LMFDB - Embedded newform 209.4.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,4,Mod(1,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("209.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	209.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$12.3313991912$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 91 x^{11} + 176 x^{10} + 3117 x^{9} - 5786 x^{8} - 49725 x^{7} + 87196 x^{6} + \cdots - 86016 $ x^13 - 2x^12 - 91x^11 + 176x^10 + 3117x^9 - 5786x^8 - 49725x^7 + 87196x^6 + 366602x^5 - 590896x^4 - 1017888x^3 + 1444096x^2 + 115200x - 86016
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-3.02090$ of defining polynomial
Character	$\chi$	$=$	209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.02090 q^{2} -8.02896 q^{3} +1.12583 q^{4} -20.1089 q^{5} -24.2547 q^{6} +33.1653 q^{7} -20.7662 q^{8} +37.4642 q^{9} -60.7468 q^{10} -11.0000 q^{11} -9.03920 q^{12} +53.7348 q^{13} +100.189 q^{14} +161.453 q^{15} -71.7391 q^{16} +27.9300 q^{17} +113.175 q^{18} -19.0000 q^{19} -22.6391 q^{20} -266.283 q^{21} -33.2299 q^{22} +104.096 q^{23} +166.731 q^{24} +279.366 q^{25} +162.327 q^{26} -84.0162 q^{27} +37.3383 q^{28} +82.7061 q^{29} +487.734 q^{30} -11.0218 q^{31} -50.5871 q^{32} +88.3185 q^{33} +84.3736 q^{34} -666.916 q^{35} +42.1781 q^{36} +63.2850 q^{37} -57.3971 q^{38} -431.435 q^{39} +417.584 q^{40} -100.073 q^{41} -804.413 q^{42} -58.5957 q^{43} -12.3841 q^{44} -753.361 q^{45} +314.463 q^{46} -322.672 q^{47} +575.990 q^{48} +756.937 q^{49} +843.937 q^{50} -224.248 q^{51} +60.4960 q^{52} +478.924 q^{53} -253.804 q^{54} +221.197 q^{55} -688.717 q^{56} +152.550 q^{57} +249.847 q^{58} -717.320 q^{59} +181.768 q^{60} -598.511 q^{61} -33.2956 q^{62} +1242.51 q^{63} +421.094 q^{64} -1080.55 q^{65} +266.801 q^{66} +652.627 q^{67} +31.4443 q^{68} -835.782 q^{69} -2014.69 q^{70} +577.080 q^{71} -777.987 q^{72} +1102.66 q^{73} +191.178 q^{74} -2243.02 q^{75} -21.3907 q^{76} -364.818 q^{77} -1303.32 q^{78} +1026.47 q^{79} +1442.59 q^{80} -336.969 q^{81} -302.312 q^{82} +1307.91 q^{83} -299.788 q^{84} -561.640 q^{85} -177.012 q^{86} -664.044 q^{87} +228.428 q^{88} +5.18117 q^{89} -2275.83 q^{90} +1782.13 q^{91} +117.194 q^{92} +88.4932 q^{93} -974.759 q^{94} +382.068 q^{95} +406.162 q^{96} +336.438 q^{97} +2286.63 q^{98} -412.106 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 2 q^{2} + 11 q^{3} + 82 q^{4} + 8 q^{5} + 13 q^{6} + 39 q^{7} + 6 q^{8} + 156 q^{9} + 124 q^{10} - 143 q^{11} + 247 q^{12} - 23 q^{13} + 47 q^{14} + 278 q^{15} + 526 q^{16} + 73 q^{17} - 165 q^{18}+ \cdots - 1716 q^{99}+O(q^{100}) $ 13 * q - 2 * q^2 + 11 * q^3 + 82 * q^4 + 8 * q^5 + 13 * q^6 + 39 * q^7 + 6 * q^8 + 156 * q^9 + 124 * q^10 - 143 * q^11 + 247 * q^12 - 23 * q^13 + 47 * q^14 + 278 * q^15 + 526 * q^16 + 73 * q^17 - 165 * q^18 - 247 * q^19 + 142 * q^20 + 77 * q^21 + 22 * q^22 + 185 * q^23 - 251 * q^24 + 641 * q^25 - 47 * q^26 + 1109 * q^27 + 289 * q^28 - 41 * q^29 + 520 * q^30 + 930 * q^31 - 194 * q^32 - 121 * q^33 - 333 * q^34 + 122 * q^35 + 1469 * q^36 + 1094 * q^37 + 38 * q^38 + 543 * q^39 + 2084 * q^40 - 766 * q^41 - 1277 * q^42 + 1024 * q^43 - 902 * q^44 - 348 * q^45 + 1927 * q^46 + 516 * q^47 + 3067 * q^48 + 1966 * q^49 + 3066 * q^50 + 1975 * q^51 - 553 * q^52 + 1017 * q^53 - 2231 * q^54 - 88 * q^55 - 1793 * q^56 - 209 * q^57 - 159 * q^58 + 15 * q^59 - 3158 * q^60 - 862 * q^61 - 3298 * q^62 + 552 * q^63 + 3694 * q^64 - 1640 * q^65 - 143 * q^66 + 621 * q^67 - 1533 * q^68 + 335 * q^69 - 3250 * q^70 + 632 * q^71 - 8349 * q^72 - 629 * q^73 - 4086 * q^74 - 2759 * q^75 - 1558 * q^76 - 429 * q^77 - 5813 * q^78 + 2444 * q^79 + 2810 * q^80 + 2265 * q^81 - 846 * q^82 + 732 * q^83 - 761 * q^84 - 3786 * q^85 - 4664 * q^86 - 1185 * q^87 - 66 * q^88 + 3178 * q^89 - 6174 * q^90 + 1349 * q^91 - 1677 * q^92 + 1328 * q^93 + 3156 * q^94 - 152 * q^95 - 13811 * q^96 + 1410 * q^97 - 6273 * q^98 - 1716 * 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 $

$2$	3.02090	1.06805	0.534024	−	0.845469i	$-0.320679\pi$
$2$	3.02090	1.06805	0.534024	+	0.845469i	$0.320679\pi$
$3$	−8.02896	−1.54517	−0.772587	−	0.634909i	$-0.781037\pi$
$3$	−8.02896	−1.54517	−0.772587	+	0.634909i	$0.781037\pi$
$4$	1.12583	0.140728
$5$	−20.1089	−1.79859	−0.899295	−	0.437342i	$-0.855920\pi$
$5$	−20.1089	−1.79859	−0.899295	+	0.437342i	$0.855920\pi$
$6$	−24.2547	−1.65032
$7$	33.1653	1.79076	0.895379	−	0.445305i	$-0.146905\pi$
$7$	33.1653	1.79076	0.895379	+	0.445305i	$0.146905\pi$
$8$	−20.7662	−0.917744
$9$	37.4642	1.38756
$10$	−60.7468	−1.92098
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−9.03920	−0.217449
$13$	53.7348	1.14641	0.573206	−	0.819411i	$-0.305699\pi$
$13$	53.7348	1.14641	0.573206	+	0.819411i	$0.305699\pi$
$14$	100.189	1.91262
$15$	161.453	2.77914
$16$	−71.7391	−1.12092
$17$	27.9300	0.398471	0.199236	−	0.979952i	$-0.436154\pi$
$17$	27.9300	0.398471	0.199236	+	0.979952i	$0.436154\pi$
$18$	113.175	1.48198
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−22.6391	−0.253112
$21$	−266.283	−2.76703
$22$	−33.2299	−0.322029
$23$	104.096	0.943718	0.471859	−	0.881674i	$-0.343583\pi$
$23$	104.096	0.943718	0.471859	+	0.881674i	$0.343583\pi$
$24$	166.731	1.41807
$25$	279.366	2.23493
$26$	162.327	1.22442
$27$	−84.0162	−0.598849
$28$	37.3383	0.252010
$29$	82.7061	0.529591	0.264795	−	0.964305i	$-0.414696\pi$
$29$	82.7061	0.529591	0.264795	+	0.964305i	$0.414696\pi$
$30$	487.734	2.96825
$31$	−11.0218	−0.0638570	−0.0319285	−	0.999490i	$-0.510165\pi$
$31$	−11.0218	−0.0638570	−0.0319285	+	0.999490i	$0.510165\pi$
$32$	−50.5871	−0.279457
$33$	88.3185	0.465887
$34$	84.3736	0.425587
$35$	−666.916	−3.22084
$36$	42.1781	0.195269
$37$	63.2850	0.281189	0.140594	−	0.990067i	$-0.455099\pi$
$37$	63.2850	0.281189	0.140594	+	0.990067i	$0.455099\pi$
$38$	−57.3971	−0.245027
$39$	−431.435	−1.77141
$40$	417.584	1.65065
$41$	−100.073	−0.381191	−0.190596	−	0.981669i	$-0.561042\pi$
$41$	−100.073	−0.381191	−0.190596	+	0.981669i	$0.561042\pi$
