LMFDB - Embedded newform 16.28.e.a.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,28,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$73.8968919741$
Analytic rank:	$0$
Dimension:	$106$
Relative dimension:	$53$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	16.5
Dual form			16.28.e.a.13.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10534.4 - 4821.21i) q^{2} +(923601. - 923601. i) q^{3} +(8.77296e7 + 1.01577e8i) q^{4} +(-5.91123e8 - 5.91123e8i) q^{5} +(-1.41825e10 + 5.27671e9i) q^{6} -1.68267e11i q^{7} +(-4.34455e11 - 1.49302e12i) q^{8} +5.91952e12i q^{9} +O(q^{10})$	\(q+(-10534.4 - 4821.21i) q^{2} +(923601. - 923601. i) q^{3} +(8.77296e7 + 1.01577e8i) q^{4} +(-5.91123e8 - 5.91123e8i) q^{5} +(-1.41825e10 + 5.27671e9i) q^{6} -1.68267e11i q^{7} +(-4.34455e11 - 1.49302e12i) q^{8} +5.91952e12i q^{9} +(3.37720e12 + 9.07706e12i) q^{10} +(2.74936e13 + 2.74936e13i) q^{11} +(1.74844e14 + 1.27896e13i) q^{12} +(1.38682e15 - 1.38682e15i) q^{13} +(-8.11252e14 + 1.77260e15i) q^{14} -1.09192e15 q^{15} +(-2.62143e15 + 1.78226e16i) q^{16} -3.15275e16 q^{17} +(2.85392e16 - 6.23586e16i) q^{18} +(-1.04132e17 + 1.04132e17i) q^{19} +(8.18560e15 - 1.11904e17i) q^{20} +(-1.55412e17 - 1.55412e17i) q^{21} +(-1.57076e17 - 4.22181e17i) q^{22} -3.43797e17i q^{23} +(-1.78022e18 - 9.77690e17i) q^{24} -6.75173e18i q^{25} +(-2.12955e19 + 7.92320e18i) q^{26} +(1.25103e19 + 1.25103e19i) q^{27} +(1.70921e19 - 1.47620e19i) q^{28} +(1.02772e19 - 1.02772e19i) q^{29} +(1.15028e19 + 5.26440e18i) q^{30} +1.13930e20 q^{31} +(1.13542e20 - 1.75112e20i) q^{32} +5.07862e19 q^{33} +(3.32124e20 + 1.52001e20i) q^{34} +(-9.94667e19 + 9.94667e19i) q^{35} +(-6.01288e20 + 5.19317e20i) q^{36} +(6.08847e20 + 6.08847e20i) q^{37} +(1.59901e21 - 5.94926e20i) q^{38} -2.56175e21i q^{39} +(-6.25741e20 + 1.13937e21i) q^{40} +1.10002e22i q^{41} +(8.87898e20 + 2.38644e21i) q^{42} +(-2.43287e21 - 2.43287e21i) q^{43} +(-3.80718e20 + 5.20472e21i) q^{44} +(3.49917e21 - 3.49917e21i) q^{45} +(-1.65752e21 + 3.62169e21i) q^{46} +7.19867e22 q^{47} +(1.40399e22 + 1.88822e22i) q^{48} +3.73985e22 q^{49} +(-3.25515e22 + 7.11254e22i) q^{50} +(-2.91189e22 + 2.91189e22i) q^{51} +(2.62535e23 + 1.92041e22i) q^{52} +(-9.49959e22 - 9.49959e22i) q^{53} +(-7.14737e22 - 1.92103e23i) q^{54} -3.25042e22i q^{55} +(-2.51226e23 + 7.31045e22i) q^{56} +1.92353e23i q^{57} +(-1.57813e23 + 5.87159e22i) q^{58} +(-8.82273e23 - 8.82273e23i) q^{59} +(-9.57941e22 - 1.10915e23i) q^{60} +(1.05981e24 - 1.05981e24i) q^{61} +(-1.20018e24 - 5.49279e23i) q^{62} +9.96061e23 q^{63} +(-2.04035e24 + 1.29730e24i) q^{64} -1.63957e24 q^{65} +(-5.35002e23 - 2.44851e23i) q^{66} +(-1.24651e24 + 1.24651e24i) q^{67} +(-2.76590e24 - 3.20248e24i) q^{68} +(-3.17531e23 - 3.17531e23i) q^{69} +(1.52737e24 - 5.68273e23i) q^{70} -2.48171e24i q^{71} +(8.83794e24 - 2.57176e24i) q^{72} -1.30905e25i q^{73} +(-3.47846e24 - 9.34922e24i) q^{74} +(-6.23590e24 - 6.23590e24i) q^{75} +(-1.97129e25 - 1.44197e24i) q^{76} +(4.62627e24 - 4.62627e24i) q^{77} +(-1.23507e25 + 2.69865e25i) q^{78} -2.27814e25 q^{79} +(1.20850e25 - 8.98579e24i) q^{80} -2.20308e25 q^{81} +(5.30345e25 - 1.15881e26i) q^{82} +(5.57430e24 - 5.57430e24i) q^{83} +(2.15207e24 - 2.94205e25i) q^{84} +(1.86367e25 + 1.86367e25i) q^{85} +(1.38994e25 + 3.73582e25i) q^{86} -1.89842e25i q^{87} +(2.91037e25 - 5.29931e25i) q^{88} -4.83355e25i q^{89} +(-5.37318e25 + 1.99914e25i) q^{90} +(-2.33357e26 - 2.33357e26i) q^{91} +(3.49219e25 - 3.01612e25i) q^{92} +(1.05226e26 - 1.05226e26i) q^{93} +(-7.58337e26 - 3.47063e26i) q^{94} +1.23110e26 q^{95} +(-5.68667e25 - 2.66602e26i) q^{96} -8.11154e26 q^{97} +(-3.93971e26 - 1.80306e26i) q^{98} +(-1.62749e26 + 1.62749e26i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) $ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8	$ 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) $ 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−10534.4	−	4821.21i	−0.909295	−	0.416151i
$2$	−10534.4	−	4821.21i	−0.909295	−	0.416151i
$3$	923601.	−	923601.i	0.334463	−	0.334463i	−0.519816	−	0.854278i	$-0.673999\pi$
$3$	923601.	−	923601.i	0.334463	−	0.334463i	0.854278	+	0.519816i	$0.173999\pi$
$4$	8.77296e7	+	1.01577e8i	0.653637	+	0.756809i
$5$	−5.91123e8	−	5.91123e8i	−0.216562	−	0.216562i	0.590486	−	0.807048i	$-0.298936\pi$
$5$	−5.91123e8	−	5.91123e8i	−0.216562	−	0.216562i	−0.807048	+	0.590486i	$0.798936\pi$
$6$	−1.41825e10	+	5.27671e9i	−0.443312	+	0.164938i
$7$		−	1.68267e11i		−	0.656411i	−0.944606	−	0.328206i	$-0.893556\pi$
$7$		−	1.68267e11i		−	0.656411i	0.944606	−	0.328206i	$-0.106444\pi$
$8$	−4.34455e11	−	1.49302e12i	−0.279402	−	0.960174i
$9$			5.91952e12i			0.776270i
$10$	3.37720e12	+	9.07706e12i	0.106797	+	0.287042i
$11$	2.74936e13	+	2.74936e13i	0.240121	+	0.240121i	0.816900	−	0.576779i	$-0.195691\pi$
$11$	2.74936e13	+	2.74936e13i	0.240121	+	0.240121i	−0.576779	+	0.816900i	$0.695691\pi$
$12$	1.74844e14	+	1.27896e13i	0.471741	+	0.0345072i
$13$	1.38682e15	−	1.38682e15i	1.26995	−	1.26995i	0.323836	−	0.946113i	$-0.395027\pi$
$13$	1.38682e15	−	1.38682e15i	1.26995	−	1.26995i	0.946113	−	0.323836i	$-0.104973\pi$
$14$	−8.11252e14	+	1.77260e15i	−0.273166	+	0.596872i
$15$	−1.09192e15			−0.144864
$16$	−2.62143e15	+	1.78226e16i	−0.145519	+	0.989356i
$17$	−3.15275e16			−0.772022			−0.386011	−	0.922494i	$-0.626147\pi$
$17$	−3.15275e16			−0.772022			−0.386011	+	0.922494i	$0.626147\pi$
$18$	2.85392e16	−	6.23586e16i	0.323045	−	0.705858i
$19$	−1.04132e17	+	1.04132e17i	−0.568081	+	0.568081i	−0.931590	−	0.363510i	$-0.881578\pi$
$19$	−1.04132e17	+	1.04132e17i	−0.568081	+	0.568081i	0.363510	+	0.931590i	$0.381578\pi$
$20$	8.18560e15	−	1.11904e17i	0.0223432	−	0.305449i
$21$	−1.55412e17	−	1.55412e17i	−0.219545	−	0.219545i
$22$	−1.57076e17	−	4.22181e17i	−0.118414	−	0.318267i
$23$		−	3.43797e17i		−	0.142225i	−0.997468	−	0.0711125i	$-0.977345\pi$
$23$		−	3.43797e17i		−	0.142225i	0.997468	−	0.0711125i	$-0.0226549\pi$
$24$	−1.78022e18	−	9.77690e17i	−0.414592	−	0.227693i
$25$		−	6.75173e18i		−	0.906201i
$26$	−2.12955e19	+	7.92320e18i	−1.68325	+	0.626268i
$27$	1.25103e19	+	1.25103e19i	0.594096	+	0.594096i
$28$	1.70921e19	−	1.47620e19i	0.496778	−	0.429054i
$29$	1.02772e19	−	1.02772e19i	0.185996	−	0.185996i	−0.607967	−	0.793963i	$-0.708015\pi$
$29$	1.02772e19	−	1.02772e19i	0.185996	−	0.185996i	0.793963	+	0.607967i	$0.208015\pi$
$30$	1.15028e19	+	5.26440e18i	0.131724	+	0.0602853i
$31$	1.13930e20			0.838020			0.419010	−	0.907982i	$-0.362377\pi$
$31$	1.13930e20			0.838020			0.419010	+	0.907982i	$0.362377\pi$
$32$	1.13542e20	−	1.75112e20i	0.544041	−	0.839059i
$33$	5.07862e19			0.160623
$34$	3.32124e20	+	1.52001e20i	0.701996	+	0.321278i
$35$	−9.94667e19	+	9.94667e19i	−0.142154	+	0.142154i
$36$	−6.01288e20	+	5.19317e20i	−0.587487	+	0.507398i
$37$	6.08847e20	+	6.08847e20i	0.410946	+	0.410946i	0.882068	−	0.471122i	$-0.156151\pi$
$37$	6.08847e20	+	6.08847e20i	0.410946	+	0.410946i	−0.471122	+	0.882068i	$0.656151\pi$
$38$	1.59901e21	−	5.94926e20i	0.752961	−	0.280146i
$39$		−	2.56175e21i		−	0.849501i
$40$	−6.25741e20	+	1.13937e21i	−0.147430	+	0.268446i
$41$			1.10002e22i			1.85704i	0.371287	+	0.928518i	$0.378916\pi$
$41$			1.10002e22i			1.85704i	−0.371287	+	0.928518i	$0.621084\pi$
$42$	8.87898e20	+	2.38644e21i	0.108267	+	0.290995i
$43$	−2.43287e21	−	2.43287e21i	−0.215921	−	0.215921i	0.590856	−	0.806777i	$-0.298790\pi$
$43$	−2.43287e21	−	2.43287e21i	−0.215921	−	0.215921i	−0.806777	+	0.590856i	$0.798790\pi$
$44$	−3.80718e20	+	5.20472e21i	−0.0247738	+	0.338677i
$45$	3.49917e21	−	3.49917e21i	0.168111	−	0.168111i
$46$	−1.65752e21	+	3.62169e21i	−0.0591871	+	0.129325i
