LMFDB - Embedded newform 38.10.e.a.23.1

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			23.1
Character	$\chi$	$=$	38.23
Dual form			38.10.e.a.5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(15.0351 + 5.47232i) q^{2} +(-40.8678 - 231.773i) q^{3} +(196.107 + 164.554i) q^{4} +(1498.95 - 1257.77i) q^{5} +(653.886 - 3708.37i) q^{6} +(4614.74 - 7992.96i) q^{7} +(2048.00 + 3547.24i) q^{8} +(-33552.6 + 12212.2i) q^{9} +O(q^{10})$	\(q+(15.0351 + 5.47232i) q^{2} +(-40.8678 - 231.773i) q^{3} +(196.107 + 164.554i) q^{4} +(1498.95 - 1257.77i) q^{5} +(653.886 - 3708.37i) q^{6} +(4614.74 - 7992.96i) q^{7} +(2048.00 + 3547.24i) q^{8} +(-33552.6 + 12212.2i) q^{9} +(29419.8 - 10707.9i) q^{10} +(28104.0 + 48677.6i) q^{11} +(30124.6 - 52177.4i) q^{12} +(4970.79 - 28190.7i) q^{13} +(113123. - 94921.5i) q^{14} +(-352776. - 296014. i) q^{15} +(11380.2 + 64540.4i) q^{16} +(307210. + 111815. i) q^{17} -571295. q^{18} +(-565801. - 50562.0i) q^{19} +500926. q^{20} +(-2.04115e6 - 742917. i) q^{21} +(156167. + 885666. i) q^{22} +(-1.27457e6 - 1.06950e6i) q^{23} +(738457. - 619639. i) q^{24} +(325714. - 1.84722e6i) q^{25} +(229005. - 396648. i) q^{26} +(1.88549e6 + 3.26576e6i) q^{27} +(2.22025e6 - 808106. i) q^{28} +(4.94722e6 - 1.80064e6i) q^{29} +(-3.68413e6 - 6.38110e6i) q^{30} +(-4.32408e6 + 7.48952e6i) q^{31} +(-182083. + 1.03265e6i) q^{32} +(1.01336e7 - 8.50311e6i) q^{33} +(4.00703e6 + 3.36230e6i) q^{34} +(-3.13603e6 - 1.77853e7i) q^{35} +(-8.58947e6 - 3.12631e6i) q^{36} -8.65237e6 q^{37} +(-8.23018e6 - 3.85645e6i) q^{38} -6.73700e6 q^{39} +(7.53146e6 + 2.74123e6i) q^{40} +(5.38288e6 + 3.05278e7i) q^{41} +(-2.66233e7 - 2.23396e7i) q^{42} +(1.15676e7 - 9.70638e6i) q^{43} +(-2.49867e6 + 1.41707e7i) q^{44} +(-3.49337e7 + 6.05069e7i) q^{45} +(-1.33107e7 - 2.30548e7i) q^{46} +(1.55086e6 - 564467. i) q^{47} +(1.44936e7 - 5.27525e6i) q^{48} +(-2.24148e7 - 3.88235e7i) q^{49} +(1.50057e7 - 2.59906e7i) q^{50} +(1.33608e7 - 7.57726e7i) q^{51} +(5.61370e6 - 4.71045e6i) q^{52} +(7.90004e7 + 6.62892e7i) q^{53} +(1.04772e7 + 5.94190e7i) q^{54} +(1.03352e8 + 3.76170e7i) q^{55} +3.78039e7 q^{56} +(1.14042e7 + 1.33204e8i) q^{57} +8.42355e7 q^{58} +(20072.4 + 7305.75i) q^{59} +(-2.04718e7 - 1.16101e8i) q^{60} +(-5.93046e7 - 4.97625e7i) q^{61} +(-1.05998e8 + 8.89429e7i) q^{62} +(-5.72252e7 + 3.24541e8i) q^{63} +(-8.38861e6 + 1.45295e7i) q^{64} +(-2.80065e7 - 4.85086e7i) q^{65} +(1.98891e8 - 7.23905e7i) q^{66} +(1.41877e8 - 5.16390e7i) q^{67} +(4.18465e7 + 7.24803e7i) q^{68} +(-1.95791e8 + 3.39120e8i) q^{69} +(5.01765e7 - 2.84565e8i) q^{70} +(-1.04149e8 + 8.73917e7i) q^{71} +(-1.12035e8 - 9.40087e7i) q^{72} +(1.24888e6 + 7.08273e6i) q^{73} +(-1.30089e8 - 4.73485e7i) q^{74} -4.41446e8 q^{75} +(-1.02638e8 - 1.03020e8i) q^{76} +5.18771e8 q^{77} +(-1.01291e8 - 3.68670e7i) q^{78} +(-3.51951e7 - 1.99602e8i) q^{79} +(9.82352e7 + 8.24292e7i) q^{80} +(1.41484e8 - 1.18719e8i) q^{81} +(-8.61261e7 + 4.88445e8i) q^{82} +(2.94929e8 - 5.10832e8i) q^{83} +(-2.78034e8 - 4.81570e8i) q^{84} +(6.01130e8 - 2.18793e8i) q^{85} +(2.27036e8 - 8.26345e7i) q^{86} +(-6.19522e8 - 1.07304e9i) q^{87} +(-1.15114e8 + 1.99383e8i) q^{88} +(-3.33097e7 + 1.88909e8i) q^{89} +(-8.56343e8 + 7.18557e8i) q^{90} +(-2.02389e8 - 1.69824e8i) q^{91} +(-7.39642e7 - 4.19472e8i) q^{92} +(1.91259e9 + 6.96124e8i) q^{93} +2.64063e7 q^{94} +(-9.11704e8 + 6.35858e8i) q^{95} +2.46781e8 q^{96} +(-2.75018e8 - 1.00098e8i) q^{97} +(-1.24553e8 - 7.06376e8i) q^{98} +(-1.53742e9 - 1.29005e9i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{1}{9}\right)$

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
$3$	−40.8678	−	231.773i	−0.291297	−	1.65203i	−0.681883	−	0.731461i	$-0.738839\pi$
$3$	−40.8678	−	231.773i	−0.291297	−	1.65203i	0.390586	−	0.920567i	$-0.372272\pi$
$4$	196.107	+	164.554i	0.383022	+	0.321394i
$5$	1498.95	−	1257.77i	1.07256	−	0.899986i	0.0772798	−	0.997009i	$-0.475377\pi$
$5$	1498.95	−	1257.77i	1.07256	−	0.899986i	0.995282	+	0.0970231i	$0.0309321\pi$
$6$	653.886	−	3708.37i	0.205978	−	1.16816i
$7$	4614.74	−	7992.96i	0.726450	−	1.25825i	−0.231924	−	0.972734i	$-0.574502\pi$
$7$	4614.74	−	7992.96i	0.726450	−	1.25825i	0.958374	−	0.285514i	$-0.0921645\pi$
$8$	2048.00	+	3547.24i	0.176777	+	0.306186i
$9$	−33552.6	+	12212.2i	−1.70465	+	0.620442i
$10$	29419.8	−	10707.9i	0.930335	−	0.338614i
$11$	28104.0	+	48677.6i	0.578764	+	1.00245i	0.995621	+	0.0934767i	$0.0297981\pi$
$11$	28104.0	+	48677.6i	0.578764	+	1.00245i	−0.416858	+	0.908972i	$0.636869\pi$
$12$	30124.6	−	52177.4i	0.419378	−	0.726384i
$13$	4970.79	−	28190.7i	0.0482703	−	0.273755i	−0.951114	−	0.308840i	$-0.900059\pi$
$13$	4970.79	−	28190.7i	0.0482703	−	0.273755i	0.999384	+	0.0350854i	$0.0111703\pi$
$14$	113123.	−	94921.5i	0.787000	−	0.660371i
$15$	−352776.	−	296014.i	−1.79924	−	1.50974i
$16$	11380.2	+	64540.4i	0.0434120	+	0.246202i
$17$	307210.	+	111815.i	0.892103	+	0.324699i	0.747084	−	0.664730i	$-0.231453\pi$
$17$	307210.	+	111815.i	0.892103	+	0.324699i	0.145019	+	0.989429i	$0.453676\pi$
$18$	−571295.			−1.28273
$19$	−565801.	−	50562.0i	−0.996031	−	0.0890088i
$19$	−565801.	−	50562.0i	−0.996031	−	0.0890088i
$20$	500926.			0.700065
$21$	−2.04115e6	−	742917.i	−2.29027	−	0.833592i
$22$	156167.	+	885666.i	0.142130	+	0.806061i
$23$	−1.27457e6	−	1.06950e6i	−0.949708	−	0.796900i	0.0295403	−	0.999564i	$-0.490596\pi$
$23$	−1.27457e6	−	1.06950e6i	−0.949708	−	0.796900i	−0.979248	+	0.202664i	$0.935040\pi$
$24$	738457.	−	619639.i	0.454334	−	0.381231i
$25$	325714.	−	1.84722e6i	0.166766	−	0.945774i
$26$	229005.	−	396648.i	0.0982800	−	0.170226i
$27$	1.88549e6	+	3.26576e6i	0.682790	+	1.18263i
$28$	2.22025e6	−	808106.i	0.682640	−	0.248461i
$29$	4.94722e6	−	1.80064e6i	1.29888	−	0.472755i	0.402251	−	0.915530i	$-0.368228\pi$
$29$	4.94722e6	−	1.80064e6i	1.29888	−	0.472755i	0.896633	+	0.442775i	$0.146006\pi$
$30$	−3.68413e6	−	6.38110e6i	−0.830404	−	1.43830i
$31$	−4.32408e6	+	7.48952e6i	−0.840942	+	1.45655i	0.0481575	+	0.998840i	$0.484665\pi$
$31$	−4.32408e6	+	7.48952e6i	−0.840942	+	1.45655i	−0.889099	+	0.457714i	$0.848668\pi$
$32$	−182083.	+	1.03265e6i	−0.0306970	+	0.174091i
$33$	1.01336e7	−	8.50311e6i	1.48748	−	1.24814i
$34$	4.00703e6	+	3.36230e6i	0.514243	+	0.431501i
$35$	−3.13603e6	−	1.77853e7i	−0.353244	−	2.00334i
$36$	−8.58947e6	−	3.12631e6i	−0.852325	−	0.310221i
$37$	−8.65237e6			−0.758974			−0.379487	−	0.925197i	$-0.623900\pi$
$37$	−8.65237e6			−0.758974			−0.379487	+	0.925197i	$0.623900\pi$
$38$	−8.23018e6	−	3.85645e6i	−0.640299	−	0.300028i
$39$	−6.73700e6			−0.466311
$40$	7.53146e6	+	2.74123e6i	0.465167	+	0.169307i
$41$	5.38288e6	+	3.05278e7i	0.297500	+	1.68721i	0.656863	+	0.754010i	$0.271883\pi$
$41$	5.38288e6	+	3.05278e7i	0.297500	+	1.68721i	−0.359363	+	0.933198i	$0.617006\pi$
$42$	−2.66233e7	−	2.23396e7i	−1.32020	−	1.10778i
$43$	1.15676e7	−	9.70638e6i	0.515983	−	0.432961i	−0.347246	−	0.937774i	$-0.612883\pi$
$43$	1.15676e7	−	9.70638e6i	0.515983	−	0.432961i	0.863229	+	0.504813i	$0.168439\pi$
$44$	−2.49867e6	+	1.41707e7i	−0.100501	+	0.569971i
$45$	−3.49337e7	+	6.05069e7i	−1.26995	+	2.19962i
$46$	−1.33107e7	−	2.30548e7i	−0.438320	−	0.759192i
$47$	1.55086e6	−	564467.i	0.0463588	−	0.0168732i	−0.318737	−	0.947843i	$-0.603259\pi$
$47$	1.55086e6	−	564467.i	0.0463588	−	0.0168732i	0.365095	+	0.930970i	$0.381036\pi$
$48$	1.44936e7	−	5.27525e6i	0.394087	−	0.143436i
$49$	−2.24148e7	−	3.88235e7i	−0.555459	−	0.962083i
$50$	1.50057e7	−	2.59906e7i	0.339540	−	0.588101i
$51$	1.33608e7	−	7.57726e7i	0.276545	−	1.56836i
$52$	5.61370e6	−	4.71045e6i	0.106472	−	0.0893403i
$53$	7.90004e7	+	6.62892e7i	1.37527	+	1.15399i	0.970925	+	0.239382i	$0.0769448\pi$
$53$	7.90004e7	+	6.62892e7i	1.37527	+	1.15399i	0.404345	+	0.914607i	$0.367500\pi$
$54$	1.04772e7	+	5.94190e7i	0.167677	+	0.950941i
$55$	1.03352e8	+	3.76170e7i	1.52295	+	0.554309i
$56$	3.78039e7			0.513678
$57$	1.14042e7	+	1.33204e8i	0.143096	+	1.67140i
$58$	8.42355e7			0.977393
$59$	20072.4	+	7305.75i	0.000215658	+	7.84929e-5i	0.342128	−	0.939653i	$-0.388852\pi$
$59$	20072.4	+	7305.75i	0.000215658	+	7.84929e-5i	−0.341912	+	0.939732i	$0.611075\pi$
$60$	−2.04718e7	−	1.16101e8i	−0.203927	−	1.15653i
$61$	−5.93046e7	−	4.97625e7i	−0.548408	−	0.460169i	0.325993	−	0.945372i	$-0.394301\pi$
$61$	−5.93046e7	−	4.97625e7i	−0.548408	−	0.460169i	−0.874402	+	0.485203i	$0.838746\pi$
$62$	−1.05998e8	+	8.89429e7i	−0.911035	+	0.764449i
$63$	−5.72252e7	+	3.24541e8i	−0.457673	+	2.59559i
$64$	−8.38861e6	+	1.45295e7i	−0.0625000	+	0.108253i
$65$	−2.80065e7	−	4.85086e7i	−0.194602	−	0.337061i
$66$	1.98891e8	−	7.23905e7i	1.29023	−	0.469606i
$67$	1.41877e8	−	5.16390e7i	0.860152	−	0.313070i	0.125980	−	0.992033i	$-0.459793\pi$
$67$	1.41877e8	−	5.16390e7i	0.860152	−	0.313070i	0.734172	+	0.678963i	$0.237570\pi$
$68$	4.18465e7	+	7.24803e7i	0.237339	+	0.411083i
$69$	−1.95791e8	+	3.39120e8i	−1.03985	+	1.80108i
$70$	5.01765e7	−	2.84565e8i	0.249781	−	1.41658i
$71$	−1.04149e8	+	8.73917e7i	−0.486400	+	0.408138i	−0.852734	−	0.522345i	$-0.825057\pi$
$71$	−1.04149e8	+	8.73917e7i	−0.486400	+	0.408138i	0.366334	+	0.930484i	$0.380613\pi$
$72$	−1.12035e8	−	9.40087e7i	−0.491313	−	0.412261i
$73$	1.24888e6	+	7.08273e6i	0.00514715	+	0.0291909i	0.987273	−	0.159034i	$-0.0508378\pi$
$73$	1.24888e6	+	7.08273e6i	0.00514715	+	0.0291909i	−0.982126	+	0.188225i	$0.939727\pi$
$74$	−1.30089e8	−	4.73485e7i	−0.504310	−	0.183554i
$75$	−4.41446e8			−1.61102
$76$	−1.02638e8	−	1.03020e8i	−0.352895	−	0.354210i
$77$	5.18771e8			1.68177
$78$	−1.01291e8	−	3.68670e7i	−0.309847	−	0.112775i
$79$	−3.51951e7	−	1.99602e8i	−0.101662	−	0.576557i	−0.992501	−	0.122237i	$-0.960993\pi$
$79$	−3.51951e7	−	1.99602e8i	−0.101662	−	0.576557i	0.890839	−	0.454320i	$-0.150118\pi$
$80$	9.82352e7	+	8.24292e7i	0.268140	+	0.224997i
$81$	1.41484e8	−	1.18719e8i	0.365195	−	0.306435i
