LMFDB - Embedded newform 1058.4.a.t.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1058,4,Mod(1,1058)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1058.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1058, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1058 = 2 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1058.a (trivial)

Newform invariants

comment:select newform

sage:traces = [15,-30,1,60,0,-2,-80] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	yes
Analytic conductor:	$62.4240207861$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 242 x^{13} + 347 x^{12} + 22092 x^{11} - 27616 x^{10} - 966502 x^{9} + \cdots - 23850793 $ x^15 - 2x^14 - 242x^13 + 347x^12 + 22092x^11 - 27616x^10 - 966502x^9 + 1237405x^8 + 20608820x^7 - 29345287x^6 - 180363581x^5 + 286025276x^4 + 239879120x^3 - 265419860x^2 - 193980531x - 23850793
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 23^{4} $
Twist minimal:	no (minimal twist has level 46)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-7.94917$ of defining polynomial
Character	$\chi$	$=$	1058.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +6.26666 q^{3} +4.00000 q^{4} +10.4231 q^{5} -12.5333 q^{6} -11.8502 q^{7} -8.00000 q^{8} +12.2711 q^{9} -20.8461 q^{10} -35.3884 q^{11} +25.0667 q^{12} +3.85975 q^{13} +23.7004 q^{14} +65.3178 q^{15} +16.0000 q^{16} +30.9194 q^{17} -24.5421 q^{18} -134.172 q^{19} +41.6922 q^{20} -74.2611 q^{21} +70.7768 q^{22} -50.1333 q^{24} -16.3599 q^{25} -7.71950 q^{26} -92.3012 q^{27} -47.4007 q^{28} +62.7371 q^{29} -130.636 q^{30} +258.765 q^{31} -32.0000 q^{32} -221.767 q^{33} -61.8388 q^{34} -123.515 q^{35} +49.0843 q^{36} +327.190 q^{37} +268.344 q^{38} +24.1878 q^{39} -83.3845 q^{40} -69.1568 q^{41} +148.522 q^{42} -297.588 q^{43} -141.554 q^{44} +127.902 q^{45} -502.104 q^{47} +100.267 q^{48} -202.573 q^{49} +32.7198 q^{50} +193.761 q^{51} +15.4390 q^{52} -577.436 q^{53} +184.602 q^{54} -368.855 q^{55} +94.8014 q^{56} -840.811 q^{57} -125.474 q^{58} -447.008 q^{59} +261.271 q^{60} -354.178 q^{61} -517.530 q^{62} -145.414 q^{63} +64.0000 q^{64} +40.2304 q^{65} +443.534 q^{66} -1006.32 q^{67} +123.678 q^{68} +247.030 q^{70} +754.659 q^{71} -98.1686 q^{72} +707.721 q^{73} -654.381 q^{74} -102.522 q^{75} -536.688 q^{76} +419.359 q^{77} -48.3755 q^{78} -114.160 q^{79} +166.769 q^{80} -909.740 q^{81} +138.314 q^{82} -258.777 q^{83} -297.044 q^{84} +322.274 q^{85} +595.175 q^{86} +393.153 q^{87} +283.107 q^{88} -340.860 q^{89} -255.804 q^{90} -45.7388 q^{91} +1621.59 q^{93} +1004.21 q^{94} -1398.48 q^{95} -200.533 q^{96} +629.323 q^{97} +405.146 q^{98} -434.254 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 30 q^{2} + q^{3} + 60 q^{4} - 2 q^{6} - 80 q^{7} - 120 q^{8} + 96 q^{9} + 15 q^{11} + 4 q^{12} + 52 q^{13} + 160 q^{14} - 224 q^{15} + 240 q^{16} + 72 q^{17} - 192 q^{18} - 145 q^{19} - 57 q^{21}+ \cdots + 1569 q^{99}+O(q^{100}) $ 15 * q - 30 * q^2 + q^3 + 60 * q^4 - 2 * q^6 - 80 * q^7 - 120 * q^8 + 96 * q^9 + 15 * q^11 + 4 * q^12 + 52 * q^13 + 160 * q^14 - 224 * q^15 + 240 * q^16 + 72 * q^17 - 192 * q^18 - 145 * q^19 - 57 * q^21 - 30 * q^22 - 8 * q^24 + 671 * q^25 - 104 * q^26 + 85 * q^27 - 320 * q^28 - 202 * q^29 + 448 * q^30 - 320 * q^31 - 480 * q^32 - 114 * q^33 - 144 * q^34 + 500 * q^35 + 384 * q^36 - 768 * q^37 + 290 * q^38 + 653 * q^39 - 247 * q^41 + 114 * q^42 - 1210 * q^43 + 60 * q^44 + 24 * q^45 - 754 * q^47 + 16 * q^48 + 1553 * q^49 - 1342 * q^50 - 779 * q^51 + 208 * q^52 + 277 * q^53 - 170 * q^54 - 1238 * q^55 + 640 * q^56 - 1239 * q^57 + 404 * q^58 - 660 * q^59 - 896 * q^60 - 592 * q^61 + 640 * q^62 - 1665 * q^63 + 960 * q^64 + 546 * q^65 + 228 * q^66 - 1958 * q^67 + 288 * q^68 - 1000 * q^70 + 3626 * q^71 - 768 * q^72 - 2459 * q^73 + 1536 * q^74 - 4597 * q^75 - 580 * q^76 - 2198 * q^77 - 1306 * q^78 - 1038 * q^79 + 139 * q^81 + 494 * q^82 - 1192 * q^83 - 228 * q^84 + 3324 * q^85 + 2420 * q^86 + 547 * q^87 - 120 * q^88 + 70 * q^89 - 48 * q^90 - 2067 * q^91 + 2465 * q^93 + 1508 * q^94 - 4756 * q^95 - 32 * q^96 - 3856 * q^97 - 3106 * q^98 + 1569 * q^99

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	6.26666	1.20602	0.603010	−	0.797734i	$-0.293968\pi$
$3$	6.26666	1.20602	0.603010	+	0.797734i	$0.293968\pi$
$4$	4.00000	0.500000
$5$	10.4231	0.932267	0.466133	−	0.884715i	$-0.345647\pi$
$5$	10.4231	0.932267	0.466133	+	0.884715i	$0.345647\pi$
$6$	−12.5333	−0.852785
$7$	−11.8502	−0.639850	−0.319925	−	0.947443i	$-0.603658\pi$
$7$	−11.8502	−0.639850	−0.319925	+	0.947443i	$0.603658\pi$
$8$	−8.00000	−0.353553
$9$	12.2711	0.454484
$10$	−20.8461	−0.659212
$11$	−35.3884	−0.970000	−0.485000	−	0.874514i	$-0.661180\pi$
$11$	−35.3884	−0.970000	−0.485000	+	0.874514i	$0.661180\pi$
$12$	25.0667	0.603010
$13$	3.85975	0.0823463	0.0411732	−	0.999152i	$-0.486890\pi$
$13$	3.85975	0.0823463	0.0411732	+	0.999152i	$0.486890\pi$
$14$	23.7004	0.452442
$15$	65.3178	1.12433
$16$	16.0000	0.250000
$17$	30.9194	0.441121	0.220560	−	0.975373i	$-0.429211\pi$
$17$	30.9194	0.441121	0.220560	+	0.975373i	$0.429211\pi$
$18$	−24.5421	−0.321369
$19$	−134.172	−1.62006	−0.810031	−	0.586387i	$-0.800550\pi$
$19$	−134.172	−1.62006	−0.810031	+	0.586387i	$0.800550\pi$
$20$	41.6922	0.466133
$21$	−74.2611	−0.771671
$22$	70.7768	0.685894
$23$	0	0
$23$	0	0
$24$	−50.1333	−0.426392
$25$	−16.3599	−0.130879
$26$	−7.71950	−0.0582277
$27$	−92.3012	−0.657903
$28$	−47.4007	−0.319925
$29$	62.7371	0.401724	0.200862	−	0.979620i	$-0.435626\pi$
$29$	62.7371	0.401724	0.200862	+	0.979620i	$0.435626\pi$
$30$	−130.636	−0.795023
$31$	258.765	1.49921	0.749606	−	0.661884i	$-0.230243\pi$
$31$	258.765	1.49921	0.749606	+	0.661884i	$0.230243\pi$
$32$	−32.0000	−0.176777
$33$	−221.767	−1.16984
$34$	−61.8388	−0.311919
$35$	−123.515	−0.596510
$36$	49.0843	0.227242
$37$	327.190	1.45378	0.726889	−	0.686755i	$-0.240966\pi$
$37$	327.190	1.45378	0.726889	+	0.686755i	$0.240966\pi$
$38$	268.344	1.14556
