LMFDB - Embedded newform 76.8.f.a.27.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,8,Mod(27,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("76.27");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	76.f (of order $6$, 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:	$23.7412619368$
Analytic rank:	$0$
Dimension:	$136$
Relative dimension:	$68$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.7
Character	$\chi$	$=$	76.27
Dual form			76.8.f.a.31.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.9017 + 3.02556i) q^{2} +(10.5842 - 18.3323i) q^{3} +(109.692 - 65.9672i) q^{4} +(-226.342 + 392.035i) q^{5} +(-59.9194 + 231.876i) q^{6} +671.124i q^{7} +(-996.236 + 1051.03i) q^{8} +(869.451 + 1505.93i) q^{9} +O(q^{10})$	\(q+(-10.9017 + 3.02556i) q^{2} +(10.5842 - 18.3323i) q^{3} +(109.692 - 65.9672i) q^{4} +(-226.342 + 392.035i) q^{5} +(-59.9194 + 231.876i) q^{6} +671.124i q^{7} +(-996.236 + 1051.03i) q^{8} +(869.451 + 1505.93i) q^{9} +(1281.37 - 4958.64i) q^{10} -3157.75i q^{11} +(-48.3337 - 2709.12i) q^{12} +(-1860.94 + 1074.42i) q^{13} +(-2030.53 - 7316.36i) q^{14} +(4791.28 + 8298.74i) q^{15} +(7680.65 - 14472.1i) q^{16} +(-2563.92 + 4440.84i) q^{17} +(-14034.7 - 13786.6i) q^{18} +(21512.8 + 20762.3i) q^{19} +(1033.61 + 57934.3i) q^{20} +(12303.3 + 7103.29i) q^{21} +(9553.95 + 34424.6i) q^{22} +(7314.16 - 4222.83i) q^{23} +(8723.51 + 29387.6i) q^{24} +(-63398.7 - 109810. i) q^{25} +(17036.7 - 17343.3i) q^{26} +83104.8 q^{27} +(44272.2 + 73616.9i) q^{28} +(-121934. + 70398.8i) q^{29} +(-77341.2 - 75973.6i) q^{30} -200106. q^{31} +(-39945.4 + 181009. i) q^{32} +(-57888.8 - 33422.1i) q^{33} +(14514.9 - 56169.8i) q^{34} +(-263104. - 151903. i) q^{35} +(194714. + 107834. i) q^{36} -448853. i q^{37} +(-297342. - 161255. i) q^{38} +45487.2i q^{39} +(-186552. - 628452. i) q^{40} +(-419077. - 241954. i) q^{41} +(-155617. - 40213.3i) q^{42} +(-208680. - 120481. i) q^{43} +(-208308. - 346379. i) q^{44} -787172. q^{45} +(-66960.0 + 68165.3i) q^{46} +(205230. - 118489. i) q^{47} +(-184015. - 293980. i) q^{48} +373136. q^{49} +(1.02339e6 + 1.00529e6i) q^{50} +(54274.0 + 94005.3i) q^{51} +(-133254. + 240616. i) q^{52} +(-1.47695e6 + 852719. i) q^{53} +(-905979. + 251439. i) q^{54} +(1.23795e6 + 714730. i) q^{55} +(-705372. - 668598. i) q^{56} +(608316. - 174627. i) q^{57} +(1.11629e6 - 1.13638e6i) q^{58} +(-1.31619e6 + 2.27971e6i) q^{59} +(1.07301e6 + 594238. i) q^{60} +(-347784. - 602379. i) q^{61} +(2.18148e6 - 605432. i) q^{62} +(-1.01067e6 + 583509. i) q^{63} +(-112181. - 2.09415e6i) q^{64} -972742. i q^{65} +(732204. + 189210. i) q^{66} +(-636360. - 1.10221e6i) q^{67} +(11708.4 + 656260. i) q^{68} -178781. i q^{69} +(3.32786e6 + 859959. i) q^{70} +(-1.43429e6 + 2.48426e6i) q^{71} +(-2.44896e6 - 586444. i) q^{72} +(2.97623e6 - 5.15499e6i) q^{73} +(1.35803e6 + 4.89324e6i) q^{74} -2.68409e6 q^{75} +(3.72941e6 + 858320. i) q^{76} +2.11924e6 q^{77} +(-137624. - 495886. i) q^{78} +(-1.86435e6 + 3.22915e6i) q^{79} +(3.93514e6 + 6.28674e6i) q^{80} +(-1.02189e6 + 1.76997e6i) q^{81} +(5.30067e6 + 1.36976e6i) q^{82} -5.82477e6i q^{83} +(1.81815e6 - 32437.9i) q^{84} +(-1.16065e6 - 2.01030e6i) q^{85} +(2.63948e6 + 682073. i) q^{86} +2.98045e6i q^{87} +(3.31889e6 + 3.14586e6i) q^{88} +(2.95619e6 - 1.70676e6i) q^{89} +(8.58148e6 - 2.38164e6i) q^{90} +(-721067. - 1.24892e6i) q^{91} +(523736. - 945706. i) q^{92} +(-2.11795e6 + 3.66840e6i) q^{93} +(-1.87884e6 + 1.91266e6i) q^{94} +(-1.30088e7 + 3.73439e6i) q^{95} +(2.89552e6 + 2.64812e6i) q^{96} +(-8.14320e6 - 4.70148e6i) q^{97} +(-4.06779e6 + 1.12894e6i) q^{98} +(4.75535e6 - 2.74550e6i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	$ 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) $ 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−10.9017	+	3.02556i	−0.963579	+	0.267424i
$2$	−10.9017	+	3.02556i	−0.963579	+	0.267424i
$3$	10.5842	−	18.3323i	0.226325	−	0.392006i	−0.730391	−	0.683029i	$-0.760662\pi$
$3$	10.5842	−	18.3323i	0.226325	−	0.392006i	0.956716	+	0.291023i	$0.0939956\pi$
$4$	109.692	−	65.9672i	0.856968	−	0.515369i
$5$	−226.342	+	392.035i	−0.809785	+	1.40259i	0.103228	+	0.994658i	$0.467083\pi$
$5$	−226.342	+	392.035i	−0.809785	+	1.40259i	−0.913013	+	0.407931i	$0.866250\pi$
$6$	−59.9194	+	231.876i	−0.113250	+	0.438254i
$7$			671.124i			0.739536i	0.929124	+	0.369768i	$0.120563\pi$
$7$			671.124i			0.739536i	−0.929124	+	0.369768i	$0.879437\pi$
$8$	−996.236	+	1051.03i	−0.687935	+	0.725773i
$9$	869.451	+	1505.93i	0.397554	+	0.688584i
$10$	1281.37	−	4958.64i	0.405205	−	1.56806i
$11$		−	3157.75i		−	0.715324i	−0.933851	−	0.357662i	$-0.883574\pi$
$11$		−	3157.75i		−	0.715324i	0.933851	−	0.357662i	$-0.116426\pi$
$12$	−48.3337	−	2709.12i	−0.00807449	−	0.452578i
$13$	−1860.94	+	1074.42i	−0.234926	+	0.135635i	−0.612843	−	0.790205i	$-0.709974\pi$
$13$	−1860.94	+	1074.42i	−0.234926	+	0.135635i	0.377916	+	0.925840i	$0.376641\pi$
$14$	−2030.53	−	7316.36i	−0.197770	−	0.712602i
$15$	4791.28	+	8298.74i	0.366549	+	0.634881i
$16$	7680.65	−	14472.1i	0.468790	−	0.883310i
$17$	−2563.92	+	4440.84i	−0.126571	+	0.219227i	−0.922346	−	0.386365i	$-0.873730\pi$
$17$	−2563.92	+	4440.84i	−0.126571	+	0.219227i	0.795775	+	0.605592i	$0.207064\pi$
$18$	−14034.7	−	13786.6i	−0.567219	−	0.557189i
$19$	21512.8	+	20762.3i	0.719546	+	0.694445i
$19$	21512.8	+	20762.3i	0.719546	+	0.694445i
$20$	1033.61	+	57934.3i	0.0288903	+	1.61931i
$21$	12303.3	+	7103.29i	0.289903	+	0.167375i
$22$	9553.95	+	34424.6i	0.191295	+	0.689271i
$23$	7314.16	−	4222.83i	0.125348	−	0.0723697i	−0.436015	−	0.899939i	$-0.643611\pi$
$23$	7314.16	−	4222.83i	0.125348	−	0.0723697i	0.561363	+	0.827570i	$0.310277\pi$
$24$	8723.51	+	29387.6i	0.128811	+	0.433935i
$25$	−63398.7	−	109810.i	−0.811503	−	1.40557i
$26$	17036.7	−	17343.3i	0.190098	−	0.193520i
$27$	83104.8			0.812555
$28$	44272.2	+	73616.9i	0.381134	+	0.633759i
$29$	−121934.	+	70398.8i	−0.928395	+	0.536009i	−0.886304	−	0.463105i	$-0.846735\pi$
$29$	−121934.	+	70398.8i	−0.928395	+	0.536009i	−0.0420915	+	0.999114i	$0.513402\pi$
$30$	−77341.2	−	75973.6i	−0.522982	−	0.513734i
$31$	−200106.			−1.20641			−0.603203	−	0.797587i	$-0.706109\pi$
$31$	−200106.			−1.20641			−0.603203	+	0.797587i	$0.706109\pi$
$32$	−39945.4	+	181009.i	−0.215498	+	0.976504i
$33$	−57888.8	−	33422.1i	−0.280411	−	0.161896i
$34$	14514.9	−	56169.8i	0.0633343	−	0.245091i
$35$	−263104.	−	151903.i	−1.03727	−	0.598865i
$36$	194714.	+	107834.i	0.695566	+	0.385208i
$37$		−	448853.i		−	1.45679i	−0.685155	−	0.728397i	$-0.740265\pi$
$37$		−	448853.i		−	1.45679i	0.685155	−	0.728397i	$-0.259735\pi$
$38$	−297342.	−	161255.i	−0.879051	−	0.476728i
$39$			45487.2i			0.122790i
$40$	−186552.	−	628452.i	−0.460882	−	1.55261i
$41$	−419077.	−	241954.i	−0.949620	−	0.548264i	−0.0566573	−	0.998394i	$-0.518044\pi$
$41$	−419077.	−	241954.i	−0.949620	−	0.548264i	−0.892963	+	0.450130i	$0.851378\pi$
$42$	−155617.	−	40213.3i	−0.324105	−	0.0837524i
$43$	−208680.	−	120481.i	−0.400259	−	0.231090i	0.286337	−	0.958129i	$-0.407562\pi$
$43$	−208680.	−	120481.i	−0.400259	−	0.231090i	−0.686596	+	0.727039i	$0.740896\pi$
$44$	−208308.	−	346379.i	−0.368656	−	0.613010i
$45$	−787172.			−1.28773
$46$	−66960.0	+	68165.3i	−0.101429	+	0.103255i
$47$	205230.	−	118489.i	0.288335	−	0.166470i	−0.348856	−	0.937176i	$-0.613430\pi$
$47$	205230.	−	118489.i	0.288335	−	0.166470i	0.637191	+	0.770706i	$0.280096\pi$
$48$	−184015.	−	293980.i	−0.240164	−	0.383683i
$49$	373136.			0.453086
$50$	1.02339e6	+	1.00529e6i	1.15783	+	1.13736i
$51$	54274.0	+	94005.3i	0.0572923	+	0.0992331i
$52$	−133254.	+	240616.i	−0.131423	+	0.237308i
$53$	−1.47695e6	+	852719.i	−1.36270	+	0.786756i	−0.989983	−	0.141188i	$-0.954908\pi$
$53$	−1.47695e6	+	852719.i	−1.36270	+	0.786756i	−0.372719	+	0.927944i	$0.621574\pi$
$54$	−905979.	+	251439.i	−0.782961	+	0.217297i
$55$	1.23795e6	+	714730.i	1.00331	+	0.579259i
$56$	−705372.	−	668598.i	−0.536735	−	0.508753i
$57$	608316.	−	174627.i	0.435078	−	0.124896i
$58$	1.11629e6	−	1.13638e6i	0.751240	−	0.764763i
$59$	−1.31619e6	+	2.27971e6i	−0.834328	+	1.44510i	0.0602488	+	0.998183i	$0.480811\pi$
$59$	−1.31619e6	+	2.27971e6i	−0.834328	+	1.44510i	−0.894577	+	0.446915i	$0.852523\pi$
$60$	1.07301e6	+	594238.i	0.641319	+	0.355165i
$61$	−347784.	−	602379.i	−0.196180	−	0.339794i	0.751107	−	0.660181i	$-0.229520\pi$
$61$	−347784.	−	602379.i	−0.196180	−	0.339794i	−0.947287	+	0.320387i	$0.896187\pi$
$62$	2.18148e6	−	605432.i	1.16247	−	0.322623i
$63$	−1.01067e6	+	583509.i	−0.509233	+	0.294006i
$64$	−112181.	−	2.09415e6i	−0.0534921	−	0.998568i
$65$		−	972742.i		−	0.439340i
$66$	732204.	+	189210.i	0.313493	+	0.0810103i
$67$	−636360.	−	1.10221e6i	−0.258488	−	0.447715i	0.707349	−	0.706865i	$-0.249891\pi$
$67$	−636360.	−	1.10221e6i	−0.258488	−	0.447715i	−0.965837	+	0.259150i	$0.916558\pi$
$68$	11708.4	+	656260.i	0.00451561	+	0.253101i
$69$		−	178781.i		−	0.0655162i
$70$	3.32786e6	+	859959.i	1.15964	+	0.299664i
$71$	−1.43429e6	+	2.48426e6i	−0.475589	+	0.823744i	−0.999609	−	0.0279616i	$-0.991098\pi$
$71$	−1.43429e6	+	2.48426e6i	−0.475589	+	0.823744i	0.524020	+	0.851706i	$0.324432\pi$
$72$	−2.44896e6	−	586444.i	−0.773247	−	0.185167i
$73$	2.97623e6	−	5.15499e6i	0.895441	−	1.55095i	0.0621836	−	0.998065i	$-0.480194\pi$
$73$	2.97623e6	−	5.15499e6i	0.895441	−	1.55095i	0.833258	−	0.552885i	$-0.186473\pi$
$74$	1.35803e6	+	4.89324e6i	0.389582	+	1.40374i
$75$	−2.68409e6			−0.734654
$76$	3.72941e6	+	858320.i	0.974523	+	0.224286i
$77$	2.11924e6			0.529008
$78$	−137624.	−	495886.i	−0.0328371	−	0.118318i
$79$	−1.86435e6	+	3.22915e6i	−0.425434	+	0.736874i	−0.996461	−	0.0840579i	$-0.973212\pi$
$79$	−1.86435e6	+	3.22915e6i	−0.425434	+	0.736874i	0.571027	+	0.820931i	$0.306545\pi$
