LMFDB - Embedded newform 7381.2.a.l.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

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

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

chi := DirichletCharacter("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.a (trivial)

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:	yes
Analytic conductor:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.461995 q^{2} -3.03307 q^{3} -1.78656 q^{4} -2.42205 q^{5} -1.40126 q^{6} -0.344105 q^{7} -1.74937 q^{8} +6.19953 q^{9} +O(q^{10})$	\(q+0.461995 q^{2} -3.03307 q^{3} -1.78656 q^{4} -2.42205 q^{5} -1.40126 q^{6} -0.344105 q^{7} -1.74937 q^{8} +6.19953 q^{9} -1.11898 q^{10} +5.41877 q^{12} +2.06526 q^{13} -0.158975 q^{14} +7.34626 q^{15} +2.76492 q^{16} +1.43746 q^{17} +2.86415 q^{18} +4.86026 q^{19} +4.32714 q^{20} +1.04369 q^{21} -0.690105 q^{23} +5.30597 q^{24} +0.866332 q^{25} +0.954142 q^{26} -9.70440 q^{27} +0.614764 q^{28} +6.16274 q^{29} +3.39393 q^{30} +9.07409 q^{31} +4.77612 q^{32} +0.664099 q^{34} +0.833439 q^{35} -11.0758 q^{36} -0.240540 q^{37} +2.24542 q^{38} -6.26410 q^{39} +4.23707 q^{40} +1.57394 q^{41} +0.482182 q^{42} +0.272409 q^{43} -15.0156 q^{45} -0.318825 q^{46} -6.07484 q^{47} -8.38620 q^{48} -6.88159 q^{49} +0.400241 q^{50} -4.35992 q^{51} -3.68972 q^{52} -1.80639 q^{53} -4.48339 q^{54} +0.601967 q^{56} -14.7415 q^{57} +2.84715 q^{58} +4.53059 q^{59} -13.1245 q^{60} -1.00000 q^{61} +4.19218 q^{62} -2.13329 q^{63} -3.32329 q^{64} -5.00217 q^{65} -5.27712 q^{67} -2.56811 q^{68} +2.09314 q^{69} +0.385045 q^{70} +4.61072 q^{71} -10.8453 q^{72} -7.47817 q^{73} -0.111128 q^{74} -2.62765 q^{75} -8.68315 q^{76} -2.89398 q^{78} +0.695558 q^{79} -6.69678 q^{80} +10.8356 q^{81} +0.727153 q^{82} +0.407912 q^{83} -1.86462 q^{84} -3.48160 q^{85} +0.125851 q^{86} -18.6920 q^{87} +3.76697 q^{89} -6.93712 q^{90} -0.710667 q^{91} +1.23291 q^{92} -27.5224 q^{93} -2.80655 q^{94} -11.7718 q^{95} -14.4863 q^{96} +12.5351 q^{97} -3.17926 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9}+O(q^{10}) $ 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9} + 12 q^{10} + q^{12} + 3 q^{13} - q^{14} - 5 q^{15} + 17 q^{16} + 8 q^{17} + 20 q^{18} + 8 q^{19} + 16 q^{20} + 11 q^{21} + 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 13 q^{27} - 7 q^{28} + 43 q^{29} + 30 q^{30} - 4 q^{31} + 23 q^{32} + 31 q^{35} - 35 q^{36} - 4 q^{37} - 13 q^{38} + 11 q^{39} + 57 q^{40} + 29 q^{41} + 48 q^{42} + 10 q^{43} - 10 q^{45} - 14 q^{46} - 13 q^{47} + 42 q^{48} + 26 q^{49} - 6 q^{50} + 56 q^{51} + 25 q^{52} - 15 q^{53} + 35 q^{54} - 9 q^{56} - 3 q^{57} - 84 q^{58} - 13 q^{59} + 34 q^{60} - 24 q^{61} + 55 q^{62} + 22 q^{63} + 61 q^{64} + 41 q^{65} - q^{67} - 4 q^{68} - 27 q^{69} + 55 q^{70} - 6 q^{71} + 22 q^{72} + 18 q^{73} + 28 q^{74} + 47 q^{75} + 36 q^{76} - 10 q^{78} + 9 q^{79} - 40 q^{80} + 40 q^{81} + 15 q^{82} + 10 q^{83} + 93 q^{84} - 9 q^{85} + 38 q^{86} + 51 q^{87} - 17 q^{89} - 44 q^{90} - 22 q^{91} + 11 q^{92} + 32 q^{93} - 47 q^{94} + 54 q^{95} + 44 q^{96} - q^{97} + 45 q^{98}+O(q^{100}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9 + 12 * q^10 + q^12 + 3 * q^13 - q^14 - 5 * q^15 + 17 * q^16 + 8 * q^17 + 20 * q^18 + 8 * q^19 + 16 * q^20 + 11 * q^21 + 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 13 * q^27 - 7 * q^28 + 43 * q^29 + 30 * q^30 - 4 * q^31 + 23 * q^32 + 31 * q^35 - 35 * q^36 - 4 * q^37 - 13 * q^38 + 11 * q^39 + 57 * q^40 + 29 * q^41 + 48 * q^42 + 10 * q^43 - 10 * q^45 - 14 * q^46 - 13 * q^47 + 42 * q^48 + 26 * q^49 - 6 * q^50 + 56 * q^51 + 25 * q^52 - 15 * q^53 + 35 * q^54 - 9 * q^56 - 3 * q^57 - 84 * q^58 - 13 * q^59 + 34 * q^60 - 24 * q^61 + 55 * q^62 + 22 * q^63 + 61 * q^64 + 41 * q^65 - q^67 - 4 * q^68 - 27 * q^69 + 55 * q^70 - 6 * q^71 + 22 * q^72 + 18 * q^73 + 28 * q^74 + 47 * q^75 + 36 * q^76 - 10 * q^78 + 9 * q^79 - 40 * q^80 + 40 * q^81 + 15 * q^82 + 10 * q^83 + 93 * q^84 - 9 * q^85 + 38 * q^86 + 51 * q^87 - 17 * q^89 - 44 * q^90 - 22 * q^91 + 11 * q^92 + 32 * q^93 - 47 * q^94 + 54 * q^95 + 44 * q^96 - q^97 + 45 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	0.461995	0.326680	0.163340	−	0.986570i	$-0.447773\pi$
$2$	0.461995	0.326680	0.163340	+	0.986570i	$0.447773\pi$
$3$	−3.03307	−1.75115	−0.875573	−	0.483087i	$-0.839516\pi$
$3$	−3.03307	−1.75115	−0.875573	+	0.483087i	$0.839516\pi$
$4$	−1.78656	−0.893280
$5$	−2.42205	−1.08317	−0.541587	−	0.840645i	$-0.682176\pi$
$5$	−2.42205	−1.08317	−0.541587	+	0.840645i	$0.682176\pi$
$6$	−1.40126	−0.572064
$7$	−0.344105	−0.130059	−0.0650297	−	0.997883i	$-0.520714\pi$
$7$	−0.344105	−0.130059	−0.0650297	+	0.997883i	$0.520714\pi$
$8$	−1.74937	−0.618497
$9$	6.19953	2.06651
$10$	−1.11898	−0.353851
$11$	0	0
$11$	0	0
$12$	5.41877	1.56426
$13$	2.06526	0.572801	0.286401	−	0.958110i	$-0.407541\pi$
$13$	2.06526	0.572801	0.286401	+	0.958110i	$0.407541\pi$
$14$	−0.158975	−0.0424878
$15$	7.34626	1.89680
$16$	2.76492	0.691230
$17$	1.43746	0.348635	0.174317	−	0.984690i	$-0.444228\pi$
$17$	1.43746	0.348635	0.174317	+	0.984690i	$0.444228\pi$
$18$	2.86415	0.675087
$19$	4.86026	1.11502	0.557510	−	0.830170i	$-0.311757\pi$
$19$	4.86026	1.11502	0.557510	+	0.830170i	$0.311757\pi$
$20$	4.32714	0.967578
$21$	1.04369	0.227753
$22$	0	0
$23$	−0.690105	−0.143897	−0.0719484	−	0.997408i	$-0.522922\pi$
$23$	−0.690105	−0.143897	−0.0719484	+	0.997408i	$0.522922\pi$
$24$	5.30597	1.08308
$25$	0.866332	0.173266
$26$	0.954142	0.187123
$27$	−9.70440	−1.86761
$28$	0.614764	0.116179
$29$	6.16274	1.14439	0.572196	−	0.820117i	$-0.306092\pi$
$29$	6.16274	1.14439	0.572196	+	0.820117i	$0.306092\pi$
$30$	3.39393	0.619645
$31$	9.07409	1.62975	0.814877	−	0.579634i	$-0.196804\pi$
$31$	9.07409	1.62975	0.814877	+	0.579634i	$0.196804\pi$
$32$	4.77612	0.844307
$33$	0	0
$34$	0.664099	0.113892
$35$	0.833439	0.140877
$36$	−11.0758	−1.84597
$37$	−0.240540	−0.0395445	−0.0197722	−	0.999805i	$-0.506294\pi$
