LMFDB - Embedded newform 2209.2.a.m.1.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2209,2,Mod(1,2209)] 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("2209.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2209, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2209 = 47^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2209.a (trivial)

Newform invariants

comment:select newform

sage:traces = [33,1,2,25,19] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$17.6389538065$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	no (minimal twist has level 47)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	2209.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.97824 q^{2} -0.674958 q^{3} +1.91343 q^{4} -0.886577 q^{5} +1.33523 q^{6} +0.812871 q^{7} +0.171258 q^{8} -2.54443 q^{9} +1.75386 q^{10} -4.01129 q^{11} -1.29148 q^{12} -3.01783 q^{13} -1.60805 q^{14} +0.598403 q^{15} -4.16565 q^{16} -7.05262 q^{17} +5.03349 q^{18} -2.14336 q^{19} -1.69640 q^{20} -0.548654 q^{21} +7.93529 q^{22} +0.780791 q^{23} -0.115592 q^{24} -4.21398 q^{25} +5.96999 q^{26} +3.74226 q^{27} +1.55537 q^{28} +9.37850 q^{29} -1.18378 q^{30} -5.83699 q^{31} +7.89813 q^{32} +2.70745 q^{33} +13.9518 q^{34} -0.720673 q^{35} -4.86859 q^{36} -5.26898 q^{37} +4.24007 q^{38} +2.03691 q^{39} -0.151833 q^{40} +0.957187 q^{41} +1.08537 q^{42} +4.28723 q^{43} -7.67532 q^{44} +2.25584 q^{45} -1.54459 q^{46} +2.81164 q^{48} -6.33924 q^{49} +8.33626 q^{50} +4.76022 q^{51} -5.77441 q^{52} +9.00820 q^{53} -7.40308 q^{54} +3.55632 q^{55} +0.139211 q^{56} +1.44668 q^{57} -18.5529 q^{58} -4.24118 q^{59} +1.14500 q^{60} -4.14621 q^{61} +11.5470 q^{62} -2.06830 q^{63} -7.29309 q^{64} +2.67554 q^{65} -5.35599 q^{66} -11.9527 q^{67} -13.4947 q^{68} -0.527002 q^{69} +1.42566 q^{70} +2.88595 q^{71} -0.435754 q^{72} +5.56955 q^{73} +10.4233 q^{74} +2.84426 q^{75} -4.10116 q^{76} -3.26066 q^{77} -4.02950 q^{78} -8.06751 q^{79} +3.69317 q^{80} +5.10743 q^{81} -1.89354 q^{82} -16.6444 q^{83} -1.04981 q^{84} +6.25269 q^{85} -8.48116 q^{86} -6.33009 q^{87} -0.686965 q^{88} +1.12900 q^{89} -4.46258 q^{90} -2.45311 q^{91} +1.49399 q^{92} +3.93972 q^{93} +1.90025 q^{95} -5.33091 q^{96} +7.11379 q^{97} +12.5405 q^{98} +10.2065 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + q^{2} + 2 q^{3} + 25 q^{4} + 19 q^{5} + 10 q^{6} + 2 q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 37 q^{11} - 38 q^{12} + 20 q^{13} - 43 q^{14} + 33 q^{15} + 13 q^{16} + 6 q^{17} - 46 q^{18} + 36 q^{19}+ \cdots + 62 q^{99}+O(q^{100}) $ 33 * q + q^2 + 2 * q^3 + 25 * q^4 + 19 * q^5 + 10 * q^6 + 2 * q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 37 * q^11 - 38 * q^12 + 20 * q^13 - 43 * q^14 + 33 * q^15 + 13 * q^16 + 6 * q^17 - 46 * q^18 + 36 * q^19 + 48 * q^20 + 14 * q^21 + 7 * q^22 + 54 * q^23 - 21 * q^24 - 4 * q^25 + 56 * q^26 + 26 * q^27 + 20 * q^28 + 49 * q^29 + 15 * q^30 + 49 * q^31 - 31 * q^32 + 28 * q^33 + 32 * q^34 + 58 * q^35 + 17 * q^36 + 14 * q^37 + 38 * q^38 + 55 * q^39 + 17 * q^40 + 74 * q^41 - 2 * q^42 + 25 * q^43 + 58 * q^44 + 13 * q^45 + 42 * q^46 - 79 * q^48 - 7 * q^49 + 39 * q^50 - 75 * q^51 + 22 * q^52 + 30 * q^53 + 5 * q^54 + 44 * q^55 - 56 * q^56 + 11 * q^57 - 26 * q^58 + 5 * q^59 + 31 * q^60 + 11 * q^61 + 36 * q^62 - 71 * q^63 + 33 * q^64 + 11 * q^65 + 36 * q^66 + 17 * q^67 - 16 * q^68 + 41 * q^69 - 41 * q^70 + 19 * q^71 - 31 * q^72 + 20 * q^73 + 48 * q^74 + 50 * q^75 + 33 * q^76 + 39 * q^77 - 52 * q^78 + 7 * q^79 + 62 * q^80 + q^81 - 27 * q^82 - 83 * q^83 + 64 * q^84 - 9 * q^85 + 68 * q^86 + 72 * q^87 - 20 * q^88 + 25 * q^89 + 29 * q^90 + 25 * q^91 + 38 * q^92 + 14 * q^93 - 63 * q^95 - 2 * q^96 + 34 * q^97 - 45 * q^98 + 62 * 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 $

$2$	−1.97824	−1.39883	−0.699413	−	0.714718i	$-0.746555\pi$
$2$	−1.97824	−1.39883	−0.699413	+	0.714718i	$0.746555\pi$
$3$	−0.674958	−0.389687	−0.194844	−	0.980834i	$-0.562420\pi$
$3$	−0.674958	−0.389687	−0.194844	+	0.980834i	$0.562420\pi$
$4$	1.91343	0.956715
$5$	−0.886577	−0.396489	−0.198245	−	0.980153i	$-0.563524\pi$
$5$	−0.886577	−0.396489	−0.198245	+	0.980153i	$0.563524\pi$
$6$	1.33523	0.545105
$7$	0.812871	0.307237	0.153618	−	0.988130i	$-0.450907\pi$
$7$	0.812871	0.307237	0.153618	+	0.988130i	$0.450907\pi$
$8$	0.171258	0.0605488
$9$	−2.54443	−0.848144
$10$	1.75386	0.554620
$11$	−4.01129	−1.20945	−0.604725	−	0.796435i	$-0.706717\pi$
$11$	−4.01129	−1.20945	−0.604725	+	0.796435i	$0.706717\pi$
$12$	−1.29148	−0.372819
$13$	−3.01783	−0.836996	−0.418498	−	0.908218i	$-0.637443\pi$
$13$	−3.01783	−0.836996	−0.418498	+	0.908218i	$0.637443\pi$
$14$	−1.60805	−0.429770
$15$	0.598403	0.154507
$16$	−4.16565	−1.04141
$17$	−7.05262	−1.71051	−0.855256	−	0.518207i	$-0.826600\pi$
$17$	−7.05262	−1.71051	−0.855256	+	0.518207i	$0.826600\pi$
$18$	5.03349	1.18641
$19$	−2.14336	−0.491720	−0.245860	−	0.969305i	$-0.579070\pi$
$19$	−2.14336	−0.491720	−0.245860	+	0.969305i	$0.579070\pi$
$20$	−1.69640	−0.379327
$21$	−0.548654	−0.119726
$22$	7.93529	1.69181
$23$	0.780791	0.162806	0.0814031	−	0.996681i	$-0.474060\pi$
$23$	0.780791	0.162806	0.0814031	+	0.996681i	$0.474060\pi$
$24$	−0.115592	−0.0235951
$25$	−4.21398	−0.842796
$26$	5.96999	1.17081
$27$	3.74226	0.720198
$28$	1.55537	0.293938
$29$	9.37850	1.74154	0.870771	−	0.491688i	$-0.163620\pi$
$29$	9.37850	1.74154	0.870771	+	0.491688i	$0.163620\pi$
$30$	−1.18378	−0.216128
$31$	−5.83699	−1.04835	−0.524177	−	0.851609i	$-0.675627\pi$
$31$	−5.83699	−1.04835	−0.524177	+	0.851609i	$0.675627\pi$
$32$	7.89813	1.39621
$33$	2.70745	0.471307
$34$	13.9518	2.39271
$35$	−0.720673	−0.121816
$36$	−4.86859	−0.811432
$37$	−5.26898	−0.866214	−0.433107	−	0.901342i	$-0.642583\pi$
$37$	−5.26898	−0.866214	−0.433107	+	0.901342i	$0.642583\pi$
$38$	4.24007	0.687831
$39$	2.03691	0.326167
$40$	−0.151833	−0.0240070
$41$	0.957187	0.149487	0.0747437	−	0.997203i	$-0.476186\pi$
$41$	0.957187	0.149487	0.0747437	+	0.997203i	$0.476186\pi$
