LMFDB - Embedded newform 529.4.a.m.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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			1.3
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)

$f(q)$	$=$	\(q-4.35590 q^{2} -1.21507 q^{3} +10.9738 q^{4} +6.90715 q^{5} +5.29273 q^{6} -2.81570 q^{7} -12.9537 q^{8} -25.5236 q^{9} -30.0868 q^{10} +61.2825 q^{11} -13.3340 q^{12} -10.5135 q^{13} +12.2649 q^{14} -8.39268 q^{15} -31.3657 q^{16} -104.181 q^{17} +111.178 q^{18} +70.5546 q^{19} +75.7979 q^{20} +3.42128 q^{21} -266.940 q^{22} +15.7397 q^{24} -77.2913 q^{25} +45.7959 q^{26} +63.8200 q^{27} -30.8990 q^{28} -124.008 q^{29} +36.5576 q^{30} -144.754 q^{31} +240.255 q^{32} -74.4626 q^{33} +453.802 q^{34} -19.4484 q^{35} -280.092 q^{36} +230.338 q^{37} -307.328 q^{38} +12.7747 q^{39} -89.4731 q^{40} +20.1480 q^{41} -14.9027 q^{42} +221.808 q^{43} +672.503 q^{44} -176.295 q^{45} +487.718 q^{47} +38.1116 q^{48} -335.072 q^{49} +336.673 q^{50} +126.588 q^{51} -115.374 q^{52} +377.462 q^{53} -277.993 q^{54} +423.287 q^{55} +36.4737 q^{56} -85.7289 q^{57} +540.167 q^{58} -667.749 q^{59} -92.0999 q^{60} -74.6976 q^{61} +630.531 q^{62} +71.8667 q^{63} -795.601 q^{64} -72.6186 q^{65} +324.351 q^{66} +65.7167 q^{67} -1143.27 q^{68} +84.7154 q^{70} +654.734 q^{71} +330.625 q^{72} -602.684 q^{73} -1003.33 q^{74} +93.9145 q^{75} +774.254 q^{76} -172.553 q^{77} -55.6453 q^{78} -116.793 q^{79} -216.648 q^{80} +611.591 q^{81} -87.7624 q^{82} -311.073 q^{83} +37.5445 q^{84} -719.595 q^{85} -966.174 q^{86} +150.679 q^{87} -793.834 q^{88} -1520.85 q^{89} +767.924 q^{90} +29.6030 q^{91} +175.886 q^{93} -2124.45 q^{94} +487.331 q^{95} -291.927 q^{96} -832.982 q^{97} +1459.54 q^{98} -1564.15 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.35590	−1.54004	−0.770021	−	0.638019i	$-0.779754\pi$
$2$	−4.35590	−1.54004	−0.770021	+	0.638019i	$0.779754\pi$
$3$	−1.21507	−0.233841	−0.116920	−	0.993141i	$-0.537302\pi$
$3$	−1.21507	−0.233841	−0.116920	+	0.993141i	$0.537302\pi$
$4$	10.9738	1.37173
$5$	6.90715	0.617794	0.308897	−	0.951095i	$-0.400040\pi$
$5$	6.90715	0.617794	0.308897	+	0.951095i	$0.400040\pi$
$6$	5.29273	0.360124
$7$	−2.81570	−0.152033	−0.0760167	−	0.997107i	$-0.524220\pi$
$7$	−2.81570	−0.152033	−0.0760167	+	0.997107i	$0.524220\pi$
$8$	−12.9537	−0.572478
$9$	−25.5236	−0.945319
$10$	−30.0868	−0.951429
$11$	61.2825	1.67976	0.839880	−	0.542772i	$-0.182625\pi$
$11$	61.2825	1.67976	0.839880	+	0.542772i	$0.182625\pi$
$12$	−13.3340	−0.320766
$13$	−10.5135	−0.224303	−0.112151	−	0.993691i	$-0.535774\pi$
$13$	−10.5135	−0.224303	−0.112151	+	0.993691i	$0.535774\pi$
$14$	12.2649	0.234138
$15$	−8.39268	−0.144465
$16$	−31.3657	−0.490089
$17$	−104.181	−1.48633	−0.743166	−	0.669107i	$-0.766677\pi$
$17$	−104.181	−1.48633	−0.743166	+	0.669107i	$0.766677\pi$
$18$	111.178	1.45583
$19$	70.5546	0.851912	0.425956	−	0.904744i	$-0.359938\pi$
$19$	70.5546	0.851912	0.425956	+	0.904744i	$0.359938\pi$
$20$	75.7979	0.847446
$21$	3.42128	0.0355516
$22$	−266.940	−2.58690
$23$	0	0
$23$	0	0
$24$	15.7397	0.133869
$25$	−77.2913	−0.618331
$26$	45.7959	0.345435
$27$	63.8200	0.454895
$28$	−30.8990	−0.208549
$29$	−124.008	−0.794061	−0.397031	−	0.917805i	$-0.629959\pi$
$29$	−124.008	−0.794061	−0.397031	+	0.917805i	$0.629959\pi$
$30$	36.5576	0.222483
$31$	−144.754	−0.838661	−0.419331	−	0.907834i	$-0.637735\pi$
$31$	−144.754	−0.838661	−0.419331	+	0.907834i	$0.637735\pi$
$32$	240.255	1.32724
$33$	−74.4626	−0.392796
$34$	453.802	2.28901
$35$	−19.4484	−0.0939253
$36$	−280.092	−1.29672
$37$	230.338	1.02344	0.511721	−	0.859152i	$-0.329008\pi$
$37$	230.338	1.02344	0.511721	+	0.859152i	$0.329008\pi$
$38$	−307.328	−1.31198
$39$	12.7747	0.0524511
$40$	−89.4731	−0.353673
$41$	20.1480	0.0767459	0.0383730	−	0.999263i	$-0.487783\pi$
$41$	20.1480	0.0767459	0.0383730	+	0.999263i	$0.487783\pi$
$42$	−14.9027	−0.0547509
$43$	221.808	0.786638	0.393319	−	0.919402i	$-0.371327\pi$
$43$	221.808	0.786638	0.393319	+	0.919402i	$0.371327\pi$
$44$	672.503	2.30418
$45$	−176.295	−0.584012
$46$	0	0
$47$	487.718	1.51364	0.756819	−	0.653625i	$-0.226753\pi$
$47$	487.718	1.51364	0.756819	+	0.653625i	$0.226753\pi$
$48$	38.1116	0.114603
$49$	−335.072	−0.976886
$50$	336.673	0.952255
$51$	126.588	0.347565
$52$	−115.374	−0.307682
$53$	377.462	0.978273	0.489136	−	0.872207i	$-0.337312\pi$
$53$	377.462	0.978273	0.489136	+	0.872207i	$0.337312\pi$
$54$	−277.993	−0.700557
$55$	423.287	1.03775
$56$	36.4737	0.0870357
$57$	−85.7289	−0.199212
$58$	540.167	1.22289
$59$	−667.749	−1.47345	−0.736725	−	0.676193i	$-0.763629\pi$
$59$	−667.749	−1.47345	−0.736725	+	0.676193i	$0.763629\pi$
$60$	−92.0999	−0.198167
$61$	−74.6976	−0.156788	−0.0783938	−	0.996922i	$-0.524979\pi$
$61$	−74.6976	−0.156788	−0.0783938	+	0.996922i	$0.524979\pi$
$62$	630.531	1.29157
$63$	71.8667	0.143720
$64$	−795.601	−1.55391
$65$	−72.6186	−0.138573
$66$	324.351	0.604923
$67$	65.7167	0.119829	0.0599147	−	0.998203i	$-0.480917\pi$
$67$	65.7167	0.119829	0.0599147	+	0.998203i	$0.480917\pi$
$68$	−1143.27	−2.03884
$69$	0	0
$70$	84.7154	0.144649
$71$	654.734	1.09440	0.547202	−	0.837001i	$-0.315693\pi$
$71$	654.734	1.09440	0.547202	+	0.837001i	$0.315693\pi$
$72$	330.625	0.541174
$73$	−602.684	−0.966285	−0.483142	−	0.875542i	$-0.660505\pi$
$73$	−602.684	−0.966285	−0.483142	+	0.875542i	$0.660505\pi$
$74$	−1003.33	−1.57614
$75$	93.9145	0.144591
$76$	774.254	1.16859
$77$	−172.553	−0.255380
$78$	−55.6453	−0.0807768
$79$	−116.793	−0.166332	−0.0831658	−	0.996536i	$-0.526503\pi$
