LMFDB - Embedded newform 1183.2.c.f.337.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(337,1183)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.399424.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 $ x^6 - 2x^5 + 3x^4 - 6x^3 + 6x^2 - 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.2
Root			$1.40680 + 0.144584i$ of defining polynomial
Character	$\chi$	$=$	1183.337
Dual form			1183.2.c.f.337.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.81361i q^{2} -3.10278 q^{3} -1.28917 q^{4} +2.81361i q^{5} +5.62721i q^{6} +1.00000i q^{7} -1.28917i q^{8} +6.62721 q^{9} +O(q^{10})$	\(q-1.81361i q^{2} -3.10278 q^{3} -1.28917 q^{4} +2.81361i q^{5} +5.62721i q^{6} +1.00000i q^{7} -1.28917i q^{8} +6.62721 q^{9} +5.10278 q^{10} -3.10278i q^{11} +4.00000 q^{12} +1.81361 q^{14} -8.72999i q^{15} -4.91638 q^{16} +0.524438 q^{17} -12.0192i q^{18} +0.813607i q^{19} -3.62721i q^{20} -3.10278i q^{21} -5.62721 q^{22} -7.33804 q^{23} +4.00000i q^{24} -2.91638 q^{25} -11.2544 q^{27} -1.28917i q^{28} +8.28917 q^{29} -15.8328 q^{30} +1.39194i q^{31} +6.33804i q^{32} +9.62721i q^{33} -0.951124i q^{34} -2.81361 q^{35} -8.54359 q^{36} +6.15165i q^{37} +1.47556 q^{38} +3.62721 q^{40} -4.20555i q^{41} -5.62721 q^{42} -6.75971 q^{43} +4.00000i q^{44} +18.6464i q^{45} +13.3083i q^{46} +5.97028i q^{47} +15.2544 q^{48} -1.00000 q^{49} +5.28917i q^{50} -1.62721 q^{51} -2.49472 q^{53} +20.4111i q^{54} +8.72999 q^{55} +1.28917 q^{56} -2.52444i q^{57} -15.0333i q^{58} +4.47054i q^{59} +11.2544i q^{60} -2.00000 q^{61} +2.52444 q^{62} +6.62721i q^{63} +1.66196 q^{64} +17.4600 q^{66} +10.0383i q^{67} -0.676089 q^{68} +22.7683 q^{69} +5.10278i q^{70} -8.72999i q^{71} -8.54359i q^{72} +2.34307i q^{73} +11.1567 q^{74} +9.04888 q^{75} -1.04888i q^{76} +3.10278 q^{77} -13.5436 q^{79} -13.8328i q^{80} +15.0383 q^{81} -7.62721 q^{82} +16.4791i q^{83} +4.00000i q^{84} +1.47556i q^{85} +12.2594i q^{86} -25.7194 q^{87} -4.00000 q^{88} +10.6464i q^{89} +33.8172 q^{90} +9.45998 q^{92} -4.31889i q^{93} +10.8277 q^{94} -2.28917 q^{95} -19.6655i q^{96} -1.18639i q^{97} +1.81361i q^{98} -20.5628i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9}+O(q^{10}) $ 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9	$ 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9} + 16 q^{10} + 24 q^{12} - 2 q^{14} - 2 q^{16} - 8 q^{17} - 8 q^{22} - 20 q^{23} + 10 q^{25} - 16 q^{27} + 48 q^{29} - 40 q^{30} - 4 q^{35} + 2 q^{36} + 20 q^{38} - 4 q^{40} - 8 q^{42} - 20 q^{43} + 40 q^{48} - 6 q^{49} + 16 q^{51} + 16 q^{53} + 12 q^{55} + 6 q^{56} - 12 q^{61} + 4 q^{62} + 34 q^{64} + 24 q^{66} + 44 q^{68} + 12 q^{69} + 60 q^{74} + 32 q^{75} + 4 q^{77} - 28 q^{79} + 6 q^{81} - 20 q^{82} - 52 q^{87} - 24 q^{88} + 56 q^{90} - 24 q^{92} - 20 q^{94} - 12 q^{95}+O(q^{100}) $ 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9 + 16 * q^10 + 24 * q^12 - 2 * q^14 - 2 * q^16 - 8 * q^17 - 8 * q^22 - 20 * q^23 + 10 * q^25 - 16 * q^27 + 48 * q^29 - 40 * q^30 - 4 * q^35 + 2 * q^36 + 20 * q^38 - 4 * q^40 - 8 * q^42 - 20 * q^43 + 40 * q^48 - 6 * q^49 + 16 * q^51 + 16 * q^53 + 12 * q^55 + 6 * q^56 - 12 * q^61 + 4 * q^62 + 34 * q^64 + 24 * q^66 + 44 * q^68 + 12 * q^69 + 60 * q^74 + 32 * q^75 + 4 * q^77 - 28 * q^79 + 6 * q^81 - 20 * q^82 - 52 * q^87 - 24 * q^88 + 56 * q^90 - 24 * q^92 - 20 * q^94 - 12 * q^95

Display 100 coefficients 10 coefficients

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 $

$2$	− 1.81361i	− 1.28241i	−0.767368	−	0.641207i	$-0.778434\pi$
$2$	− 1.81361i	− 1.28241i	0.767368	−	0.641207i	$-0.221566\pi$
$3$	−3.10278	−1.79139	−0.895694	−	0.444671i	$-0.853321\pi$
$3$	−3.10278	−1.79139	−0.895694	+	0.444671i	$0.853321\pi$
$4$	−1.28917	−0.644584
$5$	2.81361i	1.25828i	0.777291	+	0.629142i	$0.216593\pi$
$5$	2.81361i	1.25828i	−0.777291	+	0.629142i	$0.783407\pi$
$6$	5.62721i	2.29730i
$7$	1.00000i	0.377964i
$7$	1.00000i	0.377964i
$8$	− 1.28917i	− 0.455790i
$9$	6.62721	2.20907
$10$	5.10278	1.61364
$11$	− 3.10278i	− 0.935522i	−0.883855	−	0.467761i	$-0.845061\pi$
$11$	− 3.10278i	− 0.935522i	0.883855	−	0.467761i	$-0.154939\pi$
$12$	4.00000	1.15470
$13$	0	0
$13$	0	0
$14$	1.81361	0.484707
$15$	− 8.72999i	− 2.25407i
$16$	−4.91638	−1.22910
$17$	0.524438	0.127195	0.0635974	−	0.997976i	$-0.479743\pi$
$17$	0.524438	0.127195	0.0635974	+	0.997976i	$0.479743\pi$
$18$	− 12.0192i	− 2.83294i
$19$	0.813607i	0.186654i	0.995636	+	0.0933271i	$0.0297502\pi$
$19$	0.813607i	0.186654i	−0.995636	+	0.0933271i	$0.970250\pi$
$20$	− 3.62721i	− 0.811069i
$21$	− 3.10278i	− 0.677081i
$22$	−5.62721	−1.19973
$23$	−7.33804	−1.53009	−0.765044	−	0.643978i	$-0.777283\pi$
$23$	−7.33804	−1.53009	−0.765044	+	0.643978i	$0.777283\pi$
$24$	4.00000i	0.816497i
$25$	−2.91638	−0.583276
$26$	0	0
$27$	−11.2544	−2.16592
$28$	− 1.28917i	− 0.243630i
$29$	8.28917	1.53926	0.769630	−	0.638490i	$-0.220441\pi$
$29$	8.28917	1.53926	0.769630	+	0.638490i	$0.220441\pi$
$30$	−15.8328	−2.89065
$31$	1.39194i	0.250000i	0.992157	+	0.125000i	$0.0398932\pi$
$31$	1.39194i	0.250000i	−0.992157	+	0.125000i	$0.960107\pi$
$32$	6.33804i	1.12042i
$33$	9.62721i	1.67588i
$34$	− 0.951124i	− 0.163116i
$35$	−2.81361	−0.475586
$36$	−8.54359	−1.42393
$37$	6.15165i	1.01133i	0.862731	+	0.505663i	$0.168752\pi$
$37$	6.15165i	1.01133i	−0.862731	+	0.505663i	$0.831248\pi$
$38$	1.47556	0.239368
$39$	0	0
$40$	3.62721	0.573513
$41$	− 4.20555i	− 0.656797i	−0.944539	−	0.328398i	$-0.893491\pi$
$41$	− 4.20555i	− 0.656797i	0.944539	−	0.328398i	$-0.106509\pi$
$42$	−5.62721	−0.868298
$43$	−6.75971	−1.03085	−0.515423	−	0.856936i	$-0.672365\pi$
$43$	−6.75971	−1.03085	−0.515423	+	0.856936i	$0.672365\pi$
$44$	4.00000i	0.603023i
$45$	18.6464i	2.77964i
$46$	13.3083i	1.96221i
$47$	5.97028i	0.870855i	0.900224	+	0.435427i	$0.143403\pi$
$47$	5.97028i	0.870855i	−0.900224	+	0.435427i	$0.856597\pi$
$48$	15.2544	2.20179
$49$	−1.00000	−0.142857
$50$	5.28917i	0.748001i
$51$	−1.62721	−0.227855
$52$	0	0
$53$	−2.49472	−0.342676	−0.171338	−	0.985212i	$-0.554809\pi$
