LMFDB - Embedded newform 4002.2.a.bj.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4002,2,Mod(1,4002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4002, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4002 = 2 \cdot 3 \cdot 23 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4002.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:	$31.9561308889$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 26x^{6} + 4x^{5} + 209x^{4} + 113x^{3} - 436x^{2} - 360x - 16 $ x^8 - x^7 - 26x^6 + 4x^5 + 209x^4 + 113x^3 - 436x^2 - 360x - 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.09236$ of defining polynomial
Character	$\chi$	$=$	4002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.09236 q^{5} -1.00000 q^{6} +1.21381 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.09236 q^{10} +4.27762 q^{11} -1.00000 q^{12} -5.32951 q^{13} +1.21381 q^{14} +2.09236 q^{15} +1.00000 q^{16} +5.49805 q^{17} +1.00000 q^{18} +1.21381 q^{19} -2.09236 q^{20} -1.21381 q^{21} +4.27762 q^{22} +1.00000 q^{23} -1.00000 q^{24} -0.622024 q^{25} -5.32951 q^{26} -1.00000 q^{27} +1.21381 q^{28} +1.00000 q^{29} +2.09236 q^{30} -3.40605 q^{31} +1.00000 q^{32} -4.27762 q^{33} +5.49805 q^{34} -2.53973 q^{35} +1.00000 q^{36} +3.04782 q^{37} +1.21381 q^{38} +5.32951 q^{39} -2.09236 q^{40} -3.69517 q^{41} -1.21381 q^{42} +8.96466 q^{43} +4.27762 q^{44} -2.09236 q^{45} +1.00000 q^{46} -2.76153 q^{47} -1.00000 q^{48} -5.52666 q^{49} -0.622024 q^{50} -5.49805 q^{51} -5.32951 q^{52} -3.94985 q^{53} -1.00000 q^{54} -8.95033 q^{55} +1.21381 q^{56} -1.21381 q^{57} +1.00000 q^{58} +4.90938 q^{59} +2.09236 q^{60} -10.3699 q^{61} -3.40605 q^{62} +1.21381 q^{63} +1.00000 q^{64} +11.1513 q^{65} -4.27762 q^{66} +13.7621 q^{67} +5.49805 q^{68} -1.00000 q^{69} -2.53973 q^{70} +8.59299 q^{71} +1.00000 q^{72} +6.48055 q^{73} +3.04782 q^{74} +0.622024 q^{75} +1.21381 q^{76} +5.19222 q^{77} +5.32951 q^{78} +14.2172 q^{79} -2.09236 q^{80} +1.00000 q^{81} -3.69517 q^{82} +2.28424 q^{83} -1.21381 q^{84} -11.5039 q^{85} +8.96466 q^{86} -1.00000 q^{87} +4.27762 q^{88} +2.82204 q^{89} -2.09236 q^{90} -6.46902 q^{91} +1.00000 q^{92} +3.40605 q^{93} -2.76153 q^{94} -2.53973 q^{95} -1.00000 q^{96} +3.02327 q^{97} -5.52666 q^{98} +4.27762 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + q^{5} - 8 q^{6} + 8 q^{8} + 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} + 9 q^{13} - q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + q^{20} + 3 q^{22} + 8 q^{23} - 8 q^{24}+ \cdots + 3 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + q^5 - 8 * q^6 + 8 * q^8 + 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 + 9 * q^13 - q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + q^20 + 3 * q^22 + 8 * q^23 - 8 * q^24 + 13 * q^25 + 9 * q^26 - 8 * q^27 + 8 * q^29 - q^30 - 9 * q^31 + 8 * q^32 - 3 * q^33 + 8 * q^34 - 2 * q^35 + 8 * q^36 + 7 * q^37 - 9 * q^39 + q^40 + 3 * q^41 + 16 * q^43 + 3 * q^44 + q^45 + 8 * q^46 + 24 * q^47 - 8 * q^48 + 6 * q^49 + 13 * q^50 - 8 * q^51 + 9 * q^52 + 8 * q^53 - 8 * q^54 + 13 * q^55 + 8 * q^58 - 3 * q^59 - q^60 + 31 * q^61 - 9 * q^62 + 8 * q^64 + 13 * q^65 - 3 * q^66 - 11 * q^67 + 8 * q^68 - 8 * q^69 - 2 * q^70 + 7 * q^71 + 8 * q^72 + 14 * q^73 + 7 * q^74 - 13 * q^75 + 10 * q^77 - 9 * q^78 + 12 * q^79 + q^80 + 8 * q^81 + 3 * q^82 - 8 * q^83 + 22 * q^85 + 16 * q^86 - 8 * q^87 + 3 * q^88 - 12 * q^89 + q^90 + 28 * q^91 + 8 * q^92 + 9 * q^93 + 24 * q^94 - 2 * q^95 - 8 * q^96 + 16 * q^97 + 6 * q^98 + 3 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.09236	−0.935732	−0.467866	−	0.883799i	$-0.654977\pi$
$5$	−2.09236	−0.935732	−0.467866	+	0.883799i	$0.654977\pi$
$6$	−1.00000	−0.408248
$7$	1.21381	0.458778	0.229389	−	0.973335i	$-0.426327\pi$
$7$	1.21381	0.458778	0.229389	+	0.973335i	$0.426327\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.09236	−0.661663
$11$	4.27762	1.28975	0.644876	−	0.764288i	$-0.276909\pi$
$11$	4.27762	1.28975	0.644876	+	0.764288i	$0.276909\pi$
$12$	−1.00000	−0.288675
$13$	−5.32951	−1.47814	−0.739070	−	0.673628i	$-0.764735\pi$
$13$	−5.32951	−1.47814	−0.739070	+	0.673628i	$0.764735\pi$
$14$	1.21381	0.324405
$15$	2.09236	0.540245
$16$	1.00000	0.250000
$17$	5.49805	1.33347	0.666737	−	0.745293i	$-0.267690\pi$
$17$	5.49805	1.33347	0.666737	+	0.745293i	$0.267690\pi$
$18$	1.00000	0.235702
$19$	1.21381	0.278467	0.139234	−	0.990260i	$-0.455536\pi$
$19$	1.21381	0.278467	0.139234	+	0.990260i	$0.455536\pi$
$20$	−2.09236	−0.467866
$21$	−1.21381	−0.264875
$22$	4.27762	0.911992
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	−0.622024	−0.124405
$26$	−5.32951	−1.04520
$27$	−1.00000	−0.192450
$28$	1.21381	0.229389
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.09236	0.382011
$31$	−3.40605	−0.611744	−0.305872	−	0.952073i	$-0.598948\pi$
$31$	−3.40605	−0.611744	−0.305872	+	0.952073i	$0.598948\pi$
$32$	1.00000	0.176777
$33$	−4.27762	−0.744638
$34$	5.49805	0.942908
$35$	−2.53973	−0.429293
$36$	1.00000	0.166667
$37$	3.04782	0.501058	0.250529	−	0.968109i	$-0.419395\pi$
$37$	3.04782	0.501058	0.250529	+	0.968109i	$0.419395\pi$
$38$	1.21381	0.196906
$39$	5.32951	0.853405
$40$	−2.09236	−0.330831
$41$	−3.69517	−0.577089	−0.288545	−	0.957466i	$-0.593171\pi$
$41$	−3.69517	−0.577089	−0.288545	+	0.957466i	$0.593171\pi$
$42$	−1.21381	−0.187295
$43$	8.96466	1.36710	0.683549	−	0.729905i	$-0.260436\pi$
$43$	8.96466	1.36710	0.683549	+	0.729905i	$0.260436\pi$
$44$	4.27762	0.644876
$45$	−2.09236	−0.311911
$46$	1.00000	0.147442
$47$	−2.76153	−0.402811	−0.201406	−	0.979508i	$-0.564551\pi$
$47$	−2.76153	−0.402811	−0.201406	+	0.979508i	$0.564551\pi$
$48$	−1.00000	−0.144338
$49$	−5.52666	−0.789523
$50$	−0.622024	−0.0879675
$51$	−5.49805	−0.769881
$52$	−5.32951	−0.739070
$53$	−3.94985	−0.542554	−0.271277	−	0.962501i	$-0.587446\pi$
$53$	−3.94985	−0.542554	−0.271277	+	0.962501i	$0.587446\pi$
