LMFDB - Embedded newform 6025.2.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6025,2,Mod(1,6025)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6025, 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("6025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6025 = 5^{2} \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6025.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:	$48.1098672178$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 16 x^{13} + 31 x^{12} + 99 x^{11} - 184 x^{10} - 296 x^{9} + 519 x^{8} + 437 x^{7} + \cdots - 1 $ x^15 - 2x^14 - 16x^13 + 31x^12 + 99x^11 - 184x^10 - 296x^9 + 519x^8 + 437x^7 - 699x^6 - 297x^5 + 394x^4 + 89x^3 - 57x^2 - 17x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1205)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-0.324166$ of defining polynomial
Character	$\chi$	$=$	6025.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.324166 q^{2} +1.44456 q^{3} -1.89492 q^{4} +0.468276 q^{6} -1.26380 q^{7} -1.26260 q^{8} -0.913251 q^{9} +O(q^{10})$	\(q+0.324166 q^{2} +1.44456 q^{3} -1.89492 q^{4} +0.468276 q^{6} -1.26380 q^{7} -1.26260 q^{8} -0.913251 q^{9} +3.90034 q^{11} -2.73732 q^{12} +2.19950 q^{13} -0.409681 q^{14} +3.38054 q^{16} -2.31885 q^{17} -0.296045 q^{18} -4.30079 q^{19} -1.82563 q^{21} +1.26436 q^{22} +0.680609 q^{23} -1.82390 q^{24} +0.713004 q^{26} -5.65292 q^{27} +2.39480 q^{28} +1.08274 q^{29} +8.23090 q^{31} +3.62105 q^{32} +5.63426 q^{33} -0.751693 q^{34} +1.73053 q^{36} -7.53252 q^{37} -1.39417 q^{38} +3.17731 q^{39} -11.6671 q^{41} -0.591808 q^{42} -2.36061 q^{43} -7.39081 q^{44} +0.220630 q^{46} +13.4784 q^{47} +4.88339 q^{48} -5.40281 q^{49} -3.34972 q^{51} -4.16788 q^{52} +4.49036 q^{53} -1.83248 q^{54} +1.59567 q^{56} -6.21275 q^{57} +0.350989 q^{58} -0.807999 q^{59} -13.4378 q^{61} +2.66818 q^{62} +1.15417 q^{63} -5.58726 q^{64} +1.82644 q^{66} +11.2241 q^{67} +4.39403 q^{68} +0.983180 q^{69} +1.73959 q^{71} +1.15307 q^{72} -0.282467 q^{73} -2.44179 q^{74} +8.14964 q^{76} -4.92925 q^{77} +1.02998 q^{78} -0.599814 q^{79} -5.42622 q^{81} -3.78208 q^{82} +2.56262 q^{83} +3.45943 q^{84} -0.765227 q^{86} +1.56409 q^{87} -4.92456 q^{88} -3.32629 q^{89} -2.77974 q^{91} -1.28970 q^{92} +11.8900 q^{93} +4.36923 q^{94} +5.23082 q^{96} +1.37094 q^{97} -1.75140 q^{98} -3.56199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	$ 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) $ 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

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 $

$2$	0.324166	0.229220	0.114610	−	0.993411i	$-0.463438\pi$
$2$	0.324166	0.229220	0.114610	+	0.993411i	$0.463438\pi$
$3$	1.44456	0.834016	0.417008	−	0.908903i	$-0.363079\pi$
$3$	1.44456	0.834016	0.417008	+	0.908903i	$0.363079\pi$
$4$	−1.89492	−0.947458
$5$	0	0
$5$	0	0
$6$	0.468276	0.191173
$7$	−1.26380	−0.477672	−0.238836	−	0.971060i	$-0.576766\pi$
$7$	−1.26380	−0.477672	−0.238836	+	0.971060i	$0.576766\pi$
$8$	−1.26260	−0.446396
$9$	−0.913251	−0.304417
$10$	0	0
$11$	3.90034	1.17600	0.587998	−	0.808863i	$-0.299916\pi$
$11$	3.90034	1.17600	0.587998	+	0.808863i	$0.299916\pi$
$12$	−2.73732	−0.790196
$13$	2.19950	0.610033	0.305016	−	0.952347i	$-0.401338\pi$
$13$	2.19950	0.610033	0.305016	+	0.952347i	$0.401338\pi$
$14$	−0.409681	−0.109492
$15$	0	0
$16$	3.38054	0.845135
$17$	−2.31885	−0.562404	−0.281202	−	0.959649i	$-0.590733\pi$
$17$	−2.31885	−0.562404	−0.281202	+	0.959649i	$0.590733\pi$
$18$	−0.296045	−0.0697784
$19$	−4.30079	−0.986670	−0.493335	−	0.869840i	$-0.664222\pi$
$19$	−4.30079	−0.986670	−0.493335	+	0.869840i	$0.664222\pi$
$20$	0	0
$21$	−1.82563	−0.398386
$22$	1.26436	0.269561
$23$	0.680609	0.141917	0.0709584	−	0.997479i	$-0.477394\pi$
$23$	0.680609	0.141917	0.0709584	+	0.997479i	$0.477394\pi$
$24$	−1.82390	−0.372301
$25$	0	0
$26$	0.713004	0.139832
$27$	−5.65292	−1.08790
$28$	2.39480	0.452574
$29$	1.08274	0.201061	0.100530	−	0.994934i	$-0.467946\pi$
$29$	1.08274	0.201061	0.100530	+	0.994934i	$0.467946\pi$
$30$	0	0
$31$	8.23090	1.47831	0.739157	−	0.673533i	$-0.235224\pi$
$31$	8.23090	1.47831	0.739157	+	0.673533i	$0.235224\pi$
$32$	3.62105	0.640118
$33$	5.63426	0.980799
$34$	−0.751693	−0.128914
$35$	0	0
$36$	1.73053	0.288422
$37$	−7.53252	−1.23834	−0.619169	−	0.785257i	$-0.712531\pi$
$37$	−7.53252	−1.23834	−0.619169	+	0.785257i	$0.712531\pi$
$38$	−1.39417	−0.226164
$39$	3.17731	0.508777
$40$	0	0
$41$	−11.6671	−1.82210	−0.911048	−	0.412301i	$-0.864725\pi$
$41$	−11.6671	−1.82210	−0.911048	+	0.412301i	$0.864725\pi$
$42$	−0.591808	−0.0913180
$43$	−2.36061	−0.359989	−0.179994	−	0.983668i	$-0.557608\pi$
$43$	−2.36061	−0.359989	−0.179994	+	0.983668i	$0.557608\pi$
$44$	−7.39081	−1.11421
$45$	0	0
$46$	0.220630	0.0325301
$47$	13.4784	1.96602	0.983012	−	0.183542i	$-0.0587564\pi$
$47$	13.4784	1.96602	0.983012	+	0.183542i	$0.0587564\pi$
$48$	4.88339	0.704857
$49$	−5.40281	−0.771829
$50$	0	0
$51$	−3.34972	−0.469054
$52$	−4.16788	−0.577981
$53$	4.49036	0.616798	0.308399	−	0.951257i	$-0.400207\pi$
$53$	4.49036	0.616798	0.308399	+	0.951257i	$0.400207\pi$
$54$	−1.83248	−0.249369
$55$	0	0
$56$	1.59567	0.213231
$57$	−6.21275	−0.822898
$58$	0.350989	0.0460871
$59$	−0.807999	−0.105193	−0.0525963	−	0.998616i	$-0.516750\pi$
$59$	−0.807999	−0.105193	−0.0525963	+	0.998616i	$0.516750\pi$
$60$	0	0
$61$	−13.4378	−1.72054	−0.860268	−	0.509843i	$-0.829704\pi$
$61$	−13.4378	−1.72054	−0.860268	+	0.509843i	$0.829704\pi$
$62$	2.66818	0.338859
$63$	1.15417	0.145411
$64$	−5.58726	−0.698408
