LMFDB - Embedded newform 7381.2.a.v.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:	$64$
Twist minimal:	no (minimal twist has level 671)
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)

$f(q)$	$=$	$q-1.98800 q^{2} +2.79573 q^{3} +1.95214 q^{4} +2.00486 q^{5} -5.55790 q^{6} -4.55995 q^{7} +0.0951428 q^{8} +4.81608 q^{9} +O(q^{10})$	\(q-1.98800 q^{2} +2.79573 q^{3} +1.95214 q^{4} +2.00486 q^{5} -5.55790 q^{6} -4.55995 q^{7} +0.0951428 q^{8} +4.81608 q^{9} -3.98567 q^{10} +5.45765 q^{12} -3.01519 q^{13} +9.06519 q^{14} +5.60505 q^{15} -4.09343 q^{16} +5.80852 q^{17} -9.57436 q^{18} -0.600022 q^{19} +3.91378 q^{20} -12.7484 q^{21} -5.86355 q^{23} +0.265993 q^{24} -0.980519 q^{25} +5.99421 q^{26} +5.07726 q^{27} -8.90168 q^{28} -6.35691 q^{29} -11.1428 q^{30} +4.05081 q^{31} +7.94744 q^{32} -11.5473 q^{34} -9.14209 q^{35} +9.40167 q^{36} -8.31230 q^{37} +1.19284 q^{38} -8.42966 q^{39} +0.190748 q^{40} -3.40983 q^{41} +25.3438 q^{42} +8.59613 q^{43} +9.65558 q^{45} +11.6567 q^{46} -7.42886 q^{47} -11.4441 q^{48} +13.7932 q^{49} +1.94927 q^{50} +16.2390 q^{51} -5.88609 q^{52} +9.05823 q^{53} -10.0936 q^{54} -0.433847 q^{56} -1.67750 q^{57} +12.6375 q^{58} +13.1652 q^{59} +10.9418 q^{60} +1.00000 q^{61} -8.05300 q^{62} -21.9611 q^{63} -7.61266 q^{64} -6.04506 q^{65} +10.6629 q^{67} +11.3391 q^{68} -16.3929 q^{69} +18.1745 q^{70} +2.41047 q^{71} +0.458215 q^{72} +10.1527 q^{73} +16.5248 q^{74} -2.74126 q^{75} -1.17133 q^{76} +16.7582 q^{78} +15.0339 q^{79} -8.20676 q^{80} -0.253622 q^{81} +6.77874 q^{82} +11.9457 q^{83} -24.8866 q^{84} +11.6453 q^{85} -17.0891 q^{86} -17.7722 q^{87} +10.6956 q^{89} -19.1953 q^{90} +13.7492 q^{91} -11.4465 q^{92} +11.3249 q^{93} +14.7686 q^{94} -1.20296 q^{95} +22.2189 q^{96} +5.96152 q^{97} -27.4208 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * 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 $

$2$	−1.98800	−1.40573	−0.702864	−	0.711324i	$-0.748096\pi$
$2$	−1.98800	−1.40573	−0.702864	+	0.711324i	$0.748096\pi$
$3$	2.79573	1.61411	0.807056	−	0.590474i	$-0.201059\pi$
$3$	2.79573	1.61411	0.807056	+	0.590474i	$0.201059\pi$
$4$	1.95214	0.976071
$5$	2.00486	0.896603	0.448301	−	0.893883i	$-0.352029\pi$
$5$	2.00486	0.896603	0.448301	+	0.893883i	$0.352029\pi$
$6$	−5.55790	−2.26900
$7$	−4.55995	−1.72350	−0.861750	−	0.507332i	$-0.830632\pi$
$7$	−4.55995	−1.72350	−0.861750	+	0.507332i	$0.830632\pi$
$8$	0.0951428	0.0336381
$9$	4.81608	1.60536
$10$	−3.98567	−1.26038
$11$	0	0
$11$	0	0
$12$	5.45765	1.57549
$13$	−3.01519	−0.836265	−0.418132	−	0.908386i	$-0.637315\pi$
$13$	−3.01519	−0.836265	−0.418132	+	0.908386i	$0.637315\pi$
$14$	9.06519	2.42277
$15$	5.60505	1.44722
$16$	−4.09343	−1.02336
$17$	5.80852	1.40877	0.704387	−	0.709816i	$-0.251222\pi$
$17$	5.80852	1.40877	0.704387	+	0.709816i	$0.251222\pi$
$18$	−9.57436	−2.25670
$19$	−0.600022	−0.137655	−0.0688273	−	0.997629i	$-0.521926\pi$
$19$	−0.600022	−0.137655	−0.0688273	+	0.997629i	$0.521926\pi$
$20$	3.91378	0.875147
$21$	−12.7484	−2.78192
$22$	0	0
$23$	−5.86355	−1.22263	−0.611317	−	0.791386i	$-0.709360\pi$
$23$	−5.86355	−1.22263	−0.611317	+	0.791386i	$0.709360\pi$
$24$	0.265993	0.0542956
$25$	−0.980519	−0.196104
$26$	5.99421	1.17556
$27$	5.07726	0.977118
$28$	−8.90168	−1.68226
$29$	−6.35691	−1.18045	−0.590225	−	0.807239i	$-0.700961\pi$
$29$	−6.35691	−1.18045	−0.590225	+	0.807239i	$0.700961\pi$
$30$	−11.1428	−2.03439
$31$	4.05081	0.727547	0.363773	−	0.931488i	$-0.381488\pi$
$31$	4.05081	0.727547	0.363773	+	0.931488i	$0.381488\pi$
$32$	7.94744	1.40492
$33$	0	0
$34$	−11.5473	−1.98035
$35$	−9.14209	−1.54530
$36$	9.40167	1.56694
$37$	−8.31230	−1.36653	−0.683267	−	0.730169i	$-0.739441\pi$
$37$	−8.31230	−1.36653	−0.683267	+	0.730169i	$0.739441\pi$
$38$	1.19284	0.193505
$39$	−8.42966	−1.34983
$40$	0.190748	0.0301600
$41$	−3.40983	−0.532526	−0.266263	−	0.963900i	$-0.585789\pi$
$41$	−3.40983	−0.532526	−0.266263	+	0.963900i	$0.585789\pi$
$42$	25.3438	3.91063
$43$	8.59613	1.31090	0.655449	−	0.755240i	$-0.272480\pi$
$43$	8.59613	1.31090	0.655449	+	0.755240i	$0.272480\pi$
$44$	0	0
$45$	9.65558	1.43937
$46$	11.6567	1.71869
$47$	−7.42886	−1.08361	−0.541805	−	0.840504i	$-0.682259\pi$
$47$	−7.42886	−1.08361	−0.541805	+	0.840504i	$0.682259\pi$
$48$	−11.4441	−1.65181
$49$	13.7932	1.97046
$50$	1.94927	0.275669
$51$	16.2390	2.27392
$52$	−5.88609	−0.816253
$53$	9.05823	1.24424	0.622122	−	0.782920i	$-0.286271\pi$
$53$	9.05823	1.24424	0.622122	+	0.782920i	$0.286271\pi$
$54$	−10.0936	−1.37356
$55$	0	0
$56$	−0.433847	−0.0579752
$57$	−1.67750	−0.222190
$58$	12.6375	1.65939
$59$	13.1652	1.71397	0.856984	−	0.515344i	$-0.172336\pi$
$59$	13.1652	1.71397	0.856984	+	0.515344i	$0.172336\pi$
$60$	10.9418	1.41259
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−8.05300	−1.02273
$63$	−21.9611	−2.76684
$64$	−7.61266	−0.951583
$65$	−6.04506	−0.749797
$66$	0	0
$67$	10.6629	1.30268	0.651338	−	0.758787i	$-0.274208\pi$
$67$	10.6629	1.30268	0.651338	+	0.758787i	$0.274208\pi$
$68$	11.3391	1.37506
$69$	−16.3929	−1.97347
$70$	18.1745	2.17226
$71$	2.41047	0.286070	0.143035	−	0.989718i	$-0.454314\pi$
$71$	2.41047	0.286070	0.143035	+	0.989718i	$0.454314\pi$
$72$	0.458215	0.0540012
$73$	10.1527	1.18828	0.594141	−	0.804361i	$-0.297492\pi$
$73$	10.1527	1.18828	0.594141	+	0.804361i	$0.297492\pi$
$74$	16.5248	1.92097
$75$	−2.74126	−0.316534
