LMFDB - Embedded newform 38.10.e.a.17.6

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			17.6
Character	$\chi$	$=$	38.17
Dual form			38.10.e.a.9.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.77837 + 15.7569i) q^{2} +(117.543 + 98.6302i) q^{3} +(-240.561 - 87.5572i) q^{4} +(-1860.80 + 677.275i) q^{5} +(-1880.69 + 1578.08i) q^{6} +(-1980.53 - 3430.38i) q^{7} +(2048.00 - 3547.24i) q^{8} +(670.500 + 3802.60i) q^{9} +O(q^{10})$	\(q+(-2.77837 + 15.7569i) q^{2} +(117.543 + 98.6302i) q^{3} +(-240.561 - 87.5572i) q^{4} +(-1860.80 + 677.275i) q^{5} +(-1880.69 + 1578.08i) q^{6} +(-1980.53 - 3430.38i) q^{7} +(2048.00 - 3547.24i) q^{8} +(670.500 + 3802.60i) q^{9} +(-5501.78 - 31202.1i) q^{10} +(21705.4 - 37594.9i) q^{11} +(-19640.5 - 34018.3i) q^{12} +(31908.2 - 26774.2i) q^{13} +(59554.9 - 21676.2i) q^{14} +(-285523. - 103922. i) q^{15} +(50203.5 + 42125.7i) q^{16} +(-21965.0 + 124570. i) q^{17} -61780.1 q^{18} +(-563277. + 73531.6i) q^{19} +506936. q^{20} +(105542. - 598557. i) q^{21} +(532074. + 446463. i) q^{22} +(717634. + 261198. i) q^{23} +(590593. - 214958. i) q^{24} +(1.50768e6 - 1.26510e6i) q^{25} +(333226. + 577164. i) q^{26} +(1.21386e6 - 2.10246e6i) q^{27} +(176085. + 998627. i) q^{28} +(-1.15548e6 - 6.55307e6i) q^{29} +(2.43078e6 - 4.21023e6i) q^{30} +(-174065. - 301490. i) q^{31} +(-803256. + 674012. i) q^{32} +(6.25931e6 - 2.27820e6i) q^{33} +(-1.90181e6 - 692201. i) q^{34} +(6.00868e6 + 5.04188e6i) q^{35} +(171648. - 973465. i) q^{36} +539830. q^{37} +(406361. - 9.07981e6i) q^{38} +6.39132e6 q^{39} +(-1.40846e6 + 7.98775e6i) q^{40} +(-5.62806e6 - 4.72250e6i) q^{41} +(9.13819e6 + 3.32603e6i) q^{42} +(-1.78211e7 + 6.48636e6i) q^{43} +(-8.51319e6 + 7.14341e6i) q^{44} +(-3.82307e6 - 6.62174e6i) q^{45} +(-6.10952e6 + 1.05820e7i) q^{46} +(-4.20680e6 - 2.38579e7i) q^{47} +(1.74619e6 + 9.90316e6i) q^{48} +(1.23318e7 - 2.13593e7i) q^{49} +(1.57451e7 + 2.72713e7i) q^{50} +(-1.48682e7 + 1.24759e7i) q^{51} +(-1.00201e7 + 3.64703e6i) q^{52} +(-9.56618e7 - 3.48181e7i) q^{53} +(2.97557e7 + 2.49680e7i) q^{54} +(-1.49273e7 + 8.46570e7i) q^{55} -1.62245e7 q^{56} +(-7.34616e7 - 4.69130e7i) q^{57} +1.06467e8 q^{58} +(6.13196e6 - 3.47761e7i) q^{59} +(5.95867e7 + 4.99992e7i) q^{60} +(-4.84419e7 - 1.76314e7i) q^{61} +(5.23417e6 - 1.90508e6i) q^{62} +(1.17164e7 - 9.83124e6i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(-4.12412e7 + 7.14319e7i) q^{65} +(1.85068e7 + 1.04957e8i) q^{66} +(5.42040e7 + 3.07406e8i) q^{67} +(1.61909e7 - 2.80435e7i) q^{68} +(5.85909e7 + 1.01482e8i) q^{69} +(-9.61388e7 + 8.06701e7i) q^{70} +(1.56978e7 - 5.71354e6i) q^{71} +(1.48619e7 + 5.40929e6i) q^{72} +(-3.27339e8 - 2.74670e8i) q^{73} +(-1.49985e6 + 8.50606e6i) q^{74} +3.01994e8 q^{75} +(1.41941e8 + 3.16301e7i) q^{76} -1.71953e8 q^{77} +(-1.77575e7 + 1.00708e8i) q^{78} +(-3.41554e8 - 2.86598e8i) q^{79} +(-1.21949e8 - 4.43859e7i) q^{80} +(4.21464e8 - 1.53400e8i) q^{81} +(9.00490e7 - 7.55601e7i) q^{82} +(-8.31499e7 - 1.44020e8i) q^{83} +(-7.77973e7 + 1.34749e8i) q^{84} +(-4.34955e7 - 2.46675e8i) q^{85} +(-5.26914e7 - 2.98828e8i) q^{86} +(5.10512e8 - 8.84233e8i) q^{87} +(-8.89054e7 - 1.53989e8i) q^{88} +(1.21793e8 - 1.02196e8i) q^{89} +(1.14960e8 - 4.18421e7i) q^{90} +(-1.55041e8 - 5.64302e7i) q^{91} +(-1.49765e8 - 1.25668e8i) q^{92} +(9.27587e6 - 5.26061e7i) q^{93} +3.87616e8 q^{94} +(9.98342e8 - 5.18320e8i) q^{95} -1.60895e8 q^{96} +(-2.50398e8 + 1.42008e9i) q^{97} +(3.02294e8 + 2.53655e8i) q^{98} +(1.57512e8 + 5.73296e7i) 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 $\left(\mathbb{Z}/38\mathbb{Z}\right)^\times$.

$n$	$21$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−2.77837	+	15.7569i	−0.122788	+	0.696364i
$2$	−2.77837	+	15.7569i	−0.122788	+	0.696364i
$3$	117.543	+	98.6302i	0.837820	+	0.703015i	0.957072	−	0.289849i	$-0.0936052\pi$
$3$	117.543	+	98.6302i	0.837820	+	0.703015i	−0.119252	+	0.992864i	$0.538050\pi$
$4$	−240.561	−	87.5572i	−0.469846	−	0.171010i
$5$	−1860.80	+	677.275i	−1.33148	+	0.484618i	−0.907118	−	0.420876i	$-0.861723\pi$
$5$	−1860.80	+	677.275i	−1.33148	+	0.484618i	−0.424359	+	0.905494i	$0.639501\pi$
$6$	−1880.69	+	1578.08i	−0.592428	+	0.497106i
$7$	−1980.53	−	3430.38i	−0.311775	−	0.540009i	0.666972	−	0.745083i	$-0.267590\pi$
$7$	−1980.53	−	3430.38i	−0.311775	−	0.540009i	−0.978747	+	0.205073i	$0.934257\pi$
$8$	2048.00	−	3547.24i	0.176777	−	0.306186i
$9$	670.500	+	3802.60i	0.0340649	+	0.193192i
$10$	−5501.78	−	31202.1i	−0.173982	−	0.986699i
$11$	21705.4	−	37594.9i	0.446993	−	0.774215i	−0.551195	−	0.834376i	$-0.685828\pi$
$11$	21705.4	−	37594.9i	0.446993	−	0.774215i	0.998189	+	0.0601610i	$0.0191614\pi$
$12$	−19640.5	−	34018.3i	−0.273424	−	0.473585i
$13$	31908.2	−	26774.2i	0.309854	−	0.259998i	−0.474578	−	0.880214i	$-0.657399\pi$
$13$	31908.2	−	26774.2i	0.309854	−	0.259998i	0.784432	+	0.620215i	$0.212955\pi$
$14$	59554.9	−	21676.2i	0.414325	−	0.150802i
$15$	−285523.	−	103922.i	−1.45623	−	0.530025i
$16$	50203.5	+	42125.7i	0.191511	+	0.160697i
$17$	−21965.0	+	124570.i	−0.0637839	+	0.361736i	0.936164	+	0.351563i	$0.114350\pi$
$17$	−21965.0	+	124570.i	−0.0637839	+	0.361736i	−0.999948	+	0.0101737i	$0.996762\pi$
$18$	−61780.1			−0.138715
$19$	−563277.	+	73531.6i	−0.991587	+	0.129444i
$19$	−563277.	+	73531.6i	−0.991587	+	0.129444i
$20$	506936.			0.708464
$21$	105542.	−	598557.i	0.118423	−	0.671613i
$22$	532074.	+	446463.i	0.484250	+	0.406334i
$23$	717634.	+	261198.i	0.534722	+	0.194623i	0.595245	−	0.803544i	$-0.297055\pi$
$23$	717634.	+	261198.i	0.534722	+	0.194623i	−0.0605236	+	0.998167i	$0.519277\pi$
$24$	590593.	−	214958.i	0.363360	−	0.132252i
$25$	1.50768e6	−	1.26510e6i	0.771933	−	0.647729i
$26$	333226.	+	577164.i	0.143007	+	0.247696i
$27$	1.21386e6	−	2.10246e6i	0.439572	−	0.761361i
$28$	176085.	+	998627.i	0.0541391	+	0.307038i
$29$	−1.15548e6	−	6.55307e6i	−0.303370	−	1.72050i	−0.631079	−	0.775718i	$-0.717388\pi$
$29$	−1.15548e6	−	6.55307e6i	−0.303370	−	1.72050i	0.327709	−	0.944779i	$-0.393723\pi$
$30$	2.43078e6	−	4.21023e6i	0.547898	−	0.948988i
$31$	−174065.	−	301490.i	−0.0338520	−	0.0586334i	0.848603	−	0.529030i	$-0.177444\pi$
$31$	−174065.	−	301490.i	−0.0338520	−	0.0586334i	−0.882455	+	0.470397i	$0.844111\pi$
$32$	−803256.	+	674012.i	−0.135419	+	0.113630i
$33$	6.25931e6	−	2.27820e6i	0.918785	−	0.334410i
$34$	−1.90181e6	−	692201.i	−0.244068	−	0.0888336i
$35$	6.00868e6	+	5.04188e6i	0.676819	+	0.567919i
$36$	171648.	−	973465.i	0.0170325	−	0.0965959i
$37$	539830.			0.0473532			0.0236766	−	0.999720i	$-0.492463\pi$
$37$	539830.			0.0473532			0.0236766	+	0.999720i	$0.492463\pi$
$38$	406361.	−	9.07981e6i	0.0316144	−	0.706400i
$39$	6.39132e6			0.442385
$40$	−1.40846e6	+	7.98775e6i	−0.0869908	+	0.493349i
$41$	−5.62806e6	−	4.72250e6i	−0.311051	−	0.261003i	0.473875	−	0.880592i	$-0.342855\pi$
$41$	−5.62806e6	−	4.72250e6i	−0.311051	−	0.261003i	−0.784926	+	0.619589i	$0.787299\pi$
$42$	9.13819e6	+	3.32603e6i	0.453146	+	0.164932i
$43$	−1.78211e7	+	6.48636e6i	−0.794927	+	0.289330i	−0.707383	−	0.706831i	$-0.750124\pi$
$43$	−1.78211e7	+	6.48636e6i	−0.794927	+	0.289330i	−0.0875444	+	0.996161i	$0.527902\pi$
$44$	−8.51319e6	+	7.14341e6i	−0.342417	+	0.287322i
$45$	−3.82307e6	−	6.62174e6i	−0.138981	−	0.240722i
$46$	−6.10952e6	+	1.05820e7i	−0.201186	+	0.348464i
$47$	−4.20680e6	−	2.38579e7i	−0.125751	−	0.713169i	−0.980859	−	0.194719i	$-0.937620\pi$
$47$	−4.20680e6	−	2.38579e7i	−0.125751	−	0.713169i	0.855108	−	0.518450i	$-0.173491\pi$
$48$	1.74619e6	+	9.90316e6i	0.0474796	+	0.269270i
$49$	1.23318e7	−	2.13593e7i	0.305593	−	0.529303i
$50$	1.57451e7	+	2.72713e7i	0.356271	+	0.617080i
$51$	−1.48682e7	+	1.24759e7i	−0.307745	+	0.258229i
$52$	−1.00201e7	+	3.64703e6i	−0.190046	+	0.0691711i
$53$	−9.56618e7	−	3.48181e7i	−1.66532	−	0.606126i	−0.674133	−	0.738610i	$-0.735483\pi$
$53$	−9.56618e7	−	3.48181e7i	−1.66532	−	0.606126i	−0.991185	+	0.132483i	$0.957705\pi$
$54$	2.97557e7	+	2.49680e7i	0.476210	+	0.399588i
$55$	−1.49273e7	+	8.46570e7i	−0.219963	+	1.24747i
$56$	−1.62245e7			−0.220458
$57$	−7.34616e7	−	4.69130e7i	−0.921773	−	0.588649i
$58$	1.06467e8			1.23534
$59$	6.13196e6	−	3.47761e7i	0.0658817	−	0.373634i	−0.933985	−	0.357312i	$-0.883693\pi$
$59$	6.13196e6	−	3.47761e7i	0.0658817	−	0.373634i	0.999867	−	0.0163218i	$-0.00519564\pi$
$60$	5.95867e7	+	4.99992e7i	0.593566	+	0.498061i
$61$	−4.84419e7	−	1.76314e7i	−0.447958	−	0.163043i	0.108184	−	0.994131i	$-0.465497\pi$
$61$	−4.84419e7	−	1.76314e7i	−0.447958	−	0.163043i	−0.556142	+	0.831088i	$0.687719\pi$
$62$	5.23417e6	−	1.90508e6i	0.0449868	−	0.0163739i
$63$	1.17164e7	−	9.83124e6i	0.0937049	−	0.0786277i
$64$	−8.38861e6	−	1.45295e7i	−0.0625000	−	0.108253i
$65$	−4.12412e7	+	7.14319e7i	−0.286564	+	0.496343i
$66$	1.85068e7	+	1.04957e8i	0.120056	+	0.680870i
$67$	5.42040e7	+	3.07406e8i	0.328620	+	1.86370i	0.482905	+	0.875673i	$0.339582\pi$
$67$	5.42040e7	+	3.07406e8i	0.328620	+	1.86370i	−0.154285	+	0.988026i	$0.549307\pi$
$68$	1.61909e7	−	2.80435e7i	0.0918292	−	0.159053i
$69$	5.85909e7	+	1.01482e8i	0.311178	+	0.538976i
$70$	−9.61388e7	+	8.06701e7i	−0.478583	+	0.401579i
$71$	1.56978e7	−	5.71354e6i	0.0733122	−	0.0266835i	−0.305104	−	0.952319i	$-0.598691\pi$
$71$	1.56978e7	−	5.71354e6i	0.0733122	−	0.0266835i	0.378416	+	0.925636i	$0.376469\pi$
$72$	1.48619e7	+	5.40929e6i	0.0651746	+	0.0237216i
$73$	−3.27339e8	−	2.74670e8i	−1.34910	−	1.13203i	−0.979186	−	0.202964i	$-0.934943\pi$
$73$	−3.27339e8	−	2.74670e8i	−1.34910	−	1.13203i	−0.369914	−	0.929066i	$-0.620613\pi$
$74$	−1.49985e6	+	8.50606e6i	−0.00581440	+	0.0329751i
$75$	3.01994e8			1.10210
$76$	1.41941e8	+	3.16301e7i	0.488030	+	0.108752i
$77$	−1.71953e8			−0.557445
$78$	−1.77575e7	+	1.00708e8i	−0.0543194	+	0.308061i
$79$	−3.41554e8	−	2.86598e8i	−0.986592	−	0.827849i	−0.00152126	−	0.999999i	$-0.500484\pi$
$79$	−3.41554e8	−	2.86598e8i	−0.986592	−	0.827849i	−0.985071	+	0.172150i	$0.944929\pi$
