LMFDB - Embedded newform 50.18.b.f.49.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,18,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, 18, names="a")

//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);

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

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

Self dual:	no
Analytic conductor:	$91.6110436723$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{2941})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1471x^{2} + 540225 $ x^4 + 1471*x^2 + 540225
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			49.4
Root			$27.6155i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.18.b.f.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+256.000i q^{2} +4201.44i q^{3} -65536.0 q^{4} -1.07557e6 q^{6} +1.23193e7i q^{7} -1.67772e7i q^{8} +1.11488e8 q^{9} +1.21513e9 q^{11} -2.75345e8i q^{12} -2.42392e9i q^{13} -3.15374e9 q^{14} +4.29497e9 q^{16} -1.73631e10i q^{17} +2.85410e10i q^{18} -1.15322e11 q^{19} -5.17587e10 q^{21} +3.11072e11i q^{22} -5.47905e11i q^{23} +7.04884e10 q^{24} +6.20524e11 q^{26} +1.01098e12i q^{27} -8.07357e11i q^{28} -2.02736e12 q^{29} -3.37643e12 q^{31} +1.09951e12i q^{32} +5.10528e12i q^{33} +4.44497e12 q^{34} -7.30648e12 q^{36} -2.48073e13i q^{37} -2.95225e13i q^{38} +1.01840e13 q^{39} -5.37038e13 q^{41} -1.32502e13i q^{42} +2.49397e13i q^{43} -7.96345e13 q^{44} +1.40264e14 q^{46} -1.57049e14i q^{47} +1.80450e13i q^{48} +8.08656e13 q^{49} +7.29502e13 q^{51} +1.58854e14i q^{52} -5.06856e14i q^{53} -2.58812e14 q^{54} +2.06683e14 q^{56} -4.84519e14i q^{57} -5.19005e14i q^{58} -1.29796e15 q^{59} +4.35989e14 q^{61} -8.64366e14i q^{62} +1.37345e15i q^{63} -2.81475e14 q^{64} -1.30695e15 q^{66} -2.50888e15i q^{67} +1.13791e15i q^{68} +2.30199e15 q^{69} -3.06603e15 q^{71} -1.87046e15i q^{72} -4.56009e15i q^{73} +6.35068e15 q^{74} +7.55776e15 q^{76} +1.49695e16i q^{77} +2.60709e15i q^{78} -1.40515e16 q^{79} +1.01500e16 q^{81} -1.37482e16i q^{82} -2.52434e16i q^{83} +3.39206e15 q^{84} -6.38456e15 q^{86} -8.51784e15i q^{87} -2.03864e16i q^{88} +6.68155e16 q^{89} +2.98610e16 q^{91} +3.59075e16i q^{92} -1.41859e16i q^{93} +4.02045e16 q^{94} -4.61953e15 q^{96} +6.24209e16i q^{97} +2.07016e16i q^{98} +1.35472e17 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 262144 q^{4} + 9025536 q^{6} - 471792132 q^{9} + 129030528 q^{11} - 14174308352 q^{14} + 17179869184 q^{16} - 88427425520 q^{19} + 567296955888 q^{21} - 591497527296 q^{24} + 1482669295616 q^{26}+ \cdots + 10\!\cdots\!76 q^{99}+O(q^{100}) $ 4 * q - 262144 * q^4 + 9025536 * q^6 - 471792132 * q^9 + 129030528 * q^11 - 14174308352 * q^14 + 17179869184 * q^16 - 88427425520 * q^19 + 567296955888 * q^21 - 591497527296 * q^24 + 1482669295616 * q^26 - 7974629727000 * q^29 - 10984522678672 * q^31 - 809068849152 * q^34 + 30919369162752 * q^36 - 235491790704 * q^39 + 46822954554648 * q^41 - 8456144683008 * q^44 + 249625488807936 * q^46 + 154831593772812 * q^49 + 972946158829488 * q^51 - 2956865506283520 * q^54 + 928927472156672 * q^56 - 1804358340721200 * q^59 - 3128845837935352 * q^61 - 1125899906842624 * q^64 - 15473907141378048 * q^66 + 7239025962797616 * q^69 - 135177120868272 * q^71 + 32110227270596608 * q^74 + 5795179758878720 * q^76 - 38005312793104160 * q^79 + 138574652902270164 * q^81 - 37178373301075968 * q^84 - 63926744673839104 * q^86 + 194999044384444440 * q^89 + 74223914931837328 * q^91 + 95204665407264768 * q^94 + 38764381948870656 * q^96 + 1070352562589582976 * 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
$3$	4201.44i	0.369715i	0.982765	+	0.184858i	$0.0591824\pi$
$3$	4201.44i	0.369715i	−0.982765	+	0.184858i	$0.940818\pi$
$4$	−65536.0	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.07557e6	−0.261428
$7$	1.23193e7i	0.807704i	0.914824	+	0.403852i	$0.132329\pi$
$7$	1.23193e7i	0.807704i	−0.914824	+	0.403852i	$0.867671\pi$
$8$	− 1.67772e7i	− 0.353553i
$9$	1.11488e8	0.863311
$10$	0	0
$11$	1.21513e9	1.70916	0.854582	−	0.519317i	$-0.173813\pi$
$11$	1.21513e9	1.70916	0.854582	+	0.519317i	$0.173813\pi$
$12$	− 2.75345e8i	− 0.184858i
$13$	− 2.42392e9i	− 0.824138i	−0.911153	−	0.412069i	$-0.864806\pi$
$13$	− 2.42392e9i	− 0.824138i	0.911153	−	0.412069i	$-0.135194\pi$
$14$	−3.15374e9	−0.571133
$15$	0	0
$16$	4.29497e9	0.250000
$17$	− 1.73631e10i	− 0.603688i	−0.953357	−	0.301844i	$-0.902398\pi$
$17$	− 1.73631e10i	− 0.603688i	0.953357	−	0.301844i	$-0.0976022\pi$
$18$	2.85410e10i	0.610453i
$19$	−1.15322e11	−1.55779	−0.778893	−	0.627157i	$-0.784218\pi$
$19$	−1.15322e11	−1.55779	−0.778893	+	0.627157i	$0.784218\pi$
$20$	0	0
$21$	−5.17587e10	−0.298620
$22$	3.11072e11i	1.20856i
$23$	− 5.47905e11i	− 1.45888i	−0.684046	−	0.729439i	$-0.739781\pi$
$23$	− 5.47905e11i	− 1.45888i	0.684046	−	0.729439i	$-0.260219\pi$
$24$	7.04884e10	0.130714
$25$	0	0
$26$	6.20524e11	0.582754
$27$	1.01098e12i	0.688894i
$28$	− 8.07357e11i	− 0.403852i
$29$	−2.02736e12	−0.752573	−0.376286	−	0.926503i	$-0.622799\pi$
$29$	−2.02736e12	−0.752573	−0.376286	+	0.926503i	$0.622799\pi$
$30$	0	0
$31$	−3.37643e12	−0.711022	−0.355511	−	0.934672i	$-0.615693\pi$
$31$	−3.37643e12	−0.711022	−0.355511	+	0.934672i	$0.615693\pi$
$32$	1.09951e12i	0.176777i
$33$	5.10528e12i	0.631904i
$34$	4.44497e12	0.426872
$35$	0	0
$36$	−7.30648e12	−0.431655
$37$	− 2.48073e13i	− 1.16109i	−0.814228	−	0.580545i	$-0.802840\pi$
$37$	− 2.48073e13i	− 1.16109i	0.814228	−	0.580545i	$-0.197160\pi$
$38$	− 2.95225e13i	− 1.10152i
$39$	1.01840e13	0.304696
$40$	0	0
$41$	−5.37038e13	−1.05037	−0.525185	−	0.850988i	$-0.676004\pi$
$41$	−5.37038e13	−1.05037	−0.525185	+	0.850988i	$0.676004\pi$
$42$	− 1.32502e13i	− 0.211157i
$43$	2.49397e13i	0.325394i	0.986676	+	0.162697i	$0.0520193\pi$
$43$	2.49397e13i	0.325394i	−0.986676	+	0.162697i	$0.947981\pi$
$44$	−7.96345e13	−0.854582
$45$	0	0
$46$	1.40264e14	1.03158
$47$	− 1.57049e14i	− 0.962062i	−0.876704	−	0.481031i	$-0.840262\pi$
$47$	− 1.57049e14i	− 0.962062i	0.876704	−	0.481031i	$-0.159738\pi$
$48$	1.80450e13i	0.0924288i
$49$	8.08656e13	0.347614
$50$	0	0
$51$	7.29502e13	0.223193
$52$	1.58854e14i	0.412069i
