LMFDB - Embedded newform 42.12.f.a.5.19

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			5.19
Character	$\chi$	$=$	42.5
Dual form			42.12.f.a.17.19

$q$-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} +(-320.266 - 273.087i) 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} +(27994.1 + 174921. i) q^{9} +(231494. - 133653. i) q^{10} +(844173. - 487383. i) q^{11} +(78199.8 - 423836. 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} +(-2.02294e6 + 5.29546e6i) q^{18} +(-171378. - 98945.2i) q^{19} +8.55380e6 q^{20} +(1.73654e7 - 6.98009e6i) q^{21} +3.11925e7 q^{22} +(-4.85553e7 - 2.80334e7i) q^{23} +(8.94851e6 - 1.04945e7i) 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} +(-1.10639e8 - 2.04134e7i) q^{30} +(1.97006e8 - 1.13742e8i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(-4.03458e8 - 7.44400e7i) 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} +(6.89581e7 - 8.08716e7i) q^{39} +(2.37050e8 + 1.36861e8i) q^{40} +1.04529e9 q^{41} +(5.92924e8 + 8.44080e7i) q^{42} -1.10632e9 q^{43} +(8.64433e8 + 4.99081e8i) q^{44} +(1.38233e9 + 5.28071e8i) 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} +(-2.02618e8 + 1.09817e9i) q^{51} +(-2.23932e8 + 1.29287e8i) q^{52} +(-4.09998e9 + 2.36713e9i) q^{53} +(2.09400e9 - 1.14352e9i) 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} +(-2.73949e9 - 2.33593e9i) q^{60} +(6.99890e9 + 4.04081e9i) q^{61} +7.27947e9 q^{62} +(-7.46771e9 - 2.50677e9i) q^{63} -1.07374e9 q^{64} +(1.82673e9 + 1.05466e9i) q^{65} +(-9.98992e9 - 8.51827e9i) 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} +(-5.73181e9 + 9.17310e8i) q^{72} +(6.75151e9 - 3.89799e9i) q^{73} +(1.28085e10 - 7.39497e9i) q^{74} +(-1.59988e9 + 8.67118e9i) 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} +(-2.98137e10 + 9.79351e9i) q^{81} +(2.89679e10 + 1.67247e10i) q^{82} -1.84043e10 q^{83} +(1.50811e10 + 1.18260e10i) q^{84} -2.21631e10 q^{85} +(-3.06593e10 - 1.77012e10i) q^{86} +(-4.91704e10 + 5.76652e10i) 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} +(-9.41559e10 - 1.73722e10i) q^{93} +(3.00241e10 - 1.73344e10i) q^{94} +(-1.43158e9 + 8.26521e8i) q^{95} +(1.38883e10 + 2.56245e9i) 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
$3$	−320.266	−	273.087i	−0.760930	−	0.648835i
$3$	−320.266	−	273.087i	−0.760930	−	0.648835i
$4$	512.000	+	886.810i	0.250000	+	0.433013i
$5$	4176.66	−	7234.19i	0.597715	−	1.03527i	−0.395443	−	0.918491i	$-0.629409\pi$
$5$	4176.66	−	7234.19i	0.597715	−	1.03527i	0.993158	−	0.116782i	$-0.0372579\pi$
$6$	−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
$9$	27994.1	+	174921.i	0.158027	+	0.987435i
$10$	231494.	−	133653.i	0.732048	−	0.422648i
$11$	844173.	−	487383.i	1.58042	−	0.912454i	0.585619	−	0.810587i	$-0.300852\pi$
$11$	844173.	−	487383.i	1.58042	−	0.912454i	0.994798	−	0.101867i	$-0.0324817\pi$
$12$	78199.8	−	423836.i	0.0907212	−	0.491701i
$13$			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	0.730194	−	0.683240i	$-0.239430\pi$
$17$	−1.32660e6	−	2.29775e6i	−0.226607	−	0.392494i	−0.956800	+	0.290746i	$0.906096\pi$
$18$	−2.02294e6	+	5.29546e6i	−0.252339	+	0.660549i
$19$	−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
$21$	1.73654e7	−	6.98009e6i	0.927850	−	0.372954i
$22$	3.11925e7			1.29040
$23$	−4.85553e7	−	2.80334e7i	−1.57302	−	0.908182i	−0.995796	−	0.0915948i	$-0.970804\pi$
$23$	−4.85553e7	−	2.80334e7i	−1.57302	−	0.908182i	−0.577222	−	0.816588i	$-0.695863\pi$
$24$	8.94851e6	−	1.04945e7i	0.229398	−	0.269029i
$25$	−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	$-0.696710\pi$
$29$		−	1.80054e8i		−	1.63010i	0.579392	−	0.815049i	$-0.303290\pi$
$30$	−1.10639e8	−	2.04134e7i	−0.831266	−	0.153373i
$31$	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
$33$	−4.03458e8	−	7.44400e7i	−1.79462	−	0.331116i
$34$		−	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
$39$	6.89581e7	−	8.08716e7i	0.122386	−	0.143529i
$40$	2.37050e8	+	1.36861e8i	0.366024	+	0.211324i
$41$	1.04529e9			1.40905			0.704524	−	0.709680i	$-0.251160\pi$
$41$	1.04529e9			1.40905			0.704524	+	0.709680i	$0.251160\pi$
$42$	5.92924e8	+	8.44080e7i	0.700049	+	0.0996580i
$43$	−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
$45$	1.38233e9	+	5.28071e8i	1.11672	+	0.426603i
$46$	−8.97070e8	−	1.55377e9i	−0.642182	−	1.11229i
$47$	5.41700e8	−	9.38253e8i	0.344525	−	0.596735i	−0.640742	−	0.767756i	$-0.721373\pi$
$47$	5.41700e8	−	9.38253e8i	0.344525	−	0.596735i	0.985267	+	0.171021i	$0.0547066\pi$
$48$	4.15900e8	−	1.47656e8i	0.235593	−	0.0836418i
$49$	−1.12575e9	−	1.62558e9i	−0.569328	−	0.822111i
$50$		−	6.70394e8i		−	0.303386i
$51$	−2.02618e8	+	1.09817e9i	−0.0822321	+	0.445691i
$52$	−2.23932e8	+	1.29287e8i	−0.0816765	+	0.0471559i
$53$	−4.09998e9	+	2.36713e9i	−1.34668	+	0.777507i	−0.987778	−	0.155868i	$-0.950183\pi$
$53$	−4.09998e9	+	2.36713e9i	−1.34668	+	0.777507i	−0.358903	+	0.933375i	$0.616849\pi$
$54$	2.09400e9	−	1.14352e9i	0.620599	−	0.338905i
$55$		−	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	0.580297	−	0.814405i	$-0.302937\pi$
$59$	−2.27976e9	−	3.94865e9i	−0.415147	−	0.719056i	−0.995444	+	0.0953491i	$0.969603\pi$
$60$	−2.73949e9	−	2.33593e9i	−0.454819	−	0.387818i
$61$	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
$63$	−7.46771e9	−	2.50677e9i	−0.948014	−	0.318230i
$64$	−1.07374e9			−0.125000
$65$	1.82673e9	+	1.05466e9i	0.195277	+	0.112743i
$66$	−9.98992e9	−	8.51827e9i	−0.981907	−	0.837259i
$67$	−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	$-0.939925\pi$
$71$		−	5.70444e9i		−	0.375225i	0.982243	−	0.187613i	$-0.0600750\pi$
$72$	−5.73181e9	+	9.17310e8i	−0.349111	+	0.0558711i
$73$	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
$75$	−1.59988e9	+	8.67118e9i	−0.0778483	+	0.421931i
$76$		−	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
$81$	−2.98137e10	+	9.79351e9i	−0.950055	+	0.312084i
$82$	2.89679e10	+	1.67247e10i	0.862862	+	0.498174i
$83$	−1.84043e10			−0.512851			−0.256425	−	0.966564i	$-0.582545\pi$
