LMFDB - Embedded newform 25.14.b.b.24.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [25,14,Mod(24,25)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25.24"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$26.8077322380$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 8933x^{4} + 19907716x^{2} + 350438400 $ x^6 + 8933x^4 + 19907716x^2 + 350438400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{9}\cdot 5^{6} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-64.1084i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.14.b.b.24.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-176.217i q^{2} -573.185i q^{3} -22860.4 q^{4} -101005. q^{6} +201493. i q^{7} +2.58481e6i q^{8} +1.26578e6 q^{9} -3.34359e6 q^{11} +1.31032e7i q^{12} -7.80359e6i q^{13} +3.55065e7 q^{14} +2.68215e8 q^{16} +8.71750e7i q^{17} -2.23052e8i q^{18} +1.66766e7 q^{19} +1.15493e8 q^{21} +5.89196e8i q^{22} +1.13518e9i q^{23} +1.48158e9 q^{24} -1.37512e9 q^{26} -1.63937e9i q^{27} -4.60620e9i q^{28} -2.60673e9 q^{29} +8.33139e8 q^{31} -2.60892e10i q^{32} +1.91649e9i q^{33} +1.53617e10 q^{34} -2.89362e10 q^{36} +1.05494e10i q^{37} -2.93870e9i q^{38} -4.47290e9 q^{39} -4.33030e9 q^{41} -2.03518e10i q^{42} +1.93854e9i q^{43} +7.64356e10 q^{44} +2.00038e11 q^{46} -2.85468e10i q^{47} -1.53737e11i q^{48} +5.62896e10 q^{49} +4.99674e10 q^{51} +1.78393e11i q^{52} +1.23249e11i q^{53} -2.88884e11 q^{54} -5.20821e11 q^{56} -9.55879e9i q^{57} +4.59349e11i q^{58} +5.55404e11 q^{59} -4.10476e11 q^{61} -1.46813e11i q^{62} +2.55046e11i q^{63} -2.40014e12 q^{64} +3.37718e11 q^{66} -3.36861e11i q^{67} -1.99285e12i q^{68} +6.50671e11 q^{69} +1.57323e12 q^{71} +3.27181e12i q^{72} +2.05372e12i q^{73} +1.85898e12 q^{74} -3.81234e11 q^{76} -6.73709e11i q^{77} +7.88201e11i q^{78} +6.93000e11 q^{79} +1.07840e12 q^{81} +7.63071e11i q^{82} +2.01116e12i q^{83} -2.64021e12 q^{84} +3.41604e11 q^{86} +1.49414e12i q^{87} -8.64253e12i q^{88} +8.51832e12 q^{89} +1.57237e12 q^{91} -2.59507e13i q^{92} -4.77543e11i q^{93} -5.03042e12 q^{94} -1.49540e13 q^{96} +7.99814e12i q^{97} -9.91916e12i q^{98} -4.23225e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 35752 q^{4} + 240752 q^{6} - 2572238 q^{9} - 13208008 q^{11} + 93125856 q^{14} + 399824416 q^{16} - 194982200 q^{19} + 876401472 q^{21} + 7780718400 q^{24} - 7493628088 q^{26} - 4472343700 q^{29}+ \cdots - 253574733016 q^{99}+O(q^{100}) $ 6 * q - 35752 * q^4 + 240752 * q^6 - 2572238 * q^9 - 13208008 * q^11 + 93125856 * q^14 + 399824416 * q^16 - 194982200 * q^19 + 876401472 * q^21 + 7780718400 * q^24 - 7493628088 * q^26 - 4472343700 * q^29 + 14965988752 * q^31 + 60472147976 * q^34 - 86723667704 * q^36 + 140377142144 * q^39 - 21505768868 * q^41 + 136791650336 * q^44 + 493656408672 * q^46 + 77913853258 * q^49 - 258739765888 * q^51 - 492243874400 * q^54 - 1045752902400 * q^56 + 110872847800 * q^59 + 992322785492 * q^61 - 6595130988672 * q^64 - 45767750336 * q^66 + 666758585664 * q^69 + 1043995756672 * q^71 + 4836647173016 * q^74 + 1243376100000 * q^76 - 5981273766400 * q^79 + 641098105526 * q^81 + 1628468261376 * q^84 + 4686627290192 * q^86 + 38846051916900 * q^89 - 13585044740368 * q^91 + 14007115751936 * q^94 - 4416662428928 * q^96 - 253574733016 * q^99

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 $

$2$	− 176.217i	− 1.94694i	−0.228817	−	0.973469i	$-0.573486\pi$
$2$	− 176.217i	− 1.94694i	0.228817	−	0.973469i	$-0.426514\pi$
$3$	− 573.185i	− 0.453949i	−0.973901	−	0.226974i	$-0.927117\pi$
$3$	− 573.185i	− 0.453949i	0.973901	−	0.226974i	$-0.0728834\pi$
$4$	−22860.4	−2.79057
$5$	0	0
$5$	0	0
$6$	−101005.	−0.883810
$7$	201493.i	0.647326i	0.946172	+	0.323663i	$0.104914\pi$
$7$	201493.i	0.647326i	−0.946172	+	0.323663i	$0.895086\pi$
$8$	2.58481e6i	3.48613i
$9$	1.26578e6	0.793931
$10$	0	0
$11$	−3.34359e6	−0.569062	−0.284531	−	0.958667i	$-0.591838\pi$
$11$	−3.34359e6	−0.569062	−0.284531	+	0.958667i	$0.591838\pi$
$12$	1.31032e7i	1.26678i
$13$	− 7.80359e6i	− 0.448397i	−0.974544	−	0.224198i	$-0.928024\pi$
$13$	− 7.80359e6i	− 0.448397i	0.974544	−	0.224198i	$-0.0719764\pi$
$14$	3.55065e7	1.26030
$15$	0	0
$16$	2.68215e8	3.99671
$17$	8.71750e7i	0.875939i	0.898990	+	0.437969i	$0.144302\pi$
$17$	8.71750e7i	0.875939i	−0.898990	+	0.437969i	$0.855698\pi$
$18$	− 2.23052e8i	− 1.54573i
$19$	1.66766e7	0.0813223	0.0406612	−	0.999173i	$-0.487054\pi$
$19$	1.66766e7	0.0813223	0.0406612	+	0.999173i	$0.487054\pi$
$20$	0	0
$21$	1.15493e8	0.293853
$22$	5.89196e8i	1.10793i
$23$	1.13518e9i	1.59895i	0.600698	+	0.799476i	$0.294889\pi$
$23$	1.13518e9i	1.59895i	−0.600698	+	0.799476i	$0.705111\pi$
$24$	1.48158e9	1.58253
$25$	0	0
$26$	−1.37512e9	−0.873002
$27$	− 1.63937e9i	− 0.814352i
$28$	− 4.60620e9i	− 1.80641i
$29$	−2.60673e9	−0.813783	−0.406891	−	0.913477i	$-0.633387\pi$
$29$	−2.60673e9	−0.813783	−0.406891	+	0.913477i	$0.633387\pi$
$30$	0	0
$31$	8.33139e8	0.168604	0.0843018	−	0.996440i	$-0.473134\pi$
$31$	8.33139e8	0.168604	0.0843018	+	0.996440i	$0.473134\pi$
$32$	− 2.60892e10i	− 4.29523i
$33$	1.91649e9i	0.258325i
$34$	1.53617e10	1.70540
$35$	0	0
$36$	−2.89362e10	−2.21552
$37$	1.05494e10i	0.675953i	0.941155	+	0.337976i	$0.109742\pi$
$37$	1.05494e10i	0.675953i	−0.941155	+	0.337976i	$0.890258\pi$
$38$	− 2.93870e9i	− 0.158330i
$39$	−4.47290e9	−0.203549
$40$	0	0
$41$	−4.33030e9	−0.142371	−0.0711857	−	0.997463i	$-0.522678\pi$
$41$	−4.33030e9	−0.142371	−0.0711857	+	0.997463i	$0.522678\pi$
$42$	− 2.03518e10i	− 0.572113i
$43$	1.93854e9i	0.0467660i	0.999727	+	0.0233830i	$0.00744372\pi$
$43$	1.93854e9i	0.0467660i	−0.999727	+	0.0233830i	$0.992556\pi$
$44$	7.64356e10	1.58801
$45$	0	0
$46$	2.00038e11	3.11306
$47$	− 2.85468e10i	− 0.386296i	−0.981170	−	0.193148i	$-0.938130\pi$
$47$	− 2.85468e10i	− 0.386296i	0.981170	−	0.193148i	$-0.0618698\pi$
$48$	− 1.53737e11i	− 1.81430i
$49$	5.62896e10	0.580969
$50$	0	0
$51$	4.99674e10	0.397631
$52$	1.78393e11i	1.25128i
$53$	1.23249e11i	0.763819i	0.924200	+	0.381910i	$0.124733\pi$
$53$	1.23249e11i	0.763819i	−0.924200	+	0.381910i	$0.875267\pi$
