LMFDB - Embedded newform 48.9.l.a.43.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [48,9,Mod(19,48)]

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, 3, 0]))

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("48.19");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 48 = 2^{4} \cdot 3 $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	48.l (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:	$19.5541732829$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			43.11
Character	$\chi$	$=$	48.43
Dual form			48.9.l.a.19.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.30885 - 14.2331i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-149.162 + 208.055i) q^{4} +(-206.104 - 206.104i) q^{5} +(-228.972 + 712.351i) q^{6} +3383.34 q^{7} +(4051.46 + 602.388i) q^{8} +2187.00i q^{9} +O(q^{10})$	\(q+(-7.30885 - 14.2331i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-149.162 + 208.055i) q^{4} +(-206.104 - 206.104i) q^{5} +(-228.972 + 712.351i) q^{6} +3383.34 q^{7} +(4051.46 + 602.388i) q^{8} +2187.00i q^{9} +(-1427.12 + 4439.88i) q^{10} +(754.555 - 754.555i) q^{11} +(11812.5 - 1947.49i) q^{12} +(25576.5 - 25576.5i) q^{13} +(-24728.3 - 48155.4i) q^{14} +13631.0i q^{15} +(-21037.7 - 62067.6i) q^{16} -2352.11 q^{17} +(31127.8 - 15984.4i) q^{18} +(130755. + 130755. i) q^{19} +(73623.8 - 12138.2i) q^{20} +(-111881. - 111881. i) q^{21} +(-16254.6 - 5224.72i) q^{22} -334976. q^{23} +(-114054. - 153894. i) q^{24} -305667. i q^{25} +(-550967. - 177098. i) q^{26} +(72320.0 - 72320.0i) q^{27} +(-504665. + 703921. i) q^{28} +(-426267. + 426267. i) q^{29} +(194011. - 99626.5i) q^{30} -1.67376e6i q^{31} +(-729652. + 753073. i) q^{32} -49903.4 q^{33} +(17191.2 + 33477.7i) q^{34} +(-697321. - 697321. i) q^{35} +(-455016. - 326216. i) q^{36} +(556451. + 556451. i) q^{37} +(905382. - 2.81672e6i) q^{38} -1.69153e6 q^{39} +(-710869. - 959178. i) q^{40} -2.16908e6i q^{41} +(-774689. + 2.41013e6i) q^{42} +(-796456. + 796456. i) q^{43} +(44438.3 + 269539. i) q^{44} +(450750. - 450750. i) q^{45} +(2.44829e6 + 4.76774e6i) q^{46} -7.68391e6i q^{47} +(-1.35678e6 + 2.74813e6i) q^{48} +5.68220e6 q^{49} +(-4.35059e6 + 2.23407e6i) q^{50} +(77779.7 + 77779.7i) q^{51} +(1.50629e6 + 9.13634e6i) q^{52} +(2.01803e6 + 2.01803e6i) q^{53} +(-1.55791e6 - 500761. i) q^{54} -311034. q^{55} +(1.37075e7 + 2.03808e6i) q^{56} -8.64767e6i q^{57} +(9.18262e6 + 2.95158e6i) q^{58} +(1.37774e7 - 1.37774e7i) q^{59} +(-2.83599e6 - 2.03321e6i) q^{60} +(7.62612e6 - 7.62612e6i) q^{61} +(-2.38228e7 + 1.22333e7i) q^{62} +7.39937e6i q^{63} +(1.60515e7 + 4.88110e6i) q^{64} -1.05428e7 q^{65} +(364736. + 710280. i) q^{66} +(3.30993e6 + 3.30993e6i) q^{67} +(350844. - 489367. i) q^{68} +(1.10770e7 + 1.10770e7i) q^{69} +(-4.82842e6 + 1.50216e7i) q^{70} +6.85661e6 q^{71} +(-1.31742e6 + 8.86055e6i) q^{72} +3.14472e7i q^{73} +(3.85300e6 - 1.19870e7i) q^{74} +(-1.01078e7 + 1.01078e7i) q^{75} +(-4.67080e7 + 7.70062e6i) q^{76} +(2.55292e6 - 2.55292e6i) q^{77} +(1.23632e7 + 2.40757e7i) q^{78} -3.62349e7i q^{79} +(-8.45643e6 + 1.71283e7i) q^{80} -4.78297e6 q^{81} +(-3.08728e7 + 1.58535e7i) q^{82} +(-4.22074e7 - 4.22074e7i) q^{83} +(3.99656e7 - 6.58903e6i) q^{84} +(484779. + 484779. i) q^{85} +(1.71572e7 + 5.51485e6i) q^{86} +2.81917e7 q^{87} +(3.51159e6 - 2.60252e6i) q^{88} -8.48391e7i q^{89} +(-9.71002e6 - 3.12110e6i) q^{90} +(8.65340e7 - 8.65340e7i) q^{91} +(4.99655e7 - 6.96934e7i) q^{92} +(-5.53482e7 + 5.53482e7i) q^{93} +(-1.09366e8 + 5.61605e7i) q^{94} -5.38985e7i q^{95} +(4.90309e7 - 774500. i) q^{96} -776204. q^{97} +(-4.15304e7 - 8.08753e7i) q^{98} +(1.65021e6 + 1.65021e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) $ 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * 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 $

$2$	−7.30885	−	14.2331i	−0.456803	−	0.889568i
$2$	−7.30885	−	14.2331i	−0.456803	−	0.889568i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$3$	−33.0681	−	33.0681i	−0.408248	−	0.408248i
$4$	−149.162	+	208.055i	−0.582662	+	0.812714i
$5$	−206.104	−	206.104i	−0.329767	−	0.329767i	0.522731	−	0.852498i	$-0.324913\pi$
$5$	−206.104	−	206.104i	−0.329767	−	0.329767i	−0.852498	+	0.522731i	$0.824913\pi$
$6$	−228.972	+	712.351i	−0.176676	+	0.549654i
$7$	3383.34			1.40914			0.704569	−	0.709635i	$-0.251140\pi$
$7$	3383.34			1.40914			0.704569	+	0.709635i	$0.251140\pi$
$8$	4051.46	+	602.388i	0.989126	+	0.147067i
$9$			2187.00i			0.333333i
$10$	−1427.12	+	4439.88i	−0.142712	+	0.443988i
$11$	754.555	−	754.555i	0.0515371	−	0.0515371i	−0.680869	−	0.732406i	$-0.738398\pi$
$11$	754.555	−	754.555i	0.0515371	−	0.0515371i	0.732406	+	0.680869i	$0.238398\pi$
$12$	11812.5	−	1947.49i	0.569660	−	0.0939184i
$13$	25576.5	−	25576.5i	0.895504	−	0.895504i	−0.0995304	−	0.995035i	$-0.531734\pi$
$13$	25576.5	−	25576.5i	0.895504	−	0.895504i	0.995035	+	0.0995304i	$0.0317340\pi$
$14$	−24728.3	−	48155.4i	−0.643699	−	1.25352i
$15$			13631.0i			0.269253i
$16$	−21037.7	−	62067.6i	−0.321009	−	0.947076i
$17$	−2352.11			−0.0281619			−0.0140809	−	0.999901i	$-0.504482\pi$
$17$	−2352.11			−0.0281619			−0.0140809	+	0.999901i	$0.504482\pi$
$18$	31127.8	−	15984.4i	0.296523	−	0.152268i
$19$	130755.	+	130755.i	1.00333	+	1.00333i	0.999994	+	0.00333878i	$0.00106277\pi$
$19$	130755.	+	130755.i	1.00333	+	1.00333i	0.00333878	+	0.999994i	$0.498937\pi$
$20$	73623.8	−	12138.2i	0.460149	−	0.0758635i
$21$	−111881.	−	111881.i	−0.575279	−	0.575279i
$22$	−16254.6	−	5224.72i	−0.0693881	−	0.0223035i
$23$	−334976.			−1.19702			−0.598511	−	0.801115i	$-0.704241\pi$
$23$	−334976.			−1.19702			−0.598511	+	0.801115i	$0.704241\pi$
$24$	−114054.	−	153894.i	−0.343769	−	0.463849i
$25$		−	305667.i		−	0.782508i
$26$	−550967.	−	177098.i	−1.20568	−	0.387543i
$27$	72320.0	−	72320.0i	0.136083	−	0.136083i
$28$	−504665.	+	703921.i	−0.821052	+	1.14523i
$29$	−426267.	+	426267.i	−0.602685	+	0.602685i	−0.941024	−	0.338340i	$-0.890135\pi$
$29$	−426267.	+	426267.i	−0.602685	+	0.602685i	0.338340	+	0.941024i	$0.390135\pi$
$30$	194011.	−	99626.5i	0.239519	−	0.122996i
$31$		−	1.67376e6i		−	1.81237i	−0.422878	−	0.906187i	$-0.638980\pi$
$31$		−	1.67376e6i		−	1.81237i	0.422878	−	0.906187i	$-0.361020\pi$
$32$	−729652.	+	753073.i	−0.695850	+	0.718187i
$33$	−49903.4			−0.0420799
$34$	17191.2	+	33477.7i	0.0128644	+	0.0250519i
$35$	−697321.	−	697321.i	−0.464687	−	0.464687i
$36$	−455016.	−	326216.i	−0.270905	−	0.194221i
$37$	556451.	+	556451.i	0.296907	+	0.296907i	0.839801	−	0.542894i	$-0.182672\pi$
$37$	556451.	+	556451.i	0.296907	+	0.296907i	−0.542894	+	0.839801i	$0.682672\pi$
$38$	905382.	−	2.81672e6i	0.434208	−	1.35086i
$39$	−1.69153e6			−0.731176
$40$	−710869.	−	959178.i	−0.277683	−	0.374679i
$41$		−	2.16908e6i		−	0.767611i	−0.923414	−	0.383805i	$-0.874613\pi$
$41$		−	2.16908e6i		−	0.767611i	0.923414	−	0.383805i	$-0.125387\pi$
$42$	−774689.	+	2.41013e6i	−0.248960	+	0.774538i
$43$	−796456.	+	796456.i	−0.232964	+	0.232964i	−0.813929	−	0.580965i	$-0.802675\pi$
$43$	−796456.	+	796456.i	−0.232964	+	0.232964i	0.580965	+	0.813929i	$0.302675\pi$
$44$	44438.3	+	269539.i	0.0118562	+	0.0719137i
$45$	450750.	−	450750.i	0.109922	−	0.109922i
$46$	2.44829e6	+	4.76774e6i	0.546803	+	1.06483i
$47$		−	7.68391e6i		−	1.57467i	−0.616523	−	0.787337i	$-0.711459\pi$
$47$		−	7.68391e6i		−	1.57467i	0.616523	−	0.787337i	$-0.288541\pi$
$48$	−1.35678e6	+	2.74813e6i	−0.255591	+	0.517694i
$49$	5.68220e6			0.985672
$50$	−4.35059e6	+	2.23407e6i	−0.696094	+	0.357452i
$51$	77779.7	+	77779.7i	0.0114970	+	0.0114970i
$52$	1.50629e6	+	9.13634e6i	0.206013	+	1.24957i
$53$	2.01803e6	+	2.01803e6i	0.255756	+	0.255756i	0.823325	−	0.567570i	$-0.192116\pi$
$53$	2.01803e6	+	2.01803e6i	0.255756	+	0.255756i	−0.567570	+	0.823325i	$0.692116\pi$
$54$	−1.55791e6	−	500761.i	−0.183218	−	0.0588919i
$55$	−311034.			−0.0339905
$56$	1.37075e7	+	2.03808e6i	1.39382	+	0.207238i
$57$		−	8.64767e6i		−	0.819218i
$58$	9.18262e6	+	2.95158e6i	0.811437	+	0.260821i
$59$	1.37774e7	−	1.37774e7i	1.13699	−	1.13699i	0.148007	−	0.988986i	$-0.452714\pi$
$59$	1.37774e7	−	1.37774e7i	1.13699	−	1.13699i	0.988986	−	0.148007i	$-0.0472859\pi$
$60$	−2.83599e6	−	2.03321e6i	−0.218826	−	0.156884i
$61$	7.62612e6	−	7.62612e6i	0.550787	−	0.550787i	−0.375881	−	0.926668i	$-0.622660\pi$
$61$	7.62612e6	−	7.62612e6i	0.550787	−	0.550787i	0.926668	+	0.375881i	$0.122660\pi$
$62$	−2.38228e7	+	1.22333e7i	−1.61223	+	0.827897i
$63$			7.39937e6i			0.469713i
$64$	1.60515e7	+	4.88110e6i	0.956742	+	0.290936i
$65$	−1.05428e7			−0.590615
$66$	364736.	+	710280.i	0.0192222	+	0.0374329i
$67$	3.30993e6	+	3.30993e6i	0.164255	+	0.164255i	0.784449	−	0.620194i	$-0.212946\pi$
$67$	3.30993e6	+	3.30993e6i	0.164255	+	0.164255i	−0.620194	+	0.784449i	$0.712946\pi$
$68$	350844.	−	489367.i	0.0164089	−	0.0228876i
$69$	1.10770e7	+	1.10770e7i	0.488682	+	0.488682i
$70$	−4.82842e6	+	1.50216e7i	−0.201100	+	0.625641i
$71$	6.85661e6			0.269821			0.134911	−	0.990858i	$-0.456925\pi$
$71$	6.85661e6			0.269821			0.134911	+	0.990858i	$0.456925\pi$
$72$	−1.31742e6	+	8.86055e6i	−0.0490225	+	0.329709i
$73$			3.14472e7i			1.10736i	0.832729	+	0.553681i	$0.186777\pi$
$73$			3.14472e7i			1.10736i	−0.832729	+	0.553681i	$0.813223\pi$
$74$	3.85300e6	−	1.19870e7i	0.128491	−	0.399747i
$75$	−1.01078e7	+	1.01078e7i	−0.319457	+	0.319457i
$76$	−4.67080e7	+	7.70062e6i	−1.40003	+	0.230819i
$77$	2.55292e6	−	2.55292e6i	0.0726230	−	0.0726230i
$78$	1.23632e7	+	2.40757e7i	0.334003	+	0.650431i
$79$		−	3.62349e7i		−	0.930292i	−0.885234	−	0.465146i	$-0.846002\pi$
$79$		−	3.62349e7i		−	0.930292i	0.885234	−	0.465146i	$-0.153998\pi$
