LMFDB - Embedded newform 415.4.a.c.1.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [415,4,Mod(1,415)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("415.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(415, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 415 = 5 \cdot 83 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	415.a (trivial)

Newform invariants

comment:select newform

sage:traces = [21] 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:	$24.4857926524$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	415.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.52351 q^{2} +2.27996 q^{3} -5.67892 q^{4} -5.00000 q^{5} -3.47354 q^{6} +9.53696 q^{7} +20.8400 q^{8} -21.8018 q^{9} +7.61755 q^{10} +58.3417 q^{11} -12.9477 q^{12} -68.7822 q^{13} -14.5297 q^{14} -11.3998 q^{15} +13.6814 q^{16} +87.2391 q^{17} +33.2153 q^{18} -122.038 q^{19} +28.3946 q^{20} +21.7439 q^{21} -88.8842 q^{22} +181.049 q^{23} +47.5142 q^{24} +25.0000 q^{25} +104.790 q^{26} -111.266 q^{27} -54.1596 q^{28} +39.0467 q^{29} +17.3677 q^{30} -159.515 q^{31} -187.564 q^{32} +133.016 q^{33} -132.910 q^{34} -47.6848 q^{35} +123.811 q^{36} -174.925 q^{37} +185.926 q^{38} -156.820 q^{39} -104.200 q^{40} -232.187 q^{41} -33.1270 q^{42} -268.245 q^{43} -331.318 q^{44} +109.009 q^{45} -275.830 q^{46} +373.579 q^{47} +31.1930 q^{48} -252.046 q^{49} -38.0878 q^{50} +198.901 q^{51} +390.608 q^{52} -532.530 q^{53} +169.515 q^{54} -291.709 q^{55} +198.750 q^{56} -278.241 q^{57} -59.4880 q^{58} -492.537 q^{59} +64.7384 q^{60} +324.629 q^{61} +243.024 q^{62} -207.923 q^{63} +176.304 q^{64} +343.911 q^{65} -202.652 q^{66} +583.030 q^{67} -495.424 q^{68} +412.783 q^{69} +72.6483 q^{70} -1048.99 q^{71} -454.349 q^{72} -510.729 q^{73} +266.500 q^{74} +56.9989 q^{75} +693.043 q^{76} +556.403 q^{77} +238.917 q^{78} -1197.20 q^{79} -68.4070 q^{80} +334.967 q^{81} +353.739 q^{82} +83.0000 q^{83} -123.481 q^{84} -436.196 q^{85} +408.673 q^{86} +89.0247 q^{87} +1215.84 q^{88} -170.431 q^{89} -166.076 q^{90} -655.973 q^{91} -1028.16 q^{92} -363.688 q^{93} -569.151 q^{94} +610.190 q^{95} -427.636 q^{96} +464.590 q^{97} +383.995 q^{98} -1271.95 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 5 q^{2} - 12 q^{3} + 87 q^{4} - 105 q^{5} - 7 q^{6} - 11 q^{7} - 84 q^{8} + 153 q^{9} + 25 q^{10} - 30 q^{11} - 244 q^{12} - 89 q^{13} - 191 q^{14} + 60 q^{15} + 583 q^{16} - 357 q^{17} - 281 q^{18}+ \cdots - 5369 q^{99}+O(q^{100}) $ 21 * q - 5 * q^2 - 12 * q^3 + 87 * q^4 - 105 * q^5 - 7 * q^6 - 11 * q^7 - 84 * q^8 + 153 * q^9 + 25 * q^10 - 30 * q^11 - 244 * q^12 - 89 * q^13 - 191 * q^14 + 60 * q^15 + 583 * q^16 - 357 * q^17 - 281 * q^18 - 175 * q^19 - 435 * q^20 - 41 * q^21 - 122 * q^22 - 554 * q^23 - 136 * q^24 + 525 * q^25 - 933 * q^26 - 555 * q^27 - 773 * q^28 - 96 * q^29 + 35 * q^30 + 99 * q^31 - 1307 * q^32 - 1097 * q^33 + 393 * q^34 + 55 * q^35 - 746 * q^36 - 756 * q^37 - 1192 * q^38 + 40 * q^39 + 420 * q^40 - 1436 * q^41 - 1112 * q^42 - 1003 * q^43 - 706 * q^44 - 765 * q^45 - 775 * q^46 - 858 * q^47 - 2837 * q^48 + 1384 * q^49 - 125 * q^50 - 279 * q^51 - 1092 * q^52 - 1625 * q^53 - 269 * q^54 + 150 * q^55 - 3806 * q^56 - 1740 * q^57 - 1087 * q^58 - 1224 * q^59 + 1220 * q^60 - 794 * q^61 - 2979 * q^62 - 1236 * q^63 + 2570 * q^64 + 445 * q^65 - 1094 * q^66 - 571 * q^67 - 4064 * q^68 + 774 * q^69 + 955 * q^70 - 1078 * q^71 - 2610 * q^72 - 1986 * q^73 - 1872 * q^74 - 300 * q^75 - 2854 * q^76 - 2519 * q^77 - 2449 * q^78 - 432 * q^79 - 2915 * q^80 - 219 * q^81 - 2143 * q^82 + 1743 * q^83 - 377 * q^84 + 1785 * q^85 + 1556 * q^86 - 5681 * q^87 - 3158 * q^88 - 6252 * q^89 + 1405 * q^90 + 684 * q^91 - 7623 * q^92 - 3314 * q^93 - 3877 * q^94 + 875 * q^95 - 954 * q^96 - 4880 * q^97 - 5072 * q^98 - 5369 * q^99

Coefficient data

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

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

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

$2$	−1.52351	−0.538642	−0.269321	−	0.963050i	$-0.586799\pi$
$2$	−1.52351	−0.538642	−0.269321	+	0.963050i	$0.586799\pi$
$3$	2.27996	0.438778	0.219389	−	0.975638i	$-0.429594\pi$
$3$	2.27996	0.438778	0.219389	+	0.975638i	$0.429594\pi$
$4$	−5.67892	−0.709864
$5$	−5.00000	−0.447214
$5$	−5.00000	−0.447214
$6$	−3.47354	−0.236344
$7$	9.53696	0.514948	0.257474	−	0.966285i	$-0.417110\pi$
$7$	9.53696	0.514948	0.257474	+	0.966285i	$0.417110\pi$
$8$	20.8400	0.921005
$9$	−21.8018	−0.807474
$10$	7.61755	0.240888
$11$	58.3417	1.59915	0.799577	−	0.600564i	$-0.205057\pi$
$11$	58.3417	1.59915	0.799577	+	0.600564i	$0.205057\pi$
$12$	−12.9477	−0.311473
$13$	−68.7822	−1.46744	−0.733721	−	0.679451i	$-0.762218\pi$
$13$	−68.7822	−1.46744	−0.733721	+	0.679451i	$0.762218\pi$
$14$	−14.5297	−0.277373
$15$	−11.3998	−0.196227
$16$	13.6814	0.213772
$17$	87.2391	1.24462	0.622312	−	0.782770i	$-0.286194\pi$
$17$	87.2391	1.24462	0.622312	+	0.782770i	$0.286194\pi$
$18$	33.2153	0.434940
$19$	−122.038	−1.47355	−0.736774	−	0.676139i	$-0.763652\pi$
$19$	−122.038	−1.47355	−0.736774	+	0.676139i	$0.763652\pi$
$20$	28.3946	0.317461
$21$	21.7439	0.225947
$22$	−88.8842	−0.861372
$23$	181.049	1.64136	0.820679	−	0.571389i	$-0.193595\pi$
$23$	181.049	1.64136	0.820679	+	0.571389i	$0.193595\pi$
$24$	47.5142	0.404117
$25$	25.0000	0.200000
$26$	104.790	0.790427
$27$	−111.266	−0.793079
$28$	−54.1596	−0.365543
$29$	39.0467	0.250027	0.125014	−	0.992155i	$-0.460103\pi$
$29$	39.0467	0.250027	0.125014	+	0.992155i	$0.460103\pi$
$30$	17.3677	0.105696
$31$	−159.515	−0.924188	−0.462094	−	0.886831i	$-0.652902\pi$
$31$	−159.515	−0.924188	−0.462094	+	0.886831i	$0.652902\pi$
$32$	−187.564	−1.03615
$33$	133.016	0.701673
$34$	−132.910	−0.670407
$35$	−47.6848	−0.230292
$36$	123.811	0.573197
$37$	−174.925	−0.777230	−0.388615	−	0.921400i	$-0.627046\pi$
$37$	−174.925	−0.777230	−0.388615	+	0.921400i	$0.627046\pi$
$38$	185.926	0.793716
$39$	−156.820	−0.643881
$40$	−104.200	−0.411886
$41$	−232.187	−0.884427	−0.442213	−	0.896910i	$-0.645807\pi$