$47$	7.19867e22			1.92279			0.961393	−	0.275179i	$-0.0887372\pi$
$47$	7.19867e22			1.92279			0.961393	+	0.275179i	$0.0887372\pi$
$48$	1.40399e22	+	1.88822e22i	0.282232	+	0.379573i
$49$	3.73985e22			0.569124
$50$	−3.25515e22	+	7.11254e22i	−0.377117	+	0.824005i
$51$	−2.91189e22	+	2.91189e22i	−0.258212	+	0.258212i
$52$	2.62535e23	+	1.92041e22i	1.79119	+	0.131023i
$53$	−9.49959e22	−	9.49959e22i	−0.501165	−	0.501165i	0.410635	−	0.911800i	$-0.365307\pi$
$53$	−9.49959e22	−	9.49959e22i	−0.501165	−	0.501165i	−0.911800	+	0.410635i	$0.865307\pi$
$54$	−7.14737e22	−	1.92103e23i	−0.292975	−	0.787442i
$55$		−	3.25042e22i		−	0.104002i
$56$	−2.51226e23	+	7.31045e22i	−0.630269	+	0.183403i
$57$			1.92353e23i			0.380004i
$58$	−1.57813e23	+	5.87159e22i	−0.246528	+	0.0917229i
$59$	−8.82273e23	−	8.82273e23i	−1.09421	−	1.09421i	−0.995074	−	0.0991361i	$-0.968392\pi$
$59$	−8.82273e23	−	8.82273e23i	−1.09421	−	1.09421i	−0.0991361	−	0.995074i	$-0.531608\pi$
$60$	−9.57941e22	−	1.10915e23i	−0.0946884	−	0.109634i
$61$	1.05981e24	−	1.05981e24i	0.838064	−	0.838064i	−0.150540	−	0.988604i	$-0.548101\pi$
$61$	1.05981e24	−	1.05981e24i	0.838064	−	0.838064i	0.988604	+	0.150540i	$0.0481013\pi$
$62$	−1.20018e24	−	5.49279e23i	−0.762008	−	0.348743i
$63$	9.96061e23			0.509552
$64$	−2.04035e24	+	1.29730e24i	−0.843869	+	0.536549i
$65$	−1.63957e24			−0.550047
$66$	−5.35002e23	−	2.44851e23i	−0.146054	−	0.0668434i
$67$	−1.24651e24	+	1.24651e24i	−0.277771	+	0.277771i	−0.832219	−	0.554447i	$-0.812930\pi$
$67$	−1.24651e24	+	1.24651e24i	−0.277771	+	0.277771i	0.554447	+	0.832219i	$0.312930\pi$
$68$	−2.76590e24	−	3.20248e24i	−0.504622	−	0.584273i
$69$	−3.17531e23	−	3.17531e23i	−0.0475690	−	0.0475690i
$70$	1.52737e24	−	5.68273e23i	0.188418	−	0.0701025i
$71$		−	2.48171e24i		−	0.252792i	−0.991980	−	0.126396i	$-0.959659\pi$
$71$		−	2.48171e24i		−	0.252792i	0.991980	−	0.126396i	$-0.0403410\pi$
$72$	8.83794e24	−	2.57176e24i	0.745354	−	0.216891i
$73$		−	1.30905e25i		−	0.916428i	−0.888842	−	0.458214i	$-0.848489\pi$
$73$		−	1.30905e25i		−	0.916428i	0.888842	−	0.458214i	$-0.151511\pi$
$74$	−3.47846e24	−	9.34922e24i	−0.202656	−	0.544687i
$75$	−6.23590e24	−	6.23590e24i	−0.303091	−	0.303091i
$76$	−1.97129e25	−	1.44197e24i	−0.801247	−	0.0586101i
$77$	4.62627e24	−	4.62627e24i	0.157618	−	0.157618i
$78$	−1.23507e25	+	2.69865e25i	−0.353521	+	0.772448i
$79$	−2.27814e25			−0.549055			−0.274527	−	0.961579i	$-0.588521\pi$
$79$	−2.27814e25			−0.549055			−0.274527	+	0.961579i	$0.588521\pi$
$80$	1.20850e25	−	8.98579e24i	0.245771	−	0.182743i
$81$	−2.20308e25			−0.378864
$82$	5.30345e25	−	1.15881e26i	0.772808	−	1.68859i
$83$	5.57430e24	−	5.57430e24i	0.0689662	−	0.0689662i	−0.671782	−	0.740749i	$-0.734471\pi$
$83$	5.57430e24	−	5.57430e24i	0.0689662	−	0.0689662i	0.740749	+	0.671782i	$0.234471\pi$
$84$	2.15207e24	−	2.94205e25i	0.0226509	−	0.309656i
$85$	1.86367e25	+	1.86367e25i	0.167191	+	0.167191i
$86$	1.38994e25	+	3.73582e25i	0.106480	+	0.286191i
$87$		−	1.89842e25i		−	0.124417i
$88$	2.91037e25	−	5.29931e25i	0.163468	−	0.297648i
$89$		−	4.83355e25i		−	0.233078i	−0.993186	−	0.116539i	$-0.962820\pi$
$89$		−	4.83355e25i		−	0.233078i	0.993186	−	0.116539i	$-0.0371800\pi$
$90$	−5.37318e25	+	1.99914e25i	−0.222822	+	0.0829029i
$91$	−2.33357e26	−	2.33357e26i	−0.833609	−	0.833609i
$92$	3.49219e25	−	3.01612e25i	0.107637	−	0.0929635i
$93$	1.05226e26	−	1.05226e26i	0.280286	−	0.280286i
$94$	−7.58337e26	−	3.47063e26i	−1.74838	−	0.800169i
$95$	1.23110e26			0.246050
$96$	−5.68667e25	−	2.66602e26i	−0.0986725	−	0.462595i
$97$	−8.11154e26			−1.22373			−0.611864	−	0.790963i	$-0.709580\pi$
$97$	−8.11154e26			−1.22373			−0.611864	+	0.790963i	$0.709580\pi$
$98$	−3.93971e26	−	1.80306e26i	−0.517502	−	0.236842i
$99$	−1.62749e26	+	1.62749e26i	−0.186399	+	0.186399i
$100$	6.85821e26	−	5.92326e26i	0.685821	−	0.592326i
$101$	−3.98804e26	−	3.98804e26i	−0.348675	−	0.348675i	0.510941	−	0.859616i	$-0.329297\pi$
$101$	−3.98804e26	−	3.98804e26i	−0.348675	−	0.348675i	−0.859616	+	0.510941i	$0.829297\pi$
$102$	4.47138e26	−	1.66362e26i	0.342247	−	0.127336i
$103$		−	2.62346e27i		−	1.76024i	−0.474749	−	0.880121i	$-0.657461\pi$
$103$		−	2.62346e27i		−	1.76024i	0.474749	−	0.880121i	$-0.342539\pi$
$104$	−2.67307e27	−	1.46804e27i	−1.57420	−	0.864546i
$105$			1.83735e26i			0.0950904i
$106$	5.42730e26	+	1.45872e27i	0.247147	+	0.664267i
$107$	−9.84805e26	−	9.84805e26i	−0.395066	−	0.395066i	0.481423	−	0.876488i	$-0.340120\pi$
$107$	−9.84805e26	−	9.84805e26i	−0.395066	−	0.395066i	−0.876488	+	0.481423i	$0.840120\pi$
$108$	−1.73236e26	+	2.36828e27i	−0.0612941	+	0.837939i
$109$	−8.40465e25	+	8.40465e25i	−0.0262580	+	0.0262580i	−0.720114	−	0.693856i	$-0.755910\pi$
$109$	−8.40465e25	+	8.40465e25i	−0.0262580	+	0.0262580i	0.693856	+	0.720114i	$0.255910\pi$
$110$	−1.56710e26	+	3.42412e26i	−0.0432807	+	0.0945689i
$111$	1.12466e27			0.274892
$112$	2.99897e27	+	4.41101e26i	0.649424	+	0.0955200i
$113$	3.68683e27			0.708100			0.354050	−	0.935226i	$-0.384804\pi$
$113$	3.68683e27			0.708100			0.354050	+	0.935226i	$0.384804\pi$
$114$	9.27373e26	−	2.02632e27i	0.158139	−	0.345536i
$115$	−2.03226e26	+	2.03226e26i	−0.0308006	+	0.0308006i
$116$	1.94555e27	+	1.42314e26i	0.262337	+	0.0191896i
$117$	8.20934e27	+	8.20934e27i	0.985823	+	0.985823i
$118$	5.04060e27	+	1.35478e28i	0.539604	+	1.45032i
$119$			5.30505e27i			0.506764i
$120$	4.74392e26	+	1.63026e27i	0.0404753	+	0.139095i
$121$		−	1.15982e28i		−	0.884684i
$122$	−1.62741e28	+	6.05493e27i	−1.11081	+	0.413286i
$123$	1.01598e28	+	1.01598e28i	0.621109	+	0.621109i
$124$	9.99502e27	+	1.15727e28i	0.547761	+	0.634221i
$125$	−8.39532e27	+	8.39532e27i	−0.412812	+	0.412812i
$126$	−1.04929e28	−	4.80222e27i	−0.463333	−	0.212051i
$127$	−1.89485e28			−0.752013			−0.376007	−	0.926617i	$-0.622703\pi$
$127$	−1.89485e28			−0.752013			−0.376007	+	0.926617i	$0.622703\pi$
$128$	2.77484e28	−	3.82929e27i	0.990612	−	0.136705i
$129$	−4.49400e27			−0.144435
$130$	1.72719e28	+	7.90471e27i	0.500155	+	0.228902i
$131$	1.57384e28	−	1.57384e28i	0.410959	−	0.410959i	−0.471114	−	0.882073i	$-0.656148\pi$
$131$	1.57384e28	−	1.57384e28i	0.410959	−	0.410959i	0.882073	+	0.471114i	$0.156148\pi$
$132$	4.45545e27	+	5.15872e27i	0.104989	+	0.121561i
$133$	1.75220e28	+	1.75220e28i	0.372895	+	0.372895i
$134$	1.91410e28	−	7.12158e27i	0.368171	−	0.136981i
$135$		−	1.47902e28i		−	0.257318i
$136$	1.36973e28	+	4.70711e28i	0.215704	+	0.741275i
$137$			9.61599e28i			1.37172i	0.727732	+	0.685862i	$0.240574\pi$
$137$			9.61599e28i			1.37172i	−0.727732	+	0.685862i	$0.759426\pi$
$138$	1.81412e27	+	4.87589e27i	0.0234584	+	0.0630501i
$139$	−9.57030e28	−	9.57030e28i	−1.12260	−	1.12260i	−0.991349	−	0.131252i	$-0.958100\pi$
$139$	−9.57030e28	−	9.57030e28i	−1.12260	−	1.12260i	−0.131252	−	0.991349i	$-0.541900\pi$
$140$	−1.88297e28	−	1.37737e27i	−0.200500	−	0.0146663i
$141$	6.64870e28	−	6.64870e28i	0.643100	−	0.643100i
$142$	−1.19648e28	+	2.61433e28i	−0.105200	+	0.229863i
$143$	7.62576e28			0.609883
$144$	−1.05501e29	−	1.55176e28i	−0.768007	−	0.112962i
$145$	−1.21502e28			−0.0805595
$146$	−6.31122e28	+	1.37901e29i	−0.381373	+	0.833304i
$147$	3.45413e28	−	3.45413e28i	0.190351	−	0.190351i
$148$	−8.43103e27	+	1.15259e29i	−0.0423982	+	0.579617i
$149$	−2.68386e29	−	2.68386e29i	−1.23238	−	1.23238i	−0.963047	−	0.269334i	$-0.913197\pi$
$149$	−2.68386e29	−	2.68386e29i	−1.23238	−	1.23238i	−0.269334	−	0.963047i	$-0.586803\pi$
$150$	3.56269e28	+	9.57561e28i	0.149467	+	0.401730i
$151$			1.34097e29i			0.514318i	0.966369	+	0.257159i	$0.0827864\pi$
$151$			1.34097e29i			0.514318i	−0.966369	+	0.257159i	$0.917214\pi$
$152$	2.00711e29	+	1.10230e29i	0.704179	+	0.386734i
$153$		−	1.86628e29i		−	0.599297i
