LMFDB - Embedded newform 50.18.b.e.49.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [50,18,Mod(49,50)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("50.49"); S:= CuspForms(chi, 18); N := Newforms(S);

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

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

Newform invariants

comment:select newform

sage:traces = [4,0,0,-262144,0,3229696] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$91.6110436723$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 18031x^{2} + 81270225 $ x^4 + 18031*x^2 + 81270225
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\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			$-94.4487i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.18.b.e.49.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+256.000i q^{2} +12037.8i q^{3} -65536.0 q^{4} -3.08167e6 q^{6} +9.53475e6i q^{7} -1.67772e7i q^{8} -1.57682e7 q^{9} +4.01191e8 q^{11} -7.88908e8i q^{12} +8.56166e8i q^{13} -2.44090e9 q^{14} +4.29497e9 q^{16} +3.89127e10i q^{17} -4.03665e9i q^{18} +1.13839e11 q^{19} -1.14777e11 q^{21} +1.02705e11i q^{22} +1.64834e10i q^{23} +2.01961e11 q^{24} -2.19179e11 q^{26} +1.36475e12i q^{27} -6.24870e11i q^{28} +2.27472e12 q^{29} -1.63788e12 q^{31} +1.09951e12i q^{32} +4.82946e12i q^{33} -9.96164e12 q^{34} +1.03338e12 q^{36} +1.75967e13i q^{37} +2.91428e13i q^{38} -1.03064e13 q^{39} -2.95532e13 q^{41} -2.93830e13i q^{42} +1.37690e14i q^{43} -2.62925e13 q^{44} -4.21974e12 q^{46} +1.65452e14i q^{47} +5.17019e13i q^{48} +1.41719e14 q^{49} -4.68422e14 q^{51} -5.61097e13i q^{52} -7.25259e14i q^{53} -3.49376e14 q^{54} +1.59967e14 q^{56} +1.37037e15i q^{57} +5.82328e14i q^{58} -1.62177e15 q^{59} +2.46915e15 q^{61} -4.19296e14i q^{62} -1.50346e14i q^{63} -2.81475e14 q^{64} -1.23634e15 q^{66} +2.03244e14i q^{67} -2.55018e15i q^{68} -1.98423e14 q^{69} +9.39117e15 q^{71} +2.64546e14i q^{72} +1.54865e15i q^{73} -4.50475e15 q^{74} -7.46056e15 q^{76} +3.82526e15i q^{77} -2.63843e15i q^{78} -8.30977e15 q^{79} -1.84648e16 q^{81} -7.56562e15i q^{82} -6.14697e15i q^{83} +7.52205e15 q^{84} -3.52485e16 q^{86} +2.73826e16i q^{87} -6.73087e15i q^{88} -4.67428e15 q^{89} -8.16334e15 q^{91} -1.08025e15i q^{92} -1.97164e16i q^{93} -4.23558e16 q^{94} -1.32357e16 q^{96} -1.01799e17i q^{97} +3.62801e16i q^{98} -6.32605e15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 262144 q^{4} + 3229696 q^{6} - 446391812 q^{9} + 2378817408 q^{11} + 3350448128 q^{14} + 17179869184 q^{16} + 273409661200 q^{19} - 819503796752 q^{21} - 211661357056 q^{24} + 1033174644736 q^{26}+ \cdots - 33\!\cdots\!24 q^{99}+O(q^{100}) $ 4 * q - 262144 * q^4 + 3229696 * q^6 - 446391812 * q^9 + 2378817408 * q^11 + 3350448128 * q^14 + 17179869184 * q^16 + 273409661200 * q^19 - 819503796752 * q^21 - 211661357056 * q^24 + 1033174644736 * q^26 + 9393086840040 * q^29 + 14241734757488 * q^31 - 9602887391232 * q^34 + 29254733791232 * q^36 - 126067430445424 * q^39 + 19245423761688 * q^41 - 155898177650688 * q^44 + 332407895402496 * q^46 + 231656293774092 * q^49 - 1676437434168912 * q^51 - 1434109657968640 * q^54 - 219574968516608 * q^56 - 1309232143990320 * q^59 + 2658080770325768 * q^61 - 1125899906842624 * q^64 + 4931077776801792 * q^66 - 24823071318707664 * q^69 + 4070263898695248 * q^71 + 5085754694371328 * q^74 - 17918175556403200 * q^76 - 38376855356990240 * q^79 - 37806028031428396 * q^81 + 53707000823939072 * q^84 - 3946719238068224 * q^86 + 34917825832790040 * q^89 - 108749216422866032 * q^91 - 238629158829053952 * q^94 + 13871438696022016 * q^96 - 339648391656292224 * 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
$3$	12037.8i	1.05929i	0.848219	+	0.529646i	$0.177675\pi$
$3$	12037.8i	1.05929i	−0.848219	+	0.529646i	$0.822325\pi$
$4$	−65536.0	−0.500000
$5$	0	0
$5$	0	0
$6$	−3.08167e6	−0.749033
$7$	9.53475e6i	0.625138i	0.949895	+	0.312569i	$0.101190\pi$
$7$	9.53475e6i	0.625138i	−0.949895	+	0.312569i	$0.898810\pi$
$8$	− 1.67772e7i	− 0.353553i
$9$	−1.57682e7	−0.122101
$10$	0	0
$11$	4.01191e8	0.564305	0.282152	−	0.959370i	$-0.408952\pi$
$11$	4.01191e8	0.564305	0.282152	+	0.959370i	$0.408952\pi$
$12$	− 7.88908e8i	− 0.529646i
$13$	8.56166e8i	0.291098i	0.989351	+	0.145549i	$0.0464949\pi$
$13$	8.56166e8i	0.291098i	−0.989351	+	0.145549i	$0.953505\pi$
$14$	−2.44090e9	−0.442040
$15$	0	0
$16$	4.29497e9	0.250000
$17$	3.89127e10i	1.35293i	0.736475	+	0.676465i	$0.236489\pi$
$17$	3.89127e10i	1.35293i	−0.736475	+	0.676465i	$0.763511\pi$
$18$	− 4.03665e9i	− 0.0863385i
$19$	1.13839e11	1.53775	0.768876	−	0.639398i	$-0.220816\pi$
$19$	1.13839e11	1.53775	0.768876	+	0.639398i	$0.220816\pi$
$20$	0	0
$21$	−1.14777e11	−0.662205
$22$	1.02705e11i	0.399024i
$23$	1.64834e10i	0.0438894i	0.999759	+	0.0219447i	$0.00698577\pi$
$23$	1.64834e10i	0.0438894i	−0.999759	+	0.0219447i	$0.993014\pi$
$24$	2.01961e11	0.374517
$25$	0	0
$26$	−2.19179e11	−0.205838
$27$	1.36475e12i	0.929952i
$28$	− 6.24870e11i	− 0.312569i
$29$	2.27472e12	0.844394	0.422197	−	0.906504i	$-0.361259\pi$
$29$	2.27472e12	0.844394	0.422197	+	0.906504i	$0.361259\pi$
$30$	0	0
$31$	−1.63788e12	−0.344911	−0.172455	−	0.985017i	$-0.555170\pi$
$31$	−1.63788e12	−0.344911	−0.172455	+	0.985017i	$0.555170\pi$
$32$	1.09951e12i	0.176777i
$33$	4.82946e12i	0.597764i
$34$	−9.96164e12	−0.956665
$35$	0	0
$36$	1.03338e12	0.0610506
$37$	1.75967e13i	0.823599i	0.911275	+	0.411799i	$0.135100\pi$
$37$	1.75967e13i	0.823599i	−0.911275	+	0.411799i	$0.864900\pi$
$38$	2.91428e13i	1.08735i
$39$	−1.03064e13	−0.308358
$40$	0	0
$41$	−2.95532e13	−0.578018	−0.289009	−	0.957326i	$-0.593326\pi$
$41$	−2.95532e13	−0.578018	−0.289009	+	0.957326i	$0.593326\pi$
$42$	− 2.93830e13i	− 0.468249i
$43$	1.37690e14i	1.79647i	0.439519	+	0.898233i	$0.355149\pi$
$43$	1.37690e14i	1.79647i	−0.439519	+	0.898233i	$0.644851\pi$
$44$	−2.62925e13	−0.282152
$45$	0	0
$46$	−4.21974e12	−0.0310345
$47$	1.65452e14i	1.01354i	0.862081	+	0.506770i	$0.169161\pi$
$47$	1.65452e14i	1.01354i	−0.862081	+	0.506770i	$0.830839\pi$
$48$	5.17019e13i	0.264823i
$49$	1.41719e14	0.609202
$50$	0	0
$51$	−4.68422e14	−1.43315