$82$	−8.61261e7	+	4.88445e8i	−0.210364	+	1.19304i
$83$	2.94929e8	−	5.10832e8i	0.682128	−	1.18148i	−0.292202	−	0.956357i	$-0.594388\pi$
$83$	2.94929e8	−	5.10832e8i	0.682128	−	1.18148i	0.974330	−	0.225124i	$-0.0722786\pi$
$84$	−2.78034e8	−	4.81570e8i	−0.609315	−	1.05536i
$85$	6.01130e8	−	2.18793e8i	1.24906	−	0.454621i
$86$	2.27036e8	−	8.26345e7i	0.447561	−	0.162899i
$87$	−6.19522e8	−	1.07304e9i	−1.15937	−	2.00808i
$88$	−1.15114e8	+	1.99383e8i	−0.204624	+	0.354419i
$89$	−3.33097e7	+	1.88909e8i	−0.0562751	+	0.319152i	−0.999931	−	0.0117774i	$-0.996251\pi$
$89$	−3.33097e7	+	1.88909e8i	−0.0562751	+	0.319152i	0.943656	+	0.330929i	$0.107362\pi$
$90$	−8.56343e8	+	7.18557e8i	−1.37580	+	1.15444i
$91$	−2.02389e8	−	1.69824e8i	−0.309385	−	0.259605i
$92$	−7.39642e7	−	4.19472e8i	−0.107641	−	0.610461i
$93$	1.91259e9	+	6.96124e8i	2.65123	+	0.964969i
$94$	2.64063e7			0.0348844
$95$	−9.11704e8	+	6.35858e8i	−1.14841	+	0.800947i
$96$	2.46781e8			0.296545
$97$	−2.75018e8	−	1.00098e8i	−0.315419	−	0.114803i	0.179459	−	0.983765i	$-0.442565\pi$
$97$	−2.75018e8	−	1.00098e8i	−0.315419	−	0.114803i	−0.494878	+	0.868962i	$0.664787\pi$
$98$	−1.24553e8	−	7.06376e8i	−0.136407	−	0.773604i
$99$	−1.53742e9	−	1.29005e9i	−1.60855	−	1.34973i
$100$	3.67841e8	−	3.08655e8i	0.367841	−	0.308655i
$101$	2.05039e8	−	1.16283e9i	0.196060	−	1.11191i	−0.714840	−	0.699288i	$-0.753501\pi$
$101$	2.05039e8	−	1.16283e9i	0.196060	−	1.11191i	0.910901	−	0.412626i	$-0.135388\pi$
$102$	6.15532e8	−	1.06613e9i	0.563054	−	0.975238i
$103$	3.90397e8	+	6.76188e8i	0.341774	+	0.591970i	0.984762	−	0.173906i	$-0.0556388\pi$
$103$	3.90397e8	+	6.76188e8i	0.341774	+	0.591970i	−0.642988	+	0.765876i	$0.722306\pi$
$104$	1.10180e8	−	4.01021e7i	0.0923530	−	0.0336137i
$105$	−3.99400e9	+	1.45370e9i	−3.20668	+	1.16714i
$106$	8.25022e8	+	1.42898e9i	0.634730	+	1.09938i
$107$	4.52721e7	−	7.84136e7i	0.0333890	−	0.0578315i	−0.848848	−	0.528637i	$-0.822703\pi$
$107$	4.52721e7	−	7.84136e7i	0.0333890	−	0.0578315i	0.882237	+	0.470805i	$0.156037\pi$
$108$	−1.67635e8	+	9.50704e8i	−0.118565	+	0.672417i
$109$	1.62316e9	−	1.36200e9i	1.10139	−	0.924179i	0.103876	−	0.994590i	$-0.466875\pi$
$109$	1.62316e9	−	1.36200e9i	1.10139	−	0.924179i	0.997518	+	0.0704108i	$0.0224310\pi$
$110$	1.34805e9	+	1.13115e9i	0.877887	+	0.736635i
$111$	3.53604e8	+	2.00539e9i	0.221087	+	1.25385i
$112$	5.68385e8	+	2.06875e8i	0.341320	+	0.124230i
$113$	1.41967e9			0.819097			0.409548	−	0.912288i	$-0.365686\pi$
$113$	1.41967e9			0.819097			0.409548	+	0.912288i	$0.365686\pi$
$114$	−5.57472e8	+	2.06514e9i	−0.309137	+	1.14519i
$115$	−3.25570e9			−1.73582
$116$	1.26649e9	+	4.60964e8i	0.649442	+	0.236377i
$117$	1.77487e8	+	1.00658e9i	0.0875648	+	0.496605i
$118$	261810.	+	219685.i	0.000124313	+	0.000104311i
$119$	2.31143e9	−	1.93952e9i	1.05662	−	0.886609i
$120$	3.27548e8	−	1.85762e9i	0.144198	−	0.817788i
$121$	−4.00699e8	+	6.94031e8i	−0.169935	+	0.294337i
$122$	−6.19333e8	−	1.07272e9i	−0.253108	−	0.438395i
$123$	6.85554e9	−	2.49521e9i	2.70065	−	0.982957i
$124$	−2.08041e9	+	7.57208e8i	−0.790227	+	0.287619i
$125$	7.57387e7	+	1.31183e8i	0.0277474	+	0.0480600i
$126$	−2.63638e9	+	4.56634e9i	−0.931837	+	1.61399i
$127$	2.15026e8	−	1.21947e9i	0.0733455	−	0.415963i	−0.925923	−	0.377713i	$-0.876711\pi$
$127$	2.15026e8	−	1.21947e9i	0.0733455	−	0.415963i	0.999268	−	0.0382500i	$-0.0121783\pi$
$128$	−2.05633e8	+	1.72547e8i	−0.0677094	+	0.0568149i
$129$	−2.72242e9	−	2.28438e9i	−0.865569	−	0.726298i
$130$	−1.55625e8	−	8.82592e8i	−0.0477896	−	0.271028i
$131$	−1.75408e9	−	6.38431e8i	−0.520388	−	0.189406i	0.0684534	−	0.997654i	$-0.478194\pi$
$131$	−1.75408e9	−	6.38431e8i	−0.520388	−	0.189406i	−0.588842	+	0.808249i	$0.700416\pi$
$132$	3.38649e9			0.970884
$133$	−3.01516e9	+	4.28910e9i	−0.835562	+	1.18859i
$134$	2.41572e9			0.647253
$135$	6.93383e9	+	2.52371e9i	1.79668	+	0.653939i
$136$	2.32530e8	+	1.31874e9i	0.0582847	+	0.330549i
$137$	−1.76143e9	−	1.47801e9i	−0.427191	−	0.358456i	0.403700	−	0.914892i	$-0.367724\pi$
$137$	−1.76143e9	−	1.47801e9i	−0.427191	−	0.358456i	−0.830891	+	0.556436i	$0.812168\pi$
$138$	−4.79951e9	+	4.02727e9i	−1.12653	+	0.945267i
$139$	5.12396e7	−	2.90594e8i	0.0116423	−	0.0660268i	−0.978433	−	0.206564i	$-0.933772\pi$
$139$	5.12396e7	−	2.90594e8i	0.0116423	−	0.0660268i	0.990075	+	0.140537i	$0.0448830\pi$
$140$	2.31164e9	−	4.00388e9i	0.508562	−	0.880856i
$141$	−1.94209e8	−	3.36379e8i	−0.0413793	−	0.0716710i
$142$	−2.04413e9	+	7.44002e8i	−0.421901	+	0.153559i
$143$	1.51196e9	−	5.50307e8i	0.302362	−	0.110051i
$144$	−1.17001e9	−	2.02652e9i	−0.226756	−	0.392753i
$145$	5.15085e9	−	8.92153e9i	0.967660	−	1.67604i
$146$	−1.99820e7	+	1.13324e8i	−0.00363959	+	0.0206411i
$147$	−8.08221e9	+	6.78178e9i	−1.42759	+	1.19789i
$148$	−1.69679e9	−	1.42378e9i	−0.290704	−	0.243930i
$149$	1.38546e9	+	7.85735e9i	0.230280	+	1.30598i	0.852329	+	0.523006i	$0.175189\pi$
$149$	1.38546e9	+	7.85735e9i	0.230280	+	1.30598i	−0.622049	+	0.782979i	$0.713699\pi$
$150$	−6.63718e9	−	2.41574e9i	−1.07047	−	0.389618i
$151$	4.10289e9			0.642234			0.321117	−	0.947040i	$-0.395942\pi$
$151$	4.10289e9			0.642234			0.321117	+	0.947040i	$0.395942\pi$
$152$	−9.79406e8	−	2.11058e9i	−0.148822	−	0.320706i
$153$	−1.16732e10			−1.72218
$154$	7.79976e9	+	2.83888e9i	1.11748	+	0.406728i
$155$	2.93851e9	+	1.66651e10i	0.408916	+	2.31908i
$156$	−1.32118e9	−	1.10860e9i	−0.178608	−	0.149870i
$157$	−7.77475e9	+	6.52379e9i	−1.02126	+	0.856942i	−0.989786	−	0.142563i	$-0.954466\pi$
$157$	−7.77475e9	+	6.52379e9i	−1.02126	+	0.856942i	−0.0314777	+	0.999504i	$0.510021\pi$
$158$	5.63122e8	−	3.19362e9i	0.0718862	−	0.407687i
$159$	1.21355e10	−	2.10193e10i	1.50581	−	2.60814i
$160$	1.02590e9	+	1.77690e9i	0.123755	+	0.214350i
$161$	−1.44303e10	+	5.25218e9i	−1.69261	+	0.616061i
$162$	2.77689e9	−	1.01071e9i	0.316768	−	0.115294i
$163$	−3.71867e9	−	6.44092e9i	−0.412613	−	0.714667i	0.582562	−	0.812787i	$-0.302050\pi$
$163$	−3.71867e9	−	6.44092e9i	−0.412613	−	0.714667i	−0.995175	+	0.0981199i	$0.968717\pi$
$164$	−3.96784e9	+	6.87250e9i	−0.428309	+	0.741853i
$165$	4.49484e9	−	2.54915e10i	0.472102	−	2.67742i
$166$	7.22972e9	−	6.06645e9i	0.738984	−	0.620081i
$167$	9.63938e9	+	8.08840e9i	0.959014	+	0.804708i	0.980792	−	0.195054i	$-0.0624883\pi$
$167$	9.63938e9	+	8.08840e9i	0.959014	+	0.804708i	−0.0217782	+	0.999763i	$0.506933\pi$
$168$	−1.54496e9	−	8.76193e9i	−0.149633	−	0.848610i
$169$	9.19496e9	+	3.34669e9i	0.867081	+	0.315592i
$170$	1.02353e10			0.939902
$171$	1.96016e10	−	5.21317e9i	1.75311	−	0.466250i
$172$	3.86571e9			0.336784
$173$	−1.51597e9	−	5.51766e8i	−0.128671	−	0.0468325i	0.276882	−	0.960904i	$-0.410699\pi$
$173$	−1.51597e9	−	5.51766e8i	−0.128671	−	0.0468325i	−0.405553	+	0.914071i	$0.632921\pi$
$174$	−3.44253e9	−	1.95235e10i	−0.284712	−	1.61468i
$175$	−1.32616e10	−	1.11278e10i	−1.06887	−	0.896890i
$176$	−2.82184e9	+	2.36781e9i	−0.221679	+	0.186011i
$177$	872961.	−	4.95081e6i	6.68521e−5	−	0.000379137i
$178$	−1.53458e9	+	2.65798e9i	−0.114578	+	0.198455i
$179$	−7.77512e9	−	1.34669e10i	−0.566068	−	0.980458i	−0.996949	−	0.0780495i	$-0.975131\pi$
$179$	−7.77512e9	−	1.34669e10i	−0.566068	−	0.980458i	0.430882	−	0.902408i	$-0.358203\pi$
$180$	−1.68074e10	+	6.11738e9i	−1.19337	+	0.434350i
$181$	−2.34690e10	+	8.54203e9i	−1.62533	+	0.591572i	−0.984387	−	0.176017i	$-0.943679\pi$
$181$	−2.34690e10	+	8.54203e9i	−1.62533	+	0.591572i	−0.640943	+	0.767589i	$0.721456\pi$
$182$	−2.11360e9	−	3.66086e9i	−0.142791	−	0.247321i
$183$	−9.10995e9	+	1.57789e10i	−0.600463	+	1.04003i
$184$	1.18343e9	−	6.71155e9i	0.0761134	−	0.431661i
$185$	−1.29695e10	+	1.08827e10i	−0.814047	+	0.683066i
$186$	2.49465e10	+	2.09326e10i	1.52827	+	1.28237i
$187$	3.19093e9	+	1.80967e10i	0.190823	+	1.08221i
$188$	3.97020e8	+	1.44504e8i	0.0231794	+	0.00843662i
$189$	3.48041e10			1.98405
$190$	−1.71872e10	+	4.57103e9i	−0.956782	+	0.254462i
$191$	−2.04067e10			−1.10949			−0.554744	−	0.832021i	$-0.687184\pi$
$191$	−2.04067e10			−1.10949			−0.554744	+	0.832021i	$0.687184\pi$
$192$	3.71037e9	+	1.35046e9i	0.197043	+	0.0717179i
$193$	2.59293e9	+	1.47052e10i	0.134519	+	0.762894i	0.975194	+	0.221353i	$0.0710475\pi$
$193$	2.59293e9	+	1.47052e10i	0.134519	+	0.762894i	−0.840675	+	0.541540i	$0.817841\pi$
$194$	−3.58715e9	−	3.00997e9i	−0.181820	−	0.152565i
$195$	−1.00984e10	+	8.47359e9i	−0.500148	+	0.419674i
$196$	1.99285e9	−	1.13020e10i	0.0964545	−	0.547020i
$197$	−1.47376e10	+	2.55263e10i	−0.697156	+	1.20751i	0.272293	+	0.962214i	$0.412218\pi$
$197$	−1.47376e10	+	2.55263e10i	−0.697156	+	1.20751i	−0.969449	+	0.245295i	$0.921115\pi$
$198$	−1.60557e10	−	2.78093e10i	−0.742396	−	1.28587i
$199$	−2.01774e10	+	7.34397e9i	−0.912066	+	0.331965i	−0.755078	−	0.655636i	$-0.772401\pi$
$199$	−2.01774e10	+	7.34397e9i	−0.912066	+	0.331965i	−0.156989	+	0.987600i	$0.550179\pi$
$200$	7.21958e9	−	2.62771e9i	0.319063	−	0.116130i
$201$	−1.77667e10	−	3.07729e10i	−0.767760	−	1.32980i
$202$	9.44617e9	−	1.63612e10i	0.399185	−	0.691409i
$203$	8.43767e9	−	4.78524e10i	0.348731	−	1.97775i
$204$	1.50888e10	−	1.26610e10i	0.609985	−	0.511838i
$205$	4.64656e10	+	3.89893e10i	1.83755	+	1.54189i
$206$	2.16934e9	+	1.23029e10i	0.0839314	+	0.475999i
$207$	5.58262e10	+	2.03191e10i	2.11335	+	0.769196i
$208$	1.87601e9			0.0694944
$209$	−1.34401e10	−	2.89628e10i	−0.487240	−	1.04998i
$210$	−6.80052e10			−2.41299
$211$	3.58017e10	+	1.30307e10i	1.24346	+	0.452583i	0.878187	−	0.478317i	$-0.158753\pi$
$211$	3.58017e10	+	1.30307e10i	1.24346	+	0.452583i	0.365274	+	0.930900i	$0.380975\pi$
$212$	4.58443e9	+	2.59996e10i	0.155874	+	0.884007i
$213$	2.45114e10	+	2.05675e10i	0.815943	+	0.684658i
$214$	1.10977e9	−	9.31211e8i	0.0361720	−	0.0303519i
$215$	5.13090e9	−	2.90988e10i	0.163765	−	0.928756i
$216$	−7.72296e9	+	1.33766e10i	−0.241403	+	0.418122i
$217$	3.99090e10	+	6.91244e10i	1.22180	+	2.11623i
$218$	3.18577e10	−	1.15952e10i	0.955344	−	0.347717i
