LMFDB - Embedded newform 7381.2.a.t.1.32

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:	$1$
Dimension:	$54$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.32
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)

$f(q)$	$=$	$q+0.438301 q^{2} -2.16268 q^{3} -1.80789 q^{4} -1.47822 q^{5} -0.947905 q^{6} -4.80258 q^{7} -1.66900 q^{8} +1.67720 q^{9} +O(q^{10})$	\(q+0.438301 q^{2} -2.16268 q^{3} -1.80789 q^{4} -1.47822 q^{5} -0.947905 q^{6} -4.80258 q^{7} -1.66900 q^{8} +1.67720 q^{9} -0.647906 q^{10} +3.90990 q^{12} -1.27007 q^{13} -2.10497 q^{14} +3.19693 q^{15} +2.88426 q^{16} +2.43815 q^{17} +0.735116 q^{18} -8.40418 q^{19} +2.67247 q^{20} +10.3864 q^{21} -5.24909 q^{23} +3.60952 q^{24} -2.81486 q^{25} -0.556673 q^{26} +2.86081 q^{27} +8.68254 q^{28} -0.804322 q^{29} +1.40121 q^{30} -0.544870 q^{31} +4.60218 q^{32} +1.06864 q^{34} +7.09927 q^{35} -3.03219 q^{36} -2.79820 q^{37} -3.68356 q^{38} +2.74676 q^{39} +2.46716 q^{40} +11.3436 q^{41} +4.55239 q^{42} +2.05106 q^{43} -2.47927 q^{45} -2.30068 q^{46} +1.57356 q^{47} -6.23774 q^{48} +16.0647 q^{49} -1.23375 q^{50} -5.27294 q^{51} +2.29615 q^{52} +2.01588 q^{53} +1.25389 q^{54} +8.01551 q^{56} +18.1756 q^{57} -0.352535 q^{58} -4.50425 q^{59} -5.77970 q^{60} -1.00000 q^{61} -0.238817 q^{62} -8.05486 q^{63} -3.75139 q^{64} +1.87745 q^{65} -6.60009 q^{67} -4.40791 q^{68} +11.3521 q^{69} +3.11162 q^{70} +14.6732 q^{71} -2.79924 q^{72} +11.0318 q^{73} -1.22645 q^{74} +6.08765 q^{75} +15.1939 q^{76} +1.20391 q^{78} +12.1965 q^{79} -4.26358 q^{80} -11.2186 q^{81} +4.97189 q^{82} -14.6440 q^{83} -18.7776 q^{84} -3.60413 q^{85} +0.898979 q^{86} +1.73949 q^{87} -10.9109 q^{89} -1.08666 q^{90} +6.09962 q^{91} +9.48980 q^{92} +1.17838 q^{93} +0.689691 q^{94} +12.4232 q^{95} -9.95305 q^{96} -1.59296 q^{97} +7.04118 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) $ 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9	\( 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9} + 2 q^{10} - 27 q^{12} - 3 q^{13} - 39 q^{14} - 28 q^{15} + 23 q^{16} + 4 q^{17} - 34 q^{18} - 3 q^{19} - 37 q^{20} + 9 q^{21} - 52 q^{23} + 3 q^{24} + 24 q^{25} - 47 q^{26} - 48 q^{27} - 9 q^{28} - 2 q^{29} + 31 q^{30} - 41 q^{31} + 22 q^{32} + 11 q^{34} + 11 q^{35} - 22 q^{36} - 21 q^{37} - 4 q^{38} - 4 q^{39} - 96 q^{40} - 6 q^{41} - 8 q^{42} + 19 q^{43} - 8 q^{45} - q^{46} - 47 q^{47} - 35 q^{48} + 30 q^{49} + 20 q^{50} - 30 q^{51} + 44 q^{52} - 48 q^{53} + 46 q^{54} - 89 q^{56} - 19 q^{57} - 45 q^{58} - 135 q^{59} - 10 q^{60} - 54 q^{61} - 41 q^{62} + 34 q^{63} - 45 q^{64} + 11 q^{65} - 55 q^{67} + 41 q^{68} - 37 q^{69} - 38 q^{70} - 113 q^{71} - 72 q^{72} - 42 q^{73} + 51 q^{74} - 85 q^{75} + 34 q^{76} + 13 q^{78} - 15 q^{79} - 93 q^{80} - 38 q^{81} + 5 q^{82} - 23 q^{83} - 74 q^{84} + 9 q^{85} - 106 q^{86} + 70 q^{87} - 66 q^{89} - 7 q^{90} - 121 q^{91} - 133 q^{92} - 15 q^{93} + 17 q^{94} - 47 q^{95} + 34 q^{96} - 7 q^{97} + 61 q^{98}+O(q^{100}) \) 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9 + 2 * q^10 - 27 * q^12 - 3 * q^13 - 39 * q^14 - 28 * q^15 + 23 * q^16 + 4 * q^17 - 34 * q^18 - 3 * q^19 - 37 * q^20 + 9 * q^21 - 52 * q^23 + 3 * q^24 + 24 * q^25 - 47 * q^26 - 48 * q^27 - 9 * q^28 - 2 * q^29 + 31 * q^30 - 41 * q^31 + 22 * q^32 + 11 * q^34 + 11 * q^35 - 22 * q^36 - 21 * q^37 - 4 * q^38 - 4 * q^39 - 96 * q^40 - 6 * q^41 - 8 * q^42 + 19 * q^43 - 8 * q^45 - q^46 - 47 * q^47 - 35 * q^48 + 30 * q^49 + 20 * q^50 - 30 * q^51 + 44 * q^52 - 48 * q^53 + 46 * q^54 - 89 * q^56 - 19 * q^57 - 45 * q^58 - 135 * q^59 - 10 * q^60 - 54 * q^61 - 41 * q^62 + 34 * q^63 - 45 * q^64 + 11 * q^65 - 55 * q^67 + 41 * q^68 - 37 * q^69 - 38 * q^70 - 113 * q^71 - 72 * q^72 - 42 * q^73 + 51 * q^74 - 85 * q^75 + 34 * q^76 + 13 * q^78 - 15 * q^79 - 93 * q^80 - 38 * q^81 + 5 * q^82 - 23 * q^83 - 74 * q^84 + 9 * q^85 - 106 * q^86 + 70 * q^87 - 66 * q^89 - 7 * q^90 - 121 * q^91 - 133 * q^92 - 15 * q^93 + 17 * q^94 - 47 * q^95 + 34 * q^96 - 7 * q^97 + 61 * 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 $

$2$	0.438301	0.309925	0.154963	−	0.987920i	$-0.450474\pi$
$2$	0.438301	0.309925	0.154963	+	0.987920i	$0.450474\pi$
$3$	−2.16268	−1.24863	−0.624313	−	0.781175i	$-0.714621\pi$
$3$	−2.16268	−1.24863	−0.624313	+	0.781175i	$0.714621\pi$
$4$	−1.80789	−0.903946
$5$	−1.47822	−0.661081	−0.330541	−	0.943792i	$-0.607231\pi$
$5$	−1.47822	−0.661081	−0.330541	+	0.943792i	$0.607231\pi$
$6$	−0.947905	−0.386981
$7$	−4.80258	−1.81520	−0.907602	−	0.419833i	$-0.862089\pi$
$7$	−4.80258	−1.81520	−0.907602	+	0.419833i	$0.862089\pi$
$8$	−1.66900	−0.590081
$9$	1.67720	0.559065
$10$	−0.647906	−0.204886
$11$	0	0
$11$	0	0
$12$	3.90990	1.12869
$13$	−1.27007	−0.352255	−0.176127	−	0.984367i	$-0.556357\pi$
$13$	−1.27007	−0.352255	−0.176127	+	0.984367i	$0.556357\pi$
$14$	−2.10497	−0.562577
$15$	3.19693	0.825443
$16$	2.88426	0.721065
$17$	2.43815	0.591338	0.295669	−	0.955290i	$-0.404457\pi$
$17$	2.43815	0.591338	0.295669	+	0.955290i	$0.404457\pi$
$18$	0.735116	0.173268
$19$	−8.40418	−1.92805	−0.964026	−	0.265809i	$-0.914361\pi$
$19$	−8.40418	−1.92805	−0.964026	+	0.265809i	$0.914361\pi$
$20$	2.67247	0.597582
$21$	10.3864	2.26651
$22$	0	0
$23$	−5.24909	−1.09451	−0.547256	−	0.836965i	$-0.684328\pi$
$23$	−5.24909	−1.09451	−0.547256	+	0.836965i	$0.684328\pi$
$24$	3.60952	0.736790
$25$	−2.81486	−0.562972
$26$	−0.556673	−0.109173
$27$	2.86081	0.550562
$28$	8.68254	1.64085
$29$	−0.804322	−0.149359	−0.0746794	−	0.997208i	$-0.523793\pi$
$29$	−0.804322	−0.149359	−0.0746794	+	0.997208i	$0.523793\pi$
$30$	1.40121	0.255826
$31$	−0.544870	−0.0978615	−0.0489308	−	0.998802i	$-0.515581\pi$
$31$	−0.544870	−0.0978615	−0.0489308	+	0.998802i	$0.515581\pi$
$32$	4.60218	0.813557
$33$	0	0
$34$	1.06864	0.183271
$35$	7.09927	1.20000
$36$	−3.03219	−0.505365
$37$	−2.79820	−0.460021	−0.230010	−	0.973188i	$-0.573876\pi$
$37$	−2.79820	−0.460021	−0.230010	+	0.973188i	$0.573876\pi$
