LMFDB - Embedded newform 231.4.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,4,Mod(1,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("231.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	231.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:	$13.6294412113$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 28x^{3} - 11x^{2} + 108x - 64 $ x^5 - 28x^3 - 11x^2 + 108*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.85551$ of defining polynomial
Character	$\chi$	$=$	231.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.85551 q^{2} +3.00000 q^{3} +6.86494 q^{4} +18.0422 q^{5} +11.5665 q^{6} -7.00000 q^{7} -4.37623 q^{8} +9.00000 q^{9} +69.5618 q^{10} +11.0000 q^{11} +20.5948 q^{12} +16.8358 q^{13} -26.9886 q^{14} +54.1265 q^{15} -71.7921 q^{16} +76.0041 q^{17} +34.6996 q^{18} +11.8937 q^{19} +123.858 q^{20} -21.0000 q^{21} +42.4106 q^{22} -175.501 q^{23} -13.1287 q^{24} +200.520 q^{25} +64.9104 q^{26} +27.0000 q^{27} -48.0546 q^{28} -219.409 q^{29} +208.685 q^{30} -214.355 q^{31} -241.785 q^{32} +33.0000 q^{33} +293.035 q^{34} -126.295 q^{35} +61.7845 q^{36} +272.754 q^{37} +45.8562 q^{38} +50.5073 q^{39} -78.9567 q^{40} +204.925 q^{41} -80.9657 q^{42} +406.384 q^{43} +75.5144 q^{44} +162.380 q^{45} -676.647 q^{46} +178.653 q^{47} -215.376 q^{48} +49.0000 q^{49} +773.107 q^{50} +228.012 q^{51} +115.577 q^{52} -238.316 q^{53} +104.099 q^{54} +198.464 q^{55} +30.6336 q^{56} +35.6811 q^{57} -845.931 q^{58} -584.798 q^{59} +371.575 q^{60} -910.607 q^{61} -826.449 q^{62} -63.0000 q^{63} -357.868 q^{64} +303.754 q^{65} +127.232 q^{66} -387.749 q^{67} +521.764 q^{68} -526.504 q^{69} -486.932 q^{70} -668.091 q^{71} -39.3861 q^{72} +390.298 q^{73} +1051.60 q^{74} +601.561 q^{75} +81.6495 q^{76} -77.0000 q^{77} +194.731 q^{78} -250.647 q^{79} -1295.29 q^{80} +81.0000 q^{81} +790.090 q^{82} -54.2027 q^{83} -144.164 q^{84} +1371.28 q^{85} +1566.82 q^{86} -658.226 q^{87} -48.1385 q^{88} -906.680 q^{89} +626.056 q^{90} -117.850 q^{91} -1204.81 q^{92} -643.066 q^{93} +688.796 q^{94} +214.588 q^{95} -725.356 q^{96} +618.333 q^{97} +188.920 q^{98} +99.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 15 q^{3} + 21 q^{4} + 7 q^{5} + 15 q^{6} - 35 q^{7} + 60 q^{8} + 45 q^{9} + 55 q^{10} + 55 q^{11} + 63 q^{12} + 111 q^{13} - 35 q^{14} + 21 q^{15} + 201 q^{16} + 136 q^{17} + 45 q^{18} + 111 q^{19}+ \cdots + 495 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 15 * q^3 + 21 * q^4 + 7 * q^5 + 15 * q^6 - 35 * q^7 + 60 * q^8 + 45 * q^9 + 55 * q^10 + 55 * q^11 + 63 * q^12 + 111 * q^13 - 35 * q^14 + 21 * q^15 + 201 * q^16 + 136 * q^17 + 45 * q^18 + 111 * q^19 + 219 * q^20 - 105 * q^21 + 55 * q^22 - 28 * q^23 + 180 * q^24 + 190 * q^25 - q^26 + 135 * q^27 - 147 * q^28 + 61 * q^29 + 165 * q^30 - 280 * q^31 + 535 * q^32 + 165 * q^33 - 572 * q^34 - 49 * q^35 + 189 * q^36 - 41 * q^37 + 267 * q^38 + 333 * q^39 - 336 * q^40 + 426 * q^41 - 105 * q^42 + 424 * q^43 + 231 * q^44 + 63 * q^45 + 140 * q^46 + 75 * q^47 + 603 * q^48 + 245 * q^49 + 490 * q^50 + 408 * q^51 - 269 * q^52 + 1500 * q^53 + 135 * q^54 + 77 * q^55 - 420 * q^56 + 333 * q^57 - 1767 * q^58 + 757 * q^59 + 657 * q^60 + 658 * q^61 - 568 * q^62 - 315 * q^63 - 748 * q^64 + 537 * q^65 + 165 * q^66 - 583 * q^67 - 1650 * q^68 - 84 * q^69 - 385 * q^70 - 764 * q^71 + 540 * q^72 + 875 * q^73 - 825 * q^74 + 570 * q^75 + 213 * q^76 - 385 * q^77 - 3 * q^78 - 244 * q^79 - 2577 * q^80 + 405 * q^81 - 2006 * q^82 + 924 * q^83 - 441 * q^84 - 1402 * q^85 + 1272 * q^86 + 183 * q^87 + 660 * q^88 - 1110 * q^89 + 495 * q^90 - 777 * q^91 - 2046 * q^92 - 840 * q^93 - 3349 * q^94 + 1923 * q^95 + 1605 * q^96 - 852 * q^97 + 245 * q^98 + 495 * 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 $

$2$	3.85551	1.36313	0.681564	−	0.731759i	$-0.261300\pi$
$2$	3.85551	1.36313	0.681564	+	0.731759i	$0.261300\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	6.86494	0.858118
$5$	18.0422	1.61374	0.806871	−	0.590728i	$-0.201159\pi$
$5$	18.0422	1.61374	0.806871	+	0.590728i	$0.201159\pi$
$6$	11.5665	0.787002
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−4.37623	−0.193404
$9$	9.00000	0.333333
$10$	69.5618	2.19974
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	20.5948	0.495434
$13$	16.8358	0.359185	0.179592	−	0.983741i	$-0.442522\pi$
$13$	16.8358	0.359185	0.179592	+	0.983741i	$0.442522\pi$
$14$	−26.9886	−0.515214
$15$	54.1265	0.931694
$16$	−71.7921	−1.12175
$17$	76.0041	1.08434	0.542168	−	0.840270i	$-0.317604\pi$
$17$	76.0041	1.08434	0.542168	+	0.840270i	$0.317604\pi$
$18$	34.6996	0.454376
$19$	11.8937	0.143611	0.0718053	−	0.997419i	$-0.477124\pi$
$19$	11.8937	0.143611	0.0718053	+	0.997419i	$0.477124\pi$
$20$	123.858	1.38478
$21$	−21.0000	−0.218218
$22$	42.4106	0.410999
$23$	−175.501	−1.59107	−0.795534	−	0.605909i	$-0.792810\pi$
$23$	−175.501	−1.59107	−0.795534	+	0.605909i	$0.792810\pi$
$24$	−13.1287	−0.111662
$25$	200.520	1.60416
$26$	64.9104	0.489615
$27$	27.0000	0.192450
$28$	−48.0546	−0.324338
$29$	−219.409	−1.40494	−0.702468	−	0.711715i	$-0.747919\pi$
$29$	−219.409	−1.40494	−0.702468	+	0.711715i	$0.747919\pi$
$30$	208.685	1.27002
$31$	−214.355	−1.24192	−0.620958	−	0.783844i	$-0.713256\pi$
$31$	−214.355	−1.24192	−0.620958	+	0.783844i	$0.713256\pi$
$32$	−241.785	−1.33569
$33$	33.0000	0.174078
$34$	293.035	1.47809
$35$	−126.295	−0.609937
$36$	61.7845	0.286039
$37$	272.754	1.21190	0.605952	−	0.795501i	$-0.292792\pi$
$37$	272.754	1.21190	0.605952	+	0.795501i	$0.292792\pi$
$38$	45.8562	0.195760
$39$	50.5073	0.207375
$40$	−78.9567	−0.312104
$41$	204.925	0.780583	0.390292	−	0.920691i	$-0.372374\pi$
$41$	204.925	0.780583	0.390292	+	0.920691i	$0.372374\pi$
$42$	−80.9657	−0.297459
$43$	406.384	1.44123	0.720616	−	0.693334i	$-0.243859\pi$
$43$	406.384	1.44123	0.720616	+	0.693334i	$0.243859\pi$
$44$	75.5144	0.258732
$45$	162.380	0.537914
$46$	−676.647	−2.16883
$47$	178.653	0.554450	0.277225	−	0.960805i	$-0.410585\pi$
