LMFDB - Embedded newform 50.18.b.d.49.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,18,Mod(49,50)] 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("50.49"); S:= CuspForms(chi, 18); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(50, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 18, names="a")

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 18 $
Character orbit:	$[\chi]$	$=$	50.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,-262144,0,669696] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$91.6110436723$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 41641x^{2} + 433472400 $ x^4 + 41641*x^2 + 433472400
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.3
Root			$-144.792i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.18.b.d.49.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+256.000i q^{2} -9311.53i q^{3} -65536.0 q^{4} +2.38375e6 q^{6} +2.48655e7i q^{7} -1.67772e7i q^{8} +4.24355e7 q^{9} -1.90392e8 q^{11} +6.10241e8i q^{12} -1.57377e7i q^{13} -6.36558e9 q^{14} +4.29497e9 q^{16} +2.25502e10i q^{17} +1.08635e10i q^{18} -1.27984e11 q^{19} +2.31536e11 q^{21} -4.87405e10i q^{22} +2.59325e11i q^{23} -1.56222e11 q^{24} +4.02885e9 q^{26} -1.59763e12i q^{27} -1.62959e12i q^{28} +2.57953e12 q^{29} +7.91253e12 q^{31} +1.09951e12i q^{32} +1.77285e12i q^{33} -5.77284e12 q^{34} -2.78105e12 q^{36} +2.09888e13i q^{37} -3.27638e13i q^{38} -1.46542e11 q^{39} +1.98123e13 q^{41} +5.92733e13i q^{42} -4.60777e13i q^{43} +1.24776e13 q^{44} -6.63871e13 q^{46} -2.66827e14i q^{47} -3.99927e13i q^{48} -3.85664e14 q^{49} +2.09977e14 q^{51} +1.03139e12i q^{52} +4.00045e14i q^{53} +4.08994e14 q^{54} +4.17174e14 q^{56} +1.19172e15i q^{57} +6.60360e14i q^{58} -1.82611e15 q^{59} -1.48236e15 q^{61} +2.02561e15i q^{62} +1.05518e15i q^{63} -2.81475e14 q^{64} -4.53849e14 q^{66} +2.71410e15i q^{67} -1.47785e15i q^{68} +2.41471e15 q^{69} -3.87337e15 q^{71} -7.11949e14i q^{72} -2.85786e15i q^{73} -5.37314e15 q^{74} +8.38753e15 q^{76} -4.73421e15i q^{77} -3.75148e13i q^{78} -2.80988e15 q^{79} -9.39628e15 q^{81} +5.07194e15i q^{82} -7.04230e15i q^{83} -1.51740e16 q^{84} +1.17959e16 q^{86} -2.40194e16i q^{87} +3.19426e15i q^{88} -5.51966e16 q^{89} +3.91327e14 q^{91} -1.69951e16i q^{92} -7.36778e16i q^{93} +6.83076e16 q^{94} +1.02381e16 q^{96} -6.42662e16i q^{97} -9.87300e16i q^{98} -8.07940e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 262144 q^{4} + 669696 q^{6} + 215038188 q^{9} - 942962592 q^{11} + 309168128 q^{14} + 17179869184 q^{16} - 257345058800 q^{19} + 870762493248 q^{21} - 43889197056 q^{24} + 789419124736 q^{26} - 5086109499960 q^{29}+ \cdots - 52\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 262144 * q^4 + 669696 * q^6 + 215038188 * q^9 - 942962592 * q^11 + 309168128 * q^14 + 17179869184 * q^16 - 257345058800 * q^19 + 870762493248 * q^21 - 43889197056 * q^24 + 789419124736 * q^26 - 5086109499960 * q^29 + 15678815997488 * q^31 + 16455629088768 * q^34 - 14092742688768 * q^36 + 24135247074576 * q^39 - 75652728528312 * q^41 + 61797996429312 * q^44 - 332984247957504 * q^46 - 1603445169355908 * q^49 + 1295380982531088 * q^51 + 22095889551360 * q^54 - 20261642436608 * q^56 - 3055641434470320 * q^59 - 1263476426244232 * q^61 - 1125899906842624 * q^64 + 244151200161792 * q^66 - 1429906501577664 * q^69 - 6663803321824752 * q^71 - 14236267057948672 * q^74 + 16865365773516800 * q^76 - 16527213684110240 * q^79 - 26865367701318396 * q^81 - 57066290757500928 * q^84 - 15170792410548224 * q^86 - 111756825043809960 * q^89 - 76954793221206032 * q^91 + 113045290507266048 * q^94 + 2876322418262016 * q^96 - 52747342198192224 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$-1$

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 $

$2$	256.000i	0.707107i
$2$	256.000i	0.707107i
$3$	− 9311.53i	− 0.819390i	−0.912223	−	0.409695i	$-0.865635\pi$
$3$	− 9311.53i	− 0.819390i	0.912223	−	0.409695i	$-0.134365\pi$
$4$	−65536.0	−0.500000
$5$	0	0
$5$	0	0
$6$	2.38375e6	0.579396
$7$	2.48655e7i	1.63029i	0.579258	+	0.815144i	$0.303342\pi$
$7$	2.48655e7i	1.63029i	−0.579258	+	0.815144i	$0.696658\pi$
$8$	− 1.67772e7i	− 0.353553i
$9$	4.24355e7	0.328600
$10$	0	0
$11$	−1.90392e8	−0.267801	−0.133900	−	0.990995i	$-0.542750\pi$
$11$	−1.90392e8	−0.267801	−0.133900	+	0.990995i	$0.542750\pi$
$12$	6.10241e8i	0.409695i
$13$	− 1.57377e7i	− 0.00535085i	−0.999996	−	0.00267543i	$-0.999148\pi$
$13$	− 1.57377e7i	− 0.00535085i	0.999996	−	0.00267543i	$-0.000851616\pi$
$14$	−6.36558e9	−1.15279
$15$	0	0
$16$	4.29497e9	0.250000
$17$	2.25502e10i	0.784032i	0.919958	+	0.392016i	$0.128222\pi$
$17$	2.25502e10i	0.784032i	−0.919958	+	0.392016i	$0.871778\pi$
$18$	1.08635e10i	0.232355i
$19$	−1.27984e11	−1.72882	−0.864408	−	0.502791i	$-0.832306\pi$
$19$	−1.27984e11	−1.72882	−0.864408	+	0.502791i	$0.832306\pi$
$20$	0	0
$21$	2.31536e11	1.33584
$22$	− 4.87405e10i	− 0.189364i
$23$	2.59325e11i	0.690490i	0.938513	+	0.345245i	$0.112204\pi$
$23$	2.59325e11i	0.690490i	−0.938513	+	0.345245i	$0.887796\pi$
$24$	−1.56222e11	−0.289698
$25$	0	0
$26$	4.02885e9	0.00378363
$27$	− 1.59763e12i	− 1.08864i
$28$	− 1.62959e12i	− 0.815144i
$29$	2.57953e12	0.957542	0.478771	−	0.877940i	$-0.341082\pi$
$29$	2.57953e12	0.957542	0.478771	+	0.877940i	$0.341082\pi$
$30$	0	0
$31$	7.91253e12	1.66625	0.833126	−	0.553083i	$-0.186549\pi$
$31$	7.91253e12	1.66625	0.833126	+	0.553083i	$0.186549\pi$
$32$	1.09951e12i	0.176777i
$33$	1.77285e12i	0.219433i
$34$	−5.77284e12	−0.554395
$35$	0	0
$36$	−2.78105e12	−0.164300
$37$	2.09888e13i	0.982367i	0.871056	+	0.491184i	$0.163436\pi$
$37$	2.09888e13i	0.982367i	−0.871056	+	0.491184i	$0.836564\pi$
$38$	− 3.27638e13i	− 1.22246i
$39$	−1.46542e11	−0.00438444
$40$	0	0
$41$	1.98123e13	0.387499	0.193750	−	0.981051i	$-0.437935\pi$
$41$	1.98123e13	0.387499	0.193750	+	0.981051i	$0.437935\pi$
$42$	5.92733e13i	0.944583i
$43$	− 4.60777e13i	− 0.601186i	−0.953753	−	0.300593i	$-0.902815\pi$
$43$	− 4.60777e13i	− 0.601186i	0.953753	−	0.300593i	$-0.0971845\pi$
$44$	1.24776e13	0.133900
$45$	0	0
$46$	−6.63871e13	−0.488250
$47$	− 2.66827e14i	− 1.63455i	−0.576250	−	0.817274i	$-0.695484\pi$
