LMFDB - Embedded newform 529.4.a.m.1.17

Error: no document with id 234107538 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,4,Mod(1,529)] 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("529.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,0,-1,80,-51] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.27917 q^{2} -5.45949 q^{3} -2.80539 q^{4} -0.946196 q^{5} -12.4431 q^{6} +13.4796 q^{7} -24.6273 q^{8} +2.80604 q^{9} -2.15654 q^{10} +53.3829 q^{11} +15.3160 q^{12} +33.5635 q^{13} +30.7222 q^{14} +5.16575 q^{15} -33.6866 q^{16} +34.3481 q^{17} +6.39543 q^{18} -86.9253 q^{19} +2.65445 q^{20} -73.5916 q^{21} +121.669 q^{22} +134.453 q^{24} -124.105 q^{25} +76.4969 q^{26} +132.087 q^{27} -37.8155 q^{28} +46.3077 q^{29} +11.7736 q^{30} -210.105 q^{31} +120.241 q^{32} -291.443 q^{33} +78.2852 q^{34} -12.7543 q^{35} -7.87204 q^{36} -279.323 q^{37} -198.117 q^{38} -183.240 q^{39} +23.3023 q^{40} -329.177 q^{41} -167.728 q^{42} -341.867 q^{43} -149.760 q^{44} -2.65506 q^{45} +460.208 q^{47} +183.912 q^{48} -161.301 q^{49} -282.855 q^{50} -187.523 q^{51} -94.1590 q^{52} -243.377 q^{53} +301.048 q^{54} -50.5107 q^{55} -331.966 q^{56} +474.568 q^{57} +105.543 q^{58} +119.813 q^{59} -14.4920 q^{60} +406.566 q^{61} -478.865 q^{62} +37.8242 q^{63} +543.542 q^{64} -31.7577 q^{65} -664.248 q^{66} -870.845 q^{67} -96.3601 q^{68} -29.0692 q^{70} +287.257 q^{71} -69.1051 q^{72} -913.737 q^{73} -636.625 q^{74} +677.549 q^{75} +243.860 q^{76} +719.579 q^{77} -417.634 q^{78} +788.578 q^{79} +31.8741 q^{80} -796.889 q^{81} -750.250 q^{82} -1353.17 q^{83} +206.454 q^{84} -32.5001 q^{85} -779.173 q^{86} -252.817 q^{87} -1314.68 q^{88} -744.528 q^{89} -6.05133 q^{90} +452.422 q^{91} +1147.07 q^{93} +1048.89 q^{94} +82.2484 q^{95} -656.455 q^{96} +499.625 q^{97} -367.632 q^{98} +149.794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * 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 $

$2$	2.27917	0.805808	0.402904	−	0.915242i	$-0.368001\pi$
$2$	2.27917	0.805808	0.402904	+	0.915242i	$0.368001\pi$
$3$	−5.45949	−1.05068	−0.525340	−	0.850893i	$-0.676062\pi$
$3$	−5.45949	−1.05068	−0.525340	+	0.850893i	$0.676062\pi$
$4$	−2.80539	−0.350674
$5$	−0.946196	−0.0846304	−0.0423152	−	0.999104i	$-0.513473\pi$
$5$	−0.946196	−0.0846304	−0.0423152	+	0.999104i	$0.513473\pi$
$6$	−12.4431	−0.846645
$7$	13.4796	0.727829	0.363914	−	0.931432i	$-0.381440\pi$
$7$	13.4796	0.727829	0.363914	+	0.931432i	$0.381440\pi$
$8$	−24.6273	−1.08838
$9$	2.80604	0.103927
$10$	−2.15654	−0.0681958
$11$	53.3829	1.46323	0.731615	−	0.681718i	$-0.238767\pi$
$11$	53.3829	1.46323	0.731615	+	0.681718i	$0.238767\pi$
$12$	15.3160	0.368446
$13$	33.5635	0.716066	0.358033	−	0.933709i	$-0.383448\pi$
$13$	33.5635	0.716066	0.358033	+	0.933709i	$0.383448\pi$
$14$	30.7222	0.586490
$15$	5.16575	0.0889194
$16$	−33.6866	−0.526353
$17$	34.3481	0.490038	0.245019	−	0.969518i	$-0.421206\pi$
$17$	34.3481	0.490038	0.245019	+	0.969518i	$0.421206\pi$
$18$	6.39543	0.0837454
$19$	−86.9253	−1.04958	−0.524790	−	0.851232i	$-0.675856\pi$
$19$	−86.9253	−1.04958	−0.524790	+	0.851232i	$0.675856\pi$
$20$	2.65445	0.0296777
$21$	−73.5916	−0.764715
$22$	121.669	1.17908
$23$	0	0
$23$	0	0
$24$	134.453	1.14354
$25$	−124.105	−0.992838
$26$	76.4969	0.577011
$27$	132.087	0.941485
$28$	−37.8155	−0.255231
$29$	46.3077	0.296522	0.148261	−	0.988948i	$-0.452632\pi$
$29$	46.3077	0.296522	0.148261	+	0.988948i	$0.452632\pi$
$30$	11.7736	0.0716519
$31$	−210.105	−1.21729	−0.608646	−	0.793442i	$-0.708287\pi$
$31$	−210.105	−1.21729	−0.608646	+	0.793442i	$0.708287\pi$
$32$	120.241	0.664244
$33$	−291.443	−1.53739
$34$	78.2852	0.394876
$35$	−12.7543	−0.0615964
$36$	−7.87204	−0.0364446
$37$	−279.323	−1.24109	−0.620547	−	0.784169i	$-0.713089\pi$
$37$	−279.323	−1.24109	−0.620547	+	0.784169i	$0.713089\pi$
$38$	−198.117	−0.845760
$39$	−183.240	−0.752355
$40$	23.3023	0.0921103
$41$	−329.177	−1.25387	−0.626937	−	0.779070i	$-0.715692\pi$
$41$	−329.177	−1.25387	−0.626937	+	0.779070i	$0.715692\pi$
$42$	−167.728	−0.616213
$43$	−341.867	−1.21242	−0.606212	−	0.795303i	$-0.707312\pi$
$43$	−341.867	−1.21242	−0.606212	+	0.795303i	$0.707312\pi$
$44$	−149.760	−0.513117
$45$	−2.65506	−0.00879540
$46$	0	0
$47$	460.208	1.42826	0.714130	−	0.700013i	$-0.246823\pi$
$47$	460.208	1.42826	0.714130	+	0.700013i	$0.246823\pi$
$48$	183.912	0.553029
$49$	−161.301	−0.470265
$50$	−282.855	−0.800036
$51$	−187.523	−0.514873
$52$	−94.1590	−0.251106
$53$	−243.377	−0.630763	−0.315382	−	0.948965i	$-0.602132\pi$
$53$	−243.377	−0.630763	−0.315382	+	0.948965i	$0.602132\pi$
$54$	301.048	0.758656
$55$	−50.5107	−0.123834
$56$	−331.966	−0.792157
$57$	474.568	1.10277
$58$	105.543	0.238939
$59$	119.813	0.264379	0.132190	−	0.991224i	$-0.457799\pi$
$59$	119.813	0.264379	0.132190	+	0.991224i	$0.457799\pi$
$60$	−14.4920	−0.0311817
$61$	406.566	0.853369	0.426684	−	0.904401i	$-0.359682\pi$
$61$	406.566	0.853369	0.426684	+	0.904401i	$0.359682\pi$
$62$	−478.865	−0.980902
$63$	37.8242	0.0756413
$64$	543.542	1.06161
$65$	−31.7577	−0.0606009
$66$	−664.248	−1.23884
$67$	−870.845	−1.58792	−0.793960	−	0.607970i	$-0.791984\pi$
$67$	−870.845	−1.58792	−0.793960	+	0.607970i	$0.791984\pi$
$68$	−96.3601	−0.171844
$69$	0	0
$70$	−29.0692	−0.0496349
$71$	287.257	0.480156	0.240078	−	0.970754i	$-0.422827\pi$
$71$	287.257	0.480156	0.240078	+	0.970754i	$0.422827\pi$
$72$	−69.1051	−0.113113
$73$	−913.737	−1.46500	−0.732498	−	0.680769i	$-0.761646\pi$
$73$	−913.737	−1.46500	−0.732498	+	0.680769i	$0.761646\pi$
