LMFDB - Embedded newform 1011.4.a.c.1.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1011,4,Mod(1,1011)] 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("1011.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1011, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 1011 = 3 \cdot 337 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1011.a (trivial)

Newform invariants

comment:select newform

sage:traces = [46] 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:	$59.6509310158$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	1011.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.66818 q^{2} -3.00000 q^{3} -0.880817 q^{4} -10.8109 q^{5} +8.00454 q^{6} -4.15190 q^{7} +23.6956 q^{8} +9.00000 q^{9} +28.8455 q^{10} -22.1267 q^{11} +2.64245 q^{12} +58.4419 q^{13} +11.0780 q^{14} +32.4327 q^{15} -56.1776 q^{16} +79.5421 q^{17} -24.0136 q^{18} -16.2762 q^{19} +9.52243 q^{20} +12.4557 q^{21} +59.0381 q^{22} -26.1679 q^{23} -71.0868 q^{24} -8.12423 q^{25} -155.933 q^{26} -27.0000 q^{27} +3.65707 q^{28} +6.99657 q^{29} -86.5364 q^{30} -300.774 q^{31} -39.6729 q^{32} +66.3802 q^{33} -212.233 q^{34} +44.8858 q^{35} -7.92735 q^{36} +260.698 q^{37} +43.4279 q^{38} -175.326 q^{39} -256.171 q^{40} -2.70125 q^{41} -33.2341 q^{42} -180.960 q^{43} +19.4896 q^{44} -97.2982 q^{45} +69.8206 q^{46} -126.474 q^{47} +168.533 q^{48} -325.762 q^{49} +21.6769 q^{50} -238.626 q^{51} -51.4766 q^{52} +502.655 q^{53} +72.0409 q^{54} +239.210 q^{55} -98.3819 q^{56} +48.8286 q^{57} -18.6681 q^{58} -718.446 q^{59} -28.5673 q^{60} -832.049 q^{61} +802.518 q^{62} -37.3671 q^{63} +555.275 q^{64} -631.810 q^{65} -177.114 q^{66} +768.833 q^{67} -70.0620 q^{68} +78.5036 q^{69} -119.763 q^{70} +144.770 q^{71} +213.261 q^{72} -266.808 q^{73} -695.589 q^{74} +24.3727 q^{75} +14.3364 q^{76} +91.8680 q^{77} +467.800 q^{78} -529.783 q^{79} +607.331 q^{80} +81.0000 q^{81} +7.20743 q^{82} -662.364 q^{83} -10.9712 q^{84} -859.923 q^{85} +482.834 q^{86} -20.9897 q^{87} -524.307 q^{88} +811.608 q^{89} +259.609 q^{90} -242.645 q^{91} +23.0491 q^{92} +902.321 q^{93} +337.455 q^{94} +175.961 q^{95} +119.019 q^{96} +1227.70 q^{97} +869.191 q^{98} -199.141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) $ 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * 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 $

$2$	−2.66818	−0.943344	−0.471672	−	0.881774i	$-0.656349\pi$
$2$	−2.66818	−0.943344	−0.471672	+	0.881774i	$0.656349\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−0.880817	−0.110102
$5$	−10.8109	−0.966957	−0.483479	−	0.875356i	$-0.660627\pi$
$5$	−10.8109	−0.966957	−0.483479	+	0.875356i	$0.660627\pi$
$6$	8.00454	0.544640
$7$	−4.15190	−0.224182	−0.112091	−	0.993698i	$-0.535755\pi$
$7$	−4.15190	−0.224182	−0.112091	+	0.993698i	$0.535755\pi$
$8$	23.6956	1.04721
$9$	9.00000	0.333333
$10$	28.8455	0.912173
$11$	−22.1267	−0.606496	−0.303248	−	0.952912i	$-0.598071\pi$
$11$	−22.1267	−0.606496	−0.303248	+	0.952912i	$0.598071\pi$
$12$	2.64245	0.0635675
$13$	58.4419	1.24684	0.623418	−	0.781889i	$-0.285744\pi$
$13$	58.4419	1.24684	0.623418	+	0.781889i	$0.285744\pi$
$14$	11.0780	0.211480
$15$	32.4327	0.558273
$16$	−56.1776	−0.877775
$17$	79.5421	1.13481	0.567406	−	0.823438i	$-0.307947\pi$
$17$	79.5421	1.13481	0.567406	+	0.823438i	$0.307947\pi$
$18$	−24.0136	−0.314448
$19$	−16.2762	−0.196527	−0.0982637	−	0.995160i	$-0.531329\pi$
$19$	−16.2762	−0.196527	−0.0982637	+	0.995160i	$0.531329\pi$
$20$	9.52243	0.106464
$21$	12.4557	0.129431
$22$	59.0381	0.572135
$23$	−26.1679	−0.237234	−0.118617	−	0.992940i	$-0.537846\pi$
$23$	−26.1679	−0.237234	−0.118617	+	0.992940i	$0.537846\pi$
$24$	−71.0868	−0.604606
$25$	−8.12423	−0.0649938
$26$	−155.933	−1.17620
$27$	−27.0000	−0.192450
$28$	3.65707	0.0246829
$29$	6.99657	0.0448010	0.0224005	−	0.999749i	$-0.492869\pi$
$29$	6.99657	0.0448010	0.0224005	+	0.999749i	$0.492869\pi$
$30$	−86.5364	−0.526643
$31$	−300.774	−1.74260	−0.871299	−	0.490753i	$-0.836722\pi$
$31$	−300.774	−1.74260	−0.871299	+	0.490753i	$0.836722\pi$
$32$	−39.6729	−0.219164
$33$	66.3802	0.350161
$34$	−212.233	−1.07052
$35$	44.8858	0.216774
$36$	−7.92735	−0.0367007
$37$	260.698	1.15834	0.579168	−	0.815208i	$-0.303377\pi$
$37$	260.698	1.15834	0.579168	+	0.815208i	$0.303377\pi$
$38$	43.4279	0.185393
$39$	−175.326	−0.719861
$40$	−256.171	−1.01261
$41$	−2.70125	−0.0102894	−0.00514469	−	0.999987i	$-0.501638\pi$
$41$	−2.70125	−0.0102894	−0.00514469	+	0.999987i	$0.501638\pi$
$42$	−33.2341	−0.122098
$43$	−180.960	−0.641771	−0.320885	−	0.947118i	$-0.603980\pi$
$43$	−180.960	−0.641771	−0.320885	+	0.947118i	$0.603980\pi$
$44$	19.4896	0.0667765
$45$	−97.2982	−0.322319
$46$	69.8206	0.223793
$47$	−126.474	−0.392513	−0.196256	−	0.980553i	$-0.562878\pi$
$47$	−126.474	−0.392513	−0.196256	+	0.980553i	$0.562878\pi$
$48$	168.533	0.506784
$49$	−325.762	−0.949743
$50$	21.6769	0.0613116
$51$	−238.626	−0.655184
$52$	−51.4766	−0.137279
$53$	502.655	1.30274	0.651368	−	0.758762i	$-0.274196\pi$
$53$	502.655	1.30274	0.651368	+	0.758762i	$0.274196\pi$
$54$	72.0409	0.181547
$55$	239.210	0.586456
$56$	−98.3819	−0.234765
$57$	48.8286	0.113465
$58$	−18.6681	−0.0422628
$59$	−718.446	−1.58532	−0.792659	−	0.609666i	$-0.791304\pi$
$59$	−718.446	−1.58532	−0.792659	+	0.609666i	$0.791304\pi$
$60$	−28.5673	−0.0614670
$61$	−832.049	−1.74644	−0.873221	−	0.487324i	$-0.837973\pi$
$61$	−832.049	−1.74644	−0.873221	+	0.487324i	$0.837973\pi$
$62$	802.518	1.64387
$63$	−37.3671	−0.0747272
$64$	555.275	1.08452
$65$	−631.810	−1.20564
$66$	−177.114	−0.330322
$67$	768.833	1.40191	0.700954	−	0.713206i	$-0.252758\pi$
$67$	768.833	1.40191	0.700954	+	0.713206i	$0.252758\pi$
$68$	−70.0620	−0.124945
$69$	78.5036	0.136967
$70$	−119.763	−0.204493
$71$	144.770	0.241986	0.120993	−	0.992653i	$-0.461392\pi$