$80$	−8.45643e6	+	1.71283e7i	−0.206456	+	0.418172i
$81$	−4.78297e6			−0.111111
$82$	−3.08728e7	+	1.58535e7i	−0.682842	+	0.350647i
$83$	−4.22074e7	−	4.22074e7i	−0.889358	−	0.889358i	0.105103	−	0.994461i	$-0.466483\pi$
$83$	−4.22074e7	−	4.22074e7i	−0.889358	−	0.889358i	−0.994461	+	0.105103i	$0.966483\pi$
$84$	3.99656e7	−	6.58903e6i	0.802730	−	0.132344i
$85$	484779.	+	484779.i	0.00928685	+	0.00928685i
$86$	1.71572e7	+	5.51485e6i	0.313655	+	0.100819i
$87$	2.81917e7			0.492090
$88$	3.51159e6	−	2.60252e6i	0.0585562	−	0.0433973i
$89$		−	8.48391e7i		−	1.35218i	−0.736817	−	0.676092i	$-0.763672\pi$
$89$		−	8.48391e7i		−	1.35218i	0.736817	−	0.676092i	$-0.236328\pi$
$90$	−9.71002e6	−	3.12110e6i	−0.147996	−	0.0475705i
$91$	8.65340e7	−	8.65340e7i	1.26189	−	1.26189i
$92$	4.99655e7	−	6.96934e7i	0.697460	−	0.972837i
$93$	−5.53482e7	+	5.53482e7i	−0.739898	+	0.739898i
$94$	−1.09366e8	+	5.61605e7i	−1.40078	+	0.719316i
$95$		−	5.38985e7i		−	0.661732i
$96$	4.90309e7	−	774500.i	0.577278	−	0.00911877i
$97$	−776204.			−0.00876777			−0.00438388	−	0.999990i	$-0.501395\pi$
$97$	−776204.			−0.00876777			−0.00438388	+	0.999990i	$0.501395\pi$
$98$	−4.15304e7	−	8.08753e7i	−0.450258	−	0.876822i
$99$	1.65021e6	+	1.65021e6i	0.0171790	+	0.0171790i
$100$	6.35955e7	+	4.55938e7i	0.635955	+	0.455938i
$101$	4.12812e7	+	4.12812e7i	0.396704	+	0.396704i	0.877069	−	0.480365i	$-0.159496\pi$
$101$	4.12812e7	+	4.12812e7i	0.396704	+	0.396704i	−0.480365	+	0.877069i	$0.659496\pi$
$102$	538566.	−	1.67553e6i	0.00497551	−	0.0154793i
$103$	−1.86270e8			−1.65498			−0.827492	−	0.561477i	$-0.810233\pi$
$103$	−1.86270e8			−1.65498			−0.827492	+	0.561477i	$0.810233\pi$
$104$	1.19029e8	−	8.82152e7i	1.01747	−	0.754067i
$105$			4.61182e7i			0.379415i
$106$	1.39734e7	−	4.34724e7i	0.110682	−	0.344342i
$107$	−7.18876e7	+	7.18876e7i	−0.548427	+	0.548427i	−0.925986	−	0.377559i	$-0.876764\pi$
$107$	−7.18876e7	+	7.18876e7i	−0.548427	+	0.548427i	0.377559	+	0.925986i	$0.376764\pi$
$108$	4.25917e6	+	2.58339e7i	0.0313061	+	0.189887i
$109$	−8.55692e7	+	8.55692e7i	−0.606194	+	0.606194i	−0.941949	−	0.335755i	$-0.891008\pi$
$109$	−8.55692e7	+	8.55692e7i	−0.606194	+	0.606194i	0.335755	+	0.941949i	$0.391008\pi$
$110$	2.27330e6	+	4.42697e6i	0.0155269	+	0.0302368i
$111$		−	3.68016e7i		−	0.242423i
$112$	−7.11777e7	−	2.09996e8i	−0.452347	−	1.33456i
$113$	7.49116e7			0.459447			0.229723	−	0.973256i	$-0.426218\pi$
$113$	7.49116e7			0.459447			0.229723	+	0.973256i	$0.426218\pi$
$114$	−1.23083e8	+	6.32045e7i	−0.728750	+	0.374221i
$115$	6.90399e7	+	6.90399e7i	0.394738	+	0.394738i
$116$	−2.51043e7	−	1.52270e8i	−0.138649	−	0.840972i
$117$	5.59358e7	+	5.59358e7i	0.298501	+	0.298501i
$118$	−2.96791e8	−	9.53978e7i	−1.53081	−	0.492051i
$119$	−7.95798e6			−0.0396840
$120$	−8.21112e6	+	5.52253e7i	−0.0395984	+	0.266326i
$121$			2.13220e8i			0.994688i
$122$	−1.64281e8	−	5.28051e7i	−0.741564	−	0.238362i
$123$	−7.17275e7	+	7.17275e7i	−0.313376	+	0.313376i
$124$	3.48235e8	+	2.49661e8i	1.47294	+	1.05600i
$125$	−1.43509e8	+	1.43509e8i	−0.587812	+	0.587812i
$126$	1.05316e8	−	5.40809e7i	0.417842	−	0.214566i
$127$		−	2.20832e8i		−	0.848880i	−0.905456	−	0.424440i	$-0.860471\pi$
$127$		−	2.20832e8i		−	0.848880i	0.905456	−	0.424440i	$-0.139529\pi$
$128$	−4.78446e7	−	2.64137e8i	−0.178235	−	0.983988i
$129$	5.26746e7			0.190214
$130$	7.70560e7	+	1.50057e8i	0.269795	+	0.525392i
$131$	−2.10026e8	−	2.10026e8i	−0.713162	−	0.713162i	0.254033	−	0.967195i	$-0.418243\pi$
$131$	−2.10026e8	−	2.10026e8i	−0.713162	−	0.713162i	−0.967195	+	0.254033i	$0.918243\pi$
$132$	7.44367e6	−	1.03827e7i	0.0245184	−	0.0341989i
$133$	4.42390e8	+	4.42390e8i	1.41384	+	1.41384i
$134$	2.29187e7	−	7.13022e7i	0.0710839	−	0.221148i
$135$	−2.98109e7			−0.0897511
$136$	−9.52947e6	−	1.41688e6i	−0.0278556	−	0.00414169i
$137$			5.06655e8i			1.43824i	0.694887	+	0.719119i	$0.255454\pi$
$137$			5.06655e8i			1.43824i	−0.694887	+	0.719119i	$0.744546\pi$
$138$	7.67000e7	−	2.38620e8i	0.211485	−	0.657948i
$139$	2.06164e7	−	2.06164e7i	0.0552272	−	0.0552272i	−0.678954	−	0.734181i	$-0.737566\pi$
$139$	2.06164e7	−	2.06164e7i	0.0552272	−	0.0552272i	0.734181	+	0.678954i	$0.237566\pi$
$140$	2.49095e8	−	4.10676e7i	0.648413	−	0.106902i
$141$	−2.54092e8	+	2.54092e8i	−0.642858	+	0.642858i
$142$	−5.01139e7	−	9.75908e7i	−0.123255	−	0.240024i
$143$		−	3.85977e7i		−	0.0923034i
$144$	1.35742e8	−	4.60094e7i	0.315692	−	0.107003i
$145$	1.75711e8			0.397491
$146$	4.47590e8	−	2.29842e8i	0.985074	−	0.505846i
$147$	−1.87900e8	−	1.87900e8i	−0.402399	−	0.402399i
$148$	−1.98773e8	+	3.27713e7i	−0.414297	+	0.0683041i
$149$	4.17465e8	+	4.17465e8i	0.846984	+	0.846984i	0.989756	−	0.142772i	$-0.0456014\pi$
$149$	4.17465e8	+	4.17465e8i	0.846984	+	0.846984i	−0.142772	+	0.989756i	$0.545601\pi$
$150$	2.17742e8	+	6.99891e7i	0.430108	+	0.138250i
$151$	8.68362e8			1.67029			0.835147	−	0.550027i	$-0.185382\pi$
$151$	8.68362e8			1.67029			0.835147	+	0.550027i	$0.185382\pi$
$152$	4.50985e8	+	6.08516e8i	0.844866	+	1.13998i
$153$		−	5.14406e6i		−	0.00938729i
$154$	−5.49948e7	−	1.76770e7i	−0.0977774	−	0.0314287i
$155$	−3.44970e8	+	3.44970e8i	−0.597660	+	0.597660i
$156$	2.52312e8	−	3.51932e8i	0.426029	−	0.594237i
$157$	6.26219e8	−	6.26219e8i	1.03069	−	1.03069i	0.0311757	−	0.999514i	$-0.490075\pi$
$157$	6.26219e8	−	6.26219e8i	1.03069	−	1.03069i	0.999514	−	0.0311757i	$-0.00992515\pi$
$158$	−5.15735e8	+	2.64836e8i	−0.827558	+	0.424960i
$159$		−	1.33465e8i		−	0.208824i
$160$	3.05596e8	−	4.82724e6i	0.466302	−	0.00736578i
$161$	−1.13334e9			−1.68677
$162$	3.49580e7	+	6.80764e7i	0.0507559	+	0.0988409i
$163$	−1.03964e8	−	1.03964e8i	−0.147276	−	0.147276i	0.629624	−	0.776900i	$-0.283209\pi$
$163$	−1.03964e8	−	1.03964e8i	−0.147276	−	0.147276i	−0.776900	+	0.629624i	$0.783209\pi$
$164$	4.51289e8	+	3.23544e8i	0.623848	+	0.447258i
$165$	1.02853e7	+	1.02853e7i	0.0138765	+	0.0138765i
$166$	−2.92254e8	+	9.09230e8i	−0.384883	+	1.19741i
$167$	4.49793e8			0.578291			0.289146	−	0.957285i	$-0.406629\pi$
$167$	4.49793e8			0.578291			0.289146	+	0.957285i	$0.406629\pi$
$168$	−3.85885e8	−	5.20676e8i	−0.484419	−	0.653628i
$169$		−	4.92583e8i		−	0.603855i
$170$	3.35673e6	−	1.04431e7i	0.00401902	−	0.0125035i
$171$	−2.85962e8	+	2.85962e8i	−0.334444	+	0.334444i
$172$	−4.69060e7	−	2.84507e8i	−0.0535938	−	0.325072i
$173$	2.58287e8	−	2.58287e8i	0.288349	−	0.288349i	−0.548078	−	0.836427i	$-0.684640\pi$
$173$	2.58287e8	−	2.58287e8i	0.288349	−	0.288349i	0.836427	+	0.548078i	$0.184640\pi$
$174$	−2.06049e8	−	4.01255e8i	−0.224788	−	0.437747i
$175$		−	1.03418e9i		−	1.10266i
$176$	−6.27075e7	−	3.09593e7i	−0.0653535	−	0.0322657i
$177$	−9.11183e8			−0.928351
$178$	−1.20752e9	+	6.20076e8i	−1.20286	+	0.617682i
$179$	−4.89538e8	−	4.89538e8i	−0.476842	−	0.476842i	0.427278	−	0.904120i	$-0.359472\pi$
$179$	−4.89538e8	−	4.89538e8i	−0.476842	−	0.476842i	−0.904120	+	0.427278i	$0.859472\pi$
$180$	2.65462e7	+	1.61015e8i	0.0252878	+	0.153383i
$181$	−5.75607e8	−	5.75607e8i	−0.536305	−	0.536305i	0.386137	−	0.922442i	$-0.373809\pi$
$181$	−5.75607e8	−	5.75607e8i	−0.536305	−	0.536305i	−0.922442	+	0.386137i	$0.873809\pi$
$182$	−1.86411e9	−	5.99182e8i	−1.69897	−	0.546102i
$183$	−5.04363e8			−0.449716
$184$	−1.35714e9	−	2.01785e8i	−1.18401	−	0.176043i
$185$		−	2.29374e8i		−	0.195820i
$186$	1.19231e9	+	3.83245e8i	0.996177	+	0.320202i
$187$	−1.77479e6	+	1.77479e6i	−0.00145138	+	0.00145138i
$188$	1.59867e9	+	1.14614e9i	1.27976	+	0.917503i
$189$	2.44683e8	−	2.44683e8i	0.191760	−	0.191760i
$190$	−7.67142e8	+	3.93936e8i	−0.588655	+	0.302281i
$191$		−	3.51864e8i		−	0.264388i	−0.991224	−	0.132194i	$-0.957798\pi$
$191$		−	3.51864e8i		−	0.264388i	0.991224	−	0.132194i	$-0.0422021\pi$
$192$	−3.69383e8	−	6.92201e8i	−0.271814	−	0.509363i
$193$	3.63253e8			0.261806			0.130903	−	0.991395i	$-0.458212\pi$
$193$	3.63253e8			0.261806			0.130903	+	0.991395i	$0.458212\pi$
$194$	5.67316e6	+	1.10478e7i	0.00400514	+	0.00779952i
$195$	3.48632e8	+	3.48632e8i	0.241118	+	0.241118i
$196$	−8.47566e8	+	1.18221e9i	−0.574314	+	0.801070i
$197$	4.30119e8	+	4.30119e8i	0.285578	+	0.285578i	0.835329	−	0.549751i	$-0.185277\pi$
$197$	4.30119e8	+	4.30119e8i	0.285578	+	0.285578i	−0.549751	+	0.835329i	$0.685277\pi$
$198$	1.14265e7	−	3.55488e7i	0.00743449	−	0.0231294i
$199$	2.09883e9			1.33833			0.669167	−	0.743112i	$-0.266651\pi$
$199$	2.09883e9			1.33833			0.669167	+	0.743112i	$0.266651\pi$
$200$	1.84130e8	−	1.23840e9i	0.115081	−	0.773999i
$201$		−	2.18906e8i		−	0.134114i
$202$	2.85841e8	−	8.89276e8i	0.171680	−	0.534110i
$203$	−1.44221e9	+	1.44221e9i	−0.849266	+	0.849266i
$204$	−2.77842e7	+	4.58071e6i	−0.0160427	+	0.00264492i
$205$	−4.47057e8	+	4.47057e8i	−0.253132	+	0.253132i
$206$	1.36142e9	+	2.65120e9i	0.756002	+	1.47222i
$207$		−	7.32592e8i		−	0.399007i
$208$	−2.12554e9	−	1.04940e9i	−1.13558	−	0.560645i
$209$	1.97324e8			0.103418
$210$	6.56404e8	−	3.37071e8i	0.337516	−	0.173318i
$211$	−1.21243e9	−	1.21243e9i	−0.611685	−	0.611685i	0.331700	−	0.943385i	$-0.392378\pi$
$211$	−1.21243e9	−	1.21243e9i	−0.611685	−	0.611685i	−0.943385	+	0.331700i	$0.892378\pi$
$212$	−7.20875e8	+	1.18849e8i	−0.356875	+	0.0588371i
$213$	−2.26735e8	−	2.26735e8i	−0.110154	−	0.110154i
$214$	1.54860e9	+	4.97767e8i	0.738386	+	0.237340i
$215$	3.28306e8			0.153647
$216$	3.36566e8	−	2.49437e8i	0.154616	−	0.114590i
$217$		−	5.66292e9i		−	2.55389i
$218$	1.84333e9	+	5.92502e8i	0.816162	+	0.262340i
$219$	1.03990e9	−	1.03990e9i	0.452079	−	0.452079i
$220$	4.63943e7	−	6.47121e7i	0.0198050	−	0.0276245i
$221$	−6.01587e7	+	6.01587e7i	−0.0252191	+	0.0252191i
$222$	−5.23800e8	+	2.68977e8i	−0.215652	+	0.110740i
