LMFDB - Embedded newform 62.8.d.a.33.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,8,Mod(33,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.33"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	62.d (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$19.3678715800$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			33.1
Character	$\chi$	$=$	62.33
Dual form			62.8.d.a.47.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-6.47214 - 4.70228i) q^{2} +(-63.6525 + 46.2463i) q^{3} +(19.7771 + 60.8676i) q^{4} -282.324 q^{5} +629.431 q^{6} +(-452.897 - 1393.87i) q^{7} +(158.217 - 486.941i) q^{8} +(1237.11 - 3807.42i) q^{9} +(1827.24 + 1327.57i) q^{10} +(-1464.77 - 4508.09i) q^{11} +(-4073.76 - 2959.76i) q^{12} +(-6573.69 + 4776.07i) q^{13} +(-3623.18 + 11151.0i) q^{14} +(17970.6 - 13056.4i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-1781.90 + 5484.12i) q^{17} +(-25910.3 + 18824.9i) q^{18} +(-31271.2 - 22719.8i) q^{19} +(-5583.54 - 17184.4i) q^{20} +(93289.5 + 67778.8i) q^{21} +(-11718.1 + 36064.7i) q^{22} +(-11933.2 + 36726.5i) q^{23} +(12448.3 + 38311.9i) q^{24} +1581.69 q^{25} +65004.3 q^{26} +(44161.3 + 135914. i) q^{27} +(75884.8 - 55133.5i) q^{28} +(-146015. - 106086. i) q^{29} -177703. q^{30} +(159905. + 44078.3i) q^{31} +32768.0 q^{32} +(301718. + 219211. i) q^{33} +(37320.5 - 27115.0i) q^{34} +(127864. + 393524. i) q^{35} +256215. q^{36} +30079.5 q^{37} +(95556.2 + 294092. i) q^{38} +(197557. - 608017. i) q^{39} +(-44668.3 + 137475. i) q^{40} +(-360607. - 261997. i) q^{41} +(-285067. - 877347. i) q^{42} +(395574. + 287401. i) q^{43} +(245428. - 178314. i) q^{44} +(-349264. + 1.07493e6i) q^{45} +(249931. - 181586. i) q^{46} +(-422764. + 307156. i) q^{47} +(99586.4 - 306496. i) q^{48} +(-1.07151e6 + 778497. i) q^{49} +(-10236.9 - 7437.57i) q^{50} +(-140198. - 431484. i) q^{51} +(-420716. - 305668. i) q^{52} +(-33086.4 + 101830. i) q^{53} +(353290. - 1.08732e6i) q^{54} +(413538. + 1.27274e6i) q^{55} -750390. q^{56} +3.04120e6 q^{57} +(446182. + 1.37321e6i) q^{58} +(-1.53350e6 + 1.11415e6i) q^{59} +(1.15012e6 + 835611. i) q^{60} -1.22750e6 q^{61} +(-827661. - 1.03720e6i) q^{62} -5.86735e6 q^{63} +(-212079. - 154084. i) q^{64} +(1.85591e6 - 1.34840e6i) q^{65} +(-921969. - 2.83753e6i) q^{66} +4.22106e6 q^{67} -369046. q^{68} +(-938887. - 2.88960e6i) q^{69} +(1.02291e6 - 3.14819e6i) q^{70} +(605825. - 1.86454e6i) q^{71} +(-1.65826e6 - 1.20479e6i) q^{72} +(-1.80717e6 - 5.56190e6i) q^{73} +(-194679. - 141442. i) q^{74} +(-100679. + 73147.4i) q^{75} +(764449. - 2.35273e6i) q^{76} +(-5.62032e6 + 4.08340e6i) q^{77} +(-4.13768e6 + 3.00620e6i) q^{78} +(1.30919e6 - 4.02926e6i) q^{79} +(935546. - 679714. i) q^{80} +(-2.01329e6 - 1.46274e6i) q^{81} +(1.10192e6 + 3.39136e6i) q^{82} +(5.91807e6 + 4.29973e6i) q^{83} +(-2.28054e6 + 7.01878e6i) q^{84} +(503072. - 1.54830e6i) q^{85} +(-1.20877e6 - 3.72020e6i) q^{86} +1.42003e7 q^{87} -2.42692e6 q^{88} +(2.47845e6 + 7.62788e6i) q^{89} +(7.31509e6 - 5.31472e6i) q^{90} +(9.63445e6 + 6.99983e6i) q^{91} -2.47146e6 q^{92} +(-1.22168e7 + 4.58933e6i) q^{93} +4.18052e6 q^{94} +(8.82859e6 + 6.41435e6i) q^{95} +(-2.08577e6 + 1.51540e6i) q^{96} +(-4.35002e6 - 1.33880e7i) q^{97} +1.05957e7 q^{98} -1.89763e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) $ 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$2$	−6.47214	−	4.70228i	−0.572061	−	0.415627i
$3$	−63.6525	+	46.2463i	−1.36110	+	0.988900i	−0.362730	+	0.931894i	$0.618155\pi$
$3$	−63.6525	+	46.2463i	−1.36110	+	0.988900i	−0.998374	+	0.0570051i	$0.981845\pi$
$4$	19.7771	+	60.8676i	0.154508	+	0.475528i
$5$	−282.324			−1.01007			−0.505036	−	0.863098i	$-0.668521\pi$
$5$	−282.324			−1.01007			−0.505036	+	0.863098i	$0.668521\pi$
$6$	629.431			1.18965
$7$	−452.897	−	1393.87i	−0.499064	−	1.53596i	−0.810526	−	0.585703i	$-0.800818\pi$
$7$	−452.897	−	1393.87i	−0.499064	−	1.53596i	0.311461	−	0.950259i	$-0.399182\pi$
$8$	158.217	−	486.941i	0.109254	−	0.336249i
$9$	1237.11	−	3807.42i	0.565663	−	1.74093i
$10$	1827.24	+	1327.57i	0.577823	+	0.419813i
$11$	−1464.77	−	4508.09i	−0.331813	−	1.02122i	−0.968270	−	0.249905i	$-0.919601\pi$
$11$	−1464.77	−	4508.09i	−0.331813	−	1.02122i	0.636457	−	0.771312i	$-0.280399\pi$
$12$	−4073.76	−	2959.76i	−0.680552	−	0.494450i
$13$	−6573.69	+	4776.07i	−0.829866	+	0.602933i	−0.919521	−	0.393040i	$-0.871423\pi$
$13$	−6573.69	+	4776.07i	−0.829866	+	0.602933i	0.0896557	+	0.995973i	$0.471423\pi$
$14$	−3623.18	+	11151.0i	−0.352892	+	1.08609i
$15$	17970.6	−	13056.4i	1.37481	−	0.998860i
$16$	−3313.73	+	2407.57i	−0.202254	+	0.146946i
$17$	−1781.90	+	5484.12i	−0.0879653	+	0.270729i	−0.985357	−	0.170506i	$-0.945460\pi$
$17$	−1781.90	+	5484.12i	−0.0879653	+	0.270729i	0.897391	+	0.441236i	$0.145460\pi$
$18$	−25910.3	+	18824.9i	−1.04717	+	0.760816i
$19$	−31271.2	−	22719.8i	−1.04594	−	0.759919i	−0.0745032	−	0.997221i	$-0.523737\pi$
$19$	−31271.2	−	22719.8i	−1.04594	−	0.759919i	−0.971436	+	0.237301i	$0.923737\pi$
$20$	−5583.54	−	17184.4i	−0.156065	−	0.480318i
$21$	93289.5	+	67778.8i	2.19819	+	1.59708i
$22$	−11718.1	+	36064.7i	−0.234628	+	0.722109i
$23$	−11933.2	+	36726.5i	−0.204507	+	0.629408i	0.795226	+	0.606313i	$0.207352\pi$
$23$	−11933.2	+	36726.5i	−0.204507	+	0.629408i	−0.999733	+	0.0230951i	$0.992648\pi$
$24$	12448.3	+	38311.9i	0.183811	+	0.565711i
$25$	1581.69			0.0202457
$26$	65004.3			0.725329
$27$	44161.3	+	135914.i	0.431786	+	1.32890i
$28$	75884.8	−	55133.5i	0.653284	−	0.474638i
$29$	−146015.	−	106086.i	−1.11174	−	0.807729i	−0.128806	−	0.991670i	$-0.541115\pi$
$29$	−146015.	−	106086.i	−1.11174	−	0.807729i	−0.982937	+	0.183941i	$0.941115\pi$
$30$	−177703.			−1.20163
$31$	159905.	+	44078.3i	0.964044	+	0.265741i
$31$	159905.	+	44078.3i	0.964044	+	0.265741i
$32$	32768.0			0.176777
$33$	301718.	+	219211.i	1.46151	+	1.06185i
$34$	37320.5	−	27115.0i	0.162844	−	0.118313i
$35$	127864.	+	393524.i	0.504091	+	1.55143i
$36$	256215.			0.915263
$37$	30079.5			0.0976259			0.0488130	−	0.998808i	$-0.484456\pi$
$37$	30079.5			0.0976259			0.0488130	+	0.998808i	$0.484456\pi$
$38$	95556.2	+	294092.i	0.282499	+	0.869441i
$39$	197557.	−	608017.i	0.533293	−	1.64131i
$40$	−44668.3	+	137475.i	−0.110354	+	0.339636i
$41$	−360607.	−	261997.i	−0.817130	−	0.593680i	0.0987589	−	0.995111i	$-0.468513\pi$
$41$	−360607.	−	261997.i	−0.817130	−	0.593680i	−0.915889	+	0.401432i	$0.868513\pi$
$42$	−285067.	−	877347.i	−0.593711	−	1.82725i
$43$	395574.	+	287401.i	0.758731	+	0.551251i	0.898521	−	0.438931i	$-0.144643\pi$
$43$	395574.	+	287401.i	0.758731	+	0.551251i	−0.139790	+	0.990181i	$0.544643\pi$
$44$	245428.	−	178314.i	0.434349	−	0.315573i
$45$	−349264.	+	1.07493e6i	−0.571361	+	1.75847i
$46$	249931.	−	181586.i	0.378589	−	0.275061i
$47$	−422764.	+	307156.i	−0.593958	+	0.431536i	−0.843729	−	0.536769i	$-0.819645\pi$
$47$	−422764.	+	307156.i	−0.593958	+	0.431536i	0.249771	+	0.968305i	$0.419645\pi$
$48$	99586.4	−	306496.i	0.129974	−	0.400018i
$49$	−1.07151e6	+	778497.i	−1.30110	+	0.945302i
$50$	−10236.9	−	7437.57i	−0.0115818	−	0.00841465i
$51$	−140198.	−	431484.i	−0.147994	−	0.455480i
$52$	−420716.	−	305668.i	−0.414933	−	0.301466i
$53$	−33086.4	+	101830.i	−0.0305270	+	0.0939524i	−0.965159	−	0.261664i	$-0.915729\pi$
$53$	−33086.4	+	101830.i	−0.0305270	+	0.0939524i	0.934632	+	0.355616i	$0.115729\pi$
$54$	353290.	−	1.08732e6i	0.305319	−	0.939675i
$55$	413538.	+	1.27274e6i	0.335155	+	1.03150i
$56$	−750390.			−0.570991
$57$	3.04120e6			2.17512
$58$	446182.	+	1.37321e6i	0.300272	+	0.924141i
$59$	−1.53350e6	+	1.11415e6i	−0.972081	+	0.706258i	−0.955925	−	0.293611i	$-0.905143\pi$
$59$	−1.53350e6	+	1.11415e6i	−0.972081	+	0.706258i	−0.0161560	+	0.999869i	$0.505143\pi$
$60$	1.15012e6	+	835611.i	0.687406	+	0.499430i
$61$	−1.22750e6			−0.692418			−0.346209	−	0.938157i	$-0.612531\pi$
$61$	−1.22750e6			−0.692418			−0.346209	+	0.938157i	$0.612531\pi$
$62$	−827661.	−	1.03720e6i	−0.441044	−	0.552703i
$63$	−5.86735e6			−2.95631
$64$	−212079.	−	154084.i	−0.101127	−	0.0734732i
$65$	1.85591e6	−	1.34840e6i	0.838224	−	0.609005i
$66$	−921969.	−	2.83753e6i	−0.394741	−	1.21489i
$67$	4.22106e6			1.71459			0.857294	−	0.514828i	$-0.172144\pi$
$67$	4.22106e6			1.71459			0.857294	+	0.514828i	$0.172144\pi$
$68$	−369046.			−0.142331
$69$	−938887.	−	2.88960e6i	−0.344066	−	1.05893i
$70$	1.02291e6	−	3.14819e6i	0.356446	−	1.09703i
$71$	605825.	−	1.86454e6i	0.200883	−	0.618254i	−0.798975	−	0.601365i	$-0.794624\pi$
$71$	605825.	−	1.86454e6i	0.200883	−	0.618254i	0.999857	−	0.0168888i	$-0.00537612\pi$
$72$	−1.65826e6	−	1.20479e6i	−0.523586	−	0.380408i
$73$	−1.80717e6	−	5.56190e6i	−0.543713	−	1.67338i	−0.724031	−	0.689767i	$-0.757713\pi$
$73$	−1.80717e6	−	5.56190e6i	−0.543713	−	1.67338i	0.180319	−	0.983608i	$-0.442287\pi$
$74$	−194679.	−	141442.i	−0.0558480	−	0.0405760i
$75$	−100679.	+	73147.4i	−0.0275565	+	0.0200210i
$76$	764449.	−	2.35273e6i	0.199757	−	0.614788i
$77$	−5.62032e6	+	4.08340e6i	−1.40295	+	1.01931i
$78$	−4.13768e6	+	3.00620e6i	−0.987248	+	0.717278i
$79$	1.30919e6	−	4.02926e6i	0.298749	−	0.919456i	−0.683187	−	0.730244i	$-0.739407\pi$
$79$	1.30919e6	−	4.02926e6i	0.298749	−	0.919456i	0.981936	−	0.189212i	$-0.0605935\pi$
$80$	935546.	−	679714.i	0.204291	−	0.148426i
$81$	−2.01329e6	−	1.46274e6i	−0.420929	−	0.305823i
$82$	1.10192e6	+	3.39136e6i	0.220699	+	0.679243i
$83$	5.91807e6	+	4.29973e6i	1.13607	+	0.825406i	0.986567	−	0.163355i	$-0.0522314\pi$
$83$	5.91807e6	+	4.29973e6i	1.13607	+	0.825406i	0.149507	+	0.988761i	$0.452231\pi$