$37$	−0.240540	−0.0395445	−0.0197722	+	0.999805i	$0.506294\pi$
$38$	2.24542	0.364255
$39$	−6.26410	−1.00306
$40$	4.23707	0.669940
$41$	1.57394	0.245808	0.122904	−	0.992419i	$-0.460779\pi$
$41$	1.57394	0.245808	0.122904	+	0.992419i	$0.460779\pi$
$42$	0.482182	0.0744023
$43$	0.272409	0.0415419	0.0207710	−	0.999784i	$-0.493388\pi$
$43$	0.272409	0.0415419	0.0207710	+	0.999784i	$0.493388\pi$
$44$	0	0
$45$	−15.0156	−2.23839
$46$	−0.318825	−0.0470082
$47$	−6.07484	−0.886106	−0.443053	−	0.896495i	$-0.646105\pi$
$47$	−6.07484	−0.886106	−0.443053	+	0.896495i	$0.646105\pi$
$48$	−8.38620	−1.21044
$49$	−6.88159	−0.983085
$50$	0.400241	0.0566026
$51$	−4.35992	−0.610510
$52$	−3.68972	−0.511672
$53$	−1.80639	−0.248127	−0.124064	−	0.992274i	$-0.539593\pi$
$53$	−1.80639	−0.248127	−0.124064	+	0.992274i	$0.539593\pi$
$54$	−4.48339	−0.610112
$55$	0	0
$56$	0.601967	0.0804413
$57$	−14.7415	−1.95256
$58$	2.84715	0.373850
$59$	4.53059	0.589833	0.294917	−	0.955523i	$-0.404708\pi$
$59$	4.53059	0.589833	0.294917	+	0.955523i	$0.404708\pi$
$60$	−13.1245	−1.69437
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	4.19218	0.532408
$63$	−2.13329	−0.268769
$64$	−3.32329	−0.415412
$65$	−5.00217	−0.620443
$66$	0	0
$67$	−5.27712	−0.644703	−0.322351	−	0.946620i	$-0.604473\pi$
$67$	−5.27712	−0.644703	−0.322351	+	0.946620i	$0.604473\pi$
$68$	−2.56811	−0.311429
$69$	2.09314	0.251984
$70$	0.385045	0.0460217
$71$	4.61072	0.547192	0.273596	−	0.961845i	$-0.411787\pi$
$71$	4.61072	0.547192	0.273596	+	0.961845i	$0.411787\pi$
$72$	−10.8453	−1.27813
$73$	−7.47817	−0.875254	−0.437627	−	0.899157i	$-0.644181\pi$
$73$	−7.47817	−0.875254	−0.437627	+	0.899157i	$0.644181\pi$
$74$	−0.111128	−0.0129184
$75$	−2.62765	−0.303415
$76$	−8.68315	−0.996025
$77$	0	0
$78$	−2.89398	−0.327679
$79$	0.695558	0.0782564	0.0391282	−	0.999234i	$-0.487542\pi$
$79$	0.695558	0.0782564	0.0391282	+	0.999234i	$0.487542\pi$
$80$	−6.69678	−0.748722
$81$	10.8356	1.20395
$82$	0.727153	0.0803006
$83$	0.407912	0.0447741	0.0223871	−	0.999749i	$-0.492873\pi$
$83$	0.407912	0.0447741	0.0223871	+	0.999749i	$0.492873\pi$
$84$	−1.86462	−0.203447
$85$	−3.48160	−0.377632
$86$	0.125851	0.0135709
$87$	−18.6920	−2.00400
$88$	0	0
$89$	3.76697	0.399298	0.199649	−	0.979868i	$-0.436020\pi$
$89$	3.76697	0.399298	0.199649	+	0.979868i	$0.436020\pi$
$90$	−6.93712	−0.731237
$91$	−0.710667	−0.0744981
$92$	1.23291	0.128540
$93$	−27.5224	−2.85394
$94$	−2.80655	−0.289473
$95$	−11.7718	−1.20776
$96$	−14.4863	−1.47850
$97$	12.5351	1.27274	0.636371	−	0.771383i	$-0.280435\pi$
$97$	12.5351	1.27274	0.636371	+	0.771383i	$0.280435\pi$
$98$	−3.17926	−0.321154
$99$	0	0
$100$	−1.54775	−0.154775
$101$	1.23357	0.122744	0.0613722	−	0.998115i	$-0.480452\pi$
$101$	1.23357	0.122744	0.0613722	+	0.998115i	$0.480452\pi$
$102$	−2.01426	−0.199441
$103$	15.2533	1.50295	0.751477	−	0.659759i	$-0.229342\pi$
$103$	15.2533	1.50295	0.751477	+	0.659759i	$0.229342\pi$
$104$	−3.61292	−0.354276
$105$	−2.52788	−0.246696
$106$	−0.834545	−0.0810582
$107$	−3.37813	−0.326576	−0.163288	−	0.986578i	$-0.552210\pi$
$107$	−3.37813	−0.326576	−0.163288	+	0.986578i	$0.552210\pi$
$108$	17.3375	1.66830
$109$	−0.822095	−0.0787424	−0.0393712	−	0.999225i	$-0.512535\pi$
$109$	−0.822095	−0.0787424	−0.0393712	+	0.999225i	$0.512535\pi$
$110$	0	0
$111$	0.729574	0.0692481
$112$	−0.951422	−0.0899009
$113$	−4.24078	−0.398939	−0.199469	−	0.979904i	$-0.563922\pi$
$113$	−4.24078	−0.398939	−0.199469	+	0.979904i	$0.563922\pi$
$114$	−6.81051	−0.637863
$115$	1.67147	0.155865
$116$	−11.0101	−1.02226
$117$	12.8037	1.18370
$118$	2.09311	0.192687
$119$	−0.494636	−0.0453432
$120$	−12.8513	−1.17316
$121$	0	0
$122$	−0.461995	−0.0418271
$123$	−4.77387	−0.430446
$124$	−16.2114	−1.45583
$125$	10.0120	0.895497
$126$	−0.985568	−0.0878014
$127$	−19.2525	−1.70838	−0.854190	−	0.519961i	$-0.825946\pi$
$127$	−19.2525	−1.70838	−0.854190	+	0.519961i	$0.825946\pi$
$128$	−11.0876	−0.980014
$129$	−0.826235	−0.0727459
$130$	−2.31098	−0.202686
$131$	6.20071	0.541759	0.270879	−	0.962613i	$-0.412686\pi$
$131$	6.20071	0.541759	0.270879	+	0.962613i	$0.412686\pi$
$132$	0	0
$133$	−1.67244	−0.145019
$134$	−2.43800	−0.210611
$135$	23.5046	2.02295
$136$	−2.51465	−0.215629
$137$	19.3748	1.65530	0.827649	−	0.561245i	$-0.189678\pi$
$137$	19.3748	1.65530	0.827649	+	0.561245i	$0.189678\pi$
$138$	0.967020	0.0823182
$139$	−1.56475	−0.132720	−0.0663602	−	0.997796i	$-0.521139\pi$
$139$	−1.56475	−0.132720	−0.0663602	+	0.997796i	$0.521139\pi$
$140$	−1.48899	−0.125843
$141$	18.4254	1.55170
$142$	2.13013	0.178757
$143$	0	0
$144$	17.1412	1.42843
$145$	−14.9265	−1.23958
$146$	−3.45488	−0.285928
$147$	20.8724	1.72152
$148$	0.429739	0.0353243
$149$	18.2176	1.49244	0.746220	−	0.665699i	$-0.231867\pi$
$149$	18.2176	1.49244	0.746220	+	0.665699i	$0.231867\pi$
$150$	−1.21396	−0.0991194
$151$	14.2504	1.15968	0.579842	−	0.814729i	$-0.303114\pi$
$151$	14.2504	1.15968	0.579842	+	0.814729i	$0.303114\pi$
$152$	−8.50241	−0.689636
$153$	8.91156	0.720457
$154$	0	0
$155$	−21.9779	−1.76531
$156$	11.1912	0.896012
$157$	−8.78709	−0.701286	−0.350643	−	0.936509i	$-0.614037\pi$
$157$	−8.78709	−0.701286	−0.350643	+	0.936509i	$0.614037\pi$
$158$	0.321344	0.0255648
$159$	5.47892	0.434507
$160$	−11.5680	−0.914532
$161$	0.237468	0.0187151
$162$	5.00598	0.393307
$163$	4.79334	0.375443	0.187722	−	0.982222i	$-0.439890\pi$
$163$	4.79334	0.375443	0.187722	+	0.982222i	$0.439890\pi$
$164$	−2.81194	−0.219576
$165$	0	0
$166$	0.188453	0.0146268
$167$	−21.0240	−1.62688	−0.813442	−	0.581646i	$-0.802409\pi$
$167$	−21.0240	−1.62688	−0.813442	+	0.581646i	$0.802409\pi$
$168$	−1.82581	−0.140864
$169$	−8.73468	−0.671899
$170$	−1.60848	−0.123365
$171$	30.1313	2.30420
$172$	−0.486674	−0.0371086
$173$	−22.3340	−1.69802	−0.849011	−	0.528375i	$-0.822801\pi$
$173$	−22.3340	−1.69802	−0.849011	+	0.528375i	$0.822801\pi$
$174$	−8.63563	−0.654665
$175$	−0.298109	−0.0225349
$176$	0	0
$177$	−13.7416	−1.03288
