LMFDB - Embedded newform 7595.2.a.bf.1.7

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			1.7
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)

$f(q)$	$=$	$q-1.54789 q^{2} -2.28009 q^{3} +0.395964 q^{4} +1.00000 q^{5} +3.52934 q^{6} +2.48287 q^{8} +2.19883 q^{9} +O(q^{10})$	\(q-1.54789 q^{2} -2.28009 q^{3} +0.395964 q^{4} +1.00000 q^{5} +3.52934 q^{6} +2.48287 q^{8} +2.19883 q^{9} -1.54789 q^{10} +5.50582 q^{11} -0.902836 q^{12} -3.50098 q^{13} -2.28009 q^{15} -4.63514 q^{16} -2.26269 q^{17} -3.40355 q^{18} +0.659063 q^{19} +0.395964 q^{20} -8.52240 q^{22} +5.48680 q^{23} -5.66118 q^{24} +1.00000 q^{25} +5.41914 q^{26} +1.82674 q^{27} +1.83732 q^{29} +3.52934 q^{30} -1.00000 q^{31} +2.20895 q^{32} -12.5538 q^{33} +3.50240 q^{34} +0.870658 q^{36} +9.39924 q^{37} -1.02016 q^{38} +7.98257 q^{39} +2.48287 q^{40} -6.10653 q^{41} -7.49359 q^{43} +2.18011 q^{44} +2.19883 q^{45} -8.49296 q^{46} -3.21110 q^{47} +10.5686 q^{48} -1.54789 q^{50} +5.15915 q^{51} -1.38626 q^{52} +0.151524 q^{53} -2.82760 q^{54} +5.50582 q^{55} -1.50273 q^{57} -2.84397 q^{58} -11.2937 q^{59} -0.902836 q^{60} +14.4743 q^{61} +1.54789 q^{62} +5.85108 q^{64} -3.50098 q^{65} +19.4319 q^{66} -12.4795 q^{67} -0.895945 q^{68} -12.5104 q^{69} -6.50108 q^{71} +5.45941 q^{72} -13.5553 q^{73} -14.5490 q^{74} -2.28009 q^{75} +0.260965 q^{76} -12.3561 q^{78} +6.97785 q^{79} -4.63514 q^{80} -10.7616 q^{81} +9.45223 q^{82} -16.8665 q^{83} -2.26269 q^{85} +11.5992 q^{86} -4.18926 q^{87} +13.6702 q^{88} +9.48335 q^{89} -3.40355 q^{90} +2.17258 q^{92} +2.28009 q^{93} +4.97043 q^{94} +0.659063 q^{95} -5.03661 q^{96} -6.36860 q^{97} +12.1064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.54789	−1.09452	−0.547262	−	0.836961i	$-0.684330\pi$
$2$	−1.54789	−1.09452	−0.547262	+	0.836961i	$0.684330\pi$
$3$	−2.28009	−1.31641	−0.658207	−	0.752837i	$-0.728685\pi$
$3$	−2.28009	−1.31641	−0.658207	+	0.752837i	$0.728685\pi$
$4$	0.395964	0.197982
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	3.52934	1.44085
$7$	0	0
$7$	0	0
$8$	2.48287	0.877828
$9$	2.19883	0.732943
$10$	−1.54789	−0.489486
$11$	5.50582	1.66007	0.830033	−	0.557714i	$-0.188321\pi$
$11$	5.50582	1.66007	0.830033	+	0.557714i	$0.188321\pi$
$12$	−0.902836	−0.260626
$13$	−3.50098	−0.970998	−0.485499	−	0.874237i	$-0.661362\pi$
$13$	−3.50098	−0.970998	−0.485499	+	0.874237i	$0.661362\pi$
$14$	0	0
$15$	−2.28009	−0.588718
$16$	−4.63514	−1.15879
$17$	−2.26269	−0.548783	−0.274392	−	0.961618i	$-0.588476\pi$
$17$	−2.26269	−0.548783	−0.274392	+	0.961618i	$0.588476\pi$
$18$	−3.40355	−0.802224
$19$	0.659063	0.151199	0.0755997	−	0.997138i	$-0.475913\pi$
$19$	0.659063	0.151199	0.0755997	+	0.997138i	$0.475913\pi$
$20$	0.395964	0.0885403
$21$	0	0
$22$	−8.52240	−1.81698
$23$	5.48680	1.14408	0.572038	−	0.820227i	$-0.306153\pi$
$23$	5.48680	1.14408	0.572038	+	0.820227i	$0.306153\pi$
$24$	−5.66118	−1.15558
$25$	1.00000	0.200000
$26$	5.41914	1.06278
$27$	1.82674	0.351557
$28$	0	0
$29$	1.83732	0.341182	0.170591	−	0.985342i	$-0.445432\pi$
$29$	1.83732	0.341182	0.170591	+	0.985342i	$0.445432\pi$
$30$	3.52934	0.644366
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	2.20895	0.390490
$33$	−12.5538	−2.18533
$34$	3.50240	0.600656
$35$	0	0
$36$	0.870658	0.145110
$37$	9.39924	1.54522	0.772612	−	0.634878i	$-0.218950\pi$
$37$	9.39924	1.54522	0.772612	+	0.634878i	$0.218950\pi$
$38$	−1.02016	−0.165491
$39$	7.98257	1.27823
$40$	2.48287	0.392576
$41$	−6.10653	−0.953679	−0.476840	−	0.878990i	$-0.658218\pi$
$41$	−6.10653	−0.953679	−0.476840	+	0.878990i	$0.658218\pi$
$42$	0	0
$43$	−7.49359	−1.14276	−0.571381	−	0.820685i	$-0.693592\pi$
$43$	−7.49359	−1.14276	−0.571381	+	0.820685i	$0.693592\pi$
$44$	2.18011	0.328663
$45$	2.19883	0.327782
$46$	−8.49296	−1.25222
$47$	−3.21110	−0.468387	−0.234193	−	0.972190i	$-0.575245\pi$
$47$	−3.21110	−0.468387	−0.234193	+	0.972190i	$0.575245\pi$
$48$	10.5686	1.52544
$49$	0	0
$50$	−1.54789	−0.218905
$51$	5.15915	0.722426
$52$	−1.38626	−0.192240
$53$	0.151524	0.0208134	0.0104067	−	0.999946i	$-0.496687\pi$
$53$	0.151524	0.0208134	0.0104067	+	0.999946i	$0.496687\pi$
$54$	−2.82760	−0.384787
$55$	5.50582	0.742404
$56$	0	0
$57$	−1.50273	−0.199041
$58$	−2.84397	−0.373432
$59$	−11.2937	−1.47031	−0.735157	−	0.677897i	$-0.762892\pi$
$59$	−11.2937	−1.47031	−0.735157	+	0.677897i	$0.762892\pi$
$60$	−0.902836	−0.116556
$61$	14.4743	1.85325	0.926624	−	0.375989i	$-0.122697\pi$
$61$	14.4743	1.85325	0.926624	+	0.375989i	$0.122697\pi$
$62$	1.54789	0.196582
$63$	0	0
$64$	5.85108	0.731384
$65$	−3.50098	−0.434243
$66$	19.4319	2.39190
$67$	−12.4795	−1.52461	−0.762306	−	0.647216i	$-0.775933\pi$
$67$	−12.4795	−1.52461	−0.762306	+	0.647216i	$0.775933\pi$
$68$	−0.895945	−0.108649
$69$	−12.5104	−1.50608
$70$	0	0
$71$	−6.50108	−0.771537	−0.385768	−	0.922596i	$-0.626064\pi$
$71$	−6.50108	−0.771537	−0.385768	+	0.922596i	$0.626064\pi$
$72$	5.45941	0.643398
$73$	−13.5553	−1.58653	−0.793266	−	0.608875i	$-0.791621\pi$
$73$	−13.5553	−1.58653	−0.793266	+	0.608875i	$0.791621\pi$
$74$	−14.5490	−1.69129
$75$	−2.28009	−0.263283
$76$	0.260965	0.0299348
$77$	0	0
$78$	−12.3561	−1.39906
$79$	6.97785	0.785069	0.392535	−	0.919737i	$-0.371598\pi$
$79$	6.97785	0.785069	0.392535	+	0.919737i	$0.371598\pi$