$84$	−2.28054e6	+	7.01878e6i	−0.419817	+	1.29206i
$85$	503072.	−	1.54830e6i	0.0888513	−	0.273456i
$86$	−1.20877e6	−	3.72020e6i	−0.204926	−	0.630698i
$87$	1.42003e7			2.31196
$88$	−2.42692e6			−0.379635
$89$	2.47845e6	+	7.62788e6i	0.372662	+	1.14694i	0.945043	+	0.326947i	$0.106020\pi$
$89$	2.47845e6	+	7.62788e6i	0.372662	+	1.14694i	−0.572381	+	0.819988i	$0.693980\pi$
$90$	7.31509e6	−	5.31472e6i	1.05772	−	0.768479i
$91$	9.63445e6	+	6.99983e6i	1.34024	+	0.973740i
$92$	−2.47146e6			−0.330899
$93$	−1.22168e7	+	4.58933e6i	−1.57496	+	0.591642i
$94$	4.18052e6			0.519139
$95$	8.82859e6	+	6.41435e6i	1.05647	+	0.767573i
$96$	−2.08577e6	+	1.51540e6i	−0.240611	+	0.174814i
$97$	−4.35002e6	−	1.33880e7i	−0.483939	−	1.48941i	−0.833512	−	0.552501i	$-0.813673\pi$
$97$	−4.35002e6	−	1.33880e7i	−0.483939	−	1.48941i	0.349573	−	0.936909i	$-0.386327\pi$
$98$	1.05957e7			1.13720
$99$	−1.89763e7			−1.96556
$100$	31281.3	+	96274.0i	0.00312813	+	0.00962740i
$101$	−5.38599e6	+	1.65764e7i	−0.520165	+	1.60090i	0.253518	+	0.967331i	$0.418412\pi$
$101$	−5.38599e6	+	1.65764e7i	−0.520165	+	1.60090i	−0.773683	+	0.633572i	$0.781588\pi$
$102$	−1.12158e6	+	3.45187e6i	−0.104648	+	0.322073i
$103$	7.44436e6	+	5.40864e6i	0.671270	+	0.487706i	0.870450	−	0.492257i	$-0.163828\pi$
$103$	7.44436e6	+	5.40864e6i	0.671270	+	0.487706i	−0.199180	+	0.979963i	$0.563828\pi$
$104$	1.28559e6	+	3.95665e6i	0.112070	+	0.344914i
$105$	−2.63378e7	−	1.91356e7i	−2.22033	−	1.61316i
$106$	692971.	−	503473.i	0.0565125	−	0.0410587i
$107$	−6.80553e6	+	2.09453e7i	−0.537055	+	1.65289i	0.202112	+	0.979362i	$0.435220\pi$
$107$	−6.80553e6	+	2.09453e7i	−0.537055	+	1.65289i	−0.739167	+	0.673523i	$0.764780\pi$
$108$	−7.39941e6	+	5.37599e6i	−0.565215	+	0.410653i
$109$	1.30660e7	−	9.49299e6i	0.966383	−	0.702119i	0.0117589	−	0.999931i	$-0.496257\pi$
$109$	1.30660e7	−	9.49299e6i	0.966383	−	0.702119i	0.954624	+	0.297812i	$0.0962570\pi$
$110$	3.30831e6	−	1.01819e7i	0.236991	−	0.729382i
$111$	−1.91464e6	+	1.39107e6i	−0.132879	+	0.0965422i
$112$	4.85663e6	+	3.52855e6i	0.326642	+	0.237319i
$113$	−2.63686e6	−	8.11543e6i	−0.171915	−	0.529099i	0.827564	−	0.561371i	$-0.189726\pi$
$113$	−2.63686e6	−	8.11543e6i	−0.171915	−	0.529099i	−0.999479	+	0.0322717i	$0.989726\pi$
$114$	−1.96830e7	−	1.43006e7i	−1.24430	−	0.904037i
$115$	3.36902e6	−	1.03688e7i	0.206567	−	0.635747i
$116$	3.56946e6	−	1.09857e7i	0.212324	−	0.653467i
$117$	1.00521e7	+	3.09373e7i	0.580241	+	1.78580i
$118$	1.51641e7			0.849630
$119$	8.45118e6			0.459730
$120$	−3.51445e6	−	1.08164e7i	−0.185662	−	0.571409i
$121$	−2.41186e6	+	1.75232e6i	−0.123766	+	0.0899215i
$122$	7.94457e6	+	5.77207e6i	0.396106	+	0.287788i
$123$	3.50699e7			1.69929
$124$	479523.	+	1.06048e7i	0.0225857	+	0.499490i
$125$	2.16100e7			0.989623
$126$	3.79743e7	+	2.75899e7i	1.69119	+	1.22872i
$127$	2.07927e7	−	1.51068e7i	0.900736	−	0.654423i	−0.0379189	−	0.999281i	$-0.512073\pi$
$127$	2.07927e7	−	1.51068e7i	0.900736	−	0.654423i	0.938655	+	0.344858i	$0.112073\pi$
$128$	648056.	+	1.99451e6i	0.0273135	+	0.0840623i
$129$	−3.84705e7			−1.57784
$130$	−1.83522e7			−0.732635
$131$	−1.30842e7	−	4.02689e7i	−0.508507	−	1.56502i	−0.794794	−	0.606879i	$-0.792421\pi$
$131$	−1.30842e7	−	4.02689e7i	−0.508507	−	1.56502i	0.286287	−	0.958144i	$-0.407579\pi$
$132$	−7.37575e6	+	2.27002e7i	−0.279124	+	0.859056i
$133$	−1.75060e7	+	5.38778e7i	−0.645216	+	1.98577i
$134$	−2.73193e7	−	1.98486e7i	−0.980849	−	0.712629i
$135$	−1.24678e7	−	3.83719e7i	−0.436135	−	1.34229i
$136$	2.38851e6	+	1.73536e6i	0.0814220	+	0.0591565i
$137$	3.27668e7	−	2.38065e7i	1.08871	−	0.790994i	0.109528	−	0.993984i	$-0.465066\pi$
$137$	3.27668e7	−	2.38065e7i	1.08871	−	0.790994i	0.979181	+	0.202990i	$0.0650659\pi$
$138$	−7.51110e6	+	2.31168e7i	−0.243291	+	0.748774i
$139$	−3.50455e7	+	2.54620e7i	−1.10683	+	0.804158i	−0.982161	−	0.188041i	$-0.939786\pi$
$139$	−3.50455e7	+	2.54620e7i	−1.10683	+	0.804158i	−0.124667	+	0.992199i	$0.539786\pi$
$140$	−2.14241e7	+	1.55655e7i	−0.659864	+	0.479419i
$141$	1.27052e7	−	3.91025e7i	0.381693	−	1.17473i
$142$	−1.26886e7	+	9.21877e6i	−0.371880	+	0.270187i
$143$	3.11599e7	+	2.26390e7i	0.891085	+	0.647411i
$144$	5.06719e6	+	1.55952e7i	0.141416	+	0.435233i
$145$	4.12235e7	+	2.99506e7i	1.12294	+	0.815865i
$146$	−1.44574e7	+	4.44952e7i	−0.384463	+	1.18326i
$147$	3.22017e7	−	9.91066e7i	0.836118	−	2.57331i
$148$	594886.	+	1.83087e6i	0.0150840	+	0.0464239i
$149$	−4.67212e7			−1.15708			−0.578538	−	0.815655i	$-0.696377\pi$
$149$	−4.67212e7			−1.15708			−0.578538	+	0.815655i	$0.696377\pi$
$150$	995567.			0.0240852
$151$	−1.17869e7	−	3.62764e7i	−0.278600	−	0.857443i	−0.988244	−	0.152883i	$-0.951144\pi$
$151$	−1.17869e7	−	3.62764e7i	−0.278600	−	0.857443i	0.709644	−	0.704560i	$-0.248856\pi$
$152$	−1.60108e7	+	1.16326e7i	−0.369795	+	0.268672i
$153$	1.86759e7	+	1.35689e7i	0.421563	+	0.306283i
$154$	5.55768e7			1.22623
$155$	−4.51451e7	−	1.24443e7i	−0.973754	−	0.268418i
$156$	4.09157e7			0.862886
$157$	−1.38975e7	−	1.00971e7i	−0.286608	−	0.208233i	0.435187	−	0.900340i	$-0.356682\pi$
$157$	−1.38975e7	−	1.00971e7i	−0.286608	−	0.208233i	−0.721794	+	0.692107i	$0.756682\pi$
$158$	−2.74200e7	+	1.99218e7i	−0.553054	+	0.401817i
$159$	−2.60320e6	−	8.01183e6i	−0.0513591	−	0.158067i
$160$	−9.25118e6			−0.178557
$161$	5.65966e7			1.06881
$162$	6.15207e6	+	1.89341e7i	0.113689	+	0.349899i
$163$	−3.41525e6	+	1.05110e7i	−0.0617683	+	0.190103i	−0.977179	−	0.212418i	$-0.931866\pi$
$163$	−3.41525e6	+	1.05110e7i	−0.0617683	+	0.190103i	0.915411	+	0.402521i	$0.131866\pi$
$164$	8.81535e6	−	2.71308e7i	0.156058	−	0.480297i
$165$	−8.51822e7	−	6.18885e7i	−1.47623	−	1.07255i
$166$	−1.80840e7	−	5.56569e7i	−0.306843	−	0.944366i
$167$	2.49859e7	+	1.81533e7i	0.415133	+	0.301612i	0.775676	−	0.631131i	$-0.217409\pi$
$167$	2.49859e7	+	1.81533e7i	0.415133	+	0.301612i	−0.360544	+	0.932742i	$0.617409\pi$
$168$	4.77642e7	−	3.47027e7i	0.777178	−	0.564653i
$169$	1.01227e6	−	3.11543e6i	0.0161321	−	0.0496495i
$170$	−1.05365e7	+	7.65520e6i	−0.164484	+	0.119505i
$171$	−1.25190e8	+	9.09556e7i	−1.91462	+	1.39105i
$172$	−9.67013e6	+	2.97616e7i	−0.144905	+	0.445971i
$173$	−8.60933e7	+	6.25504e7i	−1.26418	+	0.918478i	−0.998955	−	0.0457091i	$-0.985445\pi$
$173$	−8.60933e7	+	6.25504e7i	−1.26418	+	0.918478i	−0.265222	+	0.964187i	$0.585445\pi$
$174$	−9.19064e7	−	6.67739e7i	−1.32258	−	0.960913i
$175$	−716345.	−	2.20468e6i	−0.0101039	−	0.0310966i
$176$	1.57074e7	+	1.14121e7i	0.217175	+	0.157787i
$177$	4.60858e7	−	1.41837e8i	0.624684	−	1.92258i
$178$	1.98276e7	−	6.10231e7i	0.263512	−	0.811006i
$179$	−2.50311e7	−	7.70377e7i	−0.326207	−	1.00396i	−0.970893	−	0.239515i	$-0.923012\pi$
$179$	−2.50311e7	−	7.70377e7i	−0.326207	−	1.00396i	0.644685	−	0.764448i	$-0.276988\pi$
$180$	−7.23356e7			−0.924481
$181$	4.69832e7			0.588935			0.294468	−	0.955661i	$-0.404858\pi$
$181$	4.69832e7			0.588935			0.294468	+	0.955661i	$0.404858\pi$
$182$	−2.94402e7	−	9.06078e7i	−0.361986	−	1.11408i
$183$	7.81337e7	−	5.67674e7i	0.942452	−	0.684732i
$184$	1.59956e7	+	1.16215e7i	0.189295	+	0.137531i
$185$	−8.49217e6			−0.0986092
$186$	1.00649e8	+	2.77442e7i	1.14687	+	0.316138i
$187$	2.73329e7			0.305661
$188$	−2.70569e7	−	1.96580e7i	−0.296979	−	0.215768i
$189$	1.69447e8	−	1.23111e8i	1.82565	−	1.32641i
$190$	−2.69778e7	−	8.30291e7i	−0.285344	−	0.878198i
$191$	−1.22399e8			−1.27105			−0.635525	−	0.772080i	$-0.719216\pi$
$191$	−1.22399e8			−1.27105			−0.635525	+	0.772080i	$0.719216\pi$
$192$	2.06252e7			0.210302
$193$	9.86845e6	+	3.03720e7i	0.0988094	+	0.304104i	0.988228	−	0.152990i	$-0.0488902\pi$
$193$	9.86845e6	+	3.03720e7i	0.0988094	+	0.304104i	−0.889418	+	0.457094i	$0.848890\pi$
$194$	−3.48002e7	+	1.07104e8i	−0.342196	+	1.05317i
$195$	−5.57750e7	+	1.71658e8i	−0.538664	+	1.65784i
$196$	−6.85766e7	−	4.98238e7i	−0.650548	−	0.472651i
$197$	1.50546e7	+	4.63333e7i	0.140294	+	0.431779i	0.996376	−	0.0850604i	$-0.0271083\pi$
$197$	1.50546e7	+	4.63333e7i	0.140294	+	0.431779i	−0.856082	+	0.516840i	$0.827108\pi$
$198$	1.22817e8	+	8.92317e7i	1.12442	+	0.816941i
$199$	6.60313e7	−	4.79745e7i	0.593969	−	0.431544i	−0.249764	−	0.968307i	$-0.580353\pi$
$199$	6.60313e7	−	4.79745e7i	0.593969	−	0.431544i	0.843733	+	0.536763i	$0.180353\pi$
$200$	250250.	−	770192.i	0.00221192	−	0.00680760i
$201$	−2.68681e8	+	1.95208e8i	−2.33373	+	1.69555i
$202$	1.12806e8	−	8.19582e7i	0.962945	−	0.699620i
$203$	−8.17409e7	+	2.51573e8i	−0.685810	+	2.11070i
$204$	2.34907e7	−	1.70670e7i	0.193727	−	0.140751i
$205$	1.01808e8	+	7.39679e7i	0.825360	+	0.599659i
$206$	−2.27479e7	−	7.00109e7i	−0.181304	−	0.557995i
$207$	1.25071e8	+	9.08691e7i	0.980075	+	0.712066i
$208$	1.02848e7	−	3.16532e7i	0.0792451	−	0.243891i
$209$	−5.66180e7	+	1.74252e8i	−0.428986	+	1.32028i
$210$	8.04813e7	+	2.47696e8i	0.599691	+	1.84566i
$211$	−2.81438e7			−0.206250			−0.103125	−	0.994668i	$-0.532884\pi$
$211$	−2.81438e7			−0.206250			−0.103125	+	0.994668i	$0.532884\pi$
$212$	−6.85247e6			−0.0493937
$213$	4.76656e7	+	1.46700e8i	0.337968	+	1.04016i
$214$	1.42537e8	−	1.03559e8i	0.994212	−	0.722337i
$215$	−1.11680e8	−	8.11402e7i	−0.766373	−	0.556803i
$216$	7.31694e7			0.494016
$217$	−1.09811e7	−	2.42851e8i	−0.0729521	−	1.61336i
$218$	−1.29204e8			−0.844650
$219$	3.72248e8	+	2.70454e8i	2.39485	+	1.73996i
$220$	−6.92901e7	+	5.03422e7i	−0.438724	+	0.318752i
$221$	−1.44789e7	−	4.45614e7i	−0.0902322	−	0.277706i
$222$	1.89330e7			0.116140
