LMFDB - Embedded newform 42.12.f.a.5.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [42,12,Mod(5,42)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("42.5"); S:= CuspForms(chi, 12); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(42, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5])) N = Newforms(chi, 12, names="a")

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$32.2704135835$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-27.7128 - 16.0000i) q^{2} +(76.3670 + 413.902i) q^{3} +(512.000 + 886.810i) q^{4} +(-4176.66 + 7234.19i) q^{5} +(4506.09 - 12692.3i) q^{6} +(-20634.7 + 39389.6i) q^{7} -32768.0i q^{8} +(-165483. + 63217.0i) q^{9} +(231494. - 133653. i) q^{10} +(-844173. + 487383. i) q^{11} +(-327953. + 279641. i) q^{12} +252514. i q^{13} +(1.20208e6 - 761440. i) q^{14} +(-3.31321e6 - 1.17628e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.32660e6 + 2.29775e6i) q^{17} +(5.59748e6 + 895811. i) q^{18} +(-171378. - 98945.2i) q^{19} -8.55380e6 q^{20} +(-1.78792e7 - 5.53268e6i) q^{21} +3.11925e7 q^{22} +(4.85553e7 + 2.80334e7i) q^{23} +(1.35627e7 - 2.50239e6i) q^{24} +(-1.04749e7 - 1.81431e7i) q^{25} +(4.04022e6 - 6.99786e6i) q^{26} +(-3.88031e7 - 6.36662e7i) q^{27} +(-4.54960e7 + 1.86841e6i) q^{28} +1.80054e8i q^{29} +(7.29978e7 + 8.56092e7i) q^{30} +(1.97006e8 - 1.13742e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-2.66196e8 - 3.12185e8i) q^{33} -8.49027e7i q^{34} +(-1.98767e8 - 3.13792e8i) q^{35} +(-1.40789e8 - 1.14385e8i) q^{36} +(2.31093e8 - 4.00264e8i) q^{37} +(3.16625e6 + 5.48410e6i) q^{38} +(-1.04516e8 + 1.92837e7i) q^{39} +(2.37050e8 + 1.36861e8i) q^{40} -1.04529e9 q^{41} +(4.06961e8 + 4.39394e8i) q^{42} -1.10632e9 q^{43} +(-8.64433e8 - 4.99081e8i) q^{44} +(2.33844e8 - 1.46117e9i) q^{45} +(-8.97070e8 - 1.55377e9i) q^{46} +(-5.41700e8 + 9.38253e8i) q^{47} +(-4.15900e8 - 1.47656e8i) q^{48} +(-1.12575e9 - 1.62558e9i) q^{49} +6.70394e8i q^{50} +(-8.49734e8 + 7.24557e8i) q^{51} +(-2.23932e8 + 1.29287e8i) q^{52} +(4.09998e9 - 2.36713e9i) q^{53} +(5.66843e7 + 2.38522e9i) q^{54} -8.14254e9i q^{55} +(1.29072e9 + 6.76157e8i) q^{56} +(2.78660e7 - 7.84899e7i) q^{57} +(2.88086e9 - 4.98980e9i) q^{58} +(2.27976e9 + 3.94865e9i) q^{59} +(-6.53228e8 - 3.54044e9i) q^{60} +(6.99890e9 + 4.04081e9i) q^{61} -7.27947e9 q^{62} +(9.24604e8 - 7.82277e9i) q^{63} -1.07374e9 q^{64} +(-1.82673e9 - 1.05466e9i) q^{65} +(2.38208e9 + 1.29107e10i) q^{66} +(-1.35256e9 - 2.34270e9i) q^{67} +(-1.35844e9 + 2.35289e9i) q^{68} +(-7.89507e9 + 2.22380e10i) q^{69} +(4.87732e8 + 1.18763e10i) q^{70} +5.70444e9i q^{71} +(2.07149e9 + 5.42255e9i) q^{72} +(6.75151e9 - 3.89799e9i) q^{73} +(-1.28085e10 + 7.39497e9i) q^{74} +(6.70952e9 - 5.72112e9i) q^{75} -2.02640e8i q^{76} +(-1.77858e9 - 4.33086e10i) q^{77} +(3.20497e9 + 1.13785e9i) q^{78} +(-8.75989e9 + 1.51726e10i) q^{79} +(-4.37955e9 - 7.58559e9i) q^{80} +(2.33883e10 - 2.09227e10i) q^{81} +(2.89679e10 + 1.67247e10i) q^{82} +1.84043e10 q^{83} +(-4.24773e9 - 1.86882e10i) q^{84} -2.21631e10 q^{85} +(3.06593e10 + 1.77012e10i) q^{86} +(-7.45247e10 + 1.37502e10i) q^{87} +(1.59706e10 + 2.76619e10i) q^{88} +(-2.19482e10 + 3.80155e10i) q^{89} +(-2.98592e10 + 3.67517e10i) q^{90} +(-9.94640e9 - 5.21054e9i) q^{91} +5.74125e10i q^{92} +(6.21227e10 + 7.28553e10i) q^{93} +(3.00241e10 - 1.73344e10i) q^{94} +(1.43158e9 - 8.26521e8i) q^{95} +(9.16328e9 + 1.07464e10i) q^{96} +1.61761e10i q^{97} +(5.18831e9 + 6.30614e10i) q^{98} +(1.08885e11 - 1.34020e11i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) $ 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$2$	−27.7128	−	16.0000i	−0.612372	−	0.353553i
$3$	76.3670	+	413.902i	0.181442	+	0.983402i
$3$	76.3670	+	413.902i	0.181442	+	0.983402i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	−4176.66	+	7234.19i	−0.597715	+	1.03527i	0.395443	+	0.918491i	$0.370591\pi$
$5$	−4176.66	+	7234.19i	−0.597715	+	1.03527i	−0.993158	+	0.116782i	$0.962742\pi$
$6$	4506.09	−	12692.3i	0.236575	−	0.666358i
$7$	−20634.7	+	39389.6i	−0.464043	+	0.885813i
$7$	−20634.7	+	39389.6i	−0.464043	+	0.885813i
$8$		−	32768.0i		−	0.353553i
$9$	−165483.	+	63217.0i	−0.934157	+	0.356862i
$10$	231494.	−	133653.i	0.732048	−	0.422648i
$11$	−844173.	+	487383.i	−1.58042	+	0.912454i	−0.585619	+	0.810587i	$0.699148\pi$
$11$	−844173.	+	487383.i	−1.58042	+	0.912454i	−0.994798	+	0.101867i	$0.967518\pi$
$12$	−327953.	+	279641.i	−0.380465	+	0.324417i
$13$			252514.i			0.188624i	0.995543	+	0.0943118i	$0.0300651\pi$
$13$			252514.i			0.188624i	−0.995543	+	0.0943118i	$0.969935\pi$
$14$	1.20208e6	−	761440.i	0.597349	−	0.378383i
$15$	−3.31321e6	−	1.17628e6i	−1.12654	−	0.399951i
$16$	−524288.	+	908093.i	−0.125000	+	0.216506i
$17$	1.32660e6	+	2.29775e6i	0.226607	+	0.392494i	0.956800	−	0.290746i	$-0.0939035\pi$
$17$	1.32660e6	+	2.29775e6i	0.226607	+	0.392494i	−0.730194	+	0.683240i	$0.760570\pi$
$18$	5.59748e6	+	895811.i	0.698222	+	0.111742i
$19$	−171378.	−	98945.2i	−0.0158785	−	0.00916748i	0.492040	−	0.870573i	$-0.336251\pi$
$19$	−171378.	−	98945.2i	−0.0158785	−	0.00916748i	−0.507918	+	0.861405i	$0.669585\pi$
$20$	−8.55380e6			−0.597715
$21$	−1.78792e7	−	5.53268e6i	−0.955307	−	0.295617i
$22$	3.11925e7			1.29040
$23$	4.85553e7	+	2.80334e7i	1.57302	+	0.908182i	0.995796	+	0.0915948i	$0.0291965\pi$
$23$	4.85553e7	+	2.80334e7i	1.57302	+	0.908182i	0.577222	+	0.816588i	$0.304137\pi$
$24$	1.35627e7	−	2.50239e6i	0.347685	−	0.0641496i
$25$	−1.04749e7	−	1.81431e7i	−0.214526	−	0.371570i
$26$	4.04022e6	−	6.99786e6i	0.0666885	−	0.115508i
$27$	−3.88031e7	−	6.36662e7i	−0.520434	−	0.853902i
$28$	−4.54960e7	+	1.86841e6i	−0.499579	+	0.0205165i
$29$			1.80054e8i			1.63010i	0.579392	+	0.815049i	$0.303290\pi$
$29$			1.80054e8i			1.63010i	−0.579392	+	0.815049i	$0.696710\pi$
$30$	7.29978e7	+	8.56092e7i	0.548458	+	0.643211i
$31$	1.97006e8	−	1.13742e8i	1.23592	−	0.713560i	0.267663	−	0.963512i	$-0.413748\pi$
$31$	1.97006e8	−	1.13742e8i	1.23592	−	0.713560i	0.968258	+	0.249953i	$0.0804151\pi$
$32$	2.90590e7	−	1.67772e7i	0.153093	−	0.0883883i
$33$	−2.66196e8	−	3.12185e8i	−1.18406	−	1.38863i
$34$		−	8.49027e7i		−	0.320470i
$35$	−1.98767e8	−	3.13792e8i	−0.639692	−	1.00987i
$36$	−1.40789e8	−	1.14385e8i	−0.388065	−	0.315287i
$37$	2.31093e8	−	4.00264e8i	0.547869	−	0.948937i	−0.450551	−	0.892751i	$-0.648772\pi$
$37$	2.31093e8	−	4.00264e8i	0.547869	−	0.948937i	0.998420	−	0.0561867i	$-0.0178942\pi$
$38$	3.16625e6	+	5.48410e6i	0.00648239	+	0.0112278i
$39$	−1.04516e8	+	1.92837e7i	−0.185493	+	0.0342243i
$40$	2.37050e8	+	1.36861e8i	0.366024	+	0.211324i
$41$	−1.04529e9			−1.40905			−0.704524	−	0.709680i	$-0.748840\pi$
$41$	−1.04529e9			−1.40905			−0.704524	+	0.709680i	$0.748840\pi$
$42$	4.06961e8	+	4.39394e8i	0.480487	+	0.518780i
$43$	−1.10632e9			−1.14764			−0.573819	−	0.818982i	$-0.694539\pi$
$43$	−1.10632e9			−1.14764			−0.573819	+	0.818982i	$0.694539\pi$
$44$	−8.64433e8	−	4.99081e8i	−0.790208	−	0.456227i
$45$	2.33844e8	−	1.46117e9i	0.188911	−	1.18041i
$46$	−8.97070e8	−	1.55377e9i	−0.642182	−	1.11229i
$47$	−5.41700e8	+	9.38253e8i	−0.344525	+	0.596735i	−0.985267	−	0.171021i	$-0.945293\pi$
$47$	−5.41700e8	+	9.38253e8i	−0.344525	+	0.596735i	0.640742	+	0.767756i	$0.278627\pi$
$48$	−4.15900e8	−	1.47656e8i	−0.235593	−	0.0836418i
$49$	−1.12575e9	−	1.62558e9i	−0.569328	−	0.822111i
$50$			6.70394e8i			0.303386i
$51$	−8.49734e8	+	7.24557e8i	−0.344863	+	0.294060i
$52$	−2.23932e8	+	1.29287e8i	−0.0816765	+	0.0471559i
$53$	4.09998e9	−	2.36713e9i	1.34668	−	0.777507i	0.358903	−	0.933375i	$-0.383151\pi$
$53$	4.09998e9	−	2.36713e9i	1.34668	−	0.777507i	0.987778	+	0.155868i	$0.0498175\pi$
$54$	5.66843e7	+	2.38522e9i	0.0167995	+	0.706907i
$55$		−	8.14254e9i		−	2.18155i
$56$	1.29072e9	+	6.76157e8i	0.313182	+	0.164064i
$57$	2.78660e7	−	7.84899e7i	0.00613427	−	0.0172783i
$58$	2.88086e9	−	4.98980e9i	0.576326	−	0.998227i
$59$	2.27976e9	+	3.94865e9i	0.415147	+	0.719056i	0.995444	−	0.0953491i	$-0.0303967\pi$
$59$	2.27976e9	+	3.94865e9i	0.415147	+	0.719056i	−0.580297	+	0.814405i	$0.697063\pi$
$60$	−6.53228e8	−	3.54044e9i	−0.108451	−	0.587794i
$61$	6.99890e9	+	4.04081e9i	1.06100	+	0.612569i	0.925709	−	0.378237i	$-0.123470\pi$
$61$	6.99890e9	+	4.04081e9i	1.06100	+	0.612569i	0.135291	+	0.990806i	$0.456803\pi$
$62$	−7.27947e9			−1.00913
$63$	9.24604e8	−	7.82277e9i	0.117377	−	0.993087i
$64$	−1.07374e9			−0.125000
$65$	−1.82673e9	−	1.05466e9i	−0.195277	−	0.112743i
$66$	2.38208e9	+	1.29107e10i	0.234134	+	1.26899i
$67$	−1.35256e9	−	2.34270e9i	−0.122390	−	0.211985i	0.798320	−	0.602233i	$-0.205722\pi$
$67$	−1.35256e9	−	2.34270e9i	−0.122390	−	0.211985i	−0.920710	+	0.390249i	$0.872389\pi$
$68$	−1.35844e9	+	2.35289e9i	−0.113303	+	0.196247i
$69$	−7.89507e9	+	2.22380e10i	−0.607696	+	1.71169i
$70$	4.87732e8	+	1.18763e10i	0.0346850	+	0.844585i
$71$			5.70444e9i			0.375225i	0.982243	+	0.187613i	$0.0600750\pi$
$71$			5.70444e9i			0.375225i	−0.982243	+	0.187613i	$0.939925\pi$
$72$	2.07149e9	+	5.42255e9i	0.126170	+	0.330274i
$73$	6.75151e9	−	3.89799e9i	0.381176	−	0.220072i	−0.297154	−	0.954830i	$-0.596037\pi$
$73$	6.75151e9	−	3.89799e9i	0.381176	−	0.220072i	0.678330	+	0.734758i	$0.262704\pi$
$74$	−1.28085e10	+	7.39497e9i	−0.671000	+	0.387402i
$75$	6.70952e9	−	5.72112e9i	0.326479	−	0.278384i
$76$		−	2.02640e8i		−	0.00916748i
$77$	−1.77858e9	−	4.33086e10i	−0.0748814	−	1.82337i
$78$	3.20497e9	+	1.13785e9i	0.125691	+	0.0446236i
$79$	−8.75989e9	+	1.51726e10i	−0.320295	+	0.554767i	−0.980549	−	0.196276i	$-0.937115\pi$
$79$	−8.75989e9	+	1.51726e10i	−0.320295	+	0.554767i	0.660254	+	0.751042i	$0.270449\pi$
$80$	−4.37955e9	−	7.58559e9i	−0.149429	−	0.258818i
$81$	2.33883e10	−	2.09227e10i	0.745300	−	0.666730i
$82$	2.89679e10	+	1.67247e10i	0.862862	+	0.498174i
