LMFDB - Embedded newform 4001.2.a.b.1.111

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4001,2,Mod(1,4001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4001, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("4001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4001.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:	$31.9481458487$
Analytic rank:	$0$
Dimension:	$184$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.111
Character	$\chi$	$=$	4001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.799211 q^{2} -0.343685 q^{3} -1.36126 q^{4} +3.87367 q^{5} -0.274677 q^{6} +3.67019 q^{7} -2.68636 q^{8} -2.88188 q^{9} +3.09588 q^{10} +3.19124 q^{11} +0.467846 q^{12} -5.30234 q^{13} +2.93325 q^{14} -1.33132 q^{15} +0.575560 q^{16} -1.86790 q^{17} -2.30323 q^{18} -2.90630 q^{19} -5.27309 q^{20} -1.26139 q^{21} +2.55047 q^{22} -3.28077 q^{23} +0.923261 q^{24} +10.0054 q^{25} -4.23769 q^{26} +2.02152 q^{27} -4.99609 q^{28} +8.38478 q^{29} -1.06401 q^{30} +1.37034 q^{31} +5.83271 q^{32} -1.09678 q^{33} -1.49285 q^{34} +14.2171 q^{35} +3.92300 q^{36} +10.9621 q^{37} -2.32274 q^{38} +1.82234 q^{39} -10.4061 q^{40} -5.18605 q^{41} -1.00812 q^{42} +9.49354 q^{43} -4.34412 q^{44} -11.1635 q^{45} -2.62203 q^{46} +8.49904 q^{47} -0.197812 q^{48} +6.47028 q^{49} +7.99638 q^{50} +0.641971 q^{51} +7.21788 q^{52} +11.4174 q^{53} +1.61562 q^{54} +12.3618 q^{55} -9.85943 q^{56} +0.998852 q^{57} +6.70120 q^{58} +6.65086 q^{59} +1.81228 q^{60} -5.18931 q^{61} +1.09519 q^{62} -10.5770 q^{63} +3.51044 q^{64} -20.5396 q^{65} -0.876560 q^{66} -3.20048 q^{67} +2.54271 q^{68} +1.12755 q^{69} +11.3625 q^{70} -5.41447 q^{71} +7.74176 q^{72} +5.64575 q^{73} +8.76106 q^{74} -3.43869 q^{75} +3.95623 q^{76} +11.7125 q^{77} +1.45643 q^{78} -7.91117 q^{79} +2.22953 q^{80} +7.95088 q^{81} -4.14474 q^{82} +0.854088 q^{83} +1.71708 q^{84} -7.23565 q^{85} +7.58734 q^{86} -2.88172 q^{87} -8.57281 q^{88} -8.87532 q^{89} -8.92196 q^{90} -19.4606 q^{91} +4.46599 q^{92} -0.470965 q^{93} +6.79252 q^{94} -11.2581 q^{95} -2.00462 q^{96} +6.76528 q^{97} +5.17111 q^{98} -9.19678 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18}+ \cdots + 53 q^{99}+O(q^{100}) $ 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * 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 $

$2$	0.799211	0.565127	0.282564	−	0.959249i	$-0.408815\pi$
$2$	0.799211	0.565127	0.282564	+	0.959249i	$0.408815\pi$
$3$	−0.343685	−0.198427	−0.0992134	−	0.995066i	$-0.531633\pi$
$3$	−0.343685	−0.198427	−0.0992134	+	0.995066i	$0.531633\pi$
$4$	−1.36126	−0.680631
$5$	3.87367	1.73236	0.866180	−	0.499732i	$-0.166568\pi$
$5$	3.87367	1.73236	0.866180	+	0.499732i	$0.166568\pi$
$6$	−0.274677	−0.112136
$7$	3.67019	1.38720	0.693600	−	0.720360i	$-0.256023\pi$
$7$	3.67019	1.38720	0.693600	+	0.720360i	$0.256023\pi$
$8$	−2.68636	−0.949770
$9$	−2.88188	−0.960627
$10$	3.09588	0.979004
$11$	3.19124	0.962195	0.481098	−	0.876667i	$-0.340238\pi$
$11$	3.19124	0.962195	0.481098	+	0.876667i	$0.340238\pi$
$12$	0.467846	0.135055
$13$	−5.30234	−1.47061	−0.735303	−	0.677739i	$-0.762960\pi$
$13$	−5.30234	−1.47061	−0.735303	+	0.677739i	$0.762960\pi$
$14$	2.93325	0.783945
$15$	−1.33132	−0.343747
$16$	0.575560	0.143890
$17$	−1.86790	−0.453033	−0.226516	−	0.974007i	$-0.572734\pi$
$17$	−1.86790	−0.453033	−0.226516	+	0.974007i	$0.572734\pi$
$18$	−2.30323	−0.542876
$19$	−2.90630	−0.666751	−0.333375	−	0.942794i	$-0.608188\pi$
$19$	−2.90630	−0.666751	−0.333375	+	0.942794i	$0.608188\pi$
$20$	−5.27309	−1.17910
$21$	−1.26139	−0.275258
$22$	2.55047	0.543763
$23$	−3.28077	−0.684088	−0.342044	−	0.939684i	$-0.611119\pi$
$23$	−3.28077	−0.684088	−0.342044	+	0.939684i	$0.611119\pi$
$24$	0.923261	0.188460
$25$	10.0054	2.00107
$26$	−4.23769	−0.831079
$27$	2.02152	0.389041
$28$	−4.99609	−0.944172
$29$	8.38478	1.55701	0.778507	−	0.627636i	$-0.215977\pi$
$29$	8.38478	1.55701	0.778507	+	0.627636i	$0.215977\pi$
$30$	−1.06401	−0.194261
$31$	1.37034	0.246120	0.123060	−	0.992399i	$-0.460729\pi$
$31$	1.37034	0.246120	0.123060	+	0.992399i	$0.460729\pi$
$32$	5.83271	1.03109
$33$	−1.09678	−0.190925
$34$	−1.49285	−0.256021
$35$	14.2171	2.40313
$36$	3.92300	0.653833
$37$	10.9621	1.80216	0.901082	−	0.433648i	$-0.142774\pi$
$37$	10.9621	1.80216	0.901082	+	0.433648i	$0.142774\pi$
$38$	−2.32274	−0.376799
$39$	1.82234	0.291808
$40$	−10.4061	−1.64534
$41$	−5.18605	−0.809925	−0.404962	−	0.914333i	$-0.632715\pi$
$41$	−5.18605	−0.809925	−0.404962	+	0.914333i	$0.632715\pi$
$42$	−1.00812	−0.155556
$43$	9.49354	1.44775	0.723876	−	0.689931i	$-0.242359\pi$
$43$	9.49354	1.44775	0.723876	+	0.689931i	$0.242359\pi$
$44$	−4.34412	−0.654900
$45$	−11.1635	−1.66415
$46$	−2.62203	−0.386597
$47$	8.49904	1.23971	0.619856	−	0.784716i	$-0.287191\pi$
$47$	8.49904	1.23971	0.619856	+	0.784716i	$0.287191\pi$
$48$	−0.197812	−0.0285516
$49$	6.47028	0.924325
$50$	7.99638	1.13086
$51$	0.641971	0.0898939
$52$	7.21788	1.00094
$53$	11.4174	1.56830	0.784152	−	0.620569i	$-0.213098\pi$
$53$	11.4174	1.56830	0.784152	+	0.620569i	$0.213098\pi$
$54$	1.61562	0.219858
$55$	12.3618	1.66687
$56$	−9.85943	−1.31752
$57$	0.998852	0.132301
$58$	6.70120	0.879911
$59$	6.65086	0.865869	0.432934	−	0.901425i	$-0.357478\pi$
$59$	6.65086	0.865869	0.432934	+	0.901425i	$0.357478\pi$
$60$	1.81228	0.233965
$61$	−5.18931	−0.664423	−0.332212	−	0.943205i	$-0.607795\pi$
$61$	−5.18931	−0.664423	−0.332212	+	0.943205i	$0.607795\pi$
$62$	1.09519	0.139089
$63$	−10.5770	−1.33258
$64$	3.51044	0.438805
$65$	−20.5396	−2.54762
$66$	−0.876560	−0.107897
$67$	−3.20048	−0.391000	−0.195500	−	0.980704i	$-0.562633\pi$
$67$	−3.20048	−0.391000	−0.195500	+	0.980704i	$0.562633\pi$
$68$	2.54271	0.308348
$69$	1.12755	0.135741
$70$	11.3625	1.35807
$71$	−5.41447	−0.642579	−0.321290	−	0.946981i	$-0.604116\pi$
