LMFDB - Embedded newform 7381.2.a.j.1.17

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:	$21$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q+2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} +2.49129 q^{6} -3.34814 q^{7} +1.77494 q^{8} -1.70949 q^{9} +O(q^{10})$	\(q+2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} +2.49129 q^{6} -3.34814 q^{7} +1.77494 q^{8} -1.70949 q^{9} -8.50160 q^{10} +3.19145 q^{12} -3.33150 q^{13} -7.34255 q^{14} -4.40390 q^{15} -1.72622 q^{16} -2.42548 q^{17} -3.74895 q^{18} +7.48304 q^{19} -10.8909 q^{20} -3.80351 q^{21} +6.20068 q^{23} +2.01635 q^{24} +10.0285 q^{25} -7.30607 q^{26} -5.35001 q^{27} -9.40612 q^{28} +2.67585 q^{29} -9.65787 q^{30} +8.31622 q^{31} -7.33554 q^{32} -5.31914 q^{34} +12.9796 q^{35} -4.80257 q^{36} +5.59361 q^{37} +16.4105 q^{38} -3.78461 q^{39} -6.88084 q^{40} -0.632514 q^{41} -8.34118 q^{42} -5.14454 q^{43} +6.62710 q^{45} +13.5982 q^{46} +6.95884 q^{47} -1.96100 q^{48} +4.21003 q^{49} +21.9926 q^{50} -2.75536 q^{51} -9.35939 q^{52} -10.8778 q^{53} -11.7327 q^{54} -5.94275 q^{56} +8.50078 q^{57} +5.86821 q^{58} +0.797395 q^{59} -12.3721 q^{60} -1.00000 q^{61} +18.2377 q^{62} +5.72361 q^{63} -12.6346 q^{64} +12.9151 q^{65} +13.0038 q^{67} -6.81405 q^{68} +7.04401 q^{69} +28.4645 q^{70} +15.1395 q^{71} -3.03425 q^{72} -4.09379 q^{73} +12.2669 q^{74} +11.3924 q^{75} +21.0225 q^{76} -8.29974 q^{78} -11.2765 q^{79} +6.69197 q^{80} -0.949176 q^{81} -1.38712 q^{82} -6.06669 q^{83} -10.6854 q^{84} +9.40276 q^{85} -11.2821 q^{86} +3.03979 q^{87} +16.4725 q^{89} +14.5334 q^{90} +11.1543 q^{91} +17.4199 q^{92} +9.44728 q^{93} +15.2609 q^{94} -29.0092 q^{95} -8.33321 q^{96} -3.95096 q^{97} +9.23269 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9}+O(q^{10}) $ 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9} - q^{10} + 6 q^{12} - 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} - q^{17} + 5 q^{18} - 15 q^{19} - 2 q^{20} - 16 q^{21} + 11 q^{23} + 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} + 16 q^{28} + 9 q^{29} - 16 q^{30} + 22 q^{31} - 3 q^{32} + 33 q^{34} + 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} + 28 q^{39} + 16 q^{40} - 7 q^{41} - 55 q^{42} - 16 q^{43} + 44 q^{45} + 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} + 33 q^{50} + 19 q^{51} - 60 q^{52} + 9 q^{53} - 13 q^{54} + 44 q^{56} - 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} - 21 q^{61} + 23 q^{62} - 24 q^{63} + 66 q^{64} - 25 q^{65} + 38 q^{67} + 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} + 75 q^{72} - 20 q^{73} + 12 q^{74} - 10 q^{75} - 59 q^{76} - 14 q^{78} - q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} + 19 q^{83} + 14 q^{84} - 38 q^{85} - 3 q^{86} - 4 q^{87} + 37 q^{89} + 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} + 64 q^{94} + 43 q^{95} + 38 q^{96} + 68 q^{97} + 2 q^{98}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9 - q^10 + 6 * q^12 - 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 - q^17 + 5 * q^18 - 15 * q^19 - 2 * q^20 - 16 * q^21 + 11 * q^23 + 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 + 16 * q^28 + 9 * q^29 - 16 * q^30 + 22 * q^31 - 3 * q^32 + 33 * q^34 + 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 + 28 * q^39 + 16 * q^40 - 7 * q^41 - 55 * q^42 - 16 * q^43 + 44 * q^45 + 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 + 33 * q^50 + 19 * q^51 - 60 * q^52 + 9 * q^53 - 13 * q^54 + 44 * q^56 - 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 - 21 * q^61 + 23 * q^62 - 24 * q^63 + 66 * q^64 - 25 * q^65 + 38 * q^67 + 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 + 75 * q^72 - 20 * q^73 + 12 * q^74 - 10 * q^75 - 59 * q^76 - 14 * q^78 - q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 + 19 * q^83 + 14 * q^84 - 38 * q^85 - 3 * q^86 - 4 * q^87 + 37 * q^89 + 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 + 64 * q^94 + 43 * q^95 + 38 * q^96 + 68 * q^97 + 2 * 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 $

$2$	2.19302	1.55070	0.775351	−	0.631530i	$-0.217573\pi$
$2$	2.19302	1.55070	0.775351	+	0.631530i	$0.217573\pi$
$3$	1.13601	0.655874	0.327937	−	0.944700i	$-0.393647\pi$
$3$	1.13601	0.655874	0.327937	+	0.944700i	$0.393647\pi$
$4$	2.80936	1.40468
$5$	−3.87665	−1.73369	−0.866846	−	0.498575i	$-0.833857\pi$
$5$	−3.87665	−1.73369	−0.866846	+	0.498575i	$0.833857\pi$
$6$	2.49129	1.01706
$7$	−3.34814	−1.26548	−0.632739	−	0.774365i	$-0.718069\pi$
$7$	−3.34814	−1.26548	−0.632739	+	0.774365i	$0.718069\pi$
$8$	1.77494	0.627537
$9$	−1.70949	−0.569830
$10$	−8.50160	−2.68844
$11$	0	0
$11$	0	0
$12$	3.19145	0.921292
$13$	−3.33150	−0.923993	−0.461996	−	0.886882i	$-0.652867\pi$
$13$	−3.33150	−0.923993	−0.461996	+	0.886882i	$0.652867\pi$
$14$	−7.34255	−1.96238
$15$	−4.40390	−1.13708
$16$	−1.72622	−0.431556
$17$	−2.42548	−0.588266	−0.294133	−	0.955765i	$-0.595031\pi$
$17$	−2.42548	−0.588266	−0.294133	+	0.955765i	$0.595031\pi$
$18$	−3.74895	−0.883637
$19$	7.48304	1.71673	0.858364	−	0.513041i	$-0.171481\pi$
$19$	7.48304	1.71673	0.858364	+	0.513041i	$0.171481\pi$
$20$	−10.8909	−2.43528
$21$	−3.80351	−0.829993
$22$	0	0
$23$	6.20068	1.29293	0.646466	−	0.762943i	$-0.276246\pi$
$23$	6.20068	1.29293	0.646466	+	0.762943i	$0.276246\pi$
$24$	2.01635	0.411585
$25$	10.0285	2.00569
$26$	−7.30607	−1.43284
$27$	−5.35001	−1.02961
$28$	−9.40612	−1.77759
$29$	2.67585	0.496893	0.248447	−	0.968646i	$-0.420080\pi$
$29$	2.67585	0.496893	0.248447	+	0.968646i	$0.420080\pi$
$30$	−9.65787	−1.76328
$31$	8.31622	1.49364	0.746819	−	0.665028i	$-0.231580\pi$
$31$	8.31622	1.49364	0.746819	+	0.665028i	$0.231580\pi$
$32$	−7.33554	−1.29675
$33$	0	0
$34$	−5.31914	−0.912226
$35$	12.9796	2.19395
$36$	−4.80257	−0.800428
$37$	5.59361	0.919584	0.459792	−	0.888027i	$-0.347924\pi$
$37$	5.59361	0.919584	0.459792	+	0.888027i	$0.347924\pi$
