LMFDB - Embedded newform 50.26.b.h.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,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, 26, names="a")

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

chi := DirichletCharacter("50.49");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 5211818408605 x^{8} + \cdots + 28\!\cdots\!01 $ x^10 + 5211818408605x^8 + 9550013044828576501383210x^6 + 6973841556383605813216495597740002010x^4 + 1502492440761809172497027825025593423345236688805x^2 + 2808409106992010919468023850302956778869454001951219661401
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{38}\cdot 3^{10}\cdot 5^{24} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.1
Root			$-1.22241e6i$ of defining polynomial
Character	$\chi$	$=$	50.49
Dual form			50.26.b.h.49.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00i q^{2} -1.22241e6i q^{3} -1.67772e7 q^{4} -5.00697e9 q^{6} -6.80801e10i q^{7} +6.87195e10i q^{8} -6.46987e11 q^{9} -1.63529e13 q^{11} +2.05086e13i q^{12} +1.23277e14i q^{13} -2.78856e14 q^{14} +2.81475e14 q^{16} -1.24327e15i q^{17} +2.65006e15i q^{18} -1.08089e16 q^{19} -8.32215e16 q^{21} +6.69815e16i q^{22} +1.26942e17i q^{23} +8.40031e16 q^{24} +5.04942e17 q^{26} -2.44849e17i q^{27} +1.14219e18i q^{28} +1.19617e18 q^{29} +3.33827e18 q^{31} -1.15292e18i q^{32} +1.99899e19i q^{33} -5.09242e18 q^{34} +1.08546e19 q^{36} -5.02410e19i q^{37} +4.42734e19i q^{38} +1.50694e20 q^{39} -2.63431e20 q^{41} +3.40875e20i q^{42} +1.36754e20i q^{43} +2.74356e20 q^{44} +5.19955e20 q^{46} +7.03907e20i q^{47} -3.44077e20i q^{48} -3.29383e21 q^{49} -1.51978e21 q^{51} -2.06824e21i q^{52} -3.75972e21i q^{53} -1.00290e21 q^{54} +4.67843e21 q^{56} +1.32129e22i q^{57} -4.89952e21i q^{58} +6.89657e21 q^{59} +1.54607e22 q^{61} -1.36736e22i q^{62} +4.40470e22i q^{63} -4.72237e21 q^{64} +8.18786e22 q^{66} +8.66895e22i q^{67} +2.08585e22i q^{68} +1.55175e23 q^{69} +4.41872e22 q^{71} -4.44606e22i q^{72} -8.03151e22i q^{73} -2.05787e23 q^{74} +1.81344e23 q^{76} +1.11331e24i q^{77} -6.17244e23i q^{78} +5.07310e23 q^{79} -8.47490e23 q^{81} +1.07901e24i q^{82} +5.22032e23i q^{83} +1.39623e24 q^{84} +5.60143e23 q^{86} -1.46221e24i q^{87} -1.12376e24i q^{88} +1.15373e24 q^{89} +8.39270e24 q^{91} -2.12974e24i q^{92} -4.08072e24i q^{93} +2.88320e24 q^{94} -1.40934e24 q^{96} +4.89110e24i q^{97} +1.34915e25i q^{98} +1.05801e25 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 167772160 q^{4} + 5930967040 q^{6} - 1950750722780 q^{9} - 17674067967630 q^{11} - 403201115668480 q^{14} + 28\!\cdots\!60 q^{16} - 13\!\cdots\!50 q^{19} - 11\!\cdots\!80 q^{21} - 99\!\cdots\!40 q^{24}+ \cdots + 46\!\cdots\!40 q^{99}+O(q^{100}) $ 10 * q - 167772160 * q^4 + 5930967040 * q^6 - 1950750722780 * q^9 - 17674067967630 * q^11 - 403201115668480 * q^14 + 2814749767106560 * q^16 - 13656410902154450 * q^19 - 112914117637521980 * q^21 - 99505115118960640 * q^24 + 553861034690314240 * q^26 - 5233921758503439600 * q^29 + 2763842594495258420 * q^31 - 12643869681446215680 * q^34 + 32728166238236180480 * q^36 + 152836894182107254040 * q^39 + 221293530514434412770 * q^41 + 296521655891609518080 * q^44 + 1438969030306499543040 * q^46 - 9942833167487211475170 * q^49 - 1909885137421531933230 * q^51 - 9030562925524734976000 * q^54 + 6764592209011073351680 * q^56 - 66083072776331191921200 * q^59 - 23179743393488009953180 * q^61 - 47223664828696452136960 * q^64 + 120286140832874083246080 * q^66 - 135923250107652130550460 * q^69 + 355679240938654866836520 * q^71 - 557504464959852709396480 * q^74 + 229116555490200073011200 * q^76 + 440397207411103561820500 * q^79 - 3190456286426028454480390 * q^81 + 1894384541054115963207680 * q^84 - 1385876056255558046351360 * q^86 + 11864662755859110806369850 * q^89 + 6710519214620433441429520 * q^91 + 13547865247217718455992320 * q^94 + 1669418809455668352778240 * q^96 + 46393873036575245993852340 * 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 $

$2$	− 4096.00i	− 0.707107i
$2$	− 4096.00i	− 0.707107i
$3$	− 1.22241e6i	− 1.32801i	−0.747730	−	0.664003i	$-0.768856\pi$
$3$	− 1.22241e6i	− 1.32801i	0.747730	−	0.664003i	$-0.231144\pi$
$4$	−1.67772e7	−0.500000
$5$	0	0
$5$	0	0
$6$	−5.00697e9	−0.939041
$7$	− 6.80801e10i	− 1.85907i	−0.368739	−	0.929533i	$-0.620211\pi$
$7$	− 6.80801e10i	− 1.85907i	0.368739	−	0.929533i	$-0.379789\pi$
$8$	6.87195e10i	0.353553i
$9$	−6.46987e11	−0.763597
$10$	0	0
$11$	−1.63529e13	−1.57104	−0.785519	−	0.618838i	$-0.787604\pi$
$11$	−1.63529e13	−1.57104	−0.785519	+	0.618838i	$0.787604\pi$
$12$	2.05086e13i	0.664003i
$13$	1.23277e14i	1.46754i	0.679399	+	0.733769i	$0.262241\pi$
$13$	1.23277e14i	1.46754i	−0.679399	+	0.733769i	$0.737759\pi$
$14$	−2.78856e14	−1.31456
$15$	0	0
$16$	2.81475e14	0.250000
$17$	− 1.24327e15i	− 0.517550i	−0.965938	−	0.258775i	$-0.916681\pi$
$17$	− 1.24327e15i	− 0.517550i	0.965938	−	0.258775i	$-0.0833189\pi$
$18$	2.65006e15i	0.539945i
$19$	−1.08089e16	−1.12037	−0.560187	−	0.828366i	$-0.689271\pi$
$19$	−1.08089e16	−1.12037	−0.560187	+	0.828366i	$0.689271\pi$
$20$	0	0
$21$	−8.32215e16	−2.46885
$22$	6.69815e16i	1.11089i
$23$	1.26942e17i	1.20784i	0.797046	+	0.603918i	$0.206395\pi$
$23$	1.26942e17i	1.20784i	−0.797046	+	0.603918i	$0.793605\pi$
$24$	8.40031e16	0.469521
$25$	0	0
$26$	5.04942e17	1.03771
$27$	− 2.44849e17i	− 0.313944i
$28$	1.14219e18i	0.929533i
$29$	1.19617e18	0.627797	0.313898	−	0.949457i	$-0.398365\pi$
$29$	1.19617e18	0.627797	0.313898	+	0.949457i	$0.398365\pi$
$30$	0	0
$31$	3.33827e18	0.761203	0.380602	−	0.924739i	$-0.375717\pi$
$31$	3.33827e18	0.761203	0.380602	+	0.924739i	$0.375717\pi$
$32$	− 1.15292e18i	− 0.176777i
$33$	1.99899e19i	2.08635i
$34$	−5.09242e18	−0.365963
$35$	0	0
$36$	1.08546e19	0.381799
$37$	− 5.02410e19i	− 1.25469i	−0.778741	−	0.627346i	$-0.784141\pi$
$37$	− 5.02410e19i	− 1.25469i	0.778741	−	0.627346i	$-0.215859\pi$
$38$	4.42734e19i	0.792224i
$39$	1.50694e20	1.94890
$40$	0	0
$41$	−2.63431e20	−1.82335	−0.911673	−	0.410917i	$-0.865209\pi$
$41$	−2.63431e20	−1.82335	−0.911673	+	0.410917i	$0.865209\pi$
$42$	3.40875e20i	1.74574i
$43$	1.36754e20i	0.521895i	0.965353	+	0.260947i	$0.0840349\pi$