$47$	− 2.66827e14i	− 1.63455i	0.576250	−	0.817274i	$-0.304516\pi$
$48$	− 3.99927e13i	− 0.204847i
$49$	−3.85664e14	−1.65784
$50$	0	0
$51$	2.09977e14	0.642428
$52$	1.03139e12i	0.00267543i
$53$	4.00045e14i	0.882599i	0.897360	+	0.441300i	$0.145482\pi$
$53$	4.00045e14i	0.882599i	−0.897360	+	0.441300i	$0.854518\pi$
$54$	4.08994e14	0.769786
$55$	0	0
$56$	4.17174e14	0.576394
$57$	1.19172e15i	1.41657i
$58$	6.60360e14i	0.677084i
$59$	−1.82611e15	−1.61914	−0.809570	−	0.587024i	$-0.800299\pi$
$59$	−1.82611e15	−1.61914	−0.809570	+	0.587024i	$0.800299\pi$
$60$	0	0
$61$	−1.48236e15	−0.990035	−0.495017	−	0.868883i	$-0.664838\pi$
$61$	−1.48236e15	−0.990035	−0.495017	+	0.868883i	$0.664838\pi$
$62$	2.02561e15i	1.17822i
$63$	1.05518e15i	0.535713i
$64$	−2.81475e14	−0.125000
$65$	0	0
$66$	−4.53849e14	−0.155163
$67$	2.71410e15i	0.816563i	0.912856	+	0.408282i	$0.133872\pi$
$67$	2.71410e15i	0.816563i	−0.912856	+	0.408282i	$0.866128\pi$
$68$	− 1.47785e15i	− 0.392016i
$69$	2.41471e15	0.565780
$70$	0	0
$71$	−3.87337e15	−0.711858	−0.355929	−	0.934513i	$-0.615836\pi$
$71$	−3.87337e15	−0.711858	−0.355929	+	0.934513i	$0.615836\pi$
$72$	− 7.11949e14i	− 0.116178i
$73$	− 2.85786e15i	− 0.414759i	−0.978261	−	0.207380i	$-0.933506\pi$
$73$	− 2.85786e15i	− 0.414759i	0.978261	−	0.207380i	$-0.0664935\pi$
$74$	−5.37314e15	−0.694638
$75$	0	0
$76$	8.38753e15	0.864408
$77$	− 4.73421e15i	− 0.436593i
$78$	− 3.75148e13i	− 0.00310026i
$79$	−2.80988e15	−0.208381	−0.104190	−	0.994557i	$-0.533225\pi$
$79$	−2.80988e15	−0.208381	−0.104190	+	0.994557i	$0.533225\pi$
$80$	0	0
$81$	−9.39628e15	−0.563422
$82$	5.07194e15i	0.274003i
$83$	− 7.04230e15i	− 0.343203i	−0.985166	−	0.171601i	$-0.945106\pi$
$83$	− 7.04230e15i	− 0.343203i	0.985166	−	0.171601i	$-0.0548941\pi$
$84$	−1.51740e16	−0.667921
$85$	0	0
$86$	1.17959e16	0.425103
$87$	− 2.40194e16i	− 0.784600i
$88$	3.19426e15i	0.0946819i
$89$	−5.51966e16	−1.48627	−0.743135	−	0.669142i	$-0.766662\pi$
$89$	−5.51966e16	−1.48627	−0.743135	+	0.669142i	$0.766662\pi$
$90$	0	0
$91$	3.91327e14	0.00872343
$92$	− 1.69951e16i	− 0.345245i
$93$	− 7.36778e16i	− 1.36531i
$94$	6.83076e16	1.15580
$95$	0	0
$96$	1.02381e16	0.144849
$97$	− 6.42662e16i	− 0.832574i	−0.909233	−	0.416287i	$-0.863331\pi$
$97$	− 6.42662e16i	− 0.832574i	0.909233	−	0.416287i	$-0.136669\pi$
$98$	− 9.87300e16i	− 1.17227i
$99$	−8.07940e15	−0.0879994
$100$	0	0
$101$	−1.56405e17	−1.43721	−0.718603	−	0.695421i	$-0.755218\pi$
$101$	−1.56405e17	−1.43721	−0.718603	+	0.695421i	$0.755218\pi$
$102$	5.37540e16i	0.454265i
$103$	− 2.33166e17i	− 1.81363i	−0.421527	−	0.906816i	$-0.638506\pi$
$103$	− 2.33166e17i	− 1.81363i	0.421527	−	0.906816i	$-0.361494\pi$
$104$	−2.64035e14	−0.00189181
$105$	0	0
$106$	−1.02411e17	−0.624092
$107$	1.05397e17i	0.593017i	0.955030	+	0.296509i	$0.0958224\pi$
$107$	1.05397e17i	0.593017i	−0.955030	+	0.296509i	$0.904178\pi$
$108$	1.04702e17i	0.544321i
$109$	−2.51895e17	−1.21086	−0.605431	−	0.795898i	$-0.706999\pi$
$109$	−2.51895e17	−1.21086	−0.605431	+	0.795898i	$0.706999\pi$
$110$	0	0
$111$	1.95438e17	0.804942
$112$	1.06797e17i	0.407572i
$113$	4.09395e17i	1.44869i	0.689436	+	0.724346i	$0.257858\pi$
$113$	4.09395e17i	1.44869i	−0.689436	+	0.724346i	$0.742142\pi$
$114$	−3.05081e17	−1.00167
$115$	0	0
$116$	−1.69052e17	−0.478771
$117$	− 6.67838e14i	− 0.00175829i
$118$	− 4.67483e17i	− 1.14490i
$119$	−5.60722e17	−1.27820
$120$	0	0
$121$	−4.69198e17	−0.928283
$122$	− 3.79484e17i	− 0.700060i
$123$	− 1.84482e17i	− 0.317513i
$124$	−5.18555e17	−0.833126
$125$	0	0
$126$	−2.70126e17	−0.378806
$127$	6.42410e17i	0.842327i	0.906985	+	0.421164i	$0.138378\pi$
$127$	6.42410e17i	0.842327i	−0.906985	+	0.421164i	$0.861622\pi$
$128$	− 7.20576e16i	− 0.0883883i
$129$	−4.29054e17	−0.492606
$130$	0	0
$131$	3.57323e17	0.359961	0.179980	−	0.983670i	$-0.442397\pi$
$131$	3.57323e17	0.359961	0.179980	+	0.983670i	$0.442397\pi$
$132$	− 1.16185e17i	− 0.109717i
$133$	− 3.18238e18i	− 2.81847i
$134$	−6.94809e17	−0.577397
$135$	0	0
$136$	3.78329e17	0.277197
$137$	1.23821e18i	0.852454i	0.904616	+	0.426227i	$0.140158\pi$
$137$	1.23821e18i	0.852454i	−0.904616	+	0.426227i	$0.859842\pi$
$138$	6.18166e17i	0.400067i
$139$	−1.95129e18	−1.18767	−0.593836	−	0.804586i	$-0.702387\pi$
$139$	−1.95129e18	−1.18767	−0.593836	+	0.804586i	$0.702387\pi$
$140$	0	0
$141$	−2.48457e18	−1.33933
$142$	− 9.91584e17i	− 0.503360i
$143$	2.99634e15i	0.00143296i
$144$	1.82259e17	0.0821501
$145$	0	0
$146$	7.31611e17	0.293279
$147$	3.59112e18i	1.35842i
$148$	− 1.37552e18i	− 0.491184i
$149$	−1.86793e18	−0.629908	−0.314954	−	0.949107i	$-0.601989\pi$
$149$	−1.86793e18	−0.629908	−0.314954	+	0.949107i	$0.601989\pi$
$150$	0	0
$151$	5.18884e18	1.56231	0.781154	−	0.624339i	$-0.214632\pi$
$151$	5.18884e18	1.56231	0.781154	+	0.624339i	$0.214632\pi$
$152$	2.14721e18i	0.611229i
$153$	9.56927e17i	0.257633i
$154$	1.21196e18	0.308718
$155$	0	0
$156$	9.60379e15	0.00219222
$157$	− 7.78987e18i	− 1.68416i	−0.539353	−	0.842080i	$-0.681331\pi$
$157$	− 7.78987e18i	− 1.68416i	0.539353	−	0.842080i	$-0.318669\pi$
$158$	− 7.19330e17i	− 0.147347i
$159$	3.72503e18	0.723193
$160$	0	0
$161$	−6.44825e18	−1.12570
$162$	− 2.40545e18i	− 0.398399i
$163$	6.16891e18i	0.969647i	0.874612	+	0.484824i	$0.161116\pi$
$163$	6.16891e18i	0.969647i	−0.874612	+	0.484824i	$0.838884\pi$
$164$	−1.29842e18	−0.193750
$165$	0	0
$166$	1.80283e18	0.242681
$167$	− 1.24726e19i	− 1.59539i	−0.603064	−	0.797693i	$-0.706054\pi$
$167$	− 1.24726e19i	− 1.59539i	0.603064	−	0.797693i	$-0.293946\pi$
$168$	− 3.88453e18i	− 0.472291i
$169$	8.65017e18	0.999971
$170$	0	0
$171$	−5.43105e18	−0.568089
$172$	3.01975e18i	0.300593i
$173$	1.64494e19i	1.55869i	0.626596	+	0.779344i	$0.284448\pi$
$173$	1.64494e19i	1.55869i	−0.626596	+	0.779344i	$0.715552\pi$
$174$	6.14896e18	0.554796
$175$	0	0
$176$	−8.17729e17	−0.0669502
$177$	1.70039e19i	1.32671i
$178$	− 1.41303e19i	− 1.05095i
$179$	1.53067e18	0.108550	0.0542751	−	0.998526i	$-0.482715\pi$
$179$	1.53067e18	0.108550	0.0542751	+	0.998526i	$0.482715\pi$
$180$	0	0
$181$	−8.51444e18	−0.549399	−0.274700	−	0.961530i	$-0.588578\pi$
$181$	−8.51444e18	−0.549399	−0.274700	+	0.961530i	$0.588578\pi$
$182$	1.00180e17i	0.00616840i