$41$	−232.187	−0.884427	−0.442213	+	0.896910i	$0.645807\pi$
$42$	−33.1270	−0.121705
$43$	−268.245	−0.951324	−0.475662	−	0.879628i	$-0.657791\pi$
$43$	−268.245	−0.951324	−0.475662	+	0.879628i	$0.657791\pi$
$44$	−331.318	−1.13518
$45$	109.009	0.361113
$46$	−275.830	−0.884105
$47$	373.579	1.15941	0.579703	−	0.814828i	$-0.303169\pi$
$47$	373.579	1.15941	0.579703	+	0.814828i	$0.303169\pi$
$48$	31.1930	0.0937983
$49$	−252.046	−0.734829
$50$	−38.0878	−0.107728
$51$	198.901	0.546113
$52$	390.608	1.04169
$53$	−532.530	−1.38016	−0.690081	−	0.723732i	$-0.742425\pi$
$53$	−532.530	−1.38016	−0.690081	+	0.723732i	$0.742425\pi$
$54$	169.515	0.427186
$55$	−291.709	−0.715163
$56$	198.750	0.474270
$57$	−278.241	−0.646560
$58$	−59.4880	−0.134675
$59$	−492.537	−1.08683	−0.543414	−	0.839465i	$-0.682869\pi$
$59$	−492.537	−1.08683	−0.543414	+	0.839465i	$0.682869\pi$
$60$	64.7384	0.139295
$61$	324.629	0.681386	0.340693	−	0.940175i	$-0.389338\pi$
$61$	324.629	0.681386	0.340693	+	0.940175i	$0.389338\pi$
$62$	243.024	0.497807
$63$	−207.923	−0.415807
$64$	176.304	0.344344
$65$	343.911	0.656260
$66$	−202.652	−0.377951
$67$	583.030	1.06311	0.531556	−	0.847023i	$-0.321608\pi$
$67$	583.030	1.06311	0.531556	+	0.847023i	$0.321608\pi$
$68$	−495.424	−0.883514
$69$	412.783	0.720191
$70$	72.6483	0.124045
$71$	−1048.99	−1.75340	−0.876702	−	0.481034i	$-0.840261\pi$
$71$	−1048.99	−1.75340	−0.876702	+	0.481034i	$0.840261\pi$
$72$	−454.349	−0.743688
$73$	−510.729	−0.818854	−0.409427	−	0.912343i	$-0.634271\pi$
$73$	−510.729	−0.818854	−0.409427	+	0.912343i	$0.634271\pi$
$74$	266.500	0.418649
$75$	56.9989	0.0877555
$76$	693.043	1.04602
$77$	556.403	0.823480
$78$	238.917	0.346821
$79$	−1197.20	−1.70501	−0.852505	−	0.522719i	$-0.824918\pi$
$79$	−1197.20	−1.70501	−0.852505	+	0.522719i	$0.824918\pi$
$80$	−68.4070	−0.0956017
$81$	334.967	0.459489
$82$	353.739	0.476390
$83$	83.0000	0.109764
$83$	83.0000	0.109764
$84$	−123.481	−0.160392
$85$	−436.196	−0.556612
$86$	408.673	0.512423
$87$	89.0247	0.109706
$88$	1215.84	1.47283
$89$	−170.431	−0.202985	−0.101493	−	0.994836i	$-0.532362\pi$
$89$	−170.431	−0.202985	−0.101493	+	0.994836i	$0.532362\pi$
$90$	−166.076	−0.194511
$91$	−655.973	−0.755656
$92$	−1028.16	−1.16514
$93$	−363.688	−0.405513
$94$	−569.151	−0.624505
$95$	610.190	0.658991
$96$	−427.636	−0.454640
$97$	464.590	0.486309	0.243155	−	0.969988i	$-0.421818\pi$
$97$	464.590	0.486309	0.243155	+	0.969988i	$0.421818\pi$
$98$	383.995	0.395810
$99$	−1271.95	−1.29128
$100$	−141.973	−0.141973
$101$	−1050.82	−1.03525	−0.517624	−	0.855608i	$-0.673183\pi$
$101$	−1050.82	−1.03525	−0.517624	+	0.855608i	$0.673183\pi$
$102$	−303.028	−0.294159
$103$	−1435.65	−1.37339	−0.686694	−	0.726947i	$-0.740939\pi$
$103$	−1435.65	−1.37339	−0.686694	+	0.726947i	$0.740939\pi$
$104$	−1433.42	−1.35152
$105$	−108.719	−0.101047
$106$	811.315	0.743414
$107$	−636.749	−0.575297	−0.287649	−	0.957736i	$-0.592874\pi$
$107$	−636.749	−0.575297	−0.287649	+	0.957736i	$0.592874\pi$
$108$	631.870	0.562979
$109$	2104.83	1.84960	0.924799	−	0.380456i	$-0.124233\pi$
$109$	2104.83	1.84960	0.924799	+	0.380456i	$0.124233\pi$
$110$	444.421	0.385217
$111$	−398.821	−0.341031
$112$	130.479	0.110081
$113$	−156.174	−0.130015	−0.0650073	−	0.997885i	$-0.520707\pi$
$113$	−156.174	−0.130015	−0.0650073	+	0.997885i	$0.520707\pi$
$114$	423.903	0.348265
$115$	−905.243	−0.734038
$116$	−221.743	−0.177485
$117$	1499.58	1.18492
$118$	750.385	0.585411
$119$	831.996	0.640916
$120$	−237.571	−0.180726
$121$	2072.76	1.55729
$122$	−494.576	−0.367023
$123$	−529.376	−0.388067
$124$	905.875	0.656048
$125$	−125.000	−0.0894427
$126$	316.773	0.223971
$127$	−2480.31	−1.73301	−0.866505	−	0.499168i	$-0.833639\pi$
$127$	−2480.31	−1.73301	−0.866505	+	0.499168i	$0.833639\pi$
$128$	1231.91	0.850674
$129$	−611.586	−0.417419
$130$	−523.952	−0.353490
$131$	124.301	0.0829024	0.0414512	−	0.999141i	$-0.486802\pi$
$131$	124.301	0.0829024	0.0414512	+	0.999141i	$0.486802\pi$
$132$	−755.389	−0.498092
$133$	−1163.87	−0.758800
$134$	−888.252	−0.572637
$135$	556.330	0.354676
$136$	1818.06	1.14630
$137$	−1442.09	−0.899317	−0.449659	−	0.893200i	$-0.648454\pi$
$137$	−1442.09	−0.899317	−0.449659	+	0.893200i	$0.648454\pi$
$138$	−628.879	−0.387926
$139$	−434.791	−0.265313	−0.132656	−	0.991162i	$-0.542351\pi$
$139$	−434.791	−0.265313	−0.132656	+	0.991162i	$0.542351\pi$
$140$	270.798	0.163476
$141$	851.743	0.508721
$142$	1598.14	0.944458
$143$	−4012.87	−2.34667
$144$	−298.279	−0.172615
$145$	−195.233	−0.111815
$146$	778.102	0.441069
$147$	−574.654	−0.322426
$148$	993.385	0.551728
$149$	2831.58	1.55686	0.778429	−	0.627732i	$-0.216017\pi$
$149$	2831.58	1.55686	0.778429	+	0.627732i	$0.216017\pi$
$150$	−86.8384	−0.0472688
$151$	1287.43	0.693840	0.346920	−	0.937895i	$-0.387227\pi$
$151$	1287.43	0.693840	0.346920	+	0.937895i	$0.387227\pi$
$152$	−2543.27	−1.35715
$153$	−1901.97	−1.00500
$154$	−847.686	−0.443561
$155$	797.577	0.413309
$156$	890.569	0.457068
$157$	−1550.95	−0.788403	−0.394201	−	0.919024i	$-0.628979\pi$
$157$	−1550.95	−0.788403	−0.394201	+	0.919024i	$0.628979\pi$
$158$	1823.95	0.918391
$159$	−1214.14	−0.605584
$160$	937.818	0.463381
$161$	1726.65	0.845214
$162$	−510.326	−0.247500
$163$	−1681.15	−0.807840	−0.403920	−	0.914794i	$-0.632353\pi$
$163$	−1681.15	−0.807840	−0.403920	+	0.914794i	$0.632353\pi$
$164$	1318.57	0.627823
$165$	−665.082	−0.313798
$166$	−126.451	−0.0591237
$167$	311.253	0.144224	0.0721122	−	0.997397i	$-0.477026\pi$
$167$	311.253	0.144224	0.0721122	+	0.997397i	$0.477026\pi$
$168$	453.141	0.208099
$169$	2533.99	1.15339
$170$	664.549	0.299815
$171$	2660.65	1.18985
$172$	1523.34	0.675311
$173$	3487.62	1.53271	0.766355	−	0.642418i	$-0.222069\pi$
$173$	3487.62	1.53271	0.766355	+	0.642418i	$0.222069\pi$
$174$	−135.630	−0.0590924
$175$	238.424	0.102990
$176$	798.196	0.341854
$177$	−1122.96	−0.476876
$178$	259.654	0.109336
$179$	2671.46	1.11550	0.557749	−	0.830010i	$-0.311665\pi$
$179$	2671.46	1.11550	0.557749	+	0.830010i	$0.311665\pi$