$76$	−1.17133	−0.134361
$77$	0	0
$78$	16.7582	1.89749
$79$	15.0339	1.69145	0.845724	−	0.533621i	$-0.179169\pi$
$79$	15.0339	1.69145	0.845724	+	0.533621i	$0.179169\pi$
$80$	−8.20676	−0.917544
$81$	−0.253622	−0.0281803
$82$	6.77874	0.748587
$83$	11.9457	1.31121	0.655604	−	0.755105i	$-0.272414\pi$
$83$	11.9457	1.31121	0.655604	+	0.755105i	$0.272414\pi$
$84$	−24.8866	−2.71535
$85$	11.6453	1.26311
$86$	−17.0891	−1.84276
$87$	−17.7722	−1.90538
$88$	0	0
$89$	10.6956	1.13373	0.566864	−	0.823811i	$-0.308157\pi$
$89$	10.6956	1.13373	0.566864	+	0.823811i	$0.308157\pi$
$90$	−19.1953	−2.02336
$91$	13.7492	1.44130
$92$	−11.4465	−1.19338
$93$	11.3249	1.17434
$94$	14.7686	1.52326
$95$	−1.20296	−0.123421
$96$	22.2189	2.26770
$97$	5.96152	0.605300	0.302650	−	0.953102i	$-0.402129\pi$
$97$	5.96152	0.605300	0.302650	+	0.953102i	$0.402129\pi$
$98$	−27.4208	−2.76992
$99$	0	0
$100$	−1.91411	−0.191411
$101$	8.81272	0.876898	0.438449	−	0.898756i	$-0.355528\pi$
$101$	8.81272	0.876898	0.438449	+	0.898756i	$0.355528\pi$
$102$	−32.2832	−3.19651
$103$	12.2857	1.21055	0.605275	−	0.796016i	$-0.293063\pi$
$103$	12.2857	1.21055	0.605275	+	0.796016i	$0.293063\pi$
$104$	−0.286874	−0.0281303
$105$	−25.5588	−2.49428
$106$	−18.0078	−1.74907
$107$	4.63551	0.448132	0.224066	−	0.974574i	$-0.428067\pi$
$107$	4.63551	0.448132	0.224066	+	0.974574i	$0.428067\pi$
$108$	9.91152	0.953737
$109$	7.21369	0.690946	0.345473	−	0.938429i	$-0.387718\pi$
$109$	7.21369	0.690946	0.345473	+	0.938429i	$0.387718\pi$
$110$	0	0
$111$	−23.2389	−2.20574
$112$	18.6658	1.76376
$113$	1.61059	0.151511	0.0757556	−	0.997126i	$-0.475863\pi$
$113$	1.61059	0.151511	0.0757556	+	0.997126i	$0.475863\pi$
$114$	3.33486	0.312339
$115$	−11.7556	−1.09622
$116$	−12.4096	−1.15220
$117$	−14.5214	−1.34251
$118$	−26.1725	−2.40937
$119$	−26.4866	−2.42802
$120$	0.533280	0.0486816
$121$	0	0
$122$	−1.98800	−0.179985
$123$	−9.53295	−0.859557
$124$	7.90775	0.710137
$125$	−11.9901	−1.07243
$126$	43.6587	3.88942
$127$	2.12773	0.188806	0.0944030	−	0.995534i	$-0.469906\pi$
$127$	2.12773	0.188806	0.0944030	+	0.995534i	$0.469906\pi$
$128$	−0.760925	−0.0672569
$129$	24.0324	2.11594
$130$	12.0176	1.05401
$131$	−11.1919	−0.977837	−0.488919	−	0.872329i	$-0.662609\pi$
$131$	−11.1919	−0.977837	−0.488919	+	0.872329i	$0.662609\pi$
$132$	0	0
$133$	2.73607	0.237248
$134$	−21.1978	−1.83121
$135$	10.1792	0.876087
$136$	0.552639	0.0473884
$137$	−7.77997	−0.664688	−0.332344	−	0.943158i	$-0.607839\pi$
$137$	−7.77997	−0.664688	−0.332344	+	0.943158i	$0.607839\pi$
$138$	32.5890	2.77416
$139$	11.3706	0.964444	0.482222	−	0.876049i	$-0.339830\pi$
$139$	11.3706	0.964444	0.482222	+	0.876049i	$0.339830\pi$
$140$	−17.8467	−1.50832
$141$	−20.7691	−1.74907
$142$	−4.79202	−0.402137
$143$	0	0
$144$	−19.7143	−1.64286
$145$	−12.7447	−1.05839
$146$	−20.1835	−1.67040
$147$	38.5620	3.18054
$148$	−16.2268	−1.33383
$149$	20.4866	1.67833	0.839166	−	0.543876i	$-0.183044\pi$
$149$	20.4866	1.67833	0.839166	+	0.543876i	$0.183044\pi$
$150$	5.44963	0.444960
$151$	−2.53941	−0.206654	−0.103327	−	0.994647i	$-0.532949\pi$
$151$	−2.53941	−0.206654	−0.103327	+	0.994647i	$0.532949\pi$
$152$	−0.0570878	−0.00463043
$153$	27.9743	2.26159
$154$	0	0
$155$	8.12132	0.652320
$156$	−16.4559	−1.31752
$157$	10.5249	0.839979	0.419990	−	0.907529i	$-0.362034\pi$
$157$	10.5249	0.839979	0.419990	+	0.907529i	$0.362034\pi$
$158$	−29.8874	−2.37771
$159$	25.3243	2.00835
$160$	15.9335	1.25966
$161$	26.7375	2.10721
$162$	0.504201	0.0396138
$163$	−1.86988	−0.146460	−0.0732300	−	0.997315i	$-0.523331\pi$
$163$	−1.86988	−0.146460	−0.0732300	+	0.997315i	$0.523331\pi$
$164$	−6.65647	−0.519783
$165$	0	0
$166$	−23.7480	−1.84320
$167$	−0.894406	−0.0692112	−0.0346056	−	0.999401i	$-0.511018\pi$
$167$	−0.894406	−0.0692112	−0.0346056	+	0.999401i	$0.511018\pi$
$168$	−1.21292	−0.0935786
$169$	−3.90860	−0.300662
$170$	−23.1508	−1.77559
$171$	−2.88976	−0.220985
$172$	16.7809	1.27953
$173$	−12.3166	−0.936417	−0.468208	−	0.883618i	$-0.655100\pi$
$173$	−12.3166	−0.936417	−0.468208	+	0.883618i	$0.655100\pi$
$174$	35.3311	2.67844
$175$	4.47112	0.337985
$176$	0	0
$177$	36.8064	2.76654
$178$	−21.2628	−1.59371
$179$	−6.90165	−0.515854	−0.257927	−	0.966164i	$-0.583039\pi$
$179$	−6.90165	−0.515854	−0.257927	+	0.966164i	$0.583039\pi$
$180$	18.8491	1.40493
$181$	1.60552	0.119337	0.0596687	−	0.998218i	$-0.480996\pi$
$181$	1.60552	0.119337	0.0596687	+	0.998218i	$0.480996\pi$
$182$	−27.3333	−2.02608
$183$	2.79573	0.206666
$184$	−0.557875	−0.0411271
$185$	−16.6650	−1.22524
$186$	−22.5140	−1.65081
$187$	0	0
$188$	−14.5022	−1.05768
$189$	−23.1521	−1.68406
$190$	2.39149	0.173497
$191$	17.7510	1.28442	0.642209	−	0.766530i	$-0.278018\pi$
$191$	17.7510	1.28442	0.642209	+	0.766530i	$0.278018\pi$
$192$	−21.2829	−1.53596
$193$	−7.02829	−0.505907	−0.252954	−	0.967478i	$-0.581402\pi$
$193$	−7.02829	−0.505907	−0.252954	+	0.967478i	$0.581402\pi$
$194$	−11.8515	−0.850887
$195$	−16.9003	−1.21026
$196$	26.9262	1.92330
$197$	−8.40332	−0.598712	−0.299356	−	0.954142i	$-0.596772\pi$
$197$	−8.40332	−0.598712	−0.299356	+	0.954142i	$0.596772\pi$
$198$	0	0
$199$	−11.0242	−0.781488	−0.390744	−	0.920499i	$-0.627782\pi$
$199$	−11.0242	−0.781488	−0.390744	+	0.920499i	$0.627782\pi$
$200$	−0.0932894	−0.00659656
$201$	29.8104	2.10267
$202$	−17.5197	−1.23268
$203$	28.9872	2.03451
$204$	31.7009	2.21951