$80$	3.93514e6	+	6.28674e6i	0.859301	+	1.37281i
$81$	−1.02189e6	+	1.76997e6i	−0.213653	+	0.370057i
$82$	5.30067e6	+	1.36976e6i	1.06165	+	0.274344i
$83$		−	5.82477e6i		−	1.11816i	−0.829112	−	0.559082i	$-0.811154\pi$
$83$		−	5.82477e6i		−	1.11816i	0.829112	−	0.559082i	$-0.188846\pi$
$84$	1.81815e6	−	32437.9i	0.334698	−	0.00597138i
$85$	−1.16065e6	−	2.01030e6i	−0.204990	−	0.355054i
$86$	2.63948e6	+	682073.i	0.447480	+	0.115634i
$87$			2.98045e6i			0.485249i
$88$	3.31889e6	+	3.14586e6i	0.519163	+	0.492096i
$89$	2.95619e6	−	1.70676e6i	0.444495	−	0.256629i	−0.261007	−	0.965337i	$-0.584055\pi$
$89$	2.95619e6	−	1.70676e6i	0.444495	−	0.256629i	0.705503	+	0.708707i	$0.250721\pi$
$90$	8.58148e6	−	2.38164e6i	1.24083	−	0.344371i
$91$	−721067.	−	1.24892e6i	−0.100307	−	0.173737i
$92$	523736.	−	945706.i	0.0701222	−	0.126619i
$93$	−2.11795e6	+	3.66840e6i	−0.273040	+	0.472919i
$94$	−1.87884e6	+	1.91266e6i	−0.233315	+	0.237515i
$95$	−1.30088e7	+	3.73439e6i	−1.55670	+	0.446876i
$96$	2.89552e6	+	2.64812e6i	0.334023	+	0.305484i
$97$	−8.14320e6	−	4.70148e6i	−0.905929	−	0.523038i	−0.0268097	−	0.999641i	$-0.508535\pi$
$97$	−8.14320e6	−	4.70148e6i	−0.905929	−	0.523038i	−0.879119	+	0.476602i	$0.841868\pi$
$98$	−4.06779e6	+	1.12894e6i	−0.436584	+	0.121166i
$99$	4.75535e6	−	2.74550e6i	0.492561	−	0.284380i
$100$	−1.41982e7	−	7.86301e6i	−1.41982	−	0.786301i
$101$	791788.	+	1.37142e6i	0.0764688	+	0.132448i	0.901724	−	0.432312i	$-0.142302\pi$
$101$	791788.	+	1.37142e6i	0.0764688	+	0.132448i	−0.825255	+	0.564760i	$0.808969\pi$
$102$	−876095.	−	860603.i	−0.0817430	−	0.0802976i
$103$	1.15591e7			1.04230			0.521150	−	0.853465i	$-0.325503\pi$
$103$	1.15591e7			1.04230			0.521150	+	0.853465i	$0.325503\pi$
$104$	724694.	−	3.02628e6i	0.0631739	−	0.263811i
$105$	−5.56948e6	+	3.21554e6i	−0.469518	+	0.271076i
$106$	1.35213e7	−	1.37646e7i	1.10267	−	1.12252i
$107$	7.68186e6			0.606210			0.303105	−	0.952957i	$-0.401977\pi$
$107$	7.68186e6			0.606210			0.303105	+	0.952957i	$0.401977\pi$
$108$	9.11593e6	−	5.48219e6i	0.696334	−	0.418766i
$109$	−1.11281e7	−	6.42483e6i	−0.823056	−	0.475192i	0.0284130	−	0.999596i	$-0.490955\pi$
$109$	−1.11281e7	−	6.42483e6i	−0.823056	−	0.475192i	−0.851469	+	0.524405i	$0.824288\pi$
$110$	−1.56581e7	−	4.04625e6i	−1.12167	−	0.289853i
$111$	−8.22852e6	−	4.75074e6i	−0.571073	−	0.329709i
$112$	9.71260e6	+	5.15467e6i	0.653240	+	0.346687i
$113$			1.20952e6i			0.0788567i	0.999222	+	0.0394284i	$0.0125537\pi$
$113$			1.20952e6i			0.0788567i	−0.999222	+	0.0394284i	$0.987446\pi$
$114$	−6.10330e6	+	3.74422e6i	−0.385831	+	0.236698i
$115$			3.82322e6i			0.234416i
$116$	−8.73120e6	+	1.57658e7i	−0.519363	+	0.937809i
$117$	−3.23600e6	−	1.86831e6i	−0.186792	−	0.107844i
$118$	7.45125e6	−	2.88348e7i	0.417486	−	1.61559i
$119$	−2.98036e6	−	1.72071e6i	−0.162126	−	0.0936038i
$120$	−1.34955e7	−	3.23171e6i	−0.712941	−	0.170726i
$121$	9.51581e6			0.488312
$122$	5.61395e6	+	5.51469e6i	0.279904	+	0.274955i
$123$	−8.87115e6	+	5.12176e6i	−0.429845	+	0.248171i
$124$	−2.19500e7	+	1.32004e7i	−1.03385	+	0.621745i
$125$	2.20332e7			1.00900
$126$	9.25250e6	−	9.41905e6i	0.412062	−	0.419479i
$127$	1.42752e7	+	2.47253e7i	0.618397	+	1.07110i	0.989778	+	0.142615i	$0.0455511\pi$
$127$	1.42752e7	+	2.47253e7i	0.618397	+	1.07110i	−0.371381	+	0.928481i	$0.621116\pi$
$128$	7.55894e6	+	2.24903e7i	0.318585	+	0.947894i
$129$	−4.41741e6	+	2.55039e6i	−0.181177	+	0.104603i
$130$	2.94309e6	+	1.06045e7i	0.117490	+	0.423339i
$131$	−2.32426e7	−	1.34191e7i	−0.903308	−	0.521525i	−0.0250363	−	0.999687i	$-0.507970\pi$
$131$	−2.32426e7	−	1.34191e7i	−0.903308	−	0.521525i	−0.878272	+	0.478161i	$0.841303\pi$
$132$	−8.55470e6	+	152625.i	−0.323740	+	0.00577588i
$133$	−1.39341e7	+	1.44377e7i	−0.513567	+	0.532130i
$134$	1.02722e7	+	1.00905e7i	0.368804	+	0.362283i
$135$	−1.88101e7	+	3.25800e7i	−0.657995	+	1.13968i
$136$	−2.11320e6	−	7.11889e6i	−0.0720366	−	0.242676i
$137$	7.42344e6	+	1.28578e7i	0.246651	+	0.427213i	0.962595	−	0.270946i	$-0.0873364\pi$
$137$	7.42344e6	+	1.28578e7i	0.246651	+	0.427213i	−0.715943	+	0.698158i	$0.754003\pi$
$138$	540912.	+	1.94901e6i	0.0175206	+	0.0631301i
$139$	4.20019e7	−	2.42498e7i	1.32653	−	0.765872i	0.341768	−	0.939784i	$-0.388974\pi$
$139$	4.20019e7	−	2.42498e7i	1.32653	−	0.765872i	0.984761	+	0.173912i	$0.0556410\pi$
$140$	−3.88811e7	+	693682.i	−1.19754	+	0.0213655i
$141$		−	5.01644e6i		−	0.150705i
$142$	8.11982e6	−	3.14220e7i	0.237978	−	0.920927i
$143$	3.39274e6	+	5.87639e6i	0.0970228	+	0.168048i
$144$	2.84720e7	−	1.01627e6i	0.794602	−	0.0283622i
$145$		−	6.37368e7i		−	1.73621i
$146$	−1.68491e7	+	6.52027e7i	−0.448067	+	1.73393i
$147$	3.94933e6	−	6.84044e6i	0.102545	−	0.177612i
$148$	−2.96096e7	−	4.92356e7i	−0.750787	−	1.24843i
$149$	1.25641e7	−	2.17616e7i	0.311157	−	0.538939i	−0.667456	−	0.744649i	$-0.732617\pi$
$149$	1.25641e7	−	2.17616e7i	0.311157	−	0.538939i	0.978613	+	0.205710i	$0.0659503\pi$
$150$	2.92610e7	−	8.12088e6i	0.707897	−	0.196464i
$151$	−1.64981e7			−0.389954			−0.194977	−	0.980808i	$-0.562463\pi$
$151$	−1.64981e7			−0.389954			−0.194977	+	0.980808i	$0.562463\pi$
$152$	−4.32536e7	+	1.92644e6i	−0.999010	+	0.0444942i
$153$	−8.91682e6			−0.201275
$154$	−2.31032e7	+	6.41189e6i	−0.509741	+	0.141470i
$155$	4.52923e7	−	7.84486e7i	0.976930	−	1.69209i
$156$	3.00067e6	+	4.98958e6i	0.0632822	+	0.105227i
$157$	−3.86956e7	+	6.70228e7i	−0.798018	+	1.38221i	0.122886	+	0.992421i	$0.460785\pi$
$157$	−3.86956e7	+	6.70228e7i	−0.798018	+	1.38221i	−0.920905	+	0.389788i	$0.872548\pi$
$158$	1.05545e7	−	4.08437e7i	0.212881	−	0.823807i
$159$			3.61013e7i			0.712250i
$160$	−6.19205e7	−	5.66298e7i	−1.19513	−	1.09301i
$161$	2.83405e6	+	4.90871e6i	0.0535200	+	0.0926994i
$162$	5.78517e6	−	2.23874e7i	0.106909	−	0.413715i
$163$		−	6.34743e7i		−	1.14800i	−0.818856	−	0.573999i	$-0.805391\pi$
$163$		−	6.34743e7i		−	1.14800i	0.818856	−	0.573999i	$-0.194609\pi$
$164$	−6.19304e7	+	1.10491e6i	−1.09635	+	0.0195602i
$165$	2.62053e7	−	1.51296e7i	0.454146	−	0.262201i
$166$	1.76232e7	+	6.34996e7i	0.299024	+	1.07744i
$167$	−2.59702e7	−	4.49817e7i	−0.431487	−	0.747357i	0.565515	−	0.824738i	$-0.308677\pi$
$167$	−2.59702e7	−	4.49817e7i	−0.431487	−	0.747357i	−0.997002	+	0.0773813i	$0.975344\pi$
$168$	−1.97227e7	+	5.85456e6i	−0.320911	+	0.0952602i
$169$	−2.90655e7	+	5.03429e7i	−0.463206	+	0.802297i
$170$	1.87352e7	+	1.84040e7i	0.292474	+	0.287303i
$171$	−1.25623e7	+	5.04486e7i	−0.192125	+	0.771547i
$172$	−3.08383e7	+	550191.i	−0.462106	+	0.00824449i
$173$	4.41890e7	+	2.55125e7i	0.648863	+	0.374621i	0.788020	−	0.615649i	$-0.211106\pi$
$173$	4.41890e7	+	2.55125e7i	0.648863	+	0.374621i	−0.139158	+	0.990270i	$0.544439\pi$
$174$	−9.01753e6	−	3.24918e7i	−0.129767	−	0.467576i
$175$	7.36960e7	−	4.25484e7i	1.03947	−	0.600136i
$176$	−4.56994e7	−	2.42536e7i	−0.631853	−	0.335337i
$177$	2.78616e7	+	4.82576e7i	0.377658	+	0.654123i
$178$	−2.70634e7	+	2.75506e7i	−0.359677	+	0.366152i
$179$	1.44220e8			1.87949			0.939744	−	0.341879i	$-0.111063\pi$
$179$	1.44220e8			1.87949			0.939744	+	0.341879i	$0.111063\pi$
$180$	−8.63465e7	+	5.19276e7i	−1.10355	+	0.663658i
$181$	−7.74691e7	+	4.47268e7i	−0.971077	+	0.560651i	−0.899564	−	0.436788i	$-0.856116\pi$
$181$	−7.74691e7	+	4.47268e7i	−0.971077	+	0.560651i	−0.0715125	+	0.997440i	$0.522783\pi$
$182$	1.16395e7	+	1.14337e7i	0.143115	+	0.140584i
$183$	−1.47240e7			−0.177602
$184$	−2.84830e6	+	1.18944e7i	−0.0337073	+	0.140760i
$185$	1.75966e8	+	1.01594e8i	2.04328	+	1.17969i
$186$	1.19902e7	−	4.63996e7i	0.136625	−	0.528712i
$187$	1.40231e7	+	8.09622e6i	0.156818	+	0.0905392i
$188$	1.46956e7	−	2.65358e7i	0.161300	−	0.291259i
$189$			5.57736e7i			0.600914i
$190$	1.30519e8	−	8.00699e7i	1.38050	−	0.846899i
$191$			3.98067e7i			0.413371i	0.978407	+	0.206685i	$0.0662676\pi$
$191$			3.98067e7i			0.413371i	−0.978407	+	0.206685i	$0.933732\pi$
$192$	−3.95779e7	−	2.01083e7i	−0.403552	−	0.205032i
$193$	−6.40357e7	−	3.69710e7i	−0.641167	−	0.370178i	0.143897	−	0.989593i	$-0.454037\pi$
$193$	−6.40357e7	−	3.69710e7i	−0.641167	−	0.370178i	−0.785064	+	0.619414i	$0.787370\pi$
$194$	1.02999e8	+	2.66161e7i	1.01281	+	0.261721i
$195$	−1.78326e7	−	1.02957e7i	−0.172224	−	0.0994336i
$196$	4.09300e7	−	2.46147e7i	0.388280	−	0.233506i
$197$	−1.77954e6			−0.0165835			−0.00829176	−	0.999966i	$-0.502639\pi$
$197$	−1.77954e6			−0.0165835			−0.00829176	+	0.999966i	$0.502639\pi$
$198$	−4.35345e7	+	4.43181e7i	−0.398571	+	0.405745i
$199$	−1.92391e7	+	1.11077e7i	−0.173061	+	0.0999168i	−0.584028	−	0.811733i	$-0.698524\pi$
$199$	−1.92391e7	+	1.11077e7i	−0.173061	+	0.0999168i	0.410967	+	0.911650i	$0.365191\pi$
$200$	1.78574e8	+	4.27624e7i	1.57838	+	0.377970i
$201$	−2.69414e7			−0.234009
$202$	−1.27811e7	−	1.25551e7i	−0.109103	−	0.107174i
$203$	−4.72463e7	−	8.18330e7i	−0.396398	−	0.686582i
$204$	1.21547e7	+	6.73132e6i	0.100239	+	0.0555130i
$205$	1.89709e8	−	1.09529e8i	1.53798	−	0.887951i
$206$	−1.26013e8	+	3.49727e7i	−1.00434	+	0.278736i
$207$	1.27186e7	+	7.34309e6i	0.0996652	+	0.0575417i
$208$	1.25585e6	+	3.51841e7i	0.00967643	+	0.271097i
$209$	6.55621e7	−	6.79318e7i	0.496753	−	0.514708i
$210$	5.09877e7	−	5.19055e7i	0.379925	−	0.386764i
$211$	−9.94653e7	+	1.72279e8i	−0.728925	+	1.26254i	0.228412	+	0.973564i	$0.426647\pi$
$211$	−9.94653e7	+	1.72279e8i	−0.728925	+	1.26254i	−0.957338	+	0.288971i	$0.906687\pi$
$212$	−1.05758e8	+	1.90967e8i	−0.762323	+	1.37652i
$213$	3.03615e7	+	5.25876e7i	0.215275	+	0.372868i
$214$	−8.37450e7	+	2.32419e7i	−0.584131	+	0.162115i
$215$	9.44660e7	−	5.45400e7i	0.648248	−	0.374266i
$216$	−8.27920e7	+	8.73457e7i	−0.558985	+	0.589730i
$217$		−	1.34296e8i		−	0.892182i
$218$	1.40754e8	+	3.63724e7i	0.920157	+	0.237779i
