LMFDB - Embedded newform 16.28.e.a.13.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [16,28,Mod(5,16)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			13.20
Character	$\chi$	$=$	16.13
Dual form			16.28.e.a.5.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4567.90 - 10646.7i) q^{2} +(-1.19622e6 - 1.19622e6i) q^{3} +(-9.24863e7 + 9.72661e7i) q^{4} +(-1.71680e9 + 1.71680e9i) q^{5} +(-7.27159e9 + 1.82001e10i) q^{6} +4.18265e11i q^{7} +(1.45803e12 + 5.40371e11i) q^{8} -4.76369e12i q^{9} +(2.61205e13 + 1.04361e13i) q^{10} +(-1.15090e14 + 1.15090e14i) q^{11} +(2.26986e14 - 5.71770e12i) q^{12} +(1.30631e15 + 1.30631e15i) q^{13} +(4.45313e15 - 1.91059e15i) q^{14} +4.10736e15 q^{15} +(-9.06977e14 - 1.79916e16i) q^{16} +4.40408e16 q^{17} +(-5.07176e16 + 2.17601e16i) q^{18} +(-2.59621e16 - 2.59621e16i) q^{19} +(-8.20596e15 - 3.25767e17i) q^{20} +(5.00338e17 - 5.00338e17i) q^{21} +(1.75104e18 + 6.99606e17i) q^{22} +1.89933e18i q^{23} +(-1.09773e18 - 2.39053e18i) q^{24} +1.55576e18i q^{25} +(7.94080e18 - 1.98750e19i) q^{26} +(-1.48204e19 + 1.48204e19i) q^{27} +(-4.06830e19 - 3.86837e19i) q^{28} +(2.84932e19 + 2.84932e19i) q^{29} +(-1.87620e19 - 4.37298e19i) q^{30} -2.18343e19 q^{31} +(-1.87407e20 + 9.18399e19i) q^{32} +2.75346e20 q^{33} +(-2.01174e20 - 4.68888e20i) q^{34} +(-7.18078e20 - 7.18078e20i) q^{35} +(4.63346e20 + 4.40576e20i) q^{36} +(1.66700e20 - 1.66700e20i) q^{37} +(-1.57818e20 + 3.95002e20i) q^{38} -3.12528e21i q^{39} +(-3.43086e21 + 1.57544e21i) q^{40} +7.02406e21i q^{41} +(-7.61244e21 - 3.04145e21i) q^{42} +(7.90701e21 - 7.90701e21i) q^{43} +(-5.50105e20 - 2.18385e22i) q^{44} +(8.17832e21 + 8.17832e21i) q^{45} +(2.02216e22 - 8.67594e21i) q^{46} -1.97489e22 q^{47} +(-2.04370e22 + 2.26069e22i) q^{48} -1.09233e23 q^{49} +(1.65637e22 - 7.10655e21i) q^{50} +(-5.26826e22 - 5.26826e22i) q^{51} +(-2.47876e23 + 6.24390e21i) q^{52} +(1.95000e23 - 1.95000e23i) q^{53} +(2.25486e23 + 9.00899e22i) q^{54} -3.95173e23i q^{55} +(-2.26018e23 + 6.09842e23i) q^{56} +6.21129e22i q^{57} +(1.73204e23 - 4.33512e23i) q^{58} +(1.10914e22 - 1.10914e22i) q^{59} +(-3.79875e23 + 3.99507e23i) q^{60} +(1.44870e24 + 1.44870e24i) q^{61} +(9.97372e22 + 2.32464e23i) q^{62} +1.99248e24 q^{63} +(1.83385e24 + 1.57575e24i) q^{64} -4.48536e24 q^{65} +(-1.25775e24 - 2.93152e24i) q^{66} +(4.20584e24 + 4.20584e24i) q^{67} +(-4.07316e24 + 4.28367e24i) q^{68} +(2.27202e24 - 2.27202e24i) q^{69} +(-4.36504e24 + 1.09253e25i) q^{70} +1.80821e25i q^{71} +(2.57416e24 - 6.94561e24i) q^{72} +2.74303e24i q^{73} +(-2.53628e24 - 1.01334e24i) q^{74} +(1.86103e24 - 1.86103e24i) q^{75} +(4.92636e24 - 1.24093e23i) q^{76} +(-4.81380e25 - 4.81380e25i) q^{77} +(-3.32739e25 + 1.42760e25i) q^{78} -1.31583e25 q^{79} +(3.24450e25 + 2.93308e25i) q^{80} -8.69063e23 q^{81} +(7.47830e25 - 3.20852e25i) q^{82} +(9.23513e24 + 9.23513e24i) q^{83} +(2.39151e24 + 9.49403e25i) q^{84} +(-7.56093e25 + 7.56093e25i) q^{85} +(-1.20302e26 - 4.80650e25i) q^{86} -6.81685e25i q^{87} +(-2.29995e26 + 1.05613e26i) q^{88} +3.89739e26i q^{89} +(4.97143e25 - 1.24430e26i) q^{90} +(-5.46384e26 + 5.46384e26i) q^{91} +(-1.84740e26 - 1.75662e26i) q^{92} +(2.61188e25 + 2.61188e25i) q^{93} +(9.02108e25 + 2.10260e26i) q^{94} +8.91435e25 q^{95} +(3.34042e26 + 1.14320e26i) q^{96} +7.54323e26 q^{97} +(4.98965e26 + 1.16297e27i) q^{98} +(5.48252e26 + 5.48252e26i) 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} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12} - 2 q^{13} - 71\!\cdots\!60 q^{14} - 15\!\cdots\!04 q^{15}+ \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

Character values

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

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−4567.90	−	10646.7i	−0.394286	−	0.918988i
$2$	−4567.90	−	10646.7i	−0.394286	−	0.918988i
$3$	−1.19622e6	−	1.19622e6i	−0.433187	−	0.433187i	0.456524	−	0.889711i	$-0.349094\pi$
$3$	−1.19622e6	−	1.19622e6i	−0.433187	−	0.433187i	−0.889711	+	0.456524i	$0.849094\pi$
$4$	−9.24863e7	+	9.72661e7i	−0.689076	+	0.724689i
$5$	−1.71680e9	+	1.71680e9i	−0.628963	+	0.628963i	−0.947807	−	0.318844i	$-0.896705\pi$
$5$	−1.71680e9	+	1.71680e9i	−0.628963	+	0.628963i	0.318844	+	0.947807i	$0.396705\pi$
$6$	−7.27159e9	+	1.82001e10i	−0.227294	+	0.568893i
$7$			4.18265e11i			1.63165i	0.578297	+	0.815826i	$0.303717\pi$
$7$			4.18265e11i			1.63165i	−0.578297	+	0.815826i	$0.696283\pi$
$8$	1.45803e12	+	5.40371e11i	0.937673	+	0.347518i
$9$		−	4.76369e12i		−	0.624698i
$10$	2.61205e13	+	1.04361e13i	0.826001	+	0.330018i
$11$	−1.15090e14	+	1.15090e14i	−1.00516	+	1.00516i	−0.00517337	+	0.999987i	$0.501647\pi$
$11$	−1.15090e14	+	1.15090e14i	−1.00516	+	1.00516i	−0.999987	+	0.00517337i	$0.998353\pi$
$12$	2.26986e14	−	5.71770e12i	0.612425	−	0.0154268i
$13$	1.30631e15	+	1.30631e15i	1.19622	+	1.19622i	0.975289	+	0.220933i	$0.0709102\pi$
$13$	1.30631e15	+	1.30631e15i	1.19622	+	1.19622i	0.220933	+	0.975289i	$0.429090\pi$
$14$	4.45313e15	−	1.91059e15i	1.49947	−	0.643338i
$15$	4.10736e15			0.544918
$16$	−9.06977e14	−	1.79916e16i	−0.0503473	−	0.998732i
$17$	4.40408e16			1.07844			0.539218	−	0.842166i	$-0.318720\pi$
$17$	4.40408e16			1.07844			0.539218	+	0.842166i	$0.318720\pi$
$18$	−5.07176e16	+	2.17601e16i	−0.574090	+	0.246310i
$19$	−2.59621e16	−	2.59621e16i	−0.141633	−	0.141633i	0.632735	−	0.774368i	$-0.281932\pi$
$19$	−2.59621e16	−	2.59621e16i	−0.141633	−	0.141633i	−0.774368	+	0.632735i	$0.781932\pi$
$20$	−8.20596e15	−	3.25767e17i	−0.0223988	−	0.889206i
$21$	5.00338e17	−	5.00338e17i	0.706811	−	0.706811i
$22$	1.75104e18	+	6.99606e17i	1.32005	+	0.527409i
$23$			1.89933e18i			0.785731i	0.919596	+	0.392866i	$0.128516\pi$
$23$			1.89933e18i			0.785731i	−0.919596	+	0.392866i	$0.871484\pi$
$24$	−1.09773e18	−	2.39053e18i	−0.255648	−	0.556728i
$25$			1.55576e18i			0.208810i
$26$	7.94080e18	−	1.98750e19i	0.627659	−	1.57097i
$27$	−1.48204e19	+	1.48204e19i	−0.703798	+	0.703798i
$28$	−4.06830e19	−	3.86837e19i	−1.18244	−	1.12433i
$29$	2.84932e19	+	2.84932e19i	0.515666	+	0.515666i	0.916257	−	0.400591i	$-0.131195\pi$
$29$	2.84932e19	+	2.84932e19i	0.515666	+	0.515666i	−0.400591	+	0.916257i	$0.631195\pi$
$30$	−1.87620e19	−	4.37298e19i	−0.214854	−	0.500773i
$31$	−2.18343e19			−0.160604			−0.0803022	−	0.996771i	$-0.525589\pi$
$31$	−2.18343e19			−0.160604			−0.0803022	+	0.996771i	$0.525589\pi$
$32$	−1.87407e20	+	9.18399e19i	−0.897971	+	0.440055i
$33$	2.75346e20			0.870845
$34$	−2.01174e20	−	4.68888e20i	−0.425213	−	0.991069i
$35$	−7.18078e20	−	7.18078e20i	−1.02625	−	1.02625i
$36$	4.63346e20	+	4.40576e20i	0.452711	+	0.430465i
$37$	1.66700e20	−	1.66700e20i	0.112516	−	0.112516i	−0.648607	−	0.761123i	$-0.724648\pi$
$37$	1.66700e20	−	1.66700e20i	0.112516	−	0.112516i	0.761123	+	0.648607i	$0.224648\pi$
$38$	−1.57818e20	+	3.95002e20i	−0.0743152	+	0.186003i
$39$		−	3.12528e21i		−	1.03638i
$40$	−3.43086e21	+	1.57544e21i	−0.808338	+	0.371186i
$41$			7.02406e21i			1.18579i	0.805281	+	0.592893i	$0.202014\pi$
$41$			7.02406e21i			1.18579i	−0.805281	+	0.592893i	$0.797986\pi$
$42$	−7.61244e21	−	3.04145e21i	−0.928236	−	0.370864i
$43$	7.90701e21	−	7.90701e21i	0.701759	−	0.701759i	−0.263029	−	0.964788i	$-0.584721\pi$
$43$	7.90701e21	−	7.90701e21i	0.701759	−	0.701759i	0.964788	+	0.263029i	$0.0847214\pi$
$44$	−5.50105e20	−	2.18385e22i	−0.0357960	−	1.42106i
$45$	8.17832e21	+	8.17832e21i	0.392912	+	0.392912i
$46$	2.02216e22	−	8.67594e21i	0.722077	−	0.309803i
$47$	−1.97489e22			−0.527498			−0.263749	−	0.964591i	$-0.584959\pi$
$47$	−1.97489e22			−0.527498			−0.263749	+	0.964591i	$0.584959\pi$
$48$	−2.04370e22	+	2.26069e22i	−0.410828	+	0.454448i
$49$	−1.09233e23			−1.66229
$50$	1.65637e22	−	7.10655e21i	0.191894	−	0.0823310i
$51$	−5.26826e22	−	5.26826e22i	−0.467164	−	0.467164i
$52$	−2.47876e23	+	6.24390e21i	−1.69118	+	0.0426001i
$53$	1.95000e23	−	1.95000e23i	1.02875	−	1.02875i	0.0291795	−	0.999574i	$-0.490711\pi$
$53$	1.95000e23	−	1.95000e23i	1.02875	−	1.02875i	0.999574	−	0.0291795i	$-0.00928944\pi$
$54$	2.25486e23	+	9.00899e22i	0.924280	+	0.369284i
$55$		−	3.95173e23i		−	1.26442i
$56$	−2.26018e23	+	6.09842e23i	−0.567028	+	1.52996i
$57$			6.21129e22i			0.122708i
$58$	1.73204e23	−	4.33512e23i	0.270570	−	0.677210i
$59$	1.10914e22	−	1.10914e22i	0.0137558	−	0.0137558i	−0.700195	−	0.713951i	$-0.746904\pi$
$59$	1.10914e22	−	1.10914e22i	0.0137558	−	0.0137558i	0.713951	+	0.700195i	$0.246904\pi$
$60$	−3.79875e23	+	3.99507e23i	−0.375490	+	0.394896i
$61$	1.44870e24	+	1.44870e24i	1.14558	+	1.14558i	0.987412	+	0.158172i	$0.0505601\pi$
$61$	1.44870e24	+	1.44870e24i	1.14558	+	1.14558i	0.158172	+	0.987412i	$0.449440\pi$
$62$	9.97372e22	+	2.32464e23i	0.0633241	+	0.147593i
$63$	1.99248e24			1.01929
$64$	1.83385e24	+	1.57575e24i	0.758463	+	0.651716i
$65$	−4.48536e24			−1.50476
$66$	−1.25775e24	−	2.93152e24i	−0.343362	−	0.800295i
$67$	4.20584e24	+	4.20584e24i	0.937222	+	0.937222i	0.998143	−	0.0609202i	$-0.0194035\pi$
$67$	4.20584e24	+	4.20584e24i	0.937222	+	0.937222i	−0.0609202	+	0.998143i	$0.519404\pi$
$68$	−4.07316e24	+	4.28367e24i	−0.743125	+	0.781530i
$69$	2.27202e24	−	2.27202e24i	0.340369	−	0.340369i
$70$	−4.36504e24	+	1.09253e25i	−0.538474	+	1.34775i
$71$			1.80821e25i			1.84187i	0.389711	+	0.920937i	$0.372575\pi$
$71$			1.80821e25i			1.84187i	−0.389711	+	0.920937i	$0.627425\pi$
$72$	2.57416e24	−	6.94561e24i	0.217094	−	0.585763i
$73$			2.74303e24i			0.192031i	0.995380	+	0.0960157i	$0.0306099\pi$
