LMFDB - Embedded newform 5.24.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,24,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 24, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	5.a (trivial)

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:	yes
Analytic conductor:	$16.7602018673$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\mathbb{Q}[x]/(x^{3} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 215756x + 18660756 $ x^3 - x^2 - 215756*x + 18660756
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-502.392$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2794.35 q^{2} -370647. q^{3} -580214. q^{4} +4.88281e7 q^{5} +1.03572e9 q^{6} +2.05641e9 q^{7} +2.50620e10 q^{8} +4.32361e10 q^{9} +O(q^{10})$	\(q-2794.35 q^{2} -370647. q^{3} -580214. q^{4} +4.88281e7 q^{5} +1.03572e9 q^{6} +2.05641e9 q^{7} +2.50620e10 q^{8} +4.32361e10 q^{9} -1.36443e11 q^{10} +6.42732e11 q^{11} +2.15055e11 q^{12} +3.10398e12 q^{13} -5.74633e12 q^{14} -1.80980e13 q^{15} -6.51649e13 q^{16} -2.44063e14 q^{17} -1.20817e14 q^{18} +3.84362e14 q^{19} -2.83308e13 q^{20} -7.62203e14 q^{21} -1.79602e15 q^{22} -4.73954e15 q^{23} -9.28917e15 q^{24} +2.38419e15 q^{25} -8.67359e15 q^{26} +1.88686e16 q^{27} -1.19316e15 q^{28} +1.15421e17 q^{29} +5.05722e16 q^{30} +4.06480e16 q^{31} -2.81420e16 q^{32} -2.38227e17 q^{33} +6.81997e17 q^{34} +1.00411e17 q^{35} -2.50862e16 q^{36} -1.35601e18 q^{37} -1.07404e18 q^{38} -1.15048e18 q^{39} +1.22373e18 q^{40} -5.05305e17 q^{41} +2.12986e18 q^{42} -5.96439e18 q^{43} -3.72922e17 q^{44} +2.11114e18 q^{45} +1.32439e19 q^{46} -2.55219e19 q^{47} +2.41532e19 q^{48} -2.31399e19 q^{49} -6.66225e18 q^{50} +9.04612e19 q^{51} -1.80097e18 q^{52} +9.91283e19 q^{53} -5.27253e19 q^{54} +3.13834e19 q^{55} +5.15378e19 q^{56} -1.42463e20 q^{57} -3.22528e20 q^{58} -2.33633e20 q^{59} +1.05007e19 q^{60} -1.54254e20 q^{61} -1.13585e20 q^{62} +8.89112e19 q^{63} +6.25281e20 q^{64} +1.51561e20 q^{65} +6.65689e20 q^{66} -5.45272e20 q^{67} +1.41609e20 q^{68} +1.75670e21 q^{69} -2.80583e20 q^{70} -2.35184e21 q^{71} +1.08359e21 q^{72} -7.49385e20 q^{73} +3.78916e21 q^{74} -8.83692e20 q^{75} -2.23012e20 q^{76} +1.32172e21 q^{77} +3.21484e21 q^{78} -7.69798e21 q^{79} -3.18188e21 q^{80} -1.10640e22 q^{81} +1.41200e21 q^{82} +8.79858e21 q^{83} +4.42241e20 q^{84} -1.19171e22 q^{85} +1.66666e22 q^{86} -4.27806e22 q^{87} +1.61082e22 q^{88} +2.96864e22 q^{89} -5.89926e21 q^{90} +6.38305e21 q^{91} +2.74995e21 q^{92} -1.50661e22 q^{93} +7.13172e22 q^{94} +1.87677e22 q^{95} +1.04307e22 q^{96} -6.40973e22 q^{97} +6.46611e22 q^{98} +2.77892e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9}+O(q^{10}) $ 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9	$ 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9} + 32519531250 q^{10} - 165286030404 q^{11} - 2460925191744 q^{12} - 3554970733998 q^{13} + 1638464466408 q^{14} - 6808007812500 q^{15} - 68987884476912 q^{16} - 416105769269514 q^{17} - 302723670254238 q^{18} - 975704043068460 q^{19} - 463062304687500 q^{20} - 51\!\cdots\!84 q^{21}+ \cdots + 19\!\cdots\!32 q^{99}+O(q^{100}) $ 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9 + 32519531250 * q^10 - 165286030404 * q^11 - 2460925191744 * q^12 - 3554970733998 * q^13 + 1638464466408 * q^14 - 6808007812500 * q^15 - 68987884476912 * q^16 - 416105769269514 * q^17 - 302723670254238 * q^18 - 975704043068460 * q^19 - 463062304687500 * q^20 - 5102384337991584 * q^21 - 5786145456383688 * q^22 - 4979666912332368 * q^23 - 10409810708926080 * q^24 + 7152557373046875 * q^25 - 17675137590787524 * q^26 + 20047178078003160 * q^27 + 71220956974215888 * q^28 + 95526863867406210 * q^29 + 46870059375000000 * q^30 + 203997528720796176 * q^31 + 170287635059993376 * q^32 + 322079222096408304 * q^33 + 716918393922501108 * q^34 - 118783366406250000 * q^35 - 220893376245027372 * q^36 - 483030177185234454 * q^37 - 3922824866561525640 * q^38 - 2555750058791490648 * q^39 - 626973708984375000 * q^40 - 4358124871734570834 * q^41 - 2559620302421551488 * q^42 - 5324153686845536508 * q^43 - 5745533240877106512 * q^44 + 82670114794921875 * q^45 + 10292691411163504536 * q^46 + 12258262539323374776 * q^47 + 52185334595839679232 * q^48 + 53865950980476272379 * q^49 + 1587867736816406250 * q^50 - 13305294839256933384 * q^51 + 36561029094508759896 * q^52 + 71640983942760085722 * q^53 - 8722300088406303360 * q^54 - 8070606953320312500 * q^55 + 32773217861089510560 * q^56 - 174702718819675136880 * q^57 - 258910443213048121860 * q^58 - 420843416438104506180 * q^59 - 120162362878125000000 * q^60 - 581725337824220015454 * q^61 - 6386866856435690928 * q^62 - 701377962769300673808 * q^63 + 910193477718092702784 * q^64 - 173582555370996093750 * q^65 + 1527698529319557146112 * q^66 - 1399668543169120673364 * q^67 + 2058346167335115118728 * q^68 + 2368452906957113559072 * q^69 + 80003147773828125000 * q^70 - 409151675006970497064 * q^71 + 2624939937107847919080 * q^72 + 3254958507976741960782 * q^73 + 5024018202030699806508 * q^74 - 332422256469726562500 * q^75 + 4116463921392566297520 * q^76 - 17679177187365753067008 * q^77 + 2659161203582354699904 * q^78 - 10163548547854309111440 * q^79 - 3368549046724218750000 * q^80 - 17599804703176322735397 * q^81 - 12650907933669059897148 * q^82 - 14365350009027465650388 * q^83 + 29520686861588838037248 * q^84 - 20317664515112988281250 * q^85 + 26606188682127536075856 * q^86 - 69805465343858969988120 * q^87 + 49185500030908263850080 * q^88 + 55263110999125019200830 * q^89 - 14781429211632714843750 * q^90 + 41561600612192918902176 * q^91 - 4955822257768756710864 * q^92 + 48060187726233171700224 * q^93 + 160261789932669635237208 * q^94 - 47641798977952148437500 * q^95 + 56188621559544366859776 * q^96 - 231524977804298299798074 * q^97 + 129877246807137874291338 * q^98 + 195725739081953651557932 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−2794.35	−0.964797	−0.482398	−	0.875952i	$-0.660234\pi$
$2$	−2794.35	−0.964797	−0.482398	+	0.875952i	$0.660234\pi$
$3$	−370647.	−1.20800	−0.603999	−	0.796985i	$-0.706427\pi$
$3$	−370647.	−1.20800	−0.603999	+	0.796985i	$0.706427\pi$
$4$	−580214.	−0.0691669
$5$	4.88281e7	0.447214
$5$	4.88281e7	0.447214
$6$	1.03572e9	1.16547
$7$	2.05641e9	0.393081	0.196541	−	0.980496i	$-0.437029\pi$
$7$	2.05641e9	0.393081	0.196541	+	0.980496i	$0.437029\pi$
$8$	2.50620e10	1.03153
$9$	4.32361e10	0.459259
$10$	−1.36443e11	−0.431470
$11$	6.42732e11	0.679226	0.339613	−	0.940565i	$-0.389704\pi$
$11$	6.42732e11	0.679226	0.339613	+	0.940565i	$0.389704\pi$
$12$	2.15055e11	0.0835535
$13$	3.10398e12	0.480363	0.240182	−	0.970728i	$-0.422793\pi$
$13$	3.10398e12	0.480363	0.240182	+	0.970728i	$0.422793\pi$
$14$	−5.74633e12	−0.379244
$15$	−1.80980e13	−0.540233
$16$	−6.51649e13	−0.926049
$17$	−2.44063e14	−1.72719	−0.863593	−	0.504190i	$-0.831791\pi$
$17$	−2.44063e14	−1.72719	−0.863593	+	0.504190i	$0.831791\pi$
$18$	−1.20817e14	−0.443092