$53$	− 5.06856e14i	− 1.11825i	−0.829083	−	0.559126i	$-0.811137\pi$
$53$	− 5.06856e14i	− 1.11825i	0.829083	−	0.559126i	$-0.188863\pi$
$54$	−2.58812e14	−0.487122
$55$	0	0
$56$	2.06683e14	0.285567
$57$	− 4.84519e14i	− 0.575937i
$58$	− 5.19005e14i	− 0.532149i
$59$	−1.29796e15	−1.15085	−0.575424	−	0.817856i	$-0.695163\pi$
$59$	−1.29796e15	−1.15085	−0.575424	+	0.817856i	$0.695163\pi$
$60$	0	0
$61$	4.35989e14	0.291187	0.145593	−	0.989344i	$-0.453491\pi$
$61$	4.35989e14	0.291187	0.145593	+	0.989344i	$0.453491\pi$
$62$	− 8.64366e14i	− 0.502769i
$63$	1.37345e15i	0.697300i
$64$	−2.81475e14	−0.125000
$65$	0	0
$66$	−1.30695e15	−0.446823
$67$	− 2.50888e15i	− 0.754820i	−0.926046	−	0.377410i	$-0.876815\pi$
$67$	− 2.50888e15i	− 0.754820i	0.926046	−	0.377410i	$-0.123185\pi$
$68$	1.13791e15i	0.301844i
$69$	2.30199e15	0.539369
$70$	0	0
$71$	−3.06603e15	−0.563483	−0.281742	−	0.959490i	$-0.590912\pi$
$71$	−3.06603e15	−0.563483	−0.281742	+	0.959490i	$0.590912\pi$
$72$	− 1.87046e15i	− 0.305226i
$73$	− 4.56009e15i	− 0.661804i	−0.943665	−	0.330902i	$-0.892647\pi$
$73$	− 4.56009e15i	− 0.661804i	0.943665	−	0.330902i	$-0.107353\pi$
$74$	6.35068e15	0.821014
$75$	0	0
$76$	7.55776e15	0.778893
$77$	1.49695e16i	1.38050i
$78$	2.60709e15i	0.215453i
$79$	−1.40515e16	−1.04206	−0.521031	−	0.853538i	$-0.674452\pi$
$79$	−1.40515e16	−1.04206	−0.521031	+	0.853538i	$0.674452\pi$
$80$	0	0
$81$	1.01500e16	0.608616
$82$	− 1.37482e16i	− 0.742724i
$83$	− 2.52434e16i	− 1.23023i	−0.788439	−	0.615113i	$-0.789111\pi$
$83$	− 2.52434e16i	− 1.23023i	0.788439	−	0.615113i	$-0.210889\pi$
$84$	3.39206e15	0.149310
$85$	0	0
$86$	−6.38456e15	−0.230088
$87$	− 8.51784e15i	− 0.278237i
$88$	− 2.03864e16i	− 0.604281i
$89$	6.68155e16	1.79913	0.899564	−	0.436790i	$-0.143885\pi$
$89$	6.68155e16	1.79913	0.899564	+	0.436790i	$0.143885\pi$
$90$	0	0
$91$	2.98610e16	0.665660
$92$	3.59075e16i	0.729439i
$93$	− 1.41859e16i	− 0.262876i
$94$	4.02045e16	0.680281
$95$	0	0
$96$	−4.61953e15	−0.0653570
$97$	6.24209e16i	0.808667i	0.914612	+	0.404334i	$0.132497\pi$
$97$	6.24209e16i	0.808667i	−0.914612	+	0.404334i	$0.867503\pi$
$98$	2.07016e16i	0.245800i
$99$	1.35472e17	1.47554
$100$	0	0
$101$	−1.29437e17	−1.18940	−0.594701	−	0.803947i	$-0.702729\pi$
$101$	−1.29437e17	−1.18940	−0.594701	+	0.803947i	$0.702729\pi$
$102$	1.86752e16i	0.157821i
$103$	1.62161e16i	0.126134i	0.998009	+	0.0630668i	$0.0200881\pi$
$103$	1.62161e16i	0.126134i	−0.998009	+	0.0630668i	$0.979912\pi$
$104$	−4.06666e16	−0.291377
$105$	0	0
$106$	1.29755e17	0.790724
$107$	7.54294e16i	0.424403i	0.977226	+	0.212201i	$0.0680633\pi$
$107$	7.54294e16i	0.424403i	−0.977226	+	0.212201i	$0.931937\pi$
$108$	− 6.62559e16i	− 0.344447i
$109$	3.29149e17	1.58222	0.791112	−	0.611672i	$-0.209503\pi$
$109$	3.29149e17	1.58222	0.791112	+	0.611672i	$0.209503\pi$
$110$	0	0
$111$	1.04227e17	0.429272
$112$	5.29110e16i	0.201926i
$113$	− 4.37906e17i	− 1.54958i	−0.632217	−	0.774791i	$-0.717855\pi$
$113$	− 4.37906e17i	− 1.54958i	0.632217	−	0.774791i	$-0.282145\pi$
$114$	1.24037e17	0.407249
$115$	0	0
$116$	1.32865e17	0.376286
$117$	− 2.70238e17i	− 0.711487i
$118$	− 3.32277e17i	− 0.813772i
$119$	2.13902e17	0.487602
$120$	0	0
$121$	9.71086e17	1.92124
$122$	1.11613e17i	0.205900i
$123$	− 2.25633e17i	− 0.388338i
$124$	2.21278e17	0.355511
$125$	0	0
$126$	−3.51604e17	−0.493065
$127$	4.26464e17i	0.559179i	0.960120	+	0.279590i	$0.0901984\pi$
$127$	4.26464e17i	0.559179i	−0.960120	+	0.279590i	$0.909802\pi$
$128$	− 7.20576e16i	− 0.0883883i
$129$	−1.04783e17	−0.120303
$130$	0	0
$131$	−1.99048e17	−0.200517	−0.100259	−	0.994961i	$-0.531967\pi$
$131$	−1.99048e17	−0.200517	−0.100259	+	0.994961i	$0.531967\pi$
$132$	− 3.34579e17i	− 0.315952i
$133$	− 1.42069e18i	− 1.25823i
$134$	6.42272e17	0.533738
$135$	0	0
$136$	−2.91305e17	−0.213436
$137$	− 2.15800e18i	− 1.48569i	−0.669465	−	0.742844i	$-0.733476\pi$
$137$	− 2.15800e18i	− 1.48569i	0.669465	−	0.742844i	$-0.266524\pi$
$138$	5.89309e17i	0.381391i
$139$	2.69991e18	1.64332	0.821662	−	0.569975i	$-0.193047\pi$
$139$	2.69991e18	1.64332	0.821662	+	0.569975i	$0.193047\pi$
$140$	0	0
$141$	6.59831e17	0.355689
$142$	− 7.84905e17i	− 0.398443i
$143$	− 2.94537e18i	− 1.40859i
$144$	4.78838e17	0.215828
$145$	0	0
$146$	1.16738e18	0.467966
$147$	3.39752e17i	0.128518i
$148$	1.62577e18i	0.580545i
$149$	−1.38331e18	−0.466484	−0.233242	−	0.972419i	$-0.574934\pi$
$149$	−1.38331e18	−0.466484	−0.233242	+	0.972419i	$0.574934\pi$
$150$	0	0
$151$	−3.60449e18	−1.08528	−0.542638	−	0.839967i	$-0.682574\pi$
$151$	−3.60449e18	−1.08528	−0.542638	+	0.839967i	$0.682574\pi$
$152$	1.93479e18i	0.550760i
$153$	− 1.93578e18i	− 0.521170i
$154$	−3.83219e18	−0.976160
$155$	0	0
$156$	−6.67415e17	−0.152348
$157$	6.76512e18i	1.46261i	0.682051	+	0.731305i	$0.261088\pi$
$157$	6.76512e18i	1.46261i	−0.682051	+	0.731305i	$0.738912\pi$
$158$	− 3.59719e18i	− 0.736849i
$159$	2.12952e18	0.413435
$160$	0	0
$161$	6.74980e18	1.17834
$162$	2.59840e18i	0.430357i
$163$	1.06804e19i	1.67877i	0.543536	+	0.839386i	$0.317085\pi$
$163$	1.06804e19i	1.67877i	−0.543536	+	0.839386i	$0.682915\pi$
$164$	3.51953e18	0.525185
$165$	0	0
$166$	6.46232e18	0.869900
$167$	− 2.93736e18i	− 0.375722i	−0.982196	−	0.187861i	$-0.939845\pi$
$167$	− 2.93736e18i	− 0.375722i	0.982196	−	0.187861i	$-0.0601554\pi$
$168$	8.68367e17i	0.105578i
$169$	2.77502e18	0.320797
$170$	0	0
$171$	−1.28571e19	−1.34485
$172$	− 1.63445e18i	− 0.162697i
$173$	3.04250e18i	0.288296i	0.989556	+	0.144148i	$0.0460442\pi$
$173$	3.04250e18i	0.288296i	−0.989556	+	0.144148i	$0.953956\pi$
$174$	2.18057e18	0.196744
$175$	0	0
$176$	5.21893e18	0.427291
$177$	− 5.45328e18i	− 0.425486i
$178$	1.71048e19i	1.27218i
$179$	−1.82741e19	−1.29594	−0.647970	−	0.761666i	$-0.724382\pi$
$179$	−1.82741e19	−1.29594	−0.647970	+	0.761666i	$0.724382\pi$
$180$	0	0
$181$	−1.73562e19	−1.11992	−0.559959	−	0.828520i	$-0.689183\pi$
$181$	−1.73562e19	−1.11992	−0.559959	+	0.828520i	$0.689183\pi$
$182$	7.64441e18i	0.470693i
$183$	1.83178e18i	0.107656i
$184$	−9.19232e18	−0.515791
$185$	0	0
$186$	3.63158e18	0.185881
$187$	− 2.10984e19i	− 1.03180i
$188$	1.02924e19i	0.481031i