$54$	−1.00000	−0.136083
$55$	−8.95033	−1.20686
$56$	1.21381	0.162202
$57$	−1.21381	−0.160773
$58$	1.00000	0.131306
$59$	4.90938	0.639147	0.319573	−	0.947562i	$-0.396460\pi$
$59$	4.90938	0.639147	0.319573	+	0.947562i	$0.396460\pi$
$60$	2.09236	0.270123
$61$	−10.3699	−1.32773	−0.663863	−	0.747854i	$-0.731084\pi$
$61$	−10.3699	−1.32773	−0.663863	+	0.747854i	$0.731084\pi$
$62$	−3.40605	−0.432568
$63$	1.21381	0.152926
$64$	1.00000	0.125000
$65$	11.1513	1.38314
$66$	−4.27762	−0.526539
$67$	13.7621	1.68130	0.840652	−	0.541576i	$-0.182172\pi$
$67$	13.7621	1.68130	0.840652	+	0.541576i	$0.182172\pi$
$68$	5.49805	0.666737
$69$	−1.00000	−0.120386
$70$	−2.53973	−0.303556
$71$	8.59299	1.01980	0.509900	−	0.860234i	$-0.329682\pi$
$71$	8.59299	1.01980	0.509900	+	0.860234i	$0.329682\pi$
$72$	1.00000	0.117851
$73$	6.48055	0.758491	0.379245	−	0.925296i	$-0.376184\pi$
$73$	6.48055	0.758491	0.379245	+	0.925296i	$0.376184\pi$
$74$	3.04782	0.354302
$75$	0.622024	0.0718252
$76$	1.21381	0.139234
$77$	5.19222	0.591709
$78$	5.32951	0.603448
$79$	14.2172	1.59956	0.799782	−	0.600291i	$-0.204949\pi$
$79$	14.2172	1.59956	0.799782	+	0.600291i	$0.204949\pi$
$80$	−2.09236	−0.233933
$81$	1.00000	0.111111
$82$	−3.69517	−0.408064
$83$	2.28424	0.250728	0.125364	−	0.992111i	$-0.459990\pi$
$83$	2.28424	0.250728	0.125364	+	0.992111i	$0.459990\pi$
$84$	−1.21381	−0.132438
$85$	−11.5039	−1.24777
$86$	8.96466	0.966684
$87$	−1.00000	−0.107211
$88$	4.27762	0.455996
$89$	2.82204	0.299135	0.149568	−	0.988751i	$-0.452212\pi$
$89$	2.82204	0.299135	0.149568	+	0.988751i	$0.452212\pi$
$90$	−2.09236	−0.220554
$91$	−6.46902	−0.678138
$92$	1.00000	0.104257
$93$	3.40605	0.353191
$94$	−2.76153	−0.284830
$95$	−2.53973	−0.260571
$96$	−1.00000	−0.102062
$97$	3.02327	0.306967	0.153483	−	0.988151i	$-0.450951\pi$
$97$	3.02327	0.306967	0.153483	+	0.988151i	$0.450951\pi$
$98$	−5.52666	−0.558277
$99$	4.27762	0.429917
$100$	−0.622024	−0.0622024
$101$	4.04050	0.402045	0.201022	−	0.979587i	$-0.435574\pi$
$101$	4.04050	0.402045	0.201022	+	0.979587i	$0.435574\pi$
$102$	−5.49805	−0.544388
$103$	−3.18341	−0.313671	−0.156835	−	0.987625i	$-0.550129\pi$
$103$	−3.18341	−0.313671	−0.156835	+	0.987625i	$0.550129\pi$
$104$	−5.32951	−0.522602
$105$	2.53973	0.247852
$106$	−3.94985	−0.383643
$107$	7.00698	0.677390	0.338695	−	0.940896i	$-0.390014\pi$
$107$	7.00698	0.677390	0.338695	+	0.940896i	$0.390014\pi$
$108$	−1.00000	−0.0962250
$109$	17.0266	1.63085	0.815427	−	0.578859i	$-0.196502\pi$
$109$	17.0266	1.63085	0.815427	+	0.578859i	$0.196502\pi$
$110$	−8.95033	−0.853380
$111$	−3.04782	−0.289286
$112$	1.21381	0.114694
$113$	−7.11887	−0.669687	−0.334843	−	0.942274i	$-0.608683\pi$
$113$	−7.11887	−0.669687	−0.334843	+	0.942274i	$0.608683\pi$
$114$	−1.21381	−0.113684
$115$	−2.09236	−0.195114
$116$	1.00000	0.0928477
$117$	−5.32951	−0.492714
$118$	4.90938	0.451945
$119$	6.67360	0.611768
$120$	2.09236	0.191006
$121$	7.29804	0.663458
$122$	−10.3699	−0.938844
$123$	3.69517	0.333183
$124$	−3.40605	−0.305872
$125$	11.7633	1.05214
$126$	1.21381	0.108135
$127$	4.15476	0.368676	0.184338	−	0.982863i	$-0.440986\pi$
$127$	4.15476	0.368676	0.184338	+	0.982863i	$0.440986\pi$
$128$	1.00000	0.0883883
$129$	−8.96466	−0.789295
$130$	11.1513	0.978031
$131$	−7.81885	−0.683136	−0.341568	−	0.939857i	$-0.610958\pi$
$131$	−7.81885	−0.683136	−0.341568	+	0.939857i	$0.610958\pi$
$132$	−4.27762	−0.372319
$133$	1.47334	0.127755
$134$	13.7621	1.18886
$135$	2.09236	0.180082
$136$	5.49805	0.471454
$137$	−0.349193	−0.0298336	−0.0149168	−	0.999889i	$-0.504748\pi$
$137$	−0.349193	−0.0298336	−0.0149168	+	0.999889i	$0.504748\pi$
$138$	−1.00000	−0.0851257
$139$	6.86046	0.581897	0.290948	−	0.956739i	$-0.406029\pi$
$139$	6.86046	0.581897	0.290948	+	0.956739i	$0.406029\pi$
$140$	−2.53973	−0.214647
$141$	2.76153	0.232563
$142$	8.59299	0.721108
$143$	−22.7976	−1.90643
$144$	1.00000	0.0833333
$145$	−2.09236	−0.173761
$146$	6.48055	0.536334
$147$	5.52666	0.455831
$148$	3.04782	0.250529
$149$	11.8766	0.972968	0.486484	−	0.873689i	$-0.338279\pi$
$149$	11.8766	0.972968	0.486484	+	0.873689i	$0.338279\pi$
$150$	0.622024	0.0507881
$151$	−3.82181	−0.311014	−0.155507	−	0.987835i	$-0.549701\pi$
$151$	−3.82181	−0.311014	−0.155507	+	0.987835i	$0.549701\pi$
$152$	1.21381	0.0984531
$153$	5.49805	0.444491
$154$	5.19222	0.418401
$155$	7.12668	0.572429
$156$	5.32951	0.426702
$157$	21.7574	1.73643	0.868214	−	0.496190i	$-0.165268\pi$
$157$	21.7574	1.73643	0.868214	+	0.496190i	$0.165268\pi$
$158$	14.2172	1.13106
$159$	3.94985	0.313244
$160$	−2.09236	−0.165416
$161$	1.21381	0.0956617
$162$	1.00000	0.0785674
$163$	11.8622	0.929123	0.464562	−	0.885541i	$-0.346212\pi$
$163$	11.8622	0.929123	0.464562	+	0.885541i	$0.346212\pi$
$164$	−3.69517	−0.288545
$165$	8.95033	0.696782
$166$	2.28424	0.177292
$167$	−12.7215	−0.984418	−0.492209	−	0.870477i	$-0.663810\pi$
$167$	−12.7215	−0.984418	−0.492209	+	0.870477i	$0.663810\pi$
$168$	−1.21381	−0.0936476
$169$	15.4037	1.18490
$170$	−11.5039	−0.882310
$171$	1.21381	0.0928225
$172$	8.96466	0.683549
$173$	−7.24363	−0.550723	−0.275361	−	0.961341i	$-0.588797\pi$
$173$	−7.24363	−0.550723	−0.275361	+	0.961341i	$0.588797\pi$
$174$	−1.00000	−0.0758098
$175$	−0.755020	−0.0570742
$176$	4.27762	0.322438
$177$	−4.90938	−0.369012
$178$	2.82204	0.211521
$179$	9.90582	0.740395	0.370198	−	0.928953i	$-0.379290\pi$
$179$	9.90582	0.740395	0.370198	+	0.928953i	$0.379290\pi$
$180$	−2.09236	−0.155955
$181$	12.3380	0.917073	0.458537	−	0.888675i	$-0.348374\pi$
$181$	12.3380	0.917073	0.458537	+	0.888675i	$0.348374\pi$
$182$	−6.46902	−0.479516
$183$	10.3699	0.766563
$184$	1.00000	0.0737210
$185$	−6.37714	−0.468857
$186$	3.40605	0.249744
$187$	23.5186	1.71985
$188$	−2.76153	−0.201406
$189$	−1.21381	−0.0882918
$190$	−2.53973	−0.184252
$191$	−6.11363	−0.442367	−0.221183	−	0.975232i	$-0.570992\pi$
