LMFDB - Embedded newform 7595.2.a.bf.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.239569 q^{2} +1.70292 q^{3} -1.94261 q^{4} +1.00000 q^{5} +0.407968 q^{6} -0.944527 q^{8} -0.100048 q^{9} +O(q^{10})$	\(q+0.239569 q^{2} +1.70292 q^{3} -1.94261 q^{4} +1.00000 q^{5} +0.407968 q^{6} -0.944527 q^{8} -0.100048 q^{9} +0.239569 q^{10} +5.19399 q^{11} -3.30811 q^{12} -6.25906 q^{13} +1.70292 q^{15} +3.65893 q^{16} +5.57339 q^{17} -0.0239685 q^{18} -7.11374 q^{19} -1.94261 q^{20} +1.24432 q^{22} -3.61033 q^{23} -1.60846 q^{24} +1.00000 q^{25} -1.49948 q^{26} -5.27915 q^{27} +8.27304 q^{29} +0.407968 q^{30} -1.00000 q^{31} +2.76562 q^{32} +8.84497 q^{33} +1.33521 q^{34} +0.194355 q^{36} +3.38680 q^{37} -1.70423 q^{38} -10.6587 q^{39} -0.944527 q^{40} -10.1966 q^{41} -10.2038 q^{43} -10.0899 q^{44} -0.100048 q^{45} -0.864925 q^{46} -4.10601 q^{47} +6.23089 q^{48} +0.239569 q^{50} +9.49106 q^{51} +12.1589 q^{52} -4.22249 q^{53} -1.26472 q^{54} +5.19399 q^{55} -12.1142 q^{57} +1.98197 q^{58} -0.482536 q^{59} -3.30811 q^{60} -1.65374 q^{61} -0.239569 q^{62} -6.65531 q^{64} -6.25906 q^{65} +2.11898 q^{66} +3.31448 q^{67} -10.8269 q^{68} -6.14812 q^{69} +6.58780 q^{71} +0.0944984 q^{72} -13.9619 q^{73} +0.811373 q^{74} +1.70292 q^{75} +13.8192 q^{76} -2.55350 q^{78} +4.32480 q^{79} +3.65893 q^{80} -8.68985 q^{81} -2.44278 q^{82} +12.1598 q^{83} +5.57339 q^{85} -2.44451 q^{86} +14.0884 q^{87} -4.90587 q^{88} +15.5248 q^{89} -0.0239685 q^{90} +7.01346 q^{92} -1.70292 q^{93} -0.983674 q^{94} -7.11374 q^{95} +4.70965 q^{96} +7.50753 q^{97} -0.519650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.239569	0.169401	0.0847005	−	0.996406i	$-0.473007\pi$
$2$	0.239569	0.169401	0.0847005	+	0.996406i	$0.473007\pi$
$3$	1.70292	0.983184	0.491592	−	0.870826i	$-0.336415\pi$
$3$	1.70292	0.983184	0.491592	+	0.870826i	$0.336415\pi$
$4$	−1.94261	−0.971303
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.407968	0.166552
$7$	0	0
$7$	0	0
$8$	−0.944527	−0.333941
$9$	−0.100048	−0.0333494
$10$	0.239569	0.0757585
$11$	5.19399	1.56605	0.783023	−	0.621992i	$-0.213676\pi$
$11$	5.19399	1.56605	0.783023	+	0.621992i	$0.213676\pi$
$12$	−3.30811	−0.954970
$13$	−6.25906	−1.73595	−0.867976	−	0.496607i	$-0.834579\pi$
$13$	−6.25906	−1.73595	−0.867976	+	0.496607i	$0.834579\pi$
$14$	0	0
$15$	1.70292	0.439693
$16$	3.65893	0.914733
$17$	5.57339	1.35175	0.675873	−	0.737018i	$-0.263767\pi$
$17$	5.57339	1.35175	0.675873	+	0.737018i	$0.263767\pi$
$18$	−0.0239685	−0.00564943
$19$	−7.11374	−1.63200	−0.816002	−	0.578049i	$-0.803814\pi$
$19$	−7.11374	−1.63200	−0.816002	+	0.578049i	$0.803814\pi$
$20$	−1.94261	−0.434380
$21$	0	0
$22$	1.24432	0.265290
$23$	−3.61033	−0.752806	−0.376403	−	0.926456i	$-0.622839\pi$
$23$	−3.61033	−0.752806	−0.376403	+	0.926456i	$0.622839\pi$
$24$	−1.60846	−0.328325
$25$	1.00000	0.200000
$26$	−1.49948	−0.294072
$27$	−5.27915	−1.01597
$28$	0	0
$29$	8.27304	1.53627	0.768133	−	0.640290i	$-0.221186\pi$
$29$	8.27304	1.53627	0.768133	+	0.640290i	$0.221186\pi$
$30$	0.407968	0.0744845
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	2.76562	0.488898
$33$	8.84497	1.53971
$34$	1.33521	0.228987
$35$	0	0
$36$	0.194355	0.0323924
$37$	3.38680	0.556787	0.278393	−	0.960467i	$-0.410198\pi$
$37$	3.38680	0.556787	0.278393	+	0.960467i	$0.410198\pi$
$38$	−1.70423	−0.276463
$39$	−10.6587	−1.70676
$40$	−0.944527	−0.149343
$41$	−10.1966	−1.59243	−0.796217	−	0.605011i	$-0.793169\pi$
$41$	−10.1966	−1.59243	−0.796217	+	0.605011i	$0.793169\pi$
$42$	0	0
$43$	−10.2038	−1.55606	−0.778030	−	0.628227i	$-0.783781\pi$
$43$	−10.2038	−1.55606	−0.778030	+	0.628227i	$0.783781\pi$
$44$	−10.0899	−1.52111
$45$	−0.100048	−0.0149143
$46$	−0.864925	−0.127526
$47$	−4.10601	−0.598923	−0.299462	−	0.954108i	$-0.596807\pi$
$47$	−4.10601	−0.598923	−0.299462	+	0.954108i	$0.596807\pi$
$48$	6.23089	0.899351
$49$	0	0
$50$	0.239569	0.0338802
$51$	9.49106	1.32901
$52$	12.1589	1.68614
$53$	−4.22249	−0.580003	−0.290001	−	0.957026i	$-0.593656\pi$
$53$	−4.22249	−0.580003	−0.290001	+	0.957026i	$0.593656\pi$
$54$	−1.26472	−0.172107
$55$	5.19399	0.700357
$56$	0	0
$57$	−12.1142	−1.60456
$58$	1.98197	0.260245
$59$	−0.482536	−0.0628208	−0.0314104	−	0.999507i	$-0.510000\pi$
$59$	−0.482536	−0.0628208	−0.0314104	+	0.999507i	$0.510000\pi$
$60$	−3.30811	−0.427075
$61$	−1.65374	−0.211740	−0.105870	−	0.994380i	$-0.533763\pi$
$61$	−1.65374	−0.211740	−0.105870	+	0.994380i	$0.533763\pi$
$62$	−0.239569	−0.0304253
$63$	0	0
$64$	−6.65531	−0.831914
$65$	−6.25906	−0.776341
$66$	2.11898	0.260829
$67$	3.31448	0.404928	0.202464	−	0.979290i	$-0.435105\pi$
$67$	3.31448	0.404928	0.202464	+	0.979290i	$0.435105\pi$
$68$	−10.8269	−1.31295
$69$	−6.14812	−0.740147
$70$	0	0
$71$	6.58780	0.781828	0.390914	−	0.920427i	$-0.372159\pi$
$71$	6.58780	0.781828	0.390914	+	0.920427i	$0.372159\pi$
$72$	0.0944984	0.0111367
$73$	−13.9619	−1.63411	−0.817056	−	0.576558i	$-0.804395\pi$
$73$	−13.9619	−1.63411	−0.817056	+	0.576558i	$0.804395\pi$
$74$	0.811373	0.0943202
$75$	1.70292	0.196637
$76$	13.8192	1.58517
$77$	0	0
$78$	−2.55350	−0.289127
$79$	4.32480	0.486578	0.243289	−	0.969954i	$-0.421774\pi$
$79$	4.32480	0.486578	0.243289	+	0.969954i	$0.421774\pi$
$80$	3.65893	0.409081
$81$	−8.68985	−0.965538