$205$	−6.83625	−0.477464
$206$	−24.4241	−1.70170
$207$	−28.2393	−1.96277
$208$	12.3425	0.855797
$209$	0	0
$210$	50.8108	3.50628
$211$	7.27543	0.500861	0.250431	−	0.968135i	$-0.419428\pi$
$211$	7.27543	0.500861	0.250431	+	0.968135i	$0.419428\pi$
$212$	17.6829	1.21447
$213$	6.73902	0.461750
$214$	−9.21540	−0.629952
$215$	17.2341	1.17535
$216$	0.483065	0.0328684
$217$	−18.4715	−1.25393
$218$	−14.3408	−0.971282
$219$	28.3841	1.91802
$220$	0	0
$221$	−17.5138	−1.17811
$222$	46.1989	3.10067
$223$	2.92340	0.195765	0.0978825	−	0.995198i	$-0.468793\pi$
$223$	2.92340	0.195765	0.0978825	+	0.995198i	$0.468793\pi$
$224$	−36.2400	−2.42139
$225$	−4.72226	−0.314817
$226$	−3.20185	−0.212984
$227$	−16.8571	−1.11884	−0.559421	−	0.828884i	$-0.688976\pi$
$227$	−16.8571	−1.11884	−0.559421	+	0.828884i	$0.688976\pi$
$228$	−3.27471	−0.216873
$229$	0.382431	0.0252718	0.0126359	−	0.999920i	$-0.495978\pi$
$229$	0.382431	0.0252718	0.0126359	+	0.999920i	$0.495978\pi$
$230$	23.3702	1.54098
$231$	0	0
$232$	−0.604815	−0.0397080
$233$	28.0266	1.83608	0.918042	−	0.396484i	$-0.129770\pi$
$233$	28.0266	1.83608	0.918042	+	0.396484i	$0.129770\pi$
$234$	28.8686	1.88720
$235$	−14.8939	−0.971568
$236$	25.7004	1.67295
$237$	42.0307	2.73019
$238$	52.6553	3.41314
$239$	3.20292	0.207180	0.103590	−	0.994620i	$-0.466967\pi$
$239$	3.20292	0.207180	0.103590	+	0.994620i	$0.466967\pi$
$240$	−22.9439	−1.48102
$241$	9.45524	0.609065	0.304533	−	0.952502i	$-0.401500\pi$
$241$	9.45524	0.609065	0.304533	+	0.952502i	$0.401500\pi$
$242$	0	0
$243$	−15.9408	−1.02260
$244$	1.95214	0.124973
$245$	27.6535	1.76672
$246$	18.9515	1.20830
$247$	1.80918	0.115116
$248$	0.385405	0.0244733
$249$	33.3968	2.11644
$250$	23.8364	1.50754
$251$	−14.9755	−0.945248	−0.472624	−	0.881264i	$-0.656693\pi$
$251$	−14.9755	−0.945248	−0.472624	+	0.881264i	$0.656693\pi$
$252$	−42.8712	−2.70063
$253$	0	0
$254$	−4.22994	−0.265410
$255$	32.5571	2.03880
$256$	16.7380	1.04613
$257$	0.408572	0.0254860	0.0127430	−	0.999919i	$-0.495944\pi$
$257$	0.408572	0.0254860	0.0127430	+	0.999919i	$0.495944\pi$
$258$	−47.7764	−2.97443
$259$	37.9037	2.35522
$260$	−11.8008	−0.731855
$261$	−30.6154	−1.89505
$262$	22.2494	1.37457
$263$	−16.9746	−1.04670	−0.523349	−	0.852118i	$-0.675318\pi$
$263$	−16.9746	−1.04670	−0.523349	+	0.852118i	$0.675318\pi$
$264$	0	0
$265$	18.1605	1.11559
$266$	−5.43932	−0.333506
$267$	29.9019	1.82996
$268$	20.8154	1.27150
$269$	−0.670366	−0.0408729	−0.0204365	−	0.999791i	$-0.506506\pi$
$269$	−0.670366	−0.0408729	−0.0204365	+	0.999791i	$0.506506\pi$
$270$	−20.2363	−1.23154
$271$	−19.0661	−1.15818	−0.579091	−	0.815263i	$-0.696592\pi$
$271$	−19.0661	−1.15818	−0.579091	+	0.815263i	$0.696592\pi$
$272$	−23.7768	−1.44168
$273$	38.4388	2.32642
$274$	15.4666	0.934370
$275$	0	0
$276$	−32.0012	−1.92625
$277$	8.42615	0.506279	0.253139	−	0.967430i	$-0.418537\pi$
$277$	8.42615	0.506279	0.253139	+	0.967430i	$0.418537\pi$
$278$	−22.6048	−1.35575
$279$	19.5090	1.16797
$280$	−0.869804	−0.0519807
$281$	0.111725	0.00666496	0.00333248	−	0.999994i	$-0.498939\pi$
$281$	0.111725	0.00666496	0.00333248	+	0.999994i	$0.498939\pi$
$282$	41.2889	2.45872
$283$	6.07583	0.361171	0.180585	−	0.983559i	$-0.442201\pi$
$283$	6.07583	0.361171	0.180585	+	0.983559i	$0.442201\pi$
$284$	4.70558	0.279225
$285$	−3.36316	−0.199216
$286$	0	0
$287$	15.5487	0.917809
$288$	38.2755	2.25541
$289$	16.7389	0.984644
$290$	25.3366	1.48781
$291$	16.6668	0.977023
$292$	19.8195	1.15985
$293$	−11.6560	−0.680953	−0.340477	−	0.940253i	$-0.610588\pi$
$293$	−11.6560	−0.680953	−0.340477	+	0.940253i	$0.610588\pi$
$294$	−76.6611	−4.47097
$295$	26.3945	1.53675
$296$	−0.790855	−0.0459675
$297$	0	0
$298$	−40.7274	−2.35928
$299$	17.6797	1.02245
$300$	−5.35133	−0.308959
$301$	−39.1980	−2.25933
$302$	5.04834	0.290499
$303$	24.6379	1.41541
$304$	2.45615	0.140870
$305$	2.00486	0.114798
$306$	−55.6129	−3.17918
$307$	−14.5063	−0.827920	−0.413960	−	0.910295i	$-0.635855\pi$
$307$	−14.5063	−0.827920	−0.413960	+	0.910295i	$0.635855\pi$
$308$	0	0
$309$	34.3476	1.95397
$310$	−16.1452	−0.916985
$311$	18.5839	1.05380	0.526899	−	0.849928i	$-0.323355\pi$
$311$	18.5839	1.05380	0.526899	+	0.849928i	$0.323355\pi$
$312$	−0.802021	−0.0454055
$313$	12.7189	0.718915	0.359457	−	0.933161i	$-0.382962\pi$
$313$	12.7189	0.718915	0.359457	+	0.933161i	$0.382962\pi$
$314$	−20.9235	−1.18078
$315$	−44.0290	−2.48075
$316$	29.3483	1.65097
$317$	25.6939	1.44311	0.721557	−	0.692355i	$-0.243427\pi$
$317$	25.6939	1.44311	0.721557	+	0.692355i	$0.243427\pi$
$318$	−50.3447	−2.82319
$319$	0	0
$320$	−15.2624	−0.853191
$321$	12.9596	0.723335
$322$	−53.1542	−2.96217
$323$	−3.48524	−0.193924
$324$	−0.495107	−0.0275059
$325$	2.95646	0.163995
$326$	3.71731	0.205883
$327$	20.1675	1.11526
$328$	−0.324421	−0.0179131
$329$	33.8753	1.86760
$330$	0	0
$331$	11.7026	0.643232	0.321616	−	0.946870i	$-0.395774\pi$
$331$	11.7026	0.643232	0.321616	+	0.946870i	$0.395774\pi$
$332$	23.3197	1.27983
$333$	−40.0327	−2.19378
$334$	1.77808	0.0972921
$335$	21.3776	1.16798
$336$	52.1846	2.84690
$337$	23.1194	1.25940	0.629698	−	0.776840i	$-0.283179\pi$
$337$	23.1194	1.25940	0.629698	+	0.776840i	$0.283179\pi$
$338$	7.77029	0.422648
$339$	4.50276	0.244556
$340$	22.7333	1.23288
$341$	0	0
$342$	5.74483	0.310645
$343$	−30.9766	−1.67258
$344$	0.817860	0.0440961
$345$	−32.8655	−1.76942