$191$	−6.11363	−0.442367	−0.221183	+	0.975232i	$0.570992\pi$
$192$	−1.00000	−0.0721688
$193$	−11.0150	−0.792880	−0.396440	−	0.918061i	$-0.629754\pi$
$193$	−11.0150	−0.792880	−0.396440	+	0.918061i	$0.629754\pi$
$194$	3.02327	0.217058
$195$	−11.1513	−0.798559
$196$	−5.52666	−0.394762
$197$	−23.5736	−1.67955	−0.839774	−	0.542935i	$-0.817313\pi$
$197$	−23.5736	−1.67955	−0.839774	+	0.542935i	$0.817313\pi$
$198$	4.27762	0.303997
$199$	−1.80591	−0.128017	−0.0640087	−	0.997949i	$-0.520389\pi$
$199$	−1.80591	−0.128017	−0.0640087	+	0.997949i	$0.520389\pi$
$200$	−0.622024	−0.0439838
$201$	−13.7621	−0.970701
$202$	4.04050	0.284289
$203$	1.21381	0.0851929
$204$	−5.49805	−0.384941
$205$	7.73164	0.540001
$206$	−3.18341	−0.221799
$207$	1.00000	0.0695048
$208$	−5.32951	−0.369535
$209$	5.19222	0.359154
$210$	2.53973	0.175258
$211$	18.9339	1.30346	0.651730	−	0.758451i	$-0.274043\pi$
$211$	18.9339	1.30346	0.651730	+	0.758451i	$0.274043\pi$
$212$	−3.94985	−0.271277
$213$	−8.59299	−0.588782
$214$	7.00698	0.478987
$215$	−18.7573	−1.27924
$216$	−1.00000	−0.0680414
$217$	−4.13430	−0.280654
$218$	17.0266	1.15319
$219$	−6.48055	−0.437915
$220$	−8.95033	−0.603431
$221$	−29.3019	−1.97106
$222$	−3.04782	−0.204556
$223$	13.8070	0.924585	0.462292	−	0.886728i	$-0.347027\pi$
$223$	13.8070	0.924585	0.462292	+	0.886728i	$0.347027\pi$
$224$	1.21381	0.0811012
$225$	−0.622024	−0.0414683
$226$	−7.11887	−0.473540
$227$	8.41935	0.558812	0.279406	−	0.960173i	$-0.409862\pi$
$227$	8.41935	0.558812	0.279406	+	0.960173i	$0.409862\pi$
$228$	−1.21381	−0.0803866
$229$	−21.7567	−1.43773	−0.718863	−	0.695152i	$-0.755337\pi$
$229$	−21.7567	−1.43773	−0.718863	+	0.695152i	$0.755337\pi$
$230$	−2.09236	−0.137966
$231$	−5.19222	−0.341623
$232$	1.00000	0.0656532
$233$	−5.35837	−0.351038	−0.175519	−	0.984476i	$-0.556160\pi$
$233$	−5.35837	−0.351038	−0.175519	+	0.984476i	$0.556160\pi$
$234$	−5.32951	−0.348401
$235$	5.77813	0.376923
$236$	4.90938	0.319573
$237$	−14.2172	−0.923508
$238$	6.67360	0.432585
$239$	−8.22679	−0.532147	−0.266073	−	0.963953i	$-0.585726\pi$
$239$	−8.22679	−0.532147	−0.266073	+	0.963953i	$0.585726\pi$
$240$	2.09236	0.135061
$241$	16.7123	1.07653	0.538267	−	0.842774i	$-0.319079\pi$
$241$	16.7123	1.07653	0.538267	+	0.842774i	$0.319079\pi$
$242$	7.29804	0.469136
$243$	−1.00000	−0.0641500
$244$	−10.3699	−0.663863
$245$	11.5638	0.738782
$246$	3.69517	0.235596
$247$	−6.46902	−0.411614
$248$	−3.40605	−0.216284
$249$	−2.28424	−0.144758
$250$	11.7633	0.743977
$251$	12.4578	0.786330	0.393165	−	0.919468i	$-0.371380\pi$
$251$	12.4578	0.786330	0.393165	+	0.919468i	$0.371380\pi$
$252$	1.21381	0.0764629
$253$	4.27762	0.268932
$254$	4.15476	0.260693
$255$	11.5039	0.720403
$256$	1.00000	0.0625000
$257$	−11.0347	−0.688325	−0.344162	−	0.938910i	$-0.611837\pi$
$257$	−11.0347	−0.688325	−0.344162	+	0.938910i	$0.611837\pi$
$258$	−8.96466	−0.558116
$259$	3.69948	0.229874
$260$	11.1513	0.691572
$261$	1.00000	0.0618984
$262$	−7.81885	−0.483050
$263$	18.9683	1.16964	0.584819	−	0.811164i	$-0.301165\pi$
$263$	18.9683	1.16964	0.584819	+	0.811164i	$0.301165\pi$
$264$	−4.27762	−0.263269
$265$	8.26451	0.507685
$266$	1.47334	0.0903361
$267$	−2.82204	−0.172706
$268$	13.7621	0.840652
$269$	−5.98519	−0.364923	−0.182462	−	0.983213i	$-0.558407\pi$
$269$	−5.98519	−0.364923	−0.182462	+	0.983213i	$0.558407\pi$
$270$	2.09236	0.127337
$271$	24.1545	1.46728	0.733642	−	0.679536i	$-0.237819\pi$
$271$	24.1545	1.46728	0.733642	+	0.679536i	$0.237819\pi$
$272$	5.49805	0.333368
$273$	6.46902	0.391523
$274$	−0.349193	−0.0210955
$275$	−2.66078	−0.160451
$276$	−1.00000	−0.0601929
$277$	10.7423	0.645445	0.322722	−	0.946494i	$-0.395402\pi$
$277$	10.7423	0.645445	0.322722	+	0.946494i	$0.395402\pi$
$278$	6.86046	0.411463
$279$	−3.40605	−0.203915
$280$	−2.53973	−0.151778
$281$	−9.94896	−0.593505	−0.296753	−	0.954954i	$-0.595904\pi$
$281$	−9.94896	−0.593505	−0.296753	+	0.954954i	$0.595904\pi$
$282$	2.76153	0.164447
$283$	8.56549	0.509165	0.254583	−	0.967051i	$-0.418062\pi$
$283$	8.56549	0.509165	0.254583	+	0.967051i	$0.418062\pi$
$284$	8.59299	0.509900
$285$	2.53973	0.150441
$286$	−22.7976	−1.34805
$287$	−4.48524	−0.264756
$288$	1.00000	0.0589256
$289$	13.2286	0.778152
$290$	−2.09236	−0.122868
$291$	−3.02327	−0.177227
$292$	6.48055	0.379245
$293$	27.1351	1.58525	0.792624	−	0.609711i	$-0.208714\pi$
$293$	27.1351	1.58525	0.792624	+	0.609711i	$0.208714\pi$
$294$	5.52666	0.322321
$295$	−10.2722	−0.598070
$296$	3.04782	0.177151
$297$	−4.27762	−0.248213
$298$	11.8766	0.687993
$299$	−5.32951	−0.308214
$300$	0.622024	0.0359126
$301$	10.8814	0.627194
$302$	−3.82181	−0.219920
$303$	−4.04050	−0.232121
$304$	1.21381	0.0696169
$305$	21.6975	1.24240
$306$	5.49805	0.314303
$307$	−21.7245	−1.23988	−0.619942	−	0.784648i	$-0.712844\pi$
$307$	−21.7245	−1.23988	−0.619942	+	0.784648i	$0.712844\pi$
$308$	5.19222	0.295854
$309$	3.18341	0.181098
$310$	7.12668	0.404768
$311$	−32.3619	−1.83508	−0.917538	−	0.397648i	$-0.869827\pi$
$311$	−32.3619	−1.83508	−0.917538	+	0.397648i	$0.869827\pi$
$312$	5.32951	0.301724
$313$	13.0739	0.738979	0.369489	−	0.929235i	$-0.379533\pi$
$313$	13.0739	0.738979	0.369489	+	0.929235i	$0.379533\pi$
$314$	21.7574	1.22784
$315$	−2.53973	−0.143098
$316$	14.2172	0.799782
$317$	−28.2743	−1.58804	−0.794022	−	0.607888i	$-0.792017\pi$
$317$	−28.2743	−1.58804	−0.794022	+	0.607888i	$0.792017\pi$
$318$	3.94985	0.221497
$319$	4.27762	0.239501
$320$	−2.09236	−0.116967
$321$	−7.00698	−0.391092
$322$	1.21381	0.0676431
$323$	6.67360	0.371329
$324$	1.00000	0.0555556
$325$	3.31509	0.183888
$326$	11.8622	0.656989
$327$	−17.0266	−0.941574
$328$	−3.69517	−0.204032
$329$	−3.35198	−0.184801
$330$	8.95033	0.492699
$331$	−3.05261	−0.167787	−0.0838934	−	0.996475i	$-0.526736\pi$
$331$	−3.05261	−0.167787	−0.0838934	+	0.996475i	$0.526736\pi$
$332$	2.28424	0.125364
