LMFDB - Embedded newform 9386.2.a.bp.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9386,2,Mod(1,9386)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9386.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9386, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 9386 = 2 \cdot 13 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9386.a (trivial)

Newform invariants

comment:select newform

sage:traces = [9,9,-3,9,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$74.9475873372$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 12x^{7} + 34x^{6} + 51x^{5} - 123x^{4} - 81x^{3} + 138x^{2} + 15x - 1 $ x^9 - 3x^8 - 12x^7 + 34x^6 + 51x^5 - 123x^4 - 81x^3 + 138x^2 + 15x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 494)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.147896$ of defining polynomial
Character	$\chi$	$=$	9386.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +0.147896 q^{3} +1.00000 q^{4} +1.20058 q^{5} +0.147896 q^{6} -3.26215 q^{7} +1.00000 q^{8} -2.97813 q^{9} +1.20058 q^{10} +1.44577 q^{11} +0.147896 q^{12} +1.00000 q^{13} -3.26215 q^{14} +0.177560 q^{15} +1.00000 q^{16} +7.42399 q^{17} -2.97813 q^{18} +1.20058 q^{20} -0.482457 q^{21} +1.44577 q^{22} -7.20751 q^{23} +0.147896 q^{24} -3.55862 q^{25} +1.00000 q^{26} -0.884138 q^{27} -3.26215 q^{28} -5.59186 q^{29} +0.177560 q^{30} +1.07736 q^{31} +1.00000 q^{32} +0.213822 q^{33} +7.42399 q^{34} -3.91646 q^{35} -2.97813 q^{36} +1.48402 q^{37} +0.147896 q^{39} +1.20058 q^{40} +5.67671 q^{41} -0.482457 q^{42} +0.300246 q^{43} +1.44577 q^{44} -3.57547 q^{45} -7.20751 q^{46} +1.48371 q^{47} +0.147896 q^{48} +3.64162 q^{49} -3.55862 q^{50} +1.09797 q^{51} +1.00000 q^{52} -5.02488 q^{53} -0.884138 q^{54} +1.73575 q^{55} -3.26215 q^{56} -5.59186 q^{58} -9.80311 q^{59} +0.177560 q^{60} -10.7846 q^{61} +1.07736 q^{62} +9.71510 q^{63} +1.00000 q^{64} +1.20058 q^{65} +0.213822 q^{66} -2.68576 q^{67} +7.42399 q^{68} -1.06596 q^{69} -3.91646 q^{70} +1.23491 q^{71} -2.97813 q^{72} -14.9720 q^{73} +1.48402 q^{74} -0.526303 q^{75} -4.71631 q^{77} +0.147896 q^{78} -7.31528 q^{79} +1.20058 q^{80} +8.80362 q^{81} +5.67671 q^{82} +9.69833 q^{83} -0.482457 q^{84} +8.91306 q^{85} +0.300246 q^{86} -0.827011 q^{87} +1.44577 q^{88} -13.6896 q^{89} -3.57547 q^{90} -3.26215 q^{91} -7.20751 q^{92} +0.159336 q^{93} +1.48371 q^{94} +0.147896 q^{96} +7.86960 q^{97} +3.64162 q^{98} -4.30568 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 9 q^{2} - 3 q^{3} + 9 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} + 9 q^{8} + 6 q^{9} - 3 q^{10} - 6 q^{11} - 3 q^{12} + 9 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 6 q^{18} - 3 q^{20} - 9 q^{21} - 6 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 9 * q + 9 * q^2 - 3 * q^3 + 9 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 + 9 * q^8 + 6 * q^9 - 3 * q^10 - 6 * q^11 - 3 * q^12 + 9 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 6 * q^18 - 3 * q^20 - 9 * q^21 - 6 * q^22 - 3 * q^23 - 3 * q^24 + 9 * q^26 - 15 * q^27 - 6 * q^28 - 21 * q^29 - 3 * q^30 - 3 * q^31 + 9 * q^32 - 18 * q^33 - 27 * q^35 + 6 * q^36 - 12 * q^37 - 3 * q^39 - 3 * q^40 - 9 * q^42 - 3 * q^43 - 6 * q^44 + 3 * q^45 - 3 * q^46 - 3 * q^48 + 3 * q^49 - 3 * q^51 + 9 * q^52 + 6 * q^53 - 15 * q^54 - 9 * q^55 - 6 * q^56 - 21 * q^58 - 12 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 + 6 * q^63 + 9 * q^64 - 3 * q^65 - 18 * q^66 - 21 * q^67 - 21 * q^69 - 27 * q^70 - 21 * q^71 + 6 * q^72 - 45 * q^73 - 12 * q^74 + 18 * q^75 - 15 * q^77 - 3 * q^78 + 9 * q^79 - 3 * q^80 - 27 * q^81 + 15 * q^83 - 9 * q^84 - 9 * q^85 - 3 * q^86 + 9 * q^87 - 6 * q^88 + 3 * q^89 + 3 * q^90 - 6 * q^91 - 3 * q^92 + 21 * q^93 - 3 * q^96 + 3 * q^97 + 3 * q^98 + 18 * 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
$3$	0.147896	0.0853875	0.0426938	−	0.999088i	$-0.486406\pi$
$3$	0.147896	0.0853875	0.0426938	+	0.999088i	$0.486406\pi$
$4$	1.00000	0.500000
$5$	1.20058	0.536914	0.268457	−	0.963292i	$-0.413486\pi$
$5$	1.20058	0.536914	0.268457	+	0.963292i	$0.413486\pi$
$6$	0.147896	0.0603781
$7$	−3.26215	−1.23298	−0.616488	−	0.787364i	$-0.711445\pi$
$7$	−3.26215	−1.23298	−0.616488	+	0.787364i	$0.711445\pi$
$8$	1.00000	0.353553
$9$	−2.97813	−0.992709
$10$	1.20058	0.379656
$11$	1.44577	0.435915	0.217958	−	0.975958i	$-0.430061\pi$
$11$	1.44577	0.435915	0.217958	+	0.975958i	$0.430061\pi$
$12$	0.147896	0.0426938
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.26215	−0.871846
$15$	0.177560	0.0458458
$16$	1.00000	0.250000
$17$	7.42399	1.80058	0.900291	−	0.435289i	$-0.143354\pi$
$17$	7.42399	1.80058	0.900291	+	0.435289i	$0.143354\pi$
$18$	−2.97813	−0.701951
$19$	0	0
$19$	0	0
$20$	1.20058	0.268457
$21$	−0.482457	−0.105281
$22$	1.44577	0.308239
$23$	−7.20751	−1.50287	−0.751435	−	0.659807i	$-0.770638\pi$
$23$	−7.20751	−1.50287	−0.751435	+	0.659807i	$0.770638\pi$
$24$	0.147896	0.0301890
$25$	−3.55862	−0.711723
$26$	1.00000	0.196116
$27$	−0.884138	−0.170152
$28$	−3.26215	−0.616488
$29$	−5.59186	−1.03838	−0.519191	−	0.854658i	$-0.673767\pi$
$29$	−5.59186	−1.03838	−0.519191	+	0.854658i	$0.673767\pi$
$30$	0.177560	0.0324179
$31$	1.07736	0.193499	0.0967496	−	0.995309i	$-0.469155\pi$
$31$	1.07736	0.193499	0.0967496	+	0.995309i	$0.469155\pi$
$32$	1.00000	0.176777
$33$	0.213822	0.0372217
$34$	7.42399	1.27320
$35$	−3.91646	−0.662003
$36$	−2.97813	−0.496354
$37$	1.48402	0.243971	0.121986	−	0.992532i	$-0.461074\pi$
$37$	1.48402	0.243971	0.121986	+	0.992532i	$0.461074\pi$
$38$	0	0
$39$	0.147896	0.0236822
$40$	1.20058	0.189828
$41$	5.67671	0.886554	0.443277	−	0.896385i	$-0.353816\pi$
$41$	5.67671	0.886554	0.443277	+	0.896385i	$0.353816\pi$
$42$	−0.482457	−0.0744448
$43$	0.300246	0.0457871	0.0228935	−	0.999738i	$-0.492712\pi$
$43$	0.300246	0.0457871	0.0228935	+	0.999738i	$0.492712\pi$
$44$	1.44577	0.217958
$45$	−3.57547	−0.533000