$47$	178.653	0.554450	0.277225	+	0.960805i	$0.410585\pi$
$48$	−215.376	−0.647644
$49$	49.0000	0.142857
$50$	773.107	2.18668
$51$	228.012	0.626042
$52$	115.577	0.308223
$53$	−238.316	−0.617646	−0.308823	−	0.951120i	$-0.599935\pi$
$53$	−238.316	−0.617646	−0.308823	+	0.951120i	$0.599935\pi$
$54$	104.099	0.262334
$55$	198.464	0.486561
$56$	30.6336	0.0730998
$57$	35.6811	0.0829136
$58$	−845.931	−1.91511
$59$	−584.798	−1.29041	−0.645205	−	0.764009i	$-0.723228\pi$
$59$	−584.798	−1.29041	−0.645205	+	0.764009i	$0.723228\pi$
$60$	371.575	0.799503
$61$	−910.607	−1.91133	−0.955666	−	0.294452i	$-0.904863\pi$
$61$	−910.607	−1.91133	−0.955666	+	0.294452i	$0.904863\pi$
$62$	−826.449	−1.69289
$63$	−63.0000	−0.125988
$64$	−357.868	−0.698961
$65$	303.754	0.579631
$66$	127.232	0.237290
$67$	−387.749	−0.707030	−0.353515	−	0.935429i	$-0.615014\pi$
$67$	−387.749	−0.707030	−0.353515	+	0.935429i	$0.615014\pi$
$68$	521.764	0.930488
$69$	−526.504	−0.918603
$70$	−486.932	−0.831422
$71$	−668.091	−1.11673	−0.558365	−	0.829595i	$-0.688571\pi$
$71$	−668.091	−1.11673	−0.558365	+	0.829595i	$0.688571\pi$
$72$	−39.3861	−0.0644679
$73$	390.298	0.625766	0.312883	−	0.949792i	$-0.398705\pi$
$73$	390.298	0.625766	0.312883	+	0.949792i	$0.398705\pi$
$74$	1051.60	1.65198
$75$	601.561	0.926163
$76$	81.6495	0.123235
$77$	−77.0000	−0.113961
$78$	194.731	0.282679
$79$	−250.647	−0.356962	−0.178481	−	0.983943i	$-0.557118\pi$
$79$	−250.647	−0.356962	−0.178481	+	0.983943i	$0.557118\pi$
$80$	−1295.29	−1.81022
$81$	81.0000	0.111111
$82$	790.090	1.06403
$83$	−54.2027	−0.0716809	−0.0358404	−	0.999358i	$-0.511411\pi$
$83$	−54.2027	−0.0716809	−0.0358404	+	0.999358i	$0.511411\pi$
$84$	−144.164	−0.187257
$85$	1371.28	1.74984
$86$	1566.82	1.96458
$87$	−658.226	−0.811140
$88$	−48.1385	−0.0583134
$89$	−906.680	−1.07986	−0.539932	−	0.841709i	$-0.681550\pi$
$89$	−906.680	−1.07986	−0.539932	+	0.841709i	$0.681550\pi$
$90$	626.056	0.733245
$91$	−117.850	−0.135759
$92$	−1204.81	−1.36532
$93$	−643.066	−0.717020
$94$	688.796	0.755786
$95$	214.588	0.231750
$96$	−725.356	−0.771159
$97$	618.333	0.647239	0.323620	−	0.946187i	$-0.395100\pi$
$97$	618.333	0.647239	0.323620	+	0.946187i	$0.395100\pi$
$98$	188.920	0.194733
$99$	99.0000	0.100504
$100$	1376.56	1.37656
$101$	443.731	0.437157	0.218578	−	0.975819i	$-0.429858\pi$
$101$	443.731	0.437157	0.218578	+	0.975819i	$0.429858\pi$
$102$	879.104	0.853375
$103$	−1893.39	−1.81128	−0.905638	−	0.424051i	$-0.860608\pi$
$103$	−1893.39	−1.81128	−0.905638	+	0.424051i	$0.860608\pi$
$104$	−73.6771	−0.0694677
$105$	−378.886	−0.352147
$106$	−918.830	−0.841930
$107$	966.336	0.873077	0.436538	−	0.899686i	$-0.356204\pi$
$107$	966.336	0.873077	0.436538	+	0.899686i	$0.356204\pi$
$108$	185.353	0.165145
$109$	86.9483	0.0764049	0.0382025	−	0.999270i	$-0.487837\pi$
$109$	86.9483	0.0764049	0.0382025	+	0.999270i	$0.487837\pi$
$110$	765.179	0.663245
$111$	818.261	0.699693
$112$	502.545	0.423982
$113$	1645.50	1.36987	0.684937	−	0.728602i	$-0.259830\pi$
$113$	1645.50	1.36987	0.684937	+	0.728602i	$0.259830\pi$
$114$	137.569	0.113022
$115$	−3166.43	−2.56757
$116$	−1506.23	−1.20560
$117$	151.522	0.119728
$118$	−2254.69	−1.75899
$119$	−532.029	−0.409840
$120$	−236.870	−0.180193
$121$	121.000	0.0909091
$122$	−3510.85	−2.60539
$123$	614.775	0.450670
$124$	−1471.54	−1.06571
$125$	1362.55	0.974961
$126$	−242.897	−0.171738
$127$	−978.550	−0.683719	−0.341859	−	0.939751i	$-0.611057\pi$
$127$	−978.550	−0.683719	−0.341859	+	0.939751i	$0.611057\pi$
$128$	554.519	0.382914
$129$	1219.15	0.832096
$130$	1171.13	0.790112
$131$	1494.86	0.996993	0.498497	−	0.866892i	$-0.333886\pi$
$131$	1494.86	0.996993	0.498497	+	0.866892i	$0.333886\pi$
$132$	226.543	0.149379
$133$	−83.2559	−0.0542797
$134$	−1494.97	−0.963773
$135$	487.139	0.310565
$136$	−332.611	−0.209715
$137$	2397.79	1.49530	0.747652	−	0.664091i	$-0.231181\pi$
$137$	2397.79	1.49530	0.747652	+	0.664091i	$0.231181\pi$
$138$	−2029.94	−1.25217
$139$	2672.65	1.63087	0.815436	−	0.578847i	$-0.196497\pi$
$139$	2672.65	1.63087	0.815436	+	0.578847i	$0.196497\pi$
$140$	−867.009	−0.523398
$141$	535.958	0.320112
$142$	−2575.83	−1.52225
$143$	185.193	0.108298
$144$	−646.129	−0.373917
$145$	−3958.61	−2.26720
$146$	1504.80	0.853000
$147$	147.000	0.0824786
$148$	1872.44	1.03996
$149$	2052.12	1.12830	0.564149	−	0.825673i	$-0.309204\pi$
$149$	2052.12	1.12830	0.564149	+	0.825673i	$0.309204\pi$
$150$	2319.32	1.26248
$151$	2366.66	1.27547	0.637734	−	0.770256i	$-0.279872\pi$
$151$	2366.66	1.27547	0.637734	+	0.770256i	$0.279872\pi$
$152$	−52.0495	−0.0277748
$153$	684.037	0.361445
$154$	−296.874	−0.155343
$155$	−3867.44	−2.00413
$156$	346.730	0.177952
$157$	−3763.06	−1.91290	−0.956450	−	0.291897i	$-0.905714\pi$
$157$	−3763.06	−1.91290	−0.956450	+	0.291897i	$0.905714\pi$
$158$	−966.371	−0.486584
$159$	−714.948	−0.356598
$160$	−4362.33	−2.15545
$161$	1228.51	0.601367
$162$	312.296	0.151459
$163$	1394.64	0.670166	0.335083	−	0.942189i	$-0.391236\pi$
$163$	1394.64	0.670166	0.335083	+	0.942189i	$0.391236\pi$
$164$	1406.80	0.669832
$165$	595.392	0.280916
$166$	−208.979	−0.0977102
$167$	−384.184	−0.178018	−0.0890091	−	0.996031i	$-0.528370\pi$
$167$	−384.184	−0.178018	−0.0890091	+	0.996031i	$0.528370\pi$
$168$	91.9008	0.0422042
$169$	−1913.56	−0.870986
$170$	5286.98	2.38525
$171$	107.043	0.0478702
$172$	2789.80	1.23675
$173$	1156.21	0.508121	0.254061	−	0.967188i	$-0.418234\pi$
$173$	1156.21	0.508121	0.254061	+	0.967188i	$0.418234\pi$
$174$	−2537.79	−1.10569
$175$	−1403.64	−0.606316
$176$	−789.713	−0.338221
$177$	−1754.39	−0.745019
$178$	−3495.71	−1.47199
$179$	141.765	0.0591956	0.0295978	−	0.999562i	$-0.490577\pi$
$179$	141.765	0.0591956	0.0295978	+	0.999562i	$0.490577\pi$
$180$	1114.73	0.461593
$181$	1359.83	0.558428	0.279214	−	0.960229i	$-0.409926\pi$
$181$	1359.83	0.558428	0.279214	+	0.960229i	$0.409926\pi$
$182$	−454.373	−0.185057
$183$	−2731.82	−1.10351