$71$	144.770	0.241986	0.120993	+	0.992653i	$0.461392\pi$
$72$	213.261	0.349069
$73$	−266.808	−0.427774	−0.213887	−	0.976858i	$-0.568612\pi$
$73$	−266.808	−0.427774	−0.213887	+	0.976858i	$0.568612\pi$
$74$	−695.589	−1.09271
$75$	24.3727	0.0375242
$76$	14.3364	0.0216381
$77$	91.8680	0.135965
$78$	467.800	0.679077
$79$	−529.783	−0.754497	−0.377248	−	0.926112i	$-0.623130\pi$
$79$	−529.783	−0.754497	−0.377248	+	0.926112i	$0.623130\pi$
$80$	607.331	0.848771
$81$	81.0000	0.111111
$82$	7.20743	0.00970643
$83$	−662.364	−0.875950	−0.437975	−	0.898987i	$-0.644304\pi$
$83$	−662.364	−0.875950	−0.437975	+	0.898987i	$0.644304\pi$
$84$	−10.9712	−0.0142507
$85$	−859.923	−1.09731
$86$	482.834	0.605411
$87$	−20.9897	−0.0258659
$88$	−524.307	−0.635128
$89$	811.608	0.966633	0.483316	−	0.875446i	$-0.339432\pi$
$89$	811.608	0.966633	0.483316	+	0.875446i	$0.339432\pi$
$90$	259.609	0.304058
$91$	−242.645	−0.279518
$92$	23.0491	0.0261200
$93$	902.321	1.00609
$94$	337.455	0.370274
$95$	175.961	0.190034
$96$	119.019	0.126534
$97$	1227.70	1.28509	0.642547	−	0.766246i	$-0.277878\pi$
$97$	1227.70	1.28509	0.642547	+	0.766246i	$0.277878\pi$
$98$	869.191	0.895934
$99$	−199.141	−0.202165
$100$	7.15596	0.00715596
$101$	1080.54	1.06453	0.532267	−	0.846576i	$-0.321340\pi$
$101$	1080.54	1.06453	0.532267	+	0.846576i	$0.321340\pi$
$102$	636.698	0.618064
$103$	−221.040	−0.211453	−0.105727	−	0.994395i	$-0.533717\pi$
$103$	−221.040	−0.211453	−0.105727	+	0.994395i	$0.533717\pi$
$104$	1384.82	1.30570
$105$	−134.658	−0.125155
$106$	−1341.17	−1.22893
$107$	−1822.61	−1.64672	−0.823358	−	0.567522i	$-0.807902\pi$
$107$	−1822.61	−1.64672	−0.823358	+	0.567522i	$0.807902\pi$
$108$	23.7821	0.0211892
$109$	1.22945	0.00108037	0.000540184	−	1.00000i	$-0.499828\pi$
$109$	1.22945	0.00108037	0.000540184		1.00000i	$0.499828\pi$
$110$	−638.256	−0.553230
$111$	−782.093	−0.668766
$112$	233.244	0.196781
$113$	1508.05	1.25544	0.627722	−	0.778437i	$-0.283987\pi$
$113$	1508.05	1.25544	0.627722	+	0.778437i	$0.283987\pi$
$114$	−130.284	−0.107037
$115$	282.899	0.229395
$116$	−6.16270	−0.00493269
$117$	525.977	0.415612
$118$	1916.94	1.49550
$119$	−330.251	−0.254404
$120$	768.513	0.584628
$121$	−841.408	−0.632162
$122$	2220.06	1.64750
$123$	8.10376	0.00594058
$124$	264.926	0.191864
$125$	1439.19	1.02980
$126$	99.7022	0.0704935
$127$	−559.576	−0.390979	−0.195489	−	0.980706i	$-0.562630\pi$
$127$	−559.576	−0.390979	−0.195489	+	0.980706i	$0.562630\pi$
$128$	−1164.19	−0.803914
$129$	542.880	0.370526
$130$	1685.78	1.13733
$131$	−696.733	−0.464686	−0.232343	−	0.972634i	$-0.574639\pi$
$131$	−696.733	−0.464686	−0.232343	+	0.972634i	$0.574639\pi$
$132$	−58.4688	−0.0385535
$133$	67.5773	0.0440578
$134$	−2051.38	−1.32248
$135$	291.895	0.186091
$136$	1884.80	1.18838
$137$	1796.79	1.12051	0.560255	−	0.828320i	$-0.310703\pi$
$137$	1796.79	1.12051	0.560255	+	0.828320i	$0.310703\pi$
$138$	−209.462	−0.129207
$139$	−2587.99	−1.57921	−0.789604	−	0.613616i	$-0.789714\pi$
$139$	−2587.99	−1.57921	−0.789604	+	0.613616i	$0.789714\pi$
$140$	−39.5362	−0.0238673
$141$	379.421	0.226617
$142$	−386.271	−0.228276
$143$	−1293.13	−0.756201
$144$	−505.599	−0.292592
$145$	−75.6393	−0.0433207
$146$	711.891	0.403538
$147$	977.285	0.548334
$148$	−229.627	−0.127535
$149$	−588.204	−0.323406	−0.161703	−	0.986839i	$-0.551699\pi$
$149$	−588.204	−0.323406	−0.161703	+	0.986839i	$0.551699\pi$
$150$	−65.0307	−0.0353982
$151$	−1720.92	−0.927458	−0.463729	−	0.885977i	$-0.653489\pi$
$151$	−1720.92	−0.927458	−0.463729	+	0.885977i	$0.653489\pi$
$152$	−385.675	−0.205805
$153$	715.879	0.378271
$154$	−245.120	−0.128262
$155$	3251.64	1.68502
$156$	154.430	0.0792582
$157$	−172.709	−0.0877940	−0.0438970	−	0.999036i	$-0.513977\pi$
$157$	−172.709	−0.0877940	−0.0438970	+	0.999036i	$0.513977\pi$
$158$	1413.56	0.711750
$159$	−1507.97	−0.752135
$160$	428.900	0.211922
$161$	108.646	0.0531835
$162$	−216.123	−0.104816
$163$	3902.69	1.87535	0.937675	−	0.347513i	$-0.112974\pi$
$163$	3902.69	1.87535	0.937675	+	0.347513i	$0.112974\pi$
$164$	2.37931	0.00113288
$165$	−717.630	−0.338591
$166$	1767.31	0.826322
$167$	1630.47	0.755505	0.377752	−	0.925907i	$-0.376697\pi$
$167$	1630.47	0.755505	0.377752	+	0.925907i	$0.376697\pi$
$168$	295.146	0.135542
$169$	1218.45	0.554599
$170$	2294.43	1.03514
$171$	−146.486	−0.0655091
$172$	159.393	0.0706603
$173$	−1152.51	−0.506496	−0.253248	−	0.967401i	$-0.581499\pi$
$173$	−1152.51	−0.506496	−0.253248	+	0.967401i	$0.581499\pi$
$174$	56.0043	0.0244004
$175$	33.7310	0.0145704
$176$	1243.03	0.532368
$177$	2155.34	0.915283
$178$	−2165.52	−0.911867
$179$	836.909	0.349461	0.174730	−	0.984616i	$-0.444095\pi$
$179$	836.909	0.349461	0.174730	+	0.984616i	$0.444095\pi$
$180$	85.7019	0.0354880
$181$	−2895.93	−1.18924	−0.594622	−	0.804006i	$-0.702698\pi$
$181$	−2895.93	−1.18924	−0.594622	+	0.804006i	$0.702698\pi$
$182$	647.421	0.263681
$183$	2496.15	1.00831
$184$	−620.064	−0.248433
$185$	−2818.38	−1.12006
$186$	−2407.55	−0.949088
$187$	−1760.01	−0.688259
$188$	111.400	0.0432165
$189$	112.101	0.0431438
$190$	−469.495	−0.179267
$191$	4584.97	1.73695	0.868473	−	0.495736i	$-0.165102\pi$
$191$	4584.97	1.73695	0.868473	+	0.495736i	$0.165102\pi$
$192$	−1665.83	−0.626149
$193$	3510.75	1.30937	0.654687	−	0.755900i	$-0.272800\pi$
$193$	3510.75	1.30937	0.654687	+	0.755900i	$0.272800\pi$
$194$	−3275.73	−1.21229
$195$	1895.43	0.696075
$196$	286.936	0.104569
$197$	1375.03	0.497293	0.248647	−	0.968594i	$-0.420014\pi$
$197$	1375.03	0.497293	0.248647	+	0.968594i	$0.420014\pi$
$198$	531.343	0.190712
$199$	−272.560	−0.0970917	−0.0485458	−	0.998821i	$-0.515459\pi$
$199$	−272.560	−0.0970917	−0.0485458	+	0.998821i	$0.515459\pi$
$200$	−192.509	−0.0680621
$201$	−2306.50	−0.809392
$202$	−2883.08	−1.00422
$203$	−29.0491	−0.0100436
$204$	210.186	0.0721371
