LMFDB - Embedded newform 7865.2.a.u.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7865,2,Mod(1,7865)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7865.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7865, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7865 = 5 \cdot 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7865.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,1,-5,7,-8,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$62.8023411897$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 11x^{6} + 9x^{5} + 34x^{4} - 13x^{3} - 35x^{2} - 3x + 5 $ x^8 - x^7 - 11x^6 + 9x^5 + 34x^4 - 13x^3 - 35x^2 - 3x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-0.652625$ of defining polynomial
Character	$\chi$	$=$	7865.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.652625 q^{2} +1.46424 q^{3} -1.57408 q^{4} -1.00000 q^{5} -0.955597 q^{6} +0.0215714 q^{7} +2.33253 q^{8} -0.856014 q^{9} +0.652625 q^{10} -2.30483 q^{12} -1.00000 q^{13} -0.0140780 q^{14} -1.46424 q^{15} +1.62589 q^{16} -0.943312 q^{17} +0.558656 q^{18} +4.14101 q^{19} +1.57408 q^{20} +0.0315856 q^{21} +6.12899 q^{23} +3.41538 q^{24} +1.00000 q^{25} +0.652625 q^{26} -5.64611 q^{27} -0.0339551 q^{28} +0.897861 q^{29} +0.955597 q^{30} +10.2470 q^{31} -5.72617 q^{32} +0.615629 q^{34} -0.0215714 q^{35} +1.34743 q^{36} +0.0527321 q^{37} -2.70252 q^{38} -1.46424 q^{39} -2.33253 q^{40} -7.32799 q^{41} -0.0206136 q^{42} +3.30725 q^{43} +0.856014 q^{45} -3.99993 q^{46} -2.20356 q^{47} +2.38069 q^{48} -6.99953 q^{49} -0.652625 q^{50} -1.38123 q^{51} +1.57408 q^{52} +2.37453 q^{53} +3.68479 q^{54} +0.0503160 q^{56} +6.06341 q^{57} -0.585967 q^{58} -2.53023 q^{59} +2.30483 q^{60} -8.11828 q^{61} -6.68746 q^{62} -0.0184654 q^{63} +0.485257 q^{64} +1.00000 q^{65} -11.5771 q^{67} +1.48485 q^{68} +8.97429 q^{69} +0.0140780 q^{70} -14.4740 q^{71} -1.99668 q^{72} +4.38236 q^{73} -0.0344143 q^{74} +1.46424 q^{75} -6.51828 q^{76} +0.955597 q^{78} +1.43091 q^{79} -1.62589 q^{80} -5.69920 q^{81} +4.78243 q^{82} +6.35117 q^{83} -0.0497183 q^{84} +0.943312 q^{85} -2.15840 q^{86} +1.31468 q^{87} -4.01534 q^{89} -0.558656 q^{90} -0.0215714 q^{91} -9.64753 q^{92} +15.0041 q^{93} +1.43810 q^{94} -4.14101 q^{95} -8.38446 q^{96} +7.88347 q^{97} +4.56807 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} - 5 q^{3} + 7 q^{4} - 8 q^{5} - 7 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9} - q^{10} - 15 q^{12} - 8 q^{13} - 7 q^{14} + 5 q^{15} + 9 q^{16} + 4 q^{17} + 8 q^{18} + 16 q^{19} - 7 q^{20} - 23 q^{21}+ \cdots + 41 q^{98}+O(q^{100}) $ 8 * q + q^2 - 5 * q^3 + 7 * q^4 - 8 * q^5 - 7 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9 - q^10 - 15 * q^12 - 8 * q^13 - 7 * q^14 + 5 * q^15 + 9 * q^16 + 4 * q^17 + 8 * q^18 + 16 * q^19 - 7 * q^20 - 23 * q^21 - 9 * q^23 + 5 * q^24 + 8 * q^25 - q^26 - 11 * q^27 + 11 * q^28 - 13 * q^29 + 7 * q^30 - 28 * q^32 + 13 * q^34 - 9 * q^35 + 12 * q^36 - 5 * q^37 + 55 * q^38 + 5 * q^39 - 3 * q^40 + 13 * q^41 - 5 * q^42 + 5 * q^43 - 3 * q^45 + 27 * q^46 + 10 * q^47 - 36 * q^48 + 23 * q^49 + q^50 - 37 * q^51 - 7 * q^52 + 14 * q^53 - 45 * q^54 - 18 * q^56 - 21 * q^57 + 3 * q^58 - 20 * q^59 + 15 * q^60 + 6 * q^61 + 25 * q^62 + 26 * q^63 - 3 * q^64 + 8 * q^65 + 4 * q^67 - 9 * q^69 + 7 * q^70 - 9 * q^71 + 35 * q^72 + 10 * q^73 + 42 * q^74 - 5 * q^75 + 19 * q^76 + 7 * q^78 + 13 * q^79 - 9 * q^80 + 16 * q^82 + 26 * q^83 - 58 * q^84 - 4 * q^85 + 26 * q^86 + 11 * q^87 - 6 * q^89 - 8 * q^90 - 9 * q^91 - 16 * q^92 + 3 * q^93 + 23 * q^94 - 16 * q^95 + 21 * q^96 + 26 * q^97 + 41 * q^98

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 $

$2$	−0.652625	−0.461476	−0.230738	−	0.973016i	$-0.574114\pi$
$2$	−0.652625	−0.461476	−0.230738	+	0.973016i	$0.574114\pi$
$3$	1.46424	0.845377	0.422688	−	0.906275i	$-0.361086\pi$
$3$	1.46424	0.845377	0.422688	+	0.906275i	$0.361086\pi$
$4$	−1.57408	−0.787040
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.955597	−0.390121
$7$	0.0215714	0.00815322	0.00407661	−	0.999992i	$-0.498702\pi$
$7$	0.0215714	0.00815322	0.00407661	+	0.999992i	$0.498702\pi$
$8$	2.33253	0.824675
$9$	−0.856014	−0.285338
$10$	0.652625	0.206378
$11$	0	0
$11$	0	0
$12$	−2.30483	−0.665346
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.0140780	−0.00376251
$15$	−1.46424	−0.378064
$16$	1.62589	0.406473
$17$	−0.943312	−0.228787	−0.114393	−	0.993436i	$-0.536492\pi$
$17$	−0.943312	−0.228787	−0.114393	+	0.993436i	$0.536492\pi$
$18$	0.558656	0.131676
$19$	4.14101	0.950012	0.475006	−	0.879983i	$-0.342446\pi$
$19$	4.14101	0.950012	0.475006	+	0.879983i	$0.342446\pi$
$20$	1.57408	0.351975
$21$	0.0315856	0.00689255
$22$	0	0
$23$	6.12899	1.27798	0.638992	−	0.769214i	$-0.279352\pi$
$23$	6.12899	1.27798	0.638992	+	0.769214i	$0.279352\pi$
$24$	3.41538	0.697162
$25$	1.00000	0.200000
$26$	0.652625	0.127990
$27$	−5.64611	−1.08659
$28$	−0.0339551	−0.00641692
$29$	0.897861	0.166729	0.0833643	−	0.996519i	$-0.473433\pi$
$29$	0.897861	0.166729	0.0833643	+	0.996519i	$0.473433\pi$
$30$	0.955597	0.174467
$31$	10.2470	1.84042	0.920210	−	0.391425i	$-0.128018\pi$
$31$	10.2470	1.84042	0.920210	+	0.391425i	$0.128018\pi$
$32$	−5.72617	−1.01225
$33$	0	0
$34$	0.615629	0.105580
$35$	−0.0215714	−0.00364623
$36$	1.34743	0.224572
$37$	0.0527321	0.00866910	0.00433455	−	0.999991i	$-0.498620\pi$
$37$	0.0527321	0.00866910	0.00433455	+	0.999991i	$0.498620\pi$
$38$	−2.70252	−0.438407
$39$	−1.46424	−0.234465
$40$	−2.33253	−0.368806
$41$	−7.32799	−1.14444	−0.572220	−	0.820100i	$-0.693918\pi$
$41$	−7.32799	−1.14444	−0.572220	+	0.820100i	$0.693918\pi$
$42$	−0.0206136	−0.00318074
$43$	3.30725	0.504352	0.252176	−	0.967681i	$-0.418854\pi$
$43$	3.30725	0.504352	0.252176	+	0.967681i	$0.418854\pi$
$44$	0	0
$45$	0.856014	0.127607
$46$	−3.99993	−0.589758