$83$	1.84043e10			0.512851			0.256425	−	0.966564i	$-0.417455\pi$
$83$	1.84043e10			0.512851			0.256425	+	0.966564i	$0.417455\pi$
$84$	−4.24773e9	−	1.86882e10i	−0.110821	−	0.487564i
$85$	−2.21631e10			−0.541785
$86$	3.06593e10	+	1.77012e10i	0.702782	+	0.405752i
$87$	−7.45247e10	+	1.37502e10i	−1.60304	+	0.295769i
$88$	1.59706e10	+	2.76619e10i	0.322601	+	0.558762i
$89$	−2.19482e10	+	3.80155e10i	−0.416634	+	0.721631i	−0.995598	−	0.0937217i	$-0.970124\pi$
$89$	−2.19482e10	+	3.80155e10i	−0.416634	+	0.721631i	0.578965	+	0.815353i	$0.303457\pi$
$90$	−2.98592e10	+	3.67517e10i	−0.533021	+	0.656060i
$91$	−9.94640e9	−	5.21054e9i	−0.167085	−	0.0875296i
$92$			5.74125e10i			0.908182i
$93$	6.21227e10	+	7.28553e10i	0.925964	+	1.08594i
$94$	3.00241e10	−	1.73344e10i	0.421955	−	0.243616i
$95$	1.43158e9	−	8.26521e8i	0.0189817	−	0.0109591i
$96$	9.16328e9	+	1.07464e10i	0.114699	+	0.134515i
$97$			1.61761e10i			0.191262i	0.995417	+	0.0956310i	$0.0304869\pi$
$97$			1.61761e10i			0.191262i	−0.995417	+	0.0956310i	$0.969513\pi$
$98$	5.18831e9	+	6.30614e10i	0.0579805	+	0.704726i
$99$	1.08885e11	−	1.34020e11i	1.15074	−	1.41637i
$100$	1.07263e10	−	1.85785e10i	0.107263	−	0.185785i
$101$	−7.22548e10	−	1.25149e11i	−0.684067	−	1.18484i	−0.973729	−	0.227710i	$-0.926876\pi$
$101$	−7.22548e10	−	1.25149e11i	−0.684067	−	1.18484i	0.289661	−	0.957129i	$-0.406457\pi$
$102$	3.51414e10	−	6.48377e9i	0.315151	−	0.0581469i
$103$	4.06157e10	+	2.34495e10i	0.345215	+	0.199310i	0.662576	−	0.748995i	$-0.269463\pi$
$103$	4.06157e10	+	2.34495e10i	0.345215	+	0.199310i	−0.317361	+	0.948305i	$0.602797\pi$
$104$	8.27436e9			0.0666885
$105$	1.14700e11	−	1.06234e11i	0.877045	−	0.812308i
$106$	−1.51496e11			−1.09956
$107$	4.91976e10	+	2.84042e10i	0.339104	+	0.195782i	0.659876	−	0.751375i	$-0.270609\pi$
$107$	4.91976e10	+	2.84042e10i	0.339104	+	0.195782i	−0.320772	+	0.947157i	$0.603942\pi$
$108$	3.65926e10	−	6.70080e10i	0.239642	−	0.438830i
$109$	1.08749e10	+	1.88358e10i	0.0676983	+	0.117257i	0.897888	−	0.440224i	$-0.145101\pi$
$109$	1.08749e10	+	1.88358e10i	0.0676983	+	0.117257i	−0.830189	+	0.557481i	$0.811768\pi$
$110$	−1.30281e11	+	2.25653e11i	−0.771294	+	1.33592i
$111$	1.83318e11	+	6.50828e10i	1.03259	+	0.366598i
$112$	−2.49509e10	−	3.93897e10i	−0.133779	−	0.211195i
$113$		−	5.52049e9i		−	0.0281868i	−0.999901	−	0.0140934i	$-0.995514\pi$
$113$		−	5.52049e9i		−	0.0281868i	0.999901	−	0.0140934i	$-0.00448622\pi$
$114$	−2.02808e9	+	1.72932e9i	−0.00986528	+	0.00841199i
$115$	−4.05598e11	+	2.34172e11i	−1.88043	+	1.08567i
$116$	−1.59674e11	+	9.21876e10i	−0.705853	+	0.407524i
$117$	−1.59631e10	−	4.17867e10i	−0.0673125	−	0.176204i
$118$		−	1.45904e11i		−	0.587107i
$119$	−1.17881e11	+	4.84110e9i	−0.452831	+	0.0185967i
$120$	−3.85442e10	+	1.08567e11i	−0.141404	+	0.398292i
$121$	3.32429e11	−	5.75784e11i	1.16514	−	2.01809i
$122$	−1.29306e11	−	2.23965e11i	−0.433151	−	0.750240i
$123$	−7.98257e10	−	4.32648e11i	−0.255661	−	1.38566i
$124$	2.01734e11	+	1.16471e11i	0.617961	+	0.356780i
$125$	−2.32876e11			−0.682528
$126$	−1.50788e11	+	2.01997e11i	−0.422988	+	0.566640i
$127$	1.30644e11			0.350889			0.175445	−	0.984489i	$-0.443864\pi$
$127$	1.30644e11			0.350889			0.175445	+	0.984489i	$0.443864\pi$
$128$	2.97564e10	+	1.71799e10i	0.0765466	+	0.0441942i
$129$	−8.44865e10	−	4.57909e11i	−0.208230	−	1.12859i
$130$	3.37492e10	+	5.84554e10i	0.0797215	+	0.138082i
$131$	−1.73966e11	+	3.01318e11i	−0.393979	+	0.682391i	−0.992970	−	0.118364i	$-0.962235\pi$
$131$	−1.73966e11	+	3.01318e11i	−0.393979	+	0.682391i	0.598992	+	0.800755i	$0.295568\pi$
$132$	1.40556e11	−	3.95904e11i	0.305277	−	0.859871i
$133$	7.43374e9	−	4.70880e9i	0.0154890	−	0.00981130i
$134$			8.65637e10i			0.173085i
$135$	6.22640e11	−	1.47970e10i	1.19509	−	0.0284012i
$136$	7.52926e10	−	4.34702e10i	0.138768	−	0.0801175i
$137$	−4.88936e11	+	2.82287e11i	−0.865544	+	0.499722i	−0.865865	−	0.500278i	$-0.833231\pi$
$137$	−4.88936e11	+	2.82287e11i	−0.865544	+	0.499722i	0.000321066		1.00000i	$0.499898\pi$
$138$	5.74602e11	−	4.89956e11i	0.977310	−	0.833340i
$139$			4.47169e11i			0.730954i	0.930820	+	0.365477i	$0.119094\pi$
$139$			4.47169e11i			0.730954i	−0.930820	+	0.365477i	$0.880906\pi$
$140$	1.76505e11	−	3.36930e11i	0.277366	−	0.529463i
$141$	−4.29713e11	−	1.52559e11i	−0.649342	−	0.230533i
$142$	9.12710e10	−	1.58086e11i	0.132662	−	0.229778i
$143$	−1.23071e11	−	2.13165e11i	−0.172110	−	0.298104i
$144$	2.93539e10	−	1.83418e11i	0.0395069	−	0.246859i
$145$	−1.30254e12	−	7.52024e11i	−1.68760	−	0.974334i
$146$	−2.49471e11			−0.311229
$147$	5.86862e11	−	5.90090e11i	0.705165	−	0.709043i
$148$	4.73278e11			0.547869
$149$	−1.35391e11	−	7.81680e10i	−0.151031	−	0.0871976i	0.422580	−	0.906326i	$-0.361124\pi$
$149$	−1.35391e11	−	7.81680e10i	−0.151031	−	0.0871976i	−0.573611	+	0.819128i	$0.694458\pi$
$150$	−2.77478e11	+	5.11960e10i	−0.298350	+	0.0550471i
$151$	3.33689e11	+	5.77967e11i	0.345915	+	0.599142i	0.985520	−	0.169562i	$-0.0542353\pi$
$151$	3.33689e11	+	5.77967e11i	0.345915	+	0.599142i	−0.639605	+	0.768704i	$0.720902\pi$
$152$	−3.24224e9	+	5.61572e9i	−0.00324119	+	0.00561391i
$153$	−3.64787e11	−	2.96375e11i	−0.351752	−	0.285784i
$154$	−6.43648e11	+	1.22866e12i	−0.598804	+	1.14306i
$155$			1.90024e12i			1.70602i
$156$	−7.06131e10	−	8.28125e10i	−0.0611928	−	0.0717647i
$157$	6.29617e10	−	3.63510e10i	0.0526779	−	0.0304136i	−0.473430	−	0.880832i	$-0.656984\pi$
$157$	6.29617e10	−	3.63510e10i	0.0526779	−	0.0304136i	0.526108	+	0.850418i	$0.323651\pi$
$158$	4.85523e11	−	2.80317e11i	0.392279	−	0.226483i
$159$	1.29286e12	+	1.51622e12i	1.00895	+	1.18326i
$160$			2.80291e11i			0.211324i
$161$	−2.10615e12	+	1.33411e12i	−1.53443	+	0.971963i
$162$	−9.82918e11	+	2.05614e11i	−0.692125	+	0.144784i
$163$	−5.11552e11	+	8.86033e11i	−0.348223	+	0.603140i	−0.985934	−	0.167136i	$-0.946548\pi$
$163$	−5.11552e11	+	8.86033e11i	−0.348223	+	0.603140i	0.637711	+	0.770276i	$0.279882\pi$
$164$	−5.35189e11	−	9.26974e11i	−0.352262	−	0.610136i
$165$	3.37022e12	−	6.21821e11i	2.14534	−	0.395826i
$166$	−5.10036e11	−	2.94470e11i	−0.314056	−	0.181320i
$167$	6.15264e11			0.366539			0.183270	−	0.983063i	$-0.441332\pi$
$167$	6.15264e11			0.366539			0.183270	+	0.983063i	$0.441332\pi$
$168$	−1.81295e11	+	5.85867e11i	−0.104516	+	0.337752i
$169$	1.72840e12			0.964421
$170$	6.14202e11	+	3.54610e11i	0.331774	+	0.191550i
$171$	3.46152e10	+	5.53976e9i	0.0181046	+	0.00289743i
$172$	−5.66437e11	−	9.81098e11i	−0.286910	−	0.496942i
$173$	−1.29543e12	+	2.24374e12i	−0.635564	+	1.10083i	0.350831	+	0.936439i	$0.385899\pi$
$173$	−1.29543e12	+	2.24374e12i	−0.635564	+	1.10083i	−0.986395	+	0.164390i	$0.947434\pi$
$174$	2.28529e12	+	8.11339e11i	1.08623	+	0.385640i
$175$	9.30794e11	−	3.82255e10i	0.428691	−	0.0176053i
$176$		−	1.02212e12i		−	0.456227i
$177$	−1.46026e12	+	1.24514e12i	−0.631796	+	0.538724i
$178$	1.21649e12	−	7.02343e11i	0.510270	−	0.294605i
$179$	3.69396e12	−	2.13271e12i	1.50245	−	0.867441i	0.502456	−	0.864603i	$-0.332430\pi$
$179$	3.69396e12	−	2.13271e12i	1.50245	−	0.867441i	0.999996	−	0.00283810i	$-0.000903397\pi$
$180$	1.41551e12	−	5.40745e11i	0.558360	−	0.213301i
$181$			3.37176e12i			1.29010i	0.764139	+	0.645052i	$0.223164\pi$
$181$			3.37176e12i			1.29010i	−0.764139	+	0.645052i	$0.776836\pi$
$182$	1.92274e11	+	3.03541e11i	0.0713720	+	0.112674i
$183$	−1.13802e12	+	3.20544e12i	−0.409891	+	1.15454i
$184$	9.18599e11	−	1.59106e12i	0.321091	−	0.556146i
$185$	1.93039e12	+	3.34354e12i	0.654939	+	1.13439i
$186$	−5.55911e11	−	3.01299e12i	−0.183098	−	0.992376i
$187$	−2.23977e12	−	1.29313e12i	−0.716266	−	0.413536i
$188$	−1.10940e12			−0.344525
$189$	3.30847e12	−	2.14706e11i	0.997901	−	0.0647595i
$190$	−5.28973e10			−0.0154985
$191$	−3.27190e12	−	1.88903e12i	−0.931358	−	0.537720i	−0.0441172	−	0.999026i	$-0.514047\pi$
$191$	−3.27190e12	−	1.88903e12i	−0.931358	−	0.537720i	−0.887241	+	0.461307i	$0.847381\pi$
$192$	−8.19985e10	−	4.44424e11i	−0.0226803	−	0.122925i
$193$	3.50536e11	+	6.07145e11i	0.0942252	+	0.163203i	0.909285	−	0.416174i	$-0.136629\pi$
$193$	3.50536e11	+	6.07145e11i	0.0942252	+	0.163203i	−0.815060	+	0.579377i	$0.803296\pi$
$194$	2.58817e11	−	4.48285e11i	0.0676213	−	0.117124i
$195$	2.97026e11	−	8.36629e11i	0.0754403	−	0.212492i
$196$	8.65200e11	−	1.83062e12i	0.213652	−	0.452054i
$197$			7.19845e11i			0.172852i	0.996258	+	0.0864261i	$0.0275446\pi$
$197$			7.19845e11i			0.172852i	−0.996258	+	0.0864261i	$0.972455\pi$
$198$	−5.16184e12	+	1.97190e12i	−1.20544	+	0.460496i
$199$	−9.56662e11	+	5.52329e11i	−0.217303	+	0.125460i	−0.604701	−	0.796453i	$-0.706707\pi$
$199$	−9.56662e11	+	5.52329e11i	−0.217303	+	0.125460i	0.387398	+	0.921913i	$0.373374\pi$
$200$	−5.94512e11	+	3.43242e11i	−0.131370	+	0.0758465i
$201$	8.66357e11	−	7.38731e11i	0.186260	−	0.158821i
$202$			4.62430e12i			0.967417i
$203$	−7.09224e12	−	3.71535e12i	−1.44396	−	0.756436i
$204$	−1.07761e12	−	3.82579e11i	−0.213548	−	0.0758151i
$205$	4.36582e12	−	7.56183e12i	0.842209	−	1.45875i
$206$	−7.50384e11	−	1.29970e12i	−0.140933	−	0.244104i
$207$	−9.80727e12	−	1.56954e12i	−1.79354	−	0.287035i
$208$	−2.29306e11	−	1.32390e11i	−0.0408382	−	0.0235780i
$209$	1.92897e11			0.0334596
$210$	−4.87839e12	+	1.10883e12i	−0.824272	+	0.187353i
$211$	−3.66503e12			−0.603287			−0.301643	−	0.953421i	$-0.597535\pi$
$211$	−3.66503e12			−0.603287			−0.301643	+	0.953421i	$0.597535\pi$
$212$	4.19838e12	+	2.42394e12i	0.673341	+	0.388753i
$213$	−2.36108e12	+	4.35631e11i	−0.368997	+	0.0680818i
$214$	−9.08935e11	−	1.57432e12i	−0.138439	−	0.239783i
$215$	4.62073e12	−	8.00334e12i	0.685961	−	1.18812i
$216$	−2.08621e12	+	1.27150e12i	−0.301900	+	0.184001i
$217$	4.15071e11	+	1.01070e13i	0.0585590	+	1.42592i
$218$		−	6.95991e11i		−	0.0957398i
$219$	2.12898e12	+	2.49679e12i	0.285581	+	0.334919i