$223$		−	3.52094e9i		−	1.42377i	−0.702296	−	0.711885i	$-0.747842\pi$
$223$		−	3.52094e9i		−	1.42377i	0.702296	−	0.711885i	$-0.252158\pi$
$224$	−2.46866e9	+	2.54790e9i	−0.980550	+	1.01202i
$225$	6.68494e8			0.260836
$226$	−5.47517e8	−	1.06622e9i	−0.209877	−	0.408709i
$227$	3.25998e9	+	3.25998e9i	1.22775	+	1.22775i	0.964812	+	0.262942i	$0.0846928\pi$
$227$	3.25998e9	+	3.25998e9i	1.22775	+	1.22775i	0.262942	+	0.964812i	$0.415307\pi$
$228$	1.79919e9	+	1.28990e9i	0.665790	+	0.477327i
$229$	3.57036e9	+	3.57036e9i	1.29828	+	1.29828i	0.929525	+	0.368758i	$0.120217\pi$
$229$	3.57036e9	+	3.57036e9i	1.29828	+	1.29828i	0.368758	+	0.929525i	$0.379783\pi$
$230$	4.78049e8	−	1.48725e9i	0.170829	−	0.531464i
$231$	−1.68840e8			−0.0592964
$232$	−1.98378e9	+	1.47023e9i	−0.684767	+	0.507496i
$233$		−	4.93129e9i		−	1.67316i	−0.547847	−	0.836579i	$-0.684552\pi$
$233$		−	4.93129e9i		−	1.67316i	0.547847	−	0.836579i	$-0.315448\pi$
$234$	3.87313e8	−	1.20497e9i	0.129181	−	0.401894i
$235$	−1.58369e9	+	1.58369e9i	−0.519275	+	0.519275i
$236$	8.11395e8	+	4.92150e9i	0.261568	+	1.58653i
$237$	−1.19822e9	+	1.19822e9i	−0.379790	+	0.379790i
$238$	5.81637e7	+	1.13267e8i	0.0181278	+	0.0353016i
$239$			5.29507e9i			1.62286i	0.584451	+	0.811429i	$0.301310\pi$
$239$			5.29507e9i			1.62286i	−0.584451	+	0.811429i	$0.698690\pi$
$240$	8.46040e8	−	2.86764e8i	0.255003	−	0.0864329i
$241$	−2.85450e9			−0.846179			−0.423090	−	0.906088i	$-0.639054\pi$
$241$	−2.85450e9			−0.846179			−0.423090	+	0.906088i	$0.639054\pi$
$242$	3.03478e9	−	1.55839e9i	0.884842	−	0.454376i
$243$	1.58164e8	+	1.58164e8i	0.0453609	+	0.0453609i
$244$	4.49128e8	+	2.72417e9i	0.126710	+	0.768556i
$245$	−1.17113e9	−	1.17113e9i	−0.325042	−	0.325042i
$246$	1.54515e9	+	4.96659e8i	0.421920	+	0.135618i
$247$	6.68853e9			1.79698
$248$	1.00826e9	−	6.78119e9i	0.266541	−	1.79267i
$249$			2.79144e9i			0.726158i
$250$	3.09146e9	+	9.93689e8i	0.791413	+	0.254384i
$251$	−5.20610e9	+	5.20610e9i	−1.31165	+	1.31165i	−0.391448	+	0.920200i	$0.628026\pi$
$251$	−5.20610e9	+	5.20610e9i	−1.31165	+	1.31165i	−0.920200	+	0.391448i	$0.871974\pi$
$252$	−1.53947e9	−	1.10370e9i	−0.381742	−	0.273684i
$253$	−2.52758e8	+	2.52758e8i	−0.0616911	+	0.0616911i
$254$	−3.14312e9	+	1.61402e9i	−0.755136	+	0.387771i
$255$		−	3.20615e7i		−	0.00758268i
$256$	−3.40980e9	+	2.61151e9i	−0.793906	+	0.608041i
$257$	−2.97177e8			−0.0681212			−0.0340606	−	0.999420i	$-0.510844\pi$
$257$	−2.97177e8			−0.0681212			−0.0340606	+	0.999420i	$0.510844\pi$
$258$	−3.84991e8	−	7.49722e8i	−0.0868903	−	0.169208i
$259$	1.88266e9	+	1.88266e9i	0.418383	+	0.418383i
$260$	1.57259e9	−	2.19349e9i	0.344129	−	0.480001i
$261$	−9.32247e8	−	9.32247e8i	−0.200895	−	0.200895i
$262$	−1.45427e9	+	4.52437e9i	−0.308632	+	0.960181i
$263$	−4.79130e9			−1.00145			−0.500726	−	0.865606i	$-0.666934\pi$
$263$	−4.79130e9			−1.00145			−0.500726	+	0.865606i	$0.666934\pi$
$264$	−2.02182e8	−	3.00612e7i	−0.0416223	−	0.00618858i
$265$		−	8.31851e8i		−	0.168679i
$266$	3.06322e9	−	9.52994e9i	0.611859	−	1.90355i
$267$	−2.80547e9	+	2.80547e9i	−0.552027	+	0.552027i
$268$	−1.18236e9	+	1.94933e8i	−0.229198	+	0.0377873i
$269$	5.52133e9	−	5.52133e9i	1.05447	−	1.05447i	0.0560427	−	0.998428i	$-0.482152\pi$
$269$	5.52133e9	−	5.52133e9i	1.05447	−	1.05447i	0.998428	−	0.0560427i	$-0.0178483\pi$
$270$	2.17883e8	+	4.24301e8i	0.0409986	+	0.0798397i
$271$			6.51113e9i			1.20720i	0.797287	+	0.603600i	$0.206268\pi$
$271$			6.51113e9i			1.20720i	−0.797287	+	0.603600i	$0.793732\pi$
$272$	4.94829e7	+	1.45990e8i	0.00904022	+	0.0266714i
$273$	−5.72303e9			−1.03033
$274$	7.21127e9	−	3.70307e9i	1.27941	−	0.656991i
$275$	−2.30643e8	−	2.30643e8i	−0.0403282	−	0.0403282i
$276$	−3.95689e9	+	6.52363e8i	−0.681896	+	0.112422i
$277$	6.03539e9	+	6.03539e9i	1.02515	+	1.02515i	0.999676	+	0.0254719i	$0.00810882\pi$
$277$	6.03539e9	+	6.03539e9i	1.02515	+	1.02515i	0.0254719	+	0.999676i	$0.491891\pi$
$278$	−4.44117e8	−	1.42753e8i	−0.0743563	−	0.0239004i
$279$	3.66052e9			0.604124
$280$	−2.40511e9	−	3.24523e9i	−0.391294	−	0.527975i
$281$		−	7.25155e9i		−	1.16307i	−0.813522	−	0.581535i	$-0.802452\pi$
$281$		−	7.25155e9i		−	1.16307i	0.813522	−	0.581535i	$-0.197548\pi$
$282$	5.47364e9	+	1.75940e9i	0.865525	+	0.278206i
$283$	1.68761e9	−	1.68761e9i	0.263104	−	0.263104i	−0.563210	−	0.826314i	$-0.690434\pi$
$283$	1.68761e9	−	1.68761e9i	0.263104	−	0.263104i	0.826314	+	0.563210i	$0.190434\pi$
$284$	−1.02274e9	+	1.42655e9i	−0.157215	+	0.219288i
$285$	−1.78232e9	+	1.78232e9i	−0.270151	+	0.270151i
$286$	−5.49365e8	+	2.82105e8i	−0.0821102	+	0.0421645i
$287$		−	7.33876e9i		−	1.08167i
$288$	−1.64697e9	−	1.59575e9i	−0.239396	−	0.231950i
$289$	−6.97023e9			−0.999207
$290$	−1.28424e9	−	2.50091e9i	−0.181575	−	0.353595i
$291$	2.56676e7	+	2.56676e7i	0.00357943	+	0.00357943i
$292$	−6.54273e9	−	4.69071e9i	−0.899970	−	0.645218i
$293$	3.45572e9	+	3.45572e9i	0.468887	+	0.468887i	0.901554	−	0.432667i	$-0.142427\pi$
$293$	3.45572e9	+	3.45572e9i	0.468887	+	0.468887i	−0.432667	+	0.901554i	$0.642427\pi$
$294$	−1.30106e9	+	4.04772e9i	−0.174144	+	0.541778i
$295$	−5.67914e9			−0.749885
$296$	1.91924e9	+	2.58964e9i	0.250013	+	0.337344i
$297$		−	1.09139e8i		−	0.0140266i
$298$	2.89063e9	−	8.99301e9i	0.366545	−	1.14035i
$299$	−8.56751e9	+	8.56751e9i	−1.07194	+	1.07194i
$300$	−5.95284e8	−	3.61068e9i	−0.0734919	−	0.445764i
$301$	−2.69468e9	+	2.69468e9i	−0.328278	+	0.328278i
$302$	−6.34672e9	−	1.23595e10i	−0.762995	−	1.48584i
$303$		−	2.73018e9i		−	0.323907i
$304$	5.36488e9	−	1.08665e10i	0.628153	−	1.27231i
$305$	−3.14355e9			−0.363263
$306$	−7.32158e7	+	3.75971e7i	−0.00835063	+	0.00428814i
$307$	2.19069e9	+	2.19069e9i	0.246620	+	0.246620i	0.819582	−	0.572962i	$-0.194206\pi$
$307$	2.19069e9	+	2.19069e9i	0.246620	+	0.246620i	−0.572962	+	0.819582i	$0.694206\pi$
$308$	1.50350e8	+	9.11944e8i	0.0167071	+	0.101336i
$309$	6.15959e9	+	6.15959e9i	0.675644	+	0.675644i
$310$	7.43132e9	+	2.38865e9i	0.804672	+	0.258646i
$311$	1.38987e10			1.48570			0.742851	−	0.669457i	$-0.233473\pi$
$311$	1.38987e10			1.48570			0.742851	+	0.669457i	$0.233473\pi$
$312$	−6.85318e9	−	1.01896e9i	−0.723226	−	0.107532i
$313$			7.55347e9i			0.786990i	0.919327	+	0.393495i	$0.128734\pi$
$313$			7.55347e9i			0.786990i	−0.919327	+	0.393495i	$0.871266\pi$
$314$	−1.34900e10	−	4.33609e9i	−1.38769	−	0.446046i
$315$	1.52504e9	−	1.52504e9i	0.154896	−	0.154896i
$316$	7.53886e9	+	5.40486e9i	0.756062	+	0.542046i
$317$	−5.34731e9	+	5.34731e9i	−0.529539	+	0.529539i	−0.920435	−	0.390896i	$-0.872165\pi$
$317$	−5.34731e9	+	5.34731e9i	−0.529539	+	0.529539i	0.390896	+	0.920435i	$0.372165\pi$
$318$	−1.89962e9	+	9.75476e8i	−0.185763	+	0.0953912i
$319$			6.43284e8i			0.0621213i
$320$	−2.30226e9	−	4.31429e9i	−0.219561	−	0.411443i
$321$	4.75437e9			0.447789
$322$	8.28339e9	+	1.61309e10i	0.770522	+	1.50050i
$323$	−3.07551e8	−	3.07551e8i	−0.0282557	−	0.0282557i
$324$	7.13435e8	−	9.95120e8i	0.0647402	−	0.0903016i
$325$	−7.81789e9	−	7.81789e9i	−0.700739	−	0.700739i
$326$	−7.19872e8	+	2.23959e9i	−0.0637360	+	0.198288i
$327$	5.65923e9			0.494955
$328$	1.30663e9	−	8.78796e9i	0.112890	−	0.759264i
$329$		−	2.59973e10i		−	2.21893i
$330$	7.12179e7	−	2.21565e8i	0.00600528	−	0.0186830i
$331$	−9.98413e9	+	9.98413e9i	−0.831761	+	0.831761i	−0.987758	−	0.155997i	$-0.950141\pi$
$331$	−9.98413e9	+	9.98413e9i	−0.831761	+	0.831761i	0.155997	+	0.987758i	$0.450141\pi$
$332$	1.50772e10	−	2.48574e9i	1.24099	−	0.204599i
$333$	−1.21696e9	+	1.21696e9i	−0.0989689	+	0.0989689i
$334$	−3.28747e9	−	6.40194e9i	−0.264165	−	0.514429i
$335$		−	1.36438e9i		−	0.108332i
$336$	−4.59046e9	+	9.29788e9i	−0.360163	+	0.729502i
$337$	−1.25826e10			−0.975557			−0.487778	−	0.872968i	$-0.662193\pi$
$337$	−1.25826e10			−0.975557			−0.487778	+	0.872968i	$0.662193\pi$
$338$	−7.01098e9	+	3.60022e9i	−0.537170	+	0.275843i
$339$	−2.47719e9	−	2.47719e9i	−0.187568	−	0.187568i
$340$	−1.73171e8	+	2.85503e7i	−0.0129586	+	0.00213646i
$341$	−1.26295e9	−	1.26295e9i	−0.0934045	−	0.0934045i
$342$	6.16017e9	+	1.98007e9i	0.450286	+	0.144736i
$343$	−2.79455e8			−0.0201900
$344$	−3.70659e9	+	2.74704e9i	−0.264692	+	0.196169i
$345$		−	4.56604e9i		−	0.322302i
$346$	−5.56400e9	−	1.78844e9i	−0.388224	−	0.124787i
$347$	4.38065e9	−	4.38065e9i	0.302149	−	0.302149i	−0.539705	−	0.841854i	$-0.681464\pi$
$347$	4.38065e9	−	4.38065e9i	0.302149	−	0.302149i	0.841854	+	0.539705i	$0.181464\pi$
$348$	−4.20512e9	+	5.86542e9i	−0.286722	+	0.399929i
$349$	5.14565e9	−	5.14565e9i	0.346847	−	0.346847i	−0.512086	−	0.858934i	$-0.671127\pi$
$349$	5.14565e9	−	5.14565e9i	0.346847	−	0.346847i	0.858934	+	0.512086i	$0.171127\pi$
$350$	−1.47195e10	+	7.55864e9i	−0.980893	+	0.503699i
$351$		−	3.69938e9i		−	0.243725i
$352$	1.76727e7	+	1.11880e9i	0.00115115	+	0.0728754i
$353$	1.57990e10			1.01749			0.508746	−	0.860917i	$-0.330109\pi$
$353$	1.57990e10			1.01749			0.508746	+	0.860917i	$0.330109\pi$
$354$	6.65969e9	+	1.29689e10i	0.424074	+	0.825832i
$355$	−1.41318e9	−	1.41318e9i	−0.0889781	−	0.0889781i
$356$	1.76512e10	+	1.26547e10i	1.09894	+	0.787867i
$357$	2.63155e8	+	2.63155e8i	0.0162009	+	0.0162009i
$358$	−3.38968e9	+	1.05456e10i	−0.206360	+	0.642006i
$359$	−1.31222e10			−0.790002			−0.395001	−	0.918681i	$-0.629256\pi$
$359$	−1.31222e10			−0.790002			−0.395001	+	0.918681i	$0.629256\pi$
$360$	2.09772e9	−	1.55467e9i	0.124893	−	0.0925610i
$361$			1.72104e10i			1.01336i
$362$	−3.98564e9	+	1.23997e10i	−0.232094	+	0.722065i
$363$	7.05079e9	−	7.05079e9i	0.406080	−	0.406080i
$364$	5.09628e9	+	3.09114e10i	0.290300	+	1.76081i
$365$	6.48139e9	−	6.48139e9i	0.365171	−	0.365171i
$366$	3.68631e9	+	7.17864e9i	0.205432	+	0.400053i
