LMFDB - Embedded newform 7381.2.a.o.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:	$25$
Twist minimal:	yes
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)

$f(q)$	$=$	$q-0.589503 q^{2} +0.0839224 q^{3} -1.65249 q^{4} -0.856992 q^{5} -0.0494725 q^{6} +3.14113 q^{7} +2.15315 q^{8} -2.99296 q^{9} +O(q^{10})$	\(q-0.589503 q^{2} +0.0839224 q^{3} -1.65249 q^{4} -0.856992 q^{5} -0.0494725 q^{6} +3.14113 q^{7} +2.15315 q^{8} -2.99296 q^{9} +0.505200 q^{10} -0.138681 q^{12} -1.46242 q^{13} -1.85170 q^{14} -0.0719208 q^{15} +2.03568 q^{16} -5.02048 q^{17} +1.76436 q^{18} +0.707248 q^{19} +1.41617 q^{20} +0.263611 q^{21} +7.30023 q^{23} +0.180698 q^{24} -4.26557 q^{25} +0.862102 q^{26} -0.502943 q^{27} -5.19066 q^{28} -1.90920 q^{29} +0.0423975 q^{30} +0.843122 q^{31} -5.50635 q^{32} +2.95959 q^{34} -2.69192 q^{35} +4.94582 q^{36} +0.681437 q^{37} -0.416925 q^{38} -0.122730 q^{39} -1.84523 q^{40} -1.39407 q^{41} -0.155399 q^{42} -0.116108 q^{43} +2.56494 q^{45} -4.30351 q^{46} +0.0286233 q^{47} +0.170839 q^{48} +2.86667 q^{49} +2.51457 q^{50} -0.421331 q^{51} +2.41663 q^{52} -0.375357 q^{53} +0.296487 q^{54} +6.76332 q^{56} +0.0593539 q^{57} +1.12548 q^{58} +1.10489 q^{59} +0.118848 q^{60} -1.00000 q^{61} -0.497023 q^{62} -9.40125 q^{63} -0.825350 q^{64} +1.25328 q^{65} +7.45182 q^{67} +8.29628 q^{68} +0.612653 q^{69} +1.58690 q^{70} -2.51132 q^{71} -6.44429 q^{72} -0.865830 q^{73} -0.401710 q^{74} -0.357976 q^{75} -1.16872 q^{76} +0.0723496 q^{78} +3.45646 q^{79} -1.74456 q^{80} +8.93666 q^{81} +0.821809 q^{82} +14.4970 q^{83} -0.435613 q^{84} +4.30251 q^{85} +0.0684459 q^{86} -0.160225 q^{87} +3.44775 q^{89} -1.51204 q^{90} -4.59365 q^{91} -12.0635 q^{92} +0.0707568 q^{93} -0.0168735 q^{94} -0.606106 q^{95} -0.462106 q^{96} -15.1583 q^{97} -1.68991 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 4 q^{7} + 21 q^{8} + 24 q^{9}+O(q^{10}) $ 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 4 * q^7 + 21 * q^8 + 24 * q^9	$ 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 4 q^{7} + 21 q^{8} + 24 q^{9} - q^{12} + 4 q^{13} - q^{14} - 2 q^{15} + 21 q^{16} + 10 q^{17} + 40 q^{18} + 17 q^{19} - 6 q^{20} + 15 q^{21} - 4 q^{23} - 9 q^{24} + 40 q^{25} - 18 q^{26} + 8 q^{27} - 29 q^{28} + 35 q^{29} - 6 q^{30} - 12 q^{31} + 47 q^{32} + 45 q^{35} + 41 q^{36} - 14 q^{37} - 13 q^{38} + 20 q^{39} + 69 q^{40} + 24 q^{41} - 32 q^{42} + 24 q^{43} - 16 q^{45} + 10 q^{46} + 22 q^{47} - 54 q^{48} + 23 q^{49} + 26 q^{50} + 76 q^{51} + q^{52} - 27 q^{53} + 13 q^{54} - 9 q^{56} + 4 q^{57} + 76 q^{58} - 21 q^{59} + 28 q^{60} - 25 q^{61} + 25 q^{62} + 4 q^{63} + 5 q^{64} + 20 q^{65} + 13 q^{67} - 34 q^{68} - 7 q^{69} - 41 q^{70} - 24 q^{71} + 54 q^{72} + 39 q^{73} + 56 q^{74} + 7 q^{75} + 42 q^{76} + 30 q^{78} + 5 q^{79} + 92 q^{80} + 9 q^{81} - 9 q^{82} + 51 q^{83} + 125 q^{84} + 5 q^{85} - 10 q^{86} + 3 q^{87} + 17 q^{89} - 104 q^{90} + 8 q^{91} - 23 q^{92} - 36 q^{93} - 29 q^{94} + 81 q^{95} - 48 q^{96} - 15 q^{97} + 25 q^{98}+O(q^{100}) $ 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 4 * q^7 + 21 * q^8 + 24 * q^9 - q^12 + 4 * q^13 - q^14 - 2 * q^15 + 21 * q^16 + 10 * q^17 + 40 * q^18 + 17 * q^19 - 6 * q^20 + 15 * q^21 - 4 * q^23 - 9 * q^24 + 40 * q^25 - 18 * q^26 + 8 * q^27 - 29 * q^28 + 35 * q^29 - 6 * q^30 - 12 * q^31 + 47 * q^32 + 45 * q^35 + 41 * q^36 - 14 * q^37 - 13 * q^38 + 20 * q^39 + 69 * q^40 + 24 * q^41 - 32 * q^42 + 24 * q^43 - 16 * q^45 + 10 * q^46 + 22 * q^47 - 54 * q^48 + 23 * q^49 + 26 * q^50 + 76 * q^51 + q^52 - 27 * q^53 + 13 * q^54 - 9 * q^56 + 4 * q^57 + 76 * q^58 - 21 * q^59 + 28 * q^60 - 25 * q^61 + 25 * q^62 + 4 * q^63 + 5 * q^64 + 20 * q^65 + 13 * q^67 - 34 * q^68 - 7 * q^69 - 41 * q^70 - 24 * q^71 + 54 * q^72 + 39 * q^73 + 56 * q^74 + 7 * q^75 + 42 * q^76 + 30 * q^78 + 5 * q^79 + 92 * q^80 + 9 * q^81 - 9 * q^82 + 51 * q^83 + 125 * q^84 + 5 * q^85 - 10 * q^86 + 3 * q^87 + 17 * q^89 - 104 * q^90 + 8 * q^91 - 23 * q^92 - 36 * q^93 - 29 * q^94 + 81 * q^95 - 48 * q^96 - 15 * q^97 + 25 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−0.589503	−0.416842	−0.208421	−	0.978039i	$-0.566832\pi$
$2$	−0.589503	−0.416842	−0.208421	+	0.978039i	$0.566832\pi$
$3$	0.0839224	0.0484526	0.0242263	−	0.999707i	$-0.492288\pi$
$3$	0.0839224	0.0484526	0.0242263	+	0.999707i	$0.492288\pi$
$4$	−1.65249	−0.826243
$5$	−0.856992	−0.383258	−0.191629	−	0.981467i	$-0.561377\pi$
$5$	−0.856992	−0.383258	−0.191629	+	0.981467i	$0.561377\pi$
$6$	−0.0494725	−0.0201971
$7$	3.14113	1.18723	0.593617	−	0.804748i	$-0.297699\pi$
$7$	3.14113	1.18723	0.593617	+	0.804748i	$0.297699\pi$
$8$	2.15315	0.761255
$9$	−2.99296	−0.997652
$10$	0.505200	0.159758
$11$	0	0
$11$	0	0
$12$	−0.138681	−0.0400336
$13$	−1.46242	−0.405602	−0.202801	−	0.979220i	$-0.565005\pi$
$13$	−1.46242	−0.405602	−0.202801	+	0.979220i	$0.565005\pi$
$14$	−1.85170	−0.494889
$15$	−0.0719208	−0.0185699
$16$	2.03568	0.508920
$17$	−5.02048	−1.21765	−0.608823	−	0.793306i	$-0.708358\pi$
$17$	−5.02048	−1.21765	−0.608823	+	0.793306i	$0.708358\pi$
$18$	1.76436	0.415863
$19$	0.707248	0.162254	0.0811269	−	0.996704i	$-0.474148\pi$
$19$	0.707248	0.162254	0.0811269	+	0.996704i	$0.474148\pi$
$20$	1.41617	0.316664
$21$	0.263611	0.0575246
$22$	0	0
$23$	7.30023	1.52220	0.761102	−	0.648632i	$-0.224659\pi$
$23$	7.30023	1.52220	0.761102	+	0.648632i	$0.224659\pi$
$24$	0.180698	0.0368848
$25$	−4.26557	−0.853113
$26$	0.862102	0.169072
$27$	−0.502943	−0.0967915
$28$	−5.19066	−0.980943
$29$	−1.90920	−0.354530	−0.177265	−	0.984163i	$-0.556725\pi$
$29$	−1.90920	−0.354530	−0.177265	+	0.984163i	$0.556725\pi$
$30$	0.0423975	0.00774070
$31$	0.843122	0.151429	0.0757146	−	0.997130i	$-0.475876\pi$
$31$	0.843122	0.151429	0.0757146	+	0.997130i	$0.475876\pi$
$32$	−5.50635	−0.973394
$33$	0	0
$34$	2.95959	0.507566
$35$	−2.69192	−0.455017
$36$	4.94582	0.824303
$37$	0.681437	0.112028	0.0560138	−	0.998430i	$-0.482161\pi$
$37$	0.681437	0.112028	0.0560138	+	0.998430i	$0.482161\pi$
$38$	−0.416925	−0.0676342
$39$	−0.122730	−0.0196525
