LMFDB - Embedded newform 48.8.k.a.11.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,8,Mod(11,48)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(48, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("48.11");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	48.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$14.9944812232$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$54$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			11.9
Character	$\chi$	$=$	48.11
Dual form			48.8.k.a.35.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.3435 - 4.58397i) q^{2} +(45.5791 + 10.4665i) q^{3} +(85.9744 + 94.8283i) q^{4} +(25.0262 - 25.0262i) q^{5} +(-423.468 - 317.193i) q^{6} -1569.84 q^{7} +(-454.583 - 1374.96i) q^{8} +(1967.91 + 954.104i) q^{9} +O(q^{10})$	\(q+(-10.3435 - 4.58397i) q^{2} +(45.5791 + 10.4665i) q^{3} +(85.9744 + 94.8283i) q^{4} +(25.0262 - 25.0262i) q^{5} +(-423.468 - 317.193i) q^{6} -1569.84 q^{7} +(-454.583 - 1374.96i) q^{8} +(1967.91 + 954.104i) q^{9} +(-373.577 + 144.138i) q^{10} +(-2008.55 - 2008.55i) q^{11} +(2926.12 + 5222.03i) q^{12} +(6734.71 - 6734.71i) q^{13} +(16237.6 + 7196.12i) q^{14} +(1402.61 - 878.735i) q^{15} +(-1600.81 + 16305.6i) q^{16} -11311.5i q^{17} +(-15981.4 - 18889.6i) q^{18} +(-22153.6 - 22153.6i) q^{19} +(4524.80 + 221.579i) q^{20} +(-71552.0 - 16430.7i) q^{21} +(11568.2 + 29982.5i) q^{22} -67536.9i q^{23} +(-6328.51 - 67427.2i) q^{24} +76872.4i q^{25} +(-100532. + 38788.5i) q^{26} +(79709.3 + 64084.2i) q^{27} +(-134966. - 148866. i) q^{28} +(-178633. - 178633. i) q^{29} +(-18535.9 + 2659.65i) q^{30} -150154. i q^{31} +(91302.4 - 161318. i) q^{32} +(-70525.5 - 112570. i) q^{33} +(-51851.8 + 117001. i) q^{34} +(-39287.2 + 39287.2i) q^{35} +(78713.5 + 268642. i) q^{36} +(19560.6 + 19560.6i) q^{37} +(127593. + 330696. i) q^{38} +(377451. - 236473. i) q^{39} +(-45786.4 - 23033.5i) q^{40} -26965.0 q^{41} +(664778. + 497943. i) q^{42} +(-297319. + 297319. i) q^{43} +(17783.5 - 363151. i) q^{44} +(73126.8 - 25371.6i) q^{45} +(-309587. + 698566. i) q^{46} -173836. q^{47} +(-243625. + 726440. i) q^{48} +1.64086e6 q^{49} +(352381. - 795126. i) q^{50} +(118392. - 515570. i) q^{51} +(1.21765e6 + 59628.5i) q^{52} +(-816830. + 816830. i) q^{53} +(-530709. - 1.02824e6i) q^{54} -100533. q^{55} +(713623. + 2.15847e6i) q^{56} +(-777869. - 1.24161e6i) q^{57} +(1.02884e6 + 2.66654e6i) q^{58} +(-1.70171e6 - 1.70171e6i) q^{59} +(203917. + 57458.1i) q^{60} +(1.47422e6 - 1.47422e6i) q^{61} +(-688303. + 1.55312e6i) q^{62} +(-3.08930e6 - 1.49779e6i) q^{63} +(-1.68386e6 + 1.25006e6i) q^{64} -337089. i q^{65} +(213458. + 1.48765e6i) q^{66} +(819300. + 819300. i) q^{67} +(1.07265e6 - 972503. i) q^{68} +(706873. - 3.07827e6i) q^{69} +(586457. - 226274. i) q^{70} +195694. i q^{71} +(417276. - 3.13951e6i) q^{72} +2.35222e6i q^{73} +(-112659. - 291990. i) q^{74} +(-804582. + 3.50377e6i) q^{75} +(196145. - 4.00542e6i) q^{76} +(3.15311e6 + 3.15311e6i) q^{77} +(-4.98814e6 + 715730. i) q^{78} +1.16965e6i q^{79} +(368005. + 448130. i) q^{80} +(2.96234e6 + 3.75517e6i) q^{81} +(278912. + 123607. i) q^{82} +(841153. - 841153. i) q^{83} +(-4.59354e6 - 8.19778e6i) q^{84} +(-283085. - 283085. i) q^{85} +(4.43821e6 - 1.71240e6i) q^{86} +(-6.27228e6 - 1.00116e7i) q^{87} +(-1.84862e6 + 3.67472e6i) q^{88} +1.16031e7 q^{89} +(-872687. - 72780.9i) q^{90} +(-1.05724e7 + 1.05724e7i) q^{91} +(6.40441e6 - 5.80645e6i) q^{92} +(1.57159e6 - 6.84390e6i) q^{93} +(1.79807e6 + 796861. i) q^{94} -1.10884e6 q^{95} +(5.84991e6 - 6.39713e6i) q^{96} +2.71643e6 q^{97} +(-1.69722e7 - 7.52168e6i) q^{98} +(-2.03627e6 - 5.86900e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	$ 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) $ 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/48\mathbb{Z}\right)^\times$.

$n$	$17$	$31$	$37$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−10.3435	−	4.58397i	−0.914241	−	0.405170i
$2$	−10.3435	−	4.58397i	−0.914241	−	0.405170i
$3$	45.5791	+	10.4665i	0.974633	+	0.223808i
$3$	45.5791	+	10.4665i	0.974633	+	0.223808i
$4$	85.9744	+	94.8283i	0.671675	+	0.740846i
$5$	25.0262	−	25.0262i	0.0895364	−	0.0895364i	−0.660920	−	0.750456i	$-0.729834\pi$
$5$	25.0262	−	25.0262i	0.0895364	−	0.0895364i	0.750456	+	0.660920i	$0.229834\pi$
$6$	−423.468	−	317.193i	−0.800370	−	0.599507i
$7$	−1569.84			−1.72987			−0.864934	−	0.501885i	$-0.832640\pi$
$7$	−1569.84			−1.72987			−0.864934	+	0.501885i	$0.832640\pi$
$8$	−454.583	−	1374.96i	−0.313905	−	0.949455i
$9$	1967.91	+	954.104i	0.899820	+	0.436262i
$10$	−373.577	+	144.138i	−0.118135	+	0.0455805i
$11$	−2008.55	−	2008.55i	−0.454997	−	0.454997i	0.442012	−	0.897009i	$-0.354265\pi$
$11$	−2008.55	−	2008.55i	−0.454997	−	0.454997i	−0.897009	+	0.442012i	$0.854265\pi$
$12$	2926.12	+	5222.03i	0.488829	+	0.872379i
$13$	6734.71	−	6734.71i	0.850193	−	0.850193i	−0.139964	−	0.990157i	$-0.544699\pi$
$13$	6734.71	−	6734.71i	0.850193	−	0.850193i	0.990157	+	0.139964i	$0.0446986\pi$
$14$	16237.6	+	7196.12i	1.58152	+	0.700890i
$15$	1402.61	−	878.735i	0.107304	−	0.0672262i
$16$	−1600.81	+	16305.6i	−0.0977056	+	0.995215i
$17$		−	11311.5i		−	0.558407i	−0.960232	−	0.279203i	$-0.909930\pi$
$17$		−	11311.5i		−	0.558407i	0.960232	−	0.279203i	$-0.0900704\pi$
$18$	−15981.4	−	18889.6i	−0.645893	−	0.763428i
$19$	−22153.6	−	22153.6i	−0.740979	−	0.740979i	0.231787	−	0.972766i	$-0.425543\pi$
$19$	−22153.6	−	22153.6i	−0.740979	−	0.740979i	−0.972766	+	0.231787i	$0.925543\pi$
$20$	4524.80	+	221.579i	0.126472	+	0.00619333i
$21$	−71552.0	−	16430.7i	−1.68599	−	0.387159i
$22$	11568.2	+	29982.5i	0.231626	+	0.600328i
$23$		−	67536.9i		−	1.15743i	−0.815531	−	0.578714i	$-0.803555\pi$
$23$		−	67536.9i		−	1.15743i	0.815531	−	0.578714i	$-0.196445\pi$
$24$	−6328.51	−	67427.2i	−0.0934464	−	0.995624i
$25$			76872.4i			0.983966i
$26$	−100532.	+	38788.5i	−1.12175	+	0.432809i
$27$	79709.3	+	64084.2i	0.779356	+	0.626582i
$28$	−134966.	−	148866.i	−1.16191	−	1.28157i
$29$	−178633.	−	178633.i	−1.36010	−	1.36010i	−0.873787	−	0.486309i	$-0.838343\pi$
$29$	−178633.	−	178633.i	−1.36010	−	1.36010i	−0.486309	−	0.873787i	$-0.661657\pi$
$30$	−18535.9	+	2659.65i	−0.125340	+	0.0179846i
$31$		−	150154.i		−	0.905257i	−0.891699	−	0.452628i	$-0.850486\pi$
$31$		−	150154.i		−	0.905257i	0.891699	−	0.452628i	$-0.149514\pi$
$32$	91302.4	−	161318.i	0.492558	−	0.870280i
$33$	−70525.5	−	112570.i	−0.341623	−	0.545287i
$34$	−51851.8	+	117001.i	−0.226250	+	0.510519i
$35$	−39287.2	+	39287.2i	−0.154886	+	0.154886i
$36$	78713.5	+	268642.i	0.281184	+	0.959654i
$37$	19560.6	+	19560.6i	0.0634859	+	0.0634859i	0.738137	−	0.674651i	$-0.235706\pi$
$37$	19560.6	+	19560.6i	0.0634859	+	0.0634859i	−0.674651	+	0.738137i	$0.735706\pi$
$38$	127593.	+	330696.i	0.377211	+	0.977656i
$39$	377451.	−	236473.i	1.01891	−	0.638346i
$40$	−45786.4	−	23033.5i	−0.113117	−	0.0569049i
$41$	−26965.0			−0.0611022			−0.0305511	−	0.999533i	$-0.509726\pi$
$41$	−26965.0			−0.0611022			−0.0305511	+	0.999533i	$0.509726\pi$
$42$	664778.	+	497943.i	1.38453	+	1.03707i
$43$	−297319.	+	297319.i	−0.570273	+	0.570273i	−0.932205	−	0.361932i	$-0.882117\pi$
$43$	−297319.	+	297319.i	−0.570273	+	0.570273i	0.361932	+	0.932205i	$0.382117\pi$
$44$	17783.5	−	363151.i	0.0314726	−	0.642692i
$45$	73126.8	−	25371.6i	0.119628	−	0.0415054i
$46$	−309587.	+	698566.i	−0.468955	+	1.05817i
$47$	−173836.			−0.244230			−0.122115	−	0.992516i	$-0.538968\pi$
$47$	−173836.			−0.244230			−0.122115	+	0.992516i	$0.538968\pi$
$48$	−243625.	+	726440.i	−0.317964	+	0.948103i
$49$	1.64086e6			1.99245
$50$	352381.	−	795126.i	0.398673	−	0.899583i
$51$	118392.	−	515570.i	0.124976	−	0.544242i
$52$	1.21765e6	+	59628.5i	1.20092	+	0.0588087i
$53$	−816830.	+	816830.i	−0.753644	+	0.753644i	−0.975157	−	0.221514i	$-0.928900\pi$
$53$	−816830.	+	816830.i	−0.753644	+	0.753644i	0.221514	+	0.975157i	$0.428900\pi$
$54$	−530709.	−	1.02824e6i	−0.458647	−	0.888618i
$55$	−100533.			−0.0814776
$56$	713623.	+	2.15847e6i	0.543014	+	1.64243i
$57$	−777869.	−	1.24161e6i	−0.556346	−	0.888020i
$58$	1.02884e6	+	2.66654e6i	0.692386	+	1.79453i
$59$	−1.70171e6	−	1.70171e6i	−1.07871	−	1.07871i	−0.996626	−	0.0820800i	$-0.973844\pi$
$59$	−1.70171e6	−	1.70171e6i	−1.07871	−	1.07871i	−0.0820800	−	0.996626i	$-0.526156\pi$
$60$	203917.	+	57458.1i	0.121878	+	0.0343417i
$61$	1.47422e6	−	1.47422e6i	0.831585	−	0.831585i	−0.156149	−	0.987734i	$-0.549908\pi$
$61$	1.47422e6	−	1.47422e6i	0.831585	−	0.831585i	0.987734	+	0.156149i	$0.0499080\pi$
$62$	−688303.	+	1.55312e6i	−0.366783	+	0.827623i
$63$	−3.08930e6	−	1.49779e6i	−1.55657	−	0.754675i
$64$	−1.68386e6	+	1.25006e6i	−0.802928	+	0.596076i
$65$		−	337089.i		−	0.152246i
$66$	213458.	+	1.48765e6i	0.0913922	+	0.636939i
$67$	819300.	+	819300.i	0.332798	+	0.332798i	0.853648	−	0.520850i	$-0.174385\pi$
$67$	819300.	+	819300.i	0.332798	+	0.332798i	−0.520850	+	0.853648i	$0.674385\pi$
$68$	1.07265e6	−	972503.i	0.413693	−	0.375068i
$69$	706873.	−	3.07827e6i	0.259042	−	1.12807i
$70$	586457.	−	226274.i	0.204359	−	0.0788482i
$71$			195694.i			0.0648893i	0.999474	+	0.0324447i	$0.0103293\pi$
$71$			195694.i			0.0648893i	−0.999474	+	0.0324447i	$0.989671\pi$
$72$	417276.	−	3.13951e6i	0.131753	−	0.991283i
$73$			2.35222e6i			0.707697i	0.935303	+	0.353848i	$0.115127\pi$
$73$			2.35222e6i			0.707697i	−0.935303	+	0.353848i	$0.884873\pi$
$74$	−112659.	−	291990.i	−0.0323189	−	0.0837640i
$75$	−804582.	+	3.50377e6i	−0.220220	+	0.959006i
$76$	196145.	−	4.00542e6i	0.0512543	−	1.04665i