$53$	−2.49472	−0.342676	−0.171338	+	0.985212i	$0.554809\pi$
$54$	20.4111i	2.77760i
$55$	8.72999	1.17715
$56$	1.28917	0.172272
$57$	− 2.52444i	− 0.334370i
$58$	− 15.0333i	− 1.97397i
$59$	4.47054i	0.582015i	0.956721	+	0.291007i	$0.0939904\pi$
$59$	4.47054i	0.582015i	−0.956721	+	0.291007i	$0.906010\pi$
$60$	11.2544i	1.45294i
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.52444	0.320604
$63$	6.62721i	0.834950i
$64$	1.66196	0.207744
$65$	0	0
$66$	17.4600	2.14917
$67$	10.0383i	1.22638i	0.789937	+	0.613188i	$0.210113\pi$
$67$	10.0383i	1.22638i	−0.789937	+	0.613188i	$0.789887\pi$
$68$	−0.676089	−0.0819878
$69$	22.7683	2.74098
$70$	5.10278i	0.609898i
$71$	− 8.72999i	− 1.03606i	−0.855363	−	0.518029i	$-0.826666\pi$
$71$	− 8.72999i	− 1.03606i	0.855363	−	0.518029i	$-0.173334\pi$
$72$	− 8.54359i	− 1.00687i
$73$	2.34307i	0.274235i	0.990555	+	0.137118i	$0.0437838\pi$
$73$	2.34307i	0.274235i	−0.990555	+	0.137118i	$0.956216\pi$
$74$	11.1567	1.29694
$75$	9.04888	1.04487
$76$	− 1.04888i	− 0.120314i
$77$	3.10278	0.353594
$78$	0	0
$79$	−13.5436	−1.52377	−0.761887	−	0.647710i	$-0.775727\pi$
$79$	−13.5436	−1.52377	−0.761887	+	0.647710i	$0.775727\pi$
$80$	− 13.8328i	− 1.54655i
$81$	15.0383	1.67092
$82$	−7.62721	−0.842285
$83$	16.4791i	1.80882i	0.426665	+	0.904410i	$0.359688\pi$
$83$	16.4791i	1.80882i	−0.426665	+	0.904410i	$0.640312\pi$
$84$	4.00000i	0.436436i
$85$	1.47556i	0.160047i
$86$	12.2594i	1.32197i
$87$	−25.7194	−2.75741
$88$	−4.00000	−0.426401
$89$	10.6464i	1.12851i	0.825600	+	0.564256i	$0.190837\pi$
$89$	10.6464i	1.12851i	−0.825600	+	0.564256i	$0.809163\pi$
$90$	33.8172	3.56464
$91$	0	0
$92$	9.45998	0.986271
$93$	− 4.31889i	− 0.447848i
$94$	10.8277	1.11680
$95$	−2.28917	−0.234864
$96$	− 19.6655i	− 2.00710i
$97$	− 1.18639i	− 0.120460i	−0.998185	−	0.0602300i	$-0.980817\pi$
$97$	− 1.18639i	− 0.120460i	0.998185	−	0.0602300i	$-0.0191834\pi$
$98$	1.81361i	0.183202i
$99$	− 20.5628i	− 2.06663i
$100$	3.75971	0.375971
$101$	−13.1028	−1.30377	−0.651887	−	0.758316i	$-0.726023\pi$
$101$	−13.1028	−1.30377	−0.651887	+	0.758316i	$0.726023\pi$
$102$	2.95112i	0.292205i
$103$	−4.41110	−0.434639	−0.217319	−	0.976101i	$-0.569731\pi$
$103$	−4.41110	−0.434639	−0.217319	+	0.976101i	$0.569731\pi$
$104$	0	0
$105$	8.72999	0.851960
$106$	4.52444i	0.439452i
$107$	0.578337	0.0559100	0.0279550	−	0.999609i	$-0.491100\pi$
$107$	0.578337	0.0559100	0.0279550	+	0.999609i	$0.491100\pi$
$108$	14.5089	1.39611
$109$	5.57331i	0.533827i	0.963721	+	0.266913i	$0.0860037\pi$
$109$	5.57331i	0.533827i	−0.963721	+	0.266913i	$0.913996\pi$
$110$	− 15.8328i	− 1.50959i
$111$	− 19.0872i	− 1.81168i
$112$	− 4.91638i	− 0.464554i
$113$	5.44584	0.512302	0.256151	−	0.966637i	$-0.417546\pi$
$113$	5.44584	0.512302	0.256151	+	0.966637i	$0.417546\pi$
$114$	−4.57834	−0.428801
$115$	− 20.6464i	− 1.92528i
$116$	−10.6861	−0.992183
$117$	0	0
$118$	8.10780	0.746383
$119$	0.524438i	0.0480751i
$120$	−11.2544	−1.02738
$121$	1.37279	0.124799
$122$	3.62721i	0.328392i
$123$	13.0489i	1.17658i
$124$	− 1.79445i	− 0.161146i
$125$	5.86248i	0.524356i
$126$	12.0192	1.07075
$127$	12.8816	1.14306	0.571530	−	0.820581i	$-0.306350\pi$
$127$	12.8816	1.14306	0.571530	+	0.820581i	$0.306350\pi$
$128$	9.66196i	0.854004i
$129$	20.9739	1.84664
$130$	0	0
$131$	9.04888	0.790604	0.395302	−	0.918551i	$-0.370640\pi$
$131$	9.04888	0.790604	0.395302	+	0.918551i	$0.370640\pi$
$132$	− 12.4111i	− 1.08025i
$133$	−0.813607	−0.0705486
$134$	18.2056	1.57272
$135$	− 31.6655i	− 2.72533i
$136$	− 0.676089i	− 0.0579741i
$137$	6.25945i	0.534781i	0.963588	+	0.267390i	$0.0861613\pi$
$137$	6.25945i	0.534781i	−0.963588	+	0.267390i	$0.913839\pi$
$138$	− 41.2927i	− 3.51507i
$139$	−11.5733	−0.981636	−0.490818	−	0.871262i	$-0.663302\pi$
$139$	−11.5733	−0.981636	−0.490818	+	0.871262i	$0.663302\pi$
$140$	3.62721	0.306555
$141$	− 18.5244i	− 1.56004i
$142$	−15.8328	−1.32866
$143$	0	0
$144$	−32.5819	−2.71516
$145$	23.3225i	1.93682i
$146$	4.24940	0.351683
$147$	3.10278	0.255913
$148$	− 7.93051i	− 0.651884i
$149$	8.52444i	0.698349i	0.937058	+	0.349175i	$0.113538\pi$
$149$	8.52444i	0.698349i	−0.937058	+	0.349175i	$0.886462\pi$
$150$	− 16.4111i	− 1.33996i
$151$	11.9844i	0.975278i	0.873045	+	0.487639i	$0.162142\pi$
$151$	11.9844i	0.975278i	−0.873045	+	0.487639i	$0.837858\pi$
$152$	1.04888	0.0850751
$153$	3.47556	0.280983
$154$	− 5.62721i	− 0.453454i
$155$	−3.91638	−0.314571
$156$	0	0
$157$	−12.8277	−1.02377	−0.511883	−	0.859055i	$-0.671052\pi$
$157$	−12.8277	−1.02377	−0.511883	+	0.859055i	$0.671052\pi$
$158$	24.5628i	1.95411i
$159$	7.74055	0.613866
$160$	−17.8328	−1.40980
$161$	− 7.33804i	− 0.578319i
$162$	− 27.2736i	− 2.14282i
$163$	13.4600i	1.05427i	0.849783	+	0.527133i	$0.176733\pi$
$163$	13.4600i	1.05427i	−0.849783	+	0.527133i	$0.823267\pi$
$164$	5.42166i	0.423361i
$165$	−27.0872	−2.10873
$166$	29.8867	2.31965
$167$	2.02972i	0.157064i	0.996912	+	0.0785322i	$0.0250233\pi$
$167$	2.02972i	0.157064i	−0.996912	+	0.0785322i	$0.974977\pi$
$168$	−4.00000	−0.308607
$169$	0	0
$170$	2.67609	0.205247
$171$	5.39194i	0.412332i
$172$	8.71440	0.664467
$173$	−20.2978	−1.54321	−0.771605	−	0.636102i	$-0.780546\pi$
$173$	−20.2978	−1.54321	−0.771605	+	0.636102i	$0.780546\pi$
$174$	46.6449i	3.53614i
$175$	− 2.91638i	− 0.220458i
$176$	15.2544i	1.14985i
$177$	− 13.8711i	− 1.04261i
$178$	19.3083	1.44722
$179$	11.0036	0.822445	0.411223	−	0.911535i	$-0.365102\pi$
$179$	11.0036	0.822445	0.411223	+	0.911535i	$0.365102\pi$
$180$	− 24.0383i	− 1.79171i
$181$	−0.691675	−0.0514118	−0.0257059	−	0.999670i	$-0.508183\pi$
$181$	−0.691675	−0.0514118	−0.0257059	+	0.999670i	$0.508183\pi$
$182$	0	0
$183$	6.20555	0.458727
$184$	9.45998i	0.697399i
$185$	−17.3083	−1.27253
$186$	−7.83276	−0.574326
$187$	− 1.62721i	− 0.118994i
$188$	− 7.69670i	− 0.561339i
$189$	− 11.2544i	− 0.818639i
$190$	4.15165i	0.301192i
$191$	7.83276	0.566759	0.283379	−	0.959008i	$-0.408544\pi$
$191$	7.83276	0.566759	0.283379	+	0.959008i	$0.408544\pi$
$192$	−5.15667	−0.372151
$193$	12.2056i	0.878575i	0.898347	+	0.439287i	$0.144769\pi$