$54$	−2.88884e11	−1.58549
$55$	0	0
$56$	−5.20821e11	−2.25666
$57$	− 9.55879e9i	− 0.0369162i
$58$	4.59349e11i	1.58439i
$59$	5.55404e11	1.71424	0.857118	−	0.515120i	$-0.172253\pi$
$59$	5.55404e11	1.71424	0.857118	+	0.515120i	$0.172253\pi$
$60$	0	0
$61$	−4.10476e11	−1.02010	−0.510051	−	0.860144i	$-0.670373\pi$
$61$	−4.10476e11	−1.02010	−0.510051	+	0.860144i	$0.670373\pi$
$62$	− 1.46813e11i	− 0.328261i
$63$	2.55046e11i	0.513932i
$64$	−2.40014e12	−4.36583
$65$	0	0
$66$	3.37718e11	0.502943
$67$	− 3.36861e11i	− 0.454951i	−0.973784	−	0.227475i	$-0.926953\pi$
$67$	− 3.36861e11i	− 0.454951i	0.973784	−	0.227475i	$-0.0730471\pi$
$68$	− 1.99285e12i	− 2.44437i
$69$	6.50671e11	0.725842
$70$	0	0
$71$	1.57323e12	1.45751	0.728757	−	0.684772i	$-0.240098\pi$
$71$	1.57323e12	1.45751	0.728757	+	0.684772i	$0.240098\pi$
$72$	3.27181e12i	2.76775i
$73$	2.05372e12i	1.58834i	0.607695	+	0.794170i	$0.292094\pi$
$73$	2.05372e12i	1.58834i	−0.607695	+	0.794170i	$0.707906\pi$
$74$	1.85898e12	1.31604
$75$	0	0
$76$	−3.81234e11	−0.226936
$77$	− 6.73709e11i	− 0.368369i
$78$	7.88201e11i	0.396298i
$79$	6.93000e11	0.320743	0.160372	−	0.987057i	$-0.448731\pi$
$79$	6.93000e11	0.320743	0.160372	+	0.987057i	$0.448731\pi$
$80$	0	0
$81$	1.07840e12	0.424256
$82$	7.63071e11i	0.277188i
$83$	2.01116e12i	0.675212i	0.941288	+	0.337606i	$0.109617\pi$
$83$	2.01116e12i	0.675212i	−0.941288	+	0.337606i	$0.890383\pi$
$84$	−2.64021e12	−0.820017
$85$	0	0
$86$	3.41604e11	0.0910505
$87$	1.49414e12i	0.369416i
$88$	− 8.64253e12i	− 1.98383i
$89$	8.51832e12	1.81685	0.908424	−	0.418050i	$-0.137286\pi$
$89$	8.51832e12	1.81685	0.908424	+	0.418050i	$0.137286\pi$
$90$	0	0
$91$	1.57237e12	0.290259
$92$	− 2.59507e13i	− 4.46199i
$93$	− 4.77543e11i	− 0.0765374i
$94$	−5.03042e12	−0.752096
$95$	0	0
$96$	−1.49540e13	−1.94981
$97$	7.99814e12i	0.974929i	0.873143	+	0.487464i	$0.162078\pi$
$97$	7.99814e12i	0.974929i	−0.873143	+	0.487464i	$0.837922\pi$
$98$	− 9.91916e12i	− 1.13111i
$99$	−4.23225e12	−0.451796
$100$	0	0
$101$	−1.60387e13	−1.50342	−0.751710	−	0.659494i	$-0.770771\pi$
$101$	−1.60387e13	−1.50342	−0.751710	+	0.659494i	$0.770771\pi$
$102$	− 8.80509e12i	− 0.774164i
$103$	1.72566e13i	1.42401i	0.702176	+	0.712004i	$0.252212\pi$
$103$	1.72566e13i	1.42401i	−0.702176	+	0.712004i	$0.747788\pi$
$104$	2.01708e13	1.56317
$105$	0	0
$106$	2.17186e13	1.48711
$107$	3.98196e11i	0.0256509i	0.999918	+	0.0128254i	$0.00408258\pi$
$107$	3.98196e11i	0.0256509i	−0.999918	+	0.0128254i	$0.995917\pi$
$108$	3.74766e13i	2.27251i
$109$	−1.09886e13	−0.627582	−0.313791	−	0.949492i	$-0.601599\pi$
$109$	−1.09886e13	−0.627582	−0.313791	+	0.949492i	$0.601599\pi$
$110$	0	0
$111$	6.04676e12	0.306848
$112$	5.40435e13i	2.58718i
$113$	− 2.06154e13i	− 0.931497i	−0.884917	−	0.465748i	$-0.845785\pi$
$113$	− 2.06154e13i	− 0.931497i	0.884917	−	0.465748i	$-0.154215\pi$
$114$	−1.68442e12	−0.0718735
$115$	0	0
$116$	5.95907e13	2.27092
$117$	− 9.87764e12i	− 0.355996i
$118$	− 9.78714e13i	− 3.33751i
$119$	−1.75651e13	−0.567018
$120$	0	0
$121$	−2.33431e13	−0.676168
$122$	7.23327e13i	1.98608i
$123$	2.48206e12i	0.0646293i
$124$	−1.90459e13	−0.470500
$125$	0	0
$126$	4.49434e13	1.00059
$127$	− 3.03181e13i	− 0.641177i	−0.947219	−	0.320588i	$-0.896119\pi$
$127$	− 3.03181e13i	− 0.641177i	0.947219	−	0.320588i	$-0.103881\pi$
$128$	2.09222e14i	4.20478i
$129$	1.11114e12	0.0212294
$130$	0	0
$131$	−7.79100e13	−1.34688	−0.673441	−	0.739241i	$-0.735185\pi$
$131$	−7.79100e13	−1.34688	−0.673441	+	0.739241i	$0.735185\pi$
$132$	− 4.38117e13i	− 0.720875i
$133$	3.36022e12i	0.0526420i
$134$	−5.93605e13	−0.885761
$135$	0	0
$136$	−2.25331e14	−3.05364
$137$	1.01051e14i	1.30574i	0.757469	+	0.652871i	$0.226436\pi$
$137$	1.01051e14i	1.30574i	−0.757469	+	0.652871i	$0.773564\pi$
$138$	− 1.14659e14i	− 1.41317i
$139$	−1.42505e14	−1.67585	−0.837924	−	0.545787i	$-0.816231\pi$
$139$	−1.42505e14	−1.67585	−0.837924	+	0.545787i	$0.816231\pi$
$140$	0	0
$141$	−1.63626e13	−0.175359
$142$	− 2.77230e14i	− 2.83769i
$143$	2.60920e13i	0.255166i
$144$	3.39502e14	3.17311
$145$	0	0
$146$	3.61901e14	3.09240
$147$	− 3.22643e13i	− 0.263730i
$148$	− 2.41163e14i	− 1.88629i
$149$	6.15555e13	0.460846	0.230423	−	0.973091i	$-0.425989\pi$
$149$	6.15555e13	0.460846	0.230423	+	0.973091i	$0.425989\pi$
$150$	0	0
$151$	−4.43226e13	−0.304281	−0.152141	−	0.988359i	$-0.548617\pi$
$151$	−4.43226e13	−0.304281	−0.152141	+	0.988359i	$0.548617\pi$
$152$	4.31059e13i	0.283500i
$153$	1.10344e14i	0.695435i
$154$	−1.18719e14	−0.717191
$155$	0	0
$156$	1.02252e14	0.568019
$157$	1.81701e14i	0.968301i	0.874985	+	0.484150i	$0.160871\pi$
$157$	1.81701e14i	0.968301i	−0.874985	+	0.484150i	$0.839129\pi$
$158$	− 1.22118e14i	− 0.624467i
$159$	7.06446e13	0.346735
$160$	0	0
$161$	−2.28732e14	−1.03504
$162$	− 1.90033e14i	− 0.826001i
$163$	9.09336e13i	0.379756i	0.981808	+	0.189878i	$0.0608093\pi$
$163$	9.09336e13i	0.379756i	−0.981808	+	0.189878i	$0.939191\pi$
$164$	9.89921e13	0.397297
$165$	0	0
$166$	3.54401e14	1.31460
$167$	2.40022e14i	0.856237i	0.903723	+	0.428118i	$0.140823\pi$
$167$	2.40022e14i	0.856237i	−0.903723	+	0.428118i	$0.859177\pi$
$168$	2.98527e14i	1.02441i
$169$	2.41979e14	0.798940
$170$	0	0
$171$	2.11090e13	0.0645643
$172$	− 4.43158e13i	− 0.130504i
$173$	4.10274e14i	1.16352i	0.813360	+	0.581760i	$0.197636\pi$
$173$	4.10274e14i	1.16352i	−0.813360	+	0.581760i	$0.802364\pi$
$174$	2.63292e14	0.719230
$175$	0	0
$176$	−8.96800e14	−2.27438
$177$	− 3.18349e14i	− 0.778175i
$178$	− 1.50107e15i	− 3.53729i
$179$	2.37588e14	0.539858	0.269929	−	0.962880i	$-0.413000\pi$
$179$	2.37588e14	0.539858	0.269929	+	0.962880i	$0.413000\pi$
$180$	0	0
$181$	5.41620e14	1.14494	0.572472	−	0.819924i	$-0.305985\pi$
$181$	5.41620e14	1.14494	0.572472	+	0.819924i	$0.305985\pi$
$182$	− 2.77078e14i	− 0.565116i
$183$	2.35279e14i	0.463074i
$184$	−2.93424e15	−5.57416
$185$	0	0
$186$	−8.41511e13	−0.149014
$187$	− 2.91477e14i	− 0.498464i
$188$	6.52589e14i	1.07799i
$189$	3.30322e14	0.527151
$190$	0	0
$191$	−2.56027e12	−0.00381565	−0.00190782	−	0.999998i	$-0.500607\pi$