$154$	−7.10392e28	+	2.64308e28i	−0.208914	+	0.0777285i
$155$	−6.73466e28	−	6.73466e28i	−0.181484	−	0.181484i
$156$	2.60215e29	−	2.24741e29i	0.642910	−	0.555265i
$157$	3.04964e29	−	3.04964e29i	0.691199	−	0.691199i	−0.271296	−	0.962496i	$-0.587452\pi$
$157$	3.04964e29	−	3.04964e29i	0.691199	−	0.691199i	0.962496	+	0.271296i	$0.0874524\pi$
$158$	2.39989e29	+	1.09834e29i	0.499253	+	0.228490i
$159$	−1.75477e29			−0.335242
$160$	−1.70630e29	+	3.63958e28i	−0.299527	+	0.0638898i
$161$	−5.78498e28			−0.0933581
$162$	2.32082e29	+	1.06215e29i	0.344499	+	0.157665i
$163$	6.95720e29	−	6.95720e29i	0.950390	−	0.950390i	−0.0484363	−	0.998826i	$-0.515424\pi$
$163$	6.95720e29	−	6.95720e29i	0.950390	−	0.950390i	0.998826	+	0.0484363i	$0.0154238\pi$
$164$	−1.11737e30	+	9.65047e29i	−1.40542	+	1.21383i
$165$	−3.00209e28	−	3.00209e28i	−0.0347849	−	0.0347849i
$166$	−8.55968e28	+	3.18471e28i	−0.0914110	+	0.0340103i
$167$		−	1.20348e30i		−	1.18513i	−0.805523	−	0.592565i	$-0.798115\pi$
$167$		−	1.20348e30i		−	1.18513i	0.805523	−	0.592565i	$-0.201885\pi$
$168$	−1.64513e29	+	2.99552e29i	−0.149460	+	0.272143i
$169$		−	2.65403e30i		−	2.22554i
$170$	−1.06475e29	−	2.86177e29i	−0.0824492	−	0.221603i
$171$	−6.16411e29	−	6.16411e29i	−0.440984	−	0.440984i
$172$	3.36892e28	−	4.60558e29i	0.0222770	−	0.304544i
$173$	−7.26364e29	+	7.26364e29i	−0.444152	+	0.444152i	−0.893405	−	0.449252i	$-0.851690\pi$
$173$	−7.26364e29	+	7.26364e29i	−0.444152	+	0.444152i	0.449252	+	0.893405i	$0.351690\pi$
$174$	−9.15266e28	+	1.99987e29i	−0.0517765	+	0.113132i
$175$	−1.13609e30			−0.594841
$176$	−5.62081e29	+	4.17936e29i	−0.272507	+	0.202623i
$177$	−1.62974e30			−0.731945
$178$	−2.33036e29	+	5.09186e29i	−0.0969957	+	0.211937i
$179$	−2.09463e29	+	2.09463e29i	−0.0808333	+	0.0808333i	−0.746367	−	0.665534i	$-0.768204\pi$
$179$	−2.09463e29	+	2.09463e29i	−0.0808333	+	0.0808333i	0.665534	+	0.746367i	$0.268204\pi$
$180$	6.62416e29	+	4.84548e28i	0.237111	+	0.0173443i
$181$	−2.45212e30	−	2.45212e30i	−0.814481	−	0.814481i	0.170821	−	0.985302i	$-0.445358\pi$
$181$	−2.45212e30	−	2.45212e30i	−0.814481	−	0.814481i	−0.985302	+	0.170821i	$0.945358\pi$
$182$	1.33322e30	+	3.58334e30i	0.411090	+	1.10490i
$183$		−	1.95769e30i		−	0.560602i
$184$	−5.13295e29	+	1.49364e29i	−0.136561	+	0.0397380i
$185$		−	7.19808e29i		−	0.177991i
$186$	−1.61581e30	+	6.01175e29i	−0.371505	+	0.138222i
$187$	−8.66805e29	−	8.66805e29i	−0.185379	−	0.185379i
$188$	6.31536e30	+	7.31220e30i	1.25680	+	1.45518i
$189$	2.10507e30	−	2.10507e30i	0.389971	−	0.389971i
$190$	−1.29689e30	−	5.93537e29i	−0.223732	−	0.102394i
$191$	5.61971e30			0.903158			0.451579	−	0.892231i	$-0.350861\pi$
$191$	5.61971e30			0.903158			0.451579	+	0.892231i	$0.350861\pi$
$192$	−6.86285e29	+	3.08265e30i	−0.102787	+	0.461698i
$193$	8.09906e30			1.13087			0.565433	−	0.824795i	$-0.308709\pi$
$193$	8.09906e30			1.13087			0.565433	+	0.824795i	$0.308709\pi$
$194$	8.54503e30	+	3.91074e30i	1.11273	+	0.509256i
$195$	−1.51431e30	+	1.51431e30i	−0.183970	+	0.183970i
$196$	3.28096e30	+	3.79883e30i	0.372000	+	0.430718i
$197$	−1.20588e29	−	1.20588e29i	−0.0127647	−	0.0127647i	0.700696	−	0.713460i	$-0.252873\pi$
$197$	−1.20588e29	−	1.20588e29i	−0.0127647	−	0.0127647i	−0.713460	+	0.700696i	$0.752873\pi$
$198$	2.49911e30	−	9.29815e29i	0.247061	−	0.0919214i
$199$			8.33886e29i			0.0770176i	0.999258	+	0.0385088i	$0.0122608\pi$
$199$			8.33886e29i			0.0770176i	−0.999258	+	0.0385088i	$0.987739\pi$
$200$	−1.00804e31	+	2.93332e30i	−0.870111	+	0.253194i
$201$			2.30256e30i			0.185808i
$202$	2.27845e30	+	6.12388e30i	0.171947	+	0.462151i
$203$	−1.72932e30	−	1.72932e30i	−0.122090	−	0.122090i
$204$	−5.51240e30	−	4.03224e29i	−0.364194	−	0.0266403i
$205$	6.50250e30	−	6.50250e30i	0.402164	−	0.402164i
$206$	−1.26483e31	+	2.76366e31i	−0.732527	+	1.60058i
$207$	2.03511e30			0.110405
$208$	2.10814e31	+	2.83524e31i	1.07163	+	1.44123i
$209$	−5.72592e30			−0.272816
$210$	8.85826e29	−	1.93554e30i	0.0395720	−	0.0864653i
$211$	1.35224e31	−	1.35224e31i	0.566553	−	0.566553i	−0.364608	−	0.931161i	$-0.618797\pi$
$211$	1.35224e31	−	1.35224e31i	0.566553	−	0.566553i	0.931161	+	0.364608i	$0.118797\pi$
$212$	1.31546e30	−	1.79834e31i	0.0517062	−	0.706866i
$213$	−2.29211e30	−	2.29211e30i	−0.0845495	−	0.0845495i
$214$	5.62638e30	+	1.51223e31i	0.194824	+	0.523638i
$215$			2.87625e30i			0.0935206i
$216$	1.32429e31	−	2.41132e31i	0.404444	−	0.736427i
$217$		−	1.91707e31i		−	0.550086i
$218$	1.29059e30	−	4.80174e29i	0.0348036	−	0.0129490i
$219$	−1.20904e31	−	1.20904e31i	−0.306511	−	0.306511i
$220$	3.30168e30	−	2.85158e30i	0.0787099	−	0.0679797i
$221$	−4.37232e31	+	4.37232e31i	−0.980428	+	0.980428i
$222$	−1.18477e31	−	5.42224e30i	−0.249958	−	0.114397i
$223$	−3.99657e31			−0.793545			−0.396772	−	0.917917i	$-0.629870\pi$
$223$	−3.99657e31			−0.793545			−0.396772	+	0.917917i	$0.629870\pi$
$224$	−2.94657e31	−	1.91054e31i	−0.550768	−	0.357115i
$225$	3.99670e31			0.703457
$226$	−3.88386e31	−	1.77750e31i	−0.643872	−	0.294677i
$227$	4.59003e31	−	4.59003e31i	0.716914	−	0.716914i	−0.251058	−	0.967972i	$-0.580779\pi$
$227$	4.59003e31	−	4.59003e31i	0.716914	−	0.716914i	0.967972	+	0.251058i	$0.0807786\pi$
$228$	−1.95386e31	+	1.68750e31i	−0.287590	+	0.248384i
$229$	−4.09681e31	−	4.09681e31i	−0.568417	−	0.568417i	0.363268	−	0.931685i	$-0.381661\pi$
$229$	−4.09681e31	−	4.09681e31i	−0.568417	−	0.568417i	−0.931685	+	0.363268i	$0.881661\pi$
$230$	3.12067e30	−	1.16107e30i	0.0408246	−	0.0151891i
$231$		−	8.54566e30i		−	0.105435i
$232$	−1.98091e31	−	1.08791e31i	−0.230556	−	0.126621i
$233$			7.01051e31i			0.769919i	0.922934	+	0.384959i	$0.125785\pi$
$233$			7.01051e31i			0.769919i	−0.922934	+	0.384959i	$0.874215\pi$
$234$	−4.69015e31	−	1.26059e32i	−0.486153	−	1.30666i
$235$	−4.25530e31	−	4.25530e31i	−0.416403	−	0.416403i
$236$	1.22173e31	−	1.67020e32i	0.112892	−	1.54332i
$237$	−2.10410e31	+	2.10410e31i	−0.183638	+	0.183638i
$238$	2.55768e31	−	5.58855e31i	0.210890	−	0.460798i
$239$	7.12208e31			0.554926			0.277463	−	0.960736i	$-0.410506\pi$
$239$	7.12208e31			0.554926			0.277463	+	0.960736i	$0.410506\pi$
$240$	2.86240e30	−	1.94610e31i	0.0210804	−	0.143322i
$241$	1.88918e31			0.131536			0.0657678	−	0.997835i	$-0.479050\pi$
$241$	1.88918e31			0.131536			0.0657678	+	0.997835i	$0.479050\pi$
$242$	−5.59174e31	+	1.22180e32i	−0.368162	+	0.804439i
$243$	−1.15746e32	+	1.15746e32i	−0.720812	+	0.720812i
$244$	2.00630e32	+	1.46758e31i	1.18204	+	0.0864648i
$245$	−2.21071e31	−	2.21071e31i	−0.123251	−	0.123251i
$246$	−5.80452e31	−	1.56011e32i	−0.306296	−	0.823247i
$247$			2.88825e32i			1.44287i
$248$	−4.94973e31	−	1.70099e32i	−0.234145	−	0.804645i
$249$		−	1.02969e31i		−	0.0461332i
$250$	1.28915e32	−	4.79641e31i	0.547160	−	0.203576i
$251$	2.24340e32	+	2.24340e32i	0.902217	+	0.902217i	0.995628	−	0.0934109i	$-0.0297770\pi$
$251$	2.24340e32	+	2.24340e32i	0.902217	+	0.902217i	−0.0934109	+	0.995628i	$0.529777\pi$
$252$	8.73841e31	+	1.01177e32i	0.333062	+	0.385633i
$253$	9.45221e30	−	9.45221e30i	0.0341512	−	0.0341512i
$254$	1.99612e32	+	9.13549e31i	0.683802	+	0.312951i
$255$	3.44257e31			0.111838
$256$	−3.10775e32	−	9.34416e31i	−0.957649	−	0.287939i
$257$	7.03417e30			0.0205644			0.0102822	−	0.999947i	$-0.496727\pi$
$257$	7.03417e30			0.0205644			0.0102822	+	0.999947i	$0.496727\pi$
$258$	4.73416e31	+	2.16665e31i	0.131334	+	0.0601067i
$259$	1.02449e32	−	1.02449e32i	0.269750	−	0.269750i
$260$	−1.43839e32	−	1.66543e32i	−0.359531	−	0.416280i
$261$	6.08363e31	+	6.08363e31i	0.144383	+	0.144383i
$262$	−2.41673e32	+	8.99166e31i	−0.544704	+	0.202662i
$263$			4.03623e32i			0.864118i	0.901845	+	0.432059i	$0.142213\pi$
$263$			4.03623e32i			0.864118i	−0.901845	+	0.432059i	$0.857787\pi$