$189$	−1.24546e19	−0.556423
$190$	0	0
$191$	−1.78696e19	−0.730015	−0.365007	−	0.931005i	$-0.618934\pi$
$191$	−1.78696e19	−0.730015	−0.365007	+	0.931005i	$0.618934\pi$
$192$	− 1.18260e18i	− 0.0462144i
$193$	− 9.94962e18i	− 0.372023i	−0.982548	−	0.186011i	$-0.940444\pi$
$193$	− 9.94962e18i	− 0.372023i	0.982548	−	0.186011i	$-0.0595561\pi$
$194$	−1.59797e19	−0.571814
$195$	0	0
$196$	−5.29961e18	−0.173807
$197$	5.27173e19i	1.65573i	0.560925	+	0.827866i	$0.310446\pi$
$197$	5.27173e19i	1.65573i	−0.560925	+	0.827866i	$0.689554\pi$
$198$	3.46809e19i	1.04336i
$199$	−2.02822e18	−0.0584606	−0.0292303	−	0.999573i	$-0.509306\pi$
$199$	−2.02822e18	−0.0584606	−0.0292303	+	0.999573i	$0.509306\pi$
$200$	0	0
$201$	1.05409e19	0.279068
$202$	− 3.31360e19i	− 0.841034i
$203$	− 2.49757e19i	− 0.607856i
$204$	−4.78086e18	−0.111596
$205$	0	0
$206$	−4.15133e18	−0.0891899
$207$	− 6.10849e19i	− 1.25946i
$208$	− 1.04107e19i	− 0.206034i
$209$	−1.40131e20	−2.66251
$210$	0	0
$211$	−2.55219e19	−0.447211	−0.223606	−	0.974680i	$-0.571783\pi$
$211$	−2.55219e19	−0.447211	−0.223606	+	0.974680i	$0.571783\pi$
$212$	3.32173e19i	0.559126i
$213$	− 1.28817e19i	− 0.208328i
$214$	−1.93099e19	−0.300098
$215$	0	0
$216$	1.69615e19	0.243561
$217$	− 4.15952e19i	− 0.574296i
$218$	8.42622e19i	1.11880i
$219$	1.91589e19	0.244679
$220$	0	0
$221$	−4.20869e19	−0.497522
$222$	2.66820e19i	0.303541i
$223$	3.50141e19i	0.383399i	0.981454	+	0.191700i	$0.0613999\pi$
$223$	3.50141e19i	0.383399i	−0.981454	+	0.191700i	$0.938600\pi$
$224$	−1.35452e19	−0.142783
$225$	0	0
$226$	1.12104e20	1.09572
$227$	− 1.19657e20i	− 1.12647i	−0.826298	−	0.563233i	$-0.809557\pi$
$227$	− 1.19657e20i	− 1.12647i	0.826298	−	0.563233i	$-0.190443\pi$
$228$	3.17535e19i	0.287968i
$229$	1.50518e20	1.31518	0.657591	−	0.753375i	$-0.271576\pi$
$229$	1.50518e20	1.31518	0.657591	+	0.753375i	$0.271576\pi$
$230$	0	0
$231$	−6.28934e19	−0.510391
$232$	3.40135e19i	0.266075i
$233$	− 1.80295e20i	− 1.35975i	−0.733328	−	0.679875i	$-0.762034\pi$
$233$	− 1.80295e20i	− 1.35975i	0.733328	−	0.679875i	$-0.237966\pi$
$234$	6.91810e19	0.503097
$235$	0	0
$236$	8.50628e19	0.575424
$237$	− 5.90367e19i	− 0.385266i
$238$	5.47588e19i	0.344786i
$239$	1.50864e20	0.916650	0.458325	−	0.888785i	$-0.348450\pi$
$239$	1.50864e20	0.916650	0.458325	+	0.888785i	$0.348450\pi$
$240$	0	0
$241$	−1.11959e20	−0.633747	−0.316874	−	0.948468i	$-0.602633\pi$
$241$	−1.11959e20	−0.633747	−0.316874	+	0.948468i	$0.602633\pi$
$242$	2.48598e20i	1.35852i
$243$	1.73203e20i	0.913909i
$244$	−2.85730e19	−0.145593
$245$	0	0
$246$	5.77621e19	0.274596
$247$	2.79532e20i	1.28383i
$248$	5.66471e19i	0.251384i
$249$	1.06059e20	0.454833
$250$	0	0
$251$	2.00695e20	0.804098	0.402049	−	0.915618i	$-0.368298\pi$
$251$	2.00695e20	0.804098	0.402049	+	0.915618i	$0.368298\pi$
$252$	− 9.00107e19i	− 0.348650i
$253$	− 6.65774e20i	− 2.49346i
$254$	−1.09175e20	−0.395400
$255$	0	0
$256$	1.84467e19	0.0625000
$257$	1.70143e20i	0.557678i	0.960338	+	0.278839i	$0.0899496\pi$
$257$	1.70143e20i	0.557678i	−0.960338	+	0.278839i	$0.910050\pi$
$258$	− 2.68243e19i	− 0.0850671i
$259$	3.05609e20	0.937817
$260$	0	0
$261$	−2.26027e20	−0.649704
$262$	− 5.09563e19i	− 0.141787i
$263$	− 5.78686e20i	− 1.55890i	−0.626462	−	0.779452i	$-0.715498\pi$
$263$	− 5.78686e20i	− 1.55890i	0.626462	−	0.779452i	$-0.284502\pi$
$264$	8.56523e19	0.223412
$265$	0	0
$266$	3.63696e20	0.889703
$267$	2.80721e20i	0.665165i
$268$	1.64422e20i	0.377410i
$269$	5.13106e20	1.14107	0.570536	−	0.821273i	$-0.306736\pi$
$269$	5.13106e20	1.14107	0.570536	+	0.821273i	$0.306736\pi$
$270$	0	0
$271$	−4.64533e20	−0.970013	−0.485006	−	0.874511i	$-0.661183\pi$
$271$	−4.64533e20	−0.970013	−0.485006	+	0.874511i	$0.661183\pi$
$272$	− 7.45742e19i	− 0.150922i
$273$	1.25459e20i	0.246104i
$274$	5.52449e20	1.05054
$275$	0	0
$276$	−1.50863e20	−0.269684
$277$	− 9.72733e20i	− 1.68623i	−0.537737	−	0.843113i	$-0.680721\pi$
$277$	− 9.72733e20i	− 1.68623i	0.537737	−	0.843113i	$-0.319279\pi$
$278$	6.91177e20i	1.16201i
$279$	−3.76432e20	−0.613833
$280$	0	0
$281$	6.76588e20	1.03830	0.519148	−	0.854685i	$-0.326249\pi$
$281$	6.76588e20	1.03830	0.519148	+	0.854685i	$0.326249\pi$
$282$	1.68917e20i	0.251510i
$283$	− 1.12202e21i	− 1.62112i	−0.585656	−	0.810560i	$-0.699163\pi$
$283$	− 1.12202e21i	− 1.62112i	0.585656	−	0.810560i	$-0.300837\pi$
$284$	2.00936e20	0.281742
$285$	0	0
$286$	7.54015e20	0.996021
$287$	− 6.61593e20i	− 0.848389i
$288$	1.22582e20i	0.152613i
$289$	5.25761e20	0.635561
$290$	0	0
$291$	−2.62257e20	−0.298977
$292$	2.98850e20i	0.330902i
$293$	3.05309e20i	0.328371i	0.986429	+	0.164185i	$0.0524995\pi$
$293$	3.05309e20i	0.328371i	−0.986429	+	0.164185i	$0.947500\pi$
$294$	−8.69764e19	−0.0908760
$295$	0	0
$296$	−4.16198e20	−0.410507
$297$	1.22847e21i	1.17743i
$298$	− 3.54128e20i	− 0.329854i
$299$	−1.32808e21	−1.20232
$300$	0	0
$301$	−3.07239e20	−0.262822
$302$	− 9.22750e20i	− 0.767406i
$303$	− 5.43823e20i	− 0.439740i
$304$	−4.95305e20	−0.389446
$305$	0	0
$306$	4.95561e20	0.368523
$307$	− 3.66561e20i	− 0.265137i	−0.991174	−	0.132569i	$-0.957678\pi$
$307$	− 3.66561e20i	− 0.265137i	0.991174	−	0.132569i	$-0.0423225\pi$
$308$	− 9.81041e20i	− 0.690250i
$309$	−6.81310e19	−0.0466335
$310$	0	0
$311$	−3.12925e19	−0.0202758	−0.0101379	−	0.999949i	$-0.503227\pi$
$311$	−3.12925e19	−0.0202758	−0.0101379	+	0.999949i	$0.503227\pi$
$312$	− 1.70858e20i	− 0.107726i
$313$	2.54969e21i	1.56444i	0.623000	+	0.782222i	$0.285914\pi$
$313$	2.54969e21i	1.56444i	−0.623000	+	0.782222i	$0.714086\pi$
$314$	−1.73187e21	−1.03422
$315$	0	0
$316$	9.20882e20	0.521031
$317$	− 1.42704e21i	− 0.786018i	−0.919535	−	0.393009i	$-0.871434\pi$
$317$	− 1.42704e21i	− 0.786018i	0.919535	−	0.393009i	$-0.128566\pi$
$318$	5.45158e20i	0.292343i
$319$	−2.46350e21	−1.28627
$320$	0	0
$321$	−3.16912e20	−0.156908
$322$	1.72795e21i	0.833213i
$323$	2.00236e21i	0.940416i
$324$	−6.65191e20	−0.304308
$325$	0	0
$326$	−2.73417e21	−1.18707
$327$	1.38290e21i	0.584972i
$328$	9.01001e20i	0.371362i
$329$	1.93473e21	0.777062
$330$	0	0
$331$	−1.65282e20	−0.0630503	−0.0315251	−	0.999503i	$-0.510036\pi$
$331$	−1.65282e20	−0.0630503	−0.0315251	+	0.999503i	$0.510036\pi$