$19$	3.84362e14	0.756961	0.378481	−	0.925609i	$-0.376447\pi$
$19$	3.84362e14	0.756961	0.378481	+	0.925609i	$0.376447\pi$
$20$	−2.83308e13	−0.0309324
$21$	−7.62203e14	−0.474841
$22$	−1.79602e15	−0.655315
$23$	−4.73954e15	−1.03721	−0.518604	−	0.855014i	$-0.673548\pi$
$23$	−4.73954e15	−1.03721	−0.518604	+	0.855014i	$0.673548\pi$
$24$	−9.28917e15	−1.24608
$25$	2.38419e15	0.200000
$26$	−8.67359e15	−0.463453
$27$	1.88686e16	0.653214
$28$	−1.19316e15	−0.0271882
$29$	1.15421e17	1.75675	0.878374	−	0.477975i	$-0.158629\pi$
$29$	1.15421e17	1.75675	0.878374	+	0.477975i	$0.158629\pi$
$30$	5.05722e16	0.521215
$31$	4.06480e16	0.287330	0.143665	−	0.989626i	$-0.454111\pi$
$31$	4.06480e16	0.287330	0.143665	+	0.989626i	$0.454111\pi$
$32$	−2.81420e16	−0.138080
$33$	−2.38227e17	−0.820503
$34$	6.81997e17	1.66638
$35$	1.00411e17	0.175791
$36$	−2.50862e16	−0.0317656
$37$	−1.35601e18	−1.25297	−0.626487	−	0.779432i	$-0.715508\pi$
$37$	−1.35601e18	−1.25297	−0.626487	+	0.779432i	$0.715508\pi$
$38$	−1.07404e18	−0.730314
$39$	−1.15048e18	−0.580278
$40$	1.22373e18	0.461314
$41$	−5.05305e17	−0.143397	−0.0716984	−	0.997426i	$-0.522842\pi$
$41$	−5.05305e17	−0.143397	−0.0716984	+	0.997426i	$0.522842\pi$
$42$	2.12986e18	0.458125
$43$	−5.96439e18	−0.978766	−0.489383	−	0.872069i	$-0.662778\pi$
$43$	−5.96439e18	−0.978766	−0.489383	+	0.872069i	$0.662778\pi$
$44$	−3.72922e17	−0.0469799
$45$	2.11114e18	0.205387
$46$	1.32439e19	1.00070
$47$	−2.55219e19	−1.50587	−0.752936	−	0.658093i	$-0.771363\pi$
$47$	−2.55219e19	−1.50587	−0.752936	+	0.658093i	$0.771363\pi$
$48$	2.41532e19	1.11867
$49$	−2.31399e19	−0.845487
$50$	−6.66225e18	−0.192959
$51$	9.04612e19	2.08644
$52$	−1.80097e18	−0.0332252
$53$	9.91283e19	1.46901	0.734506	−	0.678602i	$-0.237414\pi$
$53$	9.91283e19	1.46901	0.734506	+	0.678602i	$0.237414\pi$
$54$	−5.27253e19	−0.630219
$55$	3.13834e19	0.303759
$56$	5.15378e19	0.405475
$57$	−1.42463e20	−0.914407
$58$	−3.22528e20	−1.69490
$59$	−2.33633e20	−1.00864	−0.504321	−	0.863516i	$-0.668257\pi$
$59$	−2.33633e20	−1.00864	−0.504321	+	0.863516i	$0.668257\pi$
$60$	1.05007e19	0.0373663
$61$	−1.54254e20	−0.453881	−0.226941	−	0.973909i	$-0.572872\pi$
$61$	−1.54254e20	−0.453881	−0.226941	+	0.973909i	$0.572872\pi$
$62$	−1.13585e20	−0.277215
$63$	8.89112e19	0.180526
$64$	6.25281e20	1.05927
$65$	1.51561e20	0.214825
$66$	6.65689e20	0.791619
$67$	−5.45272e20	−0.545447	−0.272724	−	0.962092i	$-0.587924\pi$
$67$	−5.45272e20	−0.545447	−0.272724	+	0.962092i	$0.587924\pi$
$68$	1.41609e20	0.119464
$69$	1.75670e21	1.25295
$70$	−2.80583e20	−0.169603
$71$	−2.35184e21	−1.20764	−0.603820	−	0.797121i	$-0.706355\pi$
$71$	−2.35184e21	−1.20764	−0.603820	+	0.797121i	$0.706355\pi$
$72$	1.08359e21	0.473739
$73$	−7.49385e20	−0.279571	−0.139786	−	0.990182i	$-0.544641\pi$
$73$	−7.49385e20	−0.279571	−0.139786	+	0.990182i	$0.544641\pi$
$74$	3.78916e21	1.20887
$75$	−8.83692e20	−0.241600
$76$	−2.23012e20	−0.0523567
$77$	1.32172e21	0.266991
$78$	3.21484e21	0.559850
$79$	−7.69798e21	−1.15788	−0.578942	−	0.815368i	$-0.696534\pi$
$79$	−7.69798e21	−1.15788	−0.578942	+	0.815368i	$0.696534\pi$
$80$	−3.18188e21	−0.414142
$81$	−1.10640e22	−1.24834
$82$	1.41200e21	0.138349
$83$	8.79858e21	0.749920	0.374960	−	0.927041i	$-0.377656\pi$
$83$	8.79858e21	0.749920	0.374960	+	0.927041i	$0.377656\pi$
$84$	4.42241e20	0.0328433
$85$	−1.19171e22	−0.772421
$86$	1.66666e22	0.944310
$87$	−4.27806e22	−2.12215
$88$	1.61082e22	0.700641
$89$	2.96864e22	1.13389	0.566946	−	0.823755i	$-0.308125\pi$
$89$	2.96864e22	1.13389	0.566946	+	0.823755i	$0.308125\pi$
$90$	−5.89926e21	−0.198157
$91$	6.38305e21	0.188822
$92$	2.74995e21	0.0717405
$93$	−1.50661e22	−0.347093
$94$	7.13172e22	1.45286
$95$	1.87677e22	0.338523
$96$	1.04307e22	0.166800
$97$	−6.40973e22	−0.909839	−0.454920	−	0.890532i	$-0.650332\pi$
$97$	−6.40973e22	−0.909839	−0.454920	+	0.890532i	$0.650332\pi$
$98$	6.46611e22	0.815723
$99$	2.77892e22	0.311941
$100$	−1.38334e21	−0.0138334
$101$	1.66180e23	1.48212	0.741060	−	0.671439i	$-0.234323\pi$
$101$	1.66180e23	1.48212	0.741060	+	0.671439i	$0.234323\pi$
$102$	−2.52780e23	−2.01299
$103$	−1.36985e23	−0.975093	−0.487546	−	0.873097i	$-0.662108\pi$
$103$	−1.36985e23	−0.975093	−0.487546	+	0.873097i	$0.662108\pi$
$104$	7.77919e22	0.495508
$105$	−3.72169e22	−0.212356
$106$	−2.76999e23	−1.41730
$107$	−4.17882e23	−1.91929	−0.959644	−	0.281219i	$-0.909261\pi$
$107$	−4.17882e23	−1.91929	−0.959644	+	0.281219i	$0.909261\pi$
$108$	−1.09478e22	−0.0451808
$109$	2.54506e23	0.944699	0.472350	−	0.881411i	$-0.343406\pi$
$109$	2.54506e23	0.944699	0.472350	+	0.881411i	$0.343406\pi$
$110$	−8.76962e22	−0.293066
$111$	5.02600e23	1.51359
$112$	−1.34006e23	−0.364012
$113$	6.15168e23	1.50866	0.754331	−	0.656495i	$-0.227962\pi$
$113$	6.15168e23	1.50866	0.754331	+	0.656495i	$0.227962\pi$
$114$	3.98090e23	0.882218
$115$	−2.31423e23	−0.463854
$116$	−6.69691e22	−0.121509
$117$	1.34204e23	0.220611
$118$	6.52854e23	0.973134
$119$	−5.01893e23	−0.678924
$120$	−4.53573e23	−0.557266
$121$	−4.82326e23	−0.538653
$122$	4.31038e23	0.437903
$123$	1.87290e23	0.173223
$124$	−2.35846e22	−0.0198737
$125$	1.16415e23	0.0894427
$126$	−2.48449e23	−0.174171
$127$	−2.46372e23	−0.157706	−0.0788529	−	0.996886i	$-0.525126\pi$
$127$	−2.46372e23	−0.157706	−0.0788529	+	0.996886i	$0.525126\pi$
$128$	−1.51118e24	−0.883899
$129$	2.21068e24	1.18235
$130$	−4.23515e23	−0.207262
$131$	−8.95139e23	−0.401117	−0.200558	−	0.979682i	$-0.564276\pi$
$131$	−8.95139e23	−0.401117	−0.200558	+	0.979682i	$0.564276\pi$
$132$	1.38223e23	0.0567517
$133$	7.90405e23	0.297547
$134$	1.52368e24	0.526246
$135$	9.21316e23	0.292126
$136$	−6.11671e24	−1.78164
$137$	−3.04273e24	−0.814661	−0.407331	−	0.913281i	$-0.633540\pi$
$137$	−3.04273e24	−0.814661	−0.407331	+	0.913281i	$0.633540\pi$
$138$	−4.90883e24	−1.20884
$139$	−2.27560e24	−0.515734	−0.257867	−	0.966180i	$-0.583020\pi$
$139$	−2.27560e24	−0.515734	−0.257867	+	0.966180i	$0.583020\pi$
$140$	−5.82597e22	−0.0121589
$141$	9.45963e24	1.81909
$142$	6.57188e24	1.16513
$143$	1.99502e24	0.326275
$144$	−2.81748e24	−0.425297
$145$	5.63581e24	0.785641
$146$	2.09405e24	0.269729
$147$	8.57675e24	1.02135
$148$	7.86775e23	0.0866644
$149$	−1.49592e25	−1.52499	−0.762493	−	0.646997i	$-0.776025\pi$
$149$	−1.49592e25	−1.52499	−0.762493	+	0.646997i	$0.776025\pi$
$150$	2.46934e24	0.233095
$151$	9.47592e24	0.828679	0.414340	−	0.910122i	$-0.364013\pi$
$151$	9.47592e24	0.828679	0.414340	+	0.910122i	$0.364013\pi$
$152$	9.63288e24	0.780827
$153$	−1.05523e25	−0.793226
$154$	−3.69335e24	−0.257592
$155$	1.98477e24	0.128498
$156$	6.67525e23	0.0401360
$157$	−2.70485e25	−1.51111	−0.755556	−	0.655084i	$-0.772633\pi$
$157$	−2.70485e25	−1.51111	−0.755556	+	0.655084i	$0.772633\pi$
$158$	2.15109e25	1.11712
$159$	−3.67416e25	−1.77456
$160$	−1.37412e24	−0.0617511
$161$	−9.74644e24	−0.407707
$162$	3.09166e25	1.20439
$163$	−2.53457e25	−0.919912	−0.459956	−	0.887942i	$-0.652135\pi$
$163$	−2.53457e25	−0.919912	−0.459956	+	0.887942i	$0.652135\pi$
$164$	2.93185e23	0.00991831
