LMFDB - Embedded newform 6025.2.a.o.1.8

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:	$0$
Dimension:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q-1.44334 q^{2} -2.75896 q^{3} +0.0832441 q^{4} +3.98213 q^{6} +1.64702 q^{7} +2.76654 q^{8} +4.61187 q^{9} +O(q^{10})$	\(q-1.44334 q^{2} -2.75896 q^{3} +0.0832441 q^{4} +3.98213 q^{6} +1.64702 q^{7} +2.76654 q^{8} +4.61187 q^{9} -2.45824 q^{11} -0.229667 q^{12} +0.225525 q^{13} -2.37722 q^{14} -4.15956 q^{16} +5.45215 q^{17} -6.65652 q^{18} +4.16394 q^{19} -4.54407 q^{21} +3.54809 q^{22} +1.41953 q^{23} -7.63278 q^{24} -0.325510 q^{26} -4.44710 q^{27} +0.137105 q^{28} -0.147625 q^{29} +1.53138 q^{31} +0.470598 q^{32} +6.78220 q^{33} -7.86934 q^{34} +0.383911 q^{36} +11.1762 q^{37} -6.01000 q^{38} -0.622215 q^{39} -2.94197 q^{41} +6.55866 q^{42} +10.1529 q^{43} -0.204634 q^{44} -2.04888 q^{46} +7.51645 q^{47} +11.4761 q^{48} -4.28732 q^{49} -15.0423 q^{51} +0.0187736 q^{52} +14.4535 q^{53} +6.41870 q^{54} +4.55655 q^{56} -11.4882 q^{57} +0.213074 q^{58} +4.70568 q^{59} +2.54627 q^{61} -2.21031 q^{62} +7.59586 q^{63} +7.63988 q^{64} -9.78905 q^{66} -9.13811 q^{67} +0.453859 q^{68} -3.91644 q^{69} +14.9420 q^{71} +12.7589 q^{72} -5.54388 q^{73} -16.1310 q^{74} +0.346623 q^{76} -4.04878 q^{77} +0.898071 q^{78} +15.2219 q^{79} -1.56624 q^{81} +4.24627 q^{82} +8.01520 q^{83} -0.378267 q^{84} -14.6541 q^{86} +0.407293 q^{87} -6.80083 q^{88} +14.7136 q^{89} +0.371445 q^{91} +0.118168 q^{92} -4.22501 q^{93} -10.8488 q^{94} -1.29836 q^{96} -11.9794 q^{97} +6.18808 q^{98} -11.3371 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9}+O(q^{10}) $ 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9	$ 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9} + q^{11} + 14 q^{12} + 9 q^{13} - q^{14} + 43 q^{16} + 12 q^{17} + 42 q^{18} + 2 q^{21} + 5 q^{22} + 77 q^{23} - 2 q^{24} + 2 q^{26} + 38 q^{27} + 42 q^{28} + 2 q^{29} + q^{31} + 72 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 28 q^{37} + 23 q^{38} - 2 q^{39} - 2 q^{41} + 37 q^{42} + 31 q^{43} + 3 q^{44} + 14 q^{46} + 96 q^{47} + 13 q^{48} + 40 q^{49} - 10 q^{51} + 42 q^{52} + 54 q^{53} + 4 q^{54} - 15 q^{56} + 37 q^{57} + 27 q^{58} + q^{59} + 5 q^{61} + 39 q^{62} + 70 q^{63} + 65 q^{64} - 52 q^{66} + 34 q^{67} + 52 q^{68} + 21 q^{69} - 9 q^{71} + 70 q^{72} + 25 q^{73} + 22 q^{74} - 47 q^{76} + 54 q^{77} + 58 q^{78} + 13 q^{79} + 12 q^{81} - 5 q^{82} + 63 q^{83} + 95 q^{84} - 18 q^{86} + 47 q^{87} + 13 q^{88} + 19 q^{89} - 31 q^{91} + 137 q^{92} + 52 q^{93} + 120 q^{94} - 49 q^{96} + 36 q^{97} + 64 q^{98} + 16 q^{99}+O(q^{100}) $ 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9 + q^11 + 14 * q^12 + 9 * q^13 - q^14 + 43 * q^16 + 12 * q^17 + 42 * q^18 + 2 * q^21 + 5 * q^22 + 77 * q^23 - 2 * q^24 + 2 * q^26 + 38 * q^27 + 42 * q^28 + 2 * q^29 + q^31 + 72 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 28 * q^37 + 23 * q^38 - 2 * q^39 - 2 * q^41 + 37 * q^42 + 31 * q^43 + 3 * q^44 + 14 * q^46 + 96 * q^47 + 13 * q^48 + 40 * q^49 - 10 * q^51 + 42 * q^52 + 54 * q^53 + 4 * q^54 - 15 * q^56 + 37 * q^57 + 27 * q^58 + q^59 + 5 * q^61 + 39 * q^62 + 70 * q^63 + 65 * q^64 - 52 * q^66 + 34 * q^67 + 52 * q^68 + 21 * q^69 - 9 * q^71 + 70 * q^72 + 25 * q^73 + 22 * q^74 - 47 * q^76 + 54 * q^77 + 58 * q^78 + 13 * q^79 + 12 * q^81 - 5 * q^82 + 63 * q^83 + 95 * q^84 - 18 * q^86 + 47 * q^87 + 13 * q^88 + 19 * q^89 - 31 * q^91 + 137 * q^92 + 52 * q^93 + 120 * q^94 - 49 * q^96 + 36 * q^97 + 64 * q^98 + 16 * 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 $

$2$	−1.44334	−1.02060	−0.510299	−	0.859997i	$-0.670465\pi$
$2$	−1.44334	−1.02060	−0.510299	+	0.859997i	$0.670465\pi$
$3$	−2.75896	−1.59289	−0.796444	−	0.604712i	$-0.793288\pi$
$3$	−2.75896	−1.59289	−0.796444	+	0.604712i	$0.793288\pi$
$4$	0.0832441	0.0416220
$5$	0	0
$5$	0	0
$6$	3.98213	1.62570
$7$	1.64702	0.622516	0.311258	−	0.950325i	$-0.399250\pi$
$7$	1.64702	0.622516	0.311258	+	0.950325i	$0.399250\pi$
$8$	2.76654	0.978119
$9$	4.61187	1.53729
$10$	0	0
$11$	−2.45824	−0.741188	−0.370594	−	0.928795i	$-0.620846\pi$
$11$	−2.45824	−0.741188	−0.370594	+	0.928795i	$0.620846\pi$
$12$	−0.229667	−0.0662992
$13$	0.225525	0.0625494	0.0312747	−	0.999511i	$-0.490043\pi$
$13$	0.225525	0.0625494	0.0312747	+	0.999511i	$0.490043\pi$
$14$	−2.37722	−0.635339
$15$	0	0
$16$	−4.15956	−1.03989
$17$	5.45215	1.32234	0.661171	−	0.750236i	$-0.270060\pi$
$17$	5.45215	1.32234	0.661171	+	0.750236i	$0.270060\pi$
$18$	−6.65652	−1.56896
$19$	4.16394	0.955273	0.477637	−	0.878557i	$-0.341494\pi$
$19$	4.16394	0.955273	0.477637	+	0.878557i	$0.341494\pi$
$20$	0	0
$21$	−4.54407	−0.991598
$22$	3.54809	0.756456
$23$	1.41953	0.295993	0.147997	−	0.988988i	$-0.452717\pi$
$23$	1.41953	0.295993	0.147997	+	0.988988i	$0.452717\pi$
$24$	−7.63278	−1.55803
$25$	0	0
$26$	−0.325510	−0.0638378
$27$	−4.44710	−0.855845
$28$	0.137105	0.0259104
$29$	−0.147625	−0.0274134	−0.0137067	−	0.999906i	$-0.504363\pi$
$29$	−0.147625	−0.0274134	−0.0137067	+	0.999906i	$0.504363\pi$
$30$	0	0
$31$	1.53138	0.275043	0.137522	−	0.990499i	$-0.456086\pi$
$31$	1.53138	0.275043	0.137522	+	0.990499i	$0.456086\pi$
$32$	0.470598	0.0831907
$33$	6.78220	1.18063
$34$	−7.86934	−1.34958
$35$	0	0
$36$	0.383911	0.0639852
$37$	11.1762	1.83735	0.918675	−	0.395015i	$-0.129261\pi$
$37$	11.1762	1.83735	0.918675	+	0.395015i	$0.129261\pi$
$38$	−6.01000	−0.974951
$39$	−0.622215	−0.0996342
$40$	0	0
$41$	−2.94197	−0.459458	−0.229729	−	0.973255i	$-0.573784\pi$
$41$	−2.94197	−0.459458	−0.229729	+	0.973255i	$0.573784\pi$
$42$	6.55866	1.01202
$43$	10.1529	1.54830	0.774149	−	0.633003i	$-0.218178\pi$