$77$	3.15311e6	+	3.15311e6i	0.787085	+	0.787085i
$78$	−4.98814e6	+	715730.i	−1.19016	+	0.170773i
$79$			1.16965e6i			0.266907i	0.991055	+	0.133454i	$0.0426068\pi$
$79$			1.16965e6i			0.266907i	−0.991055	+	0.133454i	$0.957393\pi$
$80$	368005.	+	448130.i	0.0803598	+	0.0978563i
$81$	2.96234e6	+	3.75517e6i	0.619352	+	0.785114i
$82$	278912.	+	123607.i	0.0558622	+	0.0247568i
$83$	841153.	−	841153.i	0.161474	−	0.161474i	−0.621746	−	0.783219i	$-0.713576\pi$
$83$	841153.	−	841153.i	0.161474	−	0.161474i	0.783219	+	0.621746i	$0.213576\pi$
$84$	−4.59354e6	−	8.19778e6i	−0.845611	−	1.50910i
$85$	−283085.	−	283085.i	−0.0499978	−	0.0499978i
$86$	4.43821e6	−	1.71240e6i	0.752425	−	0.290310i
$87$	−6.27228e6	−	1.00116e7i	−1.02119	−	1.63000i
$88$	−1.84862e6	+	3.67472e6i	−0.289173	+	0.574824i
$89$	1.16031e7			1.74465			0.872325	−	0.488927i	$-0.162612\pi$
$89$	1.16031e7			1.74465			0.872325	+	0.488927i	$0.162612\pi$
$90$	−872687.	−	72780.9i	−0.126186	−	0.0105237i
$91$	−1.05724e7	+	1.05724e7i	−1.47072	+	1.47072i
$92$	6.40441e6	−	5.80645e6i	0.857476	−	0.777415i
$93$	1.57159e6	−	6.84390e6i	0.202604	−	0.882294i
$94$	1.79807e6	+	796861.i	0.223285	+	0.0989544i
$95$	−1.10884e6			−0.132689
$96$	5.84991e6	−	6.39713e6i	0.674839	−	0.737965i
$97$	2.71643e6			0.302202			0.151101	−	0.988518i	$-0.451718\pi$
$97$	2.71643e6			0.302202			0.151101	+	0.988518i	$0.451718\pi$
$98$	−1.69722e7	−	7.52168e6i	−1.82158	−	0.807279i
$99$	−2.03627e6	−	5.86900e6i	−0.210918	−	0.607913i
$100$	−7.28968e6	+	6.60906e6i	−0.728968	+	0.660906i
$101$	−1.00800e7	+	1.00800e7i	−0.973500	+	0.973500i	−0.999658	−	0.0261576i	$-0.991673\pi$
$101$	−1.00800e7	+	1.00800e7i	−0.973500	+	0.973500i	0.0261576	+	0.999658i	$0.491673\pi$
$102$	−3.58794e6	+	4.79007e6i	−0.334769	+	0.446932i
$103$	−2.69177e6			−0.242721			−0.121361	−	0.992608i	$-0.538726\pi$
$103$	−2.69177e6			−0.242721			−0.121361	+	0.992608i	$0.538726\pi$
$104$	−1.23214e7	−	6.19846e6i	−1.07410	−	0.540340i
$105$	−2.20187e6	+	1.37948e6i	−0.185622	+	0.116293i
$106$	1.21932e7	−	4.70452e6i	0.994366	−	0.383659i
$107$	8.10790e6	+	8.10790e6i	0.639831	+	0.639831i	0.950514	−	0.310683i	$-0.100558\pi$
$107$	8.10790e6	+	8.10790e6i	0.639831	+	0.639831i	−0.310683	+	0.950514i	$0.600558\pi$
$108$	775960.	+	1.30683e7i	0.0592729	+	0.998242i
$109$	4.75466e6	−	4.75466e6i	0.351663	−	0.351663i	−0.509065	−	0.860728i	$-0.670009\pi$
$109$	4.75466e6	−	4.75466e6i	0.351663	−	0.351663i	0.860728	+	0.509065i	$0.170009\pi$
$110$	1.03986e6	+	460839.i	0.0744902	+	0.0330123i
$111$	686825.	+	1.09629e6i	0.0476668	+	0.0760841i
$112$	2.51302e6	−	2.55972e7i	0.169018	−	1.72159i
$113$			2.31903e7i			1.51193i	0.654612	+	0.755965i	$0.272832\pi$
$113$			2.31903e7i			1.51193i	−0.654612	+	0.755965i	$0.727168\pi$
$114$	2.35436e6	+	1.64083e7i	0.148836	+	1.03728i
$115$	−1.69019e6	−	1.69019e6i	−0.103632	−	0.103632i
$116$	1.58160e6	−	3.22974e7i	0.0940793	−	1.92116i
$117$	1.96789e7	−	6.82767e6i	1.13593	−	0.394114i
$118$	9.80097e6	+	2.54021e7i	0.549139	+	1.42326i
$119$			1.77574e7i			0.965970i
$120$	−1.84582e6	−	1.52907e6i	−0.0975115	−	0.0807778i
$121$		−	1.14186e7i		−	0.585956i
$122$	−2.20062e7	+	8.49073e6i	−1.09720	+	0.423336i
$123$	−1.22904e6	−	282228.i	−0.0595523	−	0.0136752i
$124$	1.42389e7	−	1.29094e7i	0.670656	−	0.608038i
$125$	3.87899e6	+	3.87899e6i	0.177637	+	0.177637i
$126$	2.50883e7	+	2.96537e7i	1.11731	+	1.32063i
$127$			2.82558e6i			0.122404i	0.998125	+	0.0612019i	$0.0194934\pi$
$127$			2.82558e6i			0.122404i	−0.998125	+	0.0612019i	$0.980507\pi$
$128$	2.31472e7	−	5.21120e6i	0.975582	−	0.219636i
$129$	−1.66634e7	+	1.04396e7i	−0.683439	+	0.428175i
$130$	−1.54520e6	+	3.48666e6i	−0.0616857	+	0.139190i
$131$	1.07447e7	−	1.07447e7i	0.417584	−	0.417584i	−0.466786	−	0.884370i	$-0.654588\pi$
$131$	1.07447e7	−	1.07447e7i	0.417584	−	0.417584i	0.884370	+	0.466786i	$0.154588\pi$
$132$	4.61147e6	−	1.63660e7i	0.174514	−	0.619346i
$133$	3.47776e7	+	3.47776e7i	1.28180	+	1.28180i
$134$	−4.71875e6	−	1.22300e7i	−0.169418	−	0.439098i
$135$	3.59860e6	−	391036.i	0.125883	−	0.0136788i
$136$	−1.55529e7	+	5.14203e6i	−0.530182	+	0.175287i
$137$	−2.88082e7			−0.957183			−0.478591	−	0.878038i	$-0.658852\pi$
$137$	−2.88082e7			−0.957183			−0.478591	+	0.878038i	$0.658852\pi$
$138$	−2.14222e7	+	2.85997e7i	−0.693885	+	0.926370i
$139$	6.57594e6	−	6.57594e6i	0.207685	−	0.207685i	−0.595598	−	0.803283i	$-0.703085\pi$
$139$	6.57594e6	−	6.57594e6i	0.207685	−	0.207685i	0.803283	+	0.595598i	$0.203085\pi$
$140$	−7.10323e6	−	347845.i	−0.218780	−	0.0107137i
$141$	−7.92330e6	−	1.81945e6i	−0.238034	−	0.0546605i
$142$	897056.	−	2.02415e6i	0.0262912	−	0.0593245i
$143$	−2.70540e7			−0.773670
$144$	−1.87075e7	+	3.05606e7i	−0.522092	+	0.852889i
$145$	−8.94103e6			−0.243556
$146$	1.07825e7	−	2.43301e7i	0.286737	−	0.647006i
$147$	7.47891e7	+	1.71741e7i	1.94190	+	0.445925i
$148$	−173188.	+	3.53662e6i	−0.00439139	+	0.0896751i
$149$	4.85468e7	−	4.85468e7i	1.20229	−	1.20229i	0.228820	−	0.973469i	$-0.426513\pi$
$149$	4.85468e7	−	4.85468e7i	1.20229	−	1.20229i	0.973469	−	0.228820i	$-0.0734867\pi$
$150$	2.43834e7	−	3.25530e7i	0.589894	−	0.787537i
$151$	−8.03628e7			−1.89948			−0.949742	−	0.313033i	$-0.898655\pi$
$151$	−8.03628e7			−1.89948			−0.949742	+	0.313033i	$0.898655\pi$
$152$	−2.03896e7	+	4.05308e7i	−0.470929	+	0.936123i
$153$	1.07924e7	−	2.22601e7i	0.243611	−	0.502466i
$154$	−1.81603e7	−	4.70678e7i	−0.400683	−	1.03849i
$155$	−3.75779e6	−	3.75779e6i	−0.0810535	−	0.0810535i
$156$	5.48755e7	+	1.54623e7i	1.15729	+	0.326091i
$157$	4.12261e7	−	4.12261e7i	0.850205	−	0.850205i	−0.139953	−	0.990158i	$-0.544695\pi$
$157$	4.12261e7	−	4.12261e7i	0.850205	−	0.850205i	0.990158	+	0.139953i	$0.0446952\pi$
$158$	5.36164e6	−	1.20982e7i	0.108143	−	0.244018i
$159$	−4.57797e7	+	2.86810e7i	−0.903198	+	0.565855i
$160$	−1.75223e6	−	6.32214e6i	−0.0338199	−	0.122024i
$161$			1.06022e8i			2.00220i
$162$	−1.34272e7	−	5.24208e7i	−0.248133	−	0.968726i
$163$	−2.51867e7	−	2.51867e7i	−0.455527	−	0.455527i	0.441657	−	0.897184i	$-0.354391\pi$
$163$	−2.51867e7	−	2.51867e7i	−0.455527	−	0.455527i	−0.897184	+	0.441657i	$0.854391\pi$
$164$	−2.31830e6	−	2.55705e6i	−0.0410408	−	0.0452673i
$165$	−4.58219e6	−	1.05222e6i	−0.0794108	−	0.0182353i
$166$	−1.25563e7	+	4.84461e6i	−0.213050	+	0.0822017i
$167$			804614.i			0.0133684i	0.999978	+	0.00668421i	$0.00212766\pi$
$167$			804614.i			0.0133684i	−0.999978	+	0.00668421i	$0.997872\pi$
$168$	9.93478e6	+	1.05850e8i	0.161650	+	1.72230i
$169$		−	2.79642e7i		−	0.445655i
$170$	1.63042e6	+	4.22573e6i	0.0254524	+	0.0659676i
$171$	−2.24593e7	−	6.47329e7i	−0.343487	−	0.990008i
$172$	−5.37560e7	−	2.63243e6i	−0.805523	−	0.0394464i
$173$	−4.57770e7	−	4.57770e7i	−0.672181	−	0.672181i	0.286038	−	0.958218i	$-0.407662\pi$
$173$	−4.57770e7	−	4.57770e7i	−0.672181	−	0.672181i	−0.958218	+	0.286038i	$0.907662\pi$
$174$	1.89842e7	+	1.32307e8i	0.273193	+	1.90397i
$175$		−	1.20678e8i		−	1.70213i
$176$	3.59659e7	−	2.95353e7i	0.497275	−	0.408364i
$177$	−5.97514e7	−	9.53732e7i	−0.809919	−	1.29277i
$178$	−1.20016e8	−	5.31882e7i	−1.59503	−	0.706879i
$179$	−1.03973e7	+	1.03973e7i	−0.135499	+	0.135499i	−0.771603	−	0.636104i	$-0.780545\pi$
$179$	−1.03973e7	+	1.03973e7i	−0.135499	+	0.135499i	0.636104	+	0.771603i	$0.280545\pi$
$180$	8.69298e6	+	4.75318e6i	0.111100	+	0.0607478i
$181$	−1.41689e7	−	1.41689e7i	−0.177608	−	0.177608i	0.612705	−	0.790312i	$-0.290082\pi$
$181$	−1.41689e7	−	1.41689e7i	−0.177608	−	0.177608i	−0.790312	+	0.612705i	$0.790082\pi$
$182$	1.57819e8	−	6.08919e7i	1.94049	−	0.748703i
$183$	8.26232e7	−	5.17636e7i	0.996605	−	0.624375i
$184$	−9.28604e7	+	3.07011e7i	−1.09892	+	0.363322i
$185$	979057.			0.0113686
$186$	−4.76279e7	+	6.35855e7i	−0.542707	+	0.724540i
$187$	−2.27198e7	+	2.27198e7i	−0.254073	+	0.254073i
$188$	−1.49455e7	−	1.64846e7i	−0.164043	−	0.180936i
$189$	−1.25131e8	−	1.00602e8i	−1.34818	−	1.08390i
$190$	1.14692e7	+	5.08289e6i	0.121310	+	0.0537617i
$191$	−1.79887e8			−1.86803			−0.934014	−	0.357236i	$-0.883719\pi$
$191$	−1.79887e8			−1.86803			−0.934014	+	0.357236i	$0.883719\pi$
$192$	−8.98326e7	+	3.93526e7i	−0.915967	+	0.401254i
$193$	−1.08695e8			−1.08833			−0.544163	−	0.838980i	$-0.683153\pi$
$193$	−1.08695e8			−1.08833			−0.544163	+	0.838980i	$0.683153\pi$
$194$	−2.80973e7	−	1.24520e7i	−0.276285	−	0.122443i
$195$	3.52813e6	−	1.53642e7i	0.0340740	−	0.148384i
$196$	1.41072e8	+	1.55600e8i	1.33828	+	1.47610i
$197$	4.18481e7	−	4.18481e7i	0.389981	−	0.389981i	−0.484699	−	0.874681i	$-0.661071\pi$
$197$	4.18481e7	−	4.18481e7i	0.389981	−	0.389981i	0.874681	+	0.484699i	$0.161071\pi$
$198$	−5.84125e6	+	7.00400e7i	−0.0534783	+	0.641236i
$199$	2.02161e8			1.81850			0.909248	−	0.416254i	$-0.136657\pi$
$199$	2.02161e8			1.81850			0.909248	+	0.416254i	$0.136657\pi$
$200$	1.05696e8	−	3.49448e7i	0.934231	−	0.308872i
$201$	2.87678e7	+	4.59181e7i	0.249873	+	0.398839i
$202$	1.50469e8	−	5.80557e7i	1.28445	−	0.495581i
$203$	2.80426e8	+	2.80426e8i	2.35279	+	2.35279i
$204$	5.90693e7	−	3.30989e7i	0.487143	−	0.272966i
$205$	−674832.	+	674832.i	−0.00547088	+	0.00547088i
$206$	2.78422e7	+	1.23390e7i	0.221906	+	0.0983434i
$207$	6.44372e7	−	1.32906e8i	0.504941	−	1.04148i
$208$	9.90326e7	+	1.20595e8i	0.763056	+	0.929193i
$209$			8.89931e7i			0.674286i
$210$	2.90985e7	−	4.17524e6i	0.216822	−	0.0311110i
$211$	1.04076e8	+	1.04076e8i	0.762711	+	0.762711i	0.976812	−	0.214100i	$-0.0686820\pi$
$211$	1.04076e8	+	1.04076e8i	0.762711	+	0.762711i	−0.214100	+	0.976812i	$0.568682\pi$
$212$	−1.47685e8	−	7.23213e6i	−1.06454	−	0.0521303i