$74$	−636.625	−1.00008
$75$	677.549	1.04315
$76$	243.860	0.368061
$77$	719.579	1.06498
$78$	−417.634	−0.606254
$79$	788.578	1.12306	0.561532	−	0.827455i	$-0.310212\pi$
$79$	788.578	1.12306	0.561532	+	0.827455i	$0.310212\pi$
$80$	31.8741	0.0445455
$81$	−796.889	−1.09313
$82$	−750.250	−1.01038
$83$	−1353.17	−1.78951	−0.894757	−	0.446552i	$-0.852652\pi$
$83$	−1353.17	−1.78951	−0.894757	+	0.446552i	$0.852652\pi$
$84$	206.454	0.268166
$85$	−32.5001	−0.0414721
$86$	−779.173	−0.976981
$87$	−252.817	−0.311549
$88$	−1314.68	−1.59256
$89$	−744.528	−0.886739	−0.443369	−	0.896339i	$-0.646217\pi$
$89$	−744.528	−0.886739	−0.443369	+	0.896339i	$0.646217\pi$
$90$	−6.05133	−0.00708740
$91$	452.422	0.521173
$92$	0	0
$93$	1147.07	1.27898
$94$	1048.89	1.15090
$95$	82.2484	0.0888264
$96$	−656.455	−0.697908
$97$	499.625	0.522982	0.261491	−	0.965206i	$-0.415786\pi$
$97$	499.625	0.522982	0.261491	+	0.965206i	$0.415786\pi$
$98$	−367.632	−0.378943
$99$	149.794	0.152070
$100$	348.163	0.348163
$101$	419.522	0.413307	0.206653	−	0.978414i	$-0.433743\pi$
$101$	419.522	0.413307	0.206653	+	0.978414i	$0.433743\pi$
$102$	−427.397	−0.414889
$103$	−311.123	−0.297630	−0.148815	−	0.988865i	$-0.547546\pi$
$103$	−311.123	−0.297630	−0.148815	+	0.988865i	$0.547546\pi$
$104$	−826.580	−0.779354
$105$	69.6321	0.0647181
$106$	−554.698	−0.508274
$107$	−705.495	−0.637409	−0.318704	−	0.947854i	$-0.603248\pi$
$107$	−705.495	−0.637409	−0.318704	+	0.947854i	$0.603248\pi$
$108$	−370.555	−0.330155
$109$	−687.862	−0.604452	−0.302226	−	0.953236i	$-0.597730\pi$
$109$	−687.862	−0.604452	−0.302226	+	0.953236i	$0.597730\pi$
$110$	−115.122	−0.0997862
$111$	1524.96	1.30399
$112$	−454.081	−0.383095
$113$	969.886	0.807427	0.403713	−	0.914885i	$-0.367719\pi$
$113$	969.886	0.807427	0.403713	+	0.914885i	$0.367719\pi$
$114$	1081.62	0.888623
$115$	0	0
$116$	−129.911	−0.103983
$117$	94.1805	0.0744188
$118$	273.075	0.213039
$119$	462.998	0.356664
$120$	−127.218	−0.0967784
$121$	1518.73	1.14104
$122$	926.633	0.687651
$123$	1797.14	1.31742
$124$	589.428	0.426873
$125$	235.702	0.168655
$126$	86.2077	0.0609523
$127$	−1422.09	−0.993623	−0.496811	−	0.867859i	$-0.665496\pi$
$127$	−1422.09	−0.993623	−0.496811	+	0.867859i	$0.665496\pi$
$128$	276.896	0.191206
$129$	1866.42	1.27387
$130$	−72.3811	−0.0488327
$131$	−2006.39	−1.33816	−0.669079	−	0.743191i	$-0.733311\pi$
$131$	−2006.39	−1.33816	−0.669079	+	0.743191i	$0.733311\pi$
$132$	817.613	0.539122
$133$	−1171.72	−0.763915
$134$	−1984.80	−1.27956
$135$	−124.980	−0.0796782
$136$	−845.902	−0.533349
$137$	1517.23	0.946170	0.473085	−	0.881017i	$-0.343140\pi$
$137$	1517.23	0.946170	0.473085	+	0.881017i	$0.343140\pi$
$138$	0	0
$139$	188.684	0.115136	0.0575681	−	0.998342i	$-0.481665\pi$
$139$	188.684	0.115136	0.0575681	+	0.998342i	$0.481665\pi$
$140$	35.7809	0.0216003
$141$	−2512.50	−1.50064
$142$	654.706	0.386914
$143$	1791.72	1.04777
$144$	−94.5259	−0.0547025
$145$	−43.8162	−0.0250947
$146$	−2082.56	−1.18051
$147$	880.621	0.494098
$148$	783.612	0.435220
$149$	−559.526	−0.307639	−0.153819	−	0.988099i	$-0.549157\pi$
$149$	−559.526	−0.307639	−0.153819	+	0.988099i	$0.549157\pi$
$150$	1544.25	0.840581
$151$	2970.36	1.60082	0.800411	−	0.599451i	$-0.204614\pi$
$151$	2970.36	1.60082	0.800411	+	0.599451i	$0.204614\pi$
$152$	2140.74	1.14235
$153$	96.3822	0.0509283
$154$	1640.04	0.858170
$155$	198.801	0.103020
$156$	514.060	0.263832
$157$	926.873	0.471162	0.235581	−	0.971855i	$-0.424301\pi$
$157$	926.873	0.471162	0.235581	+	0.971855i	$0.424301\pi$
$158$	1797.30	0.904973
$159$	1328.72	0.662730
$160$	−113.772	−0.0562152
$161$	0	0
$162$	−1816.24	−0.880849
$163$	−2243.11	−1.07788	−0.538939	−	0.842345i	$-0.681175\pi$
$163$	−2243.11	−1.07788	−0.538939	+	0.842345i	$0.681175\pi$
$164$	923.472	0.439701
$165$	275.763	0.130110
$166$	−3084.10	−1.44200
$167$	−1285.77	−0.595786	−0.297893	−	0.954599i	$-0.596284\pi$
$167$	−1285.77	−0.595786	−0.297893	+	0.954599i	$0.596284\pi$
$168$	1812.36	0.832303
$169$	−1070.49	−0.487250
$170$	−74.0731	−0.0334185
$171$	−243.916	−0.109080
$172$	959.072	0.425166
$173$	203.210	0.0893051	0.0446525	−	0.999003i	$-0.485782\pi$
$173$	203.210	0.0893051	0.0446525	+	0.999003i	$0.485782\pi$
$174$	−576.211	−0.251049
$175$	−1672.88	−0.722616
$176$	−1798.29	−0.770176
$177$	−654.120	−0.277778
$178$	−1696.90	−0.714541
$179$	445.875	0.186180	0.0930902	−	0.995658i	$-0.470326\pi$
$179$	445.875	0.186180	0.0930902	+	0.995658i	$0.470326\pi$
$180$	7.44849	0.00308432
$181$	3542.58	1.45479	0.727397	−	0.686217i	$-0.240730\pi$
$181$	3542.58	1.45479	0.727397	+	0.686217i	$0.240730\pi$
$182$	1031.15	0.419965
$183$	−2219.65	−0.896617
$184$	0	0
$185$	264.295	0.105034
$186$	2614.36	1.03061
$187$	1833.60	0.717039
$188$	−1291.06	−0.500854
$189$	1780.47	0.685240
$190$	187.458	0.0715770
$191$	−1969.94	−0.746283	−0.373142	−	0.927774i	$-0.621719\pi$
$191$	−1969.94	−0.746283	−0.373142	+	0.927774i	$0.621719\pi$
$192$	−2967.46	−1.11541
$193$	−914.565	−0.341098	−0.170549	−	0.985349i	$-0.554554\pi$
$193$	−914.565	−0.341098	−0.170549	+	0.985349i	$0.554554\pi$
$194$	1138.73	0.421423
$195$	173.381	0.0636721
$196$	452.513	0.164910
$197$	−3140.74	−1.13588	−0.567940	−	0.823070i	$-0.692259\pi$
$197$	−3140.74	−1.13588	−0.567940	+	0.823070i	$0.692259\pi$
$198$	341.406	0.122539
$199$	380.763	0.135636	0.0678181	−	0.997698i	$-0.478396\pi$
$199$	380.763	0.135636	0.0678181	+	0.997698i	$0.478396\pi$
$200$	3056.36	1.08059
$201$	4754.37	1.66839
$202$	956.161	0.333046
$203$	624.209	0.215817