$332$	1.65435e21i	0.615113i
$333$	− 2.76572e21i	− 1.00238i
$334$	7.51963e20	0.265676
$335$	0	0
$336$	−2.22302e20	−0.0746551
$337$	− 1.56766e21i	− 0.513332i	−0.966500	−	0.256666i	$-0.917376\pi$
$337$	− 1.56766e21i	− 0.513332i	0.966500	−	0.256666i	$-0.0826240\pi$
$338$	7.10406e20i	0.226837i
$339$	1.83984e21	0.572904
$340$	0	0
$341$	−4.10279e21	−1.21525
$342$	− 3.29141e21i	− 0.950954i
$343$	3.86205e21i	1.08847i
$344$	4.18419e20	0.115044
$345$	0	0
$346$	−7.78881e20	−0.203856
$347$	1.62532e21i	0.415086i	0.978226	+	0.207543i	$0.0665467\pi$
$347$	1.62532e21i	0.415086i	−0.978226	+	0.207543i	$0.933453\pi$
$348$	5.58225e20i	0.139119i
$349$	−3.60380e21	−0.876486	−0.438243	−	0.898857i	$-0.644399\pi$
$349$	−3.60380e21	−0.876486	−0.438243	+	0.898857i	$0.644399\pi$
$350$	0	0
$351$	2.45055e21	0.567744
$352$	1.33605e21i	0.302140i
$353$	7.99561e21i	1.76509i	0.470230	+	0.882544i	$0.344171\pi$
$353$	7.99561e21i	1.76509i	−0.470230	+	0.882544i	$0.655829\pi$
$354$	1.39604e21	0.300864
$355$	0	0
$356$	−4.37882e21	−0.899564
$357$	8.98694e20i	0.180274i
$358$	− 4.67817e21i	− 0.916368i
$359$	−7.69221e21	−1.47146	−0.735730	−	0.677275i	$-0.763161\pi$
$359$	−7.69221e21	−1.47146	−0.735730	+	0.677275i	$0.763161\pi$
$360$	0	0
$361$	7.81884e21	1.42669
$362$	− 4.44318e21i	− 0.791902i
$363$	4.07995e21i	0.710312i
$364$	−1.95697e21	−0.332830
$365$	0	0
$366$	−4.68936e20	−0.0761244
$367$	4.40761e21i	0.699104i	0.936917	+	0.349552i	$0.113666\pi$
$367$	4.40761e21i	0.699104i	−0.936917	+	0.349552i	$0.886334\pi$
$368$	− 2.35323e21i	− 0.364719i
$369$	−5.98734e21	−0.906796
$370$	0	0
$371$	6.24411e21	0.903217
$372$	9.29684e20i	0.131438i
$373$	− 7.73260e21i	− 1.06856i	−0.845306	−	0.534282i	$-0.820582\pi$
$373$	− 7.73260e21i	− 1.06856i	0.845306	−	0.534282i	$-0.179418\pi$
$374$	5.40120e21	0.729594
$375$	0	0
$376$	−2.63484e21	−0.340140
$377$	4.91417e21i	0.620224i
$378$	− 3.18838e21i	− 0.393450i
$379$	6.86035e21	0.827776	0.413888	−	0.910328i	$-0.364171\pi$
$379$	6.86035e21	0.827776	0.413888	+	0.910328i	$0.364171\pi$
$380$	0	0
$381$	−1.79176e21	−0.206737
$382$	− 4.57462e21i	− 0.516198i
$383$	4.86654e21i	0.537070i	0.963270	+	0.268535i	$0.0865395\pi$
$383$	4.86654e21i	0.537070i	−0.963270	+	0.268535i	$0.913461\pi$
$384$	3.02745e20	0.0326785
$385$	0	0
$386$	2.54710e21	0.263060
$387$	2.78048e21i	0.280916i
$388$	− 4.09081e21i	− 0.404334i
$389$	9.98351e21	0.965410	0.482705	−	0.875783i	$-0.339654\pi$
$389$	9.98351e21	0.965410	0.482705	+	0.875783i	$0.339654\pi$
$390$	0	0
$391$	−9.51336e21	−0.880707
$392$	− 1.35670e21i	− 0.122900i
$393$	− 8.36288e20i	− 0.0741343i
$394$	−1.34956e22	−1.17078
$395$	0	0
$396$	−8.87830e21	−0.737770
$397$	− 5.08435e21i	− 0.413539i	−0.978390	−	0.206769i	$-0.933705\pi$
$397$	− 5.08435e21i	− 0.413539i	0.978390	−	0.206769i	$-0.0662949\pi$
$398$	− 5.19224e20i	− 0.0413379i
$399$	5.96893e21	0.465187
$400$	0	0
$401$	1.05661e22	0.789198	0.394599	−	0.918853i	$-0.370883\pi$
$401$	1.05661e22	0.789198	0.394599	+	0.918853i	$0.370883\pi$
$402$	2.69847e21i	0.197331i
$403$	8.18420e21i	0.585980i
$404$	8.48281e21	0.594701
$405$	0	0
$406$	6.39377e21	0.429819
$407$	− 3.01441e22i	− 1.98449i
$408$	− 1.22390e21i	− 0.0789105i
$409$	−1.73559e21	−0.109597	−0.0547985	−	0.998497i	$-0.517452\pi$
$409$	−1.73559e21	−0.109597	−0.0547985	+	0.998497i	$0.517452\pi$
$410$	0	0
$411$	9.06672e21	0.549281
$412$	− 1.06274e21i	− 0.0630668i
$413$	− 1.59899e22i	− 0.929544i
$414$	1.56377e22	0.890576
$415$	0	0
$416$	2.66513e21	0.145688
$417$	1.13435e22i	0.607562i
$418$	− 3.58736e22i	− 1.88268i
$419$	1.13030e22	0.581264	0.290632	−	0.956835i	$-0.406134\pi$
$419$	1.13030e22	0.581264	0.290632	+	0.956835i	$0.406134\pi$
$420$	0	0
$421$	−1.06234e21	−0.0524643	−0.0262321	−	0.999656i	$-0.508351\pi$
$421$	−1.06234e21	−0.0524643	−0.0262321	+	0.999656i	$0.508351\pi$
$422$	− 6.53361e21i	− 0.316226i
$423$	− 1.75091e22i	− 0.830559i
$424$	−8.50363e21	−0.395362
$425$	0	0
$426$	3.29773e21	0.147310
$427$	5.37108e21i	0.235193i
$428$	− 4.94334e21i	− 0.212201i
$429$	1.23748e22	0.520776
$430$	0	0
$431$	3.61567e22	1.46262	0.731310	−	0.682045i	$-0.238909\pi$
$431$	3.61567e22	1.46262	0.731310	+	0.682045i	$0.238909\pi$
$432$	4.34215e21i	0.172224i
$433$	2.15292e22i	0.837298i	0.908148	+	0.418649i	$0.137496\pi$
$433$	2.15292e22i	0.837298i	−0.908148	+	0.418649i	$0.862504\pi$
$434$	1.06484e22	0.406088
$435$	0	0
$436$	−2.15711e22	−0.791112
$437$	6.31857e22i	2.27262i
$438$	4.90469e21i	0.173014i
$439$	2.88882e22	0.999476	0.499738	−	0.866177i	$-0.333430\pi$
$439$	2.88882e22	0.999476	0.499738	+	0.866177i	$0.333430\pi$
$440$	0	0
$441$	9.01555e21	0.300099
$442$	− 1.07742e22i	− 0.351801i
$443$	− 3.43476e21i	− 0.110018i	−0.998486	−	0.0550091i	$-0.982481\pi$
$443$	− 3.43476e21i	− 0.110018i	0.998486	−	0.0550091i	$-0.0175188\pi$
$444$	−6.83059e21	−0.214636
$445$	0	0
$446$	−8.96360e21	−0.271104
$447$	− 5.81190e21i	− 0.172466i
$448$	− 3.46757e21i	− 0.100963i
$449$	−3.08875e22	−0.882447	−0.441223	−	0.897397i	$-0.645455\pi$
$449$	−3.08875e22	−0.882447	−0.441223	+	0.897397i	$0.645455\pi$
$450$	0	0
$451$	−6.52570e22	−1.79526
$452$	2.86986e22i	0.774791i
$453$	− 1.51440e22i	− 0.401243i
$454$	3.06322e22	0.796532
$455$	0	0
$456$	−8.12888e21	−0.203624
$457$	− 3.83285e22i	− 0.942398i	−0.882027	−	0.471199i	$-0.843821\pi$
$457$	− 3.83285e22i	− 0.942398i	0.882027	−	0.471199i	$-0.156179\pi$
$458$	3.85325e22i	0.929974i
$459$	1.75539e22	0.415877
$460$	0	0
$461$	6.80144e22	1.55290	0.776449	−	0.630180i	$-0.217019\pi$
$461$	6.80144e22	1.55290	0.776449	+	0.630180i	$0.217019\pi$
$462$	− 1.61007e22i	− 0.360901i
$463$	− 4.57341e21i	− 0.100647i	−0.998733	−	0.0503236i	$-0.983975\pi$
$463$	− 4.57341e21i	− 0.100647i	0.998733	−	0.0503236i	$-0.0160253\pi$
$464$	−8.70746e21	−0.188143
$465$	0	0
$466$	4.61556e22	0.961489
$467$	4.97766e22i	1.01820i	0.860708	+	0.509099i	$0.170021\pi$
$467$	4.97766e22i	1.01820i	−0.860708	+	0.509099i	$0.829979\pi$
$468$	1.77103e22i	0.355744i
$469$	3.09076e22	0.609671
$470$	0	0
$471$	−2.84232e22	−0.540749
$472$	2.17761e22i	0.406886i
$473$	3.03049e22i	0.556151i
$474$	1.51134e22	0.272424
$475$	0	0
$476$	−1.40183e22	−0.243801