$165$	−1.16322e25	−0.366940
$166$	−2.45863e25	−0.723520
$167$	4.42055e25	1.21405	0.607026	−	0.794682i	$-0.292362\pi$
$167$	4.42055e25	1.21405	0.607026	+	0.794682i	$0.292362\pi$
$168$	−1.91023e25	−0.489813
$169$	−3.21192e25	−0.769251
$170$	3.33006e25	0.745229
$171$	1.66183e25	0.347641
$172$	3.46062e24	0.0676982
$173$	2.87109e25	0.525431	0.262716	−	0.964873i	$-0.415382\pi$
$173$	2.87109e25	0.525431	0.262716	+	0.964873i	$0.415382\pi$
$174$	1.19544e26	2.04744
$175$	4.90286e24	0.0786162
$176$	−4.18836e25	−0.628996
$177$	8.65956e25	1.21844
$178$	−8.29541e25	−1.09398
$179$	8.78557e25	1.08633	0.543163	−	0.839627i	$-0.317227\pi$
$179$	8.78557e25	1.08633	0.543163	+	0.839627i	$0.317227\pi$
$180$	−1.22491e24	−0.0142060
$181$	−9.88209e25	−1.07534	−0.537669	−	0.843156i	$-0.680695\pi$
$181$	−9.88209e25	−1.07534	−0.537669	+	0.843156i	$0.680695\pi$
$182$	−1.78365e25	−0.182175
$183$	5.71736e25	0.548287
$184$	−1.18783e26	−1.06991
$185$	−6.62113e25	−0.560347
$186$	4.20999e25	0.334875
$187$	−1.56867e26	−1.17315
$188$	1.48082e25	0.104157
$189$	3.88015e25	0.256766
$190$	−5.24434e25	−0.326606
$191$	1.07642e26	0.631101	0.315551	−	0.948909i	$-0.397811\pi$
$191$	1.07642e26	0.631101	0.315551	+	0.948909i	$0.397811\pi$
$192$	−2.31759e26	−1.27959
$193$	2.05927e26	1.07104	0.535518	−	0.844524i	$-0.320117\pi$
$193$	2.05927e26	1.07104	0.535518	+	0.844524i	$0.320117\pi$
$194$	1.79110e26	0.877810
$195$	−5.61758e25	−0.259508
$196$	1.34261e25	0.0584797
$197$	2.96638e25	0.121861	0.0609305	−	0.998142i	$-0.480593\pi$
$197$	2.96638e25	0.121861	0.0609305	+	0.998142i	$0.480593\pi$
$198$	−7.76529e25	−0.300959
$199$	−2.62425e26	−0.959830	−0.479915	−	0.877315i	$-0.659333\pi$
$199$	−2.62425e26	−0.959830	−0.479915	+	0.877315i	$0.659333\pi$
$200$	5.97525e25	0.206306
$201$	2.02103e26	0.658899
$202$	−4.64366e26	−1.42995
$203$	2.37354e26	0.690544
$204$	−5.24869e25	−0.144312
$205$	−2.46731e25	−0.0641290
$206$	3.82785e26	0.940766
$207$	−2.04919e26	−0.476348
$208$	−2.02270e26	−0.444840
$209$	2.47041e26	0.514147
$210$	1.03997e26	0.204880
$211$	−5.67775e25	−0.105908	−0.0529539	−	0.998597i	$-0.516864\pi$
$211$	−5.67775e25	−0.105908	−0.0529539	+	0.998597i	$0.516864\pi$
$212$	−5.75157e25	−0.101607
$213$	8.71704e26	1.45883
$214$	1.16771e27	1.85172
$215$	−2.91230e26	−0.437717
$216$	4.72884e26	0.673809
$217$	8.35891e25	0.112944
$218$	−7.11179e26	−0.911443
$219$	2.77758e26	0.337721
$220$	−1.82091e25	−0.0210101
$221$	−7.57565e26	−0.829677
$222$	−1.40444e27	−1.46031
$223$	−1.10925e27	−1.09527	−0.547636	−	0.836717i	$-0.684472\pi$
$223$	−1.10925e27	−1.09527	−0.547636	+	0.836717i	$0.684472\pi$
$224$	−5.78714e25	−0.0542765
$225$	1.03083e26	0.0918519
$226$	−1.71900e27	−1.45555
$227$	2.64261e26	0.212684	0.106342	−	0.994330i	$-0.466086\pi$
$227$	2.64261e26	0.212684	0.106342	+	0.994330i	$0.466086\pi$
$228$	8.26588e25	0.0632467
$229$	−6.00712e26	−0.437078	−0.218539	−	0.975828i	$-0.570129\pi$
$229$	−6.00712e26	−0.437078	−0.218539	+	0.975828i	$0.570129\pi$
$230$	6.46677e26	0.447525
$231$	−4.89892e26	−0.322524
$232$	2.89269e27	1.81214
$233$	−5.65690e26	−0.337276	−0.168638	−	0.985678i	$-0.553937\pi$
$233$	−5.65690e26	−0.337276	−0.168638	+	0.985678i	$0.553937\pi$
$234$	−3.75013e26	−0.212845
$235$	−1.24619e27	−0.673447
$236$	1.35557e26	0.0697646
$237$	2.85324e27	1.39872
$238$	1.40247e27	0.655024
$239$	−2.87909e27	−1.28138	−0.640692	−	0.767798i	$-0.721353\pi$
$239$	−2.87909e27	−1.28138	−0.640692	+	0.767798i	$0.721353\pi$
$240$	1.17935e27	0.500282
$241$	1.85367e27	0.749610	0.374805	−	0.927104i	$-0.377710\pi$
$241$	1.85367e27	0.749610	0.374805	+	0.927104i	$0.377710\pi$
$242$	1.34779e27	0.519690
$243$	2.32448e27	0.854779
$244$	8.95001e25	0.0313936
$245$	−1.12988e27	−0.378113
$246$	−5.23354e26	−0.167125
$247$	1.19305e27	0.363616
$248$	1.01872e27	0.296389
$249$	−3.26117e27	−0.905902
$250$	−3.25305e26	−0.0862941
$251$	−2.41423e26	−0.0611689	−0.0305845	−	0.999532i	$-0.509737\pi$
$251$	−2.41423e26	−0.0611689	−0.0305845	+	0.999532i	$0.509737\pi$
$252$	−5.15876e25	−0.0124864
$253$	−3.04625e27	−0.704499
$254$	6.88449e26	0.152154
$255$	4.41705e27	0.933083
$256$	−1.02247e27	−0.206485
$257$	−1.29308e27	−0.249685	−0.124843	−	0.992177i	$-0.539843\pi$
$257$	−1.29308e27	−0.249685	−0.124843	+	0.992177i	$0.539843\pi$
$258$	−6.17742e27	−1.14072
$259$	−2.78851e27	−0.492521
$260$	−8.79380e25	−0.0148588
$261$	4.99037e27	0.806803
$262$	2.50133e27	0.386996
$263$	−4.80949e27	−0.712210	−0.356105	−	0.934446i	$-0.615895\pi$
$263$	−4.80949e27	−0.712210	−0.356105	+	0.934446i	$0.615895\pi$
$264$	−5.97045e27	−0.846373
$265$	4.84025e27	0.656962
$266$	−2.20867e27	−0.287073
$267$	−1.10032e28	−1.36974
$268$	3.16374e26	0.0377269
$269$	2.03295e27	0.232260	0.116130	−	0.993234i	$-0.462951\pi$
$269$	2.03295e27	0.232260	0.116130	+	0.993234i	$0.462951\pi$
$270$	−2.57448e27	−0.281842
$271$	4.33212e27	0.454521	0.227261	−	0.973834i	$-0.427023\pi$
$271$	4.33212e27	0.454521	0.227261	+	0.973834i	$0.427023\pi$
$272$	1.59043e28	1.59946
$273$	−2.36586e27	−0.228096
$274$	8.50246e27	0.785983
$275$	1.53239e27	0.135845
$276$	−1.01926e27	−0.0866624
$277$	2.19433e27	0.178972	0.0894861	−	0.995988i	$-0.471478\pi$
$277$	2.19433e27	0.178972	0.0894861	+	0.995988i	$0.471478\pi$
$278$	6.35882e27	0.497578
$279$	1.75746e27	0.131959
$280$	2.51650e27	0.181334
$281$	−2.32028e27	−0.160479	−0.0802396	−	0.996776i	$-0.525569\pi$
$281$	−2.32028e27	−0.160479	−0.0802396	+	0.996776i	$0.525569\pi$
$282$	−2.64335e28	−1.75505
$283$	9.74061e27	0.620929	0.310465	−	0.950585i	$-0.399515\pi$
$283$	9.74061e27	0.620929	0.310465	+	0.950585i	$0.399515\pi$
$284$	1.36457e27	0.0835287
$285$	−6.95618e27	−0.408935
$286$	−5.57480e27	−0.314789
$287$	−1.03911e27	−0.0563666
$288$	−1.21675e27	−0.0634144
$289$	3.95991e28	1.98317
$290$	−1.57484e28	−0.757984
$291$	2.37575e28	1.09908
$292$	4.34804e26	0.0193371
$293$	2.30606e28	0.986036	0.493018	−	0.870019i	$-0.335894\pi$
$293$	2.30606e28	0.986036	0.493018	+	0.870019i	$0.335894\pi$
$294$	−2.39664e28	−0.985392
$295$	−1.14079e28	−0.451078
$296$	−3.39843e28	−1.29248
$297$	1.21274e28	0.443679
$298$	4.18012e28	1.47130
$299$	−1.47114e28	−0.498237
$300$	5.12730e26	0.0167107
$301$	−1.22652e28	−0.384734
$302$	−2.64790e28	−0.799507
$303$	−6.15942e28	−1.79040
$304$	−2.50469e28	−0.700983
$305$	−7.53191e27	−0.202982
$306$	2.94869e28	0.765302
$307$	−5.75499e27	−0.143864	−0.0719322	−	0.997410i	$-0.522917\pi$
$307$	−5.75499e27	−0.143864	−0.0719322	+	0.997410i	$0.522917\pi$
$308$	−7.66881e26	−0.0184669
$309$	5.07732e28	1.17791
$310$	−5.54614e27	−0.123974
$311$	−7.84965e28	−1.69085	−0.845427	−	0.534091i	$-0.820654\pi$
$311$	−7.84965e28	−1.69085	−0.845427	+	0.534091i	$0.820654\pi$
$312$	−2.88334e28	−0.598573
$313$	−1.33439e28	−0.267006	−0.133503	−	0.991048i	$-0.542623\pi$
$313$	−1.33439e28	−0.267006	−0.133503	+	0.991048i	$0.542623\pi$
$314$	7.55829e28	1.45792
$315$	4.34137e27	0.0807338
$316$	4.46648e27	0.0800873
$317$	−2.40509e28	−0.415862	−0.207931	−	0.978143i	$-0.566673\pi$