$47$	−2.20356	−0.321423	−0.160711	−	0.987001i	$-0.551379\pi$
$47$	−2.20356	−0.321423	−0.160711	+	0.987001i	$0.551379\pi$
$48$	2.38069	0.343623
$49$	−6.99953	−0.999934
$50$	−0.652625	−0.0922951
$51$	−1.38123	−0.193411
$52$	1.57408	0.218286
$53$	2.37453	0.326167	0.163084	−	0.986612i	$-0.447856\pi$
$53$	2.37453	0.326167	0.163084	+	0.986612i	$0.447856\pi$
$54$	3.68479	0.501437
$55$	0	0
$56$	0.0503160	0.00672376
$57$	6.06341	0.803118
$58$	−0.585967	−0.0769412
$59$	−2.53023	−0.329408	−0.164704	−	0.986343i	$-0.552667\pi$
$59$	−2.53023	−0.329408	−0.164704	+	0.986343i	$0.552667\pi$
$60$	2.30483	0.297552
$61$	−8.11828	−1.03944	−0.519719	−	0.854337i	$-0.673964\pi$
$61$	−8.11828	−1.03944	−0.519719	+	0.854337i	$0.673964\pi$
$62$	−6.68746	−0.849309
$63$	−0.0184654	−0.00232642
$64$	0.485257	0.0606571
$65$	1.00000	0.124035
$66$	0	0
$67$	−11.5771	−1.41437	−0.707184	−	0.707029i	$-0.750035\pi$
$67$	−11.5771	−1.41437	−0.707184	+	0.707029i	$0.750035\pi$
$68$	1.48485	0.180064
$69$	8.97429	1.08038
$70$	0.0140780	0.00168265
$71$	−14.4740	−1.71775	−0.858873	−	0.512188i	$-0.828835\pi$
$71$	−14.4740	−1.71775	−0.858873	+	0.512188i	$0.828835\pi$
$72$	−1.99668	−0.235311
$73$	4.38236	0.512916	0.256458	−	0.966555i	$-0.417444\pi$
$73$	4.38236	0.512916	0.256458	+	0.966555i	$0.417444\pi$
$74$	−0.0344143	−0.00400058
$75$	1.46424	0.169075
$76$	−6.51828	−0.747698
$77$	0	0
$78$	0.955597	0.108200
$79$	1.43091	0.160990	0.0804951	−	0.996755i	$-0.474350\pi$
$79$	1.43091	0.160990	0.0804951	+	0.996755i	$0.474350\pi$
$80$	−1.62589	−0.181780
$81$	−5.69920	−0.633244
$82$	4.78243	0.528131
$83$	6.35117	0.697131	0.348566	−	0.937284i	$-0.386669\pi$
$83$	6.35117	0.697131	0.348566	+	0.937284i	$0.386669\pi$
$84$	−0.0497183	−0.00542471
$85$	0.943312	0.102317
$86$	−2.15840	−0.232746
$87$	1.31468	0.140949
$88$	0	0
$89$	−4.01534	−0.425626	−0.212813	−	0.977093i	$-0.568262\pi$
$89$	−4.01534	−0.425626	−0.212813	+	0.977093i	$0.568262\pi$
$90$	−0.558656	−0.0588875
$91$	−0.0215714	−0.00226130
$92$	−9.64753	−1.00582
$93$	15.0041	1.55585
$94$	1.43810	0.148329
$95$	−4.14101	−0.424858
$96$	−8.38446	−0.855735
$97$	7.88347	0.800445	0.400223	−	0.916418i	$-0.368933\pi$
$97$	7.88347	0.800445	0.400223	+	0.916418i	$0.368933\pi$
$98$	4.56807	0.461445
$99$	0	0
$100$	−1.57408	−0.157408
$101$	−0.213280	−0.0212221	−0.0106111	−	0.999944i	$-0.503378\pi$
$101$	−0.213280	−0.0212221	−0.0106111	+	0.999944i	$0.503378\pi$
$102$	0.901426	0.0892545
$103$	−15.2477	−1.50240	−0.751200	−	0.660075i	$-0.770524\pi$
$103$	−15.2477	−1.50240	−0.751200	+	0.660075i	$0.770524\pi$
$104$	−2.33253	−0.228724
$105$	−0.0315856	−0.00308244
$106$	−1.54968	−0.150518
$107$	17.9039	1.73084	0.865419	−	0.501049i	$-0.167052\pi$
$107$	17.9039	1.73084	0.865419	+	0.501049i	$0.167052\pi$
$108$	8.88744	0.855194
$109$	11.4522	1.09692	0.548462	−	0.836175i	$-0.315214\pi$
$109$	11.4522	1.09692	0.548462	+	0.836175i	$0.315214\pi$
$110$	0	0
$111$	0.0772122	0.00732865
$112$	0.0350728	0.00331406
$113$	−4.94962	−0.465621	−0.232811	−	0.972522i	$-0.574792\pi$
$113$	−4.94962	−0.465621	−0.232811	+	0.972522i	$0.574792\pi$
$114$	−3.95713	−0.370619
$115$	−6.12899	−0.571532
$116$	−1.41331	−0.131222
$117$	0.856014	0.0791385
$118$	1.65129	0.152014
$119$	−0.0203486	−0.00186535
$120$	−3.41538	−0.311780
$121$	0	0
$122$	5.29819	0.479676
$123$	−10.7299	−0.967483
$124$	−16.1296	−1.44848
$125$	−1.00000	−0.0894427
$126$	0.0120510	0.00107359
$127$	1.43069	0.126953	0.0634767	−	0.997983i	$-0.479781\pi$
$127$	1.43069	0.126953	0.0634767	+	0.997983i	$0.479781\pi$
$128$	11.1356	0.984261
$129$	4.84260	0.426367
$130$	−0.652625	−0.0572390
$131$	12.4613	1.08875	0.544375	−	0.838842i	$-0.316767\pi$
$131$	12.4613	1.08875	0.544375	+	0.838842i	$0.316767\pi$
$132$	0	0
$133$	0.0893273	0.00774566
$134$	7.55551	0.652696
$135$	5.64611	0.485940
$136$	−2.20031	−0.188675
$137$	−0.0752519	−0.00642920	−0.00321460	−	0.999995i	$-0.501023\pi$
$137$	−0.0752519	−0.00642920	−0.00321460	+	0.999995i	$0.501023\pi$
$138$	−5.85685	−0.498568
$139$	17.6716	1.49888	0.749441	−	0.662071i	$-0.230322\pi$
$139$	17.6716	1.49888	0.749441	+	0.662071i	$0.230322\pi$
$140$	0.0339551	0.00286973
$141$	−3.22654	−0.271723
$142$	9.44609	0.792698
$143$	0	0
$144$	−1.39179	−0.115982
$145$	−0.897861	−0.0745633
$146$	−2.86004	−0.236698
$147$	−10.2490	−0.845321
$148$	−0.0830045	−0.00682293
$149$	4.43435	0.363276	0.181638	−	0.983365i	$-0.441860\pi$
$149$	4.43435	0.363276	0.181638	+	0.983365i	$0.441860\pi$
$150$	−0.955597	−0.0780241
$151$	10.8635	0.884060	0.442030	−	0.897000i	$-0.354258\pi$
$151$	10.8635	0.884060	0.442030	+	0.897000i	$0.354258\pi$
$152$	9.65904	0.783451
$153$	0.807488	0.0652816
$154$	0	0
$155$	−10.2470	−0.823061
$156$	2.30483	0.184534
$157$	8.74067	0.697582	0.348791	−	0.937201i	$-0.386592\pi$
$157$	8.74067	0.697582	0.348791	+	0.937201i	$0.386592\pi$
$158$	−0.933849	−0.0742930
$159$	3.47688	0.275734
$160$	5.72617	0.452693
$161$	0.132211	0.0104197
$162$	3.71944	0.292227
$163$	19.6690	1.54059	0.770296	−	0.637686i	$-0.220108\pi$
$163$	19.6690	1.54059	0.770296	+	0.637686i	$0.220108\pi$
$164$	11.5348	0.900720
$165$	0	0
$166$	−4.14493	−0.321709
$167$	−14.7325	−1.14003	−0.570017	−	0.821633i	$-0.693063\pi$
$167$	−14.7325	−1.14003	−0.570017	+	0.821633i	$0.693063\pi$
$168$	0.0736745	0.00568411
$169$	1.00000	0.0769231
$170$	−0.615629	−0.0472166
$171$	−3.54476	−0.271074
$172$	−5.20589	−0.396945
$173$	12.1295	0.922185	0.461093	−	0.887352i	$-0.347458\pi$
$173$	12.1295	0.922185	0.461093	+	0.887352i	$0.347458\pi$
$174$	−0.857993	−0.0650443
$175$	0.0215714	0.00163064
$176$	0	0
$177$	−3.70485	−0.278474
$178$	2.62051	0.196416
$179$	1.23274	0.0921397	0.0460698	−	0.998938i	$-0.485330\pi$
$179$	1.23274	0.0921397	0.0460698	+	0.998938i	$0.485330\pi$
$180$	−1.34743	−0.100432
$181$	13.4693	1.00117	0.500584	−	0.865688i	$-0.333119\pi$
$181$	13.4693	1.00117	0.500584	+	0.865688i	$0.333119\pi$
