LMFDB - Embedded newform 1003.2.a.e.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.229.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 4x - 1 $ x^3 - 4*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.11491$ of defining polynomial
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.357926 q^{3} -1.00000 q^{4} +2.58774 q^{5} -0.357926 q^{6} -0.357926 q^{7} +3.00000 q^{8} -2.87189 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.357926 q^{3} -1.00000 q^{4} +2.58774 q^{5} -0.357926 q^{6} -0.357926 q^{7} +3.00000 q^{8} -2.87189 q^{9} -2.58774 q^{10} -0.357926 q^{12} -4.94567 q^{13} +0.357926 q^{14} +0.926221 q^{15} -1.00000 q^{16} -1.00000 q^{17} +2.87189 q^{18} -2.35793 q^{19} -2.58774 q^{20} -0.128111 q^{21} -2.94567 q^{23} +1.07378 q^{24} +1.69641 q^{25} +4.94567 q^{26} -2.10170 q^{27} +0.357926 q^{28} +3.30359 q^{29} -0.926221 q^{30} -1.77018 q^{31} -5.00000 q^{32} +1.00000 q^{34} -0.926221 q^{35} +2.87189 q^{36} -5.89134 q^{37} +2.35793 q^{38} -1.77018 q^{39} +7.76322 q^{40} +9.15604 q^{41} +0.128111 q^{42} -6.22982 q^{43} -7.43171 q^{45} +2.94567 q^{46} +11.4053 q^{47} -0.357926 q^{48} -6.87189 q^{49} -1.69641 q^{50} -0.357926 q^{51} +4.94567 q^{52} -5.41226 q^{53} +2.10170 q^{54} -1.07378 q^{56} -0.843964 q^{57} -3.30359 q^{58} -1.00000 q^{59} -0.926221 q^{60} -5.51396 q^{61} +1.77018 q^{62} +1.02792 q^{63} +7.00000 q^{64} -12.7981 q^{65} -2.56829 q^{67} +1.00000 q^{68} -1.05433 q^{69} +0.926221 q^{70} -6.71585 q^{71} -8.61567 q^{72} -0.715853 q^{73} +5.89134 q^{74} +0.607188 q^{75} +2.35793 q^{76} +1.77018 q^{78} -13.9930 q^{79} -2.58774 q^{80} +7.86341 q^{81} -9.15604 q^{82} -8.45963 q^{83} +0.128111 q^{84} -2.58774 q^{85} +6.22982 q^{86} +1.18244 q^{87} -3.05433 q^{89} +7.43171 q^{90} +1.77018 q^{91} +2.94567 q^{92} -0.633596 q^{93} -11.4053 q^{94} -6.10170 q^{95} -1.78963 q^{96} +4.33848 q^{97} +6.87189 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 9 q^{8} + 5 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 9 * q^8 + 5 * q^9	$ 3 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 9 q^{8} + 5 q^{9} + 4 q^{10} - 2 q^{12} - 4 q^{13} + 2 q^{14} - 3 q^{16} - 3 q^{17} - 5 q^{18} - 8 q^{19} + 4 q^{20} - 14 q^{21} + 2 q^{23} + 6 q^{24} + 15 q^{25} + 4 q^{26} + 20 q^{27} + 2 q^{28} - 18 q^{31} - 15 q^{32} + 3 q^{34} - 5 q^{36} + 4 q^{37} + 8 q^{38} - 18 q^{39} - 12 q^{40} + 12 q^{41} + 14 q^{42} - 6 q^{43} - 26 q^{45} - 2 q^{46} - 2 q^{47} - 2 q^{48} - 7 q^{49} - 15 q^{50} - 2 q^{51} + 4 q^{52} - 28 q^{53} - 20 q^{54} - 6 q^{56} - 18 q^{57} - 3 q^{59} - 2 q^{61} + 18 q^{62} - 26 q^{63} + 21 q^{64} - 22 q^{65} - 4 q^{67} + 3 q^{68} - 14 q^{69} - 22 q^{71} + 15 q^{72} - 4 q^{73} - 4 q^{74} - 18 q^{75} + 8 q^{76} + 18 q^{78} + 6 q^{79} + 4 q^{80} + 31 q^{81} - 12 q^{82} + 14 q^{84} + 4 q^{85} + 6 q^{86} + 28 q^{87} - 20 q^{89} + 26 q^{90} + 18 q^{91} - 2 q^{92} - 22 q^{93} + 2 q^{94} + 8 q^{95} - 10 q^{96} + 22 q^{97} + 7 q^{98}+O(q^{100}) $ 3 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 9 * q^8 + 5 * q^9 + 4 * q^10 - 2 * q^12 - 4 * q^13 + 2 * q^14 - 3 * q^16 - 3 * q^17 - 5 * q^18 - 8 * q^19 + 4 * q^20 - 14 * q^21 + 2 * q^23 + 6 * q^24 + 15 * q^25 + 4 * q^26 + 20 * q^27 + 2 * q^28 - 18 * q^31 - 15 * q^32 + 3 * q^34 - 5 * q^36 + 4 * q^37 + 8 * q^38 - 18 * q^39 - 12 * q^40 + 12 * q^41 + 14 * q^42 - 6 * q^43 - 26 * q^45 - 2 * q^46 - 2 * q^47 - 2 * q^48 - 7 * q^49 - 15 * q^50 - 2 * q^51 + 4 * q^52 - 28 * q^53 - 20 * q^54 - 6 * q^56 - 18 * q^57 - 3 * q^59 - 2 * q^61 + 18 * q^62 - 26 * q^63 + 21 * q^64 - 22 * q^65 - 4 * q^67 + 3 * q^68 - 14 * q^69 - 22 * q^71 + 15 * q^72 - 4 * q^73 - 4 * q^74 - 18 * q^75 + 8 * q^76 + 18 * q^78 + 6 * q^79 + 4 * q^80 + 31 * q^81 - 12 * q^82 + 14 * q^84 + 4 * q^85 + 6 * q^86 + 28 * q^87 - 20 * q^89 + 26 * q^90 + 18 * q^91 - 2 * q^92 - 22 * q^93 + 2 * q^94 + 8 * q^95 - 10 * q^96 + 22 * q^97 + 7 * q^98

Display 100 coefficients 10 coefficients

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	−0.353553	−	0.935414i	$-0.615027\pi$
$2$	−1.00000	−0.707107	−0.353553	+	0.935414i	$0.615027\pi$
$3$	0.357926	0.206649	0.103324	−	0.994648i	$-0.467052\pi$
$3$	0.357926	0.206649	0.103324	+	0.994648i	$0.467052\pi$
$4$	−1.00000	−0.500000
$5$	2.58774	1.15727	0.578637	−	0.815586i	$-0.303585\pi$
$5$	2.58774	1.15727	0.578637	+	0.815586i	$0.303585\pi$
$6$	−0.357926	−0.146123
$7$	−0.357926	−0.135283	−0.0676417	−	0.997710i	$-0.521547\pi$
$7$	−0.357926	−0.135283	−0.0676417	+	0.997710i	$0.521547\pi$
$8$	3.00000	1.06066
$9$	−2.87189	−0.957296
$10$	−2.58774	−0.818316
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−0.357926	−0.103324
$13$	−4.94567	−1.37168	−0.685841	−	0.727752i	$-0.740565\pi$
$13$	−4.94567	−1.37168	−0.685841	+	0.727752i	$0.740565\pi$
$14$	0.357926	0.0956598
$15$	0.926221	0.239149
$16$	−1.00000	−0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.87189	0.676911
$19$	−2.35793	−0.540945	−0.270473	−	0.962728i	$-0.587180\pi$
$19$	−2.35793	−0.540945	−0.270473	+	0.962728i	$0.587180\pi$
$20$	−2.58774	−0.578637
$21$	−0.128111	−0.0279562
$22$	0	0
$23$	−2.94567	−0.614214	−0.307107	−	0.951675i	$-0.599361\pi$
$23$	−2.94567	−0.614214	−0.307107	+	0.951675i	$0.599361\pi$
$24$	1.07378	0.219184
$25$	1.69641	0.339281
$26$	4.94567	0.969925
$27$	−2.10170	−0.404473
$28$	0.357926	0.0676417
$29$	3.30359	0.613462	0.306731	−	0.951796i	$-0.400765\pi$
$29$	3.30359	0.613462	0.306731	+	0.951796i	$0.400765\pi$
$30$	−0.926221	−0.169104
$31$	−1.77018	−0.317935	−0.158967	−	0.987284i	$-0.550816\pi$
$31$	−1.77018	−0.317935	−0.158967	+	0.987284i	$0.550816\pi$
$32$	−5.00000	−0.883883
$33$	0	0
$34$	1.00000	0.171499
$35$	−0.926221	−0.156560
$36$	2.87189	0.478648
$37$	−5.89134	−0.968530	−0.484265	−	0.874921i	$-0.660913\pi$
$37$	−5.89134	−0.968530	−0.484265	+	0.874921i	$0.660913\pi$
$38$	2.35793	0.382506
$39$	−1.77018	−0.283456
$40$	7.76322	1.22747
$41$	9.15604	1.42993	0.714966	−	0.699159i	$-0.246442\pi$