$43$	1.36754e20i	0.521895i	−0.965353	+	0.260947i	$0.915965\pi$
$44$	2.74356e20	0.785519
$45$	0	0
$46$	5.19955e20	0.854069
$47$	7.03907e20i	0.883674i	0.897095	+	0.441837i	$0.145673\pi$
$47$	7.03907e20i	0.883674i	−0.897095	+	0.441837i	$0.854327\pi$
$48$	− 3.44077e20i	− 0.332001i
$49$	−3.29383e21	−2.45613
$50$	0	0
$51$	−1.51978e21	−0.687309
$52$	− 2.06824e21i	− 0.733769i
$53$	− 3.75972e21i	− 1.05125i	−0.850716	−	0.525626i	$-0.823831\pi$
$53$	− 3.75972e21i	− 1.05125i	0.850716	−	0.525626i	$-0.176169\pi$
$54$	−1.00290e21	−0.221992
$55$	0	0
$56$	4.67843e21	0.657279
$57$	1.32129e22i	1.48786i
$58$	− 4.89952e21i	− 0.443919i
$59$	6.89657e21	0.504642	0.252321	−	0.967644i	$-0.418806\pi$
$59$	6.89657e21	0.504642	0.252321	+	0.967644i	$0.418806\pi$
$60$	0	0
$61$	1.54607e22	0.745773	0.372886	−	0.927877i	$-0.378368\pi$
$61$	1.54607e22	0.745773	0.372886	+	0.927877i	$0.378368\pi$
$62$	− 1.36736e22i	− 0.538252i
$63$	4.40470e22i	1.41958i
$64$	−4.72237e21	−0.125000
$65$	0	0
$66$	8.18786e22	1.47527
$67$	8.66895e22i	1.29429i	0.762367	+	0.647145i	$0.224037\pi$
$67$	8.66895e22i	1.29429i	−0.762367	+	0.647145i	$0.775963\pi$
$68$	2.08585e22i	0.258775i
$69$	1.55175e23	1.60401
$70$	0	0
$71$	4.41872e22	0.319571	0.159785	−	0.987152i	$-0.448920\pi$
$71$	4.41872e22	0.319571	0.159785	+	0.987152i	$0.448920\pi$
$72$	− 4.44606e22i	− 0.269972i
$73$	− 8.03151e22i	− 0.410451i	−0.978715	−	0.205226i	$-0.934207\pi$
$73$	− 8.03151e22i	− 0.410451i	0.978715	−	0.205226i	$-0.0657928\pi$
$74$	−2.05787e23	−0.887201
$75$	0	0
$76$	1.81344e23	0.560187
$77$	1.11331e24i	2.92066i
$78$	− 6.17244e23i	− 1.37808i
$79$	5.07310e23	0.965906	0.482953	−	0.875646i	$-0.339564\pi$
$79$	5.07310e23	0.965906	0.482953	+	0.875646i	$0.339564\pi$
$80$	0	0
$81$	−8.47490e23	−1.18052
$82$	1.07901e24i	1.28930i
$83$	5.22032e23i	0.536070i	0.963409	+	0.268035i	$0.0863743\pi$
$83$	5.22032e23i	0.536070i	−0.963409	+	0.268035i	$0.913626\pi$
$84$	1.39623e24	1.23442
$85$	0	0
$86$	5.60143e23	0.369035
$87$	− 1.46221e24i	− 0.833717i
$88$	− 1.12376e24i	− 0.555446i
$89$	1.15373e24	0.495142	0.247571	−	0.968870i	$-0.420368\pi$
$89$	1.15373e24	0.495142	0.247571	+	0.968870i	$0.420368\pi$
$90$	0	0
$91$	8.39270e24	2.72825
$92$	− 2.12974e24i	− 0.603918i
$93$	− 4.08072e24i	− 1.01088i
$94$	2.88320e24	0.624852
$95$	0	0
$96$	−1.40934e24	−0.234760
$97$	4.89110e24i	0.715748i	0.933770	+	0.357874i	$0.116498\pi$
$97$	4.89110e24i	0.715748i	−0.933770	+	0.357874i	$0.883502\pi$
$98$	1.34915e25i	1.73674i
$99$	1.05801e25	1.19964
$100$	0	0
$101$	1.39348e25	1.23051	0.615255	−	0.788328i	$-0.289053\pi$
$101$	1.39348e25	1.23051	0.615255	+	0.788328i	$0.289053\pi$
$102$	6.22500e24i	0.486001i
$103$	1.11068e25i	0.767579i	0.923421	+	0.383789i	$0.125381\pi$
$103$	1.11068e25i	0.767579i	−0.923421	+	0.383789i	$0.874619\pi$
$104$	−8.47152e24	−0.518853
$105$	0	0
$106$	−1.53998e25	−0.743348
$107$	− 2.28767e25i	− 0.981967i	−0.871169	−	0.490983i	$-0.836638\pi$
$107$	− 2.28767e25i	− 0.981967i	0.871169	−	0.490983i	$-0.163362\pi$
$108$	4.10789e24i	0.156972i
$109$	−3.92414e25	−1.33633	−0.668164	−	0.744014i	$-0.732919\pi$
$109$	−3.92414e25	−1.33633	−0.668164	+	0.744014i	$0.732919\pi$
$110$	0	0
$111$	−6.14149e25	−1.66624
$112$	− 1.91628e25i	− 0.464766i
$113$	2.95166e25i	0.640599i	0.947316	+	0.320299i	$0.103784\pi$
$113$	2.95166e25i	0.640599i	−0.947316	+	0.320299i	$0.896216\pi$
$114$	5.41201e25	1.05208
$115$	0	0
$116$	−2.00685e25	−0.313898
$117$	− 7.97585e25i	− 1.12061i
$118$	− 2.82484e25i	− 0.356835i
$119$	−8.46417e25	−0.962160
$120$	0	0
$121$	1.59071e26	1.46816
$122$	− 6.33271e25i	− 0.527341i
$123$	3.22020e26i	2.42141i
$124$	−5.60069e25	−0.380602
$125$	0	0
$126$	1.80416e26	1.00379
$127$	− 3.71288e25i	− 0.187139i	−0.995613	−	0.0935696i	$-0.970172\pi$
$127$	− 3.71288e25i	− 0.187139i	0.995613	−	0.0935696i	$-0.0298277\pi$
$128$	1.93428e25i	0.0883883i
$129$	1.67168e26	0.693079
$130$	0	0
$131$	−2.02734e26	−0.693482	−0.346741	−	0.937961i	$-0.612712\pi$
$131$	−2.02734e26	−0.693482	−0.346741	+	0.937961i	$0.612712\pi$
$132$	− 3.35375e26i	− 1.04317i
$133$	7.35874e26i	2.08285i
$134$	3.55080e26	0.915201
$135$	0	0
$136$	8.54366e25	0.182982
$137$	− 4.21478e26i	− 0.823697i	−0.911252	−	0.411848i	$-0.864883\pi$
$137$	− 4.21478e26i	− 0.823697i	0.911252	−	0.411848i	$-0.135117\pi$
$138$	− 6.35596e26i	− 1.13421i
$139$	2.61876e26	0.426983	0.213491	−	0.976945i	$-0.431516\pi$
$139$	2.61876e26	0.426983	0.213491	+	0.976945i	$0.431516\pi$
$140$	0	0
$141$	8.60460e26	1.17352
$142$	− 1.80991e26i	− 0.225971i
$143$	− 2.01593e27i	− 2.30556i
$144$	−1.82111e26	−0.190899
$145$	0	0
$146$	−3.28971e26	−0.290233
$147$	4.02640e27i	3.26175i
$148$	8.42905e26i	0.627346i
$149$	−5.33091e26	−0.364732	−0.182366	−	0.983231i	$-0.558375\pi$
$149$	−5.33091e26	−0.364732	−0.182366	+	0.983231i	$0.558375\pi$
$150$	0	0
$151$	−1.15195e26	−0.0667148	−0.0333574	−	0.999443i	$-0.510620\pi$
$151$	−1.15195e26	−0.0667148	−0.0333574	+	0.999443i	$0.510620\pi$
$152$	− 7.42784e26i	− 0.396112i
$153$	8.04377e26i	0.395200i
$154$	4.56011e27	2.06522
$155$	0	0
$156$	−2.52823e27	−0.974449
$157$	− 7.11181e26i	− 0.253066i	−0.991962	−	0.126533i	$-0.959615\pi$
$157$	− 7.11181e26i	− 0.253066i	0.991962	−	0.126533i	$-0.0403850\pi$
$158$	− 2.07794e27i	− 0.682999i
$159$	−4.59590e27	−1.39607
$160$	0	0
$161$	8.64224e27	2.24545
$162$	3.47132e27i	0.834751i
$163$	4.92749e27i	1.09719i	0.836089	+	0.548594i	$0.184837\pi$
$163$	4.92749e27i	1.09719i	−0.836089	+	0.548594i	$0.815163\pi$
$164$	4.41964e27	0.911673
$165$	0	0
$166$	2.13825e27	0.379059
$167$	− 1.54847e26i	− 0.0254651i	−0.999919	−	0.0127326i	$-0.995947\pi$
$167$	− 1.54847e26i	− 0.0254651i	0.999919	−	0.0127326i	$-0.00405301\pi$
$168$	− 5.71894e27i	− 0.872870i
$169$	−8.14076e27	−1.15367
$170$	0	0
$171$	6.99325e27	0.855515
$172$	− 2.29434e27i	− 0.260947i
$173$	− 1.24940e28i	− 1.32168i	−0.750527	−	0.660840i	$-0.770200\pi$
$173$	− 1.24940e28i	− 1.32168i	0.750527	−	0.660840i	$-0.229800\pi$
$174$	−5.98921e27	−0.589527
$175$	0	0
$176$	−4.60293e27	−0.392759
$177$	− 8.43041e27i	− 0.670167i
$178$	− 4.72569e27i	− 0.350118i
$179$	−1.81393e28	−1.25302	−0.626509	−	0.779414i	$-0.715517\pi$
$179$	−1.81393e28	−1.25302	−0.626509	+	0.779414i	$0.715517\pi$
