LMFDB - Embedded newform 7381.2.a.u.1.31

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			1.31
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)

$f(q)$	$=$	$q-0.160201 q^{2} -1.99014 q^{3} -1.97434 q^{4} +0.944293 q^{5} +0.318822 q^{6} -2.45884 q^{7} +0.636692 q^{8} +0.960669 q^{9} +O(q^{10})$	\(q-0.160201 q^{2} -1.99014 q^{3} -1.97434 q^{4} +0.944293 q^{5} +0.318822 q^{6} -2.45884 q^{7} +0.636692 q^{8} +0.960669 q^{9} -0.151277 q^{10} +3.92921 q^{12} +1.49006 q^{13} +0.393909 q^{14} -1.87928 q^{15} +3.84667 q^{16} +4.43934 q^{17} -0.153900 q^{18} +8.13002 q^{19} -1.86435 q^{20} +4.89345 q^{21} +2.72360 q^{23} -1.26711 q^{24} -4.10831 q^{25} -0.238708 q^{26} +4.05856 q^{27} +4.85458 q^{28} +0.129575 q^{29} +0.301062 q^{30} -6.71223 q^{31} -1.88962 q^{32} -0.711185 q^{34} -2.32187 q^{35} -1.89668 q^{36} +9.55837 q^{37} -1.30243 q^{38} -2.96543 q^{39} +0.601224 q^{40} -2.01868 q^{41} -0.783934 q^{42} +5.42082 q^{43} +0.907154 q^{45} -0.436324 q^{46} +12.1877 q^{47} -7.65543 q^{48} -0.954093 q^{49} +0.658155 q^{50} -8.83492 q^{51} -2.94187 q^{52} -4.25955 q^{53} -0.650184 q^{54} -1.56552 q^{56} -16.1799 q^{57} -0.0207581 q^{58} -1.18350 q^{59} +3.71033 q^{60} -1.00000 q^{61} +1.07530 q^{62} -2.36214 q^{63} -7.39063 q^{64} +1.40705 q^{65} -5.70593 q^{67} -8.76474 q^{68} -5.42036 q^{69} +0.371965 q^{70} -13.8714 q^{71} +0.611650 q^{72} -6.56559 q^{73} -1.53126 q^{74} +8.17613 q^{75} -16.0514 q^{76} +0.475064 q^{78} -1.69050 q^{79} +3.63239 q^{80} -10.9591 q^{81} +0.323394 q^{82} -0.566676 q^{83} -9.66131 q^{84} +4.19204 q^{85} -0.868419 q^{86} -0.257874 q^{87} -2.01271 q^{89} -0.145327 q^{90} -3.66382 q^{91} -5.37731 q^{92} +13.3583 q^{93} -1.95248 q^{94} +7.67712 q^{95} +3.76062 q^{96} +9.22607 q^{97} +0.152847 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.160201	−0.113279	−0.0566395	−	0.998395i	$-0.518039\pi$
$2$	−0.160201	−0.113279	−0.0566395	+	0.998395i	$0.518039\pi$
$3$	−1.99014	−1.14901	−0.574505	−	0.818501i	$-0.694805\pi$
$3$	−1.99014	−1.14901	−0.574505	+	0.818501i	$0.694805\pi$
$4$	−1.97434	−0.987168
$5$	0.944293	0.422301	0.211150	−	0.977454i	$-0.432279\pi$
$5$	0.944293	0.422301	0.211150	+	0.977454i	$0.432279\pi$
$6$	0.318822	0.130159
$7$	−2.45884	−0.929355	−0.464678	−	0.885480i	$-0.653830\pi$
$7$	−2.45884	−0.929355	−0.464678	+	0.885480i	$0.653830\pi$
$8$	0.636692	0.225105
$9$	0.960669	0.320223
$10$	−0.151277	−0.0478378
$11$	0	0
$11$	0	0
$12$	3.92921	1.13427
$13$	1.49006	0.413268	0.206634	−	0.978418i	$-0.433749\pi$
$13$	1.49006	0.413268	0.206634	+	0.978418i	$0.433749\pi$
$14$	0.393909	0.105276
$15$	−1.87928	−0.485228
$16$	3.84667	0.961668
$17$	4.43934	1.07670	0.538349	−	0.842722i	$-0.319048\pi$
$17$	4.43934	1.07670	0.538349	+	0.842722i	$0.319048\pi$
$18$	−0.153900	−0.0362746
$19$	8.13002	1.86515	0.932577	−	0.360972i	$-0.117555\pi$
$19$	8.13002	1.86515	0.932577	+	0.360972i	$0.117555\pi$
$20$	−1.86435	−0.416882
$21$	4.89345	1.06784
$22$	0	0
$23$	2.72360	0.567911	0.283955	−	0.958837i	$-0.408353\pi$
$23$	2.72360	0.567911	0.283955	+	0.958837i	$0.408353\pi$
$24$	−1.26711	−0.258647
$25$	−4.10831	−0.821662
$26$	−0.238708	−0.0468146
$27$	4.05856	0.781070
$28$	4.85458	0.917430
$29$	0.129575	0.0240616	0.0120308	−	0.999928i	$-0.496170\pi$
$29$	0.129575	0.0240616	0.0120308	+	0.999928i	$0.496170\pi$
$30$	0.301062	0.0549661
$31$	−6.71223	−1.20555	−0.602776	−	0.797911i	$-0.705939\pi$
$31$	−6.71223	−1.20555	−0.602776	+	0.797911i	$0.705939\pi$
$32$	−1.88962	−0.334041
$33$	0	0
$34$	−0.711185	−0.121967
$35$	−2.32187	−0.392467
$36$	−1.89668	−0.316114
$37$	9.55837	1.57139	0.785693	−	0.618616i	$-0.212306\pi$
$37$	9.55837	1.57139	0.785693	+	0.618616i	$0.212306\pi$
$38$	−1.30243	−0.211283
$39$	−2.96543	−0.474849
$40$	0.601224	0.0950618
$41$	−2.01868	−0.315265	−0.157633	−	0.987498i	$-0.550386\pi$
$41$	−2.01868	−0.315265	−0.157633	+	0.987498i	$0.550386\pi$
$42$	−0.783934	−0.120964
$43$	5.42082	0.826667	0.413333	−	0.910580i	$-0.364364\pi$
$43$	5.42082	0.826667	0.413333	+	0.910580i	$0.364364\pi$
$44$	0	0
$45$	0.907154	0.135230
$46$	−0.436324	−0.0643324
$47$	12.1877	1.77776	0.888880	−	0.458140i	$-0.151484\pi$
$47$	12.1877	1.77776	0.888880	+	0.458140i	$0.151484\pi$
$48$	−7.65543	−1.10497
$49$	−0.954093	−0.136299
$50$	0.658155	0.0930771
$51$	−8.83492	−1.23714
$52$	−2.94187	−0.407965
$53$	−4.25955	−0.585094	−0.292547	−	0.956251i	$-0.594503\pi$
$53$	−4.25955	−0.585094	−0.292547	+	0.956251i	$0.594503\pi$
$54$	−0.650184	−0.0884789
$55$	0	0
$56$	−1.56552	−0.209202
$57$	−16.1799	−2.14308
$58$	−0.0207581	−0.00272567
$59$	−1.18350	−0.154078	−0.0770390	−	0.997028i	$-0.524547\pi$
$59$	−1.18350	−0.154078	−0.0770390	+	0.997028i	$0.524547\pi$
$60$	3.71033	0.479001
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	1.07530	0.136564
$63$	−2.36214	−0.297601
$64$	−7.39063	−0.923828
$65$	1.40705	0.174523
$66$	0	0
$67$	−5.70593	−0.697090	−0.348545	−	0.937292i	$-0.613324\pi$
$67$	−5.70593	−0.697090	−0.348545	+	0.937292i	$0.613324\pi$
$68$	−8.76474	−1.06288
$69$	−5.42036	−0.652535
$70$	0.371965	0.0444583
$71$	−13.8714	−1.64624	−0.823118	−	0.567870i	$-0.807768\pi$
$71$	−13.8714	−1.64624	−0.823118	+	0.567870i	$0.807768\pi$
$72$	0.611650	0.0720837
$73$	−6.56559	−0.768444	−0.384222	−	0.923241i	$-0.625530\pi$
$73$	−6.56559	−0.768444	−0.384222	+	0.923241i	$0.625530\pi$
$74$	−1.53126	−0.178005
$75$	8.17613	0.944098
$76$	−16.0514	−1.84122
$77$	0	0
$78$	0.475064	0.0537904