$82$	−2.44278	−0.269760
$83$	12.1598	1.33471	0.667354	−	0.744741i	$-0.267427\pi$
$83$	12.1598	1.33471	0.667354	+	0.744741i	$0.267427\pi$
$84$	0	0
$85$	5.57339	0.604519
$86$	−2.44451	−0.263598
$87$	14.0884	1.51043
$88$	−4.90587	−0.522967
$89$	15.5248	1.64562	0.822812	−	0.568313i	$-0.192404\pi$
$89$	15.5248	1.64562	0.822812	+	0.568313i	$0.192404\pi$
$90$	−0.0239685	−0.00252650
$91$	0	0
$92$	7.01346	0.731203
$93$	−1.70292	−0.176585
$94$	−0.983674	−0.101458
$95$	−7.11374	−0.729854
$96$	4.70965	0.480676
$97$	7.50753	0.762274	0.381137	−	0.924519i	$-0.375533\pi$
$97$	7.50753	0.762274	0.381137	+	0.924519i	$0.375533\pi$
$98$	0	0
$99$	−0.519650	−0.0522268
$100$	−1.94261	−0.194261
$101$	−10.3103	−1.02591	−0.512955	−	0.858416i	$-0.671449\pi$
$101$	−10.3103	−1.02591	−0.512955	+	0.858416i	$0.671449\pi$
$102$	2.27377	0.225136
$103$	0.881099	0.0868172	0.0434086	−	0.999057i	$-0.486178\pi$
$103$	0.881099	0.0868172	0.0434086	+	0.999057i	$0.486178\pi$
$104$	5.91185	0.579705
$105$	0	0
$106$	−1.01158	−0.0982531
$107$	−3.69141	−0.356862	−0.178431	−	0.983952i	$-0.557102\pi$
$107$	−3.69141	−0.356862	−0.178431	+	0.983952i	$0.557102\pi$
$108$	10.2553	0.986817
$109$	−14.6337	−1.40166	−0.700829	−	0.713329i	$-0.747187\pi$
$109$	−14.6337	−1.40166	−0.700829	+	0.713329i	$0.747187\pi$
$110$	1.24432	0.118641
$111$	5.76747	0.547424
$112$	0	0
$113$	−11.5618	−1.08764	−0.543821	−	0.839201i	$-0.683023\pi$
$113$	−11.5618	−1.08764	−0.543821	+	0.839201i	$0.683023\pi$
$114$	−2.90218	−0.271814
$115$	−3.61033	−0.336665
$116$	−16.0713	−1.49218
$117$	0.626209	0.0578930
$118$	−0.115601	−0.0106419
$119$	0	0
$120$	−1.60846	−0.146832
$121$	15.9775	1.45250
$122$	−0.396186	−0.0358690
$123$	−17.3640	−1.56566
$124$	1.94261	0.174451
$125$	1.00000	0.0894427
$126$	0	0
$127$	−11.5350	−1.02356	−0.511782	−	0.859115i	$-0.671014\pi$
$127$	−11.5350	−1.02356	−0.511782	+	0.859115i	$0.671014\pi$
$128$	−7.12565	−0.629825
$129$	−17.3763	−1.52989
$130$	−1.49948	−0.131513
$131$	−13.0398	−1.13929	−0.569644	−	0.821891i	$-0.692919\pi$
$131$	−13.0398	−1.13929	−0.569644	+	0.821891i	$0.692919\pi$
$132$	−17.1823	−1.49553
$133$	0	0
$134$	0.794048	0.0685953
$135$	−5.27915	−0.454357
$136$	−5.26422	−0.451403
$137$	−8.81843	−0.753410	−0.376705	−	0.926333i	$-0.622943\pi$
$137$	−8.81843	−0.753410	−0.376705	+	0.926333i	$0.622943\pi$
$138$	−1.47290	−0.125382
$139$	−11.0136	−0.934161	−0.467080	−	0.884215i	$-0.654694\pi$
$139$	−11.0136	−0.934161	−0.467080	+	0.884215i	$0.654694\pi$
$140$	0	0
$141$	−6.99223	−0.588852
$142$	1.57823	0.132442
$143$	−32.5095	−2.71858
$144$	−0.366070	−0.0305058
$145$	8.27304	0.687039
$146$	−3.34483	−0.276820
$147$	0	0
$148$	−6.57922	−0.540809
$149$	0.300376	0.0246077	0.0123039	−	0.999924i	$-0.496083\pi$
$149$	0.300376	0.0246077	0.0123039	+	0.999924i	$0.496083\pi$
$150$	0.407968	0.0333105
$151$	13.1249	1.06809	0.534044	−	0.845457i	$-0.320672\pi$
$151$	13.1249	1.06809	0.534044	+	0.845457i	$0.320672\pi$
$152$	6.71912	0.544993
$153$	−0.557608	−0.0450800
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	20.7057	1.65778
$157$	−14.1342	−1.12803	−0.564016	−	0.825764i	$-0.690744\pi$
$157$	−14.1342	−1.12803	−0.564016	+	0.825764i	$0.690744\pi$
$158$	1.03609	0.0824268
$159$	−7.19057	−0.570250
$160$	2.76562	0.218642
$161$	0	0
$162$	−2.08182	−0.163563
$163$	3.62955	0.284288	0.142144	−	0.989846i	$-0.454600\pi$
$163$	3.62955	0.284288	0.142144	+	0.989846i	$0.454600\pi$
$164$	19.8079	1.54674
$165$	8.84497	0.688580
$166$	2.91311	0.226101
$167$	−9.77397	−0.756332	−0.378166	−	0.925738i	$-0.623445\pi$
$167$	−9.77397	−0.756332	−0.378166	+	0.925738i	$0.623445\pi$
$168$	0	0
$169$	26.1758	2.01353
$170$	1.33521	0.102406
$171$	0.711718	0.0544264
$172$	19.8219	1.51141
$173$	3.77874	0.287292	0.143646	−	0.989629i	$-0.454117\pi$
$173$	3.77874	0.287292	0.143646	+	0.989629i	$0.454117\pi$
$174$	3.37514	0.255869
$175$	0	0
$176$	19.0045	1.43252
$177$	−0.821722	−0.0617644
$178$	3.71926	0.278771
$179$	2.24410	0.167732	0.0838659	−	0.996477i	$-0.473273\pi$
$179$	2.24410	0.167732	0.0838659	+	0.996477i	$0.473273\pi$
$180$	0.194355	0.0144863
$181$	8.89881	0.661443	0.330722	−	0.943728i	$-0.392708\pi$
$181$	8.89881	0.661443	0.330722	+	0.943728i	$0.392708\pi$
$182$	0	0
$183$	−2.81620	−0.208179
$184$	3.41006	0.251393
$185$	3.38680	0.249003
$186$	−0.407968	−0.0299137
$187$	28.9481	2.11690
$188$	7.97636	0.581736
$189$	0	0
$190$	−1.70423	−0.123638
$191$	−2.57884	−0.186598	−0.0932991	−	0.995638i	$-0.529741\pi$
$191$	−2.57884	−0.186598	−0.0932991	+	0.995638i	$0.529741\pi$
$192$	−11.3335	−0.817924
$193$	−2.28065	−0.164165	−0.0820824	−	0.996626i	$-0.526157\pi$
$193$	−2.28065	−0.164165	−0.0820824	+	0.996626i	$0.526157\pi$
$194$	1.79857	0.129130
$195$	−10.6587	−0.763286
$196$	0	0
$197$	−20.2903	−1.44563	−0.722813	−	0.691044i	$-0.757151\pi$
$197$	−20.2903	−1.44563	−0.722813	+	0.691044i	$0.757151\pi$
$198$	−0.124492	−0.00884727
$199$	18.3517	1.30091	0.650457	−	0.759543i	$-0.274577\pi$
$199$	18.3517	1.30091	0.650457	+	0.759543i	$0.274577\pi$
$200$	−0.944527	−0.0667882
$201$	5.64431	0.398119
$202$	−2.47002	−0.173790
$203$	0	0
$204$	−18.4374	−1.29088
$205$	−10.1966	−0.712158
$206$	0.211084	0.0147069
$207$	0.361208	0.0251057
$208$	−22.9015	−1.58793
$209$	−36.9487	−2.55579
$210$	0	0
$211$	−3.03057	−0.208633	−0.104316	−	0.994544i	$-0.533265\pi$