$42$	1.08537	0.167476
$43$	4.28723	0.653796	0.326898	−	0.945060i	$-0.393997\pi$
$43$	4.28723	0.653796	0.326898	+	0.945060i	$0.393997\pi$
$44$	−7.67532	−1.15710
$45$	2.25584	0.336280
$46$	−1.54459	−0.227738
$47$	0	0
$47$	0	0
$48$	2.81164	0.405825
$49$	−6.33924	−0.905606
$50$	8.33626	1.17893
$51$	4.76022	0.666564
$52$	−5.77441	−0.800766
$53$	9.00820	1.23737	0.618686	−	0.785639i	$-0.287665\pi$
$53$	9.00820	1.23737	0.618686	+	0.785639i	$0.287665\pi$
$54$	−7.40308	−1.00743
$55$	3.55632	0.479534
$56$	0.139211	0.0186028
$57$	1.44668	0.191617
$58$	−18.5529	−2.43612
$59$	−4.24118	−0.552154	−0.276077	−	0.961135i	$-0.589035\pi$
$59$	−4.24118	−0.552154	−0.276077	+	0.961135i	$0.589035\pi$
$60$	1.14500	0.147819
$61$	−4.14621	−0.530868	−0.265434	−	0.964129i	$-0.585515\pi$
$61$	−4.14621	−0.530868	−0.265434	+	0.964129i	$0.585515\pi$
$62$	11.5470	1.46647
$63$	−2.06830	−0.260581
$64$	−7.29309	−0.911637
$65$	2.67554	0.331860
$66$	−5.35599	−0.659277
$67$	−11.9527	−1.46026	−0.730129	−	0.683310i	$-0.760540\pi$
$67$	−11.9527	−1.46026	−0.730129	+	0.683310i	$0.760540\pi$
$68$	−13.4947	−1.63647
$69$	−0.527002	−0.0634435
$70$	1.42566	0.170399
$71$	2.88595	0.342499	0.171250	−	0.985228i	$-0.445220\pi$
$71$	2.88595	0.342499	0.171250	+	0.985228i	$0.445220\pi$
$72$	−0.435754	−0.0513541
$73$	5.56955	0.651866	0.325933	−	0.945393i	$-0.394322\pi$
$73$	5.56955	0.651866	0.325933	+	0.945393i	$0.394322\pi$
$74$	10.4233	1.21168
$75$	2.84426	0.328427
$76$	−4.10116	−0.470436
$77$	−3.26066	−0.371587
$78$	−4.02950	−0.456250
$79$	−8.06751	−0.907666	−0.453833	−	0.891087i	$-0.649944\pi$
$79$	−8.06751	−0.907666	−0.453833	+	0.891087i	$0.649944\pi$
$80$	3.69317	0.412909
$81$	5.10743	0.567492
$82$	−1.89354	−0.209107
$83$	−16.6444	−1.82696	−0.913482	−	0.406880i	$-0.866617\pi$
$83$	−16.6444	−1.82696	−0.913482	+	0.406880i	$0.866617\pi$
$84$	−1.04981	−0.114544
$85$	6.25269	0.678200
$86$	−8.48116	−0.914547
$87$	−6.33009	−0.678657
$88$	−0.686965	−0.0732308
$89$	1.12900	0.119674	0.0598371	−	0.998208i	$-0.480942\pi$
$89$	1.12900	0.119674	0.0598371	+	0.998208i	$0.480942\pi$
$90$	−4.46258	−0.470397
$91$	−2.45311	−0.257156
$92$	1.49399	0.155759
$93$	3.93972	0.408530
$94$	0	0
$95$	1.90025	0.194962
$96$	−5.33091	−0.544083
$97$	7.11379	0.722296	0.361148	−	0.932508i	$-0.382385\pi$
$97$	7.11379	0.722296	0.361148	+	0.932508i	$0.382385\pi$
$98$	12.5405	1.26678
$99$	10.2065	1.02579
$100$	−8.06315	−0.806315
$101$	3.57625	0.355851	0.177925	−	0.984044i	$-0.443061\pi$
$101$	3.57625	0.355851	0.177925	+	0.984044i	$0.443061\pi$
$102$	−9.41686	−0.932408
$103$	11.6041	1.14339	0.571695	−	0.820466i	$-0.306286\pi$
$103$	11.6041	1.14339	0.571695	+	0.820466i	$0.306286\pi$
$104$	−0.516828	−0.0506791
$105$	0.486424	0.0474702
$106$	−17.8204	−1.73087
$107$	−3.45553	−0.334058	−0.167029	−	0.985952i	$-0.553417\pi$
$107$	−3.45553	−0.334058	−0.167029	+	0.985952i	$0.553417\pi$
$108$	7.16055	0.689024
$109$	−6.16183	−0.590197	−0.295098	−	0.955467i	$-0.595352\pi$
$109$	−6.16183	−0.590197	−0.295098	+	0.955467i	$0.595352\pi$
$110$	−7.03525	−0.670785
$111$	3.55634	0.337553
$112$	−3.38614	−0.319960
$113$	15.7614	1.48271	0.741354	−	0.671114i	$-0.234184\pi$
$113$	15.7614	1.48271	0.741354	+	0.671114i	$0.234184\pi$
$114$	−2.86187	−0.268039
$115$	−0.692232	−0.0645510
$116$	17.9451	1.66616
$117$	7.67867	0.709893
$118$	8.39006	0.772368
$119$	−5.73287	−0.525531
$120$	0.102481	0.00935521
$121$	5.09045	0.462768
$122$	8.20219	0.742592
$123$	−0.646061	−0.0582533
$124$	−11.1687	−1.00298
$125$	8.16891	0.730649
$126$	4.09158	0.364507
$127$	−14.2831	−1.26742	−0.633711	−	0.773570i	$-0.718469\pi$
$127$	−14.2831	−1.26742	−0.633711	+	0.773570i	$0.718469\pi$
$128$	−1.36878	−0.120984
$129$	−2.89370	−0.254776
$130$	−5.29286	−0.464215
$131$	11.6814	1.02061	0.510304	−	0.859994i	$-0.329533\pi$
$131$	11.6814	1.02061	0.510304	+	0.859994i	$0.329533\pi$
$132$	5.18052	0.450906
$133$	−1.74227	−0.151074
$134$	23.6453	2.04265
$135$	−3.31780	−0.285551
$136$	−1.20782	−0.103569
$137$	14.3296	1.22426	0.612129	−	0.790758i	$-0.290313\pi$
$137$	14.3296	1.22426	0.612129	+	0.790758i	$0.290313\pi$
$138$	1.04253	0.0887465
$139$	22.0064	1.86656	0.933279	−	0.359153i	$-0.116934\pi$
$139$	22.0064	1.86656	0.933279	+	0.359153i	$0.116934\pi$
$140$	−1.37896	−0.116543
$141$	0	0
$142$	−5.70910	−0.479097
$143$	12.1054	1.01230
$144$	10.5992	0.883267
$145$	−8.31476	−0.690503
$146$	−11.0179	−0.911848
$147$	4.27872	0.352903
$148$	−10.0818	−0.828720
$149$	−1.69666	−0.138996	−0.0694980	−	0.997582i	$-0.522140\pi$
$149$	−1.69666	−0.138996	−0.0694980	+	0.997582i	$0.522140\pi$
$150$	−5.62663	−0.459412
$151$	−8.96582	−0.729628	−0.364814	−	0.931080i	$-0.618867\pi$
$151$	−8.96582	−0.729628	−0.364814	+	0.931080i	$0.618867\pi$
$152$	−0.367067	−0.0297731
$153$	17.9449	1.45076
$154$	6.45037	0.519786
$155$	5.17494	0.415661
$156$	3.89748	0.312048
$157$	−7.61965	−0.608115	−0.304057	−	0.952654i	$-0.598341\pi$
$157$	−7.61965	−0.608115	−0.304057	+	0.952654i	$0.598341\pi$
$158$	15.9595	1.26967
$159$	−6.08016	−0.482188
$160$	−7.00230	−0.553581
$161$	0.634683	0.0500200
$162$	−10.1037	−0.793822
$163$	−7.52324	−0.589266	−0.294633	−	0.955611i	$-0.595197\pi$
$163$	−7.52324	−0.589266	−0.294633	+	0.955611i	$0.595197\pi$
$164$	1.83151	0.143017
$165$	−2.40037	−0.186868
$166$	32.9267	2.55560
$167$	−3.91775	−0.303165	−0.151582	−	0.988445i	$-0.548437\pi$
$167$	−3.91775	−0.303165	−0.151582	+	0.988445i	$0.548437\pi$
$168$	−0.0939614	−0.00724928
$169$	−3.89269	−0.299438
$170$	−12.3693	−0.948683
$171$	5.45363	0.417049
$172$	8.20331	0.625496
$173$	−15.3122	−1.16416	−0.582082	−	0.813130i	$-0.697762\pi$
$173$	−15.3122	−1.16416	−0.582082	+	0.813130i	$0.697762\pi$
$174$	12.5224	0.949323
$175$	−3.42542	−0.258938
$176$	16.7096	1.25953
$177$	2.86262	0.215168
$178$	−2.23344	−0.167403
$179$	17.2902	1.29233	0.646164	−	0.763199i	$-0.276372\pi$
$179$	17.2902	1.29233	0.646164	+	0.763199i	$0.276372\pi$
$180$	4.31638	0.321724
$181$	−13.4895	−1.00267	−0.501335	−	0.865254i	$-0.667157\pi$
