LMFDB - Embedded newform 50.24.b.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,24,Mod(49,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	50.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$167.602018673$
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} + 58675x^{2} + 860659569 $ x^4 + 58675*x^2 + 860659569
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\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			49.1
Root			$171.781i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.24.b.b.49.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2048.00i q^{2} -589887. i q^{3} -4.19430e6 q^{4} -1.20809e9 q^{6} -8.65943e9i q^{7} +8.58993e9i q^{8} -2.53823e11 q^{9} -3.41600e11 q^{11} +2.47417e12i q^{12} -9.37599e12i q^{13} -1.77345e13 q^{14} +1.75922e13 q^{16} +1.26651e14i q^{17} +5.19830e14i q^{18} -2.68434e14 q^{19} -5.10808e15 q^{21} +6.99597e14i q^{22} -4.00352e15i q^{23} +5.06709e15 q^{24} -1.92020e16 q^{26} +9.41933e16i q^{27} +3.63203e16i q^{28} -7.20419e16 q^{29} +8.44456e16 q^{31} -3.60288e16i q^{32} +2.01505e17i q^{33} +2.59382e17 q^{34} +1.06461e18 q^{36} -8.22837e17i q^{37} +5.49753e17i q^{38} -5.53078e18 q^{39} -1.49837e18 q^{41} +1.04614e19i q^{42} -4.28965e18i q^{43} +1.43277e18 q^{44} -8.19921e18 q^{46} -8.20255e18i q^{47} -1.03774e19i q^{48} -4.76169e19 q^{49} +7.47099e19 q^{51} +3.93258e19i q^{52} +1.87100e19i q^{53} +1.92908e20 q^{54} +7.43839e19 q^{56} +1.58346e20i q^{57} +1.47542e20i q^{58} +1.04739e20 q^{59} -1.53791e20 q^{61} -1.72945e20i q^{62} +2.19797e21i q^{63} -7.37870e19 q^{64} +4.12683e20 q^{66} +1.63830e21i q^{67} -5.31214e20i q^{68} -2.36163e21 q^{69} +2.80919e21 q^{71} -2.18033e21i q^{72} +1.84822e21i q^{73} -1.68517e21 q^{74} +1.12589e21 q^{76} +2.95806e21i q^{77} +1.13270e22i q^{78} +8.75087e21 q^{79} +3.16676e22 q^{81} +3.06866e21i q^{82} -6.73667e21i q^{83} +2.14249e22 q^{84} -8.78520e21 q^{86} +4.24965e22i q^{87} -2.93432e21i q^{88} -1.65512e22 q^{89} -8.11907e22 q^{91} +1.67920e22i q^{92} -4.98134e22i q^{93} -1.67988e22 q^{94} -2.12529e22 q^{96} -4.48228e22i q^{97} +9.75195e22i q^{98} +8.67060e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16777216 q^{4} - 2811838464 q^{6} - 338022453348 q^{9} + 1873114539648 q^{11} - 14457221562368 q^{14} + 70368744177664 q^{16} + 513828480996400 q^{19} - 92\!\cdots\!72 q^{21} + 11\!\cdots\!56 q^{24}+ \cdots + 39\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 16777216 * q^4 - 2811838464 * q^6 - 338022453348 * q^9 + 1873114539648 * q^11 - 14457221562368 * q^14 + 70368744177664 * q^16 + 513828480996400 * q^19 - 9225112870917072 * q^21 + 11793705316909056 * q^24 - 40803722828529664 * q^26 - 390940010512005240 * q^29 + 337622787144424208 * q^31 - 6593371092860928 * q^34 + 1417768928167329792 * q^36 - 11174735998921715856 * q^39 + 3888451075379183448 * q^41 - 7856411806103764992 * q^44 - 14721443128002822144 * q^46 - 93126752671041347892 * q^49 + 124640539856501238288 * q^51 + 315009919262194237440 * q^54 + 60637982227926351872 * q^56 + 522526165771612251120 * q^59 - 681844237989141919192 * q^61 - 295147905179352825856 * q^64 + 319648046470575685632 * q^66 - 4644153579423826559376 * q^69 + 11431143241632899537328 * q^71 + 3747347916299749507072 * q^74 - 2155152853157124505600 * q^76 + 10222735538368045918240 * q^79 + 75964601237753871574164 * q^81 + 38692927814938958757888 * q^84 - 8855676726813586898944 * q^86 - 48669597539922410067240 * q^89 - 156370838392176790603472 * q^91 + 85604056909379500818432 * q^94 - 49466385385532921217024 * q^96 + 390218701442070249201024 * 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 $

$2$	− 2048.00i	− 0.707107i
$2$	− 2048.00i	− 0.707107i
$3$	− 589887.i	− 1.92254i	−0.275616	−	0.961268i	$-0.588882\pi$
$3$	− 589887.i	− 1.92254i	0.275616	−	0.961268i	$-0.411118\pi$
$4$	−4.19430e6	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.20809e9	−1.35944
$7$	− 8.65943e9i	− 1.65524i	−0.561287	−	0.827621i	$-0.689693\pi$
$7$	− 8.65943e9i	− 1.65524i	0.561287	−	0.827621i	$-0.310307\pi$
$8$	8.58993e9i	0.353553i
$9$	−2.53823e11	−2.69614
$10$	0	0
$11$	−3.41600e11	−0.360996	−0.180498	−	0.983575i	$-0.557771\pi$
$11$	−3.41600e11	−0.360996	−0.180498	+	0.983575i	$0.557771\pi$
$12$	2.47417e12i	0.961268i
$13$	− 9.37599e12i	− 1.45100i	−0.688220	−	0.725502i	$-0.741608\pi$
$13$	− 9.37599e12i	− 1.45100i	0.688220	−	0.725502i	$-0.258392\pi$
$14$	−1.77345e13	−1.17043
$15$	0	0
$16$	1.75922e13	0.250000
$17$	1.26651e14i	0.896286i	0.893962	+	0.448143i	$0.147915\pi$
$17$	1.26651e14i	0.896286i	−0.893962	+	0.448143i	$0.852085\pi$
$18$	5.19830e14i	1.90646i
$19$	−2.68434e14	−0.528654	−0.264327	−	0.964433i	$-0.585150\pi$
$19$	−2.68434e14	−0.528654	−0.264327	+	0.964433i	$0.585150\pi$
$20$	0	0
$21$	−5.10808e15	−3.18226
$22$	6.99597e14i	0.255262i
$23$	− 4.00352e15i	− 0.876137i	−0.898942	−	0.438069i	$-0.855663\pi$
$23$	− 4.00352e15i	− 0.876137i	0.898942	−	0.438069i	$-0.144337\pi$
$24$	5.06709e15	0.679719
$25$	0	0
$26$	−1.92020e16	−1.02602
$27$	9.41933e16i	3.26089i
$28$	3.63203e16i	0.827621i
$29$	−7.20419e16	−1.09650	−0.548249	−	0.836315i	$-0.684705\pi$
$29$	−7.20419e16	−1.09650	−0.548249	+	0.836315i	$0.684705\pi$
$30$	0	0
$31$	8.44456e16	0.596922	0.298461	−	0.954422i	$-0.403527\pi$
$31$	8.44456e16	0.596922	0.298461	+	0.954422i	$0.403527\pi$
$32$	− 3.60288e16i	− 0.176777i
$33$	2.01505e17i	0.694027i
$34$	2.59382e17	0.633770
$35$	0	0
$36$	1.06461e18	1.34807
$37$	− 8.22837e17i	− 0.760316i	−0.924922	−	0.380158i	$-0.875870\pi$
$37$	− 8.22837e17i	− 0.760316i	0.924922	−	0.380158i	$-0.124130\pi$
$38$	5.49753e17i	0.373815i
$39$	−5.53078e18	−2.78961
$40$	0	0
$41$	−1.49837e18	−0.425211	−0.212605	−	0.977138i	$-0.568195\pi$
$41$	−1.49837e18	−0.425211	−0.212605	+	0.977138i	$0.568195\pi$
$42$	1.04614e19i	2.25020i
$43$	− 4.28965e18i	− 0.703938i	−0.936012	−	0.351969i	$-0.885512\pi$
$43$	− 4.28965e18i	− 0.703938i	0.936012	−	0.351969i	$-0.114488\pi$
$44$	1.43277e18	0.180498
$45$	0	0
$46$	−8.19921e18	−0.619523
$47$	− 8.20255e18i	− 0.483976i	−0.970279	−	0.241988i	$-0.922201\pi$
$47$	− 8.20255e18i	− 0.483976i	0.970279	−	0.241988i	$-0.0777994\pi$