$180$	−619.053	−0.256342
$181$	2311.46	0.949222	0.474611	−	0.880196i	$-0.342589\pi$
$181$	2311.46	0.949222	0.474611	+	0.880196i	$0.342589\pi$
$182$	999.383	0.407028
$183$	740.140	0.298977
$184$	3773.05	1.51170
$185$	874.626	0.347588
$186$	554.083	0.218426
$187$	5089.68	1.99034
$188$	−2121.52	−0.823021
$189$	−1061.14	−0.408394
$190$	−929.630	−0.354960
$191$	2619.04	0.992184	0.496092	−	0.868270i	$-0.334768\pi$
$191$	2619.04	0.992184	0.496092	+	0.868270i	$0.334768\pi$
$192$	401.965	0.151090
$193$	−1752.12	−0.653474	−0.326737	−	0.945115i	$-0.605949\pi$
$193$	−1752.12	−0.653474	−0.326737	+	0.945115i	$0.605949\pi$
$194$	−707.809	−0.261947
$195$	784.102	0.287952
$196$	1431.35	0.521629
$197$	3723.06	1.34648	0.673241	−	0.739423i	$-0.264902\pi$
$197$	3723.06	1.34648	0.673241	+	0.739423i	$0.264902\pi$
$198$	1937.84	0.695536
$199$	−3665.93	−1.30589	−0.652943	−	0.757407i	$-0.726466\pi$
$199$	−3665.93	−1.30589	−0.652943	+	0.757407i	$0.726466\pi$
$200$	520.999	0.184201
$201$	1329.28	0.466469
$202$	1600.93	0.557628
$203$	372.387	0.128751
$204$	−1129.54	−0.387666
$205$	1160.93	0.395528
$206$	2187.23	0.739765
$207$	−3947.19	−1.32535
$208$	−941.037	−0.313698
$209$	−7119.90	−2.35643
$210$	165.635	0.0544281
$211$	5551.32	1.81123	0.905613	−	0.424104i	$-0.139411\pi$
$211$	5551.32	1.81123	0.905613	+	0.424104i	$0.139411\pi$
$212$	3024.19	0.979728
$213$	−2391.64	−0.769354
$214$	970.094	0.309880
$215$	1341.22	0.425445
$216$	−2318.78	−0.730430
$217$	−1521.29	−0.475908
$218$	−3206.73	−0.996272
$219$	−1164.44	−0.359295
$220$	1656.59	0.507669
$221$	−6000.50	−1.82641
$222$	607.609	0.183694
$223$	−345.414	−0.103725	−0.0518623	−	0.998654i	$-0.516516\pi$
$223$	−345.414	−0.103725	−0.0518623	+	0.998654i	$0.516516\pi$
$224$	−1788.79	−0.533564
$225$	−545.045	−0.161495
$226$	237.933	0.0700314
$227$	−3965.94	−1.15960	−0.579798	−	0.814760i	$-0.696869\pi$
$227$	−3965.94	−1.15960	−0.579798	+	0.814760i	$0.696869\pi$
$228$	1580.11	0.458970
$229$	775.056	0.223656	0.111828	−	0.993728i	$-0.464329\pi$
$229$	775.056	0.223656	0.111828	+	0.993728i	$0.464329\pi$
$230$	1379.15	0.395384
$231$	1268.57	0.361325
$232$	813.732	0.230276
$233$	1470.86	0.413559	0.206780	−	0.978388i	$-0.433702\pi$
$233$	1470.86	0.413559	0.206780	+	0.978388i	$0.433702\pi$
$234$	−2284.62	−0.638249
$235$	−1867.89	−0.518502
$236$	2797.07	0.771500
$237$	−2729.57	−0.748120
$238$	−1267.56	−0.345224
$239$	11.3141	0.00306214	0.00153107	−	0.999999i	$-0.499513\pi$
$239$	11.3141	0.00306214	0.00153107	+	0.999999i	$0.499513\pi$
$240$	−155.965	−0.0419479
$241$	−2035.05	−0.543939	−0.271969	−	0.962306i	$-0.587675\pi$
$241$	−2035.05	−0.543939	−0.271969	+	0.962306i	$0.587675\pi$
$242$	−3157.86	−0.838823
$243$	3767.89	0.994693
$244$	−1843.54	−0.483692
$245$	1260.23	0.328625
$246$	806.510	0.209029
$247$	8394.04	2.16235
$248$	−3324.30	−0.851182
$249$	189.236	0.0481621
$250$	190.439	0.0481776
$251$	392.845	0.0987894	0.0493947	−	0.998779i	$-0.484271\pi$
$251$	392.845	0.0987894	0.0493947	+	0.998779i	$0.484271\pi$
$252$	1180.78	0.295167
$253$	10562.7	2.62478
$254$	3778.79	0.933473
$255$	−994.506	−0.244229
$256$	−3287.26	−0.802553
$257$	−1734.89	−0.421087	−0.210543	−	0.977585i	$-0.567523\pi$
$257$	−1734.89	−0.421087	−0.210543	+	0.977585i	$0.567523\pi$
$258$	931.757	0.224840
$259$	−1668.25	−0.400233
$260$	−1953.04	−0.465856
$261$	−851.288	−0.201890
$262$	−189.374	−0.0446547
$263$	191.388	0.0448725	0.0224363	−	0.999748i	$-0.492858\pi$
$263$	191.388	0.0448725	0.0224363	+	0.999748i	$0.492858\pi$
$264$	2772.06	0.646244
$265$	2662.65	0.617227
$266$	1773.17	0.408722
$267$	−388.576	−0.0890653
$268$	−3310.98	−0.754665
$269$	3106.75	0.704171	0.352085	−	0.935968i	$-0.385473\pi$
$269$	3106.75	0.704171	0.352085	+	0.935968i	$0.385473\pi$
$270$	−847.574	−0.191043
$271$	−8143.14	−1.82532	−0.912658	−	0.408723i	$-0.865974\pi$
$271$	−8143.14	−1.82532	−0.912658	+	0.408723i	$0.865974\pi$
$272$	1193.55	0.266065
$273$	−1495.59	−0.331565
$274$	2197.05	0.484410
$275$	1458.54	0.319831
$276$	−2344.16	−0.511238
$277$	−6428.64	−1.39444	−0.697219	−	0.716858i	$-0.745579\pi$
$277$	−6428.64	−1.39444	−0.697219	+	0.716858i	$0.745579\pi$
$278$	662.409	0.142909
$279$	3477.73	0.746258
$280$	−993.750	−0.212100
$281$	−6379.48	−1.35433	−0.677167	−	0.735830i	$-0.736792\pi$
$281$	−6379.48	−1.35433	−0.677167	+	0.735830i	$0.736792\pi$
$282$	−1297.64	−0.274019
$283$	−1477.39	−0.310325	−0.155163	−	0.987889i	$-0.549590\pi$
$283$	−1477.39	−0.310325	−0.155163	+	0.987889i	$0.549590\pi$
$284$	5957.10	1.24468
$285$	1391.21	0.289150
$286$	6113.65	1.26401
$287$	−2214.36	−0.455434
$288$	4089.22	0.836666
$289$	2697.66	0.549087
$290$	297.440	0.0602286
$291$	1059.25	0.213382
$292$	2900.39	0.581275
$293$	3391.39	0.676202	0.338101	−	0.941110i	$-0.390215\pi$
$293$	3391.39	0.676202	0.338101	+	0.941110i	$0.390215\pi$
$294$	875.492	0.173673
$295$	2462.68	0.486044
$296$	−3645.43	−0.715833
$297$	−6491.44	−1.26826
$298$	−4313.94	−0.838590
$299$	−12452.9	−2.40860
$300$	−323.692	−0.0622945
$301$	−2558.24	−0.489882
$302$	−1961.42	−0.373732
$303$	−2395.81	−0.454244
$304$	−1669.65	−0.315003
$305$	−1623.15	−0.304725
$306$	2897.67	0.541336
$307$	−7178.81	−1.33458	−0.667291	−	0.744798i	$-0.732546\pi$
$307$	−7178.81	−1.33458	−0.667291	+	0.744798i	$0.732546\pi$
$308$	−3159.76	−0.584559
$309$	−3273.22	−0.602612
$310$	−1215.12	−0.222626
$311$	4757.32	0.867404	0.433702	−	0.901056i	$-0.357207\pi$
$311$	4757.32	0.867404	0.433702	+	0.901056i	$0.357207\pi$
$312$	−3268.13	−0.593018
$313$	−1566.01	−0.282799	−0.141399	−	0.989953i	$-0.545160\pi$
$313$	−1566.01	−0.282799	−0.141399	+	0.989953i	$0.545160\pi$
$314$	2362.89	0.424667
$315$	1039.62	0.185955
$316$	6798.81	1.21033
$317$	−9079.93	−1.60877	−0.804384	−	0.594109i	$-0.797505\pi$
$317$	−9079.93	−1.60877	−0.804384	+	0.594109i	$0.797505\pi$
$318$	1849.76	0.326193
$319$	2278.05	0.399832
$320$	−881.519	−0.153995
$321$	−1451.76	−0.252428
$322$	−2630.58	−0.455268
$323$	−10646.5	−1.83401
$324$	−1902.25	−0.326175
$325$	−1719.56	−0.293488