$223$	−2.10435e7			−0.127072			−0.0635362	−	0.997980i	$-0.520238\pi$
$223$	−2.10435e7			−0.127072			−0.0635362	+	0.997980i	$0.520238\pi$
$224$	−1.48405e7	−	4.56745e7i	−0.0882229	−	0.271522i
$225$	1.95672e6	−	6.02218e6i	0.0114522	−	0.0352464i
$226$	−2.10949e7	+	6.49234e7i	−0.121562	+	0.374130i
$227$	6.24587e7	+	4.53789e7i	0.354407	+	0.257492i	0.750715	−	0.660626i	$-0.229709\pi$
$227$	6.24587e7	+	4.53789e7i	0.354407	+	0.257492i	−0.396309	+	0.918117i	$0.629709\pi$
$228$	6.01460e7	+	1.85110e8i	0.336074	+	1.03433i
$229$	3.24189e7	+	2.35537e7i	0.178391	+	0.129609i	0.673398	−	0.739280i	$-0.264834\pi$
$229$	3.24189e7	+	2.35537e7i	0.178391	+	0.129609i	−0.495006	+	0.868889i	$0.664834\pi$
$230$	−7.05616e7	+	5.12660e7i	−0.382403	+	0.277832i
$231$	1.68905e8	−	5.19837e8i	0.901574	−	2.77476i
$232$	−7.47597e7	+	5.43161e7i	−0.393061	+	0.285575i
$233$	−1.17231e8	+	8.51733e7i	−0.607151	+	0.441121i	−0.848410	−	0.529340i	$-0.822440\pi$
$233$	−1.17231e8	+	8.51733e7i	−0.607151	+	0.441121i	0.241259	+	0.970461i	$0.422440\pi$
$234$	8.04171e7	−	2.47499e8i	0.410292	−	1.26275i
$235$	1.19356e8	−	8.67175e7i	0.599941	−	0.435882i
$236$	−9.81441e7	−	7.13059e7i	−0.486040	−	0.353129i
$237$	1.03005e8	+	3.17018e8i	0.502621	+	1.54691i
$238$	−5.46972e7	−	3.97398e7i	−0.262994	−	0.191076i
$239$	4.68626e7	−	1.44228e8i	0.222041	−	0.683373i	−0.776537	−	0.630072i	$-0.783026\pi$
$239$	4.68626e7	−	1.44228e8i	0.222041	−	0.683373i	0.998578	−	0.0533015i	$-0.0169744\pi$
$240$	−2.81156e7	+	8.65310e7i	−0.131283	+	0.404047i
$241$	5.15021e7	+	1.58507e8i	0.237009	+	0.729439i	0.996849	+	0.0793283i	$0.0252775\pi$
$241$	5.15021e7	+	1.58507e8i	0.237009	+	0.729439i	−0.759839	+	0.650111i	$0.774722\pi$
$242$	2.38497e7			0.108176
$243$	−1.16745e8			−0.521933
$244$	−2.42764e7	−	7.47152e7i	−0.106984	−	0.329264i
$245$	3.02512e8	−	2.19788e8i	1.31420	−	0.954823i
$246$	−2.26977e8	−	1.64909e8i	−0.972097	−	0.706270i
$247$	3.14079e8			1.32617
$248$	4.67632e7	−	7.08905e7i	0.194681	−	0.295126i
$249$	−5.75546e8			−2.36256
$250$	−1.39863e8	−	1.01616e8i	−0.566125	−	0.411314i
$251$	2.39226e8	−	1.73808e8i	0.954885	−	0.693765i	0.00292799	−	0.999996i	$-0.499068\pi$
$251$	2.39226e8	−	1.73808e8i	0.954885	−	0.693765i	0.951957	+	0.306231i	$0.0990680\pi$
$252$	−1.16039e8	−	3.57131e8i	−0.456775	−	1.40581i
$253$	1.83046e8			0.710620
$254$	−2.05609e8			−0.787272
$255$	3.95811e7	+	1.21818e8i	0.149485	+	0.460067i
$256$	5.18444e6	−	1.59561e7i	0.0193136	−	0.0594410i
$257$	−1.93325e7	+	5.94993e7i	−0.0710431	+	0.218648i	−0.980274	−	0.197645i	$-0.936671\pi$
$257$	−1.93325e7	+	5.94993e7i	−0.0710431	+	0.218648i	0.909231	+	0.416293i	$0.136671\pi$
$258$	2.48986e8	+	1.80899e8i	0.902623	+	0.655794i
$259$	−1.36229e7	−	4.19271e7i	−0.0487216	−	0.149950i
$260$	1.18778e8	+	8.62974e7i	0.419112	+	0.304503i
$261$	−5.84551e8	+	4.24701e8i	−2.03507	+	1.47857i
$262$	−1.04673e8	+	3.22152e8i	−0.359569	+	1.10664i
$263$	−1.56495e8	+	1.13701e8i	−0.530464	+	0.385405i	−0.820531	−	0.571601i	$-0.806322\pi$
$263$	−1.56495e8	+	1.13701e8i	−0.530464	+	0.385405i	0.290067	+	0.957006i	$0.406322\pi$
$264$	1.54480e8	−	1.12236e8i	0.516723	−	0.375421i
$265$	9.34108e6	−	2.87489e7i	0.0308345	−	0.0948987i
$266$	3.66650e8	−	2.66387e8i	1.19444	−	0.867814i
$267$	−5.10520e8	−	3.70915e8i	−1.64144	−	1.19257i
$268$	8.34803e7	+	2.56926e8i	0.264918	+	0.815335i
$269$	2.14370e8	+	1.55749e8i	0.671477	+	0.487856i	0.870519	−	0.492134i	$-0.163783\pi$
$269$	2.14370e8	+	1.55749e8i	0.671477	+	0.487856i	−0.199042	+	0.979991i	$0.563783\pi$
$270$	−9.97423e7	+	3.06975e8i	−0.308394	+	0.949139i
$271$	1.29047e8	−	3.97167e8i	0.393873	−	1.21222i	−0.535962	−	0.844242i	$-0.680051\pi$
$271$	1.29047e8	−	3.97167e8i	0.393873	−	1.21222i	0.929835	−	0.367975i	$-0.119949\pi$
$272$	−7.29865e6	−	2.24629e7i	−0.0219913	−	0.0676823i
$273$	−9.36973e8			−2.78713
$274$	−3.24016e8			−0.951567
$275$	−2.31681e6	−	7.13042e6i	−0.00671779	−	0.0206752i
$276$	1.57315e8	−	1.14296e8i	0.450388	−	0.327226i
$277$	−2.19494e8	−	1.59471e8i	−0.620501	−	0.450821i	0.232595	−	0.972574i	$-0.425278\pi$
$277$	−2.19494e8	−	1.59471e8i	−0.620501	−	0.450821i	−0.853097	+	0.521753i	$0.825278\pi$
$278$	3.46549e8			0.967403
$279$	3.65644e8	−	5.54297e8i	1.00796	−	1.52802i
$280$	2.11853e8			0.576742
$281$	−4.47460e8	−	3.25099e8i	−1.20305	−	0.874065i	−0.208466	−	0.978030i	$-0.566847\pi$
$281$	−4.47460e8	−	3.25099e8i	−1.20305	−	0.874065i	−0.994581	+	0.103965i	$0.966847\pi$
$282$	−2.66101e8	+	1.93334e8i	−0.706601	+	0.513376i
$283$	2.14122e8	+	6.59000e8i	0.561576	+	1.72835i	0.677911	+	0.735144i	$0.262885\pi$
$283$	2.14122e8	+	6.59000e8i	0.561576	+	1.72835i	−0.116335	+	0.993210i	$0.537115\pi$
$284$	1.25471e8			0.325035
$285$	−8.58602e8			−2.19702
$286$	−9.52160e7	−	2.93045e8i	−0.240674	−	0.740718i
$287$	−2.01872e8	+	6.21299e8i	−0.504069	+	1.55137i
$288$	4.05375e7	−	1.24762e8i	0.0999961	−	0.307756i
$289$	3.05071e8	+	2.21647e8i	0.743461	+	0.540156i
$290$	−1.25968e8	−	3.87689e8i	−0.303296	−	0.933449i
$291$	8.96034e8	+	6.51007e8i	2.13157	+	1.54867i
$292$	3.02799e8	−	2.19996e8i	0.711729	−	0.517101i
$293$	−1.04810e8	+	3.22571e8i	−0.243424	+	0.749183i	0.752467	+	0.658630i	$0.228864\pi$
$293$	−1.04810e8	+	3.22571e8i	−0.243424	+	0.749183i	−0.995892	+	0.0905535i	$0.971136\pi$
$294$	−6.74441e8	+	4.90010e8i	−1.54785	+	1.12458i
$295$	4.32944e8	−	3.14552e8i	0.981872	−	0.713372i
$296$	4.75908e6	−	1.46470e7i	0.0106660	−	0.0328266i
$297$	5.48028e8	−	3.98166e8i	1.21382	−	0.881894i
$298$	3.02386e8	+	2.19696e8i	0.661919	+	0.480912i
$299$	−9.69633e7	−	2.98422e8i	−0.209777	−	0.645628i
$300$	−6.44344e6	−	4.68144e6i	−0.0137782	−	0.0100105i
$301$	2.21447e8	−	6.81543e8i	0.468044	−	1.44049i
$302$	−9.42954e7	+	2.90211e8i	−0.197000	+	0.606304i
$303$	−4.23764e8	−	1.30421e9i	−0.875134	−	2.69339i
$304$	1.58324e8			0.323213
$305$	3.46553e8			0.699392
$306$	−5.70686e7	−	1.75639e8i	−0.113860	−	0.350426i
$307$	−2.26703e8	+	1.64709e8i	−0.447170	+	0.324888i	−0.788477	−	0.615064i	$-0.789130\pi$
$307$	−2.26703e8	+	1.64709e8i	−0.447170	+	0.324888i	0.341308	+	0.939952i	$0.389130\pi$
$308$	−3.59700e8	−	2.61338e8i	−0.701477	−	0.509653i
$309$	−7.23981e8			−1.39596
$310$	2.33668e8	+	2.92826e8i	0.445486	+	0.558270i
$311$	3.47288e8			0.654680			0.327340	−	0.944907i	$-0.393848\pi$
$311$	3.47288e8			0.654680			0.327340	+	0.944907i	$0.393848\pi$
$312$	−2.64812e8	−	1.92397e8i	−0.493624	−	0.358639i
$313$	−3.57824e8	+	2.59974e8i	−0.659575	+	0.479209i	−0.866519	−	0.499143i	$-0.833648\pi$
$313$	−3.57824e8	+	2.59974e8i	−0.659575	+	0.479209i	0.206944	+	0.978353i	$0.433648\pi$
$314$	4.24670e7	+	1.30700e8i	0.0774101	+	0.238244i
$315$	1.65649e9			2.98609
$316$	2.71144e8			0.483387
$317$	−1.87650e8	−	5.77527e8i	−0.330857	−	1.01827i	−0.968727	−	0.248130i	$-0.920184\pi$
$317$	−1.87650e8	−	5.77527e8i	−0.330857	−	1.01827i	0.637869	−	0.770144i	$-0.279816\pi$
$318$	−2.08256e7	+	6.40946e7i	−0.0363164	+	0.111770i
$319$	−2.64368e8	+	8.13640e8i	−0.455975	+	1.40335i
$320$	5.98749e7	+	4.35017e7i	0.102146	+	0.0742132i
$321$	−5.35451e8	−	1.64795e9i	−0.903550	−	2.78084i
$322$	−3.66301e8	−	2.66133e8i	−0.611424	−	0.444226i
$323$	1.80320e8	−	1.31010e8i	0.297739	−	0.216320i
$324$	4.92166e7	−	1.51473e8i	0.0803903	−	0.247416i
$325$	−1.03976e7	+	7.55428e6i	−0.0168012	+	0.0122068i
$326$	7.15298e7	−	5.19695e7i	0.114347	−	0.0830781i
$327$	−3.92667e8	+	1.20851e9i	−0.621023	+	1.91131i
$328$	−1.84631e8	+	1.34142e8i	−0.288899	+	0.209897i
$329$	6.19606e8	+	4.50170e8i	0.959246	+	0.696933i
$330$	2.60294e8	+	8.01102e8i	0.398717	+	1.22712i
$331$	4.71392e8	+	3.42486e8i	0.714471	+	0.519093i	0.884613	−	0.466326i	$-0.154423\pi$
$331$	4.71392e8	+	3.42486e8i	0.714471	+	0.519093i	−0.170142	+	0.985420i	$0.554423\pi$
$332$	−1.44672e8	+	4.45255e8i	−0.216971	+	0.667768i
$333$	3.72116e7	−	1.14525e8i	0.0552234	−	0.169960i
$334$	−7.63501e7	−	2.34981e8i	−0.112124	−	0.345081i
$335$	−1.19171e9			−1.73186
$336$	−4.72319e8			−0.679278
$337$	−2.09200e8	−	6.43851e8i	−0.297753	−	0.916391i	−0.982283	−	0.187405i	$-0.939992\pi$
$337$	−2.09200e8	−	6.43851e8i	−0.297753	−	0.916391i	0.684529	−	0.728985i	$-0.260008\pi$
$338$	−2.12012e7	+	1.54035e7i	−0.0298642	+	0.0216976i
$339$	5.43151e8	+	3.94622e8i	0.757220	+	0.550152i
$340$	1.04190e8			0.143764
$341$	−3.55153e7	−	7.85432e8i	−0.0485038	−	1.07267i
$342$	1.23794e9			1.67344
$343$	5.93935e8	+	4.31519e8i	0.794712	+	0.577392i
$344$	2.02534e8	−	1.47149e8i	0.268252	−	0.194897i
$345$	2.65070e8	+	8.15802e8i	0.347531	+	1.06959i
$346$	8.51337e8			1.10493
$347$	9.45135e7			0.121434			0.0607171	−	0.998155i	$-0.480661\pi$
$347$	9.45135e7			0.121434			0.0607171	+	0.998155i	$0.480661\pi$
$348$	2.80841e8	+	8.64339e8i	0.357218	+	1.09940i
$349$	3.63718e8	−	1.11941e9i	0.458011	−	1.40961i	−0.409552	−	0.912287i	$-0.634315\pi$
$349$	3.63718e8	−	1.11941e9i	0.458011	−	1.40961i	0.867563	−	0.497327i	$-0.165685\pi$
$350$	−5.73076e6	+	1.76375e7i	−0.00714454	+	0.0219886i
$351$	−9.39440e8	−	6.82543e8i	−1.15956	−	0.842471i
$352$	−4.79975e7	−	1.47721e8i	−0.0586569	−	0.180527i
$353$	1.79031e7	+	1.30073e7i	0.0216629	+	0.0157390i	0.598564	−	0.801075i	$-0.295738\pi$
$353$	1.79031e7	+	1.30073e7i	0.0216629	+	0.0157390i	−0.576901	+	0.816814i	$0.695738\pi$
$354$	−9.65233e8	+	7.01283e8i	−1.15643	+	0.840199i
$355$	−1.71039e8	+	5.26403e8i	−0.202906	+	0.624481i
$356$	−4.15274e8	+	3.01715e8i	−0.487821	+	0.354423i
$357$	−5.37939e8	+	3.90836e8i	−0.625741	+	0.454627i
$358$	−2.00249e8	+	6.16302e8i	−0.230663	+	0.709909i
$359$	7.95975e8	−	5.78310e8i	0.907964	−	0.659675i	−0.0325348	−	0.999471i	$-0.510358\pi$