$65$	0	0
$66$	1.82644	0.224819
$67$	11.2241	1.37124	0.685622	−	0.727958i	$-0.259530\pi$
$67$	11.2241	1.37124	0.685622	+	0.727958i	$0.259530\pi$
$68$	4.39403	0.532855
$69$	0.983180	0.118361
$70$	0	0
$71$	1.73959	0.206452	0.103226	−	0.994658i	$-0.467084\pi$
$71$	1.73959	0.206452	0.103226	+	0.994658i	$0.467084\pi$
$72$	1.15307	0.135891
$73$	−0.282467	−0.0330602	−0.0165301	−	0.999863i	$-0.505262\pi$
$73$	−0.282467	−0.0330602	−0.0165301	+	0.999863i	$0.505262\pi$
$74$	−2.44179	−0.283852
$75$	0	0
$76$	8.14964	0.934828
$77$	−4.92925	−0.561740
$78$	1.02998	0.116622
$79$	−0.599814	−0.0674844	−0.0337422	−	0.999431i	$-0.510743\pi$
$79$	−0.599814	−0.0674844	−0.0337422	+	0.999431i	$0.510743\pi$
$80$	0	0
$81$	−5.42622	−0.602913
$82$	−3.78208	−0.417660
$83$	2.56262	0.281284	0.140642	−	0.990060i	$-0.455083\pi$
$83$	2.56262	0.281284	0.140642	+	0.990060i	$0.455083\pi$
$84$	3.45943	0.377454
$85$	0	0
$86$	−0.765227	−0.0825166
$87$	1.56409	0.167688
$88$	−4.92456	−0.524960
$89$	−3.32629	−0.352586	−0.176293	−	0.984338i	$-0.556411\pi$
$89$	−3.32629	−0.352586	−0.176293	+	0.984338i	$0.556411\pi$
$90$	0	0
$91$	−2.77974	−0.291396
$92$	−1.28970	−0.134460
$93$	11.8900	1.23294
$94$	4.36923	0.450652
$95$	0	0
$96$	5.23082	0.533869
$97$	1.37094	0.139197	0.0695987	−	0.997575i	$-0.477828\pi$
$97$	1.37094	0.139197	0.0695987	+	0.997575i	$0.477828\pi$
$98$	−1.75140	−0.176919
$99$	−3.56199	−0.357993
$100$	0	0
$101$	−9.93332	−0.988403	−0.494201	−	0.869347i	$-0.664539\pi$
$101$	−9.93332	−0.988403	−0.494201	+	0.869347i	$0.664539\pi$
$102$	−1.08586	−0.107517
$103$	−6.65151	−0.655392	−0.327696	−	0.944783i	$-0.606272\pi$
$103$	−6.65151	−0.655392	−0.327696	+	0.944783i	$0.606272\pi$
$104$	−2.77709	−0.272316
$105$	0	0
$106$	1.45562	0.141382
$107$	−4.21615	−0.407590	−0.203795	−	0.979014i	$-0.565328\pi$
$107$	−4.21615	−0.407590	−0.203795	+	0.979014i	$0.565328\pi$
$108$	10.7118	1.03074
$109$	−18.4774	−1.76982	−0.884908	−	0.465766i	$-0.845779\pi$
$109$	−18.4774	−1.76982	−0.884908	+	0.465766i	$0.845779\pi$
$110$	0	0
$111$	−10.8812	−1.03279
$112$	−4.27233	−0.403698
$113$	−13.4024	−1.26079	−0.630394	−	0.776275i	$-0.717107\pi$
$113$	−13.4024	−1.26079	−0.630394	+	0.776275i	$0.717107\pi$
$114$	−2.01396	−0.188625
$115$	0	0
$116$	−2.05171	−0.190496
$117$	−2.00870	−0.185704
$118$	−0.261926	−0.0241122
$119$	2.93057	0.268645
$120$	0	0
$121$	4.21262	0.382965
$122$	−4.35608	−0.394381
$123$	−16.8538	−1.51966
$124$	−15.5969	−1.40064
$125$	0	0
$126$	0.374142	0.0333312
$127$	13.3225	1.18218	0.591092	−	0.806604i	$-0.298697\pi$
$127$	13.3225	1.18218	0.591092	+	0.806604i	$0.298697\pi$
$128$	−9.05331	−0.800207
$129$	−3.41003	−0.300237
$130$	0	0
$131$	−1.45712	−0.127309	−0.0636545	−	0.997972i	$-0.520276\pi$
$131$	−1.45712	−0.127309	−0.0636545	+	0.997972i	$0.520276\pi$
$132$	−10.6765	−0.929266
$133$	5.43535	0.471304
$134$	3.63848	0.314316
$135$	0	0
$136$	2.92778	0.251055
$137$	−20.8783	−1.78376	−0.891878	−	0.452277i	$-0.850612\pi$
$137$	−20.8783	−1.78376	−0.891878	+	0.452277i	$0.850612\pi$
$138$	0.318713	0.0271307
$139$	3.01213	0.255486	0.127743	−	0.991807i	$-0.459227\pi$
$139$	3.01213	0.255486	0.127743	+	0.991807i	$0.459227\pi$
$140$	0	0
$141$	19.4703	1.63970
$142$	0.563916	0.0473228
$143$	8.57881	0.717396
$144$	−3.08728	−0.257274
$145$	0	0
$146$	−0.0915661	−0.00757806
$147$	−7.80467	−0.643718
$148$	14.2735	1.17327
$149$	17.9662	1.47185	0.735924	−	0.677064i	$-0.236748\pi$
$149$	17.9662	1.47185	0.735924	+	0.677064i	$0.236748\pi$
$150$	0	0
$151$	−0.472147	−0.0384228	−0.0192114	−	0.999815i	$-0.506116\pi$
$151$	−0.472147	−0.0384228	−0.0192114	+	0.999815i	$0.506116\pi$
$152$	5.43017	0.440445
$153$	2.11769	0.171205
$154$	−1.59789	−0.128762
$155$	0	0
$156$	−6.02074	−0.482045
$157$	−9.61270	−0.767177	−0.383588	−	0.923504i	$-0.625312\pi$
$157$	−9.61270	−0.767177	−0.383588	+	0.923504i	$0.625312\pi$
$158$	−0.194439	−0.0154688
$159$	6.48658	0.514420
$160$	0	0
$161$	−0.860155	−0.0677897
$162$	−1.75899	−0.138200
$163$	11.7832	0.922934	0.461467	−	0.887157i	$-0.347323\pi$
$163$	11.7832	0.922934	0.461467	+	0.887157i	$0.347323\pi$
$164$	22.1082	1.72636
$165$	0	0
$166$	0.830714	0.0644759
$167$	−4.40429	−0.340814	−0.170407	−	0.985374i	$-0.554508\pi$
$167$	−4.40429	−0.340814	−0.170407	+	0.985374i	$0.554508\pi$
$168$	2.30504	0.177838
$169$	−8.16218	−0.627860
$170$	0	0
$171$	3.92770	0.300359
$172$	4.47315	0.341074
$173$	−6.89947	−0.524557	−0.262278	−	0.964992i	$-0.584474\pi$
$173$	−6.89947	−0.524557	−0.262278	+	0.964992i	$0.584474\pi$
$174$	0.507024	0.0384374
$175$	0	0
$176$	13.1852	0.993876
$177$	−1.16720	−0.0877323
$178$	−1.07827	−0.0808198
$179$	−2.64741	−0.197877	−0.0989383	−	0.995094i	$-0.531545\pi$
$179$	−2.64741	−0.197877	−0.0989383	+	0.995094i	$0.531545\pi$
$180$	0	0
$181$	−14.0837	−1.04683	−0.523416	−	0.852077i	$-0.675343\pi$
$181$	−14.0837	−1.04683	−0.523416	+	0.852077i	$0.675343\pi$
$182$	−0.901096	−0.0667936
$183$	−19.4117	−1.43495
$184$	−0.859336	−0.0633511
$185$	0	0
$186$	3.85434	0.282614
$187$	−9.04431	−0.661385
$188$	−25.5404	−1.86273
$189$	7.14417	0.519662
$190$	0	0
$191$	−0.355103	−0.0256944	−0.0128472	−	0.999917i	$-0.504089\pi$
$191$	−0.355103	−0.0256944	−0.0128472	+	0.999917i	$0.504089\pi$
$192$	−8.07113	−0.582483
$193$	−14.4780	−1.04215	−0.521075	−	0.853511i	$-0.674469\pi$
$193$	−14.4780	−1.04215	−0.521075	+	0.853511i	$0.674469\pi$
$194$	0.444411	0.0319068
$195$	0	0
$196$	10.2379	0.731276
$197$	2.66867	0.190135	0.0950676	−	0.995471i	$-0.469693\pi$
$197$	2.66867	0.190135	0.0950676	+	0.995471i	$0.469693\pi$
