LMFDB - Embedded newform 161.4.a.d.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(1,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.49930751092$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} - 76 x^{10} + 311 x^{9} + 1979 x^{8} - 8466 x^{7} - 19942 x^{6} + 95647 x^{5} + \cdots - 70656 $ x^12 - 4x^11 - 76x^10 + 311x^9 + 1979x^8 - 8466x^7 - 19942x^6 + 95647x^5 + 50294x^4 - 400320x^3 + 178432x^2 + 227072*x - 70656
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$2.11879$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.11879 q^{2} -9.53944 q^{3} -3.51074 q^{4} -13.8523 q^{5} -20.2120 q^{6} +7.00000 q^{7} -24.3888 q^{8} +64.0009 q^{9} -29.3501 q^{10} +44.5055 q^{11} +33.4905 q^{12} -14.0229 q^{13} +14.8315 q^{14} +132.143 q^{15} -23.5887 q^{16} +73.5438 q^{17} +135.604 q^{18} -144.613 q^{19} +48.6320 q^{20} -66.7761 q^{21} +94.2977 q^{22} +23.0000 q^{23} +232.656 q^{24} +66.8868 q^{25} -29.7116 q^{26} -352.967 q^{27} -24.5752 q^{28} -151.668 q^{29} +279.984 q^{30} +267.975 q^{31} +145.131 q^{32} -424.558 q^{33} +155.824 q^{34} -96.9662 q^{35} -224.691 q^{36} +217.992 q^{37} -306.405 q^{38} +133.771 q^{39} +337.842 q^{40} +292.091 q^{41} -141.484 q^{42} +258.749 q^{43} -156.247 q^{44} -886.560 q^{45} +48.7321 q^{46} -134.287 q^{47} +225.023 q^{48} +49.0000 q^{49} +141.719 q^{50} -701.567 q^{51} +49.2310 q^{52} -358.121 q^{53} -747.863 q^{54} -616.505 q^{55} -170.722 q^{56} +1379.53 q^{57} -321.353 q^{58} +726.500 q^{59} -463.921 q^{60} -22.6555 q^{61} +567.781 q^{62} +448.006 q^{63} +496.211 q^{64} +194.250 q^{65} -899.547 q^{66} +441.251 q^{67} -258.194 q^{68} -219.407 q^{69} -205.451 q^{70} -42.7849 q^{71} -1560.90 q^{72} -414.175 q^{73} +461.878 q^{74} -638.062 q^{75} +507.700 q^{76} +311.539 q^{77} +283.432 q^{78} +1245.64 q^{79} +326.759 q^{80} +1639.09 q^{81} +618.878 q^{82} -235.942 q^{83} +234.434 q^{84} -1018.75 q^{85} +548.234 q^{86} +1446.83 q^{87} -1085.44 q^{88} -229.308 q^{89} -1878.43 q^{90} -98.1606 q^{91} -80.7471 q^{92} -2556.33 q^{93} -284.525 q^{94} +2003.23 q^{95} -1384.47 q^{96} -548.410 q^{97} +103.821 q^{98} +2848.39 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) $ 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.11879	0.749104	0.374552	−	0.927206i	$-0.377796\pi$
$2$	2.11879	0.749104	0.374552	+	0.927206i	$0.377796\pi$
$3$	−9.53944	−1.83587	−0.917933	−	0.396736i	$-0.870143\pi$
$3$	−9.53944	−1.83587	−0.917933	+	0.396736i	$0.870143\pi$
$4$	−3.51074	−0.438843
$5$	−13.8523	−1.23899	−0.619495	−	0.785001i	$-0.712662\pi$
$5$	−13.8523	−1.23899	−0.619495	+	0.785001i	$0.712662\pi$
$6$	−20.2120	−1.37525
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−24.3888	−1.07784
$9$	64.0009	2.37040
$10$	−29.3501	−0.928132
$11$	44.5055	1.21990	0.609951	−	0.792439i	$-0.291189\pi$
$11$	44.5055	1.21990	0.609951	+	0.792439i	$0.291189\pi$
$12$	33.4905	0.805657
$13$	−14.0229	−0.299174	−0.149587	−	0.988749i	$-0.547794\pi$
$13$	−14.0229	−0.299174	−0.149587	+	0.988749i	$0.547794\pi$
$14$	14.8315	0.283135
$15$	132.143	2.27462
$16$	−23.5887	−0.368574
$17$	73.5438	1.04924	0.524618	−	0.851338i	$-0.324208\pi$
$17$	73.5438	1.04924	0.524618	+	0.851338i	$0.324208\pi$
$18$	135.604	1.77568
$19$	−144.613	−1.74613	−0.873067	−	0.487599i	$-0.837873\pi$
$19$	−144.613	−1.74613	−0.873067	+	0.487599i	$0.837873\pi$
$20$	48.6320	0.543722
$21$	−66.7761	−0.693892
$22$	94.2977	0.913833
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	232.656	1.97878
$25$	66.8868	0.535094
$26$	−29.7116	−0.224113
$27$	−352.967	−2.51587
$28$	−24.5752	−0.165867
$29$	−151.668	−0.971176	−0.485588	−	0.874188i	$-0.661395\pi$
$29$	−151.668	−0.971176	−0.485588	+	0.874188i	$0.661395\pi$
$30$	279.984	1.70393
$31$	267.975	1.55257	0.776285	−	0.630382i	$-0.217102\pi$
$31$	267.975	1.55257	0.776285	+	0.630382i	$0.217102\pi$
$32$	145.131	0.801743
$33$	−424.558	−2.23958
$34$	155.824	0.785986
$35$	−96.9662	−0.468294
$36$	−224.691	−1.04023
$37$	217.992	0.968584	0.484292	−	0.874906i	$-0.339077\pi$
$37$	217.992	0.968584	0.484292	+	0.874906i	$0.339077\pi$
$38$	−306.405	−1.30804
$39$	133.771	0.549244
$40$	337.842	1.33544
$41$	292.091	1.11261	0.556304	−	0.830979i	$-0.312219\pi$
$41$	292.091	1.11261	0.556304	+	0.830979i	$0.312219\pi$
$42$	−141.484	−0.519797
$43$	258.749	0.917647	0.458824	−	0.888527i	$-0.348271\pi$
$43$	258.749	0.917647	0.458824	+	0.888527i	$0.348271\pi$
$44$	−156.247	−0.535345
$45$	−886.560	−2.93690
$46$	48.7321	0.156199
$47$	−134.287	−0.416761	−0.208380	−	0.978048i	$-0.566819\pi$
$47$	−134.287	−0.416761	−0.208380	+	0.978048i	$0.566819\pi$
$48$	225.023	0.676652
$49$	49.0000	0.142857
$50$	141.719	0.400841
$51$	−701.567	−1.92625
$52$	49.2310	0.131291
$53$	−358.121	−0.928145	−0.464072	−	0.885797i	$-0.653612\pi$
$53$	−358.121	−0.928145	−0.464072	+	0.885797i	$0.653612\pi$
$54$	−747.863	−1.88465
$55$	−616.505	−1.51145
$56$	−170.722	−0.407386
$57$	1379.53	3.20567
$58$	−321.353	−0.727512
$59$	726.500	1.60309	0.801545	−	0.597935i	$-0.204012\pi$
$59$	726.500	1.60309	0.801545	+	0.597935i	$0.204012\pi$
$60$	−463.921	−0.998200
$61$	−22.6555	−0.0475531	−0.0237765	−	0.999717i	$-0.507569\pi$
$61$	−22.6555	−0.0475531	−0.0237765	+	0.999717i	$0.507569\pi$
$62$	567.781	1.16304
$63$	448.006	0.895928
$64$	496.211	0.969163
$65$	194.250	0.370674
$66$	−899.547	−1.67768
$67$	441.251	0.804587	0.402294	−	0.915511i	$-0.368213\pi$
$67$	441.251	0.804587	0.402294	+	0.915511i	$0.368213\pi$
$68$	−258.194	−0.460450
$69$	−219.407	−0.382804
$70$	−205.451	−0.350801
$71$	−42.7849	−0.0715159	−0.0357580	−	0.999360i	$-0.511385\pi$
$71$	−42.7849	−0.0715159	−0.0357580	+	0.999360i	$0.511385\pi$
$72$	−1560.90	−2.55492
$73$	−414.175	−0.664048	−0.332024	−	0.943271i	$-0.607731\pi$