$46$	−7.20751	−1.06269
$47$	1.48371	0.216421	0.108210	−	0.994128i	$-0.465488\pi$
$47$	1.48371	0.216421	0.108210	+	0.994128i	$0.465488\pi$
$48$	0.147896	0.0213469
$49$	3.64162	0.520232
$50$	−3.55862	−0.503264
$51$	1.09797	0.153747
$52$	1.00000	0.138675
$53$	−5.02488	−0.690220	−0.345110	−	0.938562i	$-0.612158\pi$
$53$	−5.02488	−0.690220	−0.345110	+	0.938562i	$0.612158\pi$
$54$	−0.884138	−0.120316
$55$	1.73575	0.234049
$56$	−3.26215	−0.435923
$57$	0	0
$58$	−5.59186	−0.734247
$59$	−9.80311	−1.27626	−0.638128	−	0.769930i	$-0.720291\pi$
$59$	−9.80311	−1.27626	−0.638128	+	0.769930i	$0.720291\pi$
$60$	0.177560	0.0229229
$61$	−10.7846	−1.38083	−0.690413	−	0.723416i	$-0.742571\pi$
$61$	−10.7846	−1.38083	−0.690413	+	0.723416i	$0.742571\pi$
$62$	1.07736	0.136825
$63$	9.71510	1.22399
$64$	1.00000	0.125000
$65$	1.20058	0.148913
$66$	0.213822	0.0263197
$67$	−2.68576	−0.328118	−0.164059	−	0.986451i	$-0.552459\pi$
$67$	−2.68576	−0.328118	−0.164059	+	0.986451i	$0.552459\pi$
$68$	7.42399	0.900291
$69$	−1.06596	−0.128326
$70$	−3.91646	−0.468107
$71$	1.23491	0.146557	0.0732786	−	0.997312i	$-0.476654\pi$
$71$	1.23491	0.146557	0.0732786	+	0.997312i	$0.476654\pi$
$72$	−2.97813	−0.350976
$73$	−14.9720	−1.75234	−0.876169	−	0.482005i	$-0.839909\pi$
$73$	−14.9720	−1.75234	−0.876169	+	0.482005i	$0.839909\pi$
$74$	1.48402	0.172514
$75$	−0.526303	−0.0607723
$76$	0	0
$77$	−4.71631	−0.537473
$78$	0.147896	0.0167459
$79$	−7.31528	−0.823034	−0.411517	−	0.911402i	$-0.635001\pi$
$79$	−7.31528	−0.823034	−0.411517	+	0.911402i	$0.635001\pi$
$80$	1.20058	0.134229
$81$	8.80362	0.978180
$82$	5.67671	0.626888
$83$	9.69833	1.06453	0.532265	−	0.846578i	$-0.321341\pi$
$83$	9.69833	1.06453	0.532265	+	0.846578i	$0.321341\pi$
$84$	−0.482457	−0.0526404
$85$	8.91306	0.966758
$86$	0.300246	0.0323764
$87$	−0.827011	−0.0886649
$88$	1.44577	0.154119
$89$	−13.6896	−1.45110	−0.725549	−	0.688171i	$-0.758414\pi$
$89$	−13.6896	−1.45110	−0.725549	+	0.688171i	$0.758414\pi$
$90$	−3.57547	−0.376888
$91$	−3.26215	−0.341966
$92$	−7.20751	−0.751435
$93$	0.159336	0.0165224
$94$	1.48371	0.153033
$95$	0	0
$96$	0.147896	0.0150945
$97$	7.86960	0.799037	0.399518	−	0.916725i	$-0.369177\pi$
$97$	7.86960	0.799037	0.399518	+	0.916725i	$0.369177\pi$
$98$	3.64162	0.367859
$99$	−4.30568	−0.432737
$100$	−3.55862	−0.355862
$101$	−5.74493	−0.571642	−0.285821	−	0.958283i	$-0.592266\pi$
$101$	−5.74493	−0.571642	−0.285821	+	0.958283i	$0.592266\pi$
$102$	1.09797	0.108716
$103$	12.1340	1.19560	0.597801	−	0.801645i	$-0.296041\pi$
$103$	12.1340	1.19560	0.597801	+	0.801645i	$0.296041\pi$
$104$	1.00000	0.0980581
$105$	−0.579227	−0.0565268
$106$	−5.02488	−0.488059
$107$	15.7633	1.52389	0.761947	−	0.647640i	$-0.224244\pi$
$107$	15.7633	1.52389	0.761947	+	0.647640i	$0.224244\pi$
$108$	−0.884138	−0.0850762
$109$	4.25725	0.407771	0.203885	−	0.978995i	$-0.434643\pi$
$109$	4.25725	0.407771	0.203885	+	0.978995i	$0.434643\pi$
$110$	1.73575	0.165498
$111$	0.219480	0.0208321
$112$	−3.26215	−0.308244
$113$	1.07121	0.100771	0.0503853	−	0.998730i	$-0.483955\pi$
$113$	1.07121	0.100771	0.0503853	+	0.998730i	$0.483955\pi$
$114$	0	0
$115$	−8.65317	−0.806913
$116$	−5.59186	−0.519191
$117$	−2.97813	−0.275328
$118$	−9.80311	−0.902450
$119$	−24.2182	−2.22007
$120$	0.177560	0.0162089
$121$	−8.90976	−0.809978
$122$	−10.7846	−0.976391
$123$	0.839560	0.0757006
$124$	1.07736	0.0967496
$125$	−10.2753	−0.919048
$126$	9.71510	0.865490
$127$	1.84226	0.163474	0.0817371	−	0.996654i	$-0.473953\pi$
$127$	1.84226	0.163474	0.0817371	+	0.996654i	$0.473953\pi$
$128$	1.00000	0.0883883
$129$	0.0444050	0.00390965
$130$	1.20058	0.105298
$131$	15.1808	1.32635	0.663175	−	0.748465i	$-0.269209\pi$
$131$	15.1808	1.32635	0.663175	+	0.748465i	$0.269209\pi$
$132$	0.213822	0.0186109
$133$	0	0
$134$	−2.68576	−0.232015
$135$	−1.06148	−0.0913573
$136$	7.42399	0.636602
$137$	−6.98685	−0.596927	−0.298463	−	0.954421i	$-0.596474\pi$
$137$	−6.98685	−0.596927	−0.298463	+	0.954421i	$0.596474\pi$
$138$	−1.06596	−0.0907405
$139$	13.5030	1.14531	0.572653	−	0.819798i	$-0.305914\pi$
$139$	13.5030	1.14531	0.572653	+	0.819798i	$0.305914\pi$
$140$	−3.91646	−0.331001
$141$	0.219434	0.0184797
$142$	1.23491	0.103632
$143$	1.44577	0.120901
$144$	−2.97813	−0.248177
$145$	−6.71346	−0.557522
$146$	−14.9720	−1.23909
$147$	0.538580	0.0444213
$148$	1.48402	0.121986
$149$	5.89805	0.483187	0.241594	−	0.970378i	$-0.422330\pi$
$149$	5.89805	0.483187	0.241594	+	0.970378i	$0.422330\pi$
$150$	−0.526303	−0.0429725
$151$	−10.3170	−0.839586	−0.419793	−	0.907620i	$-0.637897\pi$
$151$	−10.3170	−0.839586	−0.419793	+	0.907620i	$0.637897\pi$
$152$	0	0
$153$	−22.1096	−1.78745
$154$	−4.71631	−0.380051
$155$	1.29345	0.103892
$156$	0.147896	0.0118411
$157$	−13.7730	−1.09920	−0.549602	−	0.835426i	$-0.685221\pi$
$157$	−13.7730	−1.09920	−0.549602	+	0.835426i	$0.685221\pi$
$158$	−7.31528	−0.581973
$159$	−0.743157	−0.0589362
$160$	1.20058	0.0949139
$161$	23.5120	1.85300
$162$	8.80362	0.691678
$163$	−1.17427	−0.0919756	−0.0459878	−	0.998942i	$-0.514644\pi$
$163$	−1.17427	−0.0919756	−0.0459878	+	0.998942i	$0.514644\pi$
$164$	5.67671	0.443277
$165$	0.256710	0.0199849
$166$	9.69833	0.752737
$167$	−25.0106	−1.93538	−0.967689	−	0.252147i	$-0.918863\pi$
$167$	−25.0106	−1.93538	−0.967689	+	0.252147i	$0.918863\pi$
$168$	−0.482457	−0.0372224
$169$	1.00000	0.0769231
$170$	8.91306	0.683601
$171$	0	0
$172$	0.300246	0.0228935
$173$	−9.21409	−0.700534	−0.350267	−	0.936650i	$-0.613909\pi$
$173$	−9.21409	−0.700534	−0.350267	+	0.936650i	$0.613909\pi$
$174$	−0.827011	−0.0626956
$175$	11.6087	0.877538
$176$	1.44577	0.108979
$177$	−1.44984	−0.108976
$178$	−13.6896	−1.02608
$179$	−12.9958	−0.971355	−0.485678	−	0.874138i	$-0.661427\pi$
$179$	−12.9958	−0.971355	−0.485678	+	0.874138i	$0.661427\pi$
$180$	−3.57547	−0.266500
$181$	−11.2678	−0.837532	−0.418766	−	0.908094i	$-0.637537\pi$