$191$	−2.56027e12	−0.00381565	−0.00190782	+	0.999998i	$0.500607\pi$
$192$	1.37572e15i	1.98186i
$193$	1.10496e15i	1.53895i	0.638677	+	0.769475i	$0.279482\pi$
$193$	1.10496e15i	1.53895i	−0.638677	+	0.769475i	$0.720518\pi$
$194$	1.40941e15	1.89813
$195$	0	0
$196$	−1.28680e15	−1.62124
$197$	− 7.90145e14i	− 0.963110i	−0.876416	−	0.481555i	$-0.840072\pi$
$197$	− 7.90145e14i	− 0.963110i	0.876416	−	0.481555i	$-0.159928\pi$
$198$	7.45793e14i	0.879619i
$199$	2.97088e14	0.339109	0.169555	−	0.985521i	$-0.445767\pi$
$199$	2.97088e14	0.339109	0.169555	+	0.985521i	$0.445767\pi$
$200$	0	0
$201$	−1.93084e14	−0.206524
$202$	2.82629e15i	2.92707i
$203$	− 5.25237e14i	− 0.526782i
$204$	−1.14227e15	−1.10962
$205$	0	0
$206$	3.04090e15	2.77246
$207$	1.43689e15i	1.26946i
$208$	− 2.09304e15i	− 1.79211i
$209$	−5.57597e13	−0.0462775
$210$	0	0
$211$	−1.25602e15	−0.979851	−0.489926	−	0.871764i	$-0.662976\pi$
$211$	−1.25602e15	−0.979851	−0.489926	+	0.871764i	$0.662976\pi$
$212$	− 2.81752e15i	− 2.13149i
$213$	− 9.01752e14i	− 0.661637i
$214$	7.01688e13	0.0499407
$215$	0	0
$216$	4.23746e15	2.83894
$217$	1.67872e14i	0.109141i
$218$	1.93638e15i	1.22186i
$219$	1.17716e15	0.721025
$220$	0	0
$221$	6.80278e14	0.392768
$222$	− 1.06554e15i	− 0.597414i
$223$	− 1.17841e15i	− 0.641676i	−0.947134	−	0.320838i	$-0.896036\pi$
$223$	− 1.17841e15i	− 0.641676i	0.947134	−	0.320838i	$-0.103964\pi$
$224$	5.25680e15	2.78041
$225$	0	0
$226$	−3.63278e15	−1.81357
$227$	− 4.91498e14i	− 0.238426i	−0.992869	−	0.119213i	$-0.961963\pi$
$227$	− 4.91498e14i	− 0.238426i	0.992869	−	0.119213i	$-0.0380372\pi$
$228$	2.18517e14i	0.103017i
$229$	−3.17657e15	−1.45555	−0.727777	−	0.685814i	$-0.759446\pi$
$229$	−3.17657e15	−1.45555	−0.727777	+	0.685814i	$0.759446\pi$
$230$	0	0
$231$	−3.86160e14	−0.167221
$232$	− 6.73789e15i	− 2.83695i
$233$	− 2.05201e14i	− 0.0840168i	−0.999117	−	0.0420084i	$-0.986624\pi$
$233$	− 2.05201e14i	− 0.0840168i	0.999117	−	0.0420084i	$-0.0133756\pi$
$234$	−1.74061e15	−0.693103
$235$	0	0
$236$	−1.26967e16	−4.78370
$237$	− 3.97218e14i	− 0.145601i
$238$	3.09527e15i	1.10395i
$239$	−4.78414e15	−1.66042	−0.830209	−	0.557453i	$-0.811779\pi$
$239$	−4.78414e15	−1.66042	−0.830209	+	0.557453i	$0.811779\pi$
$240$	0	0
$241$	2.83675e15	0.932633	0.466316	−	0.884618i	$-0.345581\pi$
$241$	2.83675e15	0.932633	0.466316	+	0.884618i	$0.345581\pi$
$242$	4.11345e15i	1.31646i
$243$	− 3.23181e15i	− 1.00694i
$244$	9.38362e15	2.84667
$245$	0	0
$246$	4.37381e14	0.125829
$247$	− 1.30138e14i	− 0.0364647i
$248$	2.15351e15i	0.587774i
$249$	1.15277e15	0.306512
$250$	0	0
$251$	3.50075e15	0.883654	0.441827	−	0.897100i	$-0.354331\pi$
$251$	3.50075e15	0.883654	0.441827	+	0.897100i	$0.354331\pi$
$252$	− 5.83045e15i	− 1.43416i
$253$	− 3.79558e15i	− 0.909903i
$254$	−5.34256e15	−1.24833
$255$	0	0
$256$	1.72065e16	3.82061
$257$	7.14451e14i	0.154670i	0.997005	+	0.0773352i	$0.0246412\pi$
$257$	7.14451e14i	0.154670i	−0.997005	+	0.0773352i	$0.975359\pi$
$258$	− 1.95802e14i	− 0.0413323i
$259$	−2.12563e15	−0.437562
$260$	0	0
$261$	−3.29955e15	−0.646087
$262$	1.37290e16i	2.62230i
$263$	− 6.41873e15i	− 1.19601i	−0.801491	−	0.598007i	$-0.795959\pi$
$263$	− 6.41873e15i	− 1.19601i	0.801491	−	0.598007i	$-0.204041\pi$
$264$	−4.95377e15	−0.900556
$265$	0	0
$266$	5.92128e14	0.102491
$267$	− 4.88257e15i	− 0.824756i
$268$	7.70076e15i	1.26957i
$269$	1.09876e15	0.176813	0.0884063	−	0.996084i	$-0.471823\pi$
$269$	1.09876e15	0.176813	0.0884063	+	0.996084i	$0.471823\pi$
$270$	0	0
$271$	1.60206e15	0.245684	0.122842	−	0.992426i	$-0.460799\pi$
$271$	1.60206e15	0.245684	0.122842	+	0.992426i	$0.460799\pi$
$272$	2.33816e16i	3.50088i
$273$	− 9.01259e14i	− 0.131763i
$274$	1.78069e16	2.54220
$275$	0	0
$276$	−1.48746e16	−2.02551
$277$	6.91414e14i	0.0919644i	0.998942	+	0.0459822i	$0.0146417\pi$
$277$	6.91414e14i	0.0919644i	−0.998942	+	0.0459822i	$0.985358\pi$
$278$	2.51118e16i	3.26277i
$279$	1.05457e15	0.133860
$280$	0	0
$281$	2.20744e15	0.267484	0.133742	−	0.991016i	$-0.457301\pi$
$281$	2.20744e15	0.267484	0.133742	+	0.991016i	$0.457301\pi$
$282$	2.88336e15i	0.341413i
$283$	8.67634e15i	1.00398i	0.864873	+	0.501990i	$0.167399\pi$
$283$	8.67634e15i	1.00398i	−0.864873	+	0.501990i	$0.832601\pi$
$284$	−3.59646e16	−4.06730
$285$	0	0
$286$	4.59784e15	0.496792
$287$	− 8.72525e14i	− 0.0921606i
$288$	− 3.30233e16i	− 3.41011i
$289$	2.30511e15	0.232731
$290$	0	0
$291$	4.58442e15	0.442568
$292$	− 4.69489e16i	− 4.43238i
$293$	− 7.81345e15i	− 0.721445i	−0.932673	−	0.360723i	$-0.882530\pi$
$293$	− 7.81345e15i	− 0.721445i	0.932673	−	0.360723i	$-0.117470\pi$
$294$	−5.68552e15	−0.513467
$295$	0	0
$296$	−2.72682e16	−2.35646
$297$	5.48137e15i	0.463417i
$298$	− 1.08471e16i	− 0.897239i
$299$	8.85851e15	0.716965
$300$	0	0
$301$	−3.90603e14	−0.0302728
$302$	7.81039e15i	0.592417i
$303$	9.19315e15i	0.682475i
$304$	4.47292e15	0.325022
$305$	0	0
$306$	1.94445e16	1.35397
$307$	− 1.73583e16i	− 1.18334i	−0.806182	−	0.591668i	$-0.798470\pi$
$307$	− 1.73583e16i	− 1.18334i	0.806182	−	0.591668i	$-0.201530\pi$
$308$	1.54012e16i	1.02796i
$309$	9.89120e15	0.646426
$310$	0	0
$311$	−2.64097e15	−0.165509	−0.0827543	−	0.996570i	$-0.526372\pi$
$311$	−2.64097e15	−0.165509	−0.0827543	+	0.996570i	$0.526372\pi$
$312$	− 1.15616e16i	− 0.709599i
$313$	1.04071e16i	0.625594i	0.949820	+	0.312797i	$0.101266\pi$
$313$	1.04071e16i	0.625594i	−0.949820	+	0.312797i	$0.898734\pi$
$314$	3.20188e16	1.88522
$315$	0	0
$316$	−1.58422e16	−0.895057
$317$	1.64664e16i	0.911410i	0.890131	+	0.455705i	$0.150613\pi$
$317$	1.64664e16i	0.911410i	−0.890131	+	0.455705i	$0.849387\pi$
$318$	− 1.24488e16i	− 0.675071i
$319$	8.71581e15	0.463093
$320$	0	0
$321$	2.28240e14	0.0116442
$322$	4.03064e16i	2.01516i
$323$	1.45378e15i	0.0712334i
$324$	−2.46527e16	−1.18392
$325$	0	0
$326$	1.60240e16	0.739362
$327$	6.29851e15i	0.284890i
$328$	− 1.11930e16i	− 0.496325i
$329$	5.75197e15	0.250060
$330$	0	0
$331$	1.40904e16	0.588900	0.294450	−	0.955667i	$-0.404863\pi$
$331$	1.40904e16	0.588900	0.294450	+	0.955667i	$0.404863\pi$
$332$	− 4.59759e16i	− 1.88423i