$39$	24.1878	0.0993113
$40$	−83.3845	−0.329606
$41$	−69.1568	−0.263426	−0.131713	−	0.991288i	$-0.542048\pi$
$41$	−69.1568	−0.263426	−0.131713	+	0.991288i	$0.542048\pi$
$42$	148.522	0.545654
$43$	−297.588	−1.05539	−0.527694	−	0.849435i	$-0.676943\pi$
$43$	−297.588	−1.05539	−0.527694	+	0.849435i	$0.676943\pi$
$44$	−141.554	−0.485000
$45$	127.902	0.423700
$46$	0	0
$47$	−502.104	−1.55828	−0.779142	−	0.626847i	$-0.784345\pi$
$47$	−502.104	−1.55828	−0.779142	+	0.626847i	$0.784345\pi$
$48$	100.267	0.301505
$49$	−202.573	−0.590593
$50$	32.7198	0.0925455
$51$	193.761	0.532000
$52$	15.4390	0.0411732
$53$	−577.436	−1.49655	−0.748273	−	0.663391i	$-0.769116\pi$
$53$	−577.436	−1.49655	−0.748273	+	0.663391i	$0.769116\pi$
$54$	184.602	0.465208
$55$	−368.855	−0.904299
$56$	94.8014	0.226221
$57$	−840.811	−1.95383
$58$	−125.474	−0.284062
$59$	−447.008	−0.986365	−0.493183	−	0.869926i	$-0.664167\pi$
$59$	−447.008	−0.986365	−0.493183	+	0.869926i	$0.664167\pi$
$60$	261.271	0.562166
$61$	−354.178	−0.743407	−0.371703	−	0.928352i	$-0.621226\pi$
$61$	−354.178	−0.743407	−0.371703	+	0.928352i	$0.621226\pi$
$62$	−517.530	−1.06010
$63$	−145.414	−0.290802
$64$	64.0000	0.125000
$65$	40.2304	0.0767687
$66$	443.534	0.827201
$67$	−1006.32	−1.83495	−0.917476	−	0.397792i	$-0.869777\pi$
$67$	−1006.32	−1.83495	−0.917476	+	0.397792i	$0.869777\pi$
$68$	123.678	0.220560
$69$	0	0
$70$	247.030	0.421796
$71$	754.659	1.26143	0.630715	−	0.776014i	$-0.282762\pi$
$71$	754.659	1.26143	0.630715	+	0.776014i	$0.282762\pi$
$72$	−98.1686	−0.160684
$73$	707.721	1.13469	0.567346	−	0.823480i	$-0.307970\pi$
$73$	707.721	1.13469	0.567346	+	0.823480i	$0.307970\pi$
$74$	−654.381	−1.02798
$75$	−102.522	−0.157843
$76$	−536.688	−0.810031
$77$	419.359	0.620654
$78$	−48.3755	−0.0702237
$79$	−114.160	−0.162583	−0.0812914	−	0.996690i	$-0.525904\pi$
$79$	−114.160	−0.162583	−0.0812914	+	0.996690i	$0.525904\pi$
$80$	166.769	0.233067
$81$	−909.740	−1.24793
$82$	138.314	0.186271
$83$	−258.777	−0.342223	−0.171112	−	0.985252i	$-0.554736\pi$
$83$	−258.777	−0.342223	−0.171112	+	0.985252i	$0.554736\pi$
$84$	−297.044	−0.385836
$85$	322.274	0.411242
$86$	595.175	0.746272
$87$	393.153	0.484487
$88$	283.107	0.342947
$89$	−340.860	−0.405967	−0.202983	−	0.979182i	$-0.565064\pi$
$89$	−340.860	−0.405967	−0.202983	+	0.979182i	$0.565064\pi$
$90$	−255.804	−0.299601
$91$	−45.7388	−0.0526893
$92$	0	0
$93$	1621.59	1.80808
$94$	1004.21	1.10187
$95$	−1398.48	−1.51033
$96$	−200.533	−0.213196
$97$	629.323	0.658743	0.329372	−	0.944200i	$-0.393163\pi$
$97$	629.323	0.658743	0.329372	+	0.944200i	$0.393163\pi$
$98$	405.146	0.417612
$99$	−434.254	−0.440850
$100$	−65.4396	−0.0654396
$101$	1129.01	1.11229	0.556143	−	0.831087i	$-0.312281\pi$
$101$	1129.01	1.11229	0.556143	+	0.831087i	$0.312281\pi$
$102$	−387.523	−0.376181
$103$	−1110.76	−1.06258	−0.531291	−	0.847189i	$-0.678293\pi$
$103$	−1110.76	−1.06258	−0.531291	+	0.847189i	$0.678293\pi$
$104$	−30.8780	−0.0291138
$105$	−774.028	−0.719403
$106$	1154.87	1.05822
$107$	−440.151	−0.397673	−0.198836	−	0.980033i	$-0.563716\pi$
$107$	−440.151	−0.397673	−0.198836	+	0.980033i	$0.563716\pi$
$108$	−369.205	−0.328951
$109$	537.373	0.472211	0.236105	−	0.971727i	$-0.424129\pi$
$109$	537.373	0.472211	0.236105	+	0.971727i	$0.424129\pi$
$110$	737.710	0.639436
$111$	2050.39	1.75328
$112$	−189.603	−0.159962
$113$	−858.783	−0.714934	−0.357467	−	0.933926i	$-0.616360\pi$
$113$	−858.783	−0.714934	−0.357467	+	0.933926i	$0.616360\pi$
$114$	1681.62	1.38156
$115$	0	0
$116$	250.949	0.200862
$117$	47.3633	0.0374251
$118$	894.017	0.697465
$119$	−366.400	−0.282251
$120$	−522.542	−0.397511
$121$	−78.6617	−0.0590997
$122$	708.356	0.525668
$123$	−433.383	−0.317698
$124$	1035.06	0.749606
$125$	−1473.40	−1.05428
$126$	290.829	0.205628
$127$	2604.41	1.81971	0.909857	−	0.414921i	$-0.136191\pi$
$127$	2604.41	1.81971	0.909857	+	0.414921i	$0.136191\pi$
$128$	−128.000	−0.0883883
$129$	−1864.88	−1.27282
$130$	−80.4608	−0.0542837
$131$	−1530.41	−1.02071	−0.510354	−	0.859965i	$-0.670485\pi$
$131$	−1530.41	−1.02071	−0.510354	+	0.859965i	$0.670485\pi$
$132$	−887.069	−0.584920
$133$	1589.96	1.03660
$134$	2012.64	1.29751
$135$	−962.061	−0.613341
$136$	−247.355	−0.155960
$137$	436.585	0.272262	0.136131	−	0.990691i	$-0.456533\pi$
$137$	436.585	0.272262	0.136131	+	0.990691i	$0.456533\pi$
$138$	0	0
$139$	842.549	0.514130	0.257065	−	0.966394i	$-0.417245\pi$
$139$	842.549	0.514130	0.257065	+	0.966394i	$0.417245\pi$
$140$	−494.060	−0.298255
$141$	−3146.51	−1.87932
$142$	−1509.32	−0.891966
$143$	−136.590	−0.0798760
$144$	196.337	0.113621
$145$	653.913	0.374514
$146$	−1415.44	−0.802348
$147$	−1269.46	−0.712266
$148$	1308.76	0.726889
$149$	2082.06	1.14476	0.572380	−	0.819989i	$-0.306020\pi$
$149$	2082.06	1.14476	0.572380	+	0.819989i	$0.306020\pi$
$150$	205.044	0.111612
$151$	−1383.49	−0.745606	−0.372803	−	0.927911i	$-0.621603\pi$
$151$	−1383.49	−0.745606	−0.372803	+	0.927911i	$0.621603\pi$
$152$	1073.38	0.572778
$153$	379.414	0.200482
$154$	−838.718	−0.438869
$155$	2697.12	1.39767
$156$	96.7511	0.0496557
$157$	16.0299	0.00814857	0.00407429	−	0.999992i	$-0.498703\pi$
$157$	16.0299	0.00814857	0.00407429	+	0.999992i	$0.498703\pi$
$158$	228.321	0.114963
$159$	−3618.60	−1.80486
$160$	−333.538	−0.164803
$161$	0	0
$162$	1819.48	0.882419
$163$	−740.637	−0.355897	−0.177948	−	0.984040i	$-0.556946\pi$
$163$	−740.637	−0.355897	−0.177948	+	0.984040i	$0.556946\pi$
$164$	−276.627	−0.131713
$165$	−2311.49	−1.09060
$166$	517.555	0.241988
$167$	−185.971	−0.0861727	−0.0430864	−	0.999071i	$-0.513719\pi$
$167$	−185.971	−0.0861727	−0.0430864	+	0.999071i	$0.513719\pi$
$168$	594.089	0.272827
$169$	−2182.10	−0.993219
$170$	−644.549	−0.290792
$171$	−1646.43	−0.736292
$172$	−1190.35	−0.527694
$173$	4409.37	1.93779	0.968896	−	0.247468i	$-0.0795984\pi$
$173$	4409.37	1.93779	0.968896	+	0.247468i	$0.0795984\pi$
$174$	−786.305	−0.342584
$175$	193.868	0.0837430