$193$	12.2056i	0.878575i	−0.898347	+	0.439287i	$0.855231\pi$
$194$	−2.15165	−0.154480
$195$	0	0
$196$	1.28917	0.0920835
$197$	− 18.8222i	− 1.34103i	−0.741898	−	0.670513i	$-0.766074\pi$
$197$	− 18.8222i	− 1.34103i	0.741898	−	0.670513i	$-0.233926\pi$
$198$	−37.2927	−2.65028
$199$	−21.6116	−1.53201	−0.766004	−	0.642836i	$-0.777758\pi$
$199$	−21.6116	−1.53201	−0.766004	+	0.642836i	$0.777758\pi$
$200$	3.75971i	0.265851i
$201$	− 31.1466i	− 2.19691i
$202$	23.7633i	1.67198i
$203$	8.28917i	0.581786i
$204$	2.09775	0.146872
$205$	11.8328	0.826436
$206$	8.00000i	0.557386i
$207$	−48.6308	−3.38007
$208$	0	0
$209$	2.52444	0.174619
$210$	− 15.8328i	− 1.09256i
$211$	−17.3764	−1.19624	−0.598119	−	0.801407i	$-0.704085\pi$
$211$	−17.3764	−1.19624	−0.598119	+	0.801407i	$0.704085\pi$
$212$	3.21611	0.220884
$213$	27.0872i	1.85598i
$214$	− 1.04888i	− 0.0716997i
$215$	− 19.0192i	− 1.29710i
$216$	14.5089i	0.987202i
$217$	−1.39194	−0.0944913
$218$	10.1078	0.684586
$219$	− 7.27001i	− 0.491262i
$220$	−11.2544	−0.758773
$221$	0	0
$222$	−34.6167	−2.32332
$223$	− 10.5486i	− 0.706388i	−0.935550	−	0.353194i	$-0.885096\pi$
$223$	− 10.5486i	− 0.706388i	0.935550	−	0.353194i	$-0.114904\pi$
$224$	−6.33804	−0.423478
$225$	−19.3275	−1.28850
$226$	− 9.87662i	− 0.656983i
$227$	− 6.95112i	− 0.461362i	−0.973029	−	0.230681i	$-0.925905\pi$
$227$	− 6.95112i	− 0.461362i	0.973029	−	0.230681i	$-0.0740954\pi$
$228$	3.25443i	0.215530i
$229$	21.0872i	1.39348i	0.717323	+	0.696740i	$0.245367\pi$
$229$	21.0872i	1.39348i	−0.717323	+	0.696740i	$0.754633\pi$
$230$	−37.4444	−2.46901
$231$	−9.62721	−0.633424
$232$	− 10.6861i	− 0.701579i
$233$	−6.08362	−0.398551	−0.199276	−	0.979943i	$-0.563859\pi$
$233$	−6.08362	−0.398551	−0.199276	+	0.979943i	$0.563859\pi$
$234$	0	0
$235$	−16.7980	−1.09578
$236$	− 5.76328i	− 0.375157i
$237$	42.0227	2.72967
$238$	0.951124	0.0616522
$239$	− 14.2056i	− 0.918881i	−0.888209	−	0.459440i	$-0.848050\pi$
$239$	− 14.2056i	− 0.918881i	0.888209	−	0.459440i	$-0.151950\pi$
$240$	42.9200i	2.77047i
$241$	− 8.44082i	− 0.543721i	−0.962337	−	0.271860i	$-0.912361\pi$
$241$	− 8.44082i	− 0.543721i	0.962337	−	0.271860i	$-0.0876389\pi$
$242$	− 2.48970i	− 0.160044i
$243$	−12.8972	−0.827357
$244$	2.57834	0.165061
$245$	− 2.81361i	− 0.179755i
$246$	23.6655	1.50886
$247$	0	0
$248$	1.79445	0.113948
$249$	− 51.1310i	− 3.24030i
$250$	10.6322	0.672442
$251$	23.9844	1.51388	0.756941	−	0.653483i	$-0.226693\pi$
$251$	23.9844	1.51388	0.756941	+	0.653483i	$0.226693\pi$
$252$	− 8.54359i	− 0.538196i
$253$	22.7683i	1.43143i
$254$	− 23.3622i	− 1.46588i
$255$	− 4.57834i	− 0.286707i
$256$	20.8469	1.30293
$257$	−15.6116	−0.973827	−0.486913	−	0.873450i	$-0.661877\pi$
$257$	−15.6116	−0.973827	−0.486913	+	0.873450i	$0.661877\pi$
$258$	− 38.0383i	− 2.36816i
$259$	−6.15165	−0.382245
$260$	0	0
$261$	54.9341	3.40033
$262$	− 16.4111i	− 1.01388i
$263$	−15.1708	−0.935472	−0.467736	−	0.883868i	$-0.654930\pi$
$263$	−15.1708	−0.935472	−0.467736	+	0.883868i	$0.654930\pi$
$264$	12.4111	0.763850
$265$	− 7.01916i	− 0.431183i
$266$	1.47556i	0.0904725i
$267$	− 33.0333i	− 2.02160i
$268$	− 12.9411i	− 0.790502i
$269$	23.2927	1.42018	0.710092	−	0.704109i	$-0.248653\pi$
$269$	23.2927	1.42018	0.710092	+	0.704109i	$0.248653\pi$
$270$	−57.4288	−3.49501
$271$	− 12.7456i	− 0.774238i	−0.922030	−	0.387119i	$-0.873470\pi$
$271$	− 12.7456i	− 0.774238i	0.922030	−	0.387119i	$-0.126530\pi$
$272$	−2.57834	−0.156335
$273$	0	0
$274$	11.3522	0.685810
$275$	9.04888i	0.545668i
$276$	−29.3522	−1.76679
$277$	−8.12193	−0.488000	−0.244000	−	0.969775i	$-0.578460\pi$
$277$	−8.12193	−0.488000	−0.244000	+	0.969775i	$0.578460\pi$
$278$	20.9894i	1.25886i
$279$	9.22471i	0.552269i
$280$	3.62721i	0.216767i
$281$	− 19.0333i	− 1.13543i	−0.823225	−	0.567715i	$-0.807827\pi$
$281$	− 19.0333i	− 1.13543i	0.823225	−	0.567715i	$-0.192173\pi$
$282$	−33.5960	−2.00062
$283$	−11.1466	−0.662598	−0.331299	−	0.943526i	$-0.607487\pi$
$283$	−11.1466	−0.662598	−0.331299	+	0.943526i	$0.607487\pi$
$284$	11.2544i	0.667827i
$285$	7.10278	0.420732
$286$	0	0
$287$	4.20555	0.248246
$288$	42.0036i	2.47508i
$289$	−16.7250	−0.983821
$290$	42.2978	2.48381
$291$	3.68111i	0.215791i
$292$	− 3.02061i	− 0.176768i
$293$	14.1758i	0.828161i	0.910240	+	0.414080i	$0.135897\pi$
$293$	14.1758i	0.828161i	−0.910240	+	0.414080i	$0.864103\pi$
$294$	− 5.62721i	− 0.328186i
$295$	−12.5783	−0.732339
$296$	7.93051	0.460952
$297$	34.9200i	2.02626i
$298$	15.4600	0.895572
$299$	0	0
$300$	−11.6655	−0.673509
$301$	− 6.75971i	− 0.389623i
$302$	21.7350	1.25071
$303$	40.6550	2.33557
$304$	− 4.00000i	− 0.229416i
$305$	− 5.62721i	− 0.322213i
$306$	− 6.30330i	− 0.360336i
$307$	− 13.5592i	− 0.773863i	−0.922108	−	0.386932i	$-0.873535\pi$
$307$	− 13.5592i	− 0.773863i	0.922108	−	0.386932i	$-0.126465\pi$
$308$	−4.00000	−0.227921
$309$	13.6867	0.778606
$310$	7.10278i	0.403411i
$311$	−0.426686	−0.0241952	−0.0120976	−	0.999927i	$-0.503851\pi$
$311$	−0.426686	−0.0241952	−0.0120976	+	0.999927i	$0.503851\pi$
$312$	0	0
$313$	−18.1517	−1.02599	−0.512996	−	0.858391i	$-0.671464\pi$
$313$	−18.1517	−1.02599	−0.512996	+	0.858391i	$0.671464\pi$
$314$	23.2645i	1.31289i
$315$	−18.6464	−1.05060
$316$	17.4600	0.982200
$317$	9.42166i	0.529173i	0.964362	+	0.264587i	$0.0852355\pi$
$317$	9.42166i	0.529173i	−0.964362	+	0.264587i	$0.914764\pi$
$318$	− 14.0383i	− 0.787230i
$319$	− 25.7194i	− 1.44001i
$320$	4.67609i	0.261401i
$321$	−1.79445	−0.100156
$322$	−13.3083	−0.741644
$323$	0.426686i	0.0237415i
$324$	−19.3869	−1.07705
$325$	0	0
$326$	24.4111	1.35201
$327$	− 17.2927i	− 0.956291i
$328$	−5.42166	−0.299361
$329$	−5.97028	−0.329152
$330$	49.1255i	2.70427i
$331$	− 17.4005i	− 0.956420i	−0.878246	−	0.478210i	$-0.841286\pi$
$331$	− 17.4005i	− 0.956420i	0.878246	−	0.478210i	$-0.158714\pi$
$332$	− 21.2444i	− 1.16594i
$333$	40.7683i	2.23409i
$334$	3.68111	0.201421
$335$	−28.2439	−1.54313
$336$	15.2544i	0.832197i
$337$	−22.0524	−1.20127	−0.600637	−	0.799522i	$-0.705086\pi$
$337$	−22.0524	−1.20127	−0.600637	+	0.799522i	$0.705086\pi$
