LMFDB - Embedded newform 2366.2.a.bg.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2366,2,Mod(1,2366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2366, 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("2366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2366 = 2 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2366.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:	$18.8926051182$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.6052921.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 11x^{4} + 7x^{3} + 33x^{2} - 9x - 27 $ x^6 - x^5 - 11x^4 + 7x^3 + 33x^2 - 9x - 27
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.05140$ of defining polynomial
Character	$\chi$	$=$	2366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.05140 q^{3} +1.00000 q^{4} +2.26985 q^{5} -1.05140 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.89456 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.05140 q^{3} +1.00000 q^{4} +2.26985 q^{5} -1.05140 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.89456 q^{9} +2.26985 q^{10} +0.977125 q^{11} -1.05140 q^{12} +1.00000 q^{14} -2.38653 q^{15} +1.00000 q^{16} +0.963254 q^{17} -1.89456 q^{18} -5.10479 q^{19} +2.26985 q^{20} -1.05140 q^{21} +0.977125 q^{22} +8.11859 q^{23} -1.05140 q^{24} +0.152241 q^{25} +5.14614 q^{27} +1.00000 q^{28} +9.77952 q^{29} -2.38653 q^{30} +5.15994 q^{31} +1.00000 q^{32} -1.02735 q^{33} +0.963254 q^{34} +2.26985 q^{35} -1.89456 q^{36} +0.794311 q^{37} -5.10479 q^{38} +2.26985 q^{40} -1.49967 q^{41} -1.05140 q^{42} -7.93286 q^{43} +0.977125 q^{44} -4.30037 q^{45} +8.11859 q^{46} +5.04879 q^{47} -1.05140 q^{48} +1.00000 q^{49} +0.152241 q^{50} -1.01277 q^{51} +3.68079 q^{53} +5.14614 q^{54} +2.21793 q^{55} +1.00000 q^{56} +5.36718 q^{57} +9.77952 q^{58} +12.8260 q^{59} -2.38653 q^{60} -3.93268 q^{61} +5.15994 q^{62} -1.89456 q^{63} +1.00000 q^{64} -1.02735 q^{66} +0.0496112 q^{67} +0.963254 q^{68} -8.53589 q^{69} +2.26985 q^{70} -3.71940 q^{71} -1.89456 q^{72} -8.87873 q^{73} +0.794311 q^{74} -0.160066 q^{75} -5.10479 q^{76} +0.977125 q^{77} -6.98214 q^{79} +2.26985 q^{80} +0.273022 q^{81} -1.49967 q^{82} +6.24779 q^{83} -1.05140 q^{84} +2.18645 q^{85} -7.93286 q^{86} -10.2822 q^{87} +0.977125 q^{88} -5.92385 q^{89} -4.30037 q^{90} +8.11859 q^{92} -5.42516 q^{93} +5.04879 q^{94} -11.5871 q^{95} -1.05140 q^{96} +7.29137 q^{97} +1.00000 q^{98} -1.85122 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9	$ 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9} + 4 q^{10} + 6 q^{11} + q^{12} + 6 q^{14} - 5 q^{15} + 6 q^{16} - 9 q^{17} + 5 q^{18} + 10 q^{19} + 4 q^{20} + q^{21} + 6 q^{22} + 21 q^{23} + q^{24} + 8 q^{25} + 7 q^{27} + 6 q^{28} - q^{29} - 5 q^{30} + 20 q^{31} + 6 q^{32} + 9 q^{33} - 9 q^{34} + 4 q^{35} + 5 q^{36} + 16 q^{37} + 10 q^{38} + 4 q^{40} + 2 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} + 17 q^{45} + 21 q^{46} - 5 q^{47} + q^{48} + 6 q^{49} + 8 q^{50} - 15 q^{51} + 28 q^{53} + 7 q^{54} - 29 q^{55} + 6 q^{56} + 22 q^{57} - q^{58} - 12 q^{59} - 5 q^{60} - 27 q^{61} + 20 q^{62} + 5 q^{63} + 6 q^{64} + 9 q^{66} + 16 q^{67} - 9 q^{68} - 15 q^{69} + 4 q^{70} + 5 q^{72} + 38 q^{73} + 16 q^{74} - 7 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} + 4 q^{80} - 26 q^{81} + 2 q^{82} - 6 q^{83} + q^{84} + 9 q^{85} + 2 q^{86} - 39 q^{87} + 6 q^{88} - q^{89} + 17 q^{90} + 21 q^{92} - 7 q^{93} - 5 q^{94} + 3 q^{95} + q^{96} + 16 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9 + 4 * q^10 + 6 * q^11 + q^12 + 6 * q^14 - 5 * q^15 + 6 * q^16 - 9 * q^17 + 5 * q^18 + 10 * q^19 + 4 * q^20 + q^21 + 6 * q^22 + 21 * q^23 + q^24 + 8 * q^25 + 7 * q^27 + 6 * q^28 - q^29 - 5 * q^30 + 20 * q^31 + 6 * q^32 + 9 * q^33 - 9 * q^34 + 4 * q^35 + 5 * q^36 + 16 * q^37 + 10 * q^38 + 4 * q^40 + 2 * q^41 + q^42 + 2 * q^43 + 6 * q^44 + 17 * q^45 + 21 * q^46 - 5 * q^47 + q^48 + 6 * q^49 + 8 * q^50 - 15 * q^51 + 28 * q^53 + 7 * q^54 - 29 * q^55 + 6 * q^56 + 22 * q^57 - q^58 - 12 * q^59 - 5 * q^60 - 27 * q^61 + 20 * q^62 + 5 * q^63 + 6 * q^64 + 9 * q^66 + 16 * q^67 - 9 * q^68 - 15 * q^69 + 4 * q^70 + 5 * q^72 + 38 * q^73 + 16 * q^74 - 7 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 + 4 * q^80 - 26 * q^81 + 2 * q^82 - 6 * q^83 + q^84 + 9 * q^85 + 2 * q^86 - 39 * q^87 + 6 * q^88 - q^89 + 17 * q^90 + 21 * q^92 - 7 * q^93 - 5 * q^94 + 3 * q^95 + q^96 + 16 * q^97 + 6 * q^98 - 4 * q^99

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
$2$	1.00000	0.707107
$3$	−1.05140	−0.607026	−0.303513	−	0.952827i	$-0.598160\pi$
$3$	−1.05140	−0.607026	−0.303513	+	0.952827i	$0.598160\pi$
$4$	1.00000	0.500000
$5$	2.26985	1.01511	0.507555	−	0.861619i	$-0.330549\pi$
$5$	2.26985	1.01511	0.507555	+	0.861619i	$0.330549\pi$
$6$	−1.05140	−0.429232
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	−1.89456	−0.631519
$10$	2.26985	0.717791
$11$	0.977125	0.294614	0.147307	−	0.989091i	$-0.452939\pi$
$11$	0.977125	0.294614	0.147307	+	0.989091i	$0.452939\pi$
$12$	−1.05140	−0.303513
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−2.38653	−0.616198
$16$	1.00000	0.250000
$17$	0.963254	0.233623	0.116812	−	0.993154i	$-0.462733\pi$
$17$	0.963254	0.233623	0.116812	+	0.993154i	$0.462733\pi$
$18$	−1.89456	−0.446552
$19$	−5.10479	−1.17112	−0.585560	−	0.810629i	$-0.699125\pi$
$19$	−5.10479	−1.17112	−0.585560	+	0.810629i	$0.699125\pi$
$20$	2.26985	0.507555
$21$	−1.05140	−0.229434
$22$	0.977125	0.208324
$23$	8.11859	1.69284	0.846422	−	0.532513i	$-0.178752\pi$
$23$	8.11859	1.69284	0.846422	+	0.532513i	$0.178752\pi$
$24$	−1.05140	−0.214616
$25$	0.152241	0.0304482
$26$	0	0
$27$	5.14614	0.990375
$28$	1.00000	0.188982
$29$	9.77952	1.81601	0.908005	−	0.418959i	$-0.137605\pi$
$29$	9.77952	1.81601	0.908005	+	0.418959i	$0.137605\pi$
$30$	−2.38653	−0.435718
$31$	5.15994	0.926752	0.463376	−	0.886162i	$-0.346638\pi$
$31$	5.15994	0.926752	0.463376	+	0.886162i	$0.346638\pi$
$32$	1.00000	0.176777
$33$	−1.02735	−0.178839
$34$	0.963254	0.165197
$35$	2.26985	0.383675