$42$	−804.413	−2.95532
$43$	−58.5957	−0.207808	−0.103904	−	0.994587i	$-0.533134\pi$
$43$	−58.5957	−0.207808	−0.103904	+	0.994587i	$0.533134\pi$
$44$	−12.3841	−0.0424311
$45$	−753.361	−2.49565
$46$	314.463	1.00794
$47$	−322.672	−1.00142	−0.500708	−	0.865616i	$-0.666927\pi$
$47$	−322.672	−1.00142	−0.500708	+	0.865616i	$0.666927\pi$
$48$	575.990	1.73202
$49$	756.937	2.20681
$50$	843.937	2.38701
$51$	−224.248	−0.615707
$52$	60.4960	0.161332
$53$	478.924	1.24123	0.620616	−	0.784115i	$-0.286883\pi$
$53$	478.924	1.24123	0.620616	+	0.784115i	$0.286883\pi$
$54$	−253.804	−0.639600
$55$	221.197	0.542296
$56$	−688.717	−1.64346
$57$	152.550	0.354487
$58$	249.847	0.565629
$59$	−717.320	−1.58283	−0.791416	−	0.611278i	$-0.790656\pi$
$59$	−717.320	−1.58283	−0.791416	+	0.611278i	$0.790656\pi$
$60$	181.768	0.391103
$61$	−598.511	−1.25625	−0.628126	−	0.778111i	$-0.716178\pi$
$61$	−598.511	−1.25625	−0.628126	+	0.778111i	$0.716178\pi$
$62$	−33.2956	−0.0682024
$63$	1242.51	2.48479
$64$	421.094	0.822450
$65$	−1080.55	−2.06193
$66$	266.801	0.497590
$67$	652.627	1.19002	0.595008	−	0.803720i	$-0.297149\pi$
$67$	652.627	1.19002	0.595008	+	0.803720i	$0.297149\pi$
$68$	31.4443	0.0560761
$69$	−835.782	−1.45821
$70$	−2014.69	−3.44001
$71$	577.080	0.964603	0.482301	−	0.876005i	$-0.339801\pi$
$71$	577.080	0.964603	0.482301	+	0.876005i	$0.339801\pi$
$72$	−777.987	−1.27343
$73$	1102.66	1.76790	0.883952	−	0.467577i	$-0.154873\pi$
$73$	1102.66	1.76790	0.883952	+	0.467577i	$0.154873\pi$
$74$	191.178	0.300323
$75$	−2243.02	−3.45335
$76$	−21.3907	−0.0322853
$77$	−364.818	−0.539934
$78$	−1303.32	−1.89195
$79$	1026.47	1.46186	0.730929	−	0.682453i	$-0.239087\pi$
$79$	1026.47	1.46186	0.730929	+	0.682453i	$0.239087\pi$
$80$	1442.59	2.01608
$81$	−336.969	−0.462235
$82$	−302.312	−0.407131
$83$	1307.91	1.72966	0.864830	−	0.502066i	$-0.167426\pi$
$83$	1307.91	1.72966	0.864830	+	0.502066i	$0.167426\pi$
$84$	−299.788	−0.389399
$85$	−561.640	−0.716687
$86$	−177.012	−0.221950
$87$	−664.044	−0.818310
$88$	228.428	0.276710
$89$	5.18117	0.00617082	0.00308541	−	0.999995i	$-0.499018\pi$
$89$	5.18117	0.00617082	0.00308541	+	0.999995i	$0.499018\pi$
$90$	−2275.83	−2.66548
$91$	1782.13	2.05295
$92$	117.194	0.132808
$93$	88.4932	0.0986701
$94$	−974.759	−1.06956
$95$	382.068	0.412625
$96$	406.162	0.431810
$97$	336.438	0.352166	0.176083	−	0.984375i	$-0.443657\pi$
$97$	336.438	0.352166	0.176083	+	0.984375i	$0.443657\pi$
$98$	2286.63	2.35698
$99$	−412.106	−0.418365
$100$	314.517	0.314517
$101$	600.569	0.591672	0.295836	−	0.955239i	$-0.404402\pi$
$101$	600.569	0.591672	0.295836	+	0.955239i	$0.404402\pi$
$102$	−677.432	−0.657605
$103$	568.289	0.543643	0.271821	−	0.962348i	$-0.412374\pi$
$103$	568.289	0.543643	0.271821	+	0.962348i	$0.412374\pi$
$104$	−1115.87	−1.05211
$105$	5354.64	4.97676
$106$	1446.78	1.32570
$107$	362.013	0.327076	0.163538	−	0.986537i	$-0.447709\pi$
$107$	362.013	0.327076	0.163538	+	0.986537i	$0.447709\pi$
$108$	−94.5876	−0.0842750
$109$	−121.435	−0.106710	−0.0533549	−	0.998576i	$-0.516991\pi$
$109$	−121.435	−0.106710	−0.0533549	+	0.998576i	$0.516991\pi$
$110$	668.215	0.579198
$111$	−508.113	−0.434486
$112$	−2379.25	−2.00730
$113$	−1918.51	−1.59715	−0.798577	−	0.601892i	$-0.794414\pi$
$113$	−1918.51	−1.59715	−0.798577	+	0.601892i	$0.794414\pi$
$114$	460.839	0.378610
$115$	−2093.25	−1.69736
$116$	93.1126	0.0745283
$117$	2013.13	1.59072
$118$	−2166.95	−1.69054
$119$	926.305	0.713565
$120$	−3352.77	−2.55054
$121$	121.000	0.0909091
$122$	−1808.04	−1.34174
$123$	803.485	0.589007
$124$	−12.4086	−0.00898648
$125$	−3104.13	−2.22113
$126$	3753.50	2.65387
$127$	2419.55	1.69056	0.845278	−	0.534328i	$-0.179435\pi$
$127$	2419.55	1.69056	0.845278	+	0.534328i	$0.179435\pi$
$128$	1676.78	1.15787
$129$	470.462	0.321100
$130$	−3264.22	−2.20224
$131$	1561.14	1.04120	0.520601	−	0.853800i	$-0.325708\pi$
$131$	1561.14	1.04120	0.520601	+	0.853800i	$0.325708\pi$
$132$	99.4312	0.0655635
$133$	−630.141	−0.410828
$134$	1971.52	1.27100
$135$	1689.47	1.07708
$136$	−579.999	−0.365695
$137$	1187.46	0.740522	0.370261	−	0.928928i	$-0.379268\pi$
$137$	1187.46	0.740522	0.370261	+	0.928928i	$0.379268\pi$
$138$	−2524.81	−1.55744
$139$	−1577.59	−0.962655	−0.481327	−	0.876541i	$-0.659845\pi$
$139$	−1577.59	−0.962655	−0.481327	+	0.876541i	$0.659845\pi$
$140$	−750.831	−0.453263
$141$	2590.72	1.54736
$142$	1743.30	1.03024
$143$	−591.083	−0.345656
$144$	−2687.65	−1.55535
$145$	−1663.12	−0.952517
$146$	3331.03	1.88821
$147$	−6077.41	−3.40991
$148$	71.2478	0.0395712
$149$	−2126.58	−1.16924	−0.584618	−	0.811308i	$-0.698756\pi$
$149$	−2126.58	−1.16924	−0.584618	+	0.811308i	$0.698756\pi$
$150$	−6775.93	−3.68835
$151$	−2279.54	−1.22852	−0.614260	−	0.789104i	$-0.710545\pi$
$151$	−2279.54	−1.22852	−0.614260	+	0.789104i	$0.710545\pi$
$152$	394.557	0.210545
$153$	1046.37	0.552903
$154$	−1102.08	−0.576676
$155$	221.635	0.114853
$156$	−485.720	−0.249287
$157$	−3165.23	−1.60900	−0.804501	−	0.593952i	$-0.797567\pi$
$157$	−3165.23	−1.60900	−0.804501	+	0.593952i	$0.797567\pi$
$158$	3100.86	1.56134
$159$	−3845.26	−1.91792
$160$	1017.25	0.502629
$161$	3452.37	1.68997
$162$	−1017.95	−0.493690
$163$	−386.062	−0.185514	−0.0927569	−	0.995689i	$-0.529568\pi$
$163$	−386.062	−0.185514	−0.0927569	+	0.995689i	$0.529568\pi$
$164$	−112.665	−0.0536443
$165$	−1775.98	−0.837941
$166$	3951.06	1.84736
$167$	−3129.08	−1.44991	−0.724957	−	0.688794i	$-0.758141\pi$
$167$	−3129.08	−1.44991	−0.724957	+	0.688794i	$0.758141\pi$
$168$	5529.68	2.53943
$169$	690.430	0.314260
$170$	−1696.66	−0.765456
$171$	−711.819	−0.318328
$172$	−65.9685	−0.0292445
$173$	−1068.60	−0.469618	−0.234809	−	0.972041i	$-0.575447\pi$
$173$	−1068.60	−0.469618	−0.234809	+	0.972041i	$0.575447\pi$
$174$	−2006.01	−0.873995
$175$	9265.26	4.00222
$176$	789.130	0.337971
$177$	5759.33	2.44575
$178$	15.6518	0.00659074
$179$	4264.59	1.78073	0.890363	−	0.455250i	$-0.150450\pi$
$179$	4264.59	1.78073	0.890363	+	0.455250i	$0.150450\pi$