$71$	−5.41447	−0.642579	−0.321290	+	0.946981i	$0.604116\pi$
$72$	7.74176	0.912375
$73$	5.64575	0.660785	0.330393	−	0.943844i	$-0.392819\pi$
$73$	5.64575	0.660785	0.330393	+	0.943844i	$0.392819\pi$
$74$	8.76106	1.01845
$75$	−3.43869	−0.397066
$76$	3.95623	0.453811
$77$	11.7125	1.33476
$78$	1.45643	0.164908
$79$	−7.91117	−0.890076	−0.445038	−	0.895512i	$-0.646810\pi$
$79$	−7.91117	−0.890076	−0.445038	+	0.895512i	$0.646810\pi$
$80$	2.22953	0.249269
$81$	7.95088	0.883431
$82$	−4.14474	−0.457710
$83$	0.854088	0.0937483	0.0468742	−	0.998901i	$-0.485074\pi$
$83$	0.854088	0.0937483	0.0468742	+	0.998901i	$0.485074\pi$
$84$	1.71708	0.187349
$85$	−7.23565	−0.784816
$86$	7.58734	0.818163
$87$	−2.88172	−0.308953
$88$	−8.57281	−0.913865
$89$	−8.87532	−0.940782	−0.470391	−	0.882458i	$-0.655887\pi$
$89$	−8.87532	−0.940782	−0.470391	+	0.882458i	$0.655887\pi$
$90$	−8.92196	−0.940457
$91$	−19.4606	−2.04002
$92$	4.46599	0.465612
$93$	−0.470965	−0.0488368
$94$	6.79252	0.700595
$95$	−11.2581	−1.15505
$96$	−2.00462	−0.204595
$97$	6.76528	0.686910	0.343455	−	0.939169i	$-0.388403\pi$
$97$	6.76528	0.686910	0.343455	+	0.939169i	$0.388403\pi$
$98$	5.17111	0.522361
$99$	−9.19678	−0.924311
$100$	−13.6199	−1.36199
$101$	−2.81714	−0.280316	−0.140158	−	0.990129i	$-0.544761\pi$
$101$	−2.81714	−0.280316	−0.140158	+	0.990129i	$0.544761\pi$
$102$	0.513070	0.0508015
$103$	7.68494	0.757219	0.378610	−	0.925556i	$-0.376402\pi$
$103$	7.68494	0.757219	0.378610	+	0.925556i	$0.376402\pi$
$104$	14.2440	1.39674
$105$	−4.88621	−0.476845
$106$	9.12492	0.886291
$107$	7.65215	0.739761	0.369881	−	0.929079i	$-0.379399\pi$
$107$	7.65215	0.739761	0.369881	+	0.929079i	$0.379399\pi$
$108$	−2.75181	−0.264793
$109$	17.2747	1.65462	0.827309	−	0.561748i	$-0.189871\pi$
$109$	17.2747	1.65462	0.827309	+	0.561748i	$0.189871\pi$
$110$	9.87971	0.941993
$111$	−3.76753	−0.357598
$112$	2.11241	0.199604
$113$	−1.72226	−0.162017	−0.0810085	−	0.996713i	$-0.525814\pi$
$113$	−1.72226	−0.162017	−0.0810085	+	0.996713i	$0.525814\pi$
$114$	0.798293	0.0747670
$115$	−12.7086	−1.18509
$116$	−11.4139	−1.05975
$117$	15.2807	1.41270
$118$	5.31544	0.489326
$119$	−6.85555	−0.628447
$120$	3.57641	0.326480
$121$	−0.815978	−0.0741798
$122$	−4.14735	−0.375484
$123$	1.78237	0.160711
$124$	−1.86539	−0.167517
$125$	19.3891	1.73421
$126$	−8.45328	−0.753078
$127$	−18.0570	−1.60230	−0.801148	−	0.598466i	$-0.795777\pi$
$127$	−18.0570	−1.60230	−0.801148	+	0.598466i	$0.795777\pi$
$128$	−8.85983	−0.783106
$129$	−3.26279	−0.287273
$130$	−16.4154	−1.43973
$131$	−10.5580	−0.922460	−0.461230	−	0.887281i	$-0.652592\pi$
$131$	−10.5580	−0.922460	−0.461230	+	0.887281i	$0.652592\pi$
$132$	1.49301	0.129950
$133$	−10.6667	−0.924917
$134$	−2.55785	−0.220965
$135$	7.83069	0.673959
$136$	5.01785	0.430277
$137$	8.10539	0.692490	0.346245	−	0.938144i	$-0.387457\pi$
$137$	8.10539	0.692490	0.346245	+	0.938144i	$0.387457\pi$
$138$	0.901153	0.0767112
$139$	4.10403	0.348099	0.174050	−	0.984737i	$-0.444315\pi$
$139$	4.10403	0.348099	0.174050	+	0.984737i	$0.444315\pi$
$140$	−19.3532	−1.63565
$141$	−2.92099	−0.245992
$142$	−4.32730	−0.363139
$143$	−16.9211	−1.41501
$144$	−1.65870	−0.138225
$145$	32.4799	2.69731
$146$	4.51214	0.373428
$147$	−2.22374	−0.183411
$148$	−14.9223	−1.22661
$149$	6.90041	0.565303	0.282652	−	0.959223i	$-0.408786\pi$
$149$	6.90041	0.565303	0.282652	+	0.959223i	$0.408786\pi$
$150$	−2.74824	−0.224393
$151$	−13.2984	−1.08221	−0.541105	−	0.840955i	$-0.681994\pi$
$151$	−13.2984	−1.08221	−0.541105	+	0.840955i	$0.681994\pi$
$152$	7.80735	0.633260
$153$	5.38307	0.435196
$154$	9.36072	0.754308
$155$	5.30824	0.426368
$156$	−2.48068	−0.198613
$157$	−16.2712	−1.29858	−0.649290	−	0.760541i	$-0.724934\pi$
$157$	−16.2712	−1.29858	−0.649290	+	0.760541i	$0.724934\pi$
$158$	−6.32269	−0.503006
$159$	−3.92400	−0.311193
$160$	22.5940	1.78621
$161$	−12.0411	−0.948968
$162$	6.35442	0.499251
$163$	7.66346	0.600248	0.300124	−	0.953900i	$-0.402972\pi$
$163$	7.66346	0.600248	0.300124	+	0.953900i	$0.402972\pi$
$164$	7.05957	0.551260
$165$	−4.24858	−0.330751
$166$	0.682596	0.0529797
$167$	−2.57642	−0.199370	−0.0996848	−	0.995019i	$-0.531783\pi$
$167$	−2.57642	−0.199370	−0.0996848	+	0.995019i	$0.531783\pi$
$168$	3.38854	0.261432
$169$	15.1148	1.16268
$170$	−5.78281	−0.443521
$171$	8.37560	0.640498
$172$	−12.9232	−0.985385
$173$	18.8031	1.42958	0.714788	−	0.699341i	$-0.246523\pi$
$173$	18.8031	1.42958	0.714788	+	0.699341i	$0.246523\pi$
$174$	−2.30310	−0.174598
$175$	36.7215	2.77589
$176$	1.83675	0.138450
$177$	−2.28580	−0.171812
$178$	−7.09325	−0.531662
$179$	−1.47358	−0.110140	−0.0550701	−	0.998482i	$-0.517538\pi$
$179$	−1.47358	−0.110140	−0.0550701	+	0.998482i	$0.517538\pi$
$180$	15.1964	1.13267
$181$	17.9164	1.33171	0.665856	−	0.746080i	$-0.268067\pi$
$181$	17.9164	1.33171	0.665856	+	0.746080i	$0.268067\pi$
$182$	−15.5531	−1.15287
$183$	1.78349	0.131839
$184$	8.81333	0.649727
$185$	42.4638	3.12200
$186$	−0.376400	−0.0275990
$187$	−5.96093	−0.435906
$188$	−11.5694	−0.843787
$189$	7.41934	0.539678
$190$	−8.99756	−0.652751
$191$	−4.70493	−0.340437	−0.170218	−	0.985406i	$-0.554447\pi$
$191$	−4.70493	−0.340437	−0.170218	+	0.985406i	$0.554447\pi$
$192$	−1.20649	−0.0870707
$193$	−17.1110	−1.23168	−0.615839	−	0.787872i	$-0.711183\pi$
$193$	−17.1110	−1.23168	−0.615839	+	0.787872i	$0.711183\pi$
$194$	5.40688	0.388192
$195$	7.05914	0.505516
$196$	−8.80774	−0.629125
$197$	19.4059	1.38262	0.691308	−	0.722560i	$-0.257035\pi$
$197$	19.4059	1.38262	0.691308	+	0.722560i	$0.257035\pi$
$198$	−7.35016	−0.522353
$199$	13.0210	0.923031	0.461516	−	0.887132i	$-0.347306\pi$
$199$	13.0210	0.923031	0.461516	+	0.887132i	$0.347306\pi$
$200$	−26.8779	−1.90056
$201$	1.09996	0.0775849
$202$	−2.25149	−0.158414
$203$	30.7737	2.15989
$204$	−0.873890	−0.0611846
