LMFDB - Embedded newform 7381.2.a.u.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.32237 q^{2} +3.21773 q^{3} +3.39339 q^{4} -3.99960 q^{5} -7.47274 q^{6} -2.64706 q^{7} -3.23597 q^{8} +7.35376 q^{9} +O(q^{10})$	\(q-2.32237 q^{2} +3.21773 q^{3} +3.39339 q^{4} -3.99960 q^{5} -7.47274 q^{6} -2.64706 q^{7} -3.23597 q^{8} +7.35376 q^{9} +9.28854 q^{10} +10.9190 q^{12} +2.19078 q^{13} +6.14745 q^{14} -12.8696 q^{15} +0.728335 q^{16} -0.144193 q^{17} -17.0781 q^{18} -5.90861 q^{19} -13.5722 q^{20} -8.51751 q^{21} +7.47309 q^{23} -10.4125 q^{24} +10.9968 q^{25} -5.08779 q^{26} +14.0092 q^{27} -8.98252 q^{28} -5.80294 q^{29} +29.8880 q^{30} -7.78575 q^{31} +4.78049 q^{32} +0.334869 q^{34} +10.5872 q^{35} +24.9542 q^{36} -0.202732 q^{37} +13.7220 q^{38} +7.04931 q^{39} +12.9426 q^{40} -0.440547 q^{41} +19.7808 q^{42} -2.55280 q^{43} -29.4121 q^{45} -17.3553 q^{46} -9.64444 q^{47} +2.34358 q^{48} +0.00692413 q^{49} -25.5386 q^{50} -0.463974 q^{51} +7.43417 q^{52} +8.16478 q^{53} -32.5345 q^{54} +8.56582 q^{56} -19.0123 q^{57} +13.4766 q^{58} +1.39715 q^{59} -43.6717 q^{60} -1.00000 q^{61} +18.0814 q^{62} -19.4658 q^{63} -12.5587 q^{64} -8.76223 q^{65} +7.45420 q^{67} -0.489304 q^{68} +24.0463 q^{69} -24.5873 q^{70} +4.91095 q^{71} -23.7966 q^{72} +4.94988 q^{73} +0.470818 q^{74} +35.3847 q^{75} -20.0502 q^{76} -16.3711 q^{78} +1.07094 q^{79} -2.91305 q^{80} +23.0164 q^{81} +1.02311 q^{82} +13.0610 q^{83} -28.9033 q^{84} +0.576715 q^{85} +5.92855 q^{86} -18.6723 q^{87} -7.41041 q^{89} +68.3057 q^{90} -5.79911 q^{91} +25.3591 q^{92} -25.0524 q^{93} +22.3979 q^{94} +23.6321 q^{95} +15.3823 q^{96} +3.57772 q^{97} -0.0160804 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.32237	−1.64216	−0.821081	−	0.570811i	$-0.806629\pi$
$2$	−2.32237	−1.64216	−0.821081	+	0.570811i	$0.806629\pi$
$3$	3.21773	1.85775	0.928877	−	0.370388i	$-0.120775\pi$
$3$	3.21773	1.85775	0.928877	+	0.370388i	$0.120775\pi$
$4$	3.39339	1.69670
$5$	−3.99960	−1.78868	−0.894338	−	0.447392i	$-0.852353\pi$
$5$	−3.99960	−1.78868	−0.894338	+	0.447392i	$0.852353\pi$
$6$	−7.47274	−3.05073
$7$	−2.64706	−1.00049	−0.500247	−	0.865883i	$-0.666758\pi$
$7$	−2.64706	−1.00049	−0.500247	+	0.865883i	$0.666758\pi$
$8$	−3.23597	−1.14409
$9$	7.35376	2.45125
$10$	9.28854	2.93730
$11$	0	0
$11$	0	0
$12$	10.9190	3.15205
$13$	2.19078	0.607612	0.303806	−	0.952734i	$-0.401743\pi$
$13$	2.19078	0.607612	0.303806	+	0.952734i	$0.401743\pi$
$14$	6.14745	1.64297
$15$	−12.8696	−3.32292
$16$	0.728335	0.182084
$17$	−0.144193	−0.0349720	−0.0174860	−	0.999847i	$-0.505566\pi$
$17$	−0.144193	−0.0349720	−0.0174860	+	0.999847i	$0.505566\pi$
$18$	−17.0781	−4.02535
$19$	−5.90861	−1.35553	−0.677764	−	0.735280i	$-0.737051\pi$
$19$	−5.90861	−1.35553	−0.677764	+	0.735280i	$0.737051\pi$
$20$	−13.5722	−3.03484
$21$	−8.51751	−1.85867
$22$	0	0
$23$	7.47309	1.55825	0.779123	−	0.626870i	$-0.215664\pi$
$23$	7.47309	1.55825	0.779123	+	0.626870i	$0.215664\pi$
$24$	−10.4125	−2.12544
$25$	10.9968	2.19936
$26$	−5.08779	−0.997797
$27$	14.0092	2.69607
$28$	−8.98252	−1.69754
$29$	−5.80294	−1.07758	−0.538790	−	0.842440i	$-0.681118\pi$
$29$	−5.80294	−1.07758	−0.538790	+	0.842440i	$0.681118\pi$
$30$	29.8880	5.45677
$31$	−7.78575	−1.39836	−0.699181	−	0.714945i	$-0.746452\pi$
$31$	−7.78575	−1.39836	−0.699181	+	0.714945i	$0.746452\pi$
$32$	4.78049	0.845078
$33$	0	0
$34$	0.334869	0.0574296
$35$	10.5872	1.78956
$36$	24.9542	4.15903
$37$	−0.202732	−0.0333289	−0.0166645	−	0.999861i	$-0.505305\pi$
$37$	−0.202732	−0.0333289	−0.0166645	+	0.999861i	$0.505305\pi$
$38$	13.7220	2.22600
$39$	7.04931	1.12879
$40$	12.9426	2.04641
$41$	−0.440547	−0.0688018	−0.0344009	−	0.999408i	$-0.510952\pi$
$41$	−0.440547	−0.0688018	−0.0344009	+	0.999408i	$0.510952\pi$
$42$	19.7808	3.05224
$43$	−2.55280	−0.389299	−0.194649	−	0.980873i	$-0.562357\pi$
$43$	−2.55280	−0.389299	−0.194649	+	0.980873i	$0.562357\pi$
$44$	0	0
$45$	−29.4121	−4.38449
$46$	−17.3553	−2.55889
$47$	−9.64444	−1.40679	−0.703393	−	0.710801i	$-0.748332\pi$
$47$	−9.64444	−1.40679	−0.703393	+	0.710801i	$0.748332\pi$
$48$	2.34358	0.338267
$49$	0.00692413	0.000989162 0
$50$	−25.5386	−3.61171
$51$	−0.463974	−0.0649693
$52$	7.43417	1.03093
$53$	8.16478	1.12152	0.560759	−	0.827979i	$-0.310509\pi$
$53$	8.16478	1.12152	0.560759	+	0.827979i	$0.310509\pi$
$54$	−32.5345	−4.42738
$55$	0	0
$56$	8.56582	1.14466
$57$	−19.0123	−2.51824
$58$	13.4766	1.76956
$59$	1.39715	0.181893	0.0909465	−	0.995856i	$-0.471011\pi$
$59$	1.39715	0.181893	0.0909465	+	0.995856i	$0.471011\pi$
$60$	−43.6717	−5.63799
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	18.0814	2.29634
$63$	−19.4658	−2.45246
$64$	−12.5587	−1.56984
$65$	−8.76223	−1.08682
$66$	0	0
$67$	7.45420	0.910675	0.455338	−	0.890319i	$-0.349519\pi$
$67$	7.45420	0.910675	0.455338	+	0.890319i	$0.349519\pi$
$68$	−0.489304	−0.0593368
$69$	24.0463	2.89484
$70$	−24.5873	−2.93875
$71$	4.91095	0.582823	0.291411	−	0.956598i	$-0.405875\pi$
$71$	4.91095	0.582823	0.291411	+	0.956598i	$0.405875\pi$
$72$	−23.7966	−2.80445
$73$	4.94988	0.579339	0.289670	−	0.957127i	$-0.406455\pi$
$73$	4.94988	0.579339	0.289670	+	0.957127i	$0.406455\pi$
$74$	0.470818	0.0547315
$75$	35.3847	4.08587
$76$	−20.0502	−2.29992
$77$	0	0
$78$	−16.3711	−1.85366
$79$	1.07094	0.120490	0.0602449	−	0.998184i	$-0.480812\pi$
$79$	1.07094	0.120490	0.0602449	+	0.998184i	$0.480812\pi$