$80$	−1.21949e8	−	4.43859e7i	−0.332869	−	0.121155i
$81$	4.21464e8	−	1.53400e8i	1.08787	−	0.395953i
$82$	9.00490e7	−	7.55601e7i	0.219946	−	0.184557i
$83$	−8.31499e7	−	1.44020e8i	−0.192314	−	0.333097i	0.753703	−	0.657215i	$-0.228266\pi$
$83$	−8.31499e7	−	1.44020e8i	−0.192314	−	0.333097i	−0.946017	+	0.324118i	$0.894932\pi$
$84$	−7.77973e7	+	1.34749e8i	−0.170493	+	0.295303i
$85$	−4.34955e7	−	2.46675e8i	−0.0903772	−	0.512555i
$86$	−5.26914e7	−	2.98828e8i	−0.103872	−	0.589085i
$87$	5.10512e8	−	8.84233e8i	0.955365	−	1.65474i
$88$	−8.89054e7	−	1.53989e8i	−0.158036	−	0.273726i
$89$	1.21793e8	−	1.02196e8i	0.205762	−	0.172655i	−0.534083	−	0.845432i	$-0.679343\pi$
$89$	1.21793e8	−	1.02196e8i	0.205762	−	0.172655i	0.739845	+	0.672777i	$0.234899\pi$
$90$	1.14960e8	−	4.18421e7i	0.184695	−	0.0672237i
$91$	−1.55041e8	−	5.64302e7i	−0.237006	−	0.0862632i
$92$	−1.49765e8	−	1.25668e8i	−0.217955	−	0.182886i
$93$	9.27587e6	−	5.26061e7i	0.0128582	−	0.0729227i
$94$	3.87616e8			0.512066
$95$	9.98342e8	−	5.18320e8i	1.25754	−	0.652893i
$96$	−1.60895e8			−0.193340
$97$	−2.50398e8	+	1.42008e9i	−0.287182	+	1.62869i	0.410202	+	0.911995i	$0.365458\pi$
$97$	−2.50398e8	+	1.42008e9i	−0.287182	+	1.62869i	−0.697384	+	0.716697i	$0.745653\pi$
$98$	3.02294e8	+	2.53655e8i	0.331065	+	0.277796i
$99$	1.57512e8	+	5.73296e7i	0.164799	+	0.0599819i
$100$	−4.73458e8	+	1.72325e8i	−0.473458	+	0.172325i
$101$	−8.24088e7	+	6.91492e7i	−0.0788002	+	0.0661212i	−0.681337	−	0.731970i	$-0.738601\pi$
$101$	−8.24088e7	+	6.91492e7i	−0.0788002	+	0.0661212i	0.602537	+	0.798091i	$0.294157\pi$
$102$	−1.55272e8	−	2.68939e8i	−0.142034	−	0.246010i
$103$	−2.26422e8	+	3.92175e8i	−0.198222	+	0.343330i	−0.947952	−	0.318413i	$-0.896850\pi$
$103$	−2.26422e8	+	3.92175e8i	−0.198222	+	0.343330i	0.749730	+	0.661744i	$0.230183\pi$
$104$	−2.96264e7	−	1.68019e8i	−0.0248330	−	0.140835i
$105$	2.08996e8	+	1.18527e9i	0.167798	+	0.951628i
$106$	8.14410e8	−	1.41060e9i	0.626566	−	1.08524i
$107$	7.74535e8	+	1.34153e9i	0.571234	+	0.989406i	0.996440	+	0.0843094i	$0.0268684\pi$
$107$	7.74535e8	+	1.34153e9i	0.571234	+	0.989406i	−0.425206	+	0.905097i	$0.639798\pi$
$108$	−4.76092e8	+	3.99488e8i	−0.336732	+	0.282551i
$109$	5.50014e8	−	2.00189e8i	0.373211	−	0.135838i	−0.148603	−	0.988897i	$-0.547478\pi$
$109$	5.50014e8	−	2.00189e8i	0.373211	−	0.135838i	0.521814	+	0.853059i	$0.325255\pi$
$110$	−1.29246e9	−	4.70417e8i	−0.841686	−	0.306349i
$111$	6.34532e7	+	5.32436e7i	0.0396735	+	0.0332900i
$112$	4.50777e7	−	2.55648e8i	0.0270695	−	0.153519i
$113$	1.78304e8			0.102875			0.0514373	−	0.998676i	$-0.483620\pi$
$113$	1.78304e8			0.102875			0.0514373	+	0.998676i	$0.483620\pi$
$114$	9.43308e8	−	1.02719e9i	0.523097	−	0.569611i
$115$	−1.51227e9			−0.806288
$116$	−2.95804e8	+	1.67759e9i	−0.151685	+	0.860249i
$117$	1.23206e8	+	1.03382e8i	0.0607847	+	0.0510045i
$118$	5.30927e8	+	1.93242e8i	0.252096	+	0.0917554i
$119$	4.70824e8	−	1.71366e8i	0.215227	−	0.0783363i
$120$	−9.53388e8	+	7.99987e8i	−0.419714	+	0.352182i
$121$	2.36723e8	+	4.10017e8i	0.100394	+	0.173887i
$122$	4.12407e8	−	7.14309e8i	0.168541	−	0.291922i
$123$	−1.95757e8	−	1.11019e9i	−0.0771160	−	0.437347i
$124$	1.54758e7	+	8.77674e7i	0.00587834	+	0.0333377i
$125$	−1.48656e7	+	2.57480e7i	−0.00544613	+	0.00943297i
$126$	1.22357e8	+	2.11929e8i	0.0432477	+	0.0749072i
$127$	−3.81166e9	+	3.19836e9i	−1.30016	+	1.09097i	−0.310046	+	0.950722i	$0.600344\pi$
$127$	−3.81166e9	+	3.19836e9i	−1.30016	+	1.09097i	−0.990117	+	0.140244i	$0.955211\pi$
$128$	2.52247e8	−	9.18103e7i	0.0830579	−	0.0302306i
$129$	−2.73450e9	−	9.95276e8i	−0.869409	−	0.316439i
$130$	−1.01096e9	−	8.48299e8i	−0.310449	−	0.260498i
$131$	2.87436e8	−	1.63013e9i	0.0852747	−	0.483617i	−0.912022	−	0.410141i	$-0.865480\pi$
$131$	2.87436e8	−	1.63013e9i	0.0852747	−	0.483617i	0.997297	−	0.0734762i	$-0.0234093\pi$
$132$	−1.70522e9			−0.488875
$133$	1.36783e9	+	1.78662e9i	0.379053	+	0.495109i
$134$	−4.99437e9			−1.33816
$135$	−8.34795e8	+	4.73436e9i	−0.216311	+	1.22676i
$136$	3.96894e8	+	3.33034e8i	0.0994832	+	0.0834763i
$137$	−6.68194e8	−	2.43203e8i	−0.162054	−	0.0589829i	0.259719	−	0.965684i	$-0.416370\pi$
$137$	−6.68194e8	−	2.43203e8i	−0.162054	−	0.0589829i	−0.421773	+	0.906701i	$0.638592\pi$
$138$	−1.76184e9	+	6.41256e8i	−0.413533	+	0.150514i
$139$	−2.35255e8	+	1.97402e8i	−0.0534529	+	0.0448523i	−0.669123	−	0.743152i	$-0.733330\pi$
$139$	−2.35255e8	+	1.97402e8i	−0.0534529	+	0.0448523i	0.615670	+	0.788004i	$0.288886\pi$
$140$	−1.00400e9	−	1.73898e9i	−0.220881	−	0.382577i
$141$	1.85863e9	−	3.21925e9i	0.396012	−	0.685912i
$142$	4.64134e7	+	2.63223e8i	0.00957957	+	0.0543284i
$143$	−3.13991e8	−	1.78073e9i	−0.0627920	−	0.356111i
$144$	−1.26526e8	+	2.19149e8i	−0.0245215	+	0.0424725i
$145$	6.58835e9	+	1.14114e10i	1.23771	+	2.14378i
$146$	5.23742e9	−	4.39471e9i	0.953958	−	0.800466i
$147$	3.55619e9	−	1.29435e9i	0.628140	−	0.228624i
$148$	−1.29862e8	−	4.72660e7i	−0.0222487	−	0.00809788i
$149$	−1.38318e9	−	1.16063e9i	−0.229901	−	0.192910i	0.520559	−	0.853826i	$-0.325724\pi$
$149$	−1.38318e9	−	1.16063e9i	−0.229901	−	0.192910i	−0.750460	+	0.660916i	$0.770168\pi$
$150$	−8.39051e8	+	4.75850e9i	−0.135325	+	0.767466i
$151$	6.04760e9			0.946645			0.473322	−	0.880889i	$-0.343055\pi$
$151$	6.04760e9			0.946645			0.473322	+	0.880889i	$0.343055\pi$
$152$	−8.92757e8	+	2.14867e9i	−0.135655	+	0.326493i
$153$	−4.88416e8			−0.0720573
$154$	4.77749e8	−	2.70945e9i	0.0684474	−	0.388185i
$155$	5.28091e8	+	4.43121e8i	0.0734880	+	0.0616637i
$156$	−1.53751e9	−	5.59606e8i	−0.207853	−	0.0756522i
$157$	1.39268e10	−	5.06893e9i	1.82937	−	0.665836i	0.836306	−	0.548263i	$-0.184711\pi$
$157$	1.39268e10	−	5.06893e9i	1.82937	−	0.665836i	0.993064	−	0.117573i	$-0.0375115\pi$
$158$	5.46487e9	−	4.58557e9i	0.697626	−	0.585378i
$159$	−7.81026e9	−	1.35278e10i	−0.969122	−	1.67857i
$160$	1.03820e9	−	1.79822e9i	0.125240	−	0.216922i
$161$	−5.25290e8	−	2.97907e9i	−0.0616145	−	0.349433i
$162$	1.24613e9	+	7.06717e9i	0.142150	+	0.806173i
$163$	6.87542e8	−	1.19086e9i	0.0762878	−	0.132134i	−0.825358	−	0.564610i	$-0.809027\pi$
$163$	6.87542e8	−	1.19086e9i	0.0762878	−	0.132134i	0.901646	+	0.432476i	$0.142360\pi$
$164$	9.40405e8	+	1.62883e9i	0.101512	+	0.175824i
$165$	−1.01043e10	+	8.47854e9i	−1.06128	+	0.890520i
$166$	2.50033e9	−	9.10047e8i	0.255571	−	0.0930202i
$167$	−1.46473e10	−	5.33118e9i	−1.45725	−	0.530395i	−0.512642	−	0.858602i	$-0.671333\pi$
$167$	−1.46473e10	−	5.33118e9i	−1.45725	−	0.530395i	−0.944606	+	0.328207i	$0.893556\pi$
$168$	−1.90708e9	−	1.60023e9i	−0.184704	−	0.154985i
$169$	−1.54017e9	+	8.73476e9i	−0.145238	+	0.823685i
$170$	4.00769e9			0.368022
$171$	−6.57288e8	−	2.09261e9i	−0.0587859	−	0.187157i
$172$	4.85500e9			0.422972
$173$	3.20179e9	−	1.81583e10i	0.271760	−	1.54123i	−0.477308	−	0.878736i	$-0.658387\pi$
$173$	3.20179e9	−	1.81583e10i	0.271760	−	1.54123i	0.749068	−	0.662493i	$-0.230502\pi$
$174$	1.25144e10	+	1.05008e10i	1.03500	+	0.868464i
$175$	−7.32577e9	−	2.66636e9i	−0.590449	−	0.214906i
$176$	2.67340e9	−	9.73038e8i	0.210018	−	0.0764404i
$177$	4.15074e9	−	3.48288e9i	0.317867	−	0.266722i
$178$	1.27191e9	+	2.20302e9i	0.0949658	+	0.164486i
$179$	1.02322e10	−	1.77226e10i	0.744953	−	1.29030i	−0.205263	−	0.978707i	$-0.565805\pi$
$179$	1.02322e10	−	1.77226e10i	0.744953	−	1.29030i	0.950217	−	0.311590i	$-0.100862\pi$
$180$	3.39901e8	+	1.92767e9i	0.0241338	+	0.136870i
$181$	−2.15581e9	−	1.22262e10i	−0.149299	−	0.846715i	−0.963815	−	0.266574i	$-0.914108\pi$
$181$	−2.15581e9	−	1.22262e10i	−0.149299	−	0.846715i	0.814516	−	0.580141i	$-0.197003\pi$
$182$	1.31993e9	−	2.28618e9i	0.0891721	−	0.154451i
$183$	−3.95502e9	−	6.85029e9i	−0.260686	−	0.451522i
$184$	2.39625e9	−	2.01069e9i	0.154117	−	0.129320i
$185$	−1.00451e9	+	3.65613e8i	−0.0630497	+	0.0229482i
$186$	8.03138e8	+	2.92318e8i	0.0492019	+	0.0179080i
$187$	4.20642e9	+	3.52961e9i	0.251551	+	0.211076i
$188$	−1.07694e9	+	6.10763e9i	−0.0628755	+	0.356585i
$189$	−9.61631e9			−0.548189
$190$	5.39337e9	+	1.71709e10i	0.300240	+	0.955876i
$191$	−2.05078e10			−1.11498			−0.557492	−	0.830182i	$-0.688236\pi$
$191$	−2.05078e10			−1.11498			−0.557492	+	0.830182i	$0.688236\pi$
$192$	4.47026e8	−	2.53521e9i	0.0237398	−	0.134635i
$193$	1.98029e10	+	1.66166e10i	1.02736	+	0.862055i	0.990534	−	0.137266i	$-0.0438316\pi$
$193$	1.98029e10	+	1.66166e10i	1.02736	+	0.862055i	0.0368234	+	0.999322i	$0.488276\pi$
$194$	−2.16803e10	−	7.89100e9i	−1.09890	−	0.399967i
$195$	−1.18930e10	+	4.32868e9i	−0.589025	+	0.214388i
$196$	−4.83671e9	+	4.05848e9i	−0.234098	+	0.196432i
$197$	2.06092e10	+	3.56962e10i	0.974906	+	1.68859i	0.680244	+	0.732986i	$0.261874\pi$
$197$	2.06092e10	+	3.56962e10i	0.974906	+	1.68859i	0.294662	+	0.955601i	$0.404793\pi$
$198$	−1.34096e9	+	2.32262e9i	−0.0620045	+	0.107395i
$199$	−7.15570e9	−	4.05820e10i	−0.323455	−	1.83440i	−0.520319	−	0.853972i	$-0.674187\pi$
$199$	−7.15570e9	−	4.05820e10i	−0.323455	−	1.83440i	0.196865	−	0.980431i	$-0.436924\pi$
$200$	−1.39986e9	−	7.93903e9i	−0.0618659	−	0.350859i
$201$	−2.39482e10	+	4.14796e10i	−1.03488	+	1.79247i
$202$	−8.60616e8	−	1.49063e9i	−0.0363688	−	0.0629925i
$203$	−2.01911e10	+	1.69423e10i	−0.834501	+	0.700230i
$204$	4.66906e9	−	1.69940e9i	0.188753	−	0.0687004i
$205$	1.36711e10	+	4.97588e9i	0.540644	+	0.196778i
$206$	−5.55038e9	−	4.65732e9i	−0.214744	−	0.180191i
$207$	−5.12055e8	+	2.90401e9i	−0.0193843	+	0.109934i
$208$	2.72978e9			0.101121
$209$	−9.46175e9	+	2.27724e10i	−0.343015	+	0.825562i
$210$	−1.92569e10			−0.683283
$211$	−6.11408e9	+	3.46747e10i	−0.212354	+	1.20432i	0.673086	+	0.739564i	$0.264968\pi$
$211$	−6.11408e9	+	3.46747e10i	−0.212354	+	1.20432i	−0.885440	+	0.464754i	$0.846143\pi$
$212$	1.99640e10	+	1.67518e10i	0.678790	+	0.569573i
$213$	2.40869e9	+	8.76693e8i	0.0801813	+	0.0291836i
$214$	−2.32904e10	+	8.47701e9i	−0.759128	+	0.276300i
$215$	2.87685e10	−	2.41396e10i	0.918213	−	0.770472i
