LMFDB - Embedded newform 538.4.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,4,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, 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("538.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	538.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:	$31.7430275831$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.00000 q^{2} -1.07079 q^{3} +4.00000 q^{4} +3.57975 q^{5} -2.14158 q^{6} +21.8456 q^{7} +8.00000 q^{8} -25.8534 q^{9} +7.15950 q^{10} -8.22614 q^{11} -4.28316 q^{12} +58.2254 q^{13} +43.6912 q^{14} -3.83316 q^{15} +16.0000 q^{16} +96.3094 q^{17} -51.7068 q^{18} -60.2758 q^{19} +14.3190 q^{20} -23.3921 q^{21} -16.4523 q^{22} -6.40795 q^{23} -8.56633 q^{24} -112.185 q^{25} +116.451 q^{26} +56.5949 q^{27} +87.3825 q^{28} -4.93073 q^{29} -7.66633 q^{30} +233.572 q^{31} +32.0000 q^{32} +8.80847 q^{33} +192.619 q^{34} +78.2019 q^{35} -103.414 q^{36} +412.339 q^{37} -120.552 q^{38} -62.3472 q^{39} +28.6380 q^{40} +164.282 q^{41} -46.7842 q^{42} -370.699 q^{43} -32.9045 q^{44} -92.5487 q^{45} -12.8159 q^{46} +280.972 q^{47} -17.1327 q^{48} +134.231 q^{49} -224.371 q^{50} -103.127 q^{51} +232.901 q^{52} -538.290 q^{53} +113.190 q^{54} -29.4475 q^{55} +174.765 q^{56} +64.5428 q^{57} -9.86146 q^{58} +109.523 q^{59} -15.3327 q^{60} +94.6721 q^{61} +467.143 q^{62} -564.784 q^{63} +64.0000 q^{64} +208.432 q^{65} +17.6169 q^{66} +886.190 q^{67} +385.238 q^{68} +6.86157 q^{69} +156.404 q^{70} +785.631 q^{71} -206.827 q^{72} +397.954 q^{73} +824.679 q^{74} +120.127 q^{75} -241.103 q^{76} -179.705 q^{77} -124.694 q^{78} -860.750 q^{79} +57.2760 q^{80} +637.441 q^{81} +328.564 q^{82} +546.057 q^{83} -93.5684 q^{84} +344.764 q^{85} -741.399 q^{86} +5.27978 q^{87} -65.8091 q^{88} +774.506 q^{89} -185.097 q^{90} +1271.97 q^{91} -25.6318 q^{92} -250.106 q^{93} +561.944 q^{94} -215.772 q^{95} -34.2653 q^{96} -815.667 q^{97} +268.463 q^{98} +212.674 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 42 q^{2} + 6 q^{3} + 84 q^{4} + 54 q^{5} + 12 q^{6} + 52 q^{7} + 168 q^{8} + 309 q^{9} + 108 q^{10} + 99 q^{11} + 24 q^{12} + 81 q^{13} + 104 q^{14} + 277 q^{15} + 336 q^{16} + 228 q^{17} + 618 q^{18}+ \cdots - 4470 q^{99}+O(q^{100}) $ 21 * q + 42 * q^2 + 6 * q^3 + 84 * q^4 + 54 * q^5 + 12 * q^6 + 52 * q^7 + 168 * q^8 + 309 * q^9 + 108 * q^10 + 99 * q^11 + 24 * q^12 + 81 * q^13 + 104 * q^14 + 277 * q^15 + 336 * q^16 + 228 * q^17 + 618 * q^18 + 51 * q^19 + 216 * q^20 + 235 * q^21 + 198 * q^22 + 691 * q^23 + 48 * q^24 + 1035 * q^25 + 162 * q^26 + 291 * q^27 + 208 * q^28 + 540 * q^29 + 554 * q^30 + 312 * q^31 + 672 * q^32 + 513 * q^33 + 456 * q^34 + 410 * q^35 + 1236 * q^36 + 1120 * q^37 + 102 * q^38 + 904 * q^39 + 432 * q^40 + 731 * q^41 + 470 * q^42 + 788 * q^43 + 396 * q^44 + 1771 * q^45 + 1382 * q^46 + 1570 * q^47 + 96 * q^48 + 2337 * q^49 + 2070 * q^50 + 973 * q^51 + 324 * q^52 + 1801 * q^53 + 582 * q^54 + 1191 * q^55 + 416 * q^56 + 2122 * q^57 + 1080 * q^58 + 1352 * q^59 + 1108 * q^60 + 1868 * q^61 + 624 * q^62 + 2302 * q^63 + 1344 * q^64 + 2552 * q^65 + 1026 * q^66 + 1968 * q^67 + 912 * q^68 + 823 * q^69 + 820 * q^70 + 868 * q^71 + 2472 * q^72 + 1587 * q^73 + 2240 * q^74 - 1978 * q^75 + 204 * q^76 - 2020 * q^77 + 1808 * q^78 + 1168 * q^79 + 864 * q^80 + 3069 * q^81 + 1462 * q^82 - 1506 * q^83 + 940 * q^84 + 871 * q^85 + 1576 * q^86 - 6155 * q^87 + 792 * q^88 + 1471 * q^89 + 3542 * q^90 - 2157 * q^91 + 2764 * q^92 - 677 * q^93 + 3140 * q^94 + 544 * q^95 + 192 * q^96 - 801 * q^97 + 4674 * q^98 - 4470 * q^99

Coefficient data

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

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

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

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	−1.07079	−0.206074	−0.103037	−	0.994678i	$-0.532856\pi$
$3$	−1.07079	−0.206074	−0.103037	+	0.994678i	$0.532856\pi$
$4$	4.00000	0.500000
$5$	3.57975	0.320183	0.160091	−	0.987102i	$-0.448821\pi$
$5$	3.57975	0.320183	0.160091	+	0.987102i	$0.448821\pi$
$6$	−2.14158	−0.145716
$7$	21.8456	1.17955	0.589776	−	0.807567i	$-0.299216\pi$
$7$	21.8456	1.17955	0.589776	+	0.807567i	$0.299216\pi$
$8$	8.00000	0.353553
$9$	−25.8534	−0.957534
$10$	7.15950	0.226403
$11$	−8.22614	−0.225479	−0.112740	−	0.993625i	$-0.535963\pi$
$11$	−8.22614	−0.225479	−0.112740	+	0.993625i	$0.535963\pi$
$12$	−4.28316	−0.103037
$13$	58.2254	1.24222	0.621108	−	0.783725i	$-0.286683\pi$
$13$	58.2254	1.24222	0.621108	+	0.783725i	$0.286683\pi$
$14$	43.6912	0.834070
$15$	−3.83316	−0.0659812
$16$	16.0000	0.250000
$17$	96.3094	1.37403	0.687014	−	0.726644i	$-0.258921\pi$
$17$	96.3094	1.37403	0.687014	+	0.726644i	$0.258921\pi$
$18$	−51.7068	−0.677078
$19$	−60.2758	−0.727801	−0.363901	−	0.931438i	$-0.618555\pi$
$19$	−60.2758	−0.727801	−0.363901	+	0.931438i	$0.618555\pi$
$20$	14.3190	0.160091
$21$	−23.3921	−0.243075
$22$	−16.4523	−0.159438
$23$	−6.40795	−0.0580935	−0.0290467	−	0.999578i	$-0.509247\pi$
$23$	−6.40795	−0.0580935	−0.0290467	+	0.999578i	$0.509247\pi$
$24$	−8.56633	−0.0728581
$25$	−112.185	−0.897483
$26$	116.451	0.878379
$27$	56.5949	0.403396
$28$	87.3825	0.589776
$29$	−4.93073	−0.0315729	−0.0157864	−	0.999875i	$-0.505025\pi$
$29$	−4.93073	−0.0315729	−0.0157864	+	0.999875i	$0.505025\pi$
$30$	−7.66633	−0.0466558
$31$	233.572	1.35325	0.676625	−	0.736328i	$-0.263442\pi$
$31$	233.572	1.35325	0.676625	+	0.736328i	$0.263442\pi$
$32$	32.0000	0.176777
$33$	8.80847	0.0464654
$34$	192.619	0.971584
$35$	78.2019	0.377672
$36$	−103.414	−0.478767
$37$	412.339	1.83211	0.916056	−	0.401049i	$-0.131354\pi$
$37$	412.339	1.83211	0.916056	+	0.401049i	$0.131354\pi$
$38$	−120.552	−0.514633
$39$	−62.3472	−0.255988
$40$	28.6380	0.113202
$41$	164.282	0.625769	0.312885	−	0.949791i	$-0.398705\pi$
$41$	164.282	0.625769	0.312885	+	0.949791i	$0.398705\pi$
$42$	−46.7842	−0.171880
$43$	−370.699	−1.31468	−0.657339	−	0.753595i	$-0.728318\pi$
