LMFDB - Embedded newform 538.4.a.b.1.2

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 4 x^{14} - 262 x^{13} + 870 x^{12} + 26403 x^{11} - 73750 x^{10} - 1270273 x^{9} + \cdots + 4484581281 $ x^15 - 4x^14 - 262x^13 + 870x^12 + 26403x^11 - 73750x^10 - 1270273x^9 + 3200221x^8 + 29622219x^7 - 76420071x^6 - 306845604x^5 + 880769133x^4 + 1044220086x^3 - 3558788460x^2 - 957997854x + 4484581281
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$9.56722$ of defining polynomial
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)

$f(q)$	$=$	\(q-2.00000 q^{2} -8.56722 q^{3} +4.00000 q^{4} -3.91913 q^{5} +17.1344 q^{6} -8.79649 q^{7} -8.00000 q^{8} +46.3972 q^{9} +7.83826 q^{10} -20.7785 q^{11} -34.2689 q^{12} -4.62558 q^{13} +17.5930 q^{14} +33.5760 q^{15} +16.0000 q^{16} -65.4047 q^{17} -92.7944 q^{18} -65.6710 q^{19} -15.6765 q^{20} +75.3614 q^{21} +41.5570 q^{22} +102.572 q^{23} +68.5377 q^{24} -109.640 q^{25} +9.25116 q^{26} -166.180 q^{27} -35.1859 q^{28} -294.284 q^{29} -67.1520 q^{30} -236.193 q^{31} -32.0000 q^{32} +178.014 q^{33} +130.809 q^{34} +34.4746 q^{35} +185.589 q^{36} -349.271 q^{37} +131.342 q^{38} +39.6284 q^{39} +31.3530 q^{40} -213.966 q^{41} -150.723 q^{42} +439.249 q^{43} -83.1139 q^{44} -181.837 q^{45} -205.144 q^{46} -408.782 q^{47} -137.075 q^{48} -265.622 q^{49} +219.281 q^{50} +560.336 q^{51} -18.5023 q^{52} +563.247 q^{53} +332.360 q^{54} +81.4335 q^{55} +70.3719 q^{56} +562.618 q^{57} +588.567 q^{58} +707.804 q^{59} +134.304 q^{60} -530.692 q^{61} +472.387 q^{62} -408.132 q^{63} +64.0000 q^{64} +18.1282 q^{65} -356.028 q^{66} -404.851 q^{67} -261.619 q^{68} -878.757 q^{69} -68.9491 q^{70} -393.079 q^{71} -371.178 q^{72} +319.407 q^{73} +698.542 q^{74} +939.313 q^{75} -262.684 q^{76} +182.778 q^{77} -79.2567 q^{78} +1263.45 q^{79} -62.7060 q^{80} +170.975 q^{81} +427.933 q^{82} +956.077 q^{83} +301.446 q^{84} +256.329 q^{85} -878.499 q^{86} +2521.19 q^{87} +166.228 q^{88} -625.916 q^{89} +363.673 q^{90} +40.6889 q^{91} +410.288 q^{92} +2023.52 q^{93} +817.564 q^{94} +257.373 q^{95} +274.151 q^{96} -18.2342 q^{97} +531.244 q^{98} -964.063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 30 q^{2} + 11 q^{3} + 60 q^{4} + 29 q^{5} - 22 q^{6} + 5 q^{7} - 120 q^{8} + 142 q^{9} - 58 q^{10} + 79 q^{11} + 44 q^{12} - 14 q^{13} - 10 q^{14} + 67 q^{15} + 240 q^{16} + 94 q^{17} - 284 q^{18}+ \cdots + 7068 q^{99}+O(q^{100}) $ 15 * q - 30 * q^2 + 11 * q^3 + 60 * q^4 + 29 * q^5 - 22 * q^6 + 5 * q^7 - 120 * q^8 + 142 * q^9 - 58 * q^10 + 79 * q^11 + 44 * q^12 - 14 * q^13 - 10 * q^14 + 67 * q^15 + 240 * q^16 + 94 * q^17 - 284 * q^18 + 124 * q^19 + 116 * q^20 + 69 * q^21 - 158 * q^22 + 545 * q^23 - 88 * q^24 + 192 * q^25 + 28 * q^26 + 431 * q^27 + 20 * q^28 + 200 * q^29 - 134 * q^30 + 159 * q^31 - 480 * q^32 + 531 * q^33 - 188 * q^34 + 146 * q^35 + 568 * q^36 + 303 * q^37 - 248 * q^38 - 164 * q^39 - 232 * q^40 + 606 * q^41 - 138 * q^42 + 442 * q^43 + 316 * q^44 + 644 * q^45 - 1090 * q^46 + 618 * q^47 + 176 * q^48 + 286 * q^49 - 384 * q^50 - 251 * q^51 - 56 * q^52 + 916 * q^53 - 862 * q^54 + 53 * q^55 - 40 * q^56 + 190 * q^57 - 400 * q^58 + 1377 * q^59 + 268 * q^60 - 1373 * q^61 - 318 * q^62 + 1067 * q^63 + 960 * q^64 + 158 * q^65 - 1062 * q^66 + 1330 * q^67 + 376 * q^68 + 737 * q^69 - 292 * q^70 + 2291 * q^71 - 1136 * q^72 + 924 * q^73 - 606 * q^74 + 4337 * q^75 + 496 * q^76 + 4170 * q^77 + 328 * q^78 + 610 * q^79 + 464 * q^80 + 2255 * q^81 - 1212 * q^82 + 5191 * q^83 + 276 * q^84 + 1517 * q^85 - 884 * q^86 + 7295 * q^87 - 632 * q^88 + 3198 * q^89 - 1288 * q^90 + 4289 * q^91 + 2180 * q^92 + 5255 * q^93 - 1236 * q^94 + 4706 * q^95 - 352 * q^96 + 3806 * q^97 - 572 * q^98 + 7068 * 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
$3$	−8.56722	−1.64876	−0.824381	−	0.566036i	$-0.808476\pi$
$3$	−8.56722	−1.64876	−0.824381	+	0.566036i	$0.808476\pi$
$4$	4.00000	0.500000
$5$	−3.91913	−0.350537	−0.175269	−	0.984521i	$-0.556079\pi$
$5$	−3.91913	−0.350537	−0.175269	+	0.984521i	$0.556079\pi$
$6$	17.1344	1.16585
$7$	−8.79649	−0.474966	−0.237483	−	0.971392i	$-0.576322\pi$
$7$	−8.79649	−0.474966	−0.237483	+	0.971392i	$0.576322\pi$
$8$	−8.00000	−0.353553
$9$	46.3972	1.71841
$10$	7.83826	0.247867
$11$	−20.7785	−0.569541	−0.284770	−	0.958596i	$-0.591917\pi$
$11$	−20.7785	−0.569541	−0.284770	+	0.958596i	$0.591917\pi$
$12$	−34.2689	−0.824381
$13$	−4.62558	−0.0986850	−0.0493425	−	0.998782i	$-0.515713\pi$
$13$	−4.62558	−0.0986850	−0.0493425	+	0.998782i	$0.515713\pi$
$14$	17.5930	0.335851
$15$	33.5760	0.577953
$16$	16.0000	0.250000
$17$	−65.4047	−0.933115	−0.466558	−	0.884491i	$-0.654506\pi$
$17$	−65.4047	−0.933115	−0.466558	+	0.884491i	$0.654506\pi$
$18$	−92.7944	−1.21510
$19$	−65.6710	−0.792945	−0.396473	−	0.918047i	$-0.629766\pi$
$19$	−65.6710	−0.792945	−0.396473	+	0.918047i	$0.629766\pi$
$20$	−15.6765	−0.175269
$21$	75.3614	0.783105
$22$	41.5570	0.402726
$23$	102.572	0.929902	0.464951	−	0.885336i	$-0.346072\pi$
$23$	102.572	0.929902	0.464951	+	0.885336i	$0.346072\pi$
$24$	68.5377	0.582925
$25$	−109.640	−0.877124
$26$	9.25116	0.0697808
$27$	−166.180	−1.18449
$28$	−35.1859	−0.237483
$29$	−294.284	−1.88438	−0.942192	−	0.335074i	$-0.891239\pi$
$29$	−294.284	−1.88438	−0.942192	+	0.335074i	$0.891239\pi$
$30$	−67.1520	−0.408674
$31$	−236.193	−1.36844	−0.684219	−	0.729277i	$-0.739857\pi$
$31$	−236.193	−1.36844	−0.684219	+	0.729277i	$0.739857\pi$
$32$	−32.0000	−0.176777
$33$	178.014	0.939037
$34$	130.809	0.659812
$35$	34.4746	0.166493
$36$	185.589	0.859207
$37$	−349.271	−1.55189	−0.775944	−	0.630802i	$-0.782726\pi$
$37$	−349.271	−1.55189	−0.775944	+	0.630802i	$0.782726\pi$
$38$	131.342	0.560697
$39$	39.6284	0.162708
$40$	31.3530	0.123934
$41$	−213.966	−0.815022	−0.407511	−	0.913200i	$-0.633603\pi$
$41$	−213.966	−0.815022	−0.407511	+	0.913200i	$0.633603\pi$
$42$	−150.723	−0.553739
$43$	439.249	1.55779	0.778894	−	0.627155i	$-0.215781\pi$