$219$	1.59055e9	−	5.78912e8i	0.0467249	−	0.0170065i
$220$	1.40780e10	+	2.43839e10i	0.405172	+	0.701779i
$221$	4.67923e9	−	8.10466e9i	0.131950	−	0.228544i
$222$	−5.65766e9	+	3.20862e10i	−0.156332	+	0.886604i
$223$	−2.33978e10	+	1.96331e10i	−0.633583	+	0.531639i	−0.902040	−	0.431653i	$-0.857931\pi$
$223$	−2.33978e10	+	1.96331e10i	−0.633583	+	0.531639i	0.268457	+	0.963292i	$0.413486\pi$
$224$	7.41363e9	+	6.22077e9i	0.196750	+	0.165093i
$225$	1.16299e10	+	6.59566e10i	0.302521	+	1.71568i
$226$	2.13449e10	+	7.76890e9i	0.544259	+	0.198094i
$227$	−1.94898e10			−0.487182			−0.243591	−	0.969878i	$-0.578325\pi$
$227$	−1.94898e10			−0.487182			−0.243591	+	0.969878i	$0.578325\pi$
$228$	−1.96827e10	+	2.79989e10i	−0.482368	+	0.686173i
$229$	−5.41262e9			−0.130061			−0.0650306	−	0.997883i	$-0.520715\pi$
$229$	−5.41262e9			−0.130061			−0.0650306	+	0.997883i	$0.520715\pi$
$230$	−4.89498e10	−	1.78163e10i	−1.15339	−	0.419799i
$231$	−2.12010e10	−	1.20237e11i	−0.489895	−	2.77833i
$232$	1.65192e10	+	1.38613e10i	0.374363	+	0.314128i
$233$	5.76266e10	−	4.83545e10i	1.28092	−	1.07482i	0.287802	−	0.957690i	$-0.407075\pi$
$233$	5.76266e10	−	4.83545e10i	1.28092	−	1.07482i	0.993117	−	0.117129i	$-0.0373691\pi$
$234$	−2.83979e9	+	1.61052e10i	−0.0619177	+	0.351152i
$235$	1.61470e9	−	2.79673e9i	0.0345370	−	0.0598199i
$236$	2.73415e6	+	4.73569e6i	5.73745e−5	+	9.93755e-5i
$237$	−4.48239e10	+	1.63146e10i	−0.922874	+	0.335899i
$238$	4.53661e10	−	1.65119e10i	0.916507	−	0.333581i
$239$	−3.07703e10	−	5.32958e10i	−0.610017	−	1.05658i	−0.991237	−	0.132096i	$-0.957829\pi$
$239$	−3.07703e10	−	5.32958e10i	−0.610017	−	1.05658i	0.381220	−	0.924484i	$-0.375504\pi$
$240$	1.50902e10	−	2.61370e10i	0.293592	−	0.508516i
$241$	−1.14884e9	+	6.51538e9i	−0.0219372	+	0.124412i	−0.993810	−	0.111095i	$-0.964564\pi$
$241$	−1.14884e9	+	6.51538e9i	−0.0219372	+	0.124412i	0.971873	+	0.235508i	$0.0756752\pi$
$242$	−9.82250e9	+	8.24205e9i	−0.184100	+	0.154478i
$243$	2.35610e10	+	1.97700e10i	0.433476	+	0.363730i
$244$	−3.44147e9	−	1.95176e10i	−0.0621570	−	0.352510i
$245$	−8.24297e10	−	3.00020e10i	−1.46163	−	0.531988i
$246$	1.16728e11			2.03221
$247$	−4.23786e9	+	1.56990e10i	−0.0724453	+	0.268372i
$248$	−3.54229e10			−0.594636
$249$	−1.30450e11	−	4.74800e10i	−2.15054	−	0.782733i
$250$	4.20861e8	+	2.38682e9i	0.00681410	+	0.0386447i
$251$	3.44579e10	+	2.89136e10i	0.547971	+	0.459802i	0.874253	−	0.485470i	$-0.161352\pi$
$251$	3.44579e10	+	2.89136e10i	0.547971	+	0.459802i	−0.326282	+	0.945272i	$0.605796\pi$
$252$	−6.46266e10	+	5.42282e10i	−1.00951	+	0.847076i
$253$	1.62398e10	−	9.21004e10i	0.249194	−	1.41325i
$254$	9.90627e9	−	1.71582e10i	0.149334	−	0.258654i
$255$	−7.52773e10	−	1.30384e11i	−1.11489	−	1.93105i
$256$	−4.03595e9	+	1.46897e9i	−0.0587308	+	0.0213763i
$257$	−8.87409e10	+	3.22990e10i	−1.26889	+	0.461839i	−0.886743	−	0.462262i	$-0.847038\pi$
$257$	−8.87409e10	+	3.22990e10i	−1.26889	+	0.461839i	−0.382148	+	0.924101i	$0.624816\pi$
$258$	−2.84309e10	−	4.92438e10i	−0.399487	−	0.691932i
$259$	−3.99284e10	+	6.91580e10i	−0.551357	+	0.954978i
$260$	2.49000e9	−	1.41215e10i	0.0337924	−	0.191646i
$261$	−1.44002e11	+	1.20832e11i	−1.92082	+	1.61176i
$262$	−2.28790e10	−	1.91977e10i	−0.299972	−	0.251706i
$263$	−2.21731e10	−	1.25750e11i	−0.285776	−	1.62071i	−0.702502	−	0.711682i	$-0.747934\pi$
$263$	−2.21731e10	−	1.25750e11i	−0.285776	−	1.62071i	0.416726	−	0.909032i	$-0.363178\pi$
$264$	5.09162e10	+	1.85320e10i	0.645117	+	0.234803i
$265$	2.01794e11			2.51364
$266$	−6.88046e10	+	4.79870e10i	−0.842655	+	0.587700i
$267$	4.51453e10			0.543640
$268$	3.63205e10	+	1.32196e10i	0.430076	+	0.156535i
$269$	3.90988e9	+	2.21740e10i	0.0455280	+	0.258202i	0.999073	−	0.0430486i	$-0.0137070\pi$
$269$	3.90988e9	+	2.21740e10i	0.0455280	+	0.258202i	−0.953545	+	0.301251i	$0.902596\pi$
$270$	9.04402e10	+	7.58883e10i	1.03568	+	0.869036i
$271$	1.01350e11	−	8.50426e10i	1.14146	−	0.957800i	0.141976	−	0.989870i	$-0.454655\pi$
$271$	1.01350e11	−	8.50426e10i	1.14146	−	0.957800i	0.999486	+	0.0320704i	$0.0102101\pi$
$272$	−3.72048e9	+	2.10999e10i	−0.0412135	+	0.233733i
$273$	−3.10895e10	+	5.38486e10i	−0.338752	+	0.586735i
$274$	−1.83950e10	−	3.18611e10i	−0.197162	−	0.341494i
$275$	9.90719e10	−	3.60592e10i	1.04461	−	0.380206i
$276$	−9.41995e10	+	3.42858e10i	−0.977142	+	0.355651i
$277$	3.52557e10	+	6.10647e10i	0.359808	+	0.623206i	0.987929	−	0.154910i	$-0.0495088\pi$
$277$	3.52557e10	+	6.10647e10i	0.359808	+	0.623206i	−0.628120	+	0.778116i	$0.716176\pi$
$278$	2.36062e9	−	4.08871e9i	0.0237041	−	0.0410567i
$279$	5.36209e10	−	3.04099e11i	0.529804	−	3.00467i
$280$	5.66662e10	−	4.75486e10i	0.550951	−	0.462303i
$281$	−1.31021e11	−	1.09940e11i	−1.25361	−	1.05190i	−0.996333	−	0.0855651i	$-0.972730\pi$
$281$	−1.31021e11	−	1.09940e11i	−1.25361	−	1.05190i	−0.257277	−	0.966338i	$-0.582825\pi$
$282$	−1.07917e9	−	6.12026e9i	−0.0101617	−	0.0576301i
$283$	−4.09778e10	−	1.49147e10i	−0.379761	−	0.138222i	0.145085	−	0.989419i	$-0.453655\pi$
$283$	−4.09778e10	−	1.49147e10i	−0.379761	−	0.138222i	−0.524845	+	0.851198i	$0.675877\pi$
$284$	−3.48051e10			−0.317475
$285$	1.84634e11	+	1.85322e11i	1.65772	+	1.66389i
$286$	2.57439e10			0.227524
$287$	2.68848e11	+	9.78527e10i	2.33904	+	0.851343i
$288$	−6.50146e9	−	3.68716e10i	−0.0556858	−	0.315810i
$289$	−8.96840e9	−	7.52538e9i	−0.0756266	−	0.0634582i
$290$	1.26265e11	−	1.05949e11i	1.04831	−	0.879641i
$291$	−1.19607e10	+	6.78326e10i	−0.0977774	+	0.554523i
$292$	−9.20576e8	+	1.59448e9i	−0.00741031	+	0.0128350i
$293$	5.49877e10	+	9.52416e10i	0.435875	+	0.754957i	0.997367	−	0.0725252i	$-0.0231058\pi$
$293$	5.49877e10	+	9.52416e10i	0.435875	+	0.754957i	−0.561492	+	0.827482i	$0.689772\pi$
$294$	−1.58629e11	+	5.77361e10i	−1.23828	+	0.450697i
$295$	3.92764e7	−	1.42955e7i	0.000301949	−	0.000109900i
$296$	−1.77200e10	−	3.06920e10i	−0.134169	−	0.232387i
$297$	−1.05980e11	+	1.83562e11i	−0.790348	+	1.36892i
$298$	−2.21674e10	+	1.25718e11i	−0.162833	+	0.923471i
$299$	−3.64855e10	+	3.06150e10i	−0.263998	+	0.221520i
$300$	−8.65708e10	−	7.26416e10i	−0.617058	−	0.517773i
$301$	−2.42012e10	−	1.37252e11i	−0.169937	−	0.963760i
$302$	6.16872e10	+	2.24523e10i	0.426741	+	0.155321i
$303$	−2.77893e11			−1.89402
$304$	−3.17565e9	−	3.70924e10i	−0.0213256	−	0.249089i
$305$	−1.51484e11			−1.00235
$306$	−1.75507e11	−	6.38795e10i	−1.14432	−	0.416500i
$307$	9.43098e9	+	5.34858e10i	0.0605947	+	0.343649i	1.00000		0.000839998i	$0.000267380\pi$
$307$	9.43098e9	+	5.34858e10i	0.0605947	+	0.343649i	−0.939405	+	0.342809i	$0.888622\pi$
$308$	1.01735e11	+	8.53656e10i	0.644156	+	0.540511i
$309$	1.40768e11	−	1.18118e11i	0.878394	−	0.737060i
$310$	−4.70162e10	+	2.66642e11i	−0.289148	+	1.63984i
$311$	−1.36117e11	+	2.35762e11i	−0.825070	+	1.42906i	0.0767963	+	0.997047i	$0.475531\pi$
$311$	−1.36117e11	+	2.35762e11i	−0.825070	+	1.42906i	−0.901866	+	0.432016i	$0.857802\pi$
$312$	−1.37974e10	−	2.38978e10i	−0.0824330	−	0.142778i
$313$	8.95160e10	−	3.25812e10i	0.527171	−	0.191874i	−0.0647039	−	0.997905i	$-0.520610\pi$
$313$	8.95160e10	−	3.25812e10i	0.527171	−	0.191874i	0.591875	+	0.806030i	$0.298388\pi$
$314$	−1.52594e11	+	5.55398e10i	−0.885839	+	0.322419i
$315$	3.22419e11	+	5.58446e11i	1.84511	+	3.19583i
$316$	2.59431e10	−	4.49348e10i	0.146363	−	0.253508i
$317$	1.34834e10	−	7.64680e10i	0.0749949	−	0.425317i	−0.924076	−	0.382210i	$-0.875163\pi$
$317$	1.34834e10	−	7.64680e10i	0.0749949	−	0.425317i	0.999070	−	0.0431073i	$-0.0137257\pi$
$318$	2.97482e11	−	2.49617e11i	1.63132	−	1.36884i
$319$	2.26688e11	+	1.90214e11i	1.22566	+	1.02845i
$320$	5.70064e9	+	3.23299e10i	0.0303913	+	0.172357i
$321$	−2.00243e10	−	7.28826e9i	−0.105265	−	0.0383134i
$322$	−2.45702e11			−1.27367
$323$	−1.68166e11	−	7.87983e10i	−0.859661	−	0.402815i
$324$	4.72817e10			0.238364
$325$	−5.04553e10	−	1.83642e10i	−0.250860	−	0.0913057i
$326$	−2.06637e10	−	1.17189e11i	−0.101328	−	0.574658i
$327$	−3.82009e11	−	3.20544e11i	−1.84760	−	1.55032i
$328$	−9.72654e10	+	8.16153e10i	−0.464009	+	0.389349i
$329$	2.64505e9	−	1.50008e10i	0.0124467	−	0.0705885i
$330$	2.07078e11	−	3.58669e11i	0.961216	−	1.66487i
$331$	1.63803e11	+	2.83715e11i	0.750060	+	1.29914i	0.947793	+	0.318887i	$0.103309\pi$
$331$	1.63803e11	+	2.83715e11i	0.750060	+	1.29914i	−0.197732	+	0.980256i	$0.563358\pi$
$332$	1.41897e11	−	5.16463e10i	0.640991	−	0.233301i
$333$	2.90309e11	−	1.05664e11i	1.29379	−	0.470899i
$334$	1.00667e11	+	1.74360e11i	0.442615	+	0.766632i
$335$	1.47717e11	−	2.55853e11i	0.640808	−	1.10991i
$336$	2.47194e10	−	1.40191e11i	0.105806	−	0.600058i
$337$	9.99223e10	−	8.38448e10i	0.422015	−	0.354113i	−0.406914	−	0.913466i	$-0.633395\pi$
$337$	9.99223e10	−	8.38448e10i	0.422015	−	0.354113i	0.828929	+	0.559354i	$0.188951\pi$
$338$	1.19933e11	+	1.00636e11i	0.499819	+	0.419398i
$339$	−5.80189e10	−	3.29042e11i	−0.238600	−	1.35317i
$340$	1.53889e11	+	5.60111e10i	0.624530	+	0.227310i
$341$	−4.86096e11			−1.94683
$342$	3.23240e11	+	2.88858e10i	1.27764	+	0.114174i
$343$	−4.13107e10			−0.161153
$344$	5.81213e10	+	2.11544e10i	0.223781	+	0.0814495i
$345$	1.33054e11	+	7.54584e11i	0.505639	+	2.86762i
$346$	−1.97732e10	−	1.65917e10i	−0.0741711	−	0.0622370i
$347$	−2.04477e11	+	1.71576e11i	−0.757113	+	0.635294i	−0.937374	−	0.348325i	$-0.886750\pi$
$347$	−2.04477e11	+	1.71576e11i	−0.757113	+	0.635294i	0.180260	+	0.983619i	$0.442306\pi$
$348$	5.50804e10	−	3.12376e11i	0.201322	−	1.14175i
$349$	−6.52473e10	+	1.13012e11i	−0.235422	+	0.407764i	−0.959395	−	0.282065i	$-0.908981\pi$
$349$	−6.52473e10	+	1.13012e11i	−0.235422	+	0.407764i	0.723973	+	0.689828i	$0.242314\pi$
$350$	−1.38495e11	−	2.39880e11i	−0.493318	−	0.854452i
$351$	1.01437e11	−	3.69199e10i	0.356708	−	0.129831i
$352$	−5.53840e10	+	2.01581e10i	−0.192284	+	0.0699855i
$353$	5.10042e10	+	8.83419e10i	0.174832	+	0.302817i	0.940103	−	0.340890i	$-0.110729\pi$