$216$	−4.97195e9	−	8.61167e9i	−0.155412	−	0.269182i
$217$	−6.89483e8	+	1.19422e9i	−0.0211084	+	0.0365608i
$218$	1.62622e9	+	9.22273e9i	0.0487668	+	0.276570i
$219$	−1.13856e10	−	6.45709e10i	−0.334470	−	1.89687i
$220$	1.10033e10	−	1.90582e10i	0.316679	−	0.548504i
$221$	2.63438e9	+	4.56289e9i	0.0742872	+	0.128669i
$222$	−1.01525e9	+	8.51897e8i	−0.0280534	+	0.0235396i
$223$	3.33060e10	−	1.21224e10i	0.901885	−	0.328259i	0.150877	−	0.988553i	$-0.451790\pi$
$223$	3.33060e10	−	1.21224e10i	0.901885	−	0.328259i	0.751008	+	0.660293i	$0.229568\pi$
$224$	3.90299e9	+	1.42057e9i	0.103581	+	0.0377005i
$225$	5.82155e9	+	4.88486e9i	0.151432	+	0.127066i
$226$	−4.95395e8	+	2.80952e9i	−0.0126317	+	0.0716382i
$227$	5.69288e10			1.42303			0.711517	−	0.702669i	$-0.248008\pi$
$227$	5.69288e10			1.42303			0.711517	+	0.702669i	$0.248008\pi$
$228$	1.35645e10	+	1.77175e10i	0.332427	+	0.434207i
$229$	1.31945e10			0.317054			0.158527	−	0.987355i	$-0.449326\pi$
$229$	1.31945e10			0.317054			0.158527	+	0.987355i	$0.449326\pi$
$230$	4.20166e9	−	2.38288e10i	0.0990023	−	0.561470i
$231$	−2.02119e10	−	1.69598e10i	−0.467038	−	0.391892i
$232$	−2.56117e10	−	9.32191e9i	−0.580421	−	0.211256i
$233$	−4.35682e10	+	1.58575e10i	−0.968429	+	0.352479i	−0.777331	−	0.629092i	$-0.783427\pi$
$233$	−4.35682e10	+	1.58575e10i	−0.968429	+	0.352479i	−0.191098	+	0.981571i	$0.561205\pi$
$234$	−1.97129e9	+	1.65411e9i	−0.0429813	+	0.0360656i
$235$	2.39864e10	+	4.15456e10i	0.513049	+	0.888628i
$236$	−4.52000e9	+	7.82888e9i	−0.0948495	+	0.164284i
$237$	−1.18801e10	−	6.73751e10i	−0.244597	−	1.38718i
$238$	1.39208e9	+	7.89485e9i	0.0281233	+	0.159495i
$239$	−2.49762e10	+	4.32601e10i	−0.495150	+	0.857625i	−0.999984	−	0.00559148i	$-0.998220\pi$
$239$	−2.49762e10	+	4.32601e10i	−0.495150	+	0.857625i	0.504835	+	0.863216i	$0.331554\pi$
$240$	−9.95647e9	−	1.72451e10i	−0.193711	−	0.335518i
$241$	−4.15968e10	+	3.49039e10i	−0.794298	+	0.666495i	−0.946805	−	0.321807i	$-0.895710\pi$
$241$	−4.15968e10	+	3.49039e10i	−0.794298	+	0.666495i	0.152507	+	0.988302i	$0.451265\pi$
$242$	−7.11831e9	+	2.59085e9i	−0.133416	+	0.0485595i
$243$	1.97671e10	+	7.19464e9i	0.363676	+	0.132367i
$244$	1.01095e10	+	8.48288e9i	0.182589	+	0.153211i
$245$	−8.48085e9	+	4.80973e10i	−0.150381	+	0.852851i
$246$	1.80371e10			0.314021
$247$	−1.60044e10	+	1.74275e10i	−0.273592	+	0.297920i
$248$	−1.42594e9			−0.0239370
$249$	4.43103e9	−	2.51296e10i	0.0730479	−	0.414275i
$250$	−3.64407e8	−	3.05774e8i	−0.00590007	−	0.00495074i
$251$	−2.70961e10	−	9.86218e9i	−0.430899	−	0.156834i	0.117460	−	0.993078i	$-0.462525\pi$
$251$	−2.70961e10	−	9.86218e9i	−0.430899	−	0.156834i	−0.548359	+	0.836243i	$0.684747\pi$
$252$	−3.67931e9	+	1.33916e9i	−0.0574730	+	0.0209185i
$253$	2.53962e10	−	2.13100e10i	0.389697	−	0.326995i
$254$	−3.98062e10	−	6.89463e10i	−0.600066	−	1.03934i
$255$	1.92170e10	−	3.32849e10i	0.284614	−	0.492965i
$256$	7.45813e8	+	4.22972e9i	0.0108530	+	0.0615505i
$257$	6.87579e9	+	3.89945e10i	0.0983158	+	0.557577i	0.993681	+	0.112243i	$0.0358036\pi$
$257$	6.87579e9	+	3.89945e10i	0.0983158	+	0.557577i	−0.895365	+	0.445333i	$0.853085\pi$
$258$	2.32799e10	−	4.03221e10i	0.327110	−	0.566571i
$259$	−1.06915e9	−	1.85182e9i	−0.0147635	−	0.0255712i
$260$	1.61754e10	−	1.35728e10i	0.219521	−	0.184200i
$261$	2.41439e10	−	8.78767e9i	0.322052	−	0.117217i
$262$	2.48872e10	+	9.05821e9i	0.326303	+	0.118765i
$263$	−2.02888e10	−	1.70243e10i	−0.261490	−	0.219416i	0.502611	−	0.864513i	$-0.332373\pi$
$263$	−2.02888e10	−	1.70243e10i	−0.261490	−	0.219416i	−0.764101	+	0.645096i	$0.776817\pi$
$264$	4.73774e9	−	2.68690e10i	0.0600279	−	0.340435i
$265$	2.01589e11			2.51107
$266$	−3.19520e10	+	1.65889e10i	−0.391319	+	0.203165i
$267$	2.43955e10			0.293771
$268$	1.38762e10	−	7.86960e10i	0.164310	−	0.931850i
$269$	−7.39636e10	−	6.20628e10i	−0.861256	−	0.722680i	0.100982	−	0.994888i	$-0.467802\pi$
$269$	−7.39636e10	−	6.20628e10i	−0.861256	−	0.722680i	−0.962238	+	0.272208i	$0.912246\pi$
$270$	−7.22796e10	−	2.63076e10i	−0.827711	−	0.301262i
$271$	9.93545e10	−	3.61621e10i	1.11899	−	0.407278i	0.284705	−	0.958615i	$-0.408104\pi$
$271$	9.93545e10	−	3.61621e10i	1.11899	−	0.407278i	0.834283	+	0.551337i	$0.185882\pi$
$272$	−6.35031e9	+	5.32854e9i	−0.0703452	+	0.0590267i
$273$	−1.26582e10	−	2.19247e10i	−0.137924	−	0.238892i
$274$	5.68862e9	−	9.85298e9i	0.0609719	−	0.105606i
$275$	−1.48363e10	−	8.41406e10i	−0.156433	−	0.887173i
$276$	−5.20919e9	−	2.95428e10i	−0.0540355	−	0.306451i
$277$	−3.86363e10	+	6.69200e10i	−0.394308	+	0.682962i	−0.993013	−	0.118008i	$-0.962349\pi$
$277$	−3.86363e10	+	6.69200e10i	−0.394308	+	0.682962i	0.598704	+	0.800970i	$0.295682\pi$
$278$	−2.45682e9	−	4.25535e9i	−0.0246702	−	0.0427300i
$279$	1.02973e9	−	8.64048e8i	0.0101743	−	0.00853727i
$280$	3.01905e10	−	1.09885e10i	0.293535	−	0.106838i
$281$	−7.99528e10	−	2.91005e10i	−0.764989	−	0.278433i	−0.0700904	−	0.997541i	$-0.522329\pi$
$281$	−7.99528e10	−	2.91005e10i	−0.764989	−	0.278433i	−0.694899	+	0.719107i	$0.744551\pi$
$282$	4.55615e10	+	3.82306e10i	0.429019	+	0.359990i
$283$	1.35502e10	−	7.68469e10i	0.125576	−	0.712176i	−0.855388	−	0.517987i	$-0.826681\pi$
$283$	1.35502e10	−	7.68469e10i	0.125576	−	0.712176i	0.980964	−	0.194189i	$-0.0622075\pi$
$284$	−4.27655e9			−0.0390086
$285$	1.68470e11	+	3.75419e10i	1.51259	+	0.337065i
$286$	2.89312e10			0.255693
$287$	−5.05344e9	+	2.86595e10i	−0.0439661	+	0.249344i
$288$	−3.10158e9	−	2.60253e9i	−0.0265654	−	0.0222910i
$289$	9.64010e10	+	3.50871e10i	0.812908	+	0.295874i
$290$	−1.98113e11	+	7.21071e10i	−1.64483	+	0.598670i
$291$	−1.69495e11	+	1.42223e11i	−1.38560	+	1.16266i
$292$	5.46957e10	+	9.47357e10i	0.440281	+	0.762590i
$293$	−3.93594e10	+	6.81724e10i	−0.311992	+	0.540386i	−0.978794	−	0.204849i	$-0.934330\pi$
$293$	−3.93594e10	+	6.81724e10i	−0.311992	+	0.540386i	0.666801	+	0.745236i	$0.267663\pi$
$294$	1.05145e10	+	5.96307e10i	0.0820778	+	0.465486i
$295$	1.21426e10	+	6.88642e10i	0.0933497	+	0.529413i
$296$	1.10557e9	−	1.91491e9i	0.00837094	−	0.0144989i
$297$	−5.26945e10	−	9.12695e10i	−0.392971	−	0.680646i
$298$	2.21309e10	−	1.85700e10i	0.162564	−	0.136408i
$299$	2.98918e10	−	1.08797e10i	0.216287	−	0.0787222i
$300$	−7.26481e10	−	2.64417e10i	−0.517820	−	0.188471i
$301$	5.75460e10	+	4.82869e10i	0.404079	+	0.339062i
$302$	−1.68025e10	+	9.52916e10i	−0.116236	+	0.659210i
$303$	−1.65068e10			−0.112505
$304$	−3.13760e10	−	2.00369e10i	−0.210701	−	0.134555i
$305$	1.02082e11			0.675460
$306$	1.35700e9	−	7.69593e9i	0.00884776	−	0.0501781i
$307$	2.86017e10	+	2.39997e10i	0.183768	+	0.154199i	0.730031	−	0.683414i	$-0.239506\pi$
$307$	2.86017e10	+	2.39997e10i	0.183768	+	0.154199i	−0.546263	+	0.837614i	$0.683950\pi$
$308$	4.13653e10	+	1.50557e10i	0.261913	+	0.0953287i
$309$	−6.52946e10	+	2.37653e10i	−0.407440	+	0.148296i
$310$	−8.44946e9	+	7.08994e9i	−0.0519638	+	0.0436028i
$311$	−1.28300e11	−	2.22222e11i	−0.777687	−	1.34699i	−0.933272	−	0.359172i	$-0.883059\pi$
$311$	−1.28300e11	−	2.22222e11i	−0.777687	−	1.34699i	0.155584	−	0.987823i	$-0.450274\pi$
$312$	1.30894e10	−	2.26716e10i	0.0782033	−	0.135452i
$313$	2.80369e10	+	1.59005e11i	0.165113	+	0.936400i	0.948948	+	0.315432i	$0.102149\pi$
$313$	2.80369e10	+	1.59005e11i	0.165113	+	0.936400i	−0.783836	+	0.620968i	$0.786740\pi$
$314$	4.11770e10	+	2.33526e11i	0.239040	+	1.35566i
$315$	−1.51434e10	+	2.62292e10i	−0.0866615	+	0.150102i
$316$	5.70710e10	+	9.88499e10i	0.321976	+	0.557679i
$317$	−1.57245e11	+	1.31944e11i	−0.874600	+	0.733877i	−0.965062	−	0.262023i	$-0.915610\pi$
$317$	−1.57245e11	+	1.31944e11i	−0.874600	+	0.733877i	0.0904615	+	0.995900i	$0.471166\pi$
$318$	2.34856e11	−	8.54805e10i	1.28789	−	0.468754i
$319$	−2.71442e11	−	9.87969e10i	−1.46764	−	0.534177i
$320$	2.54499e10	+	2.13550e10i	0.135679	+	0.113848i
$321$	−4.12747e10	+	2.34080e11i	−0.216976	+	1.23053i
$322$	4.84004e10			0.250898
$323$	3.21257e9	−	7.17823e10i	0.0164226	−	0.366949i
$324$	−1.14819e11			−0.578844
$325$	1.42356e10	−	8.07338e10i	0.0707781	−	0.401403i
$326$	1.68540e10	+	1.41422e10i	0.0826464	+	0.0693486i
$327$	8.43949e10	+	3.07172e10i	0.408180	+	0.148565i
$328$	−2.82781e10	+	1.02924e10i	−0.134902	+	0.0491003i
$329$	−7.35102e10	+	6.16824e10i	−0.345912	+	0.290255i
$330$	−1.05522e11	−	1.82770e11i	−0.489814	−	0.848382i
$331$	−5.54660e10	+	9.60698e10i	−0.253981	+	0.439907i	−0.964618	−	0.263651i	$-0.915073\pi$
$331$	−5.54660e10	+	9.60698e10i	−0.253981	+	0.439907i	0.710638	+	0.703558i	$0.248407\pi$
$332$	7.39268e9	+	4.19260e10i	0.0333949	+	0.189392i
$333$	3.61956e8	+	2.05276e9i	0.00161308	+	0.00914826i
$334$	1.24699e11	−	2.15984e11i	0.548280	−	0.949649i
$335$	−3.09061e11	−	5.35309e11i	−1.34073	−	2.32222i
$336$	3.05132e10	−	2.56036e10i	0.130606	−	0.109591i
$337$	−1.58508e11	+	5.76921e10i	−0.669447	+	0.243659i	−0.654310	−	0.756227i	$-0.727041\pi$
$337$	−1.58508e11	+	5.76921e10i	−0.669447	+	0.243659i	−0.0151372	+	0.999885i	$0.504819\pi$
$338$	−1.33354e11	−	4.85368e10i	−0.555751	−	0.202277i
$339$	2.09584e10	+	1.75862e10i	0.0861904	+	0.0723223i
$340$	−1.11348e10	+	6.31488e10i	−0.0451886	+	0.256277i
$341$	−1.51126e10			−0.0605265
$342$	3.47993e10	−	4.54279e9i	0.137548	−	0.0179558i
$343$	−2.57537e11			−1.00465
$344$	−1.34890e10	+	7.64999e10i	−0.0519358	+	0.294542i
$345$	−1.77757e11	−	1.49156e11i	−0.675524	−	0.566832i
$346$	2.77223e11	+	1.00901e11i	1.03989	+	0.378488i
$347$	2.67386e11	−	9.73207e10i	0.990049	−	0.360348i	0.204310	−	0.978906i	$-0.434505\pi$
$347$	2.67386e11	−	9.73207e10i	0.990049	−	0.360348i	0.785739	+	0.618558i	$0.212283\pi$
$348$	−2.00230e11	+	1.68013e11i	−0.731852	+	0.614097i
$349$	1.36180e11	+	2.35871e11i	0.491359	+	0.851059i	0.999951	−	0.00994880i	$-0.00316685\pi$
$349$	1.36180e11	+	2.35871e11i	0.491359	+	0.851059i	−0.508591	+	0.861008i	$0.669834\pi$
$350$	6.23674e10	−	1.08024e11i	0.222153	−	0.384780i
$351$	−1.75596e10	−	9.95856e10i	−0.0617495	−	0.350199i
$352$	7.90439e9	+	4.48280e10i	0.0274427	+	0.155635i