$38$	−3.68356	−0.597552
$39$	2.74676	0.439834
$40$	2.46716	0.390091
$41$	11.3436	1.77157	0.885784	−	0.464098i	$-0.153621\pi$
$41$	11.3436	1.77157	0.885784	+	0.464098i	$0.153621\pi$
$42$	4.55239	0.702448
$43$	2.05106	0.312783	0.156392	−	0.987695i	$-0.450014\pi$
$43$	2.05106	0.312783	0.156392	+	0.987695i	$0.450014\pi$
$44$	0	0
$45$	−2.47927	−0.369587
$46$	−2.30068	−0.339217
$47$	1.57356	0.229527	0.114764	−	0.993393i	$-0.463389\pi$
$47$	1.57356	0.229527	0.114764	+	0.993393i	$0.463389\pi$
$48$	−6.23774	−0.900340
$49$	16.0647	2.29496
$50$	−1.23375	−0.174479
$51$	−5.27294	−0.738359
$52$	2.29615	0.318419
$53$	2.01588	0.276902	0.138451	−	0.990369i	$-0.455788\pi$
$53$	2.01588	0.276902	0.138451	+	0.990369i	$0.455788\pi$
$54$	1.25389	0.170633
$55$	0	0
$56$	8.01551	1.07112
$57$	18.1756	2.40741
$58$	−0.352535	−0.0462901
$59$	−4.50425	−0.586404	−0.293202	−	0.956051i	$-0.594721\pi$
$59$	−4.50425	−0.586404	−0.293202	+	0.956051i	$0.594721\pi$
$60$	−5.77970	−0.746156
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−0.238817	−0.0303298
$63$	−8.05486	−1.01482
$64$	−3.75139	−0.468923
$65$	1.87745	0.232869
$66$	0	0
$67$	−6.60009	−0.806330	−0.403165	−	0.915127i	$-0.632090\pi$
$67$	−6.60009	−0.806330	−0.403165	+	0.915127i	$0.632090\pi$
$68$	−4.40791	−0.534538
$69$	11.3521	1.36664
$70$	3.11162	0.371909
$71$	14.6732	1.74139	0.870694	−	0.491825i	$-0.163670\pi$
$71$	14.6732	1.74139	0.870694	+	0.491825i	$0.163670\pi$
$72$	−2.79924	−0.329894
$73$	11.0318	1.29118	0.645590	−	0.763684i	$-0.276612\pi$
$73$	11.0318	1.29118	0.645590	+	0.763684i	$0.276612\pi$
$74$	−1.22645	−0.142572
$75$	6.08765	0.702941
$76$	15.1939	1.74285
$77$	0	0
$78$	1.20391	0.136316
$79$	12.1965	1.37221	0.686104	−	0.727504i	$-0.259320\pi$
$79$	12.1965	1.37221	0.686104	+	0.727504i	$0.259320\pi$
$80$	−4.26358	−0.476683
$81$	−11.2186	−1.24651
$82$	4.97189	0.549054
$83$	−14.6440	−1.60739	−0.803695	−	0.595042i	$-0.797135\pi$
$83$	−14.6440	−1.60739	−0.803695	+	0.595042i	$0.797135\pi$
$84$	−18.7776	−2.04880
$85$	−3.60413	−0.390922
$86$	0.898979	0.0969394
$87$	1.73949	0.186493
$88$	0	0
$89$	−10.9109	−1.15655	−0.578276	−	0.815841i	$-0.696274\pi$
$89$	−10.9109	−1.15655	−0.578276	+	0.815841i	$0.696274\pi$
$90$	−1.08666	−0.114544
$91$	6.09962	0.639414
$92$	9.48980	0.989380
$93$	1.17838	0.122192
$94$	0.689691	0.0711362
$95$	12.4232	1.27460
$96$	−9.95305	−1.01583
$97$	−1.59296	−0.161741	−0.0808705	−	0.996725i	$-0.525770\pi$
$97$	−1.59296	−0.161741	−0.0808705	+	0.996725i	$0.525770\pi$
$98$	7.04118	0.711267
$99$	0	0
$100$	5.08896	0.508896
$101$	8.87975	0.883568	0.441784	−	0.897121i	$-0.354346\pi$
$101$	8.87975	0.883568	0.441784	+	0.897121i	$0.354346\pi$
$102$	−2.31113	−0.228836
$103$	14.0087	1.38032	0.690158	−	0.723659i	$-0.257541\pi$
$103$	14.0087	1.38032	0.690158	+	0.723659i	$0.257541\pi$
$104$	2.11975	0.207859
$105$	−15.3535	−1.49835
$106$	0.883560	0.0858189
$107$	12.2549	1.18473	0.592365	−	0.805670i	$-0.298195\pi$
$107$	12.2549	1.18473	0.592365	+	0.805670i	$0.298195\pi$
$108$	−5.17203	−0.497679
$109$	−1.13964	−0.109158	−0.0545790	−	0.998509i	$-0.517382\pi$
$109$	−1.13964	−0.109158	−0.0545790	+	0.998509i	$0.517382\pi$
$110$	0	0
$111$	6.05161	0.574394
$112$	−13.8519	−1.30888
$113$	11.7259	1.10308	0.551540	−	0.834149i	$-0.314040\pi$
$113$	11.7259	1.10308	0.551540	+	0.834149i	$0.314040\pi$
$114$	7.96636	0.746118
$115$	7.75933	0.723561
$116$	1.45413	0.135012
$117$	−2.13016	−0.196933
$118$	−1.97422	−0.181741
$119$	−11.7094	−1.07340
$120$	−5.33567	−0.487078
$121$	0	0
$122$	−0.438301	−0.0396819
$123$	−24.5325	−2.21202
$124$	0.985066	0.0884616
$125$	11.5521	1.03325
$126$	−3.53045	−0.314517
$127$	−14.5142	−1.28793	−0.643965	−	0.765055i	$-0.722712\pi$
$127$	−14.5142	−1.28793	−0.643965	+	0.765055i	$0.722712\pi$
$128$	−10.8486	−0.958889
$129$	−4.43578	−0.390549
$130$	0.822887	0.0721720
$131$	2.55064	0.222851	0.111425	−	0.993773i	$-0.464458\pi$
$131$	2.55064	0.222851	0.111425	+	0.993773i	$0.464458\pi$
$132$	0	0
$133$	40.3617	3.49980
$134$	−2.89282	−0.249902
$135$	−4.22891	−0.363966
$136$	−4.06927	−0.348937
$137$	2.05986	0.175985	0.0879927	−	0.996121i	$-0.471955\pi$
$137$	2.05986	0.175985	0.0879927	+	0.996121i	$0.471955\pi$
$138$	4.97564	0.423555
$139$	−22.9248	−1.94445	−0.972227	−	0.234039i	$-0.924806\pi$
$139$	−22.9248	−1.94445	−0.972227	+	0.234039i	$0.924806\pi$
$140$	−12.8347	−1.08473
$141$	−3.40311	−0.286593
$142$	6.43127	0.539700
$143$	0	0
$144$	4.83747	0.403122
$145$	1.18897	0.0987383
$146$	4.83526	0.400169
$147$	−34.7429	−2.86555
$148$	5.05884	0.415834
$149$	17.8098	1.45904	0.729519	−	0.683960i	$-0.239744\pi$
$149$	17.8098	1.45904	0.729519	+	0.683960i	$0.239744\pi$
$150$	2.66822	0.217859
$151$	−21.5538	−1.75402	−0.877011	−	0.480470i	$-0.840466\pi$
$151$	−21.5538	−1.75402	−0.877011	+	0.480470i	$0.840466\pi$
$152$	14.0266	1.13771
$153$	4.08925	0.330596
$154$	0	0
$155$	0.805439	0.0646944
$156$	−4.96585	−0.397586
$157$	−1.71037	−0.136502	−0.0682511	−	0.997668i	$-0.521742\pi$
$157$	−1.71037	−0.136502	−0.0682511	+	0.997668i	$0.521742\pi$
$158$	5.34571	0.425282
$159$	−4.35970	−0.345747
$160$	−6.80304	−0.537827
$161$	25.2092	1.98676
$162$	−4.91712	−0.386325
$163$	17.8373	1.39712	0.698562	−	0.715549i	$-0.253824\pi$
$163$	17.8373	1.39712	0.698562	+	0.715549i	$0.253824\pi$
$164$	−20.5080	−1.60140
$165$	0	0
$166$	−6.41848	−0.498171
$167$	20.4955	1.58599	0.792995	−	0.609228i	$-0.208521\pi$
$167$	20.4955	1.58599	0.792995	+	0.609228i	$0.208521\pi$
$168$	−17.3350	−1.33742
$169$	−11.3869	−0.875917
$170$	−1.57969	−0.121157
$171$	−14.0955	−1.07791
$172$	−3.70809	−0.282739
$173$	12.3416	0.938316	0.469158	−	0.883114i	$-0.344558\pi$
$173$	12.3416	0.938316	0.469158	+	0.883114i	$0.344558\pi$
$174$	0.762421	0.0577990
$175$	13.5186	1.02191
$176$	0	0
$177$	9.74127	0.732199
$178$	−4.78225	−0.358445
$179$	−13.1326	−0.981577	−0.490789	−	0.871279i	$-0.663291\pi$
$179$	−13.1326	−0.981577	−0.490789	+	0.871279i	$0.663291\pi$
$180$	4.48225	0.334087