$43$	−370.699	−1.31468	−0.657339	+	0.753595i	$0.728318\pi$
$44$	−32.9045	−0.112740
$45$	−92.5487	−0.306586
$46$	−12.8159	−0.0410783
$47$	280.972	0.871999	0.436000	−	0.899947i	$-0.356395\pi$
$47$	280.972	0.871999	0.436000	+	0.899947i	$0.356395\pi$
$48$	−17.1327	−0.0515184
$49$	134.231	0.391345
$50$	−224.371	−0.634616
$51$	−103.127	−0.283151
$52$	232.901	0.621108
$53$	−538.290	−1.39509	−0.697545	−	0.716541i	$-0.745724\pi$
$53$	−538.290	−1.39509	−0.697545	+	0.716541i	$0.745724\pi$
$54$	113.190	0.285244
$55$	−29.4475	−0.0721946
$56$	174.765	0.417035
$57$	64.5428	0.149981
$58$	−9.86146	−0.0223254
$59$	109.523	0.241673	0.120837	−	0.992672i	$-0.461442\pi$
$59$	109.523	0.241673	0.120837	+	0.992672i	$0.461442\pi$
$60$	−15.3327	−0.0329906
$61$	94.6721	0.198713	0.0993567	−	0.995052i	$-0.468322\pi$
$61$	94.6721	0.198713	0.0993567	+	0.995052i	$0.468322\pi$
$62$	467.143	0.956892
$63$	−564.784	−1.12946
$64$	64.0000	0.125000
$65$	208.432	0.397736
$66$	17.6169	0.0328560
$67$	886.190	1.61590	0.807950	−	0.589251i	$-0.200577\pi$
$67$	886.190	1.61590	0.807950	+	0.589251i	$0.200577\pi$
$68$	385.238	0.687014
$69$	6.86157	0.0119715
$70$	156.404	0.267055
$71$	785.631	1.31320	0.656600	−	0.754239i	$-0.271994\pi$
$71$	785.631	1.31320	0.656600	+	0.754239i	$0.271994\pi$
$72$	−206.827	−0.338539
$73$	397.954	0.638041	0.319020	−	0.947748i	$-0.396646\pi$
$73$	397.954	0.638041	0.319020	+	0.947748i	$0.396646\pi$
$74$	824.679	1.29550
$75$	120.127	0.184948
$76$	−241.103	−0.363901
$77$	−179.705	−0.265965
$78$	−124.694	−0.181011
$79$	−860.750	−1.22585	−0.612924	−	0.790142i	$-0.710007\pi$
$79$	−860.750	−1.22585	−0.612924	+	0.790142i	$0.710007\pi$
$80$	57.2760	0.0800456
$81$	637.441	0.874404
$82$	328.564	0.442486
$83$	546.057	0.722140	0.361070	−	0.932539i	$-0.382412\pi$
$83$	546.057	0.722140	0.361070	+	0.932539i	$0.382412\pi$
$84$	−93.5684	−0.121537
$85$	344.764	0.439940
$86$	−741.399	−0.929617
$87$	5.27978	0.00650634
$88$	−65.8091	−0.0797190
$89$	774.506	0.922443	0.461222	−	0.887285i	$-0.347411\pi$
$89$	774.506	0.922443	0.461222	+	0.887285i	$0.347411\pi$
$90$	−185.097	−0.216789
$91$	1271.97	1.46526
$92$	−25.6318	−0.0290467
$93$	−250.106	−0.278869
$94$	561.944	0.616597
$95$	−215.772	−0.233029
$96$	−34.2653	−0.0364290
$97$	−815.667	−0.853798	−0.426899	−	0.904299i	$-0.640394\pi$
$97$	−815.667	−0.853798	−0.426899	+	0.904299i	$0.640394\pi$
$98$	268.463	0.276723
$99$	212.674	0.215904
$100$	−448.742	−0.448742
$101$	502.110	0.494671	0.247336	−	0.968930i	$-0.420445\pi$
$101$	502.110	0.494671	0.247336	+	0.968930i	$0.420445\pi$
$102$	−206.254	−0.200218
$103$	−185.721	−0.177666	−0.0888331	−	0.996047i	$-0.528314\pi$
$103$	−185.721	−0.177666	−0.0888331	+	0.996047i	$0.528314\pi$
$104$	465.803	0.439190
$105$	−83.7379	−0.0778284
$106$	−1076.58	−0.986477
$107$	−1365.90	−1.23408	−0.617042	−	0.786930i	$-0.711669\pi$
$107$	−1365.90	−1.23408	−0.617042	+	0.786930i	$0.711669\pi$
$108$	226.380	0.201698
$109$	−2096.35	−1.84215	−0.921074	−	0.389388i	$-0.872686\pi$
$109$	−2096.35	−1.84215	−0.921074	+	0.389388i	$0.872686\pi$
$110$	−58.8950	−0.0510493
$111$	−441.529	−0.377550
$112$	349.530	0.294888
$113$	2208.72	1.83875	0.919374	−	0.393385i	$-0.128696\pi$
$113$	2208.72	1.83875	0.919374	+	0.393385i	$0.128696\pi$
$114$	129.086	0.106052
$115$	−22.9389	−0.0186005
$116$	−19.7229	−0.0157864
$117$	−1505.32	−1.18946
$118$	219.046	0.170889
$119$	2103.94	1.62074
$120$	−30.6653	−0.0233279
$121$	−1263.33	−0.949159
$122$	189.344	0.140512
$123$	−175.912	−0.128955
$124$	934.287	0.676625
$125$	−849.064	−0.607541
$126$	−1129.57	−0.798650
$127$	−1467.93	−1.02565	−0.512826	−	0.858493i	$-0.671401\pi$
$127$	−1467.93	−1.02565	−0.512826	+	0.858493i	$0.671401\pi$
$128$	128.000	0.0883883
$129$	396.942	0.270921
$130$	416.864	0.281242
$131$	1897.13	1.26529	0.632645	−	0.774442i	$-0.281969\pi$
$131$	1897.13	1.26529	0.632645	+	0.774442i	$0.281969\pi$
$132$	35.2339	0.0232327
$133$	−1316.76	−0.858480
$134$	1772.38	1.14261
$135$	202.596	0.129160
$136$	770.475	0.485792
$137$	−2858.81	−1.78281	−0.891404	−	0.453210i	$-0.850279\pi$
$137$	−2858.81	−1.78281	−0.891404	+	0.453210i	$0.850279\pi$
$138$	13.7231	0.00846516
$139$	617.009	0.376504	0.188252	−	0.982121i	$-0.439718\pi$
$139$	617.009	0.376504	0.188252	+	0.982121i	$0.439718\pi$
$140$	312.807	0.188836
$141$	−300.862	−0.179696
$142$	1571.26	0.928573
$143$	−478.970	−0.280094
$144$	−413.655	−0.239383
$145$	−17.6508	−0.0101091
$146$	795.908	0.451163
$147$	−143.734	−0.0806459
$148$	1649.36	0.916056
$149$	−62.6156	−0.0344273	−0.0172137	−	0.999852i	$-0.505480\pi$
$149$	−62.6156	−0.0344273	−0.0172137	+	0.999852i	$0.505480\pi$
$150$	240.254	0.130778
$151$	−1001.39	−0.539683	−0.269841	−	0.962905i	$-0.586971\pi$
$151$	−1001.39	−0.539683	−0.269841	+	0.962905i	$0.586971\pi$
$152$	−482.207	−0.257317
$153$	−2489.93	−1.31568
$154$	−359.410	−0.188066
$155$	836.128	0.433287
$156$	−249.389	−0.127994
$157$	2783.04	1.41472	0.707358	−	0.706855i	$-0.249887\pi$
$157$	2783.04	1.41472	0.707358	+	0.706855i	$0.249887\pi$
$158$	−1721.50	−0.866805
$159$	576.396	0.287491
$160$	114.552	0.0566008
$161$	−139.986	−0.0685243
$162$	1274.88	0.618297
$163$	−2128.83	−1.02296	−0.511480	−	0.859295i	$-0.670903\pi$
$163$	−2128.83	−1.02296	−0.511480	+	0.859295i	$0.670903\pi$
$164$	657.128	0.312885
$165$	31.5321	0.0148774
$166$	1092.11	0.510630
$167$	−325.804	−0.150967	−0.0754834	−	0.997147i	$-0.524050\pi$
$167$	−325.804	−0.150967	−0.0754834	+	0.997147i	$0.524050\pi$
$168$	−187.137	−0.0859400
$169$	1193.19	0.543101
$170$	689.527	0.311084
$171$	1558.34	0.696894
$172$	−1482.80	−0.657339
$173$	−3267.42	−1.43594	−0.717969	−	0.696075i	$-0.754928\pi$
$173$	−3267.42	−1.43594	−0.717969	+	0.696075i	$0.754928\pi$
$174$	10.5596	0.00460068
$175$	−2450.76	−1.05863
$176$	−131.618	−0.0563698
$177$	−117.276	−0.0498025
$178$	1549.01	0.652266
$179$	−3804.63	−1.58867	−0.794335	−	0.607481i	$-0.792180\pi$
$179$	−3804.63	−1.58867	−0.794335	+	0.607481i	$0.792180\pi$
$180$	−370.195	−0.153293