$211$	−3.03057	−0.208633	−0.104316	+	0.994544i	$0.533265\pi$
$212$	8.20263	0.563359
$213$	11.2185	0.768681
$214$	−0.884349	−0.0604529
$215$	−10.2038	−0.695892
$216$	4.98630	0.339275
$217$	0	0
$218$	−3.50580	−0.237442
$219$	−23.7760	−1.60663
$220$	−10.0899	−0.680259
$221$	−34.8842	−2.34656
$222$	1.38171	0.0927341
$223$	−24.1650	−1.61821	−0.809103	−	0.587667i	$-0.800047\pi$
$223$	−24.1650	−1.61821	−0.809103	+	0.587667i	$0.800047\pi$
$224$	0	0
$225$	−0.100048	−0.00666989
$226$	−2.76985	−0.184248
$227$	−21.5548	−1.43064	−0.715320	−	0.698797i	$-0.753719\pi$
$227$	−21.5548	−1.43064	−0.715320	+	0.698797i	$0.753719\pi$
$228$	23.5330	1.55851
$229$	−17.4529	−1.15332	−0.576661	−	0.816984i	$-0.695644\pi$
$229$	−17.4529	−1.15332	−0.576661	+	0.816984i	$0.695644\pi$
$230$	−0.864925	−0.0570315
$231$	0	0
$232$	−7.81412	−0.513022
$233$	7.64027	0.500531	0.250265	−	0.968177i	$-0.419482\pi$
$233$	7.64027	0.500531	0.250265	+	0.968177i	$0.419482\pi$
$234$	0.150020	0.00980714
$235$	−4.10601	−0.267847
$236$	0.937378	0.0610181
$237$	7.36481	0.478396
$238$	0	0
$239$	−12.2939	−0.795225	−0.397613	−	0.917553i	$-0.630161\pi$
$239$	−12.2939	−0.795225	−0.397613	+	0.917553i	$0.630161\pi$
$240$	6.23089	0.402202
$241$	−6.44457	−0.415131	−0.207566	−	0.978221i	$-0.566554\pi$
$241$	−6.44457	−0.415131	−0.207566	+	0.978221i	$0.566554\pi$
$242$	3.82772	0.246055
$243$	1.03929	0.0666708
$244$	3.21257	0.205664
$245$	0	0
$246$	−4.15987	−0.265224
$247$	44.5253	2.83308
$248$	0.944527	0.0599775
$249$	20.7072	1.31226
$250$	0.239569	0.0151517
$251$	25.9904	1.64050	0.820249	−	0.572007i	$-0.193835\pi$
$251$	25.9904	1.64050	0.820249	+	0.572007i	$0.193835\pi$
$252$	0	0
$253$	−18.7520	−1.17893
$254$	−2.76343	−0.173393
$255$	9.49106	0.594353
$256$	11.6035	0.725221
$257$	−18.2908	−1.14095	−0.570476	−	0.821314i	$-0.693241\pi$
$257$	−18.2908	−1.14095	−0.570476	+	0.821314i	$0.693241\pi$
$258$	−4.16282	−0.259166
$259$	0	0
$260$	12.1589	0.754063
$261$	−0.827704	−0.0512336
$262$	−3.12392	−0.192997
$263$	6.40694	0.395069	0.197534	−	0.980296i	$-0.436707\pi$
$263$	6.40694	0.395069	0.197534	+	0.980296i	$0.436707\pi$
$264$	−8.35432	−0.514173
$265$	−4.22249	−0.259385
$266$	0	0
$267$	26.4376	1.61795
$268$	−6.43873	−0.393308
$269$	2.83564	0.172892	0.0864459	−	0.996257i	$-0.472449\pi$
$269$	2.83564	0.172892	0.0864459	+	0.996257i	$0.472449\pi$
$270$	−1.26472	−0.0769685
$271$	−6.58978	−0.400300	−0.200150	−	0.979765i	$-0.564143\pi$
$271$	−6.58978	−0.400300	−0.200150	+	0.979765i	$0.564143\pi$
$272$	20.3927	1.23649
$273$	0	0
$274$	−2.11263	−0.127628
$275$	5.19399	0.313209
$276$	11.9434	0.718907
$277$	10.4179	0.625951	0.312975	−	0.949761i	$-0.398674\pi$
$277$	10.4179	0.625951	0.312975	+	0.949761i	$0.398674\pi$
$278$	−2.63852	−0.158248
$279$	0.100048	0.00598974
$280$	0	0
$281$	3.55010	0.211781	0.105891	−	0.994378i	$-0.466231\pi$
$281$	3.55010	0.211781	0.105891	+	0.994378i	$0.466231\pi$
$282$	−1.67512	−0.0997521
$283$	−6.05765	−0.360090	−0.180045	−	0.983658i	$-0.557624\pi$
$283$	−6.05765	−0.360090	−0.180045	+	0.983658i	$0.557624\pi$
$284$	−12.7975	−0.759392
$285$	−12.1142	−0.717581
$286$	−7.78828	−0.460530
$287$	0	0
$288$	−0.276696	−0.0163045
$289$	14.0627	0.827215
$290$	1.98197	0.116385
$291$	12.7847	0.749455
$292$	27.1224	1.58722
$293$	−3.50522	−0.204777	−0.102389	−	0.994744i	$-0.532648\pi$
$293$	−3.50522	−0.204777	−0.102389	+	0.994744i	$0.532648\pi$
$294$	0	0
$295$	−0.482536	−0.0280943
$296$	−3.19893	−0.185934
$297$	−27.4198	−1.59106
$298$	0.0719608	0.00416857
$299$	22.5973	1.30684
$300$	−3.30811	−0.190994
$301$	0	0
$302$	3.14432	0.180935
$303$	−17.5576	−1.00866
$304$	−26.0287	−1.49285
$305$	−1.65374	−0.0946930
$306$	−0.133586	−0.00763659
$307$	−19.0939	−1.08974	−0.544872	−	0.838519i	$-0.683422\pi$
$307$	−19.0939	−1.08974	−0.544872	+	0.838519i	$0.683422\pi$
$308$	0	0
$309$	1.50044	0.0853573
$310$	−0.239569	−0.0136066
$311$	−15.8274	−0.897492	−0.448746	−	0.893659i	$-0.648129\pi$
$311$	−15.8274	−0.897492	−0.448746	+	0.893659i	$0.648129\pi$
$312$	10.0674	0.569957
$313$	−21.9018	−1.23796	−0.618982	−	0.785405i	$-0.712455\pi$
$313$	−21.9018	−1.23796	−0.618982	+	0.785405i	$0.712455\pi$
$314$	−3.38612	−0.191090
$315$	0	0
$316$	−8.40138	−0.472615
$317$	1.83418	0.103018	0.0515090	−	0.998673i	$-0.483597\pi$
$317$	1.83418	0.103018	0.0515090	+	0.998673i	$0.483597\pi$
$318$	−1.72264	−0.0966009
$319$	42.9701	2.40586
$320$	−6.65531	−0.372043
$321$	−6.28620	−0.350861
$322$	0	0
$323$	−39.6476	−2.20605
$324$	16.8810	0.937831
$325$	−6.25906	−0.347190
$326$	0.869529	0.0481588
$327$	−24.9202	−1.37809
$328$	9.63092	0.531779
$329$	0	0
$330$	2.11898	0.116646
$331$	13.4757	0.740692	0.370346	−	0.928894i	$-0.379239\pi$
$331$	13.4757	0.740692	0.370346	+	0.928894i	$0.379239\pi$
$332$	−23.6217	−1.29641
$333$	−0.338844	−0.0185685
$334$	−2.34154	−0.128124
$335$	3.31448	0.181089
$336$	0	0
$337$	2.90623	0.158312	0.0791562	−	0.996862i	$-0.474777\pi$
$337$	2.90623	0.158312	0.0791562	+	0.996862i	$0.474777\pi$
$338$	6.27093	0.341094
$339$	−19.6889	−1.06935
$340$	−10.8269	−0.587171
$341$	−5.19399	−0.281270
$342$	0.170506	0.00921989
$343$	0	0
$344$	9.63774	0.519632
$345$	−6.14812	−0.331004
$346$	0.905270	0.0486676
$347$	5.23124	0.280828	0.140414	−	0.990093i	$-0.455157\pi$