$80$	−4.63514	−0.518224
$81$	−10.7616	−1.19574
$82$	9.45223	1.04382
$83$	−16.8665	−1.85134	−0.925669	−	0.378336i	$-0.876497\pi$
$83$	−16.8665	−1.85134	−0.925669	+	0.378336i	$0.876497\pi$
$84$	0	0
$85$	−2.26269	−0.245423
$86$	11.5992	1.25078
$87$	−4.18926	−0.449136
$88$	13.6702	1.45725
$89$	9.48335	1.00523	0.502616	−	0.864510i	$-0.332371\pi$
$89$	9.48335	1.00523	0.502616	+	0.864510i	$0.332371\pi$
$90$	−3.40355	−0.358765
$91$	0	0
$92$	2.17258	0.226507
$93$	2.28009	0.236435
$94$	4.97043	0.512660
$95$	0.659063	0.0676184
$96$	−5.03661	−0.514046
$97$	−6.36860	−0.646633	−0.323317	−	0.946291i	$-0.604798\pi$
$97$	−6.36860	−0.646633	−0.323317	+	0.946291i	$0.604798\pi$
$98$	0	0
$99$	12.1064	1.21673
$100$	0.395964	0.0395964
$101$	−7.16898	−0.713340	−0.356670	−	0.934230i	$-0.616088\pi$
$101$	−7.16898	−0.713340	−0.356670	+	0.934230i	$0.616088\pi$
$102$	−7.98580	−0.790712
$103$	−1.60204	−0.157854	−0.0789268	−	0.996880i	$-0.525149\pi$
$103$	−1.60204	−0.157854	−0.0789268	+	0.996880i	$0.525149\pi$
$104$	−8.69249	−0.852369
$105$	0	0
$106$	−0.234542	−0.0227807
$107$	−9.39372	−0.908125	−0.454063	−	0.890970i	$-0.650026\pi$
$107$	−9.39372	−0.908125	−0.454063	+	0.890970i	$0.650026\pi$
$108$	0.723325	0.0696020
$109$	−0.658076	−0.0630323	−0.0315161	−	0.999503i	$-0.510034\pi$
$109$	−0.658076	−0.0630323	−0.0315161	+	0.999503i	$0.510034\pi$
$110$	−8.52240	−0.812579
$111$	−21.4311	−2.03415
$112$	0	0
$113$	−4.19428	−0.394565	−0.197282	−	0.980347i	$-0.563212\pi$
$113$	−4.19428	−0.394565	−0.197282	+	0.980347i	$0.563212\pi$
$114$	2.32605	0.217855
$115$	5.48680	0.511647
$116$	0.727513	0.0675479
$117$	−7.69806	−0.711686
$118$	17.4814	1.60929
$119$	0	0
$120$	−5.66118	−0.516793
$121$	19.3140	1.75582
$122$	−22.4047	−2.02842
$123$	13.9235	1.25544
$124$	−0.395964	−0.0355586
$125$	1.00000	0.0894427
$126$	0	0
$127$	0.405614	0.0359924	0.0179962	−	0.999838i	$-0.494271\pi$
$127$	0.405614	0.0359924	0.0179962	+	0.999838i	$0.494271\pi$
$128$	−13.4747	−1.19101
$129$	17.0861	1.50435
$130$	5.41914	0.475290
$131$	15.3228	1.33876	0.669378	−	0.742922i	$-0.266561\pi$
$131$	15.3228	1.33876	0.669378	+	0.742922i	$0.266561\pi$
$132$	−4.97085	−0.432657
$133$	0	0
$134$	19.3169	1.66872
$135$	1.82674	0.157221
$136$	−5.61797	−0.481737
$137$	6.25650	0.534529	0.267264	−	0.963623i	$-0.413880\pi$
$137$	6.25650	0.534529	0.267264	+	0.963623i	$0.413880\pi$
$138$	19.3648	1.64844
$139$	16.9729	1.43962	0.719810	−	0.694172i	$-0.244229\pi$
$139$	16.9729	1.43962	0.719810	+	0.694172i	$0.244229\pi$
$140$	0	0
$141$	7.32161	0.616591
$142$	10.0630	0.844465
$143$	−19.2758	−1.61192
$144$	−10.1919	−0.849324
$145$	1.83732	0.152581
$146$	20.9822	1.73650
$147$	0	0
$148$	3.72176	0.305927
$149$	−9.73968	−0.797905	−0.398953	−	0.916972i	$-0.630626\pi$
$149$	−9.73968	−0.797905	−0.398953	+	0.916972i	$0.630626\pi$
$150$	3.52934	0.288169
$151$	−11.5032	−0.936117	−0.468058	−	0.883698i	$-0.655046\pi$
$151$	−11.5032	−0.936117	−0.468058	+	0.883698i	$0.655046\pi$
$152$	1.63637	0.132727
$153$	−4.97527	−0.402227
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	3.16081	0.253067
$157$	13.4330	1.07207	0.536035	−	0.844196i	$-0.319921\pi$
$157$	13.4330	1.07207	0.536035	+	0.844196i	$0.319921\pi$
$158$	−10.8009	−0.859277
$159$	−0.345488	−0.0273990
$160$	2.20895	0.174633
$161$	0	0
$162$	16.6578	1.30876
$163$	−21.0713	−1.65043	−0.825217	−	0.564816i	$-0.808947\pi$
$163$	−21.0713	−1.65043	−0.825217	+	0.564816i	$0.808947\pi$
$164$	−2.41797	−0.188811
$165$	−12.5538	−0.977311
$166$	26.1075	2.02633
$167$	3.45837	0.267617	0.133808	−	0.991007i	$-0.457279\pi$
$167$	3.45837	0.267617	0.133808	+	0.991007i	$0.457279\pi$
$168$	0	0
$169$	−0.743122	−0.0571632
$170$	3.50240	0.268622
$171$	1.44917	0.110821
$172$	−2.96719	−0.226246
$173$	−3.36388	−0.255751	−0.127875	−	0.991790i	$-0.540816\pi$
$173$	−3.36388	−0.255751	−0.127875	+	0.991790i	$0.540816\pi$
$174$	6.48452	0.491590
$175$	0	0
$176$	−25.5202	−1.92366
$177$	25.7507	1.93554
$178$	−14.6792	−1.10025
$179$	16.4073	1.22634	0.613169	−	0.789952i	$-0.289894\pi$
$179$	16.4073	1.22634	0.613169	+	0.789952i	$0.289894\pi$
$180$	0.870658	0.0648950
$181$	1.97277	0.146635	0.0733175	−	0.997309i	$-0.476641\pi$
$181$	1.97277	0.146635	0.0733175	+	0.997309i	$0.476641\pi$
$182$	0	0
$183$	−33.0028	−2.43964
$184$	13.6230	1.00430
$185$	9.39924	0.691046
$186$	−3.52934	−0.258783
$187$	−12.4580	−0.911017
$188$	−1.27148	−0.0927322
$189$	0	0
$190$	−1.02016	−0.0740100
$191$	−7.14928	−0.517304	−0.258652	−	0.965971i	$-0.583278\pi$
$191$	−7.14928	−0.517304	−0.258652	+	0.965971i	$0.583278\pi$
$192$	−13.3410	−0.962804
$193$	20.6879	1.48915	0.744575	−	0.667539i	$-0.232652\pi$
$193$	20.6879	1.48915	0.744575	+	0.667539i	$0.232652\pi$
$194$	9.85789	0.707755
$195$	7.98257	0.571644
$196$	0	0
$197$	11.6752	0.831826	0.415913	−	0.909404i	$-0.363462\pi$
$197$	11.6752	0.831826	0.415913	+	0.909404i	$0.363462\pi$
$198$	−18.7393	−1.33174
$199$	3.79354	0.268917	0.134459	−	0.990919i	$-0.457070\pi$
$199$	3.79354	0.268917	0.134459	+	0.990919i	$0.457070\pi$
$200$	2.48287	0.175566
$201$	28.4544	2.00702
$202$	11.0968	0.780768
$203$	0	0
$204$	2.04284	0.143027
$205$	−6.10653	−0.426498
$206$	2.47978	0.172774
$207$	12.0645	0.838543
$208$	16.2275	1.12518
$209$	3.62868	0.251001
$210$	0	0