$79$	−116.793	−0.166332	−0.0831658	+	0.996536i	$0.526503\pi$
$80$	−216.648	−0.302774
$81$	611.591	0.838946
$82$	−87.7624	−0.118192
$83$	−311.073	−0.411382	−0.205691	−	0.978617i	$-0.565944\pi$
$83$	−311.073	−0.411382	−0.205691	+	0.978617i	$0.565944\pi$
$84$	37.5445	0.0487671
$85$	−719.595	−0.918247
$86$	−966.174	−1.21146
$87$	150.679	0.185684
$88$	−793.834	−0.961625
$89$	−1520.85	−1.81135	−0.905675	−	0.423974i	$-0.860635\pi$
$89$	−1520.85	−1.81135	−0.905675	+	0.423974i	$0.860635\pi$
$90$	767.924	0.899403
$91$	29.6030	0.0341015
$92$	0	0
$93$	175.886	0.196113
$94$	−2124.45	−2.33106
$95$	487.331	0.526306
$96$	−291.927	−0.310362
$97$	−832.982	−0.871922	−0.435961	−	0.899965i	$-0.643591\pi$
$97$	−832.982	−0.871922	−0.435961	+	0.899965i	$0.643591\pi$
$98$	1459.54	1.50445
$99$	−1564.15	−1.58791
$100$	−848.182	−0.848182
$101$	−1600.56	−1.57685	−0.788423	−	0.615133i	$-0.789102\pi$
$101$	−1600.56	−1.57685	−0.788423	+	0.615133i	$0.789102\pi$
$102$	−551.403	−0.535265
$103$	−444.216	−0.424951	−0.212475	−	0.977166i	$-0.568152\pi$
$103$	−444.216	−0.424951	−0.212475	+	0.977166i	$0.568152\pi$
$104$	136.189	0.128408
$105$	23.6313	0.0219636
$106$	−1644.19	−1.50658
$107$	−1083.67	−0.979091	−0.489546	−	0.871978i	$-0.662837\pi$
$107$	−1083.67	−0.979091	−0.489546	+	0.871978i	$0.662837\pi$
$108$	700.349	0.623992
$109$	72.7978	0.0639703	0.0319851	−	0.999488i	$-0.489817\pi$
$109$	72.7978	0.0639703	0.0319851	+	0.999488i	$0.489817\pi$
$110$	−1843.79	−1.59817
$111$	−279.877	−0.239322
$112$	88.3163	0.0745099
$113$	−1912.46	−1.59212	−0.796058	−	0.605221i	$-0.793085\pi$
$113$	−1912.46	−1.59212	−0.796058	+	0.605221i	$0.793085\pi$
$114$	373.426	0.306794
$115$	0	0
$116$	−1360.85	−1.08924
$117$	268.344	0.212037
$118$	2908.65	2.26917
$119$	293.343	0.225972
$120$	108.716	0.0827032
$121$	2424.54	1.82159
$122$	325.375	0.241459
$123$	−24.4812	−0.0179463
$124$	−1588.50	−1.15042
$125$	−1397.26	−0.999795
$126$	−313.044	−0.221335
$127$	1664.03	1.16267	0.581333	−	0.813666i	$-0.302531\pi$
$127$	1664.03	1.16267	0.581333	+	0.813666i	$0.302531\pi$
$128$	1543.51	1.06585
$129$	−269.513	−0.183948
$130$	316.319	0.213408
$131$	−1258.76	−0.839528	−0.419764	−	0.907633i	$-0.637887\pi$
$131$	−1258.76	−0.839528	−0.419764	+	0.907633i	$0.637887\pi$
$132$	−817.140	−0.538810
$133$	−198.660	−0.129519
$134$	−286.255	−0.184542
$135$	440.814	0.281031
$136$	1349.53	0.850892
$137$	393.094	0.245141	0.122570	−	0.992460i	$-0.460886\pi$
$137$	393.094	0.245141	0.122570	+	0.992460i	$0.460886\pi$
$138$	0	0
$139$	1845.42	1.12609	0.563045	−	0.826426i	$-0.309630\pi$
$139$	1845.42	1.12609	0.563045	+	0.826426i	$0.309630\pi$
$140$	−213.424	−0.128840
$141$	−592.612	−0.353950
$142$	−2851.96	−1.68543
$143$	−644.296	−0.376774
$144$	800.566	0.463290
$145$	−856.544	−0.490566
$146$	2625.23	1.48812
$147$	407.136	0.228436
$148$	2527.69	1.40388
$149$	−2855.51	−1.57001	−0.785007	−	0.619486i	$-0.787341\pi$
$149$	−2855.51	−1.57001	−0.785007	+	0.619486i	$0.787341\pi$
$150$	−409.082	−0.222676
$151$	49.1327	0.0264792	0.0132396	−	0.999912i	$-0.495786\pi$
$151$	49.1327	0.0264792	0.0132396	+	0.999912i	$0.495786\pi$
$152$	−913.942	−0.487701
$153$	2659.08	1.40506
$154$	751.623	0.393295
$155$	−999.834	−0.518120
$156$	140.188	0.0719486
$157$	667.957	0.339546	0.169773	−	0.985483i	$-0.445697\pi$
$157$	667.957	0.339546	0.169773	+	0.985483i	$0.445697\pi$
$158$	508.736	0.256158
$159$	−458.644	−0.228760
$160$	1659.48	0.819958
$161$	0	0
$162$	−2664.03	−1.29201
$163$	1160.73	0.557765	0.278882	−	0.960325i	$-0.410036\pi$
$163$	1160.73	0.557765	0.278882	+	0.960325i	$0.410036\pi$
$164$	221.100	0.105275
$165$	−514.324	−0.242667
$166$	1355.00	0.633545
$167$	−3689.38	−1.70954	−0.854769	−	0.519009i	$-0.826301\pi$
$167$	−3689.38	−1.70954	−0.854769	+	0.519009i	$0.826301\pi$
$168$	−44.3182	−0.0203525
$169$	−2086.47	−0.949688
$170$	3134.48	1.41414
$171$	−1800.81	−0.805328
$172$	2434.09	1.07905
$173$	−217.205	−0.0954554	−0.0477277	−	0.998860i	$-0.515198\pi$
$173$	−217.205	−0.0954554	−0.0477277	+	0.998860i	$0.515198\pi$
$174$	−656.342	−0.285961
$175$	217.629	0.0940069
$176$	−1922.17	−0.823232
$177$	811.363	0.344553
$178$	6624.68	2.78955
$179$	−1207.71	−0.504291	−0.252146	−	0.967689i	$-0.581136\pi$
$179$	−1207.71	−0.504291	−0.252146	+	0.967689i	$0.581136\pi$
$180$	−1934.63	−0.801106
$181$	−2449.70	−1.00599	−0.502997	−	0.864288i	$-0.667769\pi$
$181$	−2449.70	−1.00599	−0.502997	+	0.864288i	$0.667769\pi$
$182$	−128.947	−0.0525177
$183$	90.7629	0.0366633
$184$	0	0
$185$	1590.98	0.632276
$186$	−766.141	−0.302022
$187$	−6384.48	−2.49668
$188$	5352.13	2.07630
$189$	−179.698	−0.0691592
$190$	−2122.76	−0.810534
$191$	−770.064	−0.291727	−0.145864	−	0.989305i	$-0.546596\pi$
$191$	−770.064	−0.291727	−0.145864	+	0.989305i	$0.546596\pi$
$192$	966.713	0.363367
$193$	1399.89	0.522105	0.261053	−	0.965325i	$-0.415930\pi$
$193$	1399.89	0.522105	0.261053	+	0.965325i	$0.415930\pi$
$194$	3628.38	1.34280
$195$	88.2368	0.0324040
$196$	−3677.02	−1.34002
$197$	−1934.20	−0.699524	−0.349762	−	0.936839i	$-0.613738\pi$
$197$	−1934.20	−0.699524	−0.349762	+	0.936839i	$0.613738\pi$
$198$	6813.27	2.44545
$199$	1830.37	0.652019	0.326009	−	0.945367i	$-0.394296\pi$
$199$	1830.37	0.652019	0.326009	+	0.945367i	$0.394296\pi$
$200$	1001.21	0.353980
$201$	−79.8506	−0.0280210
$202$	6971.87	2.42841
$203$	349.170	0.120724
$204$	1389.15	0.476765
$205$	139.165	0.0474132
$206$	1934.96	0.654442
$207$	0	0
$208$	329.765	0.109928
$209$	4323.76	1.43101
