LMFDB - Embedded newform 1015.2.a.l.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1015,2,Mod(1,1015)] 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("1015.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1015, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1015 = 5 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1015.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,1,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$8.10481580516$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 10x^{6} + 11x^{5} + 25x^{4} - 25x^{3} - 16x^{2} + 9x + 4 $ x^8 - x^7 - 10x^6 + 11x^5 + 25x^4 - 25x^3 - 16x^2 + 9x + 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.90142$ of defining polynomial
Character	$\chi$	$=$	1015.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.90142 q^{2} +2.54699 q^{3} +1.61538 q^{4} +1.00000 q^{5} +4.84289 q^{6} +1.00000 q^{7} -0.731315 q^{8} +3.48717 q^{9} +1.90142 q^{10} +0.728522 q^{11} +4.11437 q^{12} +3.13413 q^{13} +1.90142 q^{14} +2.54699 q^{15} -4.62130 q^{16} -2.84289 q^{17} +6.63056 q^{18} -5.77754 q^{19} +1.61538 q^{20} +2.54699 q^{21} +1.38522 q^{22} -4.48221 q^{23} -1.86265 q^{24} +1.00000 q^{25} +5.95929 q^{26} +1.24082 q^{27} +1.61538 q^{28} +1.00000 q^{29} +4.84289 q^{30} -5.44093 q^{31} -7.32439 q^{32} +1.85554 q^{33} -5.40552 q^{34} +1.00000 q^{35} +5.63312 q^{36} +2.63378 q^{37} -10.9855 q^{38} +7.98261 q^{39} -0.731315 q^{40} +3.86096 q^{41} +4.84289 q^{42} +6.24486 q^{43} +1.17684 q^{44} +3.48717 q^{45} -8.52254 q^{46} -1.56179 q^{47} -11.7704 q^{48} +1.00000 q^{49} +1.90142 q^{50} -7.24083 q^{51} +5.06283 q^{52} +9.73567 q^{53} +2.35931 q^{54} +0.728522 q^{55} -0.731315 q^{56} -14.7153 q^{57} +1.90142 q^{58} +6.37795 q^{59} +4.11437 q^{60} +13.1438 q^{61} -10.3455 q^{62} +3.48717 q^{63} -4.68411 q^{64} +3.13413 q^{65} +3.52816 q^{66} -7.17801 q^{67} -4.59236 q^{68} -11.4162 q^{69} +1.90142 q^{70} -0.416727 q^{71} -2.55022 q^{72} -6.24986 q^{73} +5.00792 q^{74} +2.54699 q^{75} -9.33294 q^{76} +0.728522 q^{77} +15.1783 q^{78} -15.5074 q^{79} -4.62130 q^{80} -7.30115 q^{81} +7.34129 q^{82} -3.86824 q^{83} +4.11437 q^{84} -2.84289 q^{85} +11.8741 q^{86} +2.54699 q^{87} -0.532780 q^{88} -3.83025 q^{89} +6.63056 q^{90} +3.13413 q^{91} -7.24049 q^{92} -13.8580 q^{93} -2.96962 q^{94} -5.77754 q^{95} -18.6552 q^{96} -3.75306 q^{97} +1.90142 q^{98} +2.54048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 4 q^{3} + 5 q^{4} + 8 q^{5} - 6 q^{6} + 8 q^{7} - 6 q^{8} + 14 q^{9} + q^{10} + q^{11} - 7 q^{12} - q^{13} + q^{14} + 4 q^{15} + 3 q^{16} + 22 q^{17} + 13 q^{18} + 8 q^{19} + 5 q^{20}+ \cdots - 63 q^{99}+O(q^{100}) $ 8 * q + q^2 + 4 * q^3 + 5 * q^4 + 8 * q^5 - 6 * q^6 + 8 * q^7 - 6 * q^8 + 14 * q^9 + q^10 + q^11 - 7 * q^12 - q^13 + q^14 + 4 * q^15 + 3 * q^16 + 22 * q^17 + 13 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 - 3 * q^22 + 9 * q^23 + 16 * q^24 + 8 * q^25 + 27 * q^26 + q^27 + 5 * q^28 + 8 * q^29 - 6 * q^30 + 3 * q^31 - 26 * q^32 + 14 * q^33 + q^34 + 8 * q^35 - 13 * q^36 + 9 * q^37 - 5 * q^38 + 3 * q^39 - 6 * q^40 + 24 * q^41 - 6 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 - 27 * q^46 + 21 * q^47 - 8 * q^48 + 8 * q^49 + q^50 - 8 * q^51 - 7 * q^52 - 2 * q^53 - 33 * q^54 + q^55 - 6 * q^56 - 10 * q^57 + q^58 + 18 * q^59 - 7 * q^60 + 26 * q^61 + 15 * q^62 + 14 * q^63 + 4 * q^64 - q^65 + 55 * q^66 - 8 * q^67 + 6 * q^68 - 2 * q^69 + q^70 - 12 * q^71 + 9 * q^72 - q^73 + 14 * q^74 + 4 * q^75 + 15 * q^76 + q^77 + 8 * q^78 - 14 * q^79 + 3 * q^80 + 40 * q^81 - 42 * q^82 - 10 * q^83 - 7 * q^84 + 22 * q^85 + 19 * q^86 + 4 * q^87 - 29 * q^88 - 4 * q^89 + 13 * q^90 - q^91 + 47 * q^92 - 24 * q^93 - 30 * q^94 + 8 * q^95 - q^96 - 11 * q^97 + q^98 - 63 * 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 $

$2$	1.90142	1.34450	0.672252	−	0.740322i	$-0.265327\pi$
$2$	1.90142	1.34450	0.672252	+	0.740322i	$0.265327\pi$
$3$	2.54699	1.47051	0.735253	−	0.677792i	$-0.237063\pi$
$3$	2.54699	1.47051	0.735253	+	0.677792i	$0.237063\pi$
$4$	1.61538	0.807692
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	4.84289	1.97710
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−0.731315	−0.258559
$9$	3.48717	1.16239
$10$	1.90142	0.601281
$11$	0.728522	0.219658	0.109829	−	0.993951i	$-0.464970\pi$
$11$	0.728522	0.219658	0.109829	+	0.993951i	$0.464970\pi$
$12$	4.11437	1.18772
$13$	3.13413	0.869252	0.434626	−	0.900611i	$-0.356881\pi$
$13$	3.13413	0.869252	0.434626	+	0.900611i	$0.356881\pi$
$14$	1.90142	0.508175
$15$	2.54699	0.657631
$16$	−4.62130	−1.15533
$17$	−2.84289	−0.689503	−0.344751	−	0.938694i	$-0.612037\pi$
$17$	−2.84289	−0.689503	−0.344751	+	0.938694i	$0.612037\pi$
$18$	6.63056	1.56284
$19$	−5.77754	−1.32546	−0.662729	−	0.748859i	$-0.730602\pi$
$19$	−5.77754	−1.32546	−0.662729	+	0.748859i	$0.730602\pi$
$20$	1.61538	0.361211
$21$	2.54699	0.555799
$22$	1.38522	0.295331
$23$	−4.48221	−0.934605	−0.467303	−	0.884097i	$-0.654774\pi$
$23$	−4.48221	−0.934605	−0.467303	+	0.884097i	$0.654774\pi$
$24$	−1.86265	−0.380213
$25$	1.00000	0.200000
$26$	5.95929	1.16871
$27$	1.24082	0.238796
$28$	1.61538	0.305279
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	4.84289	0.884187
$31$	−5.44093	−0.977220	−0.488610	−	0.872502i	$-0.662496\pi$
$31$	−5.44093	−0.977220	−0.488610	+	0.872502i	$0.662496\pi$
$32$	−7.32439	−1.29478
$33$	1.85554	0.323008
$34$	−5.40552	−0.927040
$35$	1.00000	0.169031
$36$	5.63312	0.938853
$37$	2.63378	0.432991	0.216496	−	0.976284i	$-0.430537\pi$
$37$	2.63378	0.432991	0.216496	+	0.976284i	$0.430537\pi$
$38$	−10.9855	−1.78208
$39$	7.98261	1.27824
$40$	−0.731315	−0.115631
$41$	3.86096	0.602981	0.301490	−	0.953469i	$-0.402516\pi$
$41$	3.86096	0.602981	0.301490	+	0.953469i	$0.402516\pi$
$42$	4.84289	0.747275
$43$	6.24486	0.952332	0.476166	−	0.879355i	$-0.342026\pi$
$43$	6.24486	0.952332	0.476166	+	0.879355i	$0.342026\pi$
$44$	1.17684	0.177416
$45$	3.48717	0.519837
