LMFDB - Embedded newform 25.32.b.d.24.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,32,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 32, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 32);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 32 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$152.192832048$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 31744631285 x^{18} + \cdots + 44\!\cdots\!76 $ x^20 + 31744631285x^18 + 423995446048816955620x^16 + 3106660218935921984013646488320x^14 + 13679821305153710111607135094389308047360x^12 + 37419679386629476838773772412098413830656205258752x^10 + 63707874511296353108940435672939178007105193685468693135360x^8 + 65620084284125021841421007310187065070306024480775464183860108984320x^6 + 37775995554700393131526739494592845101051457450908182983023372016238586757120x^4 + 9856176069614755897219321656662541127308373856626415513724188348201805841367732060160*x^2 + 445381155028366614454549079146794001318264794519412068859186461287727744559592982842626277376
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	multiple of $ 2^{80}\cdot 3^{22}\cdot 5^{110} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.16
Root			$50468.3i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.32.b.d.24.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+50468.3i q^{2} -3.54185e7i q^{3} -3.99569e8 q^{4} +1.78751e12 q^{6} +7.37897e12i q^{7} +8.82143e13i q^{8} -6.36795e14 q^{9} +O(q^{10})$	\(q+50468.3i q^{2} -3.54185e7i q^{3} -3.99569e8 q^{4} +1.78751e12 q^{6} +7.37897e12i q^{7} +8.82143e13i q^{8} -6.36795e14 q^{9} -2.56911e16 q^{11} +1.41521e16i q^{12} -1.59954e17i q^{13} -3.72404e17 q^{14} -5.31010e18 q^{16} -5.12967e18i q^{17} -3.21380e19i q^{18} -6.46616e19 q^{19} +2.61352e20 q^{21} -1.29658e21i q^{22} +1.49288e21i q^{23} +3.12442e21 q^{24} +8.07260e21 q^{26} +6.77267e20i q^{27} -2.94841e21i q^{28} +5.23737e22 q^{29} +2.77195e22 q^{31} -7.85529e22i q^{32} +9.09938e23i q^{33} +2.58886e23 q^{34} +2.54443e23 q^{36} -6.74592e23i q^{37} -3.26336e24i q^{38} -5.66532e24 q^{39} -6.66926e24 q^{41} +1.31900e25i q^{42} -2.14950e25i q^{43} +1.02653e25 q^{44} -7.53434e25 q^{46} -1.75727e25i q^{47} +1.88076e26i q^{48} +1.03326e26 q^{49} -1.81685e26 q^{51} +6.39125e25i q^{52} +3.62828e26i q^{53} -3.41806e25 q^{54} -6.50931e26 q^{56} +2.29022e27i q^{57} +2.64322e27i q^{58} +4.99188e27 q^{59} -7.77843e27 q^{61} +1.39896e27i q^{62} -4.69890e27i q^{63} -7.43891e27 q^{64} -4.59231e28 q^{66} +2.47542e28i q^{67} +2.04966e27i q^{68} +5.28757e28 q^{69} +8.55888e28 q^{71} -5.61745e28i q^{72} +7.99777e28i q^{73} +3.40455e28 q^{74} +2.58368e28 q^{76} -1.89574e29i q^{77} -2.85919e29i q^{78} +1.78848e29 q^{79} -3.69344e29 q^{81} -3.36586e29i q^{82} -8.73583e29i q^{83} -1.04428e29 q^{84} +1.08481e30 q^{86} -1.85500e30i q^{87} -2.26632e30i q^{88} +2.53778e30 q^{89} +1.18029e30 q^{91} -5.96510e29i q^{92} -9.81782e29i q^{93} +8.86867e29 q^{94} -2.78223e30 q^{96} -2.82605e30i q^{97} +5.21470e30i q^{98} +1.63599e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20539589610 q^{4} + 686623832090 q^{6} - 36\!\cdots\!40 q^{9}+O(q^{10}) $ 20 * q - 20539589610 * q^4 + 686623832090 * q^6 - 3631559863498040 * q^9	$ 20 q - 20539589610 q^{4} + 686623832090 q^{6} - 36\!\cdots\!40 q^{9}+ \cdots - 12\!\cdots\!80 q^{99}+O(q^{100}) $ 20 * q - 20539589610 * q^4 + 686623832090 * q^6 - 3631559863498040 * q^9 + 14698263410387040 * q^11 - 3585430984535446020 * q^14 + 2668707436521071970 * q^16 - 92704745745734472000 * q^19 - 1433956230663012048360 * q^21 - 7629774658866586147950 * q^24 + 32856089868200755271640 * q^26 + 87725502776009659186800 * q^29 - 222796998479461581232960 * q^31 - 1924324021312734888556570 * q^34 - 5025054501215053083856580 * q^36 - 15450618695652181209461680 * q^39 - 47909930935503157644691260 * q^41 - 145310690902340893702475970 * q^44 - 252836584120338157033164660 * q^46 - 1246276182399196031444904260 * q^49 - 1849897927683754577276692960 * q^51 + 2591153317777144376506605250 * q^54 + 5799317051948263540741982700 * q^56 + 6066159147123348006692515200 * q^59 + 8463634058261727404238573240 * q^61 + 9517358906702440359771160990 * q^64 + 41883496723623582695134585930 * q^66 + 141421493056144218523923301320 * q^69 + 118845453796062103335338131440 * q^71 - 467772945250325662075867676820 * q^74 - 862330218554817908331535050350 * q^76 - 839661308397414799907136990800 * q^79 - 46356956658731639668114605580 * q^81 - 3067463374376454313718938994820 * q^84 - 1760036218098267190164891359160 * q^86 + 2972172090363405141073742262900 * q^89 + 14623549158011964101986521147040 * q^91 + 20460655315576187327400332153480 * q^94 + 12710573490967896478118960330590 * q^96 - 12487277792345774005972560542080 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	50468.3i	1.08907i	0.838740	+	0.544533i	$0.183293\pi$
$2$	50468.3i	1.08907i	−0.838740	+	0.544533i	$0.816707\pi$
$3$	− 3.54185e7i	− 1.42512i	−0.701613	−	0.712558i	$-0.747536\pi$
$3$	− 3.54185e7i	− 1.42512i	0.701613	−	0.712558i	$-0.252464\pi$
$4$	−3.99569e8	−0.186064
$5$	0	0
$5$	0	0
$6$	1.78751e12	1.55205
$7$	7.37897e12i	0.587457i	0.955889	+	0.293729i	$0.0948962\pi$
$7$	7.37897e12i	0.587457i	−0.955889	+	0.293729i	$0.905104\pi$
$8$	8.82143e13i	0.886430i
$9$	−6.36795e14	−1.03096
$10$	0	0
$11$	−2.56911e16	−1.85437	−0.927183	−	0.374609i	$-0.877777\pi$
$11$	−2.56911e16	−1.85437	−0.927183	+	0.374609i	$0.877777\pi$
$12$	1.41521e16i	0.265163i
$13$	− 1.59954e17i	− 0.866708i	−0.901224	−	0.433354i	$-0.857330\pi$
$13$	− 1.59954e17i	− 0.866708i	0.901224	−	0.433354i	$-0.142670\pi$
$14$	−3.72404e17	−0.639780
$15$	0	0
$16$	−5.31010e18	−1.15144
$17$	− 5.12967e18i	− 0.434642i	−0.976100	−	0.217321i	$-0.930268\pi$
$17$	− 5.12967e18i	− 0.434642i	0.976100	−	0.217321i	$-0.0697318\pi$
$18$	− 3.21380e19i	− 1.12278i
$19$	−6.46616e19	−0.977160	−0.488580	−	0.872519i	$-0.662485\pi$
$19$	−6.46616e19	−0.977160	−0.488580	+	0.872519i	$0.662485\pi$
$20$	0	0
$21$	2.61352e20	0.837195
$22$	− 1.29658e21i	− 2.01953i
$23$	1.49288e21i	1.16747i	0.811945	+	0.583734i	$0.198409\pi$
$23$	1.49288e21i	1.16747i	−0.811945	+	0.583734i	$0.801591\pi$
$24$	3.12442e21	1.26327
$25$	0	0
$26$	8.07260e21	0.943901
$27$	6.77267e20i	0.0441186i
$28$	− 2.94841e21i	− 0.109304i
$29$	5.23737e22	1.12705	0.563527	−	0.826098i	$-0.309444\pi$