$346$	24.4855	1.31635
$347$	−9.44333	−0.506945	−0.253472	−	0.967343i	$-0.581573\pi$
$347$	−9.44333	−0.506945	−0.253472	+	0.967343i	$0.581573\pi$
$348$	−34.6938	−1.85978
$349$	−21.3394	−1.14227	−0.571136	−	0.820856i	$-0.693497\pi$
$349$	−21.3394	−1.14227	−0.571136	+	0.820856i	$0.693497\pi$
$350$	−8.88859	−0.475115
$351$	−15.3089	−0.817130
$352$	0	0
$353$	7.89233	0.420066	0.210033	−	0.977694i	$-0.432643\pi$
$353$	7.89233	0.420066	0.210033	+	0.977694i	$0.432643\pi$
$354$	−73.1710	−3.88900
$355$	4.83267	0.256492
$356$	20.8793	1.10660
$357$	−74.0493	−3.91910
$358$	13.7205	0.725150
$359$	0.445768	0.0235267	0.0117634	−	0.999931i	$-0.496256\pi$
$359$	0.445768	0.0235267	0.0117634	+	0.999931i	$0.496256\pi$
$360$	0.918660	0.0484176
$361$	−18.6400	−0.981051
$362$	−3.19177	−0.167756
$363$	0	0
$364$	26.8403	1.40681
$365$	20.3548	1.06542
$366$	−5.55790	−0.290516
$367$	8.56541	0.447111	0.223555	−	0.974691i	$-0.428234\pi$
$367$	8.56541	0.447111	0.223555	+	0.974691i	$0.428234\pi$
$368$	24.0020	1.25119
$369$	−16.4220	−0.854896
$370$	33.1301	1.72235
$371$	−41.3051	−2.14445
$372$	22.1079	1.14624
$373$	−19.9889	−1.03498	−0.517492	−	0.855688i	$-0.673134\pi$
$373$	−19.9889	−1.03498	−0.517492	+	0.855688i	$0.673134\pi$
$374$	0	0
$375$	−33.5211	−1.73102
$376$	−0.706803	−0.0364506
$377$	19.1673	0.987168
$378$	46.0263	2.36734
$379$	−26.0959	−1.34045	−0.670227	−	0.742156i	$-0.733803\pi$
$379$	−26.0959	−1.34045	−0.670227	+	0.742156i	$0.733803\pi$
$380$	−2.34835	−0.120468
$381$	5.94856	0.304754
$382$	−35.2890	−1.80554
$383$	−31.0038	−1.58422	−0.792111	−	0.610378i	$-0.791018\pi$
$383$	−31.0038	−1.58422	−0.792111	+	0.610378i	$0.791018\pi$
$384$	−2.12734	−0.108560
$385$	0	0
$386$	13.9722	0.711168
$387$	41.3996	2.10446
$388$	11.6377	0.590816
$389$	13.1471	0.666583	0.333291	−	0.942824i	$-0.391841\pi$
$389$	13.1471	0.666583	0.333291	+	0.942824i	$0.391841\pi$
$390$	33.5978	1.70129
$391$	−34.0586	−1.72242
$392$	1.31232	0.0662823
$393$	−31.2894	−1.57834
$394$	16.7058	0.841626
$395$	30.1410	1.51656
$396$	0	0
$397$	−32.8947	−1.65094	−0.825469	−	0.564448i	$-0.809089\pi$
$397$	−32.8947	−1.65094	−0.825469	+	0.564448i	$0.809089\pi$
$398$	21.9162	1.09856
$399$	7.64931	0.382945
$400$	4.01368	0.200684
$401$	−16.1542	−0.806701	−0.403351	−	0.915046i	$-0.632154\pi$
$401$	−16.1542	−0.806701	−0.403351	+	0.915046i	$0.632154\pi$
$402$	−59.2632	−2.95578
$403$	−12.2140	−0.608421
$404$	17.2037	0.855915
$405$	−0.508478	−0.0252665
$406$	−57.6266	−2.85996
$407$	0	0
$408$	1.54503	0.0764903
$409$	−1.07984	−0.0533945	−0.0266973	−	0.999644i	$-0.508499\pi$
$409$	−1.07984	−0.0533945	−0.0266973	+	0.999644i	$0.508499\pi$
$410$	13.5905	0.671185
$411$	−21.7507	−1.07288
$412$	23.9835	1.18158
$413$	−60.0329	−2.95402
$414$	56.1397	2.75912
$415$	23.9495	1.17563
$416$	−23.9631	−1.17489
$417$	31.7891	1.55672
$418$	0	0
$419$	6.83044	0.333689	0.166844	−	0.985983i	$-0.446642\pi$
$419$	6.83044	0.333689	0.166844	+	0.985983i	$0.446642\pi$
$420$	−49.8943	−2.43459
$421$	19.9353	0.971588	0.485794	−	0.874073i	$-0.338531\pi$
$421$	19.9353	0.971588	0.485794	+	0.874073i	$0.338531\pi$
$422$	−14.4635	−0.704075
$423$	−35.7780	−1.73959
$424$	0.861826	0.0418539
$425$	−5.69537	−0.276266
$426$	−13.3972	−0.649095
$427$	−4.55995	−0.220672
$428$	9.04918	0.437408
$429$	0	0
$430$	−34.2613	−1.65223
$431$	19.8278	0.955070	0.477535	−	0.878613i	$-0.341530\pi$
$431$	19.8278	0.955070	0.477535	+	0.878613i	$0.341530\pi$
$432$	−20.7834	−0.999941
$433$	−16.7213	−0.803573	−0.401786	−	0.915733i	$-0.631611\pi$
$433$	−16.7213	−0.803573	−0.401786	+	0.915733i	$0.631611\pi$
$434$	36.7213	1.76268
$435$	−35.6308	−1.70837
$436$	14.0821	0.674412
$437$	3.51826	0.168301
$438$	−56.4276	−2.69622
$439$	−9.33005	−0.445299	−0.222650	−	0.974899i	$-0.571471\pi$
$439$	−9.33005	−0.445299	−0.222650	+	0.974899i	$0.571471\pi$
$440$	0	0
$441$	66.4291	3.16329
$442$	34.8175	1.65610
$443$	3.51989	0.167235	0.0836175	−	0.996498i	$-0.473353\pi$
$443$	3.51989	0.167235	0.0836175	+	0.996498i	$0.473353\pi$
$444$	−45.3656	−2.15296
$445$	21.4432	1.01650
$446$	−5.81171	−0.275192
$447$	57.2750	2.70902
$448$	34.7134	1.64005
$449$	37.3054	1.76055	0.880274	−	0.474465i	$-0.157358\pi$
$449$	37.3054	1.76055	0.880274	+	0.474465i	$0.157358\pi$
$450$	9.38785	0.442547
$451$	0	0
$452$	3.14409	0.147886
$453$	−7.09948	−0.333563
$454$	33.5118	1.57279
$455$	27.5652	1.29228
$456$	−0.159602	−0.00747404
$457$	13.1820	0.616628	0.308314	−	0.951285i	$-0.400235\pi$
$457$	13.1820	0.616628	0.308314	+	0.951285i	$0.400235\pi$
$458$	−0.760273	−0.0355252
$459$	29.4914	1.37654
$460$	−22.9486	−1.06999
$461$	−38.7254	−1.80362	−0.901811	−	0.432130i	$-0.857762\pi$
$461$	−38.7254	−1.80362	−0.901811	+	0.432130i	$0.857762\pi$
$462$	0	0
$463$	1.88131	0.0874319	0.0437160	−	0.999044i	$-0.486080\pi$
$463$	1.88131	0.0874319	0.0437160	+	0.999044i	$0.486080\pi$
$464$	26.0216	1.20802
$465$	22.7050	1.05292
$466$	−55.7168	−2.58103
$467$	7.94105	0.367468	0.183734	−	0.982976i	$-0.441181\pi$
$467$	7.94105	0.367468	0.183734	+	0.982976i	$0.441181\pi$
$468$	−28.3479	−1.31038
$469$	−48.6222	−2.24516
$470$	29.6090	1.36576
$471$	29.4247	1.35582
$472$	1.25258	0.0576546
$473$	0	0
$474$	−83.5570	−3.83790
$475$	0.588334	0.0269946
$476$	−51.7056	−2.36992
$477$	43.6251	1.99746
$478$	−6.36741	−0.291239
$479$	−35.4526	−1.61987	−0.809936	−	0.586518i	$-0.800498\pi$