$205$	29.2030	0.00994940
$206$	589.774	0.199473
$207$	−235.511	−0.0790780
$208$	−3283.13	−1.09444
$209$	360.139	0.119193
$210$	359.290	0.118064
$211$	2057.02	0.671142	0.335571	−	0.942015i	$-0.391071\pi$
$211$	2057.02	0.671142	0.335571	+	0.942015i	$0.391071\pi$
$212$	−442.747	−0.143434
$213$	−434.309	−0.139711
$214$	4863.06	1.55342
$215$	1956.34	0.620565
$216$	−639.782	−0.201535
$217$	1248.78	0.390658
$218$	−3.28040	−0.00101916
$219$	800.423	0.246975
$220$	−210.700	−0.0645701
$221$	4648.59	1.41492
$222$	2086.77	0.630876
$223$	−4534.58	−1.36169	−0.680847	−	0.732426i	$-0.738388\pi$
$223$	−4534.58	−1.36169	−0.680847	+	0.732426i	$0.738388\pi$
$224$	164.718	0.0491325
$225$	−73.1181	−0.0216646
$226$	−4023.74	−1.18432
$227$	4522.98	1.32247	0.661235	−	0.750179i	$-0.270033\pi$
$227$	4522.98	1.32247	0.661235	+	0.750179i	$0.270033\pi$
$228$	−43.0091	−0.0124927
$229$	−3951.37	−1.14024	−0.570118	−	0.821563i	$-0.693102\pi$
$229$	−3951.37	−1.14024	−0.570118	+	0.821563i	$0.693102\pi$
$230$	−754.824	−0.216398
$231$	−275.604	−0.0784997
$232$	165.788	0.0469160
$233$	−5024.10	−1.41262	−0.706309	−	0.707904i	$-0.749641\pi$
$233$	−5024.10	−1.41262	−0.706309	+	0.707904i	$0.749641\pi$
$234$	−1403.40	−0.392065
$235$	1367.30	0.379543
$236$	632.819	0.174547
$237$	1589.35	0.435609
$238$	881.169	0.239990
$239$	6007.84	1.62600	0.813002	−	0.582260i	$-0.197832\pi$
$239$	6007.84	1.62600	0.813002	+	0.582260i	$0.197832\pi$
$240$	−1821.99	−0.490038
$241$	6016.87	1.60822	0.804110	−	0.594481i	$-0.202642\pi$
$241$	6016.87	1.60822	0.804110	+	0.594481i	$0.202642\pi$
$242$	2245.03	0.596346
$243$	−243.000	−0.0641500
$244$	732.883	0.192287
$245$	3521.78	0.918360
$246$	−21.6223	−0.00560401
$247$	−951.213	−0.245037
$248$	−7127.02	−1.82486
$249$	1987.09	0.505730
$250$	−3840.03	−0.971459
$251$	5698.06	1.43290	0.716451	−	0.697637i	$-0.245765\pi$
$251$	5698.06	1.43290	0.716451	+	0.697637i	$0.245765\pi$
$252$	32.9136	0.00822762
$253$	579.010	0.143882
$254$	1493.05	0.368828
$255$	2579.77	0.633535
$256$	−1335.93	−0.326155
$257$	7538.19	1.82965	0.914823	−	0.403854i	$-0.132330\pi$
$257$	7538.19	1.82965	0.914823	+	0.403854i	$0.132330\pi$
$258$	−1448.50	−0.349534
$259$	−1082.39	−0.259678
$260$	556.509	0.132743
$261$	62.9691	0.0149337
$262$	1859.01	0.438358
$263$	8438.30	1.97843	0.989216	−	0.146464i	$-0.0467892\pi$
$263$	8438.30	1.97843	0.989216	+	0.146464i	$0.0467892\pi$
$264$	1572.92	0.366691
$265$	−5434.16	−1.25969
$266$	−180.308	−0.0415617
$267$	−2434.83	−0.558086
$268$	−677.201	−0.154353
$269$	2094.94	0.474834	0.237417	−	0.971408i	$-0.423699\pi$
$269$	2094.94	0.474834	0.237417	+	0.971408i	$0.423699\pi$
$270$	−778.827	−0.175548
$271$	−2956.59	−0.662732	−0.331366	−	0.943502i	$-0.607509\pi$
$271$	−2956.59	−0.662732	−0.331366	+	0.943502i	$0.607509\pi$
$272$	−4468.49	−0.996110
$273$	727.935	0.161380
$274$	−4794.15	−1.05703
$275$	179.763	0.0394185
$276$	−69.1473	−0.0150804
$277$	1408.78	0.305580	0.152790	−	0.988259i	$-0.451174\pi$
$277$	1408.78	0.305580	0.152790	+	0.988259i	$0.451174\pi$
$278$	6905.21	1.48974
$279$	−2706.96	−0.580866
$280$	1063.60	0.227008
$281$	−5380.24	−1.14220	−0.571100	−	0.820881i	$-0.693483\pi$
$281$	−5380.24	−1.14220	−0.571100	+	0.820881i	$0.693483\pi$
$282$	−1012.36	−0.213778
$283$	−6287.12	−1.32060	−0.660301	−	0.751001i	$-0.729571\pi$
$283$	−6287.12	−1.32060	−0.660301	+	0.751001i	$0.729571\pi$
$284$	−127.515	−0.0266431
$285$	−527.882	−0.109716
$286$	3450.30	0.713358
$287$	11.2153	0.00230669
$288$	−357.056	−0.0730547
$289$	1413.95	0.287797
$290$	201.819	0.0408663
$291$	−3683.10	−0.741949
$292$	235.009	0.0470988
$293$	3209.48	0.639930	0.319965	−	0.947429i	$-0.396329\pi$
$293$	3209.48	0.639930	0.319965	+	0.947429i	$0.396329\pi$
$294$	−2607.57	−0.517268
$295$	7767.06	1.53293
$296$	6177.40	1.21302
$297$	597.422	0.116720
$298$	1569.43	0.305083
$299$	−1529.30	−0.295792
$300$	−21.4679	−0.00413149
$301$	751.328	0.143873
$302$	4591.71	0.874912
$303$	−3241.63	−0.614609
$304$	914.359	0.172507
$305$	8995.21	1.68873
$306$	−1910.09	−0.356839
$307$	−1004.27	−0.186700	−0.0933500	−	0.995633i	$-0.529758\pi$
$307$	−1004.27	−0.186700	−0.0933500	+	0.995633i	$0.529758\pi$
$308$	−80.9189	−0.0149701
$309$	663.119	0.122083
$310$	−8675.95	−1.58955
$311$	2863.74	0.522147	0.261073	−	0.965319i	$-0.415924\pi$
$311$	2863.74	0.522147	0.261073	+	0.965319i	$0.415924\pi$
$312$	−4154.45	−0.753844
$313$	8989.50	1.62338	0.811688	−	0.584092i	$-0.198549\pi$
$313$	8989.50	1.62338	0.811688	+	0.584092i	$0.198549\pi$
$314$	460.818	0.0828199
$315$	403.973	0.0722580
$316$	466.642	0.0830717
$317$	−11231.0	−1.98990	−0.994948	−	0.100388i	$-0.967991\pi$
$317$	−11231.0	−1.98990	−0.994948	+	0.100388i	$0.967991\pi$
$318$	4023.52	0.709522
$319$	−154.811	−0.0271717
$320$	−6003.03	−1.04869
$321$	5467.84	0.950732
$322$	−289.888	−0.0501703
$323$	−1294.64	−0.223022
$324$	−71.3462	−0.0122336
$325$	−474.795	−0.0810366
$326$	−10413.1	−1.76910
$327$	−3.68836	−0.000623751 0
$328$	−64.0079	−0.0107751
$329$	525.107	0.0879941
$330$	1914.77	0.319407
$331$	1323.77	0.219821	0.109911	−	0.993941i	$-0.464944\pi$
$331$	1323.77	0.219821	0.109911	+	0.993941i	$0.464944\pi$
$332$	583.421	0.0964440
$333$	2346.28	0.386112
$334$	−4350.38	−0.712701
$335$	−8311.78	−1.35559
$336$	−699.732	−0.113612
$337$	−337.000	−0.0544735
$337$	−337.000	−0.0544735
$338$	−3251.06	−0.523178
$339$	−4524.15	−0.724831
$340$	757.434	0.120817
$341$	6655.14	1.05688
$342$	390.851	0.0617976
$343$	2776.63	0.437097
$344$	−4287.96	−0.672067
$345$	−848.696	−0.132441
$346$	3075.11	0.477800
$347$	−7509.68	−1.16179	−0.580894	−	0.813979i	$-0.697297\pi$
$347$	−7509.68	−1.16179	−0.580894	+	0.813979i	$0.697297\pi$
$348$	18.4881	0.00284789
$349$	−3000.36	−0.460188	−0.230094	−	0.973168i	$-0.573903\pi$
$349$	−3000.36	−0.460188	−0.230094	+	0.973168i	$0.573903\pi$