$184$	768.034	0.307719
$185$	4921.07	1.95570
$186$	−2479.35	−0.977390
$187$	836.045	0.326940
$188$	1226.44	0.475783
$189$	−189.000	−0.0727393
$190$	827.347	0.315905
$191$	3678.06	1.39338	0.696689	−	0.717373i	$-0.254656\pi$
$191$	3678.06	1.39338	0.696689	+	0.717373i	$0.254656\pi$
$192$	−1073.60	−0.403545
$193$	1107.52	0.413064	0.206532	−	0.978440i	$-0.433782\pi$
$193$	1107.52	0.413064	0.206532	+	0.978440i	$0.433782\pi$
$194$	2383.99	0.882270
$195$	911.262	0.334650
$196$	336.382	0.122588
$197$	−693.069	−0.250655	−0.125328	−	0.992115i	$-0.539998\pi$
$197$	−693.069	−0.250655	−0.125328	+	0.992115i	$0.539998\pi$
$198$	381.695	0.137000
$199$	145.818	0.0519437	0.0259718	−	0.999663i	$-0.491732\pi$
$199$	145.818	0.0519437	0.0259718	+	0.999663i	$0.491732\pi$
$200$	−877.522	−0.310251
$201$	−1163.25	−0.408204
$202$	1710.81	0.595901
$203$	1535.86	0.531016
$204$	1565.29	0.537217
$205$	3697.29	1.25966
$206$	−7299.99	−2.46900
$207$	−1579.51	−0.530356
$208$	−1208.68	−0.402916
$209$	130.831	0.0433002
$210$	−1460.80	−0.480022
$211$	−3518.11	−1.14785	−0.573927	−	0.818907i	$-0.694580\pi$
$211$	−3518.11	−1.14785	−0.573927	+	0.818907i	$0.694580\pi$
$212$	−1636.03	−0.530013
$213$	−2004.27	−0.644744
$214$	3725.72	1.19012
$215$	7332.05	2.32578
$216$	−118.158	−0.0372206
$217$	1500.49	0.469400
$218$	335.230	0.104150
$219$	1170.89	0.361286
$220$	1362.44	0.417527
$221$	1279.59	0.389477
$222$	3154.81	0.953771
$223$	1630.18	0.489530	0.244765	−	0.969582i	$-0.421289\pi$
$223$	1630.18	0.489530	0.244765	+	0.969582i	$0.421289\pi$
$224$	1692.50	0.504842
$225$	1804.68	0.534721
$226$	6344.24	1.86731
$227$	1841.48	0.538428	0.269214	−	0.963080i	$-0.413236\pi$
$227$	1841.48	0.538428	0.269214	+	0.963080i	$0.413236\pi$
$228$	244.949	0.0711496
$229$	4468.48	1.28945	0.644727	−	0.764413i	$-0.276971\pi$
$229$	4468.48	1.28945	0.644727	+	0.764413i	$0.276971\pi$
$230$	−12208.2	−3.49993
$231$	−231.000	−0.0657952
$232$	960.182	0.271720
$233$	−1914.60	−0.538323	−0.269162	−	0.963095i	$-0.586747\pi$
$233$	−1914.60	−0.538323	−0.269162	+	0.963095i	$0.586747\pi$
$234$	584.194	0.163205
$235$	3223.28	0.894739
$236$	−4014.60	−1.10732
$237$	−751.940	−0.206092
$238$	−2051.24	−0.558665
$239$	6454.45	1.74688	0.873438	−	0.486935i	$-0.161885\pi$
$239$	6454.45	1.74688	0.873438	+	0.486935i	$0.161885\pi$
$240$	−3885.86	−1.04513
$241$	−3461.21	−0.925129	−0.462564	−	0.886586i	$-0.653071\pi$
$241$	−3461.21	−0.925129	−0.462564	+	0.886586i	$0.653071\pi$
$242$	466.516	0.123921
$243$	243.000	0.0641500
$244$	−6251.26	−1.64015
$245$	884.067	0.230535
$246$	2370.27	0.614321
$247$	200.240	0.0515827
$248$	938.068	0.240191
$249$	−162.608	−0.0413850
$250$	5253.32	1.32900
$251$	−3579.75	−0.900207	−0.450104	−	0.892976i	$-0.648613\pi$
$251$	−3579.75	−0.900207	−0.450104	+	0.892976i	$0.648613\pi$
$252$	−432.491	−0.108113
$253$	−1930.51	−0.479725
$254$	−3772.81	−0.931996
$255$	4113.84	1.01027
$256$	5000.90	1.22092
$257$	3780.31	0.917545	0.458773	−	0.888554i	$-0.348289\pi$
$257$	3780.31	0.917545	0.458773	+	0.888554i	$0.348289\pi$
$258$	4700.45	1.13425
$259$	−1909.28	−0.458057
$260$	2085.25	0.497392
$261$	−1974.68	−0.468312
$262$	5763.43	1.35903
$263$	−5063.37	−1.18715	−0.593575	−	0.804778i	$-0.702284\pi$
$263$	−5063.37	−1.18715	−0.593575	+	0.804778i	$0.702284\pi$
$264$	−144.416	−0.0336673
$265$	−4299.74	−0.996721
$266$	−320.994	−0.0739902
$267$	−2720.04	−0.623460
$268$	−2661.87	−0.606715
$269$	2910.06	0.659589	0.329795	−	0.944053i	$-0.393021\pi$
$269$	2910.06	0.659589	0.329795	+	0.944053i	$0.393021\pi$
$270$	1878.17	0.423339
$271$	5442.93	1.22005	0.610027	−	0.792381i	$-0.291159\pi$
$271$	5442.93	1.22005	0.610027	+	0.792381i	$0.291159\pi$
$272$	−5456.50	−1.21636
$273$	−353.551	−0.0783805
$274$	9244.68	2.03829
$275$	2205.72	0.483673
$276$	−3614.42	−0.788270
$277$	4044.19	0.877226	0.438613	−	0.898676i	$-0.355470\pi$
$277$	4044.19	0.877226	0.438613	+	0.898676i	$0.355470\pi$
$278$	10304.4	2.22309
$279$	−1929.20	−0.413972
$280$	552.697	0.117964
$281$	−8172.77	−1.73504	−0.867520	−	0.497402i	$-0.834287\pi$
$281$	−8172.77	−1.73504	−0.867520	+	0.497402i	$0.834287\pi$
$282$	2066.39	0.436353
$283$	2182.31	0.458391	0.229196	−	0.973380i	$-0.426390\pi$
$283$	2182.31	0.458391	0.229196	+	0.973380i	$0.426390\pi$
$284$	−4586.41	−0.958286
$285$	643.765	0.133801
$286$	714.015	0.147624
$287$	−1434.48	−0.295033
$288$	−2176.07	−0.445229
$289$	863.627	0.175784
$290$	−15262.4	−3.09049
$291$	1855.00	0.373684
$292$	2679.37	0.536981
$293$	1709.43	0.340839	0.170420	−	0.985372i	$-0.445488\pi$
$293$	1709.43	0.340839	0.170420	+	0.985372i	$0.445488\pi$
$294$	566.760	0.112429
$295$	−10551.0	−2.08239
$296$	−1193.63	−0.234387
$297$	297.000	0.0580259
$298$	7911.98	1.53801
$299$	−2954.70	−0.571487
$300$	4129.68	0.794757
$301$	−2844.69	−0.544735
$302$	9124.66	1.73863
$303$	1331.19	0.252393
$304$	−853.874	−0.161095
$305$	−16429.3	−3.08440
$306$	2637.31	0.492696
$307$	5485.85	1.01985	0.509925	−	0.860219i	$-0.329673\pi$
$307$	5485.85	1.01985	0.509925	+	0.860219i	$0.329673\pi$
$308$	−528.600	−0.0977916
$309$	−5680.18	−1.04574
$310$	−14910.9	−2.73189
$311$	476.818	0.0869385	0.0434693	−	0.999055i	$-0.486159\pi$
$311$	476.818	0.0869385	0.0434693	+	0.999055i	$0.486159\pi$
$312$	−221.031	−0.0401072
$313$	779.948	0.140848	0.0704238	−	0.997517i	$-0.477565\pi$
$313$	779.948	0.140848	0.0704238	+	0.997517i	$0.477565\pi$
$314$	−14508.5	−2.60753
$315$	−1136.66	−0.203312
$316$	−1720.68	−0.306315
$317$	6398.10	1.13361	0.566803	−	0.823853i	$-0.308180\pi$
$317$	6398.10	1.13361	0.566803	+	0.823853i	$0.308180\pi$
$318$	−2756.49	−0.486089
$319$	−2413.49	−0.423604
$320$	−6456.72	−1.12794
$321$	2899.01	0.504071
$322$	4736.53	0.819740
$323$	903.970	0.155722
$324$	556.060	0.0953464
$325$	3375.91	0.576190
$326$	5377.06	0.913522
$327$	260.845	0.0441124
$328$	−896.799	−0.150968
$329$	−1250.57	−0.209562
$330$	2295.54	0.382925
$331$	−7792.92	−1.29407	−0.647036	−	0.762460i	$-0.723991\pi$
