LMFDB - Embedded newform 543.4.a.c.1.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [543,4,Mod(1,543)] 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("543.1"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(543, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 543 = 3 \cdot 181 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	543.a (trivial)

Newform invariants

comment:select newform

sage:traces = [23] 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:	$32.0380371331$
Analytic rank:	$0$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	543.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.91929 q^{2} -3.00000 q^{3} -4.31632 q^{4} -17.8997 q^{5} -5.75788 q^{6} -9.33325 q^{7} -23.6386 q^{8} +9.00000 q^{9} -34.3548 q^{10} -56.1277 q^{11} +12.9490 q^{12} -52.8683 q^{13} -17.9132 q^{14} +53.6991 q^{15} -10.8389 q^{16} -45.4222 q^{17} +17.2736 q^{18} -26.3643 q^{19} +77.2608 q^{20} +27.9998 q^{21} -107.725 q^{22} +173.853 q^{23} +70.9158 q^{24} +195.399 q^{25} -101.470 q^{26} -27.0000 q^{27} +40.2853 q^{28} -133.466 q^{29} +103.064 q^{30} -187.129 q^{31} +168.306 q^{32} +168.383 q^{33} -87.1784 q^{34} +167.062 q^{35} -38.8469 q^{36} -114.278 q^{37} -50.6008 q^{38} +158.605 q^{39} +423.124 q^{40} -49.4326 q^{41} +53.7397 q^{42} -379.975 q^{43} +242.265 q^{44} -161.097 q^{45} +333.674 q^{46} +366.733 q^{47} +32.5166 q^{48} -255.890 q^{49} +375.028 q^{50} +136.266 q^{51} +228.196 q^{52} -313.361 q^{53} -51.8209 q^{54} +1004.67 q^{55} +220.625 q^{56} +79.0930 q^{57} -256.160 q^{58} +185.879 q^{59} -231.782 q^{60} +314.519 q^{61} -359.154 q^{62} -83.9993 q^{63} +409.739 q^{64} +946.326 q^{65} +323.176 q^{66} -830.782 q^{67} +196.056 q^{68} -521.558 q^{69} +320.642 q^{70} +657.110 q^{71} -212.748 q^{72} +552.051 q^{73} -219.333 q^{74} -586.198 q^{75} +113.797 q^{76} +523.853 q^{77} +304.409 q^{78} -124.685 q^{79} +194.013 q^{80} +81.0000 q^{81} -94.8756 q^{82} -973.588 q^{83} -120.856 q^{84} +813.043 q^{85} -729.284 q^{86} +400.398 q^{87} +1326.78 q^{88} +291.060 q^{89} -309.193 q^{90} +493.433 q^{91} -750.403 q^{92} +561.386 q^{93} +703.868 q^{94} +471.913 q^{95} -504.918 q^{96} -862.897 q^{97} -491.129 q^{98} -505.149 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q + 7 q^{2} - 69 q^{3} + 79 q^{4} + 29 q^{5} - 21 q^{6} - 6 q^{7} + 84 q^{8} + 207 q^{9} + 41 q^{10} + 45 q^{11} - 237 q^{12} + 166 q^{13} - 23 q^{14} - 87 q^{15} + 195 q^{16} + 369 q^{17} + 63 q^{18}+ \cdots + 405 q^{99}+O(q^{100}) $ 23 * q + 7 * q^2 - 69 * q^3 + 79 * q^4 + 29 * q^5 - 21 * q^6 - 6 * q^7 + 84 * q^8 + 207 * q^9 + 41 * q^10 + 45 * q^11 - 237 * q^12 + 166 * q^13 - 23 * q^14 - 87 * q^15 + 195 * q^16 + 369 * q^17 + 63 * q^18 - 115 * q^19 + 162 * q^20 + 18 * q^21 - 130 * q^22 + 221 * q^23 - 252 * q^24 + 712 * q^25 + 227 * q^26 - 621 * q^27 - 265 * q^28 + 599 * q^29 - 123 * q^30 - 8 * q^31 + 1084 * q^32 - 135 * q^33 + 409 * q^34 + 210 * q^35 + 711 * q^36 + 400 * q^37 + 507 * q^38 - 498 * q^39 + 806 * q^40 + 1329 * q^41 + 69 * q^42 - 656 * q^43 + 344 * q^44 + 261 * q^45 + 146 * q^46 + 1079 * q^47 - 585 * q^48 + 2033 * q^49 + 3481 * q^50 - 1107 * q^51 + 2191 * q^52 + 1218 * q^53 - 189 * q^54 + 1470 * q^55 + 3224 * q^56 + 345 * q^57 + 3488 * q^58 + 2075 * q^59 - 486 * q^60 + 249 * q^61 + 4385 * q^62 - 54 * q^63 + 2556 * q^64 + 4512 * q^65 + 390 * q^66 + 1020 * q^67 + 6214 * q^68 - 663 * q^69 + 264 * q^70 + 571 * q^71 + 756 * q^72 + 3247 * q^73 + 3078 * q^74 - 2136 * q^75 + 2386 * q^76 + 3290 * q^77 - 681 * q^78 - 1627 * q^79 + 7008 * q^80 + 1863 * q^81 + 3929 * q^82 + 4312 * q^83 + 795 * q^84 + 2298 * q^85 + 2775 * q^86 - 1797 * q^87 + 1476 * q^88 + 5539 * q^89 + 369 * q^90 - 1488 * q^91 + 5387 * q^92 + 24 * q^93 + 1645 * q^94 + 1796 * q^95 - 3252 * q^96 + 4202 * q^97 + 10181 * q^98 + 405 * q^99

Coefficient data

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

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

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

$2$	1.91929	0.678572	0.339286	−	0.940683i	$-0.389815\pi$
$2$	1.91929	0.678572	0.339286	+	0.940683i	$0.389815\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.31632	−0.539540
$5$	−17.8997	−1.60100	−0.800499	−	0.599334i	$-0.795432\pi$
$5$	−17.8997	−1.60100	−0.800499	+	0.599334i	$0.795432\pi$
$6$	−5.75788	−0.391774
$7$	−9.33325	−0.503948	−0.251974	−	0.967734i	$-0.581080\pi$
$7$	−9.33325	−0.503948	−0.251974	+	0.967734i	$0.581080\pi$
$8$	−23.6386	−1.04469
$9$	9.00000	0.333333
$10$	−34.3548	−1.08639
$11$	−56.1277	−1.53847	−0.769233	−	0.638968i	$-0.779361\pi$
$11$	−56.1277	−1.53847	−0.769233	+	0.638968i	$0.779361\pi$
$12$	12.9490	0.311503
$13$	−52.8683	−1.12792	−0.563962	−	0.825800i	$-0.690724\pi$
$13$	−52.8683	−1.12792	−0.563962	+	0.825800i	$0.690724\pi$
$14$	−17.9132	−0.341965
$15$	53.6991	0.924336
$16$	−10.8389	−0.169357
$17$	−45.4222	−0.648029	−0.324015	−	0.946052i	$-0.605033\pi$
$17$	−45.4222	−0.648029	−0.324015	+	0.946052i	$0.605033\pi$
$18$	17.2736	0.226191
$19$	−26.3643	−0.318336	−0.159168	−	0.987251i	$-0.550881\pi$
$19$	−26.3643	−0.318336	−0.159168	+	0.987251i	$0.550881\pi$
$20$	77.2608	0.863802
$21$	27.9998	0.290955
$22$	−107.725	−1.04396
$23$	173.853	1.57612	0.788060	−	0.615598i	$-0.211086\pi$
$23$	173.853	1.57612	0.788060	+	0.615598i	$0.211086\pi$
$24$	70.9158	0.603151
$25$	195.399	1.56319
$26$	−101.470	−0.765379
$27$	−27.0000	−0.192450
$28$	40.2853	0.271900
$29$	−133.466	−0.854621	−0.427311	−	0.904105i	$-0.640539\pi$
$29$	−133.466	−0.854621	−0.427311	+	0.904105i	$0.640539\pi$
$30$	103.064	0.627229
$31$	−187.129	−1.08417	−0.542085	−	0.840323i	$-0.682365\pi$
$31$	−187.129	−1.08417	−0.542085	+	0.840323i	$0.682365\pi$
$32$	168.306	0.929768
$33$	168.383	0.888234
$34$	−87.1784	−0.439735
$35$	167.062	0.806820
$36$	−38.8469	−0.179847
$37$	−114.278	−0.507761	−0.253881	−	0.967236i	$-0.581707\pi$
$37$	−114.278	−0.507761	−0.253881	+	0.967236i	$0.581707\pi$
$38$	−50.6008	−0.216014
$39$	158.605	0.651208
$40$	423.124	1.67254
