LMFDB - Embedded newform 1338.2.a.f.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(1,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,3,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$10.6839837904$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{14})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 2x + 1 $ x^3 - x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.24698$ of defining polynomial
Character	$\chi$	$=$	1338.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.753020 q^{5} +1.00000 q^{6} -4.69202 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.753020 q^{10} -5.51573 q^{11} +1.00000 q^{12} -4.13706 q^{13} -4.69202 q^{14} -0.753020 q^{15} +1.00000 q^{16} +4.34481 q^{17} +1.00000 q^{18} +5.65279 q^{19} -0.753020 q^{20} -4.69202 q^{21} -5.51573 q^{22} -5.69202 q^{23} +1.00000 q^{24} -4.43296 q^{25} -4.13706 q^{26} +1.00000 q^{27} -4.69202 q^{28} -0.417895 q^{29} -0.753020 q^{30} -1.55496 q^{31} +1.00000 q^{32} -5.51573 q^{33} +4.34481 q^{34} +3.53319 q^{35} +1.00000 q^{36} -8.89977 q^{37} +5.65279 q^{38} -4.13706 q^{39} -0.753020 q^{40} -9.36658 q^{41} -4.69202 q^{42} +1.04892 q^{43} -5.51573 q^{44} -0.753020 q^{45} -5.69202 q^{46} +2.57673 q^{47} +1.00000 q^{48} +15.0151 q^{49} -4.43296 q^{50} +4.34481 q^{51} -4.13706 q^{52} -8.32304 q^{53} +1.00000 q^{54} +4.15346 q^{55} -4.69202 q^{56} +5.65279 q^{57} -0.417895 q^{58} +13.0586 q^{59} -0.753020 q^{60} -15.5036 q^{61} -1.55496 q^{62} -4.69202 q^{63} +1.00000 q^{64} +3.11529 q^{65} -5.51573 q^{66} +11.5646 q^{67} +4.34481 q^{68} -5.69202 q^{69} +3.53319 q^{70} +10.0858 q^{71} +1.00000 q^{72} +1.53319 q^{73} -8.89977 q^{74} -4.43296 q^{75} +5.65279 q^{76} +25.8799 q^{77} -4.13706 q^{78} +6.46011 q^{79} -0.753020 q^{80} +1.00000 q^{81} -9.36658 q^{82} +2.93900 q^{83} -4.69202 q^{84} -3.27173 q^{85} +1.04892 q^{86} -0.417895 q^{87} -5.51573 q^{88} -4.59419 q^{89} -0.753020 q^{90} +19.4112 q^{91} -5.69202 q^{92} -1.55496 q^{93} +2.57673 q^{94} -4.25667 q^{95} +1.00000 q^{96} +3.37867 q^{97} +15.0151 q^{98} -5.51573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 7 q^{5} + 3 q^{6} - 9 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} - 4 q^{11} + 3 q^{12} - 7 q^{13} - 9 q^{14} - 7 q^{15} + 3 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - 7 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 7 * q^5 + 3 * q^6 - 9 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 - 4 * q^11 + 3 * q^12 - 7 * q^13 - 9 * q^14 - 7 * q^15 + 3 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - 7 * q^20 - 9 * q^21 - 4 * q^22 - 12 * q^23 + 3 * q^24 + 6 * q^25 - 7 * q^26 + 3 * q^27 - 9 * q^28 - 7 * q^29 - 7 * q^30 - 5 * q^31 + 3 * q^32 - 4 * q^33 - 10 * q^34 + 14 * q^35 + 3 * q^36 - 4 * q^37 - q^38 - 7 * q^39 - 7 * q^40 - 2 * q^41 - 9 * q^42 - 6 * q^43 - 4 * q^44 - 7 * q^45 - 12 * q^46 + 5 * q^47 + 3 * q^48 + 20 * q^49 + 6 * q^50 - 10 * q^51 - 7 * q^52 - 5 * q^53 + 3 * q^54 + 7 * q^55 - 9 * q^56 - q^57 - 7 * q^58 + 8 * q^59 - 7 * q^60 - 15 * q^61 - 5 * q^62 - 9 * q^63 + 3 * q^64 + 7 * q^65 - 4 * q^66 + 13 * q^67 - 10 * q^68 - 12 * q^69 + 14 * q^70 - 7 * q^71 + 3 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^75 - q^76 - 2 * q^77 - 7 * q^78 - 6 * q^79 - 7 * q^80 + 3 * q^81 - 2 * q^82 - q^83 - 9 * q^84 + 42 * q^85 - 6 * q^86 - 7 * q^87 - 4 * q^88 - 27 * q^89 - 7 * q^90 + 42 * q^91 - 12 * q^92 - 5 * q^93 + 5 * q^94 + 14 * q^95 + 3 * q^96 + 3 * q^97 + 20 * q^98 - 4 * 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
$5$	−0.753020	−0.336761	−0.168380	−	0.985722i	$-0.553854\pi$
$5$	−0.753020	−0.336761	−0.168380	+	0.985722i	$0.553854\pi$
$6$	1.00000	0.408248
$7$	−4.69202	−1.77342	−0.886709	−	0.462329i	$-0.847014\pi$
$7$	−4.69202	−1.77342	−0.886709	+	0.462329i	$0.847014\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.753020	−0.238126
$11$	−5.51573	−1.66306	−0.831528	−	0.555484i	$-0.812533\pi$
$11$	−5.51573	−1.66306	−0.831528	+	0.555484i	$0.812533\pi$
$12$	1.00000	0.288675
$13$	−4.13706	−1.14741	−0.573707	−	0.819060i	$-0.694495\pi$
$13$	−4.13706	−1.14741	−0.573707	+	0.819060i	$0.694495\pi$
$14$	−4.69202	−1.25400
$15$	−0.753020	−0.194429
$16$	1.00000	0.250000
$17$	4.34481	1.05377	0.526886	−	0.849936i	$-0.323359\pi$
$17$	4.34481	1.05377	0.526886	+	0.849936i	$0.323359\pi$
$18$	1.00000	0.235702
$19$	5.65279	1.29684	0.648420	−	0.761283i	$-0.275430\pi$
$19$	5.65279	1.29684	0.648420	+	0.761283i	$0.275430\pi$
$20$	−0.753020	−0.168380
$21$	−4.69202	−1.02388
$22$	−5.51573	−1.17596
$23$	−5.69202	−1.18687	−0.593434	−	0.804882i	$-0.702228\pi$
$23$	−5.69202	−1.18687	−0.593434	+	0.804882i	$0.702228\pi$
$24$	1.00000	0.204124
$25$	−4.43296	−0.886592
$26$	−4.13706	−0.811345
$27$	1.00000	0.192450
$28$	−4.69202	−0.886709
$29$	−0.417895	−0.0776011	−0.0388006	−	0.999247i	$-0.512354\pi$
$29$	−0.417895	−0.0776011	−0.0388006	+	0.999247i	$0.512354\pi$
$30$	−0.753020	−0.137482
$31$	−1.55496	−0.279279	−0.139639	−	0.990202i	$-0.544594\pi$
$31$	−1.55496	−0.279279	−0.139639	+	0.990202i	$0.544594\pi$
$32$	1.00000	0.176777
$33$	−5.51573	−0.960165
$34$	4.34481	0.745130
$35$	3.53319	0.597218
$36$	1.00000	0.166667
$37$	−8.89977	−1.46311	−0.731557	−	0.681781i	$-0.761206\pi$
$37$	−8.89977	−1.46311	−0.731557	+	0.681781i	$0.761206\pi$
$38$	5.65279	0.917004
$39$	−4.13706	−0.662460
$40$	−0.753020	−0.119063
$41$	−9.36658	−1.46281	−0.731407	−	0.681941i	$-0.761136\pi$
$41$	−9.36658	−1.46281	−0.731407	+	0.681941i	$0.761136\pi$
$42$	−4.69202	−0.723995
$43$	1.04892	0.159958	0.0799792	−	0.996797i	$-0.474515\pi$
$43$	1.04892	0.159958	0.0799792	+	0.996797i	$0.474515\pi$
$44$	−5.51573	−0.831528
$45$	−0.753020	−0.112254
$46$	−5.69202	−0.839243
$47$	2.57673	0.375854	0.187927	−	0.982183i	$-0.439823\pi$
$47$	2.57673	0.375854	0.187927	+	0.982183i	$0.439823\pi$
$48$	1.00000	0.144338
$49$	15.0151	2.14501
$50$	−4.43296	−0.626915
$51$	4.34481	0.608396