$210$	−102.935	−0.0338248
$211$	256.335	0.0836343	0.0418172	−	0.999125i	$-0.486685\pi$
$211$	256.335	0.0836343	0.0418172	+	0.999125i	$0.486685\pi$
$212$	4142.21	1.34192
$213$	−795.550	−0.255916
$214$	4720.37	1.50784
$215$	1532.06	0.485980
$216$	−826.704	−0.260417
$217$	407.582	0.127505
$218$	−317.100	−0.0985169
$219$	732.304	0.225957
$220$	4645.08	1.42351
$221$	1095.31	0.333388
$222$	1219.12	0.368566
$223$	−2476.81	−0.743763	−0.371882	−	0.928280i	$-0.621287\pi$
$223$	−2476.81	−0.743763	−0.371882	+	0.928280i	$0.621287\pi$
$224$	−676.486	−0.201784
$225$	1972.75	0.584519
$226$	8330.47	2.45192
$227$	1231.38	0.360042	0.180021	−	0.983663i	$-0.442383\pi$
$227$	1231.38	0.360042	0.180021	+	0.983663i	$0.442383\pi$
$228$	−940.774	−0.273264
$229$	−1448.21	−0.417906	−0.208953	−	0.977926i	$-0.567006\pi$
$229$	−1448.21	−0.417906	−0.208953	+	0.977926i	$0.567006\pi$
$230$	0	0
$231$	209.664	0.0597182
$232$	1606.37	0.454582
$233$	−3319.77	−0.933415	−0.466707	−	0.884412i	$-0.654560\pi$
$233$	−3319.77	−0.933415	−0.466707	+	0.884412i	$0.654560\pi$
$234$	−1168.88	−0.326546
$235$	3368.74	0.935116
$236$	−7327.77	−2.02117
$237$	141.911	0.0388951
$238$	−1277.77	−0.348007
$239$	−1895.45	−0.512998	−0.256499	−	0.966545i	$-0.582569\pi$
$239$	−1895.45	−0.512998	−0.256499	+	0.966545i	$0.582569\pi$
$240$	263.242	0.0708009
$241$	6551.95	1.75124	0.875618	−	0.483004i	$-0.160454\pi$
$241$	6551.95	1.75124	0.875618	+	0.483004i	$0.160454\pi$
$242$	−10561.1	−2.80533
$243$	−2466.27	−0.651074
$244$	−819.718	−0.215070
$245$	−2314.39	−0.603514
$246$	106.638	0.0276381
$247$	−741.779	−0.191086
$248$	1875.09	0.480115
$249$	377.976	0.0961978
$250$	6086.30	1.53973
$251$	−5181.59	−1.30302	−0.651512	−	0.758638i	$-0.725865\pi$
$251$	−5181.59	−1.30302	−0.651512	+	0.758638i	$0.725865\pi$
$252$	788.653	0.197145
$253$	0	0
$254$	−7248.33	−1.79055
$255$	874.359	0.214724
$256$	−358.578	−0.0875435
$257$	5889.87	1.42957	0.714786	−	0.699344i	$-0.246524\pi$
$257$	5889.87	1.42957	0.714786	+	0.699344i	$0.246524\pi$
$258$	1173.97	0.283288
$259$	−648.562	−0.155597
$260$	−796.904	−0.190084
$261$	3165.14	0.750641
$262$	5483.02	1.29291
$263$	−3363.44	−0.788588	−0.394294	−	0.918984i	$-0.629011\pi$
$263$	−3363.44	−0.788588	−0.394294	+	0.918984i	$0.629011\pi$
$264$	964.566	0.224867
$265$	2607.19	0.604371
$266$	865.344	0.199465
$267$	1847.95	0.423567
$268$	721.164	0.164374
$269$	−894.130	−0.202662	−0.101331	−	0.994853i	$-0.532310\pi$
$269$	−894.130	−0.202662	−0.101331	+	0.994853i	$0.532310\pi$
$270$	−1920.14	−0.432800
$271$	5532.27	1.24008	0.620039	−	0.784571i	$-0.287117\pi$
$271$	5532.27	1.24008	0.620039	+	0.784571i	$0.287117\pi$
$272$	3267.72	0.728435
$273$	−35.9697	−0.00797431
$274$	−1712.28	−0.377527
$275$	−4736.60	−1.03865
$276$	0	0
$277$	7236.06	1.56958	0.784788	−	0.619764i	$-0.212772\pi$
$277$	7236.06	1.56958	0.784788	+	0.619764i	$0.212772\pi$
$278$	−8038.45	−1.73422
$279$	3694.63	0.792802
$280$	251.929	0.0537702
$281$	494.245	0.104926	0.0524629	−	0.998623i	$-0.483293\pi$
$281$	494.245	0.104926	0.0524629	+	0.998623i	$0.483293\pi$
$282$	2581.36	0.545098
$283$	−1950.85	−0.409774	−0.204887	−	0.978786i	$-0.565683\pi$
$283$	−1950.85	−0.409774	−0.204887	+	0.978786i	$0.565683\pi$
$284$	7184.94	1.50123
$285$	−592.142	−0.123072
$286$	2806.49	0.580248
$287$	−56.7306	−0.0116679
$288$	−6132.18	−1.25466
$289$	5940.72	1.20918
$290$	3731.02	0.755492
$291$	1012.13	0.203891
$292$	−6613.75	−1.32548
$293$	−571.874	−0.114025	−0.0570123	−	0.998373i	$-0.518157\pi$
$293$	−571.874	−0.114025	−0.0570123	+	0.998373i	$0.518157\pi$
$294$	−1773.44	−0.351801
$295$	−4612.24	−0.910288
$296$	−2983.73	−0.585898
$297$	3911.05	0.764114
$298$	12438.3	2.41789
$299$	0	0
$300$	1030.60	0.198339
$301$	−624.545	−0.119595
$302$	−214.017	−0.0407791
$303$	1944.79	0.368731
$304$	−2212.99	−0.417513
$305$	−515.947	−0.0968624
$306$	−11582.7	−2.16385
$307$	−7821.66	−1.45409	−0.727045	−	0.686590i	$-0.759107\pi$
$307$	−7821.66	−1.45409	−0.727045	+	0.686590i	$0.759107\pi$
$308$	−1893.57	−0.350312
$309$	539.755	0.0993707
$310$	4355.17	0.797926
$311$	−1985.57	−0.362031	−0.181015	−	0.983480i	$-0.557938\pi$
$311$	−1985.57	−0.362031	−0.181015	+	0.983480i	$0.557938\pi$
$312$	−165.480	−0.0300271
$313$	−7292.61	−1.31694	−0.658470	−	0.752607i	$-0.728796\pi$
$313$	−7292.61	−1.31694	−0.658470	+	0.752607i	$0.728796\pi$
$314$	−2909.55	−0.522915
$315$	496.394	0.0887893
$316$	−1281.66	−0.228162
$317$	372.809	0.0660537	0.0330269	−	0.999454i	$-0.489485\pi$
$317$	372.809	0.0660537	0.0330269	+	0.999454i	$0.489485\pi$
$318$	1997.81	0.352300
$319$	−7599.54	−1.33383
$320$	−5495.34	−0.959996
$321$	1316.74	0.228951
$322$	0	0
$323$	−7350.46	−1.26622
$324$	6711.50	1.15081
$325$	812.606	0.138693
$326$	−5056.03	−0.858981
$327$	−88.4545	−0.0149589
$328$	−260.990	−0.0439353
$329$	−1373.27	−0.230123
$330$	2240.34	0.373718
$331$	−4472.35	−0.742667	−0.371333	−	0.928500i	$-0.621099\pi$
$331$	−4472.35	−0.742667	−0.371333	+	0.928500i	$0.621099\pi$
$332$	−3413.66	−0.564304
$333$	−5879.06	−0.967479
$334$	16070.6	2.63276
$335$	453.915	0.0740299
$336$	−107.311	−0.0174234
$337$	716.498	0.115816	0.0579082	−	0.998322i	$-0.481557\pi$
$337$	716.498	0.115816	0.0579082	+	0.998322i	$0.481557\pi$
$338$	9088.43	1.46256
$339$	2323.78	0.372301
$340$	−7896.71	−1.25959
$341$	−8870.85	−1.40875
$342$	7844.13	1.24024
$343$	1909.25	0.300553
$344$	−2873.24	−0.450333
$345$	0	0
$346$	946.122	0.147005
$347$	5002.34	0.773890	0.386945	−	0.922103i	$-0.373530\pi$