$29$	5.23737e22	1.12705	0.563527	+	0.826098i	$0.309444\pi$
$30$	0	0
$31$	2.77195e22	0.212168	0.106084	−	0.994357i	$-0.466169\pi$
$31$	2.77195e22	0.212168	0.106084	+	0.994357i	$0.466169\pi$
$32$	− 7.85529e22i	− 0.367568i
$33$	9.09938e23i	2.64269i
$34$	2.58886e23	0.473353
$35$	0	0
$36$	2.54443e23	0.191824
$37$	− 6.74592e23i	− 0.332594i	−0.986076	−	0.166297i	$-0.946819\pi$
$37$	− 6.74592e23i	− 0.332594i	0.986076	−	0.166297i	$-0.0531811\pi$
$38$	− 3.26336e24i	− 1.06419i
$39$	−5.66532e24	−1.23516
$40$	0	0
$41$	−6.66926e24	−0.669773	−0.334887	−	0.942258i	$-0.608698\pi$
$41$	−6.66926e24	−0.669773	−0.334887	+	0.942258i	$0.608698\pi$
$42$	1.31900e25i	0.911761i
$43$	− 2.14950e25i	− 1.03175i	−0.856663	−	0.515876i	$-0.827466\pi$
$43$	− 2.14950e25i	− 1.03175i	0.856663	−	0.515876i	$-0.172534\pi$
$44$	1.02653e25	0.345030
$45$	0	0
$46$	−7.53434e25	−1.27145
$47$	− 1.75727e25i	− 0.212482i	−0.994340	−	0.106241i	$-0.966118\pi$
$47$	− 1.75727e25i	− 0.212482i	0.994340	−	0.106241i	$-0.0338815\pi$
$48$	1.88076e26i	1.64094i
$49$	1.03326e26	0.654894
$50$	0	0
$51$	−1.81685e26	−0.619415
$52$	6.39125e25i	0.161263i
$53$	3.62828e26i	0.681436i	0.940166	+	0.340718i	$0.110670\pi$
$53$	3.62828e26i	0.681436i	−0.940166	+	0.340718i	$0.889330\pi$
$54$	−3.41806e25	−0.0480481
$55$	0	0
$56$	−6.50931e26	−0.520740
$57$	2.29022e27i	1.39257i
$58$	2.64322e27i	1.22744i
$59$	4.99188e27	1.77852	0.889258	−	0.457407i	$-0.151222\pi$
$59$	4.99188e27	1.77852	0.889258	+	0.457407i	$0.151222\pi$
$60$	0	0
$61$	−7.77843e27	−1.65302	−0.826512	−	0.562918i	$-0.809679\pi$
$61$	−7.77843e27	−1.65302	−0.826512	+	0.562918i	$0.809679\pi$
$62$	1.39896e27i	0.231064i
$63$	− 4.69890e27i	− 0.605644i
$64$	−7.43891e27	−0.751138
$65$	0	0
$66$	−4.59231e28	−2.87806
$67$	2.47542e28i	1.22883i	0.788985	+	0.614413i	$0.210607\pi$
$67$	2.47542e28i	1.22883i	−0.788985	+	0.614413i	$0.789393\pi$
$68$	2.04966e27i	0.0808710i
$69$	5.28757e28	1.66378
$70$	0	0
$71$	8.55888e28	1.72947	0.864734	−	0.502229i	$-0.167487\pi$
$71$	8.55888e28	1.72947	0.864734	+	0.502229i	$0.167487\pi$
$72$	− 5.61745e28i	− 0.913872i
$73$	7.99777e28i	1.05067i	0.850897	+	0.525333i	$0.176059\pi$
$73$	7.99777e28i	1.05067i	−0.850897	+	0.525333i	$0.823941\pi$
$74$	3.40455e28	0.362217
$75$	0	0
$76$	2.58368e28	0.181814
$77$	− 1.89574e29i	− 1.08936i
$78$	− 2.85919e29i	− 1.34517i
$79$	1.78848e29	0.690661	0.345330	−	0.938481i	$-0.387767\pi$
$79$	1.78848e29	0.690661	0.345330	+	0.938481i	$0.387767\pi$
$80$	0	0
$81$	−3.69344e29	−0.968084
$82$	− 3.36586e29i	− 0.729427i
$83$	− 8.73583e29i	− 1.56889i	−0.620196	−	0.784447i	$-0.712947\pi$
$83$	− 8.73583e29i	− 1.56889i	0.620196	−	0.784447i	$-0.287053\pi$
$84$	−1.04428e29	−0.155772
$85$	0	0
$86$	1.08481e30	1.12365
$87$	− 1.85500e30i	− 1.60618i
$88$	− 2.26632e30i	− 1.64377i
$89$	2.53778e30	1.54493	0.772464	−	0.635058i	$-0.219024\pi$
$89$	2.53778e30	1.54493	0.772464	+	0.635058i	$0.219024\pi$
$90$	0	0
$91$	1.18029e30	0.509154
$92$	− 5.96510e29i	− 0.217223i
$93$	− 9.81782e29i	− 0.302364i
$94$	8.86867e29	0.231407
$95$	0	0
$96$	−2.78223e30	−0.523827
$97$	− 2.82605e30i	− 0.453125i	−0.973997	−	0.226563i	$-0.927251\pi$
$97$	− 2.82605e30i	− 0.453125i	0.973997	−	0.226563i	$-0.0727488\pi$
$98$	5.21470e30i	0.713222i
$99$	1.63599e31	1.91177
$100$	0	0
$101$	−1.71242e31	−1.46767	−0.733834	−	0.679328i	$-0.762271\pi$
$101$	−1.71242e31	−1.46767	−0.733834	+	0.679328i	$0.762271\pi$
$102$	− 9.16935e30i	− 0.674583i
$103$	− 1.58163e30i	− 0.100029i	−0.998748	−	0.0500146i	$-0.984073\pi$
$103$	− 1.58163e30i	− 0.100029i	0.998748	−	0.0500146i	$-0.0159268\pi$
$104$	1.41102e31	0.768276
$105$	0	0
$106$	−1.83113e31	−0.742128
$107$	5.00191e31i	1.75262i	0.481748	+	0.876310i	$0.340002\pi$
$107$	5.00191e31i	1.75262i	−0.481748	+	0.876310i	$0.659998\pi$
$108$	− 2.70615e29i	− 0.00820887i
$109$	5.02620e30	0.132169	0.0660844	−	0.997814i	$-0.478949\pi$
$109$	5.02620e30	0.132169	0.0660844	+	0.997814i	$0.478949\pi$
$110$	0	0
$111$	−2.38930e31	−0.473986
$112$	− 3.91831e31i	− 0.676424i
$113$	− 4.36896e31i	− 0.657146i	−0.944479	−	0.328573i	$-0.893432\pi$
$113$	− 4.36896e31i	− 0.657146i	0.944479	−	0.328573i	$-0.106568\pi$
$114$	−1.15583e32	−1.51660
$115$	0	0
$116$	−2.09269e31	−0.209704
$117$	1.01858e32i	0.893539i
$118$	2.51932e32i	1.93692i
$119$	3.78517e31	0.255333
$120$	0	0
$121$	4.68087e32	2.43867
$122$	− 3.92564e32i	− 1.80025i
$123$	2.36215e32i	0.954505i
$124$	−1.10758e31	−0.0394767
$125$	0	0
$126$	2.37145e32	0.659586
$127$	7.87167e32i	1.93691i	0.249191	+	0.968454i	$0.419835\pi$
$127$	7.87167e32i	1.93691i	−0.249191	+	0.968454i	$0.580165\pi$
$128$	− 5.44121e32i	− 1.18561i
$129$	−7.61319e32	−1.47037
$130$	0	0
$131$	4.96406e32	0.755322	0.377661	−	0.925944i	$-0.376728\pi$
$131$	4.96406e32	0.755322	0.377661	+	0.925944i	$0.376728\pi$
$132$	− 3.63583e32i	− 0.491708i
$133$	− 4.77136e32i	− 0.574040i
$134$	−1.24931e33	−1.33827
$135$	0	0
$136$	4.52511e32	0.385279
$137$	− 1.28980e33i	− 0.980291i	−0.871640	−	0.490146i	$-0.836944\pi$
$137$	− 1.28980e33i	− 0.980291i	0.871640	−	0.490146i	$-0.163056\pi$
$138$	2.66855e33i	1.81196i
$139$	1.17433e33	0.712952	0.356476	−	0.934304i	$-0.383978\pi$
$139$	1.17433e33	0.712952	0.356476	+	0.934304i	$0.383978\pi$
$140$	0	0
$141$	−6.22400e32	−0.302812
$142$	4.31953e33i	1.88350i
$143$	4.10938e33i	1.60719i
$144$	3.38145e33	1.18709
$145$	0	0
$146$	−4.03634e33	−1.14424
$147$	− 3.65965e33i	− 0.933300i
$148$	2.69546e32i	0.0618837i
$149$	6.31685e33	1.30651	0.653256	−	0.757137i	$-0.273403\pi$
$149$	6.31685e33	1.30651	0.653256	+	0.757137i	$0.273403\pi$
$150$	0	0
$151$	3.39621e33	0.571283	0.285642	−	0.958336i	$-0.407793\pi$
$151$	3.39621e33	0.571283	0.285642	+	0.958336i	$0.407793\pi$
$152$	− 5.70408e33i	− 0.866184i
$153$	3.26655e33i	0.448097i
$154$	9.56746e33	1.18639
$155$	0	0
$156$	2.26368e33	0.229818
$157$	− 1.12435e33i	− 0.103385i	−0.998663	−	0.0516925i	$-0.983538\pi$
$157$	− 1.12435e33i	− 0.103385i	0.998663	−	0.0516925i	$-0.0164616\pi$
$158$	9.02617e33i	0.752175i
$159$	1.28508e34	0.971126
$160$	0	0
$161$	−1.10160e34	−0.685837
$162$	− 1.86402e34i	− 1.05431i
$163$	− 1.80084e34i	− 0.925907i	−0.886383	−	0.462954i	$-0.846790\pi$
$163$	− 1.80084e34i	− 0.925907i	0.886383	−	0.462954i	$-0.153210\pi$
$164$	2.66483e33	0.124620
$165$	0	0
$166$	4.40883e34	1.70863
$167$	− 1.75097e34i	− 0.618262i	−0.951019	−	0.309131i	$-0.899962\pi$