$80$	−2.91305	−0.325689
$81$	23.0164	2.55738
$82$	1.02311	0.112984
$83$	13.0610	1.43363	0.716817	−	0.697261i	$-0.245598\pi$
$83$	13.0610	1.43363	0.716817	+	0.697261i	$0.245598\pi$
$84$	−28.9033	−3.15361
$85$	0.576715	0.0625535
$86$	5.92855	0.639292
$87$	−18.6723	−2.00188
$88$	0	0
$89$	−7.41041	−0.785502	−0.392751	−	0.919645i	$-0.628477\pi$
$89$	−7.41041	−0.785502	−0.392751	+	0.919645i	$0.628477\pi$
$90$	68.3057	7.20005
$91$	−5.79911	−0.607912
$92$	25.3591	2.64387
$93$	−25.0524	−2.59781
$94$	22.3979	2.31017
$95$	23.6321	2.42460
$96$	15.3823	1.56995
$97$	3.57772	0.363263	0.181631	−	0.983367i	$-0.441862\pi$
$97$	3.57772	0.363263	0.181631	+	0.983367i	$0.441862\pi$
$98$	−0.0160804	−0.00162436
$99$	0	0
$100$	37.3165	3.73165
$101$	−0.963352	−0.0958571	−0.0479286	−	0.998851i	$-0.515262\pi$
$101$	−0.963352	−0.0958571	−0.0479286	+	0.998851i	$0.515262\pi$
$102$	1.07752	0.106690
$103$	0.440854	0.0434387	0.0217193	−	0.999764i	$-0.493086\pi$
$103$	0.440854	0.0434387	0.0217193	+	0.999764i	$0.493086\pi$
$104$	−7.08929	−0.695163
$105$	34.0666	3.32456
$106$	−18.9616	−1.84172
$107$	−10.7741	−1.04157	−0.520786	−	0.853687i	$-0.674361\pi$
$107$	−10.7741	−1.04157	−0.520786	+	0.853687i	$0.674361\pi$
$108$	47.5387	4.57441
$109$	16.4956	1.58000	0.789998	−	0.613110i	$-0.210082\pi$
$109$	16.4956	1.58000	0.789998	+	0.613110i	$0.210082\pi$
$110$	0	0
$111$	−0.652335	−0.0619169
$112$	−1.92795	−0.182174
$113$	18.3568	1.72686	0.863432	−	0.504465i	$-0.168310\pi$
$113$	18.3568	1.72686	0.863432	+	0.504465i	$0.168310\pi$
$114$	44.1535	4.13535
$115$	−29.8894	−2.78720
$116$	−19.6917	−1.82833
$117$	16.1104	1.48941
$118$	−3.24469	−0.298698
$119$	0.381688	0.0349892
$120$	41.6457	3.80172
$121$	0	0
$122$	2.32237	0.210257
$123$	−1.41756	−0.127817
$124$	−26.4201	−2.37260
$125$	−23.9848	−2.14527
$126$	45.2068	4.02734
$127$	−8.17923	−0.725789	−0.362895	−	0.931830i	$-0.618212\pi$
$127$	−8.17923	−0.725789	−0.362895	+	0.931830i	$0.618212\pi$
$128$	19.6050	1.73285
$129$	−8.21422	−0.723222
$130$	20.3491	1.78474
$131$	8.76352	0.765672	0.382836	−	0.923816i	$-0.374947\pi$
$131$	8.76352	0.765672	0.382836	+	0.923816i	$0.374947\pi$
$132$	0	0
$133$	15.6404	1.35620
$134$	−17.3114	−1.49548
$135$	−56.0311	−4.82239
$136$	0.466605	0.0400111
$137$	1.34539	0.114945	0.0574723	−	0.998347i	$-0.481696\pi$
$137$	1.34539	0.114945	0.0574723	+	0.998347i	$0.481696\pi$
$138$	−55.8445	−4.75380
$139$	−3.68422	−0.312491	−0.156246	−	0.987718i	$-0.549939\pi$
$139$	−3.68422	−0.312491	−0.156246	+	0.987718i	$0.549939\pi$
$140$	35.9265	3.03634
$141$	−31.0331	−2.61346
$142$	−11.4050	−0.957090
$143$	0	0
$144$	5.35600	0.446333
$145$	23.2095	1.92744
$146$	−11.4954	−0.951369
$147$	0.0222800	0.00183762
$148$	−0.687949	−0.0565491
$149$	9.92869	0.813390	0.406695	−	0.913564i	$-0.366681\pi$
$149$	9.92869	0.813390	0.406695	+	0.913564i	$0.366681\pi$
$150$	−82.1763	−6.70966
$151$	−10.1970	−0.829821	−0.414911	−	0.909862i	$-0.636187\pi$
$151$	−10.1970	−0.829821	−0.414911	+	0.909862i	$0.636187\pi$
$152$	19.1201	1.55085
$153$	−1.06036	−0.0857251
$154$	0	0
$155$	31.1399	2.50122
$156$	23.9211	1.91522
$157$	−5.12366	−0.408913	−0.204456	−	0.978876i	$-0.565543\pi$
$157$	−5.12366	−0.408913	−0.204456	+	0.978876i	$0.565543\pi$
$158$	−2.48711	−0.197864
$159$	26.2720	2.08351
$160$	−19.1200	−1.51157
$161$	−19.7817	−1.55902
$162$	−53.4527	−4.19964
$163$	2.04437	0.160128	0.0800638	−	0.996790i	$-0.474488\pi$
$163$	2.04437	0.160128	0.0800638	+	0.996790i	$0.474488\pi$
$164$	−1.49495	−0.116736
$165$	0	0
$166$	−30.3325	−2.35426
$167$	−1.76458	−0.136548	−0.0682738	−	0.997667i	$-0.521749\pi$
$167$	−1.76458	−0.136548	−0.0682738	+	0.997667i	$0.521749\pi$
$168$	27.5624	2.12649
$169$	−8.20050	−0.630808
$170$	−1.33934	−0.102723
$171$	−43.4505	−3.32274
$172$	−8.66267	−0.660522
$173$	−8.09556	−0.615494	−0.307747	−	0.951468i	$-0.599575\pi$
$173$	−8.09556	−0.615494	−0.307747	+	0.951468i	$0.599575\pi$
$174$	43.3639	3.28741
$175$	−29.1092	−2.20045
$176$	0	0
$177$	4.49563	0.337912
$178$	17.2097	1.28992
$179$	15.6254	1.16790	0.583949	−	0.811791i	$-0.301507\pi$
$179$	15.6254	1.16790	0.583949	+	0.811791i	$0.301507\pi$
$180$	−99.8068	−7.43916
$181$	−15.7432	−1.17019	−0.585093	−	0.810966i	$-0.698942\pi$
$181$	−15.7432	−1.17019	−0.585093	+	0.810966i	$0.698942\pi$
$182$	13.4677	0.998291
$183$	−3.21773	−0.237861
$184$	−24.1827	−1.78277
$185$	0.810846	0.0596146
$186$	58.1809	4.26603
$187$	0	0
$188$	−32.7274	−2.38689
$189$	−37.0832	−2.69740
$190$	−54.8824	−3.98159
$191$	−9.48574	−0.686364	−0.343182	−	0.939269i	$-0.611505\pi$
$191$	−9.48574	−0.686364	−0.343182	+	0.939269i	$0.611505\pi$
$192$	−40.4105	−2.91638
$193$	16.0055	1.15210	0.576050	−	0.817414i	$-0.304593\pi$
$193$	16.0055	1.15210	0.576050	+	0.817414i	$0.304593\pi$
$194$	−8.30879	−0.596536
$195$	−28.1944	−2.01905
$196$	0.0234963	0.00167831
$197$	−1.48202	−0.105589	−0.0527947	−	0.998605i	$-0.516813\pi$
$197$	−1.48202	−0.105589	−0.0527947	+	0.998605i	$0.516813\pi$
$198$	0	0
$199$	−8.55704	−0.606592	−0.303296	−	0.952896i	$-0.598087\pi$
$199$	−8.55704	−0.606592	−0.303296	+	0.952896i	$0.598087\pi$
$200$	−35.5854	−2.51627
$201$	23.9856	1.69181
$202$	2.23726	0.157413
$203$	15.3607	1.07811
$204$	−1.57445	−0.110233
$205$	1.76201	0.123064
$206$	−1.02383	−0.0713333
$207$	54.9553	3.81966
$208$	1.59562	0.110636
$209$	0	0
$210$	−79.1153	−5.45947