$40$	−1.84523	−0.291757
$41$	−1.39407	−0.217717	−0.108859	−	0.994057i	$-0.534720\pi$
$41$	−1.39407	−0.217717	−0.108859	+	0.994057i	$0.534720\pi$
$42$	−0.155399	−0.0239786
$43$	−0.116108	−0.0177063	−0.00885313	−	0.999961i	$-0.502818\pi$
$43$	−0.116108	−0.0177063	−0.00885313	+	0.999961i	$0.502818\pi$
$44$	0	0
$45$	2.56494	0.382359
$46$	−4.30351	−0.634518
$47$	0.0286233	0.00417513	0.00208757	−	0.999998i	$-0.499336\pi$
$47$	0.0286233	0.00417513	0.00208757	+	0.999998i	$0.499336\pi$
$48$	0.170839	0.0246585
$49$	2.86667	0.409524
$50$	2.51457	0.355613
$51$	−0.421331	−0.0589981
$52$	2.41663	0.335126
$53$	−0.375357	−0.0515592	−0.0257796	−	0.999668i	$-0.508207\pi$
$53$	−0.375357	−0.0515592	−0.0257796	+	0.999668i	$0.508207\pi$
$54$	0.296487	0.0403467
$55$	0	0
$56$	6.76332	0.903787
$57$	0.0593539	0.00786162
$58$	1.12548	0.147783
$59$	1.10489	0.143845	0.0719223	−	0.997410i	$-0.477087\pi$
$59$	1.10489	0.143845	0.0719223	+	0.997410i	$0.477087\pi$
$60$	0.118848	0.0153432
$61$	−1.00000	−0.128037
$61$	−1.00000	−0.128037
$62$	−0.497023	−0.0631220
$63$	−9.40125	−1.18445
$64$	−0.825350	−0.103169
$65$	1.25328	0.155451
$66$	0	0
$67$	7.45182	0.910385	0.455192	−	0.890393i	$-0.349571\pi$
$67$	7.45182	0.910385	0.455192	+	0.890393i	$0.349571\pi$
$68$	8.29628	1.00607
$69$	0.612653	0.0737548
$70$	1.58690	0.189670
$71$	−2.51132	−0.298039	−0.149019	−	0.988834i	$-0.547612\pi$
$71$	−2.51132	−0.298039	−0.149019	+	0.988834i	$0.547612\pi$
$72$	−6.44429	−0.759467
$73$	−0.865830	−0.101338	−0.0506689	−	0.998716i	$-0.516135\pi$
$73$	−0.865830	−0.101338	−0.0506689	+	0.998716i	$0.516135\pi$
$74$	−0.401710	−0.0466978
$75$	−0.357976	−0.0413355
$76$	−1.16872	−0.134061
$77$	0	0
$78$	0.0723496	0.00819198
$79$	3.45646	0.388882	0.194441	−	0.980914i	$-0.437711\pi$
$79$	3.45646	0.388882	0.194441	+	0.980914i	$0.437711\pi$
$80$	−1.74456	−0.195048
$81$	8.93666	0.992963
$82$	0.821809	0.0907536
$83$	14.4970	1.59125	0.795624	−	0.605791i	$-0.207143\pi$
$83$	14.4970	1.59125	0.795624	+	0.605791i	$0.207143\pi$
$84$	−0.435613	−0.0475293
$85$	4.30251	0.466673
$86$	0.0684459	0.00738071
$87$	−0.160225	−0.0171779
$88$	0	0
$89$	3.44775	0.365461	0.182730	−	0.983163i	$-0.441506\pi$
$89$	3.44775	0.365461	0.182730	+	0.983163i	$0.441506\pi$
$90$	−1.51204	−0.159383
$91$	−4.59365	−0.481545
$92$	−12.0635	−1.25771
$93$	0.0707568	0.00733713
$94$	−0.0168735	−0.00174037
$95$	−0.606106	−0.0621852
$96$	−0.462106	−0.0471635
$97$	−15.1583	−1.53909	−0.769547	−	0.638590i	$-0.779518\pi$
$97$	−15.1583	−1.53909	−0.769547	+	0.638590i	$0.779518\pi$
$98$	−1.68991	−0.170707
$99$	0	0
$100$	7.04879	0.704879
$101$	−3.19721	−0.318134	−0.159067	−	0.987268i	$-0.550849\pi$
$101$	−3.19721	−0.318134	−0.159067	+	0.987268i	$0.550849\pi$
$102$	0.248376	0.0245929
$103$	−10.0007	−0.985396	−0.492698	−	0.870200i	$-0.663989\pi$
$103$	−10.0007	−0.985396	−0.492698	+	0.870200i	$0.663989\pi$
$104$	−3.14881	−0.308767
$105$	−0.225912	−0.0220468
$106$	0.221274	0.0214920
$107$	−15.5300	−1.50134	−0.750671	−	0.660677i	$-0.770269\pi$
$107$	−15.5300	−1.50134	−0.750671	+	0.660677i	$0.770269\pi$
$108$	0.831106	0.0799732
$109$	1.49401	0.143100	0.0715500	−	0.997437i	$-0.477205\pi$
$109$	1.49401	0.143100	0.0715500	+	0.997437i	$0.477205\pi$
$110$	0	0
$111$	0.0571878	0.00542803
$112$	6.39433	0.604207
$113$	4.12434	0.387985	0.193993	−	0.981003i	$-0.437856\pi$
$113$	4.12434	0.387985	0.193993	+	0.981003i	$0.437856\pi$
$114$	−0.0349894	−0.00327705
$115$	−6.25624	−0.583397
$116$	3.15493	0.292928
$117$	4.37696	0.404650
$118$	−0.651337	−0.0599605
$119$	−15.7700	−1.44563
$120$	−0.154856	−0.0141364
$121$	0	0
$122$	0.589503	0.0533711
$123$	−0.116994	−0.0105490
$124$	−1.39325	−0.125117
$125$	7.94051	0.710221
$126$	5.54207	0.493727
$127$	1.55498	0.137982	0.0689909	−	0.997617i	$-0.478022\pi$
$127$	1.55498	0.137982	0.0689909	+	0.997617i	$0.478022\pi$
$128$	11.4992	1.01640
$129$	−0.00974403	−0.000857914 0
$130$	−0.738814	−0.0647983
$131$	−11.2712	−0.984771	−0.492385	−	0.870377i	$-0.663875\pi$
$131$	−11.2712	−0.984771	−0.492385	+	0.870377i	$0.663875\pi$
$132$	0	0
$133$	2.22156	0.192633
$134$	−4.39287	−0.379486
$135$	0.431018	0.0370961
$136$	−10.8099	−0.926939
$137$	13.6782	1.16860	0.584302	−	0.811536i	$-0.301368\pi$
$137$	13.6782	1.16860	0.584302	+	0.811536i	$0.301368\pi$
$138$	−0.361161	−0.0307441
$139$	0.718599	0.0609508	0.0304754	−	0.999536i	$-0.490298\pi$
$139$	0.718599	0.0609508	0.0304754	+	0.999536i	$0.490298\pi$
$140$	4.44836	0.375955
$141$	0.00240213	0.000202296 0
$142$	1.48043	0.124235
$143$	0	0
$144$	−6.09270	−0.507725
$145$	1.63617	0.135877
$146$	0.510410	0.0422418
$147$	0.240578	0.0198425
$148$	−1.12607	−0.0925620
$149$	11.8833	0.973517	0.486759	−	0.873536i	$-0.338179\pi$
$149$	11.8833	0.973517	0.486759	+	0.873536i	$0.338179\pi$
$150$	0.211028	0.0172304
$151$	18.5558	1.51005	0.755025	−	0.655696i	$-0.227625\pi$
$151$	18.5558	1.51005	0.755025	+	0.655696i	$0.227625\pi$
$152$	1.52281	0.123516
$153$	15.0261	1.21479
$154$	0	0
$155$	−0.722548	−0.0580365
$156$	0.202809	0.0162377
$157$	9.78029	0.780552	0.390276	−	0.920698i	$-0.372380\pi$
$157$	9.78029	0.780552	0.390276	+	0.920698i	$0.372380\pi$
$158$	−2.03760	−0.162102
$159$	−0.0315008	−0.00249818
$160$	4.71889	0.373061
$161$	22.9310	1.80721
$162$	−5.26819	−0.413908
$163$	−24.2025	−1.89569	−0.947844	−	0.318735i	$-0.896742\pi$
$163$	−24.2025	−1.89569	−0.947844	+	0.318735i	$0.896742\pi$
$164$	2.30368	0.179887
$165$	0	0
$166$	−8.54600	−0.663299
$167$	−6.92226	−0.535661	−0.267830	−	0.963466i	$-0.586307\pi$
$167$	−6.92226	−0.535661	−0.267830	+	0.963466i	$0.586307\pi$
$168$	0.567594	0.0437908
$169$	−10.8613	−0.835487
$170$	−2.53635	−0.194529
$171$	−2.11676	−0.161873
$172$	0.191866	0.0146297
$173$	7.89199	0.600017	0.300008	−	0.953937i	$-0.403011\pi$
$173$	7.89199	0.600017	0.300008	+	0.953937i	$0.403011\pi$
$174$	0.0944531	0.00716047
$175$	−13.3987	−1.01284
$176$	0	0
$177$	0.0927251	0.00696965
$178$	−2.03246	−0.152339
$179$	−0.859856	−0.0642686	−0.0321343	−	0.999484i	$-0.510230\pi$
$179$	−0.859856	−0.0642686	−0.0321343	+	0.999484i	$0.510230\pi$