$367$		−	2.39513e10i		−	1.32028i	−0.751143	−	0.660139i	$-0.770497\pi$
$367$		−	2.39513e10i		−	1.32028i	0.751143	−	0.660139i	$-0.229503\pi$
$368$	7.04711e9	+	2.07911e10i	0.384255	+	1.13367i
$369$	4.74379e9			0.255870
$370$	−3.26470e9	+	1.67646e9i	−0.174195	+	0.0894511i
$371$	6.82770e9	+	6.82770e9i	0.360395	+	0.360395i
$372$	−3.25964e9	−	1.97713e10i	−0.170215	−	1.03244i
$373$	1.33953e7	+	1.33953e7i	0.000692017	+	0.000692017i	0.707453	−	0.706761i	$-0.249844\pi$
$373$	1.33953e7	+	1.33953e7i	0.000692017	+	0.000692017i	−0.706761	+	0.707453i	$0.749844\pi$
$374$	3.82325e7	+	1.22891e7i	0.00195410	+	0.000628107i
$375$	9.49113e9			0.479946
$376$	4.62869e9	−	3.11311e10i	0.231583	−	1.55755i
$377$			2.18048e10i			1.07941i
$378$	−5.27095e9	−	1.69425e9i	−0.258179	−	0.0829868i
$379$	1.86685e10	−	1.86685e10i	0.904801	−	0.904801i	−0.0910453	−	0.995847i	$-0.529021\pi$
$379$	1.86685e10	−	1.86685e10i	0.904801	−	0.904801i	0.995847	+	0.0910453i	$0.0290208\pi$
$380$	1.12138e10	+	8.03958e9i	0.537799	+	0.385566i
$381$	−7.30248e9	+	7.30248e9i	−0.346554	+	0.346554i
$382$	−5.00811e9	+	2.57172e9i	−0.235191	+	0.120773i
$383$			1.21999e8i			0.00566972i	0.999996	+	0.00283486i	$0.000902365\pi$
$383$			1.21999e8i			0.00566972i	−0.999996	+	0.00283486i	$0.999098\pi$
$384$	−7.15239e9	+	1.03167e10i	−0.328947	+	0.474476i
$385$	−1.05233e9			−0.0478973
$386$	−2.65496e9	−	5.17022e9i	−0.119594	−	0.232895i
$387$	−1.74185e9	−	1.74185e9i	−0.0776545	−	0.0776545i
$388$	1.15780e8	−	1.61493e8i	0.00510865	−	0.00712569i
$389$	1.26818e10	+	1.26818e10i	0.553839	+	0.553839i	0.927547	−	0.373708i	$-0.121914\pi$
$389$	1.26818e10	+	1.26818e10i	0.553839	+	0.553839i	−0.373708	+	0.927547i	$0.621914\pi$
$390$	2.41401e9	−	7.51021e9i	0.104347	−	0.324634i
$391$	7.87899e8			0.0337104
$392$	2.30212e10	+	3.42289e9i	0.974954	+	0.144960i
$393$			1.38903e10i			0.582294i
$394$	2.97825e9	−	9.26560e9i	0.123588	−	0.384493i
$395$	−7.46817e9	+	7.46817e9i	−0.306779	+	0.306779i
$396$	−5.89483e8	+	9.71865e7i	−0.0239712	+	0.00395208i
$397$	−1.54867e10	+	1.54867e10i	−0.623445	+	0.623445i	−0.946411	−	0.322966i	$-0.895320\pi$
$397$	−1.54867e10	+	1.54867e10i	−0.623445	+	0.623445i	0.322966	+	0.946411i	$0.395320\pi$
$398$	−1.53400e10	−	2.98728e10i	−0.611355	−	1.19054i
$399$		−	2.92580e10i		−	1.15439i
$400$	−1.89720e10	+	6.43053e9i	−0.741094	+	0.251192i
$401$	4.48490e10			1.73450			0.867252	−	0.497870i	$-0.165884\pi$
$401$	4.48490e10			1.73450			0.867252	+	0.497870i	$0.165884\pi$
$402$	−3.11571e9	+	1.59995e9i	−0.119303	+	0.0612636i
$403$	−4.28090e10	−	4.28090e10i	−1.62299	−	1.62299i
$404$	−1.47463e10	+	2.43119e9i	−0.553551	+	0.0912626i
$405$	9.85790e8	+	9.85790e8i	0.0366407	+	0.0366407i
$406$	3.10680e10	+	9.98620e9i	1.14343	+	0.367533i
$407$	8.39746e8			0.0306034
$408$	2.68268e8	+	3.61975e8i	0.00968118	+	0.0130629i
$409$			2.70846e10i			0.967896i	0.875097	+	0.483948i	$0.160798\pi$
$409$			2.70846e10i			0.967896i	−0.875097	+	0.483948i	$0.839202\pi$
$410$	9.63048e9	+	3.09553e9i	0.340810	+	0.109547i
$411$	1.67541e10	−	1.67541e10i	0.587158	−	0.587158i
$412$	2.77843e10	−	3.87544e10i	0.964297	−	1.34503i
$413$	4.66135e10	−	4.66135e10i	1.60218	−	1.60218i
$414$	−1.04270e10	+	5.35440e9i	−0.354944	+	0.182268i
$415$			1.73983e10i			0.586561i
$416$	5.99036e8	+	3.79229e10i	0.0200023	+	1.26628i
$417$	−1.36349e9			−0.0450928
$418$	−1.44221e9	−	2.80853e9i	−0.0472416	−	0.0919972i
$419$	−3.09058e10	−	3.09058e10i	−1.00273	−	1.00273i	−0.999996	−	0.00273208i	$-0.999130\pi$
$419$	−3.09058e10	−	3.09058e10i	−1.00273	−	1.00273i	−0.00273208	−	0.999996i	$-0.500870\pi$
$420$	−9.59511e9	−	6.87906e9i	−0.308356	−	0.221071i
$421$	2.02837e10	+	2.02837e10i	0.645681	+	0.645681i	0.951946	−	0.306265i	$-0.0990795\pi$
$421$	2.02837e10	+	2.02837e10i	0.645681	+	0.645681i	−0.306265	+	0.951946i	$0.599079\pi$
$422$	−8.39518e9	+	2.61182e10i	−0.264716	+	0.823555i
$423$	1.68047e10			0.524891
$424$	6.96035e9	+	9.39163e9i	0.215361	+	0.290588i
$425$			7.18962e8i			0.0220369i
$426$	−1.56997e9	+	4.88432e9i	−0.0476708	+	0.148308i
$427$	2.58018e10	−	2.58018e10i	0.776136	−	0.776136i
$428$	−4.23370e9	−	2.56794e10i	−0.126167	−	0.765262i
$429$	−1.27635e9	+	1.27635e9i	−0.0376827	+	0.0376827i
$430$	−2.39954e9	−	4.67281e9i	−0.0701865	−	0.136680i
$431$			4.29559e10i			1.24484i	0.782683	+	0.622421i	$0.213851\pi$
$431$			4.29559e10i			1.24484i	−0.782683	+	0.622421i	$0.786149\pi$
$432$	−6.01017e9	−	2.96728e9i	−0.172565	−	0.0851969i
$433$	−4.97007e10			−1.41388			−0.706938	−	0.707276i	$-0.749924\pi$
$433$	−4.97007e10			−1.41388			−0.706938	+	0.707276i	$0.749924\pi$
$434$	−8.06008e10	+	4.13894e10i	−2.27185	+	1.16662i
$435$	−5.81043e9	−	5.81043e9i	−0.162275	−	0.162275i
$436$	−5.03946e9	−	3.05667e10i	−0.139456	−	0.845869i
$437$	−4.37999e10	−	4.37999e10i	−1.20101	−	1.20101i
$438$	−2.24014e10	−	7.20050e9i	−0.608666	−	0.195644i
$439$	−4.08883e10			−1.10088			−0.550442	−	0.834874i	$-0.685541\pi$
$439$	−4.08883e10			−1.10088			−0.550442	+	0.834874i	$0.685541\pi$
$440$	−1.26014e9	−	1.87363e8i	−0.0336209	−	0.00499889i
$441$			1.24270e10i			0.328557i
$442$	1.29593e9	+	4.16553e8i	0.0339542	+	0.0109139i
$443$	−3.50068e10	+	3.50068e10i	−0.908945	+	0.908945i	−0.996187	−	0.0872422i	$-0.972195\pi$
$443$	−3.50068e10	+	3.50068e10i	−0.908945	+	0.908945i	0.0872422	+	0.996187i	$0.472195\pi$
$444$	7.65675e9	+	5.48938e9i	0.197021	+	0.141251i
$445$	−1.74857e10	+	1.74857e10i	−0.445905	+	0.445905i
$446$	−5.01139e10	+	2.57340e10i	−1.26654	+	0.650382i
$447$		−	2.76096e10i		−	0.691560i
$448$	5.43076e10	+	1.65144e10i	1.34818	+	0.409970i
$449$	−3.02527e9			−0.0744352			−0.0372176	−	0.999307i	$-0.511849\pi$
$449$	−3.02527e9			−0.0744352			−0.0372176	+	0.999307i	$0.511849\pi$
$450$	−4.88592e9	−	9.51473e9i	−0.119151	−	0.232031i
$451$	−1.63669e9	−	1.63669e9i	−0.0395605	−	0.0395605i
$452$	−1.11739e10	+	1.55857e10i	−0.267702	+	0.373399i
$453$	−2.87151e10	−	2.87151e10i	−0.681895	−	0.681895i
$454$	2.25729e10	−	7.02262e10i	0.531329	−	1.65301i
$455$	−3.56701e10			−0.832258
$456$	5.20925e9	−	3.50357e10i	0.120480	−	0.810310i
$457$			1.11331e10i			0.255242i	0.991823	+	0.127621i	$0.0407342\pi$
$457$			1.11331e10i			0.255242i	−0.991823	+	0.127621i	$0.959266\pi$
$458$	2.47220e10	−	7.69124e10i	0.561852	−	1.74797i
$459$	−1.70104e8	+	1.70104e8i	−0.00383234	+	0.00383234i
$460$	−2.46622e10	+	4.06599e9i	−0.550808	+	0.0908103i
$461$	−4.20635e10	+	4.20635e10i	−0.931326	+	0.931326i	−0.997789	−	0.0664629i	$-0.978829\pi$
$461$	−4.20635e10	+	4.20635e10i	−0.931326	+	0.931326i	0.0664629	+	0.997789i	$0.478829\pi$
$462$	1.23403e9	+	2.40312e9i	0.0270868	+	0.0527482i
$463$			2.34606e10i			0.510524i	0.966872	+	0.255262i	$0.0821617\pi$
$463$			2.34606e10i			0.510524i	−0.966872	+	0.255262i	$0.917838\pi$
$464$	3.54251e10	+	1.74897e10i	0.764256	+	0.377321i
$465$	2.28150e10			0.487988
$466$	−7.01875e10	+	3.60420e10i	−1.48839	+	0.764303i
$467$	5.74918e10	+	5.74918e10i	1.20875	+	1.20875i	0.971431	+	0.237324i	$0.0762703\pi$
$467$	5.74918e10	+	5.74918e10i	1.20875	+	1.20875i	0.237324	+	0.971431i	$0.423730\pi$
$468$	−1.99812e10	+	3.29425e9i	−0.416522	+	0.0686709i
$469$	1.11986e10	+	1.11986e10i	0.231458	+	0.231458i
$470$	3.41156e10	+	1.09658e10i	0.699137	+	0.224724i
$471$	−4.14158e10			−0.841555
$472$	6.41178e10	−	4.75191e10i	1.29185	−	0.957416i
$473$			1.20194e9i			0.0240125i
$474$	2.58120e10	+	8.29677e9i	0.511338	+	0.164360i
$475$	3.99676e10	−	3.99676e10i	0.785116	−	0.785116i
$476$	1.18702e9	−	1.65570e9i	0.0231224	−	0.0322517i
$477$	−4.41344e9	+	4.41344e9i	−0.0852518	+	0.0852518i
$478$	7.53653e10	−	3.87009e10i	1.44364	−	0.741326i
$479$			1.21308e10i			0.230434i	0.993340	+	0.115217i	$0.0367564\pi$
$479$			1.21308e10i			0.230434i	−0.993340	+	0.115217i	$0.963244\pi$
$480$	−1.02651e10	−	9.94585e9i	−0.193374	−	0.187360i
$481$	2.84641e10			0.531763
$482$	2.08631e10	+	4.06284e10i	0.386537	+	0.752734i
$483$	3.74773e10	+	3.74773e10i	0.688621	+	0.688621i
$484$	−4.43615e10	−	3.18042e10i	−0.808397	−	0.579567i
$485$	1.59979e8	+	1.59979e8i	0.00289132	+	0.00289132i
$486$	1.09516e9	−	3.40715e9i	0.0196306	−	0.0610726i
$487$	6.38998e9			0.113601			0.0568007	−	0.998386i	$-0.481910\pi$
$487$	6.38998e9			0.113601			0.0568007	+	0.998386i	$0.481910\pi$
$488$	3.54908e10	−	2.63030e10i	0.625801	−	0.463796i
$489$			6.87579e9i			0.120251i
$490$	−8.10916e9	+	2.52283e10i	−0.140667	+	0.437627i
$491$	4.90938e10	−	4.90938e10i	0.844696	−	0.844696i	−0.144770	−	0.989465i	$-0.546244\pi$
$491$	4.90938e10	−	4.90938e10i	0.844696	−	0.844696i	0.989465	+	0.144770i	$0.0462441\pi$
$492$	−4.22428e9	−	2.56223e10i	−0.0720928	−	0.437277i
$493$	1.00263e9	−	1.00263e9i	0.0169727	−	0.0169727i
$494$	−4.88854e10	−	9.51984e10i	−0.820865	−	1.59853i
$495$		−	6.80231e8i		−	0.0113302i
$496$	−1.03887e11	+	3.52121e10i	−1.71646	+	0.581789i
$497$	2.31983e10			0.380216
$498$	3.97308e10	−	2.04022e10i	0.645967	−	0.331711i
$499$	4.26632e10	+	4.26632e10i	0.688099	+	0.688099i	0.961812	−	0.273712i	$-0.0882517\pi$
$499$	4.26632e10	+	4.26632e10i	0.688099	+	0.688099i	−0.273712	+	0.961812i	$0.588252\pi$
$500$	−8.45171e9	−	5.12637e10i	−0.135227	−	0.820219i
$501$	−1.48738e10	−	1.48738e10i	−0.236086	−	0.236086i
$502$	1.12149e11	+	3.60483e10i	1.76597	+	0.567636i
$503$	−2.94896e10			−0.460678			−0.230339	−	0.973110i	$-0.573984\pi$
$503$	−2.94896e10			−0.460678			−0.230339	+	0.973110i	$0.573984\pi$
$504$	−4.45729e9	+	2.99783e10i	−0.0690794	+	0.464605i
$505$		−	1.70164e10i		−	0.261639i
$506$	5.44489e9	+	1.75016e9i	0.0830591	+	0.0266977i
$507$	−1.62888e10	+	1.62888e10i	−0.246523	+	0.246523i
$508$	4.59451e10	+	3.29396e10i	0.689897	+	0.494610i
$509$	1.75731e10	−	1.75731e10i	0.261804	−	0.261804i	−0.563982	−	0.825787i	$-0.690731\pi$