$331$	−7792.92	−1.29407	−0.647036	+	0.762460i	$0.723991\pi$
$332$	−372.098	−0.0615106
$333$	2454.78	0.403968
$334$	−1481.22	−0.242662
$335$	−6995.83	−1.14096
$336$	1507.63	0.244786
$337$	−4106.13	−0.663724	−0.331862	−	0.943328i	$-0.607677\pi$
$337$	−4106.13	−0.663724	−0.331862	+	0.943328i	$0.607677\pi$
$338$	−7377.73	−1.18727
$339$	4936.51	0.790897
$340$	9413.76	1.50157
$341$	−2357.91	−0.374452
$342$	412.706	0.0652532
$343$	−343.000	−0.0539949
$344$	−1778.43	−0.278740
$345$	−9499.28	−1.48239
$346$	4457.77	0.692634
$347$	−3014.89	−0.466421	−0.233210	−	0.972426i	$-0.574923\pi$
$347$	−3014.89	−0.466421	−0.233210	+	0.972426i	$0.574923\pi$
$348$	−4518.68	−0.696054
$349$	8717.58	1.33708	0.668541	−	0.743675i	$-0.266919\pi$
$349$	8717.58	1.33708	0.668541	+	0.743675i	$0.266919\pi$
$350$	−5411.75	−0.826486
$351$	454.566	0.0691251
$352$	−2659.64	−0.402725
$353$	−248.227	−0.0374272	−0.0187136	−	0.999825i	$-0.505957\pi$
$353$	−248.227	−0.0374272	−0.0187136	+	0.999825i	$0.505957\pi$
$354$	−6764.08	−1.01556
$355$	−12053.8	−1.80211
$356$	−6224.31	−0.926650
$357$	−1596.09	−0.236621
$358$	546.576	0.0806912
$359$	−9850.33	−1.44814	−0.724068	−	0.689729i	$-0.757730\pi$
$359$	−9850.33	−1.44814	−0.724068	+	0.689729i	$0.757730\pi$
$360$	−710.610	−0.104035
$361$	−6717.54	−0.979376
$362$	5242.84	0.761209
$363$	363.000	0.0524864
$364$	−809.036	−0.116497
$365$	7041.83	1.00983
$366$	−10532.6	−1.50422
$367$	−3597.52	−0.511686	−0.255843	−	0.966718i	$-0.582353\pi$
$367$	−3597.52	−0.511686	−0.255843	+	0.966718i	$0.582353\pi$
$368$	12599.6	1.78478
$369$	1844.33	0.260194
$370$	18973.2	2.66587
$371$	1668.21	0.233448
$372$	−4414.61	−0.615288
$373$	2275.67	0.315897	0.157949	−	0.987447i	$-0.449512\pi$
$373$	2275.67	0.315897	0.157949	+	0.987447i	$0.449512\pi$
$374$	3223.38	0.445660
$375$	4087.65	0.562894
$376$	−781.824	−0.107233
$377$	−3693.91	−0.504632
$378$	−728.691	−0.0991530
$379$	3964.58	0.537326	0.268663	−	0.963234i	$-0.413418\pi$
$379$	3964.58	0.537326	0.268663	+	0.963234i	$0.413418\pi$
$380$	1473.14	0.198869
$381$	−2935.65	−0.394745
$382$	14180.8	1.89935
$383$	−9289.55	−1.23936	−0.619679	−	0.784855i	$-0.712737\pi$
$383$	−9289.55	−1.23936	−0.619679	+	0.784855i	$0.712737\pi$
$384$	1663.56	0.221076
$385$	−1389.25	−0.183903
$386$	4270.07	0.563059
$387$	3657.46	0.480411
$388$	4244.82	0.555407
$389$	15086.8	1.96640	0.983201	−	0.182528i	$-0.0584282\pi$
$389$	15086.8	1.96640	0.983201	+	0.182528i	$0.0584282\pi$
$390$	3513.38	0.456171
$391$	−13338.8	−1.72525
$392$	−214.435	−0.0276291
$393$	4484.57	0.575614
$394$	−2672.13	−0.341675
$395$	−4522.21	−0.576044
$396$	679.629	0.0862441
$397$	−10215.5	−1.29144	−0.645722	−	0.763572i	$-0.723444\pi$
$397$	−10215.5	−1.29144	−0.645722	+	0.763572i	$0.723444\pi$
$398$	562.204	0.0708059
$399$	−249.768	−0.0313384
$400$	−14395.8	−1.79947
$401$	−4143.18	−0.515962	−0.257981	−	0.966150i	$-0.583057\pi$
$401$	−4143.18	−0.515962	−0.257981	+	0.966150i	$0.583057\pi$
$402$	−4484.90	−0.556435
$403$	−3608.84	−0.446077
$404$	3046.18	0.375132
$405$	1461.42	0.179305
$406$	5921.52	0.723843
$407$	3000.29	0.365403
$408$	−997.834	−0.121079
$409$	−1958.71	−0.236801	−0.118401	−	0.992966i	$-0.537777\pi$
$409$	−1958.71	−0.236801	−0.118401	+	0.992966i	$0.537777\pi$
$410$	14254.9	1.71708
$411$	7193.36	0.863314
$412$	−12998.0	−1.55429
$413$	4093.59	0.487729
$414$	−6089.82	−0.722943
$415$	−977.934	−0.115674
$416$	−4070.64	−0.479758
$417$	8017.95	0.941585
$418$	504.419	0.0590237
$419$	616.552	0.0718868	0.0359434	−	0.999354i	$-0.488556\pi$
$419$	616.552	0.0718868	0.0359434	+	0.999354i	$0.488556\pi$
$420$	−2601.03	−0.302184
$421$	−612.327	−0.0708859	−0.0354430	−	0.999372i	$-0.511284\pi$
$421$	−612.327	−0.0708859	−0.0354430	+	0.999372i	$0.511284\pi$
$422$	−13564.1	−1.56467
$423$	1607.87	0.184817
$424$	1042.93	0.119455
$425$	15240.4	1.73945
$426$	−7727.49	−0.878869
$427$	6374.25	0.722416
$428$	6633.84	0.749203
$429$	555.580	0.0625260
$430$	28268.8	3.17033
$431$	−2316.95	−0.258941	−0.129470	−	0.991583i	$-0.541328\pi$
$431$	−2316.95	−0.258941	−0.129470	+	0.991583i	$0.541328\pi$
$432$	−1938.39	−0.215881
$433$	−9187.01	−1.01963	−0.509815	−	0.860284i	$-0.670286\pi$
$433$	−9187.01	−1.01963	−0.509815	+	0.860284i	$0.670286\pi$
$434$	5785.14	0.639852
$435$	−11875.8	−1.30897
$436$	596.895	0.0655644
$437$	−2087.36	−0.228494
$438$	4514.39	0.492480
$439$	1907.40	0.207369	0.103685	−	0.994610i	$-0.466937\pi$
$439$	1907.40	0.207369	0.103685	+	0.994610i	$0.466937\pi$
$440$	−868.524	−0.0941028
$441$	441.000	0.0476190
$442$	4933.46	0.530907
$443$	7657.14	0.821223	0.410611	−	0.911810i	$-0.365315\pi$
$443$	7657.14	0.821223	0.410611	+	0.911810i	$0.365315\pi$
$444$	5617.31	0.600419
$445$	−16358.5	−1.74262
$446$	6285.19	0.667292
$447$	6156.37	0.651423
$448$	2505.08	0.264182
$449$	2156.86	0.226701	0.113350	−	0.993555i	$-0.463842\pi$
$449$	2156.86	0.226701	0.113350	+	0.993555i	$0.463842\pi$
$450$	6957.97	0.728893
$451$	2254.18	0.235355
$452$	11296.3	1.17551
$453$	7099.97	0.736392
$454$	7099.83	0.733946
$455$	−2126.28	−0.219080
$456$	−156.149	−0.0160358
$457$	18073.5	1.84998	0.924990	−	0.379990i	$-0.124073\pi$
$457$	18073.5	1.84998	0.924990	+	0.379990i	$0.124073\pi$
$458$	17228.2	1.75769
$459$	2052.11	0.208681
$460$	−21737.3	−2.20328
$461$	3559.83	0.359648	0.179824	−	0.983699i	$-0.442447\pi$
$461$	3559.83	0.359648	0.179824	+	0.983699i	$0.442447\pi$
$462$	−890.622	−0.0896872
$463$	−11741.3	−1.17855	−0.589273	−	0.807934i	$-0.700586\pi$
$463$	−11741.3	−1.17855	−0.589273	+	0.807934i	$0.700586\pi$
$464$	15751.8	1.57599
$465$	−11602.3	−1.15708
$466$	−7381.74	−0.733804
$467$	15624.4	1.54821	0.774103	−	0.633060i	$-0.218201\pi$
$467$	15624.4	1.54821	0.774103	+	0.633060i	$0.218201\pi$
$468$	1040.19	0.102741
$469$	2714.24	0.267232
$470$	12427.4	1.21964
$471$	−11289.2	−1.10441
$472$	2559.21	0.249570
$473$	4470.22	0.434548
$474$	−2899.11	−0.280930
$475$	2384.93	0.230375
$476$	−3652.35	−0.351691
$477$	−2144.84	−0.205882