$73$	−414.175	−0.664048	−0.332024	+	0.943271i	$0.607731\pi$
$74$	461.878	0.725570
$75$	−638.062	−0.982361
$76$	507.700	0.766279
$77$	311.539	0.461079
$78$	283.432	0.411441
$79$	1245.64	1.77399	0.886997	−	0.461775i	$-0.152787\pi$
$79$	1245.64	1.77399	0.886997	+	0.461775i	$0.152787\pi$
$80$	326.759	0.456659
$81$	1639.09	2.24840
$82$	618.878	0.833459
$83$	−235.942	−0.312024	−0.156012	−	0.987755i	$-0.549864\pi$
$83$	−235.942	−0.312024	−0.156012	+	0.987755i	$0.549864\pi$
$84$	234.434	0.304510
$85$	−1018.75	−1.29999
$86$	548.234	0.687413
$87$	1446.83	1.78295
$88$	−1085.44	−1.31486
$89$	−229.308	−0.273108	−0.136554	−	0.990633i	$-0.543603\pi$
$89$	−229.308	−0.273108	−0.136554	+	0.990633i	$0.543603\pi$
$90$	−1878.43	−2.20005
$91$	−98.1606	−0.113077
$92$	−80.7471	−0.0915051
$93$	−2556.33	−2.85031
$94$	−284.525	−0.312197
$95$	2003.23	2.16344
$96$	−1384.47	−1.47189
$97$	−548.410	−0.574047	−0.287024	−	0.957924i	$-0.592666\pi$
$97$	−548.410	−0.574047	−0.287024	+	0.957924i	$0.592666\pi$
$98$	103.821	0.107015
$99$	2848.39	2.89166
$100$	−234.822	−0.234822
$101$	650.714	0.641074	0.320537	−	0.947236i	$-0.396137\pi$
$101$	650.714	0.641074	0.320537	+	0.947236i	$0.396137\pi$
$102$	−1486.47	−1.44297
$103$	−440.196	−0.421105	−0.210552	−	0.977583i	$-0.567526\pi$
$103$	−440.196	−0.421105	−0.210552	+	0.977583i	$0.567526\pi$
$104$	342.003	0.322463
$105$	925.003	0.859725
$106$	−758.781	−0.695277
$107$	−1727.26	−1.56056	−0.780282	−	0.625428i	$-0.784924\pi$
$107$	−1727.26	−1.56056	−0.780282	+	0.625428i	$0.784924\pi$
$108$	1239.18	1.10407
$109$	574.975	0.505254	0.252627	−	0.967564i	$-0.418706\pi$
$109$	574.975	0.505254	0.252627	+	0.967564i	$0.418706\pi$
$110$	−1306.24	−1.13223
$111$	−2079.52	−1.77819
$112$	−165.121	−0.139308
$113$	−1821.69	−1.51655	−0.758274	−	0.651936i	$-0.773957\pi$
$113$	−1821.69	−1.51655	−0.758274	+	0.651936i	$0.773957\pi$
$114$	2922.93	2.40138
$115$	−318.603	−0.258347
$116$	532.469	0.426194
$117$	−897.481	−0.709163
$118$	1539.30	1.20088
$119$	514.807	0.396574
$120$	−3222.82	−2.45168
$121$	649.741	0.488160
$122$	−48.0022	−0.0356222
$123$	−2786.38	−2.04260
$124$	−940.791	−0.681335
$125$	805.003	0.576013
$126$	949.229	0.671143
$127$	1831.16	1.27944	0.639722	−	0.768606i	$-0.279050\pi$
$127$	1831.16	1.27944	0.639722	+	0.768606i	$0.279050\pi$
$128$	−109.682	−0.0757392
$129$	−2468.32	−1.68468
$130$	411.575	0.277673
$131$	1414.78	0.943584	0.471792	−	0.881710i	$-0.343607\pi$
$131$	1414.78	0.943584	0.471792	+	0.881710i	$0.343607\pi$
$132$	1490.51	0.982822
$133$	−1012.29	−0.659977
$134$	934.916	0.602719
$135$	4889.42	3.11714
$136$	−1793.65	−1.13091
$137$	1761.45	1.09847	0.549237	−	0.835667i	$-0.314919\pi$
$137$	1761.45	1.09847	0.549237	+	0.835667i	$0.314919\pi$
$138$	−464.877	−0.286760
$139$	553.261	0.337605	0.168802	−	0.985650i	$-0.446010\pi$
$139$	553.261	0.337605	0.168802	+	0.985650i	$0.446010\pi$
$140$	340.424	0.205508
$141$	1281.02	0.765117
$142$	−90.6520	−0.0535729
$143$	−624.098	−0.364963
$144$	−1509.70	−0.873668
$145$	2100.96	1.20328
$146$	−877.548	−0.497441
$147$	−467.432	−0.262267
$148$	−765.313	−0.425056
$149$	−2178.19	−1.19761	−0.598806	−	0.800894i	$-0.704358\pi$
$149$	−2178.19	−1.19761	−0.598806	+	0.800894i	$0.704358\pi$
$150$	−1351.92	−0.735891
$151$	2997.34	1.61537	0.807683	−	0.589617i	$-0.200721\pi$
$151$	2997.34	1.61537	0.807683	+	0.589617i	$0.200721\pi$
$152$	3526.95	1.88206
$153$	4706.87	2.48711
$154$	660.084	0.345397
$155$	−3712.07	−1.92362
$156$	−469.636	−0.241032
$157$	1672.84	0.850363	0.425182	−	0.905108i	$-0.360210\pi$
$157$	1672.84	0.850363	0.425182	+	0.905108i	$0.360210\pi$
$158$	2639.25	1.32891
$159$	3416.27	1.70395
$160$	−2010.40	−0.993351
$161$	161.000	0.0788110
$162$	3472.88	1.68429
$163$	3152.11	1.51468	0.757338	−	0.653023i	$-0.226500\pi$
$163$	3152.11	1.51468	0.757338	+	0.653023i	$0.226500\pi$
$164$	−1025.46	−0.488260
$165$	5881.11	2.77481
$166$	−499.910	−0.233738
$167$	1302.51	0.603541	0.301771	−	0.953381i	$-0.402422\pi$
$167$	1302.51	0.603541	0.301771	+	0.953381i	$0.402422\pi$
$168$	1628.59	0.747907
$169$	−2000.36	−0.910495
$170$	−2158.52	−0.973829
$171$	−9255.38	−4.13904
$172$	−908.401	−0.402703
$173$	1687.46	0.741590	0.370795	−	0.928715i	$-0.379085\pi$
$173$	1687.46	0.741590	0.370795	+	0.928715i	$0.379085\pi$
$174$	3065.53	1.33561
$175$	468.208	0.202247
$176$	−1049.83	−0.449624
$177$	−6930.41	−2.94306
$178$	−485.855	−0.204586
$179$	2056.74	0.858815	0.429408	−	0.903111i	$-0.358722\pi$
$179$	2056.74	0.858815	0.429408	+	0.903111i	$0.358722\pi$
$180$	3112.49	1.28884
$181$	3211.59	1.31887	0.659435	−	0.751762i	$-0.270796\pi$
$181$	3211.59	1.31887	0.659435	+	0.751762i	$0.270796\pi$
$182$	−207.981	−0.0847066
$183$	216.121	0.0873011
$184$	−560.943	−0.224746
$185$	−3019.69	−1.20006
$186$	−5416.31	−2.13518
$187$	3273.11	1.27996
$188$	471.447	0.182893
$189$	−2470.77	−0.950911
$190$	4244.42	1.62064
$191$	−117.239	−0.0444141	−0.0222070	−	0.999753i	$-0.507069\pi$
$191$	−117.239	−0.0444141	−0.0222070	+	0.999753i	$0.507069\pi$
$192$	−4733.58	−1.77925
$193$	−3443.46	−1.28428	−0.642138	−	0.766589i	$-0.721952\pi$
$193$	−3443.46	−1.28428	−0.642138	+	0.766589i	$0.721952\pi$
$194$	−1161.96	−0.430021
$195$	−1853.04	−0.680507
$196$	−172.026	−0.0626919
$197$	−5035.34	−1.82108	−0.910541	−	0.413418i	$-0.864335\pi$
$197$	−5035.34	−1.82108	−0.910541	+	0.413418i	$0.864335\pi$
$198$	6035.13	2.16615
$199$	1094.67	0.389945	0.194973	−	0.980809i	$-0.437538\pi$
$199$	1094.67	0.389945	0.194973	+	0.980809i	$0.437538\pi$
$200$	−1631.29	−0.576748
$201$	−4209.28	−1.47711
$202$	1378.72	0.480231
$203$	−1061.68	−0.367070
$204$	2463.02	0.845323
$205$	−4046.13	−1.37851
$206$	−932.682	−0.315451
$207$	1472.02	0.494263
$208$	330.783	0.110268
$209$	−6436.09	−2.13011
$210$	1959.88	0.644023