$338$	0	0
$339$	−16.8972	−0.917731
$340$	− 1.90225i	− 0.103164i
$341$	4.31889	0.233881
$342$	9.77886	0.528780
$343$	− 1.00000i	− 0.0539949i
$344$	8.71440i	0.469849i
$345$	64.0610i	3.44893i
$346$	36.8122i	1.97903i
$347$	25.3522	1.36098	0.680488	−	0.732759i	$-0.261768\pi$
$347$	25.3522	1.36098	0.680488	+	0.732759i	$0.261768\pi$
$348$	33.1567	1.77738
$349$	5.70529i	0.305397i	0.988273	+	0.152699i	$0.0487964\pi$
$349$	5.70529i	0.305397i	−0.988273	+	0.152699i	$0.951204\pi$
$350$	−5.28917	−0.282718
$351$	0	0
$352$	19.6655	1.04818
$353$	− 28.6761i	− 1.52627i	−0.646237	−	0.763137i	$-0.723658\pi$
$353$	− 28.6761i	− 1.52627i	0.646237	−	0.763137i	$-0.276342\pi$
$354$	−25.1567	−1.33706
$355$	24.5628	1.30366
$356$	− 13.7250i	− 0.727422i
$357$	− 1.62721i	− 0.0861212i
$358$	− 19.9561i	− 1.05472i
$359$	− 11.0433i	− 0.582845i	−0.956594	−	0.291423i	$-0.905871\pi$
$359$	− 11.0433i	− 0.582845i	0.956594	−	0.291423i	$-0.0941285\pi$
$360$	24.0383	1.26693
$361$	18.3380	0.965160
$362$	1.25443i	0.0659312i
$363$	−4.25945	−0.223563
$364$	0	0
$365$	−6.59247	−0.345066
$366$	− 11.2544i	− 0.588278i
$367$	27.3466	1.42748	0.713741	−	0.700409i	$-0.246999\pi$
$367$	27.3466	1.42748	0.713741	+	0.700409i	$0.246999\pi$
$368$	36.0766	1.88062
$369$	− 27.8711i	− 1.45091i
$370$	31.3905i	1.63191i
$371$	− 2.49472i	− 0.129519i
$372$	5.56777i	0.288676i
$373$	16.1461	0.836014	0.418007	−	0.908444i	$-0.362729\pi$
$373$	16.1461	0.836014	0.418007	+	0.908444i	$0.362729\pi$
$374$	−2.95112	−0.152599
$375$	− 18.1900i	− 0.939326i
$376$	7.69670	0.396927
$377$	0	0
$378$	−20.4111	−1.04983
$379$	26.1305i	1.34223i	0.741351	+	0.671117i	$0.234185\pi$
$379$	26.1305i	1.34223i	−0.741351	+	0.671117i	$0.765815\pi$
$380$	2.95112	0.151389
$381$	−39.9688	−2.04767
$382$	− 14.2056i	− 0.726819i
$383$	− 21.0489i	− 1.07555i	−0.843089	−	0.537774i	$-0.819265\pi$
$383$	− 21.0489i	− 1.07555i	0.843089	−	0.537774i	$-0.180735\pi$
$384$	− 29.9789i	− 1.52985i
$385$	8.72999i	0.444921i
$386$	22.1361	1.12670
$387$	−44.7980	−2.27721
$388$	1.52946i	0.0776466i
$389$	21.6061	1.09547	0.547736	−	0.836651i	$-0.315490\pi$
$389$	21.6061	1.09547	0.547736	+	0.836651i	$0.315490\pi$
$390$	0	0
$391$	−3.84835	−0.194619
$392$	1.28917i	0.0651128i
$393$	−28.0766	−1.41628
$394$	−34.1361	−1.71975
$395$	− 38.1063i	− 1.91734i
$396$	26.5089i	1.33212i
$397$	27.6952i	1.38998i	0.719017	+	0.694992i	$0.244592\pi$
$397$	27.6952i	1.38998i	−0.719017	+	0.694992i	$0.755408\pi$
$398$	39.1950i	1.96467i
$399$	2.52444	0.126380
$400$	14.3380	0.716902
$401$	2.57834i	0.128756i	0.997926	+	0.0643780i	$0.0205063\pi$
$401$	2.57834i	0.128756i	−0.997926	+	0.0643780i	$0.979494\pi$
$402$	−56.4877	−2.81735
$403$	0	0
$404$	16.8917	0.840393
$405$	42.3119i	2.10250i
$406$	15.0333	0.746090
$407$	19.0872	0.946117
$408$	2.09775i	0.103854i
$409$	15.1169i	0.747483i	0.927533	+	0.373742i	$0.121925\pi$
$409$	15.1169i	0.747483i	−0.927533	+	0.373742i	$0.878075\pi$
$410$	− 21.4600i	− 1.05983i
$411$	− 19.4217i	− 0.958000i
$412$	5.68665	0.280161
$413$	−4.47054	−0.219981
$414$	88.1971i	4.33465i
$415$	−46.3658	−2.27601
$416$	0	0
$417$	35.9094	1.75849
$418$	− 4.57834i	− 0.223934i
$419$	−9.99446	−0.488261	−0.244131	−	0.969742i	$-0.578503\pi$
$419$	−9.99446	−0.488261	−0.244131	+	0.969742i	$0.578503\pi$
$420$	−11.2544	−0.549160
$421$	− 25.9250i	− 1.26351i	−0.775170	−	0.631753i	$-0.782336\pi$
$421$	− 25.9250i	− 1.26351i	0.775170	−	0.631753i	$-0.217664\pi$
$422$	31.5139i	1.53407i
$423$	39.5663i	1.92378i
$424$	3.21611i	0.156188i
$425$	−1.52946	−0.0741898
$426$	49.1255	2.38014
$427$	− 2.00000i	− 0.0967868i
$428$	−0.745574	−0.0360387
$429$	0	0
$430$	−34.4933	−1.66341
$431$	30.6761i	1.47762i	0.673916	+	0.738808i	$0.264611\pi$
$431$	30.6761i	1.47762i	−0.673916	+	0.738808i	$0.735389\pi$
$432$	55.3311	2.66212
$433$	3.51941	0.169132	0.0845661	−	0.996418i	$-0.473050\pi$
$433$	3.51941	0.169132	0.0845661	+	0.996418i	$0.473050\pi$
$434$	2.52444i	0.121177i
$435$	− 72.3643i	− 3.46960i
$436$	− 7.18494i	− 0.344096i
$437$	− 5.97028i	− 0.285597i
$438$	−13.1849	−0.630001
$439$	−32.3517	−1.54406	−0.772030	−	0.635586i	$-0.780759\pi$
$439$	−32.3517	−1.54406	−0.772030	+	0.635586i	$0.780759\pi$
$440$	− 11.2544i	− 0.536534i
$441$	−6.62721	−0.315582
$442$	0	0
$443$	15.4458	0.733854	0.366927	−	0.930250i	$-0.380410\pi$
$443$	15.4458	0.733854	0.366927	+	0.930250i	$0.380410\pi$
$444$	24.6066i	1.16778i
$445$	−29.9547	−1.41999
$446$	−19.1310	−0.905881
$447$	− 26.4494i	− 1.25101i
$448$	1.66196i	0.0785200i
$449$	14.4705i	0.682907i	0.939899	+	0.341453i	$0.110919\pi$
$449$	14.4705i	0.682907i	−0.939899	+	0.341453i	$0.889081\pi$
$450$	35.0524i	1.65239i
$451$	−13.0489	−0.614448
$452$	−7.02061	−0.330222
$453$	− 37.1849i	− 1.74710i
$454$	−12.6066	−0.591657
$455$	0	0
$456$	−3.25443	−0.152402
$457$	− 34.6705i	− 1.62182i	−0.585171	−	0.810910i	$-0.698973\pi$
$457$	− 34.6705i	− 1.62182i	0.585171	−	0.810910i	$-0.301027\pi$
$458$	38.2439	1.78702
$459$	−5.90225	−0.275493
$460$	26.6167i	1.24101i
$461$	12.5400i	0.584047i	0.956411	+	0.292024i	$0.0943286\pi$
$461$	12.5400i	0.584047i	−0.956411	+	0.292024i	$0.905671\pi$
$462$	17.4600i	0.812312i
$463$	− 12.1517i	− 0.564735i	−0.959306	−	0.282368i	$-0.908880\pi$
$463$	− 12.1517i	− 0.564735i	0.959306	−	0.282368i	$-0.0911198\pi$
$464$	−40.7527	−1.89190
$465$	12.1517	0.563519
$466$	11.0333i	0.511107i
$467$	37.0333	1.71370	0.856848	−	0.515569i	$-0.172419\pi$
$467$	37.0333	1.71370	0.856848	+	0.515569i	$0.172419\pi$
$468$	0	0
$469$	−10.0383	−0.463526
$470$	30.4650i	1.40525i
$471$	39.8016	1.83396
$472$	5.76328	0.265276
$473$	20.9739i	0.964379i
$474$	− 76.2127i	− 3.50056i
$475$	− 2.37279i	− 0.108871i
$476$	− 0.676089i	− 0.0309885i
$477$	−16.5330	−0.756996
$478$	−25.7633	−1.17838
$479$	− 12.0086i	− 0.548687i	−0.961632	−	0.274343i	$-0.911540\pi$
$479$	− 12.0086i	− 0.548687i	0.961632	−	0.274343i	$-0.0884605\pi$
$480$	55.3311	2.52551
$481$	0	0
$482$	−15.3083	−0.697275
$483$	22.7683i	1.03599i
$484$	−1.76975	−0.0804434
$485$	3.33804	0.151573
$486$	23.3905i	1.06101i
