LMFDB - Embedded newform 841.2.b.e.840.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [841,2,Mod(840,841)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(841, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("841.840");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.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:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.7877952219361.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3x^{11} + 13x^{9} - 18x^{8} - 14x^{7} + 57x^{6} - 28x^{5} - 72x^{4} + 104x^{3} - 96x + 64 $ x^12 - 3x^11 + 13x^9 - 18x^8 - 14x^7 + 57x^6 - 28x^5 - 72x^4 + 104x^3 - 96*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			840.12
Root			$0.911180 - 1.08155i$ of defining polynomial
Character	$\chi$	$=$	841.840
Dual form			841.2.b.e.840.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.60244i q^{2} +0.439339i q^{3} -4.77269 q^{4} -2.58042 q^{5} -1.14335 q^{6} +0.0751311 q^{7} -7.21577i q^{8} +2.80698 q^{9} -6.71540i q^{10} -3.77836i q^{11} -2.09683i q^{12} -0.880995 q^{13} +0.195524i q^{14} -1.13368i q^{15} +9.23322 q^{16} -3.94108i q^{17} +7.30500i q^{18} -0.713617i q^{19} +12.3156 q^{20} +0.0330080i q^{21} +9.83294 q^{22} +1.17764 q^{23} +3.17017 q^{24} +1.65858 q^{25} -2.29274i q^{26} +2.55123i q^{27} -0.358578 q^{28} +2.95033 q^{30} -5.15087i q^{31} +9.59735i q^{32} +1.65998 q^{33} +10.2564 q^{34} -0.193870 q^{35} -13.3969 q^{36} -3.08751i q^{37} +1.85714 q^{38} -0.387055i q^{39} +18.6197i q^{40} +6.67122i q^{41} -0.0859013 q^{42} +8.31364i q^{43} +18.0329i q^{44} -7.24320 q^{45} +3.06474i q^{46} -10.5920i q^{47} +4.05651i q^{48} -6.99436 q^{49} +4.31637i q^{50} +1.73147 q^{51} +4.20472 q^{52} +5.55608 q^{53} -6.63943 q^{54} +9.74976i q^{55} -0.542129i q^{56} +0.313519 q^{57} +9.91885 q^{59} +5.41071i q^{60} -3.56734i q^{61} +13.4048 q^{62} +0.210892 q^{63} -6.51010 q^{64} +2.27334 q^{65} +4.31999i q^{66} -4.93956 q^{67} +18.8096i q^{68} +0.517383i q^{69} -0.504535i q^{70} -4.90681 q^{71} -20.2545i q^{72} -8.90215i q^{73} +8.03505 q^{74} +0.728681i q^{75} +3.40587i q^{76} -0.283872i q^{77} +1.00729 q^{78} -13.1895i q^{79} -23.8256 q^{80} +7.30009 q^{81} -17.3615 q^{82} +16.9864 q^{83} -0.157537i q^{84} +10.1697i q^{85} -21.6357 q^{86} -27.2637 q^{88} -6.79655i q^{89} -18.8500i q^{90} -0.0661901 q^{91} -5.62052 q^{92} +2.26298 q^{93} +27.5652 q^{94} +1.84143i q^{95} -4.21649 q^{96} -11.4171i q^{97} -18.2024i q^{98} -10.6058i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} - 8 q^{5} - 24 q^{6} + 10 q^{7} - 10 q^{9} - 12 q^{13} + 16 q^{16} + 24 q^{20} + 38 q^{22} + 30 q^{23} + 10 q^{24} - 8 q^{25} + 12 q^{28} + 2 q^{30} + 4 q^{33} - 6 q^{34} - 44 q^{35} + 16 q^{36}+ \cdots + 58 q^{96}+O(q^{100}) $ 12 * q - 8 * q^4 - 8 * q^5 - 24 * q^6 + 10 * q^7 - 10 * q^9 - 12 * q^13 + 16 * q^16 + 24 * q^20 + 38 * q^22 + 30 * q^23 + 10 * q^24 - 8 * q^25 + 12 * q^28 + 2 * q^30 + 4 * q^33 - 6 * q^34 - 44 * q^35 + 16 * q^36 - 6 * q^42 - 12 * q^45 + 6 * q^49 - 8 * q^51 - 6 * q^52 + 32 * q^53 + 32 * q^54 - 14 * q^57 + 44 * q^59 + 16 * q^62 - 34 * q^63 + 2 * q^64 + 8 * q^65 - 30 * q^67 - 70 * q^71 + 56 * q^74 - 4 * q^78 - 34 * q^80 + 8 * q^81 - 62 * q^82 + 82 * q^83 - 44 * q^86 - 66 * q^88 + 32 * q^91 + 22 * q^92 + 12 * q^93 + 10 * q^94 + 58 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	2.60244i	1.84020i	0.391680	+	0.920101i	$0.371894\pi$
$2$	2.60244i	1.84020i	−0.391680	+	0.920101i	$0.628106\pi$
$3$	0.439339i	0.253652i	0.991925	+	0.126826i	$0.0404790\pi$
$3$	0.439339i	0.253652i	−0.991925	+	0.126826i	$0.959521\pi$
$4$	−4.77269	−2.38635
$5$	−2.58042	−1.15400	−0.577000	−	0.816744i	$-0.695777\pi$
$5$	−2.58042	−1.15400	−0.577000	+	0.816744i	$0.695777\pi$
$6$	−1.14335	−0.466772
$7$	0.0751311	0.0283969	0.0141984	−	0.999899i	$-0.495480\pi$
$7$	0.0751311	0.0283969	0.0141984	+	0.999899i	$0.495480\pi$
$8$	− 7.21577i	− 2.55116i
$9$	2.80698	0.935660
$10$	− 6.71540i	− 2.12359i
$11$	− 3.77836i	− 1.13922i	−0.821916	−	0.569609i	$-0.807095\pi$
$11$	− 3.77836i	− 1.13922i	0.821916	−	0.569609i	$-0.192905\pi$
$12$	− 2.09683i	− 0.605302i
$13$	−0.880995	−0.244344	−0.122172	−	0.992509i	$-0.538986\pi$
$13$	−0.880995	−0.244344	−0.122172	+	0.992509i	$0.538986\pi$
$14$	0.195524i	0.0522560i
$15$	− 1.13368i	− 0.292715i
$16$	9.23322	2.30830
$17$	− 3.94108i	− 0.955854i	−0.878400	−	0.477927i	$-0.841388\pi$
$17$	− 3.94108i	− 0.955854i	0.878400	−	0.477927i	$-0.158612\pi$
$18$	7.30500i	1.72181i
$19$	− 0.713617i	− 0.163715i	−0.996644	−	0.0818574i	$-0.973915\pi$
$19$	− 0.713617i	− 0.163715i	0.996644	−	0.0818574i	$-0.0260852\pi$
$20$	12.3156	2.75385
$21$	0.0330080i	0.00720294i
$22$	9.83294	2.09639
$23$	1.17764	0.245555	0.122778	−	0.992434i	$-0.460820\pi$
$23$	1.17764	0.245555	0.122778	+	0.992434i	$0.460820\pi$
$24$	3.17017	0.647108
$25$	1.65858	0.331717
$26$	− 2.29274i	− 0.449643i
$27$	2.55123i	0.490985i
$28$	−0.358578	−0.0677648
$29$	0	0
$29$	0	0
$30$	2.95033	0.538655
$31$	− 5.15087i	− 0.925124i	−0.886587	−	0.462562i	$-0.846930\pi$
$31$	− 5.15087i	− 0.925124i	0.886587	−	0.462562i	$-0.153070\pi$
$32$	9.59735i	1.69659i
$33$	1.65998	0.288965
$34$	10.2564	1.75896
$35$	−0.193870	−0.0327700
$36$	−13.3969	−2.23281
$37$	− 3.08751i	− 0.507583i	−0.967259	−	0.253791i	$-0.918322\pi$
$37$	− 3.08751i	− 0.507583i	0.967259	−	0.253791i	$-0.0816777\pi$
$38$	1.85714	0.301269
$39$	− 0.387055i	− 0.0619785i
$40$	18.6197i	2.94404i
$41$	6.67122i	1.04187i	0.853596	+	0.520935i	$0.174417\pi$
$41$	6.67122i	1.04187i	−0.853596	+	0.520935i	$0.825583\pi$
$42$	−0.0859013	−0.0132549
$43$	8.31364i	1.26782i	0.773408	+	0.633909i	$0.218551\pi$
$43$	8.31364i	1.26782i	−0.773408	+	0.633909i	$0.781449\pi$
$44$	18.0329i	2.71857i
$45$	−7.24320	−1.07975
$46$	3.06474i	0.451871i
$47$	− 10.5920i	− 1.54501i	−0.635010	−	0.772504i	$-0.719004\pi$
$47$	− 10.5920i	− 1.54501i	0.635010	−	0.772504i	$-0.280996\pi$
$48$	4.05651i	0.585507i
$49$	−6.99436	−0.999194
$50$	4.31637i	0.610427i
$51$	1.73147	0.242454
$52$	4.20472	0.583090
$53$	5.55608	0.763186	0.381593	−	0.924331i	$-0.375376\pi$
$53$	5.55608	0.763186	0.381593	+	0.924331i	$0.375376\pi$
$54$	−6.63943	−0.903512
$55$	9.74976i	1.31466i
$56$	− 0.542129i	− 0.0724450i
$57$	0.313519	0.0415267
$58$	0	0
$59$	9.91885	1.29132	0.645662	−	0.763623i	$-0.276582\pi$
$59$	9.91885	1.29132	0.645662	+	0.763623i	$0.276582\pi$