$211$	−385.635	−0.125821	−0.0629105	−	0.998019i	$-0.520038\pi$
$211$	−385.635	−0.125821	−0.0629105	+	0.998019i	$0.520038\pi$
$212$	1257.27	0.407310
$213$	408.144	0.131294
$214$	−3659.69	−1.16902
$215$	−3584.27	−1.13696
$216$	8608.45	2.71172
$217$	1875.82	0.586817
$218$	1218.25	0.378487
$219$	3951.00	1.21910
$220$	2164.39	0.663287
$221$	−1031.30	−0.313904
$222$	−4406.05	−1.33205
$223$	2595.36	0.779365	0.389682	−	0.920949i	$-0.372585\pi$
$223$	2595.36	0.779365	0.389682	+	0.920949i	$0.372585\pi$
$224$	1015.92	0.303030
$225$	4280.81	1.26839
$226$	−3859.76	−1.13605
$227$	−1542.42	−0.450985	−0.225493	−	0.974245i	$-0.572399\pi$
$227$	−1542.42	−0.450985	−0.225493	+	0.974245i	$0.572399\pi$
$228$	−4843.17	−1.40679
$229$	3735.57	1.07796	0.538981	−	0.842318i	$-0.318810\pi$
$229$	3735.57	1.07796	0.538981	+	0.842318i	$0.318810\pi$
$230$	−675.053	−0.193529
$231$	−2971.90	−0.846480
$232$	3699.01	1.04678
$233$	1302.43	0.366201	0.183100	−	0.983094i	$-0.441387\pi$
$233$	1302.43	0.366201	0.183100	+	0.983094i	$0.441387\pi$
$234$	−1901.57	−0.531237
$235$	1860.19	0.516362
$236$	−2550.56	−0.703505
$237$	−11882.7	−3.25681
$238$	1090.77	0.297075
$239$	−2933.35	−0.793901	−0.396951	−	0.917840i	$-0.629932\pi$
$239$	−2933.35	−0.793901	−0.396951	+	0.917840i	$0.629932\pi$
$240$	−3117.09	−0.838365
$241$	−5856.33	−1.56531	−0.782654	−	0.622457i	$-0.786135\pi$
$241$	−5856.33	−1.56531	−0.782654	+	0.622457i	$0.786135\pi$
$242$	1376.66	0.365683
$243$	−6105.85	−1.61189
$244$	79.5376	0.0208683
$245$	−678.764	−0.176998
$246$	−5903.75	−1.53012
$247$	2027.90	0.522399
$248$	−6535.59	−1.67343
$249$	2250.75	0.572834
$250$	1705.63	0.431494
$251$	1074.97	0.270324	0.135162	−	0.990823i	$-0.456844\pi$
$251$	1074.97	0.270324	0.135162	+	0.990823i	$0.456844\pi$
$252$	−1572.83	−0.393172
$253$	1023.63	0.254367
$254$	3879.84	0.958437
$255$	9718.33	2.38661
$256$	−4202.08	−1.02590
$257$	−1924.24	−0.467046	−0.233523	−	0.972351i	$-0.575025\pi$
$257$	−1924.24	−0.467046	−0.233523	+	0.972351i	$0.575025\pi$
$258$	−5229.84	−1.26200
$259$	1525.94	0.366090
$260$	−681.963	−0.162668
$261$	−9706.91	−2.30208
$262$	2997.61	0.706843
$263$	1355.10	0.317716	0.158858	−	0.987301i	$-0.449219\pi$
$263$	1355.10	0.317716	0.158858	+	0.987301i	$0.449219\pi$
$264$	10354.5	2.41391
$265$	4960.80	1.14996
$266$	−2144.83	−0.494391
$267$	2187.47	0.501390
$268$	−1549.12	−0.353087
$269$	6417.79	1.45464	0.727322	−	0.686296i	$-0.240765\pi$
$269$	6417.79	1.45464	0.727322	+	0.686296i	$0.240765\pi$
$270$	10359.6	2.33506
$271$	−159.049	−0.0356513	−0.0178257	−	0.999841i	$-0.505674\pi$
$271$	−159.049	−0.0356513	−0.0178257	+	0.999841i	$0.505674\pi$
$272$	−1734.81	−0.386721
$273$	936.397	0.207595
$274$	3732.14	0.822871
$275$	2976.83	0.652763
$276$	770.282	0.167991
$277$	−4435.96	−0.962206	−0.481103	−	0.876664i	$-0.659764\pi$
$277$	−4435.96	−0.962206	−0.481103	+	0.876664i	$0.659764\pi$
$278$	1172.24	0.252901
$279$	17150.6	3.68022
$280$	2364.89	0.504747
$281$	4684.51	0.994499	0.497250	−	0.867608i	$-0.334343\pi$
$281$	4684.51	0.994499	0.497250	+	0.867608i	$0.334343\pi$
$282$	2714.21	0.573152
$283$	8081.92	1.69760	0.848799	−	0.528716i	$-0.177326\pi$
$283$	8081.92	1.69760	0.848799	+	0.528716i	$0.177326\pi$
$284$	150.207	0.0313843
$285$	−19109.7	−3.97179
$286$	−1322.33	−0.273395
$287$	2044.63	0.420526
$288$	9288.51	1.90045
$289$	495.696	0.100895
$290$	4451.48	0.901380
$291$	5231.52	1.05387
$292$	1454.06	0.291413
$293$	−1228.27	−0.244901	−0.122451	−	0.992475i	$-0.539075\pi$
$293$	−1228.27	−0.244901	−0.122451	+	0.992475i	$0.539075\pi$
$294$	−990.389	−0.196465
$295$	−10063.7	−1.98621
$296$	−5316.56	−1.04398
$297$	−15709.0	−3.06912
$298$	−4615.12	−0.897136
$299$	−322.528	−0.0623821
$300$	2240.07	0.431102
$301$	1811.24	0.346838
$302$	6350.73	1.21008
$303$	−6207.44	−1.17693
$304$	3411.24	0.643580
$305$	313.831	0.0589178
$306$	9972.85	1.86310
$307$	−5765.16	−1.07178	−0.535888	−	0.844289i	$-0.680023\pi$
$307$	−5765.16	−1.07178	−0.535888	+	0.844289i	$0.680023\pi$
$308$	−1093.73	−0.202342
$309$	4199.22	0.773092
$310$	−7865.09	−1.44099
$311$	−3700.45	−0.674705	−0.337352	−	0.941378i	$-0.609531\pi$
$311$	−3700.45	−0.674705	−0.337352	+	0.941378i	$0.609531\pi$
$312$	−3262.52	−0.591999
$313$	2567.89	0.463725	0.231863	−	0.972749i	$-0.425518\pi$
$313$	2567.89	0.463725	0.231863	+	0.972749i	$0.425518\pi$
$314$	3544.39	0.637011
$315$	−6205.92	−1.11004
$316$	−4373.13	−0.778505
$317$	−6942.20	−1.23001	−0.615004	−	0.788524i	$-0.710846\pi$
$317$	−6942.20	−1.23001	−0.615004	+	0.788524i	$0.710846\pi$
$318$	7238.35	1.27643
$319$	−6750.08	−1.18474
$320$	−6873.68	−1.20078
$321$	16477.1	2.86498
$322$	341.125	0.0590377
$323$	−10635.4	−1.83211
$324$	−5754.42	−0.986697
$325$	−937.950	−0.160086
$326$	6678.64	1.13465
$327$	−5484.94	−0.927578
$328$	−7123.74	−1.19922
$329$	−940.008	−0.157521
$330$	12460.8	2.07862
$331$	7221.99	1.19926	0.599632	−	0.800276i	$-0.295313\pi$
$331$	7221.99	1.19926	0.599632	+	0.800276i	$0.295313\pi$
$332$	828.332	0.136930
$333$	13951.7	2.29593
$334$	2759.74	0.452115
$335$	−6112.34	−0.996875
$336$	1575.16	0.255750
$337$	3896.04	0.629766	0.314883	−	0.949131i	$-0.398035\pi$
$337$	3896.04	0.629766	0.314883	+	0.949131i	$0.398035\pi$
$338$	−4238.33	−0.682055
$339$	17377.9	2.78418
$340$	3576.58	0.570492
$341$	11926.4	1.89398
$342$	−19610.2	−3.10057
$343$	343.000	0.0539949
$344$	−6310.58	−0.989080
$345$	3039.30	0.474291
$346$	3575.36	0.555528
$347$	−7244.93	−1.12083	−0.560415	−	0.828212i	$-0.689358\pi$
$347$	−7244.93	−1.12083	−0.560415	+	0.828212i	$0.689358\pi$
$348$	−5079.45	−0.782435
$349$	−7008.45	−1.07494	−0.537469	−	0.843283i	$-0.680620\pi$
$349$	−7008.45	−1.07494	−0.537469	+	0.843283i	$0.680620\pi$
$350$	992.032	0.151504
$351$	4949.64	0.752685
$352$	6459.13	0.978048