$205$	−20.0891	−1.40308
$206$	6.14188	0.427925
$207$	9.45480	0.657154
$208$	−3.05182	−0.211606
$209$	−9.27470	−0.641544
$210$	−3.90511	−0.269478
$211$	−16.5761	−1.14115	−0.570574	−	0.821246i	$-0.693279\pi$
$211$	−16.5761	−1.14115	−0.570574	+	0.821246i	$0.693279\pi$
$212$	−15.5421	−1.06744
$213$	1.86087	0.127505
$214$	6.11568	0.418059
$215$	36.7749	2.50803
$216$	−5.43051	−0.369500
$217$	5.02940	0.341418
$218$	13.8061	0.935069
$219$	−1.94036	−0.131117
$220$	−16.8277	−1.13452
$221$	9.90426	0.666233
$222$	−3.01105	−0.202088
$223$	27.0170	1.80919	0.904595	−	0.426271i	$-0.140173\pi$
$223$	27.0170	1.80919	0.904595	+	0.426271i	$0.140173\pi$
$224$	21.4071	1.43032
$225$	−28.8342	−1.92228
$226$	−1.37645	−0.0915602
$227$	23.9463	1.58937	0.794686	−	0.607021i	$-0.207636\pi$
$227$	23.9463	1.58937	0.794686	+	0.607021i	$0.207636\pi$
$228$	−1.35970	−0.0900483
$229$	−18.7119	−1.23652	−0.618259	−	0.785974i	$-0.712162\pi$
$229$	−18.7119	−1.23652	−0.618259	+	0.785974i	$0.712162\pi$
$230$	−10.1569	−0.669725
$231$	−4.02540	−0.264852
$232$	−22.5245	−1.47881
$233$	−4.72056	−0.309254	−0.154627	−	0.987973i	$-0.549418\pi$
$233$	−4.72056	−0.309254	−0.154627	+	0.987973i	$0.549418\pi$
$234$	12.2125	0.798357
$235$	32.9225	2.14763
$236$	−9.05357	−0.589337
$237$	2.71895	0.176615
$238$	−5.47903	−0.355153
$239$	−2.50872	−0.162276	−0.0811378	−	0.996703i	$-0.525855\pi$
$239$	−2.50872	−0.162276	−0.0811378	+	0.996703i	$0.525855\pi$
$240$	−0.766258	−0.0494617
$241$	−7.52384	−0.484653	−0.242326	−	0.970195i	$-0.577910\pi$
$241$	−7.52384	−0.484653	−0.242326	+	0.970195i	$0.577910\pi$
$242$	−0.652139	−0.0419211
$243$	−8.79715	−0.564337
$244$	7.06401	0.452227
$245$	25.0637	1.60126
$246$	1.42449	0.0908220
$247$	15.4102	0.980527
$248$	−3.68122	−0.233758
$249$	−0.293537	−0.0186022
$250$	15.4960	0.980052
$251$	15.8611	1.00115	0.500573	−	0.865694i	$-0.333123\pi$
$251$	15.8611	1.00115	0.500573	+	0.865694i	$0.333123\pi$
$252$	14.3981	0.906997
$253$	−10.4697	−0.658227
$254$	−14.4313	−0.905501
$255$	2.48679	0.155729
$256$	−14.1018	−0.881360
$257$	−4.01579	−0.250498	−0.125249	−	0.992125i	$-0.539973\pi$
$257$	−4.01579	−0.250498	−0.125249	+	0.992125i	$0.539973\pi$
$258$	−2.60766	−0.162346
$259$	40.2331	2.49996
$260$	27.9597	1.73399
$261$	−24.1639	−1.49571
$262$	−8.43809	−0.521307
$263$	−31.2535	−1.92717	−0.963586	−	0.267397i	$-0.913836\pi$
$263$	−31.2535	−1.92717	−0.963586	+	0.267397i	$0.913836\pi$
$264$	2.94635	0.181335
$265$	44.2274	2.71687
$266$	−8.52491	−0.522696
$267$	3.05032	0.186676
$268$	4.35669	0.266127
$269$	−25.5110	−1.55543	−0.777717	−	0.628615i	$-0.783622\pi$
$269$	−25.5110	−1.55543	−0.777717	+	0.628615i	$0.783622\pi$
$270$	6.25837	0.380872
$271$	−13.9885	−0.849740	−0.424870	−	0.905254i	$-0.639680\pi$
$271$	−13.9885	−0.849740	−0.424870	+	0.905254i	$0.639680\pi$
$272$	−1.07509	−0.0651870
$273$	6.68832	0.404796
$274$	6.47791	0.391345
$275$	31.9295	1.92542
$276$	−1.53490	−0.0923899
$277$	−8.40331	−0.504906	−0.252453	−	0.967609i	$-0.581237\pi$
$277$	−8.40331	−0.504906	−0.252453	+	0.967609i	$0.581237\pi$
$278$	3.27999	0.196720
$279$	−3.94915	−0.236430
$280$	−38.1922	−2.28242
$281$	−17.1106	−1.02074	−0.510368	−	0.859956i	$-0.670491\pi$
$281$	−17.1106	−1.02074	−0.510368	+	0.859956i	$0.670491\pi$
$282$	−2.33449	−0.139017
$283$	−20.5108	−1.21924	−0.609622	−	0.792693i	$-0.708679\pi$
$283$	−20.5108	−1.21924	−0.609622	+	0.792693i	$0.708679\pi$
$284$	7.37051	0.437359
$285$	3.86923	0.229193
$286$	−13.5235	−0.799661
$287$	−19.0338	−1.12353
$288$	−16.8092	−0.990489
$289$	−13.5109	−0.794761
$290$	25.9583	1.52432
$291$	−2.32513	−0.136301
$292$	−7.68535	−0.449751
$293$	12.3203	0.719758	0.359879	−	0.932999i	$-0.382818\pi$
$293$	12.3203	0.719758	0.359879	+	0.932999i	$0.382818\pi$
$294$	−1.77724	−0.103650
$295$	25.7633	1.50000
$296$	−29.4482	−1.71164
$297$	6.45114	0.374333
$298$	5.51488	0.319468
$299$	17.3958	1.00602
$300$	4.68096	0.270256
$301$	34.8431	2.00832
$302$	−10.6282	−0.611587
$303$	0.968211	0.0556223
$304$	−1.67275	−0.0959388
$305$	−20.1017	−1.15102
$306$	4.30221	0.245941
$307$	11.7775	0.672177	0.336089	−	0.941830i	$-0.390896\pi$
$307$	11.7775	0.672177	0.336089	+	0.941830i	$0.390896\pi$
$308$	−15.9437	−0.908478
$309$	−2.64120	−0.150253
$310$	4.24241	0.240952
$311$	−7.55577	−0.428448	−0.214224	−	0.976785i	$-0.568722\pi$
$311$	−7.55577	−0.428448	−0.214224	+	0.976785i	$0.568722\pi$
$312$	−4.89545	−0.277150
$313$	−24.4768	−1.38351	−0.691754	−	0.722133i	$-0.743162\pi$
$313$	−24.4768	−1.38351	−0.691754	+	0.722133i	$0.743162\pi$
$314$	−13.0041	−0.733863
$315$	−40.9720	−2.30851
$316$	10.7692	0.605814
$317$	−30.8030	−1.73007	−0.865035	−	0.501712i	$-0.832704\pi$
$317$	−30.8030	−1.73007	−0.865035	+	0.501712i	$0.832704\pi$
$318$	−3.13610	−0.175864
$319$	26.7579	1.49815
$320$	13.5983	0.760168
$321$	−2.62993	−0.146788
$322$	−9.62334	−0.536288
$323$	5.42868	0.302060
$324$	−10.8232	−0.601291
$325$	−53.0518	−2.94279
$326$	6.12472	0.339217
$327$	−5.93706	−0.328320
$328$	13.9316	0.769242
$329$	31.1931	1.71973
$330$	−3.39551	−0.186917
$331$	14.4320	0.793252	0.396626	−	0.917980i	$-0.370181\pi$
$331$	14.4320	0.793252	0.396626	+	0.917980i	$0.370181\pi$
$332$	−1.16264	−0.0638080
$333$	−31.5916	−1.73121
$334$	−2.05910	−0.112669
$335$	−12.3976	−0.677353
$336$	−0.726006	−0.0396069
$337$	−23.0575	−1.25602	−0.628011	−	0.778204i	$-0.716131\pi$
$337$	−23.0575	−1.25602	−0.628011	+	0.778204i	$0.716131\pi$
$338$	12.0799	0.657062
$339$	0.591917	0.0321485
$340$	9.84961	0.534170
$341$	4.37308	0.236816
$342$	6.69387	0.361963
$343$	−1.94419	−0.104976
$344$	−25.5030	−1.37503
$345$	4.36777	0.235153
$346$	15.0277	0.807893
$347$	−7.97576	−0.428161	−0.214081	−	0.976816i	$-0.568676\pi$
$347$	−7.97576	−0.428161	−0.214081	+	0.976816i	$0.568676\pi$
$348$	3.92278	0.210283