$52$	− 5.61097e13i	− 0.145549i
$53$	− 7.25259e14i	− 1.60010i	−0.599931	−	0.800052i	$-0.704805\pi$
$53$	− 7.25259e14i	− 1.60010i	0.599931	−	0.800052i	$-0.295195\pi$
$54$	−3.49376e14	−0.657575
$55$	0	0
$56$	1.59967e14	0.221020
$57$	1.37037e15i	1.62893i
$58$	5.82328e14i	0.597076i
$59$	−1.62177e15	−1.43796	−0.718981	−	0.695030i	$-0.755391\pi$
$59$	−1.62177e15	−1.43796	−0.718981	+	0.695030i	$0.755391\pi$
$60$	0	0
$61$	2.46915e15	1.64909	0.824545	−	0.565796i	$-0.191431\pi$
$61$	2.46915e15	1.64909	0.824545	+	0.565796i	$0.191431\pi$
$62$	− 4.19296e14i	− 0.243889i
$63$	− 1.50346e14i	− 0.0763301i
$64$	−2.81475e14	−0.125000
$65$	0	0
$66$	−1.23634e15	−0.422683
$67$	2.03244e14i	0.0611479i	0.999533	+	0.0305739i	$0.00973350\pi$
$67$	2.03244e14i	0.0611479i	−0.999533	+	0.0305739i	$0.990266\pi$
$68$	− 2.55018e15i	− 0.676465i
$69$	−1.98423e14	−0.0464917
$70$	0	0
$71$	9.39117e15	1.72593	0.862966	−	0.505262i	$-0.168604\pi$
$71$	9.39117e15	1.72593	0.862966	+	0.505262i	$0.168604\pi$
$72$	2.64546e14i	0.0431693i
$73$	1.54865e15i	0.224754i	0.993666	+	0.112377i	$0.0358465\pi$
$73$	1.54865e15i	0.224754i	−0.993666	+	0.112377i	$0.964153\pi$
$74$	−4.50475e15	−0.582372
$75$	0	0
$76$	−7.46056e15	−0.768876
$77$	3.82526e15i	0.352769i
$78$	− 2.63843e15i	− 0.218042i
$79$	−8.30977e15	−0.616252	−0.308126	−	0.951345i	$-0.599702\pi$
$79$	−8.30977e15	−0.616252	−0.308126	+	0.951345i	$0.599702\pi$
$80$	0	0
$81$	−1.84648e16	−1.10719
$82$	− 7.56562e15i	− 0.408721i
$83$	− 6.14697e15i	− 0.299569i	−0.988719	−	0.149785i	$-0.952142\pi$
$83$	− 6.14697e15i	− 0.299569i	0.988719	−	0.149785i	$-0.0478580\pi$
$84$	7.52205e15	0.331102
$85$	0	0
$86$	−3.52485e16	−1.27029
$87$	2.73826e16i	0.894460i
$88$	− 6.73087e15i	− 0.199512i
$89$	−4.67428e15	−0.125863	−0.0629317	−	0.998018i	$-0.520045\pi$
$89$	−4.67428e15	−0.125863	−0.0629317	+	0.998018i	$0.520045\pi$
$90$	0	0
$91$	−8.16334e15	−0.181977
$92$	− 1.08025e15i	− 0.0219447i
$93$	− 1.97164e16i	− 0.365362i
$94$	−4.23558e16	−0.716681
$95$	0	0
$96$	−1.32357e16	−0.187258
$97$	− 1.01799e17i	− 1.31881i	−0.751786	−	0.659407i	$-0.770808\pi$
$97$	− 1.01799e17i	− 1.31881i	0.751786	−	0.659407i	$-0.229192\pi$
$98$	3.62801e16i	0.430771i
$99$	−6.32605e15	−0.0689023
$100$	0	0
$101$	3.11898e16	0.286603	0.143302	−	0.989679i	$-0.454228\pi$
$101$	3.11898e16	0.286603	0.143302	+	0.989679i	$0.454228\pi$
$102$	− 1.19916e17i	− 1.01339i
$103$	− 1.71633e17i	− 1.33501i	−0.744606	−	0.667505i	$-0.767362\pi$
$103$	− 1.71633e17i	− 1.33501i	0.744606	−	0.667505i	$-0.232638\pi$
$104$	1.43641e16	0.102919
$105$	0	0
$106$	1.85666e17	1.13144
$107$	1.64074e17i	0.923159i	0.887099	+	0.461579i	$0.152717\pi$
$107$	1.64074e17i	0.923159i	−0.887099	+	0.461579i	$0.847283\pi$
$108$	− 8.94401e16i	− 0.464976i
$109$	−2.80332e17	−1.34756	−0.673779	−	0.738933i	$-0.735330\pi$
$109$	−2.80332e17	−1.34756	−0.673779	+	0.738933i	$0.735330\pi$
$110$	0	0
$111$	−2.11825e17	−0.872432
$112$	4.09515e16i	0.156285i
$113$	− 5.30659e17i	− 1.87780i	−0.344193	−	0.938899i	$-0.611847\pi$
$113$	− 5.30659e17i	− 1.87780i	0.344193	−	0.938899i	$-0.388153\pi$
$114$	−3.50815e17	−1.15183
$115$	0	0
$116$	−1.49076e17	−0.422197
$117$	− 1.35002e16i	− 0.0355434i
$118$	− 4.15173e17i	− 1.01679i
$119$	−3.71023e17	−0.845768
$120$	0	0
$121$	−3.44493e17	−0.681560
$122$	6.32103e17i	1.16608i
$123$	− 3.55755e17i	− 0.612291i
$124$	1.07340e17	0.172455
$125$	0	0
$126$	3.84885e16	0.0539735
$127$	− 3.45518e17i	− 0.453043i	−0.974006	−	0.226522i	$-0.927265\pi$
$127$	− 3.45518e17i	− 0.453043i	0.974006	−	0.226522i	$-0.0727354\pi$
$128$	− 7.20576e16i	− 0.0883883i
$129$	−1.65748e18	−1.90298
$130$	0	0
$131$	−5.92983e17	−0.597360	−0.298680	−	0.954353i	$-0.596546\pi$
$131$	−5.92983e17	−0.597360	−0.298680	+	0.954353i	$0.596546\pi$
$132$	− 3.16503e17i	− 0.298882i
$133$	1.08543e18i	0.961307i
$134$	−5.20304e16	−0.0432381
$135$	0	0
$136$	6.52846e17	0.478333
$137$	5.64525e17i	0.388650i	0.980937	+	0.194325i	$0.0622516\pi$
$137$	5.64525e17i	0.388650i	−0.980937	+	0.194325i	$0.937748\pi$
$138$	− 5.07964e16i	− 0.0328746i
$139$	−2.13511e18	−1.29956	−0.649778	−	0.760124i	$-0.725138\pi$
$139$	−2.13511e18	−1.29956	−0.649778	+	0.760124i	$0.725138\pi$
$140$	0	0
$141$	−1.99168e18	−1.07364
$142$	2.40414e18i	1.22042i
$143$	3.43487e17i	0.164268i
$144$	−6.77237e16	−0.0305253
$145$	0	0
$146$	−3.96454e17	−0.158925
$147$	1.70598e18i	0.645323i
$148$	− 1.15321e18i	− 0.411799i
$149$	−2.11167e18	−0.712103	−0.356051	−	0.934466i	$-0.615877\pi$
$149$	−2.11167e18	−0.712103	−0.356051	+	0.934466i	$0.615877\pi$
$150$	0	0
$151$	1.09446e18	0.329532	0.164766	−	0.986333i	$-0.447313\pi$
$151$	1.09446e18	0.329532	0.164766	+	0.986333i	$0.447313\pi$
$152$	− 1.90990e18i	− 0.543677i
$153$	− 6.13581e17i	− 0.165194i
$154$	−9.79267e17	−0.249445
$155$	0	0
$156$	6.75437e17	0.154179
$157$	− 2.67975e18i	− 0.579359i	−0.957124	−	0.289680i	$-0.906451\pi$
$157$	− 2.67975e18i	− 0.579359i	0.957124	−	0.289680i	$-0.0935487\pi$
$158$	− 2.12730e18i	− 0.435756i
$159$	8.73051e18	1.69498
$160$	0	0
$161$	−1.57165e17	−0.0274369
$162$	− 4.72700e18i	− 0.782903i
$163$	− 9.47539e18i	− 1.48937i	−0.667416	−	0.744685i	$-0.732600\pi$
$163$	− 9.47539e18i	− 1.48937i	0.667416	−	0.744685i	$-0.267400\pi$
$164$	1.93680e18	0.289009
$165$	0	0
$166$	1.57362e18	0.211827
$167$	6.70665e18i	0.857859i	0.903338	+	0.428929i	$0.141109\pi$
$167$	6.70665e18i	0.857859i	−0.903338	+	0.428929i	$0.858891\pi$
$168$	1.92564e18i	0.234125i
$169$	7.91739e18	0.915262
$170$	0	0
$171$	−1.79503e18	−0.187761
$172$	− 9.02362e18i	− 0.898233i
$173$	1.05695e19i	1.00152i	0.865585	+	0.500762i	$0.166947\pi$
$173$	1.05695e19i	1.00152i	−0.865585	+	0.500762i	$0.833053\pi$
$174$	−7.00994e18	−0.632479
$175$	0	0
$176$	1.72310e18	0.141076
$177$	− 1.95225e19i	− 1.52322i
$178$	− 1.19662e18i	− 0.0889989i
$179$	1.98718e19	1.40924	0.704621	−	0.709583i	$-0.251117\pi$
$179$	1.98718e19	1.40924	0.704621	+	0.709583i	$0.251117\pi$
$180$	0	0
$181$	2.50176e19	1.61428	0.807138	−	0.590363i	$-0.201015\pi$
$181$	2.50176e19	1.61428	0.807138	+	0.590363i	$0.201015\pi$
$182$	− 2.08981e18i	− 0.128677i
$183$	2.97231e19i	1.74687i
$184$	2.76545e17	0.0155172
$185$	0	0
$186$	5.04740e18	0.258350