$353$	1.95805e11	−	3.39144e11i	0.671178	−	1.16251i	−0.306392	−	0.951905i	$-0.599122\pi$
$353$	1.95805e11	−	3.39144e11i	0.671178	−	1.16251i	0.977570	−	0.210609i	$-0.0675448\pi$
$354$	4.33472e10	+	7.50796e10i	0.146706	+	0.254102i
$355$	−2.53408e10	+	2.12635e10i	−0.0846823	+	0.0710569i
$356$	−3.82466e10	+	1.39206e10i	−0.126202	+	0.0459339i
$357$	7.22439e10	+	2.62946e10i	0.235393	+	0.0856761i
$358$	2.50825e11	+	2.10468e11i	0.807045	+	0.677192i
$359$	8.56405e10	−	4.85691e11i	0.272116	−	1.54325i	−0.475860	−	0.879521i	$-0.657863\pi$
$359$	8.56405e10	−	4.85691e11i	0.272116	−	1.54325i	0.747976	−	0.663726i	$-0.231026\pi$
$360$	−3.13186e10			−0.0982744
$361$	3.11874e11	−	8.28373e10i	0.966488	−	0.256710i
$362$	1.98637e11			0.607954
$363$	−1.26149e10	+	7.15427e10i	−0.0381333	+	0.216265i
$364$	3.23559e10	+	2.71499e10i	0.0966046	+	0.0810609i
$365$	7.95137e11	+	2.89406e11i	2.34490	+	0.853473i
$366$	1.18928e11	−	4.32863e10i	0.346433	−	0.126091i
$367$	−2.65507e11	+	2.22787e11i	−0.763974	+	0.641050i	−0.939158	−	0.343485i	$-0.888392\pi$
$367$	−2.65507e11	+	2.22787e11i	−0.763974	+	0.641050i	0.175184	+	0.984536i	$0.443948\pi$
$368$	2.50246e10	+	4.33439e10i	0.0711299	+	0.123201i
$369$	1.41842e10	−	2.45677e10i	0.0398277	−	0.0689836i
$370$	−2.97003e9	−	1.68439e10i	−0.00823859	−	0.0467233i
$371$	7.00221e10	+	3.97115e11i	0.191890	+	1.08826i
$372$	−6.83745e9	+	1.18428e10i	−0.0185119	+	0.0320636i
$373$	−2.15865e11	−	3.73890e11i	−0.577422	−	1.00012i	−0.995774	−	0.0918390i	$-0.970725\pi$
$373$	−2.15865e11	−	3.73890e11i	−0.577422	−	1.00012i	0.418352	−	0.908285i	$-0.362608\pi$
$374$	−6.73028e10	+	5.64737e10i	−0.177873	+	0.149253i
$375$	−4.28688e9	+	1.56030e9i	−0.0111944	+	0.00407443i
$376$	−9.32454e10	−	3.39385e10i	−0.240592	−	0.0875685i
$377$	−2.12322e11	−	1.78160e11i	−0.541327	−	0.454227i
$378$	2.67177e10	−	1.51524e11i	0.0673110	−	0.381739i
$379$	5.74229e11			1.42958			0.714790	−	0.699339i	$-0.246522\pi$
$379$	5.74229e11			1.42958			0.714790	+	0.699339i	$0.246522\pi$
$380$	−2.85545e11	+	3.72758e10i	−0.702504	+	0.0917066i
$381$	−7.63489e11			−1.85627
$382$	5.69782e10	−	3.23140e11i	0.136906	−	0.776435i
$383$	2.59236e11	+	2.17525e11i	0.615603	+	0.516552i	0.896418	−	0.443210i	$-0.146160\pi$
$383$	2.59236e11	+	2.17525e11i	0.615603	+	0.516552i	−0.280815	+	0.959762i	$0.590605\pi$
$384$	3.87051e10	+	1.40875e10i	0.0908401	+	0.0330631i
$385$	3.19970e11	−	1.16459e11i	0.742225	−	0.270148i
$386$	−3.16847e11	+	2.65866e11i	−0.726452	+	0.609565i
$387$	−3.66141e10	−	6.34175e10i	−0.0829753	−	0.143717i
$388$	1.84574e11	−	3.19691e11i	0.413454	−	0.716124i
$389$	7.82837e8	+	4.43969e9i	0.00173340	+	0.00983058i	0.985662	−	0.168731i	$-0.0539668\pi$
$389$	7.82837e8	+	4.43969e9i	0.00173340	+	0.00983058i	−0.983929	+	0.178561i	$0.942856\pi$
$390$	−3.51637e10	−	1.99423e11i	−0.0769668	−	0.436500i
$391$	−4.83001e10	+	8.36583e10i	−0.104509	+	0.181015i
$392$	−5.05110e10	−	8.74876e10i	−0.108044	−	0.187137i
$393$	1.94566e11	−	1.63260e11i	0.411435	−	0.345235i
$394$	−6.19722e11	+	2.25560e11i	−1.29558	+	0.471552i
$395$	8.29668e11	+	3.01975e11i	1.71482	+	0.624142i
$396$	−3.28716e10	−	2.75825e10i	−0.0671727	−	0.0563645i
$397$	5.78600e10	−	3.28140e11i	0.116902	−	0.662983i	−0.868889	−	0.495006i	$-0.835166\pi$
$397$	5.78600e10	−	3.28140e11i	0.116902	−	0.662983i	0.985791	−	0.167976i	$-0.0537232\pi$
$398$	6.59329e11			1.31713
$399$	−1.54364e10	+	3.44914e11i	−0.0304907	+	0.681292i
$400$	1.28984e11			0.251922
$401$	1.00513e11	−	5.70040e11i	0.194122	−	1.10092i	−0.719542	−	0.694449i	$-0.755648\pi$
$401$	1.00513e11	−	5.70040e11i	0.194122	−	1.10092i	0.913664	−	0.406471i	$-0.133241\pi$
$402$	−5.87053e11	−	4.92596e11i	−1.12114	−	0.940749i
$403$	−1.36262e10	−	4.95954e9i	−0.0257338	−	0.00936632i
$404$	2.58789e10	−	9.41914e9i	0.0483314	−	0.0175912i
$405$	−6.80364e11	+	5.70893e11i	−1.25659	+	1.05440i
$406$	−2.10861e11	−	3.65221e11i	−0.385148	−	0.667097i
$407$	1.17172e10	−	2.02949e10i	0.0211666	−	0.0366616i
$408$	1.38049e10	+	7.82915e10i	0.0246640	+	0.139876i
$409$	−2.03932e10	−	1.15655e11i	−0.0360354	−	0.204367i	0.961474	−	0.274894i	$-0.0886429\pi$
$409$	−2.03932e10	−	1.15655e11i	−0.0360354	−	0.204367i	−0.997510	+	0.0705273i	$0.977532\pi$
$410$	−1.16388e11	+	2.01590e11i	−0.203414	+	0.352323i
$411$	−5.45544e10	−	9.44909e10i	−0.0943064	−	0.163344i
$412$	8.88061e10	−	7.45172e10i	0.151847	−	0.127415i
$413$	−1.31440e11	+	4.78401e10i	−0.222306	+	0.0809128i
$414$	−4.43355e10	−	1.61368e10i	−0.0741738	−	0.0269970i
$415$	2.52266e11	+	2.11676e11i	0.417487	+	0.350313i
$416$	−7.58435e9	+	4.30130e10i	−0.0124165	+	0.0704173i
$417$	−4.71223e10			−0.0763158
$418$	−3.32534e11	−	2.12358e11i	−0.532774	−	0.340232i
$419$	−6.35388e10			−0.100711			−0.0503554	−	0.998731i	$-0.516035\pi$
$419$	−6.35388e10			−0.100711			−0.0503554	+	0.998731i	$0.516035\pi$
$420$	5.35029e10	−	3.03430e11i	0.0838988	−	0.475814i
$421$	−2.38154e11	−	1.99835e11i	−0.369478	−	0.310029i	0.439077	−	0.898449i	$-0.355306\pi$
$421$	−2.38154e11	−	1.99835e11i	−0.369478	−	0.310029i	−0.808555	+	0.588420i	$0.799750\pi$
$422$	−5.29379e11	−	1.92678e11i	−0.812570	−	0.295751i
$423$	8.79015e10	−	3.19935e10i	0.133495	−	0.0485881i
$424$	−3.19423e11	+	2.68028e11i	−0.479977	+	0.402749i
$425$	1.24476e11	+	2.15599e11i	0.185070	+	0.320551i
$426$	−2.05062e10	+	3.55178e10i	−0.0301677	+	0.0522520i
$427$	3.54583e10	+	2.01094e11i	0.0516170	+	0.292734i
$428$	−6.88622e10	−	3.90537e11i	−0.0991937	−	0.562556i
$429$	1.38726e11	−	2.40281e11i	0.197743	−	0.342501i
$430$	3.00436e11	+	5.20371e11i	0.423784	+	0.734015i
$431$	−6.22105e11	+	5.22008e11i	−0.868393	+	0.728668i	−0.963759	−	0.266774i	$-0.914042\pi$
$431$	−6.22105e11	+	5.22008e11i	−0.868393	+	0.728668i	0.0953662	+	0.995442i	$0.469598\pi$
$432$	1.49507e11	−	5.44162e10i	0.206531	−	0.0751712i
$433$	2.95903e10	+	1.07700e10i	0.0404533	+	0.0147238i	0.362168	−	0.932113i	$-0.382037\pi$
$433$	2.95903e10	+	1.07700e10i	0.0404533	+	0.0147238i	−0.321714	+	0.946837i	$0.604259\pi$
$434$	−1.69016e10	−	1.41821e10i	−0.0228678	−	0.0191883i
$435$	−3.51091e11	+	1.99113e12i	−0.470130	+	2.66624i
$436$	−1.49840e11			−0.198581
$437$	−4.23433e11	−	9.43578e10i	−0.555416	−	0.123769i
$438$	1.04907e12			1.36198
$439$	−1.59023e11	+	9.01865e11i	−0.204348	+	1.15891i	0.694115	+	0.719864i	$0.255796\pi$
$439$	−1.59023e11	+	9.01865e11i	−0.204348	+	1.15891i	−0.898463	+	0.439050i	$0.855315\pi$
$440$	2.69727e11	+	2.26328e11i	0.343074	+	0.287873i
$441$	8.94892e10	+	3.25714e10i	0.112667	+	0.0410075i
$442$	−7.92164e10	+	2.88324e10i	−0.0987222	+	0.0359319i
$443$	1.68458e11	−	1.41353e11i	0.207815	−	0.174377i	−0.532940	−	0.846153i	$-0.678913\pi$
$443$	1.68458e11	−	1.41353e11i	0.207815	−	0.174377i	0.740754	+	0.671776i	$0.234468\pi$
$444$	−1.06025e10	−	1.83641e10i	−0.0129475	−	0.0224257i
$445$	−1.57416e11	+	2.72653e11i	−0.190296	+	0.329603i
$446$	9.84753e10	+	5.58481e11i	0.117848	+	0.668347i
$447$	−4.81102e10	−	2.72847e11i	−0.0569972	−	0.323247i
$448$	−3.32278e10	+	5.75523e10i	−0.0389718	+	0.0675012i
$449$	−6.64556e11	−	1.15104e12i	−0.771655	−	1.33655i	−0.936656	−	0.350252i	$-0.886096\pi$
$449$	−6.64556e11	−	1.15104e12i	−0.771655	−	1.33655i	0.165001	−	0.986293i	$-0.447237\pi$
$450$	−9.31448e10	+	7.81577e10i	−0.107078	+	0.0898495i
$451$	−2.99701e11	+	1.09082e11i	−0.341110	+	0.124154i
$452$	−4.28930e10	−	1.56118e10i	−0.0483352	−	0.0175926i
$453$	7.10853e11	+	5.96477e11i	0.793118	+	0.665505i
$454$	−1.58169e11	+	8.97022e11i	−0.174731	+	0.990950i
$455$	3.26718e11			0.357373
$456$	−3.16861e11	+	1.64508e11i	−0.343184	+	0.178175i
$457$	−1.40230e12			−1.50390			−0.751950	−	0.659221i	$-0.770886\pi$
$457$	−1.40230e12			−1.50390			−0.751950	+	0.659221i	$0.770886\pi$
$458$	−3.66592e10	+	2.07905e11i	−0.0389303	+	0.220785i
$459$	2.35240e11	+	1.97390e11i	0.247374	+	0.207572i
$460$	3.63795e11	+	1.32410e11i	0.378831	+	0.137883i
$461$	−4.51797e11	+	1.64441e11i	−0.465896	+	0.169572i	−0.564293	−	0.825575i	$-0.690851\pi$
$461$	−4.51797e11	+	1.64441e11i	−0.465896	+	0.169572i	0.0983961	+	0.995147i	$0.468629\pi$
$462$	3.23390e11	−	2.71356e11i	0.330246	−	0.277109i
$463$	2.45909e11	+	4.25926e11i	0.248691	+	0.430745i	0.963163	−	0.268919i	$-0.0866664\pi$
$463$	2.45909e11	+	4.25926e11i	0.248691	+	0.430745i	−0.714472	+	0.699664i	$0.753333\pi$
$464$	2.18044e11	−	3.77663e11i	0.218380	−	0.378245i
$465$	1.83682e10	+	1.04171e11i	0.0182192	+	0.103326i
$466$	−1.28817e11	−	7.30559e11i	−0.126543	−	0.717659i
$467$	8.88321e11	−	1.53862e12i	0.864259	−	1.49694i	−0.00352188	−	0.999994i	$-0.501121\pi$
$467$	8.88321e11	−	1.53862e12i	0.864259	−	1.49694i	0.867781	−	0.496947i	$-0.165546\pi$
$468$	−2.05867e10	−	3.56572e10i	−0.0198372	−	0.0343591i
$469$	9.47168e11	−	7.94768e11i	0.903960	−	0.758512i
$470$	−7.21274e11	+	2.62522e11i	−0.681805	+	0.248157i
$471$	2.13694e12	+	7.77783e11i	2.00078	+	0.728223i
$472$	−1.10801e11	−	9.29729e10i	−0.102755	−	0.0862219i
$473$	−1.42961e11	+	8.10773e11i	−0.131324	+	0.744773i
$474$	1.09463e12			0.996014
$475$	−7.56218e11	+	8.23461e11i	−0.681594	+	0.742202i
$476$	−1.28266e11			−0.114520
$477$	6.82577e10	−	3.87109e11i	0.0603697	−	0.342374i
$478$	−6.12253e11	−	5.13742e11i	−0.536421	−	0.450110i
$479$	6.80952e11	+	2.47846e11i	0.591026	+	0.215116i	0.620181	−	0.784459i	$-0.287059\pi$
$479$	6.80952e11	+	2.47846e11i	0.591026	+	0.215116i	−0.0291545	+	0.999575i	$0.509281\pi$
$480$	2.99393e11	−	1.08970e11i	0.257428	−	0.0936961i
$481$	1.72250e10	−	1.44535e10i	0.0146726	−	0.0123118i
$482$	−4.34406e11	−	7.52414e11i	−0.366593	−	0.634958i
$483$	2.32082e11	−	4.01978e11i	0.194035	−	0.336078i
$484$	−2.10466e10	−	1.19361e11i	−0.0174332	−	0.0988686i
$485$	−4.95842e11	−	2.81206e12i	−0.406917	−	2.30774i
$486$	−1.68286e11	+	2.91480e11i	−0.136831	+	0.236998i
$487$	−9.31386e11	−	1.61321e12i	−0.750325	−	1.29960i	−0.947665	−	0.319266i	$-0.896564\pi$
$487$	−9.31386e11	−	1.61321e12i	−0.750325	−	1.29960i	0.197340	−	0.980335i	$-0.436770\pi$