$167$	− 1.75097e34i	− 0.618262i	0.951019	−	0.309131i	$-0.100038\pi$
$168$	2.30550e34i	0.742115i
$169$	8.47473e33	0.248818
$170$	0	0
$171$	4.11762e34	1.00741
$172$	8.58871e33i	0.191972i
$173$	2.82466e34i	0.577101i	0.957465	+	0.288550i	$0.0931733\pi$
$173$	2.82466e34i	0.577101i	−0.957465	+	0.288550i	$0.906827\pi$
$174$	9.36187e34	1.74924
$175$	0	0
$176$	1.36422e35	2.13520
$177$	− 1.76805e35i	− 2.53459i
$178$	1.28077e35i	1.68253i
$179$	1.63675e34	0.197134	0.0985668	−	0.995130i	$-0.468574\pi$
$179$	1.63675e34	0.197134	0.0985668	+	0.995130i	$0.468574\pi$
$180$	0	0
$181$	4.55817e33	0.0462139	0.0231069	−	0.999733i	$-0.492644\pi$
$181$	4.55817e33	0.0462139	0.0231069	+	0.999733i	$0.492644\pi$
$182$	5.95675e34i	0.554502i
$183$	2.75500e35i	2.35575i
$184$	−1.31694e35	−1.03488
$185$	0	0
$186$	4.95489e34	0.329294
$187$	1.31787e35i	0.805984i
$188$	7.02152e33i	0.0395352i
$189$	−4.99754e33	−0.0259178
$190$	0	0
$191$	−1.84946e35	−0.814755	−0.407377	−	0.913260i	$-0.633557\pi$
$191$	−1.84946e35	−0.814755	−0.407377	+	0.913260i	$0.633557\pi$
$192$	2.63475e35i	1.07046i
$193$	3.01732e35i	1.13105i	0.824730	+	0.565527i	$0.191327\pi$
$193$	3.01732e35i	1.13105i	−0.824730	+	0.565527i	$0.808673\pi$
$194$	1.42626e35	0.493483
$195$	0	0
$196$	−4.12859e34	−0.121852
$197$	3.75808e35i	1.02504i	0.858676	+	0.512519i	$0.171288\pi$
$197$	3.75808e35i	1.02504i	−0.858676	+	0.512519i	$0.828712\pi$
$198$	8.25659e35i	2.08205i
$199$	2.95593e35	0.689401	0.344700	−	0.938713i	$-0.387980\pi$
$199$	2.95593e35	0.689401	0.344700	+	0.938713i	$0.387980\pi$
$200$	0	0
$201$	8.76758e35	1.75122
$202$	− 8.64228e35i	− 1.59839i
$203$	3.86464e35i	0.662096i
$204$	7.25957e34	0.115251
$205$	0	0
$206$	7.98220e34	0.108938
$207$	− 9.50662e35i	− 1.20361i
$208$	8.49370e35i	0.997965i
$209$	1.66123e36	1.81201
$210$	0	0
$211$	8.80125e35	0.828259	0.414129	−	0.910218i	$-0.364086\pi$
$211$	8.80125e35	0.828259	0.414129	+	0.910218i	$0.364086\pi$
$212$	− 1.44975e35i	− 0.126790i
$213$	− 3.03143e36i	− 2.46470i
$214$	−2.52438e36	−1.90872
$215$	0	0
$216$	−5.97447e34	−0.0391081
$217$	2.04541e35i	0.124639i
$218$	2.53664e35i	0.143940i
$219$	2.83269e36	1.49732
$220$	0	0
$221$	−8.20510e35	−0.376707
$222$	− 1.20584e36i	− 0.516201i
$223$	− 1.84633e36i	− 0.737196i	−0.929589	−	0.368598i	$-0.879838\pi$
$223$	− 1.84633e36i	− 0.737196i	0.929589	−	0.368598i	$-0.120162\pi$
$224$	5.79640e35	0.215931
$225$	0	0
$226$	2.20494e36	0.715675
$227$	− 3.93136e36i	− 1.19163i	−0.803121	−	0.595816i	$-0.796829\pi$
$227$	− 3.93136e36i	− 1.19163i	0.803121	−	0.595816i	$-0.203171\pi$
$228$	− 9.15099e35i	− 0.259106i
$229$	−1.69716e35	−0.0449028	−0.0224514	−	0.999748i	$-0.507147\pi$
$229$	−1.69716e35	−0.0449028	−0.0224514	+	0.999748i	$0.507147\pi$
$230$	0	0
$231$	−6.71441e36	−1.55247
$232$	4.62012e36i	0.999054i
$233$	− 7.56158e36i	− 1.52966i	−0.644231	−	0.764831i	$-0.722822\pi$
$233$	− 7.56158e36i	− 1.52966i	0.644231	−	0.764831i	$-0.277178\pi$
$234$	−5.14059e36	−0.973122
$235$	0	0
$236$	−1.99460e36	−0.330917
$237$	− 6.33453e36i	− 0.984272i
$238$	1.91031e36i	0.278075i
$239$	9.22168e36	1.25789	0.628945	−	0.777450i	$-0.283487\pi$
$239$	9.22168e36	1.25789	0.628945	+	0.777450i	$0.283487\pi$
$240$	0	0
$241$	−4.75610e36	−0.570147	−0.285073	−	0.958506i	$-0.592018\pi$
$241$	−4.75610e36	−0.570147	−0.285073	+	0.958506i	$0.592018\pi$
$242$	2.36236e37i	2.65587i
$243$	1.34999e37i	1.42375i
$244$	3.10802e36	0.307568
$245$	0	0
$246$	−1.19214e37	−1.03952
$247$	1.03429e37i	0.846912i
$248$	2.44526e36i	0.188072i
$249$	−3.09410e37	−2.23586
$250$	0	0
$251$	−6.37631e36	−0.407030	−0.203515	−	0.979072i	$-0.565237\pi$
$251$	−6.37631e36	−0.407030	−0.203515	+	0.979072i	$0.565237\pi$
$252$	1.87753e36i	0.112688i
$253$	− 3.83538e37i	− 2.16491i
$254$	−3.97270e37	−2.10942
$255$	0	0
$256$	1.14859e37	0.540065
$257$	1.08857e37i	0.481831i	0.970546	+	0.240915i	$0.0774476\pi$
$257$	1.08857e37i	0.481831i	−0.970546	+	0.240915i	$0.922552\pi$
$258$	− 3.84225e37i	− 1.60133i
$259$	4.97780e36	0.195385
$260$	0	0
$261$	−3.33514e37	−1.16194
$262$	2.50528e37i	0.822596i
$263$	6.84363e36i	0.211823i	0.994376	+	0.105911i	$0.0337760\pi$
$263$	6.84363e36i	0.211823i	−0.994376	+	0.105911i	$0.966224\pi$
$264$	−8.02696e37	−2.34256
$265$	0	0
$266$	2.40803e37	0.625167
$267$	− 8.98842e37i	− 2.20170i
$268$	− 9.89102e36i	− 0.228640i
$269$	3.81449e37	0.832293	0.416147	−	0.909297i	$-0.363380\pi$
$269$	3.81449e37	0.832293	0.416147	+	0.909297i	$0.363380\pi$
$270$	0	0
$271$	9.16564e37	1.78295	0.891474	−	0.453072i	$-0.149672\pi$
$271$	9.16564e37	1.78295	0.891474	+	0.453072i	$0.149672\pi$
$272$	2.72391e37i	0.500465i
$273$	− 4.18042e37i	− 0.725603i
$274$	6.50943e37	1.06760
$275$	0	0
$276$	−2.11275e37	−0.309568
$277$	5.62673e37i	0.779507i	0.920919	+	0.389753i	$0.127440\pi$
$277$	5.62673e37i	0.779507i	−0.920919	+	0.389753i	$0.872560\pi$
$278$	5.92664e37i	0.776451i
$279$	−1.76516e37	−0.218736
$280$	0	0
$281$	−4.25587e37	−0.472107	−0.236053	−	0.971740i	$-0.575854\pi$
$281$	−4.25587e37	−0.472107	−0.236053	+	0.971740i	$0.575854\pi$
$282$	− 3.14115e37i	− 0.329782i
$283$	− 1.21210e38i	− 1.20461i	−0.798266	−	0.602306i	$-0.794249\pi$
$283$	− 1.21210e38i	− 1.20461i	0.798266	−	0.602306i	$-0.205751\pi$
$284$	−3.41986e37	−0.321791
$285$	0	0
$286$	−2.07394e38	−1.75034
$287$	− 4.92123e37i	− 0.393463i
$288$	5.00221e37i	0.378947i
$289$	1.12975e38	0.811087
$290$	0	0
$291$	−1.00094e38	−0.645756
$292$	− 3.19566e37i	− 0.195491i
$293$	− 2.43751e38i	− 1.41416i	−0.707134	−	0.707080i	$-0.750012\pi$
$293$	− 2.43751e38i	− 1.41416i	0.707134	−	0.707080i	$-0.249988\pi$
$294$	1.84697e38	1.01643
$295$	0	0
$296$	5.95087e37	0.294821
$297$	− 1.73997e37i	− 0.0818120i
$298$	3.18801e38i	1.42288i
$299$	2.38792e38	1.01185
$300$	0	0
$301$	1.58611e38	0.606111
$302$	1.71401e38i	0.622165i
$303$	6.06512e38i	2.09160i
$304$	3.43360e38	1.12515
$305$	0	0
$306$	−1.64857e38	−0.488007
$307$	− 2.30206e38i	− 0.647845i	−0.946084	−	0.323922i	$-0.894998\pi$
$307$	− 2.30206e38i	− 0.647845i	0.946084	−	0.323922i	$-0.105002\pi$
$308$	7.57477e37i	0.202690i
$309$	−5.60188e37	−0.142553
$310$	0	0
$311$	6.45531e38	1.48638	0.743192	−	0.669078i	$-0.233311\pi$
$311$	6.45531e38	1.48638	0.743192	+	0.669078i	$0.233311\pi$
$312$	− 4.99763e38i	− 1.09488i
$313$	2.25998e38i	0.471159i	0.971855	+	0.235580i	$0.0756988\pi$
$313$	2.25998e38i	0.471159i	−0.971855	+	0.235580i	$0.924301\pi$