$219$	−6.30019e7	−	1.09123e8i	−0.405321	−	0.702037i
$220$	1.82942e8	−	3.26389e6i	1.15833	−	0.0206660i
$221$		−	1.10189e7i		−	0.0686696i
$222$	1.04078e8	+	2.68950e7i	0.638446	+	0.164982i
$223$	7.04105e7	−	1.21955e8i	0.425178	−	0.736430i	−0.571259	−	0.820770i	$-0.693545\pi$
$223$	7.04105e7	−	1.21955e8i	0.425178	−	0.736430i	0.996437	+	0.0843402i	$0.0268782\pi$
$224$	−1.21479e8	−	2.68083e7i	−0.722161	−	0.159368i
$225$	1.10244e8	−	1.90948e8i	0.645233	−	1.11758i
$226$	−3.65948e6	−	1.31858e7i	−0.0210882	−	0.0759847i
$227$	−1.93135e8			−1.09590			−0.547949	−	0.836512i	$-0.684591\pi$
$227$	−1.93135e8			−1.09590			−0.547949	+	0.836512i	$0.684591\pi$
$228$	5.52077e7	−	5.92841e7i	0.308480	−	0.331258i
$229$	1.29811e8			0.714311			0.357156	−	0.934045i	$-0.383747\pi$
$229$	1.29811e8			0.714311			0.357156	+	0.934045i	$0.383747\pi$
$230$	−1.15674e7	−	4.16794e7i	−0.0626884	−	0.225878i
$231$	2.24304e7	−	3.88506e7i	0.119728	−	0.207374i
$232$	4.74840e7	−	1.98291e8i	0.249654	−	1.04254i
$233$	−1.46698e8	+	2.54088e8i	−0.759761	+	1.31595i	0.183211	+	0.983074i	$0.441351\pi$
$233$	−1.46698e8	+	2.54088e8i	−0.759761	+	1.31595i	−0.942972	+	0.332872i	$0.891982\pi$
$234$	4.09304e7	+	1.05769e7i	0.208829	+	0.0539638i
$235$			1.07276e8i			0.539221i
$236$	6.01052e6	+	3.36891e8i	0.0297659	+	1.66839i
$237$	3.94652e7	+	6.83557e7i	0.192573	+	0.333546i
$238$	3.76969e7	+	9.74133e6i	0.181254	+	0.0468380i
$239$			1.51808e8i			0.719288i	0.933090	+	0.359644i	$0.117102\pi$
$239$			1.51808e8i			0.719288i	−0.933090	+	0.359644i	$0.882898\pi$
$240$	1.56901e8	−	5.60035e6i	0.732631	−	0.0261503i
$241$	−7.68139e7	+	4.43485e7i	−0.353492	+	0.204089i	−0.666222	−	0.745753i	$-0.732090\pi$
$241$	−7.68139e7	+	4.43485e7i	−0.353492	+	0.204089i	0.312730	+	0.949842i	$0.398757\pi$
$242$	−1.03738e8	+	2.87907e7i	−0.470527	+	0.130586i
$243$	1.12507e8	+	1.94868e8i	0.502987	+	0.871200i
$244$	−7.78864e7	−	4.31338e7i	−0.343239	−	0.190088i
$245$	−8.44562e7	+	1.46282e8i	−0.366902	+	0.635493i
$246$	8.12140e7	−	8.26759e7i	0.347823	−	0.354084i
$247$	−6.23414e7	−	1.55238e7i	−0.263231	−	0.0655479i
$248$	1.99353e8	−	2.10317e8i	0.829929	−	0.875577i
$249$	−1.06782e8	−	6.16503e7i	−0.438327	−	0.253068i
$250$	−2.40198e8	+	6.66628e7i	−0.972254	+	0.269832i
$251$	−3.81995e8	+	2.20545e8i	−1.52475	+	0.880317i	−0.525185	+	0.850988i	$0.676004\pi$
$251$	−3.81995e8	+	2.20545e8i	−1.52475	+	0.880317i	−0.999570	+	0.0293292i	$0.990663\pi$
$252$	−7.23696e7	+	1.30677e8i	−0.284875	+	0.514396i
$253$	−1.33346e7	−	2.30963e7i	−0.0517678	−	0.0896644i
$254$	−2.30431e8	−	2.26356e8i	−0.882312	−	0.866711i
$255$	−4.91379e7			−0.185578
$256$	−1.50451e8	−	2.22311e8i	−0.560472	−	0.828173i
$257$	−3.33241e8	+	1.92397e8i	−1.22459	+	0.707019i	−0.965894	−	0.258938i	$-0.916627\pi$
$257$	−3.33241e8	+	1.92397e8i	−1.22459	+	0.707019i	−0.258700	+	0.965958i	$0.583294\pi$
$258$	4.04407e7	−	4.11686e7i	0.146605	−	0.149244i
$259$	3.01236e8			1.07735
$260$	−6.41691e7	−	1.06702e8i	−0.226422	−	0.376501i
$261$	−2.12032e8	−	1.22417e8i	−0.738175	−	0.426185i
$262$	2.93984e8	+	7.59688e7i	1.00988	+	0.260964i
$263$	1.83378e8	+	1.05873e8i	0.621586	+	0.358873i	0.777486	−	0.628900i	$-0.216495\pi$
$263$	1.83378e8	+	1.05873e8i	0.621586	+	0.358873i	−0.155900	+	0.987773i	$0.549828\pi$
$264$	9.27986e7	−	2.75466e7i	0.310404	−	0.0921414i
$265$		−	7.72023e8i		−	2.54841i
$266$	1.08222e8	−	1.99553e8i	0.352558	−	0.650090i
$267$		−	7.22584e7i		−	0.232326i
$268$	−1.42513e8	−	7.89245e7i	−0.452255	−	0.250461i
$269$	−4.24518e8	−	2.45096e8i	−1.32973	−	0.767719i	−0.344471	−	0.938797i	$-0.611942\pi$
$269$	−4.24518e8	−	2.45096e8i	−1.32973	−	0.767719i	−0.985258	+	0.171078i	$0.945275\pi$
$270$	1.06488e8	−	4.12087e8i	0.329252	−	1.27414i
$271$	2.79787e8	+	1.61535e8i	0.853954	+	0.493031i	0.861983	−	0.506937i	$-0.169222\pi$
$271$	2.79787e8	+	1.61535e8i	0.853954	+	0.493031i	−0.00802893	+	0.999968i	$0.502556\pi$
$272$	4.45759e7	+	7.12141e7i	0.134310	+	0.214573i
$273$	−3.05276e7			−0.0908077
$274$	−1.19830e8	−	1.17711e8i	−0.351915	−	0.345692i
$275$	−3.46751e8	+	2.00197e8i	−1.00543	+	0.580488i
$276$	−1.17937e7	−	1.96108e7i	−0.0337650	−	0.0561453i
$277$	−5.37533e8			−1.51959			−0.759794	−	0.650163i	$-0.774700\pi$
$277$	−5.37533e8			−1.51959			−0.759794	+	0.650163i	$0.774700\pi$
$278$	−3.84520e8	+	3.91442e8i	−1.07340	+	1.09272i
$279$	−1.73982e8	−	3.01346e8i	−0.479612	−	0.830712i
$280$	4.21769e8	−	1.25199e8i	1.14821	−	0.340839i
$281$	1.68341e7	−	9.71917e6i	0.0452603	−	0.0261311i	−0.477199	−	0.878795i	$-0.658348\pi$
$281$	1.68341e7	−	9.71917e6i	0.0452603	−	0.0261311i	0.522459	+	0.852664i	$0.325015\pi$
$282$	1.51776e7	+	5.46875e7i	0.0403023	+	0.145217i
$283$	−1.44142e8	−	8.32202e7i	−0.378039	−	0.218261i	0.298926	−	0.954276i	$-0.403372\pi$
$283$	−1.44142e8	−	8.32202e7i	−0.378039	−	0.218261i	−0.676965	+	0.736015i	$0.736705\pi$
$284$	6.54982e6	+	3.67119e8i	0.0169674	+	0.951027i
$285$	−6.92272e7	+	2.78007e8i	−0.177141	+	0.711374i
$286$	−5.47658e7	−	5.37974e7i	−0.138429	−	0.135982i
$287$	1.62381e8	−	2.81252e8i	0.405461	−	0.702279i
$288$	−3.07317e8	+	9.72229e7i	−0.758077	+	0.239825i
$289$	1.92022e8	+	3.32592e8i	0.467960	+	0.810530i
$290$	1.92839e8	+	6.94836e8i	0.464304	+	1.67297i
$291$	−1.72378e8	+	9.95225e7i	−0.410068	+	0.236753i
$292$	−1.35913e7	−	7.61795e8i	−0.0319463	−	1.79060i
$293$		−	4.25501e8i		−	0.988243i	−0.869393	−	0.494122i	$-0.835490\pi$
$293$		−	4.25501e8i		−	0.988243i	0.869393	−	0.494122i	$-0.164510\pi$
$294$	−2.23580e7	+	8.65210e7i	−0.0513119	+	0.198567i
$295$	−5.95818e8	−	1.03199e9i	−1.35125	−	2.34044i
$296$	4.71759e8	+	4.47164e8i	1.05730	+	1.00218i
$297$		−	2.62424e8i		−	0.581240i
$298$	−7.11281e7	+	2.75251e8i	−0.155699	+	0.602521i
$299$	−9.07417e6	+	1.57169e7i	−0.0196317	+	0.0340031i
$300$	−2.94423e8	+	1.77062e8i	−0.629575	+	0.378618i
$301$	8.08580e7	−	1.40050e8i	0.170899	−	0.296006i
$302$	1.79856e8	−	4.99159e7i	0.375752	−	0.104283i
$303$	3.35217e7			0.0692271
$304$	4.65707e8	−	1.51868e8i	0.950726	−	0.310033i
$305$	3.14872e8			0.635455
$306$	9.72081e7	−	2.69784e7i	0.193944	−	0.0538258i
$307$	−2.79712e8	+	4.84475e8i	−0.551730	+	0.955624i	0.446420	+	0.894823i	$0.352699\pi$
$307$	−2.79712e8	+	4.84475e8i	−0.551730	+	0.955624i	−0.998150	+	0.0608003i	$0.980635\pi$
$308$	2.32463e8	−	1.39800e8i	0.453343	−	0.272634i
$309$	1.22343e8	−	2.11905e8i	0.235898	−	0.408588i
$310$	−2.56410e8	+	9.92254e8i	−0.488843	+	1.89172i
$311$			1.04314e9i			1.96644i	0.182418	+	0.983221i	$0.441608\pi$
$311$			1.04314e9i			1.96644i	−0.182418	+	0.983221i	$0.558392\pi$
$312$	−4.78085e7	−	4.53160e7i	−0.0891177	−	0.0844715i
$313$	−1.95105e8	−	3.37932e8i	−0.359636	−	0.622908i	0.628264	−	0.778000i	$-0.283766\pi$
$313$	−1.95105e8	−	3.37932e8i	−0.359636	−	0.622908i	−0.987900	+	0.155092i	$0.950433\pi$
$314$	2.19065e8	−	8.47735e8i	0.399318	−	1.54528i
$315$		−	5.28290e8i		−	0.952326i
$316$	8.51374e6	+	4.77197e8i	0.0151780	+	0.850733i
$317$	−2.58299e8	+	1.49129e8i	−0.455423	+	0.262938i	−0.710118	−	0.704083i	$-0.751358\pi$
$317$	−2.58299e8	+	1.49129e8i	−0.455423	+	0.262938i	0.254695	+	0.967021i	$0.418025\pi$
$318$	−1.09227e8	−	3.93563e8i	−0.190473	−	0.686309i
$319$	2.22302e8	+	3.85038e8i	0.383420	+	0.664103i
$320$	8.46372e8	+	4.30015e8i	1.44390	+	0.733598i
$321$	8.13061e7	−	1.40826e8i	0.137200	−	0.237638i
$322$	−4.57474e7	−	4.49385e7i	−0.0763608	−	0.0750106i
$323$	−1.47359e8	+	4.23019e7i	−0.243315	+	0.0698475i
$324$	4.66658e6	+	2.61563e8i	0.00762239	+	0.427237i
$325$	2.35963e8	+	1.36233e8i	0.381287	+	0.220136i
$326$	1.92045e8	+	6.91975e8i	0.307003	+	1.10619i
$327$	−2.35564e8	+	1.36003e8i	−0.372556	+	0.215095i
$328$	6.71800e8	−	1.99419e8i	1.05119	−	0.312039i
$329$	7.95210e7	+	1.37734e8i	0.123111	+	0.213234i
$330$	−2.39905e8	+	2.44224e8i	−0.367486	+	0.374101i
$331$	2.12466e8			0.322026			0.161013	−	0.986952i	$-0.448524\pi$
$331$	2.12466e8			0.322026			0.161013	+	0.986952i	$0.448524\pi$
$332$	−3.84244e8	−	6.38930e8i	−0.576267	−	0.958231i
$333$	6.75943e8	−	3.90256e8i	1.00313	−	0.579155i
$334$	4.19213e8	+	4.11800e8i	0.615633	+	0.604747i
$335$	5.76140e8			0.837280
$336$	1.97297e8	−	1.23497e8i	0.283748	−	0.177610i
$337$	8.91781e8	+	5.14870e8i	1.26927	+	0.732813i	0.974850	−	0.222864i	$-0.0715405\pi$
$337$	8.91781e8	+	5.14870e8i	1.26927	+	0.732813i	0.294419	+	0.955676i	$0.404874\pi$
$338$	1.64546e8	−	6.36761e8i	0.231782	−	0.896949i
$339$	2.21733e7	+	1.28018e7i	0.0309123	+	0.0178472i
$340$	−2.59927e8	−	1.43949e8i	−0.358654	−	0.198624i
$341$			6.31883e8i			0.862972i
$342$	−1.56850e7	−	5.87981e8i	−0.0212028	−	0.794825i
$343$			8.03120e8i			1.07461i
$344$	3.34524e8	−	9.93013e7i	0.443071	−	0.131523i
$345$	7.00884e7	+	4.04656e7i	0.0918923	+	0.0530541i
$346$	−5.58923e8	−	1.44432e8i	−0.725413	−	0.187455i
$347$	1.15859e9	+	6.68909e8i	1.48859	+	0.859437i	0.999915	−	0.0130292i	$-0.00414746\pi$
$347$	1.15859e9	+	6.68909e8i	1.48859	+	0.859437i	0.488674	+	0.872467i	$0.337481\pi$
$348$	1.96612e8	+	3.26931e8i	0.250082	+	0.415843i
$349$	−6.68159e7			−0.0841377			−0.0420688	−	0.999115i	$-0.513395\pi$
$349$	−6.68159e7			−0.0841377			−0.0420688	+	0.999115i	$0.513395\pi$
$350$	−6.74675e8	+	6.86819e8i	−0.841117	+	0.856257i
$351$	−1.54653e8	+	8.92892e7i	−0.190891	+	0.110211i
$352$	5.71579e8	+	1.26138e8i	0.698517	+	0.154151i
$353$	−3.96125e8			−0.479315			−0.239658	−	0.970857i	$-0.577035\pi$
$353$	−3.96125e8			−0.479315			−0.239658	+	0.970857i	$0.577035\pi$
$354$	−4.49743e8	−	4.41791e8i	−0.538832	−	0.529304i
$355$	−6.49278e8	−	1.12458e9i	−0.770250	−	1.33411i
$356$	2.11680e8	−	3.82229e8i	0.248660	−	0.449002i
$357$	−6.30892e7	+	3.64246e7i	−0.0733865	+	0.0423697i
$358$	−1.57223e9	+	4.36346e8i	−1.81103	+	0.502621i
$359$	1.11489e8	+	6.43679e7i	0.127174	+	0.0734242i	0.562238	−	0.826976i	$-0.309941\pi$