$41$	−49.4326	−0.188294	−0.0941472	−	0.995558i	$-0.530012\pi$
$41$	−49.4326	−0.188294	−0.0941472	+	0.995558i	$0.530012\pi$
$42$	53.7397	0.197434
$43$	−379.975	−1.34757	−0.673787	−	0.738925i	$-0.735334\pi$
$43$	−379.975	−1.34757	−0.673787	+	0.738925i	$0.735334\pi$
$44$	242.265	0.830063
$45$	−161.097	−0.533666
$46$	333.674	1.06951
$47$	366.733	1.13816	0.569080	−	0.822282i	$-0.307299\pi$
$47$	366.733	1.13816	0.569080	+	0.822282i	$0.307299\pi$
$48$	32.5166	0.0977785
$49$	−255.890	−0.746036
$50$	375.028	1.06074
$51$	136.266	0.374140
$52$	228.196	0.608560
$53$	−313.361	−0.812140	−0.406070	−	0.913842i	$-0.633101\pi$
$53$	−313.361	−0.812140	−0.406070	+	0.913842i	$0.633101\pi$
$54$	−51.8209	−0.130591
$55$	1004.67	2.46308
$56$	220.625	0.526469
$57$	79.0930	0.183792
$58$	−256.160	−0.579922
$59$	185.879	0.410160	0.205080	−	0.978745i	$-0.434255\pi$
$59$	185.879	0.410160	0.205080	+	0.978745i	$0.434255\pi$
$60$	−231.782	−0.498716
$61$	314.519	0.660164	0.330082	−	0.943952i	$-0.392924\pi$
$61$	314.519	0.660164	0.330082	+	0.943952i	$0.392924\pi$
$62$	−359.154	−0.735688
$63$	−83.9993	−0.167983
$64$	409.739	0.800272
$65$	946.326	1.80581
$66$	323.176	0.602731
$67$	−830.782	−1.51487	−0.757435	−	0.652911i	$-0.773548\pi$
$67$	−830.782	−1.51487	−0.757435	+	0.652911i	$0.773548\pi$
$68$	196.056	0.349637
$69$	−521.558	−0.909974
$70$	320.642	0.547486
$71$	657.110	1.09837	0.549187	−	0.835699i	$-0.314937\pi$
$71$	657.110	1.09837	0.549187	+	0.835699i	$0.314937\pi$
$72$	−212.748	−0.348230
$73$	552.051	0.885105	0.442552	−	0.896743i	$-0.354073\pi$
$73$	552.051	0.885105	0.442552	+	0.896743i	$0.354073\pi$
$74$	−219.333	−0.344553
$75$	−586.198	−0.902510
$76$	113.797	0.171755
$77$	523.853	0.775307
$78$	304.409	0.441892
$79$	−124.685	−0.177571	−0.0887855	−	0.996051i	$-0.528299\pi$
$79$	−124.685	−0.177571	−0.0887855	+	0.996051i	$0.528299\pi$
$80$	194.013	0.271141
$81$	81.0000	0.111111
$82$	−94.8756	−0.127771
$83$	−973.588	−1.28753	−0.643766	−	0.765223i	$-0.722629\pi$
$83$	−973.588	−1.28753	−0.643766	+	0.765223i	$0.722629\pi$
$84$	−120.856	−0.156982
$85$	813.043	1.03749
$86$	−729.284	−0.914427
$87$	400.398	0.493416
$88$	1326.78	1.60722
$89$	291.060	0.346655	0.173327	−	0.984864i	$-0.444548\pi$
$89$	291.060	0.346655	0.173327	+	0.984864i	$0.444548\pi$
$90$	−309.193	−0.362131
$91$	493.433	0.568416
$92$	−750.403	−0.850379
$93$	561.386	0.625946
$94$	703.868	0.772324
$95$	471.913	0.509656
$96$	−504.918	−0.536802
$97$	−862.897	−0.903236	−0.451618	−	0.892211i	$-0.649153\pi$
$97$	−862.897	−0.903236	−0.451618	+	0.892211i	$0.649153\pi$
$98$	−491.129	−0.506240
$99$	−505.149	−0.512822
$100$	−843.405	−0.843405
$101$	−297.950	−0.293536	−0.146768	−	0.989171i	$-0.546887\pi$
$101$	−297.950	−0.293536	−0.146768	+	0.989171i	$0.546887\pi$
$102$	261.535	0.253881
$103$	676.140	0.646816	0.323408	−	0.946260i	$-0.395171\pi$
$103$	676.140	0.646816	0.323408	+	0.946260i	$0.395171\pi$
$104$	1249.73	1.17833
$105$	−501.187	−0.465818
$106$	−601.431	−0.551096
$107$	−1704.19	−1.53972	−0.769861	−	0.638212i	$-0.779674\pi$
$107$	−1704.19	−1.53972	−0.769861	+	0.638212i	$0.779674\pi$
$108$	116.541	0.103834
$109$	−1857.97	−1.63268	−0.816338	−	0.577575i	$-0.803999\pi$
$109$	−1857.97	−1.63268	−0.816338	+	0.577575i	$0.803999\pi$
$110$	1928.25	1.67138
$111$	342.834	0.293156
$112$	101.162	0.0853473
$113$	−609.016	−0.507003	−0.253502	−	0.967335i	$-0.581582\pi$
$113$	−609.016	−0.507003	−0.253502	+	0.967335i	$0.581582\pi$
$114$	151.803	0.124716
$115$	−3111.91	−2.52337
$116$	576.082	0.461102
$117$	−475.815	−0.375975
$118$	356.757	0.278323
$119$	423.936	0.326573
$120$	−1269.37	−0.965644
$121$	1819.31	1.36688
$122$	603.653	0.447969
$123$	148.298	0.108712
$124$	807.706	0.584953
$125$	−1260.12	−0.901671
$126$	−161.219	−0.113988
$127$	−475.597	−0.332302	−0.166151	−	0.986100i	$-0.553134\pi$
$127$	−475.597	−0.332302	−0.166151	+	0.986100i	$0.553134\pi$
$128$	−560.038	−0.386725
$129$	1139.93	0.778022
$130$	1816.28	1.22537
$131$	2459.31	1.64023	0.820117	−	0.572195i	$-0.193908\pi$
$131$	2459.31	1.64023	0.820117	+	0.572195i	$0.193908\pi$
$132$	−726.794	−0.479237
$133$	246.065	0.160425
$134$	−1594.51	−1.02795
$135$	483.292	0.308112
$136$	1073.72	0.676989
$137$	−1367.08	−0.852539	−0.426269	−	0.904596i	$-0.640172\pi$
$137$	−1367.08	−0.852539	−0.426269	+	0.904596i	$0.640172\pi$
$138$	−1001.02	−0.617483
$139$	−922.129	−0.562690	−0.281345	−	0.959607i	$-0.590781\pi$
$139$	−922.129	−0.562690	−0.281345	+	0.959607i	$0.590781\pi$
$140$	−721.094	−0.435311
$141$	−1100.20	−0.657117
$142$	1261.19	0.745326
$143$	2967.37	1.73527
$144$	−97.5498	−0.0564525
$145$	2389.00	1.36825
$146$	1059.55	0.600607
$147$	767.671	0.430724
$148$	493.260	0.273957
$149$	−1403.31	−0.771565	−0.385783	−	0.922590i	$-0.626069\pi$
$149$	−1403.31	−0.771565	−0.385783	+	0.922590i	$0.626069\pi$
$150$	−1125.08	−0.612418
$151$	−2957.18	−1.59372	−0.796860	−	0.604164i	$-0.793507\pi$
$151$	−2957.18	−1.59372	−0.796860	+	0.604164i	$0.793507\pi$
$152$	623.216	0.332562
$153$	−408.799	−0.216010
$154$	1005.43	0.526102
$155$	3349.55	1.73575
$156$	−684.589	−0.351352
$157$	736.658	0.374469	0.187235	−	0.982315i	$-0.440048\pi$
$157$	736.658	0.374469	0.187235	+	0.982315i	$0.440048\pi$
$158$	−239.306	−0.120495
$159$	940.082	0.468889
$160$	−3012.63	−1.48856
$161$	−1622.61	−0.794283
$162$	155.463	0.0753969
$163$	2207.52	1.06077	0.530387	−	0.847755i	$-0.322046\pi$
$163$	2207.52	1.06077	0.530387	+	0.847755i	$0.322046\pi$
$164$	213.367	0.101592
$165$	−3014.00	−1.42206
$166$	−1868.60	−0.873683
$167$	−2640.85	−1.22368	−0.611841	−	0.790981i	$-0.709571\pi$
$167$	−2640.85	−1.22368	−0.611841	+	0.790981i	$0.709571\pi$
$168$	−661.875	−0.303957
$169$	598.055	0.272214
$170$	1560.47	0.704014
$171$	−237.279	−0.106112
$172$	1640.09	0.727070
$173$	−2061.26	−0.905865	−0.452933	−	0.891545i	$-0.649622\pi$
$173$	−2061.26	−0.905865	−0.452933	+	0.891545i	$0.649622\pi$
$174$	768.481	0.334818
$175$	−1823.71	−0.787769
$176$	608.360	0.260551
$177$	−557.638	−0.236806
$178$	558.629	0.235230