$317$	−2.40509e28	−0.415862	−0.207931	+	0.978143i	$0.566673\pi$
$318$	1.02669e29	1.71209
$319$	7.41850e28	1.19323
$320$	3.05313e28	0.473719
$321$	1.54887e29	2.31850
$322$	2.72350e28	0.393355
$323$	−9.38084e28	−1.30741
$324$	6.41947e27	0.0863438
$325$	7.40045e27	0.0960726
$326$	7.08247e28	0.887528
$327$	−9.43320e28	−1.14120
$328$	−1.26640e28	−0.147918
$329$	−5.24836e28	−0.591930
$330$	3.25043e28	0.354023
$331$	−1.49781e29	−1.57556	−0.787779	−	0.615958i	$-0.788769\pi$
$331$	−1.49781e29	−1.57556	−0.787779	+	0.615958i	$0.788769\pi$
$332$	−5.10506e27	−0.0518696
$333$	−5.86285e28	−0.575440
$334$	−1.23526e29	−1.17131
$335$	−2.66246e28	−0.243931
$336$	4.96689e28	0.439726
$337$	1.52123e29	1.30152	0.650761	−	0.759282i	$-0.274450\pi$
$337$	1.52123e29	1.30152	0.650761	+	0.759282i	$0.274450\pi$
$338$	8.97524e28	0.742171
$339$	−2.28010e29	−1.82246
$340$	6.91449e27	0.0534260
$341$	2.61258e28	0.195162
$342$	−4.64374e28	−0.335403
$343$	−1.03867e29	−0.725426
$344$	−1.49480e29	−1.00962
$345$	8.57763e28	0.560335
$346$	−8.02282e28	−0.506935
$347$	2.37122e29	1.44938	0.724692	−	0.689072i	$-0.241982\pi$
$347$	2.37122e29	1.44938	0.724692	+	0.689072i	$0.241982\pi$
$348$	2.48219e28	0.146782
$349$	2.08845e29	1.19490	0.597449	−	0.801907i	$-0.296181\pi$
$349$	2.08845e29	1.19490	0.597449	+	0.801907i	$0.296181\pi$
$350$	−1.37003e28	−0.0758487
$351$	5.85675e28	0.313780
$352$	−1.80877e28	−0.0937873
$353$	1.15969e29	0.582011	0.291005	−	0.956721i	$-0.406010\pi$
$353$	1.15969e29	0.582011	0.291005	+	0.956721i	$0.406010\pi$
$354$	−2.41978e29	−1.17554
$355$	−1.14836e29	−0.540073
$356$	−1.72244e28	−0.0784278
$357$	1.86025e29	0.820139
$358$	−2.45500e29	−1.04808
$359$	8.66375e28	0.358195	0.179098	−	0.983831i	$-0.442682\pi$
$359$	8.66375e28	0.358195	0.179098	+	0.983831i	$0.442682\pi$
$360$	5.29094e28	0.211863
$361$	−1.10096e29	−0.427010
$362$	2.76140e29	1.03748
$363$	1.78773e29	0.650691
$364$	−3.70353e27	−0.0130602
$365$	−3.65911e28	−0.125028
$366$	−1.59763e29	−0.528986
$367$	3.48935e28	0.111966	0.0559829	−	0.998432i	$-0.482171\pi$
$367$	3.48935e28	0.111966	0.0559829	+	0.998432i	$0.482171\pi$
$368$	3.08852e29	0.960506
$369$	−2.18474e28	−0.0658563
$370$	1.85018e29	0.540621
$371$	2.03848e29	0.577441
$372$	8.74156e27	0.0240074
$373$	−5.07465e29	−1.35131	−0.675654	−	0.737219i	$-0.736139\pi$
$373$	−5.07465e29	−1.35131	−0.675654	+	0.737219i	$0.736139\pi$
$374$	4.38341e29	1.13185
$375$	−4.31490e28	−0.108047
$376$	−6.39631e29	−1.55335
$377$	3.58265e29	0.843877
$378$	−1.08425e29	−0.247727
$379$	−2.15102e29	−0.476754	−0.238377	−	0.971173i	$-0.576615\pi$
$379$	−2.15102e29	−0.476754	−0.238377	+	0.971173i	$0.576615\pi$
$380$	−1.08893e28	−0.0234146
$381$	9.13169e28	0.190508
$382$	−3.00790e29	−0.608885
$383$	−5.33160e29	−1.04730	−0.523651	−	0.851933i	$-0.675430\pi$
$383$	−5.33160e29	−1.04730	−0.523651	+	0.851933i	$0.675430\pi$
$384$	5.60116e29	1.06775
$385$	6.45371e28	0.119402
$386$	−5.75432e29	−1.03333
$387$	−2.57877e29	−0.449507
$388$	3.71902e28	0.0629308
$389$	−3.60016e29	−0.591427	−0.295714	−	0.955277i	$-0.595557\pi$
$389$	−3.60016e29	−0.591427	−0.295714	+	0.955277i	$0.595557\pi$
$390$	1.56975e29	0.250373
$391$	1.15675e30	1.79145
$392$	−5.79934e29	−0.872144
$393$	3.31781e29	0.484548
$394$	−8.28910e28	−0.117571
$395$	−3.75878e29	−0.517822
$396$	−1.61237e28	−0.0215760
$397$	−1.06721e30	−1.38726	−0.693631	−	0.720331i	$-0.743990\pi$
$397$	−1.06721e30	−1.38726	−0.693631	+	0.720331i	$0.743990\pi$
$398$	7.33307e29	0.926041
$399$	−2.92961e29	−0.359436
$400$	−1.55365e29	−0.185210
$401$	1.62022e30	1.87678	0.938390	−	0.345577i	$-0.112317\pi$
$401$	1.62022e30	1.87678	0.938390	+	0.345577i	$0.112317\pi$
$402$	−5.64748e29	−0.635704
$403$	1.26171e29	0.138023
$404$	−9.64201e28	−0.102514
$405$	−5.40233e29	−0.558275
$406$	−6.63249e29	−0.666235
$407$	−8.71549e29	−0.851052
$408$	2.26714e30	2.15222
$409$	1.60567e30	1.48197	0.740983	−	0.671523i	$-0.234360\pi$
$409$	1.60567e30	1.48197	0.740983	+	0.671523i	$0.234360\pi$
$410$	6.89453e28	0.0618714
$411$	1.12778e30	0.984109
$412$	7.94808e28	0.0674442
$413$	−4.80446e29	−0.396478
$414$	5.72617e29	0.459579
$415$	4.29618e29	0.335374
$416$	−8.73520e28	−0.0663284
$417$	8.43444e29	0.623005
$418$	−6.90320e29	−0.496048
$419$	−2.10606e30	−1.47234	−0.736171	−	0.676796i	$-0.763368\pi$
$419$	−2.10606e30	−1.47234	−0.736171	+	0.676796i	$0.763368\pi$
$420$	2.15938e28	0.0146880
$421$	8.03431e29	0.531746	0.265873	−	0.964008i	$-0.414340\pi$
$421$	8.03431e29	0.531746	0.265873	+	0.964008i	$0.414340\pi$
$422$	1.58656e29	0.102180
$423$	−1.10347e30	−0.691586
$424$	2.48436e30	1.51533
$425$	−5.81891e29	−0.345437
$426$	−2.43585e30	−1.40747
$427$	−3.17209e29	−0.178412
$428$	2.42461e29	0.132751
$429$	−7.39450e29	−0.394139
$430$	8.13798e29	0.422308
$431$	−2.91928e30	−1.47498	−0.737492	−	0.675356i	$-0.763990\pi$
$431$	−2.91928e30	−1.47498	−0.737492	+	0.675356i	$0.763990\pi$
$432$	−1.22957e30	−0.604908
$433$	−1.57900e30	−0.756435	−0.378218	−	0.925717i	$-0.623463\pi$
$433$	−1.57900e30	−0.756435	−0.378218	+	0.925717i	$0.623463\pi$
$434$	−2.33577e29	−0.108968
$435$	−2.08890e30	−0.949053
$436$	−1.47668e29	−0.0653419
$437$	−1.82170e30	−0.785127
$438$	−7.76152e29	−0.325833
$439$	2.68486e30	1.09794	0.548971	−	0.835842i	$-0.315020\pi$
$439$	2.68486e30	1.09794	0.548971	+	0.835842i	$0.315020\pi$
$440$	7.86532e29	0.313336
$441$	−1.00048e30	−0.388298
$442$	2.11690e30	0.800469
$443$	2.07814e30	0.765651	0.382826	−	0.923821i	$-0.374951\pi$
$443$	2.07814e30	0.765651	0.382826	+	0.923821i	$0.374951\pi$
$444$	−2.91616e29	−0.104690
$445$	1.44953e30	0.507092
$446$	3.09962e30	1.05672
$447$	5.54458e30	1.84218
$448$	1.28584e30	0.416378
$449$	1.96752e30	0.620992	0.310496	−	0.950575i	$-0.399505\pi$
$449$	1.96752e30	0.620992	0.310496	+	0.950575i	$0.399505\pi$
$450$	−2.88050e29	−0.0886184
$451$	−3.24776e29	−0.0973987
$452$	−3.56929e29	−0.104349
$453$	−3.51222e30	−1.00104
$454$	−7.38437e29	−0.205197
$455$	3.11672e29	0.0844436
$456$	−3.57040e30	−0.943238
$457$	4.27737e30	1.10189	0.550947	−	0.834540i	$-0.314266\pi$
$457$	4.27737e30	1.10189	0.550947	+	0.834540i	$0.314266\pi$
$458$	1.67860e30	0.421691
$459$	−4.60511e30	−1.12822
$460$	1.34275e29	0.0320833
$461$	−4.08340e28	−0.00951616	−0.00475808	−	0.999989i	$-0.501515\pi$
$461$	−4.08340e28	−0.00951616	−0.00475808	+	0.999989i	$0.501515\pi$
$462$	1.36893e30	0.311171
$463$	−1.05535e30	−0.233999	−0.117000	−	0.993132i	$-0.537328\pi$
$463$	−1.05535e30	−0.233999	−0.117000	+	0.993132i	$0.537328\pi$
$464$	−7.52142e30	−1.62683
$465$	−7.35649e29	−0.155225
$466$	1.58074e30	0.325403
$467$	4.55310e30	0.914457	0.457228	−	0.889349i	$-0.348842\pi$
$467$	4.55310e30	0.914457	0.457228	+	0.889349i	$0.348842\pi$
$468$	−7.78670e28	−0.0152590
$469$	−1.12130e30	−0.214405
$470$	3.48229e30	0.649739
$471$	1.00254e31	1.82542
$472$	−5.85533e30	−1.04044
$473$	−3.83350e30	−0.664803
$474$	−7.97294e30	−1.34948
$475$	9.16389e29	0.151392
$476$	2.91206e29	0.0469591
$477$	4.28593e30	0.674657
$478$	8.04519e30	1.23628
$479$	−5.19701e30	−0.779641	−0.389821	−	0.920891i	$-0.627463\pi$