$181$	1711.08	0.702674	0.351337	−	0.936249i	$-0.385727\pi$
$181$	1711.08	0.702674	0.351337	+	0.936249i	$0.385727\pi$
$182$	2543.94	1.03609
$183$	−101.374	−0.0409496
$184$	−51.2636	−0.0205391
$185$	1476.07	0.586611
$186$	−500.213	−0.197190
$187$	−792.254	−0.309815
$188$	1123.89	0.436000
$189$	1236.35	0.475827
$190$	−431.545	−0.164777
$191$	152.979	0.0579536	0.0289768	−	0.999580i	$-0.490775\pi$
$191$	152.979	0.0579536	0.0289768	+	0.999580i	$0.490775\pi$
$192$	−68.5306	−0.0257592
$193$	−1941.96	−0.724275	−0.362138	−	0.932125i	$-0.617953\pi$
$193$	−1941.96	−0.724275	−0.362138	+	0.932125i	$0.617953\pi$
$194$	−1631.33	−0.603727
$195$	−223.187	−0.0819630
$196$	536.925	0.195672
$197$	−3797.57	−1.37343	−0.686715	−	0.726927i	$-0.740948\pi$
$197$	−3797.57	−1.37343	−0.686715	+	0.726927i	$0.740948\pi$
$198$	425.347	0.152667
$199$	−3201.64	−1.14049	−0.570246	−	0.821474i	$-0.693152\pi$
$199$	−3201.64	−1.14049	−0.570246	+	0.821474i	$0.693152\pi$
$200$	−897.483	−0.317308
$201$	−948.924	−0.332995
$202$	1004.22	0.349785
$203$	−107.715	−0.0372419
$204$	−412.509	−0.141576
$205$	588.088	0.200360
$206$	−371.442	−0.125629
$207$	165.667	0.0556264
$208$	931.606	0.310554
$209$	495.837	0.164104
$210$	−167.476	−0.0550330
$211$	−3485.21	−1.13712	−0.568559	−	0.822642i	$-0.692499\pi$
$211$	−3485.21	−1.13712	−0.568559	+	0.822642i	$0.692499\pi$
$212$	−2153.16	−0.697545
$213$	−841.246	−0.270616
$214$	−2731.81	−0.872629
$215$	−1327.01	−0.420937
$216$	452.760	0.142622
$217$	5102.52	1.59623
$218$	−4192.70	−1.30259
$219$	−426.125	−0.131483
$220$	−117.790	−0.0360973
$221$	5607.65	1.70684
$222$	−883.059	−0.266968
$223$	−4524.34	−1.35862	−0.679309	−	0.733852i	$-0.737721\pi$
$223$	−4524.34	−1.35862	−0.679309	+	0.733852i	$0.737721\pi$
$224$	699.060	0.208517
$225$	2900.37	0.859370
$226$	4417.43	1.30019
$227$	−5620.04	−1.64324	−0.821620	−	0.570036i	$-0.806929\pi$
$227$	−5620.04	−1.64324	−0.821620	+	0.570036i	$0.806929\pi$
$228$	258.171	0.0749904
$229$	6124.22	1.76725	0.883624	−	0.468198i	$-0.155097\pi$
$229$	6124.22	1.76725	0.883624	+	0.468198i	$0.155097\pi$
$230$	−45.8777	−0.0131526
$231$	192.427	0.0548084
$232$	−39.4458	−0.0111627
$233$	2786.25	0.783404	0.391702	−	0.920092i	$-0.371886\pi$
$233$	2786.25	0.783404	0.391702	+	0.920092i	$0.371886\pi$
$234$	−3010.65	−0.841078
$235$	1005.81	0.279199
$236$	438.093	0.120837
$237$	921.684	0.252615
$238$	4207.88	1.14603
$239$	−4121.43	−1.11545	−0.557727	−	0.830025i	$-0.688326\pi$
$239$	−4121.43	−1.11545	−0.557727	+	0.830025i	$0.688326\pi$
$240$	−61.3306	−0.0164953
$241$	−3587.84	−0.958976	−0.479488	−	0.877548i	$-0.659178\pi$
$241$	−3587.84	−0.958976	−0.479488	+	0.877548i	$0.659178\pi$
$242$	−2526.66	−0.671157
$243$	−2210.63	−0.583588
$244$	378.688	0.0993567
$245$	480.515	0.125302
$246$	−351.823	−0.0911847
$247$	−3509.58	−0.904086
$248$	1868.57	0.478446
$249$	−584.713	−0.148814
$250$	−1698.13	−0.429596
$251$	−741.237	−0.186400	−0.0932001	−	0.995647i	$-0.529710\pi$
$251$	−741.237	−0.186400	−0.0932001	+	0.995647i	$0.529710\pi$
$252$	−2259.14	−0.564731
$253$	52.7127	0.0130989
$254$	−2935.86	−0.725245
$255$	−369.170	−0.0906600
$256$	256.000	0.0625000
$257$	4479.55	1.08726	0.543632	−	0.839324i	$-0.317049\pi$
$257$	4479.55	1.08726	0.543632	+	0.839324i	$0.317049\pi$
$258$	793.883	0.191570
$259$	9007.81	2.16107
$260$	833.729	0.198868
$261$	127.476	0.0302321
$262$	3794.26	0.894695
$263$	−4976.09	−1.16669	−0.583343	−	0.812226i	$-0.698256\pi$
$263$	−4976.09	−1.16669	−0.583343	+	0.812226i	$0.698256\pi$
$264$	70.4678	0.0164280
$265$	−1926.94	−0.446683
$266$	−2633.53	−0.607037
$267$	−829.334	−0.190091
$268$	3544.76	0.807950
$269$	269.000	0.0609711
$269$	269.000	0.0609711
$270$	405.192	0.0913303
$271$	7800.47	1.74850	0.874252	−	0.485472i	$-0.161352\pi$
$271$	7800.47	1.74850	0.874252	+	0.485472i	$0.161352\pi$
$272$	1540.95	0.343507
$273$	−1362.01	−0.301952
$274$	−5717.62	−1.26064
$275$	922.852	0.202364
$276$	27.4463	0.00598577
$277$	−613.914	−0.133164	−0.0665821	−	0.997781i	$-0.521209\pi$
$277$	−613.914	−0.133164	−0.0665821	+	0.997781i	$0.521209\pi$
$278$	1234.02	0.266228
$279$	−6038.62	−1.29578
$280$	625.615	0.133527
$281$	6835.54	1.45115	0.725576	−	0.688142i	$-0.241573\pi$
$281$	6835.54	1.45115	0.725576	+	0.688142i	$0.241573\pi$
$282$	−601.724	−0.127064
$283$	−4487.09	−0.942508	−0.471254	−	0.881998i	$-0.656198\pi$
$283$	−4487.09	−0.942508	−0.471254	+	0.881998i	$0.656198\pi$
$284$	3142.52	0.656600
$285$	231.047	0.0480212
$286$	−957.939	−0.198056
$287$	3588.84	0.738128
$288$	−827.309	−0.169270
$289$	4362.50	0.887951
$290$	−35.3016	−0.00714820
$291$	873.409	0.175945
$292$	1591.82	0.319020
$293$	2822.15	0.562703	0.281351	−	0.959605i	$-0.409217\pi$
$293$	2822.15	0.562703	0.281351	+	0.959605i	$0.409217\pi$
$294$	−287.467	−0.0570253
$295$	392.066	0.0773795
$296$	3298.72	0.647750
$297$	−465.558	−0.0909576
$298$	−125.231	−0.0243438
$299$	−373.105	−0.0721646
$300$	480.508	0.0924739
$301$	−8098.16	−1.55073
$302$	−2002.78	−0.381613
$303$	−537.654	−0.101939
$304$	−964.413	−0.181950
$305$	338.902	0.0636246
$306$	−4979.85	−0.930324
$307$	−4371.54	−0.812694	−0.406347	−	0.913719i	$-0.633198\pi$
$307$	−4371.54	−0.812694	−0.406347	+	0.913719i	$0.633198\pi$
$308$	−718.820	−0.132982
$309$	198.868	0.0366124
$310$	1672.26	0.306380
$311$	2304.21	0.420127	0.210064	−	0.977688i	$-0.432633\pi$
$311$	2304.21	0.420127	0.210064	+	0.977688i	$0.432633\pi$
$312$	−498.777	−0.0905055
$313$	−1436.95	−0.259493	−0.129747	−	0.991547i	$-0.541416\pi$
$313$	−1436.95	−0.259493	−0.129747	+	0.991547i	$0.541416\pi$
$314$	5566.07	1.00036
$315$	−2021.78	−0.361634
$316$	−3443.00	−0.612924
$317$	1132.55	0.200664	0.100332	−	0.994954i	$-0.468010\pi$
$317$	1132.55	0.200664	0.100332	+	0.994954i	$0.468010\pi$
$318$	1152.79	0.203287
$319$	40.5609	0.00711903
$320$	229.104	0.0400228
$321$	1462.60	0.254312
$322$	−279.971	−0.0484540
$323$	−5805.13	−1.00002
$324$	2549.76	0.437202
$325$	−6532.03	−1.11487
$326$	−4257.65	−0.723343
$327$	2244.75	0.379618
$328$	1314.26	0.221243