$350$	−90.0004	−0.0137449
$351$	−1577.93	−0.239954
$352$	877.832	0.132922
$353$	−11274.7	−1.69997	−0.849987	−	0.526804i	$-0.823390\pi$
$353$	−11274.7	−1.69997	−0.849987	+	0.526804i	$0.823390\pi$
$354$	−5750.83	−0.863427
$355$	−1565.09	−0.233990
$356$	−714.878	−0.106428
$357$	990.753	0.146880
$358$	−2233.02	−0.329662
$359$	−961.024	−0.141284	−0.0706420	−	0.997502i	$-0.522505\pi$
$359$	−961.024	−0.141284	−0.0706420	+	0.997502i	$0.522505\pi$
$360$	−2305.54	−0.337535
$361$	−6594.08	−0.961377
$362$	7726.87	1.12187
$363$	2524.22	0.364979
$364$	213.726	0.0307755
$365$	2884.43	0.413639
$366$	−6660.17	−0.951182
$367$	3896.14	0.554161	0.277080	−	0.960847i	$-0.410633\pi$
$367$	3896.14	0.554161	0.277080	+	0.960847i	$0.410633\pi$
$368$	1470.05	0.208238
$369$	−24.3113	−0.00342980
$370$	7519.95	1.05660
$371$	−2086.97	−0.292049
$372$	−794.779	−0.110773
$373$	−1503.11	−0.208654	−0.104327	−	0.994543i	$-0.533269\pi$
$373$	−1503.11	−0.208654	−0.104327	+	0.994543i	$0.533269\pi$
$374$	4696.02	0.649265
$375$	−4317.58	−0.594557
$376$	−2996.87	−0.411042
$377$	408.893	0.0558595
$378$	−299.107	−0.0406994
$379$	7124.27	0.965565	0.482782	−	0.875740i	$-0.339626\pi$
$379$	7124.27	0.965565	0.482782	+	0.875740i	$0.339626\pi$
$380$	−154.989	−0.0209231
$381$	1678.73	0.225732
$382$	−12233.5	−1.63854
$383$	4395.52	0.586425	0.293212	−	0.956047i	$-0.405276\pi$
$383$	4395.52	0.586425	0.293212	+	0.956047i	$0.405276\pi$
$384$	3492.57	0.464140
$385$	−993.177	−0.131473
$386$	−9367.31	−1.23519
$387$	−1628.64	−0.213924
$388$	−1081.38	−0.141492
$389$	−13907.0	−1.81263	−0.906314	−	0.422604i	$-0.861116\pi$
$389$	−13907.0	−1.81263	−0.906314	+	0.422604i	$0.861116\pi$
$390$	−5057.35	−0.656638
$391$	−2081.45	−0.269216
$392$	−7719.12	−0.994578
$393$	2090.20	0.268286
$394$	−3668.82	−0.469119
$395$	5727.44	0.729566
$396$	175.406	0.0222588
$397$	9440.40	1.19345	0.596726	−	0.802445i	$-0.296468\pi$
$397$	9440.40	1.19345	0.596726	+	0.802445i	$0.296468\pi$
$398$	727.238	0.0915908
$399$	−202.732	−0.0254368
$400$	456.400	0.0570500
$401$	−10917.3	−1.35956	−0.679778	−	0.733418i	$-0.737924\pi$
$401$	−10917.3	−1.35956	−0.679778	+	0.733418i	$0.737924\pi$
$402$	6154.15	0.763536
$403$	−17577.8	−2.17273
$404$	−951.760	−0.117207
$405$	−875.684	−0.107440
$406$	77.5081	0.00947454
$407$	−5768.39	−0.702527
$408$	−5654.40	−0.686114
$409$	−2699.27	−0.326334	−0.163167	−	0.986599i	$-0.552171\pi$
$409$	−2699.27	−0.326334	−0.163167	+	0.986599i	$0.552171\pi$
$410$	−77.9189	−0.00938571
$411$	−5390.37	−0.646927
$412$	194.695	0.0232815
$413$	2982.92	0.355399
$414$	628.386	0.0745977
$415$	7160.76	0.847006
$416$	−2318.56	−0.273262
$417$	7763.96	0.911757
$418$	−960.917	−0.112440
$419$	6559.97	0.764859	0.382429	−	0.923985i	$-0.375088\pi$
$419$	6559.97	0.764859	0.382429	+	0.923985i	$0.375088\pi$
$420$	118.609	0.0137798
$421$	4742.93	0.549064	0.274532	−	0.961578i	$-0.411477\pi$
$421$	4742.93	0.549064	0.274532	+	0.961578i	$0.411477\pi$
$422$	−5488.49	−0.633118
$423$	−1138.26	−0.130838
$424$	11910.7	1.36424
$425$	−646.218	−0.0737558
$426$	1158.81	0.131795
$427$	3454.59	0.391520
$428$	1605.39	0.181307
$429$	3879.38	0.436593
$430$	−5219.87	−0.585406
$431$	−494.267	−0.0552390	−0.0276195	−	0.999619i	$-0.508793\pi$
$431$	−494.267	−0.0552390	−0.0276195	+	0.999619i	$0.508793\pi$
$432$	1516.80	0.168928
$433$	−82.9718	−0.00920871	−0.00460436	−	0.999989i	$-0.501466\pi$
$433$	−82.9718	−0.00920871	−0.00460436	+	0.999989i	$0.501466\pi$
$434$	−3331.98	−0.368525
$435$	226.918	0.0250112
$436$	−1.08292	−0.000118951 0
$437$	425.914	0.0466230
$438$	−2135.67	−0.232983
$439$	−16468.2	−1.79039	−0.895197	−	0.445671i	$-0.852965\pi$
$439$	−16468.2	−1.79039	−0.895197	+	0.445671i	$0.852965\pi$
$440$	5668.23	0.614142
$441$	−2931.86	−0.316581
$442$	−12403.3	−1.33476
$443$	5925.81	0.635539	0.317770	−	0.948168i	$-0.397066\pi$
$443$	5925.81	0.635539	0.317770	+	0.948168i	$0.397066\pi$
$444$	688.881	0.0736325
$445$	−8774.23	−0.934692
$446$	12099.1	1.28455
$447$	1764.61	0.186719
$448$	−2305.45	−0.243130
$449$	1693.19	0.177965	0.0889827	−	0.996033i	$-0.471638\pi$
$449$	1693.19	0.177965	0.0889827	+	0.996033i	$0.471638\pi$
$450$	195.092	0.0204372
$451$	59.7699	0.00624048
$452$	−1328.31	−0.138227
$453$	5162.75	0.535468
$454$	−12068.1	−1.24754
$455$	2623.21	0.270282
$456$	1157.02	0.118822
$457$	−4395.47	−0.449916	−0.224958	−	0.974368i	$-0.572224\pi$
$457$	−4395.47	−0.449916	−0.224958	+	0.974368i	$0.572224\pi$
$458$	10543.0	1.07563
$459$	−2147.64	−0.218395
$460$	−249.182	−0.0252569
$461$	12637.3	1.27674	0.638372	−	0.769728i	$-0.279608\pi$
$461$	12637.3	1.27674	0.638372	+	0.769728i	$0.279608\pi$
$462$	735.361	0.0740522
$463$	18196.6	1.82650	0.913251	−	0.407398i	$-0.133564\pi$
$463$	18196.6	1.82650	0.913251	+	0.407398i	$0.133564\pi$
$464$	−393.051	−0.0393252
$465$	−9754.91	−0.972845
$466$	13405.2	1.33258
$467$	3398.56	0.336760	0.168380	−	0.985722i	$-0.446146\pi$
$467$	3398.56	0.336760	0.168380	+	0.985722i	$0.446146\pi$
$468$	−463.289	−0.0457597
$469$	−3192.12	−0.314282
$470$	−3648.19	−0.358040
$471$	518.126	0.0506879
$472$	−17024.0	−1.66016
$473$	4004.05	0.389232
$474$	−4240.67	−0.410929
$475$	132.232	0.0127731
$476$	290.891	0.0280104
$477$	4523.90	0.434245
$478$	−16030.0	−1.53388
$479$	11318.9	1.07970	0.539849	−	0.841762i	$-0.318481\pi$
$479$	11318.9	1.07970	0.539849	+	0.841762i	$0.318481\pi$
$480$	−1286.70	−0.122353
$481$	15235.7	1.44426
$482$	−16054.1	−1.51710
$483$	−325.939	−0.0307055
$484$	741.126	0.0696024
$485$	−13272.6	−1.24263
$486$	648.368	0.0605155
$487$	−13915.5	−1.29481	−0.647404	−	0.762147i	$-0.724145\pi$
$487$	−13915.5	−1.29481	−0.647404	+	0.762147i	$0.724145\pi$
$488$	−19715.9	−1.82889
$489$	−11708.1	−1.08273
$490$	−9396.74	−0.866330
$491$	9647.58	0.886740	0.443370	−	0.896339i	$-0.353783\pi$