$83$	−1.84043e10			−0.512851			−0.256425	+	0.966564i	$0.582545\pi$
$84$	1.50811e10	+	1.18260e10i	0.393456	+	0.308532i
$85$	−2.21631e10			−0.541785
$86$	−3.06593e10	−	1.77012e10i	−0.702782	−	0.405752i
$87$	−4.91704e10	+	5.76652e10i	−1.05766	+	1.24039i
$88$	1.59706e10	+	2.76619e10i	0.322601	+	0.558762i
$89$	2.19482e10	−	3.80155e10i	0.416634	−	0.721631i	−0.578965	−	0.815353i	$-0.696543\pi$
$89$	2.19482e10	−	3.80155e10i	0.416634	−	0.721631i	0.995598	+	0.0937217i	$0.0298764\pi$
$90$	2.98592e10	+	3.67517e10i	0.533021	+	0.656060i
$91$	−9.94640e9	−	5.21054e9i	−0.167085	−	0.0875296i
$92$		−	5.74125e10i		−	0.908182i
$93$	−9.41559e10	−	1.73722e10i	−1.40343	−	0.258940i
$94$	3.00241e10	−	1.73344e10i	0.421955	−	0.243616i
$95$	−1.43158e9	+	8.26521e8i	−0.0189817	+	0.0109591i
$96$	1.38883e10	+	2.56245e9i	0.173842	+	0.0320748i
$97$			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	$0.0731240\pi$
$101$	7.22548e10	+	1.25149e11i	0.684067	+	1.18484i	−0.289661	+	0.957129i	$0.593543\pi$
$102$	−2.31858e10	+	2.71915e10i	−0.207932	+	0.243855i
$103$	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
$105$	2.20340e10	−	1.54778e11i	0.168481	−	1.18350i
$106$	−1.51496e11			−1.09956
$107$	−4.91976e10	−	2.84042e10i	−0.339104	−	0.195782i	0.320772	−	0.947157i	$-0.396058\pi$
$107$	−4.91976e10	−	2.84042e10i	−0.339104	−	0.195782i	−0.659876	+	0.751375i	$0.729391\pi$
$108$	7.63270e10	+	1.81390e9i	0.499859	+	0.0118791i
$109$	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	$0.00448622\pi$
$113$			5.52049e9i			0.0281868i	−0.999901	+	0.0140934i	$0.995514\pi$
$114$	−4.83593e8	+	2.62103e9i	−0.00235236	+	0.0127496i
$115$	−4.05598e11	+	2.34172e11i	−1.88043	+	1.08567i
$116$	1.59674e11	−	9.21876e10i	0.705853	−	0.407524i
$117$	−4.41699e10	+	7.06889e9i	−0.186254	+	0.0298077i
$118$		−	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
$123$	−3.34771e11	−	2.85455e11i	−1.07219	−	0.914239i
$124$	2.01734e11	+	1.16471e11i	0.617961	+	0.356780i
$125$	2.32876e11			0.682528
$126$	−1.66843e11	−	1.88953e11i	−0.468026	−	0.530049i
$127$	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
$129$	3.54318e11	+	3.02122e11i	0.873272	+	0.744628i
$130$	3.37492e10	+	5.84554e10i	0.0797215	+	0.138082i
$131$	1.73966e11	−	3.01318e11i	0.393979	−	0.682391i	−0.598992	−	0.800755i	$-0.704432\pi$
$131$	1.73966e11	−	3.01318e11i	0.393979	−	0.682391i	0.992970	+	0.118364i	$0.0377651\pi$
$132$	−1.40556e11	−	3.95904e11i	−0.305277	−	0.859871i
$133$	7.43374e9	−	4.70880e9i	0.0154890	−	0.00981130i
$134$		−	8.65637e10i		−	0.173085i
$135$	−2.98506e11	−	5.46621e11i	−0.572950	−	1.04918i
$136$	7.52926e10	−	4.34702e10i	0.138768	−	0.0801175i
$137$	4.88936e11	−	2.82287e11i	0.865544	−	0.499722i	−0.000321066	−	1.00000i	$-0.500102\pi$
$137$	4.88936e11	−	2.82287e11i	0.865544	−	0.499722i	0.865865	+	0.500278i	$0.166769\pi$
$138$	−1.37013e11	+	7.42598e11i	−0.233038	+	1.26305i
$139$			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
$144$	−1.73522e11	−	6.62878e10i	−0.233539	−	0.0892154i
$145$	−1.30254e12	−	7.52024e11i	−1.68760	−	0.974334i
$146$	2.49471e11			0.311229
$147$	−8.33862e10	+	8.28046e11i	−0.100196	+	0.994968i
$148$	4.73278e11			0.547869
$149$	1.35391e11	+	7.81680e10i	0.151031	+	0.0871976i	0.573611	−	0.819128i	$-0.305542\pi$
$149$	1.35391e11	+	7.81680e10i	0.151031	+	0.0871976i	−0.422580	+	0.906326i	$0.638876\pi$
$150$	−1.83076e11	+	2.14705e11i	−0.196847	+	0.230855i
$151$	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
$156$	1.07024e11	+	1.97465e10i	0.0927464	+	0.0171122i
$157$	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
$159$	1.95952e12	+	3.61541e11i	1.52920	+	0.282145i
$160$			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
$165$	−2.22362e12	+	2.60778e12i	−1.41546	+	1.66001i
$166$	−5.10036e11	−	2.94470e11i	−0.314056	−	0.181320i
$167$	−6.15264e11			−0.366539			−0.183270	−	0.983063i	$-0.558668\pi$
$167$	−6.15264e11			−0.366539			−0.183270	+	0.983063i	$0.558668\pi$
$168$	2.28724e11	+	5.69028e11i	0.131859	+	0.328045i
$169$	1.72840e12			0.964421
$170$	−6.14202e11	−	3.54610e11i	−0.331774	−	0.191550i
$171$	1.25100e10	−	3.27475e10i	0.00654304	−	0.0171277i
$172$	−5.66437e11	−	9.81098e11i	−0.286910	−	0.496942i
$173$	1.29543e12	−	2.24374e12i	0.635564	−	1.10083i	−0.350831	−	0.936439i	$-0.614101\pi$
$173$	1.29543e12	−	2.24374e12i	0.635564	−	1.10083i	0.986395	−	0.164390i	$-0.0525657\pi$
$174$	−2.28529e12	+	8.11339e11i	−1.08623	+	0.385640i
$175$	9.30794e11	−	3.82255e10i	0.428691	−	0.0176053i
$176$			1.02212e12i			0.456227i
$177$	−3.48196e11	+	1.88719e12i	−0.150651	+	0.816513i
$178$	1.21649e12	−	7.02343e11i	0.510270	−	0.294605i
$179$	−3.69396e12	+	2.13271e12i	−1.50245	+	0.867441i	−0.502456	+	0.864603i	$0.667570\pi$
$179$	−3.69396e12	+	2.13271e12i	−1.50245	+	0.867441i	−0.999996	+	0.00283810i	$0.999097\pi$
$180$	2.39456e11	+	1.49624e12i	0.0944554	+	0.590204i
$181$			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
$186$	−2.33137e12	−	1.98793e12i	−0.767873	−	0.654756i
$187$	−2.23977e12	−	1.29313e12i	−0.716266	−	0.413536i
$188$	1.10940e12			0.344525
$189$	1.70709e12	+	2.84217e12i	0.514893	+	0.857254i
$190$	−5.28973e10			−0.0154985
$191$	3.27190e12	+	1.88903e12i	0.931358	+	0.537720i	0.887241	−	0.461307i	$-0.152619\pi$
$191$	3.27190e12	+	1.88903e12i	0.931358	+	0.537720i	0.0441172	+	0.999026i	$0.485953\pi$
$192$	3.43883e11	+	2.93225e11i	0.0951162	+	0.0811043i
$193$	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	$-0.972455\pi$
$197$		−	7.19845e11i		−	0.172852i	0.996258	−	0.0864261i	$-0.0275446\pi$
$198$	8.73207e11	+	5.45623e12i	0.203919	+	1.27419i
$199$	−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
$201$	−2.06581e11	+	1.11965e12i	−0.0444133	+	0.240716i
$202$			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
$207$	3.54438e12	−	9.27812e12i	0.648191	−	1.69677i
$208$	−2.29306e11	−	1.32390e11i	−0.0408382	−	0.0235780i
$209$	−1.92897e11			−0.0334596
$210$	3.08707e12	−	3.93678e12i	0.521603	−	0.665174i
$211$	−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