$41$	9.15604	1.42993	0.714966	+	0.699159i	$0.246442\pi$
$42$	0.128111	0.0197680
$43$	−6.22982	−0.950038	−0.475019	−	0.879976i	$-0.657559\pi$
$43$	−6.22982	−0.950038	−0.475019	+	0.879976i	$0.657559\pi$
$44$	0	0
$45$	−7.43171	−1.10785
$46$	2.94567	0.434315
$47$	11.4053	1.66363	0.831817	−	0.555050i	$-0.187301\pi$
$47$	11.4053	1.66363	0.831817	+	0.555050i	$0.187301\pi$
$48$	−0.357926	−0.0516622
$49$	−6.87189	−0.981698
$50$	−1.69641	−0.239908
$51$	−0.357926	−0.0501197
$52$	4.94567	0.685841
$53$	−5.41226	−0.743431	−0.371715	−	0.928347i	$-0.621230\pi$
$53$	−5.41226	−0.743431	−0.371715	+	0.928347i	$0.621230\pi$
$54$	2.10170	0.286006
$55$	0	0
$56$	−1.07378	−0.143490
$57$	−0.843964	−0.111786
$58$	−3.30359	−0.433783
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	−0.926221	−0.119575
$61$	−5.51396	−0.705991	−0.352995	−	0.935625i	$-0.614837\pi$
$61$	−5.51396	−0.705991	−0.352995	+	0.935625i	$0.614837\pi$
$62$	1.77018	0.224814
$63$	1.02792	0.129506
$64$	7.00000	0.875000
$65$	−12.7981	−1.58741
$66$	0	0
$67$	−2.56829	−0.313767	−0.156884	−	0.987617i	$-0.550145\pi$
$67$	−2.56829	−0.313767	−0.156884	+	0.987617i	$0.550145\pi$
$68$	1.00000	0.121268
$69$	−1.05433	−0.126927
$70$	0.926221	0.110705
$71$	−6.71585	−0.797025	−0.398513	−	0.917163i	$-0.630473\pi$
$71$	−6.71585	−0.797025	−0.398513	+	0.917163i	$0.630473\pi$
$72$	−8.61567	−1.01537
$73$	−0.715853	−0.0837842	−0.0418921	−	0.999122i	$-0.513339\pi$
$73$	−0.715853	−0.0837842	−0.0418921	+	0.999122i	$0.513339\pi$
$74$	5.89134	0.684854
$75$	0.607188	0.0701121
$76$	2.35793	0.270473
$77$	0	0
$78$	1.77018	0.200434
$79$	−13.9930	−1.57434	−0.787170	−	0.616736i	$-0.788455\pi$
$79$	−13.9930	−1.57434	−0.787170	+	0.616736i	$0.788455\pi$
$80$	−2.58774	−0.289318
$81$	7.86341	0.873712
$82$	−9.15604	−1.01112
$83$	−8.45963	−0.928565	−0.464283	−	0.885687i	$-0.653688\pi$
$83$	−8.45963	−0.928565	−0.464283	+	0.885687i	$0.653688\pi$
$84$	0.128111	0.0139781
$85$	−2.58774	−0.280680
$86$	6.22982	0.671778
$87$	1.18244	0.126771
$88$	0	0
$89$	−3.05433	−0.323759	−0.161879	−	0.986811i	$-0.551756\pi$
$89$	−3.05433	−0.323759	−0.161879	+	0.986811i	$0.551756\pi$
$90$	7.43171	0.783371
$91$	1.77018	0.185566
$92$	2.94567	0.307107
$93$	−0.633596	−0.0657008
$94$	−11.4053	−1.17637
$95$	−6.10170	−0.626022
$96$	−1.78963	−0.182654
$97$	4.33848	0.440506	0.220253	−	0.975443i	$-0.429312\pi$
$97$	4.33848	0.440506	0.220253	+	0.975443i	$0.429312\pi$
$98$	6.87189	0.694166
$99$	0	0
$100$	−1.69641	−0.169641
$101$	−7.17548	−0.713987	−0.356994	−	0.934107i	$-0.616198\pi$
$101$	−7.17548	−0.713987	−0.356994	+	0.934107i	$0.616198\pi$
$102$	0.357926	0.0354400
$103$	3.66152	0.360780	0.180390	−	0.983595i	$-0.442264\pi$
$103$	3.66152	0.360780	0.180390	+	0.983595i	$0.442264\pi$
$104$	−14.8370	−1.45489
$105$	−0.331519	−0.0323529
$106$	5.41226	0.525685
$107$	4.35793	0.421297	0.210648	−	0.977562i	$-0.432443\pi$
$107$	4.35793	0.421297	0.210648	+	0.977562i	$0.432443\pi$
$108$	2.10170	0.202237
$109$	−5.17548	−0.495721	−0.247861	−	0.968796i	$-0.579728\pi$
$109$	−5.17548	−0.495721	−0.247861	+	0.968796i	$0.579728\pi$
$110$	0	0
$111$	−2.10866	−0.200146
$112$	0.357926	0.0338209
$113$	−8.37737	−0.788077	−0.394038	−	0.919094i	$-0.628922\pi$
$113$	−8.37737	−0.788077	−0.394038	+	0.919094i	$0.628922\pi$
$114$	0.843964	0.0790445
$115$	−7.62263	−0.710814
$116$	−3.30359	−0.306731
$117$	14.2034	1.31311
$118$	1.00000	0.0920575
$119$	0.357926	0.0328111
$120$	2.77866	0.253656
$121$	−11.0000	−1.00000
$122$	5.51396	0.499211
$123$	3.27719	0.295494
$124$	1.77018	0.158967
$125$	−8.54885	−0.764632
$126$	−1.02792	−0.0915748
$127$	6.10170	0.541439	0.270719	−	0.962658i	$-0.412738\pi$
$127$	6.10170	0.541439	0.270719	+	0.962658i	$0.412738\pi$
$128$	3.00000	0.265165
$129$	−2.22982	−0.196324
$130$	12.7981	1.12247
$131$	−3.74378	−0.327095	−0.163548	−	0.986535i	$-0.552294\pi$
$131$	−3.74378	−0.327095	−0.163548	+	0.986535i	$0.552294\pi$
$132$	0	0
$133$	0.843964	0.0731810
$134$	2.56829	0.221867
$135$	−5.43867	−0.468086
$136$	−3.00000	−0.257248
$137$	10.5877	0.904572	0.452286	−	0.891873i	$-0.350609\pi$
$137$	10.5877	0.904572	0.452286	+	0.891873i	$0.350609\pi$
$138$	1.05433	0.0897507
$139$	4.14756	0.351791	0.175896	−	0.984409i	$-0.443718\pi$
$139$	4.14756	0.351791	0.175896	+	0.984409i	$0.443718\pi$
$140$	0.926221	0.0782800
$141$	4.08226	0.343788
$142$	6.71585	0.563582
$143$	0	0
$144$	2.87189	0.239324
$145$	8.54885	0.709943
$146$	0.715853	0.0592444
$147$	−2.45963	−0.202867
$148$	5.89134	0.484265
$149$	3.09323	0.253407	0.126703	−	0.991941i	$-0.459560\pi$
$149$	3.09323	0.253407	0.126703	+	0.991941i	$0.459560\pi$
$150$	−0.607188	−0.0495767
$151$	20.4596	1.66498	0.832491	−	0.554039i	$-0.186914\pi$
$151$	20.4596	1.66498	0.832491	+	0.554039i	$0.186914\pi$
$152$	−7.07378	−0.573759
$153$	2.87189	0.232178
$154$	0	0
$155$	−4.58078	−0.367937
$156$	1.77018	0.141728
$157$	0.229815	0.0183412	0.00917062	−	0.999958i	$-0.497081\pi$
$157$	0.229815	0.0183412	0.00917062	+	0.999958i	$0.497081\pi$
$158$	13.9930	1.11323
$159$	−1.93719	−0.153629
$160$	−12.9387	−1.02289
$161$	1.05433	0.0830930
$162$	−7.86341	−0.617808
$163$	2.71585	0.212722	0.106361	−	0.994328i	$-0.466080\pi$
$163$	2.71585	0.212722	0.106361	+	0.994328i	$0.466080\pi$
$164$	−9.15604	−0.714966
$165$	0	0
$166$	8.45963	0.656595
$167$	1.53341	0.118659	0.0593294	−	0.998238i	$-0.481104\pi$
$167$	1.53341	0.118659	0.0593294	+	0.998238i	$0.481104\pi$
$168$	−0.384334	−0.0296520
$169$	11.4596	0.881510
$170$	2.58774	0.198471
$171$	6.77170	0.517845
$172$	6.22982	0.475019
$173$	2.68945	0.204475	0.102237	−	0.994760i	$-0.467400\pi$
$173$	2.68945	0.204475	0.102237	+	0.994760i	$0.467400\pi$
$174$	−1.18244	−0.0896408
$175$	−0.607188	−0.0458991
$176$	0	0
$177$	−0.357926	−0.0269034
$178$	3.05433	0.228932
$179$	−6.48604	−0.484789	−0.242395	−	0.970178i	$-0.577933\pi$
$179$	−6.48604	−0.484789	−0.242395	+	0.970178i	$0.577933\pi$
$180$	7.43171	0.553927