$79$	−1.69050	−0.190196	−0.0950978	−	0.995468i	$-0.530316\pi$
$79$	−1.69050	−0.190196	−0.0950978	+	0.995468i	$0.530316\pi$
$80$	3.63239	0.406113
$81$	−10.9591	−1.21768
$82$	0.323394	0.0357129
$83$	−0.566676	−0.0622008	−0.0311004	−	0.999516i	$-0.509901\pi$
$83$	−0.566676	−0.0622008	−0.0311004	+	0.999516i	$0.509901\pi$
$84$	−9.66131	−1.05414
$85$	4.19204	0.454690
$86$	−0.868419	−0.0936440
$87$	−0.257874	−0.0276470
$88$	0	0
$89$	−2.01271	−0.213347	−0.106673	−	0.994294i	$-0.534020\pi$
$89$	−2.01271	−0.213347	−0.106673	+	0.994294i	$0.534020\pi$
$90$	−0.145327	−0.0153188
$91$	−3.66382	−0.384072
$92$	−5.37731	−0.560623
$93$	13.3583	1.38519
$94$	−1.95248	−0.201383
$95$	7.67712	0.787656
$96$	3.76062	0.383817
$97$	9.22607	0.936765	0.468383	−	0.883526i	$-0.344837\pi$
$97$	9.22607	0.936765	0.468383	+	0.883526i	$0.344837\pi$
$98$	0.152847	0.0154398
$99$	0	0
$100$	8.11118	0.811118
$101$	17.0193	1.69349	0.846744	−	0.532001i	$-0.178560\pi$
$101$	17.0193	1.69349	0.846744	+	0.532001i	$0.178560\pi$
$102$	1.41536	0.140142
$103$	16.9074	1.66594	0.832969	−	0.553320i	$-0.186639\pi$
$103$	16.9074	1.66594	0.832969	+	0.553320i	$0.186639\pi$
$104$	0.948707	0.0930284
$105$	4.62085	0.450949
$106$	0.682383	0.0662789
$107$	1.43952	0.139163	0.0695817	−	0.997576i	$-0.477834\pi$
$107$	1.43952	0.139163	0.0695817	+	0.997576i	$0.477834\pi$
$108$	−8.01296	−0.771047
$109$	−7.46538	−0.715054	−0.357527	−	0.933903i	$-0.616380\pi$
$109$	−7.46538	−0.715054	−0.357527	+	0.933903i	$0.616380\pi$
$110$	0	0
$111$	−19.0225	−1.80554
$112$	−9.45836	−0.893731
$113$	−6.21092	−0.584275	−0.292137	−	0.956376i	$-0.594366\pi$
$113$	−6.21092	−0.584275	−0.292137	+	0.956376i	$0.594366\pi$
$114$	2.59203	0.242766
$115$	2.57188	0.239829
$116$	−0.255825	−0.0237528
$117$	1.43145	0.132338
$118$	0.189597	0.0174538
$119$	−10.9156	−1.00063
$120$	−1.19652	−0.109227
$121$	0	0
$122$	0.160201	0.0145039
$123$	4.01746	0.362243
$124$	13.2522	1.19008
$125$	−8.60092	−0.769289
$126$	0.378416	0.0337120
$127$	3.89454	0.345585	0.172792	−	0.984958i	$-0.444721\pi$
$127$	3.89454	0.345585	0.172792	+	0.984958i	$0.444721\pi$
$128$	4.96323	0.438692
$129$	−10.7882	−0.949848
$130$	−0.225411	−0.0197698
$131$	5.02079	0.438669	0.219334	−	0.975650i	$-0.429611\pi$
$131$	5.02079	0.438669	0.219334	+	0.975650i	$0.429611\pi$
$132$	0	0
$133$	−19.9904	−1.73339
$134$	0.914094	0.0789657
$135$	3.83247	0.329847
$136$	2.82649	0.242369
$137$	16.9186	1.44545	0.722726	−	0.691135i	$-0.242889\pi$
$137$	16.9186	1.44545	0.722726	+	0.691135i	$0.242889\pi$
$138$	0.868346	0.0739186
$139$	−22.8309	−1.93649	−0.968244	−	0.250007i	$-0.919567\pi$
$139$	−22.8309	−1.93649	−0.968244	+	0.250007i	$0.919567\pi$
$140$	4.58415	0.387431
$141$	−24.2553	−2.04266
$142$	2.22221	0.186484
$143$	0	0
$144$	3.69538	0.307948
$145$	0.122357	0.0101612
$146$	1.05181	0.0870486
$147$	1.89878	0.156609
$148$	−18.8714	−1.55122
$149$	8.87344	0.726941	0.363470	−	0.931606i	$-0.381592\pi$
$149$	8.87344	0.726941	0.363470	+	0.931606i	$0.381592\pi$
$150$	−1.30982	−0.106946
$151$	5.51819	0.449064	0.224532	−	0.974467i	$-0.427915\pi$
$151$	5.51819	0.449064	0.224532	+	0.974467i	$0.427915\pi$
$152$	5.17631	0.419854
$153$	4.26474	0.344783
$154$	0	0
$155$	−6.33831	−0.509105
$156$	5.85475	0.468755
$157$	−14.1464	−1.12900	−0.564502	−	0.825431i	$-0.690932\pi$
$157$	−14.1464	−1.12900	−0.564502	+	0.825431i	$0.690932\pi$
$158$	0.270819	0.0215452
$159$	8.47711	0.672278
$160$	−1.78436	−0.141066
$161$	−6.69691	−0.527791
$162$	1.75566	0.137938
$163$	9.87155	0.773200	0.386600	−	0.922248i	$-0.373649\pi$
$163$	9.87155	0.773200	0.386600	+	0.922248i	$0.373649\pi$
$164$	3.98555	0.311220
$165$	0	0
$166$	0.0907820	0.00704605
$167$	23.0318	1.78225	0.891127	−	0.453754i	$-0.149915\pi$
$167$	23.0318	1.78225	0.891127	+	0.453754i	$0.149915\pi$
$168$	3.11562	0.240375
$169$	−10.7797	−0.829210
$170$	−0.671568	−0.0515069
$171$	7.81026	0.597265
$172$	−10.7025	−0.816059
$173$	−17.3046	−1.31565	−0.657824	−	0.753172i	$-0.728523\pi$
$173$	−17.3046	−1.31565	−0.657824	+	0.753172i	$0.728523\pi$
$174$	0.0413116	0.00313182
$175$	10.1017	0.763616
$176$	0	0
$177$	2.35533	0.177037
$178$	0.322437	0.0241677
$179$	−0.174246	−0.0130238	−0.00651189	−	0.999979i	$-0.502073\pi$
$179$	−0.174246	−0.0130238	−0.00651189	+	0.999979i	$0.502073\pi$
$180$	−1.79103	−0.133495
$181$	−11.4415	−0.850442	−0.425221	−	0.905090i	$-0.639804\pi$
$181$	−11.4415	−0.850442	−0.425221	+	0.905090i	$0.639804\pi$
$182$	0.586946	0.0435074
$183$	1.99014	0.147116
$184$	1.73410	0.127839
$185$	9.02591	0.663598
$186$	−2.14001	−0.156913
$187$	0	0
$188$	−24.0626	−1.75495
$189$	−9.97936	−0.725892
$190$	−1.22988	−0.0892249
$191$	−22.9972	−1.66402	−0.832011	−	0.554759i	$-0.812810\pi$
$191$	−22.9972	−1.66402	−0.832011	+	0.554759i	$0.812810\pi$
$192$	14.7084	1.06149
$193$	6.43492	0.463196	0.231598	−	0.972812i	$-0.425605\pi$
$193$	6.43492	0.463196	0.231598	+	0.972812i	$0.425605\pi$
$194$	−1.47802	−0.106116
$195$	−2.80023	−0.200529
$196$	1.88370	0.134550
$197$	−2.27791	−0.162294	−0.0811472	−	0.996702i	$-0.525858\pi$
$197$	−2.27791	−0.162294	−0.0811472	+	0.996702i	$0.525858\pi$
$198$	0	0
$199$	17.6788	1.25322	0.626610	−	0.779333i	$-0.284442\pi$
$199$	17.6788	1.25322	0.626610	+	0.779333i	$0.284442\pi$
$200$	−2.61573	−0.184960
$201$	11.3556	0.800963
$202$	−2.72651	−0.191837
$203$	−0.318606	−0.0223617
$204$	17.4431	1.22126
$205$	−1.90623	−0.133137
$206$	−2.70858	−0.188716
$207$	2.61648	0.181858
$208$	5.73176	0.397426