$347$	5002.34	0.773890	0.386945	+	0.922103i	$0.373530\pi$
$348$	1653.53	0.254708
$349$	−9318.44	−1.42924	−0.714620	−	0.699513i	$-0.753400\pi$
$349$	−9318.44	−1.42924	−0.714620	+	0.699513i	$0.753400\pi$
$350$	−947.969	−0.144775
$351$	−670.974	−0.102034
$352$	14723.4	2.22944
$353$	2698.03	0.406804	0.203402	−	0.979095i	$-0.434800\pi$
$353$	2698.03	0.406804	0.203402	+	0.979095i	$0.434800\pi$
$354$	−3534.21	−0.530625
$355$	4522.35	0.676116
$356$	−16689.6	−2.48468
$357$	−356.433	−0.0528415
$358$	5260.64	0.776630
$359$	−9845.40	−1.44741	−0.723705	−	0.690109i	$-0.757563\pi$
$359$	−9845.40	−1.44741	−0.723705	+	0.690109i	$0.757563\pi$
$360$	2283.67	0.334334
$361$	−1881.05	−0.274246
$362$	10670.6	1.54927
$363$	−2945.99	−0.425963
$364$	324.858	0.0467780
$365$	−4162.82	−0.596965
$366$	−395.354	−0.0564630
$367$	614.211	0.0873612	0.0436806	−	0.999046i	$-0.486092\pi$
$367$	614.211	0.0873612	0.0436806	+	0.999046i	$0.486092\pi$
$368$	0	0
$369$	−514.248	−0.0725493
$370$	−6930.14	−0.973732
$371$	−1062.82	−0.148730
$372$	1930.14	0.269014
$373$	5940.84	0.824679	0.412339	−	0.911030i	$-0.364712\pi$
$373$	5940.84	0.824679	0.412339	+	0.911030i	$0.364712\pi$
$374$	27810.1	3.84499
$375$	1697.77	0.233793
$376$	−6317.75	−0.866523
$377$	1303.77	0.178110
$378$	782.745	0.106508
$379$	−9409.56	−1.27529	−0.637647	−	0.770328i	$-0.720092\pi$
$379$	−9409.56	−1.27529	−0.637647	+	0.770328i	$0.720092\pi$
$380$	5347.89	0.721949
$381$	−2021.91	−0.271879
$382$	3354.32	0.449272
$383$	11899.0	1.58749	0.793746	−	0.608250i	$-0.208128\pi$
$383$	11899.0	1.58749	0.793746	+	0.608250i	$0.208128\pi$
$384$	−1875.48	−0.249239
$385$	−1191.85	−0.157772
$386$	−6097.78	−0.804064
$387$	−5661.35	−0.743624
$388$	−9141.00	−1.19604
$389$	11759.3	1.53270	0.766348	−	0.642426i	$-0.222072\pi$
$389$	11759.3	1.53270	0.766348	+	0.642426i	$0.222072\pi$
$390$	−384.350	−0.0499034
$391$	0	0
$392$	4340.42	0.559245
$393$	1529.48	0.196316
$394$	8425.19	1.07730
$395$	−806.704	−0.102759
$396$	−17164.7	−2.17818
$397$	−10853.1	−1.37204	−0.686019	−	0.727584i	$-0.740643\pi$
$397$	−10853.1	−1.37204	−0.686019	+	0.727584i	$0.740643\pi$
$398$	−7972.91	−1.00414
$399$	241.387	0.0302868
$400$	2424.30	0.303037
$401$	−1378.13	−0.171623	−0.0858113	−	0.996311i	$-0.527348\pi$
$401$	−1378.13	−0.171623	−0.0858113	+	0.996311i	$0.527348\pi$
$402$	347.821	0.0431535
$403$	1521.87	0.188114
$404$	−17564.3	−2.16301
$405$	4224.35	0.518296
$406$	−1520.95	−0.185920
$407$	14115.7	1.71914
$408$	−1639.78	−0.198973
$409$	−11977.0	−1.44799	−0.723993	−	0.689807i	$-0.757695\pi$
$409$	−11977.0	−1.44799	−0.723993	+	0.689807i	$0.757695\pi$
$410$	−606.188	−0.0730183
$411$	−477.637	−0.0573238
$412$	−4874.75	−0.582917
$413$	1880.18	0.224014
$414$	0	0
$415$	−2148.63	−0.254149
$416$	−2525.93	−0.297702
$417$	−2242.32	−0.263326
$418$	−18833.8	−2.20381
$419$	−5975.13	−0.696669	−0.348334	−	0.937370i	$-0.613253\pi$
$419$	−5975.13	−0.696669	−0.348334	+	0.937370i	$0.613253\pi$
$420$	259.325	0.0301281
$421$	9072.18	1.05024	0.525120	−	0.851028i	$-0.324021\pi$
$421$	9072.18	1.05024	0.525120	+	0.851028i	$0.324021\pi$
$422$	−1116.57	−0.128800
$423$	−12448.3	−1.43087
$424$	−4889.53	−0.560039
$425$	8052.30	0.919045
$426$	3465.33	0.394122
$427$	210.326	0.0238369
$428$	−11892.1	−1.34305
$429$	782.866	0.0881052
$430$	−6673.50	−0.748430
$431$	−674.927	−0.0754295	−0.0377147	−	0.999289i	$-0.512008\pi$
$431$	−674.927	−0.0754295	−0.0377147	+	0.999289i	$0.512008\pi$
$432$	−2001.76	−0.222939
$433$	−961.281	−0.106689	−0.0533444	−	0.998576i	$-0.516988\pi$
$433$	−961.281	−0.106689	−0.0533444	+	0.998576i	$0.516988\pi$
$434$	−1775.39	−0.196362
$435$	1040.76	0.114714
$436$	798.870	0.0877499
$437$	0	0
$438$	−3189.84	−0.347983
$439$	−12697.1	−1.38041	−0.690204	−	0.723615i	$-0.742479\pi$
$439$	−12697.1	−1.38041	−0.690204	+	0.723615i	$0.742479\pi$
$440$	−5483.13	−0.594086
$441$	8552.24	0.923468
$442$	−4771.07	−0.513432
$443$	3182.99	0.341374	0.170687	−	0.985325i	$-0.445401\pi$
$443$	3182.99	0.341374	0.170687	+	0.985325i	$0.445401\pi$
$444$	−3071.33	−0.328285
$445$	−10504.8	−1.11904
$446$	10788.7	1.14543
$447$	3469.65	0.367133
$448$	2240.17	0.236246
$449$	8524.62	0.895995	0.447997	−	0.894035i	$-0.352137\pi$
$449$	8524.62	0.895995	0.447997	+	0.894035i	$0.352137\pi$
$450$	−8593.11	−0.900184
$451$	1234.72	0.128915
$452$	−20987.0	−2.18395
$453$	−59.6997	−0.00619192
$454$	−5363.77	−0.554480
$455$	204.472	0.0210677
$456$	1110.51	0.114044
$457$	2794.23	0.286015	0.143007	−	0.989722i	$-0.454323\pi$
$457$	2794.23	0.286015	0.143007	+	0.989722i	$0.454323\pi$
$458$	6308.26	0.643593
$459$	−6648.84	−0.676125
$460$	0	0
$461$	−4244.49	−0.428819	−0.214410	−	0.976744i	$-0.568783\pi$
$461$	−4244.49	−0.428819	−0.214410	+	0.976744i	$0.568783\pi$
$462$	−913.276	−0.0919685
$463$	8144.21	0.817480	0.408740	−	0.912651i	$-0.365968\pi$
$463$	8144.21	0.817480	0.408740	+	0.912651i	$0.365968\pi$
$464$	3889.61	0.389161
$465$	1214.87	0.121158
$466$	14460.6	1.43750
$467$	−9091.45	−0.900861	−0.450430	−	0.892812i	$-0.648729\pi$
$467$	−9091.45	−0.900861	−0.450430	+	0.892812i	$0.648729\pi$
$468$	2944.76	0.290858
$469$	−185.038	−0.0182181
$470$	−14673.9	−1.44012
$471$	−811.616	−0.0793997
$472$	8649.82	0.843517
$473$	13593.0	1.32136
$474$	−618.151	−0.0599001
$475$	−5453.26	−0.526763
$476$	3219.09	0.309972
$477$	−9634.20	−0.924779
$478$	8256.38	0.790038
$479$	−15793.5	−1.50652	−0.753259	−	0.657724i	$-0.771519\pi$
$479$	−15793.5	−1.50652	−0.753259	+	0.657724i	$0.771519\pi$
$480$	−2016.39	−0.191740
$481$	−2421.67	−0.229561