$347$	5.23124	0.280828	0.140414	+	0.990093i	$0.455157\pi$
$348$	−27.3682	−1.46709
$349$	9.33216	0.499539	0.249770	−	0.968305i	$-0.419645\pi$
$349$	9.33216	0.499539	0.249770	+	0.968305i	$0.419645\pi$
$350$	0	0
$351$	33.0425	1.76368
$352$	14.3646	0.765637
$353$	−1.01398	−0.0539689	−0.0269844	−	0.999636i	$-0.508590\pi$
$353$	−1.01398	−0.0539689	−0.0269844	+	0.999636i	$0.508590\pi$
$354$	−0.196859	−0.0104630
$355$	6.58780	0.349644
$356$	−30.1586	−1.59840
$357$	0	0
$358$	0.537617	0.0284140
$359$	−24.7319	−1.30530	−0.652651	−	0.757659i	$-0.726343\pi$
$359$	−24.7319	−1.30530	−0.652651	+	0.757659i	$0.726343\pi$
$360$	0.0944984	0.00498050
$361$	31.6053	1.66344
$362$	2.13188	0.112049
$363$	27.2085	1.42808
$364$	0	0
$365$	−13.9619	−0.730797
$366$	−0.674675	−0.0352658
$367$	32.5156	1.69730	0.848650	−	0.528955i	$-0.177416\pi$
$367$	32.5156	1.69730	0.848650	+	0.528955i	$0.177416\pi$
$368$	−13.2100	−0.688617
$369$	1.02015	0.0531068
$370$	0.811373	0.0421813
$371$	0	0
$372$	3.30811	0.171518
$373$	12.3086	0.637313	0.318656	−	0.947870i	$-0.396768\pi$
$373$	12.3086	0.637313	0.318656	+	0.947870i	$0.396768\pi$
$374$	6.93508	0.358604
$375$	1.70292	0.0879386
$376$	3.87824	0.200005
$377$	−51.7815	−2.66688
$378$	0	0
$379$	19.9390	1.02420	0.512098	−	0.858927i	$-0.328869\pi$
$379$	19.9390	1.02420	0.512098	+	0.858927i	$0.328869\pi$
$380$	13.8192	0.708910
$381$	−19.6432	−1.00635
$382$	−0.617810	−0.0316099
$383$	−20.3068	−1.03763	−0.518813	−	0.854887i	$-0.673626\pi$
$383$	−20.3068	−1.03763	−0.518813	+	0.854887i	$0.673626\pi$
$384$	−12.1344	−0.619233
$385$	0	0
$386$	−0.546374	−0.0278097
$387$	1.02087	0.0518938
$388$	−14.5842	−0.740399
$389$	−23.5746	−1.19528	−0.597639	−	0.801765i	$-0.703895\pi$
$389$	−23.5746	−1.19528	−0.597639	+	0.801765i	$0.703895\pi$
$390$	−2.55350	−0.129301
$391$	−20.1218	−1.01760
$392$	0	0
$393$	−22.2057	−1.12013
$394$	−4.86094	−0.244890
$395$	4.32480	0.217604
$396$	1.00948	0.0507281
$397$	14.2207	0.713719	0.356859	−	0.934158i	$-0.383848\pi$
$397$	14.2207	0.713719	0.356859	+	0.934158i	$0.383848\pi$
$398$	4.39649	0.220376
$399$	0	0
$400$	3.65893	0.182947
$401$	−12.7468	−0.636543	−0.318272	−	0.948000i	$-0.603102\pi$
$401$	−12.7468	−0.636543	−0.318272	+	0.948000i	$0.603102\pi$
$402$	1.35220	0.0674418
$403$	6.25906	0.311786
$404$	20.0288	0.996469
$405$	−8.68985	−0.431802
$406$	0	0
$407$	17.5910	0.871954
$408$	−8.96457	−0.443812
$409$	3.17893	0.157188	0.0785940	−	0.996907i	$-0.474957\pi$
$409$	3.17893	0.157188	0.0785940	+	0.996907i	$0.474957\pi$
$410$	−2.44278	−0.120640
$411$	−15.0171	−0.740740
$412$	−1.71163	−0.0843258
$413$	0	0
$414$	0.0865343	0.00425293
$415$	12.1598	0.596900
$416$	−17.3102	−0.848703
$417$	−18.7553	−0.918452
$418$	−8.85177	−0.432954
$419$	−14.8926	−0.727552	−0.363776	−	0.931487i	$-0.618513\pi$
$419$	−14.8926	−0.727552	−0.363776	+	0.931487i	$0.618513\pi$
$420$	0	0
$421$	−16.9923	−0.828154	−0.414077	−	0.910242i	$-0.635896\pi$
$421$	−16.9923	−0.828154	−0.414077	+	0.910242i	$0.635896\pi$
$422$	−0.726031	−0.0353426
$423$	0.410799	0.0199738
$424$	3.98825	0.193687
$425$	5.57339	0.270349
$426$	2.68761	0.130215
$427$	0	0
$428$	7.17096	0.346622
$429$	−55.3612	−2.67286
$430$	−2.44451	−0.117885
$431$	−0.826075	−0.0397906	−0.0198953	−	0.999802i	$-0.506333\pi$
$431$	−0.826075	−0.0397906	−0.0198953	+	0.999802i	$0.506333\pi$
$432$	−19.3161	−0.929344
$433$	8.85201	0.425400	0.212700	−	0.977118i	$-0.431774\pi$
$433$	8.85201	0.425400	0.212700	+	0.977118i	$0.431774\pi$
$434$	0	0
$435$	14.0884	0.675486
$436$	28.4276	1.36144
$437$	25.6830	1.22858
$438$	−5.69600	−0.272165
$439$	20.7368	0.989713	0.494856	−	0.868975i	$-0.335221\pi$
$439$	20.7368	0.989713	0.494856	+	0.868975i	$0.335221\pi$
$440$	−4.90587	−0.233878
$441$	0	0
$442$	−8.35718	−0.397510
$443$	9.97858	0.474096	0.237048	−	0.971498i	$-0.423820\pi$
$443$	9.97858	0.474096	0.237048	+	0.971498i	$0.423820\pi$
$444$	−11.2039	−0.531714
$445$	15.5248	0.735946
$446$	−5.78919	−0.274126
$447$	0.511517	0.0241939
$448$	0	0
$449$	−21.5292	−1.01603	−0.508014	−	0.861349i	$-0.669620\pi$
$449$	−21.5292	−1.01603	−0.508014	+	0.861349i	$0.669620\pi$
$450$	−0.0239685	−0.00112989
$451$	−52.9608	−2.49383
$452$	22.4600	1.05643
$453$	22.3507	1.05013
$454$	−5.16386	−0.242352
$455$	0	0
$456$	11.4422	0.535828
$457$	24.0687	1.12589	0.562944	−	0.826495i	$-0.309669\pi$
$457$	24.0687	1.12589	0.562944	+	0.826495i	$0.309669\pi$
$458$	−4.18118	−0.195374
$459$	−29.4227	−1.37334
$460$	7.01346	0.327004
$461$	−14.7243	−0.685779	−0.342890	−	0.939376i	$-0.611406\pi$
$461$	−14.7243	−0.685779	−0.342890	+	0.939376i	$0.611406\pi$
$462$	0	0
$463$	−12.3389	−0.573437	−0.286719	−	0.958015i	$-0.592564\pi$
$463$	−12.3389	−0.573437	−0.286719	+	0.958015i	$0.592564\pi$
$464$	30.2705	1.40527
$465$	−1.70292	−0.0789712
$466$	1.83037	0.0847905
$467$	17.5493	0.812083	0.406042	−	0.913855i	$-0.366909\pi$
$467$	17.5493	0.812083	0.406042	+	0.913855i	$0.366909\pi$
$468$	−1.21648	−0.0562317
$469$	0	0
$470$	−0.983674	−0.0453735
$471$	−24.0695	−1.10906
$472$	0.455768	0.0209784
$473$	−52.9983	−2.43686
$474$	1.76438	0.0810407
$475$	−7.11374	−0.326401
$476$	0	0
$477$	0.422453	0.0193428
$478$	−2.94524	−0.134712
$479$	−3.74409	−0.171072	−0.0855360	−	0.996335i	$-0.527260\pi$
$479$	−3.74409	−0.171072	−0.0855360	+	0.996335i	$0.527260\pi$