$180$	−4.23853	−0.315921
$181$	−0.949317	−0.0705621	−0.0352811	−	0.999377i	$-0.511233\pi$
$181$	−0.949317	−0.0705621	−0.0352811	+	0.999377i	$0.511233\pi$
$182$	2.70797	0.200728
$183$	−0.0839224	−0.00620372
$184$	15.7185	1.15878
$185$	−0.583986	−0.0429355
$186$	−0.0417114	−0.00305842
$187$	0	0
$188$	−0.0472995	−0.00344967
$189$	−1.57981	−0.114914
$190$	0.357302	0.0259214
$191$	−5.08628	−0.368030	−0.184015	−	0.982923i	$-0.558910\pi$
$191$	−5.08628	−0.368030	−0.184015	+	0.982923i	$0.558910\pi$
$192$	−0.0692653	−0.00499879
$193$	11.5671	0.832620	0.416310	−	0.909223i	$-0.363323\pi$
$193$	11.5671	0.832620	0.416310	+	0.909223i	$0.363323\pi$
$194$	8.93588	0.641559
$195$	0.105178	0.00753198
$196$	−4.73713	−0.338366
$197$	15.6855	1.11755	0.558773	−	0.829320i	$-0.311272\pi$
$197$	15.6855	1.11755	0.558773	+	0.829320i	$0.311272\pi$
$198$	0	0
$199$	9.49572	0.673134	0.336567	−	0.941660i	$-0.390734\pi$
$199$	9.49572	0.673134	0.336567	+	0.941660i	$0.390734\pi$
$200$	−9.18441	−0.649436
$201$	0.625374	0.0441105
$202$	1.88477	0.132612
$203$	−5.99705	−0.420910
$204$	0.696243	0.0487468
$205$	1.19471	0.0834419
$206$	5.89544	0.410755
$207$	−21.8493	−1.51863
$208$	−2.97702	−0.206419
$209$	0	0
$210$	0.133176	0.00919002
$211$	1.64780	0.113439	0.0567197	−	0.998390i	$-0.481936\pi$
$211$	1.64780	0.113439	0.0567197	+	0.998390i	$0.481936\pi$
$212$	0.620271	0.0426004
$213$	−0.210756	−0.0144407
$214$	9.15499	0.625822
$215$	0.0995033	0.00678607
$216$	−1.08291	−0.0736829
$217$	2.64835	0.179782
$218$	−0.880723	−0.0596501
$219$	−0.0726625	−0.00491008
$220$	0	0
$221$	7.34206	0.493880
$222$	−0.0337124	−0.00226263
$223$	−1.26089	−0.0844356	−0.0422178	−	0.999108i	$-0.513442\pi$
$223$	−1.26089	−0.0844356	−0.0422178	+	0.999108i	$0.513442\pi$
$224$	−17.2961	−1.15565
$225$	12.7667	0.851110
$226$	−2.43131	−0.161729
$227$	−24.8663	−1.65043	−0.825216	−	0.564817i	$-0.808947\pi$
$227$	−24.8663	−1.65043	−0.825216	+	0.564817i	$0.808947\pi$
$228$	−0.0980815	−0.00649561
$229$	−8.24270	−0.544693	−0.272346	−	0.962199i	$-0.587800\pi$
$229$	−8.24270	−0.544693	−0.272346	+	0.962199i	$0.587800\pi$
$230$	3.68808	0.243185
$231$	0	0
$232$	−4.11081	−0.269888
$233$	6.94220	0.454799	0.227399	−	0.973802i	$-0.426978\pi$
$233$	6.94220	0.454799	0.227399	+	0.973802i	$0.426978\pi$
$234$	−2.58023	−0.168675
$235$	−0.0245299	−0.00160015
$236$	−1.82582	−0.118851
$237$	0.290074	0.0188424
$238$	9.29645	0.602599
$239$	−3.08764	−0.199723	−0.0998613	−	0.995001i	$-0.531840\pi$
$239$	−3.08764	−0.199723	−0.0998613	+	0.995001i	$0.531840\pi$
$240$	−0.146408	−0.00945058
$241$	10.0207	0.645491	0.322745	−	0.946486i	$-0.395394\pi$
$241$	10.0207	0.645491	0.322745	+	0.946486i	$0.395394\pi$
$242$	0	0
$243$	2.25882	0.144903
$244$	1.65249	0.105790
$245$	−2.45671	−0.156953
$246$	0.0689682	0.00439725
$247$	−1.03429	−0.0658106
$248$	1.81537	0.115276
$249$	1.21662	0.0771001
$250$	−4.68096	−0.296050
$251$	5.24096	0.330806	0.165403	−	0.986226i	$-0.447107\pi$
$251$	5.24096	0.330806	0.165403	+	0.986226i	$0.447107\pi$
$252$	15.5354	0.978640
$253$	0	0
$254$	−0.916664	−0.0575166
$255$	0.361077	0.0226115
$256$	−5.12814	−0.320509
$257$	−1.53662	−0.0958518	−0.0479259	−	0.998851i	$-0.515261\pi$
$257$	−1.53662	−0.0958518	−0.0479259	+	0.998851i	$0.515261\pi$
$258$	0.00574414	0.000357615 0
$259$	2.14048	0.133003
$260$	−2.07103	−0.128440
$261$	5.71417	0.353698
$262$	6.64442	0.410494
$263$	21.7172	1.33914	0.669570	−	0.742749i	$-0.266478\pi$
$263$	21.7172	1.33914	0.669570	+	0.742749i	$0.266478\pi$
$264$	0	0
$265$	0.321678	0.0197605
$266$	−1.30961	−0.0802976
$267$	0.289343	0.0177075
$268$	−12.3140	−0.752199
$269$	12.2326	0.745834	0.372917	−	0.927865i	$-0.378358\pi$
$269$	12.2326	0.745834	0.372917	+	0.927865i	$0.378358\pi$
$270$	−0.254087	−0.0154632
$271$	18.1748	1.10404	0.552022	−	0.833830i	$-0.313857\pi$
$271$	18.1748	1.10404	0.552022	+	0.833830i	$0.313857\pi$
$272$	−10.2201	−0.619685
$273$	−0.385510	−0.0233321
$274$	−8.06332	−0.487123
$275$	0	0
$276$	−1.01240	−0.0609393
$277$	13.7084	0.823658	0.411829	−	0.911261i	$-0.364890\pi$
$277$	13.7084	0.823658	0.411829	+	0.911261i	$0.364890\pi$
$278$	−0.423617	−0.0254069
$279$	−2.52343	−0.151074
$280$	−5.79611	−0.346384
$281$	3.61868	0.215872	0.107936	−	0.994158i	$-0.465576\pi$
$281$	3.61868	0.215872	0.107936	+	0.994158i	$0.465576\pi$
$282$	−0.00141607	−8.43255e−5 0
$283$	16.0343	0.953138	0.476569	−	0.879137i	$-0.341880\pi$
$283$	16.0343	0.953138	0.476569	+	0.879137i	$0.341880\pi$
$284$	4.14992	0.246252
$285$	−0.0508658	−0.00301303
$286$	0	0
$287$	−4.37895	−0.258481
$288$	16.4803	0.971109
$289$	8.20526	0.482663
$290$	−0.964529	−0.0566391
$291$	−1.27212	−0.0745731
$292$	1.43077	0.0837296
$293$	−4.89166	−0.285774	−0.142887	−	0.989739i	$-0.545638\pi$
$293$	−4.89166	−0.285774	−0.142887	+	0.989739i	$0.545638\pi$
$294$	−0.141821	−0.00827119
$295$	−0.946883	−0.0551296
$296$	1.46724	0.0852815
$297$	0	0
$298$	−7.00524	−0.405803
$299$	−10.6760	−0.617410
$300$	0.591551	0.0341532
$301$	−0.364709	−0.0210215
$302$	−10.9387	−0.629452
$303$	−0.268317	−0.0154144
$304$	1.43973	0.0825742
$305$	0.856992	0.0490712
$306$	−8.85793	−0.506374
$307$	11.6957	0.667508	0.333754	−	0.942660i	$-0.391685\pi$
$307$	11.6957	0.667508	0.333754	+	0.942660i	$0.391685\pi$
$308$	0	0
$309$	−0.839281	−0.0477450
$310$	0.425945	0.0241920
$311$	17.1104	0.970240	0.485120	−	0.874448i	$-0.338776\pi$
$311$	17.1104	0.970240	0.485120	+	0.874448i	$0.338776\pi$
$312$	−0.264256	−0.0149605
$313$	−21.1318	−1.19444	−0.597219	−	0.802079i	$-0.703728\pi$
$313$	−21.1318	−1.19444	−0.597219	+	0.802079i	$0.703728\pi$
$314$	−5.76552	−0.325367
$315$	8.05680	0.453949
$316$	−5.71175	−0.321311
$317$	2.33675	0.131245	0.0656226	−	0.997845i	$-0.479097\pi$
$317$	2.33675	0.131245	0.0656226	+	0.997845i	$0.479097\pi$
$318$	0.0185698	0.00104135
$319$	0	0
$320$	0.707318	0.0395403
$321$	−1.30331	−0.0727439
$322$	−13.5179	−0.753322
$323$	−3.55073	−0.197568
$324$	−14.7677	−0.820428
$325$	6.23805	0.346025
$326$	14.2675	0.790202
$327$	0.125381	0.00693357