$43$	439.249	1.55779	0.778894	+	0.627155i	$0.215781\pi$
$44$	−83.1139	−0.284770
$45$	−181.837	−0.602369
$46$	−205.144	−0.657540
$47$	−408.782	−1.26866	−0.634330	−	0.773063i	$-0.718724\pi$
$47$	−408.782	−1.26866	−0.634330	+	0.773063i	$0.718724\pi$
$48$	−137.075	−0.412190
$49$	−265.622	−0.774408
$50$	219.281	0.620220
$51$	560.336	1.53848
$52$	−18.5023	−0.0493425
$53$	563.247	1.45977	0.729886	−	0.683569i	$-0.239573\pi$
$53$	563.247	1.45977	0.729886	+	0.683569i	$0.239573\pi$
$54$	332.360	0.837564
$55$	81.4335	0.199645
$56$	70.3719	0.167926
$57$	562.618	1.30738
$58$	588.567	1.33246
$59$	707.804	1.56183	0.780917	−	0.624635i	$-0.214752\pi$
$59$	707.804	1.56183	0.780917	+	0.624635i	$0.214752\pi$
$60$	134.304	0.288976
$61$	−530.692	−1.11390	−0.556952	−	0.830545i	$-0.688029\pi$
$61$	−530.692	−1.11390	−0.556952	+	0.830545i	$0.688029\pi$
$62$	472.387	0.967632
$63$	−408.132	−0.816188
$64$	64.0000	0.125000
$65$	18.1282	0.0345928
$66$	−356.028	−0.663999
$67$	−404.851	−0.738216	−0.369108	−	0.929387i	$-0.620337\pi$
$67$	−404.851	−0.738216	−0.369108	+	0.929387i	$0.620337\pi$
$68$	−261.619	−0.466558
$69$	−878.757	−1.53319
$70$	−68.9491	−0.117728
$71$	−393.079	−0.657041	−0.328521	−	0.944497i	$-0.606550\pi$
$71$	−393.079	−0.657041	−0.328521	+	0.944497i	$0.606550\pi$
$72$	−371.178	−0.607551
$73$	319.407	0.512107	0.256054	−	0.966663i	$-0.417578\pi$
$73$	319.407	0.512107	0.256054	+	0.966663i	$0.417578\pi$
$74$	698.542	1.09735
$75$	939.313	1.44617
$76$	−262.684	−0.396473
$77$	182.778	0.270512
$78$	−79.2567	−0.115052
$79$	1263.45	1.79935	0.899676	−	0.436559i	$-0.143803\pi$
$79$	1263.45	1.79935	0.899676	+	0.436559i	$0.143803\pi$
$80$	−62.7060	−0.0876344
$81$	170.975	0.234534
$82$	427.933	0.576308
$83$	956.077	1.26437	0.632187	−	0.774816i	$-0.282157\pi$
$83$	956.077	1.26437	0.632187	+	0.774816i	$0.282157\pi$
$84$	301.446	0.391552
$85$	256.329	0.327092
$86$	−878.499	−1.10152
$87$	2521.19	3.10690
$88$	166.228	0.201363
$89$	−625.916	−0.745471	−0.372736	−	0.927938i	$-0.621580\pi$
$89$	−625.916	−0.745471	−0.372736	+	0.927938i	$0.621580\pi$
$90$	363.673	0.425939
$91$	40.6889	0.0468720
$92$	410.288	0.464951
$93$	2023.52	2.25623
$94$	817.564	0.897078
$95$	257.373	0.277957
$96$	274.151	0.291463
$97$	−18.2342	−0.0190866	−0.00954331	−	0.999954i	$-0.503038\pi$
$97$	−18.2342	−0.0190866	−0.00954331	+	0.999954i	$0.503038\pi$
$98$	531.244	0.547589
$99$	−964.063	−0.978707
$100$	−438.562	−0.438562
$101$	−336.934	−0.331942	−0.165971	−	0.986131i	$-0.553076\pi$
$101$	−336.934	−0.331942	−0.165971	+	0.986131i	$0.553076\pi$
$102$	−1120.67	−1.08787
$103$	−1864.34	−1.78349	−0.891744	−	0.452540i	$-0.850518\pi$
$103$	−1864.34	−1.78349	−0.891744	+	0.452540i	$0.850518\pi$
$104$	37.0046	0.0348904
$105$	−295.351	−0.274508
$106$	−1126.49	−1.03222
$107$	1070.55	0.967232	0.483616	−	0.875280i	$-0.339323\pi$
$107$	1070.55	0.967232	0.483616	+	0.875280i	$0.339323\pi$
$108$	−664.720	−0.592247
$109$	1007.69	0.885493	0.442747	−	0.896647i	$-0.354004\pi$
$109$	1007.69	0.885493	0.442747	+	0.896647i	$0.354004\pi$
$110$	−162.867	−0.141171
$111$	2992.28	2.55869
$112$	−140.744	−0.118741
$113$	2365.30	1.96911	0.984553	−	0.175087i	$-0.0560208\pi$
$113$	2365.30	1.96911	0.984553	+	0.175087i	$0.0560208\pi$
$114$	−1125.24	−0.924456
$115$	−401.993	−0.325965
$116$	−1177.13	−0.942192
$117$	−214.614	−0.169582
$118$	−1415.61	−1.10438
$119$	575.331	0.443198
$120$	−268.608	−0.204337
$121$	−899.255	−0.675623
$122$	1061.38	0.787649
$123$	1833.10	1.34378
$124$	−944.773	−0.684219
$125$	919.586	0.658002
$126$	816.265	0.577132
$127$	477.027	0.333302	0.166651	−	0.986016i	$-0.446705\pi$
$127$	477.027	0.333302	0.166651	+	0.986016i	$0.446705\pi$
$128$	−128.000	−0.0883883
$129$	−3763.14	−2.56842
$130$	−36.2565	−0.0244608
$131$	−347.246	−0.231595	−0.115798	−	0.993273i	$-0.536942\pi$
$131$	−347.246	−0.231595	−0.115798	+	0.993273i	$0.536942\pi$
$132$	712.055	0.469519
$133$	577.674	0.376622
$134$	809.703	0.521997
$135$	651.280	0.415210
$136$	523.237	0.329906
$137$	−1343.23	−0.837660	−0.418830	−	0.908065i	$-0.637560\pi$
$137$	−1343.23	−0.837660	−0.418830	+	0.908065i	$0.637560\pi$
$138$	1757.51	1.08413
$139$	1170.49	0.714245	0.357123	−	0.934058i	$-0.383758\pi$
$139$	1170.49	0.714245	0.357123	+	0.934058i	$0.383758\pi$
$140$	137.898	0.0832466
$141$	3502.12	2.09172
$142$	786.158	0.464598
$143$	96.1126	0.0562052
$144$	742.355	0.429604
$145$	1153.34	0.660547
$146$	−638.815	−0.362114
$147$	2275.64	1.27681
$148$	−1397.08	−0.775944
$149$	−18.6408	−0.0102491	−0.00512454	−	0.999987i	$-0.501631\pi$
$149$	−18.6408	−0.0102491	−0.00512454	+	0.999987i	$0.501631\pi$
$150$	−1878.63	−1.02259
$151$	319.970	0.172442	0.0862212	−	0.996276i	$-0.472521\pi$
$151$	319.970	0.172442	0.0862212	+	0.996276i	$0.472521\pi$
$152$	525.368	0.280349
$153$	−3034.59	−1.60348
$154$	−365.555	−0.191281
$155$	925.672	0.479689
$156$	158.513	0.0813540
$157$	−1752.68	−0.890947	−0.445474	−	0.895295i	$-0.646965\pi$
$157$	−1752.68	−0.890947	−0.445474	+	0.895295i	$0.646965\pi$
$158$	−2526.89	−1.27233
$159$	−4825.46	−2.40682
$160$	125.412	0.0619668
$161$	−902.273	−0.441671
$162$	−341.951	−0.165841
$163$	814.914	0.391589	0.195794	−	0.980645i	$-0.437272\pi$
$163$	814.914	0.391589	0.195794	+	0.980645i	$0.437272\pi$
$164$	−855.865	−0.407511
$165$	−697.659	−0.329168
$166$	−1912.15	−0.894048
$167$	2659.81	1.23247	0.616234	−	0.787563i	$-0.288657\pi$
$167$	2659.81	1.23247	0.616234	+	0.787563i	$0.288657\pi$
$168$	−602.891	−0.276869
$169$	−2175.60	−0.990261
$170$	−512.658	−0.231289
$171$	−3046.95	−1.36261
$172$	1757.00	0.778894
$173$	−2002.84	−0.880190	−0.440095	−	0.897951i	$-0.645055\pi$
$173$	−2002.84	−0.880190	−0.440095	+	0.897951i	$0.645055\pi$
$174$	−5042.38	−2.19691
$175$	964.451	0.416603
$176$	−332.456	−0.142385
$177$	−6063.91	−2.57509
$178$	1251.83	0.527128
$179$	−3258.26	−1.36052	−0.680262	−	0.732969i	$-0.738134\pi$
$179$	−3258.26	−1.36052	−0.680262	+	0.732969i	$0.738134\pi$
$180$	−727.346	−0.301184