$477$	− 5.65084e22i	− 0.965399i
$478$	3.86212e22i	0.648169i
$479$	−9.35494e22	−1.54237	−0.771186	−	0.636610i	$-0.780336\pi$
$479$	−9.35494e22	−1.54237	−0.771186	+	0.636610i	$0.780336\pi$
$480$	0	0
$481$	−6.01310e22	−0.956898
$482$	− 2.86616e22i	− 0.448127i
$483$	2.83589e22i	0.435651i
$484$	−6.36411e22	−0.960621
$485$	0	0
$486$	−4.43400e22	−0.646231
$487$	− 1.63934e22i	− 0.234786i	−0.993086	−	0.117393i	$-0.962546\pi$
$487$	− 1.63934e22i	− 0.234786i	0.993086	−	0.117393i	$-0.0374537\pi$
$488$	− 7.31468e21i	− 0.102950i
$489$	−4.48729e22	−0.620667
$490$	0	0
$491$	−2.62500e22	−0.350700	−0.175350	−	0.984506i	$-0.556106\pi$
$491$	−2.62500e22	−0.350700	−0.175350	+	0.984506i	$0.556106\pi$
$492$	1.47871e22i	0.194169i
$493$	3.52014e22i	0.454319i
$494$	−7.15602e22	−0.907805
$495$	0	0
$496$	−1.45017e22	−0.177756
$497$	− 3.77714e22i	− 0.455128i
$498$	2.71510e22i	0.321615i
$499$	−1.91458e22	−0.222956	−0.111478	−	0.993767i	$-0.535558\pi$
$499$	−1.91458e22	−0.222956	−0.111478	+	0.993767i	$0.535558\pi$
$500$	0	0
$501$	1.23411e22	0.138910
$502$	5.13778e22i	0.568583i
$503$	− 3.67210e22i	− 0.399564i	−0.979840	−	0.199782i	$-0.935977\pi$
$503$	− 3.67210e22i	− 0.399564i	0.979840	−	0.199782i	$-0.0640234\pi$
$504$	2.30427e22	0.246533
$505$	0	0
$506$	1.70438e23	1.76314
$507$	1.16591e22i	0.118603i
$508$	− 2.79488e22i	− 0.279590i
$509$	−6.75737e22	−0.664778	−0.332389	−	0.943142i	$-0.607855\pi$
$509$	−6.75737e22	−0.664778	−0.332389	+	0.943142i	$0.607855\pi$
$510$	0	0
$511$	5.61771e22	0.534542
$512$	4.72237e21i	0.0441942i
$513$	− 1.16589e23i	− 1.07315i
$514$	−4.35567e22	−0.394338
$515$	0	0
$516$	6.86703e21	0.0601515
$517$	− 1.90834e23i	− 1.64432i
$518$	7.82359e22i	0.663137i
$519$	−1.27829e22	−0.106588
$520$	0	0
$521$	−2.39219e23	−1.93052	−0.965262	−	0.261284i	$-0.915854\pi$
$521$	−2.39219e23	−1.93052	−0.965262	+	0.261284i	$0.915854\pi$
$522$	− 5.78629e22i	− 0.459410i
$523$	1.23467e22i	0.0964465i	0.998837	+	0.0482233i	$0.0153559\pi$
$523$	1.23467e22i	0.0964465i	−0.998837	+	0.0482233i	$0.984644\pi$
$524$	1.30448e22	0.100259
$525$	0	0
$526$	1.48144e23	1.10231
$527$	5.86254e22i	0.429236i
$528$	2.19270e22i	0.157976i
$529$	−1.59150e23	−1.12832
$530$	0	0
$531$	−1.44707e23	−0.993539
$532$	9.31063e22i	0.629115i
$533$	1.30174e23i	0.865650i
$534$	−7.18646e22	−0.470342
$535$	0	0
$536$	−4.20919e22	−0.266869
$537$	− 7.67774e22i	− 0.479128i
$538$	1.31355e23i	0.806859i
$539$	9.82619e22	0.594129
$540$	0	0
$541$	−2.47773e23	−1.45170	−0.725851	−	0.687851i	$-0.758554\pi$
$541$	−2.47773e23	−1.45170	−0.725851	+	0.687851i	$0.758554\pi$
$542$	− 1.18920e23i	− 0.685903i
$543$	− 7.29209e22i	− 0.414051i
$544$	1.90910e22	0.106718
$545$	0	0
$546$	−3.21175e22	−0.174022
$547$	5.48101e22i	0.292394i	0.989256	+	0.146197i	$0.0467033\pi$
$547$	5.48101e22i	0.292394i	−0.989256	+	0.146197i	$0.953297\pi$
$548$	1.41427e23i	0.742844i
$549$	4.86076e22	0.251385
$550$	0	0
$551$	2.33800e23	1.17235
$552$	− 3.86210e22i	− 0.190696i
$553$	− 1.73105e23i	− 0.841678i
$554$	2.49020e23	1.19234
$555$	0	0
$556$	−1.76941e23	−0.821662
$557$	2.57560e23i	1.17790i	0.808168	+	0.588952i	$0.200459\pi$
$557$	2.57560e23i	1.17790i	−0.808168	+	0.588952i	$0.799541\pi$
$558$	− 9.63665e22i	− 0.434046i
$559$	6.04519e22	0.268169
$560$	0	0
$561$	8.86437e22	0.381473
$562$	1.73207e23i	0.734186i
$563$	− 6.37462e22i	− 0.266154i	−0.991106	−	0.133077i	$-0.957514\pi$
$563$	− 6.37462e22i	− 0.266154i	0.991106	−	0.133077i	$-0.0424858\pi$
$564$	−4.32427e22	−0.177844
$565$	0	0
$566$	2.87237e23	1.14630
$567$	1.25041e23i	0.491582i
$568$	5.14395e22i	0.199221i
$569$	2.97128e23	1.13368	0.566839	−	0.823829i	$-0.308166\pi$
$569$	2.97128e23	1.13368	0.566839	+	0.823829i	$0.308166\pi$
$570$	0	0
$571$	3.65472e23	1.35347	0.676733	−	0.736228i	$-0.263395\pi$
$571$	3.65472e23	1.35347	0.676733	+	0.736228i	$0.263395\pi$
$572$	1.93028e23i	0.704293i
$573$	− 7.50781e22i	− 0.269898i
$574$	1.69368e23	0.599901
$575$	0	0
$576$	−3.13811e22	−0.107914
$577$	1.73713e23i	0.588623i	0.955710	+	0.294312i	$0.0950904\pi$
$577$	1.73713e23i	0.588623i	−0.955710	+	0.294312i	$0.904910\pi$
$578$	1.34595e23i	0.449409i
$579$	4.18027e22	0.137542
$580$	0	0
$581$	3.10981e23	0.993658
$582$	− 6.71379e22i	− 0.211408i
$583$	− 6.15894e23i	− 1.91128i
$584$	−7.65056e22	−0.233983
$585$	0	0
$586$	−7.81590e22	−0.232193
$587$	− 4.20741e23i	− 1.23194i	−0.787768	−	0.615972i	$-0.788763\pi$
$587$	− 4.20741e23i	− 1.23194i	0.787768	−	0.615972i	$-0.211237\pi$
$588$	− 2.22660e22i	− 0.0642590i
$589$	3.89377e23	1.10762
$590$	0	0
$591$	−2.21488e23	−0.612149
$592$	− 1.06547e23i	− 0.290272i
$593$	4.26727e23i	1.14600i	0.819555	+	0.573000i	$0.194221\pi$
$593$	4.26727e23i	1.14600i	−0.819555	+	0.573000i	$0.805779\pi$
$594$	−3.14489e23	−0.832571
$595$	0	0
$596$	9.06568e22	0.233242
$597$	− 8.52143e21i	− 0.0216138i
$598$	− 3.39988e23i	− 0.850166i
$599$	1.66085e23	0.409451	0.204726	−	0.978819i	$-0.434370\pi$
$599$	1.66085e23	0.409451	0.204726	+	0.978819i	$0.434370\pi$
$600$	0	0
$601$	−3.30613e23	−0.792294	−0.396147	−	0.918187i	$-0.629653\pi$
$601$	−3.30613e23	−0.792294	−0.396147	+	0.918187i	$0.629653\pi$
$602$	− 7.86533e22i	− 0.185843i
$603$	− 2.79710e23i	− 0.651644i
$604$	2.36224e23	0.542638
$605$	0	0
$606$	1.39219e23	0.310943
$607$	3.28253e23i	0.722944i	0.932383	+	0.361472i	$0.117726\pi$
$607$	3.28253e23i	0.722944i	−0.932383	+	0.361472i	$0.882274\pi$
$608$	− 1.26798e23i	− 0.275380i
$609$	1.04934e23	0.224734
$610$	0	0
$611$	−3.80674e23	−0.792872
$612$	1.26864e23i	0.260585i
$613$	− 4.83476e23i	− 0.979401i	−0.871891	−	0.489701i	$-0.837106\pi$
$613$	− 4.83476e23i	− 0.979401i	0.871891	−	0.489701i	$-0.162894\pi$
$614$	9.38397e22	0.187480
$615$	0	0
$616$	2.51147e23	0.488080
$617$	− 4.09399e23i	− 0.784736i	−0.919808	−	0.392368i	$-0.871656\pi$
$617$	− 4.09399e23i	− 0.784736i	0.919808	−	0.392368i	$-0.128344\pi$
$618$	− 1.74415e22i	− 0.0329748i
$619$	5.33004e23	0.993940	0.496970	−	0.867768i	$-0.334446\pi$
$619$	5.33004e23	0.993940	0.496970	+	0.867768i	$0.334446\pi$
$620$	0	0
$621$	5.53924e23	1.00501
$622$	− 8.01089e21i	− 0.0143371i
$623$	8.23119e23i	1.45316i
$624$	4.37397e22	0.0761741
$625$	0	0