$359$	7.95975e8	−	5.78310e8i	0.907964	−	0.659675i	0.940499	+	0.339796i	$0.110358\pi$
$360$	4.68166e8	+	3.40142e8i	0.528860	+	0.384239i
$361$	1.85474e8	+	5.70829e8i	0.207495	+	0.638603i
$362$	−3.04082e8	−	2.20928e8i	−0.336907	−	0.244777i
$363$	7.24827e7	−	2.23079e8i	0.0795355	−	0.244785i
$364$	−2.35522e8	+	7.24862e8i	−0.255963	+	0.787772i
$365$	5.10208e8	+	1.57026e9i	0.549189	+	1.69023i
$366$	−7.72628e8			−0.823734
$367$	1.25950e9			1.33005			0.665025	−	0.746821i	$-0.268421\pi$
$367$	1.25950e9			1.33005			0.665025	+	0.746821i	$0.268421\pi$
$368$	−4.88782e7	−	1.50432e8i	−0.0511268	−	0.157352i
$369$	−1.44364e9	+	1.04887e9i	−1.49578	+	1.08675i
$370$	5.49625e7	+	3.99326e7i	0.0564105	+	0.0409846i
$371$	1.56922e8			0.159542
$372$	−5.20955e8	−	6.52846e8i	−0.524687	−	0.657522i
$373$	−8.12878e7			−0.0811044			−0.0405522	−	0.999177i	$-0.512912\pi$
$373$	−8.12878e7			−0.0811044			−0.0405522	+	0.999177i	$0.512912\pi$
$374$	−1.76902e8	−	1.28527e8i	−0.174857	−	0.127041i
$375$	−1.37553e9	+	9.99381e8i	−1.34698	+	0.978637i
$376$	8.26786e7	+	2.54459e8i	0.0802113	+	0.246865i
$377$	1.46653e9			1.40960
$378$	−1.67559e9			−1.59568
$379$	−4.82330e8	−	1.48446e9i	−0.455100	−	1.40065i	−0.871017	−	0.491252i	$-0.836539\pi$
$379$	−4.82330e8	−	1.48446e9i	−0.455100	−	1.40065i	0.415917	−	0.909402i	$-0.363461\pi$
$380$	−2.15822e8	+	6.64233e8i	−0.201769	+	0.620980i
$381$	−6.24875e8	+	1.92317e9i	−0.578836	+	1.78148i
$382$	7.92186e8	+	5.75557e8i	0.727118	+	0.528282i
$383$	−5.21990e8	−	1.60652e9i	−0.474751	−	1.46113i	−0.846293	−	0.532718i	$-0.821171\pi$
$383$	−5.21990e8	−	1.60652e9i	−0.474751	−	1.46113i	0.371541	−	0.928416i	$-0.378829\pi$
$384$	−1.33489e8	−	9.69854e7i	−0.120306	−	0.0874072i
$385$	1.58675e9	−	1.15284e9i	1.41708	−	1.02957i
$386$	7.89476e7	−	2.42976e8i	0.0698688	−	0.215034i
$387$	1.58362e9	−	1.15057e9i	1.38888	−	1.00908i
$388$	7.28864e8	−	5.29551e8i	0.633484	−	0.460253i
$389$	−1.79985e8	+	5.53935e8i	−0.155028	+	0.477129i	−0.998164	−	0.0605729i	$-0.980707\pi$
$389$	−1.79985e8	+	5.53935e8i	−0.155028	+	0.477129i	0.843135	+	0.537701i	$0.180707\pi$
$390$	1.16817e9	−	8.48723e8i	0.997192	−	0.724502i
$391$	−1.80149e8	−	1.30886e8i	−0.152410	−	0.110732i
$392$	2.09551e8	+	6.44933e8i	0.175707	+	0.540771i
$393$	2.69513e9	+	1.95813e9i	2.23978	+	1.62730i
$394$	1.20437e8	−	3.70667e8i	0.0992026	−	0.305314i
$395$	−3.69615e8	+	1.13756e9i	−0.301758	+	0.928717i
$396$	−3.75295e8	−	1.15504e9i	−0.303696	−	0.934681i
$397$	8.26312e7			0.0662792			0.0331396	−	0.999451i	$-0.489449\pi$
$397$	8.26312e7			0.0662792			0.0331396	+	0.999451i	$0.489449\pi$
$398$	−6.52953e8			−0.519148
$399$	−1.37735e9	−	4.23904e9i	−1.08552	−	3.34089i
$400$	−5.24131e6	+	3.80804e6i	−0.00409478	+	0.00297503i
$401$	−8.90605e8	−	6.47062e8i	−0.689731	−	0.501119i	0.186841	−	0.982390i	$-0.440175\pi$
$401$	−8.90605e8	−	6.47062e8i	−0.689731	−	0.501119i	−0.876572	+	0.481271i	$0.840175\pi$
$402$	2.65686e9			2.03976
$403$	−1.26169e9	+	4.73962e8i	−0.960251	+	0.360725i
$404$	−1.11548e9			−0.841645
$405$	5.68400e8	+	4.12967e8i	0.425169	+	0.308903i
$406$	1.71200e9	−	1.24384e9i	1.26959	−	0.922412i
$407$	−4.40595e7	−	1.35601e8i	−0.0323936	−	0.0996972i
$408$	−2.32289e8			−0.169324
$409$	−2.25114e9			−1.62694			−0.813470	−	0.581607i	$-0.802424\pi$
$409$	−2.25114e9			−1.62694			−0.813470	+	0.581607i	$0.802424\pi$
$410$	−3.11098e8	−	9.57460e8i	−0.222922	−	0.686084i
$411$	−9.84729e8	+	3.03068e9i	−0.699633	+	2.15325i
$412$	−1.81983e8	+	5.60087e8i	−0.128201	+	0.394562i
$413$	2.24751e9	+	1.63291e9i	1.56992	+	1.14061i
$414$	−3.82182e8	−	1.17623e9i	−0.264709	−	0.814691i
$415$	−1.67081e9	−	1.21392e9i	−1.14752	−	0.833720i
$416$	−2.15407e8	+	1.56502e8i	−0.146701	+	0.106584i
$417$	1.05321e9	−	3.24145e9i	0.711277	−	2.18908i
$418$	1.18582e9	−	8.61551e8i	0.794151	−	0.576984i
$419$	−5.80595e8	+	4.21827e8i	−0.385588	+	0.280146i	−0.763645	−	0.645636i	$-0.776592\pi$
$419$	−5.80595e8	+	4.21827e8i	−0.385588	+	0.280146i	0.378057	+	0.925782i	$0.376592\pi$
$420$	6.43850e8	−	1.98157e9i	0.424045	−	1.30508i
$421$	3.67294e8	−	2.66855e8i	0.239898	−	0.174296i	−0.461340	−	0.887224i	$-0.652631\pi$
$421$	3.67294e8	−	2.66855e8i	0.239898	−	0.174296i	0.701238	+	0.712927i	$0.252631\pi$
$422$	1.82150e8	+	1.32340e8i	0.117988	+	0.0857229i
$423$	6.46469e8	+	1.98963e9i	0.415295	+	1.27815i
$424$	4.43501e7	+	3.22223e7i	0.0282562	+	0.0205294i
$425$	−2.81842e6	+	8.67419e6i	−0.00178092	+	0.00548110i
$426$	3.81325e8	−	1.17360e9i	0.238980	−	0.735504i
$427$	5.55933e8	+	1.71099e9i	0.345561	+	1.06353i
$428$	−1.40948e9			−0.868973
$429$	−3.03037e9			−1.85308
$430$	3.41263e8	+	1.05030e9i	0.206990	+	0.637051i
$431$	5.65103e8	−	4.10571e8i	0.339983	−	0.247012i	−0.404672	−	0.914462i	$-0.632614\pi$
$431$	5.65103e8	−	4.10571e8i	0.339983	−	0.247012i	0.744655	+	0.667450i	$0.232614\pi$
$432$	−4.73562e8	−	3.44063e8i	−0.282608	−	0.205326i
$433$	−2.15112e9			−1.27338			−0.636688	−	0.771121i	$-0.719696\pi$
$433$	−2.15112e9			−1.27338			−0.636688	+	0.771121i	$0.719696\pi$
$434$	−1.07088e9	+	1.62340e9i	−0.628822	+	0.953260i
$435$	−4.00909e9			−2.33525
$436$	8.36223e8	+	6.07552e8i	0.483192	+	0.351059i
$437$	1.20758e9	−	8.77361e8i	0.692201	−	0.502914i
$438$	−1.13749e9	−	3.50083e9i	−0.646827	−	1.99073i
$439$	2.21965e9			1.25216			0.626079	−	0.779760i	$-0.284659\pi$
$439$	2.21965e9			1.25216			0.626079	+	0.779760i	$0.284659\pi$
$440$	6.85178e8			0.383459
$441$	1.63849e9	+	5.04277e9i	0.909725	+	2.79984i
$442$	−1.15831e8	+	3.56491e8i	−0.0638038	+	0.196368i
$443$	9.44347e7	−	2.90640e8i	0.0516082	−	0.158834i	−0.921931	−	0.387355i	$-0.873389\pi$
$443$	9.44347e7	−	2.90640e8i	0.0516082	−	0.158834i	0.973539	+	0.228521i	$0.0733889\pi$
$444$	−1.22537e8	−	8.90282e7i	−0.0664395	−	0.0482711i
$445$	−6.99725e8	−	2.15353e9i	−0.376415	−	1.15849i
$446$	1.36196e8	+	9.89525e7i	0.0726932	+	0.0528147i
$447$	2.97392e9	−	2.16068e9i	1.57490	−	1.14423i
$448$	−1.18724e8	+	3.65396e8i	−0.0623830	+	0.191995i
$449$	−1.68904e9	+	1.22716e9i	−0.880600	+	0.639793i	−0.933410	−	0.358811i	$-0.883182\pi$
$449$	−1.68904e9	+	1.22716e9i	−0.880600	+	0.639793i	0.0528103	+	0.998605i	$0.483182\pi$
$450$	−4.09821e7	+	2.97753e7i	−0.0212007	+	0.0154032i
$451$	−6.52898e8	+	2.00941e9i	−0.335141	+	1.03146i
$452$	4.41817e8	−	3.20999e8i	0.225039	−	0.163501i
$453$	2.42792e9	+	1.76398e9i	1.22713	+	0.891561i
$454$	−1.90857e8	−	5.87397e8i	−0.0957220	−	0.294602i
$455$	−2.72003e9	−	1.97622e9i	−1.35374	−	0.983547i
$456$	4.81168e8	−	1.48088e9i	0.237640	−	0.731381i
$457$	−4.37767e8	+	1.34731e9i	−0.214554	+	0.660329i	0.784631	+	0.619963i	$0.212852\pi$
$457$	−4.37767e8	+	1.34731e9i	−0.214554	+	0.660329i	−0.999185	+	0.0403661i	$0.987148\pi$
$458$	−9.90633e7	−	3.04886e8i	−0.0481819	−	0.148289i
$459$	−8.24062e8			−0.397755
$460$	6.97751e8			0.334232
$461$	−2.21306e8	−	6.81108e8i	−0.105206	−	0.323790i	0.884573	−	0.466402i	$-0.154450\pi$
$461$	−2.21306e8	−	6.81108e8i	−0.105206	−	0.323790i	−0.989779	+	0.142612i	$0.954450\pi$
$462$	−3.53760e9	+	2.57022e9i	−1.66902	+	1.21261i
$463$	1.77984e9	+	1.29313e9i	0.833387	+	0.605491i	0.920515	−	0.390706i	$-0.127769\pi$
$463$	1.77984e9	+	1.29313e9i	0.833387	+	0.605491i	−0.0871287	+	0.996197i	$0.527769\pi$
$464$	7.39265e8			0.343548
$465$	3.44910e9	−	1.29568e9i	1.59082	−	0.597601i
$466$	1.15924e9			0.530669
$467$	−1.37164e9	−	9.96557e8i	−0.623207	−	0.452786i	0.230833	−	0.972993i	$-0.425855\pi$
$467$	−1.37164e9	−	9.96557e8i	−0.623207	−	0.452786i	−0.854040	+	0.520207i	$0.825855\pi$
$468$	−1.68428e9	+	1.22370e9i	−0.759545	+	0.551842i
$469$	−1.91171e9	−	5.88363e9i	−0.855689	−	2.63354i
$470$	−1.18026e9			−0.524367
$471$	1.35157e9			0.596024
$472$	2.99902e8	+	9.23003e8i	0.131275	+	0.404023i
$473$	7.16207e8	−	2.20426e9i	0.311189	−	0.957741i
$474$	8.24043e8	−	2.53614e9i	0.355407	−	1.09383i
$475$	−4.94614e7	−	3.59358e7i	−0.0211758	−	0.0153851i
$476$	1.67140e8	+	5.14403e8i	0.0710322	+	0.218615i
$477$	3.46776e8	+	2.51948e8i	0.146297	+	0.106291i
$478$	−9.81503e8	+	7.13104e8i	−0.411050	+	0.298645i
$479$	1.56636e8	−	4.82076e8i	0.0651204	−	0.200420i	−0.913202	−	0.407507i	$-0.866398\pi$
$479$	1.56636e8	−	4.82076e8i	0.0651204	−	0.200420i	0.978323	+	0.207087i	$0.0663983\pi$
$480$	5.88861e8	−	4.27833e8i	0.243035	−	0.176575i
$481$	−1.97734e8	+	1.43662e8i	−0.0810164	+	0.0588618i
$482$	4.12017e8	−	1.26806e9i	0.167591	−	0.515791i
$483$	−3.60252e9	+	2.61738e9i	−1.45476	+	1.05694i
$484$	−1.54359e8	−	1.12148e8i	−0.0618832	−	0.0449608i
$485$	1.22811e9	+	3.77975e9i	0.488813	+	1.50441i
$486$	7.55586e8	+	5.48966e8i	0.298578	+	0.216929i
$487$	−6.08550e8	+	1.87292e9i	−0.238751	+	0.734799i	0.757851	+	0.652428i	$0.226249\pi$
$487$	−6.08550e8	+	1.87292e9i	−0.238751	+	0.734799i	−0.996602	+	0.0823715i	$0.973751\pi$
$488$	−1.94212e8	+	5.97722e8i	−0.0756494	+	0.232825i
$489$	−2.68708e8	−	8.26997e8i	−0.103920	−	0.319833i
$490$	−2.99141e9			−1.14865
$491$	5.67771e8			0.216465			0.108233	−	0.994126i	$-0.465481\pi$
$491$	5.67771e8			0.216465			0.108233	+	0.994126i	$0.465481\pi$
$492$	6.93581e8	+	2.13462e9i	0.262554	+	0.808060i
$493$	8.41973e8	−	6.11729e8i	0.316471	−	0.229930i
$494$	−2.03276e9	−	1.47689e9i	−0.758650	−	0.551192i
$495$	5.35745e9			1.98536
$496$	−6.36005e8	+	2.38919e8i	−0.234032	+	0.0879155i
$497$	−2.87331e9			−1.04987
$498$	3.72501e9	+	2.70638e9i	1.35153	+	0.981943i
$499$	−1.42461e9	+	1.03504e9i	−0.513267	+	0.372910i	−0.814062	−	0.580779i	$-0.802748\pi$
$499$	−1.42461e9	+	1.03504e9i	−0.513267	+	0.372910i	0.300794	+	0.953689i	$0.402748\pi$