$329$	6138.01	1.02857
$330$	63.0642	0.0105199
$331$	7127.43	1.18356	0.591781	−	0.806099i	$-0.298425\pi$
$331$	7127.43	1.18356	0.591781	+	0.806099i	$0.298425\pi$
$332$	2184.23	0.361070
$333$	−10660.4	−1.75431
$334$	−651.607	−0.106750
$335$	3172.34	0.517383
$336$	−374.274	−0.0607687
$337$	823.690	0.133143	0.0665716	−	0.997782i	$-0.478794\pi$
$337$	823.690	0.133143	0.0665716	+	0.997782i	$0.478794\pi$
$338$	2386.38	0.384030
$339$	−2365.07	−0.378918
$340$	1379.05	0.219970
$341$	−1921.39	−0.305130
$342$	3116.67	0.492778
$343$	−4560.68	−0.717941
$344$	−2965.60	−0.464809
$345$	24.5627	0.00383308
$346$	−6534.84	−1.01536
$347$	690.577	0.106836	0.0534180	−	0.998572i	$-0.482988\pi$
$347$	690.577	0.106836	0.0534180	+	0.998572i	$0.482988\pi$
$348$	21.1191	0.00325317
$349$	−12611.4	−1.93430	−0.967151	−	0.254204i	$-0.918186\pi$
$349$	−12611.4	−1.93430	−0.967151	+	0.254204i	$0.918186\pi$
$350$	−4901.52	−0.748564
$351$	3295.26	0.501105
$352$	−263.236	−0.0398595
$353$	6730.47	1.01481	0.507403	−	0.861709i	$-0.330606\pi$
$353$	6730.47	1.01481	0.507403	+	0.861709i	$0.330606\pi$
$354$	−234.553	−0.0352157
$355$	2812.36	0.420464
$356$	3098.02	0.461222
$357$	−2252.88	−0.333992
$358$	−7609.27	−1.12336
$359$	−9445.25	−1.38858	−0.694292	−	0.719694i	$-0.744282\pi$
$359$	−9445.25	−1.38858	−0.694292	+	0.719694i	$0.744282\pi$
$360$	−740.390	−0.108394
$361$	−3225.83	−0.470306
$362$	3422.17	0.496865
$363$	1352.76	0.195597
$364$	5087.88	0.732630
$365$	1424.58	0.204290
$366$	−202.748	−0.0289558
$367$	−4695.88	−0.667910	−0.333955	−	0.942589i	$-0.608383\pi$
$367$	−4695.88	−0.667910	−0.333955	+	0.942589i	$0.608383\pi$
$368$	−102.527	−0.0145234
$369$	−4247.25	−0.599195
$370$	2952.14	0.414796
$371$	−11759.3	−1.64558
$372$	−1000.43	−0.139435
$373$	9084.77	1.26110	0.630552	−	0.776147i	$-0.282829\pi$
$373$	9084.77	1.26110	0.630552	+	0.776147i	$0.282829\pi$
$374$	−1584.51	−0.219072
$375$	909.170	0.125198
$376$	2247.78	0.308298
$377$	−287.094	−0.0392203
$378$	2472.70	0.336461
$379$	5892.69	0.798647	0.399324	−	0.916810i	$-0.369245\pi$
$379$	5892.69	0.798647	0.399324	+	0.916810i	$0.369245\pi$
$380$	−863.089	−0.116515
$381$	1571.85	0.211360
$382$	305.957	0.0409794
$383$	−933.493	−0.124541	−0.0622706	−	0.998059i	$-0.519834\pi$
$383$	−933.493	−0.124541	−0.0622706	+	0.998059i	$0.519834\pi$
$384$	−137.061	−0.0182145
$385$	−643.299	−0.0851573
$386$	−3883.91	−0.512140
$387$	9583.84	1.25885
$388$	−3262.67	−0.426899
$389$	2777.53	0.362022	0.181011	−	0.983481i	$-0.442063\pi$
$389$	2777.53	0.362022	0.181011	+	0.983481i	$0.442063\pi$
$390$	−446.375	−0.0579566
$391$	−617.146	−0.0798220
$392$	1073.85	0.138361
$393$	−2031.43	−0.260743
$394$	−7595.14	−0.971161
$395$	−3081.27	−0.392495
$396$	850.695	0.107952
$397$	−7805.98	−0.986828	−0.493414	−	0.869794i	$-0.664251\pi$
$397$	−7805.98	−0.986828	−0.493414	+	0.869794i	$0.664251\pi$
$398$	−6403.28	−0.806450
$399$	1409.98	0.176910
$400$	−1794.97	−0.224371
$401$	8022.81	0.999103	0.499551	−	0.866284i	$-0.333498\pi$
$401$	8022.81	0.999103	0.499551	+	0.866284i	$0.333498\pi$
$402$	−1897.85	−0.235463
$403$	13599.8	1.68103
$404$	2008.44	0.247336
$405$	2281.88	0.279969
$406$	−215.430	−0.0263340
$407$	−3391.96	−0.413104
$408$	−825.018	−0.100109
$409$	9213.29	1.11386	0.556929	−	0.830560i	$-0.311980\pi$
$409$	9213.29	1.11386	0.556929	+	0.830560i	$0.311980\pi$
$410$	1176.18	0.141676
$411$	3061.19	0.367390
$412$	−742.884	−0.0888331
$413$	2392.60	0.285066
$414$	331.335	0.0393338
$415$	1954.75	0.231217
$416$	1863.21	0.219595
$417$	−660.687	−0.0775875
$418$	991.674	0.116039
$419$	11521.7	1.34337	0.671684	−	0.740838i	$-0.265571\pi$
$419$	11521.7	1.34337	0.671684	+	0.740838i	$0.265571\pi$
$420$	−334.951	−0.0389142
$421$	8085.69	0.936038	0.468019	−	0.883718i	$-0.344968\pi$
$421$	8085.69	0.936038	0.468019	+	0.883718i	$0.344968\pi$
$422$	−6970.42	−0.804064
$423$	−7264.08	−0.834969
$424$	−4306.32	−0.493239
$425$	−10804.5	−1.23317
$426$	−1682.49	−0.191354
$427$	2068.17	0.234393
$428$	−5463.62	−0.617042
$429$	512.876	0.0577201
$430$	−2654.02	−0.297647
$431$	−4853.07	−0.542376	−0.271188	−	0.962526i	$-0.587417\pi$
$431$	−4853.07	−0.542376	−0.271188	+	0.962526i	$0.587417\pi$
$432$	905.519	0.100849
$433$	13920.7	1.54500	0.772500	−	0.635015i	$-0.219006\pi$
$433$	13920.7	1.54500	0.772500	+	0.635015i	$0.219006\pi$
$434$	10205.0	1.12870
$435$	18.9003	0.00208322
$436$	−8385.41	−0.921074
$437$	386.244	0.0422805
$438$	−852.251	−0.0929729
$439$	−3973.50	−0.431993	−0.215996	−	0.976394i	$-0.569300\pi$
$439$	−3973.50	−0.431993	−0.215996	+	0.976394i	$0.569300\pi$
$440$	−235.580	−0.0255246
$441$	−3470.34	−0.374726
$442$	11215.3	1.20692
$443$	−6421.16	−0.688665	−0.344332	−	0.938848i	$-0.611895\pi$
$443$	−6421.16	−0.688665	−0.344332	+	0.938848i	$0.611895\pi$
$444$	−1766.12	−0.188775
$445$	2772.54	0.295350
$446$	−9048.67	−0.960688
$447$	67.0482	0.00709456
$448$	1398.12	0.147444
$449$	2952.10	0.310285	0.155143	−	0.987892i	$-0.450416\pi$
$449$	2952.10	0.310285	0.155143	+	0.987892i	$0.450416\pi$
$450$	5800.75	0.607667
$451$	−1351.41	−0.141098
$452$	8834.86	0.919374
$453$	1072.28	0.111214
$454$	−11240.1	−1.16195
$455$	4553.33	0.469151
$456$	516.342	0.0530262
$457$	−8150.75	−0.834302	−0.417151	−	0.908837i	$-0.636971\pi$
$457$	−8150.75	−0.834302	−0.417151	+	0.908837i	$0.636971\pi$
$458$	12248.4	1.24963
$459$	5450.63	0.554278
$460$	−91.7554	−0.00930026
$461$	7658.84	0.773769	0.386885	−	0.922128i	$-0.373551\pi$
$461$	7658.84	0.773769	0.386885	+	0.922128i	$0.373551\pi$
$462$	384.853	0.0387554
$463$	−4448.60	−0.446532	−0.223266	−	0.974758i	$-0.571672\pi$
$463$	−4448.60	−0.446532	−0.223266	+	0.974758i	$0.571672\pi$
$464$	−78.8917	−0.00789322
$465$	−895.319	−0.0892890
$466$	5572.49	0.553950
$467$	12558.2	1.24437	0.622187	−	0.782869i	$-0.286244\pi$
$467$	12558.2	1.24437	0.622187	+	0.782869i	$0.286244\pi$
$468$	−6021.30	−0.594732
$469$	19359.4	1.90604
$470$	2011.62	0.197423
$471$	−2980.05	−0.291536
$472$	876.186	0.0854443
$473$	3049.42	0.296433