$211$	−3.13037	−0.215504	−0.107752	−	0.994178i	$-0.534365\pi$
$211$	−3.13037	−0.215504	−0.107752	+	0.994178i	$0.534365\pi$
$212$	27.7063	1.90288
$213$	15.8021	1.08274
$214$	25.0214	1.71043
$215$	10.2102	0.696329
$216$	−45.3334	−3.08455
$217$	20.6093	1.39905
$218$	−38.3089	−2.59461
$219$	15.9273	1.07627
$220$	0	0
$221$	−0.315895	−0.0212494
$222$	1.51496	0.101678
$223$	−14.2736	−0.955831	−0.477916	−	0.878406i	$-0.658608\pi$
$223$	−14.2736	−0.955831	−0.477916	+	0.878406i	$0.658608\pi$
$224$	−12.6542	−0.845496
$225$	80.8678	5.39118
$226$	−42.6313	−2.83579
$227$	10.0220	0.665186	0.332593	−	0.943070i	$-0.392076\pi$
$227$	10.0220	0.665186	0.332593	+	0.943070i	$0.392076\pi$
$228$	−64.5161	−4.27269
$229$	−16.2335	−1.07274	−0.536371	−	0.843982i	$-0.680205\pi$
$229$	−16.2335	−1.07274	−0.536371	+	0.843982i	$0.680205\pi$
$230$	69.4141	4.57703
$231$	0	0
$232$	18.7782	1.23285
$233$	−11.2887	−0.739548	−0.369774	−	0.929122i	$-0.620565\pi$
$233$	−11.2887	−0.739548	−0.369774	+	0.929122i	$0.620565\pi$
$234$	−37.4143	−2.44585
$235$	38.5739	2.51628
$236$	4.74107	0.308617
$237$	3.44598	0.223841
$238$	−0.886419	−0.0574580
$239$	15.0799	0.975438	0.487719	−	0.873001i	$-0.337829\pi$
$239$	15.0799	0.975438	0.487719	+	0.873001i	$0.337829\pi$
$240$	−9.37340	−0.605050
$241$	2.57689	0.165992	0.0829961	−	0.996550i	$-0.473551\pi$
$241$	2.57689	0.165992	0.0829961	+	0.996550i	$0.473551\pi$
$242$	0	0
$243$	32.0330	2.05492
$244$	−3.39339	−0.217240
$245$	−0.0276938	−0.00176929
$246$	3.29209	0.209896
$247$	−12.9444	−0.823635
$248$	25.1945	1.59985
$249$	42.0268	2.66334
$250$	55.7015	3.52287
$251$	−5.49581	−0.346893	−0.173446	−	0.984843i	$-0.555490\pi$
$251$	−5.49581	−0.346893	−0.173446	+	0.984843i	$0.555490\pi$
$252$	−66.0552	−4.16109
$253$	0	0
$254$	18.9952	1.19186
$255$	1.85571	0.116209
$256$	−20.4126	−1.27579
$257$	25.7465	1.60602	0.803012	−	0.595963i	$-0.203229\pi$
$257$	25.7465	1.60602	0.803012	+	0.595963i	$0.203229\pi$
$258$	19.0764	1.18765
$259$	0.536643	0.0333454
$260$	−29.7337	−1.84401
$261$	−42.6734	−2.64142
$262$	−20.3521	−1.25736
$263$	11.9017	0.733888	0.366944	−	0.930243i	$-0.380404\pi$
$263$	11.9017	0.733888	0.366944	+	0.930243i	$0.380404\pi$
$264$	0	0
$265$	−32.6559	−2.00603
$266$	−36.3229	−2.22710
$267$	−23.8447	−1.45927
$268$	25.2950	1.54514
$269$	4.54672	0.277219	0.138609	−	0.990347i	$-0.455737\pi$
$269$	4.54672	0.277219	0.138609	+	0.990347i	$0.455737\pi$
$270$	130.125	7.91915
$271$	−8.72945	−0.530276	−0.265138	−	0.964210i	$-0.585418\pi$
$271$	−8.72945	−0.530276	−0.265138	+	0.964210i	$0.585418\pi$
$272$	−0.105021	−0.00636783
$273$	−18.6600	−1.12935
$274$	−3.12450	−0.188758
$275$	0	0
$276$	81.5987	4.91167
$277$	15.9638	0.959170	0.479585	−	0.877495i	$-0.340787\pi$
$277$	15.9638	0.959170	0.479585	+	0.877495i	$0.340787\pi$
$278$	8.55611	0.513161
$279$	−57.2545	−3.42774
$280$	−34.2598	−2.04742
$281$	20.9507	1.24981	0.624907	−	0.780699i	$-0.285137\pi$
$281$	20.9507	1.24981	0.624907	+	0.780699i	$0.285137\pi$
$282$	72.0704	4.29173
$283$	11.2388	0.668077	0.334039	−	0.942559i	$-0.391588\pi$
$283$	11.2388	0.668077	0.334039	+	0.942559i	$0.391588\pi$
$284$	16.6648	0.988874
$285$	76.0415	4.50431
$286$	0	0
$287$	1.16615	0.0688358
$288$	35.1545	2.07150
$289$	−16.9792	−0.998777
$290$	−53.9009	−3.16517
$291$	11.5121	0.674853
$292$	16.7969	0.982963
$293$	0.824582	0.0481726	0.0240863	−	0.999710i	$-0.492332\pi$
$293$	0.824582	0.0481726	0.0240863	+	0.999710i	$0.492332\pi$
$294$	−0.0517423	−0.00301767
$295$	−5.58802	−0.325347
$296$	0.656035	0.0381313
$297$	0	0
$298$	−23.0581	−1.33572
$299$	16.3719	0.946809
$300$	120.074	6.93249
$301$	6.75742	0.389491
$302$	23.6812	1.36270
$303$	−3.09980	−0.178079
$304$	−4.30345	−0.246820
$305$	3.99960	0.229016
$306$	2.46255	0.140774
$307$	25.7354	1.46879	0.734397	−	0.678720i	$-0.237465\pi$
$307$	25.7354	1.46879	0.734397	+	0.678720i	$0.237465\pi$
$308$	0	0
$309$	1.41855	0.0806984
$310$	−72.3183	−4.10740
$311$	18.9182	1.07275	0.536376	−	0.843979i	$-0.319793\pi$
$311$	18.9182	1.07275	0.536376	+	0.843979i	$0.319793\pi$
$312$	−22.8114	−1.29144
$313$	−10.5704	−0.597476	−0.298738	−	0.954335i	$-0.596566\pi$
$313$	−10.5704	−0.597476	−0.298738	+	0.954335i	$0.596566\pi$
$314$	11.8990	0.671501
$315$	77.8555	4.38666
$316$	3.63411	0.204435
$317$	11.4717	0.644314	0.322157	−	0.946686i	$-0.395592\pi$
$317$	11.4717	0.644314	0.322157	+	0.946686i	$0.395592\pi$
$318$	−61.0133	−3.42146
$319$	0	0
$320$	50.2298	2.80793
$321$	−34.6681	−1.93498
$322$	45.9404	2.56016
$323$	0.851980	0.0474055
$324$	78.1039	4.33910
$325$	24.0915	1.33636
$326$	−4.74779	−0.262956
$327$	53.0784	2.93524
$328$	1.42560	0.0787154
$329$	25.5294	1.40748
$330$	0	0
$331$	9.72976	0.534796	0.267398	−	0.963586i	$-0.413836\pi$
$331$	9.72976	0.534796	0.267398	+	0.963586i	$0.413836\pi$
$332$	44.3212	2.43244
$333$	−1.49084	−0.0816976
$334$	4.09801	0.224233
$335$	−29.8138	−1.62890
$336$	−6.20360	−0.338434
$337$	17.6146	0.959528	0.479764	−	0.877397i	$-0.340722\pi$
$337$	17.6146	0.959528	0.479764	+	0.877397i	$0.340722\pi$
$338$	19.0446	1.03589
$339$	59.0672	3.20809
$340$	1.95702	0.106134
$341$	0	0
$342$	100.908	5.45648
$343$	18.5111	0.999505
$344$	8.26081	0.445393
$345$	−96.1758	−5.17793
$346$	18.8009	1.01074
$347$	27.9625	1.50111	0.750553	−	0.660811i	$-0.229787\pi$
$347$	27.9625	1.50111	0.750553	+	0.660811i	$0.229787\pi$
$348$	−63.3624	−3.39658
