LMFDB - Embedded newform 1183.2.c.i.337.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(337,1183)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1183.337"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.c (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.58891012706304.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 $ x^12 - 5x^10 - 2x^9 + 15x^8 + 2x^7 - 30x^6 + 4x^5 + 60x^4 - 16x^3 - 80*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.6
Root			$1.34408 + 0.439820i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.i.337.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.120360i q^{2} -0.582292 q^{3} +1.98551 q^{4} +1.68817i q^{5} +0.0700846i q^{6} -1.00000i q^{7} -0.479696i q^{8} -2.66094 q^{9} +0.203187 q^{10} -0.364618i q^{11} -1.15615 q^{12} -0.120360 q^{14} -0.983005i q^{15} +3.91329 q^{16} +3.18555 q^{17} +0.320270i q^{18} -1.44391i q^{19} +3.35188i q^{20} +0.582292i q^{21} -0.0438854 q^{22} +5.08321 q^{23} +0.279323i q^{24} +2.15010 q^{25} +3.29632 q^{27} -1.98551i q^{28} +8.19662 q^{29} -0.118314 q^{30} +4.69775i q^{31} -1.43040i q^{32} +0.212314i q^{33} -0.383412i q^{34} +1.68817 q^{35} -5.28332 q^{36} +6.31584i q^{37} -0.173789 q^{38} +0.809806 q^{40} -5.82732i q^{41} +0.0700846 q^{42} +0.773122 q^{43} -0.723954i q^{44} -4.49210i q^{45} -0.611815i q^{46} +12.7905i q^{47} -2.27868 q^{48} -1.00000 q^{49} -0.258786i q^{50} -1.85492 q^{51} +1.37110 q^{53} -0.396744i q^{54} +0.615536 q^{55} -0.479696 q^{56} +0.840776i q^{57} -0.986544i q^{58} +9.36197i q^{59} -1.95177i q^{60} -9.02484 q^{61} +0.565421 q^{62} +2.66094i q^{63} +7.65442 q^{64} +0.0255541 q^{66} -13.4759i q^{67} +6.32495 q^{68} -2.95991 q^{69} -0.203187i q^{70} +7.08115i q^{71} +1.27644i q^{72} -2.16083i q^{73} +0.760173 q^{74} -1.25198 q^{75} -2.86690i q^{76} -0.364618 q^{77} -6.88781 q^{79} +6.60628i q^{80} +6.06339 q^{81} -0.701376 q^{82} -0.567380i q^{83} +1.15615i q^{84} +5.37773i q^{85} -0.0930528i q^{86} -4.77282 q^{87} -0.174906 q^{88} -1.13893i q^{89} -0.540669 q^{90} +10.0928 q^{92} -2.73547i q^{93} +1.53947 q^{94} +2.43755 q^{95} +0.832908i q^{96} -7.92785i q^{97} +0.120360i q^{98} +0.970225i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 8 q^{4} + 8 q^{9} - 24 q^{10} - 4 q^{12} - 8 q^{14} + 16 q^{16} + 8 q^{17} - 12 q^{22} + 24 q^{23} - 20 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{30} - 12 q^{35} + 20 q^{36} + 4 q^{38} + 92 q^{40} - 8 q^{42}+ \cdots + 44 q^{95}+O(q^{100}) $ 12 * q - 8 * q^4 + 8 * q^9 - 24 * q^10 - 4 * q^12 - 8 * q^14 + 16 * q^16 + 8 * q^17 - 12 * q^22 + 24 * q^23 - 20 * q^25 + 12 * q^27 - 16 * q^29 - 16 * q^30 - 12 * q^35 + 20 * q^36 + 4 * q^38 + 92 * q^40 - 8 * q^42 - 4 * q^43 + 4 * q^48 - 12 * q^49 + 52 * q^51 - 44 * q^53 + 12 * q^55 + 24 * q^56 - 28 * q^61 + 8 * q^62 - 52 * q^64 - 52 * q^66 + 16 * q^68 - 8 * q^69 - 12 * q^74 - 92 * q^75 + 8 * q^77 - 56 * q^79 - 4 * q^81 - 28 * q^82 + 4 * q^87 + 28 * q^88 + 24 * q^90 + 24 * q^92 - 8 * q^94 + 44 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$1$	$-1$

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 $

$2$	− 0.120360i	− 0.0851073i	−0.999094	−	0.0425536i	$-0.986451\pi$
$2$	− 0.120360i	− 0.0851073i	0.999094	−	0.0425536i	$-0.0135493\pi$
$3$	−0.582292	−0.336186	−0.168093	−	0.985771i	$-0.553761\pi$
$3$	−0.582292	−0.336186	−0.168093	+	0.985771i	$0.553761\pi$
$4$	1.98551	0.992757
$5$	1.68817i	0.754971i	0.926016	+	0.377485i	$0.123211\pi$
$5$	1.68817i	0.754971i	−0.926016	+	0.377485i	$0.876789\pi$
$6$	0.0700846i	0.0286119i
$7$	− 1.00000i	− 0.377964i
$7$	− 1.00000i	− 0.377964i
$8$	− 0.479696i	− 0.169598i
$9$	−2.66094	−0.886979
$10$	0.203187	0.0642535
$11$	− 0.364618i	− 0.109936i	−0.998488	−	0.0549682i	$-0.982494\pi$
$11$	− 0.364618i	− 0.109936i	0.998488	−	0.0549682i	$-0.0175058\pi$
$12$	−1.15615	−0.333751
$13$	0	0
$13$	0	0
$14$	−0.120360	−0.0321675
$15$	− 0.983005i	− 0.253811i
$16$	3.91329	0.978323
$17$	3.18555	0.772609	0.386304	−	0.922371i	$-0.373751\pi$
$17$	3.18555	0.772609	0.386304	+	0.922371i	$0.373751\pi$
$18$	0.320270i	0.0754884i
$19$	− 1.44391i	− 0.331255i	−0.986188	−	0.165628i	$-0.947035\pi$
$19$	− 1.44391i	− 0.331255i	0.986188	−	0.165628i	$-0.0529649\pi$
$20$	3.35188i	0.749502i
$21$	0.582292i	0.127067i
$22$	−0.0438854	−0.00935640
$23$	5.08321	1.05992	0.529962	−	0.848022i	$-0.322206\pi$
$23$	5.08321	1.05992	0.529962	+	0.848022i	$0.322206\pi$
$24$	0.279323i	0.0570166i
$25$	2.15010	0.430020
$26$	0	0
$27$	3.29632	0.634377
$28$	− 1.98551i	− 0.375227i
$29$	8.19662	1.52207	0.761037	−	0.648709i	$-0.224691\pi$
$29$	8.19662	1.52207	0.761037	+	0.648709i	$0.224691\pi$
$30$	−0.118314	−0.0216012
$31$	4.69775i	0.843742i	0.906656	+	0.421871i	$0.138626\pi$
$31$	4.69775i	0.843742i	−0.906656	+	0.421871i	$0.861374\pi$
$32$	− 1.43040i	− 0.252861i
$33$	0.212314i	0.0369592i
$34$	− 0.383412i	− 0.0657546i
$35$	1.68817	0.285352
$36$	−5.28332	−0.880554
$37$	6.31584i	1.03832i	0.854678	+	0.519159i	$0.173755\pi$
$37$	6.31584i	1.03832i	−0.854678	+	0.519159i	$0.826245\pi$
$38$	−0.173789	−0.0281922
$39$	0	0
$40$	0.809806	0.128042
$41$	− 5.82732i	− 0.910074i	−0.890472	−	0.455037i	$-0.849626\pi$
$41$	− 5.82732i	− 0.910074i	0.890472	−	0.455037i	$-0.150374\pi$
$42$	0.0700846	0.0108143
$43$	0.773122	0.117900	0.0589500	−	0.998261i	$-0.481225\pi$
$43$	0.773122	0.117900	0.0589500	+	0.998261i	$0.481225\pi$
$44$	− 0.723954i	− 0.109140i
$45$	− 4.49210i	− 0.669643i
$46$	− 0.611815i	− 0.0902072i
$47$	12.7905i	1.86569i	0.360275	+	0.932846i	$0.382683\pi$
$47$	12.7905i	1.86569i	−0.360275	+	0.932846i	$0.617317\pi$
$48$	−2.27868	−0.328899
$49$	−1.00000	−0.142857
$50$	− 0.258786i	− 0.0365978i
$51$	−1.85492	−0.259741
$52$	0	0
$53$	1.37110	0.188334	0.0941672	−	0.995556i	$-0.469981\pi$
$53$	1.37110	0.188334	0.0941672	+	0.995556i	$0.469981\pi$
$54$	− 0.396744i	− 0.0539901i
$55$	0.615536	0.0829988
$56$	−0.479696	−0.0641021
$57$	0.840776i	0.111363i
$58$	− 0.986544i	− 0.129540i
$59$	9.36197i	1.21882i	0.792854	+	0.609412i	$0.208595\pi$
$59$	9.36197i	1.21882i	−0.792854	+	0.609412i	$0.791405\pi$
$60$	− 1.95177i	− 0.251972i