$181$	−11.2678	−0.837532	−0.418766	+	0.908094i	$0.637537\pi$
$182$	−3.26215	−0.241807
$183$	−1.59499	−0.117905
$184$	−7.20751	−0.531345
$185$	1.78168	0.130992
$186$	0.159336	0.0116831
$187$	10.7334	0.784900
$188$	1.48371	0.108210
$189$	2.88419	0.209794
$190$	0	0
$191$	16.8655	1.22034	0.610171	−	0.792270i	$-0.291101\pi$
$191$	16.8655	1.22034	0.610171	+	0.792270i	$0.291101\pi$
$192$	0.147896	0.0106734
$193$	−16.2332	−1.16849	−0.584244	−	0.811578i	$-0.698609\pi$
$193$	−16.2332	−1.16849	−0.584244	+	0.811578i	$0.698609\pi$
$194$	7.86960	0.565004
$195$	0.177560	0.0127153
$196$	3.64162	0.260116
$197$	−18.2105	−1.29745	−0.648724	−	0.761024i	$-0.724697\pi$
$197$	−18.2105	−1.29745	−0.648724	+	0.761024i	$0.724697\pi$
$198$	−4.30568	−0.305991
$199$	−14.4442	−1.02392	−0.511961	−	0.859008i	$-0.671081\pi$
$199$	−14.4442	−1.02392	−0.511961	+	0.859008i	$0.671081\pi$
$200$	−3.55862	−0.251632
$201$	−0.397212	−0.0280172
$202$	−5.74493	−0.404212
$203$	18.2415	1.28030
$204$	1.09797	0.0768736
$205$	6.81533	0.476003
$206$	12.1340	0.845418
$207$	21.4649	1.49191
$208$	1.00000	0.0693375
$209$	0	0
$210$	−0.579227	−0.0399705
$211$	15.9741	1.09970	0.549851	−	0.835263i	$-0.314685\pi$
$211$	15.9741	1.09970	0.549851	+	0.835263i	$0.314685\pi$
$212$	−5.02488	−0.345110
$213$	0.182638	0.0125142
$214$	15.7633	1.07756
$215$	0.360468	0.0245837
$216$	−0.884138	−0.0601580
$217$	−3.51450	−0.238580
$218$	4.25725	0.288337
$219$	−2.21429	−0.149628
$220$	1.73575	0.117024
$221$	7.42399	0.499391
$222$	0.219480	0.0147305
$223$	−19.5067	−1.30627	−0.653133	−	0.757243i	$-0.726546\pi$
$223$	−19.5067	−1.30627	−0.653133	+	0.757243i	$0.726546\pi$
$224$	−3.26215	−0.217962
$225$	10.5980	0.706534
$226$	1.07121	0.0712556
$227$	−12.0844	−0.802067	−0.401034	−	0.916063i	$-0.631349\pi$
$227$	−12.0844	−0.802067	−0.401034	+	0.916063i	$0.631349\pi$
$228$	0	0
$229$	5.62571	0.371757	0.185879	−	0.982573i	$-0.440487\pi$
$229$	5.62571	0.371757	0.185879	+	0.982573i	$0.440487\pi$
$230$	−8.65317	−0.570573
$231$	−0.697521	−0.0458935
$232$	−5.59186	−0.367124
$233$	−14.3449	−0.939767	−0.469883	−	0.882729i	$-0.655704\pi$
$233$	−14.3449	−0.939767	−0.469883	+	0.882729i	$0.655704\pi$
$234$	−2.97813	−0.194686
$235$	1.78130	0.116200
$236$	−9.80311	−0.638128
$237$	−1.08190	−0.0702768
$238$	−24.2182	−1.56983
$239$	−15.5343	−1.00483	−0.502416	−	0.864626i	$-0.667555\pi$
$239$	−15.5343	−1.00483	−0.502416	+	0.864626i	$0.667555\pi$
$240$	0.177560	0.0114614
$241$	13.9211	0.896739	0.448370	−	0.893848i	$-0.352005\pi$
$241$	13.9211	0.896739	0.448370	+	0.893848i	$0.352005\pi$
$242$	−8.90976	−0.572741
$243$	3.95443	0.253677
$244$	−10.7846	−0.690413
$245$	4.37205	0.279320
$246$	0.839560	0.0535284
$247$	0	0
$248$	1.07736	0.0684123
$249$	1.43434	0.0908976
$250$	−10.2753	−0.649865
$251$	−3.84319	−0.242580	−0.121290	−	0.992617i	$-0.538703\pi$
$251$	−3.84319	−0.242580	−0.121290	+	0.992617i	$0.538703\pi$
$252$	9.71510	0.611994
$253$	−10.4204	−0.655124
$254$	1.84226	0.115594
$255$	1.31820	0.0825490
$256$	1.00000	0.0625000
$257$	−28.4562	−1.77505	−0.887525	−	0.460760i	$-0.847577\pi$
$257$	−28.4562	−1.77505	−0.887525	+	0.460760i	$0.847577\pi$
$258$	0.0444050	0.00276454
$259$	−4.84109	−0.300811
$260$	1.20058	0.0744566
$261$	16.6533	1.03081
$262$	15.1808	0.937871
$263$	17.2621	1.06442	0.532212	−	0.846611i	$-0.321361\pi$
$263$	17.2621	1.06442	0.532212	+	0.846611i	$0.321361\pi$
$264$	0.213822	0.0131599
$265$	−6.03275	−0.370589
$266$	0	0
$267$	−2.02463	−0.123906
$268$	−2.68576	−0.164059
$269$	12.7732	0.778797	0.389399	−	0.921069i	$-0.372683\pi$
$269$	12.7732	0.778797	0.389399	+	0.921069i	$0.372683\pi$
$270$	−1.06148	−0.0645993
$271$	5.62977	0.341984	0.170992	−	0.985272i	$-0.445303\pi$
$271$	5.62977	0.341984	0.170992	+	0.985272i	$0.445303\pi$
$272$	7.42399	0.450145
$273$	−0.482457	−0.0291996
$274$	−6.98685	−0.422091
$275$	−5.14493	−0.310251
$276$	−1.06596	−0.0641632
$277$	−20.9621	−1.25949	−0.629746	−	0.776801i	$-0.716841\pi$
$277$	−20.9621	−1.25949	−0.629746	+	0.776801i	$0.716841\pi$
$278$	13.5030	0.809853
$279$	−3.20851	−0.192088
$280$	−3.91646	−0.234053
$281$	−8.90538	−0.531250	−0.265625	−	0.964076i	$-0.585578\pi$
$281$	−8.90538	−0.531250	−0.265625	+	0.964076i	$0.585578\pi$
$282$	0.219434	0.0130671
$283$	19.9127	1.18369	0.591844	−	0.806052i	$-0.298400\pi$
$283$	19.9127	1.18369	0.591844	+	0.806052i	$0.298400\pi$
$284$	1.23491	0.0732786
$285$	0	0
$286$	1.44577	0.0854900
$287$	−18.5183	−1.09310
$288$	−2.97813	−0.175488
$289$	38.1156	2.24209
$290$	−6.71346	−0.394228
$291$	1.16388	0.0682278
$292$	−14.9720	−0.876169
$293$	−19.2008	−1.12172	−0.560860	−	0.827911i	$-0.689529\pi$
$293$	−19.2008	−1.12172	−0.560860	+	0.827911i	$0.689529\pi$
$294$	0.538580	0.0314106
$295$	−11.7694	−0.685240
$296$	1.48402	0.0862568
$297$	−1.27826	−0.0741720
$298$	5.89805	0.341665
$299$	−7.20751	−0.416821
$300$	−0.526303	−0.0303861
$301$	−0.979448	−0.0564544
$302$	−10.3170	−0.593677
$303$	−0.849649	−0.0488111
$304$	0	0
$305$	−12.9477	−0.741385
$306$	−22.1096	−1.26392
$307$	−16.5882	−0.946737	−0.473368	−	0.880865i	$-0.656962\pi$
$307$	−16.5882	−0.946737	−0.473368	+	0.880865i	$0.656962\pi$
$308$	−4.71631	−0.268737
$309$	1.79457	0.102089
$310$	1.29345	0.0734630
$311$	15.5297	0.880607	0.440304	−	0.897849i	$-0.354871\pi$
$311$	15.5297	0.880607	0.440304	+	0.897849i	$0.354871\pi$
$312$	0.147896	0.00837293
$313$	−17.3696	−0.981788	−0.490894	−	0.871219i	$-0.663330\pi$
$313$	−17.3696	−0.981788	−0.490894	+	0.871219i	$0.663330\pi$
$314$	−13.7730	−0.777255
$315$	11.6637	0.657176
$316$	−7.31528	−0.411517
$317$	−30.8243	−1.73126	−0.865632	−	0.500681i	$-0.833083\pi$
$317$	−30.8243	−1.73126	−0.865632	+	0.500681i	$0.833083\pi$
$318$	−0.743157	−0.0416742
$319$	−8.08453	−0.452647
$320$	1.20058	0.0671143
$321$	2.33132	0.130121
$322$	23.5120	1.31027
$323$	0	0
$324$	8.80362	0.489090
$325$	−3.55862	−0.197396
$326$	−1.17427	−0.0650366