$182$	0.0140780	0.00104353
$183$	−11.8871	−0.878718
$184$	14.2961	1.05392
$185$	−0.0527321	−0.00387694
$186$	−9.79202	−0.717986
$187$	0	0
$188$	3.46859	0.252973
$189$	−0.121795	−0.00885925
$190$	2.70252	0.196062
$191$	−0.381949	−0.0276369	−0.0138184	−	0.999905i	$-0.504399\pi$
$191$	−0.381949	−0.0276369	−0.0138184	+	0.999905i	$0.504399\pi$
$192$	0.710530	0.0512781
$193$	5.24636	0.377641	0.188821	−	0.982012i	$-0.439534\pi$
$193$	5.24636	0.377641	0.188821	+	0.982012i	$0.439534\pi$
$194$	−5.14495	−0.369386
$195$	1.46424	0.104856
$196$	11.0178	0.786988
$197$	1.63178	0.116260	0.0581298	−	0.998309i	$-0.481486\pi$
$197$	1.63178	0.116260	0.0581298	+	0.998309i	$0.481486\pi$
$198$	0	0
$199$	15.3354	1.08710	0.543548	−	0.839378i	$-0.317080\pi$
$199$	15.3354	1.08710	0.543548	+	0.839378i	$0.317080\pi$
$200$	2.33253	0.164935
$201$	−16.9516	−1.19567
$202$	0.139192	0.00979350
$203$	0.0193681	0.00135938
$204$	2.17417	0.152222
$205$	7.32799	0.511809
$206$	9.95102	0.693321
$207$	−5.24650	−0.364657
$208$	−1.62589	−0.112735
$209$	0	0
$210$	0.0206136	0.00142247
$211$	27.9079	1.92126	0.960630	−	0.277830i	$-0.0896150\pi$
$211$	27.9079	1.92126	0.960630	+	0.277830i	$0.0896150\pi$
$212$	−3.73771	−0.256707
$213$	−21.1933	−1.45214
$214$	−11.6845	−0.798739
$215$	−3.30725	−0.225553
$216$	−13.1698	−0.896088
$217$	0.221043	0.0150054
$218$	−7.47401	−0.506204
$219$	6.41681	0.433608
$220$	0	0
$221$	0.943312	0.0634540
$222$	−0.0503906	−0.00338199
$223$	−10.5762	−0.708234	−0.354117	−	0.935201i	$-0.615218\pi$
$223$	−10.5762	−0.708234	−0.354117	+	0.935201i	$0.615218\pi$
$224$	−0.123521	−0.00825312
$225$	−0.856014	−0.0570676
$226$	3.23025	0.214873
$227$	10.0865	0.669464	0.334732	−	0.942313i	$-0.391354\pi$
$227$	10.0865	0.669464	0.334732	+	0.942313i	$0.391354\pi$
$228$	−9.54429	−0.632086
$229$	23.2527	1.53658	0.768291	−	0.640101i	$-0.221108\pi$
$229$	23.2527	1.53658	0.768291	+	0.640101i	$0.221108\pi$
$230$	3.99993	0.263748
$231$	0	0
$232$	2.09429	0.137497
$233$	8.00823	0.524636	0.262318	−	0.964981i	$-0.415513\pi$
$233$	8.00823	0.524636	0.262318	+	0.964981i	$0.415513\pi$
$234$	−0.558656	−0.0365205
$235$	2.20356	0.143745
$236$	3.98278	0.259257
$237$	2.09519	0.136097
$238$	0.0132800	0.000860813 0
$239$	−18.6226	−1.20460	−0.602298	−	0.798271i	$-0.705748\pi$
$239$	−18.6226	−1.20460	−0.602298	+	0.798271i	$0.705748\pi$
$240$	−2.38069	−0.153673
$241$	19.6117	1.26330	0.631652	−	0.775252i	$-0.282377\pi$
$241$	19.6117	1.26330	0.631652	+	0.775252i	$0.282377\pi$
$242$	0	0
$243$	8.59337	0.551265
$244$	12.7788	0.818080
$245$	6.99953	0.447184
$246$	7.00260	0.446470
$247$	−4.14101	−0.263486
$248$	23.9015	1.51775
$249$	9.29961	0.589339
$250$	0.652625	0.0412756
$251$	10.3402	0.652666	0.326333	−	0.945255i	$-0.394187\pi$
$251$	10.3402	0.652666	0.326333	+	0.945255i	$0.394187\pi$
$252$	0.0290661	0.00183099
$253$	0	0
$254$	−0.933705	−0.0585859
$255$	1.38123	0.0864960
$256$	−8.23791	−0.514869
$257$	−17.8434	−1.11304	−0.556519	−	0.830835i	$-0.687863\pi$
$257$	−17.8434	−1.11304	−0.556519	+	0.830835i	$0.687863\pi$
$258$	−3.16040	−0.196758
$259$	0.00113750	7.06811e−5 0
$260$	−1.57408	−0.0976203
$261$	−0.768582	−0.0475740
$262$	−8.13257	−0.502432
$263$	−7.62715	−0.470310	−0.235155	−	0.971958i	$-0.575560\pi$
$263$	−7.62715	−0.470310	−0.235155	+	0.971958i	$0.575560\pi$
$264$	0	0
$265$	−2.37453	−0.145866
$266$	−0.0582972	−0.00357443
$267$	−5.87941	−0.359814
$268$	18.2233	1.11316
$269$	14.4445	0.880697	0.440349	−	0.897827i	$-0.354855\pi$
$269$	14.4445	0.880697	0.440349	+	0.897827i	$0.354855\pi$
$270$	−3.68479	−0.224249
$271$	−25.5527	−1.55221	−0.776107	−	0.630601i	$-0.782808\pi$
$271$	−25.5527	−1.55221	−0.776107	+	0.630601i	$0.782808\pi$
$272$	−1.53372	−0.0929956
$273$	−0.0315856	−0.00191165
$274$	0.0491113	0.00296692
$275$	0	0
$276$	−14.1263	−0.850301
$277$	−10.4471	−0.627704	−0.313852	−	0.949472i	$-0.601620\pi$
$277$	−10.4471	−0.627704	−0.313852	+	0.949472i	$0.601620\pi$
$278$	−11.5329	−0.691697
$279$	−8.77159	−0.525142
$280$	−0.0503160	−0.00300696
$281$	23.3473	1.39278	0.696392	−	0.717662i	$-0.254788\pi$
$281$	23.3473	1.39278	0.696392	+	0.717662i	$0.254788\pi$
$282$	2.10572	0.125394
$283$	−24.7762	−1.47279	−0.736397	−	0.676550i	$-0.763474\pi$
$283$	−24.7762	−1.47279	−0.736397	+	0.676550i	$0.763474\pi$
$284$	22.7832	1.35194
$285$	−6.06341	−0.359165
$286$	0	0
$287$	−0.158075	−0.00933087
$288$	4.90168	0.288834
$289$	−16.1102	−0.947657
$290$	0.585967	0.0344091
$291$	11.5433	0.676678
$292$	−6.89819	−0.403686
$293$	29.5575	1.72677	0.863383	−	0.504550i	$-0.168342\pi$
$293$	29.5575	1.72677	0.863383	+	0.504550i	$0.168342\pi$
$294$	6.68873	0.390095
$295$	2.53023	0.147316
$296$	0.122999	0.00714919
$297$	0	0
$298$	−2.89397	−0.167643
$299$	−6.12899	−0.354449
$300$	−2.30483	−0.133069
$301$	0.0713421	0.00411209
$302$	−7.08980	−0.407972
$303$	−0.312292	−0.0179407
$304$	6.73282	0.386154
$305$	8.11828	0.464851
$306$	−0.526987	−0.0301258
$307$	−9.51282	−0.542925	−0.271463	−	0.962449i	$-0.587507\pi$
$307$	−9.51282	−0.542925	−0.271463	+	0.962449i	$0.587507\pi$
$308$	0	0
$309$	−22.3262	−1.27009
$310$	6.68746	0.379822
$311$	−14.1294	−0.801202	−0.400601	−	0.916253i	$-0.631199\pi$
$311$	−14.1294	−0.801202	−0.400601	+	0.916253i	$0.631199\pi$
$312$	−3.41538	−0.193358
$313$	−8.98201	−0.507693	−0.253847	−	0.967245i	$-0.581696\pi$
$313$	−8.98201	−0.507693	−0.253847	+	0.967245i	$0.581696\pi$
$314$	−5.70438	−0.321917
$315$	0.0184654	0.00104041
$316$	−2.25237	−0.126706
$317$	−1.74260	−0.0978743	−0.0489372	−	0.998802i	$-0.515583\pi$
$317$	−1.74260	−0.0978743	−0.0489372	+	0.998802i	$0.515583\pi$
$318$	−2.26910	−0.127245
$319$	0	0
$320$	−0.485257	−0.0271267
$321$	26.2156	1.46321
$322$	−0.0862842	−0.00480843
$323$	−3.90626	−0.217350
$324$	8.97100	0.498389
$325$	−1.00000	−0.0554700
$326$	−12.8365	−0.710946