$183$	1.38031e19i	0.811224i
$184$	4.35075e18	0.244125
$185$	0	0
$186$	1.88615e19	0.965420
$187$	− 4.29338e18i	− 0.209965i
$188$	1.74868e19i	0.817274i
$189$	3.97260e19	1.77480
$190$	0	0
$191$	1.05921e19	0.432710	0.216355	−	0.976315i	$-0.430583\pi$
$191$	1.05921e19	0.432710	0.216355	+	0.976315i	$0.430583\pi$
$192$	2.62096e18i	0.102424i
$193$	− 1.55768e19i	− 0.582425i	−0.956658	−	0.291213i	$-0.905941\pi$
$193$	− 1.55768e19i	− 0.582425i	0.956658	−	0.291213i	$-0.0940587\pi$
$194$	1.64521e19	0.588719
$195$	0	0
$196$	2.52749e19	0.828920
$197$	− 8.47320e18i	− 0.266124i	−0.991108	−	0.133062i	$-0.957519\pi$
$197$	− 8.47320e18i	− 0.266124i	0.991108	−	0.133062i	$-0.0424810\pi$
$198$	− 2.06833e18i	− 0.0622250i
$199$	−9.48640e18	−0.273433	−0.136716	−	0.990610i	$-0.543655\pi$
$199$	−9.48640e18	−0.273433	−0.136716	+	0.990610i	$0.543655\pi$
$200$	0	0
$201$	2.52724e19	0.669083
$202$	− 4.00397e19i	− 1.01626i
$203$	6.41414e19i	1.56107i
$204$	−1.37610e19	−0.321214
$205$	0	0
$206$	5.96905e19	1.28243
$207$	1.10046e19i	0.226895i
$208$	− 6.75930e16i	− 0.00133771i
$209$	2.43671e19	0.462978
$210$	0	0
$211$	−5.06102e19	−0.886824	−0.443412	−	0.896318i	$-0.646232\pi$
$211$	−5.06102e19	−0.886824	−0.443412	+	0.896318i	$0.646232\pi$
$212$	− 2.62173e19i	− 0.441300i
$213$	3.60671e19i	0.583289i
$214$	−2.69817e19	−0.419327
$215$	0	0
$216$	−2.68038e19	−0.384893
$217$	1.96749e20i	2.71647i
$218$	− 6.44851e19i	− 0.856208i
$219$	−2.66110e19	−0.339849
$220$	0	0
$221$	3.54888e17	0.00419524
$222$	5.00322e19i	0.569180i
$223$	1.13017e20i	1.23752i	0.785581	+	0.618759i	$0.212364\pi$
$223$	1.13017e20i	1.23752i	−0.785581	+	0.618759i	$0.787636\pi$
$224$	−2.73399e19	−0.288197
$225$	0	0
$226$	−1.04805e20	−1.02438
$227$	− 1.34057e20i	− 1.26203i	−0.775770	−	0.631016i	$-0.782638\pi$
$227$	− 1.34057e20i	− 1.26203i	0.775770	−	0.631016i	$-0.217362\pi$
$228$	− 7.81008e19i	− 0.708287i
$229$	1.53092e20	1.33768	0.668840	−	0.743406i	$-0.266791\pi$
$229$	1.53092e20	1.33768	0.668840	+	0.743406i	$0.266791\pi$
$230$	0	0
$231$	−4.40828e19	−0.357740
$232$	− 4.32773e19i	− 0.338542i
$233$	1.54095e20i	1.16215i	0.813849	+	0.581076i	$0.197368\pi$
$233$	1.54095e20i	1.16215i	−0.813849	+	0.581076i	$0.802632\pi$
$234$	1.70966e17	0.00124330
$235$	0	0
$236$	1.19676e20	0.809570
$237$	2.61643e19i	0.170745i
$238$	− 1.43545e20i	− 0.903823i
$239$	−1.10626e20	−0.672161	−0.336081	−	0.941833i	$-0.609101\pi$
$239$	−1.10626e20	−0.672161	−0.336081	+	0.941833i	$0.609101\pi$
$240$	0	0
$241$	−1.68590e20	−0.954303	−0.477152	−	0.878821i	$-0.658331\pi$
$241$	−1.68590e20	−0.954303	−0.477152	+	0.878821i	$0.658331\pi$
$242$	− 1.20115e20i	− 0.656395i
$243$	− 1.18825e20i	− 0.626980i
$244$	9.71480e19	0.495017
$245$	0	0
$246$	4.72275e19	0.224516
$247$	2.01417e18i	0.00925064i
$248$	− 1.32750e20i	− 0.589109i
$249$	−6.55746e19	−0.281217
$250$	0	0
$251$	−8.71684e19	−0.349247	−0.174623	−	0.984635i	$-0.555871\pi$
$251$	−8.71684e19	−0.349247	−0.174623	+	0.984635i	$0.555871\pi$
$252$	− 6.91523e19i	− 0.267857i
$253$	− 4.93735e19i	− 0.184914i
$254$	−1.64457e20	−0.595615
$255$	0	0
$256$	1.84467e19	0.0625000
$257$	− 2.57989e20i	− 0.845610i	−0.906221	−	0.422805i	$-0.861046\pi$
$257$	− 2.57989e20i	− 0.845610i	0.906221	−	0.422805i	$-0.138954\pi$
$258$	− 1.09838e20i	− 0.348325i
$259$	−5.21899e20	−1.60154
$260$	0	0
$261$	1.09464e20	0.314648
$262$	9.14747e19i	0.254531i
$263$	− 4.12838e20i	− 1.11213i	−0.831139	−	0.556065i	$-0.812311\pi$
$263$	− 4.12838e20i	− 1.11213i	0.831139	−	0.556065i	$-0.187689\pi$
$264$	2.97434e19	0.0775814
$265$	0	0
$266$	8.14689e20	1.99296
$267$	5.13965e20i	1.21783i
$268$	− 1.77871e20i	− 0.408282i
$269$	−3.61622e20	−0.804194	−0.402097	−	0.915597i	$-0.631718\pi$
$269$	−3.61622e20	−0.804194	−0.402097	+	0.915597i	$0.631718\pi$
$270$	0	0
$271$	−6.61685e20	−1.38170	−0.690848	−	0.723000i	$-0.742762\pi$
$271$	−6.61685e20	−1.38170	−0.690848	+	0.723000i	$0.742762\pi$
$272$	9.68522e19i	0.196008i
$273$	− 3.64385e18i	− 0.00714789i
$274$	−3.16983e20	−0.602776
$275$	0	0
$276$	−1.58250e20	−0.282890
$277$	− 2.43700e20i	− 0.422452i	−0.977437	−	0.211226i	$-0.932254\pi$
$277$	− 2.43700e20i	− 0.422452i	0.977437	−	0.211226i	$-0.0677456\pi$
$278$	− 4.99531e20i	− 0.839812i
$279$	3.35772e20	0.547531
$280$	0	0
$281$	−9.47052e20	−1.45335	−0.726675	−	0.686981i	$-0.758935\pi$
$281$	−9.47052e20	−1.45335	−0.726675	+	0.686981i	$0.758935\pi$
$282$	− 6.36049e20i	− 0.947050i
$283$	− 3.67504e20i	− 0.530979i	−0.964114	−	0.265489i	$-0.914466\pi$
$283$	− 3.67504e20i	− 0.530979i	0.964114	−	0.265489i	$-0.0855335\pi$
$284$	2.53845e20	0.355929
$285$	0	0
$286$	−7.67064e17	−0.00101326
$287$	4.92642e20i	0.631736i
$288$	4.66583e19i	0.0580889i
$289$	3.18730e20	0.385293
$290$	0	0
$291$	−5.98417e20	−0.682203
$292$	1.87292e20i	0.207380i
$293$	1.20904e21i	1.30037i	0.759778	+	0.650183i	$0.225308\pi$
$293$	1.20904e21i	1.30037i	−0.759778	+	0.650183i	$0.774692\pi$
$294$	−9.19328e20	−0.960546
$295$	0	0
$296$	3.52134e20	0.347319
$297$	3.04177e20i	0.291539i
$298$	− 4.78190e20i	− 0.445412i
$299$	4.08118e18	0.00369471
$300$	0	0
$301$	1.14575e21	0.980106
$302$	1.32834e21i	1.10472i
$303$	1.45637e21i	1.17763i
$304$	−5.49685e20	−0.432204
$305$	0	0
$306$	−2.44973e20	−0.182174
$307$	4.76931e20i	0.344969i	0.985012	+	0.172484i	$0.0551794\pi$
$307$	4.76931e20i	0.344969i	−0.985012	+	0.172484i	$0.944821\pi$
$308$	3.10261e20i	0.218296i
$309$	−2.17114e21	−1.48607
$310$	0	0
$311$	3.50418e20	0.227051	0.113525	−	0.993535i	$-0.463786\pi$
$311$	3.50418e20	0.227051	0.113525	+	0.993535i	$0.463786\pi$
$312$	2.45857e18i	0.00155013i
$313$	2.04751e21i	1.25631i	0.778087	+	0.628157i	$0.216190\pi$
$313$	2.04751e21i	1.25631i	−0.778087	+	0.628157i	$0.783810\pi$
$314$	1.99421e21	1.19088
$315$	0	0
$316$	1.84148e20	0.104190
$317$	− 1.31663e21i	− 0.725205i	−0.931944	−	0.362602i	$-0.881888\pi$
$317$	− 1.31663e21i	− 0.725205i	0.931944	−	0.362602i	$-0.118112\pi$
$318$	9.53607e20i	0.511375i
$319$	−4.91123e20	−0.256430
$320$	0	0
$321$	9.81411e20	0.485912
$322$	− 1.65075e21i	− 0.795988i
$323$	− 2.88605e21i	− 1.35545i
$324$	6.15795e20	0.281711
$325$	0	0
$326$	−1.57924e21	−0.685644
$327$	2.34553e21i	0.992167i
$328$	− 3.32394e20i	− 0.137002i