$487$	11.1184i	0.503821i	0.967751	+	0.251911i	$0.0810589\pi$
$487$	11.1184i	0.503821i	−0.967751	+	0.251911i	$0.918941\pi$
$488$	2.57834i	0.116716i
$489$	− 41.7633i	− 1.88860i
$490$	−5.10278	−0.230520
$491$	−0.0594386	−0.00268243	−0.00134121	−	0.999999i	$-0.500427\pi$
$491$	−0.0594386	−0.00268243	−0.00134121	+	0.999999i	$0.500427\pi$
$492$	− 16.8222i	− 0.758403i
$493$	4.34715	0.195786
$494$	0	0
$495$	57.8555	2.60041
$496$	− 6.84333i	− 0.307274i
$497$	8.72999	0.391593
$498$	−92.7316	−4.15540
$499$	10.2978i	0.460991i	0.973073	+	0.230496i	$0.0740347\pi$
$499$	10.2978i	0.460991i	−0.973073	+	0.230496i	$0.925965\pi$
$500$	− 7.55773i	− 0.337992i
$501$	− 6.29776i	− 0.281363i
$502$	− 43.4983i	− 1.94142i
$503$	−9.32391	−0.415733	−0.207866	−	0.978157i	$-0.566652\pi$
$503$	−9.32391	−0.415733	−0.207866	+	0.978157i	$0.566652\pi$
$504$	8.54359	0.380562
$505$	− 36.8661i	− 1.64052i
$506$	41.2927	1.83569
$507$	0	0
$508$	−16.6066	−0.736799
$509$	39.6952i	1.75946i	0.475473	+	0.879730i	$0.342277\pi$
$509$	39.6952i	1.75946i	−0.475473	+	0.879730i	$0.657723\pi$
$510$	−8.30330	−0.367676
$511$	−2.34307	−0.103651
$512$	− 18.4842i	− 0.816892i
$513$	− 9.15667i	− 0.404277i
$514$	28.3133i	1.24885i
$515$	− 12.4111i	− 0.546898i
$516$	−27.0388	−1.19032
$517$	18.5244	0.814704
$518$	11.1567i	0.490196i
$519$	62.9794	2.76449
$520$	0	0
$521$	22.3627	0.979729	0.489865	−	0.871798i	$-0.337046\pi$
$521$	22.3627	0.979729	0.489865	+	0.871798i	$0.337046\pi$
$522$	− 99.6288i	− 4.36063i
$523$	−20.6550	−0.903178	−0.451589	−	0.892226i	$-0.649143\pi$
$523$	−20.6550	−0.903178	−0.451589	+	0.892226i	$0.649143\pi$
$524$	−11.6655	−0.509611
$525$	9.04888i	0.394925i
$526$	27.5139i	1.19966i
$527$	0.729988i	0.0317988i
$528$	− 47.3311i	− 2.05982i
$529$	30.8469	1.34117
$530$	−12.7300	−0.552955
$531$	29.6272i	1.28571i
$532$	1.04888	0.0454745
$533$	0	0
$534$	−59.9094	−2.59253
$535$	1.62721i	0.0703506i
$536$	12.9411	0.558969
$537$	−34.1416	−1.47332
$538$	− 42.2439i	− 1.82126i
$539$	3.10278i	0.133646i
$540$	40.8222i	1.75671i
$541$	− 5.62167i	− 0.241695i	−0.992671	−	0.120847i	$-0.961439\pi$
$541$	− 5.62167i	− 0.241695i	0.992671	−	0.120847i	$-0.0385611\pi$
$542$	−23.1155	−0.992894
$543$	2.14611	0.0920985
$544$	3.32391i	0.142512i
$545$	−15.6811	−0.671705
$546$	0	0
$547$	−10.3970	−0.444542	−0.222271	−	0.974985i	$-0.571347\pi$
$547$	−10.3970	−0.444542	−0.222271	+	0.974985i	$0.571347\pi$
$548$	− 8.06949i	− 0.344711i
$549$	−13.2544	−0.565685
$550$	16.4111	0.699772
$551$	6.74412i	0.287309i
$552$	− 29.3522i	− 1.24931i
$553$	− 13.5436i	− 0.575932i
$554$	14.7300i	0.625817i
$555$	53.7038	2.27960
$556$	14.9200	0.632747
$557$	− 14.6550i	− 0.620951i	−0.950581	−	0.310475i	$-0.899512\pi$
$557$	− 14.6550i	− 0.620951i	0.950581	−	0.310475i	$-0.100488\pi$
$558$	16.7300	0.708237
$559$	0	0
$560$	13.8328	0.584541
$561$	5.04888i	0.213164i
$562$	−34.5189	−1.45609
$563$	24.7456	1.04290	0.521451	−	0.853281i	$-0.325391\pi$
$563$	24.7456	1.04290	0.521451	+	0.853281i	$0.325391\pi$
$564$	23.8811i	1.00558i
$565$	15.3225i	0.644621i
$566$	20.2156i	0.849725i
$567$	15.0383i	0.631550i
$568$	−11.2544	−0.472225
$569$	20.5330	0.860789	0.430395	−	0.902641i	$-0.358374\pi$
$569$	20.5330	0.860789	0.430395	+	0.902641i	$0.358374\pi$
$570$	− 12.8816i	− 0.539552i
$571$	41.8953	1.75326	0.876631	−	0.481163i	$-0.159786\pi$
$571$	41.8953	1.75326	0.876631	+	0.481163i	$0.159786\pi$
$572$	0	0
$573$	−24.3033	−1.01529
$574$	− 7.62721i	− 0.318354i
$575$	21.4005	0.892464
$576$	11.0141	0.458922
$577$	− 20.1744i	− 0.839870i	−0.907554	−	0.419935i	$-0.862053\pi$
$577$	− 20.1744i	− 0.839870i	0.907554	−	0.419935i	$-0.137947\pi$
$578$	30.3325i	1.26167i
$579$	− 37.8711i	− 1.57387i
$580$	− 30.0666i	− 1.24845i
$581$	−16.4791	−0.683670
$582$	6.67609	0.276733
$583$	7.74055i	0.320581i
$584$	3.02061	0.124994
$585$	0	0
$586$	25.7094	1.06204
$587$	− 18.7441i	− 0.773653i	−0.922153	−	0.386826i	$-0.873571\pi$
$587$	− 18.7441i	− 0.773653i	0.922153	−	0.386826i	$-0.126429\pi$
$588$	−4.00000	−0.164957
$589$	−1.13249	−0.0466636
$590$	22.8122i	0.939162i
$591$	58.4011i	2.40230i
$592$	− 30.2439i	− 1.24302i
$593$	2.98084i	0.122409i	0.998125	+	0.0612043i	$0.0194941\pi$
$593$	2.98084i	0.122409i	−0.998125	+	0.0612043i	$0.980506\pi$
$594$	63.3311	2.59850
$595$	−1.47556	−0.0604921
$596$	− 10.9894i	− 0.450145i
$597$	67.0560	2.74442
$598$	0	0
$599$	7.47411	0.305384	0.152692	−	0.988274i	$-0.451206\pi$
$599$	7.47411	0.305384	0.152692	+	0.988274i	$0.451206\pi$
$600$	− 11.6655i	− 0.476243i
$601$	21.4700	0.875780	0.437890	−	0.899028i	$-0.355726\pi$
$601$	21.4700	0.875780	0.437890	+	0.899028i	$0.355726\pi$
$602$	−12.2594	−0.499658
$603$	66.5260i	2.70915i
$604$	− 15.4499i	− 0.628649i
$605$	3.86248i	0.157032i
$606$	− 73.7321i	− 2.99516i
$607$	−22.9044	−0.929660	−0.464830	−	0.885400i	$-0.653884\pi$
$607$	−22.9044	−0.929660	−0.464830	+	0.885400i	$0.653884\pi$
$608$	−5.15667	−0.209131
$609$	− 25.7194i	− 1.04220i
$610$	−10.2056	−0.413211
$611$	0	0
$612$	−4.48059	−0.181117
$613$	− 20.1461i	− 0.813694i	−0.913496	−	0.406847i	$-0.866628\pi$
$613$	− 20.1461i	− 0.813694i	0.913496	−	0.406847i	$-0.133372\pi$
$614$	−24.5910	−0.992413
$615$	−36.7144	−1.48047
$616$	− 4.00000i	− 0.161165i
$617$	− 13.7844i	− 0.554939i	−0.960734	−	0.277470i	$-0.910504\pi$
$617$	− 13.7844i	− 0.554939i	0.960734	−	0.277470i	$-0.0894958\pi$
$618$	− 24.8222i	− 0.998495i
$619$	19.6655i	0.790424i	0.918590	+	0.395212i	$0.129329\pi$
$619$	19.6655i	0.790424i	−0.918590	+	0.395212i	$0.870671\pi$
$620$	5.04888	0.202768
$621$	82.5855	3.31404
$622$	0.773841i	0.0310282i
$623$	−10.6464	−0.426538
$624$	0	0
$625$	−31.0766	−1.24307
$626$	32.9200i	1.31575i
$627$	−7.83276	−0.312810
$628$	16.5371	0.659903
$629$	3.22616i	0.128635i
$630$	33.8172i	1.34731i
$631$	16.1672i	0.643608i	0.946806	+	0.321804i	$0.104289\pi$
$631$	16.1672i	0.643608i	−0.946806	+	0.321804i	$0.895711\pi$
$632$	17.4600i	0.694521i
$633$	53.9149	2.14293
$634$	17.0872	0.678619
$635$	36.2439i	1.43829i
$636$	−9.97887	−0.395688
$637$	0	0
$638$	−46.6449	−1.84669
$639$	− 57.8555i	− 2.28873i