$48$	− 1.03774e19i	− 0.480634i
$49$	−4.76169e19	−1.73983
$50$	0	0
$51$	7.47099e19	1.72314
$52$	3.93258e19i	0.725502i
$53$	1.87100e19i	0.277269i	0.990344	+	0.138635i	$0.0442714\pi$
$53$	1.87100e19i	0.277269i	−0.990344	+	0.138635i	$0.955729\pi$
$54$	1.92908e20	2.30580
$55$	0	0
$56$	7.43839e19	0.585217
$57$	1.58346e20i	1.01636i
$58$	1.47542e20i	0.775341i
$59$	1.04739e20	0.452178	0.226089	−	0.974107i	$-0.427406\pi$
$59$	1.04739e20	0.452178	0.226089	+	0.974107i	$0.427406\pi$
$60$	0	0
$61$	−1.53791e20	−0.452519	−0.226259	−	0.974067i	$-0.572650\pi$
$61$	−1.53791e20	−0.452519	−0.226259	+	0.974067i	$0.572650\pi$
$62$	− 1.72945e20i	− 0.422088i
$63$	2.19797e21i	4.46277i
$64$	−7.37870e19	−0.125000
$65$	0	0
$66$	4.12683e20	0.490751
$67$	1.63830e21i	1.63883i	0.573200	+	0.819415i	$0.305702\pi$
$67$	1.63830e21i	1.63883i	−0.573200	+	0.819415i	$0.694298\pi$
$68$	− 5.31214e20i	− 0.448143i
$69$	−2.36163e21	−1.68440
$70$	0	0
$71$	2.80919e21	1.44248	0.721241	−	0.692684i	$-0.243572\pi$
$71$	2.80919e21	1.44248	0.721241	+	0.692684i	$0.243572\pi$
$72$	− 2.18033e21i	− 0.953230i
$73$	1.84822e21i	0.689510i	0.938693	+	0.344755i	$0.112038\pi$
$73$	1.84822e21i	0.689510i	−0.938693	+	0.344755i	$0.887962\pi$
$74$	−1.68517e21	−0.537625
$75$	0	0
$76$	1.12589e21	0.264327
$77$	2.95806e21i	0.597535i
$78$	1.13270e22i	1.97255i
$79$	8.75087e21	1.31625	0.658127	−	0.752907i	$-0.271349\pi$
$79$	8.75087e21	1.31625	0.658127	+	0.752907i	$0.271349\pi$
$80$	0	0
$81$	3.16676e22	3.57304
$82$	3.06866e21i	0.300669i
$83$	− 6.73667e21i	− 0.574179i	−0.957904	−	0.287090i	$-0.907312\pi$
$83$	− 6.73667e21i	− 0.574179i	0.957904	−	0.287090i	$-0.0926877\pi$
$84$	2.14249e22	1.59113
$85$	0	0
$86$	−8.78520e21	−0.497759
$87$	4.24965e22i	2.10806i
$88$	− 2.93432e21i	− 0.127631i
$89$	−1.65512e22	−0.632185	−0.316092	−	0.948728i	$-0.602371\pi$
$89$	−1.65512e22	−0.632185	−0.316092	+	0.948728i	$0.602371\pi$
$90$	0	0
$91$	−8.11907e22	−2.40176
$92$	1.67920e22i	0.438069i
$93$	− 4.98134e22i	− 1.14760i
$94$	−1.67988e22	−0.342223
$95$	0	0
$96$	−2.12529e22	−0.339859
$97$	− 4.48228e22i	− 0.636244i	−0.948050	−	0.318122i	$-0.896948\pi$
$97$	− 4.48228e22i	− 0.636244i	0.948050	−	0.318122i	$-0.103052\pi$
$98$	9.75195e22i	1.23024i
$99$	8.67060e22	0.973295
$100$	0	0
$101$	−1.48622e23	−1.32552	−0.662760	−	0.748832i	$-0.730615\pi$
$101$	−1.48622e23	−1.32552	−0.662760	+	0.748832i	$0.730615\pi$
$102$	− 1.53006e23i	− 1.21845i
$103$	− 6.64435e22i	− 0.472960i	−0.971636	−	0.236480i	$-0.924006\pi$
$103$	− 6.64435e22i	− 0.472960i	0.971636	−	0.236480i	$-0.0759937\pi$
$104$	8.05392e22	0.513008
$105$	0	0
$106$	3.83181e22	0.196059
$107$	3.18955e22i	0.146493i	0.997314	+	0.0732463i	$0.0233359\pi$
$107$	3.18955e22i	0.146493i	−0.997314	+	0.0732463i	$0.976664\pi$
$108$	− 3.95075e23i	− 1.63045i
$109$	−1.27271e22	−0.0472418	−0.0236209	−	0.999721i	$-0.507519\pi$
$109$	−1.27271e22	−0.0472418	−0.0236209	+	0.999721i	$0.507519\pi$
$110$	0	0
$111$	−4.85381e23	−1.46173
$112$	− 1.52338e23i	− 0.413811i
$113$	− 1.29270e23i	− 0.317027i	−0.987357	−	0.158513i	$-0.949330\pi$
$113$	− 1.29270e23i	− 0.317027i	0.987357	−	0.158513i	$-0.0506701\pi$
$114$	3.24292e23	0.718672
$115$	0	0
$116$	3.02165e23	0.548249
$117$	2.37985e24i	3.91211i
$118$	− 2.14505e23i	− 0.319738i
$119$	1.09673e24	1.48357
$120$	0	0
$121$	−7.78740e23	−0.869682
$122$	3.14963e23i	0.319979i
$123$	8.83868e23i	0.817482i
$124$	−3.54191e23	−0.298461
$125$	0	0
$126$	4.50143e24	3.15566
$127$	− 2.37120e24i	− 1.51784i	−0.651187	−	0.758918i	$-0.725729\pi$
$127$	− 2.37120e24i	− 1.51784i	0.651187	−	0.758918i	$-0.274271\pi$
$128$	1.51116e23i	0.0883883i
$129$	−2.53041e24	−1.35335
$130$	0	0
$131$	2.08233e24	0.933103	0.466551	−	0.884494i	$-0.345496\pi$
$131$	2.08233e24	0.933103	0.466551	+	0.884494i	$0.345496\pi$
$132$	− 8.45175e23i	− 0.347013i
$133$	2.32449e24i	0.875051i
$134$	3.35525e24	1.15883
$135$	0	0
$136$	−1.08793e24	−0.316885
$137$	− 2.45853e24i	− 0.658248i	−0.944287	−	0.329124i	$-0.893247\pi$
$137$	− 2.45853e24i	− 0.658248i	0.944287	−	0.329124i	$-0.106753\pi$
$138$	4.83661e24i	1.19105i
$139$	−2.83898e24	−0.643417	−0.321708	−	0.946839i	$-0.604257\pi$
$139$	−2.83898e24	−0.643417	−0.321708	+	0.946839i	$0.604257\pi$
$140$	0	0
$141$	−4.83858e24	−0.930461
$142$	− 5.75323e24i	− 1.01999i
$143$	3.20284e24i	0.523806i
$144$	−4.46531e24	−0.674036
$145$	0	0
$146$	3.78515e24	0.487557
$147$	2.80886e25i	3.34488i
$148$	3.45123e24i	0.380158i
$149$	1.04342e25	1.06370	0.531849	−	0.846839i	$-0.321497\pi$
$149$	1.04342e25	1.06370	0.531849	+	0.846839i	$0.321497\pi$
$150$	0	0
$151$	−3.94859e24	−0.345308	−0.172654	−	0.984982i	$-0.555234\pi$
$151$	−3.94859e24	−0.345308	−0.172654	+	0.984982i	$0.555234\pi$
$152$	− 2.30583e24i	− 0.186907i
$153$	− 3.21470e25i	− 2.41652i
$154$	6.05811e24	0.422521
$155$	0	0
$156$	2.31978e25	1.39480
$157$	− 1.85824e25i	− 1.03814i	−0.854732	−	0.519070i	$-0.826278\pi$
$157$	− 1.85824e25i	− 1.03814i	0.854732	−	0.519070i	$-0.173722\pi$
$158$	− 1.79218e25i	− 0.930732i
$159$	1.10368e25	0.533060
$160$	0	0
$161$	−3.46682e25	−1.45022
$162$	− 6.48553e25i	− 2.52652i
$163$	− 4.00527e25i	− 1.45370i	−0.686798	−	0.726849i	$-0.740984\pi$
$163$	− 4.00527e25i	− 1.45370i	0.686798	−	0.726849i	$-0.259016\pi$
$164$	6.28461e24	0.212605
$165$	0	0
$166$	−1.37967e25	−0.406006
$167$	7.99548e24i	0.219586i	0.993954	+	0.109793i	$0.0350188\pi$
$167$	7.99548e24i	0.219586i	−0.993954	+	0.109793i	$0.964981\pi$
$168$	− 4.38781e25i	− 1.12510i
$169$	−4.61554e25	−1.10541
$170$	0	0
$171$	6.81349e25	1.42533
$172$	1.79921e25i	0.351969i
$173$	− 8.98445e25i	− 1.64423i	−0.569325	−	0.822113i	$-0.692795\pi$
$173$	− 8.98445e25i	− 1.64423i	0.569325	−	0.822113i	$-0.307205\pi$
$174$	8.70329e25	1.49062
$175$	0	0
$176$	−6.00949e24	−0.0902489
$177$	− 6.17841e25i	− 0.869329i
$178$	3.38968e25i	0.447022i
$179$	−1.18230e26	−1.46190	−0.730949	−	0.682433i	$-0.760922\pi$
$179$	−1.18230e26	−1.46190	−0.730949	+	0.682433i	$0.760922\pi$
$180$	0	0
$181$	−1.17668e26	−1.28043	−0.640213	−	0.768198i	$-0.721154\pi$
$181$	−1.17668e26	−1.28043	−0.640213	+	0.768198i	$0.721154\pi$
$182$	1.66279e26i	1.69830i
$183$	9.07191e25i	0.869983i