$209$	0	0
$210$	−0.740264	−0.0510831
$211$	2.50617	0.172532	0.0862659	−	0.996272i	$-0.472507\pi$
$211$	2.50617	0.172532	0.0862659	+	0.996272i	$0.472507\pi$
$212$	8.40977	0.577586
$213$	27.6061	1.89154
$214$	−0.230612	−0.0157643
$215$	5.11884	0.349102
$216$	2.58405	0.175822
$217$	16.5043	1.12039
$218$	1.19596	0.0810006
$219$	13.0665	0.882950
$220$	0	0
$221$	6.61487	0.444964
$222$	3.04742	0.204530
$223$	18.8877	1.26481	0.632407	−	0.774637i	$-0.282067\pi$
$223$	18.8877	1.26481	0.632407	+	0.774637i	$0.282067\pi$
$224$	4.64629	0.310443
$225$	−3.94673	−0.263115
$226$	0.994995	0.0661861
$227$	−13.9957	−0.928924	−0.464462	−	0.885593i	$-0.653752\pi$
$227$	−13.9957	−0.928924	−0.464462	+	0.885593i	$0.653752\pi$
$228$	31.9445	2.11558
$229$	8.23448	0.544149	0.272075	−	0.962276i	$-0.412290\pi$
$229$	8.23448	0.544149	0.272075	+	0.962276i	$0.412290\pi$
$230$	−0.412017	−0.0271676
$231$	0	0
$232$	0.0824996	0.00541636
$233$	2.69478	0.176541	0.0882704	−	0.996097i	$-0.471866\pi$
$233$	2.69478	0.176541	0.0882704	+	0.996097i	$0.471866\pi$
$234$	−0.229320	−0.0149911
$235$	11.5088	0.750749
$236$	2.33662	0.152101
$237$	3.36433	0.218537
$238$	1.74869	0.113351
$239$	5.82241	0.376620	0.188310	−	0.982110i	$-0.439699\pi$
$239$	5.82241	0.376620	0.188310	+	0.982110i	$0.439699\pi$
$240$	−7.22897	−0.466628
$241$	26.8223	1.72778	0.863890	−	0.503681i	$-0.168021\pi$
$241$	26.8223	1.72778	0.863890	+	0.503681i	$0.168021\pi$
$242$	0	0
$243$	9.63454	0.618056
$244$	1.97434	0.126394
$245$	−0.900944	−0.0575592
$246$	−0.643601	−0.0410345
$247$	12.1142	0.770808
$248$	−4.27362	−0.271375
$249$	1.12777	0.0714693
$250$	1.37787	0.0871444
$251$	16.7295	1.05596	0.527979	−	0.849258i	$-0.322950\pi$
$251$	16.7295	1.05596	0.527979	+	0.849258i	$0.322950\pi$
$252$	4.66365	0.293782
$253$	0	0
$254$	−0.623909	−0.0391475
$255$	−8.34275	−0.522443
$256$	13.9861	0.874134
$257$	−19.7602	−1.23261	−0.616305	−	0.787508i	$-0.711371\pi$
$257$	−19.7602	−1.23261	−0.616305	+	0.787508i	$0.711371\pi$
$258$	1.72828	0.107598
$259$	−23.5025	−1.46038
$260$	−2.77799	−0.172284
$261$	0.124479	0.00770507
$262$	−0.804335	−0.0496920
$263$	−14.9063	−0.919162	−0.459581	−	0.888136i	$-0.652000\pi$
$263$	−14.9063	−0.919162	−0.459581	+	0.888136i	$0.652000\pi$
$264$	0	0
$265$	−4.02226	−0.247086
$266$	3.20248	0.196357
$267$	4.00558	0.245137
$268$	11.2654	0.688145
$269$	25.0288	1.52603	0.763015	−	0.646380i	$-0.223718\pi$
$269$	25.0288	1.52603	0.763015	+	0.646380i	$0.223718\pi$
$270$	−0.613965	−0.0373647
$271$	22.1508	1.34557	0.672783	−	0.739840i	$-0.265099\pi$
$271$	22.1508	1.34557	0.672783	+	0.739840i	$0.265099\pi$
$272$	17.0767	1.03543
$273$	7.29152	0.441303
$274$	−2.71037	−0.163739
$275$	0	0
$276$	10.7016	0.644162
$277$	−28.9218	−1.73774	−0.868871	−	0.495038i	$-0.835154\pi$
$277$	−28.9218	−1.73774	−0.868871	+	0.495038i	$0.835154\pi$
$278$	3.65752	0.219364
$279$	−6.44823	−0.386046
$280$	−1.47831	−0.0883462
$281$	−18.0958	−1.07950	−0.539752	−	0.841824i	$-0.681482\pi$
$281$	−18.0958	−1.07950	−0.539752	+	0.841824i	$0.681482\pi$
$282$	3.88572	0.231391
$283$	−6.65551	−0.395629	−0.197815	−	0.980239i	$-0.563384\pi$
$283$	−6.65551	−0.395629	−0.197815	+	0.980239i	$0.563384\pi$
$284$	27.3869	1.62511
$285$	−15.2786	−0.905024
$286$	0	0
$287$	4.96362	0.292993
$288$	−1.81530	−0.106968
$289$	2.70772	0.159278
$290$	−0.0196017	−0.00115105
$291$	−18.3612	−1.07635
$292$	12.9627	0.758583
$293$	−24.0011	−1.40216	−0.701080	−	0.713083i	$-0.747298\pi$
$293$	−24.0011	−1.40216	−0.701080	+	0.713083i	$0.747298\pi$
$294$	−0.304186	−0.0177405
$295$	−1.11757	−0.0650673
$296$	6.08574	0.353726
$297$	0	0
$298$	−1.42153	−0.0823472
$299$	4.05833	0.234699
$300$	−16.1424	−0.931983
$301$	−13.3289	−0.768267
$302$	−0.884018	−0.0508695
$303$	−33.8709	−1.94583
$304$	31.2735	1.79366
$305$	−0.944293	−0.0540701
$306$	−0.683214	−0.0390568
$307$	−12.4957	−0.713169	−0.356584	−	0.934263i	$-0.616059\pi$
$307$	−12.4957	−0.713169	−0.356584	+	0.934263i	$0.616059\pi$
$308$	0	0
$309$	−33.6482	−1.91418
$310$	1.01540	0.0576710
$311$	3.13143	0.177567	0.0887836	−	0.996051i	$-0.471702\pi$
$311$	3.13143	0.177567	0.0887836	+	0.996051i	$0.471702\pi$
$312$	−1.88806	−0.106891
$313$	21.0389	1.18919	0.594593	−	0.804027i	$-0.297313\pi$
$313$	21.0389	1.18919	0.594593	+	0.804027i	$0.297313\pi$
$314$	2.26626	0.127893
$315$	−2.23055	−0.125677
$316$	3.33761	0.187755
$317$	16.9026	0.949343	0.474672	−	0.880163i	$-0.342567\pi$
$317$	16.9026	0.949343	0.474672	+	0.880163i	$0.342567\pi$
$318$	−1.35804	−0.0761551
$319$	0	0
$320$	−6.97892	−0.390133
$321$	−2.86484	−0.159900
$322$	1.07285	0.0597877
$323$	36.0919	2.00821
$324$	21.6370	1.20205
$325$	−6.12162	−0.339566
$326$	−1.58143	−0.0875873
$327$	14.8572	0.821604
$328$	−1.28528	−0.0709676
$329$	−29.9677	−1.65217
$330$	0	0
$331$	−9.05971	−0.497967	−0.248983	−	0.968508i	$-0.580096\pi$
$331$	−9.05971	−0.497967	−0.248983	+	0.968508i	$0.580096\pi$
$332$	1.11881	0.0614027
$333$	9.18244	0.503194
$334$	−3.68971	−0.201892
$335$	−5.38807	−0.294382
$336$	18.8235	1.02691
$337$	−7.83185	−0.426628	−0.213314	−	0.976984i	$-0.568426\pi$
$337$	−7.83185	−0.426628	−0.213314	+	0.976984i	$0.568426\pi$
$338$	1.72692	0.0939321
$339$	12.3606	0.671337
$340$	−8.27649	−0.448856
$341$	0	0
$342$	−1.25121	−0.0676577
$343$	19.5579	1.05603
$344$	3.45139	0.186086
$345$	−5.11841	−0.275566
$346$	2.77222	0.149035
$347$	−29.8251	−1.60110	−0.800548	−	0.599268i	$-0.795458\pi$
$347$	−29.8251	−1.60110	−0.800548	+	0.599268i	$0.795458\pi$