$314$	5.67441e37	0.112593
$315$	0	0
$316$	−7.14622e37	−0.128507
$317$	3.33447e38i	0.570964i	0.958384	+	0.285482i	$0.0921537\pi$
$317$	3.33447e38i	0.570964i	−0.958384	+	0.285482i	$0.907846\pi$
$318$	6.48560e38i	1.05762i
$319$	−1.34554e39	−2.08997
$320$	0	0
$321$	1.77160e39	2.49769
$322$	− 5.55957e38i	− 0.746922i
$323$	3.31693e38i	0.424714i
$324$	1.47578e38	0.180125
$325$	0	0
$326$	9.08854e38	1.00837
$327$	− 1.78020e38i	− 0.188356i
$328$	− 5.88324e38i	− 0.593707i
$329$	1.29669e38	0.124824
$330$	0	0
$331$	5.21055e38	0.456614	0.228307	−	0.973589i	$-0.426681\pi$
$331$	5.21055e38	0.456614	0.228307	+	0.973589i	$0.426681\pi$
$332$	3.49056e38i	0.291914i
$333$	4.29577e38i	0.342891i
$334$	8.83684e38	0.673328
$335$	0	0
$336$	−1.38780e39	−0.963984
$337$	1.07632e39i	0.713968i	0.934110	+	0.356984i	$0.116195\pi$
$337$	1.07632e39i	0.713968i	−0.934110	+	0.356984i	$0.883805\pi$
$338$	4.27705e38i	0.270979i
$339$	−1.54742e39	−0.936510
$340$	0	0
$341$	−7.12143e38	−0.393436
$342$	2.07810e39i	1.09714i
$343$	1.92666e39i	0.972180i
$344$	1.89616e39	0.914576
$345$	0	0
$346$	−1.42556e39	−0.628500
$347$	− 4.50521e39i	− 1.89937i	−0.313213	−	0.949683i	$-0.601405\pi$
$347$	− 4.50521e39i	− 1.89937i	0.313213	−	0.949683i	$-0.398595\pi$
$348$	7.41199e38i	0.298852i
$349$	−1.00452e39	−0.387405	−0.193703	−	0.981060i	$-0.562050\pi$
$349$	−1.00452e39	−0.387405	−0.193703	+	0.981060i	$0.562050\pi$
$350$	0	0
$351$	1.08331e38	0.0382379
$352$	2.01811e39i	0.681605i
$353$	2.32272e39i	0.750738i	0.926876	+	0.375369i	$0.122484\pi$
$353$	2.32272e39i	0.750738i	−0.926876	+	0.375369i	$0.877516\pi$
$354$	8.92304e39	2.76034
$355$	0	0
$356$	−1.01402e39	−0.287455
$357$	− 1.34065e39i	− 0.363880i
$358$	8.26041e38i	0.214691i
$359$	−7.12748e39	−1.77408	−0.887038	−	0.461696i	$-0.847241\pi$
$359$	−7.12748e39	−1.77408	−0.887038	+	0.461696i	$0.847241\pi$
$360$	0	0
$361$	−1.97739e38	−0.0451576
$362$	2.30043e38i	0.0503299i
$363$	− 1.65789e40i	− 3.47539i
$364$	−4.71609e38	−0.0947350
$365$	0	0
$366$	−1.39040e40	−2.56557
$367$	5.20594e39i	0.920821i	0.887706	+	0.460411i	$0.152298\pi$
$367$	5.20594e39i	0.920821i	−0.887706	+	0.460411i	$0.847702\pi$
$368$	− 7.92736e39i	− 1.34427i
$369$	4.24695e39	0.690508
$370$	0	0
$371$	−2.67730e39	−0.400315
$372$	3.92289e38i	0.0562589i
$373$	− 8.13982e39i	− 1.11977i	−0.828571	−	0.559884i	$-0.810846\pi$
$373$	− 8.13982e39i	− 1.11977i	0.828571	−	0.559884i	$-0.189154\pi$
$374$	−6.65105e39	−0.877770
$375$	0	0
$376$	1.55017e39	0.188351
$377$	− 8.37738e39i	− 0.976826i
$378$	− 2.52217e38i	− 0.0282262i
$379$	5.97264e38	0.0641592	0.0320796	−	0.999485i	$-0.489787\pi$
$379$	5.97264e38	0.0641592	0.0320796	+	0.999485i	$0.489787\pi$
$380$	0	0
$381$	2.78803e40	2.76032
$382$	− 9.33390e39i	− 0.887322i
$383$	2.19654e39i	0.200520i	0.994961	+	0.100260i	$0.0319675\pi$
$383$	2.19654e39i	0.200520i	−0.994961	+	0.100260i	$0.968032\pi$
$384$	−1.92719e40	−1.68963
$385$	0	0
$386$	−1.52279e40	−1.23179
$387$	1.36879e40i	1.06369i
$388$	1.12920e39i	0.0843101i
$389$	7.52607e39	0.539945	0.269973	−	0.962868i	$-0.412985\pi$
$389$	7.52607e39	0.539945	0.269973	+	0.962868i	$0.412985\pi$
$390$	0	0
$391$	7.65800e39	0.507430
$392$	9.11485e39i	0.580518i
$393$	− 1.75820e40i	− 1.07642i
$394$	−1.89664e40	−1.11633
$395$	0	0
$396$	−6.53692e39	−0.355712
$397$	− 9.21070e39i	− 0.481992i	−0.970526	−	0.240996i	$-0.922526\pi$
$397$	− 9.21070e39i	− 0.481992i	0.970526	−	0.240996i	$-0.0774740\pi$
$398$	1.49181e40i	0.750803i
$399$	−1.68994e40	−0.818074
$400$	0	0
$401$	3.82642e39	0.171417	0.0857087	−	0.996320i	$-0.472685\pi$
$401$	3.82642e39	0.171417	0.0857087	+	0.996320i	$0.472685\pi$
$402$	4.42485e40i	1.90719i
$403$	− 4.43384e39i	− 0.183887i
$404$	6.84228e39	0.273080
$405$	0	0
$406$	−1.95042e40	−0.721066
$407$	1.73310e40i	0.616751i
$408$	− 1.60272e40i	− 0.549068i
$409$	−3.63528e40	−1.19902	−0.599510	−	0.800367i	$-0.704638\pi$
$409$	−3.63528e40	−1.19902	−0.599510	+	0.800367i	$0.704638\pi$
$410$	0	0
$411$	−4.56829e40	−1.39703
$412$	6.31968e38i	0.0186118i
$413$	3.68349e40i	1.04480i
$414$	4.79783e40	1.31081
$415$	0	0
$416$	−1.25648e40	−0.318574
$417$	− 4.15929e40i	− 1.01604i
$418$	8.38393e40i	1.97340i
$419$	−9.79817e38	−0.0222243	−0.0111121	−	0.999938i	$-0.503537\pi$
$419$	−9.79817e38	−0.0222243	−0.0111121	+	0.999938i	$0.503537\pi$
$420$	0	0
$421$	−5.79926e40	−1.22180	−0.610900	−	0.791708i	$-0.709192\pi$
$421$	−5.79926e40	−1.22180	−0.610900	+	0.791708i	$0.709192\pi$
$422$	4.44184e40i	0.902028i
$423$	1.11902e40i	0.219060i
$424$	−3.20067e40	−0.604045
$425$	0	0
$426$	1.52991e41	2.68421
$427$	− 5.73968e40i	− 0.971082i
$428$	− 1.99861e40i	− 0.326099i
$429$	1.45548e41	2.29044
$430$	0	0
$431$	1.23157e41	1.80327	0.901633	−	0.432502i	$-0.142369\pi$
$431$	1.23157e41	1.80327	0.901633	+	0.432502i	$0.142369\pi$
$432$	− 3.59636e39i	− 0.0508001i
$433$	− 1.08651e41i	− 1.48072i	−0.672211	−	0.740360i	$-0.734655\pi$
$433$	− 1.08651e41i	− 1.48072i	0.672211	−	0.740360i	$-0.265345\pi$
$434$	−1.03229e40	−0.135740
$435$	0	0
$436$	−2.00831e39	−0.0245918
$437$	− 9.65323e40i	− 1.14080i
$438$	1.42961e41i	1.63068i
$439$	1.31452e41	1.44732	0.723662	−	0.690154i	$-0.242457\pi$
$439$	1.31452e41	1.44732	0.723662	+	0.690154i	$0.242457\pi$
$440$	0	0
$441$	−6.57976e40	−0.675168
$442$	− 4.14098e40i	− 0.410259i
$443$	7.34404e40i	0.702550i	0.936272	+	0.351275i	$0.114252\pi$
$443$	7.34404e40i	0.702550i	−0.936272	+	0.351275i	$0.885748\pi$
$444$	9.54691e39	0.0881915
$445$	0	0
$446$	9.31810e40	0.802855
$447$	− 2.23733e41i	− 1.86193i
$448$	− 5.48915e40i	− 0.441262i
$449$	−8.88276e39	−0.0689810	−0.0344905	−	0.999405i	$-0.510981\pi$
$449$	−8.88276e39	−0.0689810	−0.0344905	+	0.999405i	$0.510981\pi$
$450$	0	0
$451$	1.71340e41	1.24200
$452$	1.74570e40i	0.122271i
$453$	− 1.20289e41i	− 0.814146i
$454$	1.98409e41	1.29776
$455$	0	0
$456$	−2.02030e41	−1.23441
$457$	1.73624e41i	1.02544i	0.858556	+	0.512719i	$0.171362\pi$
$457$	1.73624e41i	1.02544i	−0.858556	+	0.512719i	$0.828638\pi$
$458$	− 8.56530e39i	− 0.0489021i
$459$	3.47416e39	0.0191758
$460$	0	0
$461$	−1.69460e41	−0.874384	−0.437192	−	0.899368i	$-0.644027\pi$
$461$	−1.69460e41	−0.874384	−0.437192	+	0.899368i	$0.644027\pi$
$462$	− 3.38865e41i	− 1.69074i
$463$	1.59616e41i	0.770141i	0.922887	+	0.385070i	$0.125823\pi$
$463$	1.59616e41i	0.770141i	−0.922887	+	0.385070i	$0.874177\pi$
$464$	−2.78110e41	−1.29774