$179$	−466.392	−0.194747	−0.0973737	−	0.995248i	$-0.531044\pi$
$179$	−466.392	−0.194747	−0.0973737	+	0.995248i	$0.531044\pi$
$180$	695.347	0.287934
$181$	−181.000	−0.0743294
$181$	−181.000	−0.0743294
$182$	947.042	0.385711
$183$	−943.556	−0.381146
$184$	−4109.63	−1.64656
$185$	2045.54	0.812925
$186$	1077.46	0.424750
$187$	2549.44	0.996970
$188$	−1582.94	−0.614083
$189$	251.998	0.0969849
$190$	905.740	0.345838
$191$	−1137.33	−0.430860	−0.215430	−	0.976519i	$-0.569115\pi$
$191$	−1137.33	−0.430860	−0.215430	+	0.976519i	$0.569115\pi$
$192$	−1229.22	−0.462037
$193$	−330.564	−0.123288	−0.0616438	−	0.998098i	$-0.519634\pi$
$193$	−330.564	−0.123288	−0.0616438	+	0.998098i	$0.519634\pi$
$194$	−1656.15	−0.612911
$195$	−2838.98	−1.04258
$196$	1104.50	0.402516
$197$	3983.77	1.44077	0.720385	−	0.693575i	$-0.243965\pi$
$197$	3983.77	1.44077	0.720385	+	0.693575i	$0.243965\pi$
$198$	−969.528	−0.347987
$199$	126.519	0.0450688	0.0225344	−	0.999746i	$-0.492826\pi$
$199$	126.519	0.0450688	0.0225344	+	0.999746i	$0.492826\pi$
$200$	−4618.97	−1.63305
$201$	2492.35	0.874610
$202$	−571.853	−0.199185
$203$	1245.67	0.430685
$204$	−588.169	−0.201863
$205$	884.828	0.301459
$206$	1297.71	0.438911
$207$	1564.67	0.525373
$208$	573.033	0.191022
$209$	1479.77	0.489750
$210$	−961.925	−0.316091
$211$	−1067.29	−0.348223	−0.174112	−	0.984726i	$-0.555705\pi$
$211$	−1067.29	−0.348223	−0.174112	+	0.984726i	$0.555705\pi$
$212$	1352.56	0.438182
$213$	−1971.33	−0.634147
$214$	−3270.84	−1.04481
$215$	6801.44	2.15746
$216$	638.243	0.201050
$217$	1746.52	0.546366
$218$	−3566.00	−1.10789
$219$	−1656.15	−0.511015
$220$	−4336.47	−1.32893
$221$	2401.39	0.730928
$222$	657.998	0.198928
$223$	−725.792	−0.217949	−0.108975	−	0.994045i	$-0.534757\pi$
$223$	−725.792	−0.217949	−0.108975	+	0.994045i	$0.534757\pi$
$224$	−1570.84	−0.468555
$225$	1758.59	0.521065
$226$	−1168.88	−0.344038
$227$	2043.12	0.597385	0.298693	−	0.954349i	$-0.403449\pi$
$227$	2043.12	0.597385	0.298693	+	0.954349i	$0.403449\pi$
$228$	−341.390	−0.0991628
$229$	−1829.51	−0.527935	−0.263968	−	0.964532i	$-0.585031\pi$
$229$	−1829.51	−0.527935	−0.263968	+	0.964532i	$0.585031\pi$
$230$	−5972.66	−1.71229
$231$	−1571.56	−0.447624
$232$	3154.95	0.892813
$233$	2548.04	0.716428	0.358214	−	0.933639i	$-0.383386\pi$
$233$	2548.04	0.716428	0.358214	+	0.933639i	$0.383386\pi$
$234$	−913.227	−0.255126
$235$	−6564.41	−1.82219
$236$	−802.315	−0.221298
$237$	374.054	0.102521
$238$	813.658	0.221603
$239$	1554.00	0.420585	0.210293	−	0.977638i	$-0.432558\pi$
$239$	1554.00	0.420585	0.210293	+	0.977638i	$0.432558\pi$
$240$	−582.038	−0.156543
$241$	−4707.35	−1.25820	−0.629102	−	0.777323i	$-0.716577\pi$
$241$	−4707.35	−1.25820	−0.629102	+	0.777323i	$0.716577\pi$
$242$	3491.79	0.927525
$243$	−243.000	−0.0641500
$244$	−1357.56	−0.356184
$245$	4580.36	1.19440
$246$	284.627	0.0737689
$247$	1393.84	0.359059
$248$	4423.46	1.13262
$249$	2920.76	0.743357
$250$	−2418.55	−0.611849
$251$	3157.56	0.794038	0.397019	−	0.917810i	$-0.370045\pi$
$251$	3157.56	0.794038	0.397019	+	0.917810i	$0.370045\pi$
$252$	362.567	0.0906333
$253$	−9757.94	−2.42481
$254$	−912.809	−0.225491
$255$	−2439.13	−0.598997
$256$	−4352.79	−1.06269
$257$	7952.97	1.93032	0.965160	−	0.261659i	$-0.0842697\pi$
$257$	7952.97	1.93032	0.965160	+	0.261659i	$0.0842697\pi$
$258$	2187.85	0.527944
$259$	1066.58	0.255885
$260$	−4084.64	−0.974303
$261$	−1201.19	−0.284874
$262$	4720.13	1.11302
$263$	−3955.26	−0.927344	−0.463672	−	0.886007i	$-0.653468\pi$
$263$	−3955.26	−0.927344	−0.463672	+	0.886007i	$0.653468\pi$
$264$	−3980.34	−0.927928
$265$	5609.06	1.30023
$266$	472.270	0.108860
$267$	−873.179	−0.200141
$268$	3585.92	0.817332
$269$	3982.59	0.902686	0.451343	−	0.892351i	$-0.350945\pi$
$269$	3982.59	0.902686	0.451343	+	0.892351i	$0.350945\pi$
$270$	927.578	0.209076
$271$	−2930.71	−0.656931	−0.328465	−	0.944516i	$-0.606531\pi$
$271$	−2930.71	−0.656931	−0.328465	+	0.944516i	$0.606531\pi$
$272$	492.325	0.109748
$273$	−1480.30	−0.328175
$274$	−2623.83	−0.578509
$275$	−10967.3	−2.40492
$276$	2251.21	0.490967
$277$	6179.33	1.34036	0.670180	−	0.742199i	$-0.266217\pi$
$277$	6179.33	1.34036	0.670180	+	0.742199i	$0.266217\pi$
$278$	−1769.83	−0.381826
$279$	−1684.16	−0.361390
$280$	−3949.12	−0.842876
$281$	4110.88	0.872720	0.436360	−	0.899772i	$-0.356267\pi$
$281$	4110.88	0.872720	0.436360	+	0.899772i	$0.356267\pi$
$282$	−2111.60	−0.445902
$283$	−1097.57	−0.230543	−0.115271	−	0.993334i	$-0.536774\pi$
$283$	−1097.57	−0.230543	−0.115271	+	0.993334i	$0.536774\pi$
$284$	−2836.29	−0.592616
$285$	−1415.74	−0.294250
$286$	5695.26	1.17751
$287$	461.367	0.0948907
$288$	1514.75	0.309923
$289$	−2849.83	−0.580058
$290$	4585.19	0.928454
$291$	2588.69	0.521484
$292$	−2382.83	−0.477549
$293$	2388.52	0.476241	0.238121	−	0.971236i	$-0.423469\pi$
$293$	2388.52	0.476241	0.238121	+	0.971236i	$0.423469\pi$
$294$	1473.39	0.292278
$295$	−3327.19	−0.656665
$296$	2701.37	0.530453
$297$	1515.45	0.296078
$298$	−2693.35	−0.523563
$299$	−9191.29	−1.77775
$300$	2530.21	0.486940
$301$	3546.41	0.679108
$302$	−5675.69	−1.08145
$303$	893.849	0.169473
$304$	285.759	0.0539126
$305$	−5629.79	−1.05692
$306$	−784.606	−0.146578
$307$	2096.37	0.389728	0.194864	−	0.980830i	$-0.437574\pi$
$307$	2096.37	0.389728	0.194864	+	0.980830i	$0.437574\pi$
$308$	−2261.12	−0.418309
$309$	−2028.42	−0.373439
$310$	6428.76	1.17784
$311$	6079.47	1.10847	0.554237	−	0.832359i	$-0.313010\pi$
$311$	6079.47	1.10847	0.554237	+	0.832359i	$0.313010\pi$
$312$	−3749.20	−0.680309
$313$	−10614.5	−1.91683	−0.958416	−	0.285374i	$-0.907882\pi$
$313$	−10614.5	−1.91683	−0.958416	+	0.285374i	$0.907882\pi$
$314$	1413.86	0.254105
$315$	1503.56	0.268940
$316$	538.178	0.0958066
$317$	−8429.82	−1.49358	−0.746791	−	0.665058i	$-0.768407\pi$
$317$	−8429.82	−1.49358	−0.746791	+	0.665058i	$0.768407\pi$
$318$	1804.29	0.318175
$319$	7491.13	1.31481
$320$	−7334.21	−1.28123
$321$	5112.57	0.888959
$322$	−3114.26	−0.538978
$323$	1197.52	0.206291
$324$	−349.622	−0.0599488