$479$	−35.4526	−1.61987	−0.809936	+	0.586518i	$0.800498\pi$
$480$	44.5458	2.03323
$481$	25.0632	1.14278
$482$	−18.7970	−0.856180
$483$	74.7507	3.40128
$484$	0	0
$485$	11.9520	0.542714
$486$	31.6904	1.43750
$487$	10.3407	0.468583	0.234291	−	0.972166i	$-0.424723\pi$
$487$	10.3407	0.468583	0.234291	+	0.972166i	$0.424723\pi$
$488$	0.0951428	0.00430691
$489$	−5.22766	−0.236403
$490$	−54.9751	−2.48352
$491$	−17.3982	−0.785168	−0.392584	−	0.919716i	$-0.628419\pi$
$491$	−17.3982	−0.785168	−0.392584	+	0.919716i	$0.628419\pi$
$492$	−18.6097	−0.838988
$493$	−36.9243	−1.66299
$494$	−3.59666	−0.161821
$495$	0	0
$496$	−16.5817	−0.744540
$497$	−10.9916	−0.493043
$498$	−66.3929	−2.97514
$499$	−0.211288	−0.00945854	−0.00472927	−	0.999989i	$-0.501505\pi$
$499$	−0.211288	−0.00945854	−0.00472927	+	0.999989i	$0.501505\pi$
$500$	−23.4064	−1.04677
$501$	−2.50051	−0.111715
$502$	29.7714	1.32876
$503$	0.263245	0.0117375	0.00586875	−	0.999983i	$-0.498132\pi$
$503$	0.263245	0.0117375	0.00586875	+	0.999983i	$0.498132\pi$
$504$	−2.08944	−0.0930711
$505$	17.6683	0.786229
$506$	0	0
$507$	−10.9274	−0.485302
$508$	4.15364	0.184288
$509$	32.9591	1.46089	0.730443	−	0.682973i	$-0.239314\pi$
$509$	32.9591	1.46089	0.730443	+	0.682973i	$0.239314\pi$
$510$	−64.7234	−2.86600
$511$	−46.2958	−2.04801
$512$	−31.7534	−1.40331
$513$	−3.04647	−0.134505
$514$	−0.812240	−0.0358264
$515$	24.6313	1.08538
$516$	46.9147	2.06530
$517$	0	0
$518$	−75.3525	−3.31080
$519$	−34.4339	−1.51148
$520$	−0.575144	−0.0252217
$521$	0.187488	0.00821401	0.00410701	−	0.999992i	$-0.498693\pi$
$521$	0.187488	0.00821401	0.00410701	+	0.999992i	$0.498693\pi$
$522$	60.8634	2.66392
$523$	9.83592	0.430095	0.215047	−	0.976604i	$-0.431009\pi$
$523$	9.83592	0.430095	0.215047	+	0.976604i	$0.431009\pi$
$524$	−21.8481	−0.954439
$525$	12.5000	0.545546
$526$	33.7455	1.47137
$527$	23.5292	1.02495
$528$	0	0
$529$	11.3812	0.494835
$530$	−36.1031	−1.56822
$531$	63.4048	2.75153
$532$	5.34121	0.231571
$533$	10.2813	0.445333
$534$	−59.4449	−2.57243
$535$	9.29357	0.401796
$536$	1.01450	0.0438195
$537$	−19.2951	−0.832646
$538$	1.33269	0.0574562
$539$	0	0
$540$	19.8713	0.855123
$541$	9.52604	0.409557	0.204778	−	0.978808i	$-0.434353\pi$
$541$	9.52604	0.409557	0.204778	+	0.978808i	$0.434353\pi$
$542$	37.9034	1.62809
$543$	4.48859	0.192624
$544$	46.1629	1.97922
$545$	14.4625	0.619504
$546$	−76.4164	−3.27032
$547$	−8.09643	−0.346178	−0.173089	−	0.984906i	$-0.555375\pi$
$547$	−8.09643	−0.346178	−0.173089	+	0.984906i	$0.555375\pi$
$548$	−15.1876	−0.648782
$549$	4.81608	0.205545
$550$	0	0
$551$	3.81429	0.162494
$552$	−1.55966	−0.0663837
$553$	−68.5540	−2.91521
$554$	−16.7512	−0.711690
$555$	−46.5908	−1.97767
$556$	22.1971	0.941365
$557$	−6.91691	−0.293079	−0.146539	−	0.989205i	$-0.546814\pi$
$557$	−6.91691	−0.293079	−0.146539	+	0.989205i	$0.546814\pi$
$558$	−38.7839	−1.64185
$559$	−25.9190	−1.09626
$560$	37.4225	1.58139
$561$	0	0
$562$	−0.222109	−0.00936912
$563$	26.9620	1.13631	0.568157	−	0.822920i	$-0.307657\pi$
$563$	26.9620	1.13631	0.568157	+	0.822920i	$0.307657\pi$
$564$	−40.5441	−1.70722
$565$	3.22901	0.135845
$566$	−12.0788	−0.507708
$567$	1.15651	0.0485687
$568$	0.229339	0.00962286
$569$	−0.919445	−0.0385451	−0.0192726	−	0.999814i	$-0.506135\pi$
$569$	−0.919445	−0.0385451	−0.0192726	+	0.999814i	$0.506135\pi$
$570$	6.68595	0.280044
$571$	20.8580	0.872882	0.436441	−	0.899733i	$-0.356239\pi$
$571$	20.8580	0.872882	0.436441	+	0.899733i	$0.356239\pi$
$572$	0	0
$573$	49.6269	2.07320
$574$	−30.9107	−1.29019
$575$	5.74932	0.239763
$576$	−36.6632	−1.52763
$577$	−41.7293	−1.73721	−0.868607	−	0.495502i	$-0.834984\pi$
$577$	−41.7293	−1.73721	−0.868607	+	0.495502i	$0.834984\pi$
$578$	−33.2770	−1.38414
$579$	−19.6492	−0.816591
$580$	−24.8796	−1.03307
$581$	−54.4718	−2.25987
$582$	−33.1335	−1.37343
$583$	0	0
$584$	0.965955	0.0399715
$585$	−29.1135	−1.20369
$586$	23.1722	0.957235
$587$	−20.4088	−0.842361	−0.421180	−	0.906977i	$-0.638384\pi$
$587$	−20.4088	−0.842361	−0.421180	+	0.906977i	$0.638384\pi$
$588$	75.2784	3.10443
$589$	−2.43058	−0.100150
$590$	−52.4723	−2.16025
$591$	−23.4934	−0.966388
$592$	34.0258	1.39845
$593$	−24.6661	−1.01291	−0.506457	−	0.862265i	$-0.669045\pi$
$593$	−24.6661	−1.01291	−0.506457	+	0.862265i	$0.669045\pi$
$594$	0	0
$595$	−53.1020	−2.17697
$596$	39.9928	1.63817
$597$	−30.8208	−1.26141
$598$	−35.1473	−1.43728
$599$	−11.2990	−0.461665	−0.230832	−	0.972994i	$-0.574145\pi$
$599$	−11.2990	−0.461665	−0.230832	+	0.972994i	$0.574145\pi$
$600$	−0.260811	−0.0106476
$601$	−29.5878	−1.20691	−0.603457	−	0.797396i	$-0.706210\pi$
$601$	−29.5878	−1.20691	−0.603457	+	0.797396i	$0.706210\pi$
$602$	77.9255	3.17601
$603$	51.3532	2.09126
$604$	−4.95728	−0.201709
$605$	0	0
$606$	−48.9802	−1.98968
$607$	31.4865	1.27800	0.638998	−	0.769208i	$-0.279349\pi$
$607$	31.4865	1.27800	0.638998	+	0.769208i	$0.279349\pi$
$608$	−4.76864	−0.193394
$609$	81.0403	3.28392
$610$	−3.98567	−0.161375
$611$	22.3995	0.906185
$612$	54.6098	2.20747
$613$	15.2776	0.617055	0.308527	−	0.951215i	$-0.400164\pi$
$613$	15.2776	0.617055	0.308527	+	0.951215i	$0.400164\pi$
$614$	28.8386	1.16383
$615$	−19.1123	−0.770681
$616$	0	0
$617$	46.4039	1.86815	0.934075	−	0.357077i	$-0.116227\pi$
$617$	46.4039	1.86815	0.934075	+	0.357077i	$0.116227\pi$
$618$	−68.2830	−2.74674
$619$	44.0425	1.77022	0.885109	−	0.465384i	$-0.154084\pi$