$60$	5.41071i	0.698519i
$61$	− 3.56734i	− 0.456751i	−0.973573	−	0.228375i	$-0.926659\pi$
$61$	− 3.56734i	− 0.456751i	0.973573	−	0.228375i	$-0.0733413\pi$
$62$	13.4048	1.70242
$63$	0.210892	0.0265698
$64$	−6.51010	−0.813763
$65$	2.27334	0.281973
$66$	4.31999i	0.531754i
$67$	−4.93956	−0.603464	−0.301732	−	0.953393i	$-0.597565\pi$
$67$	−4.93956	−0.603464	−0.301732	+	0.953393i	$0.597565\pi$
$68$	18.8096i	2.28100i
$69$	0.517383i	0.0622856i
$70$	− 0.504535i	− 0.0603035i
$71$	−4.90681	−0.582331	−0.291166	−	0.956673i	$-0.594043\pi$
$71$	−4.90681	−0.582331	−0.291166	+	0.956673i	$0.594043\pi$
$72$	− 20.2545i	− 2.38702i
$73$	− 8.90215i	− 1.04192i	−0.853582	−	0.520959i	$-0.825574\pi$
$73$	− 8.90215i	− 1.04192i	0.853582	−	0.520959i	$-0.174426\pi$
$74$	8.03505	0.934056
$75$	0.728681i	0.0841408i
$76$	3.40587i	0.390680i
$77$	− 0.283872i	− 0.0323502i
$78$	1.00729	0.114053
$79$	− 13.1895i	− 1.48394i	−0.670435	−	0.741969i	$-0.733892\pi$
$79$	− 13.1895i	− 1.48394i	0.670435	−	0.741969i	$-0.266108\pi$
$80$	−23.8256	−2.66378
$81$	7.30009	0.811121
$82$	−17.3615	−1.91725
$83$	16.9864	1.86450	0.932249	−	0.361818i	$-0.117844\pi$
$83$	16.9864	1.86450	0.932249	+	0.361818i	$0.117844\pi$
$84$	− 0.157537i	− 0.0171887i
$85$	10.1697i	1.10306i
$86$	−21.6357	−2.33304
$87$	0	0
$88$	−27.2637	−2.90632
$89$	− 6.79655i	− 0.720433i	−0.932869	−	0.360216i	$-0.882703\pi$
$89$	− 6.79655i	− 0.720433i	0.932869	−	0.360216i	$-0.117297\pi$
$90$	− 18.8500i	− 1.98696i
$91$	−0.0661901	−0.00693861
$92$	−5.62052	−0.585980
$93$	2.26298	0.234660
$94$	27.5652	2.84313
$95$	1.84143i	0.188927i
$96$	−4.21649	−0.430344
$97$	− 11.4171i	− 1.15923i	−0.814890	−	0.579615i	$-0.803203\pi$
$97$	− 11.4171i	− 1.15923i	0.814890	−	0.579615i	$-0.196797\pi$
$98$	− 18.2024i	− 1.83872i
$99$	− 10.6058i	− 1.06592i
$100$	−7.91592	−0.791592
$101$	− 9.43826i	− 0.939142i	−0.882895	−	0.469571i	$-0.844409\pi$
$101$	− 9.43826i	− 0.939142i	0.882895	−	0.469571i	$-0.155591\pi$
$102$	4.50605i	0.446165i
$103$	−9.18317	−0.904845	−0.452422	−	0.891804i	$-0.649440\pi$
$103$	−9.18317	−0.904845	−0.452422	+	0.891804i	$0.649440\pi$
$104$	6.35706i	0.623361i
$105$	− 0.0851746i	− 0.00831219i
$106$	14.4594i	1.40442i
$107$	−4.86820	−0.470627	−0.235313	−	0.971920i	$-0.575612\pi$
$107$	−4.86820	−0.470627	−0.235313	+	0.971920i	$0.575612\pi$
$108$	− 12.1762i	− 1.17166i
$109$	−4.33423	−0.415144	−0.207572	−	0.978220i	$-0.566556\pi$
$109$	−4.33423	−0.415144	−0.207572	+	0.978220i	$0.566556\pi$
$110$	−25.3732	−2.41924
$111$	1.35646	0.128750
$112$	0.693702	0.0655486
$113$	4.52309i	0.425496i	0.977107	+	0.212748i	$0.0682414\pi$
$113$	4.52309i	0.425496i	−0.977107	+	0.212748i	$0.931759\pi$
$114$	0.815916i	0.0764175i
$115$	−3.03881	−0.283371
$116$	0	0
$117$	−2.47294	−0.228623
$118$	25.8132i	2.37630i
$119$	− 0.296098i	− 0.0271433i
$120$	−8.18037	−0.746762
$121$	−3.27597	−0.297816
$122$	9.28378	0.840514
$123$	−2.93093	−0.264273
$124$	24.5835i	2.20767i
$125$	8.62227	0.771199
$126$	0.548833i	0.0488939i
$127$	− 5.83762i	− 0.518005i	−0.965877	−	0.259003i	$-0.916606\pi$
$127$	− 5.83762i	− 0.518005i	0.965877	−	0.259003i	$-0.0833939\pi$
$128$	2.25255i	0.199099i
$129$	−3.65250	−0.321585
$130$	5.91623i	0.518888i
$131$	− 6.62441i	− 0.578777i	−0.957212	−	0.289389i	$-0.906548\pi$
$131$	− 6.62441i	− 0.578777i	0.957212	−	0.289389i	$-0.0934520\pi$
$132$	−7.92257	−0.689571
$133$	− 0.0536148i	− 0.00464899i
$134$	− 12.8549i	− 1.11050i
$135$	− 6.58326i	− 0.566597i
$136$	−28.4380	−2.43853
$137$	− 1.55881i	− 0.133178i	−0.997780	−	0.0665890i	$-0.978788\pi$
$137$	− 1.55881i	− 0.133178i	0.997780	−	0.0665890i	$-0.0212116\pi$
$138$	−1.34646	−0.114618
$139$	10.6416	0.902607	0.451303	−	0.892371i	$-0.350959\pi$
$139$	10.6416	0.902607	0.451303	+	0.892371i	$0.350959\pi$
$140$	0.925282	0.0782006
$141$	4.65349	0.391895
$142$	− 12.7697i	− 1.07161i
$143$	3.32871i	0.278361i
$144$	25.9175	2.15979
$145$	0	0
$146$	23.1673	1.91734
$147$	− 3.07289i	− 0.253448i
$148$	14.7357i	1.21127i
$149$	−5.43253	−0.445050	−0.222525	−	0.974927i	$-0.571430\pi$
$149$	−5.43253	−0.445050	−0.222525	+	0.974927i	$0.571430\pi$
$150$	−1.89635	−0.154836
$151$	−17.8418	−1.45194	−0.725971	−	0.687725i	$-0.758610\pi$
$151$	−17.8418	−1.45194	−0.725971	+	0.687725i	$0.758610\pi$
$152$	−5.14929	−0.417663
$153$	− 11.0626i	− 0.894354i
$154$	0.738760	0.0595310
$155$	13.2914i	1.06759i
$156$	1.84730i	0.147902i
$157$	9.46360i	0.755278i	0.925953	+	0.377639i	$0.123264\pi$
$157$	9.46360i	0.755278i	−0.925953	+	0.377639i	$0.876736\pi$
$158$	34.3249	2.73075
$159$	2.44100i	0.193584i
$160$	− 24.7652i	− 1.95786i
$161$	0.0884774	0.00697300
$162$	18.9980i	1.49263i
$163$	10.4578i	0.819116i	0.912284	+	0.409558i	$0.134317\pi$
$163$	10.4578i	0.819116i	−0.912284	+	0.409558i	$0.865683\pi$
$164$	− 31.8397i	− 2.48626i
$165$	−4.28345	−0.333466
$166$	44.2060i	3.43105i
$167$	−0.170436	−0.0131888	−0.00659438	−	0.999978i	$-0.502099\pi$
$167$	−0.170436	−0.0131888	−0.00659438	+	0.999978i	$0.502099\pi$
$168$	0.238178	0.0183758
$169$	−12.2238	−0.940296
$170$	−26.4659	−2.02985
$171$	− 2.00311i	− 0.153182i
$172$	− 39.6785i	− 3.02545i
$173$	12.0694	0.917616	0.458808	−	0.888535i	$-0.348277\pi$
$173$	12.0694	0.917616	0.458808	+	0.888535i	$0.348277\pi$
$174$	0	0
$175$	0.124611	0.00941973
$176$	− 34.8864i	− 2.62966i
$177$	4.35773i	0.327547i
$178$	17.6876	1.32574
$179$	1.67483	0.125183	0.0625913	−	0.998039i	$-0.480064\pi$
$179$	1.67483	0.125183	0.0625913	+	0.998039i	$0.480064\pi$
$180$	34.5696	2.57666
$181$	−15.3626	−1.14190	−0.570948	−	0.820986i	$-0.693424\pi$
$181$	−15.3626	−1.14190	−0.570948	+	0.820986i	$0.693424\pi$
$182$	− 0.172256i	− 0.0127685i
$183$	1.56727	0.115856
$184$	− 8.49758i	− 0.626450i
$185$	7.96707i	0.585751i
$186$	5.88926i	0.431822i
$187$	−14.8908	−1.08892
$188$	50.5526i	3.68693i
$189$	0.191677i	0.0139424i
$190$	−4.79222	−0.347664
$191$	− 20.4783i	− 1.48176i	−0.671640	−	0.740878i	$-0.734410\pi$
$191$	− 20.4783i	− 1.48176i	0.671640	−	0.740878i	$-0.265590\pi$
$192$	− 2.86014i	− 0.206413i
$193$	3.13441i	0.225620i	0.993617	+	0.112810i	$0.0359851\pi$
$193$	3.13441i	0.225620i	−0.993617	+	0.112810i	$0.964015\pi$
$194$	29.7123	2.13322
$195$	0.998767i	0.0715232i
$196$	33.3819	2.38442
$197$	2.84040	0.202370	0.101185	−	0.994868i	$-0.467737\pi$
$197$	2.84040	0.202370	0.101185	+	0.994868i	$0.467737\pi$