$349$	36.7783	1.96870	0.984348	−	0.176238i	$-0.0563929\pi$
$349$	36.7783	1.96870	0.984348	+	0.176238i	$0.0563929\pi$
$350$	29.3482	1.56873
$351$	−10.7188	−0.572126
$352$	18.6136	0.992107
$353$	7.13482	0.379748	0.189874	−	0.981808i	$-0.439192\pi$
$353$	7.13482	0.379748	0.189874	+	0.981808i	$0.439192\pi$
$354$	−1.82684	−0.0970954
$355$	−20.9739	−1.11318
$356$	12.0816	0.640326
$357$	2.35615	0.124701
$358$	−1.17770	−0.0622432
$359$	−11.6337	−0.614006	−0.307003	−	0.951709i	$-0.599326\pi$
$359$	−11.6337	−0.614006	−0.307003	+	0.951709i	$0.599326\pi$
$360$	29.9891	1.58056
$361$	−10.5534	−0.555444
$362$	14.3189	0.752587
$363$	0.280440	0.0147193
$364$	26.4910	1.38850
$365$	21.8698	1.14472
$366$	1.42538	0.0745060
$367$	2.71666	0.141808	0.0709042	−	0.997483i	$-0.477412\pi$
$367$	2.71666	0.141808	0.0709042	+	0.997483i	$0.477412\pi$
$368$	−1.88828	−0.0984336
$369$	14.9456	0.778035
$370$	33.9375	1.76433
$371$	41.9041	2.17555
$372$	0.641107	0.0332399
$373$	17.1756	0.889317	0.444658	−	0.895700i	$-0.353325\pi$
$373$	17.1756	0.889317	0.444658	+	0.895700i	$0.353325\pi$
$374$	−4.76404	−0.246342
$375$	−6.66375	−0.344115
$376$	−22.8314	−1.17744
$377$	−44.4590	−2.28975
$378$	5.92962	0.304987
$379$	2.70576	0.138986	0.0694928	−	0.997582i	$-0.477862\pi$
$379$	2.70576	0.138986	0.0694928	+	0.997582i	$0.477862\pi$
$380$	15.3252	0.786164
$381$	6.20591	0.317939
$382$	−3.76023	−0.192390
$383$	15.7574	0.805167	0.402583	−	0.915383i	$-0.368112\pi$
$383$	15.7574	0.805167	0.402583	+	0.915383i	$0.368112\pi$
$384$	3.04499	0.155389
$385$	45.3702	2.31228
$386$	−13.6753	−0.696055
$387$	−27.3592	−1.39075
$388$	−9.20932	−0.467533
$389$	28.7970	1.46007	0.730033	−	0.683412i	$-0.239505\pi$
$389$	28.7970	1.46007	0.730033	+	0.683412i	$0.239505\pi$
$390$	5.64174	0.285681
$391$	6.12816	0.309915
$392$	−17.3815	−0.877897
$393$	3.62864	0.183041
$394$	15.5094	0.781354
$395$	−30.6453	−1.54193
$396$	12.5192	0.629115
$397$	33.5009	1.68136	0.840681	−	0.541531i	$-0.182155\pi$
$397$	33.5009	1.68136	0.840681	+	0.541531i	$0.182155\pi$
$398$	10.4065	0.521630
$399$	3.66597	0.183528
$400$	5.75869	0.287934
$401$	24.2934	1.21316	0.606578	−	0.795024i	$-0.292542\pi$
$401$	24.2934	1.21316	0.606578	+	0.795024i	$0.292542\pi$
$402$	0.879097	0.0438454
$403$	−7.26600	−0.361945
$404$	3.83487	0.190792
$405$	30.7991	1.53042
$406$	24.5947	1.22061
$407$	34.9828	1.73403
$408$	−1.72456	−0.0853785
$409$	−24.6078	−1.21677	−0.608387	−	0.793640i	$-0.708183\pi$
$409$	−24.6078	−1.21677	−0.608387	+	0.793640i	$0.708183\pi$
$410$	−16.0554	−0.792919
$411$	−2.78570	−0.137409
$412$	−10.4612	−0.515387
$413$	24.4099	1.20113
$414$	7.55637	0.371375
$415$	3.30846	0.162406
$416$	−30.9270	−1.51632
$417$	−1.41050	−0.0690722
$418$	−7.41244	−0.362554
$419$	24.3309	1.18864	0.594320	−	0.804228i	$-0.297421\pi$
$419$	24.3309	1.18864	0.594320	+	0.804228i	$0.297421\pi$
$420$	6.65142	0.324556
$421$	−27.4818	−1.33938	−0.669691	−	0.742640i	$-0.733574\pi$
$421$	−27.4818	−1.33938	−0.669691	+	0.742640i	$0.733574\pi$
$422$	−13.2478	−0.644894
$423$	−24.4932	−1.19090
$424$	−30.6713	−1.48953
$425$	−18.6890	−0.906551
$426$	1.48723	0.0720565
$427$	−19.0457	−0.921688
$428$	−10.4166	−0.503504
$429$	5.81552	0.280776
$430$	29.3909	1.41735
$431$	−20.4450	−0.984799	−0.492399	−	0.870369i	$-0.663880\pi$
$431$	−20.4450	−0.984799	−0.492399	+	0.870369i	$0.663880\pi$
$432$	1.16350	0.0559791
$433$	9.69415	0.465871	0.232936	−	0.972492i	$-0.425167\pi$
$433$	9.69415	0.465871	0.232936	+	0.972492i	$0.425167\pi$
$434$	4.01955	0.192945
$435$	−11.1629	−0.535218
$436$	−23.5154	−1.12618
$437$	9.53490	0.456116
$438$	−1.55076	−0.0740981
$439$	32.8481	1.56776	0.783878	−	0.620915i	$-0.213239\pi$
$439$	32.8481	1.56776	0.783878	+	0.620915i	$0.213239\pi$
$440$	−33.2083	−1.58314
$441$	−18.6466	−0.887932
$442$	7.91559	0.376506
$443$	12.7383	0.605217	0.302608	−	0.953115i	$-0.402143\pi$
$443$	12.7383	0.605217	0.302608	+	0.953115i	$0.402143\pi$
$444$	5.12859	0.243392
$445$	−34.3801	−1.62977
$446$	21.5923	1.02242
$447$	−2.37157	−0.112171
$448$	12.8840	0.608711
$449$	−20.7693	−0.980166	−0.490083	−	0.871676i	$-0.663034\pi$
$449$	−20.7693	−0.980166	−0.490083	+	0.871676i	$0.663034\pi$
$450$	−23.0446	−1.08633
$451$	−16.5499	−0.779306
$452$	2.34445	0.110274
$453$	4.57047	0.214740
$454$	19.1381	0.898197
$455$	−75.3840	−3.53406
$456$	−2.68327	−0.125656
$457$	5.13421	0.240168	0.120084	−	0.992764i	$-0.461684\pi$
$457$	5.13421	0.240168	0.120084	+	0.992764i	$0.461684\pi$
$458$	−14.9548	−0.698790
$459$	−3.77599	−0.176248
$460$	17.2998	0.806607
$461$	−23.8909	−1.11271	−0.556356	−	0.830944i	$-0.687801\pi$
$461$	−23.8909	−1.11271	−0.556356	+	0.830944i	$0.687801\pi$
$462$	−3.21714	−0.149675
$463$	−39.1998	−1.82177	−0.910885	−	0.412660i	$-0.864600\pi$
$463$	−39.1998	−1.82177	−0.910885	+	0.412660i	$0.864600\pi$
$464$	4.82595	0.224039
$465$	−1.82437	−0.0846029
$466$	−3.77272	−0.174768
$467$	−13.0036	−0.601734	−0.300867	−	0.953666i	$-0.597276\pi$
$467$	−13.0036	−0.601734	−0.300867	+	0.953666i	$0.597276\pi$
$468$	−20.8011	−0.961530
$469$	−11.7463	−0.542396
$470$	26.3120	1.21368
$471$	5.59216	0.257673
$472$	−17.8666	−0.822377
$473$	30.2962	1.39302
$474$	2.17302	0.0998099
$475$	−29.0785	−1.33421
$476$	9.33221	0.427741
$477$	−32.9036	−1.50655
$478$	−2.00499	−0.0917063
$479$	14.3062	0.653668	0.326834	−	0.945082i	$-0.394018\pi$
$479$	14.3062	0.653668	0.326834	+	0.945082i	$0.394018\pi$
$480$	−7.76523	−0.354433
$481$	−58.1250	−2.65027
$482$	−6.01313	−0.273891
$483$	4.13833	0.188301
$484$	1.11076	0.0504891
$485$	26.2065	1.18998
$486$	−7.03077	−0.318922
$487$	−17.0617	−0.773139	−0.386569	−	0.922260i	$-0.626340\pi$
$487$	−17.0617	−0.773139	−0.386569	+	0.922260i	$0.626340\pi$
$488$	13.9403	0.631049
$489$	−2.63382	−0.119105
$490$	20.0312	0.904918
$491$	35.3313	1.59448	0.797240	−	0.603663i	$-0.206293\pi$