$211$	16.7321	1.15189	0.575943	−	0.817490i	$-0.304635\pi$
$211$	16.7321	1.15189	0.575943	+	0.817490i	$0.304635\pi$
$212$	0.0599980	0.00412068
$213$	14.8231	1.01566
$214$	14.5405	0.993965
$215$	−7.49359	−0.511058
$216$	4.53557	0.308606
$217$	0	0
$218$	1.01863	0.0689903
$219$	30.9074	2.08853
$220$	2.18011	0.146983
$221$	7.92164	0.532867
$222$	33.1731	2.22643
$223$	17.7759	1.19036	0.595181	−	0.803592i	$-0.297080\pi$
$223$	17.7759	1.19036	0.595181	+	0.803592i	$0.297080\pi$
$224$	0	0
$225$	2.19883	0.146589
$226$	6.49228	0.431860
$227$	17.3484	1.15145	0.575727	−	0.817642i	$-0.304719\pi$
$227$	17.3484	1.15145	0.575727	+	0.817642i	$0.304719\pi$
$228$	−0.595025	−0.0394065
$229$	−17.0933	−1.12956	−0.564779	−	0.825242i	$-0.691039\pi$
$229$	−17.0933	−1.12956	−0.564779	+	0.825242i	$0.691039\pi$
$230$	−8.49296	−0.560009
$231$	0	0
$232$	4.56183	0.299499
$233$	−29.5448	−1.93555	−0.967773	−	0.251823i	$-0.918970\pi$
$233$	−29.5448	−1.93555	−0.967773	+	0.251823i	$0.918970\pi$
$234$	11.9158	0.778958
$235$	−3.21110	−0.209469
$236$	−4.47190	−0.291096
$237$	−15.9102	−1.03348
$238$	0	0
$239$	3.51114	0.227117	0.113559	−	0.993531i	$-0.463775\pi$
$239$	3.51114	0.227117	0.113559	+	0.993531i	$0.463775\pi$
$240$	10.5686	0.682197
$241$	−14.2799	−0.919850	−0.459925	−	0.887958i	$-0.652124\pi$
$241$	−14.2799	−0.919850	−0.459925	+	0.887958i	$0.652124\pi$
$242$	−29.8960	−1.92179
$243$	19.0573	1.22253
$244$	5.73132	0.366910
$245$	0	0
$246$	−21.5520	−1.37410
$247$	−2.30737	−0.146814
$248$	−2.48287	−0.157662
$249$	38.4572	2.43712
$250$	−1.54789	−0.0978972
$251$	−16.5619	−1.04538	−0.522690	−	0.852523i	$-0.675072\pi$
$251$	−16.5619	−1.04538	−0.522690	+	0.852523i	$0.675072\pi$
$252$	0	0
$253$	30.2093	1.89924
$254$	−0.627845	−0.0393945
$255$	5.15915	0.323079
$256$	9.15523	0.572202
$257$	4.47848	0.279360	0.139680	−	0.990197i	$-0.455393\pi$
$257$	4.47848	0.279360	0.139680	+	0.990197i	$0.455393\pi$
$258$	−26.4474	−1.64654
$259$	0	0
$260$	−1.38626	−0.0859724
$261$	4.03995	0.250067
$262$	−23.7179	−1.46530
$263$	−9.86910	−0.608555	−0.304277	−	0.952583i	$-0.598415\pi$
$263$	−9.86910	−0.608555	−0.304277	+	0.952583i	$0.598415\pi$
$264$	−31.1694	−1.91835
$265$	0.151524	0.00930803
$266$	0	0
$267$	−21.6229	−1.32330
$268$	−4.94143	−0.301846
$269$	8.50542	0.518585	0.259292	−	0.965799i	$-0.416511\pi$
$269$	8.50542	0.518585	0.259292	+	0.965799i	$0.416511\pi$
$270$	−2.82760	−0.172082
$271$	31.9230	1.93918	0.969592	−	0.244725i	$-0.0786978\pi$
$271$	31.9230	1.93918	0.969592	+	0.244725i	$0.0786978\pi$
$272$	10.4879	0.635922
$273$	0	0
$274$	−9.68438	−0.585055
$275$	5.50582	0.332013
$276$	−4.95368	−0.298176
$277$	21.3962	1.28557	0.642787	−	0.766045i	$-0.277778\pi$
$277$	21.3962	1.28557	0.642787	+	0.766045i	$0.277778\pi$
$278$	−26.2721	−1.57570
$279$	−2.19883	−0.131640
$280$	0	0
$281$	−2.06621	−0.123260	−0.0616298	−	0.998099i	$-0.519630\pi$
$281$	−2.06621	−0.123260	−0.0616298	+	0.998099i	$0.519630\pi$
$282$	−11.3330	−0.674873
$283$	−8.79967	−0.523086	−0.261543	−	0.965192i	$-0.584231\pi$
$283$	−8.79967	−0.523086	−0.261543	+	0.965192i	$0.584231\pi$
$284$	−2.57420	−0.152750
$285$	−1.50273	−0.0890138
$286$	29.8368	1.76429
$287$	0	0
$288$	4.85710	0.286207
$289$	−11.8802	−0.698837
$290$	−2.84397	−0.167004
$291$	14.5210	0.851236
$292$	−5.36743	−0.314105
$293$	−16.4137	−0.958899	−0.479450	−	0.877569i	$-0.659164\pi$
$293$	−16.4137	−0.958899	−0.479450	+	0.877569i	$0.659164\pi$
$294$	0	0
$295$	−11.2937	−0.657544
$296$	23.3371	1.35644
$297$	10.0577	0.583608
$298$	15.0759	0.873326
$299$	−19.2092	−1.11090
$300$	−0.902836	−0.0521252
$301$	0	0
$302$	17.8057	1.02460
$303$	16.3459	0.939050
$304$	−3.05485	−0.175208
$305$	14.4743	0.828798
$306$	7.70118	0.440247
$307$	4.85418	0.277042	0.138521	−	0.990359i	$-0.455765\pi$
$307$	4.85418	0.277042	0.138521	+	0.990359i	$0.455765\pi$
$308$	0	0
$309$	3.65280	0.207800
$310$	1.54789	0.0879143
$311$	18.8152	1.06691	0.533455	−	0.845829i	$-0.320893\pi$
$311$	18.8152	1.06691	0.533455	+	0.845829i	$0.320893\pi$
$312$	19.8197	1.12207
$313$	−25.2101	−1.42496	−0.712479	−	0.701694i	$-0.752427\pi$
$313$	−25.2101	−1.42496	−0.712479	+	0.701694i	$0.752427\pi$
$314$	−20.7928	−1.17341
$315$	0	0
$316$	2.76298	0.155430
$317$	24.1699	1.35751	0.678757	−	0.734363i	$-0.262519\pi$
$317$	24.1699	1.35751	0.678757	+	0.734363i	$0.262519\pi$
$318$	0.534778	0.0299889
$319$	10.1160	0.566385
$320$	5.85108	0.327085
$321$	21.4186	1.19547
$322$	0	0
$323$	−1.49126	−0.0829757
$324$	−4.26122	−0.236735
$325$	−3.50098	−0.194200
$326$	32.6161	1.80644
$327$	1.50048	0.0829765
$328$	−15.1617	−0.837166
$329$	0	0
$330$	19.4319	1.06969
$331$	−7.55808	−0.415430	−0.207715	−	0.978189i	$-0.566603\pi$
$331$	−7.55808	−0.415430	−0.207715	+	0.978189i	$0.566603\pi$
$332$	−6.67852	−0.366532
$333$	20.6673	1.13256
$334$	−5.35317	−0.292913
$335$	−12.4795	−0.681827
$336$	0	0
$337$	−19.4435	−1.05916	−0.529578	−	0.848261i	$-0.677650\pi$
$337$	−19.4435	−1.05916	−0.529578	+	0.848261i	$0.677650\pi$
$338$	1.15027	0.0625665
$339$	9.56335	0.519410
$340$	−0.895945	−0.0485894
$341$	−5.50582	−0.298157
$342$	−2.24315	−0.121296
$343$	0	0
$344$	−18.6056	−1.00315
$345$	−12.5104	−0.673538
$346$	5.20691	0.279925
$347$	−17.0339	−0.914429	−0.457215	−	0.889356i	$-0.651153\pi$
$347$	−17.0339	−0.914429	−0.457215	+	0.889356i	$0.651153\pi$