$329$	6.63479e21	2.66478
$330$	0	0
$331$	3.85862e21	1.47195	0.735977	−	0.677007i	$-0.236723\pi$
$331$	3.85862e21	1.47195	0.735977	+	0.677007i	$0.236723\pi$
$332$	4.61524e20i	0.171601i
$333$	8.90672e20i	0.322806i
$334$	3.19298e21	1.12811
$335$	0	0
$336$	9.94441e20	0.333960
$337$	− 4.69149e21i	− 1.53623i	−0.640312	−	0.768115i	$-0.721195\pi$
$337$	− 4.69149e21i	− 1.53623i	0.640312	−	0.768115i	$-0.278805\pi$
$338$	2.21444e21i	0.707087i
$339$	3.81210e21	1.18704
$340$	0	0
$341$	−1.50649e21	−0.446224
$342$	− 1.39035e21i	− 0.401700i
$343$	− 3.80526e21i	− 1.07247i
$344$	−7.73055e20	−0.212551
$345$	0	0
$346$	−4.21106e21	−1.10216
$347$	− 2.51637e21i	− 0.642648i	−0.946969	−	0.321324i	$-0.895872\pi$
$347$	− 2.51637e21i	− 0.642648i	0.946969	−	0.321324i	$-0.104128\pi$
$348$	1.57413e21i	0.392300i
$349$	2.20222e21	0.535606	0.267803	−	0.963474i	$-0.413702\pi$
$349$	2.20222e21	0.535606	0.267803	+	0.963474i	$0.413702\pi$
$350$	0	0
$351$	−2.51431e19	−0.00582516
$352$	− 2.09339e20i	− 0.0473410i
$353$	1.30214e21i	0.287456i	0.989617	+	0.143728i	$0.0459091\pi$
$353$	1.30214e21i	0.287456i	−0.989617	+	0.143728i	$0.954091\pi$
$354$	−4.35299e21	−0.938123
$355$	0	0
$356$	3.61737e21	0.743135
$357$	5.22118e21i	1.04734i
$358$	3.91851e20i	0.0767566i
$359$	−2.07162e21	−0.396285	−0.198143	−	0.980173i	$-0.563491\pi$
$359$	−2.07162e21	−0.396285	−0.198143	+	0.980173i	$0.563491\pi$
$360$	0	0
$361$	1.08994e22	1.98880
$362$	− 2.17970e21i	− 0.388484i
$363$	4.36895e21i	0.760625i
$364$	−2.56460e19	−0.00436172
$365$	0	0
$366$	−3.53358e21	−0.573622
$367$	− 4.69137e21i	− 0.744111i	−0.928210	−	0.372056i	$-0.878653\pi$
$367$	− 4.69137e21i	− 0.744111i	0.928210	−	0.372056i	$-0.121347\pi$
$368$	1.11379e21i	0.172622i
$369$	8.40743e20	0.127332
$370$	0	0
$371$	−9.94732e21	−1.43889
$372$	4.82855e21i	0.682655i
$373$	− 7.77652e20i	− 0.107463i	−0.998555	−	0.0537317i	$-0.982888\pi$
$373$	− 7.77652e20i	− 0.107463i	0.998555	−	0.0537317i	$-0.0171116\pi$
$374$	1.09911e21	0.148467
$375$	0	0
$376$	−4.47661e21	−0.577900
$377$	− 4.05959e19i	− 0.00512367i
$378$	1.01699e22i	1.25497i
$379$	−3.50054e20	−0.0422379	−0.0211189	−	0.999777i	$-0.506723\pi$
$379$	−3.50054e20	−0.0422379	−0.0211189	+	0.999777i	$0.506723\pi$
$380$	0	0
$381$	5.98183e21	0.690194
$382$	2.71157e21i	0.305972i
$383$	− 1.02315e22i	− 1.12914i	−0.825385	−	0.564570i	$-0.809042\pi$
$383$	− 1.02315e22i	− 1.12914i	0.825385	−	0.564570i	$-0.190958\pi$
$384$	−6.70967e20	−0.0724245
$385$	0	0
$386$	3.98765e21	0.411837
$387$	− 1.95533e21i	− 0.197550i
$388$	4.21175e21i	0.416287i
$389$	4.13104e21	0.399473	0.199737	−	0.979850i	$-0.435991\pi$
$389$	4.13104e21	0.399473	0.199737	+	0.979850i	$0.435991\pi$
$390$	0	0
$391$	−5.84781e21	−0.541366
$392$	6.47037e21i	0.586135i
$393$	− 3.32723e21i	− 0.294948i
$394$	2.16914e21	0.188178
$395$	0	0
$396$	5.29491e20	0.0439997
$397$	7.65334e21i	0.622489i	0.950330	+	0.311244i	$0.100746\pi$
$397$	7.65334e21i	0.622489i	−0.950330	+	0.311244i	$0.899254\pi$
$398$	− 2.42852e21i	− 0.193346i
$399$	−2.96328e22	−2.30942
$400$	0	0
$401$	−4.08273e20	−0.0304947	−0.0152473	−	0.999884i	$-0.504854\pi$
$401$	−4.08273e20	−0.0304947	−0.0152473	+	0.999884i	$0.504854\pi$
$402$	6.46974e21i	0.473113i
$403$	− 1.24525e20i	− 0.00891588i
$404$	1.02502e22	0.718603
$405$	0	0
$406$	−1.64202e22	−1.10384
$407$	− 3.99612e21i	− 0.263079i
$408$	− 3.52282e21i	− 0.227133i
$409$	−2.00923e22	−1.26877	−0.634383	−	0.773019i	$-0.718746\pi$
$409$	−2.00923e22	−1.26877	−0.634383	+	0.773019i	$0.718746\pi$
$410$	0	0
$411$	1.15297e22	0.698493
$412$	1.52808e22i	0.906816i
$413$	− 4.54071e22i	− 2.63966i
$414$	−2.81717e21	−0.160439
$415$	0	0
$416$	1.73038e19	0.000945906 0
$417$	1.81695e22i	0.973167i
$418$	6.23798e21i	0.327375i
$419$	−3.31114e22	−1.70278	−0.851390	−	0.524533i	$-0.824240\pi$
$419$	−3.31114e22	−1.70278	−0.851390	+	0.524533i	$0.824240\pi$
$420$	0	0
$421$	−2.31325e22	−1.14242	−0.571208	−	0.820805i	$-0.693525\pi$
$421$	−2.31325e22	−1.14242	−0.571208	+	0.820805i	$0.693525\pi$
$422$	− 1.29562e22i	− 0.627079i
$423$	− 1.13229e22i	− 0.537113i
$424$	6.71163e21	0.312046
$425$	0	0
$426$	−9.23317e21	−0.412448
$427$	− 3.68597e22i	− 1.61404i
$428$	− 6.90732e21i	− 0.296509i
$429$	2.79005e19	0.00117416
$430$	0	0
$431$	4.44596e22	1.79849	0.899247	−	0.437440i	$-0.144115\pi$
$431$	4.44596e22	1.79849	0.899247	+	0.437440i	$0.144115\pi$
$432$	− 6.86178e21i	− 0.272160i
$433$	2.85304e22i	1.10959i	0.831989	+	0.554793i	$0.187202\pi$
$433$	2.85304e22i	1.10959i	−0.831989	+	0.554793i	$0.812798\pi$
$434$	−5.03678e22	−1.92084
$435$	0	0
$436$	1.65082e22	0.605431
$437$	− 3.31893e22i	− 1.19373i
$438$	− 6.81242e21i	− 0.240310i
$439$	4.28578e22	1.48279	0.741397	−	0.671066i	$-0.234163\pi$
$439$	4.28578e22	1.48279	0.741397	+	0.671066i	$0.234163\pi$
$440$	0	0
$441$	−1.63658e22	−0.544767
$442$	9.08513e19i	0.00296648i
$443$	− 1.40464e22i	− 0.449919i	−0.974368	−	0.224959i	$-0.927775\pi$
$443$	− 1.40464e22i	− 0.449919i	0.974368	−	0.224959i	$-0.0722249\pi$
$444$	−1.28082e22	−0.402471
$445$	0	0
$446$	−2.89323e22	−0.875057
$447$	1.73933e22i	0.516140i
$448$	− 6.99902e21i	− 0.203786i
$449$	3.88401e22	1.10965	0.554826	−	0.831966i	$-0.312785\pi$
$449$	3.88401e22	1.10965	0.554826	+	0.831966i	$0.312785\pi$
$450$	0	0
$451$	−3.77210e21	−0.103773
$452$	− 2.68301e22i	− 0.724346i
$453$	− 4.83161e22i	− 1.28014i
$454$	3.43186e22	0.892391
$455$	0	0
$456$	1.99938e22	0.500835
$457$	2.21160e22i	0.543774i	0.962329	+	0.271887i	$0.0876477\pi$
$457$	2.21160e22i	0.543774i	−0.962329	+	0.271887i	$0.912352\pi$
$458$	3.91917e22i	0.945883i
$459$	3.60269e22	0.853530
$460$	0	0
$461$	1.69257e22	0.386446	0.193223	−	0.981155i	$-0.438106\pi$
$461$	1.69257e22	0.386446	0.193223	+	0.981155i	$0.438106\pi$
$462$	− 1.12852e22i	− 0.252960i
$463$	5.00810e22i	1.10213i	0.834461	+	0.551067i	$0.185779\pi$
$463$	5.00810e22i	1.10213i	−0.834461	+	0.551067i	$0.814221\pi$
$464$	1.10790e22	0.239385
$465$	0	0
$466$	−3.94483e22	−0.821765
$467$	6.87611e22i	1.40653i	0.710927	+	0.703266i	$0.248276\pi$
$467$	6.87611e22i	1.40653i	−0.710927	+	0.703266i	$0.751724\pi$
$468$	4.37674e19i	0 0.000879146i
$469$	−6.74875e22	−1.33123
$470$	0	0
$471$	−7.25357e22	−1.37998
$472$	3.06370e22i	0.572452i