$359$	1.11489e8	+	6.43679e7i	0.127174	+	0.0734242i	−0.435063	+	0.900400i	$0.643274\pi$
$360$	7.84209e8	−	8.27343e8i	0.885876	−	0.934602i
$361$	3.17259e7	+	8.93309e8i	0.0354926	+	0.999370i
$362$	7.09218e8	−	7.21984e8i	0.785777	−	0.799921i
$363$	1.00717e8	−	1.74447e8i	0.110517	−	0.191421i
$364$	−1.61483e8	−	8.94302e7i	−0.175498	−	0.0971917i
$365$	1.34729e9	+	2.33358e9i	1.45023	+	2.51187i
$366$	1.60516e8	−	4.45484e7i	0.171133	−	0.0474950i
$367$	5.56194e8	−	3.21119e8i	0.587347	−	0.339105i	−0.176701	−	0.984265i	$-0.556542\pi$
$367$	5.56194e8	−	3.21119e8i	0.587347	−	0.339105i	0.764048	+	0.645160i	$0.223209\pi$
$368$	−4.93592e6	−	1.38286e8i	−0.00516298	−	0.144647i
$369$		−	8.41469e8i		−	0.871858i
$370$	−2.22570e9	−	5.75148e8i	−2.28434	−	0.590301i
$371$	−5.72280e8	−	9.91218e8i	−0.581835	−	1.00777i
$372$	9.67185e6	+	5.42110e8i	0.00974112	+	0.545993i
$373$			4.48287e8i			0.447275i	0.974672	+	0.223638i	$0.0717932\pi$
$373$			4.48287e8i			0.447275i	−0.974672	+	0.223638i	$0.928207\pi$
$374$	−1.77370e8	−	4.58345e7i	−0.175319	−	0.0453046i
$375$	2.33203e8	−	4.03920e8i	0.228362	−	0.395535i
$376$	−7.99210e7	+	3.33746e8i	−0.0775360	+	0.323786i
$377$	1.51275e8	−	2.62017e8i	0.145403	−	0.251845i
$378$	−1.68746e8	−	6.08024e8i	−0.160699	−	0.579028i
$379$	9.77907e8			0.922700			0.461350	−	0.887218i	$-0.347365\pi$
$379$	9.77907e8			0.922700			0.461350	+	0.887218i	$0.347365\pi$
$380$	−1.18061e9	+	1.26779e9i	−1.10374	+	1.18523i
$381$	6.04362e8			0.559835
$382$	−1.20438e8	−	4.33959e8i	−0.110545	−	0.398315i
$383$	1.49759e8	−	2.59391e8i	0.136207	−	0.235917i	−0.789851	−	0.613299i	$-0.789842\pi$
$383$	1.49759e8	−	2.59391e8i	0.136207	−	0.235917i	0.926058	+	0.377382i	$0.123176\pi$
$384$	4.92304e8	+	9.94680e7i	0.443684	+	0.0896446i
$385$	−4.79672e8	+	8.30817e8i	−0.428383	+	0.741981i
$386$	8.09953e8	+	2.09301e8i	0.716810	+	0.185232i
$387$		−	4.19011e8i		−	0.367483i
$388$	−1.20339e9	+	2.14698e7i	−1.04591	+	0.0186602i
$389$	−3.91757e8	−	6.78543e8i	−0.337438	−	0.584459i	0.646512	−	0.762903i	$-0.276227\pi$
$389$	−3.91757e8	−	6.78543e8i	−0.337438	−	0.584459i	−0.983950	+	0.178444i	$0.942894\pi$
$390$	2.25555e8	+	5.82860e7i	0.192542	+	0.0497552i
$391$			4.33081e7i			0.0366396i
$392$	−3.71731e8	+	3.92177e8i	−0.311693	+	0.328837i
$393$	−4.92008e8	+	2.84061e8i	−0.408882	+	0.236068i
$394$	1.94000e7	−	5.38411e6i	0.0159795	−	0.00443484i
$395$	−8.43960e8	−	1.46178e9i	−0.689020	−	1.19342i
$396$	3.40511e8	−	6.14857e8i	0.275548	−	0.497555i
$397$	7.71302e8	−	1.33594e9i	0.618668	−	1.07157i	−0.371061	−	0.928609i	$-0.621006\pi$
$397$	7.71302e8	−	1.33594e9i	0.618668	−	1.07157i	0.989729	−	0.142956i	$-0.0456609\pi$
$398$	1.76131e8	−	1.79301e8i	0.140038	−	0.142558i
$399$	1.17196e8	+	4.08255e8i	0.0923654	+	0.321756i
$400$	−2.07613e9	+	7.41044e7i	−1.62197	+	0.0578941i
$401$	1.09220e9	+	6.30581e8i	0.845855	+	0.488355i	0.859250	−	0.511555i	$-0.170931\pi$
$401$	1.09220e9	+	6.30581e8i	0.845855	+	0.488355i	−0.0133948	+	0.999910i	$0.504264\pi$
$402$	2.93705e8	−	8.15128e7i	0.225487	−	0.0625798i
$403$	3.72386e8	−	2.14997e8i	0.283417	−	0.163631i
$404$	1.77321e8	+	9.82014e7i	0.133791	+	0.0740939i
$405$	−4.62595e8	−	8.01237e8i	−0.346025	−	0.599334i
$406$	7.62654e8	+	7.49168e8i	0.565570	+	0.555569i
$407$	−1.41736e9			−1.04208
$408$	−1.52872e8	−	3.66078e7i	−0.111434	−	0.0266847i
$409$	−1.34925e9	+	7.78990e8i	−0.975126	+	0.562989i	−0.900795	−	0.434244i	$-0.857015\pi$
$409$	−1.34925e9	+	7.78990e8i	−0.975126	+	0.562989i	−0.0743309	+	0.997234i	$0.523682\pi$
$410$	−1.73676e9	+	1.76802e9i	−1.24450	+	1.26690i
$411$	3.14284e8			0.223293
$412$	1.26794e9	−	7.62520e8i	0.893218	−	0.537169i
$413$	−1.52997e9	−	8.83327e8i	−1.06870	−	0.617016i
$414$	−1.60871e8	−	4.15709e7i	−0.111423	−	0.0287931i
$415$	2.28352e9	+	1.31839e9i	1.56832	+	0.905472i
$416$	−1.20142e8	−	3.79765e8i	−0.0818219	−	0.258636i
$417$		−	1.02666e9i		−	0.693343i
$418$	−5.09203e8	+	9.38931e8i	−0.341015	+	0.628806i
$419$		−	1.33155e9i		−	0.884316i	−0.896937	−	0.442158i	$-0.854213\pi$
$419$		−	1.33155e9i		−	0.884316i	0.896937	−	0.442158i	$-0.145787\pi$
$420$	−3.98807e8	+	7.20122e8i	−0.262658	+	0.474279i
$421$	−3.74460e8	−	2.16195e8i	−0.244578	−	0.141207i	0.372701	−	0.927952i	$-0.378432\pi$
$421$	−3.74460e8	−	2.16195e8i	−0.244578	−	0.141207i	−0.617279	+	0.786744i	$0.711765\pi$
$422$	5.63096e8	−	2.17906e9i	0.364744	−	1.41149i
$423$	3.56874e8	+	2.06041e8i	0.229258	+	0.132362i
$424$	5.75158e8	−	2.40183e9i	0.366443	−	1.53025i
$425$	6.50198e8			0.410851
$426$	−4.90097e8	−	4.81431e8i	−0.307149	−	0.301718i
$427$	4.04271e8	−	2.33406e8i	0.251290	−	0.145082i
$428$	8.42638e8	−	5.06751e8i	0.519503	−	0.312422i
$429$	1.43637e8			0.0878347
$430$	−8.64821e8	+	8.80388e8i	−0.524550	+	0.533992i
$431$	−1.21298e8	−	2.10095e8i	−0.0729768	−	0.126400i	0.827228	−	0.561867i	$-0.189917\pi$
$431$	−1.21298e8	−	2.10095e8i	−0.0729768	−	0.126400i	−0.900205	+	0.435467i	$0.856583\pi$
$432$	6.38299e8	−	1.20270e9i	0.380918	−	0.717738i
$433$	1.68347e9	−	9.71952e8i	0.996547	−	0.575357i	0.0893225	−	0.996003i	$-0.471530\pi$
$433$	1.68347e9	−	9.71952e8i	0.996547	−	0.575357i	0.907225	+	0.420646i	$0.138196\pi$
$434$	4.06320e8	+	1.46405e9i	0.238591	+	0.859688i
$435$	−1.16844e9	−	6.74600e8i	−0.680605	−	0.392947i
$436$	−1.64449e9	+	2.93396e7i	−0.950232	+	0.0169532i
$437$	2.45024e8	+	6.10140e7i	0.140450	+	0.0349739i
$438$	1.01698e9	+	9.98999e8i	0.578301	+	0.568075i
$439$	−1.60959e9	+	2.78789e9i	−0.908008	+	1.57272i	−0.0911792	+	0.995835i	$0.529064\pi$
$439$	−1.60959e9	+	2.78789e9i	−0.908008	+	1.57272i	−0.816828	+	0.576881i	$0.804270\pi$
$440$	−1.98449e9	+	5.89083e8i	−1.11062	+	0.329680i
$441$	3.24423e8	+	5.61917e8i	0.180126	+	0.311988i
$442$	3.33383e7	+	1.20124e8i	0.0183639	+	0.0661686i
$443$	2.15588e9	−	1.24470e9i	1.17818	−	0.680221i	0.222585	−	0.974913i	$-0.428550\pi$
$443$	2.15588e9	−	1.24470e9i	1.17818	−	0.680221i	0.955592	+	0.294692i	$0.0952170\pi$
$444$	−1.21600e9	+	2.16947e7i	−0.659313	+	0.0117629i
$445$			1.54524e9i			0.831259i
$446$	−3.98610e8	+	1.54254e9i	−0.212753	+	0.823311i
$447$	−2.65961e8	−	4.60658e8i	−0.140845	−	0.243951i
$448$	1.40543e9	−	7.52874e7i	0.738478	−	0.0395594i
$449$			2.91307e9i			1.51876i	0.650647	+	0.759380i	$0.274498\pi$
$449$			2.91307e9i			1.51876i	−0.650647	+	0.759380i	$0.725502\pi$
$450$	−6.24117e8	+	2.41520e9i	−0.322866	+	1.24942i
$451$	−7.64029e8	+	1.32334e9i	−0.392186	+	0.679286i
$452$	7.97887e7	+	1.32675e8i	0.0406403	+	0.0675777i
$453$	−1.74618e8	+	3.02448e8i	−0.0882563	+	0.152864i
$454$	2.10549e9	−	5.84341e8i	1.05598	−	0.293070i
$455$	6.52830e8			0.324908
$456$	−4.22487e8	+	8.13328e8i	−0.208659	+	0.401688i
$457$	−2.54550e9			−1.24757			−0.623786	−	0.781595i	$-0.714406\pi$
$457$	−2.54550e9			−1.24757			−0.623786	+	0.781595i	$0.714406\pi$
$458$	−1.41515e9	+	3.92751e8i	−0.688295	+	0.191024i
$459$	−2.13074e8	+	3.69055e8i	−0.102846	+	0.178134i
$460$	2.52207e8	+	4.19376e8i	0.120810	+	0.200887i
$461$	−3.02789e8	+	5.24445e8i	−0.143942	+	0.249314i	−0.928978	−	0.370136i	$-0.879311\pi$
$461$	−3.02789e8	+	5.24445e8i	−0.143942	+	0.249314i	0.785036	+	0.619450i	$0.212644\pi$
$462$	−1.26983e8	+	4.91400e8i	−0.0599101	+	0.231840i
$463$			2.51701e9i			1.17856i	0.807930	+	0.589279i	$0.200588\pi$
$463$			2.51701e9i			1.17856i	−0.807930	+	0.589279i	$0.799412\pi$
$464$	8.22866e7	+	2.30536e9i	0.0382398	+	1.07134i
$465$	−9.58763e8	−	1.66063e9i	−0.442207	−	0.765925i
$466$	8.30488e8	−	3.21382e9i	0.380174	−	1.47120i
$467$		−	1.75112e8i		−	0.0795624i	−0.999208	−	0.0397812i	$-0.987334\pi$
$467$		−	1.75112e8i		−	0.0795624i	0.999208	−	0.0397812i	$-0.0126661\pi$
$468$	−4.78210e8	+	8.53180e6i	−0.215654	+	0.00384751i
$469$	7.39718e8	−	4.27077e8i	0.331102	−	0.191162i
$470$	−3.24571e8	−	1.16949e9i	−0.144201	−	0.519582i
$471$	8.19122e8	+	1.41876e9i	0.361223	+	0.625656i
$472$	−1.08481e9	−	3.65448e9i	−0.474850	−	1.59967i
$473$	−3.80450e8	+	6.58958e8i	−0.165304	+	0.286315i
$474$	−6.37050e8	−	6.25785e8i	−0.274757	−	0.269899i
$475$	9.16022e8	−	3.67861e9i	0.392174	−	1.57491i
$476$	−4.40432e8	+	7.85779e6i	−0.187178	+	0.00333946i
$477$	−2.56827e9	−	1.48279e9i	−1.08350	−	0.625556i
$478$	−4.59305e8	−	1.65496e9i	−0.192355	−	0.693091i
$479$	3.63181e9	−	2.09683e9i	1.50990	−	0.871744i	0.509971	−	0.860192i	$-0.329656\pi$
$479$	3.63181e9	−	2.09683e9i	1.50990	−	0.871744i	0.999933	−	0.0115519i	$-0.00367716\pi$
$480$	−1.69353e9	+	5.35766e8i	−0.698955	+	0.221121i
$481$	4.82256e8	+	8.35291e8i	0.197592	+	0.342239i
$482$	7.03219e8	−	7.15877e8i	0.286039	−	0.291188i
$483$	1.19984e8			0.0484516
$484$	1.04381e9	−	6.27732e8i	0.418468	−	0.251661i
$485$	3.68629e9	−	2.12828e9i	1.46721	−	0.847097i
$486$	−1.81609e9	−	1.78398e9i	−0.717648	−	0.704959i
$487$	1.28710e9			0.504963			0.252481	−	0.967602i	$-0.418753\pi$
$487$	1.28710e9			0.504963			0.252481	+	0.967602i	$0.418753\pi$
$488$	9.79594e8	+	2.34580e8i	0.381572	+	0.0913738i
$489$	−1.16363e9	−	6.71823e8i	−0.450023	−	0.259821i
$490$	4.78126e8	−	1.85025e9i	0.183593	−	0.710466i
$491$	−3.97966e9	−	2.29766e9i	−1.51726	−	0.875992i	−0.999794	−	0.0202898i	$-0.993541\pi$
$491$	−3.97966e9	−	2.29766e9i	−1.51726	−	0.875992i	−0.517469	−	0.855702i	$-0.673126\pi$
$492$	−6.35226e8	+	1.14702e9i	−0.240464	+	0.434204i
$493$		−	7.21988e8i		−	0.271373i
$494$	7.26592e8	−	1.93826e7i	0.271173	−	0.00723381i
$495$			2.48569e9i			0.921147i
$496$	−1.53694e9	+	2.89596e9i	−0.565551	+	1.06563i
$497$	−1.66724e9	−	9.62584e8i	−0.609189	−	0.351715i
$498$	1.35062e9	+	3.49016e8i	0.490039	+	0.126632i
$499$	−3.47792e9	−	2.00798e9i	−1.25305	−	0.723447i	−0.281334	−	0.959610i	$-0.590777\pi$
$499$	−3.47792e9	−	2.00798e9i	−1.25305	−	0.723447i	−0.971714	+	0.236163i	$0.924110\pi$
$500$	2.41686e9	−	1.45347e9i	0.864684	−	0.520009i
$501$	−1.09949e9			−0.390625
$502$	3.49711e9	−	3.56005e9i	1.23380	−	1.25601i
