LMFDB - Embedded newform 38.10.e.a.5.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [38,10,Mod(5,38)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(38, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("38.5");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 38 = 2 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	38.e (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$19.5713617742$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$7$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			5.7
Character	$\chi$	$=$	38.5
Dual form			38.10.e.a.23.7

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.0351 - 5.47232i) q^{2} +(34.3807 - 194.983i) q^{3} +(196.107 - 164.554i) q^{4} +(317.823 + 266.685i) q^{5} +(-550.092 - 3119.72i) q^{6} +(-2691.74 - 4662.22i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-18340.3 - 6675.31i) q^{9} +O(q^{10})$	\(q+(15.0351 - 5.47232i) q^{2} +(34.3807 - 194.983i) q^{3} +(196.107 - 164.554i) q^{4} +(317.823 + 266.685i) q^{5} +(-550.092 - 3119.72i) q^{6} +(-2691.74 - 4662.22i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-18340.3 - 6675.31i) q^{9} +(6237.88 + 2270.40i) q^{10} +(27343.6 - 47360.4i) q^{11} +(-25342.8 - 43895.0i) q^{12} +(-1925.52 - 10920.2i) q^{13} +(-65983.7 - 55366.9i) q^{14} +(62926.0 - 52801.2i) q^{15} +(11380.2 - 64540.4i) q^{16} +(-433813. + 157895. i) q^{17} -312277. q^{18} +(9565.28 + 567976. i) q^{19} +106211. q^{20} +(-1.00160e6 + 364552. i) q^{21} +(151941. - 861701. i) q^{22} +(-463854. + 389220. i) q^{23} +(-621239. - 521281. i) q^{24} +(-309266. - 1.75394e6i) q^{25} +(-88708.9 - 153648. i) q^{26} +(16402.7 - 28410.3i) q^{27} +(-1.29506e6 - 471362. i) q^{28} +(2.79986e6 + 1.01907e6i) q^{29} +(657153. - 1.13822e6i) q^{30} +(-660133. - 1.14338e6i) q^{31} +(-182083. - 1.03265e6i) q^{32} +(-8.29438e6 - 6.95981e6i) q^{33} +(-5.65836e6 + 4.74793e6i) q^{34} +(387850. - 2.19961e6i) q^{35} +(-4.69511e6 + 1.70888e6i) q^{36} -95486.6 q^{37} +(3.25196e6 + 8.48721e6i) q^{38} -2.19544e6 q^{39} +(1.59690e6 - 581223. i) q^{40} +(1.40378e6 - 7.96121e6i) q^{41} +(-1.30642e7 + 1.09621e7i) q^{42} +(-2.68301e6 - 2.25131e6i) q^{43} +(-2.43106e6 - 1.37872e7i) q^{44} +(-4.04875e6 - 7.01265e6i) q^{45} +(-4.84415e6 + 8.39031e6i) q^{46} +(1.52552e7 + 5.55244e6i) q^{47} +(-1.21930e7 - 4.43789e6i) q^{48} +(5.68592e6 - 9.84829e6i) q^{49} +(-1.42479e7 - 2.46782e7i) q^{50} +(1.58720e7 + 9.00146e7i) q^{51} +(-2.17456e6 - 1.82467e6i) q^{52} +(5.01299e7 - 4.20640e7i) q^{53} +(91145.5 - 516912. i) q^{54} +(2.13207e7 - 7.76012e6i) q^{55} -2.20507e7 q^{56} +(1.11074e8 + 1.76623e7i) q^{57} +4.76728e7 q^{58} +(1.35194e8 - 4.92065e7i) q^{59} +(3.65163e6 - 2.07094e7i) q^{60} +(-5.88534e7 + 4.93839e7i) q^{61} +(-1.61821e7 - 1.35784e7i) q^{62} +(1.82454e7 + 1.03475e8i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(2.30027e6 - 3.98418e6i) q^{65} +(-1.62793e8 - 5.92518e7i) q^{66} +(2.37290e8 + 8.63664e7i) q^{67} +(-5.90918e7 + 1.02350e8i) q^{68} +(5.99435e7 + 1.03825e8i) q^{69} +(-6.20561e6 - 3.51937e7i) q^{70} +(2.55758e8 + 2.14606e8i) q^{71} +(-6.12398e7 + 5.13863e7i) q^{72} +(1.13151e7 - 6.41713e7i) q^{73} +(-1.43565e6 + 522534. i) q^{74} -3.52620e8 q^{75} +(9.53383e7 + 1.09810e8i) q^{76} -2.94407e8 q^{77} +(-3.30087e7 + 1.20142e7i) q^{78} +(6.69743e7 - 3.79830e8i) q^{79} +(2.08289e7 - 1.74775e7i) q^{80} +(-2.99259e8 - 2.51108e8i) q^{81} +(-2.24604e7 - 1.27379e8i) q^{82} +(-5.86957e7 - 1.01664e8i) q^{83} +(-1.36432e8 + 2.36308e8i) q^{84} +(-1.79984e8 - 6.55089e7i) q^{85} +(-5.26591e7 - 1.91663e7i) q^{86} +(2.94961e8 - 5.10888e8i) q^{87} +(-1.11999e8 - 1.93988e8i) q^{88} +(-1.89360e8 - 1.07391e9i) q^{89} +(-9.92488e7 - 8.32797e7i) q^{90} +(-4.57292e7 + 3.83714e7i) q^{91} +(-2.69177e7 + 1.52658e8i) q^{92} +(-2.45636e8 + 8.94042e7i) q^{93} +2.59748e8 q^{94} +(-1.48431e8 + 1.83067e8i) q^{95} -2.07608e8 q^{96} +(-1.45712e8 + 5.30348e7i) q^{97} +(3.15952e7 - 1.79185e8i) q^{98} +(-8.17634e8 + 6.86076e8i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9}+O(q^{10}) $ 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9	\( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9} + 32625 q^{11} - 62208 q^{12} + 351237 q^{13} + 165264 q^{14} - 834165 q^{15} + 1075035 q^{17} - 3364608 q^{18} + 696762 q^{19} - 1396224 q^{20} - 3148065 q^{21} - 1462656 q^{22} - 4882824 q^{23} + 1032192 q^{24} - 483270 q^{25} - 70176 q^{26} + 2570400 q^{27} + 1519104 q^{28} + 13670499 q^{29} - 2263968 q^{31} - 5777733 q^{33} - 9526080 q^{34} + 43019613 q^{35} + 3290112 q^{36} - 50105184 q^{37} - 692160 q^{38} - 89820600 q^{39} - 94033860 q^{41} - 43526160 q^{42} + 30524217 q^{43} + 23402496 q^{44} + 39789630 q^{45} - 18312576 q^{46} + 81865791 q^{47} + 33030144 q^{48} + 40421580 q^{49} - 16761600 q^{50} - 28132314 q^{51} - 91666176 q^{52} + 126049077 q^{53} - 106214544 q^{54} + 553870071 q^{55} + 117743616 q^{56} + 384197394 q^{57} - 63148512 q^{58} + 135312639 q^{59} - 129611520 q^{60} + 132517452 q^{61} - 419324112 q^{62} + 577860735 q^{63} - 352321536 q^{64} - 184218951 q^{65} + 413765760 q^{66} + 229749621 q^{67} + 152743680 q^{68} - 517946637 q^{69} - 688313808 q^{70} - 2107934406 q^{71} + 105283584 q^{72} - 26577420 q^{73} + 322027248 q^{74} + 941894730 q^{75} - 107163648 q^{76} + 620006124 q^{77} + 122597280 q^{78} - 624601023 q^{79} - 1037387736 q^{81} + 1504541760 q^{82} + 907729401 q^{83} - 604998912 q^{84} + 1462808898 q^{85} + 222950208 q^{86} + 63648732 q^{87} - 133632000 q^{88} - 847590846 q^{89} - 4481693280 q^{90} + 957045924 q^{91} + 648163584 q^{92} + 2438307564 q^{93} + 2205393024 q^{94} - 208077987 q^{95} - 509607936 q^{96} + 535342599 q^{97} + 1861154832 q^{98} - 11757151095 q^{99}+O(q^{100}) \) 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9 + 32625 * q^11 - 62208 * q^12 + 351237 * q^13 + 165264 * q^14 - 834165 * q^15 + 1075035 * q^17 - 3364608 * q^18 + 696762 * q^19 - 1396224 * q^20 - 3148065 * q^21 - 1462656 * q^22 - 4882824 * q^23 + 1032192 * q^24 - 483270 * q^25 - 70176 * q^26 + 2570400 * q^27 + 1519104 * q^28 + 13670499 * q^29 - 2263968 * q^31 - 5777733 * q^33 - 9526080 * q^34 + 43019613 * q^35 + 3290112 * q^36 - 50105184 * q^37 - 692160 * q^38 - 89820600 * q^39 - 94033860 * q^41 - 43526160 * q^42 + 30524217 * q^43 + 23402496 * q^44 + 39789630 * q^45 - 18312576 * q^46 + 81865791 * q^47 + 33030144 * q^48 + 40421580 * q^49 - 16761600 * q^50 - 28132314 * q^51 - 91666176 * q^52 + 126049077 * q^53 - 106214544 * q^54 + 553870071 * q^55 + 117743616 * q^56 + 384197394 * q^57 - 63148512 * q^58 + 135312639 * q^59 - 129611520 * q^60 + 132517452 * q^61 - 419324112 * q^62 + 577860735 * q^63 - 352321536 * q^64 - 184218951 * q^65 + 413765760 * q^66 + 229749621 * q^67 + 152743680 * q^68 - 517946637 * q^69 - 688313808 * q^70 - 2107934406 * q^71 + 105283584 * q^72 - 26577420 * q^73 + 322027248 * q^74 + 941894730 * q^75 - 107163648 * q^76 + 620006124 * q^77 + 122597280 * q^78 - 624601023 * q^79 - 1037387736 * q^81 + 1504541760 * q^82 + 907729401 * q^83 - 604998912 * q^84 + 1462808898 * q^85 + 222950208 * q^86 + 63648732 * q^87 - 133632000 * q^88 - 847590846 * q^89 - 4481693280 * q^90 + 957045924 * q^91 + 648163584 * q^92 + 2438307564 * q^93 + 2205393024 * q^94 - 208077987 * q^95 - 509607936 * q^96 + 535342599 * q^97 + 1861154832 * q^98 - 11757151095 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	15.0351	−	5.47232i	0.664463	−	0.241845i
$2$	15.0351	−	5.47232i	0.664463	−	0.241845i
$3$	34.3807	−	194.983i	0.245058	−	1.38979i	−0.575299	−	0.817943i	$-0.695114\pi$
$3$	34.3807	−	194.983i	0.245058	−	1.38979i	0.820357	−	0.571851i	$-0.193775\pi$
$4$	196.107	−	164.554i	0.383022	−	0.321394i
$5$	317.823	+	266.685i	0.227416	+	0.190824i	0.749375	−	0.662146i	$-0.230354\pi$
$5$	317.823	+	266.685i	0.227416	+	0.190824i	−0.521959	+	0.852971i	$0.674799\pi$
$6$	−550.092	−	3119.72i	−0.173282	−	0.982733i
$7$	−2691.74	−	4662.22i	−0.423732	−	0.733925i	0.572569	−	0.819857i	$-0.305947\pi$
$7$	−2691.74	−	4662.22i	−0.423732	−	0.733925i	−0.996301	+	0.0859311i	$0.972614\pi$
$8$	2048.00	−	3547.24i	0.176777	−	0.306186i
$9$	−18340.3	−	6675.31i	−0.931782	−	0.339141i
$10$	6237.88	+	2270.40i	0.197259	+	0.0717965i
$11$	27343.6	−	47360.4i	0.563103	−	0.975323i	−0.434120	−	0.900855i	$-0.642941\pi$
$11$	27343.6	−	47360.4i	0.563103	−	0.975323i	0.997223	−	0.0744684i	$-0.0237260\pi$
$12$	−25342.8	−	43895.0i	−0.352809	−	0.611082i
$13$	−1925.52	−	10920.2i	−0.0186983	−	0.106043i	0.974030	−	0.226418i	$-0.0727015\pi$
$13$	−1925.52	−	10920.2i	−0.0186983	−	0.106043i	−0.992729	+	0.120375i	$0.961590\pi$
$14$	−65983.7	−	55366.9i	−0.459050	−	0.385189i
$15$	62926.0	−	52801.2i	0.320937	−	0.269298i
$16$	11380.2	−	64540.4i	0.0434120	−	0.246202i
$17$	−433813.	+	157895.i	−1.25974	+	0.458510i	−0.883683	−	0.468085i	$-0.844944\pi$
$17$	−433813.	+	157895.i	−1.25974	+	0.458510i	−0.376061	+	0.926595i	$0.622722\pi$
$18$	−312277.			−0.701154
$19$	9565.28	+	567976.i	0.0168386	+	0.999858i
$19$	9565.28	+	567976.i	0.0168386	+	0.999858i
$20$	106211.			0.148435
$21$	−1.00160e6	+	364552.i	−1.12384	+	0.409046i
$22$	151941.	−	861701.i	0.138284	−	0.784250i
$23$	−463854.	+	389220.i	−0.345626	+	0.290014i	−0.799031	−	0.601290i	$-0.794654\pi$
$23$	−463854.	+	389220.i	−0.345626	+	0.290014i	0.453405	+	0.891305i	$0.350209\pi$
$24$	−621239.	−	521281.i	−0.382215	−	0.320717i
$25$	−309266.	−	1.75394e6i	−0.158344	−	0.898015i
$26$	−88708.9	−	153648.i	−0.0380704	−	0.0659398i
$27$	16402.7	−	28410.3i	0.00593988	−	0.0102882i
$28$	−1.29506e6	−	471362.i	−0.398178	−	0.144925i
$29$	2.79986e6	+	1.01907e6i	0.735098	+	0.267554i	0.682321	−	0.731053i	$-0.260971\pi$
$29$	2.79986e6	+	1.01907e6i	0.735098	+	0.267554i	0.0527767	+	0.998606i	$0.483193\pi$
$30$	657153.	−	1.13822e6i	0.148122	−	0.256555i
$31$	−660133.	−	1.14338e6i	−0.128382	−	0.222364i	0.794668	−	0.607044i	$-0.207645\pi$
$31$	−660133.	−	1.14338e6i	−0.128382	−	0.222364i	−0.923050	+	0.384680i	$0.874312\pi$
$32$	−182083.	−	1.03265e6i	−0.0306970	−	0.174091i
$33$	−8.29438e6	−	6.95981e6i	−1.21751	−	1.02161i
$34$	−5.65836e6	+	4.74793e6i	−0.726166	+	0.609325i
$35$	387850.	−	2.19961e6i	0.0436876	−	0.247765i
$36$	−4.69511e6	+	1.70888e6i	−0.465891	+	0.169571i
$37$	−95486.6			−0.00837597			−0.00418798	−	0.999991i	$-0.501333\pi$
$37$	−95486.6			−0.00837597			−0.00418798	+	0.999991i	$0.501333\pi$
$38$	3.25196e6	+	8.48721e6i	0.252999	+	0.660296i
$39$	−2.19544e6			−0.151961
$40$	1.59690e6	−	581223.i	0.0986296	−	0.0358982i
$41$	1.40378e6	−	7.96121e6i	0.0775837	−	0.439999i	−0.921128	−	0.389259i	$-0.872731\pi$
$41$	1.40378e6	−	7.96121e6i	0.0775837	−	0.439999i	0.998712	−	0.0507396i	$-0.0161579\pi$
$42$	−1.30642e7	+	1.09621e7i	−0.647828	+	0.543592i
$43$	−2.68301e6	−	2.25131e6i	−0.119678	−	0.100422i	0.580985	−	0.813915i	$-0.302668\pi$