$36$	−1.89456	−0.315760
$37$	0.794311	0.130584	0.0652920	−	0.997866i	$-0.479202\pi$
$37$	0.794311	0.130584	0.0652920	+	0.997866i	$0.479202\pi$
$38$	−5.10479	−0.828107
$39$	0	0
$40$	2.26985	0.358896
$41$	−1.49967	−0.234208	−0.117104	−	0.993120i	$-0.537361\pi$
$41$	−1.49967	−0.234208	−0.117104	+	0.993120i	$0.537361\pi$
$42$	−1.05140	−0.162235
$43$	−7.93286	−1.20975	−0.604875	−	0.796321i	$-0.706777\pi$
$43$	−7.93286	−1.20975	−0.604875	+	0.796321i	$0.706777\pi$
$44$	0.977125	0.147307
$45$	−4.30037	−0.641061
$46$	8.11859	1.19702
$47$	5.04879	0.736442	0.368221	−	0.929738i	$-0.379967\pi$
$47$	5.04879	0.736442	0.368221	+	0.929738i	$0.379967\pi$
$48$	−1.05140	−0.151757
$49$	1.00000	0.142857
$50$	0.152241	0.0215301
$51$	−1.01277	−0.141816
$52$	0	0
$53$	3.68079	0.505596	0.252798	−	0.967519i	$-0.418649\pi$
$53$	3.68079	0.505596	0.252798	+	0.967519i	$0.418649\pi$
$54$	5.14614	0.700301
$55$	2.21793	0.299066
$56$	1.00000	0.133631
$57$	5.36718	0.710900
$58$	9.77952	1.28411
$59$	12.8260	1.66980	0.834898	−	0.550404i	$-0.185526\pi$
$59$	12.8260	1.66980	0.834898	+	0.550404i	$0.185526\pi$
$60$	−2.38653	−0.308099
$61$	−3.93268	−0.503528	−0.251764	−	0.967789i	$-0.581011\pi$
$61$	−3.93268	−0.503528	−0.251764	+	0.967789i	$0.581011\pi$
$62$	5.15994	0.655313
$63$	−1.89456	−0.238692
$64$	1.00000	0.125000
$65$	0	0
$66$	−1.02735	−0.126458
$67$	0.0496112	0.00606097	0.00303049	−	0.999995i	$-0.499035\pi$
$67$	0.0496112	0.00606097	0.00303049	+	0.999995i	$0.499035\pi$
$68$	0.963254	0.116812
$69$	−8.53589	−1.02760
$70$	2.26985	0.271300
$71$	−3.71940	−0.441412	−0.220706	−	0.975340i	$-0.570836\pi$
$71$	−3.71940	−0.441412	−0.220706	+	0.975340i	$0.570836\pi$
$72$	−1.89456	−0.223276
$73$	−8.87873	−1.03918	−0.519588	−	0.854417i	$-0.673915\pi$
$73$	−8.87873	−1.03918	−0.519588	+	0.854417i	$0.673915\pi$
$74$	0.794311	0.0923368
$75$	−0.160066	−0.0184829
$76$	−5.10479	−0.585560
$77$	0.977125	0.111354
$78$	0	0
$79$	−6.98214	−0.785552	−0.392776	−	0.919634i	$-0.628485\pi$
$79$	−6.98214	−0.785552	−0.392776	+	0.919634i	$0.628485\pi$
$80$	2.26985	0.253777
$81$	0.273022	0.0303357
$82$	−1.49967	−0.165610
$83$	6.24779	0.685785	0.342892	−	0.939375i	$-0.388593\pi$
$83$	6.24779	0.685785	0.342892	+	0.939375i	$0.388593\pi$
$84$	−1.05140	−0.114717
$85$	2.18645	0.237153
$86$	−7.93286	−0.855422
$87$	−10.2822	−1.10237
$88$	0.977125	0.104162
$89$	−5.92385	−0.627927	−0.313964	−	0.949435i	$-0.601657\pi$
$89$	−5.92385	−0.627927	−0.313964	+	0.949435i	$0.601657\pi$
$90$	−4.30037	−0.453299
$91$	0	0
$92$	8.11859	0.846422
$93$	−5.42516	−0.562563
$94$	5.04879	0.520743
$95$	−11.5871	−1.18882
$96$	−1.05140	−0.107308
$97$	7.29137	0.740326	0.370163	−	0.928967i	$-0.379302\pi$
$97$	7.29137	0.740326	0.370163	+	0.928967i	$0.379302\pi$
$98$	1.00000	0.101015
$99$	−1.85122	−0.186055
$100$	0.152241	0.0152241
$101$	−18.1884	−1.80981	−0.904906	−	0.425611i	$-0.860059\pi$
$101$	−18.1884	−1.80981	−0.904906	+	0.425611i	$0.860059\pi$
$102$	−1.01277	−0.100279
$103$	5.63247	0.554984	0.277492	−	0.960728i	$-0.410497\pi$
$103$	5.63247	0.554984	0.277492	+	0.960728i	$0.410497\pi$
$104$	0	0
$105$	−2.38653	−0.232901
$106$	3.68079	0.357510
$107$	11.6580	1.12702	0.563510	−	0.826110i	$-0.309451\pi$
$107$	11.6580	1.12702	0.563510	+	0.826110i	$0.309451\pi$
$108$	5.14614	0.495187
$109$	14.8986	1.42703	0.713515	−	0.700640i	$-0.247102\pi$
$109$	14.8986	1.42703	0.713515	+	0.700640i	$0.247102\pi$
$110$	2.21793	0.211471
$111$	−0.835139	−0.0792679
$112$	1.00000	0.0944911
$113$	11.4817	1.08010	0.540052	−	0.841632i	$-0.318405\pi$
$113$	11.4817	1.08010	0.540052	+	0.841632i	$0.318405\pi$
$114$	5.36718	0.502682
$115$	18.4280	1.71842
$116$	9.77952	0.908005
$117$	0	0
$118$	12.8260	1.18072
$119$	0.963254	0.0883014
$120$	−2.38653	−0.217859
$121$	−10.0452	−0.913202
$122$	−3.93268	−0.356048
$123$	1.57675	0.142171
$124$	5.15994	0.463376
$125$	−11.0037	−0.984202
$126$	−1.89456	−0.168781
$127$	−7.13960	−0.633537	−0.316768	−	0.948503i	$-0.602598\pi$
$127$	−7.13960	−0.633537	−0.316768	+	0.948503i	$0.602598\pi$
$128$	1.00000	0.0883883
$129$	8.34061	0.734350
$130$	0	0
$131$	20.0739	1.75387	0.876933	−	0.480613i	$-0.159586\pi$
$131$	20.0739	1.75387	0.876933	+	0.480613i	$0.159586\pi$
$132$	−1.02735	−0.0894193
$133$	−5.10479	−0.442642
$134$	0.0496112	0.00428575
$135$	11.6810	1.00534
$136$	0.963254	0.0825984
$137$	14.5252	1.24097	0.620485	−	0.784218i	$-0.286936\pi$
$137$	14.5252	1.24097	0.620485	+	0.784218i	$0.286936\pi$
$138$	−8.53589	−0.726623
$139$	−7.51577	−0.637479	−0.318740	−	0.947842i	$-0.603260\pi$
$139$	−7.51577	−0.637479	−0.318740	+	0.947842i	$0.603260\pi$
$140$	2.26985	0.191838
$141$	−5.30830	−0.447039
$142$	−3.71940	−0.312125
$143$	0	0
$144$	−1.89456	−0.157880
$145$	22.1981	1.84345
$146$	−8.87873	−0.734809
$147$	−1.05140	−0.0867180
$148$	0.794311	0.0652920
$149$	−5.10994	−0.418622	−0.209311	−	0.977849i	$-0.567122\pi$
$149$	−5.10994	−0.418622	−0.209311	+	0.977849i	$0.567122\pi$
$150$	−0.160066	−0.0130693
$151$	22.3477	1.81863	0.909314	−	0.416110i	$-0.136607\pi$
$151$	22.3477	1.81863	0.909314	+	0.416110i	$0.136607\pi$
$152$	−5.10479	−0.414053
$153$	−1.82494	−0.147538
$154$	0.977125	0.0787390
$155$	11.7123	0.940755
$156$	0	0
$157$	−10.2561	−0.818528	−0.409264	−	0.912416i	$-0.634214\pi$
$157$	−10.2561	−0.818528	−0.409264	+	0.912416i	$0.634214\pi$
$158$	−6.98214	−0.555469
$159$	−3.86999	−0.306910
$160$	2.26985	0.179448
$161$	8.11859	0.639835
$162$	0.273022	0.0214506
$163$	−16.7390	−1.31110	−0.655550	−	0.755151i	$-0.727563\pi$
$163$	−16.7390	−1.31110	−0.655550	+	0.755151i	$0.727563\pi$
$164$	−1.49967	−0.117104
$165$	−2.33193	−0.181541
$166$	6.24779	0.484923
$167$	−12.8583	−0.995002	−0.497501	−	0.867463i	$-0.665749\pi$
$167$	−12.8583	−0.995002	−0.497501	+	0.867463i	$0.665749\pi$
$168$	−1.05140	−0.0811173
$169$	0	0
$170$	2.18645	0.167693
$171$	9.67132	0.739584
$172$	−7.93286	−0.604875
$173$	−1.45155	−0.110359	−0.0551795	−	0.998476i	$-0.517573\pi$
$173$	−1.45155	−0.110359	−0.0551795	+	0.998476i	$0.517573\pi$
$174$	−10.2822	−0.779490