$38$	16.4105	2.66213
$39$	−3.78461	−0.606022
$40$	−6.88084	−1.08796
$41$	−0.632514	−0.0987820	−0.0493910	−	0.998780i	$-0.515728\pi$
$41$	−0.632514	−0.0987820	−0.0493910	+	0.998780i	$0.515728\pi$
$42$	−8.34118	−1.28707
$43$	−5.14454	−0.784535	−0.392267	−	0.919851i	$-0.628309\pi$
$43$	−5.14454	−0.784535	−0.392267	+	0.919851i	$0.628309\pi$
$44$	0	0
$45$	6.62710	0.987910
$46$	13.5982	2.00495
$47$	6.95884	1.01505	0.507526	−	0.861637i	$-0.330560\pi$
$47$	6.95884	1.01505	0.507526	+	0.861637i	$0.330560\pi$
$48$	−1.96100	−0.283046
$49$	4.21003	0.601432
$50$	21.9926	3.11023
$51$	−2.75536	−0.385828
$52$	−9.35939	−1.29791
$53$	−10.8778	−1.49418	−0.747091	−	0.664721i	$-0.768550\pi$
$53$	−10.8778	−1.49418	−0.747091	+	0.664721i	$0.768550\pi$
$54$	−11.7327	−1.59662
$55$	0	0
$56$	−5.94275	−0.794134
$57$	8.50078	1.12596
$58$	5.86821	0.770534
$59$	0.797395	0.103812	0.0519060	−	0.998652i	$-0.483470\pi$
$59$	0.797395	0.103812	0.0519060	+	0.998652i	$0.483470\pi$
$60$	−12.3721	−1.59724
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	18.2377	2.31619
$63$	5.72361	0.721107
$64$	−12.6346	−1.57932
$65$	12.9151	1.60192
$66$	0	0
$67$	13.0038	1.58867	0.794336	−	0.607479i	$-0.207819\pi$
$67$	13.0038	1.58867	0.794336	+	0.607479i	$0.207819\pi$
$68$	−6.81405	−0.826325
$69$	7.04401	0.847999
$70$	28.4645	3.40216
$71$	15.1395	1.79673	0.898367	−	0.439246i	$-0.144754\pi$
$71$	15.1395	1.79673	0.898367	+	0.439246i	$0.144754\pi$
$72$	−3.03425	−0.357589
$73$	−4.09379	−0.479142	−0.239571	−	0.970879i	$-0.577007\pi$
$73$	−4.09379	−0.479142	−0.239571	+	0.970879i	$0.577007\pi$
$74$	12.2669	1.42600
$75$	11.3924	1.31548
$76$	21.0225	2.41145
$77$	0	0
$78$	−8.29974	−0.939761
$79$	−11.2765	−1.26870	−0.634352	−	0.773045i	$-0.718733\pi$
$79$	−11.2765	−1.26870	−0.634352	+	0.773045i	$0.718733\pi$
$80$	6.69197	0.748185
$81$	−0.949176	−0.105464
$82$	−1.38712	−0.153182
$83$	−6.06669	−0.665906	−0.332953	−	0.942943i	$-0.608045\pi$
$83$	−6.06669	−0.665906	−0.332953	+	0.942943i	$0.608045\pi$
$84$	−10.6854	−1.16587
$85$	9.40276	1.01987
$86$	−11.2821	−1.21658
$87$	3.03979	0.325899
$88$	0	0
$89$	16.4725	1.74608	0.873041	−	0.487647i	$-0.162145\pi$
$89$	16.4725	1.74608	0.873041	+	0.487647i	$0.162145\pi$
$90$	14.5334	1.53195
$91$	11.1543	1.16929
$92$	17.4199	1.81615
$93$	9.44728	0.979637
$94$	15.2609	1.57404
$95$	−29.0092	−2.97628
$96$	−8.33321	−0.850505
$97$	−3.95096	−0.401159	−0.200579	−	0.979677i	$-0.564282\pi$
$97$	−3.95096	−0.401159	−0.200579	+	0.979677i	$0.564282\pi$
$98$	9.23269	0.932643
$99$	0	0
$100$	28.1735	2.81735
$101$	−4.24862	−0.422753	−0.211377	−	0.977405i	$-0.567795\pi$
$101$	−4.24862	−0.422753	−0.211377	+	0.977405i	$0.567795\pi$
$102$	−6.04258	−0.598305
$103$	−11.0222	−1.08605	−0.543026	−	0.839716i	$-0.682722\pi$
$103$	−11.0222	−1.08605	−0.543026	+	0.839716i	$0.682722\pi$
$104$	−5.91323	−0.579840
$105$	14.7449	1.43895
$106$	−23.8553	−2.31703
$107$	−10.4279	−1.00810	−0.504052	−	0.863673i	$-0.668158\pi$
$107$	−10.4279	−1.00810	−0.504052	+	0.863673i	$0.668158\pi$
$108$	−15.0301	−1.44627
$109$	5.49290	0.526124	0.263062	−	0.964779i	$-0.415268\pi$
$109$	5.49290	0.526124	0.263062	+	0.964779i	$0.415268\pi$
$110$	0	0
$111$	6.35438	0.603131
$112$	5.77963	0.546124
$113$	−12.2934	−1.15647	−0.578234	−	0.815871i	$-0.696258\pi$
$113$	−12.2934	−1.15647	−0.578234	+	0.815871i	$0.696258\pi$
$114$	18.6424	1.74602
$115$	−24.0379	−2.24155
$116$	7.51743	0.697976
$117$	5.69517	0.526519
$118$	1.74871	0.160981
$119$	8.12085	0.744437
$120$	−7.81668	−0.713562
$121$	0	0
$122$	−2.19302	−0.198547
$123$	−0.718539	−0.0647885
$124$	23.3632	2.09808
$125$	−19.4936	−1.74356
$126$	12.5520	1.11822
$127$	2.89882	0.257228	0.128614	−	0.991695i	$-0.458947\pi$
$127$	2.89882	0.257228	0.128614	+	0.991695i	$0.458947\pi$
$128$	−13.0368	−1.15231
$129$	−5.84423	−0.514555
$130$	28.3231	2.48410
$131$	12.2543	1.07066	0.535331	−	0.844642i	$-0.320187\pi$
$131$	12.2543	1.07066	0.535331	+	0.844642i	$0.320187\pi$
$132$	0	0
$133$	−25.0543	−2.17248
$134$	28.5177	2.46356
$135$	20.7401	1.78503
$136$	−4.30509	−0.369159
$137$	17.8925	1.52866	0.764332	−	0.644823i	$-0.223069\pi$
$137$	17.8925	1.52866	0.764332	+	0.644823i	$0.223069\pi$
$138$	15.4477	1.31499
$139$	12.6337	1.07158	0.535788	−	0.844353i	$-0.320015\pi$
$139$	12.6337	1.07158	0.535788	+	0.844353i	$0.320015\pi$
$140$	36.4643	3.08179
$141$	7.90529	0.665745
$142$	33.2014	2.78620
$143$	0	0
$144$	2.95096	0.245913
$145$	−10.3734	−0.861461
$146$	−8.97779	−0.743007
$147$	4.78262	0.394464
$148$	15.7145	1.29172
$149$	18.7862	1.53903	0.769513	−	0.638632i	$-0.220499\pi$
$149$	18.7862	1.53903	0.769513	+	0.638632i	$0.220499\pi$
$150$	24.9838	2.03992
$151$	14.2055	1.15602	0.578012	−	0.816028i	$-0.303829\pi$
$151$	14.2055	1.15602	0.578012	+	0.816028i	$0.303829\pi$
$152$	13.2820	1.07731
$153$	4.14634	0.335211
$154$	0	0
$155$	−32.2391	−2.58951
$156$	−10.6323	−0.851267
$157$	0.168712	0.0134647	0.00673235	−	0.999977i	$-0.497857\pi$
$157$	0.168712	0.0134647	0.00673235	+	0.999977i	$0.497857\pi$
$158$	−24.7296	−1.96738
$159$	−12.3573	−0.979995
$160$	28.4373	2.24817
$161$	−20.7607	−1.63617
$162$	−2.08157	−0.163543
$163$	7.00919	0.549002	0.274501	−	0.961587i	$-0.411487\pi$
$163$	7.00919	0.549002	0.274501	+	0.961587i	$0.411487\pi$
$164$	−1.77696	−0.138757
$165$	0	0
$166$	−13.3044	−1.03262
$167$	−14.2000	−1.09883	−0.549414	−	0.835550i	$-0.685149\pi$
$167$	−14.2000	−1.09883	−0.549414	+	0.835550i	$0.685149\pi$
$168$	−6.75100	−0.520851
$169$	−1.90108	−0.146237
$170$	20.6205	1.58152
$171$	−12.7922	−0.978243
$172$	−14.4528	−1.10202
$173$	19.2874	1.46639	0.733196	−	0.680017i	$-0.238028\pi$
$173$	19.2874	1.46639	0.733196	+	0.680017i	$0.238028\pi$
$174$	6.66633	0.505373
$175$	−33.5766	−2.53816
$176$	0	0
$177$	0.905845	0.0680875
$178$	36.1246	2.70765
$179$	14.6949	1.09835	0.549175	−	0.835708i	$-0.314942\pi$
$179$	14.6949	1.09835	0.549175	+	0.835708i	$0.314942\pi$