$479$	−5.19701e30	−0.779641	−0.389821	+	0.920891i	$0.627463\pi$
$480$	5.09314e29	0.0745952
$481$	−4.20901e30	−0.601883
$482$	−5.17979e30	−0.723222
$483$	3.61249e30	0.492510
$484$	2.79852e29	0.0372569
$485$	−3.12975e30	−0.406892
$486$	−6.49541e30	−0.824688
$487$	−4.95710e30	−0.614673	−0.307337	−	0.951601i	$-0.599438\pi$
$487$	−4.95710e30	−0.614673	−0.307337	+	0.951601i	$0.599438\pi$
$488$	−3.86591e30	−0.468191
$489$	9.39430e30	1.11125
$490$	3.15728e30	0.364803
$491$	1.52512e31	1.72134	0.860668	−	0.509167i	$-0.170046\pi$
$491$	1.52512e31	1.72134	0.860668	+	0.509167i	$0.170046\pi$
$492$	−1.08668e29	−0.0119813
$493$	−2.81701e31	−3.03423
$494$	−3.33380e30	−0.350816
$495$	1.35690e30	0.139504
$496$	−2.64883e30	−0.266081
$497$	−4.83636e30	−0.474701
$498$	9.11285e30	0.874011
$499$	2.08591e31	1.95496	0.977482	−	0.211018i	$-0.0676780\pi$
$499$	2.08591e31	1.95496	0.977482	+	0.211018i	$0.0676780\pi$
$500$	−6.75458e28	−0.00618648
$501$	−1.63847e31	−1.46657
$502$	6.74620e29	0.0590156
$503$	1.11364e31	0.952165	0.476082	−	0.879401i	$-0.342056\pi$
$503$	1.11364e31	0.952165	0.476082	+	0.879401i	$0.342056\pi$
$504$	2.22830e30	0.186218
$505$	8.11427e30	0.662824
$506$	8.51230e30	0.679698
$507$	1.19049e31	0.929254
$508$	1.42948e29	0.0109080
$509$	8.58904e30	0.640752	0.320376	−	0.947290i	$-0.396191\pi$
$509$	8.58904e30	0.640752	0.320376	+	0.947290i	$0.396191\pi$
$510$	−1.23428e31	−0.900236
$511$	−1.54104e30	−0.109894
$512$	1.55338e31	1.08311
$513$	7.25235e30	0.494457
$514$	3.61331e30	0.240896
$515$	−6.68874e30	−0.436075
$516$	−1.28267e30	−0.0817793
$517$	−1.64038e31	−1.02283
$518$	7.79207e30	0.475183
$519$	−1.06416e31	−0.634720
$520$	3.79843e30	0.221598
$521$	−1.40028e31	−0.799064	−0.399532	−	0.916719i	$-0.630827\pi$
$521$	−1.40028e31	−0.799064	−0.399532	+	0.916719i	$0.630827\pi$
$522$	−1.39449e31	−0.778401
$523$	−9.34334e30	−0.510191	−0.255095	−	0.966916i	$-0.582107\pi$
$523$	−9.34334e30	−0.510191	−0.255095	+	0.966916i	$0.582107\pi$
$524$	5.19373e29	0.0277440
$525$	−1.81723e30	−0.0949683
$526$	1.34394e31	0.687138
$527$	−9.92068e30	−0.496272
$528$	1.55240e31	0.759826
$529$	1.58279e30	0.0758024
$530$	−1.35254e31	−0.633835
$531$	−1.01014e31	−0.463228
$532$	−4.58604e29	−0.0205804
$533$	−1.56845e30	−0.0688825
$534$	3.07467e31	1.32152
$535$	−2.04044e31	−0.858331
$536$	−1.36656e31	−0.562645
$537$	−3.25635e31	−1.31228
$538$	−5.68076e30	−0.224084
$539$	−1.48728e31	−0.574276
$540$	−5.34561e29	−0.0202055
$541$	−2.59721e30	−0.0961033	−0.0480516	−	0.998845i	$-0.515301\pi$
$541$	−2.59721e30	−0.0961033	−0.0480516	+	0.998845i	$0.515301\pi$
$542$	−1.21055e31	−0.438521
$543$	3.66277e31	1.29901
$544$	6.86841e30	0.238489
$545$	1.24271e31	0.422482
$546$	6.61104e30	0.220067
$547$	−1.15651e31	−0.376960	−0.188480	−	0.982077i	$-0.560356\pi$
$547$	−1.15651e31	−0.376960	−0.188480	+	0.982077i	$0.560356\pi$
$548$	1.76544e30	0.0563476
$549$	−6.66933e30	−0.208449
$550$	−4.28204e30	−0.131063
$551$	4.43635e31	1.32979
$552$	4.40264e31	1.29245
$553$	−1.58302e31	−0.455143
$554$	−6.13174e30	−0.172672
$555$	2.45410e31	0.676899
$556$	1.32033e30	0.0356717
$557$	1.43957e31	0.380976	0.190488	−	0.981689i	$-0.438993\pi$
$557$	1.43957e31	0.380976	0.190488	+	0.981689i	$0.438993\pi$
$558$	−4.91097e30	−0.127313
$559$	−1.85133e31	−0.470163
$560$	−6.54325e30	−0.162791
$561$	5.81423e31	1.41716
$562$	6.48369e30	0.154830
$563$	3.50531e31	0.820125	0.410063	−	0.912057i	$-0.365507\pi$
$563$	3.50531e31	0.820125	0.410063	+	0.912057i	$0.365507\pi$
$564$	−5.48861e30	−0.125821
$565$	3.00375e31	0.674694
$566$	−2.72187e31	−0.599071
$567$	−2.27520e31	−0.490699
$568$	−5.89420e31	−1.24572
$569$	6.60409e31	1.36780	0.683899	−	0.729576i	$-0.260283\pi$
$569$	6.60409e31	1.36780	0.683899	+	0.729576i	$0.260283\pi$
$570$	1.94380e31	0.394540
$571$	−4.70874e31	−0.936676	−0.468338	−	0.883549i	$-0.655147\pi$
$571$	−4.70874e31	−0.936676	−0.468338	+	0.883549i	$0.655147\pi$
$572$	−1.15754e30	−0.0225674
$573$	−3.98973e31	−0.762369
$574$	2.90365e30	0.0543823
$575$	−1.12999e31	−0.207442
$576$	2.70348e31	0.486479
$577$	−2.61393e31	−0.461076	−0.230538	−	0.973063i	$-0.574049\pi$
$577$	−2.61393e31	−0.461076	−0.230538	+	0.973063i	$0.574049\pi$
$578$	−1.10654e32	−1.91336
$579$	−7.63262e31	−1.29381
$580$	−3.26998e30	−0.0543404
$581$	1.80935e31	0.294779
$582$	−6.63867e31	−1.06039
$583$	6.37129e31	0.997790
$584$	−1.87811e31	−0.288386
$585$	6.55292e30	0.0986604
$586$	−6.44393e31	−0.951324
$587$	1.10640e32	1.60167	0.800836	−	0.598884i	$-0.204389\pi$
$587$	1.10640e32	1.60167	0.800836	+	0.598884i	$0.204389\pi$
$588$	−4.97635e30	−0.0706434
$589$	1.56235e31	0.217497
$590$	3.18776e31	0.435199
$591$	−1.09948e31	−0.147208
$592$	8.83641e31	1.16032
$593$	6.01006e31	0.774016	0.387008	−	0.922076i	$-0.373509\pi$
$593$	6.01006e31	0.774016	0.387008	+	0.922076i	$0.373509\pi$
$594$	−3.38883e31	−0.428060
$595$	−2.45065e31	−0.303624
$596$	8.67953e30	0.105479
$597$	9.72670e31	1.15947
$598$	4.11089e31	0.480697
$599$	−1.30398e32	−1.49577	−0.747883	−	0.663831i	$-0.768930\pi$
$599$	−1.30398e32	−1.49577	−0.747883	+	0.663831i	$0.768930\pi$
$600$	−2.21471e31	−0.249217
$601$	−1.35644e32	−1.49742	−0.748712	−	0.662896i	$-0.769327\pi$
$601$	−1.35644e32	−1.49742	−0.748712	+	0.662896i	$0.769327\pi$
$602$	3.42733e31	0.371191
$603$	−2.35754e31	−0.250502
$604$	−5.49806e30	−0.0573172
$605$	−2.35511e31	−0.240893
$606$	1.72116e32	1.72737
$607$	4.51302e31	0.444424	0.222212	−	0.974998i	$-0.428672\pi$
$607$	4.51302e31	0.444424	0.222212	+	0.974998i	$0.428672\pi$
$608$	−1.08167e31	−0.104521
$609$	−8.79745e31	−0.834176
$610$	2.10468e31	0.195836
$611$	−7.92194e31	−0.723366
$612$	6.12261e30	0.0548650
$613$	1.14195e32	1.00427	0.502136	−	0.864789i	$-0.332548\pi$
$613$	1.14195e32	1.00427	0.502136	+	0.864789i	$0.332548\pi$
$614$	1.60815e31	0.138800
$615$	9.14501e30	0.0774677
$616$	3.31250e31	0.275409
$617$	1.59841e31	0.130440	0.0652199	−	0.997871i	$-0.479225\pi$
$617$	1.59841e31	0.130440	0.0652199	+	0.997871i	$0.479225\pi$
$618$	−1.41878e32	−1.13644
$619$	−1.70436e31	−0.134004	−0.0670020	−	0.997753i	$-0.521343\pi$
$619$	−1.70436e31	−0.134004	−0.0670020	+	0.997753i	$0.521343\pi$
$620$	−1.15159e30	−0.00888779
$621$	−8.94283e31	−0.677519
$622$	2.19347e32	1.63133
$623$	6.10473e31	0.445712
$624$	7.49709e31	0.537366
$625$	5.68434e30	0.0400000
$626$	3.72874e31	0.257607
$627$	−9.15652e31	−0.621089
$628$	1.56939e31	0.104519
$629$	3.30951e32	2.16412
$630$	−1.21313e31	−0.0778917
$631$	1.15753e31	0.0729781	0.0364891	−	0.999334i	$-0.488383\pi$
$631$	1.15753e31	0.0729781	0.0364891	+	0.999334i	$0.488383\pi$
$632$	−1.92927e32	−1.19439
$633$	2.10444e31	0.127937
$634$	6.72066e31	0.401222
$635$	−1.20299e31	−0.0705282
$636$	2.13180e31	0.122741
$637$	−7.18257e31	−0.406141
$638$	−2.07299e32	−1.15122
$639$	−1.01685e32	−0.554620
$640$	−7.37882e31	−0.395292
$641$	−2.37913e32	−1.25184	−0.625922	−	0.779886i	$-0.715277\pi$
$641$	−2.37913e32	−1.25184	−0.625922	+	0.779886i	$0.715277\pi$
$642$	−4.32808e32	−2.23688