$175$	0.152241	0.0115083
$176$	0.977125	0.0736536
$177$	−13.4852	−1.01361
$178$	−5.92385	−0.444012
$179$	2.71291	0.202772	0.101386	−	0.994847i	$-0.467672\pi$
$179$	2.71291	0.202772	0.101386	+	0.994847i	$0.467672\pi$
$180$	−4.30037	−0.320531
$181$	−22.5406	−1.67543	−0.837715	−	0.546107i	$-0.816109\pi$
$181$	−22.5406	−1.67543	−0.837715	+	0.546107i	$0.816109\pi$
$182$	0	0
$183$	4.13482	0.305655
$184$	8.11859	0.598510
$185$	1.80297	0.132557
$186$	−5.42516	−0.397792
$187$	0.941220	0.0688288
$188$	5.04879	0.368221
$189$	5.14614	0.374327
$190$	−11.5871	−0.840619
$191$	−6.68377	−0.483621	−0.241810	−	0.970324i	$-0.577741\pi$
$191$	−6.68377	−0.483621	−0.241810	+	0.970324i	$0.577741\pi$
$192$	−1.05140	−0.0758783
$193$	18.0081	1.29625	0.648126	−	0.761534i	$-0.275553\pi$
$193$	18.0081	1.29625	0.648126	+	0.761534i	$0.275553\pi$
$194$	7.29137	0.523490
$195$	0	0
$196$	1.00000	0.0714286
$197$	−2.56211	−0.182543	−0.0912715	−	0.995826i	$-0.529093\pi$
$197$	−2.56211	−0.182543	−0.0912715	+	0.995826i	$0.529093\pi$
$198$	−1.85122	−0.131560
$199$	8.54978	0.606078	0.303039	−	0.952978i	$-0.401999\pi$
$199$	8.54978	0.606078	0.303039	+	0.952978i	$0.401999\pi$
$200$	0.152241	0.0107651
$201$	−0.0521612	−0.00367917
$202$	−18.1884	−1.27973
$203$	9.77952	0.686388
$204$	−1.01277	−0.0709078
$205$	−3.40402	−0.237747
$206$	5.63247	0.392433
$207$	−15.3811	−1.06906
$208$	0	0
$209$	−4.98802	−0.345028
$210$	−2.38653	−0.164686
$211$	14.4132	0.992242	0.496121	−	0.868253i	$-0.334757\pi$
$211$	14.4132	0.992242	0.496121	+	0.868253i	$0.334757\pi$
$212$	3.68079	0.252798
$213$	3.91058	0.267949
$214$	11.6580	0.796923
$215$	−18.0064	−1.22803
$216$	5.14614	0.350150
$217$	5.15994	0.350279
$218$	14.8986	1.00906
$219$	9.33510	0.630807
$220$	2.21793	0.149533
$221$	0	0
$222$	−0.835139	−0.0560508
$223$	−5.56995	−0.372992	−0.186496	−	0.982456i	$-0.559713\pi$
$223$	−5.56995	−0.372992	−0.186496	+	0.982456i	$0.559713\pi$
$224$	1.00000	0.0668153
$225$	−0.288429	−0.0192286
$226$	11.4817	0.763749
$227$	7.08232	0.470070	0.235035	−	0.971987i	$-0.424480\pi$
$227$	7.08232	0.470070	0.235035	+	0.971987i	$0.424480\pi$
$228$	5.36718	0.355450
$229$	13.9978	0.924999	0.462500	−	0.886619i	$-0.346953\pi$
$229$	13.9978	0.924999	0.462500	+	0.886619i	$0.346953\pi$
$230$	18.4280	1.21511
$231$	−1.02735	−0.0675946
$232$	9.77952	0.642057
$233$	−23.6892	−1.55193	−0.775964	−	0.630777i	$-0.782736\pi$
$233$	−23.6892	−1.55193	−0.775964	+	0.630777i	$0.782736\pi$
$234$	0	0
$235$	11.4600	0.747569
$236$	12.8260	0.834898
$237$	7.34102	0.476851
$238$	0.963254	0.0624385
$239$	−8.32300	−0.538370	−0.269185	−	0.963088i	$-0.586754\pi$
$239$	−8.32300	−0.538370	−0.269185	+	0.963088i	$0.586754\pi$
$240$	−2.38653	−0.154050
$241$	−27.7146	−1.78525	−0.892627	−	0.450796i	$-0.851140\pi$
$241$	−27.7146	−1.78525	−0.892627	+	0.450796i	$0.851140\pi$
$242$	−10.0452	−0.645732
$243$	−15.7255	−1.00879
$244$	−3.93268	−0.251764
$245$	2.26985	0.145016
$246$	1.57675	0.100530
$247$	0	0
$248$	5.15994	0.327656
$249$	−6.56893	−0.416289
$250$	−11.0037	−0.695936
$251$	−15.4094	−0.972634	−0.486317	−	0.873782i	$-0.661660\pi$
$251$	−15.4094	−0.972634	−0.486317	+	0.873782i	$0.661660\pi$
$252$	−1.89456	−0.119346
$253$	7.93288	0.498736
$254$	−7.13960	−0.447978
$255$	−2.29883	−0.143958
$256$	1.00000	0.0625000
$257$	−28.6449	−1.78682	−0.893411	−	0.449241i	$-0.851695\pi$
$257$	−28.6449	−1.78682	−0.893411	+	0.449241i	$0.851695\pi$
$258$	8.34061	0.519264
$259$	0.794311	0.0493561
$260$	0	0
$261$	−18.5279	−1.14685
$262$	20.0739	1.24017
$263$	24.8105	1.52988	0.764942	−	0.644100i	$-0.222768\pi$
$263$	24.8105	1.52988	0.764942	+	0.644100i	$0.222768\pi$
$264$	−1.02735	−0.0632290
$265$	8.35487	0.513235
$266$	−5.10479	−0.312995
$267$	6.22834	0.381168
$268$	0.0496112	0.00303049
$269$	−27.2428	−1.66103	−0.830513	−	0.556999i	$-0.811953\pi$
$269$	−27.2428	−1.66103	−0.830513	+	0.556999i	$0.811953\pi$
$270$	11.6810	0.710882
$271$	−0.406075	−0.0246673	−0.0123336	−	0.999924i	$-0.503926\pi$
$271$	−0.406075	−0.0246673	−0.0123336	+	0.999924i	$0.503926\pi$
$272$	0.963254	0.0584059
$273$	0	0
$274$	14.5252	0.877498
$275$	0.148758	0.00897047
$276$	−8.53589	−0.513800
$277$	24.6439	1.48071	0.740355	−	0.672216i	$-0.234657\pi$
$277$	24.6439	1.48071	0.740355	+	0.672216i	$0.234657\pi$
$278$	−7.51577	−0.450766
$279$	−9.77580	−0.585262
$280$	2.26985	0.135650
$281$	−2.06017	−0.122899	−0.0614497	−	0.998110i	$-0.519572\pi$
$281$	−2.06017	−0.122899	−0.0614497	+	0.998110i	$0.519572\pi$
$282$	−5.30830	−0.316105
$283$	−7.94702	−0.472401	−0.236201	−	0.971704i	$-0.575902\pi$
$283$	−7.94702	−0.472401	−0.236201	+	0.971704i	$0.575902\pi$
$284$	−3.71940	−0.220706
$285$	12.1827	0.721642
$286$	0	0
$287$	−1.49967	−0.0885225
$288$	−1.89456	−0.111638
$289$	−16.0721	−0.945420
$290$	22.1981	1.30352
$291$	−7.66614	−0.449397
$292$	−8.87873	−0.519588
$293$	29.3231	1.71307	0.856537	−	0.516086i	$-0.172612\pi$
$293$	29.3231	1.71307	0.856537	+	0.516086i	$0.172612\pi$
$294$	−1.05140	−0.0613189
$295$	29.1130	1.69503
$296$	0.794311	0.0461684
$297$	5.02842	0.291779
$298$	−5.10994	−0.296011
$299$	0	0
$300$	−0.160066	−0.00924143
$301$	−7.93286	−0.457242
$302$	22.3477	1.28596
$303$	19.1233	1.09860
$304$	−5.10479	−0.292780
$305$	−8.92662	−0.511137
$306$	−1.82494	−0.104325
$307$	14.0749	0.803299	0.401649	−	0.915793i	$-0.368437\pi$
$307$	14.0749	0.803299	0.401649	+	0.915793i	$0.368437\pi$
$308$	0.977125	0.0556769
$309$	−5.92198	−0.336890
$310$	11.7123	0.665215
$311$	−27.2622	−1.54589	−0.772947	−	0.634470i	$-0.781218\pi$
$311$	−27.2622	−1.54589	−0.772947	+	0.634470i	$0.781218\pi$
$312$	0	0
$313$	−20.8963	−1.18113	−0.590564	−	0.806991i	$-0.701095\pi$
$313$	−20.8963	−1.18113	−0.590564	+	0.806991i	$0.701095\pi$
$314$	−10.2561	−0.578787
$315$	−4.30037	−0.242298
$316$	−6.98214	−0.392776
$317$	−15.7420	−0.884161	−0.442081	−	0.896975i	$-0.645759\pi$
$317$	−15.7420	−0.884161	−0.442081	+	0.896975i	$0.645759\pi$
$318$	−3.86999	−0.217018
$319$	9.55581	0.535023
$320$	2.26985	0.126889
$321$	−12.2572	−0.684130
$322$	8.11859	0.452431