$509$	1.75731e10	−	1.75731e10i	0.261804	−	0.261804i	0.825787	+	0.563982i	$0.190731\pi$
$510$	−4.56334e8	+	2.34332e8i	−0.00674531	+	0.00346379i
$511$			1.06396e11i			1.56043i
$512$	6.20916e10	+	2.94448e10i	0.903552	+	0.428479i
$513$	1.89124e10			0.273073
$514$	2.17202e9	+	4.22974e9i	0.0311179	+	0.0605984i
$515$	3.83910e10	+	3.83910e10i	0.545759	+	0.545759i
$516$	−7.85703e9	+	1.09592e10i	−0.110831	+	0.154590i
$517$	−5.79793e9	−	5.79793e9i	−0.0811542	−	0.0811542i
$518$	1.30360e10	−	4.05562e10i	0.181062	−	0.563299i
$519$	−1.70821e10			−0.235436
$520$	−4.27139e10	−	6.35088e9i	−0.584193	−	0.0868602i
$521$			1.08869e11i			1.47759i	0.673931	+	0.738795i	$0.264605\pi$
$521$			1.08869e11i			1.47759i	−0.673931	+	0.738795i	$0.735395\pi$
$522$	−6.45510e9	+	2.00824e10i	−0.0869403	+	0.270479i
$523$	−3.36439e9	+	3.36439e9i	−0.0449676	+	0.0449676i	−0.729233	−	0.684265i	$-0.760123\pi$
$523$	−3.36439e9	+	3.36439e9i	−0.0449676	+	0.0449676i	0.684265	+	0.729233i	$0.260123\pi$
$524$	7.50248e10	−	1.23691e10i	0.995130	−	0.164064i
$525$	−3.41983e10	+	3.41983e10i	−0.450160	+	0.450160i
$526$	3.50189e10	+	6.81950e10i	0.457466	+	0.890860i
$527$			3.93687e9i			0.0510398i
$528$	1.04985e9	+	3.09738e9i	0.0135080	+	0.0398528i
$529$	3.38979e10			0.432862
$530$	−1.18398e10	+	6.07987e9i	−0.150052	+	0.0770532i
$531$	3.01311e10	+	3.01311e10i	0.378998	+	0.378998i
$532$	−1.58029e11	+	2.60538e10i	−1.97283	+	0.325256i
$533$	−5.54776e10	−	5.54776e10i	−0.687399	−	0.687399i
$534$	6.04352e10	+	1.94257e10i	0.743233	+	0.238898i
$535$	2.96327e10			0.361706
$536$	1.14162e10	+	1.54039e10i	0.138313	+	0.186626i
$537$			3.23762e10i			0.389340i
$538$	−1.18940e11	−	3.82310e10i	−1.41971	−	0.456338i
$539$	4.28754e9	−	4.28754e9i	0.0507987	−	0.0507987i
$540$	4.44664e9	−	6.20230e9i	0.0522946	−	0.0729420i
$541$	1.50201e9	−	1.50201e9i	0.0175341	−	0.0175341i	−0.698285	−	0.715819i	$-0.746053\pi$
$541$	1.50201e9	−	1.50201e9i	0.0175341	−	0.0175341i	0.715819	+	0.698285i	$0.246053\pi$
$542$	9.26735e10	−	4.75889e10i	1.07389	−	0.551453i
$543$			3.80685e10i			0.437891i
$544$	1.71622e9	−	1.77131e9i	0.0195964	−	0.0202255i
$545$	3.52724e10			0.399805
$546$	4.18288e10	+	8.14564e10i	0.470657	+	0.916547i
$547$	−5.59310e10	−	5.59310e10i	−0.624746	−	0.624746i	0.321996	−	0.946741i	$-0.395646\pi$
$547$	−5.59310e10	−	5.59310e10i	−0.624746	−	0.624746i	−0.946741	+	0.321996i	$0.895646\pi$
$548$	−1.05412e11	−	7.55735e10i	−1.16888	−	0.838006i
$549$	1.66783e10	+	1.66783e10i	0.183596	+	0.183596i
$550$	−1.59703e9	+	4.96849e9i	−0.0174526	+	0.0542967i
$551$	−1.11474e11			−1.20939
$552$	3.82055e10	+	5.15508e10i	0.411499	+	0.555238i
$553$		−	1.22595e11i		−	1.31091i
$554$	4.17905e10	−	1.30014e11i	0.443648	−	1.38023i
$555$	−7.58496e9	+	7.58496e9i	−0.0799432	+	0.0799432i
$556$	1.21417e9	+	7.36451e9i	0.0127051	+	0.0770628i
$557$	1.10211e10	−	1.10211e10i	0.114500	−	0.114500i	−0.647535	−	0.762035i	$-0.724200\pi$
$557$	1.10211e10	−	1.10211e10i	0.114500	−	0.114500i	0.762035	+	0.647535i	$0.224200\pi$
$558$	−2.67542e10	−	5.21005e10i	−0.275966	−	0.537410i
$559$			4.07411e10i			0.417240i
$560$	−2.86110e10	+	5.79510e10i	−0.290925	+	0.589263i
$561$	1.17378e8			0.00118505
$562$	−1.03212e11	+	5.30005e10i	−1.03463	+	0.531294i
$563$	1.67878e10	+	1.67878e10i	0.167093	+	0.167093i	0.785700	−	0.618607i	$-0.212303\pi$
$563$	1.67878e10	+	1.67878e10i	0.167093	+	0.167093i	−0.618607	+	0.785700i	$0.712303\pi$
$564$	−1.49643e10	−	9.07659e10i	−0.147891	−	0.897029i
$565$	−1.54396e10	−	1.54396e10i	−0.151510	−	0.151510i
$566$	−3.63544e10	−	1.16854e10i	−0.354235	−	0.113862i
$567$	−1.61824e10			−0.156571
$568$	2.77793e10	+	4.13034e9i	0.266887	+	0.0396819i
$569$		−	1.66490e11i		−	1.58832i	−0.607707	−	0.794161i	$-0.707911\pi$
$569$		−	1.66490e11i		−	1.58832i	0.607707	−	0.794161i	$-0.292089\pi$
$570$	3.83946e10	+	1.23412e10i	0.363723	+	0.116912i
$571$	5.46377e10	−	5.46377e10i	0.513982	−	0.513982i	−0.401762	−	0.915744i	$-0.631602\pi$
$571$	5.46377e10	−	5.46377e10i	0.513982	−	0.513982i	0.915744	+	0.401762i	$0.131602\pi$
$572$	8.03045e9	+	5.75730e9i	0.0750163	+	0.0537817i
$573$	−1.16355e10	+	1.16355e10i	−0.107936	+	0.107936i
$574$	−1.04453e11	+	5.36378e10i	−0.962219	+	0.494110i
$575$			1.02391e11i			0.936679i
$576$	−1.06750e10	+	3.51046e10i	−0.0969788	+	0.318914i
$577$	−1.06818e11			−0.963700			−0.481850	−	0.876254i	$-0.660035\pi$
$577$	−1.06818e11			−0.963700			−0.481850	+	0.876254i	$0.660035\pi$
$578$	5.09443e10	+	9.92078e10i	0.456441	+	0.888862i
$579$	−1.20121e10	−	1.20121e10i	−0.106882	−	0.106882i
$580$	−2.62093e10	+	3.65575e10i	−0.231603	+	0.323046i
$581$	−1.42802e11	−	1.42802e11i	−1.25323	−	1.25323i
$582$	1.77729e8	−	5.52930e8i	0.00154905	−	0.00481923i
$583$	3.04544e9			0.0263618
$584$	−1.89434e10	+	1.27407e11i	−0.162857	+	1.09532i
$585$		−	2.30572e10i		−	0.196872i
$586$	2.39282e10	−	7.44429e10i	0.202918	−	0.631296i
$587$	1.16574e10	−	1.16574e10i	0.0981863	−	0.0981863i	−0.656307	−	0.754494i	$-0.727883\pi$
$587$	1.16574e10	−	1.16574e10i	0.0981863	−	0.0981863i	0.754494	+	0.656307i	$0.227883\pi$
$588$	6.71209e10	−	1.10660e10i	0.561498	−	0.0925728i
$589$	2.18854e11	−	2.18854e11i	1.81841	−	1.81841i
$590$	4.15080e10	+	8.08317e10i	0.342550	+	0.667074i
$591$		−	2.84465e10i		−	0.233173i
$592$	2.28311e10	−	4.62440e10i	0.185883	−	0.376503i
$593$	7.84313e10			0.634265			0.317132	−	0.948381i	$-0.397280\pi$
$593$	7.84313e10			0.634265			0.317132	+	0.948381i	$0.397280\pi$
$594$	−1.55338e9	+	7.97679e8i	−0.0124776	+	0.00640740i
$595$	1.64017e9	+	1.64017e9i	0.0130865	+	0.0130865i
$596$	−1.49125e11	+	2.45859e10i	−1.18186	+	0.194851i
$597$	−6.94043e10	−	6.94043e10i	−0.546372	−	0.546372i
$598$	1.84561e11	+	5.93235e10i	1.44323	+	0.463897i
$599$	7.89671e10			0.613393			0.306697	−	0.951807i	$-0.400776\pi$
$599$	7.89671e10			0.613393			0.306697	+	0.951807i	$0.400776\pi$
$600$	−4.70403e10	+	3.48627e10i	−0.362966	+	0.269002i
$601$			1.39344e11i			1.06805i	0.845469	+	0.534025i	$0.179321\pi$
$601$			1.39344e11i			1.06805i	−0.845469	+	0.534025i	$0.820679\pi$
$602$	5.80487e10	+	1.86586e10i	0.441984	+	0.142067i
$603$	−7.23881e9	+	7.23881e9i	−0.0547517	+	0.0547517i
$604$	−1.29526e11	+	1.80667e11i	−0.973217	+	1.35747i
$605$	4.39456e10	−	4.39456e10i	0.328015	−	0.328015i
$606$	−3.88589e10	+	1.99545e10i	−0.288138	+	0.147962i
$607$			1.64246e11i			1.20987i	0.796274	+	0.604937i	$0.206802\pi$
$607$			1.64246e11i			1.20987i	−0.796274	+	0.604937i	$0.793198\pi$
$608$	−1.93874e11	+	3.06247e9i	−1.41875	+	0.0224108i
$609$	9.53822e10			0.693423
$610$	2.29757e10	+	4.47424e10i	0.165939	+	0.323147i
$611$	−1.96527e11	−	1.96527e11i	−1.41013	−	1.41013i
$612$	1.07025e9	+	7.67296e8i	0.00762918	+	0.00546962i
$613$	−9.08403e10	−	9.08403e10i	−0.643334	−	0.643334i	0.308039	−	0.951374i	$-0.400327\pi$
$613$	−9.08403e10	−	9.08403e10i	−0.643334	−	0.643334i	−0.951374	+	0.308039i	$0.900327\pi$
$614$	1.51689e10	−	4.71918e10i	0.106728	−	0.332042i
$615$	2.95667e10			0.206682
$616$	1.18809e10	−	8.80520e9i	0.0825138	−	0.0611528i
$617$			5.91847e10i			0.408384i	0.978931	+	0.204192i	$0.0654567\pi$
$617$			5.91847e10i			0.408384i	−0.978931	+	0.204192i	$0.934543\pi$
$618$	4.26505e10	−	1.32690e11i	0.292395	−	0.909668i
$619$	1.70195e11	−	1.70195e11i	1.15927	−	1.15927i	0.174640	−	0.984632i	$-0.444124\pi$
$619$	1.70195e11	−	1.70195e11i	1.15927	−	1.15927i	0.984632	−	0.174640i	$-0.0558762\pi$
$620$	−2.03164e10	−	1.23229e11i	−0.137493	−	0.833961i
$621$	−2.42254e10	+	2.42254e10i	−0.162894	+	0.162894i
$622$	−1.01583e11	−	1.97821e11i	−0.678673	−	1.32163i
$623$		−	2.87040e11i		−	1.90542i
$624$	3.55859e10	+	1.04989e11i	0.234714	+	0.692479i
$625$	−6.02457e10			−0.394826
$626$	1.07509e11	−	5.52072e10i	0.700081	−	0.359499i
$627$	−6.52514e9	−	6.52514e9i	−0.0422201	−	0.0422201i
$628$	3.68802e10	+	2.23696e11i	0.237112	+	1.43820i
$629$	−1.30883e9	−	1.30883e9i	−0.00836145	−	0.00836145i
$630$	−3.28523e10	−	1.05598e10i	−0.208547	−	0.0670334i
$631$	−4.91483e10			−0.310021			−0.155010	−	0.987913i	$-0.549541\pi$
$631$	−4.91483e10			−0.310021			−0.155010	+	0.987913i	$0.549541\pi$
$632$	2.18275e10	−	1.46804e11i	0.136816	−	0.920176i
$633$			8.01857e10i			0.499439i
$634$	1.15191e11	+	3.70261e10i	0.712956	+	0.229166i
$635$	−4.55143e10	+	4.55143e10i	−0.279932	+	0.279932i
$636$	2.77681e10	+	1.99079e10i	0.169714	+	0.121674i
$637$	1.45331e11	−	1.45331e11i	0.882673	−	0.882673i
$638$	9.15592e9	−	4.70167e9i	0.0552611	−	0.0283772i
$639$			1.49954e10i			0.0899404i
$640$	−4.45788e10	+	6.43008e10i	−0.265711	+	0.383262i
$641$	−7.71923e10			−0.457238			−0.228619	−	0.973516i	$-0.573421\pi$
$641$	−7.71923e10			−0.457238			−0.228619	+	0.973516i	$0.573421\pi$
$642$	−3.47490e10	−	6.76694e10i	−0.204551	−	0.398338i
$643$	−1.63479e10	−	1.63479e10i	−0.0956352	−	0.0956352i	0.657671	−	0.753306i	$-0.271542\pi$
$643$	−1.63479e10	−	1.63479e10i	−0.0956352	−	0.0956352i	−0.753306	+	0.657671i	$0.771542\pi$
$644$	1.69050e11	−	2.35797e11i	0.982817	−	1.37086i
$645$	−1.08565e10	−	1.08565e10i	−0.0627262	−	0.0627262i
$646$	−2.12955e9	+	6.62524e9i	−0.0122281	+	0.0380427i
$647$	1.61295e11			0.920455			0.460228	−	0.887801i	$-0.347768\pi$
$647$	1.61295e11			0.920455			0.460228	+	0.887801i	$0.347768\pi$
$648$	−1.93780e10	−	2.88120e9i	−0.109903	−	0.0163408i
$649$		−	2.07916e10i		−	0.117195i
$650$	−5.41330e10	+	1.68413e11i	−0.303255	+	0.943455i
$651$	−1.87262e11	+	1.87262e11i	−1.04262	+	1.04262i
$652$	3.71376e10	−	6.12279e9i	0.205506	−	0.0338812i
$653$	−2.41259e11	+	2.41259e11i	−1.32687	+	1.32687i	−0.418793	+	0.908082i	$0.637547\pi$
$653$	−2.41259e11	+	2.41259e11i	−1.32687	+	1.32687i	−0.908082	+	0.418793i	$0.862453\pi$