$349$	34.6700	1.85584	0.927922	−	0.372775i	$-0.121594\pi$
$349$	34.6700	1.85584	0.927922	+	0.372775i	$0.121594\pi$
$350$	67.6022	3.61349
$351$	30.6910	1.63816
$352$	0	0
$353$	30.2462	1.60984	0.804920	−	0.593383i	$-0.202208\pi$
$353$	30.2462	1.60984	0.804920	+	0.593383i	$0.202208\pi$
$354$	−10.4405	−0.554907
$355$	−19.6418	−1.04248
$356$	−25.1464	−1.33276
$357$	1.22817	0.0650014
$358$	−36.2879	−1.91788
$359$	29.9255	1.57941	0.789704	−	0.613488i	$-0.210234\pi$
$359$	29.9255	1.57941	0.789704	+	0.613488i	$0.210234\pi$
$360$	95.1767	5.01625
$361$	15.9117	0.837455
$362$	36.5616	1.92163
$363$	0	0
$364$	−19.6787	−1.03144
$365$	−19.7975	−1.03625
$366$	7.47274	0.390607
$367$	20.3508	1.06230	0.531151	−	0.847277i	$-0.321760\pi$
$367$	20.3508	1.06230	0.531151	+	0.847277i	$0.321760\pi$
$368$	5.44292	0.283732
$369$	−3.23967	−0.168651
$370$	−1.88308	−0.0978969
$371$	−21.6127	−1.12207
$372$	−85.0127	−4.40770
$373$	−8.35966	−0.432847	−0.216423	−	0.976300i	$-0.569439\pi$
$373$	−8.35966	−0.432847	−0.216423	+	0.976300i	$0.569439\pi$
$374$	0	0
$375$	−77.1765	−3.98538
$376$	31.2091	1.60949
$377$	−12.7130	−0.654750
$378$	86.1207	4.42957
$379$	−13.7047	−0.703961	−0.351980	−	0.936007i	$-0.614492\pi$
$379$	−13.7047	−0.703961	−0.351980	+	0.936007i	$0.614492\pi$
$380$	80.1929	4.11381
$381$	−26.3185	−1.34834
$382$	22.0294	1.12712
$383$	4.14891	0.211999	0.106000	−	0.994366i	$-0.466196\pi$
$383$	4.14891	0.211999	0.106000	+	0.994366i	$0.466196\pi$
$384$	63.0835	3.21922
$385$	0	0
$386$	−37.1706	−1.89194
$387$	−18.7727	−0.954270
$388$	12.1406	0.616347
$389$	−5.36604	−0.272069	−0.136035	−	0.990704i	$-0.543436\pi$
$389$	−5.36604	−0.272069	−0.136035	+	0.990704i	$0.543436\pi$
$390$	65.4779	3.31560
$391$	−1.07757	−0.0544949
$392$	−0.0224063	−0.00113169
$393$	28.1986	1.42243
$394$	3.44179	0.173395
$395$	−4.28332	−0.215517
$396$	0	0
$397$	−30.9283	−1.55225	−0.776123	−	0.630581i	$-0.782817\pi$
$397$	−30.9283	−1.55225	−0.776123	+	0.630581i	$0.782817\pi$
$398$	19.8726	0.996123
$399$	50.3266	2.51948
$400$	8.00936	0.400468
$401$	−10.2912	−0.513917	−0.256958	−	0.966422i	$-0.582720\pi$
$401$	−10.2912	−0.513917	−0.256958	+	0.966422i	$0.582720\pi$
$402$	−55.7033	−2.77823
$403$	−17.0568	−0.849661
$404$	−3.26903	−0.162640
$405$	−92.0566	−4.57433
$406$	−35.6733	−1.77044
$407$	0	0
$408$	1.50141	0.0743307
$409$	8.53555	0.422056	0.211028	−	0.977480i	$-0.432319\pi$
$409$	8.53555	0.422056	0.211028	+	0.977480i	$0.432319\pi$
$410$	−4.09204	−0.202091
$411$	4.32911	0.213539
$412$	1.49599	0.0737022
$413$	−3.69833	−0.181983
$414$	−127.626	−6.27249
$415$	−52.2389	−2.56431
$416$	10.4730	0.513480
$417$	−11.8548	−0.580532
$418$	0	0
$419$	−4.96324	−0.242470	−0.121235	−	0.992624i	$-0.538685\pi$
$419$	−4.96324	−0.242470	−0.121235	+	0.992624i	$0.538685\pi$
$420$	115.602	5.64078
$421$	−28.6529	−1.39646	−0.698228	−	0.715876i	$-0.746028\pi$
$421$	−28.6529	−1.39646	−0.698228	+	0.715876i	$0.746028\pi$
$422$	7.26988	0.353892
$423$	−70.9228	−3.44839
$424$	−26.4210	−1.28312
$425$	−1.58566	−0.0769159
$426$	−36.6983	−1.77804
$427$	2.64706	0.128100
$428$	−36.5608	−1.76723
$429$	0	0
$430$	−23.7118	−1.14349
$431$	16.2313	0.781835	0.390918	−	0.920426i	$-0.372158\pi$
$431$	16.2313	0.781835	0.390918	+	0.920426i	$0.372158\pi$
$432$	10.2034	0.490911
$433$	0.242631	0.0116601	0.00583005	−	0.999983i	$-0.498144\pi$
$433$	0.242631	0.0116601	0.00583005	+	0.999983i	$0.498144\pi$
$434$	−47.8625	−2.29747
$435$	74.6816	3.58071
$436$	55.9762	2.68077
$437$	−44.1556	−2.11225
$438$	−36.9892	−1.76741
$439$	−5.09967	−0.243394	−0.121697	−	0.992567i	$-0.538834\pi$
$439$	−5.09967	−0.243394	−0.121697	+	0.992567i	$0.538834\pi$
$440$	0	0
$441$	0.0509184	0.00242468
$442$	0.733624	0.0348949
$443$	37.7653	1.79428	0.897142	−	0.441743i	$-0.145640\pi$
$443$	37.7653	1.79428	0.897142	+	0.441743i	$0.145640\pi$
$444$	−2.21363	−0.105054
$445$	29.6387	1.40501
$446$	33.1486	1.56963
$447$	31.9478	1.51108
$448$	33.2437	1.57062
$449$	12.3535	0.582996	0.291498	−	0.956571i	$-0.405846\pi$
$449$	12.3535	0.582996	0.291498	+	0.956571i	$0.405846\pi$
$450$	−187.805	−8.85320
$451$	0	0
$452$	62.2919	2.92997
$453$	−32.8112	−1.54160
$454$	−23.2749	−1.09234
$455$	23.1941	1.08736
$456$	61.5232	2.88109
$457$	−37.0440	−1.73284	−0.866422	−	0.499312i	$-0.833586\pi$
$457$	−37.0440	−1.73284	−0.866422	+	0.499312i	$0.833586\pi$
$458$	37.7003	1.76162
$459$	−2.02003	−0.0942868
$460$	−101.426	−4.72903
$461$	24.2030	1.12725	0.563623	−	0.826032i	$-0.309407\pi$
$461$	24.2030	1.12725	0.563623	+	0.826032i	$0.309407\pi$
$462$	0	0
$463$	32.6864	1.51907	0.759533	−	0.650468i	$-0.225427\pi$
$463$	32.6864	1.51907	0.759533	+	0.650468i	$0.225427\pi$
$464$	−4.22649	−0.196210
$465$	100.200	4.64664
$466$	26.2165	1.21446
$467$	21.2250	0.982176	0.491088	−	0.871110i	$-0.336599\pi$
$467$	21.2250	0.982176	0.491088	+	0.871110i	$0.336599\pi$
$468$	54.6690	2.52708
$469$	−19.7317	−0.911125
$470$	−89.5828	−4.13214
$471$	−16.4865	−0.759659
$472$	−4.52113	−0.208102
$473$	0	0
$474$	−8.00284	−0.367583
$475$	−64.9758	−2.98129
$476$	1.29522	0.0593662
$477$	60.0418	2.74913
$478$	−35.0211	−1.60183
$479$	7.35783	0.336188	0.168094	−	0.985771i	$-0.446239\pi$
$479$	7.35783	0.336188	0.168094	+	0.985771i	$0.446239\pi$
$480$	−61.5230	−2.80813
$481$	−0.444140	−0.0202510
$482$	−5.98449	−0.272586
$483$	−63.6521	−2.89627
$484$	0	0
$485$	−14.3095	−0.649759