$176$	−566.214	−0.242500
$177$	−2801.25	−1.18958
$178$	681.719	0.287062
$179$	−3063.62	−1.27925	−0.639625	−	0.768687i	$-0.720911\pi$
$179$	−3063.62	−1.27925	−0.639625	+	0.768687i	$0.720911\pi$
$180$	511.608	0.211850
$181$	−3179.95	−1.30588	−0.652938	−	0.757411i	$-0.726464\pi$
$181$	−3179.95	−1.30588	−0.652938	+	0.757411i	$0.726464\pi$
$182$	91.4775	0.0372569
$183$	−2219.51	−0.896563
$184$	0	0
$185$	3410.32	1.35531
$186$	−3243.19	−1.27851
$187$	−1094.19	−0.427887
$188$	−2008.41	−0.779142
$189$	1093.79	0.420959
$190$	2796.96	1.06796
$191$	−1111.39	−0.421031	−0.210516	−	0.977590i	$-0.567514\pi$
$191$	−1111.39	−0.421031	−0.210516	+	0.977590i	$0.567514\pi$
$192$	401.066	0.150752
$193$	3834.50	1.43012	0.715061	−	0.699062i	$-0.246399\pi$
$193$	3834.50	1.43012	0.715061	+	0.699062i	$0.246399\pi$
$194$	−1258.65	−0.465802
$195$	252.110	0.0925846
$196$	−810.293	−0.295296
$197$	3454.23	1.24926	0.624628	−	0.780922i	$-0.285251\pi$
$197$	3454.23	1.24926	0.624628	+	0.780922i	$0.285251\pi$
$198$	868.507	0.311728
$199$	960.188	0.342040	0.171020	−	0.985268i	$-0.445294\pi$
$199$	960.188	0.342040	0.171020	+	0.985268i	$0.445294\pi$
$200$	130.879	0.0462728
$201$	−6306.28	−2.21299
$202$	−2258.02	−0.786504
$203$	−743.446	−0.257043
$204$	775.045	0.266000
$205$	−720.826	−0.245584
$206$	2221.51	0.751359
$207$	0	0
$208$	61.7560	0.0205866
$209$	4748.13	1.57146
$210$	1548.06	0.508695
$211$	3439.42	1.12218	0.561088	−	0.827756i	$-0.310383\pi$
$211$	3439.42	1.12218	0.561088	+	0.827756i	$0.310383\pi$
$212$	−2309.74	−0.748273
$213$	4729.20	1.52131
$214$	880.301	0.281197
$215$	−3101.77	−0.983903
$216$	738.410	0.232604
$217$	−3066.41	−0.959271
$218$	−1074.75	−0.333903
$219$	4435.05	1.36846
$220$	−1475.42	−0.452149
$221$	119.341	0.0363247
$222$	−4100.78	−1.23976
$223$	−2070.40	−0.621723	−0.310862	−	0.950455i	$-0.600618\pi$
$223$	−2070.40	−0.621723	−0.310862	+	0.950455i	$0.600618\pi$
$224$	379.206	0.113110
$225$	−200.753	−0.0594825
$226$	1717.57	0.505535
$227$	−672.154	−0.196531	−0.0982653	−	0.995160i	$-0.531329\pi$
$227$	−672.154	−0.196531	−0.0982653	+	0.995160i	$0.531329\pi$
$228$	−3363.24	−0.976913
$229$	−1899.18	−0.548042	−0.274021	−	0.961724i	$-0.588354\pi$
$229$	−1899.18	−0.548042	−0.274021	+	0.961724i	$0.588354\pi$
$230$	0	0
$231$	2627.98	0.748521
$232$	−501.897	−0.142031
$233$	−2375.86	−0.668017	−0.334009	−	0.942570i	$-0.608401\pi$
$233$	−2375.86	−0.668017	−0.334009	+	0.942570i	$0.608401\pi$
$234$	−94.7266	−0.0264636
$235$	−5233.45	−1.45274
$236$	−1788.03	−0.493183
$237$	−715.404	−0.196078
$238$	732.800	0.199581
$239$	−3173.27	−0.858837	−0.429418	−	0.903106i	$-0.641281\pi$
$239$	−3173.27	−0.858837	−0.429418	+	0.903106i	$0.641281\pi$
$240$	1045.08	0.281083
$241$	−6620.09	−1.76945	−0.884725	−	0.466113i	$-0.845654\pi$
$241$	−6620.09	−1.76945	−0.884725	+	0.466113i	$0.845654\pi$
$242$	157.323	0.0417898
$243$	−3208.90	−0.847124
$244$	−1416.71	−0.371703
$245$	−2111.43	−0.550590
$246$	866.765	0.224646
$247$	−517.871	−0.133406
$248$	−2070.12	−0.530052
$249$	−1621.67	−0.412728
$250$	2946.80	0.745489
$251$	3556.87	0.894454	0.447227	−	0.894421i	$-0.352412\pi$
$251$	3556.87	0.894454	0.447227	+	0.894421i	$0.352412\pi$
$252$	−581.658	−0.145401
$253$	0	0
$254$	−5208.82	−1.28673
$255$	2019.59	0.495966
$256$	256.000	0.0625000
$257$	−4655.56	−1.12998	−0.564992	−	0.825097i	$-0.691121\pi$
$257$	−4655.56	−1.12998	−0.564992	+	0.825097i	$0.691121\pi$
$258$	3729.76	0.900019
$259$	−3877.27	−0.930199
$260$	160.922	0.0383844
$261$	769.852	0.182577
$262$	3060.82	0.721749
$263$	1537.77	0.360544	0.180272	−	0.983617i	$-0.442302\pi$
$263$	1537.77	0.360544	0.180272	+	0.983617i	$0.442302\pi$
$264$	1774.14	0.413601
$265$	−6018.65	−1.39518
$266$	−3179.92	−0.732984
$267$	−2136.05	−0.489604
$268$	−4025.29	−0.917476
$269$	2820.10	0.639199	0.319600	−	0.947553i	$-0.396452\pi$
$269$	2820.10	0.639199	0.319600	+	0.947553i	$0.396452\pi$
$270$	1924.12	0.433697
$271$	−2811.85	−0.630288	−0.315144	−	0.949044i	$-0.602053\pi$
$271$	−2811.85	−0.630288	−0.315144	+	0.949044i	$0.602053\pi$
$272$	494.710	0.110280
$273$	−286.629	−0.0635443
$274$	−873.169	−0.192519
$275$	578.950	0.126953
$276$	0	0
$277$	4489.62	0.973845	0.486923	−	0.873445i	$-0.338119\pi$
$277$	4489.62	0.973845	0.486923	+	0.873445i	$0.338119\pi$
$278$	−1685.10	−0.363545
$279$	3175.33	0.681369
$280$	988.121	0.210898
$281$	−6627.18	−1.40692	−0.703460	−	0.710735i	$-0.748362\pi$
$281$	−6627.18	−1.40692	−0.703460	+	0.710735i	$0.748362\pi$
$282$	6293.03	1.32888
$283$	−8092.99	−1.69992	−0.849962	−	0.526844i	$-0.823375\pi$
$283$	−8092.99	−1.69992	−0.849962	+	0.526844i	$0.823375\pi$
$284$	3018.64	0.630715
$285$	−8763.82	−1.82149
$286$	273.181	0.0564808
$287$	819.521	0.168553
$288$	−392.674	−0.0803422
$289$	−3956.99	−0.805413
$290$	−1307.83	−0.264821
$291$	3943.76	0.794458
$292$	2830.88	0.567346
$293$	−543.785	−0.108424	−0.0542120	−	0.998529i	$-0.517265\pi$
$293$	−543.785	−0.108424	−0.0542120	+	0.998529i	$0.517265\pi$
$294$	2538.92	0.503648
$295$	−4659.19	−0.919555
$296$	−2617.52	−0.513988
$297$	3266.39	0.638166
$298$	−4164.13	−0.809468
$299$	0	0
$300$	−410.088	−0.0789214
$301$	3526.47	0.675289
$302$	2766.97	0.527223
$303$	7075.13	1.34144
$304$	−2146.75	−0.405015
$305$	−3691.61	−0.693053
$306$	−758.828	−0.141762
$307$	5451.41	1.01345	0.506724	−	0.862108i	$-0.330856\pi$
$307$	5451.41	1.01345	0.506724	+	0.862108i	$0.330856\pi$
$308$	1677.44	0.310327
$309$	−6960.73	−1.28150
$310$	−5394.25	−0.988299
$311$	−180.570	−0.0329234	−0.0164617	−	0.999864i	$-0.505240\pi$
$311$	−180.570	−0.0329234	−0.0164617	+	0.999864i	$0.505240\pi$
$312$	−193.502	−0.0351119
$313$	3596.62	0.649498	0.324749	−	0.945800i	$-0.394720\pi$
$313$	3596.62	0.649498	0.324749	+	0.945800i	$0.394720\pi$
$314$	−32.0598	−0.00576191
$315$	−1515.66	−0.271105
$316$	−456.641	−0.0812914
$317$	8723.83	1.54568	0.772838	−	0.634604i	$-0.218837\pi$
$317$	8723.83	1.54568	0.772838	+	0.634604i	$0.218837\pi$
$318$	7237.19	1.27623