$178$	1.74032	0.130443
$179$	3.12870	0.233850	0.116925	−	0.993141i	$-0.462696\pi$
$179$	3.12870	0.233850	0.116925	+	0.993141i	$0.462696\pi$
$180$	26.8262	1.99951
$181$	18.1947	1.35240	0.676201	−	0.736718i	$-0.263625\pi$
$181$	18.1947	1.35240	0.676201	+	0.736718i	$0.263625\pi$
$182$	−0.328325	−0.0243370
$183$	3.03307	0.224211
$184$	1.20725	0.0889997
$185$	0.582599	0.0428336
$186$	−12.7152	−0.932323
$187$	0	0
$188$	10.8531	0.791541
$189$	3.33933	0.242901
$190$	−5.43851	−0.394551
$191$	5.40086	0.390793	0.195396	−	0.980724i	$-0.437401\pi$
$191$	5.40086	0.390793	0.195396	+	0.980724i	$0.437401\pi$
$192$	10.0798	0.727446
$193$	−23.6780	−1.70438	−0.852188	−	0.523235i	$-0.824725\pi$
$193$	−23.6780	−1.70438	−0.852188	+	0.523235i	$0.824725\pi$
$194$	5.79114	0.415779
$195$	15.1720	1.08649
$196$	12.2944	0.878170
$197$	22.5015	1.60317	0.801584	−	0.597882i	$-0.203991\pi$
$197$	22.5015	1.60317	0.801584	+	0.597882i	$0.203991\pi$
$198$	0	0
$199$	4.24981	0.301261	0.150630	−	0.988590i	$-0.451870\pi$
$199$	4.24981	0.301261	0.150630	+	0.988590i	$0.451870\pi$
$200$	−1.51554	−0.107165
$201$	16.0059	1.12897
$202$	0.569901	0.0400981
$203$	−2.12063	−0.148839
$204$	7.78925	0.545357
$205$	−3.81216	−0.266253
$206$	7.04696	0.490985
$207$	−4.27833	−0.297364
$208$	5.71029	0.395937
$209$	0	0
$210$	−1.16787	−0.0805906
$211$	−20.4908	−1.41064	−0.705322	−	0.708887i	$-0.749198\pi$
$211$	−20.4908	−1.41064	−0.705322	+	0.708887i	$0.749198\pi$
$212$	3.22723	0.221647
$213$	−13.9847	−0.958213
$214$	−1.56068	−0.106686
$215$	−0.659787	−0.0449971
$216$	16.9766	1.15511
$217$	−3.12244	−0.211965
$218$	−0.379804	−0.0257236
$219$	22.6818	1.53270
$220$	0	0
$221$	2.96873	0.199698
$222$	0.337060	0.0226220
$223$	−27.0181	−1.80926	−0.904632	−	0.426193i	$-0.859854\pi$
$223$	−27.0181	−1.80926	−0.904632	+	0.426193i	$0.859854\pi$
$224$	−1.64349	−0.109810
$225$	5.37085	0.358057
$226$	−1.95922	−0.130325
$227$	0.793675	0.0526781	0.0263390	−	0.999653i	$-0.491615\pi$
$227$	0.793675	0.0526781	0.0263390	+	0.999653i	$0.491615\pi$
$228$	26.3366	1.74419
$229$	−17.9781	−1.18803	−0.594013	−	0.804456i	$-0.702457\pi$
$229$	−17.9781	−1.18803	−0.594013	+	0.804456i	$0.702457\pi$
$230$	0.772211	0.0509181
$231$	0	0
$232$	−10.7809	−0.707802
$233$	−14.7546	−0.966606	−0.483303	−	0.875453i	$-0.660563\pi$
$233$	−14.7546	−0.966606	−0.483303	+	0.875453i	$0.660563\pi$
$234$	5.91523	0.386691
$235$	14.7136	0.959808
$236$	−8.09418	−0.526886
$237$	−2.10968	−0.137038
$238$	−0.228520	−0.0148127
$239$	−9.72216	−0.628874	−0.314437	−	0.949278i	$-0.601816\pi$
$239$	−9.72216	−0.628874	−0.314437	+	0.949278i	$0.601816\pi$
$240$	20.3118	1.31112
$241$	−24.9239	−1.60549	−0.802745	−	0.596322i	$-0.796628\pi$
$241$	−24.9239	−1.60549	−0.802745	+	0.596322i	$0.796628\pi$
$242$	0	0
$243$	−3.75187	−0.240682
$244$	1.78656	0.114373
$245$	16.6676	1.06485
$246$	−2.20551	−0.140618
$247$	10.0377	0.638685
$248$	−15.8740	−1.00800
$249$	−1.23723	−0.0784060
$250$	4.62547	0.292541
$251$	−21.4126	−1.35155	−0.675776	−	0.737107i	$-0.736192\pi$
$251$	−21.4126	−1.35155	−0.675776	+	0.737107i	$0.736192\pi$
$252$	3.81125	0.240086
$253$	0	0
$254$	−8.89454	−0.558093
$255$	10.5599	0.661289
$256$	1.52417	0.0952608
$257$	15.4128	0.961423	0.480712	−	0.876879i	$-0.340378\pi$
$257$	15.4128	0.961423	0.480712	+	0.876879i	$0.340378\pi$
$258$	−0.381717	−0.0237646
$259$	0.0827708	0.00514313
$260$	8.93669	0.554230
$261$	38.2061	2.36490
$262$	2.86470	0.176982
$263$	29.3148	1.80763	0.903814	−	0.427926i	$-0.140756\pi$
$263$	29.3148	1.80763	0.903814	+	0.427926i	$0.140756\pi$
$264$	0	0
$265$	4.37518	0.268765
$266$	−0.772658	−0.0473747
$267$	−11.4255	−0.699228
$268$	9.42789	0.575900
$269$	20.4770	1.24851	0.624253	−	0.781222i	$-0.285403\pi$
$269$	20.4770	1.24851	0.624253	+	0.781222i	$0.285403\pi$
$270$	10.8590	0.660857
$271$	6.63222	0.402879	0.201439	−	0.979501i	$-0.435438\pi$
$271$	6.63222	0.402879	0.201439	+	0.979501i	$0.435438\pi$
$272$	3.97446	0.240987
$273$	2.15550	0.130457
$274$	8.95105	0.540753
$275$	0	0
$276$	−3.73952	−0.225093
$277$	−2.40610	−0.144569	−0.0722844	−	0.997384i	$-0.523029\pi$
$277$	−2.40610	−0.144569	−0.0722844	+	0.997384i	$0.523029\pi$
$278$	−0.722907	−0.0433571
$279$	56.2551	3.36790
$280$	−1.45800	−0.0871319
$281$	27.0506	1.61370	0.806851	−	0.590755i	$-0.201170\pi$
$281$	27.0506	1.61370	0.806851	+	0.590755i	$0.201170\pi$
$282$	8.51246	0.506909
$283$	26.5207	1.57649	0.788246	−	0.615360i	$-0.210989\pi$
$283$	26.5207	1.57649	0.788246	+	0.615360i	$0.210989\pi$
$284$	−8.23734	−0.488796
$285$	35.7047	2.11497
$286$	0	0
$287$	−0.541600	−0.0319696
$288$	29.6097	1.74477
$289$	−14.9337	−0.878454
$290$	−6.89595	−0.404944
$291$	−38.0197	−2.22876
$292$	13.3602	0.781847
$293$	−21.8631	−1.27726	−0.638628	−	0.769516i	$-0.720498\pi$
$293$	−21.8631	−1.27726	−0.638628	+	0.769516i	$0.720498\pi$
$294$	9.64293	0.562387
$295$	−10.9733	−0.638892
$296$	0.420793	0.0244581
$297$	0	0
$298$	8.41642	0.487550
$299$	−1.42525	−0.0824243
$300$	4.69445	0.271034
$301$	−0.0937371	−0.00540291
$302$	6.58363	0.378845
$303$	−3.74149	−0.214943
$304$	13.4382	0.770735
$305$	2.42205	0.138686
$306$	4.11710	0.235359
$307$	28.1500	1.60661	0.803303	−	0.595571i	$-0.203074\pi$
$307$	28.1500	1.60661	0.803303	+	0.595571i	$0.203074\pi$
$308$	0	0
$309$	−46.2644	−2.63189
$310$	−10.1537	−0.576690
$311$	−2.57987	−0.146291	−0.0731455	−	0.997321i	$-0.523304\pi$
$311$	−2.57987	−0.146291	−0.0731455	+	0.997321i	$0.523304\pi$
$312$	10.9582	0.620388
$313$	2.62065	0.148128	0.0740638	−	0.997254i	$-0.476403\pi$
$313$	2.62065	0.148128	0.0740638	+	0.997254i	$0.476403\pi$
$314$	−4.05959	−0.229096
$315$	5.16693	0.291124
$316$	−1.24266	−0.0699049
$317$	10.3372	0.580596	0.290298	−	0.956936i	$-0.406246\pi$
$317$	10.3372	0.580596	0.290298	+	0.956936i	$0.406246\pi$
$318$	2.53124	0.141945
$319$	0	0
$320$	8.04919	0.449963
$321$	10.2461	0.571883
$322$	0.109709	0.00611386
$323$	6.98642	0.388735
$324$	−19.3584	−1.07547
$325$	1.78920	0.0992472