$181$	−13.4895	−1.00267	−0.501335	+	0.865254i	$0.667157\pi$
$182$	4.85284	0.359716
$183$	2.79852	0.206872
$184$	0.133717	0.00985773
$185$	4.67135	0.343445
$186$	−7.79372	−0.571463
$187$	28.2901	2.06878
$188$	0	0
$189$	3.04198	0.221271
$190$	−3.75915	−0.272718
$191$	−10.0199	−0.725018	−0.362509	−	0.931980i	$-0.618080\pi$
$191$	−10.0199	−0.725018	−0.362509	+	0.931980i	$0.618080\pi$
$192$	4.92253	0.355253
$193$	−10.9760	−0.790072	−0.395036	−	0.918666i	$-0.629268\pi$
$193$	−10.9760	−0.790072	−0.395036	+	0.918666i	$0.629268\pi$
$194$	−14.0728	−1.01037
$195$	−1.80588	−0.129322
$196$	−12.1297	−0.866406
$197$	−6.64706	−0.473583	−0.236792	−	0.971560i	$-0.576096\pi$
$197$	−6.64706	−0.473583	−0.236792	+	0.971560i	$0.576096\pi$
$198$	−20.1908	−1.43490
$199$	24.6854	1.74990	0.874951	−	0.484211i	$-0.160893\pi$
$199$	24.6854	1.74990	0.874951	+	0.484211i	$0.160893\pi$
$200$	−0.721678	−0.0510303
$201$	8.06759	0.569044
$202$	−7.07468	−0.497773
$203$	7.62351	0.535066
$204$	9.10835	0.637712
$205$	−0.848620	−0.0592702
$206$	−22.9558	−1.59940
$207$	−1.98667	−0.138083
$208$	12.5712	0.871658
$209$	8.59763	0.594710
$210$	−0.962264	−0.0664025
$211$	22.0841	1.52033	0.760165	−	0.649730i	$-0.225118\pi$
$211$	22.0841	1.52033	0.760165	+	0.649730i	$0.225118\pi$
$212$	17.2366	1.18381
$213$	−1.94790	−0.133468
$214$	6.83586	0.467290
$215$	−3.80096	−0.259223
$216$	0.640892	0.0436072
$217$	−4.74472	−0.322093
$218$	12.1896	0.825583
$219$	−3.75921	−0.254024
$220$	6.80476	0.458777
$221$	21.2836	1.43169
$222$	−7.03529	−0.472178
$223$	14.6249	0.979356	0.489678	−	0.871903i	$-0.337114\pi$
$223$	14.6249	0.979356	0.489678	+	0.871903i	$0.337114\pi$
$224$	6.42016	0.428965
$225$	10.7222	0.714812
$226$	−31.1798	−2.07405
$227$	21.7231	1.44181	0.720905	−	0.693034i	$-0.243726\pi$
$227$	21.7231	1.44181	0.720905	+	0.693034i	$0.243726\pi$
$228$	2.76811	0.183323
$229$	19.1403	1.26483	0.632415	−	0.774630i	$-0.282064\pi$
$229$	19.1403	1.26483	0.632415	+	0.774630i	$0.282064\pi$
$230$	1.36940	0.0902956
$231$	2.20081	0.144803
$232$	1.60614	0.105448
$233$	1.89820	0.124355	0.0621775	−	0.998065i	$-0.480196\pi$
$233$	1.89820	0.124355	0.0621775	+	0.998065i	$0.480196\pi$
$234$	−15.1902	−0.993017
$235$	0	0
$236$	−8.11519	−0.528254
$237$	5.44523	0.353706
$238$	11.3410	0.735127
$239$	−22.9906	−1.48714	−0.743570	−	0.668658i	$-0.766869\pi$
$239$	−22.9906	−1.48714	−0.743570	+	0.668658i	$0.766869\pi$
$240$	−2.49273	−0.160905
$241$	8.78729	0.566039	0.283019	−	0.959114i	$-0.408664\pi$
$241$	8.78729	0.566039	0.283019	+	0.959114i	$0.408664\pi$
$242$	−10.0701	−0.647332
$243$	−14.6741	−0.941342
$244$	−7.93348	−0.507889
$245$	5.62023	0.359063
$246$	1.27806	0.0814863
$247$	6.46829	0.411568
$248$	−0.999631	−0.0634766
$249$	11.2343	0.711944
$250$	−16.1600	−1.02205
$251$	0.363357	0.0229349	0.0114675	−	0.999934i	$-0.496350\pi$
$251$	0.363357	0.0229349	0.0114675	+	0.999934i	$0.496350\pi$
$252$	−3.95754	−0.249301
$253$	−3.13198	−0.196906
$254$	28.2554	1.77290
$255$	−4.22030	−0.264286
$256$	17.2940	1.08087
$257$	−8.40284	−0.524155	−0.262077	−	0.965047i	$-0.584408\pi$
$257$	−8.40284	−0.524155	−0.262077	+	0.965047i	$0.584408\pi$
$258$	5.72443	0.356387
$259$	−4.28300	−0.266133
$260$	5.11946	0.317495
$261$	−23.8629	−1.47708
$262$	−23.1086	−1.42765
$263$	−10.1035	−0.623007	−0.311504	−	0.950245i	$-0.600833\pi$
$263$	−10.1035	−0.623007	−0.311504	+	0.950245i	$0.600833\pi$
$264$	0.463673	0.0285371
$265$	−7.98647	−0.490605
$266$	3.44663	0.211327
$267$	−0.762031	−0.0466355
$268$	−22.8707	−1.39705
$269$	−11.1302	−0.678618	−0.339309	−	0.940675i	$-0.610193\pi$
$269$	−11.1302	−0.678618	−0.339309	+	0.940675i	$0.610193\pi$
$270$	6.56341	0.399436
$271$	26.8601	1.63164	0.815819	−	0.578308i	$-0.196287\pi$
$271$	26.8601	1.63164	0.815819	+	0.578308i	$0.196287\pi$
$272$	29.3787	1.78135
$273$	1.65575	0.100210
$274$	−28.3473	−1.71252
$275$	16.9035	1.01932
$276$	−1.00838	−0.0606974
$277$	0.811728	0.0487720	0.0243860	−	0.999703i	$-0.492237\pi$
$277$	0.811728	0.0487720	0.0243860	+	0.999703i	$0.492237\pi$
$278$	−43.5339	−2.61099
$279$	14.8518	0.889155
$280$	−0.123421	−0.00737582
$281$	18.7418	1.11804	0.559021	−	0.829153i	$-0.311177\pi$
$281$	18.7418	1.11804	0.559021	+	0.829153i	$0.311177\pi$
$282$	0	0
$283$	6.53621	0.388537	0.194269	−	0.980948i	$-0.437767\pi$
$283$	6.53621	0.388537	0.194269	+	0.980948i	$0.437767\pi$
$284$	5.52206	0.327674
$285$	−1.28259	−0.0759741
$286$	−23.9474	−1.41604
$287$	0.778070	0.0459280
$288$	−20.0962	−1.18418
$289$	32.7394	1.92585
$290$	16.4486	0.965894
$291$	−4.80151	−0.281470
$292$	10.6569	0.623650
$293$	8.21316	0.479818	0.239909	−	0.970795i	$-0.422882\pi$
$293$	8.21316	0.479818	0.239909	+	0.970795i	$0.422882\pi$
$294$	−8.46433	−0.493650
$295$	3.76013	0.218923
$296$	−0.902354	−0.0524483
$297$	−15.0113	−0.871043
$298$	3.35640	0.194431
$299$	−2.35630	−0.136268
$300$	5.44229	0.314211
$301$	3.48497	0.200870
$302$	17.7365	1.02062
$303$	−2.41382	−0.138670
$304$	8.92847	0.512083
$305$	3.67593	0.210483
$306$	−35.4993	−2.02936
$307$	9.83386	0.561248	0.280624	−	0.959818i	$-0.409459\pi$
$307$	9.83386	0.561248	0.280624	+	0.959818i	$0.409459\pi$
$308$	−6.23905	−0.355503
$309$	−7.83231	−0.445565
$310$	−10.2373	−0.581438
$311$	14.7011	0.833625	0.416812	−	0.908993i	$-0.363147\pi$
$311$	14.7011	0.833625	0.416812	+	0.908993i	$0.363147\pi$
$312$	0.348837	0.0197490
$313$	−3.48577	−0.197027	−0.0985136	−	0.995136i	$-0.531409\pi$
$313$	−3.48577	−0.197027	−0.0985136	+	0.995136i	$0.531409\pi$
$314$	15.0735	0.850647
$315$	1.83370	0.103318
$316$	−15.4366	−0.868377
$317$	−0.287635	−0.0161552	−0.00807760	−	0.999967i	$-0.502571\pi$
$317$	−0.287635	−0.0161552	−0.00807760	+	0.999967i	$0.502571\pi$
$318$	12.0280	0.674497
$319$	−37.6199	−2.10631
$320$	6.46589	0.361454
$321$	2.33234	0.130178
$322$	−1.25555	−0.0699693
$323$	15.1163	0.841092
$324$	9.77270	0.542928
$325$	12.7171	0.705417
$326$	14.8828	0.824280
$327$	4.15898	0.229992
$328$	0.163926	0.00905129
$329$	0	0
$330$	4.74850	0.261396