$198$	27.6009	1.96151
$199$	−19.1189	−1.35530	−0.677652	−	0.735383i	$-0.737002\pi$
$199$	−19.1189	−1.35530	−0.677652	+	0.735383i	$0.737002\pi$
$200$	− 11.9680i	− 0.846263i
$201$	− 2.17014i	− 0.153070i
$202$	24.5625	1.72821
$203$	0	0
$204$	−8.26378	−0.578580
$205$	− 17.2146i	− 1.20232i
$206$	− 23.8987i	− 1.66510i
$207$	3.30562	0.229756
$208$	−8.13442	−0.564021
$209$	−2.69630	−0.186507
$210$	0.221662	0.0152961
$211$	17.8936i	1.23184i	0.787807	+	0.615922i	$0.211216\pi$
$211$	17.8936i	1.23184i	−0.787807	+	0.615922i	$0.788784\pi$
$212$	−26.5174	−1.82123
$213$	− 2.15575i	− 0.147710i
$214$	− 12.6692i	− 0.866049i
$215$	− 21.4527i	− 1.46306i
$216$	18.4091	1.25258
$217$	− 0.386991i	− 0.0262706i
$218$	− 11.2796i	− 0.763949i
$219$	3.91106	0.264285
$220$	− 46.5326i	− 3.13723i
$221$	3.47208i	0.233557i
$222$	3.53011i	0.236925i
$223$	17.7308	1.18735	0.593673	−	0.804707i	$-0.297677\pi$
$223$	17.7308	1.18735	0.593673	+	0.804707i	$0.297677\pi$
$224$	0.721060i	0.0481778i
$225$	4.65562	0.310374
$226$	−11.7711	−0.783000
$227$	22.2116	1.47424	0.737119	−	0.675763i	$-0.236186\pi$
$227$	22.2116	1.47424	0.737119	+	0.675763i	$0.236186\pi$
$228$	−1.49633	−0.0990970
$229$	− 9.96812i	− 0.658712i	−0.944206	−	0.329356i	$-0.893168\pi$
$229$	− 9.96812i	− 0.658712i	0.944206	−	0.329356i	$-0.106832\pi$
$230$	− 7.90832i	− 0.521459i
$231$	0.124716	0.00820571
$232$	0	0
$233$	−20.0765	−1.31525	−0.657627	−	0.753344i	$-0.728440\pi$
$233$	−20.0765	−1.31525	−0.657627	+	0.753344i	$0.728440\pi$
$234$	− 6.43567i	− 0.420713i
$235$	27.3320i	1.78294i
$236$	−47.3396	−3.08155
$237$	5.79467	0.376404
$238$	0.770577	0.0499491
$239$	−1.18085	−0.0763830	−0.0381915	−	0.999270i	$-0.512160\pi$
$239$	−1.18085	−0.0763830	−0.0381915	+	0.999270i	$0.512160\pi$
$240$	− 10.4675i	− 0.675675i
$241$	−11.8311	−0.762110	−0.381055	−	0.924552i	$-0.624439\pi$
$241$	−11.8311	−0.762110	−0.381055	+	0.924552i	$0.624439\pi$
$242$	− 8.52552i	− 0.548041i
$243$	10.8609i	0.696728i
$244$	17.0258i	1.08997i
$245$	18.0484	1.15307
$246$	− 7.62756i	− 0.486316i
$247$	0.628693i	0.0400028i
$248$	−37.1675	−2.36014
$249$	7.46278i	0.472934i
$250$	22.4389i	1.41916i
$251$	7.66497i	0.483809i	0.970300	+	0.241904i	$0.0777720\pi$
$251$	7.66497i	0.483809i	−0.970300	+	0.241904i	$0.922228\pi$
$252$	−1.00652	−0.0634049
$253$	− 4.44955i	− 0.279741i
$254$	15.1921	0.953235
$255$	−4.46793	−0.279793
$256$	−18.8823	−1.18015
$257$	11.3728	0.709415	0.354707	−	0.934977i	$-0.384580\pi$
$257$	11.3728	0.709415	0.354707	+	0.934977i	$0.384580\pi$
$258$	− 9.50542i	− 0.591782i
$259$	− 0.231968i	− 0.0144138i
$260$	−10.8500	−0.672886
$261$	0	0
$262$	17.2396	1.06507
$263$	16.7464i	1.03263i	0.856399	+	0.516315i	$0.172697\pi$
$263$	16.7464i	1.03263i	−0.856399	+	0.516315i	$0.827303\pi$
$264$	− 11.9780i	− 0.737196i
$265$	−14.3370	−0.880717
$266$	0.139529	0.00855509
$267$	2.98599	0.182739
$268$	23.5750	1.44007
$269$	− 21.9337i	− 1.33732i	−0.743568	−	0.668660i	$-0.766868\pi$
$269$	− 21.9337i	− 1.33732i	0.743568	−	0.668660i	$-0.233132\pi$
$270$	17.1325	1.04265
$271$	− 6.54431i	− 0.397539i	−0.980046	−	0.198769i	$-0.936306\pi$
$271$	− 6.54431i	− 0.397539i	0.980046	−	0.198769i	$-0.0636945\pi$
$272$	− 36.3889i	− 2.20640i
$273$	− 0.0290799i	− 0.00176000i
$274$	4.05670	0.245074
$275$	− 6.26672i	− 0.377898i
$276$	− 2.46931i	− 0.148635i
$277$	21.5277	1.29347	0.646736	−	0.762714i	$-0.276134\pi$
$277$	21.5277	1.29347	0.646736	+	0.762714i	$0.276134\pi$
$278$	27.6941i	1.66098i
$279$	− 14.4584i	− 0.865602i
$280$	1.39892i	0.0836015i
$281$	−8.69715	−0.518828	−0.259414	−	0.965766i	$-0.583529\pi$
$281$	−8.69715	−0.518828	−0.259414	+	0.965766i	$0.583529\pi$
$282$	12.1104i	0.721166i
$283$	−21.9887	−1.30709	−0.653545	−	0.756888i	$-0.726719\pi$
$283$	−21.9887	−1.30709	−0.653545	+	0.756888i	$0.726719\pi$
$284$	23.4187	1.38964
$285$	−0.809013	−0.0479218
$286$	−8.66278	−0.512241
$287$	0.501216i	0.0295859i
$288$	26.9396i	1.58743i
$289$	1.46785	0.0863441
$290$	0	0
$291$	5.01597	0.294042
$292$	42.4872i	2.48638i
$293$	2.22609i	0.130050i	0.997884	+	0.0650249i	$0.0207127\pi$
$293$	2.22609i	0.130050i	−0.997884	+	0.0650249i	$0.979287\pi$
$294$	7.99702	0.466395
$295$	−25.5948	−1.49019
$296$	−22.2787	−1.29493
$297$	9.63946	0.559338
$298$	− 14.1378i	− 0.818982i
$299$	−1.03750	−0.0599999
$300$	− 3.47777i	− 0.200789i
$301$	0.624613i	0.0360021i
$302$	− 46.4321i	− 2.67187i
$303$	4.14659	0.238216
$304$	− 6.58898i	− 0.377904i
$305$	9.20524i	0.527090i
$306$	28.7896	1.64579
$307$	13.8760i	0.791945i	0.918262	+	0.395972i	$0.129592\pi$
$307$	13.8760i	0.791945i	−0.918262	+	0.395972i	$0.870408\pi$
$308$	1.35483i	0.0771988i
$309$	− 4.03452i	− 0.229516i
$310$	−34.5901	−1.96459
$311$	1.41217i	0.0800768i	0.999198	+	0.0400384i	$0.0127480\pi$
$311$	1.41217i	0.0800768i	−0.999198	+	0.0400384i	$0.987252\pi$
$312$	−2.79290	−0.158117
$313$	−28.7487	−1.62497	−0.812487	−	0.582980i	$-0.801887\pi$
$313$	−28.7487	−1.62497	−0.812487	+	0.582980i	$0.801887\pi$
$314$	−24.6285	−1.38986
$315$	−0.544190	−0.0306616
$316$	62.9496i	3.54119i
$317$	− 22.3203i	− 1.25363i	−0.779168	−	0.626815i	$-0.784358\pi$
$317$	− 22.3203i	− 1.25363i	0.779168	−	0.626815i	$-0.215642\pi$
$318$	−6.35255	−0.356234
$319$	0	0
$320$	16.7988	0.939083
$321$	− 2.13879i	− 0.119376i
$322$	0.230257i	0.0128317i
$323$	−2.81242	−0.156487
$324$	−34.8411	−1.93562
$325$	−1.46121	−0.0810531
$326$	−27.2157	−1.50734
$327$	− 1.90420i	− 0.105302i
$328$	48.1380	2.65798
$329$	− 0.795792i	− 0.0438734i
$330$	− 11.1474i	− 0.613645i
$331$	9.34951i	0.513895i	0.966425	+	0.256948i	$0.0827168\pi$
$331$	9.34951i	0.513895i	−0.966425	+	0.256948i	$0.917283\pi$
$332$	−81.0708	−4.44934
$333$	− 8.66657i	− 0.474925i
$334$	− 0.443550i	− 0.0242700i
$335$	12.7462	0.696397
$336$	0.304770i	0.0166266i
$337$	− 15.4311i	− 0.840583i	−0.907389	−	0.420292i	$-0.861928\pi$
$337$	− 15.4311i	− 0.840583i	0.907389	−	0.420292i	$-0.138072\pi$
$338$	− 31.8118i	− 1.73034i
$339$	−1.98717	−0.107928
$340$	− 48.5367i	− 2.63227i
$341$	−19.4618	−1.05392
$342$	5.21297	0.281885
$343$	−1.05141	−0.0567709
$344$	59.9893	3.23441
$345$	− 1.33507i	− 0.0718776i
$346$	31.4098i	1.68860i
$347$	9.39939	0.504586	0.252293	−	0.967651i	$-0.418815\pi$
$347$	9.39939	0.504586	0.252293	+	0.967651i	$0.418815\pi$
$348$	0	0
$349$	−24.5072	−1.31184	−0.655921	−	0.754830i	$-0.727720\pi$
$349$	−24.5072	−1.31184	−0.655921	+	0.754830i	$0.727720\pi$