$333$	3.04782	0.167019
$334$	−12.7215	−0.696089
$335$	−28.7952	−1.57325
$336$	−1.21381	−0.0662188
$337$	−7.45247	−0.405962	−0.202981	−	0.979183i	$-0.565063\pi$
$337$	−7.45247	−0.405962	−0.202981	+	0.979183i	$0.565063\pi$
$338$	15.4037	0.837851
$339$	7.11887	0.386644
$340$	−11.5039	−0.623887
$341$	−14.5698	−0.788998
$342$	1.21381	0.0656354
$343$	−15.2050	−0.820993
$344$	8.96466	0.483342
$345$	2.09236	0.112649
$346$	−7.24363	−0.389420
$347$	30.3831	1.63105	0.815526	−	0.578720i	$-0.196447\pi$
$347$	30.3831	1.63105	0.815526	+	0.578720i	$0.196447\pi$
$348$	−1.00000	−0.0536056
$349$	32.8532	1.75859	0.879296	−	0.476276i	$-0.158014\pi$
$349$	32.8532	1.75859	0.879296	+	0.476276i	$0.158014\pi$
$350$	−0.755020	−0.0403575
$351$	5.32951	0.284468
$352$	4.27762	0.227998
$353$	15.1861	0.808276	0.404138	−	0.914698i	$-0.367572\pi$
$353$	15.1861	0.808276	0.404138	+	0.914698i	$0.367572\pi$
$354$	−4.90938	−0.260931
$355$	−17.9796	−0.954260
$356$	2.82204	0.149568
$357$	−6.67360	−0.353204
$358$	9.90582	0.523539
$359$	−27.9725	−1.47633	−0.738166	−	0.674619i	$-0.764308\pi$
$359$	−27.9725	−1.47633	−0.738166	+	0.674619i	$0.764308\pi$
$360$	−2.09236	−0.110277
$361$	−17.5267	−0.922456
$362$	12.3380	0.648469
$363$	−7.29804	−0.383048
$364$	−6.46902	−0.339069
$365$	−13.5597	−0.709745
$366$	10.3699	0.542042
$367$	1.69827	0.0886488	0.0443244	−	0.999017i	$-0.485886\pi$
$367$	1.69827	0.0886488	0.0443244	+	0.999017i	$0.485886\pi$
$368$	1.00000	0.0521286
$369$	−3.69517	−0.192363
$370$	−6.37714	−0.331532
$371$	−4.79437	−0.248911
$372$	3.40605	0.176595
$373$	−23.1053	−1.19635	−0.598173	−	0.801367i	$-0.704106\pi$
$373$	−23.1053	−1.19635	−0.598173	+	0.801367i	$0.704106\pi$
$374$	23.5186	1.21612
$375$	−11.7633	−0.607455
$376$	−2.76153	−0.142415
$377$	−5.32951	−0.274484
$378$	−1.21381	−0.0624317
$379$	−7.96124	−0.408942	−0.204471	−	0.978873i	$-0.565547\pi$
$379$	−7.96124	−0.408942	−0.204471	+	0.978873i	$0.565547\pi$
$380$	−2.53973	−0.130285
$381$	−4.15476	−0.212855
$382$	−6.11363	−0.312801
$383$	20.2496	1.03471	0.517354	−	0.855772i	$-0.326917\pi$
$383$	20.2496	1.03471	0.517354	+	0.855772i	$0.326917\pi$
$384$	−1.00000	−0.0510310
$385$	−10.8640	−0.553681
$386$	−11.0150	−0.560651
$387$	8.96466	0.455699
$388$	3.02327	0.153483
$389$	6.60450	0.334861	0.167431	−	0.985884i	$-0.446453\pi$
$389$	6.60450	0.334861	0.167431	+	0.985884i	$0.446453\pi$
$390$	−11.1513	−0.564666
$391$	5.49805	0.278049
$392$	−5.52666	−0.279139
$393$	7.81885	0.394409
$394$	−23.5736	−1.18762
$395$	−29.7476	−1.49676
$396$	4.27762	0.214959
$397$	1.35739	0.0681253	0.0340626	−	0.999420i	$-0.489155\pi$
$397$	1.35739	0.0681253	0.0340626	+	0.999420i	$0.489155\pi$
$398$	−1.80591	−0.0905220
$399$	−1.47334	−0.0737591
$400$	−0.622024	−0.0311012
$401$	−26.0349	−1.30012	−0.650061	−	0.759882i	$-0.725256\pi$
$401$	−26.0349	−1.30012	−0.650061	+	0.759882i	$0.725256\pi$
$402$	−13.7621	−0.686390
$403$	18.1526	0.904244
$404$	4.04050	0.201022
$405$	−2.09236	−0.103970
$406$	1.21381	0.0602404
$407$	13.0374	0.646241
$408$	−5.49805	−0.272194
$409$	4.89450	0.242018	0.121009	−	0.992651i	$-0.461387\pi$
$409$	4.89450	0.242018	0.121009	+	0.992651i	$0.461387\pi$
$410$	7.73164	0.381839
$411$	0.349193	0.0172244
$412$	−3.18341	−0.156835
$413$	5.95906	0.293226
$414$	1.00000	0.0491473
$415$	−4.77946	−0.234614
$416$	−5.32951	−0.261301
$417$	−6.86046	−0.335958
$418$	5.19222	0.253960
$419$	−8.89184	−0.434395	−0.217197	−	0.976128i	$-0.569692\pi$
$419$	−8.89184	−0.434395	−0.217197	+	0.976128i	$0.569692\pi$
$420$	2.53973	0.123926
$421$	−32.0524	−1.56214	−0.781068	−	0.624446i	$-0.785325\pi$
$421$	−32.0524	−1.56214	−0.781068	+	0.624446i	$0.785325\pi$
$422$	18.9339	0.921686
$423$	−2.76153	−0.134270
$424$	−3.94985	−0.191822
$425$	−3.41992	−0.165891
$426$	−8.59299	−0.416332
$427$	−12.5871	−0.609131
$428$	7.00698	0.338695
$429$	22.7976	1.10068
$430$	−18.7573	−0.904558
$431$	24.4317	1.17683	0.588416	−	0.808558i	$-0.299752\pi$
$431$	24.4317	1.17683	0.588416	+	0.808558i	$0.299752\pi$
$432$	−1.00000	−0.0481125
$433$	26.8156	1.28868	0.644338	−	0.764741i	$-0.277133\pi$
$433$	26.8156	1.28868	0.644338	+	0.764741i	$0.277133\pi$
$434$	−4.13430	−0.198453
$435$	2.09236	0.100321
$436$	17.0266	0.815427
$437$	1.21381	0.0580645
$438$	−6.48055	−0.309653
$439$	0.906930	0.0432854	0.0216427	−	0.999766i	$-0.493110\pi$
$439$	0.906930	0.0432854	0.0216427	+	0.999766i	$0.493110\pi$
$440$	−8.95033	−0.426690
$441$	−5.52666	−0.263174
$442$	−29.3019	−1.39375
$443$	8.31784	0.395193	0.197596	−	0.980283i	$-0.436687\pi$
$443$	8.31784	0.395193	0.197596	+	0.980283i	$0.436687\pi$
$444$	−3.04782	−0.144643
$445$	−5.90472	−0.279911
$446$	13.8070	0.653780
$447$	−11.8766	−0.561744
$448$	1.21381	0.0573472
$449$	−17.5982	−0.830513	−0.415256	−	0.909704i	$-0.636308\pi$
$449$	−17.5982	−0.830513	−0.415256	+	0.909704i	$0.636308\pi$
$450$	−0.622024	−0.0293225
$451$	−15.8066	−0.744302
$452$	−7.11887	−0.334843
$453$	3.82181	0.179564
$454$	8.41935	0.395140
$455$	13.5355	0.634555
$456$	−1.21381	−0.0568419
$457$	13.9960	0.654704	0.327352	−	0.944902i	$-0.393844\pi$
$457$	13.9960	0.654704	0.327352	+	0.944902i	$0.393844\pi$
$458$	−21.7567	−1.01663
$459$	−5.49805	−0.256627
$460$	−2.09236	−0.0975568
$461$	−9.65966	−0.449895	−0.224948	−	0.974371i	$-0.572221\pi$
$461$	−9.65966	−0.449895	−0.224948	+	0.974371i	$0.572221\pi$
$462$	−5.19222	−0.241564
$463$	0.597286	0.0277583	0.0138791	−	0.999904i	$-0.495582\pi$
$463$	0.597286	0.0277583	0.0138791	+	0.999904i	$0.495582\pi$
$464$	1.00000	0.0464238
$465$	−7.12668	−0.330492
$466$	−5.35837	−0.248222
$467$	15.3211	0.708977	0.354488	−	0.935060i	$-0.384655\pi$
$467$	15.3211	0.708977	0.354488	+	0.935060i	$0.384655\pi$
$468$	−5.32951	−0.246357
$469$	16.7046	0.771345
$470$	5.77813	0.266525
$471$	−21.7574	−1.00253
$472$	4.90938	0.225973
$473$	38.3474	1.76322
$474$	−14.2172	−0.653019
$475$	−0.755020	−0.0346427