$181$	4096.45	1.68225	0.841124	−	0.540842i	$-0.181894\pi$
$181$	4096.45	1.68225	0.841124	+	0.540842i	$0.181894\pi$
$182$	−81.3777	−0.0331435
$183$	4546.55	1.83656
$184$	−820.576	−0.328770
$185$	1368.84	0.543994
$186$	−4047.04	−1.59539
$187$	1359.01	0.531447
$188$	−1635.13	−0.634330
$189$	1461.80	0.562594
$190$	−514.746	−0.196545
$191$	−4880.90	−1.84906	−0.924528	−	0.381113i	$-0.875541\pi$
$191$	−4880.90	−1.84906	−0.924528	+	0.381113i	$0.875541\pi$
$192$	−548.302	−0.206095
$193$	−3673.29	−1.37000	−0.684998	−	0.728545i	$-0.740197\pi$
$193$	−3673.29	−1.37000	−0.684998	+	0.728545i	$0.740197\pi$
$194$	36.4684	0.0134963
$195$	−155.309	−0.0570353
$196$	−1062.49	−0.387204
$197$	4320.60	1.56259	0.781295	−	0.624162i	$-0.214559\pi$
$197$	4320.60	1.56259	0.781295	+	0.624162i	$0.214559\pi$
$198$	1928.13	0.692051
$199$	−4624.68	−1.64741	−0.823706	−	0.567017i	$-0.808097\pi$
$199$	−4624.68	−1.64741	−0.823706	+	0.567017i	$0.808097\pi$
$200$	877.124	0.310110
$201$	3468.45	1.21714
$202$	673.868	0.234719
$203$	2588.66	0.895017
$204$	2241.34	0.769242
$205$	838.561	0.285696
$206$	3728.69	1.26112
$207$	4759.05	1.59796
$208$	−74.0093	−0.0246713
$209$	1364.54	0.451615
$210$	590.702	0.194106
$211$	−2887.80	−0.942201	−0.471100	−	0.882080i	$-0.656143\pi$
$211$	−2887.80	−0.942201	−0.471100	+	0.882080i	$0.656143\pi$
$212$	2252.99	0.729886
$213$	3367.59	1.08330
$214$	−2141.10	−0.683936
$215$	−1721.47	−0.546063
$216$	1329.44	0.418782
$217$	2077.67	0.649961
$218$	−2015.37	−0.626138
$219$	−2736.43	−0.844342
$220$	325.734	0.0998227
$221$	302.535	0.0920845
$222$	−5984.56	−1.80927
$223$	−876.910	−0.263328	−0.131664	−	0.991294i	$-0.542032\pi$
$223$	−876.910	−0.263328	−0.131664	+	0.991294i	$0.542032\pi$
$224$	281.488	0.0839628
$225$	−5087.01	−1.50726
$226$	−4730.61	−1.39237
$227$	1639.66	0.479419	0.239710	−	0.970845i	$-0.422948\pi$
$227$	1639.66	0.479419	0.239710	+	0.970845i	$0.422948\pi$
$228$	2250.47	0.653689
$229$	1903.72	0.549351	0.274675	−	0.961537i	$-0.411430\pi$
$229$	1903.72	0.549351	0.274675	+	0.961537i	$0.411430\pi$
$230$	803.986	0.230492
$231$	−1565.90	−0.446010
$232$	2354.27	0.666230
$233$	6193.76	1.74149	0.870743	−	0.491738i	$-0.163638\pi$
$233$	6193.76	1.74149	0.870743	+	0.491738i	$0.163638\pi$
$234$	429.228	0.119912
$235$	1602.07	0.444713
$236$	2831.21	0.780917
$237$	−10824.2	−2.96670
$238$	−1150.66	−0.313388
$239$	4914.38	1.33006	0.665031	−	0.746816i	$-0.268418\pi$
$239$	4914.38	1.33006	0.665031	+	0.746816i	$0.268418\pi$
$240$	537.216	0.144488
$241$	4839.50	1.29353	0.646763	−	0.762691i	$-0.276122\pi$
$241$	4839.50	1.29353	0.646763	+	0.762691i	$0.276122\pi$
$242$	1798.51	0.477738
$243$	3022.08	0.797803
$244$	−2122.77	−0.556952
$245$	1041.01	0.271459
$246$	−3666.19	−0.950194
$247$	303.767	0.0782518
$248$	1889.55	0.483816
$249$	−8190.92	−2.08465
$250$	−1839.17	−0.465278
$251$	−3118.20	−0.784139	−0.392070	−	0.919935i	$-0.628241\pi$
$251$	−3118.20	−0.784139	−0.392070	+	0.919935i	$0.628241\pi$
$252$	−1632.53	−0.408094
$253$	−2131.29	−0.529617
$254$	−954.054	−0.235680
$255$	−2196.03	−0.539296
$256$	256.000	0.0625000
$257$	4360.89	1.05846	0.529231	−	0.848478i	$-0.322480\pi$
$257$	4360.89	1.05846	0.529231	+	0.848478i	$0.322480\pi$
$258$	7526.29	1.81615
$259$	3072.36	0.737093
$260$	72.5130	0.0172964
$261$	−13653.9	−3.23815
$262$	694.491	0.163763
$263$	−3762.86	−0.882236	−0.441118	−	0.897449i	$-0.645418\pi$
$263$	−3762.86	−0.882236	−0.441118	+	0.897449i	$0.645418\pi$
$264$	−1424.11	−0.332000
$265$	−2207.44	−0.511705
$266$	−1155.35	−0.266312
$267$	5362.35	1.22910
$268$	−1619.41	−0.369108
$269$	−269.000	−0.0609711
$269$	−269.000	−0.0609711
$270$	−1302.56	−0.293598
$271$	3124.09	0.700276	0.350138	−	0.936698i	$-0.386135\pi$
$271$	3124.09	0.700276	0.350138	+	0.936698i	$0.386135\pi$
$272$	−1046.47	−0.233279
$273$	−348.590	−0.0772807
$274$	2686.45	0.592315
$275$	2278.16	0.499558
$276$	−3515.03	−0.766593
$277$	−3145.09	−0.682203	−0.341102	−	0.940026i	$-0.610800\pi$
$277$	−3145.09	−0.682203	−0.341102	+	0.940026i	$0.610800\pi$
$278$	−2340.99	−0.505048
$279$	−10958.7	−2.35154
$280$	−275.796	−0.0588642
$281$	2281.22	0.484293	0.242147	−	0.970240i	$-0.422148\pi$
$281$	2281.22	0.484293	0.242147	+	0.970240i	$0.422148\pi$
$282$	−7004.25	−1.47907
$283$	4220.93	0.886602	0.443301	−	0.896373i	$-0.353807\pi$
$283$	4220.93	0.886602	0.443301	+	0.896373i	$0.353807\pi$
$284$	−1572.32	−0.328521
$285$	−2204.97	−0.458285
$286$	−192.225	−0.0397430
$287$	1882.15	0.387108
$288$	−1484.71	−0.303776
$289$	−635.230	−0.129296
$290$	−2306.67	−0.467077
$291$	156.216	0.0314693
$292$	1277.63	0.256054
$293$	−2543.56	−0.507155	−0.253577	−	0.967315i	$-0.581607\pi$
$293$	−2543.56	−0.507155	−0.253577	+	0.967315i	$0.581607\pi$
$294$	−4551.28	−0.902844
$295$	−2773.97	−0.547481
$296$	2794.17	0.548675
$297$	3452.97	0.674618
$298$	37.2816	0.00724719
$299$	−474.455	−0.0917674
$300$	3757.25	0.723084
$301$	−3863.85	−0.739896
$302$	−639.940	−0.121935
$303$	2886.59	0.547294
$304$	−1050.74	−0.198236
$305$	2079.85	0.390465
$306$	6069.19	1.13383
$307$	−104.075	−0.0193481	−0.00967403	−	0.999953i	$-0.503079\pi$
$307$	−104.075	−0.0193481	−0.00967403	+	0.999953i	$0.503079\pi$
$308$	731.111	0.135256
$309$	15972.2	2.94055
$310$	−1851.34	−0.339191
$311$	4174.21	0.761086	0.380543	−	0.924763i	$-0.375737\pi$
$311$	4174.21	0.761086	0.380543	+	0.924763i	$0.375737\pi$
$312$	−317.027	−0.0575260
$313$	−6030.19	−1.08897	−0.544483	−	0.838772i	$-0.683274\pi$
$313$	−6030.19	−1.08897	−0.544483	+	0.838772i	$0.683274\pi$
$314$	3505.35	0.629995
$315$	1599.52	0.286104
$316$	5053.78	0.899676
$317$	4123.80	0.730649	0.365324	−	0.930880i	$-0.380958\pi$
$317$	4123.80	0.730649	0.365324	+	0.930880i	$0.380958\pi$
$318$	9650.92	1.70188
$319$	6114.77	1.07323
$320$	−250.824	−0.0438172
$321$	−9171.62	−1.59473
$322$	1804.55	0.312309
$323$	4295.19	0.739909
$324$	683.902	0.117267
$325$	507.151	0.0865590
$326$	−1629.83	−0.276895
$327$	−8633.06	−1.45997