$43$	−2.68301e6	−	2.25131e6i	−0.119678	−	0.100422i	−0.700662	+	0.713493i	$0.747112\pi$
$44$	−2.43106e6	−	1.37872e7i	−0.0977818	−	0.554548i
$45$	−4.04875e6	−	7.01265e6i	−0.147186	−	0.254933i
$46$	−4.84415e6	+	8.39031e6i	−0.159517	+	0.276292i
$47$	1.52552e7	+	5.55244e6i	0.456013	+	0.165975i	0.559806	−	0.828624i	$-0.310876\pi$
$47$	1.52552e7	+	5.55244e6i	0.456013	+	0.165975i	−0.103793	+	0.994599i	$0.533098\pi$
$48$	−1.21930e7	−	4.43789e6i	−0.331532	−	0.120668i
$49$	5.68592e6	−	9.84829e6i	0.140902	−	0.244050i
$50$	−1.42479e7	−	2.46782e7i	−0.322394	−	0.558403i
$51$	1.58720e7	+	9.00146e7i	0.328523	+	1.86315i
$52$	−2.17456e6	−	1.82467e6i	−0.0412436	−	0.0346075i
$53$	5.01299e7	−	4.20640e7i	0.872681	−	0.732266i	−0.0919802	−	0.995761i	$-0.529320\pi$
$53$	5.01299e7	−	4.20640e7i	0.872681	−	0.732266i	0.964661	+	0.263495i	$0.0848752\pi$
$54$	91145.5	−	516912.i	0.00145869	−	0.00827264i
$55$	2.13207e7	−	7.76012e6i	0.314174	−	0.114350i
$56$	−2.20507e7			−0.299624
$57$	1.11074e8	+	1.76623e7i	1.39372	+	0.221621i
$58$	4.76728e7			0.553152
$59$	1.35194e8	−	4.92065e7i	1.45252	−	0.528674i	0.509226	−	0.860633i	$-0.329932\pi$
$59$	1.35194e8	−	4.92065e7i	1.45252	−	0.528674i	0.943294	+	0.331958i	$0.107709\pi$
$60$	3.65163e6	−	2.07094e7i	0.0363752	−	0.206294i
$61$	−5.88534e7	+	4.93839e7i	−0.544236	+	0.456669i	−0.872984	−	0.487749i	$-0.837818\pi$
$61$	−5.88534e7	+	4.93839e7i	−0.544236	+	0.456669i	0.328747	+	0.944418i	$0.393374\pi$
$62$	−1.61821e7	−	1.35784e7i	−0.139083	−	0.116704i
$63$	1.82454e7	+	1.03475e8i	0.145922	+	0.827564i
$64$	−8.38861e6	−	1.45295e7i	−0.0625000	−	0.108253i
$65$	2.30027e6	−	3.98418e6i	0.0159834	−	0.0276840i
$66$	−1.62793e8	−	5.92518e7i	−1.05606	−	0.384374i
$67$	2.37290e8	+	8.63664e7i	1.43861	+	0.523610i	0.939385	−	0.342864i	$-0.111397\pi$
$67$	2.37290e8	+	8.63664e7i	1.43861	+	0.523610i	0.499222	+	0.866474i	$0.333619\pi$
$68$	−5.90918e7	+	1.02350e8i	−0.335148	+	0.580494i
$69$	5.99435e7	+	1.03825e8i	0.318362	+	0.551419i
$70$	−6.20561e6	−	3.51937e7i	−0.0308918	−	0.175196i
$71$	2.55758e8	+	2.14606e8i	1.19445	+	1.00226i	0.999771	+	0.0213910i	$0.00680950\pi$
$71$	2.55758e8	+	2.14606e8i	1.19445	+	1.00226i	0.194674	+	0.980868i	$0.437635\pi$
$72$	−6.12398e7	+	5.13863e7i	−0.268558	+	0.225347i
$73$	1.13151e7	−	6.41713e7i	0.0466344	−	0.264477i	−0.952572	−	0.304314i	$-0.901573\pi$
$73$	1.13151e7	−	6.41713e7i	0.0466344	−	0.264477i	0.999206	+	0.0398370i	$0.0126839\pi$
$74$	−1.43565e6	+	522534.i	−0.00556552	+	0.00202568i
$75$	−3.52620e8			−1.28686
$76$	9.53383e7	+	1.09810e8i	0.327798	+	0.377556i
$77$	−2.94407e8			−0.954419
$78$	−3.30087e7	+	1.20142e7i	−0.100972	+	0.0367509i
$79$	6.69743e7	−	3.79830e8i	0.193458	−	1.09715i	−0.721140	−	0.692790i	$-0.756381\pi$
$79$	6.69743e7	−	3.79830e8i	0.193458	−	1.09715i	0.914598	−	0.404365i	$-0.132507\pi$
$80$	2.08289e7	−	1.74775e7i	0.0568539	−	0.0477061i
$81$	−2.99259e8	−	2.51108e8i	−0.772439	−	0.648153i
$82$	−2.24604e7	−	1.27379e8i	−0.0548599	−	0.311126i
$83$	−5.86957e7	−	1.01664e8i	−0.135755	−	0.235134i	0.790131	−	0.612938i	$-0.210013\pi$
$83$	−5.86957e7	−	1.01664e8i	−0.135755	−	0.235134i	−0.925885	+	0.377804i	$0.876679\pi$
$84$	−1.36432e8	+	2.36308e8i	−0.298993	+	0.517870i
$85$	−1.79984e8	−	6.55089e7i	−0.373981	−	0.136118i
$86$	−5.26591e7	−	1.91663e7i	−0.103808	−	0.0377830i
$87$	2.94961e8	−	5.10888e8i	0.551986	−	0.956068i
$88$	−1.11999e8	−	1.93988e8i	−0.199087	−	0.344829i
$89$	−1.89360e8	−	1.07391e9i	−0.319914	−	1.81432i	−0.543239	−	0.839578i	$-0.682802\pi$
$89$	−1.89360e8	−	1.07391e9i	−0.319914	−	1.81432i	0.223325	−	0.974744i	$-0.428309\pi$
$90$	−9.92488e7	−	8.32797e7i	−0.159454	−	0.133797i
$91$	−4.57292e7	+	3.83714e7i	−0.0699049	+	0.0586572i
$92$	−2.69177e7	+	1.52658e8i	−0.0391735	+	0.222164i
$93$	−2.45636e8	+	8.94042e7i	−0.340501	+	0.123932i
$94$	2.59748e8			0.343144
$95$	−1.48431e8	+	1.83067e8i	−0.186968	+	0.230597i
$96$	−2.07608e8			−0.249473
$97$	−1.45712e8	+	5.30348e7i	−0.167118	+	0.0608259i	−0.424224	−	0.905557i	$-0.639453\pi$
$97$	−1.45712e8	+	5.30348e7i	−0.167118	+	0.0608259i	0.257106	+	0.966383i	$0.417231\pi$
$98$	3.15952e7	−	1.79185e8i	0.0346022	−	0.196239i
$99$	−8.17634e8	+	6.86076e8i	−0.855462	+	0.717818i
$100$	−3.49266e8	−	2.93069e8i	−0.349266	−	0.293069i
$101$	1.81406e7	+	1.02880e8i	0.0173462	+	0.0983755i	0.992252	−	0.124244i	$-0.0396505\pi$
$101$	1.81406e7	+	1.02880e8i	0.0173462	+	0.0983755i	−0.974905	+	0.222619i	$0.928539\pi$
$102$	7.31226e8	+	1.26652e9i	0.668884	+	1.15854i
$103$	−6.85721e8	+	1.18770e9i	−0.600316	+	1.03978i	0.392457	+	0.919770i	$0.371625\pi$
$103$	−6.85721e8	+	1.18770e9i	−0.600316	+	1.03978i	−0.992773	+	0.120007i	$0.961708\pi$
$104$	−4.26799e7	−	1.55342e7i	−0.0357745	−	0.0130208i
$105$	−4.15551e8	−	1.51248e8i	−0.333636	−	0.121434i
$106$	5.23519e8	−	9.06762e8i	0.402769	−	0.697617i
$107$	8.26400e8	+	1.43137e9i	0.609485	+	1.05566i	0.991325	+	0.131431i	$0.0419572\pi$
$107$	8.26400e8	+	1.43137e9i	0.609485	+	1.05566i	−0.381840	+	0.924228i	$0.624709\pi$
$108$	−1.45833e6	−	8.27058e6i	−0.00103145	−	0.00584964i
$109$	6.87292e8	+	5.76706e8i	0.466361	+	0.391323i	0.845465	−	0.534031i	$-0.179323\pi$
$109$	6.87292e8	+	5.76706e8i	0.466361	+	0.391323i	−0.379104	+	0.925354i	$0.623768\pi$
$110$	2.78093e8	−	2.33348e8i	0.181102	−	0.151963i
$111$	−3.28290e6	+	1.86182e7i	−0.00205260	+	0.0116409i
$112$	−3.31534e8	+	1.20669e8i	−0.199089	+	0.0724625i
$113$	1.54518e8			0.0891512			0.0445756	−	0.999006i	$-0.485806\pi$
$113$	1.54518e8			0.0891512			0.0445756	+	0.999006i	$0.485806\pi$
$114$	1.76667e9	−	3.42280e8i	0.979676	−	0.189806i
$115$	−2.51223e8			−0.133943
$116$	7.16764e8	−	2.60881e8i	0.367549	−	0.133777i
$117$	−3.75809e7	+	2.13132e8i	−0.0185409	+	0.105151i
$118$	1.76337e9	−	1.47965e9i	0.837289	−	0.702569i
$119$	1.90385e9	+	1.59752e9i	0.870306	+	0.730274i
$120$	−5.84260e7	−	3.31351e8i	−0.0257212	−	0.145872i
$121$	−3.16367e8	−	5.47963e8i	−0.134170	−	0.232390i
$122$	−6.14622e8	+	1.06456e9i	−0.251182	+	0.435060i
$123$	−1.50404e9	−	5.47424e8i	−0.592495	−	0.215651i
$124$	−3.17605e8	−	1.15599e8i	−0.120640	−	0.0439092i
$125$	7.74621e8	−	1.34168e9i	0.283788	−	0.491536i
$126$	8.40567e8	+	1.45591e9i	0.297102	+	0.514595i
$127$	−9.02068e8	−	5.11588e9i	−0.307697	−	1.74503i	−0.610532	−	0.791991i	$-0.709044\pi$
$127$	−9.02068e8	−	5.11588e9i	−0.307697	−	1.74503i	0.302836	−	0.953043i	$-0.402067\pi$
$128$	−2.05633e8	−	1.72547e8i	−0.0677094	−	0.0568149i
$129$	−5.31210e8	+	4.45738e8i	−0.168893	+	0.141718i
$130$	1.27820e7	−	7.24904e7i	0.00392513	−	0.0222605i
$131$	−6.46456e8	+	2.35291e8i	−0.191787	+	0.0698046i	−0.436128	−	0.899885i	$-0.643650\pi$
$131$	−6.46456e8	+	2.35291e8i	−0.191787	+	0.0698046i	0.244341	+	0.969689i	$0.421428\pi$
$132$	−2.77185e9			−0.794670
$133$	2.62228e9	−	1.57344e9i	0.726686	−	0.436030i
$134$	4.04029e9			1.08253
$135$	1.27898e7	−	4.65509e6i	0.00331406	−	0.00120622i
$136$	−3.28358e8	+	1.86221e9i	−0.0823042	+	0.466770i
$137$	−1.80782e9	+	1.51694e9i	−0.438443	+	0.367898i	−0.835127	−	0.550058i	$-0.814606\pi$
$137$	−1.80782e9	+	1.51694e9i	−0.438443	+	0.367898i	0.396683	+	0.917956i	$0.370161\pi$
$138$	1.46942e9	+	1.23299e9i	0.344898	+	0.289403i
$139$	5.42093e8	+	3.07436e9i	0.123171	+	0.698536i	0.982378	+	0.186907i	$0.0598465\pi$
$139$	5.42093e8	+	3.07436e9i	0.123171	+	0.698536i	−0.859207	+	0.511628i	$0.829042\pi$
$140$	−2.85893e8	−	4.95182e8i	−0.0628967	−	0.108940i
$141$	1.60711e9	−	2.78360e9i	0.342421	−	0.593091i
$142$	5.01974e9	+	1.82703e9i	1.03606	+	0.377094i
$143$	−5.69834e8	−	2.07403e8i	−0.113956	−	0.0414765i
$144$	−6.39543e8	+	1.10772e9i	−0.123948	+	0.214684i
$145$	6.18090e8	+	1.07056e9i	0.116117	+	0.201121i
$146$	−1.81042e8	−	1.02674e9i	−0.0329755	−	0.187014i
$147$	−1.72476e9	−	1.44725e9i	−0.304650	−	0.255632i
$148$	−1.87256e7	+	1.57127e7i	−0.00320818	+	0.00269198i
$149$	−1.77044e9	+	1.00407e10i	−0.294268	+	1.66888i	0.375895	+	0.926662i	$0.377335\pi$
$149$	−1.77044e9	+	1.00407e10i	−0.294268	+	1.66888i	−0.670163	+	0.742214i	$0.733776\pi$
$150$	−5.30167e9	+	1.92965e9i	−0.855071	+	0.311220i
$151$	−1.04328e10			−1.63307			−0.816537	−	0.577293i	$-0.804109\pi$
$151$	−1.04328e10			−1.63307			−0.816537	+	0.577293i	$0.804109\pi$
$152$	2.03434e9	+	1.12928e9i	0.309119	+	0.171596i
$153$	9.01025e9			1.32931
$154$	−4.42643e9	+	1.61109e9i	−0.634176	+	0.230821i
$155$	9.51181e7	−	5.39442e8i	0.0132364	−	0.0750675i
$156$	−4.30542e8	+	3.61268e8i	−0.0582043	+	0.0488392i
$157$	5.91082e9	+	4.95977e9i	0.776424	+	0.651497i	0.942345	−	0.334642i	$-0.108615\pi$
$157$	5.91082e9	+	4.95977e9i	0.776424	+	0.651497i	−0.165921	+	0.986139i	$0.553060\pi$
$158$	−1.07159e9	−	6.07729e9i	−0.136795	−	0.775805i
$159$	−6.47825e9	−	1.12207e10i	−0.803842	−	1.39229i
$160$	2.17521e8	−	3.76758e8i	0.0262399	−	0.0454488i
$161$	3.06320e9	+	1.11491e9i	0.359302	+	0.130775i
$162$	−5.87352e9	−	2.13779e9i	−0.670009	−	0.243863i
$163$	2.40207e9	−	4.16050e9i	0.266527	−	0.461638i	−0.701436	−	0.712733i	$-0.747457\pi$
$163$	2.40207e9	−	4.16050e9i	0.266527	−	0.461638i	0.967963	+	0.251095i	$0.0807906\pi$
$164$	−1.03475e9	−	1.79225e9i	−0.111697	−	0.193464i
$165$	−7.80066e8	−	4.42398e9i	−0.0819320	−	0.464660i
$166$	−1.43883e9	−	1.20732e9i	−0.147070	−	0.123406i
$167$	−6.90912e9	+	5.79744e9i	−0.687383	+	0.576783i	−0.918153	−	0.396225i	$-0.870320\pi$
$167$	−6.90912e9	+	5.79744e9i	−0.687383	+	0.576783i	0.230770	+	0.973008i	$0.425875\pi$
$168$	−7.58119e8	+	4.29951e9i	−0.0734253	+	0.416415i
$169$	9.84943e9	−	3.58490e9i	0.928797	−	0.338054i
$170$	−3.06456e9			−0.281416
$171$	3.61598e9	−	1.04807e10i	0.323403	−	0.937361i
$172$	−8.96618e8			−0.0781141
$173$	−5.47501e9	+	1.99274e9i	−0.464705	+	0.169139i	−0.563752	−	0.825944i	$-0.690643\pi$
$173$	−5.47501e9	+	1.99274e9i	−0.464705	+	0.169139i	0.0990470	+	0.995083i	$0.468421\pi$
$174$	1.63902e9	−	9.29536e9i	0.135554	−	0.768767i
$175$	−7.34478e9	+	6.16300e9i	−0.591980	+	0.496731i
$176$	−2.74548e9	−	2.30373e9i	−0.215681	−	0.180978i
$177$	−4.94636e9	−	2.80522e10i	−0.378796	−	2.14826i
$178$	−8.72385e9	−	1.51101e10i	−0.651355	−	1.12818i
$179$	−6.42499e9	+	1.11284e10i	−0.467772	+	0.810204i	−0.999322	−	0.0368227i	$-0.988276\pi$
$179$	−6.42499e9	+	1.11284e10i	−0.467772	+	0.810204i	0.531550	+	0.847027i	$0.321610\pi$
$180$	−1.94795e9	−	7.08995e8i	−0.138309	−	0.0503404i
$181$	1.49249e10	+	5.43221e9i	1.03361	+	0.376204i	0.802455	−	0.596713i	$-0.203527\pi$
$181$	1.49249e10	+	5.43221e9i	1.03361	+	0.376204i	0.231157	+	0.972917i	$0.425749\pi$
$182$	−4.77562e8	+	8.27162e8i	−0.0322633	+	0.0558816i
$183$	7.60558e9	+	1.31733e10i	0.501306	+	0.868287i
$184$	4.30683e8	+	2.44252e9i	0.0276998	+	0.157094i
$185$	−3.03479e7	−	2.54649e7i	−0.00190483	−	0.00159834i
$186$	−3.20391e9	+	2.68840e9i	−0.196278	+	0.164697i
$187$	−4.38402e9	+	2.48630e10i	−0.262171	+	1.48685i
$188$	3.90533e9	−	1.42142e9i	0.228007	−	0.0829876i
$189$	−1.76607e8			−0.0100677