$180$	−848.153	−0.351209
$181$	−81.3880	−0.0334228	−0.0167114	−	0.999860i	$-0.505320\pi$
$181$	−81.3880	−0.0334228	−0.0167114	+	0.999860i	$0.505320\pi$
$182$	5383.64	2.19265
$183$	4805.42	1.94113
$184$	−2161.68	−0.866092
$185$	−1272.59	−0.505744
$186$	267.329	0.105385
$187$	−307.230	−0.120144
$188$	−363.272	−0.140927
$189$	−2786.42	−1.07239
$190$	1154.19	0.440704
$191$	−3976.16	−1.50631	−0.753154	−	0.657844i	$-0.771469\pi$
$191$	−3976.16	−1.50631	−0.753154	+	0.657844i	$0.771469\pi$
$192$	−3380.95	−1.27083
$193$	2762.18	1.03019	0.515094	−	0.857134i	$-0.327757\pi$
$193$	2762.18	1.03019	0.515094	+	0.857134i	$0.327757\pi$
$194$	1016.35	0.376131
$195$	8675.66	3.18603
$196$	852.179	0.310561
$197$	1765.73	0.638593	0.319297	−	0.947655i	$-0.396553\pi$
$197$	1765.73	0.638593	0.319297	+	0.947655i	$0.396553\pi$
$198$	−1244.93	−0.446835
$199$	2717.24	0.967940	0.483970	−	0.875085i	$-0.339194\pi$
$199$	2717.24	0.967940	0.483970	+	0.875085i	$0.339194\pi$
$200$	−5801.37	−2.05109
$201$	−5239.91	−1.83878
$202$	1814.26	0.631935
$203$	2742.97	0.948369
$204$	−252.465	−0.0866473
$205$	2012.36	0.685607
$206$	1716.74	0.580637
$207$	3899.87	1.30947
$208$	−3854.89	−1.28504
$209$	209.000	0.0691714
$210$	16175.8	5.31542
$211$	1179.97	0.384988	0.192494	−	0.981298i	$-0.438342\pi$
$211$	1179.97	0.384988	0.192494	+	0.981298i	$0.438342\pi$
$212$	539.185	0.174676
$213$	−4633.35	−1.49048
$214$	1093.61	0.349333
$215$	1178.29	0.373762
$216$	1744.70	0.549590
$217$	−365.540	−0.114352
$218$	−366.843	−0.113971
$219$	−8853.24	−2.73172
$220$	249.030	0.0763163
$221$	1500.81	0.456812
$222$	−1534.96	−0.464052
$223$	2626.18	0.788618	0.394309	−	0.918978i	$-0.370984\pi$
$223$	2626.18	0.788618	0.394309	+	0.918978i	$0.370984\pi$
$224$	−1677.74	−0.500440
$225$	10466.2	3.10110
$226$	−5795.63	−1.70584
$227$	−1059.38	−0.309751	−0.154876	−	0.987934i	$-0.549498\pi$
$227$	−1059.38	−0.309751	−0.154876	+	0.987934i	$0.549498\pi$
$228$	171.745	0.0498863
$229$	−1748.59	−0.504586	−0.252293	−	0.967651i	$-0.581185\pi$
$229$	−1748.59	−0.504586	−0.252293	+	0.967651i	$0.581185\pi$
$230$	−6323.50	−1.81287
$231$	2929.11	0.834291
$232$	−1717.49	−0.486029
$233$	587.803	0.165271	0.0826357	−	0.996580i	$-0.473666\pi$
$233$	587.803	0.165271	0.0826357	+	0.996580i	$0.473666\pi$
$234$	6081.46	1.69896
$235$	6488.56	1.80114
$236$	−807.576	−0.222749
$237$	−8241.48	−2.25883
$238$	2798.27	0.762123
$239$	4392.65	1.18886	0.594428	−	0.804149i	$-0.297378\pi$
$239$	4392.65	1.18886	0.594428	+	0.804149i	$0.297378\pi$
$240$	−11582.5	−3.11520
$241$	−439.180	−0.117386	−0.0586931	−	0.998276i	$-0.518693\pi$
$241$	−439.180	−0.117386	−0.0586931	+	0.998276i	$0.518693\pi$
$242$	365.529	0.0970953
$243$	4973.95	1.31308
$244$	−673.818	−0.176790
$245$	−15221.1	−3.96915
$246$	2427.25	0.629088
$247$	−1020.96	−0.263005
$248$	228.880	0.0586044
$249$	−10501.1	−2.67262
$250$	−9377.25	−2.37228
$251$	1482.33	0.372764	0.186382	−	0.982477i	$-0.440324\pi$
$251$	1482.33	0.372764	0.186382	+	0.982477i	$0.440324\pi$
$252$	1398.85	0.349679
$253$	−1145.06	−0.284542
$254$	7309.22	1.80560
$255$	4509.38	1.10741
$256$	1696.63	0.414216
$257$	−3958.76	−0.960860	−0.480430	−	0.877033i	$-0.659519\pi$
$257$	−3958.76	−0.960860	−0.480430	+	0.877033i	$0.659519\pi$
$258$	1421.22	0.342951
$259$	2098.87	0.503541
$260$	−1216.51	−0.290171
$261$	3098.51	0.734840
$262$	4716.04	1.11205
$263$	−5878.13	−1.37818	−0.689089	−	0.724677i	$-0.741989\pi$
$263$	−5878.13	−1.37818	−0.689089	+	0.724677i	$0.741989\pi$
$264$	−1834.04	−0.427565
$265$	−9630.62	−2.23247
$266$	−1903.59	−0.438784
$267$	−41.5994	−0.00953499
$268$	734.744	0.167469
$269$	2753.10	0.624014	0.312007	−	0.950080i	$-0.398999\pi$
$269$	2753.10	0.624014	0.312007	+	0.950080i	$0.398999\pi$
$270$	5103.72	1.15038
$271$	2057.27	0.461145	0.230572	−	0.973055i	$-0.425940\pi$
$271$	2057.27	0.461145	0.230572	+	0.973055i	$0.425940\pi$
$272$	−2003.67	−0.446656
$273$	−14308.7	−3.17216
$274$	3587.20	0.790914
$275$	−3073.03	−0.673857
$276$	−940.945	−0.205211
$277$	787.784	0.170879	0.0854393	−	0.996343i	$-0.472771\pi$
$277$	787.784	0.170879	0.0854393	+	0.996343i	$0.472771\pi$
$278$	−4765.72	−1.02816
$279$	−412.921	−0.0886055
$280$	13849.3	2.95591
$281$	1496.27	0.317652	0.158826	−	0.987307i	$-0.449229\pi$
$281$	1496.27	0.317652	0.158826	+	0.987307i	$0.449229\pi$
$282$	7826.30	1.65266
$283$	8586.05	1.80349	0.901745	−	0.432268i	$-0.142287\pi$
$283$	8586.05	1.80349	0.901745	+	0.432268i	$0.142287\pi$
$284$	649.691	0.135747
$285$	−3067.61	−0.637577
$286$	−1785.60	−0.369178
$287$	−3318.96	−0.682621
$288$	−1895.20	−0.387764
$289$	−4132.92	−0.841221
$290$	−5024.13	−1.01733
$291$	−2701.25	−0.544158
$292$	1241.41	0.248794
$293$	1971.90	0.393173	0.196586	−	0.980486i	$-0.437014\pi$
$293$	1971.90	0.393173	0.196586	+	0.980486i	$0.437014\pi$
$294$	−18359.2	−3.64195
$295$	14424.5	2.84687
$296$	−1314.19	−0.258059
$297$	924.179	0.180560
$298$	−6424.18	−1.24880
$299$	5593.58	1.08189
$300$	−2525.25	−0.485984
$301$	−1943.34	−0.372135
$302$	−6886.27	−1.31212
$303$	−4821.95	−0.914236
$304$	1363.04	0.257158
$305$	12035.4	2.25949
$306$	3160.98	0.590528
$307$	−7238.32	−1.34564	−0.672822	−	0.739804i	$-0.734918\pi$
$307$	−7238.32	−1.34564	−0.672822	+	0.739804i	$0.734918\pi$
$308$	−410.722	−0.0759839
$309$	−4562.77	−0.840023
$310$	669.537	0.122668
$311$	2043.10	0.372520	0.186260	−	0.982500i	$-0.440363\pi$
$311$	2043.10	0.372520	0.186260	+	0.982500i	$0.440363\pi$
$312$	8959.25	1.62570
$313$	−4268.16	−0.770769	−0.385384	−	0.922756i	$-0.625931\pi$
$313$	−4268.16	−0.770769	−0.385384	+	0.922756i	$0.625931\pi$
$314$	−9561.85	−1.71849
$315$	−24985.4	−4.46911
$316$	1155.63	0.205725
$317$	−1484.41	−0.263006	−0.131503	−	0.991316i	$-0.541980\pi$
$317$	−1484.41	−0.263006	−0.131503	+	0.991316i	$0.541980\pi$
$318$	−11616.1	−2.04843
$319$	−909.767	−0.159678
$320$	−8467.73	−1.47925
$321$	−2906.59	−0.505389
$322$	10429.3	1.80497
$323$	−530.669	−0.0914156
$324$	−379.369	−0.0650495
$325$	15011.7	2.56215