$328$	−3.00165	−0.165738
$329$	0.0899093	0.00495686
$330$	0	0
$331$	−10.0859	−0.554369	−0.277184	−	0.960817i	$-0.589401\pi$
$331$	−10.0859	−0.554369	−0.277184	+	0.960817i	$0.589401\pi$
$332$	−23.9560	−1.31476
$333$	−2.03951	−0.111765
$334$	4.08070	0.223286
$335$	−6.38615	−0.348913
$336$	0.536627	0.0292754
$337$	−10.9301	−0.595400	−0.297700	−	0.954660i	$-0.596219\pi$
$337$	−10.9301	−0.595400	−0.297700	+	0.954660i	$0.596219\pi$
$338$	6.40279	0.348266
$339$	0.346125	0.0187989
$340$	−7.10984	−0.385585
$341$	0	0
$342$	1.24784	0.0674754
$343$	−12.9833	−0.701033
$344$	−0.249998	−0.0134790
$345$	−0.525039	−0.0282671
$346$	−4.65235	−0.250112
$347$	23.4967	1.26137	0.630684	−	0.776039i	$-0.282774\pi$
$347$	23.4967	1.26137	0.630684	+	0.776039i	$0.282774\pi$
$348$	0.264769	0.0141931
$349$	−12.7882	−0.684537	−0.342269	−	0.939602i	$-0.611195\pi$
$349$	−12.7882	−0.684537	−0.342269	+	0.939602i	$0.611195\pi$
$350$	7.89856	0.422196
$351$	0.735514	0.0392588
$352$	0	0
$353$	24.5654	1.30748	0.653742	−	0.756718i	$-0.273198\pi$
$353$	24.5654	1.30748	0.653742	+	0.756718i	$0.273198\pi$
$354$	−0.0546618	−0.00290524
$355$	2.15218	0.114226
$356$	−5.69735	−0.301959
$357$	−1.32345	−0.0700446
$358$	0.506888	0.0267899
$359$	13.4573	0.710248	0.355124	−	0.934819i	$-0.384439\pi$
$359$	13.4573	0.710248	0.355124	+	0.934819i	$0.384439\pi$
$360$	5.52271	0.291072
$361$	−18.4998	−0.973674
$362$	0.559625	0.0294133
$363$	0	0
$364$	7.59093	0.397873
$365$	0.742009	0.0388385
$366$	0.0494725	0.00258597
$367$	−14.4398	−0.753749	−0.376875	−	0.926264i	$-0.623001\pi$
$367$	−14.4398	−0.753749	−0.376875	+	0.926264i	$0.623001\pi$
$368$	14.8609	0.774680
$369$	4.17239	0.217206
$370$	0.344262	0.0178973
$371$	−1.17904	−0.0612128
$372$	−0.116925	−0.00606225
$373$	27.6462	1.43147	0.715733	−	0.698374i	$-0.246093\pi$
$373$	27.6462	1.43147	0.715733	+	0.698374i	$0.246093\pi$
$374$	0	0
$375$	0.666387	0.0344121
$376$	0.0616303	0.00317834
$377$	2.79206	0.143798
$378$	0.931302	0.0479010
$379$	3.78906	0.194631	0.0973156	−	0.995254i	$-0.468974\pi$
$379$	3.78906	0.194631	0.0973156	+	0.995254i	$0.468974\pi$
$380$	1.00158	0.0513800
$381$	0.130497	0.00668558
$382$	2.99838	0.153410
$383$	21.2097	1.08377	0.541883	−	0.840454i	$-0.317712\pi$
$383$	21.2097	1.08377	0.541883	+	0.840454i	$0.317712\pi$
$384$	0.965043	0.0492472
$385$	0	0
$386$	−6.81886	−0.347071
$387$	0.347505	0.0176647
$388$	25.0489	1.27167
$389$	−18.7641	−0.951378	−0.475689	−	0.879614i	$-0.657801\pi$
$389$	−18.7641	−0.951378	−0.475689	+	0.879614i	$0.657801\pi$
$390$	−0.0620030	−0.00313965
$391$	−36.6507	−1.85351
$392$	6.17237	0.311752
$393$	−0.945907	−0.0477147
$394$	−9.24666	−0.465840
$395$	−2.96216	−0.149042
$396$	0	0
$397$	33.4507	1.67884	0.839421	−	0.543482i	$-0.182894\pi$
$397$	33.4507	1.67884	0.839421	+	0.543482i	$0.182894\pi$
$398$	−5.59776	−0.280590
$399$	0.186438	0.00933358
$400$	−8.68333	−0.434166
$401$	5.74787	0.287035	0.143517	−	0.989648i	$-0.454159\pi$
$401$	5.74787	0.287035	0.143517	+	0.989648i	$0.454159\pi$
$402$	−0.368660	−0.0183871
$403$	−1.23300	−0.0614200
$404$	5.28334	0.262856
$405$	−7.65865	−0.380561
$406$	3.53528	0.175453
$407$	0	0
$408$	−0.907190	−0.0449126
$409$	15.6469	0.773688	0.386844	−	0.922145i	$-0.373565\pi$
$409$	15.6469	0.773688	0.386844	+	0.922145i	$0.373565\pi$
$410$	−0.704284	−0.0347821
$411$	1.14790	0.0566219
$412$	16.5260	0.814177
$413$	3.47060	0.170777
$414$	12.8802	0.633029
$415$	−12.4238	−0.609859
$416$	8.05259	0.394811
$417$	0.0603066	0.00295323
$418$	0	0
$419$	8.69030	0.424549	0.212275	−	0.977210i	$-0.431913\pi$
$419$	8.69030	0.424549	0.212275	+	0.977210i	$0.431913\pi$
$420$	0.373317	0.0182160
$421$	23.1013	1.12589	0.562945	−	0.826495i	$-0.309668\pi$
$421$	23.1013	1.12589	0.562945	+	0.826495i	$0.309668\pi$
$422$	−0.971386	−0.0472863
$423$	−0.0856682	−0.00416533
$424$	−0.808200	−0.0392497
$425$	21.4152	1.03879
$426$	0.124241	0.00601951
$427$	−3.14113	−0.152010
$428$	25.6631	1.24047
$429$	0	0
$430$	−0.0586576	−0.00282872
$431$	−1.71203	−0.0824656	−0.0412328	−	0.999150i	$-0.513129\pi$
$431$	−1.71203	−0.0824656	−0.0412328	+	0.999150i	$0.513129\pi$
$432$	−1.02383	−0.0492591
$433$	−11.3253	−0.544258	−0.272129	−	0.962261i	$-0.587728\pi$
$433$	−11.3253	−0.544258	−0.272129	+	0.962261i	$0.587728\pi$
$434$	−1.56121	−0.0749406
$435$	0.137311	0.00658358
$436$	−2.46883	−0.118235
$437$	5.16308	0.246984
$438$	0.0428348	0.00204673
$439$	−8.79631	−0.419825	−0.209912	−	0.977720i	$-0.567318\pi$
$439$	−8.79631	−0.419825	−0.209912	+	0.977720i	$0.567318\pi$
$440$	0	0
$441$	−8.57981	−0.408562
$442$	−4.32817	−0.205870
$443$	−1.44641	−0.0687211	−0.0343606	−	0.999410i	$-0.510939\pi$
$443$	−1.44641	−0.0687211	−0.0343606	+	0.999410i	$0.510939\pi$
$444$	−0.0945021	−0.00448487
$445$	−2.95469	−0.140066
$446$	0.743300	0.0351963
$447$	0.997274	0.0471695
$448$	−2.59253	−0.122485
$449$	34.6398	1.63475	0.817376	−	0.576104i	$-0.195428\pi$
$449$	34.6398	1.63475	0.817376	+	0.576104i	$0.195428\pi$
$450$	−7.52599	−0.354778
$451$	0	0
$452$	−6.81542	−0.320570
$453$	1.55725	0.0731658
$454$	14.6588	0.687970
$455$	3.93672	0.184556
$456$	0.127798	0.00598470
$457$	−29.7024	−1.38942	−0.694709	−	0.719290i	$-0.744467\pi$
$457$	−29.7024	−1.38942	−0.694709	+	0.719290i	$0.744467\pi$
$458$	4.85910	0.227051
$459$	2.52502	0.117858
$460$	10.3383	0.482028
$461$	12.2652	0.571249	0.285625	−	0.958342i	$-0.407799\pi$
$461$	12.2652	0.571249	0.285625	+	0.958342i	$0.407799\pi$
$462$	0	0
$463$	39.4855	1.83505	0.917524	−	0.397681i	$-0.130185\pi$
$463$	39.4855	1.83505	0.917524	+	0.397681i	$0.130185\pi$
$464$	−3.88653	−0.180428
$465$	−0.0606380	−0.00281202
$466$	−4.09245	−0.189579
$467$	−3.34689	−0.154876	−0.0774378	−	0.996997i	$-0.524674\pi$
$467$	−3.34689	−0.154876	−0.0774378	+	0.996997i	$0.524674\pi$
$468$	−7.23287	−0.334339
$469$	23.4071	1.08084
$470$	0.0144605	0.000667012 0
$471$	0.820785	0.0378198
$472$	2.37900	0.109502
$473$	0	0
$474$	−0.171000	−0.00785428
$475$	−3.01681	−0.138421
$476$	26.0596	1.19444
$477$	1.12343	0.0514382
$478$	1.82017	0.0832528