$46$	−8.52254	−1.25658
$47$	−1.56179	−0.227811	−0.113905	−	0.993492i	$-0.536336\pi$
$47$	−1.56179	−0.227811	−0.113905	+	0.993492i	$0.536336\pi$
$48$	−11.7704	−1.69891
$49$	1.00000	0.142857
$50$	1.90142	0.268901
$51$	−7.24083	−1.01392
$52$	5.06283	0.702088
$53$	9.73567	1.33730	0.668649	−	0.743578i	$-0.266873\pi$
$53$	9.73567	1.33730	0.668649	+	0.743578i	$0.266873\pi$
$54$	2.35931	0.321062
$55$	0.728522	0.0982339
$56$	−0.731315	−0.0977261
$57$	−14.7153	−1.94910
$58$	1.90142	0.249668
$59$	6.37795	0.830338	0.415169	−	0.909744i	$-0.363722\pi$
$59$	6.37795	0.830338	0.415169	+	0.909744i	$0.363722\pi$
$60$	4.11437	0.531163
$61$	13.1438	1.68289	0.841445	−	0.540343i	$-0.181705\pi$
$61$	13.1438	1.68289	0.841445	+	0.540343i	$0.181705\pi$
$62$	−10.3455	−1.31388
$63$	3.48717	0.439342
$64$	−4.68411	−0.585514
$65$	3.13413	0.388741
$66$	3.52816	0.434286
$67$	−7.17801	−0.876933	−0.438466	−	0.898748i	$-0.644478\pi$
$67$	−7.17801	−0.876933	−0.438466	+	0.898748i	$0.644478\pi$
$68$	−4.59236	−0.556906
$69$	−11.4162	−1.37434
$70$	1.90142	0.227263
$71$	−0.416727	−0.0494564	−0.0247282	−	0.999694i	$-0.507872\pi$
$71$	−0.416727	−0.0494564	−0.0247282	+	0.999694i	$0.507872\pi$
$72$	−2.55022	−0.300546
$73$	−6.24986	−0.731490	−0.365745	−	0.930715i	$-0.619186\pi$
$73$	−6.24986	−0.731490	−0.365745	+	0.930715i	$0.619186\pi$
$74$	5.00792	0.582159
$75$	2.54699	0.294101
$76$	−9.33294	−1.07056
$77$	0.728522	0.0830228
$78$	15.1783	1.71860
$79$	−15.5074	−1.74471	−0.872357	−	0.488869i	$-0.837409\pi$
$79$	−15.5074	−1.74471	−0.872357	+	0.488869i	$0.837409\pi$
$80$	−4.62130	−0.516677
$81$	−7.30115	−0.811239
$82$	7.34129	0.810710
$83$	−3.86824	−0.424595	−0.212297	−	0.977205i	$-0.568095\pi$
$83$	−3.86824	−0.424595	−0.212297	+	0.977205i	$0.568095\pi$
$84$	4.11437	0.448915
$85$	−2.84289	−0.308355
$86$	11.8741	1.28041
$87$	2.54699	0.273066
$88$	−0.532780	−0.0567945
$89$	−3.83025	−0.406005	−0.203003	−	0.979178i	$-0.565070\pi$
$89$	−3.83025	−0.406005	−0.203003	+	0.979178i	$0.565070\pi$
$90$	6.63056	0.698923
$91$	3.13413	0.328546
$92$	−7.24049	−0.754873
$93$	−13.8580	−1.43701
$94$	−2.96962	−0.306293
$95$	−5.77754	−0.592763
$96$	−18.6552	−1.90398
$97$	−3.75306	−0.381066	−0.190533	−	0.981681i	$-0.561022\pi$
$97$	−3.75306	−0.381066	−0.190533	+	0.981681i	$0.561022\pi$
$98$	1.90142	0.192072
$99$	2.54048	0.255328
$100$	1.61538	0.161538
$101$	7.41208	0.737529	0.368765	−	0.929523i	$-0.379781\pi$
$101$	7.41208	0.737529	0.368765	+	0.929523i	$0.379781\pi$
$102$	−13.7678	−1.36322
$103$	9.80016	0.965638	0.482819	−	0.875720i	$-0.339613\pi$
$103$	9.80016	0.965638	0.482819	+	0.875720i	$0.339613\pi$
$104$	−2.29204	−0.224753
$105$	2.54699	0.248561
$106$	18.5116	1.79800
$107$	−0.235944	−0.0228096	−0.0114048	−	0.999935i	$-0.503630\pi$
$107$	−0.235944	−0.0228096	−0.0114048	+	0.999935i	$0.503630\pi$
$108$	2.00440	0.192873
$109$	−2.90415	−0.278168	−0.139084	−	0.990281i	$-0.544416\pi$
$109$	−2.90415	−0.278168	−0.139084	+	0.990281i	$0.544416\pi$
$110$	1.38522	0.132076
$111$	6.70823	0.636717
$112$	−4.62130	−0.436672
$113$	0.412291	0.0387850	0.0193925	−	0.999812i	$-0.493827\pi$
$113$	0.412291	0.0387850	0.0193925	+	0.999812i	$0.493827\pi$
$114$	−27.9800	−2.62057
$115$	−4.48221	−0.417968
$116$	1.61538	0.149985
$117$	10.9293	1.01041
$118$	12.1271	1.11639
$119$	−2.84289	−0.260608
$120$	−1.86265	−0.170036
$121$	−10.4693	−0.951750
$122$	24.9918	2.26265
$123$	9.83384	0.886687
$124$	−8.78919	−0.789292
$125$	1.00000	0.0894427
$126$	6.63056	0.590697
$127$	2.84410	0.252373	0.126186	−	0.992007i	$-0.459726\pi$
$127$	2.84410	0.252373	0.126186	+	0.992007i	$0.459726\pi$
$128$	5.74234	0.507556
$129$	15.9056	1.40041
$130$	5.95929	0.522664
$131$	2.54530	0.222384	0.111192	−	0.993799i	$-0.464533\pi$
$131$	2.54530	0.222384	0.111192	+	0.993799i	$0.464533\pi$
$132$	2.99741	0.260891
$133$	−5.77754	−0.500976
$134$	−13.6484	−1.17904
$135$	1.24082	0.106793
$136$	2.07905	0.178277
$137$	12.2175	1.04381	0.521907	−	0.853002i	$-0.325221\pi$
$137$	12.2175	1.04381	0.521907	+	0.853002i	$0.325221\pi$
$138$	−21.7069	−1.84781
$139$	−2.42528	−0.205710	−0.102855	−	0.994696i	$-0.532798\pi$
$139$	−2.42528	−0.205710	−0.102855	+	0.994696i	$0.532798\pi$
$140$	1.61538	0.136525
$141$	−3.97787	−0.334997
$142$	−0.792372	−0.0664944
$143$	2.28329	0.190938
$144$	−16.1153	−1.34294
$145$	1.00000	0.0830455
$146$	−11.8836	−0.983492
$147$	2.54699	0.210072
$148$	4.25457	0.349724
$149$	−9.60374	−0.786769	−0.393384	−	0.919374i	$-0.628696\pi$
$149$	−9.60374	−0.786769	−0.393384	+	0.919374i	$0.628696\pi$
$150$	4.84289	0.395421
$151$	−21.6983	−1.76578	−0.882891	−	0.469577i	$-0.844406\pi$
$151$	−21.6983	−1.76578	−0.882891	+	0.469577i	$0.844406\pi$
$152$	4.22520	0.342709
$153$	−9.91365	−0.801471
$154$	1.38522	0.111625
$155$	−5.44093	−0.437026
$156$	12.8950	1.03242
$157$	−16.7980	−1.34063	−0.670314	−	0.742078i	$-0.733841\pi$
$157$	−16.7980	−1.34063	−0.670314	+	0.742078i	$0.733841\pi$
$158$	−29.4859	−2.34578
$159$	24.7967	1.96651
$160$	−7.32439	−0.579044
$161$	−4.48221	−0.353248
$162$	−13.8825	−1.09071
$163$	23.3686	1.83037	0.915186	−	0.403031i	$-0.132043\pi$
$163$	23.3686	1.83037	0.915186	+	0.403031i	$0.132043\pi$
$164$	6.23693	0.487023
$165$	1.85554	0.144454
$166$	−7.35514	−0.570869
$167$	−5.65077	−0.437270	−0.218635	−	0.975807i	$-0.570160\pi$
$167$	−5.65077	−0.437270	−0.218635	+	0.975807i	$0.570160\pi$
$168$	−1.86265	−0.143707
$169$	−3.17721	−0.244401
$170$	−5.40552	−0.414585
$171$	−20.1473	−1.54070
$172$	10.0878	0.769191
$173$	22.3388	1.69839	0.849193	−	0.528083i	$-0.177089\pi$
$173$	22.3388	1.69839	0.849193	+	0.528083i	$0.177089\pi$
$174$	4.84289	0.367139
$175$	1.00000	0.0755929
$176$	−3.36672	−0.253776
$177$	16.2446	1.22102
$178$	−7.28290	−0.545876
$179$	−4.44330	−0.332108	−0.166054	−	0.986117i	$-0.553103\pi$
$179$	−4.44330	−0.332108	−0.166054	+	0.986117i	$0.553103\pi$
$180$	5.63312	0.419868
$181$	9.78079	0.727001	0.363500	−	0.931594i	$-0.381582\pi$
$181$	9.78079	0.727001	0.363500	+	0.931594i	$0.381582\pi$