$181$	−10.0726	−0.748694	−0.374347	−	0.927289i	$-0.622133\pi$
$181$	−10.0726	−0.748694	−0.374347	+	0.927289i	$0.622133\pi$
$182$	2.67347	0.198170
$183$	2.16268	0.159870
$184$	8.76075	0.645851
$185$	4.13636	0.304111
$186$	0.516485	0.0378705
$187$	0	0
$188$	−2.84482	−0.207480
$189$	−13.7392	−0.999383
$190$	5.44512	0.395030
$191$	12.7010	0.919015	0.459507	−	0.888174i	$-0.348026\pi$
$191$	12.7010	0.919015	0.459507	+	0.888174i	$0.348026\pi$
$192$	8.11306	0.585509
$193$	−13.3674	−0.962206	−0.481103	−	0.876664i	$-0.659764\pi$
$193$	−13.3674	−0.962206	−0.481103	+	0.876664i	$0.659764\pi$
$194$	−0.698197	−0.0501276
$195$	−4.06033	−0.290766
$196$	−29.0433	−2.07452
$197$	−0.864792	−0.0616139	−0.0308069	−	0.999525i	$-0.509808\pi$
$197$	−0.864792	−0.0616139	−0.0308069	+	0.999525i	$0.509808\pi$
$198$	0	0
$199$	−14.6728	−1.04013	−0.520065	−	0.854127i	$-0.674092\pi$
$199$	−14.6728	−1.04013	−0.520065	+	0.854127i	$0.674092\pi$
$200$	4.69800	0.332199
$201$	14.2739	1.00680
$202$	3.89200	0.273840
$203$	3.86282	0.271117
$204$	9.53291	0.667437
$205$	−16.7683	−1.17115
$206$	6.14001	0.427795
$207$	−8.80376	−0.611904
$208$	−3.66322	−0.253999
$209$	0	0
$210$	−6.72944	−0.464375
$211$	−16.5035	−1.13615	−0.568073	−	0.822978i	$-0.692311\pi$
$211$	−16.5035	−1.13615	−0.568073	+	0.822978i	$0.692311\pi$
$212$	−3.64449	−0.250304
$213$	−31.7335	−2.17434
$214$	5.37134	0.367177
$215$	−3.03192	−0.206775
$216$	−4.77469	−0.324876
$217$	2.61678	0.177639
$218$	−0.499506	−0.0338308
$219$	−23.8584	−1.61220
$220$	0	0
$221$	−3.09662	−0.208302
$222$	2.65242	0.178019
$223$	−5.22004	−0.349560	−0.174780	−	0.984608i	$-0.555921\pi$
$223$	−5.22004	−0.349560	−0.174780	+	0.984608i	$0.555921\pi$
$224$	−22.1023	−1.47677
$225$	−4.72107	−0.314738
$226$	5.13947	0.341872
$227$	−1.94964	−0.129402	−0.0647012	−	0.997905i	$-0.520609\pi$
$227$	−1.94964	−0.129402	−0.0647012	+	0.997905i	$0.520609\pi$
$228$	−32.8595	−2.17617
$229$	−27.9151	−1.84468	−0.922342	−	0.386374i	$-0.873727\pi$
$229$	−27.9151	−1.84468	−0.922342	+	0.386374i	$0.873727\pi$
$230$	3.40092	0.224250
$231$	0	0
$232$	1.34241	0.0881339
$233$	20.2176	1.32450	0.662249	−	0.749284i	$-0.269602\pi$
$233$	20.2176	1.32450	0.662249	+	0.749284i	$0.269602\pi$
$234$	−0.933650	−0.0610346
$235$	−2.32607	−0.151736
$236$	8.14321	0.530078
$237$	−26.3771	−1.71337
$238$	−5.13223	−0.332673
$239$	−15.5241	−1.00417	−0.502085	−	0.864818i	$-0.667434\pi$
$239$	−15.5241	−1.00417	−0.502085	+	0.864818i	$0.667434\pi$
$240$	9.22077	0.595198
$241$	6.48279	0.417594	0.208797	−	0.977959i	$-0.433045\pi$
$241$	6.48279	0.417594	0.208797	+	0.977959i	$0.433045\pi$
$242$	0	0
$243$	15.6799	1.00586
$244$	1.80789	0.115738
$245$	−23.7473	−1.51716
$246$	−10.7526	−0.685562
$247$	10.6739	0.679165
$248$	0.909389	0.0577463
$249$	31.6703	2.00703
$250$	5.06329	0.320231
$251$	17.9058	1.13020	0.565100	−	0.825022i	$-0.308837\pi$
$251$	17.9058	1.13020	0.565100	+	0.825022i	$0.308837\pi$
$252$	14.5623	0.917340
$253$	0	0
$254$	−6.36160	−0.399162
$255$	7.79458	0.488115
$256$	2.74783	0.171739
$257$	−3.72272	−0.232217	−0.116109	−	0.993237i	$-0.537042\pi$
$257$	−3.72272	−0.232217	−0.116109	+	0.993237i	$0.537042\pi$
$258$	−1.94421	−0.121041
$259$	13.4386	0.835031
$260$	−3.39423	−0.210501
$261$	−1.34901	−0.0835014
$262$	1.11795	0.0690671
$263$	8.44206	0.520560	0.260280	−	0.965533i	$-0.416185\pi$
$263$	8.44206	0.520560	0.260280	+	0.965533i	$0.416185\pi$
$264$	0	0
$265$	−2.97991	−0.183055
$266$	17.6906	1.08468
$267$	23.5968	1.44410
$268$	11.9323	0.728879
$269$	−11.6239	−0.708722	−0.354361	−	0.935109i	$-0.615302\pi$
$269$	−11.6239	−0.708722	−0.354361	+	0.935109i	$0.615302\pi$
$270$	−1.85353	−0.112802
$271$	−10.9603	−0.665792	−0.332896	−	0.942964i	$-0.608026\pi$
$271$	−10.9603	−0.665792	−0.332896	+	0.942964i	$0.608026\pi$
$272$	7.03226	0.426393
$273$	−13.1915	−0.798388
$274$	0.902836	0.0545423
$275$	0	0
$276$	−20.5234	−1.23536
$277$	−7.32788	−0.440290	−0.220145	−	0.975467i	$-0.570653\pi$
$277$	−7.32788	−0.440290	−0.220145	+	0.975467i	$0.570653\pi$
$278$	−10.0479	−0.602636
$279$	−0.913854	−0.0547110
$280$	−11.8487	−0.708095
$281$	−3.22433	−0.192348	−0.0961738	−	0.995365i	$-0.530660\pi$
$281$	−3.22433	−0.192348	−0.0961738	+	0.995365i	$0.530660\pi$
$282$	−1.49158	−0.0888225
$283$	7.03217	0.418019	0.209010	−	0.977914i	$-0.432976\pi$
$283$	7.03217	0.418019	0.209010	+	0.977914i	$0.432976\pi$
$284$	−26.5276	−1.57412
$285$	−26.8675	−1.59150
$286$	0	0
$287$	−54.4784	−3.21576
$288$	7.71875	0.454832
$289$	−11.0554	−0.650319
$290$	0.521125	0.0306015
$291$	3.44508	0.201954
$292$	−19.9444	−1.16716
$293$	13.4294	0.784552	0.392276	−	0.919848i	$-0.371688\pi$
$293$	13.4294	0.784552	0.392276	+	0.919848i	$0.371688\pi$
$294$	−15.2278	−0.888106
$295$	6.65829	0.387660
$296$	4.67020	0.271450
$297$	0	0
$298$	7.80606	0.452193
$299$	6.66673	0.385547
$300$	−11.0058	−0.635421
$301$	−9.85035	−0.567765
$302$	−9.44704	−0.543616
$303$	−19.2041	−1.10325
$304$	−24.2399	−1.39025
$305$	1.47822	0.0846428
$306$	1.79232	0.102460
$307$	11.8518	0.676417	0.338209	−	0.941071i	$-0.390179\pi$
$307$	11.8518	0.676417	0.338209	+	0.941071i	$0.390179\pi$
$308$	0	0
$309$	−30.2963	−1.72350
$310$	0.353024	0.0200504
$311$	2.72860	0.154725	0.0773625	−	0.997003i	$-0.475350\pi$
$311$	2.72860	0.154725	0.0773625	+	0.997003i	$0.475350\pi$
$312$	−4.58435	−0.259538
$313$	22.0756	1.24779	0.623895	−	0.781509i	$-0.285549\pi$
$313$	22.0756	1.24779	0.623895	+	0.781509i	$0.285549\pi$
$314$	−0.749655	−0.0423055
$315$	11.9069	0.670876
$316$	−22.0499	−1.24040
$317$	−11.9746	−0.672560	−0.336280	−	0.941762i	$-0.609169\pi$
$317$	−11.9746	−0.672560	−0.336280	+	0.941762i	$0.609169\pi$
$318$	−1.91086	−0.107156
$319$	0	0
$320$	5.54538	0.309996
$321$	−26.5035	−1.47928
$322$	11.0492	0.615748
$323$	−20.4906	−1.14013
$324$	20.2820	1.12678
$325$	3.57507	0.198309
$326$	7.81809	0.433004
$327$	2.46469	0.136297
$328$	−18.9324	−1.04537
$329$	−7.55713	−0.416638
$330$	0	0