$326$	2.21450	0.122650
$327$	2.49347	0.137889
$328$	−2.75341	−0.152031
$329$	2.09038	0.115246
$330$	0	0
$331$	8.77865	0.482518	0.241259	−	0.970461i	$-0.422440\pi$
$331$	8.77865	0.482518	0.241259	+	0.970461i	$0.422440\pi$
$332$	−0.728759	−0.0399959
$333$	−1.49123	−0.0817190
$334$	−9.71297	−0.531470
$335$	12.7815	0.698325
$336$	2.88573	0.157430
$337$	20.7906	1.13254	0.566268	−	0.824221i	$-0.308387\pi$
$337$	20.7906	1.13254	0.566268	+	0.824221i	$0.308387\pi$
$338$	−4.03538	−0.219496
$339$	12.8626	0.698600
$340$	6.22008	0.337331
$341$	0	0
$342$	13.9205	0.752736
$343$	4.77672	0.257919
$344$	−0.476544	−0.0256935
$345$	−5.06969	−0.272943
$346$	−10.3182	−0.554710
$347$	23.4137	1.25691	0.628456	−	0.777845i	$-0.283687\pi$
$347$	23.4137	1.25691	0.628456	+	0.777845i	$0.283687\pi$
$348$	33.3944	1.79013
$349$	−18.4036	−0.985121	−0.492561	−	0.870278i	$-0.663939\pi$
$349$	−18.4036	−0.985121	−0.492561	+	0.870278i	$0.663939\pi$
$350$	−0.137725	−0.00736170
$351$	−20.0422	−1.06977
$352$	0	0
$353$	16.8353	0.896053	0.448027	−	0.894020i	$-0.352127\pi$
$353$	16.8353	0.896053	0.448027	+	0.894020i	$0.352127\pi$
$354$	−6.34856	−0.337422
$355$	−11.1674	−0.592705
$356$	−6.72991	−0.356685
$357$	1.50027	0.0794026
$358$	1.44544	0.0763941
$359$	31.9372	1.68558	0.842792	−	0.538240i	$-0.180911\pi$
$359$	31.9372	1.68558	0.842792	+	0.538240i	$0.180911\pi$
$360$	26.2678	1.38444
$361$	4.62213	0.243270
$362$	8.40586	0.441802
$363$	0	0
$364$	1.26965	0.0665477
$365$	18.1125	0.948052
$366$	1.40126	0.0732453
$367$	−4.53051	−0.236491	−0.118245	−	0.992984i	$-0.537727\pi$
$367$	−4.53051	−0.236491	−0.118245	+	0.992984i	$0.537727\pi$
$368$	−1.90808	−0.0994658
$369$	9.75769	0.507965
$370$	0.269158	0.0139929
$371$	0.621588	0.0322713
$372$	49.1704	2.54936
$373$	−28.6610	−1.48401	−0.742006	−	0.670394i	$-0.766125\pi$
$373$	−28.6610	−1.48401	−0.742006	+	0.670394i	$0.766125\pi$
$374$	0	0
$375$	−30.3670	−1.56814
$376$	10.6272	0.548054
$377$	12.7277	0.655509
$378$	1.54275	0.0793507
$379$	26.1537	1.34342	0.671712	−	0.740812i	$-0.265559\pi$
$379$	26.1537	1.34342	0.671712	+	0.740812i	$0.265559\pi$
$380$	21.0310	1.07887
$381$	58.3941	2.99162
$382$	2.49517	0.127664
$383$	15.9563	0.815327	0.407664	−	0.913132i	$-0.366344\pi$
$383$	15.9563	0.815327	0.407664	+	0.913132i	$0.366344\pi$
$384$	33.6295	1.71615
$385$	0	0
$386$	−10.9391	−0.556786
$387$	1.68880	0.0858468
$388$	−22.3946	−1.13692
$389$	−29.4689	−1.49413	−0.747066	−	0.664750i	$-0.768538\pi$
$389$	−29.4689	−1.49413	−0.747066	+	0.664750i	$0.768538\pi$
$390$	7.00937	0.354933
$391$	−0.991997	−0.0501675
$392$	12.0385	0.608034
$393$	−18.8072	−0.948698
$394$	10.3956	0.523723
$395$	−1.68468	−0.0847653
$396$	0	0
$397$	−24.1867	−1.21390	−0.606948	−	0.794741i	$-0.707607\pi$
$397$	−24.1867	−1.21390	−0.606948	+	0.794741i	$0.707607\pi$
$398$	1.96339	0.0984158
$399$	5.07263	0.253949
$400$	2.39534	0.119767
$401$	19.5369	0.975624	0.487812	−	0.872949i	$-0.337795\pi$
$401$	19.5369	0.975624	0.487812	+	0.872949i	$0.337795\pi$
$402$	7.39464	0.368811
$403$	18.7404	0.933525
$404$	−2.20384	−0.109645
$405$	−26.2443	−1.30409
$406$	−0.979719	−0.0486227
$407$	0	0
$408$	7.62712	0.377599
$409$	1.10197	0.0544889	0.0272444	−	0.999629i	$-0.491327\pi$
$409$	1.10197	0.0544889	0.0272444	+	0.999629i	$0.491327\pi$
$410$	−1.76120	−0.0869795
$411$	−58.7651	−2.89867
$412$	−27.2510	−1.34256
$413$	−1.55900	−0.0767133
$414$	−1.97657	−0.0971429
$415$	−0.987983	−0.0484982
$416$	9.86396	0.483620
$417$	4.74600	0.232413
$418$	0	0
$419$	−7.81269	−0.381675	−0.190838	−	0.981622i	$-0.561120\pi$
$419$	−7.81269	−0.381675	−0.190838	+	0.981622i	$0.561120\pi$
$420$	4.51621	0.220369
$421$	29.9916	1.46170	0.730850	−	0.682538i	$-0.239124\pi$
$421$	29.9916	1.46170	0.730850	+	0.682538i	$0.239124\pi$
$422$	−9.46665	−0.460829
$423$	−37.6611	−1.83115
$424$	3.16005	0.153466
$425$	1.24532	0.0604067
$426$	−6.46084	−0.313029
$427$	0.344105	0.0166524
$428$	6.03524	0.291724
$429$	0	0
$430$	−0.304819	−0.0146997
$431$	25.5293	1.22970	0.614851	−	0.788644i	$-0.289216\pi$
$431$	25.5293	1.22970	0.614851	+	0.788644i	$0.289216\pi$
$432$	−26.8319	−1.29095
$433$	−16.5781	−0.796693	−0.398347	−	0.917235i	$-0.630416\pi$
$433$	−16.5781	−0.796693	−0.398347	+	0.917235i	$0.630416\pi$
$434$	−1.44255	−0.0692446
$435$	45.2731	2.17068
$436$	1.46872	0.0703391
$437$	−3.35409	−0.160448
$438$	10.4789	0.500701
$439$	10.9429	0.522275	0.261137	−	0.965302i	$-0.415902\pi$
$439$	10.9429	0.522275	0.261137	+	0.965302i	$0.415902\pi$
$440$	0	0
$441$	−42.6626	−2.03155
$442$	1.37154	0.0652375
$443$	−6.28980	−0.298837	−0.149419	−	0.988774i	$-0.547740\pi$
$443$	−6.28980	−0.298837	−0.149419	+	0.988774i	$0.547740\pi$
$444$	−1.30343	−0.0618580
$445$	−9.12379	−0.432509
$446$	−12.4822	−0.591050
$447$	−55.2552	−2.61348
$448$	1.14356	0.0540282
$449$	−12.7781	−0.603035	−0.301517	−	0.953461i	$-0.597493\pi$
$449$	−12.7781	−0.603035	−0.301517	+	0.953461i	$0.597493\pi$
$450$	2.48131	0.116970
$451$	0	0
$452$	7.57641	0.356364
$453$	−43.2226	−2.03078
$454$	0.366674	0.0172089
$455$	1.72127	0.0806945
$456$	25.7884	1.20765
$457$	−31.2144	−1.46015	−0.730074	−	0.683368i	$-0.760515\pi$
$457$	−31.2144	−1.46015	−0.730074	+	0.683368i	$0.760515\pi$
$458$	−8.30579	−0.388104
$459$	−13.9497	−0.651115
$460$	−2.98618	−0.139231
$461$	−34.5739	−1.61027	−0.805133	−	0.593094i	$-0.797906\pi$
$461$	−34.5739	−1.61027	−0.805133	+	0.593094i	$0.797906\pi$
$462$	0	0
$463$	21.6861	1.00784	0.503919	−	0.863751i	$-0.331891\pi$
$463$	21.6861	1.00784	0.503919	+	0.863751i	$0.331891\pi$
$464$	17.0395	0.791038
$465$	66.6606	3.09131
$466$	−6.81655	−0.315771
$467$	20.1364	0.931802	0.465901	−	0.884837i	$-0.345730\pi$
$467$	20.1364	0.931802	0.465901	+	0.884837i	$0.345730\pi$
$468$	−22.8745	−1.05738
$469$	1.81588	0.0838496
$470$	6.79760	0.313550
$471$	26.6519	1.22805
$472$	−7.92570	−0.364810
$473$	0	0
$474$	−0.974661	−0.0447677
$475$	4.21060	0.193195
$476$	0.883697	0.0405042
$477$	−11.1988	−0.512757