$479$	33.8256	1.54553	0.772766	−	0.634691i	$-0.218873\pi$
$479$	33.8256	1.54553	0.772766	+	0.634691i	$0.218873\pi$
$480$	0.396021	0.0180758
$481$	−0.996548	−0.0454387
$482$	−5.90725	−0.269068
$483$	1.92442	0.0875641
$484$	0	0
$485$	12.9906	0.589871
$486$	−1.33158	−0.0604017
$487$	23.9947	1.08730	0.543652	−	0.839311i	$-0.317041\pi$
$487$	23.9947	1.08730	0.543652	+	0.839311i	$0.317041\pi$
$488$	−2.15315	−0.0974687
$489$	−2.03113	−0.0918510
$490$	1.44824	0.0654248
$491$	−3.85290	−0.173879	−0.0869394	−	0.996214i	$-0.527709\pi$
$491$	−3.85290	−0.173879	−0.0869394	+	0.996214i	$0.527709\pi$
$492$	0.193330	0.00871601
$493$	9.58513	0.431692
$494$	0.609720	0.0274326
$495$	0	0
$496$	1.71633	0.0770653
$497$	−7.88836	−0.353841
$498$	−0.717201	−0.0321385
$499$	28.9221	1.29473	0.647365	−	0.762180i	$-0.275871\pi$
$499$	28.9221	1.29473	0.647365	+	0.762180i	$0.275871\pi$
$500$	−13.1216	−0.586815
$501$	−0.580933	−0.0259542
$502$	−3.08956	−0.137894
$503$	22.2269	0.991047	0.495524	−	0.868594i	$-0.334976\pi$
$503$	22.2269	0.991047	0.495524	+	0.868594i	$0.334976\pi$
$504$	−20.2423	−0.901665
$505$	2.73998	0.121928
$506$	0	0
$507$	−0.911508	−0.0404815
$508$	−2.56958	−0.114007
$509$	4.49674	0.199315	0.0996574	−	0.995022i	$-0.468225\pi$
$509$	4.49674	0.199315	0.0996574	+	0.995022i	$0.468225\pi$
$510$	−0.212856	−0.00942543
$511$	−2.71968	−0.120312
$512$	−19.9754	−0.882797
$513$	−0.355706	−0.0157048
$514$	0.905844	0.0399551
$515$	8.57050	0.377661
$516$	0.0161019	0.000708845 0
$517$	0	0
$518$	−1.26182	−0.0554412
$519$	0.662314	0.0290724
$520$	2.69851	0.118337
$521$	36.3616	1.59303	0.796515	−	0.604618i	$-0.206674\pi$
$521$	36.3616	1.59303	0.796515	+	0.604618i	$0.206674\pi$
$522$	−3.36852	−0.147436
$523$	23.0561	1.00817	0.504086	−	0.863653i	$-0.331829\pi$
$523$	23.0561	1.00817	0.504086	+	0.863653i	$0.331829\pi$
$524$	18.6255	0.813660
$525$	−1.12445	−0.0490750
$526$	−12.8024	−0.558210
$527$	−4.23288	−0.184387
$528$	0	0
$529$	30.2934	1.31711
$530$	−0.189630	−0.00823700
$531$	−3.30689	−0.143507
$532$	−3.67109	−0.159162
$533$	2.03872	0.0883066
$534$	−0.170569	−0.00738123
$535$	13.3091	0.575402
$536$	16.0449	0.693034
$537$	−0.0721611	−0.00311398
$538$	−7.21116	−0.310895
$539$	0	0
$540$	−0.712251	−0.0306504
$541$	−32.4797	−1.39641	−0.698205	−	0.715898i	$-0.746018\pi$
$541$	−32.4797	−1.39641	−0.698205	+	0.715898i	$0.746018\pi$
$542$	−10.7141	−0.460212
$543$	−0.0796689	−0.00341892
$544$	27.6445	1.18525
$545$	−1.28035	−0.0548443
$546$	0.227259	0.00972580
$547$	13.9059	0.594574	0.297287	−	0.954788i	$-0.403918\pi$
$547$	13.9059	0.594574	0.297287	+	0.954788i	$0.403918\pi$
$548$	−22.6030	−0.965550
$549$	2.99296	0.127736
$550$	0	0
$551$	−1.35028	−0.0575239
$552$	1.31914	0.0561461
$553$	10.8572	0.461694
$554$	−8.08115	−0.343335
$555$	−0.0490095	−0.00208034
$556$	−1.18748	−0.0503602
$557$	13.0713	0.553848	0.276924	−	0.960892i	$-0.410685\pi$
$557$	13.0713	0.553848	0.276924	+	0.960892i	$0.410685\pi$
$558$	1.48757	0.0629738
$559$	0.169798	0.00718170
$560$	−5.47988	−0.231567
$561$	0	0
$562$	−2.13323	−0.0899847
$563$	27.0066	1.13819	0.569097	−	0.822270i	$-0.307293\pi$
$563$	27.0066	1.13819	0.569097	+	0.822270i	$0.307293\pi$
$564$	−0.00396949	−0.000167146 0
$565$	−3.53453	−0.148699
$566$	−9.45225	−0.397308
$567$	28.0712	1.17888
$568$	−5.40725	−0.226883
$569$	−12.1123	−0.507774	−0.253887	−	0.967234i	$-0.581709\pi$
$569$	−12.1123	−0.507774	−0.253887	+	0.967234i	$0.581709\pi$
$570$	0.0299856	0.00125596
$571$	−28.6374	−1.19844	−0.599218	−	0.800586i	$-0.704522\pi$
$571$	−28.6374	−1.19844	−0.599218	+	0.800586i	$0.704522\pi$
$572$	0	0
$573$	−0.426853	−0.0178320
$574$	2.58141	0.107746
$575$	−31.1396	−1.29861
$576$	2.47024	0.102927
$577$	−13.2379	−0.551102	−0.275551	−	0.961286i	$-0.588860\pi$
$577$	−13.2379	−0.551102	−0.275551	+	0.961286i	$0.588860\pi$
$578$	−4.83703	−0.201194
$579$	0.970740	0.0403426
$580$	−2.70375	−0.112267
$581$	45.5367	1.88918
$582$	0.749920	0.0310852
$583$	0	0
$584$	−1.86426	−0.0771438
$585$	−3.75102	−0.155086
$586$	2.88365	0.119122
$587$	−31.9714	−1.31960	−0.659801	−	0.751440i	$-0.729359\pi$
$587$	−31.9714	−1.31960	−0.659801	+	0.751440i	$0.729359\pi$
$588$	−0.397551	−0.0163947
$589$	0.596296	0.0245700
$590$	0.558191	0.0229803
$591$	1.31637	0.0541480
$592$	1.38719	0.0570131
$593$	2.33051	0.0957026	0.0478513	−	0.998854i	$-0.484763\pi$
$593$	2.33051	0.0957026	0.0478513	+	0.998854i	$0.484763\pi$
$594$	0	0
$595$	13.5147	0.554050
$596$	−19.6370	−0.804362
$597$	0.796904	0.0326151
$598$	6.29355	0.257362
$599$	−5.85677	−0.239301	−0.119651	−	0.992816i	$-0.538177\pi$
$599$	−5.85677	−0.239301	−0.119651	+	0.992816i	$0.538177\pi$
$600$	−0.770778	−0.0314669
$601$	42.3803	1.72873	0.864365	−	0.502866i	$-0.167721\pi$
$601$	42.3803	1.72873	0.864365	+	0.502866i	$0.167721\pi$
$602$	0.214997	0.00876263
$603$	−22.3030	−0.908247
$604$	−30.6632	−1.24767
$605$	0	0
$606$	0.158174	0.00642538
$607$	41.8498	1.69863	0.849316	−	0.527885i	$-0.177015\pi$
$607$	41.8498	1.69863	0.849316	+	0.527885i	$0.177015\pi$
$608$	−3.89435	−0.157937
$609$	−0.503287	−0.0203942
$610$	−0.505200	−0.0204549
$611$	−0.0418593	−0.00169344
$612$	−24.8304	−1.00371
$613$	26.4219	1.06717	0.533586	−	0.845746i	$-0.320844\pi$
$613$	26.4219	1.06717	0.533586	+	0.845746i	$0.320844\pi$
$614$	−6.89464	−0.278245
$615$	0.100263	0.00404298
$616$	0	0
$617$	38.9547	1.56826	0.784128	−	0.620599i	$-0.213111\pi$
$617$	38.9547	1.56826	0.784128	+	0.620599i	$0.213111\pi$
$618$	0.494759	0.0199021
$619$	−30.2867	−1.21732	−0.608662	−	0.793430i	$-0.708293\pi$
$619$	−30.2867	−1.21732	−0.608662	+	0.793430i	$0.708293\pi$
$620$	1.19400	0.0479522
$621$	−3.67160	−0.147336
$622$	−10.0866	−0.404437
$623$	10.8298	0.433887
$624$	−0.249839	−0.0100015
$625$	14.5229	0.580915
$626$	12.4572	0.497891
$627$	0	0
$628$	−16.1618	−0.644926
$629$	−3.42115	−0.136410
$630$	−4.74951	−0.189225
$631$	24.6489	0.981257	0.490629	−	0.871369i	$-0.336767\pi$
$631$	24.6489	0.981257	0.490629	+	0.871369i	$0.336767\pi$
$632$	7.44229	0.296038
$633$	0.138288	0.00549644
$634$	−1.37752	−0.0547085
