LMFDB - Embedded newform 91.8.g.a.81.56

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,Mod(9,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("91.9");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	91.g (of order $3$, 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:	$28.4270373191$
Analytic rank:	$0$
Dimension:	$126$
Relative dimension:	$63$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.56
Character	$\chi$	$=$	91.81
Dual form			91.8.g.a.9.56

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(9.08678 - 15.7388i) q^{2} -12.4690 q^{3} +(-101.139 - 175.178i) q^{4} +(-132.496 - 229.490i) q^{5} +(-113.303 + 196.247i) q^{6} +(-891.511 - 169.560i) q^{7} -1349.91 q^{8} -2031.52 q^{9} +O(q^{10})$	\(q+(9.08678 - 15.7388i) q^{2} -12.4690 q^{3} +(-101.139 - 175.178i) q^{4} +(-132.496 - 229.490i) q^{5} +(-113.303 + 196.247i) q^{6} +(-891.511 - 169.560i) q^{7} -1349.91 q^{8} -2031.52 q^{9} -4815.86 q^{10} +5527.63 q^{11} +(1261.11 + 2184.31i) q^{12} +(-890.416 + 7871.19i) q^{13} +(-10769.6 + 12490.5i) q^{14} +(1652.10 + 2861.52i) q^{15} +(679.518 - 1176.96i) q^{16} +(-13072.3 - 22641.9i) q^{17} +(-18460.0 + 31973.7i) q^{18} +18432.9 q^{19} +(-26801.2 + 46421.0i) q^{20} +(11116.3 + 2114.25i) q^{21} +(50228.4 - 86998.1i) q^{22} +(-50140.2 + 86845.3i) q^{23} +16832.0 q^{24} +(3951.98 - 6845.03i) q^{25} +(115792. + 85537.9i) q^{26} +52600.9 q^{27} +(60463.5 + 173323. i) q^{28} +(63073.9 + 109247. i) q^{29} +60049.2 q^{30} +(-136119. + 235766. i) q^{31} +(-98743.3 - 171028. i) q^{32} -68924.3 q^{33} -475142. q^{34} +(79209.5 + 227059. i) q^{35} +(205467. + 355879. i) q^{36} +(123345. - 213640. i) q^{37} +(167495. - 290111. i) q^{38} +(11102.6 - 98146.2i) q^{39} +(178858. + 309790. i) q^{40} +(-85514.4 - 148115. i) q^{41} +(134287. - 155745. i) q^{42} +(-191958. + 332481. i) q^{43} +(-559061. - 968322. i) q^{44} +(269169. + 466215. i) q^{45} +(911226. + 1.57829e6i) q^{46} +(-357673. - 619508. i) q^{47} +(-8472.94 + 14675.6i) q^{48} +(766042. + 302330. i) q^{49} +(-71821.6 - 124399. i) q^{50} +(162999. + 282323. i) q^{51} +(1.46892e6 - 640105. i) q^{52} +(151236. - 261949. i) q^{53} +(477973. - 827874. i) q^{54} +(-732391. - 1.26854e6i) q^{55} +(1.20346e6 + 228891. i) q^{56} -229840. q^{57} +2.29255e6 q^{58} +(-1.35133e6 - 2.34058e6i) q^{59} +(334185. - 578825. i) q^{60} -556204. q^{61} +(2.47377e6 + 4.28470e6i) q^{62} +(1.81113e6 + 344466. i) q^{63} -3.41508e6 q^{64} +(1.92434e6 - 838562. i) q^{65} +(-626300. + 1.08478e6i) q^{66} -2.74453e6 q^{67} +(-2.64425e6 + 4.57998e6i) q^{68} +(625200. - 1.08288e6i) q^{69} +(4.29339e6 + 816578. i) q^{70} +(-2.75108e6 + 4.76501e6i) q^{71} +2.74237e6 q^{72} +(-4070.79 + 7050.82i) q^{73} +(-2.24162e6 - 3.88260e6i) q^{74} +(-49277.4 + 85350.9i) q^{75} +(-1.86429e6 - 3.22904e6i) q^{76} +(-4.92795e6 - 937267. i) q^{77} +(-1.44381e6 - 1.06658e6i) q^{78} +(2.03666e6 + 3.52760e6i) q^{79} -360135. q^{80} +3.78706e6 q^{81} -3.10820e6 q^{82} -9.45254e6 q^{83} +(-753922. - 2.16117e6i) q^{84} +(-3.46407e6 + 5.99994e6i) q^{85} +(3.48856e6 + 6.04237e6i) q^{86} +(-786471. - 1.36221e6i) q^{87} -7.46179e6 q^{88} +(-4.19248e6 + 7.26159e6i) q^{89} +9.78353e6 q^{90} +(2.12846e6 - 6.86628e6i) q^{91} +2.02846e7 q^{92} +(1.69728e6 - 2.93977e6i) q^{93} -1.30004e7 q^{94} +(-2.44229e6 - 4.23016e6i) q^{95} +(1.23123e6 + 2.13256e6i) q^{96} +(-2.17337e6 + 3.76439e6i) q^{97} +(1.17192e7 - 9.30935e6i) q^{98} -1.12295e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 126 q + q^{2} + 160 q^{3} - 3839 q^{4} - 2 q^{5} - 258 q^{6} - 1816 q^{7} - 264 q^{8} + 83414 q^{9}+O(q^{10}) $ 126 * q + q^2 + 160 * q^3 - 3839 * q^4 - 2 * q^5 - 258 * q^6 - 1816 * q^7 - 264 * q^8 + 83414 * q^9	\( 126 q + q^{2} + 160 q^{3} - 3839 q^{4} - 2 q^{5} - 258 q^{6} - 1816 q^{7} - 264 q^{8} + 83414 q^{9} + 8510 q^{10} - 14846 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} - 205147 q^{16} - 49637 q^{17} - 21111 q^{18} + 9688 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} - 17065 q^{23} + 260608 q^{24} - 810669 q^{25} - 7812 q^{26} + 416614 q^{27} + 425466 q^{28} + 191096 q^{29} - 141332 q^{30} + 183609 q^{31} - 347673 q^{32} - 357182 q^{33} - 742000 q^{34} + 145247 q^{35} - 1732409 q^{36} + 681449 q^{37} - 877438 q^{38} - 1822261 q^{39} - 1502882 q^{40} + 593701 q^{41} - 1525674 q^{42} - 592188 q^{43} + 1254066 q^{44} - 977113 q^{45} + 692726 q^{46} + 98278 q^{47} - 374916 q^{48} - 747844 q^{49} + 289562 q^{50} - 281250 q^{51} - 1459588 q^{52} - 1256681 q^{53} + 146907 q^{54} - 3015554 q^{55} - 5896005 q^{56} + 2743072 q^{57} - 3702938 q^{58} + 1139729 q^{59} + 1031485 q^{60} + 2255272 q^{61} - 7724680 q^{62} - 8617558 q^{63} + 11827496 q^{64} + 487948 q^{65} + 435059 q^{66} - 8746696 q^{67} - 4368561 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} + 23321902 q^{72} - 5060877 q^{73} - 592001 q^{74} - 11318627 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} + 247136 q^{80} + 61513790 q^{81} - 17253904 q^{82} - 18679806 q^{83} + 14270544 q^{84} + 5330093 q^{85} - 8512356 q^{86} + 8254381 q^{87} + 12876438 q^{88} + 3088342 q^{89} + 53481084 q^{90} - 38127665 q^{91} + 2460546 q^{92} - 13841202 q^{93} + 34843588 q^{94} - 19776699 q^{95} + 26667066 q^{96} + 7705262 q^{97} - 58123667 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q + q^2 + 160 * q^3 - 3839 * q^4 - 2 * q^5 - 258 * q^6 - 1816 * q^7 - 264 * q^8 + 83414 * q^9 + 8510 * q^10 - 14846 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 - 205147 * q^16 - 49637 * q^17 - 21111 * q^18 + 9688 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 - 17065 * q^23 + 260608 * q^24 - 810669 * q^25 - 7812 * q^26 + 416614 * q^27 + 425466 * q^28 + 191096 * q^29 - 141332 * q^30 + 183609 * q^31 - 347673 * q^32 - 357182 * q^33 - 742000 * q^34 + 145247 * q^35 - 1732409 * q^36 + 681449 * q^37 - 877438 * q^38 - 1822261 * q^39 - 1502882 * q^40 + 593701 * q^41 - 1525674 * q^42 - 592188 * q^43 + 1254066 * q^44 - 977113 * q^45 + 692726 * q^46 + 98278 * q^47 - 374916 * q^48 - 747844 * q^49 + 289562 * q^50 - 281250 * q^51 - 1459588 * q^52 - 1256681 * q^53 + 146907 * q^54 - 3015554 * q^55 - 5896005 * q^56 + 2743072 * q^57 - 3702938 * q^58 + 1139729 * q^59 + 1031485 * q^60 + 2255272 * q^61 - 7724680 * q^62 - 8617558 * q^63 + 11827496 * q^64 + 487948 * q^65 + 435059 * q^66 - 8746696 * q^67 - 4368561 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 + 23321902 * q^72 - 5060877 * q^73 - 592001 * q^74 - 11318627 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 + 247136 * q^80 + 61513790 * q^81 - 17253904 * q^82 - 18679806 * q^83 + 14270544 * q^84 + 5330093 * q^85 - 8512356 * q^86 + 8254381 * q^87 + 12876438 * q^88 + 3088342 * q^89 + 53481084 * q^90 - 38127665 * q^91 + 2460546 * q^92 - 13841202 * q^93 + 34843588 * q^94 - 19776699 * q^95 + 26667066 * q^96 + 7705262 * q^97 - 58123667 * q^98 - 60531432 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	9.08678	−	15.7388i	0.803166	−	1.39112i	−0.114357	−	0.993440i	$-0.536481\pi$
$2$	9.08678	−	15.7388i	0.803166	−	1.39112i	0.917522	−	0.397684i	$-0.130186\pi$
$3$	−12.4690			−0.266630			−0.133315	−	0.991074i	$-0.542562\pi$
$3$	−12.4690			−0.266630			−0.133315	+	0.991074i	$0.542562\pi$
$4$	−101.139	−	175.178i	−0.790151	−	1.36858i
$5$	−132.496	−	229.490i	−0.474033	−	0.821049i	0.525525	−	0.850778i	$-0.323869\pi$
$5$	−132.496	−	229.490i	−0.474033	−	0.821049i	−0.999558	+	0.0297289i	$0.990536\pi$
$6$	−113.303	+	196.247i	−0.214148	+	0.370915i
$7$	−891.511	−	169.560i	−0.982389	−	0.186845i
$7$	−891.511	−	169.560i	−0.982389	−	0.186845i
$8$	−1349.91			−0.932156
$9$	−2031.52			−0.928909
$10$	−4815.86			−1.52291
$11$	5527.63			1.25217			0.626087	−	0.779753i	$-0.284655\pi$
$11$	5527.63			1.25217			0.626087	+	0.779753i	$0.284655\pi$
$12$	1261.11	+	2184.31i	0.210678	+	0.364905i
$13$	−890.416	+	7871.19i	−0.112406	+	0.993662i
$13$	−890.416	+	7871.19i	−0.112406	+	0.993662i
$14$	−10769.6	+	12490.5i	−1.04895	+	1.21656i
$15$	1652.10	+	2861.52i	0.126391	+	0.218916i
$16$	679.518	−	1176.96i	0.0414745	−	0.0718360i
$17$	−13072.3	−	22641.9i	−0.645330	−	1.11774i	−0.984225	−	0.176920i	$-0.943387\pi$
$17$	−13072.3	−	22641.9i	−0.645330	−	1.11774i	0.338895	−	0.940824i	$-0.389947\pi$
$18$	−18460.0	+	31973.7i	−0.746068	+	1.29223i
$19$	18432.9			0.616531			0.308266	−	0.951300i	$-0.400251\pi$
$19$	18432.9			0.616531			0.308266	+	0.951300i	$0.400251\pi$
$20$	−26801.2	+	46421.0i	−0.749115	+	1.29751i
$21$	11116.3	+	2114.25i	0.261934	+	0.0498184i
$22$	50228.4	−	86998.1i	1.00570	−	1.74193i
$23$	−50140.2	+	86845.3i	−0.859287	+	1.48833i	0.0133227	+	0.999911i	$0.495759\pi$
$23$	−50140.2	+	86845.3i	−0.859287	+	1.48833i	−0.872610	+	0.488418i	$0.837574\pi$
$24$	16832.0			0.248541
$25$	3951.98	−	6845.03i	0.0505853	−	0.0876164i
$26$	115792.	+	85537.9i	1.29203	+	0.954447i
$27$	52600.9			0.514304
$28$	60463.5	+	173323.i	0.520523	+	1.49212i
$29$	63073.9	+	109247.i	0.480238	+	0.831797i	0.999743	−	0.0226709i	$-0.00721698\pi$
$29$	63073.9	+	109247.i	0.480238	+	0.831797i	−0.519505	+	0.854467i	$0.673884\pi$
$30$	60049.2			0.406053
$31$	−136119.	+	235766.i	−0.820642	+	1.42139i	0.0845628	+	0.996418i	$0.473051\pi$
$31$	−136119.	+	235766.i	−0.820642	+	1.42139i	−0.905205	+	0.424976i	$0.860283\pi$
$32$	−98743.3	−	171028.i	−0.532700	−	0.922663i
$33$	−68924.3			−0.333867
$34$	−475142.			−2.07323
$35$	79209.5	+	227059.i	0.312276	+	0.895161i
$36$	205467.	+	355879.i	0.733978	+	1.27129i
$37$	123345.	−	213640.i	0.400328	−	0.693388i	−0.593437	−	0.804880i	$-0.702230\pi$
$37$	123345.	−	213640.i	0.400328	−	0.693388i	0.993765	+	0.111492i	$0.0355629\pi$
$38$	167495.	−	290111.i	0.495177	−	0.857672i
$39$	11102.6	−	98146.2i	0.0299709	−	0.264940i
$40$	178858.	+	309790.i	0.441873	+	0.765346i
$41$	−85514.4	−	148115.i	−0.193774	−	0.335627i	0.752724	−	0.658336i	$-0.228740\pi$