$465$	0	0
$466$	3.81620e41	1.66590
$467$	3.56199e41i	1.50411i	0.659098	+	0.752057i	$0.270938\pi$
$467$	3.56199e41i	1.50411i	−0.659098	+	0.752057i	$0.729062\pi$
$468$	− 4.06992e40i	− 0.166255i
$469$	−1.82661e41	−0.721883
$470$	0	0
$471$	−3.98228e40	−0.147336
$472$	4.40355e41i	1.57653i
$473$	5.52228e41i	1.91325i
$474$	3.19693e41	1.07194
$475$	0	0
$476$	−1.51244e40	−0.0475083
$477$	− 2.31047e41i	− 0.702532i
$478$	4.65403e41i	1.36992i
$479$	2.77088e41	0.789619	0.394809	−	0.918763i	$-0.370811\pi$
$479$	2.77088e41	0.789619	0.394809	+	0.918763i	$0.370811\pi$
$480$	0	0
$481$	−1.07904e41	−0.288262
$482$	− 2.40032e41i	− 0.620927i
$483$	3.90168e41i	0.977398i
$484$	−1.87033e41	−0.453748
$485$	0	0
$486$	−6.81319e41	−1.55056
$487$	8.87356e41i	1.95614i	0.208285	+	0.978068i	$0.433212\pi$
$487$	8.87356e41i	1.95614i	−0.208285	+	0.978068i	$0.566788\pi$
$488$	− 6.86169e41i	− 1.46529i
$489$	−6.37830e41	−1.31953
$490$	0	0
$491$	1.02124e41	0.198319	0.0991596	−	0.995072i	$-0.468385\pi$
$491$	1.02124e41	0.198319	0.0991596	+	0.995072i	$0.468385\pi$
$492$	− 9.43841e40i	− 0.177599i
$493$	− 2.68660e41i	− 0.489864i
$494$	−5.21988e41	−0.922343
$495$	0	0
$496$	−1.47193e41	−0.244299
$497$	6.31558e41i	1.01599i
$498$	− 1.56154e42i	− 2.43499i
$499$	−1.15532e42	−1.74640	−0.873202	−	0.487359i	$-0.837960\pi$
$499$	−1.15532e42	−1.74640	−0.873202	+	0.487359i	$0.837960\pi$
$500$	0	0
$501$	−6.20166e41	−0.881096
$502$	− 3.21802e41i	− 0.443282i
$503$	− 8.98250e41i	− 1.19976i	−0.800091	−	0.599878i	$-0.795216\pi$
$503$	− 8.98250e41i	− 1.19976i	0.800091	−	0.599878i	$-0.204784\pi$
$504$	4.14510e41	0.536861
$505$	0	0
$506$	1.93565e42	2.35773
$507$	− 3.00162e41i	− 0.354595i
$508$	− 3.14527e41i	− 0.360388i
$509$	2.04179e41	0.226927	0.113463	−	0.993542i	$-0.463806\pi$
$509$	2.04179e41	0.226927	0.113463	+	0.993542i	$0.463806\pi$
$510$	0	0
$511$	−5.90153e41	−0.617221
$512$	− 5.88815e41i	− 0.597440i
$513$	− 4.37932e40i	− 0.0431110i
$514$	−5.49385e41	−0.524745
$515$	0	0
$516$	3.04199e41	0.273582
$517$	4.51462e41i	0.394020i
$518$	2.51221e41i	0.212787i
$519$	1.00045e42	0.822436
$520$	0	0
$521$	−4.50719e41	−0.349077	−0.174538	−	0.984650i	$-0.555843\pi$
$521$	−4.50719e41	−0.349077	−0.174538	+	0.984650i	$0.555843\pi$
$522$	− 1.68319e42i	− 1.26543i
$523$	3.50199e41i	0.255587i	0.991801	+	0.127794i	$0.0407895\pi$
$523$	3.50199e41i	0.255587i	−0.991801	+	0.127794i	$0.959210\pi$
$524$	−1.98349e41	−0.140538
$525$	0	0
$526$	−3.45387e41	−0.230689
$527$	− 1.42192e41i	− 0.0922168i
$528$	− 4.83186e42i	− 3.04291i
$529$	−5.93533e41	−0.362979
$530$	0	0
$531$	−3.17880e42	−1.83357
$532$	1.90649e41i	0.106808i
$533$	1.06677e42i	0.580498i
$534$	4.53631e42	2.39780
$535$	0	0
$536$	−2.18368e42	−1.08927
$537$	− 5.79712e41i	− 0.280938i
$538$	1.92511e42i	0.906422i
$539$	−2.65456e42	−1.21441
$540$	0	0
$541$	1.03013e42	0.444974	0.222487	−	0.974936i	$-0.428583\pi$
$541$	1.03013e42	0.444974	0.222487	+	0.974936i	$0.428583\pi$
$542$	4.62574e42i	1.94175i
$543$	− 1.61443e41i	− 0.0658601i
$544$	−4.02951e41	−0.159760
$545$	0	0
$546$	2.10979e42	0.790230
$547$	− 2.42722e42i	− 0.883701i	−0.897089	−	0.441851i	$-0.854322\pi$
$547$	− 2.42722e42i	− 0.883701i	0.897089	−	0.441851i	$-0.145678\pi$
$548$	5.15366e41i	0.182397i
$549$	4.95327e42	1.70420
$550$	0	0
$551$	−3.38657e42	−1.10131
$552$	4.66439e42i	1.47482i
$553$	1.31972e42i	0.405734i
$554$	−2.83972e42	−0.848934
$555$	0	0
$556$	−4.69225e41	−0.132654
$557$	− 8.00704e41i	− 0.220149i	−0.993923	−	0.110074i	$-0.964891\pi$
$557$	− 8.00704e41i	− 0.220149i	0.993923	−	0.110074i	$-0.0351089\pi$
$558$	− 8.90849e41i	− 0.238218i
$559$	−3.43820e42	−0.894228
$560$	0	0
$561$	4.66768e42	1.14862
$562$	− 2.14787e42i	− 0.514155i
$563$	5.81315e42i	1.35373i	0.736108	+	0.676864i	$0.236661\pi$
$563$	5.81315e42i	1.35373i	−0.736108	+	0.676864i	$0.763339\pi$
$564$	2.48691e41	0.0563423
$565$	0	0
$566$	6.11724e42	1.31190
$567$	− 2.72538e42i	− 0.568708i
$568$	7.55016e42i	1.53305i
$569$	−3.55543e42	−0.702510	−0.351255	−	0.936280i	$-0.614245\pi$
$569$	−3.55543e42	−0.702510	−0.351255	+	0.936280i	$0.614245\pi$
$570$	0	0
$571$	−1.36185e42	−0.254840	−0.127420	−	0.991849i	$-0.540670\pi$
$571$	−1.36185e42	−0.254840	−0.127420	+	0.991849i	$0.540670\pi$
$572$	− 1.64198e42i	− 0.299040i
$573$	6.55049e42i	1.16112i
$574$	2.48366e42	0.428507
$575$	0	0
$576$	4.73707e42	0.774392
$577$	3.39833e42i	0.540805i	0.962747	+	0.270403i	$0.0871568\pi$
$577$	3.39833e42i	0.540805i	−0.962747	+	0.270403i	$0.912843\pi$
$578$	5.70168e42i	0.883327i
$579$	1.06869e43	1.61188
$580$	0	0
$581$	6.44614e42	0.921658
$582$	− 5.05160e42i	− 0.703271i
$583$	− 9.32144e42i	− 1.26363i
$584$	−7.05518e42	−0.931342
$585$	0	0
$586$	1.23017e43	1.54011
$587$	− 6.84778e42i	− 0.834948i	−0.908689	−	0.417474i	$-0.862916\pi$
$587$	− 6.84778e42i	− 0.834948i	0.908689	−	0.417474i	$-0.137084\pi$
$588$	1.46228e42i	0.173653i
$589$	−1.79239e42	−0.207322
$590$	0	0
$591$	1.33106e43	1.46080
$592$	3.58215e42i	0.382964i
$593$	− 5.19197e42i	− 0.540735i	−0.962757	−	0.270367i	$-0.912855\pi$
$593$	− 5.19197e42i	− 0.540735i	0.962757	−	0.270367i	$-0.0871452\pi$
$594$	8.78135e41	0.0890987
$595$	0	0
$596$	−2.52402e42	−0.243094
$597$	− 1.04695e43i	− 0.982477i
$598$	1.20515e43i	1.10197i
$599$	−3.82744e42	−0.341030	−0.170515	−	0.985355i	$-0.554543\pi$
$599$	−3.82744e42	−0.341030	−0.170515	+	0.985355i	$0.554543\pi$
$600$	0	0
$601$	−2.00425e43	−1.69589	−0.847944	−	0.530086i	$-0.822159\pi$
$601$	−2.00425e43	−1.69589	−0.847944	+	0.530086i	$0.822159\pi$
$602$	8.00482e42i	0.660094i
$603$	− 1.57634e43i	− 1.26687i
$604$	−1.35702e42	−0.106295
$605$	0	0
$606$	−3.06096e43	−2.27789
$607$	5.42746e42i	0.393706i	0.980433	+	0.196853i	$0.0630722\pi$
$607$	5.42746e42i	0.393706i	−0.980433	+	0.196853i	$0.936928\pi$
$608$	5.07936e42i	0.359173i
$609$	1.36880e43	0.943564
$610$	0	0
$611$	−2.81083e42	−0.184160
$612$	− 1.30521e42i	− 0.0833746i
$613$	9.70689e42i	0.604565i	0.953218	+	0.302282i	$0.0977485\pi$
$613$	9.70689e42i	0.604565i	−0.953218	+	0.302282i	$0.902251\pi$
$614$	1.16181e43	0.705545
$615$	0	0
$616$	1.67231e43	0.965642
$617$	− 2.73058e42i	− 0.153757i	−0.997040	−	0.0768786i	$-0.975505\pi$
$617$	− 2.73058e42i	− 0.153757i	0.997040	−	0.0768786i	$-0.0244954\pi$
$618$	− 2.82717e42i	− 0.155250i
$619$	2.73719e43	1.46588	0.732942	−	0.680291i	$-0.238147\pi$
$619$	2.73719e43	1.46588	0.732942	+	0.680291i	$0.238147\pi$