$333$	1.33532e16i	0.536660i
$334$	4.22959e16	1.66704
$335$	0	0
$336$	3.09769e16	1.17445
$337$	− 1.51673e16i	− 0.564044i	−0.959408	−	0.282022i	$-0.908995\pi$
$337$	− 1.51673e16i	− 0.564044i	0.959408	−	0.282022i	$-0.0910051\pi$
$338$	− 4.26408e16i	− 1.55549i
$339$	−1.18164e16	−0.422852
$340$	0	0
$341$	−2.78567e15	−0.0959460
$342$	− 3.71975e15i	− 0.125703i
$343$	3.08644e16i	1.02340i
$344$	−5.01076e15	−0.163032
$345$	0	0
$346$	7.22971e16	2.26530
$347$	− 3.87222e15i	− 0.119074i	−0.998226	−	0.0595372i	$-0.981038\pi$
$347$	− 3.87222e15i	− 0.119074i	0.998226	−	0.0595372i	$-0.0189625\pi$
$348$	− 3.41565e16i	− 1.03088i
$349$	−5.50673e16	−1.63128	−0.815640	−	0.578560i	$-0.803615\pi$
$349$	−5.50673e16	−1.63128	−0.815640	+	0.578560i	$0.803615\pi$
$350$	0	0
$351$	−1.27930e16	−0.365153
$352$	8.72315e16i	2.44425i
$353$	− 4.84424e15i	− 0.133257i	−0.997778	−	0.0666285i	$-0.978776\pi$
$353$	− 4.84424e15i	− 0.133257i	0.997778	−	0.0666285i	$-0.0212242\pi$
$354$	−5.60985e16	−1.51506
$355$	0	0
$356$	−1.94732e17	−5.07004
$357$	1.00681e16i	0.257397i
$358$	− 4.18670e16i	− 1.05107i
$359$	5.71730e16	1.40954	0.704770	−	0.709436i	$-0.251050\pi$
$359$	5.71730e16	1.40954	0.704770	+	0.709436i	$0.251050\pi$
$360$	0	0
$361$	−4.17749e16	−0.993387
$362$	− 9.54426e16i	− 2.22914i
$363$	1.33799e16i	0.306946i
$364$	−3.59449e16	−0.809988
$365$	0	0
$366$	4.14600e16	0.901576
$367$	3.48286e16i	0.744057i	0.928221	+	0.372028i	$0.121338\pi$
$367$	3.48286e16i	0.744057i	−0.928221	+	0.372028i	$0.878662\pi$
$368$	3.04473e17i	6.39055i
$369$	−5.48121e15	−0.113033
$370$	0	0
$371$	−2.48338e16	−0.494440
$372$	1.09168e16i	0.213583i
$373$	− 2.14588e16i	− 0.412570i	−0.978492	−	0.206285i	$-0.933863\pi$
$373$	− 2.14588e16i	− 0.412570i	0.978492	−	0.206285i	$-0.0661375\pi$
$374$	−5.13631e16	−0.970479
$375$	0	0
$376$	7.37880e16	1.34668
$377$	2.03418e16i	0.364898i
$378$	− 5.82082e16i	− 1.02633i
$379$	1.90361e16	0.329930	0.164965	−	0.986299i	$-0.447249\pi$
$379$	1.90361e16	0.329930	0.164965	+	0.986299i	$0.447249\pi$
$380$	0	0
$381$	−1.73779e16	−0.291061
$382$	4.51162e14i	0.00742884i
$383$	− 1.03414e17i	− 1.67412i	−0.547112	−	0.837059i	$-0.684273\pi$
$383$	− 1.03414e17i	− 1.67412i	0.547112	−	0.837059i	$-0.315727\pi$
$384$	1.19923e17	1.90875
$385$	0	0
$386$	1.94713e17	2.99624
$387$	2.45377e15i	0.0371290i
$388$	− 1.82840e17i	− 2.72061i
$389$	−9.11608e16	−1.33394	−0.666969	−	0.745085i	$-0.732409\pi$
$389$	−9.11608e16	−1.33394	−0.666969	+	0.745085i	$0.732409\pi$
$390$	0	0
$391$	−9.89596e16	−1.40058
$392$	1.45498e17i	2.02534i
$393$	4.46568e16i	0.611416i
$394$	−1.39237e17	−1.87512
$395$	0	0
$396$	9.67507e16	1.26077
$397$	− 7.19989e15i	− 0.0922970i	−0.998935	−	0.0461485i	$-0.985305\pi$
$397$	− 7.19989e15i	− 0.0922970i	0.998935	−	0.0461485i	$-0.0146947\pi$
$398$	− 5.23518e16i	− 0.660225i
$399$	1.92603e15	0.0238968
$400$	0	0
$401$	1.06602e17	1.28034	0.640172	−	0.768231i	$-0.278863\pi$
$401$	1.06602e17	1.28034	0.640172	+	0.768231i	$0.278863\pi$
$402$	3.40246e16i	0.402090i
$403$	− 6.50148e15i	− 0.0756013i
$404$	3.66650e17	4.19540
$405$	0	0
$406$	−9.25556e16	−1.02561
$407$	− 3.52728e16i	− 0.384659i
$408$	1.29156e17i	1.38620i
$409$	−6.00154e16	−0.633959	−0.316980	−	0.948432i	$-0.602669\pi$
$409$	−6.00154e16	−0.633959	−0.316980	+	0.948432i	$0.602669\pi$
$410$	0	0
$411$	5.79210e16	0.592740
$412$	− 3.94491e17i	− 3.97379i
$413$	1.11910e17i	1.10967i
$414$	2.53205e17	2.47155
$415$	0	0
$416$	−2.03590e17	−1.92597
$417$	8.16819e16i	0.760749i
$418$	9.82580e15i	0.0900994i
$419$	−1.22532e17	−1.10626	−0.553130	−	0.833095i	$-0.686567\pi$
$419$	−1.22532e17	−1.10626	−0.553130	+	0.833095i	$0.686567\pi$
$420$	0	0
$421$	−1.19508e17	−1.04607	−0.523037	−	0.852310i	$-0.675201\pi$
$421$	−1.19508e17	−1.04607	−0.523037	+	0.852310i	$0.675201\pi$
$422$	2.21332e17i	1.90771i
$423$	− 3.61340e16i	− 0.306693i
$424$	−3.18576e17	−2.66277
$425$	0	0
$426$	−1.58904e17	−1.28817
$427$	− 8.27080e16i	− 0.660338i
$428$	− 9.10290e15i	− 0.0715806i
$429$	1.49555e16	0.115832
$430$	0	0
$431$	−3.18425e16	−0.239279	−0.119640	−	0.992817i	$-0.538174\pi$
$431$	−3.18425e16	−0.239279	−0.119640	+	0.992817i	$0.538174\pi$
$432$	− 4.39704e17i	− 3.25473i
$433$	1.24850e16i	0.0910366i	0.998964	+	0.0455183i	$0.0144939\pi$
$433$	1.24850e16i	0.0910366i	−0.998964	+	0.0455183i	$0.985506\pi$
$434$	2.95818e16	0.212492
$435$	0	0
$436$	2.51204e17	1.75131
$437$	1.89310e16i	0.130030i
$438$	− 2.07436e17i	− 1.40379i
$439$	2.58876e17	1.72613	0.863063	−	0.505095i	$-0.168543\pi$
$439$	2.58876e17	1.72613	0.863063	+	0.505095i	$0.168543\pi$
$440$	0	0
$441$	7.12503e16	0.461249
$442$	− 1.19876e17i	− 0.764696i
$443$	1.53844e17i	0.967068i	0.875326	+	0.483534i	$0.160647\pi$
$443$	1.53844e17i	0.967068i	−0.875326	+	0.483534i	$0.839353\pi$
$444$	−1.38231e17	−0.856281
$445$	0	0
$446$	−2.07656e17	−1.24930
$447$	− 3.52827e16i	− 0.209201i
$448$	− 4.83612e17i	− 2.82611i
$449$	9.02887e16	0.520034	0.260017	−	0.965604i	$-0.416272\pi$
$449$	9.02887e16	0.520034	0.260017	+	0.965604i	$0.416272\pi$
$450$	0	0
$451$	1.44787e16	0.0810182
$452$	4.71275e17i	2.59941i
$453$	2.54051e16i	0.138128i
$454$	−8.66102e16	−0.464201
$455$	0	0
$456$	2.47077e16	0.128695
$457$	9.78643e16i	0.502538i	0.967917	+	0.251269i	$0.0808479\pi$
$457$	9.78643e16i	0.502538i	−0.967917	+	0.251269i	$0.919152\pi$
$458$	5.59765e17i	2.83387i
$459$	1.42912e17	0.713323
$460$	0	0
$461$	2.08140e17	1.00995	0.504976	−	0.863134i	$-0.331501\pi$
$461$	2.08140e17	1.00995	0.504976	+	0.863134i	$0.331501\pi$
$462$	6.80479e16i	0.325568i
$463$	− 2.44823e17i	− 1.15498i	−0.816397	−	0.577491i	$-0.804032\pi$
$463$	− 2.44823e17i	− 1.15498i	0.816397	−	0.577491i	$-0.195968\pi$
$464$	−6.99163e17	−3.25246
$465$	0	0
$466$	−3.61599e16	−0.163576
$467$	− 3.54401e17i	− 1.58101i	−0.612454	−	0.790506i	$-0.709818\pi$
$467$	− 3.54401e17i	− 1.58101i	0.612454	−	0.790506i	$-0.290182\pi$
$468$	2.25806e17i	0.993432i
$469$	6.78751e16	0.294501
$470$	0	0
$471$	1.04148e17	0.439559
$472$	1.43561e18i	5.97605i
$473$	− 6.48168e15i	− 0.0266128i
$474$	−6.99964e16	−0.283476
$475$	0	0
$476$	4.01546e17	1.58230