$213$	−2.04822e6	+	8.91955e6i	−0.0145228	+	0.0632433i
$214$	−4.66974e7	−	1.21030e8i	−0.325720	−	0.844200i
$215$			1.48815e7i			0.102120i
$216$	5.18786e7	−	1.38728e8i	0.350268	−	0.936650i
$217$			2.35719e8i			1.56598i
$218$	−7.09749e7	+	2.73844e7i	−0.463989	+	0.179022i
$219$	−2.46194e7	+	1.07212e8i	−0.158388	+	0.689745i
$220$	−8.64324e6	−	9.53335e6i	−0.0547264	−	0.0603623i
$221$	−7.61800e7	−	7.61800e7i	−0.474753	−	0.474753i
$222$	−2.07880e6	−	1.44878e7i	−0.0127520	−	0.0888724i
$223$		−	9.49167e7i		−	0.573159i	−0.958056	−	0.286580i	$-0.907482\pi$
$223$		−	9.49167e7i		−	0.573159i	0.958056	−	0.286580i	$-0.0925183\pi$
$224$	−1.43330e8	+	2.53245e8i	−0.852060	+	1.50547i
$225$	−7.33442e7	+	1.51278e8i	−0.429267	+	0.885393i
$226$	1.06304e8	−	2.39868e8i	0.612588	−	1.38227i
$227$	1.79007e8	−	1.79007e8i	1.01574	−	1.01574i	0.0158608	−	0.999874i	$-0.494951\pi$
$227$	1.79007e8	−	1.79007e8i	1.01574	−	1.01574i	0.999874	−	0.0158608i	$-0.00504887\pi$
$228$	5.08627e7	−	1.80511e8i	0.284202	−	1.00863i
$229$	5.41101e7	+	5.41101e7i	0.297752	+	0.297752i	0.840133	−	0.542381i	$-0.182477\pi$
$229$	5.41101e7	+	5.41101e7i	0.297752	+	0.297752i	−0.542381	+	0.840133i	$0.682477\pi$
$230$	9.73464e6	+	2.52302e7i	0.0527561	+	0.136733i
$231$	1.10714e8	+	1.76718e8i	0.590963	+	0.943275i
$232$	−1.64410e8	+	3.26817e8i	−0.864409	+	1.71829i
$233$	−1.25288e8			−0.648878			−0.324439	−	0.945907i	$-0.605176\pi$
$233$	−1.25288e8			−0.648878			−0.324439	+	0.945907i	$0.605176\pi$
$234$	−2.34846e8	−	1.95858e7i	−1.19819	−	0.0999278i
$235$	−4.35046e6	+	4.35046e6i	−0.0218674	+	0.0218674i
$236$	1.50667e7	−	3.07673e8i	0.0746152	−	1.52369i
$237$	−1.22421e7	+	5.33115e7i	−0.0597360	+	0.260137i
$238$	8.13992e7	−	1.83672e8i	0.391382	−	0.883130i
$239$	−9.62220e7			−0.455913			−0.227956	−	0.973671i	$-0.573204\pi$
$239$	−9.62220e7			−0.455913			−0.227956	+	0.973671i	$0.573204\pi$
$240$	1.20830e7	+	2.42770e7i	0.0564203	+	0.113359i
$241$	7.26620e7			0.334386			0.167193	−	0.985924i	$-0.446530\pi$
$241$	7.26620e7			0.334386			0.167193	+	0.985924i	$0.446530\pi$
$242$	−5.23427e7	+	1.18108e8i	−0.237412	+	0.535705i
$243$	9.57174e7	+	2.02163e8i	0.427926	+	0.903814i
$244$	2.66542e8	+	1.30525e7i	1.17463	+	0.0575216i
$245$	4.10646e7	−	4.10646e7i	0.178397	−	0.178397i
$246$	1.14188e7	+	8.55311e6i	0.0489044	+	0.0366312i
$247$	−2.98396e8			−1.25995
$248$	−2.06456e8	+	6.82575e7i	−0.859500	+	0.284164i
$249$	4.71429e7	−	2.95351e7i	0.193517	−	0.121239i
$250$	−2.23410e7	−	5.79034e7i	−0.0904301	−	0.234377i
$251$	−6.00748e7	−	6.00748e7i	−0.239792	−	0.239792i	0.576972	−	0.816764i	$-0.304234\pi$
$251$	−6.00748e7	−	6.00748e7i	−0.239792	−	0.239792i	−0.816764	+	0.576972i	$0.804234\pi$
$252$	−1.23568e8	−	4.21725e8i	−0.486411	−	1.66008i
$253$	−1.35651e8	+	1.35651e8i	−0.526626	+	0.526626i
$254$	1.29524e7	−	2.92263e7i	0.0495943	−	0.111907i
$255$	−9.93985e6	−	1.58657e7i	−0.0375396	−	0.0599194i
$256$	−2.63310e8	−	5.22043e7i	−0.980907	−	0.194476i
$257$		−	1.77627e8i		−	0.652744i	−0.945241	−	0.326372i	$-0.894174\pi$
$257$		−	1.77627e8i		−	0.652744i	0.945241	−	0.326372i	$-0.105826\pi$
$258$	2.20212e8	−	3.15975e7i	0.798312	−	0.114547i
$259$	−3.07071e7	−	3.07071e7i	−0.109822	−	0.109822i
$260$	3.19655e7	−	2.89810e7i	0.112791	−	0.102260i
$261$	−1.81099e8	−	5.21968e8i	−0.630484	−	1.81720i
$262$	−1.60391e8	+	6.18839e7i	−0.550965	+	0.212580i
$263$			3.35731e8i			1.13801i	0.822334	+	0.569006i	$0.192672\pi$
$263$			3.35731e8i			1.13801i	−0.822334	+	0.569006i	$0.807328\pi$
$264$	−1.22720e8	+	1.48142e8i	−0.410488	+	0.495524i
$265$			4.08843e7i			0.134957i
$266$	−2.00301e8	−	5.19141e8i	−0.652526	−	1.69122i
$267$	5.28858e8	+	1.21443e8i	1.70039	+	0.390467i
$268$	−7.25400e6	+	1.48132e8i	−0.0230200	+	0.470085i
$269$	5.28833e7	+	5.28833e7i	0.165648	+	0.165648i	0.785063	−	0.619416i	$-0.212630\pi$
$269$	5.28833e7	+	5.28833e7i	0.165648	+	0.165648i	−0.619416	+	0.785063i	$0.712630\pi$
$270$	−3.90145e7	−	1.24512e7i	−0.120629	−	0.0384981i
$271$		−	2.68132e8i		−	0.818382i	−0.912449	−	0.409191i	$-0.865811\pi$
$271$		−	2.68132e8i		−	0.818382i	0.912449	−	0.409191i	$-0.134189\pi$
$272$	1.84442e8	+	1.81076e7i	0.555735	+	0.0545595i
$273$	−5.92538e8	+	3.71226e8i	−1.76257	+	1.10426i
$274$	2.97977e8	+	1.32056e8i	0.875096	+	0.387821i
$275$	1.54402e8	−	1.54402e8i	0.447702	−	0.447702i
$276$	3.52680e8	−	1.97621e8i	1.00972	−	0.565785i
$277$	3.49838e8	+	3.49838e8i	0.988982	+	0.988982i	0.999940	−	0.0109580i	$-0.00348812\pi$
$277$	3.49838e8	+	3.49838e8i	0.988982	+	0.988982i	−0.0109580	+	0.999940i	$0.503488\pi$
$278$	−9.81619e7	+	3.78741e7i	−0.274023	+	0.105727i
$279$	1.43263e8	−	2.95490e8i	0.394929	−	0.814568i
$280$	7.18775e7	+	3.61589e7i	0.195677	+	0.0984380i
$281$	2.42786e8			0.652756			0.326378	−	0.945239i	$-0.394172\pi$
$281$	2.42786e8			0.652756			0.326378	+	0.945239i	$0.394172\pi$
$282$	7.36141e7	+	5.51396e7i	0.195474	+	0.146417i
$283$	−4.76441e8	+	4.76441e8i	−1.24956	+	1.24956i	−0.293645	+	0.955915i	$0.594868\pi$
$283$	−4.76441e8	+	4.76441e8i	−1.24956	+	1.24956i	−0.955915	+	0.293645i	$0.905132\pi$
$284$	−1.85573e7	+	1.68247e7i	−0.0480730	+	0.0435845i
$285$	−5.05398e7	−	1.16056e7i	−0.129323	−	0.0296969i
$286$	2.79832e8	+	1.24015e8i	0.707321	+	0.313468i
$287$	4.23308e7			0.105699
$288$	3.33589e8	−	2.30347e8i	0.822883	−	0.568211i
$289$	2.82388e8			0.688182
$290$	9.24812e7	+	4.09854e7i	0.222669	+	0.0986817i
$291$	1.23812e8	+	2.84314e7i	0.294536	+	0.0676352i
$292$	−2.23057e8	+	2.02230e8i	−0.524294	+	0.475342i
$293$	2.91427e7	−	2.91427e7i	0.0676851	−	0.0676851i	−0.672454	−	0.740139i	$-0.734760\pi$
$293$	2.91427e7	−	2.91427e7i	0.0676851	−	0.0676851i	0.740139	+	0.672454i	$0.234760\pi$
$294$	−6.94853e8	−	5.20470e8i	−1.59469	−	1.19448i
$295$	−8.51746e7			−0.193167
$296$	1.80031e7	−	3.57870e7i	0.0403484	−	0.0802055i
$297$	−3.13837e7	−	2.88816e8i	−0.0695115	−	0.639697i
$298$	−7.24679e8	+	2.79605e8i	−1.58631	+	0.612051i
$299$	−4.54842e8	−	4.54842e8i	−0.984037	−	0.984037i
$300$	−4.01430e8	+	2.24938e8i	−0.858392	+	0.480992i
$301$	4.66744e8	−	4.66744e8i	0.986497	−	0.986497i
$302$	8.31230e8	+	3.68381e8i	1.73659	+	0.769614i
$303$	−5.64940e8	+	3.53935e8i	−1.16668	+	0.730929i
$304$	3.96691e8	−	3.25764e8i	0.809831	−	0.665036i
$305$		−	7.37880e7i		−	0.148914i
$306$	−2.13670e8	+	1.80774e8i	−0.426303	+	0.360671i
$307$	−5.65069e8	−	5.65069e8i	−1.11460	−	1.11460i	−0.992521	−	0.122075i	$-0.961045\pi$
$307$	−5.65069e8	−	5.65069e8i	−1.11460	−	1.11460i	−0.122075	−	0.992521i	$-0.538955\pi$
$308$	−2.79173e7	+	5.70091e8i	−0.0544435	+	1.11177i
$309$	−1.22689e8	−	2.81734e7i	−0.236564	−	0.0543230i
$310$	2.16430e7	+	5.60942e7i	0.0412620	+	0.106943i
$311$		−	6.47977e8i		−	1.22151i	−0.791819	−	0.610756i	$-0.790866\pi$
$311$		−	6.47977e8i		−	1.22151i	0.791819	−	0.610756i	$-0.209134\pi$
$312$	−4.96723e8	−	4.11482e8i	−0.925920	−	0.767025i
$313$		−	3.03248e8i		−	0.558976i	−0.960149	−	0.279488i	$-0.909835\pi$
$313$		−	3.03248e8i		−	0.558976i	0.960149	−	0.279488i	$-0.0901647\pi$
$314$	−6.15400e8	+	2.37441e8i	−1.12177	+	0.432815i
$315$	−1.14798e8	+	3.98295e7i	−0.206941	+	0.0717988i
$316$	−1.10916e8	+	1.00560e8i	−0.197737	+	0.179275i
$317$	4.12457e7	+	4.12457e7i	0.0727229	+	0.0727229i	0.742533	−	0.669810i	$-0.233624\pi$
$317$	4.12457e7	+	4.12457e7i	0.0727229	+	0.0727229i	−0.669810	+	0.742533i	$0.733624\pi$
$318$	6.04993e8	−	8.68084e7i	1.05501	−	0.151379i
$319$			7.17588e8i			1.23768i
$320$	−1.08563e7	+	7.34250e7i	−0.0185207	+	0.125262i
$321$	2.84690e8	+	4.54412e8i	0.480401	+	0.766800i
$322$	4.86004e8	−	1.09664e9i	0.811230	−	1.83049i
$323$	−2.50591e8	+	2.50591e8i	−0.413768	+	0.413768i
$324$	−1.01411e8	+	6.03762e8i	−0.165645	+	0.986185i
$325$	5.17713e8	+	5.17713e8i	0.836561	+	0.836561i
$326$	1.45062e8	+	3.75973e8i	0.231896	+	0.601028i
$327$	2.66478e8	−	1.66949e8i	0.421448	−	0.264038i
$328$	1.22578e7	+	3.70757e7i	0.0191803	+	0.0580138i
$329$	2.72896e8			0.422485
$330$	4.25724e7	+	3.18883e7i	0.0652122	+	0.0488463i
$331$	3.40548e8	−	3.40548e8i	0.516155	−	0.516155i	−0.400251	−	0.916406i	$-0.631077\pi$
$331$	3.40548e8	−	3.40548e8i	0.516155	−	0.516155i	0.916406	+	0.400251i	$0.131077\pi$
$332$	1.52083e8	+	7.44748e6i	0.228085	+	0.0111693i
$333$	1.98306e7	+	5.71564e7i	0.0294294	+	0.0848223i
$334$	3.68833e6	−	8.32249e6i	0.00541648	−	0.0122220i
$335$	4.10079e7			0.0595952
$336$	3.82454e8	−	1.14040e9i	0.550037	−	1.64009i
$337$	8.51776e8			1.21233			0.606165	−	0.795339i	$-0.292707\pi$
$337$	8.51776e8			1.21233			0.606165	+	0.795339i	$0.292707\pi$
$338$	−1.28187e8	+	2.89247e8i	−0.180566	+	0.407437i
$339$	−2.42720e8	+	1.05699e9i	−0.338382	+	1.47358i
$340$	2.50640e6	−	5.11825e7i	0.00345840	−	0.0706229i
$341$	−3.01592e8	+	3.01592e8i	−0.411889	+	0.411889i
$342$	−6.44268e7	+	7.72515e8i	−0.0870913	+	1.04428i
$343$	−1.28307e9			−1.71680
$344$	5.43957e8	+	2.73645e8i	0.720460	+	0.362437i
$345$	−5.93471e7	−	9.47278e7i	−0.0778095	−	0.124197i
$346$	2.63652e8	+	6.83333e8i	0.342188	+	0.886883i
$347$	−7.11592e8	−	7.11592e8i	−0.914278	−	0.914278i	0.0823277	−	0.996605i	$-0.473765\pi$
$347$	−7.11592e8	−	7.11592e8i	−0.914278	−	0.914278i	−0.996605	+	0.0823277i	$0.973765\pi$
$348$	4.10127e8	−	1.45553e9i	0.521665	−	1.85137i
$349$	6.28430e8	−	6.28430e8i	0.791349	−	0.791349i	−0.190365	−	0.981713i	$-0.560967\pi$
$349$	6.28430e8	−	6.28430e8i	0.791349	−	0.791349i	0.981713	+	0.190365i	$0.0609671\pi$
$350$	−5.53183e8	+	1.24822e9i	−0.689653	+	1.55616i
$351$	9.68408e8	−	1.05230e8i	1.19532	−	0.129887i
$352$	−5.07401e8	+	1.40631e8i	−0.620087	+	0.171862i
$353$		−	9.26898e8i		−	1.12155i	−0.827967	−	0.560777i	$-0.810502\pi$