$640$	−27.1849	−1.07458
$641$	29.0036	1.14557	0.572786	−	0.819705i	$-0.305863\pi$
$641$	29.0036	1.14557	0.572786	+	0.819705i	$0.305863\pi$
$642$	3.25443i	0.128442i
$643$	− 39.2233i	− 1.54681i	−0.633910	−	0.773407i	$-0.718551\pi$
$643$	− 39.2233i	− 1.54681i	0.633910	−	0.773407i	$-0.281449\pi$
$644$	9.45998i	0.372775i
$645$	59.0122i	2.32360i
$646$	0.773841	0.0304464
$647$	11.9844	0.471156	0.235578	−	0.971855i	$-0.424302\pi$
$647$	11.9844	0.471156	0.235578	+	0.971855i	$0.424302\pi$
$648$	− 19.3869i	− 0.761590i
$649$	13.8711	0.544487
$650$	0	0
$651$	4.31889	0.169271
$652$	− 17.3522i	− 0.679564i
$653$	45.3311	1.77394	0.886971	−	0.461826i	$-0.152806\pi$
$653$	45.3311	1.77394	0.886971	+	0.461826i	$0.152806\pi$
$654$	−31.3622	−1.22636
$655$	25.4600i	0.994804i
$656$	20.6761i	0.807266i
$657$	15.5280i	0.605805i
$658$	10.8277i	0.422109i
$659$	6.12193	0.238477	0.119238	−	0.992866i	$-0.461955\pi$
$659$	6.12193	0.238477	0.119238	+	0.992866i	$0.461955\pi$
$660$	34.9200	1.35926
$661$	27.5280i	1.07072i	0.844625	+	0.535358i	$0.179823\pi$
$661$	27.5280i	1.07072i	−0.844625	+	0.535358i	$0.820177\pi$
$662$	−31.5577	−1.22653
$663$	0	0
$664$	21.2444	0.824442
$665$	− 2.28917i	− 0.0887701i
$666$	73.9377	2.86503
$667$	−60.8263	−2.35520
$668$	− 2.61665i	− 0.101241i
$669$	32.7300i	1.26541i
$670$	51.2233i	1.97893i
$671$	6.20555i	0.239563i
$672$	19.6655	0.758614
$673$	−27.9547	−1.07757	−0.538787	−	0.842442i	$-0.681117\pi$
$673$	−27.9547	−1.07757	−0.538787	+	0.842442i	$0.681117\pi$
$674$	39.9945i	1.54053i
$675$	32.8222	1.26333
$676$	0	0
$677$	−12.6605	−0.486583	−0.243291	−	0.969953i	$-0.578227\pi$
$677$	−12.6605	−0.486583	−0.243291	+	0.969953i	$0.578227\pi$
$678$	30.6449i	1.17691i
$679$	1.18639	0.0455296
$680$	1.90225	0.0729479
$681$	21.5678i	0.826479i
$682$	− 7.83276i	− 0.299932i
$683$	28.3033i	1.08300i	0.840702	+	0.541498i	$0.182143\pi$
$683$	28.3033i	1.08300i	−0.840702	+	0.541498i	$0.817857\pi$
$684$	− 6.95112i	− 0.265783i
$685$	−17.6116	−0.672906
$686$	−1.81361	−0.0692438
$687$	− 65.4288i	− 2.49626i
$688$	33.2333	1.26701
$689$	0	0
$690$	116.182	4.42295
$691$	12.2353i	0.465452i	0.972542	+	0.232726i	$0.0747645\pi$
$691$	12.2353i	0.465452i	−0.972542	+	0.232726i	$0.925236\pi$
$692$	26.1672	0.994729
$693$	20.5628	0.781114
$694$	− 45.9789i	− 1.74533i
$695$	− 32.5628i	− 1.23518i
$696$	33.1567i	1.25680i
$697$	− 2.20555i	− 0.0835412i
$698$	10.3472	0.391646
$699$	18.8761	0.713960
$700$	3.75971i	0.142104i
$701$	−51.0419	−1.92783	−0.963913	−	0.266219i	$-0.914226\pi$
$701$	−51.0419	−1.92783	−0.963913	+	0.266219i	$0.914226\pi$
$702$	0	0
$703$	−5.00502	−0.188768
$704$	− 5.15667i	− 0.194349i
$705$	52.1205	1.96297
$706$	−52.0071	−1.95731
$707$	− 13.1028i	− 0.492781i
$708$	17.8822i	0.672053i
$709$	− 42.5910i	− 1.59954i	−0.600307	−	0.799770i	$-0.704955\pi$
$709$	− 42.5910i	− 1.59954i	0.600307	−	0.799770i	$-0.295045\pi$
$710$	− 44.5472i	− 1.67183i
$711$	−89.7563	−3.36612
$712$	13.7250	0.514365
$713$	− 10.2141i	− 0.382523i
$714$	−2.95112	−0.110443
$715$	0	0
$716$	−14.1855	−0.530135
$717$	44.0766i	1.64607i
$718$	−20.0283	−0.747448
$719$	42.4933	1.58473	0.792366	−	0.610046i	$-0.208849\pi$
$719$	42.4933	1.58473	0.792366	+	0.610046i	$0.208849\pi$
$720$	− 91.6727i	− 3.41644i
$721$	− 4.41110i	− 0.164278i
$722$	− 33.2580i	− 1.23773i
$723$	26.1900i	0.974015i
$724$	0.891685	0.0331392
$725$	−24.1744	−0.897814
$726$	7.72496i	0.286700i
$727$	3.75614	0.139307	0.0696537	−	0.997571i	$-0.477811\pi$
$727$	3.75614	0.139307	0.0696537	+	0.997571i	$0.477811\pi$
$728$	0	0
$729$	−5.09775	−0.188806
$730$	11.9561i	0.442517i
$731$	−3.54505	−0.131118
$732$	−8.00000	−0.295689
$733$	45.7819i	1.69099i	0.533980	+	0.845497i	$0.320696\pi$
$733$	45.7819i	1.69099i	−0.533980	+	0.845497i	$0.679304\pi$
$734$	− 49.5960i	− 1.83062i
$735$	8.72999i	0.322010i
$736$	− 46.5089i	− 1.71434i
$737$	31.1466	1.14730
$738$	−50.5472	−1.86067
$739$	14.0539i	0.516981i	0.966014	+	0.258491i	$0.0832251\pi$
$739$	14.0539i	0.516981i	−0.966014	+	0.258491i	$0.916775\pi$
$740$	22.3133	0.820255
$741$	0	0
$742$	−4.52444	−0.166097
$743$	4.74557i	0.174098i	0.996204	+	0.0870491i	$0.0277437\pi$
$743$	4.74557i	0.174098i	−0.996204	+	0.0870491i	$0.972256\pi$
$744$	−5.56777	−0.204125
$745$	−23.9844	−0.878721
$746$	− 29.2827i	− 1.07212i
$747$	109.211i	3.99581i
$748$	2.09775i	0.0767014i
$749$	0.578337i	0.0211320i
$750$	−32.9894	−1.20460
$751$	−36.1008	−1.31734	−0.658669	−	0.752433i	$-0.728880\pi$
$751$	−36.1008	−1.31734	−0.658669	+	0.752433i	$0.728880\pi$
$752$	− 29.3522i	− 1.07036i
$753$	−74.4182	−2.71195
$754$	0	0
$755$	−33.7194	−1.22718
$756$	14.5089i	0.527682i
$757$	−1.03474	−0.0376084	−0.0188042	−	0.999823i	$-0.505986\pi$
$757$	−1.03474	−0.0376084	−0.0188042	+	0.999823i	$0.505986\pi$
$758$	47.3905	1.72130
$759$	− 70.6449i	− 2.56425i
$760$	2.95112i	0.107049i
$761$	− 29.8414i	− 1.08175i	−0.841104	−	0.540874i	$-0.818094\pi$
$761$	− 29.8414i	− 1.08175i	0.841104	−	0.540874i	$-0.181906\pi$
$762$	72.4877i	2.62595i
$763$	−5.57331	−0.201768
$764$	−10.0978	−0.365324
$765$	9.77886i	0.353556i
$766$	−38.1744	−1.37930
$767$	0	0
$768$	−64.6832	−2.33406
$769$	23.6358i	0.852329i	0.904646	+	0.426164i	$0.140136\pi$
$769$	23.6358i	0.852329i	−0.904646	+	0.426164i	$0.859864\pi$
$770$	15.8328	0.570573
$771$	48.4394	1.74450
$772$	− 15.7350i	− 0.566315i
$773$	13.0278i	0.468576i	0.972167	+	0.234288i	$0.0752758\pi$
$773$	13.0278i	0.468576i	−0.972167	+	0.234288i	$0.924724\pi$
$774$	81.2460i	2.92033i
$775$	− 4.05944i	− 0.145819i
$776$	−1.52946	−0.0549045
$777$	19.0872	0.684749
$778$	− 39.1849i	− 1.40485i
$779$	3.42166	0.122594
$780$	0	0
$781$	−27.0872	−0.969256
$782$	6.97939i	0.249583i
$783$	−93.2898	−3.33391
$784$	4.91638	0.175585
$785$	− 36.0922i	− 1.28819i
$786$	50.9200i	1.81625i
$787$	− 46.2141i	− 1.64736i	−0.567058	−	0.823678i	$-0.691918\pi$
$787$	− 46.2141i	− 1.64736i	0.567058	−	0.823678i	$-0.308082\pi$
$788$	24.2650i	0.864404i
$789$	47.0716	1.67579
$790$	−69.1099	−2.45882
$791$	5.44584i	0.193632i
$792$	−26.5089	−0.941951
$793$	0	0
$794$	50.2283	1.78253