$348$	−1.65880	−0.0889209
$349$	−34.4438	−1.84374	−0.921868	−	0.387503i	$-0.873338\pi$
$349$	−34.4438	−1.84374	−0.921868	+	0.387503i	$0.873338\pi$
$350$	0	0
$351$	−6.39540	−0.341361
$352$	12.1621	0.648240
$353$	−19.1989	−1.02186	−0.510928	−	0.859624i	$-0.670698\pi$
$353$	−19.1989	−1.02186	−0.510928	+	0.859624i	$0.670698\pi$
$354$	−39.8592	−2.11849
$355$	−6.50108	−0.345042
$356$	3.75507	0.199018
$357$	0	0
$358$	−25.3967	−1.34226
$359$	22.4418	1.18443	0.592216	−	0.805779i	$-0.298253\pi$
$359$	22.4418	1.18443	0.592216	+	0.805779i	$0.298253\pi$
$360$	5.45941	0.287736
$361$	−18.5656	−0.977139
$362$	−3.05364	−0.160496
$363$	−44.0378	−2.31139
$364$	0	0
$365$	−13.5553	−0.709519
$366$	51.0848	2.67024
$367$	−10.5900	−0.552795	−0.276397	−	0.961043i	$-0.589141\pi$
$367$	−10.5900	−0.552795	−0.276397	+	0.961043i	$0.589141\pi$
$368$	−25.4321	−1.32574
$369$	−13.4272	−0.698993
$370$	−14.5490	−0.756366
$371$	0	0
$372$	0.902836	0.0468098
$373$	34.9117	1.80766	0.903828	−	0.427895i	$-0.140745\pi$
$373$	34.9117	1.80766	0.903828	+	0.427895i	$0.140745\pi$
$374$	19.2836	0.997130
$375$	−2.28009	−0.117744
$376$	−7.97274	−0.411163
$377$	−6.43243	−0.331287
$378$	0	0
$379$	26.8982	1.38167	0.690834	−	0.723014i	$-0.257244\pi$
$379$	26.8982	1.38167	0.690834	+	0.723014i	$0.257244\pi$
$380$	0.260965	0.0133872
$381$	−0.924837	−0.0473809
$382$	11.0663	0.566201
$383$	−13.6362	−0.696775	−0.348388	−	0.937351i	$-0.613271\pi$
$383$	−13.6362	−0.696775	−0.348388	+	0.937351i	$0.613271\pi$
$384$	30.7236	1.56786
$385$	0	0
$386$	−32.0226	−1.62991
$387$	−16.4771	−0.837579
$388$	−2.52174	−0.128022
$389$	−23.1711	−1.17482	−0.587409	−	0.809290i	$-0.699852\pi$
$389$	−23.1711	−1.17482	−0.587409	+	0.809290i	$0.699852\pi$
$390$	−12.3561	−0.625678
$391$	−12.4149	−0.627850
$392$	0	0
$393$	−34.9373	−1.76236
$394$	−18.0720	−0.910454
$395$	6.97785	0.351094
$396$	4.79368	0.240892
$397$	−10.0484	−0.504315	−0.252158	−	0.967686i	$-0.581140\pi$
$397$	−10.0484	−0.504315	−0.252158	+	0.967686i	$0.581140\pi$
$398$	−5.87199	−0.294336
$399$	0	0
$400$	−4.63514	−0.231757
$401$	9.20785	0.459818	0.229909	−	0.973212i	$-0.426157\pi$
$401$	9.20785	0.459818	0.229909	+	0.973212i	$0.426157\pi$
$402$	−44.0443	−2.19673
$403$	3.50098	0.174396
$404$	−2.83866	−0.141229
$405$	−10.7616	−0.534750
$406$	0	0
$407$	51.7505	2.56518
$408$	12.8095	0.634165
$409$	−24.9030	−1.23137	−0.615687	−	0.787991i	$-0.711121\pi$
$409$	−24.9030	−1.23137	−0.615687	+	0.787991i	$0.711121\pi$
$410$	9.45223	0.466812
$411$	−14.2654	−0.703661
$412$	−0.634350	−0.0312522
$413$	0	0
$414$	−18.6746	−0.917806
$415$	−16.8665	−0.827943
$416$	−7.73348	−0.379165
$417$	−38.6997	−1.89513
$418$	−5.61680	−0.274727
$419$	−15.0451	−0.735003	−0.367501	−	0.930023i	$-0.619787\pi$
$419$	−15.0451	−0.735003	−0.367501	+	0.930023i	$0.619787\pi$
$420$	0	0
$421$	−14.3659	−0.700149	−0.350074	−	0.936722i	$-0.613844\pi$
$421$	−14.3659	−0.700149	−0.350074	+	0.936722i	$0.613844\pi$
$422$	−25.8995	−1.26077
$423$	−7.06066	−0.343301
$424$	0.376214	0.0182706
$425$	−2.26269	−0.109757
$426$	−22.9445	−1.11166
$427$	0	0
$428$	−3.71958	−0.179793
$429$	43.9506	2.12195
$430$	11.5992	0.559365
$431$	6.25088	0.301094	0.150547	−	0.988603i	$-0.451896\pi$
$431$	6.25088	0.301094	0.150547	+	0.988603i	$0.451896\pi$
$432$	−8.46721	−0.407379
$433$	−18.4479	−0.886548	−0.443274	−	0.896386i	$-0.646183\pi$
$433$	−18.4479	−0.886548	−0.443274	+	0.896386i	$0.646183\pi$
$434$	0	0
$435$	−4.18926	−0.200860
$436$	−0.260575	−0.0124793
$437$	3.61615	0.172984
$438$	−47.8413	−2.28595
$439$	−30.2391	−1.44323	−0.721617	−	0.692293i	$-0.756601\pi$
$439$	−30.2391	−1.44323	−0.721617	+	0.692293i	$0.756601\pi$
$440$	13.6702	0.651703
$441$	0	0
$442$	−12.2618	−0.583236
$443$	−13.1992	−0.627115	−0.313557	−	0.949569i	$-0.601521\pi$
$443$	−13.1992	−0.627115	−0.313557	+	0.949569i	$0.601521\pi$
$444$	−8.48596	−0.402726
$445$	9.48335	0.449554
$446$	−27.5151	−1.30288
$447$	22.2074	1.05037
$448$	0	0
$449$	22.3159	1.05315	0.526577	−	0.850128i	$-0.323475\pi$
$449$	22.3159	1.05315	0.526577	+	0.850128i	$0.323475\pi$
$450$	−3.40355	−0.160445
$451$	−33.6214	−1.58317
$452$	−1.66078	−0.0781167
$453$	26.2284	1.23232
$454$	−26.8534	−1.26029
$455$	0	0
$456$	−3.73107	−0.174724
$457$	−26.9409	−1.26024	−0.630120	−	0.776498i	$-0.716994\pi$
$457$	−26.9409	−1.26024	−0.630120	+	0.776498i	$0.716994\pi$
$458$	26.4586	1.23633
$459$	−4.13336	−0.192929
$460$	2.17258	0.101297
$461$	17.8260	0.830238	0.415119	−	0.909767i	$-0.363740\pi$
$461$	17.8260	0.830238	0.415119	+	0.909767i	$0.363740\pi$
$462$	0	0
$463$	37.4269	1.73938	0.869688	−	0.493601i	$-0.164320\pi$
$463$	37.4269	1.73938	0.869688	+	0.493601i	$0.164320\pi$
$464$	−8.51624	−0.395356
$465$	2.28009	0.105737
$466$	45.7322	2.11850
$467$	−19.0936	−0.883544	−0.441772	−	0.897127i	$-0.645650\pi$
$467$	−19.0936	−0.883544	−0.441772	+	0.897127i	$0.645650\pi$
$468$	−3.04816	−0.140901
$469$	0	0
$470$	4.97043	0.229269
$471$	−30.6285	−1.41129
$472$	−28.0408	−1.29068
$473$	−41.2583	−1.89706
$474$	24.6272	1.13116
$475$	0.659063	0.0302399
$476$	0	0
$477$	0.333175	0.0152550
$478$	−5.43487	−0.248585
$479$	18.0382	0.824186	0.412093	−	0.911142i	$-0.364798\pi$
$479$	18.0382	0.824186	0.412093	+	0.911142i	$0.364798\pi$
$480$	−5.03661	−0.229889
$481$	−32.9066	−1.50041