$182$	5.95929	0.441732
$183$	33.4771	2.47470
$184$	3.27791	0.241651
$185$	2.63378	0.193640
$186$	−26.3498	−1.93206
$187$	−2.07111	−0.151455
$188$	−2.52289	−0.184001
$189$	1.24082	0.0902563
$190$	−10.9855	−0.796972
$191$	−18.9046	−1.36789	−0.683946	−	0.729533i	$-0.739738\pi$
$191$	−18.9046	−1.36789	−0.683946	+	0.729533i	$0.739738\pi$
$192$	−11.9304	−0.861002
$193$	15.5798	1.12146	0.560729	−	0.827999i	$-0.310521\pi$
$193$	15.5798	1.12146	0.560729	+	0.827999i	$0.310521\pi$
$194$	−7.13613	−0.512345
$195$	7.98261	0.571647
$196$	1.61538	0.115385
$197$	−15.5935	−1.11099	−0.555495	−	0.831520i	$-0.687471\pi$
$197$	−15.5935	−1.11099	−0.555495	+	0.831520i	$0.687471\pi$
$198$	4.83051	0.343290
$199$	−0.403048	−0.0285713	−0.0142856	−	0.999898i	$-0.504547\pi$
$199$	−0.403048	−0.0285713	−0.0142856	+	0.999898i	$0.504547\pi$
$200$	−0.731315	−0.0517118
$201$	−18.2823	−1.28954
$202$	14.0934	0.991611
$203$	1.00000	0.0701862
$204$	−11.6967	−0.818934
$205$	3.86096	0.269661
$206$	18.6342	1.29830
$207$	−15.6302	−1.08638
$208$	−14.4838	−1.00427
$209$	−4.20907	−0.291147
$210$	4.84289	0.334191
$211$	23.0587	1.58742	0.793712	−	0.608294i	$-0.208146\pi$
$211$	23.0587	1.58742	0.793712	+	0.608294i	$0.208146\pi$
$212$	15.7268	1.08012
$213$	−1.06140	−0.0727260
$214$	−0.448629	−0.0306676
$215$	6.24486	0.425896
$216$	−0.907430	−0.0617428
$217$	−5.44093	−0.369354
$218$	−5.52201	−0.373998
$219$	−15.9183	−1.07566
$220$	1.17684	0.0793428
$221$	−8.91000	−0.599352
$222$	12.7551	0.856069
$223$	8.59802	0.575766	0.287883	−	0.957666i	$-0.407049\pi$
$223$	8.59802	0.575766	0.287883	+	0.957666i	$0.407049\pi$
$224$	−7.32439	−0.489381
$225$	3.48717	0.232478
$226$	0.783936	0.0521467
$227$	11.5139	0.764203	0.382101	−	0.924120i	$-0.375201\pi$
$227$	11.5139	0.764203	0.382101	+	0.924120i	$0.375201\pi$
$228$	−23.7709	−1.57427
$229$	15.6307	1.03290	0.516452	−	0.856316i	$-0.327252\pi$
$229$	15.6307	1.03290	0.516452	+	0.856316i	$0.327252\pi$
$230$	−8.52254	−0.561960
$231$	1.85554	0.122086
$232$	−0.731315	−0.0480132
$233$	4.87126	0.319127	0.159563	−	0.987188i	$-0.448991\pi$
$233$	4.87126	0.319127	0.159563	+	0.987188i	$0.448991\pi$
$234$	20.7811	1.35850
$235$	−1.56179	−0.101880
$236$	10.3028	0.670658
$237$	−39.4971	−2.56561
$238$	−5.40552	−0.350388
$239$	4.40727	0.285083	0.142541	−	0.989789i	$-0.454473\pi$
$239$	4.40727	0.285083	0.142541	+	0.989789i	$0.454473\pi$
$240$	−11.7704	−0.759778
$241$	13.7374	0.884905	0.442452	−	0.896792i	$-0.354109\pi$
$241$	13.7374	0.884905	0.442452	+	0.896792i	$0.354109\pi$
$242$	−19.9064	−1.27963
$243$	−22.3184	−1.43173
$244$	21.2323	1.35926
$245$	1.00000	0.0638877
$246$	18.6982	1.19215
$247$	−18.1076	−1.15216
$248$	3.97903	0.252669
$249$	−9.85238	−0.624369
$250$	1.90142	0.120256
$251$	26.3747	1.66475	0.832377	−	0.554209i	$-0.186979\pi$
$251$	26.3747	1.66475	0.832377	+	0.554209i	$0.186979\pi$
$252$	5.63312	0.354853
$253$	−3.26539	−0.205293
$254$	5.40781	0.339316
$255$	−7.24083	−0.453438
$256$	20.2868	1.26792
$257$	25.2286	1.57372	0.786860	−	0.617132i	$-0.211705\pi$
$257$	25.2286	1.57372	0.786860	+	0.617132i	$0.211705\pi$
$258$	30.2432	1.88286
$259$	2.63378	0.163655
$260$	5.06283	0.313983
$261$	3.48717	0.215850
$262$	4.83967	0.298996
$263$	6.71900	0.414311	0.207156	−	0.978308i	$-0.433579\pi$
$263$	6.71900	0.414311	0.207156	+	0.978308i	$0.433579\pi$
$264$	−1.35699	−0.0835167
$265$	9.73567	0.598058
$266$	−10.9855	−0.673565
$267$	−9.75561	−0.597034
$268$	−11.5952	−0.708292
$269$	16.4506	1.00301	0.501507	−	0.865154i	$-0.332779\pi$
$269$	16.4506	1.00301	0.501507	+	0.865154i	$0.332779\pi$
$270$	2.35931	0.143583
$271$	10.5078	0.638302	0.319151	−	0.947704i	$-0.396602\pi$
$271$	10.5078	0.638302	0.319151	+	0.947704i	$0.396602\pi$
$272$	13.1379	0.796600
$273$	7.98261	0.483130
$274$	23.2306	1.40341
$275$	0.728522	0.0439315
$276$	−18.4415	−1.11005
$277$	−28.4609	−1.71005	−0.855025	−	0.518587i	$-0.826458\pi$
$277$	−28.4609	−1.71005	−0.855025	+	0.518587i	$0.826458\pi$
$278$	−4.61148	−0.276578
$279$	−18.9734	−1.13591
$280$	−0.731315	−0.0437045
$281$	−7.90549	−0.471602	−0.235801	−	0.971801i	$-0.575771\pi$
$281$	−7.90549	−0.471602	−0.235801	+	0.971801i	$0.575771\pi$
$282$	−7.56359	−0.450405
$283$	20.8806	1.24122	0.620612	−	0.784118i	$-0.286884\pi$
$283$	20.8806	1.24122	0.620612	+	0.784118i	$0.286884\pi$
$284$	−0.673174	−0.0399455
$285$	−14.7153	−0.871662
$286$	4.34148	0.256717
$287$	3.86096	0.227905
$288$	−25.5414	−1.50504
$289$	−8.91796	−0.524586
$290$	1.90142	0.111655
$291$	−9.55902	−0.560360
$292$	−10.0959	−0.590819
$293$	11.5150	0.672714	0.336357	−	0.941735i	$-0.390805\pi$
$293$	11.5150	0.672714	0.336357	+	0.941735i	$0.390805\pi$
$294$	4.84289	0.282443
$295$	6.37795	0.371339
$296$	−1.92613	−0.111954
$297$	0.903965	0.0524533
$298$	−18.2607	−1.05781
$299$	−14.0478	−0.812407
$300$	4.11437	0.237543
$301$	6.24486	0.359948
$302$	−41.2575	−2.37410
$303$	18.8785	1.08454
$304$	26.6998	1.53134
$305$	13.1438	0.752611
$306$	−18.8500	−1.07758
$307$	1.70062	0.0970592	0.0485296	−	0.998822i	$-0.484546\pi$
$307$	1.70062	0.0970592	0.0485296	+	0.998822i	$0.484546\pi$
$308$	1.17684	0.0670569
$309$	24.9609	1.41998
$310$	−10.3455	−0.587583
$311$	0.169230	0.00959613	0.00479806	−	0.999988i	$-0.498473\pi$
$311$	0.169230	0.00959613	0.00479806	+	0.999988i	$0.498473\pi$
$312$	−5.83781	−0.330501
$313$	−29.9696	−1.69398	−0.846990	−	0.531609i	$-0.821588\pi$
$313$	−29.9696	−1.69398	−0.846990	+	0.531609i	$0.821588\pi$
$314$	−31.9400	−1.80248
$315$	3.48717	0.196480
$316$	−25.0503	−1.40919
$317$	−17.3308	−0.973396	−0.486698	−	0.873570i	$-0.661799\pi$
$317$	−17.3308	−0.973396	−0.486698	+	0.873570i	$0.661799\pi$
$318$	47.1488	2.64397
$319$	0.728522	0.0407894
$320$	−4.68411	−0.261850
$321$	−0.600949	−0.0335417
$322$	−8.52254	−0.474943
$323$	16.4249	0.913907
$324$	−11.7942	−0.655231
$325$	3.13413	0.173850
$326$	44.4335	2.46094
$327$	−7.39686	−0.409047
$328$	−2.82358	−0.155906
$329$	−1.56179	−0.0861044