$491$	35.3313	1.59448	0.797240	+	0.603663i	$0.206293\pi$
$492$	−2.42627	−0.109385
$493$	−15.6619	−0.705379
$494$	12.3160	0.554122
$495$	−35.6253	−1.60124
$496$	0.788712	0.0354142
$497$	−19.8721	−0.891386
$498$	−0.234598	−0.0105126
$499$	4.92390	0.220424	0.110212	−	0.993908i	$-0.464847\pi$
$499$	4.92390	0.220424	0.110212	+	0.993908i	$0.464847\pi$
$500$	−26.3937	−1.18036
$501$	0.885479	0.0395603
$502$	12.6764	0.565775
$503$	41.7709	1.86247	0.931235	−	0.364419i	$-0.118732\pi$
$503$	41.7709	1.86247	0.931235	+	0.364419i	$0.118732\pi$
$504$	28.4137	1.26565
$505$	−10.9127	−0.485609
$506$	−8.36753	−0.371982
$507$	−5.19475	−0.230707
$508$	24.5803	1.09057
$509$	31.8541	1.41191	0.705954	−	0.708257i	$-0.250518\pi$
$509$	31.8541	1.41191	0.705954	+	0.708257i	$0.250518\pi$
$510$	1.98746	0.0880064
$511$	20.7210	0.916642
$512$	6.44940	0.285026
$513$	−5.87513	−0.259393
$514$	−3.20946	−0.141563
$515$	29.7689	1.31178
$516$	4.44151	0.195527
$517$	27.1225	1.19285
$518$	32.1547	1.41280
$519$	−6.46236	−0.283666
$520$	55.1766	2.41965
$521$	16.4247	0.719581	0.359791	−	0.933033i	$-0.382848\pi$
$521$	16.4247	0.719581	0.359791	+	0.933033i	$0.382848\pi$
$522$	−19.3121	−0.845266
$523$	−32.1244	−1.40470	−0.702351	−	0.711831i	$-0.747866\pi$
$523$	−32.1244	−1.40470	−0.702351	+	0.711831i	$0.747866\pi$
$524$	14.3723	0.627855
$525$	−12.6206	−0.550810
$526$	−24.9781	−1.08910
$527$	−2.55966	−0.111500
$528$	−0.631265	−0.0274723
$529$	−12.2365	−0.532023
$530$	35.3470	1.53537
$531$	−19.1670	−0.831777
$532$	14.5201	0.629527
$533$	27.4982	1.19108
$534$	2.43785	0.105496
$535$	29.6419	1.28153
$536$	8.59762	0.371361
$537$	0.506446	0.0218548
$538$	−20.3887	−0.879018
$539$	20.6482	0.889381
$540$	−10.6596	−0.458717
$541$	−42.9660	−1.84725	−0.923626	−	0.383295i	$-0.874789\pi$
$541$	−42.9660	−1.84725	−0.923626	+	0.383295i	$0.874789\pi$
$542$	−11.1797	−0.480211
$543$	−6.15759	−0.264247
$544$	−10.8949	−0.467116
$545$	66.9166	2.86639
$546$	5.34538	0.228761
$547$	−4.22060	−0.180460	−0.0902300	−	0.995921i	$-0.528760\pi$
$547$	−4.22060	−0.180460	−0.0902300	+	0.995921i	$0.528760\pi$
$548$	−11.0336	−0.471330
$549$	14.9550	0.638263
$550$	25.5184	1.08811
$551$	−24.3687	−1.03814
$552$	−3.02901	−0.128923
$553$	−29.0355	−1.23471
$554$	−6.71601	−0.285336
$555$	−14.5942	−0.619488
$556$	−5.58666	−0.236927
$557$	−9.71101	−0.411469	−0.205734	−	0.978608i	$-0.565958\pi$
$557$	−9.71101	−0.411469	−0.205734	+	0.978608i	$0.565958\pi$
$558$	−3.15620	−0.133613
$559$	−50.3380	−2.12907
$560$	8.18281	0.345787
$561$	2.04868	0.0864955
$562$	−13.6750	−0.576846
$563$	−14.9696	−0.630892	−0.315446	−	0.948944i	$-0.602154\pi$
$563$	−14.9696	−0.630892	−0.315446	+	0.948944i	$0.602154\pi$
$564$	3.97624	0.167430
$565$	−6.67149	−0.280672
$566$	−16.3925	−0.689027
$567$	29.1812	1.22550
$568$	14.5452	0.610303
$569$	−7.63840	−0.320218	−0.160109	−	0.987099i	$-0.551185\pi$
$569$	−7.63840	−0.320218	−0.160109	+	0.987099i	$0.551185\pi$
$570$	3.09233	0.129523
$571$	35.6631	1.49246	0.746228	−	0.665691i	$-0.231863\pi$
$571$	35.6631	1.49246	0.746228	+	0.665691i	$0.231863\pi$
$572$	23.0340	0.963100
$573$	1.61701	0.0675517
$574$	−15.2120	−0.634936
$575$	−32.8253	−1.36891
$576$	−10.1167	−0.421528
$577$	14.7976	0.616031	0.308015	−	0.951381i	$-0.400335\pi$
$577$	14.7976	0.616031	0.308015	+	0.951381i	$0.400335\pi$
$578$	−10.7981	−0.449141
$579$	5.88081	0.244398
$580$	−44.2137	−1.83587
$581$	3.13466	0.130048
$582$	−1.85827	−0.0770276
$583$	36.4357	1.50901
$584$	−15.1665	−0.627594
$585$	59.1925	2.44731
$586$	9.84649	0.406755
$587$	−1.44039	−0.0594513	−0.0297256	−	0.999558i	$-0.509463\pi$
$587$	−1.44039	−0.0594513	−0.0297256	+	0.999558i	$0.509463\pi$
$588$	3.02709	0.124835
$589$	−3.98261	−0.164101
$590$	20.5903	0.847689
$591$	−6.66954	−0.274348
$592$	6.30937	0.259314
$593$	−34.9216	−1.43406	−0.717029	−	0.697044i	$-0.754498\pi$
$593$	−34.9216	−1.43406	−0.717029	+	0.697044i	$0.754498\pi$
$594$	5.15582	0.211546
$595$	−26.5562	−1.08870
$596$	−9.39326	−0.384763
$597$	−4.47511	−0.183154
$598$	13.9029	0.568532
$599$	12.8169	0.523685	0.261843	−	0.965111i	$-0.415670\pi$
$599$	12.8169	0.523685	0.261843	+	0.965111i	$0.415670\pi$
$600$	9.23755	0.377122
$601$	15.3503	0.626152	0.313076	−	0.949728i	$-0.398640\pi$
$601$	15.3503	0.626152	0.313076	+	0.949728i	$0.398640\pi$
$602$	27.8469	1.13496
$603$	9.22339	0.375605
$604$	18.1026	0.736586
$605$	−3.16083	−0.128506
$606$	0.773804	0.0314337
$607$	44.7202	1.81514	0.907569	−	0.419903i	$-0.137936\pi$
$607$	44.7202	1.81514	0.907569	+	0.419903i	$0.137936\pi$
$608$	−16.9516	−0.687478
$609$	−10.5765	−0.428580
$610$	−16.0655	−0.650473
$611$	−45.0648	−1.82313
$612$	−7.32777	−0.296208
$613$	−23.0227	−0.929877	−0.464939	−	0.885343i	$-0.653924\pi$
$613$	−23.0227	−0.929877	−0.464939	+	0.885343i	$0.653924\pi$
$614$	9.41270	0.379866
$615$	6.90431	0.278409
$616$	−31.4638	−1.26771
$617$	−37.9062	−1.52604	−0.763022	−	0.646372i	$-0.776285\pi$
$617$	−37.9062	−1.52604	−0.763022	+	0.646372i	$0.776285\pi$
$618$	−2.11087	−0.0849118
$619$	−23.4726	−0.943442	−0.471721	−	0.881748i	$-0.656367\pi$
$619$	−23.4726	−0.943442	−0.471721	+	0.881748i	$0.656367\pi$
$620$	−7.22591	−0.290200
$621$	−6.63213	−0.266138
$622$	−6.03865	−0.242128
$623$	−32.5741	−1.30505
$624$	1.04887	0.0419882
$625$	25.0803	1.00321
$626$	−19.5621	−0.781858
$627$	3.18758	0.127300
$628$	22.1493	0.883854
$629$	−20.4762	−0.816440
$630$	−32.7453	−1.30460
$631$	3.95729	0.157537	0.0787687	−	0.996893i	$-0.474901\pi$
$631$	3.95729	0.157537	0.0787687	+	0.996893i	$0.474901\pi$
$632$	21.2522	0.845368
$633$	5.69698	0.226435
$634$	−24.6181	−0.977709
$635$	−69.9468	−2.77575
$636$	5.34159	0.211808
$637$	−34.3076	−1.35932
$638$	21.3852	0.846646
$639$	15.6038	0.617279
$640$	−34.3201	−1.35662
$641$	27.5441	1.08792	0.543962	−	0.839110i	$-0.316923\pi$