$328$	1711.73	0.288154
$329$	3595.85	0.602570
$330$	1395.32	0.232757
$331$	2336.11	0.387928	0.193964	−	0.981009i	$-0.437866\pi$
$331$	2336.11	0.387928	0.193964	+	0.981009i	$0.437866\pi$
$332$	3824.31	0.632187
$333$	−16205.2	−2.66679
$334$	−5319.62	−0.871487
$335$	1586.66	0.258772
$336$	1205.78	0.195776
$337$	−7892.98	−1.27584	−0.637920	−	0.770103i	$-0.720205\pi$
$337$	−7892.98	−1.27584	−0.637920	+	0.770103i	$0.720205\pi$
$338$	4351.21	0.700220
$339$	−20264.1	−3.24659
$340$	1025.32	0.163546
$341$	4907.74	0.779381
$342$	6093.90	0.963510
$343$	5353.73	0.842783
$344$	−3514.00	−0.550761
$345$	3443.96	0.537439
$346$	4005.67	0.622388
$347$	3891.02	0.601962	0.300981	−	0.953630i	$-0.402686\pi$
$347$	3891.02	0.601962	0.300981	+	0.953630i	$0.402686\pi$
$348$	10084.8	1.55345
$349$	−11706.2	−1.79547	−0.897736	−	0.440534i	$-0.854789\pi$
$349$	−11706.2	−1.79547	−0.897736	+	0.440534i	$0.854789\pi$
$350$	−1928.90	−0.294583
$351$	768.679	0.116892
$352$	664.912	0.100682
$353$	3176.80	0.478991	0.239495	−	0.970897i	$-0.423018\pi$
$353$	3176.80	0.478991	0.239495	+	0.970897i	$0.423018\pi$
$354$	12127.8	1.82086
$355$	1540.53	0.230318
$356$	−2503.66	−0.372736
$357$	−4928.99	−0.730727
$358$	6516.52	0.962036
$359$	4871.15	0.716127	0.358064	−	0.933697i	$-0.383437\pi$
$359$	4871.15	0.716127	0.358064	+	0.933697i	$0.383437\pi$
$360$	1454.69	0.212969
$361$	−2546.32	−0.371238
$362$	−8192.90	−1.18953
$363$	7704.11	1.11394
$364$	162.755	0.0234360
$365$	−1251.80	−0.179513
$366$	−9093.11	−1.29865
$367$	2226.29	0.316652	0.158326	−	0.987387i	$-0.449390\pi$
$367$	2226.29	0.316652	0.158326	+	0.987387i	$0.449390\pi$
$368$	1641.15	0.232475
$369$	−9927.44	−1.40055
$370$	−2737.68	−0.384662
$371$	−4954.60	−0.693342
$372$	8094.08	1.12811
$373$	−8816.62	−1.22388	−0.611940	−	0.790904i	$-0.709610\pi$
$373$	−8816.62	−1.22388	−0.611940	+	0.790904i	$0.709610\pi$
$374$	−2718.02	−0.375790
$375$	−7878.29	−1.08489
$376$	3270.26	0.448539
$377$	1361.23	0.185960
$378$	−2923.60	−0.397814
$379$	9053.02	1.22697	0.613486	−	0.789705i	$-0.289767\pi$
$379$	9053.02	1.22697	0.613486	+	0.789705i	$0.289767\pi$
$380$	1029.49	0.138979
$381$	−4086.79	−0.549535
$382$	9761.81	1.30748
$383$	−7441.05	−0.992741	−0.496370	−	0.868111i	$-0.665334\pi$
$383$	−7441.05	−0.992741	−0.496370	+	0.868111i	$0.665334\pi$
$384$	1096.60	0.145731
$385$	−716.329	−0.0948247
$386$	7346.58	0.968733
$387$	20379.9	2.67693
$388$	−72.9368	−0.00954331
$389$	9412.93	1.22687	0.613437	−	0.789743i	$-0.289786\pi$
$389$	9412.93	1.22687	0.613437	+	0.789743i	$0.289786\pi$
$390$	310.617	0.0403300
$391$	−6708.69	−0.867706
$392$	2124.97	0.273794
$393$	2974.93	0.381845
$394$	−8641.21	−1.10492
$395$	−4951.61	−0.630740
$396$	−3856.25	−0.489354
$397$	2461.26	0.311151	0.155575	−	0.987824i	$-0.450277\pi$
$397$	2461.26	0.311151	0.155575	+	0.987824i	$0.450277\pi$
$398$	9249.36	1.16490
$399$	−4949.06	−0.620959
$400$	−1754.25	−0.219281
$401$	−1975.56	−0.246021	−0.123011	−	0.992405i	$-0.539255\pi$
$401$	−1975.56	−0.246021	−0.123011	+	0.992405i	$0.539255\pi$
$402$	−6936.90	−0.860649
$403$	1092.53	0.135044
$404$	−1347.74	−0.165971
$405$	−670.075	−0.0822130
$406$	−5177.33	−0.632873
$407$	7257.33	0.883863
$408$	−4482.69	−0.543936
$409$	−2506.50	−0.303028	−0.151514	−	0.988455i	$-0.548415\pi$
$409$	−2506.50	−0.303028	−0.151514	+	0.988455i	$0.548415\pi$
$410$	−1677.12	−0.202017
$411$	11507.7	1.38110
$412$	−7457.37	−0.891744
$413$	−6226.18	−0.741817
$414$	−9518.11	−1.12993
$415$	−3746.99	−0.443211
$416$	148.019	0.0174452
$417$	−10027.9	−1.17762
$418$	−2729.09	−0.319340
$419$	8566.84	0.998849	0.499424	−	0.866358i	$-0.333545\pi$
$419$	8566.84	0.998849	0.499424	+	0.866358i	$0.333545\pi$
$420$	−1181.40	−0.137254
$421$	8177.17	0.946630	0.473315	−	0.880893i	$-0.343057\pi$
$421$	8177.17	0.946630	0.473315	+	0.880893i	$0.343057\pi$
$422$	5775.60	0.666237
$423$	−18966.3	−2.18008
$424$	−4505.98	−0.516108
$425$	7171.00	0.818457
$426$	−6735.19	−0.766012
$427$	4668.23	0.529066
$428$	4282.19	0.483616
$429$	−823.417	−0.0926689
$430$	3442.95	0.386125
$431$	13772.5	1.53921	0.769605	−	0.638520i	$-0.220453\pi$
$431$	13772.5	1.53921	0.769605	+	0.638520i	$0.220453\pi$
$432$	−2658.88	−0.296124
$433$	−130.033	−0.0144319	−0.00721595	−	0.999974i	$-0.502297\pi$
$433$	−130.033	−0.0144319	−0.00721595	+	0.999974i	$0.502297\pi$
$434$	−4155.34	−0.459592
$435$	−9880.87	−1.08908
$436$	4030.74	0.442747
$437$	−6736.01	−0.737361
$438$	5472.87	0.597040
$439$	−10139.8	−1.10238	−0.551189	−	0.834380i	$-0.685826\pi$
$439$	−10139.8	−1.10238	−0.551189	+	0.834380i	$0.685826\pi$
$440$	−651.468	−0.0705853
$441$	−12324.1	−1.33075
$442$	−605.069	−0.0651136
$443$	−4992.22	−0.535412	−0.267706	−	0.963501i	$-0.586266\pi$
$443$	−4992.22	−0.535412	−0.267706	+	0.963501i	$0.586266\pi$
$444$	11969.1	1.27935
$445$	2453.04	0.261316
$446$	1753.82	0.186201
$447$	159.700	0.0168983
$448$	−562.975	−0.0593707
$449$	12347.0	1.29776	0.648878	−	0.760893i	$-0.275239\pi$
$449$	12347.0	1.29776	0.648878	+	0.760893i	$0.275239\pi$
$450$	10174.0	1.06580
$451$	4445.90	0.464189
$452$	9461.21	0.984553
$453$	−2741.25	−0.284316
$454$	−3279.32	−0.339001
$455$	−159.465	−0.0164304
$456$	−4500.94	−0.462228
$457$	−1742.55	−0.178365	−0.0891825	−	0.996015i	$-0.528425\pi$
$457$	−1742.55	−0.178365	−0.0891825	+	0.996015i	$0.528425\pi$
$458$	−3807.44	−0.388450
$459$	10868.9	1.10527
$460$	−1607.97	−0.162983
$461$	−3993.01	−0.403413	−0.201706	−	0.979446i	$-0.564649\pi$
$461$	−3993.01	−0.403413	−0.201706	+	0.979446i	$0.564649\pi$
$462$	3131.79	0.315377
$463$	11933.7	1.19785	0.598924	−	0.800806i	$-0.295595\pi$
$463$	11933.7	1.19785	0.598924	+	0.800806i	$0.295595\pi$
$464$	−4708.54	−0.471096
$465$	−7930.43	−0.790892
$466$	−12387.5	−1.23142
$467$	7008.75	0.694489	0.347244	−	0.937775i	$-0.387117\pi$
$467$	7008.75	0.694489	0.347244	+	0.937775i	$0.387117\pi$
$468$	−858.456	−0.0847909
$469$	3561.27	0.350627
$470$	−3204.14	−0.314459
$471$	15015.5	1.46896
$472$	−5662.43	−0.552192