$264$	−2.20643e31	−	7.58247e31i	−0.0448784	−	0.154226i
$265$			1.12309e32i			0.217067i
$266$	−1.00107e32	−	2.69061e32i	−0.183891	−	0.494252i
$267$	−4.46428e31	−	4.46428e31i	−0.0779559	−	0.0779559i
$268$	−2.35974e32	−	1.72611e31i	−0.391781	−	0.0286583i
$269$	−4.98473e32	+	4.98473e32i	−0.787020	+	0.787020i	−0.981005	−	0.193985i	$-0.937859\pi$
$269$	−4.98473e32	+	4.98473e32i	−0.787020	+	0.787020i	0.193985	+	0.981005i	$0.437859\pi$
$270$	−7.13069e31	+	1.55806e32i	−0.107083	+	0.233978i
$271$	3.55365e32			0.507679			0.253839	−	0.967246i	$-0.418307\pi$
$271$	3.55365e32			0.507679			0.253839	+	0.967246i	$0.418307\pi$
$272$	8.26472e31	−	5.61904e32i	0.112343	−	0.763804i
$273$	−4.31058e32			−0.557622
$274$	4.63607e32	−	1.01299e33i	0.570844	−	1.24730i
$275$	1.85629e32	−	1.85629e32i	0.217598	−	0.217598i
$276$	4.39702e30	−	6.01108e31i	0.00490779	−	0.0670934i
$277$	4.19499e32	+	4.19499e32i	0.445917	+	0.445917i	0.893995	−	0.448078i	$-0.147891\pi$
$277$	4.19499e32	+	4.19499e32i	0.445917	+	0.445917i	−0.448078	+	0.893995i	$0.647891\pi$
$278$	5.46770e32	+	1.46958e33i	0.553605	+	1.48795i
$279$			6.74410e32i			0.650530i
$280$	1.91719e32	+	1.05292e32i	0.176211	+	0.0967745i
$281$			5.29489e31i			0.0463790i	0.999731	+	0.0231895i	$0.00738211\pi$
$281$			5.29489e31i			0.0463790i	−0.999731	+	0.0231895i	$0.992618\pi$
$282$	−1.02095e33	+	3.79853e32i	−0.852395	+	0.317141i
$283$	1.05080e33	+	1.05080e33i	0.836381	+	0.836381i	0.988381	−	0.151999i	$-0.0485712\pi$
$283$	1.05080e33	+	1.05080e33i	0.836381	+	0.836381i	−0.151999	+	0.988381i	$0.548571\pi$
$284$	2.52085e32	−	2.17720e32i	0.191315	−	0.165234i
$285$	1.13704e32	−	1.13704e32i	0.0822945	−	0.0822945i
$286$	−8.03328e32	−	3.67654e32i	−0.554564	−	0.253803i
$287$	1.85098e33			1.21898
$288$	1.03658e33	+	6.72113e32i	0.651336	+	0.422322i
$289$	−6.73726e32			−0.403983
$290$	1.27996e32	+	5.85788e31i	0.0732524	+	0.0335249i
$291$	−7.49183e32	+	7.49183e32i	−0.409291	+	0.409291i
$292$	1.32970e33	−	1.14843e33i	0.693561	−	0.599011i
$293$	−1.35817e33	−	1.35817e33i	−0.676456	−	0.676456i	0.282740	−	0.959196i	$-0.408757\pi$
$293$	−1.35817e33	−	1.35817e33i	−0.676456	−	0.676456i	−0.959196	+	0.282740i	$0.908757\pi$
$294$	−5.30403e32	+	1.97341e32i	−0.252300	+	0.0938704i
$295$			1.04306e33i			0.473930i
$296$	6.44503e32	−	1.17354e33i	0.279761	−	0.509399i
$297$			6.87905e32i			0.285310i
$298$	1.53334e33	+	4.12123e33i	0.607742	+	1.63345i
$299$	−4.76786e32	−	4.76786e32i	−0.180619	−	0.180619i
$300$	8.63518e31	−	1.18050e33i	0.0312705	−	0.427493i
$301$	−4.09372e32	+	4.09372e32i	−0.141733	+	0.141733i
$302$	6.46512e32	−	1.41264e33i	0.214034	−	0.467667i
$303$	−7.36672e32			−0.233238
$304$	−1.58293e33	−	2.12888e33i	−0.479368	−	0.644700i
$305$	−1.25296e33			−0.362986
$306$	−8.99772e32	+	1.96601e33i	−0.249398	+	0.544938i
$307$	2.59634e33	−	2.59634e33i	0.688641	−	0.688641i	−0.273290	−	0.961932i	$-0.588112\pi$
$307$	2.59634e33	−	2.59634e33i	0.688641	−	0.688641i	0.961932	+	0.273290i	$0.0881120\pi$
$308$	8.75784e32	+	6.40624e31i	0.222312	+	0.0162618i
$309$	−2.42303e33	−	2.42303e33i	−0.588735	−	0.588735i
$310$	3.84764e32	+	1.03415e33i	0.0894977	+	0.240547i
$311$		−	7.31852e33i		−	1.62989i	−0.579539	−	0.814944i	$-0.696767\pi$
$311$		−	7.31852e33i		−	1.62989i	0.579539	−	0.814944i	$-0.303233\pi$
$312$	−3.82473e33	+	1.11296e33i	−0.815669	+	0.237352i
$313$		−	3.84059e33i		−	0.784422i	−0.919875	−	0.392211i	$-0.871710\pi$
$313$		−	3.84059e33i		−	0.784422i	0.919875	−	0.392211i	$-0.128290\pi$
$314$	−4.68291e33	+	1.74232e33i	−0.916148	+	0.340861i
$315$	−5.88795e32	−	5.88795e32i	−0.110350	−	0.110350i
$316$	−1.99861e33	−	2.31407e33i	−0.358882	−	0.415529i
$317$	7.03783e32	−	7.03783e32i	0.121098	−	0.121098i	−0.643960	−	0.765059i	$-0.722710\pi$
$317$	7.03783e32	−	7.03783e32i	0.121098	−	0.121098i	0.765059	+	0.643960i	$0.222710\pi$
$318$	1.84854e33	+	8.46010e32i	0.304834	+	0.139511i
$319$	5.65116e32			0.0893231
$320$	1.97296e33	+	4.39237e32i	0.298947	+	0.0665539i
$321$	−1.81913e33			−0.264269
$322$	6.09413e32	+	2.78906e32i	0.0848901	+	0.0388511i
$323$	3.28302e33	−	3.28302e33i	0.438571	−	0.438571i
$324$	−1.93276e33	−	2.23783e33i	−0.247639	−	0.286727i
$325$	−9.36346e33	−	9.36346e33i	−1.15083	−	1.15083i
$326$	−1.06832e34	+	3.97478e33i	−1.25969	+	0.468679i
$327$			1.55251e32i			0.0175647i
$328$	1.64236e34	−	4.77911e33i	1.78308	−	0.518860i
$329$		−	1.21130e34i		−	1.26214i
$330$	1.71515e32	+	4.60990e32i	0.0171540	+	0.0461055i
$331$	6.23114e33	+	6.23114e33i	0.598260	+	0.598260i	0.939849	−	0.341590i	$-0.110965\pi$
$331$	6.23114e33	+	6.23114e33i	0.598260	+	0.598260i	−0.341590	+	0.939849i	$0.610965\pi$
$332$	1.05525e33	+	7.71902e31i	0.0972730	+	0.00711538i
$333$	−3.60408e33	+	3.60408e33i	−0.319005	+	0.319005i
$334$	−5.80222e33	+	1.26779e34i	−0.493193	+	1.07763i
$335$	1.47369e33			0.120310
$336$	3.17725e33	−	2.36245e33i	0.249156	−	0.185260i
$337$	−1.52002e34			−1.14510			−0.572552	−	0.819868i	$-0.694046\pi$
$337$	−1.52002e34			−1.14510			−0.572552	+	0.819868i	$0.694046\pi$
$338$	−1.27957e34	+	2.79587e34i	−0.926162	+	2.02368i
$339$	3.40517e33	−	3.40517e33i	0.236833	−	0.236833i
$340$	−2.58072e32	+	3.52805e33i	−0.0172494	+	0.235814i
$341$	3.13234e33	+	3.13234e33i	0.201226	+	0.201226i
$342$	3.52167e33	+	9.46536e33i	0.217469	+	0.584500i
$343$		−	1.73502e34i		−	1.02999i
$344$	−2.57534e33	+	4.68928e33i	−0.146993	+	0.267650i
$345$			3.75400e32i			0.0206033i
$346$	1.11538e34	−	4.14986e33i	0.588700	−	0.219031i
$347$	1.90236e34	+	1.90236e34i	0.965706	+	0.965706i	0.999431	−	0.0337251i	$-0.0107371\pi$
$347$	1.90236e34	+	1.90236e34i	0.965706	+	0.965706i	−0.0337251	+	0.999431i	$0.510737\pi$
$348$	1.92836e33	−	1.66547e33i	0.0941602	−	0.0813238i
$349$	8.36695e33	−	8.36695e33i	0.393028	−	0.393028i	−0.482737	−	0.875765i	$-0.660357\pi$
$349$	8.36695e33	−	8.36695e33i	0.393028	−	0.393028i	0.875765	+	0.482737i	$0.160357\pi$
$350$	1.19681e34	+	5.47735e33i	0.540886	+	0.247544i
$351$	3.46992e34			1.50894
$352$	7.93614e33	−	1.69280e33i	0.332111	−	0.0708400i
$353$	−2.62591e34			−1.05760			−0.528800	−	0.848747i	$-0.677358\pi$
$353$	−2.62591e34			−1.05760			−0.528800	+	0.848747i	$0.677358\pi$
$354$	1.71683e34	+	7.85730e33i	0.665554	+	0.304600i
$355$	−1.46700e33	+	1.46700e33i	−0.0547453	+	0.0547453i
$356$	4.90978e33	−	4.24046e33i	0.176395	−	0.152348i
$357$	4.89975e33	+	4.89975e33i	0.169494	+	0.169494i
$358$	3.21643e33	−	1.19670e33i	0.107140	−	0.0398625i
$359$			4.61066e34i			1.47907i	0.673119	+	0.739534i	$0.264954\pi$
$359$			4.61066e34i			1.47907i	−0.673119	+	0.739534i	$0.735046\pi$
$360$	−6.74454e33	−	3.70409e33i	−0.208386	−	0.114445i
$361$			1.19137e34i			0.354568i
$362$	1.40094e34	+	3.76538e34i	0.401656	+	1.07955i
$363$	−1.07121e34	−	1.07121e34i	−0.295894	−	0.295894i
$364$	3.23142e33	−	4.41761e34i	0.0860052	−	1.17576i
$365$	−7.73812e33	+	7.73812e33i	−0.198464	+	0.198464i
$366$	−9.43844e33	+	2.06231e34i	−0.233295	+	0.509753i
$367$	8.07754e34			1.92436			0.962181	−	0.272409i	$-0.0878204\pi$
$367$	8.07754e34			1.92436			0.962181	+	0.272409i	$0.0878204\pi$
$368$	6.12737e33	+	9.01239e32i	0.140711	+	0.0206964i
$369$	−6.51162e34			−1.44156
$370$	−3.47034e33	+	7.58274e33i	−0.0740712	+	0.161846i
$371$	−1.59847e34	+	1.59847e34i	−0.328970	+	0.328970i
$372$	1.99199e34	+	1.45712e33i	0.395329	+	0.0289177i
$373$	−5.77223e34	−	5.77223e34i	−1.10478	−	1.10478i	−0.993826	−	0.110950i	$-0.964611\pi$
$373$	−5.77223e34	−	5.77223e34i	−1.10478	−	1.10478i	−0.110950	−	0.993826i	$-0.535389\pi$
$374$	4.95222e33	+	1.33103e34i	0.0914184	+	0.245709i
$375$			1.55079e34i			0.276140i
$376$	−3.12749e34	−	1.07477e35i	−0.537230	−	1.84621i
$377$		−	2.85055e34i		−	0.472411i
$378$	−3.23247e34	+	1.20267e34i	−0.516886	+	0.192312i