$474$	1843.37	0.178626
$475$	6762.07	0.653189
$476$	8415.76	0.810369
$477$	13916.6	1.33585
$478$	−8242.87	−0.788745
$479$	3513.52	0.335150	0.167575	−	0.985859i	$-0.446406\pi$
$479$	3513.52	0.335150	0.167575	+	0.985859i	$0.446406\pi$
$480$	−122.661	−0.0116639
$481$	24008.6	2.27588
$482$	−7175.68	−0.678098
$483$	149.895	0.0141211
$484$	−5053.32	−0.474580
$485$	−2919.88	−0.273371
$486$	−4421.26	−0.412659
$487$	3237.81	0.301271	0.150636	−	0.988589i	$-0.451868\pi$
$487$	3237.81	0.301271	0.150636	+	0.988589i	$0.451868\pi$
$488$	757.377	0.0702558
$489$	2279.53	0.210805
$490$	961.029	0.0886018
$491$	10817.6	0.994283	0.497141	−	0.867670i	$-0.334383\pi$
$491$	10817.6	0.994283	0.497141	+	0.867670i	$0.334383\pi$
$492$	−703.647	−0.0644773
$493$	−474.876	−0.0433820
$494$	−7019.16	−0.639285
$495$	761.318	0.0691287
$496$	3737.15	0.338312
$497$	17162.6	1.54899
$498$	−1169.43	−0.105227
$499$	1503.59	0.134890	0.0674448	−	0.997723i	$-0.478515\pi$
$499$	1503.59	0.134890	0.0674448	+	0.997723i	$0.478515\pi$
$500$	−3396.26	−0.303771
$501$	348.868	0.0311103
$502$	−1482.47	−0.131805
$503$	6539.69	0.579702	0.289851	−	0.957072i	$-0.406394\pi$
$503$	6539.69	0.579702	0.289851	+	0.957072i	$0.406394\pi$
$504$	−4518.27	−0.399325
$505$	1797.43	0.158385
$506$	105.425	0.00926231
$507$	−1277.66	−0.111919
$508$	−5871.72	−0.512826
$509$	−20298.1	−1.76758	−0.883791	−	0.467882i	$-0.845017\pi$
$509$	−20298.1	−1.76758	−0.883791	+	0.467882i	$0.845017\pi$
$510$	−738.340	−0.0641063
$511$	8693.55	0.752603
$512$	512.000	0.0441942
$513$	−3411.31	−0.293592
$514$	8959.10	0.768811
$515$	−664.834	−0.0568856
$516$	1587.77	0.135460
$517$	−2311.31	−0.196618
$518$	18015.6	1.52811
$519$	3498.72	0.295909
$520$	1667.46	0.140621
$521$	−11072.1	−0.931048	−0.465524	−	0.885035i	$-0.654134\pi$
$521$	−11072.1	−0.931048	−0.465524	+	0.885035i	$0.654134\pi$
$522$	254.952	0.0213773
$523$	17025.7	1.42348	0.711741	−	0.702442i	$-0.247907\pi$
$523$	17025.7	1.42348	0.711741	+	0.702442i	$0.247907\pi$
$524$	7588.52	0.632645
$525$	2624.25	0.218156
$526$	−9952.17	−0.824972
$527$	22495.2	1.85940
$528$	140.936	0.0116163
$529$	−12125.9	−0.996625
$530$	−3853.88	−0.315853
$531$	−2831.55	−0.231410
$532$	−5267.05	−0.429240
$533$	9565.38	0.777340
$534$	−1658.67	−0.134415
$535$	−4889.60	−0.395132
$536$	7089.52	0.571307
$537$	4073.97	0.327383
$538$	538.000	0.0431131
$539$	−1104.20	−0.0882402
$540$	810.383	0.0645802
$541$	−18983.3	−1.50861	−0.754304	−	0.656525i	$-0.772026\pi$
$541$	−18983.3	−1.50861	−0.754304	+	0.656525i	$0.772026\pi$
$542$	15600.9	1.23638
$543$	−1832.21	−0.144803
$544$	3081.90	0.242896
$545$	−7504.41	−0.589823
$546$	−2724.03	−0.213512
$547$	−15459.3	−1.20839	−0.604197	−	0.796835i	$-0.706506\pi$
$547$	−15459.3	−1.20839	−0.604197	+	0.796835i	$0.706506\pi$
$548$	−11435.2	−0.891404
$549$	−2447.60	−0.190275
$550$	1845.70	0.143093
$551$	297.204	0.0229788
$552$	54.8926	0.00423258
$553$	−18803.6	−1.44595
$554$	−1227.83	−0.0941613
$555$	−1580.56	−0.120885
$556$	2468.03	0.188252
$557$	1001.16	0.0761588	0.0380794	−	0.999275i	$-0.487876\pi$
$557$	1001.16	0.0761588	0.0380794	+	0.999275i	$0.487876\pi$
$558$	−12077.2	−0.916256
$559$	−21584.1	−1.63311
$560$	1251.23	0.0944181
$561$	848.339	0.0638447
$562$	13671.1	1.02612
$563$	−17512.2	−1.31093	−0.655463	−	0.755227i	$-0.727527\pi$
$563$	−17512.2	−1.31093	−0.655463	+	0.755227i	$0.727527\pi$
$564$	−1203.45	−0.0898481
$565$	7906.65	0.588735
$566$	−8974.18	−0.666454
$567$	13925.3	1.03141
$568$	6285.04	0.464286
$569$	−2267.59	−0.167069	−0.0835346	−	0.996505i	$-0.526621\pi$
$569$	−2267.59	−0.167069	−0.0835346	+	0.996505i	$0.526621\pi$
$570$	462.094	0.0339561
$571$	−18349.0	−1.34481	−0.672403	−	0.740186i	$-0.734738\pi$
$571$	−18349.0	−1.34481	−0.672403	+	0.740186i	$0.734738\pi$
$572$	−1915.88	−0.140047
$573$	−163.808	−0.0119427
$574$	7177.68	0.521935
$575$	718.878	0.0521379
$576$	−1654.62	−0.119692
$577$	19403.1	1.39993	0.699966	−	0.714176i	$-0.253198\pi$
$577$	19403.1	1.39993	0.699966	+	0.714176i	$0.253198\pi$
$578$	8725.01	0.627876
$579$	2079.43	0.149254
$580$	−70.6031	−0.00505454
$581$	11929.0	0.851802
$582$	1746.82	0.124412
$583$	4428.04	0.314564
$584$	3183.63	0.225581
$585$	−5388.68	−0.380846
$586$	5644.30	0.397891
$587$	323.054	0.0227153	0.0113576	−	0.999935i	$-0.496385\pi$
$587$	323.054	0.0227153	0.0113576	+	0.999935i	$0.496385\pi$
$588$	−574.935	−0.0403230
$589$	−14078.7	−0.984896
$590$	784.132	0.0547156
$591$	4066.40	0.283028
$592$	6597.43	0.458028
$593$	−8308.92	−0.575390	−0.287695	−	0.957722i	$-0.592889\pi$
$593$	−8308.92	−0.575390	−0.287695	+	0.957722i	$0.592889\pi$
$594$	−931.115	−0.0643167
$595$	7531.58	0.518932
$596$	−250.462	−0.0172137
$597$	3428.28	0.235026
$598$	−746.210	−0.0510281
$599$	11217.2	0.765145	0.382572	−	0.923925i	$-0.375038\pi$
$599$	11217.2	0.765145	0.382572	+	0.923925i	$0.375038\pi$
$600$	961.017	0.0653889
$601$	20658.0	1.40209	0.701046	−	0.713116i	$-0.252717\pi$
$601$	20658.0	1.40209	0.701046	+	0.713116i	$0.252717\pi$
$602$	−16196.3	−1.09653
$603$	−22911.0	−1.54728
$604$	−4005.57	−0.269841
$605$	−4522.41	−0.303904
$606$	−1075.31	−0.0720816
$607$	−18832.4	−1.25928	−0.629642	−	0.776885i	$-0.716798\pi$
$607$	−18832.4	−1.25928	−0.629642	+	0.776885i	$0.716798\pi$
$608$	−1928.83	−0.128658
$609$	115.340	0.00767458
$610$	677.805	0.0449894
$611$	16359.7	1.08321
$612$	−9959.71	−0.657839
$613$	526.582	0.0346956	0.0173478	−	0.999850i	$-0.494478\pi$
$613$	526.582	0.0346956	0.0173478	+	0.999850i	$0.494478\pi$
$614$	−8743.08	−0.574661
$615$	−629.720	−0.0412890
$616$	−1437.64	−0.0940328
$617$	24329.0	1.58744	0.793718	−	0.608286i	$-0.208143\pi$
$617$	24329.0	1.58744	0.793718	+	0.608286i	$0.208143\pi$
$618$	397.736	0.0258888
$619$	−2155.18	−0.139942	−0.0699709	−	0.997549i	$-0.522291\pi$
$619$	−2155.18	−0.139942	−0.0699709	+	0.997549i	$0.522291\pi$
$620$	3344.51	0.216643
$621$	−362.658	−0.0234347
$622$	4608.42	0.297075
$623$	16919.6	1.08807
$624$	−997.555	−0.0639970
$625$	10983.7	0.702959