$643$	2.45460e32	1.24610	0.623051	−	0.782181i	$-0.285893\pi$
$643$	2.45460e32	1.24610	0.623051	+	0.782181i	$0.285893\pi$
$644$	5.65502e30	0.0281999
$645$	1.07944e32	0.528762
$646$	2.62133e32	1.26139
$647$	−2.17221e32	−1.02684	−0.513421	−	0.858137i	$-0.671622\pi$
$647$	−2.17221e32	−1.02684	−0.513421	+	0.858137i	$0.671622\pi$
$648$	−2.77285e32	−1.28770
$649$	−1.50164e32	−0.685095
$650$	−2.06795e31	−0.0926906
$651$	−3.09821e31	−0.136436
$652$	1.47059e31	0.0636275
$653$	−1.38562e32	−0.589038	−0.294519	−	0.955646i	$-0.595160\pi$
$653$	−1.38562e32	−0.589038	−0.294519	+	0.955646i	$0.595160\pi$
$654$	2.63597e32	1.10102
$655$	−4.37080e31	−0.179385
$656$	3.29282e31	0.132792
$657$	−3.24005e31	−0.128396
$658$	1.46657e32	0.571092
$659$	−7.26940e31	−0.278174	−0.139087	−	0.990280i	$-0.544417\pi$
$659$	−7.26940e31	−0.278174	−0.139087	+	0.990280i	$0.544417\pi$
$660$	6.74915e30	0.0253801
$661$	3.78029e32	1.39704	0.698519	−	0.715592i	$-0.253843\pi$
$661$	3.78029e32	1.39704	0.698519	+	0.715592i	$0.253843\pi$
$662$	4.18540e32	1.52009
$663$	2.80789e32	1.00225
$664$	2.20510e32	0.773564
$665$	3.85940e31	0.133067
$666$	1.63829e32	0.555183
$667$	−5.47044e32	−1.82211
$668$	−2.56487e31	−0.0839722
$669$	4.11139e32	1.32309
$670$	7.43985e31	0.235344
$671$	−9.91437e31	−0.308288
$672$	2.14499e31	0.0655660
$673$	2.41230e31	0.0724866	0.0362433	−	0.999343i	$-0.488461\pi$
$673$	2.41230e31	0.0724866	0.0362433	+	0.999343i	$0.488461\pi$
$674$	−4.25086e32	−1.25570
$675$	4.49861e31	0.130643
$676$	1.86360e31	0.0532067
$677$	−1.00530e32	−0.282178	−0.141089	−	0.989997i	$-0.545060\pi$
$677$	−1.00530e32	−0.282178	−0.141089	+	0.989997i	$0.545060\pi$
$678$	6.37141e32	1.75830
$679$	−1.31810e32	−0.357641
$680$	−2.98668e32	−0.796775
$681$	−9.79475e31	−0.256922
$682$	−7.30046e31	−0.188291
$683$	−2.04955e32	−0.519781	−0.259890	−	0.965638i	$-0.583686\pi$
$683$	−2.04955e32	−0.519781	−0.259890	+	0.965638i	$0.583686\pi$
$684$	−9.64218e30	−0.0240453
$685$	−1.48571e32	−0.364328
$686$	2.90240e32	0.699889
$687$	2.22652e32	0.527989
$688$	3.88669e32	0.906385
$689$	3.07692e32	0.705659
$690$	−2.39689e32	−0.540609
$691$	−2.53141e32	−0.561519	−0.280759	−	0.959778i	$-0.590586\pi$
$691$	−2.53141e32	−0.561519	−0.280759	+	0.959778i	$0.590586\pi$
$692$	−1.66584e31	−0.0363425
$693$	5.71461e31	0.122618
$694$	−6.62603e32	−1.39836
$695$	−1.11113e32	−0.230643
$696$	−1.07217e33	−2.18906
$697$	1.23326e32	0.247673
$698$	−5.83585e32	−1.15283
$699$	2.09671e32	0.407429
$700$	−2.84471e30	−0.00543764
$701$	5.72089e32	1.07574	0.537869	−	0.843029i	$-0.319230\pi$
$701$	5.72089e32	1.07574	0.537869	+	0.843029i	$0.319230\pi$
$702$	−1.63658e32	−0.302734
$703$	−5.21197e32	−0.948453
$704$	4.01888e32	0.719482
$705$	4.61896e32	0.813522
$706$	−3.24057e32	−0.561522
$707$	3.41735e32	0.582594
$708$	−5.02440e31	−0.0842755
$709$	−5.26420e32	−0.868761	−0.434381	−	0.900729i	$-0.643033\pi$
$709$	−5.26420e32	−0.868761	−0.434381	+	0.900729i	$0.643033\pi$
$710$	3.20892e32	0.521061
$711$	−3.32831e32	−0.531769
$712$	7.44001e32	1.16964
$713$	−1.92653e32	−0.298021
$714$	−5.19820e32	−0.791268
$715$	9.74133e31	0.145915
$716$	−5.09751e31	−0.0751378
$717$	1.06713e33	1.54791
$718$	−2.42096e32	−0.345586
$719$	9.47630e32	1.33124	0.665620	−	0.746291i	$-0.268167\pi$
$719$	9.47630e32	1.33124	0.665620	+	0.746291i	$0.268167\pi$
$720$	−1.37572e32	−0.190198
$721$	−2.81698e32	−0.383291
$722$	3.07646e32	0.411978
$723$	−6.87056e32	−0.905528
$724$	5.73373e31	0.0743778
$725$	2.75186e32	0.351349
$726$	−4.99554e32	−0.627785
$727$	−7.13068e31	−0.0882034	−0.0441017	−	0.999027i	$-0.514043\pi$
$727$	−7.13068e31	−0.0882034	−0.0441017	+	0.999027i	$0.514043\pi$
$728$	1.59972e32	0.194775
$729$	1.80034e32	0.215769
$730$	1.02248e32	0.120627
$731$	1.45569e33	1.69051
$732$	−3.31730e31	−0.0379234
$733$	1.25781e33	1.41553	0.707763	−	0.706450i	$-0.249705\pi$
$733$	1.25781e33	1.41553	0.707763	+	0.706450i	$0.249705\pi$
$734$	−9.75047e31	−0.108024
$735$	4.18786e32	0.456760
$736$	1.33380e32	0.143218
$737$	−3.50464e32	−0.370482
$738$	6.10494e31	0.0635379
$739$	−1.36187e33	−1.39548	−0.697742	−	0.716349i	$-0.745812\pi$
$739$	−1.36187e33	−1.39548	−0.697742	+	0.716349i	$0.745812\pi$
$740$	3.84167e31	0.0387575
$741$	−4.42200e32	−0.439248
$742$	−5.69624e32	−0.557113
$743$	−1.24800e33	−1.20183	−0.600914	−	0.799313i	$-0.705197\pi$
$743$	−1.24800e33	−1.20183	−0.600914	+	0.799313i	$0.705197\pi$
$744$	−3.77587e32	−0.358037
$745$	−7.30429e32	−0.681994
$746$	1.41803e33	1.30374
$747$	3.80417e32	0.344408
$748$	9.10165e31	0.0811431
$749$	−8.59336e32	−0.754436
$750$	1.20573e32	0.104243
$751$	−2.67128e32	−0.227436	−0.113718	−	0.993513i	$-0.536276\pi$
$751$	−2.67128e32	−0.227436	−0.113718	+	0.993513i	$0.536276\pi$
$752$	1.66313e33	1.39451
$753$	8.94827e31	0.0738919
$754$	−1.00112e33	−0.814170
$755$	4.62691e32	0.370597
$756$	−2.25132e31	−0.0177597
$757$	−1.99769e33	−1.55212	−0.776062	−	0.630656i	$-0.782786\pi$
$757$	−1.99769e33	−1.55212	−0.776062	+	0.630656i	$0.782786\pi$
$758$	6.01071e32	0.459970
$759$	1.12909e33	0.851033
$760$	4.70356e32	0.349197
$761$	5.39735e31	0.0394691	0.0197346	−	0.999805i	$-0.493718\pi$
$761$	5.39735e31	0.0394691	0.0197346	+	0.999805i	$0.493718\pi$
$762$	−2.55171e32	−0.183802
$763$	5.23369e32	0.371344
$764$	−6.24556e31	−0.0436513
$765$	−5.15251e32	−0.354742
$766$	1.48984e33	1.01043
$767$	−7.25192e32	−0.484514
$768$	3.78974e32	0.249434
$769$	−2.60865e33	−1.69147	−0.845733	−	0.533606i	$-0.820837\pi$
$769$	−2.60865e33	−1.69147	−0.845733	+	0.533606i	$0.820837\pi$
$770$	−1.80339e32	−0.115199
$771$	4.79275e32	0.301619
$772$	−1.19482e32	−0.0740802
$773$	−2.83829e33	−1.73377	−0.866887	−	0.498505i	$-0.833882\pi$
$773$	−2.83829e33	−1.73377	−0.866887	+	0.498505i	$0.833882\pi$
$774$	7.20599e32	0.433683
$775$	9.69125e31	0.0574659
$776$	−1.60641e33	−0.938526
$777$	1.03355e33	0.594964
$778$	1.00601e33	0.570607
$779$	−1.94220e32	−0.108546
$780$	3.25940e31	0.0179494
$781$	−1.51161e33	−0.820260
$782$	−3.23235e33	−1.72839
$783$	2.17783e33	1.14753
$784$	1.50791e33	0.782963
$785$	−1.32073e33	−0.675790
$786$	−9.27112e32	−0.467491
$787$	3.30676e33	1.64321	0.821606	−	0.570056i	$-0.193078\pi$
$787$	3.30676e33	1.64321	0.821606	+	0.570056i	$0.193078\pi$
$788$	−1.72113e31	−0.00842875
$789$	1.78262e33	0.860348
$790$	1.05033e33	0.499593
$791$	1.26504e33	0.593026
$792$	6.96455e32	0.321776
$793$	−4.78799e32	−0.218028
$794$	2.98215e33	1.33843
$795$	−1.79402e33	−0.793609
$796$	1.52263e32	0.0663885
$797$	4.49635e32	0.193237	0.0966183	−	0.995322i	$-0.469197\pi$
$797$	4.49635e32	0.193237	0.0966183	+	0.995322i	$0.469197\pi$
$798$	8.18637e32	0.346783
$799$	6.22896e33	2.60092
$800$	−6.70957e31	−0.0276159
$801$	1.28352e33	0.520751
$802$	−4.52746e33	−1.81071
$803$	−4.81654e32	−0.189892
$804$	−1.17263e32	−0.0455740
$805$	−4.75901e32	−0.182332
$806$	−3.52565e32	−0.133164
$807$	−7.53506e32	−0.280570
$808$	4.16481e33	1.52885
$809$	−4.86821e31	−0.0176182	−0.00880910	−	0.999961i	$-0.502804\pi$
$809$	−4.86821e31	−0.0176182	−0.00880910	+	0.999961i	$0.502804\pi$