$213$	−1.55781e12	+	1.82694e12i	−0.243459	+	0.285520i
$214$	−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
$219$	−3.22677e12	−	5.95355e11i	−0.432838	−	0.0798608i
$220$	7.22088e12	−	4.16898e12i	0.944639	−	0.545387i
$221$	5.80212e11	−	3.34986e11i	0.0740337	−	0.0427434i
$222$	−6.12159e12	−	1.12946e12i	−0.761944	−	0.140582i
$223$		−	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	0.854342	−	0.519711i	$-0.173960\pi$
$227$	−2.08065e11	−	3.60380e11i	−0.0229117	−	0.0396842i	−0.877254	+	0.480027i	$0.840627\pi$
$228$	−5.53383e10	+	6.48987e10i	−0.00594818	+	0.00697580i
$229$	−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
$231$	1.12574e13	−	1.43560e13i	1.12609	−	1.43604i
$232$	5.90001e12			0.576326
$233$	5.03974e12	+	2.90969e12i	0.480784	+	0.277581i	0.720743	−	0.693202i	$-0.243801\pi$
$233$	5.03974e12	+	2.90969e12i	0.480784	+	0.277581i	−0.239959	+	0.970783i	$0.577134\pi$
$234$	−1.33718e12	−	5.10820e11i	−0.124595	−	0.0475972i
$235$	−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	$-0.994892\pi$
$239$		−	3.86877e11i		−	0.0320911i	0.999871	−	0.0160455i	$-0.00510767\pi$
$240$	6.68906e11	−	3.62541e12i	0.0542254	−	0.293897i
$241$	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
$243$	1.22228e13	+	5.00520e12i	0.925415	+	0.378955i
$244$			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
$249$	5.89429e12	+	5.02599e12i	0.390243	+	0.332755i
$250$	6.45366e12	+	3.72602e12i	0.417961	+	0.241310i
$251$	−2.69200e13			−1.70557			−0.852786	−	0.522260i	$-0.825089\pi$
$251$	−2.69200e13			−1.70557			−0.852786	+	0.522260i	$0.825089\pi$
$252$	−1.60044e12	−	7.90591e12i	−0.0992059	−	0.490059i
$253$	−5.46521e13			−3.31470
$254$	3.62052e12	+	2.09031e12i	0.214875	+	0.124058i
$255$	7.09810e12	+	6.05245e12i	0.412260	+	0.351529i
$256$	−5.49756e11	−	9.52205e11i	−0.0312500	−	0.0541266i
$257$	1.99454e12	−	3.45465e12i	0.110972	−	0.192208i	−0.805191	−	0.593016i	$-0.797937\pi$
$257$	1.99454e12	−	3.45465e12i	0.110972	−	0.192208i	0.916162	+	0.400808i	$0.131270\pi$
$258$	4.98519e12	+	1.40417e13i	0.271502	+	0.764738i
$259$	1.09977e13	+	1.73620e13i	0.586346	+	0.925657i
$260$			2.15995e12i			0.112743i
$261$	3.14952e13	−	5.04044e12i	1.60961	−	0.257600i
$262$	9.64218e12	−	5.56692e12i	0.482523	−	0.278585i
$263$	−2.86958e13	+	1.65675e13i	−1.40625	+	0.811897i	−0.995024	−	0.0996385i	$-0.968231\pi$
$263$	−2.86958e13	+	1.65675e13i	−1.40625	+	0.811897i	−0.411222	+	0.911535i	$0.634898\pi$
$264$	2.43925e12	−	1.32205e13i	0.117067	−	0.634493i
$265$			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	$0.000610293\pi$
$269$	1.15890e13	+	2.00728e13i	0.501660	+	0.868900i	−0.498339	+	0.866982i	$0.666056\pi$
$270$	4.73502e11	−	1.99245e13i	0.0200827	−	0.845058i
$271$	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
$273$	1.76257e12	+	4.38499e12i	0.0703479	+	0.175014i
$274$	1.80664e13			0.706714
$275$	−1.76853e13	−	1.02106e13i	−0.678081	−	0.391491i
$276$	−1.56786e13	+	1.83873e13i	−0.589260	+	0.691063i
$277$	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	$0.0754816\pi$
$281$			1.37984e13i			0.469833i	−0.972016	+	0.234916i	$0.924518\pi$
$282$	−1.43495e13	−	2.64755e12i	−0.479145	−	0.0884046i
$283$	−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
$285$	6.84198e11	+	1.26238e11i	0.0215543	+	0.00397688i
$286$			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
$291$	4.41748e12	−	5.18065e12i	0.124097	−	0.145537i
$292$	6.91355e12	+	3.99154e12i	0.190588	+	0.110036i
$293$	6.70453e12			0.181383			0.0906915	−	0.995879i	$-0.471092\pi$
$293$	6.70453e12			0.181383			0.0906915	+	0.995879i	$0.471092\pi$
$294$	−1.55596e13	+	2.16133e13i	−0.413131	+	0.573866i
$295$	−3.80870e13			−0.992559
$296$	1.31159e13	+	7.57245e12i	0.335500	+	0.193701i
$297$	1.72669e12	−	7.26572e13i	0.0433564	−	1.82439i
$298$	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
$303$	1.10358e13	−	5.98128e13i	0.248238	−	1.34543i
$304$	1.79703e11	−	1.03752e11i	0.00396963	−	0.00229187i
$305$	5.84640e13	−	3.37542e13i	1.26835	−	0.732283i
$306$	1.48513e13	−	2.37677e12i	0.316443	−	0.0506431i
$307$			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	$-0.995973\pi$
$311$	−2.62139e13	−	4.54037e13i	−0.510915	−	0.884931i	0.489005	−	0.872281i	$-0.337360\pi$
$312$	2.65000e12	+	2.25962e12i	0.0507453	+	0.0432698i
$313$	−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
$315$	−4.93245e13	+	4.35529e13i	−0.896096	+	0.791242i
$316$	−1.79403e13			−0.320295
$317$	1.96848e13	+	1.13650e13i	0.345387	+	0.199409i	0.662651	−	0.748928i	$-0.269431\pi$
$317$	1.96848e13	+	1.13650e13i	0.345387	+	0.199409i	−0.317265	+	0.948337i	$0.602764\pi$
$318$	4.85191e13	+	4.13716e13i	0.836688	+	0.713433i
$319$	−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
$324$	−2.39496e13	−	2.14248e13i	−0.372650	−	0.333365i
$325$	4.58137e12	−	2.64506e12i	0.0700870	−	0.0404647i
$326$	−2.83531e13	+	1.63696e13i	−0.426484	+	0.246231i
$327$	1.66096e12	−	9.00225e12i	0.0245667	−	0.133149i
$328$			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
$333$	7.64839e13	+	2.92180e13i	1.02359	+	0.391027i
$334$	−1.70507e13	−	9.84422e12i	−0.224459	−	0.129591i
$335$	−2.25967e13			−0.292616
$336$	−2.76588e12	+	1.94289e13i	−0.0352344	+	0.247505i
$337$	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
$339$	1.50757e12	−	1.76803e12i	0.0182886	−	0.0214482i
$340$	−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
$345$	1.93849e14	+	3.57661e13i	2.13530	+	0.393973i
$346$	7.17998e13	−	4.14536e13i	0.778404	−	0.449412i
$347$	1.99817e13	−	1.15364e13i	0.213216	−	0.123100i	−0.389589	−	0.920989i	$-0.627383\pi$
$347$	1.99817e13	−	1.15364e13i	0.213216	−	0.123100i	0.602805	+	0.797888i	$0.294050\pi$
$348$	−7.63133e13	−	1.40802e13i	−0.801520	−	0.147884i
$349$			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	$0.0526693\pi$
$353$	6.54774e13	+	1.13410e14i	0.635815	+	1.10126i	−0.350527	+	0.936553i	$0.613997\pi$
$354$	−3.98446e13	+	4.67282e13i	−0.380935	+	0.446747i
$355$	−4.12670e13	−	2.38255e13i	−0.388460	−	0.224278i