$187$	1.56114e19i	0.763464i
$188$	− 1.08431e19i	− 0.506770i
$189$	−1.30125e19	−0.581349
$190$	0	0
$191$	−2.63385e19	−1.07599	−0.537995	−	0.842948i	$-0.680818\pi$
$191$	−2.63385e19	−1.07599	−0.537995	+	0.842948i	$0.680818\pi$
$192$	− 3.38834e18i	− 0.132412i
$193$	3.68856e19i	1.37918i	0.724201	+	0.689589i	$0.242209\pi$
$193$	3.68856e19i	1.37918i	−0.724201	+	0.689589i	$0.757791\pi$
$194$	2.60605e19	0.932542
$195$	0	0
$196$	−9.28769e18	−0.304601
$197$	4.04920e19i	1.27176i	0.771786	+	0.635882i	$0.219364\pi$
$197$	4.04920e19i	1.27176i	−0.771786	+	0.635882i	$0.780636\pi$
$198$	− 1.61947e18i	− 0.0487212i
$199$	3.32772e19	0.959171	0.479586	−	0.877495i	$-0.340787\pi$
$199$	3.32772e19	0.959171	0.479586	+	0.877495i	$0.340787\pi$
$200$	0	0
$201$	−2.44660e18	−0.0647735
$202$	7.98459e18i	0.202659i
$203$	2.16889e19i	0.527863i
$204$	3.06985e19	0.716574
$205$	0	0
$206$	4.39380e19	0.943994
$207$	− 2.59912e17i	− 0.00535894i
$208$	3.67721e18i	0.0727746i
$209$	4.56713e19	0.867761
$210$	0	0
$211$	−2.42162e19	−0.424331	−0.212166	−	0.977234i	$-0.568052\pi$
$211$	−2.42162e19	−0.424331	−0.212166	+	0.977234i	$0.568052\pi$
$212$	4.75306e19i	0.800052i
$213$	1.13049e20i	1.82827i
$214$	−4.20028e19	−0.652772
$215$	0	0
$216$	2.28967e19	0.328788
$217$	− 1.56168e19i	− 0.215617i
$218$	− 7.17650e19i	− 0.952867i
$219$	−1.86423e19	−0.238081
$220$	0	0
$221$	−3.33157e19	−0.393835
$222$	− 5.42272e19i	− 0.616903i
$223$	7.42273e19i	0.812779i	0.913700	+	0.406390i	$0.133212\pi$
$223$	7.42273e19i	0.812779i	−0.913700	+	0.406390i	$0.866788\pi$
$224$	−1.04836e19	−0.110510
$225$	0	0
$226$	1.35849e20	1.32780
$227$	− 9.57531e18i	− 0.0901432i	−0.998984	−	0.0450716i	$-0.985648\pi$
$227$	− 9.57531e18i	− 0.0901432i	0.998984	−	0.0450716i	$-0.0143516\pi$
$228$	− 8.98087e19i	− 0.814464i
$229$	−1.97753e20	−1.72791	−0.863955	−	0.503569i	$-0.832020\pi$
$229$	−1.97753e20	−1.72791	−0.863955	+	0.503569i	$0.832020\pi$
$230$	0	0
$231$	−4.60477e19	−0.373685
$232$	− 3.81635e19i	− 0.298538i
$233$	− 1.79778e20i	− 1.35585i	−0.735131	−	0.677925i	$-0.762880\pi$
$233$	− 1.79778e20i	− 1.35585i	0.735131	−	0.677925i	$-0.237120\pi$
$234$	3.45604e18	0.0251330
$235$	0	0
$236$	1.06284e20	0.718981
$237$	− 1.00031e20i	− 0.652792i
$238$	− 9.49818e19i	− 0.598048i
$239$	2.00207e20	1.21646	0.608229	−	0.793761i	$-0.291880\pi$
$239$	2.00207e20	1.21646	0.608229	+	0.793761i	$0.291880\pi$
$240$	0	0
$241$	−1.81616e20	−1.02804	−0.514018	−	0.857779i	$-0.671844\pi$
$241$	−1.81616e20	−1.02804	−0.514018	+	0.857779i	$0.671844\pi$
$242$	− 8.81901e19i	− 0.481936i
$243$	− 4.60321e19i	− 0.242889i
$244$	−1.61818e20	−0.824545
$245$	0	0
$246$	9.10733e19	0.432955
$247$	9.74653e19i	0.447637i
$248$	2.74790e19i	0.121944i
$249$	7.39959e19	0.317332
$250$	0	0
$251$	−3.20192e20	−1.28288	−0.641438	−	0.767175i	$-0.721662\pi$
$251$	−3.20192e20	−1.28288	−0.641438	+	0.767175i	$0.721662\pi$
$252$	9.85304e18i	0.0381651i
$253$	6.61299e18i	0.0247670i
$254$	8.84527e19	0.320350
$255$	0	0
$256$	1.84467e19	0.0625000
$257$	3.34539e20i	1.09652i	0.836309	+	0.548259i	$0.184709\pi$
$257$	3.34539e20i	1.09652i	−0.836309	+	0.548259i	$0.815291\pi$
$258$	− 4.24314e20i	− 1.34561i
$259$	−1.67780e20	−0.514863
$260$	0	0
$261$	−3.58681e19	−0.103101
$262$	− 1.51804e20i	− 0.422397i
$263$	2.95034e20i	0.794782i	0.917649	+	0.397391i	$0.130084\pi$
$263$	2.95034e20i	0.794782i	−0.917649	+	0.397391i	$0.869916\pi$
$264$	8.10248e19	0.211341
$265$	0	0
$266$	−2.77870e20	−0.679747
$267$	− 5.62680e19i	− 0.133326i
$268$	− 1.33198e19i	− 0.0305739i
$269$	−7.56967e20	−1.68338	−0.841690	−	0.539960i	$-0.818439\pi$
$269$	−7.56967e20	−1.68338	−0.841690	+	0.539960i	$0.818439\pi$
$270$	0	0
$271$	−1.18908e20	−0.248298	−0.124149	−	0.992264i	$-0.539620\pi$
$271$	−1.18908e20	−0.248298	−0.124149	+	0.992264i	$0.539620\pi$
$272$	1.67129e20i	0.338232i
$273$	− 9.82685e19i	− 0.192767i
$274$	−1.44518e20	−0.274817
$275$	0	0
$276$	1.30039e19	0.0232458
$277$	1.96379e20i	0.340421i	0.985408	+	0.170211i	$0.0544448\pi$
$277$	1.96379e20i	0.340421i	−0.985408	+	0.170211i	$0.945555\pi$
$278$	− 5.46589e20i	− 0.918925i
$279$	2.58263e19	0.0421140
$280$	0	0
$281$	−3.39035e20	−0.520284	−0.260142	−	0.965570i	$-0.583769\pi$
$281$	−3.39035e20	−0.520284	−0.260142	+	0.965570i	$0.583769\pi$
$282$	− 5.09870e20i	− 0.759175i
$283$	4.03445e20i	0.582908i	0.956585	+	0.291454i	$0.0941390\pi$
$283$	4.03445e20i	0.582908i	−0.956585	+	0.291454i	$0.905861\pi$
$284$	−6.15460e20	−0.862966
$285$	0	0
$286$	−8.79326e19	−0.116155
$287$	− 2.81782e20i	− 0.361341i
$288$	− 1.73373e19i	− 0.0215846i
$289$	−6.86955e20	−0.830418
$290$	0	0
$291$	1.22543e21	1.39701
$292$	− 1.01492e20i	− 0.112377i
$293$	− 1.05777e20i	− 0.113767i	−0.998381	−	0.0568836i	$-0.981884\pi$
$293$	− 1.05777e20i	− 0.113767i	0.998381	−	0.0568836i	$-0.0181164\pi$
$294$	−4.36732e20	−0.456312
$295$	0	0
$296$	2.95223e20	0.291186
$297$	5.47525e20i	0.524776i
$298$	− 5.40587e20i	− 0.503533i
$299$	−1.41125e19	−0.0127761
$300$	0	0
$301$	−1.31284e21	−1.12304
$302$	2.80183e20i	0.233014i
$303$	3.75456e20i	0.303597i
$304$	4.88936e20	0.384438
$305$	0	0
$306$	1.57077e20	0.116810
$307$	1.82911e21i	1.32301i	0.749941	+	0.661504i	$0.230082\pi$
$307$	1.82911e21i	1.32301i	−0.749941	+	0.661504i	$0.769918\pi$
$308$	− 2.50692e20i	− 0.176384i
$309$	2.06608e21	1.41417
$310$	0	0
$311$	2.00748e21	1.30073	0.650366	−	0.759621i	$-0.274616\pi$
$311$	2.00748e21	1.30073	0.650366	+	0.759621i	$0.274616\pi$
$312$	1.72912e20i	0.109021i
$313$	− 2.84834e21i	− 1.74769i	−0.486203	−	0.873846i	$-0.661619\pi$
$313$	− 2.84834e21i	− 1.74769i	0.486203	−	0.873846i	$-0.338381\pi$
$314$	6.86017e20	0.409669
$315$	0	0
$316$	5.44589e20	0.308126
$317$	− 2.74347e20i	− 0.151111i	−0.997142	−	0.0755554i	$-0.975927\pi$
$317$	− 2.74347e20i	− 0.151111i	0.997142	−	0.0755554i	$-0.0240730\pi$
$318$	2.23501e21i	1.19853i
$319$	9.12598e20	0.476495
$320$	0	0
$321$	−1.97508e21	−0.977895
$322$	− 4.02342e19i	− 0.0194008i
$323$	4.42979e21i	2.08047i
$324$	1.21011e21	0.553596
$325$	0	0
$326$	2.42570e21	1.05314
$327$	− 3.37458e21i	− 1.42746i
$328$	4.95820e20i	0.204360i
$329$	−1.57755e21	−0.633603
$330$	0	0
$331$	1.83521e20	0.0700082	0.0350041	−	0.999387i	$-0.488856\pi$