$319$	−2220.17	−0.389672
$320$	667.076	0.116533
$321$	−2758.28	−0.479601
$322$	0	0
$323$	−4148.52	−0.714643
$324$	−3638.96	−0.623964
$325$	−63.1451	−0.0107774
$326$	1481.27	0.251657
$327$	3367.53	0.569495
$328$	553.255	0.0931353
$329$	5950.02	0.997067
$330$	4622.98	0.771172
$331$	−2232.10	−0.370657	−0.185328	−	0.982677i	$-0.559335\pi$
$331$	−2232.10	−0.370657	−0.185328	+	0.982677i	$0.559335\pi$
$332$	−1035.11	−0.171112
$333$	4014.98	0.660719
$334$	371.941	0.0609333
$335$	−10488.9	−1.71066
$336$	−1188.18	−0.192918
$337$	8186.87	1.32334	0.661672	−	0.749793i	$-0.269847\pi$
$337$	8186.87	1.32334	0.661672	+	0.749793i	$0.269847\pi$
$338$	4364.20	0.702312
$339$	−5381.71	−0.862225
$340$	1289.10	0.205621
$341$	−9157.28	−1.45424
$342$	3292.87	0.520637
$343$	6465.14	1.01774
$344$	2380.70	0.373136
$345$	0	0
$346$	−8818.74	−1.37023
$347$	12226.6	1.89152	0.945758	−	0.324872i	$-0.105321\pi$
$347$	12226.6	1.89152	0.945758	+	0.324872i	$0.105321\pi$
$348$	1572.61	0.242244
$349$	2436.18	0.373655	0.186827	−	0.982393i	$-0.440179\pi$
$349$	2436.18	0.373655	0.186827	+	0.982393i	$0.440179\pi$
$350$	−387.735	−0.0592152
$351$	−356.260	−0.0541759
$352$	1132.43	0.171473
$353$	−11761.8	−1.77342	−0.886708	−	0.462330i	$-0.847014\pi$
$353$	−11761.8	−1.77342	−0.886708	+	0.462330i	$0.847014\pi$
$354$	5602.50	0.841157
$355$	7865.86	1.17599
$356$	−1363.44	−0.202983
$357$	−2296.11	−0.340400
$358$	6127.25	0.904567
$359$	10480.8	1.54082	0.770408	−	0.637551i	$-0.220052\pi$
$359$	10480.8	1.54082	0.770408	+	0.637551i	$0.220052\pi$
$360$	−1023.22	−0.149801
$361$	11143.1	1.62460
$362$	6359.90	0.923394
$363$	−492.947	−0.0712754
$364$	−182.955	−0.0263446
$365$	7376.62	1.05783
$366$	4439.03	0.633966
$367$	−3780.54	−0.537718	−0.268859	−	0.963180i	$-0.586647\pi$
$367$	−3780.54	−0.537718	−0.268859	+	0.963180i	$0.586647\pi$
$368$	0	0
$369$	−848.629	−0.119723
$370$	−6820.65	−0.958348
$371$	6842.72	0.957564
$372$	6486.38	0.904040
$373$	4263.73	0.591870	0.295935	−	0.955208i	$-0.404369\pi$
$373$	4263.73	0.591870	0.295935	+	0.955208i	$0.404369\pi$
$374$	2188.37	0.302562
$375$	−9233.32	−1.27148
$376$	4016.83	0.550937
$377$	242.150	0.0330805
$378$	−2187.57	−0.297663
$379$	6290.45	0.852556	0.426278	−	0.904592i	$-0.359825\pi$
$379$	6290.45	0.852556	0.426278	+	0.904592i	$0.359825\pi$
$380$	−5593.93	−0.755165
$381$	16320.9	2.19461
$382$	2222.77	0.297714
$383$	5684.88	0.758443	0.379221	−	0.925306i	$-0.376192\pi$
$383$	5684.88	0.758443	0.379221	+	0.925306i	$0.376192\pi$
$384$	−802.133	−0.106598
$385$	4371.00	0.578615
$386$	−7669.01	−1.01125
$387$	−3651.72	−0.479657
$388$	2517.29	0.329372
$389$	645.659	0.0841547	0.0420774	−	0.999114i	$-0.486602\pi$
$389$	645.659	0.0841547	0.0420774	+	0.999114i	$0.486602\pi$
$390$	−504.221	−0.0654672
$391$	0	0
$392$	1620.59	0.208806
$393$	−9590.57	−1.23099
$394$	−6908.45	−0.883358
$395$	−1189.90	−0.151570
$396$	−1737.01	−0.220425
$397$	−7859.82	−0.993635	−0.496817	−	0.867855i	$-0.665498\pi$
$397$	−7859.82	−0.993635	−0.496817	+	0.867855i	$0.665498\pi$
$398$	−1920.38	−0.241859
$399$	9963.76	1.25016
$400$	−261.758	−0.0327198
$401$	2713.86	0.337965	0.168982	−	0.985619i	$-0.445952\pi$
$401$	2713.86	0.337965	0.168982	+	0.985619i	$0.445952\pi$
$402$	12612.6	1.56482
$403$	998.769	0.123455
$404$	4516.04	0.556143
$405$	−9482.27	−1.16340
$406$	1486.89	0.181757
$407$	−11578.7	−1.41016
$408$	−1550.09	−0.188091
$409$	5061.05	0.611865	0.305933	−	0.952053i	$-0.401032\pi$
$409$	5061.05	0.611865	0.305933	+	0.952053i	$0.401032\pi$
$410$	1441.65	0.173654
$411$	2735.93	0.328354
$412$	−4443.02	−0.531291
$413$	5297.13	0.631125
$414$	0	0
$415$	−2697.25	−0.319043
$416$	−123.512	−0.0145569
$417$	5279.97	0.620051
$418$	−9496.26	−1.11119
$419$	15258.9	1.77911	0.889554	−	0.456829i	$-0.151015\pi$
$419$	15258.9	1.77911	0.889554	+	0.456829i	$0.151015\pi$
$420$	−3096.11	−0.359702
$421$	2185.44	0.252997	0.126499	−	0.991967i	$-0.459626\pi$
$421$	2185.44	0.252997	0.126499	+	0.991967i	$0.459626\pi$
$422$	−6878.83	−0.793498
$423$	−6161.35	−0.708215
$424$	4619.49	0.529109
$425$	−505.838	−0.0577335
$426$	−9458.39	−1.07573
$427$	4197.07	0.475669
$428$	−1760.60	−0.198836
$429$	−855.966	−0.0963320
$430$	6203.54	0.695724
$431$	41.9648	0.00468997	0.00234498	−	0.999997i	$-0.499254\pi$
$431$	41.9648	0.00468997	0.00234498	+	0.999997i	$0.499254\pi$
$432$	−1476.82	−0.164476
$433$	−12351.8	−1.37087	−0.685436	−	0.728133i	$-0.740388\pi$
$433$	−12351.8	−1.37087	−0.685436	+	0.728133i	$0.740388\pi$
$434$	6132.83	0.678307
$435$	4097.85	0.451671
$436$	2149.49	0.236105
$437$	0	0
$438$	−8870.10	−0.967648
$439$	−10231.9	−1.11239	−0.556197	−	0.831050i	$-0.687740\pi$
$439$	−10231.9	−1.11239	−0.556197	+	0.831050i	$0.687740\pi$
$440$	2950.84	0.319718
$441$	−2485.79	−0.268415
$442$	−238.682	−0.0256854
$443$	−15181.0	−1.62815	−0.814073	−	0.580762i	$-0.802755\pi$
$443$	−15181.0	−1.62815	−0.814073	+	0.580762i	$0.802755\pi$
$444$	8201.57	0.876642
$445$	−3552.80	−0.378469
$446$	4140.80	0.439625
$447$	13047.6	1.38060
$448$	−758.411	−0.0799812
$449$	−3772.38	−0.396502	−0.198251	−	0.980151i	$-0.563526\pi$
$449$	−3772.38	−0.396502	−0.198251	+	0.980151i	$0.563526\pi$
$450$	401.507	0.0420605
$451$	2447.35	0.255524
$452$	−3435.13	−0.357467
$453$	−8669.84	−0.899216
$454$	1344.31	0.138968
$455$	−476.738	−0.0491204
$456$	6726.49	0.690782
$457$	−5578.15	−0.570974	−0.285487	−	0.958383i	$-0.592155\pi$
$457$	−5578.15	−0.570974	−0.285487	+	0.958383i	$0.592155\pi$
$458$	3798.36	0.387524
$459$	−2853.90	−0.290215
$460$	0	0
$461$	−5688.78	−0.574735	−0.287367	−	0.957820i	$-0.592780\pi$
$461$	−5688.78	−0.574735	−0.287367	+	0.957820i	$0.592780\pi$
$462$	−5255.96	−0.529285
$463$	−13452.6	−1.35031	−0.675156	−	0.737675i	$-0.735924\pi$
$463$	−13452.6	−1.35031	−0.675156	+	0.737675i	$0.735924\pi$
$464$	1003.79	0.100431
$465$	16902.0	1.68561
$466$	4751.73	0.472360
$467$	20024.0	1.98416	0.992078	−	0.125625i	$-0.0400937\pi$
$467$	20024.0	1.98416	0.992078	+	0.125625i	$0.0400937\pi$