$220$	7.22088e12	−	4.16898e12i	0.944639	−	0.545387i
$221$	−5.80212e11	+	3.34986e11i	−0.0740337	+	0.0427434i
$222$	−4.03894e12	−	4.73672e12i	−0.502720	−	0.589571i
$223$		−	1.51342e13i		−	1.83773i	−0.394571	−	0.918866i	$-0.629107\pi$
$223$		−	1.51342e13i		−	1.83773i	0.394571	−	0.918866i	$-0.370893\pi$
$224$	6.12241e10	+	1.49081e12i	0.00725368	+	0.176628i
$225$	2.88037e12	+	2.34018e12i	0.333000	+	0.270549i
$226$	−8.83278e10	+	1.52988e11i	−0.00996554	+	0.0172608i
$227$	2.08065e11	+	3.60380e11i	0.0229117	+	0.0396842i	0.877254	−	0.480027i	$-0.159373\pi$
$227$	2.08065e11	+	3.60380e11i	0.0229117	+	0.0396842i	−0.854342	+	0.519711i	$0.826040\pi$
$228$	8.38730e10	−	1.54750e10i	0.00901531	−	0.00166337i
$229$	−1.08930e13	−	6.28911e12i	−1.14302	−	0.659924i	−0.195844	−	0.980635i	$-0.562745\pi$
$229$	−1.08930e13	−	6.28911e12i	−1.14302	−	0.659924i	−0.947177	+	0.320711i	$0.896078\pi$
$230$	1.49870e13			1.53537
$231$	1.77897e13	−	4.04351e12i	1.77952	−	0.404475i
$232$	5.90001e12			0.576326
$233$	−5.03974e12	−	2.90969e12i	−0.480784	−	0.277581i	0.239959	−	0.970783i	$-0.422866\pi$
$233$	−5.03974e12	−	2.90969e12i	−0.480784	−	0.277581i	−0.720743	+	0.693202i	$0.756199\pi$
$234$	−2.26204e11	+	1.41344e12i	−0.0210772	+	0.131701i
$235$	−4.52500e12	−	7.83752e12i	−0.411856	−	0.713355i
$236$	−2.33447e12	+	4.04342e12i	−0.207574	+	0.359528i
$237$	−6.94893e12	−	2.46706e12i	−0.603674	−	0.214320i
$238$	3.34428e12	+	1.75194e12i	0.283876	+	0.148712i
$239$			3.86877e11i			0.0320911i	0.999871	+	0.0160455i	$0.00510767\pi$
$239$			3.86877e11i			0.0320911i	−0.999871	+	0.0160455i	$0.994892\pi$
$240$	2.80524e12	−	2.39199e12i	0.227409	−	0.193909i
$241$	1.89850e12	−	1.09610e12i	0.150424	−	0.0868472i	−0.422899	−	0.906177i	$-0.638987\pi$
$241$	1.89850e12	−	1.09610e12i	0.150424	−	0.0868472i	0.573323	+	0.819330i	$0.305654\pi$
$242$	−1.84251e13	+	1.06377e13i	−1.42700	+	0.823882i
$243$	1.04460e13	+	8.08266e12i	0.790892	+	0.611956i
$244$			8.27559e12i			0.612569i
$245$	1.64616e13	−	1.35436e12i	1.19140	−	0.0980215i
$246$	−4.71018e12	+	1.32671e13i	−0.333345	+	0.938930i
$247$	2.49850e10	−	4.32753e10i	0.00172920	−	0.00299507i
$248$	−3.72709e12	−	6.45550e12i	−0.252281	−	0.436964i
$249$	1.40548e12	+	7.61760e12i	0.0930529	+	0.504338i
$250$	6.45366e12	+	3.72602e12i	0.417961	+	0.241310i
$251$	2.69200e13			1.70557			0.852786	−	0.522260i	$-0.174911\pi$
$251$	2.69200e13			1.70557			0.852786	+	0.522260i	$0.174911\pi$
$252$	7.41071e12	−	3.18531e12i	0.459364	−	0.197446i
$253$	−5.46521e13			−3.31470
$254$	−3.62052e12	−	2.09031e12i	−0.214875	−	0.124058i
$255$	−1.69253e12	−	9.17336e12i	−0.0983027	−	0.532792i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	−1.99454e12	+	3.45465e12i	−0.110972	+	0.192208i	−0.916162	−	0.400808i	$-0.868730\pi$
$257$	−1.99454e12	+	3.45465e12i	−0.110972	+	0.192208i	0.805191	+	0.593016i	$0.202063\pi$
$258$	−4.98519e12	+	1.40417e13i	−0.271502	+	0.764738i
$259$	1.09977e13	+	1.73620e13i	0.586346	+	0.925657i
$260$		−	2.15995e12i		−	0.112743i
$261$	−1.13825e13	−	2.97959e13i	−0.581719	−	1.52277i
$262$	9.64218e12	−	5.56692e12i	0.482523	−	0.278585i
$263$	2.86958e13	−	1.65675e13i	1.40625	−	0.811897i	0.411222	−	0.911535i	$-0.365102\pi$
$263$	2.86958e13	−	1.65675e13i	1.40625	−	0.811897i	0.995024	+	0.0996385i	$0.0317686\pi$
$264$	−1.02297e13	+	8.72271e12i	−0.490954	+	0.418630i
$265$			3.95467e13i			1.85891i
$266$	−2.81351e11	+	1.15544e10i	−0.0129539	+	0.000531983i
$267$	−1.74108e13	−	6.18130e12i	−0.785248	−	0.278784i
$268$	1.38502e12	−	2.39892e12i	0.0611948	−	0.105992i
$269$	−1.15890e13	−	2.00728e13i	−0.501660	−	0.868900i	−0.999998	−	0.00191729i	$-0.999390\pi$
$269$	−1.15890e13	−	2.00728e13i	−0.501660	−	0.868900i	0.498339	−	0.866982i	$-0.333944\pi$
$270$	−1.74919e13	−	9.55218e12i	−0.741883	−	0.405137i
$271$	1.02934e13	+	5.94292e12i	0.427789	+	0.246984i	0.698404	−	0.715704i	$-0.253894\pi$
$271$	1.02934e13	+	5.94292e12i	0.427789	+	0.246984i	−0.270615	+	0.962688i	$0.587227\pi$
$272$	−2.78209e12			−0.113303
$273$	1.39708e12	−	4.51475e12i	0.0557604	−	0.180193i
$274$	1.80664e13			0.706714
$275$	1.76853e13	+	1.02106e13i	0.678081	+	0.391491i
$276$	−2.37631e13	+	4.38442e12i	−0.893108	+	0.164783i
$277$	2.64815e13	+	4.58673e13i	0.975672	+	1.68991i	0.677699	+	0.735340i	$0.262977\pi$
$277$	2.64815e13	+	4.58673e13i	0.975672	+	1.68991i	0.297973	+	0.954574i	$0.403689\pi$
$278$	7.15470e12	−	1.23923e13i	0.258431	−	0.447616i
$279$	−2.54108e13	+	3.12765e13i	−0.899903	+	1.10763i
$280$	−1.02823e13	+	6.51321e12i	−0.357045	+	0.226165i
$281$		−	1.37984e13i		−	0.469833i	−0.972016	−	0.234916i	$-0.924518\pi$
$281$		−	1.37984e13i		−	0.469833i	0.972016	−	0.234916i	$-0.0754816\pi$
$282$	9.46760e12	+	1.11033e13i	0.316133	+	0.370749i
$283$	−5.57153e12	+	3.21672e12i	−0.182452	+	0.105339i	−0.588444	−	0.808538i	$-0.700259\pi$
$283$	−5.57153e12	+	3.21672e12i	−0.182452	+	0.105339i	0.405992	+	0.913877i	$0.366926\pi$
$284$	−5.05875e12	+	2.92067e12i	−0.162477	+	0.0938063i
$285$	4.51424e11	+	5.29414e11i	0.0142213	+	0.0166782i
$286$			7.87654e12i			0.243401i
$287$	2.15692e13	−	4.11735e13i	0.653859	−	1.24815i
$288$	−3.74817e12	+	4.61337e12i	−0.111471	+	0.137202i
$289$	1.36162e13	−	2.35839e13i	0.397299	−	0.688142i
$290$	2.40648e13	+	4.16814e13i	0.688958	+	1.19331i
$291$	−6.69532e12	+	1.23532e12i	−0.188087	+	0.0347031i
$292$	6.91355e12	+	3.99154e12i	0.190588	+	0.110036i
$293$	−6.70453e12			−0.181383			−0.0906915	−	0.995879i	$-0.528908\pi$
$293$	−6.70453e12			−0.181383			−0.0906915	+	0.995879i	$0.528908\pi$
$294$	−2.57050e13	+	6.96326e12i	−0.682508	+	0.184885i
$295$	−3.80870e13			−0.992559
$296$	−1.31159e13	−	7.57245e12i	−0.335500	−	0.193701i
$297$	6.37863e13	+	3.48333e13i	1.60165	+	0.874649i
$298$	2.50138e12	+	4.33251e12i	0.0616580	+	0.106795i
$299$	−7.07882e12	+	1.22609e13i	−0.171305	+	0.296708i
$300$	8.50882e12	+	3.02086e12i	0.202163	+	0.0717734i
$301$	2.28286e13	−	4.35775e13i	0.532554	−	1.01659i
$302$		−	2.13561e13i		−	0.489197i
$303$	4.62815e13	−	3.94637e13i	1.04105	−	0.887693i
$304$	1.79703e11	−	1.03752e11i	0.00396963	−	0.00229187i
$305$	−5.84640e13	+	3.37542e13i	−1.26835	+	0.732283i
$306$	5.36729e12	+	1.40500e13i	0.114363	+	0.299369i
$307$			7.62425e13i			1.59564i	0.602893	+	0.797822i	$0.294015\pi$
$307$			7.62425e13i			1.59564i	−0.602893	+	0.797822i	$0.705985\pi$
$308$	3.74959e13	−	2.37513e13i	0.770822	−	0.488267i
$309$	−6.60410e12	+	1.86017e13i	−0.133365	+	0.375648i
$310$	3.04039e13	−	5.26610e13i	0.603169	−	1.04472i
$311$	2.62139e13	+	4.54037e13i	0.510915	+	0.884931i	0.999920	+	0.0126498i	$0.00402668\pi$
$311$	2.62139e13	+	4.54037e13i	0.510915	+	0.884931i	−0.489005	+	0.872281i	$0.662640\pi$
$312$	6.31888e11	+	3.42478e12i	0.0121001	+	0.0655816i
$313$	−5.81936e13	−	3.35981e13i	−1.09492	−	0.632151i	−0.160036	−	0.987111i	$-0.551161\pi$
$313$	−5.81936e13	−	3.35981e13i	−1.09492	−	0.632151i	−0.934881	+	0.354961i	$0.884494\pi$
$314$	−2.32646e12			−0.0430113
$315$	5.27296e13	+	3.93618e13i	0.957958	+	0.715100i
$316$	−1.79403e13			−0.320295
$317$	−1.96848e13	−	1.13650e13i	−0.345387	−	0.199409i	0.317265	−	0.948337i	$-0.397236\pi$
$317$	−1.96848e13	−	1.13650e13i	−0.345387	−	0.199409i	−0.662651	+	0.748928i	$0.730569\pi$
$318$	−1.15693e13	−	6.27046e13i	−0.199507	−	1.08131i
$319$	−8.77553e13	−	1.51997e14i	−1.48739	−	2.57623i
$320$	4.48465e12	−	7.76765e12i	0.0747144	−	0.129409i
$321$	−7.99950e12	+	2.25321e13i	−0.131004	+	0.368998i
$322$	7.97131e13	−	3.27362e12i	1.28328	−	0.0527013i
$323$		−	5.25045e11i		−	0.00830964i
$324$	3.05293e13	+	1.00286e13i	0.475027	+	0.156042i
$325$	4.58137e12	−	2.64506e12i	0.0700870	−	0.0404647i
$326$	2.83531e13	−	1.63696e13i	0.426484	−	0.246231i
$327$	−6.96570e12	+	5.93956e12i	−0.103027	+	0.0878500i
$328$			3.42521e13i			0.498174i
$329$	−2.57795e13	−	4.06979e13i	−0.368721	−	0.582096i
$330$	−1.03347e14	−	3.66910e13i	−1.45369	−	0.516099i
$331$	1.73215e13	−	3.00018e13i	0.239625	−	0.415043i	−0.720982	−	0.692954i	$-0.756309\pi$
$331$	1.73215e13	−	3.00018e13i	0.239625	−	0.415043i	0.960607	+	0.277911i	$0.0896421\pi$
$332$	9.42303e12	+	1.63212e13i	0.128213	+	0.222071i
$333$	−1.29385e13	+	8.08460e13i	−0.173157	+	1.08197i
$334$	−1.70507e13	−	9.84422e12i	−0.224459	−	0.129591i
$335$	2.25967e13			0.292616
$336$	1.43981e13	−	1.33353e13i	0.183416	−	0.169878i
$337$	1.39006e13			0.174208			0.0871040	−	0.996199i	$-0.472239\pi$
$337$	1.39006e13			0.174208			0.0871040	+	0.996199i	$0.472239\pi$
$338$	−4.78988e13	−	2.76544e13i	−0.590585	−	0.340974i
$339$	2.28494e12	−	4.21583e11i	0.0277189	−	0.00511428i
$340$	−1.13475e13	−	1.96545e13i	−0.135446	−	0.234600i
$341$	−1.10872e14	+	1.92035e14i	−1.30218	+	2.25544i
$342$	−8.70648e11	−	7.07366e11i	−0.0100623	−	0.00817524i
$343$	8.72603e13	−	1.07993e13i	0.992429	−	0.122823i
$344$			3.62520e13i			0.405752i
$345$	−1.27899e14	−	1.49995e14i	−1.40884	−	1.65223i
$346$	7.17998e13	−	4.14536e13i	0.778404	−	0.449412i
$347$	−1.99817e13	+	1.15364e13i	−0.213216	+	0.123100i	−0.602805	−	0.797888i	$-0.705950\pi$
$347$	−1.99817e13	+	1.15364e13i	−0.213216	+	0.123100i	0.389589	+	0.920989i	$0.372617\pi$
$348$	−5.03505e13	−	5.90492e13i	−0.528832	−	0.620195i
$349$			4.44997e13i			0.460063i	0.973183	+	0.230031i	$0.0738829\pi$
$349$			4.44997e13i			0.460063i	−0.973183	+	0.230031i	$0.926117\pi$
$350$	−2.64065e13	−	1.38334e13i	−0.268743	−	0.140784i
$351$	1.60766e13	−	9.79831e12i	0.161066	−	0.0981662i
$352$	−1.63539e13	+	2.83257e13i	−0.161301	+	0.279381i
$353$	−6.54774e13	−	1.13410e14i	−0.635815	−	1.10126i	−0.986342	−	0.164711i	$-0.947331\pi$
$353$	−6.54774e13	−	1.13410e14i	−0.635815	−	1.10126i	0.350527	−	0.936553i	$-0.386003\pi$
$354$	6.03901e13	−	1.11423e13i	0.577362	−	0.106526i
$355$	−4.12670e13	−	2.38255e13i	−0.388460	−	0.224278i
$356$	−4.49500e13			−0.416634