$476$	6.67360	0.305884
$477$	−3.94985	−0.180851
$478$	−8.22679	−0.376285
$479$	−35.4073	−1.61780	−0.808901	−	0.587945i	$-0.799937\pi$
$479$	−35.4073	−1.61780	−0.808901	+	0.587945i	$0.799937\pi$
$480$	2.09236	0.0955028
$481$	−16.2434	−0.740635
$482$	16.7123	0.761225
$483$	−1.21381	−0.0552303
$484$	7.29804	0.331729
$485$	−6.32578	−0.287239
$486$	−1.00000	−0.0453609
$487$	−26.4538	−1.19873	−0.599367	−	0.800474i	$-0.704581\pi$
$487$	−26.4538	−1.19873	−0.599367	+	0.800474i	$0.704581\pi$
$488$	−10.3699	−0.469422
$489$	−11.8622	−0.536429
$490$	11.5638	0.522398
$491$	−36.7051	−1.65648	−0.828238	−	0.560377i	$-0.810656\pi$
$491$	−36.7051	−1.65648	−0.828238	+	0.560377i	$0.810656\pi$
$492$	3.69517	0.166591
$493$	5.49805	0.247620
$494$	−6.46902	−0.291055
$495$	−8.95033	−0.402287
$496$	−3.40605	−0.152936
$497$	10.4303	0.467862
$498$	−2.28424	−0.102359
$499$	−13.5721	−0.607570	−0.303785	−	0.952741i	$-0.598251\pi$
$499$	−13.5721	−0.607570	−0.303785	+	0.952741i	$0.598251\pi$
$500$	11.7633	0.526071
$501$	12.7215	0.568354
$502$	12.4578	0.556019
$503$	−14.9130	−0.664938	−0.332469	−	0.943114i	$-0.607882\pi$
$503$	−14.9130	−0.664938	−0.332469	+	0.943114i	$0.607882\pi$
$504$	1.21381	0.0540675
$505$	−8.45418	−0.376206
$506$	4.27762	0.190163
$507$	−15.4037	−0.684102
$508$	4.15476	0.184338
$509$	−10.0137	−0.443850	−0.221925	−	0.975064i	$-0.571234\pi$
$509$	−10.0137	−0.443850	−0.221925	+	0.975064i	$0.571234\pi$
$510$	11.5039	0.509402
$511$	7.86616	0.347979
$512$	1.00000	0.0441942
$513$	−1.21381	−0.0535911
$514$	−11.0347	−0.486719
$515$	6.66084	0.293512
$516$	−8.96466	−0.394647
$517$	−11.8128	−0.519526
$518$	3.69948	0.162546
$519$	7.24363	0.317960
$520$	11.1513	0.489015
$521$	26.1433	1.14536	0.572679	−	0.819779i	$-0.305904\pi$
$521$	26.1433	1.14536	0.572679	+	0.819779i	$0.305904\pi$
$522$	1.00000	0.0437688
$523$	−40.0908	−1.75305	−0.876525	−	0.481356i	$-0.840144\pi$
$523$	−40.0908	−1.75305	−0.876525	+	0.481356i	$0.840144\pi$
$524$	−7.81885	−0.341568
$525$	0.755020	0.0329518
$526$	18.9683	0.827059
$527$	−18.7266	−0.815745
$528$	−4.27762	−0.186160
$529$	1.00000	0.0434783
$530$	8.26451	0.358988
$531$	4.90938	0.213049
$532$	1.47334	0.0638773
$533$	19.6935	0.853019
$534$	−2.82204	−0.122122
$535$	−14.6611	−0.633856
$536$	13.7621	0.594431
$537$	−9.90582	−0.427468
$538$	−5.98519	−0.258040
$539$	−23.6410	−1.01829
$540$	2.09236	0.0900409
$541$	−15.4106	−0.662552	−0.331276	−	0.943534i	$-0.607479\pi$
$541$	−15.4106	−0.662552	−0.331276	+	0.943534i	$0.607479\pi$
$542$	24.1545	1.03753
$543$	−12.3380	−0.529473
$544$	5.49805	0.235727
$545$	−35.6258	−1.52604
$546$	6.46902	0.276849
$547$	−19.2806	−0.824379	−0.412190	−	0.911098i	$-0.635236\pi$
$547$	−19.2806	−0.824379	−0.412190	+	0.911098i	$0.635236\pi$
$548$	−0.349193	−0.0149168
$549$	−10.3699	−0.442575
$550$	−2.66078	−0.113456
$551$	1.21381	0.0517101
$552$	−1.00000	−0.0425628
$553$	17.2570	0.733844
$554$	10.7423	0.456399
$555$	6.37714	0.270695
$556$	6.86046	0.290948
$557$	1.61098	0.0682596	0.0341298	−	0.999417i	$-0.489134\pi$
$557$	1.61098	0.0682596	0.0341298	+	0.999417i	$0.489134\pi$
$558$	−3.40605	−0.144189
$559$	−47.7773	−2.02076
$560$	−2.53973	−0.107323
$561$	−23.5186	−0.992956
$562$	−9.94896	−0.419672
$563$	−1.14503	−0.0482572	−0.0241286	−	0.999709i	$-0.507681\pi$
$563$	−1.14503	−0.0482572	−0.0241286	+	0.999709i	$0.507681\pi$
$564$	2.76153	0.116282
$565$	14.8952	0.626648
$566$	8.56549	0.360034
$567$	1.21381	0.0509753
$568$	8.59299	0.360554
$569$	−24.1326	−1.01169	−0.505845	−	0.862624i	$-0.668819\pi$
$569$	−24.1326	−1.01169	−0.505845	+	0.862624i	$0.668819\pi$
$570$	2.53973	0.106378
$571$	14.1131	0.590614	0.295307	−	0.955402i	$-0.404578\pi$
$571$	14.1131	0.590614	0.295307	+	0.955402i	$0.404578\pi$
$572$	−22.7976	−0.953217
$573$	6.11363	0.255401
$574$	−4.48524	−0.187210
$575$	−0.622024	−0.0259402
$576$	1.00000	0.0416667
$577$	17.5599	0.731027	0.365513	−	0.930806i	$-0.380893\pi$
$577$	17.5599	0.731027	0.365513	+	0.930806i	$0.380893\pi$
$578$	13.2286	0.550237
$579$	11.0150	0.457769
$580$	−2.09236	−0.0868806
$581$	2.77264	0.115028
$582$	−3.02327	−0.125319
$583$	−16.8960	−0.699759
$584$	6.48055	0.268167
$585$	11.1513	0.461048
$586$	27.1351	1.12094
$587$	11.1455	0.460026	0.230013	−	0.973188i	$-0.426123\pi$
$587$	11.1455	0.460026	0.230013	+	0.973188i	$0.426123\pi$
$588$	5.52666	0.227916
$589$	−4.13430	−0.170351
$590$	−10.2722	−0.422900
$591$	23.5736	0.969688
$592$	3.04782	0.125265
$593$	8.80425	0.361547	0.180774	−	0.983525i	$-0.442140\pi$
$593$	8.80425	0.361547	0.180774	+	0.983525i	$0.442140\pi$
$594$	−4.27762	−0.175513
$595$	−13.9636	−0.572451
$596$	11.8766	0.486484
$597$	1.80591	0.0739109
$598$	−5.32951	−0.217940
$599$	21.5453	0.880315	0.440158	−	0.897921i	$-0.354923\pi$
$599$	21.5453	0.880315	0.440158	+	0.897921i	$0.354923\pi$
$600$	0.622024	0.0253940
$601$	−12.9212	−0.527066	−0.263533	−	0.964650i	$-0.584888\pi$
$601$	−12.9212	−0.527066	−0.263533	+	0.964650i	$0.584888\pi$
$602$	10.8814	0.443493
$603$	13.7621	0.560435
$604$	−3.82181	−0.155507
$605$	−15.2701	−0.620819
$606$	−4.04050	−0.164134
$607$	−42.9237	−1.74222	−0.871110	−	0.491088i	$-0.836600\pi$
$607$	−42.9237	−1.74222	−0.871110	+	0.491088i	$0.836600\pi$
$608$	1.21381	0.0492265
$609$	−1.21381	−0.0491861
$610$	21.6975	0.878507
$611$	14.7176	0.595412
$612$	5.49805	0.222246
$613$	−18.9477	−0.765290	−0.382645	−	0.923895i	$-0.624987\pi$
$613$	−18.9477	−0.765290	−0.382645	+	0.923895i	$0.624987\pi$
$614$	−21.7245	−0.876730
$615$	−7.73164	−0.311770
$616$	5.19222	0.209201
$617$	−3.80346	−0.153122	−0.0765608	−	0.997065i	$-0.524394\pi$
$617$	−3.80346	−0.153122	−0.0765608	+	0.997065i	$0.524394\pi$
$618$	3.18341	0.128056
$619$	6.07400	0.244135	0.122067	−	0.992522i	$-0.461048\pi$
$619$	6.07400	0.244135	0.122067	+	0.992522i	$0.461048\pi$
$620$	7.12668	0.286214
$621$	−1.00000	−0.0401286
$622$	−32.3619	−1.29759