$43$	10.1529	1.54830	0.774149	+	0.633003i	$0.218178\pi$
$44$	−0.204634	−0.0308498
$45$	0	0
$46$	−2.04888	−0.302091
$47$	7.51645	1.09639	0.548194	−	0.836352i	$-0.315316\pi$
$47$	7.51645	1.09639	0.548194	+	0.836352i	$0.315316\pi$
$48$	11.4761	1.65643
$49$	−4.28732	−0.612474
$50$	0	0
$51$	−15.0423	−2.10634
$52$	0.0187736	0.00260343
$53$	14.4535	1.98534	0.992672	−	0.120836i	$-0.0385576\pi$
$53$	14.4535	1.98534	0.992672	+	0.120836i	$0.0385576\pi$
$54$	6.41870	0.873474
$55$	0	0
$56$	4.55655	0.608895
$57$	−11.4882	−1.52164
$58$	0.213074	0.0279780
$59$	4.70568	0.612627	0.306314	−	0.951931i	$-0.400904\pi$
$59$	4.70568	0.612627	0.306314	+	0.951931i	$0.400904\pi$
$60$	0	0
$61$	2.54627	0.326017	0.163008	−	0.986625i	$-0.447880\pi$
$61$	2.54627	0.326017	0.163008	+	0.986625i	$0.447880\pi$
$62$	−2.21031	−0.280709
$63$	7.59586	0.956988
$64$	7.63988	0.954985
$65$	0	0
$66$	−9.78905	−1.20495
$67$	−9.13811	−1.11640	−0.558199	−	0.829707i	$-0.688507\pi$
$67$	−9.13811	−1.11640	−0.558199	+	0.829707i	$0.688507\pi$
$68$	0.453859	0.0550385
$69$	−3.91644	−0.471484
$70$	0	0
$71$	14.9420	1.77329	0.886647	−	0.462448i	$-0.153029\pi$
$71$	14.9420	1.77329	0.886647	+	0.462448i	$0.153029\pi$
$72$	12.7589	1.50365
$73$	−5.54388	−0.648862	−0.324431	−	0.945909i	$-0.605173\pi$
$73$	−5.54388	−0.648862	−0.324431	+	0.945909i	$0.605173\pi$
$74$	−16.1310	−1.87520
$75$	0	0
$76$	0.346623	0.0397604
$77$	−4.04878	−0.461401
$78$	0.898071	0.101687
$79$	15.2219	1.71260	0.856301	−	0.516476i	$-0.172757\pi$
$79$	15.2219	1.71260	0.856301	+	0.516476i	$0.172757\pi$
$80$	0	0
$81$	−1.56624	−0.174027
$82$	4.24627	0.468922
$83$	8.01520	0.879782	0.439891	−	0.898051i	$-0.355017\pi$
$83$	8.01520	0.879782	0.439891	+	0.898051i	$0.355017\pi$
$84$	−0.378267	−0.0412723
$85$	0	0
$86$	−14.6541	−1.58019
$87$	0.407293	0.0436664
$88$	−6.80083	−0.724971
$89$	14.7136	1.55964	0.779821	−	0.626002i	$-0.215310\pi$
$89$	14.7136	1.55964	0.779821	+	0.626002i	$0.215310\pi$
$90$	0	0
$91$	0.371445	0.0389380
$92$	0.118168	0.0123199
$93$	−4.22501	−0.438113
$94$	−10.8488	−1.11897
$95$	0	0
$96$	−1.29836	−0.132514
$97$	−11.9794	−1.21633	−0.608164	−	0.793811i	$-0.708094\pi$
$97$	−11.9794	−1.21633	−0.608164	+	0.793811i	$0.708094\pi$
$98$	6.18808	0.625090
$99$	−11.3371	−1.13942
$100$	0	0
$101$	−17.3352	−1.72492	−0.862459	−	0.506126i	$-0.831077\pi$
$101$	−17.3352	−1.72492	−0.862459	+	0.506126i	$0.831077\pi$
$102$	21.7112	2.14973
$103$	0.781262	0.0769800	0.0384900	−	0.999259i	$-0.487745\pi$
$103$	0.781262	0.0769800	0.0384900	+	0.999259i	$0.487745\pi$
$104$	0.623924	0.0611808
$105$	0	0
$106$	−20.8614	−2.02624
$107$	−9.08155	−0.877946	−0.438973	−	0.898500i	$-0.644658\pi$
$107$	−9.08155	−0.877946	−0.438973	+	0.898500i	$0.644658\pi$
$108$	−0.370195	−0.0356220
$109$	−1.64207	−0.157282	−0.0786408	−	0.996903i	$-0.525058\pi$
$109$	−1.64207	−0.157282	−0.0786408	+	0.996903i	$0.525058\pi$
$110$	0	0
$111$	−30.8346	−2.92669
$112$	−6.85088	−0.647348
$113$	14.2820	1.34354	0.671771	−	0.740759i	$-0.265534\pi$
$113$	14.2820	1.34354	0.671771	+	0.740759i	$0.265534\pi$
$114$	16.5814	1.55299
$115$	0	0
$116$	−0.0122889	−0.00114100
$117$	1.04009	0.0961566
$118$	−6.79192	−0.625247
$119$	8.97981	0.823178
$120$	0	0
$121$	−4.95704	−0.450640
$122$	−3.67515	−0.332732
$123$	8.11677	0.731865
$124$	0.127478	0.0114479
$125$	0	0
$126$	−10.9634	−0.976701
$127$	11.8480	1.05134	0.525668	−	0.850690i	$-0.323815\pi$
$127$	11.8480	1.05134	0.525668	+	0.850690i	$0.323815\pi$
$128$	−11.9682	−1.05785
$129$	−28.0114	−2.46627
$130$	0	0
$131$	−7.67360	−0.670445	−0.335223	−	0.942139i	$-0.608812\pi$
$131$	−7.67360	−0.670445	−0.335223	+	0.942139i	$0.608812\pi$
$132$	0.564578	0.0491402
$133$	6.85810	0.594673
$134$	13.1894	1.13939
$135$	0	0
$136$	15.0836	1.29341
$137$	−7.37050	−0.629705	−0.314852	−	0.949141i	$-0.601955\pi$
$137$	−7.37050	−0.629705	−0.314852	+	0.949141i	$0.601955\pi$
$138$	5.65278	0.481196
$139$	−5.61434	−0.476202	−0.238101	−	0.971240i	$-0.576525\pi$
$139$	−5.61434	−0.476202	−0.238101	+	0.971240i	$0.576525\pi$
$140$	0	0
$141$	−20.7376	−1.74642
$142$	−21.5665	−1.80982
$143$	−0.554395	−0.0463609
$144$	−19.1834	−1.59861
$145$	0	0
$146$	8.00173	0.662228
$147$	11.8286	0.975603
$148$	0.930349	0.0764742
$149$	−0.264724	−0.0216870	−0.0108435	−	0.999941i	$-0.503452\pi$
$149$	−0.264724	−0.0216870	−0.0108435	+	0.999941i	$0.503452\pi$
$150$	0	0
$151$	−1.15925	−0.0943386	−0.0471693	−	0.998887i	$-0.515020\pi$
$151$	−1.15925	−0.0943386	−0.0471693	+	0.998887i	$0.515020\pi$
$152$	11.5197	0.934371
$153$	25.1446	2.03282
$154$	5.84378	0.470906
$155$	0	0
$156$	−0.0517957	−0.00414698
$157$	6.80215	0.542870	0.271435	−	0.962457i	$-0.412502\pi$
$157$	6.80215	0.542870	0.271435	+	0.962457i	$0.412502\pi$
$158$	−21.9705	−1.74788
$159$	−39.8767	−3.16243
$160$	0	0
$161$	2.33800	0.184261
$162$	2.26062	0.177611
$163$	−0.874753	−0.0685160	−0.0342580	−	0.999413i	$-0.510907\pi$
$163$	−0.874753	−0.0685160	−0.0342580	+	0.999413i	$0.510907\pi$
$164$	−0.244901	−0.0191236
$165$	0	0
$166$	−11.5687	−0.897905
$167$	−7.64858	−0.591865	−0.295932	−	0.955209i	$-0.595630\pi$
$167$	−7.64858	−0.591865	−0.295932	+	0.955209i	$0.595630\pi$
$168$	−12.5714	−0.969901
$169$	−12.9491	−0.996088
$170$	0	0
$171$	19.2036	1.46853
$172$	0.845166	0.0644433
$173$	−15.1779	−1.15396	−0.576978	−	0.816760i	$-0.695768\pi$
$173$	−15.1779	−1.15396	−0.576978	+	0.816760i	$0.695768\pi$
$174$	−0.587864	−0.0445659
$175$	0	0
$176$	10.2252	0.770754
$177$	−12.9828	−0.975846
$178$	−21.2369	−1.59177
$179$	3.91906	0.292924	0.146462	−	0.989216i	$-0.453211\pi$
$179$	3.91906	0.292924	0.146462	+	0.989216i	$0.453211\pi$
$180$	0	0
$181$	−21.0049	−1.56128	−0.780640	−	0.624981i	$-0.785107\pi$