$184$	3.43900e25	0.309761
$185$	0	0
$186$	−1.02018e26	−0.811478
$187$	− 4.32640e25i	− 0.323555i
$188$	3.44040e25i	0.241988i
$189$	8.15660e26	5.39757
$190$	0	0
$191$	2.94896e26	1.72896	0.864480	−	0.502668i	$-0.167648\pi$
$191$	2.94896e26	1.72896	0.864480	+	0.502668i	$0.167648\pi$
$192$	4.35260e25i	0.240317i
$193$	− 1.41854e26i	− 0.737789i	−0.929471	−	0.368894i	$-0.879736\pi$
$193$	− 1.41854e26i	− 0.737789i	0.929471	−	0.368894i	$-0.120264\pi$
$194$	−9.17970e25	−0.449892
$195$	0	0
$196$	1.99720e26	0.869915
$197$	− 1.89037e25i	− 0.0776580i	−0.999246	−	0.0388290i	$-0.987637\pi$
$197$	− 1.89037e25i	− 0.0776580i	0.999246	−	0.0388290i	$-0.0123628\pi$
$198$	− 1.77574e26i	− 0.688224i
$199$	4.29000e26	1.56909	0.784543	−	0.620074i	$-0.212898\pi$
$199$	4.29000e26	1.56909	0.784543	+	0.620074i	$0.212898\pi$
$200$	0	0
$201$	9.66414e26	3.15071
$202$	3.04377e26i	0.937284i
$203$	6.23841e26i	1.81497i
$204$	−3.13356e26	−0.861571
$205$	0	0
$206$	−1.36076e26	−0.334433
$207$	1.01619e27i	2.36219i
$208$	− 1.64944e26i	− 0.362751i
$209$	9.16971e25	0.190842
$210$	0	0
$211$	−5.54819e26	−1.03491	−0.517456	−	0.855710i	$-0.673121\pi$
$211$	−5.54819e26	−1.03491	−0.517456	+	0.855710i	$0.673121\pi$
$212$	− 7.84756e25i	− 0.138635i
$213$	− 1.65711e27i	− 2.77322i
$214$	6.53220e25	0.103586
$215$	0	0
$216$	−8.09114e26	−1.15290
$217$	− 7.31251e26i	− 0.988051i
$218$	2.60652e25i	0.0334050i
$219$	1.09024e27	1.32561
$220$	0	0
$221$	1.18748e27	1.30052
$222$	9.94060e26i	1.03360i
$223$	1.18597e26i	0.117103i	0.998284	+	0.0585517i	$0.0186483\pi$
$223$	1.18597e26i	0.117103i	−0.998284	+	0.0585517i	$0.981352\pi$
$224$	−3.11989e26	−0.292608
$225$	0	0
$226$	−2.64745e26	−0.224172
$227$	− 4.65610e26i	− 0.374736i	−0.982290	−	0.187368i	$-0.940004\pi$
$227$	− 4.65610e26i	− 0.374736i	0.982290	−	0.187368i	$-0.0599956\pi$
$228$	− 6.64151e26i	− 0.508178i
$229$	9.14229e26	0.665192	0.332596	−	0.943069i	$-0.392075\pi$
$229$	9.14229e26	0.665192	0.332596	+	0.943069i	$0.392075\pi$
$230$	0	0
$231$	1.74492e27	1.14878
$232$	− 6.18835e26i	− 0.387671i
$233$	− 1.71939e25i	− 0.0102514i	−0.999987	−	0.00512569i	$-0.998368\pi$
$233$	− 1.71939e25i	− 0.0102514i	0.999987	−	0.00512569i	$-0.00163156\pi$
$234$	4.87393e27	2.76628
$235$	0	0
$236$	−4.39307e26	−0.226089
$237$	− 5.16203e27i	− 2.53055i
$238$	− 2.24610e27i	− 1.04904i
$239$	1.37899e27	0.613741	0.306870	−	0.951751i	$-0.400718\pi$
$239$	1.37899e27	0.613741	0.306870	+	0.951751i	$0.400718\pi$
$240$	0	0
$241$	−4.72718e27	−1.91164	−0.955821	−	0.293950i	$-0.905030\pi$
$241$	−4.72718e27	−1.91164	−0.955821	+	0.293950i	$0.905030\pi$
$242$	1.59486e27i	0.614958i
$243$	− 9.81267e27i	− 3.60840i
$244$	6.45044e26	0.226259
$245$	0	0
$246$	1.81016e27	0.578047
$247$	2.51684e27i	0.767079i
$248$	7.25382e26i	0.211044i
$249$	−3.97388e27	−1.10388
$250$	0	0
$251$	−4.79993e27	−1.21615	−0.608075	−	0.793879i	$-0.708058\pi$
$251$	−4.79993e27	−1.21615	−0.608075	+	0.793879i	$0.708058\pi$
$252$	− 9.21894e27i	− 2.23139i
$253$	1.36760e27i	0.316282i
$254$	−4.85621e27	−1.07327
$255$	0	0
$256$	3.09485e26	0.0625000
$257$	9.07525e27i	1.75238i	0.481968	+	0.876189i	$0.339922\pi$
$257$	9.07525e27i	1.75238i	−0.481968	+	0.876189i	$0.660078\pi$
$258$	5.18228e27i	0.956960i
$259$	−7.12530e27	−1.25851
$260$	0	0
$261$	1.82859e28	2.95632
$262$	− 4.26461e27i	− 0.659803i
$263$	8.09758e25i	0.0119912i	0.999982	+	0.00599562i	$0.00190848\pi$
$263$	8.09758e25i	0.0119912i	−0.999982	+	0.00599562i	$0.998092\pi$
$264$	−1.73092e27	−0.245375
$265$	0	0
$266$	4.76055e27	0.618754
$267$	9.76333e27i	1.21540i
$268$	− 6.87154e27i	− 0.819415i
$269$	1.72812e28	1.97435	0.987173	−	0.159656i	$-0.0510384\pi$
$269$	1.72812e28	1.97435	0.987173	+	0.159656i	$0.0510384\pi$
$270$	0	0
$271$	−1.25531e28	−1.31706	−0.658528	−	0.752557i	$-0.728820\pi$
$271$	−1.25531e28	−1.31706	−0.658528	+	0.752557i	$0.728820\pi$
$272$	2.22807e27i	0.224072i
$273$	4.78934e28i	4.61748i
$274$	−5.03507e27	−0.465451
$275$	0	0
$276$	9.90538e27	0.842202
$277$	− 5.00554e27i	− 0.408257i	−0.978944	−	0.204129i	$-0.934564\pi$
$277$	− 5.00554e27i	− 0.408257i	0.978944	−	0.204129i	$-0.0654361\pi$
$278$	5.81423e27i	0.454964i
$279$	−2.14343e28	−1.60939
$280$	0	0
$281$	−2.40666e27	−0.166453	−0.0832265	−	0.996531i	$-0.526522\pi$
$281$	−2.40666e27	−0.166453	−0.0832265	+	0.996531i	$0.526522\pi$
$282$	9.90941e27i	0.657935i
$283$	− 2.62143e28i	− 1.67107i	−0.549438	−	0.835535i	$-0.685158\pi$
$283$	− 2.62143e28i	− 1.67107i	0.549438	−	0.835535i	$-0.314842\pi$
$284$	−1.17826e28	−0.721241
$285$	0	0
$286$	6.55941e27	0.370387
$287$	1.29750e28i	0.703827i
$288$	9.14495e27i	0.476615i
$289$	3.92704e27	0.196671
$290$	0	0
$291$	−2.64404e28	−1.22320
$292$	− 7.75199e27i	− 0.344755i
$293$	3.01791e27i	0.129041i	0.997916	+	0.0645206i	$0.0205518\pi$
$293$	3.01791e27i	0.129041i	−0.997916	+	0.0645206i	$0.979448\pi$
$294$	5.75255e28	2.36519
$295$	0	0
$296$	7.06812e27	0.268812
$297$	− 3.21764e28i	− 1.17717i
$298$	− 2.13693e28i	− 0.752149i
$299$	−3.75370e28	−1.27128
$300$	0	0
$301$	−3.71459e28	−1.16519
$302$	8.08671e27i	0.244170i
$303$	8.76699e28i	2.54836i
$304$	−4.72235e27	−0.132164
$305$	0	0
$306$	−6.58371e28	−1.70873
$307$	− 2.03128e28i	− 0.507784i	−0.967233	−	0.253892i	$-0.918289\pi$
$307$	− 2.03128e28i	− 0.507784i	0.967233	−	0.253892i	$-0.0817107\pi$
$308$	− 1.24070e28i	− 0.298768i
$309$	−3.91941e28	−0.909282
$310$	0	0
$311$	6.48885e28	1.39773	0.698865	−	0.715254i	$-0.253689\pi$
$311$	6.48885e28	1.39773	0.698865	+	0.715254i	$0.253689\pi$
$312$	− 4.75090e28i	− 0.986275i
$313$	− 4.80190e28i	− 0.960845i	−0.877037	−	0.480423i	$-0.840483\pi$
$313$	− 4.80190e28i	− 0.960845i	0.877037	−	0.480423i	$-0.159517\pi$
$314$	−3.80568e28	−0.734076
$315$	0	0
$316$	−3.67038e28	−0.658127
$317$	5.25019e28i	0.907807i	0.891051	+	0.453903i	$0.149969\pi$
$317$	5.25019e28i	0.907807i	−0.891051	+	0.453903i	$0.850031\pi$
$318$	− 2.26034e28i	− 0.376931i
$319$	2.46095e28	0.395831
$320$	0	0
$321$	1.88147e28	0.281637
$322$	7.10005e28i	1.02546i
$323$	− 3.39975e28i	− 0.473825i
$324$	−1.32824e29	−1.78652
$325$	0	0
$326$	−8.20279e28	−1.02792
$327$	7.50758e27i	0.0908240i
$328$	− 1.28709e28i	− 0.150335i