$623$	3.42542	0.137237
$624$	5.32951	0.213351
$625$	−21.5030	−0.860119
$626$	13.0739	0.522537
$627$	−5.19222	−0.207357
$628$	21.7574	0.868214
$629$	16.7571	0.668148
$630$	−2.53973	−0.101185
$631$	−49.5454	−1.97237	−0.986186	−	0.165640i	$-0.947031\pi$
$631$	−49.5454	−1.97237	−0.986186	+	0.165640i	$0.947031\pi$
$632$	14.2172	0.565531
$633$	−18.9339	−0.752553
$634$	−28.2743	−1.12292
$635$	−8.69326	−0.344982
$636$	3.94985	0.156622
$637$	29.4544	1.16703
$638$	4.27762	0.169353
$639$	8.59299	0.339934
$640$	−2.09236	−0.0827078
$641$	33.8597	1.33738	0.668690	−	0.743541i	$-0.266855\pi$
$641$	33.8597	1.33738	0.668690	+	0.743541i	$0.266855\pi$
$642$	−7.00698	−0.276544
$643$	3.55721	0.140283	0.0701414	−	0.997537i	$-0.477655\pi$
$643$	3.55721	0.140283	0.0701414	+	0.997537i	$0.477655\pi$
$644$	1.21381	0.0478309
$645$	18.7573	0.738568
$646$	6.67360	0.262569
$647$	−33.3672	−1.31180	−0.655899	−	0.754849i	$-0.727710\pi$
$647$	−33.3672	−1.31180	−0.655899	+	0.754849i	$0.727710\pi$
$648$	1.00000	0.0392837
$649$	21.0005	0.824340
$650$	3.31509	0.130028
$651$	4.13430	0.162036
$652$	11.8622	0.464562
$653$	36.5638	1.43085	0.715425	−	0.698689i	$-0.246233\pi$
$653$	36.5638	1.43085	0.715425	+	0.698689i	$0.246233\pi$
$654$	−17.0266	−0.665794
$655$	16.3599	0.639232
$656$	−3.69517	−0.144272
$657$	6.48055	0.252830
$658$	−3.35198	−0.130674
$659$	−29.8465	−1.16265	−0.581327	−	0.813670i	$-0.697466\pi$
$659$	−29.8465	−1.16265	−0.581327	+	0.813670i	$0.697466\pi$
$660$	8.95033	0.348391
$661$	−11.4400	−0.444965	−0.222482	−	0.974937i	$-0.571416\pi$
$661$	−11.4400	−0.444965	−0.222482	+	0.974937i	$0.571416\pi$
$662$	−3.05261	−0.118643
$663$	29.3019	1.13799
$664$	2.28424	0.0886458
$665$	−3.08276	−0.119544
$666$	3.04782	0.118101
$667$	1.00000	0.0387202
$668$	−12.7215	−0.492209
$669$	−13.8070	−0.533809
$670$	−28.7952	−1.11246
$671$	−44.3584	−1.71244
$672$	−1.21381	−0.0468238
$673$	24.0229	0.926016	0.463008	−	0.886354i	$-0.346770\pi$
$673$	24.0229	0.926016	0.463008	+	0.886354i	$0.346770\pi$
$674$	−7.45247	−0.287059
$675$	0.622024	0.0239417
$676$	15.4037	0.592450
$677$	25.4903	0.979673	0.489836	−	0.871814i	$-0.337057\pi$
$677$	25.4903	0.979673	0.489836	+	0.871814i	$0.337057\pi$
$678$	7.11887	0.273399
$679$	3.66968	0.140829
$680$	−11.5039	−0.441155
$681$	−8.41935	−0.322630
$682$	−14.5698	−0.557906
$683$	4.36220	0.166915	0.0834575	−	0.996511i	$-0.473404\pi$
$683$	4.36220	0.166915	0.0834575	+	0.996511i	$0.473404\pi$
$684$	1.21381	0.0464112
$685$	0.730638	0.0279162
$686$	−15.2050	−0.580530
$687$	21.7567	0.830071
$688$	8.96466	0.341775
$689$	21.0508	0.801971
$690$	2.09236	0.0796548
$691$	−7.63496	−0.290448	−0.145224	−	0.989399i	$-0.546390\pi$
$691$	−7.63496	−0.290448	−0.145224	+	0.989399i	$0.546390\pi$
$692$	−7.24363	−0.275361
$693$	5.19222	0.197236
$694$	30.3831	1.15333
$695$	−14.3546	−0.544500
$696$	−1.00000	−0.0379049
$697$	−20.3163	−0.769534
$698$	32.8532	1.24351
$699$	5.35837	0.202672
$700$	−0.755020	−0.0285371
$701$	14.2419	0.537908	0.268954	−	0.963153i	$-0.413322\pi$
$701$	14.2419	0.537908	0.268954	+	0.963153i	$0.413322\pi$
$702$	5.32951	0.201149
$703$	3.69948	0.139528
$704$	4.27762	0.161219
$705$	−5.77813	−0.217617
$706$	15.1861	0.571537
$707$	4.90440	0.184449
$708$	−4.90938	−0.184506
$709$	49.2524	1.84971	0.924856	−	0.380316i	$-0.124185\pi$
$709$	49.2524	1.84971	0.924856	+	0.380316i	$0.124185\pi$
$710$	−17.9796	−0.674764
$711$	14.2172	0.533188
$712$	2.82204	0.105760
$713$	−3.40605	−0.127557
$714$	−6.67360	−0.249753
$715$	47.7009	1.78391
$716$	9.90582	0.370198
$717$	8.22679	0.307235
$718$	−27.9725	−1.04392
$719$	−4.21837	−0.157319	−0.0786594	−	0.996902i	$-0.525064\pi$
$719$	−4.21837	−0.157319	−0.0786594	+	0.996902i	$0.525064\pi$
$720$	−2.09236	−0.0779777
$721$	−3.86406	−0.143905
$722$	−17.5267	−0.652275
$723$	−16.7123	−0.621538
$724$	12.3380	0.458537
$725$	−0.622024	−0.0231014
$726$	−7.29804	−0.270856
$727$	17.0789	0.633420	0.316710	−	0.948522i	$-0.397422\pi$
$727$	17.0789	0.633420	0.316710	+	0.948522i	$0.397422\pi$
$728$	−6.46902	−0.239758
$729$	1.00000	0.0370370
$730$	−13.5597	−0.501865
$731$	49.2882	1.82299
$732$	10.3699	0.383282
$733$	−28.0285	−1.03526	−0.517628	−	0.855606i	$-0.673185\pi$
$733$	−28.0285	−1.03526	−0.517628	+	0.855606i	$0.673185\pi$
$734$	1.69827	0.0626842
$735$	−11.5638	−0.426536
$736$	1.00000	0.0368605
$737$	58.8689	2.16846
$738$	−3.69517	−0.136021
$739$	8.50957	0.313029	0.156515	−	0.987676i	$-0.449974\pi$
$739$	8.50957	0.313029	0.156515	+	0.987676i	$0.449974\pi$
$740$	−6.37714	−0.234428
$741$	6.46902	0.237645
$742$	−4.79437	−0.176007
$743$	−42.6202	−1.56358	−0.781792	−	0.623539i	$-0.785694\pi$
$743$	−42.6202	−1.56358	−0.781792	+	0.623539i	$0.785694\pi$
$744$	3.40605	0.124872
$745$	−24.8501	−0.910438
$746$	−23.1053	−0.845944
$747$	2.28424	0.0835761
$748$	23.5186	0.859925
$749$	8.50515	0.310772
$750$	−11.7633	−0.429535
$751$	−37.1522	−1.35570	−0.677852	−	0.735199i	$-0.737089\pi$
$751$	−37.1522	−1.35570	−0.677852	+	0.735199i	$0.737089\pi$
$752$	−2.76153	−0.100703
$753$	−12.4578	−0.453988
$754$	−5.32951	−0.194089
$755$	7.99660	0.291026
$756$	−1.21381	−0.0441459
$757$	22.4227	0.814967	0.407484	−	0.913213i	$-0.366406\pi$
$757$	22.4227	0.814967	0.407484	+	0.913213i	$0.366406\pi$
$758$	−7.96124	−0.289165
$759$	−4.27762	−0.155268
$760$	−2.53973	−0.0921258
$761$	−27.5129	−0.997342	−0.498671	−	0.866791i	$-0.666178\pi$
$761$	−27.5129	−0.997342	−0.498671	+	0.866791i	$0.666178\pi$
$762$	−4.15476	−0.150511
$763$	20.6671	0.748199
$764$	−6.11363	−0.221183
$765$	−11.5039	−0.415925
$766$	20.2496	0.731649
$767$	−26.1646	−0.944749
$768$	−1.00000	−0.0360844
$769$	25.9471	0.935678	0.467839	−	0.883814i	$-0.345033\pi$
$769$	25.9471	0.935678	0.467839	+	0.883814i	$0.345033\pi$
$770$	−10.8640	−0.391512
$771$	11.0347	0.397405
$772$	−11.0150	−0.396440
$773$	−10.9440	−0.393629	−0.196814	−	0.980441i	$-0.563060\pi$