$348$	0.509129	0.0272922
$349$	25.0554	1.34118	0.670592	−	0.741826i	$-0.266040\pi$
$349$	25.0554	1.34118	0.670592	+	0.741826i	$0.266040\pi$
$350$	−1.61830	−0.0865017
$351$	6.04749	0.322791
$352$	0	0
$353$	−11.1541	−0.593671	−0.296835	−	0.954929i	$-0.595931\pi$
$353$	−11.1541	−0.593671	−0.296835	+	0.954929i	$0.595931\pi$
$354$	−0.377325	−0.0200546
$355$	−13.0987	−0.695207
$356$	3.97376	0.210609
$357$	21.7237	1.14974
$358$	0.0279144	0.00147532
$359$	−5.42920	−0.286542	−0.143271	−	0.989683i	$-0.545762\pi$
$359$	−5.42920	−0.286542	−0.143271	+	0.989683i	$0.545762\pi$
$360$	0.577577	0.0304410
$361$	47.0972	2.47880
$362$	1.83294	0.0963372
$363$	0	0
$364$	7.23361	0.379144
$365$	−6.19984	−0.324515
$366$	−0.318822	−0.0166651
$367$	4.29312	0.224099	0.112050	−	0.993703i	$-0.464258\pi$
$367$	4.29312	0.224099	0.112050	+	0.993703i	$0.464258\pi$
$368$	10.4768	0.546142
$369$	−1.93929	−0.100955
$370$	−1.44596	−0.0751717
$371$	10.4736	0.543760
$372$	−26.3738	−1.36742
$373$	−10.9013	−0.564450	−0.282225	−	0.959348i	$-0.591072\pi$
$373$	−10.9013	−0.564450	−0.282225	+	0.959348i	$0.591072\pi$
$374$	0	0
$375$	17.1171	0.883921
$376$	7.75981	0.400182
$377$	0.193075	0.00994386
$378$	1.59870	0.0822283
$379$	17.1139	0.879084	0.439542	−	0.898222i	$-0.355141\pi$
$379$	17.1139	0.879084	0.439542	+	0.898222i	$0.355141\pi$
$380$	−15.1572	−0.777548
$381$	−7.75070	−0.397080
$382$	3.68418	0.188499
$383$	30.5201	1.55950	0.779751	−	0.626089i	$-0.215345\pi$
$383$	30.5201	1.55950	0.779751	+	0.626089i	$0.215345\pi$
$384$	−9.87754	−0.504061
$385$	0	0
$386$	−1.03088	−0.0524704
$387$	5.20761	0.264718
$388$	−18.2154	−0.924744
$389$	2.52152	0.127846	0.0639231	−	0.997955i	$-0.479639\pi$
$389$	2.52152	0.127846	0.0639231	+	0.997955i	$0.479639\pi$
$390$	0.448600	0.0227157
$391$	12.0910	0.611468
$392$	−0.607463	−0.0306815
$393$	−9.99210	−0.504035
$394$	0.364923	0.0183845
$395$	−1.59632	−0.0803197
$396$	0	0
$397$	23.7002	1.18948	0.594739	−	0.803919i	$-0.297255\pi$
$397$	23.7002	1.18948	0.594739	+	0.803919i	$0.297255\pi$
$398$	−2.83216	−0.141964
$399$	39.7838	1.99168
$400$	−15.8033	−0.790166
$401$	29.0075	1.44857	0.724283	−	0.689503i	$-0.242171\pi$
$401$	29.0075	1.44857	0.724283	+	0.689503i	$0.242171\pi$
$402$	−1.81918	−0.0907324
$403$	−10.0016	−0.498216
$404$	−33.6019	−1.67176
$405$	−10.3486	−0.514227
$406$	0.0510409	0.00253312
$407$	0	0
$408$	−5.62512	−0.278485
$409$	−33.0563	−1.63453	−0.817265	−	0.576262i	$-0.804511\pi$
$409$	−33.0563	−1.63453	−0.817265	+	0.576262i	$0.804511\pi$
$410$	0.305379	0.0150816
$411$	−33.6704	−1.66084
$412$	−33.3809	−1.64456
$413$	2.91003	0.143193
$414$	−0.419163	−0.0206007
$415$	−0.535109	−0.0262675
$416$	−2.81565	−0.138048
$417$	45.4367	2.22504
$418$	0	0
$419$	20.3884	0.996041	0.498020	−	0.867165i	$-0.334061\pi$
$419$	20.3884	0.996041	0.498020	+	0.867165i	$0.334061\pi$
$420$	−9.12311	−0.445162
$421$	4.42114	0.215473	0.107737	−	0.994179i	$-0.465640\pi$
$421$	4.42114	0.215473	0.107737	+	0.994179i	$0.465640\pi$
$422$	−0.401490	−0.0195442
$423$	11.7084	0.569280
$424$	−2.71202	−0.131707
$425$	−18.2382	−0.884681
$426$	−4.42253	−0.214272
$427$	2.45884	0.118992
$428$	−2.84209	−0.137378
$429$	0	0
$430$	−0.820042	−0.0395460
$431$	−14.6916	−0.707671	−0.353835	−	0.935308i	$-0.615123\pi$
$431$	−14.6916	−0.707671	−0.353835	+	0.935308i	$0.615123\pi$
$432$	15.6120	0.751130
$433$	−3.42961	−0.164816	−0.0824082	−	0.996599i	$-0.526261\pi$
$433$	−3.42961	−0.164816	−0.0824082	+	0.996599i	$0.526261\pi$
$434$	−2.64400	−0.126916
$435$	−0.243508	−0.0116753
$436$	14.7392	0.705878
$437$	22.1429	1.05924
$438$	−2.09326	−0.100020
$439$	2.87188	0.137067	0.0685337	−	0.997649i	$-0.478168\pi$
$439$	2.87188	0.137067	0.0685337	+	0.997649i	$0.478168\pi$
$440$	0	0
$441$	−0.916568	−0.0436461
$442$	−1.05971	−0.0504051
$443$	−10.9468	−0.520096	−0.260048	−	0.965596i	$-0.583738\pi$
$443$	−10.9468	−0.520096	−0.260048	+	0.965596i	$0.583738\pi$
$444$	37.5569	1.78237
$445$	−1.90059	−0.0900965
$446$	−3.02582	−0.143277
$447$	−17.6594	−0.835262
$448$	18.1724	0.858565
$449$	8.44948	0.398756	0.199378	−	0.979923i	$-0.436108\pi$
$449$	8.44948	0.398756	0.199378	+	0.979923i	$0.436108\pi$
$450$	0.632269	0.0298054
$451$	0	0
$452$	12.2624	0.576777
$453$	−10.9820	−0.515978
$454$	2.24211	0.105228
$455$	−3.45972	−0.162194
$456$	−10.3016	−0.482417
$457$	−34.9160	−1.63330	−0.816650	−	0.577134i	$-0.804171\pi$
$457$	−34.9160	−1.63330	−0.816650	+	0.577134i	$0.804171\pi$
$458$	−1.31917	−0.0616407
$459$	18.0173	0.840976
$460$	−5.07776	−0.236752
$461$	13.1355	0.611783	0.305892	−	0.952066i	$-0.401045\pi$
$461$	13.1355	0.611783	0.305892	+	0.952066i	$0.401045\pi$
$462$	0	0
$463$	4.51104	0.209646	0.104823	−	0.994491i	$-0.466572\pi$
$463$	4.51104	0.209646	0.104823	+	0.994491i	$0.466572\pi$
$464$	0.498434	0.0231392
$465$	12.6141	0.584967
$466$	−0.431706	−0.0199984
$467$	−11.7603	−0.544202	−0.272101	−	0.962269i	$-0.587718\pi$
$467$	−11.7603	−0.544202	−0.272101	+	0.962269i	$0.587718\pi$
$468$	−2.82617	−0.130640
$469$	14.0300	0.647844
$470$	−1.84371	−0.0850442
$471$	28.1533	1.29724
$472$	−0.753522	−0.0346837
$473$	0	0
$474$	−0.538968	−0.0247556
$475$	−33.4006	−1.53253
$476$	21.5511	0.987794
$477$	−4.09202	−0.187361
$478$	−0.932755	−0.0426632
$479$	30.8171	1.40807	0.704033	−	0.710167i	$-0.251380\pi$
$479$	30.8171	1.40807	0.704033	+	0.710167i	$0.251380\pi$
$480$	3.55113	0.162086
$481$	14.2425	0.649403
$482$	−4.29696	−0.195721