$326$	−1166.26	−0.198138
$327$	974.998	0.164885
$328$	2078.14	0.349836
$329$	−10701.5	−1.79329
$330$	−5365.07	−0.894962
$331$	−6834.20	−1.13487	−0.567434	−	0.823419i	$-0.692064\pi$
$331$	−6834.20	−1.13487	−0.567434	+	0.823419i	$0.692064\pi$
$332$	1472.48	0.243412
$333$	2370.92	0.390167
$334$	−9452.64	−1.54858
$335$	−13123.6	−2.14035
$336$	19102.9	3.10163
$337$	3538.42	0.571959	0.285979	−	0.958236i	$-0.407681\pi$
$337$	3538.42	0.571959	0.285979	+	0.958236i	$0.407681\pi$
$338$	2085.72	0.335645
$339$	15403.7	2.46788
$340$	−632.308	−0.100858
$341$	121.239	0.0192536
$342$	−2150.33	−0.339990
$343$	13728.3	2.16111
$344$	1216.81	0.190715
$345$	16806.6	2.62272
$346$	−3228.13	−0.501575
$347$	4587.35	0.709688	0.354844	−	0.934926i	$-0.384534\pi$
$347$	4587.35	0.709688	0.354844	+	0.934926i	$0.384534\pi$
$348$	−747.597	−0.115159
$349$	−4643.30	−0.712178	−0.356089	−	0.934452i	$-0.615890\pi$
$349$	−4643.30	−0.712178	−0.356089	+	0.934452i	$0.615890\pi$
$350$	27989.4	4.27456
$351$	−4514.60	−0.686528
$352$	556.458	0.0842594
$353$	−10052.1	−1.51564	−0.757821	−	0.652462i	$-0.773736\pi$
$353$	−10052.1	−1.51564	−0.757821	+	0.652462i	$0.773736\pi$
$354$	17398.3	2.61218
$355$	−11604.4	−1.73493
$356$	5.83309	0.000868408 0
$357$	−7437.27	−1.10258
$358$	12882.9	1.90190
$359$	−3099.77	−0.455709	−0.227854	−	0.973695i	$-0.573171\pi$
$359$	−3099.77	−0.455709	−0.227854	+	0.973695i	$0.573171\pi$
$360$	15644.4	2.29037
$361$	361.000	0.0526316
$362$	−245.865	−0.0356971
$363$	−971.504	−0.140470
$364$	2006.37	0.288907
$365$	−22173.3	−3.17974
$366$	14516.7	2.07322
$367$	1900.26	0.270280	0.135140	−	0.990827i	$-0.456852\pi$
$367$	1900.26	0.270280	0.135140	+	0.990827i	$0.456852\pi$
$368$	−7467.75	−1.05784
$369$	−3749.17	−0.528926
$370$	−3844.36	−0.540159
$371$	15883.7	2.22274
$372$	99.6279	0.0138857
$373$	−3441.59	−0.477745	−0.238872	−	0.971051i	$-0.576778\pi$
$373$	−3441.59	−0.477745	−0.238872	+	0.971051i	$0.576778\pi$
$374$	−928.109	−0.128319
$375$	24922.9	3.43204
$376$	6700.66	0.919043
$377$	4444.20	0.607129
$378$	−8417.50	−1.14537
$379$	9560.54	1.29576	0.647878	−	0.761744i	$-0.275656\pi$
$379$	9560.54	1.29576	0.647878	+	0.761744i	$0.275656\pi$
$380$	430.142	0.0580680
$381$	−19426.5	−2.61220
$382$	−12011.6	−1.60881
$383$	−4409.84	−0.588335	−0.294168	−	0.955754i	$-0.595042\pi$
$383$	−4409.84	−0.588335	−0.294168	+	0.955754i	$0.595042\pi$
$384$	−13462.8	−1.78912
$385$	7336.08	0.971120
$386$	8344.27	1.10029
$387$	−2195.24	−0.288347
$388$	378.771	0.0495597
$389$	10734.7	1.39916	0.699578	−	0.714556i	$-0.253371\pi$
$389$	10734.7	1.39916	0.699578	+	0.714556i	$0.253371\pi$
$390$	26208.3	3.40284
$391$	2907.40	0.376044
$392$	−15718.7	−2.02529
$393$	−12534.3	−1.60884
$394$	5334.08	0.682049
$395$	−20641.1	−2.62929
$396$	−463.959	−0.0588758
$397$	−7337.36	−0.927586	−0.463793	−	0.885944i	$-0.653512\pi$
$397$	−7337.36	−0.927586	−0.463793	+	0.885944i	$0.653512\pi$
$398$	8208.50	1.03381
$399$	5059.37	0.634800
$400$	−20041.5	−2.50519
$401$	10828.0	1.34844	0.674221	−	0.738530i	$-0.264480\pi$
$401$	10828.0	1.34844	0.674221	+	0.738530i	$0.264480\pi$
$402$	−15829.2	−1.96391
$403$	−592.252	−0.0732064
$404$	676.136	0.0832649
$405$	6776.07	0.831372
$406$	8286.24	1.01290
$407$	−696.135	−0.0847816
$408$	4656.78	0.565062
$409$	2281.31	0.275803	0.137901	−	0.990446i	$-0.455964\pi$
$409$	2281.31	0.275803	0.137901	+	0.990446i	$0.455964\pi$
$410$	6079.14	0.732262
$411$	−9534.07	−1.14424
$412$	639.795	0.0765059
$413$	−23790.1	−2.83447
$414$	11781.1	1.39857
$415$	−26300.6	−3.11095
$416$	−2718.29	−0.320373
$417$	12666.4	1.48747
$418$	631.368	0.0738785
$419$	6420.27	0.748570	0.374285	−	0.927314i	$-0.377888\pi$
$419$	6420.27	0.748570	0.374285	+	0.927314i	$0.377888\pi$
$420$	6028.39	0.700370
$421$	9310.51	1.07783	0.538915	−	0.842360i	$-0.318834\pi$
$421$	9310.51	1.07783	0.538915	+	0.842360i	$0.318834\pi$
$422$	3564.57	0.411186
$423$	−12088.6	−1.38953
$424$	−9945.42	−1.13913
$425$	7802.69	0.890555
$426$	−13996.9	−1.59190
$427$	−19849.8	−2.24964
$428$	407.564	0.0460288
$429$	4745.78	0.534099
$430$	3559.50	0.399196
$431$	6421.57	0.717671	0.358836	−	0.933401i	$-0.383174\pi$
$431$	6421.57	0.717671	0.358836	+	0.933401i	$0.383174\pi$
$432$	6027.25	0.671264
$433$	−6990.77	−0.775878	−0.387939	−	0.921685i	$-0.626813\pi$
$433$	−6990.77	−0.775878	−0.387939	+	0.921685i	$0.626813\pi$
$434$	−1104.26	−0.122134
$435$	13353.2	1.47180
$436$	−136.715	−0.0150171
$437$	−1977.82	−0.216504
$438$	−26744.7	−2.91761
$439$	5319.50	0.578327	0.289164	−	0.957280i	$-0.406623\pi$
$439$	5319.50	0.578327	0.289164	+	0.957280i	$0.406623\pi$
$440$	−4593.43	−0.497689
$441$	28358.0	3.06209
$442$	4533.80	0.487898
$443$	104.923	0.0112529	0.00562647	−	0.999984i	$-0.498209\pi$
$443$	104.923	0.0112529	0.00562647	+	0.999984i	$0.498209\pi$
$444$	−572.046	−0.0611444
$445$	−104.187	−0.0110988
$446$	7933.42	0.842283
$447$	17074.2	1.80667
$448$	13965.7	1.47281
$449$	16239.5	1.70689	0.853443	−	0.521186i	$-0.174510\pi$
$449$	16239.5	1.70689	0.853443	+	0.521186i	$0.174510\pi$
$450$	31617.4	3.31213
$451$	1100.81	0.114933
$452$	−2159.91	−0.224765
$453$	18302.4	1.89828
$454$	−3200.28	−0.330830
$455$	−35836.6	−3.69241
$456$	−3167.88	−0.325329
$457$	994.277	0.101773	0.0508865	−	0.998704i	$-0.483795\pi$
$457$	994.277	0.101773	0.0508865	+	0.998704i	$0.483795\pi$
$458$	−5282.31	−0.538922
$459$	−2346.57	−0.238624
$460$	−2356.64	−0.238867
$461$	−8645.56	−0.873458	−0.436729	−	0.899593i	$-0.643863\pi$
$461$	−8645.56	−0.873458	−0.436729	+	0.899593i	$0.643863\pi$
$462$	8848.54	0.891064
$463$	4818.01	0.483611	0.241806	−	0.970325i	$-0.422260\pi$
$463$	4818.01	0.483611	0.241806	+	0.970325i	$0.422260\pi$
$464$	−5933.26	−0.593631
$465$	−1779.50	−0.177467
$466$	1775.69	0.176518
$467$	−6978.48	−0.691489	−0.345745	−	0.938329i	$-0.612374\pi$
$467$	−6978.48	−0.691489	−0.345745	+	0.938329i	$0.612374\pi$
$468$	2266.43	0.223859
$469$	21644.6	2.13103
$470$	19601.3	1.92370
$471$	25413.5	2.48619
$472$	14896.0	1.45263
$473$	644.553	0.0626566