$810$	1.50960e33	0.538622
$811$	−2.63403e33	−0.926574	−0.463287	−	0.886208i	$-0.653330\pi$
$811$	−2.63403e33	−0.926574	−0.463287	+	0.886208i	$0.653330\pi$
$812$	−1.37716e32	−0.0477628
$813$	−1.60569e33	−0.549061
$814$	2.43541e33	0.821093
$815$	−1.23758e33	−0.411397
$816$	−5.89490e33	−1.93214
$817$	−2.29248e33	−0.740887
$818$	−4.48681e33	−1.42980
$819$	2.75978e32	0.0867182
$820$	1.43157e31	0.00443560
$821$	2.21277e33	0.676067	0.338034	−	0.941134i	$-0.390238\pi$
$821$	2.21277e33	0.676067	0.338034	+	0.941134i	$0.390238\pi$
$822$	−3.15141e33	−0.949466
$823$	−3.50816e33	−1.04227	−0.521136	−	0.853474i	$-0.674492\pi$
$823$	−3.50816e33	−1.04227	−0.521136	+	0.853474i	$0.674492\pi$
$824$	−3.43313e33	−1.00584
$825$	−5.67977e32	−0.164101
$826$	1.34253e33	0.382521
$827$	4.27681e33	1.20173	0.600864	−	0.799351i	$-0.294823\pi$
$827$	4.27681e33	1.20173	0.600864	+	0.799351i	$0.294823\pi$
$828$	1.18897e32	0.0329475
$829$	−6.30687e33	−1.72360	−0.861801	−	0.507246i	$-0.830663\pi$
$829$	−6.30687e33	−1.72360	−0.861801	+	0.507246i	$0.830663\pi$
$830$	−1.20050e33	−0.323568
$831$	−8.13324e32	−0.216198
$832$	1.94086e33	0.508833
$833$	5.64760e33	1.46031
$834$	−2.35688e33	−0.601073
$835$	2.15847e33	0.542941
$836$	−1.43337e32	−0.0355620
$837$	7.66970e32	0.187688
$838$	5.88506e33	1.42051
$839$	6.90038e32	0.164290	0.0821448	−	0.996620i	$-0.473823\pi$
$839$	6.90038e32	0.164290	0.0821448	+	0.996620i	$0.473823\pi$
$840$	−9.32732e32	−0.219051
$841$	9.00537e33	2.08616
$842$	−2.24507e33	−0.513027
$843$	8.60007e32	0.193859
$844$	3.29431e31	0.00732532
$845$	−1.56832e33	−0.344020
$846$	3.08348e33	0.667240
$847$	−9.91860e32	−0.211734
$848$	−6.45969e33	−1.36038
$849$	−3.61033e33	−0.750081
$850$	1.62601e33	0.333277
$851$	6.42686e33	1.29960
$852$	−5.05775e32	−0.100903
$853$	3.36514e33	0.662353	0.331176	−	0.943569i	$-0.392554\pi$
$853$	3.36514e33	0.662353	0.331176	+	0.943569i	$0.392554\pi$
$854$	8.86392e32	0.172131
$855$	8.11441e32	0.155470
$856$	−1.04730e34	−1.97980
$857$	1.99307e33	0.371743	0.185872	−	0.982574i	$-0.440489\pi$
$857$	1.99307e33	0.371743	0.185872	+	0.982574i	$0.440489\pi$
$858$	2.06628e33	0.380265
$859$	3.62598e33	0.658422	0.329211	−	0.944256i	$-0.393217\pi$
$859$	3.62598e33	0.658422	0.329211	+	0.944256i	$0.393217\pi$
$860$	1.68976e32	0.0302756
$861$	3.85145e32	0.0680907
$862$	8.15750e33	1.42306
$863$	−2.55511e33	−0.439831	−0.219916	−	0.975519i	$-0.570578\pi$
$863$	−2.55511e33	−0.439831	−0.219916	+	0.975519i	$0.570578\pi$
$864$	−5.30998e32	−0.0901955
$865$	1.40190e33	0.234980
$866$	4.41228e33	0.729806
$867$	−1.46773e34	−2.39567
$868$	−4.84996e31	−0.00781198
$869$	−4.94774e33	−0.786465
$870$	5.83711e33	0.915644
$871$	−1.69251e33	−0.262013
$872$	6.37844e33	0.974485
$873$	−2.77132e33	−0.417852
$874$	5.09046e33	0.757488
$875$	2.39398e32	0.0351583
$876$	−1.61159e32	−0.0233591
$877$	3.10273e33	0.443863	0.221932	−	0.975062i	$-0.428764\pi$
$877$	3.10273e33	0.443863	0.221932	+	0.975062i	$0.428764\pi$
$878$	−7.50243e33	−1.05929
$879$	−8.54734e33	−1.19113
$880$	−2.04510e33	−0.281296
$881$	4.09430e33	0.555848	0.277924	−	0.960603i	$-0.410354\pi$
$881$	4.09430e33	0.555848	0.277924	+	0.960603i	$0.410354\pi$
$882$	2.79569e33	0.374629
$883$	−1.14207e34	−1.51058	−0.755291	−	0.655389i	$-0.772505\pi$
$883$	−1.14207e34	−1.51058	−0.755291	+	0.655389i	$0.772505\pi$
$884$	4.39550e32	0.0573862
$885$	4.22830e33	0.544902
$886$	−5.80704e33	−0.738698
$887$	1.51286e34	1.89967	0.949834	−	0.312755i	$-0.101252\pi$
$887$	1.51286e34	1.89967	0.949834	+	0.312755i	$0.101252\pi$
$888$	1.25962e34	1.56131
$889$	−5.06641e32	−0.0619912
$890$	−4.05049e33	−0.489241
$891$	−7.11116e33	−0.847905
$892$	6.43601e32	0.0757566
$893$	−9.80965e33	−1.13989
$894$	−1.54935e34	−1.77733
$895$	4.28983e33	0.485820
$896$	−3.10761e33	−0.347444
$897$	5.45275e33	0.601869
$898$	−5.49794e33	−0.599131
$899$	4.69165e33	0.504765
$900$	−5.98102e31	−0.00635311
$901$	−2.41935e34	−2.53726
$902$	9.07537e32	0.0939700
$903$	4.54607e33	0.464758
$904$	1.54174e34	1.55623
$905$	−4.82524e33	−0.480906
$906$	9.81438e33	0.965803
$907$	−9.27877e33	−0.901585	−0.450792	−	0.892629i	$-0.648859\pi$
$907$	−9.27877e33	−0.901585	−0.450792	+	0.892629i	$0.648859\pi$
$908$	−1.53328e32	−0.0147107
$909$	7.18499e33	0.680678
$910$	−8.70921e32	−0.0814710
$911$	9.56887e33	0.883893	0.441946	−	0.897042i	$-0.354288\pi$
$911$	9.56887e33	0.883893	0.441946	+	0.897042i	$0.354288\pi$
$912$	9.28356e33	0.846786
$913$	5.65513e33	0.509365
$914$	−1.19525e34	−1.06310
$915$	2.79168e33	0.245202
$916$	3.48542e32	0.0302313
$917$	−1.84077e33	−0.157671
$918$	1.28683e34	1.08850
$919$	6.94402e33	0.580073	0.290036	−	0.957016i	$-0.406333\pi$
$919$	6.94402e33	0.580073	0.290036	+	0.957016i	$0.406333\pi$
$920$	−5.79993e33	−0.478479
$921$	2.13307e33	0.173788
$922$	1.14105e32	0.00918116
$923$	−7.30006e33	−0.580106
$924$	2.84242e32	0.0223080
$925$	−3.23297e33	−0.250595
$926$	2.94901e33	0.225762
$927$	−5.92272e33	−0.447820
$928$	−3.24819e33	−0.242571
$929$	6.78312e32	0.0500321	0.0250160	−	0.999687i	$-0.492036\pi$
$929$	6.78312e32	0.0500321	0.0250160	+	0.999687i	$0.492036\pi$
$930$	2.05566e33	0.149761
$931$	−8.89410e33	−0.640001
$932$	3.28221e32	0.0233283
$933$	2.90945e34	2.04255
$934$	−1.27230e34	−0.882265
$935$	−7.65952e33	−0.524648
$936$	3.36342e33	0.227567
$937$	1.30982e34	0.875397	0.437699	−	0.899122i	$-0.355794\pi$
$937$	1.30982e34	0.875397	0.437699	+	0.899122i	$0.355794\pi$
$938$	3.13331e33	0.206857
$939$	4.94586e33	0.322543
$940$	7.23056e32	0.0465802
$941$	1.70578e34	1.08553	0.542766	−	0.839884i	$-0.317377\pi$
$941$	1.70578e34	1.08553	0.542766	+	0.839884i	$0.317377\pi$
$942$	−2.80146e34	−1.76116
$943$	2.39491e33	0.148732
$944$	1.52247e34	0.934051
$945$	1.89460e33	0.114829
$946$	1.07121e34	0.641399
$947$	1.73521e32	0.0102643	0.00513213	−	0.999987i	$-0.498366\pi$
$947$	1.73521e32	0.0102643	0.00513213	+	0.999987i	$0.498366\pi$
$948$	−1.65549e33	−0.0967453
$949$	−2.32607e33	−0.134296
$950$	−2.56071e33	−0.146063
$951$	8.91439e33	0.502361
$952$	−1.25785e34	−0.700330
$953$	−1.88418e34	−1.03646	−0.518231	−	0.855240i	$-0.673409\pi$
$953$	−1.88418e34	−1.03646	−0.518231	+	0.855240i	$0.673409\pi$
$954$	−1.19764e34	−0.650907
$955$	5.25597e33	0.282237
$956$	1.67049e33	0.0886294
$957$	−2.74965e34	−1.44142
$958$	1.45223e34	0.752195
$959$	−6.25710e33	−0.320228
$960$	−1.13163e34	−0.572252
$961$	−1.83610e34	−0.917442
$962$	1.17615e34	0.580695
$963$	−1.80676e34	−0.881451
$964$	−1.07552e33	−0.0518482
$965$	1.00550e34	0.478982
$966$	−1.00946e34	−0.475172
$967$	−2.89121e34	−1.34485	−0.672427	−	0.740164i	$-0.734748\pi$
$967$	−2.89121e34	−1.34485	−0.672427	+	0.740164i	$0.734748\pi$
$968$	−1.20881e34	−0.555636
$969$	3.47698e34	1.57935
$970$	8.74562e33	0.392569
$971$	−2.58459e34	−1.14649	−0.573246	−	0.819384i	$-0.694316\pi$
$971$	−2.58459e34	−1.14649	−0.573246	+	0.819384i	$0.694316\pi$
$972$	−1.34870e33	−0.0591224
$973$	−4.67956e33	−0.202725
$974$	1.38519e34	0.593035
$975$	−2.74296e33	−0.116056
$976$	1.00519e34	0.420316