$477$	1.56006e17i	0.606419i
$478$	8.43045e17i	3.23273i
$479$	1.54040e17	0.582712	0.291356	−	0.956615i	$-0.405894\pi$
$479$	1.54040e17	0.582712	0.291356	+	0.956615i	$0.405894\pi$
$480$	0	0
$481$	8.23232e16	0.303095
$482$	− 4.99883e17i	− 1.81578i
$483$	1.31106e17i	0.469856i
$484$	5.33633e17	1.88689
$485$	0	0
$486$	−5.69499e17	−1.96046
$487$	− 2.11302e17i	− 0.717736i	−0.933388	−	0.358868i	$-0.883163\pi$
$487$	− 2.11302e17i	− 0.717736i	0.933388	−	0.358868i	$-0.116837\pi$
$488$	− 1.06100e18i	− 3.55621i
$489$	5.21218e16	0.172390
$490$	0	0
$491$	2.61474e17	0.842167	0.421083	−	0.907022i	$-0.361650\pi$
$491$	2.61474e17	0.842167	0.421083	+	0.907022i	$0.361650\pi$
$492$	− 5.67408e16i	− 0.180353i
$493$	− 2.27241e17i	− 0.712824i
$494$	−2.29324e16	−0.0709945
$495$	0	0
$496$	2.23460e17	0.673860
$497$	3.16995e17i	0.943487i
$498$	− 2.03137e17i	− 0.596759i
$499$	−3.87524e17	−1.12369	−0.561843	−	0.827244i	$-0.689908\pi$
$499$	−3.87524e17	−1.12369	−0.561843	+	0.827244i	$0.689908\pi$
$500$	0	0
$501$	1.37577e17	0.388688
$502$	− 6.16891e17i	− 1.72042i
$503$	− 4.12680e17i	− 1.13611i	−0.822990	−	0.568056i	$-0.807696\pi$
$503$	− 4.12680e17i	− 1.13611i	0.822990	−	0.568056i	$-0.192304\pi$
$504$	−6.59246e17	−1.79163
$505$	0	0
$506$	−6.68846e17	−1.77153
$507$	− 1.38699e17i	− 0.362678i
$508$	6.93083e17i	1.78925i
$509$	−8.09532e16	−0.206333	−0.103166	−	0.994664i	$-0.532897\pi$
$509$	−8.09532e16	−0.206333	−0.103166	+	0.994664i	$0.532897\pi$
$510$	0	0
$511$	−4.13811e17	−1.02817
$512$	− 1.31813e18i	− 3.23372i
$513$	− 2.73391e16i	− 0.0662250i
$514$	1.25898e17	0.301134
$515$	0	0
$516$	−2.54011e16	−0.0592420
$517$	9.54485e16i	0.219827i
$518$	3.74572e17i	0.851906i
$519$	2.35163e17	0.528178
$520$	0	0
$521$	−2.79201e17	−0.611607	−0.305803	−	0.952095i	$-0.598925\pi$
$521$	−2.79201e17	−0.611607	−0.305803	+	0.952095i	$0.598925\pi$
$522$	5.81436e17i	1.25789i
$523$	9.97401e16i	0.213112i	0.994307	+	0.106556i	$0.0339824\pi$
$523$	9.97401e16i	0.213112i	−0.994307	+	0.106556i	$0.966018\pi$
$524$	1.78105e18	3.75857
$525$	0	0
$526$	−1.13109e18	−2.32857
$527$	7.26289e16i	0.147686i
$528$	5.14032e17i	1.03245i
$529$	−7.84606e17	−1.55665
$530$	0	0
$531$	7.03020e17	1.36098
$532$	− 7.68159e16i	− 0.146901i
$533$	3.37919e16i	0.0638389i
$534$	−8.60391e17	−1.60575
$535$	0	0
$536$	8.70721e17	1.58602
$537$	− 1.36182e17i	− 0.245068i
$538$	− 1.93620e17i	− 0.344243i
$539$	−1.88209e17	−0.330608
$540$	0	0
$541$	−2.15125e17	−0.368899	−0.184450	−	0.982842i	$-0.559050\pi$
$541$	−2.15125e17	−0.368899	−0.184450	+	0.982842i	$0.559050\pi$
$542$	− 2.82309e17i	− 0.478332i
$543$	− 3.10449e17i	− 0.519746i
$544$	2.27433e18	3.76236
$545$	0	0
$546$	−1.58817e17	−0.256534
$547$	− 9.04541e17i	− 1.44381i	−0.691991	−	0.721906i	$-0.743266\pi$
$547$	− 9.04541e17i	− 1.44381i	0.691991	−	0.721906i	$-0.256734\pi$
$548$	− 2.31007e18i	− 3.64377i
$549$	−5.19573e17	−0.809890
$550$	0	0
$551$	−4.34714e16	−0.0661787
$552$	1.68186e18i	2.53038i
$553$	1.39635e17i	0.207625i
$554$	1.21839e17	0.179049
$555$	0	0
$556$	3.25772e18	4.67657
$557$	9.25130e17i	1.31263i	0.754485	+	0.656317i	$0.227887\pi$
$557$	9.25130e17i	1.31263i	−0.754485	+	0.656317i	$0.772113\pi$
$558$	− 1.85833e17i	− 0.260616i
$559$	1.51276e16	0.0209697
$560$	0	0
$561$	−1.67070e17	−0.226277
$562$	− 3.88987e17i	− 0.520774i
$563$	− 7.77258e17i	− 1.02863i	−0.857600	−	0.514317i	$-0.828046\pi$
$563$	− 7.77258e17i	− 1.02863i	0.857600	−	0.514317i	$-0.171954\pi$
$564$	3.74054e17	0.489351
$565$	0	0
$566$	1.52892e18	1.95469
$567$	2.17291e17i	0.274632i
$568$	4.06650e18i	5.08109i
$569$	−5.27222e17	−0.651274	−0.325637	−	0.945495i	$-0.605579\pi$
$569$	−5.27222e17	−0.651274	−0.325637	+	0.945495i	$0.605579\pi$
$570$	0	0
$571$	−8.57655e17	−1.03557	−0.517783	−	0.855512i	$-0.673243\pi$
$571$	−8.57655e17	−1.03557	−0.517783	+	0.855512i	$0.673243\pi$
$572$	− 5.96472e17i	− 0.712059i
$573$	1.46751e15i	0.00173211i
$574$	−1.53753e17	−0.179431
$575$	0	0
$576$	−3.03805e18	−3.46617
$577$	6.01001e17i	0.678004i	0.940786	+	0.339002i	$0.110089\pi$
$577$	6.01001e17i	0.678004i	−0.940786	+	0.339002i	$0.889911\pi$
$578$	− 4.06198e17i	− 0.453114i
$579$	6.33347e17	0.698604
$580$	0	0
$581$	−4.05236e17	−0.437082
$582$	− 8.07851e17i	− 0.861652i
$583$	− 4.12094e17i	− 0.434661i
$584$	−5.30849e18	−5.53716
$585$	0	0
$586$	−1.37686e18	−1.40461
$587$	− 2.25235e17i	− 0.227241i	−0.993524	−	0.113621i	$-0.963755\pi$
$587$	− 2.25235e17i	− 0.227241i	0.993524	−	0.113621i	$-0.0362449\pi$
$588$	7.37574e17i	0.735958i
$589$	1.38940e16	0.0137112
$590$	0	0
$591$	−4.52899e17	−0.437203
$592$	2.82951e18i	2.70159i
$593$	8.69033e17i	0.820693i	0.911930	+	0.410347i	$0.134592\pi$
$593$	8.69033e17i	0.820693i	−0.911930	+	0.410347i	$0.865408\pi$
$594$	9.65910e17	0.902245
$595$	0	0
$596$	−1.40718e18	−1.28602
$597$	− 1.70286e17i	− 0.153938i
$598$	− 1.56102e18i	− 1.39589i
$599$	1.94567e18	1.72105	0.860527	−	0.509405i	$-0.170134\pi$
$599$	1.94567e18	1.72105	0.860527	+	0.509405i	$0.170134\pi$
$600$	0	0
$601$	2.96725e17	0.256844	0.128422	−	0.991720i	$-0.459009\pi$
$601$	2.96725e17	0.256844	0.128422	+	0.991720i	$0.459009\pi$
$602$	6.88307e16i	0.0589393i
$603$	− 4.26392e17i	− 0.361199i
$604$	1.01323e18	0.849118
$605$	0	0
$606$	1.61999e18	1.32874
$607$	− 2.06953e18i	− 1.67937i	−0.543076	−	0.839683i	$-0.682741\pi$
$607$	− 2.06953e18i	− 1.67937i	0.543076	−	0.839683i	$-0.317259\pi$
$608$	− 4.35080e17i	− 0.349298i
$609$	−3.01058e17	−0.239132
$610$	0	0
$611$	−2.22767e17	−0.173214
$612$	− 2.52251e18i	− 1.94066i
$613$	2.27988e18i	1.73548i	0.497022	+	0.867738i	$0.334427\pi$
$613$	2.27988e18i	1.73548i	−0.497022	+	0.867738i	$0.665573\pi$
$614$	−3.05883e18	−2.30388
$615$	0	0
$616$	1.74141e18	1.28418
$617$	2.03478e18i	1.48479i	0.669964	+	0.742394i	$0.266310\pi$
$617$	2.03478e18i	1.48479i	−0.669964	+	0.742394i	$0.733690\pi$
$618$	− 1.74300e18i	− 1.25855i
$619$	7.79671e17	0.557086	0.278543	−	0.960424i	$-0.410149\pi$
$619$	7.79671e17	0.557086	0.278543	+	0.960424i	$0.410149\pi$
$620$	0	0
$621$	1.86099e18	1.30211
$622$	4.65383e17i	0.322235i
$623$	1.71638e18i	1.17609i
$624$	−1.19970e18	−0.813528