$474$	−24896.7	−2.41254
$475$	−5307.96	−0.512728
$476$	1042.86	0.100419
$477$	17942.5	1.72228
$478$	13269.7	1.26976
$479$	7316.33	0.697895	0.348947	−	0.937142i	$-0.386539\pi$
$479$	7316.33	0.697895	0.348947	+	0.937142i	$0.386539\pi$
$480$	−8167.45	−0.776649
$481$	3400.61	0.322358
$482$	−1326.72	−0.125374
$483$	−27719.0	−2.61130
$484$	136.225	0.0127935
$485$	−6765.39	−0.633403
$486$	15025.8	1.40244
$487$	1795.41	0.167059	0.0835293	−	0.996505i	$-0.473381\pi$
$487$	1795.41	0.167059	0.0835293	+	0.996505i	$0.473381\pi$
$488$	12428.8	1.15292
$489$	3099.68	0.286651
$490$	−45981.5	−4.23925
$491$	−13897.1	−1.27733	−0.638664	−	0.769486i	$-0.720513\pi$
$491$	−13897.1	−1.27733	−0.638664	+	0.769486i	$0.720513\pi$
$492$	904.584	0.0828898
$493$	2309.98	0.211027
$494$	−3084.22	−0.280902
$495$	8286.97	0.752468
$496$	790.691	0.0715788
$497$	19139.0	1.72737
$498$	−31722.9	−2.85449
$499$	−11916.6	−1.06906	−0.534528	−	0.845151i	$-0.679511\pi$
$499$	−11916.6	−1.06906	−0.534528	+	0.845151i	$0.679511\pi$
$500$	−3494.70	−0.312576
$501$	25123.3	2.24037
$502$	4477.97	0.398130
$503$	10936.1	0.969419	0.484709	−	0.874675i	$-0.338925\pi$
$503$	10936.1	0.969419	0.484709	+	0.874675i	$0.338925\pi$
$504$	−25802.2	−2.28040
$505$	−12076.8	−1.06418
$506$	−3459.10	−0.303904
$507$	−5543.43	−0.485587
$508$	2723.99	0.237909
$509$	9826.31	0.855685	0.427842	−	0.903853i	$-0.359274\pi$
$509$	9826.31	0.855685	0.427842	+	0.903853i	$0.359274\pi$
$510$	13622.4	1.18276
$511$	36570.2	3.16589
$512$	−8288.91	−0.715471
$513$	1596.31	0.137385
$514$	−11959.0	−1.02624
$515$	−11427.7	−0.977791
$516$	529.658	0.0451878
$517$	3549.39	0.301938
$518$	6340.46	0.537807
$519$	8579.73	0.725642
$520$	22438.8	1.89232
$521$	−4280.73	−0.359965	−0.179983	−	0.983670i	$-0.557604\pi$
$521$	−4280.73	−0.359965	−0.179983	+	0.983670i	$0.557604\pi$
$522$	9360.29	0.784845
$523$	16829.3	1.40706	0.703530	−	0.710665i	$-0.251606\pi$
$523$	16829.3	1.40706	0.703530	+	0.710665i	$0.251606\pi$
$524$	1757.57	0.146526
$525$	−74390.4	−6.18412
$526$	−17757.2	−1.47196
$527$	−307.837	−0.0254452
$528$	−6335.89	−0.522224
$529$	−1331.03	−0.109396
$530$	−29093.1	−2.38438
$531$	−26873.8	−2.19628
$532$	−709.428	−0.0578151
$533$	−5377.43	−0.437002
$534$	−125.668	−0.0101838
$535$	−7279.67	−0.588276
$536$	−13552.6	−1.09213
$537$	−34240.2	−2.75153
$538$	8316.84	0.666477
$539$	−8326.30	−0.665379
$540$	1902.05	0.151576
$541$	−17854.5	−1.41890	−0.709450	−	0.704756i	$-0.751056\pi$
$541$	−17854.5	−1.41890	−0.709450	+	0.704756i	$0.751056\pi$
$542$	6214.80	0.492525
$543$	653.460	0.0516440
$544$	−1412.90	−0.111356
$545$	2441.92	0.191927
$546$	−43225.0	−3.38802
$547$	−707.278	−0.0552852	−0.0276426	−	0.999618i	$-0.508800\pi$
$547$	−707.278	−0.0552852	−0.0276426	+	0.999618i	$0.508800\pi$
$548$	1336.87	0.104212
$549$	−22422.7	−1.74313
$550$	−9283.30	−0.719712
$551$	−1571.42	−0.121496
$552$	17356.0	1.33826
$553$	34043.2	2.61783
$554$	2379.82	0.182507
$555$	10217.6	0.781462
$556$	−1776.09	−0.135473
$557$	2995.26	0.227851	0.113926	−	0.993489i	$-0.463657\pi$
$557$	2995.26	0.227851	0.113926	+	0.993489i	$0.463657\pi$
$558$	−1247.39	−0.0946350
$559$	−3148.63	−0.238234
$560$	47844.0	3.61032
$561$	2466.73	0.185643
$562$	4520.09	0.339268
$563$	15356.0	1.14952	0.574758	−	0.818323i	$-0.305096\pi$
$563$	15356.0	1.14952	0.574758	+	0.818323i	$0.305096\pi$
$564$	2916.70	0.217757
$565$	38579.1	2.87263
$566$	25937.6	1.92622
$567$	−11175.7	−0.827751
$568$	−11983.7	−0.885259
$569$	−4459.09	−0.328532	−0.164266	−	0.986416i	$-0.552526\pi$
$569$	−4459.09	−0.328532	−0.164266	+	0.986416i	$0.552526\pi$
$570$	−9266.94	−0.680964
$571$	20286.6	1.48681	0.743404	−	0.668842i	$-0.233210\pi$
$571$	20286.6	1.48681	0.743404	+	0.668842i	$0.233210\pi$
$572$	−665.456	−0.0486436
$573$	31924.4	2.32751
$574$	−10026.3	−0.729073
$575$	29080.9	2.10914
$576$	15775.9	1.14120
$577$	−48.7580	−0.00351789	−0.00175895	−	0.999998i	$-0.500560\pi$
$577$	−48.7580	−0.00351789	−0.00175895	+	0.999998i	$0.500560\pi$
$578$	−12485.1	−0.898465
$579$	−22177.4	−1.59182
$580$	−1872.39	−0.134046
$581$	43377.2	3.09740
$582$	−8160.19	−0.581187
$583$	−5268.16	−0.374245
$584$	−22898.1	−1.62248
$585$	−40481.7	−2.86105
$586$	5956.91	0.419928
$587$	8763.15	0.616174	0.308087	−	0.951358i	$-0.400311\pi$
$587$	8763.15	0.616174	0.308087	+	0.951358i	$0.400311\pi$
$588$	−6842.10	−0.479870
$589$	209.413	0.0146498
$590$	43574.9	3.04059
$591$	−14177.0	−0.986738
$592$	−4540.01	−0.315191
$593$	−9164.58	−0.634644	−0.317322	−	0.948318i	$-0.602784\pi$
$593$	−9164.58	−0.634644	−0.317322	+	0.948318i	$0.602784\pi$
$594$	2791.85	0.192847
$595$	−18626.9	−1.28341
$596$	−2394.16	−0.164545
$597$	−21816.6	−1.49563
$598$	16897.6	1.15551
$599$	−11023.0	−0.751896	−0.375948	−	0.926641i	$-0.622683\pi$
$599$	−11023.0	−0.751896	−0.375948	+	0.926641i	$0.622683\pi$
$600$	46578.9	3.16930
$601$	7851.38	0.532886	0.266443	−	0.963851i	$-0.414152\pi$
$601$	7851.38	0.532886	0.266443	+	0.963851i	$0.414152\pi$
$602$	−5870.64	−0.397458
$603$	24450.1	1.65122
$604$	−2566.37	−0.172887
$605$	−2433.17	−0.163508
$606$	−14566.6	−0.976449
$607$	16438.8	1.09923	0.549613	−	0.835419i	$-0.314775\pi$
$607$	16438.8	1.09923	0.549613	+	0.835419i	$0.314775\pi$
$608$	961.155	0.0641118
$609$	−22023.2	−1.46539
$610$	36357.6	2.41324
$611$	−17338.7	−1.14803
$612$	1178.03	0.0778090
$613$	2609.28	0.171921	0.0859606	−	0.996299i	$-0.472604\pi$
$613$	2609.28	0.171921	0.0859606	+	0.996299i	$0.472604\pi$
$614$	−21866.2	−1.43721
$615$	−16157.2	−1.05938
$616$	7575.88	0.495521
$617$	−10673.7	−0.696443	−0.348222	−	0.937412i	$-0.613214\pi$
$617$	−10673.7	−0.696443	−0.348222	+	0.937412i	$0.613214\pi$
$618$	−13783.7	−0.897185
$619$	−14303.1	−0.928739	−0.464369	−	0.885642i	$-0.653719\pi$
$619$	−14303.1	−0.928739	−0.464369	+	0.885642i	$0.653719\pi$
$620$	249.522	0.0161630
$621$	−8745.75	−0.565145
$622$	6172.01	0.397870
$623$	171.835	0.0110504
$624$	30950.7	1.98561
$625$	27499.7	1.75998
$626$	−12893.7	−0.823219
$627$	−1678.05	−0.106882