$488$	−1.61752e11	+	1.35726e11i	−0.129110	+	0.108336i
$489$	1.98270e11	−	7.21645e10i	0.156808	−	0.0570734i
$490$	−7.34302e11	−	2.67264e11i	−0.575430	−	0.209439i
$491$	6.83165e11	+	5.73244e11i	0.530468	+	0.445115i	0.868263	−	0.496104i	$-0.165237\pi$
$491$	6.83165e11	+	5.73244e11i	0.530468	+	0.445115i	−0.337795	+	0.941220i	$0.609681\pi$
$492$	−5.01138e10	+	2.84210e11i	−0.0385580	+	0.218673i
$493$	8.41694e11			0.641716
$494$	−2.30138e11	−	3.00600e11i	−0.173867	−	0.227100i
$495$	−3.31925e11			−0.248494
$496$	3.96179e9	−	2.24685e10i	0.00293917	−	0.0166689i
$497$	−5.06896e10	−	4.25336e10i	−0.0372662	−	0.0312701i
$498$	3.83654e11	+	1.39639e11i	0.279517	+	0.101736i
$499$	1.17072e11	−	4.26106e10i	0.0845277	−	0.0307656i	−0.299410	−	0.954124i	$-0.596790\pi$
$499$	1.17072e11	−	4.26106e10i	0.0845277	−	0.0307656i	0.383938	+	0.923359i	$0.374568\pi$
$500$	5.83052e9	−	4.89238e9i	0.00417198	−	0.00350070i
$501$	−1.19587e12	−	2.07131e12i	−0.848036	−	1.46884i
$502$	2.30681e11	−	3.99551e11i	0.162123	−	0.280805i
$503$	−6.35847e9	−	3.60607e10i	−0.00442891	−	0.0251176i	0.982513	−	0.186193i	$-0.0596149\pi$
$503$	−6.35847e9	−	3.60607e10i	−0.00442891	−	0.0251176i	−0.986942	+	0.161075i	$0.948504\pi$
$504$	−1.08785e10	−	6.16953e10i	−0.00750989	−	0.0425907i
$505$	1.06513e11	−	1.84486e11i	0.0728772	−	0.126227i
$506$	2.65220e11	+	4.59374e11i	0.179857	+	0.311522i
$507$	−1.04255e12	+	8.74802e11i	−0.700746	+	0.587995i
$508$	1.19698e12	−	4.35664e11i	0.797443	−	0.290245i
$509$	1.58263e12	+	5.76030e11i	1.04508	+	0.380378i	0.806804	−	0.590820i	$-0.201196\pi$
$509$	1.58263e12	+	5.76030e11i	1.04508	+	0.380378i	0.238276	+	0.971198i	$0.423418\pi$
$510$	4.71075e11	+	3.95279e11i	0.308336	+	0.258725i
$511$	−2.93917e11	+	1.66689e12i	−0.190691	+	1.08146i
$512$	−6.87195e10			−0.0441942
$513$	−5.29139e11	+	1.27352e12i	−0.337320	+	0.811855i
$514$	−6.33537e11			−0.400348
$515$	1.55716e11	−	8.83107e11i	0.0975438	−	0.553198i
$516$	5.70671e11	+	4.78850e11i	0.354374	+	0.297355i
$517$	−9.88247e11	−	3.59693e11i	−0.608356	−	0.221424i
$518$	3.21495e10	−	1.17015e10i	0.0196196	−	0.00714096i
$519$	2.16730e12	−	1.81858e12i	1.31119	−	1.10022i
$520$	1.68924e11	+	2.92585e11i	0.101316	+	0.175484i
$521$	−1.16401e12	+	2.01612e12i	−0.692127	+	1.19880i	0.279012	+	0.960287i	$0.409993\pi$
$521$	−1.16401e12	+	2.01612e12i	−0.692127	+	1.19880i	−0.971140	+	0.238512i	$0.923340\pi$
$522$	7.13859e10	+	4.04850e11i	0.0420819	+	0.238658i
$523$	−4.20848e11	−	2.38675e12i	−0.245962	−	1.39492i	−0.818248	−	0.574865i	$-0.805055\pi$
$523$	−4.20848e11	−	2.38675e12i	−0.245962	−	1.39492i	0.572286	−	0.820054i	$-0.306057\pi$
$524$	−2.11876e11	+	3.66979e11i	−0.122769	+	0.212643i
$525$	−5.98109e11	−	1.03595e12i	−0.343608	−	0.595147i
$526$	3.24620e11	−	2.72389e11i	0.184901	−	0.155151i
$527$	4.13798e10	−	1.50610e10i	0.0233690	−	0.00850563i
$528$	4.10210e11	+	1.49304e11i	0.229696	+	0.0836026i
$529$	−9.32988e11	−	7.82870e11i	−0.517995	−	0.434649i
$530$	−5.60088e11	+	3.17642e12i	−0.308329	+	1.74862i
$531$	1.36351e11			0.0744273
$532$	−1.72615e11	−	5.49556e11i	−0.0934279	−	0.297447i
$533$	−3.06022e11			−0.164241
$534$	−6.77797e10	+	3.84398e11i	−0.0360715	+	0.204572i
$535$	−2.34984e12	−	1.97175e12i	−1.24007	−	1.04054i
$536$	1.20145e12	+	4.37293e11i	0.628731	+	0.228840i
$537$	2.95071e12	−	1.07397e12i	1.53123	−	0.557324i
$538$	1.18342e12	−	9.93005e11i	0.609000	−	0.511012i
$539$	−5.35333e11	−	9.27225e11i	−0.273196	−	0.473190i
$540$	6.15347e11	−	1.06581e12i	0.311421	−	0.539397i
$541$	2.90876e11	+	1.64964e12i	0.145989	+	0.827945i	0.966568	+	0.256412i	$0.0825403\pi$
$541$	2.90876e11	+	1.64964e12i	0.145989	+	0.827945i	−0.820579	+	0.571534i	$0.806349\pi$
$542$	2.93759e11	+	1.66599e12i	0.146216	+	0.829232i
$543$	9.52471e11	−	1.64973e12i	0.470167	−	0.814354i
$544$	−6.63179e10	−	1.14866e11i	−0.0324665	−	0.0562337i
$545$	−8.87881e11	+	7.45021e11i	−0.431093	+	0.361730i
$546$	3.80635e11	−	1.38540e11i	0.183291	−	0.0667125i
$547$	−2.81293e12	−	1.02382e12i	−1.34343	−	0.488970i	−0.432541	−	0.901614i	$-0.642383\pi$
$547$	−2.81293e12	−	1.02382e12i	−1.34343	−	0.488970i	−0.910892	+	0.412644i	$0.864605\pi$
$548$	1.39448e11	+	1.17010e11i	0.0660539	+	0.0554258i
$549$	3.45649e10	−	1.96027e11i	0.0162390	−	0.0920959i
$550$	1.36702e12			0.637004
$551$	1.13271e12	+	3.60623e12i	0.523526	+	1.66675i
$552$	4.79976e11			0.220036
$553$	−3.06682e11	+	1.73928e12i	−0.139452	+	0.790871i
$554$	−9.47107e11	−	7.94717e11i	−0.427174	−	0.358442i
$555$	−1.54134e11	−	5.61002e10i	−0.0689573	−	0.0250984i
$556$	7.38771e10	−	2.68891e10i	0.0327849	−	0.0119327i
$557$	1.26552e12	−	1.06190e12i	0.557084	−	0.467449i	−0.320247	−	0.947334i	$-0.603766\pi$
$557$	1.26552e12	−	1.06190e12i	0.557084	−	0.467449i	0.877331	+	0.479885i	$0.159322\pi$
$558$	1.07538e10	+	1.86261e10i	0.00469577	+	0.00813331i
$559$	−3.94973e11	+	6.84114e11i	−0.171086	+	0.296330i
$560$	8.92637e10	+	5.06240e11i	0.0383556	+	0.217525i
$561$	1.46309e11	+	8.29761e11i	0.0623647	+	0.353688i
$562$	6.80672e11	−	1.17896e12i	0.287822	−	0.498523i
$563$	1.80915e12	+	3.13353e12i	0.758903	+	1.31446i	0.943411	+	0.331627i	$0.107597\pi$
$563$	1.80915e12	+	3.13353e12i	0.758903	+	1.31446i	−0.184508	+	0.982831i	$0.559069\pi$
$564$	−7.28984e11	+	6.11690e11i	−0.303363	+	0.254551i
$565$	−3.31787e11	+	1.20761e11i	−0.136975	+	0.0498549i
$566$	1.17322e12	+	4.27018e11i	0.480515	+	0.174893i
$567$	−1.36094e12	−	1.14197e12i	−0.552989	−	0.464013i
$568$	1.18818e10	−	6.73852e10i	0.00478978	−	0.0271642i
$569$	2.58483e12			1.03378			0.516888	−	0.856053i	$-0.327090\pi$
$569$	2.58483e12			1.03378			0.516888	+	0.856053i	$0.327090\pi$
$570$	−1.05962e12	+	2.55027e12i	−0.420448	+	1.01193i
$571$	−3.57888e12			−1.40892			−0.704458	−	0.709746i	$-0.748810\pi$
$571$	−3.57888e12			−1.40892			−0.704458	+	0.709746i	$0.748810\pi$
$572$	−8.03816e10	+	4.55867e11i	−0.0313960	+	0.178056i
$573$	−2.41054e12	−	2.02269e12i	−0.934156	−	0.783850i
$574$	−4.37545e11	−	1.59253e11i	−0.168236	−	0.0612329i
$575$	1.41240e12	−	5.14073e11i	0.538832	−	0.196119i
$576$	4.96252e10	−	4.16405e10i	0.0187846	−	0.0157621i
$577$	−5.74912e11	−	9.95777e11i	−0.215929	−	0.374000i	0.737631	−	0.675204i	$-0.235945\pi$
$577$	−5.74912e11	−	9.95777e11i	−0.215929	−	0.374000i	−0.953559	+	0.301205i	$0.902611\pi$
$578$	−8.20703e11	+	1.42150e12i	−0.305851	+	0.529750i
$579$	6.88792e11	+	3.90634e12i	0.254703	+	1.44449i
$580$	−5.85756e11	−	3.32199e12i	−0.214927	−	1.21891i
$581$	−3.29362e11	+	5.70472e11i	−0.119917	+	0.207703i
$582$	−1.77008e12	−	3.06587e12i	−0.639498	−	1.10764i
$583$	−3.38536e12	+	2.84066e12i	−1.21366	+	1.01838i
$584$	−1.64471e12	+	5.98625e11i	−0.585101	+	0.212959i
$585$	−2.99279e11	−	1.08929e11i	−0.105651	−	0.0384539i
$586$	−9.64833e11	−	8.09591e11i	−0.337997	−	0.283613i
$587$	6.61721e9	−	3.75280e10i	0.00230040	−	0.0130462i	−0.983636	−	0.180167i	$-0.942336\pi$
$587$	6.61721e9	−	3.75280e10i	0.00230040	−	0.0130462i	0.985936	+	0.167121i	$0.0534471\pi$
$588$	−9.68810e11			−0.334226
$589$	1.20216e11	+	1.57023e11i	0.0411569	+	0.0537581i
$590$	−1.11882e12			−0.380126
$591$	−1.09826e12	+	6.22852e12i	−0.370305	+	2.10011i
$592$	2.71014e10	+	2.27407e10i	0.00906867	+	0.00760951i
$593$	3.76087e12	+	1.36884e12i	1.24894	+	0.454577i	0.880044	−	0.474893i	$-0.157513\pi$
$593$	3.76087e12	+	1.36884e12i	1.24894	+	0.454577i	0.368898	+	0.929470i	$0.379735\pi$
$594$	1.58453e12	−	5.76722e11i	0.522230	−	0.190076i
$595$	−7.60046e11	+	6.37754e11i	−0.248607	+	0.208606i
$596$	2.31118e11	+	4.00309e11i	0.0750285	+	0.129953i
$597$	3.16151e12	−	5.47590e12i	1.01861	−	1.76429i
$598$	8.83804e10	+	5.01230e11i	0.0282618	+	0.160281i
$599$	−5.54134e11	−	3.14265e12i	−0.175871	−	0.997414i	−0.937134	−	0.348970i	$-0.886531\pi$
$599$	−5.54134e11	−	3.14265e12i	−0.175871	−	0.997414i	0.761263	−	0.648444i	$-0.224580\pi$
$600$	6.18484e11	−	1.07125e12i	0.194826	−	0.337449i
$601$	1.32168e12	+	2.28922e12i	0.413229	+	0.715734i	0.995241	−	0.0974463i	$-0.0310674\pi$
$601$	1.32168e12	+	2.28922e12i	0.413229	+	0.715734i	−0.582011	+	0.813181i	$0.697734\pi$
$602$	−9.20736e11	+	7.72590e11i	−0.285727	+	0.239753i
$603$	−1.13260e12	+	4.12232e11i	−0.348857	+	0.126974i
$604$	−1.45482e12	−	5.29511e11i	−0.444778	−	0.161886i
$605$	−7.18188e11	−	6.02631e11i	−0.217941	−	0.182874i
$606$	4.58619e10	−	2.60096e11i	0.0138142	−	0.0783442i
$607$	4.50126e12			1.34581			0.672907	−	0.739727i	$-0.265045\pi$
$607$	4.50126e12			1.34581			0.672907	+	0.739727i	$0.265045\pi$
$608$	4.02894e11	−	4.38720e11i	0.119571	−	0.130203i
$609$	−4.04434e12			−1.19143
$610$	−2.83621e11	+	1.60850e12i	−0.0829382	+	0.470366i
$611$	−7.73008e11	−	6.48630e11i	−0.224387	−	0.188283i
$612$	1.17494e11	+	4.27643e10i	0.0338559	+	0.0123225i
$613$	2.37694e11	−	8.65136e10i	0.0679902	−	0.0247464i	−0.307801	−	0.951451i	$-0.599593\pi$
$613$	2.37694e11	−	8.65136e10i	0.0679902	−	0.0247464i	0.375791	+	0.926704i	$0.377371\pi$
$614$	−4.57627e11	+	3.83994e11i	−0.129943	+	0.109035i
$615$	1.11617e12	+	1.93326e12i	0.314624	+	0.544945i
$616$	−3.52160e11	+	6.09959e11i	−0.0985432	+	0.170682i
$617$	8.50397e11	+	4.82284e12i	0.236232	+	1.33974i	0.840004	+	0.542580i	$0.182553\pi$
$617$	8.50397e11	+	4.82284e12i	0.236232	+	1.33974i	−0.603772	+	0.797157i	$0.706336\pi$
$618$	−1.93055e11	−	1.09487e12i	−0.0532395	−	0.301936i
$619$	2.90881e12	−	5.03820e12i	0.796356	−	1.37933i	−0.125619	−	0.992079i	$-0.540092\pi$
$619$	2.90881e12	−	5.03820e12i	0.796356	−	1.37933i	0.921975	−	0.387250i	$-0.126575\pi$
$620$	−8.82399e10	−	1.52836e11i	−0.0239829	−	0.0415397i
$621$	1.42026e12	−	1.19174e12i	0.383227	−	0.321566i
$622$	3.85800e12	−	1.40420e12i	1.03349	−	0.376159i
$623$	−5.91786e11	−	2.15393e11i	−0.157387	−	0.0572841i
$624$	3.20867e11	+	2.69239e11i	0.0847216	+	0.0710898i
$625$	−6.57284e11	+	3.72764e12i	−0.172303	+	0.977179i
$626$	−2.58333e12			−0.672350
$627$	−3.35820e12	+	1.74352e12i	−0.867767	+	0.450528i
$628$	−3.79406e12			−0.973388
$629$	−1.18574e10	+	6.72465e10i	−0.00302037	+	0.0171294i
