LMFDB - Embedded newform 2366.2.a.be.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:	$1$
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	$-0.669451\pi$
$5$	−2.26985	−1.01511	−0.507555	+	0.861619i	$0.669451\pi$
$6$	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	$-0.547061\pi$
$11$	−0.977125	−0.294614	−0.147307	+	0.989091i	$0.547061\pi$
$12$	−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	$-0.300875\pi$
$19$	5.10479	1.17112	0.585560	+	0.810629i	$0.300875\pi$
$20$	−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	$-0.653362\pi$
$31$	−5.15994	−0.926752	−0.463376	+	0.886162i	$0.653362\pi$
$32$	−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	$-0.520798\pi$
$37$	−0.794311	−0.130584	−0.0652920	+	0.997866i	$0.520798\pi$
$38$	−5.10479	−0.828107
$39$	0	0
$40$	2.26985	0.358896
$41$	1.49967	0.234208	0.117104	−	0.993120i	$-0.462639\pi$
$41$	1.49967	0.234208	0.117104	+	0.993120i	$0.462639\pi$
$42$	−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	$-0.620033\pi$
$47$	−5.04879	−0.736442	−0.368221	+	0.929738i	$0.620033\pi$
$48$	−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	$-0.814474\pi$
$59$	−12.8260	−1.66980	−0.834898	+	0.550404i	$0.814474\pi$
$60$	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	$-0.500965\pi$
$67$	−0.0496112	−0.00606097	−0.00303049	+	0.999995i	$0.500965\pi$
$68$	0.963254	0.116812
$69$	−8.53589	−1.02760
$70$	−2.26985	−0.271300
$71$	3.71940	0.441412	0.220706	−	0.975340i	$-0.429164\pi$
$71$	3.71940	0.441412	0.220706	+	0.975340i	$0.429164\pi$
$72$	1.89456	0.223276
$73$	8.87873	1.03918	0.519588	−	0.854417i	$-0.326085\pi$
$73$	8.87873	1.03918	0.519588	+	0.854417i	$0.326085\pi$
$74$	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	$-0.611407\pi$
$83$	−6.24779	−0.685785	−0.342892	+	0.939375i	$0.611407\pi$
$84$	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	$-0.398343\pi$
$89$	5.92385	0.627927	0.313964	+	0.949435i	$0.398343\pi$
$90$	−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	$-0.620698\pi$
$97$	−7.29137	−0.740326	−0.370163	+	0.928967i	$0.620698\pi$
$98$	−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	$-0.752898\pi$
$109$	−14.8986	−1.42703	−0.713515	+	0.700640i	$0.752898\pi$
$110$	−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	$-0.713064\pi$
$137$	−14.5252	−1.24097	−0.620485	+	0.784218i	$0.713064\pi$
$138$	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	$-0.432878\pi$
$149$	5.10994	0.418622	0.209311	+	0.977849i	$0.432878\pi$
$150$	0.160066	0.0130693
$151$	−22.3477	−1.81863	−0.909314	−	0.416110i	$-0.863393\pi$
$151$	−22.3477	−1.81863	−0.909314	+	0.416110i	$0.863393\pi$
$152$	−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	$-0.272437\pi$
$163$	16.7390	1.31110	0.655550	+	0.755151i	$0.272437\pi$
$164$	1.49967	0.117104
$165$	−2.33193	−0.181541
$166$	6.24779	0.484923
$167$	12.8583	0.995002	0.497501	−	0.867463i	$-0.334251\pi$
$167$	12.8583	0.995002	0.497501	+	0.867463i	$0.334251\pi$
$168$	−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	$-0.724447\pi$
$193$	−18.0081	−1.29625	−0.648126	+	0.761534i	$0.724447\pi$
$194$	7.29137	0.523490
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.56211	0.182543	0.0912715	−	0.995826i	$-0.470907\pi$
$197$	2.56211	0.182543	0.0912715	+	0.995826i	$0.470907\pi$
$198$	−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	$-0.440287\pi$
$223$	5.56995	0.372992	0.186496	+	0.982456i	$0.440287\pi$
$224$	1.00000	0.0668153
$225$	−0.288429	−0.0192286
$226$	−11.4817	−0.763749
$227$	−7.08232	−0.470070	−0.235035	−	0.971987i	$-0.575520\pi$
$227$	−7.08232	−0.470070	−0.235035	+	0.971987i	$0.575520\pi$
$228$	−5.36718	−0.355450
$229$	−13.9978	−0.924999	−0.462500	−	0.886619i	$-0.653047\pi$
$229$	−13.9978	−0.924999	−0.462500	+	0.886619i	$0.653047\pi$
$230$	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	$-0.413246\pi$
$239$	8.32300	0.538370	0.269185	+	0.963088i	$0.413246\pi$
$240$	2.38653	0.154050
$241$	27.7146	1.78525	0.892627	−	0.450796i	$-0.148860\pi$
$241$	27.7146	1.78525	0.892627	+	0.450796i	$0.148860\pi$
$242$	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	$-0.496074\pi$
$271$	0.406075	0.0246673	0.0123336	+	0.999924i	$0.496074\pi$