$628$	−3563.50	−0.226432
$629$	1767.55	0.112046
$630$	−75478.5	−4.77323
$631$	−11490.5	−0.724927	−0.362463	−	0.931998i	$-0.618064\pi$
$631$	−11490.5	−0.724927	−0.362463	+	0.931998i	$0.618064\pi$
$632$	−21315.8	−1.34161
$633$	−9473.94	−0.594874
$634$	−4484.26	−0.280903
$635$	−48654.4	−3.04062
$636$	−4329.09	−0.269905
$637$	40673.9	2.52992
$638$	−2748.31	−0.170544
$639$	21619.8	1.33845
$640$	−33718.1	−2.08254
$641$	−14840.9	−0.914477	−0.457238	−	0.889344i	$-0.651161\pi$
$641$	−14840.9	−0.914477	−0.457238	+	0.889344i	$0.651161\pi$
$642$	−8780.51	−0.539781
$643$	−5505.56	−0.337664	−0.168832	−	0.985645i	$-0.554000\pi$
$643$	−5505.56	−0.337664	−0.168832	+	0.985645i	$0.554000\pi$
$644$	3886.77	0.237826
$645$	−9460.46	−0.577528
$646$	−1603.10	−0.0976363
$647$	−3214.30	−0.195312	−0.0976561	−	0.995220i	$-0.531135\pi$
$647$	−3214.30	−0.195312	−0.0976561	+	0.995220i	$0.531135\pi$
$648$	6997.57	0.424214
$649$	7890.52	0.477242
$650$	45348.8	2.73650
$651$	2934.90	0.176694
$652$	−434.639	−0.0261070
$653$	−25969.5	−1.55630	−0.778151	−	0.628077i	$-0.783842\pi$
$653$	−25969.5	−1.55630	−0.778151	+	0.628077i	$0.783842\pi$
$654$	2945.37	0.176106
$655$	−31392.7	−1.87270
$656$	7179.18	0.427286
$657$	41310.4	2.45308
$658$	−32328.2	−1.91532
$659$	23185.8	1.37054	0.685272	−	0.728287i	$-0.259683\pi$
$659$	23185.8	1.37054	0.685272	+	0.728287i	$0.259683\pi$
$660$	−1999.45	−0.117922
$661$	−17201.4	−1.01219	−0.506094	−	0.862478i	$-0.668911\pi$
$661$	−17201.4	−1.01219	−0.506094	+	0.862478i	$0.668911\pi$
$662$	−20645.4	−1.21210
$663$	−12049.9	−0.705854
$664$	−27160.3	−1.58738
$665$	12671.4	0.738911
$666$	7162.30	0.416717
$667$	8609.37	0.499784
$668$	−3522.80	−0.204044
$669$	−21085.5	−1.21855
$670$	−39645.0	−2.28600
$671$	6583.62	0.378775
$672$	13470.5	0.773266
$673$	17592.1	1.00762	0.503809	−	0.863815i	$-0.331931\pi$
$673$	17592.1	1.00762	0.503809	+	0.863815i	$0.331931\pi$
$674$	10689.2	0.610880
$675$	−23471.3	−1.33839
$676$	777.304	0.0442253
$677$	18276.0	1.03752	0.518762	−	0.854919i	$-0.326393\pi$
$677$	18276.0	1.03752	0.518762	+	0.854919i	$0.326393\pi$
$678$	46532.9	2.63582
$679$	11158.1	0.630644
$680$	11663.1	0.657735
$681$	8505.72	0.478620
$682$	366.252	0.0205638
$683$	19656.4	1.10122	0.550610	−	0.834763i	$-0.314395\pi$
$683$	19656.4	1.10122	0.550610	+	0.834763i	$0.314395\pi$
$684$	−801.384	−0.0447978
$685$	−23878.5	−1.33190
$686$	41471.9	2.30817
$687$	14039.4	0.779673
$688$	4203.60	0.232937
$689$	25734.9	1.42296
$690$	50771.1	2.80119
$691$	−16507.6	−0.908794	−0.454397	−	0.890799i	$-0.650145\pi$
$691$	−16507.6	−0.908794	−0.454397	+	0.890799i	$0.650145\pi$
$692$	−1203.05	−0.0660885
$693$	−13667.6	−0.749191
$694$	13857.9	0.757981
$695$	31723.4	1.73142
$696$	13789.6	0.750999
$697$	−2795.05	−0.151894
$698$	−14026.9	−0.760641
$699$	−4719.44	−0.255373
$700$	10431.1	0.563225
$701$	−17434.9	−0.939381	−0.469690	−	0.882831i	$-0.655634\pi$
$701$	−17434.9	−0.939381	−0.469690	+	0.882831i	$0.655634\pi$
$702$	−13638.1	−0.733245
$703$	−1202.41	−0.0645092
$704$	−4632.04	−0.247978
$705$	−52096.4	−2.78307
$706$	−30366.5	−1.61878
$707$	19918.1	1.05954
$708$	6484.00	0.344186
$709$	−7296.09	−0.386475	−0.193237	−	0.981152i	$-0.561899\pi$
$709$	−7296.09	−0.386475	−0.193237	+	0.981152i	$0.561899\pi$
$710$	−35055.8	−1.85299
$711$	38455.8	2.02842
$712$	−107.593	−0.00566324
$713$	−1147.32	−0.0602630
$714$	−22467.2	−1.17761
$715$	11886.0	0.621694
$716$	4801.18	0.250598
$717$	−35268.4	−1.83699
$718$	−9364.08	−0.486719
$719$	23481.2	1.21794	0.608972	−	0.793192i	$-0.291582\pi$
$719$	23481.2	1.21794	0.608972	+	0.793192i	$0.291582\pi$
$720$	54045.5	2.79744
$721$	18847.5	0.973533
$722$	1090.54	0.0562131
$723$	3526.16	0.181382
$724$	−91.6286	−0.00470352
$725$	23105.3	1.18360
$726$	−2934.81	−0.150029
$727$	−37543.3	−1.91527	−0.957637	−	0.287979i	$-0.907017\pi$
$727$	−37543.3	−1.91527	−0.957637	+	0.287979i	$0.907017\pi$
$728$	−37008.1	−1.88408
$729$	−30837.5	−1.56671
$730$	−66983.3	−3.39611
$731$	−1636.58	−0.0828057
$732$	5410.06	0.273171
$733$	−27235.8	−1.37241	−0.686205	−	0.727408i	$-0.740725\pi$
$733$	−27235.8	−1.37241	−0.686205	+	0.727408i	$0.740725\pi$
$734$	5740.49	0.288672
$735$	122210.	6.13303
$736$	−5265.92	−0.263729
$737$	−7178.90	−0.358803
$738$	−11325.8	−0.564919
$739$	−941.766	−0.0468788	−0.0234394	−	0.999725i	$-0.507462\pi$
$739$	−941.766	−0.0468788	−0.0234394	+	0.999725i	$0.507462\pi$
$740$	−1432.71	−0.0711724
$741$	8197.26	0.406388
$742$	47982.9	2.37400
$743$	9417.06	0.464978	0.232489	−	0.972599i	$-0.425313\pi$
$743$	9417.06	0.464978	0.232489	+	0.972599i	$0.425313\pi$
$744$	−1837.67	−0.0905539
$745$	42763.1	2.10298
$746$	−10396.7	−0.510255
$747$	48999.7	2.40001
$748$	−345.887	−0.0169076
$749$	12006.3	0.585714
$750$	75289.6	3.66558
$751$	−34968.9	−1.69911	−0.849557	−	0.527498i	$-0.823130\pi$
$751$	−34968.9	−1.69911	−0.849557	+	0.527498i	$0.823130\pi$
$752$	23148.2	1.12251
$753$	−11901.6	−0.575986
$754$	13425.5	0.648444
$755$	45839.0	2.20961
$756$	−3137.03	−0.150916
$757$	−8652.21	−0.415416	−0.207708	−	0.978191i	$-0.566600\pi$
$757$	−8652.21	−0.415416	−0.207708	+	0.978191i	$0.566600\pi$
$758$	28881.4	1.38393
$759$	9193.60	0.439666
$760$	−7934.10	−0.378684
$761$	12889.6	0.613990	0.306995	−	0.951711i	$-0.400676\pi$
$761$	12889.6	0.613990	0.306995	+	0.951711i	$0.400676\pi$
$762$	−58685.4	−2.78996
$763$	−4027.43	−0.191092
$764$	−4476.46	−0.211980
$765$	−21041.4	−0.994447
$766$	−13321.7	−0.628370
$767$	−38545.0	−1.81458
$768$	−13622.1	−0.640035
$769$	−8873.14	−0.416091	−0.208045	−	0.978119i	$-0.566710\pi$
$769$	−8873.14	−0.416091	−0.208045	+	0.978119i	$0.566710\pi$
$770$	22161.5	1.03720
$771$	31784.7	1.48469
$772$	3109.74	0.144976
$773$	−7548.76	−0.351242	−0.175621	−	0.984458i	$-0.556193\pi$
$773$	−7548.76	−0.351242	−0.175621	+	0.984458i	$0.556193\pi$
$774$	−6631.59	−0.307969
$775$	−3079.11	−0.142716
$776$	−6986.54	−0.323199
$777$	−16851.7	−0.778058
$778$	32428.5	1.49437
$779$	1901.39	0.0874513
$780$	9767.27	0.448365