$473$	8.77284e21i	0.160998i
$474$	−6.69806e21	−0.120735
$475$	0	0
$476$	3.67475e22	0.639099
$477$	1.69761e22i	0.290022i
$478$	− 2.83201e22i	− 0.475290i
$479$	3.44291e22	0.567641	0.283821	−	0.958877i	$-0.408398\pi$
$479$	3.44291e22	0.567641	0.283821	+	0.958877i	$0.408398\pi$
$480$	0	0
$481$	3.30316e20	0.00525650
$482$	− 4.31590e22i	− 0.674794i
$483$	6.00431e22i	0.922385i
$484$	3.07493e22	0.464141
$485$	0	0
$486$	3.04191e22	0.443342
$487$	− 8.83844e20i	− 0.0126584i	−0.999980	−	0.00632921i	$-0.997985\pi$
$487$	− 8.83844e20i	− 0.0126584i	0.999980	−	0.00632921i	$-0.00201466\pi$
$488$	2.48699e22i	0.350030i
$489$	5.74420e22	0.794519
$490$	0	0
$491$	1.04515e23	1.39632	0.698158	−	0.715943i	$-0.254003\pi$
$491$	1.04515e23	1.39632	0.698158	+	0.715943i	$0.254003\pi$
$492$	1.20902e22i	0.158757i
$493$	5.81688e22i	0.750744i
$494$	−5.15627e20	−0.00654119
$495$	0	0
$496$	3.39841e22	0.416563
$497$	− 9.63135e22i	− 1.16053i
$498$	− 1.67871e22i	− 0.198850i
$499$	5.12067e22	0.596310	0.298155	−	0.954518i	$-0.403629\pi$
$499$	5.12067e22	0.596310	0.298155	+	0.954518i	$0.403629\pi$
$500$	0	0
$501$	−1.16139e23	−1.30724
$502$	− 2.23151e22i	− 0.246955i
$503$	5.06660e22i	0.551301i	0.961258	+	0.275650i	$0.0888932\pi$
$503$	5.06660e22i	0.551301i	−0.961258	+	0.275650i	$0.911107\pi$
$504$	1.77030e22	0.189403
$505$	0	0
$506$	1.26396e22	0.130754
$507$	− 8.05463e22i	− 0.819366i
$508$	− 4.21010e22i	− 0.421164i
$509$	−1.68111e23	−1.65385	−0.826923	−	0.562316i	$-0.809911\pi$
$509$	−1.68111e23	−1.65385	−0.826923	+	0.562316i	$0.809911\pi$
$510$	0	0
$511$	7.10621e22	0.676177
$512$	4.72237e21i	0.0441942i
$513$	2.04471e23i	1.88206i
$514$	6.60452e22	0.597936
$515$	0	0
$516$	2.81185e22	0.246303
$517$	5.08018e22i	0.437733i
$518$	− 1.33606e23i	− 1.13246i
$519$	1.53170e23	1.27717
$520$	0	0
$521$	1.13516e23	0.916085	0.458042	−	0.888930i	$-0.348551\pi$
$521$	1.13516e23	0.916085	0.458042	+	0.888930i	$0.348551\pi$
$522$	2.80227e22i	0.222490i
$523$	3.13139e22i	0.244609i	0.992493	+	0.122305i	$0.0390285\pi$
$523$	3.13139e22i	0.244609i	−0.992493	+	0.122305i	$0.960972\pi$
$524$	−2.34175e22	−0.179980
$525$	0	0
$526$	1.05686e23	0.786394
$527$	1.78429e23i	1.30640i
$528$	7.61432e21i	0.0548583i
$529$	7.38008e22	0.523224
$530$	0	0
$531$	−7.74918e22	−0.532050
$532$	2.08560e23i	1.40923i
$533$	− 3.11800e20i	− 0.00207345i
$534$	−1.31575e23	−0.861139
$535$	0	0
$536$	4.55350e22	0.288699
$537$	− 1.42529e22i	− 0.0889449i
$538$	− 9.25753e22i	− 0.568651i
$539$	7.34275e22	0.443971
$540$	0	0
$541$	−1.32903e23	−0.778680	−0.389340	−	0.921094i	$-0.627297\pi$
$541$	−1.32903e23	−0.778680	−0.389340	+	0.921094i	$0.627297\pi$
$542$	− 1.69391e23i	− 0.977006i
$543$	7.92825e22i	0.450172i
$544$	−2.47942e22	−0.138599
$545$	0	0
$546$	9.32826e20	0.00505432
$547$	− 3.86923e22i	− 0.206411i	−0.994660	−	0.103205i	$-0.967090\pi$
$547$	− 3.86923e22i	− 0.206411i	0.994660	−	0.103205i	$-0.0329099\pi$
$548$	− 8.11477e22i	− 0.426227i
$549$	−6.29047e22	−0.325326
$550$	0	0
$551$	−3.30138e23	−1.65541
$552$	− 4.05121e22i	− 0.200034i
$553$	− 6.98692e22i	− 0.339721i
$554$	6.23872e22	0.298719
$555$	0	0
$556$	1.27880e23	0.593836
$557$	1.53384e23i	0.701475i	0.936474	+	0.350737i	$0.114069\pi$
$557$	1.53384e23i	0.701475i	−0.936474	+	0.350737i	$0.885931\pi$
$558$	8.59576e22i	0.387163i
$559$	−7.25157e20	−0.00321686
$560$	0	0
$561$	−3.99780e22	−0.172043
$562$	− 2.42445e23i	− 1.02767i
$563$	− 1.19252e23i	− 0.497904i	−0.968516	−	0.248952i	$-0.919914\pi$
$563$	− 1.19252e23i	− 0.497904i	0.968516	−	0.248952i	$-0.0800862\pi$
$564$	1.62829e23	0.669666
$565$	0	0
$566$	9.40810e22	0.375459
$567$	− 2.33644e23i	− 0.918540i
$568$	6.49844e22i	0.251680i
$569$	1.07363e23	0.409638	0.204819	−	0.978800i	$-0.434339\pi$
$569$	1.07363e23	0.409638	0.204819	+	0.978800i	$0.434339\pi$
$570$	0	0
$571$	−2.25644e23	−0.835634	−0.417817	−	0.908531i	$-0.637205\pi$
$571$	−2.25644e23	−0.835634	−0.417817	+	0.908531i	$0.637205\pi$
$572$	− 1.96368e20i	0 0.000716482i
$573$	− 9.86284e22i	− 0.354558i
$574$	−1.26116e23	−0.446705
$575$	0	0
$576$	−1.19445e22	−0.0410750
$577$	1.29594e23i	0.439127i	0.975598	+	0.219563i	$0.0704633\pi$
$577$	1.29594e23i	0.439127i	−0.975598	+	0.219563i	$0.929537\pi$
$578$	8.15949e22i	0.272444i
$579$	−1.45044e23	−0.477233
$580$	0	0
$581$	1.75111e23	0.559519
$582$	− 1.53195e23i	− 0.482390i
$583$	− 7.61655e22i	− 0.236361i
$584$	−4.79469e22	−0.146640
$585$	0	0
$586$	−3.09514e23	−0.919498
$587$	− 3.21537e23i	− 0.941471i	−0.882274	−	0.470735i	$-0.843989\pi$
$587$	− 3.21537e23i	− 0.941471i	0.882274	−	0.470735i	$-0.156011\pi$
$588$	− 2.35348e23i	− 0.679208i
$589$	−1.01267e24	−2.88064
$590$	0	0
$591$	−7.88985e22	−0.218060
$592$	9.01464e22i	0.245592i
$593$	− 8.23836e22i	− 0.221246i	−0.993862	−	0.110623i	$-0.964715\pi$
$593$	− 8.23836e22i	− 0.221246i	0.993862	−	0.110623i	$-0.0352847\pi$
$594$	−7.78694e22	−0.206149
$595$	0	0
$596$	1.22417e23	0.314954
$597$	8.83330e22i	0.224048i
$598$	1.04478e21i	0.00261255i
$599$	7.29015e22	0.179725	0.0898625	−	0.995954i	$-0.471357\pi$
$599$	7.29015e22	0.179725	0.0898625	+	0.995954i	$0.471357\pi$
$600$	0	0
$601$	3.79880e23	0.910361	0.455180	−	0.890399i	$-0.349575\pi$
$601$	3.79880e23	0.910361	0.455180	+	0.890399i	$0.349575\pi$
$602$	2.93311e23i	0.693040i
$603$	1.15174e23i	0.268323i
$604$	−3.40056e23	−0.781154
$605$	0	0
$606$	−3.72831e23	−0.832711
$607$	3.76245e23i	0.828641i	0.910131	+	0.414321i	$0.135981\pi$
$607$	3.76245e23i	0.828641i	−0.910131	+	0.414321i	$0.864019\pi$
$608$	− 1.40719e23i	− 0.305614i
$609$	5.97255e23	1.27912
$610$	0	0
$611$	−4.19924e21	−0.00874623
$612$	− 6.27132e22i	− 0.128817i
$613$	− 4.60370e23i	− 0.932595i	−0.884628	−	0.466298i	$-0.845588\pi$
$613$	− 4.60370e23i	− 0.932595i	0.884628	−	0.466298i	$-0.154412\pi$
$614$	−1.22094e23	−0.243930
$615$	0	0
$616$	−7.94269e22	−0.154359
$617$	3.36863e23i	0.645698i	0.946451	+	0.322849i	$0.104641\pi$
$617$	3.36863e23i	0.645698i	−0.946451	+	0.322849i	$0.895359\pi$
$618$	− 5.55811e23i	− 1.05081i
$619$	−1.49640e23	−0.279047	−0.139523	−	0.990219i	$-0.544557\pi$
$619$	−1.49640e23	−0.279047	−0.139523	+	0.990219i	$0.544557\pi$
$620$	0	0
$621$	4.14306e23	0.751696
$622$	8.97070e22i	0.160549i
$623$	− 1.37249e24i	− 2.42305i