$620$	0	0
$621$	−1.01108e42	−0.0515070
$622$	3.25789e43i	1.61877i
$623$	1.87262e43i	0.907580i
$624$	3.00834e43	1.42222
$625$	0	0
$626$	−1.14058e43	−0.513123
$627$	− 5.88381e43i	− 2.58233i
$628$	4.49256e41i	0.0192362i
$629$	−3.46044e42	−0.144559
$630$	0	0
$631$	−2.09278e43	−0.832280	−0.416140	−	0.909301i	$-0.636617\pi$
$631$	−2.09278e43	−0.832280	−0.416140	+	0.909301i	$0.636617\pi$
$632$	1.57770e43i	0.612222i
$633$	− 3.11727e43i	− 1.18037i
$634$	−1.68285e43	−0.621817
$635$	0	0
$636$	−5.13479e42	−0.180691
$637$	− 1.65274e43i	− 0.567601i
$638$	− 6.79070e43i	− 2.27611i
$639$	−5.45026e43	−1.78301
$640$	0	0
$641$	−8.79186e41	−0.0274019	−0.0137010	−	0.999906i	$-0.504361\pi$
$641$	−8.79186e41	−0.0274019	−0.0137010	+	0.999906i	$0.504361\pi$
$642$	8.94098e43i	2.72015i
$643$	− 4.86507e42i	− 0.144484i	−0.997387	−	0.0722418i	$-0.976985\pi$
$643$	− 4.86507e42i	− 0.144484i	0.997387	−	0.0722418i	$-0.0230153\pi$
$644$	4.40163e42	0.127609
$645$	0	0
$646$	−1.67400e43	−0.462542
$647$	− 3.20540e43i	− 0.864701i	−0.901706	−	0.432351i	$-0.857684\pi$
$647$	− 3.20540e43i	− 0.864701i	0.901706	−	0.432351i	$-0.142316\pi$
$648$	− 3.25814e43i	− 0.858138i
$649$	−1.28247e44	−3.29802
$650$	0	0
$651$	7.24454e42	0.177626
$652$	7.19560e42i	0.172278i
$653$	− 2.55276e43i	− 0.596838i	−0.954435	−	0.298419i	$-0.903541\pi$
$653$	− 2.55276e43i	− 0.596838i	0.954435	−	0.298419i	$-0.0964592\pi$
$654$	8.98439e42	0.205132
$655$	0	0
$656$	3.54144e43	0.771206
$657$	− 5.09294e43i	− 1.08319i
$658$	6.54417e42i	0.135942i
$659$	−4.03603e43	−0.818900	−0.409450	−	0.912333i	$-0.634279\pi$
$659$	−4.03603e43	−0.818900	−0.409450	+	0.912333i	$0.634279\pi$
$660$	0	0
$661$	−2.96661e43	−0.574299	−0.287149	−	0.957886i	$-0.592708\pi$
$661$	−2.96661e43	−0.574299	−0.287149	+	0.957886i	$0.592708\pi$
$662$	2.62968e43i	0.497283i
$663$	2.90612e43i	0.536852i
$664$	7.70625e43	1.39071
$665$	0	0
$666$	−2.16800e43	−0.373430
$667$	7.81879e43i	1.31580i
$668$	6.99632e42i	0.115036i
$669$	−6.53940e43	−1.05059
$670$	0	0
$671$	1.99836e44	3.06531
$672$	− 2.05300e43i	− 0.307726i
$673$	9.75824e42i	0.142935i	0.997443	+	0.0714674i	$0.0227682\pi$
$673$	9.75824e42i	0.142935i	−0.997443	+	0.0714674i	$0.977232\pi$
$674$	−5.43202e43	−0.777558
$675$	0	0
$676$	−3.38624e42	−0.0462960
$677$	5.75918e43i	0.769549i	0.923011	+	0.384775i	$0.125721\pi$
$677$	5.75918e43i	0.769549i	−0.923011	+	0.384775i	$0.874279\pi$
$678$	− 7.80956e43i	− 1.01992i
$679$	2.08534e43	0.266192
$680$	0	0
$681$	−1.39243e44	−1.69821
$682$	− 3.59407e43i	− 0.428478i
$683$	− 1.28137e42i	− 0.0149332i	−0.999972	−	0.00746659i	$-0.997623\pi$
$683$	− 1.28137e42i	− 0.0149332i	0.999972	−	0.00746659i	$-0.00237671\pi$
$684$	−1.64527e43	−0.187443
$685$	0	0
$686$	−9.72354e43	−1.05877
$687$	6.01110e42i	0.0639918i
$688$	1.14140e44i	1.18801i
$689$	5.80357e43	0.590606
$690$	0	0
$691$	−1.04701e44	−1.01869	−0.509344	−	0.860563i	$-0.670112\pi$
$691$	−1.04701e44	−1.01869	−0.509344	+	0.860563i	$0.670112\pi$
$692$	− 1.12865e43i	− 0.107377i
$693$	1.20720e44i	1.12308i
$694$	2.27371e44	2.06853
$695$	0	0
$696$	1.63637e44	1.42377
$697$	3.42111e43i	0.291111i
$698$	− 5.06966e43i	− 0.421910i
$699$	−2.67820e44	−2.17995
$700$	0	0
$701$	−2.97574e43	−0.231721	−0.115861	−	0.993265i	$-0.536963\pi$
$701$	−2.97574e43	−0.231721	−0.115861	+	0.993265i	$0.536963\pi$
$702$	5.46731e42i	0.0416436i
$703$	4.36202e43i	0.324998i
$704$	1.91114e44	1.39289
$705$	0	0
$706$	−1.17224e44	−0.817603
$707$	− 1.26359e44i	− 0.862193i
$708$	7.06456e43i	0.471596i
$709$	1.24196e44	0.811132	0.405566	−	0.914066i	$-0.367074\pi$
$709$	1.24196e44	0.811132	0.405566	+	0.914066i	$0.367074\pi$
$710$	0	0
$711$	−1.13890e44	−0.712042
$712$	2.23868e44i	1.36947i
$713$	4.13820e43i	0.247699i
$714$	6.76604e43	0.396289
$715$	0	0
$716$	−6.53994e42	−0.0366794
$717$	− 3.26618e44i	− 1.79264i
$718$	− 3.59712e44i	− 1.93209i
$719$	2.70426e44	1.42151	0.710755	−	0.703439i	$-0.248353\pi$
$719$	2.70426e44	1.42151	0.710755	+	0.703439i	$0.248353\pi$
$720$	0	0
$721$	1.16708e43	0.0587629
$722$	− 9.97956e42i	− 0.0491796i
$723$	1.68454e44i	0.812526i
$724$	−1.82130e42	−0.00859872
$725$	0	0
$726$	8.36711e44	3.78493
$727$	− 2.23994e44i	− 0.991867i	−0.868360	−	0.495934i	$-0.834826\pi$
$727$	− 2.23994e44i	− 0.991867i	0.868360	−	0.495934i	$-0.165174\pi$
$728$	1.04119e44i	0.451329i
$729$	2.50013e44	1.06093
$730$	0	0
$731$	−1.10262e44	−0.448443
$732$	− 1.10081e44i	− 0.438320i
$733$	3.60937e44i	1.40708i	0.710655	+	0.703541i	$0.248399\pi$
$733$	3.60937e44i	1.40708i	−0.710655	+	0.703541i	$0.751601\pi$
$734$	−2.62735e44	−1.00283
$735$	0	0
$736$	1.17270e44	0.429124
$737$	− 6.35963e44i	− 2.27869i
$738$	2.14337e44i	0.752008i
$739$	1.34591e44	0.462409	0.231205	−	0.972905i	$-0.425733\pi$
$739$	1.34591e44	0.462409	0.231205	+	0.972905i	$0.425733\pi$
$740$	0	0
$741$	3.66329e44	1.20695
$742$	− 1.35119e44i	− 0.435969i
$743$	− 2.29970e44i	− 0.726682i	−0.931656	−	0.363341i	$-0.881636\pi$
$743$	− 2.29970e44i	− 0.726682i	0.931656	−	0.363341i	$-0.118364\pi$
$744$	8.66073e43	0.268024
$745$	0	0
$746$	4.10803e44	1.21950
$747$	5.56293e44i	1.61746i
$748$	− 5.26578e43i	− 0.149964i
$749$	−3.69090e44	−1.02959
$750$	0	0
$751$	−6.82476e44	−1.82671	−0.913353	−	0.407169i	$-0.866516\pi$
$751$	−6.82476e44	−1.82671	−0.913353	+	0.407169i	$0.866516\pi$
$752$	9.33130e43i	0.244661i
$753$	2.25839e44i	0.580065i
$754$	4.22792e44	1.06383
$755$	0	0
$756$	1.99686e42	0.00482236
$757$	5.83963e44i	1.38165i	0.723020	+	0.690827i	$0.242753\pi$
$757$	5.83963e44i	1.38165i	−0.723020	+	0.690827i	$0.757247\pi$
$758$	3.01429e43i	0.0698736i
$759$	−1.35843e45	−3.08525
$760$	0	0
$761$	−4.47927e44	−0.976664	−0.488332	−	0.872658i	$-0.662394\pi$
$761$	−4.47927e44	−0.976664	−0.488332	+	0.872658i	$0.662394\pi$
$762$	1.40707e45i	3.00617i
$763$	3.70882e43i	0.0776435i
$764$	7.38985e43	0.151596
$765$	0	0
$766$	−1.10856e44	−0.218380
$767$	− 7.98469e44i	− 1.54145i
$768$	− 4.06814e44i	− 0.769656i
$769$	5.08233e44	0.942334	0.471167	−	0.882044i	$-0.343833\pi$
$769$	5.08233e44	0.942334	0.471167	+	0.882044i	$0.343833\pi$
$770$	0	0
$771$	3.85556e44	0.686665
$772$	− 1.20563e44i	− 0.210448i
$773$	2.24846e44i	0.384682i	0.981328	+	0.192341i	$0.0616080\pi$
$773$	2.24846e44i	0.384682i	−0.981328	+	0.192341i	$0.938392\pi$
$774$	−6.90805e44	−1.15843
$775$	0	0
$776$	2.49298e44	0.401664
$777$	− 1.76306e44i	− 0.278446i