$635$	−1.33260	−0.0528827
$636$	0.0520547	0.00206410
$637$	−4.19227	−0.166104
$638$	0	0
$639$	7.51627	0.297339
$640$	−9.85475	−0.389543
$641$	21.8120	0.861520	0.430760	−	0.902466i	$-0.358245\pi$
$641$	21.8120	0.861520	0.430760	+	0.902466i	$0.358245\pi$
$642$	0.768308	0.0303227
$643$	−24.4435	−0.963958	−0.481979	−	0.876183i	$-0.660082\pi$
$643$	−24.4435	−0.963958	−0.481979	+	0.876183i	$0.660082\pi$
$644$	−37.8931	−1.49320
$645$	0.00835055	0.000328803 0
$646$	2.09317	0.0823546
$647$	18.7205	0.735980	0.367990	−	0.929830i	$-0.380046\pi$
$647$	18.7205	0.735980	0.367990	+	0.929830i	$0.380046\pi$
$648$	19.2420	0.755897
$649$	0	0
$650$	−3.67735	−0.144238
$651$	0.222256	0.00871089
$652$	39.9943	1.56630
$653$	20.1156	0.787183	0.393591	−	0.919285i	$-0.371232\pi$
$653$	20.1156	0.787183	0.393591	+	0.919285i	$0.371232\pi$
$654$	−0.0739123	−0.00289020
$655$	9.65934	0.377422
$656$	−2.83788	−0.110801
$657$	2.59139	0.101100
$658$	−0.0530018	−0.00206623
$659$	−12.2516	−0.477254	−0.238627	−	0.971111i	$-0.576697\pi$
$659$	−12.2516	−0.477254	−0.238627	+	0.971111i	$0.576697\pi$
$660$	0	0
$661$	−13.7882	−0.536298	−0.268149	−	0.963377i	$-0.586412\pi$
$661$	−13.7882	−0.536298	−0.268149	+	0.963377i	$0.586412\pi$
$662$	5.94564	0.231084
$663$	0.616163	0.0239298
$664$	31.2142	1.21134
$665$	−1.90385	−0.0738283
$666$	1.20230	0.0465882
$667$	−13.9376	−0.539667
$668$	11.4389	0.442586
$669$	−0.105817	−0.00409112
$670$	3.76466	0.145441
$671$	0	0
$672$	−1.45153	−0.0559941
$673$	38.6982	1.49171	0.745853	−	0.666111i	$-0.232042\pi$
$673$	38.6982	1.49171	0.745853	+	0.666111i	$0.232042\pi$
$674$	6.44332	0.248187
$675$	2.14534	0.0825741
$676$	17.9482	0.690315
$677$	39.2596	1.50887	0.754435	−	0.656374i	$-0.227911\pi$
$677$	39.2596	1.50887	0.754435	+	0.656374i	$0.227911\pi$
$678$	−0.204042	−0.00783617
$679$	−47.6142	−1.82726
$680$	9.26397	0.355257
$681$	−2.08684	−0.0799678
$682$	0	0
$683$	−6.42411	−0.245812	−0.122906	−	0.992418i	$-0.539221\pi$
$683$	−6.42411	−0.245812	−0.122906	+	0.992418i	$0.539221\pi$
$684$	3.49792	0.133746
$685$	−11.7221	−0.447877
$686$	7.65371	0.292220
$687$	−0.691747	−0.0263918
$688$	−0.236358	−0.00901107
$689$	0.548929	0.0209125
$690$	0.309512	0.0117829
$691$	−12.9096	−0.491103	−0.245552	−	0.969384i	$-0.578969\pi$
$691$	−12.9096	−0.491103	−0.245552	+	0.969384i	$0.578969\pi$
$692$	−13.0414	−0.495760
$693$	0	0
$694$	−13.8514	−0.525791
$695$	−0.615834	−0.0233599
$696$	−0.344989	−0.0130768
$697$	6.99891	0.265103
$698$	7.53870	0.285344
$699$	0.582606	0.0220362
$700$	22.1411	0.836856
$701$	17.0840	0.645254	0.322627	−	0.946526i	$-0.395434\pi$
$701$	17.0840	0.645254	0.322627	+	0.946526i	$0.395434\pi$
$702$	−0.433588	−0.0163647
$703$	0.481945	0.0181769
$704$	0	0
$705$	−0.00205861	−7.75317e−5 0
$706$	−14.4814	−0.545014
$707$	−10.0428	−0.377700
$708$	−0.153227	−0.00575862
$709$	28.6285	1.07517	0.537583	−	0.843211i	$-0.319337\pi$
$709$	28.6285	1.07517	0.537583	+	0.843211i	$0.319337\pi$
$710$	−1.26872	−0.0476141
$711$	−10.3450	−0.387969
$712$	7.42353	0.278208
$713$	6.15499	0.230506
$714$	0.780180	0.0291975
$715$	0	0
$716$	1.42090	0.0531015
$717$	−0.259122	−0.00967708
$718$	−7.93311	−0.296061
$719$	−48.0355	−1.79142	−0.895710	−	0.444638i	$-0.853332\pi$
$719$	−48.0355	−1.79142	−0.895710	+	0.444638i	$0.853332\pi$
$720$	5.22140	0.194590
$721$	−31.4134	−1.16990
$722$	10.9057	0.405868
$723$	0.840962	0.0312757
$724$	1.56873	0.0583015
$725$	8.14383	0.302454
$726$	0	0
$727$	−44.3450	−1.64467	−0.822333	−	0.569007i	$-0.807328\pi$
$727$	−44.3450	−1.64467	−0.822333	+	0.569007i	$0.807328\pi$
$728$	−9.89082	−0.366578
$729$	−26.6204	−0.985942
$730$	−0.437417	−0.0161895
$731$	0.582917	0.0215600
$732$	0.138681	0.00512578
$733$	17.0312	0.629063	0.314531	−	0.949247i	$-0.398153\pi$
$733$	17.0312	0.629063	0.314531	+	0.949247i	$0.398153\pi$
$734$	8.51229	0.314194
$735$	−0.206173	−0.00760480
$736$	−40.1976	−1.48170
$737$	0	0
$738$	−2.45964	−0.0905406
$739$	34.6716	1.27542	0.637708	−	0.770278i	$-0.279883\pi$
$739$	34.6716	1.27542	0.637708	+	0.770278i	$0.279883\pi$
$740$	0.965029	0.0354752
$741$	−0.0868004	−0.00318869
$742$	0.695049	0.0255161
$743$	37.0096	1.35775	0.678876	−	0.734253i	$-0.262467\pi$
$743$	37.0096	1.35775	0.678876	+	0.734253i	$0.262467\pi$
$744$	0.152350	0.00558543
$745$	−10.1839	−0.373109
$746$	−16.2975	−0.596695
$747$	−43.3888	−1.58751
$748$	0	0
$749$	−48.7817	−1.78244
$750$	−0.392837	−0.0143444
$751$	−43.8238	−1.59915	−0.799577	−	0.600564i	$-0.794943\pi$
$751$	−43.8238	−1.59915	−0.799577	+	0.600564i	$0.794943\pi$
$752$	0.0582678	0.00212481
$753$	0.439834	0.0160284
$754$	−1.64593	−0.0599412
$755$	−15.9022	−0.578739
$756$	2.61061	0.0949469
$757$	−20.8931	−0.759374	−0.379687	−	0.925115i	$-0.623968\pi$
$757$	−20.8931	−0.759374	−0.379687	+	0.925115i	$0.623968\pi$
$758$	−2.23367	−0.0811304
$759$	0	0
$760$	−1.30504	−0.0473387
$761$	−31.1900	−1.13064	−0.565319	−	0.824872i	$-0.691247\pi$
$761$	−31.1900	−1.13064	−0.565319	+	0.824872i	$0.691247\pi$
$762$	−0.0769286	−0.00278683
$763$	4.69287	0.169893
$764$	8.40500	0.304082
$765$	−12.8772	−0.465578
$766$	−12.5032	−0.451759
$767$	−1.61582	−0.0583437
$768$	−0.430366	−0.0155295
$769$	−5.81563	−0.209717	−0.104858	−	0.994487i	$-0.533439\pi$
$769$	−5.81563	−0.209717	−0.104858	+	0.994487i	$0.533439\pi$
$770$	0	0
$771$	−0.128957	−0.00464427
$772$	−19.1145	−0.687946
$773$	−10.4129	−0.374527	−0.187264	−	0.982310i	$-0.559962\pi$
$773$	−10.4129	−0.374527	−0.187264	+	0.982310i	$0.559962\pi$
$774$	−0.204856	−0.00736338
$775$	−3.59639	−0.129186
$776$	−32.6382	−1.17164
$777$	0.179634	0.00644434
$778$	11.0615	0.396574
$779$	−0.985954	−0.0353255
$780$	−0.173806	−0.00622325
$781$	0	0
$782$	21.6057	0.772619
$783$	0.960221	0.0343155
$784$	5.83562	0.208415
$785$	−8.38163	−0.299153
$786$	0.557616	0.0198895
$787$	5.40493	0.192665	0.0963325	−	0.995349i	$-0.469289\pi$
$787$	5.40493	0.192665	0.0963325	+	0.995349i	$0.469289\pi$
$788$	−25.9201	−0.923365
$789$	1.82256	0.0648849
$790$	1.74620	0.0621271
$791$	12.9551	0.460629
$792$	0	0
$793$	1.46242	0.0519321