$482$	−28539.6	−2.69698
$483$	0	0
$484$	26606.5	2.49873
$485$	−5753.53	−0.538668
$486$	10742.8	1.00268
$487$	12182.4	1.13355	0.566775	−	0.823873i	$-0.308191\pi$
$487$	12182.4	1.13355	0.566775	+	0.823873i	$0.308191\pi$
$488$	967.609	0.0897574
$489$	−1410.37	−0.130428
$490$	10081.2	0.929437
$491$	7794.55	0.716422	0.358211	−	0.933641i	$-0.383387\pi$
$491$	7794.55	0.716422	0.358211	+	0.933641i	$0.383387\pi$
$492$	−268.653	−0.0246175
$493$	12919.3	1.18024
$494$	3231.11	0.294281
$495$	−10803.8	−0.981000
$496$	4540.29	0.411019
$497$	−1843.53	−0.166386
$498$	−1646.42	−0.148149
$499$	−2936.52	−0.263440	−0.131720	−	0.991287i	$-0.542050\pi$
$499$	−2936.52	−0.263440	−0.131720	+	0.991287i	$0.542050\pi$
$500$	−15333.2	−1.37145
$501$	4482.86	0.399760
$502$	22570.5	2.00671
$503$	12992.3	1.15168	0.575841	−	0.817561i	$-0.304675\pi$
$503$	12992.3	1.15168	0.575841	+	0.817561i	$0.304675\pi$
$504$	−930.940	−0.0822765
$505$	−11055.3	−0.974166
$506$	0	0
$507$	2535.21	0.222076
$508$	18260.8	1.59486
$509$	9151.18	0.796894	0.398447	−	0.917191i	$-0.369549\pi$
$509$	9151.18	0.796894	0.398447	+	0.917191i	$0.369549\pi$
$510$	−3808.62	−0.330683
$511$	1696.97	0.146908
$512$	−10786.2	−0.931029
$513$	4502.79	0.387530
$514$	−25655.6	−2.20160
$515$	−3068.27	−0.262532
$516$	−2957.59	−0.252327
$517$	29888.5	2.54255
$518$	2825.07	0.239626
$519$	263.920	0.0223214
$520$	940.679	0.0793298
$521$	7732.59	0.650232	0.325116	−	0.945674i	$-0.394597\pi$
$521$	7732.59	0.650232	0.325116	+	0.945674i	$0.394597\pi$
$522$	−13787.0	−1.15602
$523$	−10321.1	−0.862926	−0.431463	−	0.902131i	$-0.642002\pi$
$523$	−10321.1	−0.862926	−0.431463	+	0.902131i	$0.642002\pi$
$524$	−13813.4	−1.15160
$525$	−264.435	−0.0219826
$526$	14650.8	1.21446
$527$	15080.6	1.24653
$528$	2335.57	0.192505
$529$	0	0
$530$	−11356.6	−0.930757
$531$	17043.4	1.39288
$532$	−2180.07	−0.177665
$533$	−211.826	−0.0172143
$534$	−8049.46	−0.652311
$535$	−7485.10	−0.604877
$536$	−851.274	−0.0685997
$537$	1467.45	0.117924
$538$	3894.74	0.312108
$539$	−20534.0	−1.64093
$540$	4837.42	0.385499
$541$	−4989.41	−0.396509	−0.198255	−	0.980151i	$-0.563527\pi$
$541$	−4989.41	−0.396509	−0.198255	+	0.980151i	$0.563527\pi$
$542$	−24098.0	−1.90977
$543$	2976.56	0.235242
$544$	−25030.1	−1.97271
$545$	502.825	0.0395205
$546$	156.680	0.0122808
$547$	10608.8	0.829250	0.414625	−	0.909992i	$-0.363913\pi$
$547$	10608.8	0.829250	0.414625	+	0.909992i	$0.363913\pi$
$548$	4313.74	0.336266
$549$	1906.55	0.148214
$550$	20632.2	1.59956
$551$	−8749.36	−0.676470
$552$	0	0
$553$	328.853	0.0252880
$554$	−31519.5	−2.41721
$555$	−1933.15	−0.147852
$556$	20251.3	1.54469
$557$	21645.4	1.64658	0.823290	−	0.567621i	$-0.192136\pi$
$557$	21645.4	1.64658	0.823290	+	0.567621i	$0.192136\pi$
$558$	−16093.4	−1.22095
$559$	−2331.99	−0.176445
$560$	610.014	0.0460318
$561$	7757.60	0.583826
$562$	−2152.88	−0.161590
$563$	5654.04	0.423250	0.211625	−	0.977351i	$-0.432125\pi$
$563$	5654.04	0.423250	0.211625	+	0.977351i	$0.432125\pi$
$564$	−6503.22	−0.485523
$565$	−13209.6	−0.983599
$566$	8497.71	0.631069
$567$	−1722.06	−0.127548
$568$	−8481.23	−0.626522
$569$	6738.40	0.496465	0.248232	−	0.968701i	$-0.420150\pi$
$569$	6738.40	0.496465	0.248232	+	0.968701i	$0.420150\pi$
$570$	2579.31	0.189536
$571$	2474.50	0.181357	0.0906783	−	0.995880i	$-0.471097\pi$
$571$	2474.50	0.181357	0.0906783	+	0.995880i	$0.471097\pi$
$572$	−7070.40	−0.516832
$573$	935.684	0.0682177
$574$	247.112	0.0179691
$575$	0	0
$576$	20306.6	1.46894
$577$	−2875.12	−0.207440	−0.103720	−	0.994607i	$-0.533075\pi$
$577$	−2875.12	−0.207440	−0.103720	+	0.994607i	$0.533075\pi$
$578$	−25877.1	−1.86219
$579$	−1700.97	−0.122089
$580$	−9399.57	−0.672924
$581$	875.888	0.0625438
$582$	−4408.74	−0.314001
$583$	23131.8	1.64326
$584$	7806.98	0.553176
$585$	1853.49	0.130995
$586$	2491.02	0.175603
$587$	−5764.27	−0.405310	−0.202655	−	0.979250i	$-0.564957\pi$
$587$	−5764.27	−0.405310	−0.202655	+	0.979250i	$0.564957\pi$
$588$	4467.85	0.313352
$589$	−10213.0	−0.714466
$590$	20090.4	1.40188
$591$	2350.20	0.163577
$592$	−7224.72	−0.501578
$593$	16156.4	1.11883	0.559414	−	0.828888i	$-0.311026\pi$
$593$	16156.4	1.11883	0.559414	+	0.828888i	$0.311026\pi$
$594$	−17036.1	−1.17677
$595$	2026.16	0.139604
$596$	−31335.8	−2.15363
$597$	−2224.04	−0.152468
$598$	0	0
$599$	−5962.96	−0.406744	−0.203372	−	0.979102i	$-0.565190\pi$
$599$	−5962.96	−0.406744	−0.203372	+	0.979102i	$0.565190\pi$
$600$	−1216.54	−0.0827751
$601$	−9334.47	−0.633546	−0.316773	−	0.948501i	$-0.602599\pi$
$601$	−9334.47	−0.633546	−0.316773	+	0.948501i	$0.602599\pi$
$602$	2720.45	0.184182
$603$	−1677.33	−0.113277
$604$	539.173	0.0363223
$605$	16746.7	1.12537
$606$	−8471.32	−0.567861
$607$	22294.8	1.49080	0.745402	−	0.666615i	$-0.232258\pi$
$607$	22294.8	1.49080	0.745402	+	0.666615i	$0.232258\pi$
$608$	16951.1	1.13069
$609$	−424.267	−0.0282301
$610$	2247.41	0.149172
$611$	−5127.64	−0.339513
$612$	29180.3	1.92736
$613$	2608.93	0.171899	0.0859493	−	0.996300i	$-0.472608\pi$
$613$	2608.93	0.171899	0.0859493	+	0.996300i	$0.472608\pi$
$614$	34070.3	2.23936
$615$	−169.095	−0.0110871
$616$	2235.20	0.146199
$617$	14919.0	0.973447	0.486724	−	0.873556i	$-0.338192\pi$
$617$	14919.0	0.973447	0.486724	+	0.873556i	$0.338192\pi$
$618$	−2351.11	−0.153035
$619$	10937.8	0.710223	0.355112	−	0.934824i	$-0.384443\pi$
$619$	10937.8	0.710223	0.355112	+	0.934824i	$0.384443\pi$
$620$	−10972.0	−0.710720
$621$	0	0
$622$	8648.95	0.557542
$623$	4282.26	0.275386
$624$	−400.688	−0.0257057