$781$	−6347.88	−0.290839
$782$	8782.95	0.401634
$783$	−6948.65	−0.317145
$784$	−54302.0	−2.47367
$785$	63649.3	2.89394
$786$	−37864.9	−1.71832
$787$	−10222.6	−0.463018	−0.231509	−	0.972833i	$-0.574366\pi$
$787$	−10222.6	−0.463018	−0.231509	+	0.972833i	$0.574366\pi$
$788$	1987.90	0.0898681
$789$	47195.2	2.12952
$790$	−62354.7	−2.80821
$791$	−63628.0	−2.86012
$792$	8557.86	0.383952
$793$	−32160.9	−1.44018
$794$	−22165.4	−0.990707
$795$	77323.8	3.44955
$796$	3059.14	0.136216
$797$	21763.8	0.967268	0.483634	−	0.875270i	$-0.339317\pi$
$797$	21763.8	0.967268	0.483634	+	0.875270i	$0.339317\pi$
$798$	15283.8	0.677998
$799$	−9012.21	−0.399035
$800$	−14132.3	−0.624567
$801$	194.108	0.00856239
$802$	32710.3	1.44020
$803$	−12129.3	−0.533043
$804$	−5899.23	−0.258768
$805$	−69423.3	−3.03956
$806$	−1789.13	−0.0781880
$807$	−22104.5	−0.964209
$808$	−12471.5	−0.543004
$809$	10357.5	0.450124	0.225062	−	0.974344i	$-0.427741\pi$
$809$	10357.5	0.450124	0.225062	+	0.974344i	$0.427741\pi$
$810$	20469.8	0.887946
$811$	33252.4	1.43977	0.719883	−	0.694096i	$-0.244196\pi$
$811$	33252.4	1.43977	0.719883	+	0.694096i	$0.244196\pi$
$812$	3088.11	0.133462
$813$	−16517.7	−0.712548
$814$	−2102.95	−0.0905509
$815$	7763.27	0.333663
$816$	16087.4	0.690161
$817$	1113.32	0.0476745
$818$	6891.60	0.294571
$819$	66766.0	2.84859
$820$	2265.57	0.0964842
$821$	−15293.1	−0.650102	−0.325051	−	0.945697i	$-0.605381\pi$
$821$	−15293.1	−0.650102	−0.325051	+	0.945697i	$0.605381\pi$
$822$	−28801.4	−1.22210
$823$	−38928.2	−1.64879	−0.824393	−	0.566017i	$-0.808484\pi$
$823$	−38928.2	−1.64879	−0.824393	+	0.566017i	$0.808484\pi$
$824$	−11801.2	−0.498925
$825$	24673.2	1.04123
$826$	−71867.5	−3.02735
$827$	27259.5	1.14620	0.573099	−	0.819486i	$-0.305741\pi$
$827$	27259.5	1.14620	0.573099	+	0.819486i	$0.305741\pi$
$828$	4390.57	0.184279
$829$	24738.3	1.03643	0.518213	−	0.855251i	$-0.326597\pi$
$829$	24738.3	1.03643	0.518213	+	0.855251i	$0.326597\pi$
$830$	−79451.3	−3.32265
$831$	−6325.08	−0.264037
$832$	22627.4	0.942867
$833$	21141.2	0.879351
$834$	38263.8	1.58869
$835$	62922.3	2.60780
$836$	235.297	0.00973437
$837$	926.007	0.0382407
$838$	19395.0	0.799510
$839$	30458.1	1.25331	0.626656	−	0.779296i	$-0.284423\pi$
$839$	30458.1	1.25331	0.626656	+	0.779296i	$0.284423\pi$
$840$	−111195.	−4.56739
$841$	−17548.7	−0.719534
$842$	28126.1	1.15117
$843$	−12013.5	−0.490828
$844$	1328.44	0.0541787
$845$	−13883.8	−0.565226
$846$	−36518.5	−1.48408
$847$	4013.00	0.162796
$848$	−34357.6	−1.39133
$849$	−68937.0	−2.78671
$850$	23571.1	0.951156
$851$	6587.71	0.265363
$852$	−5216.34	−0.209752
$853$	12483.2	0.501076	0.250538	−	0.968107i	$-0.419392\pi$
$853$	12483.2	0.501076	0.250538	+	0.968107i	$0.419392\pi$
$854$	−59964.2	−2.40273
$855$	14313.9	0.572543
$856$	−7517.63	−0.300172
$857$	−14799.9	−0.589914	−0.294957	−	0.955511i	$-0.595305\pi$
$857$	−14799.9	−0.589914	−0.294957	+	0.955511i	$0.595305\pi$
$858$	14336.5	0.570444
$859$	−12561.9	−0.498960	−0.249480	−	0.968380i	$-0.580260\pi$
$859$	−12561.9	−0.498960	−0.249480	+	0.968380i	$0.580260\pi$
$860$	1326.55	0.0525989
$861$	26647.8	1.05477
$862$	19398.9	0.766508
$863$	−29702.4	−1.17159	−0.585795	−	0.810460i	$-0.699217\pi$
$863$	−29702.4	−1.17159	−0.585795	+	0.810460i	$0.699217\pi$
$864$	4250.14	0.167353
$865$	21488.3	0.844652
$866$	−21118.4	−0.828675
$867$	33183.0	1.29983
$868$	−411.534	−0.0160926
$869$	−11291.2	−0.440767
$870$	40338.5	1.57196
$871$	35068.8	1.36425
$872$	2521.74	0.0979324
$873$	12604.4	0.488652
$874$	−5974.80	−0.231237
$875$	−102949.	−3.97751
$876$	−9967.20	−0.384430
$877$	−3455.14	−0.133035	−0.0665175	−	0.997785i	$-0.521189\pi$
$877$	−3455.14	−0.133035	−0.0665175	+	0.997785i	$0.521189\pi$
$878$	16069.7	0.617682
$879$	−15832.3	−0.607520
$880$	−15868.5	−0.607872
$881$	25856.9	0.988810	0.494405	−	0.869232i	$-0.335386\pi$
$881$	25856.9	0.988810	0.494405	+	0.869232i	$0.335386\pi$
$882$	85666.6	3.27046
$883$	30864.0	1.17628	0.588140	−	0.808759i	$-0.299860\pi$
$883$	30864.0	1.17628	0.588140	+	0.808759i	$0.299860\pi$
$884$	1689.65	0.0642863
$885$	−115814.	−4.39890
$886$	316.963	0.0120187
$887$	29488.1	1.11625	0.558126	−	0.829756i	$-0.311521\pi$
$887$	29488.1	1.11625	0.558126	+	0.829756i	$0.311521\pi$
$888$	10551.6	0.398747
$889$	80245.1	3.02737
$890$	−314.740	−0.0118540
$891$	3706.66	0.139369
$892$	2956.62	0.110981
$893$	6130.77	0.229740
$894$	51579.5	1.92962
$895$	−85756.0	−3.20280
$896$	55610.9	2.07347
$897$	−44910.6	−1.67171
$898$	49058.0	1.82304
$899$	−911.567	−0.0338181
$900$	11783.1	0.436412
$901$	13376.3	0.494595
$902$	3325.43	0.122755
$903$	15603.0	0.575012
$904$	39840.2	1.46578
$905$	1636.62	0.0601139
$906$	55289.5	2.02745
$907$	−2539.54	−0.0929703	−0.0464851	−	0.998919i	$-0.514802\pi$
$907$	−2539.54	−0.0929703	−0.0464851	+	0.998919i	$0.514802\pi$
$908$	−1192.68	−0.0435908
$909$	22499.8	0.820981
$910$	−108259.	−3.94367
$911$	−38095.0	−1.38545	−0.692725	−	0.721202i	$-0.743590\pi$
$911$	−38095.0	−1.38545	−0.692725	+	0.721202i	$0.743590\pi$
$912$	−10943.8	−0.397353
$913$	−14387.0	−0.521512
$914$	3003.61	0.108699
$915$	−96631.4	−3.49130
$916$	−1968.61	−0.0710094
$917$	51775.6	1.86454
$918$	−7088.75	−0.254862
$919$	40134.8	1.44061	0.720307	−	0.693656i	$-0.244001\pi$
$919$	40134.8	1.44061	0.720307	+	0.693656i	$0.244001\pi$
$920$	43468.8	1.55774
$921$	58116.2	2.07925
$922$	−26117.4	−0.932895
$923$	31009.3	1.10583
$924$	3297.67	0.117408
$925$	17679.7	0.628437
$926$	14554.7	0.516520
$927$	21290.5	0.754338
$928$	−4183.86	−0.147998
$929$	−39198.6	−1.38435	−0.692177	−	0.721728i	$-0.743348\pi$
$929$	−39198.6	−1.38435	−0.692177	+	0.721728i	$0.743348\pi$
$930$	−5375.68	−0.189544
$931$	−14381.8	−0.506278
$932$	661.763	0.0232583
$933$	−16404.0	−0.575609
$934$	−21081.3	−0.738544
$935$	6178.04	0.216089
$936$	−41805.0	−1.45987
$937$	−5253.97	−0.183180	−0.0915900	−	0.995797i	$-0.529195\pi$
$937$	−5253.97	−0.183180	−0.0915900	+	0.995797i	$0.529195\pi$
$938$	65386.0	2.27604
$939$	34268.9	1.19097
$940$	7304.99	0.253471