$483$	13.3278	0.606437
$484$	0	0
$485$	8.71211	0.395597
$486$	−1.54346	−0.0700128
$487$	9.25458	0.419365	0.209682	−	0.977770i	$-0.432757\pi$
$487$	9.25458	0.419365	0.209682	+	0.977770i	$0.432757\pi$
$488$	−0.636692	−0.0288217
$489$	−19.6458	−0.888414
$490$	0.144332	0.00652025
$491$	−31.1017	−1.40360	−0.701801	−	0.712373i	$-0.747620\pi$
$491$	−31.1017	−1.40360	−0.701801	+	0.712373i	$0.747620\pi$
$492$	−7.93182	−0.357594
$493$	0.575229	0.0259070
$494$	−1.94070	−0.0873164
$495$	0	0
$496$	−25.8197	−1.15934
$497$	34.1077	1.52994
$498$	−0.180669	−0.00809598
$499$	33.1250	1.48288	0.741439	−	0.671020i	$-0.234144\pi$
$499$	33.1250	1.48288	0.741439	+	0.671020i	$0.234144\pi$
$500$	16.9811	0.759418
$501$	−45.8366	−2.04783
$502$	−2.68008	−0.119618
$503$	7.11565	0.317271	0.158636	−	0.987337i	$-0.449290\pi$
$503$	7.11565	0.317271	0.158636	+	0.987337i	$0.449290\pi$
$504$	−1.50395	−0.0669913
$505$	16.0713	0.715161
$506$	0	0
$507$	21.4532	0.952770
$508$	−7.68914	−0.341150
$509$	0.658501	0.0291875	0.0145938	−	0.999894i	$-0.495354\pi$
$509$	0.658501	0.0291875	0.0145938	+	0.999894i	$0.495354\pi$
$510$	1.33652	0.0591819
$511$	16.1437	0.714157
$512$	−12.1671	−0.537713
$513$	32.9962	1.45682
$514$	3.16560	0.139629
$515$	15.9656	0.703527
$516$	21.2995	0.937659
$517$	0	0
$518$	3.76512	0.165430
$519$	34.4387	1.51169
$520$	0.895858	0.0392860
$521$	−40.5892	−1.77825	−0.889123	−	0.457669i	$-0.848684\pi$
$521$	−40.5892	−1.77825	−0.889123	+	0.457669i	$0.848684\pi$
$522$	−0.0199417	−0.000872823 0
$523$	−0.978083	−0.0427686	−0.0213843	−	0.999771i	$-0.506807\pi$
$523$	−0.978083	−0.0427686	−0.0213843	+	0.999771i	$0.506807\pi$
$524$	−9.91273	−0.433040
$525$	−20.1038	−0.877402
$526$	2.38800	0.104122
$527$	−29.7978	−1.29801
$528$	0	0
$529$	−15.5820	−0.677477
$530$	0.644369	0.0279896
$531$	−1.13695	−0.0493394
$532$	39.4678	1.71115
$533$	−3.00795	−0.130289
$534$	−0.641697	−0.0277689
$535$	1.35933	0.0587688
$536$	−3.63292	−0.156918
$537$	0.346775	0.0149644
$538$	−4.00963	−0.172867
$539$	0	0
$540$	−7.56658	−0.325614
$541$	20.3077	0.873098	0.436549	−	0.899681i	$-0.356201\pi$
$541$	20.3077	0.873098	0.436549	+	0.899681i	$0.356201\pi$
$542$	−3.54858	−0.152425
$543$	22.7703	0.977166
$544$	−8.38868	−0.359662
$545$	−7.04951	−0.301968
$546$	−1.16811	−0.0499904
$547$	39.3824	1.68387	0.841936	−	0.539578i	$-0.181416\pi$
$547$	39.3824	1.68387	0.841936	+	0.539578i	$0.181416\pi$
$548$	−33.4030	−1.42690
$549$	−0.960669	−0.0410004
$550$	0	0
$551$	1.05345	0.0448785
$552$	−3.45110	−0.146889
$553$	4.15666	0.176759
$554$	4.63330	0.196850
$555$	−17.9628	−0.762480
$556$	45.0758	1.91164
$557$	−22.6890	−0.961364	−0.480682	−	0.876895i	$-0.659611\pi$
$557$	−22.6890	−0.961364	−0.480682	+	0.876895i	$0.659611\pi$
$558$	1.03301	0.0437309
$559$	8.07733	0.341635
$560$	−8.93147	−0.377423
$561$	0	0
$562$	2.89896	0.122285
$563$	43.1631	1.81911	0.909554	−	0.415586i	$-0.136423\pi$
$563$	43.1631	1.81911	0.909554	+	0.415586i	$0.136423\pi$
$564$	47.8881	2.01645
$565$	−5.86493	−0.246740
$566$	1.06622	0.0448165
$567$	26.9468	1.13166
$568$	−8.83183	−0.370575
$569$	4.60536	0.193067	0.0965333	−	0.995330i	$-0.469225\pi$
$569$	4.60536	0.193067	0.0965333	+	0.995330i	$0.469225\pi$
$570$	2.44764	0.102520
$571$	2.33936	0.0978991	0.0489495	−	0.998801i	$-0.484413\pi$
$571$	2.33936	0.0978991	0.0489495	+	0.998801i	$0.484413\pi$
$572$	0	0
$573$	45.7678	1.91198
$574$	−0.795176	−0.0331900
$575$	−11.1894	−0.466631
$576$	−7.09995	−0.295831
$577$	−16.0826	−0.669528	−0.334764	−	0.942302i	$-0.608657\pi$
$577$	−16.0826	−0.669528	−0.334764	+	0.942302i	$0.608657\pi$
$578$	−0.433779	−0.0180428
$579$	−12.8064	−0.532216
$580$	−0.241574	−0.0100308
$581$	1.39337	0.0578067
$582$	2.94148	0.121928
$583$	0	0
$584$	−4.18026	−0.172980
$585$	1.35171	0.0558864
$586$	3.84500	0.158835
$587$	−10.1005	−0.416891	−0.208445	−	0.978034i	$-0.566840\pi$
$587$	−10.1005	−0.416891	−0.208445	+	0.978034i	$0.566840\pi$
$588$	−3.74883	−0.154599
$589$	−54.5705	−2.24854
$590$	0.179035	0.00737076
$591$	4.53337	0.186478
$592$	36.7679	1.51115
$593$	36.4212	1.49564	0.747820	−	0.663902i	$-0.231101\pi$
$593$	36.4212	1.49564	0.747820	+	0.663902i	$0.231101\pi$
$594$	0	0
$595$	−10.3076	−0.422569
$596$	−17.5192	−0.717613
$597$	−35.1834	−1.43996
$598$	−0.650147	−0.0265865
$599$	35.0428	1.43181	0.715906	−	0.698197i	$-0.246014\pi$
$599$	35.0428	1.43181	0.715906	+	0.698197i	$0.246014\pi$
$600$	5.20567	0.212521
$601$	38.6817	1.57786	0.788929	−	0.614485i	$-0.210636\pi$
$601$	38.6817	1.57786	0.788929	+	0.614485i	$0.210636\pi$
$602$	2.13531	0.0870286
$603$	−5.48151	−0.223224
$604$	−10.8948	−0.443301
$605$	0	0
$606$	5.42615	0.220422
$607$	11.6556	0.473086	0.236543	−	0.971621i	$-0.423986\pi$
$607$	11.6556	0.473086	0.236543	+	0.971621i	$0.423986\pi$
$608$	−15.3627	−0.623038
$609$	0.634071	0.0256938
$610$	0.151277	0.00612501
$611$	18.1604	0.734691
$612$	−8.42002	−0.340359
$613$	−40.0506	−1.61763	−0.808815	−	0.588063i	$-0.799891\pi$
$613$	−40.0506	−1.61763	−0.808815	+	0.588063i	$0.799891\pi$
$614$	2.00182	0.0807871
$615$	3.79366	0.152975
$616$	0	0
$617$	33.1010	1.33260	0.666299	−	0.745685i	$-0.267877\pi$
$617$	33.1010	1.33260	0.666299	+	0.745685i	$0.267877\pi$
$618$	5.39047	0.216836
$619$	33.4246	1.34345	0.671724	−	0.740801i	$-0.265554\pi$
$619$	33.4246	1.34345	0.671724	+	0.740801i	$0.265554\pi$
$620$	12.5140	0.502573
$621$	11.0539	0.443578
$622$	−0.501658	−0.0201146
$623$	4.94893	0.198275
$624$	−11.4070	−0.456647