$353$	5.10042e10	+	8.83419e10i	0.174832	+	0.302817i	−0.765271	+	0.643708i	$0.777395\pi$
$354$	4.02174e7	−	6.96587e7i	0.000136113	−	0.000235755i
$355$	−4.61962e10	+	2.61992e11i	−0.154376	+	0.875507i
$356$	−3.76179e10	+	3.15652e10i	−0.124128	+	0.104156i
$357$	−5.43991e11	−	4.56463e11i	−1.77249	−	1.48730i
$358$	−4.32043e10	−	2.45024e11i	−0.139012	−	0.788378i
$359$	2.25793e10	+	8.21821e9i	0.0717441	+	0.0261127i	0.377643	−	0.925951i	$-0.376735\pi$
$359$	2.25793e10	+	8.21821e9i	0.0717441	+	0.0261127i	−0.305899	+	0.952064i	$0.598957\pi$
$360$	−2.86176e11			−0.897992
$361$	3.17575e11	+	5.72161e10i	0.984155	+	0.177311i
$362$	−3.99603e11			−1.22304
$363$	1.77233e11	+	6.45077e10i	0.535754	+	0.194999i
$364$	−1.17447e10	−	6.66075e10i	−0.0350660	−	0.198869i
$365$	1.07805e10	+	9.04587e9i	0.0317921	+	0.0266767i
$366$	−2.23316e11	+	1.87384e11i	−0.650512	+	0.545844i
$367$	−7.79760e10	+	4.42224e11i	−0.224369	+	1.27246i	0.639518	+	0.768776i	$0.279134\pi$
$367$	−7.79760e10	+	4.42224e11i	−0.224369	+	1.27246i	−0.863887	+	0.503686i	$0.831977\pi$
$368$	5.45207e10	−	9.44326e10i	0.154969	−	0.268415i
$369$	−5.53420e11	−	9.58552e11i	−1.55395	−	2.69152i
$370$	−2.54551e11	+	9.26488e10i	−0.706100	+	0.256999i
$371$	8.94413e11	−	3.25540e11i	2.45107	−	0.892116i
$372$	2.60522e11	+	4.51238e11i	0.705345	+	1.22169i
$373$	1.87058e10	−	3.23994e10i	0.0500364	−	0.0866656i	−0.839922	−	0.542707i	$-0.817400\pi$
$373$	1.87058e10	−	3.23994e10i	0.0500364	−	0.0866656i	0.889959	+	0.456041i	$0.150733\pi$
$374$	−5.10550e10	+	2.89547e11i	−0.134932	+	0.765239i
$375$	2.73095e10	−	2.29154e10i	0.0713137	−	0.0598393i
$376$	5.17846e9	+	4.34525e9i	0.0133615	+	0.0112116i
$377$	−2.61698e10	−	1.48416e11i	−0.0667213	−	0.378395i
$378$	5.23283e11	+	1.90459e11i	1.31833	+	0.479832i
$379$	−1.76315e11			−0.438948			−0.219474	−	0.975618i	$-0.570434\pi$
$379$	−1.76315e11			−0.438948			−0.219474	+	0.975618i	$0.570434\pi$
$380$	−2.83424e11	−	2.53278e10i	−0.697286	−	0.0623119i
$381$	−2.91428e11			−0.708548
$382$	−3.06816e11	−	1.11672e11i	−0.737214	−	0.268324i
$383$	−6.94649e10	−	3.93955e11i	−0.164957	−	0.935519i	−0.949109	−	0.314949i	$-0.898013\pi$
$383$	−6.94649e10	−	3.93955e11i	−0.164957	−	0.935519i	0.784151	−	0.620570i	$-0.213099\pi$
$384$	4.83955e10	+	4.06087e10i	0.113583	+	0.0953078i
$385$	7.77612e11	−	6.52494e11i	1.80380	−	1.51357i
$386$	−4.14869e10	+	2.35284e11i	−0.0951191	+	0.539447i
$387$	−2.69588e11	+	4.66940e11i	−0.610943	+	1.05818i
$388$	−3.74615e10	−	6.48852e10i	−0.0839155	−	0.145346i
$389$	−3.24423e11	+	1.18080e11i	−0.718354	+	0.261459i	−0.675227	−	0.737610i	$-0.735954\pi$
$389$	−3.24423e11	+	1.18080e11i	−0.718354	+	0.261459i	−0.0431271	+	0.999070i	$0.513732\pi$
$390$	−1.98201e11	+	7.21393e10i	−0.433826	+	0.157900i
$391$	−2.71976e11	−	4.71076e11i	−0.588485	−	1.01929i
$392$	9.18109e10	−	1.59021e11i	0.196384	−	0.340148i
$393$	−7.62859e10	+	4.32639e11i	−0.161316	+	0.914869i
$394$	−3.61270e11	+	3.03141e11i	−0.755264	+	0.633742i
$395$	−3.03808e11	−	2.54926e11i	−0.627932	−	0.526898i
$396$	−8.92173e10	−	5.05977e11i	−0.182314	−	1.03396i
$397$	1.38896e11	+	5.05540e10i	0.280629	+	0.102141i	0.478500	−	0.878087i	$-0.341181\pi$
$397$	1.38896e11	+	5.05540e10i	0.280629	+	0.102141i	−0.197871	+	0.980228i	$0.563403\pi$
$398$	−3.43557e11			−0.686318
$399$	1.11732e12	+	5.23548e11i	2.20699	+	1.03414i
$400$	1.22927e11			0.240091
$401$	5.80102e11	+	2.11140e11i	1.12035	+	0.407775i	0.834781	−	0.550583i	$-0.185594\pi$
$401$	5.80102e11	+	2.11140e11i	1.12035	+	0.407775i	0.285571	+	0.958357i	$0.407817\pi$
$402$	−9.87251e10	−	5.59898e11i	−0.188543	−	1.06928i
$403$	1.89641e11	+	1.59128e11i	0.358146	+	0.300520i
$404$	2.31558e11	−	1.94300e11i	0.432458	−	0.362875i
$405$	6.27562e10	−	3.55908e11i	0.115907	−	0.657340i
$406$	3.88725e11	−	6.73291e11i	0.710027	−	1.22980i
$407$	−2.43166e11	−	4.21176e11i	−0.439267	−	0.760833i
$408$	2.96146e11	−	1.07788e11i	0.529098	−	0.192576i
$409$	−4.93284e11	+	1.79541e11i	−0.871650	+	0.317255i	−0.738835	−	0.673886i	$-0.764624\pi$
$409$	−4.93284e11	+	1.79541e11i	−0.871650	+	0.317255i	−0.132815	+	0.991141i	$0.542401\pi$
$410$	4.85252e11	+	8.40482e11i	0.848087	+	1.46893i
$411$	−2.70578e11	+	4.68654e11i	−0.467739	+	0.810148i
$412$	−3.47094e10	+	1.96847e11i	−0.0593485	+	0.336582i
$413$	1.51023e8	−	1.26724e8i	0.000255428	−	0.000214330i
$414$	7.28159e11	+	6.10998e11i	1.21822	+	1.02220i
$415$	−2.00425e11	−	1.13666e12i	−0.331692	−	1.88112i
$416$	2.82060e10	+	1.02661e10i	0.0461765	+	0.0168069i
$417$	−6.94460e10			−0.112470
$418$	−4.35784e10	−	5.09007e11i	−0.0698197	−	0.815512i
$419$	4.59499e11			0.728319			0.364159	−	0.931337i	$-0.381356\pi$
$419$	4.59499e11			0.728319			0.364159	+	0.931337i	$0.381356\pi$
$420$	−1.02246e12	−	3.72146e11i	−1.60334	−	0.583568i
$421$	1.51319e11	+	8.58172e11i	0.234760	+	1.33139i	0.843119	+	0.537727i	$0.180717\pi$
$421$	1.51319e11	+	8.58172e11i	0.234760	+	1.33139i	−0.608359	+	0.793662i	$0.708172\pi$
$422$	4.66973e11	+	3.91837e11i	0.716780	+	0.601449i
$423$	−4.51421e10	+	3.78787e10i	−0.0685567	+	0.0575259i
$424$	−7.33509e10	+	4.15994e11i	−0.110220	+	0.625087i
$425$	3.06609e11	−	5.31063e11i	0.455864	−	0.789579i
$426$	2.55979e11	+	4.43368e11i	0.376583	+	0.652261i
$427$	−6.71424e11	+	2.44378e11i	−0.977398	+	0.355744i
$428$	2.17814e10	−	7.92779e9i	0.0313754	−	0.0114197i
$429$	−1.89337e11	−	3.27941e11i	−0.269884	−	0.467453i
$430$	2.36381e11	−	4.09424e11i	0.333430	−	0.577518i
$431$	−1.54207e11	+	8.74551e11i	−0.215257	+	1.22078i	0.665204	+	0.746662i	$0.268344\pi$
$431$	−1.54207e11	+	8.74551e11i	−0.215257	+	1.22078i	−0.880461	+	0.474119i	$0.842767\pi$
$432$	−1.89316e11	+	1.58855e11i	−0.261524	+	0.219444i
$433$	−2.26110e10	−	1.89728e10i	−0.0309117	−	0.0259380i	0.627201	−	0.778858i	$-0.284200\pi$
$433$	−2.26110e10	−	1.89728e10i	−0.0309117	−	0.0259380i	−0.658113	+	0.752919i	$0.728645\pi$
$434$	2.21764e11	+	1.25769e12i	0.300045	+	1.70164i
$435$	−2.27827e12	−	8.29224e11i	−3.05074	−	1.11038i
$436$	5.42435e11			0.718884
$437$	6.67080e11	+	6.69567e11i	0.875007	+	0.878269i
$438$	2.70820e10			0.0351599
$439$	−1.04774e12	−	3.81345e11i	−1.34636	−	0.490036i	−0.434552	−	0.900647i	$-0.643093\pi$
$439$	−1.04774e12	−	3.81345e11i	−1.34636	−	0.490036i	−0.911811	+	0.410611i	$0.865315\pi$
$440$	7.82280e10	+	4.43653e11i	0.0995005	+	0.564295i
$441$	1.22619e12	+	1.02890e12i	1.54378	+	1.29539i
$442$	1.14704e11	−	9.62480e10i	0.142948	−	0.119948i
$443$	1.99761e11	−	1.13290e12i	0.246430	−	1.39758i	−0.570717	−	0.821147i	$-0.693335\pi$
$443$	1.99761e11	−	1.13290e12i	0.246430	−	1.39758i	0.817148	−	0.576429i	$-0.195554\pi$
$444$	−2.60649e11	+	4.51458e11i	−0.318297	+	0.551307i
$445$	1.87674e11	+	3.25061e11i	0.226874	+	0.392957i
$446$	−4.59227e11	+	1.67145e11i	−0.549566	+	0.200026i
$447$	1.76450e12	−	6.42226e11i	2.09044	−	0.760859i
$448$	7.74224e10	+	1.34100e11i	0.0908062	+	0.157281i
$449$	−2.43816e9	+	4.22301e9i	−0.00283109	+	0.00490359i	−0.867437	−	0.497546i	$-0.834234\pi$
$449$	−2.43816e9	+	4.22301e9i	−0.00283109	+	0.00490359i	0.864606	+	0.502450i	$0.167568\pi$
$450$	−1.86079e11	+	1.05531e12i	−0.213915	+	1.21317i
$451$	−1.33474e12	+	1.11998e12i	−1.51916	+	1.27472i
$452$	2.78408e11	+	2.33612e11i	0.313732	+	0.263253i
$453$	−1.67676e11	−	9.50939e11i	−0.187081	−	1.06099i
$454$	−2.93031e11	−	1.06654e11i	−0.323714	−	0.117822i
$455$	−5.16970e11			−0.565476
$456$	−4.49150e11	+	3.13255e11i	−0.486463	+	0.339278i
$457$	2.96706e11			0.318203			0.159101	−	0.987262i	$-0.449140\pi$
$457$	2.96706e11			0.318203			0.159101	+	0.987262i	$0.449140\pi$
$458$	−8.13792e10	−	2.96196e10i	−0.0864209	−	0.0314546i
$459$	2.14079e11	+	1.21410e12i	0.225121	+	1.27673i
$460$	−6.38467e11	−	5.35738e11i	−0.664857	−	0.557882i
$461$	−2.90808e11	+	2.44017e11i	−0.299883	+	0.251632i	−0.780296	−	0.625411i	$-0.784931\pi$
$461$	−2.90808e11	+	2.44017e11i	−0.299883	+	0.251632i	0.480413	+	0.877043i	$0.340487\pi$
$462$	3.39217e11	−	1.92379e12i	0.346408	−	1.96458i
$463$	−8.62569e11	+	1.49401e12i	−0.872327	+	1.51092i	−0.0127444	+	0.999919i	$0.504057\pi$
$463$	−8.62569e11	+	1.49401e12i	−0.872327	+	1.51092i	−0.859583	+	0.510996i	$0.829277\pi$
$464$	1.72514e11	+	2.98804e11i	0.172780	+	0.299264i
$465$	3.74244e12	−	1.36214e12i	3.71207	−	1.35108i
$466$	1.13103e12	−	4.11662e11i	1.11106	−	0.404394i
$467$	−7.68137e11	−	1.33045e12i	−0.747331	−	1.29442i	−0.949098	−	0.314982i	$-0.898002\pi$
$467$	−7.68137e11	−	1.33045e12i	−0.747331	−	1.29442i	0.201767	−	0.979434i	$-0.435332\pi$
$468$	−1.30829e11	+	2.26603e11i	−0.126066	+	0.218353i
$469$	2.41976e11	−	1.37232e12i	0.230938	−	1.30971i
$470$	3.95817e10	−	3.32130e10i	0.0374157	−	0.0313955i
$471$	1.82978e12	+	1.53536e12i	1.71318	+	1.43753i
$472$	1.51930e7	+	8.61637e7i	1.40898e−5	+	7.99071e-5i
$473$	7.97580e11	+	2.90295e11i	0.732654	+	0.266664i
$474$	−7.63210e11			−0.694451
$475$	−2.77688e11	+	1.02869e12i	−0.250286	+	0.927177i
$476$	7.72442e11			0.689660
$477$	−3.46020e12	−	1.25941e12i	−3.06034	−	1.11387i
$478$	−1.70983e11	−	9.69692e11i	−0.149805	−	0.849588i
$479$	5.92398e11	+	4.97081e11i	0.514166	+	0.431437i	0.862592	−	0.505900i	$-0.168839\pi$
$479$	5.92398e11	+	4.97081e11i	0.514166	+	0.431437i	−0.348426	+	0.937336i	$0.613284\pi$
$480$	3.69912e11	−	3.10393e11i	0.318063	−	0.266887i
$481$	−4.30091e10	+	2.43917e11i	−0.0366359	+	0.207773i
$482$	−5.29271e10	+	9.16725e10i	−0.0446649	+	0.0773620i
$483$	1.80705e12	+	3.12990e12i	1.51080	+	2.61679i
$484$	−1.92785e11	+	7.01681e10i	−0.159687	+	0.0581213i
$485$	−5.38139e11	+	1.95867e11i	−0.441628	+	0.160739i
$486$	2.46053e11	+	4.26177e11i	0.200063	+	0.346519i
$487$	9.85411e11	−	1.70678e12i	0.793847	−	1.37498i	−0.129721	−	0.991551i	$-0.541408\pi$
$487$	9.85411e11	−	1.70678e12i	0.793847	−	1.37498i	0.923569	−	0.383433i	$-0.125258\pi$
$488$	5.50636e10	−	3.12281e11i	0.0439517	−	0.249262i
$489$	−1.34086e12	+	1.12511e12i	−1.06046	+	0.889828i