$977$	−1.18490e34	−0.489659	−0.244829	−	0.969566i	$-0.578732\pi$
$977$	−1.18490e34	−0.489659	−0.244829	+	0.969566i	$0.578732\pi$
$978$	−2.62510e34	−1.07213
$979$	1.90804e34	0.770169
$980$	6.55572e32	0.0261529
$981$	1.10039e34	0.433862
$982$	−4.26171e34	−1.66074
$983$	3.47338e34	1.33779	0.668893	−	0.743359i	$-0.266769\pi$
$983$	3.47338e34	1.33779	0.668893	+	0.743359i	$0.266769\pi$
$984$	4.69386e33	0.178685
$985$	1.44843e33	0.0544979
$986$	7.87171e34	2.92742
$987$	1.94529e34	0.715051
$988$	−6.92224e32	−0.0251502
$989$	2.82685e34	1.01518
$990$	−3.79164e33	−0.134593
$991$	−2.20622e34	−0.774108	−0.387054	−	0.922057i	$-0.626507\pi$
$991$	−2.20622e34	−0.774108	−0.387054	+	0.922057i	$0.626507\pi$
$992$	−1.14392e33	−0.0396744
$993$	5.55158e34	1.90327
$994$	1.35145e34	0.457990
$995$	−1.28137e34	−0.429249
$996$	1.89218e33	0.0626584
$997$	1.73938e34	0.569377	0.284689	−	0.958620i	$-0.408110\pi$
$997$	1.73938e34	0.569377	0.284689	+	0.958620i	$0.408110\pi$
$998$	−5.82876e34	−1.88614
$999$	−2.55859e34	−0.818460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.24.a.a.1.1	✓	3
3.2	odd	2		45.24.a.a.1.3		3
5.2	odd	4		25.24.b.b.24.1		6
5.3	odd	4		25.24.b.b.24.6		6
5.4	even	2		25.24.a.b.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.a.a.1.1	✓	3	1.1	even	1	trivial
25.24.a.b.1.3		3	5.4	even	2
25.24.b.b.24.1		6	5.2	odd	4
25.24.b.b.24.6		6	5.3	odd	4
45.24.a.a.1.3		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-2794.35 q^{2} -370647. q^{3} -580214. q^{4} +4.88281e7 q^{5} +1.03572e9 q^{6} +2.05641e9 q^{7} +2.50620e10 q^{8} +4.32361e10 q^{9} +O(q^{10})\)	\(q-2794.35 q^{2} -370647. q^{3} -580214. q^{4} +4.88281e7 q^{5} +1.03572e9 q^{6} +2.05641e9 q^{7} +2.50620e10 q^{8} +4.32361e10 q^{9} -1.36443e11 q^{10} +6.42732e11 q^{11} +2.15055e11 q^{12} +3.10398e12 q^{13} -5.74633e12 q^{14} -1.80980e13 q^{15} -6.51649e13 q^{16} -2.44063e14 q^{17} -1.20817e14 q^{18} +3.84362e14 q^{19} -2.83308e13 q^{20} -7.62203e14 q^{21} -1.79602e15 q^{22} -4.73954e15 q^{23} -9.28917e15 q^{24} +2.38419e15 q^{25} -8.67359e15 q^{26} +1.88686e16 q^{27} -1.19316e15 q^{28} +1.15421e17 q^{29} +5.05722e16 q^{30} +4.06480e16 q^{31} -2.81420e16 q^{32} -2.38227e17 q^{33} +6.81997e17 q^{34} +1.00411e17 q^{35} -2.50862e16 q^{36} -1.35601e18 q^{37} -1.07404e18 q^{38} -1.15048e18 q^{39} +1.22373e18 q^{40} -5.05305e17 q^{41} +2.12986e18 q^{42} -5.96439e18 q^{43} -3.72922e17 q^{44} +2.11114e18 q^{45} +1.32439e19 q^{46} -2.55219e19 q^{47} +2.41532e19 q^{48} -2.31399e19 q^{49} -6.66225e18 q^{50} +9.04612e19 q^{51} -1.80097e18 q^{52} +9.91283e19 q^{53} -5.27253e19 q^{54} +3.13834e19 q^{55} +5.15378e19 q^{56} -1.42463e20 q^{57} -3.22528e20 q^{58} -2.33633e20 q^{59} +1.05007e19 q^{60} -1.54254e20 q^{61} -1.13585e20 q^{62} +8.89112e19 q^{63} +6.25281e20 q^{64} +1.51561e20 q^{65} +6.65689e20 q^{66} -5.45272e20 q^{67} +1.41609e20 q^{68} +1.75670e21 q^{69} -2.80583e20 q^{70} -2.35184e21 q^{71} +1.08359e21 q^{72} -7.49385e20 q^{73} +3.78916e21 q^{74} -8.83692e20 q^{75} -2.23012e20 q^{76} +1.32172e21 q^{77} +3.21484e21 q^{78} -7.69798e21 q^{79} -3.18188e21 q^{80} -1.10640e22 q^{81} +1.41200e21 q^{82} +8.79858e21 q^{83} +4.42241e20 q^{84} -1.19171e22 q^{85} +1.66666e22 q^{86} -4.27806e22 q^{87} +1.61082e22 q^{88} +2.96864e22 q^{89} -5.89926e21 q^{90} +6.38305e21 q^{91} +2.74995e21 q^{92} -1.50661e22 q^{93} +7.13172e22 q^{94} +1.87677e22 q^{95} +1.04307e22 q^{96} -6.40973e22 q^{97} +6.46611e22 q^{98} +2.77892e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9}+O(q^{10}) \) 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9	\( 3 q + 666 q^{2} - 139428 q^{3} - 9483516 q^{4} + 146484375 q^{5} + 959898816 q^{6} - 2432683344 q^{7} - 12840421560 q^{8} + 1693083951 q^{9} + 32519531250 q^{10} - 165286030404 q^{11} - 2460925191744 q^{12} - 3554970733998 q^{13} + 1638464466408 q^{14} - 6808007812500 q^{15} - 68987884476912 q^{16} - 416105769269514 q^{17} - 302723670254238 q^{18} - 975704043068460 q^{19} - 463062304687500 q^{20} - 51\!\cdots\!84 q^{21}+ \cdots + 19\!\cdots\!32 q^{99}+O(q^{100}) \) 3 * q + 666 * q^2 - 139428 * q^3 - 9483516 * q^4 + 146484375 * q^5 + 959898816 * q^6 - 2432683344 * q^7 - 12840421560 * q^8 + 1693083951 * q^9 + 32519531250 * q^10 - 165286030404 * q^11 - 2460925191744 * q^12 - 3554970733998 * q^13 + 1638464466408 * q^14 - 6808007812500 * q^15 - 68987884476912 * q^16 - 416105769269514 * q^17 - 302723670254238 * q^18 - 975704043068460 * q^19 - 463062304687500 * q^20 - 5102384337991584 * q^21 - 5786145456383688 * q^22 - 4979666912332368 * q^23 - 10409810708926080 * q^24 + 7152557373046875 * q^25 - 17675137590787524 * q^26 + 20047178078003160 * q^27 + 71220956974215888 * q^28 + 95526863867406210 * q^29 + 46870059375000000 * q^30 + 203997528720796176 * q^31 + 170287635059993376 * q^32 + 322079222096408304 * q^33 + 716918393922501108 * q^34 - 118783366406250000 * q^35 - 220893376245027372 * q^36 - 483030177185234454 * q^37 - 3922824866561525640 * q^38 - 2555750058791490648 * q^39 - 626973708984375000 * q^40 - 4358124871734570834 * q^41 - 2559620302421551488 * q^42 - 5324153686845536508 * q^43 - 5745533240877106512 * q^44 + 82670114794921875 * q^45 + 10292691411163504536 * q^46 + 12258262539323374776 * q^47 + 52185334595839679232 * q^48 + 53865950980476272379 * q^49 + 1587867736816406250 * q^50 - 13305294839256933384 * q^51 + 36561029094508759896 * q^52 + 71640983942760085722 * q^53 - 8722300088406303360 * q^54 - 8070606953320312500 * q^55 + 32773217861089510560 * q^56 - 174702718819675136880 * q^57 - 258910443213048121860 * q^58 - 420843416438104506180 * q^59 - 120162362878125000000 * q^60 - 581725337824220015454 * q^61 - 6386866856435690928 * q^62 - 701377962769300673808 * q^63 + 910193477718092702784 * q^64 - 173582555370996093750 * q^65 + 1527698529319557146112 * q^66 - 1399668543169120673364 * q^67 + 2058346167335115118728 * q^68 + 2368452906957113559072 * q^69 + 80003147773828125000 * q^70 - 409151675006970497064 * q^71 + 2624939937107847919080 * q^72 + 3254958507976741960782 * q^73 + 5024018202030699806508 * q^74 - 332422256469726562500 * q^75 + 4116463921392566297520 * q^76 - 17679177187365753067008 * q^77 + 2659161203582354699904 * q^78 - 10163548547854309111440 * q^79 - 3368549046724218750000 * q^80 - 17599804703176322735397 * q^81 - 12650907933669059897148 * q^82 - 14365350009027465650388 * q^83 + 29520686861588838037248 * q^84 - 20317664515112988281250 * q^85 + 26606188682127536075856 * q^86 - 69805465343858969988120 * q^87 + 49185500030908263850080 * q^88 + 55263110999125019200830 * q^89 - 14781429211632714843750 * q^90 + 41561600612192918902176 * q^91 - 4955822257768756710864 * q^92 + 48060187726233171700224 * q^93 + 160261789932669635237208 * q^94 - 47641798977952148437500 * q^95 + 56188621559544366859776 * q^96 - 231524977804298299798074 * q^97 + 129877246807137874291338 * q^98 + 195725739081953651557932 * q^99

Introduction

L-functions

Modular forms

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