$468$	189.453	0.0187126
$469$	11925.1	1.17409
$470$	10466.9	1.02724
$471$	100.454	0.00982734
$472$	3576.07	0.348733
$473$	10531.1	1.02373
$474$	1430.81	0.138648
$475$	2195.04	0.212032
$476$	−1465.60	−0.141125
$477$	−7085.76	−0.680156
$478$	6346.55	0.607289
$479$	2821.08	0.269099	0.134550	−	0.990907i	$-0.457041\pi$
$479$	2821.08	0.269099	0.134550	+	0.990907i	$0.457041\pi$
$480$	−2090.17	−0.198756
$481$	1262.87	0.119713
$482$	13240.2	1.25119
$483$	0	0
$484$	−314.647	−0.0295499
$485$	6559.47	0.614124
$486$	6417.80	0.599007
$487$	3992.88	0.371529	0.185765	−	0.982594i	$-0.440524\pi$
$487$	3992.88	0.371529	0.185765	+	0.982594i	$0.440524\pi$
$488$	2833.42	0.262834
$489$	−4641.32	−0.429219
$490$	4222.86	0.389326
$491$	3727.57	0.342613	0.171307	−	0.985218i	$-0.445201\pi$
$491$	3727.57	0.342613	0.171307	+	0.985218i	$0.445201\pi$
$492$	−1733.53	−0.158849
$493$	1939.79	0.177209
$494$	1035.74	0.0943324
$495$	−4526.25	−0.410989
$496$	4140.24	0.374803
$497$	−8942.85	−0.807126
$498$	3243.34	0.291843
$499$	13195.1	1.18375	0.591877	−	0.806028i	$-0.298387\pi$
$499$	13195.1	1.18375	0.591877	+	0.806028i	$0.298387\pi$
$500$	−5893.61	−0.527140
$501$	−1165.42	−0.103926
$502$	−7113.75	−0.632474
$503$	−6456.21	−0.572302	−0.286151	−	0.958185i	$-0.592376\pi$
$503$	−6456.21	−0.572302	−0.286151	+	0.958185i	$0.592376\pi$
$504$	1163.32	0.102814
$505$	11767.7	1.03695
$506$	0	0
$507$	−13674.5	−1.19784
$508$	10417.6	0.909857
$509$	−8218.62	−0.715685	−0.357843	−	0.933782i	$-0.616488\pi$
$509$	−8218.62	−0.715685	−0.357843	+	0.933782i	$0.616488\pi$
$510$	−4039.17	−0.350701
$511$	−8386.62	−0.726032
$512$	−512.000	−0.0441942
$513$	12384.2	1.06584
$514$	9311.12	0.799019
$515$	−11577.5	−0.990610
$516$	−7459.52	−0.636409
$517$	17768.6	1.51154
$518$	7754.53	0.657750
$519$	27632.0	2.33702
$520$	−321.843	−0.0271418
$521$	826.499	0.0695001	0.0347501	−	0.999396i	$-0.488936\pi$
$521$	826.499	0.0695001	0.0347501	+	0.999396i	$0.488936\pi$
$522$	−1539.70	−0.129102
$523$	9741.52	0.814469	0.407234	−	0.913324i	$-0.366493\pi$
$523$	9741.52	0.814469	0.407234	+	0.913324i	$0.366493\pi$
$524$	−6121.64	−0.510354
$525$	1214.90	0.100996
$526$	−3075.55	−0.254943
$527$	8000.86	0.661334
$528$	−3548.27	−0.292460
$529$	0	0
$530$	12037.3	0.986541
$531$	−5485.27	−0.448287
$532$	6359.85	0.518298
$533$	−266.928	−0.0216922
$534$	4272.10	0.346202
$535$	−4587.71	−0.370737
$536$	8050.57	0.648753
$537$	−19198.7	−1.54280
$538$	−5640.20	−0.451982
$539$	7168.74	0.572875
$540$	−3848.24	−0.306670
$541$	−5957.17	−0.473417	−0.236709	−	0.971581i	$-0.576069\pi$
$541$	−5957.17	−0.473417	−0.236709	+	0.971581i	$0.576069\pi$
$542$	5623.71	0.445681
$543$	−19927.7	−1.57491
$544$	−989.420	−0.0779798
$545$	5601.06	0.440226
$546$	573.259	0.0449326
$547$	−9191.61	−0.718473	−0.359237	−	0.933247i	$-0.616963\pi$
$547$	−9191.61	−0.718473	−0.359237	+	0.933247i	$0.616963\pi$
$548$	1746.34	0.136131
$549$	−4346.14	−0.337867
$550$	−1157.90	−0.0897692
$551$	−8417.57	−0.650818
$552$	0	0
$553$	1352.82	0.104028
$554$	−8979.24	−0.688613
$555$	21371.4	1.63453
$556$	3370.20	0.257065
$557$	−7063.48	−0.537323	−0.268662	−	0.963235i	$-0.586581\pi$
$557$	−7063.48	−0.537323	−0.268662	+	0.963235i	$0.586581\pi$
$558$	−6350.65	−0.481800
$559$	−1148.61	−0.0869073
$560$	−1976.24	−0.149128
$561$	−6856.90	−0.516040
$562$	13254.4	0.994842
$563$	95.8736	0.00717689	0.00358845	−	0.999994i	$-0.498858\pi$
$563$	95.8736	0.00717689	0.00358845	+	0.999994i	$0.498858\pi$
$564$	−12586.1	−0.939661
$565$	−8951.15	−0.666509
$566$	16186.0	1.20203
$567$	10780.6	0.798486
$568$	−6037.27	−0.445983
$569$	22463.8	1.65506	0.827531	−	0.561419i	$-0.189745\pi$
$569$	22463.8	1.65506	0.827531	+	0.561419i	$0.189745\pi$
$570$	17527.6	1.28799
$571$	−854.824	−0.0626502	−0.0313251	−	0.999509i	$-0.509973\pi$
$571$	−854.824	−0.0626502	−0.0313251	+	0.999509i	$0.509973\pi$
$572$	−546.362	−0.0399380
$573$	−6964.68	−0.507772
$574$	−1639.04	−0.119185
$575$	0	0
$576$	785.349	0.0568105
$577$	−9001.17	−0.649434	−0.324717	−	0.945811i	$-0.605269\pi$
$577$	−9001.17	−0.649434	−0.324717	+	0.945811i	$0.605269\pi$
$578$	7913.98	0.569513
$579$	24029.6	1.72476
$580$	2615.65	0.187257
$581$	3066.56	0.218971
$582$	−7887.52	−0.561766
$583$	20434.5	1.45165
$584$	−5661.77	−0.401174
$585$	493.670	0.0348902
$586$	1087.57	0.0766674
$587$	−3169.23	−0.222842	−0.111421	−	0.993773i	$-0.535540\pi$
$587$	−3169.23	−0.222842	−0.111421	+	0.993773i	$0.535540\pi$
$588$	−5077.83	−0.356133
$589$	−34719.0	−2.42882
$590$	9318.39	0.650224
$591$	21646.5	1.50663
$592$	5235.05	0.363444
$593$	163.723	0.0113378	0.00566889	−	0.999984i	$-0.498196\pi$
$593$	163.723	0.0113378	0.00566889	+	0.999984i	$0.498196\pi$
$594$	−6532.78	−0.451251
$595$	−3819.01	−0.263133
$596$	8328.25	0.572380
$597$	6017.17	0.412507
$598$	0	0
$599$	12468.7	0.850510	0.425255	−	0.905074i	$-0.360184\pi$
$599$	12468.7	0.850510	0.425255	+	0.905074i	$0.360184\pi$
$600$	820.176	0.0558059
$601$	−6177.91	−0.419305	−0.209653	−	0.977776i	$-0.567233\pi$
$601$	−6177.91	−0.419305	−0.209653	+	0.977776i	$0.567233\pi$
$602$	−7052.93	−0.477502
$603$	−12348.6	−0.833956
$604$	−5533.94	−0.372803
$605$	−819.895	−0.0550967
$606$	−14150.3	−0.948540
$607$	14563.5	0.973831	0.486915	−	0.873449i	$-0.338122\pi$
$607$	14563.5	0.973831	0.486915	+	0.873449i	$0.338122\pi$
$608$	4293.50	0.286389
$609$	−4658.93	−0.309999
$610$	7383.23	0.490063
$611$	−1938.00	−0.128319
$612$	1517.66	0.100241
$613$	−11870.4	−0.782119	−0.391060	−	0.920365i	$-0.627891\pi$
$613$	−11870.4	−0.782119	−0.391060	+	0.920365i	$0.627891\pi$
$614$	−10902.8	−0.716616
$615$	−4517.17	−0.296179
$616$	−3354.87	−0.219434
$617$	3913.16	0.255329	0.127665	−	0.991817i	$-0.459252\pi$
$617$	3913.16	0.255329	0.127665	+	0.991817i	$0.459252\pi$
$618$	13921.5	0.906154
$619$	8978.28	0.582985	0.291492	−	0.956573i	$-0.405848\pi$
$619$	8978.28	0.582985	0.291492	+	0.956573i	$0.405848\pi$
$620$	10788.5	0.698833
$621$	0	0
$622$	361.140	0.0232804
$623$	4039.25	0.259758