$330$	3.52816	0.194219
$331$	−13.9562	−0.767104	−0.383552	−	0.923519i	$-0.625299\pi$
$331$	−13.9562	−0.767104	−0.383552	+	0.923519i	$0.625299\pi$
$332$	−6.24869	−0.342942
$333$	9.18445	0.503305
$334$	−10.7445	−0.587912
$335$	−7.17801	−0.392176
$336$	−11.7704	−0.642129
$337$	14.8801	0.810571	0.405286	−	0.914190i	$-0.367172\pi$
$337$	14.8801	0.810571	0.405286	+	0.914190i	$0.367172\pi$
$338$	−6.04121	−0.328598
$339$	1.05010	0.0570337
$340$	−4.59236	−0.249056
$341$	−3.96384	−0.214654
$342$	−38.3083	−2.07148
$343$	1.00000	0.0539949
$344$	−4.56696	−0.246234
$345$	−11.4162	−0.614625
$346$	42.4753	2.28349
$347$	−29.7336	−1.59618	−0.798092	−	0.602535i	$-0.794157\pi$
$347$	−29.7336	−1.59618	−0.798092	+	0.602535i	$0.794157\pi$
$348$	4.11437	0.220553
$349$	−12.8810	−0.689503	−0.344752	−	0.938694i	$-0.612037\pi$
$349$	−12.8810	−0.689503	−0.344752	+	0.938694i	$0.612037\pi$
$350$	1.90142	0.101635
$351$	3.88889	0.207574
$352$	−5.33598	−0.284409
$353$	−5.81067	−0.309271	−0.154635	−	0.987972i	$-0.549420\pi$
$353$	−5.81067	−0.309271	−0.154635	+	0.987972i	$0.549420\pi$
$354$	30.8877	1.64166
$355$	−0.416727	−0.0221176
$356$	−6.18732	−0.327927
$357$	−7.24083	−0.383225
$358$	−8.44856	−0.446520
$359$	−36.5012	−1.92646	−0.963229	−	0.268683i	$-0.913412\pi$
$359$	−36.5012	−1.92646	−0.963229	+	0.268683i	$0.913412\pi$
$360$	−2.55022	−0.134408
$361$	14.3800	0.756840
$362$	18.5974	0.977456
$363$	−26.6651	−1.39956
$364$	5.06283	0.265364
$365$	−6.24986	−0.327132
$366$	63.6540	3.32725
$367$	6.38217	0.333146	0.166573	−	0.986029i	$-0.446730\pi$
$367$	6.38217	0.333146	0.166573	+	0.986029i	$0.446730\pi$
$368$	20.7136	1.07977
$369$	13.4638	0.700899
$370$	5.00792	0.260349
$371$	9.73567	0.505451
$372$	−22.3860	−1.16066
$373$	−10.8278	−0.560644	−0.280322	−	0.959906i	$-0.590441\pi$
$373$	−10.8278	−0.560644	−0.280322	+	0.959906i	$0.590441\pi$
$374$	−3.93804	−0.203631
$375$	2.54699	0.131526
$376$	1.14216	0.0589025
$377$	3.13413	0.161416
$378$	2.35931	0.121350
$379$	23.2489	1.19422	0.597109	−	0.802160i	$-0.296316\pi$
$379$	23.2489	1.19422	0.597109	+	0.802160i	$0.296316\pi$
$380$	−9.33294	−0.478770
$381$	7.24389	0.371116
$382$	−35.9456	−1.83914
$383$	−17.6744	−0.903120	−0.451560	−	0.892241i	$-0.649132\pi$
$383$	−17.6744	−0.903120	−0.451560	+	0.892241i	$0.649132\pi$
$384$	14.6257	0.746364
$385$	0.728522	0.0371289
$386$	29.6237	1.50780
$387$	21.7769	1.10698
$388$	−6.06264	−0.307784
$389$	28.4890	1.44445	0.722225	−	0.691659i	$-0.243120\pi$
$389$	28.4890	1.44445	0.722225	+	0.691659i	$0.243120\pi$
$390$	15.1783	0.768581
$391$	12.7424	0.644413
$392$	−0.731315	−0.0369370
$393$	6.48285	0.327017
$394$	−29.6497	−1.49373
$395$	−15.5074	−0.780260
$396$	4.10385	0.206226
$397$	−33.7043	−1.69157	−0.845785	−	0.533523i	$-0.820868\pi$
$397$	−33.7043	−1.69157	−0.845785	+	0.533523i	$0.820868\pi$
$398$	−0.766361	−0.0384142
$399$	−14.7153	−0.736689
$400$	−4.62130	−0.231065
$401$	−26.3551	−1.31611	−0.658055	−	0.752970i	$-0.728621\pi$
$401$	−26.3551	−1.31611	−0.658055	+	0.752970i	$0.728621\pi$
$402$	−34.7623	−1.73379
$403$	−17.0526	−0.849450
$404$	11.9733	0.595696
$405$	−7.30115	−0.362797
$406$	1.90142	0.0943657
$407$	1.91877	0.0951099
$408$	5.29533	0.262158
$409$	14.2893	0.706558	0.353279	−	0.935518i	$-0.385067\pi$
$409$	14.2893	0.706558	0.353279	+	0.935518i	$0.385067\pi$
$410$	7.34129	0.362561
$411$	31.1180	1.53494
$412$	15.8310	0.779938
$413$	6.37795	0.313838
$414$	−29.7196	−1.46064
$415$	−3.86824	−0.189884
$416$	−22.9556	−1.12549
$417$	−6.17718	−0.302498
$418$	−8.00319	−0.391449
$419$	−12.6926	−0.620076	−0.310038	−	0.950724i	$-0.600342\pi$
$419$	−12.6926	−0.620076	−0.310038	+	0.950724i	$0.600342\pi$
$420$	4.11437	0.200761
$421$	24.6290	1.20035	0.600173	−	0.799870i	$-0.295098\pi$
$421$	24.6290	1.20035	0.600173	+	0.799870i	$0.295098\pi$
$422$	43.8441	2.13430
$423$	−5.44624	−0.264805
$424$	−7.11985	−0.345770
$425$	−2.84289	−0.137901
$426$	−2.01816	−0.0977804
$427$	13.1438	0.636073
$428$	−0.381141	−0.0184231
$429$	5.81551	0.280775
$430$	11.8741	0.572619
$431$	34.9325	1.68264	0.841320	−	0.540537i	$-0.181779\pi$
$431$	34.9325	1.68264	0.841320	+	0.540537i	$0.181779\pi$
$432$	−5.73420	−0.275887
$433$	6.39096	0.307130	0.153565	−	0.988139i	$-0.450925\pi$
$433$	6.39096	0.307130	0.153565	+	0.988139i	$0.450925\pi$
$434$	−10.3455	−0.496599
$435$	2.54699	0.122119
$436$	−4.69132	−0.224674
$437$	25.8961	1.23878
$438$	−30.2674	−1.44623
$439$	−13.5177	−0.645163	−0.322582	−	0.946542i	$-0.604551\pi$
$439$	−13.5177	−0.645163	−0.322582	+	0.946542i	$0.604551\pi$
$440$	−0.532780	−0.0253993
$441$	3.48717	0.166056
$442$	−16.9416	−0.805831
$443$	0.677780	0.0322023	0.0161011	−	0.999870i	$-0.494875\pi$
$443$	0.677780	0.0322023	0.0161011	+	0.999870i	$0.494875\pi$
$444$	10.8364	0.514271
$445$	−3.83025	−0.181571
$446$	16.3484	0.774120
$447$	−24.4606	−1.15695
$448$	−4.68411	−0.221303
$449$	24.4669	1.15466	0.577331	−	0.816510i	$-0.304094\pi$
$449$	24.4669	1.15466	0.577331	+	0.816510i	$0.304094\pi$
$450$	6.63056	0.312568
$451$	2.81280	0.132449
$452$	0.666008	0.0313264
$453$	−55.2654	−2.59660
$454$	21.8927	1.02747
$455$	3.13413	0.146930
$456$	10.7616	0.503956
$457$	−2.95902	−0.138417	−0.0692086	−	0.997602i	$-0.522047\pi$
$457$	−2.95902	−0.138417	−0.0692086	+	0.997602i	$0.522047\pi$
$458$	29.7204	1.38874
$459$	−3.52752	−0.164650
$460$	−7.24049	−0.337589
$461$	19.0775	0.888526	0.444263	−	0.895897i	$-0.353466\pi$
$461$	19.0775	0.888526	0.444263	+	0.895897i	$0.353466\pi$
$462$	3.52816	0.164145
$463$	−21.7261	−1.00970	−0.504848	−	0.863208i	$-0.668451\pi$
$463$	−21.7261	−1.00970	−0.504848	+	0.863208i	$0.668451\pi$
$464$	−4.62130	−0.214539
$465$	−13.8580	−0.642650
$466$	9.26228	0.429067
$467$	23.5677	1.09059	0.545293	−	0.838246i	$-0.316419\pi$
$467$	23.5677	1.09059	0.545293	+	0.838246i	$0.316419\pi$
$468$	17.6549	0.816100
$469$	−7.17801	−0.331449
$470$	−2.96962	−0.136978
$471$	−42.7844	−1.97140
$472$	−4.66429	−0.214691
$473$	4.54952	0.209187