$625$	12.4198	0.496791
$626$	−3.37044	−0.134710
$627$	0	0
$628$	27.9297	1.11452
$629$	42.4328	1.69191
$630$	0.357336	0.0142366
$631$	17.9993	0.716539	0.358270	−	0.933618i	$-0.383367\pi$
$631$	17.9993	0.716539	0.358270	+	0.933618i	$0.383367\pi$
$632$	−1.07632	−0.0428139
$633$	−4.98764	−0.198241
$634$	−2.70781	−0.107541
$635$	3.67759	0.145941
$636$	−16.7367	−0.663651
$637$	−1.42165	−0.0563280
$638$	0	0
$639$	−13.3259	−0.527163
$640$	4.68675	0.185260
$641$	−23.9835	−0.947292	−0.473646	−	0.880715i	$-0.657062\pi$
$641$	−23.9835	−0.947292	−0.473646	+	0.880715i	$0.657062\pi$
$642$	0.458950	0.0181133
$643$	1.48031	0.0583777	0.0291889	−	0.999574i	$-0.490708\pi$
$643$	1.48031	0.0583777	0.0291889	+	0.999574i	$0.490708\pi$
$644$	13.2220	0.521018
$645$	−10.1872	−0.401122
$646$	−5.78195	−0.227488
$647$	−2.87709	−0.113110	−0.0565551	−	0.998399i	$-0.518012\pi$
$647$	−2.87709	−0.113110	−0.0565551	+	0.998399i	$0.518012\pi$
$648$	−6.97758	−0.274105
$649$	0	0
$650$	0.980688	0.0384658
$651$	−32.8459	−1.28733
$652$	−19.4898	−0.763278
$653$	−30.2463	−1.18363	−0.591815	−	0.806074i	$-0.701588\pi$
$653$	−30.2463	−1.18363	−0.591815	+	0.806074i	$0.701588\pi$
$654$	−2.38013	−0.0930705
$655$	4.74110	0.185250
$656$	−7.76521	−0.303180
$657$	−6.30736	−0.246074
$658$	4.80084	0.187156
$659$	6.01148	0.234174	0.117087	−	0.993122i	$-0.462644\pi$
$659$	6.01148	0.234174	0.117087	+	0.993122i	$0.462644\pi$
$660$	0	0
$661$	9.53794	0.370983	0.185491	−	0.982646i	$-0.440612\pi$
$661$	9.53794	0.370983	0.185491	+	0.982646i	$0.440612\pi$
$662$	1.45137	0.0564092
$663$	−13.1645	−0.511268
$664$	−0.360798	−0.0140017
$665$	−18.8768	−0.732012
$666$	−1.47103	−0.0570014
$667$	0.352912	0.0136648
$668$	−45.4725	−1.75938
$669$	−37.5892	−1.45328
$670$	0.863173	0.0333473
$671$	0	0
$672$	−9.24678	−0.356702
$673$	10.4894	0.404336	0.202168	−	0.979351i	$-0.435201\pi$
$673$	10.4894	0.404336	0.202168	+	0.979351i	$0.435201\pi$
$674$	1.25467	0.0483280
$675$	−16.6738	−0.641776
$676$	21.2828	0.818569
$677$	−47.8587	−1.83936	−0.919680	−	0.392669i	$-0.871552\pi$
$677$	−47.8587	−1.83936	−0.919680	+	0.392669i	$0.871552\pi$
$678$	−1.98018	−0.0760484
$679$	−22.6854	−0.870587
$680$	2.66904	0.102353
$681$	27.8534	1.06734
$682$	0	0
$683$	−8.00998	−0.306493	−0.153247	−	0.988188i	$-0.548973\pi$
$683$	−8.00998	−0.306493	−0.153247	+	0.988188i	$0.548973\pi$
$684$	−15.4201	−0.589601
$685$	15.9761	0.610416
$686$	−3.13319	−0.119626
$687$	−16.3878	−0.625233
$688$	20.8521	0.794979
$689$	−6.34697	−0.241800
$690$	0.819974	0.0312159
$691$	−7.68357	−0.292297	−0.146148	−	0.989263i	$-0.546688\pi$
$691$	−7.68357	−0.292297	−0.146148	+	0.989263i	$0.546688\pi$
$692$	34.1652	1.29877
$693$	0	0
$694$	4.77801	0.181371
$695$	−21.5590	−0.817781
$696$	−0.164186	−0.00622346
$697$	−8.96161	−0.339445
$698$	−4.01389	−0.151928
$699$	−5.36299	−0.202847
$700$	−19.9441	−0.753817
$701$	−4.44441	−0.167863	−0.0839315	−	0.996472i	$-0.526748\pi$
$701$	−4.44441	−0.167863	−0.0839315	+	0.996472i	$0.526748\pi$
$702$	−0.968812	−0.0365655
$703$	77.7097	2.93088
$704$	0	0
$705$	−22.9041	−0.862618
$706$	1.78689	0.0672505
$707$	−41.8479	−1.57385
$708$	−4.65020	−0.174765
$709$	12.6530	0.475193	0.237596	−	0.971364i	$-0.423640\pi$
$709$	12.6530	0.475193	0.237596	+	0.971364i	$0.423640\pi$
$710$	2.09842	0.0787524
$711$	−1.62401	−0.0609050
$712$	−1.28147	−0.0480253
$713$	−18.2815	−0.684646
$714$	−3.48015	−0.130241
$715$	0	0
$716$	0.344020	0.0128566
$717$	−11.5874	−0.432741
$718$	0.869761	0.0324592
$719$	32.2707	1.20349	0.601747	−	0.798687i	$-0.294472\pi$
$719$	32.2707	1.20349	0.601747	+	0.798687i	$0.294472\pi$
$720$	3.48952	0.130047
$721$	−41.5727	−1.54825
$722$	−7.54500	−0.280796
$723$	−53.3803	−1.98523
$724$	22.5894	0.839529
$725$	−0.532336	−0.0197705
$726$	0	0
$727$	−2.89002	−0.107185	−0.0535925	−	0.998563i	$-0.517067\pi$
$727$	−2.89002	−0.107185	−0.0535925	+	0.998563i	$0.517067\pi$
$728$	−2.33272	−0.0864564
$729$	13.7032	0.507528
$730$	0.993220	0.0367607
$731$	24.0648	0.890070
$732$	−3.92921	−0.145228
$733$	25.1963	0.930646	0.465323	−	0.885141i	$-0.345938\pi$
$733$	25.1963	0.930646	0.465323	+	0.885141i	$0.345938\pi$
$734$	−0.687761	−0.0253857
$735$	1.79301	0.0661361
$736$	−5.14659	−0.189706
$737$	0	0
$738$	0.310675	0.0114361
$739$	12.1849	0.448228	0.224114	−	0.974563i	$-0.428051\pi$
$739$	12.1849	0.448228	0.224114	+	0.974563i	$0.428051\pi$
$740$	−17.8202	−0.655082
$741$	−24.1090	−0.885665
$742$	−1.67787	−0.0615966
$743$	3.55450	0.130402	0.0652010	−	0.997872i	$-0.479231\pi$
$743$	3.55450	0.130402	0.0652010	+	0.997872i	$0.479231\pi$
$744$	8.50511	0.311813
$745$	8.37913	0.306988
$746$	1.74640	0.0639403
$747$	−0.544389	−0.0199181
$748$	0	0
$749$	−3.53954	−0.129332
$750$	−2.74217	−0.100130
$751$	14.1488	0.516298	0.258149	−	0.966105i	$-0.416887\pi$
$751$	14.1488	0.516298	0.258149	+	0.966105i	$0.416887\pi$
$752$	46.8821	1.70962
$753$	−33.2941	−1.21330
$754$	−0.0309307	−0.00112643
$755$	5.21079	0.189640
$756$	19.7026	0.716577
$757$	24.3922	0.886550	0.443275	−	0.896386i	$-0.353817\pi$
$757$	24.3922	0.886550	0.443275	+	0.896386i	$0.353817\pi$
$758$	−2.74167	−0.0995818
$759$	0	0
$760$	4.88796	0.177305
$761$	−46.3497	−1.68018	−0.840088	−	0.542451i	$-0.817497\pi$
$761$	−46.3497	−1.68018	−0.840088	+	0.542451i	$0.817497\pi$
$762$	1.24167	0.0449809
$763$	18.3562	0.664539
$764$	45.4043	1.64267
$765$	4.02716	0.145602
$766$	−4.88934	−0.176659
$767$	−1.76348	−0.0636755
$768$	−27.8344	−1.00439