$52$	−4.13706	−0.573707
$53$	−8.32304	−1.14326	−0.571629	−	0.820512i	$-0.693688\pi$
$53$	−8.32304	−1.14326	−0.571629	+	0.820512i	$0.693688\pi$
$54$	1.00000	0.136083
$55$	4.15346	0.560052
$56$	−4.69202	−0.626998
$57$	5.65279	0.748731
$58$	−0.417895	−0.0548723
$59$	13.0586	1.70009	0.850043	−	0.526714i	$-0.176576\pi$
$59$	13.0586	1.70009	0.850043	+	0.526714i	$0.176576\pi$
$60$	−0.753020	−0.0972145
$61$	−15.5036	−1.98504	−0.992519	−	0.122087i	$-0.961041\pi$
$61$	−15.5036	−1.98504	−0.992519	+	0.122087i	$0.961041\pi$
$62$	−1.55496	−0.197480
$63$	−4.69202	−0.591139
$64$	1.00000	0.125000
$65$	3.11529	0.386405
$66$	−5.51573	−0.678939
$67$	11.5646	1.41285	0.706423	−	0.707790i	$-0.250308\pi$
$67$	11.5646	1.41285	0.706423	+	0.707790i	$0.250308\pi$
$68$	4.34481	0.526886
$69$	−5.69202	−0.685239
$70$	3.53319	0.422297
$71$	10.0858	1.19696	0.598479	−	0.801138i	$-0.295772\pi$
$71$	10.0858	1.19696	0.598479	+	0.801138i	$0.295772\pi$
$72$	1.00000	0.117851
$73$	1.53319	0.179446	0.0897230	−	0.995967i	$-0.471402\pi$
$73$	1.53319	0.179446	0.0897230	+	0.995967i	$0.471402\pi$
$74$	−8.89977	−1.03458
$75$	−4.43296	−0.511874
$76$	5.65279	0.648420
$77$	25.8799	2.94929
$78$	−4.13706	−0.468430
$79$	6.46011	0.726819	0.363409	−	0.931630i	$-0.381613\pi$
$79$	6.46011	0.726819	0.363409	+	0.931630i	$0.381613\pi$
$80$	−0.753020	−0.0841902
$81$	1.00000	0.111111
$82$	−9.36658	−1.03437
$83$	2.93900	0.322597	0.161299	−	0.986906i	$-0.448432\pi$
$83$	2.93900	0.322597	0.161299	+	0.986906i	$0.448432\pi$
$84$	−4.69202	−0.511942
$85$	−3.27173	−0.354869
$86$	1.04892	0.113108
$87$	−0.417895	−0.0448030
$88$	−5.51573	−0.587979
$89$	−4.59419	−0.486983	−0.243491	−	0.969903i	$-0.578293\pi$
$89$	−4.59419	−0.486983	−0.243491	+	0.969903i	$0.578293\pi$
$90$	−0.753020	−0.0793753
$91$	19.4112	2.03485
$92$	−5.69202	−0.593434
$93$	−1.55496	−0.161242
$94$	2.57673	0.265769
$95$	−4.25667	−0.436725
$96$	1.00000	0.102062
$97$	3.37867	0.343052	0.171526	−	0.985180i	$-0.445130\pi$
$97$	3.37867	0.343052	0.171526	+	0.985180i	$0.445130\pi$
$98$	15.0151	1.51675
$99$	−5.51573	−0.554352
$100$	−4.43296	−0.443296
$101$	−5.85623	−0.582717	−0.291358	−	0.956614i	$-0.594107\pi$
$101$	−5.85623	−0.582717	−0.291358	+	0.956614i	$0.594107\pi$
$102$	4.34481	0.430201
$103$	3.34050	0.329149	0.164575	−	0.986365i	$-0.447375\pi$
$103$	3.34050	0.329149	0.164575	+	0.986365i	$0.447375\pi$
$104$	−4.13706	−0.405672
$105$	3.53319	0.344804
$106$	−8.32304	−0.808405
$107$	−16.0248	−1.54917	−0.774586	−	0.632469i	$-0.782042\pi$
$107$	−16.0248	−1.54917	−0.774586	+	0.632469i	$0.782042\pi$
$108$	1.00000	0.0962250
$109$	15.9705	1.52969	0.764846	−	0.644213i	$-0.222815\pi$
$109$	15.9705	1.52969	0.764846	+	0.644213i	$0.222815\pi$
$110$	4.15346	0.396017
$111$	−8.89977	−0.844729
$112$	−4.69202	−0.443354
$113$	−15.7778	−1.48425	−0.742124	−	0.670263i	$-0.766182\pi$
$113$	−15.7778	−1.48425	−0.742124	+	0.670263i	$0.766182\pi$
$114$	5.65279	0.529433
$115$	4.28621	0.399691
$116$	−0.417895	−0.0388006
$117$	−4.13706	−0.382472
$118$	13.0586	1.20214
$119$	−20.3860	−1.86878
$120$	−0.753020	−0.0687410
$121$	19.4233	1.76575
$122$	−15.5036	−1.40363
$123$	−9.36658	−0.844556
$124$	−1.55496	−0.139639
$125$	7.10321	0.635331
$126$	−4.69202	−0.417998
$127$	−1.66487	−0.147734	−0.0738669	−	0.997268i	$-0.523534\pi$
$127$	−1.66487	−0.147734	−0.0738669	+	0.997268i	$0.523534\pi$
$128$	1.00000	0.0883883
$129$	1.04892	0.0923520
$130$	3.11529	0.273229
$131$	9.21983	0.805541	0.402770	−	0.915301i	$-0.368047\pi$
$131$	9.21983	0.805541	0.402770	+	0.915301i	$0.368047\pi$
$132$	−5.51573	−0.480083
$133$	−26.5230	−2.29984
$134$	11.5646	0.999033
$135$	−0.753020	−0.0648097
$136$	4.34481	0.372565
$137$	−18.6286	−1.59155	−0.795776	−	0.605592i	$-0.792937\pi$
$137$	−18.6286	−1.59155	−0.795776	+	0.605592i	$0.792937\pi$
$138$	−5.69202	−0.484537
$139$	8.46681	0.718146	0.359073	−	0.933310i	$-0.383093\pi$
$139$	8.46681	0.718146	0.359073	+	0.933310i	$0.383093\pi$
$140$	3.53319	0.298609
$141$	2.57673	0.217000
$142$	10.0858	0.846378
$143$	22.8189	1.90821
$144$	1.00000	0.0833333
$145$	0.314683	0.0261330
$146$	1.53319	0.126888
$147$	15.0151	1.23842
$148$	−8.89977	−0.731557
$149$	−3.73125	−0.305676	−0.152838	−	0.988251i	$-0.548841\pi$
$149$	−3.73125	−0.305676	−0.152838	+	0.988251i	$0.548841\pi$
$150$	−4.43296	−0.361950
$151$	−0.146752	−0.0119425	−0.00597125	−	0.999982i	$-0.501901\pi$
$151$	−0.146752	−0.0119425	−0.00597125	+	0.999982i	$0.501901\pi$
$152$	5.65279	0.458502
$153$	4.34481	0.351257
$154$	25.8799	2.08546
$155$	1.17092	0.0940502
$156$	−4.13706	−0.331230
$157$	8.85623	0.706804	0.353402	−	0.935472i	$-0.385025\pi$
$157$	8.85623	0.706804	0.353402	+	0.935472i	$0.385025\pi$
$158$	6.46011	0.513939
$159$	−8.32304	−0.660060
$160$	−0.753020	−0.0595315
$161$	26.7071	2.10481
$162$	1.00000	0.0785674
$163$	18.6112	1.45774	0.728870	−	0.684652i	$-0.240046\pi$
$163$	18.6112	1.45774	0.728870	+	0.684652i	$0.240046\pi$
$164$	−9.36658	−0.731407
$165$	4.15346	0.323346
$166$	2.93900	0.228111
$167$	15.9933	1.23760	0.618799	−	0.785549i	$-0.287619\pi$
$167$	15.9933	1.23760	0.618799	+	0.785549i	$0.287619\pi$
$168$	−4.69202	−0.361997
$169$	4.11529	0.316561
$170$	−3.27173	−0.250931
$171$	5.65279	0.432280
$172$	1.04892	0.0799792
$173$	−2.14914	−0.163396	−0.0816982	−	0.996657i	$-0.526034\pi$
$173$	−2.14914	−0.163396	−0.0816982	+	0.996657i	$0.526034\pi$
$174$	−0.417895	−0.0316805
$175$	20.7995	1.57230
$176$	−5.51573	−0.415764
$177$	13.0586	0.981545
$178$	−4.59419	−0.344349
$179$	−21.3032	−1.59228	−0.796138	−	0.605116i	$-0.793127\pi$
$179$	−21.3032	−1.59228	−0.796138	+	0.605116i	$0.793127\pi$
$180$	−0.753020	−0.0561268
$181$	−1.76510	−0.131199	−0.0655995	−	0.997846i	$-0.520896\pi$
$181$	−1.76510	−0.131199	−0.0655995	+	0.997846i	$0.520896\pi$
$182$	19.4112	1.43885
$183$	−15.5036	−1.14606
$184$	−5.69202	−0.419621
$185$	6.70171	0.492720
$186$	−1.55496	−0.114015