$474$	−75.1005	−3.44948
$475$	−5.77754	−0.265092
$476$	−4.59236	−0.210491
$477$	33.9500	1.55446
$478$	8.38006	0.383295
$479$	4.30567	0.196731	0.0983656	−	0.995150i	$-0.468639\pi$
$479$	4.30567	0.196731	0.0983656	+	0.995150i	$0.468639\pi$
$480$	−18.6552	−0.851488
$481$	8.25463	0.376379
$482$	26.1205	1.18976
$483$	−11.4162	−0.519453
$484$	−16.9119	−0.768721
$485$	−3.75306	−0.170418
$486$	−42.4366	−1.92497
$487$	2.97877	0.134981	0.0674905	−	0.997720i	$-0.478501\pi$
$487$	2.97877	0.134981	0.0674905	+	0.997720i	$0.478501\pi$
$488$	−9.61226	−0.435126
$489$	59.5197	2.69158
$490$	1.90142	0.0858972
$491$	24.0623	1.08592	0.542959	−	0.839759i	$-0.317304\pi$
$491$	24.0623	1.08592	0.542959	+	0.839759i	$0.317304\pi$
$492$	15.8854	0.716170
$493$	−2.84289	−0.128037
$494$	−34.4300	−1.54908
$495$	2.54048	0.114186
$496$	25.1442	1.12901
$497$	−0.416727	−0.0186928
$498$	−18.7335	−0.839467
$499$	−8.35244	−0.373906	−0.186953	−	0.982369i	$-0.559861\pi$
$499$	−8.35244	−0.373906	−0.186953	+	0.982369i	$0.559861\pi$
$500$	1.61538	0.0722422
$501$	−14.3925	−0.643009
$502$	50.1492	2.23827
$503$	23.3963	1.04319	0.521595	−	0.853193i	$-0.325337\pi$
$503$	23.3963	1.04319	0.521595	+	0.853193i	$0.325337\pi$
$504$	−2.55022	−0.113596
$505$	7.41208	0.329833
$506$	−6.20886	−0.276018
$507$	−8.09234	−0.359394
$508$	4.59431	0.203839
$509$	17.4660	0.774167	0.387084	−	0.922045i	$-0.373482\pi$
$509$	17.4660	0.774167	0.387084	+	0.922045i	$0.373482\pi$
$510$	−13.7678	−0.609650
$511$	−6.24986	−0.276477
$512$	27.0890	1.19717
$513$	−7.16888	−0.316514
$514$	47.9702	2.11587
$515$	9.80016	0.431846
$516$	25.6937	1.13110
$517$	−1.13780	−0.0500404
$518$	5.00792	0.220035
$519$	56.8967	2.49749
$520$	−2.29204	−0.100513
$521$	−25.5836	−1.12084	−0.560420	−	0.828209i	$-0.689360\pi$
$521$	−25.5836	−1.12084	−0.560420	+	0.828209i	$0.689360\pi$
$522$	6.63056	0.290212
$523$	23.6073	1.03227	0.516137	−	0.856506i	$-0.327370\pi$
$523$	23.6073	1.03227	0.516137	+	0.856506i	$0.327370\pi$
$524$	4.11163	0.179618
$525$	2.54699	0.111160
$526$	12.7756	0.557043
$527$	15.4680	0.673796
$528$	−8.57502	−0.373180
$529$	−2.90981	−0.126513
$530$	18.5116	0.804091
$531$	22.2410	0.965177
$532$	−9.33294	−0.404634
$533$	12.1008	0.524142
$534$	−18.5495	−0.802714
$535$	−0.235944	−0.0102008
$536$	5.24939	0.226739
$537$	−11.3170	−0.488367
$538$	31.2795	1.34856
$539$	0.728522	0.0313797
$540$	2.00440	0.0862556
$541$	−0.457626	−0.0196749	−0.00983743	−	0.999952i	$-0.503131\pi$
$541$	−0.457626	−0.0196749	−0.00983743	+	0.999952i	$0.503131\pi$
$542$	19.9797	0.858200
$543$	24.9116	1.06906
$544$	20.8225	0.892755
$545$	−2.90415	−0.124400
$546$	15.1783	0.649570
$547$	−26.2239	−1.12125	−0.560627	−	0.828069i	$-0.689440\pi$
$547$	−26.2239	−1.12125	−0.560627	+	0.828069i	$0.689440\pi$
$548$	19.7360	0.843081
$549$	45.8346	1.95617
$550$	1.38522	0.0590662
$551$	−5.77754	−0.246131
$552$	8.34881	0.355349
$553$	−15.5074	−0.659440
$554$	−54.1160	−2.29917
$555$	6.70823	0.284748
$556$	−3.91777	−0.166150
$557$	17.1385	0.726180	0.363090	−	0.931754i	$-0.381722\pi$
$557$	17.1385	0.726180	0.363090	+	0.931754i	$0.381722\pi$
$558$	−36.0764	−1.52724
$559$	19.5722	0.827816
$560$	−4.62130	−0.195286
$561$	−5.27510	−0.222715
$562$	−15.0316	−0.634071
$563$	−42.4701	−1.78990	−0.894951	−	0.446164i	$-0.852790\pi$
$563$	−42.4701	−1.78990	−0.894951	+	0.446164i	$0.852790\pi$
$564$	−6.42579	−0.270575
$565$	0.412291	0.0173452
$566$	39.7028	1.66883
$567$	−7.30115	−0.306620
$568$	0.304759	0.0127874
$569$	−15.4302	−0.646868	−0.323434	−	0.946251i	$-0.604837\pi$
$569$	−15.4302	−0.646868	−0.323434	+	0.946251i	$0.604837\pi$
$570$	−27.9800	−1.17195
$571$	1.34931	0.0564668	0.0282334	−	0.999601i	$-0.491012\pi$
$571$	1.34931	0.0564668	0.0282334	+	0.999601i	$0.491012\pi$
$572$	3.68838	0.154219
$573$	−48.1500	−2.01149
$574$	7.34129	0.306420
$575$	−4.48221	−0.186921
$576$	−16.3343	−0.680595
$577$	−33.5590	−1.39708	−0.698540	−	0.715571i	$-0.746167\pi$
$577$	−33.5590	−1.39708	−0.698540	+	0.715571i	$0.746167\pi$
$578$	−16.9568	−0.705308
$579$	39.6816	1.64911
$580$	1.61538	0.0670752
$581$	−3.86824	−0.160482
$582$	−18.1757	−0.753406
$583$	7.09266	0.293748
$584$	4.57062	0.189133
$585$	10.9293	0.451869
$586$	21.8948	0.904467
$587$	25.2112	1.04058	0.520290	−	0.853990i	$-0.325824\pi$
$587$	25.2112	1.04058	0.520290	+	0.853990i	$0.325824\pi$
$588$	4.11437	0.169674
$589$	31.4352	1.29526
$590$	12.1271	0.499266
$591$	−39.7165	−1.63372
$592$	−12.1715	−0.500246
$593$	−9.68172	−0.397581	−0.198790	−	0.980042i	$-0.563701\pi$
$593$	−9.68172	−0.397581	−0.198790	+	0.980042i	$0.563701\pi$
$594$	1.71881	0.0705238
$595$	−2.84289	−0.116547
$596$	−15.5137	−0.635467
$597$	−1.02656	−0.0420143
$598$	−26.7108	−1.09229
$599$	1.96995	0.0804899	0.0402449	−	0.999190i	$-0.487186\pi$
$599$	1.96995	0.0804899	0.0402449	+	0.999190i	$0.487186\pi$
$600$	−1.86265	−0.0760426
$601$	5.20772	0.212427	0.106214	−	0.994343i	$-0.466127\pi$
$601$	5.20772	0.212427	0.106214	+	0.994343i	$0.466127\pi$
$602$	11.8741	0.483951
$603$	−25.0309	−1.01934
$604$	−35.0511	−1.42621
$605$	−10.4693	−0.425636
$606$	35.8959	1.45817
$607$	−33.9026	−1.37606	−0.688031	−	0.725681i	$-0.741525\pi$
$607$	−33.9026	−1.37606	−0.688031	+	0.725681i	$0.741525\pi$
$608$	42.3169	1.71618
$609$	2.54699	0.103209
$610$	24.9918	1.01189
$611$	−4.89486	−0.198025
$612$	−16.0144	−0.647342
$613$	25.3935	1.02563	0.512816	−	0.858498i	$-0.328602\pi$
$613$	25.3935	1.02563	0.512816	+	0.858498i	$0.328602\pi$
$614$	3.23358	0.130497
$615$	9.83384	0.396539
$616$	−0.532780	−0.0214663
$617$	10.7565	0.433041	0.216520	−	0.976278i	$-0.430529\pi$
$617$	10.7565	0.433041	0.216520	+	0.976278i	$0.430529\pi$
$618$	47.4611	1.90917
$619$	0.933533	0.0375219	0.0187609	−	0.999824i	$-0.494028\pi$
$619$	0.933533	0.0375219	0.0187609	+	0.999824i	$0.494028\pi$
$620$	−8.78919	−0.352982
$621$	−5.56161	−0.223180
$622$	0.321776	0.0129020
$623$	−3.83025	−0.153456
$624$	−36.8901	−1.47678
$625$	1.00000	0.0400000
$626$	−56.9846	−2.27756