$357$	−1.10060e13	−	4.84216e13i	−0.100451	−	0.441941i
$358$	−1.36493e14			−1.22675
$359$	−4.36364e11	−	2.51935e11i	−0.00386216	−	0.00222982i	0.498068	−	0.867138i	$-0.334043\pi$
$359$	−4.36364e11	−	2.51935e11i	−0.00386216	−	0.00222982i	−0.501930	+	0.864908i	$0.667376\pi$
$360$	−4.78797e13	−	7.66259e12i	−0.417338	−	0.0667900i
$361$	−5.82255e13	−	1.00850e14i	−0.499832	−	0.865734i
$362$	5.39482e13	−	9.34410e13i	0.456121	−	0.790024i
$363$	2.63705e14	+	9.36223e13i	2.19600	+	0.779638i
$364$	−4.71799e11	−	1.14884e13i	−0.00386990	−	0.0942324i
$365$			6.51223e13i			0.526161i
$366$	8.28248e13	−	7.06236e13i	0.659196	−	0.562087i
$367$	8.98706e13	−	5.18868e13i	0.704619	−	0.406812i	−0.104447	−	0.994530i	$-0.533307\pi$
$367$	8.98706e13	−	5.18868e13i	0.704619	−	0.406812i	0.809065	+	0.587719i	$0.199974\pi$
$368$	−5.09139e13	+	2.93952e13i	−0.393254	+	0.227046i
$369$	1.72978e14	−	6.60801e13i	1.31627	−	0.502835i
$370$		−	1.23545e14i		−	0.926224i
$371$	8.63821e12	+	2.10341e14i	0.0638068	+	1.55370i
$372$	−3.28019e13	+	9.23929e13i	−0.238733	+	0.672439i
$373$	−1.03273e14	+	1.78873e14i	−0.740605	+	1.28276i	0.211616	+	0.977353i	$0.432127\pi$
$373$	−1.03273e14	+	1.78873e14i	−0.740605	+	1.28276i	−0.952220	+	0.305412i	$0.901206\pi$
$374$	4.13802e13	+	7.16726e13i	0.292414	+	0.506476i
$375$	−1.77841e13	−	9.63881e13i	−0.123840	−	0.671199i
$376$	3.07447e13	+	1.77504e13i	0.210978	+	0.121808i
$377$	−4.54661e13			−0.307475
$378$	−9.51223e13	−	4.69854e13i	−0.633983	−	0.313154i
$379$	−1.38083e14			−0.907038			−0.453519	−	0.891247i	$-0.649832\pi$
$379$	−1.38083e14			−0.907038			−0.453519	+	0.891247i	$0.649832\pi$
$380$	1.46593e12	+	8.46357e11i	0.00949084	+	0.00547954i
$381$	9.97691e12	+	5.40739e13i	0.0636662	+	0.345065i
$382$	6.04491e13	+	1.04701e14i	0.380225	+	0.658570i
$383$	8.41883e13	−	1.45818e14i	0.521986	−	0.904106i	−0.477687	−	0.878530i	$-0.658525\pi$
$383$	8.41883e13	−	1.45818e14i	0.521986	−	0.904106i	0.999673	−	0.0255758i	$-0.00814191\pi$
$384$	−4.83838e12	+	1.36282e13i	−0.0295718	+	0.0832947i
$385$	3.20731e14	+	1.68019e14i	1.93244	+	1.01233i
$386$		−	2.24343e13i		−	0.133255i
$387$	1.83078e14	−	6.99383e13i	1.07207	−	0.409548i
$388$	−1.43451e13	+	8.28215e12i	−0.0828189	+	0.0478155i
$389$	−6.03568e13	+	3.48470e13i	−0.343560	+	0.198355i	−0.661845	−	0.749640i	$-0.730226\pi$
$389$	−6.03568e13	+	3.48470e13i	−0.343560	+	0.198355i	0.318285	+	0.947995i	$0.396893\pi$
$390$	−2.16175e13	+	1.84329e13i	−0.121325	+	0.103452i
$391$			1.48757e14i			0.823200i
$392$	−5.32671e13	+	3.68885e13i	−0.290660	+	0.201288i
$393$	−1.38002e14	−	4.89942e13i	−0.742549	−	0.263624i
$394$	1.15175e13	−	1.99489e13i	0.0611125	−	0.105850i
$395$	−7.31742e13	−	1.26741e14i	−0.382890	−	0.663185i
$396$	1.74599e14	+	2.79426e13i	0.900989	+	0.144193i
$397$	1.09756e14	+	6.33676e13i	0.558573	+	0.322492i	0.752573	−	0.658509i	$-0.228813\pi$
$397$	1.09756e14	+	6.33676e13i	0.558573	+	0.322492i	−0.194000	+	0.981002i	$0.562146\pi$
$398$	3.53490e13			0.177427
$399$	2.51668e12	+	2.71724e12i	0.0124588	+	0.0134517i
$400$	2.19675e13			0.107263
$401$	−7.77840e13	−	4.49086e13i	−0.374625	−	0.216290i	0.300852	−	0.953671i	$-0.402729\pi$
$401$	−7.77840e13	−	4.49086e13i	−0.374625	−	0.216290i	−0.675477	+	0.737381i	$0.736062\pi$
$402$	−3.58289e13	+	6.61061e12i	−0.170212	+	0.0314049i
$403$	2.87213e13	+	4.97468e13i	0.134594	+	0.233124i
$404$	7.39889e13	−	1.28152e14i	0.342034	−	0.592420i
$405$	5.36737e13	+	2.56582e14i	0.244770	+	1.17010i
$406$	1.37100e14	+	2.16439e14i	0.616801	+	0.973738i
$407$			4.50523e14i			1.99962i
$408$	2.37423e13	+	2.78441e13i	0.103966	+	0.121928i
$409$	−3.59439e13	+	2.07522e13i	−0.155291	+	0.0896574i	−0.575632	−	0.817709i	$-0.695244\pi$
$409$	−3.59439e13	+	2.07522e13i	−0.155291	+	0.0896574i	0.420341	+	0.907366i	$0.361911\pi$
$410$	−2.41979e14	+	1.39706e14i	−1.03149	+	0.595532i
$411$	−1.54178e14	−	1.80814e14i	−0.648474	−	0.760506i
$412$			4.80246e13i			0.199310i
$413$	−2.02578e14	+	8.31937e12i	−0.829595	+	0.0340695i
$414$	2.46675e14	+	2.00413e14i	0.996833	+	0.809885i
$415$	−7.68687e13	+	1.33140e14i	−0.306538	+	0.530940i
$416$	4.23647e12	+	7.33779e12i	0.0166721	+	0.0288770i
$417$	−1.85084e14	+	3.41490e13i	−0.718822	+	0.132626i
$418$	−5.34572e12	−	3.08635e12i	−0.0204897	−	0.0118298i
$419$	3.07167e14			1.16198			0.580988	−	0.813912i	$-0.302666\pi$
$419$	3.07167e14			1.16198			0.580988	+	0.813912i	$0.302666\pi$
$420$	1.52935e14	+	4.73254e13i	0.571001	+	0.176695i
$421$	−3.39983e14			−1.25287			−0.626435	−	0.779474i	$-0.715487\pi$
$421$	−3.39983e14			−1.25287			−0.626435	+	0.779474i	$0.715487\pi$
$422$	1.01568e14	+	5.86405e13i	0.369436	+	0.213294i
$423$	3.03288e13	−	1.89510e14i	0.108889	−	0.680392i
$424$	−7.75660e13	−	1.34348e14i	−0.274890	−	0.476124i
$425$	2.77921e13	−	4.81374e13i	0.0972261	−	0.168401i
$426$	7.24023e13	+	2.57047e13i	0.250034	+	0.0887688i
$427$	−3.03586e14	+	1.92302e14i	−1.03497	+	0.655589i
$428$			5.81718e13i			0.195782i
$429$	7.88309e13	−	6.72181e13i	0.261928	−	0.223342i
$430$	−2.56107e14	+	1.47863e14i	−0.840127	+	0.485047i
$431$	4.99467e14	−	2.88367e14i	1.61764	−	0.933945i	0.630111	−	0.776505i	$-0.283009\pi$
$431$	4.99467e14	−	2.88367e14i	1.61764	−	0.933945i	0.987529	−	0.157439i	$-0.0503239\pi$
$432$	7.81588e13	−	1.85743e12i	0.249929	−	0.00593953i
$433$		−	1.80461e14i		−	0.569770i	−0.958562	−	0.284885i	$-0.908045\pi$
$433$		−	1.80461e14i		−	0.569770i	0.958562	−	0.284885i	$-0.0919555\pi$
$434$	1.50209e14	−	2.86735e14i	0.468278	−	0.893896i
$435$	2.11793e14	−	5.96556e14i	0.651960	−	1.83637i
$436$	−1.11358e13	+	1.92879e13i	−0.0338491	+	0.0586284i
$437$	−5.54754e12	−	9.60863e12i	−0.0166515	−	0.0288412i
$438$	−1.90514e13	−	1.03257e14i	−0.0564701	−	0.306063i
$439$	−7.83239e13	−	4.52204e13i	−0.229266	−	0.132367i	0.380967	−	0.924588i	$-0.375591\pi$
$439$	−7.83239e13	−	4.52204e13i	−0.229266	−	0.132367i	−0.610233	+	0.792222i	$0.708924\pi$
$440$	−2.66815e14			−0.771294
$441$	2.89056e14	+	1.97840e14i	0.825221	+	0.564810i
$442$	2.14391e13			0.0604483
$443$	−3.42579e14	−	1.97788e14i	−0.953981	−	0.550781i	−0.0596658	−	0.998218i	$-0.519004\pi$
$443$	−3.42579e14	−	1.97788e14i	−0.953981	−	0.550781i	−0.894315	+	0.447437i	$0.852337\pi$
$444$	3.61428e13	+	1.95891e14i	0.0994067	+	0.538775i
$445$	−1.83341e14	−	3.17555e14i	−0.498056	−	0.862659i
$446$	−2.42147e14	+	4.19411e14i	−0.649736	+	1.12538i
$447$	2.20145e13	−	6.20081e13i	0.0583469	−	0.164345i
$448$	2.21563e13	−	4.22942e13i	0.0580054	−	0.110727i
$449$		−	1.55097e14i		−	0.401096i	−0.979684	−	0.200548i	$-0.935728\pi$
$449$		−	1.55097e14i		−	0.401096i	0.979684	−	0.200548i	$-0.0642722\pi$
$450$	−4.23803e13	−	1.10939e14i	−0.108267	−	0.283410i
$451$	8.82406e14	−	5.09457e14i	2.22688	−	1.28569i
$452$	4.89562e12	−	2.82649e12i	0.0122052	−	0.00704670i
$453$	−2.13739e14	+	1.82252e14i	−0.526434	+	0.448883i
$454$		−	1.33162e13i		−	0.0324020i
$455$	7.92367e13	−	5.01914e13i	0.190486	−	0.120661i
$456$	−2.57196e12	−	9.13113e11i	−0.00610882	−	0.00216879i
$457$	2.44644e13	−	4.23735e13i	0.0574109	−	0.0994387i	−0.835892	−	0.548895i	$-0.815049\pi$
$457$	2.44644e13	−	4.23735e13i	0.0574109	−	0.0994387i	0.893302	+	0.449456i	$0.148382\pi$
$458$	2.01251e14	+	3.48578e14i	0.466637	+	0.808238i
$459$	9.48124e13	−	1.73620e14i	0.217218	−	0.397767i
$460$	−4.15332e14	−	2.39792e14i	−0.940216	−	0.542834i
$461$	−3.05686e14			−0.683787			−0.341893	−	0.939739i	$-0.611068\pi$
$461$	−3.05686e14			−0.683787			−0.341893	+	0.939739i	$0.611068\pi$
$462$	−5.57699e14	−	1.72578e14i	−1.23273	−	0.381465i
$463$	2.41549e14			0.527605			0.263803	−	0.964577i	$-0.415023\pi$
$463$	2.41549e14			0.527605			0.263803	+	0.964577i	$0.415023\pi$
$464$	−1.63506e14	−	9.44001e13i	−0.352926	−	0.203762i
$465$	−7.86514e14	+	1.45116e14i	−1.67770	+	0.309545i
$466$	9.31102e13	+	1.61272e14i	0.196279	+	0.339966i
$467$	−1.88438e14	+	3.26385e14i	−0.392579	+	0.679966i	−0.992789	−	0.119876i	$-0.961750\pi$
$467$	−1.88438e14	+	3.26385e14i	−0.392579	+	0.679966i	0.600210	+	0.799842i	$0.295084\pi$
$468$	2.88838e13	−	3.55511e13i	0.0594705	−	0.0731982i
$469$	1.20187e14	−	4.93580e12i	0.244573	−	0.0100440i
$470$			2.89600e14i			0.582452i
$471$	1.98540e13	+	2.32840e13i	0.0394668	+	0.0462852i
$472$	1.29389e14	−	7.47030e13i	0.254225	−	0.146777i
$473$	9.33927e14	−	5.39203e14i	1.81375	−	1.04717i
$474$	1.53102e14	+	1.79552e14i	0.293899	+	0.344675i
$475$			4.14577e12i			0.00786666i
$476$	−6.46484e13	−	1.02060e14i	−0.121260	−	0.191433i
$477$	−5.28836e14	+	6.50908e14i	−0.980550	+	1.20689i
$478$	6.19003e12	−	1.07214e13i	0.0113459	−	0.0196517i
$479$	−2.94522e14	−	5.10127e14i	−0.533669	−	0.924342i	−0.999227	−	0.0393242i	$-0.987480\pi$
$479$	−2.94522e14	−	5.10127e14i	−0.533669	−	0.924342i	0.465558	−	0.885018i	$-0.345854\pi$
$480$	−1.16013e14	+	2.14050e13i	−0.207816	+	0.0383432i
$481$	1.01072e14	+	5.83541e13i	0.178992	+	0.103341i
$482$	−7.01503e13			−0.122821
$483$	−7.13032e14	−	7.69857e14i	−1.23424	−	1.33260i
$484$	6.80815e14			1.16514
$485$	−1.17021e14	−	6.75620e13i	−0.198008	−	0.114320i
$486$	−1.60167e14	−	3.91130e14i	−0.267961	−	0.654367i
$487$	−2.34045e14	−	4.05378e14i	−0.387160	−	0.670580i	0.604906	−	0.796297i	$-0.293210\pi$
$487$	−2.34045e14	−	4.05378e14i	−0.387160	−	0.670580i	−0.992066	+	0.125716i	$0.959877\pi$
$488$	1.32409e14	−	2.29340e14i	0.216576	−	0.375120i
$489$	−4.05797e14	−	1.44069e14i	−0.656311	−	0.233008i
$490$	−4.77868e14	−	2.25853e14i	−0.764239	−	0.361199i
$491$		−	2.93212e13i		−	0.0463696i	−0.999731	−	0.0231848i	$-0.992619\pi$
$491$		−	2.93212e13i		−	0.0463696i	0.999731	−	0.0231848i	$-0.00738062\pi$
$492$	3.42806e14	−	2.92306e14i	0.536093	−	0.457120i
$493$	−4.13718e14	+	2.38860e14i	−0.639804	+	0.369391i
$494$	−1.38481e12	+	7.99520e11i	−0.00211783	+	0.00122273i
$495$	5.14747e14	+	1.34745e15i	0.778511	+	2.03791i