$778$	3.79828e44i	0.588036i
$779$	4.31245e44	0.654476
$780$	0	0
$781$	−2.19887e45	−3.20707
$782$	3.86487e44i	0.552624i
$783$	3.54710e43i	0.0497240i
$784$	−5.48672e44	−0.754074
$785$	0	0
$786$	8.87332e44	1.17229
$787$	− 1.36341e45i	− 1.76612i	−0.469263	−	0.883059i	$-0.655480\pi$
$787$	− 1.36341e45i	− 1.76612i	0.469263	−	0.883059i	$-0.344520\pi$
$788$	− 1.50161e44i	− 0.190722i
$789$	2.42391e44	0.301872
$790$	0	0
$791$	3.22384e44	0.386045
$792$	1.44318e45i	1.69465i
$793$	1.24419e45i	1.43269i
$794$	4.64849e44	0.524921
$795$	0	0
$796$	−1.18110e44	−0.128272
$797$	9.47512e44i	1.00921i	0.863351	+	0.504604i	$0.168362\pi$
$797$	9.47512e44i	1.00921i	−0.863351	+	0.504604i	$0.831638\pi$
$798$	− 8.52887e44i	− 0.890936i
$799$	−9.01423e43	−0.0923536
$800$	0	0
$801$	−1.61604e45	−1.59276
$802$	1.93113e44i	0.186685i
$803$	− 2.05471e45i	− 1.94832i
$804$	−3.50325e44	−0.325839
$805$	0	0
$806$	2.23768e44	0.200265
$807$	− 1.35104e45i	− 1.18612i
$808$	− 1.51060e45i	− 1.30099i
$809$	−5.00741e44	−0.423069	−0.211535	−	0.977371i	$-0.567846\pi$
$809$	−5.00741e44	−0.423069	−0.211535	+	0.977371i	$0.567846\pi$
$810$	0	0
$811$	−4.64497e44	−0.377711	−0.188856	−	0.982005i	$-0.560478\pi$
$811$	−4.64497e44	−0.377711	−0.188856	+	0.982005i	$0.560478\pi$
$812$	− 1.54419e44i	− 0.123192i
$813$	− 3.24633e45i	− 2.54091i
$814$	−8.74666e44	−0.671682
$815$	0	0
$816$	9.64766e44	0.713222
$817$	1.38990e45i	1.00819i
$818$	− 1.83466e45i	− 1.30581i
$819$	−7.51606e44	−0.524916
$820$	0	0
$821$	8.53797e44	0.574164	0.287082	−	0.957906i	$-0.407315\pi$
$821$	8.53797e44	0.574164	0.287082	+	0.957906i	$0.407315\pi$
$822$	− 2.30554e45i	− 1.52146i
$823$	1.45427e45i	0.941779i	0.882192	+	0.470890i	$0.156067\pi$
$823$	1.45427e45i	0.941779i	−0.882192	+	0.470890i	$0.843933\pi$
$824$	1.39522e44	0.0886688
$825$	0	0
$826$	−1.85900e45	−1.13786
$827$	− 2.09313e45i	− 1.25736i	−0.777663	−	0.628681i	$-0.783595\pi$
$827$	− 2.09313e45i	− 1.25736i	0.777663	−	0.628681i	$-0.216405\pi$
$828$	3.79855e44i	0.223948i
$829$	2.58269e45	1.49444	0.747219	−	0.664578i	$-0.231389\pi$
$829$	2.58269e45	1.49444	0.747219	+	0.664578i	$0.231389\pi$
$830$	0	0
$831$	1.99290e45	1.11089
$832$	1.18988e45i	0.651017i
$833$	− 5.30029e44i	− 0.284644i
$834$	2.09913e45	1.10653
$835$	0	0
$836$	−6.63774e44	−0.337150
$837$	1.87735e43i	0.00936054i
$838$	− 4.94497e43i	− 0.0242037i
$839$	−1.29282e45	−0.621192	−0.310596	−	0.950542i	$-0.600529\pi$
$839$	−1.29282e45	−0.621192	−0.310596	+	0.950542i	$0.600529\pi$
$840$	0	0
$841$	5.83585e44	0.270250
$842$	− 2.92679e45i	− 1.33062i
$843$	1.50736e45i	0.672807i
$844$	−3.51670e44	−0.154109
$845$	0	0
$846$	−5.64752e44	−0.238571
$847$	3.45400e45i	1.43262i
$848$	− 1.92665e45i	− 0.784635i
$849$	−4.29306e45	−1.71671
$850$	0	0
$851$	1.00709e45	0.388293
$852$	1.21126e45i	0.458590i
$853$	4.80470e45i	1.78631i	0.449752	+	0.893154i	$0.351512\pi$
$853$	4.80470e45i	1.78631i	−0.449752	+	0.893154i	$0.648488\pi$
$854$	2.89672e45	1.05757
$855$	0	0
$856$	−4.41241e45	−1.55357
$857$	4.21760e44i	0.145835i	0.997338	+	0.0729176i	$0.0232310\pi$
$857$	4.21760e44i	0.145835i	−0.997338	+	0.0729176i	$0.976769\pi$
$858$	7.34557e45i	2.49444i
$859$	4.58182e45	1.52807	0.764037	−	0.645172i	$-0.223214\pi$
$859$	4.58182e45	1.52807	0.764037	+	0.645172i	$0.223214\pi$
$860$	0	0
$861$	−1.74302e45	−0.560731
$862$	6.21550e45i	1.96387i
$863$	1.31315e45i	0.407518i	0.979021	+	0.203759i	$0.0653159\pi$
$863$	1.31315e45i	0.407518i	−0.979021	+	0.203759i	$0.934684\pi$
$864$	5.32013e43	0.0162166
$865$	0	0
$866$	5.48345e45	1.61260
$867$	− 4.00142e45i	− 1.15589i
$868$	− 8.17283e43i	− 0.0231909i
$869$	−4.59480e45	−1.28074
$870$	0	0
$871$	3.95954e45	1.06503
$872$	4.43383e44i	0.117158i
$873$	1.79962e45i	0.467153i
$874$	4.87183e45	1.24241
$875$	0	0
$876$	−1.13185e45	−0.278597
$877$	2.11951e45i	0.512557i	0.966603	+	0.256279i	$0.0824964\pi$
$877$	2.11951e45i	0.512557i	−0.966603	+	0.256279i	$0.917504\pi$
$878$	6.63415e45i	1.57623i
$879$	−8.63329e45	−2.01534
$880$	0	0
$881$	−2.35738e45	−0.531255	−0.265627	−	0.964076i	$-0.585579\pi$
$881$	−2.35738e45	−0.531255	−0.265627	+	0.964076i	$0.585579\pi$
$882$	− 3.32069e45i	− 0.735302i
$883$	− 3.51964e45i	− 0.765786i	−0.923793	−	0.382893i	$-0.874928\pi$
$883$	− 3.51964e45i	− 0.765786i	0.923793	−	0.382893i	$-0.125072\pi$
$884$	3.27850e44	0.0700915
$885$	0	0
$886$	−3.70641e45	−0.765123
$887$	− 1.81896e45i	− 0.368983i	−0.982834	−	0.184492i	$-0.940936\pi$
$887$	− 1.81896e45i	− 0.368983i	0.982834	−	0.184492i	$-0.0590638\pi$
$888$	− 2.10771e45i	− 0.420155i
$889$	−5.80848e45	−1.13785
$890$	0	0
$891$	9.48883e45	1.79518
$892$	7.37734e44i	0.137165i
$893$	1.13628e45i	0.207629i
$894$	1.12914e46	2.02777
$895$	0	0
$896$	4.01505e45	0.696493
$897$	− 8.45767e45i	− 1.44201i
$898$	− 4.48298e44i	− 0.0751249i
$899$	1.45177e45	0.239124
$900$	0	0
$901$	1.86119e45	0.296180
$902$	8.64726e45i	1.35262i
$903$	− 5.61775e45i	− 0.863778i
$904$	3.85405e45	0.582514
$905$	0	0
$906$	6.07076e45	0.886658
$907$	− 3.55045e45i	− 0.509765i	−0.966972	−	0.254883i	$-0.917963\pi$
$907$	− 3.55045e45i	− 0.509765i	0.966972	−	0.254883i	$-0.0820368\pi$
$908$	1.57085e45i	0.221719i
$909$	1.09046e46	1.51310
$910$	0	0
$911$	1.17856e46	1.58059	0.790293	−	0.612729i	$-0.209928\pi$
$911$	1.17856e46	1.58059	0.790293	+	0.612729i	$0.209928\pi$
$912$	− 1.21613e46i	− 1.60346i
$913$	2.24433e46i	2.90930i
$914$	−8.76254e45	−1.11677
$915$	0	0
$916$	6.78134e43	0.00835479
$917$	3.66297e45i	0.443720i
$918$	1.75335e44i	0.0208837i
$919$	3.13788e45	0.367491	0.183745	−	0.982974i	$-0.441178\pi$
$919$	3.13788e45	0.367491	0.183745	+	0.982974i	$0.441178\pi$
$920$	0	0
$921$	−8.15353e45	−0.923255
$922$	− 8.55235e45i	− 0.952261i
$923$	− 1.36903e46i	− 1.49894i
$924$	2.68287e45	0.288858
$925$	0	0
$926$	−8.05554e45	−0.838734
$927$	1.00717e45i	0.103126i
$928$	− 4.11411e45i	− 0.414269i
$929$	1.03965e46	1.02954	0.514772	−	0.857327i	$-0.327877\pi$
$929$	1.03965e46	1.02954	0.514772	+	0.857327i	$0.327877\pi$
$930$	0	0
$931$	−6.68124e45	−0.639936
$932$	3.02137e45i	0.284615i
$933$	− 2.28637e46i	− 2.11827i
$934$	−1.79768e46	−1.63808
$935$	0	0
$936$	−8.98532e45	−0.792060
$937$	1.31609e45i	0.114110i	0.998371	+	0.0570550i	$0.0181710\pi$
$937$	1.31609e45i	0.114110i	−0.998371	+	0.0570550i	$0.981829\pi$
$938$	− 9.21859e45i	− 0.786178i
$939$	8.00451e45	0.671457
$940$	0	0
$941$	−4.70374e45	−0.381772	−0.190886	−	0.981612i	$-0.561136\pi$