$350$	0.324293i	0.0173342i
$351$	− 2.24762i	− 0.119969i
$352$	36.2622	1.93278
$353$	24.1475	1.28524	0.642622	−	0.766183i	$-0.277847\pi$
$353$	24.1475	1.28524	0.642622	+	0.766183i	$0.277847\pi$
$354$	−11.3407	−0.602753
$355$	12.6616	0.672011
$356$	32.4378i	1.71920i
$357$	0.130087	0.00688495
$358$	4.35864i	0.230361i
$359$	15.2452i	0.804609i	0.915506	+	0.402304i	$0.131791\pi$
$359$	15.2452i	0.804609i	−0.915506	+	0.402304i	$0.868209\pi$
$360$	52.2653i	2.75462i
$361$	18.4908	0.973197
$362$	− 39.9803i	− 2.10132i
$363$	− 1.43926i	− 0.0755417i
$364$	0.315905	0.0165579
$365$	22.9713i	1.20237i
$366$	4.07872i	0.213198i
$367$	12.8020i	0.668261i	0.942527	+	0.334130i	$0.108443\pi$
$367$	12.8020i	0.668261i	−0.942527	+	0.334130i	$0.891557\pi$
$368$	10.8734	0.566816
$369$	18.7260i	0.974837i
$370$	−20.7338	−1.07790
$371$	0.417434	0.0216721
$372$	−10.8005	−0.559980
$373$	−0.0195746	−0.00101354	−0.000506768	−	1.00000i	$-0.500161\pi$
$373$	−0.0195746	−0.00101354	−0.000506768		1.00000i	$0.500161\pi$
$374$	− 38.7525i	− 2.00384i
$375$	3.78810i	0.195616i
$376$	−76.4297	−3.94156
$377$	0	0
$378$	−0.498827	−0.0256569
$379$	5.23573i	0.268941i	0.990918	+	0.134471i	$0.0429334\pi$
$379$	5.23573i	0.268941i	−0.990918	+	0.134471i	$0.957067\pi$
$380$	− 8.78860i	− 0.450845i
$381$	2.56469	0.131393
$382$	53.2935	2.72673
$383$	0.274844	0.0140438	0.00702192	−	0.999975i	$-0.497765\pi$
$383$	0.274844	0.0140438	0.00702192	+	0.999975i	$0.497765\pi$
$384$	−0.989633	−0.0505020
$385$	0.732510i	0.0373322i
$386$	−8.15711	−0.415186
$387$	23.3362i	1.18625i
$388$	54.4903i	2.76633i
$389$	− 7.53699i	− 0.382140i	−0.981576	−	0.191070i	$-0.938804\pi$
$389$	− 7.53699i	− 0.382140i	0.981576	−	0.191070i	$-0.0611958\pi$
$390$	−2.59923	−0.131617
$391$	− 4.64118i	− 0.234715i
$392$	50.4696i	2.54910i
$393$	2.91036	0.146808
$394$	7.39197i	0.372402i
$395$	34.0346i	1.71246i
$396$	50.6181i	2.54366i
$397$	16.7344	0.839877	0.419938	−	0.907553i	$-0.362052\pi$
$397$	16.7344	0.839877	0.419938	+	0.907553i	$0.362052\pi$
$398$	− 49.7558i	− 2.49403i
$399$	0.0235551	0.00117923
$400$	15.3141	0.765704
$401$	−8.05748	−0.402371	−0.201186	−	0.979553i	$-0.564479\pi$
$401$	−8.05748	−0.402371	−0.201186	+	0.979553i	$0.564479\pi$
$402$	5.64766	0.281680
$403$	4.53789i	0.226049i
$404$	45.0459i	2.24112i
$405$	−18.8373	−0.936034
$406$	0	0
$407$	−11.6657	−0.578247
$408$	− 12.4939i	− 0.618540i
$409$	9.50361i	0.469923i	0.972005	+	0.234962i	$0.0754964\pi$
$409$	9.50361i	0.469923i	−0.972005	+	0.234962i	$0.924504\pi$
$410$	44.7999	2.21251
$411$	0.684845	0.0337809
$412$	43.8285	2.15927
$413$	0.745214	0.0366696
$414$	8.60267i	0.422798i
$415$	−43.8321	−2.15163
$416$	− 8.45522i	− 0.414551i
$417$	4.67526i	0.228948i
$418$	− 7.01695i	− 0.343210i
$419$	−23.2480	−1.13574	−0.567870	−	0.823118i	$-0.692232\pi$
$419$	−23.2480	−1.13574	−0.567870	+	0.823118i	$0.692232\pi$
$420$	0.406512i	0.0198358i
$421$	17.4532i	0.850618i	0.905048	+	0.425309i	$0.139834\pi$
$421$	17.4532i	0.850618i	−0.905048	+	0.425309i	$0.860166\pi$
$422$	−46.5669	−2.26684
$423$	− 29.7317i	− 1.44560i
$424$	− 40.0914i	− 1.94701i
$425$	− 6.53662i	− 0.317073i
$426$	5.61022	0.271816
$427$	− 0.268018i	− 0.0129703i
$428$	23.2344	1.12308
$429$	−1.46243	−0.0706069
$430$	55.8294	2.69233
$431$	−32.7850	−1.57920	−0.789598	−	0.613624i	$-0.789711\pi$
$431$	−32.7850	−1.57920	−0.789598	+	0.613624i	$0.789711\pi$
$432$	23.5561i	1.13334i
$433$	− 5.02086i	− 0.241287i	−0.992696	−	0.120644i	$-0.961504\pi$
$433$	− 5.02086i	− 0.241287i	0.992696	−	0.120644i	$-0.0384958\pi$
$434$	1.00712	0.0483433
$435$	0	0
$436$	20.6859	0.990677
$437$	− 0.840384i	− 0.0402010i
$438$	10.1783i	0.486338i
$439$	21.3691	1.01989	0.509946	−	0.860207i	$-0.329666\pi$
$439$	21.3691	1.01989	0.509946	+	0.860207i	$0.329666\pi$
$440$	70.3520	3.35390
$441$	−19.6330	−0.934906
$442$	−9.03587	−0.429793
$443$	39.8292i	1.89234i	0.323668	+	0.946171i	$0.395084\pi$
$443$	39.8292i	1.89234i	−0.323668	+	0.946171i	$0.604916\pi$
$444$	−6.47397	−0.307241
$445$	17.5380i	0.831380i
$446$	46.1435i	2.18496i
$447$	− 2.38672i	− 0.112888i
$448$	−0.489111	−0.0231083
$449$	9.92661i	0.468466i	0.972181	+	0.234233i	$0.0752578\pi$
$449$	9.92661i	0.468466i	−0.972181	+	0.234233i	$0.924742\pi$
$450$	12.1160i	0.571152i
$451$	25.2063	1.18692
$452$	− 21.5873i	− 1.01538i
$453$	− 7.83858i	− 0.368289i
$454$	57.8044i	2.71290i
$455$	0.170799	0.00800716
$456$	− 2.26228i	− 0.105941i
$457$	−14.6244	−0.684102	−0.342051	−	0.939681i	$-0.611122\pi$
$457$	−14.6244	−0.684102	−0.342051	+	0.939681i	$0.611122\pi$
$458$	25.9414	1.21216
$459$	10.0546	0.469310
$460$	14.5033	0.676221
$461$	− 18.8523i	− 0.878037i	−0.898478	−	0.439019i	$-0.855326\pi$
$461$	− 18.8523i	− 0.878037i	0.898478	−	0.439019i	$-0.144674\pi$
$462$	0.324566i	0.0151002i
$463$	35.4987	1.64977	0.824883	−	0.565304i	$-0.191241\pi$
$463$	35.4987	1.64977	0.824883	+	0.565304i	$0.191241\pi$
$464$	0	0
$465$	−5.83944	−0.270798
$466$	− 52.2478i	− 2.42033i
$467$	6.06786i	0.280787i	0.990096	+	0.140394i	$0.0448368\pi$
$467$	6.06786i	0.280787i	−0.990096	+	0.140394i	$0.955163\pi$
$468$	11.8026	0.545574
$469$	−0.371115	−0.0171365
$470$	−71.1298	−3.28097
$471$	−4.15773	−0.191578
$472$	− 71.5721i	− 3.29437i
$473$	31.4119	1.44432
$474$	15.0803i	0.692660i
$475$	− 1.18359i	− 0.0543070i
$476$	1.41319i	0.0647732i
$477$	15.5958	0.714083
$478$	− 3.07310i	− 0.140560i
$479$	− 3.51910i	− 0.160792i	−0.996763	−	0.0803958i	$-0.974382\pi$
$479$	− 3.51910i	− 0.160792i	0.996763	−	0.0803958i	$-0.0256184\pi$
$480$	10.8803	0.496617
$481$	2.72008i	0.124025i
$482$	− 30.7898i	− 1.40244i
$483$	0.0388716i	0.00176872i
$484$	15.6352	0.710692
$485$	29.4609i	1.33775i
$486$	−28.2649	−1.28212
$487$	7.87745	0.356961	0.178481	−	0.983943i	$-0.442882\pi$
$487$	7.87745	0.356961	0.178481	+	0.983943i	$0.442882\pi$
$488$	−25.7411	−1.16524
$489$	−4.59451	−0.207771
$490$	46.9699i	2.12188i
$491$	− 21.8303i	− 0.985187i	−0.870259	−	0.492594i	$-0.836049\pi$
$491$	− 21.8303i	− 0.985187i	0.870259	−	0.492594i	$-0.163951\pi$
$492$	13.9884	0.630646
$493$	0	0
$494$	−1.63614	−0.0736132
$495$	27.3674i	1.23007i
$496$	− 47.5591i	− 2.13547i
$497$	−0.368654	−0.0165364
$498$	−19.4214	−0.870295
$499$	29.6115	1.32559	0.662796	−	0.748800i	$-0.269370\pi$
$499$	29.6115	1.32559	0.662796	+	0.748800i	$0.269370\pi$
$500$	−41.1514	−1.84035