$323$	−4.91721	−0.273601
$324$	0.273022	0.0151679
$325$	0	0
$326$	−16.7390	−0.927088
$327$	−15.6644	−0.866245
$328$	−1.49967	−0.0828052
$329$	5.04879	0.278349
$330$	−2.33193	−0.128369
$331$	2.40882	0.132401	0.0662003	−	0.997806i	$-0.478912\pi$
$331$	2.40882	0.132401	0.0662003	+	0.997806i	$0.478912\pi$
$332$	6.24779	0.342892
$333$	−1.50487	−0.0824663
$334$	−12.8583	−0.703573
$335$	0.112610	0.00615255
$336$	−1.05140	−0.0573586
$337$	19.0700	1.03881	0.519405	−	0.854528i	$-0.326154\pi$
$337$	19.0700	1.03881	0.519405	+	0.854528i	$0.326154\pi$
$338$	0	0
$339$	−12.0718	−0.655651
$340$	2.18645	0.118577
$341$	5.04190	0.273034
$342$	9.67132	0.522965
$343$	1.00000	0.0539949
$344$	−7.93286	−0.427711
$345$	−19.3752	−1.04313
$346$	−1.45155	−0.0780356
$347$	22.6224	1.21443	0.607216	−	0.794537i	$-0.292286\pi$
$347$	22.6224	1.21443	0.607216	+	0.794537i	$0.292286\pi$
$348$	−10.2822	−0.551183
$349$	−19.5678	−1.04744	−0.523719	−	0.851891i	$-0.675456\pi$
$349$	−19.5678	−1.04744	−0.523719	+	0.851891i	$0.675456\pi$
$350$	0.152241	0.00813762
$351$	0	0
$352$	0.977125	0.0520809
$353$	−4.27967	−0.227784	−0.113892	−	0.993493i	$-0.536332\pi$
$353$	−4.27967	−0.227784	−0.113892	+	0.993493i	$0.536332\pi$
$354$	−13.4852	−0.716731
$355$	−8.44250	−0.448082
$356$	−5.92385	−0.313964
$357$	−1.01277	−0.0536012
$358$	2.71291	0.143382
$359$	15.2915	0.807052	0.403526	−	0.914968i	$-0.367785\pi$
$359$	15.2915	0.807052	0.403526	+	0.914968i	$0.367785\pi$
$360$	−4.30037	−0.226649
$361$	7.05890	0.371521
$362$	−22.5406	−1.18471
$363$	10.5616	0.554338
$364$	0	0
$365$	−20.1534	−1.05488
$366$	4.13482	0.216131
$367$	−16.3870	−0.855397	−0.427698	−	0.903921i	$-0.640675\pi$
$367$	−16.3870	−0.855397	−0.427698	+	0.903921i	$0.640675\pi$
$368$	8.11859	0.423211
$369$	2.84120	0.147907
$370$	1.80297	0.0937320
$371$	3.68079	0.191097
$372$	−5.42516	−0.281281
$373$	−18.3946	−0.952436	−0.476218	−	0.879327i	$-0.657993\pi$
$373$	−18.3946	−0.952436	−0.476218	+	0.879327i	$0.657993\pi$
$374$	0.941220	0.0486693
$375$	11.5693	0.597436
$376$	5.04879	0.260371
$377$	0	0
$378$	5.14614	0.264689
$379$	−21.0316	−1.08032	−0.540161	−	0.841562i	$-0.681637\pi$
$379$	−21.0316	−1.08032	−0.540161	+	0.841562i	$0.681637\pi$
$380$	−11.5871	−0.594408
$381$	7.50657	0.384573
$382$	−6.68377	−0.341971
$383$	−14.6607	−0.749124	−0.374562	−	0.927202i	$-0.622207\pi$
$383$	−14.6607	−0.749124	−0.374562	+	0.927202i	$0.622207\pi$
$384$	−1.05140	−0.0536540
$385$	2.21793	0.113036
$386$	18.0081	0.916588
$387$	15.0293	0.763980
$388$	7.29137	0.370163
$389$	7.18271	0.364178	0.182089	−	0.983282i	$-0.441714\pi$
$389$	7.18271	0.364178	0.182089	+	0.983282i	$0.441714\pi$
$390$	0	0
$391$	7.82027	0.395488
$392$	1.00000	0.0505076
$393$	−21.1057	−1.06464
$394$	−2.56211	−0.129077
$395$	−15.8484	−0.797422
$396$	−1.85122	−0.0930273
$397$	−27.5462	−1.38250	−0.691251	−	0.722615i	$-0.742940\pi$
$397$	−27.5462	−1.38250	−0.691251	+	0.722615i	$0.742940\pi$
$398$	8.54978	0.428562
$399$	5.36718	0.268695
$400$	0.152241	0.00761205
$401$	17.8377	0.890774	0.445387	−	0.895338i	$-0.353066\pi$
$401$	17.8377	0.890774	0.445387	+	0.895338i	$0.353066\pi$
$402$	−0.0521612	−0.00260156
$403$	0	0
$404$	−18.1884	−0.904906
$405$	0.619720	0.0307941
$406$	9.77952	0.485349
$407$	0.776141	0.0384719
$408$	−1.01277	−0.0501394
$409$	33.5105	1.65699	0.828495	−	0.559997i	$-0.189198\pi$
$409$	33.5105	1.65699	0.828495	+	0.559997i	$0.189198\pi$
$410$	−3.40402	−0.168113
$411$	−15.2718	−0.753301
$412$	5.63247	0.277492
$413$	12.8260	0.631124
$414$	−15.3811	−0.755942
$415$	14.1816	0.696147
$416$	0	0
$417$	7.90208	0.386967
$418$	−4.98802	−0.243972
$419$	1.62778	0.0795225	0.0397612	−	0.999209i	$-0.487340\pi$
$419$	1.62778	0.0795225	0.0397612	+	0.999209i	$0.487340\pi$
$420$	−2.38653	−0.116451
$421$	−37.2889	−1.81735	−0.908674	−	0.417507i	$-0.862904\pi$
$421$	−37.2889	−1.81735	−0.908674	+	0.417507i	$0.862904\pi$
$422$	14.4132	0.701621
$423$	−9.56522	−0.465077
$424$	3.68079	0.178755
$425$	0.146647	0.00711341
$426$	3.91058	0.189468
$427$	−3.93268	−0.190316
$428$	11.6580	0.563510
$429$	0	0
$430$	−18.0064	−0.868348
$431$	−14.9139	−0.718376	−0.359188	−	0.933265i	$-0.616946\pi$
$431$	−14.9139	−0.718376	−0.359188	+	0.933265i	$0.616946\pi$
$432$	5.14614	0.247594
$433$	−29.2027	−1.40339	−0.701696	−	0.712476i	$-0.747574\pi$
$433$	−29.2027	−1.40339	−0.701696	+	0.712476i	$0.747574\pi$
$434$	5.15994	0.247685
$435$	−23.3391	−1.11902
$436$	14.8986	0.713515
$437$	−41.4437	−1.98252
$438$	9.33510	0.446048
$439$	−35.6807	−1.70295	−0.851473	−	0.524398i	$-0.824290\pi$
$439$	−35.6807	−1.70295	−0.851473	+	0.524398i	$0.824290\pi$
$440$	2.21793	0.105736
$441$	−1.89456	−0.0902170
$442$	0	0
$443$	−21.4240	−1.01789	−0.508943	−	0.860800i	$-0.669964\pi$
$443$	−21.4240	−1.01789	−0.508943	+	0.860800i	$0.669964\pi$
$444$	−0.835139	−0.0396339
$445$	−13.4463	−0.637415
$446$	−5.56995	−0.263745
$447$	5.37259	0.254115
$448$	1.00000	0.0472456
$449$	24.0450	1.13475	0.567376	−	0.823459i	$-0.307958\pi$
$449$	24.0450	1.13475	0.567376	+	0.823459i	$0.307958\pi$
$450$	−0.288429	−0.0135967
$451$	−1.46536	−0.0690011
$452$	11.4817	0.540052
$453$	−23.4964	−1.10396
$454$	7.08232	0.332390
$455$	0	0
$456$	5.36718	0.251341
$457$	−11.3275	−0.529880	−0.264940	−	0.964265i	$-0.585352\pi$
$457$	−11.3275	−0.529880	−0.264940	+	0.964265i	$0.585352\pi$
$458$	13.9978	0.654073
$459$	4.95704	0.231375
$460$	18.4280	0.859211
$461$	−7.54671	−0.351485	−0.175743	−	0.984436i	$-0.556233\pi$
$461$	−7.54671	−0.351485	−0.175743	+	0.984436i	$0.556233\pi$
$462$	−1.02735	−0.0477966
$463$	18.6384	0.866202	0.433101	−	0.901345i	$-0.357419\pi$
$463$	18.6384	0.866202	0.433101	+	0.901345i	$0.357419\pi$
$464$	9.77952	0.454003
$465$	−12.3143	−0.571063
$466$	−23.6892	−1.09738
$467$	−11.1505	−0.515983	−0.257992	−	0.966147i	$-0.583061\pi$
$467$	−11.1505	−0.515983	−0.257992	+	0.966147i	$0.583061\pi$
$468$	0	0
$469$	0.0496112	0.00229083
$470$	11.4600	0.528611
$471$	10.7833	0.496868
$472$	12.8260	0.590362
$473$	−7.75139	−0.356409
$474$	7.34102	0.337184
$475$	−0.777158	−0.0356585