$198$	−1.15467	−0.0820591
$199$	−23.6530	−1.67672	−0.838358	−	0.545119i	$-0.816484\pi$
$199$	−23.6530	−1.67672	−0.838358	+	0.545119i	$0.816484\pi$
$200$	0	0
$201$	16.2139	1.14364
$202$	−3.22004	−0.226561
$203$	−1.36837	−0.0960410
$204$	6.34744	0.444410
$205$	0	0
$206$	−2.15619	−0.150229
$207$	−0.621567	−0.0432019
$208$	7.43552	0.515560
$209$	−16.7745	−1.16032
$210$	0	0
$211$	−19.8800	−1.36860	−0.684299	−	0.729201i	$-0.739892\pi$
$211$	−19.8800	−1.36860	−0.684299	+	0.729201i	$0.739892\pi$
$212$	−8.50885	−0.584391
$213$	2.51294	0.172184
$214$	−1.36673	−0.0934277
$215$	0	0
$216$	7.13737	0.485636
$217$	−10.4022	−0.706149
$218$	−5.98975	−0.405677
$219$	−0.408040	−0.0275728
$220$	0	0
$221$	−5.10033	−0.343085
$222$	−3.52730	−0.236737
$223$	14.2590	0.954854	0.477427	−	0.878671i	$-0.341570\pi$
$223$	14.2590	0.954854	0.477427	+	0.878671i	$0.341570\pi$
$224$	−4.57629	−0.305766
$225$	0	0
$226$	−4.34458	−0.288997
$227$	6.05733	0.402039	0.201019	−	0.979587i	$-0.435575\pi$
$227$	6.05733	0.402039	0.201019	+	0.979587i	$0.435575\pi$
$228$	11.7726	0.779662
$229$	0.243801	0.0161109	0.00805543	−	0.999968i	$-0.497436\pi$
$229$	0.243801	0.0161109	0.00805543	+	0.999968i	$0.497436\pi$
$230$	0	0
$231$	−7.12059	−0.468500
$232$	−1.36707	−0.0897526
$233$	21.2278	1.39068	0.695341	−	0.718680i	$-0.255253\pi$
$233$	21.2278	1.39068	0.695341	+	0.718680i	$0.255253\pi$
$234$	−0.651152	−0.0425671
$235$	0	0
$236$	1.53109	0.0996656
$237$	−0.866467	−0.0562830
$238$	0.949990	0.0615787
$239$	−13.7298	−0.888104	−0.444052	−	0.896001i	$-0.646459\pi$
$239$	−13.7298	−0.888104	−0.444052	+	0.896001i	$0.646459\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	1.36559	0.0877833
$243$	9.12027	0.585065
$244$	25.4635	1.63014
$245$	0	0
$246$	−5.46343	−0.348336
$247$	−9.45961	−0.601901
$248$	−10.3923	−0.659913
$249$	3.70186	0.234596
$250$	0	0
$251$	−12.6809	−0.800408	−0.400204	−	0.916426i	$-0.631061\pi$
$251$	−12.6809	−0.800408	−0.400204	+	0.916426i	$0.631061\pi$
$252$	−2.18705	−0.137771
$253$	2.65460	0.166894
$254$	4.31871	0.270980
$255$	0	0
$256$	8.23975	0.514985
$257$	−17.7814	−1.10917	−0.554587	−	0.832125i	$-0.687124\pi$
$257$	−17.7814	−1.10917	−0.554587	+	0.832125i	$0.687124\pi$
$258$	−1.10542	−0.0688202
$259$	9.51961	0.591520
$260$	0	0
$261$	−0.988817	−0.0612063
$262$	−0.472348	−0.0291818
$263$	−31.1031	−1.91790	−0.958951	−	0.283572i	$-0.908481\pi$
$263$	−31.1031	−1.91790	−0.958951	+	0.283572i	$0.908481\pi$
$264$	−7.11381	−0.437825
$265$	0	0
$266$	1.76195	0.108032
$267$	−4.80503	−0.294063
$268$	−21.2688	−1.29920
$269$	−23.3489	−1.42360	−0.711802	−	0.702380i	$-0.752121\pi$
$269$	−23.3489	−1.42360	−0.711802	+	0.702380i	$0.752121\pi$
$270$	0	0
$271$	10.7876	0.655300	0.327650	−	0.944799i	$-0.393743\pi$
$271$	10.7876	0.655300	0.327650	+	0.944799i	$0.393743\pi$
$272$	−7.83898	−0.475308
$273$	−4.01549	−0.243029
$274$	−6.76804	−0.408872
$275$	0	0
$276$	−1.86304	−0.112142
$277$	−9.45988	−0.568389	−0.284195	−	0.958767i	$-0.591726\pi$
$277$	−9.45988	−0.568389	−0.284195	+	0.958767i	$0.591726\pi$
$278$	0.976430	0.0585624
$279$	−7.51688	−0.450024
$280$	0	0
$281$	−7.77804	−0.463999	−0.232000	−	0.972716i	$-0.574527\pi$
$281$	−7.77804	−0.463999	−0.232000	+	0.972716i	$0.574527\pi$
$282$	6.31161	0.375851
$283$	2.52159	0.149893	0.0749463	−	0.997188i	$-0.476121\pi$
$283$	2.52159	0.149893	0.0749463	+	0.997188i	$0.476121\pi$
$284$	−3.29638	−0.195604
$285$	0	0
$286$	2.78096	0.164441
$287$	14.7449	0.870364
$288$	−3.30693	−0.194863
$289$	−11.6229	−0.683701
$290$	0	0
$291$	1.98040	0.116093
$292$	0.535251	0.0313232
$293$	4.45173	0.260073	0.130036	−	0.991509i	$-0.458491\pi$
$293$	4.45173	0.260073	0.130036	+	0.991509i	$0.458491\pi$
$294$	−2.53001	−0.147553
$295$	0	0
$296$	9.51055	0.552789
$297$	−22.0483	−1.27937
$298$	5.82403	0.337377
$299$	1.49700	0.0865739
$300$	0	0
$301$	2.98334	0.171957
$302$	−0.153054	−0.00880726
$303$	−14.3493	−0.824344
$304$	−14.5390	−0.833869
$305$	0	0
$306$	0.686484	0.0392437
$307$	3.01622	0.172145	0.0860724	−	0.996289i	$-0.472568\pi$
$307$	3.01622	0.172145	0.0860724	+	0.996289i	$0.472568\pi$
$308$	9.34052	0.532225
$309$	−9.60849	−0.546608
$310$	0	0
$311$	−17.2546	−0.978418	−0.489209	−	0.872166i	$-0.662715\pi$
$311$	−17.2546	−0.978418	−0.489209	+	0.872166i	$0.662715\pi$
$312$	−4.01167	−0.227116
$313$	−9.60420	−0.542862	−0.271431	−	0.962458i	$-0.587497\pi$
$313$	−9.60420	−0.542862	−0.271431	+	0.962458i	$0.587497\pi$
$314$	−3.11611	−0.175852
$315$	0	0
$316$	1.13660	0.0639386
$317$	16.1598	0.907624	0.453812	−	0.891098i	$-0.350064\pi$
$317$	16.1598	0.907624	0.453812	+	0.891098i	$0.350064\pi$
$318$	2.10273	0.117915
$319$	4.22307	0.236446
$320$	0	0
$321$	−6.09047	−0.339937
$322$	−0.278833	−0.0155387
$323$	9.97291	0.554907
$324$	10.2822	0.571235
$325$	0	0
$326$	3.81972	0.211555
$327$	−26.6917	−1.47605
$328$	14.7309	0.813376
$329$	−17.0340	−0.939114
$330$	0	0
$331$	−34.3103	−1.88587	−0.942933	−	0.332982i	$-0.891945\pi$
$331$	−34.3103	−1.88587	−0.942933	+	0.332982i	$0.891945\pi$
$332$	−4.85596	−0.266505
$333$	6.87908	0.376971
$334$	−1.42772	−0.0781213
$335$	0	0
$336$	−6.17164	−0.336690
$337$	33.9582	1.84982	0.924910	−	0.380187i	$-0.124140\pi$
$337$	33.9582	1.84982	0.924910	+	0.380187i	$0.124140\pi$
$338$	−2.64590	−0.143918
$339$	−19.3605	−1.05152
$340$	0	0
$341$	32.1033	1.73849
$342$	1.27323	0.0688482
$343$	15.6747	0.846353
$344$	2.98050	0.160698
$345$	0	0
$346$	−2.23657	−0.120239
$347$	−17.8959	−0.960700	−0.480350	−	0.877077i	$-0.659490\pi$
$347$	−17.8959	−0.960700	−0.480350	+	0.877077i	$0.659490\pi$