$331$	−22.9134	−1.25943	−0.629716	−	0.776825i	$-0.716829\pi$
$331$	−22.9134	−1.25943	−0.629716	+	0.776825i	$0.716829\pi$
$332$	26.4748	1.45299
$333$	−4.69312	−0.257182
$334$	8.98319	0.491539
$335$	9.75641	0.533049
$336$	29.9572	1.63430
$337$	29.1055	1.58547	0.792737	−	0.609563i	$-0.208655\pi$
$337$	29.1055	1.58547	0.792737	+	0.609563i	$0.208655\pi$
$338$	−4.99089	−0.271469
$339$	−25.3594	−1.37733
$340$	6.51587	0.353373
$341$	0	0
$342$	−6.17805	−0.334070
$343$	−43.5341	−2.35062
$344$	−3.42322	−0.184567
$345$	−16.7810	−0.903457
$346$	5.40934	0.290808
$347$	−18.1454	−0.974097	−0.487049	−	0.873375i	$-0.661927\pi$
$347$	−18.1454	−0.974097	−0.487049	+	0.873375i	$0.661927\pi$
$348$	−3.14482	−0.168580
$349$	−12.1185	−0.648689	−0.324344	−	0.945939i	$-0.605144\pi$
$349$	−12.1185	−0.648689	−0.324344	+	0.945939i	$0.605144\pi$
$350$	5.92520	0.316715
$351$	−3.63343	−0.193938
$352$	0	0
$353$	−6.59988	−0.351276	−0.175638	−	0.984455i	$-0.556199\pi$
$353$	−6.59988	−0.351276	−0.175638	+	0.984455i	$0.556199\pi$
$354$	4.26960	0.226927
$355$	−21.6903	−1.15120
$356$	19.7257	1.04546
$357$	25.3237	1.34027
$358$	−5.75603	−0.304216
$359$	11.4846	0.606131	0.303066	−	0.952970i	$-0.401990\pi$
$359$	11.4846	0.606131	0.303066	+	0.952970i	$0.401990\pi$
$360$	4.13790	0.218087
$361$	51.6303	2.71738
$362$	−4.41485	−0.232039
$363$	0	0
$364$	−11.0275	−0.577996
$365$	−16.3075	−0.853574
$366$	0.947905	0.0495478
$367$	−11.8531	−0.618729	−0.309364	−	0.950944i	$-0.600116\pi$
$367$	−11.8531	−0.618729	−0.309364	+	0.950944i	$0.600116\pi$
$368$	−15.1398	−0.789215
$369$	19.0254	0.990422
$370$	1.81297	0.0942517
$371$	−9.68140	−0.502633
$372$	−2.13039	−0.110455
$373$	15.5549	0.805404	0.402702	−	0.915331i	$-0.368071\pi$
$373$	15.5549	0.805404	0.402702	+	0.915331i	$0.368071\pi$
$374$	0	0
$375$	−24.9835	−1.29014
$376$	−2.62627	−0.135440
$377$	1.02155	0.0526124
$378$	−6.02192	−0.309734
$379$	−9.11609	−0.468262	−0.234131	−	0.972205i	$-0.575225\pi$
$379$	−9.11609	−0.468262	−0.234131	+	0.972205i	$0.575225\pi$
$380$	−22.4599	−1.15217
$381$	31.3897	1.60814
$382$	5.56687	0.284826
$383$	12.4752	0.637454	0.318727	−	0.947847i	$-0.396745\pi$
$383$	12.4752	0.637454	0.318727	+	0.947847i	$0.396745\pi$
$384$	23.4620	1.19729
$385$	0	0
$386$	−5.85894	−0.298212
$387$	3.44002	0.174866
$388$	2.87991	0.146205
$389$	−3.34872	−0.169787	−0.0848934	−	0.996390i	$-0.527055\pi$
$389$	−3.34872	−0.169787	−0.0848934	+	0.996390i	$0.527055\pi$
$390$	−1.77964	−0.0901157
$391$	−12.7981	−0.647226
$392$	−26.8121	−1.35421
$393$	−5.51623	−0.278257
$394$	−0.379039	−0.0190957
$395$	−18.0291	−0.907141
$396$	0	0
$397$	−19.2362	−0.965436	−0.482718	−	0.875776i	$-0.660350\pi$
$397$	−19.2362	−0.965436	−0.482718	+	0.875776i	$0.660350\pi$
$398$	−6.43111	−0.322363
$399$	−87.2896	−4.36994
$400$	−8.11879	−0.405939
$401$	6.05830	0.302537	0.151268	−	0.988493i	$-0.451664\pi$
$401$	6.05830	0.302537	0.151268	+	0.988493i	$0.451664\pi$
$402$	6.25626	0.312034
$403$	0.692024	0.0344722
$404$	−16.0536	−0.798698
$405$	16.5836	0.824045
$406$	1.69308	0.0840259
$407$	0	0
$408$	8.80055	0.435692
$409$	17.0216	0.841662	0.420831	−	0.907139i	$-0.361739\pi$
$409$	17.0216	0.841662	0.420831	+	0.907139i	$0.361739\pi$
$410$	−7.34956	−0.362969
$411$	−4.45482	−0.219740
$412$	−25.3262	−1.24773
$413$	21.6320	1.06444
$414$	−3.85869	−0.189644
$415$	21.6471	1.06261
$416$	−5.84510	−0.286579
$417$	49.5790	2.42790
$418$	0	0
$419$	5.42763	0.265157	0.132579	−	0.991173i	$-0.457674\pi$
$419$	5.42763	0.265157	0.132579	+	0.991173i	$0.457674\pi$
$420$	27.7574	1.35442
$421$	4.60253	0.224314	0.112157	−	0.993691i	$-0.464224\pi$
$421$	4.60253	0.224314	0.112157	+	0.993691i	$0.464224\pi$
$422$	−7.23348	−0.352120
$423$	2.63916	0.128321
$424$	−3.36450	−0.163395
$425$	−6.86304	−0.332907
$426$	−13.9088	−0.673884
$427$	4.80258	0.232413
$428$	−22.1556	−1.07093
$429$	0	0
$430$	−1.32889	−0.0640848
$431$	1.61447	0.0777664	0.0388832	−	0.999244i	$-0.487620\pi$
$431$	1.61447	0.0777664	0.0388832	+	0.999244i	$0.487620\pi$
$432$	8.25131	0.396991
$433$	−4.94973	−0.237869	−0.118934	−	0.992902i	$-0.537948\pi$
$433$	−4.94973	−0.237869	−0.118934	+	0.992902i	$0.537948\pi$
$434$	1.14694	0.0550547
$435$	−2.57136	−0.123287
$436$	2.06035	0.0986730
$437$	44.1143	2.11028
$438$	−10.4571	−0.499661
$439$	5.68121	0.271149	0.135575	−	0.990767i	$-0.456712\pi$
$439$	5.68121	0.271149	0.135575	+	0.990767i	$0.456712\pi$
$440$	0	0
$441$	26.9437	1.28303
$442$	−1.35725	−0.0645579
$443$	11.1604	0.530245	0.265123	−	0.964215i	$-0.414588\pi$
$443$	11.1604	0.530245	0.265123	+	0.964215i	$0.414588\pi$
$444$	−10.9407	−0.519221
$445$	16.1287	0.764575
$446$	−2.28795	−0.108337
$447$	−38.5170	−1.82179
$448$	18.0163	0.851191
$449$	9.02684	0.426003	0.213001	−	0.977052i	$-0.431676\pi$
$449$	9.02684	0.426003	0.213001	+	0.977052i	$0.431676\pi$
$450$	−2.06925	−0.0975452
$451$	0	0
$452$	−21.1992	−0.997125
$453$	46.6140	2.19012
$454$	−0.854530	−0.0401051
$455$	−9.01659	−0.422704
$456$	−30.3351	−1.42057
$457$	−0.370385	−0.0173259	−0.00866294	−	0.999962i	$-0.502758\pi$
$457$	−0.370385	−0.0173259	−0.00866294	+	0.999962i	$0.502758\pi$
$458$	−12.2352	−0.571714
$459$	6.97507	0.325568
$460$	−14.0280	−0.654060
$461$	6.65876	0.310129	0.155065	−	0.987904i	$-0.450441\pi$
$461$	6.65876	0.310129	0.155065	+	0.987904i	$0.450441\pi$
$462$	0	0
$463$	16.9311	0.786856	0.393428	−	0.919355i	$-0.371289\pi$
$463$	16.9311	0.786856	0.393428	+	0.919355i	$0.371289\pi$
$464$	−2.31988	−0.107698
$465$	−1.74191	−0.0807791
$466$	8.86137	0.410495
$467$	−31.7374	−1.46863	−0.734316	−	0.678808i	$-0.762497\pi$
$467$	−31.7374	−1.46863	−0.734316	+	0.678808i	$0.762497\pi$
$468$	3.85110	0.178017
$469$	31.6975	1.46365
$470$	−1.01952	−0.0470268
$471$	3.69898	0.170440
$472$	7.51760	0.346026
$473$	0	0
$474$	−11.5611	−0.531018
$475$	23.6566	1.08544
$476$	21.1693	0.970295
$477$	3.38102	0.154806
$478$	−6.80422	−0.311218
$479$	29.5958	1.35227	0.676134	−	0.736779i	$-0.263654\pi$
$479$	29.5958	1.35227	0.676134	+	0.736779i	$0.263654\pi$