$61$	−9.02484	−1.15551	−0.577756	−	0.816209i	$-0.696072\pi$
$61$	−9.02484	−1.15551	−0.577756	+	0.816209i	$0.696072\pi$
$62$	0.565421	0.0718086
$63$	2.66094i	0.335246i
$64$	7.65442	0.956802
$65$	0	0
$66$	0.0255541	0.00314549
$67$	− 13.4759i	− 1.64635i	−0.567789	−	0.823174i	$-0.692201\pi$
$67$	− 13.4759i	− 1.64635i	0.567789	−	0.823174i	$-0.307799\pi$
$68$	6.32495	0.767013
$69$	−2.95991	−0.356332
$70$	− 0.203187i	− 0.0242855i
$71$	7.08115i	0.840378i	0.907437	+	0.420189i	$0.138036\pi$
$71$	7.08115i	0.840378i	−0.907437	+	0.420189i	$0.861964\pi$
$72$	1.27644i	0.150430i
$73$	− 2.16083i	− 0.252906i	−0.991973	−	0.126453i	$-0.959641\pi$
$73$	− 2.16083i	− 0.252906i	0.991973	−	0.126453i	$-0.0403592\pi$
$74$	0.760173	0.0883684
$75$	−1.25198	−0.144567
$76$	− 2.86690i	− 0.328856i
$77$	−0.364618	−0.0415521
$78$	0	0
$79$	−6.88781	−0.774940	−0.387470	−	0.921882i	$-0.626651\pi$
$79$	−6.88781	−0.774940	−0.387470	+	0.921882i	$0.626651\pi$
$80$	6.60628i	0.738605i
$81$	6.06339	0.673710
$82$	−0.701376	−0.0774540
$83$	− 0.567380i	− 0.0622780i	−0.999515	−	0.0311390i	$-0.990087\pi$
$83$	− 0.567380i	− 0.0622780i	0.999515	−	0.0311390i	$-0.00991345\pi$
$84$	1.15615i	0.126146i
$85$	5.37773i	0.583297i
$86$	− 0.0930528i	− 0.0100341i
$87$	−4.77282	−0.511700
$88$	−0.174906	−0.0186450
$89$	− 1.13893i	− 0.120727i	−0.998176	−	0.0603634i	$-0.980774\pi$
$89$	− 1.13893i	− 0.120727i	0.998176	−	0.0603634i	$-0.0192260\pi$
$90$	−0.540669	−0.0569915
$91$	0	0
$92$	10.0928	1.05225
$93$	− 2.73547i	− 0.283655i
$94$	1.53947	0.158784
$95$	2.43755	0.250088
$96$	0.832908i	0.0850083i
$97$	− 7.92785i	− 0.804952i	−0.915431	−	0.402476i	$-0.868150\pi$
$97$	− 7.92785i	− 0.804952i	0.915431	−	0.402476i	$-0.131850\pi$
$98$	0.120360i	0.0121582i
$99$	0.970225i	0.0975113i
$100$	4.26905	0.426905
$101$	15.5464	1.54693	0.773465	−	0.633839i	$-0.218522\pi$
$101$	15.5464	1.54693	0.773465	+	0.633839i	$0.218522\pi$
$102$	0.223258i	0.0221058i
$103$	−10.2982	−1.01471	−0.507354	−	0.861738i	$-0.669376\pi$
$103$	−10.2982	−1.01471	−0.507354	+	0.861738i	$0.669376\pi$
$104$	0	0
$105$	−0.983005	−0.0959315
$106$	− 0.165025i	− 0.0160286i
$107$	−13.1244	−1.26878	−0.634391	−	0.773012i	$-0.718749\pi$
$107$	−13.1244	−1.26878	−0.634391	+	0.773012i	$0.718749\pi$
$108$	6.54488	0.629782
$109$	− 10.4459i	− 1.00054i	−0.865871	−	0.500268i	$-0.833235\pi$
$109$	− 10.4459i	− 1.00054i	0.865871	−	0.500268i	$-0.166765\pi$
$110$	− 0.0740858i	− 0.00706380i
$111$	− 3.67766i	− 0.349068i
$112$	− 3.91329i	− 0.369771i
$113$	4.95262	0.465903	0.232952	−	0.972488i	$-0.425162\pi$
$113$	4.95262	0.465903	0.232952	+	0.972488i	$0.425162\pi$
$114$	0.101196	0.00947784
$115$	8.58130i	0.800211i
$116$	16.2745	1.51105
$117$	0	0
$118$	1.12681	0.103731
$119$	− 3.18555i	− 0.292019i
$120$	−0.471544	−0.0430458
$121$	10.8671	0.987914
$122$	1.08623i	0.0983425i
$123$	3.39320i	0.305955i
$124$	9.32746i	0.837630i
$125$	12.0705i	1.07962i
$126$	0.320270	0.0285319
$127$	−8.06731	−0.715858	−0.357929	−	0.933749i	$-0.616517\pi$
$127$	−8.06731	−0.715858	−0.357929	+	0.933749i	$0.616517\pi$
$128$	− 3.78208i	− 0.334291i
$129$	−0.450183	−0.0396364
$130$	0	0
$131$	18.9039	1.65164	0.825820	−	0.563934i	$-0.190713\pi$
$131$	18.9039	1.65164	0.825820	+	0.563934i	$0.190713\pi$
$132$	0.421553i	0.0366915i
$133$	−1.44391	−0.125203
$134$	−1.62196	−0.140116
$135$	5.56473i	0.478936i
$136$	− 1.52809i	− 0.131033i
$137$	− 18.2255i	− 1.55711i	−0.627577	−	0.778554i	$-0.715953\pi$
$137$	− 18.2255i	− 1.55711i	0.627577	−	0.778554i	$-0.284047\pi$
$138$	0.356255i	0.0303264i
$139$	5.25085	0.445371	0.222686	−	0.974890i	$-0.428518\pi$
$139$	5.25085	0.445371	0.222686	+	0.974890i	$0.428518\pi$
$140$	3.35188	0.283285
$141$	− 7.44783i	− 0.627220i
$142$	0.852287	0.0715223
$143$	0	0
$144$	−10.4130	−0.867751
$145$	13.8372i	1.14912i
$146$	−0.260077	−0.0215241
$147$	0.582292	0.0480266
$148$	12.5402i	1.03080i
$149$	− 9.27309i	− 0.759681i	−0.925052	−	0.379841i	$-0.875979\pi$
$149$	− 9.27309i	− 0.759681i	0.925052	−	0.379841i	$-0.124021\pi$
$150$	0.150689i	0.0123037i
$151$	− 14.0132i	− 1.14038i	−0.821513	−	0.570189i	$-0.806870\pi$
$151$	− 14.0132i	− 1.14038i	0.821513	−	0.570189i	$-0.193130\pi$
$152$	−0.692636	−0.0561802
$153$	−8.47654	−0.685287
$154$	0.0438854i	0.00353639i
$155$	−7.93059	−0.637000
$156$	0	0
$157$	−17.1825	−1.37131	−0.685656	−	0.727925i	$-0.740485\pi$
$157$	−17.1825	−1.37131	−0.685656	+	0.727925i	$0.740485\pi$
$158$	0.829017i	0.0659530i
$159$	−0.798378	−0.0633155
$160$	2.41474	0.190902
$161$	− 5.08321i	− 0.400613i
$162$	− 0.729789i	− 0.0573376i
$163$	− 11.7927i	− 0.923679i	−0.886963	−	0.461840i	$-0.847190\pi$
$163$	− 11.7927i	− 0.923679i	0.886963	−	0.461840i	$-0.152810\pi$
$164$	− 11.5702i	− 0.903482i
$165$	−0.358422	−0.0279031
$166$	−0.0682898	−0.00530031
$167$	4.31687i	0.334049i	0.985953	+	0.167025i	$0.0534159\pi$
$167$	4.31687i	0.334049i	−0.985953	+	0.167025i	$0.946584\pi$
$168$	0.279323	0.0215502
$169$	0	0
$170$	0.647263	0.0496428
$171$	3.84214i	0.293816i
$172$	1.53504	0.117046
$173$	−12.5197	−0.951855	−0.475928	−	0.879484i	$-0.657888\pi$
$173$	−12.5197	−0.951855	−0.475928	+	0.879484i	$0.657888\pi$
$174$	0.574457i	0.0435494i
$175$	− 2.15010i	− 0.162532i
$176$	− 1.42686i	− 0.107553i
$177$	− 5.45140i	− 0.409752i
$178$	−0.137082	−0.0102747
$179$	6.59534	0.492959	0.246479	−	0.969148i	$-0.420726\pi$
$179$	6.59534	0.492959	0.246479	+	0.969148i	$0.420726\pi$
$180$	− 8.91913i	− 0.664792i
$181$	−11.0157	−0.818791	−0.409395	−	0.912357i	$-0.634260\pi$
$181$	−11.0157	−0.818791	−0.409395	+	0.912357i	$0.634260\pi$
$182$	0	0
$183$	5.25509	0.388468
$184$	− 2.43840i	− 0.179761i
$185$	−10.6622	−0.783899
$186$	−0.329240	−0.0241411
$187$	− 1.16151i	− 0.0849379i
$188$	25.3958i	1.85218i
$189$	− 3.29632i	− 0.239772i
$190$	− 0.293384i	− 0.0212843i
$191$	5.93213	0.429234	0.214617	−	0.976698i	$-0.431150\pi$
$191$	5.93213	0.429234	0.214617	+	0.976698i	$0.431150\pi$
$192$	−4.45711	−0.321664
$193$	4.19595i	0.302031i	0.988531	+	0.151016i	$0.0482544\pi$
$193$	4.19595i	0.302031i	−0.988531	+	0.151016i	$0.951746\pi$
$194$	−0.954196	−0.0685073
$195$	0	0
$196$	−1.98551	−0.141822
$197$	5.78494i	0.412160i	0.978535	+	0.206080i	$0.0660707\pi$