$180$	0	0
$181$	−2.28334e28	−1.37274	−0.686369	−	0.727254i	$-0.740796\pi$
$181$	−2.28334e28	−1.37274	−0.686369	+	0.727254i	$0.740796\pi$
$182$	− 3.43765e28i	− 1.92916i
$183$	− 1.88993e28i	− 0.990390i
$184$	−8.72340e27	−0.427035
$185$	0	0
$186$	−1.67146e28	−0.714801
$187$	2.03310e28i	0.813091i
$188$	− 1.18096e28i	− 0.441837i
$189$	−1.66694e28	−0.583642
$190$	0	0
$191$	−3.88305e28	−1.19195	−0.595973	−	0.803005i	$-0.703233\pi$
$191$	−3.88305e28	−1.19195	−0.595973	+	0.803005i	$0.703233\pi$
$192$	5.77265e27i	0.166001i
$193$	5.16030e28i	1.39062i	0.718710	+	0.695310i	$0.244733\pi$
$193$	5.16030e28i	1.39062i	−0.718710	+	0.695310i	$0.755267\pi$
$194$	2.00340e28	0.506110
$195$	0	0
$196$	5.52613e28	1.22806
$197$	− 4.39578e28i	− 0.916659i	−0.888782	−	0.458330i	$-0.848448\pi$
$197$	− 4.39578e28i	− 0.916659i	0.888782	−	0.458330i	$-0.151552\pi$
$198$	− 4.33362e28i	− 0.848274i
$199$	−6.89463e28	−1.26721	−0.633604	−	0.773658i	$-0.718425\pi$
$199$	−6.89463e28	−1.26721	−0.633604	+	0.773658i	$0.718425\pi$
$200$	0	0
$201$	1.05970e29	1.71882
$202$	− 5.70771e28i	− 0.870102i
$203$	− 8.14356e28i	− 1.16712i
$204$	2.54976e28	0.343655
$205$	0	0
$206$	4.54934e28	0.542760
$207$	− 8.21300e28i	− 0.922301i
$208$	3.46993e28i	0.366885i
$209$	1.76758e29	1.76015
$210$	0	0
$211$	2.04578e29	1.80854	0.904269	−	0.426962i	$-0.140416\pi$
$211$	2.04578e29	1.80854	0.904269	+	0.426962i	$0.140416\pi$
$212$	6.30776e28i	0.525626i
$213$	− 5.40147e28i	− 0.424392i
$214$	−9.37031e28	−0.694355
$215$	0	0
$216$	1.68259e28	0.110996
$217$	− 2.27270e29i	− 1.41513i
$218$	1.60733e29i	0.944926i
$219$	−9.81777e28	−0.545081
$220$	0	0
$221$	1.53266e29	0.759525
$222$	2.51556e29i	1.17821i
$223$	− 3.97032e29i	− 1.75798i	−0.476839	−	0.878991i	$-0.658217\pi$
$223$	− 3.97032e29i	− 1.75798i	0.476839	−	0.878991i	$-0.341783\pi$
$224$	−7.84910e28	−0.328639
$225$	0	0
$226$	1.20900e29	0.452972
$227$	3.06368e29i	1.08623i	0.839660	+	0.543113i	$0.182754\pi$
$227$	3.06368e29i	1.08623i	−0.839660	+	0.543113i	$0.817246\pi$
$228$	− 2.21676e29i	− 0.743931i
$229$	−2.92488e28	−0.0929319	−0.0464660	−	0.998920i	$-0.514796\pi$
$229$	−2.92488e28	−0.0929319	−0.0464660	+	0.998920i	$0.514796\pi$
$230$	0	0
$231$	1.36091e30	3.87865
$232$	8.22004e28i	0.221960i
$233$	− 3.00032e29i	− 0.767748i	−0.923385	−	0.383874i	$-0.874590\pi$
$233$	− 3.00032e29i	− 0.767748i	0.923385	−	0.383874i	$-0.125410\pi$
$234$	−3.26691e29	−0.792390
$235$	0	0
$236$	−1.15705e29	−0.252321
$237$	− 6.20139e29i	− 1.28273i
$238$	3.46692e29i	0.680350i
$239$	7.62279e29	1.41952	0.709758	−	0.704445i	$-0.248804\pi$
$239$	7.62279e29	1.41952	0.709758	+	0.704445i	$0.248804\pi$
$240$	0	0
$241$	−5.68961e29	−0.954705	−0.477352	−	0.878712i	$-0.658403\pi$
$241$	−5.68961e29	−0.954705	−0.477352	+	0.878712i	$0.658403\pi$
$242$	− 6.51553e29i	− 1.03814i
$243$	8.28519e29i	1.25379i
$244$	−2.59388e29	−0.372886
$245$	0	0
$246$	1.31899e30	1.71220
$247$	− 1.33249e30i	− 1.64419i
$248$	2.29404e29i	0.269126i
$249$	6.38136e29	0.711903
$250$	0	0
$251$	7.84848e29	0.792253	0.396127	−	0.918196i	$-0.370354\pi$
$251$	7.84848e29	0.792253	0.396127	+	0.918196i	$0.370354\pi$
$252$	− 7.38986e29i	− 0.709789i
$253$	− 2.07587e30i	− 1.89756i
$254$	−1.52080e29	−0.132327
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	− 1.93819e30i	− 1.45624i	−0.685450	−	0.728119i	$-0.740395\pi$
$257$	− 1.93819e30i	− 1.45624i	0.685450	−	0.728119i	$-0.259605\pi$
$258$	− 6.84722e29i	− 0.490081i
$259$	−3.42041e30	−2.33255
$260$	0	0
$261$	−7.73909e29	−0.479384
$262$	8.30399e29i	0.490366i
$263$	7.76661e29i	0.437305i	0.975803	+	0.218653i	$0.0701661\pi$
$263$	7.76661e29i	0.437305i	−0.975803	+	0.218653i	$0.929834\pi$
$264$	−1.37369e30	−0.737634
$265$	0	0
$266$	3.01414e30	1.47280
$267$	− 1.41033e30i	− 0.657551i
$268$	− 1.45441e30i	− 0.647145i
$269$	−1.26958e30	−0.539209	−0.269604	−	0.962971i	$-0.586893\pi$
$269$	−1.26958e30	−0.539209	−0.269604	+	0.962971i	$0.586893\pi$
$270$	0	0
$271$	−2.59506e29	−0.100469	−0.0502344	−	0.998737i	$-0.515997\pi$
$271$	−2.59506e29	−0.100469	−0.0502344	+	0.998737i	$0.515997\pi$
$272$	− 3.49948e29i	− 0.129388i
$273$	− 1.02593e31i	− 3.62313i
$274$	−1.72637e30	−0.582442
$275$	0	0
$276$	−2.60340e30	−0.802006
$277$	− 4.20101e30i	− 1.23696i	−0.785799	−	0.618482i	$-0.787748\pi$
$277$	− 4.20101e30i	− 1.23696i	0.785799	−	0.618482i	$-0.212252\pi$
$278$	− 1.07264e30i	− 0.301922i
$279$	−2.15982e30	−0.581253
$280$	0	0
$281$	7.34654e30	1.80823	0.904115	−	0.427290i	$-0.140532\pi$
$281$	7.34654e30	1.80823	0.904115	+	0.427290i	$0.140532\pi$
$282$	− 3.52444e30i	− 0.829806i
$283$	7.45011e30i	1.67816i	0.544011	+	0.839078i	$0.316905\pi$
$283$	7.45011e30i	1.67816i	−0.544011	+	0.839078i	$0.683095\pi$
$284$	−7.41339e29	−0.159785
$285$	0	0
$286$	−8.25727e30	−1.63028
$287$	1.79344e31i	3.38972i
$288$	7.45926e29i	0.134986i
$289$	4.22492e30	0.732142
$290$	0	0
$291$	5.97891e30	0.950517
$292$	1.34746e30i	0.205226i
$293$	3.40180e30i	0.496436i	0.968704	+	0.248218i	$0.0798449\pi$
$293$	3.40180e30i	0.496436i	−0.968704	+	0.248218i	$0.920155\pi$
$294$	1.64921e31	2.30640
$295$	0	0
$296$	3.45254e30	0.443601
$297$	4.00400e30i	0.493217i
$298$	2.18354e30i	0.257904i
$299$	−1.56490e31	−1.77255
$300$	0	0
$301$	9.31020e30	0.970237
$302$	4.71839e29i	0.0471745i
$303$	− 1.70340e31i	− 1.63412i
$304$	−3.04245e30	−0.280093
$305$	0	0
$306$	3.29473e30	0.279449
$307$	− 2.05490e31i	− 1.67325i	−0.547778	−	0.836624i	$-0.684526\pi$
$307$	− 2.05490e31i	− 1.67325i	0.547778	−	0.836624i	$-0.315474\pi$
$308$	− 1.86782e31i	− 1.46033i
$309$	1.35770e31	1.01935
$310$	0	0
$311$	−7.23094e28	−0.00500829	−0.00250415	−	0.999997i	$-0.500797\pi$
$311$	−7.23094e28	−0.00500829	−0.00250415	+	0.999997i	$0.500797\pi$
$312$	1.03556e31i	0.689040i
$313$	1.14602e31i	0.732635i	0.930490	+	0.366318i	$0.119382\pi$
$313$	1.14602e31i	0.732635i	−0.930490	+	0.366318i	$0.880618\pi$
$314$	−2.91300e30	−0.178945
$315$	0	0
$316$	−8.51125e30	−0.482953
$317$	2.43704e31i	1.32929i	0.747158	+	0.664647i	$0.231418\pi$
$317$	2.43704e31i	1.32929i	−0.747158	+	0.664647i	$0.768582\pi$
$318$	1.88248e31i	0.987170i
$319$	−1.95609e31	−0.986292
$320$	0	0
$321$	−2.79646e31	−1.30406
$322$	− 3.53986e31i	− 1.58777i