$73$			2.74303e24i			0.192031i	−0.995380	+	0.0960157i	$0.969390\pi$
$74$	−2.53628e24	−	1.01334e24i	−0.147764	−	0.0590372i
$75$	1.86103e24	−	1.86103e24i	0.0904539	−	0.0904539i
$76$	4.92636e24	−	1.24093e23i	0.200236	−	0.00504388i
$77$	−4.81380e25	−	4.81380e25i	−1.64007	−	1.64007i
$78$	−3.32739e25	+	1.42760e25i	−0.952417	+	0.408629i
$79$	−1.31583e25			−0.317127			−0.158563	−	0.987349i	$-0.550686\pi$
$79$	−1.31583e25			−0.317127			−0.158563	+	0.987349i	$0.550686\pi$
$80$	3.24450e25	+	2.93308e25i	0.659832	+	0.596499i
$81$	−8.69063e23			−0.0149453
$82$	7.47830e25	−	3.20852e25i	1.08972	−	0.467539i
$83$	9.23513e24	+	9.23513e24i	0.114259	+	0.114259i	0.761924	−	0.647666i	$-0.224255\pi$
$83$	9.23513e24	+	9.23513e24i	0.114259	+	0.114259i	−0.647666	+	0.761924i	$0.724255\pi$
$84$	2.39151e24	+	9.49403e25i	0.0251711	+	0.999264i
$85$	−7.56093e25	+	7.56093e25i	−0.678297	+	0.678297i
$86$	−1.20302e26	−	4.80650e25i	−0.921602	−	0.368214i
$87$		−	6.81685e25i		−	0.446760i
$88$	−2.29995e26	+	1.05613e26i	−1.29182	+	0.593201i
$89$			3.89739e26i			1.87935i	0.342065	+	0.939676i	$0.388874\pi$
$89$			3.89739e26i			1.87935i	−0.342065	+	0.939676i	$0.611126\pi$
$90$	4.97143e25	−	1.24430e26i	0.206161	−	0.516001i
$91$	−5.46384e26	+	5.46384e26i	−1.95182	+	1.95182i
$92$	−1.84740e26	−	1.75662e26i	−0.569411	−	0.541429i
$93$	2.61188e25	+	2.61188e25i	0.0695717	+	0.0695717i
$94$	9.02108e25	+	2.10260e26i	0.207985	+	0.484764i
$95$	8.91435e25			0.178164
$96$	3.34042e26	+	1.14320e26i	0.579616	+	0.198363i
$97$	7.54323e26			1.13799			0.568996	−	0.822341i	$-0.307332\pi$
$97$	7.54323e26			1.13799			0.568996	+	0.822341i	$0.307332\pi$
$98$	4.98965e26	+	1.16297e27i	0.655418	+	1.52762i
$99$	5.48252e26	+	5.48252e26i	0.627921	+	0.627921i
$100$	−1.51322e26	−	1.43886e26i	−0.151322	−	0.143886i
$101$	1.95539e26	−	1.95539e26i	0.170960	−	0.170960i	−0.616441	−	0.787401i	$-0.711426\pi$
$101$	1.95539e26	−	1.95539e26i	0.170960	−	0.170960i	0.787401	+	0.616441i	$0.211426\pi$
$102$	−3.20246e26	+	8.01544e26i	−0.245122	+	0.613515i
$103$		−	2.03688e27i		−	1.36666i	−0.730108	−	0.683332i	$-0.760530\pi$
$103$		−	2.03688e27i		−	1.36666i	0.730108	−	0.683332i	$-0.239470\pi$
$104$	1.19875e27	+	2.61054e27i	0.705957	+	1.53737i
$105$			1.71796e27i			0.889116i
$106$	−2.96685e27	−	1.18537e27i	−1.35104	−	0.539788i
$107$	−2.22887e27	+	2.22887e27i	−0.894136	+	0.894136i	−0.994909	−	0.100774i	$-0.967868\pi$
$107$	−2.22887e27	+	2.22887e27i	−0.894136	+	0.894136i	0.100774	+	0.994909i	$0.467868\pi$
$108$	−7.08383e25	−	2.81220e27i	−0.0250638	−	0.995005i
$109$	−3.50912e27	−	3.50912e27i	−1.09633	−	1.09633i	−0.994836	−	0.101492i	$-0.967638\pi$
$109$	−3.50912e27	−	3.50912e27i	−1.09633	−	1.09633i	−0.101492	−	0.994836i	$-0.532362\pi$
$110$	−4.20728e27	+	1.80511e27i	−1.16198	+	0.498543i
$111$	−3.98822e26			−0.0974808
$112$	7.52523e27	−	3.79356e26i	1.62958	−	0.0821493i
$113$	4.32773e27			0.831192			0.415596	−	0.909549i	$-0.363573\pi$
$113$	4.32773e27			0.831192			0.415596	+	0.909549i	$0.363573\pi$
$114$	6.61297e26	−	2.83726e26i	0.112767	−	0.0483819i
$115$	−3.26077e27	−	3.26077e27i	−0.494196	−	0.494196i
$116$	−5.40665e27	+	1.36192e26i	−0.729030	+	0.0183640i
$117$	6.22287e27	−	6.22287e27i	0.747277	−	0.747277i
$118$	−1.68752e26	−	6.74225e25i	−0.0180651	−	0.00721768i
$119$			1.84207e28i			1.75963i
$120$	5.98865e27	+	2.21950e27i	0.510955	+	0.189369i
$121$		−	1.33813e28i		−	1.02069i
$122$	8.80636e27	−	2.20414e28i	0.601089	−	1.50447i
$123$	8.40235e27	−	8.40235e27i	0.513667	−	0.513667i
$124$	2.01938e27	−	2.12374e27i	0.110669	−	0.116388i
$125$	−1.54621e28	−	1.54621e28i	−0.760297	−	0.760297i
$126$	−9.10148e27	−	2.12134e28i	−0.401892	−	0.936715i
$127$	6.35132e26			0.0252066			0.0126033	−	0.999921i	$-0.495988\pi$
$127$	6.35132e26			0.0252066			0.0126033	+	0.999921i	$0.495988\pi$
$128$	8.39971e27	−	2.67223e28i	0.299868	−	0.953981i
$129$	−1.89171e28			−0.607986
$130$	2.04887e28	+	4.77543e28i	0.593306	+	1.38286i
$131$	8.71228e27	+	8.71228e27i	0.227494	+	0.227494i	0.811645	−	0.584151i	$-0.198573\pi$
$131$	8.71228e27	+	8.71228e27i	0.227494	+	0.227494i	−0.584151	+	0.811645i	$0.698573\pi$
$132$	−2.54657e28	+	2.67818e28i	−0.600079	+	0.631091i
$133$	1.08590e28	−	1.08590e28i	0.231096	−	0.231096i
$134$	2.55664e28	−	6.39901e28i	0.491762	−	1.23083i
$135$		−	5.08873e28i		−	0.885327i
$136$	6.42127e28	+	2.37983e28i	1.01122	+	0.374776i
$137$			7.00612e28i			0.999424i	0.866192	+	0.499712i	$0.166561\pi$
$137$			7.00612e28i			0.999424i	−0.866192	+	0.499712i	$0.833439\pi$
$138$	−3.45679e28	−	1.38111e28i	−0.446997	−	0.178592i
$139$	2.76867e28	−	2.76867e28i	0.324766	−	0.324766i	−0.525826	−	0.850592i	$-0.676244\pi$
$139$	2.76867e28	−	2.76867e28i	0.324766	−	0.324766i	0.850592	+	0.525826i	$0.176244\pi$
$140$	1.36257e29	−	3.43226e27i	1.45088	−	0.0365470i
$141$	2.36241e28	+	2.36241e28i	0.228505	+	0.228505i
$142$	1.92514e29	−	8.25970e28i	1.69266	−	0.726226i
$143$	−3.00686e29			−2.40479
$144$	−8.57063e28	+	4.32056e27i	−0.623906	+	0.0314519i
$145$	−9.78344e28			−0.648670
$146$	2.92042e28	−	1.25299e28i	0.176474	−	0.0757153i
$147$	1.30667e29	+	1.30667e29i	0.720082	+	0.720082i
$148$	7.96794e26	+	3.16318e28i	0.00400694	+	0.159071i
$149$	7.19434e28	−	7.19434e28i	0.330352	−	0.330352i	−0.522368	−	0.852720i	$-0.674951\pi$
$149$	7.19434e28	−	7.19434e28i	0.330352	−	0.330352i	0.852720	+	0.522368i	$0.174951\pi$
$150$	−2.83149e28	−	1.13128e28i	−0.118791	−	0.0474613i
$151$			4.99670e28i			0.191644i	0.995398	+	0.0958219i	$0.0305479\pi$
$151$			4.99670e28i			0.191644i	−0.995398	+	0.0958219i	$0.969452\pi$
$152$	−2.38243e28	−	5.18826e28i	−0.0835857	−	0.182026i
$153$		−	2.09797e29i		−	0.673696i
$154$	−2.92620e29	+	7.32399e29i	−0.860548	+	2.15386i
$155$	3.74853e28	−	3.74853e28i	0.101014	−	0.101014i
$156$	3.03984e29	+	2.89046e29i	0.751050	+	0.714142i
$157$	−2.28694e29	−	2.28694e29i	−0.518334	−	0.518334i	0.398733	−	0.917067i	$-0.369450\pi$
$157$	−2.28694e29	−	2.28694e29i	−0.518334	−	0.518334i	−0.917067	+	0.398733i	$0.869450\pi$
$158$	6.01057e28	+	1.40092e29i	0.125039	+	0.291436i
$159$	−4.66528e29			−0.891286
$160$	1.64071e29	−	4.79413e29i	0.288012	−	0.841569i
$161$	−7.94422e29			−1.28204
$162$	3.96979e27	+	9.25264e27i	0.00589271	+	0.0137345i
$163$	−4.63362e29	−	4.63362e29i	−0.632976	−	0.632976i	0.315837	−	0.948813i	$-0.397715\pi$
$163$	−4.63362e29	−	4.63362e29i	−0.632976	−	0.632976i	−0.948813	+	0.315837i	$0.897715\pi$
$164$	−6.83203e29	−	6.49629e29i	−0.859325	−	0.817097i
$165$	−4.72715e29	+	4.72715e29i	−0.547729	+	0.547729i
$166$	5.61384e28	−	1.40509e29i	0.0599516	−	0.150053i
$167$			9.86566e29i			0.971525i	0.874091	+	0.485762i	$0.161458\pi$
$167$			9.86566e29i			0.971525i	−0.874091	+	0.485762i	$0.838542\pi$
$168$	9.99876e29	−	4.59140e29i	0.908387	−	0.417128i
$169$			2.22037e30i			1.86189i
$170$	1.15036e30	+	4.59613e29i	0.890789	+	0.355903i
$171$	−1.23675e29	+	1.23675e29i	−0.0884781	+	0.0884781i
$172$	3.77939e28	+	1.50037e30i	0.0249912	+	0.992123i
$173$	2.47200e28	+	2.47200e28i	0.0151156	+	0.0151156i	0.714624	−	0.699509i	$-0.246598\pi$
$173$	2.47200e28	+	2.47200e28i	0.0151156	+	0.0151156i	−0.699509	+	0.714624i	$0.746598\pi$
$174$	−7.25769e29	+	3.11387e29i	−0.410566	+	0.176151i
$175$	−6.50718e29			−0.340706
$176$	2.17503e30	+	1.96626e30i	1.05449	+	0.953278i
$177$	−2.65357e28			−0.0119177
$178$	4.14943e30	−	1.78029e30i	1.72710	−	0.741003i
$179$	−3.32672e30	−	3.32672e30i	−1.28381	−	1.28381i	−0.938483	−	0.345325i	$-0.887769\pi$
$179$	−3.32672e30	−	3.32672e30i	−1.28381	−	1.28381i	−0.345325	−	0.938483i	$-0.612231\pi$
$180$	−1.55186e30	+	3.90907e28i	−0.555485	+	0.0139925i
$181$	−2.23550e30	+	2.23550e30i	−0.742528	+	0.742528i	−0.973064	−	0.230536i	$-0.925952\pi$
$181$	−2.23550e30	+	2.23550e30i	−0.742528	+	0.742528i	0.230536	+	0.973064i	$0.425952\pi$
$182$	8.31301e30	+	3.32135e30i	2.56327	+	1.02412i
$183$		−	3.46595e30i		−	0.992504i
$184$	−1.02634e30	+	2.76928e30i	−0.273056	+	0.736760i
$185$			5.72384e29i			0.141537i
$186$	1.58770e29	−	3.97386e29i	0.0365044	−	0.0913668i
$187$	−5.06864e30	+	5.06864e30i	−1.08400	+	1.08400i
$188$	1.82650e30	−	1.92089e30i	0.363486	−	0.382272i
$189$	−6.19884e30	−	6.19884e30i	−1.14835	−	1.14835i
$190$	−4.07199e29	−	9.49083e29i	−0.0702478	−	0.163731i
$191$	5.46306e30			0.877982			0.438991	−	0.898491i	$-0.355336\pi$
$191$	5.46306e30			0.877982			0.438991	+	0.898491i	$0.355336\pi$
$192$	−3.08742e29	−	4.07865e30i	−0.0462411	−	0.610871i
$193$	−4.87180e30			−0.680246			−0.340123	−	0.940381i	$-0.610469\pi$
$193$	−4.87180e30			−0.680246			−0.340123	+	0.940381i	$0.610469\pi$
$194$	−3.44567e30	−	8.03104e30i	−0.448694	−	1.04580i
$195$	5.36550e30	+	5.36550e30i	0.651842	+	0.651842i
$196$	1.01025e31	−	1.06247e31i	1.14544	−	1.20464i
$197$	1.42113e29	−	1.42113e29i	0.0150432	−	0.0150432i	−0.699545	−	0.714588i	$-0.746614\pi$
$197$	1.42113e29	−	1.42113e29i	0.0150432	−	0.0150432i	0.714588	+	0.699545i	$0.246614\pi$
$198$	3.33271e30	−	8.34143e30i	0.329471	−	0.824633i
$199$		−	1.17163e31i		−	1.08211i	−0.840986	−	0.541057i	$-0.818024\pi$
$199$		−	1.17163e31i		−	1.08211i	0.840986	−	0.541057i	$-0.181976\pi$
$200$	−8.40686e29	+	2.26834e30i	−0.0725653	+	0.195796i
$201$		−	1.00622e31i		−	0.811985i
$202$	−2.97504e30	−	1.18864e30i	−0.224517	−	0.0897029i
$203$	−1.19177e31	+	1.19177e31i	−0.841387	+	0.841387i
$204$	9.99665e30	−	2.51812e29i	0.660461	−	0.0166368i
$205$	−1.20589e31	−	1.20589e31i	−0.745816	−	0.745816i