$331$	−7.02027	−0.385869	−0.192934	−	0.981212i	$-0.561800\pi$
$331$	−7.02027	−0.385869	−0.192934	+	0.981212i	$0.561800\pi$
$332$	−31.8479	−1.74788
$333$	13.4065	0.734674
$334$	7.75025	0.424075
$335$	10.5970	0.578977
$336$	2.28550	0.124684
$337$	−3.84483	−0.209441	−0.104721	−	0.994502i	$-0.533395\pi$
$337$	−3.84483	−0.209441	−0.104721	+	0.994502i	$0.533395\pi$
$338$	7.70067	0.418861
$339$	−10.6383	−0.577792
$340$	11.9641	0.648843
$341$	23.4139	1.26793
$342$	−10.7886	−0.583379
$343$	−10.8431	−0.585472
$344$	0.734222	0.0395866
$345$	0.467228	0.0251547
$346$	30.2912	1.62846
$347$	3.40161	0.182608	0.0913040	−	0.995823i	$-0.470897\pi$
$347$	3.40161	0.182608	0.0913040	+	0.995823i	$0.470897\pi$
$348$	−12.1122	−0.649281
$349$	−6.33762	−0.339245	−0.169623	−	0.985509i	$-0.554255\pi$
$349$	−6.33762	−0.339245	−0.169623	+	0.985509i	$0.554255\pi$
$350$	6.77631	0.362209
$351$	−11.2935	−0.602803
$352$	−31.6817	−1.68864
$353$	−9.77559	−0.520302	−0.260151	−	0.965568i	$-0.583772\pi$
$353$	−9.77559	−0.520302	−0.260151	+	0.965568i	$0.583772\pi$
$354$	−5.66294	−0.300982
$355$	−2.55862	−0.135797
$356$	2.16027	0.114494
$357$	3.86945	0.204793
$358$	−34.2041	−1.80774
$359$	20.1907	1.06563	0.532813	−	0.846233i	$-0.321135\pi$
$359$	20.1907	1.06563	0.532813	+	0.846233i	$0.321135\pi$
$360$	0.386330	0.0203614
$361$	−14.4060	−0.758211
$362$	26.6855	1.40256
$363$	−3.43584	−0.180335
$364$	−4.69385	−0.246025
$365$	−4.93784	−0.258458
$366$	−5.53614	−0.289378
$367$	−34.4605	−1.79883	−0.899413	−	0.437100i	$-0.856006\pi$
$367$	−34.4605	−1.79883	−0.899413	+	0.437100i	$0.856006\pi$
$368$	−3.25250	−0.169548
$369$	−2.43550	−0.126787
$370$	−9.24106	−0.480420
$371$	7.32251	0.380166
$372$	7.53838	0.390847
$373$	−25.6839	−1.32986	−0.664930	−	0.746906i	$-0.731539\pi$
$373$	−25.6839	−1.32986	−0.664930	+	0.746906i	$0.731539\pi$
$374$	−55.9646	−2.89386
$375$	−5.51367	−0.284725
$376$	0	0
$377$	−28.3027	−1.45766
$378$	−6.01775	−0.309520
$379$	−10.9380	−0.561849	−0.280925	−	0.959730i	$-0.590641\pi$
$379$	−10.9380	−0.561849	−0.280925	+	0.959730i	$0.590641\pi$
$380$	3.63600	0.186523
$381$	9.64050	0.493898
$382$	19.8218	1.01417
$383$	6.96472	0.355881	0.177940	−	0.984041i	$-0.443057\pi$
$383$	6.96472	0.355881	0.177940	+	0.984041i	$0.443057\pi$
$384$	0.923869	0.0471460
$385$	2.89083	0.147330
$386$	21.7132	1.10517
$387$	−10.9086	−0.554513
$388$	13.6117	0.691031
$389$	5.77134	0.292619	0.146309	−	0.989239i	$-0.453261\pi$
$389$	5.77134	0.292619	0.146309	+	0.989239i	$0.453261\pi$
$390$	3.57246	0.180898
$391$	−5.50662	−0.278482
$392$	−1.08565	−0.0548334
$393$	−7.88446	−0.397718
$394$	13.1495	0.662461
$395$	7.15247	0.359880
$396$	19.5293	0.981385
$397$	22.9805	1.15336	0.576679	−	0.816971i	$-0.304348\pi$
$397$	22.9805	1.15336	0.576679	+	0.816971i	$0.304348\pi$
$398$	−48.8336	−2.44781
$399$	1.17596	0.0588717
$400$	17.5540	0.877698
$401$	−26.4176	−1.31923	−0.659615	−	0.751603i	$-0.729281\pi$
$401$	−26.4176	−1.31923	−0.659615	+	0.751603i	$0.729281\pi$
$402$	−15.9596	−0.795993
$403$	17.6151	0.877468
$404$	6.84291	0.340447
$405$	−4.52813	−0.225005
$406$	−15.0811	−0.748464
$407$	21.1354	1.04764
$408$	0.815226	0.0403597
$409$	−27.3412	−1.35193	−0.675967	−	0.736932i	$-0.736274\pi$
$409$	−27.3412	−1.35193	−0.675967	+	0.736932i	$0.736274\pi$
$410$	1.67877	0.0829087
$411$	−9.67186	−0.477078
$412$	22.2037	1.09390
$413$	−3.44753	−0.169642
$414$	3.93011	0.193154
$415$	14.7566	0.724372
$416$	−23.8352	−1.16862
$417$	−14.8534	−0.727374
$418$	−17.0082	−0.831896
$419$	6.83824	0.334070	0.167035	−	0.985951i	$-0.446581\pi$
$419$	6.83824	0.334070	0.167035	+	0.985951i	$0.446581\pi$
$420$	0.930739	0.0454154
$421$	11.8050	0.575339	0.287669	−	0.957730i	$-0.407120\pi$
$421$	11.8050	0.575339	0.287669	+	0.957730i	$0.407120\pi$
$422$	−43.6876	−2.12668
$423$	0	0
$424$	1.54273	0.0749214
$425$	29.7196	1.44161
$426$	3.85340	0.186698
$427$	−3.37033	−0.163102
$428$	−6.61191	−0.319599
$429$	−8.17064	−0.394482
$430$	7.51921	0.362608
$431$	9.02187	0.434568	0.217284	−	0.976108i	$-0.430280\pi$
$431$	9.02187	0.434568	0.217284	+	0.976108i	$0.430280\pi$
$432$	−15.5889	−0.750023
$433$	−1.12252	−0.0539449	−0.0269725	−	0.999636i	$-0.508587\pi$
$433$	−1.12252	−0.0539449	−0.0269725	+	0.999636i	$0.508587\pi$
$434$	9.38620	0.450552
$435$	5.61212	0.269080
$436$	−11.7902	−0.564650
$437$	−1.67352	−0.0800551
$438$	7.43662	0.355335
$439$	32.1171	1.53287	0.766433	−	0.642324i	$-0.222030\pi$
$439$	32.1171	1.53287	0.766433	+	0.642324i	$0.222030\pi$
$440$	0.609048	0.0290352
$441$	16.1298	0.768084
$442$	−42.1041	−2.00269
$443$	4.63319	0.220130	0.110065	−	0.993924i	$-0.464894\pi$
$443$	4.63319	0.220130	0.110065	+	0.993924i	$0.464894\pi$
$444$	6.80480	0.322942
$445$	−1.00095	−0.0474496
$446$	−28.9315	−1.36995
$447$	1.14518	0.0541650
$448$	−5.92835	−0.280088
$449$	7.49959	0.353927	0.176964	−	0.984217i	$-0.443372\pi$
$449$	7.49959	0.353927	0.176964	+	0.984217i	$0.443372\pi$
$450$	−21.2110	−0.999898
$451$	−3.83955	−0.180797
$452$	30.1583	1.41853
$453$	6.05156	0.284327
$454$	−42.9734	−2.01684
$455$	2.17487	0.101960
$456$	0.247755	0.0116022
$457$	12.6295	0.590783	0.295392	−	0.955376i	$-0.404550\pi$
$457$	12.6295	0.590783	0.295392	+	0.955376i	$0.404550\pi$
$458$	−37.8642	−1.76928
$459$	−26.3927	−1.23191
$460$	−1.32454	−0.0617569
$461$	22.6078	1.05295	0.526476	−	0.850190i	$-0.323513\pi$
$461$	22.6078	1.05295	0.526476	+	0.850190i	$0.323513\pi$
$462$	−4.35373	−0.202554
$463$	−25.4318	−1.18192	−0.590958	−	0.806702i	$-0.701250\pi$
$463$	−25.4318	−1.18192	−0.590958	+	0.806702i	$0.701250\pi$
$464$	−39.0675	−1.81366
$465$	−3.49287	−0.161978
$466$	−3.75509	−0.173951
$467$	1.97374	0.0913336	0.0456668	−	0.998957i	$-0.485459\pi$
$467$	1.97374	0.0913336	0.0456668	+	0.998957i	$0.485459\pi$
$468$	14.6926	0.679165
$469$	−9.71603	−0.448644
$470$	0	0
$471$	5.14295	0.236974
$472$	−0.726336	−0.0334323
$473$	−17.1973	−0.790734
$474$	−10.7720	−0.494773
$475$	9.03207	0.414420
$476$	−10.9694	−0.502784
$477$	−22.9207	−1.04947
$478$	45.4809	2.08025