$496$			2.38534e14i			0.356780i
$497$	−2.24695e14	−	1.17709e14i	−0.332379	−	0.174121i
$498$	8.29317e13	−	2.33593e14i	0.121327	−	0.341742i
$499$	3.06894e14	−	5.31557e14i	0.444054	−	0.769124i	−0.553932	−	0.832562i	$-0.686873\pi$
$499$	3.06894e14	−	5.31557e14i	0.444054	−	0.769124i	0.997986	+	0.0634378i	$0.0202065\pi$
$500$	−1.19233e14	−	2.06517e14i	−0.170632	−	0.295543i
$501$	4.69859e13	+	2.54659e14i	0.0665058	+	0.360455i
$502$	−7.46030e14	−	4.30721e14i	−1.04445	−	0.603011i
$503$	5.59756e14			0.775130			0.387565	−	0.921842i	$-0.373316\pi$
$503$	5.59756e14			0.775130			0.387565	+	0.921842i	$0.373316\pi$
$504$	−2.56336e14	−	3.02974e13i	−0.351109	−	0.0414990i
$505$	1.20713e15			1.63551
$506$	1.51456e15	+	8.74434e14i	2.02983	+	1.17192i
$507$	1.31993e14	+	7.15388e14i	0.174987	+	0.948413i
$508$	6.68898e13	+	1.15857e14i	0.0877223	+	0.151939i
$509$	−2.39005e13	+	4.13969e13i	−0.0310070	+	0.0537057i	−0.881112	−	0.472907i	$-0.843205\pi$
$509$	−2.39005e13	+	4.13969e13i	−0.0310070	+	0.0537057i	0.850105	+	0.526612i	$0.176538\pi$
$510$	−9.98690e13	+	2.81300e14i	−0.128172	+	0.361022i
$511$	1.42247e13	+	3.46373e14i	0.0180604	+	0.439773i
$512$			3.51844e13i			0.0441942i
$513$	3.50540e11	+	1.47504e13i	0.000435604	+	0.0183298i
$514$	1.10549e14	−	6.38254e13i	0.135912	−	0.0784687i
$515$	−3.39276e14	+	1.95881e14i	−0.412680	+	0.238261i
$516$	3.62821e14	−	3.09373e14i	0.436636	−	0.372314i
$517$		−	1.05606e15i		−	1.25745i
$518$	−2.69860e13	−	6.57112e14i	−0.0317925	−	0.774152i
$519$	−1.02762e15	−	3.64832e14i	−1.19788	−	0.425277i
$520$	−3.45592e13	+	5.98583e13i	−0.0398607	+	0.0690408i
$521$	2.17238e14	+	3.76268e14i	0.247930	+	0.429427i	0.962951	−	0.269675i	$-0.0869164\pi$
$521$	2.17238e14	+	3.76268e14i	0.247930	+	0.429427i	−0.715021	+	0.699103i	$0.753583\pi$
$522$	−1.61294e14	+	1.00785e15i	−0.182151	+	1.13817i
$523$	−5.40736e14	−	3.12194e14i	−0.604263	−	0.348871i	0.166454	−	0.986049i	$-0.446768\pi$
$523$	−5.40736e14	−	3.12194e14i	−0.604263	−	0.348871i	−0.770717	+	0.637178i	$0.780102\pi$
$524$	−3.56283e14			−0.393979
$525$	8.69036e13	+	3.82339e14i	0.0950958	+	0.418381i
$526$	−1.06032e15			−1.14820
$527$	5.22699e14	+	3.01780e14i	0.560136	+	0.323395i
$528$	4.23057e14	−	7.80560e13i	0.448654	−	0.0827789i
$529$	1.09534e15	+	1.89719e15i	1.14959	+	1.99115i
$530$	6.32748e14	−	1.09595e15i	0.657224	−	1.13834i
$531$	−6.26883e14	−	5.09316e14i	−0.644416	−	0.523561i
$532$	7.98189e12	+	4.18141e12i	0.00812067	+	0.00425411i
$533$		−	2.63950e14i		−	0.265780i
$534$	3.83602e14	+	4.49874e14i	0.382299	+	0.448347i
$535$	−4.10963e14	+	2.37270e14i	−0.405375	+	0.234043i
$536$	−7.67655e13	+	4.43206e13i	−0.0749480	+	0.0432712i
$537$	1.16483e15	+	1.36607e15i	1.12565	+	1.32012i
$538$			7.41697e14i			0.709454i
$539$	1.74261e15	+	8.23601e14i	1.64991	+	0.779792i
$540$	3.31914e14	+	5.44588e14i	0.311071	+	0.510390i
$541$	−2.37517e14	+	4.11391e14i	−0.220348	+	0.381654i	−0.954914	−	0.296884i	$-0.904053\pi$
$541$	−2.37517e14	+	4.11391e14i	−0.220348	+	0.381654i	0.734566	+	0.678538i	$0.237386\pi$
$542$	−1.90173e14	−	3.29390e14i	−0.174644	−	0.302492i
$543$	−1.39558e15	+	2.57491e14i	−1.26869	+	0.234080i
$544$	7.70996e13	+	4.45135e13i	0.0693838	+	0.0400588i
$545$	−1.81682e14			−0.161857
$546$	−1.10953e14	+	1.02763e14i	−0.0978541	+	0.0906312i
$547$	1.90345e15			1.66192			0.830961	−	0.556330i	$-0.187791\pi$
$547$	1.90345e15			1.66192			0.830961	+	0.556330i	$0.187791\pi$
$548$	−5.00671e14	−	2.89062e14i	−0.432772	−	0.249861i
$549$	−1.41365e15	−	2.26238e14i	−1.20974	−	0.193605i
$550$	−3.26739e14	−	5.65929e14i	−0.276826	−	0.479476i
$551$	1.78155e13	−	3.08573e13i	0.0149439	−	0.0258836i
$552$	7.28694e14	+	2.58706e14i	0.605174	+	0.214853i
$553$	−4.16884e14	−	6.58130e14i	−0.342789	−	0.541157i
$554$		−	1.69482e15i		−	1.37981i
$555$	−1.23648e15	+	1.05433e15i	−0.996725	+	0.849894i
$556$	−3.96554e14	+	2.28950e14i	−0.316512	+	0.182739i
$557$	8.48839e14	−	4.90078e14i	0.670844	−	0.387312i	−0.125552	−	0.992087i	$-0.540070\pi$
$557$	8.48839e14	−	4.90078e14i	0.670844	−	0.387312i	0.796397	+	0.604775i	$0.206737\pi$
$558$	1.20463e15	−	4.60186e14i	0.942682	−	0.360118i
$559$		−	2.79361e14i		−	0.216472i
$560$	3.89164e14	−	1.59820e13i	0.298606	−	0.0122630i
$561$	3.64185e14	−	1.02580e15i	0.276711	−	0.779410i
$562$	−2.20774e14	+	3.82392e14i	−0.166111	+	0.287713i
$563$	−9.88073e13	−	1.71139e14i	−0.0736195	−	0.127513i	0.826866	−	0.562400i	$-0.190122\pi$
$563$	−9.88073e13	−	1.71139e14i	−0.0736195	−	0.127513i	−0.900485	+	0.434887i	$0.856788\pi$
$564$	−8.47217e13	−	4.59184e14i	−0.0625115	−	0.338807i
$565$	3.99362e13	+	2.30572e13i	0.0291810	+	0.0168477i
$566$	2.05870e14			0.148972
$567$	3.41525e14	+	1.35299e15i	0.244746	+	0.969587i
$568$	1.86923e14			0.132662
$569$	−7.62649e14	−	4.40315e14i	−0.536052	−	0.309490i	0.207425	−	0.978251i	$-0.433492\pi$
$569$	−7.62649e14	−	4.40315e14i	−0.536052	−	0.309490i	−0.743477	+	0.668761i	$0.766825\pi$
$570$	−4.03961e12	−	2.18943e13i	−0.00281208	−	0.0152412i
$571$	6.27561e14	+	1.08697e15i	0.432670	+	0.749407i	0.997102	−	0.0760727i	$-0.0242381\pi$
$571$	6.27561e14	+	1.08697e15i	0.432670	+	0.749407i	−0.564432	+	0.825480i	$0.690905\pi$
$572$	1.26025e14	−	2.18281e14i	0.0860552	−	0.149052i
$573$	5.32010e14	−	1.49851e15i	0.359807	−	1.01346i
$574$	−1.25652e15	+	7.95927e14i	−0.841694	+	0.533160i
$575$		−	1.17459e15i		−	0.779316i
$576$	1.77686e14	−	6.78787e13i	0.116770	−	0.0446077i
$577$	−5.27085e14	+	3.04313e14i	−0.343094	+	0.198086i	−0.661640	−	0.749822i	$-0.730139\pi$
$577$	−5.27085e14	+	3.04313e14i	−0.343094	+	0.198086i	0.318545	+	0.947908i	$0.396806\pi$
$578$	−7.54686e14	+	4.35718e14i	−0.486590	+	0.280933i
$579$	−2.24530e14	+	1.91453e14i	−0.143397	+	0.122273i
$580$		−	1.54014e15i		−	0.974334i
$581$	−3.79768e14	+	7.24939e14i	−0.237985	+	0.454290i
$582$	2.05311e14	+	7.28909e13i	0.127449	+	0.0452477i
$583$	−2.30740e15	+	3.99653e15i	−1.41888	+	2.45757i
$584$	−1.27729e14	−	2.21234e14i	−0.0778072	−	0.134766i
$585$	3.68966e14	+	5.90487e13i	0.222653	+	0.0356330i
$586$	1.85801e14	+	1.07272e14i	0.111074	+	0.0641286i
$587$	−3.00856e15			−1.78176			−0.890879	−	0.454242i	$-0.849910\pi$
$587$	−3.00856e15			−1.78176			−0.890879	+	0.454242i	$0.849910\pi$
$588$	8.23771e14	+	2.18309e14i	0.483316	+	0.128084i
$589$	−4.50168e13			−0.0261662
$590$	1.05550e15	+	6.09393e14i	0.607816	+	0.350922i
$591$	−2.97945e14	+	5.49724e13i	−0.169983	+	0.0313627i
$592$	2.42318e14	+	4.19708e14i	0.136967	+	0.237234i
$593$	−1.36559e15	+	2.36527e15i	−0.764750	+	1.32459i	0.175629	+	0.984457i	$0.443804\pi$
$593$	−1.36559e15	+	2.36527e15i	−0.764750	+	1.32459i	−0.940379	+	0.340129i	$0.889529\pi$
$594$	−1.21037e15	−	1.98591e15i	−0.671571	−	1.10188i
$595$	4.57329e14	−	8.72995e14i	0.251411	−	0.479920i
$596$		−	1.60088e14i		−	0.0871976i
$597$	−3.01668e14	−	3.53785e14i	−0.162806	−	0.190933i
$598$	3.92348e14	−	2.26522e14i	0.209805	−	0.121131i
$599$	6.56465e14	−	3.79010e14i	0.347828	−	0.200818i	−0.315900	−	0.948792i	$-0.602307\pi$
$599$	6.56465e14	−	3.79010e14i	0.347828	−	0.200818i	0.663728	+	0.747974i	$0.268973\pi$
$600$	−1.87470e14	−	2.19858e14i	−0.0984236	−	0.115428i
$601$		−	1.88416e15i		−	0.980185i	−0.871670	−	0.490093i	$-0.836963\pi$
$601$		−	1.88416e15i		−	0.980185i	0.871670	−	0.490093i	$-0.163037\pi$
$602$	−1.32989e15	+	8.42399e14i	−0.685541	+	0.434247i
$603$	3.71924e14	+	3.02172e14i	0.189980	+	0.154351i
$604$	−3.41698e14	+	5.91838e14i	−0.172957	+	0.299571i
$605$	2.77689e15	+	4.80971e15i	1.39285	+	2.41248i
$606$	−1.91401e15	+	3.53144e14i	−0.951360	+	0.175531i
$607$	7.54997e14	+	4.35898e14i	0.371884	+	0.214707i	0.674281	−	0.738475i	$-0.264454\pi$
$607$	7.54997e14	+	4.35898e14i	0.371884	+	0.214707i	−0.302397	+	0.953182i	$0.597787\pi$
$608$	−6.64010e12			−0.00324119
$609$	9.96180e14	−	3.21923e15i	0.481884	−	1.55724i
$610$	2.16027e15			1.03560
$611$	−2.36921e14	−	1.36787e14i	−0.112558	−	0.0649856i
$612$	7.60568e13	−	4.75241e14i	0.0358101	−	0.223759i
$613$	1.24072e14	+	2.14898e14i	0.0578948	+	0.100277i	0.893520	−	0.449023i	$-0.148228\pi$
$613$	1.24072e14	+	2.14898e14i	0.0578948	+	0.100277i	−0.835625	+	0.549300i	$0.814895\pi$
$614$	1.21988e15	−	2.11289e15i	0.564145	−	0.977128i
$615$	3.46326e15	+	1.22955e15i	1.58735	+	0.563551i
$616$	−1.41914e15	+	5.82805e13i	−0.644659	+	0.0264746i
$617$		−	1.82843e15i		−	0.823208i	−0.911363	−	0.411604i	$-0.864969\pi$
$617$		−	1.82843e15i		−	0.823208i	0.911363	−	0.411604i	$-0.135031\pi$
$618$	4.80646e14	−	4.09840e14i	0.214481	−	0.182885i
$619$	3.39171e15	−	1.95821e15i	1.50010	−	0.866083i	0.500101	−	0.865967i	$-0.333296\pi$
$619$	3.39171e15	−	1.95821e15i	1.50010	−	0.866083i	1.00000		0.000116098i	$-3.69550e-5\pi$
$620$	−1.68515e15	+	9.72923e14i	−0.738729	+	0.426505i
$621$	−9.93160e13	−	4.17911e15i	−0.0431534	−	1.81585i
$622$		−	1.67769e15i		−	0.722543i
$623$	−1.04452e15	−	1.64897e15i	−0.445894	−	0.703927i
$624$	3.72850e13	−	1.05020e14i	0.0157768	−	0.0444384i
$625$	1.48412e15	−	2.57056e15i	0.622483	−	1.07817i
$626$	1.07514e15	+	1.86219e15i	0.446998	+	0.774223i
$627$	1.47310e13	+	7.98405e13i	0.00607099	+	0.0329042i
$628$	6.44728e13	+	3.72234e13i	0.0263390	+	0.0152068i
$629$	1.22628e15			0.496603
$630$	−8.31497e14	−	1.93450e15i	−0.333801	−	0.776597i
$631$	−5.38547e14			−0.214320			−0.107160	−	0.994242i	$-0.534176\pi$
$631$	−5.38547e14			−0.214320			−0.107160	+	0.994242i	$0.534176\pi$
$632$	4.97175e14	+	2.87044e14i	0.196140	+	0.113241i
$633$	−2.79887e14	−	1.51696e15i	−0.109462	−	0.593273i
$634$	3.63681e14	+	6.29914e14i	0.141004	+	0.244225i
$635$	−5.45657e14	+	9.45105e14i	−0.209732	+	0.363266i
$636$	−6.82655e14	+	1.92283e15i	−0.260128	+	0.732701i
$637$	4.10481e14	−	2.84266e14i	0.155070	−	0.107389i
$638$			5.61634e15i			2.10349i
$639$	−3.60617e14	−	9.43989e14i	−0.133903	−	0.350519i