$327$	0.629628	0.0348185
$328$	5.67671	0.313444
$329$	−4.84008	−0.266842
$330$	0.256710	0.0141314
$331$	−27.3801	−1.50495	−0.752475	−	0.658621i	$-0.771140\pi$
$331$	−27.3801	−1.50495	−0.752475	+	0.658621i	$0.771140\pi$
$332$	9.69833	0.532265
$333$	−4.41959	−0.242192
$334$	−25.0106	−1.36852
$335$	−3.22446	−0.176171
$336$	−0.482457	−0.0263202
$337$	−35.9229	−1.95685	−0.978423	−	0.206610i	$-0.933757\pi$
$337$	−35.9229	−1.95685	−0.978423	+	0.206610i	$0.933757\pi$
$338$	1.00000	0.0543928
$339$	0.158427	0.00860456
$340$	8.91306	0.483379
$341$	1.55761	0.0843492
$342$	0	0
$343$	10.9555	0.591543
$344$	0.300246	0.0161882
$345$	−1.27977	−0.0689003
$346$	−9.21409	−0.495353
$347$	−20.7791	−1.11548	−0.557741	−	0.830015i	$-0.688332\pi$
$347$	−20.7791	−1.11548	−0.557741	+	0.830015i	$0.688332\pi$
$348$	−0.827011	−0.0443324
$349$	−27.2581	−1.45909	−0.729546	−	0.683931i	$-0.760269\pi$
$349$	−27.2581	−1.45909	−0.729546	+	0.683931i	$0.760269\pi$
$350$	11.6087	0.620513
$351$	−0.884138	−0.0471918
$352$	1.44577	0.0770596
$353$	23.4930	1.25040	0.625202	−	0.780463i	$-0.285017\pi$
$353$	23.4930	1.25040	0.625202	+	0.780463i	$0.285017\pi$
$354$	−1.44984	−0.0770579
$355$	1.48261	0.0786886
$356$	−13.6896	−0.725549
$357$	−3.58176	−0.189567
$358$	−12.9958	−0.686852
$359$	13.2622	0.699954	0.349977	−	0.936758i	$-0.386189\pi$
$359$	13.2622	0.699954	0.349977	+	0.936758i	$0.386189\pi$
$360$	−3.57547	−0.188444
$361$	0	0
$362$	−11.2678	−0.592225
$363$	−1.31771	−0.0691620
$364$	−3.26215	−0.170983
$365$	−17.9750	−0.940855
$366$	−1.59499	−0.0833716
$367$	34.3445	1.79277	0.896385	−	0.443276i	$-0.146184\pi$
$367$	34.3445	1.79277	0.896385	+	0.443276i	$0.146184\pi$
$368$	−7.20751	−0.375718
$369$	−16.9060	−0.880090
$370$	1.78168	0.0926250
$371$	16.3919	0.851026
$372$	0.159336	0.00826120
$373$	19.8835	1.02953	0.514763	−	0.857332i	$-0.327880\pi$
$373$	19.8835	1.02953	0.514763	+	0.857332i	$0.327880\pi$
$374$	10.7334	0.555008
$375$	−1.51967	−0.0784753
$376$	1.48371	0.0765164
$377$	−5.59186	−0.287995
$378$	2.88419	0.148347
$379$	3.33959	0.171543	0.0857717	−	0.996315i	$-0.472664\pi$
$379$	3.33959	0.171543	0.0857717	+	0.996315i	$0.472664\pi$
$380$	0	0
$381$	0.272462	0.0139587
$382$	16.8655	0.862912
$383$	−23.5276	−1.20221	−0.601103	−	0.799171i	$-0.705272\pi$
$383$	−23.5276	−1.20221	−0.601103	+	0.799171i	$0.705272\pi$
$384$	0.147896	0.00754726
$385$	−5.66229	−0.288577
$386$	−16.2332	−0.826246
$387$	−0.894171	−0.0454533
$388$	7.86960	0.399518
$389$	25.2558	1.28052	0.640260	−	0.768159i	$-0.278827\pi$
$389$	25.2558	1.28052	0.640260	+	0.768159i	$0.278827\pi$
$390$	0.177560	0.00899109
$391$	−53.5085	−2.70604
$392$	3.64162	0.183930
$393$	2.24517	0.113254
$394$	−18.2105	−0.917434
$395$	−8.78256	−0.441898
$396$	−4.30568	−0.216368
$397$	−12.7191	−0.638352	−0.319176	−	0.947695i	$-0.603406\pi$
$397$	−12.7191	−0.638352	−0.319176	+	0.947695i	$0.603406\pi$
$398$	−14.4442	−0.724023
$399$	0	0
$400$	−3.55862	−0.177931
$401$	−5.49595	−0.274455	−0.137227	−	0.990540i	$-0.543819\pi$
$401$	−5.49595	−0.274455	−0.137227	+	0.990540i	$0.543819\pi$
$402$	−0.397212	−0.0198112
$403$	1.07736	0.0536670
$404$	−5.74493	−0.285821
$405$	10.5694	0.525199
$406$	18.2415	0.905310
$407$	2.14554	0.106351
$408$	1.09797	0.0543578
$409$	17.1252	0.846786	0.423393	−	0.905946i	$-0.360839\pi$
$409$	17.1252	0.846786	0.423393	+	0.905946i	$0.360839\pi$
$410$	6.81533	0.336585
$411$	−1.03332	−0.0509701
$412$	12.1340	0.597801
$413$	31.9792	1.57359
$414$	21.4649	1.05494
$415$	11.6436	0.571562
$416$	1.00000	0.0490290
$417$	1.99703	0.0977948
$418$	0	0
$419$	−27.4907	−1.34301	−0.671504	−	0.741001i	$-0.734351\pi$
$419$	−27.4907	−1.34301	−0.671504	+	0.741001i	$0.734351\pi$
$420$	−0.579227	−0.0282634
$421$	15.9882	0.779217	0.389608	−	0.920981i	$-0.372610\pi$
$421$	15.9882	0.779217	0.389608	+	0.920981i	$0.372610\pi$
$422$	15.9741	0.777607
$423$	−4.41867	−0.214843
$424$	−5.02488	−0.244030
$425$	−26.4191	−1.28152
$426$	0.182638	0.00884884
$427$	35.1810	1.70253
$428$	15.7633	0.761947
$429$	0.213822	0.0103234
$430$	0.360468	0.0173833
$431$	17.8523	0.859916	0.429958	−	0.902849i	$-0.358528\pi$
$431$	17.8523	0.859916	0.429958	+	0.902849i	$0.358528\pi$
$432$	−0.884138	−0.0425381
$433$	18.2809	0.878522	0.439261	−	0.898359i	$-0.355240\pi$
$433$	18.2809	0.878522	0.439261	+	0.898359i	$0.355240\pi$
$434$	−3.51450	−0.168701
$435$	−0.992890	−0.0476054
$436$	4.25725	0.203885
$437$	0	0
$438$	−2.21429	−0.105803
$439$	−19.8760	−0.948631	−0.474316	−	0.880355i	$-0.657304\pi$
$439$	−19.8760	−0.948631	−0.474316	+	0.880355i	$0.657304\pi$
$440$	1.73575	0.0827488
$441$	−10.8452	−0.516439
$442$	7.42399	0.353123
$443$	24.8341	1.17990	0.589952	−	0.807439i	$-0.299147\pi$
$443$	24.8341	1.17990	0.589952	+	0.807439i	$0.299147\pi$
$444$	0.219480	0.0104160
$445$	−16.4354	−0.779115
$446$	−19.5067	−0.923670
$447$	0.872295	0.0412582
$448$	−3.26215	−0.154122
$449$	9.18647	0.433536	0.216768	−	0.976223i	$-0.430448\pi$
$449$	9.18647	0.433536	0.216768	+	0.976223i	$0.430448\pi$
$450$	10.5980	0.499595
$451$	8.20720	0.386462
$452$	1.07121	0.0503853
$453$	−1.52584	−0.0716901
$454$	−12.0844	−0.567147
$455$	−3.91646	−0.183607
$456$	0	0
$457$	−7.90161	−0.369622	−0.184811	−	0.982774i	$-0.559167\pi$
$457$	−7.90161	−0.369622	−0.184811	+	0.982774i	$0.559167\pi$
$458$	5.62571	0.262872
$459$	−6.56383	−0.306373
$460$	−8.65317	−0.403456
$461$	7.31985	0.340920	0.170460	−	0.985365i	$-0.445475\pi$
$461$	7.31985	0.340920	0.170460	+	0.985365i	$0.445475\pi$
$462$	−0.697521	−0.0324516
$463$	−15.8660	−0.737355	−0.368677	−	0.929557i	$-0.620189\pi$
$463$	−15.8660	−0.737355	−0.368677	+	0.929557i	$0.620189\pi$
$464$	−5.59186	−0.259596
$465$	0.191295	0.00887112
$466$	−14.3449	−0.664515
$467$	6.56283	0.303692	0.151846	−	0.988404i	$-0.451478\pi$
$467$	6.56283	0.303692	0.151846	+	0.988404i	$0.451478\pi$
$468$	−2.97813	−0.137664
$469$	8.76136	0.404562
$470$	1.78130	0.0821655