$478$	24885.2	2.38122
$479$	856.272	0.0816787	0.0408393	−	0.999166i	$-0.486997\pi$
$479$	856.272	0.0816787	0.0408393	+	0.999166i	$0.486997\pi$
$480$	−13087.0	−1.24445
$481$	4592.02	0.435297
$482$	−13344.7	−1.26107
$483$	3685.53	0.347199
$484$	830.658	0.0780107
$485$	11156.1	1.04448
$486$	936.888	0.0874447
$487$	1401.75	0.130430	0.0652148	−	0.997871i	$-0.479227\pi$
$487$	1401.75	0.130430	0.0652148	+	0.997871i	$0.479227\pi$
$488$	3985.02	0.369659
$489$	4183.93	0.386920
$490$	3408.53	0.314248
$491$	−4413.29	−0.405639	−0.202820	−	0.979216i	$-0.565010\pi$
$491$	−4413.29	−0.405639	−0.202820	+	0.979216i	$0.565010\pi$
$492$	4220.40	0.386728
$493$	−16676.0	−1.52342
$494$	772.025	0.0703139
$495$	1786.18	0.162187
$496$	15389.0	1.39312
$497$	4676.64	0.422084
$498$	−626.936	−0.0564130
$499$	5105.31	0.458006	0.229003	−	0.973426i	$-0.426453\pi$
$499$	5105.31	0.458006	0.229003	+	0.973426i	$0.426453\pi$
$500$	9353.82	0.836631
$501$	−1152.55	−0.102779
$502$	−13801.8	−1.22710
$503$	−18573.1	−1.64639	−0.823195	−	0.567759i	$-0.807810\pi$
$503$	−18573.1	−1.64639	−0.823195	+	0.567759i	$0.807810\pi$
$504$	275.702	0.0243666
$505$	8005.87	0.705458
$506$	−7443.11	−0.653927
$507$	−5740.67	−0.502864
$508$	−6717.69	−0.586711
$509$	−20788.8	−1.81031	−0.905153	−	0.425086i	$-0.860244\pi$
$509$	−20788.8	−1.81031	−0.905153	+	0.425086i	$0.860244\pi$
$510$	15860.9	1.37713
$511$	−2732.09	−0.236517
$512$	14844.8	1.28136
$513$	321.130	0.0276379
$514$	14575.0	1.25073
$515$	−34160.9	−2.92293
$516$	8369.41	0.714036
$517$	1965.18	0.167173
$518$	−7361.23	−0.624390
$519$	3468.63	0.293364
$520$	−1329.30	−0.112103
$521$	−12175.6	−1.02384	−0.511921	−	0.859032i	$-0.671066\pi$
$521$	−12175.6	−1.02384	−0.511921	+	0.859032i	$0.671066\pi$
$522$	−7613.38	−0.638369
$523$	−104.134	−0.00870642	−0.00435321	−	0.999991i	$-0.501386\pi$
$523$	−104.134	−0.00870642	−0.00435321	+	0.999991i	$0.501386\pi$
$524$	10262.1	0.855538
$525$	−4210.92	−0.350057
$526$	−19521.9	−1.61824
$527$	−16291.9	−1.34665
$528$	−2369.14	−0.195272
$529$	18633.7	1.53150
$530$	−16577.7	−1.35866
$531$	−5263.18	−0.430137
$532$	−571.547	−0.0465784
$533$	3450.07	0.280374
$534$	−10487.1	−0.849855
$535$	17434.8	1.40892
$536$	1696.88	0.136742
$537$	425.295	0.0341766
$538$	11219.8	0.899104
$539$	539.000	0.0430730
$540$	3344.18	0.266501
$541$	−2741.20	−0.217844	−0.108922	−	0.994050i	$-0.534740\pi$
$541$	−2741.20	−0.217844	−0.108922	+	0.994050i	$0.534740\pi$
$542$	20985.3	1.66309
$543$	4079.50	0.322409
$544$	−18376.7	−1.44833
$545$	1568.74	0.123298
$546$	−1363.12	−0.106843
$547$	−17008.0	−1.32945	−0.664725	−	0.747089i	$-0.731451\pi$
$547$	−17008.0	−1.32945	−0.664725	+	0.747089i	$0.731451\pi$
$548$	16460.7	1.28315
$549$	−8195.46	−0.637111
$550$	8504.18	0.659308
$551$	−2609.58	−0.201764
$552$	2304.10	0.177661
$553$	1754.53	0.134919
$554$	15592.4	1.19577
$555$	14763.2	1.12912
$556$	18347.6	1.39948
$557$	−2055.20	−0.156340	−0.0781702	−	0.996940i	$-0.524908\pi$
$557$	−2055.20	−0.156340	−0.0781702	+	0.996940i	$0.524908\pi$
$558$	−7438.04	−0.564296
$559$	6841.79	0.517669
$560$	9067.00	0.684198
$561$	2508.14	0.188759
$562$	−31510.2	−2.36508
$563$	−4425.50	−0.331284	−0.165642	−	0.986186i	$-0.552970\pi$
$563$	−4425.50	−0.331284	−0.165642	+	0.986186i	$0.552970\pi$
$564$	3679.32	0.274694
$565$	29688.4	2.21062
$566$	8413.90	0.624846
$567$	−567.000	−0.0419961
$568$	2923.72	0.215980
$569$	6590.24	0.485549	0.242775	−	0.970083i	$-0.421942\pi$
$569$	6590.24	0.485549	0.242775	+	0.970083i	$0.421942\pi$
$570$	2482.04	0.182388
$571$	−24640.9	−1.80594	−0.902968	−	0.429707i	$-0.858617\pi$
$571$	−24640.9	−1.80594	−0.902968	+	0.429707i	$0.858617\pi$
$572$	1271.34	0.0929327
$573$	11034.2	0.804467
$574$	−5530.63	−0.402167
$575$	−35191.6	−2.55233
$576$	−3220.81	−0.232987
$577$	−26063.5	−1.88048	−0.940242	−	0.340507i	$-0.889401\pi$
$577$	−26063.5	−1.88048	−0.940242	+	0.340507i	$0.889401\pi$
$578$	3329.72	0.239616
$579$	3322.57	0.238482
$580$	−27175.6	−1.94553
$581$	379.419	0.0270928
$582$	7151.96	0.509379
$583$	−2621.48	−0.186227
$584$	−1708.03	−0.121026
$585$	2733.79	0.193210
$586$	6590.72	0.464607
$587$	18880.3	1.32756	0.663778	−	0.747930i	$-0.268952\pi$
$587$	18880.3	1.32756	0.663778	+	0.747930i	$0.268952\pi$
$588$	1009.15	0.0707764
$589$	−2549.48	−0.178352
$590$	−40679.6	−2.83856
$591$	−2079.21	−0.144716
$592$	−19581.6	−1.35945
$593$	20373.4	1.41085	0.705426	−	0.708783i	$-0.250756\pi$
$593$	20373.4	1.41085	0.705426	+	0.708783i	$0.250756\pi$
$594$	1145.09	0.0790967
$595$	−9598.96	−0.661376
$596$	14087.7	0.968213
$597$	437.455	0.0299897
$598$	−11391.9	−0.779010
$599$	−3953.48	−0.269674	−0.134837	−	0.990868i	$-0.543051\pi$
$599$	−3953.48	−0.269674	−0.134837	+	0.990868i	$0.543051\pi$
$600$	−2632.57	−0.179123
$601$	6736.90	0.457244	0.228622	−	0.973515i	$-0.426578\pi$
$601$	6736.90	0.457244	0.228622	+	0.973515i	$0.426578\pi$
$602$	−10967.7	−0.742543
$603$	−3489.74	−0.235677
$604$	16247.0	1.09450
$605$	2183.10	0.146704
$606$	5132.42	0.344043
$607$	−28336.7	−1.89481	−0.947406	−	0.320035i	$-0.896305\pi$
$607$	−28336.7	−1.89481	−0.947406	+	0.320035i	$0.896305\pi$
$608$	−2875.72	−0.191819
$609$	4607.58	0.306582
$610$	−63343.4	−4.20443
$611$	3007.75	0.199150
$612$	4695.87	0.310163
$613$	2767.63	0.182355	0.0911774	−	0.995835i	$-0.470937\pi$
$613$	2767.63	0.182355	0.0911774	+	0.995835i	$0.470937\pi$
$614$	21150.7	1.39019
$615$	11091.9	0.727265
$616$	336.970	0.0220404
$617$	25880.0	1.68864	0.844318	−	0.535842i	$-0.180006\pi$
$617$	25880.0	1.68864	0.844318	+	0.535842i	$0.180006\pi$
$618$	−21900.0	−1.42548
$619$	42.9744	0.00279045	0.00139522	−	0.999999i	$-0.499556\pi$
$619$	42.9744	0.00279045	0.00139522	+	0.999999i	$0.499556\pi$
$620$	−26549.7	−1.71978
$621$	−4738.54	−0.306201
$622$	1838.38	0.118508
$623$	6346.76	0.408150
$624$	−3626.03	−0.232624
$625$	−481.672	−0.0308270
$626$	3007.10	0.191993
$627$	392.492	0.0249994
$628$	−25833.2	−1.64149
$629$	20730.4	1.31411
$630$	−4382.39	−0.277141