$331$	1.83521e20	0.0700082	0.0350041	+	0.999387i	$0.488856\pi$
$332$	4.02848e20i	0.149785i
$333$	− 2.77467e20i	− 0.100562i
$334$	−1.71690e21	−0.606598
$335$	0	0
$336$	−4.92965e20	−0.165551
$337$	6.21202e20i	0.203413i	0.994814	+	0.101706i	$0.0324302\pi$
$337$	6.21202e20i	0.203413i	−0.994814	+	0.101706i	$0.967570\pi$
$338$	2.02685e21i	0.647188i
$339$	6.38796e21	1.98914
$340$	0	0
$341$	−6.57102e20	−0.194635
$342$	− 4.59529e20i	− 0.132767i
$343$	3.56933e21i	1.00597i
$344$	2.31005e21	0.635147
$345$	0	0
$346$	−2.70579e21	−0.708185
$347$	− 5.08978e21i	− 1.29987i	−0.759992	−	0.649933i	$-0.774797\pi$
$347$	− 5.08978e21i	− 1.29987i	0.759992	−	0.649933i	$-0.225203\pi$
$348$	− 1.79455e21i	− 0.447230i
$349$	3.81066e20	0.0926796	0.0463398	−	0.998926i	$-0.485244\pi$
$349$	3.81066e20	0.0926796	0.0463398	+	0.998926i	$0.485244\pi$
$350$	0	0
$351$	−1.16845e21	−0.270707
$352$	4.41115e20i	0.0997559i
$353$	2.34699e21i	0.518115i	0.965862	+	0.259058i	$0.0834120\pi$
$353$	2.34699e21i	0.518115i	−0.965862	+	0.259058i	$0.916588\pi$
$354$	4.99777e21	1.07708
$355$	0	0
$356$	3.06334e20	0.0629317
$357$	− 4.46629e21i	− 0.895916i
$358$	5.08717e21i	0.996485i
$359$	6.19792e19	0.0118561	0.00592807	−	0.999982i	$-0.498113\pi$
$359$	6.19792e19	0.0118561	0.00592807	+	0.999982i	$0.498113\pi$
$360$	0	0
$361$	7.47897e21	1.36468
$362$	6.40451e21i	1.14147i
$363$	− 4.14693e21i	− 0.721972i
$364$	5.34992e20	0.0909884
$365$	0	0
$366$	−7.60912e21	−1.23522
$367$	3.40565e21i	0.540180i	0.962835	+	0.270090i	$0.0870535\pi$
$367$	3.40565e21i	0.540180i	−0.962835	+	0.270090i	$0.912946\pi$
$368$	7.07955e19i	0.0109723i
$369$	4.65999e20	0.0705767
$370$	0	0
$371$	6.91517e21	1.00029
$372$	1.29213e21i	0.182681i
$373$	− 6.44986e21i	− 0.891302i	−0.895207	−	0.445651i	$-0.852972\pi$
$373$	− 6.44986e21i	− 0.891302i	0.895207	−	0.445651i	$-0.147028\pi$
$374$	−3.99652e21	−0.539851
$375$	0	0
$376$	2.77583e21	0.358340
$377$	1.94754e21i	0.245802i
$378$	− 3.33121e21i	− 0.411076i
$379$	5.68235e21	0.685638	0.342819	−	0.939401i	$-0.388618\pi$
$379$	5.68235e21	0.685638	0.342819	+	0.939401i	$0.388618\pi$
$380$	0	0
$381$	4.15928e21	0.479905
$382$	− 6.74266e21i	− 0.760839i
$383$	− 1.28548e22i	− 1.41865i	−0.704879	−	0.709327i	$-0.748999\pi$
$383$	− 1.28548e22i	− 1.41865i	0.704879	−	0.709327i	$-0.251001\pi$
$384$	8.67414e20	0.0936291
$385$	0	0
$386$	−9.44272e21	−0.975226
$387$	− 2.17111e21i	− 0.219351i
$388$	6.67149e21i	0.659407i
$389$	−1.70189e22	−1.64573	−0.822867	−	0.568234i	$-0.807627\pi$
$389$	−1.70189e22	−1.64573	−0.822867	+	0.568234i	$0.807627\pi$
$390$	0	0
$391$	−6.41412e20	−0.0593792
$392$	− 2.37765e21i	− 0.215385i
$393$	− 7.13820e21i	− 0.632779i
$394$	−1.03660e22	−0.899273
$395$	0	0
$396$	4.14584e20	0.0344511
$397$	1.81182e22i	1.47365i	0.676081	+	0.736827i	$0.263677\pi$
$397$	1.81182e22i	1.47365i	−0.676081	+	0.736827i	$0.736323\pi$
$398$	8.51897e21i	0.678236i
$399$	−1.30662e22	−1.01831
$400$	0	0
$401$	1.75008e22	1.30717	0.653585	−	0.756853i	$-0.273264\pi$
$401$	1.75008e22	1.30717	0.653585	+	0.756853i	$0.273264\pi$
$402$	− 6.26331e20i	− 0.0458018i
$403$	− 1.40230e21i	− 0.100403i
$404$	−2.04406e21	−0.143302
$405$	0	0
$406$	−5.55236e21	−0.373255
$407$	7.05963e21i	0.464761i
$408$	7.85882e21i	0.506694i
$409$	−9.06225e21	−0.572253	−0.286127	−	0.958192i	$-0.592368\pi$
$409$	−9.06225e21	−0.572253	−0.286127	+	0.958192i	$0.592368\pi$
$410$	0	0
$411$	−6.79563e21	−0.411694
$412$	1.12481e22i	0.667505i
$413$	− 1.54632e22i	− 0.898925i
$414$	6.65376e19	0.00378934
$415$	0	0
$416$	−9.41365e20	−0.0514594
$417$	− 2.57020e22i	− 1.37661i
$418$	1.16919e22i	0.613599i
$419$	−7.49706e21	−0.385542	−0.192771	−	0.981244i	$-0.561747\pi$
$419$	−7.49706e21	−0.385542	−0.192771	+	0.981244i	$0.561747\pi$
$420$	0	0
$421$	−2.95580e22	−1.45975	−0.729873	−	0.683583i	$-0.760421\pi$
$421$	−2.95580e22	−1.45975	−0.729873	+	0.683583i	$0.760421\pi$
$422$	− 6.19935e21i	− 0.300048i
$423$	− 2.60888e21i	− 0.123754i
$424$	−1.21678e22	−0.565722
$425$	0	0
$426$	−2.89405e22	−1.29278
$427$	2.35428e22i	1.03091i
$428$	− 1.07527e22i	− 0.461579i
$429$	−4.13482e21	−0.174008
$430$	0	0
$431$	−7.37016e21	−0.298140	−0.149070	−	0.988827i	$-0.547628\pi$
$431$	−7.37016e21	−0.298140	−0.149070	+	0.988827i	$0.547628\pi$
$432$	5.86155e21i	0.232488i
$433$	1.77584e21i	0.0690650i	0.999404	+	0.0345325i	$0.0109942\pi$
$433$	1.77584e21i	0.0690650i	−0.999404	+	0.0345325i	$0.989006\pi$
$434$	3.99789e21	0.152464
$435$	0	0
$436$	1.83718e22	0.673779
$437$	1.87645e21i	0.0674909i
$438$	− 4.77243e21i	− 0.168349i
$439$	2.92011e22	1.01030	0.505151	−	0.863031i	$-0.331437\pi$
$439$	2.92011e22	1.01030	0.505151	+	0.863031i	$0.331437\pi$
$440$	0	0
$441$	−2.23465e21	−0.0743842
$442$	− 8.52882e21i	− 0.278484i
$443$	− 4.06554e22i	− 1.30223i	−0.758980	−	0.651113i	$-0.774302\pi$
$443$	− 4.06554e22i	− 1.30223i	0.758980	−	0.651113i	$-0.225698\pi$
$444$	1.38822e22	0.436216
$445$	0	0
$446$	−1.90022e22	−0.574722
$447$	− 2.54198e22i	− 0.754325i
$448$	− 2.68379e21i	− 0.0781423i
$449$	−4.62783e21	−0.132216	−0.0661079	−	0.997812i	$-0.521058\pi$
$449$	−4.62783e21	−0.132216	−0.0661079	+	0.997812i	$0.521058\pi$
$450$	0	0
$451$	−1.18565e22	−0.326179
$452$	3.47773e22i	0.938899i
$453$	1.31749e22i	0.349071i
$454$	2.45128e21	0.0637409
$455$	0	0
$456$	2.29910e22	0.575913
$457$	− 6.30841e22i	− 1.55107i	−0.631303	−	0.775536i	$-0.717480\pi$
$457$	− 6.30841e22i	− 1.55107i	0.631303	−	0.775536i	$-0.282520\pi$
$458$	− 5.06247e22i	− 1.22182i
$459$	−5.31060e22	−1.25816
$460$	0	0
$461$	5.62982e22	1.28539	0.642697	−	0.766120i	$-0.277815\pi$
$461$	5.62982e22	1.28539	0.642697	+	0.766120i	$0.277815\pi$
$462$	− 1.17882e22i	− 0.264235i
$463$	5.90180e21i	0.129881i	0.997889	+	0.0649405i	$0.0206858\pi$
$463$	5.90180e21i	0.129881i	−0.997889	+	0.0649405i	$0.979314\pi$
$464$	9.76985e21	0.211098
$465$	0	0
$466$	4.60232e22	0.958730
$467$	− 2.51115e22i	− 0.513663i	−0.966456	−	0.256832i	$-0.917321\pi$
$467$	− 2.51115e22i	− 0.513663i	0.966456	−	0.256832i	$-0.0826786\pi$
$468$	8.84747e20i	0.0177717i
$469$	−1.93788e21	−0.0382259
$470$	0	0
$471$	3.22583e22	0.613711
$472$	2.72088e22i	0.508396i