$353$		−	9.26898e8i		−	1.12155i	0.827967	−	0.560777i	$-0.189498\pi$
$354$	1.80849e8	+	1.26039e9i	0.216672	+	1.51005i
$355$	4.89748e6	+	4.89748e6i	0.00580996	+	0.00580996i
$356$	9.97567e8	+	1.10030e9i	1.17184	+	1.29252i
$357$	−1.85857e8	+	8.09364e8i	−0.216192	+	0.941467i
$358$	1.55205e8	−	5.98833e7i	0.178779	−	0.0689787i
$359$			3.80316e8i			0.433825i	0.976191	+	0.216912i	$0.0695986\pi$
$359$			3.80316e8i			0.433825i	−0.976191	+	0.216912i	$0.930401\pi$
$360$	−6.81270e7	−	8.90127e7i	−0.0769592	−	0.100553i
$361$			8.76885e7i			0.0980996i
$362$	8.16057e7	+	2.11505e8i	0.0904150	+	0.234337i
$363$	1.19513e8	−	5.20450e8i	0.131142	−	0.571092i
$364$	−1.91153e9	−	9.36073e7i	−2.07743	−	0.101731i
$365$	5.88670e7	+	5.88670e7i	0.0633646	+	0.0633646i
$366$	−1.09189e9	+	1.56672e8i	−1.16412	+	0.167035i
$367$		−	3.60441e8i		−	0.380630i	−0.981723	−	0.190315i	$-0.939049\pi$
$367$		−	3.60441e8i		−	0.380630i	0.981723	−	0.190315i	$-0.0609509\pi$
$368$	1.10123e9	+	1.08114e8i	1.15189	+	0.113087i
$369$	−5.30646e7	−	2.57274e7i	−0.0549810	−	0.0266566i
$370$	−1.01268e7	−	4.48797e6i	−0.0103936	−	0.00460621i
$371$	1.28229e9	−	1.28229e9i	1.30370	−	1.30370i
$372$	7.84111e8	−	4.39369e8i	0.789728	−	0.442516i
$373$	−7.23473e8	−	7.23473e8i	−0.721841	−	0.721841i	0.247139	−	0.968980i	$-0.420510\pi$
$373$	−7.23473e8	−	7.23473e8i	−0.721841	−	0.721841i	−0.968980	+	0.247139i	$0.920510\pi$
$374$	3.39148e8	−	1.30854e8i	0.335227	−	0.129342i
$375$	1.36202e8	+	2.17400e8i	0.133375	+	0.212888i
$376$	7.90230e7	+	2.39018e8i	0.0766648	+	0.231885i
$377$	−2.40609e9			−2.31269
$378$	8.33131e8	+	1.61417e9i	0.793399	+	1.53719i
$379$	8.06959e8	−	8.06959e8i	0.761402	−	0.761402i	−0.215174	−	0.976576i	$-0.569032\pi$
$379$	8.06959e8	−	8.06959e8i	0.761402	−	0.761402i	0.976576	+	0.215174i	$0.0690317\pi$
$380$	−9.53317e7	−	1.05149e8i	−0.0891240	−	0.0983023i
$381$	−2.95739e7	+	1.28787e8i	−0.0273950	+	0.119299i
$382$	1.86066e9	+	8.24598e8i	1.70783	+	0.756869i
$383$	3.07589e8			0.279753			0.139877	−	0.990169i	$-0.455329\pi$
$383$	3.07589e8			0.279753			0.139877	+	0.990169i	$0.455329\pi$
$384$	1.10957e9	+	4.74766e6i	0.999991	+	0.00427879i
$385$	1.57821e8			0.140946
$386$	1.12428e9	+	4.98254e8i	0.994992	+	0.440956i
$387$	−8.68769e8	+	3.01422e8i	−0.761931	+	0.264355i
$388$	2.33543e8	+	2.57594e8i	0.202981	+	0.223885i
$389$	5.51695e8	−	5.51695e8i	0.475198	−	0.475198i	−0.428394	−	0.903592i	$-0.640920\pi$
$389$	5.51695e8	−	5.51695e8i	0.475198	−	0.475198i	0.903592	+	0.428394i	$0.140920\pi$
$390$	−1.06922e8	+	1.42746e8i	−0.0912728	+	0.121853i
$391$	−7.63947e8			−0.646315
$392$	−7.45908e8	−	2.25612e9i	−0.625438	−	1.89174i
$393$	6.02192e8	−	3.77274e8i	0.500450	−	0.313533i
$394$	−6.24684e8	+	2.41024e8i	−0.514546	+	0.198528i
$395$	2.92719e7	+	2.92719e7i	0.0238979	+	0.0238979i
$396$	3.81480e8	−	6.97680e8i	0.308702	−	0.564577i
$397$	−1.18568e9	+	1.18568e9i	−0.951047	+	0.951047i	−0.998856	−	0.0478097i	$-0.984776\pi$
$397$	−1.18568e9	+	1.18568e9i	−0.951047	+	0.951047i	0.0478097	+	0.998856i	$0.484776\pi$
$398$	−2.09105e9	−	9.26702e8i	−1.66254	−	0.736800i
$399$	1.22113e9	+	1.94913e9i	0.962405	+	1.53616i
$400$	−1.25345e9	−	1.23058e8i	−0.979259	−	0.0961390i
$401$		−	7.95231e8i		−	0.615869i	−0.951408	−	0.307934i	$-0.900362\pi$
$401$		−	7.95231e8i		−	0.615869i	0.951408	−	0.307934i	$-0.0996377\pi$
$402$	−8.70709e7	−	6.06823e8i	−0.0668470	−	0.465876i
$403$	−1.01125e9	−	1.01125e9i	−0.769643	−	0.769643i
$404$	−1.82249e9	−	8.92474e7i	−1.37509	−	0.0673381i
$405$	1.68114e8	+	1.98416e7i	0.125751	+	0.0148417i
$406$	−1.61511e9	−	4.18605e9i	−1.19774	−	3.10429i
$407$		−	7.85771e7i		−	0.0577717i
$408$	−7.62705e8	+	7.15853e7i	−0.555963	+	0.0521811i
$409$		−	1.15083e9i		−	0.831728i	−0.909427	−	0.415864i	$-0.863479\pi$
$409$		−	1.15083e9i		−	0.831728i	0.909427	−	0.415864i	$-0.136521\pi$
$410$	1.00735e7	−	3.88669e6i	0.00721834	−	0.00278507i
$411$	−1.31305e9	−	3.01521e8i	−0.932902	−	0.214225i
$412$	−2.31424e8	−	2.55256e8i	−0.163030	−	0.179819i
$413$	2.67141e9	+	2.67141e9i	1.86602	+	1.86602i
$414$	−1.27574e9	+	1.07933e9i	−0.883613	+	0.747574i
$415$		−	4.21017e7i		−	0.0289156i
$416$	−4.71538e8	−	1.70133e9i	−0.321137	−	1.15867i
$417$	3.68552e8	−	2.30898e8i	0.248899	−	0.155935i
$418$	4.07942e8	−	9.20496e8i	0.273200	−	0.616460i
$419$	−9.94957e8	+	9.94957e8i	−0.660778	+	0.660778i	−0.955563	−	0.294786i	$-0.904752\pi$
$419$	−9.94957e8	+	9.94957e8i	−0.660778	+	0.660778i	0.294786	+	0.955563i	$0.404752\pi$
$420$	−3.20118e8	−	9.02002e7i	−0.210833	−	0.0594066i
$421$	−3.96799e7	−	3.96799e7i	−0.0259169	−	0.0259169i	0.694030	−	0.719946i	$-0.255834\pi$
$421$	−3.96799e7	−	3.96799e7i	−0.0259169	−	0.0259169i	−0.719946	+	0.694030i	$0.755834\pi$
$422$	−5.99422e8	−	1.55358e9i	−0.388275	−	1.00633i
$423$	−3.42094e8	−	1.65858e8i	−0.219763	−	0.106548i
$424$	1.49442e9	+	7.51789e8i	0.952122	+	0.478978i
$425$	8.69545e8			0.549454
$426$	6.20727e7	−	8.28700e7i	0.0389016	−	0.0519355i
$427$	−2.31429e9	+	2.31429e9i	−1.43853	+	1.43853i
$428$	−7.17865e7	+	1.46593e9i	−0.0442578	+	0.903775i
$429$	−1.23310e9	−	2.83160e8i	−0.754044	−	0.173154i
$430$	6.82165e7	−	1.53926e8i	0.0413761	−	0.0933627i
$431$	−1.29862e9			−0.781286			−0.390643	−	0.920542i	$-0.627747\pi$
$431$	−1.29862e9			−0.781286			−0.390643	+	0.920542i	$0.627747\pi$
$432$	−1.17253e9	+	1.19712e9i	−0.699731	+	0.714406i
$433$	1.54820e9			0.916473			0.458236	−	0.888830i	$-0.348481\pi$
$433$	1.54820e9			0.916473			0.458236	+	0.888830i	$0.348481\pi$
$434$	1.08053e9	−	2.43815e9i	0.634486	−	1.43168i
$435$	−4.07524e8	−	9.35810e7i	−0.237378	−	0.0545099i
$436$	8.59656e8	+	4.20973e7i	0.496732	+	0.0243249i
$437$	−1.49618e9	+	1.49618e9i	−0.857630	+	0.857630i
$438$	7.46106e8	−	9.96087e8i	0.424269	−	0.566419i
$439$	1.96834e9			1.11039			0.555194	−	0.831721i	$-0.312644\pi$
$439$	1.96834e9			1.11039			0.555194	+	0.831721i	$0.312644\pi$
$440$	4.57004e7	+	1.38228e8i	0.0255762	+	0.0773593i
$441$	3.22907e9	+	1.56556e9i	1.79284	+	0.869227i
$442$	4.38758e8	+	1.13717e9i	0.241684	+	0.626395i
$443$	8.06979e8	+	8.06979e8i	0.441011	+	0.441011i	0.892352	−	0.451341i	$-0.149054\pi$
$443$	8.06979e8	+	8.06979e8i	0.441011	+	0.441011i	−0.451341	+	0.892352i	$0.649054\pi$
$444$	−4.49096e7	+	1.59383e8i	−0.0243500	+	0.0864175i
$445$	2.90381e8	−	2.90381e8i	0.156210	−	0.156210i
$446$	−4.35095e8	+	9.81767e8i	−0.232227	+	0.524006i
$447$	2.72083e9	−	1.70461e9i	1.44087	−	0.902709i
$448$	2.64340e9	−	1.96240e9i	1.38896	−	1.03113i
$449$		−	2.17934e9i		−	1.13622i	−0.822953	−	0.568110i	$-0.807675\pi$
$449$		−	2.17934e9i		−	1.13622i	0.822953	−	0.568110i	$-0.192325\pi$
$450$	1.45209e9	−	1.22853e9i	0.751188	−	0.635537i
$451$	5.41606e7	+	5.41606e7i	0.0278013	+	0.0278013i
$452$	−2.19910e9	+	1.99377e9i	−1.12011	+	1.01553i
$453$	−3.66286e9	−	8.41115e8i	−1.85130	−	0.425120i
$454$	−2.67212e9	+	1.03099e9i	−1.34017	+	0.517082i
$455$			5.29176e8i			0.263366i
$456$	−1.35355e9	+	1.63395e9i	−0.668495	+	0.806978i
$457$			3.52462e9i			1.72745i	0.503965	+	0.863724i	$0.331874\pi$
$457$			3.52462e9i			1.72745i	−0.503965	+	0.863724i	$0.668126\pi$
$458$	−3.11647e8	−	8.07725e8i	−0.151577	−	0.392857i
$459$	7.24891e8	−	9.01635e8i	0.349888	−	0.435197i
$460$	1.49648e7	−	3.05591e8i	0.00716833	−	0.146382i
$461$	9.53497e8	+	9.53497e8i	0.453280	+	0.453280i	0.896442	−	0.443162i	$-0.146143\pi$
$461$	9.53497e8	+	9.53497e8i	0.453280	+	0.453280i	−0.443162	+	0.896442i	$0.646143\pi$
$462$	−3.35096e8	−	2.33538e9i	−0.158096	−	1.10182i
$463$			2.66644e9i			1.24853i	0.781213	+	0.624264i	$0.214601\pi$
$463$			2.66644e9i			1.24853i	−0.781213	+	0.624264i	$0.785399\pi$
$464$	3.19868e9	−	2.62677e9i	1.48648	−	1.22070i
$465$	−1.31946e8	−	2.10607e8i	−0.0608570	−	0.0971379i
$466$	1.29591e9	+	5.74316e8i	0.593231	+	0.262906i
$467$	−3.26047e8	+	3.26047e8i	−0.148139	+	0.148139i	−0.777286	−	0.629147i	$-0.783404\pi$
$467$	−3.26047e8	+	3.26047e8i	−0.148139	+	0.148139i	0.629147	+	0.777286i	$0.283404\pi$
$468$	2.33934e9	+	1.27911e9i	1.05495	+	0.576830i
$469$	−1.28617e9	−	1.28617e9i	−0.575697	−	0.575697i
$470$	6.49413e7	−	2.50564e7i	0.0288522	−	0.0111321i
$471$	2.31054e9	−	1.44756e9i	1.01892	−	0.638355i
$472$	−1.56621e9	+	3.11334e9i	−0.685571	+	1.36279i
$473$	1.19436e9			0.518945
$474$	3.71004e8	−	4.95308e8i	0.160013	−	0.213625i
$475$	1.70300e9	−	1.70300e9i	0.729098	−	0.729098i
$476$	−1.68390e9	+	1.52668e9i	−0.715635	+	0.648818i
$477$	−2.38678e9	+	8.28104e8i	−1.00693	+	0.349358i
$478$	9.95269e8	+	4.41079e8i	0.416814	+	0.184722i
$479$	1.97955e9			0.822986			0.411493	−	0.911413i	$-0.365007\pi$
$479$	1.97955e9			0.822986			0.411493	+	0.911413i	$0.365007\pi$
$480$	−1.36948e7	−	3.06497e8i	−0.00565213	−	0.126497i
$481$	2.63471e8			0.107950
$482$	−7.51577e8	−	3.33081e8i	−0.305709	−	0.135483i
$483$	−1.10968e9	+	4.83240e9i	−0.448108	+	1.95141i
$484$	1.08281e9	−	9.81709e8i	0.434103	−	0.393572i
$485$	6.79819e7	−	6.79819e7i	0.0270581	−	0.0270581i
$486$	−6.33408e7	−	2.52983e9i	−0.0250298	−	0.999687i
$487$	1.94274e9			0.762190			0.381095	−	0.924536i	$-0.375547\pi$
$487$	1.94274e9			0.762190			0.381095	+	0.924536i	$0.375547\pi$
$488$	−2.69713e9	−	1.35683e9i	−1.05059	−	0.528513i
$489$	−8.84371e8	−	1.41160e9i	−0.342021	−	0.545923i
$490$	−6.12989e8	+	2.36511e8i	−0.235378	+	0.0908166i
$491$	2.24258e9	+	2.24258e9i	0.854995	+	0.854995i	0.990743	−	0.135749i	$-0.0433439\pi$
$491$	2.24258e9	+	2.24258e9i	0.854995	+	0.854995i	−0.135749	+	0.990743i	$0.543344\pi$
$492$	−7.89028e7	−	1.40812e8i	−0.0298686	−	0.0533043i
$493$	−2.02062e9	+	2.02062e9i	−0.759487	+	0.759487i
$494$	3.08644e9	+	1.36784e9i	1.15190	+	0.510494i