$187$	−23.9648	−1.75248
$188$	2.57673	0.187927
$189$	−4.69202	−0.341294
$190$	−4.25667	−0.308811
$191$	−18.9933	−1.37431	−0.687153	−	0.726512i	$-0.741140\pi$
$191$	−18.9933	−1.37431	−0.687153	+	0.726512i	$0.741140\pi$
$192$	1.00000	0.0721688
$193$	−24.8635	−1.78972	−0.894858	−	0.446351i	$-0.852723\pi$
$193$	−24.8635	−1.78972	−0.894858	+	0.446351i	$0.852723\pi$
$194$	3.37867	0.242574
$195$	3.11529	0.223091
$196$	15.0151	1.07250
$197$	−0.0706876	−0.00503628	−0.00251814	−	0.999997i	$-0.500802\pi$
$197$	−0.0706876	−0.00503628	−0.00251814	+	0.999997i	$0.500802\pi$
$198$	−5.51573	−0.391986
$199$	−11.7041	−0.829682	−0.414841	−	0.909894i	$-0.636163\pi$
$199$	−11.7041	−0.829682	−0.414841	+	0.909894i	$0.636163\pi$
$200$	−4.43296	−0.313458
$201$	11.5646	0.815707
$202$	−5.85623	−0.412043
$203$	1.96077	0.137619
$204$	4.34481	0.304198
$205$	7.05323	0.492619
$206$	3.34050	0.232744
$207$	−5.69202	−0.395623
$208$	−4.13706	−0.286854
$209$	−31.1793	−2.15672
$210$	3.53319	0.243813
$211$	−9.29350	−0.639791	−0.319896	−	0.947453i	$-0.603648\pi$
$211$	−9.29350	−0.639791	−0.319896	+	0.947453i	$0.603648\pi$
$212$	−8.32304	−0.571629
$213$	10.0858	0.691064
$214$	−16.0248	−1.09543
$215$	−0.789856	−0.0538677
$216$	1.00000	0.0680414
$217$	7.29590	0.495278
$218$	15.9705	1.08166
$219$	1.53319	0.103603
$220$	4.15346	0.280026
$221$	−17.9748	−1.20911
$222$	−8.89977	−0.597314
$223$	−1.00000	−0.0669650
$223$	−1.00000	−0.0669650
$224$	−4.69202	−0.313499
$225$	−4.43296	−0.295531
$226$	−15.7778	−1.04952
$227$	−9.17390	−0.608893	−0.304447	−	0.952529i	$-0.598471\pi$
$227$	−9.17390	−0.608893	−0.304447	+	0.952529i	$0.598471\pi$
$228$	5.65279	0.374365
$229$	21.5308	1.42279	0.711397	−	0.702790i	$-0.248063\pi$
$229$	21.5308	1.42279	0.711397	+	0.702790i	$0.248063\pi$
$230$	4.28621	0.282624
$231$	25.8799	1.70277
$232$	−0.417895	−0.0274361
$233$	15.6082	1.02253	0.511263	−	0.859424i	$-0.329178\pi$
$233$	15.6082	1.02253	0.511263	+	0.859424i	$0.329178\pi$
$234$	−4.13706	−0.270448
$235$	−1.94033	−0.126573
$236$	13.0586	0.850043
$237$	6.46011	0.419629
$238$	−20.3860	−1.32143
$239$	−18.7506	−1.21288	−0.606439	−	0.795130i	$-0.707402\pi$
$239$	−18.7506	−1.21288	−0.606439	+	0.795130i	$0.707402\pi$
$240$	−0.753020	−0.0486073
$241$	4.61463	0.297254	0.148627	−	0.988893i	$-0.452515\pi$
$241$	4.61463	0.297254	0.148627	+	0.988893i	$0.452515\pi$
$242$	19.4233	1.24858
$243$	1.00000	0.0641500
$244$	−15.5036	−0.992519
$245$	−11.3067	−0.722355
$246$	−9.36658	−0.597192
$247$	−23.3860	−1.48801
$248$	−1.55496	−0.0987399
$249$	2.93900	0.186252
$250$	7.10321	0.449247
$251$	−16.8280	−1.06218	−0.531088	−	0.847317i	$-0.678216\pi$
$251$	−16.8280	−1.06218	−0.531088	+	0.847317i	$0.678216\pi$
$252$	−4.69202	−0.295570
$253$	31.3957	1.97383
$254$	−1.66487	−0.104464
$255$	−3.27173	−0.204884
$256$	1.00000	0.0625000
$257$	−11.0513	−0.689362	−0.344681	−	0.938720i	$-0.612013\pi$
$257$	−11.0513	−0.689362	−0.344681	+	0.938720i	$0.612013\pi$
$258$	1.04892	0.0653027
$259$	41.7579	2.59471
$260$	3.11529	0.193202
$261$	−0.417895	−0.0258670
$262$	9.21983	0.569603
$263$	6.92261	0.426866	0.213433	−	0.976958i	$-0.431535\pi$
$263$	6.92261	0.426866	0.213433	+	0.976958i	$0.431535\pi$
$264$	−5.51573	−0.339470
$265$	6.26742	0.385005
$266$	−26.5230	−1.62623
$267$	−4.59419	−0.281160
$268$	11.5646	0.706423
$269$	−16.4330	−1.00194	−0.500968	−	0.865466i	$-0.667022\pi$
$269$	−16.4330	−1.00194	−0.500968	+	0.865466i	$0.667022\pi$
$270$	−0.753020	−0.0458274
$271$	5.65817	0.343709	0.171855	−	0.985122i	$-0.445024\pi$
$271$	5.65817	0.343709	0.171855	+	0.985122i	$0.445024\pi$
$272$	4.34481	0.263443
$273$	19.4112	1.17482
$274$	−18.6286	−1.12540
$275$	24.4510	1.47445
$276$	−5.69202	−0.342619
$277$	−2.23191	−0.134103	−0.0670514	−	0.997750i	$-0.521359\pi$
$277$	−2.23191	−0.134103	−0.0670514	+	0.997750i	$0.521359\pi$
$278$	8.46681	0.507806
$279$	−1.55496	−0.0930929
$280$	3.53319	0.211148
$281$	18.6015	1.10967	0.554836	−	0.831960i	$-0.312781\pi$
$281$	18.6015	1.10967	0.554836	+	0.831960i	$0.312781\pi$
$282$	2.57673	0.153442
$283$	−5.78017	−0.343595	−0.171798	−	0.985132i	$-0.554958\pi$
$283$	−5.78017	−0.343595	−0.171798	+	0.985132i	$0.554958\pi$
$284$	10.0858	0.598479
$285$	−4.25667	−0.252143
$286$	22.8189	1.34931
$287$	43.9482	2.59418
$288$	1.00000	0.0589256
$289$	1.87741	0.110436
$290$	0.314683	0.0184788
$291$	3.37867	0.198061
$292$	1.53319	0.0897230
$293$	−10.5875	−0.618527	−0.309264	−	0.950976i	$-0.600083\pi$
$293$	−10.5875	−0.618527	−0.309264	+	0.950976i	$0.600083\pi$
$294$	15.0151	0.875696
$295$	−9.83340	−0.572522
$296$	−8.89977	−0.517289
$297$	−5.51573	−0.320055
$298$	−3.73125	−0.216146
$299$	23.5483	1.36183
$300$	−4.43296	−0.255937
$301$	−4.92154	−0.283673
$302$	−0.146752	−0.00844463
$303$	−5.85623	−0.336432
$304$	5.65279	0.324210
$305$	11.6746	0.668484
$306$	4.34481	0.248377
$307$	−27.3478	−1.56082	−0.780411	−	0.625267i	$-0.784990\pi$
$307$	−27.3478	−1.56082	−0.780411	+	0.625267i	$0.784990\pi$
$308$	25.8799	1.47465
$309$	3.34050	0.190035
$310$	1.17092	0.0665035
$311$	−4.63102	−0.262601	−0.131301	−	0.991343i	$-0.541915\pi$
$311$	−4.63102	−0.262601	−0.131301	+	0.991343i	$0.541915\pi$
$312$	−4.13706	−0.234215
$313$	−21.1709	−1.19665	−0.598325	−	0.801253i	$-0.704167\pi$
$313$	−21.1709	−1.19665	−0.598325	+	0.801253i	$0.704167\pi$
$314$	8.85623	0.499786
$315$	3.53319	0.199073
$316$	6.46011	0.363409
$317$	−1.68127	−0.0944294	−0.0472147	−	0.998885i	$-0.515034\pi$
$317$	−1.68127	−0.0944294	−0.0472147	+	0.998885i	$0.515034\pi$
$318$	−8.32304	−0.466733
$319$	2.30499	0.129055
$320$	−0.753020	−0.0420951
$321$	−16.0248	−0.894415
$322$	26.7071	1.48833
$323$	24.5603	1.36657
$324$	1.00000	0.0555556
$325$	18.3394	1.01729
$326$	18.6112	1.03078
$327$	15.9705	0.883168
$328$	−9.36658	−0.517183
$329$	−12.0901	−0.666547
$330$	4.15346	0.228640
$331$	24.3394	1.33782	0.668908	−	0.743345i	$-0.266762\pi$