$204$	526.077	0.180553
$205$	311.466	0.106116
$206$	−709.103	−0.239833
$207$	0	0
$208$	−1130.64	−0.376903
$209$	−4640.32	−1.53578
$210$	158.703	0.0521503
$211$	4385.35	1.43081	0.715403	−	0.698712i	$-0.246243\pi$
$211$	4385.35	1.43081	0.715403	+	0.698712i	$0.246243\pi$
$212$	682.769	0.221192
$213$	−1568.28	−0.504490
$214$	−1607.94	−0.513629
$215$	323.474	0.102608
$216$	−3252.94	−1.02470
$217$	−2832.13	−0.885980
$218$	−1567.75	−0.487072
$219$	4988.54	1.53924
$220$	141.702	0.0434253
$221$	1152.85	0.350899
$222$	3475.65	1.05077
$223$	3849.73	1.15604	0.578020	−	0.816023i	$-0.303826\pi$
$223$	3849.73	1.15604	0.578020	+	0.816023i	$0.303826\pi$
$224$	1620.80	0.483456
$225$	−348.242	−0.103183
$226$	2210.53	0.650631
$227$	−726.650	−0.212464	−0.106232	−	0.994341i	$-0.533879\pi$
$227$	−726.650	−0.212464	−0.106232	+	0.994341i	$0.533879\pi$
$228$	−1331.35	−0.386714
$229$	−5991.20	−1.72886	−0.864432	−	0.502750i	$-0.832322\pi$
$229$	−5991.20	−1.72886	−0.864432	+	0.502750i	$0.832322\pi$
$230$	0	0
$231$	−3928.53	−1.11895
$232$	−1140.43	−0.322729
$233$	3871.65	1.08858	0.544292	−	0.838896i	$-0.316798\pi$
$233$	3871.65	1.08858	0.544292	+	0.838896i	$0.316798\pi$
$234$	214.653	0.0599672
$235$	−435.447	−0.120874
$236$	−336.124	−0.0927109
$237$	−4305.24	−1.17998
$238$	1055.25	0.287402
$239$	2952.98	0.799216	0.399608	−	0.916686i	$-0.369146\pi$
$239$	2952.98	0.799216	0.399608	+	0.916686i	$0.369146\pi$
$240$	−174.017	−0.0468030
$241$	−5796.90	−1.54942	−0.774711	−	0.632315i	$-0.782105\pi$
$241$	−5796.90	−1.54942	−0.774711	+	0.632315i	$0.782105\pi$
$242$	3461.44	0.919462
$243$	784.268	0.207040
$244$	−1140.58	−0.299254
$245$	152.622	0.0397987
$246$	4095.98	1.06159
$247$	−2917.52	−0.751569
$248$	5174.33	1.32488
$249$	7387.62	1.88021
$250$	537.204	0.135903
$251$	−2169.66	−0.545608	−0.272804	−	0.962070i	$-0.587951\pi$
$251$	−2169.66	−0.545608	−0.272804	+	0.962070i	$0.587951\pi$
$252$	−106.112	−0.0265254
$253$	0	0
$254$	−3241.18	−0.800668
$255$	177.434	0.0435739
$256$	−3717.25	−0.907531
$257$	4383.32	1.06391	0.531954	−	0.846773i	$-0.321458\pi$
$257$	4383.32	1.06391	0.531954	+	0.846773i	$0.321458\pi$
$258$	4253.89	1.02649
$259$	−3765.16	−0.903304
$260$	89.0929	0.0212512
$261$	129.941	0.0308167
$262$	−4572.89	−1.07830
$263$	−2446.80	−0.573673	−0.286836	−	0.957980i	$-0.592604\pi$
$263$	−2446.80	−0.573673	−0.286836	+	0.957980i	$0.592604\pi$
$264$	7177.46	1.67327
$265$	230.283	0.0533817
$266$	−2670.54	−0.615568
$267$	4064.74	0.931678
$268$	2443.06	0.556843
$269$	−2496.56	−0.565865	−0.282933	−	0.959140i	$-0.591307\pi$
$269$	−2496.56	−0.565865	−0.282933	+	0.959140i	$0.591307\pi$
$270$	−284.850	−0.0642053
$271$	−7251.46	−1.62544	−0.812721	−	0.582653i	$-0.802015\pi$
$271$	−7251.46	−1.62544	−0.812721	+	0.582653i	$0.802015\pi$
$272$	−1157.07	−0.257933
$273$	−2470.00	−0.547586
$274$	3458.01	0.762431
$275$	−6625.07	−1.45275
$276$	0	0
$277$	4444.85	0.964134	0.482067	−	0.876134i	$-0.339886\pi$
$277$	4444.85	0.964134	0.482067	+	0.876134i	$0.339886\pi$
$278$	430.042	0.0927776
$279$	−589.563	−0.126510
$280$	314.105	0.0670405
$281$	−4542.77	−0.964409	−0.482205	−	0.876059i	$-0.660164\pi$
$281$	−4542.77	−0.964409	−0.482205	+	0.876059i	$0.660164\pi$
$282$	−5726.41	−1.20923
$283$	−2695.66	−0.566221	−0.283111	−	0.959087i	$-0.591366\pi$
$283$	−2695.66	−0.566221	−0.283111	+	0.959087i	$0.591366\pi$
$284$	−805.868	−0.168378
$285$	−449.034	−0.0933281
$286$	4083.63	0.844300
$287$	−4437.17	−0.912606
$288$	337.401	0.0690331
$289$	−3733.21	−0.759863
$290$	−99.8645	−0.0202215
$291$	−2727.70	−0.549486
$292$	2563.39	0.513737
$293$	2392.05	0.476946	0.238473	−	0.971149i	$-0.423353\pi$
$293$	2392.05	0.476946	0.238473	+	0.971149i	$0.423353\pi$
$294$	2007.08	0.398148
$295$	−113.367	−0.0223745
$296$	6878.98	1.35079
$297$	7051.17	1.37761
$298$	−1275.25	−0.247897
$299$	0	0
$300$	−1900.79	−0.365807
$301$	−4608.23	−0.882438
$302$	6769.94	1.28995
$303$	−2290.38	−0.434253
$304$	2928.22	0.552450
$305$	−384.692	−0.0722209
$306$	219.671	0.0410384
$307$	−4881.47	−0.907493	−0.453747	−	0.891131i	$-0.649913\pi$
$307$	−4881.47	−0.907493	−0.453747	+	0.891131i	$0.649913\pi$
$308$	−2018.70	−0.373462
$309$	1698.58	0.312714
$310$	453.101	0.0830141
$311$	−2136.50	−0.389549	−0.194775	−	0.980848i	$-0.562398\pi$
$311$	−2136.50	−0.389549	−0.194775	+	0.980848i	$0.562398\pi$
$312$	4512.70	0.818851
$313$	−4233.77	−0.764559	−0.382279	−	0.924047i	$-0.624861\pi$
$313$	−4233.77	−0.764559	−0.382279	+	0.924047i	$0.624861\pi$
$314$	2112.50	0.379666
$315$	−35.7891	−0.00640155
$316$	−2212.27	−0.393829
$317$	7182.53	1.27259	0.636295	−	0.771445i	$-0.280466\pi$
$317$	7182.53	1.27259	0.636295	+	0.771445i	$0.280466\pi$
$318$	3028.37	0.534033
$319$	2472.04	0.433880
$320$	−514.298	−0.0898441
$321$	3851.64	0.669712
$322$	0	0
$323$	−2985.72	−0.514335
$324$	2235.59	0.383331
$325$	−4165.39	−0.710937
$326$	−5112.43	−0.868562
$327$	3755.38	0.635085
$328$	8106.75	1.36470
$329$	6203.41	1.03953
$330$	628.509	0.104843
$331$	7950.08	1.32017	0.660084	−	0.751192i	$-0.270521\pi$
$331$	7950.08	1.32017	0.660084	+	0.751192i	$0.270521\pi$
$332$	3796.18	0.627537
$333$	−783.791	−0.128984
$334$	−2930.49	−0.480088
$335$	823.990	0.134386
$336$	2479.05	0.402510
$337$	−3358.70	−0.542909	−0.271454	−	0.962451i	$-0.587505\pi$
$337$	−3358.70	−0.542909	−0.271454	+	0.962451i	$0.587505\pi$
$338$	−2439.82	−0.392630
$339$	−5295.09	−0.848347
$340$	91.1755	0.0145432
$341$	−11216.0	−1.78118
$342$	−555.925	−0.0878975
$343$	−6797.76	−1.07010
$344$	8419.27	1.31958