$323$	1.34384e31i	0.579850i
$324$	1.42185e31	0.590258
$325$	0	0
$326$	2.01830e31	0.775828
$327$	4.79689e31i	1.77465i
$328$	− 1.81029e31i	− 0.644650i
$329$	4.79220e31	1.64281
$330$	0	0
$331$	−3.61088e31	−1.14753	−0.573764	−	0.819021i	$-0.694517\pi$
$331$	−3.61088e31	−1.14753	−0.573764	+	0.819021i	$0.694517\pi$
$332$	− 8.75825e30i	− 0.268035i
$333$	3.25053e31i	0.958079i
$334$	−6.34252e29	−0.0180066
$335$	0	0
$336$	−2.34248e31	−0.617212
$337$	− 5.01811e31i	− 1.27399i	−0.770868	−	0.636995i	$-0.780177\pi$
$337$	− 5.01811e31i	− 1.27399i	0.770868	−	0.636995i	$-0.219823\pi$
$338$	3.33446e31i	0.815767i
$339$	3.60813e31	0.850718
$340$	0	0
$341$	−5.45905e31	−1.19588
$342$	− 2.86443e31i	− 0.604940i
$343$	1.32944e32i	2.70703i
$344$	−9.39763e30	−0.184518
$345$	0	0
$346$	−5.11756e31	−0.934569
$347$	− 2.69651e31i	− 0.474988i	−0.971389	−	0.237494i	$-0.923674\pi$
$347$	− 2.69651e31i	− 0.474988i	0.971389	−	0.237494i	$-0.0763261\pi$
$348$	2.45318e31i	0.416859i
$349$	−4.66669e31	−0.765052	−0.382526	−	0.923945i	$-0.624946\pi$
$349$	−4.66669e31	−0.765052	−0.382526	+	0.923945i	$0.624946\pi$
$350$	0	0
$351$	3.01842e31	0.460725
$352$	1.88536e31i	0.277723i
$353$	6.63592e31i	0.943446i	0.881747	+	0.471723i	$0.156368\pi$
$353$	6.63592e31i	0.943446i	−0.881747	+	0.471723i	$0.843632\pi$
$354$	−3.45310e31	−0.473879
$355$	0	0
$356$	−1.93564e31	−0.247571
$357$	1.03466e32i	1.27775i
$358$	7.42985e31i	0.886017i
$359$	7.18124e31	0.827025	0.413513	−	0.910498i	$-0.364302\pi$
$359$	7.18124e31	0.827025	0.413513	+	0.910498i	$0.364302\pi$
$360$	0	0
$361$	2.37566e31	0.255238
$362$	9.35254e31i	0.970672i
$363$	− 1.94449e32i	− 1.94972i
$364$	−1.40806e32	−1.36413
$365$	0	0
$366$	−7.74114e31	−0.700311
$367$	8.09654e31i	0.707903i	0.935264	+	0.353951i	$0.115162\pi$
$367$	8.09654e31i	0.707903i	−0.935264	+	0.353951i	$0.884838\pi$
$368$	3.57310e31i	0.301959i
$369$	1.70437e32	1.39230
$370$	0	0
$371$	−2.55962e32	−1.95435
$372$	6.84632e31i	0.505441i
$373$	− 1.63975e32i	− 1.17063i	−0.810807	−	0.585313i	$-0.800972\pi$
$373$	− 1.63975e32i	− 1.17063i	0.810807	−	0.585313i	$-0.199028\pi$
$374$	8.32758e31	0.574942
$375$	0	0
$376$	−4.83721e31	−0.312426
$377$	1.47460e32i	0.921316i
$378$	6.82777e31i	0.412697i
$379$	5.11219e31	0.298963	0.149481	−	0.988765i	$-0.452240\pi$
$379$	5.11219e31	0.298963	0.149481	+	0.988765i	$0.452240\pi$
$380$	0	0
$381$	−4.53865e31	−0.248522
$382$	1.59050e32i	0.842833i
$383$	− 2.90570e32i	− 1.49028i	−0.666911	−	0.745138i	$-0.732384\pi$
$383$	− 2.90570e32i	− 1.49028i	0.666911	−	0.745138i	$-0.267616\pi$
$384$	2.36448e31	0.117380
$385$	0	0
$386$	2.11366e32	0.983317
$387$	− 8.84778e31i	− 0.398518i
$388$	− 8.20591e31i	− 0.357874i
$389$	−9.70428e31	−0.409820	−0.204910	−	0.978781i	$-0.565690\pi$
$389$	−9.70428e31	−0.409820	−0.204910	+	0.978781i	$0.565690\pi$
$390$	0	0
$391$	1.57823e32	0.625116
$392$	− 2.26350e32i	− 0.868371i
$393$	2.47823e32i	0.920948i
$394$	−1.80051e32	−0.648176
$395$	0	0
$396$	−1.77505e32	−0.599820
$397$	4.94379e32i	1.61875i	0.587295	+	0.809373i	$0.300193\pi$
$397$	4.94379e32i	1.61875i	−0.587295	+	0.809373i	$0.699807\pi$
$398$	2.82404e32i	0.896051i
$399$	8.99536e32	2.76603
$400$	0	0
$401$	4.47162e31	0.129170	0.0645848	−	0.997912i	$-0.479428\pi$
$401$	4.47162e31	0.129170	0.0645848	+	0.997912i	$0.479428\pi$
$402$	− 4.34052e32i	− 1.21539i
$403$	4.11531e32i	1.11709i
$404$	−2.33788e32	−0.615255
$405$	0	0
$406$	−3.33560e32	−0.825275
$407$	8.21587e32i	1.97117i
$408$	− 1.04438e32i	− 0.243001i
$409$	−3.47804e32	−0.784863	−0.392431	−	0.919781i	$-0.628366\pi$
$409$	−3.47804e32	−0.784863	−0.392431	+	0.919781i	$0.628366\pi$
$410$	0	0
$411$	−5.15217e32	−1.09387
$412$	− 1.86341e32i	− 0.383789i
$413$	− 4.69519e32i	− 0.938162i
$414$	−3.36404e32	−0.652165
$415$	0	0
$416$	1.42128e32	0.259427
$417$	− 3.20119e32i	− 0.567035i
$418$	− 7.23999e32i	− 1.24461i
$419$	1.64856e32	0.275061	0.137531	−	0.990498i	$-0.456083\pi$
$419$	1.64856e32	0.275061	0.137531	+	0.990498i	$0.456083\pi$
$420$	0	0
$421$	4.59846e32	0.722914	0.361457	−	0.932389i	$-0.382279\pi$
$421$	4.59846e32	0.722914	0.361457	+	0.932389i	$0.382279\pi$
$422$	− 8.37951e32i	− 1.27883i
$423$	− 4.55419e32i	− 0.674771i
$424$	2.58366e32	0.371674
$425$	0	0
$426$	−2.21244e32	−0.300090
$427$	− 1.05257e33i	− 1.38644i
$428$	3.83808e32i	0.490983i
$429$	−2.46429e33	−3.06179
$430$	0	0
$431$	7.08014e32	0.829996	0.414998	−	0.909822i	$-0.363782\pi$
$431$	7.08014e32	0.829996	0.414998	+	0.909822i	$0.363782\pi$
$432$	− 6.89190e31i	− 0.0784860i
$433$	− 1.74438e32i	− 0.192993i	−0.995333	−	0.0964964i	$-0.969236\pi$
$433$	− 1.74438e32i	− 0.192993i	0.995333	−	0.0964964i	$-0.0307636\pi$
$434$	−9.30898e32	−1.00065
$435$	0	0
$436$	6.58361e32	0.668164
$437$	− 1.37211e33i	− 1.35323i
$438$	4.02136e32i	0.385431i
$439$	9.83917e32	0.916541	0.458271	−	0.888813i	$-0.348469\pi$
$439$	9.83917e32	0.916541	0.458271	+	0.888813i	$0.348469\pi$
$440$	0	0
$441$	2.13107e33	1.87549
$442$	− 6.27777e32i	− 0.537065i
$443$	9.66613e32i	0.803908i	0.915660	+	0.401954i	$0.131669\pi$
$443$	9.66613e32i	0.803908i	−0.915660	+	0.401954i	$0.868331\pi$
$444$	1.03037e33	0.833118
$445$	0	0
$446$	−1.62624e33	−1.24308
$447$	6.51654e32i	0.484365i
$448$	3.21499e32i	0.232383i
$449$	−5.74227e32	−0.403650	−0.201825	−	0.979422i	$-0.564687\pi$
$449$	−5.74227e32	−0.403650	−0.201825	+	0.979422i	$0.564687\pi$
$450$	0	0
$451$	4.30787e33	2.86454
$452$	− 4.95207e32i	− 0.320299i
$453$	1.40815e32i	0.0885977i
$454$	1.25488e33	0.768078
$455$	0	0
$456$	−9.07984e32	−0.526039
$457$	3.19404e33i	1.80048i	0.435398	+	0.900238i	$0.356608\pi$
$457$	3.19404e33i	1.80048i	−0.435398	+	0.900238i	$0.643392\pi$
$458$	1.19803e32i	0.0657128i
$459$	−3.04413e32	−0.162482
$460$	0	0
$461$	2.15114e33	1.08745	0.543723	−	0.839264i	$-0.317014\pi$
$461$	2.15114e33	1.08745	0.543723	+	0.839264i	$0.317014\pi$
$462$	− 5.57430e33i	− 2.74262i
$463$	− 6.57140e32i	− 0.314699i	−0.987543	−	0.157350i	$-0.949705\pi$
$463$	− 6.57140e32i	− 0.314699i	0.987543	−	0.157350i	$-0.0502950\pi$
$464$	3.36693e32	0.156949
$465$	0	0
$466$	−1.22893e33	−0.542880
$467$	1.92599e32i	0.0828312i	0.999142	+	0.0414156i	$0.0131868\pi$
$467$	1.92599e32i	0.0828312i	−0.999142	+	0.0414156i	$0.986813\pi$