$181$	3.30359	0.245554	0.122777	−	0.992434i	$-0.460820\pi$
$181$	3.30359	0.245554	0.122777	+	0.992434i	$0.460820\pi$
$182$	−1.77018	−0.131215
$183$	−1.97359	−0.145892
$184$	−8.83700	−0.651473
$185$	−15.2453	−1.12085
$186$	0.633596	0.0464575
$187$	0	0
$188$	−11.4053	−0.831817
$189$	0.752255	0.0547185
$190$	6.10170	0.442664
$191$	−4.83700	−0.349993	−0.174997	−	0.984569i	$-0.555991\pi$
$191$	−4.83700	−0.349993	−0.174997	+	0.984569i	$0.555991\pi$
$192$	2.50548	0.180818
$193$	−8.44018	−0.607538	−0.303769	−	0.952746i	$-0.598245\pi$
$193$	−8.44018	−0.607538	−0.303769	+	0.952746i	$0.598245\pi$
$194$	−4.33848	−0.311485
$195$	−4.58078	−0.328037
$196$	6.87189	0.490849
$197$	−8.56829	−0.610466	−0.305233	−	0.952278i	$-0.598734\pi$
$197$	−8.56829	−0.610466	−0.305233	+	0.952278i	$0.598734\pi$
$198$	0	0
$199$	5.99304	0.424835	0.212418	−	0.977179i	$-0.431866\pi$
$199$	5.99304	0.424835	0.212418	+	0.977179i	$0.431866\pi$
$200$	5.08922	0.359862
$201$	−0.919260	−0.0648396
$202$	7.17548	0.504865
$203$	−1.18244	−0.0829913
$204$	0.357926	0.0250599
$205$	23.6935	1.65482
$206$	−3.66152	−0.255110
$207$	8.45963	0.587985
$208$	4.94567	0.342920
$209$	0	0
$210$	0.331519	0.0228770
$211$	19.8260	1.36488	0.682440	−	0.730941i	$-0.260919\pi$
$211$	19.8260	1.36488	0.682440	+	0.730941i	$0.260919\pi$
$212$	5.41226	0.371715
$213$	−2.40378	−0.164704
$214$	−4.35793	−0.297902
$215$	−16.1212	−1.09945
$216$	−6.30511	−0.429008
$217$	0.633596	0.0430113
$218$	5.17548	0.350528
$219$	−0.256223	−0.0173139
$220$	0	0
$221$	4.94567	0.332682
$222$	2.10866	0.141524
$223$	12.4596	0.834359	0.417179	−	0.908824i	$-0.363019\pi$
$223$	12.4596	0.834359	0.417179	+	0.908824i	$0.363019\pi$
$224$	1.78963	0.119575
$225$	−4.87189	−0.324793
$226$	8.37737	0.557255
$227$	−9.85244	−0.653930	−0.326965	−	0.945037i	$-0.606026\pi$
$227$	−9.85244	−0.653930	−0.326965	+	0.945037i	$0.606026\pi$
$228$	0.843964	0.0558929
$229$	21.3230	1.40907	0.704533	−	0.709671i	$-0.251156\pi$
$229$	21.3230	1.40907	0.704533	+	0.709671i	$0.251156\pi$
$230$	7.62263	0.502621
$231$	0	0
$232$	9.91078	0.650675
$233$	−10.3510	−0.678114	−0.339057	−	0.940766i	$-0.610108\pi$
$233$	−10.3510	−0.678114	−0.339057	+	0.940766i	$0.610108\pi$
$234$	−14.2034	−0.928506
$235$	29.5140	1.92528
$236$	1.00000	0.0650945
$237$	−5.00848	−0.325336
$238$	−0.357926	−0.0232009
$239$	15.4945	1.00226	0.501128	−	0.865373i	$-0.332918\pi$
$239$	15.4945	1.00226	0.501128	+	0.865373i	$0.332918\pi$
$240$	−0.926221	−0.0597873
$241$	−5.61567	−0.361737	−0.180868	−	0.983507i	$-0.557891\pi$
$241$	−5.61567	−0.361737	−0.180868	+	0.983507i	$0.557891\pi$
$242$	11.0000	0.707107
$243$	9.11963	0.585025
$244$	5.51396	0.352995
$245$	−17.7827	−1.13609
$246$	−3.27719	−0.208946
$247$	11.6615	0.742005
$248$	−5.31055	−0.337221
$249$	−3.02792	−0.191887
$250$	8.54885	0.540677
$251$	17.1685	1.08367	0.541834	−	0.840486i	$-0.317730\pi$
$251$	17.1685	1.08367	0.541834	+	0.840486i	$0.317730\pi$
$252$	−1.02792	−0.0647532
$253$	0	0
$254$	−6.10170	−0.382855
$255$	−0.926221	−0.0580022
$256$	−17.0000	−1.06250
$257$	−11.2647	−0.702673	−0.351336	−	0.936249i	$-0.614273\pi$
$257$	−11.2647	−0.702673	−0.351336	+	0.936249i	$0.614273\pi$
$258$	2.22982	0.138822
$259$	2.10866	0.131026
$260$	12.7981	0.793705
$261$	−9.48755	−0.587265
$262$	3.74378	0.231291
$263$	8.92622	0.550414	0.275207	−	0.961385i	$-0.411254\pi$
$263$	8.92622	0.550414	0.275207	+	0.961385i	$0.411254\pi$
$264$	0	0
$265$	−14.0055	−0.860353
$266$	−0.843964	−0.0517468
$267$	−1.09323	−0.0669043
$268$	2.56829	0.156884
$269$	−16.7159	−1.01918	−0.509592	−	0.860416i	$-0.670204\pi$
$269$	−16.7159	−1.01918	−0.509592	+	0.860416i	$0.670204\pi$
$270$	5.43867	0.330987
$271$	17.6421	1.07168	0.535840	−	0.844320i	$-0.319995\pi$
$271$	17.6421	1.07168	0.535840	+	0.844320i	$0.319995\pi$
$272$	1.00000	0.0606339
$273$	0.633596	0.0383470
$274$	−10.5877	−0.639629
$275$	0	0
$276$	1.05433	0.0634633
$277$	−8.44018	−0.507121	−0.253561	−	0.967319i	$-0.581602\pi$
$277$	−8.44018	−0.507121	−0.253561	+	0.967319i	$0.581602\pi$
$278$	−4.14756	−0.248754
$279$	5.08377	0.304358
$280$	−2.77866	−0.166057
$281$	23.9666	1.42973	0.714865	−	0.699263i	$-0.246488\pi$
$281$	23.9666	1.42973	0.714865	+	0.699263i	$0.246488\pi$
$282$	−4.08226	−0.243095
$283$	13.2966	0.790403	0.395201	−	0.918594i	$-0.370675\pi$
$283$	13.2966	0.790403	0.395201	+	0.918594i	$0.370675\pi$
$284$	6.71585	0.398513
$285$	−2.18396	−0.129367
$286$	0	0
$287$	−3.27719	−0.193446
$288$	14.3594	0.846138
$289$	1.00000	0.0588235
$290$	−8.54885	−0.502006
$291$	1.55286	0.0910300
$292$	0.715853	0.0418921
$293$	−17.9108	−1.04636	−0.523180	−	0.852222i	$-0.675254\pi$
$293$	−17.9108	−1.04636	−0.523180	+	0.852222i	$0.675254\pi$
$294$	2.45963	0.143449
$295$	−2.58774	−0.150664
$296$	−17.6740	−1.02728
$297$	0	0
$298$	−3.09323	−0.179186
$299$	14.5683	0.842506
$300$	−0.607188	−0.0350560
$301$	2.22982	0.128524
$302$	−20.4596	−1.17732
$303$	−2.56829	−0.147545
$304$	2.35793	0.135236
$305$	−14.2687	−0.817024
$306$	−2.87189	−0.164175
$307$	23.0599	1.31610	0.658048	−	0.752976i	$-0.271382\pi$
$307$	23.0599	1.31610	0.658048	+	0.752976i	$0.271382\pi$
$308$	0	0
$309$	1.31055	0.0745549
$310$	4.58078	0.260171
$311$	11.6421	0.660161	0.330081	−	0.943953i	$-0.392924\pi$
$311$	11.6421	0.660161	0.330081	+	0.943953i	$0.392924\pi$
$312$	−5.31055	−0.300651
$313$	−20.8370	−1.17778	−0.588889	−	0.808214i	$-0.700434\pi$
$313$	−20.8370	−1.17778	−0.588889	+	0.808214i	$0.700434\pi$
$314$	−0.229815	−0.0129692
$315$	2.66000	0.149874
$316$	13.9930	0.787170
$317$	15.4317	0.866731	0.433365	−	0.901218i	$-0.357326\pi$
$317$	15.4317	0.866731	0.433365	+	0.901218i	$0.357326\pi$
$318$	1.93719	0.108632
$319$	0	0
$320$	18.1142	1.01261
$321$	1.55982	0.0870605
$322$	−1.05433	−0.0587556
$323$	2.35793	0.131199
$324$	−7.86341	−0.436856
$325$	−8.38986	−0.465386
$326$	−2.71585	−0.150417
$327$	−1.85244	−0.102440
$328$	27.4681	1.51667
$329$	−4.08226	−0.225062
$330$	0	0