$327$	16.7688	0.927314
$328$	−17.0928	−0.943791
$329$	−0.0475339	−0.00262063
$330$	0	0
$331$	−7.19486	−0.395465	−0.197733	−	0.980256i	$-0.563358\pi$
$331$	−7.19486	−0.395465	−0.197733	+	0.980256i	$0.563358\pi$
$332$	−9.99725	−0.548670
$333$	−0.0451394	−0.00247362
$334$	9.61478	0.526097
$335$	11.5771	0.632525
$336$	0.0513548	0.00280163
$337$	9.84432	0.536254	0.268127	−	0.963384i	$-0.413595\pi$
$337$	9.84432	0.536254	0.268127	+	0.963384i	$0.413595\pi$
$338$	−0.652625	−0.0354981
$339$	−7.24742	−0.393626
$340$	−1.48485	−0.0805273
$341$	0	0
$342$	2.31340	0.125094
$343$	−0.301990	−0.0163059
$344$	7.71429	0.415926
$345$	−8.97429	−0.483160
$346$	−7.91598	−0.425566
$347$	−5.06522	−0.271915	−0.135958	−	0.990715i	$-0.543411\pi$
$347$	−5.06522	−0.271915	−0.135958	+	0.990715i	$0.543411\pi$
$348$	−2.06941	−0.110932
$349$	−2.08696	−0.111712	−0.0558562	−	0.998439i	$-0.517789\pi$
$349$	−2.08696	−0.111712	−0.0558562	+	0.998439i	$0.517789\pi$
$350$	−0.0140780	−0.000752503 0
$351$	5.64611	0.301367
$352$	0	0
$353$	23.4745	1.24942	0.624712	−	0.780855i	$-0.285216\pi$
$353$	23.4745	1.24942	0.624712	+	0.780855i	$0.285216\pi$
$354$	2.41788	0.128509
$355$	14.4740	0.768200
$356$	6.32048	0.334985
$357$	−0.0297951	−0.00157692
$358$	−0.804520	−0.0425202
$359$	23.7498	1.25347	0.626735	−	0.779233i	$-0.284391\pi$
$359$	23.7498	1.25347	0.626735	+	0.779233i	$0.284391\pi$
$360$	1.99668	0.105234
$361$	−1.85207	−0.0974775
$362$	−8.79042	−0.462014
$363$	0	0
$364$	0.0339551	0.00177973
$365$	−4.38236	−0.229383
$366$	7.75780	0.405507
$367$	−30.1105	−1.57176	−0.785878	−	0.618381i	$-0.787789\pi$
$367$	−30.1105	−1.57176	−0.785878	+	0.618381i	$0.787789\pi$
$368$	9.96508	0.519466
$369$	6.27286	0.326552
$370$	0.0344143	0.00178911
$371$	0.0512220	0.00265931
$372$	−23.6176	−1.22452
$373$	−4.32146	−0.223757	−0.111878	−	0.993722i	$-0.535687\pi$
$373$	−4.32146	−0.223757	−0.111878	+	0.993722i	$0.535687\pi$
$374$	0	0
$375$	−1.46424	−0.0756128
$376$	−5.13989	−0.265069
$377$	−0.897861	−0.0462422
$378$	0.0794862	0.00408833
$379$	−22.5548	−1.15856	−0.579282	−	0.815127i	$-0.696667\pi$
$379$	−22.5548	−1.15856	−0.579282	+	0.815127i	$0.696667\pi$
$380$	6.51828	0.334381
$381$	2.09487	0.107323
$382$	0.249270	0.0127537
$383$	8.11000	0.414402	0.207201	−	0.978298i	$-0.433565\pi$
$383$	8.11000	0.414402	0.207201	+	0.978298i	$0.433565\pi$
$384$	16.3052	0.832071
$385$	0	0
$386$	−3.42390	−0.174272
$387$	−2.83106	−0.143911
$388$	−12.4092	−0.629983
$389$	26.9628	1.36707	0.683534	−	0.729919i	$-0.260442\pi$
$389$	26.9628	1.36707	0.683534	+	0.729919i	$0.260442\pi$
$390$	−0.955597	−0.0483885
$391$	−5.78155	−0.292386
$392$	−16.3267	−0.824621
$393$	18.2463	0.920405
$394$	−1.06494	−0.0536510
$395$	−1.43091	−0.0719970
$396$	0	0
$397$	25.9303	1.30140	0.650702	−	0.759334i	$-0.274475\pi$
$397$	25.9303	1.30140	0.650702	+	0.759334i	$0.274475\pi$
$398$	−10.0083	−0.501669
$399$	0.130796	0.00654800
$400$	1.62589	0.0812946
$401$	17.4286	0.870341	0.435170	−	0.900348i	$-0.356688\pi$
$401$	17.4286	0.870341	0.435170	+	0.900348i	$0.356688\pi$
$402$	11.0630	0.551774
$403$	−10.2470	−0.510441
$404$	0.335720	0.0167027
$405$	5.69920	0.283195
$406$	−0.0126401	−0.000627319 0
$407$	0	0
$408$	−3.22177	−0.159501
$409$	20.1361	0.995666	0.497833	−	0.867273i	$-0.334129\pi$
$409$	20.1361	0.995666	0.497833	+	0.867273i	$0.334129\pi$
$410$	−4.78243	−0.236187
$411$	−0.110186	−0.00543510
$412$	24.0011	1.18245
$413$	−0.0545806	−0.00268573
$414$	3.42400	0.168280
$415$	−6.35117	−0.311767
$416$	5.72617	0.280748
$417$	25.8753	1.26712
$418$	0	0
$419$	2.90916	0.142122	0.0710609	−	0.997472i	$-0.477362\pi$
$419$	2.90916	0.142122	0.0710609	+	0.997472i	$0.477362\pi$
$420$	0.0497183	0.00242600
$421$	−15.0667	−0.734304	−0.367152	−	0.930161i	$-0.619667\pi$
$421$	−15.0667	−0.734304	−0.367152	+	0.930161i	$0.619667\pi$
$422$	−18.2134	−0.886615
$423$	1.88628	0.0917141
$424$	5.53868	0.268982
$425$	−0.943312	−0.0457574
$426$	13.8313	0.670128
$427$	−0.175123	−0.00847478
$428$	−28.1822	−1.36224
$429$	0	0
$430$	2.15840	0.104087
$431$	13.3253	0.641859	0.320929	−	0.947103i	$-0.396005\pi$
$431$	13.3253	0.641859	0.320929	+	0.947103i	$0.396005\pi$
$432$	−9.17997	−0.441671
$433$	33.0717	1.58932	0.794661	−	0.607053i	$-0.207648\pi$
$433$	33.0717	1.58932	0.794661	+	0.607053i	$0.207648\pi$
$434$	−0.144258	−0.00692460
$435$	−1.31468	−0.0630341
$436$	−18.0267	−0.863323
$437$	25.3802	1.21410
$438$	−4.18777	−0.200099
$439$	23.0279	1.09906	0.549532	−	0.835473i	$-0.314806\pi$
$439$	23.0279	1.09906	0.549532	+	0.835473i	$0.314806\pi$
$440$	0	0
$441$	5.99170	0.285319
$442$	−0.615629	−0.0292825
$443$	−6.19307	−0.294241	−0.147121	−	0.989119i	$-0.547001\pi$
$443$	−6.19307	−0.294241	−0.147121	+	0.989119i	$0.547001\pi$
$444$	−0.121538	−0.00576795
$445$	4.01534	0.190346
$446$	6.90228	0.326833
$447$	6.49294	0.307106
$448$	0.0104677	0.000494551 0
$449$	19.4942	0.919988	0.459994	−	0.887922i	$-0.347851\pi$
$449$	19.4942	0.919988	0.459994	+	0.887922i	$0.347851\pi$
$450$	0.558656	0.0263353
$451$	0	0
$452$	7.79111	0.366463
$453$	15.9067	0.747364
$454$	−6.58270	−0.308941
$455$	0.0215714	0.00101128
$456$	14.1431	0.662312
$457$	16.7540	0.783717	0.391859	−	0.920025i	$-0.371832\pi$
$457$	16.7540	0.783717	0.391859	+	0.920025i	$0.371832\pi$
$458$	−15.1753	−0.709095
$459$	5.32605	0.248599
$460$	9.64753	0.449818
$461$	−41.9930	−1.95581	−0.977905	−	0.209049i	$-0.932963\pi$
$461$	−41.9930	−1.95581	−0.977905	+	0.209049i	$0.932963\pi$
$462$	0	0
$463$	−22.3752	−1.03987	−0.519933	−	0.854207i	$-0.674043\pi$
$463$	−22.3752	−1.03987	−0.519933	+	0.854207i	$0.674043\pi$
$464$	1.45982	0.0677706
$465$	−15.0041	−0.695797
$466$	−5.22637	−0.242107
$467$	34.1746	1.58141	0.790705	−	0.612198i	$-0.209714\pi$
$467$	34.1746	1.58141	0.790705	+	0.612198i	$0.209714\pi$
$468$	−1.34743	−0.0622852
$469$	−0.249734	−0.0115317
$470$	−1.43810	−0.0663346