$181$	−21.0049	−1.56128	−0.780640	+	0.624981i	$0.785107\pi$
$182$	−0.536123	−0.0397401
$183$	−7.02507	−0.519308
$184$	3.92720	0.289517
$185$	0	0
$186$	6.09815	0.447138
$187$	−13.4027	−0.980104
$188$	0.625700	0.0456339
$189$	−7.32447	−0.532777
$190$	0	0
$191$	−5.93234	−0.429249	−0.214624	−	0.976697i	$-0.568853\pi$
$191$	−5.93234	−0.429249	−0.214624	+	0.976697i	$0.568853\pi$
$192$	−21.0781	−1.52118
$193$	6.26083	0.450664	0.225332	−	0.974282i	$-0.427653\pi$
$193$	6.26083	0.450664	0.225332	+	0.974282i	$0.427653\pi$
$194$	17.2905	1.24138
$195$	0	0
$196$	−0.356894	−0.0254924
$197$	3.71334	0.264565	0.132282	−	0.991212i	$-0.457769\pi$
$197$	3.71334	0.264565	0.132282	+	0.991212i	$0.457769\pi$
$198$	16.3634	1.16289
$199$	17.2066	1.21974	0.609871	−	0.792501i	$-0.291221\pi$
$199$	17.2066	1.21974	0.609871	+	0.792501i	$0.291221\pi$
$200$	0	0
$201$	25.2117	1.77830
$202$	25.0207	1.76045
$203$	−0.243142	−0.0170652
$204$	−1.25218	−0.0876702
$205$	0	0
$206$	−1.12763	−0.0785657
$207$	6.54672	0.455028
$208$	−0.938085	−0.0650445
$209$	−10.2360	−0.708037
$210$	0	0
$211$	4.22632	0.290952	0.145476	−	0.989362i	$-0.453529\pi$
$211$	4.22632	0.290952	0.145476	+	0.989362i	$0.453529\pi$
$212$	1.20317	0.0826341
$213$	−41.2245	−2.82466
$214$	13.1078	0.896031
$215$	0	0
$216$	−12.3031	−0.837118
$217$	2.52221	0.171219
$218$	2.37007	0.160521
$219$	15.2953	1.03356
$220$	0	0
$221$	1.22960	0.0827116
$222$	44.5050	2.98698
$223$	−0.761791	−0.0510133	−0.0255066	−	0.999675i	$-0.508120\pi$
$223$	−0.761791	−0.0510133	−0.0255066	+	0.999675i	$0.508120\pi$
$224$	0.775085	0.0517875
$225$	0	0
$226$	−20.6139	−1.37122
$227$	−6.91558	−0.459003	−0.229502	−	0.973308i	$-0.573710\pi$
$227$	−6.91558	−0.459003	−0.229502	+	0.973308i	$0.573710\pi$
$228$	−0.956321	−0.0633339
$229$	1.84311	0.121796	0.0608980	−	0.998144i	$-0.480604\pi$
$229$	1.84311	0.121796	0.0608980	+	0.998144i	$0.480604\pi$
$230$	0	0
$231$	11.1704	0.734960
$232$	−0.408412	−0.0268135
$233$	24.9350	1.63355	0.816775	−	0.576957i	$-0.195760\pi$
$233$	24.9350	1.63355	0.816775	+	0.576957i	$0.195760\pi$
$234$	−1.50121	−0.0981373
$235$	0	0
$236$	0.391720	0.0254988
$237$	−41.9968	−2.72798
$238$	−12.9610	−0.840135
$239$	−6.11414	−0.395491	−0.197746	−	0.980253i	$-0.563362\pi$
$239$	−6.11414	−0.395491	−0.197746	+	0.980253i	$0.563362\pi$
$240$	0	0
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	7.15472	0.459923
$243$	17.6625	1.13305
$244$	0.211962	0.0135695
$245$	0	0
$246$	−11.7153	−0.746940
$247$	0.939073	0.0597518
$248$	4.23662	0.269025
$249$	−22.1136	−1.40139
$250$	0	0
$251$	5.17822	0.326846	0.163423	−	0.986556i	$-0.447746\pi$
$251$	5.17822	0.326846	0.163423	+	0.986556i	$0.447746\pi$
$252$	0.632310	0.0398318
$253$	−3.48956	−0.219387
$254$	−17.1007	−1.07299
$255$	0	0
$256$	1.99444	0.124653
$257$	28.1570	1.75639	0.878193	−	0.478306i	$-0.158749\pi$
$257$	28.1570	1.75639	0.878193	+	0.478306i	$0.158749\pi$
$258$	40.4301	2.51707
$259$	18.4074	1.14378
$260$	0	0
$261$	−0.680830	−0.0421423
$262$	11.0756	0.684256
$263$	−11.3044	−0.697060	−0.348530	−	0.937298i	$-0.613319\pi$
$263$	−11.3044	−0.697060	−0.348530	+	0.937298i	$0.613319\pi$
$264$	18.7632	1.15480
$265$	0	0
$266$	−9.89860	−0.606922
$267$	−40.5944	−2.48434
$268$	−0.760694	−0.0464668
$269$	−17.7202	−1.08042	−0.540210	−	0.841530i	$-0.681655\pi$
$269$	−17.7202	−1.08042	−0.540210	+	0.841530i	$0.681655\pi$
$270$	0	0
$271$	6.44509	0.391511	0.195756	−	0.980653i	$-0.437284\pi$
$271$	6.44509	0.391511	0.195756	+	0.980653i	$0.437284\pi$
$272$	−22.6785	−1.37509
$273$	−1.02480	−0.0620238
$274$	10.6382	0.642676
$275$	0	0
$276$	−0.326021	−0.0196241
$277$	−23.9729	−1.44039	−0.720195	−	0.693772i	$-0.755948\pi$
$277$	−23.9729	−1.44039	−0.720195	+	0.693772i	$0.755948\pi$
$278$	8.10342	0.486011
$279$	7.06252	0.422822
$280$	0	0
$281$	−29.3389	−1.75021	−0.875105	−	0.483933i	$-0.839208\pi$
$281$	−29.3389	−1.75021	−0.875105	+	0.483933i	$0.839208\pi$
$282$	29.9315	1.78240
$283$	−15.6157	−0.928255	−0.464127	−	0.885768i	$-0.653632\pi$
$283$	−15.6157	−0.928255	−0.464127	+	0.885768i	$0.653632\pi$
$284$	1.24384	0.0738081
$285$	0	0
$286$	0.800184	0.0473158
$287$	−4.84548	−0.286020
$288$	2.17034	0.127888
$289$	12.7260	0.748586
$290$	0	0
$291$	33.0508	1.93747
$292$	−0.461495	−0.0270069
$293$	6.05757	0.353887	0.176944	−	0.984221i	$-0.443379\pi$
$293$	6.05757	0.353887	0.176944	+	0.984221i	$0.443379\pi$
$294$	−17.0727	−0.995699
$295$	0	0
$296$	30.9193	1.79715
$297$	10.9321	0.634342
$298$	0.382087	0.0221337
$299$	0.320141	0.0185142
$300$	0	0
$301$	16.7220	0.963840
$302$	1.67320	0.0962819
$303$	47.8272	2.74760
$304$	−17.3202	−0.993379
$305$	0	0
$306$	−36.2924	−2.07470
$307$	−15.6112	−0.890976	−0.445488	−	0.895288i	$-0.646970\pi$
$307$	−15.6112	−0.890976	−0.445488	+	0.895288i	$0.646970\pi$
$308$	−0.337037	−0.0192045
$309$	−2.15547	−0.122621
$310$	0	0
$311$	−2.77861	−0.157561	−0.0787803	−	0.996892i	$-0.525103\pi$
$311$	−2.77861	−0.157561	−0.0787803	+	0.996892i	$0.525103\pi$
$312$	−1.72138	−0.0974541
$313$	−11.2889	−0.638086	−0.319043	−	0.947740i	$-0.603361\pi$
$313$	−11.2889	−0.638086	−0.319043	+	0.947740i	$0.603361\pi$
$314$	−9.81784	−0.554053
$315$	0	0
$316$	1.26714	0.0712820
$317$	−28.8984	−1.62310	−0.811548	−	0.584286i	$-0.801375\pi$
$317$	−28.8984	−1.62310	−0.811548	+	0.584286i	$0.801375\pi$
$318$	57.5559	3.22757
$319$	0.362899	0.0203185
$320$	0	0
$321$	25.0557	1.39847
$322$	−3.37455	−0.188056
$323$	22.7024	1.26320
$324$	−0.130380	−0.00724335
$325$	0	0
$326$	1.26257	0.0699273
$327$	4.53040	0.250532
$328$	−8.13906	−0.449405
$329$	12.3798	0.682518
$330$	0	0
$331$	10.6833	0.587206	0.293603	−	0.955927i	$-0.405146\pi$