$468$	1.33813e33i	0.560304i
$469$	5.90183e33	2.40617
$470$	0	0
$471$	−8.69352e32	−0.336074
$472$	4.73929e32i	0.178418i
$473$	− 2.23632e33i	− 0.819916i
$474$	−2.54009e33	−0.907026
$475$	0	0
$476$	1.42005e33	0.481080
$477$	2.43249e33i	0.802734i
$478$	− 3.12230e33i	− 1.00375i
$479$	−3.90669e33	−1.22353	−0.611766	−	0.791039i	$-0.709541\pi$
$479$	−3.90669e33	−1.22353	−0.611766	+	0.791039i	$0.709541\pi$
$480$	0	0
$481$	6.19355e33	1.84131
$482$	2.33046e33i	0.675078i
$483$	− 1.05643e34i	− 2.98196i
$484$	−2.66876e33	−0.734079
$485$	0	0
$486$	3.39361e33	0.886562
$487$	4.17680e33i	1.06349i	0.846906	+	0.531743i	$0.178463\pi$
$487$	4.17680e33i	1.06349i	−0.846906	+	0.531743i	$0.821537\pi$
$488$	1.06245e33i	0.263670i
$489$	6.02339e33	1.45707
$490$	0	0
$491$	−1.40550e33	−0.323083	−0.161541	−	0.986866i	$-0.551647\pi$
$491$	−1.40550e33	−0.323083	−0.161541	+	0.986866i	$0.551647\pi$
$492$	− 5.40260e33i	− 1.21071i
$493$	− 1.48716e33i	− 0.324916i
$494$	−5.45788e33	−1.16262
$495$	0	0
$496$	9.39640e32	0.190301
$497$	− 3.00827e33i	− 0.594103i
$498$	− 2.61380e33i	− 0.503392i
$499$	−8.69572e32	−0.163323	−0.0816617	−	0.996660i	$-0.526023\pi$
$499$	−8.69572e32	−0.163323	−0.0816617	+	0.996660i	$0.526023\pi$
$500$	0	0
$501$	−1.89285e32	−0.0338178
$502$	− 3.21474e33i	− 0.560208i
$503$	7.81824e33i	1.32895i	0.747310	+	0.664476i	$0.231345\pi$
$503$	7.81824e33i	1.32895i	−0.747310	+	0.664476i	$0.768655\pi$
$504$	−3.02688e33	−0.501897
$505$	0	0
$506$	−8.50278e33	−1.34177
$507$	9.95131e33i	1.53208i
$508$	6.22918e32i	0.0935696i
$509$	7.92846e33	1.16203	0.581014	−	0.813894i	$-0.302656\pi$
$509$	7.92846e33	1.16203	0.581014	+	0.813894i	$0.302656\pi$
$510$	0	0
$511$	−5.46786e33	−0.763056
$512$	− 3.24519e32i	− 0.0441942i
$513$	2.64656e33i	0.351734i
$514$	−7.93883e33	−1.02972
$515$	0	0
$516$	−2.80462e33	−0.346539
$517$	− 1.15109e34i	− 1.38828i
$518$	1.40100e34i	1.64936i
$519$	−1.52728e34	−1.75520
$520$	0	0
$521$	−3.29787e33	−0.361212	−0.180606	−	0.983556i	$-0.557806\pi$
$521$	−3.29787e33	−0.361212	−0.180606	+	0.983556i	$0.557806\pi$
$522$	3.16993e33i	0.338976i
$523$	1.60818e33i	0.167905i	0.996470	+	0.0839524i	$0.0267544\pi$
$523$	1.60818e33i	0.167905i	−0.996470	+	0.0839524i	$0.973246\pi$
$524$	3.40131e33	0.346741
$525$	0	0
$526$	3.18120e33	0.309221
$527$	− 4.15036e33i	− 0.393961i
$528$	5.62665e33i	0.521586i
$529$	−5.06855e33	−0.458868
$530$	0	0
$531$	−4.46199e33	−0.385343
$532$	− 1.23459e34i	− 1.04142i
$533$	− 3.24750e34i	− 2.67583i
$534$	−5.77671e33	−0.464959
$535$	0	0
$536$	−5.95726e33	−0.457601
$537$	2.21736e34i	1.66401i
$538$	5.20020e33i	0.381278i
$539$	5.38637e34	3.85866
$540$	0	0
$541$	−1.05559e34	−0.721990	−0.360995	−	0.932568i	$-0.617563\pi$
$541$	−1.05559e34	−0.721990	−0.360995	+	0.932568i	$0.617563\pi$
$542$	1.06294e33i	0.0710422i
$543$	2.79116e34i	1.82300i
$544$	−1.43339e33	−0.0914908
$545$	0	0
$546$	−4.20220e34	−2.56194
$547$	2.41768e34i	1.44065i	0.693638	+	0.720324i	$0.256007\pi$
$547$	2.41768e34i	1.44065i	−0.693638	+	0.720324i	$0.743993\pi$
$548$	7.07122e33i	0.411848i
$549$	−1.00029e34	−0.569470
$550$	0	0
$551$	−1.29294e34	−0.703367
$552$	1.06635e34i	0.567104i
$553$	− 3.45377e34i	− 1.79568i
$554$	−1.72073e34	−0.874665
$555$	0	0
$556$	−4.39355e33	−0.213491
$557$	− 1.98926e34i	− 0.945153i	−0.881290	−	0.472576i	$-0.843324\pi$
$557$	− 1.98926e34i	− 0.945153i	0.881290	−	0.472576i	$-0.156676\pi$
$558$	8.84662e33i	0.411008i
$559$	−1.68585e34	−0.765901
$560$	0	0
$561$	2.48527e34	1.07979
$562$	− 3.00914e34i	− 1.27861i
$563$	3.43624e34i	1.42800i	0.700145	+	0.714001i	$0.253119\pi$
$563$	3.43624e34i	1.42800i	−0.700145	+	0.714001i	$0.746881\pi$
$564$	−1.44361e34	−0.586762
$565$	0	0
$566$	3.05157e34	1.18664
$567$	5.76972e34i	2.19466i
$568$	3.03652e33i	0.112985i
$569$	4.74393e34	1.72677	0.863386	−	0.504544i	$-0.168339\pi$
$569$	4.74393e34	1.72677	0.863386	+	0.504544i	$0.168339\pi$
$570$	0	0
$571$	−4.26964e33	−0.148744	−0.0743721	−	0.997231i	$-0.523695\pi$
$571$	−4.26964e33	−0.148744	−0.0743721	+	0.997231i	$0.523695\pi$
$572$	3.38218e34i	1.15278i
$573$	4.74667e34i	1.58291i
$574$	7.34594e34	2.39689
$575$	0	0
$576$	3.05531e33	0.0954497
$577$	− 1.96194e34i	− 0.599775i	−0.953975	−	0.299887i	$-0.903051\pi$
$577$	− 1.96194e34i	− 0.599775i	0.953975	−	0.299887i	$-0.0969491\pi$
$578$	− 1.73053e34i	− 0.517702i
$579$	6.30798e34	1.84675
$580$	0	0
$581$	3.55400e34	0.996589
$582$	− 2.44896e34i	− 0.672117i
$583$	6.14824e34i	1.65156i
$584$	5.51921e33	0.145116
$585$	0	0
$586$	1.39338e34	0.351033
$587$	4.23298e34i	1.04393i	0.852968	+	0.521963i	$0.174800\pi$
$587$	4.23298e34i	1.04393i	−0.852968	+	0.521963i	$0.825200\pi$
$588$	− 6.75518e34i	− 1.63087i
$589$	−3.60832e34	−0.852832
$590$	0	0
$591$	−5.37343e34	−1.21733
$592$	− 1.41416e34i	− 0.313673i
$593$	2.29135e34i	0.497631i	0.968551	+	0.248816i	$0.0800413\pi$
$593$	2.29135e34i	0.497631i	−0.968551	+	0.248816i	$0.919959\pi$
$594$	1.64004e34	0.348757
$595$	0	0
$596$	8.94379e33	0.182366
$597$	8.42804e34i	1.68286i
$598$	6.40984e34i	1.25338i
$599$	−1.21937e34	−0.233508	−0.116754	−	0.993161i	$-0.537249\pi$
$599$	−1.21937e34	−0.233508	−0.116754	+	0.993161i	$0.537249\pi$
$600$	0	0
$601$	−2.38798e33	−0.0438631	−0.0219315	−	0.999759i	$-0.506982\pi$
$601$	−2.38798e33	−0.0438631	−0.0219315	+	0.999759i	$0.506982\pi$
$602$	− 3.81346e34i	− 0.686061i
$603$	− 5.60870e34i	− 0.988317i
$604$	1.93265e33	0.0333574
$605$	0	0
$606$	−6.97714e34	−1.15550
$607$	2.92481e34i	0.474504i	0.971448	+	0.237252i	$0.0762466\pi$
$607$	2.92481e34i	0.474504i	−0.971448	+	0.237252i	$0.923753\pi$
$608$	1.24619e34i	0.198056i
$609$	−9.95473e34	−1.54993
$610$	0	0
$611$	−8.67754e34	−1.29682
$612$	− 1.34952e34i	− 0.197600i
$613$	6.94539e34i	0.996416i	0.867057	+	0.498208i	$0.166008\pi$
$613$	6.94539e34i	0.996416i	−0.867057	+	0.498208i	$0.833992\pi$
$614$	−8.41686e34	−1.18316
$615$	0	0
$616$	−7.65059e34	−1.03261
$617$	4.20916e34i	0.556713i	0.960478	+	0.278356i	$0.0897896\pi$
$617$	4.20916e34i	0.556713i	−0.960478	+	0.278356i	$0.910210\pi$
$618$	− 5.56114e34i	− 0.720788i
$619$	−5.93194e34	−0.753466	−0.376733	−	0.926322i	$-0.622953\pi$
$619$	−5.93194e34	−0.753466	−0.376733	+	0.926322i	$0.622953\pi$
$620$	0	0