$41$	−85514.4	−	148115.i	−0.193774	−	0.335627i	−0.946498	+	0.322710i	$0.895406\pi$
$42$	134287.	−	155745.i	0.279680	−	0.324371i
$43$	−191958.	+	332481.i	−0.368186	+	0.637716i	−0.989282	−	0.146018i	$-0.953354\pi$
$43$	−191958.	+	332481.i	−0.368186	+	0.637716i	0.621096	+	0.783734i	$0.286688\pi$
$44$	−559061.	−	968322.i	−0.989406	−	1.71370i
$45$	269169.	+	466215.i	0.440333	+	0.762680i
$46$	911226.	+	1.57829e6i	1.38030	+	2.39075i
$47$	−357673.	−	619508.i	−0.502509	−	0.870371i	−0.999996	−	0.00289941i	$-0.999077\pi$
$47$	−357673.	−	619508.i	−0.502509	−	0.870371i	0.497487	−	0.867471i	$-0.334256\pi$
$48$	−8472.94	+	14675.6i	−0.0110583	+	0.0191536i
$49$	766042.	+	302330.i	0.930178	+	0.367109i
$50$	−71821.6	−	124399.i	−0.0812568	−	0.140741i
$51$	162999.	+	282323.i	0.172064	+	0.298024i
$52$	1.46892e6	−	640105.i	1.44873	−	0.631306i
$53$	151236.	−	261949.i	0.139537	−	0.241686i	−0.787784	−	0.615951i	$-0.788772\pi$
$53$	151236.	−	261949.i	0.139537	−	0.241686i	0.927322	+	0.374265i	$0.122105\pi$
$54$	477973.	−	827874.i	0.413072	−	0.715461i
$55$	−732391.	−	1.26854e6i	−0.593572	−	1.02810i
$56$	1.20346e6	+	228891.i	0.915741	+	0.174169i
$57$	−229840.			−0.164386
$58$	2.29255e6			1.54284
$59$	−1.35133e6	−	2.34058e6i	−0.856606	−	1.48368i	−0.875147	−	0.483856i	$-0.839236\pi$
$59$	−1.35133e6	−	2.34058e6i	−0.856606	−	1.48368i	0.0185418	−	0.999828i	$-0.494098\pi$
$60$	334185.	−	578825.i	0.199736	−	0.345954i
$61$	−556204.			−0.313747			−0.156874	−	0.987619i	$-0.550142\pi$
$61$	−556204.			−0.313747			−0.156874	+	0.987619i	$0.550142\pi$
$62$	2.47377e6	+	4.28470e6i	1.31822	+	2.28323i
$63$	1.81113e6	+	344466.i	0.912550	+	0.173562i
$64$	−3.41508e6			−1.62844
$65$	1.92434e6	−	838562.i	0.869130	−	0.378738i
$66$	−626300.	+	1.08478e6i	−0.268150	+	0.464450i
$67$	−2.74453e6			−1.11482			−0.557412	−	0.830236i	$-0.688206\pi$
$67$	−2.74453e6			−1.11482			−0.557412	+	0.830236i	$0.688206\pi$
$68$	−2.64425e6	+	4.57998e6i	−1.01982	+	1.76637i
$69$	625200.	−	1.08288e6i	0.229112	−	0.396833i
$70$	4.29339e6	+	816578.i	1.49609	+	0.284547i
$71$	−2.75108e6	+	4.76501e6i	−0.912220	+	1.58001i	−0.101298	+	0.994856i	$0.532300\pi$
$71$	−2.75108e6	+	4.76501e6i	−0.912220	+	1.58001i	−0.810922	+	0.585155i	$0.801034\pi$
$72$	2.74237e6			0.865888
$73$	−4070.79	+	7050.82i	−0.00122475	+	0.00212134i	−0.866637	−	0.498939i	$-0.833723\pi$
$73$	−4070.79	+	7050.82i	−0.00122475	+	0.00212134i	0.865412	+	0.501060i	$0.167057\pi$
$74$	−2.24162e6	−	3.88260e6i	−0.643059	−	1.11381i
$75$	−49277.4	+	85350.9i	−0.0134876	+	0.0233611i
$76$	−1.86429e6	−	3.22904e6i	−0.487153	−	0.843773i
$77$	−4.92795e6	−	937267.i	−1.23012	−	0.233962i
$78$	−1.44381e6	−	1.06658e6i	−0.344493	−	0.254484i
$79$	2.03666e6	+	3.52760e6i	0.464754	+	0.804978i	0.999190	−	0.0402308i	$-0.0128093\pi$
$79$	2.03666e6	+	3.52760e6i	0.464754	+	0.804978i	−0.534436	+	0.845209i	$0.679476\pi$
$80$	−360135.			−0.0786412
$81$	3.78706e6			0.791780
$82$	−3.10820e6			−0.622531
$83$	−9.45254e6			−1.81458			−0.907288	−	0.420509i	$-0.861852\pi$
$83$	−9.45254e6			−1.81458			−0.907288	+	0.420509i	$0.861852\pi$
$84$	−753922.	−	2.16117e6i	−0.138787	−	0.397842i
$85$	−3.46407e6	+	5.99994e6i	−0.611815	+	1.05970i
$86$	3.48856e6	+	6.04237e6i	0.591428	+	1.02438i
$87$	−786471.	−	1.36221e6i	−0.128046	−	0.221782i
$88$	−7.46179e6			−1.16722
$89$	−4.19248e6	+	7.26159e6i	−0.630385	+	1.09186i	0.357088	+	0.934071i	$0.383770\pi$
$89$	−4.19248e6	+	7.26159e6i	−0.630385	+	1.09186i	−0.987473	+	0.157788i	$0.949564\pi$
$90$	9.78353e6			1.41464
$91$	2.12846e6	−	6.86628e6i	0.296088	−	0.955161i
$92$	2.02846e7			2.71587
$93$	1.69728e6	−	2.93977e6i	0.218808	−	0.378986i
$94$	−1.30004e7			−1.61439
$95$	−2.44229e6	−	4.23016e6i	−0.292256	−	0.506203i
$96$	1.23123e6	+	2.13256e6i	0.142034	+	0.246010i
$97$	−2.17337e6	+	3.76439e6i	−0.241787	+	0.418788i	−0.961223	−	0.275771i	$-0.911067\pi$
$97$	−2.17337e6	+	3.76439e6i	−0.241787	+	0.418788i	0.719436	+	0.694559i	$0.244400\pi$
$98$	1.17192e7	−	9.30935e6i	1.25778	−	0.999144i
$99$	−1.12295e7			−1.16316
$100$	−1.59880e6			−0.159880
$101$	−1.70157e7			−1.64333			−0.821665	−	0.569971i	$-0.806955\pi$
$101$	−1.70157e7			−1.64333			−0.821665	+	0.569971i	$0.806955\pi$
$102$	5.92456e6			0.552784
$103$	3.86191e6	+	6.68903e6i	0.348235	+	0.603160i	0.985936	−	0.167124i	$-0.0534479\pi$
$103$	3.86191e6	+	6.68903e6i	0.348235	+	0.603160i	−0.637701	+	0.770284i	$0.720115\pi$
$104$	1.20198e6	−	1.06254e7i	0.104780	−	0.926249i
$105$	−987666.	−	2.83121e6i	−0.0832622	−	0.238677i
$106$	−2.74850e6	−	4.76055e6i	−0.224143	−	0.388228i
$107$	9.27098e6	−	1.60578e7i	0.731615	−	1.26719i	−0.224578	−	0.974456i	$-0.572100\pi$
$107$	9.27098e6	−	1.60578e7i	0.731615	−	1.26719i	0.956193	−	0.292738i	$-0.0945665\pi$
$108$	−5.32002e6	−	9.21455e6i	−0.406378	−	0.703867i
$109$	7.29532e6	−	1.26359e7i	0.539575	−	0.934571i	−0.459352	−	0.888254i	$-0.651918\pi$
$109$	7.29532e6	−	1.26359e7i	0.539575	−	0.934571i	0.998927	−	0.0463164i	$-0.0147482\pi$
$110$	−2.66203e7			−1.90695
$111$	−1.53799e6	+	2.66389e6i	−0.106739	+	0.184878i
$112$	−805364.	+	934054.i	−0.0541663	+	0.0628216i
$113$	7.50326e6	−	1.29960e7i	0.489188	−	0.847298i	−0.510735	−	0.859738i	$-0.670627\pi$
$113$	7.50326e6	−	1.29960e7i	0.489188	−	0.847298i	0.999923	+	0.0124402i	$0.00395993\pi$
$114$	−2.08851e6	+	3.61740e6i	−0.132029	+	0.228681i
$115$	2.65735e7			1.62932
$116$	1.27585e7	−	2.20984e7i	0.758921	−	1.31449i
$117$	1.80890e6	−	1.59905e7i	0.104415	−	0.923021i
$118$	−4.91171e7			−2.75199
$119$	7.81496e6	+	2.24021e7i	0.425121	+	1.21864i
$120$	−2.23018e6	−	3.86279e6i	−0.117816	−	0.204064i
$121$	1.10675e7			0.567940
$122$	−5.05411e6	+	8.75397e6i	−0.251991	+	0.436461i
$123$	1.06628e6	+	1.84686e6i	0.0516659	+	0.0894881i
$124$	5.50680e7			2.59372
$125$	−2.27970e7			−1.04398
$126$	2.18788e7	−	2.53748e7i	0.974375	−	1.13007i
$127$	3.98460e6	+	6.90152e6i	0.172612	+	0.298973i	0.939332	−	0.343008i	$-0.111446\pi$
$127$	3.98460e6	+	6.90152e6i	0.172612	+	0.298973i	−0.766720	+	0.641981i	$0.778113\pi$
$128$	−1.83929e7	+	3.18575e7i	−0.775205	+	1.34269i
$129$	2.39353e6	−	4.14572e6i	0.0981693	−	0.170034i
$130$	4.28812e6	−	3.79066e7i	0.171185	−	1.51326i
$131$	−1.81979e7	−	3.15197e7i	−0.707249	−	1.22499i	−0.965874	−	0.259014i	$-0.916603\pi$
$131$	−1.81979e7	−	3.15197e7i	−0.707249	−	1.22499i	0.258624	−	0.965978i	$-0.416731\pi$
$132$	6.97095e6	+	1.20740e7i	0.263805	+	0.456924i
$133$	−1.64331e7	−	3.12548e6i	−0.605674	−	0.115196i
$134$	−2.49390e7	+	4.31956e7i	−0.895389	+	1.55086i
$135$	−6.96943e6	−	1.20714e7i	−0.243797	−	0.422269i
$136$	1.76464e7	+	3.05645e7i	0.601548	+	1.04191i
$137$	−1.72813e7	−	2.99322e7i	−0.574190	−	0.994526i	−0.996129	−	0.0879019i	$-0.971984\pi$
$137$	−1.72813e7	−	2.99322e7i	−0.574190	−	0.994526i	0.421939	−	0.906624i	$-0.361350\pi$
$138$	−1.13621e7	−	1.96798e7i	−0.368029	−	0.637445i
$139$	3.12389e6	−	5.41074e6i	0.0986607	−	0.170885i	−0.812470	−	0.583003i	$-0.801877\pi$
$139$	3.12389e6	−	5.41074e6i	0.0986607	−	0.170885i	0.911131	+	0.412118i	$0.135211\pi$
$140$	3.17647e7	−	3.68404e7i	0.978355	−	1.13469i
$141$	4.45984e6	+	7.72467e6i	0.133984	+	0.232067i
$142$	4.99970e7	+	8.65973e7i	1.46533	+	2.53802i
$143$	−4.92189e6	+	4.35091e7i	−0.140752	+	1.24424i
$144$	−1.38046e6	+	2.39102e6i	−0.0385260	+	0.0667290i
$145$	1.67141e7	−	2.89497e7i	0.455297	−	0.788598i
$146$	73980.8	+	128139.i	0.00196736	+	0.00340757i
$147$	−9.55181e6	−	3.76976e6i	−0.248013	−	0.0978821i
$148$	−4.99001e7			−1.26528
$149$	−3.01961e7			−0.747823			−0.373912	−	0.927464i	$-0.621984\pi$
$149$	−3.01961e7			−0.747823			−0.373912	+	0.927464i	$0.621984\pi$
$150$	895546.	+	1.55113e6i	0.0216655	+	0.0375257i
$151$	−2.79820e7	+	4.84663e7i	−0.661394	+	1.14557i	0.318856	+	0.947803i	$0.396701\pi$
$151$	−2.79820e7	+	4.84663e7i	−0.661394	+	1.14557i	−0.980250	+	0.197764i	$0.936632\pi$
$152$	−2.48826e7			−0.574704
$153$	2.65567e7	+	4.59976e7i	0.599452	+	1.03828i
$154$	−5.95306e7	+	6.90431e7i	−1.31346	+	1.52334i
$155$	7.21412e7			1.55605
$156$	−1.83160e7	+	7.98150e6i	−0.386273	+	0.168325i
$157$	1.64979e6	−	2.85753e6i	0.0340236	−	0.0589307i	−0.848512	−	0.529176i	$-0.822501\pi$
$157$	1.64979e6	−	2.85753e6i	0.0340236	−	0.0589307i	0.882536	+	0.470245i	$0.155835\pi$
$158$	7.40267e7			1.49310
$159$	−1.88577e6	+	3.26625e6i	−0.0372048	+	0.0644407i
$160$	−2.61662e7	+	4.53213e7i	−0.505035	+	0.874746i
$161$	5.94260e7	−	6.89218e7i	1.12224	−	1.30157i
$162$	3.44122e7	−	5.96036e7i	0.635930	−	1.10146i
$163$	9.18248e7			1.66075			0.830373	−	0.557208i	$-0.188127\pi$
$163$	9.18248e7			1.66075			0.830373	+	0.557208i	$0.188127\pi$
$164$	−1.72977e7	+	2.99605e7i	−0.306221	+	0.530391i
$165$	9.13221e6	+	1.58174e7i	0.158264	+	0.274121i
$166$	−8.58932e7	+	1.48771e8i	−1.45741	+	2.52430i
$167$	−1.91390e6	−	3.31497e6i	−0.0317989	−	0.0550772i	0.849688	−	0.527286i	$-0.176790\pi$
$167$	−1.91390e6	−	3.31497e6i	−0.0317989	−	0.0550772i	−0.881487	+	0.472209i	$0.843457\pi$
$168$	−1.50060e7	−	2.85405e6i	−0.244164	−	0.0464385i
$169$	−6.11628e7	−	1.40173e7i	−0.974730	−	0.223388i
$170$	6.29545e7	+	1.09040e8i	0.982778	+	1.70222i
$171$	−3.74468e7			−0.572701
$172$	7.76581e7			1.16369
$173$	2.07273e7			0.304356			0.152178	−	0.988353i	$-0.451371\pi$
$173$	2.07273e7			0.304356			0.152178	+	0.988353i	$0.451371\pi$
$174$	−2.85860e7			−0.411368
$175$	−4.68388e6	+	5.43232e6i	−0.0660652	+	0.0766218i
$176$	3.75613e6	−	6.50580e6i	0.0519333	−	0.0899511i
$177$	1.68498e7	+	2.91848e7i	0.228397	+	0.395594i
$178$	7.61923e7	+	1.31969e8i	1.01261	+	1.75389i
$179$	2.98250e7			0.388682			0.194341	−	0.980934i	$-0.437743\pi$
$179$	2.98250e7			0.388682			0.194341	+	0.980934i	$0.437743\pi$
$180$	5.44472e7	−	9.43053e7i	0.695859	−	1.20526i
$181$	−1.22770e7			−0.153893			−0.0769463	−	0.997035i	$-0.524517\pi$
$181$	−1.22770e7			−0.153893			−0.0769463	+	0.997035i	$0.524517\pi$
$182$	−8.87259e7	−	9.58917e7i	−1.09094	−	1.17905i
$183$	6.93533e6			0.0836544
$184$	6.76845e7	−	1.17233e8i	0.800990	−	1.38736i