$503$	−3.76089e9	+	2.17135e9i	−1.31766	+	0.760751i	−0.983352	−	0.181713i	$-0.941836\pi$
$503$	−3.76089e9	+	2.17135e9i	−1.31766	+	0.760751i	−0.334307	+	0.942464i	$0.608502\pi$
$504$	3.93577e8	−	1.64356e9i	0.136938	−	0.571844i
$505$	−7.16859e8			−0.247693
$506$	2.15249e8	+	2.11443e8i	0.0738608	+	0.0725548i
$507$	6.15269e8	+	1.06568e9i	0.209670	+	0.363160i
$508$	3.19693e9	+	1.77047e9i	1.08196	+	0.599193i
$509$	1.04008e9	−	6.00488e8i	0.349585	−	0.201833i	−0.314917	−	0.949119i	$-0.601977\pi$
$509$	1.04008e9	−	6.00488e8i	0.349585	−	0.201833i	0.664503	+	0.747286i	$0.268643\pi$
$510$	5.35684e8	−	1.48670e8i	0.178819	−	0.0496280i
$511$	3.45964e9	+	1.99742e9i	1.14698	+	0.662211i
$512$	2.31278e9	+	1.96836e9i	0.761533	+	0.648126i
$513$	1.78781e9	+	1.72545e9i	0.584671	+	0.564275i
$514$	3.05076e9	−	3.10568e9i	0.990918	−	1.00875i
$515$	−2.61630e9	+	4.53157e9i	−0.844039	+	1.46192i
$516$	−3.16312e8	+	5.71161e8i	−0.101354	+	0.183014i
$517$	−3.74159e8	−	6.48063e8i	−0.119080	−	0.206253i
$518$	−3.28397e9	+	9.11408e8i	−1.03811	+	0.288110i
$519$	9.35407e8	−	5.40058e8i	0.293708	−	0.169572i
$520$	1.02238e9	+	9.69080e8i	0.318861	+	0.302237i
$521$			4.60906e8i			0.142784i	0.997448	+	0.0713921i	$0.0227442\pi$
$521$			4.60906e8i			0.142784i	−0.997448	+	0.0713921i	$0.977256\pi$
$522$	2.68187e9	+	6.93028e8i	0.825262	+	0.213257i
$523$	−7.78929e8	−	1.34914e9i	−0.238090	−	0.412385i	0.722076	−	0.691814i	$-0.243188\pi$
$523$	−7.78929e8	−	1.34914e9i	−0.238090	−	0.412385i	−0.960166	+	0.279429i	$0.909855\pi$
$524$	−3.43476e9	+	6.12799e7i	−1.04288	+	0.0186062i
$525$		−	1.80136e9i		−	0.543303i
$526$	−2.31944e9	−	5.99372e8i	−0.694918	−	0.179575i
$527$	5.13056e8	−	8.88639e8i	0.152696	−	0.264477i
$528$	−9.28313e8	+	5.81071e8i	−0.274458	+	0.171795i
$529$	−1.66675e9	+	2.88689e9i	−0.489525	+	0.847883i
$530$	2.33580e9	+	8.41633e9i	0.681508	+	2.45560i
$531$	−4.57745e9			−1.32676
$532$	−5.76039e8	+	2.50289e9i	−0.165868	+	0.720696i
$533$	1.03984e9			0.297454
$534$	2.18622e8	+	7.87735e8i	0.0621298	+	0.223865i
$535$	−1.73873e9	+	3.01156e9i	−0.490900	+	0.850264i
$536$	1.79242e9	+	4.29225e8i	0.502763	+	0.120395i
$537$	1.52645e9	−	2.64388e9i	0.425375	−	0.736771i
$538$	5.36950e9	+	1.38754e9i	1.48661	+	0.384156i
$539$		−	1.17827e9i		−	0.324103i
$540$	8.58981e7	+	4.81462e9i	0.0234750	+	1.31578i
$541$	2.81722e9	+	4.87957e9i	0.764945	+	1.32492i	0.940276	+	0.340414i	$0.110567\pi$
$541$	2.81722e9	+	4.87957e9i	0.764945	+	1.32492i	−0.175331	+	0.984510i	$0.556099\pi$
$542$	−3.53887e9	−	9.14486e8i	−0.954700	−	0.246706i
$543$			1.89358e9i			0.507557i
$544$	−7.01414e8	−	6.41484e8i	−0.186801	−	0.170840i
$545$	5.03752e9	−	2.90841e9i	1.33300	−	0.769606i
$546$	3.32801e8	−	9.23630e7i	0.0875004	−	0.0242842i
$547$	−1.90713e9	−	3.30324e9i	−0.498224	−	0.862949i	0.501774	−	0.864999i	$-0.332681\pi$
$547$	−1.90713e9	−	3.30324e9i	−0.498224	−	0.862949i	−0.999998	+	0.00204983i	$0.999348\pi$
$548$	1.66248e9	+	9.20691e8i	0.431544	+	0.238991i
$549$	6.04762e8	−	1.04748e9i	0.155984	−	0.270173i
$550$	3.17445e9	−	3.23159e9i	0.813579	−	0.828223i
$551$	−4.08478e9	−	1.01716e9i	−1.04025	−	0.259036i
$552$	1.87904e8	+	1.78108e8i	0.0475499	+	0.0450709i
$553$	−2.16716e9	−	1.25121e9i	−0.544945	−	0.314624i
$554$	5.86000e9	−	1.62634e9i	1.46424	−	0.406375i
$555$	3.72492e9	−	2.15058e9i	0.924892	−	0.533987i
$556$	3.00758e9	−	5.43075e9i	0.742087	−	1.33998i
$557$	−2.05890e9	−	3.56612e9i	−0.504827	−	0.874385i	−0.999984	−	0.00558221i	$-0.998223\pi$
$557$	−2.05890e9	−	3.56612e9i	−0.504827	−	0.874385i	0.495158	−	0.868803i	$-0.335110\pi$
$558$	2.80843e9	+	2.75877e9i	0.684297	+	0.672197i
$559$	5.17789e8			0.125375
$560$	−4.21918e9	+	2.64097e9i	−1.01524	+	0.635485i
$561$	2.96845e8	−	1.71383e8i	0.0709838	−	0.0409825i
$562$	−1.54113e8	+	1.56888e8i	−0.0366238	+	0.0372830i
$563$	−1.48671e9			−0.351112			−0.175556	−	0.984469i	$-0.556172\pi$
$563$	−1.48671e9			−0.351112			−0.175556	+	0.984469i	$0.556172\pi$
$564$	−3.30921e8	−	5.50264e8i	−0.0776689	−	0.129150i
$565$	−4.74175e8	−	2.73765e8i	−0.110604	−	0.0638570i
$566$	1.82317e9	+	4.71128e8i	0.422639	+	0.109215i
$567$	−1.18787e9	−	6.85818e8i	−0.273671	−	0.158004i
$568$	−1.18214e9	−	3.98239e9i	−0.270677	−	0.911852i
$569$			1.96214e9i			0.446515i	0.974759	+	0.223258i	$0.0716691\pi$
$569$			1.96214e9i			0.446515i	−0.974759	+	0.223258i	$0.928331\pi$
$570$	−8.64351e7	−	3.24018e9i	−0.0195492	−	0.732837i
$571$			3.06447e9i			0.688857i	0.938813	+	0.344429i	$0.111927\pi$
$571$			3.06447e9i			0.688857i	−0.938813	+	0.344429i	$0.888073\pi$
$572$	7.59805e8	+	4.20783e8i	0.169752	+	0.0940097i
$573$	7.29749e8	+	4.21321e8i	0.162044	+	0.0935561i
$574$	−9.19276e8	+	3.55741e9i	−0.202887	+	0.785131i
$575$	−9.27417e8	−	5.35445e8i	−0.203441	−	0.117456i
$576$	3.05611e9	−	1.98970e9i	0.666332	−	0.433819i
$577$	−3.96788e9			−0.859890			−0.429945	−	0.902855i	$-0.641467\pi$
$577$	−3.96788e9			−0.859890			−0.429945	+	0.902855i	$0.641467\pi$
$578$	−3.09963e9	−	3.04482e9i	−0.667671	−	0.655866i
$579$	−1.35553e9	+	7.82615e8i	−0.290224	+	0.167561i
$580$	−4.20454e9	−	6.99141e9i	−0.894788	−	1.48788i
$581$	3.90914e9			0.826923
$582$	1.57809e9	−	1.60650e9i	0.331820	−	0.337793i
$583$	2.69267e9	+	4.66384e9i	0.562786	+	0.974773i
$584$	2.45302e9	+	8.26370e9i	0.509632	+	1.71684i
$585$	1.46488e9	−	8.45751e8i	0.302522	−	0.174661i
$586$	1.28738e9	+	4.63866e9i	0.264280	+	0.952250i
$587$	5.38483e9	+	3.10893e9i	1.09885	+	0.634422i	0.935919	−	0.352216i	$-0.114572\pi$
$587$	5.38483e9	+	3.10893e9i	1.09885	+	0.634422i	0.162932	+	0.986637i	$0.447905\pi$
$588$	−1.80350e7	−	1.01087e9i	−0.00365844	−	0.205057i
$589$	−4.30483e9	−	4.15466e9i	−0.868065	−	0.837783i
$590$	9.61774e9	+	9.44767e9i	1.92793	+	1.89384i
$591$	−1.88350e7	+	3.26231e7i	−0.00375326	+	0.00650084i
$592$	−6.49587e9	−	3.44749e9i	−1.28680	−	0.682931i
$593$	−2.55998e9	−	4.43402e9i	−0.504133	−	0.873184i	−0.999989	−	0.00477920i	$-0.998479\pi$
$593$	−2.55998e9	−	4.43402e9i	−0.504133	−	0.873184i	0.495855	−	0.868405i	$-0.334855\pi$
$594$	7.93979e8	+	2.86085e9i	0.155438	+	0.560071i
$595$	1.34916e9	−	7.78937e8i	0.262575	−	0.151598i
$596$	−5.73752e7	−	3.21589e9i	−0.0111010	−	0.622214i
$597$			4.70263e8i			0.0904546i
$598$	5.13709e7	−	1.98795e8i	0.00982343	−	0.0380146i
$599$	1.12501e9	+	1.94857e9i	0.213876	+	0.370444i	0.952924	−	0.303208i	$-0.0980578\pi$
$599$	1.12501e9	+	1.94857e9i	0.213876	+	0.370444i	−0.739048	+	0.673652i	$0.764724\pi$
$600$	2.67399e9	−	2.82106e9i	0.505394	−	0.533192i
$601$			2.41375e8i			0.0453557i	0.999743	+	0.0226779i	$0.00721921\pi$
$601$			2.41375e8i			0.0453557i	−0.999743	+	0.0226779i	$0.992781\pi$
$602$	−4.57755e8	+	1.77142e9i	−0.0855156	+	0.330928i
$603$	1.10657e9	−	1.91663e9i	0.205526	−	0.355982i
$604$	−1.80970e9	+	1.08833e9i	−0.334178	+	0.200970i
$605$	−2.15383e9	+	3.73054e9i	−0.395427	+	0.684900i
$606$	−3.65441e8	+	1.01422e8i	−0.0667058	+	0.0185130i
$607$	6.00790e9			1.09034			0.545171	−	0.838325i	$-0.316465\pi$
$607$	6.00790e9			1.09034			0.545171	+	0.838325i	$0.316465\pi$
$608$	−4.61749e9	+	3.06463e9i	−0.833189	+	0.552989i
$609$	−2.00025e9			−0.358859
$610$	−3.43263e9	+	9.52665e8i	−0.612311	+	0.169936i
$611$	−2.54614e8	+	4.41004e8i	−0.0451583	+	0.0782165i
$612$	−9.78103e8	+	5.88218e8i	−0.172486	+	0.103731i
$613$	−5.18649e9	+	8.98326e9i	−0.909414	+	1.57515i	−0.0945346	+	0.995522i	$0.530136\pi$
$613$	−5.18649e9	+	8.98326e9i	−0.909414	+	1.57515i	−0.814880	+	0.579630i	$0.803197\pi$
$614$	1.58351e9	−	6.12786e9i	0.276078	−	1.06836i
$615$		−	4.63708e9i		−	0.803862i
$616$	−2.11126e9	+	2.22739e9i	−0.363923	+	0.383940i
$617$	−1.61411e9	−	2.79572e9i	−0.276653	−	0.479177i	0.693898	−	0.720074i	$-0.255892\pi$
$617$	−1.61411e9	−	2.79572e9i	−0.276653	−	0.479177i	−0.970551	+	0.240896i	$0.922559\pi$
$618$	−6.92612e8	+	2.68027e9i	−0.118040	+	0.456792i
$619$			6.93453e9i			1.17517i	0.809163	+	0.587584i	$0.199921\pi$
$619$			6.93453e9i			1.17517i	−0.809163	+	0.587584i	$0.800079\pi$
$620$	−2.06832e8	−	1.15930e10i	−0.0348535	−	1.95355i
$621$	6.07842e8	−	3.50938e8i	0.101852	−	0.0588044i
$622$	−3.15608e9	−	1.13719e10i	−0.525874	−	1.89482i
$623$	1.14544e9	+	1.98397e9i	0.189787	+	0.328720i
$624$	6.58298e8	+	3.49372e8i	0.108462	+	0.0575628i
$625$	−3.40097e7	+	5.89065e7i	−0.00557215	+	0.00965124i
$626$	3.14940e9	+	3.09371e9i	0.513119	+	0.504046i
$627$	−5.51428e8	−	1.92091e9i	−0.0893413	−	0.311222i
$628$	1.76707e8	+	9.90450e9i	0.0284706	+	1.59578i
$629$	1.99329e9	+	1.15083e9i	0.319369	+	0.184388i
$630$	1.59837e9	+	5.75923e9i	0.254675	+	0.917641i
$631$	9.28119e9	−	5.35850e9i	1.47062	−	0.849064i	0.471165	−	0.882045i	$-0.343833\pi$
$631$	9.28119e9	−	5.35850e9i	1.47062	−	0.849064i	0.999456	+	0.0329812i	$0.0105001\pi$
$632$	−1.53660e9	−	5.17648e9i	−0.242132	−	0.815689i
$633$	2.10552e9	+	3.64686e9i	0.329948	+	0.571487i
$634$	2.36468e9	−	2.40725e9i	0.368520	−	0.375153i
$635$	−1.29243e10			−2.00308
$636$	2.38150e9	+	3.96002e9i	0.367071	+	0.610376i
$637$	−6.94385e8	+	4.00903e8i	−0.106442	+	0.0614542i
$638$	−3.58841e9	−	3.52496e9i	−0.547053	−	0.537380i
$639$	−4.98817e9			−0.756290
$640$	−1.05279e10	−	2.12712e9i	−1.58749	−	0.320746i
$641$	1.04806e9	+	6.05099e8i	0.157175	+	0.0907451i	0.576525	−	0.817080i	$-0.304408\pi$
$641$	1.04806e9	+	6.05099e8i	0.157175	+	0.0907451i	−0.419350	+	0.907825i	$0.637742\pi$
$642$	−4.60292e8	+	1.78124e9i	−0.0686532	+	0.265674i
$643$	−3.62033e9	−	2.09020e9i	−0.537045	−	0.310063i	0.206836	−	0.978376i	$-0.433683\pi$
$643$	−3.62033e9	−	2.09020e9i	−0.537045	−	0.310063i	−0.743880	+	0.668313i	$0.767017\pi$
$644$	6.34686e8	+	3.51492e8i	0.0936393	+	0.0518579i
$645$		−	2.30904e9i		−	0.338823i
$646$	1.47847e9	−	9.07005e8i	0.215774	−	0.132372i
$647$			3.46582e9i			0.503084i	0.967846	+	0.251542i	$0.0809377\pi$
$647$			3.46582e9i			0.503084i	−0.967846	+	0.251542i	$0.919062\pi$