$180$	18.6179	1.38770
$181$	5.00787	0.372232	0.186116	−	0.982528i	$-0.440410\pi$
$181$	5.00787	0.372232	0.186116	+	0.982528i	$0.440410\pi$
$182$	24.4617	1.81322
$183$	−1.13601	−0.0839760
$184$	11.0059	0.811362
$185$	−21.6845	−1.59428
$186$	20.7181	1.51913
$187$	0	0
$188$	19.5499	1.42582
$189$	17.9126	1.30295
$190$	−63.6178	−4.61532
$191$	−0.913661	−0.0661102	−0.0330551	−	0.999454i	$-0.510524\pi$
$191$	−0.913661	−0.0661102	−0.0330551	+	0.999454i	$0.510524\pi$
$192$	−14.3529	−1.03583
$193$	11.2144	0.807229	0.403614	−	0.914929i	$-0.367754\pi$
$193$	11.2144	0.807229	0.403614	+	0.914929i	$0.367754\pi$
$194$	−8.66455	−0.622078
$195$	14.6716	1.05066
$196$	11.8275	0.844820
$197$	−13.0173	−0.927441	−0.463721	−	0.885981i	$-0.653486\pi$
$197$	−13.0173	−0.927441	−0.463721	+	0.885981i	$0.653486\pi$
$198$	0	0
$199$	−9.78075	−0.693339	−0.346669	−	0.937987i	$-0.612687\pi$
$199$	−9.78075	−0.693339	−0.346669	+	0.937987i	$0.612687\pi$
$200$	17.7999	1.25864
$201$	14.7724	1.04197
$202$	−9.31733	−0.655565
$203$	−8.95913	−0.628807
$204$	−7.74080	−0.541965
$205$	2.45204	0.171258
$206$	−24.1720	−1.68414
$207$	−10.6000	−0.736751
$208$	5.75092	0.398754
$209$	0	0
$210$	32.3359	2.23139
$211$	−3.72562	−0.256482	−0.128241	−	0.991743i	$-0.540933\pi$
$211$	−3.72562	−0.256482	−0.128241	+	0.991743i	$0.540933\pi$
$212$	−30.5597	−2.09885
$213$	17.1986	1.17843
$214$	−22.8687	−1.56327
$215$	19.9436	1.36014
$216$	−9.49596	−0.646118
$217$	−27.8439	−1.89016
$218$	12.0461	0.815862
$219$	−4.65058	−0.314257
$220$	0	0
$221$	8.08050	0.543553
$222$	13.9353	0.935277
$223$	−18.0723	−1.21021	−0.605105	−	0.796146i	$-0.706869\pi$
$223$	−18.0723	−1.21021	−0.605105	+	0.796146i	$0.706869\pi$
$224$	24.5604	1.64101
$225$	−17.1435	−1.14290
$226$	−26.9598	−1.79334
$227$	7.30933	0.485137	0.242569	−	0.970134i	$-0.422010\pi$
$227$	7.30933	0.485137	0.242569	+	0.970134i	$0.422010\pi$
$228$	23.8817	1.58161
$229$	−3.38255	−0.223525	−0.111763	−	0.993735i	$-0.535650\pi$
$229$	−3.38255	−0.223525	−0.111763	+	0.993735i	$0.535650\pi$
$230$	−52.7157	−3.47597
$231$	0	0
$232$	4.74949	0.311819
$233$	3.58756	0.235029	0.117514	−	0.993071i	$-0.462507\pi$
$233$	3.58756	0.235029	0.117514	+	0.993071i	$0.462507\pi$
$234$	12.4897	0.816474
$235$	−26.9770	−1.75979
$236$	2.24017	0.145822
$237$	−12.8102	−0.832109
$238$	17.8092	1.15440
$239$	20.9385	1.35440	0.677200	−	0.735799i	$-0.263193\pi$
$239$	20.9385	1.35440	0.677200	+	0.735799i	$0.263193\pi$
$240$	7.60212	0.490715
$241$	14.8021	0.953488	0.476744	−	0.879042i	$-0.341817\pi$
$241$	14.8021	0.953488	0.476744	+	0.879042i	$0.341817\pi$
$242$	0	0
$243$	14.9718	0.960439
$244$	−2.80936	−0.179851
$245$	−16.3208	−1.04270
$246$	−1.57577	−0.100468
$247$	−24.9298	−1.58624
$248$	14.7608	0.937313
$249$	−6.89180	−0.436750
$250$	−42.7499	−2.70374
$251$	19.9160	1.25709	0.628543	−	0.777775i	$-0.283652\pi$
$251$	19.9160	1.25709	0.628543	+	0.777775i	$0.283652\pi$
$252$	16.0797	1.01292
$253$	0	0
$254$	6.35718	0.398885
$255$	10.6816	0.668907
$256$	−3.32100	−0.207562
$257$	−22.2211	−1.38612	−0.693059	−	0.720881i	$-0.743737\pi$
$257$	−22.2211	−1.38612	−0.693059	+	0.720881i	$0.743737\pi$
$258$	−12.8165	−0.797923
$259$	−18.7282	−1.16371
$260$	36.2831	2.25018
$261$	−4.57434	−0.283145
$262$	26.8740	1.66028
$263$	1.12178	0.0691721	0.0345860	−	0.999402i	$-0.488989\pi$
$263$	1.12178	0.0691721	0.0345860	+	0.999402i	$0.488989\pi$
$264$	0	0
$265$	42.1695	2.59045
$266$	−54.9446	−3.36887
$267$	18.7129	1.14521
$268$	36.5324	2.23157
$269$	3.27958	0.199960	0.0999798	−	0.994989i	$-0.468122\pi$
$269$	3.27958	0.199960	0.0999798	+	0.994989i	$0.468122\pi$
$270$	45.4836	2.76805
$271$	0.586170	0.0356073	0.0178036	−	0.999842i	$-0.494333\pi$
$271$	0.586170	0.0356073	0.0178036	+	0.999842i	$0.494333\pi$
$272$	4.18692	0.253870
$273$	12.6714	0.766908
$274$	39.2388	2.37050
$275$	0	0
$276$	19.7892	1.19117
$277$	−15.1268	−0.908882	−0.454441	−	0.890777i	$-0.650161\pi$
$277$	−15.1268	−0.908882	−0.454441	+	0.890777i	$0.650161\pi$
$278$	27.7060	1.66170
$279$	−14.2165	−0.851119
$280$	23.0380	1.37678
$281$	−5.88779	−0.351236	−0.175618	−	0.984458i	$-0.556192\pi$
$281$	−5.88779	−0.351236	−0.175618	+	0.984458i	$0.556192\pi$
$282$	17.3365	1.03237
$283$	−29.5862	−1.75872	−0.879358	−	0.476160i	$-0.842028\pi$
$283$	−29.5862	−1.75872	−0.879358	+	0.476160i	$0.842028\pi$
$284$	42.5324	2.52383
$285$	−32.9546	−1.95206
$286$	0	0
$287$	2.11774	0.125006
$288$	12.5400	0.738928
$289$	−11.1170	−0.653943
$290$	−22.7490	−1.33587
$291$	−4.48831	−0.263110
$292$	−11.5009	−0.673041
$293$	−5.73008	−0.334755	−0.167378	−	0.985893i	$-0.553530\pi$
$293$	−5.73008	−0.334755	−0.167378	+	0.985893i	$0.553530\pi$
$294$	10.4884	0.611696
$295$	−3.09122	−0.179978
$296$	9.92834	0.577073
$297$	0	0
$298$	41.1986	2.38657
$299$	−20.6576	−1.19466
$300$	32.0053	1.84783
$301$	17.2246	0.992811
$302$	31.1529	1.79265
$303$	−4.82646	−0.277273
$304$	−12.9174	−0.740864
$305$	3.87665	0.221977
$306$	9.09302	0.519813
$307$	−20.2593	−1.15626	−0.578129	−	0.815946i	$-0.696217\pi$
$307$	−20.2593	−1.15626	−0.578129	+	0.815946i	$0.696217\pi$
$308$	0	0
$309$	−12.5213	−0.712313
$310$	−70.7012	−4.01556
$311$	−3.07029	−0.174100	−0.0870502	−	0.996204i	$-0.527744\pi$
$311$	−3.07029	−0.174100	−0.0870502	+	0.996204i	$0.527744\pi$
$312$	−6.71746	−0.380302
$313$	27.3010	1.54314	0.771572	−	0.636142i	$-0.219471\pi$
$313$	27.3010	1.54314	0.771572	+	0.636142i	$0.219471\pi$
$314$	0.369990	0.0208798
$315$	−22.1884	−1.25018
$316$	−31.6797	−1.78212
$317$	−1.40786	−0.0790732	−0.0395366	−	0.999218i	$-0.512588\pi$
$317$	−1.40786	−0.0790732	−0.0395366	+	0.999218i	$0.512588\pi$
$318$	−27.0998	−1.51968
$319$	0	0
$320$	48.9798	2.73806
$321$	−11.8462	−0.661189
$322$	−45.5288	−2.53722
$323$	−18.1500	−1.00989
$324$	−2.66658	−0.148143
$325$	−33.4098	−1.85324
$326$	15.3713	0.851339
$327$	6.23997	0.345071
$328$	−1.12268	−0.0619894
$329$	−23.2992	−1.28452
$330$	0	0