$348$	−2.96382	−0.158877
$349$	16.1850	0.866363	0.433182	−	0.901307i	$-0.357391\pi$
$349$	16.1850	0.866363	0.433182	+	0.901307i	$0.357391\pi$
$350$	0	0
$351$	−12.4336	−0.663658
$352$	14.1233	0.752776
$353$	−9.92750	−0.528387	−0.264194	−	0.964470i	$-0.585106\pi$
$353$	−9.92750	−0.528387	−0.264194	+	0.964470i	$0.585106\pi$
$354$	−0.378367	−0.0201100
$355$	0	0
$356$	6.30305	0.334061
$357$	4.23338	0.224054
$358$	−0.858199	−0.0453572
$359$	35.2159	1.85862	0.929312	−	0.369294i	$-0.120401\pi$
$359$	35.2159	1.85862	0.929312	+	0.369294i	$0.120401\pi$
$360$	0	0
$361$	−0.503182	−0.0264833
$362$	−4.56545	−0.239955
$363$	6.08538	0.319399
$364$	5.26737	0.276085
$365$	0	0
$366$	−6.29261	−0.328920
$367$	−12.2408	−0.638966	−0.319483	−	0.947592i	$-0.603509\pi$
$367$	−12.2408	−0.638966	−0.319483	+	0.947592i	$0.603509\pi$
$368$	2.30083	0.119939
$369$	10.6550	0.554677
$370$	0	0
$371$	−5.67492	−0.294627
$372$	−22.5306	−1.16816
$373$	−17.3701	−0.899392	−0.449696	−	0.893182i	$-0.648468\pi$
$373$	−17.3701	−0.899392	−0.449696	+	0.893182i	$0.648468\pi$
$374$	−2.93185	−0.151603
$375$	0	0
$376$	−17.0178	−0.877625
$377$	2.38150	0.122654
$378$	2.31589	0.119117
$379$	−24.1009	−1.23798	−0.618990	−	0.785399i	$-0.712458\pi$
$379$	−24.1009	−1.23798	−0.618990	+	0.785399i	$0.712458\pi$
$380$	0	0
$381$	19.2452	0.985960
$382$	−0.115112	−0.00588965
$383$	34.3918	1.75734	0.878669	−	0.477431i	$-0.158432\pi$
$383$	34.3918	1.75734	0.878669	+	0.477431i	$0.158432\pi$
$384$	−13.0780	−0.667385
$385$	0	0
$386$	−4.69327	−0.238881
$387$	2.15582	0.109587
$388$	−2.59781	−0.131884
$389$	36.7883	1.86524	0.932621	−	0.360856i	$-0.117516\pi$
$389$	36.7883	1.86524	0.932621	+	0.360856i	$0.117516\pi$
$390$	0	0
$391$	−1.57823	−0.0798146
$392$	6.82158	0.344542
$393$	−2.10489	−0.106178
$394$	0.865093	0.0435827
$395$	0	0
$396$	6.74967	0.339183
$397$	11.5858	0.581473	0.290737	−	0.956803i	$-0.406100\pi$
$397$	11.5858	0.581473	0.290737	+	0.956803i	$0.406100\pi$
$398$	−7.66749	−0.384337
$399$	7.85168	0.393075
$400$	0	0
$401$	28.9369	1.44504	0.722519	−	0.691351i	$-0.242984\pi$
$401$	28.9369	1.44504	0.722519	+	0.691351i	$0.242984\pi$
$402$	5.25599	0.262145
$403$	18.1039	0.901820
$404$	18.8228	0.936470
$405$	0	0
$406$	−0.443580	−0.0220145
$407$	−29.3794	−1.45628
$408$	4.22935	0.209384
$409$	37.8631	1.87221	0.936104	−	0.351723i	$-0.114404\pi$
$409$	37.8631	1.87221	0.936104	+	0.351723i	$0.114404\pi$
$410$	0	0
$411$	−30.1600	−1.48768
$412$	12.6041	0.620957
$413$	1.02115	0.0502475
$414$	−0.201491	−0.00990273
$415$	0	0
$416$	7.96452	0.390493
$417$	4.35120	0.213079
$418$	−5.43773	−0.265968
$419$	−0.0617483	−0.00301660	−0.00150830	−	0.999999i	$-0.500480\pi$
$419$	−0.0617483	−0.00301660	−0.00150830	+	0.999999i	$0.500480\pi$
$420$	0	0
$421$	−22.0071	−1.07256	−0.536280	−	0.844040i	$-0.680171\pi$
$421$	−22.0071	−1.07256	−0.536280	+	0.844040i	$0.680171\pi$
$422$	−6.44443	−0.313710
$423$	−12.3091	−0.598491
$424$	−5.66952	−0.275336
$425$	0	0
$426$	0.814610	0.0394680
$427$	16.9827	0.821851
$428$	7.98924	0.386175
$429$	12.3926	0.598320
$430$	0	0
$431$	2.32684	0.112080	0.0560400	−	0.998429i	$-0.482153\pi$
$431$	2.32684	0.112080	0.0560400	+	0.998429i	$0.482153\pi$
$432$	−19.1099	−0.919427
$433$	−17.1194	−0.822707	−0.411354	−	0.911476i	$-0.634944\pi$
$433$	−17.1194	−0.822707	−0.411354	+	0.911476i	$0.634944\pi$
$434$	−3.37204	−0.161863
$435$	0	0
$436$	35.0132	1.67683
$437$	−2.92716	−0.140025
$438$	−0.132273	−0.00632023
$439$	−2.94132	−0.140382	−0.0701908	−	0.997534i	$-0.522361\pi$
$439$	−2.94132	−0.140382	−0.0701908	+	0.997534i	$0.522361\pi$
$440$	0	0
$441$	4.93412	0.234958
$442$	−1.65335	−0.0786419
$443$	19.7048	0.936204	0.468102	−	0.883674i	$-0.344938\pi$
$443$	19.7048	0.936204	0.468102	+	0.883674i	$0.344938\pi$
$444$	20.6189	0.978530
$445$	0	0
$446$	4.62228	0.218871
$447$	25.9532	1.22755
$448$	7.06119	0.333610
$449$	−5.65848	−0.267040	−0.133520	−	0.991046i	$-0.542628\pi$
$449$	−5.65848	−0.267040	−0.133520	+	0.991046i	$0.542628\pi$
$450$	0	0
$451$	−45.5056	−2.14278
$452$	25.3963	1.19454
$453$	−0.682044	−0.0320452
$454$	1.96358	0.0921552
$455$	0	0
$456$	7.84420	0.367339
$457$	−38.1370	−1.78397	−0.891987	−	0.452061i	$-0.850689\pi$
$457$	−38.1370	−1.78397	−0.891987	+	0.452061i	$0.850689\pi$
$458$	0.0790321	0.00369293
$459$	13.1083	0.611843
$460$	0	0
$461$	−5.89347	−0.274486	−0.137243	−	0.990537i	$-0.543824\pi$
$461$	−5.89347	−0.274486	−0.137243	+	0.990537i	$0.543824\pi$
$462$	−2.30825	−0.107390
$463$	19.1462	0.889801	0.444900	−	0.895580i	$-0.353239\pi$
$463$	19.1462	0.889801	0.444900	+	0.895580i	$0.353239\pi$
$464$	3.66026	0.169923
$465$	0	0
$466$	6.88134	0.318772
$467$	30.8489	1.42752	0.713758	−	0.700392i	$-0.246992\pi$
$467$	30.8489	1.42752	0.713758	+	0.700392i	$0.246992\pi$
$468$	3.80632	0.175947
$469$	−14.1851	−0.655005
$470$	0	0
$471$	−13.8861	−0.639838
$472$	1.02018	0.0469575
$473$	−9.20715	−0.423345
$474$	−0.280879	−0.0129012
$475$	0	0
$476$	−5.55318	−0.254530
$477$	−4.10082	−0.187764
$478$	−4.45072	−0.203571
$479$	18.1857	0.830924	0.415462	−	0.909611i	$-0.363620\pi$
$479$	18.1857	0.830924	0.415462	+	0.909611i	$0.363620\pi$
$480$	0	0
$481$	−16.5678	−0.755427
$482$	−0.324166	−0.0147653
$483$	−1.24254	−0.0565377
$484$	−7.98256	−0.362844
$485$	0	0
$486$	2.95648	0.134109
$487$	−18.7953	−0.851697	−0.425848	−	0.904795i	$-0.640024\pi$
$487$	−18.7953	−0.851697	−0.425848	+	0.904795i	$0.640024\pi$
$488$	16.9666	0.768040
$489$	17.0216	0.769742
$490$	0	0
$491$	5.03453	0.227205	0.113603	−	0.993526i	$-0.463761\pi$