$769$	8.45198	0.304786	0.152393	−	0.988320i	$-0.451302\pi$
$769$	8.45198	0.304786	0.152393	+	0.988320i	$0.451302\pi$
$770$	0	0
$771$	39.3257	1.41628
$772$	−12.7047	−0.457252
$773$	−5.83136	−0.209739	−0.104870	−	0.994486i	$-0.533443\pi$
$773$	−5.83136	−0.209739	−0.104870	+	0.994486i	$0.533443\pi$
$774$	−0.834264	−0.0299870
$775$	27.5759	0.990556
$776$	5.87416	0.210870
$777$	46.7734	1.67799
$778$	−0.403950	−0.0144823
$779$	−16.4119	−0.588018
$780$	5.52860	0.197956
$781$	0	0
$782$	−1.93699	−0.0692665
$783$	0.525890	0.0187938
$784$	−3.67009	−0.131074
$785$	−13.3583	−0.476780
$786$	1.60074	0.0570966
$787$	15.8221	0.563997	0.281998	−	0.959415i	$-0.409003\pi$
$787$	15.8221	0.563997	0.281998	+	0.959415i	$0.409003\pi$
$788$	4.49736	0.160212
$789$	29.6657	1.05613
$790$	0.255732	0.00909855
$791$	15.2717	0.542999
$792$	0	0
$793$	−1.49006	−0.0529135
$794$	−3.79679	−0.134743
$795$	8.00487	0.283904
$796$	−34.9040	−1.23714
$797$	12.4030	0.439335	0.219668	−	0.975575i	$-0.429503\pi$
$797$	12.4030	0.439335	0.219668	+	0.975575i	$0.429503\pi$
$798$	−6.37340	−0.225616
$799$	54.1053	1.91411
$800$	7.76316	0.274469
$801$	−1.93355	−0.0683185
$802$	−4.64703	−0.164092
$803$	0	0
$804$	−22.4198	−0.790685
$805$	−6.32385	−0.222886
$806$	1.60227	0.0564374
$807$	−49.8108	−1.75342
$808$	10.8361	0.381212
$809$	46.8544	1.64731	0.823657	−	0.567088i	$-0.191930\pi$
$809$	46.8544	1.64731	0.823657	+	0.567088i	$0.191930\pi$
$810$	1.65786	0.0582512
$811$	−12.0879	−0.424465	−0.212232	−	0.977219i	$-0.568073\pi$
$811$	−12.0879	−0.424465	−0.212232	+	0.977219i	$0.568073\pi$
$812$	0.629034	0.0220748
$813$	−44.0833	−1.54607
$814$	0	0
$815$	9.32164	0.326523
$816$	−33.9850	−1.18971
$817$	44.0713	1.54186
$818$	5.29565	0.185158
$819$	−3.51972	−0.122989
$820$	3.76353	0.131428
$821$	−31.5046	−1.09952	−0.549759	−	0.835324i	$-0.685280\pi$
$821$	−31.5046	−1.09952	−0.549759	+	0.835324i	$0.685280\pi$
$822$	5.39403	0.188138
$823$	7.27344	0.253536	0.126768	−	0.991932i	$-0.459540\pi$
$823$	7.27344	0.253536	0.126768	+	0.991932i	$0.459540\pi$
$824$	10.7648	0.375010
$825$	0	0
$826$	−0.466189	−0.0162208
$827$	−24.0404	−0.835965	−0.417982	−	0.908455i	$-0.637263\pi$
$827$	−24.0404	−0.835965	−0.417982	+	0.908455i	$0.637263\pi$
$828$	−5.16582	−0.179525
$829$	−22.8708	−0.794336	−0.397168	−	0.917746i	$-0.630007\pi$
$829$	−22.8708	−0.794336	−0.397168	+	0.917746i	$0.630007\pi$
$830$	0.0857249	0.00297555
$831$	57.5585	1.99668
$832$	−11.0125	−0.381788
$833$	−4.23554	−0.146753
$834$	−7.27899	−0.252051
$835$	21.7488	0.752647
$836$	0	0
$837$	−27.2420	−0.941620
$838$	−3.26624	−0.112831
$839$	35.0431	1.20982	0.604912	−	0.796292i	$-0.293208\pi$
$839$	35.0431	1.20982	0.604912	+	0.796292i	$0.293208\pi$
$840$	2.94206	0.101511
$841$	−28.9832	−0.999421
$842$	−0.708270	−0.0244086
$843$	36.0132	1.24036
$844$	−4.94802	−0.170318
$845$	−10.1792	−0.350176
$846$	−1.87569	−0.0644875
$847$	0	0
$848$	−16.3851	−0.562666
$849$	13.2454	0.454582
$850$	2.92177	0.100216
$851$	26.0332	0.892407
$852$	−54.5038	−1.86727
$853$	10.6854	0.365862	0.182931	−	0.983126i	$-0.441442\pi$
$853$	10.6854	0.365862	0.182931	+	0.983126i	$0.441442\pi$
$854$	−0.393909	−0.0134793
$855$	7.37517	0.252226
$856$	0.916528	0.0313263
$857$	−25.4187	−0.868286	−0.434143	−	0.900844i	$-0.642949\pi$
$857$	−25.4187	−0.868286	−0.434143	+	0.900844i	$0.642949\pi$
$858$	0	0
$859$	−10.1605	−0.346673	−0.173337	−	0.984863i	$-0.555455\pi$
$859$	−10.1605	−0.346673	−0.173337	+	0.984863i	$0.555455\pi$
$860$	−10.1063	−0.344622
$861$	−9.87831	−0.336652
$862$	2.35361	0.0801643
$863$	39.5319	1.34568	0.672841	−	0.739787i	$-0.265074\pi$
$863$	39.5319	1.34568	0.672841	+	0.739787i	$0.265074\pi$
$864$	−7.66915	−0.260910
$865$	−16.3407	−0.555599
$866$	0.549426	0.0186702
$867$	−5.38875	−0.183011
$868$	−32.5851	−1.10601
$869$	0	0
$870$	0.0390102	0.00132257
$871$	−8.50216	−0.288085
$872$	−4.75315	−0.160962
$873$	8.86320	0.299974
$874$	−3.54732	−0.119990
$875$	21.1483	0.714943
$876$	−25.7976	−0.871619
$877$	−16.9987	−0.574005	−0.287002	−	0.957930i	$-0.592659\pi$
$877$	−16.9987	−0.574005	−0.287002	+	0.957930i	$0.592659\pi$
$878$	−0.460078	−0.0155269
$879$	47.7656	1.61110
$880$	0	0
$881$	15.5041	0.522347	0.261174	−	0.965292i	$-0.415890\pi$
$881$	15.5041	0.522347	0.261174	+	0.965292i	$0.415890\pi$
$882$	0.146835	0.00494419
$883$	−1.52136	−0.0511980	−0.0255990	−	0.999672i	$-0.508149\pi$
$883$	−1.52136	−0.0511980	−0.0255990	+	0.999672i	$0.508149\pi$
$884$	−13.0600	−0.439254
$885$	2.22412	0.0747629
$886$	1.75368	0.0589160
$887$	−34.5166	−1.15895	−0.579477	−	0.814988i	$-0.696743\pi$
$887$	−34.5166	−1.15895	−0.579477	+	0.814988i	$0.696743\pi$
$888$	−12.1115	−0.406435
$889$	−9.57607	−0.321171
$890$	0.304476	0.0102060
$891$	0	0
$892$	−37.2906	−1.24858
$893$	99.0863	3.31580
$894$	2.82905	0.0946177
$895$	−0.164540	−0.00549995
$896$	−12.2038	−0.407700
$897$	−8.07665	−0.269672
$898$	−1.35361	−0.0451707
$899$	−0.869740	−0.0290074
$900$	7.79217	0.259739
$901$	−18.9096	−0.629969
$902$	0	0
$903$	26.5265	0.882746
$904$	−3.95444	−0.131523
$905$	−10.8042	−0.359142
$906$	1.75932	0.0584495
$907$	−8.20949	−0.272591	−0.136296	−	0.990668i	$-0.543520\pi$
$907$	−8.20949	−0.272591	−0.136296	+	0.990668i	$0.543520\pi$
$908$	27.6321	0.917004
$909$	16.3500	0.542294
$910$	0.554250	0.0183732
$911$	30.4629	1.00928	0.504641	−	0.863329i	$-0.331625\pi$
$911$	30.4629	1.00928	0.504641	+	0.863329i	$0.331625\pi$
$912$	−62.2388	−2.06093
$913$	0	0
$914$	5.59356	0.185019