$627$	−10.7205	−0.428134
$628$	−27.1352	−1.08281
$629$	−7.48757	−0.298549
$630$	6.63056	0.264168
$631$	−28.7515	−1.14458	−0.572290	−	0.820051i	$-0.693945\pi$
$631$	−28.7515	−1.14458	−0.572290	+	0.820051i	$0.693945\pi$
$632$	11.3408	0.451112
$633$	58.7302	2.33432
$634$	−32.9531	−1.30874
$635$	2.84410	0.112865
$636$	40.0562	1.58833
$637$	3.13413	0.124179
$638$	1.38522	0.0548416
$639$	−1.45320	−0.0574876
$640$	5.74234	0.226986
$641$	47.4817	1.87541	0.937706	−	0.347429i	$-0.112945\pi$
$641$	47.4817	1.87541	0.937706	+	0.347429i	$0.112945\pi$
$642$	−1.14265	−0.0450969
$643$	4.20981	0.166019	0.0830093	−	0.996549i	$-0.473547\pi$
$643$	4.20981	0.166019	0.0830093	+	0.996549i	$0.473547\pi$
$644$	−7.24049	−0.285315
$645$	15.9056	0.626282
$646$	31.2306	1.22875
$647$	3.42384	0.134605	0.0673025	−	0.997733i	$-0.478561\pi$
$647$	3.42384	0.134605	0.0673025	+	0.997733i	$0.478561\pi$
$648$	5.33945	0.209753
$649$	4.64648	0.182390
$650$	5.95929	0.233743
$651$	−13.8580	−0.543138
$652$	37.7493	1.47838
$653$	−20.4473	−0.800166	−0.400083	−	0.916479i	$-0.631019\pi$
$653$	−20.4473	−0.800166	−0.400083	+	0.916479i	$0.631019\pi$
$654$	−14.0645	−0.549966
$655$	2.54530	0.0994530
$656$	−17.8427	−0.696639
$657$	−21.7943	−0.850277
$658$	−2.96962	−0.115768
$659$	33.9663	1.32314	0.661569	−	0.749884i	$-0.269891\pi$
$659$	33.9663	1.32314	0.661569	+	0.749884i	$0.269891\pi$
$660$	2.99741	0.116674
$661$	−19.2404	−0.748366	−0.374183	−	0.927355i	$-0.622077\pi$
$661$	−19.2404	−0.748366	−0.374183	+	0.927355i	$0.622077\pi$
$662$	−26.5366	−1.03137
$663$	−22.6937	−0.881351
$664$	2.82890	0.109783
$665$	−5.77754	−0.224043
$666$	17.4635	0.676696
$667$	−4.48221	−0.173552
$668$	−9.12817	−0.353180
$669$	21.8991	0.846668
$670$	−13.6484	−0.527283
$671$	9.57555	0.369660
$672$	−18.6552	−0.719639
$673$	−47.9591	−1.84869	−0.924344	−	0.381559i	$-0.875387\pi$
$673$	−47.9591	−1.84869	−0.924344	+	0.381559i	$0.875387\pi$
$674$	28.2933	1.08982
$675$	1.24082	0.0477592
$676$	−5.13242	−0.197401
$677$	−47.4804	−1.82482	−0.912411	−	0.409275i	$-0.865782\pi$
$677$	−47.4804	−1.82482	−0.912411	+	0.409275i	$0.865782\pi$
$678$	1.99668	0.0766820
$679$	−3.75306	−0.144029
$680$	2.07905	0.0797280
$681$	29.3258	1.12377
$682$	−7.53691	−0.288603
$683$	−26.3101	−1.00673	−0.503363	−	0.864075i	$-0.667904\pi$
$683$	−26.3101	−1.00673	−0.503363	+	0.864075i	$0.667904\pi$
$684$	−32.5456	−1.24441
$685$	12.2175	0.466808
$686$	1.90142	0.0725964
$687$	39.8112	1.51889
$688$	−28.8594	−1.10025
$689$	30.5129	1.16245
$690$	−21.7069	−0.826366
$691$	−42.0009	−1.59779	−0.798894	−	0.601472i	$-0.794581\pi$
$691$	−42.0009	−1.59779	−0.798894	+	0.601472i	$0.794581\pi$
$692$	36.0857	1.37177
$693$	2.54048	0.0965049
$694$	−56.5360	−2.14608
$695$	−2.42528	−0.0919963
$696$	−1.86265	−0.0706037
$697$	−10.9763	−0.415757
$698$	−24.4921	−0.927040
$699$	12.4070	0.469278
$700$	1.61538	0.0610558
$701$	6.45871	0.243942	0.121971	−	0.992534i	$-0.461079\pi$
$701$	6.45871	0.243942	0.121971	+	0.992534i	$0.461079\pi$
$702$	7.39440	0.279084
$703$	−15.2168	−0.573912
$704$	−3.41248	−0.128613
$705$	−3.97787	−0.149815
$706$	−11.0485	−0.415816
$707$	7.41208	0.278760
$708$	26.2413	0.986207
$709$	24.1580	0.907271	0.453636	−	0.891187i	$-0.350127\pi$
$709$	24.1580	0.907271	0.453636	+	0.891187i	$0.350127\pi$
$710$	−0.792372	−0.0297372
$711$	−54.0768	−2.02804
$712$	2.80112	0.104976
$713$	24.3874	0.913314
$714$	−13.7678	−0.515248
$715$	2.28329	0.0853900
$716$	−7.17763	−0.268241
$717$	11.2253	0.419216
$718$	−69.4039	−2.59013
$719$	48.3531	1.80327	0.901633	−	0.432502i	$-0.142369\pi$
$719$	48.3531	1.80327	0.901633	+	0.432502i	$0.142369\pi$
$720$	−16.1153	−0.600581
$721$	9.80016	0.364977
$722$	27.3423	1.01757
$723$	34.9891	1.30126
$724$	15.7997	0.587193
$725$	1.00000	0.0371391
$726$	−50.7015	−1.88171
$727$	35.7615	1.32632	0.663160	−	0.748478i	$-0.269215\pi$
$727$	35.7615	1.32632	0.663160	+	0.748478i	$0.269215\pi$
$728$	−2.29204	−0.0849486
$729$	−34.9414	−1.29413
$730$	−11.8836	−0.439831
$731$	−17.7535	−0.656635
$732$	54.0784	1.99880
$733$	−13.4675	−0.497432	−0.248716	−	0.968576i	$-0.580009\pi$
$733$	−13.4675	−0.497432	−0.248716	+	0.968576i	$0.580009\pi$
$734$	12.1352	0.447917
$735$	2.54699	0.0939472
$736$	32.8294	1.21011
$737$	−5.22934	−0.192625
$738$	25.6003	0.942361
$739$	14.8317	0.545595	0.272797	−	0.962072i	$-0.412051\pi$
$739$	14.8317	0.545595	0.272797	+	0.962072i	$0.412051\pi$
$740$	4.25457	0.156401
$741$	−46.1199	−1.69426
$742$	18.5116	0.679581
$743$	−51.6364	−1.89436	−0.947178	−	0.320709i	$-0.896079\pi$
$743$	−51.6364	−1.89436	−0.947178	+	0.320709i	$0.896079\pi$
$744$	10.1346	0.371551
$745$	−9.60374	−0.351854
$746$	−20.5882	−0.753789
$747$	−13.4892	−0.493545
$748$	−3.34564	−0.122329
$749$	−0.235944	−0.00862122
$750$	4.84289	0.176837
$751$	−47.4696	−1.73219	−0.866095	−	0.499879i	$-0.833378\pi$
$751$	−47.4696	−1.73219	−0.866095	+	0.499879i	$0.833378\pi$
$752$	7.21751	0.263196
$753$	67.1761	2.44803
$754$	5.95929	0.217025
$755$	−21.6983	−0.789682
$756$	2.00440	0.0728993
$757$	9.04485	0.328741	0.164370	−	0.986399i	$-0.447441\pi$
$757$	9.04485	0.328741	0.164370	+	0.986399i	$0.447441\pi$
$758$	44.2059	1.60563
$759$	−8.31692	−0.301885
$760$	4.22520	0.153264
$761$	19.6371	0.711846	0.355923	−	0.934515i	$-0.384167\pi$
$761$	19.6371	0.711846	0.355923	+	0.934515i	$0.384167\pi$
$762$	13.7737	0.498967
$763$	−2.90415	−0.105137
$764$	−30.5383	−1.10484
$765$	−9.91365	−0.358429
$766$	−33.6064	−1.21425
$767$	19.9893	0.721773
$768$	51.6703	1.86449
$769$	8.05083	0.290320	0.145160	−	0.989408i	$-0.453630\pi$
$769$	8.05083	0.290320	0.145160	+	0.989408i	$0.453630\pi$
$770$	1.38522	0.0499200
$771$	64.2572	2.31417
$772$	25.1673	0.905792
$773$	−41.1247	−1.47915	−0.739577	−	0.673072i	$-0.764974\pi$
$773$	−41.1247	−1.47915	−0.739577	+	0.673072i	$0.764974\pi$
$774$	41.4069	1.48834
$775$	−5.44093	−0.195444
$776$	2.74467	0.0985280
$777$	6.70823	0.240656
$778$	54.1694	1.94207
$779$	−22.3068	−0.799226