$331$	24.3394	1.33782	0.668908	+	0.743345i	$0.266762\pi$
$332$	2.93900	0.161299
$333$	−8.89977	−0.487705
$334$	15.9933	0.875114
$335$	−8.70841	−0.475792
$336$	−4.69202	−0.255971
$337$	28.9922	1.57931	0.789654	−	0.613553i	$-0.210260\pi$
$337$	28.9922	1.57931	0.789654	+	0.613553i	$0.210260\pi$
$338$	4.11529	0.223842
$339$	−15.7778	−0.856931
$340$	−3.27173	−0.177435
$341$	8.57673	0.464456
$342$	5.65279	0.305668
$343$	−37.6069	−2.03058
$344$	1.04892	0.0565538
$345$	4.28621	0.230762
$346$	−2.14914	−0.115539
$347$	−28.8442	−1.54844	−0.774218	−	0.632920i	$-0.781856\pi$
$347$	−28.8442	−1.54844	−0.774218	+	0.632920i	$0.781856\pi$
$348$	−0.417895	−0.0224015
$349$	19.4795	1.04271	0.521356	−	0.853339i	$-0.325426\pi$
$349$	19.4795	1.04271	0.521356	+	0.853339i	$0.325426\pi$
$350$	20.7995	1.11178
$351$	−4.13706	−0.220820
$352$	−5.51573	−0.293989
$353$	−34.7657	−1.85039	−0.925196	−	0.379491i	$-0.876099\pi$
$353$	−34.7657	−1.85039	−0.925196	+	0.379491i	$0.876099\pi$
$354$	13.0586	0.694057
$355$	−7.59478	−0.403089
$356$	−4.59419	−0.243491
$357$	−20.3860	−1.07894
$358$	−21.3032	−1.12591
$359$	12.9530	0.683633	0.341817	−	0.939767i	$-0.388958\pi$
$359$	12.9530	0.683633	0.341817	+	0.939767i	$0.388958\pi$
$360$	−0.753020	−0.0396877
$361$	12.9541	0.681793
$362$	−1.76510	−0.0927717
$363$	19.4233	1.01946
$364$	19.4112	1.01742
$365$	−1.15452	−0.0604304
$366$	−15.5036	−0.810389
$367$	−23.5265	−1.22807	−0.614036	−	0.789278i	$-0.710455\pi$
$367$	−23.5265	−1.22807	−0.614036	+	0.789278i	$0.710455\pi$
$368$	−5.69202	−0.296717
$369$	−9.36658	−0.487605
$370$	6.70171	0.348405
$371$	39.0519	2.02747
$372$	−1.55496	−0.0806208
$373$	26.4959	1.37190	0.685952	−	0.727647i	$-0.259386\pi$
$373$	26.4959	1.37190	0.685952	+	0.727647i	$0.259386\pi$
$374$	−23.9648	−1.23919
$375$	7.10321	0.366808
$376$	2.57673	0.132885
$377$	1.72886	0.0890407
$378$	−4.69202	−0.241332
$379$	−35.3642	−1.81654	−0.908268	−	0.418388i	$-0.862595\pi$
$379$	−35.3642	−1.81654	−0.908268	+	0.418388i	$0.862595\pi$
$380$	−4.25667	−0.218362
$381$	−1.66487	−0.0852941
$382$	−18.9933	−0.971782
$383$	−17.8834	−0.913798	−0.456899	−	0.889519i	$-0.651040\pi$
$383$	−17.8834	−0.913798	−0.456899	+	0.889519i	$0.651040\pi$
$384$	1.00000	0.0510310
$385$	−19.4881	−0.993206
$386$	−24.8635	−1.26552
$387$	1.04892	0.0533195
$388$	3.37867	0.171526
$389$	−12.6063	−0.639163	−0.319582	−	0.947559i	$-0.603542\pi$
$389$	−12.6063	−0.639163	−0.319582	+	0.947559i	$0.603542\pi$
$390$	3.11529	0.157749
$391$	−24.7308	−1.25069
$392$	15.0151	0.758375
$393$	9.21983	0.465079
$394$	−0.0706876	−0.00356119
$395$	−4.86459	−0.244764
$396$	−5.51573	−0.277176
$397$	10.2567	0.514767	0.257384	−	0.966309i	$-0.417140\pi$
$397$	10.2567	0.514767	0.257384	+	0.966309i	$0.417140\pi$
$398$	−11.7041	−0.586674
$399$	−26.5230	−1.32781
$400$	−4.43296	−0.221648
$401$	−15.3690	−0.767490	−0.383745	−	0.923439i	$-0.625366\pi$
$401$	−15.3690	−0.767490	−0.383745	+	0.923439i	$0.625366\pi$
$402$	11.5646	0.576792
$403$	6.43296	0.320449
$404$	−5.85623	−0.291358
$405$	−0.753020	−0.0374179
$406$	1.96077	0.0973114
$407$	49.0887	2.43324
$408$	4.34481	0.215100
$409$	34.6819	1.71491	0.857454	−	0.514561i	$-0.172045\pi$
$409$	34.6819	1.71491	0.857454	+	0.514561i	$0.172045\pi$
$410$	7.05323	0.348334
$411$	−18.6286	−0.918883
$412$	3.34050	0.164575
$413$	−61.2713	−3.01496
$414$	−5.69202	−0.279748
$415$	−2.21313	−0.108638
$416$	−4.13706	−0.202836
$417$	8.46681	0.414622
$418$	−31.1793	−1.52503
$419$	15.1250	0.738904	0.369452	−	0.929250i	$-0.379545\pi$
$419$	15.1250	0.738904	0.369452	+	0.929250i	$0.379545\pi$
$420$	3.53319	0.172402
$421$	33.2707	1.62151	0.810757	−	0.585383i	$-0.199056\pi$
$421$	33.2707	1.62151	0.810757	+	0.585383i	$0.199056\pi$
$422$	−9.29350	−0.452401
$423$	2.57673	0.125285
$424$	−8.32304	−0.404203
$425$	−19.2604	−0.934266
$426$	10.0858	0.488656
$427$	72.7434	3.52030
$428$	−16.0248	−0.774586
$429$	22.8189	1.10171
$430$	−0.789856	−0.0380902
$431$	20.0465	0.965607	0.482804	−	0.875729i	$-0.339619\pi$
$431$	20.0465	0.965607	0.482804	+	0.875729i	$0.339619\pi$
$432$	1.00000	0.0481125
$433$	−25.9734	−1.24820	−0.624102	−	0.781343i	$-0.714535\pi$
$433$	−25.9734	−1.24820	−0.624102	+	0.781343i	$0.714535\pi$
$434$	7.29590	0.350214
$435$	0.314683	0.0150879
$436$	15.9705	0.764846
$437$	−32.1758	−1.53918
$438$	1.53319	0.0732586
$439$	−14.7705	−0.704956	−0.352478	−	0.935820i	$-0.614661\pi$
$439$	−14.7705	−0.704956	−0.352478	+	0.935820i	$0.614661\pi$
$440$	4.15346	0.198008
$441$	15.0151	0.715003
$442$	−17.9748	−0.854973
$443$	−1.89440	−0.0900055	−0.0450027	−	0.998987i	$-0.514330\pi$
$443$	−1.89440	−0.0900055	−0.0450027	+	0.998987i	$0.514330\pi$
$444$	−8.89977	−0.422365
$445$	3.45952	0.163997
$446$	−1.00000	−0.0473514
$447$	−3.73125	−0.176482
$448$	−4.69202	−0.221677
$449$	14.4142	0.680247	0.340123	−	0.940381i	$-0.389531\pi$
$449$	14.4142	0.680247	0.340123	+	0.940381i	$0.389531\pi$
$450$	−4.43296	−0.208972
$451$	51.6635	2.43274
$452$	−15.7778	−0.742124
$453$	−0.146752	−0.00689501
$454$	−9.17390	−0.430552
$455$	−14.6170	−0.685257
$456$	5.65279	0.264716
$457$	6.65817	0.311456	0.155728	−	0.987800i	$-0.450228\pi$
$457$	6.65817	0.311456	0.155728	+	0.987800i	$0.450228\pi$
$458$	21.5308	1.00607
$459$	4.34481	0.202799
$460$	4.28621	0.199845
$461$	−8.91723	−0.415317	−0.207658	−	0.978201i	$-0.566584\pi$
$461$	−8.91723	−0.415317	−0.207658	+	0.978201i	$0.566584\pi$
$462$	25.8799	1.20404
$463$	11.0271	0.512475	0.256237	−	0.966614i	$-0.417517\pi$
$463$	11.0271	0.512475	0.256237	+	0.966614i	$0.417517\pi$
$464$	−0.417895	−0.0194003
$465$	1.17092	0.0542999
$466$	15.6082	0.723035
$467$	30.5478	1.41358	0.706791	−	0.707422i	$-0.250142\pi$
$467$	30.5478	1.41358	0.706791	+	0.707422i	$0.250142\pi$
$468$	−4.13706	−0.191236
$469$	−54.2616	−2.50557
$470$	−1.94033	−0.0895007
$471$	8.85623	0.408074
$472$	13.0586	0.601071
$473$	−5.78554	−0.266020
$474$	6.46011	0.296723
$475$	−25.0586	−1.14977