$626$	−2873.91	−0.183489
$627$	−530.938	−0.0338176
$628$	11132.1	0.707358
$629$	39712.2	2.51737
$630$	−4043.57	−0.255714
$631$	6719.25	0.423913	0.211957	−	0.977279i	$-0.432016\pi$
$631$	6719.25	0.423913	0.211957	+	0.977279i	$0.432016\pi$
$632$	−6886.00	−0.433403
$633$	3731.93	0.234330
$634$	2265.10	0.141891
$635$	−5254.83	−0.328396
$636$	2305.58	0.143746
$637$	7815.67	0.486135
$638$	81.1217	0.00503392
$639$	−20311.2	−1.25743
$640$	458.208	0.0283004
$641$	22238.9	1.37033	0.685167	−	0.728386i	$-0.259729\pi$
$641$	22238.9	1.37033	0.685167	+	0.728386i	$0.259729\pi$
$642$	2925.20	0.179826
$643$	11950.4	0.732934	0.366467	−	0.930431i	$-0.380567\pi$
$643$	11950.4	0.732934	0.366467	+	0.930431i	$0.380567\pi$
$644$	−559.943	−0.0342622
$645$	1420.95	0.0867440
$646$	−11610.3	−0.707120
$647$	13860.5	0.842213	0.421107	−	0.907011i	$-0.361642\pi$
$647$	13860.5	0.842213	0.421107	+	0.907011i	$0.361642\pi$
$648$	5099.53	0.309149
$649$	−900.953	−0.0544923
$650$	−13064.1	−0.788331
$651$	−5463.73	−0.328941
$652$	−8515.31	−0.511480
$653$	19213.2	1.15141	0.575706	−	0.817657i	$-0.304727\pi$
$653$	19213.2	1.15141	0.575706	+	0.817657i	$0.304727\pi$
$654$	4489.51	0.268431
$655$	6791.25	0.405124
$656$	2628.51	0.156442
$657$	−10288.5	−0.610945
$658$	12276.0	0.727308
$659$	−27657.4	−1.63487	−0.817436	−	0.576019i	$-0.804605\pi$
$659$	−27657.4	−1.63487	−0.817436	+	0.576019i	$0.804605\pi$
$660$	126.128	0.00743870
$661$	−26363.2	−1.55130	−0.775651	−	0.631162i	$-0.782578\pi$
$661$	−26363.2	−1.55130	−0.775651	+	0.631162i	$0.782578\pi$
$662$	14254.9	0.836904
$663$	−6004.62	−0.351735
$664$	4368.46	0.255315
$665$	−4713.68	−0.274870
$666$	−21320.8	−1.24048
$667$	31.5959	0.00183418
$668$	−1303.21	−0.0754834
$669$	4844.62	0.279976
$670$	6344.68	0.365845
$671$	−778.786	−0.0448058
$672$	−748.547	−0.0429700
$673$	19235.4	1.10174	0.550870	−	0.834591i	$-0.314296\pi$
$673$	19235.4	1.10174	0.550870	+	0.834591i	$0.314296\pi$
$674$	1647.38	0.0941464
$675$	−6349.13	−0.362041
$676$	4772.77	0.271550
$677$	−10104.2	−0.573614	−0.286807	−	0.957988i	$-0.592594\pi$
$677$	−10104.2	−0.573614	−0.286807	+	0.957988i	$0.592594\pi$
$678$	−4730.15	−0.267935
$679$	−17818.8	−1.00710
$680$	2758.11	0.155542
$681$	6017.89	0.338629
$682$	−3842.79	−0.215759
$683$	−28965.6	−1.62275	−0.811376	−	0.584524i	$-0.801281\pi$
$683$	−28965.6	−1.62275	−0.811376	+	0.584524i	$0.801281\pi$
$684$	6233.34	0.348447
$685$	−10233.8	−0.570824
$686$	−9121.36	−0.507661
$687$	−6557.75	−0.364183
$688$	−5931.19	−0.328669
$689$	−31342.1	−1.73300
$690$	49.1254	0.00271040
$691$	−9945.49	−0.547532	−0.273766	−	0.961796i	$-0.588269\pi$
$691$	−9945.49	−0.547532	−0.273766	+	0.961796i	$0.588269\pi$
$692$	−13069.7	−0.717969
$693$	4645.99	0.254670
$694$	1381.15	0.0755445
$695$	2208.74	0.120550
$696$	42.2382	0.00230034
$697$	15821.9	0.859824
$698$	−25222.7	−1.36776
$699$	−2983.49	−0.161439
$700$	−9803.04	−0.529314
$701$	19180.8	1.03345	0.516726	−	0.856151i	$-0.327151\pi$
$701$	19180.8	1.03345	0.516726	+	0.856151i	$0.327151\pi$
$702$	6590.52	0.354335
$703$	−24854.1	−1.33341
$704$	−526.473	−0.0281849
$705$	−1077.01	−0.0575356
$706$	13460.9	0.717576
$707$	10968.9	0.583491
$708$	−469.106	−0.0249012
$709$	−24843.9	−1.31598	−0.657992	−	0.753025i	$-0.728594\pi$
$709$	−24843.9	−1.31598	−0.657992	+	0.753025i	$0.728594\pi$
$710$	5624.72	0.297313
$711$	22253.3	1.17379
$712$	6196.05	0.326133
$713$	−1496.72	−0.0786149
$714$	−4505.76	−0.236168
$715$	−1714.59	−0.0896813
$716$	−15218.5	−0.794335
$717$	4413.19	0.229866
$718$	−18890.5	−0.981877
$719$	15118.5	0.784180	0.392090	−	0.919927i	$-0.371752\pi$
$719$	15118.5	0.784180	0.392090	+	0.919927i	$0.371752\pi$
$720$	−1480.78	−0.0766464
$721$	−4057.19	−0.209567
$722$	−6451.65	−0.332556
$723$	3841.83	0.197620
$724$	6844.34	0.351337
$725$	553.156	0.0283361
$726$	2705.53	0.138308
$727$	−25394.6	−1.29551	−0.647753	−	0.761850i	$-0.724291\pi$
$727$	−25394.6	−1.29551	−0.647753	+	0.761850i	$0.724291\pi$
$728$	10175.8	0.518047
$729$	−14843.8	−0.754142
$730$	2849.15	0.144455
$731$	−35701.8	−1.80640
$732$	−405.496	−0.0204748
$733$	−5116.13	−0.257802	−0.128901	−	0.991657i	$-0.541145\pi$
$733$	−5116.13	−0.257802	−0.128901	+	0.991657i	$0.541145\pi$
$734$	−9391.77	−0.472284
$735$	−514.531	−0.0258214
$736$	−205.054	−0.0102696
$737$	−7289.92	−0.364352
$738$	−8494.50	−0.423695
$739$	31608.5	1.57339	0.786696	−	0.617340i	$-0.211790\pi$
$739$	31608.5	1.57339	0.786696	+	0.617340i	$0.211790\pi$
$740$	5904.29	0.293305
$741$	3758.03	0.186308
$742$	−23518.5	−1.16360
$743$	−15791.3	−0.779712	−0.389856	−	0.920876i	$-0.627475\pi$
$743$	−15791.3	−0.779712	−0.389856	+	0.920876i	$0.627475\pi$
$744$	−2000.85	−0.0985951
$745$	−224.148	−0.0110230
$746$	18169.5	0.891735
$747$	−14117.4	−0.691473
$748$	−3169.02	−0.154907
$749$	−29839.0	−1.45567
$750$	1818.34	0.0885286
$751$	957.250	0.0465120	0.0232560	−	0.999730i	$-0.492597\pi$
$751$	957.250	0.0465120	0.0232560	+	0.999730i	$0.492597\pi$
$752$	4495.55	0.218000
$753$	793.710	0.0384122
$754$	−574.187	−0.0277330
$755$	−3584.73	−0.172797
$756$	4945.41	0.237914
$757$	2875.44	0.138058	0.0690288	−	0.997615i	$-0.478010\pi$
$757$	2875.44	0.138058	0.0690288	+	0.997615i	$0.478010\pi$
$758$	11785.4	0.564729
$759$	−56.4442	−0.00269934
$760$	−1726.18	−0.0823883
$761$	−23338.6	−1.11173	−0.555863	−	0.831274i	$-0.687612\pi$
$761$	−23338.6	−1.11173	−0.555863	+	0.831274i	$0.687612\pi$
$762$	3143.69	0.149454
$763$	−45796.1	−2.17291
$764$	611.914	0.0289768
$765$	−8913.31	−0.421257
$766$	−1866.99	−0.0880639
$767$	6377.03	0.300210
$768$	−274.122	−0.0128796
$769$	−23060.7	−1.08139	−0.540695	−	0.841219i	$-0.681839\pi$
$769$	−23060.7	−1.08139	−0.540695	+	0.841219i	$0.681839\pi$
$770$	−1286.60	−0.0602153
$771$	−4796.66	−0.224056
$772$	−7767.83	−0.362138
$773$	265.574	0.0123571	0.00617855	−	0.999981i	$-0.498033\pi$
$773$	265.574	0.0123571	0.00617855	+	0.999981i	$0.498033\pi$
$774$	19167.7	0.890140
$775$	−26203.3	−1.21452
$776$	−6525.34	−0.301863
$777$	−9645.48	−0.445341