$185$	−6.53711e7			−0.759075
$186$	−3.08456e7	−	5.34261e7i	−0.351478	−	0.608777i
$187$	−7.22590e7	−	1.25156e8i	−0.808065	−	1.39961i
$188$	−7.23496e7	+	1.25313e8i	−0.794115	+	1.37545i
$189$	−4.68943e7	−	8.91903e6i	−0.505247	−	0.0960951i
$190$	−8.87701e7			−0.938921
$191$	1.26333e8			1.31190			0.655949	−	0.754805i	$-0.272269\pi$
$191$	1.26333e8			1.31190			0.655949	+	0.754805i	$0.272269\pi$
$192$	4.25828e7			0.434190
$193$	1.18246e8			1.18396			0.591979	−	0.805954i	$-0.298347\pi$
$193$	1.18246e8			1.18396			0.591979	+	0.805954i	$0.298347\pi$
$194$	3.94980e7	+	6.84125e7i	0.388391	+	0.672712i
$195$	−2.39947e7	+	1.04561e7i	−0.231736	+	0.100983i
$196$	−2.45153e7	−	1.64771e8i	−0.232563	−	1.56310i
$197$	−4.63967e7	−	8.03614e7i	−0.432369	−	0.748886i	0.564708	−	0.825291i	$-0.308989\pi$
$197$	−4.63967e7	−	8.03614e7i	−0.432369	−	0.748886i	−0.997077	+	0.0764055i	$0.975656\pi$
$198$	−1.02040e8	+	1.76739e8i	−0.934206	+	1.61809i
$199$	2.56628e7	+	4.44493e7i	0.230844	+	0.399834i	0.958057	−	0.286579i	$-0.0925179\pi$
$199$	2.56628e7	+	4.44493e7i	0.230844	+	0.399834i	−0.727213	+	0.686412i	$0.759185\pi$
$200$	−5.33480e6	+	9.24015e6i	−0.0471534	+	0.0816722i
$201$	3.42217e7			0.297246
$202$	−1.54618e8	+	2.67806e8i	−1.31987	+	2.28608i
$203$	−3.77071e7	−	1.08090e8i	−0.316364	−	0.906878i
$204$	3.29713e7	−	5.71079e7i	0.271913	−	0.470967i
$205$	−2.26607e7	+	3.92494e7i	−0.183711	+	0.318196i
$206$	1.40369e8			1.11876
$207$	1.01861e8	−	1.76428e8i	0.798199	−	1.38252i
$208$	8.65903e6	+	6.39661e6i	0.0667187	+	0.0492865i
$209$	1.01890e8			0.772005
$210$	−5.35345e7	−	1.01820e7i	−0.398902	−	0.0758688i
$211$	−3.10550e7	−	5.37888e7i	−0.227584	−	0.394188i	0.729507	−	0.683973i	$-0.239749\pi$
$211$	−3.10550e7	−	5.37888e7i	−0.227584	−	0.394188i	−0.957092	+	0.289785i	$0.906416\pi$
$212$	−6.11838e7			−0.441022
$213$	3.43034e7	−	5.94152e7i	0.243225	−	0.421278i
$214$	−1.68487e8	−	2.91828e8i	−1.17522	−	2.03553i
$215$	1.01735e8			0.698129
$216$	−7.10064e7			−0.479412
$217$	1.61328e8	−	1.87107e8i	1.07177	−	1.24303i
$218$	−1.32582e8	−	2.29639e8i	−0.866736	−	1.50123i
$219$	50758.9	−	87917.0i	0.000326556	−	0.000565612i
$220$	−1.48147e8	+	2.56598e8i	−0.938022	+	1.62470i
$221$	1.89859e8	−	8.27341e7i	1.18320	−	0.515598i
$222$	2.79509e7	+	4.84123e7i	0.171459	+	0.296975i
$223$	−4.72970e7	−	8.19208e7i	−0.285605	−	0.494683i	0.687150	−	0.726515i	$-0.258861\pi$
$223$	−4.72970e7	−	8.19208e7i	−0.285605	−	0.494683i	−0.972756	+	0.231832i	$0.925528\pi$
$224$	5.90311e7	+	1.69217e8i	0.350924	+	1.00595i
$225$	−8.02854e6	+	1.39058e7i	−0.0469891	+	0.0813876i
$226$	−1.36361e8	−	2.36184e8i	−0.785798	−	1.36104i
$227$	4.75146e7	+	8.22977e7i	0.269610	+	0.466979i	0.968761	−	0.247995i	$-0.0797717\pi$
$227$	4.75146e7	+	8.22977e7i	0.269610	+	0.466979i	−0.699151	+	0.714974i	$0.746438\pi$
$228$	2.32459e7	+	4.02630e7i	0.129889	+	0.224975i
$229$	3.98709e7	+	6.90584e7i	0.219398	+	0.380008i	0.954624	−	0.297814i	$-0.0962575\pi$
$229$	3.98709e7	+	6.90584e7i	0.219398	+	0.380008i	−0.735226	+	0.677822i	$0.762924\pi$
$230$	2.41468e8	−	4.18235e8i	1.30862	−	2.26659i
$231$	6.14468e7	+	1.16868e7i	0.327987	+	0.0623813i
$232$	−8.51438e7	−	1.47473e8i	−0.447657	−	0.775364i
$233$	5.68658e7	+	9.84944e7i	0.294514	+	0.510113i	0.974872	−	0.222767i	$-0.0715090\pi$
$233$	5.68658e7	+	9.84944e7i	0.294514	+	0.510113i	−0.680358	+	0.732880i	$0.738176\pi$
$234$	−2.35234e8	−	1.73772e8i	−1.20017	−	0.886594i
$235$	−9.47807e7	+	1.64165e8i	−0.476412	+	0.825169i
$236$	−2.73346e8	+	4.73449e8i	−1.35370	+	2.34467i
$237$	−2.53952e7	−	4.39857e7i	−0.123917	−	0.214631i
$238$	4.23594e8	+	8.05651e7i	2.03672	+	0.387372i
$239$	2.93713e8			1.39165			0.695826	−	0.718210i	$-0.255038\pi$
$239$	2.93713e8			1.39165			0.695826	+	0.718210i	$0.255038\pi$
$240$	4.49053e6			0.0209681
$241$	−6.91834e7	−	1.19829e8i	−0.318377	−	0.551446i	0.661772	−	0.749705i	$-0.269805\pi$
$241$	−6.91834e7	−	1.19829e8i	−0.318377	−	0.551446i	−0.980150	+	0.198259i	$0.936471\pi$
$242$	1.00568e8	−	1.74189e8i	0.456150	−	0.790075i
$243$	−1.62259e8			−0.725417
$244$	5.62541e7	+	9.74350e7i	0.247908	+	0.429389i
$245$	−3.21159e7	−	2.15857e8i	−0.139521	−	0.937744i
$246$	3.87563e7			0.165985
$247$	−1.64129e7	+	1.45089e8i	−0.0693021	+	0.612624i
$248$	1.83748e8	−	3.18261e8i	0.764967	−	1.32496i
$249$	1.17864e8			0.483820
$250$	−2.07152e8	+	3.58797e8i	−0.838491	+	1.45231i
$251$	−3.06422e7	+	5.30738e7i	−0.122310	+	0.211847i	−0.920678	−	0.390322i	$-0.872364\pi$
$251$	−3.06422e7	+	5.30738e7i	−0.122310	+	0.211847i	0.798368	+	0.602170i	$0.205697\pi$
$252$	−1.22833e8	−	3.52109e8i	−0.483519	−	1.38604i
$253$	−2.77156e8	+	4.80049e8i	−1.07598	+	1.86365i
$254$	1.44829e8			0.554545
$255$	4.31936e7	−	7.48136e7i	0.163128	−	0.282546i
$256$	1.15700e8	+	2.00399e8i	0.431018	+	0.746544i
$257$	−4.64701e7	+	8.04886e7i	−0.170769	+	0.295780i	−0.938689	−	0.344766i	$-0.887958\pi$
$257$	−4.64701e7	+	8.04886e7i	−0.170769	+	0.295780i	0.767920	+	0.640545i	$0.221292\pi$
$258$	−4.34991e7	−	7.53426e7i	−0.157692	−	0.273131i
$259$	−1.46188e8	+	1.69548e8i	−0.522834	+	0.606378i
$260$	−3.41524e8	−	2.52291e8i	−1.20508	−	0.890215i
$261$	−1.28136e8	−	2.21938e8i	−0.446097	−	0.772663i
$262$	−6.61443e8			−2.27215
$263$	−4.46739e8			−1.51429			−0.757144	−	0.653248i	$-0.773406\pi$
$263$	−4.46739e8			−1.51429			−0.757144	+	0.653248i	$0.773406\pi$
$264$	9.30413e7			0.311216
$265$	−8.01530e7			−0.264581
$266$	−1.98515e8	+	2.30236e8i	−0.646708	+	0.750046i
$267$	5.22762e7	−	9.05451e7i	0.168079	−	0.291122i
$268$	2.77580e8	+	4.80783e8i	0.880880	+	1.52573i
$269$	1.62593e8	+	2.81619e8i	0.509294	+	0.882122i	0.999942	+	0.0107647i	$0.00342657\pi$
$269$	1.62593e8	+	2.81619e8i	0.509294	+	0.882122i	−0.490649	+	0.871358i	$0.663240\pi$
$270$	−2.53319e8			−0.783239
$271$	−9.49578e6	+	1.64472e7i	−0.0289827	+	0.0501994i	−0.880153	−	0.474690i	$-0.842560\pi$
$271$	−9.49578e6	+	1.64472e7i	−0.0289827	+	0.0501994i	0.851170	+	0.524890i	$0.175893\pi$
$272$	−3.55316e7			−0.107059
$273$	−2.65398e7	+	8.56159e7i	−0.0789458	+	0.254674i
$274$	−6.28127e8			−1.84468
$275$	2.18451e7	−	3.78368e7i	0.0633416	−	0.109711i
$276$	−2.52929e8			−0.724131
$277$	−4.26838e7	−	7.39304e7i	−0.120666	−	0.208999i	0.799365	−	0.600846i	$-0.205170\pi$
$277$	−4.26838e7	−	7.39304e7i	−0.120666	−	0.208999i	−0.920030	+	0.391847i	$0.871836\pi$
$278$	−5.67723e7	−	9.83325e7i	−0.158482	−	0.274499i
$279$	2.76529e8	−	4.78963e8i	0.762301	−	1.32034i
$280$	−1.06925e8	−	3.06509e8i	−0.291090	−	0.834430i
$281$	1.79379e8			0.482279			0.241139	−	0.970490i	$-0.422479\pi$
$281$	1.79379e8			0.482279			0.241139	+	0.970490i	$0.422479\pi$
$282$	1.62102e8			0.430445
$283$	−2.21346e8			−0.580522			−0.290261	−	0.956947i	$-0.593742\pi$
$283$	−2.21346e8			−0.580522			−0.290261	+	0.956947i	$0.593742\pi$
$284$	1.11297e9			2.88316
$285$	3.04530e7	+	5.27461e7i	0.0779242	+	0.134969i
$286$	6.40055e8	+	4.72822e8i	1.61784	+	1.19513i
$287$	5.11226e7	+	1.46546e8i	0.127652	+	0.365922i
$288$	2.00599e8	+	3.47448e8i	0.494830	+	0.857070i
$289$	−1.36602e8	+	2.36602e8i	−0.332901	+	0.576602i
$290$	−3.03755e8	−	5.26119e8i	−0.731358	−	1.26675i
$291$	2.70999e7	−	4.69384e7i	0.0644677	−	0.111661i
$292$	1.64687e6			0.00387096
$293$	1.05490e8	−	1.82715e8i	0.245006	−	0.424363i	−0.717127	−	0.696942i	$-0.754543\pi$
$293$	1.05490e8	−	1.82715e8i	0.245006	−	0.424363i	0.962133	+	0.272579i	$0.0878768\pi$
$294$	−1.46127e8	+	1.16079e8i	−0.335362	+	0.266402i
$295$	−3.58094e8	+	6.20236e8i	−0.812119	+	1.40663i
$296$	−1.66504e8	+	2.88394e8i	−0.373168	+	0.646346i
$297$	2.90759e8			0.643999
$298$	−2.74386e8	+	4.75250e8i	−0.600626	+	1.04032i
$299$	−6.38931e8	−	4.71991e8i	−1.38231	−	1.02114i
$300$	1.99355e7			0.0426288
$301$	2.27508e8	−	2.63862e8i	0.480856	−	0.557692i
$302$	5.08534e8	+	8.80806e8i	1.06242	+	1.84016i
$303$	2.12169e8			0.438161
$304$	1.25255e7	−	2.16948e7i	0.0255703	−	0.0442891i
$305$	7.36950e7	+	1.27643e8i	0.148727	+	0.257602i
$306$	9.65261e8			1.92584
$307$	9.05498e8			1.78609			0.893045	−	0.449967i	$-0.148564\pi$
$307$	9.05498e8			1.78609			0.893045	+	0.449967i	$0.148564\pi$
$308$	3.34220e8	+	9.58064e8i	0.651786	+	1.86839i
$309$	−4.81543e7	−	8.34058e7i	−0.0928498	−	0.160820i
$310$	6.55531e8	−	1.13541e9i	1.24976	−	2.16465i
$311$	2.88967e8	−	5.00505e8i	0.544736	−	0.943511i	−0.453887	−	0.891059i	$-0.649963\pi$
$311$	2.88967e8	−	5.00505e8i	0.544736	−	0.943511i	0.998623	−	0.0524515i	$-0.0167035\pi$
$312$	−1.49875e7	+	1.32488e8i	−0.0279376	+	0.246965i
$313$	−2.75442e8	−	4.77080e8i	−0.507721	−	0.879399i	−0.999960	−	0.00893875i	$-0.997155\pi$
$313$	−2.75442e8	−	4.77080e8i	−0.507721	−	0.879399i	0.492239	−	0.870460i	$-0.336179\pi$
$314$	−2.99826e7	−	5.19314e7i	−0.0546532	−	0.0946622i
$315$	−1.60916e8	−	4.61276e8i	−0.290076	−	0.831523i
$316$	4.11972e8	−	7.13557e8i	0.734452	−	1.27211i
$317$	−3.51756e8	−	6.09260e8i	−0.620204	−	1.07422i	−0.989447	−	0.144892i	$-0.953717\pi$
$317$	−3.51756e8	−	6.09260e8i	−0.620204	−	1.07422i	0.369244	−	0.929333i	$-0.379617\pi$
$318$	3.42712e7	+	5.93595e7i	0.0597633	+	0.103513i
$319$	3.48649e8	+	6.03878e8i	0.601341	+	1.04155i
$320$	4.52485e8	+	7.83727e8i	0.771933	+	1.33703i
$321$	−1.15600e8	+	2.00226e8i	−0.195070	+	0.337872i
$322$	−5.44753e8	−	1.56157e9i	−0.909293	−	2.60655i
$323$	−2.40960e8	−	4.17356e8i	−0.397866	−	0.689124i
$324$	−3.83020e8	−	6.63411e8i	−0.625625	−	1.08361i
$325$	5.03596e7	+	3.72017e7i	0.0813750	+	0.0601134i
$326$	8.34392e8	−	1.44521e9i	1.33385	−	2.31030i
$327$	−9.09656e7	+	1.57557e8i	−0.143867	+	0.249184i
$328$	1.15436e8	+	1.99942e8i	0.180628	+	0.312856i
$329$	2.13826e8	+	6.12945e8i	0.331035	+	0.948934i
$330$	3.31930e8			0.508449
$331$	−4.72211e8			−0.715712			−0.357856	−	0.933777i	$-0.616492\pi$
$331$	−4.72211e8			−0.715712			−0.357856	+	0.933777i	$0.616492\pi$
$332$	9.56024e8	+	1.65588e9i	1.43379	+	2.48340i
$333$	−2.50578e8	+	4.34014e8i	−0.371868	+	0.644094i
$334$	−6.95648e7			−0.102159
$335$	3.63640e8	+	6.29844e8i	0.528464	+	0.915326i