$471$	12.7984	0.589719
$472$	−5.90184	−0.271654
$473$	0	0
$474$	−1.36737	−0.0628056
$475$	4.14101	0.190002
$476$	0.0320303	0.00146811
$477$	−2.03263	−0.0930679
$478$	12.1536	0.555892
$479$	4.40869	0.201438	0.100719	−	0.994915i	$-0.467886\pi$
$479$	4.40869	0.201438	0.100719	+	0.994915i	$0.467886\pi$
$480$	8.38446	0.382696
$481$	−0.0527321	−0.00240438
$482$	−12.7991	−0.582984
$483$	0.193588	0.00880856
$484$	0	0
$485$	−7.88347	−0.357970
$486$	−5.60825	−0.254395
$487$	19.2373	0.871727	0.435864	−	0.900013i	$-0.356443\pi$
$487$	19.2373	0.871727	0.435864	+	0.900013i	$0.356443\pi$
$488$	−18.9362	−0.857200
$489$	28.8000	1.30238
$490$	−4.56807	−0.206364
$491$	6.25527	0.282296	0.141148	−	0.989988i	$-0.454921\pi$
$491$	6.25527	0.282296	0.141148	+	0.989988i	$0.454921\pi$
$492$	16.8897	0.761448
$493$	−0.846963	−0.0381453
$494$	2.70252	0.121592
$495$	0	0
$496$	16.6605	0.748081
$497$	−0.312224	−0.0140052
$498$	−6.06916	−0.271965
$499$	−6.25732	−0.280116	−0.140058	−	0.990143i	$-0.544729\pi$
$499$	−6.25732	−0.280116	−0.140058	+	0.990143i	$0.544729\pi$
$500$	1.57408	0.0703950
$501$	−21.5718	−0.963758
$502$	−6.74826	−0.301190
$503$	30.9182	1.37858	0.689288	−	0.724487i	$-0.257923\pi$
$503$	30.9182	1.37858	0.689288	+	0.724487i	$0.257923\pi$
$504$	−0.0430712	−0.00191854
$505$	0.213280	0.00949083
$506$	0	0
$507$	1.46424	0.0650290
$508$	−2.25202	−0.0999174
$509$	−27.5532	−1.22128	−0.610638	−	0.791910i	$-0.709087\pi$
$509$	−27.5532	−1.22128	−0.610638	+	0.791910i	$0.709087\pi$
$510$	−0.901426	−0.0399158
$511$	0.0945336	0.00418192
$512$	−16.8950	−0.746661
$513$	−23.3806	−1.03228
$514$	11.6450	0.513640
$515$	15.2477	0.671893
$516$	−7.62264	−0.335568
$517$	0	0
$518$	−0.000742364 0	−3.26176e−5 0
$519$	17.7604	0.779594
$520$	2.33253	0.102288
$521$	−16.3130	−0.714684	−0.357342	−	0.933974i	$-0.616317\pi$
$521$	−16.3130	−0.714684	−0.357342	+	0.933974i	$0.616317\pi$
$522$	0.501596	0.0219542
$523$	17.7312	0.775331	0.387666	−	0.921800i	$-0.373282\pi$
$523$	17.7312	0.775331	0.387666	+	0.921800i	$0.373282\pi$
$524$	−19.6151	−0.856891
$525$	0.0315856	0.00137851
$526$	4.97767	0.217037
$527$	−9.66614	−0.421064
$528$	0	0
$529$	14.5646	0.633242
$530$	1.54968	0.0673138
$531$	2.16591	0.0939925
$532$	−0.140608	−0.00609615
$533$	7.32799	0.317410
$534$	3.83705	0.166045
$535$	−17.9039	−0.774054
$536$	−27.0040	−1.16639
$537$	1.80503	0.0778928
$538$	−9.42684	−0.406420
$539$	0	0
$540$	−8.88744	−0.382454
$541$	8.70765	0.374371	0.187186	−	0.982325i	$-0.440063\pi$
$541$	8.70765	0.374371	0.187186	+	0.982325i	$0.440063\pi$
$542$	16.6763	0.716309
$543$	19.7223	0.846364
$544$	5.40156	0.231590
$545$	−11.4522	−0.490559
$546$	0.0206136	0.000882179 0
$547$	33.5698	1.43534	0.717671	−	0.696382i	$-0.245208\pi$
$547$	33.5698	1.43534	0.717671	+	0.696382i	$0.245208\pi$
$548$	0.118453	0.00506004
$549$	6.94936	0.296591
$550$	0	0
$551$	3.71805	0.158394
$552$	20.9328	0.890961
$553$	0.0308668	0.00131259
$554$	6.81802	0.289670
$555$	−0.0772122	−0.00327747
$556$	−27.8165	−1.17968
$557$	22.9483	0.972352	0.486176	−	0.873861i	$-0.338391\pi$
$557$	22.9483	0.972352	0.486176	+	0.873861i	$0.338391\pi$
$558$	5.72456	0.242340
$559$	−3.30725	−0.139882
$560$	−0.0350728	−0.00148209
$561$	0	0
$562$	−15.2370	−0.642735
$563$	−37.7401	−1.59056	−0.795278	−	0.606245i	$-0.792675\pi$
$563$	−37.7401	−1.59056	−0.795278	+	0.606245i	$0.792675\pi$
$564$	5.07883	0.213857
$565$	4.94962	0.208232
$566$	16.1696	0.679659
$567$	−0.122940	−0.00516298
$568$	−33.7611	−1.41658
$569$	16.9841	0.712009	0.356004	−	0.934484i	$-0.384139\pi$
$569$	16.9841	0.712009	0.356004	+	0.934484i	$0.384139\pi$
$570$	3.95713	0.165746
$571$	25.8666	1.08248	0.541242	−	0.840867i	$-0.317954\pi$
$571$	25.8666	1.08248	0.541242	+	0.840867i	$0.317954\pi$
$572$	0	0
$573$	−0.559264	−0.0233636
$574$	0.103164	0.00430597
$575$	6.12899	0.255597
$576$	−0.415386	−0.0173078
$577$	−19.8673	−0.827087	−0.413543	−	0.910484i	$-0.635709\pi$
$577$	−19.8673	−0.827087	−0.413543	+	0.910484i	$0.635709\pi$
$578$	10.5139	0.437320
$579$	7.68191	0.319249
$580$	1.41331	0.0586843
$581$	0.137004	0.00568387
$582$	−7.53342	−0.312270
$583$	0	0
$584$	10.2220	0.422989
$585$	−0.856014	−0.0353918
$586$	−19.2899	−0.796860
$587$	−21.6378	−0.893088	−0.446544	−	0.894762i	$-0.647345\pi$
$587$	−21.6378	−0.893088	−0.446544	+	0.894762i	$0.647345\pi$
$588$	16.1327	0.665301
$589$	42.4330	1.74842
$590$	−1.65129	−0.0679825
$591$	2.38931	0.0982832
$592$	0.0857366	0.00352375
$593$	13.2238	0.543038	0.271519	−	0.962433i	$-0.412474\pi$
$593$	13.2238	0.543038	0.271519	+	0.962433i	$0.412474\pi$
$594$	0	0
$595$	0.0203486	0.000834210 0
$596$	−6.98003	−0.285913
$597$	22.4546	0.919006
$598$	3.99993	0.163569
$599$	−12.3607	−0.505045	−0.252522	−	0.967591i	$-0.581260\pi$
$599$	−12.3607	−0.505045	−0.252522	+	0.967591i	$0.581260\pi$
$600$	3.41538	0.139432
$601$	−26.1446	−1.06646	−0.533230	−	0.845970i	$-0.679022\pi$
$601$	−26.1446	−1.06646	−0.533230	+	0.845970i	$0.679022\pi$
$602$	−0.0465597	−0.00189763
$603$	9.91016	0.403573
$604$	−17.1000	−0.695791
$605$	0	0
$606$	0.203810	0.00827920
$607$	21.1955	0.860297	0.430149	−	0.902758i	$-0.358461\pi$
$607$	21.1955	0.860297	0.430149	+	0.902758i	$0.358461\pi$
$608$	−23.7121	−0.961652
$609$	0.0283595	0.00114918
$610$	−5.29819	−0.214517
$611$	2.20356	0.0891466
$612$	−1.27105	−0.0513792
$613$	−17.6986	−0.714841	−0.357421	−	0.933944i	$-0.616344\pi$
$613$	−17.6986	−0.714841	−0.357421	+	0.933944i	$0.616344\pi$
$614$	6.20830	0.250547
$615$	10.7299	0.432671
$616$	0	0
$617$	13.0707	0.526205	0.263103	−	0.964768i	$-0.415254\pi$
$617$	13.0707	0.526205	0.263103	+	0.964768i	$0.415254\pi$
$618$	14.5706	0.586117
$619$	11.4550	0.460415	0.230208	−	0.973142i	$-0.426059\pi$
$619$	11.4550	0.460415	0.230208	+	0.973142i	$0.426059\pi$
$620$	16.1296	0.647782
$621$	−34.6050	−1.38865
$622$	9.22117	0.369735