$625$	10.3632	0.000663242 0
$626$	31765.8	2.02814
$627$	−5253.68	−0.334628
$628$	7330.04	0.465765
$629$	−23996.9	−1.52117
$630$	−2162.24	−0.136739
$631$	10548.7	0.665512	0.332756	−	0.943013i	$-0.392022\pi$
$631$	10548.7	0.665512	0.332756	+	0.943013i	$0.392022\pi$
$632$	1512.90	0.0952211
$633$	−311.466	−0.0195571
$634$	−1623.92	−0.101725
$635$	11493.7	0.718288
$636$	−5033.08	−0.313797
$637$	3522.79	0.219118
$638$	33102.8	2.05416
$639$	−16711.2	−1.03456
$640$	10661.3	0.658475
$641$	232.746	0.0143415	0.00717076	−	0.999974i	$-0.497717\pi$
$641$	232.746	0.0143415	0.00717076	+	0.999974i	$0.497717\pi$
$642$	−5735.59	−0.352595
$643$	23503.0	1.44148	0.720738	−	0.693207i	$-0.243803\pi$
$643$	23503.0	1.44148	0.720738	+	0.693207i	$0.243803\pi$
$644$	0	0
$645$	−1861.57	−0.113642
$646$	32017.8	1.95004
$647$	−6178.11	−0.375404	−0.187702	−	0.982226i	$-0.560104\pi$
$647$	−6178.11	−0.375404	−0.187702	+	0.982226i	$0.560104\pi$
$648$	−7922.37	−0.480278
$649$	−40921.3	−2.47504
$650$	−3539.63	−0.213593
$651$	−495.242	−0.0298157
$652$	12737.7	0.765102
$653$	−9413.36	−0.564124	−0.282062	−	0.959396i	$-0.591018\pi$
$653$	−9413.36	−0.564124	−0.282062	+	0.959396i	$0.591018\pi$
$654$	385.299	0.0230373
$655$	−8694.42	−0.518655
$656$	−631.955	−0.0376123
$657$	15382.7	0.913447
$658$	5981.80	0.354400
$659$	−4233.22	−0.250232	−0.125116	−	0.992142i	$-0.539930\pi$
$659$	−4233.22	−0.250232	−0.125116	+	0.992142i	$0.539930\pi$
$660$	−5644.11	−0.332874
$661$	31794.6	1.87090	0.935450	−	0.353458i	$-0.114994\pi$
$661$	31794.6	1.87090	0.935450	+	0.353458i	$0.114994\pi$
$662$	19481.1	1.14374
$663$	−1330.88	−0.0779597
$664$	4029.54	0.235507
$665$	−1372.18	−0.0800161
$666$	25608.6	1.48996
$667$	0	0
$668$	−40486.6	−2.34502
$669$	3009.50	0.173922
$670$	−1977.21	−0.114009
$671$	−4577.65	−0.263366
$672$	821.979	0.0471853
$673$	−6124.16	−0.350771	−0.175386	−	0.984500i	$-0.556117\pi$
$673$	−6124.16	−0.350771	−0.175386	+	0.984500i	$0.556117\pi$
$674$	−3120.99	−0.178362
$675$	−4932.73	−0.281275
$676$	−22896.5	−1.30271
$677$	18065.3	1.02556	0.512782	−	0.858519i	$-0.328615\pi$
$677$	18065.3	1.02556	0.512782	+	0.858519i	$0.328615\pi$
$678$	−10122.1	−0.573360
$679$	2345.42	0.132561
$680$	9321.41	0.525676
$681$	−1496.22	−0.0841926
$682$	38640.5	2.16953
$683$	1279.84	0.0717007	0.0358503	−	0.999357i	$-0.488586\pi$
$683$	1279.84	0.0717007	0.0358503	+	0.999357i	$0.488586\pi$
$684$	−19761.7	−1.10469
$685$	2715.16	0.151446
$686$	−8316.47	−0.462864
$687$	1759.68	0.0977234
$688$	−6957.17	−0.385523
$689$	−3968.47	−0.219429
$690$	0	0
$691$	−5556.99	−0.305930	−0.152965	−	0.988232i	$-0.548882\pi$
$691$	−5556.99	−0.305930	−0.152965	+	0.988232i	$0.548882\pi$
$692$	−2383.57	−0.130939
$693$	4404.17	0.241415
$694$	−21789.7	−1.19182
$695$	12746.6	0.695691
$696$	−1951.85	−0.106300
$697$	−2099.04	−0.114070
$698$	40590.2	2.20109
$699$	4033.77	0.218270
$700$	2388.22	0.128952
$701$	−31951.4	−1.72152	−0.860762	−	0.509007i	$-0.830013\pi$
$701$	−31951.4	−1.72152	−0.860762	+	0.509007i	$0.830013\pi$
$702$	2922.69	0.157137
$703$	16251.4	0.871883
$704$	−48756.4	−2.61019
$705$	−4093.26	−0.218668
$706$	−11752.4	−0.626495
$707$	4506.69	0.239733
$708$	8903.76	0.472633
$709$	3547.49	0.187911	0.0939555	−	0.995576i	$-0.470049\pi$
$709$	3547.49	0.187911	0.0939555	+	0.995576i	$0.470049\pi$
$710$	−19698.9	−1.04125
$711$	2980.97	0.157236
$712$	19700.7	1.03696
$713$	0	0
$714$	1552.58	0.0813781
$715$	−4450.25	−0.232769
$716$	−13253.2	−0.691751
$717$	2303.11	0.119960
$718$	42885.6	2.22907
$719$	25203.2	1.30726	0.653630	−	0.756814i	$-0.273245\pi$
$719$	25203.2	1.30726	0.653630	+	0.756814i	$0.273245\pi$
$720$	5529.62	0.286218
$721$	1250.78	0.0646067
$722$	8193.66	0.422350
$723$	−7961.09	−0.409510
$724$	−26882.6	−1.37995
$725$	9584.77	0.490992
$726$	12832.4	0.656001
$727$	21182.3	1.08062	0.540309	−	0.841467i	$-0.318307\pi$
$727$	21182.3	1.08062	0.540309	+	0.841467i	$0.318307\pi$
$728$	−383.468	−0.0195223
$729$	−13516.3	−0.686698
$730$	18132.8	0.919351
$731$	−23108.2	−1.16921
$732$	996.017	0.0502921
$733$	−17463.6	−0.879992	−0.439996	−	0.898000i	$-0.645020\pi$
$733$	−17463.6	−0.879992	−0.439996	+	0.898000i	$0.645020\pi$
$734$	−2675.44	−0.134540
$735$	2812.15	0.141126
$736$	0	0
$737$	4027.28	0.201285
$738$	2240.01	0.111729
$739$	22488.7	1.11943	0.559715	−	0.828685i	$-0.310911\pi$
$739$	22488.7	1.11943	0.559715	+	0.828685i	$0.310911\pi$
$740$	17459.1	0.867311
$741$	901.315	0.0446837
$742$	4629.53	0.229051
$743$	−23783.1	−1.17432	−0.587158	−	0.809472i	$-0.699753\pi$
$743$	−23783.1	−1.17432	−0.587158	+	0.809472i	$0.699753\pi$
$744$	−2278.37	−0.112270
$745$	−19723.4	−0.969946
$746$	−25877.7	−1.27004
$747$	7939.70	0.388887
$748$	−70062.2	−3.42477
$749$	3051.30	0.148855
$750$	−7395.29	−0.360051
$751$	11747.5	0.570804	0.285402	−	0.958408i	$-0.407873\pi$
$751$	11747.5	0.570804	0.285402	+	0.958408i	$0.407873\pi$
$752$	−15297.6	−0.741817
$753$	6296.00	0.304700
$754$	−5679.08	−0.274297
$755$	339.367	0.0163587
$756$	−1971.97	−0.0948676
$757$	−36703.7	−1.76224	−0.881122	−	0.472889i	$-0.843211\pi$
$757$	−36703.7	−1.76224	−0.881122	+	0.472889i	$0.843211\pi$
$758$	40987.1	1.96401
$759$	0	0
$760$	−6312.73	−0.301299
$761$	−28852.6	−1.37438	−0.687191	−	0.726477i	$-0.741157\pi$
$761$	−28852.6	−1.37438	−0.687191	+	0.726477i	$0.741157\pi$
$762$	8807.25	0.418705
$763$	−204.977	−0.00972562
$764$	−8450.56	−0.400171
$765$	18366.6	0.868036
$766$	−51830.7	−2.44480
$767$	7020.41	0.330499
$768$	435.698	0.0204712