$490$	−1.07516e12	−	9.02164e11i	−0.842538	−	0.706973i
$491$	−3.27556e11	−	1.85766e12i	−0.254342	−	1.44245i	−0.797755	−	0.602982i	$-0.793979\pi$
$491$	−3.27556e11	−	1.85766e12i	−0.254342	−	1.44245i	0.543412	−	0.839466i	$-0.317132\pi$
$492$	1.75502e12	+	6.38774e11i	1.35033	+	0.491479i
$493$	1.72117e12			1.31224
$494$	−1.49627e11	+	2.12845e11i	−0.113041	+	0.160802i
$495$	−3.92711e12			−2.94001
$496$	−5.32585e11	−	1.93845e11i	−0.395113	−	0.143810i
$497$	2.17896e11	+	1.23575e12i	0.160194	+	0.908505i
$498$	−1.70150e12	−	1.42773e12i	−1.23965	−	1.04019i
$499$	2.13542e11	−	1.79183e11i	0.154181	−	0.129373i	−0.562434	−	0.826842i	$-0.690135\pi$
$499$	2.13542e11	−	1.79183e11i	0.154181	−	0.129373i	0.716615	+	0.697469i	$0.245691\pi$
$500$	−6.73377e9	+	3.81891e10i	−0.00481829	+	0.0273259i
$501$	1.48073e12	−	2.56470e12i	1.05004	−	1.81873i
$502$	3.59853e11	+	6.23284e11i	0.252906	+	0.438045i
$503$	−6.26539e11	+	2.28042e11i	−0.436408	+	0.158839i	−0.550875	−	0.834588i	$-0.685706\pi$
$503$	−6.26539e11	+	2.28042e11i	−0.436408	+	0.158839i	0.114468	+	0.993427i	$0.463484\pi$
$504$	−1.26842e12	+	4.61667e11i	−0.875640	+	0.318707i
$505$	−1.15523e12	−	2.00092e12i	−0.790420	−	1.36905i
$506$	7.48169e11	−	1.29587e12i	0.507367	−	0.878786i
$507$	3.99895e11	−	2.26792e12i	0.268788	−	1.52437i
$508$	2.42837e11	−	2.03764e11i	0.161781	−	0.135750i
$509$	1.21921e12	+	1.02304e12i	0.805100	+	0.675559i	0.949433	−	0.313970i	$-0.101659\pi$
$509$	1.21921e12	+	1.02304e12i	0.805100	+	0.675559i	−0.144333	+	0.989529i	$0.546104\pi$
$510$	−4.18297e11	−	2.37228e12i	−0.273791	−	1.55274i
$511$	6.23752e10	+	2.27027e10i	0.0404686	+	0.0147294i
$512$	−6.87195e10			−0.0441942
$513$	−9.01689e11	−	1.94311e12i	−0.574816	−	1.23871i
$514$	−1.51098e12			−0.954825
$515$	1.43567e12	+	5.22543e11i	0.899339	+	0.327333i
$516$	−1.57983e11	−	8.95968e11i	−0.0981042	−	0.556377i
$517$	7.10624e10	+	5.96284e10i	0.0437454	+	0.0367067i
$518$	−9.78781e11	+	8.21295e11i	−0.597313	+	0.501205i
$519$	−6.59303e10	+	3.73909e11i	−0.0398871	+	0.226211i
$520$	1.14715e11	−	1.98691e11i	0.0688024	−	0.119169i
$521$	−8.52752e11	−	1.47701e12i	−0.507053	−	0.878241i	−0.999967	−	0.00816309i	$-0.997402\pi$
$521$	−8.52752e11	−	1.47701e12i	−0.507053	−	0.878241i	0.492914	−	0.870078i	$-0.335932\pi$
$522$	−2.82632e12	+	1.02870e12i	−1.66611	+	0.606416i
$523$	8.14243e11	−	2.96360e11i	0.475879	−	0.173206i	−0.0929348	−	0.995672i	$-0.529625\pi$
$523$	8.14243e11	−	2.96360e11i	0.475879	−	0.173206i	0.568814	+	0.822467i	$0.307403\pi$
$524$	−2.38931e11	−	4.13840e11i	−0.138446	−	0.239796i
$525$	−2.03716e12	+	3.52846e12i	−1.17033	+	2.02707i
$526$	3.54769e11	−	2.01200e12i	0.202074	−	1.14602i
$527$	−2.16584e12	+	1.81736e12i	−1.22315	+	1.02634i
$528$	6.64116e11	+	5.57260e11i	0.371870	+	0.312036i
$529$	1.67954e11	+	9.52515e11i	0.0932481	+	0.528836i
$530$	3.03399e12	+	1.10428e12i	1.67022	+	0.607910i
$531$	−7.62700e8			−0.000416321
$532$	−1.29708e12	+	3.44967e11i	−0.702045	+	0.186713i
$533$	8.87359e11			0.476241
$534$	6.78763e11	+	2.47050e11i	0.361229	+	0.131477i
$535$	−3.07655e10	−	1.74480e11i	−0.0162357	−	0.0920775i
$536$	4.73740e11	+	3.97515e11i	0.247912	+	0.208023i
$537$	−2.80351e12	+	2.35243e12i	−1.45485	+	1.22076i
$538$	−6.25581e10	+	3.54785e11i	−0.0321931	+	0.182576i
$539$	1.25989e12	−	2.18220e12i	0.642959	−	1.11364i
$540$	9.44490e11	+	1.63590e12i	0.477997	+	0.827916i
$541$	−1.51857e12	+	5.52713e11i	−0.762160	+	0.277404i	−0.693713	−	0.720251i	$-0.744027\pi$
$541$	−1.51857e12	+	5.52713e11i	−0.762160	+	0.277404i	−0.0684467	+	0.997655i	$0.521804\pi$
$542$	1.98918e12	−	7.24004e11i	0.990098	−	0.360366i
$543$	2.93894e12	+	5.09039e12i	1.45075	+	2.51277i
$544$	−1.71403e11	+	2.96879e11i	−0.0839120	+	0.145340i
$545$	7.19966e11	−	4.08313e12i	0.349565	−	1.98248i
$546$	−7.62110e11	+	6.39486e11i	−0.366987	+	0.307939i
$547$	−1.88356e12	−	1.58049e12i	−0.899573	−	0.754832i	0.0705336	−	0.997509i	$-0.477530\pi$
$547$	−1.88356e12	−	1.58049e12i	−0.899573	−	0.754832i	−0.970107	+	0.242678i	$0.921974\pi$
$548$	−1.02216e11	−	5.79698e11i	−0.0484181	−	0.274593i
$549$	2.59753e12	+	9.45424e11i	1.22035	+	0.444172i
$550$	1.68688e12			0.786054
$551$	−2.89019e12	+	7.68664e11i	−1.33581	+	0.355266i
$552$	−1.60392e12			−0.735287
$553$	−1.75782e12	−	6.39795e11i	−0.799304	−	0.290923i
$554$	1.95907e11	+	1.11104e12i	0.0883601	+	0.501115i
$555$	3.05235e12	+	2.56122e12i	1.36557	+	1.14585i
$556$	5.78668e10	−	4.85560e10i	0.0256799	−	0.0215480i
$557$	−1.38725e11	+	7.86748e11i	−0.0610669	+	0.346328i	0.938931	+	0.344107i	$0.111818\pi$
$557$	−1.38725e11	+	7.86748e11i	−0.0610669	+	0.346328i	−0.999998	+	0.00222116i	$0.999293\pi$
$558$	2.47033e12	−	4.27873e12i	1.07870	−	1.86836i
$559$	−2.16130e11	−	3.74348e11i	−0.0936185	−	0.162152i
$560$	1.11218e12	−	4.04801e11i	0.477892	−	0.173939i
$561$	4.06392e12	−	1.47915e12i	1.73226	−	0.630490i
$562$	−1.36829e12	−	2.36994e12i	−0.578580	−	1.00213i
$563$	−1.30403e12	+	2.25865e12i	−0.547018	+	0.947462i	0.451459	+	0.892292i	$0.350904\pi$
$563$	−1.30403e12	+	2.25865e12i	−0.547018	+	0.947462i	−0.998477	+	0.0551705i	$0.982430\pi$
$564$	1.72667e10	−	9.79242e10i	0.00718543	−	0.0407506i
$565$	2.12802e12	−	1.78562e12i	0.878532	−	0.737176i
$566$	−5.34487e11	−	4.48488e11i	−0.218909	−	0.183686i
$567$	−2.96006e11	−	1.67873e12i	−0.120275	−	0.682115i
$568$	−5.23297e11	−	1.90465e11i	−0.210951	−	0.0767797i
$569$	−1.02039e12			−0.408096			−0.204048	−	0.978961i	$-0.565410\pi$
$569$	−1.02039e12			−0.408096			−0.204048	+	0.978961i	$0.565410\pi$
$570$	1.76184e12	+	3.79671e12i	0.699086	+	1.50651i
$571$	−4.73554e11			−0.186426			−0.0932131	−	0.995646i	$-0.529714\pi$
$571$	−4.73554e11			−0.186426			−0.0932131	+	0.995646i	$0.529714\pi$
$572$	3.87061e11	+	1.40879e11i	0.151181	+	0.0550254i
$573$	8.33978e11	+	4.72972e12i	0.323191	+	1.83290i
$574$	3.50667e12	+	2.94245e12i	1.34832	+	1.13137i
$575$	−2.39074e12	+	2.00607e12i	−0.912066	+	0.765314i
$576$	1.04023e11	−	5.89946e11i	0.0393758	−	0.223311i
$577$	5.53944e11	−	9.59459e11i	0.208053	−	0.360359i	−0.743048	−	0.669238i	$-0.766621\pi$
$577$	5.53944e11	−	9.59459e11i	0.208053	−	0.360359i	0.951101	+	0.308879i	$0.0999539\pi$
$578$	−9.36593e10	−	1.62223e11i	−0.0349040	−	0.0604555i
$579$	3.30231e12	−	1.20194e12i	1.22114	−	0.444457i
$580$	2.47819e12	−	9.01987e11i	0.909303	−	0.330959i
$581$	−2.72204e12	−	4.71471e12i	−0.991064	−	1.71657i
$582$	−5.51032e11	+	9.54415e11i	−0.199078	+	0.344813i
$583$	−1.00657e12	+	5.70855e12i	−0.360857	+	2.04652i
$584$	−2.25665e10	+	1.89355e10i	−0.00802797	+	0.00673626i
$585$	1.53209e12	+	1.28557e12i	0.540856	+	0.453832i
$586$	3.05553e11	+	1.73288e12i	0.107040	+	0.607055i
$587$	1.12001e12	+	4.07651e11i	0.389360	+	0.141715i	0.529279	−	0.848448i	$-0.322462\pi$
$587$	1.12001e12	+	4.07651e11i	0.389360	+	0.141715i	−0.139920	+	0.990163i	$0.544685\pi$
$588$	−2.70095e12			−0.931790
$589$	2.82525e12	−	4.01895e12i	0.967250	−	1.37592i
$590$	6.68754e8			0.000227213
$591$	6.51861e12	+	2.37258e12i	2.19792	+	0.799977i
$592$	−9.84657e10	−	5.58427e11i	−0.0329486	−	0.186861i
$593$	−3.05033e12	−	2.55953e12i	−1.01298	−	0.849991i	−0.0242504	−	0.999706i	$-0.507720\pi$
$593$	−3.05033e12	−	2.55953e12i	−1.01298	−	0.849991i	−0.988729	+	0.149715i	$0.952164\pi$
$594$	−2.59792e12	+	2.17992e12i	−0.856224	+	0.718457i
$595$	1.02525e12	−	5.81448e12i	0.335354	−	1.90189i
$596$	−1.02126e12	+	1.76887e12i	−0.331533	+	0.574232i
$597$	2.52674e12	+	4.37645e12i	0.814097	+	1.41006i
$598$	−7.16098e11	+	2.60638e11i	−0.228990	+	0.0833456i
$599$	−1.66194e12	+	6.04898e11i	−0.527467	+	0.191982i	−0.592007	−	0.805933i	$-0.701664\pi$
$599$	−1.66194e12	+	6.04898e11i	−0.527467	+	0.191982i	0.0645399	+	0.997915i	$0.479442\pi$
$600$	−9.04082e11	−	1.56592e12i	−0.284791	−	0.493273i
$601$	−2.95646e12	+	5.12073e12i	−0.924349	+	1.60102i	−0.131745	+	0.991284i	$0.542058\pi$
$601$	−2.95646e12	+	5.12073e12i	−0.924349	+	1.60102i	−0.792604	+	0.609737i	$0.791275\pi$
$602$	3.87219e11	−	2.19603e12i	0.120163	−	0.681481i
$603$	−4.12972e12	+	3.46525e12i	−1.27202	+	1.06735i
$604$	8.04606e11	+	6.75145e11i	0.245990	+	0.206410i
$605$	2.72303e11	+	1.54430e12i	0.0826328	+	0.468634i
$606$	−4.17814e12	−	1.52072e12i	−1.25851	−	0.458060i
$607$	6.46890e11			0.193411			0.0967056	−	0.995313i	$-0.469169\pi$
$607$	6.46890e11			0.193411			0.0967056	+	0.995313i	$0.469169\pi$
$608$	1.55236e11	−	5.75066e11i	0.0460707	−	0.170668i
$609$	−1.14357e13			−3.36888
$610$	−2.27758e12	−	8.28971e11i	−0.666023	−	0.242413i
$611$	−8.20375e9	−	4.65258e10i	−0.00238137	−	0.0135054i
$612$	−2.28920e12	−	1.92087e12i	−0.659633	−	0.553498i
$613$	−2.77763e12	+	2.33071e12i	−0.794516	+	0.666678i	−0.946859	−	0.321649i	$-0.895763\pi$
$613$	−2.77763e12	+	2.33071e12i	−0.794516	+	0.666678i	0.152342	+	0.988328i	$0.451318\pi$
$614$	−1.50896e11	+	8.55772e11i	−0.0428469	+	0.242997i
$615$	7.13772e12	−	1.23629e13i	2.01197	−	3.48483i
$616$	1.06244e12	+	1.84020e12i	0.297298	+	0.514935i
$617$	5.19518e12	−	1.89089e12i	1.44317	−	0.525271i	0.502495	−	0.864580i	$-0.332415\pi$
$617$	5.19518e12	−	1.89089e12i	1.44317	−	0.525271i	0.940675	+	0.339309i	$0.110193\pi$
$618$	2.76283e12	−	1.00559e12i	0.761914	−	0.277314i
$619$	1.74280e12	+	3.01861e12i	0.477133	+	0.826418i	0.999657	−	0.0262067i	$-0.00834281\pi$
$619$	1.74280e12	+	3.01861e12i	0.477133	+	0.826418i	−0.522524	+	0.852625i	$0.675009\pi$
$620$	−2.16604e12	+	3.75170e12i	−0.588714	+	1.01968i
$621$	1.08952e12	−	6.17898e12i	0.293984	−	1.66727i
$622$	−3.33669e12	+	2.79982e12i	−0.893840	+	0.750021i
$623$	1.35623e12	+	1.13801e12i	0.360691	+	0.302656i
$624$	−7.66685e10	−	4.34808e11i	−0.0202435	−	0.114807i
$625$	3.72109e12	+	1.35437e12i	0.975462	+	0.355039i
$626$	1.52418e12			0.396689
$627$	−6.16354e12	+	4.29869e12i	−1.59267	+	1.11079i
$628$	−2.59820e12			−0.666582
$629$	−2.65809e12	−	9.67466e11i	−0.677083	−	0.246438i
$630$	1.79160e12	+	1.01607e13i	0.453115	+	2.56974i