$626$	−6.52720e23	−1.10623
$627$	− 5.88752e23i	− 0.984370i
$628$	− 4.43359e23i	− 0.731305i
$629$	−4.30734e23	−0.700936
$630$	0	0
$631$	−2.81823e22	−0.0446402	−0.0223201	−	0.999751i	$-0.507105\pi$
$631$	−2.81823e22	−0.0446402	−0.0223201	+	0.999751i	$0.507105\pi$
$632$	2.35746e23i	0.368425i
$633$	− 1.07229e23i	− 0.165341i
$634$	3.65322e23	0.555799
$635$	0	0
$636$	−1.39560e23	−0.206717
$637$	− 1.96012e23i	− 0.286482i
$638$	− 6.30657e23i	− 0.909530i
$639$	−3.41826e23	−0.486461
$640$	0	0
$641$	5.47552e23	0.758809	0.379404	−	0.925231i	$-0.376129\pi$
$641$	5.47552e23	0.758809	0.379404	+	0.925231i	$0.376129\pi$
$642$	− 8.11294e22i	− 0.110951i
$643$	1.13082e24i	1.52616i	0.646305	+	0.763079i	$0.276313\pi$
$643$	1.13082e24i	1.52616i	−0.646305	+	0.763079i	$0.723687\pi$
$644$	−4.42355e23	−0.589171
$645$	0	0
$646$	−5.12604e23	−0.664975
$647$	9.71467e23i	1.24377i	0.783107	+	0.621887i	$0.213634\pi$
$647$	9.71467e23i	1.24377i	−0.783107	+	0.621887i	$0.786366\pi$
$648$	− 1.70289e23i	− 0.215178i
$649$	−1.57718e24	−1.96699
$650$	0	0
$651$	1.74760e23	0.212326
$652$	− 6.99949e23i	− 0.839386i
$653$	− 8.71125e22i	− 0.103114i	−0.998670	−	0.0515571i	$-0.983582\pi$
$653$	− 8.71125e22i	− 0.103114i	0.998670	−	0.0515571i	$-0.0164184\pi$
$654$	−3.54023e23	−0.413638
$655$	0	0
$656$	−2.30656e23	−0.262593
$657$	− 5.08396e23i	− 0.571342i
$658$	4.95291e23i	0.549466i
$659$	5.51481e23	0.603955	0.301978	−	0.953315i	$-0.402353\pi$
$659$	5.51481e23	0.603955	0.301978	+	0.953315i	$0.402353\pi$
$660$	0	0
$661$	1.72983e23	0.184626	0.0923128	−	0.995730i	$-0.470574\pi$
$661$	1.72983e23	0.184626	0.0923128	+	0.995730i	$0.470574\pi$
$662$	− 4.23121e22i	− 0.0445833i
$663$	− 1.76825e23i	− 0.183942i
$664$	−4.23514e23	−0.434950
$665$	0	0
$666$	7.08025e23	0.708790
$667$	1.11080e24i	1.09791i
$668$	1.92503e23i	0.187861i
$669$	−1.47109e23	−0.141748
$670$	0	0
$671$	5.29782e23	0.497686
$672$	− 5.69093e22i	− 0.0527891i
$673$	− 9.31240e23i	− 0.852970i	−0.904495	−	0.426485i	$-0.859752\pi$
$673$	− 9.31240e23i	− 0.852970i	0.904495	−	0.426485i	$-0.140248\pi$
$674$	4.01321e23	0.362981
$675$	0	0
$676$	−1.81864e23	−0.160398
$677$	− 8.38487e21i	− 0.00730286i	−0.999993	−	0.00365143i	$-0.998838\pi$
$677$	− 8.38487e21i	− 0.00730286i	0.999993	−	0.00365143i	$-0.00116229\pi$
$678$	4.70998e23i	0.405104i
$679$	−7.68981e23	−0.653164
$680$	0	0
$681$	5.02732e23	0.416472
$682$	− 1.05031e24i	− 0.859314i
$683$	2.03510e24i	1.64440i	0.569195	+	0.822202i	$0.307255\pi$
$683$	2.03510e24i	1.64440i	−0.569195	+	0.822202i	$0.692745\pi$
$684$	8.42600e23	0.672426
$685$	0	0
$686$	−9.88685e23	−0.769667
$687$	6.32390e23i	0.486243i
$688$	1.07115e23i	0.0813485i
$689$	−1.22858e24	−0.921594
$690$	0	0
$691$	−1.51213e24	−1.10669	−0.553343	−	0.832953i	$-0.686648\pi$
$691$	−1.51213e24	−1.10669	−0.553343	+	0.832953i	$0.686648\pi$
$692$	− 1.99393e23i	− 0.144148i
$693$	1.66892e24i	1.19180i
$694$	−4.16082e23	−0.293510
$695$	0	0
$696$	−1.42906e23	−0.0983718
$697$	9.32468e23i	0.634096i
$698$	− 9.22574e23i	− 0.619769i
$699$	7.57500e23	0.502720
$700$	0	0
$701$	8.28511e23	0.536655	0.268328	−	0.963328i	$-0.413529\pi$
$701$	8.28511e23	0.536655	0.268328	+	0.963328i	$0.413529\pi$
$702$	6.27340e23i	0.401456i
$703$	2.86084e24i	1.80873i
$704$	−3.42028e23	−0.213645
$705$	0	0
$706$	−2.04688e24	−1.24811
$707$	− 1.59458e24i	− 0.960684i
$708$	3.57386e23i	0.212743i
$709$	3.32788e22	0.0195738	0.00978689	−	0.999952i	$-0.496885\pi$
$709$	3.32788e22	0.0195738	0.00978689	+	0.999952i	$0.496885\pi$
$710$	0	0
$711$	−1.56658e24	−0.899623
$712$	− 1.12098e24i	− 0.636088i
$713$	1.84996e24i	1.03729i
$714$	−2.30066e23	−0.127473
$715$	0	0
$716$	1.19761e24	0.647970
$717$	6.33846e23i	0.338899i
$718$	− 1.96921e24i	− 1.04048i
$719$	−2.74357e23	−0.143258	−0.0716292	−	0.997431i	$-0.522820\pi$
$719$	−2.74357e23	−0.143258	−0.0716292	+	0.997431i	$0.522820\pi$
$720$	0	0
$721$	−1.99771e23	−0.101879
$722$	2.00162e24i	1.00883i
$723$	− 4.70391e23i	− 0.234306i
$724$	1.13745e24	0.559959
$725$	0	0
$726$	−1.04447e24	−0.502266
$727$	3.38639e24i	1.60951i	0.593606	+	0.804756i	$0.297704\pi$
$727$	3.38639e24i	1.60951i	−0.593606	+	0.804756i	$0.702296\pi$
$728$	− 5.00984e23i	− 0.235346i
$729$	5.83070e23	0.270730
$730$	0	0
$731$	4.33032e23	0.196436
$732$	− 1.20048e23i	− 0.0538281i
$733$	− 2.34817e24i	− 1.04075i	−0.853938	−	0.520375i	$-0.825792\pi$
$733$	− 2.34817e24i	− 1.04075i	0.853938	−	0.520375i	$-0.174208\pi$
$734$	−1.12835e24	−0.494341
$735$	0	0
$736$	6.02428e23	0.257896
$737$	− 3.04860e24i	− 1.29011i
$738$	− 1.53276e24i	− 0.641202i
$739$	−2.65236e24	−1.09687	−0.548434	−	0.836194i	$-0.684776\pi$
$739$	−2.65236e24	−1.09687	−0.548434	+	0.836194i	$0.684776\pi$
$740$	0	0
$741$	−1.17444e24	−0.474651
$742$	1.59849e24i	0.638671i
$743$	− 4.48213e24i	− 1.77043i	−0.465178	−	0.885217i	$-0.654010\pi$
$743$	− 4.48213e24i	− 1.77043i	0.465178	−	0.885217i	$-0.345990\pi$
$744$	−2.37999e23	−0.0929406
$745$	0	0
$746$	1.97955e24	0.755589
$747$	− 2.81434e24i	− 1.06207i
$748$	1.38271e24i	0.515901i
$749$	−9.29236e23	−0.342792
$750$	0	0
$751$	3.89653e24	1.40520	0.702600	−	0.711585i	$-0.252022\pi$
$751$	3.89653e24	1.40520	0.702600	+	0.711585i	$0.252022\pi$
$752$	− 6.74520e23i	− 0.240516i
$753$	8.43206e23i	0.297287i
$754$	−1.25803e24	−0.438564
$755$	0	0
$756$	8.16225e23	0.278211
$757$	− 2.72183e24i	− 0.917373i	−0.888598	−	0.458687i	$-0.848320\pi$
$757$	− 2.72183e24i	− 0.917373i	0.888598	−	0.458687i	$-0.151680\pi$
$758$	1.75625e24i	0.585326i
$759$	2.79721e24	0.921870
$760$	0	0
$761$	3.88834e23	0.125312	0.0626562	−	0.998035i	$-0.480043\pi$
$761$	3.88834e23	0.125312	0.0626562	+	0.998035i	$0.480043\pi$
$762$	− 4.58691e23i	− 0.146185i
$763$	4.05489e24i	1.27797i
$764$	1.17110e24	0.365007
$765$	0	0
$766$	−1.24583e24	−0.379766
$767$	3.14614e24i	0.948457i
$768$	7.75028e22i	0.0231072i
$769$	2.20996e24	0.651645	0.325823	−	0.945431i	$-0.394359\pi$
$769$	2.20996e24	0.651645	0.325823	+	0.945431i	$0.394359\pi$
$770$	0	0
$771$	−7.14847e23	−0.206182
$772$	6.52058e23i	0.186011i
$773$	− 5.39261e24i	− 1.52151i	−0.649042	−	0.760753i	$-0.724830\pi$
$773$	− 5.39261e24i	− 1.52151i	0.649042	−	0.760753i	$-0.275170\pi$