$206$	−2.16860e31	+	9.30425e30i	−1.25595	+	0.538857i
$207$	9.04782e30			0.490845
$208$	2.23178e31	−	2.46874e31i	1.13448	−	1.25493i
$209$	5.97593e30			0.284728
$210$	1.82906e31	−	7.84749e30i	0.817087	−	0.350566i
$211$	−2.71209e31	−	2.71209e31i	−1.13629	−	1.13629i	−0.989109	−	0.147185i	$-0.952979\pi$
$211$	−2.71209e31	−	2.71209e31i	−1.13629	−	1.13629i	−0.147185	−	0.989109i	$-0.547021\pi$
$212$	9.32062e29	+	3.70018e31i	0.0366362	+	1.45442i
$213$	2.16302e31	−	2.16302e31i	0.797876	−	0.797876i
$214$	3.39113e31	+	1.35488e31i	1.17425	+	0.469154i
$215$			2.71496e31i			0.882762i
$216$	−2.96170e31	+	1.36000e31i	−0.904515	+	0.415350i
$217$		−	9.13254e30i		−	0.262050i
$218$	−2.13312e31	+	5.33899e31i	−0.575245	+	1.43978i
$219$	3.28128e30	−	3.28128e30i	0.0831855	−	0.0831855i
$220$	3.84369e31	+	3.65480e31i	0.916309	+	0.871280i
$221$	5.75310e31	+	5.75310e31i	1.29005	+	1.29005i
$222$	1.82178e30	+	4.24614e30i	0.0384354	+	0.0895836i
$223$	−4.01590e31			−0.797383			−0.398692	−	0.917085i	$-0.630536\pi$
$223$	−4.01590e31			−0.797383			−0.398692	+	0.917085i	$0.630536\pi$
$224$	−3.84134e31	−	7.83859e31i	−0.718017	−	1.46518i
$225$	7.41115e30			0.130443
$226$	−1.97687e31	−	4.60760e31i	−0.327728	−	0.763855i
$227$	−3.35058e31	−	3.35058e31i	−0.523325	−	0.523325i	0.395249	−	0.918574i	$-0.370658\pi$
$227$	−3.35058e31	−	3.35058e31i	−0.523325	−	0.523325i	−0.918574	+	0.395249i	$0.870658\pi$
$228$	−6.04148e30	−	5.74459e30i	−0.0889247	−	0.0845549i
$229$	−3.71443e31	+	3.71443e31i	−0.515364	+	0.515364i	−0.916165	−	0.400801i	$-0.868732\pi$
$229$	−3.71443e31	+	3.71443e31i	−0.515364	+	0.515364i	0.400801	+	0.916165i	$0.368732\pi$
$230$	−1.98215e31	+	4.96113e31i	−0.259305	+	0.649015i
$231$			1.15168e32i			1.42092i
$232$	2.61470e31	+	5.69408e31i	0.304323	+	0.662729i
$233$			7.84252e31i			0.861292i	0.902521	+	0.430646i	$0.141714\pi$
$233$			7.84252e31i			0.861292i	−0.902521	+	0.430646i	$0.858286\pi$
$234$	−9.46785e31	−	3.78275e31i	−0.981380	−	0.392097i
$235$	3.39049e31	−	3.39049e31i	0.331777	−	0.331777i
$236$	5.30148e28	+	2.10463e30i	0.000489874	+	0.0194475i
$237$	1.57402e31	+	1.57402e31i	0.137375	+	0.137375i
$238$	1.96119e32	−	8.41439e31i	1.61708	−	0.693799i
$239$	9.34231e31			0.727918			0.363959	−	0.931415i	$-0.381425\pi$
$239$	9.34231e31			0.727918			0.363959	+	0.931415i	$0.381425\pi$
$240$	−3.72528e30	−	7.38978e31i	−0.0274351	−	0.544227i
$241$	−1.05737e32			−0.736203			−0.368101	−	0.929786i	$-0.619992\pi$
$241$	−1.05737e32			−0.736203			−0.368101	+	0.929786i	$0.619992\pi$
$242$	−1.42466e32	+	6.11244e31i	−0.938004	+	0.402445i
$243$	1.14054e32	+	1.14054e32i	0.710272	+	0.710272i
$244$	−2.74895e32	+	6.92450e30i	−1.61959	+	0.0407968i
$245$	1.87531e32	−	1.87531e32i	1.04552	−	1.04552i
$246$	−1.27838e32	−	5.10761e31i	−0.674586	−	0.269522i
$247$		−	6.78291e31i		−	0.338850i
$248$	−3.18351e31	−	1.17986e31i	−0.150594	−	0.0558129i
$249$		−	2.20946e31i		−	0.0989907i
$250$	−9.39909e31	+	2.35250e32i	−0.398929	+	0.998479i
$251$	−2.51589e32	+	2.51589e32i	−1.01180	+	1.01180i	−0.0118735	+	0.999930i	$0.503780\pi$
$251$	−2.51589e32	+	2.51589e32i	−1.01180	+	1.01180i	−0.999930	+	0.0118735i	$0.996220\pi$
$252$	−1.84278e32	+	1.93801e32i	−0.702368	+	0.738668i
$253$	−2.18593e32	−	2.18593e32i	−0.789786	−	0.789786i
$254$	−2.90122e30	−	6.76205e30i	−0.00993861	−	0.0231645i
$255$	1.80891e32			0.587659
$256$	−3.22873e32	+	3.26358e31i	−0.994930	+	0.100567i
$257$	5.00462e32			1.46310			0.731550	−	0.681788i	$-0.238797\pi$
$257$	5.00462e32			1.46310			0.731550	+	0.681788i	$0.238797\pi$
$258$	8.64115e31	+	2.01405e32i	0.239721	+	0.558732i
$259$	6.97249e31	+	6.97249e31i	0.183587	+	0.183587i
$260$	4.14834e32	−	4.36273e32i	1.03689	−	1.09048i
$261$	1.35733e32	−	1.35733e32i	0.322135	−	0.322135i
$262$	5.29601e31	−	1.32554e32i	0.119366	−	0.298761i
$263$		−	4.98945e32i		−	1.06819i	−0.845423	−	0.534097i	$-0.820652\pi$
$263$		−	4.98945e32i		−	1.06819i	0.845423	−	0.534097i	$-0.179348\pi$
$264$	4.01463e32	+	1.48789e32i	0.816568	+	0.302634i
$265$			6.69555e32i			1.29410i
$266$	−1.65215e32	−	6.60096e31i	−0.303493	−	0.121257i
$267$	4.66215e32	−	4.66215e32i	0.814111	−	0.814111i
$268$	−7.98068e32	+	2.01030e31i	−1.32501	+	0.0333766i
$269$	−8.64308e31	−	8.64308e31i	−0.136462	−	0.136462i	0.635576	−	0.772038i	$-0.280763\pi$
$269$	−8.64308e31	−	8.64308e31i	−0.136462	−	0.136462i	−0.772038	+	0.635576i	$0.780763\pi$
$270$	−5.41781e32	+	2.32448e32i	−0.813604	+	0.349072i
$271$	1.01122e33			1.44465			0.722324	−	0.691555i	$-0.243074\pi$
$271$	1.01122e33			1.44465			0.722324	+	0.691555i	$0.243074\pi$
$272$	−3.99439e31	−	7.92361e32i	−0.0542964	−	1.07707i
$273$	1.30720e33			1.69101
$274$	7.45919e32	−	3.20032e32i	0.918458	−	0.394059i
$275$	−1.79052e32	−	1.79052e32i	−0.209888	−	0.209888i
$276$	1.08598e31	+	4.31121e32i	0.0121213	+	0.481201i
$277$	7.20261e32	−	7.20261e32i	0.765620	−	0.765620i	−0.211712	−	0.977332i	$-0.567904\pi$
$277$	7.20261e32	−	7.20261e32i	0.765620	−	0.765620i	0.977332	+	0.211712i	$0.0679039\pi$
$278$	−4.21242e32	−	1.68301e32i	−0.426507	−	0.170405i
$279$			1.04012e32i			0.100329i
$280$	−6.58951e32	−	1.43501e33i	−0.605647	−	1.31893i
$281$			1.25054e33i			1.09538i	0.836683	+	0.547688i	$0.184492\pi$
$281$			1.25054e33i			1.09538i	−0.836683	+	0.547688i	$0.815508\pi$
$282$	1.43606e32	−	3.59430e32i	0.119897	−	0.300090i
$283$	−1.14005e32	+	1.14005e32i	−0.0907418	+	0.0907418i	−0.751021	−	0.660279i	$-0.770438\pi$
$283$	−1.14005e32	+	1.14005e32i	−0.0907418	+	0.0907418i	0.660279	+	0.751021i	$0.270438\pi$
$284$	−1.75877e33	−	1.67234e33i	−1.33479	−	1.26919i
$285$	−1.06636e32	−	1.06636e32i	−0.0771785	−	0.0771785i
$286$	1.37350e33	+	3.20131e33i	0.948176	+	2.20997i
$287$	−2.93792e33			−1.93479
$288$	4.37497e32	+	8.92752e32i	0.274901	+	0.560960i
$289$	2.71876e32			0.163024
$290$	4.46898e32	+	1.04161e33i	0.255762	+	0.596119i
$291$	−9.02339e32	−	9.02339e32i	−0.492963	−	0.492963i
$292$	−2.66804e32	−	2.53693e32i	−0.139163	−	0.132324i
$293$	1.41298e33	−	1.41298e33i	0.703757	−	0.703757i	−0.261458	−	0.965215i	$-0.584203\pi$
$293$	1.41298e33	−	1.41298e33i	0.703757	−	0.703757i	0.965215	+	0.261458i	$0.0842032\pi$
$294$	7.94297e32	−	1.98805e33i	0.377828	−	0.945665i
$295$			3.80836e31i			0.0173038i
$296$	3.33134e32	−	1.52974e32i	0.144604	−	0.0664018i
$297$		−	3.41134e33i		−	1.41486i
$298$	−1.09459e33	−	4.37329e32i	−0.433842	−	0.173336i
$299$	−2.48112e33	+	2.48112e33i	−0.939909	+	0.939909i
$300$	8.89536e30	+	3.53136e32i	0.00322126	+	0.127881i
$301$	3.30722e33	+	3.30722e33i	1.14503	+	1.14503i
$302$	5.31983e32	−	2.28244e32i	0.176118	−	0.0755625i
$303$	−4.67816e32			−0.148115
$304$	−4.43551e32	+	4.90645e32i	−0.134323	+	0.148585i
$305$	−4.97428e33			−1.44106
$306$	−2.23364e33	+	9.58331e32i	−0.619119	+	0.265629i
$307$	1.08127e32	+	1.08127e32i	0.0286791	+	0.0286791i	0.721301	−	0.692622i	$-0.243544\pi$
$307$	1.08127e32	+	1.08127e32i	0.0286791	+	0.0286791i	−0.692622	+	0.721301i	$0.743544\pi$
$308$	9.13429e33	−	2.30089e32i	2.31868	−	0.0584066i
$309$	−2.43656e33	+	2.43656e33i	−0.592021	+	0.592021i
$310$	−5.70323e32	−	2.27865e32i	−0.132659	−	0.0530023i
$311$			6.52684e33i			1.45358i	0.686862	+	0.726788i	$0.258988\pi$
$311$			6.52684e33i			1.45358i	−0.686862	+	0.726788i	$0.741012\pi$
$312$	1.68881e33	−	4.55676e33i	0.360159	−	0.971782i
$313$		−	6.53232e33i		−	1.33419i	−0.744971	−	0.667097i	$-0.767537\pi$
$313$		−	6.53232e33i		−	1.33419i	0.744971	−	0.667097i	$-0.232463\pi$
$314$	−1.39018e33	+	3.47949e33i	−0.271971	+	0.680715i
$315$	−3.42070e33	+	3.42070e33i	−0.641096	+	0.641096i
$316$	1.21696e33	−	1.27985e33i	0.218525	−	0.229818i
$317$	−6.77430e32	−	6.77430e32i	−0.116564	−	0.116564i	0.646419	−	0.762983i	$-0.276266\pi$
$317$	−6.77430e32	−	6.77430e32i	−0.116564	−	0.116564i	−0.762983	+	0.646419i	$0.776266\pi$
$318$	2.13106e33	+	4.96698e33i	0.351422	+	0.819080i
$319$	−6.55855e33			−1.03665
$320$	−5.85362e33	+	4.43101e32i	−0.886951	+	0.0671396i
$321$	5.33245e33			0.774656
$322$	3.62884e33	+	8.45796e33i	0.505491	+	1.17818i
$323$	−1.14339e33	−	1.14339e33i	−0.152743	−	0.152743i
$324$	8.03764e31	−	8.45303e31i	0.0102984	−	0.0108307i
$325$	−2.03230e33	+	2.03230e33i	−0.249783	+	0.249783i
$326$	−2.81668e33	+	7.04986e33i	−0.332123	+	0.831271i
$327$			8.39539e33i			0.949831i
$328$	−3.79560e33	+	1.02413e34i	−0.412082	+	1.11188i
$329$		−	8.26025e33i		−	0.860693i
$330$	7.19216e33	+	2.87353e33i	0.719319	+	0.287394i
$331$	−1.37139e33	+	1.37139e33i	−0.131669	+	0.131669i	−0.769870	−	0.638201i	$-0.779679\pi$
$331$	−1.37139e33	+	1.37139e33i	−0.131669	+	0.131669i	0.638201	+	0.769870i	$0.279679\pi$
$332$	−1.75239e33	+	4.41420e31i	−0.161535	+	0.00406900i
$333$	−7.94110e32	−	7.94110e32i	−0.0702884	−	0.0702884i
$334$	1.05037e34	−	4.50654e33i	0.892819	−	0.383059i
$335$	−1.44412e34			−1.17896
$336$	−9.45566e33	−	8.54806e33i	−0.741500	−	0.670328i
$337$	2.25845e34			1.70140			0.850701	−	0.525651i	$-0.176178\pi$
$337$	2.25845e34			1.70140			0.850701	+	0.525651i	$0.176178\pi$
$338$	2.36396e34	−	1.01424e34i	1.71106	−	0.734120i
$339$	−5.17694e33	−	5.17694e33i	−0.360062	−	0.360062i
$340$	−3.61397e32	−	1.43470e34i	−0.0241557	−	0.958952i
$341$	2.51291e33	−	2.51291e33i	0.161433	−	0.161433i
$342$	1.88167e33	+	7.51796e32i	0.116196	+	0.0464246i
$343$		−	1.82031e34i		−	1.08063i
$344$	1.58014e34	−	7.25594e33i	0.901895	−	0.414147i
$345$			7.80123e33i			0.428159i
$346$	1.50268e32	−	3.76105e32i	0.00793119	−	0.0198510i
$347$	−1.10255e34	+	1.10255e34i	−0.559692	+	0.559692i	−0.929220	−	0.369528i	$-0.879519\pi$