$773$	−10.9440	−0.393629	−0.196814	+	0.980441i	$0.563060\pi$
$774$	8.96466	0.322228
$775$	2.11864	0.0761039
$776$	3.02327	0.108529
$777$	−3.69948	−0.132718
$778$	6.60450	0.236783
$779$	−4.48524	−0.160701
$780$	−11.1513	−0.399279
$781$	36.7576	1.31529
$782$	5.49805	0.196610
$783$	−1.00000	−0.0357371
$784$	−5.52666	−0.197381
$785$	−45.5243	−1.62483
$786$	7.81885	0.278889
$787$	−6.75972	−0.240958	−0.120479	−	0.992716i	$-0.538443\pi$
$787$	−6.75972	−0.240958	−0.120479	+	0.992716i	$0.538443\pi$
$788$	−23.5736	−0.839774
$789$	−18.9683	−0.675291
$790$	−29.7476	−1.05837
$791$	−8.64096	−0.307237
$792$	4.27762	0.151999
$793$	55.2664	1.96257
$794$	1.35739	0.0481719
$795$	−8.26451	−0.293112
$796$	−1.80591	−0.0640087
$797$	−9.11727	−0.322950	−0.161475	−	0.986877i	$-0.551625\pi$
$797$	−9.11727	−0.322950	−0.161475	+	0.986877i	$0.551625\pi$
$798$	−1.47334	−0.0521556
$799$	−15.1831	−0.537138
$800$	−0.622024	−0.0219919
$801$	2.82204	0.0997118
$802$	−26.0349	−0.919324
$803$	27.7213	0.978265
$804$	−13.7621	−0.485351
$805$	−2.53973	−0.0895138
$806$	18.1526	0.639397
$807$	5.98519	0.210689
$808$	4.04050	0.142144
$809$	−30.2514	−1.06358	−0.531791	−	0.846876i	$-0.678481\pi$
$809$	−30.2514	−1.06358	−0.531791	+	0.846876i	$0.678481\pi$
$810$	−2.09236	−0.0735181
$811$	6.92975	0.243336	0.121668	−	0.992571i	$-0.461176\pi$
$811$	6.92975	0.243336	0.121668	+	0.992571i	$0.461176\pi$
$812$	1.21381	0.0425964
$813$	−24.1545	−0.847137
$814$	13.0374	0.456961
$815$	−24.8201	−0.869411
$816$	−5.49805	−0.192470
$817$	10.8814	0.380692
$818$	4.89450	0.171132
$819$	−6.46902	−0.226046
$820$	7.73164	0.270001
$821$	13.1188	0.457849	0.228924	−	0.973444i	$-0.426479\pi$
$821$	13.1188	0.457849	0.228924	+	0.973444i	$0.426479\pi$
$822$	0.349193	0.0121795
$823$	−13.0887	−0.456243	−0.228121	−	0.973633i	$-0.573258\pi$
$823$	−13.0887	−0.456243	−0.228121	+	0.973633i	$0.573258\pi$
$824$	−3.18341	−0.110899
$825$	2.66078	0.0926366
$826$	5.95906	0.207342
$827$	−12.7616	−0.443763	−0.221882	−	0.975074i	$-0.571220\pi$
$827$	−12.7616	−0.443763	−0.221882	+	0.975074i	$0.571220\pi$
$828$	1.00000	0.0347524
$829$	45.7087	1.58753	0.793764	−	0.608226i	$-0.208119\pi$
$829$	45.7087	1.58753	0.793764	+	0.608226i	$0.208119\pi$
$830$	−4.77946	−0.165897
$831$	−10.7423	−0.372648
$832$	−5.32951	−0.184768
$833$	−30.3859	−1.05281
$834$	−6.86046	−0.237558
$835$	26.6179	0.921152
$836$	5.19222	0.179577
$837$	3.40605	0.117730
$838$	−8.89184	−0.307164
$839$	−45.5170	−1.57142	−0.785711	−	0.618593i	$-0.787703\pi$
$839$	−45.5170	−1.57142	−0.785711	+	0.618593i	$0.787703\pi$
$840$	2.53973	0.0876291
$841$	1.00000	0.0344828
$842$	−32.0524	−1.10460
$843$	9.94896	0.342660
$844$	18.9339	0.651730
$845$	−32.2301	−1.10875
$846$	−2.76153	−0.0949435
$847$	8.85844	0.304380
$848$	−3.94985	−0.135638
$849$	−8.56549	−0.293967
$850$	−3.41992	−0.117302
$851$	3.04782	0.104478
$852$	−8.59299	−0.294391
$853$	42.7292	1.46302	0.731509	−	0.681831i	$-0.238816\pi$
$853$	42.7292	1.46302	0.731509	+	0.681831i	$0.238816\pi$
$854$	−12.5871	−0.430721
$855$	−2.53973	−0.0868570
$856$	7.00698	0.239494
$857$	4.68105	0.159902	0.0799508	−	0.996799i	$-0.474524\pi$
$857$	4.68105	0.159902	0.0799508	+	0.996799i	$0.474524\pi$
$858$	22.7976	0.778298
$859$	39.7263	1.35545	0.677723	−	0.735318i	$-0.262967\pi$
$859$	39.7263	1.35545	0.677723	+	0.735318i	$0.262967\pi$
$860$	−18.7573	−0.639619
$861$	4.48524	0.152857
$862$	24.4317	0.832146
$863$	32.1628	1.09483	0.547417	−	0.836860i	$-0.315611\pi$
$863$	32.1628	1.09483	0.547417	+	0.836860i	$0.315611\pi$
$864$	−1.00000	−0.0340207
$865$	15.1563	0.515329
$866$	26.8156	0.911231
$867$	−13.2286	−0.449267
$868$	−4.13430	−0.140327
$869$	60.8159	2.06304
$870$	2.09236	0.0709377
$871$	−73.3451	−2.48520
$872$	17.0266	0.576594
$873$	3.02327	0.102322
$874$	1.21381	0.0410578
$875$	14.2784	0.482699
$876$	−6.48055	−0.218957
$877$	−33.4579	−1.12979	−0.564897	−	0.825162i	$-0.691084\pi$
$877$	−33.4579	−1.12979	−0.564897	+	0.825162i	$0.691084\pi$
$878$	0.906930	0.0306074
$879$	−27.1351	−0.915243
$880$	−8.95033	−0.301715
$881$	−36.3589	−1.22496	−0.612481	−	0.790486i	$-0.709828\pi$
$881$	−36.3589	−1.22496	−0.612481	+	0.790486i	$0.709828\pi$
$882$	−5.52666	−0.186092
$883$	−9.60552	−0.323251	−0.161626	−	0.986852i	$-0.551674\pi$
$883$	−9.60552	−0.323251	−0.161626	+	0.986852i	$0.551674\pi$
$884$	−29.3019	−0.985531
$885$	10.2722	0.345296
$886$	8.31784	0.279443
$887$	14.9948	0.503475	0.251737	−	0.967796i	$-0.418998\pi$
$887$	14.9948	0.503475	0.251737	+	0.967796i	$0.418998\pi$
$888$	−3.04782	−0.102278
$889$	5.04310	0.169140
$890$	−5.90472	−0.197927
$891$	4.27762	0.143306
$892$	13.8070	0.462292
$893$	−3.35198	−0.112170
$894$	−11.8766	−0.397213
$895$	−20.7265	−0.692812
$896$	1.21381	0.0405506
$897$	5.32951	0.177947
$898$	−17.5982	−0.587261
$899$	−3.40605	−0.113598
$900$	−0.622024	−0.0207341
$901$	−21.7165	−0.723481
$902$	−15.8066	−0.526301
$903$	−10.8814	−0.362111
$904$	−7.11887	−0.236770
$905$	−25.8155	−0.858135
$906$	3.82181	0.126971
$907$	46.7989	1.55393	0.776966	−	0.629542i	$-0.216758\pi$
$907$	46.7989	1.55393	0.776966	+	0.629542i	$0.216758\pi$
$908$	8.41935	0.279406
$909$	4.04050	0.134015
$910$	13.5355	0.448698
$911$	−7.17495	−0.237717	−0.118858	−	0.992911i	$-0.537923\pi$
$911$	−7.17495	−0.237717	−0.118858	+	0.992911i	$0.537923\pi$
$912$	−1.21381	−0.0401933
$913$	9.77112	0.323377
$914$	13.9960	0.462946
$915$	−21.6975	−0.717298
$916$	−21.7567	−0.718863
$917$	−9.49060	−0.313407
$918$	−5.49805	−0.181463
$919$	−31.7852	−1.04850	−0.524248	−	0.851566i	$-0.675654\pi$
$919$	−31.7852	−1.04850	−0.524248	+	0.851566i	$0.675654\pi$
$920$	−2.09236	−0.0689831
$921$	21.7245	0.715847
$922$	−9.65966	−0.318124
$923$	−45.7965	−1.50741
$924$	−5.19222	−0.170812
$925$	−1.89582	−0.0623341
$926$	0.597286	0.0196281
$927$	−3.18341	−0.104557
$928$	1.00000	0.0328266
$929$	−39.7708	−1.30484	−0.652419	−	0.757858i	$-0.726246\pi$