$476$	−20.3860	−0.934389
$477$	−8.32304	−0.381086
$478$	−18.7506	−0.857634
$479$	10.1032	0.461628	0.230814	−	0.972998i	$-0.425861\pi$
$479$	10.1032	0.461628	0.230814	+	0.972998i	$0.425861\pi$
$480$	−0.753020	−0.0343705
$481$	36.8189	1.67880
$482$	4.61463	0.210191
$483$	26.7071	1.21521
$484$	19.4233	0.882876
$485$	−2.54420	−0.115526
$486$	1.00000	0.0453609
$487$	−17.5961	−0.797356	−0.398678	−	0.917091i	$-0.630531\pi$
$487$	−17.5961	−0.797356	−0.398678	+	0.917091i	$0.630531\pi$
$488$	−15.5036	−0.701817
$489$	18.6112	0.841626
$490$	−11.3067	−0.510782
$491$	−22.9758	−1.03689	−0.518443	−	0.855112i	$-0.673488\pi$
$491$	−22.9758	−1.03689	−0.518443	+	0.855112i	$0.673488\pi$
$492$	−9.36658	−0.422278
$493$	−1.81568	−0.0817739
$494$	−23.3860	−1.05218
$495$	4.15346	0.186684
$496$	−1.55496	−0.0698197
$497$	−47.3226	−2.12271
$498$	2.93900	0.131700
$499$	29.5200	1.32150	0.660749	−	0.750607i	$-0.270239\pi$
$499$	29.5200	1.32150	0.660749	+	0.750607i	$0.270239\pi$
$500$	7.10321	0.317665
$501$	15.9933	0.714528
$502$	−16.8280	−0.751071
$503$	−23.4741	−1.04666	−0.523329	−	0.852130i	$-0.675310\pi$
$503$	−23.4741	−1.04666	−0.523329	+	0.852130i	$0.675310\pi$
$504$	−4.69202	−0.208999
$505$	4.40986	0.196236
$506$	31.3957	1.39571
$507$	4.11529	0.182767
$508$	−1.66487	−0.0738669
$509$	−37.2078	−1.64920	−0.824602	−	0.565713i	$-0.808601\pi$
$509$	−37.2078	−1.64920	−0.824602	+	0.565713i	$0.808601\pi$
$510$	−3.27173	−0.144875
$511$	−7.19375	−0.318233
$512$	1.00000	0.0441942
$513$	5.65279	0.249577
$514$	−11.0513	−0.487452
$515$	−2.51547	−0.110845
$516$	1.04892	0.0461760
$517$	−14.2125	−0.625067
$518$	41.7579	1.83474
$519$	−2.14914	−0.0943370
$520$	3.11529	0.136615
$521$	6.82430	0.298978	0.149489	−	0.988763i	$-0.452237\pi$
$521$	6.82430	0.298978	0.149489	+	0.988763i	$0.452237\pi$
$522$	−0.417895	−0.0182908
$523$	−19.1879	−0.839028	−0.419514	−	0.907749i	$-0.637800\pi$
$523$	−19.1879	−0.839028	−0.419514	+	0.907749i	$0.637800\pi$
$524$	9.21983	0.402770
$525$	20.7995	0.907767
$526$	6.92261	0.301840
$527$	−6.75600	−0.294296
$528$	−5.51573	−0.240041
$529$	9.39911	0.408657
$530$	6.26742	0.272239
$531$	13.0586	0.566695
$532$	−26.5230	−1.14992
$533$	38.7502	1.67846
$534$	−4.59419	−0.198810
$535$	12.0670	0.521700
$536$	11.5646	0.499517
$537$	−21.3032	−0.919301
$538$	−16.4330	−0.708475
$539$	−82.8190	−3.56727
$540$	−0.753020	−0.0324048
$541$	−17.2271	−0.740652	−0.370326	−	0.928902i	$-0.620754\pi$
$541$	−17.2271	−0.740652	−0.370326	+	0.928902i	$0.620754\pi$
$542$	5.65817	0.243039
$543$	−1.76510	−0.0757478
$544$	4.34481	0.186282
$545$	−12.0261	−0.515141
$546$	19.4112	0.830722
$547$	−11.4125	−0.487964	−0.243982	−	0.969780i	$-0.578454\pi$
$547$	−11.4125	−0.487964	−0.243982	+	0.969780i	$0.578454\pi$
$548$	−18.6286	−0.795776
$549$	−15.5036	−0.661680
$550$	24.4510	1.04259
$551$	−2.36227	−0.100636
$552$	−5.69202	−0.242269
$553$	−30.3110	−1.28895
$554$	−2.23191	−0.0948249
$555$	6.70171	0.284472
$556$	8.46681	0.359073
$557$	16.0392	0.679604	0.339802	−	0.940497i	$-0.389640\pi$
$557$	16.0392	0.679604	0.339802	+	0.940497i	$0.389640\pi$
$558$	−1.55496	−0.0658266
$559$	−4.33944	−0.183539
$560$	3.53319	0.149304
$561$	−23.9648	−1.01180
$562$	18.6015	0.784656
$563$	16.4517	0.693358	0.346679	−	0.937984i	$-0.387309\pi$
$563$	16.4517	0.693358	0.346679	+	0.937984i	$0.387309\pi$
$564$	2.57673	0.108500
$565$	11.8810	0.499837
$566$	−5.78017	−0.242959
$567$	−4.69202	−0.197046
$568$	10.0858	0.423189
$569$	6.44026	0.269990	0.134995	−	0.990846i	$-0.456898\pi$
$569$	6.44026	0.269990	0.134995	+	0.990846i	$0.456898\pi$
$570$	−4.25667	−0.178292
$571$	−23.3260	−0.976164	−0.488082	−	0.872798i	$-0.662303\pi$
$571$	−23.3260	−0.976164	−0.488082	+	0.872798i	$0.662303\pi$
$572$	22.8189	0.954107
$573$	−18.9933	−0.793456
$574$	43.9482	1.83436
$575$	25.2325	1.05227
$576$	1.00000	0.0416667
$577$	7.17092	0.298529	0.149265	−	0.988797i	$-0.452309\pi$
$577$	7.17092	0.298529	0.149265	+	0.988797i	$0.452309\pi$
$578$	1.87741	0.0780900
$579$	−24.8635	−1.03329
$580$	0.314683	0.0130665
$581$	−13.7899	−0.572100
$582$	3.37867	0.140050
$583$	45.9077	1.90130
$584$	1.53319	0.0634438
$585$	3.11529	0.128802
$586$	−10.5875	−0.437365
$587$	−43.0097	−1.77520	−0.887600	−	0.460615i	$-0.847629\pi$
$587$	−43.0097	−1.77520	−0.887600	+	0.460615i	$0.847629\pi$
$588$	15.0151	0.619211
$589$	−8.78986	−0.362180
$590$	−9.83340	−0.404835
$591$	−0.0706876	−0.00290770
$592$	−8.89977	−0.365778
$593$	14.2155	0.583761	0.291881	−	0.956455i	$-0.405719\pi$
$593$	14.2155	0.583761	0.291881	+	0.956455i	$0.405719\pi$
$594$	−5.51573	−0.226313
$595$	15.3510	0.629331
$596$	−3.73125	−0.152838
$597$	−11.7041	−0.479017
$598$	23.5483	0.962960
$599$	17.2338	0.704155	0.352078	−	0.935971i	$-0.385475\pi$
$599$	17.2338	0.704155	0.352078	+	0.935971i	$0.385475\pi$
$600$	−4.43296	−0.180975
$601$	−12.4722	−0.508751	−0.254376	−	0.967106i	$-0.581870\pi$
$601$	−12.4722	−0.508751	−0.254376	+	0.967106i	$0.581870\pi$
$602$	−4.92154	−0.200587
$603$	11.5646	0.470949
$604$	−0.146752	−0.00597125
$605$	−14.6261	−0.594636
$606$	−5.85623	−0.237893
$607$	36.6558	1.48781	0.743906	−	0.668284i	$-0.232971\pi$
$607$	36.6558	1.48781	0.743906	+	0.668284i	$0.232971\pi$
$608$	5.65279	0.229251
$609$	1.96077	0.0794545
$610$	11.6746	0.472689
$611$	−10.6601	−0.431261
$612$	4.34481	0.175629
$613$	21.6775	0.875548	0.437774	−	0.899085i	$-0.355767\pi$
$613$	21.6775	0.875548	0.437774	+	0.899085i	$0.355767\pi$
$614$	−27.3478	−1.10367
$615$	7.05323	0.284414
$616$	25.8799	1.04273
$617$	−29.6329	−1.19298	−0.596489	−	0.802622i	$-0.703438\pi$
$617$	−29.6329	−1.19298	−0.596489	+	0.802622i	$0.703438\pi$
$618$	3.34050	0.134375
$619$	26.8291	1.07835	0.539176	−	0.842193i	$-0.318736\pi$
$619$	26.8291	1.07835	0.539176	+	0.842193i	$0.318736\pi$
$620$	1.17092	0.0470251
$621$	−5.69202	−0.228413
$622$	−4.63102	−0.185687
$623$	21.5560	0.863624
$624$	−4.13706	−0.165615
$625$	16.8159	0.672638