$353$	−8242.56	−1.24280	−0.621398	−	0.783495i	$-0.713435\pi$
$353$	−8242.56	−1.24280	−0.621398	+	0.783495i	$0.713435\pi$
$354$	−14684.0	−2.20466
$355$	592.670	0.0886075
$356$	805.042	0.119852
$357$	−4910.97	−0.728056
$358$	4357.79	0.643342
$359$	1159.24	0.170424	0.0852119	−	0.996363i	$-0.472843\pi$
$359$	1159.24	0.170424	0.0852119	+	0.996363i	$0.472843\pi$
$360$	21622.2	3.16552
$361$	14054.0	2.04899
$362$	6804.67	0.987971
$363$	−6198.16	−0.896196
$364$	344.617	0.0496232
$365$	5737.28	0.822748
$366$	457.914	0.0653976
$367$	3374.09	0.479908	0.239954	−	0.970784i	$-0.422868\pi$
$367$	3374.09	0.479908	0.239954	+	0.970784i	$0.422868\pi$
$368$	−542.541	−0.0768530
$369$	18694.1	2.63733
$370$	−6398.08	−0.898974
$371$	−2506.84	−0.350806
$372$	8974.62	1.25084
$373$	4442.14	0.616637	0.308318	−	0.951283i	$-0.400234\pi$
$373$	4442.14	0.616637	0.308318	+	0.951283i	$0.400234\pi$
$374$	6935.01	0.958826
$375$	−7679.27	−1.05748
$376$	3275.10	0.449203
$377$	2126.84	0.290551
$378$	−5235.04	−0.712331
$379$	3403.89	0.461335	0.230667	−	0.973033i	$-0.425909\pi$
$379$	3403.89	0.461335	0.230667	+	0.973033i	$0.425909\pi$
$380$	−7032.83	−0.949412
$381$	−17468.3	−2.34889
$382$	−248.404	−0.0332708
$383$	4078.07	0.544072	0.272036	−	0.962287i	$-0.412303\pi$
$383$	4078.07	0.544072	0.272036	+	0.962287i	$0.412303\pi$
$384$	1046.30	0.139047
$385$	−4315.53	−0.571273
$386$	−7295.95	−0.962057
$387$	16560.1	2.17519
$388$	1925.33	0.251917
$389$	13167.6	1.71625	0.858126	−	0.513440i	$-0.171629\pi$
$389$	13167.6	1.71625	0.858126	+	0.513440i	$0.171629\pi$
$390$	−3926.19	−0.509771
$391$	1691.51	0.218781
$392$	−1195.05	−0.153978
$393$	−13496.2	−1.73229
$394$	−10668.8	−1.36418
$395$	−17255.0	−2.19796
$396$	−9999.97	−1.26898
$397$	7505.93	0.948896	0.474448	−	0.880284i	$-0.342648\pi$
$397$	7505.93	0.948896	0.474448	+	0.880284i	$0.342648\pi$
$398$	2319.37	0.292110
$399$	9656.71	1.21163
$400$	−1577.77	−0.197222
$401$	−648.404	−0.0807475	−0.0403737	−	0.999185i	$-0.512855\pi$
$401$	−648.404	−0.0807475	−0.0403737	+	0.999185i	$0.512855\pi$
$402$	−8918.57	−1.10651
$403$	−3757.80	−0.464489
$404$	−2284.49	−0.281331
$405$	−22705.2	−2.78575
$406$	−2249.47	−0.274974
$407$	9701.83	1.18158
$408$	17110.4	2.07620
$409$	7769.06	0.939255	0.469627	−	0.882865i	$-0.344388\pi$
$409$	7769.06	0.939255	0.469627	+	0.882865i	$0.344388\pi$
$410$	−8572.89	−1.03265
$411$	−16803.2	−2.01665
$412$	1545.42	0.184799
$413$	5085.50	0.605911
$414$	3118.90	0.370254
$415$	3268.34	0.386594
$416$	−2035.16	−0.239861
$417$	−5277.80	−0.619796
$418$	−13636.7	−1.59568
$419$	−14158.6	−1.65082	−0.825409	−	0.564535i	$-0.809056\pi$
$419$	−14158.6	−1.65082	−0.825409	+	0.564535i	$0.809056\pi$
$420$	−3247.45	−0.377284
$421$	5008.04	0.579755	0.289877	−	0.957064i	$-0.406385\pi$
$421$	5008.04	0.579755	0.289877	+	0.957064i	$0.406385\pi$
$422$	−817.079	−0.0942530
$423$	−8594.48	−0.987891
$424$	8734.14	1.00039
$425$	4919.11	0.561440
$426$	864.769	0.0983526
$427$	−158.588	−0.0179734
$428$	6063.96	0.684842
$429$	5953.55	0.670023
$430$	−7594.31	−0.851698
$431$	4166.53	0.465649	0.232825	−	0.972519i	$-0.425203\pi$
$431$	4166.53	0.465649	0.232825	+	0.972519i	$0.425203\pi$
$432$	8326.05	0.927285
$433$	10367.8	1.15068	0.575340	−	0.817914i	$-0.304870\pi$
$433$	10367.8	1.15068	0.575340	+	0.817914i	$0.304870\pi$
$434$	3974.47	0.439587
$435$	−20042.0	−2.20906
$436$	−2018.59	−0.221727
$437$	−3326.11	−0.364094
$438$	8371.32	0.913235
$439$	6128.16	0.666244	0.333122	−	0.942884i	$-0.391898\pi$
$439$	6128.16	0.666244	0.333122	+	0.942884i	$0.391898\pi$
$440$	15035.8	1.62910
$441$	3136.04	0.338629
$442$	−2185.11	−0.235147
$443$	−11220.6	−1.20340	−0.601700	−	0.798723i	$-0.705510\pi$
$443$	−11220.6	−1.20340	−0.601700	+	0.798723i	$0.705510\pi$
$444$	7300.65	0.780346
$445$	3176.45	0.338378
$446$	5499.02	0.583825
$447$	20778.7	2.19865
$448$	3473.48	0.366309
$449$	5409.68	0.568594	0.284297	−	0.958736i	$-0.408240\pi$
$449$	5409.68	0.568594	0.284297	+	0.958736i	$0.408240\pi$
$450$	9070.13	0.950155
$451$	12999.6	1.35727
$452$	6395.47	0.665526
$453$	−28593.0	−2.96560
$454$	−3268.05	−0.337835
$455$	1359.75	0.140101
$456$	−33645.1	−3.45521
$457$	7975.08	0.816321	0.408160	−	0.912910i	$-0.366170\pi$
$457$	7975.08	0.816321	0.408160	+	0.912910i	$0.366170\pi$
$458$	7914.87	0.807505
$459$	−25958.6	−2.63974
$460$	1118.53	0.113374
$461$	6865.48	0.693617	0.346808	−	0.937936i	$-0.387265\pi$
$461$	6865.48	0.693617	0.346808	+	0.937936i	$0.387265\pi$
$462$	−6296.83	−0.634102
$463$	−780.070	−0.0783000	−0.0391500	−	0.999233i	$-0.512465\pi$
$463$	−780.070	−0.0783000	−0.0391500	+	0.999233i	$0.512465\pi$
$464$	3577.66	0.357950
$465$	35411.1	3.53150
$466$	2759.56	0.274322
$467$	−9986.86	−0.989586	−0.494793	−	0.869011i	$-0.664756\pi$
$467$	−9986.86	−0.989586	−0.494793	+	0.869011i	$0.664756\pi$
$468$	3150.82	0.311211
$469$	3088.75	0.304105
$470$	3941.34	0.386809
$471$	−15957.9	−1.56115
$472$	−17718.5	−1.72788
$473$	11515.8	1.11944
$474$	−25176.9	−2.43969
$475$	−9672.72	−0.934347
$476$	−1807.36	−0.174034
$477$	−22920.0	−2.20008
$478$	−6215.13	−0.594715
$479$	−4096.33	−0.390743	−0.195372	−	0.980729i	$-0.562591\pi$
$479$	−4096.33	−0.390743	−0.195372	+	0.980729i	$0.562591\pi$
$480$	19178.1	1.82366
$481$	−3056.88	−0.289775
$482$	−12408.3	−1.17258
$483$	−1535.85	−0.144686
$484$	−2281.07	−0.214226
$485$	7596.75	0.711238
$486$	−12937.0	−1.20748
$487$	−5209.38	−0.484722	−0.242361	−	0.970186i	$-0.577922\pi$
$487$	−5209.38	−0.484722	−0.242361	+	0.970186i	$0.577922\pi$
$488$	552.540	0.0512548
$489$	−30069.3	−2.78074
$490$	−1438.16	−0.132590
$491$	7398.09	0.679982	0.339991	−	0.940429i	$-0.389576\pi$
$491$	7398.09	0.679982	0.339991	+	0.940429i	$0.389576\pi$
$492$	9782.27	0.896380
$493$	−11154.3	−1.01899
$494$	4296.70	0.391331