$630$	−3.71217e11	−	3.11488e11i	−0.0938848	−	0.0787787i
$631$	3.25565e12	+	1.18496e12i	0.817533	+	0.297558i	0.716732	−	0.697349i	$-0.245637\pi$
$631$	3.25565e12	+	1.18496e12i	0.817533	+	0.297558i	0.100801	+	0.994907i	$0.467859\pi$
$632$	−1.71613e12	+	6.24622e11i	−0.427882	+	0.155736i
$633$	−4.13864e12	+	3.47273e12i	−1.02457	+	0.859714i
$634$	−1.64215e12	−	2.84428e12i	−0.403655	−	0.699151i
$635$	4.92656e12	−	8.53305e12i	1.20244	−	2.08268i
$636$	6.94393e11	+	3.93810e12i	0.168286	+	0.954399i
$637$	−1.78392e11	−	1.01171e12i	−0.0429286	−	0.243460i
$638$	2.31090e12	−	4.00260e12i	0.552190	−	0.956421i
$639$	3.22517e10	+	5.58615e10i	0.00765241	+	0.0132544i
$640$	−4.07199e11	+	3.41681e11i	−0.0959394	+	0.0805027i
$641$	3.37258e12	−	1.22752e12i	0.789043	−	0.287188i	0.0841049	−	0.996457i	$-0.473197\pi$
$641$	3.37258e12	−	1.22752e12i	0.789043	−	0.287188i	0.704938	+	0.709269i	$0.250975\pi$
$642$	−3.57371e12	−	1.30072e12i	−0.830255	−	0.302188i
$643$	−3.80664e12	−	3.19415e12i	−0.878198	−	0.736896i	0.0876096	−	0.996155i	$-0.472077\pi$
$643$	−3.80664e12	−	3.19415e12i	−0.878198	−	0.736896i	−0.965808	+	0.259259i	$0.916522\pi$
$644$	−1.34474e11	+	7.62642e11i	−0.0308073	+	0.174717i
$645$	5.76242e12			1.31095
$646$	1.12214e12	+	2.50058e11i	0.253514	+	0.0564930i
$647$	2.96000e12			0.664083			0.332042	−	0.943265i	$-0.392263\pi$
$647$	2.96000e12			0.664083			0.332042	+	0.943265i	$0.392263\pi$
$648$	3.19010e11	−	1.80920e12i	0.0710750	−	0.403086i
$649$	−1.17431e12	−	9.85359e11i	−0.259824	−	0.218019i
$650$	1.23257e12	+	4.48617e11i	0.270832	+	0.0985747i
$651$	−1.98830e11	+	7.23682e10i	−0.0433878	+	0.0157919i
$652$	−2.69664e11	+	2.26275e11i	−0.0584399	+	0.0490369i
$653$	−1.62227e12	−	2.80985e12i	−0.349151	−	0.604748i	0.636948	−	0.770907i	$-0.280197\pi$
$653$	−1.62227e12	−	2.80985e12i	−0.349151	−	0.604748i	−0.986099	+	0.166159i	$0.946863\pi$
$654$	−7.18489e11	+	1.24446e12i	−0.153575	+	0.266000i
$655$	5.69186e11	+	3.22801e12i	0.120828	+	0.685251i
$656$	−8.36094e10	−	4.74172e11i	−0.0176274	−	0.0999698i
$657$	8.24977e11	−	1.42890e12i	0.172742	−	0.299198i
$658$	−7.67686e11	−	1.32967e12i	−0.159649	−	0.276521i
$659$	1.04271e12	−	8.74934e11i	0.215366	−	0.180714i	−0.528722	−	0.848795i	$-0.677329\pi$
$659$	1.04271e12	−	8.74934e11i	0.215366	−	0.180714i	0.744088	+	0.668081i	$0.232884\pi$
$660$	3.17307e12	−	1.15490e12i	0.650926	−	0.236918i
$661$	1.95956e11	+	7.13223e10i	0.0399257	+	0.0145318i	0.361906	−	0.932215i	$-0.382126\pi$
$661$	1.95956e11	+	7.13223e10i	0.0399257	+	0.0145318i	−0.321980	+	0.946746i	$0.604348\pi$
$662$	−1.35966e12	−	1.14089e12i	−0.275150	−	0.230878i
$663$	−1.40385e11	+	7.96165e11i	−0.0282170	+	0.160027i
$664$	−6.81164e11			−0.135986
$665$	−3.75529e12	−	2.39815e12i	−0.744639	−	0.475530i
$666$	−3.33508e10			−0.00656859
$667$	8.82432e11	−	5.00452e12i	0.172629	−	0.979030i
$668$	3.05679e12	+	2.56495e12i	0.593980	+	0.498408i
$669$	5.11052e12	+	1.86008e12i	0.986388	+	0.359016i
$670$	9.29351e12	−	3.38256e12i	1.78174	−	0.648499i
$671$	−1.71430e12	+	1.43847e12i	−0.326465	+	0.273937i
$672$	3.18658e11	+	5.51931e11i	0.0602785	+	0.104405i
$673$	−2.72281e12	+	4.71605e12i	−0.511623	+	0.886156i	0.488287	+	0.872683i	$0.337622\pi$
$673$	−2.72281e12	+	4.71605e12i	−0.511623	+	0.886156i	−0.999909	+	0.0134730i	$0.995711\pi$
$674$	−4.68657e11	−	2.65789e12i	−0.0874753	−	0.496097i
$675$	−8.29703e11	−	4.70548e12i	−0.153835	−	0.872443i
$676$	1.13530e12	−	1.96639e12i	0.209098	−	0.362168i
$677$	−2.07982e12	−	3.60236e12i	−0.380520	−	0.659080i	0.610617	−	0.791926i	$-0.290922\pi$
$677$	−2.07982e12	−	3.60236e12i	−0.380520	−	0.659080i	−0.991137	+	0.132846i	$0.957588\pi$
$678$	−3.35334e11	+	2.81379e11i	−0.0609458	+	0.0511396i
$679$	5.36733e12	−	1.95355e12i	0.969045	−	0.352704i
$680$	−9.64095e11	−	3.50902e11i	−0.172914	−	0.0629355i
$681$	6.69157e12	+	5.61490e12i	1.19225	+	1.00041i
$682$	4.19885e10	−	2.38129e11i	0.00743191	−	0.0421485i
$683$	4.13847e12			0.727690			0.363845	−	0.931460i	$-0.381464\pi$
$683$	4.13847e12			0.727690			0.363845	+	0.931460i	$0.381464\pi$
$684$	−2.51050e10	+	5.60952e11i	−0.00438539	+	0.0979880i
$685$	1.40809e12			0.244356
$686$	7.15534e11	−	4.05799e12i	0.123359	−	0.699605i
$687$	1.55092e12	+	1.30138e12i	0.265634	+	0.222893i
$688$	−1.16793e12	−	4.25090e11i	−0.198732	−	0.0723324i
$689$	−3.98462e12	+	1.45028e12i	−0.673598	+	0.245169i
$690$	2.84411e12	−	2.38649e12i	0.477668	−	0.400811i
$691$	8.16394e11	+	1.41404e12i	0.136222	+	0.235944i	0.926064	−	0.377367i	$-0.123170\pi$
$691$	8.16394e11	+	1.41404e12i	0.136222	+	0.235944i	−0.789841	+	0.613311i	$0.789837\pi$
$692$	−2.36012e12	+	4.08784e12i	−0.391251	+	0.677667i
$693$	−1.15295e11	−	6.53868e11i	−0.0189893	−	0.107694i
$694$	7.90576e11	+	4.48358e12i	0.129368	+	0.733681i
$695$	3.04066e11	−	5.26657e11i	0.0494351	−	0.0856242i
$696$	−2.09106e12	−	3.62182e12i	−0.337773	−	0.585039i
$697$	7.11901e11	−	5.97356e11i	0.114254	−	0.0958707i
$698$	−4.09496e12	+	1.49044e12i	−0.652980	+	0.237665i
$699$	−6.68516e12	−	2.43320e12i	−1.05917	−	0.385505i
$700$	1.52884e12	+	1.28285e12i	0.240669	+	0.201945i
$701$	−1.23622e12	+	7.01094e12i	−0.193359	+	1.09659i	0.721378	+	0.692542i	$0.243509\pi$
$701$	−1.23622e12	+	7.01094e12i	−0.193359	+	1.09659i	−0.914736	+	0.404051i	$0.867602\pi$
$702$	1.61795e12			0.251448
$703$	−3.04074e11	+	3.96946e10i	−0.0469548	+	0.00612960i
$704$	−7.28313e11			−0.111748
$705$	−1.27823e12	+	7.24917e12i	−0.194875	+	1.10519i
$706$	4.79985e12	+	4.02756e12i	0.727121	+	0.610127i
$707$	4.00421e11	+	1.45741e11i	0.0602740	+	0.0219379i
$708$	−1.30346e12	+	4.74420e11i	−0.194961	+	0.0709600i
$709$	−7.15596e12	+	6.00456e12i	−1.06355	+	0.892428i	−0.994453	−	0.105182i	$-0.966458\pi$
$709$	−7.15596e12	+	6.00456e12i	−1.06355	+	0.892428i	−0.0691013	+	0.997610i	$0.522013\pi$
$710$	−2.64640e11	−	4.58371e11i	−0.0390835	−	0.0676946i
$711$	8.60804e11	−	1.49096e12i	0.126326	−	0.218802i
$712$	−1.13083e11	−	6.41325e11i	−0.0164906	−	0.0935230i
$713$	−4.61668e10	−	2.61825e11i	−0.00669001	−	0.0379409i
$714$	−6.15043e11	+	1.06529e12i	−0.0885652	+	0.153399i
$715$	1.79032e12	+	3.10092e12i	0.256184	+	0.443724i
$716$	−4.01321e12	+	3.36748e12i	−0.570667	+	0.478847i
$717$	−7.20254e12	+	2.62151e12i	−1.01777	+	0.370438i
$718$	7.41506e12	+	2.69886e12i	1.04125	+	0.378984i
$719$	−9.79947e12	−	8.22273e12i	−1.36748	−	1.14746i	−0.973591	−	0.228300i	$-0.926683\pi$
$719$	−9.79947e12	−	8.22273e12i	−1.36748	−	1.14746i	−0.393894	−	0.919156i	$-0.628872\pi$
$720$	8.70146e10	−	4.93484e11i	0.0120669	−	0.0684348i
$721$	1.79375e12			0.247202
$722$	4.38759e11	+	5.14433e12i	0.0600909	+	0.704549i
$723$	−8.33199e12			−1.13403
$724$	−5.51886e11	+	3.12990e12i	−0.0746493	+	0.423357i
$725$	−1.00324e13	−	8.41815e12i	−1.34860	−	1.13161i
$726$	−1.09224e12	−	3.97544e11i	−0.145917	−	0.0531093i
$727$	3.79837e12	−	1.38249e12i	0.504304	−	0.183552i	−0.0773250	−	0.997006i	$-0.524638\pi$
$727$	3.79837e12	−	1.38249e12i	0.504304	−	0.183552i	0.581629	+	0.813454i	$0.302416\pi$
$728$	−5.17695e11	+	4.34398e11i	−0.0683098	+	0.0573187i
$729$	−2.80016e12	−	4.85002e12i	−0.367205	−	0.636018i
$730$	−6.76934e12	+	1.17248e13i	−0.882253	+	1.52811i
$731$	−4.16563e11	−	2.36245e12i	−0.0539576	−	0.306009i
$732$	3.51632e11	+	1.99420e12i	0.0452677	+	0.256726i
$733$	−9.89437e11	+	1.71376e12i	−0.126596	+	0.219271i	−0.922356	−	0.386342i	$-0.873739\pi$
$733$	−9.89437e11	+	1.71376e12i	−0.126596	+	0.219271i	0.795760	+	0.605613i	$0.207072\pi$
$734$	−2.77276e12	−	4.80256e12i	−0.352598	−	0.610717i
$735$	−5.74071e12	+	4.81703e12i	−0.725559	+	0.608816i
$736$	−7.52494e11	+	2.73885e11i	−0.0945264	+	0.0344048i
$737$	1.27334e13	+	4.63458e12i	1.58980	+	0.578638i
$738$	3.47702e11	+	2.91757e11i	0.0431473	+	0.0362049i
$739$	5.24971e11	−	2.97726e12i	0.0647494	−	0.367212i	−0.935166	−	0.354210i	$-0.884750\pi$
$739$	5.24971e11	−	2.97726e12i	0.0647494	−	0.367212i	0.999915	−	0.0130024i	$-0.00413892\pi$
$740$	2.73659e11			0.0335481
$741$	−3.60008e12	+	4.69964e11i	−0.438663	+	0.0572641i
$742$	−6.45186e12			−0.781389
$743$	1.77877e12	−	1.00879e13i	0.214126	−	1.21437i	−0.668289	−	0.743901i	$-0.732973\pi$
$743$	1.77877e12	−	1.00879e13i	0.214126	−	1.21437i	0.882416	−	0.470470i	$-0.155916\pi$
$744$	−1.67609e11	−	1.40641e11i	−0.0200549	−	0.0168280i
$745$	3.35988e12	+	1.22290e12i	0.399595	+	0.145441i
$746$	6.49111e12	−	2.36257e12i	0.767351	−	0.279293i
$747$	4.91898e11	−	4.12751e11i	0.0578005	−	0.0485004i
$748$	−7.02860e11	−	1.21739e12i	−0.0820941	−	0.142191i
$749$	3.06798e12	−	5.31390e12i	0.356192	−	0.616943i
$750$	−1.26749e10	−	7.18831e10i	−0.00146275	−	0.00829567i
$751$	−3.41559e11	−	1.93708e12i	−0.0391819	−	0.222212i	0.958929	−	0.283645i	$-0.0915438\pi$
$751$	−3.41559e11	−	1.93708e12i	−0.0391819	−	0.222212i	−0.998111	+	0.0614337i	$0.980433\pi$
$752$	7.93837e11	−	1.37497e12i	0.0905214	−	0.156788i
$753$	−2.21225e12	−	3.83173e12i	−0.250759	−	0.434327i
$754$	3.39716e12	−	2.85055e12i	0.382776	−	0.321187i
$755$	−1.12534e13	+	4.09589e12i	−1.26044	+	0.458761i
$756$	2.31331e12	+	8.41977e11i	0.257565	+	0.0937459i
$757$	8.06629e12	+	6.76842e12i	0.892776	+	0.749128i	0.968765	−	0.247981i	$-0.0797669\pi$
$757$	8.06629e12	+	6.76842e12i	0.892776	+	0.749128i	−0.0759889	+	0.997109i	$0.524211\pi$
$758$	−1.59542e12	+	9.04808e12i	−0.175535	+	0.995509i
$759$	5.08696e12			0.556378
$760$	2.05999e11	−	4.60288e12i	0.0223977	−	0.500459i
$761$	1.20684e13			1.30442			0.652211	−	0.758038i	$-0.273842\pi$
$761$	1.20684e13			1.30442			0.652211	+	0.758038i	$0.273842\pi$
$762$	2.12126e12	−	1.20302e13i	0.227927	−	1.29264i
$763$	−1.77604e12	−	1.49028e12i	−0.189711	−	0.159187i
$764$	4.93338e12	+	1.79560e12i	0.523871	+	0.190673i
$765$	9.08842e11	−	3.30791e11i	0.0959427	−	0.0349203i
$766$	−4.14777e12	+	3.48040e12i	−0.435297	+	0.365258i
$767$	−7.35440e11	−	1.27382e12i	−0.0767305	−	0.132901i
$768$	−3.29513e11	+	5.70733e11i	−0.0341780	+	0.0591981i