$331$	−13.6295	−0.749147	−0.374573	−	0.927197i	$-0.622211\pi$
$331$	−13.6295	−0.749147	−0.374573	+	0.927197i	$0.622211\pi$
$332$	−17.0435	−0.935384
$333$	−9.56222	−0.524006
$334$	−31.1409	−1.70396
$335$	−50.4114	−2.75427
$336$	6.56570	0.358188
$337$	23.0887	1.25772	0.628861	−	0.777518i	$-0.283521\pi$
$337$	23.0887	1.25772	0.628861	+	0.777518i	$0.283521\pi$
$338$	−4.16913	−0.226771
$339$	−13.9654	−0.758497
$340$	26.4157	1.43259
$341$	0	0
$342$	−28.0536	−1.51696
$343$	9.34122	0.504378
$344$	−9.13126	−0.492324
$345$	−27.3072	−1.47017
$346$	42.2977	2.27394
$347$	17.8829	0.960006	0.480003	−	0.877267i	$-0.340635\pi$
$347$	17.8829	0.960006	0.480003	+	0.877267i	$0.340635\pi$
$348$	8.53985	0.457784
$349$	16.5158	0.884071	0.442036	−	0.896997i	$-0.354256\pi$
$349$	16.5158	0.884071	0.442036	+	0.896997i	$0.354256\pi$
$350$	−73.6344	−3.93592
$351$	17.8236	0.951352
$352$	0	0
$353$	8.23829	0.438480	0.219240	−	0.975671i	$-0.429642\pi$
$353$	8.23829	0.438480	0.219240	+	0.975671i	$0.429642\pi$
$354$	1.98654	0.105583
$355$	−58.6908	−3.11498
$356$	46.2772	2.45268
$357$	9.22534	0.488257
$358$	32.2263	1.70321
$359$	7.15090	0.377410	0.188705	−	0.982034i	$-0.439571\pi$
$359$	7.15090	0.377410	0.188705	+	0.982034i	$0.439571\pi$
$360$	11.7627	0.619950
$361$	36.9959	1.94715
$362$	10.9824	0.577222
$363$	0	0
$364$	31.3365	1.64248
$365$	15.8702	0.830686
$366$	−2.49129	−0.130222
$367$	−29.7118	−1.55094	−0.775472	−	0.631382i	$-0.782488\pi$
$367$	−29.7118	−1.55094	−0.775472	+	0.631382i	$0.782488\pi$
$368$	−10.7038	−0.557972
$369$	1.08128	0.0562890
$370$	−47.5546	−2.47225
$371$	36.4204	1.89085
$372$	26.5408	1.37608
$373$	−15.5940	−0.807428	−0.403714	−	0.914885i	$-0.632281\pi$
$373$	−15.5940	−0.807428	−0.403714	+	0.914885i	$0.632281\pi$
$374$	0	0
$375$	−22.1448	−1.14355
$376$	12.3515	0.636982
$377$	−8.91461	−0.459126
$378$	39.2827	2.02048
$379$	3.93071	0.201907	0.100954	−	0.994891i	$-0.467811\pi$
$379$	3.93071	0.201907	0.100954	+	0.994891i	$0.467811\pi$
$380$	−81.4972	−4.18072
$381$	3.29308	0.168709
$382$	−2.00368	−0.102517
$383$	7.69912	0.393407	0.196703	−	0.980463i	$-0.436976\pi$
$383$	7.69912	0.393407	0.196703	+	0.980463i	$0.436976\pi$
$384$	−14.8099	−0.755767
$385$	0	0
$386$	24.5934	1.25177
$387$	8.79453	0.447051
$388$	−11.0997	−0.563500
$389$	12.4596	0.631727	0.315863	−	0.948805i	$-0.397706\pi$
$389$	12.4596	0.631727	0.315863	+	0.948805i	$0.397706\pi$
$390$	32.1752	1.62926
$391$	−15.0396	−0.760587
$392$	7.47256	0.377421
$393$	13.9210	0.702219
$394$	−28.5472	−1.43819
$395$	43.7150	2.19954
$396$	0	0
$397$	16.8597	0.846164	0.423082	−	0.906091i	$-0.360948\pi$
$397$	16.8597	0.846164	0.423082	+	0.906091i	$0.360948\pi$
$398$	−21.4494	−1.07516
$399$	−28.4618	−1.42487
$400$	−17.3113	−0.865567
$401$	10.0010	0.499425	0.249712	−	0.968320i	$-0.419664\pi$
$401$	10.0010	0.499425	0.249712	+	0.968320i	$0.419664\pi$
$402$	32.3963	1.61578
$403$	−27.7055	−1.38011
$404$	−11.9359	−0.593833
$405$	3.67963	0.182842
$406$	−19.6476	−0.975093
$407$	0	0
$408$	−4.89061	−0.242121
$409$	−3.37679	−0.166972	−0.0834859	−	0.996509i	$-0.526605\pi$
$409$	−3.37679	−0.166972	−0.0834859	+	0.996509i	$0.526605\pi$
$410$	5.37738	0.265570
$411$	20.3260	1.00261
$412$	−30.9654	−1.52556
$413$	−2.66979	−0.131372
$414$	−23.2461	−1.14248
$415$	23.5185	1.15448
$416$	24.4384	1.19819
$417$	14.3520	0.702818
$418$	0	0
$419$	−23.0855	−1.12780	−0.563899	−	0.825844i	$-0.690699\pi$
$419$	−23.0855	−1.12780	−0.563899	+	0.825844i	$0.690699\pi$
$420$	41.4236	2.02127
$421$	−6.13654	−0.299077	−0.149538	−	0.988756i	$-0.547779\pi$
$421$	−6.13654	−0.299077	−0.149538	+	0.988756i	$0.547779\pi$
$422$	−8.17037	−0.397727
$423$	−11.8961	−0.578407
$424$	−19.3075	−0.937655
$425$	−24.3238	−1.17988
$426$	37.7170	1.82740
$427$	3.34814	0.162028
$428$	−29.2958	−1.41606
$429$	0	0
$430$	43.7368	2.10918
$431$	−33.6449	−1.62062	−0.810308	−	0.586005i	$-0.800700\pi$
$431$	−33.6449	−1.62062	−0.810308	+	0.586005i	$0.800700\pi$
$432$	9.23531	0.444334
$433$	20.6095	0.990427	0.495214	−	0.868771i	$-0.335090\pi$
$433$	20.6095	0.990427	0.495214	+	0.868771i	$0.335090\pi$
$434$	−61.0623	−2.93108
$435$	−11.7842	−0.565009
$436$	15.4315	0.739036
$437$	46.4000	2.21961
$438$	−10.1988	−0.487319
$439$	−13.1005	−0.625254	−0.312627	−	0.949876i	$-0.601209\pi$
$439$	−13.1005	−0.625254	−0.312627	+	0.949876i	$0.601209\pi$
$440$	0	0
$441$	−7.19700	−0.342714
$442$	17.7207	0.842890
$443$	24.8810	1.18213	0.591067	−	0.806623i	$-0.298707\pi$
$443$	24.8810	1.18213	0.591067	+	0.806623i	$0.298707\pi$
$444$	17.8517	0.847205
$445$	−63.8582	−3.02717
$446$	−39.6330	−1.87668
$447$	21.3412	1.00941
$448$	42.3023	1.99859
$449$	35.4096	1.67108	0.835542	−	0.549427i	$-0.185154\pi$
$449$	35.4096	1.67108	0.835542	+	0.549427i	$0.185154\pi$
$450$	−37.5962	−1.77230
$451$	0	0
$452$	−34.5367	−1.62447
$453$	16.1375	0.758206
$454$	16.0295	0.752303
$455$	−43.2415	−2.02719
$456$	15.0884	0.706579
$457$	5.00611	0.234176	0.117088	−	0.993122i	$-0.462644\pi$
$457$	5.00611	0.234176	0.117088	+	0.993122i	$0.462644\pi$
$458$	−7.41801	−0.346621
$459$	12.9764	0.605684
$460$	−67.5311	−3.14865
$461$	31.9040	1.48592	0.742958	−	0.669338i	$-0.233422\pi$
$461$	31.9040	1.48592	0.742958	+	0.669338i	$0.233422\pi$
$462$	0	0
$463$	2.91706	0.135567	0.0677837	−	0.997700i	$-0.478407\pi$
$463$	2.91706	0.135567	0.0677837	+	0.997700i	$0.478407\pi$
$464$	−4.61912	−0.214437
$465$	−36.6238	−1.69839
$466$	7.86760	0.364459
$467$	34.3642	1.59018	0.795092	−	0.606488i	$-0.207422\pi$
$467$	34.3642	1.59018	0.795092	+	0.606488i	$0.207422\pi$
$468$	15.9998	0.739590
$469$	−43.5386	−2.01043
$470$	−59.1613	−2.72891
$471$	0.191658	0.00883115
$472$	1.41533	0.0651458
$473$	0	0
$474$	−28.0930	−1.29035
$475$	75.0433	3.44322
$476$	22.8144	1.04570
$477$	18.5955	0.851430
$478$	45.9187	2.10027
$479$	−22.7117	−1.03772	−0.518862	−	0.854858i	$-0.673644\pi$
$479$	−22.7117	−1.03772	−0.518862	+	0.854858i	$0.673644\pi$