$479$	21.4785	0.981376	0.490688	−	0.871335i	$-0.336745\pi$
$479$	21.4785	0.981376	0.490688	+	0.871335i	$0.336745\pi$
$480$	4.72626	0.215723
$481$	15.9009	0.725018
$482$	−17.3834	−0.791790
$483$	−0.428385	−0.0194922
$484$	9.74021	0.442737
$485$	−6.30693	−0.286383
$486$	29.0288	1.31677
$487$	−11.9771	−0.542733	−0.271367	−	0.962476i	$-0.587476\pi$
$487$	−11.9771	−0.542733	−0.271367	+	0.962476i	$0.587476\pi$
$488$	−0.710071	−0.0321434
$489$	5.07787	0.229629
$490$	−11.1182	−0.502267
$491$	−27.3091	−1.23244	−0.616221	−	0.787573i	$-0.711337\pi$
$491$	−27.3091	−1.23244	−0.616221	+	0.787573i	$0.711337\pi$
$492$	−1.23619	−0.0557318
$493$	−66.1429	−2.97893
$494$	−12.7958	−0.575712
$495$	−9.04881	−0.406714
$496$	24.3148	1.09177
$497$	2.34591	0.105228
$498$	−22.2241	−0.995886
$499$	37.1679	1.66386	0.831932	−	0.554878i	$-0.187235\pi$
$499$	37.1679	1.66386	0.831932	+	0.554878i	$0.187235\pi$
$500$	15.6306	0.699023
$501$	2.64432	0.118139
$502$	−0.718808	−0.0320820
$503$	−12.9258	−0.576334	−0.288167	−	0.957580i	$-0.593046\pi$
$503$	−12.9258	−0.576334	−0.288167	+	0.957580i	$0.593046\pi$
$504$	−0.354212	−0.0157779
$505$	−3.17063	−0.141091
$506$	6.19581	0.275437
$507$	2.62740	0.116687
$508$	−27.3297	−1.21256
$509$	−25.3342	−1.12292	−0.561459	−	0.827505i	$-0.689760\pi$
$509$	−25.3342	−1.12292	−0.561459	+	0.827505i	$0.689760\pi$
$510$	8.34877	0.369690
$511$	4.52733	0.200277
$512$	−31.4740	−1.39097
$513$	−8.02100	−0.354136
$514$	16.6228	0.733201
$515$	−10.2880	−0.453342
$516$	−5.53689	−0.243748
$517$	0	0
$518$	8.47280	0.372273
$519$	10.3351	0.453660
$520$	0.458208	0.0200937
$521$	36.6792	1.60695	0.803473	−	0.595342i	$-0.202983\pi$
$521$	36.6792	1.60695	0.803473	+	0.595342i	$0.202983\pi$
$522$	47.2066	2.06618
$523$	−10.3469	−0.452441	−0.226220	−	0.974076i	$-0.572637\pi$
$523$	−10.3469	−0.452441	−0.226220	+	0.974076i	$0.572637\pi$
$524$	22.3515	0.976431
$525$	2.31202	0.100905
$526$	19.9871	0.871479
$527$	41.1661	1.79322
$528$	−11.2783	−0.490825
$529$	−22.3904	−0.973494
$530$	15.7991	0.686271
$531$	10.7914	0.468306
$532$	−3.33372	−0.144535
$533$	−2.88863	−0.125120
$534$	1.50748	0.0652350
$535$	3.06359	0.132451
$536$	−2.04700	−0.0884169
$537$	−11.6701	−0.503604
$538$	22.0181	0.949268
$539$	25.4285	1.09528
$540$	−6.34838	−0.273191
$541$	1.20364	0.0517485	0.0258743	−	0.999665i	$-0.491763\pi$
$541$	1.20364	0.0517485	0.0258743	+	0.999665i	$0.491763\pi$
$542$	−53.1358	−2.28238
$543$	9.10487	0.390727
$544$	−55.7025	−2.38822
$545$	5.46294	0.234007
$546$	−3.27546	−0.140177
$547$	−21.5364	−0.920831	−0.460415	−	0.887704i	$-0.652300\pi$
$547$	−21.5364	−0.920831	−0.460415	+	0.887704i	$0.652300\pi$
$548$	27.4186	1.17127
$549$	10.5497	0.450252
$550$	−33.4392	−1.42585
$551$	−20.1015	−0.856351
$552$	−0.0902532	−0.00384143
$553$	−6.55785	−0.278868
$554$	−1.60579	−0.0682236
$555$	−3.15297	−0.133836
$556$	42.1077	1.78576
$557$	−10.2388	−0.433833	−0.216917	−	0.976190i	$-0.569600\pi$
$557$	−10.2388	−0.433833	−0.216917	+	0.976190i	$0.569600\pi$
$558$	−29.3805	−1.24377
$559$	−12.9381	−0.547225
$560$	3.00207	0.126861
$561$	−19.0946	−0.806176
$562$	−37.0758	−1.56395
$563$	−22.8402	−0.962598	−0.481299	−	0.876556i	$-0.659835\pi$
$563$	−22.8402	−0.962598	−0.481299	+	0.876556i	$0.659835\pi$
$564$	0	0
$565$	−13.9737	−0.587878
$566$	−12.9302	−0.543496
$567$	4.15168	0.174354
$568$	0.494242	0.0207379
$569$	23.1176	0.969142	0.484571	−	0.874752i	$-0.338976\pi$
$569$	23.1176	0.969142	0.484571	+	0.874752i	$0.338976\pi$
$570$	2.53727	0.106275
$571$	−20.2986	−0.849470	−0.424735	−	0.905318i	$-0.639633\pi$
$571$	−20.2986	−0.849470	−0.424735	+	0.905318i	$0.639633\pi$
$572$	23.1628	0.968486
$573$	6.76304	0.282530
$574$	−1.53921	−0.0642453
$575$	−3.29024	−0.137213
$576$	18.5568	0.773199
$577$	−11.8325	−0.492593	−0.246297	−	0.969195i	$-0.579214\pi$
$577$	−11.8325	−0.492593	−0.246297	+	0.969195i	$0.579214\pi$
$578$	−64.7664	−2.69393
$579$	7.40836	0.307881
$580$	−15.9097	−0.660615
$581$	−13.5298	−0.561310
$582$	9.49854	0.393727
$583$	−36.1345	−1.49654
$584$	0.953830	0.0394697
$585$	−6.80773	−0.281465
$586$	−16.2476	−0.671182
$587$	20.3445	0.839709	0.419855	−	0.907591i	$-0.362081\pi$
$587$	20.3445	0.839709	0.419855	+	0.907591i	$0.362081\pi$
$588$	8.18703	0.337627
$589$	12.5108	0.515497
$590$	−7.43844	−0.306236
$591$	4.48649	0.184549
$592$	21.9487	0.902086
$593$	−22.0756	−0.906536	−0.453268	−	0.891374i	$-0.649742\pi$
$593$	−22.0756	−0.906536	−0.453268	+	0.891374i	$0.649742\pi$
$594$	29.6959	1.21844
$595$	5.08263	0.208368
$596$	−3.24644	−0.132979
$597$	−16.6616	−0.681915
$598$	4.66132	0.190616
$599$	−41.1347	−1.68072	−0.840360	−	0.542029i	$-0.817656\pi$
$599$	−41.1347	−1.68072	−0.840360	+	0.542029i	$0.817656\pi$
$600$	0.487102	0.0198859
$601$	−24.4056	−0.995525	−0.497763	−	0.867313i	$-0.665845\pi$
$601$	−24.4056	−0.995525	−0.497763	+	0.867313i	$0.665845\pi$
$602$	−6.89410	−0.280982
$603$	30.4129	1.23851
$604$	−17.1555	−0.698046
$605$	−4.51308	−0.183483
$606$	4.77512	0.193976
$607$	7.54923	0.306414	0.153207	−	0.988194i	$-0.451040\pi$
$607$	7.54923	0.306414	0.153207	+	0.988194i	$0.451040\pi$
$608$	−16.9285	−0.686542
$609$	−5.14555	−0.208508
$610$	−7.27188	−0.294430
$611$	0	0
$612$	34.3363	1.38796
$613$	−29.4903	−1.19110	−0.595551	−	0.803317i	$-0.703066\pi$
$613$	−29.4903	−1.19110	−0.595551	+	0.803317i	$0.703066\pi$
$614$	−19.4537	−0.785088
$615$	0.572783	0.0230968
$616$	−0.558415	−0.0224992
$617$	9.59181	0.386152	0.193076	−	0.981184i	$-0.438154\pi$
$617$	9.59181	0.386152	0.193076	+	0.981184i	$0.438154\pi$
$618$	15.4942	0.623267
$619$	28.5555	1.14774	0.573871	−	0.818946i	$-0.305441\pi$
$619$	28.5555	1.14774	0.573871	+	0.818946i	$0.305441\pi$
$620$	9.90189	0.397669
$621$	2.92192	0.117253
$622$	−29.0824	−1.16610
$623$	0.917736	0.0367683
$624$	−8.48505	−0.339674
$625$	13.8275	0.553101
$626$	6.89568	0.275607
$627$	−5.80304	−0.231751
$628$	−14.5797	−0.581792
$629$	37.1601	1.48167
$630$	−3.62750	−0.144523
$631$	18.8880	0.751919	0.375959	−	0.926636i	$-0.377313\pi$