$478$	−4.49159	−0.205441
$479$	−1.04114	−0.0475709	−0.0237855	−	0.999717i	$-0.507572\pi$
$479$	−1.04114	−0.0475709	−0.0237855	+	0.999717i	$0.507572\pi$
$480$	35.0866	1.60148
$481$	−0.496778	−0.0226511
$482$	−11.5147	−0.524482
$483$	−0.720259	−0.0327729
$484$	0	0
$485$	−30.3606	−1.37860
$486$	−1.73334	−0.0786261
$487$	−11.3208	−0.512995	−0.256497	−	0.966545i	$-0.582569\pi$
$487$	−11.3208	−0.512995	−0.256497	+	0.966545i	$0.582569\pi$
$488$	1.74937	0.0791904
$489$	−14.5385	−0.657456
$490$	7.70033	0.347866
$491$	−13.2393	−0.597483	−0.298742	−	0.954334i	$-0.596567\pi$
$491$	−13.2393	−0.597483	−0.298742	+	0.954334i	$0.596567\pi$
$492$	8.52882	0.384509
$493$	8.85868	0.398975
$494$	4.63738	0.208645
$495$	0	0
$496$	25.0891	1.12653
$497$	−1.58657	−0.0711675
$498$	−0.571592	−0.0256137
$499$	40.4402	1.81035	0.905176	−	0.425036i	$-0.139739\pi$
$499$	40.4402	1.81035	0.905176	+	0.425036i	$0.139739\pi$
$500$	−17.8870	−0.799929
$501$	63.7672	2.84891
$502$	−9.89253	−0.441525
$503$	−23.4107	−1.04383	−0.521916	−	0.852997i	$-0.674783\pi$
$503$	−23.4107	−1.04383	−0.521916	+	0.852997i	$0.674783\pi$
$504$	3.73191	0.166233
$505$	−2.98776	−0.132954
$506$	0	0
$507$	26.4929	1.17659
$508$	34.3957	1.52606
$509$	4.00736	0.177623	0.0888116	−	0.996048i	$-0.471693\pi$
$509$	4.00736	0.177623	0.0888116	+	0.996048i	$0.471693\pi$
$510$	4.87864	0.216030
$511$	2.57327	0.113835
$512$	22.8793	1.01113
$513$	−47.1659	−2.08243
$514$	7.12063	0.314078
$515$	−36.9443	−1.62796
$516$	1.47612	0.0649825
$517$	0	0
$518$	0.0382397	0.00168016
$519$	67.7406	2.97348
$520$	8.75067	0.383742
$521$	−22.7661	−0.997401	−0.498700	−	0.866774i	$-0.666189\pi$
$521$	−22.7661	−0.997401	−0.498700	+	0.866774i	$0.666189\pi$
$522$	17.6510	0.772564
$523$	3.48752	0.152499	0.0762494	−	0.997089i	$-0.475705\pi$
$523$	3.48752	0.152499	0.0762494	+	0.997089i	$0.475705\pi$
$524$	−11.0779	−0.483942
$525$	0.904186	0.0394619
$526$	13.5433	0.590515
$527$	13.0436	0.568189
$528$	0	0
$529$	−22.5238	−0.979294
$530$	2.02131	0.0878001
$531$	28.0876	1.21890
$532$	2.98791	0.129542
$533$	3.25060	0.140799
$534$	−5.27852	−0.228424
$535$	8.18201	0.353739
$536$	9.23165	0.398746
$537$	−9.48957	−0.409505
$538$	9.46029	0.407862
$539$	0	0
$540$	−41.9923	−1.80706
$541$	19.7342	0.848441	0.424221	−	0.905559i	$-0.360548\pi$
$541$	19.7342	0.848441	0.424221	+	0.905559i	$0.360548\pi$
$542$	3.06405	0.131612
$543$	−55.1858	−2.36825
$544$	6.86548	0.294355
$545$	1.99116	0.0852918
$546$	0.995833	0.0426177
$547$	−14.5045	−0.620166	−0.310083	−	0.950710i	$-0.600357\pi$
$547$	−14.5045	−0.620166	−0.310083	+	0.950710i	$0.600357\pi$
$548$	−34.6142	−1.47865
$549$	−6.19953	−0.264589
$550$	0	0
$551$	29.9525	1.27602
$552$	−3.66168	−0.155851
$553$	−0.239345	−0.0101780
$554$	−1.11161	−0.0472277
$555$	−1.76707	−0.0750078
$556$	2.79552	0.118556
$557$	27.4856	1.16460	0.582301	−	0.812973i	$-0.302153\pi$
$557$	27.4856	1.16460	0.582301	+	0.812973i	$0.302153\pi$
$558$	25.9896	1.10023
$559$	0.562596	0.0237953
$560$	2.30439	0.0973783
$561$	0	0
$562$	12.4972	0.527164
$563$	5.90286	0.248776	0.124388	−	0.992234i	$-0.460303\pi$
$563$	5.90286	0.248776	0.124388	+	0.992234i	$0.460303\pi$
$564$	−32.9181	−1.38610
$565$	10.2714	0.432120
$566$	12.2524	0.515008
$567$	−3.72857	−0.156585
$568$	−8.06587	−0.338437
$569$	−11.9156	−0.499530	−0.249765	−	0.968306i	$-0.580353\pi$
$569$	−11.9156	−0.499530	−0.249765	+	0.968306i	$0.580353\pi$
$570$	16.4954	0.690917
$571$	14.8375	0.620928	0.310464	−	0.950585i	$-0.399516\pi$
$571$	14.8375	0.620928	0.310464	+	0.950585i	$0.399516\pi$
$572$	0	0
$573$	−16.3812	−0.684335
$574$	−0.250217	−0.0104438
$575$	−0.597860	−0.0249325
$576$	−20.6029	−0.858452
$577$	4.47516	0.186303	0.0931516	−	0.995652i	$-0.470306\pi$
$577$	4.47516	0.186303	0.0931516	+	0.995652i	$0.470306\pi$
$578$	−6.89930	−0.286973
$579$	71.8170	2.98461
$580$	26.6670	1.10729
$581$	−0.140364	−0.00582330
$582$	−17.5649	−0.728090
$583$	0	0
$584$	13.0821	0.541341
$585$	−31.0111	−1.28215
$586$	−10.1006	−0.417254
$587$	14.7539	0.608960	0.304480	−	0.952519i	$-0.401517\pi$
$587$	14.7539	0.608960	0.304480	+	0.952519i	$0.401517\pi$
$588$	−37.2897	−1.53780
$589$	44.1024	1.81721
$590$	−5.06963	−0.208713
$591$	−68.2488	−2.80738
$592$	−0.665073	−0.0273343
$593$	18.4560	0.757897	0.378948	−	0.925418i	$-0.376286\pi$
$593$	18.4560	0.757897	0.378948	+	0.925418i	$0.376286\pi$
$594$	0	0
$595$	1.19803	0.0491146
$596$	−32.5468	−1.33317
$597$	−12.8900	−0.527551
$598$	−0.658458	−0.0269264
$599$	38.8926	1.58911	0.794555	−	0.607193i	$-0.207704\pi$
$599$	38.8926	1.58911	0.794555	+	0.607193i	$0.207704\pi$
$600$	4.59673	0.187661
$601$	−15.4754	−0.631256	−0.315628	−	0.948883i	$-0.602215\pi$
$601$	−15.4754	−0.631256	−0.315628	+	0.948883i	$0.602215\pi$
$602$	−0.0433061	−0.00176502
$603$	−32.7157	−1.33228
$604$	−25.4593	−1.03592
$605$	0	0
$606$	−1.72855	−0.0702176
$607$	−6.77350	−0.274928	−0.137464	−	0.990507i	$-0.543895\pi$
$607$	−6.77350	−0.274928	−0.137464	+	0.990507i	$0.543895\pi$
$608$	23.2132	0.941420
$609$	6.43202	0.260638
$610$	1.11898	0.0453060
$611$	−12.5461	−0.507563
$612$	−15.9211	−0.643570
$613$	−5.73197	−0.231512	−0.115756	−	0.993278i	$-0.536929\pi$
$613$	−5.73197	−0.231512	−0.115756	+	0.993278i	$0.536929\pi$
$614$	13.0052	0.524846
$615$	11.5626	0.466248
$616$	0	0
$617$	−30.2689	−1.21858	−0.609291	−	0.792947i	$-0.708546\pi$
$617$	−30.2689	−1.21858	−0.609291	+	0.792947i	$0.708546\pi$
$618$	−21.3739	−0.859786
$619$	−10.1124	−0.406452	−0.203226	−	0.979132i	$-0.565143\pi$
$619$	−10.1124	−0.406452	−0.203226	+	0.979132i	$0.565143\pi$
$620$	39.2648	1.57691
$621$	6.69706	0.268744
$622$	−1.19189	−0.0477904
$623$	−1.29623	−0.0519324
$624$	−17.3197	−0.693344
$625$	−28.5811	−1.14325
$626$	1.21073	0.0483903
$627$	0	0
$628$	15.6987	0.626445
$629$	−0.345766	−0.0137866
$630$	2.38710	0.0951042
$631$	−43.7551	−1.74186	−0.870932	−	0.491404i	$-0.836484\pi$
$631$	−43.7551	−1.74186	−0.870932	+	0.491404i	$0.836484\pi$
$632$	−1.21679	−0.0484013