$780$	12.8950	0.461714
$781$	−0.303595	−0.0108635
$782$	24.2287	0.866416
$783$	1.24082	0.0443433
$784$	−4.62130	−0.165047
$785$	−16.7980	−0.599547
$786$	12.3266	0.439675
$787$	50.1393	1.78727	0.893636	−	0.448792i	$-0.148146\pi$
$787$	50.1393	1.78727	0.893636	+	0.448792i	$0.148146\pi$
$788$	−25.1895	−0.897338
$789$	17.1132	0.609247
$790$	−29.4859	−1.04906
$791$	0.412291	0.0146594
$792$	−1.85789	−0.0660174
$793$	41.1944	1.46286
$794$	−64.0859	−2.27432
$795$	24.7967	0.879448
$796$	−0.651077	−0.0230768
$797$	3.28991	0.116535	0.0582673	−	0.998301i	$-0.481442\pi$
$797$	3.28991	0.116535	0.0582673	+	0.998301i	$0.481442\pi$
$798$	−27.9800	−0.990481
$799$	4.44001	0.157076
$800$	−7.32439	−0.258956
$801$	−13.3567	−0.471937
$802$	−50.1120	−1.76952
$803$	−4.55316	−0.160678
$804$	−29.5330	−1.04155
$805$	−4.48221	−0.157977
$806$	−32.4241	−1.14209
$807$	41.8997	1.47494
$808$	−5.42057	−0.190695
$809$	31.3021	1.10052	0.550262	−	0.834992i	$-0.314528\pi$
$809$	31.3021	1.10052	0.550262	+	0.834992i	$0.314528\pi$
$810$	−13.8825	−0.487782
$811$	22.3138	0.783544	0.391772	−	0.920062i	$-0.371862\pi$
$811$	22.3138	0.783544	0.391772	+	0.920062i	$0.371862\pi$
$812$	1.61538	0.0566889
$813$	26.7632	0.938628
$814$	3.64838	0.127876
$815$	23.3686	0.818568
$816$	33.4621	1.17141
$817$	−36.0799	−1.26228
$818$	27.1698	0.949971
$819$	10.9293	0.381899
$820$	6.23693	0.217803
$821$	51.5168	1.79795	0.898974	−	0.438002i	$-0.144314\pi$
$821$	51.5168	1.79795	0.898974	+	0.438002i	$0.144314\pi$
$822$	59.1682	2.06373
$823$	−32.1092	−1.11926	−0.559628	−	0.828744i	$-0.689056\pi$
$823$	−32.1092	−1.11926	−0.559628	+	0.828744i	$0.689056\pi$
$824$	−7.16700	−0.249674
$825$	1.85554	0.0646016
$826$	12.1271	0.421957
$827$	45.8979	1.59603	0.798013	−	0.602640i	$-0.205885\pi$
$827$	45.8979	1.59603	0.798013	+	0.602640i	$0.205885\pi$
$828$	−25.2488	−0.877457
$829$	−36.2109	−1.25766	−0.628828	−	0.777544i	$-0.716465\pi$
$829$	−36.2109	−1.25766	−0.628828	+	0.777544i	$0.716465\pi$
$830$	−7.35514	−0.255300
$831$	−72.4897	−2.51464
$832$	−14.6806	−0.508959
$833$	−2.84289	−0.0985004
$834$	−11.7454	−0.406710
$835$	−5.65077	−0.195553
$836$	−6.79926	−0.235157
$837$	−6.75121	−0.233356
$838$	−24.1340	−0.833694
$839$	−24.7372	−0.854025	−0.427012	−	0.904246i	$-0.640434\pi$
$839$	−24.7372	−0.854025	−0.427012	+	0.904246i	$0.640434\pi$
$840$	−1.86265	−0.0642677
$841$	1.00000	0.0344828
$842$	46.8300	1.61387
$843$	−20.1352	−0.693494
$844$	37.2486	1.28215
$845$	−3.17721	−0.109300
$846$	−10.3556	−0.356032
$847$	−10.4693	−0.359728
$848$	−44.9915	−1.54501
$849$	53.1828	1.82523
$850$	−5.40552	−0.185408
$851$	−11.8052	−0.404676
$852$	−1.71457	−0.0587402
$853$	−35.5893	−1.21856	−0.609278	−	0.792957i	$-0.708540\pi$
$853$	−35.5893	−1.21856	−0.609278	+	0.792957i	$0.708540\pi$
$854$	24.9918	0.855202
$855$	−20.1473	−0.689022
$856$	0.172550	0.00589763
$857$	36.6218	1.25098	0.625488	−	0.780234i	$-0.284900\pi$
$857$	36.6218	1.25098	0.625488	+	0.780234i	$0.284900\pi$
$858$	11.0577	0.377504
$859$	−6.91387	−0.235898	−0.117949	−	0.993020i	$-0.537632\pi$
$859$	−6.91387	−0.235898	−0.117949	+	0.993020i	$0.537632\pi$
$860$	10.0878	0.343993
$861$	9.83384	0.335136
$862$	66.4213	2.26232
$863$	−49.7118	−1.69221	−0.846104	−	0.533018i	$-0.821058\pi$
$863$	−49.7118	−1.69221	−0.846104	+	0.533018i	$0.821058\pi$
$864$	−9.08824	−0.309188
$865$	22.3388	0.759541
$866$	12.1519	0.412937
$867$	−22.7140	−0.771407
$868$	−8.78919	−0.298325
$869$	−11.2975	−0.383240
$870$	4.84289	0.164189
$871$	−22.4968	−0.762276
$872$	2.12385	0.0719227
$873$	−13.0876	−0.442947
$874$	49.2393	1.66555
$875$	1.00000	0.0338062
$876$	−25.7142	−0.868803
$877$	37.8835	1.27924	0.639618	−	0.768693i	$-0.279092\pi$
$877$	37.8835	1.27924	0.639618	+	0.768693i	$0.279092\pi$
$878$	−25.7027	−0.867425
$879$	29.3286	0.989230
$880$	−3.36672	−0.113492
$881$	25.0332	0.843390	0.421695	−	0.906738i	$-0.361435\pi$
$881$	25.0332	0.843390	0.421695	+	0.906738i	$0.361435\pi$
$882$	6.63056	0.223263
$883$	−29.0617	−0.978006	−0.489003	−	0.872282i	$-0.662639\pi$
$883$	−29.0617	−0.978006	−0.489003	+	0.872282i	$0.662639\pi$
$884$	−14.3931	−0.484091
$885$	16.2446	0.546056
$886$	1.28874	0.0432961
$887$	22.8066	0.765772	0.382886	−	0.923796i	$-0.374930\pi$
$887$	22.8066	0.765772	0.382886	+	0.923796i	$0.374930\pi$
$888$	−4.90583	−0.164629
$889$	2.84410	0.0953879
$890$	−7.28290	−0.244123
$891$	−5.31905	−0.178195
$892$	13.8891	0.465042
$893$	9.02332	0.301954
$894$	−46.5099	−1.55552
$895$	−4.44330	−0.148523
$896$	5.74234	0.191838
$897$	−35.7797	−1.19465
$898$	46.5217	1.55245
$899$	−5.44093	−0.181465
$900$	5.63312	0.187771
$901$	−27.6775	−0.922070
$902$	5.34830	0.178079
$903$	15.9056	0.529305
$904$	−0.301515	−0.0100282
$905$	9.78079	0.325125
$906$	−105.083	−3.49113
$907$	−11.3620	−0.377268	−0.188634	−	0.982047i	$-0.560406\pi$
$907$	−11.3620	−0.377268	−0.188634	+	0.982047i	$0.560406\pi$
$908$	18.5993	0.617240
$909$	25.8472	0.857297
$910$	5.95929	0.197549
$911$	−36.9986	−1.22582	−0.612910	−	0.790153i	$-0.710001\pi$
$911$	−36.9986	−1.22582	−0.612910	+	0.790153i	$0.710001\pi$
$912$	68.0041	2.25184
$913$	−2.81810	−0.0932655
$914$	−5.62634	−0.186103
$915$	33.4771	1.10672
$916$	25.2496	0.834269
$917$	2.54530	0.0840531
$918$	−6.70728	−0.221373
$919$	−34.2345	−1.12929	−0.564647	−	0.825333i	$-0.690987\pi$
$919$	−34.2345	−1.12929	−0.564647	+	0.825333i	$0.690987\pi$
$920$	3.27791	0.108069
$921$	4.33145	0.142726
$922$	36.2742	1.19463
$923$	−1.30608	−0.0429901
$924$	2.99741	0.0986076
$925$	2.63378	0.0865983
$926$	−41.3103	−1.35754
$927$	34.1748	1.12245
$928$	−7.32439	−0.240435
$929$	−41.7101	−1.36846	−0.684231	−	0.729265i	$-0.739862\pi$
$929$	−41.7101	−1.36846	−0.684231	+	0.729265i	$0.739862\pi$
$930$	−26.3498	−0.864045
$931$	−5.77754	−0.189351
$932$	7.86895	0.257756
$933$	0.431026	0.0141112
$934$	44.8121	1.46630
$935$	−2.07111	−0.0677326
$936$	−7.99273	−0.261251
$937$	−1.75298	−0.0572674	−0.0286337	−	0.999590i	$-0.509116\pi$