$326$	2561.25	0.435137
$327$	4798.92	0.811562
$328$	−4838.77	−0.814562
$329$	3562.81	0.597033
$330$	1013.26	0.169025
$331$	5363.00	0.890565	0.445283	−	0.895390i	$-0.353103\pi$
$331$	5363.00	0.890565	0.445283	+	0.895390i	$0.353103\pi$
$332$	−471.350	−0.0779177
$333$	3813.68	0.627593
$334$	−474.197	−0.0776854
$335$	−2915.15	−0.475438
$336$	297.486	0.0483012
$337$	−10899.9	−1.76188	−0.880940	−	0.473228i	$-0.843089\pi$
$337$	−10899.9	−1.76188	−0.880940	+	0.473228i	$0.843089\pi$
$338$	−3860.56	−0.621263
$339$	−356.071	−0.0570475
$340$	2477.12	0.395119
$341$	−9306.41	−1.47792
$342$	−4053.52	−0.640905
$343$	−5674.94	−0.893346
$344$	−5590.21	−0.876174
$345$	−2063.91	−0.322079
$346$	−5313.42	−0.825582
$347$	4599.17	0.711517	0.355758	−	0.934578i	$-0.384223\pi$
$347$	4599.17	0.711517	0.355758	+	0.934578i	$0.384223\pi$
$348$	−505.563	−0.0778766
$349$	−2707.96	−0.415341	−0.207670	−	0.978199i	$-0.566588\pi$
$349$	−2707.96	−0.415341	−0.207670	+	0.978199i	$0.566588\pi$
$350$	−363.242	−0.0554745
$351$	7653.12	1.16380
$352$	−10942.8	−1.65697
$353$	−5693.22	−0.858413	−0.429206	−	0.903206i	$-0.641207\pi$
$353$	−5693.22	−0.858413	−0.429206	+	0.903206i	$0.641207\pi$
$354$	1710.84	0.256865
$355$	5244.93	0.784146
$356$	967.865	0.144092
$357$	1896.91	0.281219
$358$	−4069.99	−0.600854
$359$	11778.5	1.73160	0.865800	−	0.500389i	$-0.166810\pi$
$359$	11778.5	1.73160	0.865800	+	0.500389i	$0.166810\pi$
$360$	2271.75	0.332587
$361$	8034.26	1.17135
$362$	−3521.53	−0.511291
$363$	4725.79	0.683305
$364$	3725.22	0.536413
$365$	2553.65	0.366203
$366$	−1127.61	−0.161042
$367$	2945.24	0.418911	0.209455	−	0.977818i	$-0.432831\pi$
$367$	2945.24	0.418911	0.209455	+	0.977818i	$0.432831\pi$
$368$	2477.00	0.350876
$369$	5062.09	0.714152
$370$	−1332.50	−0.187226
$371$	−5078.72	−0.710711
$372$	2065.35	0.287859
$373$	−1706.46	−0.236882	−0.118441	−	0.992961i	$-0.537790\pi$
$373$	−1706.46	−0.236882	−0.118441	+	0.992961i	$0.537790\pi$
$374$	−7754.18	−1.07208
$375$	−284.994	−0.0392455
$376$	7785.37	1.06782
$377$	−2685.72	−0.366900
$378$	1616.66	0.219978
$379$	−11508.4	−1.55976	−0.779879	−	0.625930i	$-0.784719\pi$
$379$	−11508.4	−1.55976	−0.779879	+	0.625930i	$0.784719\pi$
$380$	−3465.22	−0.467794
$381$	−5655.01	−0.760406
$382$	−3990.14	−0.534432
$383$	11376.4	1.51777	0.758885	−	0.651225i	$-0.225745\pi$
$383$	11376.4	1.51777	0.758885	+	0.651225i	$0.225745\pi$
$384$	2808.69	0.373257
$385$	−2782.01	−0.368272
$386$	2669.37	0.351989
$387$	5848.22	0.768169
$388$	−2638.37	−0.345214
$389$	−1455.14	−0.189663	−0.0948313	−	0.995493i	$-0.530231\pi$
$389$	−1455.14	−0.189663	−0.0948313	+	0.995493i	$0.530231\pi$
$390$	−1194.59	−0.155103
$391$	15794.5	2.04287
$392$	−5252.64	−0.676781
$393$	283.400	0.0363757
$394$	−5672.12	−0.725272
$395$	5986.01	0.762504
$396$	7223.32	0.916630
$397$	10435.0	1.31919	0.659594	−	0.751622i	$-0.270728\pi$
$397$	10435.0	1.31919	0.659594	+	0.751622i	$0.270728\pi$
$398$	5585.09	0.703405
$399$	−2653.57	−0.332945
$400$	342.035	0.0427544
$401$	−4464.91	−0.556027	−0.278014	−	0.960577i	$-0.589676\pi$
$401$	−4464.91	−0.556027	−0.278014	+	0.960577i	$0.589676\pi$
$402$	−2025.18	−0.251260
$403$	10971.8	1.35619
$404$	5967.49	0.734886
$405$	−1674.84	−0.205490
$406$	−567.335	−0.0693507
$407$	−10205.4	−1.24291
$408$	4145.10	0.502973
$409$	−1305.92	−0.157882	−0.0789408	−	0.996879i	$-0.525154\pi$
$409$	−1305.92	−0.157882	−0.0789408	+	0.996879i	$0.525154\pi$
$410$	−1768.70	−0.213048
$411$	−3287.91	−0.394600
$412$	8152.94	0.974919
$413$	−4697.31	−0.559659
$414$	6013.58	0.713892
$415$	−415.000	−0.0490881
$416$	12901.0	1.52049
$417$	−991.304	−0.116413
$418$	10847.2	1.26927
$419$	−9560.35	−1.11469	−0.557343	−	0.830282i	$-0.688179\pi$
$419$	−9560.35	−1.11469	−0.557343	+	0.830282i	$0.688179\pi$
$420$	617.407	0.0717295
$421$	12725.5	1.47316	0.736581	−	0.676349i	$-0.236439\pi$
$421$	12725.5	1.47316	0.736581	+	0.676349i	$0.236439\pi$
$422$	−8457.50	−0.975603
$423$	−8144.69	−0.936190
$424$	−11097.9	−1.27114
$425$	2180.98	0.248925
$426$	3643.69	0.414407
$427$	3095.98	0.350878
$428$	3616.04	0.408383
$429$	−9149.17	−1.02966
$430$	−2043.37	−0.229163
$431$	−3802.40	−0.424954	−0.212477	−	0.977166i	$-0.568153\pi$
$431$	−3802.40	−0.424954	−0.212477	+	0.977166i	$0.568153\pi$
$432$	−1522.27	−0.169538
$433$	5008.23	0.555844	0.277922	−	0.960604i	$-0.410354\pi$
$433$	5008.23	0.555844	0.277922	+	0.960604i	$0.410354\pi$
$434$	2317.71	0.256344
$435$	−445.123	−0.0490621
$436$	−11953.2	−1.31296
$437$	−22094.8	−2.41862
$438$	1774.04	0.193531
$439$	759.014	0.0825188	0.0412594	−	0.999148i	$-0.486863\pi$
$439$	759.014	0.0825188	0.0412594	+	0.999148i	$0.486863\pi$
$440$	−6079.20	−0.658669
$441$	5495.06	0.593355
$442$	9141.82	0.983783
$443$	5220.82	0.559930	0.279965	−	0.960010i	$-0.409677\pi$
$443$	5220.82	0.559930	0.279965	+	0.960010i	$0.409677\pi$
$444$	2264.87	0.242086
$445$	852.156	0.0907777
$446$	526.241	0.0558705
$447$	6455.87	0.683115
$448$	1681.40	0.177319
$449$	144.140	0.0151501	0.00757506	−	0.999971i	$-0.497589\pi$
$449$	144.140	0.0151501	0.00757506	+	0.999971i	$0.497589\pi$
$450$	830.382	0.0869880
$451$	−13546.2	−1.41433
$452$	886.902	0.0922928
$453$	2935.29	0.304442
$454$	6042.15	0.624608
$455$	3279.87	0.337940
$456$	−5798.54	−0.595485
$457$	4176.41	0.427493	0.213747	−	0.976889i	$-0.431433\pi$
$457$	4176.41	0.427493	0.213747	+	0.976889i	$0.431433\pi$
$458$	−1180.81	−0.120470
$459$	−9706.74	−0.987085
$460$	5140.80	0.521067
$461$	10280.5	1.03864	0.519318	−	0.854581i	$-0.326186\pi$
$461$	10280.5	1.03864	0.519318	+	0.854581i	$0.326186\pi$
$462$	−1932.69	−0.194625
$463$	−63.5675	−0.00638063	−0.00319032	−	0.999995i	$-0.501016\pi$
$463$	−63.5675	−0.00638063	−0.00319032	+	0.999995i	$0.501016\pi$
$464$	534.213	0.0534487
$465$	1818.44	0.181351
$466$	−2240.87	−0.222760
$467$	−13276.1	−1.31551	−0.657754	−	0.753232i	$-0.728494\pi$
$467$	−13276.1	−1.31551	−0.657754	+	0.753232i	$0.728494\pi$
$468$	−8515.97	−0.841134
$469$	5560.34	0.547447
$470$	2845.76	0.279287
$471$	−3536.09	−0.345933
$472$	−10264.5	−1.00097