$331$	10.6833	0.587206	0.293603	+	0.955927i	$0.405146\pi$
$332$	0.667218	0.0366183
$333$	51.5430	2.82454
$334$	11.0395	0.604057
$335$	0	0
$336$	18.9013	1.03115
$337$	−14.7605	−0.804054	−0.402027	−	0.915628i	$-0.631694\pi$
$337$	−14.7605	−0.804054	−0.402027	+	0.915628i	$0.631694\pi$
$338$	18.6901	1.01661
$339$	−39.4036	−2.14011
$340$	0	0
$341$	−3.76450	−0.203859
$342$	−27.7174	−1.49878
$343$	−18.5905	−1.00379
$344$	28.0883	1.51442
$345$	0	0
$346$	21.9070	1.17773
$347$	8.25614	0.443213	0.221606	−	0.975136i	$-0.428870\pi$
$347$	8.25614	0.443213	0.221606	+	0.975136i	$0.428870\pi$
$348$	0.0339047	0.00181748
$349$	−0.275027	−0.0147219	−0.00736093	−	0.999973i	$-0.502343\pi$
$349$	−0.275027	−0.0147219	−0.00736093	+	0.999973i	$0.502343\pi$
$350$	0	0
$351$	−1.00293	−0.0535326
$352$	−1.15684	−0.0616600
$353$	−0.217232	−0.0115621	−0.00578105	−	0.999983i	$-0.501840\pi$
$353$	−0.217232	−0.0115621	−0.00578105	+	0.999983i	$0.501840\pi$
$354$	18.7386	0.995948
$355$	0	0
$356$	1.22482	0.0649155
$357$	−24.7750	−1.31123
$358$	−5.65656	−0.298958
$359$	−29.2946	−1.54611	−0.773055	−	0.634339i	$-0.781273\pi$
$359$	−29.2946	−1.54611	−0.773055	+	0.634339i	$0.781273\pi$
$360$	0	0
$361$	−1.66161	−0.0874531
$362$	30.3173	1.59344
$363$	13.6763	0.717819
$364$	0.0309206	0.00162068
$365$	0	0
$366$	10.1396	0.530005
$367$	29.2016	1.52431	0.762157	−	0.647392i	$-0.224140\pi$
$367$	29.2016	1.52431	0.762157	+	0.647392i	$0.224140\pi$
$368$	−5.90464	−0.307801
$369$	−13.5680	−0.706321
$370$	0	0
$371$	23.8053	1.23591
$372$	−0.351707	−0.0182352
$373$	−33.0815	−1.71289	−0.856447	−	0.516235i	$-0.827333\pi$
$373$	−33.0815	−1.71289	−0.856447	+	0.516235i	$0.827333\pi$
$374$	19.3447	1.00029
$375$	0	0
$376$	20.7946	1.07240
$377$	−0.0332932	−0.00171469
$378$	10.5717	0.543751
$379$	24.1530	1.24066	0.620328	−	0.784343i	$-0.287000\pi$
$379$	24.1530	1.24066	0.620328	+	0.784343i	$0.287000\pi$
$380$	0	0
$381$	−32.6881	−1.67466
$382$	8.56241	0.438091
$383$	37.9978	1.94159	0.970797	−	0.239901i	$-0.0771150\pi$
$383$	37.9978	1.94159	0.970797	+	0.239901i	$0.0771150\pi$
$384$	33.0198	1.68503
$385$	0	0
$386$	−9.03653	−0.459947
$387$	46.8238	2.38019
$388$	−0.997218	−0.0506261
$389$	30.7749	1.56035	0.780176	−	0.625561i	$-0.215130\pi$
$389$	30.7749	1.56035	0.780176	+	0.625561i	$0.215130\pi$
$390$	0	0
$391$	7.73952	0.391404
$392$	−11.8610	−0.599073
$393$	21.1712	1.06794
$394$	−5.35963	−0.270014
$395$	0	0
$396$	−0.943747	−0.0474251
$397$	33.3421	1.67339	0.836696	−	0.547667i	$-0.184484\pi$
$397$	33.3421	1.67339	0.836696	+	0.547667i	$0.184484\pi$
$398$	−24.8350	−1.24487
$399$	−18.9212	−0.947247
$400$	0	0
$401$	25.3102	1.26393	0.631965	−	0.774997i	$-0.282249\pi$
$401$	25.3102	1.26393	0.631965	+	0.774997i	$0.282249\pi$
$402$	−36.3892	−1.81493
$403$	0.345364	0.0172038
$404$	−1.44305	−0.0717946
$405$	0	0
$406$	0.350938	0.0174168
$407$	−27.4737	−1.36182
$408$	−41.6151	−2.06025
$409$	28.5752	1.41295	0.706477	−	0.707736i	$-0.250284\pi$
$409$	28.5752	1.41295	0.706477	+	0.707736i	$0.250284\pi$
$410$	0	0
$411$	20.3349	1.00305
$412$	0.0650354	0.00320407
$413$	7.75035	0.381370
$414$	−9.44917	−0.464401
$415$	0	0
$416$	0.106132	0.00520353
$417$	15.4897	0.758536
$418$	14.7740	0.722622
$419$	40.7895	1.99270	0.996349	−	0.0853741i	$-0.0272085\pi$
$419$	40.7895	1.99270	0.996349	+	0.0853741i	$0.0272085\pi$
$420$	0	0
$421$	3.35946	0.163730	0.0818650	−	0.996643i	$-0.473912\pi$
$421$	3.35946	0.163730	0.0818650	+	0.996643i	$0.473912\pi$
$422$	−6.10004	−0.296945
$423$	34.6649	1.68547
$424$	39.9863	1.94190
$425$	0	0
$426$	59.5012	2.88284
$427$	4.19376	0.202950
$428$	−0.755985	−0.0365419
$429$	1.52956	0.0738476
$430$	0	0
$431$	4.87111	0.234633	0.117317	−	0.993095i	$-0.462571\pi$
$431$	4.87111	0.234633	0.117317	+	0.993095i	$0.462571\pi$
$432$	18.4980	0.889984
$433$	−12.6736	−0.609054	−0.304527	−	0.952504i	$-0.598498\pi$
$433$	−12.6736	−0.609054	−0.304527	+	0.952504i	$0.598498\pi$
$434$	−3.64042	−0.174746
$435$	0	0
$436$	−0.136692	−0.00654638
$437$	5.91086	0.282755
$438$	−22.0765	−1.05485
$439$	9.86326	0.470748	0.235374	−	0.971905i	$-0.424369\pi$
$439$	9.86326	0.470748	0.235374	+	0.971905i	$0.424369\pi$
$440$	0	0
$441$	−19.7726	−0.941551
$442$	−1.77473	−0.0844154
$443$	22.4789	1.06801	0.534003	−	0.845483i	$-0.320687\pi$
$443$	22.4789	1.06801	0.534003	+	0.845483i	$0.320687\pi$
$444$	−2.56680	−0.121815
$445$	0	0
$446$	1.09953	0.0520641
$447$	0.730362	0.0345450
$448$	12.5831	0.594493
$449$	29.9519	1.41352	0.706760	−	0.707454i	$-0.250156\pi$
$449$	29.9519	1.41352	0.706760	+	0.707454i	$0.250156\pi$
$450$	0	0
$451$	7.23207	0.340545
$452$	1.18890	0.0559210
$453$	3.19833	0.150271
$454$	9.98157	0.468458
$455$	0	0
$456$	−31.7824	−1.48835
$457$	−12.3781	−0.579022	−0.289511	−	0.957175i	$-0.593493\pi$
$457$	−12.3781	−0.579022	−0.289511	+	0.957175i	$0.593493\pi$
$458$	−2.66024	−0.124305
$459$	−24.2463	−1.13172
$460$	0	0
$461$	−25.7753	−1.20048	−0.600238	−	0.799821i	$-0.704928\pi$
$461$	−25.7753	−1.20048	−0.600238	+	0.799821i	$0.704928\pi$
$462$	−16.1228	−0.750100
$463$	3.05091	0.141788	0.0708938	−	0.997484i	$-0.477415\pi$
$463$	3.05091	0.141788	0.0708938	+	0.997484i	$0.477415\pi$
$464$	0.614057	0.0285069
$465$	0	0
$466$	−35.9899	−1.66720
$467$	10.8914	0.503994	0.251997	−	0.967728i	$-0.418913\pi$
$467$	10.8914	0.503994	0.251997	+	0.967728i	$0.418913\pi$
$468$	0.0865816	0.00400224
$469$	−15.0507	−0.694975
$470$	0	0
$471$	−18.7669	−0.864732
$472$	13.0184	0.599223
$473$	−24.9582	−1.14758
$474$	60.6158	2.78418
$475$	0	0
$476$	0.747516	0.0342624
$477$	66.6579	3.05205
$478$	8.82482	0.403638
$479$	−24.7057	−1.12883	−0.564416	−	0.825490i	$-0.690899\pi$
$479$	−24.7057	−1.12883	−0.564416	+	0.825490i	$0.690899\pi$