$501$	− 0.0748793i	− 0.00334536i
$502$	−19.9476	−0.890306
$503$	14.0757i	0.627603i	0.949489	+	0.313802i	$0.101603\pi$
$503$	14.0757i	0.627603i	−0.949489	+	0.313802i	$0.898397\pi$
$504$	− 1.52174i	− 0.0677839i
$505$	24.3547i	1.08377i
$506$	11.5797	0.514779
$507$	− 5.37041i	− 0.238508i
$508$	27.8612i	1.23614i
$509$	−28.1153	−1.24619	−0.623095	−	0.782146i	$-0.714125\pi$
$509$	−28.1153	−1.24619	−0.623095	+	0.782146i	$0.714125\pi$
$510$	− 11.6275i	− 0.514875i
$511$	− 0.668828i	− 0.0295872i
$512$	− 44.6351i	− 1.97261i
$513$	1.82060	0.0803815
$514$	29.5970i	1.30547i
$515$	23.6965	1.04419
$516$	17.4323	0.767413
$517$	−40.0205	−1.76010
$518$	0.603682	0.0265243
$519$	5.30254i	0.232756i
$520$	− 16.4039i	− 0.719359i
$521$	−30.6374	−1.34225	−0.671125	−	0.741344i	$-0.734189\pi$
$521$	−30.6374	−1.34225	−0.671125	+	0.741344i	$0.734189\pi$
$522$	0	0
$523$	31.1728	1.36309	0.681546	−	0.731775i	$-0.261308\pi$
$523$	31.1728	1.36309	0.681546	+	0.731775i	$0.261308\pi$
$524$	31.6163i	1.38116i
$525$	0.0547466i	0.00238934i
$526$	−43.5816	−1.90025
$527$	−20.3000	−0.884283
$528$	15.3269	0.667019
$529$	−21.6132	−0.939703
$530$	− 37.3113i	− 1.62070i
$531$	27.8420	1.20824
$532$	0.255887i	0.0110941i
$533$	− 5.87732i	− 0.254575i
$534$	7.77085i	0.336278i
$535$	12.5620	0.543104
$536$	35.6427i	1.53953i
$537$	0.735817i	0.0317529i
$538$	57.0811	2.46094
$539$	26.4272i	1.13830i
$540$	31.4199i	1.35210i
$541$	− 22.3769i	− 0.962058i	−0.876705	−	0.481029i	$-0.840263\pi$
$541$	− 22.3769i	− 0.962058i	0.876705	−	0.481029i	$-0.159737\pi$
$542$	17.0312	0.731552
$543$	− 6.74940i	− 0.289645i
$544$	37.8240	1.62169
$545$	11.1841	0.479076
$546$	0.0756787	0.00323875
$547$	−12.2963	−0.525752	−0.262876	−	0.964830i	$-0.584671\pi$
$547$	−12.2963	−0.525752	−0.262876	+	0.964830i	$0.584671\pi$
$548$	7.43971i	0.317809i
$549$	− 10.0134i	− 0.427363i
$550$	16.3088	0.695408
$551$	0	0
$552$	3.73332	0.158901
$553$	− 0.990943i	− 0.0421392i
$554$	56.0244i	2.38025i
$555$	−3.50024	−0.148577
$556$	−50.7890	−2.15393
$557$	−6.00766	−0.254553	−0.127276	−	0.991867i	$-0.540623\pi$
$557$	−6.00766	−0.254553	−0.127276	+	0.991867i	$0.540623\pi$
$558$	37.6271	1.59288
$559$	− 7.32428i	− 0.309784i
$560$	−1.79004	−0.0756432
$561$	− 6.54212i	− 0.276208i
$562$	− 22.6338i	− 0.954749i
$563$	− 28.0097i	− 1.18047i	−0.807233	−	0.590233i	$-0.799036\pi$
$563$	− 28.0097i	− 1.18047i	0.807233	−	0.590233i	$-0.200964\pi$
$564$	−22.2097	−0.935197
$565$	− 11.6715i	− 0.491023i
$566$	− 57.2241i	− 2.40531i
$567$	0.548464	0.0230333
$568$	35.4064i	1.48562i
$569$	34.6764i	1.45371i	0.686790	+	0.726856i	$0.259019\pi$
$569$	34.6764i	1.45371i	−0.686790	+	0.726856i	$0.740981\pi$
$570$	− 2.10541i	− 0.0881858i
$571$	4.37818	0.183221	0.0916106	−	0.995795i	$-0.470799\pi$
$571$	4.37818	0.183221	0.0916106	+	0.995795i	$0.470799\pi$
$572$	− 15.8869i	− 0.664266i
$573$	8.99690	0.375851
$574$	−1.30439	−0.0544440
$575$	1.95322	0.0814548
$576$	−18.2737	−0.761406
$577$	− 44.8517i	− 1.86720i	−0.358317	−	0.933600i	$-0.616649\pi$
$577$	− 44.8517i	− 1.86720i	0.358317	−	0.933600i	$-0.383351\pi$
$578$	3.81999i	0.158891i
$579$	−1.37707	−0.0572289
$580$	0	0
$581$	1.27621	0.0529459
$582$	13.0538i	0.541096i
$583$	− 20.9928i	− 0.869434i
$584$	−64.2359	−2.65810
$585$	6.38123	0.263831
$586$	−5.79327	−0.239318
$587$	6.40778	0.264477	0.132239	−	0.991218i	$-0.457783\pi$
$587$	6.40778	0.264477	0.132239	+	0.991218i	$0.457783\pi$
$588$	14.6660i	0.604814i
$589$	−3.67575	−0.151457
$590$	− 66.6090i	− 2.74225i
$591$	1.24790i	0.0513317i
$592$	− 28.5076i	− 1.17166i
$593$	1.41754	0.0582114	0.0291057	−	0.999576i	$-0.490734\pi$
$593$	1.41754	0.0582114	0.0291057	+	0.999576i	$0.490734\pi$
$594$	25.0861i	1.02930i
$595$	0.764058i	0.0313233i
$596$	25.9278	1.06204
$597$	− 8.39968i	− 0.343776i
$598$	− 2.70002i	− 0.110412i
$599$	37.2538i	1.52215i	0.648663	+	0.761075i	$0.275328\pi$
$599$	37.2538i	1.52215i	−0.648663	+	0.761075i	$0.724672\pi$
$600$	5.25799	0.214657
$601$	− 25.3174i	− 1.03272i	−0.856372	−	0.516360i	$-0.827287\pi$
$601$	− 25.3174i	− 1.03272i	0.856372	−	0.516360i	$-0.172713\pi$
$602$	−1.62552	−0.0662511
$603$	−13.8653	−0.564637
$604$	85.1533	3.46484
$605$	8.45340	0.343679
$606$	10.7913i	0.438365i
$607$	29.8274i	1.21066i	0.795976	+	0.605328i	$0.206958\pi$
$607$	29.8274i	1.21066i	−0.795976	+	0.605328i	$0.793042\pi$
$608$	6.84883	0.277757
$609$	0	0
$610$	−23.9561	−0.969953
$611$	9.33154i	0.377514i
$612$	52.7982i	2.13424i
$613$	−31.5885	−1.27585	−0.637923	−	0.770100i	$-0.720206\pi$
$613$	−31.5885	−1.27585	−0.637923	+	0.770100i	$0.720206\pi$
$614$	−36.1114	−1.45734
$615$	7.56303	0.304971
$616$	−2.04835	−0.0825306
$617$	− 19.2746i	− 0.775968i	−0.921666	−	0.387984i	$-0.873172\pi$
$617$	− 19.2746i	− 0.775968i	0.921666	−	0.387984i	$-0.126828\pi$
$618$	10.4996	0.422356
$619$	− 44.9116i	− 1.80515i	−0.430534	−	0.902574i	$-0.641675\pi$
$619$	− 44.9116i	− 1.80515i	0.430534	−	0.902574i	$-0.358325\pi$
$620$	− 63.4359i	− 2.54765i
$621$	3.00443i	0.120564i
$622$	−3.67509	−0.147358
$623$	− 0.510632i	− 0.0204580i
$624$	− 3.57377i	− 0.143065i
$625$	−30.5420	−1.22168
$626$	− 74.8168i	− 2.99028i
$627$	− 1.18459i	− 0.0473079i
$628$	− 45.1669i	− 1.80235i
$629$	−12.1681	−0.485175
$630$	− 1.41622i	− 0.0564236i
$631$	38.1217	1.51760	0.758800	−	0.651324i	$-0.225786\pi$
$631$	38.1217	1.51760	0.758800	+	0.651324i	$0.225786\pi$
$632$	−95.1725	−3.78576
$633$	−7.86134	−0.312460
$634$	58.0871	2.30693
$635$	15.0635i	0.597778i
$636$	− 11.6501i	− 0.461958i
$637$	6.16199	0.244147
$638$	0	0
$639$	−13.7733	−0.544864
$640$	− 5.81254i	− 0.229761i
$641$	− 36.9753i	− 1.46044i	−0.683214	−	0.730219i	$-0.739418\pi$
$641$	− 36.9753i	− 1.46044i	0.683214	−	0.730219i	$-0.260582\pi$
$642$	5.56607	0.219675
$643$	17.0863	0.673816	0.336908	−	0.941537i	$-0.390619\pi$
$643$	17.0863	0.673816	0.336908	+	0.941537i	$0.390619\pi$
$644$	−0.422276	−0.0166400
$645$	9.42501	0.371109
$646$	− 7.31916i	− 0.287969i
$647$	−6.19335	−0.243486	−0.121743	−	0.992562i	$-0.538848\pi$
$647$	−6.19335	−0.243486	−0.121743	+	0.992562i	$0.538848\pi$
$648$	− 52.6758i	− 2.06930i
$649$	− 37.4769i	− 1.47110i
$650$	− 3.80270i	− 0.149154i
$651$	0.170020	0.00666361
$652$	− 49.9117i	− 1.95469i
$653$	15.7585i	0.616677i	0.951277	+	0.308339i	$0.0997730\pi$
$653$	15.7585i	0.616677i	−0.951277	+	0.308339i	$0.900227\pi$
$654$	4.95555	0.193777