$336$	1.00421e7	−	1.16468e7i	0.0144423	−	0.0167501i
$337$	−9.37139e8			−1.33383			−0.666913	−	0.745135i	$-0.732385\pi$
$337$	−9.37139e8			−1.33383			−0.666913	+	0.745135i	$0.732385\pi$
$338$	−7.76388e8	+	8.35256e8i	−1.09363	+	1.17655i
$339$	−9.35585e7	+	1.62048e8i	−0.130432	+	0.225915i
$340$	1.40141e9			1.93371
$341$	−7.52417e8	+	1.30322e9i	−1.02759	+	1.77983i
$342$	−3.40271e8	+	5.89366e8i	−0.459974	+	0.796699i
$343$	−6.31672e8	−	3.99421e8i	−0.845205	−	0.534443i
$344$	2.59126e8	−	4.48819e8i	0.343207	−	0.594452i
$345$	−3.31347e8			−0.434426
$346$	1.88344e8	−	3.26222e8i	0.244448	−	0.423396i
$347$	1.89263e8	+	3.27813e8i	0.243172	+	0.421186i	0.961616	−	0.274399i	$-0.0884789\pi$
$347$	1.89263e8	+	3.27813e8i	0.243172	+	0.421186i	−0.718444	+	0.695584i	$0.755146\pi$
$348$	−1.59086e8	+	2.75545e8i	−0.202351	+	0.350482i
$349$	−5.28496e8	−	9.15381e8i	−0.665507	−	1.15269i	−0.979148	−	0.203150i	$-0.934882\pi$
$349$	−5.28496e8	−	9.15381e8i	−0.665507	−	1.15269i	0.313641	−	0.949542i	$-0.398451\pi$
$350$	4.29367e7	+	1.23081e8i	0.0535291	+	0.153445i
$351$	−4.68367e7	+	4.14032e8i	−0.0578112	+	0.511045i
$352$	−5.45817e8	−	9.45382e8i	−0.667033	−	1.15534i
$353$	−1.10594e9			−1.33820			−0.669099	−	0.743173i	$-0.733320\pi$
$353$	−1.10594e9			−1.33820			−0.669099	+	0.743173i	$0.733320\pi$
$354$	6.12444e8			0.733761
$355$	1.45803e9			1.72969
$356$	1.69610e9			1.99240
$357$	−9.74450e7	−	2.79333e8i	−0.113350	−	0.324925i
$358$	2.71013e8	−	4.69408e8i	0.312176	−	0.540705i
$359$	−1.41635e8	−	2.45319e8i	−0.161562	−	0.279834i	0.773867	−	0.633348i	$-0.218320\pi$
$359$	−1.41635e8	−	2.45319e8i	−0.161562	−	0.279834i	−0.935429	+	0.353514i	$0.884987\pi$
$360$	−3.63353e8	−	6.29346e8i	−0.410460	−	0.710937i
$361$	−5.54101e8			−0.619889
$362$	−1.11559e8	+	1.93225e8i	−0.123601	+	0.214084i
$363$	−1.38002e8			−0.151430
$364$	−1.41809e9	+	3.21591e8i	−1.54117	+	0.349501i
$365$	2.15746e6			0.00232230
$366$	6.30199e7	−	1.09154e8i	0.0671883	−	0.116374i
$367$	−2.04302e8			−0.215745			−0.107873	−	0.994165i	$-0.534404\pi$
$367$	−2.04302e8			−0.215745			−0.107873	+	0.994165i	$0.534404\pi$
$368$	6.81423e7	+	1.18026e8i	0.0712770	+	0.123455i
$369$	1.73724e8	+	3.00900e8i	0.179998	+	0.311766i
$370$	−5.94013e8	+	1.02886e9i	−0.609663	+	1.05597i
$371$	−1.79245e8	+	2.07887e8i	−0.182238	+	0.211358i
$372$	−6.86646e8			−0.691564
$373$	2.45096e8			0.244543			0.122272	−	0.992497i	$-0.460982\pi$
$373$	2.45096e8			0.244543			0.122272	+	0.992497i	$0.460982\pi$
$374$	−2.62641e9			−2.59604
$375$	2.84257e8			0.278357
$376$	4.82825e8	+	8.36278e8i	0.468417	+	0.811322i
$377$	−9.16067e8	+	3.99191e8i	−0.880507	+	0.383695i
$378$	−5.66493e8	+	6.57014e8i	−0.539478	+	0.625681i
$379$	3.95021e7	+	6.84197e7i	0.0372721	+	0.0645571i	0.884060	−	0.467374i	$-0.154800\pi$
$379$	3.95021e7	+	6.84197e7i	0.0372721	+	0.0645571i	−0.846788	+	0.531931i	$0.821467\pi$
$380$	−4.94022e8	+	8.55671e8i	−0.461853	+	0.799953i
$381$	−4.96841e7	−	8.60554e7i	−0.0460235	−	0.0797151i
$382$	1.14796e9	−	1.98833e9i	1.05367	−	1.82501i
$383$	−7.48291e7			−0.0680573			−0.0340287	−	0.999421i	$-0.510834\pi$
$383$	−7.48291e7			−0.0680573			−0.0340287	+	0.999421i	$0.510834\pi$
$384$	2.29342e8	−	3.97233e8i	0.206693	−	0.358002i
$385$	4.37841e8	+	1.25510e9i	0.391024	+	1.12090i
$386$	1.07448e9	−	1.86105e9i	0.950914	−	1.64703i
$387$	3.89967e8	−	6.75443e8i	0.342011	−	0.592380i
$388$	8.79254e8			0.764194
$389$	−3.52582e8	+	6.10690e8i	−0.303694	+	0.526014i	−0.976970	−	0.213378i	$-0.931554\pi$
$389$	−3.52582e8	+	6.10690e8i	−0.303694	+	0.526014i	0.673275	+	0.739392i	$0.264887\pi$
$390$	−5.34687e7	+	4.72658e8i	−0.0456430	+	0.403479i
$391$	2.62179e9			2.21809
$392$	−1.03408e9	−	4.08117e8i	−0.867071	−	0.342203i
$393$	2.26911e8	+	3.93021e8i	0.188574	+	0.326619i
$394$	−1.68639e9			−1.38906
$395$	5.39699e8	−	9.34787e8i	0.440618	−	0.763172i
$396$	1.13574e9	+	1.96717e9i	0.919068	+	1.59187i
$397$	−5.62011e8			−0.450794			−0.225397	−	0.974267i	$-0.572368\pi$
$397$	−5.62011e8			−0.450794			−0.225397	+	0.974267i	$0.572368\pi$
$398$	9.32770e8			0.741624
$399$	2.04905e8	+	3.89718e7i	0.161491	+	0.0307146i
$400$	−5.37089e6	−	9.30265e6i	−0.00419600	−	0.00726769i
$401$	−7.72404e8	+	1.33784e9i	−0.598190	+	1.03610i	0.394898	+	0.918725i	$0.370780\pi$
$401$	−7.72404e8	+	1.33784e9i	−0.598190	+	1.03610i	−0.993088	+	0.117371i	$0.962553\pi$
$402$	3.10965e8	−	5.38607e8i	0.238737	−	0.413505i
$403$	−1.73455e9	−	1.28135e9i	−1.32014	−	0.975215i
$404$	1.72096e9	+	2.98078e9i	1.29848	+	2.24903i
$405$	−5.01771e8	−	8.69093e8i	−0.375330	−	0.650090i
$406$	−2.04384e9	−	3.88726e8i	−1.51567	−	0.288272i
$407$	6.81806e8	−	1.18092e9i	0.501280	−	0.868243i
$408$	−2.20034e8	−	3.81110e8i	−0.160391	−	0.277805i
$409$	−6.12357e8	−	1.06063e9i	−0.442561	−	0.766539i	0.555318	−	0.831638i	$-0.312597\pi$
$409$	−6.12357e8	−	1.06063e9i	−0.442561	−	0.766539i	−0.997879	+	0.0650999i	$0.979263\pi$
$410$	4.11825e8	+	7.13302e8i	0.295100	+	0.511129i
$411$	2.15482e8	+	3.73225e8i	0.153096	+	0.265170i
$412$	7.81182e8	−	1.35305e9i	0.550316	−	0.953175i
$413$	8.07861e8	+	2.31579e9i	0.564302	+	1.61761i
$414$	−1.85118e9	−	3.20633e9i	−1.28217	−	2.22079i
$415$	1.25243e9	+	2.16927e9i	0.860169	+	1.48986i
$416$	1.43412e9	−	6.24941e8i	0.976695	−	0.425611i
$417$	−3.89519e7	+	6.74668e7i	−0.0263059	+	0.0455631i
$418$	9.25853e8	−	1.60362e9i	0.620048	−	1.07395i
$419$	2.17016e8	+	3.75883e8i	0.144126	+	0.249634i	0.929047	−	0.369963i	$-0.120630\pi$
$419$	2.17016e8	+	3.75883e8i	0.144126	+	0.249634i	−0.784920	+	0.619597i	$0.787296\pi$
$420$	−3.96075e8	+	4.59364e8i	−0.260859	+	0.302541i
$421$	6.22416e8			0.406531			0.203265	−	0.979124i	$-0.434845\pi$
$421$	6.22416e8			0.406531			0.203265	+	0.979124i	$0.434845\pi$
$422$	−1.12876e9			−0.731152
$423$	7.26621e8	+	1.25854e9i	0.466785	+	0.808495i
$424$	−2.04155e8	+	3.53607e8i	−0.130071	+	0.225289i
$425$	−2.06646e8			−0.130577
$426$	−6.23414e8	−	1.07979e9i	−0.390700	−	0.676712i
$427$	4.95862e8	+	9.43101e7i	0.308222	+	0.0586220i
$428$	−3.75064e9			−2.31234
$429$	6.13713e7	−	5.42516e8i	0.0375288	−	0.331751i
$430$	9.24444e8	−	1.60118e9i	0.560713	−	0.971184i
$431$	1.97526e8			0.118838			0.0594188	−	0.998233i	$-0.481075\pi$
$431$	1.97526e8			0.118838			0.0594188	+	0.998233i	$0.481075\pi$
$432$	3.57433e7	−	6.19092e7i	0.0213305	−	0.0369456i
$433$	−3.90068e8	+	6.75617e8i	−0.230904	+	0.399938i	−0.958075	−	0.286519i	$-0.907502\pi$
$433$	−3.90068e8	+	6.75617e8i	−0.230904	+	0.399938i	0.727170	+	0.686457i	$0.240835\pi$
$434$	−1.47888e9	−	4.23931e9i	−0.868399	−	2.48932i
$435$	−2.08409e8	+	3.60975e8i	−0.121396	+	0.210264i
$436$	−2.95137e9			−1.70538
$437$	−9.24227e8	+	1.60081e9i	−0.529778	+	0.917602i
$438$	−922470.	−	1.59777e6i	−0.000524557	−	0.000908560i
$439$	−5.98579e8	+	1.03677e9i	−0.337673	+	0.584866i	−0.983995	−	0.178199i	$-0.942973\pi$
$439$	−5.98579e8	+	1.03677e9i	−0.337673	+	0.584866i	0.646322	+	0.763065i	$0.276306\pi$
$440$	9.88659e8	+	1.71241e9i	0.553302	+	0.958347i
$441$	−1.55623e9	−	6.14190e8i	−0.864050	−	0.341010i
$442$	4.23074e8	−	3.73993e9i	0.233044	−	2.06009i
$443$	−1.13593e9	−	1.96748e9i	−0.620780	−	1.07522i	−0.989341	−	0.145619i	$-0.953483\pi$
$443$	−1.13593e9	−	1.96748e9i	−0.620780	−	1.07522i	0.368561	−	0.929604i	$-0.379851\pi$
$444$	6.22207e8			0.337361
$445$	2.22195e9			1.19529
$446$	−1.71911e9			−0.917554
$447$	3.76517e8			0.199392
$448$	3.04458e9	+	5.79062e8i	1.59976	+	0.304265i
$449$	3.01713e8	−	5.22582e8i	0.157301	−	0.272454i	−0.776593	−	0.630002i	$-0.783054\pi$
$449$	3.01713e8	−	5.22582e8i	0.157301	−	0.272454i	0.933895	+	0.357549i	$0.116387\pi$
$450$	1.45907e8	+	2.52719e8i	0.0754802	+	0.130735i
$451$	−4.72692e8	−	8.18727e8i	−0.242639	−	0.420263i
$452$	−3.03550e9			−1.54613
$453$	3.48909e8	−	6.04329e8i	0.176347	−	0.305442i
$454$	1.72702e9			0.866168
$455$	−1.85776e9	+	4.21296e8i	−0.924589	+	0.209675i
$456$	3.10263e8			0.153233
$457$	4.10532e8	−	7.11063e8i	0.201206	−	0.348499i	−0.747711	−	0.664024i	$-0.768847\pi$
$457$	4.10532e8	−	7.11063e8i	0.201206	−	0.348499i	0.948917	+	0.315525i	$0.102181\pi$
$458$	1.44919e9			0.704850
$459$	−6.87617e8	−	1.19099e9i	−0.331896	−	0.574861i
$460$	−2.68763e9	−	4.65511e9i	−1.28741	−	2.22986i
$461$	4.94902e8	−	8.57196e8i	0.235270	−	0.407499i	−0.724081	−	0.689715i	$-0.757736\pi$
$461$	4.94902e8	−	8.57196e8i	0.235270	−	0.407499i	0.959351	+	0.282215i	$0.0910693\pi$
$462$	7.42290e8	−	8.60901e8i	0.350208	−	0.406169i
$463$	−6.02402e8			−0.282068			−0.141034	−	0.990005i	$-0.545043\pi$
$463$	−6.02402e8			−0.282068			−0.141034	+	0.990005i	$0.545043\pi$
$464$	1.71439e8			0.0796705
$465$	−8.99532e8			−0.414888
$466$	2.06691e9			0.946173
$467$	2.75922e8	+	4.77910e8i	0.125365	+	0.217139i	0.921876	−	0.387486i	$-0.126656\pi$
$467$	2.75922e8	+	4.77910e8i	0.125365	+	0.217139i	−0.796510	+	0.604625i	$0.793323\pi$
$468$	−2.98414e9	+	1.30039e9i	−1.34573	+	0.586425i
$469$	2.44678e9	+	4.65364e8i	1.09519	+	0.208299i
$470$	1.72250e9	+	2.98346e9i	0.765275	+	1.32550i
$471$	−2.05713e7	+	3.56306e7i	−0.00907171	+	0.0157127i
$472$	1.82418e9	+	3.15957e9i	0.798490	+	1.38303i
$473$	−1.06107e9	+	1.83783e9i	−0.461033	+	0.798532i
$474$	−9.23042e8			−0.398105
$475$	7.28463e7	−	1.26173e8i	0.0311874	−	0.0540182i
$476$	3.13396e9	−	3.63474e9i	1.33189	−	1.54472i
$477$	−3.07240e8	+	5.32156e8i	−0.129618	+	0.224504i
$478$	2.66891e9	−	4.62268e9i	1.11773	−	1.93596i
$479$	−1.85819e9			−0.772532			−0.386266	−	0.922387i	$-0.626235\pi$
$479$	−1.85819e9			−0.772532			−0.386266	+	0.922387i	$0.626235\pi$
$480$	3.26268e8	−	5.65113e8i	0.134657	−	0.233233i
$481$	1.57177e9	+	1.16110e9i	0.643994	+	0.475732i
$482$	−2.51462e9			−1.02284
$483$	−7.40986e8	+	8.59389e8i	−0.299223	+	0.347036i
$484$	−1.11936e9	−	1.93879e9i	−0.448758	−	0.777272i
$485$	1.15186e9			0.458461
$486$	−1.47441e9	+	2.55376e9i	−0.582630	+	1.00914i
$487$	−1.67305e8	−	2.89781e8i	−0.0656384	−	0.113689i	0.831339	−	0.555766i	$-0.187575\pi$