$480$	0	0
$481$	2.52050	0.114925
$482$	1.44334	0.0657426
$483$	−6.45047	−0.293506
$484$	−0.412644	−0.0187566
$485$	0	0
$486$	−25.4931	−1.15639
$487$	14.6482	0.663775	0.331887	−	0.943319i	$-0.392315\pi$
$487$	14.6482	0.663775	0.331887	+	0.943319i	$0.392315\pi$
$488$	7.04436	0.318883
$489$	2.41341	0.109138
$490$	0	0
$491$	30.4629	1.37477	0.687386	−	0.726292i	$-0.258758\pi$
$491$	30.4629	1.37477	0.687386	+	0.726292i	$0.258758\pi$
$492$	0.675673	0.0304617
$493$	−0.804877	−0.0362498
$494$	−1.35541	−0.0609826
$495$	0	0
$496$	−6.36985	−0.286015
$497$	24.6099	1.10390
$498$	31.9176	1.43026
$499$	15.7174	0.703608	0.351804	−	0.936074i	$-0.385568\pi$
$499$	15.7174	0.703608	0.351804	+	0.936074i	$0.385568\pi$
$500$	0	0
$501$	21.1021	0.942774
$502$	−7.47396	−0.333579
$503$	23.5099	1.04825	0.524126	−	0.851641i	$-0.324392\pi$
$503$	23.5099	1.04825	0.524126	+	0.851641i	$0.324392\pi$
$504$	21.0142	0.936049
$505$	0	0
$506$	5.03664	0.223906
$507$	35.7262	1.58666
$508$	0.986273	0.0437588
$509$	−14.2914	−0.633454	−0.316727	−	0.948517i	$-0.602584\pi$
$509$	−14.2914	−0.633454	−0.316727	+	0.948517i	$0.602584\pi$
$510$	0	0
$511$	−9.13089	−0.403927
$512$	21.0577	0.930627
$513$	−18.5175	−0.817566
$514$	−40.6403	−1.79257
$515$	0	0
$516$	−2.33178	−0.102651
$517$	−18.4773	−0.812629
$518$	−26.5682	−1.16734
$519$	41.8753	1.83812
$520$	0	0
$521$	19.7643	0.865888	0.432944	−	0.901421i	$-0.357475\pi$
$521$	19.7643	0.865888	0.432944	+	0.901421i	$0.357475\pi$
$522$	0.982672	0.0430104
$523$	−11.6148	−0.507882	−0.253941	−	0.967220i	$-0.581727\pi$
$523$	−11.6148	−0.507882	−0.253941	+	0.967220i	$0.581727\pi$
$524$	−0.638781	−0.0279053
$525$	0	0
$526$	16.3162	0.711418
$527$	8.34930	0.363701
$528$	−28.2110	−1.22772
$529$	−20.9849	−0.912388
$530$	0	0
$531$	21.7020	0.941786
$532$	0.570896	0.0247515
$533$	−0.663487	−0.0287388
$534$	58.5917	2.53551
$535$	0	0
$536$	−25.2810	−1.09197
$537$	−10.8125	−0.466596
$538$	25.5764	1.10268
$539$	10.5393	0.453959
$540$	0	0
$541$	−13.3419	−0.573613	−0.286807	−	0.957989i	$-0.592594\pi$
$541$	−13.3419	−0.573613	−0.286807	+	0.957989i	$0.592594\pi$
$542$	−9.30248	−0.399576
$543$	57.9517	2.48694
$544$	2.56577	0.110007
$545$	0	0
$546$	1.47914	0.0633014
$547$	−13.4875	−0.576685	−0.288343	−	0.957527i	$-0.593104\pi$
$547$	−13.4875	−0.576685	−0.288343	+	0.957527i	$0.593104\pi$
$548$	−0.613551	−0.0262096
$549$	11.7431	0.501182
$550$	0	0
$551$	−0.614704	−0.0261872
$552$	−10.8350	−0.461168
$553$	25.0709	1.06612
$554$	34.6011	1.47006
$555$	0	0
$556$	−0.467360	−0.0198205
$557$	−6.61321	−0.280211	−0.140105	−	0.990137i	$-0.544744\pi$
$557$	−6.61321	−0.280211	−0.140105	+	0.990137i	$0.544744\pi$
$558$	−10.1936	−0.431532
$559$	2.28973	0.0968451
$560$	0	0
$561$	36.9776	1.56119
$562$	42.3461	1.78626
$563$	−6.33895	−0.267155	−0.133577	−	0.991038i	$-0.542646\pi$
$563$	−6.33895	−0.267155	−0.133577	+	0.991038i	$0.542646\pi$
$564$	−1.72628	−0.0726896
$565$	0	0
$566$	22.5388	0.947376
$567$	−2.57963	−0.108334
$568$	41.3377	1.73449
$569$	−17.3303	−0.726525	−0.363263	−	0.931687i	$-0.618337\pi$
$569$	−17.3303	−0.726525	−0.363263	+	0.931687i	$0.618337\pi$
$570$	0	0
$571$	−26.3909	−1.10442	−0.552211	−	0.833704i	$-0.686216\pi$
$571$	−26.3909	−1.10442	−0.552211	+	0.833704i	$0.686216\pi$
$572$	−0.0461501	−0.00192963
$573$	16.3671	0.683745
$574$	6.99370	0.291911
$575$	0	0
$576$	35.2342	1.46809
$577$	36.1007	1.50289	0.751446	−	0.659795i	$-0.229357\pi$
$577$	36.1007	1.50289	0.751446	+	0.659795i	$0.229357\pi$
$578$	−18.3680	−0.764006
$579$	−17.2734	−0.717858
$580$	0	0
$581$	13.2012	0.547678
$582$	−47.7037	−1.97738
$583$	−35.5303	−1.47151
$584$	−15.3374	−0.634664
$585$	0	0
$586$	−8.74317	−0.361177
$587$	8.80044	0.363233	0.181617	−	0.983369i	$-0.441867\pi$
$587$	8.80044	0.363233	0.181617	+	0.983369i	$0.441867\pi$
$588$	0.984657	0.0406066
$589$	6.37656	0.262742
$590$	0	0
$591$	−10.2450	−0.421422
$592$	−46.4879	−1.91064
$593$	−8.41291	−0.345477	−0.172738	−	0.984968i	$-0.555261\pi$
$593$	−8.41291	−0.345477	−0.172738	+	0.984968i	$0.555261\pi$
$594$	−15.7787	−0.647409
$595$	0	0
$596$	−0.0220367	−0.000902657 0
$597$	−47.4723	−1.94291
$598$	−0.462073	−0.0188956
$599$	−36.9523	−1.50983	−0.754915	−	0.655822i	$-0.772322\pi$
$599$	−36.9523	−1.50983	−0.754915	+	0.655822i	$0.772322\pi$
$600$	0	0
$601$	2.16858	0.0884583	0.0442291	−	0.999021i	$-0.485917\pi$
$601$	2.16858	0.0884583	0.0442291	+	0.999021i	$0.485917\pi$
$602$	−24.1356	−0.983694
$603$	−42.1438	−1.71623
$604$	−0.0965009	−0.00392657
$605$	0	0
$606$	−69.0312	−2.80420
$607$	−37.1254	−1.50687	−0.753437	−	0.657520i	$-0.771605\pi$
$607$	−37.1254	−1.50687	−0.753437	+	0.657520i	$0.771605\pi$
$608$	1.95954	0.0794699
$609$	0.670821	0.0271830
$610$	0	0
$611$	1.69515	0.0685783
$612$	2.09314	0.0846103
$613$	−6.76953	−0.273419	−0.136709	−	0.990611i	$-0.543653\pi$
$613$	−6.76953	−0.273419	−0.136709	+	0.990611i	$0.543653\pi$
$614$	22.5323	0.909329
$615$	0	0
$616$	−11.2011	−0.451306
$617$	23.6341	0.951473	0.475737	−	0.879588i	$-0.342182\pi$
$617$	23.6341	0.951473	0.475737	+	0.879588i	$0.342182\pi$
$618$	3.11109	0.125146
$619$	16.7010	0.671270	0.335635	−	0.941992i	$-0.391049\pi$
$619$	16.7010	0.671270	0.335635	+	0.941992i	$0.391049\pi$
$620$	0	0
$621$	−6.31281	−0.253324
$622$	4.01049	0.160806
$623$	24.2337	0.970902
$624$	2.58814	0.103609
$625$	0	0
$626$	16.2938	0.651229
$627$	28.2407	1.12782
$628$	0.566238	0.0225954
$629$	60.9341	2.42960
$630$	0	0
$631$	−32.0618	−1.27636	−0.638181	−	0.769887i	$-0.720313\pi$
$631$	−32.0618	−1.27636	−0.638181	+	0.769887i	$0.720313\pi$
$632$	42.1121	1.67513
$633$	−11.6603	−0.463454
$634$	41.7104	1.65653
$635$	0	0
$636$	−3.31950	−0.131627