$329$	−7.10294e28	−0.801097
$330$	0	0
$331$	−1.29656e28	−0.136386	−0.0681930	−	0.997672i	$-0.521723\pi$
$331$	−1.29656e28	−0.136386	−0.0681930	+	0.997672i	$0.521723\pi$
$332$	2.82557e28i	0.287090i
$333$	2.08855e29i	2.04992i
$334$	1.63747e28	0.155271
$335$	0	0
$336$	−8.98624e28	−0.795566
$337$	9.04429e28i	0.773803i	0.922121	+	0.386902i	$0.126455\pi$
$337$	9.04429e28i	0.773803i	−0.922121	+	0.386902i	$0.873545\pi$
$338$	9.45262e28i	0.781646i
$339$	−7.62548e28	−0.609495
$340$	0	0
$341$	−2.88466e28	−0.215486
$342$	− 1.39540e29i	− 1.00786i
$343$	1.75338e29i	1.22460i
$344$	3.68478e28	0.248880
$345$	0	0
$346$	−1.84002e29	−1.16264
$347$	− 1.49288e29i	− 0.912504i	−0.889851	−	0.456252i	$-0.849192\pi$
$347$	− 1.49288e29i	− 0.912504i	0.889851	−	0.456252i	$-0.150808\pi$
$348$	− 1.78243e29i	− 1.05403i
$349$	1.52139e29	0.870459	0.435230	−	0.900319i	$-0.356667\pi$
$349$	1.52139e29	0.870459	0.435230	+	0.900319i	$0.356667\pi$
$350$	0	0
$351$	8.83156e29	4.73157
$352$	1.23074e28i	0.0638156i
$353$	− 2.49410e29i	− 1.25171i	−0.779938	−	0.625857i	$-0.784750\pi$
$353$	− 2.49410e29i	− 1.25171i	0.779938	−	0.625857i	$-0.215250\pi$
$354$	−1.26534e29	−0.614708
$355$	0	0
$356$	6.94207e28	0.316092
$357$	− 6.46945e29i	− 2.85222i
$358$	2.42134e29i	1.03372i
$359$	−3.91702e29	−1.61946	−0.809728	−	0.586805i	$-0.800386\pi$
$359$	−3.91702e29	−1.61946	−0.809728	+	0.586805i	$0.800386\pi$
$360$	0	0
$361$	−1.85773e29	−0.720525
$362$	2.40984e29i	0.905398i
$363$	4.59368e29i	1.67199i
$364$	3.40539e29	1.20088
$365$	0	0
$366$	1.85793e29	0.615171
$367$	1.79517e29i	0.576032i	0.957626	+	0.288016i	$0.0929956\pi$
$367$	1.79517e29i	0.576032i	−0.957626	+	0.288016i	$0.907004\pi$
$368$	− 7.04307e28i	− 0.219034i
$369$	3.80321e29	1.14643
$370$	0	0
$371$	1.62018e29	0.458948
$372$	2.08932e29i	0.573802i
$373$	7.00737e29i	1.86597i	0.359920	+	0.932983i	$0.382804\pi$
$373$	7.00737e29i	1.86597i	−0.359920	+	0.932983i	$0.617196\pi$
$374$	−8.86048e28	−0.228788
$375$	0	0
$376$	7.04594e28	0.171111
$377$	6.75464e29i	1.59102i
$378$	− 1.67047e30i	− 3.81666i
$379$	−7.85722e28	−0.174148	−0.0870739	−	0.996202i	$-0.527752\pi$
$379$	−7.85722e28	−0.174148	−0.0870739	+	0.996202i	$0.527752\pi$
$380$	0	0
$381$	−1.39874e30	−2.91809
$382$	− 6.03947e29i	− 1.22256i
$383$	− 4.36132e29i	− 0.856707i	−0.903611	−	0.428353i	$-0.859094\pi$
$383$	− 4.36132e29i	− 0.856707i	0.903611	−	0.428353i	$-0.140906\pi$
$384$	8.91412e28	0.169930
$385$	0	0
$386$	−2.90517e29	−0.521696
$387$	1.08881e30i	1.89792i
$388$	1.88000e29i	0.318122i
$389$	8.02563e28	0.131844	0.0659218	−	0.997825i	$-0.479001\pi$
$389$	8.02563e28	0.131844	0.0659218	+	0.997825i	$0.479001\pi$
$390$	0	0
$391$	5.07051e29	0.785270
$392$	− 4.09026e29i	− 0.615122i
$393$	− 1.22834e30i	− 1.79392i
$394$	−3.87148e28	−0.0549125
$395$	0	0
$396$	−3.63672e29	−0.486648
$397$	− 1.82014e29i	− 0.236600i	−0.992978	−	0.118300i	$-0.962256\pi$
$397$	− 1.82014e29i	− 0.236600i	0.992978	−	0.118300i	$-0.0377444\pi$
$398$	− 8.78592e29i	− 1.10951i
$399$	1.37118e30	1.68232
$400$	0	0
$401$	1.22321e30	1.41691	0.708454	−	0.705757i	$-0.249393\pi$
$401$	1.22321e30	1.41691	0.708454	+	0.705757i	$0.249393\pi$
$402$	− 1.97922e30i	− 2.22789i
$403$	− 7.91762e29i	− 0.866137i
$404$	6.23364e29	0.662760
$405$	0	0
$406$	1.27763e30	1.28338
$407$	2.81081e29i	0.274471i
$408$	6.41753e29i	0.609223i
$409$	1.28273e30	1.18391	0.591954	−	0.805972i	$-0.298357\pi$
$409$	1.28273e30	1.18391	0.591954	+	0.805972i	$0.298357\pi$
$410$	0	0
$411$	−1.45026e30	−1.26550
$412$	2.78684e29i	0.236480i
$413$	− 9.06979e29i	− 0.748465i
$414$	2.08115e30	1.67032
$415$	0	0
$416$	−3.37806e29	−0.256504
$417$	1.67468e30i	1.23699i
$418$	− 1.87796e29i	− 0.134946i
$419$	−3.03804e29	−0.212389	−0.106194	−	0.994345i	$-0.533867\pi$
$419$	−3.03804e29	−0.212389	−0.106194	+	0.994345i	$0.533867\pi$
$420$	0	0
$421$	1.27738e30	0.845427	0.422714	−	0.906263i	$-0.361078\pi$
$421$	1.27738e30	0.845427	0.422714	+	0.906263i	$0.361078\pi$
$422$	1.13627e30i	0.731793i
$423$	2.08200e30i	1.30487i
$424$	−1.60718e29	−0.0980296
$425$	0	0
$426$	−3.39375e30	−1.96097
$427$	1.33174e30i	0.749029i
$428$	− 1.33779e29i	− 0.0732463i
$429$	1.88931e30	1.00704
$430$	0	0
$431$	−1.22639e30	−0.619642	−0.309821	−	0.950795i	$-0.600269\pi$
$431$	−1.22639e30	−0.619642	−0.309821	+	0.950795i	$0.600269\pi$
$432$	1.65707e30i	0.815223i
$433$	2.34066e30i	1.12132i	0.828047	+	0.560658i	$0.189452\pi$
$433$	2.34066e30i	1.12132i	−0.828047	+	0.560658i	$0.810548\pi$
$434$	−1.49760e30	−0.698658
$435$	0	0
$436$	5.33815e28	0.0236209
$437$	1.07468e30i	0.463174i
$438$	− 2.23281e30i	− 0.937346i
$439$	−2.33966e30	−0.956779	−0.478389	−	0.878148i	$-0.658779\pi$
$439$	−2.33966e30	−0.956779	−0.478389	+	0.878148i	$0.658779\pi$
$440$	0	0
$441$	1.20863e31	4.69083
$442$	− 2.43196e30i	− 0.919603i
$443$	5.19485e30i	1.91395i	0.290175	+	0.956974i	$0.406286\pi$
$443$	5.19485e30i	1.91395i	−0.290175	+	0.956974i	$0.593714\pi$
$444$	2.03584e30	0.730867
$445$	0	0
$446$	2.42888e29	0.0828046
$447$	− 6.15502e30i	− 2.04500i
$448$	6.38953e29i	0.206905i
$449$	−8.46675e29	−0.267229	−0.133615	−	0.991033i	$-0.542658\pi$
$449$	−8.46675e29	−0.267229	−0.133615	+	0.991033i	$0.542658\pi$
$450$	0	0
$451$	5.11842e29	0.153499
$452$	5.42198e29i	0.158513i
$453$	2.32922e30i	0.663868i
$454$	−9.53569e29	−0.264978
$455$	0	0
$456$	−1.36018e30	−0.359336
$457$	4.30243e30i	1.10835i	0.832399	+	0.554176i	$0.186967\pi$
$457$	4.30243e30i	1.10835i	−0.832399	+	0.554176i	$0.813033\pi$
$458$	− 1.87234e30i	− 0.470362i
$459$	−1.19297e31	−2.92269
$460$	0	0
$461$	5.59904e30	1.30483	0.652413	−	0.757863i	$-0.273757\pi$
$461$	5.59904e30	1.30483	0.652413	+	0.757863i	$0.273757\pi$
$462$	− 3.57360e30i	− 0.812312i
$463$	− 6.54677e30i	− 1.45160i	−0.687908	−	0.725798i	$-0.741471\pi$
$463$	− 6.54677e30i	− 1.45160i	0.687908	−	0.725798i	$-0.258529\pi$
$464$	−1.26737e30	−0.274125
$465$	0	0
$466$	−3.52132e28	−0.00724882
$467$	− 2.46045e30i	− 0.494163i	−0.968995	−	0.247082i	$-0.920528\pi$
$467$	− 2.46045e30i	− 0.494163i	0.968995	−	0.247082i	$-0.0794716\pi$
$468$	− 9.98180e30i	− 1.95606i
$469$	1.41868e31	2.71266
$470$	0	0
$471$	−1.09615e31	−1.99586
$472$	8.99700e29i	0.159869i