$624$	387.004	0.0248278
$625$	−13312.4	−0.851991
$626$	−7193.23	−0.459264
$627$	29754.9	1.89521
$628$	64.1196	0.00407429
$629$	10116.5	0.641291
$630$	3031.33	0.191700
$631$	1550.27	0.0978057	0.0489028	−	0.998804i	$-0.484428\pi$
$631$	1550.27	0.0978057	0.0489028	+	0.998804i	$0.484428\pi$
$632$	913.282	0.0574817
$633$	21553.7	1.35337
$634$	−17447.7	−1.09296
$635$	27145.9	1.69646
$636$	−14474.4	−0.902432
$637$	−781.882	−0.0486331
$638$	4440.33	0.275540
$639$	9260.48	0.573300
$640$	−1334.15	−0.0824015
$641$	28259.7	1.74133	0.870663	−	0.491881i	$-0.163690\pi$
$641$	28259.7	1.74133	0.870663	+	0.491881i	$0.163690\pi$
$642$	5516.55	0.339129
$643$	−17966.4	−1.10191	−0.550953	−	0.834537i	$-0.685735\pi$
$643$	−17966.4	−1.10191	−0.550953	+	0.834537i	$0.685735\pi$
$644$	0	0
$645$	−19437.8	−1.18661
$646$	8297.03	0.505329
$647$	10168.8	0.617894	0.308947	−	0.951079i	$-0.400023\pi$
$647$	10168.8	0.617894	0.308947	+	0.951079i	$0.400023\pi$
$648$	7277.92	0.441209
$649$	15818.9	0.956774
$650$	126.290	0.00762079
$651$	−19216.2	−1.15690
$652$	−2962.55	−0.177948
$653$	15077.8	0.903580	0.451790	−	0.892124i	$-0.350786\pi$
$653$	15077.8	0.903580	0.451790	+	0.892124i	$0.350786\pi$
$654$	−6735.07	−0.402694
$655$	−15951.6	−0.951571
$656$	−1106.51	−0.0658566
$657$	8684.50	0.515699
$658$	−11900.0	−0.705033
$659$	9881.47	0.584108	0.292054	−	0.956402i	$-0.405661\pi$
$659$	9881.47	0.584108	0.292054	+	0.956402i	$0.405661\pi$
$660$	−9245.97	−0.545301
$661$	−19796.5	−1.16489	−0.582447	−	0.812869i	$-0.697905\pi$
$661$	−19796.5	−1.16489	−0.582447	+	0.812869i	$0.697905\pi$
$662$	4464.20	0.262094
$663$	747.871	0.0438083
$664$	2070.22	0.120994
$665$	16572.3	0.966383
$666$	−8029.96	−0.467199
$667$	0	0
$668$	−743.883	−0.0430864
$669$	−12974.5	−0.749810
$670$	20977.9	1.20962
$671$	12533.8	0.721105
$672$	2376.35	0.136414
$673$	−10472.6	−0.599833	−0.299917	−	0.953965i	$-0.596959\pi$
$673$	−10472.6	−0.599833	−0.299917	+	0.953965i	$0.596959\pi$
$674$	−16373.7	−0.935746
$675$	1510.04	0.0861058
$676$	−8728.41	−0.496610
$677$	−13712.8	−0.778471	−0.389235	−	0.921138i	$-0.627261\pi$
$677$	−13712.8	−0.778471	−0.389235	+	0.921138i	$0.627261\pi$
$678$	10763.4	0.609685
$679$	−7457.59	−0.421497
$680$	−2578.20	−0.145396
$681$	−4212.16	−0.237020
$682$	18314.6	1.02830
$683$	11812.1	0.661753	0.330876	−	0.943674i	$-0.392656\pi$
$683$	11812.1	0.661753	0.330876	+	0.943674i	$0.392656\pi$
$684$	−6585.74	−0.368146
$685$	4550.55	0.253821
$686$	−12930.3	−0.719651
$687$	−11901.5	−0.660949
$688$	−4761.40	−0.263847
$689$	−2228.76	−0.123235
$690$	0	0
$691$	−32460.7	−1.78707	−0.893533	−	0.448998i	$-0.851781\pi$
$691$	−32460.7	−1.78707	−0.893533	+	0.448998i	$0.851781\pi$
$692$	17637.5	0.968896
$693$	5145.98	0.282078
$694$	−24453.1	−1.33750
$695$	8781.94	0.479306
$696$	−3145.22	−0.171292
$697$	−2138.29	−0.116203
$698$	−4872.35	−0.264214
$699$	−14888.7	−0.805642
$700$	775.471	0.0418715
$701$	11274.6	0.607467	0.303734	−	0.952757i	$-0.401767\pi$
$701$	11274.6	0.607467	0.303734	+	0.952757i	$0.401767\pi$
$702$	712.520	0.0383081
$703$	−43899.8	−2.35521
$704$	−2264.86	−0.121250
$705$	−32796.3	−1.75203
$706$	23523.5	1.25399
$707$	−13379.0	−0.711695
$708$	−11205.0	−0.594788
$709$	15986.6	0.846814	0.423407	−	0.905940i	$-0.360834\pi$
$709$	15986.6	0.846814	0.423407	+	0.905940i	$0.360834\pi$
$710$	−15731.7	−0.831550
$711$	−1400.87	−0.0738913
$712$	2726.88	0.143531
$713$	0	0
$714$	4592.21	0.240699
$715$	−1423.69	−0.0744657
$716$	−12254.5	−0.639625
$717$	−19885.8	−1.03577
$718$	−20961.5	−1.08952
$719$	33562.3	1.74084	0.870420	−	0.492310i	$-0.163848\pi$
$719$	33562.3	1.74084	0.870420	+	0.492310i	$0.163848\pi$
$720$	2046.43	0.105925
$721$	13162.7	0.679893
$722$	−22286.3	−1.14877
$723$	−41485.9	−2.13399
$724$	−12719.8	−0.652938
$725$	−1026.37	−0.0525773
$726$	985.893	0.0503993
$727$	38677.7	1.97315	0.986573	−	0.163320i	$-0.0522203\pi$
$727$	38677.7	1.97315	0.986573	+	0.163320i	$0.0522203\pi$
$728$	365.910	0.0186285
$729$	4453.88	0.226280
$730$	−14753.2	−0.748002
$731$	−9201.22	−0.465553
$732$	−8878.05	−0.448282
$733$	784.501	0.0395310	0.0197655	−	0.999805i	$-0.493708\pi$
$733$	784.501	0.0395310	0.0197655	+	0.999805i	$0.493708\pi$
$734$	7561.08	0.380224
$735$	−13231.6	−0.664022
$736$	0	0
$737$	35612.1	1.77990
$738$	1697.26	0.0846571
$739$	−38387.1	−1.91081	−0.955407	−	0.295292i	$-0.904583\pi$
$739$	−38387.1	−1.91081	−0.955407	+	0.295292i	$0.904583\pi$
$740$	13641.3	0.677654
$741$	−3245.32	−0.160890
$742$	−13685.4	−0.677100
$743$	−13169.6	−0.650263	−0.325132	−	0.945669i	$-0.605409\pi$
$743$	−13169.6	−0.650263	−0.325132	+	0.945669i	$0.605409\pi$
$744$	−12972.8	−0.639253
$745$	21701.5	1.06722
$746$	−8527.46	−0.418515
$747$	−3175.48	−0.155535
$748$	−4376.75	−0.213944
$749$	5215.86	0.254451
$750$	18466.6	0.899075
$751$	−6602.02	−0.320787	−0.160393	−	0.987053i	$-0.551276\pi$
$751$	−6602.02	−0.320787	−0.160393	+	0.987053i	$0.551276\pi$
$752$	−8033.66	−0.389571
$753$	22289.7	1.07873
$754$	−484.300	−0.0233914
$755$	−14420.2	−0.695103
$756$	4375.14	0.210479
$757$	−4781.72	−0.229583	−0.114792	−	0.993390i	$-0.536620\pi$
$757$	−4781.72	−0.229583	−0.114792	+	0.993390i	$0.536620\pi$
$758$	−12580.9	−0.602848
$759$	0	0
$760$	11187.9	0.533982
$761$	6978.78	0.332432	0.166216	−	0.986089i	$-0.446845\pi$
$761$	6978.78	0.332432	0.166216	+	0.986089i	$0.446845\pi$
$762$	−32641.9	−1.55183
$763$	−6367.96	−0.302144
$764$	−4445.54	−0.210516
$765$	3954.65	0.186903
$766$	−11369.8	−0.536300
$767$	−1725.34	−0.0812236
$768$	1604.27	0.0753762
$769$	17006.3	0.797480	0.398740	−	0.917064i	$-0.369448\pi$
$769$	17006.3	0.797480	0.398740	+	0.917064i	$0.369448\pi$
$770$	−8742.00	−0.409143
$771$	−29174.8	−1.36278
$772$	15338.0	0.715061
$773$	−2000.60	−0.0930872	−0.0465436	−	0.998916i	$-0.514821\pi$
$773$	−2000.60	−0.0930872	−0.0465436	+	0.998916i	$0.514821\pi$
$774$	7303.44	0.339169
$775$	−4233.37	−0.196216
$776$	−5034.59	−0.232901
$777$	−24297.5	−1.12184