$491$	5.03453	0.227205	0.113603	+	0.993526i	$0.463761\pi$
$492$	31.9366	1.43981
$493$	−2.51072	−0.113077
$494$	−3.06648	−0.137968
$495$	0	0
$496$	27.8249	1.24938
$497$	−2.19850	−0.0986162
$498$	1.20002	0.0537740
$499$	−25.6170	−1.14677	−0.573387	−	0.819285i	$-0.694371\pi$
$499$	−25.6170	−1.14677	−0.573387	+	0.819285i	$0.694371\pi$
$500$	0	0
$501$	−6.36225	−0.284244
$502$	−4.11070	−0.183469
$503$	2.33960	0.104318	0.0521588	−	0.998639i	$-0.483390\pi$
$503$	2.33960	0.104318	0.0521588	+	0.998639i	$0.483390\pi$
$504$	−1.45725	−0.0649111
$505$	0	0
$506$	0.860532	0.0382553
$507$	−11.7907	−0.523645
$508$	−25.2451	−1.12007
$509$	25.6878	1.13859	0.569296	−	0.822132i	$-0.307216\pi$
$509$	25.6878	1.13859	0.569296	+	0.822132i	$0.307216\pi$
$510$	0	0
$511$	0.356982	0.0157920
$512$	20.7777	0.918251
$513$	24.3120	1.07340
$514$	−5.76413	−0.254245
$515$	0	0
$516$	6.46173	0.284462
$517$	52.5702	2.31203
$518$	3.08593	0.135588
$519$	−9.96668	−0.437489
$520$	0	0
$521$	−7.26135	−0.318126	−0.159063	−	0.987268i	$-0.550847\pi$
$521$	−7.26135	−0.318126	−0.159063	+	0.987268i	$0.550847\pi$
$522$	−0.320541	−0.0140297
$523$	34.4891	1.50810	0.754052	−	0.656815i	$-0.228097\pi$
$523$	34.4891	1.50810	0.754052	+	0.656815i	$0.228097\pi$
$524$	2.76112	0.120620
$525$	0	0
$526$	−10.0826	−0.439621
$527$	−19.0863	−0.831410
$528$	19.0469	0.828908
$529$	−22.5368	−0.979860
$530$	0	0
$531$	0.737906	0.0320224
$532$	−10.2995	−0.446541
$533$	−25.6619	−1.11154
$534$	−1.55762	−0.0674050
$535$	0	0
$536$	−14.1716	−0.612118
$537$	−3.82434	−0.165032
$538$	−7.56890	−0.326318
$539$	−21.0728	−0.907668
$540$	0	0
$541$	14.5536	0.625710	0.312855	−	0.949801i	$-0.398715\pi$
$541$	14.5536	0.625710	0.312855	+	0.949801i	$0.398715\pi$
$542$	3.49697	0.150208
$543$	−20.3447	−0.873075
$544$	−8.39669	−0.360005
$545$	0	0
$546$	−1.30169	−0.0557070
$547$	18.0719	0.772697	0.386349	−	0.922353i	$-0.373736\pi$
$547$	18.0719	0.772697	0.386349	+	0.922353i	$0.373736\pi$
$548$	39.5627	1.69003
$549$	12.2721	0.523760
$550$	0	0
$551$	−4.65666	−0.198380
$552$	−1.24136	−0.0528358
$553$	0.758046	0.0322354
$554$	−3.06657	−0.130286
$555$	0	0
$556$	−5.70774	−0.242062
$557$	31.0778	1.31681	0.658405	−	0.752664i	$-0.271232\pi$
$557$	31.0778	1.31681	0.658405	+	0.752664i	$0.271232\pi$
$558$	−2.43671	−0.103154
$559$	−5.19216	−0.219605
$560$	0	0
$561$	−13.0650	−0.551606
$562$	−2.52137	−0.106358
$563$	4.78192	0.201534	0.100767	−	0.994910i	$-0.467870\pi$
$563$	4.78192	0.201534	0.100767	+	0.994910i	$0.467870\pi$
$564$	−36.8946	−1.55354
$565$	0	0
$566$	0.817412	0.0343584
$567$	6.85766	0.287995
$568$	−2.19641	−0.0921592
$569$	−21.7600	−0.912226	−0.456113	−	0.889922i	$-0.650759\pi$
$569$	−21.7600	−0.912226	−0.456113	+	0.889922i	$0.650759\pi$
$570$	0	0
$571$	17.3790	0.727287	0.363643	−	0.931538i	$-0.381533\pi$
$571$	17.3790	0.727287	0.363643	+	0.931538i	$0.381533\pi$
$572$	−16.2561	−0.679703
$573$	−0.512967	−0.0214295
$574$	4.77979	0.199505
$575$	0	0
$576$	5.10257	0.212607
$577$	−31.3497	−1.30511	−0.652553	−	0.757743i	$-0.726302\pi$
$577$	−31.3497	−1.30511	−0.652553	+	0.757743i	$0.726302\pi$
$578$	−3.76775	−0.156718
$579$	−20.9143	−0.869169
$580$	0	0
$581$	−3.23865	−0.134362
$582$	0.641977	0.0266108
$583$	17.5139	0.725352
$584$	0.356642	0.0147580
$585$	0	0
$586$	1.44310	0.0596138
$587$	15.1944	0.627141	0.313571	−	0.949565i	$-0.398475\pi$
$587$	15.1944	0.627141	0.313571	+	0.949565i	$0.398475\pi$
$588$	14.7892	0.609896
$589$	−35.3994	−1.45861
$590$	0	0
$591$	3.85506	0.158576
$592$	−25.4640	−1.04656
$593$	6.68937	0.274699	0.137350	−	0.990523i	$-0.456142\pi$
$593$	6.68937	0.274699	0.137350	+	0.990523i	$0.456142\pi$
$594$	−7.14730	−0.293257
$595$	0	0
$596$	−34.0445	−1.39452
$597$	−34.1681	−1.39841
$598$	0.485277	0.0198445
$599$	−5.16397	−0.210994	−0.105497	−	0.994420i	$-0.533643\pi$
$599$	−5.16397	−0.210994	−0.105497	+	0.994420i	$0.533643\pi$
$600$	0	0
$601$	6.02123	0.245611	0.122805	−	0.992431i	$-0.460811\pi$
$601$	6.02123	0.245611	0.122805	+	0.992431i	$0.460811\pi$
$602$	0.967095	0.0394159
$603$	−10.2504	−0.417430
$604$	0.894679	0.0364040
$605$	0	0
$606$	−4.65154	−0.188956
$607$	42.0451	1.70656	0.853278	−	0.521456i	$-0.174611\pi$
$607$	42.0451	1.70656	0.853278	+	0.521456i	$0.174611\pi$
$608$	−15.5734	−0.631585
$609$	−1.97670	−0.0800997
$610$	0	0
$611$	29.6458	1.19934
$612$	−4.01286	−0.162210
$613$	30.0230	1.21262	0.606309	−	0.795229i	$-0.292650\pi$
$613$	30.0230	1.21262	0.606309	+	0.795229i	$0.292650\pi$
$614$	0.977755	0.0394590
$615$	0	0
$616$	6.22366	0.250759
$617$	−8.18499	−0.329515	−0.164758	−	0.986334i	$-0.552684\pi$
$617$	−8.18499	−0.329515	−0.164758	+	0.986334i	$0.552684\pi$
$618$	−3.11474	−0.125293
$619$	−22.8038	−0.916564	−0.458282	−	0.888807i	$-0.651535\pi$
$619$	−22.8038	−0.916564	−0.458282	+	0.888807i	$0.651535\pi$
$620$	0	0
$621$	−3.84743	−0.154392
$622$	−5.59335	−0.224273
$623$	4.20377	0.168421
$624$	10.7410	0.429986
$625$	0	0
$626$	−3.11335	−0.124435
$627$	−24.2318	−0.967725
$628$	18.2153	0.726868
$629$	17.4668	0.696447
$630$	0	0
$631$	20.9460	0.833849	0.416924	−	0.908941i	$-0.363108\pi$
$631$	20.9460	0.833849	0.416924	+	0.908941i	$0.363108\pi$
$632$	0.757324	0.0301247
$633$	−28.7179	−1.14143
$634$	5.23845	0.208045
$635$	0	0
$636$	−12.2915	−0.487391
$637$	−11.8835	−0.470841
$638$	1.36897	0.0541982
$639$	−1.58868	−0.0628474
$640$	0	0
$641$	43.3451	1.71203	0.856014	−	0.516952i	$-0.172933\pi$
$641$	43.3451	1.71203	0.856014	+	0.516952i	$0.172933\pi$
$642$	−1.97432	−0.0779202
$643$	10.8302	0.427100	0.213550	−	0.976932i	$-0.431497\pi$