$623$	−0.0866166	−0.00347022
$624$	−2.38069	−0.0953038
$625$	1.00000	0.0400000
$626$	5.86188	0.234288
$627$	0	0
$628$	−13.7585	−0.549025
$629$	−0.0497428	−0.00198337
$630$	−0.0120510	−0.000480123 0
$631$	28.1227	1.11955	0.559774	−	0.828645i	$-0.310888\pi$
$631$	28.1227	1.11955	0.559774	+	0.828645i	$0.310888\pi$
$632$	3.33765	0.132765
$633$	40.8638	1.62419
$634$	1.13727	0.0451666
$635$	−1.43069	−0.0567753
$636$	−5.47288	−0.217014
$637$	6.99953	0.277332
$638$	0	0
$639$	12.3899	0.490138
$640$	−11.1356	−0.440175
$641$	−36.4352	−1.43911	−0.719553	−	0.694438i	$-0.755653\pi$
$641$	−36.4352	−1.43911	−0.719553	+	0.694438i	$0.755653\pi$
$642$	−17.1089	−0.675236
$643$	−6.60860	−0.260618	−0.130309	−	0.991473i	$-0.541597\pi$
$643$	−6.60860	−0.260618	−0.130309	+	0.991473i	$0.541597\pi$
$644$	−0.208111	−0.00820071
$645$	−4.84260	−0.190677
$646$	2.54932	0.100302
$647$	−41.0715	−1.61469	−0.807343	−	0.590082i	$-0.799095\pi$
$647$	−41.0715	−1.61469	−0.807343	+	0.590082i	$0.799095\pi$
$648$	−13.2936	−0.522221
$649$	0	0
$650$	0.652625	0.0255981
$651$	0.323659	0.0126852
$652$	−30.9605	−1.21251
$653$	−0.831563	−0.0325416	−0.0162708	−	0.999868i	$-0.505179\pi$
$653$	−0.831563	−0.0325416	−0.0162708	+	0.999868i	$0.505179\pi$
$654$	−10.9437	−0.427933
$655$	−12.4613	−0.486904
$656$	−11.9145	−0.465184
$657$	−3.75136	−0.146354
$658$	0.0310218	0.00120936
$659$	−1.48271	−0.0577582	−0.0288791	−	0.999583i	$-0.509194\pi$
$659$	−1.48271	−0.0577582	−0.0288791	+	0.999583i	$0.509194\pi$
$660$	0	0
$661$	24.0990	0.937341	0.468671	−	0.883373i	$-0.344733\pi$
$661$	24.0990	0.937341	0.468671	+	0.883373i	$0.344733\pi$
$662$	4.69554	0.182497
$663$	1.38123	0.0536426
$664$	14.8143	0.574907
$665$	−0.0893273	−0.00346396
$666$	0.0294591	0.00114152
$667$	5.50299	0.213076
$668$	23.1901	0.897252
$669$	−15.4860	−0.598724
$670$	−7.55551	−0.291895
$671$	0	0
$672$	−0.180864	−0.00697700
$673$	−14.7400	−0.568186	−0.284093	−	0.958797i	$-0.591692\pi$
$673$	−14.7400	−0.568186	−0.284093	+	0.958797i	$0.591692\pi$
$674$	−6.42465	−0.247468
$675$	−5.64611	−0.217319
$676$	−1.57408	−0.0605416
$677$	−32.2136	−1.23807	−0.619035	−	0.785363i	$-0.712476\pi$
$677$	−32.2136	−1.23807	−0.619035	+	0.785363i	$0.712476\pi$
$678$	4.72984	0.181649
$679$	0.170058	0.00652621
$680$	2.20031	0.0843779
$681$	14.7690	0.565950
$682$	0	0
$683$	30.3594	1.16167	0.580836	−	0.814021i	$-0.302726\pi$
$683$	30.3594	1.16167	0.580836	+	0.814021i	$0.302726\pi$
$684$	5.57974	0.213347
$685$	0.0752519	0.00287523
$686$	0.197086	0.00752478
$687$	34.0474	1.29899
$688$	5.37724	0.205005
$689$	−2.37453	−0.0904625
$690$	5.85685	0.222966
$691$	−8.57639	−0.326261	−0.163131	−	0.986604i	$-0.552159\pi$
$691$	−8.57639	−0.326261	−0.163131	+	0.986604i	$0.552159\pi$
$692$	−19.0927	−0.725797
$693$	0	0
$694$	3.30569	0.125482
$695$	−17.6716	−0.670320
$696$	3.06654	0.116237
$697$	6.91258	0.261833
$698$	1.36200	0.0515525
$699$	11.7259	0.443515
$700$	−0.0339551	−0.00128338
$701$	6.03629	0.227988	0.113994	−	0.993481i	$-0.463636\pi$
$701$	6.03629	0.227988	0.113994	+	0.993481i	$0.463636\pi$
$702$	−3.68479	−0.139074
$703$	0.218364	0.00823575
$704$	0	0
$705$	3.22654	0.121518
$706$	−15.3201	−0.576579
$707$	−0.00460075	−0.000173029 0
$708$	5.83173	0.219170
$709$	−15.4778	−0.581280	−0.290640	−	0.956833i	$-0.593868\pi$
$709$	−15.4778	−0.581280	−0.290640	+	0.956833i	$0.593868\pi$
$710$	−9.44609	−0.354505
$711$	−1.22488	−0.0459366
$712$	−9.36593	−0.351003
$713$	62.8039	2.35203
$714$	0.0194450	0.000727712 0
$715$	0	0
$716$	−1.94044	−0.0725176
$717$	−27.2679	−1.01834
$718$	−15.4997	−0.578445
$719$	−23.9737	−0.894067	−0.447033	−	0.894517i	$-0.647520\pi$
$719$	−23.9737	−0.894067	−0.447033	+	0.894517i	$0.647520\pi$
$720$	1.39179	0.0518688
$721$	−0.328914	−0.0122494
$722$	1.20871	0.0449835
$723$	28.7162	1.06797
$724$	−21.2018	−0.787959
$725$	0.897861	0.0333457
$726$	0	0
$727$	38.7434	1.43691	0.718456	−	0.695572i	$-0.244849\pi$
$727$	38.7434	1.43691	0.718456	+	0.695572i	$0.244849\pi$
$728$	−0.0503160	−0.00186484
$729$	29.6803	1.09927
$730$	2.86004	0.105855
$731$	−3.11977	−0.115389
$732$	18.7112	0.691586
$733$	35.6170	1.31554	0.657771	−	0.753218i	$-0.271499\pi$
$733$	35.6170	1.31554	0.657771	+	0.753218i	$0.271499\pi$
$734$	19.6509	0.725327
$735$	10.2490	0.378039
$736$	−35.0956	−1.29364
$737$	0	0
$738$	−4.09383	−0.150696
$739$	−12.6216	−0.464293	−0.232146	−	0.972681i	$-0.574575\pi$
$739$	−12.6216	−0.464293	−0.232146	+	0.972681i	$0.574575\pi$
$740$	0.0830045	0.00305131
$741$	−6.06341	−0.222745
$742$	−0.0334288	−0.00122721
$743$	−1.85904	−0.0682017	−0.0341008	−	0.999418i	$-0.510857\pi$
$743$	−1.85904	−0.0682017	−0.0341008	+	0.999418i	$0.510857\pi$
$744$	34.9975	1.28307
$745$	−4.43435	−0.162462
$746$	2.82029	0.103258
$747$	−5.43669	−0.198918
$748$	0	0
$749$	0.386213	0.0141119
$750$	0.955597	0.0348935
$751$	−10.7509	−0.392306	−0.196153	−	0.980573i	$-0.562845\pi$
$751$	−10.7509	−0.392306	−0.196153	+	0.980573i	$0.562845\pi$
$752$	−3.58275	−0.130650
$753$	15.1405	0.551749
$754$	0.585967	0.0213396
$755$	−10.8635	−0.395364
$756$	0.191714	0.00697259
$757$	−19.3195	−0.702179	−0.351089	−	0.936342i	$-0.614189\pi$
$757$	−19.3195	−0.702179	−0.351089	+	0.936342i	$0.614189\pi$
$758$	14.7199	0.534649
$759$	0	0
$760$	−9.65904	−0.350370
$761$	−5.86123	−0.212469	−0.106235	−	0.994341i	$-0.533879\pi$
$761$	−5.86123	−0.212469	−0.106235	+	0.994341i	$0.533879\pi$
$762$	−1.36716	−0.0495271
$763$	0.247041	0.00894347
$764$	0.601219	0.0217513
$765$	−0.807488	−0.0291948
$766$	−5.29279	−0.191236
$767$	2.53023	0.0913613
$768$	−12.0622	−0.435259
$769$	38.9298	1.40384	0.701922	−	0.712254i	$-0.252326\pi$
$769$	38.9298	1.40384	0.701922	+	0.712254i	$0.252326\pi$
$770$	0	0
$771$	−26.1269	−0.940937
$772$	−8.25819	−0.297219
$773$	46.1552	1.66009	0.830044	−	0.557698i	$-0.188315\pi$
$773$	46.1552	1.66009	0.830044	+	0.557698i	$0.188315\pi$