$379$	8.65768e34	+	8.65768e34i	1.33589	+	1.33589i	0.899996	+	0.435899i	$0.143569\pi$
$379$	8.65768e34	+	8.65768e34i	1.33589	+	1.33589i	0.435899	+	0.899996i	$0.356431\pi$
$380$	1.08004e34	+	1.25051e34i	0.160827	+	0.186213i
$381$	−1.75009e34	+	1.75009e34i	−0.251520	+	0.251520i
$382$	−5.92003e34	−	2.70938e34i	−0.821237	−	0.375850i
$383$	−7.34112e34			−0.983058			−0.491529	−	0.870861i	$-0.663562\pi$
$383$	−7.34112e34			−0.983058			−0.491529	+	0.870861i	$0.663562\pi$
$384$	2.20917e34	−	2.91652e34i	0.285600	−	0.377045i
$385$	−5.46939e33			−0.0682683
$386$	−8.53187e34	−	3.90472e34i	−1.02829	−	0.470611i
$387$	1.44014e34	−	1.44014e34i	0.167613	−	0.167613i
$388$	−7.11622e34	−	8.23947e34i	−0.799874	−	0.926128i
$389$	1.86554e34	+	1.86554e34i	0.202528	+	0.202528i	0.801082	−	0.598554i	$-0.204258\pi$
$389$	1.86554e34	+	1.86554e34i	0.202528	+	0.202528i	−0.598554	+	0.801082i	$0.704258\pi$
$390$	2.32531e34	−	8.65154e33i	0.243842	−	0.0907238i
$391$			1.08391e34i			0.109801i
$392$	−1.62479e34	−	5.58366e34i	−0.159014	−	0.546458i
$393$		−	2.90720e34i		−	0.274901i
$394$	6.88943e32	+	1.85170e33i	0.00629483	+	0.0169189i
$395$	1.34666e34	+	1.34666e34i	0.118905	+	0.118905i
$396$	−3.08094e34	−	2.25367e33i	−0.262905	−	0.0192311i
$397$	−4.33190e34	+	4.33190e34i	−0.357278	+	0.357278i	−0.862809	−	0.505530i	$-0.831297\pi$
$397$	−4.33190e34	+	4.33190e34i	−0.357278	+	0.357278i	0.505530	+	0.862809i	$0.331297\pi$
$398$	4.02034e33	−	8.78449e33i	0.0320510	−	0.0700318i
$399$	3.23667e34			0.249439
$400$	1.20334e35	+	1.76992e34i	0.896555	+	0.131869i
$401$	9.62026e33			0.0693008			0.0346504	−	0.999399i	$-0.488968\pi$
$401$	9.62026e33			0.0693008			0.0346504	+	0.999399i	$0.488968\pi$
$402$	1.11011e34	−	2.42561e34i	0.0773243	−	0.168955i
$403$	1.58001e35	−	1.58001e35i	1.06424	−	1.06424i
$404$	5.52245e33	−	7.54963e34i	0.0359736	−	0.491788i
$405$	1.30229e34	+	1.30229e34i	0.0820477	+	0.0820477i
$406$	9.87996e33	+	2.65548e34i	0.0602080	+	0.161824i
$407$			3.34788e34i			0.197354i
$408$	5.61258e34	+	3.08241e34i	0.320074	+	0.175784i
$409$			4.96919e34i			0.274171i	0.990559	+	0.137085i	$0.0437734\pi$
$409$			4.96919e34i			0.274171i	−0.990559	+	0.137085i	$0.956227\pi$
$410$	−9.98499e34	+	3.71501e34i	−0.533047	+	0.198325i
$411$	8.88134e34	+	8.88134e34i	0.458790	+	0.458790i
$412$	2.66484e35	−	2.30155e35i	1.33217	−	1.15056i
$413$	−1.48458e35	+	1.48458e35i	−0.718252	+	0.718252i
$414$	−2.14387e34	−	9.81170e33i	−0.100391	−	0.0459452i
$415$	−6.59020e33			−0.0298710
$416$	−8.53876e34	−	4.00313e35i	−0.374658	−	1.75647i
$417$	−1.76783e35			−0.750936
$418$	6.03191e34	+	2.76058e34i	0.248071	+	0.113533i
$419$	−9.28528e34	+	9.28528e34i	−0.369748	+	0.369748i	−0.867385	−	0.497637i	$-0.834201\pi$
$419$	−9.28528e34	+	9.28528e34i	−0.369748	+	0.369748i	0.497637	+	0.867385i	$0.334201\pi$
$420$	−1.86633e34	+	1.61190e34i	−0.0719653	+	0.0621546i
$421$	−1.56428e35	−	1.56428e35i	−0.584124	−	0.584124i	0.351910	−	0.936034i	$-0.385532\pi$
$421$	−1.56428e35	−	1.56428e35i	−0.584124	−	0.584124i	−0.936034	+	0.351910i	$0.885532\pi$
$422$	−2.07645e35	+	7.72561e34i	−0.750936	+	0.279392i
$423$			4.26126e35i			1.49260i
$424$	−1.00559e35	+	1.83102e35i	−0.341179	+	0.621232i
$425$			2.12865e35i			0.699607i
$426$	1.30953e34	+	3.51968e34i	0.0416951	+	0.112066i
$427$	−1.78332e35	−	1.78332e35i	−0.550115	−	0.550115i
$428$	1.36371e34	−	1.86430e35i	0.0407597	−	0.557218i
$429$	7.04316e34	−	7.04316e34i	0.203983	−	0.203983i
$430$	1.38670e34	−	3.02996e34i	0.0389187	−	0.0850379i
$431$	4.99780e35			1.35936			0.679681	−	0.733507i	$-0.262118\pi$
$431$	4.99780e35			1.35936			0.679681	+	0.733507i	$0.262118\pi$
$432$	−2.55761e35	+	1.90172e35i	−0.674224	+	0.501320i
$433$	4.28742e35			1.09549			0.547746	−	0.836645i	$-0.315486\pi$
$433$	4.28742e35			1.09549			0.547746	+	0.836645i	$0.315486\pi$
$434$	−9.24257e34	+	2.01951e35i	−0.228919	+	0.500191i
$435$	−1.12220e34	+	1.12220e34i	−0.0269441	+	0.0269441i
$436$	−1.59106e34	−	1.16384e33i	−0.0370355	−	0.00270910i
$437$	3.58002e34	+	3.58002e34i	0.0807953	+	0.0807953i
$438$	6.90750e34	+	1.85656e35i	0.151154	+	0.406264i
$439$		−	4.00763e35i		−	0.850387i	−0.905102	−	0.425194i	$-0.860206\pi$
$439$		−	4.00763e35i		−	0.850387i	0.905102	−	0.425194i	$-0.139794\pi$
$440$	−4.85293e34	+	1.41216e34i	−0.0998604	+	0.0290585i
$441$			2.21381e35i			0.441794i
$442$	6.71396e35	−	2.49799e35i	1.29951	−	0.483493i
$443$	6.89328e34	+	6.89328e34i	0.129412	+	0.129412i	0.768846	−	0.639434i	$-0.220831\pi$
$443$	6.89328e34	+	6.89328e34i	0.129412	+	0.129412i	−0.639434	+	0.768846i	$0.720831\pi$
$444$	9.86663e34	+	1.14240e35i	0.179680	+	0.208041i
$445$	−2.85723e34	+	2.85723e34i	−0.0504759	+	0.0504759i
$446$	4.21015e35	+	1.92683e35i	0.721567	+	0.330235i
$447$	−4.95763e35			−0.824371
$448$	2.18293e35	+	3.43324e35i	0.352197	+	0.553925i
$449$	−2.55669e35			−0.400269			−0.200135	−	0.979768i	$-0.564138\pi$
$449$	−2.55669e35			−0.400269			−0.200135	+	0.979768i	$0.564138\pi$
$450$	−4.21028e35	−	1.92689e35i	−0.639650	−	0.292744i
$451$	−3.02436e35	+	3.02436e35i	−0.445913	+	0.445913i
$452$	3.23445e35	+	3.74498e35i	0.462840	+	0.535896i
$453$	1.23853e35	+	1.23853e35i	0.172020	+	0.172020i
$454$	−7.04828e35	+	2.62238e35i	−0.950231	+	0.353542i
$455$			2.75886e35i			0.361057i
$456$	2.87186e35	−	8.35685e34i	0.364870	−	0.106174i
$457$		−	1.38281e36i		−	1.70566i	−0.522185	−	0.852832i	$-0.674883\pi$
$457$		−	1.38281e36i		−	1.70566i	0.522185	−	0.852832i	$-0.325117\pi$
$458$	2.34059e35	+	6.29090e35i	0.280312	+	0.753406i
$459$	−3.94418e35	−	3.94418e35i	−0.458655	−	0.458655i
$460$	−3.84721e34	−	2.81418e33i	−0.0434426	−	0.00317776i
$461$	9.02620e34	−	9.02620e34i	0.0989788	−	0.0989788i	−0.655883	−	0.754862i	$-0.727704\pi$
$461$	9.02620e34	−	9.02620e34i	0.0989788	−	0.0989788i	0.754862	+	0.655883i	$0.227704\pi$
$462$	−4.12004e34	+	9.00234e34i	−0.0438768	+	0.0958713i
$463$	3.96731e35			0.410349			0.205174	−	0.978725i	$-0.434224\pi$
$463$	3.96731e35			0.410349			0.205174	+	0.978725i	$0.434224\pi$
$464$	1.56227e35	+	2.10109e35i	0.156950	+	0.211082i
$465$	−1.24403e35			−0.121399
$466$	3.37991e35	−	7.38516e35i	0.320402	−	0.700083i
$467$	1.34186e36	−	1.34186e36i	1.23575	−	1.23575i	0.274029	−	0.961721i	$-0.411643\pi$
$467$	1.34186e36	−	1.34186e36i	1.23575	−	1.23575i	0.961721	−	0.274029i	$-0.0883565\pi$
$468$	−1.13679e35	+	1.55408e36i	−0.101709	+	1.39045i
$469$	2.09748e35	+	2.09748e35i	0.182332	+	0.182332i
$470$	2.43114e35	+	6.53427e35i	0.205347	+	0.551920i
$471$		−	5.63330e35i		−	0.462361i
$472$	−9.33941e35	+	1.70056e36i	−0.744908	+	1.35636i
$473$		−	1.33776e35i		−	0.103694i
$474$	3.23097e35	−	1.20211e35i	0.243403	−	0.0905602i
$475$	7.03070e35	+	7.03070e35i	0.514796	+	0.514796i
$476$	−5.38872e35	+	4.65410e35i	−0.383523	+	0.331239i
$477$	5.62330e35	−	5.62330e35i	0.389039	−	0.389039i
$478$	−7.50269e35	−	3.43370e35i	−0.504592	−	0.230933i
$479$	−2.96524e36			−1.93879			−0.969396	−	0.245503i	$-0.921047\pi$
$479$	−2.96524e36			−1.93879			−0.969396	+	0.245503i	$0.921047\pi$
$480$	−1.23979e35	+	1.91210e35i	−0.0788120	+	0.121549i
$481$	1.68873e36			1.04376
$482$	−1.99014e35	−	9.10813e34i	−0.119605	−	0.0547387i
$483$	−5.34301e34	+	5.34301e34i	−0.0312248	+	0.0312248i
$484$	1.17811e36	−	1.01751e36i	0.669536	−	0.578262i
$485$	4.79492e35	+	4.79492e35i	0.265014	+	0.265014i
$486$	1.77735e36	−	6.61280e35i	0.955397	−	0.355464i
$487$		−	1.48382e36i		−	0.775785i	−0.921705	−	0.387893i	$-0.873203\pi$
$487$		−	1.48382e36i		−	0.775785i	0.921705	−	0.387893i	$-0.126797\pi$
$488$	−2.04276e36	−	1.12188e36i	−1.03884	−	0.570530i
$489$		−	1.28514e36i		−	0.635740i
$490$	1.26302e35	+	3.39468e35i	0.0607805	+	0.163362i