$500$	4.27383e8	+	1.31535e9i	0.152905	+	0.470593i
$501$	−2.42994e9			−0.863302
$502$	−2.36560e9			−0.834600
$503$	5.85679e8	+	1.80253e9i	0.205197	+	0.631532i	0.999705	+	0.0242786i	$0.00772888\pi$
$503$	5.85679e8	+	1.80253e9i	0.205197	+	0.631532i	−0.794508	+	0.607254i	$0.792271\pi$
$504$	−9.28312e8	+	2.85705e9i	−0.322989	+	0.994057i
$505$	1.52059e9	−	4.67991e9i	0.525404	−	1.61703i
$506$	−1.18470e9	−	8.60732e8i	−0.406518	−	0.295353i
$507$	7.96438e7	+	2.45119e8i	0.0271409	+	0.0835311i
$508$	1.33073e9	+	9.66833e8i	0.450368	+	0.327212i
$509$	1.86672e9	−	1.35625e9i	0.627431	−	0.455855i	−0.228078	−	0.973643i	$-0.573244\pi$
$509$	1.86672e9	−	1.35625e9i	0.627431	−	0.455855i	0.855509	+	0.517788i	$0.173244\pi$
$510$	3.16649e8	−	9.74545e8i	0.105702	−	0.325317i
$511$	−6.93413e9	+	5.03794e9i	−2.29889	+	1.67024i
$512$	−1.08584e8	+	7.88912e7i	−0.0357538	+	0.0259767i
$513$	1.70698e9	−	5.25354e9i	0.558236	−	1.71807i
$514$	4.04905e8	−	2.94181e8i	0.131517	−	0.0955527i
$515$	−2.10172e9	−	1.52699e9i	−0.678031	−	0.492618i
$516$	−7.60835e8	−	2.34161e9i	−0.243790	−	0.750309i
$517$	2.00394e9	+	1.45595e9i	0.637775	+	0.463371i
$518$	−1.08983e8	+	3.35417e8i	−0.0344514	+	0.106030i
$519$	2.58733e9	−	7.96298e9i	0.812393	−	2.50029i
$520$	−3.62954e8	−	1.11706e9i	−0.113198	−	0.348388i
$521$	3.53036e9			1.09367			0.546836	−	0.837240i	$-0.315832\pi$
$521$	3.53036e9			1.09367			0.546836	+	0.837240i	$0.315832\pi$
$522$	5.78035e9			1.77872
$523$	−1.58600e9	−	4.88120e9i	−0.484782	−	1.49201i	−0.832296	−	0.554332i	$-0.812974\pi$
$523$	−1.58600e9	−	4.88120e9i	−0.484782	−	1.49201i	0.347514	−	0.937675i	$-0.387026\pi$
$524$	2.19231e9	−	1.59280e9i	0.665644	−	0.483619i
$525$	1.47555e8	+	1.07205e8i	0.0445039	+	0.0323340i
$526$	1.54751e9			0.463643
$527$	−5.26665e8	+	7.98396e8i	−0.156746	+	0.237619i
$528$	−1.52758e9			−0.451632
$529$	1.54813e9	+	1.12478e9i	0.454686	+	0.330349i
$530$	−1.95642e8	+	1.42142e8i	−0.0570817	+	0.0414723i
$531$	2.34495e9	+	7.21701e9i	0.679677	+	2.09183i
$532$	−3.62563e9			−1.04398
$533$	3.62184e9			1.03606
$534$	1.56001e9	+	4.80122e9i	0.443336	+	1.36445i
$535$	1.92136e9	−	5.91335e9i	0.542464	−	1.66953i
$536$	6.67842e8	−	2.05541e9i	0.187326	−	0.576529i
$537$	5.15600e9	+	3.74605e9i	1.43682	+	1.04391i
$538$	−6.55056e8	−	2.01606e9i	−0.181360	−	0.558168i
$539$	5.07904e9	+	3.69014e9i	1.39708	+	1.01504i
$540$	2.08903e9	−	1.51777e9i	0.570908	−	0.414789i
$541$	−1.10940e9	+	3.41437e9i	−0.301229	+	0.927087i	0.679829	+	0.733371i	$0.262054\pi$
$541$	−1.10940e9	+	3.41437e9i	−0.301229	+	0.927087i	−0.981058	+	0.193716i	$0.937946\pi$
$542$	−2.70280e9	+	1.96370e9i	−0.729150	+	0.529758i
$543$	−2.99060e9	+	2.17280e9i	−0.801602	+	0.582398i
$544$	−5.83892e7	+	1.79703e8i	−0.0155502	+	0.0478586i
$545$	−3.68884e9	+	2.68010e9i	−0.976117	+	0.709190i
$546$	6.06422e9	+	4.40591e9i	1.59441	+	1.15841i
$547$	−3.49476e8	−	1.07558e9i	−0.0912982	−	0.280987i	0.894973	−	0.446120i	$-0.147195\pi$
$547$	−3.49476e8	−	1.07558e9i	−0.0912982	−	0.280987i	−0.986271	+	0.165133i	$0.947195\pi$
$548$	2.09707e9	+	1.52361e9i	0.544355	+	0.395497i
$549$	−1.51855e9	+	4.67362e9i	−0.391675	+	1.20545i
$550$	−1.85345e7	+	5.70433e7i	−0.00475020	+	0.0146196i
$551$	2.15580e9	+	6.63488e9i	0.549007	+	1.68967i
$552$	−1.55561e9			−0.393654
$553$	−6.20922e9			−1.56134
$554$	6.70713e8	+	2.06424e9i	0.167592	+	0.515794i
$555$	5.40548e8	−	3.92731e8i	0.134217	−	0.0975146i
$556$	−2.24291e9	−	1.62957e9i	−0.553414	−	0.402079i
$557$	−2.28630e9			−0.560582			−0.280291	−	0.959915i	$-0.590431\pi$
$557$	−2.28630e9			−0.560582			−0.280291	+	0.959915i	$0.590431\pi$
$558$	−4.97296e9	+	1.86813e9i	−1.21170	+	0.455183i
$559$	−3.97303e9			−0.962012
$560$	−1.37114e9	−	9.96193e8i	−0.329932	−	0.239709i
$561$	−1.73981e9	+	1.26405e9i	−0.416037	+	0.302268i
$562$	1.36732e9	+	4.20817e9i	0.324932	+	1.00004i
$563$	−3.23731e9			−0.764548			−0.382274	−	0.924049i	$-0.624859\pi$
$563$	−3.23731e9			−0.764548			−0.382274	+	0.924049i	$0.624859\pi$
$564$	2.63135e9			0.617592
$565$	7.44449e8	+	2.29118e9i	0.173646	+	0.534428i
$566$	1.71298e9	−	5.27200e9i	0.397094	−	1.22213i
$567$	−1.12706e9	+	3.46875e9i	−0.259662	+	0.799156i
$568$	−8.12067e8	−	5.90002e8i	−0.185940	−	0.135093i
$569$	1.72477e9	+	5.30830e9i	0.392499	+	1.20799i	0.930892	+	0.365294i	$0.119031\pi$
$569$	1.72477e9	+	5.30830e9i	0.392499	+	1.20799i	−0.538393	+	0.842694i	$0.680969\pi$
$570$	5.55699e9	+	4.03739e9i	1.25683	+	0.913142i
$571$	−1.76532e8	+	1.28258e8i	−0.0396822	+	0.0288308i	−0.607450	−	0.794358i	$-0.707807\pi$
$571$	−1.76532e8	+	1.28258e8i	−0.0396822	+	0.0288308i	0.567767	+	0.823189i	$0.307807\pi$
$572$	−7.61728e8	+	2.34436e9i	−0.170182	+	0.523767i
$573$	7.79103e9	−	5.66051e9i	1.73003	−	1.25694i
$574$	4.22807e9	−	3.07187e9i	0.933148	−	0.677971i
$575$	−1.88746e7	+	5.80901e7i	−0.00414039	+	0.0127428i
$576$	−8.49028e8	+	6.16855e8i	−0.185116	+	0.134494i
$577$	6.00175e9	+	4.36053e9i	1.30066	+	0.944983i	0.999962	−	0.00873751i	$-0.00278127\pi$
$577$	6.00175e9	+	4.36053e9i	1.30066	+	0.944983i	0.300695	+	0.953720i	$0.402781\pi$
$578$	−9.32213e8	−	2.86906e9i	−0.200802	−	0.618004i
$579$	−2.03274e9	−	1.47687e9i	−0.435218	−	0.316205i
$580$	−1.00774e9	+	3.10151e9i	−0.214463	+	0.660048i
$581$	3.31300e9	−	1.01964e10i	0.700818	−	2.15690i
$582$	−2.73804e9	−	8.42681e9i	−0.575717	−	1.77187i
$583$	5.07520e8			0.106075
$584$	−2.99424e9			−0.622074
$585$	−2.83796e9	−	8.73434e9i	−0.586085	−	1.80378i
$586$	2.19516e9	−	1.59488e9i	0.450634	−	0.327405i
$587$	1.90246e9	+	1.38222e9i	0.388224	+	0.282061i	0.764727	−	0.644354i	$-0.222874\pi$
$587$	1.90246e9	+	1.38222e9i	0.388224	+	0.282061i	−0.376503	+	0.926415i	$0.622874\pi$
$588$	6.66924e9			1.35287
$589$	−3.99898e9	−	5.01140e9i	−0.806390	−	1.01055i
$590$	−4.28119e9			−0.858187
$591$	−3.10101e9	−	2.25301e9i	−0.617940	−	0.448960i
$592$	−9.96756e7	+	7.24185e7i	−0.0197453	+	0.0143458i
$593$	1.40938e9	+	4.33762e9i	0.277547	+	0.854201i	0.988534	+	0.150996i	$0.0482481\pi$
$593$	1.40938e9	+	4.33762e9i	0.277547	+	0.854201i	−0.710988	+	0.703204i	$0.751752\pi$
$594$	−5.41920e9			−1.06092
$595$	−2.38597e9			−0.464361
$596$	−9.24009e8	−	2.84381e9i	−0.178778	−	0.550223i
$597$	−1.98441e9	+	6.10740e9i	−0.381700	+	1.17475i
$598$	−7.75707e8	+	2.38738e9i	−0.148335	+	0.456528i
$599$	1.79321e8	+	1.30285e8i	0.0340909	+	0.0247685i	0.604700	−	0.796453i	$-0.293293\pi$
$599$	1.79321e8	+	1.30285e8i	0.0340909	+	0.0247685i	−0.570609	+	0.821222i	$0.693293\pi$
$600$	1.96894e7	+	6.05978e7i	0.00372138	+	0.0114532i
$601$	−2.48595e9	−	1.80615e9i	−0.467124	−	0.339385i	0.329196	−	0.944262i	$-0.393222\pi$
$601$	−2.48595e9	−	1.80615e9i	−0.467124	−	0.339385i	−0.796319	+	0.604877i	$0.793222\pi$
$602$	−4.63804e9	+	3.36974e9i	−0.866457	+	0.629518i
$603$	5.22190e9	−	1.60713e10i	0.969879	−	2.98498i
$604$	1.97495e9	−	1.43488e9i	0.364692	−	0.264964i
$605$	6.80924e8	−	4.94721e8i	0.125013	−	0.0908272i
$606$	−3.39011e9	+	1.04337e10i	−0.618813	+	1.90451i
$607$	9.67949e8	−	7.03256e8i	0.175668	−	0.127630i	−0.496477	−	0.868050i	$-0.665373\pi$
$607$	9.67949e8	−	7.03256e8i	0.175668	−	0.127630i	0.672145	+	0.740420i	$0.265373\pi$
$608$	−1.02469e9	−	7.44483e8i	−0.184898	−	0.134336i
$609$	−6.43128e9	−	1.97935e10i	−1.15382	−	3.55108i
$610$	−2.24294e9	−	1.62959e9i	−0.400095	−	0.290686i
$611$	1.31212e9	−	4.03830e9i	0.232718	−	0.716234i
$612$	−4.56549e8	+	1.40511e9i	−0.0805113	+	0.247788i
$613$	8.53883e7	+	2.62798e8i	0.0149722	+	0.0460798i	0.958264	−	0.285886i	$-0.0922880\pi$
$613$	8.53883e7	+	2.62798e8i	0.0149722	+	0.0460798i	−0.943291	+	0.331966i	$0.892288\pi$
$614$	2.24176e9			0.390841
$615$	−9.90108e9			−1.71640
$616$	1.09915e9	+	3.38282e9i	0.189462	+	0.583105i
$617$	−1.49251e9	+	1.08437e9i	−0.255811	+	0.185858i	−0.708298	−	0.705913i	$-0.750537\pi$
$617$	−1.49251e9	+	1.08437e9i	−0.255811	+	0.185858i	0.452487	+	0.891771i	$0.350537\pi$
$618$	4.68571e9	+	3.40437e9i	0.798574	+	0.580198i
$619$	−5.23347e9			−0.886895			−0.443448	−	0.896300i	$-0.646245\pi$
$619$	−5.23347e9			−0.886895			−0.443448	+	0.896300i	$0.646245\pi$
$620$	−1.35381e8	−	2.99399e9i	−0.0228132	−	0.504521i
$621$	−5.51865e9			−0.924724
$622$	−2.24770e9	−	1.63305e9i	−0.374517	−	0.272103i
$623$	9.50982e9	−	6.90929e9i	1.57567	−	1.14479i
$624$	8.09193e8	+	2.49044e9i	0.133323	+	0.410327i
$625$	−6.22458e9			−1.01984
$626$	3.53836e9			0.576490
$627$	−4.45464e9	−	1.37100e10i	−0.721733	−	2.22126i
$628$	3.39736e8	−	1.04560e9i	0.0547372	−	0.168464i
$629$	−5.35986e7	+	1.64960e8i	−0.00858769	+	0.0264302i
$630$	−1.07210e10	−	7.78929e9i	−1.70822	−	1.24110i
$631$	2.98277e9	+	9.18003e9i	0.472626	+	1.45459i	0.849133	+	0.528179i	$0.177125\pi$
$631$	2.98277e9	+	9.18003e9i	0.472626	+	1.45459i	−0.376508	+	0.926414i	$0.622875\pi$
$632$	−1.75488e9	−	1.27499e9i	−0.276527	−	0.200909i
$633$	1.79142e9	−	1.30154e9i	0.280727	−	0.203960i
$634$	−1.50120e9	+	4.62021e9i	−0.233951	+	0.720029i
$635$	−5.87027e9	+	4.26500e9i	−0.909808	+	0.661014i
$636$	4.36177e8	−	3.16901e8i	0.0672300	−	0.0488454i
$637$	3.32562e9	−	1.02352e10i	0.509782	−	1.56895i
$638$	5.53699e9	−	4.02286e9i	0.844114	−	0.613285i
$639$	−6.34960e9	−	4.61326e9i	−0.962706	−	0.699447i
$640$	−1.82961e8	−	5.63098e8i	−0.0275886	−	0.0849090i
$641$	1.15736e9	+	8.40870e8i	0.173566	+	0.126103i	0.671177	−	0.741297i	$-0.265789\pi$
$641$	1.15736e9	+	8.40870e8i	0.173566	+	0.126103i	−0.497611	+	0.867400i	$0.665789\pi$
$642$	−4.28361e9	+	1.31836e10i	−0.638906	+	1.96635i
$643$	9.07492e8	−	2.79297e9i	0.134618	−	0.414313i	−0.860912	−	0.508754i	$-0.830106\pi$