$624$	−6.29394e20	−0.00109611
$625$	0	0
$626$	−5.24161e23	−0.888348
$627$	− 2.26895e23i	− 0.379360i
$628$	5.10517e23i	0.842080i
$629$	−4.73302e23	−0.770208
$630$	0	0
$631$	−6.17252e21	−0.00977717	−0.00488858	−	0.999988i	$-0.501556\pi$
$631$	−6.17252e21	−0.00977717	−0.00488858	+	0.999988i	$0.501556\pi$
$632$	4.71420e22i	0.0736737i
$633$	4.71259e23i	0.726654i
$634$	3.37058e23	0.512797
$635$	0	0
$636$	−2.44124e23	−0.361596
$637$	6.06947e21i	0.00887086i
$638$	− 1.25728e23i	− 0.181324i
$639$	−1.64369e23	−0.233917
$640$	0	0
$641$	−1.59514e23	−0.221057	−0.110529	−	0.993873i	$-0.535254\pi$
$641$	−1.59514e23	−0.221057	−0.110529	+	0.993873i	$0.535254\pi$
$642$	2.51241e23i	0.343592i
$643$	1.37854e24i	1.86049i	0.366941	+	0.930244i	$0.380405\pi$
$643$	1.37854e24i	1.86049i	−0.366941	+	0.930244i	$0.619595\pi$
$644$	4.22592e23	0.562849
$645$	0	0
$646$	7.38829e23	0.958446
$647$	− 3.15056e23i	− 0.403369i	−0.979451	−	0.201684i	$-0.935359\pi$
$647$	− 3.15056e23i	− 0.403369i	0.979451	−	0.201684i	$-0.0646415\pi$
$648$	1.57643e23i	0.199200i
$649$	3.47677e23	0.433607
$650$	0	0
$651$	1.83204e24	2.22585
$652$	− 4.04286e23i	− 0.484824i
$653$	− 2.27963e23i	− 0.269838i	−0.990857	−	0.134919i	$-0.956923\pi$
$653$	− 2.27963e23i	− 0.269838i	0.990857	−	0.134919i	$-0.0430774\pi$
$654$	−6.00455e23	−0.701568
$655$	0	0
$656$	8.50930e22	0.0968749
$657$	− 1.21275e23i	− 0.136290i
$658$	1.69851e24i	1.88429i
$659$	−1.18670e24	−1.29961	−0.649806	−	0.760100i	$-0.725150\pi$
$659$	−1.18670e24	−1.29961	−0.649806	+	0.760100i	$0.725150\pi$
$660$	0	0
$661$	−1.50237e24	−1.60348	−0.801741	−	0.597672i	$-0.796092\pi$
$661$	−1.50237e24	−1.60348	−0.801741	+	0.597672i	$0.796092\pi$
$662$	9.87806e23i	1.04083i
$663$	− 3.30455e21i	− 0.00343754i
$664$	−1.18150e23	−0.121340
$665$	0	0
$666$	−2.28012e23	−0.228258
$667$	6.68936e23i	0.661173i
$668$	8.17402e23i	0.797693i
$669$	1.05236e24	1.01401
$670$	0	0
$671$	2.82230e23	0.265132
$672$	2.54577e23i	0.236146i
$673$	2.53432e23i	0.232131i	0.993242	+	0.116065i	$0.0370282\pi$
$673$	2.53432e23i	0.232131i	−0.993242	+	0.116065i	$0.962972\pi$
$674$	1.20102e24	1.08628
$675$	0	0
$676$	−5.66897e23	−0.499986
$677$	− 4.60323e23i	− 0.400921i	−0.979702	−	0.200460i	$-0.935756\pi$
$677$	− 4.60323e23i	− 0.400921i	0.979702	−	0.200460i	$-0.0642438\pi$
$678$	9.75897e23i	0.839367i
$679$	1.59801e24	1.35734
$680$	0	0
$681$	−1.24828e24	−1.03410
$682$	− 3.85660e23i	− 0.315528i
$683$	− 6.27345e23i	− 0.506910i	−0.967347	−	0.253455i	$-0.918433\pi$
$683$	− 6.27345e23i	− 0.506910i	0.967347	−	0.253455i	$-0.0815670\pi$
$684$	3.55929e23	0.284045
$685$	0	0
$686$	9.74147e23	0.758349
$687$	− 1.42553e24i	− 1.09608i
$688$	− 1.97902e23i	− 0.150296i
$689$	6.29579e21	0.00472266
$690$	0	0
$691$	4.11645e23	0.301272	0.150636	−	0.988589i	$-0.451868\pi$
$691$	4.11645e23	0.301272	0.150636	+	0.988589i	$0.451868\pi$
$692$	− 1.07803e24i	− 0.779344i
$693$	− 2.00899e23i	− 0.143464i
$694$	6.44190e23	0.454421
$695$	0	0
$696$	−4.02978e23	−0.277398
$697$	4.46770e23i	0.303812i
$698$	5.63770e23i	0.378731i
$699$	1.43486e24	0.952255
$700$	0	0
$701$	2.88292e23	0.186737	0.0933683	−	0.995632i	$-0.470237\pi$
$701$	2.88292e23	0.186737	0.0933683	+	0.995632i	$0.470237\pi$
$702$	− 6.43663e21i	− 0.00411901i
$703$	− 2.68623e24i	− 1.69833i
$704$	5.35907e22	0.0334751
$705$	0	0
$706$	−3.33347e23	−0.203262
$707$	− 3.88909e24i	− 2.34306i
$708$	− 1.11436e24i	− 0.663353i
$709$	2.85869e24	1.68141	0.840707	−	0.541491i	$-0.182140\pi$
$709$	2.85869e24	1.68141	0.840707	+	0.541491i	$0.182140\pi$
$710$	0	0
$711$	−1.19239e23	−0.0684740
$712$	9.26046e23i	0.525475i
$713$	2.05191e24i	1.15053i
$714$	−1.33662e24	−0.740583
$715$	0	0
$716$	−1.00314e23	−0.0542751
$717$	1.03009e24i	0.550762i
$718$	− 5.30336e23i	− 0.280216i
$719$	1.21983e24	0.636946	0.318473	−	0.947932i	$-0.396830\pi$
$719$	1.21983e24	0.636946	0.318473	+	0.947932i	$0.396830\pi$
$720$	0	0
$721$	5.79780e24	2.95674
$722$	2.79025e24i	1.40630i
$723$	1.56983e24i	0.781947i
$724$	5.58002e23	0.274700
$725$	0	0
$726$	−1.11845e24	−0.537843
$727$	2.28060e24i	1.08394i	0.840396	+	0.541972i	$0.182322\pi$
$727$	2.28060e24i	1.08394i	−0.840396	+	0.541972i	$0.817678\pi$
$728$	− 6.56537e21i	− 0.00308420i
$729$	−2.31988e24	−1.07716
$730$	0	0
$731$	1.03906e24	0.471349
$732$	− 9.04597e23i	− 0.405612i
$733$	− 8.50533e23i	− 0.376970i	−0.982076	−	0.188485i	$-0.939642\pi$
$733$	− 8.50533e23i	− 0.376970i	0.982076	−	0.188485i	$-0.0603577\pi$
$734$	1.20099e24	0.526166
$735$	0	0
$736$	−2.85130e23	−0.122062
$737$	− 5.16744e23i	− 0.218676i
$738$	2.15230e23i	0.0900376i
$739$	−2.14385e24	−0.886578	−0.443289	−	0.896379i	$-0.646188\pi$
$739$	−2.14385e24	−0.886578	−0.443289	+	0.896379i	$0.646188\pi$
$740$	0	0
$741$	1.87550e22	0.00757988
$742$	− 2.54651e24i	− 1.01745i
$743$	2.23446e24i	0.882606i	0.897358	+	0.441303i	$0.145484\pi$
$743$	2.23446e24i	0.882606i	−0.897358	+	0.441303i	$0.854516\pi$
$744$	−1.23611e24	−0.482710
$745$	0	0
$746$	1.99079e23	0.0759880
$747$	− 2.98843e23i	− 0.112777i
$748$	2.81371e23i	0.104982i
$749$	−2.62076e24	−0.966789
$750$	0	0
$751$	−1.71798e24	−0.619555	−0.309778	−	0.950809i	$-0.600255\pi$
$751$	−1.71798e24	−0.619555	−0.309778	+	0.950809i	$0.600255\pi$
$752$	− 1.14601e24i	− 0.408637i
$753$	8.11671e23i	0.286169i
$754$	1.03926e22	0.00362298
$755$	0	0
$756$	−2.60348e24	−0.887400
$757$	1.09729e24i	0.369832i	0.982754	+	0.184916i	$0.0592014\pi$
$757$	1.09729e24i	0.369832i	−0.982754	+	0.184916i	$0.940799\pi$
$758$	− 8.96138e22i	− 0.0298667i
$759$	−4.59743e23	−0.151516
$760$	0	0
$761$	−1.70967e24	−0.550990	−0.275495	−	0.961302i	$-0.588842\pi$
$761$	−1.70967e24	−0.550990	−0.275495	+	0.961302i	$0.588842\pi$
$762$	1.53135e24i	0.488041i
$763$	− 6.26350e24i	− 1.97405i
$764$	−6.94162e23	−0.216355
$765$	0	0
$766$	2.61925e24	0.798423
$767$	2.87388e22i	0.00866378i
$768$	− 1.71767e23i	− 0.0512119i
$769$	−1.22119e24	−0.360090	−0.180045	−	0.983658i	$-0.557624\pi$
$769$	−1.22119e24	−0.360090	−0.180045	+	0.983658i	$0.557624\pi$
$770$	0	0
$771$	−2.40228e24	−0.692884
$772$	1.02084e24i	0.291213i
$773$	2.59069e24i	0.730952i	0.930821	+	0.365476i	$0.119094\pi$
$773$	2.59069e24i	0.730952i	−0.930821	+	0.365476i	$0.880906\pi$