$473$	−9126.94	−0.887224
$474$	21648.4	2.09778
$475$	7200.20	0.695511
$476$	2301.32	0.221599
$477$	26133.1	2.50849
$478$	−9828.76	−0.940496
$479$	−13942.4	−1.32995	−0.664976	−	0.746865i	$-0.731558\pi$
$479$	−13942.4	−1.32995	−0.664976	+	0.746865i	$0.731558\pi$
$480$	−1074.43	−0.102169
$481$	1615.58	0.153148
$482$	−9679.00	−0.914661
$483$	7729.97	0.728211
$484$	−3597.02	−0.337812
$485$	71.4621	0.00669057
$486$	−6044.15	−0.564132
$487$	4196.59	0.390484	0.195242	−	0.980755i	$-0.437451\pi$
$487$	4196.59	0.390484	0.195242	+	0.980755i	$0.437451\pi$
$488$	4245.54	0.393825
$489$	−6981.54	−0.645636
$490$	−2082.01	−0.191950
$491$	−2111.33	−0.194059	−0.0970295	−	0.995282i	$-0.530934\pi$
$491$	−2111.33	−0.194059	−0.0970295	+	0.995282i	$0.530934\pi$
$492$	7332.38	0.671889
$493$	19247.5	1.75835
$494$	−607.533	−0.0553324
$495$	3778.29	0.343074
$496$	−3779.09	−0.342109
$497$	3457.72	0.312072
$498$	16381.8	1.47407
$499$	20437.0	1.83344	0.916720	−	0.399531i	$-0.130827\pi$
$499$	20437.0	1.83344	0.916720	+	0.399531i	$0.130827\pi$
$500$	3678.34	0.329001
$501$	−22787.2	−2.03205
$502$	6236.40	0.554470
$503$	454.849	0.0403196	0.0201598	−	0.999797i	$-0.493583\pi$
$503$	454.849	0.0403196	0.0201598	+	0.999797i	$0.493583\pi$
$504$	3265.06	0.288566
$505$	1320.49	0.116358
$506$	4262.58	0.374496
$507$	18638.9	1.63270
$508$	1908.11	0.166651
$509$	6333.30	0.551510	0.275755	−	0.961228i	$-0.411072\pi$
$509$	6333.30	0.551510	0.275755	+	0.961228i	$0.411072\pi$
$510$	4392.06	0.381340
$511$	−2809.66	−0.243233
$512$	−512.000	−0.0441942
$513$	10913.2	0.939239
$514$	−8721.78	−0.748446
$515$	7306.60	0.625179
$516$	−15052.6	−1.28421
$517$	8493.87	0.722553
$518$	−6144.72	−0.521203
$519$	17158.7	1.45122
$520$	−145.026	−0.0122304
$521$	1590.59	0.133752	0.0668762	−	0.997761i	$-0.478697\pi$
$521$	1590.59	0.133752	0.0668762	+	0.997761i	$0.478697\pi$
$522$	27307.9	2.28972
$523$	−12164.9	−1.01708	−0.508542	−	0.861037i	$-0.669815\pi$
$523$	−12164.9	−1.01708	−0.508542	+	0.861037i	$0.669815\pi$
$524$	−1388.98	−0.115798
$525$	−8262.66	−0.686880
$526$	7525.73	0.623835
$527$	15448.1	1.27691
$528$	2848.22	0.234759
$529$	−1645.98	−0.135282
$530$	4414.87	0.361830
$531$	32840.1	2.68388
$532$	2310.70	0.188311
$533$	989.718	0.0804305
$534$	−10724.7	−0.869108
$535$	−4195.61	−0.339051
$536$	3238.81	0.260999
$537$	27914.2	2.24318
$538$	538.000	0.0431131
$539$	5519.22	0.441057
$540$	2605.12	0.207605
$541$	−6567.20	−0.521897	−0.260948	−	0.965353i	$-0.584035\pi$
$541$	−6567.20	−0.521897	−0.260948	+	0.965353i	$0.584035\pi$
$542$	−6248.17	−0.495170
$543$	−35095.2	−2.77363
$544$	2092.95	0.164953
$545$	−3949.25	−0.310399
$546$	697.180	0.0546457
$547$	−13457.3	−1.05190	−0.525951	−	0.850515i	$-0.676291\pi$
$547$	−13457.3	−1.05190	−0.525951	+	0.850515i	$0.676291\pi$
$548$	−5372.90	−0.418830
$549$	−24622.6	−1.91415
$550$	−4556.32	−0.353241
$551$	19325.9	1.49421
$552$	7030.05	0.542063
$553$	−11113.9	−0.854630
$554$	6290.19	0.482391
$555$	−11727.1	−0.896917
$556$	4681.98	0.357123
$557$	10125.6	0.770262	0.385131	−	0.922862i	$-0.374156\pi$
$557$	10125.6	0.770262	0.385131	+	0.922862i	$0.374156\pi$
$558$	21917.4	1.66279
$559$	−2031.78	−0.153730
$560$	551.593	0.0416233
$561$	−11642.9	−0.876230
$562$	−4562.45	−0.342447
$563$	−10284.4	−0.769867	−0.384933	−	0.922944i	$-0.625776\pi$
$563$	−10284.4	−0.769867	−0.384933	+	0.922944i	$0.625776\pi$
$564$	14008.5	1.04586
$565$	−9269.92	−0.690245
$566$	−8441.87	−0.626923
$567$	−1503.98	−0.111396
$568$	3144.63	0.232299
$569$	−4089.80	−0.301324	−0.150662	−	0.988585i	$-0.548141\pi$
$569$	−4089.80	−0.301324	−0.150662	+	0.988585i	$0.548141\pi$
$570$	4409.94	0.324056
$571$	5467.48	0.400712	0.200356	−	0.979723i	$-0.435790\pi$
$571$	5467.48	0.400712	0.200356	+	0.979723i	$0.435790\pi$
$572$	384.450	0.0281026
$573$	41815.8	3.04865
$574$	−3764.30	−0.273726
$575$	−11246.0	−0.815639
$576$	2969.42	0.214802
$577$	15170.9	1.09458	0.547290	−	0.836943i	$-0.315659\pi$
$577$	15170.9	1.09458	0.547290	+	0.836943i	$0.315659\pi$
$578$	1270.46	0.0914259
$579$	31469.9	2.25880
$580$	4613.34	0.330273
$581$	−8410.12	−0.600534
$582$	−312.433	−0.0222521
$583$	−11703.4	−0.831400
$584$	−2555.26	−0.181057
$585$	841.100	0.0594448
$586$	5087.12	0.358613
$587$	−15977.1	−1.12341	−0.561707	−	0.827336i	$-0.689855\pi$
$587$	−15977.1	−1.12341	−0.561707	+	0.827336i	$0.689855\pi$
$588$	9102.56	0.638407
$589$	15511.1	1.08510
$590$	5547.94	0.387128
$591$	−37015.5	−2.57634
$592$	−5588.34	−0.387972
$593$	−17473.5	−1.21003	−0.605017	−	0.796213i	$-0.706834\pi$
$593$	−17473.5	−1.21003	−0.605017	+	0.796213i	$0.706834\pi$
$594$	−6905.94	−0.477027
$595$	−2254.80	−0.155357
$596$	−74.5631	−0.00512454
$597$	39620.6	2.71619
$598$	948.910	0.0648893
$599$	1908.73	0.130198	0.0650988	−	0.997879i	$-0.479264\pi$
$599$	1908.73	0.130198	0.0650988	+	0.997879i	$0.479264\pi$
$600$	−7514.51	−0.511297
$601$	−10232.7	−0.694508	−0.347254	−	0.937771i	$-0.612886\pi$
$601$	−10232.7	−0.694508	−0.347254	+	0.937771i	$0.612886\pi$
$602$	7727.70	0.523185
$603$	−18784.0	−1.26856
$604$	1279.88	0.0862212
$605$	3524.29	0.236831
$606$	−5773.17	−0.386995
$607$	−6321.13	−0.422680	−0.211340	−	0.977413i	$-0.567783\pi$
$607$	−6321.13	−0.422680	−0.211340	+	0.977413i	$0.567783\pi$
$608$	2101.47	0.140174
$609$	−22177.6	−1.47567
$610$	−4159.70	−0.276101
$611$	1890.85	0.125198
$612$	−12138.4	−0.801740
$613$	−11014.1	−0.725702	−0.362851	−	0.931847i	$-0.618197\pi$
$613$	−11014.1	−0.725702	−0.362851	+	0.931847i	$0.618197\pi$
$614$	208.149	0.0136812
$615$	−7184.13	−0.471044
$616$	−1462.22	−0.0956405
$617$	−27706.9	−1.80784	−0.903919	−	0.427703i	$-0.859323\pi$
$617$	−27706.9	−1.80784	−0.903919	+	0.427703i	$0.859323\pi$
$618$	−31944.5	−2.07928
$619$	−13943.7	−0.905403	−0.452701	−	0.891662i	$-0.649540\pi$
$619$	−13943.7	−0.905403	−0.452701	+	0.891662i	$0.649540\pi$
$620$	3702.69	0.239844
$621$	−17045.4	−1.10146
$622$	−8348.42	−0.538169
$623$	5505.86	0.354073
$624$	634.054	0.0406770