$648$	−8.42249e8	−	2.83735e9i	−0.121598	−	0.409638i
$649$	7.19874e9	+	4.15619e9i	1.03371	+	0.596815i
$650$	−2.98457e9	−	7.71247e8i	−0.426270	−	0.110153i
$651$	−2.46195e9	−	1.42141e9i	−0.349741	−	0.201923i
$652$	−4.18722e9	−	6.96262e9i	−0.591643	−	0.983799i
$653$	−6.80035e9			−0.955730			−0.477865	−	0.878433i	$-0.658589\pi$
$653$	−6.80035e9			−0.955730			−0.477865	+	0.878433i	$0.658589\pi$
$654$	2.15655e9	−	2.19537e9i	0.301466	−	0.306892i
$655$	1.05216e10	−	6.07463e9i	1.46297	−	0.844647i
$656$	−6.72038e9	+	4.20657e9i	−0.929459	+	0.581788i
$657$	1.03508e10			1.42395
$658$	−1.28363e9	−	1.26094e9i	−0.175651	−	0.172545i
$659$	−6.30414e9	−	1.09191e10i	−0.858078	−	1.48623i	−0.873760	−	0.486358i	$-0.838325\pi$
$659$	−6.30414e9	−	1.09191e10i	−0.858078	−	1.48623i	0.0156818	−	0.999877i	$-0.495008\pi$
$660$	1.87645e9	−	3.38829e9i	0.254058	−	0.458751i
$661$	−7.94768e9	+	4.58860e9i	−1.07037	+	0.617981i	−0.928284	−	0.371873i	$-0.878716\pi$
$661$	−7.94768e9	+	4.58860e9i	−1.07037	+	0.617981i	−0.142090	+	0.989854i	$0.545382\pi$
$662$	−2.31623e9	+	6.42829e8i	−0.310298	+	0.0861177i
$663$	−2.02002e8	−	1.16626e8i	−0.0269189	−	0.0155416i
$664$	6.12201e9	+	5.80284e9i	0.811533	+	0.769223i
$665$	−2.50624e9	−	8.73051e9i	−0.330481	−	1.15123i
$666$	−6.18815e9	+	6.29954e9i	−0.811710	+	0.826321i
$667$	−5.94565e8	+	1.02982e9i	−0.0775816	+	0.134375i
$668$	−5.81604e9	−	3.22095e9i	−0.754935	−	0.418086i
$669$	−1.49047e9	−	2.58158e9i	−0.192457	−	0.333345i
$670$	−6.28087e9	+	1.74315e9i	−0.806786	+	0.223909i
$671$	−1.90216e9	+	1.09821e9i	−0.243063	+	0.140332i
$672$	−1.77721e9	+	1.94325e9i	−0.225916	+	0.247022i
$673$		−	4.85614e9i		−	0.614100i	−0.951693	−	0.307050i	$-0.900658\pi$
$673$		−	4.85614e9i		−	0.614100i	0.951693	−	0.307050i	$-0.0993418\pi$
$674$	−1.12797e10	−	2.91480e9i	−1.41901	−	0.366689i
$675$	−5.26874e9	−	9.12572e9i	−0.659391	−	1.14210i
$676$	1.32731e8	+	7.43959e9i	0.0165256	+	0.926265i
$677$		−	1.01248e10i		−	1.25409i	−0.778984	−	0.627044i	$-0.784265\pi$
$677$		−	1.01248e10i		−	1.25409i	0.778984	−	0.627044i	$-0.215735\pi$
$678$	−2.80458e8	−	7.24737e7i	−0.0345592	−	0.00893051i
$679$	3.15527e9	−	5.46510e9i	0.386806	−	0.669967i
$680$	3.26916e9	+	7.82855e8i	0.398708	+	0.0954773i
$681$	−2.04417e9	+	3.54061e9i	−0.248029	+	0.429599i
$682$	−1.91180e9	−	6.88857e9i	−0.230780	−	0.831541i
$683$	1.20546e10			1.44770			0.723852	−	0.689955i	$-0.242370\pi$
$683$	1.20546e10			1.44770			0.723852	+	0.689955i	$0.242370\pi$
$684$	1.94996e9	+	6.36251e9i	0.232986	+	0.760207i
$685$	−6.72094e9			−0.798938
$686$	−2.42989e9	−	8.75533e9i	−0.287377	−	1.03547i
$687$	1.37394e9	−	2.37974e9i	0.161666	−	0.280014i
$688$	−3.34642e9	+	2.09467e9i	−0.391761	+	0.245220i
$689$	1.83235e9	−	3.17372e9i	0.213423	−	0.369660i
$690$	−8.86510e8	−	2.29085e8i	−0.102733	−	0.0265475i
$691$		−	8.15752e7i		−	0.00940557i	−0.999989	−	0.00470278i	$-0.998503\pi$
$691$		−	8.15752e7i		−	0.00940557i	0.999989	−	0.00470278i	$-0.00149695\pi$
$692$	6.53017e9	−	1.16506e8i	0.749123	−	0.0133652i
$693$	1.84257e9	+	3.19143e9i	0.210309	+	0.364266i
$694$	−1.46543e10	−	3.78685e9i	−1.66421	−	0.430051i
$695$			2.19550e10i			2.48077i
$696$	−3.13255e9	−	2.96923e9i	−0.352180	−	0.333819i
$697$	2.14896e9	−	1.24070e9i	0.240389	−	0.138788i
$698$	7.28403e8	−	2.02155e8i	0.0810733	−	0.0225005i
$699$	3.10534e9	+	5.37861e9i	0.343906	+	0.595662i
$700$	5.27706e9	−	9.52873e9i	0.581499	−	1.05001i
$701$	−1.30899e9	+	2.26723e9i	−0.143523	+	0.248589i	−0.928821	−	0.370529i	$-0.879176\pi$
$701$	−1.30899e9	+	2.26723e9i	−0.143523	+	0.248589i	0.785298	+	0.619118i	$0.212510\pi$
$702$	1.41583e9	−	1.44131e9i	0.154465	−	0.157246i
$703$	9.31923e9	−	9.65607e9i	1.01166	−	1.04823i
$704$	−6.61279e9	+	3.54240e8i	−0.714300	+	0.0382642i
$705$	1.96662e9	+	1.13543e9i	0.211378	+	0.122039i
$706$	4.31842e9	−	1.19850e9i	0.461858	−	0.128181i
$707$	−9.20391e8	+	5.31388e8i	−0.0979499	+	0.0565514i
$708$	6.23961e9	+	3.45553e9i	0.660756	+	0.365930i
$709$	9.19979e9	+	1.59345e10i	0.969429	+	1.67910i	0.697213	+	0.716864i	$0.254423\pi$
$709$	9.19979e9	+	1.59345e10i	0.969429	+	1.67910i	0.272216	+	0.962236i	$0.412243\pi$
$710$	1.04807e10	+	1.02954e10i	1.09897	+	1.07954i
$711$	−6.48384e9			−0.676532
$712$	−1.15121e9	+	4.80738e9i	−0.119529	+	0.499147i
$713$	−1.46361e9	+	8.45014e8i	−0.151221	+	0.0873073i
$714$	5.77572e8	−	5.87968e8i	0.0593830	−	0.0604519i
$715$	−3.07167e9			−0.314270
$716$	1.58198e10	−	9.51378e9i	1.61066	−	0.968630i
$717$	2.78300e9	+	1.60677e9i	0.281966	+	0.162793i
$718$	−1.41016e9	−	3.64401e8i	−0.142178	−	0.0367404i
$719$	−2.40702e9	−	1.38969e9i	−0.241506	−	0.139434i	0.374363	−	0.927282i	$-0.377862\pi$
$719$	−2.40702e9	−	1.38969e9i	−0.241506	−	0.139434i	−0.615869	+	0.787849i	$0.711195\pi$
$720$	−6.04600e9	+	1.13921e10i	−0.603676	+	1.13747i
$721$			7.75757e9i			0.770819i
$722$	−3.04862e9	−	9.64255e9i	−0.301456	−	0.953480i
$723$			1.87757e9i			0.184762i
$724$	−5.54724e9	+	1.00166e10i	−0.543240	+	0.980923i
$725$	1.54610e10	+	8.92639e9i	1.50679	+	0.869947i
$726$	−5.70181e8	+	2.20648e9i	−0.0553012	+	0.214004i
$727$	7.57098e9	+	4.37111e9i	0.730771	+	0.421911i	0.818704	−	0.574215i	$-0.194693\pi$
$727$	7.57098e9	+	4.37111e9i	0.730771	+	0.421911i	−0.0879329	+	0.996126i	$0.528026\pi$
$728$	2.03101e9	+	4.86359e8i	0.195098	+	0.0467194i
$729$	2.93402e8			0.0280490
$730$	−2.17481e10	−	2.13635e10i	−2.06915	−	2.03256i
$731$	1.07008e9	−	6.17810e8i	0.101322	−	0.0584984i
$732$	−1.61511e9	+	9.71302e8i	−0.152199	+	0.0915304i
$733$	6.97247e9			0.653917			0.326959	−	0.945039i	$-0.393976\pi$
$733$	6.97247e9			0.653917			0.326959	+	0.945039i	$0.393976\pi$
$734$	−5.09187e9	+	5.18352e9i	−0.475270	+	0.483825i
$735$	1.78780e9	+	3.09656e9i	0.166078	+	0.287656i
$736$	4.72202e8	+	1.49261e9i	0.0436571	+	0.137998i
$737$	−3.48049e9	+	2.00946e9i	−0.320261	+	0.184903i
$738$	2.54591e9	+	9.17340e9i	0.233156	+	0.840104i
$739$	6.85144e9	+	3.95568e9i	0.624491	+	0.360550i	0.778615	−	0.627501i	$-0.215922\pi$
$739$	6.85144e9	+	3.95568e9i	0.624491	+	0.360550i	−0.154124	+	0.988051i	$0.549256\pi$
$740$	2.60040e10	−	4.63940e8i	2.35901	−	0.0420873i
$741$	−9.44419e8	+	9.78556e8i	−0.0852709	+	0.0883531i
$742$	9.23778e9	+	9.07444e9i	0.830145	+	0.815467i
$743$	4.28072e9	−	7.41443e9i	0.382874	−	0.663158i	−0.608598	−	0.793479i	$-0.708268\pi$
$743$	4.28072e9	−	7.41443e9i	0.382874	−	0.663158i	0.991472	+	0.130321i	$0.0416009\pi$
$744$	−1.74563e9	−	5.88063e9i	−0.155398	−	0.523502i
$745$	5.68756e9	+	9.85114e9i	0.503940	+	0.872849i
$746$	−1.35632e9	−	4.88707e9i	−0.119612	−	0.430985i
$747$	8.77171e9	−	5.06435e9i	0.769950	−	0.444531i
$748$	2.07230e9	−	3.69722e7i	0.181050	−	0.00323013i
$749$			5.15548e9i			0.448314i
$750$	−1.32021e9	+	5.10896e9i	−0.114269	+	0.442199i
$751$	2.33061e9	+	4.03673e9i	0.200784	+	0.347768i	0.948781	−	0.315934i	$-0.102318\pi$
$751$	2.33061e9	+	4.03673e9i	0.200784	+	0.347768i	−0.747997	+	0.663702i	$0.768984\pi$
$752$	−1.38498e8	−	3.88019e9i	−0.0118763	−	0.332729i
$753$			9.33714e9i			0.796951i
$754$	−8.56404e8	+	3.31411e9i	−0.0727577	+	0.281557i
$755$	3.73420e9	−	6.46783e9i	0.315779	−	0.546945i
$756$	3.67923e9	+	6.11792e9i	0.309692	+	0.514965i
$757$	5.93191e9	−	1.02744e10i	0.497003	−	0.860834i	−0.502991	−	0.864292i	$-0.667767\pi$
$757$	5.93191e9	−	1.02744e10i	0.497003	−	0.860834i	0.999994	+	0.00345717i	$0.00110045\pi$
$758$	−1.06608e10	+	2.95872e9i	−0.889094	+	0.246752i
$759$	−5.64544e8			−0.0468653
$760$	9.03486e9	−	1.73930e10i	0.746576	−	1.43723i
$761$	−2.02907e9			−0.166898			−0.0834488	−	0.996512i	$-0.526593\pi$
$761$	−2.02907e9			−0.166898			−0.0834488	+	0.996512i	$0.526593\pi$
$762$	−6.58855e9	+	1.82853e9i	−0.539445	+	0.149713i
$763$	4.31186e9	−	7.46836e9i	0.351422	−	0.608680i
$764$	2.62594e9	+	4.36648e9i	0.213038	+	0.354246i
$765$	2.01825e9	−	3.49571e9i	0.162990	−	0.282306i
$766$	−8.47822e8	+	3.28090e9i	−0.0681560	+	0.263750i
$767$		−	5.65655e9i		−	0.452655i
$768$	−5.66787e9	+	4.05130e8i	−0.451498	+	0.0322723i
$769$	5.33505e9	+	9.24058e9i	0.423054	+	0.732752i	0.996237	−	0.0866762i	$-0.0276246\pi$
$769$	5.33505e9	+	9.24058e9i	0.423054	+	0.732752i	−0.573182	+	0.819428i	$0.694291\pi$
$770$	2.71553e9	−	1.05086e10i	0.214357	−	0.829517i
$771$			8.14543e9i			0.640064i
$772$	−9.46308e9	+	1.68832e8i	−0.740239	+	0.0132067i
$773$	6.25169e9	−	3.60942e9i	0.486821	−	0.281066i	−0.236434	−	0.971648i	$-0.575979\pi$
$773$	6.25169e9	−	3.60942e9i	0.486821	−	0.281066i	0.723255	+	0.690581i	$0.242645\pi$
$774$	1.26774e9	+	4.56791e9i	0.0982738	+	0.354098i
$775$	1.26865e10	+	2.19736e10i	0.979003	+	1.69568i
$776$	1.30539e10	−	3.87498e9i	1.00283	−	0.297682i
$777$	3.18833e9	−	5.52236e9i	0.243832	−	0.422329i
$778$	6.32377e9	+	6.21196e9i	0.481446	+	0.472933i
$779$	−3.99197e9	−	1.39061e10i	−0.302557	−	1.05396i
$780$	−2.63527e9	+	4.70162e7i	−0.198835	+	0.00354745i
$781$	7.84466e9	+	4.52911e9i	0.589244	+	0.340200i
$782$	−1.31031e8	−	4.72130e8i	−0.00979831	−	0.0353051i
$783$	−1.01333e10	+	5.85048e9i	−0.754372	+	0.435537i
$784$	2.86593e9	−	5.40007e9i	0.212402	−	0.400215i
$785$	−1.75169e10	−	3.03401e10i	−1.29245	−	2.23858i
$786$	4.50426e9	−	4.58533e9i	0.330860	−	0.336815i
$787$	−2.44114e10			−1.78518			−0.892590	−	0.450869i	$-0.851114\pi$
$787$	−2.44114e10			−1.78518			−0.892590	+	0.450869i	$0.851114\pi$
$788$	−1.95202e8	+	1.17391e8i	−0.0142116	+	0.00854663i
$789$	3.88180e9	−	2.24116e9i	0.281361	−	0.162444i
$790$	1.36233e10	+	1.33824e10i	0.983075	+	0.965692i
$791$	−8.11738e8			−0.0583174
$792$	−1.85184e9	+	7.73319e9i	−0.132454	+	0.553122i
$793$	1.29441e9	+	7.47330e8i	0.0921757	+	0.0532177i
$794$	−4.36652e9	+	1.68975e10i	−0.309573	+	1.19798i
$795$	−1.41530e10	−	8.17122e9i	−0.998994	−	0.576769i
$796$	−1.37763e9	+	2.48758e9i	−0.0968138	+	0.174816i