$774$	5.00564e23	0.139689
$775$	0	0
$776$	−1.07821e24	−0.294359
$777$	4.85968e24i	1.31229i
$778$	1.05755e24i	0.282470i
$779$	−2.53564e24	−0.669915
$780$	0	0
$781$	7.37461e23	0.190636
$782$	− 1.49704e24i	− 0.382804i
$783$	− 4.12114e24i	− 1.04242i
$784$	−1.65641e24	−0.414460
$785$	0	0
$786$	8.51770e23	0.208560
$787$	− 2.64413e24i	− 0.640467i	−0.947339	−	0.320234i	$-0.896239\pi$
$787$	− 2.64413e24i	− 0.640467i	0.947339	−	0.320234i	$-0.103761\pi$
$788$	5.55300e23i	0.133062i
$789$	−3.84415e24	−0.911268
$790$	0	0
$791$	−1.01798e25	−2.36179
$792$	1.35550e23i	0.0311125i
$793$	2.33290e22i	0.00529753i
$794$	−1.95925e24	−0.440166
$795$	0	0
$796$	6.21701e23	0.136716
$797$	6.24909e24i	1.35963i	0.733383	+	0.679815i	$0.237940\pi$
$797$	6.24909e24i	1.35963i	−0.733383	+	0.679815i	$0.762060\pi$
$798$	− 7.58601e24i	− 1.63301i
$799$	6.01699e24	1.28154
$800$	0	0
$801$	−2.34230e24	−0.488388
$802$	− 1.04518e23i	− 0.0215630i
$803$	5.44114e23i	0.111073i
$804$	−1.65625e24	−0.334542
$805$	0	0
$806$	3.18784e22	0.00630448
$807$	3.36726e24i	0.658948i
$808$	2.62404e24i	0.508129i
$809$	−5.76985e24	−1.10561	−0.552805	−	0.833311i	$-0.686443\pi$
$809$	−5.76985e24	−1.10561	−0.552805	+	0.833311i	$0.686443\pi$
$810$	0	0
$811$	3.03433e24	0.569359	0.284679	−	0.958623i	$-0.408113\pi$
$811$	3.03433e24	0.569359	0.284679	+	0.958623i	$0.408113\pi$
$812$	− 4.20357e24i	− 0.780534i
$813$	6.16130e24i	1.13215i
$814$	1.02301e24	0.186025
$815$	0	0
$816$	9.01843e23	0.160607
$817$	5.89719e24i	1.03934i
$818$	− 5.14363e24i	− 0.897153i
$819$	1.66061e22	0.00286652
$820$	0	0
$821$	4.15299e24	0.702172	0.351086	−	0.936343i	$-0.385812\pi$
$821$	4.15299e24	0.702172	0.351086	+	0.936343i	$0.385812\pi$
$822$	2.95160e24i	0.493909i
$823$	9.22848e23i	0.152838i	0.997076	+	0.0764191i	$0.0243487\pi$
$823$	9.22848e23i	0.152838i	−0.997076	+	0.0764191i	$0.975651\pi$
$824$	−3.91188e24	−0.641216
$825$	0	0
$826$	1.16242e25	1.86652
$827$	− 7.67636e24i	− 1.22000i	−0.792403	−	0.609998i	$-0.791170\pi$
$827$	− 7.67636e24i	− 1.22000i	0.792403	−	0.609998i	$-0.208830\pi$
$828$	− 7.21195e23i	− 0.113448i
$829$	−8.23009e23	−0.128142	−0.0640709	−	0.997945i	$-0.520408\pi$
$829$	−8.23009e23	−0.128142	−0.0640709	+	0.997945i	$0.520408\pi$
$830$	0	0
$831$	−2.26922e24	−0.346153
$832$	4.42977e21i	0 0.000668857i
$833$	− 8.69679e24i	− 1.29980i
$834$	−4.65140e24	−0.688133
$835$	0	0
$836$	−1.59692e24	−0.231489
$837$	− 1.26413e25i	− 1.81395i
$838$	− 8.47652e24i	− 1.20405i
$839$	9.57083e24	1.34578	0.672888	−	0.739744i	$-0.265053\pi$
$839$	9.57083e24	1.34578	0.672888	+	0.739744i	$0.265053\pi$
$840$	0	0
$841$	−6.03171e23	−0.0831140
$842$	− 5.92192e24i	− 0.807811i
$843$	8.81851e24i	1.19086i
$844$	3.31679e24	0.443412
$845$	0	0
$846$	2.89867e24	0.379796
$847$	− 1.16669e25i	− 1.51337i
$848$	1.71818e24i	0.220650i
$849$	−3.42203e24	−0.435079
$850$	0	0
$851$	−5.44292e24	−0.678314
$852$	− 2.36369e24i	− 0.291645i
$853$	2.48597e24i	0.303690i	0.988404	+	0.151845i	$0.0485214\pi$
$853$	2.48597e24i	0.303690i	−0.988404	+	0.151845i	$0.951479\pi$
$854$	9.43608e24	1.14130
$855$	0	0
$856$	1.76827e24	0.209663
$857$	2.10495e24i	0.247118i	0.992337	+	0.123559i	$0.0394308\pi$
$857$	2.10495e24i	0.247118i	−0.992337	+	0.123559i	$0.960569\pi$
$858$	7.14254e21i	0 0.000830253i
$859$	7.58565e23	0.0873074	0.0436537	−	0.999047i	$-0.486100\pi$
$859$	7.58565e23	0.0873074	0.0436537	+	0.999047i	$0.486100\pi$
$860$	0	0
$861$	4.58725e24	0.517638
$862$	1.13817e25i	1.27173i
$863$	− 5.83299e24i	− 0.645356i	−0.946509	−	0.322678i	$-0.895417\pi$
$863$	− 5.83299e24i	− 0.645356i	0.946509	−	0.322678i	$-0.104583\pi$
$864$	1.75662e24	0.192446
$865$	0	0
$866$	−7.30378e24	−0.784595
$867$	− 2.96787e24i	− 0.315706i
$868$	− 1.28942e25i	− 1.35824i
$869$	5.34980e23	0.0558046
$870$	0	0
$871$	4.27137e22	0.00436931
$872$	4.22610e24i	0.428104i
$873$	− 2.72717e24i	− 0.273584i
$874$	8.49646e24	0.844094
$875$	0	0
$876$	1.74398e24	0.169925
$877$	1.53835e25i	1.48443i	0.670163	+	0.742214i	$0.266224\pi$
$877$	1.53835e25i	1.48443i	−0.670163	+	0.742214i	$0.733776\pi$
$878$	1.09716e25i	1.04849i
$879$	1.12580e25	1.06551
$880$	0	0
$881$	−1.57727e25	−1.46424	−0.732118	−	0.681178i	$-0.761468\pi$
$881$	−1.57727e25	−1.46424	−0.732118	+	0.681178i	$0.761468\pi$
$882$	− 4.18966e24i	− 0.385208i
$883$	1.75208e25i	1.59547i	0.603009	+	0.797734i	$0.293968\pi$
$883$	1.75208e25i	1.59547i	−0.603009	+	0.797734i	$0.706032\pi$
$884$	−2.32579e22	−0.00209762
$885$	0	0
$886$	3.59588e24	0.318140
$887$	1.05988e25i	0.928764i	0.885635	+	0.464382i	$0.153724\pi$
$887$	1.05988e25i	0.928764i	−0.885635	+	0.464382i	$0.846276\pi$
$888$	− 3.27891e24i	− 0.284590i
$889$	−1.59739e25	−1.37324
$890$	0	0
$891$	1.78898e24	0.150885
$892$	− 7.40667e24i	− 0.618759i
$893$	3.41494e25i	2.82583i
$894$	−4.45268e24	−0.364966
$895$	0	0
$896$	1.79175e24	0.144098
$897$	− 3.80020e22i	− 0.00302741i
$898$	9.94307e24i	0.784643i
$899$	2.04106e25	1.59551
$900$	0	0
$901$	−9.02107e24	−0.691986
$902$	− 9.65659e23i	− 0.0733784i
$903$	− 1.06687e25i	− 0.803089i
$904$	6.86852e24	0.512190
$905$	0	0
$906$	1.23689e25	0.905195
$907$	− 6.72762e24i	− 0.487753i	−0.969806	−	0.243876i	$-0.921581\pi$
$907$	− 6.72762e24i	− 0.487753i	0.969806	−	0.243876i	$-0.0784191\pi$
$908$	8.78557e24i	0.631016i
$909$	−6.63712e24	−0.472266
$910$	0	0
$911$	1.90734e25	1.33205	0.666027	−	0.745928i	$-0.267994\pi$
$911$	1.90734e25	1.33205	0.666027	+	0.745928i	$0.267994\pi$
$912$	5.11841e24i	0.354143i
$913$	1.34080e24i	0.0919100i
$914$	−5.66169e24	−0.384506
$915$	0	0
$916$	−1.00331e25	−0.668840
$917$	8.88503e24i	0.586840i
$918$	9.22288e24i	0.603537i
$919$	1.73304e25	1.12364	0.561818	−	0.827261i	$-0.310102\pi$
$919$	1.73304e25	1.12364	0.561818	+	0.827261i	$0.310102\pi$
$920$	0	0
$921$	4.44096e24	0.282664
$922$	4.33297e24i	0.273258i
$923$	6.09580e22i	0.00380905i
$924$	2.88901e24	0.178870
$925$	0	0
$926$	−1.28207e25	−0.779326
$927$	− 9.89452e24i	− 0.595960i
$928$	2.83622e24i	0.169271i
$929$	6.38514e24	0.377605	0.188802	−	0.982015i	$-0.439539\pi$
$929$	6.38514e24	0.377605	0.188802	+	0.982015i	$0.439539\pi$
$930$	0	0
$931$	4.93587e25	2.86610
$932$	− 1.00988e25i	− 0.581076i
$933$	− 3.26293e24i	− 0.186043i
$934$	−1.76029e25	−0.994568