$625$	10101.1	0.646469
$626$	12060.4	0.770015
$627$	−11690.3	−0.744605
$628$	−7010.70	−0.445474
$629$	22844.0	1.44809
$630$	−3199.04	−0.202306
$631$	−17734.2	−1.11884	−0.559419	−	0.828885i	$-0.688976\pi$
$631$	−17734.2	−1.11884	−0.559419	+	0.828885i	$0.688976\pi$
$632$	−10107.6	−0.636167
$633$	24740.4	1.55346
$634$	−8247.60	−0.516647
$635$	−1869.53	−0.116835
$636$	−19301.8	−1.20341
$637$	1228.66	0.0764224
$638$	−12229.5	−0.758890
$639$	−18237.8	−1.12907
$640$	501.648	0.0309834
$641$	6992.08	0.430843	0.215422	−	0.976521i	$-0.430887\pi$
$641$	6992.08	0.430843	0.215422	+	0.976521i	$0.430887\pi$
$642$	18343.2	1.12765
$643$	−23243.4	−1.42555	−0.712775	−	0.701393i	$-0.752562\pi$
$643$	−23243.4	−1.42555	−0.712775	+	0.701393i	$0.752562\pi$
$644$	−3609.09	−0.220836
$645$	14748.2	0.900328
$646$	−8590.38	−0.523195
$647$	−10308.2	−0.626361	−0.313180	−	0.949694i	$-0.601394\pi$
$647$	−10308.2	−0.626361	−0.313180	+	0.949694i	$0.601394\pi$
$648$	−1367.80	−0.0829204
$649$	−14707.1	−0.889528
$650$	−1014.30	−0.0612064
$651$	−17799.9	−1.07163
$652$	3259.65	0.195794
$653$	−19931.2	−1.19444	−0.597221	−	0.802077i	$-0.703728\pi$
$653$	−19931.2	−1.19444	−0.597221	+	0.802077i	$0.703728\pi$
$654$	17266.1	1.03235
$655$	1360.90	0.0811828
$656$	−3423.46	−0.203756
$657$	14819.6	0.880012
$658$	−7191.69	−0.426081
$659$	−8666.82	−0.512308	−0.256154	−	0.966636i	$-0.582455\pi$
$659$	−8666.82	−0.512308	−0.256154	+	0.966636i	$0.582455\pi$
$660$	−2790.63	−0.164584
$661$	−22490.5	−1.32342	−0.661710	−	0.749760i	$-0.730169\pi$
$661$	−22490.5	−1.32342	−0.661710	+	0.749760i	$0.730169\pi$
$662$	−4672.21	−0.274306
$663$	−2591.88	−0.151825
$664$	−7648.61	−0.447024
$665$	−2263.98	−0.132020
$666$	32410.4	1.88570
$667$	−30185.3	−1.75229
$668$	10639.2	0.616234
$669$	7512.68	0.434166
$670$	−3173.33	−0.182980
$671$	11027.0	0.634414
$672$	−2411.56	−0.138435
$673$	−2036.99	−0.116672	−0.0583361	−	0.998297i	$-0.518579\pi$
$673$	−2036.99	−0.116672	−0.0583361	+	0.998297i	$0.518579\pi$
$674$	15786.0	0.902155
$675$	18220.0	1.03895
$676$	−8702.42	−0.495131
$677$	20296.3	1.15221	0.576107	−	0.817374i	$-0.304571\pi$
$677$	20296.3	1.15221	0.576107	+	0.817374i	$0.304571\pi$
$678$	40528.1	2.29568
$679$	160.397	0.00906549
$680$	−2050.63	−0.115644
$681$	−14047.3	−0.790448
$682$	−9815.48	−0.551106
$683$	17867.9	1.00102	0.500509	−	0.865731i	$-0.333146\pi$
$683$	17867.9	1.00102	0.500509	+	0.865731i	$0.333146\pi$
$684$	−12187.8	−0.681304
$685$	5264.27	0.293631
$686$	−10707.5	−0.595937
$687$	−16309.6	−0.905748
$688$	7027.99	0.389447
$689$	−2605.35	−0.144058
$690$	−6887.92	−0.380027
$691$	−17376.4	−0.956626	−0.478313	−	0.878189i	$-0.658752\pi$
$691$	−17376.4	−0.956626	−0.478313	+	0.878189i	$0.658752\pi$
$692$	−8011.34	−0.440095
$693$	8480.37	0.464852
$694$	−7782.04	−0.425651
$695$	−4587.32	−0.250370
$696$	−20169.5	−1.09845
$697$	13994.4	0.760510
$698$	23412.4	1.26959
$699$	−53063.2	−2.87130
$700$	3857.80	0.208302
$701$	−26604.2	−1.43342	−0.716709	−	0.697372i	$-0.754352\pi$
$701$	−26604.2	−1.43342	−0.716709	+	0.697372i	$0.754352\pi$
$702$	−1537.36	−0.0826550
$703$	22937.0	1.23056
$704$	−1329.82	−0.0711926
$705$	−13725.3	−0.733225
$706$	−6353.59	−0.338698
$707$	2963.84	0.157661
$708$	−24255.6	−1.28755
$709$	9955.82	0.527361	0.263680	−	0.964610i	$-0.415064\pi$
$709$	9955.82	0.527361	0.263680	+	0.964610i	$0.415064\pi$
$710$	−3081.06	−0.162859
$711$	58620.4	3.09203
$712$	5007.32	0.263564
$713$	−24226.8	−1.27251
$714$	9857.97	0.516702
$715$	−376.677	−0.0197020
$716$	−13033.0	−0.680262
$717$	−42102.6	−2.19296
$718$	−9742.31	−0.506378
$719$	14511.6	0.752699	0.376350	−	0.926478i	$-0.377179\pi$
$719$	14511.6	0.752699	0.376350	+	0.926478i	$0.377179\pi$
$720$	−2909.38	−0.150592
$721$	16399.7	0.847095
$722$	5092.64	0.262505
$723$	−41461.1	−2.13272
$724$	16385.8	0.841124
$725$	32265.4	1.65284
$726$	−15408.2	−0.787676
$727$	22615.4	1.15373	0.576864	−	0.816840i	$-0.304276\pi$
$727$	22615.4	1.15373	0.576864	+	0.816840i	$0.304276\pi$
$728$	−325.511	−0.0165718
$729$	−30507.1	−1.54992
$730$	2503.60	0.126935
$731$	−28729.0	−1.45360
$732$	18186.2	0.918281
$733$	−17154.5	−0.864415	−0.432208	−	0.901774i	$-0.642265\pi$
$733$	−17154.5	−0.864415	−0.432208	+	0.901774i	$0.642265\pi$
$734$	−4452.58	−0.223907
$735$	−8918.52	−0.447571
$736$	−3282.30	−0.164385
$737$	8412.20	0.420444
$738$	19854.9	0.990336
$739$	−21558.2	−1.07312	−0.536558	−	0.843864i	$-0.680276\pi$
$739$	−21558.2	−1.07312	−0.536558	+	0.843864i	$0.680276\pi$
$740$	5475.35	0.271997
$741$	−2602.43	−0.129019
$742$	9909.19	0.490267
$743$	18289.3	0.903054	0.451527	−	0.892258i	$-0.350880\pi$
$743$	18289.3	0.903054	0.451527	+	0.892258i	$0.350880\pi$
$744$	−16188.2	−0.797697
$745$	73.0556	0.00359268
$746$	17633.2	0.865413
$747$	44359.3	2.17272
$748$	5436.04	0.265724
$749$	−9417.06	−0.459402
$750$	15756.6	0.767132
$751$	−17355.1	−0.843270	−0.421635	−	0.906766i	$-0.638544\pi$
$751$	−17355.1	−0.843270	−0.421635	+	0.906766i	$0.638544\pi$
$752$	−6540.51	−0.317165
$753$	26714.3	1.29286
$754$	−2722.47	−0.131494
$755$	−1254.00	−0.0604475
$756$	5847.20	0.281297
$757$	32246.3	1.54823	0.774115	−	0.633045i	$-0.218195\pi$
$757$	32246.3	1.54823	0.774115	+	0.633045i	$0.218195\pi$
$758$	−18106.0	−0.867601
$759$	18259.2	0.873212
$760$	−2058.98	−0.0982727
$761$	−6832.20	−0.325449	−0.162725	−	0.986672i	$-0.552028\pi$
$761$	−6832.20	−0.325449	−0.162725	+	0.986672i	$0.552028\pi$
$762$	8173.59	0.388580
$763$	−8864.09	−0.420579
$764$	−19523.6	−0.924528
$765$	11893.0	0.562079
$766$	14882.1	0.701974
$767$	−3274.00	−0.154130
$768$	−2193.21	−0.103048
$769$	14347.5	0.672800	0.336400	−	0.941719i	$-0.390791\pi$
$769$	14347.5	0.672800	0.336400	+	0.941719i	$0.390791\pi$
$770$	1432.66	0.0670512
$771$	−37360.7	−1.74515
$772$	−14693.2	−0.684998
$773$	−37191.8	−1.73052	−0.865262	−	0.501319i	$-0.832848\pi$
$773$	−37191.8	−1.73052	−0.865262	+	0.501319i	$0.832848\pi$
$774$	−40759.9	−1.89287
$775$	25896.3	1.20029