$356$	4.49500e13			0.416634
$357$	−3.90755e13	−	3.06414e13i	−0.356639	−	0.279662i
$358$	−1.36493e14			−1.22675
$359$	4.36364e11	+	2.51935e11i	0.00386216	+	0.00222982i	0.501930	−	0.864908i	$-0.332624\pi$
$359$	4.36364e11	+	2.51935e11i	0.00386216	+	0.00222982i	−0.498068	+	0.867138i	$0.665957\pi$
$360$	−1.73038e13	+	4.52963e13i	−0.150827	+	0.394820i
$361$	−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
$366$	1.97494e13	−	1.07040e14i	0.157184	−	0.851924i
$367$	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
$369$	2.92620e13	+	1.82843e14i	0.222668	+	1.39134i
$370$		−	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
$375$	−7.45825e13	−	6.35955e13i	−0.519356	−	0.442848i
$376$	3.07447e13	+	1.77504e13i	0.210978	+	0.121808i
$377$	4.54661e13			0.307475
$378$	1.83365e12	+	1.06078e14i	0.0122211	+	0.707001i
$379$	−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
$381$	−4.18410e13	−	3.56772e13i	−0.267002	−	0.227669i
$382$	6.04491e13	+	1.04701e14i	0.380225	+	0.658570i
$383$	−8.41883e13	+	1.45818e14i	−0.521986	+	0.904106i	0.477687	+	0.878530i	$0.341475\pi$
$383$	−8.41883e13	+	1.45818e14i	−0.521986	+	0.904106i	−0.999673	+	0.0255758i	$0.991858\pi$
$384$	4.83838e12	+	1.36282e13i	0.0295718	+	0.0832947i
$385$	3.20731e14	+	1.68019e14i	1.93244	+	1.01233i
$386$			2.24343e13i			0.133255i
$387$	−3.09705e13	−	1.93519e14i	−0.181358	−	1.13322i
$388$	−1.43451e13	+	8.28215e12i	−0.0828189	+	0.0478155i
$389$	6.03568e13	−	3.48470e13i	0.343560	−	0.198355i	−0.318285	−	0.947995i	$-0.603107\pi$
$389$	6.03568e13	−	3.48470e13i	0.343560	−	0.198355i	0.661845	+	0.749640i	$0.269774\pi$
$390$	5.15465e12	−	2.79378e13i	0.0289297	−	0.156796i
$391$			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
$396$	−6.31007e13	+	1.65179e14i	−0.325620	+	0.852376i
$397$	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
$399$	−3.66669e12	−	5.21985e11i	−0.0181519	−	0.00258409i
$400$	2.19675e13			0.107263
$401$	7.77840e13	+	4.49086e13i	0.374625	+	0.216290i	0.675477	−	0.737381i	$-0.263938\pi$
$401$	7.77840e13	+	4.49086e13i	0.374625	+	0.216290i	−0.300852	+	0.953671i	$0.597271\pi$
$402$	−2.36394e13	+	2.77234e13i	−0.112303	+	0.131705i
$403$	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
$408$	−3.59848e13	−	6.63938e12i	−0.157575	−	0.0290734i
$409$	−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
$411$	−2.33679e14	−	4.31149e13i	−0.982855	−	0.181342i
$412$			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
$417$	1.22116e14	−	1.43213e14i	0.474268	−	0.556205i
$418$	−5.34572e12	−	3.08635e12i	−0.0204897	−	0.0118298i
$419$	−3.07167e14			−1.16198			−0.580988	−	0.813912i	$-0.697334\pi$
$419$	−3.07167e14			−1.16198			−0.580988	+	0.813912i	$0.697334\pi$
$420$	1.48540e14	−	5.97063e13i	0.554590	−	0.222920i
$421$	−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
$423$	1.79285e14	+	6.84893e13i	0.643681	+	0.245896i
$424$	−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
$429$	1.87971e13	−	1.01879e14i	0.0624563	−	0.338507i
$430$	−2.56107e14	+	1.47863e14i	−0.840127	+	0.485047i
$431$	−4.99467e14	+	2.88367e14i	−1.61764	+	0.933945i	−0.630111	+	0.776505i	$0.716991\pi$
$431$	−4.99467e14	+	2.88367e14i	−1.61764	+	0.933945i	−0.987529	+	0.157439i	$0.949676\pi$
$432$	3.74708e13	+	6.86162e13i	0.119821	+	0.219415i
$433$		−	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
$438$	−7.98972e13	−	6.81273e13i	−0.236823	−	0.201936i
$439$	−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
$441$	2.52834e14	−	2.42424e14i	0.721811	−	0.692090i
$442$	2.14391e13			0.0604483
$443$	3.42579e14	+	1.97788e14i	0.953981	+	0.550781i	0.894315	−	0.447437i	$-0.147663\pi$
$443$	3.42579e14	+	1.97788e14i	0.953981	+	0.550781i	0.0596658	+	0.998218i	$0.480996\pi$
$444$	−1.51575e14	−	1.29246e14i	−0.416890	−	0.355477i
$445$	−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	$0.0642722\pi$
$449$			1.55097e14i			0.401096i	−0.979684	+	0.200548i	$0.935728\pi$
$450$	1.17266e14	−	1.87671e13i	0.299574	−	0.0479433i
$451$	8.82406e14	−	5.09457e14i	2.22688	−	1.28569i
$452$	−4.89562e12	+	2.82649e12i	−0.0122052	+	0.00704670i
$453$	5.09657e13	−	2.76230e14i	0.125527	−	0.680346i
$454$		−	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
$459$	−1.97765e14	−	4.69986e12i	−0.453085	−	0.0107675i
$460$	−4.15332e14	−	2.39792e14i	−0.940216	−	0.542834i
$461$	3.05686e14			0.683787			0.341893	−	0.939739i	$-0.388932\pi$
$461$	3.05686e14			0.683787			0.341893	+	0.939739i	$0.388932\pi$
$462$	5.41670e14	−	2.17727e14i	1.19730	−	0.481261i
$463$	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
$465$	−5.18931e14	+	6.08583e14i	−1.10693	+	1.29816i
$466$	9.31102e13	+	1.61272e14i	0.196279	+	0.339966i
$467$	1.88438e14	−	3.26385e14i	0.392579	−	0.679966i	−0.600210	−	0.799842i	$-0.704916\pi$
$467$	1.88438e14	−	3.26385e14i	0.392579	−	0.679966i	0.992789	+	0.119876i	$0.0382497\pi$
$468$	−2.88838e13	−	3.55511e13i	−0.0594705	−	0.0731982i
$469$	1.20187e14	−	4.93580e12i	0.244573	−	0.0100440i
$470$		−	2.89600e14i		−	0.582452i
$471$	−3.00915e13	−	5.55203e12i	−0.0598176	−	0.0110366i
$472$	1.29389e14	−	7.47030e13i	0.254225	−	0.146777i
$473$	−9.33927e14	+	5.39203e14i	−1.81375	+	1.04717i
$474$	2.32047e14	+	4.28139e13i	0.445447	+	0.0821871i
$475$			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	$0.0125205\pi$
$479$	2.94522e14	+	5.10127e14i	0.533669	+	0.924342i	−0.465558	+	0.885018i	$0.654146\pi$
$480$	7.65438e13	−	8.97677e13i	0.137114	−	0.160803i
$481$	1.01072e14	+	5.83541e13i	0.178992	+	0.103341i
$482$	7.01503e13			0.122821
$483$	−1.03886e15	−	1.47890e14i	−1.79823	−	0.255994i
$484$	6.80815e14			1.16514
$485$	1.17021e14	+	6.75620e13i	0.198008	+	0.114320i
$486$	2.58645e14	+	3.34273e14i	0.432718	+	0.559245i
$487$	−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	$0.00738062\pi$
$491$			2.93212e13i			0.0463696i	−0.999731	+	0.0231848i	$0.992619\pi$
$492$	8.17415e13	−	4.43032e14i	0.127831	−	0.692830i
$493$	−4.13718e14	+	2.38860e14i	−0.639804	+	0.369391i