$476$	0.963254	0.0441507
$477$	−6.97347	−0.319293
$478$	−8.32300	−0.380685
$479$	43.4475	1.98517	0.992584	−	0.121564i	$-0.0387908\pi$
$479$	43.4475	1.98517	0.992584	+	0.121564i	$0.0387908\pi$
$480$	−2.38653	−0.108930
$481$	0	0
$482$	−27.7146	−1.26236
$483$	−8.53589	−0.388396
$484$	−10.0452	−0.456601
$485$	16.5503	0.751512
$486$	−15.7255	−0.713322
$487$	−10.3172	−0.467515	−0.233758	−	0.972295i	$-0.575102\pi$
$487$	−10.3172	−0.467515	−0.233758	+	0.972295i	$0.575102\pi$
$488$	−3.93268	−0.178024
$489$	17.5994	0.795872
$490$	2.26985	0.102542
$491$	21.9035	0.988491	0.494246	−	0.869322i	$-0.335444\pi$
$491$	21.9035	0.988491	0.494246	+	0.869322i	$0.335444\pi$
$492$	1.57675	0.0710853
$493$	9.42016	0.424263
$494$	0	0
$495$	−4.20200	−0.188866
$496$	5.15994	0.231688
$497$	−3.71940	−0.166838
$498$	−6.56893	−0.294361
$499$	−26.6278	−1.19202	−0.596012	−	0.802975i	$-0.703249\pi$
$499$	−26.6278	−1.19202	−0.596012	+	0.802975i	$0.703249\pi$
$500$	−11.0037	−0.492101
$501$	13.5192	0.603993
$502$	−15.4094	−0.687756
$503$	5.40979	0.241211	0.120605	−	0.992701i	$-0.461516\pi$
$503$	5.40979	0.241211	0.120605	+	0.992701i	$0.461516\pi$
$504$	−1.89456	−0.0843903
$505$	−41.2850	−1.83716
$506$	7.93288	0.352659
$507$	0	0
$508$	−7.13960	−0.316768
$509$	−14.1121	−0.625507	−0.312753	−	0.949834i	$-0.601251\pi$
$509$	−14.1121	−0.625507	−0.312753	+	0.949834i	$0.601251\pi$
$510$	−2.29883	−0.101794
$511$	−8.87873	−0.392772
$512$	1.00000	0.0441942
$513$	−26.2700	−1.15985
$514$	−28.6449	−1.26347
$515$	12.7849	0.563370
$516$	8.34061	0.367175
$517$	4.93330	0.216966
$518$	0.794311	0.0349000
$519$	1.52616	0.0669908
$520$	0	0
$521$	−31.3394	−1.37300	−0.686502	−	0.727128i	$-0.740855\pi$
$521$	−31.3394	−1.37300	−0.686502	+	0.727128i	$0.740855\pi$
$522$	−18.5279	−0.810942
$523$	−20.7887	−0.909025	−0.454513	−	0.890740i	$-0.650187\pi$
$523$	−20.7887	−0.909025	−0.454513	+	0.890740i	$0.650187\pi$
$524$	20.0739	0.876933
$525$	−0.160066	−0.00698586
$526$	24.8105	1.08179
$527$	4.97033	0.216511
$528$	−1.02735	−0.0447096
$529$	42.9115	1.86572
$530$	8.35487	0.362912
$531$	−24.2995	−1.05451
$532$	−5.10479	−0.221321
$533$	0	0
$534$	6.22834	0.269527
$535$	26.4619	1.14405
$536$	0.0496112	0.00214288
$537$	−2.85235	−0.123088
$538$	−27.2428	−1.17452
$539$	0.977125	0.0420877
$540$	11.6810	0.502670
$541$	8.66839	0.372683	0.186342	−	0.982485i	$-0.440337\pi$
$541$	8.66839	0.372683	0.186342	+	0.982485i	$0.440337\pi$
$542$	−0.406075	−0.0174424
$543$	23.6992	1.01703
$544$	0.963254	0.0412992
$545$	33.8177	1.44859
$546$	0	0
$547$	28.0452	1.19913	0.599563	−	0.800328i	$-0.295341\pi$
$547$	28.0452	1.19913	0.599563	+	0.800328i	$0.295341\pi$
$548$	14.5252	0.620485
$549$	7.45069	0.317988
$550$	0.148758	0.00634308
$551$	−49.9224	−2.12677
$552$	−8.53589	−0.363312
$553$	−6.98214	−0.296911
$554$	24.6439	1.04702
$555$	−1.89564	−0.0804656
$556$	−7.51577	−0.318740
$557$	−37.8791	−1.60499	−0.802494	−	0.596660i	$-0.796494\pi$
$557$	−37.8791	−1.60499	−0.802494	+	0.596660i	$0.796494\pi$
$558$	−9.77580	−0.413843
$559$	0	0
$560$	2.26985	0.0959189
$561$	−0.989598	−0.0417809
$562$	−2.06017	−0.0869030
$563$	31.8722	1.34326	0.671628	−	0.740889i	$-0.265596\pi$
$563$	31.8722	1.34326	0.671628	+	0.740889i	$0.265596\pi$
$564$	−5.30830	−0.223520
$565$	26.0617	1.09642
$566$	−7.94702	−0.334038
$567$	0.273022	0.0114658
$568$	−3.71940	−0.156063
$569$	−23.6136	−0.989933	−0.494966	−	0.868912i	$-0.664820\pi$
$569$	−23.6136	−0.989933	−0.494966	+	0.868912i	$0.664820\pi$
$570$	12.1827	0.510278
$571$	−17.9245	−0.750116	−0.375058	−	0.927001i	$-0.622377\pi$
$571$	−17.9245	−0.750116	−0.375058	+	0.927001i	$0.622377\pi$
$572$	0	0
$573$	7.02732	0.293570
$574$	−1.49967	−0.0625948
$575$	1.23598	0.0515440
$576$	−1.89456	−0.0789399
$577$	16.6539	0.693310	0.346655	−	0.937993i	$-0.387317\pi$
$577$	16.6539	0.693310	0.346655	+	0.937993i	$0.387317\pi$
$578$	−16.0721	−0.668513
$579$	−18.9337	−0.786858
$580$	22.1981	0.921725
$581$	6.24779	0.259202
$582$	−7.66614	−0.317772
$583$	3.59659	0.148956
$584$	−8.87873	−0.367404
$585$	0	0
$586$	29.3231	1.21133
$587$	−5.78820	−0.238905	−0.119452	−	0.992840i	$-0.538114\pi$
$587$	−5.78820	−0.238905	−0.119452	+	0.992840i	$0.538114\pi$
$588$	−1.05140	−0.0433590
$589$	−26.3404	−1.08534
$590$	29.1130	1.19857
$591$	2.69381	0.110808
$592$	0.794311	0.0326460
$593$	−3.22830	−0.132570	−0.0662852	−	0.997801i	$-0.521115\pi$
$593$	−3.22830	−0.132570	−0.0662852	+	0.997801i	$0.521115\pi$
$594$	5.02842	0.206319
$595$	2.18645	0.0896356
$596$	−5.10994	−0.209311
$597$	−8.98924	−0.367905
$598$	0	0
$599$	31.7387	1.29681	0.648405	−	0.761296i	$-0.275436\pi$
$599$	31.7387	1.29681	0.648405	+	0.761296i	$0.275436\pi$
$600$	−0.160066	−0.00653467
$601$	−36.0005	−1.46849	−0.734246	−	0.678883i	$-0.762464\pi$
$601$	−36.0005	−1.46849	−0.734246	+	0.678883i	$0.762464\pi$
$602$	−7.93286	−0.323319
$603$	−0.0939912	−0.00382762
$604$	22.3477	0.909314
$605$	−22.8012	−0.927001
$606$	19.1233	0.776830
$607$	43.1875	1.75293	0.876463	−	0.481469i	$-0.159897\pi$
$607$	43.1875	1.75293	0.876463	+	0.481469i	$0.159897\pi$
$608$	−5.10479	−0.207027
$609$	−10.2822	−0.416655
$610$	−8.92662	−0.361428
$611$	0	0
$612$	−1.82494	−0.0737689
$613$	−37.4092	−1.51094	−0.755471	−	0.655182i	$-0.772592\pi$
$613$	−37.4092	−1.51094	−0.755471	+	0.655182i	$0.772592\pi$
$614$	14.0749	0.568018
$615$	3.57899	0.144319
$616$	0.977125	0.0393695
$617$	−0.959817	−0.0386408	−0.0193204	−	0.999813i	$-0.506150\pi$
$617$	−0.959817	−0.0386408	−0.0193204	+	0.999813i	$0.506150\pi$
$618$	−5.92198	−0.238217
$619$	11.1412	0.447804	0.223902	−	0.974612i	$-0.428120\pi$
$619$	11.1412	0.447804	0.223902	+	0.974612i	$0.428120\pi$
$620$	11.7123	0.470378
$621$	41.7794	1.67655
$622$	−27.2622	−1.09311
$623$	−5.92385	−0.237334
$624$	0	0
$625$	−25.7380	−1.02952
$626$	−20.8963	−0.835184
$627$	5.24440	0.209441
$628$	−10.2561	−0.409264
$629$	0.765123	0.0305075
$630$	−4.30037	−0.171331
$631$	−11.2745	−0.448831	−0.224416	−	0.974494i	$-0.572047\pi$
$631$	−11.2745	−0.448831	−0.224416	+	0.974494i	$0.572047\pi$