$625$	0	0
$626$	1.83391e18	1.21799
$627$	3.19606e16i	0.0210076i
$628$	− 4.15376e18i	− 2.70211i
$629$	−9.19643e17	−0.592093
$630$	0	0
$631$	−1.75763e18	−1.10850	−0.554252	−	0.832349i	$-0.686995\pi$
$631$	−1.75763e18	−1.10850	−0.554252	+	0.832349i	$0.686995\pi$
$632$	1.79128e18i	1.11815i
$633$	7.19931e17i	0.444802i
$634$	2.90166e18	1.77446
$635$	0	0
$636$	−1.61496e18	−0.967588
$637$	− 4.39261e17i	− 0.260505i
$638$	− 1.53587e18i	− 0.901614i
$639$	1.99137e18	1.15717
$640$	0	0
$641$	2.32621e18	1.32456	0.662279	−	0.749257i	$-0.269589\pi$
$641$	2.32621e18	1.32456	0.662279	+	0.749257i	$0.269589\pi$
$642$	− 4.02197e16i	− 0.0226705i
$643$	2.60316e18i	1.45254i	0.687408	+	0.726272i	$0.258749\pi$
$643$	2.60316e18i	1.45254i	−0.687408	+	0.726272i	$0.741251\pi$
$644$	5.22889e18	2.88836
$645$	0	0
$646$	2.56181e17	0.138687
$647$	1.20524e18i	0.645947i	0.946408	+	0.322974i	$0.104682\pi$
$647$	1.20524e18i	0.645947i	−0.946408	+	0.322974i	$0.895318\pi$
$648$	2.78747e18i	1.47901i
$649$	−1.85704e18	−0.975507
$650$	0	0
$651$	9.62216e16	0.0495446
$652$	− 2.07877e18i	− 1.05974i
$653$	1.72181e18i	0.869061i	0.900657	+	0.434531i	$0.143086\pi$
$653$	1.72181e18i	0.869061i	−0.900657	+	0.434531i	$0.856914\pi$
$654$	1.10990e18	0.554664
$655$	0	0
$656$	−1.16145e18	−0.569018
$657$	2.59957e18i	1.26103i
$658$	− 1.01359e18i	− 0.486851i
$659$	3.66491e18	1.74304	0.871521	−	0.490358i	$-0.163134\pi$
$659$	3.66491e18	1.74304	0.871521	+	0.490358i	$0.163134\pi$
$660$	0	0
$661$	−3.66523e18	−1.70920	−0.854599	−	0.519289i	$-0.826197\pi$
$661$	−3.66523e18	−1.70920	−0.854599	+	0.519289i	$0.826197\pi$
$662$	− 2.48297e18i	− 1.14655i
$663$	− 3.89925e17i	− 0.178297i
$664$	−5.19848e18	−2.35388
$665$	0	0
$666$	2.35306e18	1.04484
$667$	− 2.95911e18i	− 1.30120i
$668$	− 5.48699e18i	− 2.38939i
$669$	−6.75448e17	−0.291288
$670$	0	0
$671$	1.37246e18	0.580502
$672$	− 3.01312e18i	− 1.26216i
$673$	− 3.60071e18i	− 1.49379i	−0.664940	−	0.746897i	$-0.731543\pi$
$673$	− 3.60071e18i	− 1.49379i	0.664940	−	0.746897i	$-0.268457\pi$
$674$	−2.67273e18	−1.09816
$675$	0	0
$676$	−5.53173e18	−2.22950
$677$	− 1.46169e17i	− 0.0583484i	−0.999574	−	0.0291742i	$-0.990712\pi$
$677$	− 1.46169e17i	− 0.0583484i	0.999574	−	0.0291742i	$-0.00928776\pi$
$678$	2.08225e18i	0.823267i
$679$	−1.61157e18	−0.631097
$680$	0	0
$681$	−2.81720e17	−0.108233
$682$	4.90882e17i	0.186801i
$683$	− 2.32270e18i	− 0.875505i	−0.899095	−	0.437753i	$-0.855775\pi$
$683$	− 2.32270e18i	− 0.875505i	0.899095	−	0.437753i	$-0.144225\pi$
$684$	−4.82558e17	−0.180171
$685$	0	0
$686$	5.43883e18	1.99250
$687$	1.82076e18i	0.660747i
$688$	5.19946e17i	0.186910i
$689$	9.61786e17	0.342494
$690$	0	0
$691$	−6.92473e16	−0.0241989	−0.0120994	−	0.999927i	$-0.503851\pi$
$691$	−6.92473e16	−0.0241989	−0.0120994	+	0.999927i	$0.503851\pi$
$692$	− 9.37900e18i	− 3.24688i
$693$	− 8.52769e17i	− 0.292459i
$694$	−6.82350e17	−0.231831
$695$	0	0
$696$	−3.86206e18	−1.28783
$697$	− 3.77493e17i	− 0.124709i
$698$	9.70378e18i	3.17600i
$699$	−1.17618e17	−0.0381393
$700$	0	0
$701$	−6.22383e16	−0.0198103	−0.00990514	−	0.999951i	$-0.503153\pi$
$701$	−6.22383e16	−0.0198103	−0.00990514	+	0.999951i	$0.503153\pi$
$702$	2.25434e18i	0.710931i
$703$	1.75928e17i	0.0549700i
$704$	8.02507e18	2.48443
$705$	0	0
$706$	−8.53637e17	−0.259443
$707$	− 3.23169e18i	− 0.973202i
$708$	7.27757e18i	2.17155i
$709$	−2.94114e18	−0.869592	−0.434796	−	0.900529i	$-0.643180\pi$
$709$	−2.94114e18	−0.869592	−0.434796	+	0.900529i	$0.643180\pi$
$710$	0	0
$711$	8.77187e17	0.254648
$712$	2.20182e19i	6.33377i
$713$	9.45766e17i	0.269589i
$714$	1.77417e18	0.501136
$715$	0	0
$716$	−5.43134e18	−1.50651
$717$	2.74220e18i	0.753744i
$718$	− 1.00748e19i	− 2.74429i
$719$	−4.39694e18	−1.18690	−0.593448	−	0.804872i	$-0.702234\pi$
$719$	−4.39694e18	−1.18690	−0.593448	+	0.804872i	$0.702234\pi$
$720$	0	0
$721$	−3.47708e18	−0.921797
$722$	7.36143e18i	1.93406i
$723$	− 1.62598e18i	− 0.423367i
$724$	−1.23816e19	−3.19505
$725$	0	0
$726$	2.35777e18	0.597604
$727$	− 6.21513e18i	− 1.56126i	−0.624991	−	0.780632i	$-0.714897\pi$
$727$	− 6.21513e18i	− 1.56126i	0.624991	−	0.780632i	$-0.285103\pi$
$728$	4.06428e18i	1.01188i
$729$	−1.33103e17	−0.0328442
$730$	0	0
$731$	−1.68992e17	−0.0409641
$732$	− 5.37855e18i	− 1.29224i
$733$	− 1.54714e18i	− 0.368429i	−0.982886	−	0.184215i	$-0.941026\pi$
$733$	− 1.54714e18i	− 0.368429i	0.982886	−	0.184215i	$-0.0589742\pi$
$734$	6.13738e18	1.44863
$735$	0	0
$736$	2.96161e19	6.86786
$737$	1.12632e18i	0.258895i
$738$	9.65881e17i	0.220068i
$739$	1.96669e18	0.444167	0.222084	−	0.975028i	$-0.428714\pi$
$739$	1.96669e18	0.444167	0.222084	+	0.975028i	$0.428714\pi$
$740$	0	0
$741$	−7.45929e16	−0.0165531
$742$	4.37614e18i	0.962644i
$743$	− 5.66492e18i	− 1.23528i	−0.786460	−	0.617641i	$-0.788088\pi$
$743$	− 5.66492e18i	− 1.23528i	0.786460	−	0.617641i	$-0.211912\pi$
$744$	1.23436e18	0.266819
$745$	0	0
$746$	−3.78140e18	−0.803249
$747$	2.54570e18i	0.536071i
$748$	6.66327e18i	1.39100i
$749$	−8.02337e16	−0.0166045
$750$	0	0
$751$	4.65838e18	0.947491	0.473745	−	0.880662i	$-0.342902\pi$
$751$	4.65838e18	0.947491	0.473745	+	0.880662i	$0.342902\pi$
$752$	− 7.65667e18i	− 1.54392i
$753$	− 2.00658e18i	− 0.401133i
$754$	3.58457e18	0.710434
$755$	0	0
$756$	−7.55127e18	−1.47105
$757$	3.51348e18i	0.678602i	0.940678	+	0.339301i	$0.110190\pi$
$757$	3.51348e18i	0.678602i	−0.940678	+	0.339301i	$0.889810\pi$
$758$	− 3.35447e18i	− 0.642354i
$759$	−2.17557e18	−0.413049
$760$	0	0
$761$	4.55489e18	0.850116	0.425058	−	0.905166i	$-0.360254\pi$
$761$	4.55489e18	0.850116	0.425058	+	0.905166i	$0.360254\pi$
$762$	3.06228e18i	0.566679i
$763$	− 2.21413e18i	− 0.406250i
$764$	5.85286e16	0.0106478
$765$	0	0
$766$	−1.82232e19	−3.25941
$767$	− 4.33414e18i	− 0.768658i
$768$	− 9.86252e18i	− 1.73436i
$769$	−5.81779e18	−1.01446	−0.507232	−	0.861810i	$-0.669331\pi$
$769$	−5.81779e18	−1.01446	−0.507232	+	0.861810i	$0.669331\pi$
$770$	0	0
$771$	4.09513e17	0.0702124
$772$	− 2.52598e19i	− 4.29455i
$773$	− 3.52257e18i	− 0.593871i	−0.954897	−	0.296936i	$-0.904035\pi$