$655$	17.0938i	0.667909i
$656$	61.5968i	2.40495i
$657$	− 24.9882i	− 0.974881i
$658$	2.07100	0.0807360
$659$	16.6107i	0.647059i	0.946218	+	0.323530i	$0.104870\pi$
$659$	16.6107i	0.647059i	−0.946218	+	0.323530i	$0.895130\pi$
$660$	20.4436	0.795765
$661$	−40.0401	−1.55738	−0.778691	−	0.627408i	$-0.784116\pi$
$661$	−40.0401	−1.55738	−0.778691	+	0.627408i	$0.784116\pi$
$662$	−24.3315	−0.945672
$663$	−1.52542	−0.0592423
$664$	− 122.570i	− 4.75663i
$665$	0.138349i	0.00536494i
$666$	22.5542	0.873959
$667$	0	0
$668$	0.813440	0.0314729
$669$	7.78985i	0.301173i
$670$	33.1711i	1.28151i
$671$	−13.4787	−0.520338
$672$	−0.316789	−0.0122204
$673$	13.2244	0.509764	0.254882	−	0.966972i	$-0.417963\pi$
$673$	13.2244	0.509764	0.254882	+	0.966972i	$0.417963\pi$
$674$	40.1584	1.54684
$675$	4.23144i	0.162868i
$676$	58.3407	2.24387
$677$	− 23.8101i	− 0.915095i	−0.889185	−	0.457548i	$-0.848728\pi$
$677$	− 23.8101i	− 0.915095i	0.889185	−	0.457548i	$-0.151272\pi$
$678$	− 5.17149i	− 0.198610i
$679$	− 0.857779i	− 0.0329185i
$680$	73.3820	2.81407
$681$	9.75843i	0.373944i
$682$	− 50.6482i	− 1.93942i
$683$	28.7668	1.10073	0.550365	−	0.834924i	$-0.314489\pi$
$683$	28.7668	1.10073	0.550365	+	0.834924i	$0.314489\pi$
$684$	9.56022i	0.365544i
$685$	4.02238i	0.153687i
$686$	− 2.73623i	− 0.104470i
$687$	4.37938	0.167084
$688$	76.7616i	2.92651i
$689$	−4.89488	−0.186480
$690$	3.47443	0.132269
$691$	27.1116	1.03137	0.515686	−	0.856777i	$-0.327537\pi$
$691$	27.1116	1.03137	0.515686	+	0.856777i	$0.327537\pi$
$692$	−57.6033	−2.18975
$693$	− 0.796823i	− 0.0302688i
$694$	24.4613i	0.928540i
$695$	−27.4598	−1.04161
$696$	0	0
$697$	26.2919	0.995875
$698$	− 63.7786i	− 2.41406i
$699$	− 8.82037i	− 0.333617i
$700$	−0.594732	−0.0224787
$701$	24.5115	0.925788	0.462894	−	0.886414i	$-0.346811\pi$
$701$	24.5115	0.925788	0.462894	+	0.886414i	$0.346811\pi$
$702$	5.84930	0.220768
$703$	−2.20330	−0.0830989
$704$	24.5975i	0.927053i
$705$	−12.0080	−0.452247
$706$	62.8425i	2.36511i
$707$	− 0.709107i	− 0.0266687i
$708$	− 20.7981i	− 0.781641i
$709$	−16.5914	−0.623104	−0.311552	−	0.950229i	$-0.600849\pi$
$709$	−16.5914	−0.623104	−0.311552	+	0.950229i	$0.600849\pi$
$710$	32.9512i	1.23664i
$711$	− 37.0227i	− 1.38846i
$712$	−49.0423	−1.83794
$713$	− 6.06588i	− 0.227169i
$714$	0.338544i	0.0126697i
$715$	− 8.58949i	− 0.321229i
$716$	−7.99344	−0.298729
$717$	− 0.518795i	− 0.0193747i
$718$	−39.6746	−1.48064
$719$	40.5018	1.51046	0.755231	−	0.655458i	$-0.227525\pi$
$719$	40.5018	1.51046	0.755231	+	0.655458i	$0.227525\pi$
$720$	−66.8780	−2.49240
$721$	−0.689942	−0.0256948
$722$	48.1211i	1.79088i
$723$	− 5.19787i	− 0.193311i
$724$	73.3212	2.72496
$725$	0	0
$726$	3.74559	0.139012
$727$	31.7298i	1.17679i	0.808572	+	0.588397i	$0.200241\pi$
$727$	31.7298i	1.17679i	−0.808572	+	0.588397i	$0.799759\pi$
$728$	0.477613i	0.0177015i
$729$	17.1286	0.634394
$730$	−59.7815	−2.21261
$731$	32.7648	1.21185
$732$	−7.48009	−0.276472
$733$	1.48939i	0.0550118i	0.999622	+	0.0275059i	$0.00875650\pi$
$733$	1.48939i	0.0550118i	−0.999622	+	0.0275059i	$0.991243\pi$
$734$	−33.3165	−1.22974
$735$	7.92936i	0.292479i
$736$	11.3022i	0.416606i
$737$	18.6634i	0.687476i
$738$	−48.7333	−1.79390
$739$	36.7246i	1.35094i	0.737389	+	0.675468i	$0.236058\pi$
$739$	36.7246i	1.35094i	−0.737389	+	0.675468i	$0.763942\pi$
$740$	− 38.0244i	− 1.39780i
$741$	−0.276209	−0.0101468
$742$	1.08635i	0.0398810i
$743$	− 31.1757i	− 1.14373i	−0.820349	−	0.571863i	$-0.806221\pi$
$743$	− 31.1757i	− 1.14373i	0.820349	−	0.571863i	$-0.193779\pi$
$744$	− 16.3291i	− 0.598655i
$745$	14.0182	0.513588
$746$	− 0.0509418i	− 0.00186511i
$747$	47.6805	1.74454
$748$	71.0693	2.59855
$749$	−0.365753	−0.0133643
$750$	−9.85829	−0.359974
$751$	45.2999i	1.65302i	0.562923	+	0.826509i	$0.309677\pi$
$751$	45.2999i	1.65302i	−0.562923	+	0.826509i	$0.690323\pi$
$752$	− 97.7986i	− 3.56635i
$753$	−3.36752	−0.122719
$754$	0	0
$755$	46.0393	1.67554
$756$	− 0.914815i	− 0.0332715i
$757$	− 18.8863i	− 0.686435i	−0.939256	−	0.343218i	$-0.888483\pi$
$757$	− 18.8863i	− 0.686435i	0.939256	−	0.343218i	$-0.111517\pi$
$758$	−13.6257	−0.494906
$759$	1.95486	0.0709568
$760$	13.2874	0.481983
$761$	17.4270	0.631727	0.315863	−	0.948805i	$-0.397706\pi$
$761$	17.4270	0.631727	0.315863	+	0.948805i	$0.397706\pi$
$762$	6.67446i	0.241790i
$763$	−0.325635	−0.0117888
$764$	97.7365i	3.53598i
$765$	28.5461i	1.03209i
$766$	0.715264i	0.0258435i
$767$	−8.73846	−0.315527
$768$	− 8.29574i	− 0.299347i
$769$	27.2971i	0.984357i	0.870494	+	0.492179i	$0.163799\pi$
$769$	27.2971i	0.984357i	−0.870494	+	0.492179i	$0.836201\pi$
$770$	−1.90631	−0.0686988
$771$	4.99650i	0.179945i
$772$	− 14.9596i	− 0.538406i
$773$	5.89778i	0.212128i	0.994359	+	0.106064i	$0.0338249\pi$
$773$	5.89778i	0.212128i	−0.994359	+	0.106064i	$0.966175\pi$
$774$	−60.7311	−2.18294
$775$	− 8.54316i	− 0.306879i
$776$	−82.3831	−2.95738
$777$	0.101912	0.00365609
$778$	19.6146	0.703216
$779$	4.76070	0.170570
$780$	− 4.76681i	− 0.170679i
$781$	18.5397i	0.663402i
$782$	12.0784	0.431923
$783$	0	0
$784$	−64.5804	−2.30644
$785$	− 24.4201i	− 0.871591i
$786$	7.57403i	0.270157i
$787$	43.7976	1.56122	0.780609	−	0.625020i	$-0.214909\pi$
$787$	43.7976	1.56122	0.780609	+	0.625020i	$0.214909\pi$
$788$	−13.5564	−0.482925
$789$	−7.35736	−0.261929
$790$	−88.5729	−3.15128
$791$	0.339825i	0.0120828i
$792$	−76.5288	−2.71933
$793$	3.14281i	0.111604i
$794$	43.5503i	1.54554i
$795$	− 6.29881i	− 0.223396i
$796$	91.2487	3.23422
$797$	36.6686i	1.29887i	0.760417	+	0.649435i	$0.224994\pi$
$797$	36.6686i	1.29887i	−0.760417	+	0.649435i	$0.775006\pi$
$798$	0.0613006i	0.00217002i
$799$	−41.7441	−1.47680
$800$	15.9180i	0.562787i
$801$	− 19.0778i	− 0.674081i
$802$	− 20.9691i	− 0.740445i
$803$	−33.6355	−1.18697
$804$	10.3574i	0.365278i
$805$	−0.228309	−0.00804684
$806$	−11.8096	−0.415975
$807$	9.63632	0.339214
$808$	−68.1043	−2.39590
$809$	18.7725i	0.660007i	0.943980	+	0.330004i	$0.107050\pi$
$809$	18.7725i	0.660007i	−0.943980	+	0.330004i	$0.892950\pi$
$810$	− 49.0230i	− 1.72249i
$811$	33.9249	1.19127	0.595633	−	0.803257i	$-0.296901\pi$
$811$	33.9249	1.19127	0.595633	+	0.803257i	$0.296901\pi$
$812$	0	0
$813$	2.87517	0.100837
$814$	− 30.3593i	− 1.06409i
$815$	− 26.9855i	− 0.945260i
$816$	15.9870	0.559659
$817$	5.93275	0.207561
$818$	−24.7326	−0.864754
$819$	−0.185794	−0.00649218