$495$	−1.97839e8	−	9.59187e7i	−0.0733151	−	0.0355455i
$496$	2.44836e9	+	2.40368e8i	0.900926	+	0.0884487i
$497$		−	3.07209e8i		−	0.112250i
$498$	−6.23009e8	+	8.93934e7i	−0.226043	+	0.0324342i
$499$	−9.03855e8	−	9.03855e8i	−0.325647	−	0.325647i	0.525282	−	0.850928i	$-0.323960\pi$
$499$	−9.03855e8	−	9.03855e8i	−0.325647	−	0.325647i	−0.850928	+	0.525282i	$0.823960\pi$
$500$	−3.43442e7	+	7.01333e8i	−0.0122874	+	0.250916i
$501$	−8.42146e6	+	3.66736e7i	−0.00299196	+	0.0130293i
$502$	3.46000e8	+	8.96762e8i	0.122071	+	0.316384i
$503$			3.15328e9i			1.10478i	0.833586	+	0.552389i	$0.186284\pi$
$503$			3.15328e9i			1.10478i	−0.833586	+	0.552389i	$0.813716\pi$
$504$	−6.55058e8	+	4.92853e9i	−0.227915	+	1.71479i
$505$			5.04529e8i			0.174328i
$506$	2.02493e9	−	7.81282e8i	0.694836	−	0.268090i
$507$	2.92687e8	−	1.27458e9i	0.0997413	−	0.434351i
$508$	−2.67945e8	+	2.42928e8i	−0.0906824	+	0.0822156i
$509$	−1.97015e8	−	1.97015e8i	−0.0662198	−	0.0662198i	0.673221	−	0.739441i	$-0.264910\pi$
$509$	−1.97015e8	−	1.97015e8i	−0.0662198	−	0.0662198i	−0.739441	+	0.673221i	$0.764910\pi$
$510$	3.00848e7	+	2.09670e8i	0.0100427	+	0.0699907i
$511$		−	3.69261e9i		−	1.22422i
$512$	2.48424e9	+	1.74698e9i	0.817990	+	0.575232i
$513$	−3.46151e8	−	3.18554e9i	−0.113202	−	1.04177i
$514$	−8.14237e8	+	1.83728e9i	−0.264472	+	0.596766i
$515$	−6.73648e7	+	6.73648e7i	−0.0217324	+	0.0217324i
$516$	−2.42260e9	−	6.82620e8i	−0.776261	−	0.218728i
$517$	3.49159e8	+	3.49159e8i	0.111124	+	0.111124i
$518$	1.76857e8	+	4.58379e8i	0.0559074	+	0.144901i
$519$	−1.60735e9	−	2.56560e9i	−0.504690	−	0.805569i
$520$	−4.63482e8	+	1.53235e8i	−0.144551	+	0.0477909i
$521$	−6.25729e9			−1.93845			−0.969224	−	0.246180i	$-0.920824\pi$
$521$	−6.25729e9			−1.93845			−0.969224	+	0.246180i	$0.920824\pi$
$522$	−5.19500e8	+	6.22911e9i	−0.159860	+	1.91681i
$523$	2.26396e9	−	2.26396e9i	0.692010	−	0.692010i	−0.270664	−	0.962674i	$-0.587243\pi$
$523$	2.26396e9	−	2.26396e9i	0.692010	−	0.692010i	0.962674	+	0.270664i	$0.0872433\pi$
$524$	1.94267e9	+	9.51323e7i	0.589846	+	0.0288847i
$525$	1.26307e9	−	5.50037e9i	0.380951	−	1.65896i
$526$	1.53898e9	−	3.47262e9i	0.461088	−	1.04042i
$527$	−1.69848e9			−0.505502
$528$	1.94843e9	−	9.69757e8i	0.576056	−	0.286711i
$529$	−1.15641e9			−0.339639
$530$	1.87412e8	−	4.22885e8i	0.0546805	−	0.123383i
$531$	−1.72520e9	−	4.97241e9i	−0.500043	−	1.44124i
$532$	−3.07917e8	+	6.28789e9i	−0.0886632	+	1.81056i
$533$	−1.81602e8	+	1.81602e8i	−0.0519487	+	0.0519487i
$534$	−4.91353e9	−	3.68041e9i	−1.39636	−	1.04593i
$535$	4.05820e8			0.114576
$536$	7.54063e8	−	1.49894e9i	0.211510	−	0.420444i
$537$	−5.82724e8	+	3.65078e8i	−0.162388	+	0.101736i
$538$	−3.04581e8	−	7.89412e8i	−0.0843265	−	0.218557i
$539$	−3.29576e9	−	3.29576e9i	−0.906556	−	0.906556i
$540$	3.46469e8	+	3.07630e8i	0.0946861	+	0.0840719i
$541$	−4.33318e8	+	4.33318e8i	−0.117656	+	0.117656i	−0.763484	−	0.645827i	$-0.776513\pi$
$541$	−4.33318e8	+	4.33318e8i	−0.117656	+	0.117656i	0.645827	+	0.763484i	$0.276513\pi$
$542$	−1.22911e9	+	2.77341e9i	−0.331584	+	0.748199i
$543$	−4.97508e8	−	7.94104e8i	−0.133352	−	0.212852i
$544$	−1.82476e9	−	1.03277e9i	−0.485970	−	0.275048i
$545$		−	2.37982e8i		−	0.0629734i
$546$	7.83059e9	−	1.12358e9i	2.05883	−	0.295414i
$547$	5.08922e9	+	5.08922e9i	1.32952	+	1.32952i	0.905785	+	0.423738i	$0.139282\pi$
$547$	5.08922e9	+	5.08922e9i	1.32952	+	1.32952i	0.423738	+	0.905785i	$0.360718\pi$
$548$	−2.47677e9	−	2.73184e9i	−0.642916	−	0.709125i
$549$	4.30767e9	−	1.49456e9i	1.11106	−	0.385488i
$550$	−2.30483e9	+	8.89277e8i	−0.590702	+	0.227912i
$551$			7.91473e9i			2.01560i
$552$	−4.55382e9	+	4.27408e8i	−1.15236	+	0.108157i
$553$		−	1.83617e9i		−	0.461715i
$554$	−2.01489e9	−	5.22219e9i	−0.503463	−	1.30487i
$555$	4.46245e7	+	1.02473e7i	0.0110802	+	0.00254438i
$556$	1.18895e9	+	5.82227e7i	0.293360	+	0.0143658i
$557$	3.11905e9	+	3.11905e9i	0.764766	+	0.764766i	0.977180	−	0.212414i	$-0.0681325\pi$
$557$	3.11905e9	+	3.11905e9i	0.764766	+	0.764766i	−0.212414	+	0.977180i	$0.568132\pi$
$558$	−2.83635e9	+	2.39967e9i	−0.691099	+	0.584699i
$559$			4.00471e9i			0.969684i
$560$	−5.77711e8	−	7.03493e8i	−0.139012	−	0.169278i
$561$	−1.27334e9	+	7.97752e8i	−0.304492	+	0.190765i
$562$	−2.51124e9	−	1.11292e9i	−0.596776	−	0.264477i
$563$	5.22147e9	−	5.22147e9i	1.23314	−	1.23314i	0.270392	−	0.962750i	$-0.412847\pi$
$563$	5.22147e9	−	5.22147e9i	1.23314	−	1.23314i	0.962750	−	0.270392i	$-0.0871534\pi$
$564$	−5.08666e8	−	9.07780e8i	−0.119387	−	0.213061i
$565$	5.80365e8	+	5.80365e8i	0.135373	+	0.135373i
$566$	7.11205e9	−	2.74406e9i	1.64868	−	0.636115i
$567$	−4.65041e9	−	5.89503e9i	−1.07140	−	1.35814i
$568$	2.69071e8	−	8.89591e7i	0.0616095	−	0.0203691i
$569$	−3.45877e9			−0.787097			−0.393549	−	0.919304i	$-0.628753\pi$
$569$	−3.45877e9			−0.787097			−0.393549	+	0.919304i	$0.628753\pi$
$570$	4.69557e8	+	3.51716e8i	0.106200	+	0.0795481i
$571$	1.72135e9	−	1.72135e9i	0.386939	−	0.386939i	−0.486655	−	0.873594i	$-0.661783\pi$
$571$	1.72135e9	−	1.72135e9i	0.386939	−	0.386939i	0.873594	+	0.486655i	$0.161783\pi$
$572$	−2.32595e9	−	2.56549e9i	−0.519655	−	0.573170i
$573$	−8.19909e9	−	1.88278e9i	−1.82064	−	0.418080i
$574$	−4.37847e8	−	1.94043e8i	−0.0966343	−	0.0428260i
$575$	5.19172e9			1.13887
$576$	−4.50637e9	+	8.53427e8i	−0.982536	+	0.186075i
$577$	−7.34987e9			−1.59281			−0.796405	−	0.604763i	$-0.793268\pi$
$577$	−7.34987e9			−1.59281			−0.796405	+	0.604763i	$0.793268\pi$
$578$	−2.92087e9	−	1.29446e9i	−0.629164	−	0.278830i
$579$	−4.95421e9	−	1.13765e9i	−1.06072	−	0.243576i
$580$	−7.68699e8	−	8.47862e8i	−0.163591	−	0.180438i
$581$	−1.32048e9	+	1.32048e9i	−0.279328	+	0.279328i
$582$	−1.15032e9	−	8.61631e8i	−0.241873	−	0.181172i
$583$	3.28129e9			0.685811
$584$	3.23420e9	−	1.06928e9i	0.671926	−	0.222149i
$585$	3.21618e8	−	6.63359e8i	0.0664193	−	0.136994i
$586$	−4.35026e8	+	1.67847e8i	−0.0893045	+	0.0344566i
$587$	−1.67723e9	−	1.67723e9i	−0.342263	−	0.342263i	0.514955	−	0.857217i	$-0.327809\pi$
$587$	−1.67723e9	−	1.67723e9i	−0.342263	−	0.342263i	−0.857217	+	0.514955i	$0.827809\pi$
$588$	4.80136e9	+	8.56865e9i	0.973966	+	1.73817i
$589$	−3.32645e9	+	3.32645e9i	−0.670776	+	0.670776i
$590$	8.81000e8	+	3.90438e8i	0.176601	+	0.0782654i
$591$	2.34540e9	−	1.46940e9i	0.467370	−	0.292808i
$592$	−3.50261e8	+	2.87635e8i	−0.0693850	+	0.0569792i
$593$		−	8.67330e9i		−	1.70802i	−0.520257	−	0.854010i	$-0.674164\pi$
$593$		−	8.67330e9i		−	1.70802i	0.520257	−	0.854010i	$-0.325836\pi$
$594$	−9.99310e8	+	3.13122e9i	−0.195636	+	0.613001i
$595$	4.44399e8	+	4.44399e8i	0.0864896	+	0.0864896i
$596$	8.77739e9	+	4.29828e8i	1.69826	+	0.0831636i
$597$	9.21433e9	+	2.11592e9i	1.77237	+	0.406994i
$598$	2.61966e9	+	6.78962e9i	0.500945	+	1.29835i
$599$			1.31339e9i			0.249689i	0.992176	+	0.124844i	$0.0398431\pi$
$599$			1.31339e9i			0.249689i	−0.992176	+	0.124844i	$0.960157\pi$
$600$	5.18329e9	−	4.86488e8i	0.979661	−	0.0919481i
$601$		−	9.54271e9i		−	1.79313i	−0.442915	−	0.896564i	$-0.646056\pi$
$601$		−	9.54271e9i		−	1.79313i	0.442915	−	0.896564i	$-0.353944\pi$
$602$	−6.96729e9	+	2.68821e9i	−1.30160	+	0.502198i
$603$	8.30608e8	+	2.39400e9i	0.154271	+	0.444646i
$604$	−6.90914e9	−	7.62067e9i	−1.27584	−	1.40723i
$605$	−2.85765e8	−	2.85765e8i	−0.0524644	−	0.0524644i
$606$	7.46586e9	−	1.07125e9i	1.36278	−	0.195541i
$607$		−	5.10912e8i		−	0.0927226i	−0.998925	−	0.0463613i	$-0.985237\pi$
$607$		−	5.10912e8i		−	0.0927226i	0.998925	−	0.0463613i	$-0.0147626\pi$
$608$	−5.59645e9	+	1.55110e9i	−1.00983	+	0.279884i
$609$	9.84650e9	+	1.57166e10i	1.76653	+	2.81968i
$610$	−3.38242e8	+	7.63223e8i	−0.0603356	+	0.136144i
$611$	−1.17074e9	+	1.17074e9i	−0.207642	+	0.207642i
$612$	3.03875e9	−	8.90371e8i	0.535877	−	0.157015i
$613$	−1.90143e9	−	1.90143e9i	−0.333403	−	0.333403i	0.520475	−	0.853877i	$-0.325755\pi$
$613$	−1.90143e9	−	1.90143e9i	−0.333403	−	0.333403i	−0.853877	+	0.520475i	$0.825755\pi$
$614$	3.25451e9	+	8.43504e9i	0.567409	+	1.47061i
$615$	−3.78213e7	+	2.36951e7i	−0.00655652	+	0.00410767i
$616$	2.90204e9	−	5.76874e9i	0.500231	−	0.994371i
$617$	5.64178e9			0.966981			0.483490	−	0.875350i	$-0.339369\pi$
$617$	5.64178e9			0.966981			0.483490	+	0.875350i	$0.339369\pi$
$618$	1.13988e9	+	8.53811e8i	0.194267	+	0.145513i
$619$	2.66979e9	−	2.66979e9i	0.452439	−	0.452439i	−0.443724	−	0.896163i	$-0.646343\pi$
$619$	2.66979e9	−	2.66979e9i	0.452439	−	0.452439i	0.896163	+	0.443724i	$0.146343\pi$
$620$	3.32711e7	−	6.79419e8i	0.00560656	−	0.114490i
$621$	4.32805e9	−	5.38332e9i	0.725223	−	0.902048i
$622$	−2.97031e9	+	6.70232e9i	−0.494920	+	1.11676i
$623$	−1.82150e10			−3.01801
$624$	3.25162e9	+	6.53311e9i	0.535739	+	1.07640i
$625$	−5.81150e9			−0.952156
$626$	−1.39008e9	+	3.13664e9i	−0.226480	+	0.511039i
$627$	−9.31443e8	+	4.05622e9i	−0.150911	+	0.657182i
$628$	7.45379e9	+	3.65012e8i	1.20093	+	0.0588096i
$629$	2.21261e8	−	2.21261e8i	0.0354509	−	0.0354509i
$630$	1.36998e9	+	1.14255e8i	0.218284	+	0.0182046i
$631$	−3.38004e9			−0.535574			−0.267787	−	0.963478i	$-0.586292\pi$
$631$	−3.38004e9			−0.535574			−0.267787	+	0.963478i	$0.586292\pi$
$632$	1.60822e9	−	5.31702e8i	0.253416	−	0.0837835i
$633$	3.65437e9	+	5.83297e9i	0.572663	+	0.914065i
$634$	−2.37554e8	−	6.15692e8i	−0.0370212	−	0.0959514i
$635$	7.07136e7	+	7.07136e7i	0.0109596	+	0.0109596i
$636$	−6.65565e9	−	1.87537e9i	−1.02587	−	0.289060i
$637$	1.10508e10	−	1.10508e10i	1.69396	−	1.69396i
$638$	3.28940e9	−	7.42234e9i	0.501470	−	1.13154i
$639$	−1.86712e8	+	3.85107e8i	−0.0283087	+	0.0583887i
$640$	4.48870e8	−	7.09703e8i	0.0676847	−	0.107016i