$941$	2750.80	0.0952960	0.0476480	−	0.998864i	$-0.484827\pi$
$941$	2750.80	0.0952960	0.0476480	+	0.998864i	$0.484827\pi$
$942$	76771.7	2.65537
$943$	−10417.2	−0.359737
$944$	51459.9	1.77423
$945$	56031.8	1.92880
$946$	1947.13	0.0669203
$947$	−42599.6	−1.46177	−0.730887	−	0.682498i	$-0.760894\pi$
$947$	−42599.6	−1.46177	−0.730887	+	0.682498i	$0.760894\pi$
$948$	−9278.46	−0.317880
$949$	59251.4	2.02675
$950$	−16034.8	−0.547618
$951$	11918.3	0.406390
$952$	−19235.8	−0.654870
$953$	−45286.7	−1.53933	−0.769664	−	0.638449i	$-0.779576\pi$
$953$	−45286.7	−1.53933	−0.769664	+	0.638449i	$0.779576\pi$
$954$	54202.4	1.83948
$955$	79956.0	2.70923
$956$	4945.35	0.167306
$957$	7304.48	0.246730
$958$	22101.9	0.745386
$959$	39382.5	1.32610
$960$	67987.0	2.28570
$961$	−29669.5	−0.995922
$962$	10272.9	0.344294
$963$	13562.5	0.453838
$964$	−494.440	−0.0165196
$965$	−55544.3	−1.85289
$966$	−83736.2	−2.78899
$967$	−45539.7	−1.51444	−0.757218	−	0.653163i	$-0.773442\pi$
$967$	−45539.7	−1.51444	−0.757218	+	0.653163i	$0.773442\pi$
$968$	−2512.71	−0.0834313
$969$	4260.72	0.141253
$970$	−20437.5	−0.676505
$971$	−29550.6	−0.976647	−0.488324	−	0.872663i	$-0.662391\pi$
$971$	−29550.6	−0.976647	−0.488324	+	0.872663i	$0.662391\pi$
$972$	5599.80	0.184788
$973$	−52321.1	−1.72388
$974$	5423.74	0.178427
$975$	−120528.	−3.95897
$976$	42936.6	1.40816
$977$	15818.9	0.518007	0.259003	−	0.965876i	$-0.416606\pi$
$977$	15818.9	0.518007	0.259003	+	0.965876i	$0.416606\pi$
$978$	9363.81	0.306157
$979$	−56.9929	−0.00186057
$980$	−17136.3	−0.558572
$981$	−4549.47	−0.148067
$982$	−41981.8	−1.36425
$983$	−27453.5	−0.890774	−0.445387	−	0.895338i	$-0.646934\pi$
$983$	−27453.5	−0.890774	−0.445387	+	0.895338i	$0.646934\pi$
$984$	−16685.3	−0.540557
$985$	−35506.8	−1.14857
$986$	6978.21	0.225387
$987$	85921.9	2.77095
$988$	−1149.42	−0.0370122
$989$	−6099.58	−0.196113
$990$	25034.1	0.803673
$991$	−33079.6	−1.06035	−0.530176	−	0.847888i	$-0.677874\pi$
$991$	−33079.6	−1.06035	−0.530176	+	0.847888i	$0.677874\pi$
$992$	557.559	0.0178453
$993$	54871.5	1.75357
$994$	57817.1	1.84492
$995$	−54640.6	−1.74093
$996$	−11822.5	−0.376113
$997$	−5119.53	−0.162625	−0.0813124	−	0.996689i	$-0.525911\pi$
$997$	−5119.53	−0.162625	−0.0813124	+	0.996689i	$0.525911\pi$
$998$	−35998.7	−1.14180
$999$	−5316.97	−0.168390

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.4.a.c.1.10	✓	13
3.2	odd	2		1881.4.a.k.1.4		13
11.10	odd	2		2299.4.a.k.1.4		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.4.a.c.1.10	✓	13	1.1	even	1	trivial
1881.4.a.k.1.4		13	3.2	odd	2
2299.4.a.k.1.4		13	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	209.a (trivial)

\(f(q)\)	\(=\)	\(q+3.02090 q^{2} -8.02896 q^{3} +1.12583 q^{4} -20.1089 q^{5} -24.2547 q^{6} +33.1653 q^{7} -20.7662 q^{8} +37.4642 q^{9} -60.7468 q^{10} -11.0000 q^{11} -9.03920 q^{12} +53.7348 q^{13} +100.189 q^{14} +161.453 q^{15} -71.7391 q^{16} +27.9300 q^{17} +113.175 q^{18} -19.0000 q^{19} -22.6391 q^{20} -266.283 q^{21} -33.2299 q^{22} +104.096 q^{23} +166.731 q^{24} +279.366 q^{25} +162.327 q^{26} -84.0162 q^{27} +37.3383 q^{28} +82.7061 q^{29} +487.734 q^{30} -11.0218 q^{31} -50.5871 q^{32} +88.3185 q^{33} +84.3736 q^{34} -666.916 q^{35} +42.1781 q^{36} +63.2850 q^{37} -57.3971 q^{38} -431.435 q^{39} +417.584 q^{40} -100.073 q^{41} -804.413 q^{42} -58.5957 q^{43} -12.3841 q^{44} -753.361 q^{45} +314.463 q^{46} -322.672 q^{47} +575.990 q^{48} +756.937 q^{49} +843.937 q^{50} -224.248 q^{51} +60.4960 q^{52} +478.924 q^{53} -253.804 q^{54} +221.197 q^{55} -688.717 q^{56} +152.550 q^{57} +249.847 q^{58} -717.320 q^{59} +181.768 q^{60} -598.511 q^{61} -33.2956 q^{62} +1242.51 q^{63} +421.094 q^{64} -1080.55 q^{65} +266.801 q^{66} +652.627 q^{67} +31.4443 q^{68} -835.782 q^{69} -2014.69 q^{70} +577.080 q^{71} -777.987 q^{72} +1102.66 q^{73} +191.178 q^{74} -2243.02 q^{75} -21.3907 q^{76} -364.818 q^{77} -1303.32 q^{78} +1026.47 q^{79} +1442.59 q^{80} -336.969 q^{81} -302.312 q^{82} +1307.91 q^{83} -299.788 q^{84} -561.640 q^{85} -177.012 q^{86} -664.044 q^{87} +228.428 q^{88} +5.18117 q^{89} -2275.83 q^{90} +1782.13 q^{91} +117.194 q^{92} +88.4932 q^{93} -974.759 q^{94} +382.068 q^{95} +406.162 q^{96} +336.438 q^{97} +2286.63 q^{98} -412.106 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 2 q^{2} + 11 q^{3} + 82 q^{4} + 8 q^{5} + 13 q^{6} + 39 q^{7} + 6 q^{8} + 156 q^{9} + 124 q^{10} - 143 q^{11} + 247 q^{12} - 23 q^{13} + 47 q^{14} + 278 q^{15} + 526 q^{16} + 73 q^{17} - 165 q^{18}+ \cdots - 1716 q^{99}+O(q^{100}) \) 13 * q - 2 * q^2 + 11 * q^3 + 82 * q^4 + 8 * q^5 + 13 * q^6 + 39 * q^7 + 6 * q^8 + 156 * q^9 + 124 * q^10 - 143 * q^11 + 247 * q^12 - 23 * q^13 + 47 * q^14 + 278 * q^15 + 526 * q^16 + 73 * q^17 - 165 * q^18 - 247 * q^19 + 142 * q^20 + 77 * q^21 + 22 * q^22 + 185 * q^23 - 251 * q^24 + 641 * q^25 - 47 * q^26 + 1109 * q^27 + 289 * q^28 - 41 * q^29 + 520 * q^30 + 930 * q^31 - 194 * q^32 - 121 * q^33 - 333 * q^34 + 122 * q^35 + 1469 * q^36 + 1094 * q^37 + 38 * q^38 + 543 * q^39 + 2084 * q^40 - 766 * q^41 - 1277 * q^42 + 1024 * q^43 - 902 * q^44 - 348 * q^45 + 1927 * q^46 + 516 * q^47 + 3067 * q^48 + 1966 * q^49 + 3066 * q^50 + 1975 * q^51 - 553 * q^52 + 1017 * q^53 - 2231 * q^54 - 88 * q^55 - 1793 * q^56 - 209 * q^57 - 159 * q^58 + 15 * q^59 - 3158 * q^60 - 862 * q^61 - 3298 * q^62 + 552 * q^63 + 3694 * q^64 - 1640 * q^65 - 143 * q^66 + 621 * q^67 - 1533 * q^68 + 335 * q^69 - 3250 * q^70 + 632 * q^71 - 8349 * q^72 - 629 * q^73 - 4086 * q^74 - 2759 * q^75 - 1558 * q^76 - 429 * q^77 - 5813 * q^78 + 2444 * q^79 + 2810 * q^80 + 2265 * q^81 - 846 * q^82 + 732 * q^83 - 761 * q^84 - 3786 * q^85 - 4664 * q^86 - 1185 * q^87 - 66 * q^88 + 3178 * q^89 - 6174 * q^90 + 1349 * q^91 - 1677 * q^92 + 1328 * q^93 + 3156 * q^94 - 152 * q^95 - 13811 * q^96 + 1410 * q^97 - 6273 * q^98 - 1716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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