$491$	9647.58	0.886740	0.443370	+	0.896339i	$0.353783\pi$
$492$	−7.13793	−0.000654071 0
$493$	556.522	0.0508407
$494$	2538.01	0.231154
$495$	2152.89	0.195485
$496$	16896.7	1.52961
$497$	−601.069	−0.0542488
$498$	−5301.92	−0.477077
$499$	−16070.6	−1.44172	−0.720861	−	0.693079i	$-0.756253\pi$
$499$	−16070.6	−1.44172	−0.720861	+	0.693079i	$0.756253\pi$
$500$	−1267.67	−0.113384
$501$	−4891.40	−0.436191
$502$	−15203.5	−1.35172
$503$	3129.46	0.277407	0.138703	−	0.990334i	$-0.455707\pi$
$503$	3129.46	0.277407	0.138703	+	0.990334i	$0.455707\pi$
$504$	−885.437	−0.0782550
$505$	−11681.6	−1.02936
$506$	−1544.90	−0.135730
$507$	−3655.36	−0.320198
$508$	492.884	0.0430476
$509$	7440.14	0.647894	0.323947	−	0.946075i	$-0.394990\pi$
$509$	7440.14	0.647894	0.323947	+	0.946075i	$0.394990\pi$
$510$	−6883.28	−0.597641
$511$	1107.76	0.0958990
$512$	12878.0	1.11159
$513$	439.458	0.0378217
$514$	−20113.2	−1.72599
$515$	2389.64	0.204466
$516$	−478.178	−0.0407957
$517$	2798.45	0.238058
$518$	2888.02	0.244966
$519$	3457.53	0.292426
$520$	−14971.1	−1.26255
$521$	10707.0	0.900352	0.450176	−	0.892940i	$-0.351361\pi$
$521$	10707.0	0.900352	0.450176	+	0.892940i	$0.351361\pi$
$522$	−168.013	−0.0140876
$523$	15755.2	1.31726	0.658631	−	0.752466i	$-0.271136\pi$
$523$	15755.2	1.31726	0.658631	+	0.752466i	$0.271136\pi$
$524$	613.694	0.0511629
$525$	−101.193	−0.00841224
$526$	−22514.9	−1.86634
$527$	−23924.2	−1.97752
$528$	−3729.08	−0.307363
$529$	−11482.2	−0.943720
$530$	14499.3	1.18832
$531$	−6466.02	−0.528439
$532$	−59.5232	−0.00485086
$533$	−157.866	−0.0128292
$534$	6496.55	0.526467
$535$	19704.1	1.59230
$536$	18218.0	1.46809
$537$	−2510.73	−0.201761
$538$	−5589.66	−0.447932
$539$	7208.04	0.576016
$540$	−257.106	−0.0204890
$541$	−8963.68	−0.712345	−0.356173	−	0.934420i	$-0.615919\pi$
$541$	−8963.68	−0.712345	−0.356173	+	0.934420i	$0.615919\pi$
$542$	7888.72	0.625184
$543$	8687.80	0.686610
$544$	−3155.67	−0.248710
$545$	−13.2915	−0.00104467
$546$	−1942.26	−0.152236
$547$	15550.9	1.21555	0.607776	−	0.794109i	$-0.292062\pi$
$547$	15550.9	1.21555	0.607776	+	0.794109i	$0.292062\pi$
$548$	−1582.64	−0.123371
$549$	−7488.44	−0.582147
$550$	−479.639	−0.0371852
$551$	−113.878	−0.00880463
$552$	1860.19	0.143433
$553$	2199.61	0.169144
$554$	−3758.89	−0.288267
$555$	8455.14	0.646668
$556$	2279.54	0.173874
$557$	−3122.80	−0.237553	−0.118777	−	0.992921i	$-0.537897\pi$
$557$	−3122.80	−0.237553	−0.118777	+	0.992921i	$0.537897\pi$
$558$	7222.66	0.547956
$559$	−10575.6	−0.800183
$560$	−2521.58	−0.190279
$561$	5280.02	0.397367
$562$	14355.4	1.07749
$563$	17142.7	1.28327	0.641634	−	0.767011i	$-0.278257\pi$
$563$	17142.7	1.28327	0.641634	+	0.767011i	$0.278257\pi$
$564$	−334.201	−0.0249510
$565$	−16303.4	−1.21396
$566$	16775.2	1.24578
$567$	−336.304	−0.0249091
$568$	3430.40	0.253409
$569$	6297.48	0.463979	0.231990	−	0.972718i	$-0.425476\pi$
$569$	6297.48	0.463979	0.231990	+	0.972718i	$0.425476\pi$
$570$	1408.48	0.103500
$571$	15845.6	1.16133	0.580663	−	0.814144i	$-0.302793\pi$
$571$	15845.6	1.16133	0.580663	+	0.814144i	$0.302793\pi$
$572$	1139.01	0.0832594
$573$	−13754.9	−1.00283
$574$	−29.9245	−0.00217600
$575$	212.594	0.0154187
$576$	4997.48	0.361507
$577$	6196.55	0.447081	0.223540	−	0.974695i	$-0.428239\pi$
$577$	6196.55	0.447081	0.223540	+	0.974695i	$0.428239\pi$
$578$	−3772.67	−0.271492
$579$	−10532.2	−0.755967
$580$	66.6243	0.00476970
$581$	2750.07	0.196372
$582$	9827.18	0.699913
$583$	−11122.1	−0.790105
$584$	−6322.17	−0.447968
$585$	−5686.29	−0.401879
$586$	−8563.46	−0.603675
$587$	−19306.2	−1.35750	−0.678749	−	0.734370i	$-0.737478\pi$
$587$	−19306.2	−1.35750	−0.678749	+	0.734370i	$0.737478\pi$
$588$	−860.809	−0.0603727
$589$	4895.46	0.342468
$590$	−20723.9	−1.44608
$591$	−4125.09	−0.287112
$592$	−14645.4	−1.01676
$593$	−22969.9	−1.59066	−0.795331	−	0.606175i	$-0.792703\pi$
$593$	−22969.9	−1.59066	−0.795331	+	0.606175i	$0.792703\pi$
$594$	−1594.03	−0.110107
$595$	3570.31	0.245998
$596$	518.100	0.0356077
$597$	817.679	0.0560559
$598$	4080.45	0.279033
$599$	16710.8	1.13987	0.569937	−	0.821689i	$-0.306968\pi$
$599$	16710.8	1.13987	0.569937	+	0.821689i	$0.306968\pi$
$600$	577.526	0.0392957
$601$	13596.4	0.922812	0.461406	−	0.887189i	$-0.347345\pi$
$601$	13596.4	0.922812	0.461406	+	0.887189i	$0.347345\pi$
$602$	−2004.68	−0.135722
$603$	6919.50	0.467303
$604$	1515.81	0.102115
$605$	9096.38	0.611274
$606$	8649.24	0.579788
$607$	−13645.3	−0.912433	−0.456216	−	0.889869i	$-0.650796\pi$
$607$	−13645.3	−0.912433	−0.456216	+	0.889869i	$0.650796\pi$
$608$	645.725	0.0430717
$609$	87.1472	0.00579866
$610$	−24000.8	−1.59306
$611$	−7391.37	−0.489399
$612$	−630.558	−0.0416484
$613$	20836.8	1.37291	0.686453	−	0.727174i	$-0.259167\pi$
$613$	20836.8	1.37291	0.686453	+	0.727174i	$0.259167\pi$
$614$	2679.58	0.176122
$615$	−87.6090	−0.00574429
$616$	2176.87	0.142384
$617$	3309.41	0.215935	0.107968	−	0.994154i	$-0.465566\pi$
$617$	3309.41	0.215935	0.107968	+	0.994154i	$0.465566\pi$
$618$	−1769.32	−0.115166
$619$	13116.2	0.851674	0.425837	−	0.904800i	$-0.359980\pi$
$619$	13116.2	0.851674	0.425837	+	0.904800i	$0.359980\pi$
$620$	−2864.10	−0.185524
$621$	706.533	0.0456557
$622$	−7640.97	−0.492564
$623$	−3369.72	−0.216701
$624$	9849.38	0.631876
$625$	−14543.5	−0.930782
$626$	−23985.6	−1.53140
$627$	−1080.42	−0.0688162
$628$	152.125	0.00966630
$629$	20736.5	1.31449
$630$	−1077.87	−0.0681642
$631$	3988.37	0.251624	0.125812	−	0.992054i	$-0.459846\pi$
$631$	3988.37	0.251624	0.125812	+	0.992054i	$0.459846\pi$
$632$	−12553.5	−0.790115
$633$	−6171.05	−0.387484
$634$	29966.4	1.87716
$635$	6049.52	0.378060
$636$	1328.24	0.0828116
$637$	−19038.1	−1.18417
$638$	413.064	0.0256322
$639$	1302.93	0.0806619
$640$	12586.0	0.777350
$641$	6090.72	0.375302	0.187651	−	0.982236i	$-0.439913\pi$
$641$	6090.72	0.375302	0.187651	+	0.982236i	$0.439913\pi$