$487$	−1.67305e8	−	2.89781e8i	−0.0656384	−	0.113689i	−0.896977	+	0.442077i	$0.854242\pi$
$488$	7.50824e8			0.292462
$489$	−1.14497e9			−0.442804
$490$	−3.68915e9	−	1.45598e9i	−1.41658	−	0.559073i
$491$	1.91646e9	+	3.31940e9i	0.730657	+	1.26554i	0.956603	+	0.291395i	$0.0941195\pi$
$491$	1.91646e9	+	3.31940e9i	0.730657	+	1.26554i	−0.225946	+	0.974140i	$0.572547\pi$
$492$	2.15686e8	−	3.73579e8i	0.0816478	−	0.141418i
$493$	1.64904e9	−	2.85623e9i	0.619824	−	1.07357i
$494$	2.13438e9	+	1.57671e9i	0.796575	+	0.588447i
$495$	1.48787e9	+	2.57706e9i	0.551374	+	0.955008i
$496$	1.84991e8	+	3.20414e8i	0.0680715	+	0.117903i
$497$	3.26058e9	−	3.78159e9i	1.19137	−	1.38174i
$498$	1.07101e9	−	1.85504e9i	0.388588	−	0.673054i
$499$	7.65175e8	+	1.32532e9i	0.275682	+	0.477496i	0.970307	−	0.241876i	$-0.0777629\pi$
$499$	7.65175e8	+	1.32532e9i	0.275682	+	0.477496i	−0.694625	+	0.719372i	$0.744430\pi$
$500$	2.30568e9	+	3.99355e9i	0.824904	+	1.42877i
$501$	2.38645e7	+	4.13345e7i	0.00847852	+	0.0146852i
$502$	5.56878e8	+	9.64541e8i	0.196470	+	0.340297i
$503$	1.25123e9	−	2.16719e9i	0.438378	−	0.759292i	−0.559187	−	0.829042i	$-0.688887\pi$
$503$	1.25123e9	−	2.16719e9i	0.438378	−	0.759292i	0.997565	+	0.0697493i	$0.0222199\pi$
$504$	−2.44485e9	−	4.64996e8i	−0.850639	−	0.161787i
$505$	2.25452e9	+	3.90494e9i	0.778993	+	1.34926i
$506$	5.03692e9	+	8.72420e9i	1.72838	+	2.99364i
$507$	7.62642e8	+	1.74782e8i	0.259892	+	0.0595619i
$508$	8.05999e8	−	1.39603e9i	0.272779	−	0.472467i
$509$	1.35038e9	−	2.33893e9i	0.453883	−	0.786148i	−0.544740	−	0.838605i	$-0.683372\pi$
$509$	1.35038e9	−	2.33893e9i	0.453883	−	0.786148i	0.998623	+	0.0524567i	$0.0167051\pi$
$510$	−7.84982e8	−	1.35963e9i	−0.262038	−	0.453863i
$511$	4.82470e6	−	5.59564e6i	0.00159955	−	0.00185514i
$512$	−5.03217e8			−0.165695
$513$	9.69586e8			0.317085
$514$	8.44528e8	+	1.46277e9i	0.274311	+	0.475120i
$515$	1.02338e9	−	1.77254e9i	0.330150	−	0.571836i
$516$	−9.68321e8			−0.310274
$517$	−1.97708e9	−	3.42441e9i	−0.629229	−	1.08986i
$518$	1.34010e9	+	3.84147e9i	0.423625	+	1.21435i
$519$	−2.58450e8			−0.0811503
$520$	−2.59768e9	+	1.13198e9i	−0.810165	+	0.353043i
$521$	−6.30656e8	+	1.09233e9i	−0.195371	+	0.338393i	−0.947022	−	0.321168i	$-0.895924\pi$
$521$	−6.30656e8	+	1.09233e9i	−0.195371	+	0.338393i	0.751651	+	0.659561i	$0.229258\pi$
$522$	−4.65738e9			−1.43316
$523$	−1.88998e9	+	3.27355e9i	−0.577699	+	1.00060i	0.418043	+	0.908427i	$0.362716\pi$
$523$	−1.88998e9	+	3.27355e9i	−0.577699	+	1.00060i	−0.995743	+	0.0921777i	$0.970617\pi$
$524$	−3.68105e9	+	6.37577e9i	−1.11767	+	1.93586i
$525$	5.84035e7	−	6.77358e7i	0.0176149	−	0.0204297i
$526$	−4.05942e9	+	7.03112e9i	−1.21622	+	2.10656i
$527$	7.11758e9			2.11834
$528$	−4.68353e7	+	8.11211e7i	−0.0138470	+	0.0239837i
$529$	−3.32566e9	−	5.76021e9i	−0.976749	−	1.69178i
$530$	−7.28333e8	+	1.26151e9i	−0.212503	+	0.368066i
$531$	2.74527e9	+	4.75494e9i	0.795708	+	1.37821i
$532$	1.11452e9	+	3.19483e9i	0.320919	+	0.919936i
$533$	1.24199e9	−	5.41216e8i	0.355281	−	0.154819i
$534$	−9.50045e8	−	1.64553e9i	−0.269991	−	0.467639i
$535$	−4.91348e9			−1.38724
$536$	3.70486e9			1.03919
$537$	−3.71889e8			−0.103634
$538$	5.90978e9			1.63619
$539$	4.23440e9	+	1.67117e9i	1.16474	+	0.459684i
$540$	−1.40977e9	+	2.44179e9i	−0.385273	+	0.667313i
$541$	−2.70042e9	−	4.67727e9i	−0.733232	−	1.26999i	−0.955495	−	0.295008i	$-0.904678\pi$
$541$	−2.70042e9	−	4.67727e9i	−0.733232	−	1.26999i	0.222263	−	0.974987i	$-0.428656\pi$
$542$	1.72572e8	+	2.98904e8i	0.0465558	+	0.0806370i
$543$	1.53083e8			0.0410324
$544$	−2.58161e9	+	4.47148e9i	−0.687534	+	1.19084i
$545$	−3.86641e9			−1.02310
$546$	1.10633e9	+	1.19568e9i	0.290877	+	0.314369i
$547$	−5.72630e9			−1.49595			−0.747977	−	0.663724i	$-0.768975\pi$
$547$	−5.72630e9			−1.49595			−0.747977	+	0.663724i	$0.768975\pi$
$548$	−3.49565e9	+	6.05464e9i	−0.907393	+	1.57165i
$549$	1.12994e9			0.291443
$550$	−3.97003e8	−	6.87630e8i	−0.101748	−	0.176232i
$551$	1.16263e9	+	2.01374e9i	0.296082	+	0.512829i
$552$	−8.43961e8	+	1.46178e9i	−0.213568	+	0.369910i
$553$	−1.21756e9	−	3.49023e9i	−0.306164	−	0.877639i
$554$	−1.55143e9			−0.387658
$555$	8.15114e8			0.202392
$556$	−1.26379e9			−0.311827
$557$	3.22125e9			0.789825			0.394913	−	0.918719i	$-0.370775\pi$
$557$	3.22125e9			0.789825			0.394913	+	0.918719i	$0.370775\pi$
$558$	−5.02553e9	−	8.70447e9i	−1.22451	−	2.12091i
$559$	−2.44610e9	−	1.80699e9i	−0.592288	−	0.437536i
$560$	3.21064e8	+	6.10645e7i	0.0772562	+	0.0146937i
$561$	9.01001e8	+	1.56058e9i	0.215454	+	0.373178i
$562$	1.62997e9	−	2.82320e9i	0.387350	−	0.670910i
$563$	−2.96189e9	−	5.13015e9i	−0.699504	−	1.21158i	−0.968639	−	0.248474i	$-0.920071\pi$
$563$	−2.96189e9	−	5.13015e9i	−0.699504	−	1.21158i	0.269135	−	0.963103i	$-0.413262\pi$
$564$	9.02130e8	−	1.56254e9i	0.211735	−	0.366735i
$565$	−3.97662e9			−0.927565
$566$	−2.01132e9	+	3.48371e9i	−0.466256	+	0.807578i
$567$	−3.37620e9	−	6.42134e8i	−0.777836	−	0.147940i
$568$	3.71370e9	−	6.43233e9i	0.850331	−	1.47282i
$569$	−2.84519e9	+	4.92801e9i	−0.647467	+	1.12145i	0.336258	+	0.941770i	$0.390838\pi$
$569$	−2.84519e9	+	4.92801e9i	−0.647467	+	1.12145i	−0.983726	+	0.179677i	$0.942495\pi$
$570$	1.10688e9			0.250344
$571$	−2.09194e9	+	3.62335e9i	−0.470244	+	0.814486i	−0.999421	−	0.0340254i	$-0.989167\pi$
$571$	−2.09194e9	+	3.62335e9i	−0.470244	+	0.814486i	0.529177	+	0.848511i	$0.322501\pi$
$572$	8.11964e9	−	3.53827e9i	1.81406	−	0.790504i
$573$	−1.57525e9			−0.349791
$574$	2.77100e9	+	5.27028e8i	0.611568	+	0.116317i
$575$	3.96306e8	+	6.86422e8i	0.0869347	+	0.150575i
$576$	6.93781e9			1.51267
$577$	1.57013e9	−	2.71955e9i	0.340268	−	0.589361i	−0.644215	−	0.764845i	$-0.722816\pi$
$577$	1.57013e9	−	2.71955e9i	0.340268	−	0.589361i	0.984482	+	0.175484i	$0.0561490\pi$
$578$	2.48255e9	+	4.29990e9i	0.534749	+	0.926213i
$579$	−1.47441e9			−0.315678
$580$	−6.76181e9			−1.43901
$581$	8.42705e9	+	1.60278e9i	1.78262	+	0.339044i
$582$	−4.92502e8	−	8.53038e8i	−0.103556	−	0.179365i
$583$	8.35979e8	−	1.44796e9i	0.174725	−	0.302633i
$584$	5.49519e6	−	9.51795e6i	0.00114166	−	0.00197742i
$585$	−3.90934e9	+	1.70356e9i	−0.807342	+	0.351813i
$586$	−1.91714e9	−	3.32058e9i	−0.393561	−	0.681667i
$587$	4.00580e8	+	6.93826e8i	0.0817441	+	0.141585i	0.903999	−	0.427534i	$-0.140618\pi$
$587$	4.00580e8	+	6.93826e8i	0.0817441	+	0.141585i	−0.822255	+	0.569119i	$0.807284\pi$
$588$	3.05682e8	+	2.05454e9i	0.0620082	+	0.416768i
$589$	−2.50907e9	+	4.34583e9i	−0.505952	+	0.876334i
$590$	6.50784e9	+	1.12719e10i	1.30453	+	2.25952i
$591$	5.78522e8	+	1.00203e9i	0.115283	+	0.199675i
$592$	−1.67631e8	−	2.90345e8i	−0.0332068	−	0.0575159i
$593$	−4.08545e9	−	7.07620e9i	−0.804541	−	1.39351i	−0.916601	−	0.399804i	$-0.869078\pi$
$593$	−4.08545e9	−	7.07620e9i	−0.804541	−	1.39351i	0.112060	−	0.993701i	$-0.464255\pi$
$594$	2.64206e9	−	4.57618e9i	0.517238	−	0.895882i
$595$	4.10561e9	−	4.76165e9i	0.799039	−	0.926719i
$596$	3.05401e9	+	5.28971e9i	0.590893	+	1.02346i
$597$	−3.19991e8	−	5.54240e8i	−0.0615499	−	0.106608i
$598$	−1.32344e10	+	5.76710e9i	−2.53075	+	1.10282i
$599$	3.27459e9	−	5.67176e9i	0.622535	−	1.07826i	−0.366477	−	0.930427i	$-0.619436\pi$
$599$	3.27459e9	−	5.67176e9i	0.622535	−	1.07826i	0.989012	−	0.147835i	$-0.0472304\pi$
$600$	6.65199e7	−	1.15216e8i	0.0125725	−	0.0217762i
$601$	1.94065e9	+	3.36130e9i	0.364659	+	0.631607i	0.988721	−	0.149767i	$-0.0478523\pi$
$601$	1.94065e9	+	3.36130e9i	0.364659	+	0.631607i	−0.624063	+	0.781374i	$0.714519\pi$
$602$	−2.08555e9	−	5.97836e9i	−0.389612	−	1.11685i
$603$	5.57558e9			1.03557
$604$	1.13203e10			2.09040
$605$	−1.46641e9	−	2.53989e9i	−0.269222	−	0.466307i
$606$	1.92794e9	−	3.33929e9i	0.351916	−	0.609536i
$607$	−1.59893e9			−0.290180			−0.145090	−	0.989418i	$-0.546347\pi$
$607$	−1.59893e9			−0.290180			−0.145090	+	0.989418i	$0.546347\pi$
$608$	−1.82012e9	−	3.15254e9i	−0.328426	−	0.568851i
$609$	4.70171e8	+	1.34778e9i	0.0843520	+	0.241801i
$610$	2.67860e9			0.477808
$611$	5.19474e9	−	2.26369e9i	0.921340	−	0.401489i
$612$	5.37186e9	−	9.30433e9i	0.947315	−	1.64080i
$613$	9.66451e9			1.69460			0.847302	−	0.531112i	$-0.178226\pi$
$613$	9.66451e9			1.69460			0.847302	+	0.531112i	$0.178226\pi$
$614$	8.22807e9	−	1.42514e10i	1.43453	−	2.48467i
$615$	2.82557e8	−	4.89403e8i	0.0489827	−	0.0848406i
$616$	6.65227e9	+	1.26522e9i	1.14667	+	0.218089i
$617$	−4.70426e9	+	8.14802e9i	−0.806294	+	1.39654i	0.109120	+	0.994029i	$0.465197\pi$
$617$	−4.70426e9	+	8.14802e9i	−0.806294	+	1.39654i	−0.915414	+	0.402514i	$0.868136\pi$
$618$	−1.75027e9			−0.298295
$619$	−7.51824e8	+	1.30220e9i	−0.127409	+	0.220678i	−0.922672	−	0.385586i	$-0.873999\pi$
$619$	−7.51824e8	+	1.30220e9i	−0.127409	+	0.220678i	0.795263	+	0.606264i	$0.207333\pi$
$620$	−7.29631e9	−	1.26376e10i	−1.22951	−	2.12957i
$621$	−2.63742e9	+	4.56815e9i	−0.441935	+	0.765454i
$622$	−5.25155e9	−	9.09596e9i	−0.875027	−	1.51559i
$623$	4.96892e9	−	5.76291e9i	0.823292	−	0.954847i
$624$	−1.07970e8	−	7.97595e7i	−0.0177892	−	0.0131412i
$625$	2.71177e9	+	4.69693e9i	0.444297	+	0.769545i
$626$	−1.00115e10			−1.63114
$627$	−1.27047e9			−0.205839
$628$	−6.67436e8			−0.107535
$629$	−6.44963e9			−1.03337
$630$	−8.72213e9	−	1.65890e9i	−1.38973	−	0.264319i
$631$	−1.58034e9	+	2.73723e9i	−0.250408	+	0.433719i	−0.963638	−	0.267211i	$-0.913898\pi$
$631$	−1.58034e9	+	2.73723e9i	−0.250408	+	0.433719i	0.713230	+	0.700930i	$0.247231\pi$
$632$	−2.74930e9	−	4.76193e9i	−0.433224	−	0.750365i
$633$	3.87226e8	+	6.70695e8i	0.0606808	+	0.105102i
$634$	−1.27853e10			−1.99251
$635$	1.05589e9	−	1.82885e9i	0.163648	−	0.283446i
$636$	7.62903e8			0.117590
$637$	−3.06179e9	+	5.76046e9i	−0.469340	+	0.883018i
$638$	1.26724e10			1.93191
$639$	5.58889e9	−	9.68024e9i	0.847369	−	1.46769i
$640$	9.74799e9			1.46989
$641$	−1.27445e9	−	2.20742e9i	−0.191126	−	0.331040i	0.754497	−	0.656303i	$-0.227881\pi$
$641$	−1.27445e9	−	2.20742e9i	−0.191126	−	0.331040i	−0.945624	+	0.325262i	$0.894547\pi$