$482$	22.1037	1.00680
$483$	0	0
$484$	7.64766	0.347621
$485$	−6.36860	−0.289183
$486$	−29.4986	−1.33809
$487$	−5.28354	−0.239420	−0.119710	−	0.992809i	$-0.538196\pi$
$487$	−5.28354	−0.239420	−0.119710	+	0.992809i	$0.538196\pi$
$488$	35.9379	1.62683
$489$	48.0446	2.17265
$490$	0	0
$491$	19.9966	0.902436	0.451218	−	0.892414i	$-0.350990\pi$
$491$	19.9966	0.902436	0.451218	+	0.892414i	$0.350990\pi$
$492$	5.51319	0.248554
$493$	−4.15729	−0.187235
$494$	3.57155	0.160692
$495$	12.1064	0.544140
$496$	4.63514	0.208124
$497$	0	0
$498$	−59.5275	−2.66749
$499$	1.66707	0.0746281	0.0373140	−	0.999304i	$-0.488120\pi$
$499$	1.66707	0.0746281	0.0373140	+	0.999304i	$0.488120\pi$
$500$	0.395964	0.0177081
$501$	−7.88540	−0.352294
$502$	25.6361	1.14419
$503$	−7.35046	−0.327741	−0.163870	−	0.986482i	$-0.552398\pi$
$503$	−7.35046	−0.327741	−0.163870	+	0.986482i	$0.552398\pi$
$504$	0	0
$505$	−7.16898	−0.319015
$506$	−46.7607	−2.07877
$507$	1.69439	0.0752504
$508$	0.160608	0.00712585
$509$	26.3271	1.16693	0.583463	−	0.812139i	$-0.301697\pi$
$509$	26.3271	1.16693	0.583463	+	0.812139i	$0.301697\pi$
$510$	−7.98580	−0.353617
$511$	0	0
$512$	12.7781	0.564719
$513$	1.20394	0.0531552
$514$	−6.93219	−0.305766
$515$	−1.60204	−0.0705942
$516$	6.76548	0.297833
$517$	−17.6797	−0.777553
$518$	0	0
$519$	7.66996	0.336674
$520$	−8.69249	−0.381191
$521$	1.18497	0.0519143	0.0259572	−	0.999663i	$-0.491737\pi$
$521$	1.18497	0.0519143	0.0259572	+	0.999663i	$0.491737\pi$
$522$	−6.25341	−0.273704
$523$	27.3332	1.19520	0.597600	−	0.801795i	$-0.296121\pi$
$523$	27.3332	1.19520	0.597600	+	0.801795i	$0.296121\pi$
$524$	6.06726	0.265050
$525$	0	0
$526$	15.2763	0.666078
$527$	2.26269	0.0985644
$528$	58.1886	2.53233
$529$	7.10497	0.308912
$530$	−0.234542	−0.0101879
$531$	−24.8329	−1.07766
$532$	0	0
$533$	21.3788	0.926020
$534$	33.4699	1.44838
$535$	−9.39372	−0.406126
$536$	−30.9850	−1.33835
$537$	−37.4102	−1.61437
$538$	−13.1655	−0.567603
$539$	0	0
$540$	0.723325	0.0311270
$541$	12.1877	0.523988	0.261994	−	0.965069i	$-0.415620\pi$
$541$	12.1877	0.523988	0.261994	+	0.965069i	$0.415620\pi$
$542$	−49.4133	−2.12248
$543$	−4.49811	−0.193032
$544$	−4.99816	−0.214295
$545$	−0.658076	−0.0281889
$546$	0	0
$547$	−4.44981	−0.190260	−0.0951300	−	0.995465i	$-0.530327\pi$
$547$	−4.44981	−0.190260	−0.0951300	+	0.995465i	$0.530327\pi$
$548$	2.47735	0.105827
$549$	31.8266	1.35833
$550$	−8.52240	−0.363396
$551$	1.21091	0.0515865
$552$	−31.0618	−1.32208
$553$	0	0
$554$	−33.1190	−1.40709
$555$	−21.4311	−0.909701
$556$	6.72064	0.285019
$557$	−25.0794	−1.06265	−0.531324	−	0.847169i	$-0.678305\pi$
$557$	−25.0794	−1.06265	−0.531324	+	0.847169i	$0.678305\pi$
$558$	3.40355	0.144084
$559$	26.2349	1.10962
$560$	0	0
$561$	28.4053	1.19927
$562$	3.19826	0.134911
$563$	3.24479	0.136751	0.0683757	−	0.997660i	$-0.478218\pi$
$563$	3.24479	0.136751	0.0683757	+	0.997660i	$0.478218\pi$
$564$	2.89909	0.122074
$565$	−4.19428	−0.176455
$566$	13.6209	0.572530
$567$	0	0
$568$	−16.1414	−0.677276
$569$	−29.0240	−1.21675	−0.608376	−	0.793649i	$-0.708179\pi$
$569$	−29.0240	−1.21675	−0.608376	+	0.793649i	$0.708179\pi$
$570$	2.32605	0.0974277
$571$	−26.9001	−1.12574	−0.562868	−	0.826547i	$-0.690302\pi$
$571$	−26.9001	−1.12574	−0.562868	+	0.826547i	$0.690302\pi$
$572$	−7.63251	−0.319131
$573$	16.3010	0.680986
$574$	0	0
$575$	5.48680	0.228815
$576$	12.8655	0.536063
$577$	22.3390	0.929983	0.464992	−	0.885315i	$-0.346057\pi$
$577$	22.3390	0.929983	0.464992	+	0.885315i	$0.346057\pi$
$578$	18.3893	0.764893
$579$	−47.1704	−1.96034
$580$	0.727513	0.0302083
$581$	0	0
$582$	−22.4769	−0.931698
$583$	0.834262	0.0345516
$584$	−33.6562	−1.39270
$585$	−7.69806	−0.318276
$586$	25.4066	1.04954
$587$	9.67462	0.399314	0.199657	−	0.979866i	$-0.436017\pi$
$587$	9.67462	0.399314	0.199657	+	0.979866i	$0.436017\pi$
$588$	0	0
$589$	−0.659063	−0.0271562
$590$	17.4814	0.719698
$591$	−26.6207	−1.09503
$592$	−43.5668	−1.79058
$593$	−38.8741	−1.59637	−0.798185	−	0.602413i	$-0.794206\pi$
$593$	−38.8741	−1.59637	−0.798185	+	0.602413i	$0.794206\pi$
$594$	−15.5682	−0.638773
$595$	0	0
$596$	−3.85656	−0.157971
$597$	−8.64963	−0.354006
$598$	29.7337	1.21590
$599$	18.6962	0.763905	0.381953	−	0.924182i	$-0.375252\pi$
$599$	18.6962	0.763905	0.381953	+	0.924182i	$0.375252\pi$
$600$	−5.66118	−0.231117
$601$	12.6018	0.514038	0.257019	−	0.966406i	$-0.417260\pi$
$601$	12.6018	0.514038	0.257019	+	0.966406i	$0.417260\pi$
$602$	0	0
$603$	−27.4403	−1.11745
$604$	−4.55485	−0.185334
$605$	19.3140	0.785227
$606$	−25.3017	−1.02781
$607$	17.5302	0.711528	0.355764	−	0.934576i	$-0.384221\pi$
$607$	17.5302	0.711528	0.355764	+	0.934576i	$0.384221\pi$
$608$	1.45583	0.0590419
$609$	0	0
$610$	−22.4047	−0.907139
$611$	11.2420	0.454803
$612$	−1.97003	−0.0796337
$613$	12.7131	0.513475	0.256738	−	0.966481i	$-0.417352\pi$
$613$	12.7131	0.513475	0.256738	+	0.966481i	$0.417352\pi$
$614$	−7.51373	−0.303230
$615$	13.9235	0.561448
$616$	0	0
$617$	14.5406	0.585382	0.292691	−	0.956207i	$-0.405449\pi$
$617$	14.5406	0.585382	0.292691	+	0.956207i	$0.405449\pi$
$618$	−5.65413	−0.227442
$619$	−22.0186	−0.885002	−0.442501	−	0.896768i	$-0.645909\pi$
$619$	−22.0186	−0.885002	−0.442501	+	0.896768i	$0.645909\pi$
$620$	−0.395964	−0.0159023
$621$	10.0230	0.402208