$473$	−15649.8	−1.52131
$474$	4158.53	0.402969
$475$	−3050.95	−0.294710
$476$	−4724.84	−0.454963
$477$	11610.1	1.11445
$478$	−17.2372	−0.00164940
$479$	362.208	0.0345505	0.0172752	−	0.999851i	$-0.494501\pi$
$479$	362.208	0.0345505	0.0172752	+	0.999851i	$0.494501\pi$
$480$	2138.18	0.203321
$481$	12031.7	1.14054
$482$	3100.42	0.292989
$483$	3936.69	0.370861
$484$	−11771.0	−1.10547
$485$	−2322.95	−0.217484
$486$	−5740.42	−0.535784
$487$	4517.95	0.420386	0.210193	−	0.977660i	$-0.432591\pi$
$487$	4517.95	0.420386	0.210193	+	0.977660i	$0.432591\pi$
$488$	6765.27	0.627560
$489$	−3832.95	−0.354462
$490$	−1919.98	−0.177012
$491$	13557.8	1.24614	0.623070	−	0.782166i	$-0.285885\pi$
$491$	13557.8	1.24614	0.623070	+	0.782166i	$0.285885\pi$
$492$	3006.28	0.275475
$493$	3406.40	0.311189
$494$	−12788.4	−1.16473
$495$	6359.77	0.577476
$496$	−2182.39	−0.197565
$497$	−10004.1	−0.902911
$498$	−288.303	−0.0259421
$499$	−9368.11	−0.840429	−0.420215	−	0.907425i	$-0.638045\pi$
$499$	−9368.11	−0.840429	−0.420215	+	0.907425i	$0.638045\pi$
$500$	709.864	0.0634922
$501$	709.643	0.0632825
$502$	−598.503	−0.0532121
$503$	−14154.3	−1.25469	−0.627345	−	0.778741i	$-0.715858\pi$
$503$	−14154.3	−1.25469	−0.627345	+	0.778741i	$0.715858\pi$
$504$	−4333.11	−0.382960
$505$	5254.08	0.462977
$506$	−16092.4	−1.41382
$507$	5777.39	0.506080
$508$	14085.5	1.23020
$509$	−20074.0	−1.74806	−0.874032	−	0.485868i	$-0.838504\pi$
$509$	−20074.0	−1.74806	−0.874032	+	0.485868i	$0.838504\pi$
$510$	1515.14	0.131552
$511$	−4870.81	−0.421667
$512$	−4847.09	−0.418385
$513$	13578.7	1.16864
$514$	2643.12	0.226815
$515$	7178.26	0.614198
$516$	3473.14	0.296311
$517$	21795.2	1.85407
$518$	2541.60	0.215582
$519$	7951.61	0.672519
$520$	7167.10	0.604419
$521$	−9883.02	−0.831061	−0.415531	−	0.909579i	$-0.636404\pi$
$521$	−9883.02	−0.831061	−0.415531	+	0.909579i	$0.636404\pi$
$522$	1296.95	0.108747
$523$	11943.5	0.998573	0.499286	−	0.866437i	$-0.333596\pi$
$523$	11943.5	0.998573	0.499286	+	0.866437i	$0.333596\pi$
$524$	−705.894	−0.0588495
$525$	543.596	0.0451895
$526$	−291.581	−0.0241702
$527$	−13916.0	−1.15027
$528$	1819.85	0.149998
$529$	20611.6	1.69406
$530$	−4056.57	−0.332465
$531$	10738.2	0.877585
$532$	6609.53	0.538645
$533$	15970.3	1.29785
$534$	591.999	0.0479744
$535$	3183.74	0.257281
$536$	12150.3	0.979131
$537$	6090.80	0.489455
$538$	−4733.17	−0.379296
$539$	−14704.8	−1.17510
$540$	−3159.35	−0.251772
$541$	−12252.3	−0.973690	−0.486845	−	0.873488i	$-0.661852\pi$
$541$	−12252.3	−0.973690	−0.486845	+	0.873488i	$0.661852\pi$
$542$	12406.2	0.983193
$543$	5270.02	0.416497
$544$	−16362.9	−1.28962
$545$	−10524.2	−0.827165
$546$	2278.55	0.178595
$547$	6227.09	0.486748	0.243374	−	0.969933i	$-0.421746\pi$
$547$	6227.09	0.486748	0.243374	+	0.969933i	$0.421746\pi$
$548$	8189.53	0.638393
$549$	−7077.51	−0.550202
$550$	−2222.11	−0.172274
$551$	−4765.17	−0.368427
$552$	8602.38	0.663300
$553$	−11417.7	−0.877991
$554$	9794.09	0.751103
$555$	1994.11	0.152514
$556$	2469.14	0.188336
$557$	4186.97	0.318505	0.159253	−	0.987238i	$-0.449092\pi$
$557$	4186.97	0.318505	0.159253	+	0.987238i	$0.449092\pi$
$558$	−5298.35	−0.401966
$559$	18450.5	1.39601
$560$	−652.395	−0.0492299
$561$	11604.2	0.873318
$562$	9719.20	0.729501
$563$	−11298.2	−0.845757	−0.422878	−	0.906186i	$-0.638980\pi$
$563$	−11298.2	−0.845757	−0.422878	+	0.906186i	$0.638980\pi$
$564$	−4836.97	−0.361123
$565$	780.872	0.0581443
$566$	2250.83	0.167154
$567$	3194.57	0.236613
$568$	−21860.8	−1.61489
$569$	13663.2	1.00667	0.503333	−	0.864093i	$-0.332107\pi$
$569$	13663.2	1.00667	0.503333	+	0.864093i	$0.332107\pi$
$570$	−2119.52	−0.155749
$571$	−9967.49	−0.730519	−0.365260	−	0.930906i	$-0.619020\pi$
$571$	−9967.49	−0.730519	−0.365260	+	0.930906i	$0.619020\pi$
$572$	22788.8	1.66581
$573$	5971.30	0.435348
$574$	3373.60	0.245316
$575$	4526.22	0.328272
$576$	−3843.74	−0.278049
$577$	9794.28	0.706657	0.353329	−	0.935499i	$-0.385050\pi$
$577$	9794.28	0.706657	0.353329	+	0.935499i	$0.385050\pi$
$578$	−4109.92	−0.295761
$579$	−3994.76	−0.286730
$580$	1108.71	0.0793738
$581$	791.568	0.0565228
$582$	−1613.77	−0.114936
$583$	−31068.7	−2.20709
$584$	−10643.6	−0.754169
$585$	−7497.88	−0.529913
$586$	−5166.82	−0.364231
$587$	−7683.46	−0.540256	−0.270128	−	0.962824i	$-0.587066\pi$
$587$	−7683.46	−0.540256	−0.270128	+	0.962824i	$0.587066\pi$
$588$	3263.41	0.228879
$589$	19466.9	1.36184
$590$	−3751.92	−0.261804
$591$	8488.41	0.590806
$592$	−2393.22	−0.166150
$593$	−9643.48	−0.667808	−0.333904	−	0.942607i	$-0.608366\pi$
$593$	−9643.48	−0.667808	−0.333904	+	0.942607i	$0.608366\pi$
$594$	9889.79	0.683136
$595$	−4159.98	−0.286626
$596$	−16080.3	−1.10516
$597$	−8358.16	−0.572993
$598$	18972.2	1.29737
$599$	7857.22	0.535955	0.267978	−	0.963425i	$-0.413645\pi$
$599$	7857.22	0.535955	0.267978	+	0.963425i	$0.413645\pi$
$600$	1187.86	0.0808233
$601$	−22538.6	−1.52973	−0.764864	−	0.644191i	$-0.777194\pi$
$601$	−22538.6	−1.52973	−0.764864	+	0.644191i	$0.777194\pi$
$602$	3897.50	0.263871
$603$	−12711.1	−0.858435
$604$	−7311.23	−0.492533
$605$	−10363.8	−0.696442
$606$	3650.05	0.244675
$607$	−25082.9	−1.67724	−0.838620	−	0.544717i	$-0.816637\pi$
$607$	−25082.9	−1.67724	−0.838620	+	0.544717i	$0.816637\pi$
$608$	22889.9	1.52682
$609$	849.025	0.0564930
$610$	2472.88	0.164138
$611$	−25695.6	−1.70136
$612$	10801.1	0.713415
$613$	7745.54	0.510342	0.255171	−	0.966896i	$-0.417868\pi$
$613$	7745.54	0.510342	0.255171	+	0.966896i	$0.417868\pi$
$614$	10937.0	0.718862
$615$	2646.88	0.173549
$616$	11595.4	0.758430
$617$	−1569.47	−0.102406	−0.0512031	−	0.998688i	$-0.516306\pi$
$617$	−1569.47	−0.102406	−0.0512031	+	0.998688i	$0.516306\pi$
$618$	4986.79	0.324592
$619$	21425.6	1.39122	0.695612	−	0.718418i	$-0.255133\pi$
$619$	21425.6	1.39122	0.695612	+	0.718418i	$0.255133\pi$
$620$	−4529.37	−0.293394
$621$	−20144.5	−1.30173
$622$	−7247.83	−0.467221
$623$	−1625.40	−0.104527
$624$	−2145.52	−0.137644
$625$	625.000	0.0400000
$626$	2385.83	0.152327
$627$	−16233.1	−1.03395