$480$	14.7128	0.671545
$481$	3.55391	0.162044
$482$	2.84141	0.129423
$483$	−54.5194	−2.48072
$484$	0	0
$485$	2.35476	0.106924
$486$	6.87249	0.311742
$487$	−17.8675	−0.809655	−0.404828	−	0.914393i	$-0.632668\pi$
$487$	−17.8675	−0.809655	−0.404828	+	0.914393i	$0.632668\pi$
$488$	1.66900	0.0755521
$489$	−38.5764	−1.74448
$490$	−10.4084	−0.470205
$491$	3.09486	0.139669	0.0698346	−	0.997559i	$-0.477753\pi$
$491$	3.09486	0.139669	0.0698346	+	0.997559i	$0.477753\pi$
$492$	44.3522	1.99955
$493$	−1.96106	−0.0883216
$494$	4.67838	0.210490
$495$	0	0
$496$	−1.57155	−0.0705646
$497$	−70.4692	−3.16097
$498$	13.8811	0.622028
$499$	4.79653	0.214722	0.107361	−	0.994220i	$-0.465760\pi$
$499$	4.79653	0.214722	0.107361	+	0.994220i	$0.465760\pi$
$500$	−20.8850	−0.934004
$501$	−44.3253	−1.98031
$502$	7.84810	0.350278
$503$	−11.9306	−0.531959	−0.265979	−	0.963979i	$-0.585695\pi$
$503$	−11.9306	−0.531959	−0.265979	+	0.963979i	$0.585695\pi$
$504$	13.4436	0.598824
$505$	−13.1262	−0.584110
$506$	0	0
$507$	24.6263	1.09369
$508$	26.2402	1.16422
$509$	32.3121	1.43221	0.716104	−	0.697994i	$-0.245924\pi$
$509$	32.3121	1.43221	0.716104	+	0.697994i	$0.245924\pi$
$510$	3.41637	0.151279
$511$	−52.9813	−2.34375
$512$	22.9015	1.01212
$513$	−24.0427	−1.06151
$514$	−1.63167	−0.0719700
$515$	−20.7079	−0.912501
$516$	8.01942	0.353035
$517$	0	0
$518$	5.89013	0.258797
$519$	−26.6910	−1.17160
$520$	−3.13347	−0.137412
$521$	0.798715	0.0349923	0.0174962	−	0.999847i	$-0.494431\pi$
$521$	0.798715	0.0349923	0.0174962	+	0.999847i	$0.494431\pi$
$522$	−0.591270	−0.0258792
$523$	7.66182	0.335028	0.167514	−	0.985870i	$-0.446426\pi$
$523$	7.66182	0.335028	0.167514	+	0.985870i	$0.446426\pi$
$524$	−4.61129	−0.201445
$525$	−29.2364	−1.27598
$526$	3.70016	0.161335
$527$	−1.32847	−0.0578692
$528$	0	0
$529$	4.55300	0.197956
$530$	−1.30610	−0.0567333
$531$	−7.55451	−0.327838
$532$	−72.9697	−3.16364
$533$	−14.4072	−0.624043
$534$	10.3425	0.447563
$535$	−18.1155	−0.783202
$536$	11.0156	0.475800
$537$	28.4017	1.22562
$538$	−5.09476	−0.219651
$539$	0	0
$540$	7.64541	0.329006
$541$	10.7405	0.461772	0.230886	−	0.972981i	$-0.425838\pi$
$541$	10.7405	0.461772	0.230886	+	0.972981i	$0.425838\pi$
$542$	−4.80391	−0.206346
$543$	21.7839	0.934839
$544$	11.2208	0.481087
$545$	1.68465	0.0721623
$546$	−5.78186	−0.247441
$547$	36.2179	1.54857	0.774283	−	0.632840i	$-0.218111\pi$
$547$	36.2179	1.54857	0.774283	+	0.632840i	$0.218111\pi$
$548$	−3.72400	−0.159081
$549$	−1.67720	−0.0715810
$550$	0	0
$551$	6.75967	0.287972
$552$	−18.9467	−0.806426
$553$	−58.5744	−2.49084
$554$	−3.21181	−0.136457
$555$	−8.94563	−0.379721
$556$	41.4455	1.75768
$557$	22.5873	0.957055	0.478528	−	0.878072i	$-0.341171\pi$
$557$	22.5873	0.957055	0.478528	+	0.878072i	$0.341171\pi$
$558$	−0.400543	−0.0169563
$559$	−2.60499	−0.110179
$560$	20.4762	0.865276
$561$	0	0
$562$	−1.41323	−0.0596134
$563$	18.1855	0.766428	0.383214	−	0.923660i	$-0.374817\pi$
$563$	18.1855	0.766428	0.383214	+	0.923660i	$0.374817\pi$
$564$	6.15245	0.259065
$565$	−17.3335	−0.729225
$566$	3.08220	0.129555
$567$	53.8782	2.26267
$568$	−24.4896	−1.02756
$569$	−2.16554	−0.0907840	−0.0453920	−	0.998969i	$-0.514454\pi$
$569$	−2.16554	−0.0907840	−0.0453920	+	0.998969i	$0.514454\pi$
$570$	−11.7761	−0.493245
$571$	−8.28218	−0.346598	−0.173299	−	0.984869i	$-0.555443\pi$
$571$	−8.28218	−0.346598	−0.173299	+	0.984869i	$0.555443\pi$
$572$	0	0
$573$	−27.4683	−1.14751
$574$	−23.8779	−0.996644
$575$	14.7755	0.616179
$576$	−6.29181	−0.262159
$577$	8.96940	0.373401	0.186701	−	0.982417i	$-0.440221\pi$
$577$	8.96940	0.373401	0.186701	+	0.982417i	$0.440221\pi$
$578$	−4.84560	−0.201550
$579$	28.9094	1.20144
$580$	−2.14952	−0.0892542
$581$	70.3290	2.91774
$582$	1.50998	0.0625906
$583$	0	0
$584$	−18.4122	−0.761901
$585$	3.14885	0.130189
$586$	5.88610	0.243153
$587$	37.9092	1.56468	0.782340	−	0.622852i	$-0.214026\pi$
$587$	37.9092	1.56468	0.782340	+	0.622852i	$0.214026\pi$
$588$	62.8115	2.59030
$589$	4.57919	0.188682
$590$	2.91833	0.120146
$591$	1.87027	0.0769326
$592$	−8.07073	−0.331705
$593$	20.4825	0.841117	0.420559	−	0.907265i	$-0.361834\pi$
$593$	20.4825	0.841117	0.420559	+	0.907265i	$0.361834\pi$
$594$	0	0
$595$	17.3091	0.709603
$596$	−32.1983	−1.31889
$597$	31.7327	1.29873
$598$	2.92203	0.119491
$599$	15.7454	0.643340	0.321670	−	0.946852i	$-0.395756\pi$
$599$	15.7454	0.643340	0.321670	+	0.946852i	$0.395756\pi$
$600$	−10.1603	−0.414792
$601$	−6.30274	−0.257094	−0.128547	−	0.991703i	$-0.541031\pi$
$601$	−6.30274	−0.257094	−0.128547	+	0.991703i	$0.541031\pi$
$602$	−4.31741	−0.175965
$603$	−11.0696	−0.450791
$604$	38.9669	1.58554
$605$	0	0
$606$	−8.41716	−0.341924
$607$	−37.4587	−1.52040	−0.760201	−	0.649687i	$-0.774900\pi$
$607$	−37.4587	−1.52040	−0.760201	+	0.649687i	$0.774900\pi$
$608$	−38.6775	−1.56858
$609$	−8.35405	−0.338523
$610$	0.647906	0.0262329
$611$	−1.99853	−0.0808520
$612$	−7.39293	−0.298841
$613$	4.36886	0.176457	0.0882283	−	0.996100i	$-0.471879\pi$
$613$	4.36886	0.176457	0.0882283	+	0.996100i	$0.471879\pi$
$614$	5.19464	0.209639
$615$	36.2645	1.46233
$616$	0	0
$617$	31.1622	1.25454	0.627271	−	0.778801i	$-0.284172\pi$
$617$	31.1622	1.25454	0.627271	+	0.778801i	$0.284172\pi$
$618$	−13.2789	−0.534156
$619$	23.5990	0.948525	0.474263	−	0.880383i	$-0.342715\pi$
$619$	23.5990	0.948525	0.474263	+	0.880383i	$0.342715\pi$
$620$	−1.45615	−0.0584803
$621$	−15.0166	−0.602597
$622$	1.19595	0.0479532
$623$	52.4004	2.09938
$624$	7.92238	0.317149
$625$	−3.00227	−0.120091
$626$	9.67577	0.386721
$627$	0	0
$628$	3.09216	0.123391
$629$	−6.82242	−0.272028
$630$	5.21879	0.207922
$631$	48.7375	1.94021	0.970104	−	0.242691i	$-0.0780300\pi$
$631$	48.7375	1.94021	0.970104	+	0.242691i	$0.0780300\pi$
$632$	−20.3559	−0.809714
$633$	35.6918	1.41862
$634$	−5.24847	−0.208443
$635$	21.4553	0.851426
$636$	7.88187	0.312536
$637$	−20.4034	−0.808411
$638$	0	0
$639$	24.6098	0.973550
$640$	16.0366	0.633903