$621$	3.10817e34	0.379193
$622$	2.96179e32i	0.00354140i
$623$	− 7.85462e34i	− 0.920502i
$624$	4.24167e34	0.487225
$625$	0	0
$626$	4.69410e34	0.518051
$627$	− 2.16069e35i	− 2.33749i
$628$	1.19316e34i	0.126533i
$629$	−6.24630e34	−0.649366
$630$	0	0
$631$	1.46762e35	1.46638	0.733192	−	0.680022i	$-0.238030\pi$
$631$	1.46762e35	1.46638	0.733192	+	0.680022i	$0.238030\pi$
$632$	3.48621e34i	0.341499i
$633$	− 2.50077e35i	− 2.40175i
$634$	9.98210e34	0.939953
$635$	0	0
$636$	7.71065e34	0.698034
$637$	− 4.06053e35i	− 3.60446i
$638$	8.01215e34i	0.697414i
$639$	−2.85886e34	−0.244024
$640$	0	0
$641$	1.22792e35	1.00796	0.503982	−	0.863714i	$-0.331868\pi$
$641$	1.22792e35	1.00796	0.503982	+	0.863714i	$0.331868\pi$
$642$	1.14543e35i	0.922107i
$643$	1.26806e34i	0.100116i	0.998746	+	0.0500579i	$0.0159406\pi$
$643$	1.26806e34i	0.100116i	−0.998746	+	0.0500579i	$0.984059\pi$
$644$	−1.44993e35	−1.12272
$645$	0	0
$646$	5.50436e34	0.410016
$647$	− 3.01852e34i	− 0.220541i	−0.993902	−	0.110271i	$-0.964828\pi$
$647$	− 3.01852e34i	− 0.220541i	0.993902	−	0.110271i	$-0.0351718\pi$
$648$	− 5.82391e34i	− 0.417376i
$649$	−1.12779e35	−0.792811
$650$	0	0
$651$	−2.77816e35	−1.87930
$652$	− 8.26696e34i	− 0.548594i
$653$	1.81062e35i	1.17872i	0.807870	+	0.589361i	$0.200620\pi$
$653$	1.81062e35i	1.17872i	−0.807870	+	0.589361i	$0.799380\pi$
$654$	1.96481e35	1.25487
$655$	0	0
$656$	−7.41493e34	−0.455836
$657$	5.19629e34i	0.313420i
$658$	− 1.96289e35i	− 1.16164i
$659$	2.69289e35	1.56369	0.781847	−	0.623471i	$-0.214278\pi$
$659$	2.69289e35	1.56369	0.781847	+	0.623471i	$0.214278\pi$
$660$	0	0
$661$	3.11605e35	1.74215	0.871075	−	0.491150i	$-0.163423\pi$
$661$	3.11605e35	1.74215	0.871075	+	0.491150i	$0.163423\pi$
$662$	1.47902e35i	0.811424i
$663$	− 1.87353e35i	− 1.00865i
$664$	−3.58738e34	−0.189529
$665$	0	0
$666$	1.33142e35	0.677464
$667$	1.51845e35i	0.758276i
$668$	2.59789e33i	0.0127326i
$669$	−4.85334e35	−2.33461
$670$	0	0
$671$	−2.52828e35	−1.17164
$672$	9.59479e34i	0.436435i
$673$	− 1.24919e35i	− 0.557752i	−0.960327	−	0.278876i	$-0.910038\pi$
$673$	− 1.24919e35i	− 0.557752i	0.960327	−	0.278876i	$-0.0899618\pi$
$674$	−2.05542e35	−0.900848
$675$	0	0
$676$	1.36579e35	0.576834
$677$	− 2.88499e35i	− 1.19615i	−0.801440	−	0.598075i	$-0.795933\pi$
$677$	− 2.88499e35i	− 1.19615i	0.801440	−	0.598075i	$-0.204067\pi$
$678$	− 1.47789e35i	− 0.601549i
$679$	3.32987e35	1.33062
$680$	0	0
$681$	3.74506e35	1.44251
$682$	2.23603e35i	0.845614i
$683$	3.81708e34i	0.141733i	0.997486	+	0.0708667i	$0.0225765\pi$
$683$	3.81708e34i	0.141733i	−0.997486	+	0.0708667i	$0.977423\pi$
$684$	−1.17327e35	−0.427757
$685$	0	0
$686$	5.44540e35	1.91416
$687$	3.57539e34i	0.123414i
$688$	3.84927e34i	0.130474i
$689$	4.63486e35	1.54275
$690$	0	0
$691$	−2.01041e35	−0.645372	−0.322686	−	0.946506i	$-0.604586\pi$
$691$	−2.01041e35	−0.645372	−0.322686	+	0.946506i	$0.604586\pi$
$692$	2.09615e35i	0.660840i
$693$	− 7.20296e35i	− 2.23021i
$694$	−1.10449e35	−0.335867
$695$	0	0
$696$	1.00482e35	0.294764
$697$	3.27515e35i	0.943673i
$698$	1.91148e35i	0.540974i
$699$	−3.66761e35	−1.01957
$700$	0	0
$701$	1.78724e35	0.479411	0.239705	−	0.970846i	$-0.422949\pi$
$701$	1.78724e35	0.479411	0.239705	+	0.970846i	$0.422949\pi$
$702$	− 1.23635e35i	− 0.325781i
$703$	5.43052e35i	1.40572i
$704$	7.72244e34	0.196380
$705$	0	0
$706$	2.71807e35	0.667117
$707$	− 9.48686e35i	− 2.28760i
$708$	1.41439e35i	0.335083i
$709$	−5.59205e33	−0.0130165	−0.00650824	−	0.999979i	$-0.502072\pi$
$709$	−5.59205e33	−0.0130165	−0.00650824	+	0.999979i	$0.502072\pi$
$710$	0	0
$711$	−3.28223e35	−0.737564
$712$	7.92839e34i	0.175059i
$713$	4.23768e35i	0.919409i
$714$	4.23799e35	0.903508
$715$	0	0
$716$	3.04327e35	0.626509
$717$	− 9.31815e35i	− 1.88512i
$718$	− 2.94144e35i	− 0.584795i
$719$	−3.90750e35	−0.763463	−0.381732	−	0.924273i	$-0.624672\pi$
$719$	−3.90750e35	−0.763463	−0.381732	+	0.924273i	$0.624672\pi$
$720$	0	0
$721$	7.56151e35	1.42698
$722$	− 9.73071e34i	− 0.180480i
$723$	6.95501e35i	1.26785i
$724$	3.83080e35	0.686369
$725$	0	0
$726$	−7.96462e35	−1.37866
$727$	9.31579e35i	1.58504i	0.609848	+	0.792518i	$0.291230\pi$
$727$	9.31579e35i	1.58504i	−0.609848	+	0.792518i	$0.708770\pi$
$728$	5.76742e35i	0.964582i
$729$	2.94718e35	0.484520
$730$	0	0
$731$	1.70021e35	0.270107
$732$	3.17077e35i	0.495195i
$733$	2.49884e35i	0.383653i	0.981429	+	0.191826i	$0.0614410\pi$
$733$	2.49884e35i	0.383653i	−0.981429	+	0.191826i	$0.938559\pi$
$734$	3.31634e35	0.500563
$735$	0	0
$736$	1.46354e35	0.213517
$737$	− 1.41763e36i	− 2.03338i
$738$	− 6.98109e35i	− 0.984506i
$739$	1.12909e35	0.156558	0.0782788	−	0.996932i	$-0.475058\pi$
$739$	1.12909e35	0.156558	0.0782788	+	0.996932i	$0.475058\pi$
$740$	0	0
$741$	−1.62885e36	−2.18349
$742$	1.04842e36i	1.38193i
$743$	3.71494e35i	0.481495i	0.970588	+	0.240748i	$0.0773926\pi$
$743$	3.71494e35i	0.481495i	−0.970588	+	0.240748i	$0.922607\pi$
$744$	2.80425e35	0.357401
$745$	0	0
$746$	−6.71643e35	−0.827758
$747$	− 3.37748e35i	− 0.409342i
$748$	− 3.41098e35i	− 0.406545i
$749$	−1.55745e36	−1.82554
$750$	0	0
$751$	−6.99646e35	−0.793194	−0.396597	−	0.917993i	$-0.629809\pi$
$751$	−6.99646e35	−0.793194	−0.396597	+	0.917993i	$0.629809\pi$
$752$	1.98132e35i	0.220918i
$753$	− 9.59403e35i	− 1.05212i
$754$	6.03998e35	0.651469
$755$	0	0
$756$	2.79666e35	0.291821
$757$	− 7.64525e35i	− 0.784681i	−0.919820	−	0.392341i	$-0.871665\pi$
$757$	− 7.64525e35i	− 0.784681i	0.919820	−	0.392341i	$-0.128335\pi$
$758$	− 2.09395e35i	− 0.211399i
$759$	−2.53756e36	−2.51996
$760$	0	0
$761$	−7.74903e35	−0.744628	−0.372314	−	0.928107i	$-0.621436\pi$
$761$	−7.74903e35	−0.744628	−0.372314	+	0.928107i	$0.621436\pi$
$762$	1.85903e35i	0.175731i
$763$	2.67156e36i	2.48432i
$764$	6.51468e35	0.595973
$765$	0	0
$766$	−1.19018e36	−1.05378
$767$	8.50187e35i	0.740581i
$768$	− 9.68490e34i	− 0.0830003i
$769$	1.04301e36	0.879447	0.439723	−	0.898133i	$-0.355077\pi$
$769$	1.04301e36	0.879447	0.439723	+	0.898133i	$0.355077\pi$
$770$	0	0
$771$	−2.36926e36	−1.93389
$772$	− 8.65755e35i	− 0.695310i
$773$	− 1.42237e36i	− 1.12400i	−0.827136	−	0.562002i	$-0.810031\pi$
$773$	− 1.42237e36i	− 1.12400i	0.827136	−	0.562002i	$-0.189969\pi$