$626$	−21.1709	−0.846160
$627$	−31.1793	−1.24518
$628$	8.85623	0.353402
$629$	−38.6679	−1.54179
$630$	3.53319	0.140766
$631$	−9.14005	−0.363860	−0.181930	−	0.983312i	$-0.558234\pi$
$631$	−9.14005	−0.363860	−0.181930	+	0.983312i	$0.558234\pi$
$632$	6.46011	0.256969
$633$	−9.29350	−0.369384
$634$	−1.68127	−0.0667717
$635$	1.25368	0.0497509
$636$	−8.32304	−0.330030
$637$	−62.1183	−2.46122
$638$	2.30499	0.0912556
$639$	10.0858	0.398986
$640$	−0.753020	−0.0297657
$641$	1.45606	0.0575109	0.0287554	−	0.999586i	$-0.490846\pi$
$641$	1.45606	0.0575109	0.0287554	+	0.999586i	$0.490846\pi$
$642$	−16.0248	−0.632447
$643$	−19.0562	−0.751504	−0.375752	−	0.926720i	$-0.622615\pi$
$643$	−19.0562	−0.751504	−0.375752	+	0.926720i	$0.622615\pi$
$644$	26.7071	1.05241
$645$	−0.789856	−0.0311006
$646$	24.5603	0.966313
$647$	21.2373	0.834924	0.417462	−	0.908694i	$-0.362920\pi$
$647$	21.2373	0.834924	0.417462	+	0.908694i	$0.362920\pi$
$648$	1.00000	0.0392837
$649$	−72.0277	−2.82734
$650$	18.3394	0.719332
$651$	7.29590	0.285949
$652$	18.6112	0.728870
$653$	−3.11662	−0.121963	−0.0609814	−	0.998139i	$-0.519423\pi$
$653$	−3.11662	−0.121963	−0.0609814	+	0.998139i	$0.519423\pi$
$654$	15.9705	0.624494
$655$	−6.94272	−0.271275
$656$	−9.36658	−0.365704
$657$	1.53319	0.0598154
$658$	−12.0901	−0.471320
$659$	−17.5429	−0.683373	−0.341687	−	0.939814i	$-0.610998\pi$
$659$	−17.5429	−0.683373	−0.341687	+	0.939814i	$0.610998\pi$
$660$	4.15346	0.161673
$661$	−38.7482	−1.50713	−0.753566	−	0.657372i	$-0.771668\pi$
$661$	−38.7482	−1.50713	−0.753566	+	0.657372i	$0.771668\pi$
$662$	24.3394	0.945979
$663$	−17.9748	−0.698082
$664$	2.93900	0.114055
$665$	19.9724	0.774496
$666$	−8.89977	−0.344859
$667$	2.37867	0.0921023
$668$	15.9933	0.618799
$669$	−1.00000	−0.0386622
$670$	−8.70841	−0.336435
$671$	85.5139	3.30123
$672$	−4.69202	−0.180999
$673$	−2.55629	−0.0985376	−0.0492688	−	0.998786i	$-0.515689\pi$
$673$	−2.55629	−0.0985376	−0.0492688	+	0.998786i	$0.515689\pi$
$674$	28.9922	1.11674
$675$	−4.43296	−0.170625
$676$	4.11529	0.158281
$677$	−48.9874	−1.88274	−0.941370	−	0.337375i	$-0.890461\pi$
$677$	−48.9874	−1.88274	−0.941370	+	0.337375i	$0.890461\pi$
$678$	−15.7778	−0.605942
$679$	−15.8528	−0.608374
$680$	−3.27173	−0.125465
$681$	−9.17390	−0.351545
$682$	8.57673	0.328420
$683$	23.4077	0.895672	0.447836	−	0.894116i	$-0.352195\pi$
$683$	23.4077	0.895672	0.447836	+	0.894116i	$0.352195\pi$
$684$	5.65279	0.216140
$685$	14.0277	0.535972
$686$	−37.6069	−1.43584
$687$	21.5308	0.821451
$688$	1.04892	0.0399896
$689$	34.4330	1.31179
$690$	4.28621	0.163173
$691$	48.5357	1.84638	0.923192	−	0.384338i	$-0.125570\pi$
$691$	48.5357	1.84638	0.923192	+	0.384338i	$0.125570\pi$
$692$	−2.14914	−0.0816982
$693$	25.8799	0.983097
$694$	−28.8442	−1.09491
$695$	−6.37568	−0.241843
$696$	−0.417895	−0.0158403
$697$	−40.6961	−1.54147
$698$	19.4795	0.737309
$699$	15.6082	0.590356
$700$	20.7995	0.786149
$701$	14.1860	0.535797	0.267899	−	0.963447i	$-0.413671\pi$
$701$	14.1860	0.535797	0.267899	+	0.963447i	$0.413671\pi$
$702$	−4.13706	−0.156143
$703$	−50.3086	−1.89742
$704$	−5.51573	−0.207882
$705$	−1.94033	−0.0730770
$706$	−34.7657	−1.30842
$707$	27.4776	1.03340
$708$	13.0586	0.490772
$709$	−33.9439	−1.27479	−0.637395	−	0.770537i	$-0.719988\pi$
$709$	−33.9439	−1.27479	−0.637395	+	0.770537i	$0.719988\pi$
$710$	−7.59478	−0.285027
$711$	6.46011	0.242273
$712$	−4.59419	−0.172174
$713$	8.85086	0.331467
$714$	−20.3860	−0.762925
$715$	−17.1831	−0.642612
$716$	−21.3032	−0.796138
$717$	−18.7506	−0.700255
$718$	12.9530	0.483402
$719$	−10.4964	−0.391448	−0.195724	−	0.980659i	$-0.562706\pi$
$719$	−10.4964	−0.391448	−0.195724	+	0.980659i	$0.562706\pi$
$720$	−0.753020	−0.0280634
$721$	−15.6737	−0.583719
$722$	12.9541	0.482100
$723$	4.61463	0.171620
$724$	−1.76510	−0.0655995
$725$	1.85251	0.0688005
$726$	19.4233	0.720865
$727$	−27.3274	−1.01352	−0.506758	−	0.862088i	$-0.669156\pi$
$727$	−27.3274	−1.01352	−0.506758	+	0.862088i	$0.669156\pi$
$728$	19.4112	0.719427
$729$	1.00000	0.0370370
$730$	−1.15452	−0.0427308
$731$	4.55735	0.168560
$732$	−15.5036	−0.573031
$733$	−36.3588	−1.34294	−0.671472	−	0.741030i	$-0.734338\pi$
$733$	−36.3588	−1.34294	−0.671472	+	0.741030i	$0.734338\pi$
$734$	−23.5265	−0.868378
$735$	−11.3067	−0.417052
$736$	−5.69202	−0.209811
$737$	−63.7875	−2.34964
$738$	−9.36658	−0.344789
$739$	34.7644	1.27883	0.639414	−	0.768863i	$-0.279177\pi$
$739$	34.7644	1.27883	0.639414	+	0.768863i	$0.279177\pi$
$740$	6.70171	0.246360
$741$	−23.3860	−0.859105
$742$	39.0519	1.43364
$743$	17.2591	0.633174	0.316587	−	0.948564i	$-0.397463\pi$
$743$	17.2591	0.633174	0.316587	+	0.948564i	$0.397463\pi$
$744$	−1.55496	−0.0570075
$745$	2.80971	0.102940
$746$	26.4959	0.970083
$747$	2.93900	0.107532
$748$	−23.9648	−0.876241
$749$	75.1885	2.74733
$750$	7.10321	0.259373
$751$	12.8431	0.468651	0.234325	−	0.972158i	$-0.424712\pi$
$751$	12.8431	0.468651	0.234325	+	0.972158i	$0.424712\pi$
$752$	2.57673	0.0939636
$753$	−16.8280	−0.613247
$754$	1.72886	0.0629613
$755$	0.110507	0.00402177
$756$	−4.69202	−0.170647
$757$	2.04221	0.0742255	0.0371127	−	0.999311i	$-0.488184\pi$
$757$	2.04221	0.0742255	0.0371127	+	0.999311i	$0.488184\pi$
$758$	−35.3642	−1.28449
$759$	31.3957	1.13959
$760$	−4.25667	−0.154406
$761$	−45.6902	−1.65627	−0.828135	−	0.560529i	$-0.810598\pi$
$761$	−45.6902	−1.65627	−0.828135	+	0.560529i	$0.810598\pi$
$762$	−1.66487	−0.0603120
$763$	−74.9337	−2.71278
$764$	−18.9933	−0.687153
$765$	−3.27173	−0.118290
$766$	−17.8834	−0.646153
$767$	−54.0243	−1.95070
$768$	1.00000	0.0360844
$769$	−35.7743	−1.29005	−0.645027	−	0.764159i	$-0.723154\pi$
$769$	−35.7743	−1.29005	−0.645027	+	0.764159i	$0.723154\pi$
$770$	−19.4881	−0.702303
$771$	−11.0513	−0.398003
$772$	−24.8635	−0.894858
$773$	23.9782	0.862437	0.431218	−	0.902248i	$-0.358084\pi$
$773$	23.9782	0.862437	0.431218	+	0.902248i	$0.358084\pi$