$190$	−1.22987e9	+	3.56468e9i	−0.0684647	+	0.198440i
$191$	4.03708e9			0.219491			0.109746	−	0.993960i	$-0.464996\pi$
$191$	4.03708e9			0.219491			0.109746	+	0.993960i	$0.464996\pi$
$192$	−3.12141e9	+	1.13610e9i	−0.165766	+	0.0603338i
$193$	−6.64426e9	+	3.76815e10i	−0.344698	+	1.95488i	−0.0521037	+	0.998642i	$0.516593\pi$
$193$	−6.64426e9	+	3.76815e10i	−0.344698	+	1.95488i	−0.292594	+	0.956237i	$0.594518\pi$
$194$	−1.90057e9	+	1.59477e9i	−0.0963331	+	0.0808331i
$195$	−6.97762e8	−	5.85492e8i	−0.0345583	−	0.0289978i
$196$	−5.05523e8	−	2.86696e9i	−0.0244674	−	0.138762i
$197$	−1.04928e10	−	1.81741e10i	−0.496358	−	0.859717i	0.503633	−	0.863918i	$-0.331996\pi$
$197$	−1.04928e10	−	1.81741e10i	−0.496358	−	0.859717i	−0.999991	+	0.00420033i	$0.998663\pi$
$198$	−8.53876e9	+	1.47896e10i	−0.394822	+	0.683852i
$199$	1.36583e10	+	4.97120e9i	0.617386	+	0.224710i	0.631732	−	0.775187i	$-0.282344\pi$
$199$	1.36583e10	+	4.97120e9i	0.617386	+	0.224710i	−0.0143461	+	0.999897i	$0.504567\pi$
$200$	−6.85501e9	−	2.49502e9i	−0.302951	−	0.110265i
$201$	2.49981e10	−	4.32981e10i	1.08025	−	1.87105i
$202$	8.35741e8	+	1.44755e9i	0.0353175	+	0.0611718i
$203$	−2.78537e9	−	1.57966e10i	−0.115120	−	0.652878i
$204$	1.79249e10	+	1.50407e10i	0.724636	+	0.608042i
$205$	2.56929e9	−	2.15589e9i	0.101606	−	0.0852578i
$206$	−3.81037e9	+	2.16097e10i	−0.147423	+	0.836077i
$207$	1.11054e10	−	4.04202e9i	0.420404	−	0.153014i
$208$	−7.26703e8			−0.0269198
$209$	2.71611e10	+	1.50775e10i	0.984667	+	0.546600i
$210$	−7.07553e9			−0.251057
$211$	−8.84616e9	+	3.21974e9i	−0.307244	+	0.111828i	−0.491041	−	0.871137i	$-0.663383\pi$
$211$	−8.84616e9	+	3.21974e9i	−0.307244	+	0.111828i	0.183797	+	0.982964i	$0.441161\pi$
$212$	2.90906e9	−	1.64981e10i	0.0989103	−	0.560948i
$213$	5.06377e10	−	4.24901e10i	1.68564	−	1.41442i
$214$	2.02579e10	+	1.69984e10i	0.660286	+	0.554046i
$215$	−2.52330e8	−	1.43104e9i	−0.00805371	−	0.0456749i
$216$	−6.71854e7	−	1.16368e8i	−0.00210007	−	0.00363742i
$217$	−3.55381e9	+	6.15538e9i	−0.108799	+	0.188445i
$218$	1.34894e10	+	4.90974e9i	0.404519	+	0.147233i
$219$	−1.21233e10	−	4.41251e9i	−0.356141	−	0.129625i
$220$	2.90420e9	−	5.03022e9i	0.0835843	−	0.144772i
$221$	2.55955e9	+	4.43328e9i	0.0721770	+	0.125014i
$222$	5.25264e7	+	2.97892e8i	0.00145141	+	0.00823134i
$223$	3.47758e10	+	2.91803e10i	0.941683	+	0.790166i	0.977877	−	0.209179i	$-0.0670791\pi$
$223$	3.47758e10	+	2.91803e10i	0.941683	+	0.790166i	−0.0361943	+	0.999345i	$0.511524\pi$
$224$	−4.32431e9	+	3.62852e9i	−0.114763	+	0.0962972i
$225$	−6.03604e9	+	3.42321e10i	−0.157011	+	0.890455i
$226$	2.32320e9	−	8.45575e8i	0.0592377	−	0.0215608i
$227$	−5.60704e10			−1.40158			−0.700789	−	0.713369i	$-0.747168\pi$
$227$	−5.60704e10			−1.40158			−0.700789	+	0.713369i	$0.747168\pi$
$228$	2.46889e10	−	1.48140e10i	0.605055	−	0.363048i
$229$	3.19022e10			0.766586			0.383293	−	0.923627i	$-0.374790\pi$
$229$	3.19022e10			0.766586			0.383293	+	0.923627i	$0.374790\pi$
$230$	−3.77715e9	+	1.37477e9i	−0.0889999	+	0.0323933i
$231$	−1.01219e10	+	5.74042e10i	−0.233888	+	1.32645i
$232$	9.34898e9	−	7.84472e9i	0.211869	−	0.177780i
$233$	−2.56459e10	−	2.15195e10i	−0.570055	−	0.478333i	0.311609	−	0.950210i	$-0.399132\pi$
$233$	−2.56459e10	−	2.15195e10i	−0.570055	−	0.478333i	−0.881664	+	0.471877i	$0.843577\pi$
$234$	6.01295e8	+	3.41011e9i	0.0131104	+	0.0743528i
$235$	3.36770e9	+	5.83303e9i	0.0720324	+	0.124764i
$236$	1.84154e10	−	3.18964e10i	0.386435	−	0.669325i
$237$	−7.17577e10	−	2.61177e10i	−1.47741	−	0.537733i
$238$	3.73667e10	+	1.36004e10i	0.754899	+	0.274761i
$239$	3.41721e10	−	5.91878e10i	0.677456	−	1.17339i	−0.298288	−	0.954476i	$-0.596416\pi$
$239$	3.41721e10	−	5.91878e10i	0.677456	−	1.17339i	0.975744	−	0.218913i	$-0.0702509\pi$
$240$	−2.69170e9	−	4.66216e9i	−0.0523692	−	0.0907060i
$241$	−8.89359e8	−	5.04381e9i	−0.0169825	−	0.0963123i	0.975138	−	0.221597i	$-0.0711268\pi$
$241$	−8.89359e8	−	5.04381e9i	−0.0169825	−	0.0963123i	−0.992121	+	0.125284i	$0.960016\pi$
$242$	−7.75523e9	−	6.50741e9i	−0.145354	−	0.121966i
$243$	−5.87558e10	+	4.93019e10i	−1.08099	+	0.907060i
$244$	−3.41529e9	+	1.93691e10i	−0.0616842	+	0.349828i
$245$	4.43351e9	−	1.61367e9i	0.0786141	−	0.0286132i
$246$	−2.56090e10			−0.445845
$247$	6.18396e9	−	1.19810e9i	0.105714	−	0.0204813i
$248$	−5.40781e9			−0.0907797
$249$	−2.18407e10	+	7.94937e9i	−0.360056	+	0.131050i
$250$	4.30437e9	−	2.44113e10i	0.0696915	−	0.395240i
$251$	−2.51297e10	+	2.10863e10i	−0.399628	+	0.335327i	−0.820350	−	0.571862i	$-0.806221\pi$
$251$	−2.51297e10	+	2.10863e10i	−0.399628	+	0.335327i	0.420722	+	0.907190i	$0.361777\pi$
$252$	2.06052e10	+	1.72898e10i	0.321865	+	0.270077i
$253$	5.75020e9	+	3.26110e10i	0.0882349	+	0.500405i
$254$	−4.15584e10	−	7.19813e10i	−0.626480	−	1.08510i
$255$	−1.89611e10	+	3.28416e10i	−0.280823	+	0.486399i
$256$	−4.03595e9	−	1.46897e9i	−0.0587308	−	0.0213763i
$257$	−1.16726e11	−	4.24846e10i	−1.66904	−	0.607481i	−0.677296	−	0.735710i	$-0.736849\pi$
$257$	−1.16726e11	−	4.24846e10i	−1.66904	−	0.607481i	−0.991745	+	0.128229i	$0.959071\pi$
$258$	−5.54756e9	+	9.60866e9i	−0.0779495	+	0.135013i
$259$	2.57025e8	+	4.45180e8i	0.00354916	+	0.00614733i
$260$	−2.04512e8	−	1.15985e9i	−0.00277549	−	0.0157406i
$261$	−4.45476e10	−	3.73799e10i	−0.594213	−	0.498604i
$262$	−8.43194e9	+	7.07523e9i	−0.110553	+	0.0927652i
$263$	4.68338e9	−	2.65608e10i	0.0603613	−	0.342326i	−0.939639	−	0.342168i	$-0.888839\pi$
$263$	4.68338e9	−	2.65608e10i	0.0603613	−	0.342326i	1.00000		0.000157606i	$-5.01675e-5\pi$
$264$	−4.16750e10	+	1.51685e10i	−0.528029	+	0.192187i
$265$	2.71503e10			0.338196
$266$	3.08159e10	−	3.80067e10i	0.377405	−	0.465471i
$267$	−2.15905e11			−2.59993
$268$	6.07462e10	−	2.21098e10i	0.719304	−	0.261805i
$269$	2.61740e10	−	1.48440e11i	0.304779	−	1.72849i	−0.319762	−	0.947498i	$-0.603603\pi$
$269$	2.61740e10	−	1.48440e11i	0.304779	−	1.72849i	0.624541	−	0.780992i	$-0.285286\pi$
$270$	1.66821e8	−	1.39979e8i	0.00191035	−	0.00160298i
$271$	1.26967e11	+	1.06538e11i	1.42998	+	1.19990i	0.945724	+	0.324972i	$0.105355\pi$
$271$	1.26967e11	+	1.06538e11i	1.42998	+	1.19990i	0.484258	+	0.874925i	$0.339090\pi$
$272$	5.25372e9	+	2.97953e10i	0.0581979	+	0.330056i
$273$	5.90955e9	+	1.02356e10i	0.0643906	+	0.111528i
$274$	−1.88796e10	+	3.27004e10i	−0.202355	+	0.350490i
$275$	−9.15236e10	−	3.33119e10i	−0.965019	−	0.351238i
$276$	2.88402e10	+	1.04970e10i	0.299162	+	0.108886i
$277$	5.70764e10	−	9.88593e10i	0.582503	−	1.00892i	−0.412679	−	0.910876i	$-0.635407\pi$
$277$	5.70764e10	−	9.88593e10i	0.582503	−	1.00892i	0.995182	−	0.0980476i	$-0.0312598\pi$
$278$	2.49743e10	+	4.32568e10i	0.250780	+	0.434363i
$279$	4.47457e9	+	2.53766e10i	0.0442112	+	0.250734i
$280$	−7.00822e9	−	5.88060e9i	−0.0681392	−	0.0571755i
$281$	1.39580e11	−	1.17122e11i	1.33550	−	1.12062i	0.352747	−	0.935719i	$-0.385248\pi$
$281$	1.39580e11	−	1.17122e11i	1.33550	−	1.12062i	0.982757	−	0.184903i	$-0.0591969\pi$
$282$	8.93032e9	−	5.06463e10i	0.0840903	−	0.476900i
$283$	−1.72425e10	+	6.27575e9i	−0.159794	+	0.0581603i	−0.420679	−	0.907210i	$-0.638208\pi$
$283$	−1.72425e10	+	6.27575e9i	−0.159794	+	0.0581603i	0.260885	+	0.965370i	$0.415986\pi$
$284$	8.54702e10			0.779619
$285$	3.05917e10	+	3.52354e10i	0.274664	+	0.316357i
$286$	−9.70247e9			−0.0857502
$287$	−4.08955e10	+	1.48848e10i	−0.355801	+	0.129501i
$288$	−3.55378e9	+	2.01545e10i	−0.0304385	+	0.172626i
$289$	7.24194e10	−	6.07671e10i	0.610682	−	0.512423i
$290$	1.51515e10	+	1.27136e10i	0.125795	+	0.105555i
$291$	5.33119e9	+	3.02347e10i	0.0435819	+	0.247165i
$292$	−8.34064e9	−	1.44464e10i	−0.0671393	−	0.116289i
$293$	−7.50794e10	+	1.30041e11i	−0.595136	+	1.03081i	0.398391	+	0.917216i	$0.369569\pi$
$293$	−7.50794e10	+	1.30041e11i	−0.595136	+	1.03081i	−0.993528	+	0.113591i	$0.963765\pi$
$294$	−3.38517e10	−	1.23210e10i	−0.264252	−	0.0961798i
$295$	5.60903e10	+	2.04152e10i	0.431210	+	0.156948i
$296$	−1.95557e8	+	3.38714e8i	−0.00148068	+	0.00256461i
$297$	−8.97015e8	−	1.55368e9i	−0.00668953	−	0.0115866i
$298$	2.83270e10	+	1.60651e11i	0.208079	+	1.18007i
$299$	5.14350e9	+	4.31591e9i	0.0372167	+	0.0312285i
$300$	−6.91514e10	+	5.80249e10i	−0.492896	+	0.413589i
$301$	−3.27416e9	+	1.85687e10i	−0.0229906	+	0.130386i
$302$	−1.56859e11	+	5.70918e10i	−1.08512	+	0.394951i
$303$	2.06836e10			0.140973
$304$	3.67662e10	+	5.84633e9i	0.246898	+	0.0392602i
$305$	−3.18749e10			−0.210911
$306$	1.35470e11	−	4.93070e10i	0.883276	−	0.321486i
$307$	−1.88753e10	+	1.07047e11i	−0.121275	+	0.687784i	0.862176	+	0.506609i	$0.169101\pi$
$307$	−1.88753e10	+	1.07047e11i	−0.121275	+	0.687784i	−0.983451	+	0.181175i	$0.942010\pi$
$308$	−5.77353e10	+	4.84457e10i	−0.365564	+	0.306745i
$309$	2.08006e11	+	1.74538e11i	1.29796	+	1.08912i
$310$	−1.52189e9	−	8.63106e9i	−0.00935956	−	0.0530807i
$311$	3.66499e10	+	6.34795e10i	0.222153	+	0.384780i	0.955461	−	0.295116i	$-0.0953584\pi$
$311$	3.66499e10	+	6.34795e10i	0.222153	+	0.384780i	−0.733309	+	0.679896i	$0.762025\pi$
$312$	−4.49627e9	+	7.78776e9i	−0.0268631	+	0.0465283i
$313$	4.71079e10	+	1.71459e10i	0.277424	+	0.100974i	0.476985	−	0.878911i	$-0.341729\pi$
$313$	4.71079e10	+	1.71459e10i	0.277424	+	0.100974i	−0.199561	+	0.979885i	$0.563952\pi$
$314$	1.16011e11	+	4.22246e10i	0.673467	+	0.245122i
$315$	−2.17964e10	+	3.77524e10i	−0.124734	+	0.216046i
$316$	−4.93683e10	−	8.55084e10i	−0.278520	−	0.482411i
$317$	2.25982e10	+	1.28161e11i	0.125692	+	0.712834i	0.980895	+	0.194540i	$0.0623214\pi$
$317$	2.25982e10	+	1.28161e11i	0.125692	+	0.712834i	−0.855203	+	0.518294i	$0.826567\pi$
$318$	−1.58804e11	−	1.33252e11i	−0.870842	−	0.730723i
$319$	1.24821e11	−	1.04738e11i	0.674887	−	0.566298i
$320$	1.20871e9	−	6.85493e9i	0.00644387	−	0.0365450i
$321$	3.07504e11	−	1.11922e11i	1.61651	−	0.588361i
$322$	5.21567e10			0.270370
$323$	−9.38301e10	−	2.44885e11i	−0.479657	−	1.25185i
$324$	−1.00008e11			−0.504174
$325$	−1.85577e10	+	6.75447e9i	−0.0922678	+	0.0335827i
$326$	1.33477e10	−	7.56984e10i	0.0654525	−	0.371199i
$327$	1.36077e11	−	1.14182e11i	0.658144	−	0.552248i
$328$	−2.53654e10	−	2.12841e10i	−0.121007	−	0.101537i
$329$	−1.51763e10	−	8.60688e10i	−0.0714140	−	0.405009i
$330$	−3.59378e10	−	6.22461e10i	−0.166816	−	0.288934i
$331$	−2.45907e9	+	4.25924e9i	−0.0112602	+	0.0195032i	−0.871601	−	0.490217i	$-0.836918\pi$
$331$	−2.45907e9	+	4.25924e9i	−0.0112602	+	0.0195032i	0.860340	+	0.509720i	$0.170251\pi$
$332$	−2.82398e10	−	1.02785e10i	−0.127568	−	0.0464308i
$333$	1.75125e9	+	6.37403e8i	0.00780458	+	0.00284063i
$334$	−7.21538e10	+	1.24974e11i	−0.317249	+	0.549491i
$335$	5.23835e10	+	9.07309e10i	0.227244	+	0.393599i
$336$	1.21299e10	+	6.87921e10i	0.0519195	+	0.294450i
$337$	2.05161e11	+	1.72151e11i	0.866484	+	0.727066i	0.963355	−	0.268231i	$-0.0864389\pi$
$337$	2.05161e11	+	1.72151e11i	0.866484	+	0.727066i	−0.0968708	+	0.995297i	$0.530883\pi$