$628$	8807.71	0.559659
$629$	−15260.3	−0.967359
$630$	−1583.86	−0.100163
$631$	11830.4	0.746371	0.373186	−	0.927757i	$-0.378265\pi$
$631$	11830.4	0.746371	0.373186	+	0.927757i	$0.378265\pi$
$632$	−24949.7	−1.57032
$633$	12656.8	0.794726
$634$	13833.4	0.866551
$635$	12401.6	0.775026
$636$	6895.02	0.429883
$637$	17336.3	1.07832
$638$	−3470.63	−0.215366
$639$	22869.8	1.41583
$640$	−6159.54	−0.380433
$641$	29383.1	1.81055	0.905274	−	0.424828i	$-0.139665\pi$
$641$	29383.1	1.81055	0.905274	+	0.424828i	$0.139665\pi$
$642$	2211.77	0.135968
$643$	21889.3	1.34250	0.671251	−	0.741230i	$-0.265757\pi$
$643$	21889.3	1.34250	0.671251	+	0.741230i	$0.265757\pi$
$644$	−9805.52	−0.599987
$645$	3057.93	0.186676
$646$	16220.0	0.987877
$647$	9421.28	0.572471	0.286235	−	0.958159i	$-0.407596\pi$
$647$	9421.28	0.572471	0.286235	+	0.958159i	$0.407596\pi$
$648$	6980.71	0.423192
$649$	−28735.4	−1.73800
$650$	2619.76	0.158085
$651$	−3468.48	−0.208818
$652$	9547.11	0.573457
$653$	−1168.63	−0.0700335	−0.0350168	−	0.999387i	$-0.511148\pi$
$653$	−1168.63	−0.0700335	−0.0350168	+	0.999387i	$0.511148\pi$
$654$	−7311.20	−0.437142
$655$	−621.504	−0.0370751
$656$	−3176.64	−0.189066
$657$	11134.8	0.661204
$658$	−5427.97	−0.321587
$659$	13876.8	0.820277	0.410139	−	0.912023i	$-0.365480\pi$
$659$	13876.8	0.820277	0.410139	+	0.912023i	$0.365480\pi$
$660$	3776.95	0.222754
$661$	−6084.50	−0.358033	−0.179016	−	0.983846i	$-0.557291\pi$
$661$	−6084.50	−0.358033	−0.179016	+	0.983846i	$0.557291\pi$
$662$	−8170.59	−0.479696
$663$	−13680.9	−0.801389
$664$	1729.72	0.101093
$665$	5819.36	0.339346
$666$	−5810.19	−0.338048
$667$	7069.35	0.410384
$668$	−1767.58	−0.102380
$669$	−787.527	−0.0455121
$670$	4441.26	0.256091
$671$	18939.4	1.08964
$672$	−4078.35	−0.234116
$673$	−7481.24	−0.428500	−0.214250	−	0.976779i	$-0.568731\pi$
$673$	−7481.24	−0.428500	−0.214250	+	0.976779i	$0.568731\pi$
$674$	16606.1	0.949023
$675$	−2781.65	−0.158616
$676$	−14390.3	−0.818748
$677$	20122.6	1.14235	0.571176	−	0.820827i	$-0.306487\pi$
$677$	20122.6	1.14235	0.571176	+	0.820827i	$0.306487\pi$
$678$	542.478	0.0307282
$679$	4430.78	0.250424
$680$	−9090.30	−0.512643
$681$	−9042.16	−0.508805
$682$	14178.4	0.796069
$683$	21064.6	1.18011	0.590054	−	0.807364i	$-0.299106\pi$
$683$	21064.6	1.18011	0.590054	+	0.807364i	$0.299106\pi$
$684$	−15109.6	−0.844634
$685$	7210.47	0.402187
$686$	8645.82	0.481194
$687$	1767.09	0.0981351
$688$	−3669.96	−0.203366
$689$	36628.6	2.02531
$690$	3144.39	0.173486
$691$	11210.0	0.617145	0.308573	−	0.951201i	$-0.400149\pi$
$691$	11210.0	0.617145	0.308573	+	0.951201i	$0.400149\pi$
$692$	−19805.9	−1.08802
$693$	−12130.6	−0.664939
$694$	−7006.88	−0.383253
$695$	2173.95	0.118651
$696$	1855.27	0.101040
$697$	−20255.8	−1.10078
$698$	4125.61	0.223720
$699$	3353.50	0.181460
$700$	−1353.99	−0.0731086
$701$	10860.9	0.585178	0.292589	−	0.956238i	$-0.405483\pi$
$701$	10860.9	0.585178	0.292589	+	0.956238i	$0.405483\pi$
$702$	−11659.6	−0.626871
$703$	21347.5	1.14529
$704$	10285.9	0.550658
$705$	−4258.71	−0.227507
$706$	8673.69	0.462378
$707$	−10021.6	−0.533098
$708$	6377.20	0.338517
$709$	−14059.1	−0.744709	−0.372355	−	0.928090i	$-0.621450\pi$
$709$	−14059.1	−0.744709	−0.372355	+	0.928090i	$0.621450\pi$
$710$	−7990.70	−0.422374
$711$	26101.2	1.37675
$712$	−3551.78	−0.186950
$713$	−28880.1	−1.51692
$714$	−2889.97	−0.151477
$715$	20064.4	1.04946
$716$	−15171.0	−0.791852
$717$	25.7957	0.00134360
$718$	−17944.6	−0.932714
$719$	−12419.6	−0.644191	−0.322096	−	0.946707i	$-0.604387\pi$
$719$	−12419.6	−0.644191	−0.322096	+	0.946707i	$0.604387\pi$
$720$	1491.40	0.0771959
$721$	−13691.8	−0.707223
$722$	−12240.3	−0.630936
$723$	−4639.83	−0.238668
$724$	−13126.6	−0.673819
$725$	976.167	0.0500054
$726$	−7199.79	−0.368057
$727$	15819.2	0.807019	0.403509	−	0.914975i	$-0.367790\pi$
$727$	15819.2	0.807019	0.403509	+	0.914975i	$0.367790\pi$
$728$	−13670.5	−0.695963
$729$	−453.498	−0.0230401
$730$	−3890.51	−0.197252
$731$	−23401.4	−1.18404
$732$	−4203.20	−0.212233
$733$	−171.656	−0.00864974	−0.00432487	−	0.999991i	$-0.501377\pi$
$733$	−171.656	−0.00864974	−0.00432487	+	0.999991i	$0.501377\pi$
$734$	−4487.10	−0.225643
$735$	2873.27	0.144193
$736$	−33958.1	−1.70070
$737$	34015.0	1.70008
$738$	−7712.15	−0.384673
$739$	21681.8	1.07926	0.539632	−	0.841901i	$-0.318563\pi$
$739$	21681.8	1.07926	0.539632	+	0.841901i	$0.318563\pi$
$740$	−4966.92	−0.246740
$741$	19138.0	0.948790
$742$	7737.48	0.382819
$743$	34876.3	1.72205	0.861027	−	0.508559i	$-0.169821\pi$
$743$	34876.3	1.72205	0.861027	+	0.508559i	$0.169821\pi$
$744$	−7579.25	−0.373480
$745$	−14157.9	−0.696248
$746$	2599.81	0.127595
$747$	−1809.55	−0.0886318
$748$	−28903.9	−1.41287
$749$	−6072.65	−0.296248
$750$	434.192	0.0211393
$751$	−15466.9	−0.751524	−0.375762	−	0.926716i	$-0.622619\pi$
$751$	−15466.9	−0.751524	−0.375762	+	0.926716i	$0.622619\pi$
$752$	5111.08	0.247848
$753$	895.668	0.0433466
$754$	4091.72	0.197628
$755$	−6437.17	−0.310295
$756$	6026.12	0.289905
$757$	−24842.6	−1.19276	−0.596380	−	0.802702i	$-0.703395\pi$
$757$	−24842.6	−1.19276	−0.596380	+	0.802702i	$0.703395\pi$
$758$	17533.2	0.840152
$759$	24082.5	1.15170
$760$	12716.3	0.606934
$761$	−830.614	−0.0395660	−0.0197830	−	0.999804i	$-0.506298\pi$
$761$	−830.614	−0.0395660	−0.0197830	+	0.999804i	$0.506298\pi$
$762$	8615.46	0.409587
$763$	20073.7	0.952446
$764$	−14873.3	−0.704316
$765$	9509.85	0.449450
$766$	−17332.0	−0.817535
$767$	33877.8	1.59486
$768$	−7494.79	−0.352142
$769$	22797.1	1.06903	0.534514	−	0.845159i	$-0.320495\pi$
$769$	22797.1	1.06903	0.534514	+	0.845159i	$0.320495\pi$
$770$	4238.43	0.198367
$771$	−3955.46	−0.184763
$772$	9950.14	0.463878
$773$	−11780.8	−0.548157	−0.274079	−	0.961707i	$-0.588373\pi$
$773$	−11780.8	−0.548157	−0.274079	+	0.961707i	$0.588373\pi$
$774$	−8909.82	−0.413769
$775$	−3987.89	−0.184838
$776$	9682.05	0.447894
$777$	−3803.55	−0.175613
$778$	2216.93	0.102160
$779$	28335.6	1.30325
$780$	−4452.85	−0.204407
$781$	−61199.6	−2.80396
$782$	−24063.1	−1.10038