$642$	2.10087e9	+	3.63881e9i	0.313348	+	0.542734i
$643$	4.45614e9	−	7.71827e9i	0.661029	−	1.14494i	−0.319316	−	0.947648i	$-0.603453\pi$
$643$	4.45614e9	−	7.71827e9i	0.661029	−	1.14494i	0.980346	−	0.197288i	$-0.0632134\pi$
$644$	−1.80839e10	−	3.43946e9i	−2.66804	−	0.507445i
$645$	−1.26854e9			−0.186142
$646$	−8.75822e9			−1.27821
$647$	1.33644e8			0.0193992			0.00969962	−	0.999953i	$-0.496912\pi$
$647$	1.33644e8			0.0193992			0.00969962	+	0.999953i	$0.496912\pi$
$648$	−5.11217e9			−0.738062
$649$	−7.46968e9	−	1.29379e10i	−1.07262	−	1.85783i
$650$	1.04312e9	−	4.54555e8i	0.148983	−	0.0649216i
$651$	−2.01161e9	+	2.33305e9i	−0.285766	+	0.331429i
$652$	−9.28709e9	−	1.60857e10i	−1.31224	−	2.27287i
$653$	1.86854e9	−	3.23641e9i	0.262607	−	0.454849i	−0.704327	−	0.709876i	$-0.748751\pi$
$653$	1.86854e9	−	3.23641e9i	0.262607	−	0.454849i	0.966934	+	0.255027i	$0.0820843\pi$
$654$	1.65317e9	+	2.86337e9i	0.231098	+	0.400273i
$655$	−4.82232e9	+	8.35250e9i	−0.670519	+	1.16137i
$656$	−2.32434e8			−0.0321467
$657$	8.26991e6	−	1.43239e7i	0.00113768	−	0.00197053i
$658$	1.15900e10	+	2.20435e9i	1.58596	+	0.301641i
$659$	−1.56303e9	+	2.70725e9i	−0.212750	+	0.368493i	−0.952574	−	0.304307i	$-0.901575\pi$
$659$	−1.56303e9	+	2.70725e9i	−0.212750	+	0.368493i	0.739824	+	0.672800i	$0.234909\pi$
$660$	1.84725e9	−	3.19953e9i	0.250105	−	0.433194i
$661$	−5.28922e9			−0.712339			−0.356170	−	0.934421i	$-0.615917\pi$
$661$	−5.28922e9			−0.712339			−0.356170	+	0.934421i	$0.615917\pi$
$662$	−4.29088e9	+	7.43202e9i	−0.574835	+	0.995644i
$663$	−2.36736e9	+	1.03161e9i	−0.315476	+	0.137474i
$664$	1.27601e10			1.69147
$665$	1.46006e9	+	4.18535e9i	0.192528	+	0.551895i
$666$	4.55390e9	+	7.88759e9i	0.597343	+	1.03463i
$667$	−1.26501e10			−1.65065
$668$	−3.87141e8	+	6.70548e8i	−0.0502518	+	0.0870386i
$669$	5.89748e8	+	1.02147e9i	0.0761509	+	0.131897i
$670$	1.32173e10			1.69778
$671$	−3.07449e9			−0.392866
$672$	−7.36062e8	−	2.10997e9i	−0.0935668	−	0.268215i
$673$	−1.00617e9	−	1.74274e9i	−0.127239	−	0.220384i	0.795367	−	0.606128i	$-0.207278\pi$
$673$	−1.00617e9	−	1.74274e9i	−0.127239	−	0.220384i	−0.922606	+	0.385744i	$0.873945\pi$
$674$	−8.51558e9	+	1.47494e10i	−1.07128	+	1.85552i
$675$	2.07878e8	−	3.60055e8i	0.0260163	−	0.0450615i
$676$	3.73044e9	+	1.21321e10i	0.464458	+	1.51051i
$677$	−2.67935e9	−	4.64077e9i	−0.331871	−	0.574817i	0.651008	−	0.759071i	$-0.274346\pi$
$677$	−2.67935e9	−	4.64077e9i	−0.331871	−	0.574817i	−0.982879	+	0.184254i	$0.941013\pi$
$678$	1.70029e9	+	2.94499e9i	0.209517	+	0.362894i
$679$	2.57588e9	−	2.98748e9i	0.315778	−	0.366236i
$680$	4.67617e9	−	8.09936e9i	0.570308	−	0.987802i
$681$	−5.92462e8	−	1.02617e9i	−0.0718862	−	0.124511i
$682$	1.36741e10	+	2.36842e10i	1.65064	+	2.85900i
$683$	−2.49173e9	−	4.31581e9i	−0.299246	−	0.518310i	0.676717	−	0.736243i	$-0.263402\pi$
$683$	−2.49173e9	−	4.31581e9i	−0.299246	−	0.518310i	−0.975964	+	0.217933i	$0.930069\pi$
$684$	3.78734e9	+	6.55987e9i	0.452520	+	0.783788i
$685$	−4.57943e9	+	7.93180e9i	−0.544370	+	0.942876i
$686$	−1.20263e10	+	6.31229e9i	−1.42232	+	0.746539i
$687$	−4.97152e8	−	8.61092e8i	−0.0584979	−	0.101321i
$688$	2.60878e8	+	4.51854e8i	0.0305407	+	0.0528980i
$689$	1.92719e9	+	1.42365e9i	0.224469	+	0.165820i
$690$	−3.01087e9	+	5.21499e9i	−0.348916	+	0.604340i
$691$	−4.64282e9	+	8.04160e9i	−0.535314	+	0.927191i	0.463834	+	0.885922i	$0.346473\pi$
$691$	−4.64282e9	+	8.04160e9i	−0.535314	+	0.927191i	−0.999148	+	0.0412690i	$0.986860\pi$
$692$	−2.09634e9	−	3.63097e9i	−0.240487	−	0.416535i
$693$	1.00112e10	+	1.90408e9i	1.14267	+	0.217329i
$694$	6.87917e9			0.781228
$695$	−1.65562e9			−0.187074
$696$	1.06166e9	+	1.83885e9i	0.119359	+	0.206735i
$697$	−2.23574e9	+	3.87242e9i	−0.250096	+	0.433180i
$698$	−1.92093e10			−2.13805
$699$	−7.09062e8	−	1.22813e9i	−0.0785261	−	0.136011i
$700$	1.42535e9	+	2.71093e8i	0.157065	+	0.0298728i
$701$	−3.27292e9			−0.358858			−0.179429	−	0.983771i	$-0.557425\pi$
$701$	−3.27292e9			−0.358858			−0.179429	+	0.983771i	$0.557425\pi$
$702$	6.09076e9	+	4.49937e9i	0.664495	+	0.490876i
$703$	2.27360e9	−	3.93800e9i	0.246815	−	0.427496i
$704$	−1.88773e10			−2.03909
$705$	1.18182e9	−	2.04698e9i	0.127026	−	0.220015i
$706$	−1.00494e10	+	1.74061e10i	−1.07479	+	1.86160i
$707$	1.51697e10	+	2.88519e9i	1.61439	+	0.307048i
$708$	3.40836e9	−	5.90346e9i	0.360935	−	0.625158i
$709$	−4.07705e9			−0.429620			−0.214810	−	0.976656i	$-0.568913\pi$
$709$	−4.07705e9			−0.429620			−0.214810	+	0.976656i	$0.568913\pi$
$710$	1.32488e10	−	2.29476e10i	1.38923	−	2.40621i
$711$	−4.13752e9	−	7.16639e9i	−0.431714	−	0.747751i
$712$	5.65946e9	−	9.80247e9i	0.587618	−	1.01778i
$713$	−1.36501e10	−	2.36426e10i	−1.41033	−	2.44277i
$714$	−5.28181e9	−	1.00457e9i	−0.543049	−	0.103285i
$715$	1.06370e10	−	4.63526e9i	1.08830	−	0.474245i
$716$	−3.01648e9	−	5.22469e9i	−0.307117	−	0.531943i
$717$	−3.66232e9			−0.371056
$718$	−5.14803e9			−0.519046
$719$	1.79567e10			1.80167			0.900837	−	0.434156i	$-0.142953\pi$
$719$	1.79567e10			1.80167			0.900837	+	0.434156i	$0.142953\pi$
$720$	7.31622e8			0.0730504
$721$	−2.30874e9	−	6.61817e9i	−0.229405	−	0.657604i
$722$	−5.03500e9	+	8.72087e9i	−0.497874	+	0.862342i
$723$	8.62651e8	+	1.49416e9i	0.0848889	+	0.147032i
$724$	1.24169e9	+	2.15067e9i	0.121598	+	0.210615i
$725$	9.97066e8			0.0971720
$726$	−1.25399e9	+	2.17198e9i	−0.121623	+	0.210657i
$727$	−1.21852e8			−0.0117615			−0.00588075	−	0.999983i	$-0.501872\pi$
$727$	−1.21852e8			−0.0117615			−0.00588075	+	0.999983i	$0.501872\pi$
$728$	−2.87322e9	+	9.26883e9i	−0.276000	+	0.890359i
$729$	−6.25908e9			−0.598362
$730$	1.96044e7	−	3.39558e7i	0.00186519	−	0.00323060i
$731$	1.00374e10			0.950405
$732$	−7.01435e8	−	1.21492e9i	−0.0660996	−	0.114488i
$733$	5.80429e8	+	1.00533e9i	0.0544359	+	0.0942857i	0.891959	−	0.452116i	$-0.149331\pi$
$733$	5.80429e8	+	1.00533e9i	0.0544359	+	0.0942857i	−0.837523	+	0.546401i	$0.815997\pi$
$734$	−1.85645e9	+	3.21546e9i	−0.173279	+	0.300128i
$735$	4.00455e8	+	2.69153e9i	0.0372004	+	0.250030i
$736$	1.98040e10			1.83097
$737$	−1.51708e10			−1.39595
$738$	6.31439e9			0.578274
$739$	2.28911e9			0.208647			0.104323	−	0.994543i	$-0.466732\pi$
$739$	2.28911e9			0.208647			0.104323	+	0.994543i	$0.466732\pi$
$740$	6.61158e9	+	1.14516e10i	0.599783	+	1.03886i
$741$	2.04653e8	−	1.80912e9i	0.0184780	−	0.163344i
$742$	1.64312e9	+	4.71012e9i	0.147658	+	0.423271i
$743$	1.52769e9	+	2.64603e9i	0.136639	+	0.236665i	0.926222	−	0.376978i	$-0.123037\pi$
$743$	1.52769e9	+	2.64603e9i	0.136639	+	0.236665i	−0.789584	+	0.613643i	$0.789703\pi$
$744$	−2.29117e9	+	3.96842e9i	−0.203963	+	0.353274i
$745$	4.00087e9	+	6.92971e9i	0.354493	+	0.614000i
$746$	2.22713e9	−	3.85751e9i	0.196409	−	0.340190i
$747$	1.92031e10			1.68558
$748$	−1.46164e10	+	2.53164e10i	−1.27699	+	2.21181i
$749$	−1.09880e10	+	1.27437e10i	−0.955500	+	1.10818i
$750$	2.58298e9	−	4.47386e9i	0.223567	−	0.387229i
$751$	4.42457e9	−	7.66358e9i	0.381181	−	0.660225i	−0.610050	−	0.792363i	$-0.708851\pi$
$751$	4.42457e9	−	7.66358e9i	0.381181	−	0.660225i	0.991231	+	0.132138i	$0.0421841\pi$
$752$	−9.72182e8			−0.0833652
$753$	3.82079e8	−	6.61780e8i	0.0326115	−	0.0564847i
$754$	−2.04133e9	+	1.80451e10i	−0.173426	+	1.53306i
$755$	1.48301e10			1.25409
$756$	3.18044e9	+	9.11694e9i	0.267708	+	0.767402i
$757$	−3.55386e9	−	6.15547e9i	−0.297759	−	0.515734i	0.677864	−	0.735187i	$-0.262906\pi$
$757$	−3.55386e9	−	6.15547e9i	−0.297759	−	0.515734i	−0.975623	+	0.219454i	$0.929573\pi$
$758$	1.43579e9			0.119743
$759$	3.45587e9	−	5.98575e9i	0.286888	−	0.496904i
$760$	3.29686e9	+	5.71032e9i	0.272429	+	0.471860i
$761$	−1.20506e10			−0.991204			−0.495602	−	0.868550i	$-0.665053\pi$
$761$	−1.20506e10			−0.991204			−0.495602	+	0.868550i	$0.665053\pi$
$762$	−1.80587e9			−0.147858
$763$	−8.64640e9	+	1.00280e10i	−0.704692	+	0.817296i
$764$	−1.27772e10	−	2.21308e10i	−1.03660	−	1.79544i
$765$	7.03734e9	−	1.21890e10i	0.568320	−	0.984360i
$766$	−6.79956e8	+	1.17772e9i	−0.0546613	+	0.0946762i
$767$	1.96264e10	−	8.55253e9i	1.57057	−	0.684401i
$768$	−1.44267e9	−	2.49878e9i	−0.114922	−	0.199051i
$769$	1.03707e10	+	1.79627e10i	0.822371	+	1.42439i	0.903912	+	0.427719i	$0.140683\pi$
$769$	1.03707e10	+	1.79627e10i	0.822371	+	1.42439i	−0.0815407	+	0.996670i	$0.525984\pi$
$770$	2.37323e10	+	4.51374e9i	1.87336	+	0.356303i
$771$	5.79438e8	−	1.00362e9i	0.0455320	−	0.0788637i
$772$	−1.19593e10	−	2.07141e10i	−0.935504	−	1.62034i
$773$	4.47611e9	+	7.75284e9i	0.348556	+	0.603716i	0.985993	−	0.166786i	$-0.0533389\pi$
$773$	4.47611e9	+	7.75284e9i	0.348556	+	0.603716i	−0.637437	+	0.770502i	$0.720006\pi$
$774$	−7.08710e9	−	1.22752e10i	−0.549383	−	0.951559i
$775$	1.07588e9	+	1.86348e9i	0.0830249	+	0.143803i
$776$	2.93385e9	−	5.08158e9i	0.225384	−	0.390376i
$777$	1.82283e9	−	2.11410e9i	0.139403	−	0.161678i
$778$	6.40768e9	+	1.10984e10i	0.487834	+	0.844953i
$779$	−1.57628e9	−	2.73019e9i	−0.119468	−	0.206924i
$780$	4.25848e9	+	3.14583e9i	0.321309	+	0.237358i
$781$	−1.52070e10	+	2.63392e10i	−1.14226	+	1.97845i
$782$	2.38237e10	−	4.12638e10i	1.78150	−	3.08564i
$783$	3.31774e9	+	5.74650e9i	0.246989	+	0.427797i
$784$	8.76370e8	−	6.96162e8i	0.0649503	−	0.0515946i
$785$	−8.74366e8			−0.0645133
$786$	8.24756e9			0.605824
$787$	−5.63964e9	−	9.76814e9i	−0.412420	−	0.714332i	0.582734	−	0.812663i	$-0.301983\pi$
$787$	−5.63964e9	−	9.76814e9i	−0.412420	−	0.714332i	−0.995154	+	0.0983309i	$0.968650\pi$
$788$	−9.38505e9	+	1.62554e10i	−0.683274	+	1.18346i
$789$	5.57040e9			0.403754
$790$	−9.80826e9	−	1.69884e10i	−0.707778	−	1.22591i
$791$	−8.89285e9	+	1.03139e10i	−0.638886	+	0.740975i
$792$	1.51588e10			1.08424
$793$	4.95253e8	−	4.37799e9i	0.0352672	−	0.311759i
$794$	−5.10688e9	+	8.84537e9i	−0.362062	+	0.627111i
$795$	9.99431e8			0.0705453
$796$	5.19104e9	−	8.99114e9i	0.364803	−	0.631858i
$797$	5.89603e9	−	1.02122e10i	0.412530	−	0.714523i	−0.582635	−	0.812734i	$-0.697978\pi$