$632$	−6.98214	−0.277735
$633$	−15.1540	−0.602317
$634$	−15.7420	−0.625196
$635$	−16.2058	−0.643109
$636$	−3.86999	−0.153455
$637$	0	0
$638$	9.55581	0.378318
$639$	7.04662	0.278760
$640$	2.26985	0.0897239
$641$	−38.1624	−1.50732	−0.753661	−	0.657263i	$-0.771714\pi$
$641$	−38.1624	−1.50732	−0.753661	+	0.657263i	$0.771714\pi$
$642$	−12.2572	−0.483753
$643$	0.756725	0.0298423	0.0149212	−	0.999889i	$-0.495250\pi$
$643$	0.756725	0.0298423	0.0149212	+	0.999889i	$0.495250\pi$
$644$	8.11859	0.319917
$645$	18.9320	0.745446
$646$	−4.91721	−0.193465
$647$	−13.1973	−0.518839	−0.259419	−	0.965765i	$-0.583531\pi$
$647$	−13.1973	−0.518839	−0.259419	+	0.965765i	$0.583531\pi$
$648$	0.273022	0.0107253
$649$	12.5326	0.491946
$650$	0	0
$651$	−5.42516	−0.212629
$652$	−16.7390	−0.655550
$653$	−21.6653	−0.847829	−0.423914	−	0.905702i	$-0.639344\pi$
$653$	−21.6653	−0.847829	−0.423914	+	0.905702i	$0.639344\pi$
$654$	−15.6644	−0.612528
$655$	45.5649	1.78037
$656$	−1.49967	−0.0585521
$657$	16.8213	0.656260
$658$	5.04879	0.196822
$659$	13.5006	0.525911	0.262955	−	0.964808i	$-0.415303\pi$
$659$	13.5006	0.525911	0.262955	+	0.964808i	$0.415303\pi$
$660$	−2.33193	−0.0907704
$661$	18.9423	0.736769	0.368385	−	0.929674i	$-0.379911\pi$
$661$	18.9423	0.736769	0.368385	+	0.929674i	$0.379911\pi$
$662$	2.40882	0.0936213
$663$	0	0
$664$	6.24779	0.242461
$665$	−11.5871	−0.449330
$666$	−1.50487	−0.0583124
$667$	79.3959	3.07422
$668$	−12.8583	−0.497501
$669$	5.85625	0.226416
$670$	0.112610	0.00435051
$671$	−3.84272	−0.148347
$672$	−1.05140	−0.0405586
$673$	−3.53776	−0.136370	−0.0681852	−	0.997673i	$-0.521721\pi$
$673$	−3.53776	−0.136370	−0.0681852	+	0.997673i	$0.521721\pi$
$674$	19.0700	0.734550
$675$	0.783453	0.0301551
$676$	0	0
$677$	3.86189	0.148425	0.0742123	−	0.997242i	$-0.476356\pi$
$677$	3.86189	0.148425	0.0742123	+	0.997242i	$0.476356\pi$
$678$	−12.0718	−0.463615
$679$	7.29137	0.279817
$680$	2.18645	0.0838464
$681$	−7.44635	−0.285345
$682$	5.04190	0.193064
$683$	−9.95472	−0.380907	−0.190453	−	0.981696i	$-0.560996\pi$
$683$	−9.95472	−0.380907	−0.190453	+	0.981696i	$0.560996\pi$
$684$	9.67132	0.369792
$685$	32.9701	1.25972
$686$	1.00000	0.0381802
$687$	−14.7173	−0.561499
$688$	−7.93286	−0.302437
$689$	0	0
$690$	−19.3752	−0.737602
$691$	46.5117	1.76939	0.884695	−	0.466171i	$-0.154367\pi$
$691$	46.5117	1.76939	0.884695	+	0.466171i	$0.154367\pi$
$692$	−1.45155	−0.0551795
$693$	−1.85122	−0.0703220
$694$	22.6224	0.858733
$695$	−17.0597	−0.647111
$696$	−10.2822	−0.389745
$697$	−1.44456	−0.0547166
$698$	−19.5678	−0.740651
$699$	24.9068	0.942061
$700$	0.152241	0.00575417
$701$	20.4361	0.771861	0.385931	−	0.922528i	$-0.373880\pi$
$701$	20.4361	0.771861	0.385931	+	0.922528i	$0.373880\pi$
$702$	0	0
$703$	−4.05479	−0.152929
$704$	0.977125	0.0368268
$705$	−12.0491	−0.453794
$706$	−4.27967	−0.161067
$707$	−18.1884	−0.684045
$708$	−13.4852	−0.506805
$709$	33.7565	1.26775	0.633877	−	0.773434i	$-0.281463\pi$
$709$	33.7565	1.26775	0.633877	+	0.773434i	$0.281463\pi$
$710$	−8.44250	−0.316841
$711$	13.2281	0.496091
$712$	−5.92385	−0.222006
$713$	41.8914	1.56885
$714$	−1.01277	−0.0379018
$715$	0	0
$716$	2.71291	0.101386
$717$	8.75081	0.326805
$718$	15.2915	0.570672
$719$	26.9400	1.00469	0.502346	−	0.864667i	$-0.332470\pi$
$719$	26.9400	1.00469	0.502346	+	0.864667i	$0.332470\pi$
$720$	−4.30037	−0.160265
$721$	5.63247	0.209764
$722$	7.05890	0.262705
$723$	29.1391	1.08370
$724$	−22.5406	−0.837715
$725$	1.48884	0.0552942
$726$	10.5616	0.391976
$727$	0.192213	0.00712877	0.00356439	−	0.999994i	$-0.498865\pi$
$727$	0.192213	0.00712877	0.00356439	+	0.999994i	$0.498865\pi$
$728$	0	0
$729$	15.7147	0.582026
$730$	−20.1534	−0.745912
$731$	−7.64136	−0.282626
$732$	4.13482	0.152827
$733$	−20.1885	−0.745680	−0.372840	−	0.927896i	$-0.621616\pi$
$733$	−20.1885	−0.745680	−0.372840	+	0.927896i	$0.621616\pi$
$734$	−16.3870	−0.604857
$735$	−2.38653	−0.0880283
$736$	8.11859	0.299255
$737$	0.0484763	0.00178565
$738$	2.84120	0.104586
$739$	15.6989	0.577493	0.288747	−	0.957406i	$-0.406761\pi$
$739$	15.6989	0.577493	0.288747	+	0.957406i	$0.406761\pi$
$740$	1.80297	0.0662785
$741$	0	0
$742$	3.68079	0.135126
$743$	−37.2634	−1.36706	−0.683530	−	0.729923i	$-0.739556\pi$
$743$	−37.2634	−1.36706	−0.683530	+	0.729923i	$0.739556\pi$
$744$	−5.42516	−0.198896
$745$	−11.5988	−0.424948
$746$	−18.3946	−0.673474
$747$	−11.8368	−0.433086
$748$	0.941220	0.0344144
$749$	11.6580	0.425973
$750$	11.5693	0.422451
$751$	−42.9626	−1.56773	−0.783863	−	0.620934i	$-0.786754\pi$
$751$	−42.9626	−1.56773	−0.783863	+	0.620934i	$0.786754\pi$
$752$	5.04879	0.184110
$753$	16.2015	0.590414
$754$	0	0
$755$	50.7260	1.84611
$756$	5.14614	0.187163
$757$	−13.6113	−0.494711	−0.247355	−	0.968925i	$-0.579561\pi$
$757$	−13.6113	−0.494711	−0.247355	+	0.968925i	$0.579561\pi$
$758$	−21.0316	−0.763903
$759$	−8.34063	−0.302746
$760$	−11.5871	−0.420310
$761$	−6.91223	−0.250568	−0.125284	−	0.992121i	$-0.539984\pi$
$761$	−6.91223	−0.250568	−0.125284	+	0.992121i	$0.539984\pi$
$762$	7.50657	0.271934
$763$	14.8986	0.539367
$764$	−6.68377	−0.241810
$765$	−4.14235	−0.149767
$766$	−14.6607	−0.529711
$767$	0	0
$768$	−1.05140	−0.0379391
$769$	26.2839	0.947822	0.473911	−	0.880573i	$-0.342842\pi$
$769$	26.2839	0.947822	0.473911	+	0.880573i	$0.342842\pi$
$770$	2.21793	0.0799287
$771$	30.1173	1.08465
$772$	18.0081	0.648126
$773$	22.0986	0.794832	0.397416	−	0.917638i	$-0.369907\pi$
$773$	22.0986	0.794832	0.397416	+	0.917638i	$0.369907\pi$
$774$	15.0293	0.540216
$775$	0.785554	0.0282179
$776$	7.29137	0.261745
$777$	−0.835139	−0.0299604
$778$	7.18271	0.257513
$779$	7.65548	0.274286
$780$	0	0
$781$	−3.63432	−0.130046
$782$	7.82027	0.279652
$783$	50.3267	1.79853
$784$	1.00000	0.0357143
$785$	−23.2799	−0.830896
$786$	−21.1057	−0.752816
$787$	−46.8673	−1.67064	−0.835319	−	0.549766i	$-0.814717\pi$
$787$	−46.8673	−1.67064	−0.835319	+	0.549766i	$0.814717\pi$
$788$	−2.56211	−0.0912715
$789$	−26.0858	−0.928679
$790$	−15.8484	−0.563862
$791$	11.4817	0.408241
$792$	−1.85122	−0.0657802