$345$	0	0
$346$	463.150	0.0719627
$347$	1155.82	0.178811	0.0894057	−	0.995995i	$-0.471503\pi$
$347$	1155.82	0.178811	0.0894057	+	0.995995i	$0.471503\pi$
$348$	709.250	0.109252
$349$	6932.87	1.06335	0.531673	−	0.846949i	$-0.321563\pi$
$349$	6932.87	1.06335	0.531673	+	0.846949i	$0.321563\pi$
$350$	−3812.77	−0.582289
$351$	4433.30	0.674165
$352$	6418.81	0.971942
$353$	10113.2	1.52484	0.762421	−	0.647081i	$-0.224011\pi$
$353$	10113.2	1.52484	0.762421	+	0.647081i	$0.224011\pi$
$354$	−1490.85	−0.223835
$355$	−271.801	−0.0406358
$356$	2088.69	0.310956
$357$	−2527.74	−0.374739
$358$	1016.22	0.150026
$359$	8786.85	1.29179	0.645894	−	0.763427i	$-0.276485\pi$
$359$	8786.85	1.29179	0.645894	+	0.763427i	$0.276485\pi$
$360$	65.3870	0.00957277
$361$	697.007	0.101619
$362$	8074.13	1.17228
$363$	−8291.50	−1.19887
$364$	−1269.22	−0.182762
$365$	864.574	0.123983
$366$	−5058.94	−0.722501
$367$	10727.8	1.52585	0.762924	−	0.646488i	$-0.223763\pi$
$367$	10727.8	1.52585	0.762924	+	0.646488i	$0.223763\pi$
$368$	0	0
$369$	−923.684	−0.130312
$370$	602.372	0.0846374
$371$	−3280.62	−0.459088
$372$	−3217.98	−0.448506
$373$	−2186.47	−0.303515	−0.151758	−	0.988418i	$-0.548493\pi$
$373$	−2186.47	−0.303515	−0.151758	+	0.988418i	$0.548493\pi$
$374$	4179.09	0.577795
$375$	−1286.81	−0.177202
$376$	−11333.7	−1.55449
$377$	1554.25	0.212329
$378$	4058.00	0.552172
$379$	−7058.75	−0.956686	−0.478343	−	0.878173i	$-0.658762\pi$
$379$	−7058.75	−0.956686	−0.478343	+	0.878173i	$0.658762\pi$
$380$	−230.739	−0.0311491
$381$	7763.89	1.04398
$382$	−4489.83	−0.601361
$383$	−4792.91	−0.639442	−0.319721	−	0.947512i	$-0.603589\pi$
$383$	−4792.91	−0.639442	−0.319721	+	0.947512i	$0.603589\pi$
$384$	−1511.71	−0.200896
$385$	−680.863	−0.0901298
$386$	−2084.45	−0.274859
$387$	−959.292	−0.126004
$388$	−1401.65	−0.183396
$389$	12950.6	1.68797	0.843986	−	0.536365i	$-0.180203\pi$
$389$	12950.6	1.68797	0.843986	+	0.536365i	$0.180203\pi$
$390$	395.164	0.0513075
$391$	0	0
$392$	3972.41	0.511829
$393$	10953.8	1.40598
$394$	−7158.27	−0.915300
$395$	−746.150	−0.0950452
$396$	−420.232	−0.0533269
$397$	4307.97	0.544611	0.272306	−	0.962211i	$-0.412214\pi$
$397$	4307.97	0.544611	0.272306	+	0.962211i	$0.412214\pi$
$398$	867.824	0.109297
$399$	6396.97	0.802630
$400$	4180.67	0.522583
$401$	−14819.4	−1.84550	−0.922752	−	0.385394i	$-0.874066\pi$
$401$	−14819.4	−1.84550	−0.922752	+	0.385394i	$0.874066\pi$
$402$	10836.0	1.34440
$403$	−7051.88	−0.871660
$404$	−1176.92	−0.144936
$405$	754.014	0.0925117
$406$	1422.68	0.173907
$407$	−14911.1	−1.81601
$408$	4618.20	0.560379
$409$	−2400.40	−0.290201	−0.145101	−	0.989417i	$-0.546351\pi$
$409$	−2400.40	−0.290201	−0.145101	+	0.989417i	$0.546351\pi$
$410$	709.884	0.0855090
$411$	−8283.28	−0.994122
$412$	872.824	0.104371
$413$	1615.03	0.192423
$414$	0	0
$415$	1280.36	0.151447
$416$	4035.71	0.475642
$417$	−1030.12	−0.120971
$418$	−10576.1	−1.23754
$419$	−553.002	−0.0644771	−0.0322385	−	0.999480i	$-0.510264\pi$
$419$	−553.002	−0.0644771	−0.0322385	+	0.999480i	$0.510264\pi$
$420$	−195.346	−0.0226950
$421$	12151.1	1.40667	0.703336	−	0.710857i	$-0.251693\pi$
$421$	12151.1	1.40667	0.703336	+	0.710857i	$0.251693\pi$
$422$	9994.95	1.15295
$423$	1291.36	0.148435
$424$	5993.73	0.686512
$425$	−4262.77	−0.486528
$426$	−3574.36	−0.406522
$427$	5480.34	0.621106
$428$	1979.19	0.223523
$429$	−9781.87	−1.10087
$430$	737.250	0.0826823
$431$	−14792.8	−1.65324	−0.826618	−	0.562764i	$-0.809738\pi$
$431$	−14792.8	−1.65324	−0.826618	+	0.562764i	$0.809738\pi$
$432$	−4449.55	−0.495554
$433$	6914.74	0.767439	0.383720	−	0.923450i	$-0.374643\pi$
$433$	6914.74	0.767439	0.383720	+	0.923450i	$0.374643\pi$
$434$	−6454.90	−0.713929
$435$	239.214	0.0263665
$436$	1929.72	0.211966
$437$	0	0
$438$	11369.7	1.24033
$439$	709.848	0.0771735	0.0385868	−	0.999255i	$-0.487714\pi$
$439$	709.848	0.0771735	0.0385868	+	0.999255i	$0.487714\pi$
$440$	1243.94	0.134779
$441$	−452.617	−0.0488734
$442$	2627.53	0.282757
$443$	−12087.3	−1.29636	−0.648179	−	0.761488i	$-0.724469\pi$
$443$	−12087.3	−1.29636	−0.648179	+	0.761488i	$0.724469\pi$
$444$	−4278.12	−0.457276
$445$	704.469	0.0750450
$446$	8774.18	0.931546
$447$	3054.73	0.323229
$448$	7326.72	0.772667
$449$	−1382.65	−0.145326	−0.0726631	−	0.997357i	$-0.523150\pi$
$449$	−1382.65	−0.145326	−0.0726631	+	0.997357i	$0.523150\pi$
$450$	−793.703	−0.0831456
$451$	−17572.4	−1.83471
$452$	−2720.91	−0.283144
$453$	−16216.6	−1.68195
$454$	−1656.16	−0.171205
$455$	−428.080	−0.0441071
$456$	−11687.3	−1.20024
$457$	−4048.95	−0.414446	−0.207223	−	0.978294i	$-0.566443\pi$
$457$	−4048.95	−0.414446	−0.207223	+	0.978294i	$0.566443\pi$
$458$	−13655.0	−1.39313
$459$	4536.93	0.461364
$460$	0	0
$461$	10896.5	1.10087	0.550436	−	0.834877i	$-0.314461\pi$
$461$	10896.5	1.10087	0.550436	+	0.834877i	$0.314461\pi$
$462$	−8953.78	−0.901662
$463$	−4913.75	−0.493221	−0.246611	−	0.969115i	$-0.579317\pi$
$463$	−4913.75	−0.493221	−0.246611	+	0.969115i	$0.579317\pi$
$464$	−1559.95	−0.156075
$465$	−1085.35	−0.108241
$466$	8824.14	0.877189
$467$	−12835.4	−1.27184	−0.635922	−	0.771753i	$-0.719380\pi$
$467$	−12835.4	−1.27184	−0.635922	+	0.771753i	$0.719380\pi$
$468$	−264.214	−0.0260967
$469$	−11738.6	−1.15573
$470$	−992.457	−0.0974013
$471$	−5060.25	−0.495041
$472$	−2950.68	−0.287746
$473$	−18249.9	−1.77406
$474$	−9812.35	−0.950836
$475$	10787.8	1.04206
$476$	−1298.89	−0.125073
$477$	−682.926	−0.0655535
$478$	6730.35	0.644014
$479$	−10683.6	−1.01909	−0.509546	−	0.860444i	$-0.670186\pi$