$774$	1.04892	0.0377026
$775$	6.89307	0.247606
$776$	3.37867	0.121287
$777$	41.7579	1.49806
$778$	−12.6063	−0.451957
$779$	−52.9474	−1.89704
$780$	3.11529	0.111545
$781$	−55.6303	−1.99061
$782$	−24.7308	−0.884371
$783$	−0.417895	−0.0149343
$784$	15.0151	0.536252
$785$	−6.66892	−0.238024
$786$	9.21983	0.328861
$787$	−50.4626	−1.79880	−0.899399	−	0.437129i	$-0.855995\pi$
$787$	−50.4626	−1.79880	−0.899399	+	0.437129i	$0.855995\pi$
$788$	−0.0706876	−0.00251814
$789$	6.92261	0.246451
$790$	−4.86459	−0.173074
$791$	74.0297	2.63219
$792$	−5.51573	−0.195993
$793$	64.1396	2.27766
$794$	10.2567	0.363996
$795$	6.26742	0.222283
$796$	−11.7041	−0.414841
$797$	−15.3026	−0.542046	−0.271023	−	0.962573i	$-0.587362\pi$
$797$	−15.3026	−0.542046	−0.271023	+	0.962573i	$0.587362\pi$
$798$	−26.5230	−0.938905
$799$	11.1954	0.396065
$800$	−4.43296	−0.156729
$801$	−4.59419	−0.162328
$802$	−15.3690	−0.542697
$803$	−8.45665	−0.298429
$804$	11.5646	0.407854
$805$	−20.1110	−0.708819
$806$	6.43296	0.226591
$807$	−16.4330	−0.578468
$808$	−5.85623	−0.206022
$809$	17.5636	0.617503	0.308751	−	0.951143i	$-0.400089\pi$
$809$	17.5636	0.617503	0.308751	+	0.951143i	$0.400089\pi$
$810$	−0.753020	−0.0264584
$811$	−0.443977	−0.0155901	−0.00779507	−	0.999970i	$-0.502481\pi$
$811$	−0.443977	−0.0155901	−0.00779507	+	0.999970i	$0.502481\pi$
$812$	1.96077	0.0688096
$813$	5.65817	0.198441
$814$	49.0887	1.72056
$815$	−14.0146	−0.490910
$816$	4.34481	0.152099
$817$	5.92931	0.207440
$818$	34.6819	1.21262
$819$	19.4112	0.678282
$820$	7.05323	0.246309
$821$	16.4510	0.574144	0.287072	−	0.957909i	$-0.407318\pi$
$821$	16.4510	0.574144	0.287072	+	0.957909i	$0.407318\pi$
$822$	−18.6286	−0.649748
$823$	44.1309	1.53831	0.769154	−	0.639063i	$-0.220678\pi$
$823$	44.1309	1.53831	0.769154	+	0.639063i	$0.220678\pi$
$824$	3.34050	0.116372
$825$	24.4510	0.851275
$826$	−61.2713	−2.13190
$827$	5.58748	0.194296	0.0971479	−	0.995270i	$-0.469028\pi$
$827$	5.58748	0.194296	0.0971479	+	0.995270i	$0.469028\pi$
$828$	−5.69202	−0.197811
$829$	36.7754	1.27726	0.638631	−	0.769513i	$-0.279501\pi$
$829$	36.7754	1.27726	0.638631	+	0.769513i	$0.279501\pi$
$830$	−2.21313	−0.0768188
$831$	−2.23191	−0.0774242
$832$	−4.13706	−0.143427
$833$	65.2377	2.26035
$834$	8.46681	0.293182
$835$	−12.0433	−0.416775
$836$	−31.1793	−1.07836
$837$	−1.55496	−0.0537472
$838$	15.1250	0.522484
$839$	−15.2892	−0.527842	−0.263921	−	0.964544i	$-0.585016\pi$
$839$	−15.2892	−0.527842	−0.263921	+	0.964544i	$0.585016\pi$
$840$	3.53319	0.121907
$841$	−28.8254	−0.993978
$842$	33.2707	1.14658
$843$	18.6015	0.640669
$844$	−9.29350	−0.319896
$845$	−3.09890	−0.106605
$846$	2.57673	0.0885897
$847$	−91.1344	−3.13142
$848$	−8.32304	−0.285815
$849$	−5.78017	−0.198375
$850$	−19.2604	−0.660626
$851$	50.6577	1.73652
$852$	10.0858	0.345532
$853$	20.7090	0.709063	0.354531	−	0.935044i	$-0.384640\pi$
$853$	20.7090	0.709063	0.354531	+	0.935044i	$0.384640\pi$
$854$	72.7434	2.48923
$855$	−4.25667	−0.145575
$856$	−16.0248	−0.547715
$857$	37.2368	1.27199	0.635993	−	0.771695i	$-0.280591\pi$
$857$	37.2368	1.27199	0.635993	+	0.771695i	$0.280591\pi$
$858$	22.8189	0.779025
$859$	−1.71273	−0.0584375	−0.0292187	−	0.999573i	$-0.509302\pi$
$859$	−1.71273	−0.0584375	−0.0292187	+	0.999573i	$0.509302\pi$
$860$	−0.789856	−0.0269339
$861$	43.9482	1.49775
$862$	20.0465	0.682787
$863$	15.0731	0.513094	0.256547	−	0.966532i	$-0.417415\pi$
$863$	15.0731	0.513094	0.256547	+	0.966532i	$0.417415\pi$
$864$	1.00000	0.0340207
$865$	1.61835	0.0550255
$866$	−25.9734	−0.882614
$867$	1.87741	0.0637602
$868$	7.29590	0.247639
$869$	−35.6322	−1.20874
$870$	0.314683	0.0106688
$871$	−47.8437	−1.62112
$872$	15.9705	0.540828
$873$	3.37867	0.114351
$874$	−32.1758	−1.08836
$875$	−33.3284	−1.12671
$876$	1.53319	0.0518016
$877$	−38.7536	−1.30862	−0.654308	−	0.756228i	$-0.727040\pi$
$877$	−38.7536	−1.30862	−0.654308	+	0.756228i	$0.727040\pi$
$878$	−14.7705	−0.498480
$879$	−10.5875	−0.357107
$880$	4.15346	0.140013
$881$	19.8358	0.668285	0.334142	−	0.942523i	$-0.391553\pi$
$881$	19.8358	0.668285	0.334142	+	0.942523i	$0.391553\pi$
$882$	15.0151	0.505584
$883$	−35.0258	−1.17871	−0.589356	−	0.807873i	$-0.700619\pi$
$883$	−35.0258	−1.17871	−0.589356	+	0.807873i	$0.700619\pi$
$884$	−17.9748	−0.604557
$885$	−9.83340	−0.330546
$886$	−1.89440	−0.0636435
$887$	31.7875	1.06732	0.533659	−	0.845700i	$-0.320816\pi$
$887$	31.7875	1.06732	0.533659	+	0.845700i	$0.320816\pi$
$888$	−8.89977	−0.298657
$889$	7.81163	0.261994
$890$	3.45952	0.115963
$891$	−5.51573	−0.184784
$892$	−1.00000	−0.0334825
$893$	14.5657	0.487423
$894$	−3.73125	−0.124792
$895$	16.0417	0.536216
$896$	−4.69202	−0.156749
$897$	23.5483	0.786253
$898$	14.4142	0.481007
$899$	0.649809	0.0216723
$900$	−4.43296	−0.147765
$901$	−36.1621	−1.20473
$902$	51.6635	1.72021
$903$	−4.92154	−0.163779
$904$	−15.7778	−0.524761
$905$	1.32916	0.0441827
$906$	−0.146752	−0.00487551
$907$	8.45042	0.280592	0.140296	−	0.990110i	$-0.455195\pi$
$907$	8.45042	0.280592	0.140296	+	0.990110i	$0.455195\pi$
$908$	−9.17390	−0.304447
$909$	−5.85623	−0.194239
$910$	−14.6170	−0.484550
$911$	−9.38106	−0.310808	−0.155404	−	0.987851i	$-0.549668\pi$
$911$	−9.38106	−0.310808	−0.155404	+	0.987851i	$0.549668\pi$
$912$	5.65279	0.187183
$913$	−16.2107	−0.536497
$914$	6.65817	0.220233
$915$	11.6746	0.385949
$916$	21.5308	0.711397
$917$	−43.2597	−1.42856
$918$	4.34481	0.143400
$919$	−44.2247	−1.45884	−0.729420	−	0.684066i	$-0.760210\pi$
$919$	−44.2247	−1.45884	−0.729420	+	0.684066i	$0.760210\pi$
$920$	4.28621	0.141312
$921$	−27.3478	−0.901141
$922$	−8.91723	−0.293673
$923$	−41.7254	−1.37341
$924$	25.8799	0.851387
$925$	39.4523	1.29718
$926$	11.0271	0.362375
$927$	3.34050	0.109716
$928$	−0.417895	−0.0137181
$929$	16.8810	0.553847	0.276924	−	0.960892i	$-0.410685\pi$
$929$	16.8810	0.553847	0.276924	+	0.960892i	$0.410685\pi$
$930$	1.17092	0.0383958