$325$	−10330.4	−1.76316
$326$	4236.88	0.719812
$327$	5573.92	0.942626
$328$	1168.52	0.196709
$329$	−3422.81	−0.573574
$330$	−5784.75	−0.964971
$331$	10309.5	1.71197	0.855985	−	0.517000i	$-0.172951\pi$
$331$	10309.5	1.71197	0.855985	+	0.517000i	$0.172951\pi$
$332$	4202.31	0.694674
$333$	−1028.50	−0.169254
$334$	−5068.56	−0.830357
$335$	14870.8	2.42530
$336$	−303.486	−0.0492753
$337$	−3675.84	−0.594172	−0.297086	−	0.954851i	$-0.596015\pi$
$337$	−3675.84	−0.594172	−0.297086	+	0.954851i	$0.596015\pi$
$338$	1147.84	0.184717
$339$	1827.05	0.292718
$340$	−3509.35	−0.559769
$341$	10503.1	1.66796
$342$	−455.408	−0.0720047
$343$	5589.59	0.879912
$344$	8982.09	1.40780
$345$	9335.73	1.45687
$346$	−3956.16	−0.614695
$347$	4456.24	0.689405	0.344703	−	0.938712i	$-0.387980\pi$
$347$	4456.24	0.689405	0.344703	+	0.938712i	$0.387980\pi$
$348$	−1728.25	−0.266217
$349$	1369.42	0.210038	0.105019	−	0.994470i	$-0.466510\pi$
$349$	1369.42	0.210038	0.105019	+	0.994470i	$0.466510\pi$
$350$	−3500.23	−0.534558
$351$	1427.44	0.217069
$352$	−9446.62	−1.43042
$353$	3692.28	0.556715	0.278357	−	0.960478i	$-0.410210\pi$
$353$	3692.28	0.556715	0.278357	+	0.960478i	$0.410210\pi$
$354$	−1070.27	−0.160690
$355$	−11762.1	−1.75849
$356$	−1256.31	−0.187034
$357$	−1271.81	−0.188547
$358$	−895.143	−0.132150
$359$	9194.46	1.35171	0.675856	−	0.737033i	$-0.263774\pi$
$359$	9194.46	1.35171	0.675856	+	0.737033i	$0.263774\pi$
$360$	3808.12	0.557515
$361$	−6163.92	−0.898662
$362$	−347.392	−0.0504379
$363$	−5457.94	−0.789167
$364$	−2129.81	−0.306683
$365$	−9881.54	−1.41705
$366$	−1810.96	−0.258635
$367$	448.057	0.0637286	0.0318643	−	0.999492i	$-0.489856\pi$
$367$	448.057	0.0637286	0.0318643	+	0.999492i	$0.489856\pi$
$368$	−1884.37	−0.266928
$369$	−444.893	−0.0627648
$370$	3925.99	0.551628
$371$	2924.68	0.409276
$372$	−2423.12	−0.337723
$373$	8424.64	1.16947	0.584734	−	0.811225i	$-0.301199\pi$
$373$	8424.64	1.16947	0.584734	+	0.811225i	$0.301199\pi$
$374$	4893.12	0.676517
$375$	3780.37	0.520580
$376$	−8669.06	−1.18902
$377$	7056.12	0.963949
$378$	483.657	0.0658113
$379$	−12814.9	−1.73683	−0.868413	−	0.495842i	$-0.834859\pi$
$379$	−12814.9	−1.73683	−0.868413	+	0.495842i	$0.834859\pi$
$380$	−2036.93	−0.274979
$381$	1426.79	0.191855
$382$	−2182.87	−0.292369
$383$	−13873.8	−1.85096	−0.925480	−	0.378797i	$-0.876338\pi$
$383$	−13873.8	−1.85096	−0.925480	+	0.378797i	$0.876338\pi$
$384$	1680.11	0.223276
$385$	−9376.82	−1.24126
$386$	−634.449	−0.0836596
$387$	−3419.78	−0.449191
$388$	3724.54	0.487332
$389$	7520.78	0.980253	0.490127	−	0.871651i	$-0.336951\pi$
$389$	7520.78	0.980253	0.490127	+	0.871651i	$0.336951\pi$
$390$	−5448.83	−0.707467
$391$	−7896.76	−1.02137
$392$	6048.89	0.779376
$393$	−7377.92	−0.946990
$394$	7646.01	0.977666
$395$	2231.82	0.284291
$396$	2180.38	0.276688
$397$	−6446.95	−0.815020	−0.407510	−	0.913201i	$-0.633603\pi$
$397$	−6446.95	−0.815020	−0.407510	+	0.913201i	$0.633603\pi$
$398$	242.827	0.0305824
$399$	−738.194	−0.0926214
$400$	−2117.91	−0.264738
$401$	−13100.6	−1.63145	−0.815727	−	0.578437i	$-0.803663\pi$
$401$	−13100.6	−1.63145	−0.815727	+	0.578437i	$0.803663\pi$
$402$	4783.54	0.593486
$403$	9893.17	1.22286
$404$	1286.05	0.158374
$405$	−1449.88	−0.177889
$406$	2390.81	0.292251
$407$	6414.15	0.781173
$408$	−3221.15	−0.390860
$409$	13140.5	1.58864	0.794321	−	0.607499i	$-0.207827\pi$
$409$	13140.5	1.58864	0.794321	+	0.607499i	$0.207827\pi$
$410$	1698.24	0.204562
$411$	4101.25	0.492214
$412$	−2918.43	−0.348983
$413$	−1734.86	−0.206699
$414$	3003.07	0.356504
$415$	17426.9	2.06134
$416$	−8898.05	−1.04871
$417$	2766.39	0.324869
$418$	2840.11	0.332330
$419$	−4021.66	−0.468904	−0.234452	−	0.972128i	$-0.575330\pi$
$419$	−4021.66	−0.468904	−0.234452	+	0.972128i	$0.575330\pi$
$420$	2163.28	0.251327
$421$	−2939.00	−0.340233	−0.170117	−	0.985424i	$-0.554414\pi$
$421$	−2939.00	−0.340233	−0.170117	+	0.985424i	$0.554414\pi$
$422$	−2048.44	−0.236295
$423$	3300.60	0.379387
$424$	7407.41	0.848434
$425$	−8875.45	−1.01299
$426$	−3783.56	−0.430314
$427$	−2935.48	−0.332688
$428$	7355.82	0.830741
$429$	−8902.12	−1.00186
$430$	13054.0	1.46399
$431$	−9679.41	−1.08177	−0.540883	−	0.841098i	$-0.681910\pi$
$431$	−9679.41	−1.08177	−0.540883	+	0.841098i	$0.681910\pi$
$432$	292.650	0.0325928
$433$	−75.8532	−0.00841864	−0.00420932	−	0.999991i	$-0.501340\pi$
$433$	−75.8532	−0.00841864	−0.00420932	+	0.999991i	$0.501340\pi$
$434$	3352.08	0.370749
$435$	−7167.00	−0.789958
$436$	8019.60	0.880893
$437$	−4583.50	−0.501736
$438$	−3178.64	−0.346761
$439$	−8154.32	−0.886525	−0.443263	−	0.896392i	$-0.646179\pi$
$439$	−8154.32	−0.886525	−0.443263	+	0.896392i	$0.646179\pi$
$440$	−23749.0	−2.57315
$441$	−2303.01	−0.248679
$442$	4608.97	0.495988
$443$	3120.41	0.334662	0.167331	−	0.985901i	$-0.446485\pi$
$443$	3120.41	0.334662	0.167331	+	0.985901i	$0.446485\pi$
$444$	−1479.78	−0.158169
$445$	−5209.88	−0.554994
$446$	−1393.01	−0.147894
$447$	4209.92	0.445463
$448$	−3824.20	−0.403296
$449$	17954.3	1.88712	0.943561	−	0.331200i	$-0.107453\pi$
$449$	17954.3	1.88712	0.943561	+	0.331200i	$0.107453\pi$
$450$	3375.25	0.353580
$451$	2774.53	0.289685
$452$	2628.70	0.273548
$453$	8871.53	0.920135
$454$	3921.34	0.405369
$455$	−8832.30	−0.910032
$456$	−1869.65	−0.192005
$457$	4171.14	0.426953	0.213477	−	0.976948i	$-0.431521\pi$
$457$	4171.14	0.426953	0.213477	+	0.976948i	$0.431521\pi$
$458$	−3511.36	−0.358242
$459$	1226.40	0.124713
$460$	13432.0	1.36146
$461$	−4166.77	−0.420967	−0.210483	−	0.977597i	$-0.567504\pi$
$461$	−4166.77	−0.420967	−0.210483	+	0.977597i	$0.567504\pi$
$462$	−3016.28	−0.303745
$463$	−14769.2	−1.48247	−0.741233	−	0.671248i	$-0.765758\pi$
$463$	−14769.2	−1.48247	−0.741233	+	0.671248i	$0.765758\pi$
$464$	1446.62	0.144736
$465$	−10048.6	−1.00214
$466$	4890.44	0.486148
$467$	9126.12	0.904296	0.452148	−	0.891943i	$-0.350658\pi$
$467$	9126.12	0.904296	0.452148	+	0.891943i	$0.350658\pi$
$468$	2053.77	0.202853
$469$	7753.90	0.763416
$470$	−12599.0	−1.23649