$820$	82.1599i	2.86915i
$821$	12.5182	0.436887	0.218443	−	0.975850i	$-0.429902\pi$
$821$	12.5182	0.436887	0.218443	+	0.975850i	$0.429902\pi$
$822$	1.78227i	0.0621637i
$823$	− 27.6813i	− 0.964911i	−0.875920	−	0.482456i	$-0.839745\pi$
$823$	− 27.6813i	− 0.964911i	0.875920	−	0.482456i	$-0.160255\pi$
$824$	66.2636i	2.30840i
$825$	2.75321	0.0958546
$826$	1.93937i	0.0674794i
$827$	29.5496i	1.02754i	0.857928	+	0.513771i	$0.171752\pi$
$827$	29.5496i	1.02754i	−0.857928	+	0.513771i	$0.828248\pi$
$828$	−15.7767	−0.548278
$829$	1.28760i	0.0447203i	0.999750	+	0.0223601i	$0.00711805\pi$
$829$	1.28760i	0.0447203i	−0.999750	+	0.0223601i	$0.992882\pi$
$830$	− 114.070i	− 3.95944i
$831$	9.45793i	0.328092i
$832$	5.73537	0.198838
$833$	27.5653i	0.955083i
$834$	−12.1671	−0.421311
$835$	0.439798	0.0152198
$836$	12.8686	0.445070
$837$	13.1411	0.454222
$838$	− 60.5016i	− 2.08999i
$839$	− 16.3512i	− 0.564505i	−0.959340	−	0.282253i	$-0.908918\pi$
$839$	− 16.3512i	− 0.564505i	0.959340	−	0.282253i	$-0.0910816\pi$
$840$	−0.614600	−0.0212057
$841$	0	0
$842$	−45.4209	−1.56531
$843$	− 3.82099i	− 0.131602i
$844$	− 85.4005i	− 2.93961i
$845$	31.5427	1.08510
$846$	77.3749	2.66020
$847$	−0.246127	−0.00845704
$848$	51.3004	1.76166
$849$	− 9.66047i	− 0.331546i
$850$	17.0112	0.583478
$851$	− 3.63597i	− 0.124640i
$852$	10.2887i	0.352487i
$853$	51.4321i	1.76100i	0.474045	+	0.880501i	$0.342793\pi$
$853$	51.4321i	1.76100i	−0.474045	+	0.880501i	$0.657207\pi$
$854$	0.697500	0.0238680
$855$	5.16887i	0.176772i
$856$	35.1278i	1.20064i
$857$	−19.4262	−0.663588	−0.331794	−	0.943352i	$-0.607654\pi$
$857$	−19.4262	−0.663588	−0.331794	+	0.943352i	$0.607654\pi$
$858$	− 3.80589i	− 0.129931i
$859$	23.9218i	0.816201i	0.912937	+	0.408101i	$0.133809\pi$
$859$	23.9218i	0.816201i	−0.912937	+	0.408101i	$0.866191\pi$
$860$	102.387i	3.49137i
$861$	−0.220204	−0.00750452
$862$	− 85.3209i	− 2.90604i
$863$	28.4361	0.967977	0.483989	−	0.875074i	$-0.339188\pi$
$863$	28.4361	0.967977	0.483989	+	0.875074i	$0.339188\pi$
$864$	−24.4851	−0.832999
$865$	−31.1441	−1.05893
$866$	13.0665	0.444018
$867$	0.644883i	0.0219014i
$868$	1.84699i	0.0626908i
$869$	−49.8347	−1.69053
$870$	0	0
$871$	4.35173	0.147453
$872$	31.2748i	1.05910i
$873$	− 32.0476i	− 1.08465i
$874$	2.18705	0.0739780
$875$	0.647800	0.0218996
$876$	−18.6663	−0.630675
$877$	−3.71106	−0.125314	−0.0626568	−	0.998035i	$-0.519957\pi$
$877$	−3.71106	−0.125314	−0.0626568	+	0.998035i	$0.519957\pi$
$878$	55.6118i	1.87681i
$879$	−0.978009	−0.0329874
$880$	90.0216i	3.03463i
$881$	− 11.9260i	− 0.401796i	−0.979612	−	0.200898i	$-0.935614\pi$
$881$	− 11.9260i	− 0.401796i	0.979612	−	0.200898i	$-0.0643860\pi$
$882$	− 51.0938i	− 1.72042i
$883$	−5.89920	−0.198524	−0.0992619	−	0.995061i	$-0.531648\pi$
$883$	−5.89920	−0.198524	−0.0992619	+	0.995061i	$0.531648\pi$
$884$	− 16.5712i	− 0.557348i
$885$	− 11.2448i	− 0.377990i
$886$	−103.653	−3.48229
$887$	− 24.5541i	− 0.824445i	−0.911083	−	0.412223i	$-0.864753\pi$
$887$	− 24.5541i	− 0.824445i	0.911083	−	0.412223i	$-0.135247\pi$
$888$	− 9.78791i	− 0.328461i
$889$	− 0.438587i	− 0.0147097i
$890$	−45.6415	−1.52991
$891$	− 27.5823i	− 0.924043i
$892$	−84.6239	−2.83342
$893$	−7.55866	−0.252941
$894$	6.21129	0.207737
$895$	−4.32177	−0.144461
$896$	0.169237i	0.00565380i
$897$	− 0.455812i	− 0.0152191i
$898$	−25.8334	−0.862072
$899$	0	0
$900$	−22.2198	−0.740661
$901$	− 21.8970i	− 0.729494i
$902$	65.5978i	2.18417i
$903$	−0.274417	−0.00913201
$904$	32.6376	1.08551
$905$	39.6421	1.31775
$906$	20.3994	0.677726
$907$	40.2160i	1.33535i	0.744453	+	0.667675i	$0.232711\pi$
$907$	40.2160i	1.33535i	−0.744453	+	0.667675i	$0.767289\pi$
$908$	−106.009	−3.51804
$909$	− 26.4930i	− 0.878718i
$910$	0.444493i	0.0147348i
$911$	13.5344i	0.448415i	0.974541	+	0.224208i	$0.0719794\pi$
$911$	13.5344i	0.448415i	−0.974541	+	0.224208i	$0.928021\pi$
$912$	2.89479	0.0958562
$913$	− 64.1806i	− 2.12407i
$914$	− 38.0592i	− 1.25889i
$915$	−4.04422	−0.133698
$916$	47.5748i	1.57191i
$917$	− 0.497699i	− 0.0164355i
$918$	26.1666i	0.863625i
$919$	55.1125	1.81799	0.908997	−	0.416803i	$-0.136849\pi$
$919$	55.1125	1.81799	0.908997	+	0.416803i	$0.136849\pi$
$920$	21.9274i	0.722924i
$921$	−6.09626	−0.200879
$922$	49.0619	1.61577
$923$	4.32288	0.142289
$924$	−0.595231	−0.0195817
$925$	− 5.12089i	− 0.168374i
$926$	92.3833i	3.03590i
$927$	−25.7770	−0.846627
$928$	0	0
$929$	4.05714	0.133111	0.0665553	−	0.997783i	$-0.478799\pi$
$929$	4.05714	0.133111	0.0665553	+	0.997783i	$0.478799\pi$
$930$	− 15.1968i	− 0.498322i
$931$	4.99129i	0.163583i
$932$	95.8188	3.13865
$933$	−0.620421	−0.0203117
$934$	−15.7912	−0.516705
$935$	38.4246	1.25662
$936$	17.8441i	0.583254i
$937$	30.1884	0.986213	0.493106	−	0.869969i	$-0.335861\pi$
$937$	30.1884	0.986213	0.493106	+	0.869969i	$0.335861\pi$
$938$	− 0.965804i	− 0.0315346i
$939$	− 12.6304i	− 0.412178i
$940$	− 130.447i	− 4.25471i
$941$	8.38002	0.273181	0.136590	−	0.990628i	$-0.456386\pi$
$941$	8.38002	0.273181	0.136590	+	0.990628i	$0.456386\pi$
$942$	− 10.8202i	− 0.352542i
$943$	7.85630i	0.255836i
$944$	91.5828	2.98077
$945$	− 0.494607i	− 0.0160896i
$946$	81.7476i	2.65784i
$947$	− 1.82587i	− 0.0593328i	−0.999560	−	0.0296664i	$-0.990556\pi$
$947$	− 1.82587i	− 0.0593328i	0.999560	−	0.0296664i	$-0.00944450\pi$
$948$	−27.6562	−0.898231
$949$	7.84275i	0.254587i
$950$	3.08023	0.0999359
$951$	9.80616	0.317986
$952$	−2.13657	−0.0692468
$953$	46.8893	1.51889	0.759447	−	0.650569i	$-0.225470\pi$
$953$	46.8893	1.51889	0.759447	+	0.650569i	$0.225470\pi$
$954$	40.5871i	1.31406i
$955$	52.8426i	1.70995i
$956$	5.63585	0.182276
$957$	0	0
$958$	9.15823	0.295889
$959$	− 0.117115i	− 0.00378184i
$960$	7.38038i	0.238201i
$961$	4.46852	0.144146
$962$	−7.07884	−0.228231
$963$	−13.6650	−0.440347
$964$	56.4664	1.81866
$965$	− 8.08810i	− 0.260365i
$966$	−0.101161	−0.00325480
$967$	20.1580i	0.648239i	0.946016	+	0.324119i	$0.105068\pi$
$967$	20.1580i	0.648239i	−0.946016	+	0.324119i	$0.894932\pi$
$968$	23.6387i	0.759775i
$969$	− 1.23561i	− 0.0396934i
$970$	−76.6703	−2.46174
$971$	16.9188i	0.542949i	0.962446	+	0.271474i	$0.0875113\pi$
$971$	16.9188i	0.542949i	−0.962446	+	0.271474i	$0.912489\pi$
$972$	− 51.8358i	− 1.66263i
$973$	0.799513	0.0256312
$974$	20.5006i	0.656881i
$975$	− 0.641964i	− 0.0205593i
$976$	− 32.9380i	− 1.05432i