$654$	−4.13624e10	−	8.05482e10i	−0.226097	−	0.440296i
$655$			8.65745e10i			0.470354i
$656$	−1.34630e11	+	4.56325e10i	−0.726986	+	0.246410i
$657$	−6.87749e10			−0.369121
$658$	−3.70022e11	+	1.90010e11i	−1.97389	+	1.01362i
$659$	2.21610e11	+	2.21610e11i	1.17503	+	1.17503i	0.980996	+	0.194029i	$0.0621557\pi$
$659$	2.21610e11	+	2.21610e11i	1.17503	+	1.17503i	0.194029	+	0.980996i	$0.437844\pi$
$660$	−3.67408e9	+	6.05736e8i	−0.0193630	+	0.00319233i
$661$	1.62184e11	+	1.62184e11i	0.849573	+	0.849573i	0.990080	−	0.140506i	$-0.0448730\pi$
$661$	1.62184e11	+	1.62184e11i	0.849573	+	0.849573i	−0.140506	+	0.990080i	$0.544873\pi$
$662$	2.15078e11	+	6.91325e10i	1.11986	+	0.359957i
$663$	3.97867e9			0.0205913
$664$	−1.45577e11	−	1.96427e11i	−0.748892	−	1.01048i
$665$		−	1.82357e11i		−	0.932472i
$666$	2.62156e10	+	8.42652e9i	0.133249	+	0.0428303i
$667$	1.42789e11	−	1.42789e11i	0.721427	−	0.721427i
$668$	−6.70918e10	+	9.35816e10i	−0.336948	+	0.469986i
$669$	−1.16431e11	+	1.16431e11i	−0.581251	+	0.581251i
$670$	−1.94193e10	+	9.97204e9i	−0.0963685	+	0.0494863i
$671$		−	1.15086e10i		−	0.0567720i
$672$	1.65888e11	−	2.62040e9i	0.813465	−	0.0128496i
$673$	1.26305e11			0.615688			0.307844	−	0.951437i	$-0.400392\pi$
$673$	1.26305e11			0.615688			0.307844	+	0.951437i	$0.400392\pi$
$674$	9.19646e10	+	1.79090e11i	0.445637	+	0.867824i
$675$	−2.21058e10	−	2.21058e10i	−0.106486	−	0.106486i
$676$	1.02484e11	+	7.34745e10i	0.490762	+	0.351844i
$677$	7.06806e10	+	7.06806e10i	0.336470	+	0.336470i	0.855037	−	0.518567i	$-0.173534\pi$
$677$	7.06806e10	+	7.06806e10i	0.336470	+	0.336470i	−0.518567	+	0.855037i	$0.673534\pi$
$678$	−1.71526e10	+	5.33634e10i	−0.0811731	+	0.252537i
$679$	−2.62616e9			−0.0123550
$680$	1.67204e9	+	2.25609e9i	0.00782007	+	0.0105517i
$681$		−	2.15603e11i		−	1.00246i
$682$	−8.74495e9	+	2.72063e10i	−0.0404222	+	0.125757i
$683$	−2.16047e11	+	2.16047e11i	−0.992809	+	0.992809i	−0.999974	−	0.00716529i	$-0.997719\pi$
$683$	−2.16047e11	+	2.16047e11i	−0.992809	+	0.992809i	0.00716529	+	0.999974i	$0.497719\pi$
$684$	−1.68413e10	−	1.02150e11i	−0.0769397	−	0.466676i
$685$	1.04424e11	−	1.04424e11i	0.474283	−	0.474283i
$686$	2.04249e9	+	3.97751e9i	0.00922284	+	0.0179604i
$687$		−	2.36130e11i		−	1.06004i
$688$	6.61897e10	+	3.26785e10i	0.295418	+	0.145851i
$689$	1.03228e11			0.458060
$690$	−6.49888e10	+	3.33725e10i	−0.286710	+	0.147229i
$691$	6.60318e10	+	6.60318e10i	0.289628	+	0.289628i	0.836933	−	0.547305i	$-0.184346\pi$
$691$	6.60318e10	+	6.60318e10i	0.289628	+	0.289628i	−0.547305	+	0.836933i	$0.684346\pi$
$692$	1.52114e10	+	9.22643e10i	0.0663352	+	0.402355i
$693$	5.58323e9	+	5.58323e9i	0.0242077	+	0.0242077i
$694$	−9.43677e10	−	3.03327e10i	−0.406804	−	0.130759i
$695$	−8.49824e9			−0.0364242
$696$	1.14218e11	+	1.69823e10i	0.486739	+	0.0723704i
$697$			5.10192e9i			0.0216174i
$698$	−1.10847e11	−	3.56297e10i	−0.466985	−	0.150103i
$699$	−1.63068e11	+	1.63068e11i	−0.683064	+	0.683064i
$700$	2.15165e11	+	1.54259e11i	0.896149	+	0.642480i
$701$	−2.10986e11	+	2.10986e11i	−0.873738	+	0.873738i	−0.992877	−	0.119140i	$-0.961986\pi$
$701$	−2.10986e11	+	2.10986e11i	−0.873738	+	0.873738i	0.119140	+	0.992877i	$0.461986\pi$
$702$	−5.26536e10	+	2.70382e10i	−0.216810	+	0.111334i
$703$			1.45518e11i			0.595793i
$704$	1.57948e10	−	8.42866e9i	0.0643018	−	0.0343137i
$705$	1.04739e11			0.423986
$706$	−1.15472e11	−	2.24869e11i	−0.464793	−	0.905128i
$707$	1.39668e11	+	1.39668e11i	0.559011	+	0.559011i
$708$	1.35913e11	−	1.89576e11i	0.540915	−	0.754484i
$709$	2.71747e11	+	2.71747e11i	1.07542	+	1.07542i	0.996913	+	0.0785116i	$0.0250168\pi$
$709$	2.71747e11	+	2.71747e11i	1.07542	+	1.07542i	0.0785116	+	0.996913i	$0.474983\pi$
$710$	−9.78518e9	+	3.04426e10i	−0.0385066	+	0.119797i
$711$	7.92458e10			0.310097
$712$	5.11060e10	−	3.43722e11i	0.198862	−	1.33748i
$713$			5.60671e11i			2.16945i
$714$	1.82215e9	−	5.66888e9i	0.00701119	−	0.0218124i
$715$	−7.95516e9	+	7.95516e9i	−0.0304386	+	0.0304386i
$716$	1.74871e11	−	2.88305e10i	0.665374	−	0.109698i
$717$	1.75098e11	−	1.75098e11i	0.662529	−	0.662529i
$718$	9.59080e10	+	1.86769e11i	0.360875	+	0.702761i
$719$		−	2.97413e11i		−	1.11287i	−0.830891	−	0.556436i	$-0.812169\pi$
$719$		−	2.97413e11i		−	1.11287i	0.830891	−	0.556436i	$-0.187831\pi$
$720$	−3.74597e10	−	1.84942e10i	−0.139391	−	0.0688186i
$721$	−6.30215e11			−2.33210
$722$	2.44957e11	−	1.25788e11i	0.901448	−	0.462904i
$723$	9.43931e10	+	9.43931e10i	0.345451	+	0.345451i
$724$	2.05616e11	−	3.38994e10i	0.748347	−	0.123378i
$725$	1.30296e11	+	1.30296e11i	0.471605	+	0.471605i
$726$	−1.51888e11	−	4.88214e10i	−0.546734	−	0.175737i
$727$	1.01032e11			0.361678			0.180839	−	0.983513i	$-0.442119\pi$
$727$	1.01032e11			0.361678			0.180839	+	0.983513i	$0.442119\pi$
$728$	4.02716e11	−	2.98462e11i	1.43375	−	1.06259i
$729$		−	1.04604e10i		−	0.0370370i
$730$	−1.39622e11	−	4.48787e10i	−0.491656	−	0.158033i
$731$	1.87335e9	−	1.87335e9i	0.00656069	−	0.00656069i
$732$	7.52315e10	−	1.04935e11i	0.262033	−	0.365491i
$733$	−1.73875e10	+	1.73875e10i	−0.0602312	+	0.0602312i	−0.736581	−	0.676350i	$-0.763561\pi$
$733$	−1.73875e10	+	1.73875e10i	−0.0602312	+	0.0602312i	0.676350	+	0.736581i	$0.263561\pi$
$734$	−3.40901e11	+	1.75057e11i	−1.17448	+	0.603107i
$735$			7.74538e10i			0.265396i
$736$	2.44416e11	−	2.52261e11i	0.832948	−	0.859685i
$737$	4.99504e9			0.0169305
$738$	−3.46716e10	−	6.75187e10i	−0.116882	−	0.227614i
$739$	−3.37589e11	−	3.37589e11i	−1.13190	−	1.13190i	−0.989860	−	0.142045i	$-0.954632\pi$
$739$	−3.37589e11	−	3.37589e11i	−1.13190	−	1.13190i	−0.142045	−	0.989860i	$-0.545368\pi$
$740$	4.77223e10	+	3.42138e10i	0.159146	+	0.114097i
$741$	−2.21177e11	−	2.21177e11i	−0.733613	−	0.733613i
$742$	4.72766e10	−	1.47082e11i	0.155966	−	0.485225i
$743$	1.38154e11			0.453323			0.226662	−	0.973974i	$-0.427219\pi$
$743$	1.38154e11			0.453323			0.226662	+	0.973974i	$0.427219\pi$
$744$	−2.57582e11	+	1.90900e11i	−0.840668	+	0.623038i
$745$		−	1.72083e11i		−	0.558614i
$746$	9.27522e7	−	2.88560e8i	0.000299481	−	0.000931712i
$747$	9.23077e10	−	9.23077e10i	0.296453	−	0.296453i
$748$	−1.04524e8	−	6.33986e8i	−0.000333893	−	0.00202522i
$749$	−2.43220e11	+	2.43220e11i	−0.772810	+	0.772810i
$750$	−6.93692e10	−	1.35088e11i	−0.219241	−	0.426945i
$751$			5.38643e9i			0.0169333i	0.999964	+	0.00846664i	$0.00269505\pi$
$751$			5.38643e9i			0.0169333i	−0.999964	+	0.00846664i	$0.997305\pi$
$752$	−4.76921e11	+	1.61652e11i	−1.49134	+	0.505485i
$753$	3.44312e11			1.07096
$754$	3.10350e11	−	1.59368e11i	0.960211	−	0.493079i
$755$	−1.78973e11	−	1.78973e11i	−0.550807	−	0.550807i
$756$	1.44102e10	+	8.74048e10i	0.0441147	+	0.267577i
$757$	3.15476e11	+	3.15476e11i	0.960690	+	0.960690i	0.999256	−	0.0385664i	$-0.0122791\pi$
$757$	3.15476e11	+	3.15476e11i	0.960690	+	0.960690i	−0.0385664	+	0.999256i	$0.512279\pi$
$758$	−4.02156e11	−	1.29265e11i	−1.21820	−	0.391566i
$759$	1.67164e10			0.0503706
$760$	3.24678e10	−	2.18368e11i	0.0973191	−	0.654536i
$761$			4.32267e11i			1.28888i	0.764653	+	0.644442i	$0.222910\pi$
$761$			4.32267e11i			1.28888i	−0.764653	+	0.644442i	$0.777090\pi$
$762$	1.57310e11	+	5.05642e10i	0.466590	+	0.149976i
$763$	−2.89510e11	+	2.89510e11i	−0.854211	+	0.854211i
$764$	7.32070e10	+	5.24845e10i	0.214872	+	0.154049i
$765$	−1.06021e9	+	1.06021e9i	−0.00309562	+	0.00309562i
$766$	1.73642e9	−	8.91672e8i	0.00504360	−	0.00258994i
$767$		−	7.04753e11i		−	2.03636i
$768$	1.99114e11	+	2.63978e10i	0.572342	+	0.0758792i
$769$	−3.70146e11			−1.05844			−0.529222	−	0.848483i	$-0.677516\pi$
$769$	−3.70146e11			−1.05844			−0.529222	+	0.848483i	$0.677516\pi$
$770$	7.69135e9	+	1.49780e10i	0.0218796	+	0.0426079i
$771$	9.82707e9	+	9.82707e9i	0.0278103	+	0.0278103i
$772$	−5.41834e10	+	7.55766e10i	−0.152545	+	0.212774i
$773$	3.21513e11	+	3.21513e11i	0.900495	+	0.900495i	0.995479	−	0.0949841i	$-0.0302800\pi$
$773$	3.21513e11	+	3.21513e11i	0.900495	+	0.900495i	−0.0949841	+	0.995479i	$0.530280\pi$
$774$	−1.20610e10	+	3.75228e10i	−0.0336062	+	0.104552i
$775$	−5.11615e11			−1.41820
$776$	−3.14476e9	−	4.67576e8i	−0.00867243	−	0.00128945i
$777$		−	1.24512e11i		−	0.341608i
$778$	8.78120e10	−	2.73191e11i	0.239682	−	0.745673i
$779$	2.83619e11	−	2.83619e11i	0.770169	−	0.770169i
$780$	−1.24537e11	+	2.05321e10i	−0.336450	+	0.0554696i
$781$	5.17369e9	−	5.17369e9i	0.0139058	−	0.0139058i
$782$	−5.75863e9	−	1.12142e10i	−0.0153990	−	0.0299877i
$783$			6.16553e10i			0.164030i
$784$	−1.19540e11	−	3.52681e11i	−0.316410	−	0.933506i
$785$	−2.58133e11			−0.679774
$786$	1.97702e11	−	1.01522e11i	0.517990	−	0.265994i
$787$	−4.49296e11	−	4.49296e11i	−1.17121	−	1.17121i	−0.981922	−	0.189286i	$-0.939383\pi$
$787$	−4.49296e11	−	4.49296e11i	−1.17121	−	1.17121i	−0.189286	−	0.981922i	$-0.560617\pi$
$788$	−1.53646e11	+	2.53312e10i	−0.398488	+	0.0656977i
$789$	1.58439e11	+	1.58439e11i	0.408841	+	0.408841i
$790$	1.60879e11	+	5.17114e10i	0.413039	+	0.132763i
$791$	2.53452e11			0.647424
$792$	5.69170e9	+	7.67984e9i	0.0144658	+	0.0195187i
$793$		−	3.90099e11i		−	0.986465i
$794$	3.33614e11	+	1.07234e11i	0.839388	+	0.269805i
$795$	−2.75077e10	+	2.75077e10i	−0.0688630	+	0.0688630i
$796$	−3.13064e11	+	4.36671e11i	−0.779797	+	1.08768i
$797$	−1.96532e11	+	1.96532e11i	−0.487079	+	0.487079i	−0.907383	−	0.420304i	$-0.861923\pi$
$797$	−1.96532e11	+	1.96532e11i	−0.487079	+	0.487079i	0.420304	+	0.907383i	$0.361923\pi$
$798$	−4.16432e11	+	2.13842e11i	−1.02691	+	0.527330i
$799$			1.80734e10i			0.0443458i
$800$	2.30190e11	+	2.23031e11i	0.561987	+	0.544508i
$801$	1.85543e11			0.450728
$802$	−3.27794e11	−	6.38340e11i	−0.792326	−	1.54296i
$803$	2.37286e10	+	2.37286e10i	0.0570703	+	0.0570703i