$774$	1.84762	0.0664113
$775$	10.2470	0.368084
$776$	18.3885	0.660108
$777$	0.00166557	5.97522e−5 0
$778$	−17.5966	−0.630868
$779$	−30.3452	−1.08723
$780$	−2.30483	−0.0825260
$781$	0	0
$782$	3.77319	0.134929
$783$	−5.06943	−0.181166
$784$	−11.3805	−0.406446
$785$	−8.74067	−0.311968
$786$	−11.9080	−0.424744
$787$	−45.2311	−1.61231	−0.806157	−	0.591702i	$-0.798456\pi$
$787$	−45.2311	−1.61231	−0.806157	+	0.591702i	$0.798456\pi$
$788$	−2.56855	−0.0915010
$789$	−11.1679	−0.397589
$790$	0.933849	0.0332249
$791$	−0.106770	−0.00379632
$792$	0	0
$793$	8.11828	0.288288
$794$	−16.9227	−0.600566
$795$	−3.47688	−0.123312
$796$	−24.1391	−0.855589
$797$	−11.2911	−0.399950	−0.199975	−	0.979801i	$-0.564086\pi$
$797$	−11.2911	−0.399950	−0.199975	+	0.979801i	$0.564086\pi$
$798$	−0.0853609	−0.00302174
$799$	2.07865	0.0735373
$800$	−5.72617	−0.202451
$801$	3.43719	0.121447
$802$	−11.3743	−0.401641
$803$	0	0
$804$	26.6832	0.941044
$805$	−0.132211	−0.00465982
$806$	6.68746	0.235556
$807$	21.1502	0.744521
$808$	−0.497483	−0.0175014
$809$	−31.9482	−1.12324	−0.561620	−	0.827396i	$-0.689822\pi$
$809$	−31.9482	−1.12324	−0.561620	+	0.827396i	$0.689822\pi$
$810$	−3.71944	−0.130688
$811$	15.0932	0.529994	0.264997	−	0.964249i	$-0.414629\pi$
$811$	15.0932	0.529994	0.264997	+	0.964249i	$0.414629\pi$
$812$	−0.0304870	−0.00106988
$813$	−37.4151	−1.31221
$814$	0	0
$815$	−19.6690	−0.688974
$816$	−2.24573	−0.0786163
$817$	13.6954	0.479140
$818$	−13.1413	−0.459475
$819$	0.0184654	0.000645234 0
$820$	−11.5348	−0.402814
$821$	−51.2425	−1.78838	−0.894188	−	0.447692i	$-0.852246\pi$
$821$	−51.2425	−1.78838	−0.894188	+	0.447692i	$0.852246\pi$
$822$	0.0719105	0.00250817
$823$	15.4202	0.537514	0.268757	−	0.963208i	$-0.413387\pi$
$823$	15.4202	0.537514	0.268757	+	0.963208i	$0.413387\pi$
$824$	−35.5658	−1.23899
$825$	0	0
$826$	0.0356206	0.00123940
$827$	−28.9735	−1.00751	−0.503754	−	0.863847i	$-0.668048\pi$
$827$	−28.9735	−1.00751	−0.503754	+	0.863847i	$0.668048\pi$
$828$	8.25842	0.287000
$829$	−15.7105	−0.545649	−0.272824	−	0.962064i	$-0.587958\pi$
$829$	−15.7105	−0.545649	−0.272824	+	0.962064i	$0.587958\pi$
$830$	4.14493	0.143873
$831$	−15.2970	−0.530646
$832$	−0.485257	−0.0168232
$833$	6.60275	0.228772
$834$	−16.8869	−0.584745
$835$	14.7325	0.509838
$836$	0	0
$837$	−57.8559	−1.99979
$838$	−1.89859	−0.0655858
$839$	39.6206	1.36785	0.683927	−	0.729550i	$-0.260271\pi$
$839$	39.6206	1.36785	0.683927	+	0.729550i	$0.260271\pi$
$840$	−0.0736745	−0.00254201
$841$	−28.1938	−0.972202
$842$	9.83288	0.338864
$843$	34.1860	1.17743
$844$	−43.9293	−1.51211
$845$	−1.00000	−0.0344010
$846$	−1.23103	−0.0423238
$847$	0	0
$848$	3.86073	0.132578
$849$	−36.2782	−1.24507
$850$	0.615629	0.0211159
$851$	0.323194	0.0110790
$852$	33.3600	1.14290
$853$	33.0056	1.13009	0.565045	−	0.825060i	$-0.308859\pi$
$853$	33.0056	1.13009	0.565045	+	0.825060i	$0.308859\pi$
$854$	0.114289	0.00391090
$855$	3.54476	0.121228
$856$	41.7615	1.42738
$857$	38.3809	1.31107	0.655534	−	0.755166i	$-0.272444\pi$
$857$	38.3809	1.31107	0.655534	+	0.755166i	$0.272444\pi$
$858$	0	0
$859$	−6.59064	−0.224870	−0.112435	−	0.993659i	$-0.535865\pi$
$859$	−6.59064	−0.224870	−0.112435	+	0.993659i	$0.535865\pi$
$860$	5.20589	0.177519
$861$	−0.231459	−0.00788810
$862$	−8.69644	−0.296202
$863$	11.4710	0.390476	0.195238	−	0.980756i	$-0.437452\pi$
$863$	11.4710	0.390476	0.195238	+	0.980756i	$0.437452\pi$
$864$	32.3306	1.09991
$865$	−12.1295	−0.412414
$866$	−21.5834	−0.733433
$867$	−23.5891	−0.801127
$868$	−0.347939	−0.0118098
$869$	0	0
$870$	0.857993	0.0290887
$871$	11.5771	0.392275
$872$	26.7127	0.904606
$873$	−6.74836	−0.228397
$874$	−16.5638	−0.560277
$875$	−0.0215714	−0.000729246 0
$876$	−10.1006	−0.341267
$877$	−55.3903	−1.87040	−0.935199	−	0.354122i	$-0.884780\pi$
$877$	−55.3903	−1.87040	−0.935199	+	0.354122i	$0.884780\pi$
$878$	−15.0286	−0.507191
$879$	43.2791	1.45977
$880$	0	0
$881$	−40.3557	−1.35962	−0.679810	−	0.733389i	$-0.737938\pi$
$881$	−40.3557	−1.35962	−0.679810	+	0.733389i	$0.737938\pi$
$882$	−3.91033	−0.131668
$883$	−28.2815	−0.951747	−0.475874	−	0.879514i	$-0.657868\pi$
$883$	−28.2815	−0.951747	−0.475874	+	0.879514i	$0.657868\pi$
$884$	−1.48485	−0.0499409
$885$	3.70485	0.124537
$886$	4.04175	0.135785
$887$	54.7993	1.83998	0.919989	−	0.391943i	$-0.128197\pi$
$887$	54.7993	1.83998	0.919989	+	0.391943i	$0.128197\pi$
$888$	0.180100	0.00604376
$889$	0.0308620	0.00103508
$890$	−2.62051	−0.0878398
$891$	0	0
$892$	16.6478	0.557408
$893$	−9.12497	−0.305355
$894$	−4.23745	−0.141722
$895$	−1.23274	−0.0412061
$896$	0.240211	0.00802490
$897$	−8.97429	−0.299643
$898$	−12.7224	−0.424552
$899$	9.20040	0.306851
$900$	1.34743	0.0449145
$901$	−2.23993	−0.0746228
$902$	0	0
$903$	0.104462	0.00347627
$904$	−11.5452	−0.383987
$905$	−13.4693	−0.447736
$906$	−10.3811	−0.344890
$907$	52.7060	1.75007	0.875037	−	0.484057i	$-0.160837\pi$
$907$	52.7060	1.75007	0.875037	+	0.484057i	$0.160837\pi$
$908$	−15.8770	−0.526895
$909$	0.182571	0.00605548
$910$	−0.0140780	−0.000466682 0
$911$	−53.1427	−1.76070	−0.880348	−	0.474329i	$-0.842691\pi$
$911$	−53.1427	−1.76070	−0.880348	+	0.474329i	$0.842691\pi$
$912$	9.85844	0.326446
$913$	0	0
$914$	−10.9341	−0.361666
$915$	11.8871	0.392974
$916$	−36.6016	−1.20935
$917$	0.268808	0.00887683
$918$	−3.47591	−0.114722
$919$	5.37402	0.177272	0.0886362	−	0.996064i	$-0.471749\pi$
$919$	5.37402	0.177272	0.0886362	+	0.996064i	$0.471749\pi$
$920$	−14.2961	−0.471328
$921$	−13.9290	−0.458976
$922$	27.4057	0.902559
$923$	14.4740	0.476417
$924$	0	0
$925$	0.0527321	0.00173382
$926$	14.6026	0.479872
$927$	13.0522	0.428692
$928$	−5.14130	−0.168771
$929$	−50.9686	−1.67223	−0.836113	−	0.548558i	$-0.815177\pi$
$929$	−50.9686	−1.67223	−0.836113	+	0.548558i	$0.815177\pi$
$930$	9.79202	0.321093
$931$	−28.9851	−0.949949