$347$	−1.10255e34	+	1.10255e34i	−0.559692	+	0.559692i	0.369528	+	0.929220i	$0.379519\pi$
$348$	6.63048e33	+	6.30465e33i	0.323762	+	0.307851i
$349$	1.14090e34	+	1.14090e34i	0.535926	+	0.535926i	0.922330	−	0.386403i	$-0.126283\pi$
$349$	1.14090e34	+	1.14090e34i	0.535926	+	0.535926i	−0.386403	+	0.922330i	$0.626283\pi$
$350$	2.97242e33	+	6.92799e33i	0.134336	+	0.313104i
$351$	−3.87201e34			−1.68380
$352$	1.09988e34	−	3.21385e34i	0.460279	−	1.34493i
$353$	−2.06338e34			−0.831038			−0.415519	−	0.909584i	$-0.636400\pi$
$353$	−2.06338e34			−0.831038			−0.415519	+	0.909584i	$0.636400\pi$
$354$	1.21212e32	+	2.82517e32i	0.00469897	+	0.0109522i
$355$	−3.10433e34	−	3.10433e34i	−1.15847	−	1.15847i
$356$	−3.79083e34	−	3.60455e34i	−1.36195	−	1.29502i
$357$	2.20353e34	−	2.20353e34i	0.762250	−	0.762250i
$358$	−2.02224e34	+	5.06147e34i	−0.673616	+	1.68599i
$359$		−	1.87954e34i		−	0.602944i	−0.953475	−	0.301472i	$-0.902522\pi$
$359$		−	1.87954e34i		−	0.602944i	0.953475	−	0.301472i	$-0.0974780\pi$
$360$	7.50491e33	+	1.63436e34i	0.231879	+	0.504967i
$361$		−	3.22526e34i		−	0.959880i
$362$	3.40122e34	+	1.35891e34i	0.975143	+	0.389605i
$363$	−1.60070e34	+	1.60070e34i	−0.442151	+	0.442151i
$364$	−2.61160e33	−	1.03678e35i	−0.0695086	−	2.75941i
$365$	−4.70924e33	−	4.70924e33i	−0.120781	−	0.120781i
$366$	−3.69009e34	+	1.58321e34i	−0.912099	+	0.391331i
$367$	1.83880e34			0.438069			0.219034	−	0.975717i	$-0.429709\pi$
$367$	1.83880e34			0.438069			0.219034	+	0.975717i	$0.429709\pi$
$368$	3.41719e34	−	1.72265e33i	0.784735	−	0.0395595i
$369$	3.34605e34			0.740758
$370$	6.09399e33	−	2.61459e33i	0.130070	−	0.0558060i
$371$	8.15618e34	+	8.15618e34i	1.67857	+	1.67857i
$372$	−4.95610e33	+	1.24842e32i	−0.0983581	+	0.00247760i
$373$	6.03698e34	−	6.03698e34i	1.15545	−	1.15545i	0.170004	−	0.985443i	$-0.445622\pi$
$373$	6.03698e34	−	6.03698e34i	1.15545	−	1.15545i	0.985443	−	0.170004i	$-0.0543781\pi$
$374$	7.71172e34	+	3.08112e34i	1.42359	+	0.568776i
$375$			3.69923e34i			0.658702i
$376$	−2.87944e34	−	1.06717e34i	−0.494621	−	0.183315i
$377$			7.44420e34i			1.23370i
$378$	−3.76814e34	+	9.43127e34i	−0.602543	+	1.50810i
$379$	7.29357e32	−	7.29357e32i	0.0112541	−	0.0112541i	−0.701457	−	0.712711i	$-0.747467\pi$
$379$	7.29357e32	−	7.29357e32i	0.0112541	−	0.0112541i	0.712711	+	0.701457i	$0.247467\pi$
$380$	−8.24455e33	+	8.67064e33i	−0.122769	+	0.129114i
$381$	−7.59760e32	−	7.59760e32i	−0.0109192	−	0.0109192i
$382$	−2.49547e34	−	5.81635e34i	−0.346176	−	0.806855i
$383$	−8.28925e34			−1.11002			−0.555011	−	0.831843i	$-0.687286\pi$
$383$	−8.28925e34			−1.11002			−0.555011	+	0.831843i	$0.687286\pi$
$384$	−4.20138e34	+	2.19179e34i	−0.543151	+	0.283353i
$385$	1.65287e35			2.06309
$386$	2.22539e34	+	5.18686e34i	0.268212	+	0.625137i
$387$	−3.76666e34	−	3.76666e34i	−0.438388	−	0.438388i
$388$	−6.97645e34	+	7.33700e34i	−0.784163	+	0.824689i
$389$	−3.61349e34	+	3.61349e34i	−0.392290	+	0.392290i	−0.875503	−	0.483213i	$-0.839470\pi$
$389$	−3.61349e34	+	3.61349e34i	−0.392290	+	0.392290i	0.483213	+	0.875503i	$0.339470\pi$
$390$	3.26157e34	−	8.16338e34i	0.342023	−	0.856048i
$391$			8.36478e34i			0.847361i
$392$	−1.59265e35	−	5.90263e34i	−1.55868	−	0.577675i
$393$		−	2.08437e34i		−	0.197095i
$394$	−2.16219e33	−	8.63873e32i	−0.0197558	−	0.00789316i
$395$	2.25902e34	−	2.25902e34i	0.199461	−	0.199461i
$396$	−1.04032e35	+	2.62053e33i	−0.887733	+	0.0223617i
$397$	7.36062e34	+	7.36062e34i	0.607076	+	0.607076i	0.942181	−	0.335105i	$-0.108772\pi$
$397$	7.36062e34	+	7.36062e34i	0.607076	+	0.607076i	−0.335105	+	0.942181i	$0.608772\pi$
$398$	−1.24740e35	+	5.35188e34i	−0.994450	+	0.426663i
$399$	−2.59796e34			−0.200216
$400$	2.79905e34	−	1.41104e33i	0.208545	−	0.0105130i
$401$	5.55409e34			0.400096			0.200048	−	0.979786i	$-0.435890\pi$
$401$	5.55409e34			0.400096			0.200048	+	0.979786i	$0.435890\pi$
$402$	−1.07130e35	+	4.59634e34i	−0.746205	+	0.320155i
$403$	−2.85225e34	−	2.85225e34i	−0.192118	−	0.192118i
$404$	9.34635e32	+	3.71039e34i	0.00608826	+	0.241697i
$405$	1.49201e33	−	1.49201e33i	0.00940002	−	0.00940002i
$406$	1.81323e35	+	7.24452e34i	1.10497	+	0.441477i
$407$			3.83710e34i			0.226193i
$408$	−4.83447e34	−	1.05281e35i	−0.275700	−	0.600396i
$409$		−	2.30941e35i		−	1.27419i	−0.770784	−	0.637097i	$-0.780135\pi$
$409$		−	2.30941e35i		−	1.27419i	0.770784	−	0.637097i	$-0.219865\pi$
$410$	−7.33037e34	+	1.83472e35i	−0.391330	+	0.979460i
$411$	8.38088e34	−	8.38088e34i	0.432937	−	0.432937i
$412$	1.98119e35	+	1.88383e35i	0.990406	+	0.941736i
$413$	4.63915e33	+	4.63915e33i	0.0224447	+	0.0224447i
$414$	−4.13295e34	−	9.63293e34i	−0.193533	−	0.451080i
$415$	−3.17098e34			−0.143729
$416$	−3.64784e35	−	1.24841e35i	−1.60058	−	0.547769i
$417$	−6.62389e34			−0.281369
$418$	−2.72975e34	−	6.36239e34i	−0.112265	−	0.261662i
$419$	−3.32836e34	−	3.32836e34i	−0.132538	−	0.132538i	0.637726	−	0.770264i	$-0.279875\pi$
$419$	−3.32836e34	−	3.32836e34i	−0.132538	−	0.132538i	−0.770264	+	0.637726i	$0.779875\pi$
$420$	−1.67100e35	−	1.58888e35i	−0.644332	−	0.612669i
$421$	3.66035e35	−	3.66035e35i	1.36683	−	1.36683i	0.501912	−	0.864918i	$-0.332630\pi$
$421$	3.66035e35	−	3.66035e35i	1.36683	−	1.36683i	0.864918	−	0.501912i	$-0.167370\pi$
$422$	−1.64862e35	+	4.12633e35i	−0.596215	+	1.49227i
$423$			9.40775e34i			0.329527i
$424$	3.89689e35	−	1.78944e35i	1.32215	−	0.607125i
$425$			6.85167e34i			0.225188i
$426$	−3.29094e35	−	1.31485e35i	−1.04783	−	0.418647i
$427$	−6.05942e35	+	6.05942e35i	−1.86919	+	1.86919i
$428$	−1.06535e34	−	4.22933e35i	−0.0318422	−	1.26410i
$429$	3.59688e35	+	3.59688e35i	1.04172	+	1.04172i
$430$	2.89053e35	−	1.24017e35i	0.811247	−	0.348061i
$431$	2.62955e35			0.715217			0.357608	−	0.933872i	$-0.383592\pi$
$431$	2.62955e35			0.715217			0.357608	+	0.933872i	$0.383592\pi$
$432$	2.80083e35	+	2.53200e35i	0.738340	+	0.667471i
$433$	3.31434e34			0.0846858			0.0423429	−	0.999103i	$-0.486518\pi$
$433$	3.31434e34			0.0846858			0.0423429	+	0.999103i	$0.486518\pi$
$434$	−9.72313e34	+	4.17165e34i	−0.240821	+	0.103323i
$435$	1.17032e35	+	1.17032e35i	0.280995	+	0.280995i
$436$	6.65864e35	−	1.67729e34i	1.54995	−	0.0390427i
$437$	4.93105e34	−	4.93105e34i	0.111286	−	0.111286i
$438$	−4.99233e34	−	1.99462e34i	−0.109245	−	0.0436475i
$439$			4.55802e35i			0.967175i	0.875296	+	0.483587i	$0.160666\pi$
$439$			4.55802e35i			0.967175i	−0.875296	+	0.483587i	$0.839334\pi$
$440$	2.13540e35	−	5.76173e35i	0.439408	−	1.18561i
$441$			5.20352e35i			1.03843i
$442$	3.49719e35	−	8.75310e35i	0.676890	−	1.69419i
$443$	5.56737e35	−	5.56737e35i	1.04520	−	1.04520i	0.0462711	−	0.998929i	$-0.485266\pi$
$443$	5.56737e35	−	5.56737e35i	1.04520	−	1.04520i	0.998929	−	0.0462711i	$-0.0147338\pi$
$444$	3.68856e34	−	3.87919e34i	0.0671717	−	0.0706432i
$445$	−6.69104e35	−	6.69104e35i	−1.18204	−	1.18204i
$446$	1.83442e35	+	4.27560e35i	0.314397	+	0.732785i
$447$	−1.72121e35			−0.286208
$448$	−6.59082e35	+	7.67035e35i	−1.06337	+	1.23755i
$449$	1.27730e35			0.199971			0.0999854	−	0.994989i	$-0.468120\pi$
$449$	1.27730e35			0.199971			0.0999854	+	0.994989i	$0.468120\pi$
$450$	−3.38534e34	−	7.89042e34i	−0.0514320	−	0.119876i
$451$	−8.08397e35	−	8.08397e35i	−1.19190	−	1.19190i
$452$	−4.00256e35	+	4.20942e35i	−0.572755	+	0.602356i
$453$	5.97717e34	−	5.97717e34i	0.0830176	−	0.0830176i
$454$	−2.03675e35	+	5.09778e35i	−0.274589	+	0.687269i
$455$		−	1.87607e36i		−	2.45524i
$456$	−3.35640e34	+	9.05624e34i	−0.0426430	+	0.115060i
$457$		−	7.07752e35i		−	0.872996i	−0.899705	−	0.436498i	$-0.856219\pi$
$457$		−	7.07752e35i		−	0.872996i	0.899705	−	0.436498i	$-0.143781\pi$
$458$	5.65136e35	+	2.25793e35i	0.676814	+	0.270412i
$459$	−6.52700e35	+	6.52700e35i	−0.759001	+	0.759001i
$460$	6.18739e35	−	1.55858e34i	0.698678	−	0.0175994i
$461$	−8.29115e35	−	8.29115e35i	−0.909185	−	0.909185i	0.0870212	−	0.996206i	$-0.472265\pi$
$461$	−8.29115e35	−	8.29115e35i	−0.909185	−	0.909185i	−0.996206	+	0.0870212i	$0.972265\pi$
$462$	1.22615e36	−	5.26074e35i	1.30580	−	0.560248i
$463$	1.60221e36			1.65720			0.828600	−	0.559841i	$-0.189138\pi$
$463$	1.60221e36			1.65720			0.828600	+	0.559841i	$0.189138\pi$
$464$	4.86794e35	−	5.38480e35i	0.489049	−	0.540974i
$465$	−8.96815e34			−0.0875162
$466$	8.34968e35	−	3.58238e35i	0.791517	−	0.339596i
$467$	−7.12300e34	−	7.12300e34i	−0.0655972	−	0.0655972i	0.673547	−	0.739144i	$-0.264770\pi$
$467$	−7.12300e34	−	7.12300e34i	−0.0655972	−	0.0655972i	−0.739144	+	0.673547i	$0.764770\pi$
$468$	2.97440e34	+	1.18080e36i	0.0266122	+	1.05647i
$469$	−1.75915e36	+	1.75915e36i	−1.52922	+	1.52922i
$470$	−5.15849e35	−	2.06101e35i	−0.435714	−	0.174084i
$471$			5.47139e35i			0.449071i
$472$	2.21651e34	−	1.01782e34i	0.0176788	−	0.00811806i
$473$			1.82003e36i			1.41076i
$474$	9.56816e34	−	2.39481e35i	0.0720810	−	0.180411i
$475$	4.03907e34	−	4.03907e34i	0.0295745	−	0.0295745i
$476$	−1.79171e36	−	1.70366e36i	−1.27519	−	1.21252i
$477$	−9.28923e35	−	9.28923e35i	−0.642660	−	0.642660i
$478$	−4.26747e35	−	9.94646e35i	−0.287008	−	0.668948i
$479$	−1.12050e36			−0.732625			−0.366312	−	0.930492i	$-0.619380\pi$
$479$	−1.12050e36			−0.732625			−0.366312	+	0.930492i	$0.619380\pi$
$480$	−7.69750e35	+	3.77220e35i	−0.489320	+	0.239794i
$481$	4.35526e35			0.269188
$482$	4.82997e35	+	1.12575e36i	0.290275	+	0.676561i
$483$	9.50306e35	+	9.50306e35i	0.555363	+	0.555363i
$484$	1.30154e36	+	1.23758e36i	0.739685	+	0.703336i