$480$	4.70965	0.214965
$481$	−21.1982	−0.966554
$482$	−1.54392	−0.0703237
$483$	0	0
$484$	−31.0381	−1.41082
$485$	7.50753	0.340899
$486$	0.248983	0.0112941
$487$	31.3875	1.42230	0.711151	−	0.703039i	$-0.248174\pi$
$487$	31.3875	1.42230	0.711151	+	0.703039i	$0.248174\pi$
$488$	1.56200	0.0707086
$489$	6.18085	0.279508
$490$	0	0
$491$	16.1795	0.730170	0.365085	−	0.930974i	$-0.381040\pi$
$491$	16.1795	0.730170	0.365085	+	0.930974i	$0.381040\pi$
$492$	33.7313	1.52073
$493$	46.1089	2.07664
$494$	10.6669	0.479926
$495$	−0.519650	−0.0233565
$496$	−3.65893	−0.164291
$497$	0	0
$498$	4.96080	0.222299
$499$	−4.77873	−0.213925	−0.106963	−	0.994263i	$-0.534113\pi$
$499$	−4.77873	−0.213925	−0.106963	+	0.994263i	$0.534113\pi$
$500$	−1.94261	−0.0868760
$501$	−16.6443	−0.743614
$502$	6.22649	0.277902
$503$	−16.4645	−0.734115	−0.367057	−	0.930198i	$-0.619635\pi$
$503$	−16.4645	−0.734115	−0.367057	+	0.930198i	$0.619635\pi$
$504$	0	0
$505$	−10.3103	−0.458801
$506$	−4.49241	−0.199712
$507$	44.5755	1.97967
$508$	22.4079	0.994191
$509$	37.4338	1.65922	0.829612	−	0.558340i	$-0.188561\pi$
$509$	37.4338	1.65922	0.829612	+	0.558340i	$0.188561\pi$
$510$	2.27377	0.100684
$511$	0	0
$512$	17.0312	0.752678
$513$	37.5545	1.65807
$514$	−4.38192	−0.193278
$515$	0.881099	0.0388258
$516$	33.7552	1.48599
$517$	−21.3266	−0.937942
$518$	0	0
$519$	6.43491	0.282461
$520$	5.91185	0.259252
$521$	−37.1118	−1.62590	−0.812949	−	0.582335i	$-0.802139\pi$
$521$	−37.1118	−1.62590	−0.812949	+	0.582335i	$0.802139\pi$
$522$	−0.198293	−0.00867903
$523$	−0.294353	−0.0128712	−0.00643558	−	0.999979i	$-0.502049\pi$
$523$	−0.294353	−0.0128712	−0.00643558	+	0.999979i	$0.502049\pi$
$524$	25.3311	1.10659
$525$	0	0
$526$	1.53491	0.0669251
$527$	−5.57339	−0.242781
$528$	32.3632	1.40843
$529$	−9.96550	−0.433282
$530$	−1.01158	−0.0439401
$531$	0.0482769	0.00209504
$532$	0	0
$533$	63.8208	2.76439
$534$	6.33362	0.274083
$535$	−3.69141	−0.159594
$536$	−3.13062	−0.135222
$537$	3.82153	0.164911
$538$	0.679331	0.0292880
$539$	0	0
$540$	10.2553	0.441318
$541$	−27.2212	−1.17033	−0.585166	−	0.810913i	$-0.698971\pi$
$541$	−27.2212	−1.17033	−0.585166	+	0.810913i	$0.698971\pi$
$542$	−1.57871	−0.0678113
$543$	15.1540	0.650320
$544$	15.4139	0.660865
$545$	−14.6337	−0.626841
$546$	0	0
$547$	−43.1942	−1.84685	−0.923426	−	0.383777i	$-0.874623\pi$
$547$	−43.1942	−1.84685	−0.923426	+	0.383777i	$0.874623\pi$
$548$	17.1307	0.731789
$549$	0.165454	0.00706141
$550$	1.24432	0.0530580
$551$	−58.8523	−2.50719
$552$	5.80707	0.247165
$553$	0	0
$554$	2.49581	0.106037
$555$	5.76747	0.244815
$556$	21.3951	0.907354
$557$	−10.7080	−0.453713	−0.226856	−	0.973928i	$-0.572845\pi$
$557$	−10.7080	−0.453713	−0.226856	+	0.973928i	$0.572845\pi$
$558$	0.0239685	0.00101467
$559$	63.8660	2.70125
$560$	0	0
$561$	49.2965	2.08130
$562$	0.850495	0.0358760
$563$	8.43935	0.355676	0.177838	−	0.984060i	$-0.443090\pi$
$563$	8.43935	0.355676	0.177838	+	0.984060i	$0.443090\pi$
$564$	13.5831	0.571953
$565$	−11.5618	−0.486408
$566$	−1.45123	−0.0609997
$567$	0	0
$568$	−6.22236	−0.261084
$569$	21.8208	0.914775	0.457387	−	0.889268i	$-0.348785\pi$
$569$	21.8208	0.914775	0.457387	+	0.889268i	$0.348785\pi$
$570$	−2.90218	−0.121559
$571$	−37.8923	−1.58574	−0.792872	−	0.609388i	$-0.791415\pi$
$571$	−37.8923	−1.58574	−0.792872	+	0.609388i	$0.791415\pi$
$572$	63.1532	2.64057
$573$	−4.39157	−0.183460
$574$	0	0
$575$	−3.61033	−0.150561
$576$	0.665853	0.0277439
$577$	−16.3995	−0.682718	−0.341359	−	0.939933i	$-0.610887\pi$
$577$	−16.3995	−0.682718	−0.341359	+	0.939933i	$0.610887\pi$
$578$	3.36898	0.140131
$579$	−3.88377	−0.161404
$580$	−16.0713	−0.667323
$581$	0	0
$582$	3.06283	0.126959
$583$	−21.9315	−0.908312
$584$	13.1874	0.545697
$585$	0.626209	0.0258905
$586$	−0.839743	−0.0346895
$587$	38.8683	1.60426	0.802132	−	0.597146i	$-0.203699\pi$
$587$	38.8683	1.60426	0.802132	+	0.597146i	$0.203699\pi$
$588$	0	0
$589$	7.11374	0.293116
$590$	−0.115601	−0.00475921
$591$	−34.5529	−1.42132
$592$	12.3921	0.509311
$593$	25.5507	1.04924	0.524621	−	0.851336i	$-0.324207\pi$
$593$	25.5507	1.04924	0.524621	+	0.851336i	$0.324207\pi$
$594$	−6.56895	−0.269527
$595$	0	0
$596$	−0.583512	−0.0239016
$597$	31.2515	1.27904
$598$	5.41362	0.221379
$599$	−30.3477	−1.23997	−0.619987	−	0.784612i	$-0.712862\pi$
$599$	−30.3477	−1.23997	−0.619987	+	0.784612i	$0.712862\pi$
$600$	−1.60846	−0.0656651
$601$	−28.3617	−1.15690	−0.578449	−	0.815719i	$-0.696342\pi$
$601$	−28.3617	−1.15690	−0.578449	+	0.815719i	$0.696342\pi$
$602$	0	0
$603$	−0.331608	−0.0135041
$604$	−25.4965	−1.03744
$605$	15.9775	0.649579
$606$	−4.20626	−0.170868
$607$	−10.6987	−0.434249	−0.217124	−	0.976144i	$-0.569668\pi$
$607$	−10.6987	−0.434249	−0.217124	+	0.976144i	$0.569668\pi$
$608$	−19.6739	−0.797883
$609$	0	0
$610$	−0.396186	−0.0160411
$611$	25.6998	1.03970
$612$	1.08321	0.0437863
$613$	1.96852	0.0795079	0.0397540	−	0.999209i	$-0.487343\pi$
$613$	1.96852	0.0795079	0.0397540	+	0.999209i	$0.487343\pi$
$614$	−4.57430	−0.184604
$615$	−17.3640	−0.700182
$616$	0	0
$617$	4.35658	0.175389	0.0876946	−	0.996147i	$-0.472050\pi$
$617$	4.35658	0.175389	0.0876946	+	0.996147i	$0.472050\pi$
$618$	0.359460	0.0144596
$619$	9.90288	0.398030	0.199015	−	0.979996i	$-0.436226\pi$