$642$	−14589.2	−0.896868
$643$	−2569.28	−0.157578	−0.0787890	−	0.996891i	$-0.525105\pi$
$643$	−2569.28	−0.157578	−0.0787890	+	0.996891i	$0.525105\pi$
$644$	−95.6977	−0.00585562
$645$	−5869.03	−0.358283
$646$	3454.34	0.210386
$647$	2705.99	0.164426	0.0822128	−	0.996615i	$-0.473801\pi$
$647$	2705.99	0.164426	0.0822128	+	0.996615i	$0.473801\pi$
$648$	1919.34	0.116356
$649$	15896.9	0.961489
$650$	1266.84	0.0764454
$651$	−3746.35	−0.225547
$652$	−3437.55	−0.206480
$653$	29666.3	1.77784	0.888922	−	0.458059i	$-0.151455\pi$
$653$	29666.3	1.77784	0.888922	+	0.458059i	$0.151455\pi$
$654$	9.84120	0.000588412 0
$655$	7532.31	0.449331
$656$	151.750	0.00903177
$657$	−2401.27	−0.142591
$658$	−1401.08	−0.0830087
$659$	18573.4	1.09790	0.548950	−	0.835855i	$-0.315028\pi$
$659$	18573.4	1.09790	0.548950	+	0.835855i	$0.315028\pi$
$660$	632.101	0.0372795
$661$	24562.1	1.44532	0.722660	−	0.691204i	$-0.242919\pi$
$661$	24562.1	1.44532	0.722660	+	0.691204i	$0.242919\pi$
$662$	−3532.05	−0.207367
$663$	−13945.8	−0.816907
$664$	−15695.1	−0.917302
$665$	−730.572	−0.0426020
$666$	−6260.30	−0.364237
$667$	−183.085	−0.0106283
$668$	−1436.14	−0.0831826
$669$	13603.7	0.786174
$670$	22177.3	1.27878
$671$	18410.5	1.05921
$672$	−494.154	−0.0283667
$673$	24089.8	1.37978	0.689891	−	0.723913i	$-0.257658\pi$
$673$	24089.8	1.37978	0.689891	+	0.723913i	$0.257658\pi$
$674$	899.177	0.0513872
$675$	219.354	0.0125081
$676$	−1073.24	−0.0610626
$677$	5176.28	0.293856	0.146928	−	0.989147i	$-0.453061\pi$
$677$	5176.28	0.293856	0.146928	+	0.989147i	$0.453061\pi$
$678$	12071.2	0.683765
$679$	−5097.29	−0.288094
$680$	−20376.4	−1.14912
$681$	−13568.9	−0.763528
$682$	−17757.1	−0.997001
$683$	−2133.26	−0.119512	−0.0597561	−	0.998213i	$-0.519032\pi$
$683$	−2133.26	−0.119512	−0.0597561	+	0.998213i	$0.519032\pi$
$684$	129.027	0.00721269
$685$	−19424.9	−1.08349
$686$	−7408.56	−0.412332
$687$	11854.1	0.658315
$688$	10165.9	0.563331
$689$	29376.1	1.62430
$690$	2264.47	0.124938
$691$	−10453.1	−0.575476	−0.287738	−	0.957709i	$-0.592903\pi$
$691$	−10453.1	−0.575476	−0.287738	+	0.957709i	$0.592903\pi$
$692$	1015.15	0.0557663
$693$	826.812	0.0453218
$694$	20037.2	1.09597
$695$	27978.5	1.52703
$696$	−497.364	−0.0270870
$697$	−214.863	−0.0116765
$698$	8005.49	0.434115
$699$	15072.3	0.815575
$700$	−29.7108	−0.00160423
$701$	−11879.3	−0.640049	−0.320025	−	0.947409i	$-0.603691\pi$
$701$	−11879.3	−0.640049	−0.320025	+	0.947409i	$0.603691\pi$
$702$	4210.20	0.226359
$703$	−4243.17	−0.227645
$704$	−12286.4	−0.657759
$705$	−4101.89	−0.219129
$706$	30082.9	1.60366
$707$	−4486.30	−0.238649
$708$	−1898.46	−0.100775
$709$	10805.4	0.572364	0.286182	−	0.958175i	$-0.407614\pi$
$709$	10805.4	0.572364	0.286182	+	0.958175i	$0.407614\pi$
$710$	4175.94	0.220733
$711$	−4768.05	−0.251499
$712$	19231.6	1.01227
$713$	7870.61	0.413403
$714$	−2643.51	−0.138559
$715$	13979.9	0.731214
$716$	−737.163	−0.0384764
$717$	−18023.5	−0.938774
$718$	2564.19	0.133279
$719$	−14676.9	−0.761274	−0.380637	−	0.924724i	$-0.624295\pi$
$719$	−14676.9	−0.761274	−0.380637	+	0.924724i	$0.624295\pi$
$720$	5465.98	0.282924
$721$	917.735	0.0474039
$722$	17594.2	0.906909
$723$	−18050.6	−0.928506
$724$	2550.79	0.130938
$725$	−56.8417	−0.00291179
$726$	−6735.08	−0.344301
$727$	36873.3	1.88109	0.940547	−	0.339663i	$-0.110313\pi$
$727$	36873.3	1.88109	0.940547	+	0.339663i	$0.110313\pi$
$728$	−5749.62	−0.292713
$729$	729.000	0.0370370
$730$	−7696.19	−0.390204
$731$	−14393.9	−0.728289
$732$	−2198.65	−0.111017
$733$	5420.90	0.273159	0.136580	−	0.990629i	$-0.456389\pi$
$733$	5420.90	0.273159	0.136580	+	0.990629i	$0.456389\pi$
$734$	−10395.6	−0.522764
$735$	−10565.3	−0.530216
$736$	1038.16	0.0519931
$737$	−17011.8	−0.850253
$738$	64.8669	0.00323548
$739$	−870.476	−0.0433301	−0.0216651	−	0.999765i	$-0.506897\pi$
$739$	−870.476	−0.0433301	−0.0216651	+	0.999765i	$0.506897\pi$
$740$	2482.48	0.123321
$741$	2853.64	0.141472
$742$	5568.42	0.275503
$743$	−20288.4	−1.00176	−0.500881	−	0.865516i	$-0.666990\pi$
$743$	−20288.4	−1.00176	−0.500881	+	0.865516i	$0.666990\pi$
$744$	21381.0	1.05358
$745$	6359.02	0.312720
$746$	4010.56	0.196832
$747$	−5961.27	−0.291983
$748$	1550.24	0.0757788
$749$	7567.31	0.369164
$750$	11520.1	0.560872
$751$	−13003.6	−0.631833	−0.315917	−	0.948787i	$-0.602312\pi$
$751$	−13003.6	−0.631833	−0.315917	+	0.948787i	$0.602312\pi$
$752$	7105.00	0.344538
$753$	−17094.2	−0.827287
$754$	−1091.00	−0.0526948
$755$	18604.7	0.896812
$756$	−98.7408	−0.00475022
$757$	12802.3	0.614672	0.307336	−	0.951601i	$-0.400563\pi$
$757$	12802.3	0.614672	0.307336	+	0.951601i	$0.400563\pi$
$758$	−19008.8	−0.910860
$759$	−1737.03	−0.0830700
$760$	4169.50	0.199005
$761$	−16127.4	−0.768222	−0.384111	−	0.923287i	$-0.625492\pi$
$761$	−16127.4	−0.768222	−0.384111	+	0.923287i	$0.625492\pi$
$762$	−4479.15	−0.212943
$763$	−5.10457	−0.000242199 0
$764$	−4038.52	−0.191241
$765$	−7739.30	−0.365771
$766$	−11728.0	−0.553200
$767$	−41987.4	−1.97663
$768$	4007.80	0.188306
$769$	−7738.74	−0.362895	−0.181447	−	0.983401i	$-0.558078\pi$
$769$	−7738.74	−0.362895	−0.181447	+	0.983401i	$0.558078\pi$
$770$	2649.97	0.124024
$771$	−22614.6	−1.05635
$772$	−3092.33	−0.144165
$773$	36238.6	1.68617	0.843086	−	0.537779i	$-0.180736\pi$
$773$	36238.6	1.68617	0.843086	+	0.537779i	$0.180736\pi$
$774$	4345.50	0.201804
$775$	2443.55	0.113258
$776$	29091.1	1.34576
$777$	3247.18	0.149925
$778$	37106.4	1.70993
$779$	43.9662	0.00202215
$780$	−1669.53	−0.0766393
$781$	−3203.28	−0.146764
$782$	5553.68	0.253963
$783$	−188.907	−0.00862196
$784$	18300.5	0.833661
$785$	1867.14	0.0848930
$786$	−5577.02	−0.253086
$787$	−18259.7	−0.827048	−0.413524	−	0.910493i	$-0.635702\pi$
$787$	−18259.7	−0.827048	−0.413524	+	0.910493i	$0.635702\pi$
$788$	−1211.15	−0.0547530