$491$	−2.81120e36	−	2.81120e36i	−1.31611	−	1.31611i	−0.916828	−	0.399282i	$-0.869260\pi$
$491$	−2.81120e36	−	2.81120e36i	−1.31611	−	1.31611i	−0.399282	−	0.916828i	$-0.630740\pi$
$492$	−1.40689e35	+	1.92333e36i	−0.0640811	+	0.876040i
$493$	−3.24016e35	+	3.24016e35i	−0.143593	+	0.143593i
$494$	1.39249e36	−	3.04260e36i	0.600451	−	1.31199i
$495$	1.92409e35			0.0807339
$496$	−2.98659e35	+	2.03053e36i	−0.121948	+	0.829100i
$497$	−4.17591e35			−0.165936
$498$	−4.96433e34	+	1.08471e35i	−0.0191984	+	0.0419487i
$499$	−1.23362e36	+	1.23362e36i	−0.464326	+	0.464326i	−0.900070	−	0.435744i	$-0.856485\pi$
$499$	−1.23362e36	+	1.23362e36i	−0.464326	+	0.464326i	0.435744	+	0.900070i	$0.356485\pi$
$500$	−1.58929e36	−	1.16254e35i	−0.582248	−	0.0425906i
$501$	−1.11153e36	−	1.11153e36i	−0.396382	−	0.396382i
$502$	−1.28170e36	−	3.44487e36i	−0.444923	−	1.19584i
$503$			9.64076e35i			0.325794i	0.986643	+	0.162897i	$0.0520839\pi$
$503$			9.64076e35i			0.325794i	−0.986643	+	0.162897i	$0.947916\pi$
$504$	−4.32743e35	−	1.48714e36i	−0.142370	−	0.489259i
$505$			4.71485e35i			0.151020i
$506$	−1.45144e35	+	5.40023e34i	−0.0452656	+	0.0168415i
$507$	−2.45127e36	−	2.45127e36i	−0.744361	−	0.744361i
$508$	−1.66235e36	−	1.92474e36i	−0.491543	−	0.569130i
$509$	4.17289e36	−	4.17289e36i	1.20156	−	1.20156i	0.227873	−	0.973691i	$-0.426823\pi$
$509$	4.17289e36	−	4.17289e36i	1.20156	−	1.20156i	0.973691	−	0.227873i	$-0.0731773\pi$
$510$	−3.62654e35	−	1.65973e35i	−0.101694	−	0.0465416i
$511$	−2.20271e36			−0.601554
$512$	2.82333e36	+	2.48266e36i	0.750959	+	0.660348i
$513$	−2.60544e36			−0.674989
$514$	−7.41008e34	−	3.39132e34i	−0.0186991	−	0.00855789i
$515$	−1.55079e36	+	1.55079e36i	−0.381202	+	0.381202i
$516$	−3.94257e35	−	4.56487e35i	−0.0944079	−	0.109309i
$517$	1.97917e36	+	1.97917e36i	0.461701	+	0.461701i
$518$	−1.57317e36	+	5.85311e35i	−0.357539	+	0.133026i
$519$			1.34174e36i			0.297105i
$520$	7.12318e35	+	2.44791e36i	0.153684	+	0.528141i
$521$			5.85723e36i			1.23135i	0.787998	+	0.615677i	$0.211117\pi$
$521$			5.85723e36i			1.23135i	−0.787998	+	0.615677i	$0.788883\pi$
$522$	−3.47570e35	−	9.34179e35i	−0.0712017	−	0.191372i
$523$	2.32801e36	+	2.32801e36i	0.464741	+	0.464741i	0.900206	−	0.435465i	$-0.143416\pi$
$523$	2.32801e36	+	2.32801e36i	0.464741	+	0.464741i	−0.435465	+	0.900206i	$0.643416\pi$
$524$	2.97939e36	+	2.17938e35i	0.579635	+	0.0423995i
$525$	−1.04930e36	+	1.04930e36i	−0.198952	+	0.198952i
$526$	1.94595e36	−	4.25193e36i	0.359604	−	0.785739i
$527$	−3.59192e36			−0.646970
$528$	−1.33132e35	+	9.05145e35i	−0.0233736	+	0.158913i
$529$	5.72501e36			0.979772
$530$	5.41463e35	−	1.18310e36i	0.0903327	−	0.197378i
$531$	5.22263e36	−	5.22263e36i	0.849402	−	0.849402i
$532$	−2.42636e35	+	3.31703e36i	−0.0384723	+	0.525947i
$533$	1.52554e37	+	1.52554e37i	2.35834	+	2.35834i
$534$	2.55053e35	+	6.85517e35i	0.0384435	+	0.103326i
$535$			1.16428e36i			0.171113i
$536$	2.40262e36	+	1.31951e36i	0.344319	+	0.189099i
$537$			3.86920e35i			0.0540714i
$538$	7.65436e36	−	2.84787e36i	1.04315	−	0.388114i
$539$	1.02822e36	+	1.02822e36i	0.136659	+	0.136659i
$540$	1.50235e36	−	1.29754e36i	0.194740	−	0.168192i
$541$	−5.43522e36	+	5.43522e36i	−0.687154	+	0.687154i	−0.961602	−	0.274448i	$-0.911505\pi$
$541$	−5.43522e36	+	5.43522e36i	−0.687154	+	0.687154i	0.274448	+	0.961602i	$0.411505\pi$
$542$	−3.74356e36	−	1.71329e36i	−0.461630	−	0.211271i
$543$	−4.52956e36			−0.544827
$544$	−3.57970e36	+	5.52086e36i	−0.420011	+	0.647772i
$545$	9.93638e34			0.0113730
$546$	4.54094e36	+	2.07822e36i	0.507043	+	0.232055i
$547$	−1.08631e36	+	1.08631e36i	−0.118338	+	0.118338i	−0.763796	−	0.645458i	$-0.776667\pi$
$547$	−1.08631e36	+	1.08631e36i	−0.118338	+	0.118338i	0.645458	+	0.763796i	$0.276667\pi$
$548$	−9.76765e36	+	8.43607e36i	−1.03813	+	0.896608i
$549$	6.27359e36	+	6.27359e36i	0.650563	+	0.650563i
$550$	−2.85045e36	+	1.06054e36i	−0.288414	+	0.107307i
$551$			2.14038e36i			0.211322i
$552$	−3.36127e35	+	6.12032e35i	−0.0323836	+	0.0589654i
$553$			3.83337e36i			0.360406i
$554$	−2.39668e36	−	6.44167e36i	−0.219902	−	0.591039i
$555$	−6.64815e35	−	6.64815e35i	−0.0595313	−	0.0595313i
$556$	1.32525e36	−	1.81172e37i	0.115821	−	1.58337i
$557$	5.79702e36	−	5.79702e36i	0.494493	−	0.494493i	−0.415226	−	0.909718i	$-0.636297\pi$
$557$	5.79702e36	−	5.79702e36i	0.494493	−	0.494493i	0.909718	+	0.415226i	$0.136297\pi$
$558$	3.25147e36	−	7.10450e36i	0.270719	−	0.591524i
$559$	−6.74792e36			−0.548417
$560$	−1.51201e36	−	2.03350e36i	−0.119955	−	0.161327i
$561$	−1.60116e36			−0.124004
$562$	2.55278e35	−	5.57785e35i	0.0193007	−	0.0421722i
$563$	−1.30932e37	+	1.30932e37i	−0.966453	+	0.966453i	−0.999455	−	0.0330019i	$-0.989493\pi$
$563$	−1.30932e37	+	1.30932e37i	−0.966453	+	0.966453i	0.0330019	+	0.999455i	$0.489493\pi$
$564$	1.25864e37	+	9.20680e35i	0.907057	+	0.0663500i
$565$	−2.17937e36	−	2.17937e36i	−0.153348	−	0.153348i
$566$	−6.00344e36	−	1.61357e37i	−0.412457	−	1.10858i
$567$			3.70707e36i			0.248691i
$568$	−3.70524e36	+	1.07819e36i	−0.242724	+	0.0706306i
$569$		−	1.24564e37i		−	0.796852i	−0.917200	−	0.398426i	$-0.869557\pi$
$569$		−	1.24564e37i		−	0.796852i	0.917200	−	0.398426i	$-0.130443\pi$
$570$	−1.74600e36	+	6.49614e35i	−0.109077	+	0.0405831i
$571$	7.66328e36	+	7.66328e36i	0.467549	+	0.467549i	0.901120	−	0.433571i	$-0.142746\pi$
$571$	7.66328e36	+	7.66328e36i	0.467549	+	0.467549i	−0.433571	+	0.901120i	$0.642746\pi$
$572$	6.69005e36	+	7.74602e36i	0.398642	+	0.461565i
$573$	5.19037e36	−	5.19037e36i	0.302073	−	0.302073i
$574$	−1.94990e37	−	8.92397e36i	−1.10841	−	0.507280i
$575$	−2.32122e36			−0.128885
$576$	−7.67937e36	−	1.20779e37i	−0.416507	−	0.655070i
$577$	−5.19917e36			−0.275461			−0.137731	−	0.990470i	$-0.543981\pi$
$577$	−5.19917e36			−0.275461			−0.137731	+	0.990470i	$0.543981\pi$
$578$	7.09731e36	+	3.24818e36i	0.367340	+	0.168118i
$579$	7.48030e36	−	7.48030e36i	0.378232	−	0.378232i
$580$	−1.06594e36	−	1.23419e36i	−0.0526566	−	0.0609681i
$581$	−9.37972e35	−	9.37972e35i	−0.0452702	−	0.0452702i
$582$	1.15042e37	−	4.28023e36i	0.542494	−	0.201840i
$583$		−	5.22356e36i		−	0.240680i
$584$	−1.95444e37	+	5.68724e36i	−0.879931	+	0.256052i
$585$		−	9.70546e36i		−	0.426984i
$586$	7.75946e36	+	2.08555e37i	0.333591	+	0.896607i
$587$	−1.06501e37	−	1.06501e37i	−0.447445	−	0.447445i	0.447059	−	0.894504i	$-0.352471\pi$
$587$	−1.06501e37	−	1.06501e37i	−0.447445	−	0.447445i	−0.894504	+	0.447059i	$0.852471\pi$
$588$	6.53890e36	+	4.78311e35i	0.268479	+	0.0196389i
$589$	−1.18637e37	+	1.18637e37i	−0.476063	+	0.476063i
$590$	5.02883e36	−	1.09881e37i	0.197226	−	0.430942i
$591$	−2.22751e35			−0.00853862
$592$	−1.24473e37	+	9.25522e36i	−0.466372	+	0.346772i
$593$	−2.41135e37			−0.883124			−0.441562	−	0.897231i	$-0.645575\pi$
$593$	−2.41135e37			−0.883124			−0.441562	+	0.897231i	$0.645575\pi$
$594$	3.31653e36	−	7.24667e36i	0.118732	−	0.259431i
$595$	3.13594e36	−	3.13594e36i	0.109746	−	0.109746i
$596$	3.71648e36	−	5.08072e37i	0.127147	−	1.73821i
$597$	7.70178e35	+	7.70178e35i	0.0257595	+	0.0257595i
$598$	2.72397e36	+	7.32134e36i	0.0890711	+	0.239400i
$599$			3.52491e37i			1.12690i	0.826150	+	0.563451i	$0.190526\pi$
$599$			3.52491e37i			1.12690i	−0.826150	+	0.563451i	$0.809474\pi$
$600$	−6.60110e36	+	1.20195e37i	−0.206336	+	0.375704i
$601$		−	1.78179e37i		−	0.544566i	−0.962217	−	0.272283i	$-0.912221\pi$
$601$		−	1.78179e37i		−	0.544566i	0.962217	−	0.272283i	$-0.0877787\pi$
$602$	6.28616e36	−	2.33882e36i	0.187859	−	0.0698947i
$603$	−7.37877e36	−	7.37877e36i	−0.215625	−	0.215625i
$604$	−1.36212e37	+	1.17643e37i	−0.389240	+	0.336177i
$605$	−6.85597e36	+	6.85597e36i	−0.191589	+	0.191589i
$606$	7.76040e36	+	3.55165e36i	0.212082	+	0.0970622i