$769$	−10545.4	−0.494507	−0.247253	−	0.968951i	$-0.579528\pi$
$769$	−10545.4	−0.494507	−0.247253	+	0.968951i	$0.579528\pi$
$770$	5191.57	0.242975
$771$	−7156.61	−0.334292
$772$	15362.2	0.716187
$773$	−21237.3	−0.988166	−0.494083	−	0.869415i	$-0.664496\pi$
$773$	−21237.3	−0.988166	−0.494083	+	0.869415i	$0.664496\pi$
$774$	24660.2	1.14521
$775$	11188.2	0.518570
$776$	10790.2	0.499156
$777$	788.050	0.0363850
$778$	−51222.2	−2.36042
$779$	1421.53	0.0653808
$780$	968.296	0.0444494
$781$	40123.8	1.83834
$782$	0	0
$783$	−7914.21	−0.361214
$784$	10509.8	0.478761
$785$	4613.68	0.209770
$786$	−6662.26	−0.302335
$787$	−23004.3	−1.04195	−0.520976	−	0.853571i	$-0.674432\pi$
$787$	−23004.3	−1.04195	−0.520976	+	0.853571i	$0.674432\pi$
$788$	−21225.6	−0.959557
$789$	4086.82	0.184404
$790$	3513.92	0.158253
$791$	5384.91	0.242055
$792$	20261.5	0.909042
$793$	785.336	0.0351679
$794$	47274.8	2.11300
$795$	−3167.92	−0.141327
$796$	20086.2	0.894393
$797$	−26456.8	−1.17584	−0.587921	−	0.808918i	$-0.700054\pi$
$797$	−26456.8	−1.17584	−0.587921	+	0.808918i	$0.700054\pi$
$798$	−1051.46	−0.0466430
$799$	−50811.0	−2.24977
$800$	−18569.6	−0.820670
$801$	38817.6	1.71230
$802$	6003.00	0.264306
$803$	−36933.9	−1.62313
$804$	−876.266	−0.0384372
$805$	0	0
$806$	−6629.12	−0.289703
$807$	1086.43	0.0473906
$808$	20733.1	0.902710
$809$	−31408.6	−1.36498	−0.682490	−	0.730895i	$-0.739103\pi$
$809$	−31408.6	−1.36498	−0.682490	+	0.730895i	$0.739103\pi$
$810$	−18400.8	−0.798197
$811$	−1316.70	−0.0570104	−0.0285052	−	0.999594i	$-0.509075\pi$
$811$	−1316.70	−0.0570104	−0.0285052	+	0.999594i	$0.509075\pi$
$812$	3831.73	0.165600
$813$	−6722.10	−0.289981
$814$	−61486.5	−2.64754
$815$	8017.35	0.344584
$816$	−3970.51	−0.170338
$817$	15649.6	0.670147
$818$	52170.7	2.22996
$819$	−755.574	−0.0322368
$820$	1527.17	0.0650380
$821$	−16201.0	−0.688696	−0.344348	−	0.938842i	$-0.611900\pi$
$821$	−16201.0	−0.688696	−0.344348	+	0.938842i	$0.611900\pi$
$822$	2080.54	0.0882811
$823$	13927.7	0.589901	0.294950	−	0.955513i	$-0.404697\pi$
$823$	13927.7	0.589901	0.294950	+	0.955513i	$0.404697\pi$
$824$	5754.24	0.243275
$825$	5755.31	0.242878
$826$	−8189.87	−0.344990
$827$	12580.4	0.528974	0.264487	−	0.964389i	$-0.414797\pi$
$827$	12580.4	0.528974	0.264487	+	0.964389i	$0.414797\pi$
$828$	0	0
$829$	12109.2	0.507321	0.253660	−	0.967293i	$-0.418365\pi$
$829$	12109.2	0.507321	0.253660	+	0.967293i	$0.418365\pi$
$830$	9359.20	0.391401
$831$	−8792.34	−0.367031
$832$	8364.59	0.348546
$833$	34908.2	1.45198
$834$	9767.30	0.405532
$835$	−25483.1	−1.05614
$836$	47448.2	1.96296
$837$	−9238.16	−0.381503
$838$	26027.0	1.07290
$839$	−20504.9	−0.843753	−0.421877	−	0.906653i	$-0.638628\pi$
$839$	−20504.9	−0.843753	−0.421877	+	0.906653i	$0.638628\pi$
$840$	−306.112	−0.0125737
$841$	−9010.93	−0.369467
$842$	−39517.5	−1.61741
$843$	−600.543	−0.0245359
$844$	2812.98	0.114724
$845$	−14411.5	−0.586712
$846$	54223.6	2.20360
$847$	−6826.78	−0.276943
$848$	−11839.4	−0.479441
$849$	2370.43	0.0958219
$850$	−35075.0	−1.41537
$851$	0	0
$852$	−8730.23	−0.351048
$853$	−18615.6	−0.747228	−0.373614	−	0.927584i	$-0.621882\pi$
$853$	−18615.6	−0.747228	−0.373614	+	0.927584i	$0.621882\pi$
$854$	−916.157	−0.0367099
$855$	−12438.4	−0.497527
$856$	14037.6	0.560508
$857$	17837.6	0.710992	0.355496	−	0.934678i	$-0.384312\pi$
$857$	17837.6	0.710992	0.355496	+	0.934678i	$0.384312\pi$
$858$	−3410.08	−0.135686
$859$	32491.0	1.29055	0.645273	−	0.763952i	$-0.276744\pi$
$859$	32491.0	1.29055	0.645273	+	0.763952i	$0.276744\pi$
$860$	16812.6	0.666633
$861$	68.9317	0.00272844
$862$	2939.91	0.116165
$863$	−47564.6	−1.87615	−0.938074	−	0.346434i	$-0.887392\pi$
$863$	−47564.6	−1.87615	−0.938074	+	0.346434i	$0.887392\pi$
$864$	15333.1	0.603752
$865$	−1500.27	−0.0589718
$866$	4187.24	0.164305
$867$	−7218.40	−0.282756
$868$	4472.74	0.174902
$869$	−7157.34	−0.279397
$870$	−4533.45	−0.176665
$871$	−690.916	−0.0268781
$872$	−943.000	−0.0366216
$873$	21260.7	0.824244
$874$	0	0
$875$	3934.25	0.152002
$876$	8036.18	0.309951
$877$	−12801.2	−0.492893	−0.246447	−	0.969156i	$-0.579263\pi$
$877$	−12801.2	−0.492893	−0.246447	+	0.969156i	$0.579263\pi$
$878$	55307.2	2.12589
$879$	694.868	0.0266636
$880$	−13276.7	−0.508588
$881$	34858.0	1.33303	0.666514	−	0.745493i	$-0.267786\pi$
$881$	34858.0	1.33303	0.666514	+	0.745493i	$0.267786\pi$
$882$	−37252.7	−1.42218
$883$	15755.6	0.600472	0.300236	−	0.953865i	$-0.402935\pi$
$883$	15755.6	0.600472	0.300236	+	0.953865i	$0.402935\pi$
$884$	12019.8	0.457318
$885$	5604.21	0.212862
$886$	−13864.8	−0.525730
$887$	−21839.2	−0.826706	−0.413353	−	0.910571i	$-0.635642\pi$
$887$	−21839.2	−0.826706	−0.413353	+	0.910571i	$0.635642\pi$
$888$	3625.45	0.137007
$889$	−4685.40	−0.176764
$890$	45757.6	1.72337
$891$	37479.8	1.40923
$892$	−27180.1	−1.02024
$893$	34410.7	1.28949
$894$	−15113.4	−0.565401
$895$	−8341.80	−0.311548
$896$	−4346.07	−0.162045
$897$	0	0
$898$	−37132.4	−1.37987
$899$	17950.6	0.665948
$900$	21648.7	0.801802
$901$	−39324.5	−1.45404
$902$	−5378.30	−0.198534
$903$	758.867	0.0279662
$904$	24773.4	0.911451
$905$	−16920.4	−0.621497
$906$	260.046	0.00953581
$907$	−45581.2	−1.66869	−0.834343	−	0.551245i	$-0.814153\pi$
$907$	−45581.2	−1.66869	−0.834343	+	0.551245i	$0.814153\pi$
$908$	13513.0	0.493880
$909$	40852.0	1.49062
$910$	−890.659	−0.0324451
$911$	30487.3	1.10877	0.554384	−	0.832261i	$-0.312954\pi$
$911$	30487.3	1.10877	0.554384	+	0.832261i	$0.312954\pi$
$912$	2688.95	0.0976315
$913$	−19063.3	−0.691023