$643$	9.07492e8	−	2.79297e9i	0.134618	−	0.414313i	0.995530	+	0.0944410i	$0.0301064\pi$
$644$	1.11932e9	+	3.44490e9i	0.165140	+	0.508249i
$645$	1.08611e10			1.59374
$646$	−1.78310e9			−0.260233
$647$	3.18705e9	+	9.80873e9i	0.462619	+	1.42380i	0.861952	+	0.506990i	$0.169242\pi$
$647$	3.18705e9	+	9.80873e9i	0.462619	+	1.42380i	−0.399333	+	0.916806i	$0.630758\pi$
$648$	−1.03081e9	+	7.48924e8i	−0.148821	+	0.108125i
$649$	7.26893e9	+	5.28119e9i	1.04379	+	0.758359i
$650$	1.02817e8			0.0146848
$651$	1.19299e10	+	1.49502e10i	1.69474	+	2.12380i
$652$	−7.07326e8			−0.0999431
$653$	2.52916e9	+	1.83754e9i	0.355451	+	0.258250i	0.751152	−	0.660129i	$-0.229498\pi$
$653$	2.52916e9	+	1.83754e9i	0.355451	+	0.258250i	−0.395701	+	0.918379i	$0.629498\pi$
$654$	8.22413e9	−	5.97518e9i	1.14966	−	0.835274i
$655$	3.69397e9	+	1.13689e10i	0.513629	+	1.58079i
$656$	1.82573e9			0.252507
$657$	−2.34122e10			−3.22079
$658$	−1.89335e9	−	5.82713e9i	−0.259083	−	0.797377i
$659$	−5.79151e8	+	1.78244e9i	−0.0788303	+	0.242615i	−0.982704	−	0.185186i	$-0.940711\pi$
$659$	−5.79151e8	+	1.78244e9i	−0.0788303	+	0.242615i	0.903873	+	0.427800i	$0.140711\pi$
$660$	2.08235e9	−	6.40881e9i	0.281936	−	0.867708i
$661$	8.45755e9	+	6.14477e9i	1.13904	+	0.827562i	0.986985	−	0.160810i	$-0.0514106\pi$
$661$	8.45755e9	+	6.14477e9i	1.13904	+	0.827562i	0.152056	+	0.988372i	$0.451411\pi$
$662$	−1.44045e9	−	4.43324e9i	−0.192972	−	0.593906i
$663$	2.98241e9	+	2.16685e9i	0.397439	+	0.288756i
$664$	3.03005e9	−	2.20146e9i	0.401663	−	0.291825i
$665$	4.94235e9	−	1.52110e10i	0.651715	−	2.00577i
$666$	−7.79369e8	+	5.66245e8i	−0.102231	+	0.0742753i
$667$	5.63860e9	−	4.09668e9i	0.735750	−	0.534554i
$668$	−6.10800e8	+	1.87985e9i	−0.0792833	+	0.244009i
$669$	1.33947e9	−	9.73183e8i	0.172959	−	0.125662i
$670$	7.71288e9	+	5.60373e9i	0.990729	+	0.719806i
$671$	1.79801e9	+	5.53369e9i	0.229754	+	0.707109i
$672$	3.05691e9	+	2.22098e9i	0.388589	+	0.282326i
$673$	−1.17833e9	+	3.62654e9i	−0.149010	+	0.458606i	−0.997505	−	0.0705979i	$-0.977509\pi$
$673$	−1.17833e9	+	3.62654e9i	−0.149010	+	0.458606i	0.848495	+	0.529204i	$0.177509\pi$
$674$	−1.67360e9	+	5.15081e9i	−0.210543	+	0.647986i
$675$	6.98497e7	+	2.14975e8i	0.00874181	+	0.0269045i
$676$	2.09649e8			0.0261023
$677$	7.41514e9			0.918457			0.459229	−	0.888318i	$-0.348126\pi$
$677$	7.41514e9			0.918457			0.459229	+	0.888318i	$0.348126\pi$
$678$	−1.65972e9	−	5.10810e9i	−0.204518	−	0.629442i
$679$	−1.66911e10	+	1.21268e10i	−2.04616	+	1.48662i
$680$	−6.74334e8	−	4.89933e8i	−0.0822421	−	0.0597524i
$681$	−6.07425e9			−0.737018
$682$	−3.46346e9	+	5.25042e9i	−0.418085	+	0.633795i
$683$	1.50893e9			0.181216			0.0906082	−	0.995887i	$-0.471119\pi$
$683$	1.50893e9			0.181216			0.0906082	+	0.995887i	$0.471119\pi$
$684$	−8.01214e9	−	5.82116e9i	−0.957309	−	0.695526i
$685$	−9.25084e9	+	6.72113e9i	−1.09967	+	0.798961i
$686$	−1.81490e9	−	5.58570e9i	−0.214644	−	0.660607i
$687$	−3.15281e9			−0.370979
$688$	−2.00276e9			−0.234461
$689$	−2.68845e8	−	8.27419e8i	−0.0313137	−	0.0963736i
$690$	2.12056e9	−	6.52642e9i	0.245742	−	0.756316i
$691$	−1.65926e9	+	5.10668e9i	−0.191312	+	0.588797i	0.808688	+	0.588238i	$0.200178\pi$
$691$	−1.65926e9	+	5.10668e9i	−0.191312	+	0.588797i	−1.00000		0.000559418i	$0.999822\pi$
$692$	−5.50997e9	−	4.00323e9i	−0.632088	−	0.459239i
$693$	8.59429e9	+	2.64505e10i	0.980943	+	3.01903i
$694$	−6.11704e8	−	4.44429e8i	−0.0694678	−	0.0504713i
$695$	9.89417e9	−	7.18854e9i	1.11798	−	0.812257i
$696$	2.24673e9	−	6.91471e9i	0.252591	−	0.777395i
$697$	2.07939e9	−	1.51076e9i	0.232606	−	0.168998i
$698$	−7.61781e9	+	5.53467e9i	−0.847884	+	0.616024i
$699$	3.52310e9	−	1.08430e10i	0.390171	−	1.20082i
$700$	1.20027e8	−	8.72044e7i	0.0132262	−	0.00960938i
$701$	−6.37677e9	−	4.63299e9i	−0.699178	−	0.507982i	0.180487	−	0.983577i	$-0.442233\pi$
$701$	−6.37677e9	−	4.63299e9i	−0.699178	−	0.507982i	−0.879664	+	0.475595i	$0.842233\pi$
$702$	2.87067e9	+	8.83502e9i	0.313187	+	0.963890i
$703$	−9.40622e8	−	6.83402e8i	−0.102111	−	0.0741878i
$704$	−3.83980e8	+	1.18177e9i	−0.0414767	+	0.127652i
$705$	−3.58698e9	+	1.10396e10i	−0.385537	+	1.18656i
$706$	−5.47069e7	−	1.68370e8i	−0.00585094	−	0.0180073i
$707$	2.55447e10			2.71852
$708$	9.54475e9			1.01076
$709$	2.73974e9	+	8.43206e9i	0.288701	+	0.888530i	0.985265	+	0.171035i	$0.0547112\pi$
$709$	2.73974e9	+	8.43206e9i	0.288701	+	0.888530i	−0.696564	+	0.717495i	$0.745289\pi$
$710$	3.58228e9	−	2.60268e9i	0.375626	−	0.272908i
$711$	−1.37215e10	−	9.96925e9i	−1.43172	−	1.04021i
$712$	4.10646e9			0.426371
$713$	−3.52702e9	+	5.34677e9i	−0.364413	+	0.552431i
$714$	5.31943e9			0.546917
$715$	−8.79717e9	−	6.39152e9i	−0.900060	−	0.653932i
$716$	4.19406e9	−	3.04716e9i	0.427011	−	0.310242i
$717$	3.68710e9	+	1.13477e10i	0.373566	+	1.14972i
$718$	−7.87103e9			−0.793590
$719$	3.78758e9			0.380024			0.190012	−	0.981782i	$-0.439147\pi$
$719$	3.78758e9			0.380024			0.190012	+	0.981782i	$0.439147\pi$
$720$	−1.43059e9	−	4.40289e9i	−0.142840	−	0.439617i
$721$	4.16744e9	−	1.28261e10i	0.414091	−	1.27444i
$722$	1.48379e9	−	4.56663e9i	0.146721	−	0.451560i
$723$	−1.06086e10	−	7.70760e9i	−1.04394	−	0.758464i
$724$	9.29191e8	+	2.85975e9i	0.0909955	+	0.280055i
$725$	−2.30951e8	−	1.67796e8i	−0.0225080	−	0.0163530i
$726$	−1.51810e9	+	1.10296e9i	−0.147238	+	0.106975i
$727$	−2.25883e9	+	6.95195e9i	−0.218028	+	0.671021i	0.780897	+	0.624660i	$0.214762\pi$
$727$	−2.25883e9	+	6.95195e9i	−0.218028	+	0.671021i	−0.998925	+	0.0463611i	$0.985238\pi$
$728$	4.93284e9	−	3.58392e9i	0.473846	−	0.344269i
$729$	1.18341e10	−	8.59801e9i	1.13133	−	0.821962i
$730$	4.08166e9	−	1.25621e10i	0.388335	−	1.19517i
$731$	−2.28101e9	+	1.65725e9i	−0.215982	+	0.156920i
$732$	5.00055e9	+	3.63312e9i	0.471226	+	0.342366i
$733$	7.93343e8	+	2.44166e9i	0.0744042	+	0.228993i	0.981341	−	0.192273i	$-0.0615860\pi$
$733$	7.93343e8	+	2.44166e9i	0.0744042	+	0.228993i	−0.906937	+	0.421266i	$0.861586\pi$
$734$	−8.15167e9	−	5.92254e9i	−0.760870	−	0.552804i
$735$	−9.09130e9	+	2.79801e10i	−0.844540	+	2.59923i
$736$	−3.91026e8	+	1.20345e9i	−0.0361521	+	0.111265i
$737$	−6.18287e9	−	1.90289e10i	−0.568923	−	1.75097i
$738$	1.42755e10			1.30736
$739$	−6.28882e9			−0.573210			−0.286605	−	0.958049i	$-0.592527\pi$
$739$	−6.28882e9			−0.573210			−0.286605	+	0.958049i	$0.592527\pi$
$740$	−1.67950e8	−	5.16898e8i	−0.0152360	−	0.0468915i
$741$	−1.99919e10	+	1.45250e10i	−1.80505	+	1.31145i
$742$	−1.01562e9	−	7.37893e8i	−0.0912680	−	0.0663101i
$743$	−8.15169e9			−0.729100			−0.364550	−	0.931184i	$-0.618777\pi$
$743$	−8.15169e9			−0.729100			−0.364550	+	0.931184i	$0.618777\pi$
$744$	3.01827e8	+	6.67498e9i	0.0268691	+	0.594217i
$745$	1.31905e10			1.16873
$746$	5.26106e8	+	3.82238e8i	0.0463967	+	0.0337092i
$747$	2.36922e10	−	1.72134e10i	2.07961	−	1.51093i
$748$	5.40566e8	+	1.66369e9i	0.0472273	+	0.145351i
$749$	3.22773e10			2.80679
$750$	1.36020e10			1.17730
$751$	6.08234e9	+	1.87195e10i	0.524000	+	1.61271i	0.766285	+	0.642501i	$0.222103\pi$
$751$	6.08234e9	+	1.87195e10i	0.524000	+	1.61271i	−0.242285	+	0.970205i	$0.577897\pi$
$752$	6.61429e8	−	2.03567e9i	0.0567180	−	0.174560i
$753$	−7.18939e9	+	2.21267e10i	−0.613634	+	1.88857i
$754$	−9.49160e9	−	6.89605e9i	−0.806380	−	0.585869i
$755$	3.32773e9	+	1.02417e10i	0.281406	+	0.866079i
$756$	1.08446e10	+	7.87908e9i	0.912826	+	0.663207i
$757$	4.56286e9	−	3.31511e9i	0.382297	−	0.277755i	−0.379995	−	0.924989i	$-0.624074\pi$
$757$	4.56286e9	−	3.31511e9i	0.382297	−	0.277755i	0.762292	+	0.647234i	$0.224074\pi$
$758$	−3.85864e9	+	1.18757e10i	−0.321804	+	0.990412i
$759$	−1.16513e10	+	8.46517e9i	−0.967227	+	0.702732i
$760$	4.52024e9	−	3.28415e9i	0.373520	−	0.271378i
$761$	5.45006e8	−	1.67736e9i	0.0448286	−	0.137968i	−0.926137	−	0.377187i	$-0.876891\pi$
$761$	5.45006e8	−	1.67736e9i	0.0448286	−	0.137968i	0.970966	+	0.239219i	$0.0768914\pi$
$762$	1.30876e10	−	9.50866e9i	1.07156	−	0.778533i
$763$	−1.91496e10	−	1.39130e10i	−1.56071	−	1.13393i
$764$	−2.42070e9	−	7.45016e9i	−0.196388	−	0.604420i
$765$	−5.27266e9	−	3.83081e9i	−0.425809	−	0.309368i
$766$	−4.17592e9	+	1.28522e10i	−0.335700	+	1.03318i
$767$	4.75950e9	−	1.46482e10i	0.380870	−	1.17220i
$768$	4.07906e8	+	1.25541e9i	0.0324935	+	0.100005i
$769$	−1.71070e10			−1.35654			−0.678269	−	0.734814i	$-0.737269\pi$
$769$	−1.71070e10			−1.35654			−0.678269	+	0.734814i	$0.737269\pi$
$770$	−1.56906e10			−1.23858
$771$	−1.52106e9	−	4.68133e9i	−0.119524	−	0.367857i
$772$	−1.65350e9	+	1.20134e9i	−0.129343	+	0.0939733i
$773$	−2.20397e8	−	1.60127e8i	−0.0171623	−	0.0124692i	0.579171	−	0.815206i	$-0.303376\pi$
$773$	−2.20397e8	−	1.60127e8i	−0.0171623	−	0.0124692i	−0.596333	+	0.802737i	$0.703376\pi$
$774$	−1.56597e10			−1.21392
$775$	2.52921e8	+	6.97183e7i	0.0195177	+	0.00538011i
$776$	−7.20741e9			−0.553685
$777$	2.80610e9	+	2.03875e9i	0.214600	+	0.155916i
$778$	3.76964e9	−	2.73881e9i	0.286993	−	0.208513i
$779$	5.32410e9	+	1.63859e10i	0.403520	+	1.24191i
$780$	−1.15515e10			−0.871577
$781$	−9.29288e9			−0.698026
$782$	5.50486e8	+	1.69422e9i	0.0411644	+	0.126691i
$783$	7.97043e9	−	2.45305e10i	0.593356	−	1.82616i
$784$	1.67641e9	−	5.15946e9i	0.124244	−	0.382383i
$785$	3.92360e9	+	2.85066e9i	0.289495	+	0.210330i
$786$	−8.23558e9	−	2.53465e10i	−0.604944	−	1.86183i
$787$	−3.70279e9	−	2.69023e9i	−0.270781	−	0.196734i	0.444106	−	0.895974i	$-0.353521\pi$
$787$	−3.70279e9	−	2.69023e9i	−0.270781	−	0.196734i	−0.714886	+	0.699241i	$0.753521\pi$
$788$	−2.52246e9	+	1.83268e9i	−0.183647	+	0.133427i