$619$	9.90288	0.398030	0.199015	+	0.979996i	$0.436226\pi$
$620$	1.94261	0.0780170
$621$	19.0595	0.764831
$622$	−3.79177	−0.152036
$623$	0	0
$624$	−38.9995	−1.56123
$625$	1.00000	0.0400000
$626$	−5.24700	−0.209712
$627$	−62.9208	−2.51282
$628$	27.4572	1.09566
$629$	18.8760	0.752634
$630$	0	0
$631$	29.8031	1.18644	0.593221	−	0.805040i	$-0.297856\pi$
$631$	29.8031	1.18644	0.593221	+	0.805040i	$0.297856\pi$
$632$	−4.08489	−0.162488
$633$	−5.16083	−0.205125
$634$	0.439414	0.0174514
$635$	−11.5350	−0.457752
$636$	13.9685	0.553885
$637$	0	0
$638$	10.2943	0.407556
$639$	−0.659098	−0.0260735
$640$	−7.12565	−0.281666
$641$	28.6909	1.13322	0.566612	−	0.823985i	$-0.308254\pi$
$641$	28.6909	1.13322	0.566612	+	0.823985i	$0.308254\pi$
$642$	−1.50598	−0.0594363
$643$	41.0650	1.61945	0.809723	−	0.586813i	$-0.199617\pi$
$643$	41.0650	1.61945	0.809723	+	0.586813i	$0.199617\pi$
$644$	0	0
$645$	−17.3763	−0.684189
$646$	−9.49835	−0.373708
$647$	1.68820	0.0663702	0.0331851	−	0.999449i	$-0.489435\pi$
$647$	1.68820	0.0663702	0.0331851	+	0.999449i	$0.489435\pi$
$648$	8.20780	0.322433
$649$	−2.50629	−0.0983804
$650$	−1.49948	−0.0588144
$651$	0	0
$652$	−7.05079	−0.276130
$653$	−6.44841	−0.252346	−0.126173	−	0.992008i	$-0.540269\pi$
$653$	−6.44841	−0.252346	−0.126173	+	0.992008i	$0.540269\pi$
$654$	−5.97011	−0.233450
$655$	−13.0398	−0.509505
$656$	−37.3085	−1.45665
$657$	1.39686	0.0544967
$658$	0	0
$659$	11.1213	0.433225	0.216613	−	0.976258i	$-0.430499\pi$
$659$	11.1213	0.433225	0.216613	+	0.976258i	$0.430499\pi$
$660$	−17.1823	−0.668820
$661$	−0.679812	−0.0264416	−0.0132208	−	0.999913i	$-0.504208\pi$
$661$	−0.679812	−0.0264416	−0.0132208	+	0.999913i	$0.504208\pi$
$662$	3.22836	0.125474
$663$	−59.4051	−2.30710
$664$	−11.4852	−0.445714
$665$	0	0
$666$	−0.0811766	−0.00314553
$667$	−29.8684	−1.15651
$668$	18.9870	0.734628
$669$	−41.1511	−1.59099
$670$	0.794048	0.0306767
$671$	−8.58952	−0.331595
$672$	0	0
$673$	36.5993	1.41080	0.705400	−	0.708810i	$-0.250768\pi$
$673$	36.5993	1.41080	0.705400	+	0.708810i	$0.250768\pi$
$674$	0.696244	0.0268183
$675$	−5.27915	−0.203195
$676$	−50.8494	−1.95575
$677$	−9.96334	−0.382922	−0.191461	−	0.981500i	$-0.561323\pi$
$677$	−9.96334	−0.382922	−0.191461	+	0.981500i	$0.561323\pi$
$678$	−4.71685	−0.181149
$679$	0	0
$680$	−5.26422	−0.201874
$681$	−36.7061	−1.40658
$682$	−1.24432	−0.0476475
$683$	−19.3895	−0.741918	−0.370959	−	0.928649i	$-0.620971\pi$
$683$	−19.3895	−0.741918	−0.370959	+	0.928649i	$0.620971\pi$
$684$	−1.38259	−0.0528645
$685$	−8.81843	−0.336935
$686$	0	0
$687$	−29.7210	−1.13393
$688$	−37.3349	−1.42338
$689$	26.4288	1.00686
$690$	−1.47290	−0.0560724
$691$	31.6146	1.20268	0.601338	−	0.798995i	$-0.294635\pi$
$691$	31.6146	1.20268	0.601338	+	0.798995i	$0.294635\pi$
$692$	−7.34060	−0.279048
$693$	0	0
$694$	1.25324	0.0475725
$695$	−11.0136	−0.417769
$696$	−13.3069	−0.504395
$697$	−56.8294	−2.15257
$698$	2.23570	0.0846225
$699$	13.0108	0.492114
$700$	0	0
$701$	−36.6426	−1.38397	−0.691985	−	0.721912i	$-0.743264\pi$
$701$	−36.6426	−1.38397	−0.691985	+	0.721912i	$0.743264\pi$
$702$	7.91597	0.298769
$703$	−24.0928	−0.908678
$704$	−34.5676	−1.30282
$705$	−6.99223	−0.263342
$706$	−0.242919	−0.00914239
$707$	0	0
$708$	1.59628	0.0599920
$709$	43.1489	1.62049	0.810245	−	0.586091i	$-0.199334\pi$
$709$	43.1489	1.62049	0.810245	+	0.586091i	$0.199334\pi$
$710$	1.57823	0.0592301
$711$	−0.432689	−0.0162271
$712$	−14.6636	−0.549541
$713$	3.61033	0.135208
$714$	0	0
$715$	−32.5095	−1.21579
$716$	−4.35940	−0.162918
$717$	−20.9356	−0.781853
$718$	−5.92501	−0.221120
$719$	−14.6117	−0.544926	−0.272463	−	0.962166i	$-0.587838\pi$
$719$	−14.6117	−0.544926	−0.272463	+	0.962166i	$0.587838\pi$
$720$	−0.366070	−0.0136426
$721$	0	0
$722$	7.57165	0.281788
$723$	−10.9746	−0.408150
$724$	−17.2869	−0.642462
$725$	8.27304	0.307253
$726$	6.51833	0.241918
$727$	38.3139	1.42098	0.710491	−	0.703706i	$-0.248473\pi$
$727$	38.3139	1.42098	0.710491	+	0.703706i	$0.248473\pi$
$728$	0	0
$729$	27.8394	1.03109
$730$	−3.34483	−0.123798
$731$	−56.8696	−2.10340
$732$	5.47077	0.202205
$733$	11.6294	0.429543	0.214772	−	0.976664i	$-0.431099\pi$
$733$	11.6294	0.429543	0.214772	+	0.976664i	$0.431099\pi$
$734$	7.78973	0.287524
$735$	0	0
$736$	−9.98482	−0.368045
$737$	17.2154	0.634137
$738$	0.244396	0.00899635
$739$	−24.3103	−0.894267	−0.447134	−	0.894467i	$-0.647555\pi$
$739$	−24.3103	−0.894267	−0.447134	+	0.894467i	$0.647555\pi$
$740$	−6.57922	−0.241857
$741$	75.8233	2.78544
$742$	0	0
$743$	9.36060	0.343407	0.171704	−	0.985149i	$-0.445073\pi$
$743$	9.36060	0.343407	0.171704	+	0.985149i	$0.445073\pi$
$744$	1.60846	0.0589690
$745$	0.300376	0.0110049
$746$	2.94875	0.107961
$747$	−1.21656	−0.0445118
$748$	−56.2348	−2.05615
$749$	0	0
$750$	0.407968	0.0148969
$751$	22.5952	0.824509	0.412254	−	0.911069i	$-0.364741\pi$
$751$	22.5952	0.824509	0.412254	+	0.911069i	$0.364741\pi$
$752$	−15.0236	−0.547855
$753$	44.2596	1.61291
$754$	−12.4053	−0.451773
$755$	13.1249	0.477664
$756$	0	0
$757$	6.00136	0.218123	0.109062	−	0.994035i	$-0.465215\pi$
$757$	6.00136	0.218123	0.109062	+	0.994035i	$0.465215\pi$
$758$	4.77676	0.173500
$759$	−31.9333	−1.15911
$760$	6.71912	0.243728
$761$	15.4645	0.560586	0.280293	−	0.959914i	$-0.409568\pi$
$761$	15.4645	0.560586	0.280293	+	0.959914i	$0.409568\pi$