$797$			5.60562e9i			0.392211i	0.980583	+	0.196105i	$0.0628295\pi$
$797$			5.60562e9i			0.392211i	−0.980583	+	0.196105i	$0.937171\pi$
$798$	−2.51283e9	−	4.09607e9i	−0.175047	−	0.285336i
$799$			1.21519e9i			0.0842812i
$800$	2.24090e10	−	7.08931e9i	1.54742	−	0.489541i
$801$	5.14052e9	+	2.96788e9i	0.353422	+	0.204048i
$802$	−1.38146e10	−	3.56986e9i	−0.945646	−	0.244366i
$803$	−1.62781e10	−	9.39819e9i	−1.10943	−	0.640531i
$804$	−2.95525e9	+	1.77725e9i	−0.200539	+	0.120601i
$805$	−2.56585e9			−0.173359
$806$	−3.40913e9	+	3.47050e9i	−0.229336	+	0.233464i
$807$	−8.98634e9	+	5.18826e9i	−0.601901	+	0.347508i
$808$	−2.23021e9	−	5.34061e8i	−0.148732	−	0.0356165i
$809$	−1.54614e10			−1.02666			−0.513332	−	0.858190i	$-0.671589\pi$
$809$	−1.54614e10			−1.02666			−0.513332	+	0.858190i	$0.671589\pi$
$810$	7.46724e9	+	7.33520e9i	0.493699	+	0.484970i
$811$	−5.74801e9	−	9.95585e9i	−0.378394	−	0.655398i	0.612434	−	0.790521i	$-0.290190\pi$
$811$	−5.74801e9	−	9.95585e9i	−0.378394	−	0.655398i	−0.990829	+	0.135123i	$0.956857\pi$
$812$	−1.05808e10	−	5.85972e9i	−0.693544	−	0.384088i
$813$	5.92262e9	−	3.41942e9i	0.386542	−	0.223170i
$814$	1.54516e10	−	4.28832e9i	1.00413	−	0.278678i
$815$	2.48842e10	+	1.43669e10i	1.61017	+	0.929632i
$816$	1.77732e9	−	6.34389e7i	0.114512	−	0.00408733i
$817$	−1.98781e9	−	6.92456e9i	−0.127526	−	0.444237i
$818$	1.23522e10	−	1.25745e10i	0.789054	−	0.803257i
$819$	1.25386e9	−	2.17176e9i	0.0797548	−	0.138139i
$820$	1.35843e10	−	2.45290e10i	0.860375	−	1.55357i
$821$	−1.25021e10	−	2.16542e10i	−0.788461	−	1.36565i	−0.926909	−	0.375285i	$-0.877545\pi$
$821$	−1.25021e10	−	2.16542e10i	−0.788461	−	1.36565i	0.138448	−	0.990370i	$-0.455789\pi$
$822$	−3.42621e9	+	9.50885e8i	−0.215161	+	0.0597141i
$823$	1.21334e10	−	7.00524e9i	0.758725	−	0.438050i	−0.0701128	−	0.997539i	$-0.522336\pi$
$823$	1.21334e10	−	7.00524e9i	0.758725	−	0.438050i	0.828838	+	0.559489i	$0.189003\pi$
$824$	−1.15156e10	+	1.21489e10i	−0.717034	+	0.756473i
$825$			8.47567e9i			0.525515i
$826$	1.93517e10	+	5.00071e9i	1.19478	+	0.308746i
$827$	−1.10943e10	−	1.92158e10i	−0.682070	−	1.18138i	−0.974348	−	0.225046i	$-0.927747\pi$
$827$	−1.10943e10	−	1.92158e10i	−0.682070	−	1.18138i	0.292278	−	0.956333i	$-0.405587\pi$
$828$	1.87953e9	−	3.35330e7i	0.115065	−	0.00205289i
$829$			7.36498e9i			0.448984i	0.974476	+	0.224492i	$0.0720722\pi$
$829$			7.36498e9i			0.448984i	−0.974476	+	0.224492i	$0.927928\pi$
$830$	−2.88830e10	−	7.46370e9i	−1.75335	−	0.453086i
$831$	−5.68934e9	+	9.85423e9i	−0.343921	+	0.595688i
$832$	2.45875e9	+	3.77657e9i	0.148007	+	0.227335i
$833$	−9.56691e8	+	1.65704e9i	−0.0573475	+	0.0993287i
$834$	3.10621e9	+	1.11922e10i	0.185417	+	0.668091i
$835$	2.35125e10			1.39765
$836$	2.71036e9	−	1.17765e10i	0.160437	−	0.697100i
$837$	−1.66298e10			−0.980272
$838$	4.02868e9	+	1.45161e10i	0.236488	+	0.852108i
$839$	−1.35098e10	+	2.33997e10i	−0.789737	+	1.36786i	0.136391	+	0.990655i	$0.456450\pi$
$839$	−1.35098e10	+	2.33997e10i	−0.789737	+	1.36786i	−0.926128	+	0.377209i	$0.876884\pi$
$840$	2.16888e9	−	9.05714e9i	0.126258	−	0.527246i
$841$	1.28704e9	−	2.22922e9i	0.0746118	−	0.129231i
$842$	4.73634e9	+	1.22393e9i	0.273433	+	0.0706583i
$843$		−	4.11477e8i		−	0.0236564i
$844$	4.54218e8	+	2.54591e10i	0.0260056	+	1.45762i
$845$	−1.31575e10	−	2.27894e10i	−0.750195	−	1.29938i
$846$	−4.51391e9	−	1.16645e9i	−0.256305	−	0.0662321i
$847$			6.38629e9i			0.361124i
$848$	9.96712e8	+	2.79241e10i	0.0561286	+	1.57251i
$849$	−3.05124e9	+	1.76163e9i	−0.171119	+	0.0987958i
$850$	−7.08823e9	+	1.96721e9i	−0.395887	+	0.109871i
$851$	−1.89543e9	−	3.28299e9i	−0.105428	−	0.182606i
$852$	6.79947e9	+	3.76558e9i	0.376648	+	0.208590i
$853$	−7.81426e8	+	1.35347e9i	−0.0431088	+	0.0746667i	−0.886775	−	0.462202i	$-0.847060\pi$
$853$	−7.81426e8	+	1.35347e9i	−0.0431088	+	0.0746667i	0.843666	+	0.536869i	$0.180393\pi$
$854$	−3.70104e9	+	3.76766e9i	−0.203339	+	0.206999i
$855$	−1.69342e10	−	1.63435e10i	−0.926583	−	0.894260i
$856$	−7.65294e9	+	8.07388e9i	−0.417033	+	0.439971i
$857$	2.45924e9	+	1.41984e9i	0.133465	+	0.0770562i	0.565246	−	0.824922i	$-0.308781\pi$
$857$	2.45924e9	+	1.41984e9i	0.133465	+	0.0770562i	−0.431781	+	0.901979i	$0.642115\pi$
$858$	−1.56588e9	+	4.34583e8i	−0.0846357	+	0.0234891i
$859$	−2.72682e10	+	1.57433e10i	−1.46784	+	0.847460i	−0.999352	−	0.0360075i	$-0.988536\pi$
$859$	−2.72682e10	+	1.57433e10i	−1.46784	+	0.847460i	−0.468492	+	0.883468i	$0.655203\pi$
$860$	6.76431e9	−	1.22143e10i	0.362643	−	0.654821i
$861$	−3.43734e9	−	5.95364e9i	−0.183532	−	0.317886i
$862$	1.95801e9	+	1.92339e9i	0.104121	+	0.102280i
$863$	1.87656e10			0.993860			0.496930	−	0.867791i	$-0.334460\pi$
$863$	1.87656e10			0.993860			0.496930	+	0.867791i	$0.334460\pi$
$864$	−3.31966e9	+	1.50427e10i	−0.175104	+	0.793464i
$865$	−2.00036e10	+	1.15491e10i	−1.05088	+	0.606725i
$866$	−1.54119e10	+	1.56893e10i	−0.806388	+	0.820903i
$867$	8.12957e9			0.423644
$868$	−8.85912e9	−	1.47312e10i	−0.459803	−	0.764572i
$869$	1.01968e10	+	5.88714e9i	0.527103	+	0.304323i
$870$	1.47790e10	+	3.81907e9i	0.760900	+	0.196625i
$871$	2.36846e9	+	1.36743e9i	0.121452	+	0.0701201i
$872$	1.78389e10	−	5.29537e9i	0.911090	−	0.270451i
$873$		−	1.63508e10i		−	0.831744i
$874$	−2.85576e9	+	7.61803e7i	−0.144688	+	0.00385969i
$875$			1.47870e10i			0.746195i
$876$	−1.41093e10	−	7.81380e9i	−0.709155	−	0.392734i
$877$	−6.34443e9	−	3.66296e9i	−0.317610	−	0.183372i	0.332717	−	0.943027i	$-0.392035\pi$
$877$	−6.34443e9	−	3.66296e9i	−0.317610	−	0.183372i	−0.650327	+	0.759655i	$0.725368\pi$
$878$	9.11225e9	−	3.52625e10i	0.454355	−	1.75826i
$879$	−7.80042e9	−	4.50357e9i	−0.387397	−	0.223664i
$880$	1.98519e10	−	1.24262e10i	0.982004	−	0.614679i
$881$	2.19094e10			1.07948			0.539741	−	0.841831i	$-0.318522\pi$
$881$	2.19094e10			1.07948			0.539741	+	0.841831i	$0.318522\pi$
$882$	−5.23686e9	−	5.14426e9i	−0.256999	−	0.252455i
$883$	6.86252e9	−	3.96208e9i	0.335445	−	0.193669i	−0.322811	−	0.946463i	$-0.604628\pi$
$883$	6.86252e9	−	3.96208e9i	0.335445	−	0.193669i	0.658256	+	0.752794i	$0.271295\pi$
$884$	−7.26885e8	−	1.20868e9i	−0.0353902	−	0.0588477i
$885$	−2.52249e10			−1.22329
$886$	−1.97367e10	+	2.00920e10i	−0.953360	+	0.970520i
$887$	−5.96713e9	−	1.03354e10i	−0.287100	−	0.497272i	0.686016	−	0.727586i	$-0.259358\pi$
$887$	−5.96713e9	−	1.03354e10i	−0.287100	−	0.497272i	−0.973116	+	0.230315i	$0.926024\pi$
$888$	1.31907e10	−	3.91558e9i	0.632154	−	0.187651i
$889$	−1.65937e10	+	9.58040e9i	−0.792114	+	0.457327i
$890$	−4.67522e9	−	1.68457e10i	−0.222299	−	0.800983i
$891$	5.58912e9	+	3.22688e9i	0.264711	+	0.152831i
$892$	−3.21537e8	−	1.80222e10i	−0.0151689	−	0.850220i
$893$	6.87517e9	+	1.71200e9i	0.323075	+	0.0804498i
$894$	4.29316e9	+	4.21725e9i	0.200954	+	0.197400i
$895$	−3.26430e10	+	5.65393e10i	−1.52198	+	2.63615i
$896$	−1.50938e10	+	5.07298e9i	−0.701002	+	0.235605i
$897$	1.92085e8	+	3.32701e8i	0.00888628	+	0.0153915i
$898$	−8.81368e9	−	3.17573e10i	−0.406153	−	1.46344i
$899$	2.43998e10	−	1.40872e10i	1.12002	−	0.646645i
$900$	−5.03441e8	−	2.82180e10i	−0.0230197	−	1.29026i
$901$		−	8.74522e9i		−	0.398322i
$902$	4.32534e9	−	1.67382e10i	0.196245	−	0.759426i
$903$	−1.71163e9	−	2.96463e9i	−0.0773575	−	0.133987i
$904$	−1.27124e9	−	1.20497e9i	−0.0572321	−	0.0542483i
$905$		−	4.04942e10i		−	1.81603i
$906$	9.88553e8	−	3.82550e9i	0.0441623	−	0.170899i
$907$	−8.13884e8	+	1.40969e9i	−0.0362190	+	0.0627332i	−0.883567	−	0.468305i	$-0.844865\pi$
$907$	−8.13884e8	+	1.40969e9i	−0.0362190	+	0.0627332i	0.847348	+	0.531039i	$0.178198\pi$
$908$	−2.11853e10	+	1.27406e10i	−0.939150	+	0.564792i
$909$	−1.37684e9	+	2.38476e9i	−0.0608009	+	0.105310i
$910$	−7.11693e9	+	1.97518e9i	−0.313074	+	0.0868883i
$911$	−1.38133e10			−0.605315			−0.302658	−	0.953099i	$-0.597874\pi$
$911$	−1.38133e10			−0.605315			−0.302658	+	0.953099i	$0.597874\pi$
$912$	2.14503e9	−	1.01449e10i	0.0936380	−	0.442859i
$913$	−1.83931e10			−0.799849
$914$	2.77501e10	−	7.70155e9i	1.20213	−	0.333631i
$915$	3.33266e9	−	5.77233e9i	0.143819	−	0.249102i
$916$	1.42392e10	−	8.56327e9i	0.612142	−	0.368134i
$917$	9.00591e9	−	1.55987e10i	0.385687	−	0.668029i
$918$	1.20626e9	−	4.66798e9i	0.0514626	−	0.199150i
$919$		−	3.32200e9i		−	0.141187i	−0.997505	−	0.0705936i	$-0.977511\pi$
$919$		−	3.32200e9i		−	0.141187i	0.997505	−	0.0705936i	$-0.0224893\pi$
$920$	−4.01832e9	−	3.80882e9i	−0.170132	−	0.161263i
$921$	5.92103e9	+	1.02555e10i	0.249740	+	0.432563i
$922$	1.71415e9	−	6.63342e9i	0.0720264	−	0.278727i
$923$		−	6.16409e9i		−	0.258026i
$924$	−1.02431e8	−	5.74126e9i	−0.00427147	−	0.239417i
$925$	−4.92885e10	+	2.84567e10i	−2.04762	+	1.18219i
$926$	−7.61536e9	−	2.74395e10i	−0.315175	−	1.13563i
$927$	1.00500e10	+	1.74072e10i	0.414371	+	0.717711i
$928$	−7.87207e9	−	2.48833e10i	−0.323348	−	1.02209i
$929$	1.83701e10	−	3.18179e10i	0.751720	−	1.30202i	−0.195269	−	0.980750i	$-0.562558\pi$
$929$	1.83701e10	−	3.18179e10i	0.751720	−	1.30202i	0.946989	−	0.321267i	$-0.104109\pi$
$930$	1.54764e10	+	1.52028e10i	0.630929	+	0.619773i
$931$	8.02718e9	+	7.74715e9i	0.326016	+	0.314643i
$932$	6.69909e8	+	3.75486e10i	0.0271057	+	1.51928i
$933$	1.91232e10	+	1.10408e10i	0.770857	+	0.445055i
$934$	5.29813e8	+	1.90902e9i	0.0212769	+	0.0766647i
$935$	−6.34801e9	+	3.66502e9i	−0.253978	+	0.146635i
$936$	5.18746e9	−	1.53986e9i	0.206771	−	0.0613786i
$937$	2.01660e10	+	3.49285e10i	0.800813	+	1.38705i	0.919082	+	0.394067i	$0.128932\pi$
$937$	2.01660e10	+	3.49285e10i	0.800813	+	1.38705i	−0.118269	+	0.992982i	$0.537735\pi$
$938$	−6.77200e9	+	6.89390e9i	−0.267921	+	0.272744i
$939$	−8.26010e9			−0.325578
$940$	7.07672e9	+	1.17674e10i	0.277898	+	0.462095i
$941$	−1.41972e10	+	8.19675e9i	−0.555442	+	0.320685i	−0.751314	−	0.659945i	$-0.770580\pi$