$471$	−2209.97	−0.216200
$472$	−4393.93	−0.428490
$473$	21327.1	2.07320
$474$	717.919	0.0695677
$475$	−5151.57	−0.497621
$476$	−1829.84	−0.176199
$477$	−2820.25	−0.270713
$478$	2982.58	0.285398
$479$	−1469.89	−0.140211	−0.0701054	−	0.997540i	$-0.522334\pi$
$479$	−1469.89	−0.140211	−0.0701054	+	0.997540i	$0.522334\pi$
$480$	9037.88	0.859418
$481$	6041.67	0.572717
$482$	−9034.78	−0.853782
$483$	4867.83	0.458580
$484$	−7852.73	−0.737484
$485$	15445.6	1.44608
$486$	−466.388	−0.0435304
$487$	12909.7	1.20123	0.600613	−	0.799540i	$-0.294923\pi$
$487$	12909.7	1.20123	0.600613	+	0.799540i	$0.294923\pi$
$488$	−7434.78	−0.689666
$489$	−6622.56	−0.612439
$490$	8791.05	0.810488
$491$	18447.9	1.69560	0.847801	−	0.530314i	$-0.177926\pi$
$491$	18447.9	1.69560	0.847801	+	0.530314i	$0.177926\pi$
$492$	−640.100	−0.0586544
$493$	6062.32	0.553819
$494$	2675.18	0.243648
$495$	9042.01	0.821027
$496$	2028.26	0.183612
$497$	−6132.97	−0.553524
$498$	5605.80	0.504421
$499$	−10980.3	−0.985058	−0.492529	−	0.870296i	$-0.663928\pi$
$499$	−10980.3	−0.985058	−0.492529	+	0.870296i	$0.663928\pi$
$500$	5439.10	0.486487
$501$	7922.54	0.706493
$502$	6060.29	0.538812
$503$	−4028.20	−0.357075	−0.178537	−	0.983933i	$-0.557137\pi$
$503$	−4028.20	−0.357075	−0.178537	+	0.983933i	$0.557137\pi$
$504$	1985.63	0.175490
$505$	5333.21	0.469950
$506$	−18728.3	−1.64541
$507$	−1794.17	−0.157163
$508$	2052.83	0.179290
$509$	−2731.61	−0.237871	−0.118936	−	0.992902i	$-0.537948\pi$
$509$	−2731.61	−0.237871	−0.118936	+	0.992902i	$0.537948\pi$
$510$	−4681.40	−0.406463
$511$	−5152.43	−0.446047
$512$	−3873.97	−0.334389
$513$	711.837	0.0612639
$514$	15264.1	1.30986
$515$	−12102.7	−1.03555
$516$	−4920.28	−0.419774
$517$	−20583.9	−1.75102
$518$	2047.09	0.173637
$519$	6183.78	0.523001
$520$	−22369.8	−1.88650
$521$	16986.4	1.42838	0.714192	−	0.699950i	$-0.246795\pi$
$521$	16986.4	1.42838	0.714192	+	0.699950i	$0.246795\pi$
$522$	−2305.44	−0.193307
$523$	21093.9	1.76362	0.881810	−	0.471605i	$-0.156325\pi$
$523$	21093.9	1.76362	0.881810	+	0.471605i	$0.156325\pi$
$524$	−10615.2	−0.884972
$525$	5471.13	0.454818
$526$	−7591.29	−0.629270
$527$	8499.79	0.702574
$528$	−1825.08	−0.150429
$529$	18057.7	1.48416
$530$	10765.4	0.882303
$531$	1672.91	0.136720
$532$	−1062.09	−0.0865557
$533$	2613.42	0.212382
$534$	−1675.89	−0.135810
$535$	30504.5	2.46509
$536$	19638.5	1.58257
$537$	1399.18	0.112437
$538$	7643.75	0.612538
$539$	14362.5	1.14775
$540$	−2086.04	−0.166239
$541$	−10959.2	−0.870928	−0.435464	−	0.900206i	$-0.643416\pi$
$541$	−10959.2	−0.870928	−0.435464	+	0.900206i	$0.643416\pi$
$542$	−5624.90	−0.445775
$543$	543.000	0.0429141
$544$	−7644.82	−0.602516
$545$	33257.2	2.61391
$546$	−2841.13	−0.222690
$547$	23945.6	1.87174	0.935870	−	0.352346i	$-0.114616\pi$
$547$	23945.6	1.87174	0.935870	+	0.352346i	$0.114616\pi$
$548$	5900.77	0.459979
$549$	2830.67	0.220055
$550$	−21049.5	−1.63191
$551$	3518.74	0.272057
$552$	12328.9	0.950639
$553$	1163.71	0.0894866
$554$	11859.9	0.909531
$555$	−6136.62	−0.469342
$556$	3980.20	0.303594
$557$	11376.7	0.865437	0.432718	−	0.901529i	$-0.357554\pi$
$557$	11376.7	0.865437	0.432718	+	0.901529i	$0.357554\pi$
$558$	−3232.39	−0.245229
$559$	20088.6	1.51996
$560$	−1810.77	−0.136641
$561$	−7648.32	−0.575601
$562$	7889.97	0.592204
$563$	−19299.8	−1.44474	−0.722370	−	0.691507i	$-0.756947\pi$
$563$	−19299.8	−1.44474	−0.722370	+	0.691507i	$0.756947\pi$
$564$	4748.81	0.354541
$565$	10901.2	0.811711
$566$	−2106.55	−0.156440
$567$	−755.993	−0.0559942
$568$	−15533.2	−1.14746
$569$	10855.8	0.799820	0.399910	−	0.916554i	$-0.369041\pi$
$569$	10855.8	0.799820	0.399910	+	0.916554i	$0.369041\pi$
$570$	−2717.22	−0.199670
$571$	−12876.9	−0.943748	−0.471874	−	0.881666i	$-0.656422\pi$
$571$	−12876.9	−0.943748	−0.471874	+	0.881666i	$0.656422\pi$
$572$	−12808.1	−0.936249
$573$	3411.98	0.248757
$574$	885.498	0.0643902
$575$	33970.7	2.46378
$576$	3687.65	0.266757
$577$	16662.5	1.20220	0.601100	−	0.799174i	$-0.294729\pi$
$577$	16662.5	1.20220	0.601100	+	0.799174i	$0.294729\pi$
$578$	−5469.65	−0.393612
$579$	991.692	0.0711801
$580$	−10311.7	−0.738223
$581$	9086.74	0.648849
$582$	4968.46	0.353864
$583$	17588.2	1.24945
$584$	−13049.7	−0.924659
$585$	8516.94	0.601935
$586$	4584.27	0.323164
$587$	−9224.90	−0.648641	−0.324320	−	0.945947i	$-0.605136\pi$
$587$	−9224.90	−0.648641	−0.324320	+	0.945947i	$0.605136\pi$
$588$	−3313.51	−0.232393
$589$	4933.52	0.345131
$590$	−6385.84	−0.445595
$591$	−11951.3	−0.831829
$592$	1238.64	0.0859931
$593$	−4407.67	−0.305230	−0.152615	−	0.988286i	$-0.548769\pi$
$593$	−4407.67	−0.305230	−0.152615	+	0.988286i	$0.548769\pi$
$594$	2908.59	0.200910
$595$	−7588.34	−0.522843
$596$	6057.11	0.416290
$597$	−379.557	−0.0260205
$598$	−17640.8	−1.20633
$599$	−25472.0	−1.73749	−0.868745	−	0.495259i	$-0.835073\pi$
$599$	−25472.0	−1.73749	−0.868745	+	0.495259i	$0.835073\pi$
$600$	13856.9	0.942842
$601$	4524.23	0.307067	0.153533	−	0.988143i	$-0.450935\pi$
$601$	4524.23	0.307067	0.153533	+	0.988143i	$0.450935\pi$
$602$	6806.59	0.460824
$603$	−7477.04	−0.504956
$604$	12764.1	0.859875
$605$	−32565.2	−2.18837
$606$	1715.56	0.115000
$607$	−7020.38	−0.469437	−0.234719	−	0.972063i	$-0.575417\pi$
$607$	−7020.38	−0.469437	−0.234719	+	0.972063i	$0.575417\pi$
$608$	−4437.27	−0.295979
$609$	−3737.02	−0.248656
$610$	−10805.2	−0.717197
$611$	−19388.6	−1.28376
$612$	1764.51	0.116546
$613$	−2803.90	−0.184745	−0.0923723	−	0.995725i	$-0.529445\pi$
$613$	−2803.90	−0.184745	−0.0923723	+	0.995725i	$0.529445\pi$
$614$	4023.55	0.264458
$615$	−2654.49	−0.174047
$616$	−12383.2	−0.809955
$617$	−8131.95	−0.530599	−0.265300	−	0.964166i	$-0.585471\pi$
$617$	−8131.95	−0.530599	−0.265300	+	0.964166i	$0.585471\pi$
$618$	−3893.13	−0.253405
$619$	−21886.2	−1.42113	−0.710567	−	0.703630i	$-0.751561\pi$
$619$	−21886.2	−1.42113	−0.710567	+	0.703630i	$0.751561\pi$
$620$	−14457.7	−0.936508
$621$	−4694.02	−0.303325
$622$	11668.3	0.752179
$623$	−2716.53	−0.174696
$624$	−1719.10	−0.110287
$625$	−1869.06	−0.119620