$495$	−39456.8	−3.58273
$496$	−6321.18	−0.572237
$497$	−299.494	−0.0270305
$498$	4768.86	0.429112
$499$	1724.59	0.154716	0.0773581	−	0.997003i	$-0.475352\pi$
$499$	1724.59	0.154716	0.0773581	+	0.997003i	$0.475352\pi$
$500$	−2826.16	−0.252779
$501$	−12425.2	−1.10802
$502$	2277.63	0.202501
$503$	7101.08	0.629467	0.314733	−	0.949180i	$-0.398085\pi$
$503$	7101.08	0.629467	0.314733	+	0.949180i	$0.398085\pi$
$504$	−10926.3	−0.965670
$505$	−9013.90	−0.794284
$506$	2168.85	0.190547
$507$	19082.3	1.67155
$508$	−6428.74	−0.561475
$509$	15701.5	1.36730	0.683651	−	0.729809i	$-0.260391\pi$
$509$	15701.5	1.36730	0.683651	+	0.729809i	$0.260391\pi$
$510$	20591.1	1.78782
$511$	−2899.22	−0.250987
$512$	−8025.86	−0.692766
$513$	51043.8	4.39306
$514$	−4077.05	−0.349866
$515$	6097.74	0.521745
$516$	8665.63	0.739309
$517$	−5976.51	−0.508407
$518$	3233.14	0.274240
$519$	−16097.4	−1.36146
$520$	−4737.53	−0.399528
$521$	13698.5	1.15190	0.575951	−	0.817485i	$-0.304632\pi$
$521$	13698.5	1.15190	0.575951	+	0.817485i	$0.304632\pi$
$522$	−20566.9	−1.72450
$523$	−2295.23	−0.191899	−0.0959496	−	0.995386i	$-0.530589\pi$
$523$	−2295.23	−0.191899	−0.0959496	+	0.995386i	$0.530589\pi$
$524$	−4966.91	−0.414085
$525$	−4466.44	−0.371298
$526$	2871.17	0.238002
$527$	19707.9	1.62901
$528$	10014.8	0.825449
$529$	529.000	0.0434783
$530$	10510.9	0.861441
$531$	46496.7	3.79997
$532$	3553.90	0.289626
$533$	−4095.97	−0.332863
$534$	4634.78	0.375593
$535$	23926.5	1.93352
$536$	−10761.6	−0.867219
$537$	−19620.1	−1.57667
$538$	13597.9	1.08968
$539$	2180.77	0.174272
$540$	−17165.5	−1.36794
$541$	−12730.4	−1.01169	−0.505845	−	0.862625i	$-0.668819\pi$
$541$	−12730.4	−1.01169	−0.505845	+	0.862625i	$0.668819\pi$
$542$	−336.990	−0.0267066
$543$	−30636.7	−2.42127
$544$	10673.5	0.841217
$545$	−7964.74	−0.626004
$546$	1984.03	0.155510
$547$	−11507.3	−0.899482	−0.449741	−	0.893159i	$-0.648484\pi$
$547$	−11507.3	−0.899482	−0.449741	+	0.893159i	$0.648484\pi$
$548$	−6184.00	−0.482057
$549$	−1449.97	−0.112720
$550$	6307.27	0.488987
$551$	21933.3	1.69581
$552$	5351.08	0.412603
$553$	8719.49	0.670507
$554$	−9398.86	−0.720793
$555$	28806.1	2.20316
$556$	−1942.36	−0.148155
$557$	−23246.7	−1.76840	−0.884198	−	0.467113i	$-0.845294\pi$
$557$	−23246.7	−1.76840	−0.884198	+	0.467113i	$0.845294\pi$
$558$	36338.5	2.75687
$559$	−3628.42	−0.274536
$560$	2287.31	0.172601
$561$	−31223.6	−2.34984
$562$	9925.47	0.744984
$563$	20304.4	1.51995	0.759973	−	0.649954i	$-0.225212\pi$
$563$	20304.4	1.51995	0.759973	+	0.649954i	$0.225212\pi$
$564$	−4497.34	−0.335766
$565$	25234.6	1.87899
$566$	17123.9	1.27168
$567$	11473.6	0.849817
$568$	1043.47	0.0770830
$569$	−14444.8	−1.06425	−0.532126	−	0.846665i	$-0.678607\pi$
$569$	−14444.8	−1.06425	−0.532126	+	0.846665i	$0.678607\pi$
$570$	−40489.3	−2.97528
$571$	−17953.1	−1.31579	−0.657894	−	0.753111i	$-0.728552\pi$
$571$	−17953.1	−1.31579	−0.657894	+	0.753111i	$0.728552\pi$
$572$	2191.05	0.160162
$573$	1118.39	0.0815382
$574$	4332.14	0.315018
$575$	1538.40	0.111575
$576$	31758.0	2.29731
$577$	18672.1	1.34719	0.673596	−	0.739100i	$-0.264749\pi$
$577$	18672.1	1.34719	0.673596	+	0.739100i	$0.264749\pi$
$578$	1050.27	0.0755806
$579$	32848.6	2.35776
$580$	−7375.93	−0.528050
$581$	−1651.59	−0.117934
$582$	11084.5	0.789461
$583$	−15938.3	−1.13225
$584$	10101.2	0.715740
$585$	12432.2	0.878646
$586$	−2602.43	−0.183456
$587$	9717.16	0.683254	0.341627	−	0.939836i	$-0.389022\pi$
$587$	9717.16	0.683254	0.341627	+	0.939836i	$0.389022\pi$
$588$	1641.04	0.115094
$589$	−38752.7	−2.71100
$590$	−21322.9	−1.48788
$591$	48034.3	3.34326
$592$	−5142.14	−0.356995
$593$	−11670.0	−0.808145	−0.404073	−	0.914727i	$-0.632406\pi$
$593$	−11670.0	−0.808145	−0.404073	+	0.914727i	$0.632406\pi$
$594$	−33284.0	−2.29909
$595$	−7131.27	−0.491351
$596$	7647.06	0.525564
$597$	−10442.5	−0.715887
$598$	−683.367	−0.0467307
$599$	6190.98	0.422298	0.211149	−	0.977454i	$-0.432279\pi$
$599$	6190.98	0.422298	0.211149	+	0.977454i	$0.432279\pi$
$600$	15561.6	1.05883
$601$	−18340.9	−1.24482	−0.622412	−	0.782690i	$-0.713847\pi$
$601$	−18340.9	−1.24482	−0.622412	+	0.782690i	$0.713847\pi$
$602$	3837.63	0.259818
$603$	28240.4	1.90720
$604$	−10522.9	−0.708892
$605$	−9000.42	−0.604825
$606$	−13152.3	−0.881640
$607$	−14258.8	−0.953451	−0.476726	−	0.879052i	$-0.658176\pi$
$607$	−14258.8	−0.953451	−0.476726	+	0.879052i	$0.658176\pi$
$608$	−20987.9	−1.39995
$609$	10127.8	0.673892
$610$	664.941	0.0441355
$611$	1883.10	0.124684
$612$	−16524.6	−1.09145
$613$	12882.2	0.848790	0.424395	−	0.905477i	$-0.360487\pi$
$613$	12882.2	0.848790	0.424395	+	0.905477i	$0.360487\pi$
$614$	−12215.2	−0.802872
$615$	38597.8	2.53076
$616$	−7598.06	−0.496971
$617$	−18468.1	−1.20502	−0.602509	−	0.798112i	$-0.705832\pi$
$617$	−18468.1	−1.20502	−0.602509	+	0.798112i	$0.705832\pi$
$618$	8897.26	0.579126
$619$	7333.17	0.476163	0.238082	−	0.971245i	$-0.423481\pi$
$619$	7333.17	0.476163	0.238082	+	0.971245i	$0.423481\pi$
$620$	13032.1	0.844166
$621$	−8118.25	−0.524596
$622$	−7840.46	−0.505424
$623$	−1605.16	−0.103225
$624$	−3155.49	−0.202437
$625$	−19512.0	−1.24877
$626$	5440.82	0.347378
$627$	61396.7	3.91060
$628$	−5872.91	−0.373176
$629$	16031.9	1.01627
$630$	−13149.0	−0.831539
$631$	27310.0	1.72297	0.861486	−	0.507782i	$-0.169534\pi$
$631$	27310.0	1.72297	0.861486	+	0.507782i	$0.169534\pi$
$632$	−30379.7	−1.91209
$633$	3678.74	0.230990
$634$	−14709.0	−0.921405
$635$	−25365.8	−1.58522
$636$	−11993.6	−0.747766
$637$	−687.124	−0.0427392
$638$	−14302.0	−0.887493
$639$	−2738.27	−0.169522
$640$	1519.35	0.0938400
$641$	16514.0	1.01757	0.508786	−	0.860893i	$-0.330095\pi$
$641$	16514.0	1.01757	0.508786	+	0.860893i	$0.330095\pi$
$642$	34911.4	2.14617