$789$	−25314.9	−1.14225
$790$	−15281.8	−0.688232
$791$	−6261.27	−0.281448
$792$	−4718.76	−0.211709
$793$	−48626.5	−2.17753
$794$	−25188.7	−1.12584
$795$	16302.5	0.727282
$796$	240.075	0.0106900
$797$	10821.5	0.480951	0.240476	−	0.970655i	$-0.422697\pi$
$797$	10821.5	0.480951	0.240476	+	0.970655i	$0.422697\pi$
$798$	540.925	0.0239956
$799$	−10060.0	−0.445428
$800$	322.312	0.0142443
$801$	7304.48	0.322211
$802$	29129.2	1.28253
$803$	5903.58	0.259443
$804$	2031.60	0.0891158
$805$	−1174.57	−0.0514262
$806$	46900.7	2.04963
$807$	−6284.81	−0.274146
$808$	25604.1	1.11479
$809$	−43523.2	−1.89146	−0.945731	−	0.324949i	$-0.894653\pi$
$809$	−43523.2	−1.89146	−0.945731	+	0.324949i	$0.894653\pi$
$810$	2336.48	0.101353
$811$	44292.1	1.91776	0.958881	−	0.283807i	$-0.0915975\pi$
$811$	44292.1	1.91776	0.958881	+	0.283807i	$0.0915975\pi$
$812$	25.5869	0.00110582
$813$	8869.78	0.382628
$814$	15391.1	0.662725
$815$	−42191.6	−1.81338
$816$	13405.5	0.575104
$817$	2945.34	0.126125
$818$	7202.14	0.307845
$819$	−2183.81	−0.0931726
$820$	−25.7225	−0.00109545
$821$	6015.57	0.255718	0.127859	−	0.991792i	$-0.459189\pi$
$821$	6015.57	0.255718	0.127859	+	0.991792i	$0.459189\pi$
$822$	14382.5	0.610275
$823$	−21950.3	−0.929697	−0.464849	−	0.885390i	$-0.653891\pi$
$823$	−21950.3	−0.929697	−0.464849	+	0.885390i	$0.653891\pi$
$824$	−5237.67	−0.221436
$825$	−539.288	−0.0227583
$826$	−7958.96	−0.335264
$827$	2591.55	0.108969	0.0544843	−	0.998515i	$-0.482649\pi$
$827$	2591.55	0.108969	0.0544843	+	0.998515i	$0.482649\pi$
$828$	207.442	0.00870665
$829$	13778.9	0.577274	0.288637	−	0.957439i	$-0.406798\pi$
$829$	13778.9	0.577274	0.288637	+	0.957439i	$0.406798\pi$
$830$	−19106.2	−0.799018
$831$	−4226.35	−0.176427
$832$	32451.4	1.35222
$833$	−25911.8	−1.07778
$834$	−20715.6	−0.860100
$835$	−17626.8	−0.730540
$836$	−317.217	−0.0131234
$837$	8120.89	0.335363
$838$	−17503.2	−0.721525
$839$	8719.52	0.358798	0.179399	−	0.983776i	$-0.442585\pi$
$839$	8719.52	0.358798	0.179399	+	0.983776i	$0.442585\pi$
$840$	−3190.79	−0.131063
$841$	−24340.0	−0.997993
$842$	−12655.0	−0.517957
$843$	16140.7	0.659449
$844$	−1811.86	−0.0738942
$845$	−13172.6	−0.536274
$846$	3037.09	0.123425
$847$	3493.44	0.141719
$848$	−28238.0	−1.14351
$849$	18861.4	0.762450
$850$	1724.23	0.0695771
$851$	−6821.91	−0.274797
$852$	382.546	0.0153824
$853$	−1765.04	−0.0708487	−0.0354243	−	0.999372i	$-0.511278\pi$
$853$	−1765.04	−0.0708487	−0.0354243	+	0.999372i	$0.511278\pi$
$854$	−9217.46	−0.369338
$855$	1583.65	0.0633445
$856$	−43187.9	−1.72446
$857$	−23068.6	−0.919496	−0.459748	−	0.888049i	$-0.652060\pi$
$857$	−23068.6	−0.919496	−0.459748	+	0.888049i	$0.652060\pi$
$858$	−10350.9	−0.411858
$859$	45538.7	1.80880	0.904401	−	0.426683i	$-0.140318\pi$
$859$	45538.7	1.80880	0.904401	+	0.426683i	$0.140318\pi$
$860$	−1723.18	−0.0683255
$861$	−33.6460	−0.00133177
$862$	1318.79	0.0521094
$863$	17396.2	0.686182	0.343091	−	0.939302i	$-0.388526\pi$
$863$	17396.2	0.686182	0.343091	+	0.939302i	$0.388526\pi$
$864$	1071.17	0.0421781
$865$	12459.7	0.489760
$866$	221.384	0.00868698
$867$	−4241.84	−0.166160
$868$	−1099.95	−0.0430123
$869$	11722.4	0.457600
$870$	−605.457	−0.0235942
$871$	44932.1	1.74795
$872$	29.1326	0.00113137
$873$	11049.3	0.428365
$874$	−1136.42	−0.0439815
$875$	−5975.39	−0.230863
$876$	−705.026	−0.0271925
$877$	34399.6	1.32451	0.662254	−	0.749279i	$-0.269600\pi$
$877$	34399.6	1.32451	0.662254	+	0.749279i	$0.269600\pi$
$878$	43940.0	1.68896
$879$	−9628.43	−0.369464
$880$	−13438.3	−0.514777
$881$	32155.2	1.22967	0.614833	−	0.788657i	$-0.289223\pi$
$881$	32155.2	1.22967	0.614833	+	0.788657i	$0.289223\pi$
$882$	7822.72	0.298645
$883$	45892.3	1.74904	0.874519	−	0.484992i	$-0.161177\pi$
$883$	45892.3	1.74904	0.874519	+	0.484992i	$0.161177\pi$
$884$	−4094.56	−0.155786
$885$	−23301.2	−0.885040
$886$	−15811.1	−0.599532
$887$	−2306.90	−0.0873261	−0.0436630	−	0.999046i	$-0.513903\pi$
$887$	−2306.90	−0.0873261	−0.0436630	+	0.999046i	$0.513903\pi$
$888$	−18532.2	−0.700337
$889$	2323.30	0.0876503
$890$	23411.2	0.881737
$891$	−1792.27	−0.0673885
$892$	3994.13	0.149925
$893$	2058.51	0.0771395
$894$	−4708.30	−0.176140
$895$	−9047.74	−0.337914
$896$	4833.61	0.180223
$897$	4587.90	0.170775
$898$	−4517.73	−0.167883
$899$	−2104.38	−0.0780702
$900$	64.4036	0.00238532
$901$	39982.2	1.47836
$902$	−159.477	−0.00588692
$903$	−2253.98	−0.0830652
$904$	35734.1	1.31471
$905$	31307.7	1.14995
$906$	−13775.1	−0.505131
$907$	37028.8	1.35559	0.677796	−	0.735250i	$-0.262935\pi$
$907$	37028.8	1.35559	0.677796	+	0.735250i	$0.262935\pi$
$908$	−3983.92	−0.145607
$909$	9724.88	0.354845
$910$	−6999.21	−0.254969
$911$	4630.57	0.168406	0.0842028	−	0.996449i	$-0.473166\pi$
$911$	4630.57	0.168406	0.0842028	+	0.996449i	$0.473166\pi$
$912$	−2743.08	−0.0995969
$913$	14655.9	0.531261
$914$	11727.9	0.424425
$915$	−26985.6	−0.974992
$916$	3480.43	0.125542
$917$	2892.77	0.104174
$918$	5730.28	0.206021
$919$	16030.4	0.575402	0.287701	−	0.957720i	$-0.407109\pi$
$919$	16030.4	0.575402	0.287701	+	0.957720i	$0.407109\pi$
$920$	6703.46	0.240224
$921$	3012.82	0.107791
$922$	−33718.7	−1.20441
$923$	8460.61	0.301717
$924$	242.757	0.00864298
$925$	−2117.97	−0.0752848
$926$	−48551.9	−1.72302
$927$	−1989.36	−0.0704844
$928$	−277.574	−0.00981877
$929$	24729.7	0.873364	0.436682	−	0.899616i	$-0.356154\pi$
$929$	24729.7	0.873364	0.436682	+	0.899616i	$0.356154\pi$
$930$	26027.8	0.917728
$931$	5302.17	0.186650
$932$	4425.32	0.155532
$933$	−8591.21	−0.301462
$934$	−9067.98	−0.317680
$935$	19027.3	0.665517
$936$	12463.3	0.435232
$937$	32508.7	1.13342	0.566709	−	0.823918i	$-0.308216\pi$
$937$	32508.7	1.13342	0.566709	+	0.823918i	$0.308216\pi$
$938$	8517.15	0.296476
$939$	−26968.5	−0.937256
$940$	−1204.34	−0.0417885
$941$	−530.766	−0.0183873	−0.00919366	−	0.999958i	$-0.502926\pi$