$473$	5.52399e22i	1.01375i
$474$	2.56080e22	0.461594
$475$	0	0
$476$	2.43153e22	0.422884
$477$	1.14360e22i	0.195375i
$478$	5.12530e22i	0.860166i
$479$	3.54309e22	0.584158	0.292079	−	0.956394i	$-0.405653\pi$
$479$	3.54309e22	0.584158	0.292079	+	0.956394i	$0.405653\pi$
$480$	0	0
$481$	−1.50657e22	−0.239748
$482$	− 4.64936e22i	− 0.726931i
$483$	− 1.89192e21i	− 0.0290637i
$484$	2.25767e22	0.340780
$485$	0	0
$486$	1.17842e22	0.171748
$487$	1.51696e22i	0.217259i	0.994082	+	0.108629i	$0.0346462\pi$
$487$	1.51696e22i	0.217259i	−0.994082	+	0.108629i	$0.965354\pi$
$488$	− 4.14255e22i	− 0.583041i
$489$	1.14063e23	1.57768
$490$	0	0
$491$	−6.96906e22	−0.931068	−0.465534	−	0.885030i	$-0.654138\pi$
$491$	−6.96906e22	−0.931068	−0.465534	+	0.885030i	$0.654138\pi$
$492$	2.33148e22i	0.306145i
$493$	8.85154e22i	1.14240i
$494$	−2.49511e22	−0.316527
$495$	0	0
$496$	−7.03463e21	−0.0862277
$497$	8.95425e22i	1.07895i
$498$	1.89430e22i	0.224387i
$499$	5.10974e22	0.595037	0.297518	−	0.954716i	$-0.403841\pi$
$499$	5.10974e22	0.595037	0.297518	+	0.954716i	$0.403841\pi$
$500$	0	0
$501$	−8.07332e22	−0.908723
$502$	− 8.19693e22i	− 0.907130i
$503$	6.26474e21i	0.0681671i	0.999419	+	0.0340836i	$0.0108512\pi$
$503$	6.26474e21i	0.0681671i	−0.999419	+	0.0340836i	$0.989149\pi$
$504$	−2.52238e21	−0.0269868
$505$	0	0
$506$	−1.69292e21	−0.0175129
$507$	9.53079e22i	0.969530i
$508$	2.26439e22i	0.226522i
$509$	7.41555e22	0.729528	0.364764	−	0.931100i	$-0.381150\pi$
$509$	7.41555e22	0.729528	0.364764	+	0.931100i	$0.381150\pi$
$510$	0	0
$511$	−1.47660e22	−0.140503
$512$	4.72237e21i	0.0441942i
$513$	1.55362e23i	1.43003i
$514$	−8.56421e22	−0.775355
$515$	0	0
$516$	1.08624e23	0.951492
$517$	6.63780e22i	0.571945i
$518$	− 4.29516e22i	− 0.364063i
$519$	−1.27233e23	−1.06091
$520$	0	0
$521$	9.53386e21	0.0769393	0.0384696	−	0.999260i	$-0.487752\pi$
$521$	9.53386e21	0.0769393	0.0384696	+	0.999260i	$0.487752\pi$
$522$	− 9.18225e21i	− 0.0729037i
$523$	1.49123e23i	1.16487i	0.812876	+	0.582437i	$0.197901\pi$
$523$	1.49123e23i	1.16487i	−0.812876	+	0.582437i	$0.802099\pi$
$524$	3.88617e22	0.298680
$525$	0	0
$526$	−7.55287e22	−0.561996
$527$	− 6.37341e22i	− 0.466640i
$528$	2.07424e22i	0.149441i
$529$	1.40778e23	0.998074
$530$	0	0
$531$	2.55723e22	0.175577
$532$	− 7.11347e22i	− 0.480654i
$533$	− 2.53025e22i	− 0.168260i
$534$	1.44046e22	0.0942759
$535$	0	0
$536$	3.40986e21	0.0216190
$537$	2.39212e23i	1.49280i
$538$	− 1.93783e23i	− 1.19033i
$539$	5.68564e22	0.343776
$540$	0	0
$541$	8.46775e22	0.496125	0.248063	−	0.968744i	$-0.420206\pi$
$541$	8.46775e22	0.496125	0.248063	+	0.968744i	$0.420206\pi$
$542$	− 3.04405e22i	− 0.175573i
$543$	3.01157e23i	1.70999i
$544$	−4.27849e22	−0.239166
$545$	0	0
$546$	2.51567e22	0.136307
$547$	− 4.72359e22i	− 0.251988i	−0.992031	−	0.125994i	$-0.959788\pi$
$547$	− 4.72359e22i	− 0.251988i	0.992031	−	0.125994i	$-0.0402120\pi$
$548$	− 3.69967e22i	− 0.194325i
$549$	−3.89340e22	−0.201356
$550$	0	0
$551$	2.58952e23	1.29847
$552$	3.32899e21i	0.0164373i
$553$	− 7.92316e22i	− 0.385243i
$554$	−5.02730e22	−0.240714
$555$	0	0
$556$	1.39927e23	0.649778
$557$	− 3.77820e23i	− 1.72789i	−0.503587	−	0.863945i	$-0.667987\pi$
$557$	− 3.77820e23i	− 1.72789i	0.503587	−	0.863945i	$-0.332013\pi$
$558$	6.61153e21i	0.0297791i
$559$	−1.17885e23	−0.522949
$560$	0	0
$561$	−1.87927e23	−0.808732
$562$	− 8.67929e22i	− 0.367896i
$563$	− 4.35959e23i	− 1.82022i	−0.414363	−	0.910112i	$-0.635995\pi$
$563$	− 4.35959e23i	− 1.82022i	0.414363	−	0.910112i	$-0.364005\pi$
$564$	1.30527e23	0.536818
$565$	0	0
$566$	−1.03282e23	−0.412178
$567$	− 1.76058e23i	− 0.692149i
$568$	− 1.57558e23i	− 0.610209i
$569$	1.25095e23	0.477293	0.238647	−	0.971106i	$-0.423296\pi$
$569$	1.25095e23	0.477293	0.238647	+	0.971106i	$0.423296\pi$
$570$	0	0
$571$	−3.10316e23	−1.14920	−0.574602	−	0.818433i	$-0.694843\pi$
$571$	−3.10316e23	−1.14920	−0.574602	+	0.818433i	$0.694843\pi$
$572$	− 2.25107e22i	− 0.0821341i
$573$	− 3.17058e23i	− 1.13979i
$574$	7.21363e22	0.255507
$575$	0	0
$576$	4.43834e21	0.0152626
$577$	2.11578e23i	0.716928i	0.933544	+	0.358464i	$0.116699\pi$
$577$	2.11578e23i	0.716928i	−0.933544	+	0.358464i	$0.883301\pi$
$578$	− 1.75860e23i	− 0.587194i
$579$	−4.44021e23	−1.46095
$580$	0	0
$581$	5.86099e22	0.187272
$582$	3.13711e23i	0.987835i
$583$	− 2.90968e23i	− 0.902947i
$584$	2.59820e22	0.0794627
$585$	0	0
$586$	2.70790e22	0.0804456
$587$	− 2.15996e23i	− 0.632443i	−0.948685	−	0.316222i	$-0.897586\pi$
$587$	− 2.15996e23i	− 0.632443i	0.948685	−	0.316222i	$-0.102414\pi$
$588$	− 1.11803e23i	− 0.322662i
$589$	−1.86455e23	−0.530387
$590$	0	0
$591$	−4.87434e23	−1.34717
$592$	7.55771e22i	0.205900i
$593$	3.56471e23i	0.957326i	0.877999	+	0.478663i	$0.158878\pi$
$593$	3.56471e23i	0.957326i	−0.877999	+	0.478663i	$0.841122\pi$
$594$	−1.40166e23	−0.371073
$595$	0	0
$596$	1.38390e23	0.356051
$597$	4.00584e23i	1.01604i
$598$	− 3.61280e21i	− 0.00903408i
$599$	−3.17118e23	−0.781796	−0.390898	−	0.920434i	$-0.627835\pi$
$599$	−3.17118e23	−0.781796	−0.390898	+	0.920434i	$0.627835\pi$
$600$	0	0
$601$	−2.47473e23	−0.593055	−0.296528	−	0.955024i	$-0.595829\pi$
$601$	−2.47473e23	−0.593055	−0.296528	+	0.955024i	$0.595829\pi$
$602$	− 3.36086e23i	− 0.794109i
$603$	− 3.20478e21i	− 0.00746622i
$604$	−7.17268e22	−0.164766
$605$	0	0
$606$	−9.61168e22	−0.214675
$607$	− 1.27464e23i	− 0.280726i	−0.990100	−	0.140363i	$-0.955173\pi$
$607$	− 1.27464e23i	− 0.280726i	0.990100	−	0.140363i	$-0.0448270\pi$
$608$	1.25168e23i	0.271839i
$609$	−2.61086e23	−0.559161
$610$	0	0
$611$	−1.41655e23	−0.295040
$612$	4.02116e22i	0.0825971i
$613$	2.08992e23i	0.423366i	0.977338	+	0.211683i	$0.0678945\pi$
$613$	2.08992e23i	0.423366i	−0.977338	+	0.211683i	$0.932105\pi$
$614$	−4.68251e23	−0.935508
$615$	0	0
$616$	6.41772e22	0.124723
$617$	− 2.52173e23i	− 0.483364i	−0.970356	−	0.241682i	$-0.922301\pi$
$617$	− 2.52173e23i	− 0.483364i	0.970356	−	0.241682i	$-0.0776990\pi$
$618$	5.28917e23i	0.999966i
$619$	8.32171e23	1.55182	0.775911	−	0.630842i	$-0.217291\pi$
$619$	8.32171e23	1.55182	0.775911	+	0.630842i	$0.217291\pi$
$620$	0	0
$621$	−2.24956e22	−0.0408150
$622$	5.13915e23i	0.919756i