$640$	−2.48565e14	+	1.43509e14i	−0.0915060	+	0.0528310i
$641$	1.66600e15	−	9.61863e14i	0.608071	−	0.351070i	−0.164139	−	0.986437i	$-0.552485\pi$
$641$	1.66600e15	−	9.61863e14i	0.608071	−	0.351070i	0.772210	+	0.635367i	$0.219151\pi$
$642$	5.82203e14	−	4.96437e14i	0.210684	−	0.179647i
$643$		−	3.03288e15i		−	1.08817i	−0.839031	−	0.544083i	$-0.816878\pi$
$643$		−	3.03288e15i		−	1.08817i	0.839031	−	0.544083i	$-0.183122\pi$
$644$	−2.26145e15	−	1.18469e15i	−0.804479	−	0.421436i
$645$	3.66547e15	+	1.30134e15i	1.29286	+	0.459000i
$646$	−8.40071e12	+	1.45505e13i	−0.00293790	+	0.00508860i
$647$	4.93005e14	+	8.53909e14i	0.170953	+	0.296100i	0.938753	−	0.344590i	$-0.111982\pi$
$647$	4.93005e14	+	8.53909e14i	0.170953	+	0.296100i	−0.767800	+	0.640689i	$0.778649\pi$
$648$	−6.85595e14	−	7.66388e14i	−0.235725	−	0.263503i
$649$	−3.84901e15	−	2.22223e15i	−1.31221	−	0.757605i
$650$	−1.69284e14			−0.0572258
$651$	−4.15162e15	+	9.43641e14i	−1.39162	+	0.316309i
$652$	−1.04766e15			−0.348223
$653$	−4.92267e15	−	2.84210e15i	−1.62247	−	0.936736i	−0.986255	−	0.165228i	$-0.947164\pi$
$653$	−4.92267e15	−	2.84210e15i	−1.62247	−	0.936736i	−0.636220	−	0.771508i	$-0.719503\pi$
$654$	2.88072e14	−	5.31507e13i	0.0941507	−	0.0173713i
$655$	−1.45319e15	−	2.51701e15i	−0.470974	−	0.815750i
$656$	5.48033e14	−	9.49222e14i	0.176131	−	0.305068i
$657$	−8.70843e14	+	1.07186e15i	−0.277543	+	0.341609i
$658$	6.32574e13	+	1.54033e15i	0.0199926	+	0.486822i
$659$		−	3.22505e15i		−	1.01080i	−0.862884	−	0.505402i	$-0.831344\pi$
$659$		−	3.22505e15i		−	1.01080i	0.862884	−	0.505402i	$-0.168656\pi$
$660$	2.27699e15	+	2.67037e15i	0.707732	+	0.830003i
$661$	−4.99102e15	+	2.88157e15i	−1.53844	+	0.888221i	−0.539513	+	0.841977i	$0.681392\pi$
$661$	−4.99102e15	+	2.88157e15i	−1.53844	+	0.888221i	−0.998930	+	0.0462433i	$0.985275\pi$
$662$	−9.60057e14	+	5.54289e14i	−0.293480	+	0.169441i
$663$	−1.82960e14	−	2.14569e14i	−0.0554668	−	0.0650494i
$664$		−	6.03074e14i		−	0.181320i
$665$	3.01617e12	+	7.34441e13i	0.000899367	+	0.0218997i
$666$	1.65210e15	−	2.03346e15i	0.488571	−	0.601349i
$667$	−5.04753e15	+	8.74257e15i	−1.48043	+	2.56417i
$668$	3.15015e14	+	5.45622e14i	0.0916349	+	0.158716i
$669$	6.26407e15	−	1.15575e15i	1.80723	−	0.333442i
$670$	−6.26218e14	−	3.61547e14i	−0.179190	−	0.103455i
$671$	−7.87770e15			−2.23576
$672$	−6.12375e14	+	1.39190e14i	−0.172380	+	0.0391811i
$673$	2.19533e15			0.612939			0.306469	−	0.951881i	$-0.400852\pi$
$673$	2.19533e15			0.612939			0.306469	+	0.951881i	$0.400852\pi$
$674$	−3.85224e14	−	2.22409e14i	−0.106680	−	0.0615919i
$675$	−7.48641e14	+	1.37091e15i	−0.205638	+	0.376562i
$676$	8.84939e14	+	1.53276e15i	0.241105	+	0.417607i
$677$	−1.93052e15	+	3.34375e15i	−0.521718	+	0.903642i	0.477963	+	0.878380i	$0.341375\pi$
$677$	−1.93052e15	+	3.34375e15i	−0.521718	+	0.903642i	−0.999681	+	0.0252619i	$0.991958\pi$
$678$	−7.00675e13	−	2.48758e13i	−0.0187825	−	0.00666828i
$679$	−6.37169e14	−	3.33788e14i	−0.169422	−	0.0887539i
$680$			7.26241e14i			0.191550i
$681$	−1.33273e14	+	1.13640e14i	−0.0348684	+	0.0297318i
$682$	6.14513e15	−	3.54789e15i	1.59484	−	0.920781i
$683$	8.18819e14	−	4.72745e14i	0.210802	−	0.121706i	−0.390882	−	0.920441i	$-0.627830\pi$
$683$	8.18819e14	−	4.72745e14i	0.210802	−	0.121706i	0.601684	+	0.798734i	$0.294497\pi$
$684$	1.28103e13	+	3.35335e13i	0.00327152	+	0.00856387i
$685$		−	4.71607e15i		−	1.19476i
$686$	−2.59102e15	−	1.09689e15i	−0.651160	−	0.275663i
$687$	1.77121e15	−	4.98894e15i	0.441577	−	1.24379i
$688$	5.80032e14	−	1.00464e15i	0.143455	−	0.248471i
$689$	5.97731e14	+	1.03530e15i	0.146656	+	0.254016i
$690$	1.14451e15	+	6.20316e15i	0.278581	+	1.50988i
$691$	4.38313e15	+	2.53060e15i	1.05841	+	0.611075i	0.924993	−	0.379985i	$-0.124071\pi$
$691$	4.38313e15	+	2.53060e15i	1.05841	+	0.611075i	0.133420	+	0.991060i	$0.457404\pi$
$692$	−2.65303e15			−0.635564
$693$	3.03216e15	+	7.05441e15i	0.720642	+	1.67659i
$694$	7.38331e14			0.174090
$695$	−3.23490e15	−	1.86767e15i	−0.756737	−	0.436902i
$696$	4.50566e14	+	2.44203e15i	0.104570	+	0.566760i
$697$	−1.38669e15	−	2.40181e15i	−0.319300	−	0.553043i
$698$	7.11995e14	−	1.23321e15i	0.162657	−	0.281730i
$699$	8.19459e14	−	2.30816e15i	0.185739	−	0.523169i
$700$	5.10465e14	+	8.05866e14i	0.114796	+	0.181227i
$701$		−	4.96333e15i		−	1.10745i	−0.832700	−	0.553724i	$-0.813206\pi$
$701$		−	4.96333e15i		−	1.10745i	0.832700	−	0.553724i	$-0.186794\pi$
$702$	−6.02300e14	+	1.43136e13i	−0.133339	+	0.00316879i
$703$	−7.92085e13	+	4.57310e13i	−0.0173987	+	0.0100452i
$704$	9.06424e14	−	5.23324e14i	0.197552	−	0.114057i
$705$	2.89841e15	−	2.47143e15i	0.626786	−	0.534452i
$706$			4.19056e15i			0.899178i
$707$	6.42051e15	−	2.63675e14i	1.36698	−	0.0561387i
$708$	−1.85186e15	−	6.57458e14i	−0.391223	−	0.138895i
$709$	−3.12070e14	+	5.40521e14i	−0.0654180	+	0.113307i	−0.896879	−	0.442275i	$-0.854171\pi$
$709$	−3.12070e14	+	5.40521e14i	−0.0654180	+	0.113307i	0.831461	+	0.555583i	$0.187505\pi$
$710$	7.62416e14	+	1.32054e15i	0.158588	+	0.274683i
$711$	4.90450e14	−	3.06458e15i	0.101231	−	0.632540i
$712$	1.24569e15	+	7.19200e14i	0.255135	+	0.147302i
$713$	1.27543e16			2.59217
$714$	−4.69739e14	+	1.51800e15i	−0.0947364	+	0.306147i
$715$	2.05610e15			0.411492
$716$	3.78262e15	+	2.18389e15i	0.751226	+	0.433720i
$717$	−1.60129e14	+	2.95446e13i	−0.0315584	+	0.00582268i
$718$	8.06192e12	+	1.39637e13i	0.00157672	+	0.00273096i
$719$	−4.60261e15	+	7.97195e15i	−0.893296	+	1.54723i	−0.0573959	+	0.998351i	$0.518280\pi$
$719$	−4.60261e15	+	7.97195e15i	−0.893296	+	1.54723i	−0.835900	+	0.548882i	$0.815054\pi$
$720$	1.20428e15	+	9.78427e14i	0.231952	+	0.188451i
$721$	−1.76176e15	+	1.11596e15i	−0.336746	+	0.213307i
$722$			3.72644e15i			0.706869i
$723$	5.98661e14	+	7.02087e14i	0.112699	+	0.132169i
$724$	−2.99011e15	+	1.72634e15i	−0.558632	+	0.322526i
$725$	3.26673e15	−	1.88605e15i	0.605696	−	0.349699i
$726$	−5.81005e15	−	6.81382e15i	−1.06913	−	1.25383i
$727$			6.74923e15i			1.23258i	0.787519	+	0.616290i	$0.211365\pi$
$727$			6.74923e15i			1.23258i	−0.787519	+	0.616290i	$0.788635\pi$
$728$	−1.70739e14	+	3.25923e14i	−0.0309464	+	0.0590735i
$729$	−2.54770e15	+	4.94089e15i	−0.458297	+	0.888799i
$730$	1.04196e15	−	1.80472e15i	0.186026	−	0.322207i
$731$	−1.46765e15	−	2.54205e15i	−0.260062	−	0.450441i
$732$	−3.42528e15	+	6.31982e14i	−0.602401	+	0.111146i
$733$	7.82520e15	+	4.51788e15i	1.36591	+	0.788611i	0.990403	−	0.138206i	$-0.0441337\pi$
$733$	7.82520e15	+	4.51788e15i	1.36591	+	0.788611i	0.375511	+	0.926818i	$0.377467\pi$
$734$	−3.32075e15			−0.575319
$735$	1.81770e15	+	6.71007e15i	0.312566	+	1.15384i
$736$	1.88129e15			0.321091
$737$	2.28358e15	+	1.31843e15i	0.386853	+	0.223350i
$738$	−5.85099e15	−	9.36383e14i	−0.983828	−	0.157450i
$739$	3.53044e14	+	6.11490e14i	0.0589229	+	0.102057i	0.893982	−	0.448103i	$-0.147900\pi$
$739$	3.53044e14	+	6.11490e14i	0.0589229	+	0.102057i	−0.835059	+	0.550160i	$0.814567\pi$
$740$	−1.97672e15	+	3.42378e15i	−0.327470	+	0.567194i
$741$	1.98198e13	+	7.03654e12i	0.00325911	+	0.00115707i
$742$	3.12607e15	−	5.96736e15i	0.510244	−	0.974004i
$743$			1.11691e16i			1.80958i	0.425854	+	0.904792i	$0.359974\pi$
$743$			1.11691e16i			1.80958i	−0.425854	+	0.904792i	$0.640026\pi$
$744$	2.38732e15	−	2.03564e15i	0.383937	−	0.327378i
$745$	1.13096e15	−	6.52962e14i	0.180547	−	0.104239i
$746$	5.72395e15	−	3.30472e15i	0.907052	−	0.523687i
$747$	−3.04561e15	+	1.16347e15i	−0.479083	+	0.183017i
$748$		−	2.64833e15i		−	0.413536i
$749$	−2.13401e15	+	1.35176e15i	−0.330785	+	0.209531i
$750$	−1.04936e15	+	2.95573e15i	−0.161469	+	0.454808i
$751$	4.77158e15	−	8.26462e15i	0.728857	−	1.26242i	−0.228509	−	0.973542i	$-0.573385\pi$
$751$	4.77158e15	−	8.26462e15i	0.728857	−	1.26242i	0.957366	−	0.288876i	$-0.0932816\pi$
$752$	−5.68014e14	−	9.83829e14i	−0.0861313	−	0.149184i
$753$	2.05580e15	+	1.11423e16i	0.309463	+	1.67726i
$754$	1.25999e15	+	7.27457e14i	0.188289	+	0.108709i
$755$	−5.57483e15			−0.827034
$756$	1.88434e15	+	2.82406e15i	0.277517	+	0.415914i
$757$	−1.02166e16			−1.49375			−0.746875	−	0.664965i	$-0.768447\pi$
$757$	−1.02166e16			−1.49375			−0.746875	+	0.664965i	$0.768447\pi$
$758$	3.82668e15	+	2.20933e15i	0.555445	+	0.320686i
$759$	−4.17362e15	−	2.26206e16i	−0.601427	−	3.25968i
$760$	−2.70834e13	−	4.69099e13i	−0.00387462	−	0.00671104i
$761$	4.16266e15	−	7.20994e15i	0.591229	−	1.02404i	−0.402839	−	0.915271i	$-0.631976\pi$
$761$	4.16266e15	−	7.20994e15i	0.591229	−	1.02404i	0.994067	−	0.108767i	$-0.0346902\pi$
$762$	5.88695e14	−	1.65817e15i	0.0830114	−	0.233818i
$763$	−9.66333e14	+	3.96849e13i	−0.135283	+	0.00555573i
$764$		−	3.86874e15i		−	0.537720i
$765$	3.66762e15	−	1.40108e15i	0.506112	−	0.193342i
$766$	−4.66619e15	+	2.69403e15i	−0.639299	+	0.369100i
$767$	−9.97088e14	+	5.75669e14i	−0.135631	+	0.0783066i
$768$	3.52137e14	−	3.00262e14i	0.0475581	−	0.0405522i
$769$			6.46333e15i			0.866686i	0.901229	+	0.433343i	$0.142666\pi$
$769$			6.46333e15i			0.866686i	−0.901229	+	0.433343i	$0.857334\pi$
$770$	−6.20006e15	−	9.78796e15i	−0.825461	−	1.30315i
$771$	−1.58221e15	−	5.61725e14i	−0.209153	−	0.0742548i
$772$	−3.58948e14	+	6.21717e14i	−0.0471126	+	0.0816014i
$773$	−8.24239e13	−	1.42762e14i	−0.0107415	−	0.0186049i	0.860605	−	0.509274i	$-0.170086\pi$
$773$	−8.24239e13	−	1.42762e14i	−0.0107415	−	0.0186049i	−0.871346	+	0.490669i	$0.836753\pi$
$774$	−6.19261e15	−	9.91055e14i	−0.801306	−	0.128240i
$775$	−4.12725e15	−	2.38287e15i	−0.530275	−	0.306154i
$776$	5.30058e14			0.0676213
$777$	−6.34630e15	+	5.87786e15i	−0.803905	+	0.744567i
$778$	2.23021e15			0.280516
$779$	1.79140e14	+	1.03426e14i	0.0223736	+	0.0129174i
$780$	8.94008e14	−	1.64949e14i	0.110872	−	0.0204564i
$781$	−2.78025e15	−	4.81553e15i	−0.342376	−	0.593012i
$782$	2.38011e15	−	4.12248e15i	0.291045	−	0.504105i