$794$	−19.7193	−0.699812
$795$	0.0269959	0.000957447 0
$796$	−15.6915	−0.556172
$797$	−27.7866	−0.984252	−0.492126	−	0.870524i	$-0.663780\pi$
$797$	−27.7866	−0.984252	−0.492126	+	0.870524i	$0.663780\pi$
$798$	−0.109906	−0.00389063
$799$	−0.143703	−0.00508384
$800$	23.4877	0.830415
$801$	−10.3190	−0.364603
$802$	−3.38839	−0.119648
$803$	0	0
$804$	−1.03342	−0.0364460
$805$	−19.6516	−0.692629
$806$	0.726857	0.0256024
$807$	1.02659	0.0361376
$808$	−6.88408	−0.242181
$809$	18.7929	0.660722	0.330361	−	0.943855i	$-0.392830\pi$
$809$	18.7929	0.660722	0.330361	+	0.943855i	$0.392830\pi$
$810$	4.51480	0.158634
$811$	−9.60345	−0.337223	−0.168611	−	0.985683i	$-0.553928\pi$
$811$	−9.60345	−0.337223	−0.168611	+	0.985683i	$0.553928\pi$
$812$	9.91004	0.347774
$813$	1.52528	0.0534938
$814$	0	0
$815$	20.7414	0.726538
$816$	−0.857695	−0.0300253
$817$	−0.0821169	−0.00287291
$818$	−9.22388	−0.322505
$819$	13.7486	0.480414
$820$	−1.97424	−0.0689433
$821$	−27.0576	−0.944315	−0.472158	−	0.881514i	$-0.656525\pi$
$821$	−27.0576	−0.944315	−0.472158	+	0.881514i	$0.656525\pi$
$822$	−0.676693	−0.0236024
$823$	−17.8331	−0.621621	−0.310811	−	0.950472i	$-0.600601\pi$
$823$	−17.8331	−0.621621	−0.310811	+	0.950472i	$0.600601\pi$
$824$	−21.5330	−0.750138
$825$	0	0
$826$	−2.04593	−0.0711871
$827$	−7.37180	−0.256343	−0.128171	−	0.991752i	$-0.540911\pi$
$827$	−7.37180	−0.256343	−0.128171	+	0.991752i	$0.540911\pi$
$828$	36.1056	1.25476
$829$	−4.79813	−0.166646	−0.0833229	−	0.996523i	$-0.526553\pi$
$829$	−4.79813	−0.166646	−0.0833229	+	0.996523i	$0.526553\pi$
$830$	7.32386	0.254215
$831$	1.15044	0.0399084
$832$	1.20701	0.0418455
$833$	−14.3921	−0.498655
$834$	−0.0355509	−0.00123103
$835$	5.93232	0.205297
$836$	0	0
$837$	−0.424042	−0.0146570
$838$	−5.12296	−0.176970
$839$	30.4920	1.05270	0.526351	−	0.850267i	$-0.323560\pi$
$839$	30.4920	1.05270	0.526351	+	0.850267i	$0.323560\pi$
$840$	−0.486423	−0.0167832
$841$	−25.3549	−0.874308
$842$	−13.6183	−0.469318
$843$	0.303688	0.0104596
$844$	−2.72297	−0.0937285
$845$	9.30807	0.320207
$846$	0.0505017	0.00173628
$847$	0	0
$848$	−0.764106	−0.0262395
$849$	1.34563	0.0461820
$850$	−12.6243	−0.433011
$851$	4.97465	0.170529
$852$	0.348271	0.0119316
$853$	12.3159	0.421688	0.210844	−	0.977520i	$-0.432379\pi$
$853$	12.3159	0.421688	0.210844	+	0.977520i	$0.432379\pi$
$854$	1.85170	0.0633640
$855$	1.81405	0.0620392
$856$	−33.4385	−1.14290
$857$	0.180114	0.00615259	0.00307629	−	0.999995i	$-0.499021\pi$
$857$	0.180114	0.00615259	0.00307629	+	0.999995i	$0.499021\pi$
$858$	0	0
$859$	−42.7470	−1.45851	−0.729255	−	0.684242i	$-0.760133\pi$
$859$	−42.7470	−1.45851	−0.729255	+	0.684242i	$0.760133\pi$
$860$	−0.164428	−0.00560694
$861$	−0.367492	−0.0125241
$862$	1.00925	0.0343751
$863$	45.8252	1.55991	0.779953	−	0.625838i	$-0.215243\pi$
$863$	45.8252	1.55991	0.779953	+	0.625838i	$0.215243\pi$
$864$	2.76938	0.0942162
$865$	−6.76337	−0.229961
$866$	6.67629	0.226870
$867$	0.688605	0.0233863
$868$	−4.37636	−0.148543
$869$	0	0
$870$	−0.0809456	−0.00274431
$871$	−10.8977	−0.369254
$872$	3.21683	0.108936
$873$	45.3682	1.53548
$874$	−3.04365	−0.102953
$875$	24.9421	0.843198
$876$	0.120074	0.00405692
$877$	−46.4601	−1.56884	−0.784422	−	0.620227i	$-0.787040\pi$
$877$	−46.4601	−1.56884	−0.784422	+	0.620227i	$0.787040\pi$
$878$	5.18545	0.175001
$879$	−0.410519	−0.0138465
$880$	0	0
$881$	−33.7575	−1.13732	−0.568659	−	0.822573i	$-0.692538\pi$
$881$	−33.7575	−1.13732	−0.568659	+	0.822573i	$0.692538\pi$
$882$	5.05783	0.170306
$883$	19.8588	0.668302	0.334151	−	0.942520i	$-0.391551\pi$
$883$	19.8588	0.668302	0.334151	+	0.942520i	$0.391551\pi$
$884$	−12.1326	−0.408065
$885$	−0.0794646	−0.00267117
$886$	0.852665	0.0286458
$887$	−40.5872	−1.36278	−0.681392	−	0.731919i	$-0.738625\pi$
$887$	−40.5872	−1.36278	−0.681392	+	0.731919i	$0.738625\pi$
$888$	0.123134	0.00413211
$889$	4.88438	0.163817
$890$	1.74180	0.0583853
$891$	0	0
$892$	2.08361	0.0697643
$893$	0.0202438	0.000677432 0
$894$	−0.587897	−0.0196622
$895$	0.736889	0.0246315
$896$	36.1206	1.20670
$897$	−0.895956	−0.0299151
$898$	−20.4203	−0.681434
$899$	−1.60969	−0.0536862
$900$	−21.0967	−0.703224
$901$	1.88447	0.0627809
$902$	0	0
$903$	−0.0306072	−0.00101854
$904$	8.88034	0.295356
$905$	0.813556	0.0270435
$906$	−0.918002	−0.0304986
$907$	33.9454	1.12714	0.563570	−	0.826069i	$-0.309428\pi$
$907$	33.9454	1.12714	0.563570	+	0.826069i	$0.309428\pi$
$908$	41.0912	1.36366
$909$	9.56911	0.317387
$910$	−2.32071	−0.0769307
$911$	1.39605	0.0462533	0.0231267	−	0.999733i	$-0.492638\pi$
$911$	1.39605	0.0462533	0.0231267	+	0.999733i	$0.492638\pi$
$912$	0.120826	0.00400094
$913$	0	0
$914$	17.5097	0.579168
$915$	0.0719208	0.00237763
$916$	13.6209	0.450048
$917$	−35.4043	−1.16915
$918$	−1.48851	−0.0491281
$919$	8.34230	0.275187	0.137594	−	0.990489i	$-0.456063\pi$
$919$	8.34230	0.275187	0.137594	+	0.990489i	$0.456063\pi$
$920$	−13.4706	−0.444114
$921$	0.981529	0.0323425
$922$	−7.23040	−0.238121
$923$	3.67260	0.120885
$924$	0	0
$925$	−2.90672	−0.0955722
$926$	−23.2768	−0.764925
$927$	29.9316	0.983083
$928$	10.5127	0.345098
$929$	−31.2184	−1.02424	−0.512120	−	0.858914i	$-0.671140\pi$
$929$	−31.2184	−1.02424	−0.512120	+	0.858914i	$0.671140\pi$
$930$	0.0357463	0.00117217
$931$	2.02745	0.0664468
$932$	−11.4719	−0.375774
$933$	1.43594	0.0470106
$934$	1.97300	0.0645587
$935$	0	0
$936$	9.42427	0.308042
$937$	14.3831	0.469876	0.234938	−	0.972010i	$-0.424511\pi$
$937$	14.3831	0.469876	0.234938	+	0.972010i	$0.424511\pi$
$938$	−13.7986	−0.450539
$939$	−1.77343	−0.0578736
$940$	0.0405353	0.00132212
$941$	49.4949	1.61349	0.806744	−	0.590902i	$-0.201228\pi$
$941$	49.4949	1.61349	0.806744	+	0.590902i	$0.201228\pi$
$942$	−0.483856	−0.0157649
$943$	−10.1770	−0.331410
$944$	2.24921	0.0732054
$945$	1.35388	0.0440418
$946$	0	0
$947$	−7.75640	−0.252049	−0.126025	−	0.992027i	$-0.540222\pi$
$947$	−7.75640	−0.252049	−0.126025	+	0.992027i	$0.540222\pi$
$948$	−0.479344	−0.0155684
$949$	1.26621	0.0411028
$950$	1.77842	0.0576996
$951$	0.196106	0.00635917