$473$	1.46534e30i	0.254119i
$474$	−1.05718e31	−1.78937
$475$	0	0
$476$	−4.60001e30	−0.741786
$477$	− 4.74904e30i	− 0.747558i
$478$	− 2.82417e30i	− 0.433980i
$479$	6.11043e30	0.916671	0.458336	−	0.888779i	$-0.348446\pi$
$479$	6.11043e30	0.916671	0.458336	+	0.888779i	$0.348446\pi$
$480$	0	0
$481$	−7.71492e30	−1.10322
$482$	9.68127e30i	1.35173i
$483$	2.04503e31i	2.78810i
$484$	3.26627e30	0.434841
$485$	0	0
$486$	−2.00964e31	−2.55153
$487$	− 5.95367e30i	− 0.738247i	−0.929380	−	0.369124i	$-0.879658\pi$
$487$	− 5.95367e30i	− 0.738247i	0.929380	−	0.369124i	$-0.120342\pi$
$488$	− 1.32105e30i	− 0.159990i
$489$	−2.36265e31	−2.79478
$490$	0	0
$491$	−4.90871e30	−0.554026	−0.277013	−	0.960866i	$-0.589345\pi$
$491$	−4.90871e30	−0.554026	−0.277013	+	0.960866i	$0.589345\pi$
$492$	− 3.70721e30i	− 0.408741i
$493$	− 9.12419e30i	− 0.982776i
$494$	5.15448e30	0.542407
$495$	0	0
$496$	1.48558e30	0.149231
$497$	− 2.43260e31i	− 2.38766i
$498$	8.13850e30i	0.780561i
$499$	−1.58005e29	−0.0148087	−0.00740433	−	0.999973i	$-0.502357\pi$
$499$	−1.58005e29	−0.0148087	−0.00740433	+	0.999973i	$0.502357\pi$
$500$	0	0
$501$	4.71643e30	0.422162
$502$	9.83026e30i	0.859948i
$503$	7.88073e30i	0.673805i	0.941539	+	0.336903i	$0.109379\pi$
$503$	7.88073e30i	0.673805i	−0.941539	+	0.336903i	$0.890621\pi$
$504$	−1.88804e31	−1.57783
$505$	0	0
$506$	2.80085e30	0.223645
$507$	2.72264e31i	2.12520i
$508$	9.94552e30i	0.758918i
$509$	1.29230e31	0.964070	0.482035	−	0.876152i	$-0.339898\pi$
$509$	1.29230e31	0.964070	0.482035	+	0.876152i	$0.339898\pi$
$510$	0	0
$511$	1.60045e31	1.14131
$512$	− 6.33825e29i	− 0.0441942i
$513$	− 2.52847e31i	− 1.72388i
$514$	1.85861e31	1.23912
$515$	0	0
$516$	1.06133e31	0.676673
$517$	2.80199e30i	0.174713i
$518$	1.45926e31i	0.889899i
$519$	−5.29981e31	−3.16108
$520$	0	0
$521$	2.00059e31	1.14163	0.570814	−	0.821079i	$-0.306628\pi$
$521$	2.00059e31	1.14163	0.570814	+	0.821079i	$0.306628\pi$
$522$	− 3.74495e31i	− 2.09043i
$523$	3.24415e31i	1.77146i	0.464199	+	0.885731i	$0.346342\pi$
$523$	3.24415e31i	1.77146i	−0.464199	+	0.885731i	$0.653658\pi$
$524$	−8.73392e30	−0.466551
$525$	0	0
$526$	1.65838e29	0.00847908
$527$	1.06951e31i	0.535013i
$528$	3.54492e30i	0.173507i
$529$	4.85228e30	0.232383
$530$	0	0
$531$	−2.65852e31	−1.21914
$532$	− 9.74961e30i	− 0.437525i
$533$	1.40487e31i	0.616982i
$534$	1.99953e31	0.859416
$535$	0	0
$536$	−1.40729e31	−0.579414
$537$	6.97422e31i	2.81055i
$538$	− 3.53919e31i	− 1.39607i
$539$	1.62659e31	0.628071
$540$	0	0
$541$	−3.62031e31	−1.33961	−0.669804	−	0.742538i	$-0.733622\pi$
$541$	−3.62031e31	−1.33961	−0.669804	+	0.742538i	$0.733622\pi$
$542$	2.57087e31i	0.931299i
$543$	6.94108e31i	2.46166i
$544$	4.56309e30	0.158443
$545$	0	0
$546$	9.80856e31	3.26505
$547$	3.22624e31i	1.05158i	0.850614	+	0.525791i	$0.176231\pi$
$547$	3.22624e31i	1.05158i	−0.850614	+	0.525791i	$0.823769\pi$
$548$	1.03118e31i	0.329124i
$549$	3.90357e31	1.22006
$550$	0	0
$551$	1.93385e31	0.579668
$552$	− 2.02862e31i	− 0.595527i
$553$	− 7.57776e31i	− 2.17872i
$554$	−1.02514e31	−0.288681
$555$	0	0
$556$	1.19076e31	0.321708
$557$	4.85642e31i	1.28523i	0.766189	+	0.642616i	$0.222151\pi$
$557$	4.85642e31i	1.28523i	−0.766189	+	0.642616i	$0.777849\pi$
$558$	4.38974e31i	1.13801i
$559$	−4.02197e31	−1.02142
$560$	0	0
$561$	−2.55209e31	−0.622047
$562$	4.92884e30i	0.117700i
$563$	5.02515e31i	1.17572i	0.808964	+	0.587858i	$0.200028\pi$
$563$	5.02515e31i	1.17572i	−0.808964	+	0.587858i	$0.799972\pi$
$564$	2.02945e31	0.465230
$565$	0	0
$566$	−5.36869e31	−1.18162
$567$	− 2.74224e32i	− 5.91425i
$568$	2.41308e31i	0.509995i
$569$	7.80283e31	1.61607	0.808037	−	0.589132i	$-0.200530\pi$
$569$	7.80283e31	1.61607	0.808037	+	0.589132i	$0.200530\pi$
$570$	0	0
$571$	−4.11699e31	−0.818963	−0.409481	−	0.912319i	$-0.634290\pi$
$571$	−4.11699e31	−0.818963	−0.409481	+	0.912319i	$0.634290\pi$
$572$	− 1.34337e31i	− 0.261903i
$573$	− 1.73955e32i	− 3.32399i
$574$	2.65728e31	0.497681
$575$	0	0
$576$	1.87289e31	0.337018
$577$	7.34525e31i	1.29564i	0.761793	+	0.647820i	$0.224319\pi$
$577$	7.34525e31i	1.29564i	−0.761793	+	0.647820i	$0.775681\pi$
$578$	− 8.04257e30i	− 0.139067i
$579$	−8.36777e31	−1.41843
$580$	0	0
$581$	−5.83357e31	−0.950406
$582$	5.41499e31i	0.864934i
$583$	− 6.39134e30i	− 0.100093i
$584$	−1.58761e31	−0.243779
$585$	0	0
$586$	6.18068e30	0.0912460
$587$	5.81709e31i	0.842107i	0.907036	+	0.421054i	$0.138340\pi$
$587$	5.81709e31i	0.842107i	−0.907036	+	0.421054i	$0.861660\pi$
$588$	− 1.17812e32i	− 1.67244i
$589$	−2.26681e31	−0.315565
$590$	0	0
$591$	−1.11511e31	−0.149300
$592$	− 1.44755e31i	− 0.190079i
$593$	− 7.52337e31i	− 0.968909i	−0.874816	−	0.484455i	$-0.839018\pi$
$593$	− 7.52337e31i	− 0.968909i	0.874816	−	0.484455i	$-0.160982\pi$
$594$	−6.58973e31	−0.832384
$595$	0	0
$596$	−4.37644e31	−0.531849
$597$	− 2.53061e32i	− 3.01662i
$598$	7.68758e31i	0.898930i
$599$	5.59333e31	0.641597	0.320798	−	0.947147i	$-0.396049\pi$
$599$	5.59333e31	0.641597	0.320798	+	0.947147i	$0.396049\pi$
$600$	0	0
$601$	5.72895e31	0.632439	0.316220	−	0.948686i	$-0.397586\pi$
$601$	5.72895e31	0.632439	0.316220	+	0.948686i	$0.397586\pi$
$602$	7.60748e31i	0.823913i
$603$	− 4.15840e32i	− 4.41852i
$604$	1.65616e31	0.172654
$605$	0	0
$606$	1.79548e32	1.80196
$607$	1.73060e32i	1.70423i	0.523356	+	0.852114i	$0.324680\pi$
$607$	1.73060e32i	1.70423i	−0.523356	+	0.852114i	$0.675320\pi$
$608$	9.67136e30i	0.0934537i
$609$	3.67996e32	3.48935
$610$	0	0
$611$	−7.69071e31	−0.702251
$612$	1.34834e32i	1.20826i
$613$	4.07291e29i	0.00358186i	0.999998	+	0.00179093i	$0.000570071\pi$
$613$	4.07291e29i	0.00358186i	−0.999998	+	0.00179093i	$0.999430\pi$
$614$	−4.16006e31	−0.359057
$615$	0	0
$616$	−2.54095e31	−0.211261
$617$	− 1.95659e32i	− 1.59669i	−0.602199	−	0.798346i	$-0.705708\pi$
$617$	− 1.95659e32i	− 1.59669i	0.602199	−	0.798346i	$-0.294292\pi$
$618$	8.02696e31i	0.642959i
$619$	2.00768e32	1.57853	0.789264	−	0.614054i	$-0.210462\pi$
$619$	2.00768e32	1.57853	0.789264	+	0.614054i	$0.210462\pi$
$620$	0	0
$621$	3.77105e32	2.85699
$622$	− 1.32892e32i	− 0.988344i
$623$	1.43324e32i	1.04642i
$624$	−9.72984e31	−0.697402