$937$	−1.75298	−0.0572674	−0.0286337	+	0.999590i	$0.509116\pi$
$938$	−13.6484	−0.445635
$939$	−76.3323	−2.49101
$940$	−2.52289	−0.0822877
$941$	5.56169	0.181306	0.0906530	−	0.995883i	$-0.471105\pi$
$941$	5.56169	0.181306	0.0906530	+	0.995883i	$0.471105\pi$
$942$	−81.3510	−2.65056
$943$	−17.3056	−0.563549
$944$	−29.4744	−0.959311
$945$	1.24082	0.0403639
$946$	8.65053	0.281253
$947$	−53.7143	−1.74548	−0.872741	−	0.488184i	$-0.837659\pi$
$947$	−53.7143	−1.74548	−0.872741	+	0.488184i	$0.837659\pi$
$948$	−63.8030	−2.07223
$949$	−19.5879	−0.635849
$950$	−10.9855	−0.356417
$951$	−44.1415	−1.43139
$952$	2.07905	0.0673824
$953$	26.2751	0.851132	0.425566	−	0.904927i	$-0.360075\pi$
$953$	26.2751	0.851132	0.425566	+	0.904927i	$0.360075\pi$
$954$	64.5530	2.08998
$955$	−18.9046	−0.611740
$956$	7.11944	0.230259
$957$	1.85554	0.0599811
$958$	8.18688	0.264506
$959$	12.2175	0.394525
$960$	−11.9304	−0.385052
$961$	−1.39629	−0.0450416
$962$	15.6955	0.506043
$963$	−0.822778	−0.0265137
$964$	22.1912	0.714730
$965$	15.5798	0.501531
$966$	−21.7069	−0.698407
$967$	−10.0449	−0.323022	−0.161511	−	0.986871i	$-0.551637\pi$
$967$	−10.0449	−0.323022	−0.161511	+	0.986871i	$0.551637\pi$
$968$	7.65633	0.246084
$969$	41.8342	1.34391
$970$	−7.13613	−0.229127
$971$	−12.9787	−0.416505	−0.208253	−	0.978075i	$-0.566778\pi$
$971$	−12.9787	−0.416505	−0.208253	+	0.978075i	$0.566778\pi$
$972$	−36.0529	−1.15640
$973$	−2.42528	−0.0777511
$974$	5.66388	0.181482
$975$	7.98261	0.255648
$976$	−60.7414	−1.94429
$977$	34.9178	1.11712	0.558560	−	0.829464i	$-0.311354\pi$
$977$	34.9178	1.11712	0.558560	+	0.829464i	$0.311354\pi$
$978$	113.172	3.61884
$979$	−2.79042	−0.0891822
$980$	1.61538	0.0516015
$981$	−10.1273	−0.323339
$982$	45.7525	1.46002
$983$	−32.0694	−1.02286	−0.511428	−	0.859326i	$-0.670883\pi$
$983$	−32.0694	−1.02286	−0.511428	+	0.859326i	$0.670883\pi$
$984$	−7.19164	−0.229261
$985$	−15.5935	−0.496850
$986$	−5.40552	−0.172147
$987$	−3.97787	−0.126617
$988$	−29.2507	−0.930588
$989$	−27.9907	−0.890054
$990$	4.83051	0.153524
$991$	−39.3726	−1.25071	−0.625356	−	0.780340i	$-0.715046\pi$
$991$	−39.3726	−1.25071	−0.625356	+	0.780340i	$0.715046\pi$
$992$	39.8515	1.26529
$993$	−35.5464	−1.12803
$994$	−0.792372	−0.0251325
$995$	−0.403048	−0.0127775
$996$	−15.9154	−0.504298
$997$	−36.3834	−1.15227	−0.576137	−	0.817353i	$-0.695441\pi$
$997$	−36.3834	−1.15227	−0.576137	+	0.817353i	$0.695441\pi$
$998$	−15.8815	−0.502719
$999$	3.26805	0.103397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1015.2.a.l.1.7	✓	8
3.2	odd	2		9135.2.a.bh.1.2		8
5.4	even	2		5075.2.a.ba.1.2		8
7.6	odd	2		7105.2.a.t.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1015.2.a.l.1.7	✓	8	1.1	even	1	trivial
5075.2.a.ba.1.2		8	5.4	even	2
7105.2.a.t.1.7		8	7.6	odd	2
9135.2.a.bh.1.2		8	3.2	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:	\( N \)	\(=\)	\( 1015 = 5 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.90142 q^{2} +2.54699 q^{3} +1.61538 q^{4} +1.00000 q^{5} +4.84289 q^{6} +1.00000 q^{7} -0.731315 q^{8} +3.48717 q^{9} +1.90142 q^{10} +0.728522 q^{11} +4.11437 q^{12} +3.13413 q^{13} +1.90142 q^{14} +2.54699 q^{15} -4.62130 q^{16} -2.84289 q^{17} +6.63056 q^{18} -5.77754 q^{19} +1.61538 q^{20} +2.54699 q^{21} +1.38522 q^{22} -4.48221 q^{23} -1.86265 q^{24} +1.00000 q^{25} +5.95929 q^{26} +1.24082 q^{27} +1.61538 q^{28} +1.00000 q^{29} +4.84289 q^{30} -5.44093 q^{31} -7.32439 q^{32} +1.85554 q^{33} -5.40552 q^{34} +1.00000 q^{35} +5.63312 q^{36} +2.63378 q^{37} -10.9855 q^{38} +7.98261 q^{39} -0.731315 q^{40} +3.86096 q^{41} +4.84289 q^{42} +6.24486 q^{43} +1.17684 q^{44} +3.48717 q^{45} -8.52254 q^{46} -1.56179 q^{47} -11.7704 q^{48} +1.00000 q^{49} +1.90142 q^{50} -7.24083 q^{51} +5.06283 q^{52} +9.73567 q^{53} +2.35931 q^{54} +0.728522 q^{55} -0.731315 q^{56} -14.7153 q^{57} +1.90142 q^{58} +6.37795 q^{59} +4.11437 q^{60} +13.1438 q^{61} -10.3455 q^{62} +3.48717 q^{63} -4.68411 q^{64} +3.13413 q^{65} +3.52816 q^{66} -7.17801 q^{67} -4.59236 q^{68} -11.4162 q^{69} +1.90142 q^{70} -0.416727 q^{71} -2.55022 q^{72} -6.24986 q^{73} +5.00792 q^{74} +2.54699 q^{75} -9.33294 q^{76} +0.728522 q^{77} +15.1783 q^{78} -15.5074 q^{79} -4.62130 q^{80} -7.30115 q^{81} +7.34129 q^{82} -3.86824 q^{83} +4.11437 q^{84} -2.84289 q^{85} +11.8741 q^{86} +2.54699 q^{87} -0.532780 q^{88} -3.83025 q^{89} +6.63056 q^{90} +3.13413 q^{91} -7.24049 q^{92} -13.8580 q^{93} -2.96962 q^{94} -5.77754 q^{95} -18.6552 q^{96} -3.75306 q^{97} +1.90142 q^{98} +2.54048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 4 q^{3} + 5 q^{4} + 8 q^{5} - 6 q^{6} + 8 q^{7} - 6 q^{8} + 14 q^{9} + q^{10} + q^{11} - 7 q^{12} - q^{13} + q^{14} + 4 q^{15} + 3 q^{16} + 22 q^{17} + 13 q^{18} + 8 q^{19} + 5 q^{20}+ \cdots - 63 q^{99}+O(q^{100}) \) 8 * q + q^2 + 4 * q^3 + 5 * q^4 + 8 * q^5 - 6 * q^6 + 8 * q^7 - 6 * q^8 + 14 * q^9 + q^10 + q^11 - 7 * q^12 - q^13 + q^14 + 4 * q^15 + 3 * q^16 + 22 * q^17 + 13 * q^18 + 8 * q^19 + 5 * q^20 + 4 * q^21 - 3 * q^22 + 9 * q^23 + 16 * q^24 + 8 * q^25 + 27 * q^26 + q^27 + 5 * q^28 + 8 * q^29 - 6 * q^30 + 3 * q^31 - 26 * q^32 + 14 * q^33 + q^34 + 8 * q^35 - 13 * q^36 + 9 * q^37 - 5 * q^38 + 3 * q^39 - 6 * q^40 + 24 * q^41 - 6 * q^42 + 7 * q^43 + 10 * q^44 + 14 * q^45 - 27 * q^46 + 21 * q^47 - 8 * q^48 + 8 * q^49 + q^50 - 8 * q^51 - 7 * q^52 - 2 * q^53 - 33 * q^54 + q^55 - 6 * q^56 - 10 * q^57 + q^58 + 18 * q^59 - 7 * q^60 + 26 * q^61 + 15 * q^62 + 14 * q^63 + 4 * q^64 - q^65 + 55 * q^66 - 8 * q^67 + 6 * q^68 - 2 * q^69 + q^70 - 12 * q^71 + 9 * q^72 - q^73 + 14 * q^74 + 4 * q^75 + 15 * q^76 + q^77 + 8 * q^78 - 14 * q^79 + 3 * q^80 + 40 * q^81 - 42 * q^82 - 10 * q^83 - 7 * q^84 + 22 * q^85 + 19 * q^86 + 4 * q^87 - 29 * q^88 - 4 * q^89 + 13 * q^90 - q^91 + 47 * q^92 - 24 * q^93 - 30 * q^94 + 8 * q^95 - q^96 - 11 * q^97 + q^98 - 63 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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