$793$	0	0
$794$	−27.5462	−0.977576
$795$	−8.78431	−0.311547
$796$	8.54978	0.303039
$797$	15.4766	0.548210	0.274105	−	0.961700i	$-0.411618\pi$
$797$	15.4766	0.548210	0.274105	+	0.961700i	$0.411618\pi$
$798$	5.36718	0.189996
$799$	4.86327	0.172050
$800$	0.152241	0.00538253
$801$	11.2231	0.396548
$802$	17.8377	0.629872
$803$	−8.67563	−0.306156
$804$	−0.0521612	−0.00183958
$805$	18.4280	0.649502
$806$	0	0
$807$	28.6431	1.00829
$808$	−18.1884	−0.639865
$809$	15.4888	0.544556	0.272278	−	0.962219i	$-0.412223\pi$
$809$	15.4888	0.544556	0.272278	+	0.962219i	$0.412223\pi$
$810$	0.619720	0.0217747
$811$	44.4977	1.56252	0.781262	−	0.624203i	$-0.214576\pi$
$811$	44.4977	1.56252	0.781262	+	0.624203i	$0.214576\pi$
$812$	9.77952	0.343194
$813$	0.426947	0.0149737
$814$	0.776141	0.0272037
$815$	−37.9951	−1.33091
$816$	−1.01277	−0.0354539
$817$	40.4956	1.41676
$818$	33.5105	1.17167
$819$	0	0
$820$	−3.40402	−0.118874
$821$	38.7566	1.35261	0.676307	−	0.736619i	$-0.263579\pi$
$821$	38.7566	1.35261	0.676307	+	0.736619i	$0.263579\pi$
$822$	−15.2718	−0.532665
$823$	−27.2115	−0.948535	−0.474267	−	0.880381i	$-0.657287\pi$
$823$	−27.2115	−0.948535	−0.474267	+	0.880381i	$0.657287\pi$
$824$	5.63247	0.196216
$825$	−0.156405	−0.00544531
$826$	12.8260	0.446272
$827$	11.0276	0.383469	0.191734	−	0.981447i	$-0.438589\pi$
$827$	11.0276	0.383469	0.191734	+	0.981447i	$0.438589\pi$
$828$	−15.3811	−0.534532
$829$	9.85198	0.342173	0.171087	−	0.985256i	$-0.445272\pi$
$829$	9.85198	0.342173	0.171087	+	0.985256i	$0.445272\pi$
$830$	14.1816	0.492250
$831$	−25.9106	−0.898830
$832$	0	0
$833$	0.963254	0.0333748
$834$	7.90208	0.273627
$835$	−29.1864	−1.01004
$836$	−4.98802	−0.172514
$837$	26.5538	0.917832
$838$	1.62778	0.0562309
$839$	18.4684	0.637598	0.318799	−	0.947822i	$-0.396720\pi$
$839$	18.4684	0.637598	0.318799	+	0.947822i	$0.396720\pi$
$840$	−2.38653	−0.0823430
$841$	66.6389	2.29789
$842$	−37.2889	−1.28506
$843$	2.16606	0.0746032
$844$	14.4132	0.496121
$845$	0	0
$846$	−9.56522	−0.328859
$847$	−10.0452	−0.345158
$848$	3.68079	0.126399
$849$	8.35550	0.286760
$850$	0.146647	0.00502994
$851$	6.44869	0.221058
$852$	3.91058	0.133974
$853$	−37.6701	−1.28980	−0.644900	−	0.764267i	$-0.723101\pi$
$853$	−37.6701	−1.28980	−0.644900	+	0.764267i	$0.723101\pi$
$854$	−3.93268	−0.134574
$855$	21.9525	0.750760
$856$	11.6580	0.398461
$857$	−42.5406	−1.45316	−0.726580	−	0.687082i	$-0.758891\pi$
$857$	−42.5406	−1.45316	−0.726580	+	0.687082i	$0.758891\pi$
$858$	0	0
$859$	20.0570	0.684337	0.342168	−	0.939639i	$-0.388839\pi$
$859$	20.0570	0.684337	0.342168	+	0.939639i	$0.388839\pi$
$860$	−18.0064	−0.614014
$861$	1.57675	0.0537355
$862$	−14.9139	−0.507969
$863$	−4.27374	−0.145480	−0.0727398	−	0.997351i	$-0.523174\pi$
$863$	−4.27374	−0.145480	−0.0727398	+	0.997351i	$0.523174\pi$
$864$	5.14614	0.175075
$865$	−3.29480	−0.112027
$866$	−29.2027	−0.992348
$867$	16.8983	0.573895
$868$	5.15994	0.175140
$869$	−6.82242	−0.231435
$870$	−23.3391	−0.791269
$871$	0	0
$872$	14.8986	0.504531
$873$	−13.8139	−0.467530
$874$	−41.4437	−1.40185
$875$	−11.0037	−0.371993
$876$	9.33510	0.315404
$877$	45.0414	1.52094	0.760470	−	0.649373i	$-0.224969\pi$
$877$	45.0414	1.52094	0.760470	+	0.649373i	$0.224969\pi$
$878$	−35.6807	−1.20416
$879$	−30.8303	−1.03988
$880$	2.21793	0.0747665
$881$	30.0985	1.01405	0.507023	−	0.861933i	$-0.330746\pi$
$881$	30.0985	1.01405	0.507023	+	0.861933i	$0.330746\pi$
$882$	−1.89456	−0.0637931
$883$	−27.5493	−0.927108	−0.463554	−	0.886069i	$-0.653426\pi$
$883$	−27.5493	−0.927108	−0.463554	+	0.886069i	$0.653426\pi$
$884$	0	0
$885$	−30.6095	−1.02893
$886$	−21.4240	−0.719754
$887$	16.9861	0.570338	0.285169	−	0.958477i	$-0.407950\pi$
$887$	16.9861	0.570338	0.285169	+	0.958477i	$0.407950\pi$
$888$	−0.835139	−0.0280254
$889$	−7.13960	−0.239454
$890$	−13.4463	−0.450721
$891$	0.266776	0.00893734
$892$	−5.56995	−0.186496
$893$	−25.7730	−0.862461
$894$	5.37259	0.179686
$895$	6.15790	0.205836
$896$	1.00000	0.0334077
$897$	0	0
$898$	24.0450	0.802391
$899$	50.4617	1.68299
$900$	−0.288429	−0.00961431
$901$	3.54554	0.118119
$902$	−1.46536	−0.0487912
$903$	8.34061	0.277558
$904$	11.4817	0.381874
$905$	−51.1639	−1.70075
$906$	−23.4964	−0.780614
$907$	45.9713	1.52645	0.763226	−	0.646132i	$-0.223614\pi$
$907$	45.9713	1.52645	0.763226	+	0.646132i	$0.223614\pi$
$908$	7.08232	0.235035
$909$	34.4589	1.14293
$910$	0	0
$911$	−27.6048	−0.914588	−0.457294	−	0.889316i	$-0.651181\pi$
$911$	−27.6048	−0.914588	−0.457294	+	0.889316i	$0.651181\pi$
$912$	5.36718	0.177725
$913$	6.10488	0.202042
$914$	−11.3275	−0.374682
$915$	9.38545	0.310273
$916$	13.9978	0.462500
$917$	20.0739	0.662899
$918$	4.95704	0.163607
$919$	−25.8710	−0.853405	−0.426702	−	0.904392i	$-0.640325\pi$
$919$	−25.8710	−0.853405	−0.426702	+	0.904392i	$0.640325\pi$
$920$	18.4280	0.607554
$921$	−14.7984	−0.487623
$922$	−7.54671	−0.248538
$923$	0	0
$924$	−1.02735	−0.0337973
$925$	0.120927	0.00397604
$926$	18.6384	0.612497
$927$	−10.6710	−0.350483
$928$	9.77952	0.321028
$929$	41.9988	1.37794	0.688968	−	0.724791i	$-0.258064\pi$
$929$	41.9988	1.37794	0.688968	+	0.724791i	$0.258064\pi$
$930$	−12.3143	−0.403803
$931$	−5.10479	−0.167303
$932$	−23.6892	−0.775964
$933$	28.6634	0.938399
$934$	−11.1505	−0.364855
$935$	2.13643	0.0698688
$936$	0	0
$937$	−0.475429	−0.0155316	−0.00776579	−	0.999970i	$-0.502472\pi$
$937$	−0.475429	−0.0155316	−0.00776579	+	0.999970i	$0.502472\pi$
$938$	0.0496112	0.00161986
$939$	21.9704	0.716976
$940$	11.4600	0.373785
$941$	13.0479	0.425350	0.212675	−	0.977123i	$-0.431782\pi$
$941$	13.0479	0.425350	0.212675	+	0.977123i	$0.431782\pi$
$942$	10.7833	0.351339
$943$	−12.1752	−0.396478
$944$	12.8260	0.417449
$945$	11.6810	0.379983
$946$	−7.75139	−0.252020
$947$	−51.9018	−1.68658	−0.843291	−	0.537457i	$-0.819385\pi$
$947$	−51.9018	−1.68658	−0.843291	+	0.537457i	$0.819385\pi$
$948$	7.34102	0.238425
$949$	0	0
$950$	−0.777158	−0.0252143
$951$	16.5512	0.536709
$952$	0.963254	0.0312192
$953$	−37.4184	−1.21210	−0.606051	−	0.795426i	$-0.707247\pi$