$935$	0	0
$936$	−1.12045e22	−0.000621650 0
$937$	2.87864e25i	1.58271i	0.611358	+	0.791354i	$0.290624\pi$
$937$	2.87864e25i	1.58271i	−0.611358	+	0.791354i	$0.709376\pi$
$938$	− 1.72768e25i	− 0.941324i
$939$	1.90654e25	1.02941
$940$	0	0
$941$	−2.31234e25	−1.22614	−0.613071	−	0.790028i	$-0.710066\pi$
$941$	−2.31234e25	−1.22614	−0.613071	+	0.790028i	$0.710066\pi$
$942$	− 1.85691e25i	− 0.975796i
$943$	5.13781e24i	0.267564i
$944$	−7.84307e24	−0.404785
$945$	0	0
$946$	−2.24585e24	−0.113843
$947$	− 1.60999e25i	− 0.808816i	−0.914579	−	0.404408i	$-0.867478\pi$
$947$	− 1.60999e25i	− 0.808816i	0.914579	−	0.404408i	$-0.132522\pi$
$948$	− 1.71470e24i	− 0.0853725i
$949$	−4.49761e22	−0.00221932
$950$	0	0
$951$	−1.22599e25	−0.594225
$952$	9.40735e24i	0.451911i
$953$	− 1.12344e25i	− 0.534883i	−0.963574	−	0.267441i	$-0.913822\pi$
$953$	− 1.12344e25i	− 0.534883i	0.963574	−	0.267441i	$-0.0861781\pi$
$954$	−4.34588e24	−0.205077
$955$	0	0
$956$	7.24996e24	0.336081
$957$	4.57311e24i	0.210117i
$958$	8.81385e24i	0.401383i
$959$	−3.07889e25	−1.38975
$960$	0	0
$961$	4.00580e25	1.77640
$962$	8.45610e22i	0.00371691i
$963$	4.47259e24i	0.194866i
$964$	1.10487e25	0.477152
$965$	0	0
$966$	−1.53710e25	−0.652225
$967$	− 2.40854e24i	− 0.101305i	−0.998716	−	0.0506524i	$-0.983870\pi$
$967$	− 2.40854e24i	− 0.101305i	0.998716	−	0.0506524i	$-0.0161300\pi$
$968$	7.87183e24i	0.328197i
$969$	−2.68736e25	−1.11064
$970$	0	0
$971$	−2.55647e25	−1.03819	−0.519095	−	0.854716i	$-0.673731\pi$
$971$	−2.55647e25	−1.03819	−0.519095	+	0.854716i	$0.673731\pi$
$972$	7.78730e24i	0.313490i
$973$	− 4.85200e25i	− 1.93625i
$974$	2.26264e23	0.00895085
$975$	0	0
$976$	−6.36669e24	−0.247509
$977$	2.30301e25i	0.887547i	0.896139	+	0.443774i	$0.146361\pi$
$977$	2.30301e25i	0.887547i	−0.896139	+	0.443774i	$0.853639\pi$
$978$	1.47052e25i	0.561810i
$979$	1.05090e25	0.398024
$980$	0	0
$981$	−1.06893e25	−0.397889
$982$	2.67557e25i	0.987345i
$983$	− 2.04718e25i	− 0.748949i	−0.927237	−	0.374474i	$-0.877823\pi$
$983$	− 2.04718e25i	− 0.748949i	0.927237	−	0.374474i	$-0.122177\pi$
$984$	−3.09510e24	−0.112258
$985$	0	0
$986$	−1.48912e25	−0.530856
$987$	− 6.17801e25i	− 2.18350i
$988$	− 1.32001e23i	− 0.00462532i
$989$	1.19491e25	0.415113
$990$	0	0
$991$	1.20622e25	0.411907	0.205954	−	0.978562i	$-0.433970\pi$
$991$	1.20622e25	0.411907	0.205954	+	0.978562i	$0.433970\pi$
$992$	8.69992e24i	0.294555i
$993$	− 3.59297e25i	− 1.20610i
$994$	2.46563e25	0.820621
$995$	0	0
$996$	4.29750e24	0.140608
$997$	1.73789e23i	0.00563786i	0.999996	+	0.00281893i	$0.000897295\pi$
$997$	1.73789e23i	0.00563786i	−0.999996	+	0.00281893i	$0.999103\pi$
$998$	1.31089e25i	0.421655i
$999$	3.35325e25	1.06945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.18.b.d.49.3		4
5.2	odd	4		10.18.a.c.1.1	✓	2
5.3	odd	4		50.18.a.f.1.2		2
5.4	even	2	inner	50.18.b.d.49.2		4
15.2	even	4		90.18.a.k.1.1		2
20.7	even	4		80.18.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.c.1.1	✓	2	5.2	odd	4
50.18.a.f.1.2		2	5.3	odd	4
50.18.b.d.49.2		4	5.4	even	2	inner
50.18.b.d.49.3		4	1.1	even	1	trivial
80.18.a.d.1.2		2	20.7	even	4
90.18.a.k.1.1		2	15.2	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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 18 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+256.000i q^{2} -9311.53i q^{3} -65536.0 q^{4} +2.38375e6 q^{6} +2.48655e7i q^{7} -1.67772e7i q^{8} +4.24355e7 q^{9} -1.90392e8 q^{11} +6.10241e8i q^{12} -1.57377e7i q^{13} -6.36558e9 q^{14} +4.29497e9 q^{16} +2.25502e10i q^{17} +1.08635e10i q^{18} -1.27984e11 q^{19} +2.31536e11 q^{21} -4.87405e10i q^{22} +2.59325e11i q^{23} -1.56222e11 q^{24} +4.02885e9 q^{26} -1.59763e12i q^{27} -1.62959e12i q^{28} +2.57953e12 q^{29} +7.91253e12 q^{31} +1.09951e12i q^{32} +1.77285e12i q^{33} -5.77284e12 q^{34} -2.78105e12 q^{36} +2.09888e13i q^{37} -3.27638e13i q^{38} -1.46542e11 q^{39} +1.98123e13 q^{41} +5.92733e13i q^{42} -4.60777e13i q^{43} +1.24776e13 q^{44} -6.63871e13 q^{46} -2.66827e14i q^{47} -3.99927e13i q^{48} -3.85664e14 q^{49} +2.09977e14 q^{51} +1.03139e12i q^{52} +4.00045e14i q^{53} +4.08994e14 q^{54} +4.17174e14 q^{56} +1.19172e15i q^{57} +6.60360e14i q^{58} -1.82611e15 q^{59} -1.48236e15 q^{61} +2.02561e15i q^{62} +1.05518e15i q^{63} -2.81475e14 q^{64} -4.53849e14 q^{66} +2.71410e15i q^{67} -1.47785e15i q^{68} +2.41471e15 q^{69} -3.87337e15 q^{71} -7.11949e14i q^{72} -2.85786e15i q^{73} -5.37314e15 q^{74} +8.38753e15 q^{76} -4.73421e15i q^{77} -3.75148e13i q^{78} -2.80988e15 q^{79} -9.39628e15 q^{81} +5.07194e15i q^{82} -7.04230e15i q^{83} -1.51740e16 q^{84} +1.17959e16 q^{86} -2.40194e16i q^{87} +3.19426e15i q^{88} -5.51966e16 q^{89} +3.91327e14 q^{91} -1.69951e16i q^{92} -7.36778e16i q^{93} +6.83076e16 q^{94} +1.02381e16 q^{96} -6.42662e16i q^{97} -9.87300e16i q^{98} -8.07940e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 262144 q^{4} + 669696 q^{6} + 215038188 q^{9} - 942962592 q^{11} + 309168128 q^{14} + 17179869184 q^{16} - 257345058800 q^{19} + 870762493248 q^{21} - 43889197056 q^{24} + 789419124736 q^{26} - 5086109499960 q^{29}+ \cdots - 52\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 262144 * q^4 + 669696 * q^6 + 215038188 * q^9 - 942962592 * q^11 + 309168128 * q^14 + 17179869184 * q^16 - 257345058800 * q^19 + 870762493248 * q^21 - 43889197056 * q^24 + 789419124736 * q^26 - 5086109499960 * q^29 + 15678815997488 * q^31 + 16455629088768 * q^34 - 14092742688768 * q^36 + 24135247074576 * q^39 - 75652728528312 * q^41 + 61797996429312 * q^44 - 332984247957504 * q^46 - 1603445169355908 * q^49 + 1295380982531088 * q^51 + 22095889551360 * q^54 - 20261642436608 * q^56 - 3055641434470320 * q^59 - 1263476426244232 * q^61 - 1125899906842624 * q^64 + 244151200161792 * q^66 - 1429906501577664 * q^69 - 6663803321824752 * q^71 - 14236267057948672 * q^74 + 16865365773516800 * q^76 - 16527213684110240 * q^79 - 26865367701318396 * q^81 - 57066290757500928 * q^84 - 15170792410548224 * q^86 - 111756825043809960 * q^89 - 76954793221206032 * q^91 + 113045290507266048 * q^94 + 2876322418262016 * q^96 - 52747342198192224 * q^99

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