$485$	−1.29502e36	+	1.29502e36i	−0.715755	+	0.715755i
$486$	6.93309e35	−	1.73528e36i	0.372681	−	0.932782i
$487$		−	1.23376e35i		−	0.0645046i	−0.999480	−	0.0322523i	$-0.989732\pi$
$487$		−	1.23376e35i		−	0.0645046i	0.999480	−	0.0322523i	$-0.0102680\pi$
$488$	1.32942e36	+	2.89509e36i	0.676073	+	1.47229i
$489$			1.10857e36i			0.548394i
$490$	−2.85321e36	−	1.13996e36i	−1.37305	−	0.548585i
$491$	2.36670e36	−	2.36670e36i	1.10801	−	1.10801i	0.114598	−	0.993412i	$-0.463442\pi$
$491$	2.36670e36	−	2.36670e36i	1.10801	−	1.10801i	0.993412	−	0.114598i	$-0.0365580\pi$
$492$	4.01615e34	+	1.59437e36i	0.0182928	+	0.726205i
$493$	1.25486e36	+	1.25486e36i	0.556112	+	0.556112i
$494$	−7.22156e35	+	3.09837e35i	−0.311399	+	0.133604i
$495$	−1.88248e36			−0.789879
$496$	1.98032e34	+	3.92834e35i	0.00808600	+	0.160401i
$497$	−7.56308e36			−3.00530
$498$	−2.35234e35	+	1.00926e35i	−0.0909712	+	0.0390307i
$499$	1.17721e35	+	1.17721e35i	0.0443096	+	0.0443096i	0.728914	−	0.684605i	$-0.240025\pi$
$499$	1.17721e35	+	1.17721e35i	0.0443096	+	0.0443096i	−0.684605	+	0.728914i	$0.740025\pi$
$500$	2.93397e36	−	7.39057e34i	1.07488	−	0.0270759i
$501$	1.18015e36	−	1.18015e36i	0.420852	−	0.420852i
$502$	3.82782e36	+	1.52935e36i	1.32877	+	0.530894i
$503$			4.72412e36i			1.59644i	0.602366	+	0.798220i	$0.294225\pi$
$503$			4.72412e36i			1.59644i	−0.602366	+	0.798220i	$0.705775\pi$
$504$	2.90510e36	+	1.07668e36i	0.955761	+	0.354221i
$505$			6.71403e35i			0.215055i
$506$	−1.32878e36	+	3.32580e36i	−0.414402	+	1.03721i
$507$	2.65606e36	−	2.65606e36i	0.806549	−	0.806549i
$508$	−5.87410e34	+	6.17768e34i	−0.0173692	+	0.0182669i
$509$	−7.53150e35	−	7.53150e35i	−0.216866	−	0.216866i	0.590310	−	0.807176i	$-0.299005\pi$
$509$	−7.53150e35	−	7.53150e35i	−0.216866	−	0.216866i	−0.807176	+	0.590310i	$0.799005\pi$
$510$	−8.26294e35	−	1.92589e36i	−0.231706	−	0.540051i
$511$	−1.14731e36			−0.313328
$512$	1.82232e36	+	3.28845e36i	0.484707	+	0.874676i
$513$	7.69535e35			0.199363
$514$	−2.28606e36	−	5.32826e36i	−0.576880	−	1.34457i
$515$	3.49691e36	+	3.49691e36i	0.859582	+	0.859582i
$516$	1.74957e36	−	1.83999e36i	0.418949	−	0.440601i
$517$	2.27289e36	−	2.27289e36i	0.530220	−	0.530220i
$518$	4.23843e35	−	1.06084e36i	0.0963281	−	0.241100i
$519$		−	5.91413e34i		−	0.0130958i
$520$	−6.53979e36	−	2.42376e36i	−1.41097	−	0.522931i
$521$		−	4.65748e36i		−	0.979133i	−0.871966	−	0.489567i	$-0.837155\pi$
$521$		−	4.65748e36i		−	0.979133i	0.871966	−	0.489567i	$-0.162845\pi$
$522$	−2.06512e36	−	8.25092e35i	−0.423052	−	0.169025i
$523$	1.48713e36	−	1.48713e36i	0.296877	−	0.296877i	−0.542912	−	0.839789i	$-0.682678\pi$
$523$	1.48713e36	−	1.48713e36i	0.296877	−	0.296877i	0.839789	+	0.542912i	$0.182678\pi$
$524$	−1.65318e36	+	4.16429e34i	−0.321623	+	0.00810155i
$525$	7.78405e35	+	7.78405e35i	0.147589	+	0.147589i
$526$	−5.31211e36	+	2.27913e36i	−0.981657	+	0.421174i
$527$	−9.61601e35			−0.173201
$528$	−2.49733e35	−	4.95390e36i	−0.0438447	−	0.869740i
$529$	2.23576e36			0.382626
$530$	7.12854e36	−	3.05846e36i	1.18926	−	0.510245i
$531$	−5.28362e34	−	5.28362e34i	−0.00859321	−	0.00859321i
$532$	5.19038e34	+	2.06052e36i	0.00822986	+	0.326716i
$533$	−9.17562e36	+	9.17562e36i	−1.41846	+	1.41846i
$534$	−7.09326e36	−	2.83402e36i	−1.06915	−	0.427165i
$535$		−	7.65305e36i		−	1.12476i
$536$	3.85953e36	+	8.40495e36i	0.553107	+	1.20451i
$537$			7.95900e36i			1.11226i
$538$	−5.25395e35	+	1.31501e36i	−0.0716020	+	0.179212i
$539$	1.25716e37	−	1.25716e37i	1.67087	−	1.67087i
$540$	4.94961e36	+	4.70638e36i	0.641586	+	0.610058i
$541$	−1.58911e36	−	1.58911e36i	−0.200905	−	0.200905i	0.599483	−	0.800388i	$-0.295373\pi$
$541$	−1.58911e36	−	1.58911e36i	−0.200905	−	0.200905i	−0.800388	+	0.599483i	$0.795373\pi$
$542$	−4.61917e36	−	1.07662e37i	−0.569605	−	1.32761i
$543$	5.34831e36			0.643307
$544$	−8.25357e36	+	4.04470e36i	−0.968404	+	0.474571i
$545$	1.20489e37			1.37910
$546$	−5.97114e36	−	1.39173e37i	−0.666740	−	1.55401i
$547$	4.36044e35	+	4.36044e35i	0.0475009	+	0.0475009i	0.730458	−	0.682957i	$-0.239307\pi$
$547$	4.36044e35	+	4.36044e35i	0.0475009	+	0.0475009i	−0.682957	+	0.730458i	$0.739307\pi$
$548$	−6.81457e36	−	6.47970e36i	−0.724271	−	0.688679i
$549$	6.90118e36	−	6.90118e36i	0.715644	−	0.715644i
$550$	−1.08842e36	+	2.72420e36i	−0.110128	+	0.275640i
$551$		−	1.47948e36i		−	0.146071i
$552$	4.54041e36	−	2.08494e36i	0.437439	−	0.200871i
$553$		−	5.50364e36i		−	0.517441i
$554$	−1.09585e37	−	4.37832e36i	−1.00547	−	0.401722i
$555$	6.84699e35	−	6.84699e35i	0.0613118	−	0.0613118i
$556$	1.32337e35	+	5.25361e36i	0.0115657	+	0.459143i
$557$	−9.73906e36	−	9.73906e36i	−0.830753	−	0.830753i	0.156867	−	0.987620i	$-0.449861\pi$
$557$	−9.73906e36	−	9.73906e36i	−0.830753	−	0.830753i	−0.987620	+	0.156867i	$0.949861\pi$
$558$	1.10739e36	−	4.75117e35i	0.0922013	−	0.0395584i
$559$	2.06581e37			1.67892
$560$	−1.22681e37	+	1.35706e37i	−0.973279	+	1.07662i
$561$	1.21264e37			0.939150
$562$	1.33141e37	−	5.71235e36i	1.00664	−	0.431892i
$563$	8.92642e36	+	8.92642e36i	0.658891	+	0.658891i	0.955118	−	0.296226i	$-0.0957283\pi$
$563$	8.92642e36	+	8.92642e36i	0.658891	+	0.658891i	−0.296226	+	0.955118i	$0.595728\pi$
$564$	−4.48272e36	+	1.12918e35i	−0.323053	+	0.00813759i
$565$	−7.42986e36	+	7.42986e36i	−0.522789	+	0.522789i
$566$	1.73454e36	+	6.93013e35i	0.119169	+	0.0476123i
$567$		−	3.63498e35i		−	0.0243855i
$568$	−9.77101e36	+	2.63642e37i	−0.640084	+	1.72708i
$569$		−	2.67188e36i		−	0.170923i	−0.996341	−	0.0854616i	$-0.972764\pi$
$569$		−	2.67188e36i		−	0.170923i	0.996341	−	0.0854616i	$-0.0272365\pi$
$570$	−6.48215e35	+	1.62242e36i	−0.0404957	+	0.101357i
$571$	−1.41336e37	+	1.41336e37i	−0.862316	+	0.862316i	−0.991607	−	0.129291i	$-0.958730\pi$
$571$	−1.41336e37	+	1.41336e37i	−0.862316	+	0.862316i	0.129291	+	0.991607i	$0.458730\pi$
$572$	2.78093e37	−	2.92466e37i	1.65708	−	1.74272i
$573$	−6.53505e36	−	6.53505e36i	−0.380331	−	0.380331i
$574$	1.34201e37	+	3.12791e37i	0.762861	+	1.77805i
$575$	−2.95489e36			−0.164069
$576$	7.50641e36	−	8.73590e36i	0.407126	−	0.473810i
$577$	−1.85263e37			−0.981558			−0.490779	−	0.871284i	$-0.663288\pi$
$577$	−1.85263e37			−0.981558			−0.490779	+	0.871284i	$0.663288\pi$
$578$	−1.24190e36	−	2.89458e36i	−0.0642780	−	0.149817i
$579$	5.82776e36	+	5.82776e36i	0.294674	+	0.294674i
$580$	9.04834e36	−	9.51597e36i	0.446983	−	0.470084i
$581$	−3.86273e36	+	3.86273e36i	−0.186430	+	0.186430i
$582$	−5.48513e36	+	1.37287e37i	−0.258658	+	0.647396i
$583$			4.48851e37i			2.06812i
$584$	−1.48225e36	+	3.99942e36i	−0.0667343	+	0.180063i
$585$			2.13669e37i			0.940020i
$586$	−2.14979e37	−	8.58920e36i	−0.924226	−	0.369262i
$587$	1.14744e37	−	1.14744e37i	0.482074	−	0.482074i	−0.423719	−	0.905794i	$-0.639276\pi$
$587$	1.14744e37	−	1.14744e37i	0.482074	−	0.482074i	0.905794	+	0.423719i	$0.139276\pi$
$588$	−2.47944e37	+	6.24561e35i	−1.01803	+	0.0256437i
$589$	5.66865e35	+	5.66865e35i	0.0227469	+	0.0227469i
$590$	4.05464e35	−	1.73962e35i	0.0159020	−	0.00682264i
$591$	−3.39997e35			−0.0130330
$592$	−3.15039e36	−	2.84801e36i	−0.118038	−	0.106708i
$593$	−7.36810e36			−0.269847			−0.134923	−	0.990856i	$-0.543079\pi$
$593$	−7.36810e36			−0.269847			−0.134923	+	0.990856i	$0.543079\pi$
$594$	−3.63195e37	+	1.55827e37i	−1.30024	+	0.557860i
$595$	−3.16247e37	−	3.16247e37i	−1.10674	−	1.10674i
$596$	3.43875e35	+	1.36514e37i	0.0117646	+	0.467040i
$597$	−1.40153e37	+	1.40153e37i	−0.468758	+	0.468758i
$598$	3.77492e37	+	1.50822e37i	1.23436	+	0.493172i
$599$		−	2.75563e37i		−	0.880966i	−0.897761	−	0.440483i	$-0.854807\pi$
$599$		−	2.75563e37i		−	0.880966i	0.897761	−	0.440483i	$-0.145193\pi$
$600$	3.71909e36	−	1.70779e36i	0.116251	−	0.0533819i
$601$			4.55072e37i			1.39083i	0.718608	+	0.695416i	$0.244780\pi$
$601$			4.55072e37i			1.39083i	−0.718608	+	0.695416i	$0.755220\pi$
$602$	2.01039e37	−	5.03180e37i	0.600797	−	1.50373i
$603$	2.00353e37	−	2.00353e37i	0.585481	−	0.585481i
$604$	−4.86010e36	−	4.62126e36i	−0.138882	−	0.132057i
$605$	2.29730e37	+	2.29730e37i	0.641979	+	0.641979i
$606$	2.13694e36	+	4.98069e36i	0.0583998	+	0.136116i
$607$	−6.75868e37			−1.80640			−0.903202	−	0.429216i	$-0.858790\pi$
$607$	−6.75868e37			−1.80640			−0.903202	+	0.429216i	$0.858790\pi$
$608$	7.24984e36	+	2.48113e36i	0.189509	+	0.0648562i
$609$	2.85125e37			0.728956
$610$	2.27220e37	+	5.29596e37i	0.568191	+	1.32432i
$611$	−2.57982e37	−	2.57982e37i	−0.631005	−	0.631005i
$612$	2.04061e37	+	1.94033e37i	0.488220	+	0.464228i
$613$	4.01970e37	−	4.01970e37i	0.940757	−	0.940757i	−0.0575836	−	0.998341i	$-0.518340\pi$
$613$	4.01970e37	−	4.01970e37i	0.940757	−	0.940757i	0.998341	+	0.0575836i	$0.0183396\pi$
$614$	6.57281e35	−	1.64511e36i	0.0150480	−	0.0376636i
$615$			2.88504e37i			0.646156i
$616$	−4.41742e37	−	9.61989e37i	−0.967897	−	2.10781i
$617$		−	2.68293e37i		−	0.575121i	−0.957762	−	0.287561i	$-0.907156\pi$
$617$		−	2.68293e37i		−	0.575121i	0.957762	−	0.287561i	$-0.0928443\pi$
$618$	3.70712e37	+	1.48113e37i	0.777486	+	0.310634i
$619$	2.12714e37	−	2.12714e37i	0.436488	−	0.436488i	−0.454340	−	0.890828i	$-0.650125\pi$
$619$	2.12714e37	−	2.12714e37i	0.436488	−	0.436488i	0.890828	+	0.454340i	$0.150125\pi$
$620$	1.79172e35	+	7.11292e36i	0.00359734	+	0.142810i
$621$	−2.81487e37	−	2.81487e37i	−0.552996	−	0.552996i
$622$	6.94892e37	−	2.98140e37i	1.33582	−	0.573125i
$623$	−1.63014e38			−3.06645
$624$	−5.62287e37	+	2.83456e36i	−1.03506	+	0.0521788i
$625$	4.14995e37			0.747588