$977$	−1.03630	−0.0331543	−0.0165772	−	0.999863i	$-0.505277\pi$
$977$	−1.03630	−0.0331543	−0.0165772	+	0.999863i	$0.505277\pi$
$978$	− 11.9569i	− 0.382340i
$979$	−25.6798	−0.820729
$980$	−86.1395	−2.75162
$981$	−12.1661	−0.388434
$982$	56.8120	1.81294
$983$	− 16.2306i	− 0.517676i	−0.965921	−	0.258838i	$-0.916660\pi$
$983$	− 16.2306i	− 0.517676i	0.965921	−	0.258838i	$-0.0833395\pi$
$984$	21.1489i	0.674202i
$985$	−7.32943	−0.233535
$986$	0	0
$987$	0.349622	0.0111286
$988$	− 3.00056i	− 0.0954605i
$989$	9.79048i	0.311319i
$990$	−71.2220	−2.26358
$991$	−37.1422	−1.17986	−0.589930	−	0.807454i	$-0.700845\pi$
$991$	−37.1422	−1.17986	−0.589930	+	0.807454i	$0.700845\pi$
$992$	49.4347	1.56955
$993$	−4.10760	−0.130351
$994$	− 0.959400i	− 0.0304303i
$995$	49.3349	1.56402
$996$	− 35.6175i	− 1.12859i
$997$	− 36.1372i	− 1.14448i	−0.820088	−	0.572238i	$-0.806075\pi$
$997$	− 36.1372i	− 1.14448i	0.820088	−	0.572238i	$-0.193925\pi$
$998$	77.0621i	2.43936i
$999$	7.87695	0.249216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.b.e.840.12		12
29.2	odd	28		841.2.d.k.605.1		24
29.3	odd	28		841.2.d.m.571.1		24
29.4	even	14		29.2.e.a.13.1	yes	12
29.5	even	14		841.2.e.f.236.2		12
29.6	even	14		841.2.e.e.196.1		12
29.7	even	7		29.2.e.a.9.1	✓	12
29.8	odd	28		841.2.d.l.574.1		24
29.9	even	14		841.2.e.a.267.1		12
29.10	odd	28		841.2.d.m.190.4		24
29.11	odd	28		841.2.d.l.778.4		24
29.12	odd	4		841.2.a.k.1.1		12
29.13	even	14		841.2.e.h.63.2		12
29.14	odd	28		841.2.d.k.645.1		24
29.15	odd	28		841.2.d.k.645.4		24
29.16	even	7		841.2.e.a.63.1		12
29.17	odd	4		841.2.a.k.1.12		12
29.18	odd	28		841.2.d.l.778.1		24
29.19	odd	28		841.2.d.m.190.1		24
29.20	even	7		841.2.e.h.267.2		12
29.21	odd	28		841.2.d.l.574.4		24
29.22	even	14		841.2.e.i.270.2		12
29.23	even	7		841.2.e.f.196.2		12
29.24	even	7		841.2.e.e.236.1		12
29.25	even	7		841.2.e.i.651.2		12
29.26	odd	28		841.2.d.m.571.4		24
29.27	odd	28		841.2.d.k.605.4		24
29.28	even	2	inner	841.2.b.e.840.1		12
87.17	even	4		7569.2.a.bp.1.1		12
87.41	even	4		7569.2.a.bp.1.12		12
87.62	odd	14		261.2.o.a.100.2		12
87.65	odd	14		261.2.o.a.154.2		12
116.7	odd	14		464.2.y.d.241.1		12
116.91	odd	14		464.2.y.d.129.1		12
145.4	even	14		725.2.q.a.651.2		12
145.7	odd	28		725.2.p.a.299.4		24
145.33	odd	28		725.2.p.a.274.4		24
145.62	odd	28		725.2.p.a.274.1		24
145.94	even	14		725.2.q.a.676.2		12
145.123	odd	28		725.2.p.a.299.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.e.a.9.1	✓	12	29.7	even	7
29.2.e.a.13.1	yes	12	29.4	even	14
261.2.o.a.100.2		12	87.62	odd	14
261.2.o.a.154.2		12	87.65	odd	14
464.2.y.d.129.1		12	116.91	odd	14
464.2.y.d.241.1		12	116.7	odd	14
725.2.p.a.274.1		24	145.62	odd	28
725.2.p.a.274.4		24	145.33	odd	28
725.2.p.a.299.1		24	145.123	odd	28
725.2.p.a.299.4		24	145.7	odd	28
725.2.q.a.651.2		12	145.4	even	14
725.2.q.a.676.2		12	145.94	even	14
841.2.a.k.1.1		12	29.12	odd	4
841.2.a.k.1.12		12	29.17	odd	4
841.2.b.e.840.1		12	29.28	even	2	inner
841.2.b.e.840.12		12	1.1	even	1	trivial
841.2.d.k.605.1		24	29.2	odd	28
841.2.d.k.605.4		24	29.27	odd	28
841.2.d.k.645.1		24	29.14	odd	28
841.2.d.k.645.4		24	29.15	odd	28
841.2.d.l.574.1		24	29.8	odd	28
841.2.d.l.574.4		24	29.21	odd	28
841.2.d.l.778.1		24	29.18	odd	28
841.2.d.l.778.4		24	29.11	odd	28
841.2.d.m.190.1		24	29.19	odd	28
841.2.d.m.190.4		24	29.10	odd	28
841.2.d.m.571.1		24	29.3	odd	28
841.2.d.m.571.4		24	29.26	odd	28
841.2.e.a.63.1		12	29.16	even	7
841.2.e.a.267.1		12	29.9	even	14
841.2.e.e.196.1		12	29.6	even	14
841.2.e.e.236.1		12	29.24	even	7
841.2.e.f.196.2		12	29.23	even	7
841.2.e.f.236.2		12	29.5	even	14
841.2.e.h.63.2		12	29.13	even	14
841.2.e.h.267.2		12	29.20	even	7
841.2.e.i.270.2		12	29.22	even	14
841.2.e.i.651.2		12	29.25	even	7
7569.2.a.bp.1.1		12	87.17	even	4
7569.2.a.bp.1.12		12	87.41	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+2.60244i q^{2} +0.439339i q^{3} -4.77269 q^{4} -2.58042 q^{5} -1.14335 q^{6} +0.0751311 q^{7} -7.21577i q^{8} +2.80698 q^{9} -6.71540i q^{10} -3.77836i q^{11} -2.09683i q^{12} -0.880995 q^{13} +0.195524i q^{14} -1.13368i q^{15} +9.23322 q^{16} -3.94108i q^{17} +7.30500i q^{18} -0.713617i q^{19} +12.3156 q^{20} +0.0330080i q^{21} +9.83294 q^{22} +1.17764 q^{23} +3.17017 q^{24} +1.65858 q^{25} -2.29274i q^{26} +2.55123i q^{27} -0.358578 q^{28} +2.95033 q^{30} -5.15087i q^{31} +9.59735i q^{32} +1.65998 q^{33} +10.2564 q^{34} -0.193870 q^{35} -13.3969 q^{36} -3.08751i q^{37} +1.85714 q^{38} -0.387055i q^{39} +18.6197i q^{40} +6.67122i q^{41} -0.0859013 q^{42} +8.31364i q^{43} +18.0329i q^{44} -7.24320 q^{45} +3.06474i q^{46} -10.5920i q^{47} +4.05651i q^{48} -6.99436 q^{49} +4.31637i q^{50} +1.73147 q^{51} +4.20472 q^{52} +5.55608 q^{53} -6.63943 q^{54} +9.74976i q^{55} -0.542129i q^{56} +0.313519 q^{57} +9.91885 q^{59} +5.41071i q^{60} -3.56734i q^{61} +13.4048 q^{62} +0.210892 q^{63} -6.51010 q^{64} +2.27334 q^{65} +4.31999i q^{66} -4.93956 q^{67} +18.8096i q^{68} +0.517383i q^{69} -0.504535i q^{70} -4.90681 q^{71} -20.2545i q^{72} -8.90215i q^{73} +8.03505 q^{74} +0.728681i q^{75} +3.40587i q^{76} -0.283872i q^{77} +1.00729 q^{78} -13.1895i q^{79} -23.8256 q^{80} +7.30009 q^{81} -17.3615 q^{82} +16.9864 q^{83} -0.157537i q^{84} +10.1697i q^{85} -21.6357 q^{86} -27.2637 q^{88} -6.79655i q^{89} -18.8500i q^{90} -0.0661901 q^{91} -5.62052 q^{92} +2.26298 q^{93} +27.5652 q^{94} +1.84143i q^{95} -4.21649 q^{96} -11.4171i q^{97} -18.2024i q^{98} -10.6058i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} - 8 q^{5} - 24 q^{6} + 10 q^{7} - 10 q^{9} - 12 q^{13} + 16 q^{16} + 24 q^{20} + 38 q^{22} + 30 q^{23} + 10 q^{24} - 8 q^{25} + 12 q^{28} + 2 q^{30} + 4 q^{33} - 6 q^{34} - 44 q^{35} + 16 q^{36}+ \cdots + 58 q^{96}+O(q^{100}) \) 12 * q - 8 * q^4 - 8 * q^5 - 24 * q^6 + 10 * q^7 - 10 * q^9 - 12 * q^13 + 16 * q^16 + 24 * q^20 + 38 * q^22 + 30 * q^23 + 10 * q^24 - 8 * q^25 + 12 * q^28 + 2 * q^30 + 4 * q^33 - 6 * q^34 - 44 * q^35 + 16 * q^36 - 6 * q^42 - 12 * q^45 + 6 * q^49 - 8 * q^51 - 6 * q^52 + 32 * q^53 + 32 * q^54 - 14 * q^57 + 44 * q^59 + 16 * q^62 - 34 * q^63 + 2 * q^64 + 8 * q^65 - 30 * q^67 - 70 * q^71 + 56 * q^74 - 4 * q^78 - 34 * q^80 + 8 * q^81 - 62 * q^82 + 82 * q^83 - 44 * q^86 - 66 * q^88 + 32 * q^91 + 22 * q^92 + 12 * q^93 + 10 * q^94 + 58 * q^96

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