$929$	−39.7708	−1.30484	−0.652419	+	0.757858i	$0.726246\pi$
$930$	−7.12668	−0.233693
$931$	−6.70832	−0.219856
$932$	−5.35837	−0.175519
$933$	32.3619	1.05948
$934$	15.3211	0.501322
$935$	−49.2094	−1.60932
$936$	−5.32951	−0.174201
$937$	45.3348	1.48102	0.740512	−	0.672043i	$-0.234583\pi$
$937$	45.3348	1.48102	0.740512	+	0.672043i	$0.234583\pi$
$938$	16.7046	0.545423
$939$	−13.0739	−0.426650
$940$	5.77813	0.188462
$941$	−61.0105	−1.98888	−0.994442	−	0.105285i	$-0.966424\pi$
$941$	−61.0105	−1.98888	−0.994442	+	0.105285i	$0.966424\pi$
$942$	−21.7574	−0.708894
$943$	−3.69517	−0.120331
$944$	4.90938	0.159787
$945$	2.53973	0.0826175
$946$	38.3474	1.24678
$947$	13.3643	0.434283	0.217141	−	0.976140i	$-0.430327\pi$
$947$	13.3643	0.434283	0.217141	+	0.976140i	$0.430327\pi$
$948$	−14.2172	−0.461754
$949$	−34.5382	−1.12116
$950$	−0.755020	−0.0244961
$951$	28.2743	0.916858
$952$	6.67360	0.216293
$953$	46.0166	1.49062	0.745312	−	0.666715i	$-0.232300\pi$
$953$	46.0166	1.49062	0.745312	+	0.666715i	$0.232300\pi$
$954$	−3.94985	−0.127881
$955$	12.7919	0.413937
$956$	−8.22679	−0.266073
$957$	−4.27762	−0.138276
$958$	−35.4073	−1.14396
$959$	−0.423854	−0.0136870
$960$	2.09236	0.0675307
$961$	−19.3988	−0.625769
$962$	−16.2434	−0.523708
$963$	7.00698	0.225797
$964$	16.7123	0.538267
$965$	23.0474	0.741923
$966$	−1.21381	−0.0390537
$967$	28.5937	0.919512	0.459756	−	0.888045i	$-0.347937\pi$
$967$	28.5937	0.919512	0.459756	+	0.888045i	$0.347937\pi$
$968$	7.29804	0.234568
$969$	−6.67360	−0.214387
$970$	−6.32578	−0.203108
$971$	−28.0849	−0.901287	−0.450643	−	0.892704i	$-0.648805\pi$
$971$	−28.0849	−0.901287	−0.450643	+	0.892704i	$0.648805\pi$
$972$	−1.00000	−0.0320750
$973$	8.32730	0.266961
$974$	−26.4538	−0.847633
$975$	−3.31509	−0.106168
$976$	−10.3699	−0.331932
$977$	49.2407	1.57535	0.787674	−	0.616092i	$-0.211285\pi$
$977$	49.2407	1.57535	0.787674	+	0.616092i	$0.211285\pi$
$978$	−11.8622	−0.379313
$979$	12.0716	0.385810
$980$	11.5638	0.369391
$981$	17.0266	0.543618
$982$	−36.7051	−1.17131
$983$	−8.16426	−0.260399	−0.130200	−	0.991488i	$-0.541562\pi$
$983$	−8.16426	−0.260399	−0.130200	+	0.991488i	$0.541562\pi$
$984$	3.69517	0.117798
$985$	49.3245	1.57161
$986$	5.49805	0.175094
$987$	3.35198	0.106695
$988$	−6.46902	−0.205807
$989$	8.96466	0.285060
$990$	−8.95033	−0.284460
$991$	21.5174	0.683523	0.341761	−	0.939787i	$-0.388977\pi$
$991$	21.5174	0.683523	0.341761	+	0.939787i	$0.388977\pi$
$992$	−3.40605	−0.108142
$993$	3.05261	0.0968718
$994$	10.4303	0.330828
$995$	3.77861	0.119790
$996$	−2.28424	−0.0723790
$997$	48.4232	1.53358	0.766790	−	0.641899i	$-0.221853\pi$
$997$	48.4232	1.53358	0.766790	+	0.641899i	$0.221853\pi$
$998$	−13.5721	−0.429617
$999$	−3.04782	−0.0964287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4002.2.a.bj.1.3	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4002.2.a.bj.1.3	✓	8	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:	\( N \)	\(=\)	\( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.09236 q^{5} -1.00000 q^{6} +1.21381 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.09236 q^{10} +4.27762 q^{11} -1.00000 q^{12} -5.32951 q^{13} +1.21381 q^{14} +2.09236 q^{15} +1.00000 q^{16} +5.49805 q^{17} +1.00000 q^{18} +1.21381 q^{19} -2.09236 q^{20} -1.21381 q^{21} +4.27762 q^{22} +1.00000 q^{23} -1.00000 q^{24} -0.622024 q^{25} -5.32951 q^{26} -1.00000 q^{27} +1.21381 q^{28} +1.00000 q^{29} +2.09236 q^{30} -3.40605 q^{31} +1.00000 q^{32} -4.27762 q^{33} +5.49805 q^{34} -2.53973 q^{35} +1.00000 q^{36} +3.04782 q^{37} +1.21381 q^{38} +5.32951 q^{39} -2.09236 q^{40} -3.69517 q^{41} -1.21381 q^{42} +8.96466 q^{43} +4.27762 q^{44} -2.09236 q^{45} +1.00000 q^{46} -2.76153 q^{47} -1.00000 q^{48} -5.52666 q^{49} -0.622024 q^{50} -5.49805 q^{51} -5.32951 q^{52} -3.94985 q^{53} -1.00000 q^{54} -8.95033 q^{55} +1.21381 q^{56} -1.21381 q^{57} +1.00000 q^{58} +4.90938 q^{59} +2.09236 q^{60} -10.3699 q^{61} -3.40605 q^{62} +1.21381 q^{63} +1.00000 q^{64} +11.1513 q^{65} -4.27762 q^{66} +13.7621 q^{67} +5.49805 q^{68} -1.00000 q^{69} -2.53973 q^{70} +8.59299 q^{71} +1.00000 q^{72} +6.48055 q^{73} +3.04782 q^{74} +0.622024 q^{75} +1.21381 q^{76} +5.19222 q^{77} +5.32951 q^{78} +14.2172 q^{79} -2.09236 q^{80} +1.00000 q^{81} -3.69517 q^{82} +2.28424 q^{83} -1.21381 q^{84} -11.5039 q^{85} +8.96466 q^{86} -1.00000 q^{87} +4.27762 q^{88} +2.82204 q^{89} -2.09236 q^{90} -6.46902 q^{91} +1.00000 q^{92} +3.40605 q^{93} -2.76153 q^{94} -2.53973 q^{95} -1.00000 q^{96} +3.02327 q^{97} -5.52666 q^{98} +4.27762 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + q^{5} - 8 q^{6} + 8 q^{8} + 8 q^{9} + q^{10} + 3 q^{11} - 8 q^{12} + 9 q^{13} - q^{15} + 8 q^{16} + 8 q^{17} + 8 q^{18} + q^{20} + 3 q^{22} + 8 q^{23} - 8 q^{24}+ \cdots + 3 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + q^5 - 8 * q^6 + 8 * q^8 + 8 * q^9 + q^10 + 3 * q^11 - 8 * q^12 + 9 * q^13 - q^15 + 8 * q^16 + 8 * q^17 + 8 * q^18 + q^20 + 3 * q^22 + 8 * q^23 - 8 * q^24 + 13 * q^25 + 9 * q^26 - 8 * q^27 + 8 * q^29 - q^30 - 9 * q^31 + 8 * q^32 - 3 * q^33 + 8 * q^34 - 2 * q^35 + 8 * q^36 + 7 * q^37 - 9 * q^39 + q^40 + 3 * q^41 + 16 * q^43 + 3 * q^44 + q^45 + 8 * q^46 + 24 * q^47 - 8 * q^48 + 6 * q^49 + 13 * q^50 - 8 * q^51 + 9 * q^52 + 8 * q^53 - 8 * q^54 + 13 * q^55 + 8 * q^58 - 3 * q^59 - q^60 + 31 * q^61 - 9 * q^62 + 8 * q^64 + 13 * q^65 - 3 * q^66 - 11 * q^67 + 8 * q^68 - 8 * q^69 - 2 * q^70 + 7 * q^71 + 8 * q^72 + 14 * q^73 + 7 * q^74 - 13 * q^75 + 10 * q^77 - 9 * q^78 + 12 * q^79 + q^80 + 8 * q^81 + 3 * q^82 - 8 * q^83 + 22 * q^85 + 16 * q^86 - 8 * q^87 + 3 * q^88 - 12 * q^89 + q^90 + 28 * q^91 + 8 * q^92 + 9 * q^93 + 24 * q^94 - 2 * q^95 - 8 * q^96 + 16 * q^97 + 6 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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