$622$	−29.1238	−1.16776
$623$	0	0
$624$	−37.0003	−1.48120
$625$	1.00000	0.0400000
$626$	39.0224	1.55965
$627$	−8.27373	−0.330421
$628$	5.31899	0.212251
$629$	−21.2676	−0.847994
$630$	0	0
$631$	−25.2853	−1.00659	−0.503296	−	0.864114i	$-0.667879\pi$
$631$	−25.2853	−1.00659	−0.503296	+	0.864114i	$0.667879\pi$
$632$	17.3251	0.689156
$633$	−38.1508	−1.51636
$634$	−37.4123	−1.48583
$635$	0.405614	0.0160963
$636$	−0.136801	−0.00542451
$637$	0	0
$638$	−15.6584	−0.619921
$639$	−14.2948	−0.565493
$640$	−13.4747	−0.532635
$641$	5.83623	0.230517	0.115259	−	0.993336i	$-0.463230\pi$
$641$	5.83623	0.230517	0.115259	+	0.993336i	$0.463230\pi$
$642$	−33.1536	−1.30847
$643$	−20.5722	−0.811290	−0.405645	−	0.914031i	$-0.632953\pi$
$643$	−20.5722	−0.811290	−0.405645	+	0.914031i	$0.632953\pi$
$644$	0	0
$645$	17.0861	0.672764
$646$	2.30830	0.0908189
$647$	−8.15128	−0.320460	−0.160230	−	0.987080i	$-0.551224\pi$
$647$	−8.15128	−0.320460	−0.160230	+	0.987080i	$0.551224\pi$
$648$	−26.7198	−1.04965
$649$	−62.1810	−2.44082
$650$	5.41914	0.212556
$651$	0	0
$652$	−8.34349	−0.326756
$653$	18.6713	0.730663	0.365331	−	0.930877i	$-0.380956\pi$
$653$	18.6713	0.730663	0.365331	+	0.930877i	$0.380956\pi$
$654$	−2.32257	−0.0908197
$655$	15.3228	0.598710
$656$	28.3046	1.10511
$657$	−29.8059	−1.16284
$658$	0	0
$659$	−3.83437	−0.149366	−0.0746829	−	0.997207i	$-0.523794\pi$
$659$	−3.83437	−0.149366	−0.0746829	+	0.997207i	$0.523794\pi$
$660$	−4.97085	−0.193490
$661$	15.0005	0.583452	0.291726	−	0.956502i	$-0.405770\pi$
$661$	15.0005	0.583452	0.291726	+	0.956502i	$0.405770\pi$
$662$	11.6991	0.454698
$663$	−18.0621	−0.701474
$664$	−41.8773	−1.62515
$665$	0	0
$666$	−31.9907	−1.23962
$667$	10.0810	0.390338
$668$	1.36939	0.0529833
$669$	−40.5307	−1.56701
$670$	19.3169	0.746276
$671$	79.6930	3.07652
$672$	0	0
$673$	−40.9619	−1.57897	−0.789483	−	0.613772i	$-0.789651\pi$
$673$	−40.9619	−1.57897	−0.789483	+	0.613772i	$0.789651\pi$
$674$	30.0965	1.15927
$675$	1.82674	0.0703114
$676$	−0.294249	−0.0113173
$677$	−17.6883	−0.679817	−0.339909	−	0.940458i	$-0.610396\pi$
$677$	−17.6883	−0.679817	−0.339909	+	0.940458i	$0.610396\pi$
$678$	−14.8030	−0.568507
$679$	0	0
$680$	−5.61797	−0.215439
$681$	−39.5560	−1.51579
$682$	8.52240	0.326340
$683$	−23.2639	−0.890168	−0.445084	−	0.895489i	$-0.646826\pi$
$683$	−23.2639	−0.890168	−0.445084	+	0.895489i	$0.646826\pi$
$684$	0.573818	0.0219405
$685$	6.25650	0.239049
$686$	0	0
$687$	38.9744	1.48696
$688$	34.7338	1.32421
$689$	−0.530482	−0.0202098
$690$	19.3648	0.737204
$691$	−6.05267	−0.230254	−0.115127	−	0.993351i	$-0.536728\pi$
$691$	−6.05267	−0.230254	−0.115127	+	0.993351i	$0.536728\pi$
$692$	−1.33197	−0.0506341
$693$	0	0
$694$	26.3666	1.00086
$695$	16.9729	0.643817
$696$	−10.4014	−0.394264
$697$	13.8172	0.523363
$698$	53.3153	2.01801
$699$	67.3650	2.54798
$700$	0	0
$701$	−7.65144	−0.288991	−0.144495	−	0.989505i	$-0.546156\pi$
$701$	−7.65144	−0.288991	−0.144495	+	0.989505i	$0.546156\pi$
$702$	9.89937	0.373628
$703$	6.19469	0.233637
$704$	32.2150	1.21415
$705$	7.32161	0.275748
$706$	29.7178	1.11845
$707$	0	0
$708$	10.1963	0.383202
$709$	36.0169	1.35264	0.676322	−	0.736606i	$-0.263573\pi$
$709$	36.0169	1.35264	0.676322	+	0.736606i	$0.263573\pi$
$710$	10.0630	0.377656
$711$	15.3431	0.575411
$712$	23.5459	0.882421
$713$	−5.48680	−0.205482
$714$	0	0
$715$	−19.2758	−0.720873
$716$	6.49670	0.242793
$717$	−8.00574	−0.298980
$718$	−34.7374	−1.29639
$719$	−4.66413	−0.173943	−0.0869714	−	0.996211i	$-0.527719\pi$
$719$	−4.66413	−0.173943	−0.0869714	+	0.996211i	$0.527719\pi$
$720$	−10.1919	−0.379829
$721$	0	0
$722$	28.7376	1.06950
$723$	32.5595	1.21090
$724$	0.781147	0.0290311
$725$	1.83732	0.0682364
$726$	68.1657	2.52987
$727$	−16.8494	−0.624910	−0.312455	−	0.949933i	$-0.601151\pi$
$727$	−16.8494	−0.624910	−0.312455	+	0.949933i	$0.601151\pi$
$728$	0	0
$729$	−11.1676	−0.413613
$730$	20.9822	0.776585
$731$	16.9557	0.627128
$732$	−13.0679	−0.483005
$733$	−1.07302	−0.0396328	−0.0198164	−	0.999804i	$-0.506308\pi$
$733$	−1.07302	−0.0396328	−0.0198164	+	0.999804i	$0.506308\pi$
$734$	16.3922	0.605047
$735$	0	0
$736$	12.1200	0.446751
$737$	−68.7098	−2.53096
$738$	20.7838	0.765064
$739$	−0.561792	−0.0206659	−0.0103329	−	0.999947i	$-0.503289\pi$
$739$	−0.561792	−0.0206659	−0.0103329	+	0.999947i	$0.503289\pi$
$740$	3.72176	0.136815
$741$	5.26102	0.193268
$742$	0	0
$743$	−33.9922	−1.24705	−0.623527	−	0.781802i	$-0.714301\pi$
$743$	−33.9922	−1.24705	−0.623527	+	0.781802i	$0.714301\pi$
$744$	5.66118	0.207549
$745$	−9.73968	−0.356834
$746$	−54.0394	−1.97852
$747$	−37.0865	−1.35693
$748$	−4.93291	−0.180365
$749$	0	0
$750$	3.52934	0.128873
$751$	24.2120	0.883508	0.441754	−	0.897136i	$-0.354356\pi$
$751$	24.2120	0.883508	0.441754	+	0.897136i	$0.354356\pi$
$752$	14.8839	0.542760
$753$	37.7628	1.37615
$754$	9.95669	0.362601
$755$	−11.5032	−0.418644
$756$	0	0
$757$	−44.6814	−1.62397	−0.811987	−	0.583675i	$-0.801614\pi$
$757$	−44.6814	−1.62397	−0.811987	+	0.583675i	$0.801614\pi$
$758$	−41.6355	−1.51227
$759$	−68.8801	−2.50019
$760$	1.63637	0.0593573
$761$	35.7320	1.29529	0.647643	−	0.761944i	$-0.275755\pi$
$761$	35.7320	1.29529	0.647643	+	0.761944i	$0.275755\pi$
$762$	1.43155	0.0518595
$763$	0	0
$764$	−2.83086	−0.102417