$197$	5.78494i	0.412160i	−0.978535	+	0.206080i	$0.933929\pi$
$198$	0.116776	0.00829893
$199$	−11.9598	−0.847805	−0.423903	−	0.905708i	$-0.639340\pi$
$199$	−11.9598	−0.847805	−0.423903	+	0.905708i	$0.639340\pi$
$200$	− 1.03139i	− 0.0729305i
$201$	7.84693i	0.553480i
$202$	− 1.87117i	− 0.131655i
$203$	− 8.19662i	− 0.575290i
$204$	−3.68297	−0.257859
$205$	9.83748	0.687079
$206$	1.23949i	0.0863590i
$207$	−13.5261	−0.940129
$208$	0	0
$209$	−0.526475	−0.0364170
$210$	0.118314i	0.00816447i
$211$	−8.23591	−0.566983	−0.283492	−	0.958975i	$-0.591493\pi$
$211$	−8.23591	−0.566983	−0.283492	+	0.958975i	$0.591493\pi$
$212$	2.72233	0.186970
$213$	− 4.12330i	− 0.282524i
$214$	1.57965i	0.107983i
$215$	1.30516i	0.0890110i
$216$	− 1.58123i	− 0.107589i
$217$	4.69775	0.318904
$218$	−1.25727	−0.0851528
$219$	1.25823i	0.0850234i
$220$	1.22215	0.0823976
$221$	0	0
$222$	−0.442643	−0.0297082
$223$	15.3015i	1.02466i	0.858788	+	0.512331i	$0.171218\pi$
$223$	15.3015i	1.02466i	−0.858788	+	0.512331i	$0.828782\pi$
$224$	−1.43040	−0.0955723
$225$	−5.72127	−0.381418
$226$	− 0.596097i	− 0.0396518i
$227$	6.95467i	0.461598i	0.973002	+	0.230799i	$0.0741339\pi$
$227$	6.95467i	0.461598i	−0.973002	+	0.230799i	$0.925866\pi$
$228$	1.66937i	0.110557i
$229$	27.4219i	1.81209i	0.423180	+	0.906045i	$0.360914\pi$
$229$	27.4219i	1.81209i	−0.423180	+	0.906045i	$0.639086\pi$
$230$	1.03284	0.0681038
$231$	0.212314	0.0139693
$232$	− 3.93188i	− 0.258141i
$233$	6.85333	0.448976	0.224488	−	0.974477i	$-0.427929\pi$
$233$	6.85333	0.448976	0.224488	+	0.974477i	$0.427929\pi$
$234$	0	0
$235$	−21.5926	−1.40854
$236$	18.5883i	1.21000i
$237$	4.01072	0.260524
$238$	−0.383412	−0.0248529
$239$	− 22.0754i	− 1.42794i	−0.700177	−	0.713970i	$-0.746895\pi$
$239$	− 22.0754i	− 1.42794i	0.700177	−	0.713970i	$-0.253105\pi$
$240$	− 3.84679i	− 0.248309i
$241$	− 15.7971i	− 1.01758i	−0.860890	−	0.508790i	$-0.830093\pi$
$241$	− 15.7971i	− 1.01758i	0.860890	−	0.508790i	$-0.169907\pi$
$242$	− 1.30796i	− 0.0840787i
$243$	−13.4196	−0.860869
$244$	−17.9189	−1.14714
$245$	− 1.68817i	− 0.107853i
$246$	0.408405	0.0260390
$247$	0	0
$248$	2.25349	0.143097
$249$	0.330381i	0.0209370i
$250$	1.45281	0.0918838
$251$	−22.5567	−1.42376	−0.711882	−	0.702299i	$-0.752157\pi$
$251$	−22.5567	−1.42376	−0.711882	+	0.702299i	$0.752157\pi$
$252$	5.28332i	0.332818i
$253$	− 1.85343i	− 0.116524i
$254$	0.970981i	0.0609247i
$255$	− 3.13141i	− 0.196097i
$256$	14.8536	0.928352
$257$	−20.4129	−1.27332	−0.636660	−	0.771145i	$-0.719685\pi$
$257$	−20.4129	−1.27332	−0.636660	+	0.771145i	$0.719685\pi$
$258$	0.0541839i	0.00337334i
$259$	6.31584	0.392447
$260$	0	0
$261$	−21.8107	−1.35005
$262$	− 2.27527i	− 0.140567i
$263$	−29.5402	−1.82153	−0.910764	−	0.412927i	$-0.864506\pi$
$263$	−29.5402	−1.82153	−0.910764	+	0.412927i	$0.864506\pi$
$264$	0.101846	0.00626820
$265$	2.31464i	0.142187i
$266$	0.173789i	0.0106557i
$267$	0.663193i	0.0405867i
$268$	− 26.7567i	− 1.63442i
$269$	27.9163	1.70209	0.851043	−	0.525096i	$-0.175971\pi$
$269$	27.9163	1.70209	0.851043	+	0.525096i	$0.175971\pi$
$270$	0.669770	0.0407609
$271$	− 29.4491i	− 1.78890i	−0.447165	−	0.894451i	$-0.647566\pi$
$271$	− 29.4491i	− 1.78890i	0.447165	−	0.894451i	$-0.352434\pi$
$272$	12.4660	0.755861
$273$	0	0
$274$	−2.19362	−0.132521
$275$	− 0.783965i	− 0.0472748i
$276$	−5.87695	−0.353751
$277$	−6.85854	−0.412090	−0.206045	−	0.978543i	$-0.566059\pi$
$277$	−6.85854	−0.412090	−0.206045	+	0.978543i	$0.566059\pi$
$278$	− 0.631992i	− 0.0379043i
$279$	− 12.5004i	− 0.748381i
$280$	− 0.809806i	− 0.0483952i
$281$	29.0940i	1.73561i	0.496909	+	0.867803i	$0.334468\pi$
$281$	29.0940i	1.73561i	−0.496909	+	0.867803i	$0.665532\pi$
$282$	−0.896420	−0.0533810
$283$	−11.6102	−0.690156	−0.345078	−	0.938574i	$-0.612147\pi$
$283$	−11.6102	−0.690156	−0.345078	+	0.938574i	$0.612147\pi$
$284$	14.0597i	0.834291i
$285$	−1.41937	−0.0840761
$286$	0	0
$287$	−5.82732	−0.343976
$288$	3.80619i	0.224282i
$289$	−6.85229	−0.403076
$290$	1.66545	0.0977985
$291$	4.61633i	0.270614i
$292$	− 4.29035i	− 0.251074i
$293$	17.7886i	1.03922i	0.854403	+	0.519610i	$0.173923\pi$
$293$	17.7886i	1.03922i	−0.854403	+	0.519610i	$0.826077\pi$
$294$	− 0.0700846i	− 0.00408742i
$295$	−15.8046	−0.920177
$296$	3.02968	0.176097
$297$	− 1.20190i	− 0.0697412i
$298$	−1.11611	−0.0646544
$299$	0	0
$300$	−2.48583	−0.143520
$301$	− 0.773122i	− 0.0445620i
$302$	−1.68663	−0.0970546
$303$	−9.05257	−0.520057
$304$	− 5.65043i	− 0.324074i
$305$	− 15.2354i	− 0.872378i
$306$	1.02024i	0.0583230i
$307$	− 9.07966i	− 0.518204i	−0.965850	−	0.259102i	$-0.916573\pi$
$307$	− 9.07966i	− 0.518204i	0.965850	−	0.259102i	$-0.0834265\pi$
$308$	−0.723954	−0.0412511
$309$	5.99654	0.341131
$310$	0.954525i	0.0542134i
$311$	−1.57073	−0.0890677	−0.0445338	−	0.999008i	$-0.514180\pi$
$311$	−1.57073	−0.0890677	−0.0445338	+	0.999008i	$0.514180\pi$
$312$	0	0
$313$	20.6232	1.16569	0.582846	−	0.812582i	$-0.301939\pi$
$313$	20.6232	1.16569	0.582846	+	0.812582i	$0.301939\pi$
$314$	2.06808i	0.116709i
$315$	−4.49210	−0.253101
$316$	−13.6758	−0.769327
$317$	− 30.5435i	− 1.71549i	−0.514072	−	0.857747i	$-0.671863\pi$
$317$	− 30.5435i	− 1.71549i	0.514072	−	0.857747i	$-0.328137\pi$
$318$	0.0960927i	0.00538861i
$319$	− 2.98863i	− 0.167331i
$320$	12.9219i	0.722358i
$321$	7.64223	0.426548
$322$	−0.611815	−0.0340951
$323$	− 4.59964i	− 0.255931i
$324$	12.0389	0.668830
$325$	0	0
$326$	−1.41937	−0.0786118
$327$	6.08256i	0.336366i
$328$	−2.79534	−0.154347
$329$	12.7905	0.705165
$330$	0.0431396i	0.00237476i
$331$	25.8531i	1.42101i	0.703690	+	0.710507i	$0.251534\pi$
$331$	25.8531i	1.42101i	−0.703690	+	0.710507i	$0.748466\pi$
$332$	− 1.12654i	− 0.0618269i
$333$	− 16.8060i	− 0.920965i
$334$	0.519578	0.0284300
$335$	22.7496	1.24294
$336$	2.27868i	0.124312i
$337$	−21.3954	−1.16548	−0.582742	−	0.812657i	$-0.698020\pi$
$337$	−21.3954	−1.16548	−0.582742	+	0.812657i	$0.698020\pi$
$338$	0	0
$339$	−2.88387	−0.156630
$340$	10.6776i	0.579072i
$341$	1.71289	0.0927580
$342$	0.462440	0.0250059
$343$	1.00000i	0.0539949i
$344$	− 0.370863i	− 0.0199956i
$345$	− 4.99682i	− 0.269020i