$338$	1.28469e11	−	1.07798e11i	0.535395	−	0.449249i
$339$	5.31246e9	−	3.01284e10i	0.0218472	−	0.123902i
$340$	−4.60759e10	+	1.67703e10i	−0.186990	+	0.0680589i
$341$	−7.22015e10			−0.289169
$342$	−2.98702e9	−	1.77366e11i	−0.0118065	−	0.701055i
$343$	−2.78462e11			−1.08628
$344$	−1.34807e10	+	4.90658e9i	−0.0519039	+	0.0188915i
$345$	−8.63722e9	+	4.89841e10i	−0.0328237	+	0.186153i
$346$	−7.14124e10	+	5.99221e10i	−0.267874	+	0.224773i
$347$	−4.01999e11	−	3.37317e11i	−1.48848	−	1.24898i	−0.896512	−	0.443019i	$-0.853908\pi$
$347$	−4.01999e11	−	3.37317e11i	−1.48848	−	1.24898i	−0.591966	−	0.805963i	$-0.701648\pi$
$348$	−2.62244e10	−	1.48726e11i	−0.0958514	−	0.543600i
$349$	2.67514e11	+	4.63348e11i	0.965233	+	1.67183i	0.708988	+	0.705220i	$0.249152\pi$
$349$	2.67514e11	+	4.63348e11i	0.965233	+	1.67183i	0.256244	+	0.966612i	$0.417515\pi$
$350$	−7.67034e10	+	1.32854e11i	−0.273217	+	0.473226i
$351$	−3.41828e8	−	1.24415e8i	−0.00120206	−	0.000437514i
$352$	−5.38854e10	−	1.96127e10i	−0.187081	−	0.0680918i
$353$	−1.29730e11	+	2.24699e11i	−0.444687	+	0.770220i	−0.998030	−	0.0627329i	$-0.980018\pi$
$353$	−1.29730e11	+	2.24699e11i	−0.444687	+	0.770220i	0.553343	+	0.832953i	$0.313352\pi$
$354$	−2.27879e11	−	3.94699e11i	−0.771242	−	1.33583i
$355$	2.40534e10	+	1.36414e11i	0.0803802	+	0.455859i
$356$	−2.13851e11	−	1.79443e11i	−0.705646	−	0.592107i
$357$	3.76945e11	−	3.16295e11i	1.22821	−	1.03059i
$358$	−3.57020e10	+	2.02476e11i	−0.114873	+	0.651479i
$359$	5.65356e11	−	2.05773e11i	1.79637	−	0.653827i	0.797661	−	0.603106i	$-0.206070\pi$
$359$	5.65356e11	−	2.05773e11i	1.79637	−	0.653827i	0.998713	−	0.0507206i	$-0.0161518\pi$
$360$	−3.31674e10			−0.104076
$361$	−3.22505e11	+	1.08657e10i	−0.999433	+	0.0336725i
$362$	2.54124e11			0.777780
$363$	−1.17720e11	+	4.28467e10i	−0.355854	+	0.129520i
$364$	−2.65369e9	+	1.50498e10i	−0.00792307	+	0.0449340i
$365$	2.07098e10	−	1.73775e10i	0.0610741	−	0.0512472i
$366$	1.86439e11	+	1.56441e11i	0.543090	+	0.455706i
$367$	4.09010e10	+	2.31961e11i	0.117689	+	0.667448i	0.985384	+	0.170350i	$0.0544899\pi$
$367$	4.09010e10	+	2.31961e11i	0.117689	+	0.667448i	−0.867694	+	0.497098i	$0.834399\pi$
$368$	1.98416e10	+	3.43667e10i	0.0563978	+	0.0976838i
$369$	−7.88892e10	+	1.36640e11i	−0.221513	+	0.383671i
$370$	−5.95635e8	−	2.16793e8i	−0.00165224	−	0.000601365i
$371$	−3.31048e11	−	1.20492e11i	−0.907211	−	0.330198i
$372$	−3.34592e10	+	5.79531e10i	−0.0905885	+	0.156904i
$373$	−1.82425e11	−	3.15969e11i	−0.487971	−	0.845191i	0.511933	−	0.859025i	$-0.328930\pi$
$373$	−1.82425e11	−	3.15969e11i	−0.487971	−	0.845191i	−0.999904	+	0.0138343i	$0.995596\pi$
$374$	7.01443e10	+	3.97808e11i	0.185383	+	1.05136i
$375$	−2.34973e11	−	1.97166e11i	−0.613589	−	0.514862i
$376$	5.09385e10	−	4.27424e10i	0.131432	−	0.110284i
$377$	5.73717e9	−	3.25371e10i	0.0146272	−	0.0829551i
$378$	−2.65530e9	+	9.66449e8i	−0.00668960	+	0.00243481i
$379$	3.11446e11			0.775366			0.387683	−	0.921793i	$-0.373276\pi$
$379$	3.11446e11			0.775366			0.387683	+	0.921793i	$0.373276\pi$
$380$	1.01594e9	+	6.03255e10i	0.00249944	+	0.148414i
$381$	−1.02852e12			−2.50064
$382$	6.06978e10	−	2.20922e10i	0.145844	−	0.0530828i
$383$	−7.07997e10	+	4.01525e11i	−0.168127	+	0.953494i	0.777655	+	0.628691i	$0.216409\pi$
$383$	−7.07997e10	+	4.01525e11i	−0.168127	+	0.953494i	−0.945782	+	0.324803i	$0.894702\pi$
$384$	−4.07135e10	+	3.41627e10i	−0.0955538	+	0.0801792i
$385$	−9.35692e10	−	7.85139e10i	−0.217050	−	0.182127i
$386$	1.06308e11	+	6.02903e11i	0.243738	+	1.38231i
$387$	3.41789e10	+	5.91995e10i	0.0774565	+	0.134159i
$388$	−1.98481e10	+	3.43780e10i	−0.0444607	+	0.0770083i
$389$	−8.81918e10	−	3.20992e10i	−0.195279	−	0.0710756i	0.242529	−	0.970144i	$-0.422023\pi$
$389$	−8.81918e10	−	3.20992e10i	−0.195279	−	0.0710756i	−0.437808	+	0.899068i	$0.644245\pi$
$390$	−1.36949e10	−	4.98454e9i	−0.0299757	−	0.0109102i
$391$	1.39770e11	−	2.42089e11i	0.302426	−	0.523817i
$392$	−2.32895e10	−	4.03386e10i	−0.0498165	−	0.0862847i
$393$	2.36520e10	+	1.34137e11i	0.0500152	+	0.283650i
$394$	−2.57215e11	−	2.15829e11i	−0.537730	−	0.451209i
$395$	1.22581e11	−	1.02858e11i	0.253359	−	0.212594i
$396$	−4.74477e10	+	2.69089e11i	−0.0969587	+	0.549880i
$397$	7.03875e11	−	2.56190e11i	1.42213	−	0.517612i	0.487463	−	0.873144i	$-0.337923\pi$
$397$	7.03875e11	−	2.56190e11i	1.42213	−	0.517612i	0.934664	+	0.355532i	$0.115700\pi$
$398$	2.32557e11			0.464575
$399$	−2.16637e11	−	5.65396e11i	−0.427912	−	1.11680i
$400$	−1.16719e11			−0.227967
$401$	−2.93701e11	+	1.06898e11i	−0.567225	+	0.206453i	−0.609683	−	0.792645i	$-0.708703\pi$
$401$	−2.93701e11	+	1.06898e11i	−0.567225	+	0.206453i	0.0424584	+	0.999098i	$0.486481\pi$
$402$	1.38908e11	−	7.87788e11i	0.265284	−	1.50450i
$403$	−1.12148e10	+	9.41036e9i	−0.0211797	+	0.0177719i
$404$	2.04869e10	+	1.71905e10i	0.0382613	+	0.0321050i
$405$	−2.81446e10	−	1.59616e11i	−0.0519813	−	0.294800i
$406$	−1.28322e11	−	2.22261e11i	−0.234388	−	0.405972i
$407$	−2.61094e9	+	4.52229e9i	−0.00471653	+	0.00816927i
$408$	3.51809e11	+	1.28048e11i	0.628545	+	0.228772i
$409$	−5.07776e11	−	1.84815e11i	−0.897258	−	0.326575i	−0.148104	−	0.988972i	$-0.547317\pi$
$409$	−5.07776e11	−	1.84815e11i	−0.897258	−	0.326575i	−0.749153	+	0.662397i	$0.769539\pi$
$410$	2.68317e10	−	4.64739e10i	0.0468945	−	0.0812236i
$411$	2.33624e11	+	4.04648e11i	0.403858	+	0.699503i
$412$	6.09660e10	+	3.45755e11i	0.104244	+	0.591196i
$413$	−5.93317e11	−	4.97852e11i	−1.00349	−	0.842025i
$414$	1.44851e11	−	1.21544e11i	0.242337	−	0.203345i
$415$	8.45742e9	−	4.79644e10i	0.0139966	−	0.0793785i
$416$	−1.09260e10	+	3.97676e9i	−0.0178872	+	0.00651042i
$417$	6.18086e11			1.00101
$418$	4.90878e11	+	7.80564e10i	0.786467	+	0.125059i
$419$	−1.53493e11			−0.243291			−0.121646	−	0.992574i	$-0.538817\pi$
$419$	−1.53493e11			−0.243291			−0.121646	+	0.992574i	$0.538817\pi$
$420$	−1.06381e11	+	3.87196e10i	−0.166818	+	0.0607168i
$421$	9.67733e10	−	5.48829e11i	0.150136	−	0.851466i	−0.812962	−	0.582317i	$-0.802146\pi$
$421$	9.67733e10	−	5.48829e11i	0.150136	−	0.851466i	0.963098	−	0.269149i	$-0.0867426\pi$
$422$	−1.15383e11	+	9.68181e10i	−0.177108	+	0.148611i
$423$	−2.42720e11	−	2.03666e11i	−0.368616	−	0.309306i
$424$	−4.65450e10	−	2.63970e11i	−0.0699402	−	0.396650i
$425$	4.11101e11	+	7.12049e11i	0.611222	+	1.05867i
$426$	5.28822e11	−	9.15947e11i	0.777977	−	1.34750i
$427$	3.88657e11	+	1.41459e11i	0.565771	+	0.205924i
$428$	3.97600e11	+	1.44714e11i	0.572729	+	0.208456i
$429$	−6.00312e10	+	1.03977e11i	−0.0855696	+	0.148211i
$430$	−1.16249e10	−	2.01349e10i	−0.0163976	−	0.0284015i
$431$	7.04037e10	+	3.99279e11i	0.0982760	+	0.557351i	0.993694	+	0.112125i	$0.0357656\pi$
$431$	7.04037e10	+	3.99279e11i	0.0982760	+	0.557351i	−0.895418	+	0.445226i	$0.853123\pi$
$432$	−1.64694e9	−	1.38195e9i	−0.00227511	−	0.00190904i
$433$	−9.28209e11	+	7.78860e11i	−1.26897	+	1.06479i	−0.274300	+	0.961644i	$0.588446\pi$
$433$	−9.28209e11	+	7.78860e11i	−1.26897	+	1.06479i	−0.994666	+	0.103145i	$0.967109\pi$
$434$	−1.97476e10	+	1.11994e11i	−0.0267184	+	0.151528i
$435$	2.29992e11	−	8.37102e10i	0.307972	−	0.112092i
$436$	2.29682e11			0.304395
$437$	−2.25504e11	−	2.59735e11i	−0.295793	−	0.340693i
$438$	−2.06421e11			−0.267991
$439$	−1.26783e11	+	4.61452e10i	−0.162919	+	0.0592975i	−0.422192	−	0.906506i	$-0.638739\pi$
$439$	−1.26783e11	+	4.61452e10i	−0.162919	+	0.0592975i	0.259273	+	0.965804i	$0.416517\pi$
$440$	1.61379e10	−	9.15225e10i	0.0205263	−	0.116410i
$441$	−1.70022e11	+	1.42665e11i	−0.214058	+	0.179616i
$442$	6.27434e10	+	5.26480e10i	0.0781930	+	0.0656117i
$443$	2.20347e11	+	1.24965e12i	0.271826	+	1.54160i	0.748866	+	0.662721i	$0.230598\pi$
$443$	2.20347e11	+	1.24965e12i	0.271826	+	1.54160i	−0.477040	+	0.878881i	$0.658290\pi$
$444$	2.41990e9	+	4.19139e9i	0.00295511	+	0.00511840i
$445$	2.26214e11	−	3.91814e11i	0.273464	−	0.473653i
$446$	6.82541e11	+	2.48424e11i	0.816811	+	0.297295i
$447$	1.89689e12	+	6.90411e11i	2.24728	+	0.817944i
$448$	−4.51598e10	+	7.82191e10i	−0.0529665	+	0.0917407i
$449$	2.04662e11	+	3.54485e11i	0.237645	+	0.411613i	0.960038	−	0.279869i	$-0.0902911\pi$
$449$	2.04662e11	+	3.54485e11i	0.237645	+	0.411613i	−0.722393	+	0.691483i	$0.756958\pi$
$450$	9.65767e10	+	5.47714e11i	0.111024	+	0.629647i
$451$	−3.38662e11	−	2.84171e11i	−0.385454	−	0.323434i
$452$	3.03022e10	−	2.54266e10i	0.0341469	−	0.0286527i
$453$	−3.58688e11	+	2.03422e12i	−0.400198	+	2.26964i
$454$	−8.43023e11	+	3.06835e11i	−0.931296	+	0.338964i
$455$	−2.47669e10			−0.0270907
$456$	2.90133e11	−	3.57835e11i	0.314235	−	0.387562i
$457$	−6.56534e11			−0.704099			−0.352050	−	0.935981i	$-0.614515\pi$
$457$	−6.56534e11			−0.704099			−0.352050	+	0.935981i	$0.614515\pi$
$458$	4.79652e11	−	1.74579e11i	0.509368	−	0.185395i
$459$	−2.62986e9	+	1.49147e10i	−0.00276551	+	0.0156840i
$460$	−4.92666e10	+	4.13396e10i	−0.0513030	+	0.0430483i
$461$	−2.99762e11	−	2.51530e11i	−0.309117	−	0.259380i	0.475010	−	0.879980i	$-0.342444\pi$
$461$	−2.99762e11	−	2.51530e11i	−0.309117	−	0.259380i	−0.784127	+	0.620601i	$0.786889\pi$
$462$	1.61951e11	+	9.18467e11i	0.165384	+	0.937940i
$463$	5.81041e11	+	1.00639e12i	0.587614	+	1.01778i	0.994544	+	0.104318i	$0.0332660\pi$
$463$	5.81041e11	+	1.00639e12i	0.587614	+	1.01778i	−0.406930	+	0.913459i	$0.633401\pi$
$464$	9.76338e10	−	1.69107e11i	0.0977843	−	0.169367i
$465$	−1.01912e11	−	3.70928e10i	−0.101085	−	0.0367918i
$466$	−5.03350e11	−	1.83205e11i	−0.494463	−	0.179970i
$467$	5.20363e11	−	9.01294e11i	0.506268	−	0.876881i	−0.493706	−	0.869629i	$-0.664358\pi$
$467$	5.20363e11	−	9.01294e11i	0.506268	−	0.876881i	0.999974	−	0.00725236i	$-0.00230852\pi$
$468$	2.77017e10	+	4.79808e10i	0.0266932	+	0.0462340i
$469$	−2.36062e11	−	1.33877e12i	−0.225293	−	1.27770i
$470$	8.25538e10	+	6.92709e10i	0.0780364	+	0.0654803i
$471$	1.17029e12	−	9.81987e11i	1.09572	−	0.919415i
$472$	1.02329e11	−	5.80339e11i	0.0948990	−	0.538199i
$473$	−1.79986e11	+	6.55095e10i	−0.165334	+	0.0601768i
$474$	−1.22181e12			−1.11173
$475$	9.93234e11	−	1.92432e11i	0.895221	−	0.173443i
$476$	6.36238e11			0.568052
$477$	−1.20019e12	+	4.36832e11i	−1.06149	+	0.386351i
$478$	1.89886e11	−	1.07689e12i	0.166367	−	0.943512i
$479$	1.46954e12	−	1.23309e12i	1.27548	−	1.07025i	0.281627	−	0.959524i	$-0.409126\pi$
$479$	1.46954e12	−	1.23309e12i	1.27548	−	1.07025i	0.993851	−	0.110729i	$-0.0353186\pi$
$480$	−6.59827e10	−	5.53661e10i	−0.0567342	−	0.0476056i
$481$	1.83861e8	+	1.04273e9i	0.000156616	+	0.000888216i
$482$	−4.09729e10	−	7.09672e10i	−0.0345768	−	0.0598888i
$483$	3.22704e11	−	5.58940e11i	0.269800	−	0.467308i
$484$	−1.52211e11	−	5.54004e10i	−0.126079	−	0.0458890i
$485$	−6.04542e10	−	2.20035e10i	−0.0496123	−	0.0180574i
$486$	−6.13602e11	+	1.06279e12i	−0.498911	+	0.864140i
$487$	−9.53092e11	−	1.65080e12i	−0.767811	−	1.32989i	−0.938747	−	0.344606i	$-0.888013\pi$