$953$	−37.4184	−1.21210	−0.606051	+	0.795426i	$0.707247\pi$
$954$	−6.97347	−0.225775
$955$	−15.1712	−0.490928
$956$	−8.32300	−0.269185
$957$	−10.0470	−0.324773
$958$	43.4475	1.40373
$959$	14.5252	0.469043
$960$	−2.38653	−0.0770248
$961$	−4.37503	−0.141130
$962$	0	0
$963$	−22.0867	−0.711734
$964$	−27.7146	−0.892627
$965$	40.8758	1.31584
$966$	−8.53589	−0.274638
$967$	43.3495	1.39403	0.697013	−	0.717059i	$-0.254512\pi$
$967$	43.3495	1.39403	0.697013	+	0.717059i	$0.254512\pi$
$968$	−10.0452	−0.322866
$969$	5.16996	0.166083
$970$	16.5503	0.531399
$971$	−3.17600	−0.101923	−0.0509614	−	0.998701i	$-0.516229\pi$
$971$	−3.17600	−0.101923	−0.0509614	+	0.998701i	$0.516229\pi$
$972$	−15.7255	−0.504395
$973$	−7.51577	−0.240944
$974$	−10.3172	−0.330583
$975$	0	0
$976$	−3.93268	−0.125882
$977$	50.4739	1.61480	0.807402	−	0.590002i	$-0.200873\pi$
$977$	50.4739	1.61480	0.807402	+	0.590002i	$0.200873\pi$
$978$	17.5994	0.562767
$979$	−5.78835	−0.184996
$980$	2.26985	0.0725079
$981$	−28.2263	−0.901197
$982$	21.9035	0.698969
$983$	−41.0892	−1.31054	−0.655272	−	0.755393i	$-0.727446\pi$
$983$	−41.0892	−1.31054	−0.655272	+	0.755393i	$0.727446\pi$
$984$	1.57675	0.0502649
$985$	−5.81563	−0.185301
$986$	9.42016	0.299999
$987$	−5.30830	−0.168965
$988$	0	0
$989$	−64.4036	−2.04792
$990$	−4.20200	−0.133548
$991$	−36.3749	−1.15549	−0.577743	−	0.816219i	$-0.696066\pi$
$991$	−36.3749	−1.15549	−0.577743	+	0.816219i	$0.696066\pi$
$992$	5.15994	0.163828
$993$	−2.53263	−0.0803706
$994$	−3.71940	−0.117972
$995$	19.4068	0.615235
$996$	−6.56893	−0.208145
$997$	−39.0154	−1.23563	−0.617815	−	0.786324i	$-0.711982\pi$
$997$	−39.0154	−1.23563	−0.617815	+	0.786324i	$0.711982\pi$
$998$	−26.6278	−0.842889
$999$	4.08763	0.129327

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2366.2.a.bg.1.3	yes	6
13.5	odd	4		2366.2.d.q.337.3		12
13.8	odd	4		2366.2.d.q.337.9		12
13.12	even	2		2366.2.a.be.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2366.2.a.be.1.3	✓	6	13.12	even	2
2366.2.a.bg.1.3	yes	6	1.1	even	1	trivial
2366.2.d.q.337.3		12	13.5	odd	4
2366.2.d.q.337.9		12	13.8	odd	4

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:	\( N \)	\(=\)	\( 2366 = 2 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2366.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.05140 q^{3} +1.00000 q^{4} +2.26985 q^{5} -1.05140 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.89456 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.05140 q^{3} +1.00000 q^{4} +2.26985 q^{5} -1.05140 q^{6} +1.00000 q^{7} +1.00000 q^{8} -1.89456 q^{9} +2.26985 q^{10} +0.977125 q^{11} -1.05140 q^{12} +1.00000 q^{14} -2.38653 q^{15} +1.00000 q^{16} +0.963254 q^{17} -1.89456 q^{18} -5.10479 q^{19} +2.26985 q^{20} -1.05140 q^{21} +0.977125 q^{22} +8.11859 q^{23} -1.05140 q^{24} +0.152241 q^{25} +5.14614 q^{27} +1.00000 q^{28} +9.77952 q^{29} -2.38653 q^{30} +5.15994 q^{31} +1.00000 q^{32} -1.02735 q^{33} +0.963254 q^{34} +2.26985 q^{35} -1.89456 q^{36} +0.794311 q^{37} -5.10479 q^{38} +2.26985 q^{40} -1.49967 q^{41} -1.05140 q^{42} -7.93286 q^{43} +0.977125 q^{44} -4.30037 q^{45} +8.11859 q^{46} +5.04879 q^{47} -1.05140 q^{48} +1.00000 q^{49} +0.152241 q^{50} -1.01277 q^{51} +3.68079 q^{53} +5.14614 q^{54} +2.21793 q^{55} +1.00000 q^{56} +5.36718 q^{57} +9.77952 q^{58} +12.8260 q^{59} -2.38653 q^{60} -3.93268 q^{61} +5.15994 q^{62} -1.89456 q^{63} +1.00000 q^{64} -1.02735 q^{66} +0.0496112 q^{67} +0.963254 q^{68} -8.53589 q^{69} +2.26985 q^{70} -3.71940 q^{71} -1.89456 q^{72} -8.87873 q^{73} +0.794311 q^{74} -0.160066 q^{75} -5.10479 q^{76} +0.977125 q^{77} -6.98214 q^{79} +2.26985 q^{80} +0.273022 q^{81} -1.49967 q^{82} +6.24779 q^{83} -1.05140 q^{84} +2.18645 q^{85} -7.93286 q^{86} -10.2822 q^{87} +0.977125 q^{88} -5.92385 q^{89} -4.30037 q^{90} +8.11859 q^{92} -5.42516 q^{93} +5.04879 q^{94} -11.5871 q^{95} -1.05140 q^{96} +7.29137 q^{97} +1.00000 q^{98} -1.85122 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9	\( 6 q + 6 q^{2} + q^{3} + 6 q^{4} + 4 q^{5} + q^{6} + 6 q^{7} + 6 q^{8} + 5 q^{9} + 4 q^{10} + 6 q^{11} + q^{12} + 6 q^{14} - 5 q^{15} + 6 q^{16} - 9 q^{17} + 5 q^{18} + 10 q^{19} + 4 q^{20} + q^{21} + 6 q^{22} + 21 q^{23} + q^{24} + 8 q^{25} + 7 q^{27} + 6 q^{28} - q^{29} - 5 q^{30} + 20 q^{31} + 6 q^{32} + 9 q^{33} - 9 q^{34} + 4 q^{35} + 5 q^{36} + 16 q^{37} + 10 q^{38} + 4 q^{40} + 2 q^{41} + q^{42} + 2 q^{43} + 6 q^{44} + 17 q^{45} + 21 q^{46} - 5 q^{47} + q^{48} + 6 q^{49} + 8 q^{50} - 15 q^{51} + 28 q^{53} + 7 q^{54} - 29 q^{55} + 6 q^{56} + 22 q^{57} - q^{58} - 12 q^{59} - 5 q^{60} - 27 q^{61} + 20 q^{62} + 5 q^{63} + 6 q^{64} + 9 q^{66} + 16 q^{67} - 9 q^{68} - 15 q^{69} + 4 q^{70} + 5 q^{72} + 38 q^{73} + 16 q^{74} - 7 q^{75} + 10 q^{76} + 6 q^{77} + 6 q^{79} + 4 q^{80} - 26 q^{81} + 2 q^{82} - 6 q^{83} + q^{84} + 9 q^{85} + 2 q^{86} - 39 q^{87} + 6 q^{88} - q^{89} + 17 q^{90} + 21 q^{92} - 7 q^{93} - 5 q^{94} + 3 q^{95} + q^{96} + 16 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + q^3 + 6 * q^4 + 4 * q^5 + q^6 + 6 * q^7 + 6 * q^8 + 5 * q^9 + 4 * q^10 + 6 * q^11 + q^12 + 6 * q^14 - 5 * q^15 + 6 * q^16 - 9 * q^17 + 5 * q^18 + 10 * q^19 + 4 * q^20 + q^21 + 6 * q^22 + 21 * q^23 + q^24 + 8 * q^25 + 7 * q^27 + 6 * q^28 - q^29 - 5 * q^30 + 20 * q^31 + 6 * q^32 + 9 * q^33 - 9 * q^34 + 4 * q^35 + 5 * q^36 + 16 * q^37 + 10 * q^38 + 4 * q^40 + 2 * q^41 + q^42 + 2 * q^43 + 6 * q^44 + 17 * q^45 + 21 * q^46 - 5 * q^47 + q^48 + 6 * q^49 + 8 * q^50 - 15 * q^51 + 28 * q^53 + 7 * q^54 - 29 * q^55 + 6 * q^56 + 22 * q^57 - q^58 - 12 * q^59 - 5 * q^60 - 27 * q^61 + 20 * q^62 + 5 * q^63 + 6 * q^64 + 9 * q^66 + 16 * q^67 - 9 * q^68 - 15 * q^69 + 4 * q^70 + 5 * q^72 + 38 * q^73 + 16 * q^74 - 7 * q^75 + 10 * q^76 + 6 * q^77 + 6 * q^79 + 4 * q^80 - 26 * q^81 + 2 * q^82 - 6 * q^83 + q^84 + 9 * q^85 + 2 * q^86 - 39 * q^87 + 6 * q^88 - q^89 + 17 * q^90 + 21 * q^92 - 7 * q^93 - 5 * q^94 + 3 * q^95 + q^96 + 16 * q^97 + 6 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more