$346$	1.50687i	0.0810098i
$347$	2.20883	0.118576	0.0592882	−	0.998241i	$-0.481117\pi$
$347$	2.20883	0.118576	0.0592882	+	0.998241i	$0.481117\pi$
$348$	−9.47651	−0.507994
$349$	− 11.2912i	− 0.604402i	−0.953244	−	0.302201i	$-0.902279\pi$
$349$	− 11.2912i	− 0.604402i	0.953244	−	0.302201i	$-0.0977214\pi$
$350$	−0.258786	−0.0138327
$351$	0	0
$352$	−0.521548	−0.0277986
$353$	− 35.6433i	− 1.89710i	−0.316623	−	0.948552i	$-0.602549\pi$
$353$	− 35.6433i	− 1.89710i	0.316623	−	0.948552i	$-0.397451\pi$
$354$	−0.656130	−0.0348729
$355$	−11.9542	−0.634461
$356$	− 2.26137i	− 0.119852i
$357$	1.85492i	0.0981727i
$358$	− 0.793815i	− 0.0419544i
$359$	− 19.3218i	− 1.01976i	−0.860244	−	0.509882i	$-0.829689\pi$
$359$	− 19.3218i	− 1.01976i	0.860244	−	0.509882i	$-0.170311\pi$
$360$	−2.15484	−0.113570
$361$	16.9151	0.890270
$362$	1.32585i	0.0696851i
$363$	−6.32780	−0.332123
$364$	0	0
$365$	3.64783	0.190936
$366$	− 0.632502i	− 0.0330614i
$367$	−3.72065	−0.194216	−0.0971082	−	0.995274i	$-0.530959\pi$
$367$	−3.72065	−0.194216	−0.0971082	+	0.995274i	$0.530959\pi$
$368$	19.8921	1.03695
$369$	15.5061i	0.807217i
$370$	1.28330i	0.0667155i
$371$	− 1.37110i	− 0.0711837i
$372$	− 5.43130i	− 0.281600i
$373$	−3.51276	−0.181884	−0.0909420	−	0.995856i	$-0.528988\pi$
$373$	−3.51276	−0.181884	−0.0909420	+	0.995856i	$0.528988\pi$
$374$	−0.139799	−0.00722884
$375$	− 7.02858i	− 0.362954i
$376$	6.13557	0.316418
$377$	0	0
$378$	−0.396744	−0.0204063
$379$	25.0163i	1.28500i	0.766285	+	0.642500i	$0.222103\pi$
$379$	25.0163i	1.28500i	−0.766285	+	0.642500i	$0.777897\pi$
$380$	4.83980	0.248276
$381$	4.69753	0.240662
$382$	− 0.713990i	− 0.0365309i
$383$	22.4654i	1.14793i	0.818881	+	0.573964i	$0.194595\pi$
$383$	22.4654i	1.14793i	−0.818881	+	0.573964i	$0.805405\pi$
$384$	2.20227i	0.112384i
$385$	− 0.615536i	− 0.0313706i
$386$	0.505024	0.0257051
$387$	−2.05723	−0.104575
$388$	− 15.7409i	− 0.799121i
$389$	13.3364	0.676184	0.338092	−	0.941113i	$-0.390219\pi$
$389$	13.3364	0.676184	0.338092	+	0.941113i	$0.390219\pi$
$390$	0	0
$391$	16.1928	0.818906
$392$	0.479696i	0.0242283i
$393$	−11.0076	−0.555259
$394$	0.696274	0.0350778
$395$	− 11.6278i	− 0.585057i
$396$	1.92640i	0.0968050i
$397$	25.8333i	1.29654i	0.761412	+	0.648268i	$0.224506\pi$
$397$	25.8333i	1.29654i	−0.761412	+	0.648268i	$0.775494\pi$
$398$	1.43948i	0.0721544i
$399$	0.840776	0.0420914
$400$	8.41396	0.420698
$401$	17.5605i	0.876930i	0.898748	+	0.438465i	$0.144478\pi$
$401$	17.5605i	0.876930i	−0.898748	+	0.438465i	$0.855522\pi$
$402$	0.944456	0.0471052
$403$	0	0
$404$	30.8677	1.53572
$405$	10.2360i	0.508631i
$406$	−0.986544	−0.0489613
$407$	2.30287	0.114149
$408$	0.889797i	0.0440515i
$409$	− 14.5282i	− 0.718373i	−0.933266	−	0.359186i	$-0.883054\pi$
$409$	− 14.5282i	− 0.718373i	0.933266	−	0.359186i	$-0.116946\pi$
$410$	− 1.18404i	− 0.0584755i
$411$	10.6126i	0.523479i
$412$	−20.4471	−1.00736
$413$	9.36197	0.460672
$414$	1.62800i	0.0800119i
$415$	0.957831	0.0470181
$416$	0	0
$417$	−3.05753	−0.149728
$418$	0.0633664i	0.00309935i
$419$	−4.60192	−0.224819	−0.112409	−	0.993662i	$-0.535857\pi$
$419$	−4.60192	−0.224819	−0.112409	+	0.993662i	$0.535857\pi$
$420$	−1.95177	−0.0952366
$421$	19.2645i	0.938895i	0.882960	+	0.469447i	$0.155547\pi$
$421$	19.2645i	0.938895i	−0.882960	+	0.469447i	$0.844453\pi$
$422$	0.991273i	0.0482544i
$423$	− 34.0348i	− 1.65483i
$424$	− 0.657709i	− 0.0319412i
$425$	6.84924	0.332237
$426$	−0.496280	−0.0240448
$427$	9.02484i	0.436743i
$428$	−26.0587	−1.25959
$429$	0	0
$430$	0.157089	0.00757548
$431$	− 28.3651i	− 1.36630i	−0.730279	−	0.683149i	$-0.760610\pi$
$431$	− 28.3651i	− 1.36630i	0.730279	−	0.683149i	$-0.239390\pi$
$432$	12.8995	0.620625
$433$	12.5203	0.601686	0.300843	−	0.953674i	$-0.402732\pi$
$433$	12.5203	0.601686	0.300843	+	0.953674i	$0.402732\pi$
$434$	− 0.565421i	− 0.0271411i
$435$	− 8.05732i	− 0.386319i
$436$	− 20.7405i	− 0.993288i
$437$	− 7.33969i	− 0.351105i
$438$	0.151441	0.00723611
$439$	−31.7273	−1.51426	−0.757132	−	0.653262i	$-0.773400\pi$
$439$	−31.7273	−1.51426	−0.757132	+	0.653262i	$0.773400\pi$
$440$	− 0.295270i	− 0.0140764i
$441$	2.66094	0.126711
$442$	0	0
$443$	1.73048	0.0822177	0.0411088	−	0.999155i	$-0.486911\pi$
$443$	1.73048	0.0822177	0.0411088	+	0.999155i	$0.486911\pi$
$444$	− 7.30205i	− 0.346540i
$445$	1.92271	0.0911452
$446$	1.84168	0.0872062
$447$	5.39965i	0.255394i
$448$	− 7.65442i	− 0.361637i
$449$	10.5564i	0.498186i	0.968480	+	0.249093i	$0.0801325\pi$
$449$	10.5564i	0.498186i	−0.968480	+	0.249093i	$0.919868\pi$
$450$	0.688612i	0.0324615i
$451$	−2.12475	−0.100050
$452$	9.83349	0.462528
$453$	8.15978i	0.383380i
$454$	0.837063	0.0392853
$455$	0	0
$456$	0.403317	0.0188870
$457$	− 7.94894i	− 0.371836i	−0.982565	−	0.185918i	$-0.940474\pi$
$457$	− 7.94894i	− 0.371836i	0.982565	−	0.185918i	$-0.0595259\pi$
$458$	3.30050	0.154222
$459$	10.5006	0.490125
$460$	17.0383i	0.794415i
$461$	− 10.8918i	− 0.507284i	−0.967298	−	0.253642i	$-0.918371\pi$
$461$	− 10.8918i	− 0.507284i	0.967298	−	0.253642i	$-0.0816285\pi$
$462$	− 0.0255541i	− 0.00118889i
$463$	35.8227i	1.66482i	0.554158	+	0.832411i	$0.313040\pi$
$463$	35.8227i	1.66482i	−0.554158	+	0.832411i	$0.686960\pi$
$464$	32.0757	1.48908
$465$	4.61792	0.214151
$466$	− 0.824866i	− 0.0382112i
$467$	−19.8983	−0.920785	−0.460393	−	0.887715i	$-0.652291\pi$
$467$	−19.8983	−0.920785	−0.460393	+	0.887715i	$0.652291\pi$
$468$	0	0
$469$	−13.4759	−0.622261
$470$	2.59888i	0.119877i
$471$	10.0052	0.461017
$472$	4.49090	0.206710
$473$	− 0.281894i	− 0.0129615i
$474$	− 0.482730i	− 0.0221725i
$475$	− 3.10454i	− 0.142446i
$476$	− 6.32495i	− 0.289904i
$477$	−3.64840	−0.167049
$478$	−2.65699	−0.121528
$479$	26.2902i	1.20123i	0.799538	+	0.600615i	$0.205078\pi$
$479$	26.2902i	1.20123i	−0.799538	+	0.600615i	$0.794922\pi$
$480$	−1.40609	−0.0641788
$481$	0	0
$482$	−1.90134	−0.0866035
$483$	2.95991i	0.134681i
$484$	21.5767	0.980758
$485$	13.3835	0.607715
$486$	1.61518i	0.0732662i
$487$	− 6.37962i	− 0.289088i	−0.989498	−	0.144544i	$-0.953828\pi$
$487$	− 6.37962i	− 0.289088i	0.989498	−	0.144544i	$-0.0461716\pi$
$488$	4.32918i	0.195973i