$804$	4.55445e10	+	3.26523e10i	0.108996	+	0.0781430i
$805$	2.33586e11	+	2.33586e11i	0.556241	+	0.556241i
$806$	−2.96420e11	+	9.22189e11i	−0.702372	+	2.18514i
$807$	−3.65160e11			−0.860972
$808$	1.42382e11	+	1.92116e11i	0.334048	+	0.450732i
$809$		−	1.68544e11i		−	0.393478i	−0.980456	−	0.196739i	$-0.936965\pi$
$809$		−	1.68544e11i		−	0.393478i	0.980456	−	0.196739i	$-0.0630352\pi$
$810$	6.82585e9	−	2.12358e10i	0.0158568	−	0.0493320i
$811$	−5.24096e11	+	5.24096e11i	−1.21151	+	1.21151i	−0.240982	+	0.970530i	$0.577469\pi$
$811$	−5.24096e11	+	5.24096e11i	−1.21151	+	1.21151i	−0.970530	+	0.240982i	$0.922531\pi$
$812$	−8.49365e10	−	5.15181e11i	−0.195376	−	1.18505i
$813$	2.15311e11	−	2.15311e11i	0.492838	−	0.492838i
$814$	−6.13757e9	−	1.19522e10i	−0.0139797	−	0.0272238i
$815$			4.28548e10i			0.0971336i
$816$	3.19129e9	−	6.46390e9i	0.00719791	−	0.0145792i
$817$	−2.08282e11			−0.467480
$818$	3.85497e11	−	1.97957e11i	0.861009	−	0.442138i
$819$	1.89250e11	+	1.89250e11i	0.420630	+	0.420630i
$820$	−2.63287e10	−	1.59696e11i	−0.0582337	−	0.353215i
$821$	5.94756e10	+	5.94756e10i	0.130908	+	0.130908i	0.769525	−	0.638617i	$-0.220493\pi$
$821$	5.94756e10	+	5.94756e10i	0.130908	+	0.130908i	−0.638617	+	0.769525i	$0.720493\pi$
$822$	−3.60917e11	−	1.16010e11i	−0.790532	−	0.254101i
$823$	6.48742e11			1.41408			0.707038	−	0.707176i	$-0.250031\pi$
$823$	6.48742e11			1.41408			0.707038	+	0.707176i	$0.250031\pi$
$824$	−7.54665e11	−	1.12207e11i	−1.63699	−	0.243394i
$825$			1.52538e10i			0.0329278i
$826$	−1.00415e12	−	3.22763e11i	−2.15713	−	0.693368i
$827$	2.61981e11	−	2.61981e11i	0.560077	−	0.560077i	−0.369253	−	0.929329i	$-0.620386\pi$
$827$	2.61981e11	−	2.61981e11i	0.560077	−	0.560077i	0.929329	+	0.369253i	$0.120386\pi$
$828$	1.52419e11	+	1.09275e11i	0.324279	+	0.232487i
$829$	−1.32932e11	+	1.32932e11i	−0.281456	+	0.281456i	−0.833689	−	0.552234i	$-0.813776\pi$
$829$	−1.32932e11	+	1.32932e11i	−0.281456	+	0.281456i	0.552234	+	0.833689i	$0.313776\pi$
$830$	2.47631e11	−	1.27161e11i	0.521786	−	0.267943i
$831$		−	3.99158e11i		−	0.837029i
$832$	5.35382e11	−	2.85699e11i	1.11730	−	0.596232i
$833$	−1.33652e10			−0.0277584
$834$	9.96553e9	+	1.94067e10i	0.0205985	+	0.0401131i
$835$	−9.27042e10	−	9.27042e10i	−0.190701	−	0.190701i
$836$	−2.94332e10	+	4.10543e10i	−0.0602577	+	0.0840491i
$837$	−1.21047e11	−	1.21047e11i	−0.246633	−	0.246633i
$838$	−2.13999e11	+	6.65770e11i	−0.433946	+	1.35004i
$839$	3.18623e11			0.643027			0.321513	−	0.946905i	$-0.395809\pi$
$839$	3.18623e11			0.643027			0.321513	+	0.946905i	$0.395809\pi$
$840$	−2.77810e10	+	1.86846e11i	−0.0557996	+	0.375290i
$841$			1.36839e11i			0.273543i
$842$	1.40449e11	−	4.36949e11i	0.279428	−	0.869326i
$843$	−2.39795e11	+	2.39795e11i	−0.474821	+	0.474821i
$844$	4.33101e11	−	7.14043e10i	0.853531	−	0.140719i
$845$	−1.01523e11	+	1.01523e11i	−0.199131	+	0.199131i
$846$	−1.22823e11	−	2.39183e11i	−0.239772	−	0.466927i
$847$			7.21397e11i			1.40165i
$848$	8.27997e10	−	1.67709e11i	0.160120	−	0.324320i
$849$	−1.11612e11			−0.214823
$850$	1.02330e10	−	5.25478e9i	0.0196033	−	0.0100665i
$851$	−1.86398e11	−	1.86398e11i	−0.355404	−	0.355404i
$852$	8.09935e10	−	1.33532e10i	0.153706	−	0.0253412i
$853$	1.31894e11	+	1.31894e11i	0.249132	+	0.249132i	0.820615	−	0.571482i	$-0.193631\pi$
$853$	1.31894e11	+	1.31894e11i	0.249132	+	0.249132i	−0.571482	+	0.820615i	$0.693631\pi$
$854$	−5.55820e11	−	1.78658e11i	−1.04497	−	0.335885i
$855$	1.17876e11			0.220577
$856$	−3.34554e11	+	2.47946e11i	−0.623119	+	0.461808i
$857$		−	1.02878e12i		−	1.90722i	−0.301048	−	0.953609i	$-0.597336\pi$
$857$		−	1.02878e12i		−	1.90722i	0.301048	−	0.953609i	$-0.402664\pi$
$858$	2.74951e10	+	8.83779e9i	0.0507349	+	0.0163078i
$859$	5.68185e11	−	5.68185e11i	1.04356	−	1.04356i	0.0445515	−	0.999007i	$-0.485814\pi$
$859$	5.68185e11	−	5.68185e11i	1.04356	−	1.04356i	0.999007	−	0.0445515i	$-0.0141859\pi$
$860$	−4.89706e10	+	6.83057e10i	−0.0895245	+	0.124871i
$861$	−2.42679e11	+	2.42679e11i	−0.441590	+	0.441590i
$862$	6.11395e11	−	3.13958e11i	1.10737	−	0.568647i
$863$		−	6.86018e11i		−	1.23678i	−0.785872	−	0.618390i	$-0.787785\pi$
$863$		−	6.86018e11i		−	1.23678i	0.785872	−	0.618390i	$-0.212215\pi$
$864$	1.69383e9	+	1.07231e11i	0.00303959	+	0.192426i
$865$	−1.06468e11			−0.190176
$866$	3.63255e11	+	7.07395e11i	0.645862	+	1.25774i
$867$	2.30492e11	+	2.30492e11i	0.407925	+	0.407925i
$868$	1.17820e12	+	8.44690e11i	2.07558	+	1.48805i
$869$	−2.73413e10	−	2.73413e10i	−0.0479446	−	0.0479446i
$870$	−4.02328e10	+	1.25168e11i	−0.0702269	+	0.218482i
$871$	1.69313e11			0.294182
$872$	−3.98226e11	+	2.95135e11i	−0.688754	+	0.510451i
$873$		−	1.69756e9i		−	0.00292259i
$874$	−3.03281e11	+	9.43535e11i	−0.519756	+	1.61701i
$875$	−4.85539e11	+	4.85539e11i	−0.828308	+	0.828308i
$876$	6.12431e10	+	3.71469e11i	0.104002	+	0.630820i
$877$	3.26123e10	−	3.26123e10i	0.0551294	−	0.0551294i	−0.679005	−	0.734134i	$-0.737588\pi$
$877$	3.26123e10	−	3.26123e10i	0.0551294	−	0.0551294i	0.734134	+	0.679005i	$0.237588\pi$
$878$	2.98846e11	+	5.81967e11i	0.502887	+	0.979310i
$879$		−	2.28548e11i		−	0.382845i
$880$	6.54343e9	+	1.93051e10i	0.0109113	+	0.0321915i
$881$	6.69678e11			1.11163			0.555817	−	0.831304i	$-0.312405\pi$
$881$	6.69678e11			1.11163			0.555817	+	0.831304i	$0.312405\pi$
$882$	1.76874e11	−	9.08269e10i	0.292274	−	0.150086i
$883$	−5.24424e10	−	5.24424e10i	−0.0862660	−	0.0862660i	0.662657	−	0.748923i	$-0.269429\pi$
$883$	−5.24424e10	−	5.24424e10i	−0.0862660	−	0.0862660i	−0.748923	+	0.662657i	$0.769429\pi$
$884$	−3.54294e9	−	2.14897e10i	−0.00580170	−	0.0351901i
$885$	1.87799e11	+	1.87799e11i	0.306139	+	0.306139i
$886$	7.54114e11	+	2.42396e11i	1.22378	+	0.393360i
$887$	−1.62737e11			−0.262901			−0.131450	−	0.991323i	$-0.541963\pi$
$887$	−1.62737e11			−0.262901			−0.131450	+	0.991323i	$0.541963\pi$
$888$	2.21688e10	−	1.49100e11i	0.0356526	−	0.239787i
$889$		−	7.47149e11i		−	1.19619i
$890$	3.76676e11	+	1.21075e11i	0.600354	+	0.192972i
$891$	−3.60901e9	+	3.60901e9i	−0.00572635	+	0.00572635i
$892$	7.32549e11	+	5.25189e11i	1.15712	+	0.829577i
$893$	1.00471e12	−	1.00471e12i	1.57992	−	1.57992i
$894$	−3.92970e11	+	2.01794e11i	−0.615189	+	0.315906i
$895$			2.01792e11i			0.314493i
$896$	−1.61875e11	−	8.93667e11i	−0.251158	−	1.38658i
$897$	5.66623e11			0.875234
$898$	2.21112e10	+	4.30589e10i	0.0340022	+	0.0662152i
$899$	7.13471e11	+	7.13471e11i	1.09229	+	1.09229i
$900$	−9.97136e10	+	1.39083e11i	−0.151979	+	0.211985i
$901$	−4.74663e9	−	4.74663e9i	−0.00720255	−	0.00720255i
$902$	−1.13329e10	+	3.52575e10i	−0.0171204	+	0.0532630i
$903$	1.78216e11			0.268038
$904$	3.03502e11	+	4.51258e10i	0.454451	+	0.0675696i
$905$			2.37270e11i			0.353711i
$906$	−1.98830e11	+	6.18578e11i	−0.295100	+	0.918083i
$907$	−1.91259e11	+	1.91259e11i	−0.282613	+	0.282613i	−0.834150	−	0.551537i	$-0.814041\pi$
$907$	−1.91259e11	+	1.91259e11i	−0.282613	+	0.282613i	0.551537	+	0.834150i	$0.314041\pi$
$908$	−1.16452e12	+	1.91991e11i	−1.71318	+	0.282447i
$909$	−9.02819e10	+	9.02819e10i	−0.132235	+	0.132235i
$910$	2.60707e11	+	5.07695e11i	0.380178	+	0.740350i
$911$		−	1.24467e12i		−	1.80709i	−0.428492	−	0.903546i	$-0.640955\pi$
$911$		−	1.24467e12i		−	1.80709i	0.428492	−	0.903546i	$-0.359045\pi$
$912$	−5.36740e11	+	1.81927e11i	−0.775862	+	0.262977i
$913$	−6.36957e10			−0.0916699
$914$	1.58459e11	−	8.13704e10i	0.227055	−	0.116595i
$915$	1.03951e11	+	1.03951e11i	0.148301	+	0.148301i
$916$	−1.27539e12	+	2.10270e11i	−1.81159	+	0.298673i
$917$	−7.10590e11	−	7.10590e11i	−1.00494	−	1.00494i
$918$	3.66438e9	+	1.17784e9i	0.00515976	+	0.00165850i
$919$	−3.68509e11			−0.516638			−0.258319	−	0.966060i	$-0.583168\pi$
$919$	−3.68509e11			−0.516638			−0.258319	+	0.966060i	$0.583168\pi$
$920$	2.38124e11	+	3.21301e11i	0.332393	+	0.448499i
$921$		−	1.44884e11i		−	0.201364i
$922$	9.06129e11	+	2.91258e11i	1.25391	+	0.403045i
$923$	1.75368e11	−	1.75368e11i	0.241626	−	0.241626i
$924$	2.51845e10	−	3.51281e10i	0.0345498	−	0.0481910i
$925$	1.70089e11	−	1.70089e11i	0.232332	−	0.232332i
$926$	3.33917e11	−	1.71470e11i	0.454146	−	0.233209i
$927$		−	4.07372e11i		−	0.551661i
$928$	−9.98376e9	−	6.32037e11i	−0.0134618	−	0.852218i
$929$	−8.38412e11			−1.12563			−0.562814	−	0.826584i	$-0.690281\pi$
$929$	−8.38412e11			−1.12563			−0.562814	+	0.826584i	$0.690281\pi$
$930$	−1.66751e11	−	3.24728e11i	−0.222914	−	0.434098i
$931$	7.42979e11	+	7.42979e11i	0.988958	+	0.988958i
$932$	1.02598e12	+	7.35559e11i	1.35980	+	0.974886i
$933$	−4.59603e11	−	4.59603e11i	−0.606535	−	0.606535i
$934$	3.98087e11	−	1.23848e12i	0.523107	−	1.62743i
$935$	7.31585e8			0.000957235
$936$	1.92927e11	+	2.60317e11i	0.251356	+	0.339155i
$937$		−	1.48072e11i		−	0.192095i	−0.995377	−	0.0960473i	$-0.969380\pi$
$937$		−	1.48072e11i		−	0.192095i	0.995377	−	0.0960473i	$-0.0306200\pi$
$938$	7.75419e10	−	2.41240e11i	0.100167	−	0.311629i
$939$	2.49779e11	−	2.49779e11i	0.321287	−	0.321287i
$940$	−9.32686e10	−	5.65718e11i	−0.119460	−	0.724584i
$941$	−5.19273e11	+	5.19273e11i	−0.662273	+	0.662273i	−0.955915	−	0.293642i	$-0.905133\pi$
$941$	−5.19273e11	+	5.19273e11i	−0.662273	+	0.662273i	0.293642	+	0.955915i	$0.405133\pi$
$942$	3.02702e11	+	5.89474e11i	0.384425	+	0.748620i
$943$			7.26591e11i			0.918847i
$944$	−1.14497e12	−	5.65284e11i	−1.44180	−	0.711834i
$945$	−1.00860e11			−0.126472
$946$	1.71073e10	−	8.78480e9i	0.0213608	−	0.0109690i
$947$	−5.36780e11	−	5.36780e11i	−0.667416	−	0.667416i	0.289701	−	0.957117i	$-0.406444\pi$
$947$	−5.36780e11	−	5.36780e11i	−0.667416	−	0.667416i	−0.957117	+	0.289701i	$0.906444\pi$
$948$	−7.05673e10	−	4.28024e11i	−0.0873715	−	0.529950i