$641$	−28.9170	−1.14215	−0.571076	−	0.820897i	$-0.693474\pi$
$641$	−28.9170	−1.14215	−0.571076	+	0.820897i	$0.693474\pi$
$642$	−11.6165	−0.458467
$643$	−17.4262	−0.687222	−0.343611	−	0.939112i	$-0.611650\pi$
$643$	−17.4262	−0.687222	−0.343611	+	0.939112i	$0.611650\pi$
$644$	−45.5755	−1.79593
$645$	6.55707	0.258184
$646$	−8.98106	−0.353355
$647$	−27.2193	−1.07010	−0.535051	−	0.844820i	$-0.679707\pi$
$647$	−27.2193	−1.07010	−0.535051	+	0.844820i	$0.679707\pi$
$648$	18.7239	0.735543
$649$	0	0
$650$	1.56696	0.0614611
$651$	−5.65926	−0.221804
$652$	−32.2479	−1.26293
$653$	−44.4626	−1.73996	−0.869978	−	0.493091i	$-0.835867\pi$
$653$	−44.4626	−1.73996	−0.869978	+	0.493091i	$0.835867\pi$
$654$	1.08027	0.0422420
$655$	−3.77042	−0.147322
$656$	32.7178	1.27742
$657$	18.5026	0.721854
$658$	−3.31230	−0.129127
$659$	−0.0827962	−0.00322528	−0.00161264	−	0.999999i	$-0.500513\pi$
$659$	−0.0827962	−0.00322528	−0.00161264	+	0.999999i	$0.500513\pi$
$660$	0	0
$661$	−37.2426	−1.44857	−0.724284	−	0.689502i	$-0.757829\pi$
$661$	−37.2426	−1.44857	−0.724284	+	0.689502i	$0.757829\pi$
$662$	−10.0429	−0.390330
$663$	6.69702	0.260091
$664$	24.4409	0.948490
$665$	−59.6636	−2.31365
$666$	−2.05700	−0.0797071
$667$	4.22196	0.163475
$668$	−37.0537	−1.43365
$669$	11.2893	0.436469
$670$	4.27624	0.165205
$671$	0	0
$672$	47.8003	1.84394
$673$	−16.8650	−0.650099	−0.325050	−	0.945697i	$-0.605381\pi$
$673$	−16.8650	−0.650099	−0.325050	+	0.945697i	$0.605381\pi$
$674$	12.7569	0.491379
$675$	−8.05277	−0.309951
$676$	20.5863	0.791782
$677$	36.9779	1.42118	0.710588	−	0.703608i	$-0.248429\pi$
$677$	36.9779	1.42118	0.710588	+	0.703608i	$0.248429\pi$
$678$	−11.1150	−0.426870
$679$	7.65033	0.293593
$680$	6.01529	0.230676
$681$	4.21646	0.161575
$682$	0	0
$683$	−28.0845	−1.07462	−0.537312	−	0.843383i	$-0.680560\pi$
$683$	−28.0845	−1.07462	−0.537312	+	0.843383i	$0.680560\pi$
$684$	25.4831	0.974369
$685$	−3.04493	−0.116341
$686$	−19.0810	−0.728517
$687$	60.3716	2.30332
$688$	5.91578	0.225537
$689$	−2.56031	−0.0975400
$690$	−7.35511	−0.280004
$691$	−17.1825	−0.653654	−0.326827	−	0.945084i	$-0.605979\pi$
$691$	−17.1825	−0.653654	−0.326827	+	0.945084i	$0.605979\pi$
$692$	−22.3123	−0.848187
$693$	0	0
$694$	−7.95315	−0.301897
$695$	33.8879	1.28544
$696$	−2.90322	−0.110046
$697$	27.6573	1.04760
$698$	−5.31155	−0.201045
$699$	−43.7242	−1.65380
$700$	−24.4401	−0.923750
$701$	5.82082	0.219849	0.109925	−	0.993940i	$-0.464939\pi$
$701$	5.82082	0.219849	0.109925	+	0.993940i	$0.464939\pi$
$702$	−1.59253	−0.0601063
$703$	23.5166	0.886944
$704$	0	0
$705$	5.03055	0.189461
$706$	−2.89273	−0.108869
$707$	−42.6457	−1.60386
$708$	−17.6112	−0.661868
$709$	−1.10476	−0.0414901	−0.0207451	−	0.999785i	$-0.506604\pi$
$709$	−1.10476	−0.0414901	−0.0207451	+	0.999785i	$0.506604\pi$
$710$	−9.50685	−0.356786
$711$	20.4558	0.767154
$712$	18.2103	0.682459
$713$	2.86007	0.107111
$714$	11.0994	0.415384
$715$	0	0
$716$	23.7423	0.887293
$717$	33.5737	1.25383
$718$	5.03369	0.187855
$719$	25.2832	0.942903	0.471451	−	0.881892i	$-0.343730\pi$
$719$	25.2832	0.942903	0.471451	+	0.881892i	$0.343730\pi$
$720$	−7.15086	−0.266497
$721$	−67.2777	−2.50555
$722$	22.6296	0.842185
$723$	−14.0202	−0.521418
$724$	18.2103	0.676779
$725$	2.26405	0.0840848
$726$	0	0
$727$	−13.1987	−0.489514	−0.244757	−	0.969584i	$-0.578708\pi$
$727$	−13.1987	−0.489514	−0.244757	+	0.969584i	$0.578708\pi$
$728$	−10.1803	−0.377306
$729$	−0.254744	−0.00943498
$730$	−7.14759	−0.264544
$731$	5.00078	0.184960
$732$	−3.90990	−0.144514
$733$	−19.4837	−0.719648	−0.359824	−	0.933020i	$-0.617163\pi$
$733$	−19.4837	−0.719648	−0.359824	+	0.933020i	$0.617163\pi$
$734$	−5.19524	−0.191760
$735$	51.3578	1.89436
$736$	−24.1573	−0.890448
$737$	0	0
$738$	8.33884	0.306957
$739$	28.0417	1.03153	0.515766	−	0.856730i	$-0.327507\pi$
$739$	28.0417	1.03153	0.515766	+	0.856730i	$0.327507\pi$
$740$	−7.47809	−0.274900
$741$	−23.0843	−0.848023
$742$	−4.24336	−0.155779
$743$	−17.1946	−0.630808	−0.315404	−	0.948957i	$-0.602140\pi$
$743$	−17.1946	−0.630808	−0.315404	+	0.948957i	$0.602140\pi$
$744$	−1.96672	−0.0721034
$745$	−26.3269	−0.964543
$746$	6.81773	0.249615
$747$	−24.5609	−0.898635
$748$	0	0
$749$	−58.8552	−2.15052
$750$	−10.9503	−0.399848
$751$	2.86244	0.104452	0.0522260	−	0.998635i	$-0.483368\pi$
$751$	2.86244	0.104452	0.0522260	+	0.998635i	$0.483368\pi$
$752$	4.53855	0.165504
$753$	−38.7245	−1.41120
$754$	0.447745	0.0163059
$755$	31.8613	1.15955
$756$	24.8391	0.903388
$757$	−20.9513	−0.761487	−0.380743	−	0.924681i	$-0.624332\pi$
$757$	−20.9513	−0.761487	−0.380743	+	0.924681i	$0.624332\pi$
$758$	−3.99559	−0.145126
$759$	0	0
$760$	−20.7344	−0.752116
$761$	36.3055	1.31607	0.658037	−	0.752986i	$-0.271387\pi$
$761$	36.3055	1.31607	0.658037	+	0.752986i	$0.271387\pi$
$762$	13.7581	0.498404
$763$	5.47322	0.198144
$764$	−22.9621	−0.830740
$765$	−6.04482	−0.218551
$766$	5.46790	0.197563
$767$	5.72073	0.206563
$768$	−5.94268	−0.214438
$769$	21.4572	0.773767	0.386883	−	0.922129i	$-0.373552\pi$
$769$	21.4572	0.773767	0.386883	+	0.922129i	$0.373552\pi$
$770$	0	0
$771$	8.05107	0.289952
$772$	24.1668	0.869783
$773$	17.0278	0.612446	0.306223	−	0.951960i	$-0.400935\pi$
$773$	17.0278	0.612446	0.306223	+	0.951960i	$0.400935\pi$
$774$	1.50776	0.0541954
$775$	1.53373	0.0550933
$776$	2.65866	0.0954403
$777$	−29.0633	−1.04264
$778$	−1.46775	−0.0526212
$779$	−95.3334	−3.41567
$780$	7.34063	0.262837
$781$	0	0
$782$	−5.60940	−0.200592
$783$	−2.30101	−0.0822314
$784$	46.3349	1.65482
$785$	2.52830	0.0902391
$786$	−2.41777	−0.0862389
$787$	7.19813	0.256586	0.128293	−	0.991736i	$-0.459050\pi$
$787$	7.19813	0.256586	0.128293	+	0.991736i	$0.459050\pi$
$788$	1.56345	0.0556956
$789$	−18.2575	−0.649984
$790$	−7.90215	−0.281146
$791$	−56.3145	−2.00231
$792$	0	0
$793$	1.27007	0.0451016
$794$	−8.43122	−0.299213
$795$	6.44461	0.228567
$796$	26.5269	0.940222
$797$	24.0074	0.850387	0.425193	−	0.905103i	$-0.360206\pi$