$489$	6.86682i	0.310528i
$490$	−0.203187	−0.00917907
$491$	2.96768	0.133929	0.0669647	−	0.997755i	$-0.478669\pi$
$491$	2.96768	0.133929	0.0669647	+	0.997755i	$0.478669\pi$
$492$	6.73725i	0.303739i
$493$	26.1107	1.17597
$494$	0	0
$495$	−1.63790	−0.0736182
$496$	18.3837i	0.825452i
$497$	7.08115	0.317633
$498$	0.0397646	0.00178189
$499$	28.1331i	1.25941i	0.776835	+	0.629704i	$0.216824\pi$
$499$	28.1331i	1.25941i	−0.776835	+	0.629704i	$0.783176\pi$
$500$	23.9662i	1.07180i
$501$	− 2.51368i	− 0.112303i
$502$	2.71492i	0.121173i
$503$	−31.5376	−1.40619	−0.703097	−	0.711094i	$-0.748200\pi$
$503$	−31.5376	−1.40619	−0.703097	+	0.711094i	$0.748200\pi$
$504$	1.27644	0.0568572
$505$	26.2450i	1.16789i
$506$	−0.223079	−0.00991706
$507$	0	0
$508$	−16.0178	−0.710673
$509$	13.5944i	0.602560i	0.953536	+	0.301280i	$0.0974139\pi$
$509$	13.5944i	0.602560i	−0.953536	+	0.301280i	$0.902586\pi$
$510$	−0.376896	−0.0166892
$511$	−2.16083	−0.0955893
$512$	− 9.35193i	− 0.413301i
$513$	− 4.75958i	− 0.210140i
$514$	2.45689i	0.108369i
$515$	− 17.3850i	− 0.766074i
$516$	−0.893844	−0.0393493
$517$	4.66366	0.205108
$518$	− 0.760173i	− 0.0334001i
$519$	7.29012	0.320001
$520$	0	0
$521$	8.78344	0.384810	0.192405	−	0.981316i	$-0.438371\pi$
$521$	8.78344	0.384810	0.192405	+	0.981316i	$0.438371\pi$
$522$	2.62513i	0.114899i
$523$	32.5698	1.42418	0.712088	−	0.702090i	$-0.247749\pi$
$523$	32.5698	1.42418	0.712088	+	0.702090i	$0.247749\pi$
$524$	37.5339	1.63968
$525$	1.25198i	0.0546411i
$526$	3.55546i	0.155025i
$527$	14.9649i	0.651882i
$528$	0.830847i	0.0361580i
$529$	2.83905	0.123437
$530$	0.278589	0.0121011
$531$	− 24.9116i	− 1.08107i
$532$	−2.86690	−0.124296
$533$	0	0
$534$	0.0798218	0.00345423
$535$	− 22.1561i	− 0.957894i
$536$	−6.46435	−0.279218
$537$	−3.84041	−0.165726
$538$	− 3.36000i	− 0.144860i
$539$	0.364618i	0.0157052i
$540$	11.0488i	0.475467i
$541$	6.94870i	0.298748i	0.988781	+	0.149374i	$0.0477258\pi$
$541$	6.94870i	0.298748i	−0.988781	+	0.149374i	$0.952274\pi$
$542$	−3.54448	−0.152249
$543$	6.41436	0.275266
$544$	− 4.55659i	− 0.195362i
$545$	17.6344	0.755375
$546$	0	0
$547$	10.9095	0.466457	0.233229	−	0.972422i	$-0.425071\pi$
$547$	10.9095	0.466457	0.233229	+	0.972422i	$0.425071\pi$
$548$	− 36.1870i	− 1.54583i
$549$	24.0145	1.02491
$550$	−0.0943579	−0.00402343
$551$	− 11.8352i	− 0.504194i
$552$	1.41986i	0.0604332i
$553$	6.88781i	0.292900i
$554$	0.825493i	0.0350718i
$555$	6.20850	0.263536
$556$	10.4256	0.442145
$557$	34.6295i	1.46730i	0.679527	+	0.733650i	$0.262185\pi$
$557$	34.6295i	1.46730i	−0.679527	+	0.733650i	$0.737815\pi$
$558$	−1.50455	−0.0636927
$559$	0	0
$560$	6.60628	0.279166
$561$	0.676337i	0.0285550i
$562$	3.50176	0.147713
$563$	−9.13679	−0.385070	−0.192535	−	0.981290i	$-0.561671\pi$
$563$	−9.13679	−0.385070	−0.192535	+	0.981290i	$0.561671\pi$
$564$	− 14.7878i	− 0.622677i
$565$	8.36084i	0.351743i
$566$	1.39740i	0.0587373i
$567$	− 6.06339i	− 0.254638i
$568$	3.39680	0.142527
$569$	−18.3000	−0.767176	−0.383588	−	0.923504i	$-0.625312\pi$
$569$	−18.3000	−0.767176	−0.383588	+	0.923504i	$0.625312\pi$
$570$	0.170835i	0.00715549i
$571$	−10.1791	−0.425981	−0.212990	−	0.977054i	$-0.568320\pi$
$571$	−10.1791	−0.425981	−0.212990	+	0.977054i	$0.568320\pi$
$572$	0	0
$573$	−3.45423	−0.144303
$574$	0.701376i	0.0292748i
$575$	10.9294	0.455788
$576$	−20.3679	−0.848663
$577$	− 19.5165i	− 0.812482i	−0.913766	−	0.406241i	$-0.866839\pi$
$577$	− 19.5165i	− 0.812482i	0.913766	−	0.406241i	$-0.133161\pi$
$578$	0.824740i	0.0343047i
$579$	− 2.44327i	− 0.101539i
$580$	27.4740i	1.14080i
$581$	−0.567380	−0.0235389
$582$	0.555621	0.0230312
$583$	− 0.499926i	− 0.0207048i
$584$	−1.03654	−0.0428923
$585$	0	0
$586$	2.14103	0.0884453
$587$	− 35.3900i	− 1.46070i	−0.683072	−	0.730351i	$-0.739357\pi$
$587$	− 35.3900i	− 1.46070i	0.683072	−	0.730351i	$-0.260643\pi$
$588$	1.15615	0.0476788
$589$	6.78312	0.279494
$590$	1.90223i	0.0783137i
$591$	− 3.36852i	− 0.138562i
$592$	24.7157i	1.01581i
$593$	18.0881i	0.742790i	0.928475	+	0.371395i	$0.121120\pi$
$593$	18.0881i	0.742790i	−0.928475	+	0.371395i	$0.878880\pi$
$594$	−0.144660	−0.00593548
$595$	5.37773	0.220465
$596$	− 18.4118i	− 0.754179i
$597$	6.96407	0.285021
$598$	0	0
$599$	9.05992	0.370178	0.185089	−	0.982722i	$-0.440743\pi$
$599$	9.05992	0.370178	0.185089	+	0.982722i	$0.440743\pi$
$600$	0.600572i	0.0245182i
$601$	29.2881	1.19469	0.597343	−	0.801986i	$-0.296223\pi$
$601$	29.2881	1.19469	0.597343	+	0.801986i	$0.296223\pi$
$602$	−0.0930528	−0.00379255
$603$	35.8586i	1.46028i
$604$	− 27.8234i	− 1.13212i
$605$	18.3454i	0.745846i
$606$	1.08957i	0.0442606i
$607$	−39.3650	−1.59777	−0.798887	−	0.601481i	$-0.794578\pi$
$607$	−39.3650	−1.59777	−0.798887	+	0.601481i	$0.794578\pi$
$608$	−2.06536	−0.0837613
$609$	4.77282i	0.193405i
$610$	−1.83373	−0.0742457
$611$	0	0
$612$	−16.8303	−0.680324
$613$	5.53316i	0.223482i	0.993737	+	0.111741i	$0.0356427\pi$
$613$	5.53316i	0.223482i	−0.993737	+	0.111741i	$0.964357\pi$
$614$	−1.09283	−0.0441029
$615$	−5.72829	−0.230987
$616$	0.174906i	0.00704716i
$617$	− 12.5815i	− 0.506514i	−0.967399	−	0.253257i	$-0.918498\pi$
$617$	− 12.5815i	− 0.506514i	0.967399	−	0.253257i	$-0.0815018\pi$
$618$	− 0.721742i	− 0.0290327i
$619$	− 22.3955i	− 0.900149i	−0.892991	−	0.450075i	$-0.851397\pi$
$619$	− 22.3955i	− 0.900149i	0.892991	−	0.450075i	$-0.148603\pi$
$620$	−15.7463	−0.632386
$621$	16.7559	0.672390
$622$	0.189052i	0.00758031i
$623$	−1.13893	−0.0456305
$624$	0	0
$625$	−9.62659	−0.385064
$626$	− 2.48221i	− 0.0992090i
$627$	0.306562	0.0122429
$628$	−34.1161	−1.36138
$629$	20.1194i	0.802213i
$630$	0.540669i	0.0215408i
$631$	− 1.94888i	− 0.0775836i	−0.999247	−	0.0387918i	$-0.987649\pi$
$631$	− 1.94888i	− 0.0775836i	0.999247	−	0.0387918i	$-0.0123509\pi$
$632$	3.30406i	0.131428i
$633$	4.79570	0.190612
$634$	−3.67621	−0.146001
$635$	− 13.6190i	− 0.540452i
$636$	−1.58519	−0.0628569
$637$	0	0
$638$	−0.359712	−0.0142411
$639$	− 18.8425i	− 0.745397i
$640$	6.38477	0.252380
$641$	−10.4210	−0.411605	−0.205803	−	0.978594i	$-0.565981\pi$
$641$	−10.4210	−0.411605	−0.205803	+	0.978594i	$0.565981\pi$