$641$	27.5441	1.08792	0.543962	+	0.839110i	$0.316923\pi$
$642$	−2.10187	−0.0829541
$643$	−6.71833	−0.264945	−0.132473	−	0.991187i	$-0.542292\pi$
$643$	−6.71833	−0.264945	−0.132473	+	0.991187i	$0.542292\pi$
$644$	16.3910	0.645897
$645$	−12.6390	−0.497659
$646$	4.33866	0.170702
$647$	−13.8640	−0.545050	−0.272525	−	0.962149i	$-0.587859\pi$
$647$	−13.8640	−0.545050	−0.272525	+	0.962149i	$0.587859\pi$
$648$	−21.3589	−0.839056
$649$	21.2245	0.833135
$650$	−42.3996	−1.66305
$651$	−1.72853	−0.0677464
$652$	−10.4320	−0.408548
$653$	−0.598170	−0.0234082	−0.0117041	−	0.999932i	$-0.503726\pi$
$653$	−0.598170	−0.0234082	−0.0117041	+	0.999932i	$0.503726\pi$
$654$	−4.74496	−0.185543
$655$	−40.8984	−1.59803
$656$	−2.98488	−0.116540
$657$	−16.2704	−0.634768
$658$	24.9298	0.971866
$659$	−41.2043	−1.60509	−0.802547	−	0.596589i	$-0.796522\pi$
$659$	−41.2043	−1.60509	−0.802547	+	0.596589i	$0.796522\pi$
$660$	5.78343	0.225120
$661$	−26.9844	−1.04957	−0.524786	−	0.851234i	$-0.675855\pi$
$661$	−26.9844	−1.04957	−0.524786	+	0.851234i	$0.675855\pi$
$662$	11.5342	0.448289
$663$	−3.40395	−0.132198
$664$	−2.29438	−0.0890394
$665$	−41.3192	−1.60229
$666$	−25.2483	−0.978352
$667$	−27.5086	−1.06514
$668$	3.50719	0.135697
$669$	−9.28534	−0.358992
$670$	−9.90829	−0.382791
$671$	−16.5603	−0.639305
$672$	−7.35731	−0.283815
$673$	16.6280	0.640961	0.320481	−	0.947255i	$-0.396156\pi$
$673$	16.6280	0.640961	0.320481	+	0.947255i	$0.396156\pi$
$674$	−18.4278	−0.709813
$675$	20.2260	0.778498
$676$	−20.5753	−0.791356
$677$	−30.6961	−1.17975	−0.589874	−	0.807495i	$-0.700823\pi$
$677$	−30.6961	−1.17975	−0.589874	+	0.807495i	$0.700823\pi$
$678$	0.473066	0.0181680
$679$	24.8298	0.952882
$680$	19.4375	0.745395
$681$	−8.22999	−0.315374
$682$	3.49501	0.133831
$683$	31.6149	1.20971	0.604856	−	0.796335i	$-0.293231\pi$
$683$	31.6149	1.20971	0.604856	+	0.796335i	$0.293231\pi$
$684$	−11.4014	−0.435943
$685$	31.3976	1.19964
$686$	−1.55381	−0.0593249
$687$	6.43101	0.245358
$688$	5.46410	0.208317
$689$	−60.5391	−2.30636
$690$	3.49077	0.132891
$691$	14.3651	0.546472	0.273236	−	0.961947i	$-0.411906\pi$
$691$	14.3651	0.546472	0.273236	+	0.961947i	$0.411906\pi$
$692$	−25.5960	−0.973014
$693$	−33.7539	−1.28220
$694$	−6.37431	−0.241966
$695$	15.8977	0.603033
$696$	7.74134	0.293435
$697$	9.68703	0.366922
$698$	29.3936	1.11256
$699$	1.62239	0.0613643
$700$	−49.9876	−1.88935
$701$	2.42495	0.0915892	0.0457946	−	0.998951i	$-0.485418\pi$
$701$	2.42495	0.0915892	0.0457946	+	0.998951i	$0.485418\pi$
$702$	−8.56655	−0.323324
$703$	−31.8592	−1.20159
$704$	11.2027	0.422216
$705$	−11.3150	−0.426147
$706$	5.70223	0.214606
$707$	−10.3394	−0.388855
$708$	3.11158	0.116940
$709$	−5.13402	−0.192812	−0.0964062	−	0.995342i	$-0.530735\pi$
$709$	−5.13402	−0.192812	−0.0964062	+	0.995342i	$0.530735\pi$
$710$	−16.7625	−0.629087
$711$	22.7991	0.855031
$712$	23.8423	0.893527
$713$	−4.49577	−0.168368
$714$	1.88306	0.0704718
$715$	−65.5467	−2.45131
$716$	2.00592	0.0749649
$717$	0.862210	0.0321998
$718$	−9.29781	−0.346991
$719$	16.0731	0.599424	0.299712	−	0.954030i	$-0.403109\pi$
$719$	16.0731	0.599424	0.299712	+	0.954030i	$0.403109\pi$
$720$	−6.42525	−0.239455
$721$	28.2052	1.05041
$722$	−8.43441	−0.313896
$723$	2.58583	0.0961681
$724$	−24.3889	−0.906405
$725$	83.8927	3.11570
$726$	0.224130	0.00831826
$727$	−27.0503	−1.00324	−0.501619	−	0.865088i	$-0.667262\pi$
$727$	−27.0503	−1.00324	−0.501619	+	0.865088i	$0.667262\pi$
$728$	52.2781	1.93755
$729$	−20.8292	−0.771451
$730$	17.4786	0.646911
$731$	−17.7330	−0.655879
$732$	−2.42780	−0.0897340
$733$	−29.0016	−1.07120	−0.535600	−	0.844472i	$-0.679915\pi$
$733$	−29.0016	−1.07120	−0.535600	+	0.844472i	$0.679915\pi$
$734$	2.17118	0.0801398
$735$	−8.61404	−0.317734
$736$	−19.1358	−0.705354
$737$	−10.2135	−0.376219
$738$	11.9447	0.439689
$739$	3.90988	0.143827	0.0719136	−	0.997411i	$-0.477089\pi$
$739$	3.90988	0.143827	0.0719136	+	0.997411i	$0.477089\pi$
$740$	−57.8043	−2.12493
$741$	−5.29626	−0.194563
$742$	33.4902	1.22946
$743$	−14.3980	−0.528210	−0.264105	−	0.964494i	$-0.585077\pi$
$743$	−14.3980	−0.528210	−0.264105	+	0.964494i	$0.585077\pi$
$744$	1.26518	0.0463838
$745$	26.7299	0.979309
$746$	13.7269	0.502577
$747$	−2.46138	−0.0900572
$748$	8.11439	0.296691
$749$	28.0848	1.02620
$750$	−5.32574	−0.194469
$751$	25.7629	0.940101	0.470050	−	0.882640i	$-0.344236\pi$
$751$	25.7629	0.940101	0.470050	+	0.882640i	$0.344236\pi$
$752$	4.89171	0.178382
$753$	−5.45124	−0.198654
$754$	−35.5321	−1.29400
$755$	−51.5138	−1.87478
$756$	−10.0997	−0.367321
$757$	−10.8072	−0.392793	−0.196396	−	0.980525i	$-0.562924\pi$
$757$	−10.8072	−0.392793	−0.196396	+	0.980525i	$0.562924\pi$
$758$	2.16247	0.0785446
$759$	3.59829	0.130610
$760$	30.2431	1.09703
$761$	−6.19499	−0.224568	−0.112284	−	0.993676i	$-0.535817\pi$
$761$	−6.19499	−0.224568	−0.112284	+	0.993676i	$0.535817\pi$
$762$	4.95983	0.179676
$763$	63.4014	2.29529
$764$	6.40464	0.231712
$765$	20.8523	0.753915
$766$	12.5935	0.455022
$767$	−35.2652	−1.27335
$768$	4.84656	0.174885
$769$	−42.4384	−1.53037	−0.765184	−	0.643812i	$-0.777352\pi$
$769$	−42.4384	−1.53037	−0.765184	+	0.643812i	$0.777352\pi$
$770$	36.2604	1.30673
$771$	1.38017	0.0497055
$772$	23.2926	0.838319
$773$	15.0229	0.540335	0.270168	−	0.962813i	$-0.412921\pi$
$773$	15.0229	0.540335	0.270168	+	0.962813i	$0.412921\pi$
$774$	−21.8658	−0.785950
$775$	13.7107	0.492504
$776$	−18.1740	−0.652407
$777$	−13.8275	−0.496060
$778$	23.0149	0.825123
$779$	15.0722	0.540018
$780$	−9.60934	−0.344070
$781$	−17.2789	−0.618287
$782$	4.89769	0.175141
$783$	16.9500	0.605742
$784$	3.72403	0.133001
$785$	−63.0292	−2.24961
$786$	2.90005	0.103441
$787$	18.3800	0.655177	0.327589	−	0.944820i	$-0.393764\pi$
$787$	18.3800	0.655177	0.327589	+	0.944820i	$0.393764\pi$
$788$	−26.4166	−0.941052
$789$	10.7414	0.382403