$643$	18670.4	1.14508	0.572541	−	0.819876i	$-0.305958\pi$
$643$	18670.4	1.14508	0.572541	+	0.819876i	$0.305958\pi$
$644$	−565.230	−0.0345857
$645$	34191.9	2.08730
$646$	−22534.2	−1.37244
$647$	−25559.8	−1.55311	−0.776553	−	0.630052i	$-0.783034\pi$
$647$	−25559.8	−1.55311	−0.776553	+	0.630052i	$0.783034\pi$
$648$	−39975.4	−2.42343
$649$	32333.3	1.95561
$650$	−1987.32	−0.119921
$651$	−17894.3	−1.07732
$652$	−11066.2	−0.664705
$653$	−9362.94	−0.561103	−0.280551	−	0.959839i	$-0.590517\pi$
$653$	−9362.94	−0.561103	−0.280551	+	0.959839i	$0.590517\pi$
$654$	−11621.4	−0.694852
$655$	−19597.9	−1.16909
$656$	−6890.05	−0.410078
$657$	−26507.5	−1.57406
$658$	−1991.68	−0.117999
$659$	12620.9	0.746040	0.373020	−	0.927823i	$-0.378322\pi$
$659$	12620.9	0.746040	0.373020	+	0.927823i	$0.378322\pi$
$660$	−20647.1	−1.21771
$661$	−3724.18	−0.219143	−0.109572	−	0.993979i	$-0.534948\pi$
$661$	−3724.18	−0.219143	−0.109572	+	0.993979i	$0.534948\pi$
$662$	15301.9	0.898374
$663$	9838.03	0.576286
$664$	5754.34	0.336313
$665$	14022.6	0.817704
$666$	29560.6	1.71989
$667$	−3488.37	−0.202504
$668$	−4572.78	−0.264860
$669$	−24758.3	−1.43081
$670$	−12950.8	−0.746763
$671$	−1008.29	−0.0580101
$672$	−9691.28	−0.556323
$673$	13315.3	0.762655	0.381328	−	0.924440i	$-0.375467\pi$
$673$	13315.3	0.762655	0.381328	+	0.924440i	$0.375467\pi$
$674$	8254.89	0.471760
$675$	−23608.9	−1.34623
$676$	7022.74	0.399564
$677$	13682.3	0.776738	0.388369	−	0.921504i	$-0.373039\pi$
$677$	13682.3	0.776738	0.388369	+	0.921504i	$0.373039\pi$
$678$	36820.0	2.08564
$679$	−3838.87	−0.216969
$680$	24846.2	1.40119
$681$	14713.8	0.827949
$682$	25269.4	1.41879
$683$	−15886.7	−0.890028	−0.445014	−	0.895524i	$-0.646801\pi$
$683$	−15886.7	−0.890028	−0.445014	+	0.895524i	$0.646801\pi$
$684$	32493.3	1.81639
$685$	−24400.2	−1.36100
$686$	726.744	0.0404478
$687$	−35635.2	−1.97899
$688$	−6103.56	−0.338221
$689$	5021.91	0.277677
$690$	6439.62	0.355293
$691$	−35181.9	−1.93688	−0.968439	−	0.249250i	$-0.919816\pi$
$691$	−35181.9	−1.93688	−0.968439	+	0.249250i	$0.919816\pi$
$692$	−5924.23	−0.325442
$693$	19938.7	1.09294
$694$	−15350.5	−0.839618
$695$	−7663.96	−0.418288
$696$	−35286.5	−1.92174
$697$	21481.5	1.16739
$698$	−14849.4	−0.805241
$699$	−12424.4	−0.672295
$700$	−1643.76	−0.0887545
$701$	9560.76	0.515128	0.257564	−	0.966261i	$-0.417080\pi$
$701$	9560.76	0.515128	0.257564	+	0.966261i	$0.417080\pi$
$702$	10487.2	0.563839
$703$	−31524.5	−1.69128
$704$	22084.1	1.18228
$705$	−17745.1	−0.947971
$706$	−17464.2	−0.930984
$707$	4555.00	0.242303
$708$	24330.9	1.29154
$709$	−9643.28	−0.510806	−0.255403	−	0.966835i	$-0.582208\pi$
$709$	−9643.28	−0.510806	−0.255403	+	0.966835i	$0.582208\pi$
$710$	1255.74	0.0663762
$711$	79722.1	4.20508
$712$	5592.55	0.294368
$713$	6163.42	0.323733
$714$	−10405.3	−0.545390
$715$	8645.21	0.452185
$716$	−7220.69	−0.376885
$717$	27982.5	1.45750
$718$	2456.17	0.127665
$719$	−35086.6	−1.81990	−0.909951	−	0.414715i	$-0.863881\pi$
$719$	−35086.6	−1.81990	−0.909951	+	0.414715i	$0.863881\pi$
$720$	20912.8	1.08247
$721$	−3081.37	−0.159163
$722$	29777.4	1.53490
$723$	55866.1	2.87370
$724$	−11275.1	−0.578777
$725$	−10144.6	−0.519671
$726$	−13132.6	−0.671344
$727$	13894.3	0.708817	0.354408	−	0.935091i	$-0.384682\pi$
$727$	13894.3	0.708817	0.354408	+	0.935091i	$0.384682\pi$
$728$	2394.02	0.121880
$729$	13991.0	0.710817
$730$	12156.1	0.616324
$731$	19029.4	0.962828
$732$	−758.744	−0.0383115
$733$	−221.058	−0.0111391	−0.00556956	−	0.999984i	$-0.501773\pi$
$733$	−221.058	−0.0111391	−0.00556956	+	0.999984i	$0.501773\pi$
$734$	7148.99	0.359501
$735$	6475.02	0.324945
$736$	3338.01	0.167175
$737$	19638.1	0.981517
$738$	39608.7	1.97563
$739$	14595.1	0.726509	0.363255	−	0.931690i	$-0.381666\pi$
$739$	14595.1	0.726509	0.363255	+	0.931690i	$0.381666\pi$
$740$	10601.4	0.526640
$741$	−19345.1	−0.959054
$742$	−5311.47	−0.262790
$743$	1605.23	0.0792598	0.0396299	−	0.999214i	$-0.487382\pi$
$743$	1605.23	0.0792598	0.0396299	+	0.999214i	$0.487382\pi$
$744$	62345.8	3.07219
$745$	30173.0	1.48383
$746$	9411.96	0.461925
$747$	−15100.5	−0.739622
$748$	−11491.0	−0.561703
$749$	−12090.8	−0.589837
$750$	−16270.7	−0.792165
$751$	−7676.69	−0.373004	−0.186502	−	0.982455i	$-0.559715\pi$
$751$	−7676.69	−0.373004	−0.186502	+	0.982455i	$0.559715\pi$
$752$	3167.66	0.153607
$753$	−10254.6	−0.496279
$754$	4506.31	0.217653
$755$	−41520.2	−2.00142
$756$	8674.25	0.417301
$757$	−30629.5	−1.47061	−0.735303	−	0.677739i	$-0.762960\pi$
$757$	−30629.5	−1.47061	−0.735303	+	0.677739i	$0.762960\pi$
$758$	7212.11	0.345588
$759$	−9764.82	−0.466984
$760$	−48856.4	−2.33185
$761$	−18125.8	−0.863418	−0.431709	−	0.902013i	$-0.642089\pi$
$761$	−18125.8	−0.863418	−0.431709	+	0.902013i	$0.642089\pi$
$762$	−37011.5	−1.75956
$763$	4024.83	0.190968
$764$	411.595	0.0194908
$765$	−65201.1	−3.08150
$766$	8640.56	0.407567
$767$	−10187.7	−0.479603
$768$	40085.5	1.88341
$769$	−17335.3	−0.812908	−0.406454	−	0.913671i	$-0.633235\pi$
$769$	−17335.3	−0.812908	−0.406454	+	0.913671i	$0.633235\pi$
$770$	−9143.69	−0.427943
$771$	18356.2	0.857433
$772$	12089.1	0.563596
$773$	8133.01	0.378427	0.189213	−	0.981936i	$-0.439406\pi$
$773$	8133.01	0.378427	0.189213	+	0.981936i	$0.439406\pi$
$774$	35087.4	1.62945
$775$	17924.0	0.830772
$776$	13375.1	0.618733
$777$	−14556.6	−0.672093
$778$	27899.2	1.28565
$779$	−42240.2	−1.94276
$780$	6505.54	0.298636
$781$	−1904.16	−0.0872424
$782$	3583.94	0.163890
$783$	53534.0	2.44336
$784$	−1155.85	−0.0526534
$785$	−23172.7	−1.05359
$786$	−28595.5	−1.29767
$787$	−9653.43	−0.437240	−0.218620	−	0.975810i	$-0.570155\pi$
$787$	−9653.43	−0.437240	−0.218620	+	0.975810i	$0.570155\pi$
$788$	17677.8	0.799169
$789$	−12926.9	−0.583283
$790$	−36559.7	−1.64650
$791$	−12751.8	−0.573201