$778$	−1291.32	−0.0595064
$779$	9278.91	0.426767
$780$	1008.44	0.0462923
$781$	−26706.2	−1.22359
$782$	0	0
$783$	−5790.72	−0.264295
$784$	−3241.17	−0.147648
$785$	167.081	0.00759664
$786$	19181.1	0.870444
$787$	−40270.2	−1.82399	−0.911994	−	0.410203i	$-0.865458\pi$
$787$	−40270.2	−1.82399	−0.911994	+	0.410203i	$0.865458\pi$
$788$	13816.9	0.624628
$789$	9636.70	0.434824
$790$	2379.80	0.107176
$791$	10176.7	0.457450
$792$	3474.03	0.155864
$793$	−1367.04	−0.0612168
$794$	15719.6	0.702606
$795$	−37716.8	−1.68261
$796$	3840.75	0.171020
$797$	23173.2	1.02991	0.514954	−	0.857218i	$-0.327809\pi$
$797$	23173.2	1.02991	0.514954	+	0.857218i	$0.327809\pi$
$798$	−19927.5	−0.883993
$799$	−15524.7	−0.687391
$800$	523.517	0.0231364
$801$	−4182.71	−0.184505
$802$	−5427.73	−0.238977
$803$	−25045.1	−1.10065
$804$	−25225.1	−1.10649
$805$	0	0
$806$	−1997.54	−0.0872957
$807$	17672.6	0.770887
$808$	−9032.09	−0.393252
$809$	21370.1	0.928719	0.464359	−	0.885647i	$-0.346285\pi$
$809$	21370.1	0.928719	0.464359	+	0.885647i	$0.346285\pi$
$810$	18964.5	0.822649
$811$	−4718.19	−0.204289	−0.102144	−	0.994770i	$-0.532570\pi$
$811$	−4718.19	−0.204289	−0.102144	+	0.994770i	$0.532570\pi$
$812$	−2973.79	−0.128521
$813$	−17620.9	−0.760139
$814$	23157.5	0.997137
$815$	−7719.70	−0.331791
$816$	3100.18	0.133000
$817$	39927.9	1.70979
$818$	−10122.1	−0.432654
$819$	−561.264	−0.0239464
$820$	−2883.30	−0.122792
$821$	−36800.8	−1.56438	−0.782190	−	0.623040i	$-0.785897\pi$
$821$	−36800.8	−1.56438	−0.782190	+	0.623040i	$0.785897\pi$
$822$	−5471.86	−0.232181
$823$	−19450.2	−0.823804	−0.411902	−	0.911228i	$-0.635135\pi$
$823$	−19450.2	−0.823804	−0.411902	+	0.911228i	$0.635135\pi$
$824$	8886.05	0.375680
$825$	3628.09	0.153108
$826$	−10594.3	−0.446273
$827$	22924.2	0.963909	0.481954	−	0.876196i	$-0.339927\pi$
$827$	22924.2	0.963909	0.481954	+	0.876196i	$0.339927\pi$
$828$	0	0
$829$	−4044.07	−0.169429	−0.0847143	−	0.996405i	$-0.526998\pi$
$829$	−4044.07	−0.169429	−0.0847143	+	0.996405i	$0.526998\pi$
$830$	5394.50	0.225598
$831$	28134.9	1.17448
$832$	247.024	0.0102933
$833$	−6263.44	−0.260523
$834$	−10559.9	−0.438443
$835$	−1938.38	−0.0803360
$836$	18992.5	0.785730
$837$	−23884.3	−0.986337
$838$	−30517.8	−1.25802
$839$	−27760.8	−1.14232	−0.571161	−	0.820838i	$-0.693507\pi$
$839$	−27760.8	−1.14232	−0.571161	+	0.820838i	$0.693507\pi$
$840$	6192.22	0.254347
$841$	−20453.1	−0.838618
$842$	−4370.88	−0.178896
$843$	−41530.3	−1.69677
$844$	13757.7	0.561088
$845$	−22744.2	−0.925945
$846$	12322.7	0.500784
$847$	932.155	0.0378149
$848$	−9238.97	−0.374136
$849$	−50716.1	−2.05014
$850$	1011.68	0.0408237
$851$	0	0
$852$	18916.8	0.760655
$853$	−38562.3	−1.54789	−0.773943	−	0.633255i	$-0.781718\pi$
$853$	−38562.3	−1.54789	−0.773943	+	0.633255i	$0.781718\pi$
$854$	−8394.14	−0.336348
$855$	−17160.9	−0.686421
$856$	3521.20	0.140598
$857$	−21000.4	−0.837061	−0.418530	−	0.908203i	$-0.637455\pi$
$857$	−21000.4	−0.837061	−0.418530	+	0.908203i	$0.637455\pi$
$858$	1711.93	0.0681170
$859$	1863.30	0.0740106	0.0370053	−	0.999315i	$-0.488218\pi$
$859$	1863.30	0.0740106	0.0370053	+	0.999315i	$0.488218\pi$
$860$	−12407.1	−0.491951
$861$	5135.66	0.203279
$862$	−83.9297	−0.00331631
$863$	−4775.67	−0.188373	−0.0941864	−	0.995555i	$-0.530025\pi$
$863$	−4775.67	−0.188373	−0.0941864	+	0.995555i	$0.530025\pi$
$864$	2953.64	0.116302
$865$	45959.1	1.80654
$866$	24703.5	0.969353
$867$	−24797.1	−0.971344
$868$	−12265.7	−0.479635
$869$	4039.95	0.157705
$870$	−8195.70	−0.319380
$871$	−3884.15	−0.151102
$872$	−4298.98	−0.166952
$873$	7722.47	0.299388
$874$	0	0
$875$	17460.1	0.674581
$876$	17740.2	0.684230
$877$	23055.7	0.887726	0.443863	−	0.896095i	$-0.353608\pi$
$877$	23055.7	0.887726	0.443863	+	0.896095i	$0.353608\pi$
$878$	20463.8	0.786582
$879$	−3407.72	−0.130762
$880$	−5901.68	−0.226075
$881$	25666.1	0.981514	0.490757	−	0.871297i	$-0.336720\pi$
$881$	25666.1	0.981514	0.490757	+	0.871297i	$0.336720\pi$
$882$	4971.58	0.189798
$883$	12417.0	0.473232	0.236616	−	0.971603i	$-0.423962\pi$
$883$	12417.0	0.473232	0.236616	+	0.971603i	$0.423962\pi$
$884$	477.364	0.0181623
$885$	−29197.6	−1.10900
$886$	30361.9	1.15127
$887$	9011.52	0.341124	0.170562	−	0.985347i	$-0.445442\pi$
$887$	9011.52	0.341124	0.170562	+	0.985347i	$0.445442\pi$
$888$	−16403.1	−0.619880
$889$	−30862.7	−1.16434
$890$	7105.60	0.267618
$891$	32194.2	1.21049
$892$	−8281.60	−0.310862
$893$	67368.3	2.52452
$894$	−26095.2	−0.976234
$895$	−31932.3	−1.19260
$896$	1516.82	0.0565552
$897$	0	0
$898$	7544.76	0.280370
$899$	16234.2	0.602270
$900$	−803.014	−0.0297413
$901$	−17854.0	−0.660157
$902$	−4894.70	−0.180683
$903$	22099.2	0.814412
$904$	6870.27	0.252767
$905$	−33144.8	−1.21743
$906$	17339.7	0.635841
$907$	−7820.42	−0.286299	−0.143149	−	0.989701i	$-0.545723\pi$
$907$	−7820.42	−0.286299	−0.143149	+	0.989701i	$0.545723\pi$
$908$	−2688.62	−0.0982653
$909$	13854.2	0.505516
$910$	953.475	0.0347334
$911$	11062.1	0.402311	0.201155	−	0.979559i	$-0.435530\pi$
$911$	11062.1	0.402311	0.201155	+	0.979559i	$0.435530\pi$
$912$	−13453.0	−0.488457
$913$	9157.72	0.331956
$914$	11156.3	0.403739
$915$	−23134.1	−0.835836
$916$	−7596.73	−0.274021
$917$	18135.6	0.653099
$918$	5707.79	0.205213
$919$	33508.3	1.20276	0.601381	−	0.798962i	$-0.294617\pi$
$919$	33508.3	1.20276	0.601381	+	0.798962i	$0.294617\pi$
$920$	0	0
$921$	34162.2	1.22224
$922$	11377.6	0.406399
$923$	2912.80	0.103874
$924$	10511.9	0.374261
$925$	−5352.80	−0.190269
$926$	26905.2	0.954815
$927$	−13630.2	−0.482927
$928$	−2007.59	−0.0710154
$929$	10274.2	0.362847	0.181424	−	0.983405i	$-0.441929\pi$
$929$	10274.2	0.362847	0.181424	+	0.983405i	$0.441929\pi$
$930$	−33803.9	−1.19191
$931$	27179.7	0.956796
$932$	−9503.46	−0.334009
$933$	−1131.57	−0.0397063
$934$	−40048.0	−1.40301
$935$	−11404.8	−0.398905
$936$	−378.906	−0.0132318
$937$	20260.1	0.706369	0.353184	−	0.935554i	$-0.385099\pi$
$937$	20260.1	0.706369	0.353184	+	0.935554i	$0.385099\pi$