$479$	−10683.6	−1.01909	−0.509546	+	0.860444i	$0.670186\pi$
$480$	621.135	0.0590642
$481$	−9375.08	−0.888704
$482$	−13212.1	−1.24854
$483$	0	0
$484$	−4260.64	−0.400135
$485$	−472.743	−0.0442602
$486$	1787.48	0.166835
$487$	−2263.70	−0.210632	−0.105316	−	0.994439i	$-0.533585\pi$
$487$	−2263.70	−0.210632	−0.105316	+	0.994439i	$0.533585\pi$
$488$	−10012.6	−0.928792
$489$	12246.3	1.13250
$490$	347.852	0.0320701
$491$	681.640	0.0626517	0.0313259	−	0.999509i	$-0.490027\pi$
$491$	681.640	0.0626517	0.0313259	+	0.999509i	$0.490027\pi$
$492$	−5041.69	−0.461985
$493$	1590.58	0.145307
$494$	−6649.52	−0.605620
$495$	−141.735	−0.0128697
$496$	7077.74	0.640725
$497$	3872.10	0.349472
$498$	16837.6	1.51508
$499$	15605.8	1.40002	0.700012	−	0.714131i	$-0.253178\pi$
$499$	15605.8	1.40002	0.700012	+	0.714131i	$0.253178\pi$
$500$	−661.237	−0.0591428
$501$	7019.67	0.625980
$502$	−4945.01	−0.439655
$503$	−19205.3	−1.70243	−0.851217	−	0.524814i	$-0.824135\pi$
$503$	−19205.3	−1.70243	−0.851217	+	0.524814i	$0.824135\pi$
$504$	−931.508	−0.0823267
$505$	−396.950	−0.0349783
$506$	0	0
$507$	5844.32	0.511944
$508$	3989.52	0.348438
$509$	16690.0	1.45338	0.726692	−	0.686964i	$-0.241057\pi$
$509$	16690.0	1.45338	0.726692	+	0.686964i	$0.241057\pi$
$510$	404.402	0.0351122
$511$	−12316.8	−1.06627
$512$	−10687.4	−0.922501
$513$	−11481.7	−0.988165
$514$	9990.33	0.857305
$515$	294.384	0.0251886
$516$	−5236.05	−0.446713
$517$	24567.2	2.08987
$518$	−8581.43	−0.727889
$519$	−1109.42	−0.0938310
$520$	782.107	0.0659570
$521$	−2159.94	−0.181629	−0.0908144	−	0.995868i	$-0.528947\pi$
$521$	−2159.94	−0.181629	−0.0908144	+	0.995868i	$0.528947\pi$
$522$	296.158	0.0248323
$523$	−3348.60	−0.279969	−0.139985	−	0.990154i	$-0.544705\pi$
$523$	−3348.60	−0.279969	−0.139985	+	0.990154i	$0.544705\pi$
$524$	5628.70	0.469258
$525$	9133.07	0.759238
$526$	−5576.66	−0.462270
$527$	−7216.73	−0.596519
$528$	9817.74	0.809209
$529$	0	0
$530$	524.853	0.0430154
$531$	336.201	0.0274762
$532$	3287.13	0.267885
$533$	−11048.4	−0.897856
$534$	9264.23	0.750753
$535$	667.537	0.0539442
$536$	21446.6	1.72827
$537$	−2434.25	−0.195616
$538$	−5690.07	−0.455979
$539$	−8610.71	−0.688107
$540$	350.618	0.0279411
$541$	10603.8	0.842686	0.421343	−	0.906901i	$-0.361559\pi$
$541$	10603.8	0.842686	0.421343	+	0.906901i	$0.361559\pi$
$542$	−16527.3	−1.30979
$543$	−19340.7	−1.52852
$544$	4130.06	0.325505
$545$	650.852	0.0511550
$546$	−5629.53	−0.441249
$547$	−6892.60	−0.538769	−0.269384	−	0.963033i	$-0.586820\pi$
$547$	−6892.60	−0.538769	−0.269384	+	0.963033i	$0.586820\pi$
$548$	−4256.42	−0.331798
$549$	1140.84	0.0886883
$550$	−15099.6	−1.17064
$551$	−4025.31	−0.311223
$552$	0	0
$553$	10629.7	0.817398
$554$	10130.6	0.776907
$555$	−1442.91	−0.110357
$556$	−529.332	−0.0403753
$557$	8574.47	0.652266	0.326133	−	0.945324i	$-0.394254\pi$
$557$	8574.47	0.652266	0.326133	+	0.945324i	$0.394254\pi$
$558$	−1343.71	−0.101943
$559$	−11474.3	−0.868176
$560$	429.650	0.0324215
$561$	−10010.5	−0.753378
$562$	−10353.7	−0.777128
$563$	6599.26	0.494007	0.247003	−	0.969015i	$-0.420554\pi$
$563$	6599.26	0.494007	0.247003	+	0.969015i	$0.420554\pi$
$564$	7048.55	0.526237
$565$	−917.703	−0.0683328
$566$	−6143.87	−0.456265
$567$	−10741.7	−0.795609
$568$	−7074.36	−0.522594
$569$	19331.8	1.42431	0.712155	−	0.702022i	$-0.247719\pi$
$569$	19331.8	1.42431	0.712155	+	0.702022i	$0.247719\pi$
$570$	−1023.42	−0.0752045
$571$	−3480.72	−0.255102	−0.127551	−	0.991832i	$-0.540712\pi$
$571$	−3480.72	−0.255102	−0.127551	+	0.991832i	$0.540712\pi$
$572$	−5026.48	−0.367426
$573$	10754.9	0.784104
$574$	−10113.1	−0.735385
$575$	0	0
$576$	1525.20	0.110330
$577$	12662.2	0.913578	0.456789	−	0.889575i	$-0.348999\pi$
$577$	12662.2	0.913578	0.456789	+	0.889575i	$0.348999\pi$
$578$	−8508.60	−0.612303
$579$	4993.06	0.358384
$580$	122.922	0.00880008
$581$	−18240.2	−1.30246
$582$	−6216.88	−0.442780
$583$	−12992.2	−0.922952
$584$	22502.9	1.59448
$585$	−89.1133	−0.00629809
$586$	5451.89	0.384327
$587$	20535.9	1.44396	0.721982	−	0.691912i	$-0.243231\pi$
$587$	20535.9	1.44396	0.721982	+	0.691912i	$0.243231\pi$
$588$	−2470.49	−0.173267
$589$	18263.5	1.27765
$590$	−258.382	−0.0180295
$591$	17146.8	1.19345
$592$	9409.46	0.653254
$593$	−276.015	−0.0191139	−0.00955697	−	0.999954i	$-0.503042\pi$
$593$	−276.015	−0.0191139	−0.00955697	+	0.999954i	$0.503042\pi$
$594$	16070.8	1.11009
$595$	−438.087	−0.0301846
$596$	1569.69	0.107881
$597$	−2078.77	−0.142510
$598$	0	0
$599$	−11890.1	−0.811047	−0.405523	−	0.914085i	$-0.632911\pi$
$599$	−11890.1	−0.811047	−0.405523	+	0.914085i	$0.632911\pi$
$600$	−16686.2	−1.13535
$601$	−6361.30	−0.431752	−0.215876	−	0.976421i	$-0.569261\pi$
$601$	−6361.30	−0.431752	−0.215876	+	0.976421i	$0.569261\pi$
$602$	−10502.9	−0.711075
$603$	−2443.62	−0.165028
$604$	−8333.02	−0.561367
$605$	−1437.02	−0.0965670
$606$	−5220.15	−0.349924
$607$	−8657.05	−0.578878	−0.289439	−	0.957196i	$-0.593469\pi$
$607$	−8657.05	−0.578878	−0.289439	+	0.957196i	$0.593469\pi$
$608$	−10452.0	−0.697178
$609$	−3407.86	−0.226755
$610$	−876.777	−0.0581962
$611$	15446.2	1.02273
$612$	−270.390	−0.0178593
$613$	7651.41	0.504139	0.252070	−	0.967709i	$-0.418889\pi$
$613$	7651.41	0.504139	0.252070	+	0.967709i	$0.418889\pi$
$614$	−11125.7	−0.731265
$615$	−1700.45	−0.111494
$616$	−17721.3	−1.15911
$617$	2520.90	0.164486	0.0822428	−	0.996612i	$-0.473792\pi$
$617$	2520.90	0.164486	0.0822428	+	0.996612i	$0.473792\pi$
$618$	3871.34	0.251987
$619$	502.377	0.0326207	0.0163104	−	0.999867i	$-0.494808\pi$