$626$	−6.95476e37	+	2.98390e37i	−1.22611	+	0.526054i
$627$	−7.14855e36	−	7.14855e36i	−0.123341	−	0.123341i
$628$	4.33953e37	−	1.09311e36i	0.732803	−	0.0184590i
$629$	7.34161e36	−	7.34161e36i	0.121341	−	0.121341i
$630$	5.20446e37	+	2.07937e37i	0.841935	+	0.336384i
$631$			5.48476e37i			0.868484i	0.900796	+	0.434242i	$0.142984\pi$
$631$			5.48476e37i			0.868484i	−0.900796	+	0.434242i	$0.857016\pi$
$632$	−1.91852e37	−	7.11035e36i	−0.297361	−	0.110207i
$633$			6.48853e37i			0.984456i
$634$	−4.11795e36	+	1.03068e37i	−0.0611613	+	0.153080i
$635$	−1.09040e36	+	1.09040e36i	−0.0158540	+	0.0158540i
$636$	4.31475e37	−	4.53774e37i	0.614164	−	0.645905i
$637$	−1.42692e38	−	1.42692e38i	−1.98847	−	1.98847i
$638$	2.99588e37	+	6.98268e37i	0.408738	+	0.952671i
$639$	8.61374e37			1.15062
$640$	3.14563e37	+	6.02976e37i	0.411413	+	0.788625i
$641$	6.91474e37			0.885508			0.442754	−	0.896643i	$-0.354001\pi$
$641$	6.91474e37			0.885508			0.442754	+	0.896643i	$0.354001\pi$
$642$	−2.43581e37	−	5.67730e37i	−0.305436	−	0.711899i
$643$	6.89507e37	+	6.89507e37i	0.846624	+	0.846624i	0.989710	−	0.143086i	$-0.0457025\pi$
$643$	6.89507e37	+	6.89507e37i	0.846624	+	0.846624i	−0.143086	+	0.989710i	$0.545703\pi$
$644$	7.34731e37	−	7.72703e37i	0.883424	−	0.929080i
$645$	3.24769e37	−	3.24769e37i	0.382401	−	0.382401i
$646$	−6.95042e36	+	1.73962e37i	−0.0801442	+	0.200593i
$647$			1.07145e38i			1.20995i	0.796246	+	0.604973i	$0.206816\pi$
$647$			1.07145e38i			1.20995i	−0.796246	+	0.604973i	$0.793184\pi$
$648$	−1.26712e36	−	4.69616e35i	−0.0140138	−	0.00519374i
$649$			2.55302e36i			0.0276535i
$650$	3.09207e37	+	1.23539e37i	0.328034	+	0.131062i
$651$	−1.09246e37	+	1.09246e37i	−0.113517	+	0.113517i
$652$	8.79240e37	−	2.21477e36i	0.894880	−	0.0225417i
$653$	−6.89952e37	−	6.89952e37i	−0.687845	−	0.687845i	0.273910	−	0.961755i	$-0.411683\pi$
$653$	−6.89952e37	−	6.89952e37i	−0.687845	−	0.687845i	−0.961755	+	0.273910i	$0.911683\pi$
$654$	8.93831e37	−	3.83493e37i	0.872883	−	0.374505i
$655$	−2.99145e37			−0.286170
$656$	1.26374e38	−	6.37066e36i	1.18428	−	0.0597011i
$657$	1.30670e37			0.119962
$658$	−8.79443e37	+	3.77320e37i	−0.790967	+	0.339360i
$659$	−4.75260e37	−	4.75260e37i	−0.418772	−	0.418772i	0.466008	−	0.884780i	$-0.345692\pi$
$659$	−4.75260e37	−	4.75260e37i	−0.418772	−	0.418772i	−0.884780	+	0.466008i	$0.845692\pi$
$660$	−2.25948e36	−	8.96988e37i	−0.0195059	−	0.774361i
$661$	1.53532e38	−	1.53532e38i	1.29861	−	1.29861i	0.369296	−	0.929312i	$-0.379599\pi$
$661$	1.53532e38	−	1.53532e38i	1.29861	−	1.29861i	0.929312	−	0.369296i	$-0.120401\pi$
$662$	2.08652e37	+	8.33642e36i	0.172918	+	0.0690870i
$663$		−	1.37640e38i		−	1.11766i
$664$	8.47470e36	+	1.84555e37i	0.0674303	+	0.146844i
$665$			3.72856e37i			0.290702i
$666$	−4.82723e36	+	1.20821e37i	−0.0368804	+	0.0923079i
$667$	−5.41179e37	+	5.41179e37i	−0.405175	+	0.405175i
$668$	−9.59594e37	−	9.12438e37i	−0.704053	−	0.669455i
$669$	4.80391e37	+	4.80391e37i	0.345416	+	0.345416i
$670$	6.59659e37	+	1.53751e38i	0.464847	+	1.08345i
$671$	−3.33462e38			−2.30299
$672$	−4.78161e37	+	1.39718e38i	−0.323660	+	0.945731i
$673$	1.30104e38			0.863149			0.431575	−	0.902077i	$-0.357958\pi$
$673$	1.30104e38			0.863149			0.431575	+	0.902077i	$0.357958\pi$
$674$	−1.03164e38	−	2.40450e38i	−0.670839	−	1.56357i
$675$	−2.30569e37	−	2.30569e37i	−0.146960	−	0.146960i
$676$	−2.15967e38	−	2.05354e38i	−1.34929	−	1.28299i
$677$	2.77351e36	−	2.77351e36i	0.0169857	−	0.0169857i	−0.698563	−	0.715549i	$-0.746177\pi$
$677$	2.77351e36	−	2.77351e36i	0.0169857	−	0.0169857i	0.715549	+	0.698563i	$0.246177\pi$
$678$	−3.14695e37	+	7.87650e37i	−0.188925	+	0.472860i
$679$			3.15507e38i			1.85681i
$680$	−1.51098e38	+	6.93835e37i	−0.871741	+	0.400301i
$681$			8.01609e37i			0.453395i
$682$	−3.82329e37	−	1.52754e37i	−0.212006	−	0.0847041i
$683$	4.29135e37	−	4.29135e37i	0.233300	−	0.233300i	−0.580769	−	0.814069i	$-0.697248\pi$
$683$	4.29135e37	−	4.29135e37i	0.233300	−	0.233300i	0.814069	+	0.580769i	$0.197248\pi$
$684$	−5.91143e35	−	2.34677e37i	−0.00315090	−	0.125087i
$685$	−1.20281e38	−	1.20281e38i	−0.628601	−	0.628601i
$686$	−1.93803e38	+	8.31501e37i	−0.993082	+	0.426076i
$687$	8.88659e37			0.446498
$688$	−1.49431e38	−	1.35088e38i	−0.736201	−	0.665538i
$689$	5.09463e38			2.46124
$690$	8.30572e37	−	3.56352e37i	0.393473	−	0.168817i
$691$	−1.63822e38	−	1.63822e38i	−0.761060	−	0.761060i	0.215454	−	0.976514i	$-0.430877\pi$
$691$	−1.63822e38	−	1.63822e38i	−0.761060	−	0.761060i	−0.976514	+	0.215454i	$0.930877\pi$
$692$	−4.69068e36	+	1.18156e35i	−0.0213699	+	0.000538301i
$693$	−2.29314e38	+	2.29314e38i	−1.02455	+	1.02455i
$694$	1.67748e38	+	6.70214e37i	0.735028	+	0.293671i
$695$			9.50651e37i			0.408532i
$696$	3.68363e37	−	9.93917e37i	0.155257	−	0.418915i
$697$			3.09345e38i			1.27879i
$698$	6.93530e37	−	1.73584e38i	0.281201	−	0.703818i
$699$	9.38140e37	−	9.38140e37i	0.373101	−	0.373101i
$700$	6.01825e37	−	6.32928e37i	0.234772	−	0.246905i
$701$	7.02435e37	+	7.02435e37i	0.268790	+	0.268790i	0.828612	−	0.559823i	$-0.189131\pi$
$701$	7.02435e37	+	7.02435e37i	0.268790	+	0.268790i	−0.559823	+	0.828612i	$0.689131\pi$
$702$	1.76869e38	+	4.12240e38i	0.663899	+	1.54739i
$703$	−8.65578e36			−0.0318720
$704$	−3.92410e38	+	2.97043e37i	−1.41746	+	0.107297i
$705$	−8.11157e37			−0.287443
$706$	9.42532e37	+	2.19682e38i	0.327667	+	0.763714i
$707$	8.17869e37	+	8.17869e37i	0.278947	+	0.278947i
$708$	2.45419e36	−	2.58102e36i	0.00821218	−	0.00863659i
$709$	1.37055e38	−	1.37055e38i	0.449956	−	0.449956i	−0.445384	−	0.895340i	$-0.646933\pi$
$709$	1.37055e38	−	1.37055e38i	0.449956	−	0.449956i	0.895340	+	0.445384i	$0.146933\pi$
$710$	−1.88706e38	+	4.72311e38i	−0.607851	+	1.52139i
$711$			6.26820e37i			0.198108i
$712$	−2.10603e38	+	5.68251e38i	−0.653109	+	1.76222i
$713$		−	4.14706e37i		−	0.126192i
$714$	−3.35258e38	−	1.33948e38i	−1.00104	−	0.399953i
$715$	5.16219e38	−	5.16219e38i	1.51252	−	1.51252i
$716$	6.31253e38	−	1.59010e37i	1.81500	−	0.0457193i
$717$	−1.11755e38	−	1.11755e38i	−0.315325	−	0.315325i
$718$	−2.00109e38	+	8.58556e37i	−0.554098	+	0.237733i
$719$	−1.93805e38			−0.526652			−0.263326	−	0.964707i	$-0.584820\pi$
$719$	−1.93805e38			−0.526652			−0.263326	+	0.964707i	$0.584820\pi$
$720$	1.39723e38	−	1.54558e38i	0.372632	−	0.412196i
$721$	8.51953e38			2.22992
$722$	−3.43383e38	+	1.47327e38i	−0.882118	+	0.378468i
$723$	1.26485e38	+	1.26485e38i	0.318913	+	0.318913i
$724$	−1.06852e37	−	4.24190e38i	−0.0264431	−	1.04976i
$725$	−4.43285e37	+	4.43285e37i	−0.107676	+	0.107676i
$726$	2.43540e38	+	9.73032e37i	0.580666	+	0.231997i
$727$			5.83230e38i			1.36498i	0.730896	+	0.682489i	$0.239102\pi$
$727$			5.83230e38i			1.36498i	−0.730896	+	0.682489i	$0.760898\pi$
$728$	−1.09189e39	+	5.01394e38i	−2.50846	+	1.15188i
$729$		−	2.66241e38i		−	0.600416i
$730$	−2.86265e37	+	7.16492e37i	−0.0633738	+	0.158618i
$731$	3.48231e38	−	3.48231e38i	0.756802	−	0.756802i
$732$	3.37119e38	+	3.20553e38i	0.719257	+	0.683911i
$733$	2.84709e38	+	2.84709e38i	0.596344	+	0.596344i	0.939338	−	0.342994i	$-0.111441\pi$
$733$	2.84709e38	+	2.84709e38i	0.596344	+	0.596344i	−0.342994	+	0.939338i	$0.611441\pi$
$734$	−8.39946e37	−	1.95771e38i	−0.172725	−	0.402580i
$735$	−4.48659e38			−0.905811
$736$	−1.74434e38	−	3.55948e38i	−0.345765	−	0.705564i
$737$	−9.68097e38			−1.88412
$738$	−1.52844e38	−	3.56243e38i	−0.292071	−	0.680747i
$739$	6.68697e38	+	6.68697e38i	1.25467	+	1.25467i	0.953603	+	0.301066i	$0.0973426\pi$
$739$	6.68697e38	+	6.68697e38i	1.25467	+	1.25467i	0.301066	+	0.953603i	$0.402657\pi$
$740$	−5.56735e37	−	5.29376e37i	−0.102570	−	0.0975296i
$741$	−8.11388e37	+	8.11388e37i	−0.146785	+	0.146785i
$742$	4.95797e38	−	1.24093e39i	0.880747	−	2.20442i
$743$		−	5.43877e38i		−	0.948749i	−0.880323	−	0.474374i	$-0.842674\pi$
$743$		−	5.43877e38i		−	0.948749i	0.880323	−	0.474374i	$-0.157326\pi$
$744$	2.39681e37	+	5.21958e37i	0.0410582	+	0.0894130i
$745$			2.47025e38i			0.415558i
$746$	−9.18501e38	−	3.66975e38i	−1.51742	−	0.606265i
$747$	4.39933e37	−	4.39933e37i	0.0713771	−	0.0713771i
$748$	−2.42270e37	−	9.61786e38i	−0.0386037	−	1.53252i
$749$	−9.32257e38	−	9.32257e38i	−1.45892	−	1.45892i
$750$	3.93845e38	−	1.68977e38i	0.605339	−	0.259717i
$751$	−2.12346e38			−0.320557			−0.160279	−	0.987072i	$-0.551239\pi$
$751$	−2.12346e38			−0.320557			−0.160279	+	0.987072i	$0.551239\pi$
$752$	1.79118e37	+	3.55313e38i	0.0265581	+	0.526829i
$753$	6.01913e38			0.876600
$754$	7.92561e38	−	3.40044e38i	1.13376	−	0.486432i
$755$	−8.57835e37	−	8.57835e37i	−0.120537	−	0.120537i
$756$	1.17624e39	−	2.96291e37i	1.62350	−	0.0408954i
$757$	7.22070e37	−	7.22070e37i	0.0979005	−	0.0979005i	−0.656460	−	0.754361i	$-0.727947\pi$
$757$	7.22070e37	−	7.22070e37i	0.0979005	−	0.0979005i	0.754361	+	0.656460i	$0.227947\pi$
$758$	−1.10969e37	−	4.43361e36i	−0.0147797	−	0.00590504i
$759$			5.22972e38i			0.684250i
$760$	1.29974e38	+	4.81705e37i	0.167060	+	0.0619153i
$761$			2.50086e38i			0.315788i	0.987456	+	0.157894i	$0.0504705\pi$
$761$			2.50086e38i			0.315788i	−0.987456	+	0.157894i	$0.949529\pi$
$762$	−4.61842e36	+	1.15594e37i	−0.00572930	+	0.0143398i
$763$	1.46774e39	−	1.46774e39i	1.78883	−	1.78883i
$764$	−5.05258e38	+	5.31371e38i	−0.604997	+	0.636264i
$765$	3.60180e38	+	3.60180e38i	0.423730	+	0.423730i
$766$	3.78645e38	+	8.82531e38i	0.437667	+	1.02010i
$767$	2.89778e37			0.0329100
$768$	4.25269e38	+	3.47189e38i	0.474555	+	0.387427i