$494$	1.38481e12	−	7.99520e11i	0.00211783	−	0.00122273i
$495$	1.42430e15	−	2.27943e14i	2.15414	−	0.344745i
$496$			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
$501$	1.97048e14	+	1.68020e14i	0.278911	+	0.237823i
$502$	−7.46030e14	−	4.30721e14i	−1.04445	−	0.603011i
$503$	−5.59756e14			−0.775130			−0.387565	−	0.921842i	$-0.626684\pi$
$503$	−5.59756e14			−0.775130			−0.387565	+	0.921842i	$0.626684\pi$
$504$	8.21417e13	−	2.44702e14i	0.112511	−	0.335173i
$505$	1.20713e15			1.63551
$506$	−1.51456e15	−	8.74434e14i	−2.02983	−	1.17192i
$507$	−5.53548e14	−	4.72003e14i	−0.733856	−	0.625750i
$508$	6.68898e13	+	1.15857e14i	0.0877223	+	0.151939i
$509$	2.39005e13	−	4.13969e13i	0.0310070	−	0.0537057i	−0.850105	−	0.526612i	$-0.823462\pi$
$509$	2.39005e13	−	4.13969e13i	0.0310070	−	0.0537057i	0.881112	+	0.472907i	$0.156795\pi$
$510$	9.98690e13	+	2.81300e14i	0.128172	+	0.361022i
$511$	1.42247e13	+	3.46373e14i	0.0180604	+	0.439773i
$512$		−	3.51844e13i		−	0.0441942i
$513$	−1.29495e13	+	7.07161e12i	−0.0160919	+	0.00878765i
$514$	1.10549e14	−	6.38254e13i	0.135912	−	0.0784687i
$515$	3.39276e14	−	1.95881e14i	0.412680	−	0.238261i
$516$	−8.65142e13	+	4.68899e14i	−0.104115	+	0.564295i
$517$		−	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	0.715021	−	0.699103i	$-0.246417\pi$
$521$	−2.17238e14	−	3.76268e14i	−0.247930	−	0.429427i	−0.962951	+	0.269675i	$0.913084\pi$
$522$	9.53468e14	+	3.64239e14i	1.07676	+	0.411338i
$523$	−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
$525$	−3.08541e14	−	2.41945e14i	−0.337627	−	0.264753i
$526$	−1.06032e15			−1.14820
$527$	−5.22699e14	−	3.01780e14i	−0.560136	−	0.323395i
$528$	2.79127e14	−	3.27350e14i	0.296016	−	0.347157i
$529$	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
$534$	−5.81403e14	−	1.07272e14i	−0.579429	−	0.106908i
$535$	−4.10963e14	+	2.37270e14i	−0.405375	+	0.234043i
$536$	7.67655e13	−	4.43206e13i	0.0749480	−	0.0432712i
$537$	1.76547e15	+	3.25737e14i	1.70609	+	0.314781i
$538$			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
$543$	9.20784e14	−	1.07986e15i	0.837064	−	0.981679i
$544$	7.70996e13	+	4.45135e13i	0.0693838	+	0.0400588i
$545$	1.81682e14			0.161857
$546$	−2.13142e13	+	1.49721e14i	−0.0187979	+	0.132046i
$547$	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
$549$	−5.10896e14	+	1.33737e15i	−0.437204	+	1.14447i
$550$	−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
$555$	−2.94837e14	+	1.59799e15i	−0.237668	+	1.28814i
$556$	−3.96554e14	+	2.28950e14i	−0.316512	+	0.182739i
$557$	−8.48839e14	+	4.90078e14i	−0.670844	+	0.387312i	−0.796397	−	0.604775i	$-0.793263\pi$
$557$	−8.48839e14	+	4.90078e14i	−0.670844	+	0.387312i	0.125552	+	0.992087i	$0.459930\pi$
$558$	2.03782e14	+	1.27333e15i	0.159470	+	0.996446i
$559$		−	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	0.900485	−	0.434887i	$-0.143212\pi$
$563$	9.88073e13	+	1.71139e14i	0.0736195	+	0.127513i	−0.826866	+	0.562400i	$0.809878\pi$
$564$	−3.55304e14	−	3.02963e14i	−0.262159	−	0.223540i
$565$	3.99362e13	+	2.30572e13i	0.0291810	+	0.0168477i
$566$	−2.05870e14			−0.148972
$567$	2.29434e14	−	1.37644e15i	0.164419	−	0.986391i
$568$	1.86923e14			0.132662
$569$	7.62649e14	+	4.40315e14i	0.536052	+	0.309490i	0.743477	−	0.668761i	$-0.233175\pi$
$569$	7.62649e14	+	4.40315e14i	0.536052	+	0.309490i	−0.207425	+	0.978251i	$0.566508\pi$
$570$	1.69412e13	+	1.44456e13i	0.0117932	+	0.0100559i
$571$	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
$576$	−3.00584e13	−	1.87820e14i	−0.0197534	−	0.123429i
$577$	−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
$579$	5.35387e13	−	2.90175e14i	0.0341929	−	0.185322i
$580$		−	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
$585$	−1.33345e14	+	3.49058e14i	−0.0804674	+	0.210640i
$586$	1.85801e14	+	1.07272e14i	0.111074	+	0.0641286i
$587$	3.00856e15			1.78176			0.890879	−	0.454242i	$-0.150090\pi$
$587$	3.00856e15			1.78176			0.890879	+	0.454242i	$0.150090\pi$
$588$	−7.77013e14	+	3.50012e14i	−0.455883	+	0.205356i
$589$	−4.50168e13			−0.0261662
$590$	−1.05550e15	−	6.09393e14i	−0.607816	−	0.350922i
$591$	−1.96580e14	+	2.30542e14i	−0.112152	+	0.131528i
$592$	2.42318e14	+	4.19708e14i	0.136967	+	0.237234i
$593$	1.36559e15	−	2.36527e15i	0.764750	−	1.32459i	−0.175629	−	0.984457i	$-0.556196\pi$
$593$	1.36559e15	−	2.36527e15i	0.764750	−	1.32459i	0.940379	−	0.340129i	$-0.110471\pi$
$594$	1.21037e15	−	1.98591e15i	0.671571	−	1.10188i
$595$	4.57329e14	−	8.72995e14i	0.251411	−	0.479920i
$596$			1.60088e14i			0.0871976i
$597$	4.57220e14	+	8.43594e13i	0.246755	+	0.0455276i
$598$	3.92348e14	−	2.26522e14i	0.209805	−	0.121131i
$599$	−6.56465e14	+	3.79010e14i	−0.347828	+	0.200818i	−0.663728	−	0.747974i	$-0.731027\pi$
$599$	−6.56465e14	+	3.79010e14i	−0.347828	+	0.200818i	0.315900	+	0.948792i	$0.397693\pi$
$600$	−2.84137e14	−	5.24247e13i	−0.149175	−	0.0275235i
$601$		−	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
$606$	1.26284e15	−	1.48101e15i	0.627694	−	0.736137i
$607$	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
$609$	−1.25679e15	−	3.12670e15i	−0.607951	−	1.51249i
$610$	2.16027e15			1.03560
$611$	2.36921e14	+	1.36787e14i	0.112558	+	0.0649856i
$612$	4.49599e14	+	1.71753e14i	0.211686	+	0.0808672i
$613$	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	$0.135031\pi$
$617$			1.82843e15i			0.823208i	−0.911363	+	0.411604i	$0.864969\pi$
$618$	1.14609e14	−	6.21172e14i	0.0511426	−	0.277188i
$619$	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
$621$	−3.66888e15	+	2.00355e15i	−1.59415	+	0.870554i
$622$		−	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
$627$	6.17784e13	+	5.26776e13i	0.0254604	+	0.0217097i
$628$	6.44728e13	+	3.72234e13i	0.0263390	+	0.0152068i
$629$	−1.22628e15			−0.496603
$630$	−2.06377e15	+	4.17782e14i	−0.828491	+	0.167717i
$631$	−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
$633$	1.17379e15	+	1.00087e15i	0.459059	+	0.391433i
$634$	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
$639$	9.97827e14	−	1.59691e14i	0.370510	−	0.0592959i