$774$	−3.62405e35	−0.281794
$775$	0	0
$776$	−3.36114e35	−0.253055
$777$	4.18114e36i	3.09764i
$778$	3.97487e35i	0.289786i
$779$	2.84741e36	2.04283
$780$	0	0
$781$	−7.22590e35	−0.502058
$782$	− 6.46443e35i	− 0.442024i
$783$	− 2.92882e35i	− 0.197093i
$784$	−9.27131e35	−0.614031
$785$	0	0
$786$	1.01508e36	0.651209
$787$	2.40737e36i	1.52005i	0.649892	+	0.760026i	$0.274814\pi$
$787$	2.40737e36i	1.52005i	−0.649892	+	0.760026i	$0.725186\pi$
$788$	7.37489e35i	0.458330i
$789$	9.49395e35	0.580743
$790$	0	0
$791$	2.00949e36	1.19092
$792$	7.27061e35i	0.424137i
$793$	1.90595e36i	1.09445i
$794$	2.02498e36	1.14463
$795$	0	0
$796$	1.15673e36	0.633604
$797$	− 9.73330e35i	− 0.524845i	−0.964953	−	0.262423i	$-0.915479\pi$
$797$	− 9.73330e35i	− 0.524845i	0.964953	−	0.262423i	$-0.0845215\pi$
$798$	− 3.68450e36i	− 1.95588i
$799$	8.75143e35	0.457345
$800$	0	0
$801$	−7.46450e35	−0.378089
$802$	− 1.83158e35i	− 0.0913368i
$803$	1.31339e36i	0.644834i
$804$	−1.77788e36	−0.859412
$805$	0	0
$806$	1.68563e36	0.789905
$807$	1.55194e36i	0.716072i
$808$	9.57595e35i	0.435051i
$809$	−3.20638e36	−1.43436	−0.717179	−	0.696889i	$-0.754567\pi$
$809$	−3.20638e36	−1.43436	−0.717179	+	0.696889i	$0.754567\pi$
$810$	0	0
$811$	2.99227e36	1.29790	0.648948	−	0.760833i	$-0.275209\pi$
$811$	2.99227e36	1.29790	0.648948	+	0.760833i	$0.275209\pi$
$812$	1.36626e36i	0.583558i
$813$	3.17222e35i	0.133423i
$814$	3.36522e36	1.39383
$815$	0	0
$816$	−4.27779e35	−0.171827
$817$	− 1.47816e36i	− 0.584717i
$818$	1.42461e36i	0.554982i
$819$	−5.42997e36	−2.08328
$820$	0	0
$821$	−4.26235e36	−1.58621	−0.793103	−	0.609087i	$-0.791536\pi$
$821$	−4.26235e36	−1.58621	−0.793103	+	0.609087i	$0.791536\pi$
$822$	2.11033e36i	0.773485i
$823$	− 5.35214e36i	− 1.93210i	−0.258352	−	0.966051i	$-0.583180\pi$
$823$	− 5.35214e36i	− 1.93210i	0.258352	−	0.966051i	$-0.416820\pi$
$824$	−7.63252e35	−0.271380
$825$	0	0
$826$	−1.92315e36	−0.663381
$827$	3.57743e36i	1.21549i	0.794131	+	0.607747i	$0.207926\pi$
$827$	3.57743e36i	1.21549i	−0.794131	+	0.607747i	$0.792074\pi$
$828$	1.37791e36i	0.461150i
$829$	4.26555e36	1.40619	0.703095	−	0.711096i	$-0.251801\pi$
$829$	4.26555e36	1.40619	0.703095	+	0.711096i	$0.251801\pi$
$830$	0	0
$831$	−5.13534e36	−1.64269
$832$	− 5.82158e35i	− 0.183442i
$833$	4.09511e36i	1.27117i
$834$	−1.31121e36	−0.400955
$835$	0	0
$836$	−2.96550e36	−0.880075
$837$	− 8.17374e35i	− 0.238975i
$838$	− 6.75250e35i	− 0.194498i
$839$	5.62994e36	1.59764	0.798820	−	0.601570i	$-0.205458\pi$
$839$	5.62994e36	1.59764	0.798820	+	0.601570i	$0.205458\pi$
$840$	0	0
$841$	−2.19953e36	−0.605871
$842$	− 1.88353e36i	− 0.511177i
$843$	− 8.98045e36i	− 2.40134i
$844$	−3.43225e36	−0.904269
$845$	0	0
$846$	−1.86540e36	−0.477135
$847$	− 1.08295e37i	− 2.72940i
$848$	− 1.05827e36i	− 0.262813i
$849$	9.10706e36	2.22860
$850$	0	0
$851$	6.37771e36	1.51546
$852$	9.06217e35i	0.212196i
$853$	4.55647e36i	1.05139i	0.850672	+	0.525697i	$0.176195\pi$
$853$	4.55647e36i	1.05139i	−0.850672	+	0.525697i	$0.823805\pi$
$854$	−4.31131e36	−0.980361
$855$	0	0
$856$	1.57208e36	0.347178
$857$	7.95266e35i	0.173082i	0.996248	+	0.0865411i	$0.0275814\pi$
$857$	7.95266e35i	0.173082i	−0.996248	+	0.0865411i	$0.972419\pi$
$858$	1.00937e37i	2.16501i
$859$	−1.26545e36	−0.267505	−0.133752	−	0.991015i	$-0.542703\pi$
$859$	−1.26545e36	−0.267505	−0.133752	+	0.991015i	$0.542703\pi$
$860$	0	0
$861$	2.19231e37	4.50156
$862$	− 2.90003e36i	− 0.586896i
$863$	3.32635e36i	0.663487i	0.943370	+	0.331744i	$0.107637\pi$
$863$	3.32635e36i	0.663487i	−0.943370	+	0.331744i	$0.892363\pi$
$864$	−2.82292e35	−0.0554979
$865$	0	0
$866$	−7.14496e35	−0.136467
$867$	− 5.16456e36i	− 0.972288i
$868$	3.81296e36i	0.707563i
$869$	−8.29600e36	−1.51747
$870$	0	0
$871$	−1.06868e37	−1.89942
$872$	− 2.69665e36i	− 0.472463i
$873$	− 3.16448e36i	− 0.546543i
$874$	−5.62016e36	−0.956877
$875$	0	0
$876$	1.64715e36	0.272541
$877$	− 5.26043e36i	− 0.858078i	−0.903286	−	0.429039i	$-0.858852\pi$
$877$	− 5.26043e36i	− 0.858078i	0.903286	−	0.429039i	$-0.141148\pi$
$878$	− 4.03012e36i	− 0.648093i
$879$	4.15838e36	0.659269
$880$	0	0
$881$	5.34809e36	0.824137	0.412069	−	0.911153i	$-0.364806\pi$
$881$	5.34809e36	0.824137	0.412069	+	0.911153i	$0.364806\pi$
$882$	− 8.72885e36i	− 1.32617i
$883$	3.32166e36i	0.497560i	0.968560	+	0.248780i	$0.0800297\pi$
$883$	3.32166e36i	0.497560i	−0.968560	+	0.248780i	$0.919970\pi$
$884$	−2.57137e36	−0.379762
$885$	0	0
$886$	3.95925e36	0.568449
$887$	− 8.17924e36i	− 1.15789i	−0.815366	−	0.578945i	$-0.803464\pi$
$887$	− 8.17924e36i	− 1.15789i	0.815366	−	0.578945i	$-0.196536\pi$
$888$	− 4.22040e36i	− 0.589104i
$889$	−2.52773e36	−0.347904
$890$	0	0
$891$	1.38589e37	1.85464
$892$	6.66109e36i	0.878991i
$893$	− 7.60848e36i	− 0.990045i
$894$	2.66917e36	0.342498
$895$	0	0
$896$	1.31686e36	0.164320
$897$	1.91295e37i	2.35395i
$898$	2.35204e36i	0.285423i
$899$	3.99315e36	0.477881
$900$	0	0
$901$	−4.67433e36	−0.544076
$902$	− 1.76450e37i	− 2.02554i
$903$	− 1.13808e37i	− 1.28848i
$904$	−2.02837e36	−0.226486
$905$	0	0
$906$	5.76779e35	0.0626480
$907$	1.71298e37i	1.83511i	0.397615	+	0.917553i	$0.369838\pi$
$907$	1.71298e37i	1.83511i	−0.397615	+	0.917553i	$0.630162\pi$
$908$	− 5.14000e36i	− 0.543113i
$909$	−9.01567e36	−0.939614
$910$	0	0
$911$	6.12131e36	0.620676	0.310338	−	0.950626i	$-0.399558\pi$
$911$	6.12131e36	0.620676	0.310338	+	0.950626i	$0.399558\pi$
$912$	3.71910e36i	0.371966i
$913$	− 8.53675e36i	− 0.842186i
$914$	1.30828e37	1.27313
$915$	0	0
$916$	4.90714e35	0.0464660
$917$	1.38022e37i	1.28923i
$918$	1.24687e36i	0.114892i
$919$	1.52693e36	0.138795	0.0693977	−	0.997589i	$-0.477892\pi$
$919$	1.52693e36	0.138795	0.0693977	+	0.997589i	$0.477892\pi$
$920$	0	0
$921$	−2.51192e37	−2.22208
$922$	− 8.81109e36i	− 0.768941i
$923$	5.44726e36i	0.468983i
$924$	−2.28323e37	−1.93933
$925$	0	0
$926$	−2.69165e36	−0.222526
$927$	− 7.18595e36i	− 0.586121i
$928$	− 1.37909e36i	− 0.110980i
$929$	−1.93910e36	−0.153959	−0.0769793	−	0.997033i	$-0.524528\pi$
$929$	−1.93910e36	−0.153959	−0.0769793	+	0.997033i	$0.524528\pi$
$930$	0	0
$931$	3.56028e37	2.75178
$932$	5.03370e36i	0.383874i
$933$	8.83914e34i	0.00665104i
$934$	7.88887e35	0.0585705
$935$	0	0