$631$	18.8880	0.751919	0.375959	+	0.926636i	$0.377313\pi$
$632$	−1.38163	−0.0549581
$633$	−14.9058	−0.592453
$634$	0.569011	0.0225983
$635$	12.6631	0.502519
$636$	−11.6340	−0.461316
$637$	19.1308	0.757988
$638$	74.4211	2.94636
$639$	−7.34310	−0.290489
$640$	1.21353	0.0479690
$641$	−5.62436	−0.222149	−0.111074	−	0.993812i	$-0.535429\pi$
$641$	−5.62436	−0.222149	−0.111074	+	0.993812i	$0.535429\pi$
$642$	−4.61392	−0.182097
$643$	−29.8913	−1.17880	−0.589399	−	0.807842i	$-0.700636\pi$
$643$	−29.8913	−1.17880	−0.589399	+	0.807842i	$0.700636\pi$
$644$	1.21442	0.0478549
$645$	2.56549	0.101016
$646$	−29.9036	−1.17654
$647$	34.1394	1.34216	0.671078	−	0.741387i	$-0.265831\pi$
$647$	34.1394	1.34216	0.671078	+	0.741387i	$0.265831\pi$
$648$	0.874687	0.0343610
$649$	17.0126	0.667803
$650$	−25.1574	−0.986756
$651$	3.20249	0.125515
$652$	−14.3952	−0.563759
$653$	2.15421	0.0843007	0.0421503	−	0.999111i	$-0.486579\pi$
$653$	2.15421	0.0843007	0.0421503	+	0.999111i	$0.486579\pi$
$654$	−8.22746	−0.321719
$655$	−10.3565	−0.404661
$656$	−3.98730	−0.155678
$657$	−14.1713	−0.552876
$658$	0	0
$659$	9.04882	0.352492	0.176246	−	0.984346i	$-0.443605\pi$
$659$	9.04882	0.352492	0.176246	+	0.984346i	$0.443605\pi$
$660$	−4.59293	−0.178780
$661$	−44.0751	−1.71432	−0.857161	−	0.515048i	$-0.827774\pi$
$661$	−44.0751	−1.71432	−0.857161	+	0.515048i	$0.827774\pi$
$662$	13.8878	0.539763
$663$	−14.3655	−0.557912
$664$	−2.85049	−0.110621
$665$	1.54466	0.0598994
$666$	−26.5214	−1.02768
$667$	7.32265	0.283534
$668$	−7.49634	−0.290042
$669$	−9.87120	−0.381643
$670$	−20.9634	−0.809888
$671$	16.6316	0.642058
$672$	−4.33334	−0.167162
$673$	19.9387	0.768581	0.384291	−	0.923212i	$-0.374446\pi$
$673$	19.9387	0.768581	0.384291	+	0.923212i	$0.374446\pi$
$674$	7.60599	0.292972
$675$	−15.7698	−0.606980
$676$	−7.44839	−0.286476
$677$	4.28280	0.164601	0.0823007	−	0.996608i	$-0.473773\pi$
$677$	4.28280	0.164601	0.0823007	+	0.996608i	$0.473773\pi$
$678$	21.0451	0.808231
$679$	5.78260	0.221916
$680$	1.07082	0.0410642
$681$	−14.6622	−0.561855
$682$	−46.3182	−1.77362
$683$	−9.80795	−0.375291	−0.187645	−	0.982237i	$-0.560086\pi$
$683$	−9.80795	−0.375291	−0.187645	+	0.982237i	$0.560086\pi$
$684$	10.4351	0.398997
$685$	−12.7043	−0.485405
$686$	21.4502	0.818973
$687$	−12.9189	−0.492888
$688$	−17.8591	−0.680871
$689$	−27.1852	−1.03567
$690$	−0.924288	−0.0351870
$691$	9.81263	0.373290	0.186645	−	0.982427i	$-0.440239\pi$
$691$	9.81263	0.373290	0.186645	+	0.982427i	$0.440239\pi$
$692$	−29.2988	−1.11377
$693$	8.29653	0.315159
$694$	−6.72920	−0.255437
$695$	−19.5104	−0.740070
$696$	−1.08408	−0.0410919
$697$	−6.75067	−0.255700
$698$	12.5373	0.474545
$699$	−1.28120	−0.0484596
$700$	−6.55431	−0.247730
$701$	−27.2852	−1.03055	−0.515274	−	0.857026i	$-0.672310\pi$
$701$	−27.2852	−1.03055	−0.515274	+	0.857026i	$0.672310\pi$
$702$	22.3413	0.843216
$703$	11.2933	0.425935
$704$	29.2547	1.10258
$705$	0	0
$706$	19.3384	0.727812
$707$	2.90703	0.109330
$708$	5.47742	0.205854
$709$	−3.12606	−0.117402	−0.0587008	−	0.998276i	$-0.518696\pi$
$709$	−3.12606	−0.117402	−0.0587008	+	0.998276i	$0.518696\pi$
$710$	5.06156	0.189957
$711$	20.5272	0.769831
$712$	0.193351	0.00724614
$713$	−4.55747	−0.170679
$714$	−7.65469	−0.286470
$715$	−10.7324	−0.401368
$716$	33.0835	1.23639
$717$	15.5177	0.579519
$718$	−39.9421	−1.49062
$719$	45.2712	1.68833	0.844165	−	0.536083i	$-0.180097\pi$
$719$	45.2712	1.68833	0.844165	+	0.536083i	$0.180097\pi$
$720$	−9.39701	−0.350206
$721$	9.43268	0.351291
$722$	28.4985	1.06061
$723$	−5.93105	−0.220578
$724$	−25.8113	−0.959268
$725$	−39.5208	−1.46777
$726$	6.79691	0.252257
$727$	23.0926	0.856456	0.428228	−	0.903671i	$-0.359138\pi$
$727$	23.0926	0.856456	0.428228	+	0.903671i	$0.359138\pi$
$728$	−0.420115	−0.0155705
$729$	−5.41789	−0.200663
$730$	9.76822	0.361538
$731$	−30.2362	−1.11833
$732$	5.35476	0.197918
$733$	−41.6671	−1.53901	−0.769504	−	0.638641i	$-0.779497\pi$
$733$	−41.6671	−1.53901	−0.769504	+	0.638641i	$0.779497\pi$
$734$	68.1712	2.51624
$735$	−3.79342	−0.139922
$736$	6.16679	0.227311
$737$	47.9458	1.76611
$738$	4.81799	0.177353
$739$	18.9376	0.696631	0.348316	−	0.937377i	$-0.386754\pi$
$739$	18.9376	0.696631	0.348316	+	0.937377i	$0.386754\pi$
$740$	8.93831	0.328579
$741$	−4.36583	−0.160383
$742$	−14.4857	−0.531786
$743$	−18.0104	−0.660739	−0.330370	−	0.943852i	$-0.607173\pi$
$743$	−18.0104	−0.660739	−0.330370	+	0.943852i	$0.607173\pi$
$744$	0.674709	0.0247360
$745$	1.50422	0.0551104
$746$	50.8088	1.86024
$747$	42.3506	1.54953
$748$	54.1311	1.97923
$749$	−2.80890	−0.102635
$750$	10.9074	0.398280
$751$	−30.8610	−1.12613	−0.563067	−	0.826411i	$-0.690379\pi$
$751$	−30.8610	−1.12613	−0.563067	+	0.826411i	$0.690379\pi$
$752$	0	0
$753$	−0.245251	−0.00893744
$754$	55.9896	2.03902
$755$	7.94890	0.289290
$756$	5.82060	0.211693
$757$	−47.7663	−1.73610	−0.868048	−	0.496480i	$-0.834625\pi$
$757$	−47.7663	−1.73610	−0.868048	+	0.496480i	$0.834625\pi$
$758$	21.6380	0.785929
$759$	2.11396	0.0767317
$760$	0.325433	0.0118047
$761$	−45.1801	−1.63778	−0.818889	−	0.573952i	$-0.805410\pi$
$761$	−45.1801	−1.63778	−0.818889	+	0.573952i	$0.805410\pi$
$762$	−19.0712	−0.690877
$763$	−5.00878	−0.181330
$764$	−19.1725	−0.693635
$765$	−15.9095	−0.575211
$766$	−13.7779	−0.497815
$767$	12.7992	0.462151
$768$	−11.6727	−0.421202
$769$	−3.75129	−0.135275	−0.0676375	−	0.997710i	$-0.521546\pi$
$769$	−3.75129	−0.135275	−0.0676375	+	0.997710i	$0.521546\pi$
$770$	−5.71875	−0.206090
$771$	5.67156	0.204256
$772$	−21.0019	−0.755873
$773$	−1.54800	−0.0556777	−0.0278388	−	0.999612i	$-0.508863\pi$
$773$	−1.54800	−0.0556777	−0.0278388	+	0.999612i	$0.508863\pi$
$774$	21.5797	0.775668
$775$	24.5970	0.883549
$776$	1.21829	0.0437342
$777$	2.89085	0.103709
$778$	−11.4171	−0.409323
$779$	−2.05159	−0.0735060
$780$	−3.45542	−0.123724
$781$	−11.5764	−0.414235
$782$	10.8934	0.389548
$783$	35.0968	1.25426
$784$	26.4070	0.943109
$785$	6.75541	0.241111
$786$	15.5973	0.556339
$787$	−22.8115	−0.813141	−0.406571	−	0.913619i	$-0.633275\pi$