$631$	−2.46113e12	−	2.06513e12i	−0.618020	−	0.518580i	0.279160	−	0.960244i	$-0.409944\pi$
$631$	−2.46113e12	−	2.06513e12i	−0.618020	−	0.518580i	−0.897181	+	0.441664i	$0.854388\pi$
$632$	6.35955e11	−	5.33630e11i	0.158562	−	0.133049i
$633$	1.55704e12	−	8.83041e12i	0.385463	−	2.18607i
$634$	6.21181e11	−	1.07592e12i	0.152692	−	0.264470i
$635$	−1.21150e12	−	2.09838e12i	−0.295694	−	0.512156i
$636$	5.83865e12	−	2.12510e12i	1.41500	−	0.515017i
$637$	−1.20588e12	+	4.38906e11i	−0.290187	+	0.105619i
$638$	2.36736e12	+	4.10038e12i	0.565680	+	0.979786i
$639$	2.42724e12	−	4.20411e12i	0.575916	−	0.997516i
$640$	−9.12102e10	+	5.17279e11i	−0.0214899	+	0.121875i
$641$	−1.41042e12	+	1.18348e12i	−0.329980	+	0.276886i	−0.792692	−	0.609623i	$-0.791321\pi$
$641$	−1.41042e12	+	1.18348e12i	−0.329980	+	0.276886i	0.462712	+	0.886509i	$0.346876\pi$
$642$	−2.61184e11	−	2.19159e11i	−0.0606790	−	0.0509157i
$643$	−7.31427e11	−	4.14813e12i	−0.168741	−	0.956981i	−0.945122	−	0.326717i	$-0.894058\pi$
$643$	−7.31427e11	−	4.14813e12i	−0.168741	−	0.956981i	0.776381	−	0.630264i	$-0.217053\pi$
$644$	−3.69415e12	−	1.34456e12i	−0.846307	−	0.308030i
$645$	−6.95400e12			−1.58203
$646$	−2.09718e12	−	2.10500e12i	−0.473794	−	0.475560i
$647$	−4.98562e10			−0.0111853			−0.00559267	−	0.999984i	$-0.501780\pi$
$647$	−4.98562e10			−0.0111853			−0.00559267	+	0.999984i	$0.501780\pi$
$648$	7.10884e11	+	2.58741e11i	0.158384	+	0.0576470i
$649$	2.08488e8	+	1.18240e9i	4.61297e−5	+	0.000261615i
$650$	−6.58105e11	−	5.52216e11i	−0.144606	−	0.121338i
$651$	1.43902e13	−	1.20748e13i	3.14016	−	2.63491i
$652$	3.30619e11	−	1.87503e12i	0.0716495	−	0.406344i
$653$	−8.32273e10	+	1.44154e11i	−0.0179125	+	0.0310254i	−0.874843	−	0.484407i	$-0.839035\pi$
$653$	−8.32273e10	+	1.44154e11i	−0.0179125	+	0.0310254i	0.856930	+	0.515432i	$0.172369\pi$
$654$	−3.98942e12	−	6.90988e12i	−0.852726	−	1.47697i
$655$	−3.43227e12	+	1.24924e12i	−0.728611	+	0.265193i
$656$	−1.90902e12	+	6.94826e11i	−0.402479	+	0.146490i
$657$	−1.28399e11	−	2.22393e11i	−0.0268854	−	0.0465668i
$658$	1.21858e11	−	2.11064e11i	0.0253418	−	0.0438933i
$659$	−3.46162e11	+	1.96318e12i	−0.0714983	+	0.405487i	0.927963	+	0.372672i	$0.121558\pi$
$659$	−3.46162e11	+	1.96318e12i	−0.0714983	+	0.405487i	−0.999461	+	0.0328150i	$0.989553\pi$
$660$	5.07619e12	−	4.25943e12i	1.04133	−	0.873782i
$661$	5.69233e12	+	4.77643e12i	1.15980	+	0.973189i	0.999903	−	0.0139445i	$-0.00443882\pi$
$661$	5.69233e12	+	4.77643e12i	1.15980	+	0.973189i	0.159899	+	0.987133i	$0.448883\pi$
$662$	9.10212e11	+	5.16207e12i	0.184197	+	1.04463i
$663$	−2.06967e12	−	7.53299e11i	−0.415998	−	0.151411i
$664$	2.41606e12			0.482337
$665$	8.75111e11	+	1.02215e13i	0.173526	+	2.02683i
$666$	4.94305e12			0.973557
$667$	−8.23138e12	−	2.99598e12i	−1.61030	−	0.586101i
$668$	5.59378e11	+	3.17239e12i	0.108695	+	0.616442i
$669$	5.50664e12	+	4.62062e12i	1.06284	+	0.891831i
$670$	3.62104e12	−	3.03841e12i	0.694219	−	0.582519i
$671$	7.55619e11	−	4.28533e12i	0.143897	−	0.816081i
$672$	1.13883e12	−	1.97251e12i	0.215425	−	0.373128i
$673$	−1.42918e12	−	2.47542e12i	−0.268547	−	0.465137i	0.699940	−	0.714202i	$-0.253210\pi$
$673$	−1.42918e12	−	2.47542e12i	−0.268547	−	0.465137i	−0.968487	+	0.249065i	$0.919877\pi$
$674$	1.96117e12	−	7.13806e11i	0.366054	−	0.133233i
$675$	6.64670e12	−	2.41920e12i	1.23236	−	0.448544i
$676$	1.25249e12	+	2.16938e12i	0.230682	+	0.399553i
$677$	8.48574e10	−	1.46977e11i	0.0155253	−	0.0268907i	−0.858158	−	0.513385i	$-0.828391\pi$
$677$	8.48574e10	−	1.46977e11i	0.0155253	−	0.0268907i	0.873684	+	0.486494i	$0.161725\pi$
$678$	9.28303e11	−	5.26467e12i	0.168716	−	0.956836i
$679$	−2.06922e12	+	1.73628e12i	−0.373587	+	0.313477i
$680$	2.00723e12	+	1.68426e12i	0.360003	+	0.302079i
$681$	7.96506e11	+	4.51721e12i	0.141915	+	0.804838i
$682$	−7.30849e12	−	2.66007e12i	−1.29359	−	0.470830i
$683$	−6.79539e12			−1.19487			−0.597436	−	0.801917i	$-0.703814\pi$
$683$	−6.79539e12			−1.19487			−0.597436	+	0.801917i	$0.703814\pi$
$684$	4.70186e12	+	2.20317e12i	0.821329	+	0.384854i
$685$	−4.49929e12			−0.780794
$686$	−6.21110e11	−	2.26065e11i	−0.107080	−	0.0389741i
$687$	2.21202e11	+	1.25450e12i	0.0378865	+	0.214865i
$688$	7.58095e11	+	6.36117e11i	0.128996	+	0.108240i
$689$	2.26144e12	−	1.89757e12i	0.382294	−	0.320783i
$690$	−2.12886e12	+	1.20734e13i	−0.357541	+	2.02772i
$691$	−2.02977e12	+	3.51566e12i	−0.338684	+	0.586618i	−0.984185	−	0.177141i	$-0.943315\pi$
$691$	−2.02977e12	+	3.51566e12i	−0.338684	+	0.586618i	0.645502	+	0.763759i	$0.276648\pi$
$692$	−2.06497e11	−	3.57663e11i	−0.0342323	−	0.0592921i
$693$	−1.74061e13	+	6.33531e12i	−2.86683	+	1.04344i
$694$	−4.01324e12	+	1.46070e12i	−0.656716	+	0.239025i
$695$	−2.88695e11	−	5.00034e11i	−0.0469361	−	0.0812958i
$696$	2.53756e12	−	4.39519e12i	0.409897	−	0.709963i
$697$	−1.75980e12	+	9.98033e12i	−0.282434	+	1.60176i
$698$	−1.59943e12	+	1.34208e12i	−0.255045	+	0.214008i
$699$	−1.35623e13	−	1.13802e13i	−2.14876	−	1.80302i
$700$	−7.69579e11	−	4.36450e12i	−0.121147	−	0.687058i
$701$	1.00241e13	+	3.64848e12i	1.56789	+	0.570664i	0.972526	−	0.232794i	$-0.0747869\pi$
$701$	1.00241e13	+	3.64848e12i	1.56789	+	0.570664i	0.595361	+	0.803458i	$0.297009\pi$
$702$	1.72715e12			0.268418
$703$	4.89552e12	+	4.37481e11i	0.755962	+	0.0675554i
$704$	−9.43015e11			−0.144691
$705$	−7.14197e11	−	2.59946e11i	−0.108885	−	0.0396308i
$706$	2.83417e11	+	1.60734e12i	0.0429344	+	0.243493i
$707$	−8.34827e12	−	7.00503e12i	−1.25664	−	1.05444i
$708$	9.85867e8	−	8.27241e8i	0.000147458	−	0.000123732i
$709$	1.16076e12	−	6.58300e12i	0.172518	−	0.978399i	−0.768452	−	0.639908i	$-0.778972\pi$
$709$	1.16076e12	−	6.58300e12i	0.172518	−	0.978399i	0.940970	−	0.338491i	$-0.109916\pi$
$710$	−2.12827e12	+	3.68627e12i	−0.314314	+	0.544407i
$711$	3.61845e12	+	6.26735e12i	0.531019	+	0.919751i
$712$	−7.38323e11	+	2.68728e11i	−0.107668	+	0.0391880i
$713$	1.35214e13	−	4.92138e12i	1.95938	−	0.713155i
$714$	−5.68104e12	−	9.83984e12i	−0.818061	−	1.41692i
$715$	1.57419e12	−	2.72658e12i	0.225258	−	0.390158i
$716$	6.91269e11	−	3.92038e12i	0.0982966	−	0.557468i
$717$	−1.10950e13	+	9.30982e12i	−1.56780	+	1.31554i
$718$	2.94509e11	+	2.47123e11i	0.0413561	+	0.0347019i
$719$	3.54846e11	+	2.01243e12i	0.0495177	+	0.280829i	0.999505	−	0.0314598i	$-0.0100156\pi$
$719$	3.54846e11	+	2.01243e12i	0.0495177	+	0.280829i	−0.949987	+	0.312288i	$0.898904\pi$
$720$	−4.30269e12	−	1.56605e12i	−0.596683	−	0.217175i
$721$	7.20632e12			0.993128
$722$	4.46166e12	+	2.59812e12i	0.611053	+	0.355829i
$723$	1.55704e12			0.211923
$724$	−6.00807e12	−	2.18676e12i	−0.812665	−	0.295786i
$725$	−1.71479e12	−	9.72507e12i	−0.230510	−	1.30729i
$726$	2.31171e12	+	1.93976e12i	0.308829	+	0.259139i
$727$	−3.08500e10	+	2.58862e10i	−0.00409590	+	0.00343687i	−0.644833	−	0.764323i	$-0.723073\pi$
$727$	−3.08500e10	+	2.58862e10i	−0.00409590	+	0.00343687i	0.640737	+	0.767760i	$0.278629\pi$
$728$	1.87915e11	−	1.06572e12i	0.0247954	−	0.140622i
$729$	5.43694e12	−	9.41705e12i	0.712985	−	1.23493i
$730$	1.12583e11	+	1.95000e11i	0.0146730	+	0.0254144i
$731$	4.63900e12	−	1.68846e12i	0.600892	−	0.218707i
$732$	−4.38300e12	+	1.59528e12i	−0.564250	+	0.205370i
$733$	3.28157e12	+	5.68385e12i	0.419869	+	0.727234i	0.995926	−	0.0901752i	$-0.0287427\pi$
$733$	3.28157e12	+	5.68385e12i	0.419869	+	0.727234i	−0.576057	+	0.817410i	$0.695409\pi$
$734$	−3.59237e12	+	6.22216e12i	−0.456823	+	0.791241i
$735$	−3.58492e12	+	2.03311e13i	−0.453092	+	2.56961i
$736$	1.33649e12	−	1.12145e12i	0.167886	−	0.140873i
$737$	6.50097e12	+	5.45496e12i	0.811661	+	0.681065i
$738$	−3.07521e12	−	1.74404e13i	−0.381612	−	2.16423i
$739$	1.16871e13	+	4.25374e12i	1.44147	+	0.524652i	0.940195	−	0.340637i	$-0.110643\pi$
$739$	1.16871e13	+	4.25374e12i	1.44147	+	0.524652i	0.501274	+	0.865289i	$0.332865\pi$
$740$	−4.33419e12			−0.531331
$741$	3.81180e12	+	3.40636e11i	0.464460	+	0.0415058i
$742$	1.52290e13			1.84440
$743$	−3.11853e12	−	1.13505e12i	−0.375405	−	0.136636i	0.147425	−	0.989073i	$-0.452901\pi$
$743$	−3.11853e12	−	1.13505e12i	−0.375405	−	0.136636i	−0.522830	+	0.852437i	$0.675124\pi$
$744$	1.44766e12	+	8.21006e12i	0.173216	+	0.982355i
$745$	1.19595e13	+	1.00352e13i	1.42236	+	1.19350i
$746$	4.58543e11	−	3.84763e11i	0.0542070	−	0.0454851i
$747$	−3.65728e12	+	2.07415e13i	−0.429749	+	2.43723i
$748$	−2.35211e12	+	4.07397e12i	−0.274726	+	0.475840i
$749$	−4.17838e11	−	7.23716e11i	−0.0485109	−	0.0840233i
$750$	5.36001e11	−	1.95088e11i	0.0618571	−	0.0225142i
$751$	7.08362e12	−	2.57823e12i	0.812598	−	0.295761i	0.0979014	−	0.995196i	$-0.468787\pi$
$751$	7.08362e12	−	2.57823e12i	0.812598	−	0.295761i	0.714697	+	0.699435i	$0.246565\pi$
$752$	5.40800e10	+	9.36694e10i	0.00616676	+	0.0106811i
$753$	5.29318e12	−	9.16806e12i	0.599983	−	1.03920i
$754$	4.18717e11	−	2.37466e12i	0.0471791	−	0.267566i
$755$	6.15002e12	−	5.16048e12i	0.688836	−	0.578002i
$756$	6.82535e12	+	5.72715e12i	0.759935	+	0.637662i
$757$	−3.03683e11	−	1.72227e12i	−0.0336116	−	0.190621i	0.963379	−	0.268144i	$-0.0864101\pi$
$757$	−3.03683e11	−	1.72227e12i	−0.0336116	−	0.190621i	−0.996991	+	0.0775225i	$0.975299\pi$
$758$	−2.65091e12	−	9.64852e11i	−0.291664	−	0.106157i
$759$	−2.20101e13			−2.40732
$760$	−4.12271e12	−	1.93180e12i	−0.448251	−	0.210039i
$761$	2.23146e12			0.241189			0.120594	−	0.992702i	$-0.461520\pi$
$761$	2.23146e12			0.241189			0.120594	+	0.992702i	$0.461520\pi$
$762$	−4.38165e12	−	1.59479e12i	−0.470804	−	0.171359i
$763$	−3.39590e12	−	1.92591e13i	−0.362739	−	2.05720i
$764$	−4.00190e12	−	3.35800e12i	−0.424959	−	0.356583i
$765$	−1.74975e13	+	1.46822e13i	−1.84714	+	1.54994i
$766$	1.11144e12	−	6.30328e12i	0.116642	−	0.661512i
$767$	3.05730e8	−	5.29540e8i	3.18977e−5	−	5.52484e-5i
$768$	5.05407e11	+	8.75391e11i	0.0524223	+	0.0907981i
$769$	6.62938e12	−	2.41290e12i	0.683603	−	0.248811i	0.0232093	−	0.999731i	$-0.492612\pi$