$633$	62.1501	2.47024
$634$	4.77575	0.189669
$635$	46.6304	1.85047
$636$	−9.78843	−0.388136
$637$	−14.2123	−0.563112
$638$	0	0
$639$	28.5843	1.13078
$640$	26.8547	1.06153
$641$	−27.1617	−1.07282	−0.536411	−	0.843957i	$-0.680220\pi$
$641$	−27.1617	−1.07282	−0.536411	+	0.843957i	$0.680220\pi$
$642$	4.73366	0.186823
$643$	−2.69169	−0.106150	−0.0530750	−	0.998591i	$-0.516902\pi$
$643$	−2.69169	−0.106150	−0.0530750	+	0.998591i	$0.516902\pi$
$644$	−0.424252	−0.0167179
$645$	2.00118	0.0787965
$646$	3.22769	0.126992
$647$	−42.7404	−1.68030	−0.840148	−	0.542357i	$-0.817532\pi$
$647$	−42.7404	−1.68030	−0.840148	+	0.542357i	$0.817532\pi$
$648$	−18.9555	−0.744640
$649$	0	0
$650$	0.826603	0.0324220
$651$	9.47057	0.371181
$652$	−8.56359	−0.335376
$653$	11.4591	0.448431	0.224216	−	0.974540i	$-0.428018\pi$
$653$	11.4591	0.448431	0.224216	+	0.974540i	$0.428018\pi$
$654$	1.15197	0.0450457
$655$	−15.0184	−0.586819
$656$	4.35182	0.169910
$657$	−46.3611	−1.80872
$658$	0.965746	0.0376487
$659$	7.98889	0.311203	0.155602	−	0.987820i	$-0.450268\pi$
$659$	7.98889	0.311203	0.155602	+	0.987820i	$0.450268\pi$
$660$	0	0
$661$	−7.99672	−0.311037	−0.155518	−	0.987833i	$-0.549705\pi$
$661$	−7.99672	−0.311037	−0.155518	+	0.987833i	$0.549705\pi$
$662$	4.05569	0.157629
$663$	−9.00438	−0.349701
$664$	−0.713590	−0.0276927
$665$	4.05073	0.157081
$666$	−0.688942	−0.0266960
$667$	−4.25294	−0.164674
$668$	37.5606	1.45326
$669$	81.9478	3.16829
$670$	5.90497	0.228129
$671$	0	0
$672$	4.98481	0.192293
$673$	−28.4010	−1.09478	−0.547389	−	0.836878i	$-0.684378\pi$
$673$	−28.4010	−1.09478	−0.547389	+	0.836878i	$0.684378\pi$
$674$	9.60516	0.369977
$675$	−8.40723	−0.323595
$676$	15.6050	0.600194
$677$	−7.94935	−0.305518	−0.152759	−	0.988263i	$-0.548816\pi$
$677$	−7.94935	−0.305518	−0.152759	+	0.988263i	$0.548816\pi$
$678$	5.94245	0.228219
$679$	−4.31337	−0.165532
$680$	6.09061	0.233564
$681$	−2.40727	−0.0922470
$682$	0	0
$683$	9.06136	0.346723	0.173362	−	0.984858i	$-0.444537\pi$
$683$	9.06136	0.346723	0.173362	+	0.984858i	$0.444537\pi$
$684$	−53.8314	−2.05830
$685$	−46.9267	−1.79298
$686$	2.20682	0.0842568
$687$	54.5288	2.08040
$688$	0.753188	0.0287150
$689$	−3.73068	−0.142128
$690$	−2.34217	−0.0891649
$691$	5.59573	0.212871	0.106436	−	0.994320i	$-0.466056\pi$
$691$	5.59573	0.212871	0.106436	+	0.994320i	$0.466056\pi$
$692$	39.9010	1.51681
$693$	0	0
$694$	10.8170	0.410608
$695$	3.78990	0.143759
$696$	32.6993	1.23946
$697$	2.26247	0.0856973
$698$	−8.50236	−0.321819
$699$	44.7518	1.69267
$700$	0.532589	0.0201300
$701$	−26.9364	−1.01737	−0.508686	−	0.860952i	$-0.669869\pi$
$701$	−26.9364	−1.01737	−0.508686	+	0.860952i	$0.669869\pi$
$702$	−9.25938	−0.349473
$703$	−1.16909	−0.0440929
$704$	0	0
$705$	−44.6273	−1.68076
$706$	7.77783	0.292723
$707$	−0.424476	−0.0159641
$708$	24.5502	0.922654
$709$	30.8957	1.16031	0.580156	−	0.814505i	$-0.302991\pi$
$709$	30.8957	1.16031	0.580156	+	0.814505i	$0.302991\pi$
$710$	−5.15929	−0.193625
$711$	4.31213	0.161718
$712$	−6.58983	−0.246964
$713$	−6.26207	−0.234516
$714$	0.693116	0.0259392
$715$	0	0
$716$	−5.58961	−0.208894
$717$	29.4880	1.10125
$718$	14.7549	0.550646
$719$	5.30112	0.197698	0.0988492	−	0.995102i	$-0.468484\pi$
$719$	5.30112	0.197698	0.0988492	+	0.995102i	$0.468484\pi$
$720$	−41.5169	−1.54724
$721$	−5.24874	−0.195473
$722$	2.13540	0.0794714
$723$	75.5961	2.81145
$724$	−32.5059	−1.20807
$725$	5.33897	0.198285
$726$	0	0
$727$	21.0168	0.779471	0.389735	−	0.920927i	$-0.372566\pi$
$727$	21.0168	0.779471	0.389735	+	0.920927i	$0.372566\pi$
$728$	1.24322	0.0460768
$729$	−21.1270	−0.782483
$730$	8.36789	0.309710
$731$	0.391576	0.0144830
$732$	−5.41877	−0.200283
$733$	28.3257	1.04623	0.523116	−	0.852261i	$-0.324769\pi$
$733$	28.3257	1.04623	0.523116	+	0.852261i	$0.324769\pi$
$734$	−2.09307	−0.0772568
$735$	−50.5539	−1.86471
$736$	−3.29603	−0.121493
$737$	0	0
$738$	4.50800	0.165942
$739$	19.5300	0.718422	0.359211	−	0.933256i	$-0.383046\pi$
$739$	19.5300	0.718422	0.359211	+	0.933256i	$0.383046\pi$
$740$	−1.04085	−0.0382624
$741$	−30.4451	−1.11843
$742$	0.287171	0.0105424
$743$	−25.4314	−0.932986	−0.466493	−	0.884525i	$-0.654483\pi$
$743$	−25.4314	−0.932986	−0.466493	+	0.884525i	$0.654483\pi$
$744$	48.1469	1.76515
$745$	−44.1239	−1.61657
$746$	−13.2413	−0.484797
$747$	2.52886	0.0925262
$748$	0	0
$749$	1.16243	0.0424743
$750$	−14.0294	−0.512281
$751$	43.0212	1.56987	0.784933	−	0.619581i	$-0.212697\pi$
$751$	43.0212	1.56987	0.784933	+	0.619581i	$0.212697\pi$
$752$	−16.7964	−0.612503
$753$	64.9460	2.36677
$754$	5.88013	0.214142
$755$	−34.5153	−1.25614
$756$	−5.96592	−0.216978
$757$	49.8981	1.81358	0.906788	−	0.421587i	$-0.138527\pi$
$757$	49.8981	1.81358	0.906788	+	0.421587i	$0.138527\pi$
$758$	12.0829	0.438870
$759$	0	0
$760$	20.5933	0.746996
$761$	−8.30382	−0.301013	−0.150507	−	0.988609i	$-0.548090\pi$
$761$	−8.30382	−0.301013	−0.150507	+	0.988609i	$0.548090\pi$
$762$	26.9778	0.977302
$763$	0.282887	0.0102412
$764$	−9.64897	−0.349087
$765$	−21.5843	−0.780381
$766$	7.37172	0.266351
$767$	9.35687	0.337857
$768$	−4.62292	−0.166815
$769$	−48.4221	−1.74615	−0.873073	−	0.487590i	$-0.837876\pi$
$769$	−48.4221	−1.74615	−0.873073	+	0.487590i	$0.837876\pi$
$770$	0	0
$771$	−46.7481	−1.68359
$772$	42.3021	1.52249
$773$	4.18653	0.150579	0.0752895	−	0.997162i	$-0.476012\pi$
$773$	4.18653	0.150579	0.0752895	+	0.997162i	$0.476012\pi$
$774$	0.780220	0.0280444
$775$	7.86117	0.282381
$776$	−21.9285	−0.787187
$777$	−0.251050	−0.00900637
$778$	−13.6145	−0.488103
$779$	7.64976	0.274081
$780$	−27.1056	−0.970537
$781$	0	0
$782$	−0.458298	−0.0163887
$783$	−59.8057	−2.13728
$784$	−19.0270	−0.679537
$785$	21.2828	0.759615
$786$	−8.68884	−0.309921
$787$	−10.3189	−0.367829	−0.183915	−	0.982942i	$-0.558877\pi$
$787$	−10.3189	−0.367829	−0.183915	+	0.982942i	$0.558877\pi$
$788$	−40.2003	−1.43208
$789$	−88.9139	−3.16542
$790$	−0.778313	−0.0276911
$791$	1.45927	0.0518857
$792$	0	0