$331$	−12.7089	−0.698544	−0.349272	−	0.937021i	$-0.613571\pi$
$331$	−12.7089	−0.698544	−0.349272	+	0.937021i	$0.613571\pi$
$332$	8.45963	0.464283
$333$	16.9193	0.927170
$334$	−1.53341	−0.0839044
$335$	−6.64608	−0.363114
$336$	0.128111	0.00698904
$337$	−14.3121	−0.779628	−0.389814	−	0.920894i	$-0.627461\pi$
$337$	−14.3121	−0.779628	−0.389814	+	0.920894i	$0.627461\pi$
$338$	−11.4596	−0.623322
$339$	−2.99848	−0.162855
$340$	2.58774	0.140340
$341$	0	0
$342$	−6.77170	−0.366172
$343$	4.96511	0.268091
$344$	−18.6894	−1.00767
$345$	−2.72834	−0.146889
$346$	−2.68945	−0.144585
$347$	34.8106	1.86873	0.934365	−	0.356316i	$-0.115967\pi$
$347$	34.8106	1.86873	0.934365	+	0.356316i	$0.115967\pi$
$348$	−1.18244	−0.0633856
$349$	10.9193	0.584495	0.292247	−	0.956343i	$-0.405597\pi$
$349$	10.9193	0.584495	0.292247	+	0.956343i	$0.405597\pi$
$350$	0.607188	0.0324556
$351$	10.3943	0.554808
$352$	0	0
$353$	12.7717	0.679769	0.339885	−	0.940467i	$-0.389612\pi$
$353$	12.7717	0.679769	0.339885	+	0.940467i	$0.389612\pi$
$354$	0.357926	0.0190236
$355$	−17.3789	−0.922376
$356$	3.05433	0.161879
$357$	0.128111	0.00678037
$358$	6.48604	0.342798
$359$	−10.0628	−0.531095	−0.265547	−	0.964098i	$-0.585553\pi$
$359$	−10.0628	−0.531095	−0.265547	+	0.964098i	$0.585553\pi$
$360$	−22.2951	−1.17506
$361$	−13.4402	−0.707378
$362$	−3.30359	−0.173633
$363$	−3.93719	−0.206649
$364$	−1.77018	−0.0927829
$365$	−1.85244	−0.0969612
$366$	1.97359	0.103161
$367$	−11.3230	−0.591058	−0.295529	−	0.955334i	$-0.595496\pi$
$367$	−11.3230	−0.591058	−0.295529	+	0.955334i	$0.595496\pi$
$368$	2.94567	0.153554
$369$	−26.2951	−1.36887
$370$	15.2453	0.792563
$371$	1.93719	0.100574
$372$	0.633596	0.0328504
$373$	−31.3789	−1.62474	−0.812369	−	0.583144i	$-0.801822\pi$
$373$	−31.3789	−1.62474	−0.812369	+	0.583144i	$0.801822\pi$
$374$	0	0
$375$	−3.05986	−0.158010
$376$	34.2159	1.76455
$377$	−16.3385	−0.841475
$378$	−0.752255	−0.0386918
$379$	19.1296	0.982623	0.491312	−	0.870984i	$-0.336518\pi$
$379$	19.1296	0.982623	0.491312	+	0.870984i	$0.336518\pi$
$380$	6.10170	0.313011
$381$	2.18396	0.111888
$382$	4.83700	0.247483
$383$	4.75475	0.242956	0.121478	−	0.992594i	$-0.461237\pi$
$383$	4.75475	0.242956	0.121478	+	0.992594i	$0.461237\pi$
$384$	1.07378	0.0547961
$385$	0	0
$386$	8.44018	0.429594
$387$	17.8913	0.909468
$388$	−4.33848	−0.220253
$389$	−26.0000	−1.31825	−0.659126	−	0.752032i	$-0.729074\pi$
$389$	−26.0000	−1.31825	−0.659126	+	0.752032i	$0.729074\pi$
$390$	4.58078	0.231957
$391$	2.94567	0.148969
$392$	−20.6157	−1.04125
$393$	−1.34000	−0.0675939
$394$	8.56829	0.431664
$395$	−36.2104	−1.82194
$396$	0	0
$397$	−16.5947	−0.832864	−0.416432	−	0.909167i	$-0.636720\pi$
$397$	−16.5947	−0.832864	−0.416432	+	0.909167i	$0.636720\pi$
$398$	−5.99304	−0.300404
$399$	0.302077	0.0151228
$400$	−1.69641	−0.0848203
$401$	32.5808	1.62701	0.813503	−	0.581560i	$-0.197558\pi$
$401$	32.5808	1.62701	0.813503	+	0.581560i	$0.197558\pi$
$402$	0.919260	0.0458485
$403$	8.75475	0.436105
$404$	7.17548	0.356994
$405$	20.3485	1.01112
$406$	1.18244	0.0586837
$407$	0	0
$408$	−1.07378	−0.0531600
$409$	8.94567	0.442335	0.221167	−	0.975236i	$-0.429013\pi$
$409$	8.94567	0.442335	0.221167	+	0.975236i	$0.429013\pi$
$410$	−23.6935	−1.17014
$411$	3.78963	0.186929
$412$	−3.66152	−0.180390
$413$	0.357926	0.0176124
$414$	−8.45963	−0.415768
$415$	−21.8913	−1.07460
$416$	24.7283	1.21241
$417$	1.48452	0.0726973
$418$	0	0
$419$	−11.2019	−0.547248	−0.273624	−	0.961837i	$-0.588222\pi$
$419$	−11.2019	−0.547248	−0.273624	+	0.961837i	$0.588222\pi$
$420$	0.331519	0.0161765
$421$	30.8370	1.50290	0.751452	−	0.659788i	$-0.229354\pi$
$421$	30.8370	1.50290	0.751452	+	0.659788i	$0.229354\pi$
$422$	−19.8260	−0.965116
$423$	−32.7547	−1.59259
$424$	−16.2368	−0.788528
$425$	−1.69641	−0.0822878
$426$	2.40378	0.116464
$427$	1.97359	0.0955088
$428$	−4.35793	−0.210648
$429$	0	0
$430$	16.1212	0.777431
$431$	−32.2423	−1.55306	−0.776529	−	0.630082i	$-0.783021\pi$
$431$	−32.2423	−1.55306	−0.776529	+	0.630082i	$0.783021\pi$
$432$	2.10170	0.101118
$433$	−22.7911	−1.09527	−0.547636	−	0.836716i	$-0.684472\pi$
$433$	−22.7911	−1.09527	−0.547636	+	0.836716i	$0.684472\pi$
$434$	−0.633596	−0.0304136
$435$	3.05986	0.146709
$436$	5.17548	0.247861
$437$	6.94567	0.332256
$438$	0.256223	0.0122428
$439$	15.1755	0.724286	0.362143	−	0.932122i	$-0.382045\pi$
$439$	15.1755	0.724286	0.362143	+	0.932122i	$0.382045\pi$
$440$	0	0
$441$	19.7353	0.939776
$442$	−4.94567	−0.235241
$443$	−36.3635	−1.72768	−0.863840	−	0.503766i	$-0.831947\pi$
$443$	−36.3635	−1.72768	−0.863840	+	0.503766i	$0.831947\pi$
$444$	2.10866	0.100073
$445$	−7.90382	−0.374677
$446$	−12.4596	−0.589981
$447$	1.10715	0.0523663
$448$	−2.50548	−0.118373
$449$	−40.6436	−1.91809	−0.959045	−	0.283254i	$-0.908586\pi$
$449$	−40.6436	−1.91809	−0.959045	+	0.283254i	$0.908586\pi$
$450$	4.87189	0.229663
$451$	0	0
$452$	8.37737	0.394038
$453$	7.32304	0.344066
$454$	9.85244	0.462398
$455$	4.58078	0.214750
$456$	−2.53189	−0.118567
$457$	−18.2034	−0.851519	−0.425760	−	0.904836i	$-0.639993\pi$
$457$	−18.2034	−0.851519	−0.425760	+	0.904836i	$0.639993\pi$
$458$	−21.3230	−0.996360
$459$	2.10170	0.0980991
$460$	7.62263	0.355407
$461$	39.8385	1.85546	0.927732	−	0.373246i	$-0.121755\pi$
$461$	39.8385	1.85546	0.927732	+	0.373246i	$0.121755\pi$
$462$	0	0
$463$	−17.2966	−0.803843	−0.401921	−	0.915674i	$-0.631657\pi$
$463$	−17.2966	−0.803843	−0.401921	+	0.915674i	$0.631657\pi$
$464$	−3.30359	−0.153366
$465$	−1.63958	−0.0760338
$466$	10.3510	0.479499
$467$	13.8524	0.641015	0.320507	−	0.947246i	$-0.396147\pi$
$467$	13.8524	0.641015	0.320507	+	0.947246i	$0.396147\pi$
$468$	−14.2034	−0.656553
$469$	0.919260	0.0424475
$470$	−29.5140	−1.36138
$471$	0.0822569	0.00379020
$472$	−3.00000	−0.138086
$473$	0	0
$474$	5.00848	0.230047
$475$	−4.00000	−0.183533
$476$	−0.357926	−0.0164055
$477$	15.5434	0.711684
$478$	−15.4945	−0.708703