$640$	−2.48565e14	+	1.43509e14i	−0.0915060	+	0.0528310i
$641$	−1.66600e15	+	9.61863e14i	−0.608071	+	0.351070i	−0.772210	−	0.635367i	$-0.780849\pi$
$641$	−1.66600e15	+	9.61863e14i	−0.608071	+	0.351070i	0.164139	+	0.986437i	$0.447515\pi$
$642$	−1.38825e14	+	7.52421e14i	−0.0502373	+	0.272281i
$643$		−	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	0.767800	−	0.640689i	$-0.221351\pi$
$647$	−4.93005e14	−	8.53909e14i	−0.170953	−	0.296100i	−0.938753	+	0.344590i	$0.888018\pi$
$648$	−3.20914e14	−	9.76936e14i	−0.110338	−	0.335895i
$649$	−3.84901e15	−	2.22223e15i	−1.31221	−	0.757605i
$650$	1.69284e14			0.0572258
$651$	2.62716e15	−	3.35029e15i	0.880625	−	1.12302i
$652$	−1.04766e15			−0.348223
$653$	4.92267e15	+	2.84210e15i	1.62247	+	0.936736i	0.986255	+	0.165228i	$0.0528361\pi$
$653$	4.92267e15	+	2.84210e15i	1.62247	+	0.936736i	0.636220	+	0.771508i	$0.280497\pi$
$654$	1.90066e14	−	2.22902e14i	0.0621193	−	0.0728513i
$655$	−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	$0.168656\pi$
$659$			3.22505e15i			1.01080i	−0.862884	+	0.505402i	$0.831344\pi$
$660$	−3.45110e15	−	6.36745e14i	−1.07267	−	0.197913i
$661$	−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
$663$	−2.77303e14	−	5.11637e13i	−0.0840678	−	0.0155109i
$664$		−	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
$669$	−4.13294e15	+	4.84697e15i	−1.19238	+	1.39838i
$670$	−6.26218e14	−	3.61547e14i	−0.179190	−	0.103455i
$671$	7.87770e15			2.23576
$672$	−3.87514e14	+	4.94177e14i	−0.109083	+	0.139108i
$673$	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
$675$	−1.56156e15	−	3.71102e13i	−0.428931	−	0.0101935i
$676$	8.84939e14	+	1.53276e15i	0.241105	+	0.417607i
$677$	1.93052e15	−	3.34375e15i	0.521718	−	0.903642i	−0.477963	−	0.878380i	$-0.658625\pi$
$677$	1.93052e15	−	3.34375e15i	0.521718	−	0.903642i	0.999681	−	0.0252619i	$-0.00804195\pi$
$678$	7.00675e13	−	2.48758e13i	0.0187825	−	0.00666828i
$679$	−6.37169e14	−	3.33788e14i	−0.169422	−	0.0887539i
$680$		−	7.26241e14i		−	0.191550i
$681$	−3.17787e13	+	1.72237e14i	−0.00831431	+	0.0450628i
$682$	6.14513e15	−	3.54789e15i	1.59484	−	0.920781i
$683$	−8.18819e14	+	4.72745e14i	−0.210802	+	0.121706i	−0.601684	−	0.798734i	$-0.705503\pi$
$683$	−8.18819e14	+	4.72745e14i	−0.210802	+	0.121706i	0.390882	+	0.920441i	$0.372170\pi$
$684$	3.54460e13	−	5.67271e12i	0.00905229	−	0.00144871i
$685$		−	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
$690$	4.79984e15	+	4.09276e15i	1.16831	+	0.996199i
$691$	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
$693$	−7.52580e15	+	1.52350e15i	−1.78863	+	0.362083i
$694$	7.38331e14			0.174090
$695$	3.23490e15	+	1.86767e15i	0.756737	+	0.436902i
$696$	−1.88957e15	−	1.61121e15i	−0.438544	−	0.373941i
$697$	−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	$0.186794\pi$
$701$			4.96333e15i			1.10745i	−0.832700	+	0.553724i	$0.813206\pi$
$702$	2.88754e14	+	5.28764e14i	0.0639255	+	0.117060i
$703$	−7.92085e13	+	4.57310e13i	−0.0173987	+	0.0100452i
$704$	−9.06424e14	+	5.23324e14i	−0.197552	+	0.114057i
$705$	−6.91121e14	+	3.74581e15i	−0.149456	+	0.810039i
$706$			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
$711$	−2.89923e15	−	1.10755e15i	−0.598411	−	0.228602i
$712$	1.24569e15	+	7.19200e14i	0.255135	+	0.147302i
$713$	−1.27543e16			−2.59217
$714$	−5.92628e14	−	1.47437e15i	−0.119520	−	0.297348i
$715$	2.05610e15			0.411492
$716$	−3.78262e15	−	2.18389e15i	−0.751226	−	0.433720i
$717$	−1.05651e14	+	1.23904e14i	−0.0208218	+	0.0244190i
$718$	8.06192e12	+	1.39637e13i	0.00157672	+	0.00273096i
$719$	4.60261e15	−	7.97195e15i	0.893296	−	1.54723i	0.0573959	−	0.998351i	$-0.481720\pi$
$719$	4.60261e15	−	7.97195e15i	0.893296	−	1.54723i	0.835900	−	0.548882i	$-0.184946\pi$
$720$	−1.20428e15	+	9.78427e14i	−0.231952	+	0.188451i
$721$	−1.76176e15	+	1.11596e15i	−0.336746	+	0.213307i
$722$		−	3.72644e15i		−	0.706869i
$723$	−9.07356e14	−	1.67412e14i	−0.170811	−	0.0315156i
$724$	−2.99011e15	+	1.72634e15i	−0.558632	+	0.322526i
$725$	−3.26673e15	+	1.88605e15i	−0.605696	+	0.349699i
$726$	−8.80597e15	−	1.62474e15i	−1.62041	−	0.298974i
$727$			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
$732$	2.25995e15	−	2.65039e15i	0.397456	−	0.466122i
$733$	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
$735$	5.64196e15	+	4.06170e15i	0.970174	+	0.698437i
$736$	1.88129e15			0.321091
$737$	−2.28358e15	−	1.31843e15i	−0.386853	−	0.223350i
$738$	−2.11456e15	+	5.53530e15i	−0.355558	+	0.930745i
$739$	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	$-0.640026\pi$
$743$		−	1.11691e16i		−	1.80958i	0.425854	−	0.904792i	$-0.359974\pi$
$744$	5.69253e14	−	3.08530e15i	0.0915491	−	0.496188i
$745$	1.13096e15	−	6.52962e14i	0.180547	−	0.104239i
$746$	−5.72395e15	+	3.30472e15i	−0.907052	+	0.523687i
$747$	−5.15213e14	−	3.21931e15i	−0.0810445	−	0.506407i
$748$		−	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
$753$	8.62158e15	+	7.35151e15i	1.29782	+	1.10663i
$754$	1.25999e15	+	7.27457e14i	0.188289	+	0.108709i
$755$	5.57483e15			0.827034
$756$	−1.64643e15	+	2.96906e15i	−0.242479	+	0.437269i
$757$	−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
$759$	1.75032e16	+	1.49248e16i	2.52225	+	2.15069i
$760$	−2.70834e13	−	4.69099e13i	−0.00387462	−	0.00671104i
$761$	−4.16266e15	+	7.20994e15i	−0.591229	+	1.02404i	0.402839	+	0.915271i	$0.368024\pi$
$761$	−4.16266e15	+	7.20994e15i	−0.591229	+	1.02404i	−0.994067	+	0.108767i	$0.965310\pi$
$762$	−5.88695e14	−	1.65817e15i	−0.0830114	−	0.233818i
$763$	−9.66333e14	+	3.96849e13i	−0.135283	+	0.00555573i
$764$			3.86874e15i			0.537720i
$765$	−6.20436e14	−	3.87680e15i	−0.0856168	−	0.534977i
$766$	−4.66619e15	+	2.69403e15i	−0.639299	+	0.369100i
$767$	9.97088e14	−	5.75669e14i	0.135631	−	0.0783066i
$768$	−8.39664e13	+	4.55090e14i	−0.0113402	+	0.0614626i
$769$			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	0.871346	−	0.490669i	$-0.163247\pi$
$773$	8.24239e13	+	1.42762e14i	0.0107415	+	0.0186049i	−0.860605	+	0.509274i	$0.829914\pi$