$787$	−22.8115	−0.813141	−0.406571	+	0.913619i	$0.633275\pi$
$788$	−12.7187	−0.453084
$789$	6.81942	0.242778
$790$	−14.1493	−0.503409
$791$	12.8120	0.455542
$792$	1.74794	0.0621102
$793$	12.5126	0.444334
$794$	−45.4609	−1.61335
$795$	5.39053	0.191182
$796$	47.2338	1.67416
$797$	−13.9919	−0.495618	−0.247809	−	0.968809i	$-0.579711\pi$
$797$	−13.9919	−0.495618	−0.247809	+	0.968809i	$0.579711\pi$
$798$	−2.32633	−0.0823513
$799$	0	0
$800$	−33.2826	−1.17672
$801$	−2.87267	−0.101501
$802$	52.2603	1.84537
$803$	−22.3411	−0.788399
$804$	15.4368	0.544412
$805$	−0.562696	−0.0198324
$806$	−34.8468	−1.22743
$807$	7.51239	0.264449
$808$	0.612462	0.0215463
$809$	17.1991	0.604688	0.302344	−	0.953199i	$-0.402231\pi$
$809$	17.1991	0.604688	0.302344	+	0.953199i	$0.402231\pi$
$810$	8.95772	0.314742
$811$	−10.5928	−0.371963	−0.185982	−	0.982553i	$-0.559547\pi$
$811$	−10.5928	−0.371963	−0.185982	+	0.982553i	$0.559547\pi$
$812$	14.5870	0.511905
$813$	−18.1295	−0.635828
$814$	−41.8109	−1.46547
$815$	6.66993	0.233638
$816$	−19.8294	−0.694168
$817$	−9.18906	−0.321485
$818$	54.0874	1.89112
$819$	6.24177	0.218105
$820$	−1.62377	−0.0567047
$821$	−0.347933	−0.0121430	−0.00607148	−	0.999982i	$-0.501933\pi$
$821$	−0.347933	−0.0121430	−0.00607148	+	0.999982i	$0.501933\pi$
$822$	19.1333	0.667349
$823$	29.5127	1.02875	0.514374	−	0.857566i	$-0.328024\pi$
$823$	29.5127	1.02875	0.514374	+	0.857566i	$0.328024\pi$
$824$	1.98730	0.0692309
$825$	−11.4092	−0.397216
$826$	6.82004	0.237300
$827$	24.8879	0.865437	0.432718	−	0.901529i	$-0.357554\pi$
$827$	24.8879	0.865437	0.432718	+	0.901529i	$0.357554\pi$
$828$	−3.80135	−0.132106
$829$	24.1143	0.837525	0.418762	−	0.908096i	$-0.362464\pi$
$829$	24.1143	0.837525	0.418762	+	0.908096i	$0.362464\pi$
$830$	−29.1920	−1.01327
$831$	−0.547882	−0.0190058
$832$	22.0093	0.763036
$833$	44.7082	1.54905
$834$	29.3836	1.01747
$835$	3.47339	0.120202
$836$	16.4510	0.568968
$837$	−21.8435	−0.755023
$838$	−13.5277	−0.467306
$839$	39.4019	1.36031	0.680153	−	0.733070i	$-0.261913\pi$
$839$	39.4019	1.36031	0.680153	+	0.733070i	$0.261913\pi$
$840$	0.0833041	0.00287426
$841$	58.9562	2.03297
$842$	−23.3530	−0.804799
$843$	−12.6499	−0.435687
$844$	42.2563	1.45452
$845$	3.45117	0.118724
$846$	0	0
$847$	4.13788	0.142179
$848$	−37.5250	−1.28861
$849$	−4.41167	−0.151408
$850$	−58.7925	−2.01656
$851$	−4.11397	−0.141025
$852$	−3.72716	−0.127690
$853$	28.0980	0.962057	0.481029	−	0.876705i	$-0.340263\pi$
$853$	28.0980	0.962057	0.481029	+	0.876705i	$0.340263\pi$
$854$	6.66733	0.228151
$855$	−4.83506	−0.165356
$856$	−0.591787	−0.0202268
$857$	3.94799	0.134861	0.0674305	−	0.997724i	$-0.478520\pi$
$857$	3.94799	0.134861	0.0674305	+	0.997724i	$0.478520\pi$
$858$	16.1635	0.551812
$859$	17.2452	0.588397	0.294199	−	0.955744i	$-0.404947\pi$
$859$	17.2452	0.588397	0.294199	+	0.955744i	$0.404947\pi$
$860$	−7.27287	−0.248003
$861$	−0.525164	−0.0178976
$862$	−17.8474	−0.607886
$863$	18.5654	0.631973	0.315987	−	0.948764i	$-0.397664\pi$
$863$	18.5654	0.631973	0.315987	+	0.948764i	$0.397664\pi$
$864$	29.5568	1.00554
$865$	13.5754	0.461579
$866$	2.22061	0.0754596
$867$	−22.0977	−0.750478
$868$	−9.07869	−0.308151
$869$	32.3611	1.09778
$870$	−11.1021	−0.376397
$871$	36.0713	1.22223
$872$	−1.05526	−0.0357357
$873$	−18.1006	−0.612611
$874$	3.31061	0.111983
$875$	6.64027	0.224482
$876$	−7.19299	−0.243028
$877$	−40.2086	−1.35775	−0.678875	−	0.734254i	$-0.737532\pi$
$877$	−40.2086	−1.35775	−0.678875	+	0.734254i	$0.737532\pi$
$878$	−63.5353	−2.14421
$879$	−5.54354	−0.186979
$880$	−14.8144	−0.499392
$881$	47.4491	1.59860	0.799301	−	0.600931i	$-0.205204\pi$
$881$	47.4491	1.59860	0.799301	+	0.600931i	$0.205204\pi$
$882$	−31.9085	−1.07442
$883$	−0.917146	−0.0308644	−0.0154322	−	0.999881i	$-0.504912\pi$
$883$	−0.917146	−0.0308644	−0.0154322	+	0.999881i	$0.504912\pi$
$884$	40.7247	1.36972
$885$	−2.53793	−0.0853116
$886$	−9.16556	−0.307923
$887$	36.2772	1.21807	0.609035	−	0.793143i	$-0.291557\pi$
$887$	36.2772	1.21807	0.609035	+	0.793143i	$0.291557\pi$
$888$	0.609051	0.0204384
$889$	−11.6103	−0.389398
$890$	1.98012	0.0663737
$891$	−20.4874	−0.686353
$892$	27.9837	0.936964
$893$	0	0
$894$	−2.26543	−0.0757674
$895$	−15.3291	−0.512394
$896$	−1.11264	−0.0371708
$897$	1.59040	0.0531020
$898$	−14.8360	−0.495083
$899$	−54.7422	−1.82575
$900$	20.5161	0.683871
$901$	−63.5314	−2.11654
$902$	7.59555	0.252904
$903$	−2.35221	−0.0782765
$904$	2.69927	0.0897762
$905$	11.9595	0.397548
$906$	−11.9714	−0.397724
$907$	−9.25814	−0.307412	−0.153706	−	0.988117i	$-0.549121\pi$
$907$	−9.25814	−0.307412	−0.153706	+	0.988117i	$0.549121\pi$
$908$	41.5655	1.37940
$909$	−9.09953	−0.301812
$910$	−4.30241	−0.142624
$911$	−43.3886	−1.43753	−0.718765	−	0.695253i	$-0.755292\pi$
$911$	−43.3886	−1.43753	−0.718765	+	0.695253i	$0.755292\pi$
$912$	−6.02634	−0.199552
$913$	66.7656	2.20962
$914$	−24.9842	−0.826403
$915$	−2.48110	−0.0820227
$916$	36.6237	1.21008
$917$	9.49548	0.313568
$918$	52.2111	1.72322
$919$	37.6670	1.24252	0.621259	−	0.783605i	$-0.286621\pi$
$919$	37.6670	1.24252	0.621259	+	0.783605i	$0.286621\pi$
$920$	−0.118550	−0.00390849
$921$	−6.63744	−0.218711
$922$	−44.7237	−1.47290
$923$	−8.70931	−0.286670
$924$	4.21110	0.138535
$925$	22.2034	0.730042
$926$	50.3102	1.65330
$927$	−29.5259	−0.969759
$928$	74.0726	2.43155
$929$	39.2657	1.28826	0.644132	−	0.764914i	$-0.277219\pi$
$929$	39.2657	1.28826	0.644132	+	0.764914i	$0.277219\pi$
$930$	6.90973	0.226579
$931$	13.5873	0.445304
$932$	3.63206	0.118972
$933$	−9.92265	−0.324853
$934$	−3.90452	−0.127760
$935$	−25.0814	−0.820248
$936$	1.31503	0.0429832
$937$	−11.0658	−0.361503	−0.180752	−	0.983529i	$-0.557853\pi$
$937$	−11.0658	−0.361503	−0.180752	+	0.983529i	$0.557853\pi$
$938$	19.2206	0.627576
$939$	2.35275	0.0767790
$940$	0	0
$941$	−19.9463	−0.650231	−0.325116	−	0.945674i	$-0.605403\pi$
$941$	−19.9463	−0.650231	−0.325116	+	0.945674i	$0.605403\pi$
$942$	−10.1740	−0.331486
$943$	0.747363	0.0243375