$797$	24.0074	0.850387	0.425193	+	0.905103i	$0.360206\pi$
$798$	−38.2591	−1.35436
$799$	3.83657	0.135728
$800$	−12.9545	−0.458010
$801$	−18.2997	−0.646588
$802$	2.65536	0.0937638
$803$	0	0
$804$	−25.8057	−0.910097
$805$	−37.2648	−1.31341
$806$	0.303315	0.0106838
$807$	25.1388	0.884928
$808$	−14.8203	−0.521377
$809$	−5.71594	−0.200962	−0.100481	−	0.994939i	$-0.532038\pi$
$809$	−5.71594	−0.200962	−0.100481	+	0.994939i	$0.532038\pi$
$810$	7.26860	0.255392
$811$	−42.9052	−1.50660	−0.753302	−	0.657675i	$-0.771540\pi$
$811$	−42.9052	−1.50660	−0.753302	+	0.657675i	$0.771540\pi$
$812$	−6.98356	−0.245075
$813$	23.7037	0.831325
$814$	0	0
$815$	−26.3675	−0.923612
$816$	−15.2085	−0.532405
$817$	−17.2374	−0.603062
$818$	7.46056	0.260852
$819$	10.2303	0.357474
$820$	30.3153	1.05866
$821$	39.5206	1.37928	0.689640	−	0.724153i	$-0.257769\pi$
$821$	39.5206	1.37928	0.689640	+	0.724153i	$0.257769\pi$
$822$	−1.95255	−0.0681029
$823$	8.31614	0.289882	0.144941	−	0.989440i	$-0.453701\pi$
$823$	8.31614	0.289882	0.144941	+	0.989440i	$0.453701\pi$
$824$	−23.3805	−0.814498
$825$	0	0
$826$	9.48133	0.329898
$827$	55.6522	1.93521	0.967607	−	0.252459i	$-0.0812394\pi$
$827$	55.6522	1.93521	0.967607	+	0.252459i	$0.0812394\pi$
$828$	15.9163	0.553128
$829$	11.1295	0.386542	0.193271	−	0.981145i	$-0.438090\pi$
$829$	11.1295	0.386542	0.193271	+	0.981145i	$0.438090\pi$
$830$	9.48794	0.329331
$831$	15.8479	0.549757
$832$	4.76453	0.165180
$833$	39.1682	1.35710
$834$	21.7305	0.752466
$835$	−30.2969	−1.04847
$836$	0	0
$837$	−1.55877	−0.0538789
$838$	2.37893	0.0821789
$839$	42.2621	1.45905	0.729525	−	0.683954i	$-0.239741\pi$
$839$	42.2621	1.45905	0.729525	+	0.683954i	$0.239741\pi$
$840$	25.6250	0.884146
$841$	−28.3531	−0.977692
$842$	2.01729	0.0695205
$843$	6.97321	0.240170
$844$	29.8365	1.02702
$845$	16.8324	0.579052
$846$	1.15675	0.0397698
$847$	0	0
$848$	5.81431	0.199664
$849$	−15.2084	−0.521949
$850$	−3.00808	−0.103176
$851$	14.6880	0.503498
$852$	57.3707	1.96549
$853$	53.9290	1.84649	0.923246	−	0.384209i	$-0.125526\pi$
$853$	53.9290	1.84649	0.923246	+	0.384209i	$0.125526\pi$
$854$	2.10497	0.0720307
$855$	20.8362	0.712584
$856$	−20.4535	−0.699086
$857$	−35.7626	−1.22163	−0.610814	−	0.791774i	$-0.709157\pi$
$857$	−35.7626	−1.22163	−0.610814	+	0.791774i	$0.709157\pi$
$858$	0	0
$859$	−12.2022	−0.416335	−0.208168	−	0.978093i	$-0.566750\pi$
$859$	−12.2022	−0.416335	−0.208168	+	0.978093i	$0.566750\pi$
$860$	5.48138	0.186913
$861$	117.819	4.01527
$862$	0.707624	0.0241018
$863$	−23.4759	−0.799128	−0.399564	−	0.916705i	$-0.630838\pi$
$863$	−23.4759	−0.799128	−0.399564	+	0.916705i	$0.630838\pi$
$864$	13.1659	0.447914
$865$	−18.2436	−0.620303
$866$	−2.16947	−0.0737216
$867$	23.9094	0.812005
$868$	−4.73086	−0.160576
$869$	0	0
$870$	−1.12703	−0.0382098
$871$	8.38260	0.284033
$872$	1.90207	0.0644121
$873$	−2.67171	−0.0904238
$874$	19.3353	0.654028
$875$	−55.4798	−1.87556
$876$	43.1334	1.45734
$877$	−20.0397	−0.676693	−0.338346	−	0.941022i	$-0.609868\pi$
$877$	−20.0397	−0.676693	−0.338346	+	0.941022i	$0.609868\pi$
$878$	2.49008	0.0840360
$879$	−29.0435	−0.979612
$880$	0	0
$881$	−36.8242	−1.24064	−0.620319	−	0.784349i	$-0.712997\pi$
$881$	−36.8242	−1.24064	−0.620319	+	0.784349i	$0.712997\pi$
$882$	11.8094	0.397645
$883$	−15.6262	−0.525862	−0.262931	−	0.964815i	$-0.584689\pi$
$883$	−15.6262	−0.525862	−0.262931	+	0.964815i	$0.584689\pi$
$884$	5.59836	0.188293
$885$	−14.3998	−0.484043
$886$	4.89160	0.164336
$887$	−9.35978	−0.314271	−0.157135	−	0.987577i	$-0.550226\pi$
$887$	−9.35978	−0.314271	−0.157135	+	0.987577i	$0.550226\pi$
$888$	−10.1001	−0.338939
$889$	69.7057	2.33785
$890$	7.06923	0.236961
$891$	0	0
$892$	9.43727	0.315983
$893$	−13.2245	−0.442540
$894$	−16.8820	−0.564620
$895$	19.4129	0.648902
$896$	52.1012	1.74058
$897$	−14.4180	−0.481404
$898$	3.95647	0.132029
$899$	0.438251	0.0146165
$900$	8.53519	0.284506
$901$	4.91501	0.163743
$902$	0	0
$903$	21.3032	0.708926
$904$	−19.5705	−0.650907
$905$	14.8896	0.494948
$906$	20.4309	0.678773
$907$	−40.5591	−1.34674	−0.673371	−	0.739304i	$-0.735154\pi$
$907$	−40.5591	−1.34674	−0.673371	+	0.739304i	$0.735154\pi$
$908$	3.52475	0.116973
$909$	14.8931	0.493972
$910$	−3.95198	−0.131007
$911$	11.5591	0.382969	0.191484	−	0.981496i	$-0.438670\pi$
$911$	11.5591	0.382969	0.191484	+	0.981496i	$0.438670\pi$
$912$	52.4231	1.73590
$913$	0	0
$914$	−0.162340	−0.00536973
$915$	−3.19693	−0.105687
$916$	50.4676	1.66750
$917$	−12.2497	−0.404519
$918$	3.05718	0.100902
$919$	−40.8921	−1.34890	−0.674452	−	0.738319i	$-0.735620\pi$
$919$	−40.8921	−1.34890	−0.674452	+	0.738319i	$0.735620\pi$
$920$	−12.9503	−0.426960
$921$	−25.6316	−0.844591
$922$	2.91854	0.0961169
$923$	−18.6360	−0.613412
$924$	0	0
$925$	7.87653	0.258979
$926$	7.42092	0.243867
$927$	23.4953	0.771687
$928$	−3.70163	−0.121512
$929$	55.7195	1.82810	0.914048	−	0.405606i	$-0.132939\pi$
$929$	55.7195	1.82810	0.914048	+	0.405606i	$0.132939\pi$
$930$	−0.763480	−0.0250355
$931$	−135.011	−4.42481
$932$	−36.5512	−1.19727
$933$	−5.90110	−0.193193
$934$	−13.9105	−0.455166
$935$	0	0
$936$	3.55524	0.116207
$937$	9.41427	0.307551	0.153775	−	0.988106i	$-0.450857\pi$
$937$	9.41427	0.307551	0.153775	+	0.988106i	$0.450857\pi$
$938$	13.8930	0.453623
$939$	−47.7426	−1.55802
$940$	4.20528	0.137161
$941$	−7.03900	−0.229465	−0.114732	−	0.993396i	$-0.536601\pi$
$941$	−7.03900	−0.229465	−0.114732	+	0.993396i	$0.536601\pi$
$942$	1.62127	0.0528237
$943$	−59.5435	−1.93900
$944$	−12.9914	−0.422835
$945$	20.3096	0.660673
$946$	0	0
$947$	45.5066	1.47877	0.739384	−	0.673284i	$-0.235117\pi$
$947$	45.5066	1.47877	0.739384	+	0.673284i	$0.235117\pi$
$948$	47.6869	1.54880
$949$	−14.0112	−0.454824
$950$	10.3687	0.336405
$951$	25.8972	0.839775
$952$	19.5430	0.633392
$953$	−38.0447	−1.23239	−0.616194	−	0.787594i	$-0.711326\pi$
$953$	−38.0447	−1.23239	−0.616194	+	0.787594i	$0.711326\pi$
$954$	1.48190	0.0479784
$955$	−18.7750	−0.607543
$956$	28.0659	0.907716
$957$	0	0