$619$	44.0425	1.77022	0.885109	+	0.465384i	$0.154084\pi$
$620$	15.8540	0.636711
$621$	−29.7707	−1.19466
$622$	−36.9449	−1.48135
$623$	−48.7713	−1.95398
$624$	34.5062	1.38135
$625$	−19.1360	−0.765439
$626$	−25.2852	−1.01060
$627$	0	0
$628$	20.5461	0.819879
$629$	−48.2822	−1.92514
$630$	87.5297	3.48727
$631$	−39.9750	−1.59138	−0.795691	−	0.605703i	$-0.792892\pi$
$631$	−39.9750	−1.59138	−0.795691	+	0.605703i	$0.792892\pi$
$632$	1.43037	0.0568970
$633$	20.3401	0.808446
$634$	−51.0795	−2.02863
$635$	4.26582	0.169284
$636$	49.4367	1.96029
$637$	−41.5891	−1.64782
$638$	0	0
$639$	11.6090	0.459246
$640$	−1.52555	−0.0603027
$641$	−25.2184	−0.996066	−0.498033	−	0.867158i	$-0.665944\pi$
$641$	−25.2184	−0.996066	−0.498033	+	0.867158i	$0.665944\pi$
$642$	−25.7637	−1.01681
$643$	−5.11309	−0.201641	−0.100820	−	0.994905i	$-0.532147\pi$
$643$	−5.11309	−0.201641	−0.100820	+	0.994905i	$0.532147\pi$
$644$	52.1954	2.05679
$645$	48.1817	1.89715
$646$	6.92866	0.272605
$647$	3.28132	0.129002	0.0645010	−	0.997918i	$-0.479454\pi$
$647$	3.28132	0.129002	0.0645010	+	0.997918i	$0.479454\pi$
$648$	−0.0241304	−0.000947930 0
$649$	0	0
$650$	−5.87743	−0.230532
$651$	−51.6412	−2.02398
$652$	−3.65026	−0.142955
$653$	−16.4487	−0.643689	−0.321844	−	0.946793i	$-0.604303\pi$
$653$	−16.4487	−0.643689	−0.321844	+	0.946793i	$0.604303\pi$
$654$	−40.0930	−1.56776
$655$	−22.4382	−0.876732
$656$	13.9579	0.544964
$657$	48.8961	1.90762
$658$	−67.3440	−2.62534
$659$	−7.27733	−0.283485	−0.141742	−	0.989904i	$-0.545270\pi$
$659$	−7.27733	−0.283485	−0.141742	+	0.989904i	$0.545270\pi$
$660$	0	0
$661$	10.6629	0.414740	0.207370	−	0.978263i	$-0.433510\pi$
$661$	10.6629	0.414740	0.207370	+	0.978263i	$0.433510\pi$
$662$	−23.2647	−0.904210
$663$	−48.9638	−1.90160
$664$	1.13655	0.0441065
$665$	5.48546	0.212717
$666$	79.5849	3.08385
$667$	37.2741	1.44326
$668$	−1.74601	−0.0675550
$669$	8.17301	0.315987
$670$	−42.4987	−1.64187
$671$	0	0
$672$	−101.317	−3.90839
$673$	−47.4794	−1.83020	−0.915098	−	0.403232i	$-0.867887\pi$
$673$	−47.4794	−1.83020	−0.915098	+	0.403232i	$0.867887\pi$
$674$	−45.9614	−1.77037
$675$	−4.97835	−0.191617
$676$	−7.63014	−0.293467
$677$	12.3968	0.476446	0.238223	−	0.971210i	$-0.423435\pi$
$677$	12.3968	0.476446	0.238223	+	0.971210i	$0.423435\pi$
$678$	−8.95148	−0.343779
$679$	−27.1842	−1.04324
$680$	1.10797	0.0424886
$681$	−47.1277	−1.80594
$682$	0	0
$683$	−42.3879	−1.62193	−0.810963	−	0.585097i	$-0.801056\pi$
$683$	−42.3879	−1.62193	−0.810963	+	0.585097i	$0.801056\pi$
$684$	−5.64121	−0.215697
$685$	−15.5978	−0.595961
$686$	61.5815	2.35119
$687$	1.06917	0.0407915
$688$	−35.1876	−1.34152
$689$	−27.3123	−1.04052
$690$	65.3365	2.48732
$691$	49.1476	1.86966	0.934832	−	0.355091i	$-0.115550\pi$
$691$	49.1476	1.86966	0.934832	+	0.355091i	$0.115550\pi$
$692$	−24.0438	−0.914009
$693$	0	0
$694$	18.7733	0.712626
$695$	22.7966	0.864723
$696$	−1.69090	−0.0640932
$697$	−19.8061	−0.750209
$698$	42.4227	1.60572
$699$	78.3546	2.96364
$700$	8.72827	0.329897
$701$	36.0430	1.36133	0.680663	−	0.732597i	$-0.261692\pi$
$701$	36.0430	1.36133	0.680663	+	0.732597i	$0.261692\pi$
$702$	30.4341	1.14866
$703$	4.98756	0.188110
$704$	0	0
$705$	−41.6391	−1.56822
$706$	−15.6899	−0.590499
$707$	−40.1856	−1.51133
$708$	71.8512	2.70034
$709$	−9.26154	−0.347825	−0.173912	−	0.984761i	$-0.555641\pi$
$709$	−9.26154	−0.347825	−0.173912	+	0.984761i	$0.555641\pi$
$710$	−9.60735	−0.360557
$711$	72.4045	2.71538
$712$	1.01761	0.0381364
$713$	−23.7521	−0.889523
$714$	147.210	5.50919
$715$	0	0
$716$	−13.4730	−0.503510
$717$	8.95449	0.334412
$718$	−0.886186	−0.0330722
$719$	29.9244	1.11599	0.557996	−	0.829843i	$-0.311570\pi$
$719$	29.9244	1.11599	0.557996	+	0.829843i	$0.311570\pi$
$720$	−39.5244	−1.47299
$721$	−56.0225	−2.08639
$722$	37.0563	1.37909
$723$	26.4342	0.983100
$724$	3.13420	0.116482
$725$	6.23308	0.231491
$726$	0	0
$727$	36.4356	1.35132	0.675661	−	0.737212i	$-0.263858\pi$
$727$	36.4356	1.35132	0.675661	+	0.737212i	$0.263858\pi$
$728$	1.30813	0.0484826
$729$	−43.8053	−1.62242
$730$	−40.4652	−1.49769
$731$	49.9308	1.84676
$732$	5.45765	0.201721
$733$	−50.3595	−1.86007	−0.930034	−	0.367472i	$-0.880223\pi$
$733$	−50.3595	−1.86007	−0.930034	+	0.367472i	$0.880223\pi$
$734$	−17.0280	−0.628516
$735$	77.3115	2.85168
$736$	−46.6002	−1.71771
$737$	0	0
$738$	32.6469	1.20175
$739$	31.0703	1.14294	0.571469	−	0.820624i	$-0.306374\pi$
$739$	31.0703	1.14294	0.571469	+	0.820624i	$0.306374\pi$
$740$	−32.5325	−1.19592
$741$	5.05798	0.185810
$742$	82.1145	3.01452
$743$	−21.7324	−0.797283	−0.398641	−	0.917107i	$-0.630518\pi$
$743$	−21.7324	−0.797283	−0.398641	+	0.917107i	$0.630518\pi$
$744$	1.07749	0.0395026
$745$	41.0729	1.50480
$746$	39.7379	1.45491
$747$	57.5313	2.10496
$748$	0	0
$749$	−21.1377	−0.772356
$750$	66.6399	2.43335
$751$	−8.61359	−0.314315	−0.157157	−	0.987574i	$-0.550233\pi$
$751$	−8.61359	−0.314315	−0.157157	+	0.987574i	$0.550233\pi$
$752$	30.4095	1.10892
$753$	−41.8675	−1.52574
$754$	−38.1046	−1.38769
$755$	−5.09116	−0.185286
$756$	−45.1961	−1.64377
$757$	−34.3013	−1.24670	−0.623350	−	0.781943i	$-0.714229\pi$
$757$	−34.3013	−1.24670	−0.623350	+	0.781943i	$0.714229\pi$
$758$	51.8785	1.88431
$759$	0	0
$760$	−0.114453	−0.00415166
$761$	18.2082	0.660047	0.330023	−	0.943973i	$-0.392943\pi$
$761$	18.2082	0.660047	0.330023	+	0.943973i	$0.392943\pi$
$762$	−11.8257	−0.428401