$471$	−2.03696	−0.0938584
$472$	−9.80311	−0.451225
$473$	0.434086	0.0199593
$474$	−1.08190	−0.0496932
$475$	0	0
$476$	−24.2182	−1.11004
$477$	14.9647	0.685188
$478$	−15.5343	−0.710524
$479$	−31.2995	−1.43011	−0.715056	−	0.699067i	$-0.753599\pi$
$479$	−31.2995	−1.43011	−0.715056	+	0.699067i	$0.753599\pi$
$480$	0.177560	0.00810446
$481$	1.48402	0.0676654
$482$	13.9211	0.634090
$483$	3.47732	0.158223
$484$	−8.90976	−0.404989
$485$	9.44806	0.429014
$486$	3.95443	0.179377
$487$	37.2463	1.68779	0.843895	−	0.536509i	$-0.180257\pi$
$487$	37.2463	1.68779	0.843895	+	0.536509i	$0.180257\pi$
$488$	−10.7846	−0.488196
$489$	−0.173669	−0.00785357
$490$	4.37205	0.197509
$491$	20.2698	0.914761	0.457381	−	0.889271i	$-0.348788\pi$
$491$	20.2698	0.914761	0.457381	+	0.889271i	$0.348788\pi$
$492$	0.839560	0.0378503
$493$	−41.5139	−1.86969
$494$	0	0
$495$	−5.16929	−0.232343
$496$	1.07736	0.0483748
$497$	−4.02847	−0.180702
$498$	1.43434	0.0642743
$499$	21.4350	0.959564	0.479782	−	0.877388i	$-0.340716\pi$
$499$	21.4350	0.959564	0.479782	+	0.877388i	$0.340716\pi$
$500$	−10.2753	−0.459524
$501$	−3.69895	−0.165257
$502$	−3.84319	−0.171530
$503$	−3.01709	−0.134526	−0.0672628	−	0.997735i	$-0.521427\pi$
$503$	−3.01709	−0.134526	−0.0672628	+	0.997735i	$0.521427\pi$
$504$	9.71510	0.432745
$505$	−6.89723	−0.306922
$506$	−10.4204	−0.463243
$507$	0.147896	0.00656827
$508$	1.84226	0.0817371
$509$	−5.42969	−0.240667	−0.120333	−	0.992734i	$-0.538396\pi$
$509$	−5.42969	−0.240667	−0.120333	+	0.992734i	$0.538396\pi$
$510$	1.31820	0.0583710
$511$	48.8408	2.16059
$512$	1.00000	0.0441942
$513$	0	0
$514$	−28.4562	−1.25515
$515$	14.5678	0.641935
$516$	0.0444050	0.00195482
$517$	2.14510	0.0943412
$518$	−4.84109	−0.212705
$519$	−1.36272	−0.0598169
$520$	1.20058	0.0526488
$521$	−13.0130	−0.570108	−0.285054	−	0.958511i	$-0.592012\pi$
$521$	−13.0130	−0.570108	−0.285054	+	0.958511i	$0.592012\pi$
$522$	16.6533	0.728894
$523$	−1.28818	−0.0563283	−0.0281642	−	0.999603i	$-0.508966\pi$
$523$	−1.28818	−0.0563283	−0.0281642	+	0.999603i	$0.508966\pi$
$524$	15.1808	0.663175
$525$	1.71688	0.0749308
$526$	17.2621	0.752662
$527$	7.99829	0.348411
$528$	0.213822	0.00930543
$529$	28.9483	1.25862
$530$	−6.03275	−0.262046
$531$	29.1949	1.26695
$532$	0	0
$533$	5.67671	0.245886
$534$	−2.02463	−0.0876145
$535$	18.9250	0.818200
$536$	−2.68576	−0.116007
$537$	−1.92203	−0.0829416
$538$	12.7732	0.550693
$539$	5.26494	0.226777
$540$	−1.06148	−0.0456786
$541$	37.6826	1.62010	0.810051	−	0.586359i	$-0.199439\pi$
$541$	37.6826	1.62010	0.810051	+	0.586359i	$0.199439\pi$
$542$	5.62977	0.241819
$543$	−1.66646	−0.0715148
$544$	7.42399	0.318301
$545$	5.11115	0.218938
$546$	−0.482457	−0.0206473
$547$	20.5730	0.879638	0.439819	−	0.898086i	$-0.355043\pi$
$547$	20.5730	0.879638	0.439819	+	0.898086i	$0.355043\pi$
$548$	−6.98685	−0.298463
$549$	32.1179	1.37076
$550$	−5.14493	−0.219380
$551$	0	0
$552$	−1.06596	−0.0453702
$553$	23.8635	1.01478
$554$	−20.9621	−0.890596
$555$	0.263502	0.0111850
$556$	13.5030	0.572653
$557$	38.6141	1.63613	0.818066	−	0.575125i	$-0.195046\pi$
$557$	38.6141	1.63613	0.818066	+	0.575125i	$0.195046\pi$
$558$	−3.20851	−0.135827
$559$	0.300246	0.0126991
$560$	−3.91646	−0.165501
$561$	1.58741	0.0670207
$562$	−8.90538	−0.375651
$563$	9.79248	0.412704	0.206352	−	0.978478i	$-0.433841\pi$
$563$	9.79248	0.412704	0.206352	+	0.978478i	$0.433841\pi$
$564$	0.219434	0.00923983
$565$	1.28607	0.0541052
$566$	19.9127	0.836994
$567$	−28.7187	−1.20607
$568$	1.23491	0.0518158
$569$	−40.1136	−1.68165	−0.840824	−	0.541308i	$-0.817929\pi$
$569$	−40.1136	−1.68165	−0.840824	+	0.541308i	$0.817929\pi$
$570$	0	0
$571$	24.0783	1.00765	0.503823	−	0.863807i	$-0.331926\pi$
$571$	24.0783	1.00765	0.503823	+	0.863807i	$0.331926\pi$
$572$	1.44577	0.0604505
$573$	2.49433	0.104202
$574$	−18.5183	−0.772938
$575$	25.6488	1.06963
$576$	−2.97813	−0.124089
$577$	25.0825	1.04420	0.522100	−	0.852885i	$-0.325149\pi$
$577$	25.0825	1.04420	0.522100	+	0.852885i	$0.325149\pi$
$578$	38.1156	1.58540
$579$	−2.40081	−0.0997744
$580$	−6.71346	−0.278761
$581$	−31.6374	−1.31254
$582$	1.16388	0.0482443
$583$	−7.26480	−0.300877
$584$	−14.9720	−0.619545
$585$	−3.57547	−0.147827
$586$	−19.2008	−0.793176
$587$	−18.3805	−0.758645	−0.379322	−	0.925265i	$-0.623843\pi$
$587$	−18.3805	−0.758645	−0.379322	+	0.925265i	$0.623843\pi$
$588$	0.538580	0.0222107
$589$	0	0
$590$	−11.7694	−0.484538
$591$	−2.69326	−0.110786
$592$	1.48402	0.0609928
$593$	24.9611	1.02503	0.512515	−	0.858678i	$-0.328714\pi$
$593$	24.9611	1.02503	0.512515	+	0.858678i	$0.328714\pi$
$594$	−1.27826	−0.0524475
$595$	−29.0758	−1.19199
$596$	5.89805	0.241594
$597$	−2.13623	−0.0874302
$598$	−7.20751	−0.294737
$599$	−23.6178	−0.964997	−0.482499	−	0.875897i	$-0.660271\pi$
$599$	−23.6178	−0.964997	−0.482499	+	0.875897i	$0.660271\pi$
$600$	−0.526303	−0.0214862
$601$	18.6115	0.759181	0.379590	−	0.925155i	$-0.376065\pi$
$601$	18.6115	0.759181	0.379590	+	0.925155i	$0.376065\pi$
$602$	−0.979448	−0.0399193
$603$	7.99854	0.325726
$604$	−10.3170	−0.419793
$605$	−10.6968	−0.434889
$606$	−0.849649	−0.0345146
$607$	26.8602	1.09022	0.545112	−	0.838363i	$-0.316487\pi$
$607$	26.8602	1.09022	0.545112	+	0.838363i	$0.316487\pi$
$608$	0	0
$609$	2.69783	0.109322
$610$	−12.9477	−0.524238
$611$	1.48371	0.0600244
$612$	−22.1096	−0.893727
$613$	17.7110	0.715341	0.357671	−	0.933848i	$-0.383571\pi$
$613$	17.7110	0.715341	0.357671	+	0.933848i	$0.383571\pi$
$614$	−16.5882	−0.669444
$615$	1.00796	0.0406447
$616$	−4.71631	−0.190025
$617$	3.66322	0.147476	0.0737378	−	0.997278i	$-0.476507\pi$
$617$	3.66322	0.147476	0.0737378	+	0.997278i	$0.476507\pi$
$618$	1.79457	0.0721881
$619$	13.0426	0.524226	0.262113	−	0.965037i	$-0.415581\pi$
$619$	13.0426	0.524226	0.262113	+	0.965037i	$0.415581\pi$
$620$	1.29345	0.0519462
$621$	6.37244	0.255717
$622$	15.5297	0.622683