$769$	5.85257e11	+	3.31916e12i	0.0603501	+	0.342263i	1.00000		0.000125025i	$3.97965e-5\pi$
$769$	5.85257e11	+	3.31916e12i	0.0603501	+	0.342263i	−0.939650	+	0.342138i	$0.888849\pi$
$770$	9.46048e11	+	5.36531e12i	0.0969851	+	0.550030i
$771$	−3.03784e12	+	5.26169e12i	−0.309614	+	0.536266i
$772$	−3.30891e12	−	5.73121e12i	−0.335280	−	0.580722i
$773$	6.55769e12	−	5.50256e12i	0.660607	−	0.554315i	−0.249662	−	0.968333i	$-0.580319\pi$
$773$	6.55769e12	−	5.50256e12i	0.660607	−	0.554315i	0.910269	+	0.414018i	$0.135875\pi$
$774$	1.10099e12	−	4.00728e11i	0.110268	−	0.0401343i
$775$	−6.43848e11	−	2.34342e11i	−0.0641100	−	0.0233341i
$776$	4.52454e12	+	3.79654e12i	0.447916	+	0.375846i
$777$	5.69747e10	−	3.23119e11i	0.00560773	−	0.0318030i
$778$	−7.21308e10			−0.00705850
$779$	3.51741e12	+	2.24624e12i	0.342219	+	0.218543i
$780$	3.23999e12			0.313414
$781$	1.25928e11	−	7.14172e11i	0.0121113	−	0.0686868i
$782$	−1.18400e12	−	9.93495e11i	−0.113220	−	0.0950026i
$783$	−1.51802e13	−	5.52512e12i	−1.44327	−	0.525308i
$784$	1.51887e12	−	5.52825e11i	0.143582	−	0.0522595i
$785$	−2.24818e13	+	1.88645e13i	−2.11309	+	1.77309i
$786$	2.03190e12	+	3.51936e12i	0.189890	+	0.328899i
$787$	2.32966e12	−	4.03508e12i	0.216474	−	0.374944i	−0.737254	−	0.675616i	$-0.763878\pi$
$787$	2.32966e12	−	4.03508e12i	0.216474	−	0.374944i	0.953728	+	0.300672i	$0.0972110\pi$
$788$	−1.83232e12	−	1.03916e13i	−0.169291	−	0.960095i
$789$	−7.05691e11	−	4.00217e12i	−0.0648288	−	0.367663i
$790$	−7.06332e12	+	1.22340e13i	−0.645189	+	1.11750i
$791$	−3.53137e11	−	6.11651e11i	−0.0320737	−	0.0555532i
$792$	5.25946e11	−	4.41321e11i	0.0474982	−	0.0398558i
$793$	−2.01776e12	+	7.34405e11i	−0.181193	+	0.0659487i
$794$	5.00972e12	+	1.82339e12i	0.447323	+	0.162812i
$795$	2.36953e13	+	1.98827e13i	2.10383	+	1.76532i
$796$	−1.83186e12	+	1.03890e13i	−0.161727	+	0.917201i
$797$	−5.53353e12			−0.485780			−0.242890	−	0.970054i	$-0.578095\pi$
$797$	−5.53353e12			−0.485780			−0.242890	+	0.970054i	$0.578095\pi$
$798$	−5.39190e12	−	1.20153e12i	−0.470683	−	0.104887i
$799$	3.06438e12			0.266000
$800$	−3.58365e11	+	2.03239e12i	−0.0309329	+	0.175429i
$801$	4.70273e11	+	3.94606e11i	0.0403649	+	0.0338701i
$802$	8.70281e12	+	3.16756e12i	0.742805	+	0.270359i
$803$	−1.74312e13	+	6.34444e12i	−1.47947	+	0.538484i
$804$	9.39285e12	−	7.88154e12i	0.792766	−	0.665210i
$805$	2.99511e12	+	5.18768e12i	0.251380	+	0.435403i
$806$	1.16006e11	−	2.00928e11i	0.00968216	−	0.0167700i
$807$	−2.57263e12	−	1.45901e13i	−0.213523	−	1.21095i
$808$	7.65156e10	+	4.33941e11i	0.00631537	+	0.0358162i
$809$	2.48005e12	−	4.29558e12i	0.203560	−	0.352576i	−0.746113	−	0.665819i	$-0.768082\pi$
$809$	2.48005e12	−	4.29558e12i	0.203560	−	0.352576i	0.949673	+	0.313243i	$0.101415\pi$
$810$	−7.10522e12	−	1.23066e13i	−0.579956	−	1.00451i
$811$	−4.28403e11	+	3.59473e11i	−0.0347743	+	0.0291791i	−0.660009	−	0.751258i	$-0.729448\pi$
$811$	−4.28403e11	+	3.59473e11i	−0.0347743	+	0.0291791i	0.625235	+	0.780437i	$0.285003\pi$
$812$	6.34061e12	−	2.30779e12i	0.511834	−	0.186292i
$813$	1.52451e13	+	5.54876e12i	1.22383	+	0.445439i
$814$	2.87230e11	+	2.41014e11i	0.0229308	+	0.0192412i
$815$	−4.72838e11	+	2.68160e12i	−0.0375408	+	0.212904i
$816$	−1.27199e12			−0.100433
$817$	9.56128e12	−	4.96403e12i	0.750787	−	0.389794i
$818$	1.87903e12			0.146739
$819$	1.10626e11	−	6.27394e11i	0.00859175	−	0.0487262i
$820$	−2.85307e12	−	2.39401e12i	−0.220369	−	0.184911i
$821$	1.62920e13	+	5.92979e12i	1.25150	+	0.455507i	0.880907	−	0.473290i	$-0.156934\pi$
$821$	1.62920e13	+	5.92979e12i	1.25150	+	0.455507i	0.370589	+	0.928797i	$0.379156\pi$
$822$	1.64046e12	−	5.97078e11i	0.125326	−	0.0456150i
$823$	9.64643e12	−	8.09432e12i	0.732938	−	0.615008i	−0.197993	−	0.980204i	$-0.563442\pi$
$823$	9.64643e12	−	8.09432e12i	0.732938	−	0.615008i	0.930931	+	0.365195i	$0.118998\pi$
$824$	9.27425e11	+	1.60635e12i	0.0700820	+	0.121386i
$825$	6.55491e12	−	1.13534e13i	0.492633	−	0.853266i
$826$	−3.88625e11	−	2.20400e12i	−0.0290483	−	0.164741i
$827$	−2.55473e12	−	1.44886e13i	−0.189920	−	1.07709i	−0.919470	−	0.393161i	$-0.871381\pi$
$827$	−2.55473e12	−	1.44886e13i	−0.189920	−	1.07709i	0.729550	−	0.683928i	$-0.239730\pi$
$828$	3.77447e11	−	6.53758e11i	0.0279074	−	0.0483371i
$829$	−8.59729e12	−	1.48909e13i	−0.632217	−	1.09503i	−0.987098	−	0.160120i	$-0.948812\pi$
$829$	−8.59729e12	−	1.48909e13i	−0.632217	−	1.09503i	0.354881	−	0.934912i	$-0.384521\pi$
$830$	−4.03626e12	+	3.38682e12i	−0.295208	+	0.247709i
$831$	−1.11417e13	+	4.05526e12i	−0.810492	+	0.294995i
$832$	−6.56680e11	−	2.39012e11i	−0.0475115	−	0.0172928i
$833$	2.38985e12	+	2.00532e12i	0.171976	+	0.144305i
$834$	1.30923e11	−	7.42503e11i	0.00937065	−	0.0531436i
$835$	3.08663e13			2.19733
$836$	4.27001e12	−	4.64971e12i	0.302344	−	0.329228i
$837$	−8.45159e11			−0.0595215
$838$	1.76534e11	−	1.00118e12i	0.0123661	−	0.0701314i
$839$	−6.65693e12	−	5.58583e12i	−0.463815	−	0.389187i	0.380717	−	0.924691i	$-0.375677\pi$
$839$	−6.65693e12	−	5.58583e12i	−0.463815	−	0.389187i	−0.844532	+	0.535504i	$0.820122\pi$
$840$	4.63248e12	+	1.68608e12i	0.321038	+	0.116848i
$841$	−2.79753e13	+	1.01822e13i	−1.92838	+	0.701874i
$842$	3.81047e12	−	3.19736e12i	0.261260	−	0.219224i
$843$	−6.52771e12	−	1.13063e13i	−0.445181	−	0.771076i
$844$	4.50683e12	−	7.80605e12i	0.305724	−	0.529530i
$845$	−3.04988e12	−	1.72967e13i	−0.205792	−	1.16710i
$846$	2.59897e11	+	1.47395e12i	0.0174435	+	0.0989271i
$847$	9.37677e11	−	1.62410e12i	0.0626005	−	0.108427i
$848$	−3.33582e12	−	5.77781e12i	−0.221524	−	0.383691i
$849$	9.17216e12	−	7.69635e12i	0.605880	−	0.508394i
$850$	−3.74302e12	+	1.36235e12i	−0.245945	+	0.0895165i
$851$	3.87401e11	+	1.41002e11i	0.0253208	+	0.00921602i
$852$	−5.02678e11	−	4.21797e11i	−0.0326822	−	0.0274236i
$853$	4.46744e12	−	2.53361e13i	0.288927	−	1.63859i	−0.401983	−	0.915647i	$-0.631679\pi$
$853$	4.46744e12	−	2.53361e13i	0.288927	−	1.63859i	0.690910	−	0.722941i	$-0.257210\pi$
$854$	−3.26714e12			−0.210188
$855$	2.64035e12	+	3.44876e12i	0.168972	+	0.220707i
$856$	6.34499e12			0.403923
$857$	4.62802e12	−	2.62468e13i	0.293077	−	1.66212i	−0.381839	−	0.924229i	$-0.624709\pi$
$857$	4.62802e12	−	2.62468e13i	0.293077	−	1.66212i	0.674916	−	0.737894i	$-0.264180\pi$
$858$	3.40066e12	+	2.85349e12i	0.214225	+	0.179756i
$859$	−2.16864e13	−	7.89322e12i	−1.35900	−	0.494635i	−0.443254	−	0.896396i	$-0.646176\pi$
$859$	−2.16864e13	−	7.89322e12i	−1.35900	−	0.494635i	−0.915744	+	0.401761i	$0.868398\pi$
$860$	−9.03417e12	+	3.28817e12i	−0.563178	+	0.204980i
$861$	−3.42069e12	+	2.87030e12i	−0.212129	+	0.177997i
$862$	−6.49681e12	−	1.12528e13i	−0.400790	−	0.694189i
$863$	−2.78876e12	+	4.83027e12i	−0.171144	+	0.296431i	−0.938820	−	0.344408i	$-0.888080\pi$
$863$	−2.78876e12	+	4.83027e12i	−0.171144	+	0.296431i	0.767676	+	0.640838i	$0.221413\pi$
$864$	4.42045e11	+	2.50696e12i	0.0269870	+	0.153051i
$865$	6.34025e12	+	3.59574e13i	0.385065	+	2.18381i
$866$	−2.51915e11	+	4.36329e11i	−0.0152203	+	0.0263623i
$867$	7.87061e12	+	1.36323e13i	0.473067	+	0.819375i
$868$	2.70425e11	−	2.26914e11i	0.0161700	−	0.0135682i
$869$	−1.81882e13	+	6.61996e12i	−1.08193	+	0.393792i
$870$	−3.03987e13	−	1.10642e13i	−1.79895	−	0.654763i
$871$	9.96009e12	+	8.35751e12i	0.586383	+	0.492034i
$872$	4.16311e11	−	2.36102e12i	0.0243834	−	0.138285i
$873$	−5.56787e12			−0.324433
$874$	2.66324e12	−	6.40984e12i	0.154386	−	0.371574i
$875$	1.17767e11			0.00679186
$876$	−2.91471e12	+	1.65302e13i	−0.167235	+	0.948437i
$877$	6.58551e12	+	5.52590e12i	0.375917	+	0.315431i	0.811097	−	0.584912i	$-0.198871\pi$
$877$	6.58551e12	+	5.52590e12i	0.375917	+	0.315431i	−0.435180	+	0.900343i	$0.643315\pi$
$878$	−1.37688e13	−	5.01143e12i	−0.781935	−	0.284601i
$879$	−1.13503e13	+	4.13116e12i	−0.641293	+	0.233412i
$880$	−4.31564e12	+	3.62125e12i	−0.242590	+	0.203557i
$881$	1.45262e13	+	2.51601e13i	0.812382	+	1.40709i	0.911192	+	0.411981i	$0.135163\pi$
$881$	1.45262e13	+	2.51601e13i	0.812382	+	1.40709i	−0.0988101	+	0.995106i	$0.531504\pi$
$882$	−7.61859e11	+	1.31958e12i	−0.0423903	+	0.0734221i
$883$	3.60736e12	+	2.04583e13i	0.199695	+	1.13252i	0.905573	+	0.424191i	$0.139441\pi$
$883$	3.60736e12	+	2.04583e13i	0.199695	+	1.13252i	−0.705878	+	0.708333i	$0.749447\pi$
$884$	−2.34217e11	−	1.32831e12i	−0.0128998	−	0.0731586i
$885$	−5.36481e12	+	9.29213e12i	−0.293975	+	0.509179i
$886$	1.75926e12	+	3.04712e12i	0.0959129	+	0.166126i
$887$	9.07411e12	−	7.61408e12i	0.492207	−	0.413010i	−0.362610	−	0.931941i	$-0.618114\pi$
$887$	9.07411e12	−	7.61408e12i	0.492207	−	0.413010i	0.854816	+	0.518931i	$0.173670\pi$
$888$	3.18820e11	−	1.16041e11i	0.0172063	−	0.00626258i
$889$	1.85207e13	+	6.74099e12i	0.994490	+	0.361965i
$890$	−3.85882e12	−	3.23793e12i	−0.206157	−	0.172987i
$891$	3.38098e12	−	1.91745e13i	0.179719	−	1.01923i
$892$	−9.07355e12			−0.479883
$893$	4.12390e12	+	1.31293e13i	0.217009	+	0.690891i
$894$	4.43289e12			0.232096
$895$	−7.03689e12	+	3.99082e13i	−0.366587	+	2.07902i
$896$	−8.14527e11	−	6.83470e11i	−0.0422201	−	0.0354269i
$897$	4.58663e12	+	1.66940e12i	0.236553	+	0.0860982i
$898$	1.99833e13	−	7.27333e12i	1.02547	−	0.373241i
$899$	−1.77455e12	+	1.48903e12i	−0.0906089	+	0.0760299i
$900$	−9.72735e11	−	1.68483e12i	−0.0494201	−	0.0855980i
$901$	6.43849e12	−	1.11518e13i	0.325478	−	0.563745i
$902$	−8.86121e11	−	5.02544e12i	−0.0445722	−	0.252781i
$903$	2.00159e12	+	1.13516e13i	0.100180	+	0.568147i
$904$	3.65167e11	−	6.32487e11i	0.0181858	−	0.0314988i
$905$	1.22920e13	+	2.12904e13i	0.609121	+	1.05503i
$906$	−1.13736e13	+	9.54362e12i	−0.560819	+	0.470583i
$907$	2.39019e13	−	8.69958e12i	1.17273	−	0.426840i	0.319104	−	0.947720i	$-0.396618\pi$
$907$	2.39019e13	−	8.69958e12i	1.17273	−	0.426840i	0.853630	+	0.520879i	$0.174396\pi$
$908$	−1.36949e13	−	4.98452e12i	−0.668607	−	0.243353i
$909$	−3.18202e11	−	2.67003e11i	−0.0154584	−	0.0129711i
$910$	−9.07744e11	+	5.14807e12i	−0.0438811	+	0.248862i
$911$	−1.28164e12			−0.0616499			−0.0308250	−	0.999525i	$-0.509813\pi$