$941$	−530.766	−0.0183873	−0.00919366	+	0.999958i	$0.502926\pi$
$942$	−1382.45	−0.0478161
$943$	70.6861	0.00244099
$944$	40360.6	1.39155
$945$	−1211.92	−0.0417182
$946$	−10683.5	−0.367179
$947$	52553.0	1.80332	0.901660	−	0.432446i	$-0.142350\pi$
$947$	52553.0	1.80332	0.901660	+	0.432446i	$0.142350\pi$
$948$	−1399.93	−0.0479615
$949$	−15592.8	−0.533364
$950$	−352.818	−0.0120494
$951$	33693.1	1.14887
$952$	−7825.50	−0.266414
$953$	18880.6	0.641765	0.320883	−	0.947119i	$-0.396021\pi$
$953$	18880.6	0.641765	0.320883	+	0.947119i	$0.396021\pi$
$954$	−12070.6	−0.409643
$955$	−49567.7	−1.67955
$956$	−5291.81	−0.179027
$957$	464.434	0.0156876
$958$	−30201.0	−1.01853
$959$	−7460.09	−0.251198
$960$	18009.1	0.605460
$961$	60673.8	2.03665
$962$	−40651.5	−1.36243
$963$	−16403.5	−0.548906
$964$	−5299.76	−0.177068
$965$	−37954.4	−1.26611
$966$	869.665	0.0289659
$967$	−30050.4	−0.999334	−0.499667	−	0.866218i	$-0.666544\pi$
$967$	−30050.4	−0.999334	−0.499667	+	0.866218i	$0.666544\pi$
$968$	−19937.7	−0.662005
$969$	3883.93	0.128762
$970$	35413.6	1.17223
$971$	−21084.7	−0.696847	−0.348424	−	0.937337i	$-0.613283\pi$
$971$	−21084.7	−0.696847	−0.348424	+	0.937337i	$0.613283\pi$
$972$	214.039	0.00706305
$973$	10745.1	0.354030
$974$	37129.1	1.22145
$975$	1424.39	0.0467865
$976$	46742.5	1.53298
$977$	−6005.96	−0.196671	−0.0983356	−	0.995153i	$-0.531352\pi$
$977$	−6005.96	−0.196671	−0.0983356	+	0.995153i	$0.531352\pi$
$978$	31239.2	1.02139
$979$	−17958.2	−0.586259
$980$	−3102.04	−0.101113
$981$	11.0651	0.000360123 0
$982$	−25741.5	−0.836500
$983$	−59306.2	−1.92429	−0.962144	−	0.272542i	$-0.912136\pi$
$983$	−59306.2	−1.92429	−0.962144	+	0.272542i	$0.912136\pi$
$984$	192.024	0.00622103
$985$	−14865.3	−0.480861
$986$	−1484.90	−0.0479603
$987$	−1575.32	−0.0508034
$988$	837.844	0.0269791
$989$	4735.34	0.152250
$990$	−5744.30	−0.184410
$991$	8530.35	0.273436	0.136718	−	0.990610i	$-0.456345\pi$
$991$	8530.35	0.273436	0.136718	+	0.990610i	$0.456345\pi$
$992$	11932.6	0.381915
$993$	−3971.30	−0.126914
$994$	1603.76	0.0511753
$995$	2946.62	0.0938835
$996$	−1750.26	−0.0556820
$997$	977.326	0.0310453	0.0155227	−	0.999880i	$-0.495059\pi$
$997$	977.326	0.0310453	0.0155227	+	0.999880i	$0.495059\pi$
$998$	42879.3	1.36004
$999$	−7038.84	−0.222922

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1011.4.a.c.1.13	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1011.4.a.c.1.13	✓	46	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1011 = 3 \cdot 337 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.66818 q^{2} -3.00000 q^{3} -0.880817 q^{4} -10.8109 q^{5} +8.00454 q^{6} -4.15190 q^{7} +23.6956 q^{8} +9.00000 q^{9} +28.8455 q^{10} -22.1267 q^{11} +2.64245 q^{12} +58.4419 q^{13} +11.0780 q^{14} +32.4327 q^{15} -56.1776 q^{16} +79.5421 q^{17} -24.0136 q^{18} -16.2762 q^{19} +9.52243 q^{20} +12.4557 q^{21} +59.0381 q^{22} -26.1679 q^{23} -71.0868 q^{24} -8.12423 q^{25} -155.933 q^{26} -27.0000 q^{27} +3.65707 q^{28} +6.99657 q^{29} -86.5364 q^{30} -300.774 q^{31} -39.6729 q^{32} +66.3802 q^{33} -212.233 q^{34} +44.8858 q^{35} -7.92735 q^{36} +260.698 q^{37} +43.4279 q^{38} -175.326 q^{39} -256.171 q^{40} -2.70125 q^{41} -33.2341 q^{42} -180.960 q^{43} +19.4896 q^{44} -97.2982 q^{45} +69.8206 q^{46} -126.474 q^{47} +168.533 q^{48} -325.762 q^{49} +21.6769 q^{50} -238.626 q^{51} -51.4766 q^{52} +502.655 q^{53} +72.0409 q^{54} +239.210 q^{55} -98.3819 q^{56} +48.8286 q^{57} -18.6681 q^{58} -718.446 q^{59} -28.5673 q^{60} -832.049 q^{61} +802.518 q^{62} -37.3671 q^{63} +555.275 q^{64} -631.810 q^{65} -177.114 q^{66} +768.833 q^{67} -70.0620 q^{68} +78.5036 q^{69} -119.763 q^{70} +144.770 q^{71} +213.261 q^{72} -266.808 q^{73} -695.589 q^{74} +24.3727 q^{75} +14.3364 q^{76} +91.8680 q^{77} +467.800 q^{78} -529.783 q^{79} +607.331 q^{80} +81.0000 q^{81} +7.20743 q^{82} -662.364 q^{83} -10.9712 q^{84} -859.923 q^{85} +482.834 q^{86} -20.9897 q^{87} -524.307 q^{88} +811.608 q^{89} +259.609 q^{90} -242.645 q^{91} +23.0491 q^{92} +902.321 q^{93} +337.455 q^{94} +175.961 q^{95} +119.019 q^{96} +1227.70 q^{97} +869.191 q^{98} -199.141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q + 7 q^{2} - 138 q^{3} + 207 q^{4} + 42 q^{5} - 21 q^{6} - 72 q^{7} + 105 q^{8} + 414 q^{9} - 32 q^{10} + 126 q^{11} - 621 q^{12} + 114 q^{13} + 111 q^{14} - 126 q^{15} + 915 q^{16} + 154 q^{17} + 63 q^{18}+ \cdots + 1134 q^{99}+O(q^{100}) \) 46 * q + 7 * q^2 - 138 * q^3 + 207 * q^4 + 42 * q^5 - 21 * q^6 - 72 * q^7 + 105 * q^8 + 414 * q^9 - 32 * q^10 + 126 * q^11 - 621 * q^12 + 114 * q^13 + 111 * q^14 - 126 * q^15 + 915 * q^16 + 154 * q^17 + 63 * q^18 - 56 * q^19 + 253 * q^20 + 216 * q^21 + 115 * q^22 + 386 * q^23 - 315 * q^24 + 1278 * q^25 + 394 * q^26 - 1242 * q^27 - 780 * q^28 + 1214 * q^29 + 96 * q^30 - 306 * q^31 + 1107 * q^32 - 378 * q^33 + 280 * q^34 + 560 * q^35 + 1863 * q^36 + 694 * q^37 + 944 * q^38 - 342 * q^39 - 309 * q^40 + 1120 * q^41 - 333 * q^42 - 258 * q^43 + 2092 * q^44 + 378 * q^45 + 629 * q^46 + 258 * q^47 - 2745 * q^48 + 3490 * q^49 + 1563 * q^50 - 462 * q^51 + 816 * q^52 + 2856 * q^53 - 189 * q^54 - 1576 * q^55 + 1995 * q^56 + 168 * q^57 + 450 * q^58 + 1598 * q^59 - 759 * q^60 + 902 * q^61 + 1378 * q^62 - 648 * q^63 + 4903 * q^64 + 1760 * q^65 - 345 * q^66 + 596 * q^67 + 2161 * q^68 - 1158 * q^69 + 1334 * q^70 + 2326 * q^71 + 945 * q^72 - 1226 * q^73 + 1645 * q^74 - 3834 * q^75 + 53 * q^76 + 4494 * q^77 - 1182 * q^78 + 600 * q^79 + 159 * q^80 + 3726 * q^81 - 1535 * q^82 - 26 * q^83 + 2340 * q^84 + 3874 * q^85 + 7437 * q^86 - 3642 * q^87 + 4070 * q^88 + 3534 * q^89 - 288 * q^90 + 114 * q^91 + 12901 * q^92 + 918 * q^93 + 6808 * q^94 + 3376 * q^95 - 3321 * q^96 + 1348 * q^97 + 12735 * q^98 + 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more