$763$	−32.8941	−1.19085
$764$	34.6525	1.25368
$765$	56.0847	2.02775
$766$	61.6356	2.22698
$767$	−39.6957	−1.43333
$768$	46.7950	1.68857
$769$	33.7334	1.21646	0.608228	−	0.793762i	$-0.291881\pi$
$769$	33.7334	1.21646	0.608228	+	0.793762i	$0.291881\pi$
$770$	0	0
$771$	1.14225	0.0411373
$772$	−13.7202	−0.493801
$773$	−11.6100	−0.417583	−0.208792	−	0.977960i	$-0.566953\pi$
$773$	−11.6100	−0.417583	−0.208792	+	0.977960i	$0.566953\pi$
$774$	−82.3024	−2.95830
$775$	−3.97190	−0.142675
$776$	0.567195	0.0203611
$777$	105.968	3.80159
$778$	−26.1364	−0.937034
$779$	2.04597	0.0733046
$780$	−32.9918	−1.18130
$781$	0	0
$782$	67.7084	2.42125
$783$	−32.2757	−1.15344
$784$	−56.4614	−2.01648
$785$	21.1010	0.753127
$786$	62.2032	2.21872
$787$	29.4955	1.05140	0.525701	−	0.850669i	$-0.323803\pi$
$787$	29.4955	1.05140	0.525701	+	0.850669i	$0.323803\pi$
$788$	−16.4045	−0.584385
$789$	−47.4563	−1.68949
$790$	−59.9202	−2.13186
$791$	−7.34420	−0.261130
$792$	0	0
$793$	−3.01519	−0.107073
$794$	65.3946	2.32077
$795$	50.7718	1.80069
$796$	−21.5209	−0.762787
$797$	29.7901	1.05522	0.527610	−	0.849487i	$-0.323088\pi$
$797$	29.7901	1.05522	0.527610	+	0.849487i	$0.323088\pi$
$798$	−15.2068	−0.538316
$799$	−43.1507	−1.52656
$800$	−7.79262	−0.275511
$801$	51.5107	1.82004
$802$	32.1145	1.13400
$803$	0	0
$804$	58.1942	2.05235
$805$	53.6051	1.88933
$806$	24.2814	0.855275
$807$	−1.87416	−0.0659735
$808$	0.838467	0.0294972
$809$	29.7868	1.04725	0.523624	−	0.851950i	$-0.324580\pi$
$809$	29.7868	1.04725	0.523624	+	0.851950i	$0.324580\pi$
$810$	1.01085	0.0355178
$811$	−13.3172	−0.467630	−0.233815	−	0.972281i	$-0.575121\pi$
$811$	−13.3172	−0.467630	−0.233815	+	0.972281i	$0.575121\pi$
$812$	56.5872	1.98582
$813$	−53.3035	−1.86944
$814$	0	0
$815$	−3.74885	−0.131316
$816$	−66.4733	−2.32703
$817$	−5.15787	−0.180451
$818$	2.14672	0.0750582
$819$	66.2170	2.31381
$820$	−13.3453	−0.466039
$821$	30.9423	1.07989	0.539947	−	0.841699i	$-0.318444\pi$
$821$	30.9423	1.07989	0.539947	+	0.841699i	$0.318444\pi$
$822$	43.2403	1.50818
$823$	37.8161	1.31819	0.659093	−	0.752062i	$-0.270940\pi$
$823$	37.8161	1.31819	0.659093	+	0.752062i	$0.270940\pi$
$824$	1.16890	0.0407206
$825$	0	0
$826$	119.345	4.15255
$827$	−10.2316	−0.355788	−0.177894	−	0.984050i	$-0.556928\pi$
$827$	−10.2316	−0.355788	−0.177894	+	0.984050i	$0.556928\pi$
$828$	−55.1271	−1.91580
$829$	32.6903	1.13538	0.567691	−	0.823242i	$-0.307837\pi$
$829$	32.6903	1.13538	0.567691	+	0.823242i	$0.307837\pi$
$830$	−47.6115	−1.65262
$831$	23.5572	0.817191
$832$	22.9537	0.795775
$833$	80.1180	2.77593
$834$	−63.1968	−2.18833
$835$	−1.79316	−0.0620550
$836$	0	0
$837$	20.5670	0.710899
$838$	−13.5789	−0.469076
$839$	−25.2301	−0.871040	−0.435520	−	0.900179i	$-0.643435\pi$
$839$	−25.2301	−0.871040	−0.435520	+	0.900179i	$0.643435\pi$
$840$	−2.43173	−0.0839028
$841$	11.4104	0.393461
$842$	−39.6314	−1.36579
$843$	0.312353	0.0107580
$844$	14.2027	0.488876
$845$	−7.83621	−0.269574
$846$	71.1266	2.44538
$847$	0	0
$848$	−37.0792	−1.27330
$849$	16.9864	0.582970
$850$	11.3224	0.388355
$851$	48.7396	1.67077
$852$	13.1555	0.450701
$853$	1.17175	0.0401199	0.0200599	−	0.999799i	$-0.493614\pi$
$853$	1.17175	0.0401199	0.0200599	+	0.999799i	$0.493614\pi$
$854$	9.06519	0.310204
$855$	−5.79357	−0.198136
$856$	0.441036	0.0150743
$857$	−45.3547	−1.54929	−0.774644	−	0.632397i	$-0.782071\pi$
$857$	−45.3547	−1.54929	−0.774644	+	0.632397i	$0.782071\pi$
$858$	0	0
$859$	−3.85157	−0.131414	−0.0657069	−	0.997839i	$-0.520930\pi$
$859$	−3.85157	−0.131414	−0.0657069	+	0.997839i	$0.520930\pi$
$860$	33.6433	1.14723
$861$	43.4698	1.48145
$862$	−39.4176	−1.34257
$863$	9.72180	0.330934	0.165467	−	0.986215i	$-0.447087\pi$
$863$	9.72180	0.330934	0.165467	+	0.986215i	$0.447087\pi$
$864$	40.3512	1.37278
$865$	−24.6932	−0.839594
$866$	33.2419	1.12960
$867$	46.7975	1.58933
$868$	−36.0590	−1.22392
$869$	0	0
$870$	70.8340	2.40150
$871$	−32.1506	−1.08938
$872$	0.686331	0.0232421
$873$	28.7111	0.971725
$874$	−6.99430	−0.236586
$875$	54.6744	1.84833
$876$	55.4098	1.87212
$877$	−17.4153	−0.588074	−0.294037	−	0.955794i	$-0.594999\pi$
$877$	−17.4153	−0.588074	−0.294037	+	0.955794i	$0.594999\pi$
$878$	18.5481	0.625969
$879$	−32.5871	−1.09914
$880$	0	0
$881$	−16.6566	−0.561174	−0.280587	−	0.959829i	$-0.590529\pi$
$881$	−16.6566	−0.561174	−0.280587	+	0.959829i	$0.590529\pi$
$882$	−132.061	−4.44672
$883$	12.0297	0.404833	0.202416	−	0.979300i	$-0.435121\pi$
$883$	12.0297	0.404833	0.202416	+	0.979300i	$0.435121\pi$
$884$	−34.1895	−1.14992
$885$	73.7918	2.48048
$886$	−6.99754	−0.235087
$887$	−1.58176	−0.0531104	−0.0265552	−	0.999647i	$-0.508454\pi$
$887$	−1.58176	−0.0531104	−0.0265552	+	0.999647i	$0.508454\pi$
$888$	−2.21101	−0.0741968
$889$	−9.70237	−0.325407
$890$	−42.6290	−1.42893
$891$	0	0
$892$	5.70688	0.191081
$893$	4.45748	0.149164
$894$	−113.863	−3.80814
$895$	−13.8369	−0.462516
$896$	3.46978	0.115917
$897$	49.4277	1.65034
$898$	−74.1630	−2.47485
$899$	−25.7506	−0.858832
$900$	−9.21852	−0.307284
$901$	52.6149	1.75286
$902$	0	0
$903$	−109.587	−3.64682
$904$	0.153236	0.00509655
$905$	3.21885	0.106998
$906$	14.1138	0.468898
$907$	−50.2238	−1.66766	−0.833828	−	0.552025i	$-0.813855\pi$
$907$	−50.2238	−1.66766	−0.833828	+	0.552025i	$0.813855\pi$
$908$	−32.9073	−1.09207
$909$	42.4427	1.40774
$910$	−54.7996	−1.81659