$762$	−4.70591	−0.170477
$763$	0	0
$764$	5.00967	0.181243
$765$	−0.557608	−0.0201604
$766$	−4.86488	−0.175775
$767$	3.02022	0.109054
$768$	19.7599	0.713025
$769$	−7.20580	−0.259848	−0.129924	−	0.991524i	$-0.541473\pi$
$769$	−7.20580	−0.259848	−0.129924	+	0.991524i	$0.541473\pi$
$770$	0	0
$771$	−31.1479	−1.12177
$772$	4.43040	0.159454
$773$	−10.7447	−0.386459	−0.193230	−	0.981154i	$-0.561896\pi$
$773$	−10.7447	−0.386459	−0.193230	+	0.981154i	$0.561896\pi$
$774$	0.244569	0.00879086
$775$	−1.00000	−0.0359211
$776$	−7.09106	−0.254554
$777$	0	0
$778$	−5.64775	−0.202481
$779$	72.5356	2.59886
$780$	20.7057	0.741382
$781$	34.2170	1.22438
$782$	−4.82056	−0.172383
$783$	−43.6746	−1.56080
$784$	0	0
$785$	−14.1342	−0.504471
$786$	−5.31981	−0.189751
$787$	−6.85758	−0.244446	−0.122223	−	0.992503i	$-0.539002\pi$
$787$	−6.85758	−0.244446	−0.122223	+	0.992503i	$0.539002\pi$
$788$	39.4161	1.40414
$789$	10.9105	0.388425
$790$	1.03609	0.0368624
$791$	0	0
$792$	0.490824	0.0174407
$793$	10.3509	0.367570
$794$	3.40685	0.120905
$795$	−7.19057	−0.255023
$796$	−35.6501	−1.26358
$797$	6.13793	0.217417	0.108708	−	0.994074i	$-0.465329\pi$
$797$	6.13793	0.217417	0.108708	+	0.994074i	$0.465329\pi$
$798$	0	0
$799$	−22.8844	−0.809592
$800$	2.76562	0.0977795
$801$	−1.55323	−0.0548807
$802$	−3.05373	−0.107831
$803$	−72.5178	−2.55910
$804$	−10.9647	−0.386694
$805$	0	0
$806$	1.49948	0.0528169
$807$	4.82887	0.169984
$808$	9.73832	0.342593
$809$	30.3054	1.06548	0.532741	−	0.846278i	$-0.321162\pi$
$809$	30.3054	1.06548	0.532741	+	0.846278i	$0.321162\pi$
$810$	−2.08182	−0.0731477
$811$	−37.5896	−1.31995	−0.659974	−	0.751288i	$-0.729433\pi$
$811$	−37.5896	−1.31995	−0.659974	+	0.751288i	$0.729433\pi$
$812$	0	0
$813$	−11.2219	−0.393569
$814$	4.21426	0.147710
$815$	3.62955	0.127138
$816$	34.7272	1.21569
$817$	72.5870	2.53950
$818$	0.761574	0.0266278
$819$	0	0
$820$	19.8079	0.691722
$821$	5.14003	0.179388	0.0896942	−	0.995969i	$-0.471411\pi$
$821$	5.14003	0.179388	0.0896942	+	0.995969i	$0.471411\pi$
$822$	−3.59764	−0.125482
$823$	20.1039	0.700779	0.350389	−	0.936604i	$-0.386049\pi$
$823$	20.1039	0.700779	0.350389	+	0.936604i	$0.386049\pi$
$824$	−0.832222	−0.0289918
$825$	8.84497	0.307942
$826$	0	0
$827$	39.1070	1.35988	0.679942	−	0.733266i	$-0.262005\pi$
$827$	39.1070	1.35988	0.679942	+	0.733266i	$0.262005\pi$
$828$	−0.701685	−0.0243852
$829$	−1.85695	−0.0644945	−0.0322473	−	0.999480i	$-0.510266\pi$
$829$	−1.85695	−0.0644945	−0.0322473	+	0.999480i	$0.510266\pi$
$830$	2.91311	0.101115
$831$	17.7409	0.615424
$832$	41.6560	1.44416
$833$	0	0
$834$	−4.49320	−0.155587
$835$	−9.77397	−0.338242
$836$	71.7768	2.48245
$837$	5.27915	0.182474
$838$	−3.56781	−0.123248
$839$	−10.8017	−0.372915	−0.186458	−	0.982463i	$-0.559701\pi$
$839$	−10.8017	−0.372915	−0.186458	+	0.982463i	$0.559701\pi$
$840$	0	0
$841$	39.4433	1.36011
$842$	−4.07083	−0.140290
$843$	6.04555	0.208220
$844$	5.88720	0.202646
$845$	26.1758	0.900477
$846$	0.0984149	0.00338358
$847$	0	0
$848$	−15.4498	−0.530548
$849$	−10.3157	−0.354035
$850$	1.33521	0.0457974
$851$	−12.2275	−0.419153
$852$	−21.7932	−0.746622
$853$	13.9727	0.478416	0.239208	−	0.970968i	$-0.423112\pi$
$853$	13.9727	0.478416	0.239208	+	0.970968i	$0.423112\pi$
$854$	0	0
$855$	0.711718	0.0243402
$856$	3.48664	0.119171
$857$	−13.6245	−0.465405	−0.232703	−	0.972548i	$-0.574757\pi$
$857$	−13.6245	−0.465405	−0.232703	+	0.972548i	$0.574757\pi$
$858$	−13.2628	−0.452786
$859$	−52.3806	−1.78720	−0.893601	−	0.448862i	$-0.851829\pi$
$859$	−52.3806	−1.78720	−0.893601	+	0.448862i	$0.851829\pi$
$860$	19.8219	0.675922
$861$	0	0
$862$	−0.197902	−0.00674058
$863$	−25.5953	−0.871273	−0.435637	−	0.900123i	$-0.643477\pi$
$863$	−25.5953	−0.871273	−0.435637	+	0.900123i	$0.643477\pi$
$864$	−14.6001	−0.496707
$865$	3.77874	0.128481
$866$	2.12067	0.0720633
$867$	23.9477	0.813305
$868$	0	0
$869$	22.4630	0.762004
$870$	3.37514	0.114428
$871$	−20.7455	−0.702936
$872$	13.8220	0.468071
$873$	−0.751115	−0.0254214
$874$	6.15285	0.208123
$875$	0	0
$876$	46.1874	1.56053
$877$	−5.36475	−0.181155	−0.0905774	−	0.995889i	$-0.528871\pi$
$877$	−5.36475	−0.181155	−0.0905774	+	0.995889i	$0.528871\pi$
$878$	4.96790	0.167658
$879$	−5.96912	−0.201334
$880$	19.0045	0.640640
$881$	41.9778	1.41427	0.707133	−	0.707080i	$-0.249988\pi$
$881$	41.9778	1.41427	0.707133	+	0.707080i	$0.249988\pi$
$882$	0	0
$883$	−32.4895	−1.09336	−0.546679	−	0.837342i	$-0.684108\pi$
$883$	−32.4895	−1.09336	−0.546679	+	0.837342i	$0.684108\pi$
$884$	67.7662	2.27923
$885$	−0.821722	−0.0276219
$886$	2.39056	0.0803124
$887$	24.9574	0.837989	0.418994	−	0.907989i	$-0.362383\pi$
$887$	24.9574	0.837989	0.418994	+	0.907989i	$0.362383\pi$
$888$	−5.44753	−0.182807
$889$	0	0
$890$	3.71926	0.124670
$891$	−45.1350	−1.51208
$892$	46.9430	1.57177
$893$	29.2091	0.977445
$894$	0.122544	0.00409848
$895$	2.24410	0.0750120
$896$	0	0
$897$	38.4815	1.28486
$898$	−5.15775	−0.172116
$899$	−8.27304	−0.275921
$900$	0.194355	0.00647848
$901$	−23.5336	−0.784016
$902$	−12.6878	−0.422457
$903$	0	0
$904$	10.9204	0.363208
$905$	8.89881	0.295806
$906$	5.35454	0.177893
$907$	−33.0867	−1.09863	−0.549314	−	0.835616i	$-0.685111\pi$
$907$	−33.0867	−1.09863	−0.549314	+	0.835616i	$0.685111\pi$