$783$	1.14633e16	−	6.98665e15i	1.39194	−	0.848358i
$784$	2.06640e15	−	1.70010e14i	0.249158	−	0.0204992i
$785$			6.07303e14i			0.0727147i
$786$	3.04050e15	+	3.56579e15i	0.361511	+	0.423967i
$787$	−1.12739e16	+	6.50899e15i	−1.33111	+	0.768515i	−0.985469	−	0.169853i	$-0.945671\pi$
$787$	−1.12739e16	+	6.50899e15i	−1.33111	+	0.768515i	−0.345637	+	0.938368i	$0.612337\pi$
$788$	−6.38366e14	+	3.68561e14i	−0.0748472	+	0.0432130i
$789$	9.04874e15	+	1.06120e16i	1.05357	+	1.23559i
$790$			4.68315e15i			0.541488i
$791$	2.17449e14	+	1.13913e14i	0.0249682	+	0.0130799i
$792$	−4.39156e15	−	3.56796e15i	−0.500761	−	0.406847i
$793$	−1.02036e15	+	1.76732e15i	−0.115545	+	0.200130i
$794$	−2.02776e15	−	3.51219e15i	−0.228036	−	0.394971i
$795$	−1.63685e16	+	3.02007e15i	−1.82805	+	0.337285i
$796$	−9.79621e14	−	5.65585e14i	−0.108652	−	0.0627301i
$797$	−3.18212e15			−0.350507			−0.175253	−	0.984523i	$-0.556074\pi$
$797$	−3.18212e15			−0.350507			−0.175253	+	0.984523i	$0.556074\pi$
$798$	−2.62683e13	−	1.15569e14i	−0.00287353	−	0.0126423i
$799$	−2.87449e15			−0.312287
$800$	−6.08781e14	−	3.51480e14i	−0.0656850	−	0.0379232i
$801$	1.22884e15	−	7.67842e15i	0.131679	−	0.822797i
$802$	1.43708e15	+	2.48909e15i	0.152940	+	0.264900i
$803$	−3.79963e15	+	6.58115e15i	−0.401611	+	0.695611i
$804$	1.09869e15	+	3.90064e14i	0.115336	+	0.0409475i
$805$	−8.54550e14	−	2.08084e16i	−0.0890964	−	2.16951i
$806$		−	1.83816e15i		−	0.190345i
$807$	7.42314e15	−	6.32962e15i	0.763455	−	0.650988i
$808$	−4.10088e15	+	2.36764e15i	−0.418904	+	0.241854i
$809$	8.54281e15	−	4.93219e15i	0.866730	−	0.500407i	0.000469819	−	1.00000i	$-0.499850\pi$
$809$	8.54281e15	−	4.93219e15i	0.866730	−	0.500407i	0.866260	+	0.499593i	$0.166517\pi$
$810$	2.61787e15	−	7.96939e15i	0.263803	−	0.803078i
$811$		−	6.35863e15i		−	0.636427i	−0.948019	−	0.318213i	$-0.896917\pi$
$811$		−	6.35863e15i		−	0.636427i	0.948019	−	0.318213i	$-0.103083\pi$
$812$	−3.36415e14	−	8.19173e15i	−0.0334439	−	0.814362i
$813$	−1.67371e15	+	4.71432e15i	−0.165265	+	0.465501i
$814$	7.20837e15	−	1.24853e16i	0.706973	−	1.22451i
$815$	−4.27315e15	−	7.40132e15i	−0.416276	−	0.721012i
$816$	−2.12460e14	−	1.15151e15i	−0.0205580	−	0.111423i
$817$	1.89599e14	+	1.09465e14i	0.0182228	+	0.0105210i
$818$	1.32814e15			0.126795
$819$	1.97536e15	+	2.33475e14i	0.187320	+	0.0221401i
$820$	8.94121e15			0.842209
$821$	6.35876e13	+	3.67123e13i	0.00594957	+	0.00343498i	0.502972	−	0.864303i	$-0.332240\pi$
$821$	6.35876e13	+	3.67123e13i	0.00594957	+	0.00343498i	−0.497022	+	0.867738i	$0.665573\pi$
$822$	1.37968e15	+	7.47772e15i	0.128228	+	0.694983i
$823$	−2.94338e15	−	5.09808e15i	−0.271736	−	0.470660i	0.697571	−	0.716516i	$-0.254264\pi$
$823$	−2.94338e15	−	5.09808e15i	−0.271736	−	0.470660i	−0.969306	+	0.245856i	$0.920931\pi$
$824$	7.68394e14	−	1.33090e15i	0.0704667	−	0.122052i
$825$	−2.87562e15	+	8.09973e15i	−0.261960	+	0.737859i
$826$	5.74711e15	+	3.01069e15i	0.520067	+	0.272443i
$827$			4.08106e15i			0.366853i	0.983033	+	0.183427i	$0.0587190\pi$
$827$			4.08106e15i			0.366853i	−0.983033	+	0.183427i	$0.941281\pi$
$828$	−3.62944e15	−	9.50079e15i	−0.324095	−	0.848385i
$829$	1.19798e16	−	6.91655e15i	1.06267	−	0.613535i	0.136504	−	0.990640i	$-0.456413\pi$
$829$	1.19798e16	−	6.91655e15i	1.06267	−	0.613535i	0.926171	+	0.377104i	$0.123080\pi$
$830$	4.26050e15	−	2.45980e15i	0.375431	−	0.216755i
$831$	−1.69623e16	+	1.44635e16i	−1.48484	+	1.26610i
$832$		−	2.71134e14i		−	0.0235780i
$833$	2.24175e15	−	4.74319e15i	0.193660	−	0.409753i
$834$	5.67559e15	+	2.01498e15i	0.487077	+	0.172925i
$835$	−2.56975e15	+	4.45093e15i	−0.219086	+	0.379468i
$836$	9.87632e13	+	1.71063e14i	0.00836490	+	0.0144884i
$837$	−1.48860e16	−	8.12911e15i	−1.25253	−	0.683995i
$838$	−8.51245e15	−	4.91467e15i	−0.711562	−	0.410820i
$839$	−2.21228e15			−0.183717			−0.0918586	−	0.995772i	$-0.529281\pi$
$839$	−2.21228e15			−0.183717			−0.0918586	+	0.995772i	$0.529281\pi$
$840$	−3.48106e15	−	3.75849e15i	−0.287194	−	0.310082i
$841$	−2.02189e16			−1.65722
$842$	9.42189e15	+	5.43973e15i	0.767223	+	0.442956i
$843$	5.71118e15	−	1.05374e15i	0.462034	−	0.0852476i
$844$	−1.87649e15	−	3.25018e15i	−0.150822	−	0.261231i
$845$	−7.21893e15	+	1.25035e16i	−0.576449	+	0.998439i
$846$	−3.87265e15	+	4.76658e15i	−0.307235	+	0.378155i
$847$	1.58203e16	+	2.49754e16i	1.24697	+	1.96858i
$848$			4.96422e15i			0.388753i
$849$	−1.75689e15	−	2.06042e15i	−0.136695	−	0.160311i
$850$	−1.54040e15	+	8.89348e14i	−0.119077	+	0.0687492i
$851$	2.24416e16	−	1.29566e16i	1.72362	−	0.995130i
$852$	−1.59520e15	−	1.87079e15i	−0.121730	−	0.142760i
$853$			2.39246e16i			1.81395i	0.421185	+	0.906975i	$0.361614\pi$
$853$			2.39246e16i			1.81395i	−0.421185	+	0.906975i	$0.638386\pi$
$854$	1.14901e16	−	4.71869e14i	0.865573	−	0.0355470i
$855$	−1.84652e14	+	2.27275e14i	−0.0138210	+	0.0170113i
$856$	9.30750e14	−	1.61211e15i	0.0692193	−	0.119891i
$857$	1.19172e16	+	2.06412e16i	0.880604	+	1.52525i	0.850671	+	0.525699i	$0.176196\pi$
$857$	1.19172e16	+	2.06412e16i	0.880604	+	1.52525i	0.0299333	+	0.999552i	$0.490471\pi$
$858$	−3.26012e15	+	6.01508e14i	−0.239361	+	0.0441633i
$859$	1.02859e16	+	5.93859e15i	0.750381	+	0.433233i	0.825832	−	0.563917i	$-0.190706\pi$
$859$	1.02859e16	+	5.93859e15i	0.750381	+	0.433233i	−0.0754506	+	0.997150i	$0.524040\pi$
$860$	9.46326e15			0.685961
$861$	1.86890e16	+	5.78326e15i	1.34607	+	0.416538i
$862$	−1.84555e16			−1.32080
$863$	−1.60715e16	−	9.27889e15i	−1.14287	−	0.659837i	−0.195731	−	0.980658i	$-0.562708\pi$
$863$	−1.60715e16	−	9.27889e15i	−1.14287	−	0.659837i	−0.947140	+	0.320821i	$0.896041\pi$
$864$	−2.19572e15	−	1.19907e15i	−0.155150	−	0.0847262i
$865$	−1.08211e16	−	1.87427e16i	−0.759772	−	1.31596i
$866$	−2.88738e15	+	5.00108e15i	−0.201444	+	0.348912i
$867$	1.08013e16	+	3.83474e15i	0.748807	+	0.265846i
$868$	−8.75048e15	+	5.54288e15i	−0.602801	+	0.381836i
$869$		−	1.70777e16i		−	1.16902i
$870$	−1.54143e16	+	1.31435e16i	−1.04850	+	0.894039i
$871$	5.91563e14	−	3.41539e14i	0.0399854	−	0.0230856i
$872$	6.17211e14	−	3.56347e14i	0.0414566	−	0.0239350i
$873$	−1.02260e15	−	2.67687e15i	−0.0682541	−	0.178669i
$874$			3.55043e14i			0.0235488i
$875$	4.80533e15	−	9.17290e15i	0.316722	−	0.604592i
$876$	−1.12414e15	+	3.16636e15i	−0.0736288	+	0.207390i
$877$	1.21589e16	−	2.10598e16i	0.791398	−	1.37074i	−0.133703	−	0.991021i	$-0.542687\pi$
$877$	1.21589e16	−	2.10598e16i	0.791398	−	1.37074i	0.925101	−	0.379721i	$-0.123980\pi$
$878$	1.44705e15	+	2.50637e15i	0.0935975	+	0.162116i
$879$	−5.12005e14	−	2.77502e15i	−0.0329106	−	0.178372i
$880$	7.39419e15	+	4.26904e15i	0.472319	+	0.272694i
$881$	−5.43041e15			−0.344719			−0.172359	−	0.985034i	$-0.555139\pi$
$881$	−5.43041e15			−0.344719			−0.172359	+	0.985034i	$0.555139\pi$
$882$	−4.84513e15	−	1.01076e16i	−0.305652	−	0.637634i
$883$	4.92913e15			0.309020			0.154510	−	0.987991i	$-0.450620\pi$
$883$	4.92913e15			0.309020			0.154510	+	0.987991i	$0.450620\pi$
$884$	−5.94137e14	−	3.43025e14i	−0.0370168	−	0.0213717i
$885$	−2.90859e15	−	1.57643e16i	−0.180092	−	0.976084i
$886$	6.32921e15	+	1.09625e16i	0.389461	+	0.674567i
$887$	1.44556e16	−	2.50378e16i	0.884008	−	1.53115i	0.0371613	−	0.999309i	$-0.488168\pi$
$887$	1.44556e16	−	2.50378e16i	0.884008	−	1.53115i	0.846847	−	0.531837i	$-0.178498\pi$
$888$	2.13263e15	−	6.00697e15i	0.129612	−	0.365077i
$889$	−2.69580e15	+	5.14602e15i	−0.162828	+	0.310822i
$890$			1.17338e16i			0.704358i
$891$	−9.54639e15	+	2.90614e16i	−0.569524	+	1.73376i
$892$	1.34211e16	−	7.74870e15i	0.795761	−	0.459433i
$893$	1.85671e14	−	1.07197e14i	0.0109411	−	0.00631685i
$894$	−1.60221e15	+	1.36619e15i	−0.0938348	+	0.0800117i
$895$			3.56304e16i			2.07393i
$896$	−1.29072e15	+	8.17590e14i	−0.0746687	+	0.0472979i
$897$	−5.61539e15	−	1.99361e15i	−0.322866	−	0.114626i
$898$	−2.48155e15	+	4.29817e15i	−0.141809	+	0.245620i
$899$	2.04796e16	+	3.54718e16i	1.16317	+	2.01467i
$900$	−6.00546e14	+	3.75252e15i	−0.0339010	+	0.211831i
$901$	1.08781e16	+	6.28048e15i	0.610334	+	0.352376i
$902$	−3.26053e16			−1.81824
$903$	1.97802e16	+	6.12092e15i	1.09635	+	0.339261i
$904$	−1.80895e14			−0.00996554
$905$	−2.43920e16	−	1.40827e16i	−1.33561	−	0.771115i
$906$	8.83935e15	−	1.63090e15i	0.481078	−	0.0887612i
$907$	1.65159e16	+	2.86064e16i	0.893433	+	1.54747i	0.835732	+	0.549138i	$0.185044\pi$
$907$	1.65159e16	+	2.86064e16i	0.893433	+	1.54747i	0.0577010	+	0.998334i	$0.481623\pi$
$908$	−2.13059e14	+	3.69029e14i	−0.0114559	+	0.0198421i
$909$	1.98685e16	+	1.61423e16i	1.06185	+	0.862709i
$910$	−2.99894e15	+	1.23159e14i	−0.159309	+	0.00654242i
$911$			1.23620e16i			0.652737i	0.945243	+	0.326369i	$0.105825\pi$
$911$			1.23620e16i			0.652737i	−0.945243	+	0.326369i	$0.894175\pi$
$912$	5.66664e13	+	6.64563e13i	0.00297409	+	0.00348790i
$913$	−1.55364e16	+	8.96997e15i	−0.810518	+	0.467953i
$914$	−1.35595e15	+	7.82859e14i	−0.0703138	+	0.0405957i
$915$	−1.84357e16	−	2.16207e16i	−0.950261	−	1.11443i
$916$		−	1.28801e16i		−	0.659924i
$917$	−8.27905e15	−	1.30701e16i	−0.421647	−	0.665650i
$918$	−5.40543e15	+	3.29449e15i	−0.273650	+	0.166784i
$919$	1.69791e16	−	2.94087e16i	0.854437	−	1.47993i	−0.0227292	−	0.999742i	$-0.507236\pi$
$919$	1.69791e16	−	2.94087e16i	0.854437	−	1.47993i	0.877166	−	0.480187i	$-0.159431\pi$
$920$	7.67335e15	+	1.32906e16i	0.383842	+	0.664833i
$921$	−3.15569e16	+	5.82241e15i	−1.56916	+	0.289518i
$922$	8.47143e15	+	4.89098e15i	0.418732	+	0.241755i
$923$	−1.44045e15			−0.0707764
$924$	1.26941e16	+	1.37058e16i	0.620023	+	0.669436i
$925$	−9.68271e15			−0.470129
$926$	−6.69399e15	−	3.86478e15i	−0.323091	−	0.186537i
$927$	−8.20363e15	−	1.31290e15i	−0.393611	−	0.0629929i
$928$	3.02080e15	+	5.23218e15i	0.144082	+	0.249557i
$929$	5.51256e15	−	9.54803e15i	0.261377	−	0.452718i	−0.705231	−	0.708977i	$-0.749157\pi$