$769$	6.62938e12	−	2.41290e12i	0.683603	−	0.248811i	0.660394	+	0.750919i	$0.270389\pi$
$770$	1.52621e13	−	5.55495e12i	1.56461	−	0.569472i
$771$	1.11127e13	+	1.92478e13i	1.13260	+	1.96171i
$772$	−1.91131e12	+	3.31048e12i	−0.193666	+	0.335439i
$773$	−4.06508e11	+	2.30542e12i	−0.0409508	+	0.232243i	−0.998413	−	0.0563152i	$-0.982065\pi$
$773$	−4.06508e11	+	2.30542e12i	−0.0409508	+	0.232243i	0.957462	+	0.288558i	$0.0931759\pi$
$774$	−6.60852e12	+	5.54521e12i	−0.661866	+	0.555371i
$775$	1.24264e13	+	1.04269e13i	1.23733	+	1.03824i
$776$	−2.08164e11	−	1.18056e12i	−0.0206076	−	0.116872i
$777$	1.76607e13	+	6.42799e12i	1.73826	+	0.632675i
$778$	−5.52390e12			−0.540552
$779$	−1.50209e12	−	1.75449e13i	−0.146143	−	1.70699i
$780$	−3.37474e12			−0.326448
$781$	−7.18103e12	−	2.61368e12i	−0.690649	−	0.251376i
$782$	−1.51130e12	−	8.57101e12i	−0.144517	−	0.819599i
$783$	1.52084e13	+	1.27614e13i	1.44596	+	1.21330i
$784$	2.25060e12	−	1.88848e12i	0.212753	−	0.178521i
$785$	−3.44855e12	+	1.95577e13i	−0.324132	+	1.83825i
$786$	−3.51450e12	+	6.08730e12i	−0.328445	+	0.568883i
$787$	−8.83403e11	−	1.53010e12i	−0.0820867	−	0.142178i	0.822059	−	0.569402i	$-0.192825\pi$
$787$	−8.83403e11	−	1.53010e12i	−0.0820867	−	0.142178i	−0.904146	+	0.427223i	$0.859492\pi$
$788$	−7.09061e12	+	2.58077e12i	−0.655112	+	0.238441i
$789$	−2.82393e13	+	1.02782e13i	−2.59422	+	0.944219i
$790$	−3.17275e12	−	5.49536e12i	−0.289810	−	0.501966i
$791$	6.55141e12	−	1.13474e13i	0.595033	−	1.03063i
$792$	1.42748e12	−	8.09563e12i	0.128916	−	0.731118i
$793$	−1.69763e12	+	1.42448e12i	−0.152445	+	0.127917i
$794$	1.81167e12	+	1.52017e12i	0.161765	+	0.135737i
$795$	−8.24690e12	−	4.67705e13i	−0.732215	−	4.15260i
$796$	−5.16541e12	−	1.88006e12i	−0.456033	−	0.165982i
$797$	−2.38758e12			−0.209602			−0.104801	−	0.994493i	$-0.533421\pi$
$797$	−2.38758e12			−0.209602			−0.104801	+	0.994493i	$0.533421\pi$
$798$	1.39340e13	+	1.39859e13i	1.21636	+	1.22089i
$799$	5.39556e11			0.0468356
$800$	1.84821e12	+	6.72694e11i	0.159532	+	0.0580648i
$801$	−1.18936e12	−	6.74517e12i	−0.102086	−	0.578957i
$802$	7.56645e12	+	6.34901e12i	0.645814	+	0.541903i
$803$	−3.09672e11	+	2.59846e11i	−0.0262834	+	0.0220544i
$804$	1.57960e12	−	8.95837e12i	0.133320	−	0.756096i
$805$	−1.50242e13	+	2.60227e13i	−1.26099	+	2.18409i
$806$	1.98047e12	+	3.43028e12i	0.165295	+	0.286300i
$807$	4.97956e12	−	1.81241e12i	0.413295	−	0.150427i
$808$	4.54477e12	−	1.65416e12i	0.375111	−	0.136529i
$809$	1.20943e12	+	2.09480e12i	0.0992689	+	0.171939i	0.911382	−	0.411561i	$-0.135016\pi$
$809$	1.20943e12	+	2.09480e12i	0.0992689	+	0.171939i	−0.812113	+	0.583500i	$0.801683\pi$
$810$	2.89119e12	−	5.00768e12i	0.235990	−	0.408747i
$811$	9.74569e11	−	5.52705e12i	0.0791077	−	0.448642i	−0.919366	−	0.393404i	$-0.871297\pi$
$811$	9.74569e11	−	5.52705e12i	0.0791077	−	0.448642i	0.998473	−	0.0552376i	$-0.0175916\pi$
$812$	9.52897e12	−	7.99576e12i	0.769208	−	0.645443i
$813$	−2.38525e13	−	2.00147e13i	−1.91482	−	1.60672i
$814$	−1.35121e12	−	7.66311e12i	−0.107873	−	0.611780i
$815$	−1.36753e13	−	4.97740e12i	−1.08574	−	0.395178i
$816$	5.04244e12			0.398139
$817$	−7.03574e12	+	4.90700e12i	−0.552473	+	0.385316i
$818$	−8.39907e12			−0.655905
$819$	8.86458e12	+	3.22644e12i	0.688463	+	0.250580i
$820$	2.69642e12	+	1.52922e13i	0.208269	+	1.18115i
$821$	−1.27438e13	−	1.06933e13i	−0.978934	−	0.821423i	0.00499459	−	0.999988i	$-0.498410\pi$
$821$	−1.27438e13	−	1.06933e13i	−0.978934	−	0.821423i	−0.983928	+	0.178565i	$0.942855\pi$
$822$	−6.63278e12	+	5.56557e12i	−0.506725	+	0.425193i
$823$	−9.90987e11	+	5.62016e12i	−0.0752954	+	0.427022i	0.923736	+	0.383029i	$0.125119\pi$
$823$	−9.90987e11	+	5.62016e12i	−0.0752954	+	0.427022i	−0.999032	+	0.0439928i	$0.985992\pi$
$824$	−1.59907e12	+	2.76967e12i	−0.120835	+	0.209293i
$825$	−1.24064e13	−	2.14885e13i	−0.932403	−	1.61497i
$826$	2.96412e9	−	1.07885e9i	0.000221557	−	8.06401e-5i
$827$	−8.43825e12	+	3.07127e12i	−0.627303	+	0.228320i	−0.636057	−	0.771642i	$-0.719436\pi$
$827$	−8.43825e12	+	3.07127e12i	−0.627303	+	0.228320i	0.00875403	+	0.999962i	$0.497213\pi$
$828$	7.60435e12	+	1.31711e13i	0.562245	+	0.973837i
$829$	1.09887e12	−	1.90329e12i	0.0808070	−	0.139962i	−0.822790	−	0.568346i	$-0.807584\pi$
$829$	1.09887e12	−	1.90329e12i	0.0808070	−	0.139962i	0.903597	+	0.428384i	$0.140917\pi$
$830$	3.20679e12	−	1.81866e13i	0.234541	−	1.33015i
$831$	1.27123e13	−	1.06669e13i	0.924742	−	0.775951i
$832$	3.67899e11	+	3.08704e11i	0.0266179	+	0.0223351i
$833$	−2.54498e12	−	1.44333e13i	−0.183139	−	1.03863i
$834$	−1.04413e12	−	3.80031e11i	−0.0747318	−	0.0272002i
$835$	2.46223e13			1.75283
$836$	2.13025e12	−	7.89144e12i	0.150835	−	0.558763i
$837$	−3.26120e13			−2.29675
$838$	6.90861e12	+	2.51453e12i	0.483941	+	0.176140i
$839$	3.35383e12	+	1.90205e13i	0.233675	+	1.32524i	0.845386	+	0.534155i	$0.179370\pi$
$839$	3.35383e12	+	1.90205e13i	0.233675	+	1.32524i	−0.611712	+	0.791081i	$0.709519\pi$
$840$	−1.33363e13	−	1.11905e13i	−0.924228	−	0.775519i
$841$	1.01196e13	−	8.49131e12i	0.697556	−	0.585319i
$842$	−2.42110e12	+	1.37308e13i	−0.166000	+	0.941434i
$843$	−2.01265e13	+	3.48601e13i	−1.37260	+	2.37741i
$844$	4.87672e12	+	8.44672e12i	0.330816	+	0.572990i
$845$	1.79922e13	−	6.54861e12i	1.21403	−	0.441869i
$846$	−8.85999e11	+	3.22477e11i	−0.0594657	+	0.0216438i
$847$	3.69824e12	+	6.40554e12i	0.246899	+	0.427642i
$848$	−3.37929e12	+	5.85310e12i	−0.224411	+	0.388691i
$849$	−1.78215e12	+	1.01071e13i	−0.117723	+	0.667639i
$850$	7.51604e12	−	6.30671e12i	0.493860	−	0.414398i
$851$	1.10281e13	+	9.25366e12i	0.720804	+	0.604826i
$852$	1.42241e12	+	8.06688e12i	0.0924796	+	0.524478i
$853$	1.45896e12	+	5.31016e11i	0.0943564	+	0.0343429i	0.388767	−	0.921336i	$-0.372901\pi$
$853$	1.45896e12	+	5.31016e11i	0.0943564	+	0.0343429i	−0.294411	+	0.955679i	$0.595123\pi$
$854$	−1.14322e13			−0.735480
$855$	2.28249e13	−	3.24686e13i	1.46070	−	2.07786i
$856$	3.70869e11			0.0236096
$857$	1.36355e12	+	4.96291e11i	0.0863488	+	0.0314284i	0.384833	−	0.922986i	$-0.374259\pi$
$857$	1.36355e12	+	4.96291e11i	0.0863488	+	0.0314284i	−0.298485	+	0.954414i	$0.596481\pi$
$858$	−1.05210e12	−	5.96673e12i	−0.0662770	−	0.375875i
$859$	1.53667e13	+	1.28942e13i	0.962968	+	0.808026i	0.981433	−	0.191803i	$-0.0614336\pi$
$859$	1.53667e13	+	1.28942e13i	0.962968	+	0.808026i	−0.0184653	+	0.999830i	$0.505878\pi$
$860$	5.79451e12	−	4.86217e12i	0.361222	−	0.303101i
$861$	1.16924e13	−	6.63108e13i	0.725085	−	4.11216i
$862$	−7.10434e12	+	1.23051e13i	−0.438269	+	0.759105i
$863$	−1.10756e13	−	1.91835e13i	−0.679704	−	1.17728i	−0.975070	−	0.221897i	$-0.928775\pi$
$863$	−1.10756e13	−	1.91835e13i	−0.679704	−	1.17728i	0.295366	−	0.955384i	$-0.404558\pi$
$864$	−3.71569e12	+	1.35240e12i	−0.226844	+	0.0825646i
$865$	−2.96635e12	+	1.07966e12i	−0.180157	+	0.0655716i
$866$	−2.36132e11	−	4.08993e11i	−0.0142667	−	0.0247107i
$867$	−1.37766e12	+	2.38618e12i	−0.0828050	+	0.143422i
$868$	−3.54822e12	+	2.01230e13i	−0.212164	+	1.20324i
$869$	8.72700e12	−	7.32282e12i	0.519130	−	0.435602i
$870$	−2.97163e13	−	2.49349e13i	−1.75856	−	1.47561i
$871$	−7.50501e11	−	4.25630e12i	−0.0441845	−	0.250582i
$872$	8.15556e12	+	2.96838e12i	0.477672	+	0.173858i
$873$	1.04500e13			0.608908
$874$	6.36552e12	+	1.37175e13i	0.369005	+	0.795193i
$875$	1.39806e12			0.0806285
$876$	4.07180e11	+	1.48202e11i	0.0233624	+	0.00850324i
$877$	−3.08609e12	−	1.75021e13i	−0.176161	−	0.999061i	−0.936795	−	0.349879i	$-0.886223\pi$
$877$	−3.08609e12	−	1.75021e13i	−0.176161	−	0.999061i	0.760633	−	0.649182i	$-0.224889\pi$
$878$	−1.36660e13	−	1.14671e13i	−0.776095	−	0.651221i
$879$	1.98272e13	−	1.66370e13i	1.12024	−	0.939994i
$880$	−1.25165e12	+	7.09845e12i	−0.0703575	+	0.399017i
$881$	4.51644e12	−	7.82270e12i	0.252583	−	0.437487i	−0.711653	−	0.702531i	$-0.752053\pi$
$881$	4.51644e12	−	7.82270e12i	0.252583	−	0.437487i	0.964236	+	0.265044i	$0.0853865\pi$
$882$	1.28055e13	+	2.21797e13i	0.712503	+	1.23409i
$883$	−5.87469e12	+	2.13821e12i	−0.325208	+	0.118366i	−0.499465	−	0.866334i	$-0.666470\pi$
$883$	−5.87469e12	+	2.13821e12i	−0.325208	+	0.118366i	0.174256	+	0.984700i	$0.444248\pi$
$884$	2.25128e12	−	8.19400e11i	0.123992	−	0.0451295i
$885$	−4.91845e9	−	8.51900e9i	−0.000269515	−	0.000466814i
$886$	9.20302e12	−	1.59401e13i	0.501740	−	0.869039i
$887$	−1.35614e10	+	7.69106e10i	−0.000735612	+	0.00417186i	−0.985173	−	0.171562i	$-0.945119\pi$
$887$	−1.35614e10	+	7.69106e10i	−0.000735612	+	0.00417186i	0.984438	+	0.175734i	$0.0562298\pi$
$888$	−6.38940e12	+	5.36135e12i	−0.344828	+	0.289345i
$889$	−8.75490e12	−	7.34623e12i	−0.470103	−	0.394463i
$890$	1.04286e12	+	5.91433e12i	0.0557147	+	0.315974i
$891$	9.75522e12	+	3.55061e12i	0.518546	+	0.188735i
$892$	−7.81918e12			−0.413542
$893$	−9.06020e11	+	2.40962e11i	−0.0476767	+	0.0126799i
$894$	3.00439e13			1.57303
$895$	−2.85928e13	−	1.04069e13i	−1.48954	−	0.542149i
$896$	4.30216e11	+	2.43988e12i	0.0222998	+	0.126468i
$897$	8.58681e12	+	7.20519e12i	0.442860	+	0.371603i
$898$	−5.97676e10	+	5.01510e10i	−0.00306706	+	0.00257357i
$899$	−7.90622e12	+	4.48384e13i	−0.403692	+	2.28945i
$900$	−8.57268e12	+	1.48483e13i	−0.435537	+	0.754373i
$901$	1.68576e13	+	2.91981e13i	0.852183	+	1.47602i
$902$	−2.61968e13	+	9.53487e12i	−1.31771	+	0.479607i
$903$	−3.08222e13	+	1.12184e13i	−1.54266	+	0.561481i
$904$	2.90749e12	+	5.03592e12i	0.144797	+	0.250796i
$905$	−2.44350e13	+	4.23227e13i	−1.21086	+	2.09727i
$906$	2.68282e12	−	1.52150e13i	0.132286	−	0.750232i
$907$	−2.77131e13	+	2.32540e13i	−1.35973	+	1.14095i	−0.383661	+	0.923474i	$0.625337\pi$
$907$	−2.77131e13	+	2.32540e13i	−1.35973	+	1.14095i	−0.976066	+	0.217472i	$0.930219\pi$
$908$	−3.82209e12	−	3.20712e12i	−0.186601	−	0.156577i
$909$	7.32110e12	+	4.15200e13i	0.355663	+	2.01707i
$910$	−7.77269e12	−	2.82903e12i	−0.375738	−	0.136757i
$911$	−2.77287e13			−1.33382			−0.666909	−	0.745139i	$-0.732383\pi$