$626$	−20372.4	−1.30071
$627$	−4439.30	−0.282757
$628$	−3179.65	−0.202041
$629$	5190.75	0.329044
$630$	2885.77	0.182495
$631$	4452.70	0.280918	0.140459	−	0.990087i	$-0.455142\pi$
$631$	4452.70	0.280918	0.140459	+	0.990087i	$0.455142\pi$
$632$	2947.37	0.185507
$633$	3201.86	0.201047
$634$	−16179.3	−1.01350
$635$	8513.04	0.532015
$636$	−4057.69	−0.252984
$637$	13528.5	0.841473
$638$	14377.7	0.892191
$639$	5913.99	0.366125
$640$	10024.5	0.619146
$641$	−15513.1	−0.955899	−0.477949	−	0.878387i	$-0.658620\pi$
$641$	−15513.1	−0.955899	−0.477949	+	0.878387i	$0.658620\pi$
$642$	9812.51	0.603223
$643$	−10772.9	−0.660717	−0.330358	−	0.943856i	$-0.607170\pi$
$643$	−10772.9	−0.660717	−0.330358	+	0.943856i	$0.607170\pi$
$644$	7003.70	0.428547
$645$	−20404.3	−1.24561
$646$	2298.40	0.139983
$647$	2770.41	0.168340	0.0841701	−	0.996451i	$-0.473176\pi$
$647$	2770.41	0.168340	0.0841701	+	0.996451i	$0.473176\pi$
$648$	−1914.73	−0.116077
$649$	−10433.0	−0.631017
$650$	−19827.1	−1.19643
$651$	−5239.55	−0.315444
$652$	−9528.35	−0.572330
$653$	−31205.7	−1.87010	−0.935049	−	0.354518i	$-0.884645\pi$
$653$	−31205.7	−1.87010	−0.935049	+	0.354518i	$0.884645\pi$
$654$	10698.0	0.639640
$655$	−44020.9	−2.62601
$656$	535.793	0.0318891
$657$	4968.46	0.295035
$658$	−6569.38	−0.389211
$659$	−6071.71	−0.358908	−0.179454	−	0.983766i	$-0.557433\pi$
$659$	−6071.71	−0.358908	−0.179454	+	0.983766i	$0.557433\pi$
$660$	13009.4	0.767258
$661$	20654.8	1.21540	0.607700	−	0.794167i	$-0.292092\pi$
$661$	20654.8	1.21540	0.607700	+	0.794167i	$0.292092\pi$
$662$	19787.0	1.16170
$663$	−7204.18	−0.422001
$664$	23014.3	1.34507
$665$	−4404.49	−0.256840
$666$	−1973.99	−0.114851
$667$	−23203.4	−1.34699
$668$	11398.7	0.660225
$669$	2177.38	0.125833
$670$	28541.3	1.64574
$671$	−17653.2	−1.01564
$672$	4712.52	0.270520
$673$	−10494.7	−0.601101	−0.300551	−	0.953766i	$-0.597170\pi$
$673$	−10494.7	−0.601101	−0.300551	+	0.953766i	$0.597170\pi$
$674$	−7055.01	−0.403188
$675$	−5275.78	−0.300837
$676$	−2581.40	−0.146870
$677$	12244.8	0.695133	0.347567	−	0.937655i	$-0.387008\pi$
$677$	12244.8	0.695133	0.347567	+	0.937655i	$0.387008\pi$
$678$	3506.64	0.198631
$679$	8053.64	0.455184
$680$	−19219.2	−1.08386
$681$	−6129.35	−0.344901
$682$	20158.5	1.13183
$683$	14313.6	0.801897	0.400949	−	0.916101i	$-0.368681\pi$
$683$	14313.6	0.801897	0.400949	+	0.916101i	$0.368681\pi$
$684$	1024.17	0.0572517
$685$	24470.4	1.36491
$686$	10728.1	0.597084
$687$	5488.52	0.304804
$688$	4118.50	0.228222
$689$	16566.8	0.916033
$690$	17918.0	0.988589
$691$	−15583.7	−0.857936	−0.428968	−	0.903320i	$-0.641123\pi$
$691$	−15583.7	−0.857936	−0.428968	+	0.903320i	$0.641123\pi$
$692$	8897.05	0.488750
$693$	4714.68	0.258436
$694$	8552.83	0.467811
$695$	16505.8	0.900866
$696$	−9464.86	−0.515466
$697$	2245.34	0.122020
$698$	2628.31	0.142526
$699$	−7644.12	−0.413630
$700$	7871.71	0.425032
$701$	−28768.4	−1.55003	−0.775014	−	0.631944i	$-0.782257\pi$
$701$	−28768.4	−1.55003	−0.775014	+	0.631944i	$0.782257\pi$
$702$	2739.68	0.147297
$703$	3012.86	0.161639
$704$	−22997.7	−1.23119
$705$	19693.2	1.05204
$706$	7086.57	0.377771
$707$	2780.84	0.147927
$708$	2406.94	0.127766
$709$	9566.70	0.506749	0.253374	−	0.967368i	$-0.418460\pi$
$709$	9566.70	0.506749	0.253374	+	0.967368i	$0.418460\pi$
$710$	−22574.8	−1.19327
$711$	−1122.16	−0.0591904
$712$	−6880.25	−0.362146
$713$	−32532.8	−1.70878
$714$	−2440.97	−0.127943
$715$	−53115.1	−2.77817
$716$	2013.10	0.105074
$717$	−4662.00	−0.242825
$718$	17646.8	0.917235
$719$	−19674.1	−1.02047	−0.510237	−	0.860034i	$-0.670442\pi$
$719$	−19674.1	−1.02047	−0.510237	+	0.860034i	$0.670442\pi$
$720$	1746.11	0.0903803
$721$	−6310.58	−0.325962
$722$	−11830.4	−0.609807
$723$	14122.0	0.726424
$724$	781.253	0.0401037
$725$	−26079.2	−1.33594
$726$	−10475.4	−0.535507
$727$	−34245.6	−1.74704	−0.873520	−	0.486789i	$-0.838168\pi$
$727$	−34245.6	−1.74704	−0.873520	+	0.486789i	$0.838168\pi$
$728$	−11664.1	−0.593818
$729$	729.000	0.0370370
$730$	−18965.6	−0.961571
$731$	17259.3	0.873267
$732$	4072.69	0.205643
$733$	30906.4	1.55737	0.778685	−	0.627415i	$-0.215887\pi$
$733$	30906.4	1.55737	0.778685	+	0.627415i	$0.215887\pi$
$734$	859.953	0.0432445
$735$	−13741.1	−0.689588
$736$	29260.4	1.46543
$737$	46629.9	2.33057
$738$	−853.880	−0.0425905
$739$	−25421.1	−1.26540	−0.632699	−	0.774398i	$-0.718053\pi$
$739$	−25421.1	−1.26540	−0.632699	+	0.774398i	$0.718053\pi$
$740$	−8829.20	−0.438605
$741$	−4181.51	−0.207303
$742$	5613.31	0.277724
$743$	−33013.8	−1.63009	−0.815046	−	0.579396i	$-0.803288\pi$
$743$	−33013.8	−1.63009	−0.815046	+	0.579396i	$0.803288\pi$
$744$	−13270.4	−0.653919
$745$	25118.7	1.23527
$746$	16169.4	0.793569
$747$	−8762.29	−0.429177
$748$	−11004.2	−0.537905
$749$	15905.6	0.775940
$750$	7255.64	0.353251
$751$	−9966.57	−0.484268	−0.242134	−	0.970243i	$-0.577847\pi$
$751$	−9966.57	−0.484268	−0.242134	+	0.970243i	$0.577847\pi$
$752$	−3974.97	−0.192756
$753$	−9472.69	−0.458438
$754$	13542.8	0.654109
$755$	52932.6	2.55154
$756$	−1087.70	−0.0523272
$757$	23753.5	1.14047	0.570236	−	0.821481i	$-0.306852\pi$
$757$	23753.5	1.14047	0.570236	+	0.821481i	$0.306852\pi$
$758$	−24595.5	−1.17856
$759$	29273.8	1.39996
$760$	−11155.4	−0.532432
$761$	10526.6	0.501431	0.250716	−	0.968061i	$-0.419334\pi$
$761$	10526.6	0.501431	0.250716	+	0.968061i	$0.419334\pi$
$762$	2738.43	0.130187
$763$	17340.9	0.822784
$764$	4909.07	0.232466
$765$	7317.39	0.345831
$766$	−26627.9	−1.25601
$767$	−9827.13	−0.462630
$768$	13058.4	0.613546
$769$	2950.58	0.138362	0.0691811	−	0.997604i	$-0.477961\pi$
$769$	2950.58	0.138362	0.0691811	+	0.997604i	$0.477961\pi$
$770$	−17996.9	−0.842288
$771$	−23858.9	−1.11447
$772$	1426.82	0.0665186
$773$	−10231.2	−0.476056	−0.238028	−	0.971258i	$-0.576501\pi$
$773$	−10231.2	−0.476056	−0.238028	+	0.971258i	$0.576501\pi$
$774$	−6563.55	−0.304809
$775$	−36564.8	−1.69477
$776$	20397.7	0.943601
$777$	−3199.75	−0.147735
$778$	14434.6	0.665173
$779$	1303.26	0.0599410
$780$	12253.9	0.562514