$486$	−74.3925	−3.37451
$487$	14.2232	0.644513	0.322256	−	0.946652i	$-0.395559\pi$
$487$	14.2232	0.644513	0.322256	+	0.946652i	$0.395559\pi$
$488$	3.23597	0.146486
$489$	6.57823	0.297478
$490$	0.0643151	0.00290546
$491$	−35.3853	−1.59691	−0.798457	−	0.602052i	$-0.794350\pi$
$491$	−35.3853	−1.59691	−0.798457	+	0.602052i	$0.794350\pi$
$492$	−4.81033	−0.216866
$493$	0.836744	0.0376851
$494$	30.0617	1.35254
$495$	0	0
$496$	−5.67064	−0.254619
$497$	−12.9996	−0.583111
$498$	−97.6017	−4.37364
$499$	22.4826	1.00646	0.503230	−	0.864153i	$-0.332145\pi$
$499$	22.4826	1.00646	0.503230	+	0.864153i	$0.332145\pi$
$500$	−81.3899	−3.63987
$501$	−5.67795	−0.253672
$502$	12.7633	0.569654
$503$	36.9399	1.64707	0.823535	−	0.567266i	$-0.191999\pi$
$503$	36.9399	1.64707	0.823535	+	0.567266i	$0.191999\pi$
$504$	62.9909	2.80584
$505$	3.85302	0.171457
$506$	0	0
$507$	−26.3870	−1.17189
$508$	−27.7554	−1.23144
$509$	−14.2887	−0.633335	−0.316667	−	0.948537i	$-0.602564\pi$
$509$	−14.2887	−0.633335	−0.316667	+	0.948537i	$0.602564\pi$
$510$	−4.30964	−0.190834
$511$	−13.1026	−0.579626
$512$	8.19555	0.362195
$513$	−82.7748	−3.65460
$514$	−59.7929	−2.63735
$515$	−1.76324	−0.0776977
$516$	−27.8741	−1.22709
$517$	0	0
$518$	−1.24628	−0.0547585
$519$	−26.0493	−1.14344
$520$	28.3543	1.24342
$521$	−12.9132	−0.565737	−0.282869	−	0.959159i	$-0.591286\pi$
$521$	−12.9132	−0.565737	−0.282869	+	0.959159i	$0.591286\pi$
$522$	99.1034	4.33764
$523$	−13.4104	−0.586394	−0.293197	−	0.956052i	$-0.594719\pi$
$523$	−13.4104	−0.586394	−0.293197	+	0.956052i	$0.594719\pi$
$524$	29.7381	1.29911
$525$	−93.6654	−4.08789
$526$	−27.6400	−1.20516
$527$	1.12265	0.0489034
$528$	0	0
$529$	32.8471	1.42813
$530$	75.8389	3.29423
$531$	10.2743	0.445865
$532$	53.0742	2.30106
$533$	−0.965139	−0.0418048
$534$	55.3761	2.39636
$535$	43.0921	1.86303
$536$	−24.1216	−1.04189
$537$	50.2782	2.16967
$538$	−10.5592	−0.455238
$539$	0	0
$540$	−190.136	−8.18214
$541$	40.0928	1.72372	0.861862	−	0.507143i	$-0.169298\pi$
$541$	40.0928	1.72372	0.861862	+	0.507143i	$0.169298\pi$
$542$	20.2730	0.870800
$543$	−50.6574	−2.17392
$544$	−0.689313	−0.0295540
$545$	−65.9759	−2.82610
$546$	43.3353	1.85458
$547$	14.9709	0.640109	0.320054	−	0.947399i	$-0.396299\pi$
$547$	14.9709	0.640109	0.320054	+	0.947399i	$0.396299\pi$
$548$	4.56545	0.195026
$549$	−7.35376	−0.313851
$550$	0	0
$551$	34.2873	1.46069
$552$	−77.8134	−3.31196
$553$	−2.83484	−0.120549
$554$	−37.0738	−1.57511
$555$	2.60908	0.110749
$556$	−12.5020	−0.530203
$557$	−5.96189	−0.252613	−0.126307	−	0.991991i	$-0.540312\pi$
$557$	−5.96189	−0.252613	−0.126307	+	0.991991i	$0.540312\pi$
$558$	132.966	5.62890
$559$	−5.59262	−0.236543
$560$	7.71102	0.325850
$561$	0	0
$562$	−48.6552	−2.05240
$563$	−28.6251	−1.20640	−0.603202	−	0.797588i	$-0.706109\pi$
$563$	−28.6251	−1.20640	−0.603202	+	0.797588i	$0.706109\pi$
$564$	−105.308	−4.43425
$565$	−73.4199	−3.08880
$566$	−26.1006	−1.09709
$567$	−60.9259	−2.55865
$568$	−15.8917	−0.666802
$569$	34.5714	1.44931	0.724653	−	0.689114i	$-0.242000\pi$
$569$	34.5714	1.44931	0.724653	+	0.689114i	$0.242000\pi$
$570$	−176.596	−7.39681
$571$	36.9954	1.54821	0.774104	−	0.633058i	$-0.218200\pi$
$571$	36.9954	1.54821	0.774104	+	0.633058i	$0.218200\pi$
$572$	0	0
$573$	−30.5225	−1.27510
$574$	−2.70824	−0.113040
$575$	82.1801	3.42715
$576$	−92.3537	−3.84807
$577$	41.5219	1.72858	0.864290	−	0.502993i	$-0.167768\pi$
$577$	41.5219	1.72858	0.864290	+	0.502993i	$0.167768\pi$
$578$	39.4320	1.64015
$579$	51.5013	2.14032
$580$	78.7588	3.27028
$581$	−34.5733	−1.43434
$582$	−26.7354	−1.10822
$583$	0	0
$584$	−16.0177	−0.662816
$585$	−64.4353	−2.66407
$586$	−1.91498	−0.0791072
$587$	18.9962	0.784056	0.392028	−	0.919953i	$-0.371774\pi$
$587$	18.9962	0.784056	0.392028	+	0.919953i	$0.371774\pi$
$588$	0.0756047	0.00311788
$589$	46.0029	1.89552
$590$	12.9775	0.534273
$591$	−4.76873	−0.196159
$592$	−0.147657	−0.00606866
$593$	40.4317	1.66033	0.830166	−	0.557516i	$-0.188245\pi$
$593$	40.4317	1.66033	0.830166	+	0.557516i	$0.188245\pi$
$594$	0	0
$595$	−1.52660	−0.0625844
$596$	33.6919	1.38008
$597$	−27.5342	−1.12690
$598$	−38.0215	−1.55481
$599$	17.9220	0.732274	0.366137	−	0.930561i	$-0.380680\pi$
$599$	17.9220	0.732274	0.366137	+	0.930561i	$0.380680\pi$
$600$	−114.504	−4.67460
$601$	4.18020	0.170514	0.0852570	−	0.996359i	$-0.472829\pi$
$601$	4.18020	0.170514	0.0852570	+	0.996359i	$0.472829\pi$
$602$	−15.6932	−0.639608
$603$	54.8163	2.23229
$604$	−34.6025	−1.40796
$605$	0	0
$606$	7.19888	0.292435
$607$	38.9239	1.57987	0.789936	−	0.613190i	$-0.210114\pi$
$607$	38.9239	1.57987	0.789936	+	0.613190i	$0.210114\pi$
$608$	−28.2460	−1.14553
$609$	49.4266	2.00287
$610$	−9.28854	−0.376082
$611$	−21.1288	−0.854780
$612$	−3.59822	−0.145449
$613$	−26.0695	−1.05294	−0.526468	−	0.850195i	$-0.676484\pi$
$613$	−26.0695	−1.05294	−0.526468	+	0.850195i	$0.676484\pi$
$614$	−59.7670	−2.41200
$615$	5.66966	0.228623
$616$	0	0
$617$	−29.4793	−1.18679	−0.593395	−	0.804911i	$-0.702213\pi$
$617$	−29.4793	−1.18679	−0.593395	+	0.804911i	$0.702213\pi$
$618$	−3.29439	−0.132520
$619$	11.8955	0.478120	0.239060	−	0.971005i	$-0.423161\pi$
$619$	11.8955	0.478120	0.239060	+	0.971005i	$0.423161\pi$
$620$	105.670	4.24380
$621$	104.692	4.20114
$622$	−43.9350	−1.76163
$623$	19.6158	0.785890
$624$	5.13427	0.205535
$625$	40.9456	1.63782
$626$	24.5484	0.981152
$627$	0	0