$769$	−1.12590e39			−1.23451			−0.617255	−	0.786763i	$-0.711755\pi$
$769$	−1.12590e39			−1.23451			−0.617255	+	0.786763i	$0.711755\pi$
$770$	−7.55014e38	−	1.75976e39i	−0.813448	−	1.89595i
$771$	−5.98664e38	−	5.98664e38i	−0.633796	−	0.633796i
$772$	4.50575e38	−	4.73861e38i	0.468741	−	0.492966i
$773$	−6.60728e38	+	6.60728e38i	−0.675459	+	0.675459i	−0.958969	−	0.283510i	$-0.908501\pi$
$773$	−6.60728e38	+	6.60728e38i	−0.675459	+	0.675459i	0.283510	+	0.958969i	$0.408501\pi$
$774$	−2.28967e38	+	5.73082e38i	−0.230022	+	0.575723i
$775$		−	3.39689e37i		−	0.0335358i
$776$	1.09983e39	+	4.07614e38i	1.06706	+	0.395472i
$777$		−	1.66813e38i		−	0.159055i
$778$	5.49778e38	+	2.19657e38i	0.515185	+	0.205835i
$779$	1.82359e38	−	1.82359e38i	0.167947	−	0.167947i
$780$	−1.01812e39	+	2.56460e37i	−0.921552	+	0.0232136i
$781$	−2.08106e39	−	2.08106e39i	−1.85138	−	1.85138i
$782$	8.90572e38	−	3.82095e38i	0.778714	−	0.334103i
$783$	−8.44559e38			−0.725849
$784$	9.90718e37	+	1.96527e39i	0.0836918	+	1.66018i
$785$	7.85246e38			0.652027
$786$	−2.21916e38	+	9.52118e37i	−0.181127	+	0.0777117i
$787$	−2.82219e38	−	2.82219e38i	−0.226426	−	0.226426i	0.584772	−	0.811198i	$-0.301184\pi$
$787$	−2.82219e38	−	2.82219e38i	−0.226426	−	0.226426i	−0.811198	+	0.584772i	$0.801184\pi$
$788$	6.79270e35	+	2.69662e37i	0.000535720	+	0.0212675i
$789$	−5.96850e38	+	5.96850e38i	−0.462728	+	0.462728i
$790$	−3.43700e38	−	1.37321e38i	−0.261947	−	0.104658i
$791$			1.81014e39i			1.35622i
$792$	5.03109e38	+	1.09563e39i	0.370571	+	0.806999i
$793$			3.78492e39i			2.74074i
$794$	4.47437e38	−	1.11989e39i	0.318533	−	0.797257i
$795$	8.00937e38	−	8.00937e38i	0.560586	−	0.560586i
$796$	1.13960e39	+	1.08359e39i	0.784196	+	0.745660i
$797$	−1.45881e39	−	1.45881e39i	−0.986984	−	0.986984i	0.0129323	−	0.999916i	$-0.495883\pi$
$797$	−1.45881e39	−	1.45881e39i	−0.986984	−	0.986984i	−0.999916	+	0.0129323i	$0.995883\pi$
$798$	1.18672e38	+	2.76597e38i	0.0789425	+	0.183996i
$799$	−8.69754e38			−0.568873
$800$	−1.42881e38	−	2.91561e38i	−0.0918879	−	0.187505i
$801$	1.85660e39			1.17403
$802$	−2.53706e38	−	5.91327e38i	−0.157752	−	0.367683i
$803$	−3.15695e38	−	3.15695e38i	−0.193022	−	0.193022i
$804$	9.78715e38	+	9.30620e38i	0.588437	+	0.559520i
$805$	1.36387e39	−	1.36387e39i	0.806357	−	0.806357i
$806$	−1.73382e38	+	4.33958e38i	−0.100805	+	0.252304i
$807$			2.06781e38i			0.118227i
$808$	3.90765e38	−	1.79438e38i	0.219716	−	0.100893i
$809$			1.49786e39i			0.828257i	0.910218	+	0.414129i	$0.135914\pi$
$809$			1.49786e39i			0.828257i	−0.910218	+	0.414129i	$0.864086\pi$
$810$	−2.27003e37	−	9.06961e36i	−0.0123448	−	0.00493220i
$811$	−1.09536e39	+	1.09536e39i	−0.585834	+	0.585834i	−0.936501	−	0.350666i	$-0.885955\pi$
$811$	−1.09536e39	+	1.09536e39i	−0.585834	+	0.585834i	0.350666	+	0.936501i	$0.385955\pi$
$812$	−5.69641e37	−	2.26141e39i	−0.0299637	−	1.18952i
$813$	−1.20965e39	−	1.20965e39i	−0.625803	−	0.625803i
$814$	4.08524e38	−	1.75275e38i	0.207868	−	0.0891847i
$815$	1.59100e39			0.796238
$816$	−9.00060e38	+	9.95624e38i	−0.443052	+	0.490092i
$817$	−4.10565e38			−0.198785
$818$	−2.45875e39	+	1.05491e39i	−1.17097	+	0.502398i
$819$	2.60281e39	+	2.60281e39i	1.21930	+	1.21930i
$820$	2.28821e39	−	5.76392e37i	1.05441	−	0.0265602i
$821$	−2.16232e39	+	2.16232e39i	−0.980137	+	0.980137i	−0.999807	−	0.0196697i	$-0.993739\pi$
$821$	−2.16232e39	+	2.16232e39i	−0.980137	+	0.980137i	0.0196697	+	0.999807i	$0.493739\pi$
$822$	−1.27512e39	−	5.09456e38i	−0.568566	−	0.227163i
$823$		−	3.19936e38i		−	0.140335i	−0.997535	−	0.0701673i	$-0.977647\pi$
$823$		−	3.19936e38i		−	0.140335i	0.997535	−	0.0701673i	$-0.0223533\pi$
$824$	1.10067e39	−	2.96983e39i	0.474940	−	1.28148i
$825$			4.28372e38i			0.181841i
$826$	2.82004e37	−	7.05828e37i	0.0117767	−	0.0294760i
$827$	−6.13865e38	+	6.13865e38i	−0.252202	+	0.252202i	−0.821873	−	0.569671i	$-0.807071\pi$
$827$	−6.13865e38	+	6.13865e38i	−0.252202	+	0.252202i	0.569671	+	0.821873i	$0.307071\pi$
$828$	−8.36799e38	+	8.80046e38i	−0.338230	+	0.355710i
$829$	9.41753e38	+	9.41753e38i	0.374499	+	0.374499i	0.869113	−	0.494614i	$-0.164690\pi$
$829$	9.41753e38	+	9.41753e38i	0.374499	+	0.374499i	−0.494614	+	0.869113i	$0.664690\pi$
$830$	1.44847e38	+	3.37604e38i	0.0566704	+	0.132085i
$831$	−1.72319e39			−0.663313
$832$	3.37155e38	+	4.45401e39i	0.127692	+	1.68689i
$833$	−4.81070e39			−1.79267
$834$	3.02573e38	+	7.05225e38i	0.110940	+	0.258575i
$835$	−1.69374e39	−	1.69374e39i	−0.611053	−	0.611053i
$836$	−5.52692e38	+	5.81255e38i	−0.196200	+	0.206339i
$837$	3.23593e38	−	3.23593e38i	0.113033	−	0.113033i
$838$	−2.02324e38	+	5.06396e38i	−0.0695429	+	0.174059i
$839$		−	4.03862e39i		−	1.36599i	−0.730425	−	0.682993i	$-0.760678\pi$
$839$		−	4.03862e39i		−	1.36599i	0.730425	−	0.682993i	$-0.239322\pi$
$840$	−9.28338e38	+	2.50484e39i	−0.308984	+	0.833701i
$841$		−	1.42941e39i		−	0.468178i
$842$	−5.56908e39	−	2.22505e39i	−1.79502	−	0.717178i
$843$	1.49593e39	−	1.49593e39i	0.474502	−	0.474502i
$844$	5.14625e39	−	1.29632e38i	1.60645	−	0.0404660i
$845$	−3.81194e39	−	3.81194e39i	−1.17106	−	1.17106i
$846$	1.00161e39	−	4.29737e38i	0.302831	−	0.129928i
$847$	5.59692e39			1.66542
$848$	−3.68522e39	−	3.33150e39i	−1.07924	−	0.975654i
$849$	2.72751e38			0.0786164
$850$	7.29476e38	−	3.12978e38i	0.206945	−	0.0887887i
$851$	3.16619e38	+	3.16619e38i	0.0884072	+	0.0884072i
$852$	1.03388e38	+	4.10438e39i	0.0284142	+	1.12801i
$853$	−1.41259e39	+	1.41259e39i	−0.382123	+	0.382123i	−0.871866	−	0.489744i	$-0.837090\pi$
$853$	−1.41259e39	+	1.41259e39i	−0.382123	+	0.382123i	0.489744	+	0.871866i	$0.337090\pi$
$854$	9.21915e39	+	3.68339e39i	2.45476	+	0.980768i
$855$		−	4.24652e38i		−	0.111299i
$856$	−4.45417e39	+	2.04534e39i	−1.14914	+	0.527679i
$857$			2.38922e39i			0.606759i	0.952870	+	0.303379i	$0.0981149\pi$
$857$			2.38922e39i			0.606759i	−0.952870	+	0.303379i	$0.901885\pi$
$858$	2.18647e39	−	5.47251e39i	0.546594	−	1.36807i
$859$	1.68651e39	−	1.68651e39i	0.415030	−	0.415030i	−0.468456	−	0.883487i	$-0.655190\pi$
$859$	1.68651e39	−	1.68651e39i	0.415030	−	0.415030i	0.883487	+	0.468456i	$0.155190\pi$
$860$	−2.64073e39	−	2.51096e39i	−0.639727	−	0.608290i
$861$	3.51441e39	+	3.51441e39i	0.838126	+	0.838126i
$862$	−1.20115e39	−	2.79960e39i	−0.282000	−	0.657275i
$863$	−1.58746e39			−0.366908			−0.183454	−	0.983028i	$-0.558728\pi$
$863$	−1.58746e39			−0.366908			−0.183454	+	0.983028i	$0.558728\pi$
$864$	1.41635e39	−	4.13855e39i	0.322280	−	0.941700i
$865$	−8.48787e37			−0.0190144
$866$	−1.51396e38	−	3.52868e38i	−0.0333905	−	0.0778252i
$867$	−3.25225e38	−	3.25225e38i	−0.0706197	−	0.0706197i
$868$	8.88286e38	+	8.44634e38i	0.189905	+	0.180573i
$869$	1.51438e39	−	1.51438e39i	0.318763	−	0.318763i
$870$	7.11412e38	−	1.78059e39i	0.147439	−	0.369024i
$871$			1.09883e40i			2.24225i
$872$	−3.22018e39	−	7.01263e39i	−0.647005	−	1.40899i
$873$		−	3.59336e39i		−	0.710901i
$874$	−7.50239e38	−	2.99748e38i	−0.146149	−	0.0583918i
$875$	6.46725e39	−	6.46725e39i	1.24054	−	1.24054i
$876$	1.56838e37	+	6.22630e38i	0.00296242	+	0.117605i
$877$	6.10550e39	+	6.10550e39i	1.13560	+	1.13560i	0.989229	+	0.146373i	$0.0467601\pi$
$877$	6.10550e39	+	6.10550e39i	1.13560	+	1.13560i	0.146373	+	0.989229i	$0.453240\pi$
$878$	4.85278e39	−	2.08206e39i	0.888822	−	0.381344i
$879$	−3.38048e39			−0.609717
$880$	−7.10977e39	+	3.58412e38i	−1.26281	+	0.0636600i
$881$	8.14158e39			1.42408			0.712039	−	0.702140i	$-0.247772\pi$
$881$	8.14158e39			1.42408			0.712039	+	0.702140i	$0.247772\pi$
$882$	5.54003e39	−	2.37692e39i	0.954303	−	0.409438i
$883$	−4.34861e39	−	4.34861e39i	−0.737703	−	0.737703i	0.234430	−	0.972133i	$-0.424678\pi$
$883$	−4.34861e39	−	4.34861e39i	−0.737703	−	0.737703i	−0.972133	+	0.234430i	$0.924678\pi$
$884$	−1.09166e40	+	2.74986e38i	−1.82383	+	0.0459415i
$885$	4.55565e37	−	4.55565e37i	0.00749577	−	0.00749577i
$886$	−8.47052e39	−	3.38428e39i	−1.37263	−	0.548418i
$887$			9.73184e38i			0.155320i	0.996980	+	0.0776598i	$0.0247448\pi$
$887$			9.73184e38i			0.155320i	−0.996980	+	0.0776598i	$0.975255\pi$
$888$	−5.81495e38	−	2.15512e38i	−0.0914051	−	0.0338763i
$889$			2.65653e38i			0.0411283i
$890$	−4.06734e39	+	1.01801e40i	−0.620220	+	1.55235i
$891$	1.00020e38	−	1.00020e38i	0.0150224	−	0.0150224i
$892$	3.71415e39	−	3.90611e39i	0.549458	−	0.577855i
$893$	5.12721e38	+	5.12721e38i	0.0747113	+	0.0747113i
$894$	7.86231e38	+	1.83252e39i	0.112848	+	0.263022i
$895$	1.14226e40			1.61494
$896$	1.11770e40	+	3.51330e39i	1.55656	+	0.489280i
$897$	5.93594e39			0.814313
$898$	−5.83457e38	−	1.35990e39i	−0.0788458	−	0.183771i
$899$	−6.22131e38	−	6.22131e38i	−0.0828182	−	0.0828182i
$900$	−6.85430e38	+	7.20854e38i	−0.0898854	+	0.0945308i
$901$	8.58797e39	−	8.58797e39i	1.10944	−	1.10944i
$902$	−4.91407e39	+	1.22994e40i	−0.625394	+	1.56530i
$903$		−	7.91236e39i		−	0.992022i
$904$	6.30996e39	+	2.33858e39i	0.779387	+	0.288854i
$905$		−	7.67581e39i		−	0.934046i
$906$	−9.09403e38	−	3.63340e38i	−0.109025	−	0.0435594i
$907$	−1.58072e39	+	1.58072e39i	−0.186705	+	0.186705i	−0.794270	−	0.607565i	$-0.792146\pi$
$907$	−1.58072e39	+	1.58072e39i	−0.186705	+	0.186705i	0.607565	+	0.794270i	$0.292146\pi$
$908$	6.35781e39	−	1.60151e38i	0.739858	−	0.0186368i
$909$	−9.31487e38	−	9.31487e38i	−0.106798	−	0.106798i
$910$	−1.99739e40	+	8.56969e39i	−2.25634	+	0.968070i
$911$	−2.16461e39			−0.240925			−0.120462	−	0.992718i	$-0.538438\pi$
$911$	−2.16461e39			−0.240925			−0.120462	+	0.992718i	$0.538438\pi$