$797$	5.89603e9	−	1.02122e10i	0.412530	−	0.714523i	0.995166	+	0.0982103i	$0.0313118\pi$
$798$	2.47530e9	−	2.87083e9i	0.172432	−	0.199985i
$799$	−9.35124e9	+	1.61968e10i	−0.648568	+	1.12335i
$800$	−1.56093e9			−0.107787
$801$	8.51712e9	−	1.47521e10i	0.585570	−	1.01424i
$802$	1.40373e10	+	2.43134e10i	0.960892	+	1.66431i
$803$	−2.25018e7	+	3.89743e7i	−0.00153361	+	0.00265628i
$804$	−3.46116e9	−	5.99490e9i	−0.234869	−	0.406805i
$805$	−2.36906e10	−	4.50582e9i	−1.60063	−	0.304430i
$806$	−3.59284e10	+	1.56564e10i	−2.41694	+	1.05322i
$807$	−2.02738e9	−	3.51152e9i	−0.135793	−	0.235200i
$808$	2.29696e10			1.53184
$809$	−2.91851e9			−0.193794			−0.0968971	−	0.995294i	$-0.530892\pi$
$809$	−2.91851e9			−0.193794			−0.0968971	+	0.995294i	$0.530892\pi$
$810$	−1.82379e10			−1.20581
$811$	2.52560e10			1.66261			0.831307	−	0.555813i	$-0.187593\pi$
$811$	2.52560e10			1.66261			0.831307	+	0.555813i	$0.187593\pi$
$812$	−1.51213e10	+	1.75376e10i	−0.991161	+	1.14954i
$813$	1.18403e8	−	2.05081e8i	0.00772764	−	0.0133847i
$814$	−1.23909e10	−	2.14616e10i	−0.805222	−	1.39469i
$815$	−1.21664e10	−	2.10729e10i	−0.787249	−	1.36355i
$816$	4.43044e8			0.0285451
$817$	−3.53834e9	+	6.12858e9i	−0.226998	+	0.393172i
$818$	−2.22574e10			−1.42180
$819$	−4.32401e9	+	1.39490e10i	−0.275038	+	0.887257i
$820$	9.16754e9			0.580636
$821$	−1.77028e9	+	3.06621e9i	−0.111645	+	0.193375i	−0.916434	−	0.400186i	$-0.868945\pi$
$821$	−1.77028e9	+	3.06621e9i	−0.111645	+	0.193375i	0.804788	+	0.593562i	$0.202279\pi$
$822$	7.83215e9			0.491846
$823$	−9.31218e9	−	1.61292e10i	−0.582307	−	1.00859i	−0.995205	−	0.0978082i	$-0.968817\pi$
$823$	−9.31218e9	−	1.61292e10i	−0.582307	−	1.00859i	0.412898	−	0.910777i	$-0.364517\pi$
$824$	−5.21322e9	−	9.02956e9i	−0.324609	−	0.562240i
$825$	−2.72387e8	+	4.71789e8i	−0.0168888	+	0.0292522i
$826$	4.37885e10	+	8.32832e9i	2.70352	+	0.514194i
$827$	1.69354e10			1.04118			0.520591	−	0.853806i	$-0.325712\pi$
$827$	1.69354e10			1.04118			0.520591	+	0.853806i	$0.325712\pi$
$828$	−4.12086e10			−2.52279
$829$	7.03589e9			0.428922			0.214461	−	0.976733i	$-0.431201\pi$
$829$	7.03589e9			0.428922			0.214461	+	0.976733i	$0.431201\pi$
$830$	4.55221e10			2.76343
$831$	5.32225e8	+	9.21842e8i	0.0321730	+	0.0557253i
$832$	3.04084e9	−	2.68807e10i	0.183047	−	1.61812i
$833$	−3.16862e9	−	2.12968e10i	−0.189938	−	1.27661i
$834$	7.07896e8	+	1.22611e9i	0.0422560	+	0.0731895i
$835$	−5.07169e8	+	8.78443e8i	−0.0301474	+	0.0522169i
$836$	−1.03051e10	−	1.78489e10i	−0.610000	−	1.05655i
$837$	−7.16000e9	+	1.24015e10i	−0.422060	+	0.731029i
$838$	7.88791e9			0.463029
$839$	1.43719e10	−	2.48929e10i	0.840132	−	1.45515i	−0.0496501	−	0.998767i	$-0.515811\pi$
$839$	1.43719e10	−	2.48929e10i	0.840132	−	1.45515i	0.889782	−	0.456385i	$-0.150856\pi$
$840$	1.33326e9	+	3.82187e9i	0.0776134	+	0.222484i
$841$	6.68313e8	−	1.15755e9i	0.0387430	−	0.0671049i
$842$	5.65576e9	−	9.79606e9i	0.326512	−	0.565535i
$843$	−2.23668e9			−0.128590
$844$	−6.28175e9	+	1.08803e10i	−0.359652	+	0.622935i
$845$	4.88702e9	+	1.58935e10i	0.278641	+	0.906194i
$846$	2.64106e10			1.49962
$847$	−9.86684e9	−	1.87661e9i	−0.557938	−	0.106117i
$848$	−2.05536e8	−	3.55998e8i	−0.0115745	−	0.0200476i
$849$	2.75997e9			0.154785
$850$	−1.87775e9	+	3.25236e9i	−0.104875	+	0.181649i
$851$	1.23691e10	+	2.14239e10i	0.687993	+	1.19164i
$852$	−1.38777e10			−0.768737
$853$	2.61367e10			1.44188			0.720939	−	0.692999i	$-0.243711\pi$
$853$	2.61367e10			1.44188			0.720939	+	0.692999i	$0.243711\pi$
$854$	5.99012e9	−	6.94729e9i	0.329104	−	0.381692i
$855$	4.96156e9	+	8.59367e9i	0.271479	+	0.470216i
$856$	−1.25150e10	+	2.16766e10i	−0.681980	+	1.18122i
$857$	−1.53768e10	+	2.66335e10i	−0.834515	+	1.44542i	0.0599090	+	0.998204i	$0.480919\pi$
$857$	−1.53768e10	+	2.66335e10i	−0.834515	+	1.44542i	−0.894424	+	0.447219i	$0.852414\pi$
$858$	−7.98087e9	−	5.89564e9i	−0.431365	−	0.318658i
$859$	−2.00738e9	−	3.47688e9i	−0.108057	−	0.187160i	0.806926	−	0.590652i	$-0.201130\pi$
$859$	−2.00738e9	−	3.47688e9i	−0.108057	−	0.187160i	−0.914983	+	0.403492i	$0.867796\pi$
$860$	−1.02894e10	−	1.78218e10i	−0.551627	−	0.955446i
$861$	−6.37450e8	−	1.82729e9i	−0.0340357	−	0.0975656i
$862$	1.79488e9	−	3.10882e9i	0.0954463	−	0.165318i
$863$	1.57203e10	+	2.72284e10i	0.832576	+	1.44206i	0.895989	+	0.444077i	$0.146468\pi$
$863$	1.57203e10	+	2.72284e10i	0.832576	+	1.44206i	−0.0634125	+	0.997987i	$0.520198\pi$
$864$	−5.19399e9	−	8.99626e9i	−0.273970	−	0.474530i
$865$	−2.74629e9	−	4.75671e9i	−0.144275	−	0.249891i
$866$	7.08892e9	+	1.22784e10i	0.370909	+	0.642433i
$867$	1.70330e9	−	2.95020e9i	0.0887613	−	0.153739i
$868$	−4.90938e10	−	9.33735e9i	−2.54805	−	0.484624i
$869$	1.12579e10	+	1.94993e10i	0.581953	+	1.00797i
$870$	3.78753e9	+	6.56020e9i	0.195002	+	0.337753i
$871$	2.44378e9	−	2.16027e10i	0.125314	−	1.10776i
$872$	−9.84800e9	+	1.70572e10i	−0.502968	+	0.871166i
$873$	4.41526e9	−	7.64745e9i	0.224598	−	0.389016i
$874$	1.67965e10	+	2.90924e10i	0.850998	+	1.47397i
$875$	2.03238e10	+	3.86547e9i	1.02560	+	0.195063i
$876$	−2.05349e7			−0.00103211
$877$	−1.01552e10			−0.508383			−0.254192	−	0.967154i	$-0.581809\pi$
$877$	−1.01552e10			−0.508383			−0.254192	+	0.967154i	$0.581809\pi$
$878$	1.08783e10	+	1.88418e10i	0.542414	+	0.939489i
$879$	−1.31536e9	+	2.27828e9i	−0.0653259	+	0.113148i
$880$	−1.99069e9			−0.0984724
$881$	7.95828e9	+	1.37842e10i	0.392106	+	0.679148i	0.992727	−	0.120386i	$-0.0384132\pi$
$881$	7.95828e9	+	1.37842e10i	0.392106	+	0.679148i	−0.600621	+	0.799534i	$0.705080\pi$
$882$	−2.38077e10	+	1.89122e10i	−1.16836	+	0.928113i
$883$	1.03784e10			0.507306			0.253653	−	0.967295i	$-0.418368\pi$
$883$	1.03784e10			0.507306			0.253653	+	0.967295i	$0.418368\pi$
$884$	−3.36954e10	−	2.48915e10i	−1.64054	−	1.21190i
$885$	4.46508e9	−	7.73375e9i	0.216535	−	0.375050i
$886$	−4.12877e10			−1.99436
$887$	−5.37079e9	+	9.30248e9i	−0.258408	+	0.447575i	−0.965816	−	0.259230i	$-0.916531\pi$
$887$	−5.37079e9	+	9.30248e9i	−0.258408	+	0.447575i	0.707408	+	0.706806i	$0.249864\pi$
$888$	2.07615e9	−	3.59600e9i	0.0994978	−	0.172335i
$889$	−2.38209e9	−	6.82842e9i	−0.113711	−	0.325960i
$890$	2.01904e10	−	3.49708e10i	0.960019	−	1.66280i
$891$	2.09335e10			0.991446
$892$	−9.56717e9	+	1.65708e10i	−0.451343	+	0.781749i
$893$	−6.59294e9	−	1.14193e10i	−0.309812	−	0.536611i
$894$	3.42132e9	−	5.92591e9i	0.160145	−	0.277379i
$895$	−3.95170e9	−	6.84454e9i	−0.184248	−	0.319127i
$896$	2.17993e10	−	2.52826e10i	1.01243	−	1.17421i
$897$	7.96685e9	+	5.88528e9i	0.368564	+	0.272266i
$898$	−5.48320e9	−	9.49718e9i	−0.252678	−	0.437651i
$899$	−3.43423e10			−1.57641
$900$	3.24800e9			0.148514
$901$	−7.90805e9			−0.360191
$902$	−1.71810e10			−0.779517
$903$	−2.83681e9	+	3.29011e9i	−0.128210	+	0.148697i
$904$	−1.01287e10	+	1.75434e10i	−0.456000	+	0.789814i
$905$	1.62666e9	+	2.81746e9i	0.0729502	+	0.126353i
$906$	−6.34093e9	−	1.09828e10i	−0.283272	−	0.490642i
$907$	−1.29525e10			−0.576404			−0.288202	−	0.957570i	$-0.593058\pi$
$907$	−1.29525e10			−0.576404			−0.288202	+	0.957570i	$0.593058\pi$
$908$	9.61119e9	−	1.66471e10i	0.426066	−	0.737968i
$909$	3.45678e10			1.52650
$910$	−1.02504e10	+	3.30670e10i	−0.450914	+	1.45462i
$911$	6.77002e9			0.296671			0.148336	−	0.988937i	$-0.452608\pi$
$911$	6.77002e9			0.296671			0.148336	+	0.988937i	$0.452608\pi$
$912$	−1.56181e8	+	2.70513e8i	−0.00681781	+	0.0118088i
$913$	−5.22502e10			−2.27217
$914$	−7.46084e9	−	1.29226e10i	−0.323203	−	0.559805i
$915$	−9.18906e8	−	1.59159e9i	−0.0396549	−	0.0686844i
$916$	8.06503e9	−	1.39690e10i	0.346714	−	0.600527i
$917$	1.08792e10	+	3.11859e10i	0.465911	+	1.33556i
$918$	−2.49929e10			−1.06627
$919$	2.60169e10			1.10573			0.552867	−	0.833270i	$-0.313534\pi$
$919$	2.60169e10			1.10573			0.552867	+	0.833270i	$0.313534\pi$
$920$	−3.58718e10			−1.51878
$921$	−1.12907e10			−0.476225
$922$	−8.99414e9	−	1.55783e10i	−0.377921	−	0.654579i
$923$	−3.50567e10	−	2.58971e10i	−1.46746	−	1.08404i
$924$	−4.16740e9	−	1.19461e10i	−0.173786	−	0.498168i
$925$	−9.74914e8	−	1.68860e9i	−0.0405014	−	0.0701505i
$926$	−5.47390e9	+	9.48107e9i	−0.226547	+	0.392391i
$927$	−7.84556e9	−	1.35889e10i	−0.323478	−	0.560281i
$928$	1.24562e10	−	2.15748e10i	0.511646	−	0.886196i
$929$	−2.58745e10			−1.05881			−0.529404	−	0.848370i	$-0.677584\pi$
$929$	−2.58745e10			−1.05881			−0.529404	+	0.848370i	$0.677584\pi$
$930$	−8.17385e9	+	1.41575e10i	−0.333224	+	0.577161i
$931$	1.41203e10	+	5.57280e9i	0.573484	+	0.226334i
$932$	1.15027e10	−	1.99233e10i	0.465420	−	0.806132i
$933$	−3.60314e9	+	6.24081e9i	−0.145243	+	0.251568i
$934$	1.00290e10			0.402756
$935$	−1.91481e10	+	3.31655e10i	−0.766099	+	1.32692i
$936$	−2.44185e9	+	2.15857e10i	−0.0973314	+	0.860400i
$937$	7.38271e9			0.293175			0.146588	−	0.989198i	$-0.453171\pi$
$937$	7.38271e9			0.293175			0.146588	+	0.989198i	$0.453171\pi$
$938$	2.95576e10	−	3.42807e10i	1.16939	−	1.35625i
$939$	3.43450e9	+	5.94873e9i	0.135374	+	0.234474i
$940$	3.83442e10			1.50575
$941$	1.97851e10	−	3.42688e10i	0.774060	−	1.34071i	−0.161261	−	0.986912i	$-0.551556\pi$
$941$	1.97851e10	−	3.42688e10i	0.774060	−	1.34071i	0.935321	−	0.353800i	$-0.115111\pi$
$942$	3.73855e8	+	6.47535e8i	0.0145722	+	0.0252398i
$943$	1.71508e10			0.666030
$944$	−3.67303e9			−0.142109
$945$	4.16649e9	+	1.19435e10i	0.160605	+	0.460385i
$946$	1.92835e10	+	3.34000e10i	0.740571	+	1.28271i
$947$	2.60522e10	−	4.51237e10i	0.996825	−	1.72655i	0.429461	−	0.903085i	$-0.358704\pi$
$947$	2.60522e10	−	4.51237e10i	0.996825	−	1.72655i	0.567365	−	0.823467i	$-0.307963\pi$
$948$	−5.13690e9	+	8.89737e9i	−0.195827	+	0.339182i
$949$	−5.18737e7	−	3.83202e7i	−0.00197022	−	0.00145544i
$950$	−1.32388e9	−	2.29302e9i	−0.0500974	−	0.0867712i
$951$	4.38606e9	+	7.59688e9i	0.165365	+	0.286420i
$952$	−1.05495e10	−	3.02407e10i	−0.396279	−	1.13596i
$953$	−2.04574e10	+	3.54332e10i	−0.765641	+	1.32613i	0.174267	+	0.984699i	$0.444245\pi$