$776$	145.874	0.00674814
$777$	−26321.6	−1.21529
$778$	−18825.9	−0.867532
$779$	14051.4	0.646268
$780$	−621.234	−0.0285176
$781$	8167.59	0.374212
$782$	13417.4	0.613561
$783$	48904.1	2.23204
$784$	−4249.95	−0.193602
$785$	6868.96	0.312310
$786$	−5949.85	−0.270005
$787$	17025.9	0.771166	0.385583	−	0.922673i	$-0.374000\pi$
$787$	17025.9	0.771166	0.385583	+	0.922673i	$0.374000\pi$
$788$	17282.4	0.781295
$789$	32237.3	1.45460
$790$	9903.21	0.446001
$791$	−20806.4	−0.935257
$792$	7712.51	0.346025
$793$	2454.76	0.109926
$794$	−4922.51	−0.220017
$795$	18911.6	0.843679
$796$	−18498.7	−0.823706
$797$	33264.8	1.47842	0.739210	−	0.673475i	$-0.235199\pi$
$797$	33264.8	1.47842	0.739210	+	0.673475i	$0.235199\pi$
$798$	9898.12	0.439085
$799$	26736.3	1.18381
$800$	3508.49	0.155055
$801$	−29040.7	−1.28103
$802$	3951.11	0.173963
$803$	−6636.80	−0.291666
$804$	13873.8	0.608571
$805$	3536.12	0.154822
$806$	−2185.06	−0.0954907
$807$	2304.58	0.100527
$808$	2695.47	0.117359
$809$	−44722.8	−1.94360	−0.971798	−	0.235817i	$-0.924224\pi$
$809$	−44722.8	−1.94360	−0.971798	+	0.235817i	$0.924224\pi$
$810$	1340.15	0.0581334
$811$	18209.9	0.788453	0.394226	−	0.919013i	$-0.371013\pi$
$811$	18209.9	0.788453	0.394226	+	0.919013i	$0.371013\pi$
$812$	10354.7	0.447509
$813$	−26764.7	−1.15459
$814$	−14514.7	−0.624986
$815$	−3193.75	−0.137266
$816$	8965.37	0.384621
$817$	−28846.0	−1.23524
$818$	5013.00	0.214273
$819$	1887.85	0.0805455
$820$	3354.24	0.142848
$821$	46340.6	1.96991	0.984956	−	0.172803i	$-0.0552823\pi$
$821$	46340.6	1.96991	0.984956	+	0.172803i	$0.0552823\pi$
$822$	−23015.4	−0.976587
$823$	−18109.5	−0.767022	−0.383511	−	0.923536i	$-0.625285\pi$
$823$	−18109.5	−0.767022	−0.383511	+	0.923536i	$0.625285\pi$
$824$	14914.7	0.630558
$825$	−19517.5	−0.823651
$826$	12452.4	0.524544
$827$	−15923.6	−0.669549	−0.334775	−	0.942298i	$-0.608660\pi$
$827$	−15923.6	−0.669549	−0.334775	+	0.942298i	$0.608660\pi$
$828$	19036.2	0.798979
$829$	−29621.7	−1.24102	−0.620510	−	0.784199i	$-0.713074\pi$
$829$	−29621.7	−1.24102	−0.620510	+	0.784199i	$0.713074\pi$
$830$	7493.97	0.313397
$831$	26944.7	1.12479
$832$	−296.037	−0.0123356
$833$	17372.9	0.722612
$834$	20055.8	0.832703
$835$	−10424.1	−0.432026
$836$	5458.18	0.225807
$837$	39250.6	1.62091
$838$	−17133.7	−0.706293
$839$	−17636.8	−0.725731	−0.362866	−	0.931842i	$-0.618202\pi$
$839$	−17636.8	−0.725731	−0.362866	+	0.931842i	$0.618202\pi$
$840$	2362.81	0.0970531
$841$	62213.9	2.55090
$842$	−16354.3	−0.669368
$843$	−19543.7	−0.798484
$844$	−11551.2	−0.471100
$845$	8526.47	0.347124
$846$	37932.7	1.54155
$847$	7910.28	0.320898
$848$	9011.95	0.364943
$849$	−36161.7	−1.46180
$850$	−14342.0	−0.578737
$851$	−35825.4	−1.44310
$852$	13470.4	0.541652
$853$	19316.5	0.775365	0.387682	−	0.921793i	$-0.373276\pi$
$853$	19316.5	0.775365	0.387682	+	0.921793i	$0.373276\pi$
$854$	−9336.45	−0.374106
$855$	11941.4	0.477645
$856$	−8564.38	−0.341968
$857$	−45708.8	−1.82192	−0.910958	−	0.412498i	$-0.864656\pi$
$857$	−45708.8	−1.82192	−0.910958	+	0.412498i	$0.864656\pi$
$858$	1646.83	0.0655268
$859$	8113.87	0.322284	0.161142	−	0.986931i	$-0.448482\pi$
$859$	8113.87	0.322284	0.161142	+	0.986931i	$0.448482\pi$
$860$	−6885.90	−0.273032
$861$	−16124.8	−0.638248
$862$	−27545.1	−1.08839
$863$	30062.5	1.18579	0.592897	−	0.805279i	$-0.297984\pi$
$863$	30062.5	1.18579	0.592897	+	0.805279i	$0.297984\pi$
$864$	5317.76	0.209391
$865$	7849.37	0.308539
$866$	260.067	0.0102049
$867$	5442.15	0.213178
$868$	8310.68	0.324980
$869$	−26252.5	−1.02480
$870$	19761.7	0.770099
$871$	1872.67	0.0728508
$872$	−8061.48	−0.313069
$873$	−846.015	−0.0327987
$874$	13472.0	0.521393
$875$	−8089.12	−0.312528
$876$	−10945.7	−0.422171
$877$	−2172.86	−0.0836626	−0.0418313	−	0.999125i	$-0.513319\pi$
$877$	−2172.86	−0.0836626	−0.0418313	+	0.999125i	$0.513319\pi$
$878$	20279.5	0.779500
$879$	21791.2	0.836177
$880$	1302.94	0.0499113
$881$	−17545.9	−0.670985	−0.335492	−	0.942043i	$-0.608903\pi$
$881$	−17545.9	−0.670985	−0.335492	+	0.942043i	$0.608903\pi$
$882$	24648.2	0.940985
$883$	−16091.7	−0.613282	−0.306641	−	0.951825i	$-0.599205\pi$
$883$	−16091.7	−0.613282	−0.306641	+	0.951825i	$0.599205\pi$
$884$	1210.14	0.0460423
$885$	23765.2	0.902666
$886$	9984.43	0.378593
$887$	33265.0	1.25922	0.629610	−	0.776911i	$-0.283215\pi$
$887$	33265.0	1.25922	0.629610	+	0.776911i	$0.283215\pi$
$888$	−23938.3	−0.904634
$889$	−4196.16	−0.158307
$890$	−4906.09	−0.184778
$891$	−3552.61	−0.133577
$892$	−3507.64	−0.131664
$893$	26845.1	1.00598
$894$	−319.399	−0.0119489
$895$	12769.5	0.476915
$896$	1125.95	0.0419814
$897$	4064.76	0.151303
$898$	−24694.1	−0.917652
$899$	69507.8	2.57866
$900$	−20348.0	−0.753631
$901$	−36839.0	−1.36214
$902$	−8891.79	−0.328231
$903$	33102.5	1.21991
$904$	−18922.4	−0.696184
$905$	−16054.5	−0.589691
$906$	5482.51	0.201042
$907$	22458.2	0.822175	0.411088	−	0.911596i	$-0.365149\pi$
$907$	22458.2	0.822175	0.411088	+	0.911596i	$0.365149\pi$
$908$	6558.65	0.239710
$909$	−15632.8	−0.570415
$910$	318.930	0.0116180
$911$	−23602.6	−0.858386	−0.429193	−	0.903213i	$-0.641202\pi$
$911$	−23602.6	−0.858386	−0.429193	+	0.903213i	$0.641202\pi$
$912$	9001.88	0.326844
$913$	−19865.8	−0.720113
$914$	3485.09	0.126123
$915$	−17818.5	−0.643784
$916$	7614.88	0.274675
$917$	3054.54	0.110000
$918$	−21737.9	−0.781544
$919$	−17262.0	−0.619610	−0.309805	−	0.950800i	$-0.600264\pi$
$919$	−17262.0	−0.619610	−0.309805	+	0.950800i	$0.600264\pi$
$920$	3215.94	0.115246
$921$	891.630	0.0319004
$922$	7986.03	0.285256
$923$	1818.22	0.0648401
$924$	−6263.58	−0.223005
$925$	38294.2	1.36120
$926$	−23867.3	−0.847007
$927$	−86500.3	−3.06477
$928$	9417.08	0.333115
$929$	51716.0	1.82642	0.913211	−	0.407487i	$-0.133595\pi$
$929$	51716.0	1.82642	0.913211	+	0.407487i	$0.133595\pi$
$930$	15860.9	0.559245
$931$	17443.7	0.614063
$932$	24775.0	0.870743
$933$	−35761.4	−1.25485
$934$	−14017.5	−0.491078
$935$	−5326.13	−0.186292
$936$	1716.91	0.0599562