$480$	32.3050	1.47451
$481$	−18.6351	−0.849689
$482$	32.4614	1.47858
$483$	−23.5843	−1.07312
$484$	0	0
$485$	15.3165	0.695486
$486$	32.8334	1.48936
$487$	−13.7426	−0.622738	−0.311369	−	0.950289i	$-0.600787\pi$
$487$	−13.7426	−0.622738	−0.311369	+	0.950289i	$0.600787\pi$
$488$	−1.77494	−0.0803479
$489$	7.96248	0.360076
$490$	−35.7920	−1.61692
$491$	18.5437	0.836867	0.418434	−	0.908247i	$-0.362579\pi$
$491$	18.5437	0.836867	0.418434	+	0.908247i	$0.362579\pi$
$492$	−2.01863	−0.0910071
$493$	−6.49024	−0.292305
$494$	−54.6716	−2.45979
$495$	0	0
$496$	−14.3557	−0.644588
$497$	−50.6893	−2.27373
$498$	−15.1139	−0.677270
$499$	33.2925	1.49038	0.745190	−	0.666853i	$-0.232359\pi$
$499$	33.2925	1.49038	0.745190	+	0.666853i	$0.232359\pi$
$500$	−54.7644	−2.44914
$501$	−16.1313	−0.720693
$502$	43.6762	1.94937
$503$	−23.1519	−1.03229	−0.516146	−	0.856501i	$-0.672634\pi$
$503$	−23.1519	−1.03229	−0.516146	+	0.856501i	$0.672634\pi$
$504$	10.1591	0.452521
$505$	16.4704	0.732924
$506$	0	0
$507$	−2.15964	−0.0959132
$508$	8.14382	0.361323
$509$	−26.7406	−1.18526	−0.592629	−	0.805476i	$-0.701910\pi$
$509$	−26.7406	−1.18526	−0.592629	+	0.805476i	$0.701910\pi$
$510$	23.4250	1.03728
$511$	13.7066	0.606344
$512$	18.7907	0.830438
$513$	−40.0344	−1.76756
$514$	−48.7315	−2.14946
$515$	42.7294	1.88288
$516$	−16.4185	−0.722785
$517$	0	0
$518$	−41.0714	−1.80457
$519$	21.9106	0.961768
$520$	22.9235	1.00526
$521$	8.78354	0.384814	0.192407	−	0.981315i	$-0.438371\pi$
$521$	8.78354	0.384814	0.192407	+	0.981315i	$0.438371\pi$
$522$	−10.0316	−0.439073
$523$	43.4482	1.89986	0.949928	−	0.312470i	$-0.101156\pi$
$523$	43.4482	1.89986	0.949928	+	0.312470i	$0.101156\pi$
$524$	34.4267	1.50394
$525$	−38.1433	−1.66471
$526$	2.46010	0.107265
$527$	−20.1709	−0.878656
$528$	0	0
$529$	15.4484	0.671671
$530$	92.4788	4.01702
$531$	−1.36314	−0.0591551
$532$	−70.3864	−3.05164
$533$	2.10722	0.0912739
$534$	41.0378	1.77588
$535$	40.4254	1.74774
$536$	23.0811	0.996950
$537$	16.6935	0.720378
$538$	7.19220	0.310078
$539$	0	0
$540$	58.2665	2.50739
$541$	−0.244343	−0.0105051	−0.00525256	−	0.999986i	$-0.501672\pi$
$541$	−0.244343	−0.0105051	−0.00525256	+	0.999986i	$0.501672\pi$
$542$	1.28549	0.0552163
$543$	5.68898	0.244137
$544$	17.7922	0.762835
$545$	−21.2941	−0.912138
$546$	27.7887	1.18925
$547$	6.46011	0.276214	0.138107	−	0.990417i	$-0.455898\pi$
$547$	6.46011	0.276214	0.138107	+	0.990417i	$0.455898\pi$
$548$	50.2666	2.14728
$549$	1.70949	0.0729592
$550$	0	0
$551$	20.0235	0.853031
$552$	12.5027	0.532151
$553$	37.7552	1.60551
$554$	−33.1735	−1.40941
$555$	−24.6337	−1.04564
$556$	35.4926	1.50522
$557$	−24.5456	−1.04003	−0.520015	−	0.854157i	$-0.674074\pi$
$557$	−24.5456	−1.04003	−0.520015	+	0.854157i	$0.674074\pi$
$558$	−31.1771	−1.31983
$559$	17.1390	0.724904
$560$	−22.4056	−0.946811
$561$	0	0
$562$	−12.9121	−0.544663
$563$	10.3692	0.437009	0.218504	−	0.975836i	$-0.429882\pi$
$563$	10.3692	0.437009	0.218504	+	0.975836i	$0.429882\pi$
$564$	22.2088	0.935159
$565$	47.6574	2.00496
$566$	−64.8833	−2.72725
$567$	3.17797	0.133462
$568$	26.8718	1.12752
$569$	37.4636	1.57055	0.785277	−	0.619144i	$-0.212520\pi$
$569$	37.4636	1.57055	0.785277	+	0.619144i	$0.212520\pi$
$570$	−72.2703	−3.02707
$571$	−30.5449	−1.27826	−0.639132	−	0.769097i	$-0.720706\pi$
$571$	−30.5449	−1.27826	−0.639132	+	0.769097i	$0.720706\pi$
$572$	0	0
$573$	−1.03792	−0.0433599
$574$	4.64426	0.193848
$575$	62.1832	2.59322
$576$	21.5987	0.899944
$577$	−25.3268	−1.05437	−0.527184	−	0.849751i	$-0.676752\pi$
$577$	−25.3268	−1.05437	−0.527184	+	0.849751i	$0.676752\pi$
$578$	−24.3799	−1.01407
$579$	12.7396	0.529440
$580$	−29.1425	−1.21008
$581$	20.3121	0.842689
$582$	−9.84298	−0.408005
$583$	0	0
$584$	−7.26625	−0.300680
$585$	−22.0782	−0.912822
$586$	−12.5662	−0.519106
$587$	34.2550	1.41385	0.706927	−	0.707287i	$-0.250081\pi$
$587$	34.2550	1.41385	0.706927	+	0.707287i	$0.250081\pi$
$588$	13.4361	0.554095
$589$	62.2307	2.56417
$590$	−6.77913	−0.279092
$591$	−14.7877	−0.608284
$592$	−9.65582	−0.396852
$593$	15.8516	0.650945	0.325473	−	0.945551i	$-0.394477\pi$
$593$	15.8516	0.650945	0.325473	+	0.945551i	$0.394477\pi$
$594$	0	0
$595$	−31.4817	−1.29063
$596$	52.7772	2.16184
$597$	−11.1110	−0.454743
$598$	−45.3026	−1.85256
$599$	−11.4422	−0.467515	−0.233757	−	0.972295i	$-0.575102\pi$
$599$	−11.4422	−0.467515	−0.233757	+	0.972295i	$0.575102\pi$
$600$	20.2208	0.825512
$601$	26.8268	1.09429	0.547144	−	0.837039i	$-0.315715\pi$
$601$	26.8268	1.09429	0.547144	+	0.837039i	$0.315715\pi$
$602$	37.7740	1.53955
$603$	−22.2299	−0.905272
$604$	39.9082	1.62384
$605$	0	0
$606$	−10.5845	−0.429968
$607$	−11.8113	−0.479404	−0.239702	−	0.970847i	$-0.577050\pi$
$607$	−11.8113	−0.479404	−0.239702	+	0.970847i	$0.577050\pi$
$608$	−54.8921	−2.22617
$609$	−10.1776	−0.412418
$610$	8.50160	0.344220
$611$	−23.1834	−0.937900
$612$	11.6485	0.470865
$613$	−17.6434	−0.712609	−0.356305	−	0.934370i	$-0.615963\pi$
$613$	−17.6434	−0.712609	−0.356305	+	0.934370i	$0.615963\pi$
$614$	−44.4291	−1.79301
$615$	2.78553	0.112323
$616$	0	0
$617$	−22.6740	−0.912823	−0.456411	−	0.889769i	$-0.650865\pi$
$617$	−22.6740	−0.912823	−0.456411	+	0.889769i	$0.650865\pi$
$618$	−27.4596	−1.10459
$619$	−2.14696	−0.0862936	−0.0431468	−	0.999069i	$-0.513738\pi$
$619$	−2.14696	−0.0862936	−0.0431468	+	0.999069i	$0.513738\pi$
$620$	−90.5712	−3.63743
$621$	−33.1737	−1.33121
$622$	−6.73323	−0.269978
$623$	−55.1522	−2.20963
$624$	6.53308	0.261532
$625$	25.4276	1.01710
$626$	59.8718	2.39296
$627$	0	0
$628$	0.473973	0.0189136
$629$	−13.5672	−0.540960
$630$	−48.6598	−1.93865
$631$	16.4001	0.652876	0.326438	−	0.945219i	$-0.394151\pi$
$631$	16.4001	0.652876	0.326438	+	0.945219i	$0.394151\pi$
$632$	−20.0151	−0.796158
$633$	−4.23232	−0.168220
$634$	−3.08747	−0.122619
$635$	−11.2377	−0.445955
$636$	−34.7160	−1.37658
$637$	−14.0257	−0.555719