$793$	−2.06526	−0.0733397
$794$	−11.1741	−0.396556
$795$	−13.2702	−0.470647
$796$	−7.59254	−0.269110
$797$	42.4961	1.50529	0.752644	−	0.658428i	$-0.228778\pi$
$797$	42.4961	1.50529	0.752644	+	0.658428i	$0.228778\pi$
$798$	2.34353	0.0829600
$799$	−8.73233	−0.308928
$800$	4.13771	0.146290
$801$	23.3534	0.825152
$802$	9.02593	0.318717
$803$	0	0
$804$	−28.5955	−1.00849
$805$	−0.575161	−0.0202717
$806$	8.65796	0.304964
$807$	−62.1083	−2.18632
$808$	−2.15797	−0.0759170
$809$	13.0949	0.460391	0.230196	−	0.973144i	$-0.426063\pi$
$809$	13.0949	0.460391	0.230196	+	0.973144i	$0.426063\pi$
$810$	−12.1247	−0.426020
$811$	−50.6189	−1.77747	−0.888734	−	0.458422i	$-0.848415\pi$
$811$	−50.6189	−1.77747	−0.888734	+	0.458422i	$0.848415\pi$
$812$	3.78863	0.132955
$813$	−20.1160	−0.705499
$814$	0	0
$815$	−11.6097	−0.406670
$816$	−12.0548	−0.422003
$817$	1.32398	0.0463201
$818$	0.509104	0.0178004
$819$	−4.40580	−0.153951
$820$	6.81066	0.237839
$821$	10.5980	0.369872	0.184936	−	0.982751i	$-0.440792\pi$
$821$	10.5980	0.369872	0.184936	+	0.982751i	$0.440792\pi$
$822$	−27.1492	−0.946937
$823$	−27.1497	−0.946378	−0.473189	−	0.880961i	$-0.656897\pi$
$823$	−27.1497	−0.946378	−0.473189	+	0.880961i	$0.656897\pi$
$824$	−26.6837	−0.929572
$825$	0	0
$826$	−0.720250	−0.0250607
$827$	41.6969	1.44994	0.724971	−	0.688779i	$-0.241853\pi$
$827$	41.6969	1.44994	0.724971	+	0.688779i	$0.241853\pi$
$828$	7.64349	0.265630
$829$	−25.9232	−0.900350	−0.450175	−	0.892940i	$-0.648638\pi$
$829$	−25.9232	−0.900350	−0.450175	+	0.892940i	$0.648638\pi$
$830$	−0.456443	−0.0158434
$831$	7.29789	0.253161
$832$	−6.86348	−0.237948
$833$	−9.89200	−0.342738
$834$	2.19263	0.0759245
$835$	50.9211	1.76220
$836$	0	0
$837$	−88.0586	−3.04375
$838$	−3.60943	−0.124686
$839$	−53.2443	−1.83820	−0.919099	−	0.394027i	$-0.871082\pi$
$839$	−53.2443	−1.83820	−0.919099	+	0.394027i	$0.871082\pi$
$840$	4.42221	0.152581
$841$	8.97933	0.309632
$842$	13.8560	0.477508
$843$	−82.0463	−2.82583
$844$	36.6081	1.26010
$845$	21.1559	0.727783
$846$	−17.3993	−0.598199
$847$	0	0
$848$	−4.99453	−0.171513
$849$	−80.4392	−2.76067
$850$	0.575330	0.0197336
$851$	0.165998	0.00569033
$852$	24.9844	0.855953
$853$	−38.6463	−1.32323	−0.661613	−	0.749846i	$-0.730128\pi$
$853$	−38.6463	−1.32323	−0.661613	+	0.749846i	$0.730128\pi$
$854$	0.158975	0.00544000
$855$	−72.9796	−2.49585
$856$	5.90961	0.201986
$857$	−6.37818	−0.217874	−0.108937	−	0.994049i	$-0.534745\pi$
$857$	−6.37818	−0.217874	−0.108937	+	0.994049i	$0.534745\pi$
$858$	0	0
$859$	35.7411	1.21947	0.609736	−	0.792605i	$-0.291275\pi$
$859$	35.7411	1.21947	0.609736	+	0.792605i	$0.291275\pi$
$860$	1.17875	0.0401951
$861$	1.64271	0.0559835
$862$	11.7944	0.401719
$863$	−9.24431	−0.314680	−0.157340	−	0.987544i	$-0.550292\pi$
$863$	−9.24431	−0.314680	−0.157340	+	0.987544i	$0.550292\pi$
$864$	−46.3494	−1.57684
$865$	54.0941	1.83925
$866$	−7.65901	−0.260264
$867$	45.2950	1.53830
$868$	5.57842	0.189344
$869$	0	0
$870$	20.9159	0.709116
$871$	−10.8986	−0.369287
$872$	1.43815	0.0487019
$873$	77.7115	2.63013
$874$	−1.54957	−0.0524151
$875$	−3.44516	−0.116468
$876$	−40.5225	−1.36913
$877$	44.0937	1.48894	0.744469	−	0.667657i	$-0.232703\pi$
$877$	44.0937	1.48894	0.744469	+	0.667657i	$0.232703\pi$
$878$	5.05555	0.170617
$879$	66.3124	2.23666
$880$	0	0
$881$	24.2055	0.815503	0.407752	−	0.913093i	$-0.366313\pi$
$881$	24.2055	0.815503	0.407752	+	0.913093i	$0.366313\pi$
$882$	−19.7099	−0.663668
$883$	−29.2584	−0.984623	−0.492311	−	0.870419i	$-0.663848\pi$
$883$	−29.2584	−0.984623	−0.492311	+	0.870419i	$0.663848\pi$
$884$	−5.30382	−0.178387
$885$	33.2829	1.11879
$886$	−2.90586	−0.0976242
$887$	31.5011	1.05770	0.528852	−	0.848714i	$-0.322623\pi$
$887$	31.5011	1.05770	0.528852	+	0.848714i	$0.322623\pi$
$888$	−1.27630	−0.0428297
$889$	6.62486	0.222191
$890$	−4.21514	−0.141292
$891$	0	0
$892$	48.2694	1.61618
$893$	−29.5253	−0.988026
$894$	−25.5276	−0.853771
$895$	−7.57787	−0.253300
$896$	3.81529	0.127460
$897$	4.32288	0.144337
$898$	−5.90341	−0.196999
$899$	55.9212	1.86508
$900$	−9.59535	−0.319845
$901$	−2.59662	−0.0865058
$902$	0	0
$903$	0.284311	0.00946129
$904$	7.41870	0.246742
$905$	−44.0685	−1.46489
$906$	−19.9686	−0.663413
$907$	−0.974350	−0.0323528	−0.0161764	−	0.999869i	$-0.505149\pi$
$907$	−0.974350	−0.0323528	−0.0161764	+	0.999869i	$0.505149\pi$
$908$	−1.41795	−0.0470563
$909$	7.64753	0.253652
$910$	0.795219	0.0263613
$911$	−7.08993	−0.234900	−0.117450	−	0.993079i	$-0.537472\pi$
$911$	−7.08993	−0.234900	−0.117450	+	0.993079i	$0.537472\pi$
$912$	−40.7591	−1.34967
$913$	0	0
$914$	−14.4209	−0.477001
$915$	−7.34626	−0.242860
$916$	32.1189	1.06124
$917$	−2.13369	−0.0704608
$918$	−6.44468	−0.212706
$919$	7.01503	0.231404	0.115702	−	0.993284i	$-0.463088\pi$
$919$	7.01503	0.231404	0.115702	+	0.993284i	$0.463088\pi$
$920$	−2.92402	−0.0964022
$921$	−85.3810	−2.81340
$922$	−15.9730	−0.526042
$923$	9.52236	0.313432
$924$	0	0
$925$	−0.208387	−0.00685173
$926$	10.0189	0.329240
$927$	94.5634	3.10587
$928$	29.4340	0.966218
$929$	−32.1613	−1.05518	−0.527589	−	0.849500i	$-0.676904\pi$
$929$	−32.1613	−1.05518	−0.527589	+	0.849500i	$0.676904\pi$
$930$	30.7969	1.00987
$931$	−33.4463	−1.09616
$932$	26.3600	0.863450
$933$	7.82494	0.256177
$934$	9.30293	0.304401
$935$	0	0
$936$	−22.3984	−0.732114
$937$	−46.2662	−1.51145	−0.755725	−	0.654889i	$-0.772715\pi$
$937$	−46.2662	−1.51145	−0.755725	+	0.654889i	$0.772715\pi$
$938$	0.838929	0.0273920
$939$	−7.94861	−0.259393
$940$	−26.2867	−0.857377
$941$	42.5042	1.38560	0.692799	−	0.721130i	$-0.256377\pi$
$941$	42.5042	1.38560	0.692799	+	0.721130i	$0.256377\pi$
$942$	12.3130	0.401181
$943$	−1.08618	−0.0353710
$944$	12.5267	0.407710
$945$	−8.08803	−0.263104
$946$	0	0
$947$	−48.4151	−1.57328	−0.786640	−	0.617412i	$-0.788181\pi$
$947$	−48.4151	−1.57328	−0.786640	+	0.617412i	$0.788181\pi$
$948$	3.76907	0.122414
$949$	−15.4444	−0.501346
$950$	1.94528	0.0631131
$951$	−31.3536	−1.01671
$952$	0.865303	0.0280446