$789$	4.70310e9	−	1.44746e10i	0.340890	−	1.04915i
$790$	7.74131e9	−	5.62439e9i	0.558624	−	0.405864i
$791$	−1.01177e10	+	7.35091e9i	−0.726879	+	0.528109i
$792$	−3.00236e9	+	9.24031e9i	−0.214746	+	0.660920i
$793$	8.06923e9	−	5.86264e9i	0.574614	−	0.417481i
$794$	−5.34800e8	−	3.88555e8i	−0.0379158	−	0.0275474i
$795$	7.34945e8	+	2.26193e9i	0.0518764	+	0.159659i
$796$	4.22600e9	+	3.07037e9i	0.296985	+	0.215772i
$797$	−4.61116e9	+	1.41917e10i	−0.322631	+	0.992955i	0.649868	+	0.760047i	$0.274824\pi$
$797$	−4.61116e9	+	1.41917e10i	−0.322631	+	0.992955i	−0.972499	+	0.232908i	$0.925176\pi$
$798$	−1.10188e10	+	3.39124e10i	−0.767580	+	2.36237i
$799$	−9.31158e8	−	2.86581e9i	−0.0645817	−	0.198762i
$800$	5.18290e7			0.00357897
$801$	3.21087e10			2.20754
$802$	2.72145e9	+	8.37575e9i	0.186290	+	0.573342i
$803$	−2.24265e10	+	1.62938e10i	−1.52847	+	1.11050i
$804$	−1.71956e10	−	1.24933e10i	−1.16687	−	0.847777i
$805$	−1.59786e10			−1.07957
$806$	1.03945e10	+	2.86527e9i	0.699249	+	0.192750i
$807$	−2.08480e10			−1.39639
$808$	7.21957e9	+	5.24532e9i	0.481472	+	0.349810i
$809$	1.33941e10	−	9.73136e9i	0.889391	−	0.646180i	−0.0463284	−	0.998926i	$-0.514752\pi$
$809$	1.33941e10	−	9.73136e9i	0.889391	−	0.646180i	0.935719	+	0.352746i	$0.114752\pi$
$810$	−1.73688e9	−	5.34555e9i	−0.114834	−	0.353423i
$811$	−1.90184e10			−1.25199			−0.625996	−	0.779826i	$-0.715307\pi$
$811$	−1.90184e10			−1.25199			−0.625996	+	0.779826i	$0.715307\pi$
$812$	−1.69292e10			−1.10966
$813$	1.01533e10	+	3.12486e10i	0.662659	+	2.03945i
$814$	−3.52476e8	+	1.08481e9i	−0.0229057	+	0.0704966i
$815$	9.64205e8	−	2.96752e9i	0.0623904	−	0.192018i
$816$	1.50340e9	+	1.09229e9i	0.0968635	+	0.0703755i
$817$	−5.84035e9	−	1.79747e10i	−0.374681	−	1.15315i
$818$	1.45697e10	+	1.05855e10i	0.930709	+	0.676200i
$819$	3.85701e10	−	2.80228e10i	2.45334	−	1.78246i
$820$	−2.48878e9	+	7.65968e9i	−0.157630	+	0.485135i
$821$	−2.21866e9	+	1.61195e9i	−0.139923	+	0.101660i	−0.655545	−	0.755156i	$-0.727561\pi$
$821$	−2.21866e9	+	1.61195e9i	−0.139923	+	0.101660i	0.515622	+	0.856816i	$0.327561\pi$
$822$	2.06244e10	−	1.49845e10i	1.29518	−	0.941004i
$823$	7.57669e9	−	2.33186e10i	0.473783	−	1.45816i	−0.373808	−	0.927506i	$-0.621948\pi$
$823$	7.57669e9	−	2.33186e10i	0.473783	−	1.45816i	0.847591	−	0.530649i	$-0.178052\pi$
$824$	3.81151e9	−	2.76922e9i	0.237330	−	0.172430i
$825$	4.77226e8	+	3.46725e8i	0.0295893	+	0.0214979i
$826$	−6.86778e9	−	2.11369e10i	−0.424020	−	1.30500i
$827$	−1.63556e9	−	1.18830e9i	−0.100553	−	0.0730563i	0.536372	−	0.843981i	$-0.319794\pi$
$827$	−1.63556e9	−	1.18830e9i	−0.100553	−	0.0730563i	−0.636926	+	0.770925i	$0.719794\pi$
$828$	−3.05746e9	+	9.40988e9i	−0.187178	+	0.576073i
$829$	−4.73216e9	+	1.45641e10i	−0.288482	+	0.887857i	0.696851	+	0.717216i	$0.254584\pi$
$829$	−4.73216e9	+	1.45641e10i	−0.288482	+	0.887857i	−0.985333	+	0.170641i	$0.945416\pi$
$830$	5.10555e9	+	1.57133e10i	0.309934	+	0.953878i
$831$	2.13463e10			1.29038
$832$	2.13006e9			0.128221
$833$	−2.36005e9	−	7.26348e9i	−0.141470	−	0.435399i
$834$	−2.20587e10	+	1.60266e10i	−1.31674	+	0.956665i
$835$	−7.05411e9	−	5.12511e9i	−0.419314	−	0.304649i
$836$	−1.17261e10			−0.694113
$837$	1.07075e9	+	2.36800e10i	0.0631176	+	1.39586i
$838$	5.74124e9			0.337017
$839$	6.58392e9	+	4.78350e9i	0.384873	+	0.279627i	0.763351	−	0.645983i	$-0.223552\pi$
$839$	6.58392e9	+	4.78350e9i	0.384873	+	0.279627i	−0.378478	+	0.925610i	$0.623552\pi$
$840$	−1.34850e10	+	9.79741e9i	−0.785005	+	0.570340i
$841$	4.73562e9	+	1.45747e10i	0.274531	+	0.844919i
$842$	−3.63201e9			−0.209679
$843$	4.35166e10			2.50183
$844$	−5.56601e8	−	1.71304e9i	−0.0318673	−	0.0980776i
$845$	−2.85787e8	+	8.79560e8i	−0.0162946	+	0.0501496i
$846$	5.17175e9	−	1.59170e10i	0.293658	−	0.903785i
$847$	3.53483e9	+	2.56821e9i	0.199883	+	0.145224i
$848$	−1.35522e8	−	4.17094e8i	−0.00763175	−	0.0234881i
$849$	−4.41057e10	−	3.20446e10i	−2.47353	−	1.79713i
$850$	5.90297e7	−	4.28876e7i	0.00329689	−	0.00239533i
$851$	−3.58944e8	+	1.10472e9i	−0.0199652	+	0.0614465i
$852$	−7.98656e9	+	5.80258e9i	−0.442406	+	0.321427i
$853$	4.34527e9	−	3.15702e9i	0.239715	−	0.174163i	−0.461441	−	0.887171i	$-0.652668\pi$
$853$	4.34527e9	−	3.15702e9i	0.239715	−	0.174163i	0.701156	+	0.713008i	$0.252668\pi$
$854$	4.44746e9	−	1.36879e10i	0.244349	−	0.752027i
$855$	3.53440e10	−	2.56789e10i	1.93390	−	1.40506i
$856$	9.12236e9	+	6.62778e9i	0.497106	+	0.361169i
$857$	−7.66395e9	−	2.35872e10i	−0.415930	−	1.28010i	−0.911417	−	0.411484i	$-0.865010\pi$
$857$	−7.66395e9	−	2.35872e10i	−0.415930	−	1.28010i	0.495487	−	0.868615i	$-0.334990\pi$
$858$	1.96130e10	+	1.42497e10i	1.06008	+	0.770192i
$859$	1.10982e10	−	3.41567e10i	0.597415	−	1.83866i	0.0551001	−	0.998481i	$-0.482452\pi$
$859$	1.10982e10	−	3.41567e10i	0.597415	−	1.83866i	0.542315	−	0.840175i	$-0.317548\pi$
$860$	2.73011e9	−	8.40241e9i	0.146364	−	0.450463i
$861$	−1.58831e10	−	4.88831e10i	−0.848054	−	2.61004i
$862$	−5.58804e9			−0.297156
$863$	5.21501e9			0.276196			0.138098	−	0.990419i	$-0.455901\pi$
$863$	5.21501e9			0.276196			0.138098	+	0.990419i	$0.455901\pi$
$864$	1.44708e9	+	4.45365e9i	0.0763297	+	0.234919i
$865$	2.43062e10	−	1.76595e10i	1.27691	−	0.927729i
$866$	1.39223e10	+	1.01152e10i	0.728450	+	0.529250i
$867$	−2.96688e10			−1.54609
$868$	1.45646e10	−	5.47128e9i	0.755925	−	0.283968i
$869$	−2.00819e10			−1.03809
$870$	2.59473e10	+	1.88519e10i	1.33591	+	0.970592i
$871$	−2.77480e10	+	2.01601e10i	−1.42288	+	1.03378i
$872$	−2.55527e9	−	7.86431e9i	−0.130506	−	0.401655i
$873$	−5.63551e10			−2.86671
$874$	−1.19412e10			−0.605006
$875$	−9.78710e9	−	3.01216e10i	−0.493885	−	1.52002i
$876$	−9.09991e9	+	2.80067e10i	−0.457376	+	1.40766i
$877$	9.37075e9	−	2.88402e10i	0.469111	−	1.44378i	−0.384626	−	0.923072i	$-0.625670\pi$
$877$	9.37075e9	−	2.88402e10i	0.469111	−	1.44378i	0.853738	−	0.520704i	$-0.174330\pi$
$878$	−1.43659e10	−	1.04374e10i	−0.716311	−	0.520430i
$879$	−8.24629e9	−	2.53795e10i	−0.409541	−	1.26044i
$880$	−4.43456e9	−	3.22190e9i	−0.219362	−	0.159376i
$881$	−9.04664e8	+	6.57277e8i	−0.0445730	+	0.0323842i	−0.609849	−	0.792518i	$-0.708770\pi$
$881$	−9.04664e8	+	6.57277e8i	−0.0445730	+	0.0323842i	0.565276	+	0.824902i	$0.308770\pi$
$882$	1.31080e10	−	4.03421e10i	0.643273	−	1.97979i
$883$	−8.98375e9	+	6.52708e9i	−0.439132	+	0.319048i	−0.785290	−	0.619128i	$-0.787486\pi$
$883$	−8.98375e9	+	6.52708e9i	−0.439132	+	0.319048i	0.346158	+	0.938176i	$0.387486\pi$
$884$	2.42599e9	−	1.76259e9i	0.118115	−	0.0858159i
$885$	−1.30111e10	+	4.00441e10i	−0.630976	+	1.94195i
$886$	−1.97787e9	+	1.43700e9i	−0.0955386	+	0.0694129i
$887$	7.47021e9	+	5.42743e9i	0.359418	+	0.261133i	0.752809	−	0.658239i	$-0.228698\pi$
$887$	7.47021e9	+	5.42743e9i	0.359418	+	0.261133i	−0.393391	+	0.919371i	$0.628698\pi$
$888$	3.74439e8	+	1.15241e9i	0.0179447	+	0.0552281i
$889$	−3.04739e10	−	2.21406e10i	−1.45469	−	1.05690i
$890$	−5.59780e9	+	1.72283e10i	−0.266166	+	0.819174i
$891$	−3.64517e9	+	1.12187e10i	−0.172642	+	0.531336i
$892$	−4.16179e8	−	1.28087e9i	−0.0196338	−	0.0604265i
$893$	2.01989e10			0.949177
$894$	−2.94078e10			−1.37651
$895$	7.06687e9	+	2.17496e10i	0.329493	+	1.01408i
$896$	2.48659e9	−	1.80662e9i	0.115485	−	0.0839050i
$897$	1.99729e10	+	1.45111e10i	0.923990	+	0.671318i
$898$	1.67022e10			0.769672
$899$	−1.86725e10	−	2.33998e10i	−0.857124	−	1.07412i
$900$	4.05254e8			0.0185301
$901$	−4.99488e8	−	3.62899e8i	−0.0227504	−	0.0165291i
$902$	1.36745e10	−	9.93509e9i	0.620423	−	0.450764i
$903$	1.74232e10	+	5.36230e10i	0.787445	+	2.42351i
$904$	−4.36893e9			−0.196692
$905$	−1.32645e10			−0.594867
$906$	−7.41905e9	−	2.28335e10i	−0.331436	−	1.02006i
$907$	−7.83628e9	+	2.41176e10i	−0.348726	+	1.07327i	0.610833	+	0.791760i	$0.290835\pi$
$907$	−7.83628e9	+	2.41176e10i	−0.348726	+	1.07327i	−0.959559	+	0.281509i	$0.909165\pi$
$908$	−1.52685e9	+	4.69917e9i	−0.0676857	+	0.208315i
$909$	5.64502e10	+	4.10135e10i	2.49283	+	1.81114i
$910$	8.31168e9	+	2.55807e10i	0.365632	+	1.12530i
$911$	2.57133e10	+	1.86818e10i	1.12679	+	0.818662i	0.985225	−	0.171266i	$-0.0547859\pi$
$911$	2.57133e10	+	1.86818e10i	1.12679	+	0.818662i	0.141567	+	0.989929i	$0.454786\pi$
$912$	−1.00777e10	+	7.32189e9i	−0.439926	+	0.319625i
$913$	1.07150e10	−	3.29773e10i	0.465954	−	1.43406i
$914$	9.16872e9	−	6.66146e9i	0.397189	−	0.288574i
$915$	−2.20590e10	+	1.60268e10i	−0.951945	+	0.691628i
$916$	−7.92507e8	+	2.43908e9i	−0.0340697	+	0.104856i
$917$	−5.02041e10	+	3.64754e10i	−2.15004	+	1.56209i
$918$	5.33344e9	+	3.87497e9i	0.227540	+	0.165318i
$919$	4.88865e9	+	1.50457e10i	0.207771	+	0.639453i	0.999588	+	0.0286951i	$0.00913519\pi$
$919$	4.88865e9	+	1.50457e10i	0.207771	+	0.639453i	−0.791817	+	0.610758i	$0.790865\pi$
$920$	−4.51594e9	−	3.28102e9i	−0.191201	−	0.138916i
$921$	6.81301e9	−	2.09683e10i	0.287363	−	0.884412i
$922$	−1.77044e9	+	5.44887e9i	−0.0743916	+	0.228954i
$923$	4.92265e9	+	1.51503e10i	0.206060	+	0.634186i
$924$	3.49817e10			1.45878
$925$	4.75766e7			0.00197650
$926$	−5.43870e9	−	1.67386e10i	−0.225090	−	0.692756i
$927$	2.98024e10	−	2.16527e10i	1.22878	−	0.892758i
$928$	−4.78462e9	−	3.47623e9i	−0.196530	−	0.142788i
$929$	−2.77208e10			−1.13436			−0.567180	−	0.823594i	$-0.691966\pi$
$929$	−2.77208e10			−1.13436			−0.567180	+	0.823594i	$0.691966\pi$
$930$	−2.84157e10	−	7.83285e9i	−1.15843	−	0.319322i
$931$	5.11947e10			2.07922
$932$	−7.50278e9	−	5.45109e9i	−0.303575	−	0.220560i
$933$	−2.21058e10	+	1.60608e10i	−0.891087	+	0.647413i
$934$	4.19137e9	+	1.28997e10i	0.168322	+	0.518043i