$638$	0	0
$639$	−25.8809	−1.02383
$640$	50.5394	1.99774
$641$	17.2072	0.679645	0.339823	−	0.940490i	$-0.389633\pi$
$641$	17.2072	0.679645	0.339823	+	0.940490i	$0.389633\pi$
$642$	−25.9790	−1.02531
$643$	45.8874	1.80962	0.904811	−	0.425813i	$-0.140012\pi$
$643$	45.8874	1.80962	0.904811	+	0.425813i	$0.140012\pi$
$644$	−58.3243	−2.29830
$645$	22.6560	0.892081
$646$	−39.8034	−1.56604
$647$	−44.5350	−1.75085	−0.875426	−	0.483351i	$-0.839419\pi$
$647$	−44.5350	−1.75085	−0.875426	+	0.483351i	$0.839419\pi$
$648$	−1.68473	−0.0661826
$649$	0	0
$650$	−73.2686	−2.87383
$651$	−31.6308	−1.23971
$652$	19.6913	0.771172
$653$	−5.57274	−0.218078	−0.109039	−	0.994037i	$-0.534777\pi$
$653$	−5.57274	−0.218078	−0.109039	+	0.994037i	$0.534777\pi$
$654$	13.6844	0.535102
$655$	−47.5057	−1.85620
$656$	1.09186	0.0426300
$657$	6.99830	0.273030
$658$	−51.0956	−1.99192
$659$	39.3284	1.53202	0.766008	−	0.642831i	$-0.222240\pi$
$659$	39.3284	1.53202	0.766008	+	0.642831i	$0.222240\pi$
$660$	0	0
$661$	−2.51038	−0.0976426	−0.0488213	−	0.998808i	$-0.515546\pi$
$661$	−2.51038	−0.0976426	−0.0488213	+	0.998808i	$0.515546\pi$
$662$	−29.8899	−1.16170
$663$	9.17950	0.356502
$664$	−10.7680	−0.417881
$665$	97.1267	3.76641
$666$	−20.9702	−0.812578
$667$	16.5921	0.642449
$668$	−39.8929	−1.54350
$669$	−20.5302	−0.793744
$670$	−110.553	−4.27105
$671$	0	0
$672$	27.9007	1.07629
$673$	21.9820	0.847343	0.423671	−	0.905816i	$-0.360741\pi$
$673$	21.9820	0.847343	0.423671	+	0.905816i	$0.360741\pi$
$674$	50.6341	1.95035
$675$	−53.6523	−2.06508
$676$	−5.34083	−0.205416
$677$	18.2538	0.701552	0.350776	−	0.936459i	$-0.385918\pi$
$677$	18.2538	0.701552	0.350776	+	0.936459i	$0.385918\pi$
$678$	−30.6265	−1.17620
$679$	13.2283	0.507657
$680$	16.6894	0.640008
$681$	8.30344	0.318189
$682$	0	0
$683$	−12.3322	−0.471877	−0.235938	−	0.971768i	$-0.575816\pi$
$683$	−12.3322	−0.471877	−0.235938	+	0.971768i	$0.575816\pi$
$684$	−35.9378	−1.37412
$685$	−69.3632	−2.65023
$686$	20.4855	0.782141
$687$	−3.84260	−0.146604
$688$	8.88062	0.338570
$689$	36.2395	1.38061
$690$	−59.8854	−2.27980
$691$	−26.4275	−1.00535	−0.502675	−	0.864476i	$-0.667651\pi$
$691$	−26.4275	−1.00535	−0.502675	+	0.864476i	$0.667651\pi$
$692$	54.1852	2.05981
$693$	0	0
$694$	39.2177	1.48868
$695$	−48.9765	−1.85778
$696$	5.39545	0.204514
$697$	1.53415	0.0581101
$698$	36.2196	1.37093
$699$	4.07549	0.154149
$700$	−94.3288	−3.56529
$701$	−47.3706	−1.78916	−0.894582	−	0.446904i	$-0.852527\pi$
$701$	−47.3706	−1.78916	−0.894582	+	0.446904i	$0.852527\pi$
$702$	39.0875	1.47526
$703$	41.8572	1.57868
$704$	0	0
$705$	−30.6461	−1.15420
$706$	18.0668	0.679952
$707$	14.2250	0.534985
$708$	2.54484	0.0956411
$709$	37.5265	1.40934	0.704668	−	0.709537i	$-0.251096\pi$
$709$	37.5265	1.40934	0.704668	+	0.709537i	$0.251096\pi$
$710$	−128.710	−4.83041
$711$	19.2770	0.722945
$712$	29.2377	1.09573
$713$	51.5662	1.93117
$714$	20.2314	0.757141
$715$	0	0
$716$	41.2833	1.54283
$717$	23.7863	0.888316
$718$	15.6821	0.585251
$719$	−15.3971	−0.574216	−0.287108	−	0.957898i	$-0.592694\pi$
$719$	−15.3971	−0.574216	−0.287108	+	0.957898i	$0.592694\pi$
$720$	−11.4399	−0.426338
$721$	36.9039	1.37437
$722$	81.1330	3.01946
$723$	16.8153	0.625368
$724$	14.0689	0.522867
$725$	26.8347	0.996614
$726$	0	0
$727$	−28.1185	−1.04286	−0.521428	−	0.853295i	$-0.674600\pi$
$727$	−28.1185	−1.04286	−0.521428	+	0.853295i	$0.674600\pi$
$728$	19.7983	0.733774
$729$	19.8555	0.735390
$730$	34.8038	1.28815
$731$	12.4780	0.461515
$732$	−3.19145	−0.117959
$733$	−10.9059	−0.402817	−0.201409	−	0.979507i	$-0.564552\pi$
$733$	−10.9059	−0.402817	−0.201409	+	0.979507i	$0.564552\pi$
$734$	−65.1587	−2.40505
$735$	−18.5406	−0.683879
$736$	−45.4853	−1.67661
$737$	0	0
$738$	2.37126	0.0872874
$739$	21.1774	0.779021	0.389511	−	0.921022i	$-0.372644\pi$
$739$	21.1774	0.779021	0.389511	+	0.921022i	$0.372644\pi$
$740$	−60.9195	−2.23945
$741$	−28.3204	−1.04038
$742$	79.8709	2.93215
$743$	16.2063	0.594552	0.297276	−	0.954792i	$-0.403922\pi$
$743$	16.2063	0.594552	0.297276	+	0.954792i	$0.403922\pi$
$744$	16.7684	0.614759
$745$	−72.8276	−2.66820
$746$	−34.1981	−1.25208
$747$	10.3709	0.379453
$748$	0	0
$749$	34.9141	1.27573
$750$	−48.5641	−1.77331
$751$	3.82560	0.139598	0.0697991	−	0.997561i	$-0.477764\pi$
$751$	3.82560	0.139598	0.0697991	+	0.997561i	$0.477764\pi$
$752$	−12.0125	−0.438051
$753$	22.6247	0.824489
$754$	−19.5500	−0.711968
$755$	−55.0697	−2.00419
$756$	50.3228	1.83022
$757$	−11.4027	−0.414437	−0.207219	−	0.978295i	$-0.566441\pi$
$757$	−11.4027	−0.414437	−0.207219	+	0.978295i	$0.566441\pi$
$758$	8.62015	0.313098
$759$	0	0
$760$	−51.4896	−1.86772
$761$	8.00618	0.290224	0.145112	−	0.989415i	$-0.453646\pi$
$761$	8.00618	0.290224	0.145112	+	0.989415i	$0.453646\pi$
$762$	7.22180	0.261618
$763$	−18.3910	−0.665798
$764$	−2.56680	−0.0928636
$765$	−16.0739	−0.581154
$766$	16.8844	0.610057
$767$	−2.65652	−0.0959215
$768$	−3.77267	−0.136135
$769$	−8.44893	−0.304676	−0.152338	−	0.988328i	$-0.548680\pi$
$769$	−8.44893	−0.304676	−0.152338	+	0.988328i	$0.548680\pi$
$770$	0	0
$771$	−25.2434	−0.909117
$772$	31.5052	1.13390
$773$	−13.9443	−0.501542	−0.250771	−	0.968046i	$-0.580684\pi$
$773$	−13.9443	−0.501542	−0.250771	+	0.968046i	$0.580684\pi$
$774$	19.2866	0.693244
$775$	83.3988	2.99577
$776$	−7.01272	−0.251742
$777$	−21.2753	−0.763248
$778$	27.3242	0.979621
$779$	−4.73313	−0.169582
$780$	41.2178	1.47584
$781$	0	0
$782$	−32.9823	−1.17944
$783$	−14.3158	−0.511606
$784$	−7.26744	−0.259552
$785$	−0.654039	−0.0233437
$786$	30.5290	1.08893
$787$	6.62789	0.236259	0.118129	−	0.992998i	$-0.462310\pi$
$787$	6.62789	0.236259	0.118129	+	0.992998i	$0.462310\pi$
$788$	−36.5702	−1.30276
$789$	1.27435	0.0453681
$790$	95.8681	3.41083
$791$	41.1601	1.46348
$792$	0	0
$793$	3.33150	0.118305
$794$	36.9738	1.31215
$795$	47.9048	1.69901
$796$	−27.4776	−0.973919
$797$	−6.86668	−0.243230	−0.121615	−	0.992577i	$-0.538807\pi$