$623$	− 4.45681e22i	− 0.0786821i
$624$	−4.42654e22	−0.0770896
$625$	0	0
$626$	7.29175e23	1.23580
$627$	5.49781e23i	0.919212i
$628$	1.75620e23i	0.289680i
$629$	−6.84733e23	−1.11427
$630$	0	0
$631$	2.44878e23	0.387883	0.193942	−	0.981013i	$-0.437873\pi$
$631$	2.44878e23	0.387883	0.193942	+	0.981013i	$0.437873\pi$
$632$	1.39415e23i	0.217878i
$633$	− 2.91510e23i	− 0.449491i
$634$	7.02327e22	0.106852
$635$	0	0
$636$	−5.72163e23	−0.847489
$637$	1.21335e23i	0.177338i
$638$	2.33625e23i	0.336933i
$639$	−1.48081e23	−0.210738
$640$	0	0
$641$	8.76132e23	1.21416	0.607081	−	0.794640i	$-0.292340\pi$
$641$	8.76132e23	1.21416	0.607081	+	0.794640i	$0.292340\pi$
$642$	− 5.05621e23i	− 0.691477i
$643$	− 3.14015e23i	− 0.423796i	−0.977292	−	0.211898i	$-0.932036\pi$
$643$	− 3.14015e23i	− 0.423796i	0.977292	−	0.211898i	$-0.0679644\pi$
$644$	1.03000e22	0.0137185
$645$	0	0
$646$	−1.13403e24	−1.47111
$647$	7.19139e22i	0.0920718i	0.998940	+	0.0460359i	$0.0146589\pi$
$647$	7.19139e22i	0.0920718i	−0.998940	+	0.0460359i	$0.985341\pi$
$648$	3.09789e23i	0.391452i
$649$	−6.50640e23	−0.811448
$650$	0	0
$651$	1.87991e23	0.228402
$652$	6.20979e23i	0.744685i
$653$	− 7.53337e23i	− 0.891717i	−0.895103	−	0.445858i	$-0.852898\pi$
$653$	− 7.53337e23i	− 0.891717i	0.895103	−	0.445858i	$-0.147102\pi$
$654$	8.63892e23	1.00937
$655$	0	0
$656$	−1.26930e23	−0.144505
$657$	− 2.44193e22i	− 0.0274428i
$658$	− 4.03852e23i	− 0.448025i
$659$	1.78954e24	1.95981	0.979906	−	0.199459i	$-0.0639186\pi$
$659$	1.78954e24	1.95981	0.979906	+	0.199459i	$0.0639186\pi$
$660$	0	0
$661$	3.55263e23	0.379173	0.189586	−	0.981864i	$-0.439285\pi$
$661$	3.55263e23	0.379173	0.189586	+	0.981864i	$0.439285\pi$
$662$	4.69815e22i	0.0495033i
$663$	− 4.01047e23i	− 0.417187i
$664$	−1.03129e23	−0.105914
$665$	0	0
$666$	7.10315e22	0.0711083
$667$	3.74951e22i	0.0370599i
$668$	− 4.39527e23i	− 0.428929i
$669$	−8.93533e23	−0.860971
$670$	0	0
$671$	9.90603e23	0.930589
$672$	− 1.26199e23i	− 0.117062i
$673$	5.15130e23i	0.471833i	0.971773	+	0.235917i	$0.0758092\pi$
$673$	5.15130e23i	0.471833i	−0.971773	+	0.235917i	$0.924191\pi$
$674$	−1.59028e23	−0.143835
$675$	0	0
$676$	−5.18874e23	−0.457631
$677$	− 1.69205e23i	− 0.147370i	−0.997282	−	0.0736851i	$-0.976524\pi$
$677$	− 1.69205e23i	− 0.147370i	0.997282	−	0.0736851i	$-0.0234760\pi$
$678$	1.63532e24i	1.40653i
$679$	9.70628e23	0.824441
$680$	0	0
$681$	1.15265e23	0.0954880
$682$	− 1.68218e23i	− 0.137628i
$683$	1.97763e23i	0.159797i	0.996803	+	0.0798987i	$0.0254597\pi$
$683$	1.97763e23i	0.159797i	−0.996803	+	0.0798987i	$0.974540\pi$
$684$	1.17639e23	0.0938806
$685$	0	0
$686$	−9.13749e23	−0.711331
$687$	− 2.38051e24i	− 1.83036i
$688$	5.91372e23i	0.449117i
$689$	6.20943e23	0.465788
$690$	0	0
$691$	2.62293e24	1.91966	0.959828	−	0.280589i	$-0.0905298\pi$
$691$	2.62293e24	1.91966	0.959828	+	0.280589i	$0.0905298\pi$
$692$	− 6.92681e23i	− 0.500762i
$693$	− 6.03173e22i	− 0.0430734i
$694$	1.30298e24	0.919144
$695$	0	0
$696$	4.59404e23	0.316239
$697$	− 1.14999e24i	− 0.782018i
$698$	9.75529e22i	0.0655344i
$699$	2.16413e24	1.43624
$700$	0	0
$701$	−4.05441e22	−0.0262618	−0.0131309	−	0.999914i	$-0.504180\pi$
$701$	−4.05441e22	−0.0262618	−0.0131309	+	0.999914i	$0.504180\pi$
$702$	− 2.99124e23i	− 0.191419i
$703$	2.00319e24i	1.26649i
$704$	−1.12925e23	−0.0705381
$705$	0	0
$706$	−6.00830e23	−0.366363
$707$	2.97387e23i	0.179167i
$708$	1.27943e24i	0.761611i
$709$	7.92278e23	0.465999	0.232999	−	0.972477i	$-0.425146\pi$
$709$	7.92278e23	0.465999	0.232999	+	0.972477i	$0.425146\pi$
$710$	0	0
$711$	1.31030e23	0.0752451
$712$	7.84214e22i	0.0444995i
$713$	− 2.69977e22i	− 0.0151379i
$714$	1.14337e24	0.633508
$715$	0	0
$716$	−1.30232e24	−0.704621
$717$	2.41005e24i	1.28859i
$718$	1.58667e22i	0.00838355i
$719$	7.47670e23	0.390404	0.195202	−	0.980763i	$-0.437464\pi$
$719$	7.47670e23	0.390404	0.195202	+	0.980763i	$0.437464\pi$
$720$	0	0
$721$	1.63648e24	0.834566
$722$	1.91462e24i	0.964974i
$723$	− 2.18625e24i	− 1.08899i
$724$	−1.63955e24	−0.807138
$725$	0	0
$726$	1.06161e24	0.510511
$727$	− 5.40980e23i	− 0.257122i	−0.991702	−	0.128561i	$-0.958964\pi$
$727$	− 5.40980e23i	− 0.257122i	0.991702	−	0.128561i	$-0.0410358\pi$
$728$	1.36958e23i	0.0643385i
$729$	−1.83043e24	−0.849902
$730$	0	0
$731$	−5.35787e24	−2.43049
$732$	− 1.94794e24i	− 0.873435i
$733$	2.02014e24i	0.895361i	0.894194	+	0.447680i	$0.147750\pi$
$733$	2.02014e24i	0.895361i	−0.894194	+	0.447680i	$0.852250\pi$
$734$	−8.71847e23	−0.381965
$735$	0	0
$736$	−1.81237e22	−0.00775862
$737$	8.15396e22i	0.0345060i
$738$	1.19296e23i	0.0499053i
$739$	2.11021e24	0.872666	0.436333	−	0.899785i	$-0.356277\pi$
$739$	2.11021e24	0.872666	0.436333	+	0.899785i	$0.356277\pi$
$740$	0	0
$741$	−1.17327e24	−0.474179
$742$	1.77028e24i	0.707309i
$743$	1.34376e24i	0.530784i	0.964141	+	0.265392i	$0.0855014\pi$
$743$	1.34376e24i	0.530784i	−0.964141	+	0.265392i	$0.914499\pi$
$744$	−3.30786e23	−0.129175
$745$	0	0
$746$	1.65116e24	0.630246
$747$	9.69264e22i	0.0365777i
$748$	− 1.02311e24i	− 0.381732i
$749$	−1.56440e24	−0.577102
$750$	0	0
$751$	2.72368e24	0.982236	0.491118	−	0.871093i	$-0.336588\pi$
$751$	2.72368e24	0.982236	0.491118	+	0.871093i	$0.336588\pi$
$752$	7.10612e23i	0.253385i
$753$	− 3.85441e24i	− 1.35894i
$754$	−4.98570e23	−0.173808
$755$	0	0
$756$	8.52790e23	0.290674
$757$	3.29400e24i	1.11022i	0.831777	+	0.555109i	$0.187324\pi$
$757$	3.29400e24i	1.11022i	−0.831777	+	0.555109i	$0.812676\pi$
$758$	1.45468e24i	0.484819i
$759$	−7.96057e22	−0.0262355
$760$	0	0
$761$	−4.29576e24	−1.38443	−0.692215	−	0.721692i	$-0.743365\pi$
$761$	−4.29576e24	−1.38443	−0.692215	+	0.721692i	$0.743365\pi$
$762$	1.06477e24i	0.339344i
$763$	− 2.67290e24i	− 0.842410i
$764$	1.72612e24	0.537995
$765$	0	0
$766$	3.29083e24	1.00314
$767$	− 1.38851e24i	− 0.418588i
$768$	2.22058e23i	0.0662058i
$769$	−5.93781e24	−1.75086	−0.875432	−	0.483341i	$-0.839423\pi$
$769$	−5.93781e24	−1.75086	−0.875432	+	0.483341i	$0.839423\pi$
$770$	0	0
$771$	−4.02711e24	−1.16153
$772$	− 2.41734e24i	− 0.689589i
$773$	− 1.98352e24i	− 0.559642i	−0.960052	−	0.279821i	$-0.909725\pi$
$773$	− 1.98352e24i	− 0.559642i	0.960052	−	0.279821i	$-0.0902750\pi$