$915$	1.87928	0.0621270
$916$	−16.2576	−0.537167
$917$	−12.3453	−0.407679
$918$	−2.88639	−0.0952650
$919$	−38.8785	−1.28248	−0.641241	−	0.767339i	$-0.721580\pi$
$919$	−38.8785	−1.28248	−0.641241	+	0.767339i	$0.721580\pi$
$920$	1.63750	0.0539866
$921$	24.8683	0.819438
$922$	−2.10432	−0.0693022
$923$	−20.6692	−0.680336
$924$	0	0
$925$	−39.2688	−1.29115
$926$	−0.722671	−0.0237485
$927$	16.2424	0.533472
$928$	−0.244849	−0.00803756
$929$	−3.78496	−0.124181	−0.0620903	−	0.998071i	$-0.519777\pi$
$929$	−3.78496	−0.124181	−0.0620903	+	0.998071i	$0.519777\pi$
$930$	−2.02080	−0.0662645
$931$	−7.75679	−0.254219
$932$	−5.32040	−0.174275
$933$	−6.23199	−0.204026
$934$	1.88401	0.0616467
$935$	0	0
$936$	0.911394	0.0297899
$937$	−16.6575	−0.544176	−0.272088	−	0.962272i	$-0.587714\pi$
$937$	−16.6575	−0.544176	−0.272088	+	0.962272i	$0.587714\pi$
$938$	−2.24761	−0.0733872
$939$	−41.8703	−1.36639
$940$	−22.7222	−0.741116
$941$	22.8025	0.743341	0.371671	−	0.928365i	$-0.378785\pi$
$941$	22.8025	0.743341	0.371671	+	0.928365i	$0.378785\pi$
$942$	−4.51019	−0.146950
$943$	−5.49809	−0.179042
$944$	−4.55252	−0.148172
$945$	−9.42344	−0.306545
$946$	0	0
$947$	27.5003	0.893639	0.446819	−	0.894624i	$-0.352557\pi$
$947$	27.5003	0.893639	0.446819	+	0.894624i	$0.352557\pi$
$948$	−6.64231	−0.215732
$949$	−9.78311	−0.317573
$950$	5.35081	0.173603
$951$	−33.6385	−1.09080
$952$	−6.94989	−0.225247
$953$	22.0617	0.714648	0.357324	−	0.933980i	$-0.383689\pi$
$953$	22.0617	0.714648	0.357324	+	0.933980i	$0.383689\pi$
$954$	0.655544	0.0212240
$955$	−21.7161	−0.702718
$956$	−11.4954	−0.371788
$957$	0	0
$958$	−4.93692	−0.159505
$959$	−41.6001	−1.34334
$960$	13.8890	0.448267
$961$	14.0540	0.453355
$962$	−2.28166	−0.0735638
$963$	1.38290	0.0445633
$964$	−52.9563	−1.70561
$965$	6.07645	0.195608
$966$	−2.13513	−0.0686966
$967$	−60.9568	−1.96024	−0.980119	−	0.198413i	$-0.936421\pi$
$967$	−60.9568	−1.96024	−0.980119	+	0.198413i	$0.936421\pi$
$968$	0	0
$969$	−71.8280	−2.30745
$970$	−1.39569	−0.0448128
$971$	13.5744	0.435624	0.217812	−	0.975991i	$-0.430108\pi$
$971$	13.5744	0.435624	0.217812	+	0.975991i	$0.430108\pi$
$972$	−19.0218	−0.610125
$973$	56.1375	1.79969
$974$	−1.48259	−0.0475053
$975$	12.1829	0.390165
$976$	−3.84667	−0.123129
$977$	−13.2043	−0.422443	−0.211222	−	0.977438i	$-0.567744\pi$
$977$	−13.2043	−0.422443	−0.211222	+	0.977438i	$0.567744\pi$
$978$	3.14727	0.100639
$979$	0	0
$980$	1.77877	0.0568206
$981$	−7.17176	−0.228977
$982$	4.98252	0.158999
$983$	55.4465	1.76847	0.884234	−	0.467044i	$-0.154681\pi$
$983$	55.4465	1.76847	0.884234	+	0.467044i	$0.154681\pi$
$984$	2.55789	0.0815424
$985$	−2.15101	−0.0685370
$986$	−0.0921522	−0.00293472
$987$	59.6399	1.89836
$988$	−23.9175	−0.760916
$989$	14.7642	0.469473
$990$	0	0
$991$	16.9964	0.539910	0.269955	−	0.962873i	$-0.412991\pi$
$991$	16.9964	0.539910	0.269955	+	0.962873i	$0.412991\pi$
$992$	12.6836	0.402704
$993$	18.0301	0.572168
$994$	−5.46408	−0.173310
$995$	16.6940	0.529236
$996$	−2.22659	−0.0705522
$997$	48.7801	1.54488	0.772440	−	0.635088i	$-0.219036\pi$
$997$	48.7801	1.54488	0.772440	+	0.635088i	$0.219036\pi$
$998$	−5.30665	−0.167979
$999$	38.7932	1.22736

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.u.1.31		64
11.7	odd	10		671.2.j.c.489.18	yes	128
11.8	odd	10		671.2.j.c.306.18	✓	128
11.10	odd	2		7381.2.a.v.1.34		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.306.18	✓	128	11.8	odd	10
671.2.j.c.489.18	yes	128	11.7	odd	10
7381.2.a.u.1.31		64	1.1	even	1	trivial
7381.2.a.v.1.34		64	11.10	odd	2

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)

\(f(q)\)	\(=\)	\(q-0.160201 q^{2} -1.99014 q^{3} -1.97434 q^{4} +0.944293 q^{5} +0.318822 q^{6} -2.45884 q^{7} +0.636692 q^{8} +0.960669 q^{9} +O(q^{10})\)	\(q-0.160201 q^{2} -1.99014 q^{3} -1.97434 q^{4} +0.944293 q^{5} +0.318822 q^{6} -2.45884 q^{7} +0.636692 q^{8} +0.960669 q^{9} -0.151277 q^{10} +3.92921 q^{12} +1.49006 q^{13} +0.393909 q^{14} -1.87928 q^{15} +3.84667 q^{16} +4.43934 q^{17} -0.153900 q^{18} +8.13002 q^{19} -1.86435 q^{20} +4.89345 q^{21} +2.72360 q^{23} -1.26711 q^{24} -4.10831 q^{25} -0.238708 q^{26} +4.05856 q^{27} +4.85458 q^{28} +0.129575 q^{29} +0.301062 q^{30} -6.71223 q^{31} -1.88962 q^{32} -0.711185 q^{34} -2.32187 q^{35} -1.89668 q^{36} +9.55837 q^{37} -1.30243 q^{38} -2.96543 q^{39} +0.601224 q^{40} -2.01868 q^{41} -0.783934 q^{42} +5.42082 q^{43} +0.907154 q^{45} -0.436324 q^{46} +12.1877 q^{47} -7.65543 q^{48} -0.954093 q^{49} +0.658155 q^{50} -8.83492 q^{51} -2.94187 q^{52} -4.25955 q^{53} -0.650184 q^{54} -1.56552 q^{56} -16.1799 q^{57} -0.0207581 q^{58} -1.18350 q^{59} +3.71033 q^{60} -1.00000 q^{61} +1.07530 q^{62} -2.36214 q^{63} -7.39063 q^{64} +1.40705 q^{65} -5.70593 q^{67} -8.76474 q^{68} -5.42036 q^{69} +0.371965 q^{70} -13.8714 q^{71} +0.611650 q^{72} -6.56559 q^{73} -1.53126 q^{74} +8.17613 q^{75} -16.0514 q^{76} +0.475064 q^{78} -1.69050 q^{79} +3.63239 q^{80} -10.9591 q^{81} +0.323394 q^{82} -0.566676 q^{83} -9.66131 q^{84} +4.19204 q^{85} -0.868419 q^{86} -0.257874 q^{87} -2.01271 q^{89} -0.145327 q^{90} -3.66382 q^{91} -5.37731 q^{92} +13.3583 q^{93} -1.95248 q^{94} +7.67712 q^{95} +3.76062 q^{96} +9.22607 q^{97} +0.152847 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} + q^{6} - 6 q^{7} - 3 q^{8} + 81 q^{9}+O(q^{10}) \) 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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