$619$	502.377	0.0326207	0.0163104	+	0.999867i	$0.494808\pi$
$620$	−557.715	−0.0361264
$621$	0	0
$622$	−4869.44	−0.313902
$623$	−10035.9	−0.645394
$624$	6172.73	0.396005
$625$	15290.1	0.978564
$626$	−9649.47	−0.616087
$627$	25333.8	1.61361
$628$	−2600.24	−0.165225
$629$	−9594.24	−0.608183
$630$	−81.5694	−0.00515842
$631$	11177.6	0.705189	0.352594	−	0.935776i	$-0.385300\pi$
$631$	11177.6	0.705189	0.352594	+	0.935776i	$0.385300\pi$
$632$	−19420.6	−1.22232
$633$	−23941.8	−1.50332
$634$	16370.2	1.02546
$635$	1345.58	0.0840906
$636$	−3727.57	−0.232402
$637$	−5413.83	−0.336741
$638$	5634.19	0.349624
$639$	806.053	0.0499013
$640$	−261.998	−0.0161818
$641$	3933.27	0.242363	0.121182	−	0.992630i	$-0.461332\pi$
$641$	3933.27	0.242363	0.121182	+	0.992630i	$0.461332\pi$
$642$	8778.54	0.539659
$643$	5309.83	0.325660	0.162830	−	0.986654i	$-0.447938\pi$
$643$	5309.83	0.325660	0.162830	+	0.986654i	$0.447938\pi$
$644$	0	0
$645$	−1766.00	−0.107808
$646$	−6804.96	−0.414455
$647$	−1951.74	−0.118595	−0.0592975	−	0.998240i	$-0.518886\pi$
$647$	−1951.74	−0.118595	−0.0592975	+	0.998240i	$0.518886\pi$
$648$	19625.2	1.18974
$649$	6395.98	0.386848
$650$	−9493.63	−0.572878
$651$	15462.0	0.930881
$652$	6292.81	0.377984
$653$	16242.6	0.973387	0.486694	−	0.873573i	$-0.338203\pi$
$653$	16242.6	0.973387	0.486694	+	0.873573i	$0.338203\pi$
$654$	8559.13	0.511756
$655$	1898.43	0.113249
$656$	11088.9	0.659981
$657$	−2563.98	−0.152253
$658$	14138.6	0.837660
$659$	−5031.06	−0.297393	−0.148697	−	0.988883i	$-0.547508\pi$
$659$	−5031.06	−0.297393	−0.148697	+	0.988883i	$0.547508\pi$
$660$	−773.623	−0.0456261
$661$	−16858.0	−0.991985	−0.495992	−	0.868327i	$-0.665196\pi$
$661$	−16858.0	−0.991985	−0.495992	+	0.868327i	$0.665196\pi$
$662$	18119.6	1.06380
$663$	−6293.95	−0.368683
$664$	33324.9	1.94768
$665$	1108.67	0.0646504
$666$	−1786.39	−0.103936
$667$	0	0
$668$	3607.10	0.208927
$669$	−21017.6	−1.21463
$670$	1878.01	0.108289
$671$	21703.7	1.24868
$672$	−8848.73	−0.507957
$673$	18229.4	1.04412	0.522059	−	0.852910i	$-0.325164\pi$
$673$	18229.4	1.04412	0.522059	+	0.852910i	$0.325164\pi$
$674$	−7655.05	−0.437480
$675$	−16392.6	−0.934742
$676$	3003.14	0.170866
$677$	−6813.79	−0.386817	−0.193408	−	0.981118i	$-0.561954\pi$
$677$	−6813.79	−0.386817	−0.193408	+	0.981118i	$0.561954\pi$
$678$	−12068.4	−0.683604
$679$	6734.74	0.380641
$680$	800.390	0.0451376
$681$	3967.14	0.223232
$682$	−25563.2	−1.43529
$683$	−7491.79	−0.419715	−0.209858	−	0.977732i	$-0.567300\pi$
$683$	−7491.79	−0.419715	−0.209858	+	0.977732i	$0.567300\pi$
$684$	684.279	0.0382516
$685$	−1435.59	−0.0800747
$686$	−15493.2	−0.862296
$687$	32708.9	1.81648
$688$	11516.3	0.638164
$689$	−8168.60	−0.451668
$690$	0	0
$691$	−6514.80	−0.358661	−0.179330	−	0.983789i	$-0.557393\pi$
$691$	−6514.80	−0.358661	−0.179330	+	0.983789i	$0.557393\pi$
$692$	−570.084	−0.0313170
$693$	2019.16	0.110681
$694$	2634.30	0.144088
$695$	−178.532	−0.00974402
$696$	6226.19	0.339085
$697$	−11306.6	−0.614446
$698$	15801.2	0.856853
$699$	−21137.2	−1.14375
$700$	4693.09	0.253403
$701$	−4791.69	−0.258174	−0.129087	−	0.991633i	$-0.541205\pi$
$701$	−4791.69	−0.258174	−0.129087	+	0.991633i	$0.541205\pi$
$702$	10104.2	0.543247
$703$	24280.3	1.30263
$704$	29015.8	1.55337
$705$	2377.32	0.127000
$706$	23049.6	1.22873
$707$	5654.98	0.300817
$708$	1835.06	0.0974095
$709$	25244.9	1.33723	0.668613	−	0.743611i	$-0.266888\pi$
$709$	25244.9	1.33723	0.668613	+	0.743611i	$0.266888\pi$
$710$	−619.481	−0.0327446
$711$	2212.78	0.116717
$712$	18335.7	0.965112
$713$	0	0
$714$	−5761.13	−0.301968
$715$	−1695.32	−0.0886731
$716$	−1250.86	−0.0652887
$717$	−16121.8	−0.839720
$718$	20026.7	1.04093
$719$	−26650.4	−1.38233	−0.691164	−	0.722698i	$-0.742902\pi$
$719$	−26650.4	−1.38233	−0.691164	+	0.722698i	$0.742902\pi$
$720$	89.4400	0.00462949
$721$	−4193.81	−0.216624
$722$	1588.60	0.0818857
$723$	31648.1	1.62795
$724$	−9938.32	−0.510159
$725$	−5747.01	−0.294398
$726$	−18897.7	−0.966060
$727$	−1753.01	−0.0894297	−0.0447148	−	0.999000i	$-0.514238\pi$
$727$	−1753.01	−0.0894297	−0.0447148	+	0.999000i	$0.514238\pi$
$728$	−11141.9	−0.567236
$729$	17234.3	0.875593
$730$	1970.51	0.0999066
$731$	−11742.5	−0.594134
$732$	6226.98	0.314421
$733$	1459.90	0.0735641	0.0367821	−	0.999323i	$-0.488289\pi$
$733$	1459.90	0.0735641	0.0367821	+	0.999323i	$0.488289\pi$
$734$	24450.4	1.22954
$735$	−833.241	−0.0418157
$736$	0	0
$737$	−46488.2	−2.32349
$738$	−2105.23	−0.105006
$739$	−8682.92	−0.432214	−0.216107	−	0.976370i	$-0.569336\pi$
$739$	−8682.92	−0.432214	−0.216107	+	0.976370i	$0.569336\pi$
$740$	−741.451	−0.0368328
$741$	15928.2	0.789658
$742$	−7477.09	−0.369936
$743$	39629.4	1.95674	0.978372	−	0.206852i	$-0.0663220\pi$
$743$	39629.4	1.95674	0.978372	+	0.206852i	$0.0663220\pi$
$744$	−28249.2	−1.39202
$745$	529.421	0.0260356
$746$	−4983.33	−0.244575
$747$	−3797.05	−0.185979
$748$	−5143.98	−0.251447
$749$	−9509.77	−0.463925
$750$	−2932.86	−0.142791
$751$	28623.2	1.39078	0.695390	−	0.718633i	$-0.255232\pi$
$751$	28623.2	1.39078	0.695390	+	0.718633i	$0.255232\pi$
$752$	−15502.8	−0.751769
$753$	11845.2	0.573259
$754$	3542.40	0.171096
$755$	−2810.54	−0.135478
$756$	−4994.93	−0.240296
$757$	40054.8	1.92314	0.961569	−	0.274564i	$-0.0885337\pi$
$757$	40054.8	1.92314	0.961569	+	0.274564i	$0.0885337\pi$
$758$	−16088.1	−0.770904
$759$	0	0
$760$	−2025.56	−0.0966772
$761$	29007.4	1.38176	0.690879	−	0.722970i	$-0.257224\pi$
$761$	29007.4	1.38176	0.690879	+	0.722970i	$0.257224\pi$
$762$	17695.2	0.841246