$952$	−33.9552	−1.10049
$953$	1.79677	0.0582031	0.0291016	−	0.999576i	$-0.490735\pi$
$953$	1.79677	0.0582031	0.0291016	+	0.999576i	$0.490735\pi$
$954$	−0.662264	−0.0214416
$955$	4.35890	0.141051
$956$	5.10228	0.165019
$957$	0	0
$958$	−19.9403	−0.644242
$959$	42.9648	1.38741
$960$	0.0593598	0.00191583
$961$	−30.2891	−0.977069
$962$	0.587468	0.0189407
$963$	46.4806	1.49782
$964$	−16.5591	−0.533332
$965$	−9.91293	−0.319108
$966$	−1.13445	−0.0365004
$967$	−26.4224	−0.849687	−0.424844	−	0.905267i	$-0.639671\pi$
$967$	−26.4224	−0.849687	−0.424844	+	0.905267i	$0.639671\pi$
$968$	0	0
$969$	−0.297986	−0.00957268
$970$	−7.65798	−0.245883
$971$	−23.5226	−0.754876	−0.377438	−	0.926035i	$-0.623195\pi$
$971$	−23.5226	−0.754876	−0.377438	+	0.926035i	$0.623195\pi$
$972$	−3.73266	−0.119725
$973$	2.25721	0.0723629
$974$	−14.1450	−0.453234
$975$	0.523512	0.0167658
$976$	−2.03568	−0.0651605
$977$	−56.2143	−1.79845	−0.899227	−	0.437482i	$-0.855870\pi$
$977$	−56.2143	−1.79845	−0.899227	+	0.437482i	$0.855870\pi$
$978$	1.19736	0.0382874
$979$	0	0
$980$	4.05968	0.129682
$981$	−4.47150	−0.142764
$982$	2.27130	0.0724800
$983$	31.7818	1.01368	0.506841	−	0.862040i	$-0.330813\pi$
$983$	31.7818	1.01368	0.506841	+	0.862040i	$0.330813\pi$
$984$	−0.251905	−0.00803045
$985$	−13.4424	−0.428309
$986$	−5.65047	−0.179948
$987$	0.00754540	0.000240173 0
$988$	1.70916	0.0543755
$989$	−0.847613	−0.0269525
$990$	0	0
$991$	−42.5054	−1.35023	−0.675114	−	0.737713i	$-0.735906\pi$
$991$	−42.5054	−1.35023	−0.675114	+	0.737713i	$0.735906\pi$
$992$	−4.64252	−0.147400
$993$	−0.846429	−0.0268606
$994$	4.65022	0.147496
$995$	−8.13776	−0.257984
$996$	−2.01045	−0.0637034
$997$	35.9857	1.13968	0.569839	−	0.821757i	$-0.307006\pi$
$997$	35.9857	1.13968	0.569839	+	0.821757i	$0.307006\pi$
$998$	−17.0497	−0.539698
$999$	−0.342724	−0.0108433

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.o.1.9	yes	25
11.10	odd	2		7381.2.a.n.1.17	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7381.2.a.n.1.17	✓	25	11.10	odd	2
7381.2.a.o.1.9	yes	25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.589503 q^{2} +0.0839224 q^{3} -1.65249 q^{4} -0.856992 q^{5} -0.0494725 q^{6} +3.14113 q^{7} +2.15315 q^{8} -2.99296 q^{9} +O(q^{10})\)	\(q-0.589503 q^{2} +0.0839224 q^{3} -1.65249 q^{4} -0.856992 q^{5} -0.0494725 q^{6} +3.14113 q^{7} +2.15315 q^{8} -2.99296 q^{9} +0.505200 q^{10} -0.138681 q^{12} -1.46242 q^{13} -1.85170 q^{14} -0.0719208 q^{15} +2.03568 q^{16} -5.02048 q^{17} +1.76436 q^{18} +0.707248 q^{19} +1.41617 q^{20} +0.263611 q^{21} +7.30023 q^{23} +0.180698 q^{24} -4.26557 q^{25} +0.862102 q^{26} -0.502943 q^{27} -5.19066 q^{28} -1.90920 q^{29} +0.0423975 q^{30} +0.843122 q^{31} -5.50635 q^{32} +2.95959 q^{34} -2.69192 q^{35} +4.94582 q^{36} +0.681437 q^{37} -0.416925 q^{38} -0.122730 q^{39} -1.84523 q^{40} -1.39407 q^{41} -0.155399 q^{42} -0.116108 q^{43} +2.56494 q^{45} -4.30351 q^{46} +0.0286233 q^{47} +0.170839 q^{48} +2.86667 q^{49} +2.51457 q^{50} -0.421331 q^{51} +2.41663 q^{52} -0.375357 q^{53} +0.296487 q^{54} +6.76332 q^{56} +0.0593539 q^{57} +1.12548 q^{58} +1.10489 q^{59} +0.118848 q^{60} -1.00000 q^{61} -0.497023 q^{62} -9.40125 q^{63} -0.825350 q^{64} +1.25328 q^{65} +7.45182 q^{67} +8.29628 q^{68} +0.612653 q^{69} +1.58690 q^{70} -2.51132 q^{71} -6.44429 q^{72} -0.865830 q^{73} -0.401710 q^{74} -0.357976 q^{75} -1.16872 q^{76} +0.0723496 q^{78} +3.45646 q^{79} -1.74456 q^{80} +8.93666 q^{81} +0.821809 q^{82} +14.4970 q^{83} -0.435613 q^{84} +4.30251 q^{85} +0.0684459 q^{86} -0.160225 q^{87} +3.44775 q^{89} -1.51204 q^{90} -4.59365 q^{91} -12.0635 q^{92} +0.0707568 q^{93} -0.0168735 q^{94} -0.606106 q^{95} -0.462106 q^{96} -15.1583 q^{97} -1.68991 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 4 q^{7} + 21 q^{8} + 24 q^{9}+O(q^{10}) \) 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 4 * q^7 + 21 * q^8 + 24 * q^9	\( 25 q + 5 q^{2} - q^{3} + 25 q^{4} - q^{5} + 4 q^{7} + 21 q^{8} + 24 q^{9} - q^{12} + 4 q^{13} - q^{14} - 2 q^{15} + 21 q^{16} + 10 q^{17} + 40 q^{18} + 17 q^{19} - 6 q^{20} + 15 q^{21} - 4 q^{23} - 9 q^{24} + 40 q^{25} - 18 q^{26} + 8 q^{27} - 29 q^{28} + 35 q^{29} - 6 q^{30} - 12 q^{31} + 47 q^{32} + 45 q^{35} + 41 q^{36} - 14 q^{37} - 13 q^{38} + 20 q^{39} + 69 q^{40} + 24 q^{41} - 32 q^{42} + 24 q^{43} - 16 q^{45} + 10 q^{46} + 22 q^{47} - 54 q^{48} + 23 q^{49} + 26 q^{50} + 76 q^{51} + q^{52} - 27 q^{53} + 13 q^{54} - 9 q^{56} + 4 q^{57} + 76 q^{58} - 21 q^{59} + 28 q^{60} - 25 q^{61} + 25 q^{62} + 4 q^{63} + 5 q^{64} + 20 q^{65} + 13 q^{67} - 34 q^{68} - 7 q^{69} - 41 q^{70} - 24 q^{71} + 54 q^{72} + 39 q^{73} + 56 q^{74} + 7 q^{75} + 42 q^{76} + 30 q^{78} + 5 q^{79} + 92 q^{80} + 9 q^{81} - 9 q^{82} + 51 q^{83} + 125 q^{84} + 5 q^{85} - 10 q^{86} + 3 q^{87} + 17 q^{89} - 104 q^{90} + 8 q^{91} - 23 q^{92} - 36 q^{93} - 29 q^{94} + 81 q^{95} - 48 q^{96} - 15 q^{97} + 25 q^{98}+O(q^{100}) \) 25 * q + 5 * q^2 - q^3 + 25 * q^4 - q^5 + 4 * q^7 + 21 * q^8 + 24 * q^9 - q^12 + 4 * q^13 - q^14 - 2 * q^15 + 21 * q^16 + 10 * q^17 + 40 * q^18 + 17 * q^19 - 6 * q^20 + 15 * q^21 - 4 * q^23 - 9 * q^24 + 40 * q^25 - 18 * q^26 + 8 * q^27 - 29 * q^28 + 35 * q^29 - 6 * q^30 - 12 * q^31 + 47 * q^32 + 45 * q^35 + 41 * q^36 - 14 * q^37 - 13 * q^38 + 20 * q^39 + 69 * q^40 + 24 * q^41 - 32 * q^42 + 24 * q^43 - 16 * q^45 + 10 * q^46 + 22 * q^47 - 54 * q^48 + 23 * q^49 + 26 * q^50 + 76 * q^51 + q^52 - 27 * q^53 + 13 * q^54 - 9 * q^56 + 4 * q^57 + 76 * q^58 - 21 * q^59 + 28 * q^60 - 25 * q^61 + 25 * q^62 + 4 * q^63 + 5 * q^64 + 20 * q^65 + 13 * q^67 - 34 * q^68 - 7 * q^69 - 41 * q^70 - 24 * q^71 + 54 * q^72 + 39 * q^73 + 56 * q^74 + 7 * q^75 + 42 * q^76 + 30 * q^78 + 5 * q^79 + 92 * q^80 + 9 * q^81 - 9 * q^82 + 51 * q^83 + 125 * q^84 + 5 * q^85 - 10 * q^86 + 3 * q^87 + 17 * q^89 - 104 * q^90 + 8 * q^91 - 23 * q^92 - 36 * q^93 - 29 * q^94 + 81 * q^95 - 48 * q^96 - 15 * q^97 + 25 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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