$937$	−52471.8	−1.82943	−0.914717	−	0.404096i	$-0.867586\pi$
$937$	−52471.8	−1.82943	−0.914717	+	0.404096i	$0.867586\pi$
$938$	−7122.54	−0.247931
$939$	51661.9	1.79544
$940$	6408.28	0.222356
$941$	28142.7	0.974948	0.487474	−	0.873138i	$-0.337918\pi$
$941$	28142.7	0.974948	0.487474	+	0.873138i	$0.337918\pi$
$942$	−30031.1	−1.03871
$943$	−21947.0	−0.757891
$944$	11324.9	0.390458
$945$	−5728.98	−0.197210
$946$	18253.9	0.627362
$947$	39961.6	1.37125	0.685626	−	0.727954i	$-0.259528\pi$
$947$	39961.6	1.37125	0.685626	+	0.727954i	$0.259528\pi$
$948$	−43296.9	−1.48335
$949$	−1477.45	−0.0505373
$950$	−14400.4	−0.491801
$951$	−35329.5	−1.20467
$952$	−4602.65	−0.156694
$953$	17906.5	0.608655	0.304327	−	0.952568i	$-0.401568\pi$
$953$	17906.5	0.608655	0.304327	+	0.952568i	$0.401568\pi$
$954$	−52266.2	−1.77377
$955$	19128.9	0.648164
$956$	19657.5	0.665031
$957$	−52386.6	−1.76951
$958$	27884.9	0.940417
$959$	11815.7	0.397860
$960$	2148.86	0.0722441
$961$	25996.3	0.872622
$962$	−3231.16	−0.108292
$963$	49670.4	1.66210
$964$	19358.0	0.646763
$965$	14396.1	0.480235
$966$	−15459.9	−0.514923
$967$	−43343.4	−1.44140	−0.720698	−	0.693249i	$-0.756179\pi$
$967$	−43343.4	−1.44140	−0.720698	+	0.693249i	$0.756179\pi$
$968$	7194.04	0.238869
$969$	−36797.8	−1.21993
$970$	−142.924	−0.00473095
$971$	26889.1	0.888683	0.444341	−	0.895858i	$-0.353438\pi$
$971$	26889.1	0.888683	0.444341	+	0.895858i	$0.353438\pi$
$972$	12088.3	0.398902
$973$	−10296.2	−0.339242
$974$	−8393.18	−0.276114
$975$	−4344.87	−0.142715
$976$	−8491.07	−0.278476
$977$	−6994.03	−0.229026	−0.114513	−	0.993422i	$-0.536531\pi$
$977$	−6994.03	−0.229026	−0.114513	+	0.993422i	$0.536531\pi$
$978$	13963.1	0.456534
$979$	13005.6	0.424576
$980$	4164.02	0.135729
$981$	46753.8	1.52164
$982$	4222.66	0.137220
$983$	5952.35	0.193134	0.0965668	−	0.995327i	$-0.469214\pi$
$983$	5952.35	0.193134	0.0965668	+	0.995327i	$0.469214\pi$
$984$	−14664.8	−0.475097
$985$	−16933.0	−0.547746
$986$	−38495.1	−1.24334
$987$	−30806.4	−0.993493
$988$	1215.07	0.0391259
$989$	45054.7	1.44859
$990$	−7556.58	−0.242590
$991$	−17328.8	−0.555467	−0.277733	−	0.960658i	$-0.589583\pi$
$991$	−17328.8	−0.555467	−0.277733	+	0.960658i	$0.589583\pi$
$992$	7558.19	0.241908
$993$	−20013.9	−0.639600
$994$	−6915.43	−0.220668
$995$	18124.7	0.577480
$996$	−32763.7	−1.04233
$997$	−3393.06	−0.107783	−0.0538913	−	0.998547i	$-0.517162\pi$
$997$	−3393.06	−0.107783	−0.0538913	+	0.998547i	$0.517162\pi$
$998$	−40874.0	−1.29644
$999$	58041.9	1.83820

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.4.a.b.1.2	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.4.a.b.1.2	✓	15	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -8.56722 q^{3} +4.00000 q^{4} -3.91913 q^{5} +17.1344 q^{6} -8.79649 q^{7} -8.00000 q^{8} +46.3972 q^{9} +7.83826 q^{10} -20.7785 q^{11} -34.2689 q^{12} -4.62558 q^{13} +17.5930 q^{14} +33.5760 q^{15} +16.0000 q^{16} -65.4047 q^{17} -92.7944 q^{18} -65.6710 q^{19} -15.6765 q^{20} +75.3614 q^{21} +41.5570 q^{22} +102.572 q^{23} +68.5377 q^{24} -109.640 q^{25} +9.25116 q^{26} -166.180 q^{27} -35.1859 q^{28} -294.284 q^{29} -67.1520 q^{30} -236.193 q^{31} -32.0000 q^{32} +178.014 q^{33} +130.809 q^{34} +34.4746 q^{35} +185.589 q^{36} -349.271 q^{37} +131.342 q^{38} +39.6284 q^{39} +31.3530 q^{40} -213.966 q^{41} -150.723 q^{42} +439.249 q^{43} -83.1139 q^{44} -181.837 q^{45} -205.144 q^{46} -408.782 q^{47} -137.075 q^{48} -265.622 q^{49} +219.281 q^{50} +560.336 q^{51} -18.5023 q^{52} +563.247 q^{53} +332.360 q^{54} +81.4335 q^{55} +70.3719 q^{56} +562.618 q^{57} +588.567 q^{58} +707.804 q^{59} +134.304 q^{60} -530.692 q^{61} +472.387 q^{62} -408.132 q^{63} +64.0000 q^{64} +18.1282 q^{65} -356.028 q^{66} -404.851 q^{67} -261.619 q^{68} -878.757 q^{69} -68.9491 q^{70} -393.079 q^{71} -371.178 q^{72} +319.407 q^{73} +698.542 q^{74} +939.313 q^{75} -262.684 q^{76} +182.778 q^{77} -79.2567 q^{78} +1263.45 q^{79} -62.7060 q^{80} +170.975 q^{81} +427.933 q^{82} +956.077 q^{83} +301.446 q^{84} +256.329 q^{85} -878.499 q^{86} +2521.19 q^{87} +166.228 q^{88} -625.916 q^{89} +363.673 q^{90} +40.6889 q^{91} +410.288 q^{92} +2023.52 q^{93} +817.564 q^{94} +257.373 q^{95} +274.151 q^{96} -18.2342 q^{97} +531.244 q^{98} -964.063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 30 q^{2} + 11 q^{3} + 60 q^{4} + 29 q^{5} - 22 q^{6} + 5 q^{7} - 120 q^{8} + 142 q^{9} - 58 q^{10} + 79 q^{11} + 44 q^{12} - 14 q^{13} - 10 q^{14} + 67 q^{15} + 240 q^{16} + 94 q^{17} - 284 q^{18}+ \cdots + 7068 q^{99}+O(q^{100}) \) 15 * q - 30 * q^2 + 11 * q^3 + 60 * q^4 + 29 * q^5 - 22 * q^6 + 5 * q^7 - 120 * q^8 + 142 * q^9 - 58 * q^10 + 79 * q^11 + 44 * q^12 - 14 * q^13 - 10 * q^14 + 67 * q^15 + 240 * q^16 + 94 * q^17 - 284 * q^18 + 124 * q^19 + 116 * q^20 + 69 * q^21 - 158 * q^22 + 545 * q^23 - 88 * q^24 + 192 * q^25 + 28 * q^26 + 431 * q^27 + 20 * q^28 + 200 * q^29 - 134 * q^30 + 159 * q^31 - 480 * q^32 + 531 * q^33 - 188 * q^34 + 146 * q^35 + 568 * q^36 + 303 * q^37 - 248 * q^38 - 164 * q^39 - 232 * q^40 + 606 * q^41 - 138 * q^42 + 442 * q^43 + 316 * q^44 + 644 * q^45 - 1090 * q^46 + 618 * q^47 + 176 * q^48 + 286 * q^49 - 384 * q^50 - 251 * q^51 - 56 * q^52 + 916 * q^53 - 862 * q^54 + 53 * q^55 - 40 * q^56 + 190 * q^57 - 400 * q^58 + 1377 * q^59 + 268 * q^60 - 1373 * q^61 - 318 * q^62 + 1067 * q^63 + 960 * q^64 + 158 * q^65 - 1062 * q^66 + 1330 * q^67 + 376 * q^68 + 737 * q^69 - 292 * q^70 + 2291 * q^71 - 1136 * q^72 + 924 * q^73 - 606 * q^74 + 4337 * q^75 + 496 * q^76 + 4170 * q^77 + 328 * q^78 + 610 * q^79 + 464 * q^80 + 2255 * q^81 - 1212 * q^82 + 5191 * q^83 + 276 * q^84 + 1517 * q^85 - 884 * q^86 + 7295 * q^87 - 632 * q^88 + 3198 * q^89 - 1288 * q^90 + 4289 * q^91 + 2180 * q^92 + 5255 * q^93 - 1236 * q^94 + 4706 * q^95 - 352 * q^96 + 3806 * q^97 - 572 * q^98 + 7068 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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