$795$	21.7789i	0.772417i
$796$	27.8610	0.987508
$797$	−53.1155	−1.88145	−0.940723	−	0.339176i	$-0.889852\pi$
$797$	−53.1155	−1.88145	−0.940723	+	0.339176i	$0.889852\pi$
$798$	− 4.57834i	− 0.162071i
$799$	3.13104i	0.110768i
$800$	− 18.4842i	− 0.653514i
$801$	70.5558i	2.49297i
$802$	4.67609	0.165118
$803$	7.27001	0.256553
$804$	40.1533i	1.41610i
$805$	20.6464	0.727689
$806$	0	0
$807$	−72.2721	−2.54410
$808$	16.8917i	0.594247i
$809$	−54.4635	−1.91484	−0.957418	−	0.288705i	$-0.906775\pi$
$809$	−54.4635	−1.91484	−0.957418	+	0.288705i	$0.906775\pi$
$810$	76.7371	2.69627
$811$	38.0978i	1.33779i	0.743356	+	0.668897i	$0.233233\pi$
$811$	38.0978i	1.33779i	−0.743356	+	0.668897i	$0.766767\pi$
$812$	− 10.6861i	− 0.375010i
$813$	39.5466i	1.38696i
$814$	− 34.6167i	− 1.21331i
$815$	−37.8711	−1.32657
$816$	8.00000	0.280056
$817$	− 5.49974i	− 0.192412i
$818$	27.4161	0.958582
$819$	0	0
$820$	−15.2544	−0.532708
$821$	− 2.30330i	− 0.0803858i	−0.999192	−	0.0401929i	$-0.987203\pi$
$821$	− 2.30330i	− 0.0803858i	0.999192	−	0.0401929i	$-0.0127972\pi$
$822$	−35.2233	−1.22855
$823$	−23.6172	−0.823243	−0.411621	−	0.911355i	$-0.635037\pi$
$823$	−23.6172	−0.823243	−0.411621	+	0.911355i	$0.635037\pi$
$824$	5.68665i	0.198104i
$825$	− 28.0766i	− 0.977503i
$826$	8.10780i	0.282106i
$827$	48.1643i	1.67484i	0.546562	+	0.837419i	$0.315936\pi$
$827$	48.1643i	1.67484i	−0.546562	+	0.837419i	$0.684064\pi$
$828$	62.6933	2.17874
$829$	−13.0716	−0.453996	−0.226998	−	0.973895i	$-0.572891\pi$
$829$	−13.0716	−0.453996	−0.226998	+	0.973895i	$0.572891\pi$
$830$	84.0893i	2.91878i
$831$	25.2005	0.874197
$832$	0	0
$833$	−0.524438	−0.0181707
$834$	− 65.1255i	− 2.25511i
$835$	−5.71083	−0.197631
$836$	−3.25443	−0.112557
$837$	− 15.6655i	− 0.541480i
$838$	18.1260i	0.626153i
$839$	17.6756i	0.610229i	0.952316	+	0.305114i	$0.0986947\pi$
$839$	17.6756i	0.610229i	−0.952316	+	0.305114i	$0.901305\pi$
$840$	− 11.2544i	− 0.388315i
$841$	39.7103	1.36932
$842$	−47.0177	−1.62034
$843$	59.0560i	2.03400i
$844$	22.4011	0.771076
$845$	0	0
$846$	71.7577	2.46708
$847$	1.37279i	0.0471695i
$848$	12.2650	0.421181
$849$	34.5855	1.18697
$850$	2.77384i	0.0951420i
$851$	− 45.1411i	− 1.54742i
$852$	− 34.9200i	− 1.19634i
$853$	5.48970i	0.187964i	0.995574	+	0.0939818i	$0.0299595\pi$
$853$	5.48970i	0.187964i	−0.995574	+	0.0939818i	$0.970040\pi$
$854$	−3.62721	−0.124121
$855$	−15.1708	−0.518831
$856$	− 0.745574i	− 0.0254832i
$857$	11.0489	0.377422	0.188711	−	0.982033i	$-0.439569\pi$
$857$	11.0489	0.377422	0.188711	+	0.982033i	$0.439569\pi$
$858$	0	0
$859$	45.2616	1.54430	0.772152	−	0.635437i	$-0.219180\pi$
$859$	45.2616	1.54430	0.772152	+	0.635437i	$0.219180\pi$
$860$	24.5189i	0.836087i
$861$	−13.0489	−0.444705
$862$	55.6344	1.89491
$863$	− 5.90225i	− 0.200915i	−0.994941	−	0.100457i	$-0.967969\pi$
$863$	− 5.90225i	− 0.200915i	0.994941	−	0.100457i	$-0.0320306\pi$
$864$	− 71.3311i	− 2.42673i
$865$	− 57.1099i	− 1.94180i
$866$	− 6.38283i	− 0.216898i
$867$	51.8938	1.76241
$868$	1.79445	0.0609076
$869$	42.0227i	1.42552i
$870$	−131.240	−4.44947
$871$	0	0
$872$	7.18494	0.243313
$873$	− 7.86248i	− 0.266105i
$874$	−10.8277	−0.366254
$875$	−5.86248	−0.198188
$876$	9.37227i	0.316660i
$877$	− 4.90727i	− 0.165707i	−0.996562	−	0.0828534i	$-0.973597\pi$
$877$	− 4.90727i	− 0.165707i	0.996562	−	0.0828534i	$-0.0264033\pi$
$878$	58.6732i	1.98012i
$879$	− 43.9844i	− 1.48356i
$880$	−42.9200	−1.44683
$881$	−44.2822	−1.49190	−0.745952	−	0.665999i	$-0.768005\pi$
$881$	−44.2822	−1.49190	−0.745952	+	0.665999i	$0.768005\pi$
$882$	12.0192i	0.404706i
$883$	58.8605	1.98081	0.990407	−	0.138181i	$-0.0441256\pi$
$883$	58.8605	1.98081	0.990407	+	0.138181i	$0.0441256\pi$
$884$	0	0
$885$	39.0278	1.31190
$886$	− 28.0127i	− 0.941104i
$887$	−10.1289	−0.340096	−0.170048	−	0.985436i	$-0.554392\pi$
$887$	−10.1289	−0.340096	−0.170048	+	0.985436i	$0.554392\pi$
$888$	−24.6066	−0.825744
$889$	12.8816i	0.432036i
$890$	54.3260i	1.82101i
$891$	− 46.6605i	− 1.56319i
$892$	13.5989i	0.455326i
$893$	−4.85746	−0.162549
$894$	−47.9688	−1.60432
$895$	30.9597i	1.03487i
$896$	−9.66196	−0.322783
$897$	0	0
$898$	26.2439	0.875769
$899$	11.5381i	0.384816i
$900$	24.9164	0.830546
$901$	−1.30833	−0.0435866
$902$	23.6655i	0.787976i
$903$	20.9739i	0.697966i
$904$	− 7.02061i	− 0.233502i
$905$	− 1.94610i	− 0.0646906i
$906$	−67.4389	−2.24051
$907$	−37.9547	−1.26026	−0.630132	−	0.776488i	$-0.716999\pi$
$907$	−37.9547	−1.26026	−0.630132	+	0.776488i	$0.716999\pi$
$908$	8.96117i	0.297387i
$909$	−86.8349	−2.88013
$910$	0	0
$911$	5.57477	0.184700	0.0923501	−	0.995727i	$-0.470562\pi$
$911$	5.57477	0.184700	0.0923501	+	0.995727i	$0.470562\pi$
$912$	12.4111i	0.410973i
$913$	51.1310	1.69219
$914$	−62.8787	−2.07984
$915$	17.4600i	0.577209i
$916$	− 27.1849i	− 0.898216i
$917$	9.04888i	0.298820i
$918$	10.7044i	0.353296i
$919$	15.7844	0.520679	0.260340	−	0.965517i	$-0.416165\pi$
$919$	15.7844	0.520679	0.260340	+	0.965517i	$0.416165\pi$
$920$	−26.6167	−0.877525
$921$	42.0711i	1.38629i
$922$	22.7427	0.748990
$923$	0	0
$924$	12.4111	0.408295
$925$	− 17.9406i	− 0.589882i
$926$	−22.0383	−0.724224
$927$	−29.2333	−0.960148
$928$	52.5371i	1.72462i
$929$	− 45.2630i	− 1.48503i	−0.669829	−	0.742516i	$-0.733632\pi$
$929$	− 45.2630i	− 1.48503i	0.669829	−	0.742516i	$-0.266368\pi$
$930$	− 22.0383i	− 0.722665i
$931$	− 0.813607i	− 0.0266649i
$932$	7.84281	0.256900
$933$	1.32391	0.0433429
$934$	− 67.1638i	− 2.19767i
$935$	4.57834	0.149728
$936$	0	0
$937$	53.6188	1.75165	0.875824	−	0.482630i	$-0.160318\pi$
$937$	53.6188	1.75165	0.875824	+	0.482630i	$0.160318\pi$
$938$	18.2056i	0.594432i
$939$	56.3205	1.83795
$940$	21.6555	0.706324
$941$	20.7753i	0.677255i	0.940920	+	0.338628i	$0.109963\pi$
$941$	20.7753i	0.677255i	−0.940920	+	0.338628i	$0.890037\pi$
$942$	− 72.1844i	− 2.35190i
$943$	30.8605i	1.00496i
$944$	− 21.9789i	− 0.715351i
$945$	31.6655	1.03008
$946$	38.0383	1.23673
$947$	10.8605i	0.352919i	0.984308	+	0.176460i	$0.0564645\pi$
$947$	10.8605i	0.352919i	−0.984308	+	0.176460i	$0.943535\pi$