$781$	−36882.0	−1.68981
$782$	−15156.2	−0.693075
$783$	3603.58	0.164472
$784$	2773.56	0.126347
$785$	−13186.0	−0.599525
$786$	−14160.4	−0.642601
$787$	−27741.6	−1.25652	−0.628261	−	0.778003i	$-0.716233\pi$
$787$	−27741.6	−1.25652	−0.628261	+	0.778003i	$0.716233\pi$
$788$	−17195.2	−0.777352
$789$	11865.8	0.535402
$790$	4283.51	0.192912
$791$	5684.10	0.255503
$792$	11941.0	0.535739
$793$	−16628.1	−0.744615
$794$	−12373.6	−0.553050
$795$	−16827.2	−0.750691
$796$	−546.096	−0.0243164
$797$	−34080.0	−1.51465	−0.757326	−	0.653037i	$-0.773494\pi$
$797$	−34080.0	−1.51465	−0.757326	+	0.653037i	$0.773494\pi$
$798$	−1416.81	−0.0628503
$799$	−16657.8	−0.737561
$800$	32886.8	1.45341
$801$	2619.54	0.115552
$802$	−25143.9	−1.10706
$803$	−30985.3	−1.36170
$804$	−10757.8	−0.471887
$805$	29044.2	1.27165
$806$	18987.9	0.829801
$807$	−11947.8	−0.521166
$808$	7043.12	0.306653
$809$	−26201.8	−1.13870	−0.569348	−	0.822096i	$-0.692804\pi$
$809$	−26201.8	−1.13870	−0.569348	+	0.822096i	$0.692804\pi$
$810$	−2782.73	−0.120710
$811$	13358.8	0.578412	0.289206	−	0.957267i	$-0.406609\pi$
$811$	13358.8	0.578412	0.289206	+	0.957267i	$0.406609\pi$
$812$	−5376.72	−0.232372
$813$	8792.14	0.379279
$814$	12310.6	0.530083
$815$	−39513.9	−1.69830
$816$	−1476.98	−0.0633633
$817$	10017.8	0.428982
$818$	25220.4	1.07801
$819$	4440.90	0.189472
$820$	−3819.20	−0.162649
$821$	−35994.5	−1.53010	−0.765052	−	0.643968i	$-0.777287\pi$
$821$	−35994.5	−1.53010	−0.765052	+	0.643968i	$0.777287\pi$
$822$	7871.50	0.334002
$823$	−38743.7	−1.64097	−0.820486	−	0.571667i	$-0.806297\pi$
$823$	−38743.7	−1.64097	−0.820486	+	0.571667i	$0.806297\pi$
$824$	−15983.0	−0.675721
$825$	32901.9	1.38848
$826$	−3329.70	−0.140260
$827$	34159.4	1.43632	0.718162	−	0.695876i	$-0.244984\pi$
$827$	34159.4	1.43632	0.718162	+	0.695876i	$0.244984\pi$
$828$	−6753.63	−0.283460
$829$	35296.0	1.47875	0.739374	−	0.673295i	$-0.235122\pi$
$829$	35296.0	1.47875	0.739374	+	0.673295i	$0.235122\pi$
$830$	33447.4	1.39876
$831$	−18538.0	−0.773857
$832$	−21662.2	−0.902647
$833$	11623.1	0.483453
$834$	5309.50	0.220447
$835$	47270.4	1.95911
$836$	−6387.15	−0.264239
$837$	5052.47	0.208649
$838$	−7718.74	−0.318185
$839$	−39727.0	−1.63472	−0.817358	−	0.576129i	$-0.804562\pi$
$839$	−39727.0	−1.63472	−0.817358	+	0.576129i	$0.804562\pi$
$840$	11847.4	0.486635
$841$	−6575.82	−0.269622
$842$	−5640.80	−0.230873
$843$	−12332.6	−0.503865
$844$	4606.75	0.187880
$845$	−10705.0	−0.435815
$846$	6334.81	0.257441
$847$	−16980.1	−0.688835
$848$	3396.48	0.137542
$849$	3292.70	0.133104
$850$	−17034.6	−0.687390
$851$	−19867.5	−0.800293
$852$	8508.88	0.342147
$853$	−7068.86	−0.283743	−0.141872	−	0.989885i	$-0.545312\pi$
$853$	−7068.86	−0.283743	−0.141872	+	0.989885i	$0.545312\pi$
$854$	−5634.05	−0.225753
$855$	4247.22	0.169885
$856$	40284.7	1.60853
$857$	−7467.01	−0.297629	−0.148815	−	0.988865i	$-0.547546\pi$
$857$	−7467.01	−0.297629	−0.148815	+	0.988865i	$0.547546\pi$
$858$	−17085.8	−0.679835
$859$	−38191.8	−1.51698	−0.758490	−	0.651685i	$-0.774063\pi$
$859$	−38191.8	−1.51698	−0.758490	+	0.651685i	$0.774063\pi$
$860$	−29357.2	−1.16404
$861$	−1384.10	−0.0547851
$862$	−18577.6	−0.734056
$863$	−41733.3	−1.64614	−0.823069	−	0.567941i	$-0.807740\pi$
$863$	−41733.3	−1.64614	−0.823069	+	0.567941i	$0.807740\pi$
$864$	−4544.26	−0.178934
$865$	36895.9	1.45029
$866$	−145.584	−0.00571266
$867$	8549.48	0.334897
$868$	−7538.53	−0.294786
$869$	6998.26	0.273187
$870$	−13755.6	−0.536043
$871$	43922.0	1.70866
$872$	43919.9	1.70564
$873$	−7766.07	−0.301079
$874$	−8797.09	−0.340464
$875$	11761.1	0.454396
$876$	7148.48	0.275713
$877$	16676.0	0.642087	0.321043	−	0.947065i	$-0.395966\pi$
$877$	16676.0	0.642087	0.321043	+	0.947065i	$0.395966\pi$
$878$	−15650.5	−0.601571
$879$	−7165.56	−0.274958
$880$	−10889.5	−0.417141
$881$	−19171.1	−0.733135	−0.366567	−	0.930391i	$-0.619467\pi$
$881$	−19171.1	−0.733135	−0.366567	+	0.930391i	$0.619467\pi$
$882$	−4420.16	−0.168747
$883$	7041.22	0.268353	0.134177	−	0.990957i	$-0.457161\pi$
$883$	7041.22	0.268353	0.134177	+	0.990957i	$0.457161\pi$
$884$	−10365.2	−0.394365
$885$	9981.56	0.379126
$886$	5988.99	0.227093
$887$	41940.1	1.58761	0.793805	−	0.608173i	$-0.208097\pi$
$887$	41940.1	1.58761	0.793805	+	0.608173i	$0.208097\pi$
$888$	−8104.11	−0.306257
$889$	4438.86	0.167463
$890$	−9999.29	−0.376603
$891$	−4546.34	−0.170941
$892$	3132.75	0.117592
$893$	−9668.67	−0.362318
$894$	8080.06	0.302279
$895$	8348.28	0.311790
$896$	5226.98	0.194890
$897$	27573.9	1.02638
$898$	34459.6	1.28055
$899$	24975.3	0.926555
$900$	−7590.64	−0.281135
$901$	14233.5	0.526290
$902$	5325.14	0.196572
$903$	−10639.2	−0.392083
$904$	14396.3	0.529661
$905$	3239.85	0.119001
$906$	17027.1	0.624378
$907$	−45038.2	−1.64881	−0.824404	−	0.566001i	$-0.808490\pi$
$907$	−45038.2	−1.64881	−0.824404	+	0.566001i	$0.808490\pi$
$908$	−8818.74	−0.322313
$909$	−2681.55	−0.0978452
$910$	−16951.8	−0.617523
$911$	−48746.1	−1.77281	−0.886405	−	0.462910i	$-0.846805\pi$
$911$	−48746.1	−1.77281	−0.886405	+	0.462910i	$0.846805\pi$
$912$	−857.278	−0.0311265
$913$	54645.2	1.98082
$914$	8005.63	0.289719
$915$	16889.4	0.610213
$916$	7896.73	0.284842
$917$	−22953.3	−0.826593
$918$	2353.82	0.0846270
$919$	−37028.2	−1.32910	−0.664552	−	0.747242i	$-0.731378\pi$
$919$	−37028.2	−1.32910	−0.664552	+	0.747242i	$0.731378\pi$
$920$	73561.2	2.63613
$921$	−6289.12	−0.225009
$922$	−7997.24	−0.285656
$923$	−34740.3	−1.23888
$924$	6783.35	0.241511
$925$	−22329.8	−0.793729
$926$	−28346.3	−1.00596
$927$	6085.26	0.215605
$928$	−22463.1	−0.794599
$929$	38766.8	1.36910	0.684552	−	0.728964i	$-0.259998\pi$
$929$	38766.8	1.36910	0.684552	+	0.728964i	$0.259998\pi$
$930$	−19286.3	−0.680023
$931$	6746.38	0.237490
$932$	−10998.2	−0.386541
$933$	−18238.4	−0.639977
$934$	17515.7	0.613631
$935$	−45634.2	−1.59615
$936$	11247.6	0.392777
$937$	46941.3	1.63661	0.818306	−	0.574782i	$-0.194913\pi$
$937$	46941.3	1.63661	0.818306	+	0.574782i	$0.194913\pi$
$938$	14882.0	0.518033
$939$	31843.6	1.10668