$783$	−4344.56	−0.198291
$784$	−3448.35	−0.157086
$785$	7754.75	0.352584
$786$	−431.763	−0.0195935
$787$	−3803.40	−0.172270	−0.0861350	−	0.996283i	$-0.527452\pi$
$787$	−3803.40	−0.172270	−0.0861350	+	0.996283i	$0.527452\pi$
$788$	−21142.9	−0.955819
$789$	436.356	0.0196891
$790$	−9119.75	−0.410717
$791$	−1489.43	−0.0669508
$792$	−26507.5	−1.18927
$793$	−22328.7	−0.999894
$794$	−15897.8	−0.710570
$795$	6070.72	0.270825
$796$	20818.5	0.927001
$797$	28395.0	1.26199	0.630993	−	0.775789i	$-0.282648\pi$
$797$	28395.0	1.26199	0.630993	+	0.775789i	$0.282648\pi$
$798$	4042.75	0.179338
$799$	32590.7	1.44302
$800$	−4689.09	−0.207230
$801$	3715.71	0.163905
$802$	6802.34	0.299500
$803$	−29796.8	−1.30947
$804$	−7548.88	−0.331130
$805$	−8633.27	−0.377991
$806$	−16715.7	−0.730503
$807$	7083.25	0.308974
$808$	−21899.0	−0.953469
$809$	−21087.0	−0.916416	−0.458208	−	0.888845i	$-0.651508\pi$
$809$	−21087.0	−0.916416	−0.458208	+	0.888845i	$0.651508\pi$
$810$	2551.63	0.110685
$811$	5516.13	0.238838	0.119419	−	0.992844i	$-0.461897\pi$
$811$	5516.13	0.238838	0.119419	+	0.992844i	$0.461897\pi$
$812$	−2114.75	−0.0913956
$813$	−18566.0	−0.800908
$814$	15548.1	0.669484
$815$	8405.75	0.361277
$816$	2721.25	0.116744
$817$	32736.0	1.40182
$818$	1989.58	0.0850417
$819$	14301.4	0.610173
$820$	−6592.85	−0.280771
$821$	−9186.35	−0.390507	−0.195253	−	0.980753i	$-0.562553\pi$
$821$	−9186.35	−0.390507	−0.195253	+	0.980753i	$0.562553\pi$
$822$	5009.17	0.212548
$823$	30176.7	1.27812	0.639060	−	0.769157i	$-0.279324\pi$
$823$	30176.7	1.27812	0.639060	+	0.769157i	$0.279324\pi$
$824$	−29918.9	−1.26490
$825$	3325.41	0.140335
$826$	7156.39	0.301456
$827$	−4173.79	−0.175498	−0.0877491	−	0.996143i	$-0.527967\pi$
$827$	−4173.79	−0.175498	−0.0877491	+	0.996143i	$0.527967\pi$
$828$	22415.7	0.940822
$829$	18419.9	0.771714	0.385857	−	0.922559i	$-0.373906\pi$
$829$	18419.9	0.771714	0.385857	+	0.922559i	$0.373906\pi$
$830$	632.257	0.0264409
$831$	−14657.0	−0.611848
$832$	−12126.6	−0.505304
$833$	−21988.3	−0.914585
$834$	1510.26	0.0627051
$835$	−1556.27	−0.0644992
$836$	40433.3	1.67275
$837$	17748.6	0.732954
$838$	14565.3	0.600418
$839$	21442.5	0.882335	0.441167	−	0.897425i	$-0.354565\pi$
$839$	21442.5	0.882335	0.441167	+	0.897425i	$0.354565\pi$
$840$	−2265.71	−0.0930646
$841$	−22864.4	−0.937486
$842$	−19387.4	−0.793508
$843$	−14544.9	−0.594251
$844$	−31525.5	−1.28573
$845$	−12670.0	−0.515810
$846$	12408.5	0.504272
$847$	19767.8	0.801924
$848$	−7285.75	−0.295040
$849$	−3368.39	−0.136164
$850$	−3322.74	−0.134081
$851$	−31670.0	−1.27571
$852$	13581.9	0.546137
$853$	−27609.3	−1.10823	−0.554117	−	0.832439i	$-0.686944\pi$
$853$	−27609.3	−1.10823	−0.554117	+	0.832439i	$0.686944\pi$
$854$	−4716.76	−0.188998
$855$	−13303.2	−0.532118
$856$	−13269.8	−0.529852
$857$	−3202.65	−0.127655	−0.0638275	−	0.997961i	$-0.520331\pi$
$857$	−3202.65	−0.127655	−0.0638275	+	0.997961i	$0.520331\pi$
$858$	13938.9	0.554621
$859$	−18828.1	−0.747855	−0.373928	−	0.927458i	$-0.621989\pi$
$859$	−18828.1	−0.747855	−0.373928	+	0.927458i	$0.621989\pi$
$860$	−7616.69	−0.302008
$861$	−5048.64	−0.199834
$862$	5793.00	0.228898
$863$	−17394.9	−0.686129	−0.343064	−	0.939312i	$-0.611465\pi$
$863$	−17394.9	−0.686129	−0.343064	+	0.939312i	$0.611465\pi$
$864$	20869.4	0.821751
$865$	−17438.1	−0.685448
$866$	−7630.10	−0.299401
$867$	6150.55	0.240927
$868$	8639.30	0.337830
$869$	−69846.8	−2.72657
$870$	678.150	0.0264269
$871$	−40102.1	−1.56005
$872$	43864.6	1.70349
$873$	−10128.9	−0.392682
$874$	33661.7	1.30277
$875$	−1192.12	−0.0460583
$876$	6612.76	0.255051
$877$	−26088.8	−1.00451	−0.502255	−	0.864719i	$-0.667496\pi$
$877$	−26088.8	−1.00451	−0.502255	+	0.864719i	$0.667496\pi$
$878$	−1156.37	−0.0444481
$879$	7732.22	0.296702
$880$	−3990.98	−0.152882
$881$	42096.4	1.60983	0.804917	−	0.593388i	$-0.202210\pi$
$881$	42096.4	1.60983	0.804917	+	0.593388i	$0.202210\pi$
$882$	−8371.79	−0.319606
$883$	9252.21	0.352618	0.176309	−	0.984335i	$-0.443584\pi$
$883$	9252.21	0.352618	0.176309	+	0.984335i	$0.443584\pi$
$884$	34076.3	1.29651
$885$	5614.81	0.213265
$886$	−7953.98	−0.301602
$887$	−16116.1	−0.610062	−0.305031	−	0.952342i	$-0.598667\pi$
$887$	−16116.1	−0.610062	−0.305031	+	0.952342i	$0.598667\pi$
$888$	−8311.43	−0.314092
$889$	−23654.7	−0.892410
$890$	−1298.27	−0.0488967
$891$	19542.6	0.734793
$892$	1961.57	0.0736305
$893$	−45590.8	−1.70844
$894$	−9835.59	−0.367955
$895$	−13357.3	−0.498866
$896$	11748.7	0.438053
$897$	−28392.1	−1.05684
$898$	−219.599	−0.00816050
$899$	−6228.55	−0.231072
$900$	3095.26	0.114639
$901$	−46457.4	−1.71778
$902$	20637.8	0.761820
$903$	−5832.67	−0.214949
$904$	−3254.67	−0.119744
$905$	−11557.3	−0.424505
$906$	−4471.95	−0.163985
$907$	26185.5	0.958628	0.479314	−	0.877643i	$-0.340886\pi$
$907$	26185.5	0.958628	0.479314	+	0.877643i	$0.340886\pi$
$908$	22522.2	0.823157
$909$	22909.7	0.835936
$910$	−4996.91	−0.182029
$911$	−27823.4	−1.01189	−0.505945	−	0.862566i	$-0.668856\pi$
$911$	−27823.4	−1.01189	−0.505945	+	0.862566i	$0.668856\pi$
$912$	−3806.73	−0.138216
$913$	4842.36	0.175530
$914$	−6362.81	−0.230266
$915$	−3700.70	−0.133707
$916$	−4401.48	−0.158765
$917$	1185.45	0.0426904
$918$	14788.3	0.531686
$919$	47772.2	1.71476	0.857378	−	0.514688i	$-0.172092\pi$
$919$	47772.2	1.71476	0.857378	+	0.514688i	$0.172092\pi$
$920$	−18865.2	−0.676053
$921$	−16367.4	−0.585584
$922$	−15662.5	−0.559454
$923$	72151.5	2.57302
$924$	−7204.12	−0.256492
$925$	−4373.13	−0.155446
$926$	96.8458	0.00343688
$927$	31299.8	1.10897
$928$	−7323.73	−0.259066
$929$	1947.77	0.0687883	0.0343942	−	0.999408i	$-0.489050\pi$
$929$	1947.77	0.0687883	0.0343942	+	0.999408i	$0.489050\pi$
$930$	−2770.41	−0.0976833
$931$	30759.2	1.08281
$932$	−8352.89	−0.293571
$933$	10846.5	0.380598
$934$	20226.2	0.708589
$935$	−25448.4	−0.890109
$936$	31251.1	1.09132
$937$	−19185.4	−0.668899	−0.334449	−	0.942414i	$-0.608550\pi$
$937$	−19185.4	−0.668899	−0.334449	+	0.942414i	$0.608550\pi$
$938$	−8471.23	−0.294878
$939$	−3570.43	−0.124086
$940$	10607.6	0.368066