$765$	−4.97527	−0.179881
$766$	21.1073	0.762637
$767$	39.5390	1.42767
$768$	−20.8748	−0.753254
$769$	10.0260	0.361548	0.180774	−	0.983525i	$-0.442140\pi$
$769$	10.0260	0.361548	0.180774	+	0.983525i	$0.442140\pi$
$770$	0	0
$771$	−10.2113	−0.367753
$772$	8.19168	0.294825
$773$	4.34731	0.156362	0.0781810	−	0.996939i	$-0.475089\pi$
$773$	4.34731	0.156362	0.0781810	+	0.996939i	$0.475089\pi$
$774$	25.5048	0.916750
$775$	−1.00000	−0.0359211
$776$	−15.8124	−0.567632
$777$	0	0
$778$	35.8662	1.28587
$779$	−4.02459	−0.144196
$780$	3.16081	0.113175
$781$	−35.7938	−1.28080
$782$	19.2170	0.687197
$783$	3.35631	0.119945
$784$	0	0
$785$	13.4330	0.479444
$786$	54.0792	1.92894
$787$	−2.04208	−0.0727922	−0.0363961	−	0.999337i	$-0.511588\pi$
$787$	−2.04208	−0.0727922	−0.0363961	+	0.999337i	$0.511588\pi$
$788$	4.62298	0.164687
$789$	22.5025	0.801109
$790$	−10.8009	−0.384280
$791$	0	0
$792$	30.0585	1.06808
$793$	−50.6744	−1.79950
$794$	15.5538	0.551985
$795$	−0.345488	−0.0122532
$796$	1.50211	0.0532408
$797$	38.4808	1.36306	0.681531	−	0.731789i	$-0.261315\pi$
$797$	38.4808	1.36306	0.681531	+	0.731789i	$0.261315\pi$
$798$	0	0
$799$	7.26573	0.257043
$800$	2.20895	0.0780980
$801$	20.8523	0.736779
$802$	−14.2527	−0.503282
$803$	−74.6332	−2.63375
$804$	11.2669	0.397354
$805$	0	0
$806$	−5.41914	−0.190881
$807$	−19.3932	−0.682672
$808$	−17.7997	−0.626190
$809$	−49.6257	−1.74475	−0.872374	−	0.488840i	$-0.837420\pi$
$809$	−49.6257	−1.74475	−0.872374	+	0.488840i	$0.837420\pi$
$810$	16.6578	0.585297
$811$	−36.6822	−1.28809	−0.644043	−	0.764989i	$-0.722744\pi$
$811$	−36.6822	−1.28809	−0.644043	+	0.764989i	$0.722744\pi$
$812$	0	0
$813$	−72.7875	−2.55277
$814$	−80.1041	−2.80765
$815$	−21.0713	−0.738097
$816$	−23.9134	−0.837136
$817$	−4.93875	−0.172785
$818$	38.5471	1.34777
$819$	0	0
$820$	−2.41797	−0.0844390
$821$	5.40450	0.188618	0.0943092	−	0.995543i	$-0.469936\pi$
$821$	5.40450	0.188618	0.0943092	+	0.995543i	$0.469936\pi$
$822$	22.0813	0.770173
$823$	12.5805	0.438529	0.219265	−	0.975665i	$-0.429634\pi$
$823$	12.5805	0.438529	0.219265	+	0.975665i	$0.429634\pi$
$824$	−3.97766	−0.138568
$825$	−12.5538	−0.437067
$826$	0	0
$827$	5.25497	0.182733	0.0913665	−	0.995817i	$-0.470877\pi$
$827$	5.25497	0.182733	0.0913665	+	0.995817i	$0.470877\pi$
$828$	4.77712	0.166017
$829$	−39.7311	−1.37992	−0.689958	−	0.723849i	$-0.742371\pi$
$829$	−39.7311	−1.37992	−0.689958	+	0.723849i	$0.742371\pi$
$830$	26.1075	0.906203
$831$	−48.7854	−1.69235
$832$	−20.4845	−0.710173
$833$	0	0
$834$	59.9029	2.07427
$835$	3.45837	0.119682
$836$	1.43683	0.0496937
$837$	−1.82674	−0.0631415
$838$	23.2882	0.804478
$839$	−29.1233	−1.00545	−0.502724	−	0.864447i	$-0.667669\pi$
$839$	−29.1233	−1.00545	−0.502724	+	0.864447i	$0.667669\pi$
$840$	0	0
$841$	−25.6243	−0.883595
$842$	22.2368	0.766330
$843$	4.71115	0.162261
$844$	6.62531	0.228053
$845$	−0.743122	−0.0255642
$846$	10.9291	0.375751
$847$	0	0
$848$	−0.702334	−0.0241182
$849$	20.0641	0.688597
$850$	3.50240	0.120131
$851$	51.5717	1.76786
$852$	5.86941	0.201083
$853$	−10.6458	−0.364506	−0.182253	−	0.983252i	$-0.558339\pi$
$853$	−10.6458	−0.364506	−0.182253	+	0.983252i	$0.558339\pi$
$854$	0	0
$855$	1.44917	0.0495605
$856$	−23.3234	−0.797178
$857$	33.4890	1.14396	0.571980	−	0.820267i	$-0.306175\pi$
$857$	33.4890	1.14396	0.571980	+	0.820267i	$0.306175\pi$
$858$	−68.0307	−2.32253
$859$	−17.9224	−0.611504	−0.305752	−	0.952111i	$-0.598908\pi$
$859$	−17.9224	−0.611504	−0.305752	+	0.952111i	$0.598908\pi$
$860$	−2.96719	−0.101180
$861$	0	0
$862$	−9.67568	−0.329555
$863$	−47.1061	−1.60351	−0.801755	−	0.597653i	$-0.796100\pi$
$863$	−47.1061	−1.60351	−0.801755	+	0.597653i	$0.796100\pi$
$864$	4.03518	0.137280
$865$	−3.36388	−0.114375
$866$	28.5553	0.970348
$867$	27.0880	0.919958
$868$	0	0
$869$	38.4188	1.30327
$870$	6.48452	0.219846
$871$	43.6905	1.48040
$872$	−1.63392	−0.0553315
$873$	−14.0035	−0.473945
$874$	−5.59740	−0.189335
$875$	0	0
$876$	12.2382	0.413492
$877$	−1.31568	−0.0444273	−0.0222137	−	0.999753i	$-0.507071\pi$
$877$	−1.31568	−0.0444273	−0.0222137	+	0.999753i	$0.507071\pi$
$878$	46.8068	1.57965
$879$	37.4248	1.26231
$880$	−25.5202	−0.860287
$881$	−11.1760	−0.376530	−0.188265	−	0.982118i	$-0.560286\pi$
$881$	−11.1760	−0.376530	−0.188265	+	0.982118i	$0.560286\pi$
$882$	0	0
$883$	−45.4449	−1.52934	−0.764671	−	0.644420i	$-0.777099\pi$
$883$	−45.4449	−1.52934	−0.764671	+	0.644420i	$0.777099\pi$
$884$	3.13669	0.105498
$885$	25.7507	0.865600
$886$	20.4310	0.686392
$887$	45.9920	1.54426	0.772131	−	0.635464i	$-0.219191\pi$
$887$	45.9920	1.54426	0.772131	+	0.635464i	$0.219191\pi$
$888$	−53.2108	−1.78564
$889$	0	0
$890$	−14.6792	−0.492047
$891$	−59.2516	−1.98500
$892$	7.03862	0.235670
$893$	−2.11632	−0.0708198
$894$	−34.3746	−1.14966
$895$	16.4073	0.548435
$896$	0	0
$897$	43.7988	1.46240
$898$	−34.5426	−1.15270
$899$	−1.83732	−0.0612781
$900$	0.870658	0.0290219
$901$	−0.342852	−0.0114220
$902$	52.0423	1.73282
$903$	0	0
$904$	−10.4139	−0.346360
$905$	1.97277	0.0655772
$906$	−40.5986	−1.34880
$907$	0.506069	0.0168037	0.00840187	−	0.999965i	$-0.497326\pi$
$907$	0.506069	0.0168037	0.00840187	+	0.999965i	$0.497326\pi$
$908$	6.86934	0.227967
$909$	−15.7634	−0.522838
$910$	0	0
$911$	30.4852	1.01002	0.505009	−	0.863114i	$-0.331489\pi$