$487$	−9.53092e11	−	1.65080e12i	−0.767811	−	1.32989i	0.170936	−	0.985282i	$-0.445321\pi$
$488$	5.46447e10	+	3.09905e11i	0.0436173	+	0.247366i
$489$	−7.28641e11	−	6.11403e11i	−0.576267	−	0.483546i
$490$	5.78277e10	−	4.85232e10i	0.0453162	−	0.0380248i
$491$	−2.80513e11	+	1.59087e12i	−0.217814	+	1.23529i	0.658142	+	0.752894i	$0.271343\pi$
$491$	−2.80513e11	+	1.59087e12i	−0.217814	+	1.23529i	−0.875956	+	0.482391i	$0.839768\pi$
$492$	−3.85033e11	+	1.40141e11i	−0.296248	+	0.107825i
$493$	−1.37552e12			−1.04871
$494$	8.64200e10	−	5.18542e10i	0.0652894	−	0.0391753i
$495$	−4.42829e11			−0.331523
$496$	−8.13069e10	+	2.95933e10i	−0.0603198	+	0.0219546i
$497$	3.12110e11	−	1.77006e12i	0.229458	−	1.30132i
$498$	−2.84875e11	+	2.39039e11i	−0.207550	+	0.174155i
$499$	−1.10989e12	−	9.31310e11i	−0.801361	−	0.672422i	0.147168	−	0.989111i	$-0.452984\pi$
$499$	−1.10989e12	−	9.31310e11i	−0.801361	−	0.672422i	−0.948529	+	0.316690i	$0.897429\pi$
$500$	−6.88699e10	−	3.90581e11i	−0.0492793	−	0.279477i
$501$	8.92861e11	+	1.54648e12i	0.633161	+	1.09667i
$502$	−2.62436e11	+	4.54552e11i	−0.184441	+	0.319460i
$503$	−2.11911e12	−	7.71291e11i	−1.47603	−	0.537233i	−0.526303	−	0.850297i	$-0.676422\pi$
$503$	−2.11911e12	−	7.71291e11i	−1.47603	−	0.537233i	−0.949732	+	0.313065i	$0.898644\pi$
$504$	4.04416e11	+	1.47195e11i	0.279184	+	0.101615i
$505$	−2.16712e10	+	3.75356e10i	−0.0148276	+	0.0256822i
$506$	2.64912e11	+	4.58842e11i	0.179649	+	0.311161i
$507$	−3.60363e11	−	2.04372e12i	−0.242217	−	1.37368i
$508$	−1.01874e12	−	8.54824e11i	−0.678698	−	0.569495i
$509$	2.78915e11	−	2.34037e11i	0.184180	−	0.154545i	−0.546036	−	0.837762i	$-0.683864\pi$
$509$	2.78915e11	−	2.34037e11i	0.184180	−	0.154545i	0.730216	+	0.683217i	$0.239419\pi$
$510$	−1.05362e11	+	5.97537e11i	−0.0689632	+	0.391110i
$511$	−3.29638e11	+	1.19979e11i	−0.213867	+	0.0778412i
$512$	−6.87195e10			−0.0441942
$513$	1.62932e10	+	9.04457e9i	0.0103867	+	0.00576580i
$514$	−1.98747e12			−1.25593
$515$	−5.34681e11	+	1.94608e11i	−0.334936	+	0.121907i
$516$	−3.08264e10	+	1.74825e11i	−0.0191425	+	0.108563i
$517$	6.80097e11	−	5.70669e11i	0.418662	−	0.351299i
$518$	6.30056e9	+	5.28680e9i	0.00384499	+	0.00322633i
$519$	2.00315e11	+	1.13605e12i	0.121188	+	0.687294i
$520$	−9.42191e9	−	1.63192e10i	−0.00565098	−	0.00978778i
$521$	−4.64523e11	+	8.04577e11i	−0.276208	+	0.478407i	−0.970439	−	0.241345i	$-0.922411\pi$
$521$	−4.64523e11	+	8.04577e11i	−0.276208	+	0.478407i	0.694231	+	0.719752i	$0.255745\pi$
$522$	−8.74331e11	−	3.18231e11i	−0.515417	−	0.187596i
$523$	2.75035e12	+	1.00105e12i	1.60743	+	0.585055i	0.980929	−	0.194369i	$-0.0622658\pi$
$523$	2.75035e12	+	1.00105e12i	1.60743	+	0.585055i	0.626497	+	0.779424i	$0.284488\pi$
$524$	−8.80569e10	+	1.52519e11i	−0.0510238	+	0.0883758i
$525$	9.49160e11	+	1.64399e12i	0.545284	+	0.944459i
$526$	−7.49341e10	−	4.24972e11i	−0.0426819	−	0.242061i
$527$	4.66909e11	+	3.91783e11i	0.263684	+	0.221258i
$528$	−5.43580e11	+	4.56118e11i	−0.304376	+	0.255402i
$529$	−2.49098e11	+	1.41271e12i	−0.138299	+	0.784335i
$530$	4.08207e11	−	1.48575e11i	0.224718	−	0.0817908i
$531$	−2.80796e12			−1.53273
$532$	2.55334e11	−	7.40068e11i	0.138200	−	0.400562i
$533$	−8.96406e10			−0.0481097
$534$	−3.24615e12	+	1.18150e12i	−1.72756	+	0.628780i
$535$	−1.19075e11	+	6.75310e11i	−0.0628391	+	0.356378i
$536$	7.92332e11	−	6.64845e11i	0.414634	−	0.347920i
$537$	1.94895e12	+	1.63536e12i	1.01139	+	0.848653i
$538$	−4.18785e11	−	2.37505e12i	−0.215512	−	1.22223i
$539$	−3.10946e11	−	5.38575e11i	−0.158685	−	0.274851i
$540$	1.74215e9	−	3.01750e9i	0.000881687	−	0.00152713i
$541$	7.22961e11	+	2.63136e11i	0.362850	+	0.132067i	0.517010	−	0.855979i	$-0.327045\pi$
$541$	7.22961e11	+	2.63136e11i	0.362850	+	0.132067i	−0.154160	+	0.988046i	$0.549267\pi$
$542$	2.49198e12	+	9.07006e11i	1.24036	+	0.451454i
$543$	1.57232e12	−	2.72333e12i	0.776141	−	1.34432i
$544$	2.42040e11	+	4.19225e11i	0.118493	+	0.205235i
$545$	6.46381e10	+	3.66581e11i	0.0313837	+	0.177986i
$546$	1.44863e11	+	1.21555e11i	0.0697576	+	0.0585336i
$547$	1.82395e12	−	1.53047e12i	0.871102	−	0.730941i	−0.0932281	−	0.995645i	$-0.529719\pi$
$547$	1.82395e12	−	1.53047e12i	0.871102	−	0.730941i	0.964330	+	0.264704i	$0.0852741\pi$
$548$	−1.04909e11	+	5.94968e11i	−0.0496935	+	0.281826i
$549$	1.40904e12	−	5.12849e11i	0.661985	−	0.240943i
$550$	−1.55836e12			−0.726165
$551$	−5.52023e11	+	1.60000e12i	−0.255138	+	0.739499i
$552$	4.91057e11			0.225116
$553$	−1.95113e12	+	7.10154e11i	−0.887204	+	0.322916i
$554$	3.17159e11	−	1.79870e12i	0.143048	−	0.811268i
$555$	−6.00859e9	+	5.04181e9i	−0.00268816	+	0.00225563i
$556$	6.12206e11	+	5.13702e11i	0.271682	+	0.227968i
$557$	−1.46976e11	−	8.33544e11i	−0.0646992	−	0.366927i	−0.999917	−	0.0128554i	$-0.995908\pi$
$557$	−1.46976e11	−	8.33544e11i	−0.0646992	−	0.366927i	0.935218	−	0.354072i	$-0.115203\pi$
$558$	2.06144e11	+	3.57052e11i	0.0900155	+	0.155911i
$559$	−1.94185e10	+	3.36338e10i	−0.00841127	+	0.0145688i
$560$	−1.37550e11	−	5.00640e10i	−0.0591036	−	0.0215119i
$561$	4.69713e12	+	1.70962e12i	2.00216	+	0.728728i
$562$	1.45767e12	−	2.52476e12i	0.616377	−	1.06760i
$563$	−7.96410e11	−	1.37942e12i	−0.334079	−	0.578642i	0.649229	−	0.760593i	$-0.275092\pi$
$563$	−7.96410e11	−	1.37942e12i	−0.334079	−	0.578642i	−0.983307	+	0.181952i	$0.941759\pi$
$564$	−1.42885e11	−	8.10341e11i	−0.0594608	−	0.337219i
$565$	4.91095e10	+	4.12078e10i	0.0202744	+	0.0170122i
$566$	−2.24899e11	+	1.88713e11i	−0.0921115	+	0.0772907i
$567$	−3.65195e11	+	2.07113e12i	−0.148389	+	0.841556i
$568$	1.28505e12	−	4.67721e11i	0.518028	−	0.188547i
$569$	−4.72756e12			−1.89074			−0.945371	−	0.325997i	$-0.894300\pi$
$569$	−4.72756e12			−1.89074			−0.945371	+	0.325997i	$0.894300\pi$
$570$	6.52768e11	+	3.62359e11i	0.259013	+	0.143781i
$571$	1.18323e12			0.465809			0.232904	−	0.972500i	$-0.425177\pi$
$571$	1.18323e12			0.465809			0.232904	+	0.972500i	$0.425177\pi$
$572$	−1.45877e11	+	5.30950e10i	−0.0569778	+	0.0207382i
$573$	1.38798e11	−	7.87161e11i	0.0537881	−	0.305048i
$574$	−5.33413e11	+	4.47587e11i	−0.205098	+	0.172097i
$575$	8.26121e11	+	6.93197e11i	0.315165	+	0.264455i
$576$	5.68604e10	+	3.22471e11i	0.0215233	+	0.122065i
$577$	9.98882e11	+	1.73011e12i	0.375166	+	0.649806i	0.990352	−	0.138576i	$-0.0442525\pi$
$577$	9.98882e11	+	1.73011e12i	0.375166	+	0.649806i	−0.615186	+	0.788382i	$0.710919\pi$
$578$	7.56295e11	−	1.30994e12i	0.281849	−	0.488176i
$579$	7.11880e12	+	2.59103e12i	2.63241	+	0.958118i
$580$	2.97377e11	+	1.08236e11i	0.109114	+	0.0397143i
$581$	−3.15987e11	+	5.47305e11i	−0.115047	+	0.199268i
$582$	2.45609e11	+	4.25407e11i	0.0887341	+	0.153692i
$583$	−6.21438e11	−	3.52435e12i	−0.222787	−	1.26349i
$584$	−2.04458e11	−	1.71560e11i	−0.0727353	−	0.0610322i
$585$	−6.87833e10	+	5.77160e10i	−0.0242818	+	0.0203749i
$586$	−4.17197e11	+	2.36604e12i	−0.146151	+	0.828863i
$587$	−1.11701e10	+	4.06559e9i	−0.00388317	+	0.00141336i	−0.343961	−	0.938984i	$-0.611769\pi$
$587$	−1.11701e10	+	4.06559e9i	−0.00388317	+	0.00141336i	0.340078	+	0.940397i	$0.389547\pi$
$588$	−5.76388e11			−0.198846
$589$	6.43100e11	−	3.85876e11i	0.220171	−	0.132108i
$590$	9.55041e11			0.324480
$591$	−3.90439e12	+	1.42108e12i	−1.31647	+	0.479155i
$592$	−1.08666e9	+	6.16274e9i	−0.000363618	+	0.00206218i
$593$	2.69934e12	−	2.26501e12i	0.896419	−	0.752185i	−0.0730684	−	0.997327i	$-0.523279\pi$
$593$	2.69934e12	−	2.26501e12i	0.896419	−	0.752185i	0.969487	+	0.245142i	$0.0788347\pi$
$594$	−2.19889e10	−	1.84509e10i	−0.00724711	−	0.00608105i
$595$	1.79053e11	+	1.01546e12i	0.0585672	+	0.332151i
$596$	1.30503e12	+	2.26038e12i	0.423655	+	0.733793i
$597$	1.43888e12	−	2.49221e12i	0.463596	−	0.802972i
$598$	1.00951e11	+	3.67431e10i	0.0322816	+	0.0117495i
$599$	2.64481e12	+	9.62633e11i	0.839410	+	0.305520i	0.725715	−	0.687996i	$-0.241509\pi$
$599$	2.64481e12	+	9.62633e11i	0.839410	+	0.305520i	0.113695	+	0.993516i	$0.463731\pi$
$600$	−7.22166e11	+	1.25083e12i	−0.227487	+	0.394019i
$601$	5.27146e11	+	9.13044e11i	0.164815	+	0.285467i	0.936589	−	0.350429i	$-0.113964\pi$
$601$	5.27146e11	+	9.13044e11i	0.164815	+	0.285467i	−0.771775	+	0.635896i	$0.780631\pi$
$602$	5.23866e10	+	2.97099e11i	0.0162568	+	0.0921971i
$603$	−3.77543e12	−	3.16797e12i	−1.16289	−	0.975781i
$604$	−2.04596e12	+	1.71676e12i	−0.625504	+	0.524860i
$605$	4.55851e10	−	2.58526e11i	0.0138332	−	0.0784521i
$606$	3.10980e11	−	1.13187e11i	0.0936710	−	0.0340935i
$607$	−5.99389e12			−1.79209			−0.896045	−	0.443963i	$-0.853572\pi$
$607$	−5.99389e12			−1.79209			−0.896045	+	0.443963i	$0.853572\pi$
$608$	5.84776e11	−	1.13296e11i	0.173549	−	0.0336241i
$609$	−3.17583e12			−0.935577
$610$	−4.79242e11	+	1.74430e11i	−0.140143	+	0.0510078i
$611$	3.12593e10	−	1.77280e11i	0.00907390	−	0.0514606i
$612$	1.76698e12	−	1.48267e12i	0.509154	−	0.427231i
$613$	7.59358e11	+	6.37177e11i	0.217207	+	0.182259i	0.744899	−	0.667178i	$-0.232498\pi$
$613$	7.59358e11	+	6.37177e11i	0.217207	+	0.182259i	−0.527691	+	0.849436i	$0.676942\pi$
$614$	3.02005e11	+	1.71275e12i	0.0857543	+	0.486337i
$615$	−3.32027e11	−	5.75088e11i	−0.0935913	−	0.162105i
$616$	−6.02945e11	+	1.04433e12i	−0.168719	+	0.292230i
$617$	−5.50824e11	−	2.00484e11i	−0.153013	−	0.0556923i	0.264378	−	0.964419i	$-0.414833\pi$
$617$	−5.50824e11	−	2.00484e11i	−0.153013	−	0.0556923i	−0.417391	+	0.908727i	$0.637056\pi$
$618$	4.08252e12	+	1.48591e12i	1.12585	+	0.409775i
$619$	1.54061e11	−	2.66841e11i	0.0421779	−	0.0730542i	−0.844166	−	0.536082i	$-0.819904\pi$
$619$	1.54061e11	−	2.66841e11i	0.0421779	−	0.0730542i	0.886344	+	0.463028i	$0.153237\pi$
$620$	−7.01137e10	−	1.21440e11i	−0.0190564	−	0.0330066i
$621$	3.44939e9	+	1.95625e10i	0.000930744	+	0.00527851i
$622$	8.98415e11	+	7.53860e11i	0.240669	+	0.201945i
$623$	−4.49712e12	+	3.77353e12i	−1.19602	+	1.00358i
$624$	−2.49846e10	+	1.41695e11i	−0.00659692	+	0.0374130i
$625$	−2.66472e12	+	9.69879e11i	−0.698541	+	0.254248i
$626$	8.02099e11			0.208758
$627$	3.87366e12	−	4.77758e12i	1.00096	−	1.23454i
$628$	1.97530e12			0.506775
$629$	4.14234e10	−	1.50769e10i	0.0105516	−	0.00384046i
$630$	−1.21117e11	+	6.86887e11i	−0.0306317	+	0.173721i
$631$	−3.05479e12	+	2.56328e12i	−0.767096	+	0.643670i	−0.939964	−	0.341275i	$-0.889141\pi$
$631$	−3.05479e12	+	2.56328e12i	−0.767096	+	0.643670i	0.172867	+	0.984945i	$0.444697\pi$
$632$	−1.21019e12	−	1.01547e12i	−0.301735	−	0.253185i
$633$	3.23656e11	+	1.83555e12i	0.0801249	+	0.454411i
$634$	1.04110e12	+	1.80324e12i	0.255913	+	0.443254i
$635$	1.07763e12	−	1.86651e12i	0.263020	−	0.455564i
$636$	−3.11683e12	−	1.13443e12i	−0.755364	−	0.274930i
$637$	−1.18493e11	−	4.31280e10i	−0.0285145	−	0.0103784i
$638$	1.30354e12	−	2.25780e12i	0.311481	−	0.539502i
$639$	−3.25810e12	−	5.64320e12i	−0.773056	−	1.33897i
$640$	−1.93393e10	−	1.09679e11i	−0.00455650	−	0.0258412i