$623$	44.6576	1.78917
$624$	0.147896	0.00592056
$625$	5.45683	0.218273
$626$	−17.3696	−0.694229
$627$	0	0
$628$	−13.7730	−0.549602
$629$	11.0173	0.439290
$630$	11.6637	0.464694
$631$	−6.40055	−0.254802	−0.127401	−	0.991851i	$-0.540664\pi$
$631$	−6.40055	−0.254802	−0.127401	+	0.991851i	$0.540664\pi$
$632$	−7.31528	−0.290986
$633$	2.36250	0.0939008
$634$	−30.8243	−1.22419
$635$	2.21177	0.0877716
$636$	−0.743157	−0.0294681
$637$	3.64162	0.144286
$638$	−8.08453	−0.320069
$639$	−3.67773	−0.145489
$640$	1.20058	0.0474570
$641$	24.0962	0.951742	0.475871	−	0.879515i	$-0.342133\pi$
$641$	24.0962	0.951742	0.475871	+	0.879515i	$0.342133\pi$
$642$	2.33132	0.0920098
$643$	29.6300	1.16849	0.584247	−	0.811576i	$-0.301390\pi$
$643$	29.6300	1.16849	0.584247	+	0.811576i	$0.301390\pi$
$644$	23.5120	0.926502
$645$	0.0533117	0.00209914
$646$	0	0
$647$	−6.75705	−0.265647	−0.132823	−	0.991140i	$-0.542404\pi$
$647$	−6.75705	−0.265647	−0.132823	+	0.991140i	$0.542404\pi$
$648$	8.80362	0.345839
$649$	−14.1730	−0.556339
$650$	−3.55862	−0.139580
$651$	−0.519779	−0.0203717
$652$	−1.17427	−0.0459878
$653$	−44.9535	−1.75916	−0.879582	−	0.475747i	$-0.842178\pi$
$653$	−44.9535	−1.75916	−0.879582	+	0.475747i	$0.842178\pi$
$654$	0.629628	0.0246204
$655$	18.2257	0.712136
$656$	5.67671	0.221638
$657$	44.5884	1.73956
$658$	−4.84008	−0.188686
$659$	−26.5490	−1.03420	−0.517101	−	0.855924i	$-0.672989\pi$
$659$	−26.5490	−1.03420	−0.517101	+	0.855924i	$0.672989\pi$
$660$	0.256710	0.00999243
$661$	−15.8611	−0.616926	−0.308463	−	0.951236i	$-0.599815\pi$
$661$	−15.8611	−0.616926	−0.308463	+	0.951236i	$0.599815\pi$
$662$	−27.3801	−1.06416
$663$	1.09797	0.0426418
$664$	9.69833	0.376368
$665$	0	0
$666$	−4.41959	−0.171256
$667$	40.3034	1.56055
$668$	−25.0106	−0.967689
$669$	−2.88496	−0.111539
$670$	−3.22446	−0.124572
$671$	−15.5920	−0.601923
$672$	−0.482457	−0.0186112
$673$	17.7121	0.682752	0.341376	−	0.939927i	$-0.389107\pi$
$673$	17.7121	0.682752	0.341376	+	0.939927i	$0.389107\pi$
$674$	−35.9229	−1.38370
$675$	3.14631	0.121101
$676$	1.00000	0.0384615
$677$	30.1110	1.15726	0.578630	−	0.815590i	$-0.303588\pi$
$677$	30.1110	1.15726	0.578630	+	0.815590i	$0.303588\pi$
$678$	0.158427	0.00608434
$679$	−25.6718	−0.985194
$680$	8.91306	0.341800
$681$	−1.78722	−0.0684865
$682$	1.55761	0.0596439
$683$	−45.2179	−1.73022	−0.865108	−	0.501585i	$-0.832750\pi$
$683$	−45.2179	−1.73022	−0.865108	+	0.501585i	$0.832750\pi$
$684$	0	0
$685$	−8.38825	−0.320499
$686$	10.9555	0.418284
$687$	0.832017	0.0317434
$688$	0.300246	0.0114468
$689$	−5.02488	−0.191433
$690$	−1.27977	−0.0487198
$691$	−8.11651	−0.308766	−0.154383	−	0.988011i	$-0.549339\pi$
$691$	−8.11651	−0.308766	−0.154383	+	0.988011i	$0.549339\pi$
$692$	−9.21409	−0.350267
$693$	14.0458	0.533554
$694$	−20.7791	−0.788765
$695$	16.2113	0.614931
$696$	−0.827011	−0.0313478
$697$	42.1438	1.59631
$698$	−27.2581	−1.03173
$699$	−2.12155	−0.0802443
$700$	11.6087	0.438769
$701$	10.8337	0.409183	0.204592	−	0.978847i	$-0.434413\pi$
$701$	10.8337	0.409183	0.204592	+	0.978847i	$0.434413\pi$
$702$	−0.884138	−0.0333696
$703$	0	0
$704$	1.44577	0.0544894
$705$	0.263447	0.00992199
$706$	23.4930	0.884169
$707$	18.7408	0.704821
$708$	−1.44984	−0.0544882
$709$	16.4839	0.619066	0.309533	−	0.950889i	$-0.399827\pi$
$709$	16.4839	0.619066	0.309533	+	0.950889i	$0.399827\pi$
$710$	1.48261	0.0556413
$711$	21.7858	0.817033
$712$	−13.6896	−0.513040
$713$	−7.76507	−0.290804
$714$	−3.58176	−0.134044
$715$	1.73575	0.0649135
$716$	−12.9958	−0.485678
$717$	−2.29746	−0.0858001
$718$	13.2622	0.494942
$719$	−25.8609	−0.964451	−0.482225	−	0.876047i	$-0.660171\pi$
$719$	−25.8609	−0.964451	−0.482225	+	0.876047i	$0.660171\pi$
$720$	−3.57547	−0.133250
$721$	−39.5830	−1.47415
$722$	0	0
$723$	2.05887	0.0765703
$724$	−11.2678	−0.418766
$725$	19.8993	0.739041
$726$	−1.31771	−0.0489049
$727$	8.59757	0.318866	0.159433	−	0.987209i	$-0.449033\pi$
$727$	8.59757	0.318866	0.159433	+	0.987209i	$0.449033\pi$
$728$	−3.26215	−0.120903
$729$	−25.8260	−0.956519
$730$	−17.9750	−0.665285
$731$	2.22902	0.0824434
$732$	−1.59499	−0.0589526
$733$	43.2245	1.59653	0.798267	−	0.602304i	$-0.205751\pi$
$733$	43.2245	1.59653	0.798267	+	0.602304i	$0.205751\pi$
$734$	34.3445	1.26768
$735$	0.646606	0.0238504
$736$	−7.20751	−0.265673
$737$	−3.88299	−0.143032
$738$	−16.9060	−0.622317
$739$	0.248247	0.00913191	0.00456596	−	0.999990i	$-0.498547\pi$
$739$	0.248247	0.00913191	0.00456596	+	0.999990i	$0.498547\pi$
$740$	1.78168	0.0654958
$741$	0	0
$742$	16.3919	0.601766
$743$	20.4301	0.749506	0.374753	−	0.927125i	$-0.377727\pi$
$743$	20.4301	0.749506	0.374753	+	0.927125i	$0.377727\pi$
$744$	0.159336	0.00584155
$745$	7.08106	0.259430
$746$	19.8835	0.727985
$747$	−28.8829	−1.05677
$748$	10.7334	0.392450
$749$	−51.4222	−1.87893
$750$	−1.51967	−0.0554904
$751$	−25.9834	−0.948149	−0.474075	−	0.880485i	$-0.657217\pi$
$751$	−25.9834	−0.948149	−0.474075	+	0.880485i	$0.657217\pi$
$752$	1.48371	0.0541052
$753$	−0.568390	−0.0207133
$754$	−5.59186	−0.203644
$755$	−12.3864	−0.450785
$756$	2.88419	0.104897
$757$	−15.0463	−0.546869	−0.273434	−	0.961891i	$-0.588160\pi$
$757$	−15.0463	−0.546869	−0.273434	+	0.961891i	$0.588160\pi$
$758$	3.33959	0.121299
$759$	−1.54113	−0.0559394
$760$	0	0
$761$	45.4148	1.64629	0.823143	−	0.567834i	$-0.192219\pi$
$761$	45.4148	1.64629	0.823143	+	0.567834i	$0.192219\pi$
$762$	0.272462	0.00987026
$763$	−13.8878	−0.502772
$764$	16.8655	0.610171
$765$	−26.5442	−0.959709
$766$	−23.5276	−0.850088
$767$	−9.80311	−0.353970
$768$	0.147896	0.00533672
$769$	10.3865	0.374547	0.187273	−	0.982308i	$-0.440035\pi$
$769$	10.3865	0.374547	0.187273	+	0.982308i	$0.440035\pi$
$770$	−5.66229	−0.204055
$771$	−4.20855	−0.151567
$772$	−16.2332	−0.584244
$773$	−21.7655	−0.782850	−0.391425	−	0.920210i	$-0.628018\pi$
$773$	−21.7655	−0.782850	−0.391425	+	0.920210i	$0.628018\pi$
$774$	−0.894171	−0.0321403