$631$	−18766.2	−1.18395	−0.591974	−	0.805957i	$-0.701651\pi$
$631$	−18766.2	−1.18395	−0.591974	+	0.805957i	$0.701651\pi$
$632$	1096.89	0.0690377
$633$	−10554.3	−0.662713
$634$	24667.9	1.54525
$635$	−17655.2	−1.10335
$636$	−4908.08	−0.306003
$637$	824.953	0.0513121
$638$	−9305.25	−0.577427
$639$	−6012.82	−0.372243
$640$	10004.7	0.617925
$641$	−29882.6	−1.84133	−0.920663	−	0.390358i	$-0.872351\pi$
$641$	−29882.6	−1.84133	−0.920663	+	0.390358i	$0.872351\pi$
$642$	11177.1	0.687113
$643$	−18805.2	−1.15335	−0.576677	−	0.816973i	$-0.695651\pi$
$643$	−18805.2	−1.15335	−0.576677	+	0.816973i	$0.695651\pi$
$644$	8433.64	0.516044
$645$	21996.2	1.34279
$646$	3485.26	0.212269
$647$	−28514.1	−1.73262	−0.866309	−	0.499508i	$-0.833514\pi$
$647$	−28514.1	−1.73262	−0.866309	+	0.499508i	$0.833514\pi$
$648$	−354.474	−0.0214893
$649$	−6432.78	−0.389073
$650$	13015.9	0.785421
$651$	4501.46	0.271008
$652$	9574.15	0.575081
$653$	28136.5	1.68616	0.843082	−	0.537785i	$-0.180739\pi$
$653$	28136.5	1.68616	0.843082	+	0.537785i	$0.180739\pi$
$654$	1005.69	0.0601308
$655$	26970.4	1.60889
$656$	−14712.0	−0.875621
$657$	3512.68	0.208589
$658$	−4821.57	−0.285660
$659$	25412.3	1.50216	0.751080	−	0.660211i	$-0.229533\pi$
$659$	25412.3	1.50216	0.751080	+	0.660211i	$0.229533\pi$
$660$	4087.33	0.241059
$661$	−15015.6	−0.883569	−0.441784	−	0.897121i	$-0.645654\pi$
$661$	−15015.6	−0.883569	−0.441784	+	0.897121i	$0.645654\pi$
$662$	−30045.7	−1.76398
$663$	3838.76	0.224865
$664$	237.203	0.0138634
$665$	−1502.12	−0.0875934
$666$	9464.44	0.550660
$667$	38506.5	2.23535
$668$	−2637.40	−0.152761
$669$	4890.55	0.282630
$670$	−26972.5	−1.55528
$671$	−10016.7	−0.576289
$672$	5077.49	0.291471
$673$	21748.2	1.24566	0.622831	−	0.782357i	$-0.285983\pi$
$673$	21748.2	1.24566	0.622831	+	0.782357i	$0.285983\pi$
$674$	−15831.2	−0.904741
$675$	5414.05	0.308721
$676$	−13136.5	−0.747409
$677$	18842.5	1.06969	0.534843	−	0.844952i	$-0.320371\pi$
$677$	18842.5	1.06969	0.534843	+	0.844952i	$0.320371\pi$
$678$	19032.7	1.07809
$679$	−4328.33	−0.244633
$680$	−6001.03	−0.338425
$681$	5524.43	0.310862
$682$	−9090.94	−0.510425
$683$	−11932.7	−0.668510	−0.334255	−	0.942483i	$-0.608485\pi$
$683$	−11932.7	−0.668510	−0.334255	+	0.942483i	$0.608485\pi$
$684$	734.846	0.0410783
$685$	43261.3	2.41303
$686$	−1322.44	−0.0736020
$687$	13405.4	0.744467
$688$	−29175.2	−1.61670
$689$	−4012.23	−0.221849
$690$	−36624.5	−2.02069
$691$	11305.0	0.622376	0.311188	−	0.950348i	$-0.399273\pi$
$691$	11305.0	0.622376	0.311188	+	0.950348i	$0.399273\pi$
$692$	7937.31	0.436028
$693$	−693.000	−0.0379869
$694$	−11623.9	−0.635791
$695$	48220.4	2.63181
$696$	2880.55	0.156878
$697$	15575.1	0.846414
$698$	33610.7	1.82261
$699$	−5743.79	−0.310801
$700$	−9635.92	−0.520291
$701$	9963.42	0.536823	0.268412	−	0.963304i	$-0.413501\pi$
$701$	9963.42	0.536823	0.268412	+	0.963304i	$0.413501\pi$
$702$	1752.58	0.0942264
$703$	3244.05	0.174042
$704$	−3936.55	−0.210745
$705$	9669.84	0.516578
$706$	−957.043	−0.0510181
$707$	−3106.11	−0.165230
$708$	−12043.8	−0.639314
$709$	11000.9	0.582718	0.291359	−	0.956614i	$-0.405893\pi$
$709$	11000.9	0.582718	0.291359	+	0.956614i	$0.405893\pi$
$710$	−46473.6	−2.45651
$711$	−2255.82	−0.118987
$712$	3967.84	0.208850
$713$	37619.7	1.97597
$714$	−6153.72	−0.322545
$715$	3341.29	0.174765
$716$	973.209	0.0507968
$717$	19363.3	1.00856
$718$	−37978.0	−1.97399
$719$	−16311.5	−0.846059	−0.423030	−	0.906116i	$-0.639033\pi$
$719$	−16311.5	−0.846059	−0.423030	+	0.906116i	$0.639033\pi$
$720$	−11657.6	−0.603406
$721$	13253.7	0.684598
$722$	−25899.5	−1.33501
$723$	−10383.6	−0.534123
$724$	9335.17	0.479197
$725$	−43995.9	−2.25374
$726$	1399.55	0.0715457
$727$	−17113.7	−0.873056	−0.436528	−	0.899691i	$-0.643792\pi$
$727$	−17113.7	−0.873056	−0.436528	+	0.899691i	$0.643792\pi$
$728$	515.740	0.0262563
$729$	729.000	0.0370370
$730$	27149.8	1.37652
$731$	30886.9	1.56278
$732$	−18753.8	−0.946940
$733$	−908.468	−0.0457777	−0.0228888	−	0.999738i	$-0.507286\pi$
$733$	−908.468	−0.0457777	−0.0228888	+	0.999738i	$0.507286\pi$
$734$	−13870.3	−0.697494
$735$	2652.20	0.133099
$736$	42433.6	2.12517
$737$	−4265.24	−0.213178
$738$	7110.81	0.354678
$739$	3111.66	0.154891	0.0774453	−	0.996997i	$-0.475324\pi$
$739$	3111.66	0.154891	0.0774453	+	0.996997i	$0.475324\pi$
$740$	33782.9	1.67822
$741$	600.719	0.0297813
$742$	6431.81	0.318220
$743$	34279.0	1.69257	0.846283	−	0.532734i	$-0.178835\pi$
$743$	34279.0	1.69257	0.846283	+	0.532734i	$0.178835\pi$
$744$	2814.20	0.138674
$745$	37024.8	1.82078
$746$	8773.86	0.430608
$747$	−487.824	−0.0238936
$748$	5739.40	0.280553
$749$	−6764.35	−0.329992
$750$	15760.0	0.767296
$751$	18668.4	0.907086	0.453543	−	0.891234i	$-0.350160\pi$
$751$	18668.4	0.907086	0.453543	+	0.891234i	$0.350160\pi$
$752$	−12825.8	−0.621955
$753$	−10739.3	−0.519735
$754$	−14241.9	−0.687877
$755$	42699.6	2.05828
$756$	−1297.47	−0.0624189
$757$	8879.31	0.426320	0.213160	−	0.977017i	$-0.431624\pi$
$757$	8879.31	0.426320	0.213160	+	0.977017i	$0.431624\pi$
$758$	15285.5	0.732444
$759$	−5791.54	−0.276969
$760$	−939.087	−0.0448214
$761$	−20677.5	−0.984967	−0.492484	−	0.870322i	$-0.663911\pi$
$761$	−20677.5	−0.984967	−0.492484	+	0.870322i	$0.663911\pi$
$762$	−11318.4	−0.538088
$763$	−608.638	−0.0288783
$764$	25249.7	1.19568
$765$	12341.5	0.583279
$766$	−35816.0	−1.68940
$767$	−9845.52	−0.463496
$768$	15002.7	0.704900
$769$	−27497.6	−1.28945	−0.644725	−	0.764414i	$-0.723028\pi$
$769$	−27497.6	−1.28945	−0.644725	+	0.764414i	$0.723028\pi$
$770$	−5356.26	−0.250683
$771$	11340.9	0.529745
$772$	7603.08	0.354457
$773$	9834.49	0.457596	0.228798	−	0.973474i	$-0.426520\pi$
$773$	9834.49	0.457596	0.228798	+	0.973474i	$0.426520\pi$
$774$	14101.4	0.654861
$775$	−42982.6	−1.99223
$776$	−2705.97	−0.125179
$777$	−5727.83	−0.264459
$778$	58167.2	2.68046
$779$	2437.32	0.112100
$780$	6255.76	0.287169
$781$	−7349.00	−0.336707
$782$	−51427.9	−2.35174
$783$	−5924.03	−0.270380