$908$	41.8724	1.38959
$909$	1.03152	0.0342135
$910$	0	0
$911$	28.6511	0.949255	0.474627	−	0.880187i	$-0.342583\pi$
$911$	28.6511	0.949255	0.474627	+	0.880187i	$0.342583\pi$
$912$	−44.3249	−1.46774
$913$	63.1577	2.09022
$914$	5.76613	0.190727
$915$	−2.81620	−0.0931006
$916$	33.9042	1.12022
$917$	0	0
$918$	−7.04879	−0.232645
$919$	−28.8089	−0.950317	−0.475158	−	0.879900i	$-0.657609\pi$
$919$	−28.8089	−0.950317	−0.475158	+	0.879900i	$0.657609\pi$
$920$	3.41006	0.112426
$921$	−32.5154	−1.07142
$922$	−3.52749	−0.116172
$923$	−41.2334	−1.35722
$924$	0	0
$925$	3.38680	0.111357
$926$	−2.95602	−0.0971408
$927$	−0.0881524	−0.00289531
$928$	22.8801	0.751077
$929$	35.2753	1.15734	0.578672	−	0.815561i	$-0.303571\pi$
$929$	35.2753	1.15734	0.578672	+	0.815561i	$0.303571\pi$
$930$	−0.407968	−0.0133778
$931$	0	0
$932$	−14.8420	−0.486167
$933$	−26.9529	−0.882399
$934$	4.20427	0.137568
$935$	28.9481	0.946705
$936$	−0.591471	−0.0193328
$937$	41.9183	1.36941	0.684705	−	0.728820i	$-0.259931\pi$
$937$	41.9183	1.36941	0.684705	+	0.728820i	$0.259931\pi$
$938$	0	0
$939$	−37.2971	−1.21715
$940$	7.97636	0.260160
$941$	50.8933	1.65907	0.829536	−	0.558453i	$-0.188605\pi$
$941$	50.8933	1.65907	0.829536	+	0.558453i	$0.188605\pi$
$942$	−5.76630	−0.187876
$943$	36.8129	1.19879
$944$	−1.76557	−0.0574643
$945$	0	0
$946$	−12.6968	−0.412807
$947$	54.6355	1.77541	0.887707	−	0.460408i	$-0.152297\pi$
$947$	54.6355	1.77541	0.887707	+	0.460408i	$0.152297\pi$
$948$	−14.3069	−0.464667
$949$	87.3882	2.83674
$950$	−1.70423	−0.0552926
$951$	3.12348	0.101286
$952$	0	0
$953$	32.3306	1.04729	0.523646	−	0.851936i	$-0.324572\pi$
$953$	32.3306	1.04729	0.523646	+	0.851936i	$0.324572\pi$
$954$	0.101207	0.00327669
$955$	−2.57884	−0.0834492
$956$	23.8822	0.772405
$957$	73.1748	2.36541
$958$	−0.896969	−0.0289798
$959$	0	0
$960$	−11.3335	−0.365787
$961$	1.00000	0.0322581
$962$	−5.07844	−0.163735
$963$	0.369320	0.0119012
$964$	12.5193	0.403218
$965$	−2.28065	−0.0734167
$966$	0	0
$967$	−20.5483	−0.660789	−0.330395	−	0.943843i	$-0.607182\pi$
$967$	−20.5483	−0.660789	−0.330395	+	0.943843i	$0.607182\pi$
$968$	−15.0912	−0.485050
$969$	−67.5169	−2.16896
$970$	1.79857	0.0577487
$971$	11.9222	0.382601	0.191300	−	0.981532i	$-0.438730\pi$
$971$	11.9222	0.382601	0.191300	+	0.981532i	$0.438730\pi$
$972$	−2.01894	−0.0647575
$973$	0	0
$974$	7.51948	0.240940
$975$	−10.6587	−0.341352
$976$	−6.05093	−0.193686
$977$	22.4493	0.718217	0.359108	−	0.933296i	$-0.383081\pi$
$977$	22.4493	0.718217	0.359108	+	0.933296i	$0.383081\pi$
$978$	1.48074	0.0473489
$979$	80.6356	2.57713
$980$	0	0
$981$	1.46408	0.0467445
$982$	3.87611	0.123692
$983$	3.42792	0.109334	0.0546668	−	0.998505i	$-0.482590\pi$
$983$	3.42792	0.109334	0.0546668	+	0.998505i	$0.482590\pi$
$984$	16.4007	0.522836
$985$	−20.2903	−0.646503
$986$	11.0463	0.351785
$987$	0	0
$988$	−86.4952	−2.75178
$989$	36.8390	1.17141
$990$	−0.124492	−0.00395662
$991$	0.0482308	0.00153210	0.000766052	−	1.00000i	$-0.499756\pi$
$991$	0.0482308	0.00153210	0.000766052		1.00000i	$0.499756\pi$
$992$	−2.76562	−0.0878086
$993$	22.9481	0.728236
$994$	0	0
$995$	18.3517	0.581787
$996$	−40.2259	−1.27461
$997$	−23.0308	−0.729392	−0.364696	−	0.931127i	$-0.618827\pi$
$997$	−23.0308	−0.729392	−0.364696	+	0.931127i	$0.618827\pi$
$998$	−1.14484	−0.0362392
$999$	−17.8794	−0.565680

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.13		21
7.3	odd	6		1085.2.j.d.156.9	✓	42
7.5	odd	6		1085.2.j.d.466.9	yes	42
7.6	odd	2		7595.2.a.bg.1.13		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.9	✓	42	7.3	odd	6
1085.2.j.d.466.9	yes	42	7.5	odd	6
7595.2.a.bf.1.13		21	1.1	even	1	trivial
7595.2.a.bg.1.13		21	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q+0.239569 q^{2} +1.70292 q^{3} -1.94261 q^{4} +1.00000 q^{5} +0.407968 q^{6} -0.944527 q^{8} -0.100048 q^{9} +O(q^{10})\)	\(q+0.239569 q^{2} +1.70292 q^{3} -1.94261 q^{4} +1.00000 q^{5} +0.407968 q^{6} -0.944527 q^{8} -0.100048 q^{9} +0.239569 q^{10} +5.19399 q^{11} -3.30811 q^{12} -6.25906 q^{13} +1.70292 q^{15} +3.65893 q^{16} +5.57339 q^{17} -0.0239685 q^{18} -7.11374 q^{19} -1.94261 q^{20} +1.24432 q^{22} -3.61033 q^{23} -1.60846 q^{24} +1.00000 q^{25} -1.49948 q^{26} -5.27915 q^{27} +8.27304 q^{29} +0.407968 q^{30} -1.00000 q^{31} +2.76562 q^{32} +8.84497 q^{33} +1.33521 q^{34} +0.194355 q^{36} +3.38680 q^{37} -1.70423 q^{38} -10.6587 q^{39} -0.944527 q^{40} -10.1966 q^{41} -10.2038 q^{43} -10.0899 q^{44} -0.100048 q^{45} -0.864925 q^{46} -4.10601 q^{47} +6.23089 q^{48} +0.239569 q^{50} +9.49106 q^{51} +12.1589 q^{52} -4.22249 q^{53} -1.26472 q^{54} +5.19399 q^{55} -12.1142 q^{57} +1.98197 q^{58} -0.482536 q^{59} -3.30811 q^{60} -1.65374 q^{61} -0.239569 q^{62} -6.65531 q^{64} -6.25906 q^{65} +2.11898 q^{66} +3.31448 q^{67} -10.8269 q^{68} -6.14812 q^{69} +6.58780 q^{71} +0.0944984 q^{72} -13.9619 q^{73} +0.811373 q^{74} +1.70292 q^{75} +13.8192 q^{76} -2.55350 q^{78} +4.32480 q^{79} +3.65893 q^{80} -8.68985 q^{81} -2.44278 q^{82} +12.1598 q^{83} +5.57339 q^{85} -2.44451 q^{86} +14.0884 q^{87} -4.90587 q^{88} +15.5248 q^{89} -0.0239685 q^{90} +7.01346 q^{92} -1.70292 q^{93} -0.983674 q^{94} -7.11374 q^{95} +4.70965 q^{96} +7.50753 q^{97} -0.519650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more