$479$	24.6072	1.12433	0.562166	−	0.827025i	$-0.309968\pi$
$479$	24.6072	1.12433	0.562166	+	0.827025i	$0.309968\pi$
$480$	−4.63110	−0.211380
$481$	29.1366	1.32851
$482$	5.61567	0.255787
$483$	0.377373	0.0171711
$484$	11.0000	0.500000
$485$	11.2269	0.509786
$486$	−9.11963	−0.413675
$487$	−10.2493	−0.464438	−0.232219	−	0.972663i	$-0.574599\pi$
$487$	−10.2493	−0.464438	−0.232219	+	0.972663i	$0.574599\pi$
$488$	−16.5419	−0.748816
$489$	0.972075	0.0439588
$490$	17.7827	0.803339
$491$	2.14060	0.0966038	0.0483019	−	0.998833i	$-0.484619\pi$
$491$	2.14060	0.0966038	0.0483019	+	0.998833i	$0.484619\pi$
$492$	−3.27719	−0.147747
$493$	−3.30359	−0.148786
$494$	−11.6615	−0.524677
$495$	0	0
$496$	1.77018	0.0794836
$497$	2.40378	0.107824
$498$	3.02792	0.135685
$499$	−32.2662	−1.44443	−0.722217	−	0.691666i	$-0.756877\pi$
$499$	−32.2662	−1.44443	−0.722217	+	0.691666i	$0.756877\pi$
$500$	8.54885	0.382316
$501$	0.548848	0.0245207
$502$	−17.1685	−0.766269
$503$	−31.0279	−1.38347	−0.691733	−	0.722153i	$-0.743153\pi$
$503$	−31.0279	−1.38347	−0.691733	+	0.722153i	$0.743153\pi$
$504$	3.08377	0.137362
$505$	−18.5683	−0.826278
$506$	0	0
$507$	4.10170	0.182163
$508$	−6.10170	−0.270719
$509$	−12.2298	−0.542077	−0.271039	−	0.962569i	$-0.587367\pi$
$509$	−12.2298	−0.542077	−0.271039	+	0.962569i	$0.587367\pi$
$510$	0.926221	0.0410138
$511$	0.256223	0.0113346
$512$	11.0000	0.486136
$513$	4.95566	0.218798
$514$	11.2647	0.496865
$515$	9.47507	0.417521
$516$	2.22982	0.0981621
$517$	0	0
$518$	−2.10866	−0.0926494
$519$	0.962623	0.0422545
$520$	−38.3943	−1.68370
$521$	2.91926	0.127895	0.0639476	−	0.997953i	$-0.479631\pi$
$521$	2.91926	0.127895	0.0639476	+	0.997953i	$0.479631\pi$
$522$	9.48755	0.415259
$523$	14.0628	0.614924	0.307462	−	0.951560i	$-0.400520\pi$
$523$	14.0628	0.614924	0.307462	+	0.951560i	$0.400520\pi$
$524$	3.74378	0.163548
$525$	−0.217329	−0.00948500
$526$	−8.92622	−0.389202
$527$	1.77018	0.0771105
$528$	0	0
$529$	−14.3230	−0.622741
$530$	14.0055	0.608361
$531$	2.87189	0.124629
$532$	−0.843964	−0.0365905
$533$	−45.2827	−1.96141
$534$	1.09323	0.0473085
$535$	11.2772	0.487555
$536$	−7.70488	−0.332800
$537$	−2.32152	−0.100181
$538$	16.7159	0.720672
$539$	0	0
$540$	5.43867	0.234043
$541$	−14.9457	−0.642564	−0.321282	−	0.946983i	$-0.604114\pi$
$541$	−14.9457	−0.642564	−0.321282	+	0.946983i	$0.604114\pi$
$542$	−17.6421	−0.757792
$543$	1.18244	0.0507435
$544$	5.00000	0.214373
$545$	−13.3928	−0.573685
$546$	−0.633596	−0.0271154
$547$	4.09474	0.175079	0.0875393	−	0.996161i	$-0.472100\pi$
$547$	4.09474	0.175079	0.0875393	+	0.996161i	$0.472100\pi$
$548$	−10.5877	−0.452286
$549$	15.8355	0.675842
$550$	0	0
$551$	−7.78963	−0.331849
$552$	−3.16300	−0.134626
$553$	5.00848	0.212982
$554$	8.44018	0.358589
$555$	−5.45668	−0.231623
$556$	−4.14756	−0.175896
$557$	16.4791	0.698241	0.349120	−	0.937078i	$-0.386480\pi$
$557$	16.4791	0.698241	0.349120	+	0.937078i	$0.386480\pi$
$558$	−5.08377	−0.215213
$559$	30.8106	1.30315
$560$	0.926221	0.0391400
$561$	0	0
$562$	−23.9666	−1.01097
$563$	13.1755	0.555280	0.277640	−	0.960685i	$-0.410448\pi$
$563$	13.1755	0.555280	0.277640	+	0.960685i	$0.410448\pi$
$564$	−4.08226	−0.171894
$565$	−21.6785	−0.912020
$566$	−13.2966	−0.558899
$567$	−2.81452	−0.118199
$568$	−20.1476	−0.845373
$569$	11.3789	0.477028	0.238514	−	0.971139i	$-0.423340\pi$
$569$	11.3789	0.477028	0.238514	+	0.971139i	$0.423340\pi$
$570$	2.18396	0.0914760
$571$	−44.4846	−1.86162	−0.930811	−	0.365500i	$-0.880898\pi$
$571$	−44.4846	−1.86162	−0.930811	+	0.365500i	$0.880898\pi$
$572$	0	0
$573$	−1.73129	−0.0723257
$574$	3.27719	0.136787
$575$	−4.99705	−0.208391
$576$	−20.1032	−0.837634
$577$	−13.1560	−0.547693	−0.273846	−	0.961773i	$-0.588296\pi$
$577$	−13.1560	−0.547693	−0.273846	+	0.961773i	$0.588296\pi$
$578$	−1.00000	−0.0415945
$579$	−3.02096	−0.125547
$580$	−8.54885	−0.354972
$581$	3.02792	0.125619
$582$	−1.55286	−0.0643680
$583$	0	0
$584$	−2.14756	−0.0888666
$585$	36.7547	1.51962
$586$	17.9108	0.739888
$587$	−10.5249	−0.434410	−0.217205	−	0.976126i	$-0.569694\pi$
$587$	−10.5249	−0.434410	−0.217205	+	0.976126i	$0.569694\pi$
$588$	2.45963	0.101433
$589$	4.17397	0.171985
$590$	2.58774	0.106536
$591$	−3.06682	−0.126152
$592$	5.89134	0.242132
$593$	−11.5598	−0.474705	−0.237352	−	0.971424i	$-0.576280\pi$
$593$	−11.5598	−0.474705	−0.237352	+	0.971424i	$0.576280\pi$
$594$	0	0
$595$	0.926221	0.0379714
$596$	−3.09323	−0.126703
$597$	2.14507	0.0877917
$598$	−14.5683	−0.595742
$599$	27.5334	1.12498	0.562492	−	0.826803i	$-0.309843\pi$
$599$	27.5334	1.12498	0.562492	+	0.826803i	$0.309843\pi$
$600$	1.82157	0.0743651
$601$	−17.6740	−0.720938	−0.360469	−	0.932771i	$-0.617383\pi$
$601$	−17.6740	−0.720938	−0.360469	+	0.932771i	$0.617383\pi$
$602$	−2.22982	−0.0908805
$603$	7.37586	0.300368
$604$	−20.4596	−0.832491
$605$	−28.4652	−1.15727
$606$	2.56829	0.104330
$607$	−31.8455	−1.29257	−0.646284	−	0.763097i	$-0.723678\pi$
$607$	−31.8455	−1.29257	−0.646284	+	0.763097i	$0.723678\pi$
$608$	11.7896	0.478133
$609$	−0.423228	−0.0171501
$610$	14.2687	0.577723
$611$	−56.4068	−2.28198
$612$	−2.87189	−0.116089
$613$	−22.8370	−0.922378	−0.461189	−	0.887302i	$-0.652577\pi$
$613$	−22.8370	−0.922378	−0.461189	+	0.887302i	$0.652577\pi$
$614$	−23.0599	−0.930620
$615$	8.48051	0.341967
$616$	0	0
$617$	27.9806	1.12645	0.563227	−	0.826302i	$-0.309560\pi$
$617$	27.9806	1.12645	0.563227	+	0.826302i	$0.309560\pi$
$618$	−1.31055	−0.0527182
$619$	36.1795	1.45418	0.727088	−	0.686544i	$-0.240873\pi$
$619$	36.1795	1.45418	0.727088	+	0.686544i	$0.240873\pi$
$620$	4.58078	0.183969
$621$	6.19092	0.248433
$622$	−11.6421	−0.466805
$623$	1.09323	0.0437992
$624$	1.77018	0.0708641
$625$	−30.6042	−1.22417
$626$	20.8370	0.832814
$627$	0	0
$628$	−0.229815	−0.00917062
$629$	5.89134	0.234903
$630$	−2.66000	−0.105977
$631$	17.2144	0.685294	0.342647	−	0.939464i	$-0.388677\pi$
$631$	17.2144	0.685294	0.342647	+	0.939464i	$0.388677\pi$