$641$	−4.22347e12	−	3.54392e12i	−0.988118	−	0.829129i	−0.00282377	−	0.999996i	$-0.500899\pi$
$641$	−4.22347e12	−	3.54392e12i	−0.988118	−	0.829129i	−0.985294	+	0.170867i	$0.945343\pi$
$642$	4.01087e12	−	3.36552e12i	0.931818	−	0.781889i
$643$	−8.88628e11	+	5.03966e12i	−0.205008	+	1.16266i	0.692419	+	0.721495i	$0.256545\pi$
$643$	−8.88628e11	+	5.03966e12i	−0.205008	+	1.16266i	−0.897427	+	0.441163i	$0.854566\pi$
$644$	7.84180e11	−	2.85418e11i	0.179651	−	0.0653876i
$645$	−2.87703e11			−0.0654523
$646$	−2.75083e12	−	3.16840e12i	−0.621467	−	0.715803i
$647$	−4.91143e12			−1.10189			−0.550946	−	0.834541i	$-0.685733\pi$
$647$	−4.91143e12			−1.10189			−0.550946	+	0.834541i	$0.685733\pi$
$648$	−1.50362e12	+	5.47273e11i	−0.335005	+	0.121932i
$649$	1.36624e12	−	7.74831e12i	0.302291	−	1.71438i
$650$	−2.42055e11	+	2.03108e11i	−0.0531867	+	0.0446290i
$651$	1.07801e12	+	9.04557e11i	0.235238	+	0.197388i
$652$	−2.13563e11	−	1.21117e12i	−0.0462819	−	0.262478i
$653$	−2.38742e12	−	4.13513e12i	−0.513830	−	0.889979i	−0.999871	−	0.0160434i	$-0.994893\pi$
$653$	−2.38742e12	−	4.13513e12i	−0.513830	−	0.889979i	0.486042	−	0.873936i	$-0.338440\pi$
$654$	1.42109e12	−	2.46140e12i	0.303754	−	0.526117i
$655$	−2.68207e11	−	9.76195e10i	−0.0569357	−	0.0207229i
$656$	−4.97844e11	−	1.81200e11i	−0.104961	−	0.0382025i
$657$	−6.35886e11	+	1.10139e12i	−0.133148	+	0.230619i
$658$	−6.99173e11	−	1.21100e12i	−0.145401	−	0.251842i
$659$	1.07006e12	+	6.06864e12i	0.221017	+	1.25345i	0.870155	+	0.492779i	$0.164019\pi$
$659$	1.07006e12	+	6.06864e12i	0.221017	+	1.25345i	−0.649138	+	0.760671i	$0.724870\pi$
$660$	−8.80958e11	−	7.39212e11i	−0.180721	−	0.151643i
$661$	−3.45300e12	+	2.89741e12i	−0.703542	+	0.590342i	−0.922779	−	0.385330i	$-0.874088\pi$
$661$	−3.45300e12	+	2.89741e12i	−0.703542	+	0.590342i	0.219237	+	0.975672i	$0.429643\pi$
$662$	−1.36644e10	+	7.74948e10i	−0.00276522	+	0.0156824i
$663$	9.52412e11	−	3.46650e11i	0.191432	−	0.0696754i
$664$	−4.80835e11			−0.0959930
$665$	1.25303e12	+	1.99250e11i	0.248465	+	0.0395094i
$666$	2.98183e10			0.00587284
$667$	−1.69537e12	+	6.17063e11i	−0.331663	+	0.120716i
$668$	−4.00940e11	+	2.27384e12i	−0.0779085	+	0.441841i
$669$	6.88528e12	−	5.77743e12i	1.32894	−	1.11511i
$670$	1.28410e12	+	1.07749e12i	0.246185	+	0.206574i
$671$	7.29580e11	+	4.13766e12i	0.138938	+	0.787958i
$672$	5.58827e11	+	9.67916e11i	0.105710	+	0.183095i
$673$	2.04980e12	−	3.55035e12i	0.385162	−	0.667120i	−0.606630	−	0.794984i	$-0.707479\pi$
$673$	2.04980e12	−	3.55035e12i	0.385162	−	0.667120i	0.991792	+	0.127865i	$0.0408124\pi$
$674$	4.02668e12	+	1.46559e12i	0.751584	+	0.273554i
$675$	−5.49026e10	−	1.99829e10i	−0.0101795	−	0.00370503i
$676$	1.34164e12	−	2.32378e12i	0.247101	−	0.427992i
$677$	−6.48253e11	−	1.12281e12i	−0.118603	−	0.205426i	0.800611	−	0.599184i	$-0.204508\pi$
$677$	−6.48253e11	−	1.12281e12i	−0.118603	−	0.205426i	−0.919214	+	0.393758i	$0.871175\pi$
$678$	−8.49993e10	−	4.82055e11i	−0.0154483	−	0.0876119i
$679$	6.39479e11	+	5.36586e11i	0.115455	+	0.0968781i
$680$	−6.00983e11	+	5.04285e11i	−0.107788	+	0.0904453i
$681$	−1.92774e12	+	1.09328e13i	−0.343468	+	1.94790i
$682$	−1.08556e12	+	3.95110e11i	−0.192142	+	0.0699340i
$683$	2.07011e12			0.364000			0.182000	−	0.983299i	$-0.441743\pi$
$683$	2.07011e12			0.364000			0.182000	+	0.983299i	$0.441743\pi$
$684$	−1.01551e12	−	2.65036e12i	−0.177391	−	0.462970i
$685$	−9.79115e11			−0.169913
$686$	−4.18671e12	+	1.52384e12i	−0.721795	+	0.262712i
$687$	1.09682e12	−	6.22037e12i	0.187858	−	1.06540i
$688$	−1.75833e11	+	1.47542e11i	−0.0299194	+	0.0251054i
$689$	−5.55871e11	−	4.66431e11i	−0.0939696	−	0.0788499i
$690$	1.38195e11	+	7.83746e11i	0.0232099	+	0.131630i
$691$	2.90922e12	+	5.03892e12i	0.485428	+	0.840787i	0.999860	−	0.0167448i	$-0.00533029\pi$
$691$	2.90922e12	+	5.03892e12i	0.485428	+	0.840787i	−0.514431	+	0.857532i	$0.671997\pi$
$692$	−7.45778e11	+	1.29172e12i	−0.123632	+	0.214137i
$693$	5.39950e12	+	1.96526e12i	0.889311	+	0.323683i
$694$	−7.89000e12	−	2.87173e12i	−1.29110	−	0.469921i
$695$	−6.47598e11	+	1.12167e12i	−0.105287	+	0.182362i
$696$	−1.20816e12	−	2.09260e12i	−0.195157	−	0.338021i
$697$	6.48059e11	+	3.67533e12i	0.104008	+	0.589859i
$698$	6.55768e12	+	5.50255e12i	1.04569	+	0.877434i
$699$	−5.07766e12	+	4.26066e12i	−0.804481	+	0.675040i
$700$	−4.26221e11	+	2.41722e12i	−0.0670955	+	0.380518i
$701$	−1.19548e12	+	4.35121e11i	−0.186988	+	0.0680579i	−0.433817	−	0.901001i	$-0.642834\pi$
$701$	−1.19548e12	+	4.35121e11i	−0.186988	+	0.0680579i	0.246829	+	0.969059i	$0.420611\pi$
$702$	−5.82026e9			−0.000904534
$703$	−9.13357e8	−	5.42341e10i	−0.000141040	−	0.00837478i
$704$	−9.17498e11			−0.140776
$705$	1.25312e12	−	4.56100e11i	0.191048	−	0.0695359i
$706$	−7.20876e11	+	4.08829e12i	−0.109204	+	0.619328i
$707$	4.30822e11	−	3.61503e11i	0.0648501	−	0.0544157i
$708$	−5.58611e12	−	4.68730e12i	−0.835525	−	0.701089i
$709$	−3.27828e11	−	1.85920e12i	−0.0487234	−	0.276324i	0.950706	−	0.310093i	$-0.100360\pi$
$709$	−3.27828e11	−	1.85920e12i	−0.0487234	−	0.276324i	−0.999430	+	0.0337686i	$0.989249\pi$
$710$	1.10814e12	+	1.91936e12i	0.163657	+	0.283462i
$711$	−3.76381e12	+	6.51912e12i	−0.552351	+	0.956699i
$712$	−4.19724e12	−	1.52767e12i	−0.612074	−	0.222777i
$713$	7.51233e11	+	2.73426e11i	0.108861	+	0.0396221i
$714$	3.93654e12	−	6.81828e12i	0.566855	−	0.981822i
$715$	−1.25795e11	−	2.17884e11i	−0.0180006	−	0.0311779i
$716$	5.71232e11	+	3.23962e12i	0.0812277	+	0.460665i
$717$	−1.03657e13	−	8.69789e12i	−1.46475	−	1.22907i
$718$	7.37411e12	−	6.18762e12i	1.03550	−	0.868887i
$719$	−5.63939e11	+	3.19826e12i	−0.0786959	+	0.446306i	0.919844	+	0.392285i	$0.128315\pi$
$719$	−5.63939e11	+	3.19826e12i	−0.0786959	+	0.446306i	−0.998540	+	0.0540218i	$0.982796\pi$
$720$	−4.98675e11	+	1.81503e11i	−0.0691546	+	0.0251702i
$721$	7.38312e12			1.01749
$722$	−4.78942e12	+	1.92822e12i	−0.655943	+	0.264082i
$723$	−1.01403e12			−0.138016
$724$	3.82077e12	−	1.39065e12i	0.516806	−	0.188102i
$725$	9.21473e11	−	5.22593e12i	0.123869	−	0.702494i
$726$	−1.53546e12	+	1.28841e12i	−0.205128	+	0.172123i
$727$	−1.75833e11	−	1.47542e11i	−0.0233452	−	0.0195889i	0.631040	−	0.775750i	$-0.282628\pi$
$727$	−1.75833e11	−	1.47542e11i	−0.0233452	−	0.0195889i	−0.654386	+	0.756161i	$0.727073\pi$
$728$	4.24590e10	+	2.40797e11i	0.00560246	+	0.0317731i
$729$	3.74834e12	+	6.49231e12i	0.491547	+	0.851384i
$730$	2.16277e11	−	3.74603e11i	0.0281876	−	0.0488223i
$731$	1.51939e12	+	5.53014e11i	0.196808	+	0.0716321i
$732$	3.65922e12	+	1.33185e12i	0.471073	+	0.171457i
$733$	2.44554e12	−	4.23580e12i	0.312901	−	0.541960i	−0.666088	−	0.745873i	$-0.732033\pi$
$733$	2.44554e12	−	4.23580e12i	0.312901	−	0.541960i	0.978989	+	0.203913i	$0.0653660\pi$
$734$	1.88431e12	+	3.26373e12i	0.239619	+	0.415032i
$735$	−1.62210e11	−	9.19937e11i	−0.0205014	−	0.116269i
$736$	4.86386e11	+	4.08126e11i	0.0610986	+	0.0512678i
$737$	1.05787e13	−	8.87658e12i	1.32077	−	1.10826i
$738$	−4.38367e11	+	2.48610e12i	−0.0543981	+	0.308507i
$739$	1.39937e13	−	5.09329e12i	1.72597	−	0.628201i	0.727637	−	0.685962i	$-0.240618\pi$
$739$	1.39937e13	−	5.09329e12i	1.72597	−	0.628201i	0.998330	+	0.0577609i	$0.0183961\pi$
$740$	−1.01418e10			−0.00124329
$741$	−2.10000e10	−	1.24696e12i	−0.00255881	−	0.151939i
$742$	−5.63670e12			−0.682665
$743$	7.09536e12	−	2.58250e12i	0.854132	−	0.310879i	0.122408	−	0.992480i	$-0.460938\pi$
$743$	7.09536e12	−	2.58250e12i	0.854132	−	0.310879i	0.731724	+	0.681601i	$0.238716\pi$
$744$	−1.85924e11	+	1.05443e12i	−0.0222463	+	0.126165i
$745$	−3.24038e12	+	2.71901e12i	−0.385384	+	0.323375i
$746$	−4.47186e12	−	3.75233e12i	−0.528644	−	0.443585i
$747$	3.97856e11	+	2.25636e12i	0.0467502	+	0.265134i
$748$	3.23156e12	+	5.59722e12i	0.377446	+	0.653756i
$749$	4.44890e12	−	7.70572e12i	0.516517	−	0.894634i
$750$	−4.61180e12	−	1.67856e12i	−0.532224	−	0.193714i
$751$	8.06988e12	+	2.93720e12i	0.925737	+	0.336941i	0.760518	−	0.649316i	$-0.224945\pi$
$751$	8.06988e12	+	2.93720e12i	0.925737	+	0.336941i	0.165219	+	0.986257i	$0.447167\pi$
$752$	5.31963e11	−	9.21388e11i	0.0606599	−	0.105066i
$753$	3.24749e12	+	5.62482e12i	0.368104	+	0.637575i
$754$	−9.17947e10	−	5.20594e11i	−0.0103430	−	0.0586581i
$755$	−3.31580e12	−	2.78228e12i	−0.371387	−	0.311631i
$756$	−3.46339e10	+	2.90613e10i	−0.00385614	+	0.00323569i
$757$	2.56914e12	−	1.45703e13i	0.284352	−	1.61264i	−0.423240	−	0.906018i	$-0.639107\pi$
$757$	2.56914e12	−	1.45703e13i	0.284352	−	1.61264i	0.707592	−	0.706622i	$-0.249782\pi$
$758$	4.68262e12	−	1.70433e12i	0.515202	−	0.187518i
$759$	6.55628e12			0.717083
$760$	3.45395e11	+	9.01440e11i	0.0375539	+	0.0980111i
$761$	−1.82793e13			−1.97573			−0.987866	−	0.155311i	$-0.950362\pi$
$761$	−1.82793e13			−1.97573			−0.987866	+	0.155311i	$0.950362\pi$
$762$	−1.54639e13	+	5.62841e12i	−1.66158	+	0.604767i
$763$	8.38726e11	−	4.75665e12i	0.0895900	−	0.508090i
$764$	7.91701e11	−	6.64316e11i	0.0840700	−	0.0705431i
$765$	2.86367e12	+	2.40290e12i	0.302305	+	0.253664i
$766$	1.13279e12	+	6.42440e12i	0.118884	+	0.674222i
$767$	−7.97660e11	−	1.38159e12i	−0.0832221	−	0.144145i
$768$	−4.25182e11	+	7.36436e11i	−0.0441011	+	0.0763853i
$769$	1.09757e13	+	3.99483e12i	1.13179	+	0.411936i	0.838940	−	0.544224i	$-0.183176\pi$
$769$	1.09757e13	+	3.99483e12i	1.13179	+	0.411936i	0.292845	+	0.956160i	$0.405398\pi$
$770$	−1.83647e12	−	6.68422e11i	−0.188268	−	0.0685240i
$771$	−1.22969e13	+	2.12988e13i	−1.25329	+	2.17076i
$772$	4.89763e12	+	8.48295e12i	0.496259	+	0.859546i
$773$	9.40859e11	+	5.33588e12i	0.0947801	+	0.537524i	0.994815	+	0.101706i	$0.0324300\pi$
$773$	9.40859e11	+	5.33588e12i	0.0947801	+	0.537524i	−0.900034	+	0.435819i	$0.856459\pi$
$774$	8.37841e11	+	7.03032e11i	0.0839126	+	0.0704110i
$775$	−1.80126e12	+	1.51144e12i	−0.179358	+	0.150499i
$776$	−1.10291e11	+	6.25491e11i	−0.0109185	+	0.0619217i
$777$	9.56391e10	−	3.48098e10i	0.00941328	−	0.00342615i
$778$	−1.50163e12			−0.146945
$779$	4.53520e12	+	7.21159e11i	0.441243	+	0.0701637i
$780$	−2.33181e11			−0.0225563
$781$	1.71572e13	−	6.24470e12i	1.65012	−	0.600596i
$782$	7.76666e11	−	4.40469e12i	0.0742684	−	0.421197i
$783$	7.48771e10	−	6.28293e10i	0.00711903	−	0.00597358i
$784$	−5.70906e11	−	4.79047e11i	−0.0539687	−	0.0452851i
$785$	5.55898e11	+	3.15266e12i	0.0522495	+	0.296321i
$786$	1.08965e12	+	1.88733e12i	0.101833	+	0.176379i
$787$	−3.87794e12	+	6.71679e12i	−0.360342	+	0.624131i	−0.988017	−	0.154345i	$-0.950673\pi$
$787$	−3.87794e12	+	6.71679e12i	−0.360342	+	0.624131i	0.627675	+	0.778476i	$0.284007\pi$
$788$	−5.04834e12	−	1.83745e12i	−0.466424	−	0.169764i
$789$	−5.01787e12	−	1.82636e12i	−0.460971	−	0.167780i
$790$	1.28015e12	−	2.21728e12i	0.116933	−	0.202534i
$791$	−4.15923e11	−	7.20400e11i	−0.0377762	−	0.0654304i
$792$	7.59163e11	+	4.30543e12i	0.0685602	+	0.388824i
$793$	6.52603e11	+	5.47599e11i	0.0586030	+	0.0491737i