$637$	−0.966898	−0.0383099
$638$	−0.523789	−0.0207370
$639$	68.9108	2.72607
$640$	0	0
$641$	39.4981	1.56008	0.780041	−	0.625728i	$-0.215198\pi$
$641$	39.4981	1.56008	0.780041	+	0.625728i	$0.215198\pi$
$642$	−36.1639	−1.42728
$643$	−18.3883	−0.725164	−0.362582	−	0.931952i	$-0.618105\pi$
$643$	−18.3883	−0.725164	−0.362582	+	0.931952i	$0.618105\pi$
$644$	0.194625	0.00766930
$645$	0	0
$646$	−32.7674	−1.28922
$647$	−30.4542	−1.19728	−0.598639	−	0.801019i	$-0.704291\pi$
$647$	−30.4542	−1.19728	−0.598639	+	0.801019i	$0.704291\pi$
$648$	−4.33307	−0.170219
$649$	−11.5677	−0.454072
$650$	0	0
$651$	−6.95869	−0.272732
$652$	−0.0728180	−0.00285177
$653$	−4.69509	−0.183733	−0.0918665	−	0.995771i	$-0.529283\pi$
$653$	−4.69509	−0.183733	−0.0918665	+	0.995771i	$0.529283\pi$
$654$	−6.53893	−0.255693
$655$	0	0
$656$	12.2373	0.477785
$657$	−25.5677	−0.997490
$658$	−17.8683	−0.696577
$659$	−11.5156	−0.448585	−0.224292	−	0.974522i	$-0.572007\pi$
$659$	−11.5156	−0.448585	−0.224292	+	0.974522i	$0.572007\pi$
$660$	0	0
$661$	−20.7745	−0.808036	−0.404018	−	0.914751i	$-0.632387\pi$
$661$	−20.7745	−0.808036	−0.404018	+	0.914751i	$0.632387\pi$
$662$	−15.4196	−0.599301
$663$	−3.39241	−0.131750
$664$	22.1744	0.860532
$665$	0	0
$666$	−74.3944	−2.88272
$667$	−0.209559	−0.00811418
$668$	−0.636699	−0.0246346
$669$	2.10175	0.0812584
$670$	0	0
$671$	−6.25935	−0.241640
$672$	−2.13843	−0.0824917
$673$	−2.21790	−0.0854937	−0.0427468	−	0.999086i	$-0.513611\pi$
$673$	−2.21790	−0.0854937	−0.0427468	+	0.999086i	$0.513611\pi$
$674$	21.3045	0.820617
$675$	0	0
$676$	−1.07794	−0.0414592
$677$	−6.92193	−0.266032	−0.133016	−	0.991114i	$-0.542466\pi$
$677$	−6.92193	−0.266032	−0.133016	+	0.991114i	$0.542466\pi$
$678$	56.8730	2.18420
$679$	−19.7304	−0.757183
$680$	0	0
$681$	19.0798	0.731141
$682$	5.43347	0.208058
$683$	−17.5298	−0.670757	−0.335379	−	0.942083i	$-0.608864\pi$
$683$	−17.5298	−0.670757	−0.335379	+	0.942083i	$0.608864\pi$
$684$	1.59858	0.0611234
$685$	0	0
$686$	26.8324	1.02447
$687$	−5.08507	−0.194007
$688$	−42.2315	−1.61006
$689$	3.25963	0.124182
$690$	0	0
$691$	−15.5684	−0.592248	−0.296124	−	0.955149i	$-0.595694\pi$
$691$	−15.5684	−0.592248	−0.296124	+	0.955149i	$0.595694\pi$
$692$	−1.26347	−0.0480300
$693$	−18.6725	−0.709308
$694$	−11.9165	−0.452343
$695$	0	0
$696$	1.12679	0.0427110
$697$	−16.0400	−0.607560
$698$	0.396959	0.0150251
$699$	−68.7949	−2.60206
$700$	0	0
$701$	−30.5535	−1.15399	−0.576994	−	0.816748i	$-0.695775\pi$
$701$	−30.5535	−1.15399	−0.576994	+	0.816748i	$0.695775\pi$
$702$	1.44758	0.0546353
$703$	46.5368	1.75517
$704$	−18.7807	−0.707824
$705$	0	0
$706$	0.313541	0.0118003
$707$	−28.5515	−1.07379
$708$	−1.08074	−0.0406167
$709$	17.8130	0.668983	0.334492	−	0.942399i	$-0.391435\pi$
$709$	17.8130	0.668983	0.334492	+	0.942399i	$0.391435\pi$
$710$	0	0
$711$	70.2017	2.63277
$712$	40.7059	1.52552
$713$	2.17384	0.0814111
$714$	35.7588	1.33824
$715$	0	0
$716$	0.326239	0.0121921
$717$	16.8687	0.629973
$718$	42.2822	1.57796
$719$	−2.19390	−0.0818185	−0.0409093	−	0.999163i	$-0.513025\pi$
$719$	−2.19390	−0.0818185	−0.0409093	+	0.999163i	$0.513025\pi$
$720$	0	0
$721$	1.28676	0.0479213
$722$	2.39827	0.0892545
$723$	2.75896	0.102607
$724$	−1.74853	−0.0649837
$725$	0	0
$726$	−19.7396	−0.732605
$727$	17.5138	0.649552	0.324776	−	0.945791i	$-0.394711\pi$
$727$	17.5138	0.649552	0.324776	+	0.945791i	$0.394711\pi$
$728$	1.02762	0.0380860
$729$	−44.0314	−1.63079
$730$	0	0
$731$	55.3550	2.04738
$732$	−0.584795	−0.0216147
$733$	−50.4547	−1.86359	−0.931794	−	0.362987i	$-0.881757\pi$
$733$	−50.4547	−1.86359	−0.931794	+	0.362987i	$0.881757\pi$
$734$	−42.1480	−1.55571
$735$	0	0
$736$	0.668030	0.0246239
$737$	22.4637	0.827461
$738$	19.5833	0.720870
$739$	−25.6051	−0.941898	−0.470949	−	0.882160i	$-0.656088\pi$
$739$	−25.6051	−0.941898	−0.470949	+	0.882160i	$0.656088\pi$
$740$	0	0
$741$	−2.59087	−0.0951778
$742$	−34.3592	−1.26137
$743$	−22.6764	−0.831916	−0.415958	−	0.909384i	$-0.636554\pi$
$743$	−22.6764	−0.831916	−0.415958	+	0.909384i	$0.636554\pi$
$744$	−11.6887	−0.428527
$745$	0	0
$746$	47.7480	1.74818
$747$	36.9651	1.35248
$748$	−1.11570	−0.0407939
$749$	−14.9575	−0.546535
$750$	0	0
$751$	22.5865	0.824192	0.412096	−	0.911140i	$-0.364797\pi$
$751$	22.5865	0.824192	0.412096	+	0.911140i	$0.364797\pi$
$752$	−31.2651	−1.14012
$753$	−14.2865	−0.520630
$754$	0.0480536	0.00175001
$755$	0	0
$756$	−0.609719	−0.0221753
$757$	9.50982	0.345640	0.172820	−	0.984953i	$-0.444712\pi$
$757$	9.50982	0.345640	0.172820	+	0.984953i	$0.444712\pi$
$758$	−34.8611	−1.26621
$759$	9.62757	0.349459
$760$	0	0
$761$	21.2805	0.771417	0.385708	−	0.922621i	$-0.373957\pi$
$761$	21.2805	0.771417	0.385708	+	0.922621i	$0.373957\pi$
$762$	47.1802	1.70916
$763$	−2.70452	−0.0979102
$764$	−0.493832	−0.0178662
$765$	0	0
$766$	−54.8439	−1.98159
$767$	1.06125	0.0383195
$768$	−5.50260	−0.198558
$769$	−4.82925	−0.174147	−0.0870736	−	0.996202i	$-0.527752\pi$
$769$	−4.82925	−0.174147	−0.0870736	+	0.996202i	$0.527752\pi$
$770$	0	0
$771$	−77.6841	−2.79773
$772$	0.521177	0.0187576
$773$	−35.0577	−1.26094	−0.630468	−	0.776215i	$-0.717137\pi$
$773$	−35.0577	−1.26094	−0.630468	+	0.776215i	$0.717137\pi$
$774$	−67.5828	−2.42921
$775$	0	0
$776$	−33.1416	−1.18971
$777$	−50.7853	−1.82191
$778$	−44.4188	−1.59249
$779$	−12.2502	−0.438908
$780$	0	0
$781$	−36.7311	−1.31434
$782$	−11.1708	−0.399467
$783$	0.656505	0.0234616
$784$	17.8334	0.636906
$785$	0	0
$786$	−30.5573	−1.08994
$787$	6.28899	0.224178	0.112089	−	0.993698i	$-0.464246\pi$
$787$	6.28899	0.224178	0.112089	+	0.993698i	$0.464246\pi$
$788$	0.309114	0.0110117
$789$	31.1884	1.11034
$790$	0	0
$791$	23.5228	0.836376