$775$	−3.83390	−0.137718
$776$	7.86960	0.282502
$777$	−0.715976	−0.0256855
$778$	25.2558	0.905464
$779$	0	0
$780$	0.177560	0.00635766
$781$	1.78540	0.0638865
$782$	−53.5085	−1.91346
$783$	4.94398	0.176683
$784$	3.64162	0.130058
$785$	−16.5355	−0.590179
$786$	2.24517	0.0800825
$787$	8.37615	0.298577	0.149289	−	0.988794i	$-0.452302\pi$
$787$	8.37615	0.298577	0.149289	+	0.988794i	$0.452302\pi$
$788$	−18.2105	−0.648724
$789$	2.55298	0.0908885
$790$	−8.78256	−0.312469
$791$	−3.49444	−0.124248
$792$	−4.30568	−0.152996
$793$	−10.7846	−0.382972
$794$	−12.7191	−0.451383
$795$	−0.892217	−0.0316437
$796$	−14.4442	−0.511961
$797$	−33.6743	−1.19280	−0.596402	−	0.802686i	$-0.703404\pi$
$797$	−33.6743	−1.19280	−0.596402	+	0.802686i	$0.703404\pi$
$798$	0	0
$799$	11.0150	0.389684
$800$	−3.55862	−0.125816
$801$	40.7694	1.44052
$802$	−5.49595	−0.194069
$803$	−21.6460	−0.763870
$804$	−0.397212	−0.0140086
$805$	28.2279	0.994904
$806$	1.07736	0.0379483
$807$	1.88910	0.0664996
$808$	−5.74493	−0.202106
$809$	12.0457	0.423505	0.211752	−	0.977323i	$-0.432083\pi$
$809$	12.0457	0.423505	0.211752	+	0.977323i	$0.432083\pi$
$810$	10.5694	0.371372
$811$	32.8925	1.15501	0.577507	−	0.816386i	$-0.304026\pi$
$811$	32.8925	1.15501	0.577507	+	0.816386i	$0.304026\pi$
$812$	18.2415	0.640151
$813$	0.832618	0.0292012
$814$	2.14554	0.0752013
$815$	−1.40980	−0.0493830
$816$	1.09797	0.0384368
$817$	0	0
$818$	17.1252	0.598768
$819$	9.71510	0.339473
$820$	6.81533	0.238002
$821$	3.30171	0.115231	0.0576153	−	0.998339i	$-0.481650\pi$
$821$	3.30171	0.115231	0.0576153	+	0.998339i	$0.481650\pi$
$822$	−1.03332	−0.0360413
$823$	−9.83170	−0.342712	−0.171356	−	0.985209i	$-0.554815\pi$
$823$	−9.83170	−0.342712	−0.171356	+	0.985209i	$0.554815\pi$
$824$	12.1340	0.422709
$825$	−0.760912	−0.0264915
$826$	31.9792	1.11270
$827$	25.9646	0.902878	0.451439	−	0.892302i	$-0.350911\pi$
$827$	25.9646	0.902878	0.451439	+	0.892302i	$0.350911\pi$
$828$	21.4649	0.745957
$829$	−52.4096	−1.82026	−0.910131	−	0.414322i	$-0.864019\pi$
$829$	−52.4096	−1.82026	−0.910131	+	0.414322i	$0.864019\pi$
$830$	11.6436	0.404155
$831$	−3.10021	−0.107545
$832$	1.00000	0.0346688
$833$	27.0354	0.936720
$834$	1.99703	0.0691513
$835$	−30.0271	−1.03913
$836$	0	0
$837$	−0.952533	−0.0329244
$838$	−27.4907	−0.949650
$839$	−43.5134	−1.50225	−0.751124	−	0.660161i	$-0.770488\pi$
$839$	−43.5134	−1.50225	−0.751124	+	0.660161i	$0.770488\pi$
$840$	−0.579227	−0.0199852
$841$	2.26891	0.0782382
$842$	15.9882	0.550989
$843$	−1.31707	−0.0453621
$844$	15.9741	0.549851
$845$	1.20058	0.0413011
$846$	−4.41867	−0.151917
$847$	29.0650	0.998684
$848$	−5.02488	−0.172555
$849$	2.94500	0.101072
$850$	−26.4191	−0.906168
$851$	−10.6961	−0.366657
$852$	0.182638	0.00625708
$853$	−53.1030	−1.81821	−0.909107	−	0.416563i	$-0.863234\pi$
$853$	−53.1030	−1.81821	−0.909107	+	0.416563i	$0.863234\pi$
$854$	35.1810	1.20387
$855$	0	0
$856$	15.7633	0.538778
$857$	−32.0252	−1.09396	−0.546980	−	0.837146i	$-0.684222\pi$
$857$	−32.0252	−1.09396	−0.546980	+	0.837146i	$0.684222\pi$
$858$	0.213822	0.00729978
$859$	−0.189522	−0.00646642	−0.00323321	−	0.999995i	$-0.501029\pi$
$859$	−0.189522	−0.00646642	−0.00323321	+	0.999995i	$0.501029\pi$
$860$	0.360468	0.0122919
$861$	−2.73877	−0.0933371
$862$	17.8523	0.608052
$863$	49.0309	1.66903	0.834516	−	0.550984i	$-0.185748\pi$
$863$	49.0309	1.66903	0.834516	+	0.550984i	$0.185748\pi$
$864$	−0.884138	−0.0300790
$865$	−11.0622	−0.376127
$866$	18.2809	0.621209
$867$	5.63712	0.191447
$868$	−3.51450	−0.119290
$869$	−10.5762	−0.358773
$870$	−0.992890	−0.0336621
$871$	−2.68576	−0.0910036
$872$	4.25725	0.144169
$873$	−23.4367	−0.793211
$874$	0	0
$875$	33.5195	1.13317
$876$	−2.21429	−0.0748139
$877$	32.2540	1.08914	0.544571	−	0.838715i	$-0.316693\pi$
$877$	32.2540	1.08914	0.544571	+	0.838715i	$0.316693\pi$
$878$	−19.8760	−0.670784
$879$	−2.83970	−0.0957809
$880$	1.73575	0.0585122
$881$	0.195455	0.00658506	0.00329253	−	0.999995i	$-0.498952\pi$
$881$	0.195455	0.00658506	0.00329253	+	0.999995i	$0.498952\pi$
$882$	−10.8452	−0.365177
$883$	48.6870	1.63845	0.819224	−	0.573473i	$-0.194404\pi$
$883$	48.6870	1.63845	0.819224	+	0.573473i	$0.194404\pi$
$884$	7.42399	0.249696
$885$	−1.74064	−0.0585110
$886$	24.8341	0.834318
$887$	17.5243	0.588410	0.294205	−	0.955742i	$-0.404945\pi$
$887$	17.5243	0.588410	0.294205	+	0.955742i	$0.404945\pi$
$888$	0.219480	0.00736525
$889$	−6.00973	−0.201560
$890$	−16.4354	−0.550917
$891$	12.7280	0.426403
$892$	−19.5067	−0.653133
$893$	0	0
$894$	0.872295	0.0291739
$895$	−15.6025	−0.521534
$896$	−3.26215	−0.108981
$897$	−1.06596	−0.0355913
$898$	9.18647	0.306557
$899$	−6.02443	−0.200926
$900$	10.5980	0.353267
$901$	−37.3046	−1.24280
$902$	8.20720	0.273270
$903$	−0.144856	−0.00482050
$904$	1.07121	0.0356278
$905$	−13.5279	−0.449683
$906$	−1.52584	−0.0506926
$907$	7.13497	0.236913	0.118456	−	0.992959i	$-0.462205\pi$
$907$	7.13497	0.236913	0.118456	+	0.992959i	$0.462205\pi$
$908$	−12.0844	−0.401034
$909$	17.1091	0.567474
$910$	−3.91646	−0.129829
$911$	6.92966	0.229590	0.114795	−	0.993389i	$-0.463379\pi$
$911$	6.92966	0.229590	0.114795	+	0.993389i	$0.463379\pi$
$912$	0	0
$913$	14.0215	0.464045
$914$	−7.90161	−0.261362
$915$	−1.91491	−0.0633050
$916$	5.62571	0.185879
$917$	−49.5219	−1.63536
$918$	−6.56383	−0.216639
$919$	39.4656	1.30185	0.650924	−	0.759142i	$-0.274381\pi$
$919$	39.4656	1.30185	0.650924	+	0.759142i	$0.274381\pi$
$920$	−8.65317	−0.285287
$921$	−2.45332	−0.0808395
$922$	7.31985	0.241066
$923$	1.23491	0.0406476
$924$	−0.697521	−0.0229467
$925$	−5.28105	−0.173640
$926$	−15.8660	−0.521389
$927$	−36.1367	−1.18688
$928$	−5.59186	−0.183562
$929$	41.4126	1.35870	0.679351	−	0.733813i	$-0.262261\pi$
$929$	41.4126	1.35870	0.679351	+	0.733813i	$0.262261\pi$
$930$	0.191295	0.00627283
$931$	0	0
$932$	−14.3449	−0.469883
$933$	2.29677	0.0751929
$934$	6.56283	0.214742