$958$	12.9719	0.419102
$959$	−9.89262	−0.319449
$960$	−11.9929	−0.387069
$961$	−30.7031	−0.990423
$962$	1.55768	0.0502217
$963$	20.5539	0.662341
$964$	−11.7202	−0.377482
$965$	19.7600	0.636097
$966$	−23.8959	−0.768838
$967$	21.1052	0.678697	0.339348	−	0.940661i	$-0.389793\pi$
$967$	21.1052	0.678697	0.339348	+	0.940661i	$0.389793\pi$
$968$	0	0
$969$	44.3148	1.42359
$970$	1.03209	0.0331384
$971$	−17.8742	−0.573609	−0.286805	−	0.957989i	$-0.592593\pi$
$971$	−17.8742	−0.573609	−0.286805	+	0.957989i	$0.592593\pi$
$972$	−28.3475	−0.909246
$973$	110.098	3.52958
$974$	−7.83135	−0.250933
$975$	−7.73175	−0.247614
$976$	−2.88426	−0.0923229
$977$	27.4258	0.877430	0.438715	−	0.898626i	$-0.355434\pi$
$977$	27.4258	0.877430	0.438715	+	0.898626i	$0.355434\pi$
$978$	−16.9081	−0.540660
$979$	0	0
$980$	42.9325	1.37143
$981$	−1.91140	−0.0610264
$982$	1.35648	0.0432870
$983$	25.8598	0.824799	0.412400	−	0.911003i	$-0.364691\pi$
$983$	25.8598	0.824799	0.412400	+	0.911003i	$0.364691\pi$
$984$	40.9448	1.30527
$985$	1.27835	0.0407318
$986$	−0.859532	−0.0273731
$987$	16.3437	0.520225
$988$	−19.2973	−0.613929
$989$	−10.7662	−0.342345
$990$	0	0
$991$	−40.5690	−1.28872	−0.644359	−	0.764723i	$-0.722876\pi$
$991$	−40.5690	−1.28872	−0.644359	+	0.764723i	$0.722876\pi$
$992$	−2.50759	−0.0796160
$993$	49.5543	1.57256
$994$	−30.8867	−0.979666
$995$	21.6897	0.687610
$996$	−57.2566	−1.81424
$997$	−30.9288	−0.979524	−0.489762	−	0.871856i	$-0.662916\pi$
$997$	−30.9288	−0.979524	−0.489762	+	0.871856i	$0.662916\pi$
$998$	2.10232	0.0665479
$999$	−8.00510	−0.253270

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.t.1.32		54
11.5	even	5		671.2.j.b.245.12	✓	108
11.9	even	5		671.2.j.b.367.12	yes	108
11.10	odd	2		7381.2.a.s.1.23		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.b.245.12	✓	108	11.5	even	5
671.2.j.b.367.12	yes	108	11.9	even	5
7381.2.a.s.1.23		54	11.10	odd	2
7381.2.a.t.1.32		54	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)

\(f(q)\)	\(=\)	\(q+0.438301 q^{2} -2.16268 q^{3} -1.80789 q^{4} -1.47822 q^{5} -0.947905 q^{6} -4.80258 q^{7} -1.66900 q^{8} +1.67720 q^{9} +O(q^{10})\)	\(q+0.438301 q^{2} -2.16268 q^{3} -1.80789 q^{4} -1.47822 q^{5} -0.947905 q^{6} -4.80258 q^{7} -1.66900 q^{8} +1.67720 q^{9} -0.647906 q^{10} +3.90990 q^{12} -1.27007 q^{13} -2.10497 q^{14} +3.19693 q^{15} +2.88426 q^{16} +2.43815 q^{17} +0.735116 q^{18} -8.40418 q^{19} +2.67247 q^{20} +10.3864 q^{21} -5.24909 q^{23} +3.60952 q^{24} -2.81486 q^{25} -0.556673 q^{26} +2.86081 q^{27} +8.68254 q^{28} -0.804322 q^{29} +1.40121 q^{30} -0.544870 q^{31} +4.60218 q^{32} +1.06864 q^{34} +7.09927 q^{35} -3.03219 q^{36} -2.79820 q^{37} -3.68356 q^{38} +2.74676 q^{39} +2.46716 q^{40} +11.3436 q^{41} +4.55239 q^{42} +2.05106 q^{43} -2.47927 q^{45} -2.30068 q^{46} +1.57356 q^{47} -6.23774 q^{48} +16.0647 q^{49} -1.23375 q^{50} -5.27294 q^{51} +2.29615 q^{52} +2.01588 q^{53} +1.25389 q^{54} +8.01551 q^{56} +18.1756 q^{57} -0.352535 q^{58} -4.50425 q^{59} -5.77970 q^{60} -1.00000 q^{61} -0.238817 q^{62} -8.05486 q^{63} -3.75139 q^{64} +1.87745 q^{65} -6.60009 q^{67} -4.40791 q^{68} +11.3521 q^{69} +3.11162 q^{70} +14.6732 q^{71} -2.79924 q^{72} +11.0318 q^{73} -1.22645 q^{74} +6.08765 q^{75} +15.1939 q^{76} +1.20391 q^{78} +12.1965 q^{79} -4.26358 q^{80} -11.2186 q^{81} +4.97189 q^{82} -14.6440 q^{83} -18.7776 q^{84} -3.60413 q^{85} +0.898979 q^{86} +1.73949 q^{87} -10.9109 q^{89} -1.08666 q^{90} +6.09962 q^{91} +9.48980 q^{92} +1.17838 q^{93} +0.689691 q^{94} +12.4232 q^{95} -9.95305 q^{96} -1.59296 q^{97} +7.04118 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9}+O(q^{10}) \) 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9	\( 54 q + q^{2} - 15 q^{3} + 41 q^{4} - 14 q^{5} + 3 q^{6} + 2 q^{7} + 3 q^{8} + 27 q^{9} + 2 q^{10} - 27 q^{12} - 3 q^{13} - 39 q^{14} - 28 q^{15} + 23 q^{16} + 4 q^{17} - 34 q^{18} - 3 q^{19} - 37 q^{20} + 9 q^{21} - 52 q^{23} + 3 q^{24} + 24 q^{25} - 47 q^{26} - 48 q^{27} - 9 q^{28} - 2 q^{29} + 31 q^{30} - 41 q^{31} + 22 q^{32} + 11 q^{34} + 11 q^{35} - 22 q^{36} - 21 q^{37} - 4 q^{38} - 4 q^{39} - 96 q^{40} - 6 q^{41} - 8 q^{42} + 19 q^{43} - 8 q^{45} - q^{46} - 47 q^{47} - 35 q^{48} + 30 q^{49} + 20 q^{50} - 30 q^{51} + 44 q^{52} - 48 q^{53} + 46 q^{54} - 89 q^{56} - 19 q^{57} - 45 q^{58} - 135 q^{59} - 10 q^{60} - 54 q^{61} - 41 q^{62} + 34 q^{63} - 45 q^{64} + 11 q^{65} - 55 q^{67} + 41 q^{68} - 37 q^{69} - 38 q^{70} - 113 q^{71} - 72 q^{72} - 42 q^{73} + 51 q^{74} - 85 q^{75} + 34 q^{76} + 13 q^{78} - 15 q^{79} - 93 q^{80} - 38 q^{81} + 5 q^{82} - 23 q^{83} - 74 q^{84} + 9 q^{85} - 106 q^{86} + 70 q^{87} - 66 q^{89} - 7 q^{90} - 121 q^{91} - 133 q^{92} - 15 q^{93} + 17 q^{94} - 47 q^{95} + 34 q^{96} - 7 q^{97} + 61 q^{98}+O(q^{100}) \) 54 * q + q^2 - 15 * q^3 + 41 * q^4 - 14 * q^5 + 3 * q^6 + 2 * q^7 + 3 * q^8 + 27 * q^9 + 2 * q^10 - 27 * q^12 - 3 * q^13 - 39 * q^14 - 28 * q^15 + 23 * q^16 + 4 * q^17 - 34 * q^18 - 3 * q^19 - 37 * q^20 + 9 * q^21 - 52 * q^23 + 3 * q^24 + 24 * q^25 - 47 * q^26 - 48 * q^27 - 9 * q^28 - 2 * q^29 + 31 * q^30 - 41 * q^31 + 22 * q^32 + 11 * q^34 + 11 * q^35 - 22 * q^36 - 21 * q^37 - 4 * q^38 - 4 * q^39 - 96 * q^40 - 6 * q^41 - 8 * q^42 + 19 * q^43 - 8 * q^45 - q^46 - 47 * q^47 - 35 * q^48 + 30 * q^49 + 20 * q^50 - 30 * q^51 + 44 * q^52 - 48 * q^53 + 46 * q^54 - 89 * q^56 - 19 * q^57 - 45 * q^58 - 135 * q^59 - 10 * q^60 - 54 * q^61 - 41 * q^62 + 34 * q^63 - 45 * q^64 + 11 * q^65 - 55 * q^67 + 41 * q^68 - 37 * q^69 - 38 * q^70 - 113 * q^71 - 72 * q^72 - 42 * q^73 + 51 * q^74 - 85 * q^75 + 34 * q^76 + 13 * q^78 - 15 * q^79 - 93 * q^80 - 38 * q^81 + 5 * q^82 - 23 * q^83 - 74 * q^84 + 9 * q^85 - 106 * q^86 + 70 * q^87 - 66 * q^89 - 7 * q^90 - 121 * q^91 - 133 * q^92 - 15 * q^93 + 17 * q^94 - 47 * q^95 + 34 * q^96 - 7 * q^97 + 61 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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