$643$	10.8302	0.427100	0.213550	+	0.976932i	$0.431497\pi$
$644$	1.62992	0.0642279
$645$	0	0
$646$	3.23287	0.127196
$647$	−9.52539	−0.374482	−0.187241	−	0.982314i	$-0.559954\pi$
$647$	−9.52539	−0.374482	−0.187241	+	0.982314i	$0.559954\pi$
$648$	6.85114	0.269138
$649$	−3.15147	−0.123706
$650$	0	0
$651$	−15.0266	−0.588940
$652$	−22.3283	−0.874442
$653$	−32.1906	−1.25971	−0.629857	−	0.776711i	$-0.716887\pi$
$653$	−32.1906	−1.25971	−0.629857	+	0.776711i	$0.716887\pi$
$654$	−8.65254	−0.338341
$655$	0	0
$656$	−39.4411	−1.53992
$657$	0.257963	0.0100641
$658$	−5.52184	−0.215264
$659$	30.3610	1.18270	0.591348	−	0.806416i	$-0.298596\pi$
$659$	30.3610	1.18270	0.591348	+	0.806416i	$0.298596\pi$
$660$	0	0
$661$	16.4056	0.638104	0.319052	−	0.947737i	$-0.396636\pi$
$661$	16.4056	0.638104	0.319052	+	0.947737i	$0.396636\pi$
$662$	−11.1222	−0.432278
$663$	−7.36772	−0.286139
$664$	−3.23556	−0.125564
$665$	0	0
$666$	2.22996	0.0864093
$667$	0.736926	0.0285339
$668$	8.34575	0.322907
$669$	20.5980	0.796364
$670$	0	0
$671$	−52.4120	−2.02334
$672$	−6.61072	−0.255014
$673$	−39.0660	−1.50589	−0.752943	−	0.658086i	$-0.771366\pi$
$673$	−39.0660	−1.50589	−0.752943	+	0.658086i	$0.771366\pi$
$674$	11.0081	0.424015
$675$	0	0
$676$	15.4666	0.594871
$677$	−0.603684	−0.0232014	−0.0116007	−	0.999933i	$-0.503693\pi$
$677$	−0.603684	−0.0232014	−0.0116007	+	0.999933i	$0.503693\pi$
$678$	−6.27601	−0.241029
$679$	−1.73259	−0.0664907
$680$	0	0
$681$	8.75016	0.335307
$682$	10.4068	0.398496
$683$	−16.2310	−0.621061	−0.310531	−	0.950563i	$-0.600507\pi$
$683$	−16.2310	−0.621061	−0.310531	+	0.950563i	$0.600507\pi$
$684$	−7.44267	−0.284578
$685$	0	0
$686$	5.08120	0.194001
$687$	0.352186	0.0134367
$688$	−7.98012	−0.304239
$689$	9.87657	0.376267
$690$	0	0
$691$	−19.8729	−0.756001	−0.378001	−	0.925805i	$-0.623388\pi$
$691$	−19.8729	−0.756001	−0.378001	+	0.925805i	$0.623388\pi$
$692$	13.0739	0.496996
$693$	4.50164	0.171003
$694$	−5.80122	−0.220211
$695$	0	0
$696$	−1.97481	−0.0748551
$697$	27.0543	1.02475
$698$	5.24662	0.198588
$699$	30.6649	1.15985
$700$	0	0
$701$	25.7753	0.973521	0.486761	−	0.873535i	$-0.338178\pi$
$701$	25.7753	0.973521	0.486761	+	0.873535i	$0.338178\pi$
$702$	−4.03056	−0.152124
$703$	32.3958	1.22183
$704$	−21.7922	−0.821324
$705$	0	0
$706$	−3.21815	−0.121117
$707$	12.5537	0.472132
$708$	2.21175	0.0831227
$709$	−10.4272	−0.391603	−0.195802	−	0.980644i	$-0.562731\pi$
$709$	−10.4272	−0.391603	−0.195802	+	0.980644i	$0.562731\pi$
$710$	0	0
$711$	0.547781	0.0205434
$712$	4.19977	0.157393
$713$	5.60203	0.209798
$714$	1.37232	0.0513577
$715$	0	0
$716$	5.01662	0.187480
$717$	−19.8334	−0.740693
$718$	11.4158	0.426034
$719$	−21.8781	−0.815917	−0.407958	−	0.913001i	$-0.633759\pi$
$719$	−21.8781	−0.815917	−0.407958	+	0.913001i	$0.633759\pi$
$720$	0	0
$721$	8.40618	0.313063
$722$	−0.163114	−0.00607049
$723$	−1.44456	−0.0537237
$724$	26.6874	0.991830
$725$	0	0
$726$	1.97267	0.0732127
$727$	12.5912	0.466982	0.233491	−	0.972359i	$-0.424985\pi$
$727$	12.5912	0.466982	0.233491	+	0.972359i	$0.424985\pi$
$728$	3.50969	0.130078
$729$	29.4534	1.09087
$730$	0	0
$731$	5.47390	0.202459
$732$	36.7836	1.35956
$733$	20.0593	0.740907	0.370454	−	0.928851i	$-0.379202\pi$
$733$	20.0593	0.740907	0.370454	+	0.928851i	$0.379202\pi$
$734$	−3.96806	−0.146464
$735$	0	0
$736$	2.46452	0.0908435
$737$	43.7778	1.61258
$738$	3.45398	0.127143
$739$	−6.80886	−0.250468	−0.125234	−	0.992127i	$-0.539968\pi$
$739$	−6.80886	−0.250468	−0.125234	+	0.992127i	$0.539968\pi$
$740$	0	0
$741$	−13.6650	−0.501995
$742$	−1.83961	−0.0675344
$743$	−15.9500	−0.585150	−0.292575	−	0.956243i	$-0.594512\pi$
$743$	−15.9500	−0.585150	−0.292575	+	0.956243i	$0.594512\pi$
$744$	−15.0123	−0.550378
$745$	0	0
$746$	−5.63081	−0.206158
$747$	−2.34032	−0.0856277
$748$	17.1382	0.626635
$749$	5.32837	0.194694
$750$	0	0
$751$	22.0893	0.806048	0.403024	−	0.915189i	$-0.367959\pi$
$751$	22.0893	0.806048	0.403024	+	0.915189i	$0.367959\pi$
$752$	45.5642	1.66156
$753$	−18.3182	−0.667554
$754$	0.772001	0.0281146
$755$	0	0
$756$	−13.5376	−0.492358
$757$	45.1700	1.64173	0.820867	−	0.571120i	$-0.193491\pi$
$757$	45.1700	1.64173	0.820867	+	0.571120i	$0.193491\pi$
$758$	−7.81268	−0.283769
$759$	3.83473	0.139192
$760$	0	0
$761$	42.9320	1.55628	0.778141	−	0.628089i	$-0.216163\pi$
$761$	42.9320	1.55628	0.778141	+	0.628089i	$0.216163\pi$
$762$	6.23863	0.226002
$763$	23.3518	0.845391
$764$	0.672891	0.0243443
$765$	0	0
$766$	11.1486	0.402817
$767$	−1.77720	−0.0641709
$768$	11.9028	0.429506
$769$	−0.380430	−0.0137187	−0.00685933	−	0.999976i	$-0.502183\pi$
$769$	−0.380430	−0.0137187	−0.00685933	+	0.999976i	$0.502183\pi$
$770$	0	0
$771$	−25.6863	−0.925070
$772$	27.4346	0.987393
$773$	−16.5028	−0.593566	−0.296783	−	0.954945i	$-0.595914\pi$
$773$	−16.5028	−0.593566	−0.296783	+	0.954945i	$0.595914\pi$
$774$	0.698845	0.0251195
$775$	0	0
$776$	−1.73094	−0.0621372
$777$	13.7516	0.493337
$778$	11.9255	0.427551
$779$	50.1778	1.79781
$780$	0	0
$781$	6.78499	0.242786
$782$	−0.511609	−0.0182951
$783$	−6.12067	−0.218735
$784$	−18.2644	−0.652300
$785$	0	0
$786$	−0.682334	−0.0243381
$787$	0.632286	0.0225386	0.0112693	−	0.999936i	$-0.496413\pi$
$787$	0.632286	0.0225386	0.0112693	+	0.999936i	$0.496413\pi$
$788$	−5.05692	−0.180145
$789$	−44.9303	−1.59956
$790$	0	0
$791$	16.9379	0.602243
$792$	4.49736	0.159807
$793$	−29.5565	−1.04958
$794$	3.75571	0.133285
$795$	0	0
$796$	44.8205	1.58862
$797$	−34.4409	−1.21996	−0.609979	−	0.792418i	$-0.708822\pi$