$774$	−7.11803e23	−0.198638
$775$	0	0
$776$	1.04725e24	0.285907
$777$	1.28400e24i	0.346725i
$778$	2.55578e24i	0.682648i
$779$	6.19325e24	1.63625
$780$	0	0
$781$	−3.72562e24	−0.963085
$782$	− 2.43542e24i	− 0.622754i
$783$	− 2.04963e24i	− 0.518443i
$784$	3.47315e23	0.0869034
$785$	0	0
$786$	2.14090e23	0.0524209
$787$	− 1.11664e24i	− 0.270475i	−0.990813	−	0.135238i	$-0.956820\pi$
$787$	− 1.11664e24i	− 0.270475i	0.990813	−	0.135238i	$-0.0431798\pi$
$788$	− 3.45488e24i	− 0.827866i
$789$	2.43131e24	0.576350
$790$	0	0
$791$	5.39470e24	1.25160
$792$	− 2.27285e24i	− 0.521682i
$793$	− 1.05680e24i	− 0.239978i
$794$	1.30159e24	0.292416
$795$	0	0
$796$	1.32921e23	0.0292303
$797$	− 4.11242e24i	− 0.894751i	−0.894346	−	0.447375i	$-0.852359\pi$
$797$	− 4.11242e24i	− 0.894751i	0.894346	−	0.447375i	$-0.147641\pi$
$798$	1.52805e24i	0.328937i
$799$	−2.72686e24	−0.580786
$800$	0	0
$801$	7.44913e24	1.55321
$802$	2.70491e24i	0.558047i
$803$	− 5.54109e24i	− 1.13113i
$804$	−6.90807e23	−0.139534
$805$	0	0
$806$	−2.09515e24	−0.414351
$807$	2.15578e24i	0.421871i
$808$	2.17160e24i	0.420517i
$809$	−1.99425e24	−0.382135	−0.191068	−	0.981577i	$-0.561195\pi$
$809$	−1.99425e24	−0.382135	−0.191068	+	0.981577i	$0.561195\pi$
$810$	0	0
$811$	−6.54121e24	−1.22739	−0.613693	−	0.789545i	$-0.710317\pi$
$811$	−6.54121e24	−1.22739	−0.613693	+	0.789545i	$0.710317\pi$
$812$	1.63681e24i	0.303928i
$813$	− 1.95171e24i	− 0.358628i
$814$	7.71688e24	1.40325
$815$	0	0
$816$	3.13319e23	0.0557982
$817$	− 2.87610e24i	− 0.506894i
$818$	− 4.44311e23i	− 0.0774968i
$819$	3.32914e24	0.574671
$820$	0	0
$821$	−8.88770e24	−1.50270	−0.751351	−	0.659903i	$-0.770597\pi$
$821$	−8.88770e24	−1.50270	−0.751351	+	0.659903i	$0.770597\pi$
$822$	2.32108e24i	0.388400i
$823$	− 6.84928e24i	− 1.13435i	−0.823598	−	0.567174i	$-0.808037\pi$
$823$	− 6.84928e24i	− 1.13435i	0.823598	−	0.567174i	$-0.191963\pi$
$824$	2.72061e23	0.0445949
$825$	0	0
$826$	4.09341e24	0.657287
$827$	9.77573e24i	1.55365i	0.629718	+	0.776824i	$0.283170\pi$
$827$	9.77573e24i	1.55365i	−0.629718	+	0.776824i	$0.716830\pi$
$828$	4.00326e24i	0.629732i
$829$	−7.90775e24	−1.23123	−0.615615	−	0.788047i	$-0.711092\pi$
$829$	−7.90775e24	−1.23123	−0.615615	+	0.788047i	$0.711092\pi$
$830$	0	0
$831$	4.08688e24	0.623423
$832$	6.82273e23i	0.103017i
$833$	− 1.40408e24i	− 0.209850i
$834$	−2.90394e24	−0.429611
$835$	0	0
$836$	9.18364e24	1.33126
$837$	− 3.41352e24i	− 0.489819i
$838$	2.89356e24i	0.411016i
$839$	7.46885e24	1.05021	0.525106	−	0.851037i	$-0.324026\pi$
$839$	7.46885e24	1.05021	0.525106	+	0.851037i	$0.324026\pi$
$840$	0	0
$841$	−3.14695e24	−0.433634
$842$	− 2.71958e23i	− 0.0370978i
$843$	2.84264e24i	0.383873i
$844$	1.67260e24	0.223606
$845$	0	0
$846$	4.48233e24	0.587294
$847$	1.19631e25i	1.55179i
$848$	− 2.17693e24i	− 0.279563i
$849$	4.71409e24	0.599352
$850$	0	0
$851$	−1.35921e25	−1.69389
$852$	8.44218e23i	0.104164i
$853$	− 4.59203e24i	− 0.560967i	−0.959859	−	0.280484i	$-0.909505\pi$
$853$	− 4.59203e24i	− 0.560967i	0.959859	−	0.280484i	$-0.0904949\pi$
$854$	−1.37500e24	−0.166307
$855$	0	0
$856$	1.26549e24	0.150049
$857$	− 8.74464e24i	− 1.02661i	−0.858207	−	0.513304i	$-0.828421\pi$
$857$	− 8.74464e24i	− 1.02661i	0.858207	−	0.513304i	$-0.171579\pi$
$858$	3.16795e24i	0.368244i
$859$	1.25157e25	1.44050	0.720251	−	0.693714i	$-0.244027\pi$
$859$	1.25157e25	1.44050	0.720251	+	0.693714i	$0.244027\pi$
$860$	0	0
$861$	2.77964e24	0.313662
$862$	9.25611e24i	1.03423i
$863$	− 4.23769e22i	− 0.00468854i	−0.999997	−	0.00234427i	$-0.999254\pi$
$863$	− 4.23769e22i	− 0.00468854i	0.999997	−	0.00234427i	$-0.000746205\pi$
$864$	−1.11159e24	−0.121780
$865$	0	0
$866$	−5.51147e24	−0.592059
$867$	2.20895e24i	0.234976i
$868$	2.72598e24i	0.287148i
$869$	−1.70744e25	−1.78105
$870$	0	0
$871$	−6.08132e24	−0.622076
$872$	− 5.52221e24i	− 0.559401i
$873$	6.95918e24i	0.698131i
$874$	−1.61755e25	−1.60698
$875$	0	0
$876$	−1.25560e24	−0.122339
$877$	− 1.33197e25i	− 1.28528i	−0.766170	−	0.642638i	$-0.777840\pi$
$877$	− 1.33197e25i	− 1.28528i	0.766170	−	0.642638i	$-0.222160\pi$
$878$	7.39538e24i	0.706736i
$879$	−1.28274e24	−0.121404
$880$	0	0
$881$	3.37699e23	0.0313498	0.0156749	−	0.999877i	$-0.495010\pi$
$881$	3.37699e23	0.0313498	0.0156749	+	0.999877i	$0.495010\pi$
$882$	2.30798e24i	0.212202i
$883$	1.43309e25i	1.30499i	0.757793	+	0.652495i	$0.226278\pi$
$883$	1.43309e25i	1.30499i	−0.757793	+	0.652495i	$0.773722\pi$
$884$	2.75821e24	0.248761
$885$	0	0
$886$	8.79298e23	0.0777946
$887$	− 1.41818e25i	− 1.24274i	−0.783518	−	0.621369i	$-0.786577\pi$
$887$	− 1.41818e25i	− 1.24274i	0.783518	−	0.621369i	$-0.213423\pi$
$888$	− 1.74863e24i	− 0.151771i
$889$	−5.25374e24	−0.451652
$890$	0	0
$891$	1.23335e25	1.04022
$892$	− 2.29468e24i	− 0.191700i
$893$	1.81112e25i	1.49869i
$894$	1.48785e24	0.121952
$895$	0	0
$896$	8.87699e23	0.0713917
$897$	− 5.57984e24i	− 0.444514i
$898$	− 7.90719e24i	− 0.623984i
$899$	6.84525e24	0.535096
$900$	0	0
$901$	−8.80062e24	−0.675076
$902$	− 1.67058e25i	− 1.26944i
$903$	− 1.29085e24i	− 0.0971693i
$904$	−7.34685e24	−0.547860
$905$	0	0
$906$	3.87688e24	0.283721
$907$	2.50957e25i	1.81944i	0.415222	+	0.909720i	$0.363704\pi$
$907$	2.50957e25i	1.81944i	−0.415222	+	0.909720i	$0.636296\pi$
$908$	7.84184e24i	0.563233i
$909$	−1.44307e25	−1.02682
$910$	0	0
$911$	−2.35966e24	−0.164794	−0.0823972	−	0.996600i	$-0.526258\pi$
$911$	−2.35966e24	−0.164794	−0.0823972	+	0.996600i	$0.526258\pi$
$912$	− 2.08099e24i	− 0.143984i
$913$	− 3.06740e25i	− 2.10266i
$914$	9.81210e24	0.666376
$915$	0	0
$916$	−9.86433e24	−0.657591
$917$	− 2.45213e24i	− 0.161959i
$918$	4.49379e24i	0.294070i
$919$	−2.94936e25	−1.91226	−0.956129	−	0.292946i	$-0.905364\pi$
$919$	−2.94936e25	−1.91226	−0.956129	+	0.292946i	$0.905364\pi$
$920$	0	0
$921$	1.54008e24	0.0980252
$922$	1.74117e25i	1.09807i
$923$	7.43182e24i	0.464388i
$924$	4.12178e24	0.255196
$925$	0	0
$926$	1.17079e24	0.0711684
$927$	1.80790e24i	0.108892i
$928$	− 2.22911e24i	− 0.133037i
$929$	−1.27862e25	−0.756150	−0.378075	−	0.925775i	$-0.623414\pi$
$929$	−1.27862e25	−0.756150	−0.378075	+	0.925775i	$0.623414\pi$
$930$	0	0
$931$	−9.32560e24	−0.541508