$941$	−4.70374e45	−0.381772	−0.190886	+	0.981612i	$0.561136\pi$
$942$	− 2.00979e45i	− 0.160458i
$943$	− 9.95643e45i	− 0.781938i
$944$	−2.65074e46	−2.04786
$945$	0	0
$946$	−2.78700e46	−2.08365
$947$	− 7.16058e43i	− 0.00526652i	−0.999997	−	0.00263326i	$-0.999162\pi$
$947$	− 7.16058e43i	− 0.00526652i	0.999997	−	0.00263326i	$-0.000838194\pi$
$948$	2.53108e45i	0.183137i
$949$	1.27927e46	0.910620
$950$	0	0
$951$	1.18102e46	0.813691
$952$	3.33906e45i	0.226335i
$953$	1.01545e46i	0.677202i	0.940930	+	0.338601i	$0.109954\pi$
$953$	1.01545e46i	0.677202i	−0.940930	+	0.338601i	$0.890046\pi$
$954$	1.16606e46	0.765103
$955$	0	0
$956$	−3.68470e45	−0.234048
$957$	4.76569e46i	2.97845i
$958$	1.39842e46i	0.859946i
$959$	9.51744e45	0.575879
$960$	0	0
$961$	−1.63008e46	−0.954985
$962$	− 5.44571e45i	− 0.313936i
$963$	− 3.18520e46i	− 1.80688i
$964$	1.90039e45	0.106084
$965$	0	0
$966$	−1.96911e46	−1.06445
$967$	1.15264e46i	0.613172i	0.951843	+	0.306586i	$0.0991868\pi$
$967$	1.15264e46i	0.613172i	−0.951843	+	0.306586i	$0.900813\pi$
$968$	4.12920e46i	2.16171i
$969$	1.17481e46	0.605268
$970$	0	0
$971$	9.72203e45	0.485131	0.242565	−	0.970135i	$-0.422011\pi$
$971$	9.72203e45	0.485131	0.242565	+	0.970135i	$0.422011\pi$
$972$	− 5.39415e45i	− 0.264908i
$973$	8.66534e45i	0.418829i
$974$	−4.47834e46	−2.13036
$975$	0	0
$976$	4.13042e46	1.90337
$977$	− 1.50140e46i	− 0.680973i	−0.940249	−	0.340486i	$-0.889408\pi$
$977$	− 1.50140e46i	− 0.680973i	0.940249	−	0.340486i	$-0.110592\pi$
$978$	− 3.21902e46i	− 1.43705i
$979$	−6.51982e46	−2.86486
$980$	0	0
$981$	−3.20066e45	−0.136260
$982$	5.15403e45i	0.215983i
$983$	2.48076e45i	0.102331i	0.998690	+	0.0511653i	$0.0162935\pi$
$983$	2.48076e45i	0.102331i	−0.998690	+	0.0511653i	$0.983706\pi$
$984$	−2.08376e46	−0.846102
$985$	0	0
$986$	1.35588e46	0.533494
$987$	− 4.59267e45i	− 0.177889i
$988$	− 4.13269e45i	− 0.157580i
$989$	3.20895e46	1.20454
$990$	0	0
$991$	−2.22619e45	−0.0809879	−0.0404939	−	0.999180i	$-0.512893\pi$
$991$	−2.22619e45	−0.0809879	−0.0404939	+	0.999180i	$0.512893\pi$
$992$	− 2.17745e45i	− 0.0779860i
$993$	− 1.84550e46i	− 0.650728i
$994$	−3.18737e46	−1.10648
$995$	0	0
$996$	1.23630e46	0.416012
$997$	4.15949e46i	1.37805i	0.724738	+	0.689025i	$0.241961\pi$
$997$	4.15949e46i	1.37805i	−0.724738	+	0.689025i	$0.758039\pi$
$998$	− 5.83072e46i	− 1.90195i
$999$	4.56879e44	0.0146736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.32.b.d.24.16		20
5.2	odd	4		25.32.a.e.1.3	yes	10
5.3	odd	4		25.32.a.d.1.8	✓	10
5.4	even	2	inner	25.32.b.d.24.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.32.a.d.1.8	✓	10	5.3	odd	4
25.32.a.e.1.3	yes	10	5.2	odd	4
25.32.b.d.24.5		20	5.4	even	2	inner
25.32.b.d.24.16		20	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 32 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+50468.3i q^{2} -3.54185e7i q^{3} -3.99569e8 q^{4} +1.78751e12 q^{6} +7.37897e12i q^{7} +8.82143e13i q^{8} -6.36795e14 q^{9} +O(q^{10})\)	\(q+50468.3i q^{2} -3.54185e7i q^{3} -3.99569e8 q^{4} +1.78751e12 q^{6} +7.37897e12i q^{7} +8.82143e13i q^{8} -6.36795e14 q^{9} -2.56911e16 q^{11} +1.41521e16i q^{12} -1.59954e17i q^{13} -3.72404e17 q^{14} -5.31010e18 q^{16} -5.12967e18i q^{17} -3.21380e19i q^{18} -6.46616e19 q^{19} +2.61352e20 q^{21} -1.29658e21i q^{22} +1.49288e21i q^{23} +3.12442e21 q^{24} +8.07260e21 q^{26} +6.77267e20i q^{27} -2.94841e21i q^{28} +5.23737e22 q^{29} +2.77195e22 q^{31} -7.85529e22i q^{32} +9.09938e23i q^{33} +2.58886e23 q^{34} +2.54443e23 q^{36} -6.74592e23i q^{37} -3.26336e24i q^{38} -5.66532e24 q^{39} -6.66926e24 q^{41} +1.31900e25i q^{42} -2.14950e25i q^{43} +1.02653e25 q^{44} -7.53434e25 q^{46} -1.75727e25i q^{47} +1.88076e26i q^{48} +1.03326e26 q^{49} -1.81685e26 q^{51} +6.39125e25i q^{52} +3.62828e26i q^{53} -3.41806e25 q^{54} -6.50931e26 q^{56} +2.29022e27i q^{57} +2.64322e27i q^{58} +4.99188e27 q^{59} -7.77843e27 q^{61} +1.39896e27i q^{62} -4.69890e27i q^{63} -7.43891e27 q^{64} -4.59231e28 q^{66} +2.47542e28i q^{67} +2.04966e27i q^{68} +5.28757e28 q^{69} +8.55888e28 q^{71} -5.61745e28i q^{72} +7.99777e28i q^{73} +3.40455e28 q^{74} +2.58368e28 q^{76} -1.89574e29i q^{77} -2.85919e29i q^{78} +1.78848e29 q^{79} -3.69344e29 q^{81} -3.36586e29i q^{82} -8.73583e29i q^{83} -1.04428e29 q^{84} +1.08481e30 q^{86} -1.85500e30i q^{87} -2.26632e30i q^{88} +2.53778e30 q^{89} +1.18029e30 q^{91} -5.96510e29i q^{92} -9.81782e29i q^{93} +8.86867e29 q^{94} -2.78223e30 q^{96} -2.82605e30i q^{97} +5.21470e30i q^{98} +1.63599e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20539589610 q^{4} + 686623832090 q^{6} - 36\!\cdots\!40 q^{9}+O(q^{10}) \) 20 * q - 20539589610 * q^4 + 686623832090 * q^6 - 3631559863498040 * q^9	\( 20 q - 20539589610 q^{4} + 686623832090 q^{6} - 36\!\cdots\!40 q^{9}+ \cdots - 12\!\cdots\!80 q^{99}+O(q^{100}) \) 20 * q - 20539589610 * q^4 + 686623832090 * q^6 - 3631559863498040 * q^9 + 14698263410387040 * q^11 - 3585430984535446020 * q^14 + 2668707436521071970 * q^16 - 92704745745734472000 * q^19 - 1433956230663012048360 * q^21 - 7629774658866586147950 * q^24 + 32856089868200755271640 * q^26 + 87725502776009659186800 * q^29 - 222796998479461581232960 * q^31 - 1924324021312734888556570 * q^34 - 5025054501215053083856580 * q^36 - 15450618695652181209461680 * q^39 - 47909930935503157644691260 * q^41 - 145310690902340893702475970 * q^44 - 252836584120338157033164660 * q^46 - 1246276182399196031444904260 * q^49 - 1849897927683754577276692960 * q^51 + 2591153317777144376506605250 * q^54 + 5799317051948263540741982700 * q^56 + 6066159147123348006692515200 * q^59 + 8463634058261727404238573240 * q^61 + 9517358906702440359771160990 * q^64 + 41883496723623582695134585930 * q^66 + 141421493056144218523923301320 * q^69 + 118845453796062103335338131440 * q^71 - 467772945250325662075867676820 * q^74 - 862330218554817908331535050350 * q^76 - 839661308397414799907136990800 * q^79 - 46356956658731639668114605580 * q^81 - 3067463374376454313718938994820 * q^84 - 1760036218098267190164891359160 * q^86 + 2972172090363405141073742262900 * q^89 + 14623549158011964101986521147040 * q^91 + 20460655315576187327400332153480 * q^94 + 12710573490967896478118960330590 * q^96 - 12487277792345774005972560542080 * q^99

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