$797$	−34.4409	−1.21996	−0.609979	+	0.792418i	$0.708822\pi$
$798$	2.54524	0.0901007
$799$	−31.2544	−1.10570
$800$	0	0
$801$	3.03774	0.107333
$802$	9.38034	0.331231
$803$	−1.10172	−0.0388787
$804$	−30.7240	−1.08355
$805$	0	0
$806$	5.86867	0.206715
$807$	−33.7288	−1.18731
$808$	12.5418	0.441219
$809$	−32.9774	−1.15942	−0.579711	−	0.814822i	$-0.696835\pi$
$809$	−32.9774	−1.15942	−0.579711	+	0.814822i	$0.696835\pi$
$810$	0	0
$811$	32.2411	1.13214	0.566070	−	0.824357i	$-0.308463\pi$
$811$	32.2411	1.13214	0.566070	+	0.824357i	$0.308463\pi$
$812$	2.59295	0.0909948
$813$	15.5833	0.546531
$814$	−9.52378	−0.333808
$815$	0	0
$816$	−11.3239	−0.396415
$817$	10.1525	0.355190
$818$	12.2739	0.429147
$819$	2.53860	0.0887058
$820$	0	0
$821$	−35.8950	−1.25274	−0.626372	−	0.779524i	$-0.715461\pi$
$821$	−35.8950	−1.25274	−0.626372	+	0.779524i	$0.715461\pi$
$822$	−9.77682	−0.341006
$823$	−29.6287	−1.03279	−0.516396	−	0.856350i	$-0.672727\pi$
$823$	−29.6287	−1.03279	−0.516396	+	0.856350i	$0.672727\pi$
$824$	8.39818	0.292565
$825$	0	0
$826$	0.331022	0.0115177
$827$	51.3930	1.78711	0.893554	−	0.448955i	$-0.148204\pi$
$827$	51.3930	1.78711	0.893554	+	0.448955i	$0.148204\pi$
$828$	1.17782	0.0409320
$829$	−9.92132	−0.344582	−0.172291	−	0.985046i	$-0.555117\pi$
$829$	−9.92132	−0.344582	−0.172291	+	0.985046i	$0.555117\pi$
$830$	0	0
$831$	−13.6654	−0.474046
$832$	−12.2892	−0.426052
$833$	12.5283	0.434080
$834$	1.41051	0.0488420
$835$	0	0
$836$	31.7863	1.09935
$837$	−46.5286	−1.60826
$838$	−0.0200167	−0.000691465 0
$839$	29.5332	1.01960	0.509799	−	0.860294i	$-0.329720\pi$
$839$	29.5332	1.01960	0.509799	+	0.860294i	$0.329720\pi$
$840$	0	0
$841$	−27.8277	−0.959575
$842$	−7.13394	−0.245852
$843$	−11.2358	−0.386983
$844$	37.6710	1.29669
$845$	0	0
$846$	−3.99020	−0.137186
$847$	−5.32391	−0.182932
$848$	15.1798	0.521278
$849$	3.64258	0.125013
$850$	0	0
$851$	−5.12670	−0.175741
$852$	−4.76182	−0.163137
$853$	6.01322	0.205889	0.102944	−	0.994687i	$-0.467174\pi$
$853$	6.01322	0.205889	0.102944	+	0.994687i	$0.467174\pi$
$854$	5.50522	0.188385
$855$	0	0
$856$	5.32330	0.181947
$857$	46.3629	1.58373	0.791864	−	0.610698i	$-0.209111\pi$
$857$	46.3629	1.58373	0.791864	+	0.610698i	$0.209111\pi$
$858$	4.01725	0.137147
$859$	−14.5263	−0.495631	−0.247816	−	0.968807i	$-0.579713\pi$
$859$	−14.5263	−0.495631	−0.247816	+	0.968807i	$0.579713\pi$
$860$	0	0
$861$	21.2999	0.725898
$862$	0.754283	0.0256910
$863$	8.24781	0.280759	0.140379	−	0.990098i	$-0.455168\pi$
$863$	8.24781	0.280759	0.140379	+	0.990098i	$0.455168\pi$
$864$	−20.4695	−0.696387
$865$	0	0
$866$	−5.54953	−0.188581
$867$	−16.7900	−0.570218
$868$	19.7113	0.669047
$869$	−2.33948	−0.0793613
$870$	0	0
$871$	24.6875	0.836504
$872$	23.3296	0.790039
$873$	−1.25201	−0.0423741
$874$	−0.948884	−0.0320965
$875$	0	0
$876$	0.773202	0.0261241
$877$	−30.6215	−1.03402	−0.517008	−	0.855981i	$-0.672954\pi$
$877$	−30.6215	−1.03402	−0.517008	+	0.855981i	$0.672954\pi$
$878$	−0.953476	−0.0321782
$879$	6.43078	0.216905
$880$	0	0
$881$	−48.5924	−1.63712	−0.818559	−	0.574422i	$-0.805227\pi$
$881$	−48.5924	−1.63712	−0.818559	+	0.574422i	$0.805227\pi$
$882$	1.59947	0.0538570
$883$	−11.6564	−0.392270	−0.196135	−	0.980577i	$-0.562839\pi$
$883$	−11.6564	−0.392270	−0.196135	+	0.980577i	$0.562839\pi$
$884$	9.66470	0.325059
$885$	0	0
$886$	6.38762	0.214596
$887$	−17.2587	−0.579492	−0.289746	−	0.957104i	$-0.593571\pi$
$887$	−17.2587	−0.579492	−0.289746	+	0.957104i	$0.593571\pi$
$888$	13.7385	0.461035
$889$	−16.8370	−0.564696
$890$	0	0
$891$	−21.1641	−0.709023
$892$	−27.0196	−0.904684
$893$	−57.9677	−1.93982
$894$	8.41315	0.281378
$895$	0	0
$896$	11.4416	0.382236
$897$	2.16251	0.0722040
$898$	−1.83429	−0.0612109
$899$	8.91196	0.297231
$900$	0	0
$901$	−10.4125	−0.346890
$902$	−14.7514	−0.491167
$903$	4.30960	0.143415
$904$	16.9218	0.562811
$905$	0	0
$906$	−0.221095	−0.00734540
$907$	−52.7070	−1.75011	−0.875053	−	0.484026i	$-0.839174\pi$
$907$	−52.7070	−1.75011	−0.875053	+	0.484026i	$0.839174\pi$
$908$	−11.4781	−0.380915
$909$	9.07162	0.300887
$910$	0	0
$911$	−38.5394	−1.27687	−0.638434	−	0.769676i	$-0.720418\pi$
$911$	−38.5394	−1.27687	−0.638434	+	0.769676i	$0.720418\pi$
$912$	−21.0024	−0.695461
$913$	9.99509	0.330789
$914$	−12.3627	−0.408922
$915$	0	0
$916$	−0.461984	−0.0152644
$917$	1.84151	0.0608120
$918$	4.24926	0.140246
$919$	−0.651892	−0.0215039	−0.0107520	−	0.999942i	$-0.503423\pi$
$919$	−0.651892	−0.0215039	−0.0107520	+	0.999942i	$0.503423\pi$
$920$	0	0
$921$	4.35711	0.143572
$922$	−1.91046	−0.0629177
$923$	3.82624	0.125942
$924$	13.4929	0.443885
$925$	0	0
$926$	6.20655	0.203960
$927$	6.07450	0.199513
$928$	3.92067	0.128702
$929$	−1.74369	−0.0572086	−0.0286043	−	0.999591i	$-0.509106\pi$
$929$	−1.74369	−0.0572086	−0.0286043	+	0.999591i	$0.509106\pi$
$930$	0	0
$931$	23.2363	0.761541
$932$	−40.2250	−1.31761
$933$	−24.9253	−0.816017
$934$	10.0002	0.327215
$935$	0	0
$936$	2.53618	0.0828977
$937$	−32.3162	−1.05572	−0.527862	−	0.849330i	$-0.677006\pi$
$937$	−32.3162	−1.05572	−0.527862	+	0.849330i	$0.677006\pi$
$938$	−4.59831	−0.150140
$939$	−13.8738	−0.452755
$940$	0	0
$941$	−13.0303	−0.424777	−0.212388	−	0.977185i	$-0.568124\pi$
$941$	−13.0303	−0.424777	−0.212388	+	0.977185i	$0.568124\pi$
$942$	−4.50140	−0.146664
$943$	−7.94074	−0.258586
$944$	−2.73148	−0.0889020
$945$	0	0
$946$	−2.98464	−0.0970391
$947$	−19.2034	−0.624026	−0.312013	−	0.950078i	$-0.601003\pi$
$947$	−19.2034	−0.624026	−0.312013	+	0.950078i	$0.601003\pi$
$948$	1.64188	0.0533258
$949$	−0.621287	−0.0201678
$950$	0	0