$625$	0	0
$626$	−9.83430e31	−0.679420
$627$	− 5.40909e31i	− 0.366900i
$628$	7.79402e31i	0.519070i
$629$	1.04213e32	0.681461
$630$	0	0
$631$	2.41339e32	1.52156	0.760782	−	0.649007i	$-0.224816\pi$
$631$	2.41339e32	1.52156	0.760782	+	0.649007i	$0.224816\pi$
$632$	7.51694e31i	0.465366i
$633$	3.27281e32i	1.98965i
$634$	1.07524e32	0.641916
$635$	0	0
$636$	−4.62917e31	−0.266530
$637$	4.46456e32i	2.52450i
$638$	− 5.04002e31i	− 0.279895i
$639$	−7.13039e32	−3.88914
$640$	0	0
$641$	−1.22253e32	−0.643268	−0.321634	−	0.946864i	$-0.604232\pi$
$641$	−1.22253e32	−0.643268	−0.321634	+	0.946864i	$0.604232\pi$
$642$	− 3.85326e31i	− 0.199148i
$643$	2.71424e32i	1.37792i	0.724801	+	0.688958i	$0.241932\pi$
$643$	2.71424e32i	1.37792i	−0.724801	+	0.688958i	$0.758068\pi$
$644$	1.45409e32	0.725110
$645$	0	0
$646$	−6.96269e31	−0.335045
$647$	− 2.71917e31i	− 0.128540i	−0.997933	−	0.0642699i	$-0.979528\pi$
$647$	− 2.71917e31i	− 0.128540i	0.997933	−	0.0642699i	$-0.0204719\pi$
$648$	2.72023e32i	1.26326i
$649$	−3.57788e31	−0.163234
$650$	0	0
$651$	−4.31355e32	−1.89956
$652$	1.67993e32i	0.726849i
$653$	− 1.78163e32i	− 0.757384i	−0.925523	−	0.378692i	$-0.876374\pi$
$653$	− 1.78163e32i	− 0.757384i	0.925523	−	0.378692i	$-0.123626\pi$
$654$	1.53755e31	0.0642223
$655$	0	0
$656$	−2.63596e31	−0.106303
$657$	− 4.69121e32i	− 1.85902i
$658$	1.45468e32i	0.566461i
$659$	2.28601e32	0.874774	0.437387	−	0.899273i	$-0.355904\pi$
$659$	2.28601e32	0.874774	0.437387	+	0.899273i	$0.355904\pi$
$660$	0	0
$661$	−1.82780e32	−0.675478	−0.337739	−	0.941240i	$-0.609662\pi$
$661$	−1.82780e32	−0.675478	−0.337739	+	0.941240i	$0.609662\pi$
$662$	2.65535e31i	0.0964394i
$663$	− 7.00480e32i	− 2.50029i
$664$	5.78676e31	0.203003
$665$	0	0
$666$	4.27736e32	1.44951
$667$	2.88421e32i	0.960683i
$668$	− 3.35355e31i	− 0.109793i
$669$	6.99591e31	0.225135
$670$	0	0
$671$	5.25348e31	0.163357
$672$	1.84038e32i	0.562550i
$673$	4.40091e32i	1.32242i	0.750201	+	0.661210i	$0.229957\pi$
$673$	4.40091e32i	1.32242i	−0.750201	+	0.661210i	$0.770043\pi$
$674$	1.85227e32	0.547162
$675$	0	0
$676$	1.93590e32	0.552707
$677$	3.63271e32i	1.01967i	0.860271	+	0.509837i	$0.170294\pi$
$677$	3.63271e32i	1.01967i	−0.860271	+	0.509837i	$0.829706\pi$
$678$	1.56170e32i	0.430978i
$679$	−3.88139e32	−1.05314
$680$	0	0
$681$	−2.74657e32	−0.720443
$682$	5.90779e31i	0.152372i
$683$	− 4.83335e31i	− 0.122577i	−0.998120	−	0.0612887i	$-0.980479\pi$
$683$	− 4.83335e31i	− 0.122577i	0.998120	−	0.0612887i	$-0.0195210\pi$
$684$	−2.85779e32	−0.712663
$685$	0	0
$686$	3.59092e32	0.865921
$687$	− 5.39292e32i	− 1.27885i
$688$	− 7.54643e31i	− 0.175985i
$689$	1.75425e32	0.402319
$690$	0	0
$691$	1.13967e32	0.252802	0.126401	−	0.991979i	$-0.459657\pi$
$691$	1.13967e32	0.252802	0.126401	+	0.991979i	$0.459657\pi$
$692$	3.76835e32i	0.822113i
$693$	− 7.50825e32i	− 1.61104i
$694$	−3.05741e32	−0.645238
$695$	0	0
$696$	−3.65043e32	−0.745311
$697$	− 1.89770e32i	− 0.381110i
$698$	− 3.11581e32i	− 0.615508i
$699$	−1.01425e31	−0.0197086
$700$	0	0
$701$	−2.14787e32	−0.403879	−0.201939	−	0.979398i	$-0.564724\pi$
$701$	−2.14787e32	−0.403879	−0.201939	+	0.979398i	$0.564724\pi$
$702$	− 1.80870e33i	− 3.34573i
$703$	2.20878e32i	0.401944i
$704$	2.52056e31	0.0451244
$705$	0	0
$706$	−5.10792e32	−0.885095
$707$	1.28698e33i	2.19406i
$708$	2.59141e32i	0.434664i
$709$	2.27478e32	0.375412	0.187706	−	0.982225i	$-0.439895\pi$
$709$	2.27478e32	0.375412	0.187706	+	0.982225i	$0.439895\pi$
$710$	0	0
$711$	−2.22118e33	−3.54881
$712$	− 1.42174e32i	− 0.223511i
$713$	− 3.38080e32i	− 0.522986i
$714$	−1.32494e33	−2.01682
$715$	0	0
$716$	4.95891e32	0.730949
$717$	− 8.13448e32i	− 1.17994i
$718$	8.02205e32i	1.14513i
$719$	−8.12373e32	−1.14123	−0.570615	−	0.821217i	$-0.693295\pi$
$719$	−8.12373e32	−1.14123	−0.570615	+	0.821217i	$0.693295\pi$
$720$	0	0
$721$	−5.75362e32	−0.782863
$722$	3.80462e32i	0.509488i
$723$	2.78850e33i	3.67520i
$724$	4.93535e32	0.640213
$725$	0	0
$726$	9.40786e32	1.18228
$727$	− 8.49369e32i	− 1.05063i	−0.850907	−	0.525316i	$-0.823947\pi$
$727$	− 8.49369e32i	− 1.05063i	0.850907	−	0.525316i	$-0.176053\pi$
$728$	− 6.97423e32i	− 0.849152i
$729$	−2.80708e33	−3.36424
$730$	0	0
$731$	5.43289e32	0.630930
$732$	− 3.80503e32i	− 0.434992i
$733$	− 1.06482e33i	− 1.19834i	−0.800621	−	0.599171i	$-0.795497\pi$
$733$	− 1.06482e33i	− 1.19834i	0.800621	−	0.599171i	$-0.204503\pi$
$734$	3.67651e32	0.407316
$735$	0	0
$736$	−1.44242e32	−0.154881
$737$	− 5.59644e32i	− 0.591611i
$738$	− 7.78897e32i	− 0.810647i
$739$	4.97066e32	0.509334	0.254667	−	0.967029i	$-0.418034\pi$
$739$	4.97066e32	0.509334	0.254667	+	0.967029i	$0.418034\pi$
$740$	0	0
$741$	1.48465e33	1.47474
$742$	− 3.31813e32i	− 0.324525i
$743$	6.27596e32i	0.604379i	0.953248	+	0.302189i	$0.0977175\pi$
$743$	6.27596e32i	0.604379i	−0.953248	+	0.302189i	$0.902283\pi$
$744$	4.27894e32	0.405739
$745$	0	0
$746$	1.43511e33	1.31944
$747$	1.70993e33i	1.54807i
$748$	1.81463e32i	0.161778i
$749$	2.76197e32	0.242481
$750$	0	0
$751$	2.25567e33	1.92051	0.960254	−	0.279128i	$-0.0900455\pi$
$751$	2.25567e33	1.92051	0.960254	+	0.279128i	$0.0900455\pi$
$752$	− 1.44301e32i	− 0.120994i
$753$	2.83142e33i	2.33809i
$754$	1.38335e33	1.12502
$755$	0	0
$756$	−3.42113e33	−2.69879
$757$	− 5.24347e32i	− 0.407396i	−0.979034	−	0.203698i	$-0.934704\pi$
$757$	− 5.24347e32i	− 0.407396i	0.979034	−	0.203698i	$-0.0652960\pi$
$758$	1.60916e32i	0.123141i
$759$	8.06731e32	0.608063
$760$	0	0
$761$	−1.07047e33	−0.782799	−0.391400	−	0.920221i	$-0.628009\pi$
$761$	−1.07047e33	−0.782799	−0.391400	+	0.920221i	$0.628009\pi$
$762$	2.86461e33i	2.06340i
$763$	1.10210e32i	0.0781966i
$764$	−1.23688e33	−0.864480
$765$	0	0
$766$	−8.93199e32	−0.605783
$767$	− 9.82031e32i	− 0.656113i
$768$	− 1.82561e32i	− 0.120158i
$769$	−1.76963e32	−0.114744	−0.0573719	−	0.998353i	$-0.518272\pi$
$769$	−1.76963e32	−0.114744	−0.0573719	+	0.998353i	$0.518272\pi$
$770$	0	0
$771$	5.35337e33	3.36901
$772$	5.94978e32i	0.368894i
$773$	1.34952e32i	0.0824354i	0.999150	+	0.0412177i	$0.0131237\pi$
$773$	1.34952e32i	0.0824354i	−0.999150	+	0.0412177i	$0.986876\pi$
$774$	2.22989e33	1.34203
$775$	0	0