$784$	−3517.81	−0.160250
$785$	−67893.9	−3.08693
$786$	17290.3	0.784636
$787$	−39329.2	−1.78136	−0.890682	−	0.454627i	$-0.849773\pi$
$787$	−39329.2	−1.78136	−0.890682	+	0.454627i	$0.849773\pi$
$788$	−4757.88	−0.215092
$789$	−15190.1	−0.685402
$790$	−17435.4	−0.785221
$791$	−11518.5	−0.517764
$792$	−433.247	−0.0194378
$793$	−15330.8	−0.686522
$794$	−39386.1	−1.76040
$795$	−12899.2	−0.575457
$796$	1001.03	0.0445738
$797$	−22338.1	−0.992792	−0.496396	−	0.868096i	$-0.665344\pi$
$797$	−22338.1	−0.992792	−0.496396	+	0.868096i	$0.665344\pi$
$798$	−962.981	−0.0427183
$799$	13578.3	0.601210
$800$	−48482.8	−2.14266
$801$	−8160.12	−0.359955
$802$	−15974.1	−0.703322
$803$	4293.28	0.188676
$804$	−7985.62	−0.350287
$805$	22165.0	0.970451
$806$	−13913.9	−0.608060
$807$	8730.18	0.380814
$808$	−1941.87	−0.0845478
$809$	37494.8	1.62948	0.814739	−	0.579828i	$-0.196880\pi$
$809$	37494.8	1.62948	0.814739	+	0.579828i	$0.196880\pi$
$810$	5634.50	0.244415
$811$	−42506.0	−1.84043	−0.920214	−	0.391417i	$-0.871985\pi$
$811$	−42506.0	−1.84043	−0.920214	+	0.391417i	$0.871985\pi$
$812$	10543.6	0.455674
$813$	16328.8	0.704399
$814$	11567.6	0.498091
$815$	25162.4	1.08147
$816$	−16369.5	−0.702263
$817$	4833.41	0.206976
$818$	−7551.81	−0.322791
$819$	−1060.65	−0.0452530
$820$	25381.7	1.08094
$821$	−42443.9	−1.80427	−0.902133	−	0.431458i	$-0.857999\pi$
$821$	−42443.9	−1.80427	−0.902133	+	0.431458i	$0.857999\pi$
$822$	27734.0	1.17681
$823$	2288.06	0.0969099	0.0484549	−	0.998825i	$-0.484570\pi$
$823$	2288.06	0.0969099	0.0484549	+	0.998825i	$0.484570\pi$
$824$	8285.92	0.350308
$825$	6617.17	0.279249
$826$	15782.9	0.664837
$827$	−3182.84	−0.133831	−0.0669155	−	0.997759i	$-0.521316\pi$
$827$	−3182.84	−0.133831	−0.0669155	+	0.997759i	$0.521316\pi$
$828$	−10843.3	−0.455108
$829$	−1264.12	−0.0529609	−0.0264804	−	0.999649i	$-0.508430\pi$
$829$	−1264.12	−0.0529609	−0.0264804	+	0.999649i	$0.508430\pi$
$830$	−3770.43	−0.157679
$831$	12132.6	0.506467
$832$	−6024.98	−0.251056
$833$	3724.20	0.154905
$834$	30913.3	1.28350
$835$	−6931.52	−0.287275
$836$	898.145	0.0371567
$837$	−5787.60	−0.239007
$838$	2377.12	0.0979908
$839$	−2934.36	−0.120745	−0.0603726	−	0.998176i	$-0.519229\pi$
$839$	−2934.36	−0.120745	−0.0603726	+	0.998176i	$0.519229\pi$
$840$	1658.09	0.0681066
$841$	23751.1	0.973845
$842$	−2360.83	−0.0966266
$843$	−24518.3	−1.00173
$844$	−24151.6	−0.984993
$845$	−34524.7	−1.40555
$846$	6199.17	0.251929
$847$	−847.000	−0.0343604
$848$	17109.2	0.692845
$849$	6546.92	0.264652
$850$	58759.3	2.37109
$851$	−47868.6	−1.92822
$852$	−13759.2	−0.553266
$853$	25305.3	1.01575	0.507877	−	0.861429i	$-0.330430\pi$
$853$	25305.3	1.01575	0.507877	+	0.861429i	$0.330430\pi$
$854$	24576.0	0.984745
$855$	1931.29	0.0772501
$856$	−4228.91	−0.168856
$857$	−34699.9	−1.38311	−0.691556	−	0.722323i	$-0.743074\pi$
$857$	−34699.9	−1.38311	−0.691556	+	0.722323i	$0.743074\pi$
$858$	2142.04	0.0852310
$859$	17543.8	0.696841	0.348421	−	0.937338i	$-0.386718\pi$
$859$	17543.8	0.696841	0.348421	+	0.937338i	$0.386718\pi$
$860$	50334.1	1.99579
$861$	−4303.43	−0.170337
$862$	−8933.01	−0.352969
$863$	18985.7	0.748876	0.374438	−	0.927252i	$-0.377836\pi$
$863$	18985.7	0.748876	0.374438	+	0.927252i	$0.377836\pi$
$864$	−6528.20	−0.257053
$865$	20860.5	0.819976
$866$	−35420.6	−1.38989
$867$	2590.88	0.101489
$868$	10300.8	0.402800
$869$	−2757.11	−0.107628
$870$	−45787.3	−1.78429
$871$	−6528.05	−0.253955
$872$	−380.506	−0.0147770
$873$	5565.00	0.215746
$874$	−8047.83	−0.311467
$875$	−9537.84	−0.368501
$876$	8038.12	0.310026
$877$	4203.00	0.161830	0.0809152	−	0.996721i	$-0.474216\pi$
$877$	4203.00	0.161830	0.0809152	+	0.996721i	$0.474216\pi$
$878$	7353.98	0.282671
$879$	5128.29	0.196784
$880$	−14248.1	−0.545801
$881$	25566.7	0.977713	0.488856	−	0.872364i	$-0.337414\pi$
$881$	25566.7	0.977713	0.488856	+	0.872364i	$0.337414\pi$
$882$	1700.28	0.0649109
$883$	−39105.9	−1.49039	−0.745197	−	0.666845i	$-0.767645\pi$
$883$	−39105.9	−1.49039	−0.745197	+	0.666845i	$0.767645\pi$
$884$	8784.29	0.334217
$885$	−31653.1	−1.20227
$886$	29522.2	1.11943
$887$	−10841.1	−0.410382	−0.205191	−	0.978722i	$-0.565782\pi$
$887$	−10841.1	−0.410382	−0.205191	+	0.978722i	$0.565782\pi$
$888$	−3580.90	−0.135323
$889$	6849.85	0.258421
$890$	−63070.3	−2.37542
$891$	891.000	0.0335013
$892$	11191.1	0.420074
$893$	2124.84	0.0796249
$894$	23735.9	0.887973
$895$	2557.75	0.0955264
$896$	−3881.63	−0.144728
$897$	−8864.10	−0.329948
$898$	8315.79	0.309022
$899$	47031.4	1.74481
$900$	12389.0	0.458853
$901$	−18113.0	−0.669735
$902$	8690.99	0.320819
$903$	−8534.07	−0.314503
$904$	−7201.09	−0.264939
$905$	24534.3	0.901159
$906$	27374.0	1.00380
$907$	−21542.0	−0.788632	−0.394316	−	0.918975i	$-0.629018\pi$
$907$	−21542.0	−0.788632	−0.394316	+	0.918975i	$0.629018\pi$
$908$	12641.6	0.462035
$909$	3993.57	0.145719
$910$	−8197.88	−0.298634
$911$	16272.3	0.591794	0.295897	−	0.955220i	$-0.404382\pi$
$911$	16272.3	0.591794	0.295897	+	0.955220i	$0.404382\pi$
$912$	−2561.62	−0.0930085
$913$	−596.229	−0.0216126
$914$	69682.4	2.52176
$915$	−49288.0	−1.78078
$916$	30675.8	1.10650
$917$	−10464.0	−0.376828
$918$	7911.93	0.284458
$919$	46663.1	1.67494	0.837472	−	0.546481i	$-0.184033\pi$
$919$	46663.1	1.67494	0.837472	+	0.546481i	$0.184033\pi$
$920$	13857.0	0.496578
$921$	16457.5	0.588811
$922$	13725.0	0.490247
$923$	−11247.8	−0.401112
$924$	−1585.80	−0.0564600
$925$	54692.6	1.94409
$926$	−45268.8	−1.60651
$927$	−17040.5	−0.603759
$928$	53049.7	1.87656
$929$	37396.2	1.32070	0.660349	−	0.750959i	$-0.270408\pi$
$929$	37396.2	1.32070	0.660349	+	0.750959i	$0.270408\pi$
$930$	−44732.8	−1.57725
$931$	582.791	0.0205158
$932$	−13143.6	−0.461945
$933$	1430.45	0.0501940
$934$	60240.1	2.11040
$935$	15084.1	0.527596
$936$	−663.094	−0.0231559
$937$	−27371.8	−0.954321	−0.477161	−	0.878816i	$-0.658334\pi$
$937$	−27371.8	−0.954321	−0.477161	+	0.878816i	$0.658334\pi$
$938$	10464.8	0.364272