$792$	−69468.9	−3.11675
$793$	317.697	0.0142267
$794$	15903.5	0.710822
$795$	−47323.3	−2.11117
$796$	−3843.11	−0.171125
$797$	−9485.40	−0.421569	−0.210784	−	0.977533i	$-0.567602\pi$
$797$	−9485.40	−0.421569	−0.210784	+	0.977533i	$0.567602\pi$
$798$	20460.5	0.907636
$799$	−9875.97	−0.437280
$800$	9707.35	0.429008
$801$	−14675.9	−0.647376
$802$	−1373.83	−0.0604883
$803$	−18433.1	−0.810073
$804$	14777.7	0.648221
$805$	−2230.22	−0.0976460
$806$	−7961.97	−0.347951
$807$	−61222.1	−2.67053
$808$	−15870.1	−0.690977
$809$	13793.8	0.599461	0.299730	−	0.954024i	$-0.403103\pi$
$809$	13793.8	0.599461	0.299730	+	0.954024i	$0.403103\pi$
$810$	−48107.4	−2.08682
$811$	−17233.5	−0.746176	−0.373088	−	0.927796i	$-0.621701\pi$
$811$	−17233.5	−0.746176	−0.373088	+	0.927796i	$0.621701\pi$
$812$	3727.28	0.161086
$813$	1517.23	0.0654511
$814$	20556.1	0.885124
$815$	−43664.0	−1.87667
$816$	16549.1	0.709967
$817$	−37418.5	−1.60234
$818$	16461.0	0.703600
$819$	−6282.36	−0.268039
$820$	14204.9	0.604949
$821$	13256.2	0.563515	0.281757	−	0.959486i	$-0.409083\pi$
$821$	13256.2	0.563515	0.281757	+	0.959486i	$0.409083\pi$
$822$	−35602.5	−1.51068
$823$	15413.4	0.652827	0.326414	−	0.945227i	$-0.394160\pi$
$823$	15413.4	0.652827	0.326414	+	0.945227i	$0.394160\pi$
$824$	10735.9	0.453885
$825$	−28397.3	−1.19838
$826$	10775.1	0.453890
$827$	22153.8	0.931515	0.465757	−	0.884913i	$-0.345782\pi$
$827$	22153.8	0.931515	0.465757	+	0.884913i	$0.345782\pi$
$828$	−5167.88	−0.216904
$829$	−19856.9	−0.831917	−0.415959	−	0.909384i	$-0.636554\pi$
$829$	−19856.9	−0.831917	−0.415959	+	0.909384i	$0.636554\pi$
$830$	6924.92	0.289599
$831$	42316.6	1.76648
$832$	−6958.34	−0.289949
$833$	3603.65	0.149891
$834$	−11182.5	−0.464292
$835$	−18042.8	−0.747781
$836$	22595.5	0.934785
$837$	−94586.4	−3.90607
$838$	−29999.1	−1.23663
$839$	6674.01	0.274627	0.137314	−	0.990528i	$-0.456153\pi$
$839$	6674.01	0.274627	0.137314	+	0.990528i	$0.456153\pi$
$840$	−22559.7	−0.926648
$841$	−1385.69	−0.0568164
$842$	10611.0	0.434297
$843$	−44687.6	−1.82577
$844$	1353.87	0.0552157
$845$	27709.6	1.12809
$846$	−18209.9	−0.740033
$847$	4548.19	0.184507
$848$	8447.61	0.342090
$849$	−77097.0	−3.11656
$850$	10422.5	0.420577
$851$	5013.81	0.201964
$852$	−1432.89	−0.0576173
$853$	6439.37	0.258476	0.129238	−	0.991614i	$-0.458747\pi$
$853$	6439.37	0.258476	0.129238	+	0.991614i	$0.458747\pi$
$854$	−336.015	−0.0134639
$855$	128208.	5.12823
$856$	42125.7	1.68204
$857$	28218.7	1.12478	0.562389	−	0.826873i	$-0.309883\pi$
$857$	28218.7	1.12478	0.562389	+	0.826873i	$0.309883\pi$
$858$	12614.3	0.501917
$859$	23175.0	0.920515	0.460257	−	0.887785i	$-0.347757\pi$
$859$	23175.0	0.920515	0.460257	+	0.887785i	$0.347757\pi$
$860$	12583.5	0.498945
$861$	−19504.7	−0.772029
$862$	8827.99	0.348820
$863$	12418.8	0.489850	0.244925	−	0.969542i	$-0.421237\pi$
$863$	12418.8	0.489850	0.244925	+	0.969542i	$0.421237\pi$
$864$	−51226.5	−2.01708
$865$	−23375.2	−0.918822
$866$	21967.1	0.861979
$867$	−4728.66	−0.185229
$868$	−6585.54	−0.257520
$869$	55437.9	2.16410
$870$	−42464.7	−1.65481
$871$	−6187.63	−0.240712
$872$	−14023.0	−0.544584
$873$	−35098.7	−1.36072
$874$	−7047.31	−0.272745
$875$	5635.02	0.217712
$876$	−13870.9	−0.534995
$877$	19551.0	0.752785	0.376392	−	0.926460i	$-0.377165\pi$
$877$	19551.0	0.752785	0.376392	+	0.926460i	$0.377165\pi$
$878$	12984.3	0.499086
$879$	11717.0	0.449605
$880$	14542.6	0.557079
$881$	15487.9	0.592283	0.296141	−	0.955144i	$-0.404300\pi$
$881$	15487.9	0.592283	0.296141	+	0.955144i	$0.404300\pi$
$882$	6644.60	0.253668
$883$	16387.2	0.624545	0.312273	−	0.949992i	$-0.398910\pi$
$883$	16387.2	0.624545	0.312273	+	0.949992i	$0.398910\pi$
$884$	3620.63	0.137755
$885$	96002.2	3.64642
$886$	−23774.0	−0.901471
$887$	−26831.2	−1.01567	−0.507837	−	0.861453i	$-0.669555\pi$
$887$	−26831.2	−1.01567	−0.507837	+	0.861453i	$0.669555\pi$
$888$	50717.0	1.91661
$889$	12818.1	0.483584
$890$	6730.22	0.253480
$891$	72948.4	2.74283
$892$	−9111.66	−0.342019
$893$	19419.7	0.727721
$894$	44025.6	1.64702
$895$	−28490.6	−1.06406
$896$	−767.774	−0.0286267
$897$	3076.73	0.114525
$898$	11462.0	0.425936
$899$	−40643.3	−1.50782
$900$	−15028.8	−0.556624
$901$	−26337.6	−0.973842
$902$	27543.5	1.01674
$903$	−17278.2	−0.636748
$904$	44428.8	1.63460
$905$	−44488.0	−1.63407
$906$	−60582.4	−2.22154
$907$	−15223.9	−0.557332	−0.278666	−	0.960388i	$-0.589892\pi$
$907$	−15223.9	−0.557332	−0.278666	+	0.960388i	$0.589892\pi$
$908$	5415.03	0.197912
$909$	41646.3	1.51960
$910$	2881.02	0.104951
$911$	−4708.31	−0.171233	−0.0856165	−	0.996328i	$-0.527286\pi$
$911$	−4708.31	−0.171233	−0.0856165	+	0.996328i	$0.527286\pi$
$912$	−32541.3	−1.18153
$913$	−10500.7	−0.380638
$914$	16897.5	0.611509
$915$	−2993.77	−0.108165
$916$	−13114.6	−0.473056
$917$	9903.43	0.356641
$918$	−55000.7	−1.97744
$919$	7774.56	0.279063	0.139532	−	0.990218i	$-0.455440\pi$
$919$	7774.56	0.279063	0.139532	+	0.990218i	$0.455440\pi$
$920$	7770.36	0.278458
$921$	54996.4	1.96764
$922$	14546.5	0.519591
$923$	599.970	0.0213957
$924$	10433.6	0.371472
$925$	14580.8	0.518284
$926$	−1652.80	−0.0586549
$927$	−28172.9	−0.998188
$928$	−22011.8	−0.778634
$929$	−48808.1	−1.72373	−0.861863	−	0.507141i	$-0.830702\pi$
$929$	−48808.1	−1.72373	−0.861863	+	0.507141i	$0.830702\pi$
$930$	75028.5	2.64546
$931$	−7086.05	−0.249448
$932$	−4572.48	−0.160705
$933$	35300.2	1.23867
$934$	−21160.0	−0.741303
$935$	−45340.1	−1.58586
$936$	21888.5	0.764367
$937$	−21650.7	−0.754852	−0.377426	−	0.926040i	$-0.623191\pi$
$937$	−21650.7	−0.754852	−0.377426	+	0.926040i	$0.623191\pi$
$938$	6544.41	0.227807
$939$	−24496.3	−0.851337
$940$	−6530.63	−0.226602
$941$	−16762.2	−0.580693	−0.290346	−	0.956922i	$-0.593770\pi$
$941$	−16762.2	−0.580693	−0.290346	+	0.956922i	$0.593770\pi$