$935$	−7.71674e9			−0.308740
$936$	1.66551e10			0.663867
$937$	4.85951e9	+	1.49560e10i	0.192976	+	0.593920i	0.999994	+	0.00339303i	$0.00108004\pi$
$937$	4.85951e9	+	1.49560e10i	0.192976	+	0.593920i	−0.807018	+	0.590527i	$0.798920\pi$
$938$	−1.52936e10	+	4.70690e10i	−0.605064	+	1.86219i
$939$	1.07536e10	−	3.30960e10i	0.423860	−	1.30451i
$940$	7.63881e9	+	5.54992e9i	0.299970	+	0.217941i
$941$	−2.75653e9	−	8.48373e9i	−0.107845	−	0.331912i	0.882543	−	0.470232i	$-0.155830\pi$
$941$	−2.75653e9	−	8.48373e9i	−0.107845	−	0.331912i	−0.990388	+	0.138320i	$0.955830\pi$
$942$	−8.74752e9	−	6.35544e9i	−0.340962	−	0.247724i
$943$	1.39254e10	−	1.01174e10i	0.540776	−	0.392896i
$944$	2.39921e9	−	7.38402e9i	0.0928255	−	0.285687i
$945$	−4.78390e10	+	3.47570e10i	−1.84404	+	1.33977i
$946$	−1.50004e10	+	1.08984e10i	−0.576082	+	0.418548i
$947$	4.48711e7	−	1.38099e8i	0.00171689	−	0.00528403i	−0.950194	−	0.311658i	$-0.899116\pi$
$947$	4.48711e7	−	1.38099e8i	0.00171689	−	0.00528403i	0.951911	+	0.306374i	$0.0991157\pi$
$948$	−1.72590e10	+	1.25394e10i	−0.657939	+	0.478021i
$949$	3.84438e10	+	2.79311e10i	1.46014	+	1.06085i
$950$	1.51141e8	+	4.65163e8i	0.00571938	+	0.0176024i
$951$	3.86528e10	+	2.80829e10i	1.45730	+	1.05879i
$952$	1.33712e9	−	4.11523e9i	0.0502274	−	0.154584i
$953$	−1.25495e10	+	3.86232e10i	−0.469677	+	1.44552i	0.383326	+	0.923613i	$0.374779\pi$
$953$	−1.25495e10	+	3.86232e10i	−0.469677	+	1.44552i	−0.853003	+	0.521905i	$0.825221\pi$
$954$	−1.05965e9	−	3.26128e9i	−0.0395134	−	0.121610i
$955$	3.45563e10			1.28385
$956$	9.70564e9			0.359270
$957$	−2.08001e10	−	6.40163e10i	−0.767140	−	2.36101i
$958$	−3.28063e9	+	2.38351e9i	−0.120553	+	0.0875867i
$959$	−4.80232e10	−	3.48909e10i	−1.75827	−	1.27746i
$960$	−5.82298e9			−0.212420
$961$	2.36268e10	+	1.40967e10i	0.858763	+	0.512372i
$962$	1.95530e9			0.0708109
$963$	7.13283e10	+	5.18230e10i	2.57377	+	1.86995i
$964$	−8.62939e9	+	6.26962e9i	−0.310249	+	0.225409i
$965$	−2.78610e9	−	8.57473e9i	−0.0998046	−	0.307167i
$966$	3.56237e10			1.27151
$967$	−4.98473e10			−1.77275			−0.886377	−	0.462963i	$-0.846786\pi$
$967$	−4.98473e10			−1.77275			−0.886377	+	0.462963i	$0.846786\pi$
$968$	4.71679e8	+	1.45168e9i	0.0167141	+	0.0514406i
$969$	−5.41910e9	+	1.66783e10i	−0.191335	+	0.588868i
$970$	9.82491e9	−	3.02380e10i	0.345643	−	1.06378i
$971$	−1.70914e10	−	1.24176e10i	−0.599115	−	0.435283i	0.246450	−	0.969156i	$-0.420736\pi$
$971$	−1.70914e10	−	1.24176e10i	−0.599115	−	0.435283i	−0.845565	+	0.533873i	$0.820736\pi$
$972$	−2.30887e9	−	7.10596e9i	−0.0806430	−	0.248194i
$973$	5.13629e10	+	3.73173e10i	1.78753	+	1.29872i
$974$	1.27456e10	−	9.26024e9i	0.441982	−	0.321119i
$975$	3.12475e8	−	9.61698e8i	0.0107969	−	0.0332294i
$976$	4.06762e9	−	2.95530e9i	0.140044	−	0.101748i
$977$	−2.58830e10	+	1.88051e10i	−0.887941	+	0.645127i	−0.935340	−	0.353749i	$-0.884907\pi$
$977$	−2.58830e10	+	1.88051e10i	−0.887941	+	0.645127i	0.0473996	+	0.998876i	$0.484907\pi$
$978$	−2.14966e9	+	6.61597e9i	−0.0734825	+	0.226156i
$979$	3.07568e10	−	2.23461e10i	1.04762	−	0.761137i
$980$	1.93608e10	+	1.40664e10i	0.657101	+	0.477412i
$981$	−1.99798e10	−	6.14915e10i	−0.675694	−	2.07957i
$982$	−3.67469e9	−	2.66982e9i	−0.123831	−	0.0899688i
$983$	−7.30137e7	+	2.24713e8i	−0.00245170	+	0.00754555i	−0.952275	−	0.305242i	$-0.901263\pi$
$983$	−7.30137e7	+	2.24713e8i	−0.00245170	+	0.00754555i	0.949823	+	0.312787i	$0.101263\pi$
$984$	5.54865e9	−	1.70770e10i	0.185654	−	0.571384i
$985$	−4.25028e9	−	1.30810e10i	−0.141707	−	0.436128i
$986$	−8.32588e9			−0.276606
$987$	−6.02582e10			−1.99483
$988$	6.21156e9	+	1.91172e10i	0.204904	+	0.630631i
$989$	−1.52757e10	+	1.10984e10i	−0.502127	+	0.364817i
$990$	−3.46741e10	−	2.51922e10i	−1.13575	−	0.825170i
$991$	1.91043e10			0.623554			0.311777	−	0.950155i	$-0.399076\pi$
$991$	1.91043e10			0.623554			0.311777	+	0.950155i	$0.399076\pi$
$992$	5.23978e9	+	1.44436e9i	0.170421	+	0.0469768i
$993$	−4.58440e10			−1.48580
$994$	1.85964e10	+	1.35111e10i	0.600589	+	0.436353i
$995$	−1.86422e10	+	1.35443e10i	−0.599952	+	0.435890i
$996$	−1.13826e10	−	3.50321e10i	−0.365035	−	1.12346i
$997$	2.37387e9			0.0758618			0.0379309	−	0.999280i	$-0.487923\pi$
$997$	2.37387e9			0.0758618			0.0379309	+	0.999280i	$0.487923\pi$
$998$	1.40873e10			0.448612
$999$	1.32835e9	+	4.08824e9i	0.0421535	+	0.129735i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.8.d.a.33.1	✓	40
31.16	even	5	inner	62.8.d.a.47.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.8.d.a.33.1	✓	40	1.1	even	1	trivial
62.8.d.a.47.1	yes	40	31.16	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	62.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-6.47214 - 4.70228i) q^{2} +(-63.6525 + 46.2463i) q^{3} +(19.7771 + 60.8676i) q^{4} -282.324 q^{5} +629.431 q^{6} +(-452.897 - 1393.87i) q^{7} +(158.217 - 486.941i) q^{8} +(1237.11 - 3807.42i) q^{9} +(1827.24 + 1327.57i) q^{10} +(-1464.77 - 4508.09i) q^{11} +(-4073.76 - 2959.76i) q^{12} +(-6573.69 + 4776.07i) q^{13} +(-3623.18 + 11151.0i) q^{14} +(17970.6 - 13056.4i) q^{15} +(-3313.73 + 2407.57i) q^{16} +(-1781.90 + 5484.12i) q^{17} +(-25910.3 + 18824.9i) q^{18} +(-31271.2 - 22719.8i) q^{19} +(-5583.54 - 17184.4i) q^{20} +(93289.5 + 67778.8i) q^{21} +(-11718.1 + 36064.7i) q^{22} +(-11933.2 + 36726.5i) q^{23} +(12448.3 + 38311.9i) q^{24} +1581.69 q^{25} +65004.3 q^{26} +(44161.3 + 135914. i) q^{27} +(75884.8 - 55133.5i) q^{28} +(-146015. - 106086. i) q^{29} -177703. q^{30} +(159905. + 44078.3i) q^{31} +32768.0 q^{32} +(301718. + 219211. i) q^{33} +(37320.5 - 27115.0i) q^{34} +(127864. + 393524. i) q^{35} +256215. q^{36} +30079.5 q^{37} +(95556.2 + 294092. i) q^{38} +(197557. - 608017. i) q^{39} +(-44668.3 + 137475. i) q^{40} +(-360607. - 261997. i) q^{41} +(-285067. - 877347. i) q^{42} +(395574. + 287401. i) q^{43} +(245428. - 178314. i) q^{44} +(-349264. + 1.07493e6i) q^{45} +(249931. - 181586. i) q^{46} +(-422764. + 307156. i) q^{47} +(99586.4 - 306496. i) q^{48} +(-1.07151e6 + 778497. i) q^{49} +(-10236.9 - 7437.57i) q^{50} +(-140198. - 431484. i) q^{51} +(-420716. - 305668. i) q^{52} +(-33086.4 + 101830. i) q^{53} +(353290. - 1.08732e6i) q^{54} +(413538. + 1.27274e6i) q^{55} -750390. q^{56} +3.04120e6 q^{57} +(446182. + 1.37321e6i) q^{58} +(-1.53350e6 + 1.11415e6i) q^{59} +(1.15012e6 + 835611. i) q^{60} -1.22750e6 q^{61} +(-827661. - 1.03720e6i) q^{62} -5.86735e6 q^{63} +(-212079. - 154084. i) q^{64} +(1.85591e6 - 1.34840e6i) q^{65} +(-921969. - 2.83753e6i) q^{66} +4.22106e6 q^{67} -369046. q^{68} +(-938887. - 2.88960e6i) q^{69} +(1.02291e6 - 3.14819e6i) q^{70} +(605825. - 1.86454e6i) q^{71} +(-1.65826e6 - 1.20479e6i) q^{72} +(-1.80717e6 - 5.56190e6i) q^{73} +(-194679. - 141442. i) q^{74} +(-100679. + 73147.4i) q^{75} +(764449. - 2.35273e6i) q^{76} +(-5.62032e6 + 4.08340e6i) q^{77} +(-4.13768e6 + 3.00620e6i) q^{78} +(1.30919e6 - 4.02926e6i) q^{79} +(935546. - 679714. i) q^{80} +(-2.01329e6 - 1.46274e6i) q^{81} +(1.10192e6 + 3.39136e6i) q^{82} +(5.91807e6 + 4.29973e6i) q^{83} +(-2.28054e6 + 7.01878e6i) q^{84} +(503072. - 1.54830e6i) q^{85} +(-1.20877e6 - 3.72020e6i) q^{86} +1.42003e7 q^{87} -2.42692e6 q^{88} +(2.47845e6 + 7.62788e6i) q^{89} +(7.31509e6 - 5.31472e6i) q^{90} +(9.63445e6 + 6.99983e6i) q^{91} -2.47146e6 q^{92} +(-1.22168e7 + 4.58933e6i) q^{93} +4.18052e6 q^{94} +(8.82859e6 + 6.41435e6i) q^{95} +(-2.08577e6 + 1.51540e6i) q^{96} +(-4.35002e6 - 1.33880e7i) q^{97} +1.05957e7 q^{98} -1.89763e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 80 q^{2} + 28 q^{3} - 640 q^{4} + 168 q^{5} - 1936 q^{6} + 1402 q^{7} - 5120 q^{8} - 6164 q^{9} - 1496 q^{10} - 3402 q^{11} + 1792 q^{12} + 6413 q^{13} + 11216 q^{14} + 46465 q^{15} - 40960 q^{16}+ \cdots + 13336614 q^{99}+O(q^{100}) \) 40 * q - 80 * q^2 + 28 * q^3 - 640 * q^4 + 168 * q^5 - 1936 * q^6 + 1402 * q^7 - 5120 * q^8 - 6164 * q^9 - 1496 * q^10 - 3402 * q^11 + 1792 * q^12 + 6413 * q^13 + 11216 * q^14 + 46465 * q^15 - 40960 * q^16 + 17155 * q^17 - 98152 * q^18 + 67290 * q^19 + 6592 * q^20 + 16727 * q^21 - 27216 * q^22 + 2051 * q^23 + 47616 * q^24 + 787196 * q^25 - 214576 * q^26 + 603289 * q^27 - 62592 * q^28 + 95739 * q^29 - 369200 * q^30 + 540003 * q^31 + 1310720 * q^32 + 941656 * q^33 + 290520 * q^34 - 638364 * q^35 + 2359424 * q^36 + 843716 * q^37 - 169080 * q^38 + 827496 * q^39 + 52736 * q^40 + 175557 * q^41 + 1299656 * q^42 + 566562 * q^43 + 441152 * q^44 - 2450173 * q^45 + 484128 * q^46 - 2289258 * q^47 + 380928 * q^48 - 1290090 * q^49 - 2003912 * q^50 + 351796 * q^51 + 410432 * q^52 - 741339 * q^53 + 4826312 * q^54 - 755935 * q^55 - 434176 * q^56 - 8091472 * q^57 - 1476568 * q^58 - 8176986 * q^59 + 2973760 * q^60 - 10479540 * q^61 + 6613544 * q^62 - 10121022 * q^63 - 2621440 * q^64 + 9085330 * q^65 - 1581152 * q^66 + 7646158 * q^67 - 6844160 * q^68 - 5432460 * q^69 - 5106912 * q^70 - 24632815 * q^71 - 6281728 * q^72 - 11099311 * q^73 - 3436312 * q^74 + 11990582 * q^75 - 1352640 * q^76 + 8000688 * q^77 - 10937992 * q^78 + 10390986 * q^79 - 765952 * q^80 - 23584945 * q^81 + 2535096 * q^82 + 36507958 * q^83 + 10397248 * q^84 + 23914083 * q^85 + 5244176 * q^86 + 16619052 * q^87 - 3574784 * q^88 - 17387733 * q^89 - 2091344 * q^90 - 8973442 * q^91 - 8008576 * q^92 - 21404363 * q^93 - 137504 * q^94 - 12445576 * q^95 + 917504 * q^96 - 1428702 * q^97 + 92378560 * q^98 + 13336614 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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