$932$	−12.6056	−0.412910
$933$	−20.6887	−0.677318
$934$	−22.3032	−0.729782
$935$	0	0
$936$	1.99668	0.0652636
$937$	15.6972	0.512805	0.256403	−	0.966570i	$-0.417463\pi$
$937$	15.6972	0.512805	0.256403	+	0.966570i	$0.417463\pi$
$938$	0.162983	0.00532158
$939$	−13.1518	−0.429192
$940$	−3.46859	−0.113133
$941$	−11.7289	−0.382351	−0.191175	−	0.981556i	$-0.561230\pi$
$941$	−11.7289	−0.382351	−0.191175	+	0.981556i	$0.561230\pi$
$942$	−8.35256	−0.272141
$943$	−44.9132	−1.46258
$944$	−4.11388	−0.133895
$945$	0.121795	0.00396198
$946$	0	0
$947$	−5.92874	−0.192658	−0.0963291	−	0.995350i	$-0.530710\pi$
$947$	−5.92874	−0.192658	−0.0963291	+	0.995350i	$0.530710\pi$
$948$	−3.29800	−0.107114
$949$	−4.38236	−0.142257
$950$	−2.70252	−0.0876814
$951$	−2.55158	−0.0827407
$952$	−0.0474637	−0.00153831
$953$	−26.9527	−0.873082	−0.436541	−	0.899684i	$-0.643797\pi$
$953$	−26.9527	−0.873082	−0.436541	+	0.899684i	$0.643797\pi$
$954$	1.32655	0.0429486
$955$	0.381949	0.0123596
$956$	29.3135	0.948066
$957$	0	0
$958$	−2.87722	−0.0929589
$959$	−0.00162329	−5.24187e−5 0
$960$	−0.710530	−0.0229323
$961$	74.0015	2.38714
$962$	0.0344143	0.00110956
$963$	−15.3260	−0.493874
$964$	−30.8705	−0.994271
$965$	−5.24636	−0.168886
$966$	−0.126340	−0.00406494
$967$	36.3652	1.16942	0.584712	−	0.811241i	$-0.301207\pi$
$967$	36.3652	1.16942	0.584712	+	0.811241i	$0.301207\pi$
$968$	0	0
$969$	−5.71969	−0.183743
$970$	5.14495	0.165194
$971$	36.5391	1.17260	0.586298	−	0.810095i	$-0.300585\pi$
$971$	36.5391	1.17260	0.586298	+	0.810095i	$0.300585\pi$
$972$	−13.5267	−0.433868
$973$	0.381200	0.0122207
$974$	−12.5548	−0.402281
$975$	−1.46424	−0.0468931
$976$	−13.1994	−0.422504
$977$	23.3433	0.746817	0.373409	−	0.927667i	$-0.378189\pi$
$977$	23.3433	0.746817	0.373409	+	0.927667i	$0.378189\pi$
$978$	−18.7956	−0.601017
$979$	0	0
$980$	−11.0178	−0.351952
$981$	−9.80326	−0.312994
$982$	−4.08234	−0.130273
$983$	20.9729	0.668932	0.334466	−	0.942408i	$-0.391444\pi$
$983$	20.9729	0.668932	0.334466	+	0.942408i	$0.391444\pi$
$984$	−25.0279	−0.797859
$985$	−1.63178	−0.0519929
$986$	0.552749	0.0176031
$987$	−0.0696009	−0.00221542
$988$	6.51828	0.207374
$989$	20.2701	0.644553
$990$	0	0
$991$	−13.6667	−0.434137	−0.217068	−	0.976156i	$-0.569649\pi$
$991$	−13.6667	−0.434137	−0.217068	+	0.976156i	$0.569649\pi$
$992$	−58.6762	−1.86297
$993$	−10.5350	−0.334317
$994$	0.203765	0.00646304
$995$	−15.3354	−0.486164
$996$	−14.6383	−0.463833
$997$	−39.8342	−1.26156	−0.630780	−	0.775962i	$-0.717265\pi$
$997$	−39.8342	−1.26156	−0.630780	+	0.775962i	$0.717265\pi$
$998$	4.08368	0.129267
$999$	−0.297731	−0.00941980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7865.2.a.u.1.4	yes	8
11.10	odd	2		7865.2.a.t.1.5	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7865.2.a.t.1.5	✓	8	11.10	odd	2
7865.2.a.u.1.4	yes	8	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7865 = 5 \cdot 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7865.a (trivial)

\(f(q)\)	\(=\)	\(q-0.652625 q^{2} +1.46424 q^{3} -1.57408 q^{4} -1.00000 q^{5} -0.955597 q^{6} +0.0215714 q^{7} +2.33253 q^{8} -0.856014 q^{9} +0.652625 q^{10} -2.30483 q^{12} -1.00000 q^{13} -0.0140780 q^{14} -1.46424 q^{15} +1.62589 q^{16} -0.943312 q^{17} +0.558656 q^{18} +4.14101 q^{19} +1.57408 q^{20} +0.0315856 q^{21} +6.12899 q^{23} +3.41538 q^{24} +1.00000 q^{25} +0.652625 q^{26} -5.64611 q^{27} -0.0339551 q^{28} +0.897861 q^{29} +0.955597 q^{30} +10.2470 q^{31} -5.72617 q^{32} +0.615629 q^{34} -0.0215714 q^{35} +1.34743 q^{36} +0.0527321 q^{37} -2.70252 q^{38} -1.46424 q^{39} -2.33253 q^{40} -7.32799 q^{41} -0.0206136 q^{42} +3.30725 q^{43} +0.856014 q^{45} -3.99993 q^{46} -2.20356 q^{47} +2.38069 q^{48} -6.99953 q^{49} -0.652625 q^{50} -1.38123 q^{51} +1.57408 q^{52} +2.37453 q^{53} +3.68479 q^{54} +0.0503160 q^{56} +6.06341 q^{57} -0.585967 q^{58} -2.53023 q^{59} +2.30483 q^{60} -8.11828 q^{61} -6.68746 q^{62} -0.0184654 q^{63} +0.485257 q^{64} +1.00000 q^{65} -11.5771 q^{67} +1.48485 q^{68} +8.97429 q^{69} +0.0140780 q^{70} -14.4740 q^{71} -1.99668 q^{72} +4.38236 q^{73} -0.0344143 q^{74} +1.46424 q^{75} -6.51828 q^{76} +0.955597 q^{78} +1.43091 q^{79} -1.62589 q^{80} -5.69920 q^{81} +4.78243 q^{82} +6.35117 q^{83} -0.0497183 q^{84} +0.943312 q^{85} -2.15840 q^{86} +1.31468 q^{87} -4.01534 q^{89} -0.558656 q^{90} -0.0215714 q^{91} -9.64753 q^{92} +15.0041 q^{93} +1.43810 q^{94} -4.14101 q^{95} -8.38446 q^{96} +7.88347 q^{97} +4.56807 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} - 5 q^{3} + 7 q^{4} - 8 q^{5} - 7 q^{6} + 9 q^{7} + 3 q^{8} + 3 q^{9} - q^{10} - 15 q^{12} - 8 q^{13} - 7 q^{14} + 5 q^{15} + 9 q^{16} + 4 q^{17} + 8 q^{18} + 16 q^{19} - 7 q^{20} - 23 q^{21}+ \cdots + 41 q^{98}+O(q^{100}) \) 8 * q + q^2 - 5 * q^3 + 7 * q^4 - 8 * q^5 - 7 * q^6 + 9 * q^7 + 3 * q^8 + 3 * q^9 - q^10 - 15 * q^12 - 8 * q^13 - 7 * q^14 + 5 * q^15 + 9 * q^16 + 4 * q^17 + 8 * q^18 + 16 * q^19 - 7 * q^20 - 23 * q^21 - 9 * q^23 + 5 * q^24 + 8 * q^25 - q^26 - 11 * q^27 + 11 * q^28 - 13 * q^29 + 7 * q^30 - 28 * q^32 + 13 * q^34 - 9 * q^35 + 12 * q^36 - 5 * q^37 + 55 * q^38 + 5 * q^39 - 3 * q^40 + 13 * q^41 - 5 * q^42 + 5 * q^43 - 3 * q^45 + 27 * q^46 + 10 * q^47 - 36 * q^48 + 23 * q^49 + q^50 - 37 * q^51 - 7 * q^52 + 14 * q^53 - 45 * q^54 - 18 * q^56 - 21 * q^57 + 3 * q^58 - 20 * q^59 + 15 * q^60 + 6 * q^61 + 25 * q^62 + 26 * q^63 - 3 * q^64 + 8 * q^65 + 4 * q^67 - 9 * q^69 + 7 * q^70 - 9 * q^71 + 35 * q^72 + 10 * q^73 + 42 * q^74 - 5 * q^75 + 19 * q^76 + 7 * q^78 + 13 * q^79 - 9 * q^80 + 16 * q^82 + 26 * q^83 - 58 * q^84 - 4 * q^85 + 26 * q^86 + 11 * q^87 - 6 * q^89 - 8 * q^90 - 9 * q^91 - 16 * q^92 + 3 * q^93 + 23 * q^94 - 16 * q^95 + 21 * q^96 + 26 * q^97 + 41 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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