$774$	5.55804e23	0.155104
$775$	0	0
$776$	−1.70790e24	−0.466271
$777$	− 2.01970e24i	− 0.545391i
$778$	− 4.35684e24i	− 1.16371i
$779$	−3.36431e24	−0.888849
$780$	0	0
$781$	3.76766e24	0.973952
$782$	− 1.64201e23i	− 0.0419874i
$783$	3.10442e24i	0.785246i
$784$	6.08678e23	0.152300
$785$	0	0
$786$	1.82738e24	0.447442
$787$	− 3.61371e24i	− 0.875322i	−0.899140	−	0.437661i	$-0.855807\pi$
$787$	− 3.61371e24i	− 0.875322i	0.899140	−	0.437661i	$-0.144193\pi$
$788$	− 2.65369e24i	− 0.635882i
$789$	−3.55156e24	−0.841907
$790$	0	0
$791$	5.05970e24	1.17388
$792$	1.06133e23i	0.0243606i
$793$	2.11401e24i	0.480047i
$794$	−4.63826e24	−1.04203
$795$	0	0
$796$	−2.18086e24	−0.479586
$797$	4.63064e24i	1.00750i	0.863849	+	0.503751i	$0.168047\pi$
$797$	4.63064e24i	1.00750i	−0.863849	+	0.503751i	$0.831953\pi$
$798$	− 3.34494e24i	− 0.720051i
$799$	−6.43819e24	−1.37125
$800$	0	0
$801$	7.37048e22	0.0153681
$802$	4.48022e24i	0.924308i
$803$	6.21304e23i	0.126830i
$804$	1.60341e23	0.0323867
$805$	0	0
$806$	3.58988e23	0.0709956
$807$	− 9.11220e24i	− 1.78319i
$808$	− 5.23278e23i	− 0.101330i
$809$	1.22642e24	0.235005	0.117502	−	0.993073i	$-0.462511\pi$
$809$	1.22642e24	0.235005	0.117502	+	0.993073i	$0.462511\pi$
$810$	0	0
$811$	−2.42686e24	−0.455373	−0.227686	−	0.973735i	$-0.573116\pi$
$811$	−2.42686e24	−0.455373	−0.227686	+	0.973735i	$0.573116\pi$
$812$	− 1.42140e24i	− 0.263931i
$813$	− 1.43139e24i	− 0.263020i
$814$	−1.80726e24	−0.328635
$815$	0	0
$816$	−2.01186e24	−0.358287
$817$	1.56745e25i	2.76252i
$818$	− 2.31994e24i	− 0.404644i
$819$	1.28721e23	0.0222196
$820$	0	0
$821$	−9.87401e24	−1.66946	−0.834731	−	0.550658i	$-0.814377\pi$
$821$	−9.87401e24	−1.66946	−0.834731	+	0.550658i	$0.814377\pi$
$822$	− 1.73968e24i	− 0.291111i
$823$	− 3.09810e24i	− 0.513094i	−0.966532	−	0.256547i	$-0.917415\pi$
$823$	− 3.09810e24i	− 0.513094i	0.966532	−	0.256547i	$-0.0825849\pi$
$824$	−2.87952e24	−0.471997
$825$	0	0
$826$	3.95857e24	0.635636
$827$	3.89248e24i	0.618628i	0.950960	+	0.309314i	$0.100099\pi$
$827$	3.89248e24i	0.618628i	−0.950960	+	0.309314i	$0.899901\pi$
$828$	1.70336e22i	0.00267947i
$829$	1.04208e25	1.62251	0.811256	−	0.584691i	$-0.198784\pi$
$829$	1.04208e25	1.62251	0.811256	+	0.584691i	$0.198784\pi$
$830$	0	0
$831$	−2.36397e24	−0.360606
$832$	− 2.40989e23i	− 0.0363873i
$833$	5.51466e24i	0.824207i
$834$	6.57972e24	0.973410
$835$	0	0
$836$	−2.99311e24	−0.433880
$837$	− 2.23529e24i	− 0.320750i
$838$	− 1.91925e24i	− 0.272619i
$839$	6.67595e24	0.938721	0.469360	−	0.883007i	$-0.344485\pi$
$839$	6.67595e24	0.938721	0.469360	+	0.883007i	$0.344485\pi$
$840$	0	0
$841$	−2.08280e24	−0.286999
$842$	− 7.56685e24i	− 1.03220i
$843$	− 4.08123e24i	− 0.551133i
$844$	1.58703e24	0.212166
$845$	0	0
$846$	6.67873e23	0.0875075
$847$	− 3.28465e24i	− 0.426069i
$848$	− 3.11496e24i	− 0.400026i
$849$	−4.85659e24	−0.617470
$850$	0	0
$851$	−2.90052e23	−0.0361472
$852$	− 7.40877e24i	− 0.914134i
$853$	9.79573e24i	1.19666i	0.801250	+	0.598329i	$0.204169\pi$
$853$	9.79573e24i	1.19666i	−0.801250	+	0.598329i	$0.795831\pi$
$854$	−6.02695e24	−0.728963
$855$	0	0
$856$	2.75270e24	0.326386
$857$	4.38126e24i	0.514354i	0.966364	+	0.257177i	$0.0827923\pi$
$857$	4.38126e24i	0.514354i	−0.966364	+	0.257177i	$0.917208\pi$
$858$	− 1.05851e24i	− 0.123042i
$859$	1.50626e25	1.73364	0.866821	−	0.498620i	$-0.166159\pi$
$859$	1.50626e25	1.73364	0.866821	+	0.498620i	$0.166159\pi$
$860$	0	0
$861$	3.39204e24	0.382766
$862$	− 1.88676e24i	− 0.210817i
$863$	1.37694e25i	1.52344i	0.647909	+	0.761718i	$0.275644\pi$
$863$	1.37694e25i	1.52344i	−0.647909	+	0.761718i	$0.724356\pi$
$864$	−1.50056e24	−0.164394
$865$	0	0
$866$	−4.54616e23	−0.0488363
$867$	− 8.26942e24i	− 0.879655i
$868$	1.02346e24i	0.107808i
$869$	−3.33381e24	−0.347754
$870$	0	0
$871$	−1.74010e23	−0.0178000
$872$	4.70319e24i	0.476434i
$873$	1.60518e24i	0.161029i
$874$	−4.80372e23	−0.0477233
$875$	0	0
$876$	1.22174e24	0.119040
$877$	7.56082e24i	0.729579i	0.931090	+	0.364790i	$0.118859\pi$
$877$	7.56082e24i	0.729579i	−0.931090	+	0.364790i	$0.881141\pi$
$878$	7.47549e24i	0.714391i
$879$	1.27332e24	0.120513
$880$	0	0
$881$	5.11196e24	0.474561	0.237281	−	0.971441i	$-0.423744\pi$
$881$	5.11196e24	0.474561	0.237281	+	0.971441i	$0.423744\pi$
$882$	− 5.72070e23i	− 0.0525976i
$883$	− 1.37334e25i	− 1.25058i	−0.780393	−	0.625289i	$-0.784981\pi$
$883$	− 1.37334e25i	− 1.25058i	0.780393	−	0.625289i	$-0.215019\pi$
$884$	2.18338e24	0.196918
$885$	0	0
$886$	1.04078e25	0.920813
$887$	− 1.15450e25i	− 1.01168i	−0.862628	−	0.505838i	$-0.831183\pi$
$887$	− 1.15450e25i	− 1.01168i	0.862628	−	0.505838i	$-0.168817\pi$
$888$	3.55383e24i	0.308451i
$889$	3.29443e24	0.283215
$890$	0	0
$891$	−7.40794e24	−0.624794
$892$	− 4.86456e24i	− 0.406390i
$893$	1.88349e25i	1.55857i
$894$	6.50748e24	0.533389
$895$	0	0
$896$	6.87051e23	0.0552550
$897$	− 1.69883e23i	− 0.0135337i
$898$	− 1.18472e24i	− 0.0934907i
$899$	−3.72571e24	−0.291240
$900$	0	0
$901$	2.82218e25	2.16483
$902$	− 3.03526e24i	− 0.230643i
$903$	− 1.58036e25i	− 1.18963i
$904$	−8.90298e24	−0.663902
$905$	0	0
$906$	−3.37278e24	−0.246830
$907$	1.74990e25i	1.26868i	0.773056	+	0.634338i	$0.218727\pi$
$907$	1.74990e25i	1.26868i	−0.773056	+	0.634338i	$0.781273\pi$
$908$	6.27527e23i	0.0450716i
$909$	−4.91806e23	−0.0349946
$910$	0	0
$911$	−1.12560e25	−0.786102	−0.393051	−	0.919517i	$-0.628580\pi$
$911$	−1.12560e25	−0.786102	−0.393051	+	0.919517i	$0.628580\pi$
$912$	5.88570e24i	0.407232i
$913$	− 2.46611e24i	− 0.169048i
$914$	1.61495e25	1.09677
$915$	0	0
$916$	1.29599e25	0.863955
$917$	− 5.65395e24i	− 0.373433i
$918$	− 1.35951e25i	− 0.889653i
$919$	2.33947e24	0.151682	0.0758412	−	0.997120i	$-0.475836\pi$
$919$	2.33947e24	0.151682	0.0758412	+	0.997120i	$0.475836\pi$
$920$	0	0
$921$	−2.20184e25	−1.40145
$922$	1.44123e25i	0.908911i
$923$	8.04040e24i	0.502416i
$924$	3.01778e24	0.186843
$925$	0	0
$926$	−1.51086e24	−0.0918398
$927$	2.70634e24i	0.163006i
$928$	2.50108e24i	0.149269i
$929$	−3.62091e24	−0.214133	−0.107067	−	0.994252i	$-0.534146\pi$
$929$	−3.62091e24	−0.214133	−0.107067	+	0.994252i	$0.534146\pi$
$930$	0	0
$931$	1.61332e25	0.936801