$953$	11.8071	0.382471	0.191236	−	0.981544i	$-0.438751\pi$
$953$	11.8071	0.382471	0.191236	+	0.981544i	$0.438751\pi$
$954$	−5.17378	−0.167507
$955$	−13.0812	−0.423297
$956$	17.3692	0.561761
$957$	0	0
$958$	−0.481002	−0.0155405
$959$	−6.66695	−0.215287
$960$	−24.4138	−0.787951
$961$	51.3390	1.65610
$962$	−0.229509	−0.00739967
$963$	−20.9428	−0.674873
$964$	44.5281	1.43415
$965$	57.3492	1.84614
$966$	−0.332756	−0.0107063
$967$	−26.3486	−0.847313	−0.423657	−	0.905823i	$-0.639254\pi$
$967$	−26.3486	−0.847313	−0.423657	+	0.905823i	$0.639254\pi$
$968$	0	0
$969$	−21.1903	−0.680731
$970$	−14.0264	−0.450361
$971$	21.6570	0.695006	0.347503	−	0.937679i	$-0.387030\pi$
$971$	21.6570	0.695006	0.347503	+	0.937679i	$0.387030\pi$
$972$	6.70294	0.214997
$973$	0.538438	0.0172615
$974$	−5.23016	−0.167585
$975$	−5.42678	−0.173796
$976$	−2.76492	−0.0885029
$977$	15.3840	0.492179	0.246090	−	0.969247i	$-0.420854\pi$
$977$	15.3840	0.492179	0.246090	+	0.969247i	$0.420854\pi$
$978$	−6.71674	−0.214778
$979$	0	0
$980$	−29.7776	−0.951211
$981$	−5.09660	−0.162722
$982$	−6.11651	−0.195186
$983$	−34.3662	−1.09611	−0.548055	−	0.836442i	$-0.684632\pi$
$983$	−34.3662	−1.09611	−0.548055	+	0.836442i	$0.684632\pi$
$984$	8.35128	0.266229
$985$	−54.4999	−1.73651
$986$	4.09267	0.130337
$987$	−6.34028	−0.201813
$988$	−17.9330	−0.570525
$989$	−0.187991	−0.00597775
$990$	0	0
$991$	−7.65757	−0.243251	−0.121625	−	0.992576i	$-0.538811\pi$
$991$	−7.65757	−0.243251	−0.121625	+	0.992576i	$0.538811\pi$
$992$	43.3390	1.37601
$993$	−26.6263	−0.844960
$994$	−0.732988	−0.0232490
$995$	−10.2932	−0.326318
$996$	2.21038	0.0700385
$997$	−8.64396	−0.273757	−0.136878	−	0.990588i	$-0.543707\pi$
$997$	−8.64396	−0.273757	−0.136878	+	0.990588i	$0.543707\pi$
$998$	18.6832	0.591406
$999$	2.33429	0.0738538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.l.1.12	yes	24
11.10	odd	2		7381.2.a.k.1.13	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.k.1.13	✓	24	11.10	odd	2
7381.2.a.l.1.12	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q+0.461995 q^{2} -3.03307 q^{3} -1.78656 q^{4} -2.42205 q^{5} -1.40126 q^{6} -0.344105 q^{7} -1.74937 q^{8} +6.19953 q^{9} +O(q^{10})\)	\(q+0.461995 q^{2} -3.03307 q^{3} -1.78656 q^{4} -2.42205 q^{5} -1.40126 q^{6} -0.344105 q^{7} -1.74937 q^{8} +6.19953 q^{9} -1.11898 q^{10} +5.41877 q^{12} +2.06526 q^{13} -0.158975 q^{14} +7.34626 q^{15} +2.76492 q^{16} +1.43746 q^{17} +2.86415 q^{18} +4.86026 q^{19} +4.32714 q^{20} +1.04369 q^{21} -0.690105 q^{23} +5.30597 q^{24} +0.866332 q^{25} +0.954142 q^{26} -9.70440 q^{27} +0.614764 q^{28} +6.16274 q^{29} +3.39393 q^{30} +9.07409 q^{31} +4.77612 q^{32} +0.664099 q^{34} +0.833439 q^{35} -11.0758 q^{36} -0.240540 q^{37} +2.24542 q^{38} -6.26410 q^{39} +4.23707 q^{40} +1.57394 q^{41} +0.482182 q^{42} +0.272409 q^{43} -15.0156 q^{45} -0.318825 q^{46} -6.07484 q^{47} -8.38620 q^{48} -6.88159 q^{49} +0.400241 q^{50} -4.35992 q^{51} -3.68972 q^{52} -1.80639 q^{53} -4.48339 q^{54} +0.601967 q^{56} -14.7415 q^{57} +2.84715 q^{58} +4.53059 q^{59} -13.1245 q^{60} -1.00000 q^{61} +4.19218 q^{62} -2.13329 q^{63} -3.32329 q^{64} -5.00217 q^{65} -5.27712 q^{67} -2.56811 q^{68} +2.09314 q^{69} +0.385045 q^{70} +4.61072 q^{71} -10.8453 q^{72} -7.47817 q^{73} -0.111128 q^{74} -2.62765 q^{75} -8.68315 q^{76} -2.89398 q^{78} +0.695558 q^{79} -6.69678 q^{80} +10.8356 q^{81} +0.727153 q^{82} +0.407912 q^{83} -1.86462 q^{84} -3.48160 q^{85} +0.125851 q^{86} -18.6920 q^{87} +3.76697 q^{89} -6.93712 q^{90} -0.710667 q^{91} +1.23291 q^{92} -27.5224 q^{93} -2.80655 q^{94} -11.7718 q^{95} -14.4863 q^{96} +12.5351 q^{97} -3.17926 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9}+O(q^{10}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9	\( 24 q + 5 q^{2} - 2 q^{3} + 27 q^{4} - 4 q^{5} + 12 q^{6} + 6 q^{7} + 9 q^{8} + 26 q^{9} + 12 q^{10} + q^{12} + 3 q^{13} - q^{14} - 5 q^{15} + 17 q^{16} + 8 q^{17} + 20 q^{18} + 8 q^{19} + 16 q^{20} + 11 q^{21} + 2 q^{23} + q^{24} + 4 q^{25} + 4 q^{26} + 13 q^{27} - 7 q^{28} + 43 q^{29} + 30 q^{30} - 4 q^{31} + 23 q^{32} + 31 q^{35} - 35 q^{36} - 4 q^{37} - 13 q^{38} + 11 q^{39} + 57 q^{40} + 29 q^{41} + 48 q^{42} + 10 q^{43} - 10 q^{45} - 14 q^{46} - 13 q^{47} + 42 q^{48} + 26 q^{49} - 6 q^{50} + 56 q^{51} + 25 q^{52} - 15 q^{53} + 35 q^{54} - 9 q^{56} - 3 q^{57} - 84 q^{58} - 13 q^{59} + 34 q^{60} - 24 q^{61} + 55 q^{62} + 22 q^{63} + 61 q^{64} + 41 q^{65} - q^{67} - 4 q^{68} - 27 q^{69} + 55 q^{70} - 6 q^{71} + 22 q^{72} + 18 q^{73} + 28 q^{74} + 47 q^{75} + 36 q^{76} - 10 q^{78} + 9 q^{79} - 40 q^{80} + 40 q^{81} + 15 q^{82} + 10 q^{83} + 93 q^{84} - 9 q^{85} + 38 q^{86} + 51 q^{87} - 17 q^{89} - 44 q^{90} - 22 q^{91} + 11 q^{92} + 32 q^{93} - 47 q^{94} + 54 q^{95} + 44 q^{96} - q^{97} + 45 q^{98}+O(q^{100}) \) 24 * q + 5 * q^2 - 2 * q^3 + 27 * q^4 - 4 * q^5 + 12 * q^6 + 6 * q^7 + 9 * q^8 + 26 * q^9 + 12 * q^10 + q^12 + 3 * q^13 - q^14 - 5 * q^15 + 17 * q^16 + 8 * q^17 + 20 * q^18 + 8 * q^19 + 16 * q^20 + 11 * q^21 + 2 * q^23 + q^24 + 4 * q^25 + 4 * q^26 + 13 * q^27 - 7 * q^28 + 43 * q^29 + 30 * q^30 - 4 * q^31 + 23 * q^32 + 31 * q^35 - 35 * q^36 - 4 * q^37 - 13 * q^38 + 11 * q^39 + 57 * q^40 + 29 * q^41 + 48 * q^42 + 10 * q^43 - 10 * q^45 - 14 * q^46 - 13 * q^47 + 42 * q^48 + 26 * q^49 - 6 * q^50 + 56 * q^51 + 25 * q^52 - 15 * q^53 + 35 * q^54 - 9 * q^56 - 3 * q^57 - 84 * q^58 - 13 * q^59 + 34 * q^60 - 24 * q^61 + 55 * q^62 + 22 * q^63 + 61 * q^64 + 41 * q^65 - q^67 - 4 * q^68 - 27 * q^69 + 55 * q^70 - 6 * q^71 + 22 * q^72 + 18 * q^73 + 28 * q^74 + 47 * q^75 + 36 * q^76 - 10 * q^78 + 9 * q^79 - 40 * q^80 + 40 * q^81 + 15 * q^82 + 10 * q^83 + 93 * q^84 - 9 * q^85 + 38 * q^86 + 51 * q^87 - 17 * q^89 - 44 * q^90 - 22 * q^91 + 11 * q^92 + 32 * q^93 - 47 * q^94 + 54 * q^95 + 44 * q^96 - q^97 + 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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