$272$	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	$-0.480428\pi$
$281$	2.06017	0.122899	0.0614497	+	0.998110i	$0.480428\pi$
$282$	−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	$-0.827388\pi$
$293$	−29.3231	−1.71307	−0.856537	+	0.516086i	$0.827388\pi$
$294$	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	$-0.631563\pi$
$307$	−14.0749	−0.803299	−0.401649	+	0.915793i	$0.631563\pi$
$308$	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	$-0.354241\pi$
$317$	15.7420	0.884161	0.442081	+	0.896975i	$0.354241\pi$
$318$	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	$-0.521088\pi$
$331$	−2.40882	−0.132401	−0.0662003	+	0.997806i	$0.521088\pi$
$332$	−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	$-0.324544\pi$
$349$	19.5678	1.04744	0.523719	+	0.851891i	$0.324544\pi$
$350$	0.152241	0.00813762
$351$	0	0
$352$	0.977125	0.0520809
$353$	4.27967	0.227784	0.113892	−	0.993493i	$-0.463668\pi$
$353$	4.27967	0.227784	0.113892	+	0.993493i	$0.463668\pi$
$354$	−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	$-0.632215\pi$
$359$	−15.2915	−0.807052	−0.403526	+	0.914968i	$0.632215\pi$
$360$	−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	$-0.318363\pi$
$379$	21.0316	1.08032	0.540161	+	0.841562i	$0.318363\pi$
$380$	−11.5871	−0.594408
$381$	7.50657	0.384573
$382$	6.68377	0.341971
$383$	14.6607	0.749124	0.374562	−	0.927202i	$-0.377793\pi$
$383$	14.6607	0.749124	0.374562	+	0.927202i	$0.377793\pi$
$384$	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	$-0.257060\pi$
$397$	27.5462	1.38250	0.691251	+	0.722615i	$0.257060\pi$
$398$	−8.54978	−0.428562
$399$	5.36718	0.268695
$400$	0.152241	0.00761205
$401$	−17.8377	−0.890774	−0.445387	−	0.895338i	$-0.646934\pi$
$401$	−17.8377	−0.890774	−0.445387	+	0.895338i	$0.646934\pi$
$402$	−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	$-0.810802\pi$
$409$	−33.5105	−1.65699	−0.828495	+	0.559997i	$0.810802\pi$
$410$	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	$-0.137096\pi$
$421$	37.2889	1.81735	0.908674	+	0.417507i	$0.137096\pi$
$422$	−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	$-0.383054\pi$
$431$	14.9139	0.718376	0.359188	+	0.933265i	$0.383054\pi$
$432$	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	$-0.692042\pi$
$449$	−24.0450	−1.13475	−0.567376	+	0.823459i	$0.692042\pi$
$450$	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	$-0.414648\pi$
$457$	11.3275	0.529880	0.264940	+	0.964265i	$0.414648\pi$
$458$	13.9978	0.654073
$459$	4.95704	0.231375
$460$	−18.4280	−0.859211
$461$	7.54671	0.351485	0.175743	−	0.984436i	$-0.443767\pi$
$461$	7.54671	0.351485	0.175743	+	0.984436i	$0.443767\pi$
$462$	1.02735	0.0477966
$463$	−18.6384	−0.866202	−0.433101	−	0.901345i	$-0.642581\pi$
$463$	−18.6384	−0.866202	−0.433101	+	0.901345i	$0.642581\pi$
$464$	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	$-0.961209\pi$
$479$	−43.4475	−1.98517	−0.992584	+	0.121564i	$0.961209\pi$
$480$	−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	$-0.424898\pi$
$487$	10.3172	0.467515	0.233758	+	0.972295i	$0.424898\pi$
$488$	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	$-0.296751\pi$
$499$	26.6278	1.19202	0.596012	+	0.802975i	$0.296751\pi$
$500$	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	$-0.398749\pi$
$509$	14.1121	0.625507	0.312753	+	0.949834i	$0.398749\pi$
$510$	−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	$-0.559663\pi$
$541$	−8.66839	−0.372683	−0.186342	+	0.982485i	$0.559663\pi$
$542$	−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	$-0.203506\pi$
$557$	37.8791	1.60499	0.802494	+	0.596660i	$0.203506\pi$
$558$	−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	$-0.612683\pi$
$577$	−16.6539	−0.693310	−0.346655	+	0.937993i	$0.612683\pi$
$578$	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	$-0.461886\pi$
$587$	5.78820	0.238905	0.119452	+	0.992840i	$0.461886\pi$
$588$	−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	$-0.478885\pi$
$593$	3.22830	0.132570	0.0662852	+	0.997801i	$0.478885\pi$
$594$	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	$-0.227408\pi$
$613$	37.4092	1.51094	0.755471	+	0.655182i	$0.227408\pi$
$614$	14.0749	0.568018
$615$	3.57899	0.144319
$616$	−0.977125	−0.0393695