$642$	− 0.919818i	− 0.0363023i
$643$	− 15.2706i	− 0.602214i	−0.953590	−	0.301107i	$-0.902644\pi$
$643$	− 15.2706i	− 0.602214i	0.953590	−	0.301107i	$-0.0973562\pi$
$644$	− 10.0928i	− 0.397712i
$645$	− 0.759983i	− 0.0299243i
$646$	−0.553612	−0.0217816
$647$	−17.5066	−0.688254	−0.344127	−	0.938923i	$-0.611825\pi$
$647$	−17.5066	−0.688254	−0.344127	+	0.938923i	$0.611825\pi$
$648$	− 2.90858i	− 0.114260i
$649$	3.41354	0.133993
$650$	0	0
$651$	−2.73547	−0.107211
$652$	− 23.4147i	− 0.916989i
$653$	−10.1834	−0.398506	−0.199253	−	0.979948i	$-0.563852\pi$
$653$	−10.1834	−0.398506	−0.199253	+	0.979948i	$0.563852\pi$
$654$	0.732096	0.0286272
$655$	31.9129i	1.24694i
$656$	− 22.8040i	− 0.890346i
$657$	5.74982i	0.224322i
$658$	− 1.53947i	− 0.0600147i
$659$	−43.8587	−1.70849	−0.854247	−	0.519867i	$-0.825981\pi$
$659$	−43.8587	−1.70849	−0.854247	+	0.519867i	$0.825981\pi$
$660$	−0.711651	−0.0277010
$661$	− 32.9270i	− 1.28071i	−0.768078	−	0.640356i	$-0.778787\pi$
$661$	− 32.9270i	− 1.28071i	0.768078	−	0.640356i	$-0.221213\pi$
$662$	3.11167	0.120939
$663$	0	0
$664$	−0.272170	−0.0105622
$665$	− 2.43755i	− 0.0945243i
$666$	−2.02277	−0.0783808
$667$	41.6651	1.61328
$668$	8.57120i	0.331630i
$669$	− 8.90992i	− 0.344478i
$670$	− 2.73814i	− 0.105784i
$671$	3.29062i	0.127033i
$672$	0.832908	0.0321301
$673$	−26.6845	−1.02861	−0.514307	−	0.857606i	$-0.671951\pi$
$673$	−26.6845	−1.02861	−0.514307	+	0.857606i	$0.671951\pi$
$674$	2.57515i	0.0991912i
$675$	7.08740	0.272794
$676$	0	0
$677$	29.5328	1.13504	0.567519	−	0.823361i	$-0.307904\pi$
$677$	29.5328	1.13504	0.567519	+	0.823361i	$0.307904\pi$
$678$	0.347102i	0.0133304i
$679$	−7.92785	−0.304243
$680$	2.57968	0.0989261
$681$	− 4.04965i	− 0.155183i
$682$	− 0.206163i	− 0.00789438i
$683$	18.2880i	0.699771i	0.936793	+	0.349885i	$0.113779\pi$
$683$	18.2880i	0.699771i	−0.936793	+	0.349885i	$0.886221\pi$
$684$	7.62863i	0.291688i
$685$	30.7676	1.17557
$686$	0.120360	0.00459536
$687$	− 15.9676i	− 0.609200i
$688$	3.02545	0.115344
$689$	0	0
$690$	−0.601417	−0.0228956
$691$	− 10.3406i	− 0.393376i	−0.980466	−	0.196688i	$-0.936981\pi$
$691$	− 10.3406i	− 0.393376i	0.980466	−	0.196688i	$-0.0630186\pi$
$692$	−24.8580	−0.944961
$693$	0.970225	0.0368558
$694$	− 0.265855i	− 0.0100917i
$695$	8.86430i	0.336242i
$696$	2.28950i	0.0867834i
$697$	− 18.5632i	− 0.703131i
$698$	−1.35900	−0.0514390
$699$	−3.99064	−0.150940
$700$	− 4.26905i	− 0.161355i
$701$	41.6959	1.57483	0.787415	−	0.616423i	$-0.211419\pi$
$701$	41.6959	1.57483	0.787415	+	0.616423i	$0.211419\pi$
$702$	0	0
$703$	9.11948	0.343948
$704$	− 2.79094i	− 0.105188i
$705$	12.5732	0.473533
$706$	−4.29003	−0.161457
$707$	− 15.5464i	− 0.584684i
$708$	− 10.8238i	− 0.406784i
$709$	− 0.0109463i	0 0.000411095i	−1.00000		0.000205548i	$-0.999935\pi$
$709$	− 0.0109463i	0 0.000411095i	1.00000		0.000205548i	$-6.54279e-5\pi$
$710$	1.43880i	0.0539972i
$711$	18.3280	0.687355
$712$	−0.546342	−0.0204750
$713$	23.8797i	0.894301i
$714$	0.223258	0.00835521
$715$	0	0
$716$	13.0951	0.489388
$717$	12.8543i	0.480054i
$718$	−2.32557	−0.0867894
$719$	25.4660	0.949722	0.474861	−	0.880061i	$-0.342498\pi$
$719$	25.4660	0.949722	0.474861	+	0.880061i	$0.342498\pi$
$720$	− 17.5789i	− 0.655127i
$721$	10.2982i	0.383523i
$722$	− 2.03590i	− 0.0757685i
$723$	9.19853i	0.342097i
$724$	−21.8718	−0.812860
$725$	17.6235	0.654521
$726$	0.761613i	0.0282661i
$727$	−23.5565	−0.873663	−0.436831	−	0.899543i	$-0.643899\pi$
$727$	−23.5565	−0.873663	−0.436831	+	0.899543i	$0.643899\pi$
$728$	0	0
$729$	−10.3760	−0.384297
$730$	− 0.439053i	− 0.0162501i
$731$	2.46282	0.0910905
$732$	10.4341	0.385654
$733$	− 6.23249i	− 0.230202i	−0.993354	−	0.115101i	$-0.963281\pi$
$733$	− 6.23249i	− 0.230202i	0.993354	−	0.115101i	$-0.0367192\pi$
$734$	0.447817i	0.0165292i
$735$	0.983005i	0.0362587i
$736$	− 7.27100i	− 0.268013i
$737$	−4.91357	−0.180994
$738$	1.86632	0.0687000
$739$	1.29718i	0.0477174i	0.999715	+	0.0238587i	$0.00759517\pi$
$739$	1.29718i	0.0477174i	−0.999715	+	0.0238587i	$0.992405\pi$
$740$	−21.1699	−0.778221
$741$	0	0
$742$	−0.165025	−0.00605825
$743$	6.06942i	0.222665i	0.993783	+	0.111333i	$0.0355119\pi$
$743$	6.06942i	0.222665i	−0.993783	+	0.111333i	$0.964488\pi$
$744$	−1.31219	−0.0481073
$745$	15.6545	0.573537
$746$	0.422796i	0.0154797i
$747$	1.50976i	0.0552393i
$748$	− 2.30619i	− 0.0843227i
$749$	13.1244i	0.479555i
$750$	−0.845960	−0.0308901
$751$	36.6046	1.33572	0.667860	−	0.744287i	$-0.267210\pi$
$751$	36.6046	1.33572	0.667860	+	0.744287i	$0.267210\pi$
$752$	50.0531i	1.82525i
$753$	13.1346	0.478650
$754$	0	0
$755$	23.6566	0.860952
$756$	− 6.54488i	− 0.238035i
$757$	11.6798	0.424510	0.212255	−	0.977214i	$-0.431919\pi$
$757$	11.6798	0.424510	0.212255	+	0.977214i	$0.431919\pi$
$758$	3.01096	0.109363
$759$	1.07924i	0.0391739i
$760$	− 1.16928i	− 0.0424144i
$761$	39.7688i	1.44162i	0.693133	+	0.720810i	$0.256230\pi$
$761$	39.7688i	1.44162i	−0.693133	+	0.720810i	$0.743770\pi$
$762$	− 0.565394i	− 0.0204821i
$763$	−10.4459	−0.378167
$764$	11.7783	0.426125
$765$	− 14.3098i	− 0.517372i
$766$	2.70393	0.0976970
$767$	0	0
$768$	−8.64915	−0.312099
$769$	− 9.95937i	− 0.359144i	−0.983745	−	0.179572i	$-0.942529\pi$
$769$	− 9.95937i	− 0.359144i	0.983745	−	0.179572i	$-0.0574713\pi$
$770$	−0.0740858	−0.00266987
$771$	11.8863	0.428073
$772$	8.33112i	0.299843i
$773$	− 12.7518i	− 0.458649i	−0.973350	−	0.229324i	$-0.926348\pi$
$773$	− 12.7518i	− 0.458649i	0.973350	−	0.229324i	$-0.0736517\pi$
$774$	0.247608i	0.00890007i
$775$	10.1006i	0.362825i
$776$	−3.80296	−0.136518
$777$	−3.67766	−0.131935
$778$	− 1.60517i	− 0.0575482i
$779$	−8.41411	−0.301467
$780$	0	0
$781$	2.58192	0.0923882
$782$	− 1.94897i	− 0.0696949i
$783$	27.0186	0.965568
$784$	−3.91329	−0.139760
$785$	− 29.0069i	− 1.03530i
$786$	1.32487i	0.0472566i
$787$	− 8.68773i	− 0.309684i	−0.987939	−	0.154842i	$-0.950513\pi$
$787$	− 8.68773i	− 0.309684i	0.987939	−	0.154842i	$-0.0494869\pi$
$788$	11.4861i	0.409174i
$789$	17.2010	0.612373
$790$	−1.39952	−0.0497926
$791$	− 4.95262i	− 0.176095i
$792$	0.465413	0.0165377
$793$	0	0
$794$	3.10929	0.110345
$795$	− 1.34779i	− 0.0478013i