$797$	−6.86668	−0.243230	−0.121615	+	0.992577i	$0.538807\pi$
$798$	−62.4174	−2.20955
$799$	−16.8786	−0.597120
$800$	−73.5641	−2.60088
$801$	−28.1596	−0.994970
$802$	21.9324	0.774460
$803$	0	0
$804$	41.5011	1.46363
$805$	80.4822	2.83662
$806$	−60.7589	−2.14014
$807$	3.72562	0.131148
$808$	−7.54105	−0.265293
$809$	22.2319	0.781633	0.390817	−	0.920469i	$-0.372193\pi$
$809$	22.2319	0.781633	0.390817	+	0.920469i	$0.372193\pi$
$810$	8.06952	0.283534
$811$	−17.0512	−0.598750	−0.299375	−	0.954135i	$-0.596778\pi$
$811$	−17.0512	−0.598750	−0.299375	+	0.954135i	$0.596778\pi$
$812$	−25.1694	−0.883273
$813$	0.665893	0.0233539
$814$	0	0
$815$	−27.1722	−0.951801
$816$	4.75637	0.166506
$817$	−38.4968	−1.34683
$818$	−7.40539	−0.258924
$819$	−19.0682	−0.666297
$820$	6.88865	0.240562
$821$	−13.7365	−0.479406	−0.239703	−	0.970846i	$-0.577050\pi$
$821$	−13.7365	−0.479406	−0.239703	+	0.970846i	$0.577050\pi$
$822$	44.5755	1.55475
$823$	31.3223	1.09183	0.545914	−	0.837841i	$-0.316183\pi$
$823$	31.3223	1.09183	0.545914	+	0.837841i	$0.316183\pi$
$824$	−19.5638	−0.681538
$825$	0	0
$826$	−5.85491	−0.203718
$827$	−29.3223	−1.01964	−0.509819	−	0.860282i	$-0.670288\pi$
$827$	−29.3223	−1.01964	−0.509819	+	0.860282i	$0.670288\pi$
$828$	−29.7792	−1.03490
$829$	18.2233	0.632920	0.316460	−	0.948606i	$-0.397506\pi$
$829$	18.2233	0.632920	0.316460	+	0.948606i	$0.397506\pi$
$830$	51.5766	1.79025
$831$	−17.1842	−0.596112
$832$	42.0921	1.45928
$833$	−10.2113	−0.353802
$834$	31.4742	1.08986
$835$	55.0485	1.90503
$836$	0	0
$837$	−44.4919	−1.53786
$838$	−50.6270	−1.74888
$839$	−9.21238	−0.318047	−0.159023	−	0.987275i	$-0.550834\pi$
$839$	−9.21238	−0.318047	−0.159023	+	0.987275i	$0.550834\pi$
$840$	26.1713	0.902996
$841$	−21.8398	−0.753097
$842$	−13.4576	−0.463779
$843$	−6.68857	−0.230366
$844$	−10.4666	−0.360275
$845$	7.36985	0.253530
$846$	−26.0884	−0.896937
$847$	0	0
$848$	18.7775	0.644823
$849$	−33.6101	−1.15350
$850$	−53.3428	−1.82964
$851$	34.6842	1.18896
$852$	48.3171	1.65532
$853$	1.71618	0.0587608	0.0293804	−	0.999568i	$-0.490647\pi$
$853$	1.71618	0.0587608	0.0293804	+	0.999568i	$0.490647\pi$
$854$	7.34255	0.251257
$855$	49.5909	1.69597
$856$	−18.5090	−0.632623
$857$	−48.1201	−1.64375	−0.821876	−	0.569667i	$-0.807072\pi$
$857$	−48.1201	−1.64375	−0.821876	+	0.569667i	$0.807072\pi$
$858$	0	0
$859$	−53.3428	−1.82003	−0.910016	−	0.414573i	$-0.863931\pi$
$859$	−53.3428	−1.82003	−0.910016	+	0.414573i	$0.863931\pi$
$860$	56.0287	1.91056
$861$	2.40577	0.0819884
$862$	−73.7840	−2.51309
$863$	−11.8351	−0.402872	−0.201436	−	0.979502i	$-0.564561\pi$
$863$	−11.8351	−0.402872	−0.201436	+	0.979502i	$0.564561\pi$
$864$	39.2452	1.33515
$865$	−74.7705	−2.54227
$866$	45.1970	1.53586
$867$	−12.6290	−0.428904
$868$	−78.2234	−2.65507
$869$	0	0
$870$	−25.8430	−0.876161
$871$	−43.3223	−1.46792
$872$	9.74958	0.330162
$873$	6.75412	0.228592
$874$	101.756	3.44196
$875$	65.2671	2.20643
$876$	−13.0651	−0.441430
$877$	31.0985	1.05012	0.525062	−	0.851064i	$-0.324042\pi$
$877$	31.0985	1.05012	0.525062	+	0.851064i	$0.324042\pi$
$878$	−28.7298	−0.969583
$879$	−6.50941	−0.219557
$880$	0	0
$881$	−0.502655	−0.0169349	−0.00846744	−	0.999964i	$-0.502695\pi$
$881$	−0.502655	−0.0169349	−0.00846744	+	0.999964i	$0.502695\pi$
$882$	−15.7832	−0.531448
$883$	38.2265	1.28642	0.643211	−	0.765689i	$-0.277602\pi$
$883$	38.2265	1.28642	0.643211	+	0.765689i	$0.277602\pi$
$884$	22.7010	0.763518
$885$	−3.51165	−0.118043
$886$	54.5647	1.83314
$887$	55.2883	1.85640	0.928200	−	0.372081i	$-0.121356\pi$
$887$	55.2883	1.85640	0.928200	+	0.372081i	$0.121356\pi$
$888$	11.2787	0.378487
$889$	−9.70564	−0.325517
$890$	−140.043	−4.69424
$891$	0	0
$892$	−50.7715	−1.69996
$893$	52.0733	1.74257
$894$	46.8019	1.56529
$895$	−56.9671	−1.90420
$896$	43.6492	1.45822
$897$	−23.4671	−0.783545
$898$	77.6542	2.59135
$899$	22.2530	0.742179
$900$	−48.1623	−1.60541
$901$	26.3839	0.878977
$902$	0	0
$903$	19.5673	0.651158
$904$	−21.8201	−0.725727
$905$	−19.4138	−0.645336
$906$	35.3899	1.17575
$907$	30.6802	1.01872	0.509359	−	0.860554i	$-0.329882\pi$
$907$	30.6802	1.01872	0.509359	+	0.860554i	$0.329882\pi$
$908$	20.5345	0.681462
$909$	7.26297	0.240897
$910$	−94.8297	−3.14357
$911$	−0.197413	−0.00654057	−0.00327029	−	0.999995i	$-0.501041\pi$
$911$	−0.197413	−0.00654057	−0.00327029	+	0.999995i	$0.501041\pi$
$912$	−14.6742	−0.485913
$913$	0	0
$914$	10.9785	0.363137
$915$	4.40390	0.145589
$916$	−9.50279	−0.313981
$917$	−41.0291	−1.35490
$918$	28.4575	0.939236
$919$	44.9844	1.48390	0.741950	−	0.670456i	$-0.233901\pi$
$919$	44.9844	1.48390	0.741950	+	0.670456i	$0.233901\pi$
$920$	−42.6659	−1.40665
$921$	−23.0147	−0.758359
$922$	69.9662	2.30421
$923$	−50.4375	−1.66017
$924$	0	0
$925$	56.0953	1.84440
$926$	6.39719	0.210225
$927$	18.8424	0.618865
$928$	−19.6288	−0.644347
$929$	−7.20796	−0.236485	−0.118243	−	0.992985i	$-0.537726\pi$
$929$	−7.20796	−0.236485	−0.118243	+	0.992985i	$0.537726\pi$
$930$	−80.3170	−2.63370
$931$	31.5038	1.03250
$932$	10.0787	0.330140
$933$	−3.48787	−0.114188
$934$	75.3615	2.46590
$935$	0	0
$936$	10.1086	0.330410
$937$	10.8511	0.354489	0.177245	−	0.984167i	$-0.443282\pi$
$937$	10.8511	0.354489	0.177245	+	0.984167i	$0.443282\pi$
$938$	−95.4813	−3.11758
$939$	31.0141	1.01211
$940$	−75.7881	−2.47194
$941$	32.0924	1.04618	0.523092	−	0.852276i	$-0.324779\pi$
$941$	32.0924	1.04618	0.523092	+	0.852276i	$0.324779\pi$
$942$	0.420311	0.0136945
$943$	−3.92201	−0.127718
$944$	−1.37648	−0.0448006
$945$	−69.4408	−2.25891
$946$	0	0
$947$	−17.1736	−0.558068	−0.279034	−	0.960281i	$-0.590014\pi$
$947$	−17.1736	−0.558068	−0.279034	+	0.960281i	$0.590014\pi$
$948$	−35.9883	−1.16885
$949$	13.6385	0.442724
$950$	164.572	5.33942
$951$	−1.59934	−0.0518620
$952$	14.4140	0.467162
$953$	12.5624	0.406937	0.203468	−	0.979082i	$-0.434779\pi$
$953$	12.5624	0.406937	0.203468	+	0.979082i	$0.434779\pi$