$941$	45452.2	1.57460	0.787300	−	0.616570i	$-0.211478\pi$
$941$	45452.2	1.57460	0.787300	+	0.616570i	$0.211478\pi$
$942$	5387.28	0.186334
$943$	−42037.1	−1.45166
$944$	−6738.59	−0.232333
$945$	5305.70	0.182639
$946$	23842.7	0.819443
$947$	7896.17	0.270952	0.135476	−	0.990781i	$-0.456744\pi$
$947$	7896.17	0.270952	0.135476	+	0.990781i	$0.456744\pi$
$948$	15501.0	0.531064
$949$	35129.1	1.20162
$950$	4648.15	0.158743
$951$	−20701.8	−0.705892
$952$	17338.8	0.590287
$953$	18152.5	0.617017	0.308508	−	0.951222i	$-0.400170\pi$
$953$	18152.5	0.617017	0.308508	+	0.951222i	$0.400170\pi$
$954$	−17688.1	−0.600287
$955$	−13095.2	−0.443718
$956$	−64.2520	−0.00217370
$957$	5193.85	0.175437
$958$	−551.827	−0.0186104
$959$	−13753.2	−0.463101
$960$	−2009.82	−0.0675696
$961$	−4345.81	−0.145876
$962$	−18330.5	−0.614343
$963$	13882.3	0.464538
$964$	11556.9	0.386123
$965$	8760.60	0.292242
$966$	−5997.60	−0.199761
$967$	−23418.6	−0.778791	−0.389396	−	0.921071i	$-0.627316\pi$
$967$	−23418.6	−0.778791	−0.389396	+	0.921071i	$0.627316\pi$
$968$	43196.2	1.43427
$969$	−24273.5	−0.804724
$970$	3539.04	0.117146
$971$	43994.5	1.45402	0.727009	−	0.686628i	$-0.240910\pi$
$971$	43994.5	1.45402	0.727009	+	0.686628i	$0.240910\pi$
$972$	−21397.5	−0.706097
$973$	−4146.59	−0.136622
$974$	−6883.15	−0.226438
$975$	−3920.51	−0.128776
$976$	4441.38	0.145661
$977$	−40451.4	−1.32462	−0.662310	−	0.749230i	$-0.730424\pi$
$977$	−40451.4	−1.32462	−0.662310	+	0.749230i	$0.730424\pi$
$978$	5839.54	0.190928
$979$	−9943.25	−0.324604
$980$	−7156.75	−0.233280
$981$	−45889.1	−1.49350
$982$	−20655.4	−0.671224
$983$	−20180.4	−0.654785	−0.327393	−	0.944888i	$-0.606170\pi$
$983$	−20180.4	−0.654785	−0.327393	+	0.944888i	$0.606170\pi$
$984$	−11032.2	−0.357412
$985$	−18615.3	−0.602165
$986$	−5189.68	−0.167620
$987$	8123.04	0.261965
$988$	−47669.0	−1.53497
$989$	−48565.3	−1.56146
$990$	−9689.18	−0.311053
$991$	−37145.5	−1.19068	−0.595341	−	0.803473i	$-0.702983\pi$
$991$	−37145.5	−1.19068	−0.595341	+	0.803473i	$0.702983\pi$
$992$	29919.3	0.957599
$993$	12227.4	0.390760
$994$	15241.4	0.486346
$995$	18329.7	0.584010
$996$	−1074.66	−0.0341886
$997$	6005.07	0.190755	0.0953774	−	0.995441i	$-0.469594\pi$
$997$	6005.07	0.190755	0.0953774	+	0.995441i	$0.469594\pi$
$998$	14272.4	0.452691
$999$	19463.2	0.616405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	415.4.a.c.1.8	✓	21
5.4	even	2		2075.4.a.g.1.14		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
415.4.a.c.1.8	✓	21	1.1	even	1	trivial
2075.4.a.g.1.14		21	5.4	even	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:	\( N \)	\(=\)	\( 415 = 5 \cdot 83 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	415.a (trivial)

\(f(q)\)	\(=\)	\(q-1.52351 q^{2} +2.27996 q^{3} -5.67892 q^{4} -5.00000 q^{5} -3.47354 q^{6} +9.53696 q^{7} +20.8400 q^{8} -21.8018 q^{9} +7.61755 q^{10} +58.3417 q^{11} -12.9477 q^{12} -68.7822 q^{13} -14.5297 q^{14} -11.3998 q^{15} +13.6814 q^{16} +87.2391 q^{17} +33.2153 q^{18} -122.038 q^{19} +28.3946 q^{20} +21.7439 q^{21} -88.8842 q^{22} +181.049 q^{23} +47.5142 q^{24} +25.0000 q^{25} +104.790 q^{26} -111.266 q^{27} -54.1596 q^{28} +39.0467 q^{29} +17.3677 q^{30} -159.515 q^{31} -187.564 q^{32} +133.016 q^{33} -132.910 q^{34} -47.6848 q^{35} +123.811 q^{36} -174.925 q^{37} +185.926 q^{38} -156.820 q^{39} -104.200 q^{40} -232.187 q^{41} -33.1270 q^{42} -268.245 q^{43} -331.318 q^{44} +109.009 q^{45} -275.830 q^{46} +373.579 q^{47} +31.1930 q^{48} -252.046 q^{49} -38.0878 q^{50} +198.901 q^{51} +390.608 q^{52} -532.530 q^{53} +169.515 q^{54} -291.709 q^{55} +198.750 q^{56} -278.241 q^{57} -59.4880 q^{58} -492.537 q^{59} +64.7384 q^{60} +324.629 q^{61} +243.024 q^{62} -207.923 q^{63} +176.304 q^{64} +343.911 q^{65} -202.652 q^{66} +583.030 q^{67} -495.424 q^{68} +412.783 q^{69} +72.6483 q^{70} -1048.99 q^{71} -454.349 q^{72} -510.729 q^{73} +266.500 q^{74} +56.9989 q^{75} +693.043 q^{76} +556.403 q^{77} +238.917 q^{78} -1197.20 q^{79} -68.4070 q^{80} +334.967 q^{81} +353.739 q^{82} +83.0000 q^{83} -123.481 q^{84} -436.196 q^{85} +408.673 q^{86} +89.0247 q^{87} +1215.84 q^{88} -170.431 q^{89} -166.076 q^{90} -655.973 q^{91} -1028.16 q^{92} -363.688 q^{93} -569.151 q^{94} +610.190 q^{95} -427.636 q^{96} +464.590 q^{97} +383.995 q^{98} -1271.95 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 5 q^{2} - 12 q^{3} + 87 q^{4} - 105 q^{5} - 7 q^{6} - 11 q^{7} - 84 q^{8} + 153 q^{9} + 25 q^{10} - 30 q^{11} - 244 q^{12} - 89 q^{13} - 191 q^{14} + 60 q^{15} + 583 q^{16} - 357 q^{17} - 281 q^{18}+ \cdots - 5369 q^{99}+O(q^{100}) \) 21 * q - 5 * q^2 - 12 * q^3 + 87 * q^4 - 105 * q^5 - 7 * q^6 - 11 * q^7 - 84 * q^8 + 153 * q^9 + 25 * q^10 - 30 * q^11 - 244 * q^12 - 89 * q^13 - 191 * q^14 + 60 * q^15 + 583 * q^16 - 357 * q^17 - 281 * q^18 - 175 * q^19 - 435 * q^20 - 41 * q^21 - 122 * q^22 - 554 * q^23 - 136 * q^24 + 525 * q^25 - 933 * q^26 - 555 * q^27 - 773 * q^28 - 96 * q^29 + 35 * q^30 + 99 * q^31 - 1307 * q^32 - 1097 * q^33 + 393 * q^34 + 55 * q^35 - 746 * q^36 - 756 * q^37 - 1192 * q^38 + 40 * q^39 + 420 * q^40 - 1436 * q^41 - 1112 * q^42 - 1003 * q^43 - 706 * q^44 - 765 * q^45 - 775 * q^46 - 858 * q^47 - 2837 * q^48 + 1384 * q^49 - 125 * q^50 - 279 * q^51 - 1092 * q^52 - 1625 * q^53 - 269 * q^54 + 150 * q^55 - 3806 * q^56 - 1740 * q^57 - 1087 * q^58 - 1224 * q^59 + 1220 * q^60 - 794 * q^61 - 2979 * q^62 - 1236 * q^63 + 2570 * q^64 + 445 * q^65 - 1094 * q^66 - 571 * q^67 - 4064 * q^68 + 774 * q^69 + 955 * q^70 - 1078 * q^71 - 2610 * q^72 - 1986 * q^73 - 1872 * q^74 - 300 * q^75 - 2854 * q^76 - 2519 * q^77 - 2449 * q^78 - 432 * q^79 - 2915 * q^80 - 219 * q^81 - 2143 * q^82 + 1743 * q^83 - 377 * q^84 + 1785 * q^85 + 1556 * q^86 - 5681 * q^87 - 3158 * q^88 - 6252 * q^89 + 1405 * q^90 + 684 * q^91 - 7623 * q^92 - 3314 * q^93 - 3877 * q^94 + 875 * q^95 - 954 * q^96 - 4880 * q^97 - 5072 * q^98 - 5369 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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