$641$			7.60262e9i			1.14015i	0.821594	+	0.570073i	$0.193085\pi$
$641$			7.60262e9i			1.14015i	−0.821594	+	0.570073i	$0.806915\pi$
$642$	−8.61665e8	−	6.00520e9i	−0.128519	−	0.895684i
$643$	1.06582e9	+	1.06582e9i	0.158104	+	0.158104i	0.781726	−	0.623622i	$-0.214339\pi$
$643$	1.06582e9	+	1.06582e9i	0.158104	+	0.158104i	−0.623622	+	0.781726i	$0.714339\pi$
$644$	−1.00539e10	+	9.11521e9i	−1.48332	+	1.34483i
$645$	−1.55757e8	+	6.78286e8i	−0.0228554	+	0.0995300i
$646$	3.74068e9	−	1.44328e9i	0.545930	−	0.210637i
$647$		−	5.29388e9i		−	0.768439i	−0.923242	−	0.384219i	$-0.874471\pi$
$647$		−	5.29388e9i		−	0.768439i	0.923242	−	0.384219i	$-0.125529\pi$
$648$	3.81657e9	−	5.78013e9i	0.551012	−	0.834497i
$649$			6.83593e9i			0.981615i
$650$	−2.98176e9	−	7.72813e9i	−0.425870	−	1.10377i
$651$	−2.46714e9	+	1.07438e10i	−0.350478	+	1.52625i
$652$	2.23000e8	−	4.55382e9i	0.0315093	−	0.643442i
$653$	3.09864e9	+	3.09864e9i	0.435487	+	0.435487i	0.890490	−	0.455003i	$-0.150362\pi$
$653$	3.09864e9	+	3.09864e9i	0.435487	+	0.435487i	−0.455003	+	0.890490i	$0.650362\pi$
$654$	−3.52159e9	+	5.05301e8i	−0.492285	+	0.0706363i
$655$		−	5.37797e8i		−	0.0747780i
$656$	4.31658e7	−	4.39681e8i	0.00597003	−	0.0608099i
$657$	−2.24426e9	+	4.62894e9i	−0.308741	+	0.636800i
$658$	−2.82269e9	−	1.25095e9i	−0.386253	−	0.171178i
$659$	6.93571e9	−	6.93571e9i	0.944044	−	0.944044i	−0.0544712	−	0.998515i	$-0.517347\pi$
$659$	6.93571e9	−	6.93571e9i	0.944044	−	0.944044i	0.998515	+	0.0544712i	$0.0173473\pi$
$660$	−2.94171e8	−	5.24985e8i	−0.0398286	−	0.0710794i
$661$	−1.84135e9	−	1.84135e9i	−0.247989	−	0.247989i	0.572156	−	0.820145i	$-0.306107\pi$
$661$	−1.84135e9	−	1.84135e9i	−0.247989	−	0.247989i	−0.820145	+	0.572156i	$0.806107\pi$
$662$	−5.08350e9	+	1.96138e9i	−0.681020	+	0.262760i
$663$	−2.67488e9	−	4.26955e9i	−0.356457	−	0.568964i
$664$	−1.53892e9	−	7.74176e8i	−0.203999	−	0.102625i
$665$	1.74070e9			0.229535
$666$	5.68861e7	−	6.82098e8i	0.00746184	−	0.0894720i
$667$	−1.20643e10	+	1.20643e10i	−1.57421	+	1.57421i
$668$	−7.63001e7	+	6.91762e7i	−0.00990393	+	0.00897923i
$669$	9.93442e8	−	4.32621e9i	0.128278	−	0.558620i
$670$	−4.24164e8	−	1.87979e8i	−0.0544844	−	0.0241462i
$671$	−5.92207e9			−0.756737
$672$	−9.18344e9	+	1.00425e10i	−1.16738	+	1.27658i
$673$	5.41963e9			0.685357			0.342678	−	0.939453i	$-0.388666\pi$
$673$	5.41963e9			0.685357			0.342678	+	0.939453i	$0.388666\pi$
$674$	−8.81031e9	−	3.90452e9i	−1.10836	−	0.491199i
$675$	−4.92631e9	+	6.12744e9i	−0.616536	+	0.766860i
$676$	2.65180e9	−	2.40421e9i	0.330162	−	0.299336i
$677$	8.83712e8	−	8.83712e8i	0.109459	−	0.109459i	−0.650256	−	0.759715i	$-0.725338\pi$
$677$	8.83712e8	−	8.83712e8i	0.109459	−	0.109459i	0.759715	+	0.650256i	$0.225338\pi$
$678$	7.35579e9	−	9.82034e9i	0.906412	−	1.21010i
$679$	−4.26437e9			−0.522770
$680$	−2.60544e8	+	5.17915e8i	−0.0317761	+	0.0631651i
$681$	1.00326e10	−	6.28542e9i	1.21730	−	0.762639i
$682$	4.50200e9	−	1.73702e9i	0.543451	−	0.209681i
$683$	6.87515e9	+	6.87515e9i	0.825677	+	0.825677i	0.986915	−	0.161239i	$-0.0515490\pi$
$683$	6.87515e9	+	6.87515e9i	0.825677	+	0.825677i	−0.161239	+	0.986915i	$0.551549\pi$
$684$	4.20759e9	−	7.69515e9i	0.502732	−	0.919435i
$685$	−7.20961e8	+	7.20961e8i	−0.0857027	+	0.0857027i
$686$	1.32714e10	+	5.88154e9i	1.56957	+	0.695596i
$687$	1.89995e9	+	3.03263e9i	0.223559	+	0.356838i
$688$	−4.37201e9	−	5.32391e9i	−0.511826	−	0.623263i
$689$			1.10022e10i			1.28148i
$690$	1.79625e8	+	1.25186e9i	0.0208159	+	0.145072i
$691$	1.04279e9	+	1.04279e9i	0.120233	+	0.120233i	0.764663	−	0.644430i	$-0.222905\pi$
$691$	1.04279e9	+	1.04279e9i	0.120233	+	0.120233i	−0.644430	+	0.764663i	$0.722905\pi$
$692$	4.05305e8	−	8.27661e9i	0.0464955	−	0.949469i
$693$	3.19663e9	+	9.21342e9i	0.364860	+	1.05161i
$694$	4.09841e9	+	1.06222e10i	0.465433	+	1.20631i
$695$		−	3.29142e8i		−	0.0371908i
$696$	−1.09143e10	+	1.31752e10i	−1.22705	+	1.48124i
$697$			3.05016e8i			0.0341199i
$698$	−9.38085e9	+	3.61943e9i	−1.04411	+	0.402853i
$699$	−5.71050e9	−	1.31132e9i	−0.632418	−	0.145224i
$700$	1.14436e10	−	1.03752e10i	1.26102	−	1.14328i
$701$	8.14750e9	+	8.14750e9i	0.893329	+	0.893329i	0.994835	−	0.101506i	$-0.0323662\pi$
$701$	8.14750e9	+	8.14750e9i	0.893329	+	0.893329i	−0.101506	+	0.994835i	$0.532366\pi$
$702$	−1.04991e10	−	3.35071e9i	−1.14544	−	0.365559i
$703$		−	8.66676e8i		−	0.0940834i
$704$	5.89293e9	+	8.71306e8i	0.636542	+	0.0941167i
$705$	−2.43824e8	+	1.52756e8i	−0.0262068	+	0.0164186i
$706$	−4.24888e9	+	9.58734e9i	−0.454420	+	1.02537i
$707$	1.58240e10	−	1.58240e10i	1.68403	−	1.68403i
$708$	3.90698e9	−	1.38658e10i	0.413738	−	1.46834i
$709$	3.18374e9	+	3.18374e9i	0.335487	+	0.335487i	0.854666	−	0.519179i	$-0.173762\pi$
$709$	3.18374e9	+	3.18374e9i	0.335487	+	0.335487i	−0.519179	+	0.854666i	$0.673762\pi$
$710$	−2.82070e7	−	7.31068e7i	−0.00295769	−	0.00766573i
$711$	−1.11597e9	+	2.30176e9i	−0.116441	+	0.240169i
$712$	−5.27456e9	−	1.59537e10i	−0.547654	−	1.65647i
$713$	−1.01410e10			−1.04777
$714$	5.63250e9	−	7.51966e9i	0.579106	−	0.773134i
$715$	−6.77059e8	+	6.77059e8i	−0.0692716	+	0.0692716i
$716$	−1.87987e9	−	9.20569e7i	−0.191395	−	0.00937262i
$717$	−4.38571e9	−	1.00710e9i	−0.444348	−	0.102037i
$718$	1.74336e9	−	3.93379e9i	0.175773	−	0.396621i
$719$	2.39843e9			0.240645			0.120322	−	0.992735i	$-0.461607\pi$
$719$	2.39843e9			0.240645			0.120322	+	0.992735i	$0.461607\pi$
$720$	2.96638e8	+	1.23299e9i	0.0296185	+	0.123111i
$721$	4.22566e9			0.419876
$722$	4.01961e8	−	9.07002e8i	0.0397470	−	0.0896867i
$723$	3.31187e9	+	7.60515e8i	0.325903	+	0.0748382i
$724$	1.25450e8	−	2.56178e9i	0.0122853	−	0.250874i
$725$	1.37320e10	−	1.37320e10i	1.33829	−	1.33829i
$726$	−3.62190e9	+	4.83542e9i	−0.351284	+	0.468981i
$727$	2.58791e9			0.249793			0.124896	−	0.992170i	$-0.460140\pi$
$727$	2.58791e9			0.249793			0.124896	+	0.992170i	$0.460140\pi$
$728$	1.93427e10	+	9.73061e9i	1.85805	+	0.934717i
$729$	2.24678e9	+	1.02162e10i	0.214790	+	0.976660i
$730$	−3.39044e8	−	8.78733e8i	−0.0322571	−	0.0836040i
$731$	3.36313e9	+	3.36313e9i	0.318444	+	0.318444i
$732$	1.20121e10	+	3.38468e9i	1.13196	+	0.318954i
$733$	−4.38959e9	+	4.38959e9i	−0.411680	+	0.411680i	−0.882324	−	0.470643i	$-0.844022\pi$
$733$	−4.38959e9	+	4.38959e9i	−0.411680	+	0.411680i	0.470643	+	0.882324i	$0.344022\pi$
$734$	−1.65225e9	+	3.72821e9i	−0.154220	+	0.347987i
$735$	2.30149e9	−	1.44189e9i	0.213798	−	0.133945i
$736$	−1.08949e10	−	6.16628e9i	−1.00729	−	0.570100i
$737$		−	3.29121e9i		−	0.302844i
$738$	4.30938e8	+	5.09357e8i	0.0394655	+	0.0466472i
$739$	−3.86031e9	−	3.86031e9i	−0.351857	−	0.351857i	0.508943	−	0.860800i	$-0.330036\pi$
$739$	−3.86031e9	−	3.86031e9i	−0.351857	−	0.351857i	−0.860800	+	0.508943i	$0.830036\pi$
$740$	8.41738e7	+	9.28423e7i	0.00763600	+	0.00842238i
$741$	−1.36006e10	−	3.12315e9i	−1.22799	−	0.281987i
$742$	−1.91414e10	+	7.38536e9i	−1.72012	+	0.663679i
$743$			1.46966e10i			1.31449i	0.753678	+	0.657243i	$0.228278\pi$
$743$			1.46966e10i			1.31449i	−0.753678	+	0.657243i	$0.771722\pi$
$744$	−1.01245e10	+	9.50254e8i	−0.901296	+	0.0845930i
$745$		−	2.42988e9i		−	0.215297i
$746$	4.16684e9	+	1.07996e10i	0.367469	+	0.952405i
$747$	2.45786e9	−	8.52763e8i	0.215742	−	0.0748525i
$748$	−4.10780e9	−	2.01159e8i	−0.358884	−	0.0175745i
$749$	−1.27281e10	−	1.27281e10i	−1.10682	−	1.10682i
$750$	−4.12239e8	−	2.87302e9i	−0.0356808	−	0.248670i
$751$		−	1.56445e10i		−	1.34779i	−0.738829	−	0.673893i	$-0.764621\pi$
$751$		−	1.56445e10i		−	1.34779i	0.738829	−	0.673893i	$-0.235379\pi$
$752$	2.78279e8	−	2.83451e9i	0.0238626	−	0.243061i
$753$	−2.10938e9	−	3.36692e9i	−0.180042	−	0.287376i
$754$	2.48873e10	+	1.10294e10i	2.11435	+	0.937031i
$755$	−2.01118e9	+	2.01118e9i	−0.170073	+	0.170073i
$756$	−1.21814e9	−	2.05152e10i	−0.102534	−	1.72683i
$757$	−3.65255e9	−	3.65255e9i	−0.306028	−	0.306028i	0.537339	−	0.843367i	$-0.319430\pi$
$757$	−3.65255e9	−	3.65255e9i	−0.306028	−	0.306028i	−0.843367	+	0.537339i	$0.819430\pi$
$758$	−1.20458e10	+	4.64767e9i	−1.00460	+	0.387608i
$759$	−7.60265e9	+	4.76307e9i	−0.631130	+	0.395404i
$760$	5.04059e8	+	1.52461e9i	0.0416518	+	0.125982i
$761$	−6.74475e9			−0.554779			−0.277389	−	0.960758i	$-0.589469\pi$
$761$	−6.74475e9			−0.554779			−0.277389	+	0.960758i	$0.589469\pi$
$762$	8.96254e8	−	1.19654e9i	0.0733819	−	0.0979683i
$763$	−7.46408e9	+	7.46408e9i	−0.608331	+	0.608331i
$764$	−1.54657e10	−	1.70584e10i	−1.25471	−	1.38392i
$765$	−2.86992e8	−	8.27177e8i	−0.0231769	−	0.0668011i
$766$	−3.18154e9	−	1.40998e9i	−0.255762	−	0.113348i
$767$	−2.29210e10			−1.83422
$768$	−1.14550e10	−	5.13535e9i	−0.912499	−	0.409078i
$769$	−2.28976e10			−1.81571			−0.907857	−	0.419279i	$-0.862283\pi$
$769$	−2.28976e10			−1.81571			−0.907857	+	0.419279i	$0.862283\pi$
$770$	−1.63241e9	−	7.23446e8i	−0.128858	−	0.0571069i
$771$	1.85913e9	−	8.09607e9i	0.146089	−	0.636186i
$772$	−9.34498e9	−	1.03074e10i	−0.731001	−	0.806281i
$773$	6.97265e9	−	6.97265e9i	0.542962	−	0.542962i	−0.381434	−	0.924396i	$-0.624570\pi$
$773$	6.97265e9	−	6.97265e9i	0.542962	−	0.542962i	0.924396	+	0.381434i	$0.124570\pi$
$774$	1.03678e10	+	8.64660e8i	0.803698	+	0.0670273i
$775$	1.15427e10			0.890743
$776$	−1.23484e9	−	3.73497e9i	−0.0948626	−	0.286927i
$777$	−1.07821e9	−	1.72100e9i	−0.0824573	−	0.131615i
$778$	−8.23538e9	+	3.17748e9i	−0.626982	+	0.241910i
$779$	5.97371e8	+	5.97371e8i	0.0452755	+	0.0452755i
$780$	1.76029e9	−	9.86361e8i	0.132817	−	0.0744226i
$781$	3.93061e8	−	3.93061e8i	0.0295244	−	0.0295244i
$782$	7.90186e9	+	3.50191e9i	0.590888	+	0.261867i