$940$	28334.1	0.983145
$941$	39286.7	1.36101	0.680505	−	0.732743i	$-0.261760\pi$
$941$	39286.7	1.36101	0.680505	+	0.732743i	$0.261760\pi$
$942$	−4241.58	−0.146707
$943$	−8593.98	−0.296775
$944$	−2014.72	−0.0694636
$945$	−4510.68	−0.155273
$946$	40933.0	1.40681
$947$	10859.1	0.372622	0.186311	−	0.982491i	$-0.440347\pi$
$947$	10859.1	0.372622	0.186311	+	0.982491i	$0.440347\pi$
$948$	−1614.54	−0.0553140
$949$	−29186.0	−0.998331
$950$	−9887.36	−0.337672
$951$	25289.5	0.862320
$952$	−10021.3	−0.341167
$953$	37223.0	1.26524	0.632618	−	0.774464i	$-0.281980\pi$
$953$	37223.0	1.26524	0.632618	+	0.774464i	$0.281980\pi$
$954$	−5412.88	−0.183699
$955$	20357.8	0.689805
$956$	−6707.56	−0.226922
$957$	−22473.4	−0.759103
$958$	−2821.15	−0.0951432
$959$	12759.3	0.429635
$960$	22002.6	0.739721
$961$	5226.11	0.175426
$962$	11595.7	0.388630
$963$	−15337.7	−0.513241
$964$	20318.4	0.678851
$965$	5916.99	0.197383
$966$	9342.79	0.311179
$967$	−8408.61	−0.279630	−0.139815	−	0.990178i	$-0.544651\pi$
$967$	−8408.61	−0.279630	−0.139815	+	0.990178i	$0.544651\pi$
$968$	−43006.0	−1.42796
$969$	−3592.57	−0.119102
$970$	29644.6	0.981269
$971$	−20660.0	−0.682813	−0.341406	−	0.939916i	$-0.610903\pi$
$971$	−20660.0	−0.682813	−0.341406	+	0.939916i	$0.610903\pi$
$972$	1048.87	0.0346115
$973$	8606.46	0.283567
$974$	24777.6	0.815118
$975$	30991.3	1.01796
$976$	−3409.03	−0.111804
$977$	50316.1	1.64765	0.823825	−	0.566844i	$-0.191836\pi$
$977$	50316.1	1.64765	0.823825	+	0.566844i	$0.191836\pi$
$978$	−12710.6	−0.415584
$979$	−16336.5	−0.533317
$980$	−19770.3	−0.644427
$981$	−16721.8	−0.544225
$982$	35406.8	1.15059
$983$	1034.36	0.0335614	0.0167807	−	0.999859i	$-0.494658\pi$
$983$	1034.36	0.0335614	0.0167807	+	0.999859i	$0.494658\pi$
$984$	−3505.55	−0.113570
$985$	−71308.2	−2.30667
$986$	11635.4	0.375807
$987$	10268.4	0.331153
$988$	−6016.24	−0.193727
$989$	−66059.7	−2.12394
$990$	17354.3	0.557126
$991$	34133.6	1.09414	0.547068	−	0.837088i	$-0.315744\pi$
$991$	34133.6	1.09414	0.547068	+	0.837088i	$0.315744\pi$
$992$	−31494.9	−1.00803
$993$	−30928.6	−0.988407
$994$	−11771.0	−0.375606
$995$	−2264.65	−0.0721551
$996$	−12606.9	−0.401070
$997$	12536.8	0.398241	0.199120	−	0.979975i	$-0.436192\pi$
$997$	12536.8	0.398241	0.199120	+	0.979975i	$0.436192\pi$
$998$	−21074.3	−0.668433
$999$	3085.50	0.0977187

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	543.4.a.c.1.15	✓	23
3.2	odd	2		1629.4.a.e.1.9		23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
543.4.a.c.1.15	✓	23	1.1	even	1	trivial
1629.4.a.e.1.9		23	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 543 = 3 \cdot 181 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	543.a (trivial)

\(f(q)\)	\(=\)	\(q+1.91929 q^{2} -3.00000 q^{3} -4.31632 q^{4} -17.8997 q^{5} -5.75788 q^{6} -9.33325 q^{7} -23.6386 q^{8} +9.00000 q^{9} -34.3548 q^{10} -56.1277 q^{11} +12.9490 q^{12} -52.8683 q^{13} -17.9132 q^{14} +53.6991 q^{15} -10.8389 q^{16} -45.4222 q^{17} +17.2736 q^{18} -26.3643 q^{19} +77.2608 q^{20} +27.9998 q^{21} -107.725 q^{22} +173.853 q^{23} +70.9158 q^{24} +195.399 q^{25} -101.470 q^{26} -27.0000 q^{27} +40.2853 q^{28} -133.466 q^{29} +103.064 q^{30} -187.129 q^{31} +168.306 q^{32} +168.383 q^{33} -87.1784 q^{34} +167.062 q^{35} -38.8469 q^{36} -114.278 q^{37} -50.6008 q^{38} +158.605 q^{39} +423.124 q^{40} -49.4326 q^{41} +53.7397 q^{42} -379.975 q^{43} +242.265 q^{44} -161.097 q^{45} +333.674 q^{46} +366.733 q^{47} +32.5166 q^{48} -255.890 q^{49} +375.028 q^{50} +136.266 q^{51} +228.196 q^{52} -313.361 q^{53} -51.8209 q^{54} +1004.67 q^{55} +220.625 q^{56} +79.0930 q^{57} -256.160 q^{58} +185.879 q^{59} -231.782 q^{60} +314.519 q^{61} -359.154 q^{62} -83.9993 q^{63} +409.739 q^{64} +946.326 q^{65} +323.176 q^{66} -830.782 q^{67} +196.056 q^{68} -521.558 q^{69} +320.642 q^{70} +657.110 q^{71} -212.748 q^{72} +552.051 q^{73} -219.333 q^{74} -586.198 q^{75} +113.797 q^{76} +523.853 q^{77} +304.409 q^{78} -124.685 q^{79} +194.013 q^{80} +81.0000 q^{81} -94.8756 q^{82} -973.588 q^{83} -120.856 q^{84} +813.043 q^{85} -729.284 q^{86} +400.398 q^{87} +1326.78 q^{88} +291.060 q^{89} -309.193 q^{90} +493.433 q^{91} -750.403 q^{92} +561.386 q^{93} +703.868 q^{94} +471.913 q^{95} -504.918 q^{96} -862.897 q^{97} -491.129 q^{98} -505.149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q + 7 q^{2} - 69 q^{3} + 79 q^{4} + 29 q^{5} - 21 q^{6} - 6 q^{7} + 84 q^{8} + 207 q^{9} + 41 q^{10} + 45 q^{11} - 237 q^{12} + 166 q^{13} - 23 q^{14} - 87 q^{15} + 195 q^{16} + 369 q^{17} + 63 q^{18}+ \cdots + 405 q^{99}+O(q^{100}) \) 23 * q + 7 * q^2 - 69 * q^3 + 79 * q^4 + 29 * q^5 - 21 * q^6 - 6 * q^7 + 84 * q^8 + 207 * q^9 + 41 * q^10 + 45 * q^11 - 237 * q^12 + 166 * q^13 - 23 * q^14 - 87 * q^15 + 195 * q^16 + 369 * q^17 + 63 * q^18 - 115 * q^19 + 162 * q^20 + 18 * q^21 - 130 * q^22 + 221 * q^23 - 252 * q^24 + 712 * q^25 + 227 * q^26 - 621 * q^27 - 265 * q^28 + 599 * q^29 - 123 * q^30 - 8 * q^31 + 1084 * q^32 - 135 * q^33 + 409 * q^34 + 210 * q^35 + 711 * q^36 + 400 * q^37 + 507 * q^38 - 498 * q^39 + 806 * q^40 + 1329 * q^41 + 69 * q^42 - 656 * q^43 + 344 * q^44 + 261 * q^45 + 146 * q^46 + 1079 * q^47 - 585 * q^48 + 2033 * q^49 + 3481 * q^50 - 1107 * q^51 + 2191 * q^52 + 1218 * q^53 - 189 * q^54 + 1470 * q^55 + 3224 * q^56 + 345 * q^57 + 3488 * q^58 + 2075 * q^59 - 486 * q^60 + 249 * q^61 + 4385 * q^62 - 54 * q^63 + 2556 * q^64 + 4512 * q^65 + 390 * q^66 + 1020 * q^67 + 6214 * q^68 - 663 * q^69 + 264 * q^70 + 571 * q^71 + 756 * q^72 + 3247 * q^73 + 3078 * q^74 - 2136 * q^75 + 2386 * q^76 + 3290 * q^77 - 681 * q^78 - 1627 * q^79 + 7008 * q^80 + 1863 * q^81 + 3929 * q^82 + 4312 * q^83 + 795 * q^84 + 2298 * q^85 + 2775 * q^86 - 1797 * q^87 + 1476 * q^88 + 5539 * q^89 + 369 * q^90 - 1488 * q^91 + 5387 * q^92 + 24 * q^93 + 1645 * q^94 + 1796 * q^95 - 3252 * q^96 + 4202 * q^97 + 10181 * q^98 + 405 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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