$796$	−23.7463	−0.841664
$797$	−38.7438	−1.37237	−0.686187	−	0.727425i	$-0.740717\pi$
$797$	−38.7438	−1.37237	−0.686187	+	0.727425i	$0.740717\pi$
$798$	− 0.101196i	− 0.00358229i
$799$	40.7449i	1.44145i
$800$	− 3.07549i	− 0.108735i
$801$	3.03063i	0.107082i
$802$	2.11358	0.0746331
$803$	−0.787876	−0.0278036
$804$	15.5802i	0.549471i
$805$	8.58130	0.302451
$806$	0	0
$807$	−16.2554	−0.572218
$808$	− 7.45757i	− 0.262356i
$809$	28.8550	1.01449	0.507244	−	0.861802i	$-0.330664\pi$
$809$	28.8550	1.01449	0.507244	+	0.861802i	$0.330664\pi$
$810$	1.23200	0.0432882
$811$	12.3917i	0.435131i	0.976046	+	0.217566i	$0.0698116\pi$
$811$	12.3917i	0.435131i	−0.976046	+	0.217566i	$0.930188\pi$
$812$	− 16.2745i	− 0.571123i
$813$	17.1479i	0.601405i
$814$	− 0.277173i	− 0.00971491i
$815$	19.9081	0.697351
$816$	−7.25884	−0.254110
$817$	− 1.11632i	− 0.0390549i
$818$	−1.74861	−0.0611388
$819$	0	0
$820$	19.5324	0.682103
$821$	41.0238i	1.43174i	0.698233	+	0.715870i	$0.253970\pi$
$821$	41.0238i	1.43174i	−0.698233	+	0.715870i	$0.746030\pi$
$822$	1.27733	0.0445519
$823$	2.13613	0.0744608	0.0372304	−	0.999307i	$-0.488146\pi$
$823$	2.13613	0.0744608	0.0372304	+	0.999307i	$0.488146\pi$
$824$	4.93999i	0.172093i
$825$	0.456496i	0.0158932i
$826$	− 1.12681i	− 0.0392066i
$827$	− 8.54938i	− 0.297291i	−0.988891	−	0.148645i	$-0.952509\pi$
$827$	− 8.54938i	− 0.297291i	0.988891	−	0.148645i	$-0.0474913\pi$
$828$	−26.8563	−0.933320
$829$	14.7569	0.512528	0.256264	−	0.966607i	$-0.417508\pi$
$829$	14.7569	0.512528	0.256264	+	0.966607i	$0.417508\pi$
$830$	− 0.115284i	− 0.00400158i
$831$	3.99367	0.138539
$832$	0	0
$833$	−3.18555	−0.110373
$834$	0.368004i	0.0127429i
$835$	−7.28758	−0.252197
$836$	−1.04532	−0.0361532
$837$	15.4853i	0.535250i
$838$	0.553887i	0.0191337i
$839$	− 26.9716i	− 0.931164i	−0.885005	−	0.465582i	$-0.845845\pi$
$839$	− 26.9716i	− 0.931164i	0.885005	−	0.465582i	$-0.154155\pi$
$840$	0.471544i	0.0162698i
$841$	38.1845	1.31671
$842$	2.31867	0.0799068
$843$	− 16.9412i	− 0.583487i
$844$	−16.3525	−0.562877
$845$	0	0
$846$	−4.09643	−0.140838
$847$	− 10.8671i	− 0.373396i
$848$	5.36549	0.184252
$849$	6.76053	0.232021
$850$	− 0.824374i	− 0.0282758i
$851$	32.1047i	1.10054i
$852$	− 8.18686i	− 0.280477i
$853$	− 25.6332i	− 0.877665i	−0.898569	−	0.438832i	$-0.855392\pi$
$853$	− 25.6332i	− 0.877665i	0.898569	−	0.438832i	$-0.144608\pi$
$854$	1.08623	0.0371700
$855$	−6.48618	−0.221823
$856$	6.29572i	0.215183i
$857$	−11.7653	−0.401894	−0.200947	−	0.979602i	$-0.564402\pi$
$857$	−11.7653	−0.401894	−0.200947	+	0.979602i	$0.564402\pi$
$858$	0	0
$859$	−21.7761	−0.742992	−0.371496	−	0.928435i	$-0.621155\pi$
$859$	−21.7761	−0.742992	−0.371496	+	0.928435i	$0.621155\pi$
$860$	2.59141i	0.0883663i
$861$	3.39320	0.115640
$862$	−3.41402	−0.116282
$863$	− 41.0575i	− 1.39761i	−0.715310	−	0.698807i	$-0.753715\pi$
$863$	− 41.0575i	− 1.39761i	0.715310	−	0.698807i	$-0.246285\pi$
$864$	− 4.71504i	− 0.160409i
$865$	− 21.1353i	− 0.718623i
$866$	− 1.50694i	− 0.0512079i
$867$	3.99003	0.135509
$868$	9.32746	0.316594
$869$	2.51142i	0.0851942i
$870$	−0.969778	−0.0328785
$871$	0	0
$872$	−5.01085	−0.169689
$873$	21.0955i	0.713975i
$874$	−0.883404	−0.0298816
$875$	12.0705	0.408059
$876$	2.49824i	0.0844076i
$877$	− 6.89112i	− 0.232696i	−0.993208	−	0.116348i	$-0.962881\pi$
$877$	− 6.89112i	− 0.232696i	0.993208	−	0.116348i	$-0.0371189\pi$
$878$	3.81870i	0.128875i
$879$	− 10.3582i	− 0.349372i
$880$	2.40877	0.0811996
$881$	10.6458	0.358665	0.179332	−	0.983789i	$-0.442606\pi$
$881$	10.6458	0.358665	0.179332	+	0.983789i	$0.442606\pi$
$882$	− 0.320270i	− 0.0107841i
$883$	21.3844	0.719641	0.359821	−	0.933022i	$-0.382838\pi$
$883$	21.3844	0.719641	0.359821	+	0.933022i	$0.382838\pi$
$884$	0	0
$885$	9.20286	0.309351
$886$	− 0.208281i	− 0.00699732i
$887$	−34.1150	−1.14547	−0.572735	−	0.819740i	$-0.694118\pi$
$887$	−34.1150	−1.14547	−0.572735	+	0.819740i	$0.694118\pi$
$888$	−1.76416	−0.0592013
$889$	8.06731i	0.270569i
$890$	− 0.231417i	− 0.00775712i
$891$	− 2.21082i	− 0.0740653i
$892$	30.3813i	1.01724i
$893$	18.4684	0.618020
$894$	0.649901	0.0217359
$895$	11.1340i	0.372169i
$896$	−3.78208	−0.126350
$897$	0	0
$898$	1.27056	0.0423992
$899$	38.5057i	1.28424i
$900$	−11.3597	−0.378655
$901$	4.36769	0.145509
$902$	0.255734i	0.00851502i
$903$	0.450183i	0.0149811i
$904$	− 2.37575i	− 0.0790163i
$905$	− 18.5963i	− 0.618163i
$906$	0.982110	0.0326284
$907$	−42.1515	−1.39962	−0.699810	−	0.714329i	$-0.746732\pi$
$907$	−42.1515	−1.39962	−0.699810	+	0.714329i	$0.746732\pi$
$908$	13.8086i	0.458254i
$909$	−41.3681	−1.37209
$910$	0	0
$911$	20.9947	0.695584	0.347792	−	0.937572i	$-0.386932\pi$
$911$	20.9947	0.695584	0.347792	+	0.937572i	$0.386932\pi$
$912$	3.29020i	0.108949i
$913$	−0.206877	−0.00684663
$914$	−0.956734	−0.0316459
$915$	8.87147i	0.293282i
$916$	54.4466i	1.79897i
$917$	− 18.9039i	− 0.624261i
$918$	− 1.26385i	− 0.0417132i
$919$	−14.2940	−0.471515	−0.235757	−	0.971812i	$-0.575757\pi$
$919$	−14.2940	−0.471515	−0.235757	+	0.971812i	$0.575757\pi$
$920$	4.11642	0.135714
$921$	5.28701i	0.174213i
$922$	−1.31094	−0.0431736
$923$	0	0
$924$	0.421553	0.0138681
$925$	13.5797i	0.446497i
$926$	4.31162	0.141689
$927$	27.4027	0.900024
$928$	− 11.7244i	− 0.384872i
$929$	− 6.80723i	− 0.223338i	−0.993745	−	0.111669i	$-0.964380\pi$
$929$	− 6.80723i	− 0.223338i	0.993745	−	0.111669i	$-0.0356197\pi$
$930$	− 0.555812i	− 0.0182258i
$931$	1.44391i	0.0473221i
$932$	13.6074	0.445724
$933$	0.914621	0.0299433
$934$	2.39496i	0.0783655i
$935$	1.96082	0.0641256
$936$	0	0
$937$	−5.22890	−0.170821	−0.0854104	−	0.996346i	$-0.527220\pi$
$937$	−5.22890	−0.170821	−0.0854104	+	0.996346i	$0.527220\pi$
$938$	1.62196i	0.0529590i
$939$	−12.0087	−0.391890
$940$	−42.8723	−1.39834
$941$	56.4403i	1.83990i	0.392033	+	0.919951i	$0.371772\pi$
$941$	56.4403i	1.83990i	−0.392033	+	0.919951i	$0.628228\pi$
$942$	− 1.20423i	− 0.0392359i
$943$	− 29.6215i	− 0.964609i
$944$	36.6361i	1.19240i
$945$	5.56473	0.181021
$946$	−0.0339287	−0.00110312
$947$	− 5.85027i	− 0.190108i	−0.995472	−	0.0950541i	$-0.969698\pi$
$947$	− 5.85027i	− 0.190108i	0.995472	−	0.0950541i	$-0.0303024\pi$