$773$	− 3.52257e18i	− 0.593871i	0.954897	−	0.296936i	$-0.0959647\pi$
$774$	4.32396e17	0.0722878
$775$	0	0
$776$	−2.06737e19	−3.39873
$777$	1.21838e18i	0.198631i
$778$	1.60641e19i	2.59710i
$779$	−7.22147e16	−0.0115780
$780$	0	0
$781$	−5.26023e18	−0.829417
$782$	1.74383e19i	2.72685i
$783$	4.27339e18i	0.662706i
$784$	1.50977e19	2.32197
$785$	0	0
$786$	7.86929e18	1.19039
$787$	− 1.48350e18i	− 0.222562i	−0.993789	−	0.111281i	$-0.964505\pi$
$787$	− 1.48350e18i	− 0.222562i	0.993789	−	0.111281i	$-0.0354953\pi$
$788$	1.80630e19i	2.68763i
$789$	−3.67912e18	−0.542929
$790$	0	0
$791$	4.15386e18	0.602982
$792$	− 1.09396e19i	− 1.57502i
$793$	3.20318e18i	0.457411i
$794$	−1.26874e18	−0.179697
$795$	0	0
$796$	−6.79153e18	−0.946309
$797$	− 3.72381e18i	− 0.514645i	−0.966326	−	0.257323i	$-0.917160\pi$
$797$	− 3.72381e18i	− 0.514645i	0.966326	−	0.257323i	$-0.0828403\pi$
$798$	− 3.39399e17i	− 0.0465256i
$799$	2.48856e18	0.338372
$800$	0	0
$801$	1.07823e19	1.44245
$802$	− 1.87851e19i	− 2.49275i
$803$	− 6.86680e18i	− 0.903865i
$804$	4.41396e18	0.576320
$805$	0	0
$806$	−1.14567e18	−0.147191
$807$	− 6.29794e17i	− 0.0802639i
$808$	− 4.14570e19i	− 5.24112i
$809$	1.30799e19	1.64036	0.820181	−	0.572104i	$-0.193873\pi$
$809$	1.30799e19	1.64036	0.820181	+	0.572104i	$0.193873\pi$
$810$	0	0
$811$	−4.17968e18	−0.515832	−0.257916	−	0.966167i	$-0.583036\pi$
$811$	−4.17968e18	−0.515832	−0.257916	+	0.966167i	$0.583036\pi$
$812$	1.20071e19i	1.47002i
$813$	− 9.18274e17i	− 0.111528i
$814$	−6.21566e18	−0.748908
$815$	0	0
$816$	1.34020e19	1.58922
$817$	3.23283e16i	0.00380312i
$818$	1.05757e19i	1.23428i
$819$	1.99028e18	0.230445
$820$	0	0
$821$	5.28864e18	0.602717	0.301358	−	0.953511i	$-0.402560\pi$
$821$	5.28864e18	0.602717	0.301358	+	0.953511i	$0.402560\pi$
$822$	− 1.02067e19i	− 1.15403i
$823$	7.96616e18i	0.893614i	0.894630	+	0.446807i	$0.147439\pi$
$823$	7.96616e18i	0.893614i	−0.894630	+	0.446807i	$0.852561\pi$
$824$	−4.46049e19	−4.96428
$825$	0	0
$826$	1.97204e19	2.16046
$827$	1.49178e19i	1.62150i	0.585389	+	0.810752i	$0.300942\pi$
$827$	1.49178e19i	1.62150i	−0.585389	+	0.810752i	$0.699058\pi$
$828$	− 3.28479e19i	− 3.54251i
$829$	8.50781e18	0.910360	0.455180	−	0.890399i	$-0.349575\pi$
$829$	8.50781e18	0.910360	0.455180	+	0.890399i	$0.349575\pi$
$830$	0	0
$831$	3.96308e17	0.0417471
$832$	1.87297e19i	1.95763i
$833$	4.90704e18i	0.508894i
$834$	1.43937e19	1.48113
$835$	0	0
$836$	1.27469e18	0.129141
$837$	− 1.36582e18i	− 0.137303i
$838$	2.15921e19i	2.15382i
$839$	6.82788e18	0.675823	0.337912	−	0.941178i	$-0.390280\pi$
$839$	6.82788e18	0.675823	0.337912	+	0.941178i	$0.390280\pi$
$840$	0	0
$841$	−3.46561e18	−0.337758
$842$	2.10593e19i	2.03664i
$843$	− 1.26527e18i	− 0.121424i
$844$	2.87130e19	2.73434
$845$	0	0
$846$	−6.36741e18	−0.597112
$847$	− 4.70348e18i	− 0.437701i
$848$	3.30573e19i	3.05277i
$849$	4.97315e18	0.455755
$850$	0	0
$851$	−1.19755e19	−1.08082
$852$	2.06144e19i	1.84634i
$853$	6.17395e18i	0.548775i	0.961619	+	0.274387i	$0.0884751\pi$
$853$	6.17395e18i	0.548775i	−0.961619	+	0.274387i	$0.911525\pi$
$854$	−1.45745e19	−1.28564
$855$	0	0
$856$	−1.02926e18	−0.0894224
$857$	− 1.69937e18i	− 0.146525i	−0.997313	−	0.0732625i	$-0.976659\pi$
$857$	− 1.69937e18i	− 0.146525i	0.997313	−	0.0732625i	$-0.0233411\pi$
$858$	− 2.63542e18i	− 0.225518i
$859$	−3.92966e18	−0.333734	−0.166867	−	0.985979i	$-0.553365\pi$
$859$	−3.92966e18	−0.333734	−0.166867	+	0.985979i	$0.553365\pi$
$860$	0	0
$861$	−5.00118e17	−0.0418362
$862$	5.61118e18i	0.465862i
$863$	6.77611e18i	0.558354i	0.960240	+	0.279177i	$0.0900617\pi$
$863$	6.77611e18i	0.558354i	−0.960240	+	0.279177i	$0.909938\pi$
$864$	−4.27699e19	−3.49783
$865$	0	0
$866$	2.20006e18	0.177243
$867$	− 1.32125e18i	− 0.105648i
$868$	− 3.83761e18i	− 0.304567i
$869$	−2.31711e18	−0.182523
$870$	0	0
$871$	−2.62872e18	−0.203998
$872$	− 2.84035e19i	− 2.18783i
$873$	1.01239e19i	0.774026i
$874$	3.33597e18	0.253161
$875$	0	0
$876$	−2.69104e19	−2.01207
$877$	− 1.66517e19i	− 1.23583i	−0.786243	−	0.617917i	$-0.787977\pi$
$877$	− 1.66517e19i	− 1.23583i	0.786243	−	0.617917i	$-0.212023\pi$
$878$	− 4.56183e19i	− 3.36066i
$879$	−4.47855e18	−0.327499
$880$	0	0
$881$	1.72426e19	1.24239	0.621195	−	0.783656i	$-0.286647\pi$
$881$	1.72426e19	1.24239	0.621195	+	0.783656i	$0.286647\pi$
$882$	− 1.25555e19i	− 0.898024i
$883$	3.03788e18i	0.215688i	0.994168	+	0.107844i	$0.0343947\pi$
$883$	3.03788e18i	0.215688i	−0.994168	+	0.107844i	$0.965605\pi$
$884$	−1.55514e19	−1.09605
$885$	0	0
$886$	2.71099e19	1.88282
$887$	− 6.51405e18i	− 0.449105i	−0.974462	−	0.224552i	$-0.927908\pi$
$887$	− 6.51405e18i	− 0.449105i	0.974462	−	0.224552i	$-0.0720920\pi$
$888$	1.56297e19i	1.06971i
$889$	6.10889e18	0.415050
$890$	0	0
$891$	−3.60573e18	−0.241428
$892$	2.69389e19i	1.79064i
$893$	− 4.76063e17i	− 0.0314145i
$894$	−6.21740e18	−0.407301
$895$	0	0
$896$	−4.21568e19	−2.72186
$897$	− 5.07757e18i	− 0.325465i
$898$	− 1.59104e19i	− 1.01248i
$899$	−2.17177e18	−0.137207
$900$	0	0
$901$	−1.07442e19	−0.669059
$902$	− 2.55139e18i	− 0.157737i
$903$	2.23888e17i	0.0137423i
$904$	5.32868e19	3.24732
$905$	0	0
$906$	4.47680e18	0.268927
$907$	2.62324e19i	1.56455i	0.622931	+	0.782277i	$0.285942\pi$
$907$	2.62324e19i	1.56455i	−0.622931	+	0.782277i	$0.714058\pi$
$908$	1.12358e19i	0.665345i
$909$	−2.03015e19	−1.19361
$910$	0	0
$911$	−9.93847e18	−0.576037	−0.288018	−	0.957625i	$-0.592996\pi$
$911$	−9.93847e18	−0.576037	−0.288018	+	0.957625i	$0.592996\pi$
$912$	− 2.56381e18i	− 0.147543i
$913$	− 6.72450e18i	− 0.384238i
$914$	1.72453e19	0.978411
$915$	0	0
$916$	7.26176e19	4.06182
$917$	− 1.56983e19i	− 0.871872i
$918$	− 2.51835e19i	− 1.38880i
$919$	−1.61779e19	−0.885874	−0.442937	−	0.896553i	$-0.646063\pi$
$919$	−1.61779e19	−0.885874	−0.442937	+	0.896553i	$0.646063\pi$
$920$	0	0
$921$	−9.94953e18	−0.537174
$922$	− 3.66778e19i	− 1.96631i
$923$	− 1.22768e19i	− 0.653545i
$924$	8.82776e18	0.466641
$925$	0	0
$926$	−4.31419e19	−2.24868
$927$	2.18430e19i	1.13056i
$928$	6.80074e19i	3.49538i
$929$	−2.14431e18	−0.109442	−0.0547211	−	0.998502i	$-0.517427\pi$