$628$	−17.3866	−0.693801
$629$	0.0292325	0.00116558
$630$	−180.809	−7.20361
$631$	−1.88290	−0.0749571	−0.0374786	−	0.999297i	$-0.511933\pi$
$631$	−1.88290	−0.0749571	−0.0374786	+	0.999297i	$0.511933\pi$
$632$	−3.46553	−0.137851
$633$	−10.0727	−0.400353
$634$	−26.6415	−1.05807
$635$	32.7137	1.29820
$636$	89.1513	3.53508
$637$	0.0151692	0.000601027 0
$638$	0	0
$639$	36.1139	1.42865
$640$	−78.4121	−3.09951
$641$	−25.7884	−1.01858	−0.509290	−	0.860595i	$-0.670092\pi$
$641$	−25.7884	−1.01858	−0.509290	+	0.860595i	$0.670092\pi$
$642$	80.5121	3.17756
$643$	0.116254	0.00458462	0.00229231	−	0.999997i	$-0.499270\pi$
$643$	0.116254	0.00458462	0.00229231	+	0.999997i	$0.499270\pi$
$644$	−67.1272	−2.64518
$645$	32.8536	1.29361
$646$	−1.97861	−0.0778475
$647$	21.9432	0.862675	0.431337	−	0.902191i	$-0.358042\pi$
$647$	21.9432	0.862675	0.431337	+	0.902191i	$0.358042\pi$
$648$	−74.4806	−2.92588
$649$	0	0
$650$	−55.9494	−2.19452
$651$	66.3152	2.59910
$652$	6.93737	0.271688
$653$	14.4071	0.563792	0.281896	−	0.959445i	$-0.409037\pi$
$653$	14.4071	0.563792	0.281896	+	0.959445i	$0.409037\pi$
$654$	−123.268	−4.82015
$655$	−35.0506	−1.36954
$656$	−0.320866	−0.0125277
$657$	36.4002	1.42011
$658$	−59.2887	−2.31131
$659$	25.7669	1.00374	0.501868	−	0.864944i	$-0.332646\pi$
$659$	25.7669	1.00374	0.501868	+	0.864944i	$0.332646\pi$
$660$	0	0
$661$	44.1401	1.71685	0.858425	−	0.512939i	$-0.171443\pi$
$661$	44.1401	1.71685	0.858425	+	0.512939i	$0.171443\pi$
$662$	−22.5961	−0.878221
$663$	−1.01646	−0.0394761
$664$	−42.2651	−1.64021
$665$	−62.5555	−2.42580
$666$	3.46228	0.134161
$667$	−43.3659	−1.67914
$668$	−5.98793	−0.231680
$669$	−45.9285	−1.77570
$670$	69.2386	2.67492
$671$	0	0
$672$	−40.7178	−1.57072
$673$	11.4280	0.440518	0.220259	−	0.975441i	$-0.429310\pi$
$673$	11.4280	0.440518	0.220259	+	0.975441i	$0.429310\pi$
$674$	−40.9076	−1.57570
$675$	154.056	5.92963
$676$	−27.8275	−1.07029
$677$	−4.58790	−0.176327	−0.0881637	−	0.996106i	$-0.528100\pi$
$677$	−4.58790	−0.176327	−0.0881637	+	0.996106i	$0.528100\pi$
$678$	−137.176	−5.26820
$679$	−9.47045	−0.363442
$680$	−1.86623	−0.0715668
$681$	32.2482	1.23575
$682$	0	0
$683$	8.83712	0.338143	0.169071	−	0.985604i	$-0.445923\pi$
$683$	8.83712	0.338143	0.169071	+	0.985604i	$0.445923\pi$
$684$	−147.445	−5.63768
$685$	−5.38103	−0.205599
$686$	−42.9896	−1.64135
$687$	−52.2351	−1.99289
$688$	−1.85930	−0.0708851
$689$	17.8872	0.681448
$690$	223.356	8.50300
$691$	18.0078	0.685048	0.342524	−	0.939509i	$-0.388718\pi$
$691$	18.0078	0.685048	0.342524	+	0.939509i	$0.388718\pi$
$692$	−27.4714	−1.04431
$693$	0	0
$694$	−64.9392	−2.46506
$695$	14.7354	0.558945
$696$	60.4230	2.29033
$697$	0.0635238	0.00240613
$698$	−80.5165	−3.04760
$699$	−36.3240	−1.37390
$700$	−98.7789	−3.73349
$701$	8.23112	0.310885	0.155443	−	0.987845i	$-0.450320\pi$
$701$	8.23112	0.310885	0.155443	+	0.987845i	$0.450320\pi$
$702$	−71.2758	−2.69013
$703$	1.19786	0.0451783
$704$	0	0
$705$	124.120	4.67464
$706$	−70.2427	−2.64362
$707$	2.55005	0.0959045
$708$	15.2554	0.573335
$709$	−5.20208	−0.195368	−0.0976841	−	0.995217i	$-0.531143\pi$
$709$	−5.20208	−0.195368	−0.0976841	+	0.995217i	$0.531143\pi$
$710$	45.6156	1.71192
$711$	7.87541	0.295351
$712$	23.9799	0.898685
$713$	−58.1836	−2.17899
$714$	−2.85225	−0.106743
$715$	0	0
$716$	53.0231	1.98157
$717$	48.5230	1.81212
$718$	−69.4981	−2.59364
$719$	9.96907	0.371784	0.185892	−	0.982570i	$-0.440483\pi$
$719$	9.96907	0.371784	0.185892	+	0.982570i	$0.440483\pi$
$720$	−21.4219	−0.798346
$721$	−1.16697	−0.0434601
$722$	−36.9527	−1.37524
$723$	8.29173	0.308373
$724$	−53.4230	−1.98545
$725$	−63.8138	−2.36999
$726$	0	0
$727$	5.54034	0.205480	0.102740	−	0.994708i	$-0.467239\pi$
$727$	5.54034	0.205480	0.102740	+	0.994708i	$0.467239\pi$
$728$	18.7658	0.695506
$729$	34.0242	1.26016
$730$	45.9771	1.70169
$731$	0.368097	0.0136145
$732$	−10.9190	−0.403578
$733$	−50.1961	−1.85403	−0.927017	−	0.375018i	$-0.877636\pi$
$733$	−50.1961	−1.85403	−0.927017	+	0.375018i	$0.877636\pi$
$734$	−47.2620	−1.74447
$735$	−0.0891109	−0.00328691
$736$	35.7250	1.31684
$737$	0	0
$738$	7.52371	0.276952
$739$	5.79962	0.213343	0.106671	−	0.994294i	$-0.465981\pi$
$739$	5.79962	0.213343	0.106671	+	0.994294i	$0.465981\pi$
$740$	2.75152	0.101148
$741$	−41.6516	−1.53011
$742$	50.1926	1.84263
$743$	−28.6475	−1.05097	−0.525487	−	0.850802i	$-0.676117\pi$
$743$	−28.6475	−1.05097	−0.525487	+	0.850802i	$0.676117\pi$
$744$	81.0689	2.97213
$745$	−39.7108	−1.45489
$746$	19.4142	0.710805
$747$	96.0476	3.51420
$748$	0	0
$749$	28.5197	1.04209
$750$	179.232	6.54464
$751$	29.3189	1.06986	0.534930	−	0.844896i	$-0.320338\pi$
$751$	29.3189	1.06986	0.534930	+	0.844896i	$0.320338\pi$
$752$	−7.02438	−0.256153
$753$	−17.6840	−0.644441
$754$	29.5242	1.07521
$755$	40.7840	1.48428
$756$	−125.838	−4.57667
$757$	−0.942425	−0.0342530	−0.0171265	−	0.999853i	$-0.505452\pi$
$757$	−0.942425	−0.0342530	−0.0171265	+	0.999853i	$0.505452\pi$
$758$	31.8273	1.15602
$759$	0	0
$760$	−76.4728	−2.77396
$761$	−48.0071	−1.74026	−0.870128	−	0.492825i	$-0.835964\pi$
$761$	−48.0071	−1.74026	−0.870128	+	0.492825i	$0.835964\pi$
$762$	61.1213	2.21419
$763$	−43.6649	−1.58078
$764$	−32.1888	−1.16455
$765$	4.24102	0.153334
$766$	−9.63529	−0.348137
$767$	3.06083	0.110520
$768$	−65.6821	−2.37010
$769$	−42.3581	−1.52747	−0.763736	−	0.645529i	$-0.776637\pi$