$632$	−41.9791	−1.66984
$633$	7.09626	0.282051
$634$	−15.4317	−0.612871
$635$	15.7896	0.626592
$636$	1.93719	0.0768146
$637$	33.9861	1.34658
$638$	0	0
$639$	19.2872	0.762989
$640$	7.76322	0.306868
$641$	2.97208	0.117390	0.0586950	−	0.998276i	$-0.481306\pi$
$641$	2.97208	0.117390	0.0586950	+	0.998276i	$0.481306\pi$
$642$	−1.55982	−0.0615611
$643$	29.9541	1.18128	0.590638	−	0.806937i	$-0.298876\pi$
$643$	29.9541	1.18128	0.590638	+	0.806937i	$0.298876\pi$
$644$	−1.05433	−0.0415465
$645$	−5.77018	−0.227201
$646$	−2.35793	−0.0927714
$647$	−36.4527	−1.43310	−0.716551	−	0.697535i	$-0.754280\pi$
$647$	−36.4527	−1.43310	−0.716551	+	0.697535i	$0.754280\pi$
$648$	23.5902	0.926712
$649$	0	0
$650$	8.38986	0.329077
$651$	0.226781	0.00888823
$652$	−2.71585	−0.106361
$653$	−31.0085	−1.21346	−0.606728	−	0.794910i	$-0.707518\pi$
$653$	−31.0085	−1.21346	−0.606728	+	0.794910i	$0.707518\pi$
$654$	1.85244	0.0724362
$655$	−9.68793	−0.378539
$656$	−9.15604	−0.357483
$657$	2.05585	0.0802063
$658$	4.08226	0.159143
$659$	−30.5933	−1.19174	−0.595872	−	0.803079i	$-0.703194\pi$
$659$	−30.5933	−1.19174	−0.595872	+	0.803079i	$0.703194\pi$
$660$	0	0
$661$	10.8300	0.421240	0.210620	−	0.977568i	$-0.432452\pi$
$661$	10.8300	0.421240	0.210620	+	0.977568i	$0.432452\pi$
$662$	12.7089	0.493945
$663$	1.77018	0.0687483
$664$	−25.3789	−0.984892
$665$	2.18396	0.0846904
$666$	−16.9193	−0.655608
$667$	−9.73129	−0.376797
$668$	−1.53341	−0.0593294
$669$	4.45963	0.172419
$670$	6.64608	0.256761
$671$	0	0
$672$	0.640556	0.0247100
$673$	18.0125	0.694330	0.347165	−	0.937804i	$-0.387144\pi$
$673$	18.0125	0.694330	0.347165	+	0.937804i	$0.387144\pi$
$674$	14.3121	0.551280
$675$	−3.56534	−0.137230
$676$	−11.4596	−0.440755
$677$	−33.3230	−1.28071	−0.640354	−	0.768080i	$-0.721212\pi$
$677$	−33.3230	−1.28071	−0.640354	+	0.768080i	$0.721212\pi$
$678$	2.99848	0.115156
$679$	−1.55286	−0.0595932
$680$	−7.76322	−0.297706
$681$	−3.52645	−0.135134
$682$	0	0
$683$	−4.58078	−0.175279	−0.0876394	−	0.996152i	$-0.527932\pi$
$683$	−4.58078	−0.175279	−0.0876394	+	0.996152i	$0.527932\pi$
$684$	−6.77170	−0.258923
$685$	27.3983	1.04684
$686$	−4.96511	−0.189569
$687$	7.63208	0.291182
$688$	6.22982	0.237509
$689$	26.7672	1.01975
$690$	2.72834	0.103866
$691$	−11.7004	−0.445105	−0.222552	−	0.974921i	$-0.571439\pi$
$691$	−11.7004	−0.445105	−0.222552	+	0.974921i	$0.571439\pi$
$692$	−2.68945	−0.102237
$693$	0	0
$694$	−34.8106	−1.32139
$695$	10.7328	0.407119
$696$	3.54733	0.134461
$697$	−9.15604	−0.346810
$698$	−10.9193	−0.413300
$699$	−3.70488	−0.140132
$700$	0.607188	0.0229496
$701$	−9.91774	−0.374588	−0.187294	−	0.982304i	$-0.559972\pi$
$701$	−9.91774	−0.374588	−0.187294	+	0.982304i	$0.559972\pi$
$702$	−10.3943	−0.392309
$703$	13.8913	0.523922
$704$	0	0
$705$	10.5638	0.397857
$706$	−12.7717	−0.480669
$707$	2.56829	0.0965907
$708$	0.357926	0.0134517
$709$	49.1949	1.84755	0.923777	−	0.382930i	$-0.125085\pi$
$709$	49.1949	1.84755	0.923777	+	0.382930i	$0.125085\pi$
$710$	17.3789	0.652218
$711$	40.1865	1.50711
$712$	−9.16300	−0.343398
$713$	5.21438	0.195280
$714$	−0.128111	−0.00479444
$715$	0	0
$716$	6.48604	0.242395
$717$	5.54590	0.207115
$718$	10.0628	0.375541
$719$	−30.9317	−1.15356	−0.576780	−	0.816900i	$-0.695691\pi$
$719$	−30.9317	−1.15356	−0.576780	+	0.816900i	$0.695691\pi$
$720$	7.43171	0.276963
$721$	−1.31055	−0.0488076
$722$	13.4402	0.500192
$723$	−2.00999	−0.0747525
$724$	−3.30359	−0.122777
$725$	5.60424	0.208136
$726$	3.93719	0.146123
$727$	17.1366	0.635561	0.317780	−	0.948164i	$-0.397063\pi$
$727$	17.1366	0.635561	0.317780	+	0.948164i	$0.397063\pi$
$728$	5.31055	0.196822
$729$	−20.3261	−0.752818
$730$	1.85244	0.0685619
$731$	6.22982	0.230418
$732$	1.97359	0.0729461
$733$	41.0529	1.51632	0.758162	−	0.652067i	$-0.226098\pi$
$733$	41.0529	1.51632	0.758162	+	0.652067i	$0.226098\pi$
$734$	11.3230	0.417941
$735$	−6.36489	−0.234772
$736$	14.7283	0.542894
$737$	0	0
$738$	26.2951	0.967937
$739$	−22.9846	−0.845501	−0.422750	−	0.906246i	$-0.638935\pi$
$739$	−22.9846	−0.845501	−0.422750	+	0.906246i	$0.638935\pi$
$740$	15.2453	0.560427
$741$	4.17397	0.153334
$742$	−1.93719	−0.0711165
$743$	47.3650	1.73765	0.868826	−	0.495117i	$-0.164875\pi$
$743$	47.3650	1.73765	0.868826	+	0.495117i	$0.164875\pi$
$744$	−1.90079	−0.0696863
$745$	8.00447	0.293261
$746$	31.3789	1.14886
$747$	24.2951	0.888912
$748$	0	0
$749$	−1.55982	−0.0569945
$750$	3.05986	0.111730
$751$	24.6630	0.899967	0.449984	−	0.893037i	$-0.351430\pi$
$751$	24.6630	0.899967	0.449984	+	0.893037i	$0.351430\pi$
$752$	−11.4053	−0.415908
$753$	6.14507	0.223939
$754$	16.3385	0.595012
$755$	52.9442	1.92684
$756$	−0.752255	−0.0273593
$757$	−24.0194	−0.873002	−0.436501	−	0.899704i	$-0.643782\pi$
$757$	−24.0194	−0.873002	−0.436501	+	0.899704i	$0.643782\pi$
$758$	−19.1296	−0.694819
$759$	0	0
$760$	−18.3051	−0.663996
$761$	47.0335	1.70496	0.852481	−	0.522759i	$-0.175097\pi$
$761$	47.0335	1.70496	0.852481	+	0.522759i	$0.175097\pi$
$762$	−2.18396	−0.0791165
$763$	1.85244	0.0670629
$764$	4.83700	0.174997
$765$	7.43171	0.268694
$766$	−4.75475	−0.171796
$767$	4.94567	0.178578
$768$	−6.08475	−0.219564
$769$	47.9597	1.72947	0.864735	−	0.502228i	$-0.167486\pi$
$769$	47.9597	1.72947	0.864735	+	0.502228i	$0.167486\pi$
$770$	0	0
$771$	−4.03193	−0.145207
$772$	8.44018	0.303769
$773$	11.1366	0.400555	0.200278	−	0.979739i	$-0.435816\pi$
$773$	11.1366	0.400555	0.200278	+	0.979739i	$0.435816\pi$
$774$	−17.8913	−0.643091
$775$	−3.00295	−0.107869
$776$	13.0154	0.467227
$777$	0.754747	0.0270764
$778$	26.0000	0.932145
$779$	−21.5893	−0.773515
$780$	4.58078	0.164018
$781$	0	0
$782$	−2.94567	−0.105337
$783$	−6.94318	−0.248129
$784$	6.87189	0.245425
$785$	0.594702	0.0212258
$786$	1.34000	0.0477961
$787$	12.0947	0.431131	0.215566	−	0.976489i	$-0.430841\pi$
$787$	12.0947	0.431131	0.215566	+	0.976489i	$0.430841\pi$
$788$	8.56829	0.305233
$789$	3.19493	0.113743
$790$	36.2104	1.28831