$790$	−24.4921	−0.871388
$791$	−6.32103	−0.224750
$792$	24.7058	0.877883
$793$	27.5155	0.977104
$794$	26.7743	0.950183
$795$	−15.2003	−0.539099
$796$	−17.7249	−0.628244
$797$	7.97424	0.282462	0.141231	−	0.989977i	$-0.454894\pi$
$797$	7.97424	0.282462	0.141231	+	0.989977i	$0.454894\pi$
$798$	2.92988	0.103717
$799$	−15.8754	−0.561630
$800$	58.3583	2.06328
$801$	25.5776	0.903741
$802$	19.4156	0.685588
$803$	18.0170	0.635805
$804$	−1.49733	−0.0528067
$805$	−46.6431	−1.64395
$806$	−5.80707	−0.204545
$807$	8.76776	0.308640
$808$	7.56785	0.266236
$809$	−5.68134	−0.199745	−0.0998726	−	0.995000i	$-0.531844\pi$
$809$	−5.68134	−0.199745	−0.0998726	+	0.995000i	$0.531844\pi$
$810$	24.6150	0.864882
$811$	−33.3490	−1.17104	−0.585520	−	0.810658i	$-0.699110\pi$
$811$	−33.3490	−1.17104	−0.585520	+	0.810658i	$0.699110\pi$
$812$	−41.8911	−1.47009
$813$	4.80764	0.168611
$814$	27.9586	0.979950
$815$	29.6857	1.03985
$816$	0.369493	0.0129348
$817$	−27.5911	−0.965289
$818$	−19.6668	−0.687633
$819$	56.0831	1.95970
$820$	27.3465	0.954981
$821$	−31.9156	−1.11386	−0.556931	−	0.830559i	$-0.688021\pi$
$821$	−31.9156	−1.11386	−0.556931	+	0.830559i	$0.688021\pi$
$822$	−2.22636	−0.0776533
$823$	−15.4074	−0.537067	−0.268534	−	0.963270i	$-0.586539\pi$
$823$	−15.4074	−0.537067	−0.268534	+	0.963270i	$0.586539\pi$
$824$	−20.6445	−0.719184
$825$	−10.9737	−0.382055
$826$	19.5087	0.678793
$827$	2.04826	0.0712250	0.0356125	−	0.999366i	$-0.488662\pi$
$827$	2.04826	0.0712250	0.0356125	+	0.999366i	$0.488662\pi$
$828$	−12.8705	−0.447279
$829$	−3.08901	−0.107286	−0.0536428	−	0.998560i	$-0.517083\pi$
$829$	−3.08901	−0.107286	−0.0536428	+	0.998560i	$0.517083\pi$
$830$	2.64415	0.0917800
$831$	2.88809	0.100187
$832$	−18.6136	−0.645309
$833$	−12.0858	−0.418750
$834$	−1.12728	−0.0390346
$835$	−9.98023	−0.345380
$836$	12.6253	0.436655
$837$	2.77016	0.0957508
$838$	19.4455	0.671733
$839$	2.63584	0.0909992	0.0454996	−	0.998964i	$-0.485512\pi$
$839$	2.63584	0.0909992	0.0454996	+	0.998964i	$0.485512\pi$
$840$	13.1261	0.452894
$841$	41.3045	1.42429
$842$	−21.9638	−0.756921
$843$	5.88068	0.202541
$844$	22.5645	0.776702
$845$	58.5500	2.01418
$846$	−19.5752	−0.673010
$847$	−2.99479	−0.102902
$848$	6.57141	0.225663
$849$	7.04927	0.241930
$850$	−14.9365	−0.512317
$851$	−35.9643	−1.23284
$852$	−2.53314	−0.0867838
$853$	−7.33282	−0.251071	−0.125536	−	0.992089i	$-0.540065\pi$
$853$	−7.33282	−0.251071	−0.125536	+	0.992089i	$0.540065\pi$
$854$	−15.2216	−0.520871
$855$	32.4444	1.10957
$856$	−20.5564	−0.702603
$857$	−4.60001	−0.157133	−0.0785666	−	0.996909i	$-0.525034\pi$
$857$	−4.60001	−0.157133	−0.0785666	+	0.996909i	$0.525034\pi$
$858$	4.64782	0.158674
$859$	51.9505	1.77253	0.886265	−	0.463179i	$-0.153291\pi$
$859$	51.9505	1.77253	0.886265	+	0.463179i	$0.153291\pi$
$860$	−50.0603	−1.70704
$861$	6.54163	0.222938
$862$	−16.3398	−0.556537
$863$	−42.7089	−1.45383	−0.726915	−	0.686728i	$-0.759046\pi$
$863$	−42.7089	−1.45383	−0.726915	+	0.686728i	$0.759046\pi$
$864$	11.7909	0.401135
$865$	72.8372	2.47654
$866$	7.74767	0.263276
$867$	4.64351	0.157702
$868$	−6.84633	−0.232380
$869$	−25.2465	−0.856427
$870$	−8.92148	−0.302466
$871$	16.9700	0.575007
$872$	−46.4060	−1.57151
$873$	−19.4967	−0.659864
$874$	7.62040	0.257764
$875$	71.1617	2.40570
$876$	2.64134	0.0892427
$877$	20.6758	0.698172	0.349086	−	0.937091i	$-0.386492\pi$
$877$	20.6758	0.698172	0.349086	+	0.937091i	$0.386492\pi$
$878$	26.2526	0.885982
$879$	−4.23429	−0.142819
$880$	7.11498	0.239846
$881$	20.4765	0.689870	0.344935	−	0.938627i	$-0.387901\pi$
$881$	20.4765	0.689870	0.344935	+	0.938627i	$0.387901\pi$
$882$	−14.9025	−0.501794
$883$	−34.0898	−1.14721	−0.573607	−	0.819131i	$-0.694456\pi$
$883$	−34.0898	−1.14721	−0.573607	+	0.819131i	$0.694456\pi$
$884$	−13.4823	−0.453459
$885$	−8.85446	−0.297639
$886$	10.1806	0.342024
$887$	26.1538	0.878158	0.439079	−	0.898448i	$-0.355305\pi$
$887$	26.1538	0.878158	0.439079	+	0.898448i	$0.355305\pi$
$888$	10.1209	0.339636
$889$	−66.2724	−2.22271
$890$	−27.4769	−0.921029
$891$	25.3732	0.850033
$892$	−36.7772	−1.23139
$893$	−24.7007	−0.826579
$894$	−1.89538	−0.0633911
$895$	−5.70815	−0.190803
$896$	−32.5172	−1.08633
$897$	−5.97867	−0.199622
$898$	−16.5991	−0.553918
$899$	11.4900	0.383212
$900$	39.2510	1.30837
$901$	−21.3266	−0.710493
$902$	−13.2269	−0.440407
$903$	−11.9750	−0.398505
$904$	4.62662	0.153879
$905$	69.4021	2.30700
$906$	3.65277	0.121355
$907$	19.9329	0.661862	0.330931	−	0.943655i	$-0.392637\pi$
$907$	19.9329	0.661862	0.330931	+	0.943655i	$0.392637\pi$
$908$	−32.5972	−1.08178
$909$	8.11867	0.269279
$910$	−60.2477	−1.99719
$911$	18.2439	0.604447	0.302223	−	0.953237i	$-0.402271\pi$
$911$	18.2439	0.604447	0.302223	+	0.953237i	$0.402271\pi$
$912$	0.574900	0.0190368
$913$	2.72560	0.0902042
$914$	4.10332	0.135726
$915$	6.90866	0.228393
$916$	25.4718	0.841613
$917$	−38.7500	−1.27964
$918$	−3.01781	−0.0996027
$919$	−33.3166	−1.09901	−0.549507	−	0.835489i	$-0.685184\pi$
$919$	−33.3166	−1.09901	−0.549507	+	0.835489i	$0.685184\pi$
$920$	34.1400	1.12556
$921$	−4.04775	−0.133378
$922$	−19.0939	−0.628823
$923$	28.7094	0.944980
$924$	5.47962	0.180266
$925$	109.680	3.60626
$926$	−31.3289	−1.02953
$927$	−22.1471	−0.727405
$928$	48.9060	1.60542
$929$	19.5005	0.639791	0.319896	−	0.947453i	$-0.396352\pi$
$929$	19.5005	0.639791	0.319896	+	0.947453i	$0.396352\pi$
$930$	−1.45805	−0.0478114
$931$	−18.8046	−0.616294
$932$	6.42592	0.210488
$933$	2.59681	0.0850156
$934$	−10.3926	−0.340056
$935$	−23.0907	−0.755146
$936$	−41.0495	−1.34174
$937$	−17.2137	−0.562348	−0.281174	−	0.959657i	$-0.590724\pi$
$937$	−17.2137	−0.562348	−0.281174	+	0.959657i	$0.590724\pi$
$938$	−9.38780	−0.306523
$939$	8.41231	0.274525
$940$	−44.8162	−1.46174
$941$	49.7769	1.62268	0.811341	−	0.584573i	$-0.198738\pi$