$944$	17.6673	0.575020
$945$	−2.69695	−0.0877317
$946$	34.0204	1.10610
$947$	−54.1860	−1.76081	−0.880405	−	0.474223i	$-0.842729\pi$
$947$	−54.1860	−1.76081	−0.880405	+	0.474223i	$0.842729\pi$
$948$	10.4191	0.338395
$949$	−16.8080	−0.545609
$950$	−17.8676	−0.579701
$951$	0.194142	0.00629548
$952$	−0.981800	−0.0318203
$953$	37.8125	1.22487	0.612434	−	0.790522i	$-0.290191\pi$
$953$	37.8125	1.22487	0.612434	+	0.790522i	$0.290191\pi$
$954$	45.3427	1.46802
$955$	8.88346	0.287462
$956$	−43.9909	−1.42277
$957$	25.3918	0.820801
$958$	−42.4895	−1.37277
$959$	11.6481	0.376137
$960$	−4.36421	−0.140854
$961$	3.07046	0.0990471
$962$	−31.4557	−1.01417
$963$	8.79235	0.283330
$964$	16.8138	0.541538
$965$	9.73110	0.313255
$966$	0.847447	0.0272662
$967$	15.4930	0.498222	0.249111	−	0.968475i	$-0.419862\pi$
$967$	15.4930	0.498222	0.249111	+	0.968475i	$0.419862\pi$
$968$	0.871780	0.0280201
$969$	−10.2029	−0.327763
$970$	12.4766	0.400600
$971$	21.0305	0.674900	0.337450	−	0.941344i	$-0.390436\pi$
$971$	21.0305	0.674900	0.337450	+	0.941344i	$0.390436\pi$
$972$	−28.0778	−0.900596
$973$	17.8884	0.573475
$974$	23.6935	0.759189
$975$	−8.58350	−0.274892
$976$	17.2716	0.552852
$977$	42.1181	1.34748	0.673739	−	0.738969i	$-0.264687\pi$
$977$	42.1181	1.34748	0.673739	+	0.738969i	$0.264687\pi$
$978$	−10.0452	−0.321211
$979$	−4.52876	−0.144740
$980$	10.7539	0.343521
$981$	15.6784	0.500572
$982$	54.0239	1.72397
$983$	−17.7295	−0.565484	−0.282742	−	0.959196i	$-0.591244\pi$
$983$	−17.7295	−0.565484	−0.282742	+	0.959196i	$0.591244\pi$
$984$	−0.110643	−0.00352717
$985$	5.89313	0.187771
$986$	130.847	4.16700
$987$	0	0
$988$	12.3766	0.393753
$989$	3.34743	0.106442
$990$	17.9007	0.568922
$991$	30.1594	0.958045	0.479023	−	0.877803i	$-0.340991\pi$
$991$	30.1594	0.958045	0.479023	+	0.877803i	$0.340991\pi$
$992$	−46.1013	−1.46372
$993$	4.73839	0.150368
$994$	−4.64076	−0.147196
$995$	−21.8855	−0.693818
$996$	21.4960	0.681128
$997$	22.1158	0.700413	0.350207	−	0.936672i	$-0.386111\pi$
$997$	22.1158	0.700413	0.350207	+	0.936672i	$0.386111\pi$
$998$	−73.5270	−2.32746
$999$	−19.7179	−0.623846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2209.2.a.m.1.5		33
47.31	odd	46		47.2.c.a.21.1	yes	66
47.44	odd	46		47.2.c.a.9.1	✓	66
47.46	odd	2		2209.2.a.l.1.5		33
141.44	even	46		423.2.i.a.244.3		66
141.125	even	46		423.2.i.a.397.3		66
188.31	even	46		752.2.m.c.209.1		66
188.91	even	46		752.2.m.c.385.1		66

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
47.2.c.a.9.1	✓	66	47.44	odd	46
47.2.c.a.21.1	yes	66	47.31	odd	46
423.2.i.a.244.3		66	141.44	even	46
423.2.i.a.397.3		66	141.125	even	46
752.2.m.c.209.1		66	188.31	even	46
752.2.m.c.385.1		66	188.91	even	46
2209.2.a.l.1.5		33	47.46	odd	2
2209.2.a.m.1.5		33	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2209 = 47^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2209.a (trivial)

\(f(q)\)	\(=\)	\(q-1.97824 q^{2} -0.674958 q^{3} +1.91343 q^{4} -0.886577 q^{5} +1.33523 q^{6} +0.812871 q^{7} +0.171258 q^{8} -2.54443 q^{9} +1.75386 q^{10} -4.01129 q^{11} -1.29148 q^{12} -3.01783 q^{13} -1.60805 q^{14} +0.598403 q^{15} -4.16565 q^{16} -7.05262 q^{17} +5.03349 q^{18} -2.14336 q^{19} -1.69640 q^{20} -0.548654 q^{21} +7.93529 q^{22} +0.780791 q^{23} -0.115592 q^{24} -4.21398 q^{25} +5.96999 q^{26} +3.74226 q^{27} +1.55537 q^{28} +9.37850 q^{29} -1.18378 q^{30} -5.83699 q^{31} +7.89813 q^{32} +2.70745 q^{33} +13.9518 q^{34} -0.720673 q^{35} -4.86859 q^{36} -5.26898 q^{37} +4.24007 q^{38} +2.03691 q^{39} -0.151833 q^{40} +0.957187 q^{41} +1.08537 q^{42} +4.28723 q^{43} -7.67532 q^{44} +2.25584 q^{45} -1.54459 q^{46} +2.81164 q^{48} -6.33924 q^{49} +8.33626 q^{50} +4.76022 q^{51} -5.77441 q^{52} +9.00820 q^{53} -7.40308 q^{54} +3.55632 q^{55} +0.139211 q^{56} +1.44668 q^{57} -18.5529 q^{58} -4.24118 q^{59} +1.14500 q^{60} -4.14621 q^{61} +11.5470 q^{62} -2.06830 q^{63} -7.29309 q^{64} +2.67554 q^{65} -5.35599 q^{66} -11.9527 q^{67} -13.4947 q^{68} -0.527002 q^{69} +1.42566 q^{70} +2.88595 q^{71} -0.435754 q^{72} +5.56955 q^{73} +10.4233 q^{74} +2.84426 q^{75} -4.10116 q^{76} -3.26066 q^{77} -4.02950 q^{78} -8.06751 q^{79} +3.69317 q^{80} +5.10743 q^{81} -1.89354 q^{82} -16.6444 q^{83} -1.04981 q^{84} +6.25269 q^{85} -8.48116 q^{86} -6.33009 q^{87} -0.686965 q^{88} +1.12900 q^{89} -4.46258 q^{90} -2.45311 q^{91} +1.49399 q^{92} +3.93972 q^{93} +1.90025 q^{95} -5.33091 q^{96} +7.11379 q^{97} +12.5405 q^{98} +10.2065 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + q^{2} + 2 q^{3} + 25 q^{4} + 19 q^{5} + 10 q^{6} + 2 q^{7} + 9 q^{8} + 17 q^{9} + 10 q^{10} + 37 q^{11} - 38 q^{12} + 20 q^{13} - 43 q^{14} + 33 q^{15} + 13 q^{16} + 6 q^{17} - 46 q^{18} + 36 q^{19}+ \cdots + 62 q^{99}+O(q^{100}) \) 33 * q + q^2 + 2 * q^3 + 25 * q^4 + 19 * q^5 + 10 * q^6 + 2 * q^7 + 9 * q^8 + 17 * q^9 + 10 * q^10 + 37 * q^11 - 38 * q^12 + 20 * q^13 - 43 * q^14 + 33 * q^15 + 13 * q^16 + 6 * q^17 - 46 * q^18 + 36 * q^19 + 48 * q^20 + 14 * q^21 + 7 * q^22 + 54 * q^23 - 21 * q^24 - 4 * q^25 + 56 * q^26 + 26 * q^27 + 20 * q^28 + 49 * q^29 + 15 * q^30 + 49 * q^31 - 31 * q^32 + 28 * q^33 + 32 * q^34 + 58 * q^35 + 17 * q^36 + 14 * q^37 + 38 * q^38 + 55 * q^39 + 17 * q^40 + 74 * q^41 - 2 * q^42 + 25 * q^43 + 58 * q^44 + 13 * q^45 + 42 * q^46 - 79 * q^48 - 7 * q^49 + 39 * q^50 - 75 * q^51 + 22 * q^52 + 30 * q^53 + 5 * q^54 + 44 * q^55 - 56 * q^56 + 11 * q^57 - 26 * q^58 + 5 * q^59 + 31 * q^60 + 11 * q^61 + 36 * q^62 - 71 * q^63 + 33 * q^64 + 11 * q^65 + 36 * q^66 + 17 * q^67 - 16 * q^68 + 41 * q^69 - 41 * q^70 + 19 * q^71 - 31 * q^72 + 20 * q^73 + 48 * q^74 + 50 * q^75 + 33 * q^76 + 39 * q^77 - 52 * q^78 + 7 * q^79 + 62 * q^80 + q^81 - 27 * q^82 - 83 * q^83 + 64 * q^84 - 9 * q^85 + 68 * q^86 + 72 * q^87 - 20 * q^88 + 25 * q^89 + 29 * q^90 + 25 * q^91 + 38 * q^92 + 14 * q^93 - 63 * q^95 - 2 * q^96 + 34 * q^97 - 45 * q^98 + 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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