$912$	1.11751e39	−	5.63350e37i	0.122552	−	0.00617800i
$913$	−2.12574e39			−0.229696
$914$	−7.53521e39	+	3.23294e39i	−0.802273	+	0.344210i
$915$	5.95035e39	+	5.95035e39i	0.624249	+	0.624249i
$916$	−1.77542e38	−	7.04823e39i	−0.0183532	−	0.728603i
$917$	−3.64404e39	+	3.64404e39i	−0.371190	+	0.371190i
$918$	9.93057e39	+	3.96763e39i	0.996776	+	0.398249i
$919$			3.96068e39i			0.391751i	0.980629	+	0.195876i	$0.0627549\pi$
$919$			3.96068e39i			0.391751i	−0.980629	+	0.195876i	$0.937245\pi$
$920$	−2.99228e39	−	6.51633e39i	−0.291653	−	0.635137i
$921$		−	2.58688e38i		−	0.0248469i
$922$	−5.04002e39	+	1.26146e40i	−0.477051	+	1.19401i
$923$	−2.36208e40	+	2.36208e40i	−2.20329	+	2.20329i
$924$	−1.12019e40	−	1.06514e40i	−1.02972	−	0.979120i
$925$	2.59345e38	+	2.59345e38i	0.0234944	+	0.0234944i
$926$	−7.31872e39	−	1.70582e40i	−0.653412	−	1.52295i
$927$	−9.70305e39			−0.853752
$928$	−7.95665e39	−	2.72303e39i	−0.689974	−	0.236132i
$929$	1.39436e37			0.00119169			0.000595844	−	1.00000i	$-0.499810\pi$
$929$	1.39436e37			0.00119169			0.000595844		1.00000i	$0.499810\pi$
$930$	4.09657e38	+	9.54812e38i	0.0345064	+	0.0804263i
$931$	2.83591e39	+	2.83591e39i	0.235436	+	0.235436i
$932$	−7.62811e39	−	7.25325e39i	−0.624169	−	0.593496i
$933$	7.80756e39	−	7.80756e39i	0.629670	−	0.629670i
$934$	−4.32992e38	+	1.08374e39i	−0.0344189	+	0.0861470i
$935$		−	1.74037e40i		−	1.36359i
$936$	1.24358e40	−	5.71048e39i	0.960394	−	0.441010i
$937$		−	6.39746e39i		−	0.486993i	−0.969902	−	0.243497i	$-0.921706\pi$
$937$		−	6.39746e39i		−	0.486993i	0.969902	−	0.243497i	$-0.0782945\pi$
$938$	2.67648e40	+	1.06935e40i	2.00829	+	0.802384i
$939$	−7.81412e39	+	7.81412e39i	−0.577955	+	0.577955i
$940$	1.62058e38	+	6.43353e39i	0.0118153	+	0.469055i
$941$	−2.20712e39	−	2.20712e39i	−0.158623	−	0.158623i	0.623333	−	0.781956i	$-0.285778\pi$
$941$	−2.20712e39	−	2.20712e39i	−0.158623	−	0.158623i	−0.781956	+	0.623333i	$0.785778\pi$
$942$	5.82522e39	−	2.49928e39i	0.412691	−	0.177063i
$943$	−1.33410e40			−0.931709
$944$	−2.09612e38	−	1.89492e38i	−0.0144309	−	0.0130458i
$945$	2.12844e40			1.44455
$946$	1.93773e40	−	8.31372e39i	1.29647	−	0.556244i
$947$	5.69701e39	+	5.69701e39i	0.375770	+	0.375770i	0.869573	−	0.493804i	$-0.164394\pi$
$947$	5.69701e39	+	5.69701e39i	0.375770	+	0.375770i	−0.493804	+	0.869573i	$0.664394\pi$
$948$	−2.98675e39	+	7.52351e37i	−0.194216	+	0.00489224i
$949$	−3.58325e39	+	3.58325e39i	−0.229712	+	0.229712i
$950$	−6.14528e38	−	2.45526e38i	−0.0388394	−	0.0155178i
$951$			1.62072e39i			0.100988i
$952$	−9.95400e39	+	2.68579e40i	−0.611503	+	1.64996i
$953$			9.65797e39i			0.584967i	0.956271	+	0.292484i	$0.0944817\pi$
$953$			9.65797e39i			0.584967i	−0.956271	+	0.292484i	$0.905518\pi$
$954$	−5.64672e39	+	1.41332e40i	−0.337205	+	0.843989i
$955$	−9.37900e39	+	9.37900e39i	−0.552219	+	0.552219i
$956$	−8.64035e39	+	9.08689e39i	−0.501591	+	0.527514i
$957$	7.84549e39	+	7.84549e39i	0.449065	+	0.449065i
$958$	5.11833e39	+	1.19296e40i	0.288864	+	0.673273i
$959$	−2.93041e40			−1.63071
$960$	7.53229e39	+	6.47219e39i	0.413300	+	0.355132i
$961$	−1.80060e40			−0.974206
$962$	−1.98944e39	−	4.63691e39i	−0.106137	−	0.247380i
$963$	1.06176e40	+	1.06176e40i	0.558565	+	0.558565i
$964$	9.77923e39	−	1.02846e40i	0.507300	−	0.533518i
$965$	8.36392e39	−	8.36392e39i	0.427850	−	0.427850i
$966$	5.77671e39	−	1.44585e40i	0.291400	−	0.729344i
$967$			3.64482e39i			0.181309i	0.995882	+	0.0906544i	$0.0288959\pi$
$967$			3.64482e39i			0.181309i	−0.995882	+	0.0906544i	$0.971104\pi$
$968$	7.23085e39	−	1.95103e40i	0.354709	−	0.957077i
$969$			2.73550e39i			0.132332i
$970$	1.97033e40	+	7.87217e39i	0.939982	+	0.375557i
$971$	1.39947e40	−	1.39947e40i	0.658420	−	0.658420i	−0.296586	−	0.955006i	$-0.595848\pi$
$971$	1.39947e40	−	1.39947e40i	0.658420	−	0.658420i	0.955006	+	0.296586i	$0.0958482\pi$
$972$	−2.16420e40	+	5.45153e38i	−1.00416	+	0.0252944i
$973$	1.15804e40	+	1.15804e40i	0.529906	+	0.529906i
$974$	−1.31355e39	+	5.63570e38i	−0.0592789	+	0.0254333i
$975$	4.86218e39			0.216406
$976$	2.47505e40	−	2.73784e40i	1.08645	−	1.20181i
$977$	−3.25708e40			−1.41011			−0.705053	−	0.709154i	$-0.749077\pi$
$977$	−3.25708e40			−1.41011			−0.705053	+	0.709154i	$0.749077\pi$
$978$	1.18026e40	−	5.06383e39i	0.503968	−	0.216224i
$979$	−4.48549e40	−	4.48549e40i	−1.88905	−	1.88905i
$980$	8.96361e38	+	3.55845e40i	0.0372333	+	1.47812i
$981$	−1.67164e40	+	1.67164e40i	−0.684874	+	0.684874i
$982$	−3.60084e40	−	1.43867e40i	−1.45512	−	0.581374i
$983$			1.35303e40i			0.539306i	0.962958	+	0.269653i	$0.0869090\pi$
$983$			1.35303e40i			0.539306i	−0.962958	+	0.269653i	$0.913091\pi$
$984$	1.67913e40	−	7.71049e39i	0.660160	−	0.303143i
$985$			4.87959e38i			0.0189232i
$986$	7.62804e39	−	1.90922e40i	0.291793	−	0.730328i
$987$	−9.88111e39	+	9.88111e39i	−0.372841	+	0.372841i
$988$	6.59747e39	+	6.27326e39i	0.245561	+	0.233494i
$989$	1.50180e40	+	1.50180e40i	0.551394	+	0.551394i
$990$	8.59899e39	+	2.00422e40i	0.311439	+	0.725889i
$991$	4.27346e40			1.52681			0.763406	−	0.645919i	$-0.223526\pi$
$991$	4.27346e40			1.52681			0.763406	+	0.645919i	$0.223526\pi$
$992$	4.09192e39	−	2.00527e39i	0.144218	−	0.0706747i
$993$	3.28099e39			0.114075
$994$	3.45474e40	+	8.05218e40i	1.18495	+	2.76183i
$995$	2.01145e40	+	2.01145e40i	0.680610	+	0.680610i
$996$	2.14905e39	+	2.04344e39i	0.0717374	+	0.0682121i
$997$	−3.03870e39	+	3.03870e39i	−0.100070	+	0.100070i	−0.755369	−	0.655299i	$-0.772542\pi$
$997$	−3.03870e39	+	3.03870e39i	−0.100070	+	0.100070i	0.655299	+	0.755369i	$0.272542\pi$
$998$	7.15603e38	−	1.79108e39i	0.0232493	−	0.0581907i
$999$			4.94112e39i			0.158377i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.28.e.a.13.20	yes	106
16.5	even	4	inner	16.28.e.a.5.20	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.28.e.a.5.20	✓	106	16.5	even	4	inner
16.28.e.a.13.20	yes	106	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-4567.90 - 10646.7i) q^{2} +(-1.19622e6 - 1.19622e6i) q^{3} +(-9.24863e7 + 9.72661e7i) q^{4} +(-1.71680e9 + 1.71680e9i) q^{5} +(-7.27159e9 + 1.82001e10i) q^{6} +4.18265e11i q^{7} +(1.45803e12 + 5.40371e11i) q^{8} -4.76369e12i q^{9} +(2.61205e13 + 1.04361e13i) q^{10} +(-1.15090e14 + 1.15090e14i) q^{11} +(2.26986e14 - 5.71770e12i) q^{12} +(1.30631e15 + 1.30631e15i) q^{13} +(4.45313e15 - 1.91059e15i) q^{14} +4.10736e15 q^{15} +(-9.06977e14 - 1.79916e16i) q^{16} +4.40408e16 q^{17} +(-5.07176e16 + 2.17601e16i) q^{18} +(-2.59621e16 - 2.59621e16i) q^{19} +(-8.20596e15 - 3.25767e17i) q^{20} +(5.00338e17 - 5.00338e17i) q^{21} +(1.75104e18 + 6.99606e17i) q^{22} +1.89933e18i q^{23} +(-1.09773e18 - 2.39053e18i) q^{24} +1.55576e18i q^{25} +(7.94080e18 - 1.98750e19i) q^{26} +(-1.48204e19 + 1.48204e19i) q^{27} +(-4.06830e19 - 3.86837e19i) q^{28} +(2.84932e19 + 2.84932e19i) q^{29} +(-1.87620e19 - 4.37298e19i) q^{30} -2.18343e19 q^{31} +(-1.87407e20 + 9.18399e19i) q^{32} +2.75346e20 q^{33} +(-2.01174e20 - 4.68888e20i) q^{34} +(-7.18078e20 - 7.18078e20i) q^{35} +(4.63346e20 + 4.40576e20i) q^{36} +(1.66700e20 - 1.66700e20i) q^{37} +(-1.57818e20 + 3.95002e20i) q^{38} -3.12528e21i q^{39} +(-3.43086e21 + 1.57544e21i) q^{40} +7.02406e21i q^{41} +(-7.61244e21 - 3.04145e21i) q^{42} +(7.90701e21 - 7.90701e21i) q^{43} +(-5.50105e20 - 2.18385e22i) q^{44} +(8.17832e21 + 8.17832e21i) q^{45} +(2.02216e22 - 8.67594e21i) q^{46} -1.97489e22 q^{47} +(-2.04370e22 + 2.26069e22i) q^{48} -1.09233e23 q^{49} +(1.65637e22 - 7.10655e21i) q^{50} +(-5.26826e22 - 5.26826e22i) q^{51} +(-2.47876e23 + 6.24390e21i) q^{52} +(1.95000e23 - 1.95000e23i) q^{53} +(2.25486e23 + 9.00899e22i) q^{54} -3.95173e23i q^{55} +(-2.26018e23 + 6.09842e23i) q^{56} +6.21129e22i q^{57} +(1.73204e23 - 4.33512e23i) q^{58} +(1.10914e22 - 1.10914e22i) q^{59} +(-3.79875e23 + 3.99507e23i) q^{60} +(1.44870e24 + 1.44870e24i) q^{61} +(9.97372e22 + 2.32464e23i) q^{62} +1.99248e24 q^{63} +(1.83385e24 + 1.57575e24i) q^{64} -4.48536e24 q^{65} +(-1.25775e24 - 2.93152e24i) q^{66} +(4.20584e24 + 4.20584e24i) q^{67} +(-4.07316e24 + 4.28367e24i) q^{68} +(2.27202e24 - 2.27202e24i) q^{69} +(-4.36504e24 + 1.09253e25i) q^{70} +1.80821e25i q^{71} +(2.57416e24 - 6.94561e24i) q^{72} +2.74303e24i q^{73} +(-2.53628e24 - 1.01334e24i) q^{74} +(1.86103e24 - 1.86103e24i) q^{75} +(4.92636e24 - 1.24093e23i) q^{76} +(-4.81380e25 - 4.81380e25i) q^{77} +(-3.32739e25 + 1.42760e25i) q^{78} -1.31583e25 q^{79} +(3.24450e25 + 2.93308e25i) q^{80} -8.69063e23 q^{81} +(7.47830e25 - 3.20852e25i) q^{82} +(9.23513e24 + 9.23513e24i) q^{83} +(2.39151e24 + 9.49403e25i) q^{84} +(-7.56093e25 + 7.56093e25i) q^{85} +(-1.20302e26 - 4.80650e25i) q^{86} -6.81685e25i q^{87} +(-2.29995e26 + 1.05613e26i) q^{88} +3.89739e26i q^{89} +(4.97143e25 - 1.24430e26i) q^{90} +(-5.46384e26 + 5.46384e26i) q^{91} +(-1.84740e26 - 1.75662e26i) q^{92} +(2.61188e25 + 2.61188e25i) q^{93} +(9.02108e25 + 2.10260e26i) q^{94} +8.91435e25 q^{95} +(3.34042e26 + 1.14320e26i) q^{96} +7.54323e26 q^{97} +(4.98965e26 + 1.16297e27i) q^{98} +(5.48252e26 + 5.48252e26i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 2 q^{2} - 2 q^{3} + 125095688 q^{4} - 2 q^{5} - 59499919472 q^{6} - 287180933804 q^{8} + 8247210235372 q^{10} - 34039821810222 q^{11} + 17\!\cdots\!80 q^{12} - 2 q^{13} - 71\!\cdots\!60 q^{14} - 15\!\cdots\!04 q^{15}+ \cdots + 16\!\cdots\!66 q^{99}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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