$774$	2.23803e15	−	5.85849e15i	0.289594	−	0.758071i
$775$	−4.12725e15	−	2.38287e15i	−0.530275	−	0.306154i
$776$	−5.30058e14			−0.0676213
$777$	1.21913e15	−	8.56379e15i	0.154431	−	1.08480i
$778$	2.23021e15			0.280516
$779$	−1.79140e14	−	1.03426e14i	−0.0223736	−	0.0129174i
$780$	5.89854e14	−	6.91759e14i	0.0731517	−	0.0857896i
$781$	−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
$786$	−4.60832e15	−	8.50257e14i	−0.547922	−	0.101094i
$787$	−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
$789$	1.37147e16	+	2.53042e15i	1.59684	+	0.294625i
$790$			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
$795$	1.07997e16	−	1.26655e16i	1.20612	−	1.41450i
$796$	−9.79621e14	−	5.65585e14i	−0.108652	−	0.0627301i
$797$	3.18212e15			0.350507			0.175253	−	0.984523i	$-0.443926\pi$
$797$	3.18212e15			0.350507			0.175253	+	0.984523i	$0.443926\pi$
$798$	−9.32625e13	−	7.31327e13i	−0.0102021	−	0.00800010i
$799$	−2.87449e15			−0.312287
$800$	6.08781e14	+	3.51480e14i	0.0656850	+	0.0379232i
$801$	7.26413e15	+	2.77500e15i	0.778403	+	0.297361i
$802$	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
$807$	1.77004e15	−	9.59344e15i	0.182045	−	0.986665i
$808$	−4.10088e15	+	2.36764e15i	−0.418904	+	0.241854i
$809$	−8.54281e15	+	4.93219e15i	−0.866730	+	0.500407i	−0.866260	−	0.499593i	$-0.833483\pi$
$809$	−8.54281e15	+	4.93219e15i	−0.866730	+	0.500407i	−0.000469819		1.00000i	$0.500150\pi$
$810$	−5.59276e15	+	6.25184e15i	−0.563584	+	0.629999i
$811$		−	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
$816$	−8.91011e14	−	7.59753e14i	−0.0862158	−	0.0735151i
$817$	1.89599e14	+	1.09465e14i	0.0182228	+	0.0105210i
$818$	−1.32814e15			−0.126795
$819$	6.32992e14	−	1.88570e15i	0.0600257	−	0.178818i
$820$	8.94121e15			0.842209
$821$	−6.35876e13	−	3.67123e13i	−0.00594957	−	0.00343498i	0.497022	−	0.867738i	$-0.334427\pi$
$821$	−6.35876e13	−	3.67123e13i	−0.00594957	−	0.00343498i	−0.502972	+	0.864303i	$0.667760\pi$
$822$	−5.78606e15	−	4.93370e15i	−0.537759	−	0.458540i
$823$	−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	$-0.941281\pi$
$827$		−	4.08106e15i		−	0.366853i	0.983033	−	0.183427i	$-0.0587190\pi$
$828$	1.00426e16	−	1.60721e15i	0.896771	−	0.143518i
$829$	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
$831$	4.04463e15	−	2.19215e16i	0.354057	−	1.91896i
$832$		−	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
$837$	4.02961e14	−	1.69562e16i	0.0339057	−	1.42672i
$838$	−8.51245e15	−	4.91467e15i	−0.711562	−	0.410820i
$839$	2.21228e15			0.183717			0.0918586	−	0.995772i	$-0.470719\pi$
$839$	2.21228e15			0.183717			0.0918586	+	0.995772i	$0.470719\pi$
$840$	5.07176e15	+	7.22009e14i	0.418430	+	0.0595671i
$841$	−2.02189e16			−1.65722
$842$	−9.42189e15	−	5.43973e15i	−0.767223	−	0.442956i
$843$	3.76816e15	−	4.41916e15i	0.304844	−	0.357510i
$844$	−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
$849$	2.66282e15	+	4.91303e14i	0.207181	+	0.0382258i
$850$	−1.54040e15	+	8.89348e14i	−0.119077	+	0.0687492i
$851$	−2.24416e16	+	1.29566e16i	−1.72362	+	0.995130i
$852$	−2.41775e15	−	4.46086e14i	−0.184499	−	0.0340409i
$853$			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	$-0.823804\pi$
$857$	−1.19172e16	−	2.06412e16i	−0.880604	−	1.52525i	−0.0299333	−	0.999552i	$-0.509529\pi$
$858$	2.15098e15	−	2.52259e15i	0.157927	−	0.185211i
$859$	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
$861$	1.81519e16	−	7.29622e15i	1.30739	−	0.525510i
$862$	−1.84555e16			−1.32080
$863$	1.60715e16	+	9.27889e15i	1.14287	+	0.659837i	0.947140	−	0.320821i	$-0.103959\pi$
$863$	1.60715e16	+	9.27889e15i	1.14287	+	0.659837i	0.195731	+	0.980658i	$0.437292\pi$
$864$	−5.94378e13	+	2.50108e15i	−0.00419989	+	0.176727i
$865$	−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
$870$	−3.67551e15	+	1.99209e16i	−0.250012	+	1.35504i
$871$	5.91563e14	−	3.41539e14i	0.0399854	−	0.0230856i
$872$	−6.17211e14	+	3.56347e14i	−0.0414566	+	0.0239350i
$873$	−2.82954e15	+	4.52835e14i	−0.188859	+	0.0302247i
$874$			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
$879$	−2.14724e15	−	1.83092e15i	−0.138020	−	0.117688i
$880$	7.39419e15	+	4.26904e15i	0.472319	+	0.272694i
$881$	5.43041e15			0.344719			0.172359	−	0.985034i	$-0.444861\pi$
$881$	5.43041e15			0.344719			0.172359	+	0.985034i	$0.444861\pi$
$882$	1.08855e16	−	2.67289e15i	0.686708	−	0.168618i
$883$	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
$885$	1.21980e16	+	1.04011e16i	0.755267	+	0.644006i
$886$	6.32921e15	+	1.09625e16i	0.389461	+	0.674567i
$887$	−1.44556e16	+	2.50378e16i	−0.884008	+	1.53115i	−0.0371613	+	0.999309i	$0.511832\pi$
$887$	−1.44556e16	+	2.50378e16i	−0.884008	+	1.53115i	−0.846847	+	0.531837i	$0.821502\pi$
$888$	−2.13263e15	−	6.00697e15i	−0.129612	−	0.365077i
$889$	−2.69580e15	+	5.14602e15i	−0.162828	+	0.310822i
$890$		−	1.17338e16i		−	0.704358i
$891$	−2.03947e16	+	2.27981e16i	−1.21672	+	1.36010i
$892$	1.34211e16	−	7.74870e15i	0.795761	−	0.459433i
$893$	−1.85671e14	+	1.07197e14i	−0.0109411	+	0.00631685i
$894$	3.82045e14	−	2.07065e15i	0.0223748	−	0.121269i
$895$			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
$900$	3.55005e15	+	1.35617e15i	0.200401	+	0.0765562i
$901$	1.08781e16	+	6.28048e15i	0.610334	+	0.352376i
$902$	3.26053e16			1.81824
$903$	−1.92117e16	+	7.72223e15i	−1.06484	+	0.428016i
$904$	−1.80895e14			−0.00996554
$905$	2.43920e16	+	1.40827e16i	1.33561	+	0.771115i
$906$	5.83208e15	−	6.83965e15i	0.317408	−	0.372245i
$907$	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	$-0.894175\pi$
$911$		−	1.23620e16i		−	0.652737i	0.945243	−	0.326369i	$-0.105825\pi$
$912$	−8.58860e13	−	1.58464e13i	−0.00450766	−	0.000831685i
$913$	−1.55364e16	+	8.96997e15i	−0.810518	+	0.467953i
$914$	1.35595e15	−	7.82859e14i	0.0703138	−	0.0405957i
$915$	−2.79419e16	−	5.15542e15i	−1.44026	−	0.265734i
$916$		−	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
$921$	2.08208e16	−	2.44179e16i	1.03531	−	1.21417i
$922$	8.47143e15	+	4.89098e15i	0.418732	+	0.241755i