$941$	49.7769	1.62268	0.811341	+	0.584573i	$0.198738\pi$
$942$	4.46931	0.145618
$943$	17.0142	0.554060
$944$	3.82797	0.124590
$945$	28.7401	0.934916
$946$	24.2130	0.787233
$947$	5.46379	0.177549	0.0887746	−	0.996052i	$-0.471705\pi$
$947$	5.46379	0.177549	0.0887746	+	0.996052i	$0.471705\pi$
$948$	−3.70121	−0.120210
$949$	−29.9357	−0.971754
$950$	−23.2399	−0.754001
$951$	10.5865	0.343292
$952$	18.4165	0.596881
$953$	2.55108	0.0826376	0.0413188	−	0.999146i	$-0.486844\pi$
$953$	2.55108	0.0826376	0.0413188	+	0.999146i	$0.486844\pi$
$954$	−26.2969	−0.851395
$955$	−18.2254	−0.589759
$956$	3.41503	0.110450
$957$	−9.19628	−0.297273
$958$	11.4337	0.369405
$959$	29.7483	0.960623
$960$	−4.67354	−0.150838
$961$	−29.1222	−0.939425
$962$	−46.4541	−1.49774
$963$	−22.0526	−0.710634
$964$	10.2419	0.329870
$965$	−66.2826	−2.13371
$966$	3.30740	0.106414
$967$	37.6301	1.21010	0.605051	−	0.796186i	$-0.293153\pi$
$967$	37.6301	1.21010	0.605051	+	0.796186i	$0.293153\pi$
$968$	2.19201	0.0704538
$969$	−1.86576	−0.0599368
$970$	20.9445	0.672488
$971$	25.0620	0.804279	0.402139	−	0.915578i	$-0.368267\pi$
$971$	25.0620	0.804279	0.402139	+	0.915578i	$0.368267\pi$
$972$	11.9752	0.384106
$973$	15.0626	0.482884
$974$	−13.6359	−0.436922
$975$	18.2331	0.583927
$976$	−2.98676	−0.0956039
$977$	34.3029	1.09745	0.548724	−	0.836003i	$-0.315114\pi$
$977$	34.3029	1.09745	0.548724	+	0.836003i	$0.315114\pi$
$978$	−2.10498	−0.0673097
$979$	−28.3233	−0.905217
$980$	−34.1183	−1.08987
$981$	−49.7836	−1.58947
$982$	28.2372	0.901084
$983$	−12.8440	−0.409661	−0.204831	−	0.978797i	$-0.565664\pi$
$983$	−12.8440	−0.409661	−0.204831	+	0.978797i	$0.565664\pi$
$984$	−4.78808	−0.152638
$985$	75.1723	2.39519
$986$	−12.5172	−0.398629
$987$	−10.7206	−0.341240
$988$	−20.9773	−0.667377
$989$	−31.1461	−0.990390
$990$	−28.4721	−0.904904
$991$	15.5066	0.492584	0.246292	−	0.969196i	$-0.420788\pi$
$991$	15.5066	0.492584	0.246292	+	0.969196i	$0.420788\pi$
$992$	7.99278	0.253771
$993$	−4.96005	−0.157403
$994$	−15.8820	−0.503746
$995$	50.4389	1.59902
$996$	0.399581	0.0126612
$997$	12.9241	0.409310	0.204655	−	0.978834i	$-0.434393\pi$
$997$	12.9241	0.409310	0.204655	+	0.978834i	$0.434393\pi$
$998$	3.93523	0.124568
$999$	22.1601	0.701116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4001.2.a.b.1.111	✓	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4001.2.a.b.1.111	✓	184	1.1	even	1	trivial

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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:	\( N \)	\(=\)	\( 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4001.a (trivial)

\(f(q)\)	\(=\)	\(q+0.799211 q^{2} -0.343685 q^{3} -1.36126 q^{4} +3.87367 q^{5} -0.274677 q^{6} +3.67019 q^{7} -2.68636 q^{8} -2.88188 q^{9} +3.09588 q^{10} +3.19124 q^{11} +0.467846 q^{12} -5.30234 q^{13} +2.93325 q^{14} -1.33132 q^{15} +0.575560 q^{16} -1.86790 q^{17} -2.30323 q^{18} -2.90630 q^{19} -5.27309 q^{20} -1.26139 q^{21} +2.55047 q^{22} -3.28077 q^{23} +0.923261 q^{24} +10.0054 q^{25} -4.23769 q^{26} +2.02152 q^{27} -4.99609 q^{28} +8.38478 q^{29} -1.06401 q^{30} +1.37034 q^{31} +5.83271 q^{32} -1.09678 q^{33} -1.49285 q^{34} +14.2171 q^{35} +3.92300 q^{36} +10.9621 q^{37} -2.32274 q^{38} +1.82234 q^{39} -10.4061 q^{40} -5.18605 q^{41} -1.00812 q^{42} +9.49354 q^{43} -4.34412 q^{44} -11.1635 q^{45} -2.62203 q^{46} +8.49904 q^{47} -0.197812 q^{48} +6.47028 q^{49} +7.99638 q^{50} +0.641971 q^{51} +7.21788 q^{52} +11.4174 q^{53} +1.61562 q^{54} +12.3618 q^{55} -9.85943 q^{56} +0.998852 q^{57} +6.70120 q^{58} +6.65086 q^{59} +1.81228 q^{60} -5.18931 q^{61} +1.09519 q^{62} -10.5770 q^{63} +3.51044 q^{64} -20.5396 q^{65} -0.876560 q^{66} -3.20048 q^{67} +2.54271 q^{68} +1.12755 q^{69} +11.3625 q^{70} -5.41447 q^{71} +7.74176 q^{72} +5.64575 q^{73} +8.76106 q^{74} -3.43869 q^{75} +3.95623 q^{76} +11.7125 q^{77} +1.45643 q^{78} -7.91117 q^{79} +2.22953 q^{80} +7.95088 q^{81} -4.14474 q^{82} +0.854088 q^{83} +1.71708 q^{84} -7.23565 q^{85} +7.58734 q^{86} -2.88172 q^{87} -8.57281 q^{88} -8.87532 q^{89} -8.92196 q^{90} -19.4606 q^{91} +4.46599 q^{92} -0.470965 q^{93} +6.79252 q^{94} -11.2581 q^{95} -2.00462 q^{96} +6.76528 q^{97} +5.17111 q^{98} -9.19678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 3 q^{2} + 28 q^{3} + 217 q^{4} + 15 q^{5} + 31 q^{6} + 49 q^{7} + 6 q^{8} + 210 q^{9} + 46 q^{10} + 25 q^{11} + 61 q^{12} + 52 q^{13} + 28 q^{14} + 59 q^{15} + 279 q^{16} + 16 q^{17} - 2 q^{18}+ \cdots + 53 q^{99}+O(q^{100}) \) 184 * q + 3 * q^2 + 28 * q^3 + 217 * q^4 + 15 * q^5 + 31 * q^6 + 49 * q^7 + 6 * q^8 + 210 * q^9 + 46 * q^10 + 25 * q^11 + 61 * q^12 + 52 * q^13 + 28 * q^14 + 59 * q^15 + 279 * q^16 + 16 * q^17 - 2 * q^18 + 86 * q^19 + 26 * q^20 + 22 * q^21 + 54 * q^22 + 55 * q^23 + 72 * q^24 + 241 * q^25 + 32 * q^26 + 97 * q^27 + 75 * q^28 + 27 * q^29 - 10 * q^30 + 276 * q^31 + 20 * q^33 + 122 * q^34 + 30 * q^35 + 278 * q^36 + 42 * q^37 + 14 * q^38 + 113 * q^39 + 115 * q^40 + 39 * q^41 + 15 * q^42 + 65 * q^43 + 32 * q^44 + 54 * q^45 + 65 * q^46 + 82 * q^47 + 117 * q^48 + 297 * q^49 + 4 * q^50 + 45 * q^51 + 136 * q^52 + 21 * q^53 + 93 * q^54 + 252 * q^55 + 74 * q^56 + 14 * q^57 + 54 * q^58 + 95 * q^59 + 58 * q^60 + 131 * q^61 + 14 * q^62 + 88 * q^63 + 368 * q^64 - 9 * q^65 + 52 * q^66 + 90 * q^67 + 27 * q^68 + 101 * q^69 + 18 * q^70 + 117 * q^71 - 15 * q^72 + 72 * q^73 + 7 * q^74 + 150 * q^75 + 148 * q^76 + 7 * q^77 + 22 * q^78 + 287 * q^79 + 43 * q^80 + 244 * q^81 + 86 * q^82 + 25 * q^83 + 14 * q^84 + 41 * q^85 + 25 * q^86 + 82 * q^87 + 115 * q^88 + 48 * q^89 + 78 * q^90 + 272 * q^91 + 69 * q^92 + 44 * q^93 + 161 * q^94 + 37 * q^95 + 129 * q^96 + 106 * q^97 - 46 * q^98 + 53 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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