$607$	−1.62219e37			−0.433566			−0.216783	−	0.976220i	$-0.569556\pi$
$607$	−1.62219e37			−0.433566			−0.216783	+	0.976220i	$0.569556\pi$
$608$	6.41146e36	+	3.00581e37i	0.167594	+	0.785712i
$609$	−3.19441e36			−0.0816690
$610$	1.31992e37	+	6.04079e36i	0.330062	+	0.151057i
$611$	9.98329e37	−	9.98329e37i	2.44184	−	2.44184i
$612$	1.89571e37	−	1.63728e37i	0.453553	−	0.391722i
$613$	7.36746e36	+	7.36746e36i	0.172426	+	0.172426i	0.788044	−	0.615619i	$-0.211094\pi$
$613$	7.36746e36	+	7.36746e36i	0.172426	+	0.172426i	−0.615619	+	0.788044i	$0.711094\pi$
$614$	−3.98683e37	+	1.48334e37i	−0.912757	+	0.339600i
$615$		−	1.20114e37i		−	0.269018i
$616$	−8.91700e36	−	4.89720e36i	−0.195380	−	0.107302i
$617$		−	5.22189e37i		−	1.11938i	−0.828702	−	0.559691i	$-0.810920\pi$
$617$		−	5.22189e37i		−	1.11938i	0.828702	−	0.559691i	$-0.189080\pi$
$618$	1.38433e37	+	3.72072e37i	0.290331	+	0.780337i
$619$	6.92342e36	+	6.92342e36i	0.142068	+	0.142068i	0.774564	−	0.632496i	$-0.217969\pi$
$619$	6.92342e36	+	6.92342e36i	0.142068	+	0.142068i	−0.632496	+	0.774564i	$0.717969\pi$
$620$	9.32583e35	−	1.27492e37i	0.0187241	−	0.255973i
$621$	4.30100e36	−	4.30100e36i	0.0844953	−	0.0844953i
$622$	−3.52841e37	+	7.70962e37i	−0.678280	+	1.48205i
$623$	−8.13329e36			−0.152995
$624$	4.56571e37	+	6.71544e36i	0.840459	+	0.123618i
$625$	−4.03789e37			−0.727402
$626$	−1.85163e37	+	4.04584e37i	−0.326438	+	0.713271i
$627$	−5.28846e36	+	5.28846e36i	−0.0912468	+	0.0912468i
$628$	5.77318e37	+	4.22300e36i	0.974899	+	0.0713125i
$629$	−1.91954e37	−	1.91954e37i	−0.317259	−	0.317259i
$630$	3.36390e36	+	9.04131e36i	0.0544184	+	0.146263i
$631$			1.11321e38i			1.76271i	0.472457	+	0.881354i	$0.343367\pi$
$631$			1.11321e38i			1.76271i	−0.472457	+	0.881354i	$0.656633\pi$
$632$	9.89750e36	+	3.40131e37i	0.153407	+	0.527188i
$633$		−	2.49786e37i		−	0.378982i
$634$	−1.08070e37	+	4.02085e36i	−0.160510	+	0.0597190i
$635$	1.12009e37	+	1.12009e37i	0.162858	+	0.162858i
$636$	−1.53945e37	−	1.78244e37i	−0.219126	−	0.253714i
$637$	5.18652e37	−	5.18652e37i	0.722759	−	0.722759i
$638$	−5.95317e36	−	2.72454e36i	−0.0812211	−	0.0371719i
$639$	1.46905e37			0.196235
$640$	−1.86663e37	−	1.41392e37i	−0.244134	−	0.184924i
$641$	−1.21263e38			−1.55291			−0.776455	−	0.630172i	$-0.782984\pi$
$641$	−1.21263e38			−1.55291			−0.776455	+	0.630172i	$0.782984\pi$
$642$	1.91635e37	+	8.77043e36i	0.240299	+	0.109976i
$643$	9.56672e37	−	9.56672e37i	1.17467	−	1.17467i	0.193584	−	0.981084i	$-0.437989\pi$
$643$	9.56672e37	−	9.56672e37i	1.17467	−	1.17467i	0.981084	−	0.193584i	$-0.0620110\pi$
$644$	−5.07514e36	−	5.87621e36i	−0.0610223	−	0.0706542i
$645$	2.65651e36	+	2.65651e36i	0.0312791	+	0.0312791i
$646$	−5.04128e37	+	1.87565e37i	−0.581302	+	0.216279i
$647$		−	1.18513e37i		−	0.133831i	−0.997759	−	0.0669155i	$-0.978684\pi$
$647$		−	1.18513e37i		−	0.133831i	0.997759	−	0.0669155i	$-0.0213158\pi$
$648$	9.57140e36	+	3.28924e37i	0.105855	+	0.363775i
$649$		−	4.85137e37i		−	0.525485i
$650$	5.34953e37	+	1.43782e38i	0.567525	+	1.52536i
$651$	−1.77060e37	−	1.77060e37i	−0.183983	−	0.183983i
$652$	1.31704e38	+	9.63400e36i	1.34047	+	0.0980537i
$653$	−8.10621e37	+	8.10621e37i	−0.808146	+	0.808146i	−0.984353	−	0.176207i	$-0.943617\pi$
$653$	−8.10621e37	+	8.10621e37i	−0.808146	+	0.808146i	0.176207	+	0.984353i	$0.443617\pi$
$654$	7.48498e35	−	1.63548e36i	0.00730955	−	0.0159715i
$655$	−1.86067e37			−0.177996
$656$	−1.96053e38	−	2.88364e37i	−1.83727	−	0.270233i
$657$	7.74896e37			0.711395
$658$	−5.83993e37	+	1.27603e38i	−0.525240	+	1.14766i
$659$	−2.91777e37	+	2.91777e37i	−0.257097	+	0.257097i	−0.823873	−	0.566775i	$-0.808191\pi$
$659$	−2.91777e37	+	2.91777e37i	−0.257097	+	0.257097i	0.566775	+	0.823873i	$0.308191\pi$
$660$	4.15715e35	−	5.68316e36i	0.00358883	−	0.0490622i
$661$	5.80866e37	+	5.80866e37i	0.491311	+	0.491311i	0.908719	−	0.417408i	$-0.137061\pi$
$661$	5.80866e37	+	5.80866e37i	0.491311	+	0.491311i	−0.417408	+	0.908719i	$0.637061\pi$
$662$	−3.55997e37	−	9.56830e37i	−0.295028	−	0.792961i
$663$			8.07655e37i			0.655833i
$664$	−1.07443e37	−	5.90075e36i	−0.0854888	−	0.0469502i
$665$		−	2.07153e37i		−	0.161510i
$666$	5.53429e37	−	2.05908e37i	0.422824	−	0.157316i
$667$	−3.53328e36	−	3.53328e36i	−0.0264533	−	0.0264533i
$668$	1.22246e38	−	1.05581e38i	0.896916	−	0.774644i
$669$	−3.69123e37	+	3.69123e37i	−0.265411	+	0.265411i
$670$	−1.55244e37	−	7.10496e36i	−0.109397	−	0.0500670i
$671$	5.82762e37			0.402473
$672$	−4.48603e37	+	9.56880e36i	−0.303653	+	0.0647697i
$673$	−2.36921e38			−1.57181			−0.785906	−	0.618345i	$-0.787803\pi$
$673$	−2.36921e38			−1.57181			−0.785906	+	0.618345i	$0.787803\pi$
$674$	1.60125e38	+	7.32832e37i	1.04124	+	0.476536i
$675$	8.44660e37	−	8.44660e37i	0.538370	−	0.538370i
$676$	2.69589e38	−	2.32837e38i	1.68431	−	1.45470i
$677$	1.15968e38	+	1.15968e38i	0.710216	+	0.710216i	0.966580	−	0.256364i	$-0.0825246\pi$
$677$	1.15968e38	+	1.15968e38i	0.710216	+	0.710216i	−0.256364	+	0.966580i	$0.582525\pi$
$678$	−5.22884e37	+	1.94544e37i	−0.313910	+	0.116793i
$679$			1.36491e38i			0.803269i
$680$	1.97281e37	−	3.59216e37i	0.113819	−	0.207246i
$681$		−	8.47872e37i		−	0.479562i
$682$	−1.78957e37	−	4.80990e37i	−0.0992336	−	0.266715i
$683$	1.90359e38	+	1.90359e38i	1.03489	+	1.03489i	0.999369	+	0.0355186i	$0.0113083\pi$
$683$	1.90359e38	+	1.90359e38i	1.03489	+	1.03489i	0.0355186	+	0.999369i	$0.488692\pi$
$684$	8.53576e36	−	1.16691e38i	0.0454972	−	0.621983i
$685$	5.68424e37	−	5.68424e37i	0.297064	−	0.297064i
$686$	−8.36489e37	+	1.82774e38i	−0.428632	+	0.936566i
$687$	−7.56764e37			−0.380228
$688$	4.97377e37	−	3.69825e37i	0.245043	−	0.182202i
$689$	−2.63485e38			−1.27291
$690$	1.80988e36	−	3.95462e36i	0.00857409	−	0.0187345i
$691$	2.69028e38	−	2.69028e38i	1.24981	−	1.24981i	0.294005	−	0.955804i	$-0.405012\pi$
$691$	2.69028e38	−	2.69028e38i	1.24981	−	1.24981i	0.955804	−	0.294005i	$-0.0949884\pi$
$692$	−1.37506e38	−	1.00583e37i	−0.626453	−	0.0458241i
$693$	2.73853e37	+	2.73853e37i	0.122354	+	0.122354i
$694$	−1.08686e38	−	2.92119e38i	−0.476233	−	1.27999i
$695$			1.13145e38i			0.486227i
$696$	−2.83437e37	+	8.24775e36i	−0.119462	+	0.0347625i
$697$		−	3.46811e38i		−	1.43367i
$698$	−1.28480e38	+	4.78020e37i	−0.520938	+	0.193820i
$699$	6.47492e37	+	6.47492e37i	0.257509	+	0.257509i
$700$	−9.96691e37	−	1.15401e38i	−0.388810	−	0.450181i
$701$	−2.63674e38	+	2.63674e38i	−1.00896	+	1.00896i	−0.00899988	+	0.999960i	$0.502865\pi$
$701$	−2.63674e38	+	2.63674e38i	−1.00896	+	1.00896i	−0.999960	+	0.00899988i	$0.997135\pi$
$702$	−3.65535e38	−	1.67292e38i	−1.37208	−	0.627948i
$703$	−1.26801e38			−0.466901
$704$	−9.17638e37	−	2.04292e37i	−0.331467	−	0.0737939i
$705$	−7.86040e37			−0.278543
$706$	2.76624e38	+	1.26601e38i	0.961671	+	0.440121i
$707$	−6.71057e37	+	6.71057e37i	−0.228874	+	0.228874i
$708$	−1.42976e38	−	1.65544e38i	−0.478426	−	0.553942i
$709$	3.05283e38	+	3.05283e38i	1.00226	+	1.00226i	0.999997	+	0.00225916i	$0.000719114\pi$
$709$	3.05283e38	+	3.05283e38i	1.00226	+	1.00226i	0.00225916	+	0.999997i	$0.499281\pi$
$710$	2.25266e37	−	8.38124e36i	0.0725619	−	0.0269973i
$711$		−	1.34855e38i		−	0.426214i
$712$	−7.21658e37	+	2.09996e37i	−0.223796	+	0.0651225i
$713$		−	3.91687e37i		−	0.119187i
$714$	−2.79932e37	−	7.52387e37i	−0.0835848	−	0.224655i
$715$	−4.50776e37	−	4.50776e37i	−0.132078	−	0.132078i
$716$	−3.96527e37	−	2.90054e36i	−0.114011	−	0.00833974i
$717$	6.57796e37	−	6.57796e37i	0.185602	−	0.185602i
$718$	2.22290e38	−	4.85706e38i	0.615516	−	1.34491i
$719$	−3.91734e38			−1.06451			−0.532257	−	0.846583i	$-0.678656\pi$
$719$	−3.91734e38			−1.06451			−0.532257	+	0.846583i	$0.678656\pi$
$720$	5.31916e37	+	7.15372e37i	0.141858	+	0.190785i
$721$	−4.41443e38			−1.15544