$953$	−2.04574e10	+	3.54332e10i	−0.765641	+	1.32613i	−0.939907	+	0.341430i	$0.889089\pi$
$954$	5.58365e9	+	9.67117e9i	0.208209	+	0.360628i
$955$	−1.67386e10	−	2.89922e10i	−0.621883	−	1.07713i
$956$	−2.97059e10	−	5.14522e10i	−1.09961	−	1.90459i
$957$	−4.34732e9	−	7.52978e9i	−0.160336	−	0.277709i
$958$	−1.68850e10	+	2.92457e10i	−0.620472	+	1.07469i
$959$	1.03312e10	+	2.96151e10i	0.378256	+	1.08430i
$960$	−5.64206e9	−	9.77233e9i	−0.205820	−	0.356491i
$961$	−2.33006e10	−	4.03579e10i	−0.846907	−	1.46689i
$962$	3.25567e10	−	1.41871e10i	1.17904	−	0.513784i
$963$	−1.88342e10	+	3.26218e10i	−0.679603	+	1.17711i
$964$	−1.39943e10	+	2.42389e10i	−0.503132	+	0.871451i
$965$	−1.56672e10	−	2.71363e10i	−0.561235	−	0.972087i
$966$	6.79255e9	+	1.94713e10i	0.242445	+	0.694984i
$967$	−5.49031e9			−0.195256			−0.0976280	−	0.995223i	$-0.531126\pi$
$967$	−5.49031e9			−0.195256			−0.0976280	+	0.995223i	$0.531126\pi$
$968$	−1.49401e10			−0.529409
$969$	3.00455e9	+	5.20403e9i	0.106083	+	0.183741i
$970$	1.04667e10	−	1.81288e10i	0.368220	−	0.637776i
$971$	3.56681e10			1.25030			0.625149	−	0.780506i	$-0.285038\pi$
$971$	3.56681e10			1.25030			0.625149	+	0.780506i	$0.285038\pi$
$972$	1.64108e10	+	2.84243e10i	0.573188	+	0.992791i
$973$	−3.70243e9	+	4.29405e9i	−0.128852	+	0.149442i
$974$	−6.08107e9			−0.210874
$975$	−6.27936e8	−	4.63870e8i	−0.0216970	−	0.0160280i
$976$	−3.77951e8	+	6.54630e8i	−0.0130125	+	0.0225383i
$977$	1.96306e10			0.673446			0.336723	−	0.941604i	$-0.390681\pi$
$977$	1.96306e10			0.673446			0.336723	+	0.941604i	$0.390681\pi$
$978$	−1.04041e10	+	1.80204e10i	−0.355645	+	0.615996i
$979$	−2.31745e10	+	4.01394e10i	−0.789352	+	1.36720i
$980$	−3.45652e10	+	2.74576e10i	−1.17314	+	0.931904i
$981$	−1.48206e10	+	2.56700e10i	−0.501215	+	0.868131i
$982$	6.96577e10			2.34736
$983$	−1.33335e10	+	2.30944e10i	−0.447722	+	0.775476i	−0.998237	−	0.0593483i	$-0.981098\pi$
$983$	−1.33335e10	+	2.30944e10i	−0.447722	+	0.775476i	0.550516	+	0.834825i	$0.314431\pi$
$984$	−1.43938e9	−	2.49308e9i	−0.0481607	−	0.0834169i
$985$	−1.22948e10	+	2.12952e10i	−0.409915	+	0.709993i
$986$	−2.99690e10	−	5.19079e10i	−0.995642	−	1.72450i
$987$	−2.66620e9	−	7.64284e9i	−0.0882638	−	0.253014i
$988$	2.70764e10	−	1.17990e10i	0.893185	−	0.389220i
$989$	−1.92496e10	−	3.33413e10i	−0.632755	−	1.09596i
$990$	5.40797e10			1.77138
$991$	2.16551e10			0.706810			0.353405	−	0.935470i	$-0.385024\pi$
$991$	2.16551e10			0.706810			0.353405	+	0.935470i	$0.385024\pi$
$992$	5.37635e10			1.74862
$993$	5.88802e9			0.190830
$994$	−2.98894e10	−	8.56800e10i	−0.965306	−	2.76711i
$995$	6.80046e9	−	1.17787e10i	0.218855	−	0.379069i
$996$	−1.19207e10	−	2.06473e10i	−0.382291	−	0.662147i
$997$	−7.43364e9	−	1.28754e10i	−0.237557	−	0.411461i	0.722456	−	0.691417i	$-0.243013\pi$
$997$	−7.43364e9	−	1.28754e10i	−0.237557	−	0.411461i	−0.960013	+	0.279956i	$0.909680\pi$
$998$	2.78119e10			0.885675
$999$	6.48807e9	−	1.12377e10i	0.205890	−	0.356613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.g.a.81.56	yes	126
7.2	even	3		91.8.h.a.16.8	yes	126
13.9	even	3		91.8.h.a.74.8	yes	126
91.9	even	3	inner	91.8.g.a.9.56	✓	126

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.g.a.9.56	✓	126	91.9	even	3	inner
91.8.g.a.81.56	yes	126	1.1	even	1	trivial
91.8.h.a.16.8	yes	126	7.2	even	3
91.8.h.a.74.8	yes	126	13.9	even	3

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(9.08678 - 15.7388i) q^{2} -12.4690 q^{3} +(-101.139 - 175.178i) q^{4} +(-132.496 - 229.490i) q^{5} +(-113.303 + 196.247i) q^{6} +(-891.511 - 169.560i) q^{7} -1349.91 q^{8} -2031.52 q^{9} +O(q^{10})\)	\(q+(9.08678 - 15.7388i) q^{2} -12.4690 q^{3} +(-101.139 - 175.178i) q^{4} +(-132.496 - 229.490i) q^{5} +(-113.303 + 196.247i) q^{6} +(-891.511 - 169.560i) q^{7} -1349.91 q^{8} -2031.52 q^{9} -4815.86 q^{10} +5527.63 q^{11} +(1261.11 + 2184.31i) q^{12} +(-890.416 + 7871.19i) q^{13} +(-10769.6 + 12490.5i) q^{14} +(1652.10 + 2861.52i) q^{15} +(679.518 - 1176.96i) q^{16} +(-13072.3 - 22641.9i) q^{17} +(-18460.0 + 31973.7i) q^{18} +18432.9 q^{19} +(-26801.2 + 46421.0i) q^{20} +(11116.3 + 2114.25i) q^{21} +(50228.4 - 86998.1i) q^{22} +(-50140.2 + 86845.3i) q^{23} +16832.0 q^{24} +(3951.98 - 6845.03i) q^{25} +(115792. + 85537.9i) q^{26} +52600.9 q^{27} +(60463.5 + 173323. i) q^{28} +(63073.9 + 109247. i) q^{29} +60049.2 q^{30} +(-136119. + 235766. i) q^{31} +(-98743.3 - 171028. i) q^{32} -68924.3 q^{33} -475142. q^{34} +(79209.5 + 227059. i) q^{35} +(205467. + 355879. i) q^{36} +(123345. - 213640. i) q^{37} +(167495. - 290111. i) q^{38} +(11102.6 - 98146.2i) q^{39} +(178858. + 309790. i) q^{40} +(-85514.4 - 148115. i) q^{41} +(134287. - 155745. i) q^{42} +(-191958. + 332481. i) q^{43} +(-559061. - 968322. i) q^{44} +(269169. + 466215. i) q^{45} +(911226. + 1.57829e6i) q^{46} +(-357673. - 619508. i) q^{47} +(-8472.94 + 14675.6i) q^{48} +(766042. + 302330. i) q^{49} +(-71821.6 - 124399. i) q^{50} +(162999. + 282323. i) q^{51} +(1.46892e6 - 640105. i) q^{52} +(151236. - 261949. i) q^{53} +(477973. - 827874. i) q^{54} +(-732391. - 1.26854e6i) q^{55} +(1.20346e6 + 228891. i) q^{56} -229840. q^{57} +2.29255e6 q^{58} +(-1.35133e6 - 2.34058e6i) q^{59} +(334185. - 578825. i) q^{60} -556204. q^{61} +(2.47377e6 + 4.28470e6i) q^{62} +(1.81113e6 + 344466. i) q^{63} -3.41508e6 q^{64} +(1.92434e6 - 838562. i) q^{65} +(-626300. + 1.08478e6i) q^{66} -2.74453e6 q^{67} +(-2.64425e6 + 4.57998e6i) q^{68} +(625200. - 1.08288e6i) q^{69} +(4.29339e6 + 816578. i) q^{70} +(-2.75108e6 + 4.76501e6i) q^{71} +2.74237e6 q^{72} +(-4070.79 + 7050.82i) q^{73} +(-2.24162e6 - 3.88260e6i) q^{74} +(-49277.4 + 85350.9i) q^{75} +(-1.86429e6 - 3.22904e6i) q^{76} +(-4.92795e6 - 937267. i) q^{77} +(-1.44381e6 - 1.06658e6i) q^{78} +(2.03666e6 + 3.52760e6i) q^{79} -360135. q^{80} +3.78706e6 q^{81} -3.10820e6 q^{82} -9.45254e6 q^{83} +(-753922. - 2.16117e6i) q^{84} +(-3.46407e6 + 5.99994e6i) q^{85} +(3.48856e6 + 6.04237e6i) q^{86} +(-786471. - 1.36221e6i) q^{87} -7.46179e6 q^{88} +(-4.19248e6 + 7.26159e6i) q^{89} +9.78353e6 q^{90} +(2.12846e6 - 6.86628e6i) q^{91} +2.02846e7 q^{92} +(1.69728e6 - 2.93977e6i) q^{93} -1.30004e7 q^{94} +(-2.44229e6 - 4.23016e6i) q^{95} +(1.23123e6 + 2.13256e6i) q^{96} +(-2.17337e6 + 3.76439e6i) q^{97} +(1.17192e7 - 9.30935e6i) q^{98} -1.12295e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 126 q + q^{2} + 160 q^{3} - 3839 q^{4} - 2 q^{5} - 258 q^{6} - 1816 q^{7} - 264 q^{8} + 83414 q^{9}+O(q^{10}) \) 126 * q + q^2 + 160 * q^3 - 3839 * q^4 - 2 * q^5 - 258 * q^6 - 1816 * q^7 - 264 * q^8 + 83414 * q^9	\( 126 q + q^{2} + 160 q^{3} - 3839 q^{4} - 2 q^{5} - 258 q^{6} - 1816 q^{7} - 264 q^{8} + 83414 q^{9} + 8510 q^{10} - 14846 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} - 205147 q^{16} - 49637 q^{17} - 21111 q^{18} + 9688 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} - 17065 q^{23} + 260608 q^{24} - 810669 q^{25} - 7812 q^{26} + 416614 q^{27} + 425466 q^{28} + 191096 q^{29} - 141332 q^{30} + 183609 q^{31} - 347673 q^{32} - 357182 q^{33} - 742000 q^{34} + 145247 q^{35} - 1732409 q^{36} + 681449 q^{37} - 877438 q^{38} - 1822261 q^{39} - 1502882 q^{40} + 593701 q^{41} - 1525674 q^{42} - 592188 q^{43} + 1254066 q^{44} - 977113 q^{45} + 692726 q^{46} + 98278 q^{47} - 374916 q^{48} - 747844 q^{49} + 289562 q^{50} - 281250 q^{51} - 1459588 q^{52} - 1256681 q^{53} + 146907 q^{54} - 3015554 q^{55} - 5896005 q^{56} + 2743072 q^{57} - 3702938 q^{58} + 1139729 q^{59} + 1031485 q^{60} + 2255272 q^{61} - 7724680 q^{62} - 8617558 q^{63} + 11827496 q^{64} + 487948 q^{65} + 435059 q^{66} - 8746696 q^{67} - 4368561 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} + 23321902 q^{72} - 5060877 q^{73} - 592001 q^{74} - 11318627 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} + 247136 q^{80} + 61513790 q^{81} - 17253904 q^{82} - 18679806 q^{83} + 14270544 q^{84} + 5330093 q^{85} - 8512356 q^{86} + 8254381 q^{87} + 12876438 q^{88} + 3088342 q^{89} + 53481084 q^{90} - 38127665 q^{91} + 2460546 q^{92} - 13841202 q^{93} + 34843588 q^{94} - 19776699 q^{95} + 26667066 q^{96} + 7705262 q^{97} - 58123667 q^{98} - 60531432 q^{99}+O(q^{100}) \) 126 * q + q^2 + 160 * q^3 - 3839 * q^4 - 2 * q^5 - 258 * q^6 - 1816 * q^7 - 264 * q^8 + 83414 * q^9 + 8510 * q^10 - 14846 * q^11 - 18072 * q^12 - 1824 * q^13 - 15916 * q^14 + 11047 * q^15 - 205147 * q^16 - 49637 * q^17 - 21111 * q^18 + 9688 * q^19 + 36626 * q^20 + 73198 * q^21 - 43360 * q^22 - 17065 * q^23 + 260608 * q^24 - 810669 * q^25 - 7812 * q^26 + 416614 * q^27 + 425466 * q^28 + 191096 * q^29 - 141332 * q^30 + 183609 * q^31 - 347673 * q^32 - 357182 * q^33 - 742000 * q^34 + 145247 * q^35 - 1732409 * q^36 + 681449 * q^37 - 877438 * q^38 - 1822261 * q^39 - 1502882 * q^40 + 593701 * q^41 - 1525674 * q^42 - 592188 * q^43 + 1254066 * q^44 - 977113 * q^45 + 692726 * q^46 + 98278 * q^47 - 374916 * q^48 - 747844 * q^49 + 289562 * q^50 - 281250 * q^51 - 1459588 * q^52 - 1256681 * q^53 + 146907 * q^54 - 3015554 * q^55 - 5896005 * q^56 + 2743072 * q^57 - 3702938 * q^58 + 1139729 * q^59 + 1031485 * q^60 + 2255272 * q^61 - 7724680 * q^62 - 8617558 * q^63 + 11827496 * q^64 + 487948 * q^65 + 435059 * q^66 - 8746696 * q^67 - 4368561 * q^68 - 7610377 * q^69 - 8084578 * q^70 - 60067 * q^71 + 23321902 * q^72 - 5060877 * q^73 - 592001 * q^74 - 11318627 * q^75 + 637438 * q^76 + 21469082 * q^77 - 7230943 * q^78 - 2446486 * q^79 + 247136 * q^80 + 61513790 * q^81 - 17253904 * q^82 - 18679806 * q^83 + 14270544 * q^84 + 5330093 * q^85 - 8512356 * q^86 + 8254381 * q^87 + 12876438 * q^88 + 3088342 * q^89 + 53481084 * q^90 - 38127665 * q^91 + 2460546 * q^92 - 13841202 * q^93 + 34843588 * q^94 - 19776699 * q^95 + 26667066 * q^96 + 7705262 * q^97 - 58123667 * q^98 - 60531432 * q^99

Introduction

L-functions

Modular forms

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