$954$	40.7804	1.32031
$955$	3.54195	0.114615
$956$	58.8238	1.90250
$957$	0	0
$958$	−49.8073	−1.60920
$959$	−59.9067	−1.93449
$960$	55.6414	1.79582
$961$	38.1596	1.23095
$962$	−40.8673	−1.31762
$963$	17.8264	0.574448
$964$	41.5844	1.33934
$965$	−43.4743	−1.39949
$966$	−51.7210	−1.66410
$967$	7.96396	0.256104	0.128052	−	0.991767i	$-0.459128\pi$
$967$	7.96396	0.256104	0.128052	+	0.991767i	$0.459128\pi$
$968$	0	0
$969$	−20.6185	−0.662362
$970$	33.5895	1.07849
$971$	−5.74776	−0.184454	−0.0922272	−	0.995738i	$-0.529399\pi$
$971$	−5.74776	−0.184454	−0.0922272	+	0.995738i	$0.529399\pi$
$972$	42.0610	1.34911
$973$	−42.2993	−1.35605
$974$	−30.1379	−0.965681
$975$	−37.9538	−1.21549
$976$	1.72622	0.0552550
$977$	38.5935	1.23472	0.617358	−	0.786682i	$-0.288203\pi$
$977$	38.5935	1.23472	0.617358	+	0.786682i	$0.288203\pi$
$978$	17.4619	0.558371
$979$	0	0
$980$	−45.8510	−1.46466
$981$	−9.39005	−0.299801
$982$	40.6669	1.29773
$983$	−59.6227	−1.90167	−0.950835	−	0.309698i	$-0.899772\pi$
$983$	−59.6227	−1.90167	−0.950835	+	0.309698i	$0.899772\pi$
$984$	−1.27537	−0.0406572
$985$	50.4634	1.60790
$986$	−14.2332	−0.453279
$987$	−26.4680	−0.842486
$988$	−70.0367	−2.22816
$989$	−31.8996	−1.01435
$990$	0	0
$991$	12.3426	0.392076	0.196038	−	0.980596i	$-0.437192\pi$
$991$	12.3426	0.392076	0.196038	+	0.980596i	$0.437192\pi$
$992$	−61.0039	−1.93688
$993$	−15.4832	−0.491346
$994$	−111.163	−3.52587
$995$	37.9166	1.20204
$996$	−19.3615	−0.613494
$997$	−28.6925	−0.908699	−0.454350	−	0.890823i	$-0.650128\pi$
$997$	−28.6925	−0.908699	−0.454350	+	0.890823i	$0.650128\pi$
$998$	73.0114	2.31113
$999$	−29.9259	−0.946813

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.j.1.17		21
11.10	odd	2		671.2.a.d.1.5	✓	21
33.32	even	2		6039.2.a.l.1.17		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.a.d.1.5	✓	21	11.10	odd	2
6039.2.a.l.1.17		21	33.32	even	2
7381.2.a.j.1.17		21	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)

\(f(q)\)	\(=\)	\(q+2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} +2.49129 q^{6} -3.34814 q^{7} +1.77494 q^{8} -1.70949 q^{9} +O(q^{10})\)	\(q+2.19302 q^{2} +1.13601 q^{3} +2.80936 q^{4} -3.87665 q^{5} +2.49129 q^{6} -3.34814 q^{7} +1.77494 q^{8} -1.70949 q^{9} -8.50160 q^{10} +3.19145 q^{12} -3.33150 q^{13} -7.34255 q^{14} -4.40390 q^{15} -1.72622 q^{16} -2.42548 q^{17} -3.74895 q^{18} +7.48304 q^{19} -10.8909 q^{20} -3.80351 q^{21} +6.20068 q^{23} +2.01635 q^{24} +10.0285 q^{25} -7.30607 q^{26} -5.35001 q^{27} -9.40612 q^{28} +2.67585 q^{29} -9.65787 q^{30} +8.31622 q^{31} -7.33554 q^{32} -5.31914 q^{34} +12.9796 q^{35} -4.80257 q^{36} +5.59361 q^{37} +16.4105 q^{38} -3.78461 q^{39} -6.88084 q^{40} -0.632514 q^{41} -8.34118 q^{42} -5.14454 q^{43} +6.62710 q^{45} +13.5982 q^{46} +6.95884 q^{47} -1.96100 q^{48} +4.21003 q^{49} +21.9926 q^{50} -2.75536 q^{51} -9.35939 q^{52} -10.8778 q^{53} -11.7327 q^{54} -5.94275 q^{56} +8.50078 q^{57} +5.86821 q^{58} +0.797395 q^{59} -12.3721 q^{60} -1.00000 q^{61} +18.2377 q^{62} +5.72361 q^{63} -12.6346 q^{64} +12.9151 q^{65} +13.0038 q^{67} -6.81405 q^{68} +7.04401 q^{69} +28.4645 q^{70} +15.1395 q^{71} -3.03425 q^{72} -4.09379 q^{73} +12.2669 q^{74} +11.3924 q^{75} +21.0225 q^{76} -8.29974 q^{78} -11.2765 q^{79} +6.69197 q^{80} -0.949176 q^{81} -1.38712 q^{82} -6.06669 q^{83} -10.6854 q^{84} +9.40276 q^{85} -11.2821 q^{86} +3.03979 q^{87} +16.4725 q^{89} +14.5334 q^{90} +11.1543 q^{91} +17.4199 q^{92} +9.44728 q^{93} +15.2609 q^{94} -29.0092 q^{95} -8.33321 q^{96} -3.95096 q^{97} +9.23269 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9}+O(q^{10}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9	\( 21 q + 3 q^{3} + 32 q^{4} + 7 q^{5} - 5 q^{6} - 5 q^{7} + 6 q^{8} + 40 q^{9} - q^{10} + 6 q^{12} - 20 q^{13} + 17 q^{14} + 18 q^{15} + 50 q^{16} - q^{17} + 5 q^{18} - 15 q^{19} - 2 q^{20} - 16 q^{21} + 11 q^{23} + 16 q^{24} + 48 q^{25} - 5 q^{26} + 12 q^{27} + 16 q^{28} + 9 q^{29} - 16 q^{30} + 22 q^{31} - 3 q^{32} + 33 q^{34} + 39 q^{35} + 57 q^{36} + 21 q^{37} + 11 q^{38} + 28 q^{39} + 16 q^{40} - 7 q^{41} - 55 q^{42} - 16 q^{43} + 44 q^{45} + 3 q^{46} + 5 q^{47} - 71 q^{48} + 80 q^{49} + 33 q^{50} + 19 q^{51} - 60 q^{52} + 9 q^{53} - 13 q^{54} + 44 q^{56} - 39 q^{57} - 27 q^{58} + 13 q^{59} + 70 q^{60} - 21 q^{61} + 23 q^{62} - 24 q^{63} + 66 q^{64} - 25 q^{65} + 38 q^{67} + 74 q^{68} - 17 q^{69} - 33 q^{70} + 12 q^{71} + 75 q^{72} - 20 q^{73} + 12 q^{74} - 10 q^{75} - 59 q^{76} - 14 q^{78} - q^{79} - 38 q^{80} + 89 q^{81} + 7 q^{82} + 19 q^{83} + 14 q^{84} - 38 q^{85} - 3 q^{86} - 4 q^{87} + 37 q^{89} + 174 q^{90} + 24 q^{91} + 31 q^{92} - 15 q^{93} + 64 q^{94} + 43 q^{95} + 38 q^{96} + 68 q^{97} + 2 q^{98}+O(q^{100}) \) 21 * q + 3 * q^3 + 32 * q^4 + 7 * q^5 - 5 * q^6 - 5 * q^7 + 6 * q^8 + 40 * q^9 - q^10 + 6 * q^12 - 20 * q^13 + 17 * q^14 + 18 * q^15 + 50 * q^16 - q^17 + 5 * q^18 - 15 * q^19 - 2 * q^20 - 16 * q^21 + 11 * q^23 + 16 * q^24 + 48 * q^25 - 5 * q^26 + 12 * q^27 + 16 * q^28 + 9 * q^29 - 16 * q^30 + 22 * q^31 - 3 * q^32 + 33 * q^34 + 39 * q^35 + 57 * q^36 + 21 * q^37 + 11 * q^38 + 28 * q^39 + 16 * q^40 - 7 * q^41 - 55 * q^42 - 16 * q^43 + 44 * q^45 + 3 * q^46 + 5 * q^47 - 71 * q^48 + 80 * q^49 + 33 * q^50 + 19 * q^51 - 60 * q^52 + 9 * q^53 - 13 * q^54 + 44 * q^56 - 39 * q^57 - 27 * q^58 + 13 * q^59 + 70 * q^60 - 21 * q^61 + 23 * q^62 - 24 * q^63 + 66 * q^64 - 25 * q^65 + 38 * q^67 + 74 * q^68 - 17 * q^69 - 33 * q^70 + 12 * q^71 + 75 * q^72 - 20 * q^73 + 12 * q^74 - 10 * q^75 - 59 * q^76 - 14 * q^78 - q^79 - 38 * q^80 + 89 * q^81 + 7 * q^82 + 19 * q^83 + 14 * q^84 - 38 * q^85 - 3 * q^86 - 4 * q^87 + 37 * q^89 + 174 * q^90 + 24 * q^91 + 31 * q^92 - 15 * q^93 + 64 * q^94 + 43 * q^95 + 38 * q^96 + 68 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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