$939$	2339.85	0.0813184
$940$	22127.6	0.767791
$941$	2345.33	0.0812491	0.0406246	−	0.999174i	$-0.487065\pi$
$941$	2345.33	0.0812491	0.0406246	+	0.999174i	$0.487065\pi$
$942$	−43525.6	−1.50546
$943$	−35964.6	−1.24196
$944$	41983.9	1.44752
$945$	−3409.97	−0.117382
$946$	17235.0	0.592344
$947$	39562.8	1.35757	0.678784	−	0.734338i	$-0.262507\pi$
$947$	39562.8	1.35757	0.678784	+	0.734338i	$0.262507\pi$
$948$	−5162.03	−0.176851
$949$	6570.97	0.224766
$950$	9195.10	0.314030
$951$	19194.3	0.654488
$952$	2328.28	0.0792647
$953$	−34016.4	−1.15624	−0.578121	−	0.815951i	$-0.696214\pi$
$953$	−34016.4	−1.15624	−0.578121	+	0.815951i	$0.696214\pi$
$954$	−8269.47	−0.280643
$955$	66360.3	2.24855
$956$	44309.4	1.49903
$957$	−7240.48	−0.244568
$958$	3301.36	0.111338
$959$	−16784.5	−0.565172
$960$	−19370.2	−0.651218
$961$	16157.2	0.542353
$962$	17704.6	0.593366
$963$	8697.02	0.291026
$964$	−23761.0	−0.793869
$965$	19982.1	0.666578
$966$	14209.6	0.473277
$967$	−37016.4	−1.23099	−0.615495	−	0.788141i	$-0.711044\pi$
$967$	−37016.4	−1.23099	−0.615495	+	0.788141i	$0.711044\pi$
$968$	−529.524	−0.0175822
$969$	2711.91	0.0899062
$970$	43012.3	1.42376
$971$	43208.1	1.42803	0.714013	−	0.700133i	$-0.246876\pi$
$971$	43208.1	1.42803	0.714013	+	0.700133i	$0.246876\pi$
$972$	1668.18	0.0550483
$973$	−18708.6	−0.616412
$974$	5404.44	0.177792
$975$	10127.7	0.332664
$976$	65374.4	2.14404
$977$	12161.9	0.398253	0.199126	−	0.979974i	$-0.436190\pi$
$977$	12161.9	0.398253	0.199126	+	0.979974i	$0.436190\pi$
$978$	16131.2	0.527422
$979$	−9973.48	−0.325591
$980$	6069.07	0.197826
$981$	782.535	0.0254683
$982$	−17015.5	−0.552938
$983$	16531.0	0.536377	0.268188	−	0.963366i	$-0.413575\pi$
$983$	16531.0	0.536377	0.268188	+	0.963366i	$0.413575\pi$
$984$	−2690.40	−0.0871613
$985$	−12504.5	−0.404493
$986$	−64294.3	−2.07662
$987$	−3751.70	−0.120991
$988$	1374.63	0.0442641
$989$	−71320.9	−2.29310
$990$	6886.61	0.221082
$991$	−16088.6	−0.515712	−0.257856	−	0.966183i	$-0.583016\pi$
$991$	−16088.6	−0.515712	−0.257856	+	0.966183i	$0.583016\pi$
$992$	51828.0	1.65881
$993$	−23378.8	−0.747132
$994$	18030.8	0.575355
$995$	2630.88	0.0838237
$996$	−1116.29	−0.0355132
$997$	−31807.7	−1.01039	−0.505196	−	0.863005i	$-0.668580\pi$
$997$	−31807.7	−1.01039	−0.505196	+	0.863005i	$0.668580\pi$
$998$	19683.6	0.624321
$999$	7364.35	0.233231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.4.a.l.1.4	✓	5
3.2	odd	2		693.4.a.n.1.2		5
7.6	odd	2		1617.4.a.p.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.4.a.l.1.4	✓	5	1.1	even	1	trivial
693.4.a.n.1.2		5	3.2	odd	2
1617.4.a.p.1.4		5	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	231.a (trivial)

\(f(q)\)	\(=\)	\(q+3.85551 q^{2} +3.00000 q^{3} +6.86494 q^{4} +18.0422 q^{5} +11.5665 q^{6} -7.00000 q^{7} -4.37623 q^{8} +9.00000 q^{9} +69.5618 q^{10} +11.0000 q^{11} +20.5948 q^{12} +16.8358 q^{13} -26.9886 q^{14} +54.1265 q^{15} -71.7921 q^{16} +76.0041 q^{17} +34.6996 q^{18} +11.8937 q^{19} +123.858 q^{20} -21.0000 q^{21} +42.4106 q^{22} -175.501 q^{23} -13.1287 q^{24} +200.520 q^{25} +64.9104 q^{26} +27.0000 q^{27} -48.0546 q^{28} -219.409 q^{29} +208.685 q^{30} -214.355 q^{31} -241.785 q^{32} +33.0000 q^{33} +293.035 q^{34} -126.295 q^{35} +61.7845 q^{36} +272.754 q^{37} +45.8562 q^{38} +50.5073 q^{39} -78.9567 q^{40} +204.925 q^{41} -80.9657 q^{42} +406.384 q^{43} +75.5144 q^{44} +162.380 q^{45} -676.647 q^{46} +178.653 q^{47} -215.376 q^{48} +49.0000 q^{49} +773.107 q^{50} +228.012 q^{51} +115.577 q^{52} -238.316 q^{53} +104.099 q^{54} +198.464 q^{55} +30.6336 q^{56} +35.6811 q^{57} -845.931 q^{58} -584.798 q^{59} +371.575 q^{60} -910.607 q^{61} -826.449 q^{62} -63.0000 q^{63} -357.868 q^{64} +303.754 q^{65} +127.232 q^{66} -387.749 q^{67} +521.764 q^{68} -526.504 q^{69} -486.932 q^{70} -668.091 q^{71} -39.3861 q^{72} +390.298 q^{73} +1051.60 q^{74} +601.561 q^{75} +81.6495 q^{76} -77.0000 q^{77} +194.731 q^{78} -250.647 q^{79} -1295.29 q^{80} +81.0000 q^{81} +790.090 q^{82} -54.2027 q^{83} -144.164 q^{84} +1371.28 q^{85} +1566.82 q^{86} -658.226 q^{87} -48.1385 q^{88} -906.680 q^{89} +626.056 q^{90} -117.850 q^{91} -1204.81 q^{92} -643.066 q^{93} +688.796 q^{94} +214.588 q^{95} -725.356 q^{96} +618.333 q^{97} +188.920 q^{98} +99.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 15 q^{3} + 21 q^{4} + 7 q^{5} + 15 q^{6} - 35 q^{7} + 60 q^{8} + 45 q^{9} + 55 q^{10} + 55 q^{11} + 63 q^{12} + 111 q^{13} - 35 q^{14} + 21 q^{15} + 201 q^{16} + 136 q^{17} + 45 q^{18} + 111 q^{19}+ \cdots + 495 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 15 * q^3 + 21 * q^4 + 7 * q^5 + 15 * q^6 - 35 * q^7 + 60 * q^8 + 45 * q^9 + 55 * q^10 + 55 * q^11 + 63 * q^12 + 111 * q^13 - 35 * q^14 + 21 * q^15 + 201 * q^16 + 136 * q^17 + 45 * q^18 + 111 * q^19 + 219 * q^20 - 105 * q^21 + 55 * q^22 - 28 * q^23 + 180 * q^24 + 190 * q^25 - q^26 + 135 * q^27 - 147 * q^28 + 61 * q^29 + 165 * q^30 - 280 * q^31 + 535 * q^32 + 165 * q^33 - 572 * q^34 - 49 * q^35 + 189 * q^36 - 41 * q^37 + 267 * q^38 + 333 * q^39 - 336 * q^40 + 426 * q^41 - 105 * q^42 + 424 * q^43 + 231 * q^44 + 63 * q^45 + 140 * q^46 + 75 * q^47 + 603 * q^48 + 245 * q^49 + 490 * q^50 + 408 * q^51 - 269 * q^52 + 1500 * q^53 + 135 * q^54 + 77 * q^55 - 420 * q^56 + 333 * q^57 - 1767 * q^58 + 757 * q^59 + 657 * q^60 + 658 * q^61 - 568 * q^62 - 315 * q^63 - 748 * q^64 + 537 * q^65 + 165 * q^66 - 583 * q^67 - 1650 * q^68 - 84 * q^69 - 385 * q^70 - 764 * q^71 + 540 * q^72 + 875 * q^73 - 825 * q^74 + 570 * q^75 + 213 * q^76 - 385 * q^77 - 3 * q^78 - 244 * q^79 - 2577 * q^80 + 405 * q^81 - 2006 * q^82 + 924 * q^83 - 441 * q^84 - 1402 * q^85 + 1272 * q^86 + 183 * q^87 + 660 * q^88 - 1110 * q^89 + 495 * q^90 - 777 * q^91 - 2046 * q^92 - 840 * q^93 - 3349 * q^94 + 1923 * q^95 + 1605 * q^96 - 852 * q^97 + 245 * q^98 + 495 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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