$791$	2.99848	0.106614
$792$	0	0
$793$	27.2702	0.968394
$794$	16.5947	0.588924
$795$	−5.01295	−0.177791
$796$	−5.99304	−0.212418
$797$	−7.80908	−0.276612	−0.138306	−	0.990390i	$-0.544166\pi$
$797$	−7.80908	−0.276612	−0.138306	+	0.990390i	$0.544166\pi$
$798$	−0.302077	−0.0106934
$799$	−11.4053	−0.403490
$800$	−8.48203	−0.299885
$801$	8.77170	0.309933
$802$	−32.5808	−1.15047
$803$	0	0
$804$	0.919260	0.0324198
$805$	2.72834	0.0961613
$806$	−8.75475	−0.308373
$807$	−5.98304	−0.210613
$808$	−21.5264	−0.757298
$809$	34.7717	1.22251	0.611254	−	0.791435i	$-0.290665\pi$
$809$	34.7717	1.22251	0.611254	+	0.791435i	$0.290665\pi$
$810$	−20.3485	−0.714973
$811$	25.4317	0.893028	0.446514	−	0.894777i	$-0.352665\pi$
$811$	25.4317	0.893028	0.446514	+	0.894777i	$0.352665\pi$
$812$	1.18244	0.0414956
$813$	6.31456	0.221461
$814$	0	0
$815$	7.02792	0.246177
$816$	0.357926	0.0125299
$817$	14.6894	0.513919
$818$	−8.94567	−0.312778
$819$	−5.08377	−0.177641
$820$	−23.6935	−0.827411
$821$	13.3928	0.467412	0.233706	−	0.972307i	$-0.424915\pi$
$821$	13.3928	0.467412	0.233706	+	0.972307i	$0.424915\pi$
$822$	−3.78963	−0.132179
$823$	49.0265	1.70896	0.854478	−	0.519488i	$-0.173877\pi$
$823$	49.0265	1.70896	0.854478	+	0.519488i	$0.173877\pi$
$824$	10.9846	0.382665
$825$	0	0
$826$	−0.357926	−0.0124539
$827$	44.0947	1.53332	0.766662	−	0.642051i	$-0.221916\pi$
$827$	44.0947	1.53332	0.766662	+	0.642051i	$0.221916\pi$
$828$	−8.45963	−0.293992
$829$	−10.5349	−0.365893	−0.182947	−	0.983123i	$-0.558564\pi$
$829$	−10.5349	−0.365893	−0.182947	+	0.983123i	$0.558564\pi$
$830$	21.8913	0.759859
$831$	−3.02096	−0.104796
$832$	−34.6197	−1.20022
$833$	6.87189	0.238097
$834$	−1.48452	−0.0514047
$835$	3.96807	0.137321
$836$	0	0
$837$	3.72040	0.128596
$838$	11.2019	0.386963
$839$	10.3121	0.356012	0.178006	−	0.984029i	$-0.443035\pi$
$839$	10.3121	0.356012	0.178006	+	0.984029i	$0.443035\pi$
$840$	−0.994557	−0.0343155
$841$	−18.0863	−0.623664
$842$	−30.8370	−1.06271
$843$	8.57829	0.295452
$844$	−19.8260	−0.682440
$845$	29.6546	1.02015
$846$	32.7547	1.12613
$847$	3.93719	0.135283
$848$	5.41226	0.185858
$849$	4.75922	0.163336
$850$	1.69641	0.0581862
$851$	17.3539	0.594885
$852$	2.40378	0.0823522
$853$	−14.1281	−0.483737	−0.241869	−	0.970309i	$-0.577760\pi$
$853$	−14.1281	−0.483737	−0.241869	+	0.970309i	$0.577760\pi$
$854$	−1.97359	−0.0675349
$855$	17.5234	0.599288
$856$	13.0738	0.446853
$857$	−38.6755	−1.32113	−0.660565	−	0.750769i	$-0.729683\pi$
$857$	−38.6755	−1.32113	−0.660565	+	0.750769i	$0.729683\pi$
$858$	0	0
$859$	10.2687	0.350364	0.175182	−	0.984536i	$-0.443949\pi$
$859$	10.2687	0.350364	0.175182	+	0.984536i	$0.443949\pi$
$860$	16.1212	0.549727
$861$	−1.17299	−0.0399754
$862$	32.2423	1.09818
$863$	−49.3400	−1.67955	−0.839777	−	0.542932i	$-0.817314\pi$
$863$	−49.3400	−1.67955	−0.839777	+	0.542932i	$0.817314\pi$
$864$	10.5085	0.357507
$865$	6.95959	0.236633
$866$	22.7911	0.774475
$867$	0.357926	0.0121558
$868$	−0.633596	−0.0215056
$869$	0	0
$870$	−3.05986	−0.103739
$871$	12.7019	0.430389
$872$	−15.5264	−0.525792
$873$	−12.4596	−0.421695
$874$	−6.94567	−0.234941
$875$	3.05986	0.103442
$876$	0.256223	0.00865696
$877$	6.84396	0.231104	0.115552	−	0.993301i	$-0.463136\pi$
$877$	6.84396	0.231104	0.115552	+	0.993301i	$0.463136\pi$
$878$	−15.1755	−0.512148
$879$	−6.41074	−0.216229
$880$	0	0
$881$	35.2702	1.18828	0.594142	−	0.804360i	$-0.297492\pi$
$881$	35.2702	1.18828	0.594142	+	0.804360i	$0.297492\pi$
$882$	−19.7353	−0.664522
$883$	−20.2353	−0.680973	−0.340487	−	0.940249i	$-0.610592\pi$
$883$	−20.2353	−0.680973	−0.340487	+	0.940249i	$0.610592\pi$
$884$	−4.94567	−0.166341
$885$	−0.926221	−0.0311346
$886$	36.3635	1.22165
$887$	−0.933181	−0.0313332	−0.0156666	−	0.999877i	$-0.504987\pi$
$887$	−0.933181	−0.0313332	−0.0156666	+	0.999877i	$0.504987\pi$
$888$	−6.32599	−0.212286
$889$	−2.18396	−0.0732477
$890$	7.90382	0.264937
$891$	0	0
$892$	−12.4596	−0.417179
$893$	−26.8929	−0.899935
$894$	−1.10715	−0.0370285
$895$	−16.7842	−0.561034
$896$	−1.07378	−0.0358724
$897$	5.21438	0.174103
$898$	40.6436	1.35629
$899$	−5.84797	−0.195041
$900$	4.87189	0.162396
$901$	5.41226	0.180308
$902$	0	0
$903$	0.798110	0.0265594
$904$	−25.1321	−0.835882
$905$	8.54885	0.284173
$906$	−7.32304	−0.243292
$907$	−55.8316	−1.85386	−0.926928	−	0.375239i	$-0.877561\pi$
$907$	−55.8316	−1.85386	−0.926928	+	0.375239i	$0.877561\pi$
$908$	9.85244	0.326965
$909$	20.6072	0.683497
$910$	−4.58078	−0.151851
$911$	20.8565	0.691005	0.345503	−	0.938418i	$-0.387708\pi$
$911$	20.8565	0.691005	0.345503	+	0.938418i	$0.387708\pi$
$912$	0.843964	0.0279464
$913$	0	0
$914$	18.2034	0.602115
$915$	−5.10715	−0.168837
$916$	−21.3230	−0.704533
$917$	1.34000	0.0442506
$918$	−2.10170	−0.0693666
$919$	24.9193	0.822011	0.411005	−	0.911633i	$-0.365178\pi$
$919$	24.9193	0.822011	0.411005	+	0.911633i	$0.365178\pi$
$920$	−22.8679	−0.753932
$921$	8.25373	0.271970
$922$	−39.8385	−1.31201
$923$	33.2144	1.09326
$924$	0	0
$925$	−9.99410	−0.328604
$926$	17.2966	0.568403
$927$	−10.5155	−0.345374
$928$	−16.5180	−0.542229
$929$	−51.7299	−1.69720	−0.848601	−	0.529034i	$-0.822554\pi$
$929$	−51.7299	−1.69720	−0.848601	+	0.529034i	$0.822554\pi$
$930$	1.63958	0.0537640
$931$	16.2034	0.531045
$932$	10.3510	0.339057
$933$	4.16701	0.136422
$934$	−13.8524	−0.453266
$935$	0	0
$936$	42.6102	1.39276
$937$	−36.8634	−1.20428	−0.602138	−	0.798392i	$-0.705684\pi$
$937$	−36.8634	−1.20428	−0.602138	+	0.798392i	$0.705684\pi$
$938$	−0.919260	−0.0300149
$939$	−7.45811	−0.243386
$940$	−29.5140	−0.962639
$941$	−29.3355	−0.956311	−0.478155	−	0.878275i	$-0.658694\pi$
$941$	−29.3355	−0.956311	−0.478155	+	0.878275i	$0.658694\pi$
$942$	−0.0822569	−0.00268007
$943$	−26.9706	−0.878285
$944$	1.00000	0.0325472
$945$	1.94664	0.0633243
$946$	0	0
$947$	20.5224	0.666890	0.333445	−	0.942770i	$-0.391789\pi$
$947$	20.5224	0.666890	0.333445	+	0.942770i	$0.391789\pi$
$948$	5.00848	0.162668