$941$	−1.41972e10	+	8.19675e9i	−0.555442	+	0.320685i	0.195872	+	0.980629i	$0.437246\pi$
$942$	−1.32223e10	−	1.29885e10i	−0.515382	−	0.506269i
$943$	−4.08693e9			−0.158711
$944$	2.28831e10	+	3.65578e10i	0.885345	+	1.41442i
$945$	−2.18652e10	−	1.26239e10i	−0.842835	−	0.486611i
$946$	2.15381e9	−	8.33481e9i	0.0827159	−	0.320093i
$947$	8.30514e9	+	4.79497e9i	0.317777	+	0.183468i	0.650401	−	0.759591i	$-0.274601\pi$
$947$	8.30514e9	+	4.79497e9i	0.317777	+	0.183468i	−0.332625	+	0.943059i	$0.607934\pi$
$948$	8.83824e9	+	4.89466e9i	0.336928	+	0.186592i
$949$			1.27909e10i			0.485812i
$950$	1.14372e9	+	4.28744e10i	0.0432799	+	1.62243i
$951$			6.31362e9i			0.238038i
$952$	4.77766e9	−	1.41822e9i	0.179467	−	0.0532737i
$953$	−6.01684e9	−	3.47383e9i	−0.225187	−	0.130012i	0.383163	−	0.923681i	$-0.374835\pi$
$953$	−6.01684e9	−	3.47383e9i	−0.225187	−	0.130012i	−0.608350	+	0.793669i	$0.708168\pi$
$954$	3.24847e10	+	8.39443e9i	1.21132	+	0.313020i
$955$	−1.56056e10	−	9.00993e9i	−0.579789	−	0.334741i
$956$	1.00144e10	+	1.66522e10i	0.370699	+	0.616408i
$957$	9.41150e9			0.347110
$958$	−3.32487e10	+	3.38472e10i	−1.22179	+	1.24378i
$959$	−8.62916e9	+	4.98205e9i	−0.315939	+	0.182408i
$960$	1.68413e10	−	1.09646e10i	0.614365	−	0.399985i
$961$	1.25297e10			0.455418
$962$	−7.78461e9	−	7.64696e9i	−0.281919	−	0.276934i
$963$	6.67900e9	+	1.15684e10i	0.241001	+	0.417427i
$964$	−5.50032e9	+	9.93187e9i	−0.197751	+	0.357077i
$965$	2.89879e10	−	1.67362e10i	1.03842	−	0.599530i
$966$	−1.30802e9	+	3.63019e8i	−0.0466870	+	0.0129571i
$967$	1.06304e10	+	6.13747e9i	0.378057	+	0.218271i	0.676973	−	0.736008i	$-0.263292\pi$
$967$	1.06304e10	+	6.13747e9i	0.378057	+	0.218271i	−0.298915	+	0.954280i	$0.596625\pi$
$968$	−9.47999e9	+	1.00014e10i	−0.335926	+	0.354403i
$969$	−7.84183e8	+	3.14917e9i	−0.0276875	+	0.111189i
$970$	−3.37474e10	+	3.43549e10i	−1.18724	+	1.20861i
$971$	−5.19010e9	+	8.98951e9i	−0.181932	+	0.315115i	−0.942538	−	0.334098i	$-0.891568\pi$
$971$	−5.19010e9	+	8.98951e9i	−0.181932	+	0.315115i	0.760607	+	0.649213i	$0.224902\pi$
$972$	2.51960e10	+	1.39536e10i	0.880034	+	0.487367i
$973$	1.62746e10	+	2.81885e10i	0.566390	+	0.981017i
$974$	−1.40315e10	+	3.89419e9i	−0.486572	+	0.135039i
$975$	4.99494e9	−	2.88383e9i	0.172589	−	0.0996446i
$976$	−1.13889e10	+	4.06512e8i	−0.392111	+	0.0139958i
$977$		−	2.79220e10i		−	0.957888i	−0.877845	−	0.478944i	$-0.841020\pi$
$977$		−	2.79220e10i		−	0.957888i	0.877845	−	0.478944i	$-0.158980\pi$
$978$	1.47181e10	+	3.80334e9i	0.503115	+	0.130011i
$979$	−5.38950e9	−	9.33489e9i	−0.183573	−	0.317958i
$980$	3.85678e8	+	2.16173e10i	0.0130898	+	0.733687i
$981$		−	2.23443e10i		−	0.755658i
$982$	5.03366e10	+	1.30076e10i	1.69626	+	0.438334i
$983$	−4.82786e8	+	8.36209e8i	−0.0162113	+	0.0280787i	−0.874017	−	0.485895i	$-0.838494\pi$
$983$	−4.82786e8	+	8.36209e8i	−0.0162113	+	0.0280787i	0.857806	+	0.513974i	$0.171827\pi$
$984$	3.45463e9	−	1.44263e10i	0.115589	−	0.482696i
$985$	4.02785e8	−	6.97644e8i	0.0134291	−	0.0232599i
$986$	2.18442e9	+	7.87086e9i	0.0725716	+	0.261489i
$987$	3.36666e9			0.111452
$988$	−7.86241e9	+	2.40965e9i	−0.259362	+	0.0794886i
$989$	−2.03509e9			−0.0668955
$990$	−7.52061e9	−	2.70981e10i	−0.246337	−	0.887597i
$991$	1.92141e10	−	3.32798e10i	0.627136	−	1.08623i	−0.360988	−	0.932571i	$-0.617560\pi$
$991$	1.92141e10	−	3.32798e10i	0.627136	−	1.08623i	0.988124	−	0.153661i	$-0.0491063\pi$
$992$	7.99332e9	−	3.62209e10i	0.259978	−	1.17806i
$993$	2.24877e9	−	3.89499e9i	0.0728826	−	0.126236i
$994$	2.10881e10	+	5.44941e9i	0.681059	+	0.175994i
$995$		−	1.00565e10i		−	0.323644i
$996$	−1.57800e10	+	2.81532e8i	−0.506056	+	0.00902861i
$997$	−2.76123e10	−	4.78259e10i	−0.882409	−	1.52838i	−0.848655	−	0.528946i	$-0.822587\pi$
$997$	−2.76123e10	−	4.78259e10i	−0.882409	−	1.52838i	−0.0337532	−	0.999430i	$-0.510746\pi$
$998$	4.39903e10	+	1.13676e10i	1.40088	+	0.362003i
$999$		−	3.73019e10i		−	1.18373i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.8.f.a.27.7	✓	136
4.3	odd	2	inner	76.8.f.a.27.29	yes	136
19.12	odd	6	inner	76.8.f.a.31.29	yes	136
76.31	even	6	inner	76.8.f.a.31.7	yes	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.8.f.a.27.7	✓	136	1.1	even	1	trivial
76.8.f.a.27.29	yes	136	4.3	odd	2	inner
76.8.f.a.31.7	yes	136	76.31	even	6	inner
76.8.f.a.31.29	yes	136	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	76.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10.9017 + 3.02556i) q^{2} +(10.5842 - 18.3323i) q^{3} +(109.692 - 65.9672i) q^{4} +(-226.342 + 392.035i) q^{5} +(-59.9194 + 231.876i) q^{6} +671.124i q^{7} +(-996.236 + 1051.03i) q^{8} +(869.451 + 1505.93i) q^{9} +O(q^{10})\)	\(q+(-10.9017 + 3.02556i) q^{2} +(10.5842 - 18.3323i) q^{3} +(109.692 - 65.9672i) q^{4} +(-226.342 + 392.035i) q^{5} +(-59.9194 + 231.876i) q^{6} +671.124i q^{7} +(-996.236 + 1051.03i) q^{8} +(869.451 + 1505.93i) q^{9} +(1281.37 - 4958.64i) q^{10} -3157.75i q^{11} +(-48.3337 - 2709.12i) q^{12} +(-1860.94 + 1074.42i) q^{13} +(-2030.53 - 7316.36i) q^{14} +(4791.28 + 8298.74i) q^{15} +(7680.65 - 14472.1i) q^{16} +(-2563.92 + 4440.84i) q^{17} +(-14034.7 - 13786.6i) q^{18} +(21512.8 + 20762.3i) q^{19} +(1033.61 + 57934.3i) q^{20} +(12303.3 + 7103.29i) q^{21} +(9553.95 + 34424.6i) q^{22} +(7314.16 - 4222.83i) q^{23} +(8723.51 + 29387.6i) q^{24} +(-63398.7 - 109810. i) q^{25} +(17036.7 - 17343.3i) q^{26} +83104.8 q^{27} +(44272.2 + 73616.9i) q^{28} +(-121934. + 70398.8i) q^{29} +(-77341.2 - 75973.6i) q^{30} -200106. q^{31} +(-39945.4 + 181009. i) q^{32} +(-57888.8 - 33422.1i) q^{33} +(14514.9 - 56169.8i) q^{34} +(-263104. - 151903. i) q^{35} +(194714. + 107834. i) q^{36} -448853. i q^{37} +(-297342. - 161255. i) q^{38} +45487.2i q^{39} +(-186552. - 628452. i) q^{40} +(-419077. - 241954. i) q^{41} +(-155617. - 40213.3i) q^{42} +(-208680. - 120481. i) q^{43} +(-208308. - 346379. i) q^{44} -787172. q^{45} +(-66960.0 + 68165.3i) q^{46} +(205230. - 118489. i) q^{47} +(-184015. - 293980. i) q^{48} +373136. q^{49} +(1.02339e6 + 1.00529e6i) q^{50} +(54274.0 + 94005.3i) q^{51} +(-133254. + 240616. i) q^{52} +(-1.47695e6 + 852719. i) q^{53} +(-905979. + 251439. i) q^{54} +(1.23795e6 + 714730. i) q^{55} +(-705372. - 668598. i) q^{56} +(608316. - 174627. i) q^{57} +(1.11629e6 - 1.13638e6i) q^{58} +(-1.31619e6 + 2.27971e6i) q^{59} +(1.07301e6 + 594238. i) q^{60} +(-347784. - 602379. i) q^{61} +(2.18148e6 - 605432. i) q^{62} +(-1.01067e6 + 583509. i) q^{63} +(-112181. - 2.09415e6i) q^{64} -972742. i q^{65} +(732204. + 189210. i) q^{66} +(-636360. - 1.10221e6i) q^{67} +(11708.4 + 656260. i) q^{68} -178781. i q^{69} +(3.32786e6 + 859959. i) q^{70} +(-1.43429e6 + 2.48426e6i) q^{71} +(-2.44896e6 - 586444. i) q^{72} +(2.97623e6 - 5.15499e6i) q^{73} +(1.35803e6 + 4.89324e6i) q^{74} -2.68409e6 q^{75} +(3.72941e6 + 858320. i) q^{76} +2.11924e6 q^{77} +(-137624. - 495886. i) q^{78} +(-1.86435e6 + 3.22915e6i) q^{79} +(3.93514e6 + 6.28674e6i) q^{80} +(-1.02189e6 + 1.76997e6i) q^{81} +(5.30067e6 + 1.36976e6i) q^{82} -5.82477e6i q^{83} +(1.81815e6 - 32437.9i) q^{84} +(-1.16065e6 - 2.01030e6i) q^{85} +(2.63948e6 + 682073. i) q^{86} +2.98045e6i q^{87} +(3.31889e6 + 3.14586e6i) q^{88} +(2.95619e6 - 1.70676e6i) q^{89} +(8.58148e6 - 2.38164e6i) q^{90} +(-721067. - 1.24892e6i) q^{91} +(523736. - 945706. i) q^{92} +(-2.11795e6 + 3.66840e6i) q^{93} +(-1.87884e6 + 1.91266e6i) q^{94} +(-1.30088e7 + 3.73439e6i) q^{95} +(2.89552e6 + 2.64812e6i) q^{96} +(-8.14320e6 - 4.70148e6i) q^{97} +(-4.06779e6 + 1.12894e6i) q^{98} +(4.75535e6 - 2.74550e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9}+O(q^{10}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9	\( 136 q - 3 q^{2} - 27 q^{4} - 2 q^{5} + 309 q^{6} - 45540 q^{9} - 19464 q^{10} - 10602 q^{13} + 13602 q^{14} + 6525 q^{16} - 23974 q^{17} - 91316 q^{20} + 54264 q^{21} + 381 q^{22} - 51631 q^{24} - 937502 q^{25} + 172188 q^{26} - 165428 q^{28} - 6 q^{29} - 454352 q^{30} + 573507 q^{32} - 182106 q^{33} - 629706 q^{34} - 277130 q^{36} - 759906 q^{38} - 627504 q^{40} - 1873020 q^{41} + 332080 q^{42} - 358069 q^{44} + 321240 q^{45} - 7221687 q^{48} - 15750664 q^{49} + 2848050 q^{52} - 1027650 q^{53} + 4352085 q^{54} - 137426 q^{57} + 10387724 q^{58} + 1607094 q^{60} + 5318582 q^{61} + 3394376 q^{62} - 1319538 q^{64} + 2439607 q^{66} - 87756 q^{68} - 17825238 q^{70} + 26155014 q^{72} + 299212 q^{73} + 1895842 q^{74} + 29672379 q^{76} + 907280 q^{77} + 7456734 q^{78} + 5489562 q^{80} - 11065208 q^{81} + 1288975 q^{82} + 6118214 q^{85} + 16831518 q^{86} - 17728542 q^{89} + 52167894 q^{90} + 10184840 q^{92} - 3299132 q^{93} - 68841730 q^{96} - 9435888 q^{97} - 35100021 q^{98}+O(q^{100}) \) 136 * q - 3 * q^2 - 27 * q^4 - 2 * q^5 + 309 * q^6 - 45540 * q^9 - 19464 * q^10 - 10602 * q^13 + 13602 * q^14 + 6525 * q^16 - 23974 * q^17 - 91316 * q^20 + 54264 * q^21 + 381 * q^22 - 51631 * q^24 - 937502 * q^25 + 172188 * q^26 - 165428 * q^28 - 6 * q^29 - 454352 * q^30 + 573507 * q^32 - 182106 * q^33 - 629706 * q^34 - 277130 * q^36 - 759906 * q^38 - 627504 * q^40 - 1873020 * q^41 + 332080 * q^42 - 358069 * q^44 + 321240 * q^45 - 7221687 * q^48 - 15750664 * q^49 + 2848050 * q^52 - 1027650 * q^53 + 4352085 * q^54 - 137426 * q^57 + 10387724 * q^58 + 1607094 * q^60 + 5318582 * q^61 + 3394376 * q^62 - 1319538 * q^64 + 2439607 * q^66 - 87756 * q^68 - 17825238 * q^70 + 26155014 * q^72 + 299212 * q^73 + 1895842 * q^74 + 29672379 * q^76 + 907280 * q^77 + 7456734 * q^78 + 5489562 * q^80 - 11065208 * q^81 + 1288975 * q^82 + 6118214 * q^85 + 16831518 * q^86 - 17728542 * q^89 + 52167894 * q^90 + 10184840 * q^92 - 3299132 * q^93 - 68841730 * q^96 - 9435888 * q^97 - 35100021 * q^98

Introduction

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