$778$	5555.07	0.255988
$779$	−9902.23	−0.455435
$780$	−892.749	−0.0409815
$781$	−6462.70	−0.296100
$782$	−1234.29	−0.0564427
$783$	−279.054	−0.0127364
$784$	2147.70	0.0978362
$785$	9962.57	0.452967
$786$	−4062.86	−0.184373
$787$	6091.06	0.275887	0.137943	−	0.990440i	$-0.455951\pi$
$787$	6091.06	0.275887	0.137943	+	0.990440i	$0.455951\pi$
$788$	−15190.3	−0.686715
$789$	5328.35	0.240424
$790$	−6162.54	−0.277536
$791$	48250.8	2.16890
$792$	1701.39	0.0763336
$793$	5512.32	0.246845
$794$	−15612.0	−0.697793
$795$	2063.35	0.0920497
$796$	−12806.6	−0.570246
$797$	41859.8	1.86041	0.930206	−	0.367038i	$-0.119628\pi$
$797$	41859.8	1.86041	0.930206	+	0.367038i	$0.119628\pi$
$798$	2819.96	0.125094
$799$	27060.2	1.19815
$800$	−3589.93	−0.158654
$801$	−20023.6	−0.883270
$802$	16045.6	0.706472
$803$	−3273.62	−0.143865
$804$	−3795.70	−0.166497
$805$	−501.114	−0.0219403
$806$	27199.6	1.18867
$807$	−288.043	−0.0125645
$808$	4016.88	0.174893
$809$	43545.0	1.89241	0.946205	−	0.323569i	$-0.104883\pi$
$809$	43545.0	1.89241	0.946205	+	0.323569i	$0.104883\pi$
$810$	4563.76	0.197968
$811$	−39925.7	−1.72871	−0.864354	−	0.502884i	$-0.832272\pi$
$811$	−39925.7	−1.72871	−0.864354	+	0.502884i	$0.832272\pi$
$812$	−430.860	−0.0186209
$813$	−8352.67	−0.360321
$814$	−6783.92	−0.292108
$815$	−7620.67	−0.327534
$816$	−1650.04	−0.0707878
$817$	22344.2	0.956824
$818$	18426.6	0.787616
$819$	−32884.7	−1.40304
$820$	2352.35	0.100180
$821$	17214.7	0.731789	0.365894	−	0.930656i	$-0.380763\pi$
$821$	17214.7	0.731789	0.365894	+	0.930656i	$0.380763\pi$
$822$	6122.38	0.259784
$823$	−29224.4	−1.23779	−0.618893	−	0.785476i	$-0.712418\pi$
$823$	−29224.4	−1.23779	−0.618893	+	0.785476i	$0.712418\pi$
$824$	−1485.77	−0.0628145
$825$	−988.182	−0.0417019
$826$	4785.21	0.201572
$827$	−16267.4	−0.684008	−0.342004	−	0.939699i	$-0.611106\pi$
$827$	−16267.4	−0.684008	−0.342004	+	0.939699i	$0.611106\pi$
$828$	662.669	0.0278132
$829$	−26702.5	−1.11872	−0.559358	−	0.828926i	$-0.688952\pi$
$829$	−26702.5	−1.11872	−0.559358	+	0.828926i	$0.688952\pi$
$830$	3909.50	0.163495
$831$	657.373	0.0274417
$832$	3726.42	0.155277
$833$	12927.7	0.537719
$834$	−1321.37	−0.0548627
$835$	−1166.30	−0.0483369
$836$	1983.35	0.0820521
$837$	13219.0	0.545896
$838$	23043.4	0.949905
$839$	6917.49	0.284646	0.142323	−	0.989820i	$-0.454543\pi$
$839$	6917.49	0.284646	0.142323	+	0.989820i	$0.454543\pi$
$840$	−669.903	−0.0275165
$841$	−24364.7	−0.999003
$842$	16171.4	0.661879
$843$	−7319.43	−0.299045
$844$	−13940.8	−0.568559
$845$	4271.33	0.173891
$846$	−14528.2	−0.590412
$847$	−27598.2	−1.11958
$848$	−8612.63	−0.348772
$849$	4804.73	0.194226
$850$	−21609.0	−0.871980
$851$	−2642.25	−0.106434
$852$	−3364.98	−0.135308
$853$	34464.8	1.38341	0.691707	−	0.722178i	$-0.256859\pi$
$853$	34464.8	1.38341	0.691707	+	0.722178i	$0.256859\pi$
$854$	4136.34	0.165741
$855$	5578.45	0.223133
$856$	−10927.2	−0.436314
$857$	35655.3	1.42119	0.710595	−	0.703601i	$-0.248426\pi$
$857$	35655.3	1.42119	0.710595	+	0.703601i	$0.248426\pi$
$858$	1025.75	0.0408142
$859$	−32614.7	−1.29546	−0.647729	−	0.761871i	$-0.724281\pi$
$859$	−32614.7	−1.29546	−0.647729	+	0.761871i	$0.724281\pi$
$860$	−5308.04	−0.210468
$861$	−3842.90	−0.152109
$862$	−9706.14	−0.383518
$863$	47219.5	1.86254	0.931268	−	0.364334i	$-0.118703\pi$
$863$	47219.5	1.86254	0.931268	+	0.364334i	$0.118703\pi$
$864$	1811.04	0.0713111
$865$	−11696.5	−0.459762
$866$	27841.4	1.09248
$867$	−4671.33	−0.182983
$868$	20410.1	0.798114
$869$	7080.65	0.276403
$870$	37.8006	0.00147306
$871$	51598.7	2.00730
$872$	−16770.8	−0.651297
$873$	21087.8	0.817541
$874$	772.489	0.0298968
$875$	−18548.3	−0.716627
$876$	−1704.50	−0.0657417
$877$	−17600.9	−0.677698	−0.338849	−	0.940841i	$-0.610038\pi$
$877$	−17600.9	−0.677698	−0.338849	+	0.940841i	$0.610038\pi$
$878$	−7947.00	−0.305465
$879$	−3021.93	−0.115958
$880$	−471.160	−0.0180486
$881$	−16179.3	−0.618723	−0.309362	−	0.950944i	$-0.600115\pi$
$881$	−16179.3	−0.618723	−0.309362	+	0.950944i	$0.600115\pi$
$882$	−6940.67	−0.264971
$883$	−17880.9	−0.681472	−0.340736	−	0.940159i	$-0.610676\pi$
$883$	−17880.9	−0.681472	−0.340736	+	0.940159i	$0.610676\pi$
$884$	22430.6	0.853419
$885$	−419.820	−0.0159459
$886$	−12842.3	−0.486960
$887$	−45387.9	−1.71812	−0.859062	−	0.511872i	$-0.828952\pi$
$887$	−45387.9	−1.71812	−0.859062	+	0.511872i	$0.828952\pi$
$888$	−3532.23	−0.133484
$889$	−32067.9	−1.20981
$890$	5545.07	0.208844
$891$	−5243.67	−0.197160
$892$	−18097.3	−0.679309
$893$	−16935.8	−0.634642
$894$	134.096	0.00501661
$895$	−13619.6	−0.508664
$896$	2796.24	0.104259
$897$	399.518	0.0148712
$898$	5904.19	0.219405
$899$	−1151.68	−0.0427260
$900$	11601.5	0.429685
$901$	−51842.4	−1.91689
$902$	−2702.81	−0.0997714
$903$	8671.44	0.319565
$904$	17669.7	0.650095
$905$	6125.25	0.224984
$906$	2144.56	0.0786405
$907$	−6376.42	−0.233435	−0.116717	−	0.993165i	$-0.537237\pi$
$907$	−6376.42	−0.233435	−0.116717	+	0.993165i	$0.537237\pi$
$908$	−22480.2	−0.821620
$909$	−12981.2	−0.473664
$910$	9106.66	0.331740
$911$	−18032.0	−0.655793	−0.327896	−	0.944714i	$-0.606340\pi$
$911$	−18032.0	−0.655793	−0.327896	+	0.944714i	$0.606340\pi$
$912$	1032.68	0.0374952
$913$	−4491.94	−0.162828
$914$	−16301.5	−0.589941
$915$	−362.894	−0.0131114
$916$	24496.9	0.883624
$917$	41444.0	1.49248
$918$	10901.3	0.391934
$919$	17176.0	0.616522	0.308261	−	0.951302i	$-0.400253\pi$
$919$	17176.0	0.616522	0.308261	+	0.951302i	$0.400253\pi$
$920$	−183.511	−0.00657628
$921$	4681.01	0.167475
$922$	15317.7	0.547138
$923$	45743.6	1.63128
$924$	769.706	0.0274042
$925$	−46258.5	−1.64429
$926$	−8897.21	−0.315745
$927$	4801.52	0.170121
$928$	−157.783	−0.00558135
$929$	11842.9	0.418249	0.209124	−	0.977889i	$-0.432939\pi$
$929$	11842.9	0.418249	0.209124	+	0.977889i	$0.432939\pi$
$930$	−1790.64	−0.0631369
$931$	−8090.90	−0.284821
$932$	11145.0	0.391702
$933$	−2467.32	−0.0865773
$934$	25116.3	0.879905
$935$	−2836.07	−0.0991973
$936$	−12042.6	−0.420539