$776$	3.85025e32	0.224946
$777$	4.20312e33i	2.41953i
$778$	− 1.64365e32i	− 0.0932275i
$779$	4.02213e32	0.224789
$780$	0	0
$781$	−9.59620e32	−0.520730
$782$	− 1.03844e33i	− 0.555270i
$783$	− 6.78586e33i	− 3.57556i
$784$	−8.37686e32	−0.434957
$785$	0	0
$786$	−2.51564e33	−1.26849
$787$	2.58175e32i	0.128293i	0.997940	+	0.0641467i	$0.0204326\pi$
$787$	2.58175e32i	0.128293i	−0.997940	+	0.0641467i	$0.979567\pi$
$788$	7.92880e31i	0.0388290i
$789$	4.77665e31	0.0230536
$790$	0	0
$791$	−1.11941e33	−0.524756
$792$	7.44799e32i	0.344112i
$793$	1.44194e33i	0.656607i
$794$	−3.72765e32	−0.167301
$795$	0	0
$796$	−1.79936e33	−0.784543
$797$	4.68701e32i	0.201430i	0.994915	+	0.100715i	$0.0321131\pi$
$797$	4.68701e32i	0.201430i	−0.994915	+	0.100715i	$0.967887\pi$
$798$	− 2.80819e33i	− 1.18958i
$799$	1.03886e33	0.433781
$800$	0	0
$801$	4.20108e33	1.70446
$802$	− 2.50514e33i	− 1.00190i
$803$	− 6.31352e32i	− 0.248910i
$804$	−4.05343e33	−1.57536
$805$	0	0
$806$	−1.62153e33	−0.612451
$807$	− 1.01940e34i	− 3.79575i
$808$	− 1.27665e33i	− 0.468642i
$809$	1.32810e33	0.480643	0.240321	−	0.970693i	$-0.422747\pi$
$809$	1.32810e33	0.480643	0.240321	+	0.970693i	$0.422747\pi$
$810$	0	0
$811$	5.54203e32	0.194952	0.0974762	−	0.995238i	$-0.468923\pi$
$811$	5.54203e32	0.194952	0.0974762	+	0.995238i	$0.468923\pi$
$812$	− 2.61658e33i	− 0.907485i
$813$	7.40491e33i	2.53209i
$814$	5.75654e32	0.194080
$815$	0	0
$816$	1.31431e33	0.430786
$817$	1.15149e33i	0.372140i
$818$	− 2.62704e33i	− 0.837150i
$819$	2.06081e34	6.47550
$820$	0	0
$821$	−2.33985e33	−0.714895	−0.357448	−	0.933933i	$-0.616353\pi$
$821$	−2.33985e33	−0.714895	−0.357448	+	0.933933i	$0.616353\pi$
$822$	2.97012e33i	0.894847i
$823$	− 3.81112e33i	− 1.13228i	−0.824308	−	0.566141i	$-0.808436\pi$
$823$	− 3.81112e33i	− 1.13228i	0.824308	−	0.566141i	$-0.191564\pi$
$824$	5.70745e32	0.167217
$825$	0	0
$826$	−1.85749e33	−0.529245
$827$	3.90417e33i	1.09702i	0.836143	+	0.548511i	$0.184805\pi$
$827$	3.90417e33i	1.09702i	−0.836143	+	0.548511i	$0.815195\pi$
$828$	− 4.26220e33i	− 1.18110i
$829$	−2.55686e33	−0.698763	−0.349382	−	0.936981i	$-0.613608\pi$
$829$	−2.55686e33	−0.698763	−0.349382	+	0.936981i	$0.613608\pi$
$830$	0	0
$831$	−2.95270e33	−0.784889
$832$	6.91826e32i	0.181376i
$833$	− 6.03074e33i	− 1.55939i
$834$	3.42974e33	0.874685
$835$	0	0
$836$	−3.84606e32	−0.0954209
$837$	7.95421e33i	1.94650i
$838$	6.22190e32i	0.150182i
$839$	−5.90891e32	−0.140684	−0.0703420	−	0.997523i	$-0.522409\pi$
$839$	−5.90891e32	−0.140684	−0.0703420	+	0.997523i	$0.522409\pi$
$840$	0	0
$841$	8.73308e32	0.202308
$842$	− 2.61608e33i	− 0.597808i
$843$	1.41966e33i	0.320012i
$844$	2.32708e33	0.517456
$845$	0	0
$846$	4.26394e33	0.922681
$847$	6.74344e33i	1.43954i
$848$	3.29150e32i	0.0693174i
$849$	−1.54635e34	−3.21269
$850$	0	0
$851$	−3.29425e33	−0.666141
$852$	6.95041e33i	1.38661i
$853$	3.51995e33i	0.692823i	0.938083	+	0.346412i	$0.112600\pi$
$853$	3.51995e33i	0.692823i	−0.938083	+	0.346412i	$0.887400\pi$
$854$	2.72740e33	0.529643
$855$	0	0
$856$	−2.73980e32	−0.0517930
$857$	− 8.93522e33i	− 1.66658i	−0.552837	−	0.833289i	$-0.686455\pi$
$857$	− 8.93522e33i	− 1.66658i	0.552837	−	0.833289i	$-0.313545\pi$
$858$	− 3.86931e33i	− 0.712082i
$859$	−4.26448e33	−0.774363	−0.387181	−	0.922004i	$-0.626551\pi$
$859$	−4.26448e33	−0.774363	−0.387181	+	0.922004i	$0.626551\pi$
$860$	0	0
$861$	7.65379e33	1.35313
$862$	2.51165e33i	0.438153i
$863$	7.90521e31i	0.0136078i	0.999977	+	0.00680392i	$0.00216577\pi$
$863$	7.90521e31i	0.0136078i	−0.999977	+	0.00680392i	$0.997834\pi$
$864$	3.39367e33	0.576450
$865$	0	0
$866$	4.79368e33	0.792891
$867$	− 2.31651e33i	− 0.378107i
$868$	3.06709e33i	0.494025i
$869$	−2.98930e33	−0.475162
$870$	0	0
$871$	1.53607e34	2.37795
$872$	− 1.09325e32i	− 0.0167025i
$873$	1.13771e34i	1.71540i
$874$	2.20095e33	0.327513
$875$	0	0
$876$	−4.57280e33	−0.662804
$877$	− 5.32153e33i	− 0.761275i	−0.924724	−	0.380638i	$-0.875705\pi$
$877$	− 5.32153e33i	− 0.761275i	0.924724	−	0.380638i	$-0.124295\pi$
$878$	4.79163e33i	0.676545i
$879$	1.78023e33	0.248086
$880$	0	0
$881$	−6.10795e33	−0.829225	−0.414613	−	0.909998i	$-0.636083\pi$
$881$	−6.10795e33	−0.829225	−0.414613	+	0.909998i	$0.636083\pi$
$882$	− 2.47527e34i	− 3.31692i
$883$	− 5.57230e33i	− 0.737032i	−0.929621	−	0.368516i	$-0.879866\pi$
$883$	− 5.57230e33i	− 0.737032i	0.929621	−	0.368516i	$-0.120134\pi$
$884$	−4.98066e33	−0.650258
$885$	0	0
$886$	1.06390e34	1.35336
$887$	− 3.09075e33i	− 0.388099i	−0.980992	−	0.194050i	$-0.937838\pi$
$887$	− 3.09075e33i	− 0.388099i	0.980992	−	0.194050i	$-0.0621623\pi$
$888$	− 4.16939e33i	− 0.516801i
$889$	−2.05332e34	−2.51239
$890$	0	0
$891$	−1.08177e34	−1.28985
$892$	− 4.97434e32i	− 0.0585517i
$893$	2.20185e33i	0.255856i
$894$	−1.26055e34	−1.44603
$895$	0	0
$896$	1.30858e33	0.146304
$897$	2.21426e34i	2.44408i
$898$	1.73399e33i	0.188960i
$899$	−6.08362e33	−0.654524
$900$	0	0
$901$	−2.36965e33	−0.248513
$902$	− 1.04825e33i	− 0.108540i
$903$	2.19119e34i	2.24012i
$904$	1.11042e33	0.112086
$905$	0	0
$906$	4.77025e33	0.469425
$907$	1.19132e34i	1.15756i	0.815483	+	0.578781i	$0.196471\pi$
$907$	1.19132e34i	1.15756i	−0.815483	+	0.578781i	$0.803529\pi$
$908$	1.95291e33i	0.187368i
$909$	3.77236e34	3.57379
$910$	0	0
$911$	−1.48259e34	−1.36949	−0.684747	−	0.728781i	$-0.740087\pi$
$911$	−1.48259e34	−1.36949	−0.684747	+	0.728781i	$0.740087\pi$
$912$	2.78565e33i	0.254089i
$913$	2.30125e33i	0.207276i
$914$	8.81138e33	0.783723
$915$	0	0
$916$	−3.83455e33	−0.332596
$917$	− 1.80318e34i	− 1.54451i
$918$	2.44320e34i	2.06666i
$919$	−1.05759e34	−0.883461	−0.441731	−	0.897148i	$-0.645635\pi$
$919$	−1.05759e34	−0.883461	−0.441731	+	0.897148i	$0.645635\pi$
$920$	0	0
$921$	−1.19823e34	−0.976232
$922$	− 1.14668e34i	− 0.922652i
$923$	− 2.63390e34i	− 2.09305i
$924$	−7.31873e33	−0.574391
$925$	0	0
$926$	−1.34078e34	−1.02643
$927$	1.68649e34i	1.27517i
$928$	2.59558e33i	0.193835i
$929$	4.72412e33	0.348450	0.174225	−	0.984706i	$-0.444258\pi$
$929$	4.72412e33	0.348450	0.174225	+	0.984706i	$0.444258\pi$
$930$	0	0
$931$	1.27820e34	0.919768
$932$	7.21166e31i	0.00512569i
$933$	− 3.82769e34i	− 2.68718i