$617$	0.959817	0.0386408	0.0193204	−	0.999813i	$-0.493850\pi$
$617$	0.959817	0.0386408	0.0193204	+	0.999813i	$0.493850\pi$
$618$	5.92198	0.238217
$619$	−11.1412	−0.447804	−0.223902	−	0.974612i	$-0.571880\pi$
$619$	−11.1412	−0.447804	−0.223902	+	0.974612i	$0.571880\pi$
$620$	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	$-0.427953\pi$
$631$	11.2745	0.448831	0.224416	+	0.974494i	$0.427953\pi$
$632$	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	$-0.504750\pi$
$643$	−0.756725	−0.0298423	−0.0149212	+	0.999889i	$0.504750\pi$
$644$	−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	$-0.620089\pi$
$661$	−18.9423	−0.736769	−0.368385	+	0.929674i	$0.620089\pi$
$662$	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	$-0.439004\pi$
$683$	9.95472	0.380907	0.190453	+	0.981696i	$0.439004\pi$
$684$	−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	$-0.845633\pi$
$691$	−46.5117	−1.76939	−0.884695	+	0.466171i	$0.845633\pi$
$692$	−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	$-0.718537\pi$
$709$	−33.7565	−1.26775	−0.633877	+	0.773434i	$0.718537\pi$
$710$	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	$-0.378384\pi$
$733$	20.1885	0.745680	0.372840	+	0.927896i	$0.378384\pi$
$734$	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	$-0.593239\pi$
$739$	−15.6989	−0.577493	−0.288747	+	0.957406i	$0.593239\pi$
$740$	1.80297	0.0662785
$741$	0	0
$742$	3.68079	0.135126
$743$	37.2634	1.36706	0.683530	−	0.729923i	$-0.260444\pi$
$743$	37.2634	1.36706	0.683530	+	0.729923i	$0.260444\pi$
$744$	−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	$-0.460016\pi$
$761$	6.91223	0.250568	0.125284	+	0.992121i	$0.460016\pi$
$762$	−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	$-0.657158\pi$
$769$	−26.2839	−0.947822	−0.473911	+	0.880573i	$0.657158\pi$
$770$	2.21793	0.0799287
$771$	30.1173	1.08465
$772$	−18.0081	−0.648126
$773$	−22.0986	−0.794832	−0.397416	−	0.917638i	$-0.630093\pi$
$773$	−22.0986	−0.794832	−0.397416	+	0.917638i	$0.630093\pi$
$774$	−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	$-0.185283\pi$
$787$	46.8673	1.67064	0.835319	+	0.549766i	$0.185283\pi$
$788$	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	$-0.785424\pi$
$811$	−44.4977	−1.56252	−0.781262	+	0.624203i	$0.785424\pi$
$812$	−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	$-0.736421\pi$
$821$	−38.7566	−1.35261	−0.676307	+	0.736619i	$0.736421\pi$
$822$	−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	$-0.561411\pi$
$827$	−11.0276	−0.383469	−0.191734	+	0.981447i	$0.561411\pi$
$828$	−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	$-0.603280\pi$
$839$	−18.4684	−0.637598	−0.318799	+	0.947822i	$0.603280\pi$
$840$	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	$-0.276899\pi$
$853$	37.6701	1.28980	0.644900	+	0.764267i	$0.276899\pi$
$854$	−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	$-0.476826\pi$
$863$	4.27374	0.145480	0.0727398	+	0.997351i	$0.476826\pi$
$864$	−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	$-0.775031\pi$
$877$	−45.0414	−1.52094	−0.760470	+	0.649373i	$0.775031\pi$
$878$	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	$-0.741936\pi$
$929$	−41.9988	−1.37794	−0.688968	+	0.724791i	$0.741936\pi$
$930$	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	$-0.568218\pi$
$941$	−13.0479	−0.425350	−0.212675	+	0.977123i	$0.568218\pi$
$942$	−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	$-0.180615\pi$
$947$	51.9018	1.68658	0.843291	+	0.537457i	$0.180615\pi$
$948$	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	$-0.745488\pi$
$967$	−43.3495	−1.39403	−0.697013	+	0.717059i	$0.745488\pi$
$968$	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	$-0.799127\pi$
$977$	−50.4739	−1.61480	−0.807402	+	0.590002i	$0.799127\pi$
$978$	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	$-0.272554\pi$
$983$	41.0892	1.31054	0.655272	+	0.755393i	$0.272554\pi$
$984$	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.be.1.3	✓	6
13.5	odd	4		2366.2.d.q.337.9		12
13.8	odd	4		2366.2.d.q.337.3		12
13.12	even	2		2366.2.a.bg.1.3	yes	6

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

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