$923$	1.44045e15			0.0707764
$924$	1.84948e16	+	2.63290e15i	0.903346	+	0.128599i
$925$	−9.68271e15			−0.470129
$926$	6.69399e15	+	3.86478e15i	0.323091	+	0.186537i
$927$	−2.96481e15	+	7.76100e15i	−0.142252	+	0.372374i
$928$	3.02080e15	+	5.23218e15i	0.144082	+	0.249557i
$929$	−5.51256e15	+	9.54803e15i	−0.261377	+	0.452718i	−0.966608	−	0.256260i	$-0.917510\pi$
$929$	−5.51256e15	+	9.54803e15i	−0.261377	+	0.452718i	0.705231	+	0.708977i	$0.250843\pi$
$930$	−2.41184e16	+	8.56266e15i	−1.13682	+	0.403601i
$931$	3.20849e13	+	3.89976e14i	0.00150341	+	0.0182732i
$932$			5.95905e15i			0.277581i
$933$	−4.00375e15	+	2.16999e16i	−0.185403	+	1.00487i
$934$	1.04443e16	−	6.03003e15i	0.480809	−	0.277595i
$935$	−1.87095e16	+	1.08019e16i	−0.856245	+	0.494353i
$936$	−2.31633e14	−	1.44736e15i	−0.0105386	−	0.0658506i
$937$		−	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	0.944530	−	0.328426i	$-0.106518\pi$
$941$	4.25139e15	+	7.36362e15i	0.187840	+	0.325348i	−0.756690	+	0.653774i	$0.773185\pi$
$942$	−7.45088e14	−	6.35326e14i	−0.0327286	−	0.0279072i
$943$	−5.07544e16	−	2.93031e16i	−2.21646	−	1.27967i
$944$	4.78099e15			0.207574
$945$	2.76907e16	−	4.78658e14i	1.19525	−	0.0206609i
$946$	−3.45090e16			−1.48092
$947$	−2.75634e16	−	1.59137e16i	−1.17600	−	0.678965i	−0.220916	−	0.975293i	$-0.570905\pi$
$947$	−2.75634e16	−	1.59137e16i	−1.17600	−	0.678965i	−0.955086	+	0.296328i	$0.904238\pi$
$948$	5.74566e15	+	4.89925e15i	0.243722	+	0.207818i
$949$	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	$-0.741819\pi$
$953$		−	3.51889e16i		−	1.45009i	0.688702	−	0.725044i	$-0.258181\pi$
$954$	−4.24099e15	−	2.64999e16i	−0.173761	−	1.08574i
$955$	2.73312e16	−	1.57797e16i	1.11337	−	0.642806i
$956$	3.43086e14	−	1.98081e14i	0.0138958	−	0.00802276i
$957$	−1.34032e16	+	7.26442e16i	−0.539751	+	2.92540i
$958$			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
$963$	3.59126e15	−	9.40084e15i	0.139734	−	0.365782i
$964$	1.94406e15	+	1.12241e15i	0.0752119	+	0.0434236i
$965$	5.85627e15			0.225279
$966$	−2.64234e16	−	2.07202e16i	−1.01068	−	0.792536i
$967$	−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
$969$	1.43383e14	−	1.68154e14i	0.00539158	−	0.00632305i
$970$	2.16198e15	+	3.74467e15i	0.0808366	+	0.140013i
$971$	1.84284e16	−	3.19190e16i	0.685145	−	1.18671i	−0.288246	−	0.957556i	$-0.593072\pi$
$971$	1.84284e16	−	3.19190e16i	0.685145	−	1.18671i	0.973391	−	0.229150i	$-0.0735947\pi$
$972$	1.81941e15	+	1.34020e16i	0.0672616	+	0.495455i
$973$	−1.76138e16	−	9.22719e15i	−0.647488	−	0.339194i
$974$		−	1.49789e16i		−	0.547527i
$975$	−2.18959e15	−	4.03990e14i	−0.0795861	−	0.0146840i
$976$	−7.33887e15	+	4.23710e15i	−0.265250	+	0.153142i
$977$	1.34703e16	−	7.77707e15i	0.484124	−	0.279509i	−0.238009	−	0.971263i	$-0.576495\pi$
$977$	1.34703e16	−	7.77707e15i	0.484124	−	0.279509i	0.722134	+	0.691754i	$0.243162\pi$
$978$	1.35509e16	+	2.50020e15i	0.484288	+	0.0893535i
$979$		−	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	0.876161	−	0.482019i	$-0.160096\pi$
$983$	5.93955e14	+	1.02876e15i	0.0206400	+	0.0357495i	−0.855521	+	0.517768i	$0.826763\pi$
$984$	9.35380e15	−	1.09698e16i	0.323232	−	0.379075i
$985$	−5.20749e15	−	3.00655e15i	−0.178949	−	0.103316i
$986$	−1.52871e16			−0.522398
$987$	2.85774e15	−	2.00742e16i	0.0971132	−	0.682172i
$988$	5.11693e13			0.00172920
$989$	5.37178e16	+	3.10140e16i	1.80526	+	1.04227i
$990$	4.31185e16	+	1.64719e16i	1.44102	+	0.550490i
$991$	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
$996$	−1.43922e15	+	7.80042e15i	−0.0465264	+	0.252169i
$997$	−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
$999$	−1.65162e16	−	3.02443e16i	−0.525170	−	0.961686i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.12.f.a.5.9	✓	60	3.2	odd	2	inner
42.12.f.a.5.19	yes	60	1.1	even	1	trivial
42.12.f.a.17.9	yes	60	7.3	odd	6	inner
42.12.f.a.17.19	yes	60	21.17	even	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} +(-320.266 - 273.087i) 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} +(27994.1 + 174921. i) q^{9} +(231494. - 133653. i) q^{10} +(844173. - 487383. i) q^{11} +(78199.8 - 423836. 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} +(-2.02294e6 + 5.29546e6i) q^{18} +(-171378. - 98945.2i) q^{19} +8.55380e6 q^{20} +(1.73654e7 - 6.98009e6i) q^{21} +3.11925e7 q^{22} +(-4.85553e7 - 2.80334e7i) q^{23} +(8.94851e6 - 1.04945e7i) 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} +(-1.10639e8 - 2.04134e7i) q^{30} +(1.97006e8 - 1.13742e8i) q^{31} +(-2.90590e7 + 1.67772e7i) q^{32} +(-4.03458e8 - 7.44400e7i) 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} +(6.89581e7 - 8.08716e7i) q^{39} +(2.37050e8 + 1.36861e8i) q^{40} +1.04529e9 q^{41} +(5.92924e8 + 8.44080e7i) q^{42} -1.10632e9 q^{43} +(8.64433e8 + 4.99081e8i) q^{44} +(1.38233e9 + 5.28071e8i) 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} +(-2.02618e8 + 1.09817e9i) q^{51} +(-2.23932e8 + 1.29287e8i) q^{52} +(-4.09998e9 + 2.36713e9i) q^{53} +(2.09400e9 - 1.14352e9i) 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} +(-2.73949e9 - 2.33593e9i) q^{60} +(6.99890e9 + 4.04081e9i) q^{61} +7.27947e9 q^{62} +(-7.46771e9 - 2.50677e9i) q^{63} -1.07374e9 q^{64} +(1.82673e9 + 1.05466e9i) q^{65} +(-9.98992e9 - 8.51827e9i) 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} +(-5.73181e9 + 9.17310e8i) q^{72} +(6.75151e9 - 3.89799e9i) q^{73} +(1.28085e10 - 7.39497e9i) q^{74} +(-1.59988e9 + 8.67118e9i) 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} +(-2.98137e10 + 9.79351e9i) q^{81} +(2.89679e10 + 1.67247e10i) q^{82} -1.84043e10 q^{83} +(1.50811e10 + 1.18260e10i) q^{84} -2.21631e10 q^{85} +(-3.06593e10 - 1.77012e10i) q^{86} +(-4.91704e10 + 5.76652e10i) 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} +(-9.41559e10 - 1.73722e10i) q^{93} +(3.00241e10 - 1.73344e10i) q^{94} +(-1.43158e9 + 8.26521e8i) q^{95} +(1.38883e10 + 2.56245e9i) 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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