$763$	−9272.09	−0.439937
$764$	5526.47	0.261702
$765$	−91.1964	−0.00431008
$766$	−10923.8	−0.515267
$767$	4021.36	0.189313
$768$	20294.3	0.953524
$769$	17151.4	0.804286	0.402143	−	0.915577i	$-0.368265\pi$
$769$	17151.4	0.804286	0.402143	+	0.915577i	$0.368265\pi$
$770$	−1551.80	−0.0726273
$771$	−23930.7	−1.11783
$772$	2565.72	0.119614
$773$	14526.9	0.675933	0.337967	−	0.941158i	$-0.390261\pi$
$773$	14526.9	0.675933	0.337967	+	0.941158i	$0.390261\pi$
$774$	−2186.39	−0.101535
$775$	26075.1	1.20857
$776$	−12304.4	−0.569205
$777$	20555.9	0.949083
$778$	29516.6	1.36018
$779$	28613.8	1.31604
$780$	−486.402	−0.0223282
$781$	15334.6	0.702580
$782$	0	0
$783$	6116.64	0.279171
$784$	5433.68	0.247526
$785$	−877.003	−0.0398746
$786$	24965.6	1.13295
$787$	8984.60	0.406946	0.203473	−	0.979081i	$-0.434777\pi$
$787$	8984.60	0.406946	0.203473	+	0.979081i	$0.434777\pi$
$788$	8811.01	0.398324
$789$	13358.3	0.602746
$790$	−1700.60	−0.0765882
$791$	13073.7	0.587668
$792$	−3689.03	−0.165510
$793$	13645.8	0.611068
$794$	9818.58	0.438852
$795$	−1257.23	−0.0560871
$796$	−1068.19	−0.0475641
$797$	8740.23	0.388450	0.194225	−	0.980957i	$-0.437781\pi$
$797$	8740.23	0.388450	0.194225	+	0.980957i	$0.437781\pi$
$798$	14579.8	0.646765
$799$	15807.3	0.699902
$800$	−14922.5	−0.659486
$801$	−2089.17	−0.0921564
$802$	−33776.0	−1.48712
$803$	−48777.9	−2.14363
$804$	−13337.9	−0.585063
$805$	0	0
$806$	−16072.4	−0.702390
$807$	13629.9	0.594543
$808$	−10331.7	−0.449836
$809$	−24466.4	−1.06328	−0.531639	−	0.846971i	$-0.678424\pi$
$809$	−24466.4	−1.06328	−0.531639	+	0.846971i	$0.678424\pi$
$810$	1718.52	0.0745466
$811$	−4276.92	−0.185183	−0.0925913	−	0.995704i	$-0.529515\pi$
$811$	−4276.92	−0.185183	−0.0925913	+	0.995704i	$0.529515\pi$
$812$	−1751.15	−0.0756815
$813$	39589.3	1.70782
$814$	−33984.8	−1.46335
$815$	2122.42	0.0912212
$816$	6317.03	0.271005
$817$	29716.9	1.27254
$818$	−5470.92	−0.233846
$819$	1269.51	0.0541641
$820$	−873.786	−0.0372121
$821$	28599.1	1.21573	0.607865	−	0.794040i	$-0.292026\pi$
$821$	28599.1	1.21573	0.607865	+	0.794040i	$0.292026\pi$
$822$	−18879.0	−0.801071
$823$	−125.189	−0.00530231	−0.00265115	−	0.999996i	$-0.500844\pi$
$823$	−125.189	−0.00530231	−0.00265115	+	0.999996i	$0.500844\pi$
$824$	7662.13	0.323936
$825$	36169.5	1.52638
$826$	3680.93	0.155056
$827$	−13120.7	−0.551695	−0.275847	−	0.961201i	$-0.588958\pi$
$827$	−13120.7	−0.551695	−0.275847	+	0.961201i	$0.588958\pi$
$828$	0	0
$829$	−22359.8	−0.936776	−0.468388	−	0.883523i	$-0.655165\pi$
$829$	−22359.8	−0.936776	−0.468388	+	0.883523i	$0.655165\pi$
$830$	2918.17	0.122037
$831$	−24266.6	−1.01300
$832$	18243.2	0.760180
$833$	−5540.39	−0.230448
$834$	−2347.81	−0.0974796
$835$	1216.59	0.0504215
$836$	13017.9	0.538558
$837$	−27752.1	−1.14606
$838$	−1260.38	−0.0519561
$839$	−25200.5	−1.03697	−0.518485	−	0.855087i	$-0.673504\pi$
$839$	−25200.5	−1.03697	−0.518485	+	0.855087i	$0.673504\pi$
$840$	−1714.85	−0.0704381
$841$	−22244.6	−0.912075
$842$	27694.4	1.13351
$843$	24801.2	1.01328
$844$	−12302.6	−0.501747
$845$	1012.89	0.0412362
$846$	2943.23	0.119610
$847$	20471.8	0.830485
$848$	8198.56	0.332004
$849$	14717.0	0.594917
$850$	−9715.56	−0.392048
$851$	0	0
$852$	4399.63	0.176912
$853$	−29547.2	−1.18602	−0.593010	−	0.805195i	$-0.702061\pi$
$853$	−29547.2	−1.18602	−0.593010	+	0.805195i	$0.702061\pi$
$854$	12490.6	0.500492
$855$	230.792	0.00923149
$856$	17374.4	0.693745
$857$	−11597.2	−0.462257	−0.231128	−	0.972923i	$-0.574242\pi$
$857$	−11597.2	−0.462257	−0.231128	+	0.972923i	$0.574242\pi$
$858$	−22294.5	−0.887089
$859$	6773.87	0.269059	0.134529	−	0.990910i	$-0.457048\pi$
$859$	6773.87	0.269059	0.134529	+	0.990910i	$0.457048\pi$
$860$	−907.471	−0.0359820
$861$	24224.7	0.958856
$862$	−33715.3	−1.33219
$863$	11040.7	0.435491	0.217746	−	0.976006i	$-0.430130\pi$
$863$	11040.7	0.435491	0.217746	+	0.976006i	$0.430130\pi$
$864$	15882.2	0.625376
$865$	−192.277	−0.00755792
$866$	15759.9	0.618408
$867$	20381.4	0.798372
$868$	7945.24	0.310690
$869$	42096.6	1.64330
$870$	545.209	0.0212463
$871$	−29228.6	−1.13705
$872$	16940.2	0.657875
$873$	1401.97	0.0543521
$874$	0	0
$875$	3177.16	0.122752
$876$	−13994.8	−0.539773
$877$	40294.3	1.55147	0.775737	−	0.631057i	$-0.217378\pi$
$877$	40294.3	1.55147	0.775737	+	0.631057i	$0.217378\pi$
$878$	1617.86	0.0621870
$879$	−13059.4	−0.501118
$880$	1701.53	0.0651803
$881$	−27020.3	−1.03330	−0.516650	−	0.856197i	$-0.672821\pi$
$881$	−27020.3	−1.03330	−0.516650	+	0.856197i	$0.672821\pi$
$882$	−1031.59	−0.0393825
$883$	35464.5	1.35161	0.675806	−	0.737079i	$-0.263796\pi$
$883$	35464.5	1.35161	0.675806	+	0.737079i	$0.263796\pi$
$884$	−3234.19	−0.123051
$885$	618.926	0.0235084
$886$	−27549.1	−1.04461
$887$	−10726.1	−0.406030	−0.203015	−	0.979176i	$-0.565074\pi$
$887$	−10726.1	−0.406030	−0.203015	+	0.979176i	$0.565074\pi$
$888$	−37555.7	−1.41924
$889$	−19169.2	−0.723187
$890$	1605.60	0.0604719
$891$	−42540.2	−1.59950
$892$	−10800.0	−0.405393
$893$	−40003.7	−1.49907
$894$	6962.23	0.260461
$895$	−421.886	−0.0157565
$896$	3732.44	0.139165
$897$	0	0
$898$	−3151.30	−0.117105
$899$	−9729.50	−0.360953
$900$	976.957	0.0361836
$901$	−8359.56	−0.309098
$902$	−40050.5	−1.47842
$903$	25158.6	0.927159
$904$	−23885.7	−0.878790
$905$	−3351.97	−0.123120
$906$	−36960.4	−1.35533
$907$	−5959.29	−0.218164	−0.109082	−	0.994033i	$-0.534791\pi$
$907$	−5959.29	−0.218164	−0.109082	+	0.994033i	$0.534791\pi$
$908$	2038.54	0.0745058
$909$	1177.19	0.0429539
$910$	−975.667	−0.0355418
$911$	−1040.63	−0.0378458	−0.0189229	−	0.999821i	$-0.506024\pi$