$911$	58.7247	1.94564	0.972819	−	0.231569i	$-0.0743858\pi$
$911$	58.7247	1.94564	0.972819	+	0.231569i	$0.0743858\pi$
$912$	6.86671	0.227380
$913$	0	0
$914$	−26.2058	−0.866811
$915$	5.60505	0.185297
$916$	0.746560	0.0246670
$917$	51.0344	1.68530
$918$	−58.6288	−1.93504
$919$	11.3925	0.375805	0.187903	−	0.982188i	$-0.439831\pi$
$919$	11.3925	0.375805	0.187903	+	0.982188i	$0.439831\pi$
$920$	−1.11846	−0.0368746
$921$	−40.5557	−1.33636
$922$	76.9861	2.53540
$923$	−7.26804	−0.239231
$924$	0	0
$925$	8.15037	0.267982
$926$	−3.74005	−0.122906
$927$	59.1691	1.94337
$928$	−50.5212	−1.65844
$929$	−34.5496	−1.13353	−0.566767	−	0.823878i	$-0.691806\pi$
$929$	−34.5496	−1.13353	−0.566767	+	0.823878i	$0.691806\pi$
$930$	−45.1375	−1.48012
$931$	−8.27622	−0.271242
$932$	54.7119	1.79215
$933$	51.9556	1.70095
$934$	−15.7868	−0.516560
$935$	0	0
$936$	−1.38161	−0.0451593
$937$	−37.2303	−1.21626	−0.608131	−	0.793837i	$-0.708080\pi$
$937$	−37.2303	−1.21626	−0.608131	+	0.793837i	$0.708080\pi$
$938$	96.6609	3.15609
$939$	35.5586	1.16041
$940$	−29.0749	−0.948319
$941$	−43.0573	−1.40363	−0.701814	−	0.712361i	$-0.747626\pi$
$941$	−43.0573	−1.40363	−0.701814	+	0.712361i	$0.747626\pi$
$942$	−58.4964	−1.90591
$943$	19.9937	0.651085
$944$	−53.8909	−1.75400
$945$	−46.4167	−1.50994
$946$	0	0
$947$	14.6542	0.476198	0.238099	−	0.971241i	$-0.423476\pi$
$947$	14.6542	0.476198	0.238099	+	0.971241i	$0.423476\pi$
$948$	82.0498	2.66485
$949$	−30.6123	−0.993718
$950$	−1.16961	−0.0379471
$951$	71.8331	2.32935
$952$	−2.52001	−0.0816740
$953$	46.7114	1.51313	0.756565	−	0.653918i	$-0.226876\pi$
$953$	46.7114	1.51313	0.756565	+	0.653918i	$0.226876\pi$
$954$	−86.7268	−2.80788
$955$	35.5884	1.15161
$956$	6.25256	0.202222
$957$	0	0
$958$	70.4798	2.27710
$959$	35.4763	1.14559
$960$	−42.6693	−1.37715
$961$	−14.5910	−0.470676
$962$	−49.8256	−1.60644
$963$	22.3250	0.719413
$964$	18.4580	0.594491
$965$	−14.0908	−0.453598
$966$	−148.604	−4.78127
$967$	49.2105	1.58250	0.791252	−	0.611491i	$-0.209430\pi$
$967$	49.2105	1.58250	0.791252	+	0.611491i	$0.209430\pi$
$968$	0	0
$969$	−9.74378	−0.313015
$970$	−23.7606	−0.762908
$971$	39.7872	1.27683	0.638416	−	0.769691i	$-0.279590\pi$
$971$	39.7872	1.27683	0.638416	+	0.769691i	$0.279590\pi$
$972$	−31.1188	−0.998134
$973$	−51.8495	−1.66222
$974$	−20.5573	−0.658700
$975$	8.26544	0.264706
$976$	−4.09343	−0.131027
$977$	59.5579	1.90542	0.952712	−	0.303874i	$-0.0982801\pi$
$977$	59.5579	1.90542	0.952712	+	0.303874i	$0.0982801\pi$
$978$	10.3926	0.332318
$979$	0	0
$980$	53.9835	1.72444
$981$	34.7417	1.10922
$982$	34.5876	1.10373
$983$	0.152828	0.00487445	0.00243722	−	0.999997i	$-0.499224\pi$
$983$	0.152828	0.00487445	0.00243722	+	0.999997i	$0.499224\pi$
$984$	−0.906991	−0.0289138
$985$	−16.8475	−0.536807
$986$	73.4054	2.33771
$987$	94.7059	3.01452
$988$	3.53178	0.112361
$989$	−50.4038	−1.60275
$990$	0	0
$991$	38.0372	1.20829	0.604146	−	0.796873i	$-0.293514\pi$
$991$	38.0372	1.20829	0.604146	+	0.796873i	$0.293514\pi$
$992$	32.1936	1.02215
$993$	32.7172	1.03825
$994$	21.8514	0.693084
$995$	−22.1021	−0.700684
$996$	65.1953	2.06579
$997$	35.8902	1.13666	0.568328	−	0.822802i	$-0.307591\pi$
$997$	35.8902	1.13666	0.568328	+	0.822802i	$0.307591\pi$
$998$	0.420040	0.0132961
$999$	−42.2037	−1.33526

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.12		64
11.3	even	5		671.2.j.c.306.7	✓	128
11.4	even	5		671.2.j.c.489.7	yes	128
11.10	odd	2		7381.2.a.u.1.53		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.306.7	✓	128	11.3	even	5
671.2.j.c.489.7	yes	128	11.4	even	5
7381.2.a.u.1.53		64	11.10	odd	2
7381.2.a.v.1.12		64	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)

\(f(q)\)	\(=\)	\(q-1.98800 q^{2} +2.79573 q^{3} +1.95214 q^{4} +2.00486 q^{5} -5.55790 q^{6} -4.55995 q^{7} +0.0951428 q^{8} +4.81608 q^{9} +O(q^{10})\)	\(q-1.98800 q^{2} +2.79573 q^{3} +1.95214 q^{4} +2.00486 q^{5} -5.55790 q^{6} -4.55995 q^{7} +0.0951428 q^{8} +4.81608 q^{9} -3.98567 q^{10} +5.45765 q^{12} -3.01519 q^{13} +9.06519 q^{14} +5.60505 q^{15} -4.09343 q^{16} +5.80852 q^{17} -9.57436 q^{18} -0.600022 q^{19} +3.91378 q^{20} -12.7484 q^{21} -5.86355 q^{23} +0.265993 q^{24} -0.980519 q^{25} +5.99421 q^{26} +5.07726 q^{27} -8.90168 q^{28} -6.35691 q^{29} -11.1428 q^{30} +4.05081 q^{31} +7.94744 q^{32} -11.5473 q^{34} -9.14209 q^{35} +9.40167 q^{36} -8.31230 q^{37} +1.19284 q^{38} -8.42966 q^{39} +0.190748 q^{40} -3.40983 q^{41} +25.3438 q^{42} +8.59613 q^{43} +9.65558 q^{45} +11.6567 q^{46} -7.42886 q^{47} -11.4441 q^{48} +13.7932 q^{49} +1.94927 q^{50} +16.2390 q^{51} -5.88609 q^{52} +9.05823 q^{53} -10.0936 q^{54} -0.433847 q^{56} -1.67750 q^{57} +12.6375 q^{58} +13.1652 q^{59} +10.9418 q^{60} +1.00000 q^{61} -8.05300 q^{62} -21.9611 q^{63} -7.61266 q^{64} -6.04506 q^{65} +10.6629 q^{67} +11.3391 q^{68} -16.3929 q^{69} +18.1745 q^{70} +2.41047 q^{71} +0.458215 q^{72} +10.1527 q^{73} +16.5248 q^{74} -2.74126 q^{75} -1.17133 q^{76} +16.7582 q^{78} +15.0339 q^{79} -8.20676 q^{80} -0.253622 q^{81} +6.77874 q^{82} +11.9457 q^{83} -24.8866 q^{84} +11.6453 q^{85} -17.0891 q^{86} -17.7722 q^{87} +10.6956 q^{89} -19.1953 q^{90} +13.7492 q^{91} -11.4465 q^{92} +11.3249 q^{93} +14.7686 q^{94} -1.20296 q^{95} +22.2189 q^{96} +5.96152 q^{97} -27.4208 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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