$794$	9.18087e12	−	7.70366e12i	0.819769	−	0.687868i
$795$	9.33446e11	−	5.29384e12i	0.0828776	−	0.470022i
$796$	3.49651e12	−	1.27263e12i	0.308693	−	0.112355i
$797$	4.99629e12			0.438617			0.219308	−	0.975656i	$-0.429620\pi$
$797$	4.99629e12			0.438617			0.219308	+	0.975656i	$0.429620\pi$
$798$	−6.35118e12	−	7.31526e12i	−0.554423	−	0.638582i
$799$	−7.49461e12			−0.650561
$800$	−1.75488e12	+	6.38725e11i	−0.151476	+	0.0551326i
$801$	−3.69580e12	+	2.09599e13i	−0.317221	+	1.79905i
$802$	−3.83083e12	+	3.21445e12i	−0.326970	+	0.274361i
$803$	−2.72978e12	−	2.29056e12i	−0.231691	−	0.194412i
$804$	−2.22253e12	−	1.26046e13i	−0.187584	−	1.06384i
$805$	6.76225e11	+	1.17126e12i	0.0567558	+	0.0983039i
$806$	−1.17119e11	+	2.02857e11i	−0.00977510	+	0.0169310i
$807$	−2.80434e13	−	1.02070e13i	−2.32756	−	0.847161i
$808$	4.02094e11	+	1.46350e11i	0.0331876	+	0.0120793i
$809$	−5.65001e12	+	9.78611e12i	−0.463747	+	0.803233i	−0.999144	−	0.0413674i	$-0.986829\pi$
$809$	−5.65001e12	+	9.78611e12i	−0.463747	+	0.803233i	0.535397	+	0.844600i	$0.320162\pi$
$810$	−1.29662e12	−	2.24582e12i	−0.105836	−	0.183313i
$811$	2.37423e12	+	1.34649e13i	0.192721	+	1.09298i	0.915627	+	0.402030i	$0.131695\pi$
$811$	2.37423e12	+	1.34649e13i	0.192721	+	1.09298i	−0.722905	+	0.690947i	$0.757194\pi$
$812$	−3.14562e12	−	2.63949e12i	−0.253924	−	0.213068i
$813$	2.51384e13	−	2.10936e13i	2.01804	−	1.69334i
$814$	−1.45083e10	+	8.22809e10i	−0.00115827	+	0.00656885i
$815$	1.87298e12	−	6.81708e11i	0.148704	−	0.0541239i
$816$	5.99020e12			0.472972
$817$	1.25302e12	−	1.54542e12i	0.0983921	−	0.121352i
$818$	−8.64582e12			−0.675175
$819$	1.09483e12	−	3.98484e11i	0.0850292	−	0.0309481i
$820$	1.49097e11	−	8.45572e11i	0.0115161	−	0.0653113i
$821$	−5.91813e12	+	4.96590e12i	−0.454612	+	0.381465i	−0.841144	−	0.540811i	$-0.818117\pi$
$821$	−5.91813e12	+	4.96590e12i	−0.454612	+	0.381465i	0.386532	+	0.922276i	$0.373673\pi$
$822$	5.72692e12	+	4.80545e12i	0.437520	+	0.367123i
$823$	3.01189e12	+	1.70813e13i	0.228844	+	1.29784i	0.855199	+	0.518300i	$0.173435\pi$
$823$	3.01189e12	+	1.70813e13i	0.228844	+	1.29784i	−0.626355	+	0.779538i	$0.715454\pi$
$824$	2.80871e12	+	4.86483e12i	0.212244	+	0.367617i
$825$	−9.64188e12	+	1.67002e13i	−0.724635	+	1.25510i
$826$	−1.16450e13	−	4.23843e12i	−0.870419	−	0.316807i
$827$	−1.63166e13	−	5.93877e12i	−1.21299	−	0.441491i	−0.345247	−	0.938512i	$-0.612205\pi$
$827$	−1.63166e13	−	5.93877e12i	−1.21299	−	0.441491i	−0.867739	+	0.497021i	$0.834427\pi$
$828$	1.51272e12	−	2.62010e12i	0.111846	−	0.193723i
$829$	−8.91696e12	−	1.54446e13i	−0.655724	−	1.13575i	−0.981712	−	0.190374i	$-0.939030\pi$
$829$	−8.91696e12	−	1.54446e13i	−0.655724	−	1.13575i	0.325987	−	0.945374i	$-0.394303\pi$
$830$	−1.35319e11	−	7.67431e11i	−0.00989707	−	0.0561290i
$831$	−1.73135e13	−	1.45278e13i	−1.25945	−	1.05680i
$832$	−1.42512e11	+	1.19582e11i	−0.0103109	+	0.00865186i
$833$	−9.11628e11	+	5.17010e12i	−0.0656017	+	0.372046i
$834$	9.29297e12	−	3.38236e12i	0.665131	−	0.242088i
$835$	−3.74197e12			−0.266386
$836$	7.80755e12	−	1.51266e12i	0.552823	−	0.107106i
$837$	−4.33118e10			−0.00305029
$838$	−2.30778e12	+	8.39965e11i	−0.161658	+	0.0588387i
$839$	9.21044e11	−	5.22350e12i	0.0641729	−	0.363943i	−0.935763	−	0.352629i	$-0.885288\pi$
$839$	9.21044e11	−	5.22350e12i	0.0641729	−	0.363943i	0.999936	−	0.0113133i	$-0.00360121\pi$
$840$	−1.38756e12	+	1.16430e12i	−0.0961603	+	0.0806881i
$841$	−4.31241e12	−	3.61854e12i	−0.297261	−	0.249431i
$842$	−1.54837e12	−	8.78126e12i	−0.106163	−	0.602078i
$843$	−1.80378e13	−	3.12425e13i	−1.23016	−	2.13069i
$844$	−1.20498e12	+	2.08708e12i	−0.0817407	+	0.141579i
$845$	4.08642e12	+	1.48733e12i	0.275732	+	0.100358i
$846$	−4.76384e12	−	1.73390e12i	−0.319736	−	0.116374i
$847$	−1.70315e12	+	2.94995e12i	−0.113705	+	0.196942i
$848$	−2.14434e12	−	3.71410e12i	−0.142400	−	0.246645i
$849$	6.30854e11	+	3.57775e12i	0.0416720	+	0.236334i
$850$	1.00775e13	+	8.45603e12i	0.662167	+	0.555624i
$851$	4.42919e10	−	3.71653e10i	0.00289495	−	0.00242915i
$852$	2.93853e12	−	1.66652e13i	0.191052	−	1.08351i
$853$	−8.96067e12	+	3.26142e12i	−0.579522	+	0.210929i	−0.615115	−	0.788438i	$-0.710890\pi$
$853$	−8.96067e12	+	3.26142e12i	−0.579522	+	0.210929i	0.0355928	+	0.999366i	$0.488668\pi$
$854$	6.61760e12			0.425736
$855$	3.94429e12	−	2.36667e12i	0.252418	−	0.151457i
$856$	6.76987e12			0.430971
$857$	1.86405e13	−	6.78459e12i	1.18044	−	0.429645i	0.324083	−	0.946029i	$-0.394944\pi$
$857$	1.86405e13	−	6.78459e12i	1.18044	−	0.429645i	0.856357	+	0.516384i	$0.172722\pi$
$858$	−3.33578e11	+	1.89181e12i	−0.0210138	+	0.119175i
$859$	8.06045e12	−	6.76352e12i	0.505115	−	0.423842i	−0.354291	−	0.935135i	$-0.615278\pi$
$859$	8.06045e12	−	6.76352e12i	0.505115	−	0.423842i	0.859406	+	0.511293i	$0.170833\pi$
$860$	−2.84966e11	−	2.39115e11i	−0.0177644	−	0.0149061i
$861$	1.49625e12	+	8.48567e12i	0.0927878	+	0.526226i
$862$	3.24351e12	+	5.61792e12i	0.200093	+	0.346572i
$863$	9.96823e10	−	1.72655e11i	0.00611744	−	0.0105957i	−0.862950	−	0.505289i	$-0.831386\pi$
$863$	9.96823e10	−	1.72655e11i	0.00611744	−	0.0105957i	0.869068	+	0.494693i	$0.164719\pi$
$864$	−3.23244e10	−	1.17651e10i	−0.00197342	−	0.000718265i
$865$	−2.27152e12	−	8.26766e11i	−0.137957	−	0.0502123i
$866$	−9.69353e12	+	1.67897e13i	−0.585668	+	1.01441i
$867$	−9.35871e12	−	1.62098e13i	−0.562510	−	0.974295i
$868$	3.15961e11	+	1.79191e12i	0.0188928	+	0.107146i
$869$	−1.61576e13	−	1.35578e13i	−0.961143	−	0.806495i
$870$	2.99986e12	−	2.51718e12i	0.177527	−	0.148963i
$871$	4.86229e11	−	2.75754e12i	0.0286259	−	0.162345i
$872$	3.45329e12	−	1.25689e12i	0.202259	−	0.0736164i
$873$	3.02642e12			0.176346
$874$	−4.81183e12	−	2.67110e12i	−0.278939	−	0.154842i
$875$	−8.34031e12			−0.481001
$876$	−3.10356e12	+	1.12960e12i	−0.178070	+	0.0648123i
$877$	5.13689e11	−	2.91327e12i	0.0293226	−	0.166297i	−0.966630	−	0.256176i	$-0.917537\pi$
$877$	5.13689e11	−	2.91327e12i	0.0293226	−	0.166297i	0.995953	+	0.0898799i	$0.0286483\pi$
$878$	−1.65367e12	+	1.38759e12i	−0.0939126	+	0.0788020i
$879$	2.27745e13	+	1.91101e13i	1.28677	+	1.07972i
$880$	−2.58206e11	−	1.46436e12i	−0.0145143	−	0.0823144i
$881$	−3.07670e12	−	5.32900e12i	−0.172066	−	0.298026i	0.767076	−	0.641556i	$-0.221711\pi$
$881$	−3.07670e12	−	5.32900e12i	−0.172066	−	0.298026i	−0.939142	+	0.343530i	$0.888377\pi$
$882$	−1.77558e12	+	3.07540e12i	−0.0987942	+	0.171117i
$883$	1.82077e13	+	6.62708e12i	1.00794	+	0.366859i	0.792640	−	0.609690i	$-0.208706\pi$
$883$	1.82077e13	+	6.62708e12i	1.00794	+	0.366859i	0.215296	+	0.976549i	$0.430928\pi$
$884$	1.23146e12	+	4.48214e11i	0.0678242	+	0.0246860i
$885$	5.90904e12	−	1.02348e13i	0.323796	−	0.560832i
$886$	1.01514e13	+	1.75828e13i	0.553447	+	0.958598i
$887$	−4.49638e12	−	2.55003e13i	−0.243897	−	1.38321i	−0.823039	−	0.567984i	$-0.807723\pi$
$887$	−4.49638e12	−	2.55003e13i	−0.243897	−	1.38321i	0.579142	−	0.815227i	$-0.303388\pi$
$888$	5.93200e10	+	4.97754e10i	0.00320142	+	0.00268631i
$889$	−2.14233e13	+	1.79763e13i	−1.15034	+	0.965253i
$890$	1.25701e12	−	7.12887e12i	0.0671560	−	0.380860i
$891$	−2.00754e13	+	7.30684e12i	−1.06712	+	0.388400i
$892$	1.16215e13			0.614640
$893$	−3.00773e12	+	8.71769e12i	−0.158273	+	0.458743i
$894$	3.22980e13			1.69105
$895$	−5.00979e12	+	1.82342e12i	−0.260985	+	0.0949909i
$896$	−2.50942e11	+	1.42316e12i	−0.0130073	+	0.0737680i
$897$	1.01836e12	−	8.54510e11i	0.0525215	−	0.0440708i
$898$	5.01697e12	+	4.20974e12i	0.257453	+	0.216029i
$899$	−6.83096e11	−	3.87403e12i	−0.0348789	−	0.197808i
$900$	4.44930e12	+	7.70642e12i	0.226048	+	0.391527i
$901$	−1.51053e13	+	2.61632e13i	−0.763604	+	1.32260i
$902$	−6.64689e12	−	2.41927e12i	−0.334340	−	0.121690i
$903$	3.50801e12	+	1.27681e12i	0.175576	+	0.0639045i
$904$	3.16454e11	−	5.48114e11i	0.0157599	−	0.0272969i
$905$	3.29478e12	+	5.70673e12i	0.163271	+	0.282793i
$906$	5.73901e12	+	3.25476e13i	0.282983	+	1.60488i
$907$	2.25416e13	+	1.89147e13i	1.10599	+	0.928038i	0.997813	−	0.0660929i	$-0.0210534\pi$
$907$	2.25416e13	+	1.89147e13i	1.10599	+	0.928038i	0.108180	+	0.994131i	$0.465498\pi$
$908$	−1.09958e13	+	9.22658e12i	−0.536835	+	0.450458i
$909$	3.54056e11	−	2.00795e12i	0.0172002	−	0.0975473i
$910$	−3.72372e11	+	1.35532e11i	−0.0180008	+	0.00655174i
$911$	3.01200e13			1.44885			0.724424	−	0.689355i	$-0.242106\pi$
$911$	3.01200e13			1.44885			0.724424	+	0.689355i	$0.242106\pi$
$912$	2.40398e12	−	6.96777e12i	0.115068	−	0.333516i
$913$	−6.41980e12			−0.305776
$914$	−9.87104e12	+	3.59276e12i	−0.467848	+	0.170283i
$915$	−1.09588e12	+	6.21506e12i	−0.0516856	+	0.293123i
$916$	6.25625e12	−	5.24962e12i	0.293619	−	0.246376i
$917$	2.83707e12	+	2.38058e12i	0.132498	+	0.111179i
$918$	4.20777e10	+	2.38634e11i	0.00195551	+	0.0110902i
$919$	6.78589e12	+	1.17535e13i	0.313824	+	0.543560i	0.979187	−	0.202961i	$-0.0650563\pi$
$919$	6.78589e12	+	1.17535e13i	0.313824	+	0.543560i	−0.665362	+	0.746520i	$0.731723\pi$
$920$	−5.14504e11	+	8.91147e11i	−0.0236779	+	0.0410114i
$921$	2.02234e13	+	7.36071e12i	0.926159	+	0.337094i
$922$	−5.88340e12	−	2.14138e12i	−0.268126	−	0.0975900i
$923$	1.85107e12	−	3.20614e12i	0.0839488	−	0.145404i
$924$	7.46109e12	+	1.29230e13i	0.336727	+	0.583229i
$925$	2.95308e10	+	1.67477e11i	0.00132629	+	0.00752174i
$926$	1.42433e13	+	1.19515e13i	0.636592	+	0.534164i
$927$	2.05046e13	−	1.72054e13i	0.911995	−	0.765255i
$928$	5.42526e11	−	3.07682e12i	0.0240134	−	0.136187i
$929$	−1.15332e13	+	4.19775e12i	−0.508019	+	0.184904i	−0.583297	−	0.812259i	$-0.698238\pi$
$929$	−1.15332e13	+	4.19775e12i	−0.508019	+	0.184904i	0.0752784	+	0.997163i	$0.476015\pi$
$930$	−1.73523e12			−0.0760649
$931$	5.64798e12	+	3.13526e12i	0.246388	+	0.136773i
$932$	−8.57047e12			−0.372077
$933$	1.36375e13	−	4.96363e12i	0.589205	−	0.214453i
$934$	2.89152e12	−	1.63986e13i	0.124327	−	0.705093i
$935$	−8.02394e12	+	6.73288e12i	−0.343349	+	0.288104i
$936$	6.79065e11	+	5.69803e11i	0.0289181	+	0.0242652i
$937$	2.05467e12	+	1.16526e13i	0.0870789	+	0.493849i	0.996889	+	0.0788233i	$0.0251163\pi$
$937$	2.05467e12	+	1.16526e13i	0.0870789	+	0.493849i	−0.909810	+	0.415026i	$0.863773\pi$
$938$	−1.08754e13	−	1.88368e13i	−0.458704	−	0.794499i
$939$	4.96275e12	−	8.59574e12i	0.208318	−	0.360818i
$940$	1.62028e12	+	5.89732e11i	0.0676883	+	0.0246365i
$941$	4.78608e12	+	1.74199e12i	0.198988	+	0.0724256i	0.439592	−	0.898198i	$-0.355123\pi$
$941$	4.78608e12	+	1.74199e12i	0.198988	+	0.0724256i	−0.240604	+	0.970623i	$0.577345\pi$
$942$	1.22216e13	−	2.11684e13i	0.505707	−	0.875911i
$943$	2.44751e12	+	4.23921e12i	0.100791	+	0.174575i
$944$	−1.63727e12	−	9.28543e12i	−0.0671037	−	0.380564i
$945$	−5.61297e10	−	4.70984e10i	−0.00228955	−	0.00192116i
$946$	−2.34761e12	+	1.96988e12i	−0.0953052	+	0.0799705i
$947$	−8.64616e11	+	4.90348e12i	−0.0349340	+	0.198121i	−0.997280	−	0.0737072i	$-0.976517\pi$