$911$	−1040.63	−0.0378458	−0.0189229	+	0.999821i	$0.506024\pi$
$912$	−15986.6	−0.580448
$913$	−72236.1	−2.61847
$914$	−9228.24	−0.333964
$915$	2100.22	0.0758810
$916$	16807.7	0.606268
$917$	−27045.2	−0.973950
$918$	10340.4	0.371770
$919$	−44662.5	−1.60313	−0.801567	−	0.597904i	$-0.796000\pi$
$919$	−44662.5	−1.60313	−0.801567	+	0.597904i	$0.796000\pi$
$920$	0	0
$921$	26650.4	0.953485
$922$	24835.0	0.887092
$923$	9641.35	0.343823
$924$	11021.1	0.392388
$925$	34665.3	1.23220
$926$	−11199.3	−0.397441
$927$	−873.024	−0.0309319
$928$	5568.09	0.196963
$929$	5755.09	0.203249	0.101625	−	0.994823i	$-0.467596\pi$
$929$	5755.09	0.203249	0.101625	+	0.994823i	$0.467596\pi$
$930$	−2473.70	−0.0872212
$931$	14021.1	0.493581
$932$	−10861.5	−0.381738
$933$	11664.2	0.409291
$934$	−29254.0	−1.02486
$935$	−1734.95	−0.0606833
$936$	−2319.41	−0.0809961
$937$	37600.9	1.31096	0.655478	−	0.755214i	$-0.272467\pi$
$937$	37600.9	1.31096	0.655478	+	0.755214i	$0.272467\pi$
$938$	−26754.3	−0.931299
$939$	23114.2	0.803306
$940$	1221.60	0.0423875
$941$	−40737.4	−1.41127	−0.705633	−	0.708577i	$-0.749337\pi$
$941$	−40737.4	−1.41127	−0.705633	+	0.708577i	$0.749337\pi$
$942$	−11533.2	−0.398907
$943$	0	0
$944$	−4036.11	−0.139157
$945$	−1684.68	−0.0579921
$946$	−41594.5	−1.42955
$947$	−3278.54	−0.112501	−0.0562504	−	0.998417i	$-0.517915\pi$
$947$	−3278.54	−0.112501	−0.0562504	+	0.998417i	$0.517915\pi$
$948$	12077.9	0.413788
$949$	−30668.2	−1.04903
$950$	24587.3	0.839702
$951$	−39213.0	−1.33709
$952$	−11402.4	−0.388187
$953$	−12081.4	−0.410656	−0.205328	−	0.978693i	$-0.565826\pi$
$953$	−12081.4	−0.410656	−0.205328	+	0.978693i	$0.565826\pi$
$954$	−1556.50	−0.0528235
$955$	1863.95	0.0631582
$956$	−8284.28	−0.280265
$957$	−13496.1	−0.455868
$958$	−24349.6	−0.821191
$959$	20451.6	0.688650
$960$	2807.80	0.0943974
$961$	14353.2	0.481798
$962$	−21367.4	−0.716125
$963$	−1979.64	−0.0662442
$964$	16262.6	0.543343
$965$	865.358	0.0288672
$966$	0	0
$967$	25588.6	0.850957	0.425478	−	0.904969i	$-0.360106\pi$
$967$	25588.6	0.850957	0.425478	+	0.904969i	$0.360106\pi$
$968$	−37402.2	−1.24189
$969$	16300.5	0.540401
$970$	−1077.46	−0.0356652
$971$	−59606.8	−1.97000	−0.985001	−	0.172546i	$-0.944801\pi$
$971$	−59606.8	−1.97000	−0.985001	+	0.172546i	$0.944801\pi$
$972$	−2200.18	−0.0726037
$973$	2543.38	0.0837995
$974$	−5159.34	−0.169729
$975$	22740.9	0.746967
$976$	−13695.8	−0.449173
$977$	22401.2	0.733550	0.366775	−	0.930310i	$-0.380462\pi$
$977$	22401.2	0.733550	0.366775	+	0.930310i	$0.380462\pi$
$978$	27911.3	0.912580
$979$	−39745.0	−1.29750
$980$	−428.166	−0.0139564
$981$	−1930.17	−0.0628190
$982$	1553.57	0.0504852
$983$	26431.4	0.857610	0.428805	−	0.903397i	$-0.358935\pi$
$983$	26431.4	0.857610	0.428805	+	0.903397i	$0.358935\pi$
$984$	−44258.7	−1.43386
$985$	2971.75	0.0961299
$986$	3625.21	0.117089
$987$	−33867.4	−1.09221
$988$	8184.80	0.263556
$989$	0	0
$990$	−323.037	−0.0103705
$991$	21326.6	0.683613	0.341807	−	0.939770i	$-0.388961\pi$
$991$	21326.6	0.683613	0.341807	+	0.939770i	$0.388961\pi$
$992$	−25263.3	−0.808578
$993$	−43403.4	−1.38707
$994$	8825.16	0.281607
$995$	−360.277	−0.0114789
$996$	−20725.2	−0.659340
$997$	6170.19	0.196000	0.0979999	−	0.995186i	$-0.468756\pi$
$997$	6170.19	0.196000	0.0979999	+	0.995186i	$0.468756\pi$
$998$	35568.3	1.12815
$999$	−36894.9	−1.16847

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.17		25
23.5	odd	22		23.4.c.a.2.4	✓	50
23.14	odd	22		23.4.c.a.12.4	yes	50
23.22	odd	2		529.4.a.n.1.17		25
69.5	even	22		207.4.i.a.163.2		50
69.14	even	22		207.4.i.a.127.2		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.2.4	✓	50	23.5	odd	22
23.4.c.a.12.4	yes	50	23.14	odd	22
207.4.i.a.127.2		50	69.14	even	22
207.4.i.a.163.2		50	69.5	even	22
529.4.a.m.1.17		25	1.1	even	1	trivial
529.4.a.n.1.17		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q+2.27917 q^{2} -5.45949 q^{3} -2.80539 q^{4} -0.946196 q^{5} -12.4431 q^{6} +13.4796 q^{7} -24.6273 q^{8} +2.80604 q^{9} -2.15654 q^{10} +53.3829 q^{11} +15.3160 q^{12} +33.5635 q^{13} +30.7222 q^{14} +5.16575 q^{15} -33.6866 q^{16} +34.3481 q^{17} +6.39543 q^{18} -86.9253 q^{19} +2.65445 q^{20} -73.5916 q^{21} +121.669 q^{22} +134.453 q^{24} -124.105 q^{25} +76.4969 q^{26} +132.087 q^{27} -37.8155 q^{28} +46.3077 q^{29} +11.7736 q^{30} -210.105 q^{31} +120.241 q^{32} -291.443 q^{33} +78.2852 q^{34} -12.7543 q^{35} -7.87204 q^{36} -279.323 q^{37} -198.117 q^{38} -183.240 q^{39} +23.3023 q^{40} -329.177 q^{41} -167.728 q^{42} -341.867 q^{43} -149.760 q^{44} -2.65506 q^{45} +460.208 q^{47} +183.912 q^{48} -161.301 q^{49} -282.855 q^{50} -187.523 q^{51} -94.1590 q^{52} -243.377 q^{53} +301.048 q^{54} -50.5107 q^{55} -331.966 q^{56} +474.568 q^{57} +105.543 q^{58} +119.813 q^{59} -14.4920 q^{60} +406.566 q^{61} -478.865 q^{62} +37.8242 q^{63} +543.542 q^{64} -31.7577 q^{65} -664.248 q^{66} -870.845 q^{67} -96.3601 q^{68} -29.0692 q^{70} +287.257 q^{71} -69.1051 q^{72} -913.737 q^{73} -636.625 q^{74} +677.549 q^{75} +243.860 q^{76} +719.579 q^{77} -417.634 q^{78} +788.578 q^{79} +31.8741 q^{80} -796.889 q^{81} -750.250 q^{82} -1353.17 q^{83} +206.454 q^{84} -32.5001 q^{85} -779.173 q^{86} -252.817 q^{87} -1314.68 q^{88} -744.528 q^{89} -6.05133 q^{90} +452.422 q^{91} +1147.07 q^{93} +1048.89 q^{94} +82.2484 q^{95} -656.455 q^{96} +499.625 q^{97} -367.632 q^{98} +149.794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

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