$935$	12.8862	0.421424
$936$	−2.97813	−0.0973431
$937$	30.8438	1.00762	0.503812	−	0.863813i	$-0.331931\pi$
$937$	30.8438	1.00762	0.503812	+	0.863813i	$0.331931\pi$
$938$	8.76136	0.286069
$939$	−2.56889	−0.0838324
$940$	1.78130	0.0580998
$941$	19.7867	0.645029	0.322514	−	0.946565i	$-0.395472\pi$
$941$	19.7867	0.645029	0.322514	+	0.946565i	$0.395472\pi$
$942$	−2.03696	−0.0663679
$943$	−40.9150	−1.33238
$944$	−9.80311	−0.319064
$945$	3.46269	0.112641
$946$	0.434086	0.0141133
$947$	−14.2742	−0.463848	−0.231924	−	0.972734i	$-0.574502\pi$
$947$	−14.2742	−0.463848	−0.231924	+	0.972734i	$0.574502\pi$
$948$	−1.08190	−0.0351384
$949$	−14.9720	−0.486011
$950$	0	0
$951$	−4.55877	−0.147828
$952$	−24.2182	−0.784915
$953$	49.4499	1.60184	0.800920	−	0.598771i	$-0.204344\pi$
$953$	49.4499	1.60184	0.800920	+	0.598771i	$0.204344\pi$
$954$	14.9647	0.484501
$955$	20.2483	0.655219
$956$	−15.5343	−0.502416
$957$	−1.19567	−0.0386504
$958$	−31.2995	−1.01124
$959$	22.7922	0.735997
$960$	0.177560	0.00573072
$961$	−29.8393	−0.962558
$962$	1.48402	0.0478467
$963$	−46.9450	−1.51278
$964$	13.9211	0.448370
$965$	−19.4892	−0.627378
$966$	3.47732	0.111881
$967$	50.5368	1.62515	0.812577	−	0.582854i	$-0.198064\pi$
$967$	50.5368	1.62515	0.812577	+	0.582854i	$0.198064\pi$
$968$	−8.90976	−0.286370
$969$	0	0
$970$	9.44806	0.303359
$971$	5.78573	0.185673	0.0928364	−	0.995681i	$-0.470407\pi$
$971$	5.78573	0.185673	0.0928364	+	0.995681i	$0.470407\pi$
$972$	3.95443	0.126838
$973$	−44.0487	−1.41213
$974$	37.2463	1.19345
$975$	−0.526303	−0.0168552
$976$	−10.7846	−0.345206
$977$	25.5842	0.818512	0.409256	−	0.912419i	$-0.365788\pi$
$977$	25.5842	0.818512	0.409256	+	0.912419i	$0.365788\pi$
$978$	−0.173669	−0.00555331
$979$	−19.7920	−0.632555
$980$	4.37205	0.139660
$981$	−12.6786	−0.404797
$982$	20.2698	0.646834
$983$	−8.82077	−0.281339	−0.140669	−	0.990057i	$-0.544925\pi$
$983$	−8.82077	−0.281339	−0.140669	+	0.990057i	$0.544925\pi$
$984$	0.839560	0.0267642
$985$	−21.8632	−0.696618
$986$	−41.5139	−1.32207
$987$	−0.715826	−0.0227850
$988$	0	0
$989$	−2.16403	−0.0688121
$990$	−5.16929	−0.164291
$991$	−44.3000	−1.40723	−0.703617	−	0.710579i	$-0.748433\pi$
$991$	−44.3000	−1.40723	−0.703617	+	0.710579i	$0.748433\pi$
$992$	1.07736	0.0342061
$993$	−4.04940	−0.128504
$994$	−4.02847	−0.127775
$995$	−17.3414	−0.549759
$996$	1.43434	0.0454488
$997$	−58.4338	−1.85062	−0.925308	−	0.379215i	$-0.876194\pi$
$997$	−58.4338	−1.85062	−0.925308	+	0.379215i	$0.876194\pi$
$998$	21.4350	0.678514
$999$	−1.31208	−0.0415123

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9386.2.a.bp.1.6		9
19.4	even	9		494.2.x.b.339.2	✓	18
19.5	even	9		494.2.x.b.443.2	yes	18
19.18	odd	2		9386.2.a.bo.1.4		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
494.2.x.b.339.2	✓	18	19.4	even	9
494.2.x.b.443.2	yes	18	19.5	even	9
9386.2.a.bo.1.4		9	19.18	odd	2
9386.2.a.bp.1.6		9	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 9386 = 2 \cdot 13 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9386.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.147896 q^{3} +1.00000 q^{4} +1.20058 q^{5} +0.147896 q^{6} -3.26215 q^{7} +1.00000 q^{8} -2.97813 q^{9} +1.20058 q^{10} +1.44577 q^{11} +0.147896 q^{12} +1.00000 q^{13} -3.26215 q^{14} +0.177560 q^{15} +1.00000 q^{16} +7.42399 q^{17} -2.97813 q^{18} +1.20058 q^{20} -0.482457 q^{21} +1.44577 q^{22} -7.20751 q^{23} +0.147896 q^{24} -3.55862 q^{25} +1.00000 q^{26} -0.884138 q^{27} -3.26215 q^{28} -5.59186 q^{29} +0.177560 q^{30} +1.07736 q^{31} +1.00000 q^{32} +0.213822 q^{33} +7.42399 q^{34} -3.91646 q^{35} -2.97813 q^{36} +1.48402 q^{37} +0.147896 q^{39} +1.20058 q^{40} +5.67671 q^{41} -0.482457 q^{42} +0.300246 q^{43} +1.44577 q^{44} -3.57547 q^{45} -7.20751 q^{46} +1.48371 q^{47} +0.147896 q^{48} +3.64162 q^{49} -3.55862 q^{50} +1.09797 q^{51} +1.00000 q^{52} -5.02488 q^{53} -0.884138 q^{54} +1.73575 q^{55} -3.26215 q^{56} -5.59186 q^{58} -9.80311 q^{59} +0.177560 q^{60} -10.7846 q^{61} +1.07736 q^{62} +9.71510 q^{63} +1.00000 q^{64} +1.20058 q^{65} +0.213822 q^{66} -2.68576 q^{67} +7.42399 q^{68} -1.06596 q^{69} -3.91646 q^{70} +1.23491 q^{71} -2.97813 q^{72} -14.9720 q^{73} +1.48402 q^{74} -0.526303 q^{75} -4.71631 q^{77} +0.147896 q^{78} -7.31528 q^{79} +1.20058 q^{80} +8.80362 q^{81} +5.67671 q^{82} +9.69833 q^{83} -0.482457 q^{84} +8.91306 q^{85} +0.300246 q^{86} -0.827011 q^{87} +1.44577 q^{88} -13.6896 q^{89} -3.57547 q^{90} -3.26215 q^{91} -7.20751 q^{92} +0.159336 q^{93} +1.48371 q^{94} +0.147896 q^{96} +7.86960 q^{97} +3.64162 q^{98} -4.30568 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 9 q^{2} - 3 q^{3} + 9 q^{4} - 3 q^{5} - 3 q^{6} - 6 q^{7} + 9 q^{8} + 6 q^{9} - 3 q^{10} - 6 q^{11} - 3 q^{12} + 9 q^{13} - 6 q^{14} - 3 q^{15} + 9 q^{16} + 6 q^{18} - 3 q^{20} - 9 q^{21} - 6 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 9 * q + 9 * q^2 - 3 * q^3 + 9 * q^4 - 3 * q^5 - 3 * q^6 - 6 * q^7 + 9 * q^8 + 6 * q^9 - 3 * q^10 - 6 * q^11 - 3 * q^12 + 9 * q^13 - 6 * q^14 - 3 * q^15 + 9 * q^16 + 6 * q^18 - 3 * q^20 - 9 * q^21 - 6 * q^22 - 3 * q^23 - 3 * q^24 + 9 * q^26 - 15 * q^27 - 6 * q^28 - 21 * q^29 - 3 * q^30 - 3 * q^31 + 9 * q^32 - 18 * q^33 - 27 * q^35 + 6 * q^36 - 12 * q^37 - 3 * q^39 - 3 * q^40 - 9 * q^42 - 3 * q^43 - 6 * q^44 + 3 * q^45 - 3 * q^46 - 3 * q^48 + 3 * q^49 - 3 * q^51 + 9 * q^52 + 6 * q^53 - 15 * q^54 - 9 * q^55 - 6 * q^56 - 21 * q^58 - 12 * q^59 - 3 * q^60 - 15 * q^61 - 3 * q^62 + 6 * q^63 + 9 * q^64 - 3 * q^65 - 18 * q^66 - 21 * q^67 - 21 * q^69 - 27 * q^70 - 21 * q^71 + 6 * q^72 - 45 * q^73 - 12 * q^74 + 18 * q^75 - 15 * q^77 - 3 * q^78 + 9 * q^79 - 3 * q^80 - 27 * q^81 + 15 * q^83 - 9 * q^84 - 9 * q^85 - 3 * q^86 + 9 * q^87 - 6 * q^88 + 3 * q^89 + 3 * q^90 - 6 * q^91 - 3 * q^92 + 21 * q^93 - 3 * q^96 + 3 * q^97 + 3 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more