$929$	−2.14431e18	−0.109442	−0.0547211	+	0.998502i	$0.517427\pi$
$930$	0	0
$931$	9.38720e17	0.0472458
$932$	4.69097e18i	0.234455i
$933$	1.51376e18i	0.0751325i
$934$	−6.24514e19	−3.07813
$935$	0	0
$936$	2.55318e19	1.24105
$937$	3.39502e19i	1.63883i	0.573199	+	0.819417i	$0.305702\pi$
$937$	3.39502e19i	1.63883i	−0.573199	+	0.819417i	$0.694298\pi$
$938$	− 1.19607e19i	− 0.573376i
$939$	5.96521e18	0.283988
$940$	0	0
$941$	−1.95970e19	−0.920149	−0.460074	−	0.887880i	$-0.652177\pi$
$941$	−1.95970e19	−0.920149	−0.460074	+	0.887880i	$0.652177\pi$
$942$	− 1.83527e19i	− 0.855794i
$943$	− 4.91568e18i	− 0.227645i
$944$	1.48968e20	6.85131
$945$	0	0
$946$	−1.14218e18	−0.0518134
$947$	1.67818e19i	0.756072i	0.925791	+	0.378036i	$0.123400\pi$
$947$	1.67818e19i	0.756072i	−0.925791	+	0.378036i	$0.876600\pi$
$948$	9.08054e18i	0.406310i
$949$	1.60264e19	0.712207
$950$	0	0
$951$	9.43831e18	0.413734
$952$	− 4.54026e19i	− 1.97670i
$953$	9.68702e18i	0.418877i	0.977822	+	0.209438i	$0.0671636\pi$
$953$	9.68702e18i	0.418877i	−0.977822	+	0.209438i	$0.932836\pi$
$954$	2.74910e19	1.18066
$955$	0	0
$956$	1.09367e20	4.63351
$957$	− 4.99577e18i	− 0.210221i
$958$	− 2.71445e19i	− 1.13450i
$959$	−2.03611e19	−0.845241
$960$	0	0
$961$	−2.37234e19	−0.971573
$962$	− 1.45067e19i	− 0.590108i
$963$	5.04029e17i	0.0203650i
$964$	−6.48492e19	−2.60258
$965$	0	0
$966$	2.31030e19	0.914781
$967$	− 2.34907e18i	− 0.0923899i	−0.998932	−	0.0461949i	$-0.985290\pi$
$967$	− 2.34907e18i	− 0.0923899i	0.998932	−	0.0461949i	$-0.0147095\pi$
$968$	− 6.03376e19i	− 2.35721i
$969$	8.33287e17	0.0323363
$970$	0	0
$971$	2.00271e19	0.766818	0.383409	−	0.923579i	$-0.374750\pi$
$971$	2.00271e19	0.766818	0.383409	+	0.923579i	$0.374750\pi$
$972$	7.38803e19i	2.80995i
$973$	− 2.87138e19i	− 1.08482i
$974$	−3.72349e19	−1.39739
$975$	0	0
$976$	−1.10096e20	−4.07706
$977$	− 3.98189e19i	− 1.46479i	−0.680881	−	0.732394i	$-0.738403\pi$
$977$	− 3.98189e19i	− 1.46479i	0.680881	−	0.732394i	$-0.261597\pi$
$978$	− 9.18473e18i	− 0.335633i
$979$	−2.84817e19	−1.03390
$980$	0	0
$981$	−1.39092e19	−0.498257
$982$	− 4.60760e19i	− 1.63965i
$983$	2.29985e19i	0.813022i	0.913646	+	0.406511i	$0.133255\pi$
$983$	2.29985e19i	0.813022i	−0.913646	+	0.406511i	$0.866745\pi$
$984$	−6.41566e18	−0.225306
$985$	0	0
$986$	−4.00437e19	−1.38782
$987$	− 3.29695e18i	− 0.113514i
$988$	2.97499e18i	0.101757i
$989$	−2.20060e18	−0.0747765
$990$	0	0
$991$	8.09114e18	0.271351	0.135675	−	0.990753i	$-0.456680\pi$
$991$	8.09114e18	0.271351	0.135675	+	0.990753i	$0.456680\pi$
$992$	− 2.17360e19i	− 0.724191i
$993$	− 8.07642e18i	− 0.267331i
$994$	5.58598e19	1.83691
$995$	0	0
$996$	−2.63527e19	−0.855342
$997$	2.26704e19i	0.731039i	0.930804	+	0.365519i	$0.119109\pi$
$997$	2.26704e19i	0.731039i	−0.930804	+	0.365519i	$0.880891\pi$
$998$	6.82883e19i	2.18775i
$999$	1.72944e19	0.550464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.14.b.b.24.1		6
5.2	odd	4		5.14.a.b.1.3	✓	3
5.3	odd	4		25.14.a.b.1.1		3
5.4	even	2	inner	25.14.b.b.24.6		6
15.2	even	4		45.14.a.e.1.1		3
20.7	even	4		80.14.a.g.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.14.a.b.1.3	✓	3	5.2	odd	4
25.14.a.b.1.1		3	5.3	odd	4
25.14.b.b.24.1		6	1.1	even	1	trivial
25.14.b.b.24.6		6	5.4	even	2	inner
45.14.a.e.1.1		3	15.2	even	4
80.14.a.g.1.2		3	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-176.217i q^{2} -573.185i q^{3} -22860.4 q^{4} -101005. q^{6} +201493. i q^{7} +2.58481e6i q^{8} +1.26578e6 q^{9} -3.34359e6 q^{11} +1.31032e7i q^{12} -7.80359e6i q^{13} +3.55065e7 q^{14} +2.68215e8 q^{16} +8.71750e7i q^{17} -2.23052e8i q^{18} +1.66766e7 q^{19} +1.15493e8 q^{21} +5.89196e8i q^{22} +1.13518e9i q^{23} +1.48158e9 q^{24} -1.37512e9 q^{26} -1.63937e9i q^{27} -4.60620e9i q^{28} -2.60673e9 q^{29} +8.33139e8 q^{31} -2.60892e10i q^{32} +1.91649e9i q^{33} +1.53617e10 q^{34} -2.89362e10 q^{36} +1.05494e10i q^{37} -2.93870e9i q^{38} -4.47290e9 q^{39} -4.33030e9 q^{41} -2.03518e10i q^{42} +1.93854e9i q^{43} +7.64356e10 q^{44} +2.00038e11 q^{46} -2.85468e10i q^{47} -1.53737e11i q^{48} +5.62896e10 q^{49} +4.99674e10 q^{51} +1.78393e11i q^{52} +1.23249e11i q^{53} -2.88884e11 q^{54} -5.20821e11 q^{56} -9.55879e9i q^{57} +4.59349e11i q^{58} +5.55404e11 q^{59} -4.10476e11 q^{61} -1.46813e11i q^{62} +2.55046e11i q^{63} -2.40014e12 q^{64} +3.37718e11 q^{66} -3.36861e11i q^{67} -1.99285e12i q^{68} +6.50671e11 q^{69} +1.57323e12 q^{71} +3.27181e12i q^{72} +2.05372e12i q^{73} +1.85898e12 q^{74} -3.81234e11 q^{76} -6.73709e11i q^{77} +7.88201e11i q^{78} +6.93000e11 q^{79} +1.07840e12 q^{81} +7.63071e11i q^{82} +2.01116e12i q^{83} -2.64021e12 q^{84} +3.41604e11 q^{86} +1.49414e12i q^{87} -8.64253e12i q^{88} +8.51832e12 q^{89} +1.57237e12 q^{91} -2.59507e13i q^{92} -4.77543e11i q^{93} -5.03042e12 q^{94} -1.49540e13 q^{96} +7.99814e12i q^{97} -9.91916e12i q^{98} -4.23225e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 35752 q^{4} + 240752 q^{6} - 2572238 q^{9} - 13208008 q^{11} + 93125856 q^{14} + 399824416 q^{16} - 194982200 q^{19} + 876401472 q^{21} + 7780718400 q^{24} - 7493628088 q^{26} - 4472343700 q^{29}+ \cdots - 253574733016 q^{99}+O(q^{100}) \) 6 * q - 35752 * q^4 + 240752 * q^6 - 2572238 * q^9 - 13208008 * q^11 + 93125856 * q^14 + 399824416 * q^16 - 194982200 * q^19 + 876401472 * q^21 + 7780718400 * q^24 - 7493628088 * q^26 - 4472343700 * q^29 + 14965988752 * q^31 + 60472147976 * q^34 - 86723667704 * q^36 + 140377142144 * q^39 - 21505768868 * q^41 + 136791650336 * q^44 + 493656408672 * q^46 + 77913853258 * q^49 - 258739765888 * q^51 - 492243874400 * q^54 - 1045752902400 * q^56 + 110872847800 * q^59 + 992322785492 * q^61 - 6595130988672 * q^64 - 45767750336 * q^66 + 666758585664 * q^69 + 1043995756672 * q^71 + 4836647173016 * q^74 + 1243376100000 * q^76 - 5981273766400 * q^79 + 641098105526 * q^81 + 1628468261376 * q^84 + 4686627290192 * q^86 + 38846051916900 * q^89 - 13585044740368 * q^91 + 14007115751936 * q^94 - 4416662428928 * q^96 - 253574733016 * q^99

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