$942$	−33811.5	−1.16947
$943$	6718.09	0.231995
$944$	−17137.2	−0.590857
$945$	34225.9	1.17817
$946$	24399.4	0.838577
$947$	25007.7	0.858123	0.429062	−	0.903275i	$-0.358844\pi$
$947$	25007.7	0.858123	0.429062	+	0.903275i	$0.358844\pi$
$948$	41717.2	1.42923
$949$	5807.95	0.198666
$950$	−20494.4	−0.699923
$951$	66224.7	2.25813
$952$	−12555.5	−0.427444
$953$	24152.3	0.820955	0.410478	−	0.911871i	$-0.365362\pi$
$953$	24152.3	0.820955	0.410478	+	0.911871i	$0.365362\pi$
$954$	−48562.7	−1.64809
$955$	1624.03	0.0550285
$956$	10298.2	0.348398
$957$	64392.0	2.17502
$958$	−8679.25	−0.292707
$959$	12330.1	0.415184
$960$	65571.0	2.20447
$961$	42019.5	1.41048
$962$	−6476.89	−0.217072
$963$	−110546.	−3.69916
$964$	20560.1	0.686925
$965$	47699.8	1.59120
$966$	−3254.14	−0.108385
$967$	51912.2	1.72635	0.863177	−	0.504901i	$-0.168471\pi$
$967$	51912.2	1.72635	0.863177	+	0.504901i	$0.168471\pi$
$968$	−15846.4	−0.526160
$969$	101456.	3.36350
$970$	16095.9	0.532791
$971$	27659.9	0.914159	0.457079	−	0.889426i	$-0.348896\pi$
$971$	27659.9	0.914159	0.457079	+	0.889426i	$0.348896\pi$
$972$	21436.1	0.707369
$973$	3872.83	0.127603
$974$	−11037.6	−0.363107
$975$	8947.51	0.293897
$976$	534.414	0.0175268
$977$	8244.82	0.269985	0.134992	−	0.990847i	$-0.456899\pi$
$977$	8244.82	0.269985	0.134992	+	0.990847i	$0.456899\pi$
$978$	−63710.5	−2.08306
$979$	−10205.5	−0.333165
$980$	2382.97	0.0776745
$981$	36798.9	1.19765
$982$	15675.0	0.509378
$983$	−60043.5	−1.94821	−0.974105	−	0.226097i	$-0.927403\pi$
$983$	−60043.5	−1.94821	−0.974105	+	0.226097i	$0.927403\pi$
$984$	67956.5	2.20160
$985$	69751.2	2.25630
$986$	−23633.5	−0.763332
$987$	8967.15	0.289187
$988$	−7119.45	−0.229251
$989$	5951.22	0.191343
$990$	−83600.6	−2.68384
$991$	50596.7	1.62186	0.810928	−	0.585146i	$-0.198963\pi$
$991$	50596.7	1.62186	0.810928	+	0.585146i	$0.198963\pi$
$992$	38891.4	1.24476
$993$	−68893.7	−2.20169
$994$	−634.564	−0.0202486
$995$	−15163.7	−0.483138
$996$	−7901.82	−0.251384
$997$	−48191.9	−1.53084	−0.765422	−	0.643528i	$-0.777470\pi$
$997$	−48191.9	−1.53084	−0.765422	+	0.643528i	$0.777470\pi$
$998$	3654.04	0.115899
$999$	−76943.9	−2.43684

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.d.1.8	✓	12
3.2	odd	2		1449.4.a.o.1.5		12
7.6	odd	2		1127.4.a.h.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.d.1.8	✓	12	1.1	even	1	trivial
1127.4.a.h.1.8		12	7.6	odd	2
1449.4.a.o.1.5		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+2.11879 q^{2} -9.53944 q^{3} -3.51074 q^{4} -13.8523 q^{5} -20.2120 q^{6} +7.00000 q^{7} -24.3888 q^{8} +64.0009 q^{9} -29.3501 q^{10} +44.5055 q^{11} +33.4905 q^{12} -14.0229 q^{13} +14.8315 q^{14} +132.143 q^{15} -23.5887 q^{16} +73.5438 q^{17} +135.604 q^{18} -144.613 q^{19} +48.6320 q^{20} -66.7761 q^{21} +94.2977 q^{22} +23.0000 q^{23} +232.656 q^{24} +66.8868 q^{25} -29.7116 q^{26} -352.967 q^{27} -24.5752 q^{28} -151.668 q^{29} +279.984 q^{30} +267.975 q^{31} +145.131 q^{32} -424.558 q^{33} +155.824 q^{34} -96.9662 q^{35} -224.691 q^{36} +217.992 q^{37} -306.405 q^{38} +133.771 q^{39} +337.842 q^{40} +292.091 q^{41} -141.484 q^{42} +258.749 q^{43} -156.247 q^{44} -886.560 q^{45} +48.7321 q^{46} -134.287 q^{47} +225.023 q^{48} +49.0000 q^{49} +141.719 q^{50} -701.567 q^{51} +49.2310 q^{52} -358.121 q^{53} -747.863 q^{54} -616.505 q^{55} -170.722 q^{56} +1379.53 q^{57} -321.353 q^{58} +726.500 q^{59} -463.921 q^{60} -22.6555 q^{61} +567.781 q^{62} +448.006 q^{63} +496.211 q^{64} +194.250 q^{65} -899.547 q^{66} +441.251 q^{67} -258.194 q^{68} -219.407 q^{69} -205.451 q^{70} -42.7849 q^{71} -1560.90 q^{72} -414.175 q^{73} +461.878 q^{74} -638.062 q^{75} +507.700 q^{76} +311.539 q^{77} +283.432 q^{78} +1245.64 q^{79} +326.759 q^{80} +1639.09 q^{81} +618.878 q^{82} -235.942 q^{83} +234.434 q^{84} -1018.75 q^{85} +548.234 q^{86} +1446.83 q^{87} -1085.44 q^{88} -229.308 q^{89} -1878.43 q^{90} -98.1606 q^{91} -80.7471 q^{92} -2556.33 q^{93} -284.525 q^{94} +2003.23 q^{95} -1384.47 q^{96} -548.410 q^{97} +103.821 q^{98} +2848.39 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + q^{3} + 72 q^{4} + 16 q^{5} - 15 q^{6} + 84 q^{7} - 21 q^{8} + 203 q^{9} + 106 q^{10} + 50 q^{11} - 139 q^{12} + 21 q^{13} + 28 q^{14} + 192 q^{15} + 516 q^{16} + 26 q^{17} + 251 q^{18}+ \cdots + 2400 q^{99}+O(q^{100}) \) 12 * q + 4 * q^2 + q^3 + 72 * q^4 + 16 * q^5 - 15 * q^6 + 84 * q^7 - 21 * q^8 + 203 * q^9 + 106 * q^10 + 50 * q^11 - 139 * q^12 + 21 * q^13 + 28 * q^14 + 192 * q^15 + 516 * q^16 + 26 * q^17 + 251 * q^18 + 292 * q^19 - 12 * q^20 + 7 * q^21 + 206 * q^22 + 276 * q^23 + 42 * q^24 + 408 * q^25 + 409 * q^26 - 335 * q^27 + 504 * q^28 + 129 * q^29 + 168 * q^30 + 375 * q^31 - 54 * q^32 + 428 * q^33 + 674 * q^34 + 112 * q^35 + 2271 * q^36 + 958 * q^37 - 120 * q^38 + 89 * q^39 + 1424 * q^40 - 347 * q^41 - 105 * q^42 + 392 * q^43 - 1158 * q^44 - 1338 * q^45 + 92 * q^46 + 559 * q^47 - 4767 * q^48 + 588 * q^49 - 888 * q^50 + 204 * q^51 - 1765 * q^52 + 42 * q^53 - 1965 * q^54 + 78 * q^55 - 147 * q^56 + 156 * q^57 - 3695 * q^58 - 620 * q^59 - 1574 * q^60 - 1258 * q^61 + 489 * q^62 + 1421 * q^63 + 4335 * q^64 - 752 * q^65 - 7334 * q^66 + 2024 * q^67 - 5162 * q^68 + 23 * q^69 + 742 * q^70 + 1371 * q^71 - 2483 * q^72 - 1241 * q^73 - 4006 * q^74 + 1357 * q^75 + 4214 * q^76 + 350 * q^77 - 4787 * q^78 + 2660 * q^79 - 5734 * q^80 + 2400 * q^81 - 3551 * q^82 - 1476 * q^83 - 973 * q^84 + 408 * q^85 - 988 * q^86 + 1263 * q^87 + 3324 * q^88 + 1670 * q^89 + 1050 * q^90 + 147 * q^91 + 1656 * q^92 + 135 * q^93 - 3539 * q^94 + 2428 * q^95 - 3973 * q^96 + 1174 * q^97 + 196 * q^98 + 2400 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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