$769$	−42.3581	−1.52747	−0.763736	+	0.645529i	$0.776637\pi$
$770$	0	0
$771$	82.8452	2.98360
$772$	54.3129	1.95476
$773$	−50.2569	−1.80762	−0.903808	−	0.427938i	$-0.859240\pi$
$773$	−50.2569	−1.80762	−0.903808	+	0.427938i	$0.859240\pi$
$774$	43.5971	1.56707
$775$	−85.6183	−3.07550
$776$	−11.5774	−0.415605
$777$	1.72677	0.0619476
$778$	12.4619	0.446782
$779$	2.60302	0.0932628
$780$	−95.6748	−3.42571
$781$	0	0
$782$	2.50251	0.0894895
$783$	−81.2945	−2.90523
$784$	0.00504309	0.000180110 0
$785$	20.4926	0.731412
$786$	−65.4875	−2.33586
$787$	−21.8905	−0.780313	−0.390156	−	0.920749i	$-0.627579\pi$
$787$	−21.8905	−0.780313	−0.390156	+	0.920749i	$0.627579\pi$
$788$	−5.02907	−0.179153
$789$	38.2963	1.36338
$790$	9.94745	0.353914
$791$	−48.5916	−1.72772
$792$	0	0
$793$	−2.19078	−0.0777967
$794$	71.8269	2.54904
$795$	−105.078	−3.72672
$796$	−29.0374	−1.02920
$797$	27.3815	0.969903	0.484951	−	0.874541i	$-0.338837\pi$
$797$	27.3815	0.969903	0.484951	+	0.874541i	$0.338837\pi$
$798$	−116.877	−4.13740
$799$	1.39066	0.0491980
$800$	52.5700	1.85863
$801$	−54.4943	−1.92546
$802$	23.8999	0.843935
$803$	0	0
$804$	81.3924	2.87049
$805$	79.1189	2.78858
$806$	39.6122	1.39528
$807$	14.6301	0.515004
$808$	3.11738	0.109669
$809$	36.0983	1.26915	0.634575	−	0.772861i	$-0.281175\pi$
$809$	36.0983	1.26915	0.634575	+	0.772861i	$0.281175\pi$
$810$	213.789	7.51179
$811$	−22.5933	−0.793359	−0.396679	−	0.917957i	$-0.629838\pi$
$811$	−22.5933	−0.793359	−0.396679	+	0.917957i	$0.629838\pi$
$812$	52.1250	1.82923
$813$	−28.0890	−0.985123
$814$	0	0
$815$	−8.17668	−0.286416
$816$	−0.337928	−0.0118299
$817$	15.0835	0.527705
$818$	−19.8227	−0.693085
$819$	−42.6453	−1.49015
$820$	5.97919	0.208802
$821$	−39.0484	−1.36280	−0.681399	−	0.731912i	$-0.738628\pi$
$821$	−39.0484	−1.36280	−0.681399	+	0.731912i	$0.738628\pi$
$822$	−10.0538	−0.350666
$823$	13.2350	0.461344	0.230672	−	0.973032i	$-0.425908\pi$
$823$	13.2350	0.461344	0.230672	+	0.973032i	$0.425908\pi$
$824$	−1.42659	−0.0496977
$825$	0	0
$826$	8.58888	0.298845
$827$	−48.6358	−1.69123	−0.845617	−	0.533790i	$-0.820767\pi$
$827$	−48.6358	−1.69123	−0.845617	+	0.533790i	$0.820767\pi$
$828$	186.485	6.48080
$829$	44.7304	1.55355	0.776776	−	0.629777i	$-0.216854\pi$
$829$	44.7304	1.55355	0.776776	+	0.629777i	$0.216854\pi$
$830$	121.318	4.21101
$831$	51.3670	1.78190
$832$	−27.5133	−0.953853
$833$	−0.000998412 0	−3.45929e−5 0
$834$	27.5312	0.953328
$835$	7.05763	0.244239
$836$	0	0
$837$	−109.072	−3.77008
$838$	11.5265	0.398175
$839$	34.5382	1.19239	0.596196	−	0.802839i	$-0.296678\pi$
$839$	34.5382	1.19239	0.596196	+	0.802839i	$0.296678\pi$
$840$	−110.239	−3.80360
$841$	4.67416	0.161178
$842$	66.5425	2.29321
$843$	67.4136	2.32185
$844$	−10.6226	−0.365645
$845$	32.7987	1.12831
$846$	164.709	5.66281
$847$	0	0
$848$	5.94670	0.204210
$849$	36.1634	1.24112
$850$	3.68249	0.126308
$851$	−1.51503	−0.0519347
$852$	53.6227	1.83709
$853$	−33.2081	−1.13702	−0.568512	−	0.822675i	$-0.692481\pi$
$853$	−33.2081	−1.13702	−0.568512	+	0.822675i	$0.692481\pi$
$854$	−6.14745	−0.210361
$855$	173.784	5.94330
$856$	34.8647	1.19165
$857$	−47.7763	−1.63201	−0.816003	−	0.578047i	$-0.803815\pi$
$857$	−47.7763	−1.63201	−0.816003	+	0.578047i	$0.803815\pi$
$858$	0	0
$859$	−39.0197	−1.33133	−0.665667	−	0.746249i	$-0.731853\pi$
$859$	−39.0197	−1.33133	−0.665667	+	0.746249i	$0.731853\pi$
$860$	34.6472	1.18146
$861$	3.75236	0.127880
$862$	−37.6951	−1.28390
$863$	16.0964	0.547926	0.273963	−	0.961740i	$-0.411665\pi$
$863$	16.0964	0.547926	0.273963	+	0.961740i	$0.411665\pi$
$864$	66.9707	2.27839
$865$	32.3790	1.10092
$866$	−0.563478	−0.0191478
$867$	−54.6344	−1.85548
$868$	69.9356	2.37377
$869$	0	0
$870$	−173.438	−5.88011
$871$	16.3305	0.553337
$872$	−53.3794	−1.80766
$873$	26.3097	0.890448
$874$	102.545	3.46865
$875$	63.4892	2.14633
$876$	54.0478	1.82610
$877$	19.7831	0.668028	0.334014	−	0.942568i	$-0.391597\pi$
$877$	19.7831	0.668028	0.334014	+	0.942568i	$0.391597\pi$
$878$	11.8433	0.399692
$879$	2.65328	0.0894928
$880$	0	0
$881$	−1.77137	−0.0596790	−0.0298395	−	0.999555i	$-0.509500\pi$
$881$	−1.77137	−0.0596790	−0.0298395	+	0.999555i	$0.509500\pi$
$882$	−0.118251	−0.00398173
$883$	−40.1178	−1.35007	−0.675035	−	0.737785i	$-0.735872\pi$
$883$	−40.1178	−1.35007	−0.675035	+	0.737785i	$0.735872\pi$
$884$	−1.07196	−0.0360538
$885$	−17.9807	−0.604416
$886$	−87.7049	−2.94651
$887$	−22.4692	−0.754441	−0.377220	−	0.926124i	$-0.623120\pi$
$887$	−22.4692	−0.754441	−0.377220	+	0.926124i	$0.623120\pi$
$888$	2.11094	0.0708385
$889$	21.6509	0.726148
$890$	−68.8319	−2.30725
$891$	0	0
$892$	−48.4360	−1.62176
$893$	56.9852	1.90694
$894$	−74.1945	−2.48144
$895$	−62.4954	−2.08899
$896$	−51.8956	−1.73371
$897$	52.6802	1.75894
$898$	−28.6893	−0.957374
$899$	45.1803	1.50685
$900$	274.416	9.14721
$901$	−1.17730	−0.0392217
$902$	0	0
$903$	21.7435	0.723579
$904$	−59.4022	−1.97569
$905$	62.9667	2.09308
$906$	76.1996	2.53156
$907$	−16.7844	−0.557317	−0.278659	−	0.960390i	$-0.589890\pi$
$907$	−16.7844	−0.557317	−0.278659	+	0.960390i	$0.589890\pi$
$908$	34.0087	1.12862
$909$	−7.08426	−0.234970
$910$	−53.8653	−1.78562
$911$	−24.6670	−0.817253	−0.408626	−	0.912702i	$-0.633992\pi$
$911$	−24.6670	−0.817253	−0.408626	+	0.912702i	$0.633992\pi$
$912$	−13.8473	−0.458530
$913$	0	0
$914$	86.0298	2.84561
$915$	12.8696	0.425456
$916$	−55.0868	−1.82012