$949$	8.04308e11	+	8.04308e11i	0.991648	+	0.991648i
$950$	−8.60980e11	−	2.76745e11i	−1.05706	−	0.339771i
$951$	3.53651e11			0.432367
$952$	−3.22415e10	−	4.79379e9i	−0.0392525	−	0.00583622i
$953$			2.38943e11i			0.289683i	0.989455	+	0.144841i	$0.0462672\pi$
$953$			2.38943e11i			0.289683i	−0.989455	+	0.144841i	$0.953733\pi$
$954$	9.50740e10	+	3.05597e10i	0.114781	+	0.0368940i
$955$	−7.25206e10	+	7.25206e10i	−0.0871862	+	0.0871862i
$956$	−1.10167e12	−	7.89822e11i	−1.31892	−	0.945578i
$957$	2.12722e10	−	2.12722e10i	0.0253609	−	0.0253609i
$958$	1.72659e11	−	8.86622e10i	0.204987	−	0.105263i
$959$			1.71419e12i			2.02668i
$960$	−6.65341e10	+	2.18797e11i	−0.0783356	+	0.257606i
$961$	−1.94860e12			−2.28470
$962$	−2.08040e11	−	4.05133e11i	−0.242911	−	0.473039i
$963$	−1.57218e11	−	1.57218e11i	−0.182809	−	0.182809i
$964$	4.25782e11	−	5.93893e11i	0.493037	−	0.687702i
$965$	−7.48680e10	−	7.48680e10i	−0.0863351	−	0.0863351i
$966$	2.59502e11	−	8.07335e11i	0.298011	−	0.927139i
$967$	−5.00934e11			−0.572894			−0.286447	−	0.958096i	$-0.592474\pi$
$967$	−5.00934e11			−0.572894			−0.286447	+	0.958096i	$0.592474\pi$
$968$	−1.28441e11	+	8.63853e11i	−0.146286	+	0.983872i
$969$			2.03402e10i			0.0230707i
$970$	1.10773e9	−	3.44625e9i	0.00125126	−	0.00389279i
$971$	−5.26091e11	+	5.26091e11i	−0.591812	+	0.591812i	−0.938121	−	0.346309i	$-0.887435\pi$
$971$	−5.26091e11	+	5.26091e11i	−0.591812	+	0.591812i	0.346309	+	0.938121i	$0.387435\pi$
$972$	−5.64987e10	+	9.31479e9i	−0.0632956	+	0.0104354i
$973$	6.97522e10	−	6.97522e10i	0.0778228	−	0.0778228i
$974$	−4.67034e10	−	9.09491e10i	−0.0518934	−	0.101056i
$975$			5.17046e11i			0.572151i
$976$	−6.33770e11	−	3.12899e11i	−0.698446	−	0.344830i
$977$	1.05330e12			1.15605			0.578024	−	0.816020i	$-0.303824\pi$
$977$	1.05330e12			1.15605			0.578024	+	0.816020i	$0.303824\pi$
$978$	9.78637e10	−	5.02541e10i	0.106971	−	0.0549308i
$979$	−6.40158e10	−	6.40158e10i	−0.0696877	−	0.0696877i
$980$	4.18345e11	−	6.89715e10i	0.453556	−	0.0747766i
$981$	−1.87140e11	−	1.87140e11i	−0.202065	−	0.202065i
$982$	−1.05757e12	−	3.39937e11i	−1.13727	−	0.365555i
$983$	1.30391e12			1.39647			0.698237	−	0.715866i	$-0.253968\pi$
$983$	1.30391e12			1.39647			0.698237	+	0.715866i	$0.253968\pi$
$984$	−3.33809e11	+	2.47394e11i	−0.356056	+	0.263881i
$985$		−	1.77299e11i		−	0.188348i
$986$	−2.15985e10	−	6.94243e9i	−0.0228516	−	0.00734520i
$987$	−8.59681e11	+	8.59681e11i	−0.905876	+	0.905876i
$988$	−9.97671e11	+	1.39158e12i	−1.04703	+	1.46043i
$989$	2.66794e11	−	2.66794e11i	0.278863	−	0.278863i
$990$	−9.68179e9	+	4.97170e9i	−0.0100789	+	0.00517565i
$991$			4.23431e11i			0.439023i	0.975610	+	0.219512i	$0.0704464\pi$
$991$			4.23431e11i			0.439023i	−0.975610	+	0.219512i	$0.929554\pi$
$992$	1.26047e12	+	1.22127e12i	1.30162	+	1.26114i
$993$	6.60313e11			0.679130
$994$	−1.69553e11	−	3.30183e11i	−0.173684	−	0.338228i
$995$	−4.32577e11	−	4.32577e11i	−0.441338	−	0.441338i
$996$	−5.80773e11	−	4.16376e11i	−0.590159	−	0.423105i
$997$	−1.16859e12	−	1.16859e12i	−1.18271	−	1.18271i	−0.979038	−	0.203677i	$-0.934711\pi$
$997$	−1.16859e12	−	1.16859e12i	−1.18271	−	1.18271i	−0.203677	−	0.979038i	$-0.565289\pi$
$998$	2.95410e11	−	9.19047e11i	0.297785	−	0.926437i
$999$	8.04851e10			0.0808078

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	48.9.l.a.43.11	yes	64
4.3	odd	2		192.9.l.a.79.24		64
16.3	odd	4	inner	48.9.l.a.19.11	✓	64
16.13	even	4		192.9.l.a.175.24		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
48.9.l.a.19.11	✓	64	16.3	odd	4	inner
48.9.l.a.43.11	yes	64	1.1	even	1	trivial
192.9.l.a.79.24		64	4.3	odd	2
192.9.l.a.175.24		64	16.13	even	4

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:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	48.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.30885 - 14.2331i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-149.162 + 208.055i) q^{4} +(-206.104 - 206.104i) q^{5} +(-228.972 + 712.351i) q^{6} +3383.34 q^{7} +(4051.46 + 602.388i) q^{8} +2187.00i q^{9} +O(q^{10})\)	\(q+(-7.30885 - 14.2331i) q^{2} +(-33.0681 - 33.0681i) q^{3} +(-149.162 + 208.055i) q^{4} +(-206.104 - 206.104i) q^{5} +(-228.972 + 712.351i) q^{6} +3383.34 q^{7} +(4051.46 + 602.388i) q^{8} +2187.00i q^{9} +(-1427.12 + 4439.88i) q^{10} +(754.555 - 754.555i) q^{11} +(11812.5 - 1947.49i) q^{12} +(25576.5 - 25576.5i) q^{13} +(-24728.3 - 48155.4i) q^{14} +13631.0i q^{15} +(-21037.7 - 62067.6i) q^{16} -2352.11 q^{17} +(31127.8 - 15984.4i) q^{18} +(130755. + 130755. i) q^{19} +(73623.8 - 12138.2i) q^{20} +(-111881. - 111881. i) q^{21} +(-16254.6 - 5224.72i) q^{22} -334976. q^{23} +(-114054. - 153894. i) q^{24} -305667. i q^{25} +(-550967. - 177098. i) q^{26} +(72320.0 - 72320.0i) q^{27} +(-504665. + 703921. i) q^{28} +(-426267. + 426267. i) q^{29} +(194011. - 99626.5i) q^{30} -1.67376e6i q^{31} +(-729652. + 753073. i) q^{32} -49903.4 q^{33} +(17191.2 + 33477.7i) q^{34} +(-697321. - 697321. i) q^{35} +(-455016. - 326216. i) q^{36} +(556451. + 556451. i) q^{37} +(905382. - 2.81672e6i) q^{38} -1.69153e6 q^{39} +(-710869. - 959178. i) q^{40} -2.16908e6i q^{41} +(-774689. + 2.41013e6i) q^{42} +(-796456. + 796456. i) q^{43} +(44438.3 + 269539. i) q^{44} +(450750. - 450750. i) q^{45} +(2.44829e6 + 4.76774e6i) q^{46} -7.68391e6i q^{47} +(-1.35678e6 + 2.74813e6i) q^{48} +5.68220e6 q^{49} +(-4.35059e6 + 2.23407e6i) q^{50} +(77779.7 + 77779.7i) q^{51} +(1.50629e6 + 9.13634e6i) q^{52} +(2.01803e6 + 2.01803e6i) q^{53} +(-1.55791e6 - 500761. i) q^{54} -311034. q^{55} +(1.37075e7 + 2.03808e6i) q^{56} -8.64767e6i q^{57} +(9.18262e6 + 2.95158e6i) q^{58} +(1.37774e7 - 1.37774e7i) q^{59} +(-2.83599e6 - 2.03321e6i) q^{60} +(7.62612e6 - 7.62612e6i) q^{61} +(-2.38228e7 + 1.22333e7i) q^{62} +7.39937e6i q^{63} +(1.60515e7 + 4.88110e6i) q^{64} -1.05428e7 q^{65} +(364736. + 710280. i) q^{66} +(3.30993e6 + 3.30993e6i) q^{67} +(350844. - 489367. i) q^{68} +(1.10770e7 + 1.10770e7i) q^{69} +(-4.82842e6 + 1.50216e7i) q^{70} +6.85661e6 q^{71} +(-1.31742e6 + 8.86055e6i) q^{72} +3.14472e7i q^{73} +(3.85300e6 - 1.19870e7i) q^{74} +(-1.01078e7 + 1.01078e7i) q^{75} +(-4.67080e7 + 7.70062e6i) q^{76} +(2.55292e6 - 2.55292e6i) q^{77} +(1.23632e7 + 2.40757e7i) q^{78} -3.62349e7i q^{79} +(-8.45643e6 + 1.71283e7i) q^{80} -4.78297e6 q^{81} +(-3.08728e7 + 1.58535e7i) q^{82} +(-4.22074e7 - 4.22074e7i) q^{83} +(3.99656e7 - 6.58903e6i) q^{84} +(484779. + 484779. i) q^{85} +(1.71572e7 + 5.51485e6i) q^{86} +2.81917e7 q^{87} +(3.51159e6 - 2.60252e6i) q^{88} -8.48391e7i q^{89} +(-9.71002e6 - 3.12110e6i) q^{90} +(8.65340e7 - 8.65340e7i) q^{91} +(4.99655e7 - 6.96934e7i) q^{92} +(-5.53482e7 + 5.53482e7i) q^{93} +(-1.09366e8 + 5.61605e7i) q^{94} -5.38985e7i q^{95} +(4.90309e7 - 774500. i) q^{96} -776204. q^{97} +(-4.15304e7 - 8.08753e7i) q^{98} +(1.65021e6 + 1.65021e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 372 q^{4} + 17460 q^{8}+O(q^{10}) \) 64 * q - 372 * q^4 + 17460 * q^8	\( 64 q - 372 q^{4} + 17460 q^{8} - 13784 q^{10} + 39552 q^{11} - 22680 q^{12} + 116772 q^{14} - 161824 q^{16} - 26244 q^{18} - 167552 q^{19} + 690000 q^{20} - 1252768 q^{22} + 1691136 q^{23} - 74844 q^{24} - 1682100 q^{26} + 678600 q^{28} - 2132352 q^{29} - 2054808 q^{30} + 1407840 q^{32} - 3704544 q^{34} - 2415744 q^{35} - 1041012 q^{36} - 4720512 q^{37} + 2413320 q^{38} - 3544848 q^{40} + 9436500 q^{42} - 7244672 q^{43} - 3982056 q^{44} + 11165992 q^{46} - 9467280 q^{48} + 52706752 q^{49} + 17072676 q^{50} + 13862016 q^{51} - 22890864 q^{52} - 5358720 q^{53} - 4960116 q^{54} - 46326784 q^{55} - 9637152 q^{56} + 25732944 q^{58} + 44938752 q^{59} + 40927032 q^{60} + 24476032 q^{61} - 17024868 q^{62} - 116303448 q^{64} + 29941632 q^{65} - 56828952 q^{66} - 44244736 q^{67} - 12614400 q^{68} - 8636544 q^{69} - 60922560 q^{70} + 159664128 q^{71} - 18502020 q^{72} + 140654028 q^{74} + 12918528 q^{75} + 204842760 q^{76} - 94964352 q^{77} + 14001660 q^{78} + 38076648 q^{80} - 306110016 q^{81} - 260917000 q^{82} + 209328000 q^{83} - 127862712 q^{84} + 106960000 q^{85} - 123451824 q^{86} + 104240736 q^{88} + 53520264 q^{90} - 45401472 q^{91} + 351567216 q^{92} + 208488216 q^{94} + 49597920 q^{96} - 681890712 q^{98} + 86500224 q^{99}+O(q^{100}) \) 64 * q - 372 * q^4 + 17460 * q^8 - 13784 * q^10 + 39552 * q^11 - 22680 * q^12 + 116772 * q^14 - 161824 * q^16 - 26244 * q^18 - 167552 * q^19 + 690000 * q^20 - 1252768 * q^22 + 1691136 * q^23 - 74844 * q^24 - 1682100 * q^26 + 678600 * q^28 - 2132352 * q^29 - 2054808 * q^30 + 1407840 * q^32 - 3704544 * q^34 - 2415744 * q^35 - 1041012 * q^36 - 4720512 * q^37 + 2413320 * q^38 - 3544848 * q^40 + 9436500 * q^42 - 7244672 * q^43 - 3982056 * q^44 + 11165992 * q^46 - 9467280 * q^48 + 52706752 * q^49 + 17072676 * q^50 + 13862016 * q^51 - 22890864 * q^52 - 5358720 * q^53 - 4960116 * q^54 - 46326784 * q^55 - 9637152 * q^56 + 25732944 * q^58 + 44938752 * q^59 + 40927032 * q^60 + 24476032 * q^61 - 17024868 * q^62 - 116303448 * q^64 + 29941632 * q^65 - 56828952 * q^66 - 44244736 * q^67 - 12614400 * q^68 - 8636544 * q^69 - 60922560 * q^70 + 159664128 * q^71 - 18502020 * q^72 + 140654028 * q^74 + 12918528 * q^75 + 204842760 * q^76 - 94964352 * q^77 + 14001660 * q^78 + 38076648 * q^80 - 306110016 * q^81 - 260917000 * q^82 + 209328000 * q^83 - 127862712 * q^84 + 106960000 * q^85 - 123451824 * q^86 + 104240736 * q^88 + 53520264 * q^90 - 45401472 * q^91 + 351567216 * q^92 + 208488216 * q^94 + 49597920 * q^96 - 681890712 * q^98 + 86500224 * q^99

Introduction

L-functions

Modular forms

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