$929$	5.51256e15	−	9.54803e15i	0.261377	−	0.452718i	0.966608	+	0.256260i	$0.0824902\pi$
$930$	2.41184e16	+	8.56266e15i	1.13682	+	0.403601i
$931$	3.20849e13	+	3.89976e14i	0.00150341	+	0.0182732i
$932$		−	5.95905e15i		−	0.277581i
$933$	−1.67908e16	+	1.43173e16i	−0.777541	+	0.662999i
$934$	1.04443e16	−	6.03003e15i	0.480809	−	0.277595i
$935$	1.87095e16	−	1.08019e16i	0.856245	−	0.494353i
$936$	−1.36927e15	+	5.23080e14i	−0.0622976	+	0.0237986i
$937$		−	4.82142e15i		−	0.218076i	−0.994038	−	0.109038i	$-0.965223\pi$
$937$		−	4.82142e15i		−	0.218076i	0.994038	−	0.109038i	$-0.0347769\pi$
$938$	−3.40970e15	−	1.78621e15i	−0.153321	−	0.0803189i
$939$	9.46225e15	−	2.66522e16i	0.422994	−	1.19144i
$940$	4.63360e15	−	8.02562e15i	0.205928	−	0.356677i
$941$	−4.25139e15	−	7.36362e15i	−0.187840	−	0.325348i	0.756690	−	0.653774i	$-0.226815\pi$
$941$	−4.25139e15	−	7.36362e15i	−0.187840	−	0.325348i	−0.944530	+	0.328426i	$0.893482\pi$
$942$	−1.77665e14	−	9.62928e14i	−0.00780408	−	0.0422974i
$943$	−5.07544e16	−	2.93031e16i	−2.21646	−	1.27967i
$944$	−4.78099e15			−0.207574
$945$	−1.22651e16	+	2.48309e16i	−0.529416	+	1.07181i
$946$	−3.45090e16			−1.48092
$947$	2.75634e16	+	1.59137e16i	1.17600	+	0.678965i	0.955086	−	0.296328i	$-0.0957620\pi$
$947$	2.75634e16	+	1.59137e16i	1.17600	+	0.678965i	0.220916	+	0.975293i	$0.429095\pi$
$948$	−1.37004e15	−	7.42552e15i	−0.0581151	−	0.314978i
$949$	9.84295e14	+	1.70485e15i	0.0415108	+	0.0718988i
$950$	6.63323e13	−	1.14891e14i	0.00278128	−	0.00481732i
$951$	3.20074e15	−	9.01551e15i	0.133431	−	0.375835i
$952$	1.58633e14	+	3.86273e15i	0.00657492	+	0.160100i
$953$			3.51889e16i			1.45009i	0.688702	+	0.725044i	$0.258181\pi$
$953$			3.51889e16i			1.45009i	−0.688702	+	0.725044i	$0.741819\pi$
$954$	2.50701e16	−	9.57712e15i	1.02716	−	0.392391i
$955$	2.73312e16	−	1.57797e16i	1.11337	−	0.642806i
$956$	−3.43086e14	+	1.98081e14i	−0.0138958	+	0.00802276i
$957$	5.62101e16	−	4.79296e16i	2.26360	−	1.93014i
$958$			1.88494e16i			0.754722i
$959$	−1.03013e15	−	2.50839e16i	−0.0410102	−	0.998602i
$960$	3.55753e15	+	1.26302e15i	0.140817	+	0.0499939i
$961$	1.31701e16	−	2.28113e16i	0.518334	−	0.897782i
$962$	−1.86733e15	−	3.23431e15i	−0.0730732	−	0.126567i
$963$	−9.93700e15	−	1.59030e15i	−0.386643	−	0.0618778i
$964$	1.94406e15	+	1.12241e15i	0.0752119	+	0.0434236i
$965$	−5.85627e15			−0.225279
$966$	7.44241e15	+	3.27434e16i	0.284668	+	1.25242i
$967$	−1.52404e16			−0.579632			−0.289816	−	0.957082i	$-0.593594\pi$
$967$	−1.52404e16			−0.579632			−0.289816	+	0.957082i	$0.593594\pi$
$968$	−1.88673e16	−	1.08930e16i	−0.713502	−	0.411941i
$969$	2.17317e14	−	4.00961e13i	0.00817172	−	0.00150772i
$970$	2.16198e15	+	3.74467e15i	0.0808366	+	0.140013i
$971$	−1.84284e16	+	3.19190e16i	−0.685145	+	1.18671i	0.288246	+	0.957556i	$0.406928\pi$
$971$	−1.84284e16	+	3.19190e16i	−0.685145	+	1.18671i	−0.973391	+	0.229150i	$0.926405\pi$
$972$	−1.81941e15	+	1.34020e16i	−0.0672616	+	0.495455i
$973$	−1.76138e16	−	9.22719e15i	−0.647488	−	0.339194i
$974$			1.49789e16i			0.547527i
$975$	1.44466e15	+	1.69425e15i	0.0525098	+	0.0615816i
$976$	−7.33887e15	+	4.23710e15i	−0.265250	+	0.153142i
$977$	−1.34703e16	+	7.77707e15i	−0.484124	+	0.279509i	−0.722134	−	0.691754i	$-0.756838\pi$
$977$	−1.34703e16	+	7.77707e15i	−0.484124	+	0.279509i	0.238009	+	0.971263i	$0.423505\pi$
$978$	8.94067e15	+	1.04853e16i	0.319526	+	0.374729i
$979$		−	4.27888e16i		−	1.52064i
$980$	9.62941e15	+	1.39049e16i	0.340296	+	0.491388i
$981$	−2.99035e15	−	2.42953e15i	−0.105085	−	0.0853774i
$982$	−4.69139e14	+	8.12573e14i	−0.0163941	+	0.0283955i
$983$	−5.93955e14	−	1.02876e15i	−0.0206400	−	0.0357495i	0.855521	−	0.517768i	$-0.173237\pi$
$983$	−5.93955e14	−	1.02876e15i	−0.0206400	−	0.0357495i	−0.876161	+	0.482019i	$0.839904\pi$
$984$	−1.41770e16	+	2.61573e15i	−0.489905	+	0.0903899i
$985$	−5.20749e15	−	3.00655e15i	−0.178949	−	0.103316i
$986$	1.52871e16			0.522398
$987$	1.48762e16	−	1.37782e16i	0.505532	−	0.468217i
$988$	5.11693e13			0.00172920
$989$	−5.37178e16	−	3.10140e16i	−1.80526	−	1.04227i
$990$	7.29417e15	−	4.55777e16i	0.243771	−	1.52321i
$991$	1.14964e16	+	1.99124e16i	0.382083	+	0.661787i	0.991360	−	0.131171i	$-0.0418736\pi$
$991$	1.14964e16	+	1.99124e16i	0.382083	+	0.661787i	−0.609277	+	0.792957i	$0.708540\pi$
$992$	3.81654e15	−	6.61044e15i	0.126141	−	0.218482i
$993$	1.37406e16	+	4.87828e15i	0.451632	+	0.160341i
$994$	4.34359e15	+	6.85718e15i	0.141979	+	0.224141i
$995$		−	9.22756e15i		−	0.299958i
$996$	−6.03576e15	+	5.14661e15i	−0.195122	+	0.166378i
$997$	−4.94852e15	+	2.85703e15i	−0.159093	+	0.0918525i	−0.577433	−	0.816438i	$-0.695946\pi$
$997$	−4.94852e15	+	2.85703e15i	−0.159093	+	0.0918525i	0.418340	+	0.908291i	$0.362612\pi$
$998$	−1.70098e16	+	9.82062e15i	−0.543853	+	0.313994i
$999$	−3.44504e16	+	8.18709e14i	−1.09543	+	0.0260327i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.12.f.a.5.9	✓	60
3.2	odd	2	inner	42.12.f.a.5.19	yes	60
7.3	odd	6	inner	42.12.f.a.17.19	yes	60
21.17	even	6	inner	42.12.f.a.17.9	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.9	✓	60	1.1	even	1	trivial
42.12.f.a.5.19	yes	60	3.2	odd	2	inner
42.12.f.a.17.9	yes	60	21.17	even	6	inner
42.12.f.a.17.19	yes	60	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-27.7128 - 16.0000i) q^{2} +(76.3670 + 413.902i) q^{3} +(512.000 + 886.810i) q^{4} +(-4176.66 + 7234.19i) q^{5} +(4506.09 - 12692.3i) q^{6} +(-20634.7 + 39389.6i) q^{7} -32768.0i q^{8} +(-165483. + 63217.0i) q^{9} +(231494. - 133653. i) q^{10} +(-844173. + 487383. i) q^{11} +(-327953. + 279641. i) q^{12} +252514. i q^{13} +(1.20208e6 - 761440. i) q^{14} +(-3.31321e6 - 1.17628e6i) q^{15} +(-524288. + 908093. i) q^{16} +(1.32660e6 + 2.29775e6i) q^{17} +(5.59748e6 + 895811. i) q^{18} +(-171378. - 98945.2i) q^{19} -8.55380e6 q^{20} +(-1.78792e7 - 5.53268e6i) q^{21} +3.11925e7 q^{22} +(4.85553e7 + 2.80334e7i) q^{23} +(1.35627e7 - 2.50239e6i) q^{24} +(-1.04749e7 - 1.81431e7i) q^{25} +(4.04022e6 - 6.99786e6i) q^{26} +(-3.88031e7 - 6.36662e7i) q^{27} +(-4.54960e7 + 1.86841e6i) q^{28} +1.80054e8i q^{29} +(7.29978e7 + 8.56092e7i) q^{30} +(1.97006e8 - 1.13742e8i) q^{31} +(2.90590e7 - 1.67772e7i) q^{32} +(-2.66196e8 - 3.12185e8i) q^{33} -8.49027e7i q^{34} +(-1.98767e8 - 3.13792e8i) q^{35} +(-1.40789e8 - 1.14385e8i) q^{36} +(2.31093e8 - 4.00264e8i) q^{37} +(3.16625e6 + 5.48410e6i) q^{38} +(-1.04516e8 + 1.92837e7i) q^{39} +(2.37050e8 + 1.36861e8i) q^{40} -1.04529e9 q^{41} +(4.06961e8 + 4.39394e8i) q^{42} -1.10632e9 q^{43} +(-8.64433e8 - 4.99081e8i) q^{44} +(2.33844e8 - 1.46117e9i) q^{45} +(-8.97070e8 - 1.55377e9i) q^{46} +(-5.41700e8 + 9.38253e8i) q^{47} +(-4.15900e8 - 1.47656e8i) q^{48} +(-1.12575e9 - 1.62558e9i) q^{49} +6.70394e8i q^{50} +(-8.49734e8 + 7.24557e8i) q^{51} +(-2.23932e8 + 1.29287e8i) q^{52} +(4.09998e9 - 2.36713e9i) q^{53} +(5.66843e7 + 2.38522e9i) q^{54} -8.14254e9i q^{55} +(1.29072e9 + 6.76157e8i) q^{56} +(2.78660e7 - 7.84899e7i) q^{57} +(2.88086e9 - 4.98980e9i) q^{58} +(2.27976e9 + 3.94865e9i) q^{59} +(-6.53228e8 - 3.54044e9i) q^{60} +(6.99890e9 + 4.04081e9i) q^{61} -7.27947e9 q^{62} +(9.24604e8 - 7.82277e9i) q^{63} -1.07374e9 q^{64} +(-1.82673e9 - 1.05466e9i) q^{65} +(2.38208e9 + 1.29107e10i) q^{66} +(-1.35256e9 - 2.34270e9i) q^{67} +(-1.35844e9 + 2.35289e9i) q^{68} +(-7.89507e9 + 2.22380e10i) q^{69} +(4.87732e8 + 1.18763e10i) q^{70} +5.70444e9i q^{71} +(2.07149e9 + 5.42255e9i) q^{72} +(6.75151e9 - 3.89799e9i) q^{73} +(-1.28085e10 + 7.39497e9i) q^{74} +(6.70952e9 - 5.72112e9i) q^{75} -2.02640e8i q^{76} +(-1.77858e9 - 4.33086e10i) q^{77} +(3.20497e9 + 1.13785e9i) q^{78} +(-8.75989e9 + 1.51726e10i) q^{79} +(-4.37955e9 - 7.58559e9i) q^{80} +(2.33883e10 - 2.09227e10i) q^{81} +(2.89679e10 + 1.67247e10i) q^{82} +1.84043e10 q^{83} +(-4.24773e9 - 1.86882e10i) q^{84} -2.21631e10 q^{85} +(3.06593e10 + 1.77012e10i) q^{86} +(-7.45247e10 + 1.37502e10i) q^{87} +(1.59706e10 + 2.76619e10i) q^{88} +(-2.19482e10 + 3.80155e10i) q^{89} +(-2.98592e10 + 3.67517e10i) q^{90} +(-9.94640e9 - 5.21054e9i) q^{91} +5.74125e10i q^{92} +(6.21227e10 + 7.28553e10i) q^{93} +(3.00241e10 - 1.73344e10i) q^{94} +(1.43158e9 - 8.26521e8i) q^{95} +(9.16328e9 + 1.07464e10i) q^{96} +1.61761e10i q^{97} +(5.18831e9 + 6.30614e10i) q^{98} +(1.08885e11 - 1.34020e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 30720 q^{4} - 95298 q^{7} - 91434 q^{9} + 245184 q^{10} - 8480820 q^{15} - 31457280 q^{16} + 12170496 q^{18} + 1649724 q^{19} + 43254216 q^{21} + 20705664 q^{22} + 4521984 q^{24} - 336132444 q^{25}+ \cdots + 288758042496 q^{99}+O(q^{100}) \) 60 * q + 30720 * q^4 - 95298 * q^7 - 91434 * q^9 + 245184 * q^10 - 8480820 * q^15 - 31457280 * q^16 + 12170496 * q^18 + 1649724 * q^19 + 43254216 * q^21 + 20705664 * q^22 + 4521984 * q^24 - 336132444 * q^25 + 28121088 * q^28 - 77109120 * q^30 - 275992974 * q^31 + 1056712914 * q^33 - 187256832 * q^36 + 555437556 * q^37 - 563926680 * q^39 + 251068416 * q^40 + 1167043776 * q^42 + 2546594304 * q^43 + 544480776 * q^45 - 452472192 * q^46 - 1309143414 * q^49 + 2007979044 * q^51 + 3219419136 * q^52 - 9840998592 * q^54 + 17053196256 * q^57 + 12235419456 * q^58 - 4342179840 * q^60 - 3056592000 * q^61 - 42499692960 * q^63 - 64424509440 * q^64 + 48796070400 * q^66 + 27979853436 * q^67 - 4966503360 * q^70 - 12462587904 * q^72 - 105678747168 * q^73 + 173211633504 * q^75 - 16600538880 * q^78 - 27787555926 * q^79 - 71399556486 * q^81 + 31231064832 * q^82 - 25272410112 * q^84 + 12868048152 * q^85 + 137017459998 * q^87 + 10601299968 * q^88 + 333571182180 * q^91 - 14607989424 * q^93 - 430917051648 * q^94 + 4630511616 * q^96 + 288758042496 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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