$949$	3.54037	0.114925
$950$	4.00000	0.129777
$951$	5.52341	0.179109
$952$	1.07378	0.0348014
$953$	−13.9472	−0.451794	−0.225897	−	0.974151i	$-0.572531\pi$
$953$	−13.9472	−0.451794	−0.225897	+	0.974151i	$0.572531\pi$
$954$	−15.5434	−0.503236
$955$	−12.5169	−0.405038
$956$	−15.4945	−0.501128
$957$	0	0
$958$	−24.6072	−0.795022
$959$	−3.78963	−0.122374
$960$	6.48355	0.209256
$961$	−27.8664	−0.898918
$962$	−29.1366	−0.939401
$963$	−12.5155	−0.403306
$964$	5.61567	0.180868
$965$	−21.8410	−0.703087
$966$	−0.377373	−0.0121418
$967$	−11.3619	−0.365375	−0.182688	−	0.983171i	$-0.558480\pi$
$967$	−11.3619	−0.365375	−0.182688	+	0.983171i	$0.558480\pi$
$968$	−33.0000	−1.06066
$969$	0.843964	0.0271120
$970$	−11.2269	−0.360473
$971$	−56.3999	−1.80996	−0.904979	−	0.425457i	$-0.860113\pi$
$971$	−56.3999	−1.80996	−0.904979	+	0.425457i	$0.860113\pi$
$972$	−9.11963	−0.292512
$973$	−1.48452	−0.0475915
$974$	10.2493	0.328408
$975$	−3.00295	−0.0961714
$976$	5.51396	0.176498
$977$	−27.7952	−0.889246	−0.444623	−	0.895718i	$-0.646662\pi$
$977$	−27.7952	−0.889246	−0.444623	+	0.895718i	$0.646662\pi$
$978$	−0.972075	−0.0310835
$979$	0	0
$980$	17.7827	0.568047
$981$	14.8634	0.474552
$982$	−2.14060	−0.0683092
$983$	−29.8524	−0.952145	−0.476073	−	0.879406i	$-0.657940\pi$
$983$	−29.8524	−0.952145	−0.476073	+	0.879406i	$0.657940\pi$
$984$	9.83156	0.313419
$985$	−22.1725	−0.706476
$986$	3.30359	0.105208
$987$	−1.46115	−0.0465088
$988$	−11.6615	−0.371002
$989$	18.3510	0.583527
$990$	0	0
$991$	−61.1616	−1.94286	−0.971431	−	0.237324i	$-0.923730\pi$
$991$	−61.1616	−1.94286	−0.971431	+	0.237324i	$0.923730\pi$
$992$	8.85092	0.281017
$993$	−4.54885	−0.144353
$994$	−2.40378	−0.0762433
$995$	15.5084	0.491650
$996$	3.02792	0.0959435
$997$	10.6266	0.336549	0.168274	−	0.985740i	$-0.446181\pi$
$997$	10.6266	0.336549	0.168274	+	0.985740i	$0.446181\pi$
$998$	32.2662	1.02137
$999$	12.3818	0.391744

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.e.1.2	✓	3
3.2	odd	2		9027.2.a.h.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.e.1.2	✓	3	1.1	even	1	trivial
9027.2.a.h.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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.357926 q^{3} -1.00000 q^{4} +2.58774 q^{5} -0.357926 q^{6} -0.357926 q^{7} +3.00000 q^{8} -2.87189 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.357926 q^{3} -1.00000 q^{4} +2.58774 q^{5} -0.357926 q^{6} -0.357926 q^{7} +3.00000 q^{8} -2.87189 q^{9} -2.58774 q^{10} -0.357926 q^{12} -4.94567 q^{13} +0.357926 q^{14} +0.926221 q^{15} -1.00000 q^{16} -1.00000 q^{17} +2.87189 q^{18} -2.35793 q^{19} -2.58774 q^{20} -0.128111 q^{21} -2.94567 q^{23} +1.07378 q^{24} +1.69641 q^{25} +4.94567 q^{26} -2.10170 q^{27} +0.357926 q^{28} +3.30359 q^{29} -0.926221 q^{30} -1.77018 q^{31} -5.00000 q^{32} +1.00000 q^{34} -0.926221 q^{35} +2.87189 q^{36} -5.89134 q^{37} +2.35793 q^{38} -1.77018 q^{39} +7.76322 q^{40} +9.15604 q^{41} +0.128111 q^{42} -6.22982 q^{43} -7.43171 q^{45} +2.94567 q^{46} +11.4053 q^{47} -0.357926 q^{48} -6.87189 q^{49} -1.69641 q^{50} -0.357926 q^{51} +4.94567 q^{52} -5.41226 q^{53} +2.10170 q^{54} -1.07378 q^{56} -0.843964 q^{57} -3.30359 q^{58} -1.00000 q^{59} -0.926221 q^{60} -5.51396 q^{61} +1.77018 q^{62} +1.02792 q^{63} +7.00000 q^{64} -12.7981 q^{65} -2.56829 q^{67} +1.00000 q^{68} -1.05433 q^{69} +0.926221 q^{70} -6.71585 q^{71} -8.61567 q^{72} -0.715853 q^{73} +5.89134 q^{74} +0.607188 q^{75} +2.35793 q^{76} +1.77018 q^{78} -13.9930 q^{79} -2.58774 q^{80} +7.86341 q^{81} -9.15604 q^{82} -8.45963 q^{83} +0.128111 q^{84} -2.58774 q^{85} +6.22982 q^{86} +1.18244 q^{87} -3.05433 q^{89} +7.43171 q^{90} +1.77018 q^{91} +2.94567 q^{92} -0.633596 q^{93} -11.4053 q^{94} -6.10170 q^{95} -1.78963 q^{96} +4.33848 q^{97} +6.87189 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 9 q^{8} + 5 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 9 * q^8 + 5 * q^9	\( 3 q - 3 q^{2} + 2 q^{3} - 3 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 9 q^{8} + 5 q^{9} + 4 q^{10} - 2 q^{12} - 4 q^{13} + 2 q^{14} - 3 q^{16} - 3 q^{17} - 5 q^{18} - 8 q^{19} + 4 q^{20} - 14 q^{21} + 2 q^{23} + 6 q^{24} + 15 q^{25} + 4 q^{26} + 20 q^{27} + 2 q^{28} - 18 q^{31} - 15 q^{32} + 3 q^{34} - 5 q^{36} + 4 q^{37} + 8 q^{38} - 18 q^{39} - 12 q^{40} + 12 q^{41} + 14 q^{42} - 6 q^{43} - 26 q^{45} - 2 q^{46} - 2 q^{47} - 2 q^{48} - 7 q^{49} - 15 q^{50} - 2 q^{51} + 4 q^{52} - 28 q^{53} - 20 q^{54} - 6 q^{56} - 18 q^{57} - 3 q^{59} - 2 q^{61} + 18 q^{62} - 26 q^{63} + 21 q^{64} - 22 q^{65} - 4 q^{67} + 3 q^{68} - 14 q^{69} - 22 q^{71} + 15 q^{72} - 4 q^{73} - 4 q^{74} - 18 q^{75} + 8 q^{76} + 18 q^{78} + 6 q^{79} + 4 q^{80} + 31 q^{81} - 12 q^{82} + 14 q^{84} + 4 q^{85} + 6 q^{86} + 28 q^{87} - 20 q^{89} + 26 q^{90} + 18 q^{91} - 2 q^{92} - 22 q^{93} + 2 q^{94} + 8 q^{95} - 10 q^{96} + 22 q^{97} + 7 q^{98}+O(q^{100}) \) 3 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 9 * q^8 + 5 * q^9 + 4 * q^10 - 2 * q^12 - 4 * q^13 + 2 * q^14 - 3 * q^16 - 3 * q^17 - 5 * q^18 - 8 * q^19 + 4 * q^20 - 14 * q^21 + 2 * q^23 + 6 * q^24 + 15 * q^25 + 4 * q^26 + 20 * q^27 + 2 * q^28 - 18 * q^31 - 15 * q^32 + 3 * q^34 - 5 * q^36 + 4 * q^37 + 8 * q^38 - 18 * q^39 - 12 * q^40 + 12 * q^41 + 14 * q^42 - 6 * q^43 - 26 * q^45 - 2 * q^46 - 2 * q^47 - 2 * q^48 - 7 * q^49 - 15 * q^50 - 2 * q^51 + 4 * q^52 - 28 * q^53 - 20 * q^54 - 6 * q^56 - 18 * q^57 - 3 * q^59 - 2 * q^61 + 18 * q^62 - 26 * q^63 + 21 * q^64 - 22 * q^65 - 4 * q^67 + 3 * q^68 - 14 * q^69 - 22 * q^71 + 15 * q^72 - 4 * q^73 - 4 * q^74 - 18 * q^75 + 8 * q^76 + 18 * q^78 + 6 * q^79 + 4 * q^80 + 31 * q^81 - 12 * q^82 + 14 * q^84 + 4 * q^85 + 6 * q^86 + 28 * q^87 - 20 * q^89 + 26 * q^90 + 18 * q^91 - 2 * q^92 - 22 * q^93 + 2 * q^94 + 8 * q^95 - 10 * q^96 + 22 * q^97 + 7 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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