$792$	−31.3646	−1.11449
$793$	0.574248	0.0203921
$794$	−48.1242	−1.70786
$795$	0	0
$796$	1.43234	0.0507681
$797$	49.4271	1.75080	0.875400	−	0.483400i	$-0.160598\pi$
$797$	49.4271	1.75080	0.875400	+	0.483400i	$0.160598\pi$
$798$	27.3099	0.966759
$799$	40.9808	1.44980
$800$	0	0
$801$	67.8574	2.39762
$802$	−36.5313	−1.28996
$803$	13.6282	0.480929
$804$	2.09873	0.0740164
$805$	0	0
$806$	−0.498479	−0.0175582
$807$	48.8894	1.72099
$808$	−47.9586	−1.68718
$809$	55.5426	1.95277	0.976386	−	0.216031i	$-0.0693113\pi$
$809$	55.5426	1.95277	0.976386	+	0.216031i	$0.0693113\pi$
$810$	0	0
$811$	−49.9380	−1.75356	−0.876781	−	0.480890i	$-0.840314\pi$
$811$	−49.9380	−1.75356	−0.876781	+	0.480890i	$0.840314\pi$
$812$	−0.0202402	−0.000710290 0
$813$	−17.7817	−0.623633
$814$	39.6540	1.38987
$815$	0	0
$816$	62.5693	2.19036
$817$	42.2759	1.47905
$818$	−41.2439	−1.44206
$819$	1.71306	0.0598590
$820$	0	0
$821$	−6.33524	−0.221101	−0.110551	−	0.993870i	$-0.535261\pi$
$821$	−6.33524	−0.221101	−0.110551	+	0.993870i	$0.535261\pi$
$822$	−29.3503	−1.02371
$823$	46.0306	1.60453	0.802263	−	0.596971i	$-0.203629\pi$
$823$	46.0306	1.60453	0.802263	+	0.596971i	$0.203629\pi$
$824$	2.16139	0.0752957
$825$	0	0
$826$	−11.1864	−0.389226
$827$	−25.5389	−0.888073	−0.444037	−	0.896009i	$-0.646454\pi$
$827$	−25.5389	−0.888073	−0.444037	+	0.896009i	$0.646454\pi$
$828$	0.544975	0.0189392
$829$	−27.6145	−0.959093	−0.479546	−	0.877517i	$-0.659199\pi$
$829$	−27.6145	−0.959093	−0.479546	+	0.877517i	$0.659199\pi$
$830$	0	0
$831$	66.1402	2.29438
$832$	1.72298	0.0597337
$833$	−23.3751	−0.809900
$834$	−22.3570	−0.774161
$835$	0	0
$836$	−0.852084	−0.0294700
$837$	−6.81019	−0.235395
$838$	−58.8733	−2.03375
$839$	11.9619	0.412972	0.206486	−	0.978450i	$-0.433797\pi$
$839$	11.9619	0.412972	0.206486	+	0.978450i	$0.433797\pi$
$840$	0	0
$841$	−28.9782	−0.999249
$842$	−4.84886	−0.167103
$843$	80.9449	2.78789
$844$	0.351816	0.0121100
$845$	0	0
$846$	−50.0334	−1.72019
$847$	−8.16436	−0.280531
$848$	−60.1203	−2.06454
$849$	43.0830	1.47861
$850$	0	0
$851$	15.8649	0.543843
$852$	−3.43170	−0.117568
$853$	−18.4156	−0.630539	−0.315269	−	0.949002i	$-0.602095\pi$
$853$	−18.4156	−0.630539	−0.315269	+	0.949002i	$0.602095\pi$
$854$	−6.05305	−0.207131
$855$	0	0
$856$	−25.1245	−0.858737
$857$	22.3682	0.764083	0.382041	−	0.924145i	$-0.375221\pi$
$857$	22.3682	0.764083	0.382041	+	0.924145i	$0.375221\pi$
$858$	−2.20768	−0.0753688
$859$	−41.6353	−1.42058	−0.710288	−	0.703911i	$-0.751435\pi$
$859$	−41.6353	−1.42058	−0.710288	+	0.703911i	$0.751435\pi$
$860$	0	0
$861$	13.3685	0.455597
$862$	−7.03069	−0.239466
$863$	40.0019	1.36168	0.680840	−	0.732432i	$-0.261615\pi$
$863$	40.0019	1.36168	0.680840	+	0.732432i	$0.261615\pi$
$864$	−2.09280	−0.0711984
$865$	0	0
$866$	18.2924	0.621600
$867$	−35.1105	−1.19241
$868$	0.209959	0.00712648
$869$	−37.4192	−1.26936
$870$	0	0
$871$	−2.06087	−0.0698300
$872$	−4.54285	−0.153840
$873$	−55.2477	−1.86985
$874$	−8.53140	−0.288579
$875$	0	0
$876$	1.27325	0.0430190
$877$	−1.09857	−0.0370960	−0.0185480	−	0.999828i	$-0.505904\pi$
$877$	−1.09857	−0.0370960	−0.0185480	+	0.999828i	$0.505904\pi$
$878$	−14.2361	−0.480445
$879$	−16.7126	−0.563703
$880$	0	0
$881$	3.25152	0.109546	0.0547732	−	0.998499i	$-0.482556\pi$
$881$	3.25152	0.109546	0.0547732	+	0.998499i	$0.482556\pi$
$882$	28.5386	0.960946
$883$	24.8297	0.835588	0.417794	−	0.908542i	$-0.362803\pi$
$883$	24.8297	0.835588	0.417794	+	0.908542i	$0.362803\pi$
$884$	0.102357	0.00344263
$885$	0	0
$886$	−32.4448	−1.09001
$887$	18.7378	0.629155	0.314577	−	0.949232i	$-0.398137\pi$
$887$	18.7378	0.629155	0.314577	+	0.949232i	$0.398137\pi$
$888$	−85.3051	−2.86265
$889$	19.5139	0.654474
$890$	0	0
$891$	3.85020	0.128987
$892$	−0.0634146	−0.00212328
$893$	31.2980	1.04735
$894$	−1.05416	−0.0352565
$895$	0	0
$896$	−19.7119	−0.658527
$897$	−0.883256	−0.0294911
$898$	−43.2310	−1.44264
$899$	−0.226070	−0.00753987
$900$	0	0
$901$	78.8028	2.62530
$902$	−10.4384	−0.347560
$903$	−46.1354	−1.53529
$904$	39.5119	1.31414
$905$	0	0
$906$	−4.61630	−0.153366
$907$	−2.97151	−0.0986675	−0.0493337	−	0.998782i	$-0.515710\pi$
$907$	−2.97151	−0.0986675	−0.0493337	+	0.998782i	$0.515710\pi$
$908$	−0.575681	−0.0191047
$909$	−79.9478	−2.65170
$910$	0	0
$911$	1.36696	0.0452893	0.0226447	−	0.999744i	$-0.492791\pi$
$911$	1.36696	0.0452893	0.0226447	+	0.999744i	$0.492791\pi$
$912$	47.7856	1.58234
$913$	−19.7033	−0.652084
$914$	17.8658	0.590950
$915$	0	0
$916$	0.153428	0.00506940
$917$	−12.6386	−0.417363
$918$	34.9957	1.15503
$919$	−30.7514	−1.01440	−0.507198	−	0.861830i	$-0.669319\pi$
$919$	−30.7514	−1.01440	−0.507198	+	0.861830i	$0.669319\pi$
$920$	0	0
$921$	43.0706	1.41922
$922$	37.2027	1.22521
$923$	3.36980	0.110918
$924$	0.929872	0.0305905
$925$	0	0
$926$	−4.40351	−0.144708
$927$	3.60308	0.118341
$928$	−0.0694722	−0.00228054
$929$	20.7909	0.682126	0.341063	−	0.940040i	$-0.389213\pi$
$929$	20.7909	0.682126	0.341063	+	0.940040i	$0.389213\pi$
$930$	0	0
$931$	−17.8521	−0.585080
$932$	2.07569	0.0679916
$933$	7.66608	0.250976
$934$	−15.7200	−0.514375
$935$	0	0
$936$	2.87746	0.0940527
$937$	28.3485	0.926105	0.463052	−	0.886331i	$-0.346754\pi$
$937$	28.3485	0.926105	0.463052	+	0.886331i	$0.346754\pi$
$938$	21.7233	0.709291
$939$	31.1456	1.01640
$940$	0	0
$941$	−24.4494	−0.797028	−0.398514	−	0.917162i	$-0.630474\pi$
$941$	−24.4494	−0.797028	−0.398514	+	0.917162i	$0.630474\pi$
$942$	27.0871	0.882544
$943$	−4.17622	−0.135997
$944$	−19.5735	−0.637065
$945$	0	0
$946$	36.0233	1.17122
$947$	41.9342	1.36268	0.681340	−	0.731967i	$-0.261398\pi$
$947$	41.9342	1.36268	0.681340	+	0.731967i	$0.261398\pi$
$948$	−3.49598	−0.113544