$911$	−2.77287e13			−1.33382			−0.666909	+	0.745139i	$0.732383\pi$
$912$	−8.46725e12	+	2.25192e12i	−0.405290	+	0.107789i
$913$	3.31548e13			1.57916
$914$	4.46100e12	+	1.62367e12i	0.211434	+	0.0769556i
$915$	6.19084e12	+	3.51100e13i	0.291981	+	1.65591i
$916$	−1.06145e12	−	8.90666e11i	−0.0498163	−	0.0418009i
$917$	−1.31975e13	+	1.10741e13i	−0.616355	+	0.517184i
$918$	−3.42526e12	+	1.94256e13i	−0.159185	+	0.902781i
$919$	1.44426e13	−	2.50153e13i	0.667921	−	1.15687i	−0.310563	−	0.950553i	$-0.600518\pi$
$919$	1.44426e13	−	2.50153e13i	0.667921	−	1.15687i	0.978484	−	0.206321i	$-0.0661490\pi$
$920$	−6.66768e12	−	1.15488e13i	−0.306852	−	0.531484i
$921$	1.20111e13	−	4.37170e12i	0.550067	−	0.200208i
$922$	−5.70766e12	+	2.07742e12i	−0.260117	+	0.0946749i
$923$	1.94593e12	+	3.37045e12i	0.0882511	+	0.152855i
$924$	1.56278e13	−	2.70681e13i	0.705299	−	1.22161i
$925$	−2.81820e12	+	1.59828e13i	−0.126571	+	0.717818i
$926$	−2.11445e13	+	1.77424e13i	−0.945036	+	0.792979i
$927$	−2.13566e13	−	1.79203e13i	−0.949888	−	0.797051i
$928$	9.58618e11	+	5.43659e12i	0.0424306	+	0.240636i
$929$	−5.65759e12	−	2.05920e12i	−0.249207	−	0.0907041i	0.214396	−	0.976747i	$-0.431222\pi$
$929$	−5.65759e12	−	2.05920e12i	−0.249207	−	0.0907041i	−0.463604	+	0.886043i	$0.653444\pi$
$930$	6.37219e13			2.79329
$931$	1.07193e13	+	2.30997e13i	0.467621	+	1.00771i
$932$	1.92579e13			0.836061
$933$	6.02060e13	+	2.19132e13i	2.60119	+	0.946756i
$934$	−4.26834e12	−	2.42070e13i	−0.183526	−	1.04083i
$935$	2.75445e13	+	2.31126e13i	1.17864	+	0.989000i
$936$	−3.20708e12	+	2.69106e12i	−0.136574	+	0.114599i
$937$	6.48165e12	−	3.67592e13i	0.274699	−	1.55790i	−0.465217	−	0.885197i	$-0.654024\pi$
$937$	6.48165e12	−	3.67592e13i	0.274699	−	1.55790i	0.739916	−	0.672699i	$-0.234865\pi$
$938$	1.11479e13	−	1.93087e13i	0.470197	−	0.814405i
$939$	−1.12098e13	−	1.94159e13i	−0.470545	−	0.815008i
$940$	7.76866e11	−	2.82756e11i	0.0324542	−	0.0118124i
$941$	−5.43404e11	+	1.97783e11i	−0.0225928	+	0.00822309i	−0.353292	−	0.935513i	$-0.614938\pi$
$941$	−5.43404e11	+	1.97783e11i	−0.0225928	+	0.00822309i	0.330699	+	0.943736i	$0.392715\pi$
$942$	1.91088e13	+	3.30974e13i	0.790687	+	1.36951i
$943$	2.57885e13	−	4.46670e13i	1.06200	−	1.83943i
$944$	−2.43088e8	+	1.37862e9i	−9.96298e−6	+	5.65029e-5i
$945$	5.21697e13	−	4.37756e13i	2.12802	−	1.78562i
$946$	1.04031e13	+	8.72922e12i	0.422330	+	0.354377i
$947$	−1.75353e12	−	9.94475e12i	−0.0708497	−	0.401808i	−0.999522	−	0.0309078i	$-0.990160\pi$
$947$	−1.75353e12	−	9.94475e12i	−0.0708497	−	0.401808i	0.928673	−	0.370901i	$-0.120951\pi$
$948$	−1.14749e13	−	4.17653e12i	−0.461437	−	0.167949i
$949$	2.05875e11			0.00823961
$950$	−9.80438e12	+	1.39468e13i	−0.390539	+	0.555544i
$951$	−1.82743e13			−0.724482
$952$	1.16137e13	+	4.22705e12i	0.458253	+	0.166791i
$953$	−6.12419e12	−	3.47320e13i	−0.240509	−	1.36399i	−0.830696	−	0.556726i	$-0.812057\pi$
$953$	−6.12419e12	−	3.47320e13i	−0.240509	−	1.36399i	0.590188	−	0.807266i	$-0.299054\pi$
$954$	−4.51326e13	−	3.78707e13i	−1.76410	−	1.48025i
$955$	−3.05886e13	+	2.56669e13i	−1.18999	+	0.998524i
$956$	2.73573e12	−	1.55151e13i	0.105928	−	0.600749i
$957$	3.48221e13	−	6.03137e13i	1.34200	−	2.32441i
$958$	6.18656e12	+	1.07154e13i	0.237304	+	0.411022i
$959$	−1.99422e13	+	7.25837e12i	−0.761359	+	0.277112i
$960$	7.26024e12	−	2.64251e12i	0.275886	−	0.100414i
$961$	−2.41755e13	−	4.18732e13i	−0.914366	−	1.58373i
$962$	−1.98144e12	+	3.43195e12i	−0.0745920	+	0.129197i
$963$	−5.61399e11	+	3.18385e12i	−0.0210355	+	0.119298i
$964$	−1.29743e12	+	1.08867e12i	−0.0483878	+	0.0406022i
$965$	2.23825e13	+	1.87811e13i	0.830873	+	0.697186i
$966$	1.00413e13	+	5.69471e13i	0.371016	+	2.10414i
$967$	−2.65356e13	−	9.65818e12i	−0.975911	−	0.355203i	−0.195662	−	0.980671i	$-0.562686\pi$
$967$	−2.65356e13	−	9.65818e12i	−0.975911	−	0.355203i	−0.780249	+	0.625469i	$0.784908\pi$
$968$	−3.28252e12			−0.120162
$969$	−1.13907e13	+	4.21967e13i	−0.415045	+	1.53752i
$970$	−9.16281e12			−0.332319
$971$	1.92449e13	+	7.00457e12i	0.694751	+	0.252869i	0.665168	−	0.746694i	$-0.268360\pi$
$971$	1.92449e13	+	7.00457e12i	0.694751	+	0.252869i	0.0295828	+	0.999562i	$0.490582\pi$
$972$	1.36726e12	+	7.75409e12i	0.0491305	+	0.278633i
$973$	−2.08625e12	−	1.75057e12i	−0.0746206	−	0.0626141i
$974$	2.41558e13	−	2.02691e13i	0.860015	−	0.721638i
$975$	−2.19434e12	+	1.24447e13i	−0.0777646	+	0.441025i
$976$	2.53679e12	−	4.39385e12i	0.0894870	−	0.154996i
$977$	−7.41806e12	−	1.28485e13i	−0.260474	−	0.451154i	0.705894	−	0.708318i	$-0.250546\pi$
$977$	−7.41806e12	−	1.28485e13i	−0.260474	−	0.451154i	−0.966368	+	0.257163i	$0.917212\pi$
$978$	−2.63169e13	+	9.57856e12i	−0.919834	+	0.334792i
$979$	−1.01318e13	+	3.68766e12i	−0.352503	+	0.128301i
$980$	−1.12281e13	−	1.94477e13i	−0.388858	−	0.673521i
$981$	−3.78285e13	+	6.55208e13i	−1.30409	+	2.25875i
$982$	5.24090e12	−	2.97226e13i	0.179847	−	1.01996i
$983$	−1.45953e12	+	1.22469e12i	−0.0498565	+	0.0418346i	−0.667375	−	0.744721i	$-0.732582\pi$
$983$	−1.45953e12	+	1.22469e12i	−0.0498565	+	0.0418346i	0.617519	+	0.786556i	$0.288138\pi$
$984$	2.28913e13	+	1.92081e13i	0.778380	+	0.653139i
$985$	1.00152e13	+	5.67993e13i	0.338999	+	1.92256i
$986$	2.58780e13	+	9.41881e12i	0.871935	+	0.317358i
$987$	−3.58489e12			−0.120240
$988$	−3.41441e12	+	2.38134e12i	−0.114001	+	0.0795088i
$989$	−2.51247e13			−0.835060
$990$	−5.90443e13	−	2.14904e13i	−1.95353	−	0.711027i
$991$	−2.21397e12	−	1.25561e13i	−0.0729190	−	0.413544i	−0.999315	−	0.0369946i	$-0.988222\pi$
$991$	−2.21397e12	−	1.25561e13i	−0.0729190	−	0.413544i	0.926396	−	0.376550i	$-0.122890\pi$
$992$	−6.94668e12	−	5.82896e12i	−0.227759	−	0.191112i
$993$	5.90633e13	−	4.95600e13i	1.92773	−	1.61756i
$994$	−3.48634e12	+	1.97720e13i	−0.113274	+	0.642410i
$995$	−2.10079e13	+	3.63868e13i	−0.679483	+	1.17690i
$996$	−1.77692e13	−	3.07772e13i	−0.572139	−	0.990974i
$997$	−1.47424e13	+	5.36579e12i	−0.472541	+	0.171991i	−0.567303	−	0.823509i	$-0.692013\pi$
$997$	−1.47424e13	+	5.36579e12i	−0.472541	+	0.171991i	0.0947619	+	0.995500i	$0.469791\pi$
$998$	4.19117e12	−	1.52546e12i	0.133736	−	0.0486759i
$999$	−1.63139e13	−	2.82566e13i	−0.518220	−	0.897583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.e.a.23.1	yes	42
19.5	even	9	inner	38.10.e.a.5.1	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.e.a.5.1	✓	42	19.5	even	9	inner
38.10.e.a.23.1	yes	42	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(15.0351 + 5.47232i) q^{2} +(-40.8678 - 231.773i) q^{3} +(196.107 + 164.554i) q^{4} +(1498.95 - 1257.77i) q^{5} +(653.886 - 3708.37i) q^{6} +(4614.74 - 7992.96i) q^{7} +(2048.00 + 3547.24i) q^{8} +(-33552.6 + 12212.2i) q^{9} +O(q^{10})\)	\(q+(15.0351 + 5.47232i) q^{2} +(-40.8678 - 231.773i) q^{3} +(196.107 + 164.554i) q^{4} +(1498.95 - 1257.77i) q^{5} +(653.886 - 3708.37i) q^{6} +(4614.74 - 7992.96i) q^{7} +(2048.00 + 3547.24i) q^{8} +(-33552.6 + 12212.2i) q^{9} +(29419.8 - 10707.9i) q^{10} +(28104.0 + 48677.6i) q^{11} +(30124.6 - 52177.4i) q^{12} +(4970.79 - 28190.7i) q^{13} +(113123. - 94921.5i) q^{14} +(-352776. - 296014. i) q^{15} +(11380.2 + 64540.4i) q^{16} +(307210. + 111815. i) q^{17} -571295. q^{18} +(-565801. - 50562.0i) q^{19} +500926. q^{20} +(-2.04115e6 - 742917. i) q^{21} +(156167. + 885666. i) q^{22} +(-1.27457e6 - 1.06950e6i) q^{23} +(738457. - 619639. i) q^{24} +(325714. - 1.84722e6i) q^{25} +(229005. - 396648. i) q^{26} +(1.88549e6 + 3.26576e6i) q^{27} +(2.22025e6 - 808106. i) q^{28} +(4.94722e6 - 1.80064e6i) q^{29} +(-3.68413e6 - 6.38110e6i) q^{30} +(-4.32408e6 + 7.48952e6i) q^{31} +(-182083. + 1.03265e6i) q^{32} +(1.01336e7 - 8.50311e6i) q^{33} +(4.00703e6 + 3.36230e6i) q^{34} +(-3.13603e6 - 1.77853e7i) q^{35} +(-8.58947e6 - 3.12631e6i) q^{36} -8.65237e6 q^{37} +(-8.23018e6 - 3.85645e6i) q^{38} -6.73700e6 q^{39} +(7.53146e6 + 2.74123e6i) q^{40} +(5.38288e6 + 3.05278e7i) q^{41} +(-2.66233e7 - 2.23396e7i) q^{42} +(1.15676e7 - 9.70638e6i) q^{43} +(-2.49867e6 + 1.41707e7i) q^{44} +(-3.49337e7 + 6.05069e7i) q^{45} +(-1.33107e7 - 2.30548e7i) q^{46} +(1.55086e6 - 564467. i) q^{47} +(1.44936e7 - 5.27525e6i) q^{48} +(-2.24148e7 - 3.88235e7i) q^{49} +(1.50057e7 - 2.59906e7i) q^{50} +(1.33608e7 - 7.57726e7i) q^{51} +(5.61370e6 - 4.71045e6i) q^{52} +(7.90004e7 + 6.62892e7i) q^{53} +(1.04772e7 + 5.94190e7i) q^{54} +(1.03352e8 + 3.76170e7i) q^{55} +3.78039e7 q^{56} +(1.14042e7 + 1.33204e8i) q^{57} +8.42355e7 q^{58} +(20072.4 + 7305.75i) q^{59} +(-2.04718e7 - 1.16101e8i) q^{60} +(-5.93046e7 - 4.97625e7i) q^{61} +(-1.05998e8 + 8.89429e7i) q^{62} +(-5.72252e7 + 3.24541e8i) q^{63} +(-8.38861e6 + 1.45295e7i) q^{64} +(-2.80065e7 - 4.85086e7i) q^{65} +(1.98891e8 - 7.23905e7i) q^{66} +(1.41877e8 - 5.16390e7i) q^{67} +(4.18465e7 + 7.24803e7i) q^{68} +(-1.95791e8 + 3.39120e8i) q^{69} +(5.01765e7 - 2.84565e8i) q^{70} +(-1.04149e8 + 8.73917e7i) q^{71} +(-1.12035e8 - 9.40087e7i) q^{72} +(1.24888e6 + 7.08273e6i) q^{73} +(-1.30089e8 - 4.73485e7i) q^{74} -4.41446e8 q^{75} +(-1.02638e8 - 1.03020e8i) q^{76} +5.18771e8 q^{77} +(-1.01291e8 - 3.68670e7i) q^{78} +(-3.51951e7 - 1.99602e8i) q^{79} +(9.82352e7 + 8.24292e7i) q^{80} +(1.41484e8 - 1.18719e8i) q^{81} +(-8.61261e7 + 4.88445e8i) q^{82} +(2.94929e8 - 5.10832e8i) q^{83} +(-2.78034e8 - 4.81570e8i) q^{84} +(6.01130e8 - 2.18793e8i) q^{85} +(2.27036e8 - 8.26345e7i) q^{86} +(-6.19522e8 - 1.07304e9i) q^{87} +(-1.15114e8 + 1.99383e8i) q^{88} +(-3.33097e7 + 1.88909e8i) q^{89} +(-8.56343e8 + 7.18557e8i) q^{90} +(-2.02389e8 - 1.69824e8i) q^{91} +(-7.39642e7 - 4.19472e8i) q^{92} +(1.91259e9 + 6.96124e8i) q^{93} +2.64063e7 q^{94} +(-9.11704e8 + 6.35858e8i) q^{95} +2.46781e8 q^{96} +(-2.75018e8 - 1.00098e8i) q^{97} +(-1.24553e8 - 7.06376e8i) q^{98} +(-1.53742e9 - 1.29005e9i) 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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