$932$	1.17819e25i	0.677925i
$933$	2.41656e25i	1.37786i
$934$	6.42853e24	0.363215
$935$	0	0
$936$	−2.26495e23	−0.0125665
$937$	− 4.50917e24i	− 0.247919i	−0.992287	−	0.123960i	$-0.960441\pi$
$937$	− 4.50917e24i	− 0.247919i	0.992287	−	0.123960i	$-0.0395593\pi$
$938$	− 4.96097e23i	− 0.0270298i
$939$	3.42877e25	1.85132
$940$	0	0
$941$	2.46547e25	1.30734	0.653669	−	0.756780i	$-0.273229\pi$
$941$	2.46547e25	1.30734	0.653669	+	0.756780i	$0.273229\pi$
$942$	8.25812e24i	0.433959i
$943$	− 4.87136e23i	− 0.0253689i
$944$	−6.96545e24	−0.359490
$945$	0	0
$946$	−1.41414e25	−0.716833
$947$	− 2.52153e25i	− 1.26675i	−0.773847	−	0.633373i	$-0.781670\pi$
$947$	− 2.52153e25i	− 1.26675i	0.773847	−	0.633373i	$-0.218330\pi$
$948$	6.55565e24i	0.326396i
$949$	−1.32590e24	−0.0654257
$950$	0	0
$951$	3.30253e24	0.160071
$952$	6.22473e24i	0.299024i
$953$	2.22635e25i	1.05999i	0.848000	+	0.529996i	$0.177807\pi$
$953$	2.22635e25i	1.05999i	−0.848000	+	0.529996i	$0.822193\pi$
$954$	−2.92762e24	−0.138151
$955$	0	0
$956$	−1.31208e25	−0.608229
$957$	1.09857e25i	0.504748i
$958$	9.07031e24i	0.413062i
$959$	−5.38261e24	−0.242960
$960$	0	0
$961$	−1.98675e25	−0.881037
$962$	− 3.85681e24i	− 0.169528i
$963$	− 2.58714e24i	− 0.112719i
$964$	1.19024e25	0.514018
$965$	0	0
$966$	4.84331e23	0.0205512
$967$	4.73776e24i	0.199273i	0.995024	+	0.0996363i	$0.0317679\pi$
$967$	4.73776e24i	0.199273i	−0.995024	+	0.0996363i	$0.968232\pi$
$968$	5.77963e24i	0.240968i
$969$	−5.33248e25	−2.20383
$970$	0	0
$971$	−3.41703e25	−1.38767	−0.693833	−	0.720136i	$-0.744079\pi$
$971$	−3.41703e25	−1.38767	−0.693833	+	0.720136i	$0.744079\pi$
$972$	3.01676e24i	0.121445i
$973$	− 2.03578e25i	− 0.812402i
$974$	−3.88341e24	−0.153625
$975$	0	0
$976$	1.06049e25	0.412273
$977$	− 6.32382e24i	− 0.243711i	−0.992548	−	0.121856i	$-0.961116\pi$
$977$	− 6.32382e24i	− 0.243711i	0.992548	−	0.121856i	$-0.0388845\pi$
$978$	2.92001e25i	1.11559i
$979$	−1.87528e24	−0.0710254
$980$	0	0
$981$	4.42032e24	0.164538
$982$	− 1.78408e25i	− 0.658365i
$983$	− 5.13743e25i	− 1.87949i	−0.341870	−	0.939747i	$-0.611060\pi$
$983$	− 5.13743e25i	− 1.87949i	0.341870	−	0.939747i	$-0.388940\pi$
$984$	−5.96858e24	−0.216477
$985$	0	0
$986$	−2.26599e25	−0.807802
$987$	− 1.89902e25i	− 0.671171i
$988$	− 6.38749e24i	− 0.223818i
$989$	−2.26959e24	−0.0788458
$990$	0	0
$991$	3.11936e25	1.06522	0.532610	−	0.846361i	$-0.321211\pi$
$991$	3.11936e25	1.06522	0.532610	+	0.846361i	$0.321211\pi$
$992$	− 1.80086e24i	− 0.0609722i
$993$	2.20919e24i	0.0741592i
$994$	−2.29229e25	−0.762930
$995$	0	0
$996$	−4.84940e24	−0.158666
$997$	4.66217e25i	1.51244i	0.654315	+	0.756222i	$0.272957\pi$
$997$	4.66217e25i	1.51244i	−0.654315	+	0.756222i	$0.727043\pi$
$998$	1.30809e25i	0.420755i
$999$	−2.40150e25	−0.765907

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.18.b.e.49.4		4
5.2	odd	4		10.18.a.b.1.2	✓	2
5.3	odd	4		50.18.a.g.1.1		2
5.4	even	2	inner	50.18.b.e.49.1		4
15.2	even	4		90.18.a.n.1.1		2
20.7	even	4		80.18.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.18.a.b.1.2	✓	2	5.2	odd	4
50.18.a.g.1.1		2	5.3	odd	4
50.18.b.e.49.1		4	5.4	even	2	inner
50.18.b.e.49.4		4	1.1	even	1	trivial
80.18.a.e.1.1		2	20.7	even	4
90.18.a.n.1.1		2	15.2	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+256.000i q^{2} +12037.8i q^{3} -65536.0 q^{4} -3.08167e6 q^{6} +9.53475e6i q^{7} -1.67772e7i q^{8} -1.57682e7 q^{9} +4.01191e8 q^{11} -7.88908e8i q^{12} +8.56166e8i q^{13} -2.44090e9 q^{14} +4.29497e9 q^{16} +3.89127e10i q^{17} -4.03665e9i q^{18} +1.13839e11 q^{19} -1.14777e11 q^{21} +1.02705e11i q^{22} +1.64834e10i q^{23} +2.01961e11 q^{24} -2.19179e11 q^{26} +1.36475e12i q^{27} -6.24870e11i q^{28} +2.27472e12 q^{29} -1.63788e12 q^{31} +1.09951e12i q^{32} +4.82946e12i q^{33} -9.96164e12 q^{34} +1.03338e12 q^{36} +1.75967e13i q^{37} +2.91428e13i q^{38} -1.03064e13 q^{39} -2.95532e13 q^{41} -2.93830e13i q^{42} +1.37690e14i q^{43} -2.62925e13 q^{44} -4.21974e12 q^{46} +1.65452e14i q^{47} +5.17019e13i q^{48} +1.41719e14 q^{49} -4.68422e14 q^{51} -5.61097e13i q^{52} -7.25259e14i q^{53} -3.49376e14 q^{54} +1.59967e14 q^{56} +1.37037e15i q^{57} +5.82328e14i q^{58} -1.62177e15 q^{59} +2.46915e15 q^{61} -4.19296e14i q^{62} -1.50346e14i q^{63} -2.81475e14 q^{64} -1.23634e15 q^{66} +2.03244e14i q^{67} -2.55018e15i q^{68} -1.98423e14 q^{69} +9.39117e15 q^{71} +2.64546e14i q^{72} +1.54865e15i q^{73} -4.50475e15 q^{74} -7.46056e15 q^{76} +3.82526e15i q^{77} -2.63843e15i q^{78} -8.30977e15 q^{79} -1.84648e16 q^{81} -7.56562e15i q^{82} -6.14697e15i q^{83} +7.52205e15 q^{84} -3.52485e16 q^{86} +2.73826e16i q^{87} -6.73087e15i q^{88} -4.67428e15 q^{89} -8.16334e15 q^{91} -1.08025e15i q^{92} -1.97164e16i q^{93} -4.23558e16 q^{94} -1.32357e16 q^{96} -1.01799e17i q^{97} +3.62801e16i q^{98} -6.32605e15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 262144 q^{4} + 3229696 q^{6} - 446391812 q^{9} + 2378817408 q^{11} + 3350448128 q^{14} + 17179869184 q^{16} + 273409661200 q^{19} - 819503796752 q^{21} - 211661357056 q^{24} + 1033174644736 q^{26}+ \cdots - 33\!\cdots\!24 q^{99}+O(q^{100}) \) 4 * q - 262144 * q^4 + 3229696 * q^6 - 446391812 * q^9 + 2378817408 * q^11 + 3350448128 * q^14 + 17179869184 * q^16 + 273409661200 * q^19 - 819503796752 * q^21 - 211661357056 * q^24 + 1033174644736 * q^26 + 9393086840040 * q^29 + 14241734757488 * q^31 - 9602887391232 * q^34 + 29254733791232 * q^36 - 126067430445424 * q^39 + 19245423761688 * q^41 - 155898177650688 * q^44 + 332407895402496 * q^46 + 231656293774092 * q^49 - 1676437434168912 * q^51 - 1434109657968640 * q^54 - 219574968516608 * q^56 - 1309232143990320 * q^59 + 2658080770325768 * q^61 - 1125899906842624 * q^64 + 4931077776801792 * q^66 - 24823071318707664 * q^69 + 4070263898695248 * q^71 + 5085754694371328 * q^74 - 17918175556403200 * q^76 - 38376855356990240 * q^79 - 37806028031428396 * q^81 + 53707000823939072 * q^84 - 3946719238068224 * q^86 + 34917825832790040 * q^89 - 108749216422866032 * q^91 - 238629158829053952 * q^94 + 13871438696022016 * q^96 - 339648391656292224 * q^99

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