$936$	5.48097e36	0.396195
$937$	1.01514e37i	0.724069i	0.932165	+	0.362035i	$0.117918\pi$
$937$	1.01514e37i	0.724069i	−0.932165	+	0.362035i	$0.882082\pi$
$938$	− 2.41739e37i	− 1.70142i
$939$	1.40090e37	0.972944
$940$	0	0
$941$	4.58463e36	0.310051	0.155026	−	0.987910i	$-0.450454\pi$
$941$	4.58463e36	0.310051	0.155026	+	0.987910i	$0.450454\pi$
$942$	3.56087e36i	0.237640i
$943$	− 3.34405e37i	− 2.20230i
$944$	1.94121e36	0.126160
$945$	0	0
$946$	−9.15996e36	−0.579768
$947$	− 2.00468e37i	− 1.25219i	−0.779748	−	0.626094i	$-0.784653\pi$
$947$	− 2.00468e37i	− 1.25219i	0.779748	−	0.626094i	$-0.215347\pi$
$948$	1.04042e37i	0.641364i
$949$	9.90099e36	0.602353
$950$	0	0
$951$	2.97905e37	1.76531
$952$	− 5.81653e36i	− 0.340175i
$953$	2.53894e37i	1.46552i	0.680489	+	0.732758i	$0.261767\pi$
$953$	2.53894e37i	1.46552i	−0.680489	+	0.732758i	$0.738233\pi$
$954$	9.96348e36	0.567619
$955$	0	0
$956$	−1.27889e37	−0.709758
$957$	2.39114e37i	1.30980i
$958$	1.60018e37i	0.865168i
$959$	−2.86942e37	−1.53131
$960$	0	0
$961$	−8.08873e36	−0.420570
$962$	− 2.53688e37i	− 1.30200i
$963$	1.48010e37i	0.749827i
$964$	9.54557e36	0.477352
$965$	0	0
$966$	−4.32715e37	−2.10857
$967$	3.53299e37i	1.69946i	0.527216	+	0.849731i	$0.323236\pi$
$967$	3.53299e37i	1.69946i	−0.527216	+	0.849731i	$0.676764\pi$
$968$	1.09312e37i	0.519072i
$969$	1.64272e37	0.770043
$970$	0	0
$971$	−2.42162e37	−1.10628	−0.553141	−	0.833088i	$-0.686571\pi$
$971$	−2.42162e37	−1.10628	−0.553141	+	0.833088i	$0.686571\pi$
$972$	− 1.39002e37i	− 0.626894i
$973$	− 1.78285e37i	− 0.793789i
$974$	1.71082e37	0.751998
$975$	0	0
$976$	4.35180e36	0.186443
$977$	− 2.74750e36i	− 0.116213i	−0.998310	−	0.0581066i	$-0.981494\pi$
$977$	− 2.74750e36i	− 0.116213i	0.998310	−	0.0581066i	$-0.0185063\pi$
$978$	− 2.46718e37i	− 1.03030i
$979$	−1.88669e37	−0.777887
$980$	0	0
$981$	2.53887e37	1.02042
$982$	5.75695e36i	0.228454i
$983$	− 2.03235e37i	− 0.796303i	−0.917320	−	0.398152i	$-0.869652\pi$
$983$	− 2.03235e37i	− 0.796303i	0.917320	−	0.398152i	$-0.130348\pi$
$984$	−2.21290e37	−0.856099
$985$	0	0
$986$	−6.09141e36	−0.229751
$987$	− 5.85802e37i	− 2.18166i
$988$	2.23555e37i	0.822096i
$989$	−1.73598e37	−0.630363
$990$	0	0
$991$	1.72765e37	0.611695	0.305847	−	0.952081i	$-0.401060\pi$
$991$	1.72765e37	0.611695	0.305847	+	0.952081i	$0.401060\pi$
$992$	− 3.84877e36i	− 0.134563i
$993$	4.41396e37i	1.52392i
$994$	−1.23219e37	−0.420095
$995$	0	0
$996$	−1.07061e37	−0.355952
$997$	− 7.90582e36i	− 0.259572i	−0.991542	−	0.129786i	$-0.958571\pi$
$997$	− 7.90582e36i	− 0.259572i	0.991542	−	0.129786i	$-0.0414290\pi$
$998$	3.56177e36i	0.115487i
$999$	−1.23015e37	−0.393903

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.b.h.49.1		10
5.2	odd	4		50.26.a.j.1.1	yes	5
5.3	odd	4		50.26.a.i.1.5	✓	5
5.4	even	2	inner	50.26.b.h.49.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.26.a.i.1.5	✓	5	5.3	odd	4
50.26.a.j.1.1	yes	5	5.2	odd	4
50.26.b.h.49.1		10	1.1	even	1	trivial
50.26.b.h.49.10		10	5.4	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-4096.00i q^{2} -1.22241e6i q^{3} -1.67772e7 q^{4} -5.00697e9 q^{6} -6.80801e10i q^{7} +6.87195e10i q^{8} -6.46987e11 q^{9} -1.63529e13 q^{11} +2.05086e13i q^{12} +1.23277e14i q^{13} -2.78856e14 q^{14} +2.81475e14 q^{16} -1.24327e15i q^{17} +2.65006e15i q^{18} -1.08089e16 q^{19} -8.32215e16 q^{21} +6.69815e16i q^{22} +1.26942e17i q^{23} +8.40031e16 q^{24} +5.04942e17 q^{26} -2.44849e17i q^{27} +1.14219e18i q^{28} +1.19617e18 q^{29} +3.33827e18 q^{31} -1.15292e18i q^{32} +1.99899e19i q^{33} -5.09242e18 q^{34} +1.08546e19 q^{36} -5.02410e19i q^{37} +4.42734e19i q^{38} +1.50694e20 q^{39} -2.63431e20 q^{41} +3.40875e20i q^{42} +1.36754e20i q^{43} +2.74356e20 q^{44} +5.19955e20 q^{46} +7.03907e20i q^{47} -3.44077e20i q^{48} -3.29383e21 q^{49} -1.51978e21 q^{51} -2.06824e21i q^{52} -3.75972e21i q^{53} -1.00290e21 q^{54} +4.67843e21 q^{56} +1.32129e22i q^{57} -4.89952e21i q^{58} +6.89657e21 q^{59} +1.54607e22 q^{61} -1.36736e22i q^{62} +4.40470e22i q^{63} -4.72237e21 q^{64} +8.18786e22 q^{66} +8.66895e22i q^{67} +2.08585e22i q^{68} +1.55175e23 q^{69} +4.41872e22 q^{71} -4.44606e22i q^{72} -8.03151e22i q^{73} -2.05787e23 q^{74} +1.81344e23 q^{76} +1.11331e24i q^{77} -6.17244e23i q^{78} +5.07310e23 q^{79} -8.47490e23 q^{81} +1.07901e24i q^{82} +5.22032e23i q^{83} +1.39623e24 q^{84} +5.60143e23 q^{86} -1.46221e24i q^{87} -1.12376e24i q^{88} +1.15373e24 q^{89} +8.39270e24 q^{91} -2.12974e24i q^{92} -4.08072e24i q^{93} +2.88320e24 q^{94} -1.40934e24 q^{96} +4.89110e24i q^{97} +1.34915e25i q^{98} +1.05801e25 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 167772160 q^{4} + 5930967040 q^{6} - 1950750722780 q^{9} - 17674067967630 q^{11} - 403201115668480 q^{14} + 28\!\cdots\!60 q^{16} - 13\!\cdots\!50 q^{19} - 11\!\cdots\!80 q^{21} - 99\!\cdots\!40 q^{24}+ \cdots + 46\!\cdots\!40 q^{99}+O(q^{100}) \) 10 * q - 167772160 * q^4 + 5930967040 * q^6 - 1950750722780 * q^9 - 17674067967630 * q^11 - 403201115668480 * q^14 + 2814749767106560 * q^16 - 13656410902154450 * q^19 - 112914117637521980 * q^21 - 99505115118960640 * q^24 + 553861034690314240 * q^26 - 5233921758503439600 * q^29 + 2763842594495258420 * q^31 - 12643869681446215680 * q^34 + 32728166238236180480 * q^36 + 152836894182107254040 * q^39 + 221293530514434412770 * q^41 + 296521655891609518080 * q^44 + 1438969030306499543040 * q^46 - 9942833167487211475170 * q^49 - 1909885137421531933230 * q^51 - 9030562925524734976000 * q^54 + 6764592209011073351680 * q^56 - 66083072776331191921200 * q^59 - 23179743393488009953180 * q^61 - 47223664828696452136960 * q^64 + 120286140832874083246080 * q^66 - 135923250107652130550460 * q^69 + 355679240938654866836520 * q^71 - 557504464959852709396480 * q^74 + 229116555490200073011200 * q^76 + 440397207411103561820500 * q^79 - 3190456286426028454480390 * q^81 + 1894384541054115963207680 * q^84 - 1385876056255558046351360 * q^86 + 11864662755859110806369850 * q^89 + 6710519214620433441429520 * q^91 + 13547865247217718455992320 * q^94 + 1669418809455668352778240 * q^96 + 46393873036575245993852340 * q^99

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