$948$	7.96334	0.258637
$949$	0	0
$950$	−0.373662	−0.0121232
$951$	17.7852i	0.576726i
$952$	−1.52809	−0.0495258
$953$	21.7484	0.704499	0.352249	−	0.935906i	$-0.385417\pi$
$953$	21.7484	0.704499	0.352249	+	0.935906i	$0.385417\pi$
$954$	0.439121i	0.0142171i
$955$	10.0144i	0.324059i
$956$	− 43.8310i	− 1.41760i
$957$	1.74026i	0.0562546i
$958$	3.16429	0.102233
$959$	−18.2255	−0.588532
$960$	− 7.52433i	− 0.242847i
$961$	8.93110	0.288100
$962$	0	0
$963$	34.9232	1.12538
$964$	− 31.3654i	− 1.01021i
$965$	−7.08346	−0.228025
$966$	0.356255	0.0114623
$967$	− 13.3251i	− 0.428507i	−0.976778	−	0.214253i	$-0.931268\pi$
$967$	− 13.3251i	− 0.428507i	0.976778	−	0.214253i	$-0.0687318\pi$
$968$	− 5.21288i	− 0.167548i
$969$	2.67833i	0.0860404i
$970$	− 1.61084i	− 0.0517210i
$971$	7.46185	0.239462	0.119731	−	0.992806i	$-0.461797\pi$
$971$	7.46185	0.239462	0.119731	+	0.992806i	$0.461797\pi$
$972$	−26.6448	−0.854633
$973$	− 5.25085i	− 0.168335i
$974$	−0.767850	−0.0246035
$975$	0	0
$976$	−35.3168	−1.13046
$977$	− 10.9605i	− 0.350656i	−0.984510	−	0.175328i	$-0.943901\pi$
$977$	− 10.9605i	− 0.350656i	0.984510	−	0.175328i	$-0.0560986\pi$
$978$	0.826490	0.0264282
$979$	−0.415276	−0.0132723
$980$	− 3.35188i	− 0.107072i
$981$	27.7959i	0.887453i
$982$	− 0.357189i	− 0.0113984i
$983$	− 16.1441i	− 0.514918i	−0.966289	−	0.257459i	$-0.917115\pi$
$983$	− 16.1441i	− 0.514918i	0.966289	−	0.257459i	$-0.0828852\pi$
$984$	1.62771	0.0518893
$985$	−9.76593	−0.311168
$986$	− 3.14268i	− 0.100083i
$987$	−7.44783	−0.237067
$988$	0	0
$989$	3.92994	0.124965
$990$	0.197138i	0.00626544i
$991$	6.71496	0.213308	0.106654	−	0.994296i	$-0.465986\pi$
$991$	6.71496	0.213308	0.106654	+	0.994296i	$0.465986\pi$
$992$	6.71965	0.213349
$993$	− 15.0540i	− 0.477725i
$994$	− 0.852287i	− 0.0270329i
$995$	− 20.1901i	− 0.640068i
$996$	0.655975i	0.0207854i
$997$	−18.4411	−0.584037	−0.292018	−	0.956413i	$-0.594327\pi$
$997$	−18.4411	−0.584037	−0.292018	+	0.956413i	$0.594327\pi$
$998$	3.38609	0.107185
$999$	20.8190i	0.658684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.i.337.6		12
13.5	odd	4		1183.2.a.m.1.4		6
13.8	odd	4		1183.2.a.p.1.3		6
13.9	even	3		91.2.q.a.36.3	✓	12
13.10	even	6		91.2.q.a.43.3	yes	12
13.12	even	2	inner	1183.2.c.i.337.7		12
39.23	odd	6		819.2.ct.a.316.4		12
39.35	odd	6		819.2.ct.a.127.4		12
52.23	odd	6		1456.2.cc.c.225.3		12
52.35	odd	6		1456.2.cc.c.673.3		12
91.9	even	3		637.2.u.h.361.4		12
91.10	odd	6		637.2.u.i.30.4		12
91.23	even	6		637.2.k.h.459.4		12
91.34	even	4		8281.2.a.ch.1.3		6
91.48	odd	6		637.2.q.h.491.3		12
91.61	odd	6		637.2.u.i.361.4		12
91.62	odd	6		637.2.q.h.589.3		12
91.74	even	3		637.2.k.h.569.3		12
91.75	odd	6		637.2.k.g.459.4		12
91.83	even	4		8281.2.a.by.1.4		6
91.87	odd	6		637.2.k.g.569.3		12
91.88	even	6		637.2.u.h.30.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.3	✓	12	13.9	even	3
91.2.q.a.43.3	yes	12	13.10	even	6
637.2.k.g.459.4		12	91.75	odd	6
637.2.k.g.569.3		12	91.87	odd	6
637.2.k.h.459.4		12	91.23	even	6
637.2.k.h.569.3		12	91.74	even	3
637.2.q.h.491.3		12	91.48	odd	6
637.2.q.h.589.3		12	91.62	odd	6
637.2.u.h.30.4		12	91.88	even	6
637.2.u.h.361.4		12	91.9	even	3
637.2.u.i.30.4		12	91.10	odd	6
637.2.u.i.361.4		12	91.61	odd	6
819.2.ct.a.127.4		12	39.35	odd	6
819.2.ct.a.316.4		12	39.23	odd	6
1183.2.a.m.1.4		6	13.5	odd	4
1183.2.a.p.1.3		6	13.8	odd	4
1183.2.c.i.337.6		12	1.1	even	1	trivial
1183.2.c.i.337.7		12	13.12	even	2	inner
1456.2.cc.c.225.3		12	52.23	odd	6
1456.2.cc.c.673.3		12	52.35	odd	6
8281.2.a.by.1.4		6	91.83	even	4
8281.2.a.ch.1.3		6	91.34	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.c (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-0.120360i q^{2} -0.582292 q^{3} +1.98551 q^{4} +1.68817i q^{5} +0.0700846i q^{6} -1.00000i q^{7} -0.479696i q^{8} -2.66094 q^{9} +0.203187 q^{10} -0.364618i q^{11} -1.15615 q^{12} -0.120360 q^{14} -0.983005i q^{15} +3.91329 q^{16} +3.18555 q^{17} +0.320270i q^{18} -1.44391i q^{19} +3.35188i q^{20} +0.582292i q^{21} -0.0438854 q^{22} +5.08321 q^{23} +0.279323i q^{24} +2.15010 q^{25} +3.29632 q^{27} -1.98551i q^{28} +8.19662 q^{29} -0.118314 q^{30} +4.69775i q^{31} -1.43040i q^{32} +0.212314i q^{33} -0.383412i q^{34} +1.68817 q^{35} -5.28332 q^{36} +6.31584i q^{37} -0.173789 q^{38} +0.809806 q^{40} -5.82732i q^{41} +0.0700846 q^{42} +0.773122 q^{43} -0.723954i q^{44} -4.49210i q^{45} -0.611815i q^{46} +12.7905i q^{47} -2.27868 q^{48} -1.00000 q^{49} -0.258786i q^{50} -1.85492 q^{51} +1.37110 q^{53} -0.396744i q^{54} +0.615536 q^{55} -0.479696 q^{56} +0.840776i q^{57} -0.986544i q^{58} +9.36197i q^{59} -1.95177i q^{60} -9.02484 q^{61} +0.565421 q^{62} +2.66094i q^{63} +7.65442 q^{64} +0.0255541 q^{66} -13.4759i q^{67} +6.32495 q^{68} -2.95991 q^{69} -0.203187i q^{70} +7.08115i q^{71} +1.27644i q^{72} -2.16083i q^{73} +0.760173 q^{74} -1.25198 q^{75} -2.86690i q^{76} -0.364618 q^{77} -6.88781 q^{79} +6.60628i q^{80} +6.06339 q^{81} -0.701376 q^{82} -0.567380i q^{83} +1.15615i q^{84} +5.37773i q^{85} -0.0930528i q^{86} -4.77282 q^{87} -0.174906 q^{88} -1.13893i q^{89} -0.540669 q^{90} +10.0928 q^{92} -2.73547i q^{93} +1.53947 q^{94} +2.43755 q^{95} +0.832908i q^{96} -7.92785i q^{97} +0.120360i q^{98} +0.970225i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 8 q^{4} + 8 q^{9} - 24 q^{10} - 4 q^{12} - 8 q^{14} + 16 q^{16} + 8 q^{17} - 12 q^{22} + 24 q^{23} - 20 q^{25} + 12 q^{27} - 16 q^{29} - 16 q^{30} - 12 q^{35} + 20 q^{36} + 4 q^{38} + 92 q^{40} - 8 q^{42}+ \cdots + 44 q^{95}+O(q^{100}) \) 12 * q - 8 * q^4 + 8 * q^9 - 24 * q^10 - 4 * q^12 - 8 * q^14 + 16 * q^16 + 8 * q^17 - 12 * q^22 + 24 * q^23 - 20 * q^25 + 12 * q^27 - 16 * q^29 - 16 * q^30 - 12 * q^35 + 20 * q^36 + 4 * q^38 + 92 * q^40 - 8 * q^42 - 4 * q^43 + 4 * q^48 - 12 * q^49 + 52 * q^51 - 44 * q^53 + 12 * q^55 + 24 * q^56 - 28 * q^61 + 8 * q^62 - 52 * q^64 - 52 * q^66 + 16 * q^68 - 8 * q^69 - 12 * q^74 - 92 * q^75 + 8 * q^77 - 56 * q^79 - 4 * q^81 - 28 * q^82 + 4 * q^87 + 28 * q^88 + 24 * q^90 + 24 * q^92 - 8 * q^94 + 44 * q^95

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