$934$	−5.03900e33	−0.349426
$935$	0	0
$936$	−2.04427e34	−1.38314
$937$	− 2.82822e34i	− 1.89020i	−0.326779	−	0.945101i	$-0.605963\pi$
$937$	− 2.82822e34i	− 1.89020i	0.326779	−	0.945101i	$-0.394037\pi$
$938$	− 2.90545e34i	− 1.91814i
$939$	−2.83258e34	−1.84726
$940$	0	0
$941$	−1.69342e34	−1.07767	−0.538833	−	0.842412i	$-0.681135\pi$
$941$	−1.69342e34	−1.07767	−0.538833	+	0.842412i	$0.681135\pi$
$942$	2.24492e34i	1.41129i
$943$	5.99875e33i	0.372543i
$944$	1.84259e33	0.113045
$945$	0	0
$946$	3.00102e33	0.179689
$947$	− 8.74272e33i	− 0.517156i	−0.965990	−	0.258578i	$-0.916746\pi$
$947$	− 8.74272e33i	− 0.517156i	0.965990	−	0.258578i	$-0.0832540\pi$
$948$	2.16511e34i	1.26527i
$949$	1.73289e34	1.00048
$950$	0	0
$951$	3.09702e34	1.74529
$952$	9.42081e33i	0.524522i
$953$	2.80700e34i	1.54410i	0.635564	+	0.772048i	$0.280768\pi$
$953$	2.80700e34i	1.54410i	−0.635564	+	0.772048i	$0.719232\pi$
$954$	−9.72604e33	−0.528603
$955$	0	0
$956$	−5.78390e33	−0.306870
$957$	− 1.45168e34i	− 0.760999i
$958$	− 1.25142e34i	− 0.648185i
$959$	−2.12895e34	−1.08956
$960$	0	0
$961$	−1.28823e34	−0.643684
$962$	1.58002e34i	0.780096i
$963$	− 8.09582e33i	− 0.394965i
$964$	1.98272e34	0.955821
$965$	0	0
$966$	4.18823e34	1.97148
$967$	− 1.63293e34i	− 0.759562i	−0.925076	−	0.379781i	$-0.875999\pi$
$967$	− 1.63293e34i	− 0.759562i	0.925076	−	0.379781i	$-0.124001\pi$
$968$	− 6.68932e33i	− 0.307479i
$969$	−2.00547e34	−0.910946
$970$	0	0
$971$	−2.94646e34	−1.30701	−0.653505	−	0.756922i	$-0.726702\pi$
$971$	−2.94646e34	−1.30701	−0.653505	+	0.756922i	$0.726702\pi$
$972$	4.11573e34i	1.80420i
$973$	2.45840e34i	1.06501i
$974$	−1.21931e34	−0.522020
$975$	0	0
$976$	−2.70551e33	−0.113130
$977$	− 3.20852e34i	− 1.32592i	−0.748655	−	0.662960i	$-0.769300\pi$
$977$	− 3.20852e34i	− 1.32592i	0.748655	−	0.662960i	$-0.230700\pi$
$978$	4.83872e34i	1.97621i
$979$	5.65388e33	0.228216
$980$	0	0
$981$	3.23045e33	0.127371
$982$	1.00530e34i	0.391756i
$983$	1.27173e34i	0.489813i	0.969547	+	0.244906i	$0.0787572\pi$
$983$	1.27173e34i	0.489813i	−0.969547	+	0.244906i	$0.921243\pi$
$984$	−7.59236e33	−0.289024
$985$	0	0
$986$	−1.86863e34	−0.694928
$987$	4.18993e34i	1.54014i
$988$	− 1.05564e34i	− 0.383540i
$989$	−1.71737e34	−0.616746
$990$	0	0
$991$	−3.20701e34	−1.12526	−0.562631	−	0.826708i	$-0.690211\pi$
$991$	−3.20701e34	−1.12526	−0.562631	+	0.826708i	$0.690211\pi$
$992$	− 3.04247e33i	− 0.105522i
$993$	7.64822e33i	0.262207i
$994$	−4.98197e34	−1.68833
$995$	0	0
$996$	1.66676e34	0.551940
$997$	4.63954e34i	1.51873i	0.650665	+	0.759365i	$0.274490\pi$
$997$	4.63954e34i	1.51873i	−0.650665	+	0.759365i	$0.725510\pi$
$998$	3.23595e32i	0.0104713i
$999$	7.75057e34	2.47931

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.24.b.b.49.1		4
5.2	odd	4		50.24.a.c.1.1		2
5.3	odd	4		10.24.a.b.1.2	✓	2
5.4	even	2	inner	50.24.b.b.49.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.24.a.b.1.2	✓	2	5.3	odd	4
50.24.a.c.1.1		2	5.2	odd	4
50.24.b.b.49.1		4	1.1	even	1	trivial
50.24.b.b.49.4		4	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-2048.00i q^{2} -589887. i q^{3} -4.19430e6 q^{4} -1.20809e9 q^{6} -8.65943e9i q^{7} +8.58993e9i q^{8} -2.53823e11 q^{9} -3.41600e11 q^{11} +2.47417e12i q^{12} -9.37599e12i q^{13} -1.77345e13 q^{14} +1.75922e13 q^{16} +1.26651e14i q^{17} +5.19830e14i q^{18} -2.68434e14 q^{19} -5.10808e15 q^{21} +6.99597e14i q^{22} -4.00352e15i q^{23} +5.06709e15 q^{24} -1.92020e16 q^{26} +9.41933e16i q^{27} +3.63203e16i q^{28} -7.20419e16 q^{29} +8.44456e16 q^{31} -3.60288e16i q^{32} +2.01505e17i q^{33} +2.59382e17 q^{34} +1.06461e18 q^{36} -8.22837e17i q^{37} +5.49753e17i q^{38} -5.53078e18 q^{39} -1.49837e18 q^{41} +1.04614e19i q^{42} -4.28965e18i q^{43} +1.43277e18 q^{44} -8.19921e18 q^{46} -8.20255e18i q^{47} -1.03774e19i q^{48} -4.76169e19 q^{49} +7.47099e19 q^{51} +3.93258e19i q^{52} +1.87100e19i q^{53} +1.92908e20 q^{54} +7.43839e19 q^{56} +1.58346e20i q^{57} +1.47542e20i q^{58} +1.04739e20 q^{59} -1.53791e20 q^{61} -1.72945e20i q^{62} +2.19797e21i q^{63} -7.37870e19 q^{64} +4.12683e20 q^{66} +1.63830e21i q^{67} -5.31214e20i q^{68} -2.36163e21 q^{69} +2.80919e21 q^{71} -2.18033e21i q^{72} +1.84822e21i q^{73} -1.68517e21 q^{74} +1.12589e21 q^{76} +2.95806e21i q^{77} +1.13270e22i q^{78} +8.75087e21 q^{79} +3.16676e22 q^{81} +3.06866e21i q^{82} -6.73667e21i q^{83} +2.14249e22 q^{84} -8.78520e21 q^{86} +4.24965e22i q^{87} -2.93432e21i q^{88} -1.65512e22 q^{89} -8.11907e22 q^{91} +1.67920e22i q^{92} -4.98134e22i q^{93} -1.67988e22 q^{94} -2.12529e22 q^{96} -4.48228e22i q^{97} +9.75195e22i q^{98} +8.67060e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16777216 q^{4} - 2811838464 q^{6} - 338022453348 q^{9} + 1873114539648 q^{11} - 14457221562368 q^{14} + 70368744177664 q^{16} + 513828480996400 q^{19} - 92\!\cdots\!72 q^{21} + 11\!\cdots\!56 q^{24}+ \cdots + 39\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 16777216 * q^4 - 2811838464 * q^6 - 338022453348 * q^9 + 1873114539648 * q^11 - 14457221562368 * q^14 + 70368744177664 * q^16 + 513828480996400 * q^19 - 9225112870917072 * q^21 + 11793705316909056 * q^24 - 40803722828529664 * q^26 - 390940010512005240 * q^29 + 337622787144424208 * q^31 - 6593371092860928 * q^34 + 1417768928167329792 * q^36 - 11174735998921715856 * q^39 + 3888451075379183448 * q^41 - 7856411806103764992 * q^44 - 14721443128002822144 * q^46 - 93126752671041347892 * q^49 + 124640539856501238288 * q^51 + 315009919262194237440 * q^54 + 60637982227926351872 * q^56 + 522526165771612251120 * q^59 - 681844237989141919192 * q^61 - 295147905179352825856 * q^64 + 319648046470575685632 * q^66 - 4644153579423826559376 * q^69 + 11431143241632899537328 * q^71 + 3747347916299749507072 * q^74 - 2155152853157124505600 * q^76 + 10222735538368045918240 * q^79 + 75964601237753871574164 * q^81 + 38692927814938958757888 * q^84 - 8855676726813586898944 * q^86 - 48669597539922410067240 * q^89 - 156370838392176790603472 * q^91 + 85604056909379500818432 * q^94 - 49466385385532921217024 * q^96 + 390218701442070249201024 * q^99

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