$917$	−23.1976	−0.766051
$918$	4.69125	0.154834
$919$	49.3314	1.62729	0.813646	−	0.581360i	$-0.197479\pi$
$919$	49.3314	1.62729	0.813646	+	0.581360i	$0.197479\pi$
$920$	96.7212	3.18880
$921$	82.8093	2.72866
$922$	−56.2083	−1.85112
$923$	10.7588	0.354130
$924$	0	0
$925$	−2.22940	−0.0733023
$926$	−75.9099	−2.49455
$927$	3.24193	0.106479
$928$	−27.7409	−0.910639
$929$	5.25099	0.172279	0.0861397	−	0.996283i	$-0.472547\pi$
$929$	5.25099	0.172279	0.0861397	+	0.996283i	$0.472547\pi$
$930$	−232.700	−7.63054
$931$	−0.0409120	−0.00134084
$932$	−38.3070	−1.25479
$933$	60.8735	1.99291
$934$	−49.2923	−1.61289
$935$	0	0
$936$	−52.1329	−1.70402
$937$	−37.2323	−1.21633	−0.608163	−	0.793812i	$-0.708093\pi$
$937$	−37.2323	−1.21633	−0.608163	+	0.793812i	$0.708093\pi$
$938$	45.8243	1.49622
$939$	−34.0127	−1.10996
$940$	130.896	4.26937
$941$	−15.1286	−0.493180	−0.246590	−	0.969120i	$-0.579310\pi$
$941$	−15.1286	−0.493180	−0.246590	+	0.969120i	$0.579310\pi$
$942$	38.2878	1.24748
$943$	−3.29224	−0.107210
$944$	1.01759	0.0331198
$945$	148.318	4.82478
$946$	0	0
$947$	55.1073	1.79075	0.895374	−	0.445316i	$-0.146909\pi$
$947$	55.1073	1.79075	0.895374	+	0.445316i	$0.146909\pi$
$948$	11.6936	0.379790
$949$	10.8441	0.352013
$950$	150.898	4.89577
$951$	36.9127	1.19698
$952$	−1.23513	−0.0400308
$953$	−13.0319	−0.422145	−0.211073	−	0.977470i	$-0.567696\pi$
$953$	−13.0319	−0.422145	−0.211073	+	0.977470i	$0.567696\pi$
$954$	−139.439	−4.51451
$955$	37.9392	1.22768
$956$	51.1721	1.65502
$957$	0	0
$958$	−17.0876	−0.552075
$959$	−3.56134	−0.115002
$960$	161.626	5.21645
$961$	29.6179	0.955415
$962$	1.03146	0.0332555
$963$	−79.2301	−2.55315
$964$	8.74441	0.281639
$965$	−64.0155	−2.06073
$966$	147.824	4.75615
$967$	0.439139	0.0141218	0.00706088	−	0.999975i	$-0.497752\pi$
$967$	0.439139	0.0141218	0.00706088	+	0.999975i	$0.497752\pi$
$968$	0	0
$969$	2.74144	0.0880677
$970$	33.2318	1.06701
$971$	−49.0366	−1.57366	−0.786829	−	0.617171i	$-0.788279\pi$
$971$	−49.0366	−1.57366	−0.786829	+	0.617171i	$0.788279\pi$
$972$	108.701	3.48658
$973$	9.75234	0.312646
$974$	−33.0314	−1.05839
$975$	77.5199	2.48262
$976$	−0.728335	−0.0233134
$977$	27.9250	0.893401	0.446700	−	0.894684i	$-0.352599\pi$
$977$	27.9250	0.893401	0.446700	+	0.894684i	$0.352599\pi$
$978$	−15.2771	−0.488507
$979$	0	0
$980$	−0.0939759	−0.00300195
$981$	121.305	3.87297
$982$	82.1776	2.62239
$983$	−37.5783	−1.19856	−0.599281	−	0.800539i	$-0.704547\pi$
$983$	−37.5783	−1.19856	−0.599281	+	0.800539i	$0.704547\pi$
$984$	4.58718	0.146234
$985$	5.92748	0.188865
$986$	−1.94323	−0.0618850
$987$	82.1466	2.61475
$988$	−43.9256	−1.39746
$989$	−19.0773	−0.606624
$990$	0	0
$991$	−35.7573	−1.13587	−0.567934	−	0.823074i	$-0.692257\pi$
$991$	−35.7573	−1.13587	−0.567934	+	0.823074i	$0.692257\pi$
$992$	−37.2197	−1.18173
$993$	31.3077	0.993519
$994$	30.1898	0.957563
$995$	34.2247	1.08500
$996$	142.613	4.51888
$997$	−32.9240	−1.04272	−0.521358	−	0.853338i	$-0.674574\pi$
$997$	−32.9240	−1.04272	−0.521358	+	0.853338i	$0.674574\pi$
$998$	−52.2129	−1.65277
$999$	−2.84011	−0.0898571

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.u.1.9		64
11.7	odd	10		671.2.j.c.489.28	yes	128
11.8	odd	10		671.2.j.c.306.28	✓	128
11.10	odd	2		7381.2.a.v.1.56		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.306.28	✓	128	11.8	odd	10
671.2.j.c.489.28	yes	128	11.7	odd	10
7381.2.a.u.1.9		64	1.1	even	1	trivial
7381.2.a.v.1.56		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)

\(f(q)\)	\(=\)	\(q-2.32237 q^{2} +3.21773 q^{3} +3.39339 q^{4} -3.99960 q^{5} -7.47274 q^{6} -2.64706 q^{7} -3.23597 q^{8} +7.35376 q^{9} +O(q^{10})\)	\(q-2.32237 q^{2} +3.21773 q^{3} +3.39339 q^{4} -3.99960 q^{5} -7.47274 q^{6} -2.64706 q^{7} -3.23597 q^{8} +7.35376 q^{9} +9.28854 q^{10} +10.9190 q^{12} +2.19078 q^{13} +6.14745 q^{14} -12.8696 q^{15} +0.728335 q^{16} -0.144193 q^{17} -17.0781 q^{18} -5.90861 q^{19} -13.5722 q^{20} -8.51751 q^{21} +7.47309 q^{23} -10.4125 q^{24} +10.9968 q^{25} -5.08779 q^{26} +14.0092 q^{27} -8.98252 q^{28} -5.80294 q^{29} +29.8880 q^{30} -7.78575 q^{31} +4.78049 q^{32} +0.334869 q^{34} +10.5872 q^{35} +24.9542 q^{36} -0.202732 q^{37} +13.7220 q^{38} +7.04931 q^{39} +12.9426 q^{40} -0.440547 q^{41} +19.7808 q^{42} -2.55280 q^{43} -29.4121 q^{45} -17.3553 q^{46} -9.64444 q^{47} +2.34358 q^{48} +0.00692413 q^{49} -25.5386 q^{50} -0.463974 q^{51} +7.43417 q^{52} +8.16478 q^{53} -32.5345 q^{54} +8.56582 q^{56} -19.0123 q^{57} +13.4766 q^{58} +1.39715 q^{59} -43.6717 q^{60} -1.00000 q^{61} +18.0814 q^{62} -19.4658 q^{63} -12.5587 q^{64} -8.76223 q^{65} +7.45420 q^{67} -0.489304 q^{68} +24.0463 q^{69} -24.5873 q^{70} +4.91095 q^{71} -23.7966 q^{72} +4.94988 q^{73} +0.470818 q^{74} +35.3847 q^{75} -20.0502 q^{76} -16.3711 q^{78} +1.07094 q^{79} -2.91305 q^{80} +23.0164 q^{81} +1.02311 q^{82} +13.0610 q^{83} -28.9033 q^{84} +0.576715 q^{85} +5.92855 q^{86} -18.6723 q^{87} -7.41041 q^{89} +68.3057 q^{90} -5.79911 q^{91} +25.3591 q^{92} -25.0524 q^{93} +22.3979 q^{94} +23.6321 q^{95} +15.3823 q^{96} +3.57772 q^{97} -0.0160804 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} + q^{6} - 6 q^{7} - 3 q^{8} + 81 q^{9}+O(q^{10}) \) 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

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Database

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