$937$	45534.5	1.58756	0.793782	−	0.608202i	$-0.208109\pi$
$937$	45534.5	1.58756	0.793782	+	0.608202i	$0.208109\pi$
$938$	38718.7	1.34777
$939$	1538.68	0.0534747
$940$	4023.24	0.139599
$941$	−16808.3	−0.582291	−0.291146	−	0.956679i	$-0.594036\pi$
$941$	−16808.3	−0.582291	−0.291146	+	0.956679i	$0.594036\pi$
$942$	−5960.10	−0.206147
$943$	−1052.71	−0.0363531
$944$	1752.37	0.0604183
$945$	4425.83	0.152352
$946$	6098.85	0.209610
$947$	−10403.1	−0.356974	−0.178487	−	0.983942i	$-0.557120\pi$
$947$	−10403.1	−0.356974	−0.178487	+	0.983942i	$0.557120\pi$
$948$	3686.73	0.126308
$949$	23171.0	0.792584
$950$	13524.1	0.461874
$951$	−1212.72	−0.0413515
$952$	16831.5	0.573017
$953$	−9475.84	−0.322091	−0.161045	−	0.986947i	$-0.551487\pi$
$953$	−9475.84	−0.322091	−0.161045	+	0.986947i	$0.551487\pi$
$954$	27833.2	0.944585
$955$	547.625	0.0185557
$956$	−16485.7	−0.557727
$957$	−43.4322	−0.00146705
$958$	7027.03	0.236987
$959$	−62452.5	−2.10292
$960$	−245.322	−0.00824765
$961$	24764.8	0.831283
$962$	48017.2	1.60929
$963$	35313.3	1.18168
$964$	−14351.4	−0.479488
$965$	−6951.72	−0.231900
$966$	299.791	0.00998510
$967$	39930.0	1.32788	0.663942	−	0.747784i	$-0.268882\pi$
$967$	39930.0	1.32788	0.663942	+	0.747784i	$0.268882\pi$
$968$	−10106.6	−0.335578
$969$	6216.08	0.206078
$970$	−5839.77	−0.193303
$971$	−27957.2	−0.923984	−0.461992	−	0.886884i	$-0.652865\pi$
$971$	−27957.2	−0.923984	−0.461992	+	0.886884i	$0.652865\pi$
$972$	−8842.52	−0.291794
$973$	13478.9	0.444106
$974$	6475.62	0.213031
$975$	6994.44	0.229745
$976$	1514.75	0.0496784
$977$	−30853.6	−1.01033	−0.505166	−	0.863022i	$-0.668569\pi$
$977$	−30853.6	−1.01033	−0.505166	+	0.863022i	$0.668569\pi$
$978$	4559.06	0.149062
$979$	−6371.19	−0.207992
$980$	1922.06	0.0626509
$981$	54197.8	1.76392
$982$	21635.3	0.703064
$983$	−46.9863	−0.00152455	−0.000762274	−	1.00000i	$-0.500243\pi$
$983$	−46.9863	−0.00152455	−0.000762274		1.00000i	$0.500243\pi$
$984$	−1407.29	−0.0455923
$985$	−13594.3	−0.439748
$986$	−949.752	−0.0306757
$987$	−6572.52	−0.211961
$988$	−14038.3	−0.452043
$989$	2375.42	0.0763742
$990$	1522.64	0.0488814
$991$	−42948.4	−1.37669	−0.688346	−	0.725383i	$-0.741663\pi$
$991$	−42948.4	−1.37669	−0.688346	+	0.725383i	$0.741663\pi$
$992$	7474.30	0.239223
$993$	−7631.98	−0.243901
$994$	34325.2	1.09530
$995$	−11461.1	−0.365166
$996$	−2338.85	−0.0744070
$997$	14125.8	0.448714	0.224357	−	0.974507i	$-0.427972\pi$
$997$	14125.8	0.448714	0.224357	+	0.974507i	$0.427972\pi$
$998$	3007.18	0.0953814
$999$	23336.3	0.739068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.4.a.d.1.10	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.4.a.d.1.10	✓	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} -1.07079 q^{3} +4.00000 q^{4} +3.57975 q^{5} -2.14158 q^{6} +21.8456 q^{7} +8.00000 q^{8} -25.8534 q^{9} +7.15950 q^{10} -8.22614 q^{11} -4.28316 q^{12} +58.2254 q^{13} +43.6912 q^{14} -3.83316 q^{15} +16.0000 q^{16} +96.3094 q^{17} -51.7068 q^{18} -60.2758 q^{19} +14.3190 q^{20} -23.3921 q^{21} -16.4523 q^{22} -6.40795 q^{23} -8.56633 q^{24} -112.185 q^{25} +116.451 q^{26} +56.5949 q^{27} +87.3825 q^{28} -4.93073 q^{29} -7.66633 q^{30} +233.572 q^{31} +32.0000 q^{32} +8.80847 q^{33} +192.619 q^{34} +78.2019 q^{35} -103.414 q^{36} +412.339 q^{37} -120.552 q^{38} -62.3472 q^{39} +28.6380 q^{40} +164.282 q^{41} -46.7842 q^{42} -370.699 q^{43} -32.9045 q^{44} -92.5487 q^{45} -12.8159 q^{46} +280.972 q^{47} -17.1327 q^{48} +134.231 q^{49} -224.371 q^{50} -103.127 q^{51} +232.901 q^{52} -538.290 q^{53} +113.190 q^{54} -29.4475 q^{55} +174.765 q^{56} +64.5428 q^{57} -9.86146 q^{58} +109.523 q^{59} -15.3327 q^{60} +94.6721 q^{61} +467.143 q^{62} -564.784 q^{63} +64.0000 q^{64} +208.432 q^{65} +17.6169 q^{66} +886.190 q^{67} +385.238 q^{68} +6.86157 q^{69} +156.404 q^{70} +785.631 q^{71} -206.827 q^{72} +397.954 q^{73} +824.679 q^{74} +120.127 q^{75} -241.103 q^{76} -179.705 q^{77} -124.694 q^{78} -860.750 q^{79} +57.2760 q^{80} +637.441 q^{81} +328.564 q^{82} +546.057 q^{83} -93.5684 q^{84} +344.764 q^{85} -741.399 q^{86} +5.27978 q^{87} -65.8091 q^{88} +774.506 q^{89} -185.097 q^{90} +1271.97 q^{91} -25.6318 q^{92} -250.106 q^{93} +561.944 q^{94} -215.772 q^{95} -34.2653 q^{96} -815.667 q^{97} +268.463 q^{98} +212.674 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 42 q^{2} + 6 q^{3} + 84 q^{4} + 54 q^{5} + 12 q^{6} + 52 q^{7} + 168 q^{8} + 309 q^{9} + 108 q^{10} + 99 q^{11} + 24 q^{12} + 81 q^{13} + 104 q^{14} + 277 q^{15} + 336 q^{16} + 228 q^{17} + 618 q^{18}+ \cdots - 4470 q^{99}+O(q^{100}) \) 21 * q + 42 * q^2 + 6 * q^3 + 84 * q^4 + 54 * q^5 + 12 * q^6 + 52 * q^7 + 168 * q^8 + 309 * q^9 + 108 * q^10 + 99 * q^11 + 24 * q^12 + 81 * q^13 + 104 * q^14 + 277 * q^15 + 336 * q^16 + 228 * q^17 + 618 * q^18 + 51 * q^19 + 216 * q^20 + 235 * q^21 + 198 * q^22 + 691 * q^23 + 48 * q^24 + 1035 * q^25 + 162 * q^26 + 291 * q^27 + 208 * q^28 + 540 * q^29 + 554 * q^30 + 312 * q^31 + 672 * q^32 + 513 * q^33 + 456 * q^34 + 410 * q^35 + 1236 * q^36 + 1120 * q^37 + 102 * q^38 + 904 * q^39 + 432 * q^40 + 731 * q^41 + 470 * q^42 + 788 * q^43 + 396 * q^44 + 1771 * q^45 + 1382 * q^46 + 1570 * q^47 + 96 * q^48 + 2337 * q^49 + 2070 * q^50 + 973 * q^51 + 324 * q^52 + 1801 * q^53 + 582 * q^54 + 1191 * q^55 + 416 * q^56 + 2122 * q^57 + 1080 * q^58 + 1352 * q^59 + 1108 * q^60 + 1868 * q^61 + 624 * q^62 + 2302 * q^63 + 1344 * q^64 + 2552 * q^65 + 1026 * q^66 + 1968 * q^67 + 912 * q^68 + 823 * q^69 + 820 * q^70 + 868 * q^71 + 2472 * q^72 + 1587 * q^73 + 2240 * q^74 - 1978 * q^75 + 204 * q^76 - 2020 * q^77 + 1808 * q^78 + 1168 * q^79 + 864 * q^80 + 3069 * q^81 + 1462 * q^82 - 1506 * q^83 + 940 * q^84 + 871 * q^85 + 1576 * q^86 - 6155 * q^87 + 792 * q^88 + 1471 * q^89 + 3542 * q^90 - 2157 * q^91 + 2764 * q^92 - 677 * q^93 + 3140 * q^94 + 544 * q^95 + 192 * q^96 - 801 * q^97 + 4674 * q^98 - 4470 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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