$948$	−54.1744	−1.75950
$949$	0	0
$950$	−4.30330	−0.139618
$951$	− 29.2333i	− 0.947955i
$952$	0.676089	0.0219122
$953$	25.7180	0.833087	0.416543	−	0.909116i	$-0.363241\pi$
$953$	25.7180	0.833087	0.416543	+	0.909116i	$0.363241\pi$
$954$	29.9844i	0.970781i
$955$	22.0383i	0.713143i
$956$	18.3133i	0.592296i
$957$	79.8016i	2.57962i
$958$	−21.7789	−0.703643
$959$	−6.25945	−0.202128
$960$	− 14.5089i	− 0.468271i
$961$	29.0625	0.937500
$962$	0	0
$963$	3.83276	0.123509
$964$	10.8816i	0.350474i
$965$	−34.3416	−1.10550
$966$	41.2927	1.32857
$967$	33.5038i	1.07741i	0.842494	+	0.538705i	$0.181086\pi$
$967$	33.5038i	1.07741i	−0.842494	+	0.538705i	$0.818914\pi$
$968$	− 1.76975i	− 0.0568820i
$969$	− 1.32391i	− 0.0425302i
$970$	− 6.05390i	− 0.194379i
$971$	2.03831	0.0654126	0.0327063	−	0.999465i	$-0.489587\pi$
$971$	2.03831	0.0654126	0.0327063	+	0.999465i	$0.489587\pi$
$972$	16.6267	0.533302
$973$	− 11.5733i	− 0.371023i
$974$	20.1643	0.646107
$975$	0	0
$976$	9.83276	0.314739
$977$	15.1411i	0.484406i	0.970226	+	0.242203i	$0.0778701\pi$
$977$	15.1411i	0.484406i	−0.970226	+	0.242203i	$0.922130\pi$
$978$	−75.7422	−2.42197
$979$	33.0333	1.05575
$980$	3.62721i	0.115867i
$981$	36.9355i	1.17926i
$982$	0.107798i	0.00343998i
$983$	− 49.3124i	− 1.57282i	−0.617704	−	0.786411i	$-0.711937\pi$
$983$	− 49.3124i	− 1.57282i	0.617704	−	0.786411i	$-0.288063\pi$
$984$	16.8222	0.536272
$985$	52.9583	1.68739
$986$	− 7.88403i	− 0.251079i
$987$	18.5244	0.589639
$988$	0	0
$989$	49.6030	1.57728
$990$	− 104.927i	− 3.33480i
$991$	5.43171	0.172544	0.0862720	−	0.996272i	$-0.472505\pi$
$991$	5.43171	0.172544	0.0862720	+	0.996272i	$0.472505\pi$
$992$	−8.82220	−0.280105
$993$	53.9900i	1.71332i
$994$	− 15.8328i	− 0.502185i
$995$	− 60.8066i	− 1.92770i
$996$	65.9165i	2.08865i
$997$	−53.6061	−1.69772	−0.848861	−	0.528616i	$-0.822711\pi$
$997$	−53.6061	−1.69772	−0.848861	+	0.528616i	$0.822711\pi$
$998$	18.6761	0.591181
$999$	− 69.2333i	− 2.19044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.c.f.337.2		6
13.5	odd	4		91.2.a.d.1.1	✓	3
13.8	odd	4		1183.2.a.i.1.3		3
13.12	even	2	inner	1183.2.c.f.337.5		6
39.5	even	4		819.2.a.i.1.3		3
52.31	even	4		1456.2.a.t.1.3		3
65.44	odd	4		2275.2.a.m.1.3		3
91.5	even	12		637.2.e.i.508.3		6
91.18	odd	12		637.2.e.j.79.3		6
91.31	even	12		637.2.e.i.79.3		6
91.34	even	4		8281.2.a.bg.1.3		3
91.44	odd	12		637.2.e.j.508.3		6
91.83	even	4		637.2.a.j.1.1		3
104.5	odd	4		5824.2.a.by.1.3		3
104.83	even	4		5824.2.a.bs.1.1		3
273.83	odd	4		5733.2.a.x.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.a.d.1.1	✓	3	13.5	odd	4
637.2.a.j.1.1		3	91.83	even	4
637.2.e.i.79.3		6	91.31	even	12
637.2.e.i.508.3		6	91.5	even	12
637.2.e.j.79.3		6	91.18	odd	12
637.2.e.j.508.3		6	91.44	odd	12
819.2.a.i.1.3		3	39.5	even	4
1183.2.a.i.1.3		3	13.8	odd	4
1183.2.c.f.337.2		6	1.1	even	1	trivial
1183.2.c.f.337.5		6	13.12	even	2	inner
1456.2.a.t.1.3		3	52.31	even	4
2275.2.a.m.1.3		3	65.44	odd	4
5733.2.a.x.1.3		3	273.83	odd	4
5824.2.a.bs.1.1		3	104.83	even	4
5824.2.a.by.1.3		3	104.5	odd	4
8281.2.a.bg.1.3		3	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.81361i q^{2} -3.10278 q^{3} -1.28917 q^{4} +2.81361i q^{5} +5.62721i q^{6} +1.00000i q^{7} -1.28917i q^{8} +6.62721 q^{9} +O(q^{10})\)	\(q-1.81361i q^{2} -3.10278 q^{3} -1.28917 q^{4} +2.81361i q^{5} +5.62721i q^{6} +1.00000i q^{7} -1.28917i q^{8} +6.62721 q^{9} +5.10278 q^{10} -3.10278i q^{11} +4.00000 q^{12} +1.81361 q^{14} -8.72999i q^{15} -4.91638 q^{16} +0.524438 q^{17} -12.0192i q^{18} +0.813607i q^{19} -3.62721i q^{20} -3.10278i q^{21} -5.62721 q^{22} -7.33804 q^{23} +4.00000i q^{24} -2.91638 q^{25} -11.2544 q^{27} -1.28917i q^{28} +8.28917 q^{29} -15.8328 q^{30} +1.39194i q^{31} +6.33804i q^{32} +9.62721i q^{33} -0.951124i q^{34} -2.81361 q^{35} -8.54359 q^{36} +6.15165i q^{37} +1.47556 q^{38} +3.62721 q^{40} -4.20555i q^{41} -5.62721 q^{42} -6.75971 q^{43} +4.00000i q^{44} +18.6464i q^{45} +13.3083i q^{46} +5.97028i q^{47} +15.2544 q^{48} -1.00000 q^{49} +5.28917i q^{50} -1.62721 q^{51} -2.49472 q^{53} +20.4111i q^{54} +8.72999 q^{55} +1.28917 q^{56} -2.52444i q^{57} -15.0333i q^{58} +4.47054i q^{59} +11.2544i q^{60} -2.00000 q^{61} +2.52444 q^{62} +6.62721i q^{63} +1.66196 q^{64} +17.4600 q^{66} +10.0383i q^{67} -0.676089 q^{68} +22.7683 q^{69} +5.10278i q^{70} -8.72999i q^{71} -8.54359i q^{72} +2.34307i q^{73} +11.1567 q^{74} +9.04888 q^{75} -1.04888i q^{76} +3.10278 q^{77} -13.5436 q^{79} -13.8328i q^{80} +15.0383 q^{81} -7.62721 q^{82} +16.4791i q^{83} +4.00000i q^{84} +1.47556i q^{85} +12.2594i q^{86} -25.7194 q^{87} -4.00000 q^{88} +10.6464i q^{89} +33.8172 q^{90} +9.45998 q^{92} -4.31889i q^{93} +10.8277 q^{94} -2.28917 q^{95} -19.6655i q^{96} -1.18639i q^{97} +1.81361i q^{98} -20.5628i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9}+O(q^{10}) \) 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9	\( 6 q - 4 q^{3} - 6 q^{4} + 14 q^{9} + 16 q^{10} + 24 q^{12} - 2 q^{14} - 2 q^{16} - 8 q^{17} - 8 q^{22} - 20 q^{23} + 10 q^{25} - 16 q^{27} + 48 q^{29} - 40 q^{30} - 4 q^{35} + 2 q^{36} + 20 q^{38} - 4 q^{40} - 8 q^{42} - 20 q^{43} + 40 q^{48} - 6 q^{49} + 16 q^{51} + 16 q^{53} + 12 q^{55} + 6 q^{56} - 12 q^{61} + 4 q^{62} + 34 q^{64} + 24 q^{66} + 44 q^{68} + 12 q^{69} + 60 q^{74} + 32 q^{75} + 4 q^{77} - 28 q^{79} + 6 q^{81} - 20 q^{82} - 52 q^{87} - 24 q^{88} + 56 q^{90} - 24 q^{92} - 20 q^{94} - 12 q^{95}+O(q^{100}) \) 6 * q - 4 * q^3 - 6 * q^4 + 14 * q^9 + 16 * q^10 + 24 * q^12 - 2 * q^14 - 2 * q^16 - 8 * q^17 - 8 * q^22 - 20 * q^23 + 10 * q^25 - 16 * q^27 + 48 * q^29 - 40 * q^30 - 4 * q^35 + 2 * q^36 + 20 * q^38 - 4 * q^40 - 8 * q^42 - 20 * q^43 + 40 * q^48 - 6 * q^49 + 16 * q^51 + 16 * q^53 + 12 * q^55 + 6 * q^56 - 12 * q^61 + 4 * q^62 + 34 * q^64 + 24 * q^66 + 44 * q^68 + 12 * q^69 + 60 * q^74 + 32 * q^75 + 4 * q^77 - 28 * q^79 + 6 * q^81 - 20 * q^82 - 52 * q^87 - 24 * q^88 + 56 * q^90 - 24 * q^92 - 20 * q^94 - 12 * q^95

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