$911$	−1.28164e12			−0.0616499			−0.0308250	+	0.999525i	$0.509813\pi$
$912$	−1.71179e12	−	5.44982e12i	−0.0819356	−	0.260859i
$913$	−7.21922e12			−0.343852
$914$	3.89612e12	−	2.20960e13i	0.184660	−	1.04726i
$915$	1.19990e13	+	1.00684e13i	0.565914	+	0.474858i
$916$	−3.17408e12	−	1.15527e12i	−0.148967	−	0.0542194i
$917$	−6.16125e12	+	2.24251e12i	−0.287744	+	0.104730i
$918$	−3.76384e12	+	3.15824e12i	−0.174920	+	0.146775i
$919$	−6.12416e12	−	1.06073e13i	−0.283222	−	0.490554i	0.688955	−	0.724804i	$-0.258070\pi$
$919$	−6.12416e12	−	1.06073e13i	−0.283222	−	0.490554i	−0.972176	+	0.234250i	$0.924737\pi$
$920$	−3.09714e12	+	5.36440e12i	−0.142533	+	0.246874i
$921$	9.94833e11	+	5.64198e12i	0.0455598	+	0.258383i
$922$	−1.33582e12	−	7.57581e12i	−0.0608778	−	0.345255i
$923$	3.47914e11	−	6.02604e11i	0.0157784	−	0.0273290i
$924$	3.37724e12	+	5.84956e12i	0.152419	+	0.263997i
$925$	8.13892e11	−	6.82937e11i	0.0365535	−	0.0306720i
$926$	−7.39451e12	+	2.69138e12i	−0.330491	+	0.120289i
$927$	−1.64310e12	−	5.98039e11i	−0.0730810	−	0.0265993i
$928$	5.34500e12	+	4.48498e12i	0.236582	+	0.198516i
$929$	−9.90372e11	+	5.61668e12i	−0.0436242	+	0.247405i	−0.998820	−	0.0485702i	$-0.984534\pi$
$929$	−9.90372e11	+	5.61668e12i	−0.0436242	+	0.247405i	0.955196	+	0.295975i	$0.0956447\pi$
$930$	−1.69246e12			−0.0741898
$931$	−5.37563e12	+	1.29380e13i	−0.234507	+	0.564407i
$932$	1.18693e13			0.515290
$933$	6.83706e12	−	3.87749e13i	0.295394	−	1.67526i
$934$	2.17758e13	+	1.82721e13i	0.936295	+	0.785645i
$935$	−1.02178e13	−	3.71898e12i	−0.437226	−	0.159137i
$936$	6.19046e11	−	2.25314e11i	0.0263622	−	0.00959505i
$937$	−2.02927e13	+	1.70276e13i	−0.860028	+	0.721649i	−0.961974	−	0.273141i	$-0.911937\pi$
$937$	−2.02927e13	+	1.70276e13i	−0.860028	+	0.721649i	0.101946	+	0.994790i	$0.467493\pi$
$938$	9.89152e12	+	1.71326e13i	0.417206	+	0.722621i
$939$	−1.23872e13	+	2.14552e13i	−0.519968	+	0.900612i
$940$	−2.13258e12	−	1.20944e13i	−0.0890901	−	0.505255i
$941$	6.86220e12	+	3.89175e13i	0.285305	+	1.61805i	0.704192	+	0.710009i	$0.251309\pi$
$941$	6.86220e12	+	3.89175e13i	0.285305	+	1.61805i	−0.418887	+	0.908038i	$0.637580\pi$
$942$	−1.81927e13	+	3.15106e13i	−0.752779	+	1.30385i
$943$	−2.80538e12	−	4.85907e12i	−0.115529	−	0.200101i
$944$	1.77281e12	−	1.48757e12i	0.0726589	−	0.0609681i
$945$	1.78940e13	−	6.51288e12i	0.729902	−	0.265663i
$946$	−1.23781e13	−	4.50525e12i	−0.502508	−	0.182898i
$947$	−2.65511e13	−	2.22790e13i	−1.07277	−	0.900164i	−0.0774727	−	0.996994i	$-0.524685\pi$
$947$	−2.65511e13	−	2.22790e13i	−1.07277	−	0.900164i	−0.995301	+	0.0968305i	$0.969130\pi$
$948$	−3.04129e12	+	1.72480e13i	−0.122298	+	0.693589i
$949$	−1.77988e13			−0.712350
$950$	−1.08742e13	−	1.42035e13i	−0.433151	−	0.565771i
$951$	−3.14967e13			−1.24868
$952$	3.56371e11	−	2.02108e12i	0.0140617	−	0.0797476i
$953$	−1.17630e13	−	9.87030e12i	−0.461954	−	0.387626i	0.381895	−	0.924206i	$-0.375272\pi$
$953$	−1.17630e13	−	9.87030e12i	−0.461954	−	0.387626i	−0.843849	+	0.536580i	$0.819716\pi$
$954$	5.91000e12	+	2.15106e12i	0.231004	+	0.0840786i
$955$	3.81608e13	−	1.38894e13i	1.48458	−	0.540341i
$956$	9.79605e12	−	8.21986e12i	0.379307	−	0.318276i
$957$	−2.21618e13	−	3.83853e13i	−0.854084	−	1.47932i
$958$	−5.79723e12	+	1.00411e13i	−0.222370	+	0.385156i
$959$	4.89102e11	+	2.77383e12i	0.0186731	+	0.105900i
$960$	8.85209e11	+	5.02027e12i	0.0336376	+	0.190768i
$961$	1.31592e13	−	2.27924e13i	0.497708	−	0.862056i
$962$	1.79885e11	+	3.11570e11i	0.00677185	+	0.0117292i
$963$	−4.58198e12	+	3.84474e12i	−0.171686	+	0.144062i
$964$	1.30627e13	−	4.75442e12i	0.487175	−	0.177317i
$965$	−4.81032e13	−	1.75082e13i	−1.78567	−	0.649931i
$966$	5.68913e12	+	4.77375e12i	0.210208	+	0.176385i
$967$	4.51335e12	−	2.55965e13i	0.165989	−	0.941371i	−0.782050	−	0.623216i	$-0.785826\pi$
$967$	4.51335e12	−	2.55965e13i	0.165989	−	0.941371i	0.948039	−	0.318155i	$-0.103063\pi$
$968$	1.93924e12			0.0709892
$969$	7.45752e12	−	8.12065e12i	0.271730	−	0.295892i
$970$	4.56871e13			1.65699
$971$	−7.19118e11	+	4.07832e12i	−0.0259605	+	0.147229i	−0.995033	−	0.0995476i	$-0.968260\pi$
$971$	−7.19118e11	+	4.07832e12i	−0.0259605	+	0.147229i	0.969072	+	0.246777i	$0.0793715\pi$
$972$	−4.12526e12	−	3.46151e12i	−0.148236	−	0.124385i
$973$	1.14309e12	+	4.16052e11i	0.0408860	+	0.0148813i
$974$	2.80069e13	−	1.01937e13i	0.997127	−	0.362924i
$975$	9.63608e12	−	8.08563e12i	0.341491	−	0.286545i
$976$	−1.68922e12	−	2.92581e12i	−0.0595884	−	0.103210i
$977$	−1.77735e13	+	3.07846e13i	−0.624091	+	1.08096i	0.364625	+	0.931154i	$0.381197\pi$
$977$	−1.77735e13	+	3.07846e13i	−0.624091	+	1.08096i	−0.988716	+	0.149803i	$0.952136\pi$
$978$	5.86222e11	+	3.32463e12i	0.0204898	+	0.116203i
$979$	−1.19849e12	−	6.79699e12i	−0.0416978	−	0.236480i
$980$	6.25143e12	−	1.08278e13i	0.216502	−	0.374992i
$981$	1.13002e12	+	1.95725e12i	0.0389562	+	0.0674740i
$982$	−1.09306e13	+	9.17190e12i	−0.375098	+	0.314744i
$983$	1.43001e13	−	5.20482e12i	0.488483	−	0.177793i	−0.0860240	−	0.996293i	$-0.527416\pi$
$983$	1.43001e13	−	5.20482e12i	0.488483	−	0.177793i	0.574507	+	0.818500i	$0.305194\pi$
$984$	−4.33903e12	−	1.57928e12i	−0.147542	−	0.0537008i
$985$	−6.25256e13	−	5.24652e13i	−2.11639	−	1.77586i
$986$	−2.33854e12	+	1.32625e13i	−0.0787950	+	0.446868i
$987$	−1.47243e13			−0.493866
$988$	5.37594e12	−	2.79109e12i	0.179493	−	0.0931895i
$989$	−1.44833e13			−0.481375
$990$	9.22211e11	−	5.23012e12i	0.0305121	−	0.173043i
$991$	3.65132e13	+	3.06382e13i	1.20259	+	1.00910i	0.999552	+	0.0299249i	$0.00952683\pi$
$991$	3.65132e13	+	3.06382e13i	1.20259	+	1.00910i	0.203041	+	0.979170i	$0.434918\pi$
$992$	3.43026e11	+	1.24851e11i	0.0112467	+	0.00409346i
$993$	−1.59950e13	+	5.82171e12i	−0.522051	+	0.190011i
$994$	8.11034e11	−	6.80538e11i	0.0263512	−	0.0221113i
$995$	4.08005e13	+	7.06685e13i	1.31966	+	2.28571i
$996$	−3.26621e12	+	5.65725e12i	−0.105166	+	0.182154i
$997$	−8.37456e12	−	4.74945e13i	−0.268432	−	1.52235i	−0.759082	−	0.650995i	$-0.774352\pi$
$997$	−8.37456e12	−	4.74945e13i	−0.268432	−	1.52235i	0.490651	−	0.871356i	$-0.336759\pi$
$998$	3.46143e11	+	1.96308e12i	0.0110451	+	0.0626397i
$999$	6.55276e11	−	1.13497e12i	0.0208151	−	0.0360529i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	38.10.e.a.17.6	yes	42
19.9	even	9	inner	38.10.e.a.9.6	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.10.e.a.9.6	✓	42	19.9	even	9	inner
38.10.e.a.17.6	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)

\(f(q)\)	\(=\)	\(q+(-2.77837 + 15.7569i) q^{2} +(117.543 + 98.6302i) q^{3} +(-240.561 - 87.5572i) q^{4} +(-1860.80 + 677.275i) q^{5} +(-1880.69 + 1578.08i) q^{6} +(-1980.53 - 3430.38i) q^{7} +(2048.00 - 3547.24i) q^{8} +(670.500 + 3802.60i) q^{9} +O(q^{10})\)	\(q+(-2.77837 + 15.7569i) q^{2} +(117.543 + 98.6302i) q^{3} +(-240.561 - 87.5572i) q^{4} +(-1860.80 + 677.275i) q^{5} +(-1880.69 + 1578.08i) q^{6} +(-1980.53 - 3430.38i) q^{7} +(2048.00 - 3547.24i) q^{8} +(670.500 + 3802.60i) q^{9} +(-5501.78 - 31202.1i) q^{10} +(21705.4 - 37594.9i) q^{11} +(-19640.5 - 34018.3i) q^{12} +(31908.2 - 26774.2i) q^{13} +(59554.9 - 21676.2i) q^{14} +(-285523. - 103922. i) q^{15} +(50203.5 + 42125.7i) q^{16} +(-21965.0 + 124570. i) q^{17} -61780.1 q^{18} +(-563277. + 73531.6i) q^{19} +506936. q^{20} +(105542. - 598557. i) q^{21} +(532074. + 446463. i) q^{22} +(717634. + 261198. i) q^{23} +(590593. - 214958. i) q^{24} +(1.50768e6 - 1.26510e6i) q^{25} +(333226. + 577164. i) q^{26} +(1.21386e6 - 2.10246e6i) q^{27} +(176085. + 998627. i) q^{28} +(-1.15548e6 - 6.55307e6i) q^{29} +(2.43078e6 - 4.21023e6i) q^{30} +(-174065. - 301490. i) q^{31} +(-803256. + 674012. i) q^{32} +(6.25931e6 - 2.27820e6i) q^{33} +(-1.90181e6 - 692201. i) q^{34} +(6.00868e6 + 5.04188e6i) q^{35} +(171648. - 973465. i) q^{36} +539830. q^{37} +(406361. - 9.07981e6i) q^{38} +6.39132e6 q^{39} +(-1.40846e6 + 7.98775e6i) q^{40} +(-5.62806e6 - 4.72250e6i) q^{41} +(9.13819e6 + 3.32603e6i) q^{42} +(-1.78211e7 + 6.48636e6i) q^{43} +(-8.51319e6 + 7.14341e6i) q^{44} +(-3.82307e6 - 6.62174e6i) q^{45} +(-6.10952e6 + 1.05820e7i) q^{46} +(-4.20680e6 - 2.38579e7i) q^{47} +(1.74619e6 + 9.90316e6i) q^{48} +(1.23318e7 - 2.13593e7i) q^{49} +(1.57451e7 + 2.72713e7i) q^{50} +(-1.48682e7 + 1.24759e7i) q^{51} +(-1.00201e7 + 3.64703e6i) q^{52} +(-9.56618e7 - 3.48181e7i) q^{53} +(2.97557e7 + 2.49680e7i) q^{54} +(-1.49273e7 + 8.46570e7i) q^{55} -1.62245e7 q^{56} +(-7.34616e7 - 4.69130e7i) q^{57} +1.06467e8 q^{58} +(6.13196e6 - 3.47761e7i) q^{59} +(5.95867e7 + 4.99992e7i) q^{60} +(-4.84419e7 - 1.76314e7i) q^{61} +(5.23417e6 - 1.90508e6i) q^{62} +(1.17164e7 - 9.83124e6i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(-4.12412e7 + 7.14319e7i) q^{65} +(1.85068e7 + 1.04957e8i) q^{66} +(5.42040e7 + 3.07406e8i) q^{67} +(1.61909e7 - 2.80435e7i) q^{68} +(5.85909e7 + 1.01482e8i) q^{69} +(-9.61388e7 + 8.06701e7i) q^{70} +(1.56978e7 - 5.71354e6i) q^{71} +(1.48619e7 + 5.40929e6i) q^{72} +(-3.27339e8 - 2.74670e8i) q^{73} +(-1.49985e6 + 8.50606e6i) q^{74} +3.01994e8 q^{75} +(1.41941e8 + 3.16301e7i) q^{76} -1.71953e8 q^{77} +(-1.77575e7 + 1.00708e8i) q^{78} +(-3.41554e8 - 2.86598e8i) q^{79} +(-1.21949e8 - 4.43859e7i) q^{80} +(4.21464e8 - 1.53400e8i) q^{81} +(9.00490e7 - 7.55601e7i) q^{82} +(-8.31499e7 - 1.44020e8i) q^{83} +(-7.77973e7 + 1.34749e8i) q^{84} +(-4.34955e7 - 2.46675e8i) q^{85} +(-5.26914e7 - 2.98828e8i) q^{86} +(5.10512e8 - 8.84233e8i) q^{87} +(-8.89054e7 - 1.53989e8i) q^{88} +(1.21793e8 - 1.02196e8i) q^{89} +(1.14960e8 - 4.18421e7i) q^{90} +(-1.55041e8 - 5.64302e7i) q^{91} +(-1.49765e8 - 1.25668e8i) q^{92} +(9.27587e6 - 5.26061e7i) q^{93} +3.87616e8 q^{94} +(9.98342e8 - 5.18320e8i) q^{95} -1.60895e8 q^{96} +(-2.50398e8 + 1.42008e9i) q^{97} +(3.02294e8 + 2.53655e8i) q^{98} +(1.57512e8 + 5.73296e7i) 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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