$947$	−8.64616e11	+	4.90348e12i	−0.0349340	+	0.198121i	0.962346	+	0.271828i	$0.0876281\pi$
$948$	−1.83700e13	+	6.68613e12i	−0.738705	+	0.268867i
$949$	−7.22548e11			−0.0289180
$950$	1.38803e13	−	8.32853e12i	0.552895	−	0.331751i
$951$	2.57661e13			1.02149
$952$	9.56589e12	−	3.48170e12i	0.377450	−	0.137380i
$953$	−3.39039e12	+	1.92279e13i	−0.133147	+	0.755115i	0.842985	+	0.537937i	$0.180796\pi$
$953$	−3.39039e12	+	1.92279e13i	−0.133147	+	0.755115i	−0.976132	+	0.217178i	$0.930315\pi$
$954$	−1.56544e13	+	1.31356e13i	−0.611884	+	0.513432i
$955$	1.28308e12	+	1.07663e12i	0.0499158	+	0.0418843i
$956$	−3.03817e12	−	1.72303e13i	−0.117639	−	0.667164i
$957$	−1.61306e13	−	2.79390e13i	−0.621651	−	1.07673i
$958$	1.53468e13	−	2.65815e13i	0.588673	−	1.01961i
$959$	1.19385e13	+	4.34527e12i	0.455792	+	0.165895i
$960$	−1.29504e12	−	4.71355e11i	−0.0492109	−	0.0179113i
$961$	1.23483e13	−	2.13878e13i	0.467036	−	0.808930i
$962$	8.47052e9	+	1.46714e10i	0.000318876	+	0.000552310i
$963$	−5.60158e12	−	3.17681e13i	−0.209890	−	1.19035i
$964$	−1.00439e12	−	8.42780e11i	−0.0374588	−	0.0314317i
$965$	−1.21608e13	+	1.02041e13i	−0.451428	+	0.378793i
$966$	1.79318e12	−	1.01697e13i	0.0662564	−	0.375759i
$967$	2.79349e13	−	1.01675e13i	1.02737	−	0.373933i	0.227293	−	0.973826i	$-0.427012\pi$
$967$	2.79349e13	−	1.01675e13i	1.02737	−	0.373933i	0.800080	+	0.599893i	$0.204790\pi$
$968$	−2.59168e12			−0.0948728
$969$	−5.09743e13	+	9.87593e12i	−1.85735	+	0.359850i
$970$	−1.02935e12			−0.0373326
$971$	5.20000e11	−	1.89265e11i	0.0187723	−	0.00683255i	−0.332617	−	0.943062i	$-0.607932\pi$
$971$	5.20000e11	−	1.89265e11i	0.0187723	−	0.00683255i	0.351389	+	0.936229i	$0.385709\pi$
$972$	−3.40963e12	+	1.93370e13i	−0.122520	+	0.694848i
$973$	1.28742e13	−	1.08027e13i	0.460482	−	0.386390i
$974$	−2.33635e13	−	1.96043e13i	−0.831809	−	0.697970i
$975$	6.78976e11	+	3.85066e12i	0.0240621	+	0.136463i
$976$	2.51749e12	+	4.36042e12i	0.0888063	+	0.153817i
$977$	−2.75975e12	+	4.78003e12i	−0.0969046	+	0.167844i	−0.910402	−	0.413725i	$-0.864228\pi$
$977$	−2.75975e12	+	4.78003e12i	−0.0969046	+	0.167844i	0.813497	+	0.581569i	$0.197561\pi$
$978$	−1.43010e13	−	5.20513e12i	−0.499851	−	0.181931i
$979$	−5.60388e13	−	2.03965e13i	−1.94970	−	0.709631i
$980$	6.03909e11	−	1.04600e12i	0.0209148	−	0.0362256i
$981$	−8.75542e12	−	1.51648e13i	−0.301833	−	0.522790i
$982$	4.48821e12	+	2.54539e13i	0.154018	+	0.873479i
$983$	3.72241e13	+	3.12347e13i	1.27155	+	1.06696i	0.994351	+	0.106144i	$0.0338504\pi$
$983$	3.72241e13	+	3.12347e13i	1.27155	+	1.06696i	0.277198	+	0.960813i	$0.410594\pi$
$984$	−5.02211e12	+	4.21405e12i	−0.170769	+	0.143292i
$985$	1.51191e12	−	8.57444e12i	0.0511755	−	0.290230i
$986$	−2.06811e13	+	7.52729e12i	−0.696830	+	0.253625i
$987$	−1.73037e13			−0.580379
$988$	1.01557e12	−	1.25255e12i	0.0339081	−	0.0418205i
$989$	2.12078e12			0.0704874
$990$	−6.65798e12	+	2.42331e12i	−0.220284	+	0.0801770i
$991$	−3.53027e12	+	2.00212e13i	−0.116273	+	0.659414i	0.869840	+	0.493334i	$0.164222\pi$
$991$	−3.53027e12	+	2.00212e13i	−0.116273	+	0.659414i	−0.986112	+	0.166080i	$0.946889\pi$
$992$	−1.06051e12	+	8.89875e11i	−0.0347706	+	0.0291760i
$993$	7.45933e11	+	6.25912e11i	0.0243460	+	0.0204287i
$994$	−4.99376e12	−	2.83210e13i	−0.162252	−	0.920175i
$995$	3.01516e12	+	5.22242e12i	0.0975230	+	0.168915i
$996$	−2.97503e12	+	5.15290e12i	−0.0957908	+	0.165915i
$997$	−1.87244e13	−	6.81512e12i	−0.600177	−	0.218447i	0.0240225	−	0.999711i	$-0.492353\pi$
$997$	−1.87244e13	−	6.81512e12i	−0.600177	−	0.218447i	−0.624200	+	0.781265i	$0.714575\pi$
$998$	−2.17837e13	−	7.92863e12i	−0.695096	−	0.252994i
$999$	−1.56624e9	+	2.71280e9i	−4.97522e−5	+	8.61734e-5i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.e.a.5.7	✓	42
19.4	even	9	inner	38.10.e.a.23.7	yes	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.e.a.5.7	✓	42	1.1	even	1	trivial
38.10.e.a.23.7	yes	42	19.4	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 38 = 2 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	38.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(15.0351 - 5.47232i) q^{2} +(34.3807 - 194.983i) q^{3} +(196.107 - 164.554i) q^{4} +(317.823 + 266.685i) q^{5} +(-550.092 - 3119.72i) q^{6} +(-2691.74 - 4662.22i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-18340.3 - 6675.31i) q^{9} +O(q^{10})\)	\(q+(15.0351 - 5.47232i) q^{2} +(34.3807 - 194.983i) q^{3} +(196.107 - 164.554i) q^{4} +(317.823 + 266.685i) q^{5} +(-550.092 - 3119.72i) q^{6} +(-2691.74 - 4662.22i) q^{7} +(2048.00 - 3547.24i) q^{8} +(-18340.3 - 6675.31i) q^{9} +(6237.88 + 2270.40i) q^{10} +(27343.6 - 47360.4i) q^{11} +(-25342.8 - 43895.0i) q^{12} +(-1925.52 - 10920.2i) q^{13} +(-65983.7 - 55366.9i) q^{14} +(62926.0 - 52801.2i) q^{15} +(11380.2 - 64540.4i) q^{16} +(-433813. + 157895. i) q^{17} -312277. q^{18} +(9565.28 + 567976. i) q^{19} +106211. q^{20} +(-1.00160e6 + 364552. i) q^{21} +(151941. - 861701. i) q^{22} +(-463854. + 389220. i) q^{23} +(-621239. - 521281. i) q^{24} +(-309266. - 1.75394e6i) q^{25} +(-88708.9 - 153648. i) q^{26} +(16402.7 - 28410.3i) q^{27} +(-1.29506e6 - 471362. i) q^{28} +(2.79986e6 + 1.01907e6i) q^{29} +(657153. - 1.13822e6i) q^{30} +(-660133. - 1.14338e6i) q^{31} +(-182083. - 1.03265e6i) q^{32} +(-8.29438e6 - 6.95981e6i) q^{33} +(-5.65836e6 + 4.74793e6i) q^{34} +(387850. - 2.19961e6i) q^{35} +(-4.69511e6 + 1.70888e6i) q^{36} -95486.6 q^{37} +(3.25196e6 + 8.48721e6i) q^{38} -2.19544e6 q^{39} +(1.59690e6 - 581223. i) q^{40} +(1.40378e6 - 7.96121e6i) q^{41} +(-1.30642e7 + 1.09621e7i) q^{42} +(-2.68301e6 - 2.25131e6i) q^{43} +(-2.43106e6 - 1.37872e7i) q^{44} +(-4.04875e6 - 7.01265e6i) q^{45} +(-4.84415e6 + 8.39031e6i) q^{46} +(1.52552e7 + 5.55244e6i) q^{47} +(-1.21930e7 - 4.43789e6i) q^{48} +(5.68592e6 - 9.84829e6i) q^{49} +(-1.42479e7 - 2.46782e7i) q^{50} +(1.58720e7 + 9.00146e7i) q^{51} +(-2.17456e6 - 1.82467e6i) q^{52} +(5.01299e7 - 4.20640e7i) q^{53} +(91145.5 - 516912. i) q^{54} +(2.13207e7 - 7.76012e6i) q^{55} -2.20507e7 q^{56} +(1.11074e8 + 1.76623e7i) q^{57} +4.76728e7 q^{58} +(1.35194e8 - 4.92065e7i) q^{59} +(3.65163e6 - 2.07094e7i) q^{60} +(-5.88534e7 + 4.93839e7i) q^{61} +(-1.61821e7 - 1.35784e7i) q^{62} +(1.82454e7 + 1.03475e8i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(2.30027e6 - 3.98418e6i) q^{65} +(-1.62793e8 - 5.92518e7i) q^{66} +(2.37290e8 + 8.63664e7i) q^{67} +(-5.90918e7 + 1.02350e8i) q^{68} +(5.99435e7 + 1.03825e8i) q^{69} +(-6.20561e6 - 3.51937e7i) q^{70} +(2.55758e8 + 2.14606e8i) q^{71} +(-6.12398e7 + 5.13863e7i) q^{72} +(1.13151e7 - 6.41713e7i) q^{73} +(-1.43565e6 + 522534. i) q^{74} -3.52620e8 q^{75} +(9.53383e7 + 1.09810e8i) q^{76} -2.94407e8 q^{77} +(-3.30087e7 + 1.20142e7i) q^{78} +(6.69743e7 - 3.79830e8i) q^{79} +(2.08289e7 - 1.74775e7i) q^{80} +(-2.99259e8 - 2.51108e8i) q^{81} +(-2.24604e7 - 1.27379e8i) q^{82} +(-5.86957e7 - 1.01664e8i) q^{83} +(-1.36432e8 + 2.36308e8i) q^{84} +(-1.79984e8 - 6.55089e7i) q^{85} +(-5.26591e7 - 1.91663e7i) q^{86} +(2.94961e8 - 5.10888e8i) q^{87} +(-1.11999e8 - 1.93988e8i) q^{88} +(-1.89360e8 - 1.07391e9i) q^{89} +(-9.92488e7 - 8.32797e7i) q^{90} +(-4.57292e7 + 3.83714e7i) q^{91} +(-2.69177e7 + 1.52658e8i) q^{92} +(-2.45636e8 + 8.94042e7i) q^{93} +2.59748e8 q^{94} +(-1.48431e8 + 1.83067e8i) q^{95} -2.07608e8 q^{96} +(-1.45712e8 + 5.30348e7i) q^{97} +(3.15952e7 - 1.79185e8i) q^{98} +(-8.17634e8 + 6.86076e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9}+O(q^{10}) \) 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9	\( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9} + 32625 q^{11} - 62208 q^{12} + 351237 q^{13} + 165264 q^{14} - 834165 q^{15} + 1075035 q^{17} - 3364608 q^{18} + 696762 q^{19} - 1396224 q^{20} - 3148065 q^{21} - 1462656 q^{22} - 4882824 q^{23} + 1032192 q^{24} - 483270 q^{25} - 70176 q^{26} + 2570400 q^{27} + 1519104 q^{28} + 13670499 q^{29} - 2263968 q^{31} - 5777733 q^{33} - 9526080 q^{34} + 43019613 q^{35} + 3290112 q^{36} - 50105184 q^{37} - 692160 q^{38} - 89820600 q^{39} - 94033860 q^{41} - 43526160 q^{42} + 30524217 q^{43} + 23402496 q^{44} + 39789630 q^{45} - 18312576 q^{46} + 81865791 q^{47} + 33030144 q^{48} + 40421580 q^{49} - 16761600 q^{50} - 28132314 q^{51} - 91666176 q^{52} + 126049077 q^{53} - 106214544 q^{54} + 553870071 q^{55} + 117743616 q^{56} + 384197394 q^{57} - 63148512 q^{58} + 135312639 q^{59} - 129611520 q^{60} + 132517452 q^{61} - 419324112 q^{62} + 577860735 q^{63} - 352321536 q^{64} - 184218951 q^{65} + 413765760 q^{66} + 229749621 q^{67} + 152743680 q^{68} - 517946637 q^{69} - 688313808 q^{70} - 2107934406 q^{71} + 105283584 q^{72} - 26577420 q^{73} + 322027248 q^{74} + 941894730 q^{75} - 107163648 q^{76} + 620006124 q^{77} + 122597280 q^{78} - 624601023 q^{79} - 1037387736 q^{81} + 1504541760 q^{82} + 907729401 q^{83} - 604998912 q^{84} + 1462808898 q^{85} + 222950208 q^{86} + 63648732 q^{87} - 133632000 q^{88} - 847590846 q^{89} - 4481693280 q^{90} + 957045924 q^{91} + 648163584 q^{92} + 2438307564 q^{93} + 2205393024 q^{94} - 208077987 q^{95} - 509607936 q^{96} + 535342599 q^{97} + 1861154832 q^{98} - 11757151095 q^{99}+O(q^{100}) \) 42 * q - 252 * q^3 + 4032 * q^6 + 14373 * q^7 + 86016 * q^8 + 12852 * q^9 + 32625 * q^11 - 62208 * q^12 + 351237 * q^13 + 165264 * q^14 - 834165 * q^15 + 1075035 * q^17 - 3364608 * q^18 + 696762 * q^19 - 1396224 * q^20 - 3148065 * q^21 - 1462656 * q^22 - 4882824 * q^23 + 1032192 * q^24 - 483270 * q^25 - 70176 * q^26 + 2570400 * q^27 + 1519104 * q^28 + 13670499 * q^29 - 2263968 * q^31 - 5777733 * q^33 - 9526080 * q^34 + 43019613 * q^35 + 3290112 * q^36 - 50105184 * q^37 - 692160 * q^38 - 89820600 * q^39 - 94033860 * q^41 - 43526160 * q^42 + 30524217 * q^43 + 23402496 * q^44 + 39789630 * q^45 - 18312576 * q^46 + 81865791 * q^47 + 33030144 * q^48 + 40421580 * q^49 - 16761600 * q^50 - 28132314 * q^51 - 91666176 * q^52 + 126049077 * q^53 - 106214544 * q^54 + 553870071 * q^55 + 117743616 * q^56 + 384197394 * q^57 - 63148512 * q^58 + 135312639 * q^59 - 129611520 * q^60 + 132517452 * q^61 - 419324112 * q^62 + 577860735 * q^63 - 352321536 * q^64 - 184218951 * q^65 + 413765760 * q^66 + 229749621 * q^67 + 152743680 * q^68 - 517946637 * q^69 - 688313808 * q^70 - 2107934406 * q^71 + 105283584 * q^72 - 26577420 * q^73 + 322027248 * q^74 + 941894730 * q^75 - 107163648 * q^76 + 620006124 * q^77 + 122597280 * q^78 - 624601023 * q^79 - 1037387736 * q^81 + 1504541760 * q^82 + 907729401 * q^83 - 604998912 * q^84 + 1462808898 * q^85 + 222950208 * q^86 + 63648732 * q^87 - 133632000 * q^88 - 847590846 * q^89 - 4481693280 * q^90 + 957045924 * q^91 + 648163584 * q^92 + 2438307564 * q^93 + 2205393024 * q^94 - 208077987 * q^95 - 509607936 * q^96 + 535342599 * q^97 + 1861154832 * q^98 - 11757151095 * q^99

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