$911$	30.4852	1.01002	0.505009	+	0.863114i	$0.331489\pi$
$912$	6.96535	0.230646
$913$	−92.8638	−3.07334
$914$	41.7015	1.37936
$915$	−33.0028	−1.09104
$916$	−6.76834	−0.223632
$917$	0	0
$918$	6.39798	0.211165
$919$	−25.1796	−0.830599	−0.415300	−	0.909685i	$-0.636323\pi$
$919$	−25.1796	−0.830599	−0.415300	+	0.909685i	$0.636323\pi$
$920$	13.6230	0.449138
$921$	−11.0680	−0.364702
$922$	−27.5927	−0.908716
$923$	22.7602	0.749160
$924$	0	0
$925$	9.39924	0.309045
$926$	−57.9328	−1.90379
$927$	−3.52261	−0.115698
$928$	4.05854	0.133228
$929$	−32.9737	−1.08183	−0.540915	−	0.841077i	$-0.681922\pi$
$929$	−32.9737	−1.08183	−0.540915	+	0.841077i	$0.681922\pi$
$930$	−3.52934	−0.115731
$931$	0	0
$932$	−11.6987	−0.383204
$933$	−42.9003	−1.40449
$934$	29.5547	0.967060
$935$	−12.4580	−0.407419
$936$	−19.1133	−0.624738
$937$	2.84832	0.0930506	0.0465253	−	0.998917i	$-0.485185\pi$
$937$	2.84832	0.0930506	0.0465253	+	0.998917i	$0.485185\pi$
$938$	0	0
$939$	57.4813	1.87583
$940$	−1.27148	−0.0414711
$941$	−46.7365	−1.52357	−0.761783	−	0.647832i	$-0.775676\pi$
$941$	−46.7365	−1.52357	−0.761783	+	0.647832i	$0.775676\pi$
$942$	47.4096	1.54469
$943$	−33.5053	−1.09108
$944$	52.3479	1.70378
$945$	0	0
$946$	63.8634	2.07638
$947$	−19.0159	−0.617932	−0.308966	−	0.951073i	$-0.599983\pi$
$947$	−19.0159	−0.617932	−0.308966	+	0.951073i	$0.599983\pi$
$948$	−6.29985	−0.204610
$949$	47.4570	1.54052
$950$	−1.02016	−0.0330983
$951$	−55.1095	−1.78705
$952$	0	0
$953$	58.8382	1.90596	0.952978	−	0.303038i	$-0.0980010\pi$
$953$	58.8382	1.90596	0.952978	+	0.303038i	$0.0980010\pi$
$954$	−0.515718	−0.0166970
$955$	−7.14928	−0.231345
$956$	1.39029	0.0449651
$957$	−23.0653	−0.745596
$958$	−27.9211	−0.902091
$959$	0	0
$960$	−13.3410	−0.430579
$961$	1.00000	0.0322581
$962$	50.9357	1.64223
$963$	−20.6552	−0.665604
$964$	−5.65433	−0.182114
$965$	20.6879	0.665968
$966$	0	0
$967$	33.6630	1.08253	0.541264	−	0.840853i	$-0.317946\pi$
$967$	33.6630	1.08253	0.541264	+	0.840853i	$0.317946\pi$
$968$	47.9543	1.54131
$969$	3.40021	0.109230
$970$	9.85789	0.316518
$971$	4.10881	0.131858	0.0659290	−	0.997824i	$-0.478999\pi$
$971$	4.10881	0.131858	0.0659290	+	0.997824i	$0.478999\pi$
$972$	7.54601	0.242038
$973$	0	0
$974$	8.17834	0.262051
$975$	7.98257	0.255647
$976$	−67.0906	−2.14752
$977$	−39.3116	−1.25769	−0.628845	−	0.777531i	$-0.716472\pi$
$977$	−39.3116	−1.25769	−0.628845	+	0.777531i	$0.716472\pi$
$978$	−74.3678	−2.37802
$979$	52.2136	1.66875
$980$	0	0
$981$	−1.44700	−0.0461991
$982$	−30.9526	−0.987738
$983$	−16.2085	−0.516971	−0.258485	−	0.966015i	$-0.583223\pi$
$983$	−16.2085	−0.516971	−0.258485	+	0.966015i	$0.583223\pi$
$984$	34.5701	1.10206
$985$	11.6752	0.372004
$986$	6.43503	0.204933
$987$	0	0
$988$	−0.913635	−0.0290666
$989$	−41.1158	−1.30741
$990$	−18.7393	−0.595574
$991$	57.9932	1.84221	0.921107	−	0.389308i	$-0.127286\pi$
$991$	57.9932	1.84221	0.921107	+	0.389308i	$0.127286\pi$
$992$	−2.20895	−0.0701341
$993$	17.2331	0.546877
$994$	0	0
$995$	3.79354	0.120263
$996$	15.2277	0.482507
$997$	−39.8674	−1.26261	−0.631307	−	0.775533i	$-0.717481\pi$
$997$	−39.8674	−1.26261	−0.631307	+	0.775533i	$0.717481\pi$
$998$	−2.58043	−0.0816822
$999$	17.1700	0.543235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.7		21
7.3	odd	6		1085.2.j.d.156.15	✓	42
7.5	odd	6		1085.2.j.d.466.15	yes	42
7.6	odd	2		7595.2.a.bg.1.7		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.15	✓	42	7.3	odd	6
1085.2.j.d.466.15	yes	42	7.5	odd	6
7595.2.a.bf.1.7		21	1.1	even	1	trivial
7595.2.a.bg.1.7		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)

\(f(q)\)	\(=\)	\(q-1.54789 q^{2} -2.28009 q^{3} +0.395964 q^{4} +1.00000 q^{5} +3.52934 q^{6} +2.48287 q^{8} +2.19883 q^{9} +O(q^{10})\)	\(q-1.54789 q^{2} -2.28009 q^{3} +0.395964 q^{4} +1.00000 q^{5} +3.52934 q^{6} +2.48287 q^{8} +2.19883 q^{9} -1.54789 q^{10} +5.50582 q^{11} -0.902836 q^{12} -3.50098 q^{13} -2.28009 q^{15} -4.63514 q^{16} -2.26269 q^{17} -3.40355 q^{18} +0.659063 q^{19} +0.395964 q^{20} -8.52240 q^{22} +5.48680 q^{23} -5.66118 q^{24} +1.00000 q^{25} +5.41914 q^{26} +1.82674 q^{27} +1.83732 q^{29} +3.52934 q^{30} -1.00000 q^{31} +2.20895 q^{32} -12.5538 q^{33} +3.50240 q^{34} +0.870658 q^{36} +9.39924 q^{37} -1.02016 q^{38} +7.98257 q^{39} +2.48287 q^{40} -6.10653 q^{41} -7.49359 q^{43} +2.18011 q^{44} +2.19883 q^{45} -8.49296 q^{46} -3.21110 q^{47} +10.5686 q^{48} -1.54789 q^{50} +5.15915 q^{51} -1.38626 q^{52} +0.151524 q^{53} -2.82760 q^{54} +5.50582 q^{55} -1.50273 q^{57} -2.84397 q^{58} -11.2937 q^{59} -0.902836 q^{60} +14.4743 q^{61} +1.54789 q^{62} +5.85108 q^{64} -3.50098 q^{65} +19.4319 q^{66} -12.4795 q^{67} -0.895945 q^{68} -12.5104 q^{69} -6.50108 q^{71} +5.45941 q^{72} -13.5553 q^{73} -14.5490 q^{74} -2.28009 q^{75} +0.260965 q^{76} -12.3561 q^{78} +6.97785 q^{79} -4.63514 q^{80} -10.7616 q^{81} +9.45223 q^{82} -16.8665 q^{83} -2.26269 q^{85} +11.5992 q^{86} -4.18926 q^{87} +13.6702 q^{88} +9.48335 q^{89} -3.40355 q^{90} +2.17258 q^{92} +2.28009 q^{93} +4.97043 q^{94} +0.659063 q^{95} -5.03661 q^{96} -6.36860 q^{97} +12.1064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 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

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