$914$	−12171.4	−0.440475
$915$	626.913	0.0226504
$916$	−15892.4	−0.573254
$917$	3544.28	0.127636
$918$	28961.6	1.04126
$919$	−50947.9	−1.82875	−0.914373	−	0.404874i	$-0.867315\pi$
$919$	−50947.9	−1.82875	−0.914373	+	0.404874i	$0.867315\pi$
$920$	0	0
$921$	9503.88	0.340025
$922$	18488.6	0.660400
$923$	−6883.58	−0.245478
$924$	2300.82	0.0819171
$925$	−17803.1	−0.632825
$926$	−35475.3	−1.25895
$927$	11338.0	0.401714
$928$	−29793.7	−1.05391
$929$	42988.1	1.51819	0.759093	−	0.650982i	$-0.225643\pi$
$929$	42988.1	1.51819	0.759093	+	0.650982i	$0.225643\pi$
$930$	−5291.85	−0.186588
$931$	−23640.9	−0.832221
$932$	−36430.6	−1.28039
$933$	2412.61	0.0846575
$934$	39601.4	1.38736
$935$	−44098.5	−1.54243
$936$	−3476.04	−0.121387
$937$	30733.5	1.07152	0.535762	−	0.844369i	$-0.320024\pi$
$937$	30733.5	1.07152	0.535762	+	0.844369i	$0.320024\pi$
$938$	806.008	0.0280566
$939$	8861.04	0.307954
$940$	36968.0	1.28273
$941$	−13558.5	−0.469708	−0.234854	−	0.972031i	$-0.575461\pi$
$941$	−13558.5	−0.469708	−0.234854	+	0.972031i	$0.575461\pi$
$942$	3535.31	0.122279
$943$	0	0
$944$	20944.4	0.722122
$945$	−1241.20	−0.0427261
$946$	−59209.5	−2.03496
$947$	35185.6	1.20737	0.603685	−	0.797223i	$-0.293699\pi$
$947$	35185.6	1.20737	0.603685	+	0.797223i	$0.293699\pi$
$948$	1557.31	0.0533535
$949$	6336.34	0.216740
$950$	23753.8	0.811238
$951$	−452.990	−0.0154461
$952$	−3799.87	−0.129364
$953$	3171.12	0.107789	0.0538944	−	0.998547i	$-0.482837\pi$
$953$	3171.12	0.107789	0.0538944	+	0.998547i	$0.482837\pi$
$954$	41965.6	1.42420
$955$	−5318.95	−0.180227
$956$	−20800.3	−0.703694
$957$	9233.99	0.311904
$958$	68794.7	2.32010
$959$	−1106.83	−0.0372696
$960$	6677.23	0.224486
$961$	−8837.42	−0.296647
$962$	10548.5	0.353533
$963$	27659.3	0.925553
$964$	71900.0	2.40222
$965$	9669.25	0.322553
$966$	0	0
$967$	−7514.18	−0.249886	−0.124943	−	0.992164i	$-0.539875\pi$
$967$	−7514.18	−0.249886	−0.124943	+	0.992164i	$0.539875\pi$
$968$	−31406.8	−1.04282
$969$	8931.34	0.296095
$970$	25061.8	0.829572
$971$	−22054.6	−0.728903	−0.364452	−	0.931222i	$-0.618744\pi$
$971$	−22054.6	−0.728903	−0.364452	+	0.931222i	$0.618744\pi$
$972$	−27064.4	−0.893097
$973$	−5196.14	−0.171203
$974$	−53065.4	−1.74571
$975$	−987.375	−0.0324321
$976$	2342.94	0.0768399
$977$	−2810.32	−0.0920268	−0.0460134	−	0.998941i	$-0.514652\pi$
$977$	−2810.32	−0.0920268	−0.0460134	+	0.998941i	$0.514652\pi$
$978$	6143.44	0.200865
$979$	−93201.6	−3.04263
$980$	−25397.7	−0.827858
$981$	−1858.06	−0.0604723
$982$	−33952.3	−1.10332
$983$	29820.0	0.967559	0.483780	−	0.875190i	$-0.339264\pi$
$983$	29820.0	0.967559	0.483780	+	0.875190i	$0.339264\pi$
$984$	317.122	0.0102739
$985$	−13359.8	−0.432162
$986$	−56275.3	−1.81762
$987$	1668.62	0.0538122
$988$	−8140.16	−0.262118
$989$	0	0
$990$	47060.3	1.51078
$991$	11549.1	0.370201	0.185100	−	0.982720i	$-0.440739\pi$
$991$	11549.1	0.370201	0.185100	+	0.982720i	$0.440739\pi$
$992$	−34777.8	−1.11310
$993$	5434.23	0.173666
$994$	8030.24	0.256241
$995$	12642.7	0.402813
$996$	4147.85	0.131957
$997$	32481.6	1.03180	0.515899	−	0.856650i	$-0.327458\pi$
$997$	32481.6	1.03180	0.515899	+	0.856650i	$0.327458\pi$
$998$	12791.2	0.405709
$999$	14700.2	0.465558

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.3		25
23.7	odd	22		23.4.c.a.3.5	✓	50
23.10	odd	22		23.4.c.a.8.5	yes	50
23.22	odd	2		529.4.a.n.1.3		25
69.53	even	22		207.4.i.a.118.1		50
69.56	even	22		207.4.i.a.100.1		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.3.5	✓	50	23.7	odd	22
23.4.c.a.8.5	yes	50	23.10	odd	22
207.4.i.a.100.1		50	69.56	even	22
207.4.i.a.118.1		50	69.53	even	22
529.4.a.m.1.3		25	1.1	even	1	trivial
529.4.a.n.1.3		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)

\(f(q)\)	\(=\)	\(q-4.35590 q^{2} -1.21507 q^{3} +10.9738 q^{4} +6.90715 q^{5} +5.29273 q^{6} -2.81570 q^{7} -12.9537 q^{8} -25.5236 q^{9} -30.0868 q^{10} +61.2825 q^{11} -13.3340 q^{12} -10.5135 q^{13} +12.2649 q^{14} -8.39268 q^{15} -31.3657 q^{16} -104.181 q^{17} +111.178 q^{18} +70.5546 q^{19} +75.7979 q^{20} +3.42128 q^{21} -266.940 q^{22} +15.7397 q^{24} -77.2913 q^{25} +45.7959 q^{26} +63.8200 q^{27} -30.8990 q^{28} -124.008 q^{29} +36.5576 q^{30} -144.754 q^{31} +240.255 q^{32} -74.4626 q^{33} +453.802 q^{34} -19.4484 q^{35} -280.092 q^{36} +230.338 q^{37} -307.328 q^{38} +12.7747 q^{39} -89.4731 q^{40} +20.1480 q^{41} -14.9027 q^{42} +221.808 q^{43} +672.503 q^{44} -176.295 q^{45} +487.718 q^{47} +38.1116 q^{48} -335.072 q^{49} +336.673 q^{50} +126.588 q^{51} -115.374 q^{52} +377.462 q^{53} -277.993 q^{54} +423.287 q^{55} +36.4737 q^{56} -85.7289 q^{57} +540.167 q^{58} -667.749 q^{59} -92.0999 q^{60} -74.6976 q^{61} +630.531 q^{62} +71.8667 q^{63} -795.601 q^{64} -72.6186 q^{65} +324.351 q^{66} +65.7167 q^{67} -1143.27 q^{68} +84.7154 q^{70} +654.734 q^{71} +330.625 q^{72} -602.684 q^{73} -1003.33 q^{74} +93.9145 q^{75} +774.254 q^{76} -172.553 q^{77} -55.6453 q^{78} -116.793 q^{79} -216.648 q^{80} +611.591 q^{81} -87.7624 q^{82} -311.073 q^{83} +37.5445 q^{84} -719.595 q^{85} -966.174 q^{86} +150.679 q^{87} -793.834 q^{88} -1520.85 q^{89} +767.924 q^{90} +29.6030 q^{91} +175.886 q^{93} -2124.45 q^{94} +487.331 q^{95} -291.927 q^{96} -832.982 q^{97} +1459.54 q^{98} -1564.15 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 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

Modular forms

Varieties

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Database

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