$783$	−2.79116e9	−	2.56863e10i	−0.207787	−	1.91221i
$784$	−2.62671e9	+	2.67553e10i	−0.194673	+	1.98291i
$785$		−	2.06347e9i		−	0.152249i
$786$	−7.95816e9	+	1.14189e9i	−0.584566	+	0.0838774i
$787$	1.40086e10	+	1.40086e10i	1.02443	+	1.02443i	0.999694	+	0.0247364i	$0.00787463\pi$
$787$	1.40086e10	+	1.40086e10i	1.02443	+	1.02443i	0.0247364	+	0.999694i	$0.492125\pi$
$788$	7.56625e9	+	3.70519e8i	0.550857	+	0.0269754i
$789$	−3.51392e9	+	1.53023e10i	−0.254696	+	1.10914i
$790$	−1.68591e8	−	4.36954e8i	−0.0121658	−	0.0315312i
$791$		−	3.64051e10i		−	2.61544i
$792$	−7.14397e9	+	5.46773e9i	−0.510977	+	0.391083i
$793$		−	1.98568e10i		−	1.41401i
$794$	1.76992e10	−	6.82893e9i	1.25482	−	0.484151i
$795$	−4.27914e8	+	1.86347e9i	−0.0302045	+	0.131534i
$796$	1.73807e10	+	1.91706e10i	1.22144	+	1.34723i
$797$	−2.83276e9	−	2.83276e9i	−0.198201	−	0.198201i	0.601028	−	0.799228i	$-0.294758\pi$
$797$	−2.83276e9	−	2.83276e9i	−0.198201	−	0.198201i	−0.799228	+	0.601028i	$0.794758\pi$
$798$	−3.69598e9	−	2.57584e10i	−0.257466	−	1.79436i
$799$			1.96636e9i			0.136379i
$800$	1.24009e10	+	7.01863e9i	0.856326	+	0.484660i
$801$	2.28338e10	+	1.10705e10i	1.56987	+	0.761123i
$802$	−3.64532e9	+	8.22544e9i	−0.249531	+	0.563053i
$803$	4.72454e9	−	4.72454e9i	0.322000	−	0.322000i
$804$	−1.88105e9	+	6.67578e9i	−0.127645	+	0.453008i
$805$	2.65334e9	+	2.65334e9i	0.179270	+	0.179270i
$806$	5.82426e9	+	1.50953e10i	0.391803	+	1.01548i
$807$	1.85687e9	+	2.96387e9i	0.124372	+	0.198519i
$808$	1.84418e10	+	9.27738e9i	1.22988	+	0.618708i
$809$	−1.87752e10			−1.24671			−0.623355	−	0.781939i	$-0.714231\pi$
$809$	−1.87752e10			−1.24671			−0.623355	+	0.781939i	$0.714231\pi$
$810$	−1.64793e9	−	9.75860e8i	−0.108953	−	0.0645194i
$811$	9.85650e9	−	9.85650e9i	0.648858	−	0.648858i	−0.303859	−	0.952717i	$-0.598275\pi$
$811$	9.85650e9	−	9.85650e9i	0.648858	−	0.648858i	0.952717	+	0.303859i	$0.0982751\pi$
$812$	−2.48287e9	+	5.07018e10i	−0.162745	+	3.32336i
$813$	2.80640e9	−	1.22212e10i	0.183161	−	0.797623i
$814$	−3.60195e8	+	8.12759e8i	−0.0234074	+	0.0528173i
$815$	−1.26065e9			−0.0815726
$816$	8.21716e9	+	2.75578e9i	0.529427	+	0.177553i
$817$	1.31733e10			0.845121
$818$	−5.27540e9	+	1.19036e10i	−0.336991	+	0.760400i
$819$	−3.08928e10	+	1.07184e10i	−1.96500	+	0.681765i
$820$	−1.22011e8	−	5.97489e6i	−0.00772773	−	0.000378426i
$821$	−9.01622e9	+	9.01622e9i	−0.568622	+	0.568622i	−0.931742	−	0.363121i	$-0.881711\pi$
$821$	−9.01622e9	+	9.01622e9i	−0.568622	+	0.568622i	0.363121	+	0.931742i	$0.381711\pi$
$822$	1.21994e10	+	9.13777e9i	0.766100	+	0.573837i
$823$	1.11601e10			0.697862			0.348931	−	0.937148i	$-0.386545\pi$
$823$	1.11601e10			0.697862			0.348931	+	0.937148i	$0.386545\pi$
$824$	1.22363e9	+	3.70107e9i	0.0761914	+	0.230453i
$825$	8.65355e9	−	5.42146e9i	0.536544	−	0.336146i
$826$	−1.53860e10	−	3.98774e10i	−0.949938	−	2.46205i
$827$	−4.35934e9	−	4.35934e9i	−0.268010	−	0.268010i	0.560288	−	0.828298i	$-0.310691\pi$
$827$	−4.35934e9	−	4.35934e9i	−0.268010	−	0.268010i	−0.828298	+	0.560288i	$0.810691\pi$
$828$	1.81432e10	−	5.31607e9i	1.11073	−	0.325450i
$829$	1.01915e10	−	1.01915e10i	0.621296	−	0.621296i	−0.324567	−	0.945863i	$-0.605219\pi$
$829$	1.01915e10	−	1.01915e10i	0.621296	−	0.621296i	0.945863	+	0.324567i	$0.105219\pi$
$830$	−1.92993e8	+	4.35478e8i	−0.0117157	+	0.0264358i
$831$	1.22837e10	+	1.96069e10i	0.742553	+	1.18524i
$832$	−2.92151e9	+	1.97591e10i	−0.175863	+	1.18942i
$833$		−	1.85607e10i		−	1.11260i
$834$	−4.87054e9	+	6.98856e8i	−0.290734	+	0.0417164i
$835$	2.01364e7	+	2.01364e7i	0.00119696	+	0.00119696i
$836$	−8.43906e9	+	7.65112e9i	−0.499542	+	0.452901i
$837$	9.62252e9	−	1.19687e10i	0.567218	−	0.705517i
$838$	1.48522e10	−	5.73045e9i	0.871838	−	0.336383i
$839$			8.95450e9i			0.523449i	0.965143	+	0.261725i	$0.0842912\pi$
$839$			8.95450e9i			0.523449i	−0.965143	+	0.261725i	$0.915709\pi$
$840$	2.89765e9	+	2.40039e9i	0.168682	+	0.139735i
$841$			4.65699e10i			2.69972i
$842$	2.28536e8	+	5.92319e8i	0.0131936	+	0.0341951i
$843$	1.10659e10	+	2.54111e9i	0.636197	+	0.146092i
$844$	−9.21474e8	+	1.88171e10i	−0.0527576	+	1.07735i
$845$	−6.99838e8	−	6.99838e8i	−0.0399024	−	0.0399024i
$846$	2.77814e9	+	3.28369e9i	0.157746	+	0.186452i
$847$			1.79254e10i			1.01363i
$848$	−1.20113e10	−	1.46265e10i	−0.676402	−	0.823673i
$849$	−2.67024e10	+	1.67291e10i	−1.49752	+	0.938201i
$850$	−8.99411e9	−	3.98597e9i	−0.502333	−	0.222622i
$851$	1.32107e9	−	1.32107e9i	0.0734803	−	0.0734803i
$852$	−1.02192e9	+	5.72623e8i	−0.0566081	+	0.0317198i
$853$	−8.67029e9	−	8.67029e9i	−0.478313	−	0.478313i	0.426279	−	0.904592i	$-0.359824\pi$
$853$	−8.67029e9	−	8.67029e9i	−0.478313	−	0.478313i	−0.904592	+	0.426279i	$0.859824\pi$
$854$	3.45464e10	−	1.33291e10i	1.89802	−	0.732316i
$855$	−2.18209e9	−	1.05795e9i	−0.119396	−	0.0578872i
$856$	7.46231e9	−	1.48337e10i	0.406644	−	0.808336i
$857$	2.37705e10			1.29004			0.645022	−	0.764164i	$-0.276848\pi$
$857$	2.37705e10			1.29004			0.645022	+	0.764164i	$0.276848\pi$
$858$	1.14565e10	+	8.58134e9i	0.619222	+	0.463820i
$859$	1.25600e10	−	1.25600e10i	0.676102	−	0.676102i	−0.283014	−	0.959116i	$-0.591334\pi$
$859$	1.25600e10	−	1.25600e10i	0.676102	−	0.676102i	0.959116	+	0.283014i	$0.0913341\pi$
$860$	−1.41119e9	+	1.27943e9i	−0.0756555	+	0.0685917i
$861$	1.92940e9	+	4.43054e8i	0.103018	+	0.0236562i
$862$	1.34322e10	+	5.95282e9i	0.714284	+	0.316553i
$863$	−4.48626e9			−0.237600			−0.118800	−	0.992918i	$-0.537905\pi$
$863$	−4.48626e9			−0.237600			−0.118800	+	0.992918i	$0.537905\pi$
$864$	1.76156e10	−	7.00753e9i	0.929179	−	0.369630i
$865$	−2.29125e9			−0.120369
$866$	−1.60138e10	−	7.09691e9i	−0.837877	−	0.371327i
$867$	1.28710e10	+	2.95560e9i	0.670725	+	0.154021i
$868$	−2.23528e10	+	2.02658e10i	−1.16015	+	1.05183i
$869$	2.34930e9	−	2.34930e9i	0.121442	−	0.121442i
$870$	3.78623e9	+	2.83603e9i	0.194935	+	0.146014i
$871$	1.10355e10			0.565885
$872$	−8.69885e9	−	4.37607e9i	−0.444277	−	0.223500i
$873$	5.34568e9	+	2.59175e9i	0.271927	+	0.131839i
$874$	2.23342e10	−	8.61725e9i	1.13157	−	0.436595i
$875$	−6.08941e9	−	6.08941e9i	−0.307289	−	0.307289i
$876$	−1.22834e10	+	6.88286e9i	−0.617380	+	0.345943i
$877$	−2.01207e10	+	2.01207e10i	−1.00727	+	1.00727i	−0.00729423	+	0.999973i	$0.502322\pi$
$877$	−2.01207e10	+	2.01207e10i	−1.00727	+	1.00727i	−0.999973	+	0.00729423i	$0.997678\pi$
$878$	−2.03595e10	−	9.02283e9i	−1.01516	−	0.449896i
$879$	1.63332e9	−	1.02328e9i	0.0811167	−	0.0508197i
$880$	1.60934e8	−	1.63925e9i	0.00796081	−	0.0810877i
$881$		−	2.38745e10i		−	1.17630i	−0.808751	−	0.588151i	$-0.799856\pi$
$881$		−	2.38745e10i		−	1.17630i	0.808751	−	0.588151i	$-0.200144\pi$
$882$	−2.62233e10	−	3.09952e10i	−1.28691	−	1.52109i
$883$	1.15702e10	+	1.15702e10i	0.565560	+	0.565560i	0.930881	−	0.365321i	$-0.119041\pi$
$883$	1.15702e10	+	1.15702e10i	0.565560	+	0.565560i	−0.365321	+	0.930881i	$0.619041\pi$
$884$	6.74490e8	−	1.37736e10i	0.0328392	−	0.670599i
$885$	−3.88218e9	−	8.91477e8i	−0.188267	−	0.0432323i
$886$	−4.64779e9	−	1.20461e10i	−0.224506	−	0.581874i
$887$			3.53381e10i			1.70024i	0.526588	+	0.850120i	$0.323471\pi$
$887$			3.53381e10i			1.70024i	−0.526588	+	0.850120i	$0.676529\pi$
$888$	1.19513e9	−	1.44271e9i	0.0572756	−	0.0691406i
$889$		−	4.43572e9i		−	0.211742i
$890$	−4.33464e9	+	1.67245e9i	−0.206105	+	0.0795219i
$891$	1.59245e9	−	1.34925e10i	0.0754211	−	0.639027i
$892$	9.00078e9	−	8.16040e9i	0.424623	−	0.384977i
$893$	3.85109e9	+	3.85109e9i	0.180969	+	0.180969i
$894$	−3.59567e10	+	5.15930e9i	−1.68306	+	0.241496i
$895$			5.20411e8i			0.0242642i
$896$	−3.63375e10	+	8.18077e9i	−1.68763	+	0.379941i
$897$	−1.59707e10	−	2.54919e10i	−0.738840	−	1.17931i
$898$	−9.99002e9	+	2.25419e10i	−0.460362	+	1.03878i
$899$	−2.68226e10	+	2.68226e10i	−1.23124	+	1.23124i
$900$	−2.06511e10	+	6.05089e9i	−0.944267	+	0.276675i
$901$	9.23961e9	+	9.23961e9i	0.420840	+	0.420840i
$902$	−3.11937e8	−	8.08478e8i	−0.0141529	−	0.0366814i
$903$	2.61589e10	−	1.63886e10i	1.18226	−	0.740687i
$904$	3.18857e10	−	1.05419e10i	1.43551	−	0.474602i
$905$	−7.09188e8			−0.0318047
$906$	3.40310e10	+	2.54905e10i	1.52029	+	1.13875i
$907$	1.36134e10	−	1.36134e10i	0.605819	−	0.605819i	−0.336032	−	0.941851i	$-0.609085\pi$
$907$	1.36134e10	−	1.36134e10i	0.605819	−	0.605819i	0.941851	+	0.336032i	$0.109085\pi$
$908$	3.23650e10	+	1.58491e9i	1.43475	+	0.0702595i
$909$	−2.94539e10	+	1.02191e10i	−1.30068	+	0.451274i
$910$	2.42573e9	−	5.47351e9i	0.106708	−	0.240780i
$911$	3.09533e10			1.35641			0.678207	−	0.734871i	$-0.262757\pi$
$911$	3.09533e10			1.35641			0.678207	+	0.734871i	$0.262757\pi$
$912$	2.14904e10	−	1.06961e10i	0.938129	−	0.466919i
$913$	−3.37900e9			−0.146940
$914$	1.61567e10	−	3.64567e10i	0.699910	−	1.57930i
$915$	7.72300e8	−	3.36319e9i	0.0333282	−	0.145137i
$916$	−4.79085e8	+	9.78325e9i	−0.0205958	+	0.420580i
$917$	−1.68675e10	+	1.68675e10i	−0.722366	+	0.722366i
$918$	−1.16310e10	+	6.00314e9i	−0.496211	+	0.256112i
$919$	−3.19545e10			−1.35809			−0.679044	−	0.734097i	$-0.737606\pi$
$919$	−3.19545e10			−1.35809			−0.679044	+	0.734097i	$0.737606\pi$
$920$	−1.55561e9	+	3.09227e9i	−0.0658633	+	0.130924i
$921$	−1.98411e10	−	3.16696e10i	−0.836867	−	1.33578i
$922$	−5.49166e9	−	1.42333e10i	−0.230752	−	0.598062i
$923$	1.31794e9	+	1.31794e9i	0.0551684	+	0.0551684i
$924$	−7.23928e9	+	2.56920e10i	−0.301886	+	1.07139i
$925$	−1.50367e9	+	1.50367e9i	−0.0624680	+	0.0624680i
$926$	1.22229e10	−	2.75802e10i	0.505866	−	1.14146i
$927$	−5.29716e9	−	2.56823e9i	−0.218406	−	0.105890i
$928$	−4.51265e10	+	1.25072e10i	−1.85359	+	0.513738i