$931$	84.8771	2.78173
$932$	15.6082	0.511263
$933$	−4.63102	−0.151613
$934$	30.5478	0.999554
$935$	18.0460	0.590167
$936$	−4.13706	−0.135224
$937$	18.6021	0.607703	0.303852	−	0.952719i	$-0.401727\pi$
$937$	18.6021	0.607703	0.303852	+	0.952719i	$0.401727\pi$
$938$	−54.2616	−1.77170
$939$	−21.1709	−0.690887
$940$	−1.94033	−0.0632866
$941$	24.1545	0.787415	0.393707	−	0.919236i	$-0.371192\pi$
$941$	24.1545	0.787415	0.393707	+	0.919236i	$0.371192\pi$
$942$	8.85623	0.288552
$943$	53.3148	1.73617
$944$	13.0586	0.425021
$945$	3.53319	0.114935
$946$	−5.78554	−0.188104
$947$	12.4494	0.404550	0.202275	−	0.979329i	$-0.435167\pi$
$947$	12.4494	0.404550	0.202275	+	0.979329i	$0.435167\pi$
$948$	6.46011	0.209815
$949$	−6.34290	−0.205899
$950$	−25.0586	−0.813009
$951$	−1.68127	−0.0545188
$952$	−20.3860	−0.660713
$953$	36.7362	1.19000	0.595000	−	0.803725i	$-0.297152\pi$
$953$	36.7362	1.19000	0.595000	+	0.803725i	$0.297152\pi$
$954$	−8.32304	−0.269468
$955$	14.3023	0.462813
$956$	−18.7506	−0.606439
$957$	2.30499	0.0745099
$958$	10.1032	0.326420
$959$	87.4059	2.82248
$960$	−0.753020	−0.0243036
$961$	−28.5821	−0.922003
$962$	36.8189	1.18709
$963$	−16.0248	−0.516390
$964$	4.61463	0.148627
$965$	18.7227	0.602706
$966$	26.7071	0.859286
$967$	−9.16852	−0.294840	−0.147420	−	0.989074i	$-0.547097\pi$
$967$	−9.16852	−0.294840	−0.147420	+	0.989074i	$0.547097\pi$
$968$	19.4233	0.624288
$969$	24.5603	0.788992
$970$	−2.54420	−0.0816895
$971$	28.5327	0.915658	0.457829	−	0.889040i	$-0.348627\pi$
$971$	28.5327	0.915658	0.457829	+	0.889040i	$0.348627\pi$
$972$	1.00000	0.0320750
$973$	−39.7265	−1.27357
$974$	−17.5961	−0.563816
$975$	18.3394	0.587332
$976$	−15.5036	−0.496260
$977$	23.3593	0.747330	0.373665	−	0.927564i	$-0.378101\pi$
$977$	23.3593	0.747330	0.373665	+	0.927564i	$0.378101\pi$
$978$	18.6112	0.595120
$979$	25.3403	0.809879
$980$	−11.3067	−0.361178
$981$	15.9705	0.509898
$982$	−22.9758	−0.733188
$983$	−20.9772	−0.669068	−0.334534	−	0.942384i	$-0.608579\pi$
$983$	−20.9772	−0.669068	−0.334534	+	0.942384i	$0.608579\pi$
$984$	−9.36658	−0.298596
$985$	0.0532292	0.00169602
$986$	−1.81568	−0.0578229
$987$	−12.0901	−0.384831
$988$	−23.3860	−0.744007
$989$	−5.97046	−0.189850
$990$	4.15346	0.132006
$991$	−7.54932	−0.239812	−0.119906	−	0.992785i	$-0.538259\pi$
$991$	−7.54932	−0.239812	−0.119906	+	0.992785i	$0.538259\pi$
$992$	−1.55496	−0.0493700
$993$	24.3394	0.772389
$994$	−47.3226	−1.50098
$995$	8.81343	0.279404
$996$	2.93900	0.0931258
$997$	30.6974	0.972196	0.486098	−	0.873904i	$-0.338420\pi$
$997$	30.6974	0.972196	0.486098	+	0.873904i	$0.338420\pi$
$998$	29.5200	0.934441
$999$	−8.89977	−0.281576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.a.f.1.3	✓	3
3.2	odd	2		4014.2.a.n.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.a.f.1.3	✓	3	1.1	even	1	trivial
4014.2.a.n.1.1		3	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.753020 q^{5} +1.00000 q^{6} -4.69202 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.753020 q^{10} -5.51573 q^{11} +1.00000 q^{12} -4.13706 q^{13} -4.69202 q^{14} -0.753020 q^{15} +1.00000 q^{16} +4.34481 q^{17} +1.00000 q^{18} +5.65279 q^{19} -0.753020 q^{20} -4.69202 q^{21} -5.51573 q^{22} -5.69202 q^{23} +1.00000 q^{24} -4.43296 q^{25} -4.13706 q^{26} +1.00000 q^{27} -4.69202 q^{28} -0.417895 q^{29} -0.753020 q^{30} -1.55496 q^{31} +1.00000 q^{32} -5.51573 q^{33} +4.34481 q^{34} +3.53319 q^{35} +1.00000 q^{36} -8.89977 q^{37} +5.65279 q^{38} -4.13706 q^{39} -0.753020 q^{40} -9.36658 q^{41} -4.69202 q^{42} +1.04892 q^{43} -5.51573 q^{44} -0.753020 q^{45} -5.69202 q^{46} +2.57673 q^{47} +1.00000 q^{48} +15.0151 q^{49} -4.43296 q^{50} +4.34481 q^{51} -4.13706 q^{52} -8.32304 q^{53} +1.00000 q^{54} +4.15346 q^{55} -4.69202 q^{56} +5.65279 q^{57} -0.417895 q^{58} +13.0586 q^{59} -0.753020 q^{60} -15.5036 q^{61} -1.55496 q^{62} -4.69202 q^{63} +1.00000 q^{64} +3.11529 q^{65} -5.51573 q^{66} +11.5646 q^{67} +4.34481 q^{68} -5.69202 q^{69} +3.53319 q^{70} +10.0858 q^{71} +1.00000 q^{72} +1.53319 q^{73} -8.89977 q^{74} -4.43296 q^{75} +5.65279 q^{76} +25.8799 q^{77} -4.13706 q^{78} +6.46011 q^{79} -0.753020 q^{80} +1.00000 q^{81} -9.36658 q^{82} +2.93900 q^{83} -4.69202 q^{84} -3.27173 q^{85} +1.04892 q^{86} -0.417895 q^{87} -5.51573 q^{88} -4.59419 q^{89} -0.753020 q^{90} +19.4112 q^{91} -5.69202 q^{92} -1.55496 q^{93} +2.57673 q^{94} -4.25667 q^{95} +1.00000 q^{96} +3.37867 q^{97} +15.0151 q^{98} -5.51573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 7 q^{5} + 3 q^{6} - 9 q^{7} + 3 q^{8} + 3 q^{9} - 7 q^{10} - 4 q^{11} + 3 q^{12} - 7 q^{13} - 9 q^{14} - 7 q^{15} + 3 q^{16} - 10 q^{17} + 3 q^{18} - q^{19} - 7 q^{20}+ \cdots - 4 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 7 * q^5 + 3 * q^6 - 9 * q^7 + 3 * q^8 + 3 * q^9 - 7 * q^10 - 4 * q^11 + 3 * q^12 - 7 * q^13 - 9 * q^14 - 7 * q^15 + 3 * q^16 - 10 * q^17 + 3 * q^18 - q^19 - 7 * q^20 - 9 * q^21 - 4 * q^22 - 12 * q^23 + 3 * q^24 + 6 * q^25 - 7 * q^26 + 3 * q^27 - 9 * q^28 - 7 * q^29 - 7 * q^30 - 5 * q^31 + 3 * q^32 - 4 * q^33 - 10 * q^34 + 14 * q^35 + 3 * q^36 - 4 * q^37 - q^38 - 7 * q^39 - 7 * q^40 - 2 * q^41 - 9 * q^42 - 6 * q^43 - 4 * q^44 - 7 * q^45 - 12 * q^46 + 5 * q^47 + 3 * q^48 + 20 * q^49 + 6 * q^50 - 10 * q^51 - 7 * q^52 - 5 * q^53 + 3 * q^54 + 7 * q^55 - 9 * q^56 - q^57 - 7 * q^58 + 8 * q^59 - 7 * q^60 - 15 * q^61 - 5 * q^62 - 9 * q^63 + 3 * q^64 + 7 * q^65 - 4 * q^66 + 13 * q^67 - 10 * q^68 - 12 * q^69 + 14 * q^70 - 7 * q^71 + 3 * q^72 + 8 * q^73 - 4 * q^74 + 6 * q^75 - q^76 - 2 * q^77 - 7 * q^78 - 6 * q^79 - 7 * q^80 + 3 * q^81 - 2 * q^82 - q^83 - 9 * q^84 + 42 * q^85 - 6 * q^86 - 7 * q^87 - 4 * q^88 - 27 * q^89 - 7 * q^90 + 42 * q^91 - 12 * q^92 - 5 * q^93 + 5 * q^94 + 14 * q^95 + 3 * q^96 + 3 * q^97 + 20 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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