$932$	1.18158e25i	0.679875i
$933$	− 1.31474e23i	− 0.00749626i
$934$	−1.27428e25	−0.719975
$935$	0	0
$936$	−4.53385e24	−0.251549
$937$	5.20286e24i	0.286059i	0.989718	+	0.143029i	$0.0456844\pi$
$937$	5.20286e24i	0.286059i	−0.989718	+	0.143029i	$0.954316\pi$
$938$	7.91234e24i	0.431103i
$939$	−1.07123e25	−0.578398
$940$	0	0
$941$	2.51815e25	1.33527	0.667635	−	0.744488i	$-0.267306\pi$
$941$	2.51815e25	1.33527	0.667635	+	0.744488i	$0.267306\pi$
$942$	− 7.27635e24i	− 0.382367i
$943$	2.94246e25i	1.53236i
$944$	−5.57467e24	−0.287712
$945$	0	0
$946$	−7.75805e24	−0.393258
$947$	− 2.26103e25i	− 1.13588i	−0.823071	−	0.567939i	$-0.807741\pi$
$947$	− 2.26103e25i	− 1.13588i	0.823071	−	0.567939i	$-0.192259\pi$
$948$	3.86903e24i	0.192633i
$949$	−1.10533e25	−0.545417
$950$	0	0
$951$	5.99562e24	0.290603
$952$	− 3.58867e24i	− 0.172393i
$953$	− 2.71240e25i	− 1.29141i	−0.763586	−	0.645706i	$-0.776563\pi$
$953$	− 2.71240e25i	− 1.29141i	0.763586	−	0.645706i	$-0.223437\pi$
$954$	1.44662e25	0.682640
$955$	0	0
$956$	−9.88702e24	−0.458325
$957$	− 1.03502e25i	− 0.475553i
$958$	− 2.39486e25i	− 1.09062i
$959$	2.65851e25	1.20000
$960$	0	0
$961$	−1.11498e25	−0.494447
$962$	− 1.53935e25i	− 0.676629i
$963$	8.40947e24i	0.366392i
$964$	7.33738e24	0.316874
$965$	0	0
$966$	−7.25987e24	−0.308052
$967$	2.72568e25i	1.14644i	0.819403	+	0.573218i	$0.194305\pi$
$967$	2.72568e25i	1.14644i	−0.819403	+	0.573218i	$0.805695\pi$
$968$	− 1.62921e25i	− 0.679261i
$969$	−8.41278e24	−0.347686
$970$	0	0
$971$	−5.68052e24	−0.230688	−0.115344	−	0.993326i	$-0.536797\pi$
$971$	−5.68052e24	−0.230688	−0.115344	+	0.993326i	$0.536797\pi$
$972$	− 1.13511e25i	− 0.456954i
$973$	3.32610e25i	1.32732i
$974$	4.19670e24	0.166019
$975$	0	0
$976$	1.87256e24	0.0727967
$977$	− 2.19879e25i	− 0.847383i	−0.905807	−	0.423691i	$-0.860734\pi$
$977$	− 2.19879e25i	− 0.847383i	0.905807	−	0.423691i	$-0.139266\pi$
$978$	− 1.14875e25i	− 0.438878i
$979$	8.11892e25	3.07500
$980$	0	0
$981$	3.66962e25	1.36595
$982$	− 6.71999e24i	− 0.247983i
$983$	− 1.62023e25i	− 0.592748i	−0.955072	−	0.296374i	$-0.904222\pi$
$983$	− 1.62023e25i	− 0.592748i	0.955072	−	0.296374i	$-0.0957776\pi$
$984$	−3.78550e24	−0.137298
$985$	0	0
$986$	−9.01156e24	−0.321252
$987$	8.12865e24i	0.287291i
$988$	− 1.83194e25i	− 0.641915i
$989$	1.36646e25	0.474710
$990$	0	0
$991$	−1.63414e25	−0.558036	−0.279018	−	0.960286i	$-0.590009\pi$
$991$	−1.63414e25	−0.558036	−0.279018	+	0.960286i	$0.590009\pi$
$992$	− 3.71242e24i	− 0.125692i
$993$	− 6.94421e23i	− 0.0233106i
$994$	9.66947e24	0.321824
$995$	0	0
$996$	−6.95066e24	−0.227416
$997$	3.96008e25i	1.28468i	0.766420	+	0.642340i	$0.222036\pi$
$997$	3.96008e25i	1.28468i	−0.766420	+	0.642340i	$0.777964\pi$
$998$	− 4.90132e24i	− 0.157653i
$999$	2.50798e25	0.799868

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.18.b.f.49.4		4
5.2	odd	4		50.18.a.c.1.2		2
5.3	odd	4		10.18.a.d.1.1	✓	2
5.4	even	2	inner	50.18.b.f.49.1		4
15.8	even	4		90.18.a.j.1.1		2
20.3	even	4		80.18.a.b.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.d.1.1	✓	2	5.3	odd	4
50.18.a.c.1.2		2	5.2	odd	4
50.18.b.f.49.1		4	5.4	even	2	inner
50.18.b.f.49.4		4	1.1	even	1	trivial
80.18.a.b.1.2		2	20.3	even	4
90.18.a.j.1.1		2	15.8	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+256.000i q^{2} +4201.44i q^{3} -65536.0 q^{4} -1.07557e6 q^{6} +1.23193e7i q^{7} -1.67772e7i q^{8} +1.11488e8 q^{9} +1.21513e9 q^{11} -2.75345e8i q^{12} -2.42392e9i q^{13} -3.15374e9 q^{14} +4.29497e9 q^{16} -1.73631e10i q^{17} +2.85410e10i q^{18} -1.15322e11 q^{19} -5.17587e10 q^{21} +3.11072e11i q^{22} -5.47905e11i q^{23} +7.04884e10 q^{24} +6.20524e11 q^{26} +1.01098e12i q^{27} -8.07357e11i q^{28} -2.02736e12 q^{29} -3.37643e12 q^{31} +1.09951e12i q^{32} +5.10528e12i q^{33} +4.44497e12 q^{34} -7.30648e12 q^{36} -2.48073e13i q^{37} -2.95225e13i q^{38} +1.01840e13 q^{39} -5.37038e13 q^{41} -1.32502e13i q^{42} +2.49397e13i q^{43} -7.96345e13 q^{44} +1.40264e14 q^{46} -1.57049e14i q^{47} +1.80450e13i q^{48} +8.08656e13 q^{49} +7.29502e13 q^{51} +1.58854e14i q^{52} -5.06856e14i q^{53} -2.58812e14 q^{54} +2.06683e14 q^{56} -4.84519e14i q^{57} -5.19005e14i q^{58} -1.29796e15 q^{59} +4.35989e14 q^{61} -8.64366e14i q^{62} +1.37345e15i q^{63} -2.81475e14 q^{64} -1.30695e15 q^{66} -2.50888e15i q^{67} +1.13791e15i q^{68} +2.30199e15 q^{69} -3.06603e15 q^{71} -1.87046e15i q^{72} -4.56009e15i q^{73} +6.35068e15 q^{74} +7.55776e15 q^{76} +1.49695e16i q^{77} +2.60709e15i q^{78} -1.40515e16 q^{79} +1.01500e16 q^{81} -1.37482e16i q^{82} -2.52434e16i q^{83} +3.39206e15 q^{84} -6.38456e15 q^{86} -8.51784e15i q^{87} -2.03864e16i q^{88} +6.68155e16 q^{89} +2.98610e16 q^{91} +3.59075e16i q^{92} -1.41859e16i q^{93} +4.02045e16 q^{94} -4.61953e15 q^{96} +6.24209e16i q^{97} +2.07016e16i q^{98} +1.35472e17 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 262144 q^{4} + 9025536 q^{6} - 471792132 q^{9} + 129030528 q^{11} - 14174308352 q^{14} + 17179869184 q^{16} - 88427425520 q^{19} + 567296955888 q^{21} - 591497527296 q^{24} + 1482669295616 q^{26}+ \cdots + 10\!\cdots\!76 q^{99}+O(q^{100}) \) 4 * q - 262144 * q^4 + 9025536 * q^6 - 471792132 * q^9 + 129030528 * q^11 - 14174308352 * q^14 + 17179869184 * q^16 - 88427425520 * q^19 + 567296955888 * q^21 - 591497527296 * q^24 + 1482669295616 * q^26 - 7974629727000 * q^29 - 10984522678672 * q^31 - 809068849152 * q^34 + 30919369162752 * q^36 - 235491790704 * q^39 + 46822954554648 * q^41 - 8456144683008 * q^44 + 249625488807936 * q^46 + 154831593772812 * q^49 + 972946158829488 * q^51 - 2956865506283520 * q^54 + 928927472156672 * q^56 - 1804358340721200 * q^59 - 3128845837935352 * q^61 - 1125899906842624 * q^64 - 15473907141378048 * q^66 + 7239025962797616 * q^69 - 135177120868272 * q^71 + 32110227270596608 * q^74 + 5795179758878720 * q^76 - 38005312793104160 * q^79 + 138574652902270164 * q^81 - 37178373301075968 * q^84 - 63926744673839104 * q^86 + 194999044384444440 * q^89 + 74223914931837328 * q^91 + 95204665407264768 * q^94 + 38764381948870656 * q^96 + 1070352562589582976 * q^99

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