$929$			1.91377e10i			0.783132i	0.920150	+	0.391566i	$0.128066\pi$
$929$			1.91377e10i			0.783132i	−0.920150	+	0.391566i	$0.871934\pi$
$930$	3.99358e8	+	2.78325e9i	0.0162807	+	0.113465i
$931$	−3.63510e10	−	3.63510e10i	−1.47636	−	1.47636i
$932$	−1.07715e10	−	1.18808e10i	−0.435835	−	0.480719i
$933$	6.78203e9	−	2.95342e10i	0.273384	−	1.19053i
$934$	4.86704e9	−	1.87786e9i	0.195457	−	0.0754136i
$935$			1.13718e9i			0.0454976i
$936$	−1.83334e10	−	2.39539e10i	−0.730766	−	0.954797i
$937$		−	2.95237e10i		−	1.17242i	−0.810160	−	0.586209i	$-0.800620\pi$
$937$		−	2.95237e10i		−	1.17242i	0.810160	−	0.586209i	$-0.199380\pi$
$938$	7.40770e9	+	1.91993e10i	0.293071	+	0.759582i
$939$	3.17394e9	−	1.38218e10i	0.125103	−	0.544796i
$940$	−7.86575e8	−	3.85186e7i	−0.0308882	−	0.00151259i
$941$	2.07365e10	+	2.07365e10i	0.811284	+	0.811284i	0.984826	−	0.173543i	$-0.0555214\pi$
$941$	2.07365e10	+	2.07365e10i	0.811284	+	0.811284i	−0.173543	+	0.984826i	$0.555521\pi$
$942$	−3.05345e10	+	4.38129e9i	−1.19018	+	0.170775i
$943$			1.82113e9i			0.0707214i
$944$	3.04715e10	−	2.50233e10i	1.17894	−	0.968149i
$945$	−5.64924e9	+	6.13865e8i	−0.217760	+	0.0236625i
$946$	−1.23538e10	−	5.47491e9i	−0.474441	−	0.210261i
$947$	1.61889e10	−	1.61889e10i	0.619430	−	0.619430i	−0.325955	−	0.945385i	$-0.605686\pi$
$947$	1.61889e10	−	1.61889e10i	0.619430	−	0.619430i	0.945385	+	0.325955i	$0.105686\pi$
$948$	−6.10795e9	+	3.42253e9i	−0.232845	+	0.130472i
$949$	1.58415e10	+	1.58415e10i	0.601679	+	0.601679i
$950$	−2.54214e10	+	9.80839e9i	−0.961981	+	0.371163i
$951$	1.44824e9	+	2.31164e9i	0.0546022	+	0.0871541i
$952$	2.44156e10	−	8.07218e9i	0.917145	−	0.303223i
$953$	−2.65032e10			−0.991912			−0.495956	−	0.868348i	$-0.665182\pi$
$953$	−2.65032e10			−0.991912			−0.495956	+	0.868348i	$0.665182\pi$
$954$	2.84836e10	+	2.37550e9i	1.06213	+	0.0885799i
$955$	−4.50189e9	+	4.50189e9i	−0.167257	+	0.167257i
$956$	−8.27263e9	−	9.12457e9i	−0.306225	−	0.337761i
$957$	−7.51061e9	+	3.27070e10i	−0.277002	+	1.20628i
$958$	−2.04754e10	−	9.07421e9i	−0.752408	−	0.333449i
$959$	4.52244e10			1.65580
$960$	−1.26332e9	+	3.23302e9i	−0.0460855	+	0.117939i
$961$	4.96630e9			0.180510
$962$	−2.72520e9	−	1.20774e9i	−0.0986928	−	0.0437383i
$963$	8.21981e9	+	2.36914e10i	0.296599	+	0.854866i
$964$	6.24707e9	+	6.89041e9i	0.224599	+	0.247728i
$965$	−2.72022e9	+	2.72022e9i	−0.0974448	+	0.0974448i
$966$	3.36295e10	−	4.48970e10i	1.20033	−	1.60250i
$967$	−3.86966e10			−1.37620			−0.688098	−	0.725618i	$-0.741554\pi$
$967$	−3.86966e10			−1.37620			−0.688098	+	0.725618i	$0.741554\pi$
$968$	−1.57001e10	+	5.19071e9i	−0.556339	+	0.183934i
$969$	−1.40445e10	+	8.79890e9i	−0.495876	+	0.310667i
$970$	−1.01479e9	+	3.91541e8i	−0.0357007	+	0.0137745i
$971$	−9.97510e9	−	9.97510e9i	−0.349663	−	0.349663i	0.510321	−	0.859984i	$-0.329527\pi$
$971$	−9.97510e9	−	9.97510e9i	−0.349663	−	0.349663i	−0.859984	+	0.510321i	$0.829527\pi$
$972$	−1.09415e10	+	2.64575e10i	−0.382160	+	0.924096i
$973$	−1.03232e10	+	1.03232e10i	−0.359269	+	0.359269i
$974$	−2.00947e10	−	8.90547e9i	−0.696826	−	0.308816i
$975$	1.81783e10	+	2.90155e10i	0.628111	+	1.00257i
$976$	2.16780e10	+	2.63979e10i	0.746355	+	0.908856i
$977$		−	1.55714e10i		−	0.534192i	−0.963670	−	0.267096i	$-0.913936\pi$
$977$		−	1.55714e10i		−	0.534192i	0.963670	−	0.267096i	$-0.0860642\pi$
$978$	2.67671e9	+	1.86548e10i	0.0914987	+	0.637682i
$979$	−2.33054e10	−	2.33054e10i	−0.793810	−	0.793810i
$980$	7.42459e9	+	3.63582e8i	0.251989	+	0.0123399i
$981$	1.38932e10	−	4.82029e9i	0.469851	−	0.163017i
$982$	−1.29161e10	−	3.34760e10i	−0.435254	−	1.12809i
$983$			5.49370e10i			1.84471i	0.386348	+	0.922353i	$0.373736\pi$
$983$			5.49370e10i			1.84471i	−0.386348	+	0.922353i	$0.626264\pi$
$984$	1.70648e8	+	1.81817e9i	0.00570978	+	0.0608349i
$985$		−	2.09460e9i		−	0.0698351i
$986$	3.01627e10	−	1.16377e10i	1.00208	−	0.386633i
$987$	1.24383e10	+	2.85626e9i	0.411768	+	0.0945555i
$988$	−2.56544e10	−	2.82964e10i	−0.846277	−	0.933429i
$989$	2.00800e10	+	2.00800e10i	0.660050	+	0.660050i
$990$	1.60665e9	+	1.89902e9i	0.0526258	+	0.0622023i
$991$			7.10308e9i			0.231840i	0.993259	+	0.115920i	$0.0369817\pi$
$991$			7.10308e9i			0.231840i	−0.993259	+	0.115920i	$0.963018\pi$
$992$	−2.42226e10	−	1.37094e10i	−0.787827	−	0.445891i
$993$	1.90862e10	−	1.19575e10i	0.618581	−	0.387542i
$994$	−1.40824e9	+	3.17760e9i	−0.0454803	+	0.102624i
$995$	5.05933e9	−	5.05933e9i	0.162822	−	0.162822i
$996$	6.85384e9	+	1.93122e9i	0.219799	+	0.0619332i
$997$	−2.60683e9	−	2.60683e9i	−0.0833067	−	0.0833067i	0.664226	−	0.747532i	$-0.268761\pi$
$997$	−2.60683e9	−	2.60683e9i	−0.0833067	−	0.0833067i	−0.747532	+	0.664226i	$0.768761\pi$
$998$	5.20574e9	+	1.34922e10i	0.165778	+	0.429662i
$999$	3.05636e8	+	2.81269e9i	0.00969897	+	0.0892572i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.8.k.a.11.9	✓	108
3.2	odd	2	inner	48.8.k.a.11.46	yes	108
16.3	odd	4	inner	48.8.k.a.35.46	yes	108
48.35	even	4	inner	48.8.k.a.35.9	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.8.k.a.11.9	✓	108	1.1	even	1	trivial
48.8.k.a.11.46	yes	108	3.2	odd	2	inner
48.8.k.a.35.9	yes	108	48.35	even	4	inner
48.8.k.a.35.46	yes	108	16.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 48 = 2^{4} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	48.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.3435 - 4.58397i) q^{2} +(45.5791 + 10.4665i) q^{3} +(85.9744 + 94.8283i) q^{4} +(25.0262 - 25.0262i) q^{5} +(-423.468 - 317.193i) q^{6} -1569.84 q^{7} +(-454.583 - 1374.96i) q^{8} +(1967.91 + 954.104i) q^{9} +O(q^{10})\)	\(q+(-10.3435 - 4.58397i) q^{2} +(45.5791 + 10.4665i) q^{3} +(85.9744 + 94.8283i) q^{4} +(25.0262 - 25.0262i) q^{5} +(-423.468 - 317.193i) q^{6} -1569.84 q^{7} +(-454.583 - 1374.96i) q^{8} +(1967.91 + 954.104i) q^{9} +(-373.577 + 144.138i) q^{10} +(-2008.55 - 2008.55i) q^{11} +(2926.12 + 5222.03i) q^{12} +(6734.71 - 6734.71i) q^{13} +(16237.6 + 7196.12i) q^{14} +(1402.61 - 878.735i) q^{15} +(-1600.81 + 16305.6i) q^{16} -11311.5i q^{17} +(-15981.4 - 18889.6i) q^{18} +(-22153.6 - 22153.6i) q^{19} +(4524.80 + 221.579i) q^{20} +(-71552.0 - 16430.7i) q^{21} +(11568.2 + 29982.5i) q^{22} -67536.9i q^{23} +(-6328.51 - 67427.2i) q^{24} +76872.4i q^{25} +(-100532. + 38788.5i) q^{26} +(79709.3 + 64084.2i) q^{27} +(-134966. - 148866. i) q^{28} +(-178633. - 178633. i) q^{29} +(-18535.9 + 2659.65i) q^{30} -150154. i q^{31} +(91302.4 - 161318. i) q^{32} +(-70525.5 - 112570. i) q^{33} +(-51851.8 + 117001. i) q^{34} +(-39287.2 + 39287.2i) q^{35} +(78713.5 + 268642. i) q^{36} +(19560.6 + 19560.6i) q^{37} +(127593. + 330696. i) q^{38} +(377451. - 236473. i) q^{39} +(-45786.4 - 23033.5i) q^{40} -26965.0 q^{41} +(664778. + 497943. i) q^{42} +(-297319. + 297319. i) q^{43} +(17783.5 - 363151. i) q^{44} +(73126.8 - 25371.6i) q^{45} +(-309587. + 698566. i) q^{46} -173836. q^{47} +(-243625. + 726440. i) q^{48} +1.64086e6 q^{49} +(352381. - 795126. i) q^{50} +(118392. - 515570. i) q^{51} +(1.21765e6 + 59628.5i) q^{52} +(-816830. + 816830. i) q^{53} +(-530709. - 1.02824e6i) q^{54} -100533. q^{55} +(713623. + 2.15847e6i) q^{56} +(-777869. - 1.24161e6i) q^{57} +(1.02884e6 + 2.66654e6i) q^{58} +(-1.70171e6 - 1.70171e6i) q^{59} +(203917. + 57458.1i) q^{60} +(1.47422e6 - 1.47422e6i) q^{61} +(-688303. + 1.55312e6i) q^{62} +(-3.08930e6 - 1.49779e6i) q^{63} +(-1.68386e6 + 1.25006e6i) q^{64} -337089. i q^{65} +(213458. + 1.48765e6i) q^{66} +(819300. + 819300. i) q^{67} +(1.07265e6 - 972503. i) q^{68} +(706873. - 3.07827e6i) q^{69} +(586457. - 226274. i) q^{70} +195694. i q^{71} +(417276. - 3.13951e6i) q^{72} +2.35222e6i q^{73} +(-112659. - 291990. i) q^{74} +(-804582. + 3.50377e6i) q^{75} +(196145. - 4.00542e6i) q^{76} +(3.15311e6 + 3.15311e6i) q^{77} +(-4.98814e6 + 715730. i) q^{78} +1.16965e6i q^{79} +(368005. + 448130. i) q^{80} +(2.96234e6 + 3.75517e6i) q^{81} +(278912. + 123607. i) q^{82} +(841153. - 841153. i) q^{83} +(-4.59354e6 - 8.19778e6i) q^{84} +(-283085. - 283085. i) q^{85} +(4.43821e6 - 1.71240e6i) q^{86} +(-6.27228e6 - 1.00116e7i) q^{87} +(-1.84862e6 + 3.67472e6i) q^{88} +1.16031e7 q^{89} +(-872687. - 72780.9i) q^{90} +(-1.05724e7 + 1.05724e7i) q^{91} +(6.40441e6 - 5.80645e6i) q^{92} +(1.57159e6 - 6.84390e6i) q^{93} +(1.79807e6 + 796861. i) q^{94} -1.10884e6 q^{95} +(5.84991e6 - 6.39713e6i) q^{96} +2.71643e6 q^{97} +(-1.69722e7 - 7.52168e6i) q^{98} +(-2.03627e6 - 5.86900e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7	\( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) 108 * q - 2 * q^3 - 4 * q^4 + 172 * q^6 - 8 * q^7 - 6504 * q^10 + 12016 * q^12 - 4 * q^13 - 55280 * q^16 + 21172 * q^18 - 60588 * q^19 - 4376 * q^21 - 212744 * q^22 - 317304 * q^24 + 238042 * q^27 + 219736 * q^28 - 503852 * q^30 - 4 * q^33 - 364856 * q^34 + 867620 * q^36 - 4 * q^37 - 283948 * q^39 + 390392 * q^40 - 3022344 * q^42 + 752844 * q^43 - 156252 * q^45 - 1166824 * q^46 + 358320 * q^48 + 9882508 * q^49 + 1121592 * q^51 - 4458688 * q^52 + 203816 * q^54 + 4191000 * q^55 + 4975544 * q^58 - 4390240 * q^60 - 2279892 * q^61 + 4781432 * q^64 + 1457476 * q^66 + 1552540 * q^67 + 4372 * q^69 - 9366152 * q^70 - 1660280 * q^72 - 886066 * q^75 - 6569272 * q^76 - 13616772 * q^78 - 4 * q^81 + 11560256 * q^82 - 10944176 * q^84 + 7846496 * q^85 - 40789116 * q^87 + 24614816 * q^88 + 25746032 * q^90 - 1590680 * q^91 - 14495396 * q^93 - 6995856 * q^94 - 13927736 * q^96 - 8 * q^97 - 4701076 * q^99

Introduction

L-functions

Modular forms

Varieties

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