$951$	23.3437	0.756973
$952$	−3.70013	−0.119922
$953$	−4.30128	−0.139332	−0.0696660	−	0.997570i	$-0.522193\pi$
$953$	−4.30128	−0.139332	−0.0696660	+	0.997570i	$0.522193\pi$
$954$	−1.32935	−0.0430392
$955$	0	0
$956$	26.0167	0.841442
$957$	6.10047	0.197200
$958$	5.89517	0.190464
$959$	26.3861	0.852050
$960$	0	0
$961$	36.7478	1.18541
$962$	−5.37072	−0.173159
$963$	3.85040	0.124077
$964$	1.89492	0.0610312
$965$	0	0
$966$	−0.402790	−0.0129596
$967$	56.9756	1.83221	0.916105	−	0.400938i	$-0.131316\pi$
$967$	56.9756	1.83221	0.916105	+	0.400938i	$0.131316\pi$
$968$	−5.31885	−0.170954
$969$	14.4064	0.462802
$970$	0	0
$971$	50.6181	1.62441	0.812206	−	0.583371i	$-0.198267\pi$
$971$	50.6181	1.62441	0.812206	+	0.583371i	$0.198267\pi$
$972$	−17.2821	−0.554325
$973$	−3.80674	−0.122038
$974$	−6.09279	−0.195226
$975$	0	0
$976$	−45.4271	−1.45409
$977$	−23.0672	−0.737984	−0.368992	−	0.929433i	$-0.620297\pi$
$977$	−23.0672	−0.737984	−0.368992	+	0.929433i	$0.620297\pi$
$978$	5.51781	0.176440
$979$	−12.9737	−0.414640
$980$	0	0
$981$	16.8745	0.538762
$982$	1.63202	0.0520799
$983$	−44.8502	−1.43050	−0.715249	−	0.698870i	$-0.753687\pi$
$983$	−44.8502	−1.43050	−0.715249	+	0.698870i	$0.753687\pi$
$984$	21.2796	0.678369
$985$	0	0
$986$	−0.813891	−0.0259196
$987$	−24.6066	−0.783237
$988$	17.9252	0.570276
$989$	−1.60665	−0.0510885
$990$	0	0
$991$	3.96976	0.126104	0.0630518	−	0.998010i	$-0.479917\pi$
$991$	3.96976	0.126104	0.0630518	+	0.998010i	$0.479917\pi$
$992$	29.8045	0.946295
$993$	−49.5633	−1.57284
$994$	−0.712678	−0.0226048
$995$	0	0
$996$	−7.01471	−0.222270
$997$	6.51313	0.206273	0.103136	−	0.994667i	$-0.467112\pi$
$997$	6.51313	0.206273	0.103136	+	0.994667i	$0.467112\pi$
$998$	−8.30415	−0.262863
$999$	42.5807	1.34719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.i.1.10		15
5.4	even	2		1205.2.a.c.1.6	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.c.1.6	✓	15	5.4	even	2
6025.2.a.i.1.10		15	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:	\( N \)	\(=\)	\( 6025 = 5^{2} \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6025.a (trivial)

\(f(q)\)	\(=\)	\(q+0.324166 q^{2} +1.44456 q^{3} -1.89492 q^{4} +0.468276 q^{6} -1.26380 q^{7} -1.26260 q^{8} -0.913251 q^{9} +O(q^{10})\)	\(q+0.324166 q^{2} +1.44456 q^{3} -1.89492 q^{4} +0.468276 q^{6} -1.26380 q^{7} -1.26260 q^{8} -0.913251 q^{9} +3.90034 q^{11} -2.73732 q^{12} +2.19950 q^{13} -0.409681 q^{14} +3.38054 q^{16} -2.31885 q^{17} -0.296045 q^{18} -4.30079 q^{19} -1.82563 q^{21} +1.26436 q^{22} +0.680609 q^{23} -1.82390 q^{24} +0.713004 q^{26} -5.65292 q^{27} +2.39480 q^{28} +1.08274 q^{29} +8.23090 q^{31} +3.62105 q^{32} +5.63426 q^{33} -0.751693 q^{34} +1.73053 q^{36} -7.53252 q^{37} -1.39417 q^{38} +3.17731 q^{39} -11.6671 q^{41} -0.591808 q^{42} -2.36061 q^{43} -7.39081 q^{44} +0.220630 q^{46} +13.4784 q^{47} +4.88339 q^{48} -5.40281 q^{49} -3.34972 q^{51} -4.16788 q^{52} +4.49036 q^{53} -1.83248 q^{54} +1.59567 q^{56} -6.21275 q^{57} +0.350989 q^{58} -0.807999 q^{59} -13.4378 q^{61} +2.66818 q^{62} +1.15417 q^{63} -5.58726 q^{64} +1.82644 q^{66} +11.2241 q^{67} +4.39403 q^{68} +0.983180 q^{69} +1.73959 q^{71} +1.15307 q^{72} -0.282467 q^{73} -2.44179 q^{74} +8.14964 q^{76} -4.92925 q^{77} +1.02998 q^{78} -0.599814 q^{79} -5.42622 q^{81} -3.78208 q^{82} +2.56262 q^{83} +3.45943 q^{84} -0.765227 q^{86} +1.56409 q^{87} -4.92456 q^{88} -3.32629 q^{89} -2.77974 q^{91} -1.28970 q^{92} +11.8900 q^{93} +4.36923 q^{94} +5.23082 q^{96} +1.37094 q^{97} -1.75140 q^{98} -3.56199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9	\( 15 q - 2 q^{2} + 7 q^{3} + 6 q^{4} - 5 q^{6} + 3 q^{7} - 3 q^{8} + 6 q^{9} - 10 q^{11} + 6 q^{12} + 8 q^{13} - 5 q^{14} - 16 q^{16} + q^{17} + 3 q^{18} - 30 q^{19} - 11 q^{21} + 5 q^{22} - 19 q^{23} - 14 q^{24} - 18 q^{26} + 22 q^{27} + 20 q^{28} - 12 q^{29} - 22 q^{31} + 2 q^{32} - 4 q^{33} - 29 q^{34} - 7 q^{36} + 12 q^{37} + 18 q^{38} - 17 q^{39} - 13 q^{41} + q^{42} + 25 q^{43} - 20 q^{44} - 7 q^{46} - 16 q^{47} + 22 q^{48} - 24 q^{49} - 27 q^{51} + 15 q^{52} + 4 q^{53} - 43 q^{54} - 3 q^{56} - 22 q^{57} + 20 q^{58} - 50 q^{59} - 41 q^{61} - 12 q^{62} - 6 q^{63} - 53 q^{64} + 5 q^{66} + 43 q^{67} - 5 q^{68} - 50 q^{69} - 14 q^{71} - 32 q^{72} + 10 q^{73} - 26 q^{74} - 13 q^{76} + 7 q^{77} - 3 q^{78} - 44 q^{79} + 7 q^{81} + 19 q^{82} - 7 q^{83} - 42 q^{84} + 7 q^{86} - 10 q^{87} + 28 q^{88} + 4 q^{89} - 50 q^{91} - 25 q^{92} - 22 q^{93} - 14 q^{94} + 14 q^{96} - 9 q^{97} - 2 q^{98} - 46 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 7 * q^3 + 6 * q^4 - 5 * q^6 + 3 * q^7 - 3 * q^8 + 6 * q^9 - 10 * q^11 + 6 * q^12 + 8 * q^13 - 5 * q^14 - 16 * q^16 + q^17 + 3 * q^18 - 30 * q^19 - 11 * q^21 + 5 * q^22 - 19 * q^23 - 14 * q^24 - 18 * q^26 + 22 * q^27 + 20 * q^28 - 12 * q^29 - 22 * q^31 + 2 * q^32 - 4 * q^33 - 29 * q^34 - 7 * q^36 + 12 * q^37 + 18 * q^38 - 17 * q^39 - 13 * q^41 + q^42 + 25 * q^43 - 20 * q^44 - 7 * q^46 - 16 * q^47 + 22 * q^48 - 24 * q^49 - 27 * q^51 + 15 * q^52 + 4 * q^53 - 43 * q^54 - 3 * q^56 - 22 * q^57 + 20 * q^58 - 50 * q^59 - 41 * q^61 - 12 * q^62 - 6 * q^63 - 53 * q^64 + 5 * q^66 + 43 * q^67 - 5 * q^68 - 50 * q^69 - 14 * q^71 - 32 * q^72 + 10 * q^73 - 26 * q^74 - 13 * q^76 + 7 * q^77 - 3 * q^78 - 44 * q^79 + 7 * q^81 + 19 * q^82 - 7 * q^83 - 42 * q^84 + 7 * q^86 - 10 * q^87 + 28 * q^88 + 4 * q^89 - 50 * q^91 - 25 * q^92 - 22 * q^93 - 14 * q^94 + 14 * q^96 - 9 * q^97 - 2 * q^98 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more