$722$	5.74385e37	−	1.25504e38i	0.147554	−	0.322407i
$723$	1.74485e37	−	1.74485e37i	0.0439937	−	0.0439937i
$724$	3.39558e37	−	4.64203e38i	0.0840317	−	1.14878i
$725$	−6.93891e37	−	6.93891e37i	−0.168550	−	0.168550i
$726$	6.12004e37	+	1.64491e38i	0.145918	+	0.392191i
$727$			6.41466e38i			1.50127i	0.660716	+	0.750636i	$0.270253\pi$
$727$			6.41466e38i			1.50127i	−0.660716	+	0.750636i	$0.729747\pi$
$728$	−2.47023e38	+	4.49790e38i	−0.567498	+	1.03332i
$729$			4.58082e37i			0.103305i
$730$	1.18824e38	−	4.42094e37i	0.263053	−	0.0978714i
$731$	7.67023e37	+	7.67023e37i	0.166695	+	0.166695i
$732$	1.98857e38	−	1.71748e38i	0.424268	−	0.366430i
$733$	5.67874e38	−	5.67874e38i	1.18946	−	1.18946i	0.212237	−	0.977218i	$-0.431925\pi$
$733$	5.67874e38	−	5.67874e38i	1.18946	−	1.18946i	0.977218	−	0.212237i	$-0.0680750\pi$
$734$	−8.50920e38	−	3.89435e38i	−1.74981	−	0.800826i
$735$	−4.08363e37			−0.0824456
$736$	−6.02031e37	−	3.90353e37i	−0.119335	−	0.0773762i
$737$	−6.85423e37			−0.133397
$738$	6.85960e38	+	3.13939e38i	1.31080	+	0.599907i
$739$	4.37292e38	−	4.37292e38i	0.820486	−	0.820486i	−0.165692	−	0.986178i	$-0.552986\pi$
$739$	4.37292e38	−	4.37292e38i	0.820486	−	0.820486i	0.986178	+	0.165692i	$0.0529856\pi$
$740$	7.31160e37	−	6.31484e37i	0.134705	−	0.116341i
$741$	2.66759e38	+	2.66759e38i	0.482585	+	0.482585i
$742$	2.45455e38	−	9.13237e37i	0.436033

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-10534.4 - 4821.21i) q^{2} +(923601. - 923601. i) q^{3} +(8.77296e7 + 1.01577e8i) q^{4} +(-5.91123e8 - 5.91123e8i) q^{5} +(-1.41825e10 + 5.27671e9i) q^{6} -1.68267e11i q^{7} +(-4.34455e11 - 1.49302e12i) q^{8} +5.91952e12i q^{9} +O(q^{10})\)	\(q+(-10534.4 - 4821.21i) q^{2} +(923601. - 923601. i) q^{3} +(8.77296e7 + 1.01577e8i) q^{4} +(-5.91123e8 - 5.91123e8i) q^{5} +(-1.41825e10 + 5.27671e9i) q^{6} -1.68267e11i q^{7} +(-4.34455e11 - 1.49302e12i) q^{8} +5.91952e12i q^{9} +(3.37720e12 + 9.07706e12i) q^{10} +(2.74936e13 + 2.74936e13i) q^{11} +(1.74844e14 + 1.27896e13i) q^{12} +(1.38682e15 - 1.38682e15i) q^{13} +(-8.11252e14 + 1.77260e15i) q^{14} -1.09192e15 q^{15} +(-2.62143e15 + 1.78226e16i) q^{16} -3.15275e16 q^{17} +(2.85392e16 - 6.23586e16i) q^{18} +(-1.04132e17 + 1.04132e17i) q^{19} +(8.18560e15 - 1.11904e17i) q^{20} +(-1.55412e17 - 1.55412e17i) q^{21} +(-1.57076e17 - 4.22181e17i) q^{22} -3.43797e17i q^{23} +(-1.78022e18 - 9.77690e17i) q^{24} -6.75173e18i q^{25} +(-2.12955e19 + 7.92320e18i) q^{26} +(1.25103e19 + 1.25103e19i) q^{27} +(1.70921e19 - 1.47620e19i) q^{28} +(1.02772e19 - 1.02772e19i) q^{29} +(1.15028e19 + 5.26440e18i) q^{30} +1.13930e20 q^{31} +(1.13542e20 - 1.75112e20i) q^{32} +5.07862e19 q^{33} +(3.32124e20 + 1.52001e20i) q^{34} +(-9.94667e19 + 9.94667e19i) q^{35} +(-6.01288e20 + 5.19317e20i) q^{36} +(6.08847e20 + 6.08847e20i) q^{37} +(1.59901e21 - 5.94926e20i) q^{38} -2.56175e21i q^{39} +(-6.25741e20 + 1.13937e21i) q^{40} +1.10002e22i q^{41} +(8.87898e20 + 2.38644e21i) q^{42} +(-2.43287e21 - 2.43287e21i) q^{43} +(-3.80718e20 + 5.20472e21i) q^{44} +(3.49917e21 - 3.49917e21i) q^{45} +(-1.65752e21 + 3.62169e21i) q^{46} +7.19867e22 q^{47} +(1.40399e22 + 1.88822e22i) q^{48} +3.73985e22 q^{49} +(-3.25515e22 + 7.11254e22i) q^{50} +(-2.91189e22 + 2.91189e22i) q^{51} +(2.62535e23 + 1.92041e22i) q^{52} +(-9.49959e22 - 9.49959e22i) q^{53} +(-7.14737e22 - 1.92103e23i) q^{54} -3.25042e22i q^{55} +(-2.51226e23 + 7.31045e22i) q^{56} +1.92353e23i q^{57} +(-1.57813e23 + 5.87159e22i) q^{58} +(-8.82273e23 - 8.82273e23i) q^{59} +(-9.57941e22 - 1.10915e23i) q^{60} +(1.05981e24 - 1.05981e24i) q^{61} +(-1.20018e24 - 5.49279e23i) q^{62} +9.96061e23 q^{63} +(-2.04035e24 + 1.29730e24i) q^{64} -1.63957e24 q^{65} +(-5.35002e23 - 2.44851e23i) q^{66} +(-1.24651e24 + 1.24651e24i) q^{67} +(-2.76590e24 - 3.20248e24i) q^{68} +(-3.17531e23 - 3.17531e23i) q^{69} +(1.52737e24 - 5.68273e23i) q^{70} -2.48171e24i q^{71} +(8.83794e24 - 2.57176e24i) q^{72} -1.30905e25i q^{73} +(-3.47846e24 - 9.34922e24i) q^{74} +(-6.23590e24 - 6.23590e24i) q^{75} +(-1.97129e25 - 1.44197e24i) q^{76} +(4.62627e24 - 4.62627e24i) q^{77} +(-1.23507e25 + 2.69865e25i) q^{78} -2.27814e25 q^{79} +(1.20850e25 - 8.98579e24i) q^{80} -2.20308e25 q^{81} +(5.30345e25 - 1.15881e26i) q^{82} +(5.57430e24 - 5.57430e24i) q^{83} +(2.15207e24 - 2.94205e25i) q^{84} +(1.86367e25 + 1.86367e25i) q^{85} +(1.38994e25 + 3.73582e25i) q^{86} -1.89842e25i q^{87} +(2.91037e25 - 5.29931e25i) q^{88} -4.83355e25i q^{89} +(-5.37318e25 + 1.99914e25i) q^{90} +(-2.33357e26 - 2.33357e26i) q^{91} +(3.49219e25 - 3.01612e25i) q^{92} +(1.05226e26 - 1.05226e26i) q^{93} +(-7.58337e26 - 3.47063e26i) q^{94} +1.23110e26 q^{95} +(-5.68667e25 - 2.66602e26i) q^{96} -8.11154e26 q^{97} +(-3.93971e26 - 1.80306e26i) q^{98} +(-1.62749e26 + 1.62749e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8}+O(q^{10}) \) 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) 106 * q - 2 * q^2 - 2 * q^3 + 125095688 * q^4 - 2 * q^5 - 59499919472 * q^6 - 287180933804 * q^8 + 8247210235372 * q^10 - 34039821810222 * q^11 + 1748989708884580 * q^12 - 2 * q^13 - 7155218316814660 * q^14 - 15569560546875004 * q^15 - 11277270898466024 * q^16 - 4 * q^17 - 142926567667036386 * q^18 - 361273435637780378 * q^19 + 442470438134323004 * q^20 + 15251194969972 * q^21 - 1169169681057307068 * q^22 + 10984755246449911984 * q^24 + 17037255844415508360 * q^26 - 16968259081125930056 * q^27 - 60190300783057535720 * q^28 - 27121773564864273802 * q^29 - 676957577616991436364 * q^30 + 293010555569340511088 * q^31 - 1166901104384201893432 * q^32 - 4 * q^33 - 290590654320714186380 * q^34 - 1483431258098321642404 * q^35 + 2272823118258680645548 * q^36 - 470486119578222882250 * q^37 - 7667804020978176078752 * q^38 - 13361029860556314821176 * q^40 - 46808273599641292573640 * q^42 + 30832447383975033909242 * q^43 + 78151525061974584923236 * q^44 + 14901145942652686274 * q^45 - 30741189488837489213204 * q^46 - 109219994122411663546544 * q^47 - 189351174993879449193752 * q^48 - 882423151738888904731010 * q^49 + 548328807383867462419206 * q^50 - 115559869623218432212572 * q^51 - 870962460180776269413356 * q^52 - 5971340109916911897018 * q^53 + 1136059014139929162305056 * q^54 + 1200724087407057566405656 * q^56 - 2828993593282901350448872 * q^58 - 34394779779101149275670 * q^59 + 7255680995179605171006528 * q^60 - 2475467954128860415560434 * q^61 - 3746979776437258967395280 * q^62 + 5188426743337460248956228 * q^63 - 998638142638832585325568 * q^64 + 2911521903927484929681108 * q^65 + 19080130794608880088211092 * q^66 + 19927279436319849143450902 * q^67 - 8373829219145321982498160 * q^68 - 11740592568211854067772156 * q^69 - 5132370883366275255574400 * q^70 + 19086224804727807421919172 * q^72 + 42828123668533070044258924 * q^74 - 81164500905568543837973834 * q^75 - 105896749199037309084347596 * q^76 + 43639762623313421635882292 * q^77 - 98604570863977418199548932 * q^78 - 27720061020991987308873792 * q^79 - 62182770892870708184304728 * q^80 - 581497370030400596903901694 * q^81 - 341107120874158685100150464 * q^82 + 26201266111333778096099838 * q^83 + 507935364828252675231522472 * q^84 + 224109171520266208496093748 * q^85 - 704077428371873697577134268 * q^86 - 681166827660725136677389832 * q^88 + 482826168478152776777239896 * q^90 + 67827511015091818004015876 * q^91 - 83646902794933560160672648 * q^92 + 886600140227681407873186288 * q^93 - 168289477479668477956229936 * q^94 + 239338208955746404979764980 * q^95 - 752456785864472227742519632 * q^96 - 4 * q^97 - 1043862744854197068838248646 * q^98 + 1641925710538879681648895966 * q^99

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