$938$	−23850.2	−0.830209
$939$	22538.8	0.783307
$940$	−20933.8	−0.726368
$941$	23960.4	0.830059	0.415030	−	0.909808i	$-0.363771\pi$
$941$	23960.4	0.830059	0.415030	+	0.909808i	$0.363771\pi$
$942$	−200.908	−0.00694898
$943$	0	0
$944$	−7152.14	−0.246591
$945$	11400.6	0.392446
$946$	−21062.3	−0.723884
$947$	−39377.3	−1.35121	−0.675603	−	0.737266i	$-0.736116\pi$
$947$	−39377.3	−1.35121	−0.675603	+	0.737266i	$0.736116\pi$
$948$	−2861.62	−0.0980390
$949$	2731.63	0.0934377
$950$	−4390.08	−0.149929
$951$	54669.3	1.86412
$952$	2931.20	0.0997907
$953$	31617.1	1.07469	0.537345	−	0.843363i	$-0.319427\pi$
$953$	31617.1	1.07469	0.537345	+	0.843363i	$0.319427\pi$
$954$	14171.5	0.480943
$955$	−11584.0	−0.392514
$956$	−12693.1	−0.429418
$957$	−13913.0	−0.469953
$958$	−5642.17	−0.190282
$959$	−5173.61	−0.174207
$960$	4180.34	0.140542
$961$	37168.4	1.24764
$962$	−2525.75	−0.0846501
$963$	−5401.12	−0.180736
$964$	−26480.4	−0.884725
$965$	39967.3	1.33326
$966$	0	0
$967$	43574.2	1.44907	0.724535	−	0.689238i	$-0.242055\pi$
$967$	43574.2	1.44907	0.724535	+	0.689238i	$0.242055\pi$
$968$	629.294	0.0208949
$969$	−25997.3	−0.861873
$970$	−13118.9	−0.434252
$971$	−4745.31	−0.156832	−0.0784161	−	0.996921i	$-0.524986\pi$
$971$	−4745.31	−0.156832	−0.0784161	+	0.996921i	$0.524986\pi$
$972$	−12835.6	−0.423562
$973$	−9984.36	−0.328966
$974$	−7985.76	−0.262711
$975$	−395.709	−0.0129978
$976$	−5666.84	−0.185852
$977$	−3555.42	−0.116426	−0.0582128	−	0.998304i	$-0.518540\pi$
$977$	−3555.42	−0.116426	−0.0582128	+	0.998304i	$0.518540\pi$
$978$	9282.65	0.303503
$979$	12062.5	0.393788
$980$	−8445.73	−0.275295
$981$	6594.14	0.214612
$982$	−7455.15	−0.242264
$983$	−36878.1	−1.19657	−0.598285	−	0.801283i	$-0.704151\pi$
$983$	−36878.1	−1.19657	−0.598285	+	0.801283i	$0.704151\pi$
$984$	3467.06	0.112323
$985$	36003.6	1.16464
$986$	−3879.59	−0.125305
$987$	37286.8	1.20248
$988$	−2071.48	−0.0667031
$989$	0	0
$990$	9052.50	0.290613
$991$	−41492.7	−1.33003	−0.665014	−	0.746831i	$-0.731574\pi$
$991$	−41492.7	−1.33003	−0.665014	+	0.746831i	$0.731574\pi$
$992$	−8280.49	−0.265026
$993$	−13987.8	−0.447019
$994$	17885.7	0.570724
$995$	10008.1	0.318872
$996$	−6486.68	−0.206364
$997$	−54523.1	−1.73196	−0.865980	−	0.500079i	$-0.833304\pi$
$997$	−54523.1	−1.73196	−0.865980	+	0.500079i	$0.833304\pi$
$998$	−26390.2	−0.837041
$999$	−30200.1	−0.956445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1058.4.a.t.1.13		15
23.7	odd	22		46.4.c.b.3.3	✓	30
23.10	odd	22		46.4.c.b.31.3	yes	30
23.22	odd	2		1058.4.a.u.1.13		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.b.3.3	✓	30	23.7	odd	22
46.4.c.b.31.3	yes	30	23.10	odd	22
1058.4.a.t.1.13		15	1.1	even	1	trivial
1058.4.a.u.1.13		15	23.22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1058 = 2 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1058.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +6.26666 q^{3} +4.00000 q^{4} +10.4231 q^{5} -12.5333 q^{6} -11.8502 q^{7} -8.00000 q^{8} +12.2711 q^{9} -20.8461 q^{10} -35.3884 q^{11} +25.0667 q^{12} +3.85975 q^{13} +23.7004 q^{14} +65.3178 q^{15} +16.0000 q^{16} +30.9194 q^{17} -24.5421 q^{18} -134.172 q^{19} +41.6922 q^{20} -74.2611 q^{21} +70.7768 q^{22} -50.1333 q^{24} -16.3599 q^{25} -7.71950 q^{26} -92.3012 q^{27} -47.4007 q^{28} +62.7371 q^{29} -130.636 q^{30} +258.765 q^{31} -32.0000 q^{32} -221.767 q^{33} -61.8388 q^{34} -123.515 q^{35} +49.0843 q^{36} +327.190 q^{37} +268.344 q^{38} +24.1878 q^{39} -83.3845 q^{40} -69.1568 q^{41} +148.522 q^{42} -297.588 q^{43} -141.554 q^{44} +127.902 q^{45} -502.104 q^{47} +100.267 q^{48} -202.573 q^{49} +32.7198 q^{50} +193.761 q^{51} +15.4390 q^{52} -577.436 q^{53} +184.602 q^{54} -368.855 q^{55} +94.8014 q^{56} -840.811 q^{57} -125.474 q^{58} -447.008 q^{59} +261.271 q^{60} -354.178 q^{61} -517.530 q^{62} -145.414 q^{63} +64.0000 q^{64} +40.2304 q^{65} +443.534 q^{66} -1006.32 q^{67} +123.678 q^{68} +247.030 q^{70} +754.659 q^{71} -98.1686 q^{72} +707.721 q^{73} -654.381 q^{74} -102.522 q^{75} -536.688 q^{76} +419.359 q^{77} -48.3755 q^{78} -114.160 q^{79} +166.769 q^{80} -909.740 q^{81} +138.314 q^{82} -258.777 q^{83} -297.044 q^{84} +322.274 q^{85} +595.175 q^{86} +393.153 q^{87} +283.107 q^{88} -340.860 q^{89} -255.804 q^{90} -45.7388 q^{91} +1621.59 q^{93} +1004.21 q^{94} -1398.48 q^{95} -200.533 q^{96} +629.323 q^{97} +405.146 q^{98} -434.254 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 30 q^{2} + q^{3} + 60 q^{4} - 2 q^{6} - 80 q^{7} - 120 q^{8} + 96 q^{9} + 15 q^{11} + 4 q^{12} + 52 q^{13} + 160 q^{14} - 224 q^{15} + 240 q^{16} + 72 q^{17} - 192 q^{18} - 145 q^{19} - 57 q^{21}+ \cdots + 1569 q^{99}+O(q^{100}) \) 15 * q - 30 * q^2 + q^3 + 60 * q^4 - 2 * q^6 - 80 * q^7 - 120 * q^8 + 96 * q^9 + 15 * q^11 + 4 * q^12 + 52 * q^13 + 160 * q^14 - 224 * q^15 + 240 * q^16 + 72 * q^17 - 192 * q^18 - 145 * q^19 - 57 * q^21 - 30 * q^22 - 8 * q^24 + 671 * q^25 - 104 * q^26 + 85 * q^27 - 320 * q^28 - 202 * q^29 + 448 * q^30 - 320 * q^31 - 480 * q^32 - 114 * q^33 - 144 * q^34 + 500 * q^35 + 384 * q^36 - 768 * q^37 + 290 * q^38 + 653 * q^39 - 247 * q^41 + 114 * q^42 - 1210 * q^43 + 60 * q^44 + 24 * q^45 - 754 * q^47 + 16 * q^48 + 1553 * q^49 - 1342 * q^50 - 779 * q^51 + 208 * q^52 + 277 * q^53 - 170 * q^54 - 1238 * q^55 + 640 * q^56 - 1239 * q^57 + 404 * q^58 - 660 * q^59 - 896 * q^60 - 592 * q^61 + 640 * q^62 - 1665 * q^63 + 960 * q^64 + 546 * q^65 + 228 * q^66 - 1958 * q^67 + 288 * q^68 - 1000 * q^70 + 3626 * q^71 - 768 * q^72 - 2459 * q^73 + 1536 * q^74 - 4597 * q^75 - 580 * q^76 - 2198 * q^77 - 1306 * q^78 - 1038 * q^79 + 139 * q^81 + 494 * q^82 - 1192 * q^83 - 228 * q^84 + 3324 * q^85 + 2420 * q^86 + 547 * q^87 - 120 * q^88 + 70 * q^89 - 48 * q^90 - 2067 * q^91 + 2465 * q^93 + 1508 * q^94 - 4756 * q^95 - 32 * q^96 - 3856 * q^97 - 3106 * q^98 + 1569 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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