$949$	−1.25028	−0.0405859
$950$	0	0
$951$	79.7296	2.58541
$952$	24.8430	0.805167
$953$	−14.0181	−0.454091	−0.227045	−	0.973884i	$-0.572907\pi$
$953$	−14.0181	−0.454091	−0.227045	+	0.973884i	$0.572907\pi$
$954$	−96.2103	−3.11492
$955$	0	0
$956$	−0.508966	−0.0164611
$957$	−1.00123	−0.0323650
$958$	35.6588	1.15209
$959$	−12.1394	−0.392001
$960$	0	0
$961$	−28.6549	−0.924351
$962$	−3.63796	−0.117292
$963$	−41.8830	−1.34966
$964$	−0.0832441	−0.00268111
$965$	0	0
$966$	9.31025	0.299552
$967$	−17.3691	−0.558551	−0.279276	−	0.960211i	$-0.590094\pi$
$967$	−17.3691	−0.558551	−0.279276	+	0.960211i	$0.590094\pi$
$968$	−13.7139	−0.440780
$969$	−62.6352	−2.01213
$970$	0	0
$971$	46.9881	1.50792	0.753961	−	0.656920i	$-0.228141\pi$
$971$	46.9881	1.50792	0.753961	+	0.656920i	$0.228141\pi$
$972$	1.47030	0.0471598
$973$	−9.24693	−0.296443
$974$	−21.1424	−0.677448
$975$	0	0
$976$	−10.5914	−0.339021
$977$	16.7488	0.535843	0.267921	−	0.963441i	$-0.413663\pi$
$977$	16.7488	0.535843	0.267921	+	0.963441i	$0.413663\pi$
$978$	−3.48339	−0.111386
$979$	−36.1697	−1.15599
$980$	0	0
$981$	−7.57301	−0.241788
$982$	−43.9685	−1.40309
$983$	6.05195	0.193027	0.0965136	−	0.995332i	$-0.469231\pi$
$983$	6.05195	0.193027	0.0965136	+	0.995332i	$0.469231\pi$
$984$	22.4554	0.715851
$985$	0	0
$986$	1.16171	0.0369965
$987$	−34.1553	−1.08717
$988$	0.0781722	0.00248699
$989$	14.4124	0.458286
$990$	0	0
$991$	−18.5883	−0.590476	−0.295238	−	0.955424i	$-0.595399\pi$
$991$	−18.5883	−0.590476	−0.295238	+	0.955424i	$0.595399\pi$
$992$	0.720663	0.0228811
$993$	−29.4747	−0.935353
$994$	−35.5205	−1.12664
$995$	0	0
$996$	−1.84083	−0.0583289
$997$	28.6039	0.905894	0.452947	−	0.891537i	$-0.350373\pi$
$997$	28.6039	0.905894	0.452947	+	0.891537i	$0.350373\pi$
$998$	−22.6856	−0.718101
$999$	−49.7015	−1.57249

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6025.2.a.o.1.8	yes	40
5.4	even	2		6025.2.a.l.1.33	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6025.2.a.l.1.33	✓	40	5.4	even	2
6025.2.a.o.1.8	yes	40	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)

\(f(q)\)	\(=\)	\(q-1.44334 q^{2} -2.75896 q^{3} +0.0832441 q^{4} +3.98213 q^{6} +1.64702 q^{7} +2.76654 q^{8} +4.61187 q^{9} +O(q^{10})\)	\(q-1.44334 q^{2} -2.75896 q^{3} +0.0832441 q^{4} +3.98213 q^{6} +1.64702 q^{7} +2.76654 q^{8} +4.61187 q^{9} -2.45824 q^{11} -0.229667 q^{12} +0.225525 q^{13} -2.37722 q^{14} -4.15956 q^{16} +5.45215 q^{17} -6.65652 q^{18} +4.16394 q^{19} -4.54407 q^{21} +3.54809 q^{22} +1.41953 q^{23} -7.63278 q^{24} -0.325510 q^{26} -4.44710 q^{27} +0.137105 q^{28} -0.147625 q^{29} +1.53138 q^{31} +0.470598 q^{32} +6.78220 q^{33} -7.86934 q^{34} +0.383911 q^{36} +11.1762 q^{37} -6.01000 q^{38} -0.622215 q^{39} -2.94197 q^{41} +6.55866 q^{42} +10.1529 q^{43} -0.204634 q^{44} -2.04888 q^{46} +7.51645 q^{47} +11.4761 q^{48} -4.28732 q^{49} -15.0423 q^{51} +0.0187736 q^{52} +14.4535 q^{53} +6.41870 q^{54} +4.55655 q^{56} -11.4882 q^{57} +0.213074 q^{58} +4.70568 q^{59} +2.54627 q^{61} -2.21031 q^{62} +7.59586 q^{63} +7.63988 q^{64} -9.78905 q^{66} -9.13811 q^{67} +0.453859 q^{68} -3.91644 q^{69} +14.9420 q^{71} +12.7589 q^{72} -5.54388 q^{73} -16.1310 q^{74} +0.346623 q^{76} -4.04878 q^{77} +0.898071 q^{78} +15.2219 q^{79} -1.56624 q^{81} +4.24627 q^{82} +8.01520 q^{83} -0.378267 q^{84} -14.6541 q^{86} +0.407293 q^{87} -6.80083 q^{88} +14.7136 q^{89} +0.371445 q^{91} +0.118168 q^{92} -4.22501 q^{93} -10.8488 q^{94} -1.29836 q^{96} -11.9794 q^{97} +6.18808 q^{98} -11.3371 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9}+O(q^{10}) \) 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9	\( 40 q + 11 q^{2} + 8 q^{3} + 41 q^{4} + 3 q^{6} + 16 q^{7} + 33 q^{8} + 38 q^{9} + q^{11} + 14 q^{12} + 9 q^{13} - q^{14} + 43 q^{16} + 12 q^{17} + 42 q^{18} + 2 q^{21} + 5 q^{22} + 77 q^{23} - 2 q^{24} + 2 q^{26} + 38 q^{27} + 42 q^{28} + 2 q^{29} + q^{31} + 72 q^{32} + 20 q^{33} + 5 q^{34} + 32 q^{36} + 28 q^{37} + 23 q^{38} - 2 q^{39} - 2 q^{41} + 37 q^{42} + 31 q^{43} + 3 q^{44} + 14 q^{46} + 96 q^{47} + 13 q^{48} + 40 q^{49} - 10 q^{51} + 42 q^{52} + 54 q^{53} + 4 q^{54} - 15 q^{56} + 37 q^{57} + 27 q^{58} + q^{59} + 5 q^{61} + 39 q^{62} + 70 q^{63} + 65 q^{64} - 52 q^{66} + 34 q^{67} + 52 q^{68} + 21 q^{69} - 9 q^{71} + 70 q^{72} + 25 q^{73} + 22 q^{74} - 47 q^{76} + 54 q^{77} + 58 q^{78} + 13 q^{79} + 12 q^{81} - 5 q^{82} + 63 q^{83} + 95 q^{84} - 18 q^{86} + 47 q^{87} + 13 q^{88} + 19 q^{89} - 31 q^{91} + 137 q^{92} + 52 q^{93} + 120 q^{94} - 49 q^{96} + 36 q^{97} + 64 q^{98} + 16 q^{99}+O(q^{100}) \) 40 * q + 11 * q^2 + 8 * q^3 + 41 * q^4 + 3 * q^6 + 16 * q^7 + 33 * q^8 + 38 * q^9 + q^11 + 14 * q^12 + 9 * q^13 - q^14 + 43 * q^16 + 12 * q^17 + 42 * q^18 + 2 * q^21 + 5 * q^22 + 77 * q^23 - 2 * q^24 + 2 * q^26 + 38 * q^27 + 42 * q^28 + 2 * q^29 + q^31 + 72 * q^32 + 20 * q^33 + 5 * q^34 + 32 * q^36 + 28 * q^37 + 23 * q^38 - 2 * q^39 - 2 * q^41 + 37 * q^42 + 31 * q^43 + 3 * q^44 + 14 * q^46 + 96 * q^47 + 13 * q^48 + 40 * q^49 - 10 * q^51 + 42 * q^52 + 54 * q^53 + 4 * q^54 - 15 * q^56 + 37 * q^57 + 27 * q^58 + q^59 + 5 * q^61 + 39 * q^62 + 70 * q^63 + 65 * q^64 - 52 * q^66 + 34 * q^67 + 52 * q^68 + 21 * q^69 - 9 * q^71 + 70 * q^72 + 25 * q^73 + 22 * q^74 - 47 * q^76 + 54 * q^77 + 58 * q^78 + 13 * q^79 + 12 * q^81 - 5 * q^82 + 63 * q^83 + 95 * q^84 - 18 * q^86 + 47 * q^87 + 13 * q^88 + 19 * q^89 - 31 * q^91 + 137 * q^92 + 52 * q^93 + 120 * q^94 - 49 * q^96 + 36 * q^97 + 64 * q^98 + 16 * q^99

Introduction

L-functions

Modular forms

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Database

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