LMFDB - Embedded newform 717.2.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [717,2,Mod(1,717)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(717, 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("717.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 717 = 3 \cdot 239 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	717.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:	$5.72527382493$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	6.6.1767625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 7x^{4} - x^{3} + 11x^{2} + x - 1 $ x^6 - 7x^4 - x^3 + 11x^2 + x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.39213$ of defining polynomial
Character	$\chi$	$=$	717.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.899709 q^{2} -1.00000 q^{3} -1.19052 q^{4} +1.67380 q^{5} +0.899709 q^{6} -1.75765 q^{7} +2.87054 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.899709 q^{2} -1.00000 q^{3} -1.19052 q^{4} +1.67380 q^{5} +0.899709 q^{6} -1.75765 q^{7} +2.87054 q^{8} +1.00000 q^{9} -1.50593 q^{10} -5.08858 q^{11} +1.19052 q^{12} +6.43675 q^{13} +1.58137 q^{14} -1.67380 q^{15} -0.201602 q^{16} -2.24001 q^{17} -0.899709 q^{18} -3.96067 q^{19} -1.99270 q^{20} +1.75765 q^{21} +4.57824 q^{22} +7.71459 q^{23} -2.87054 q^{24} -2.19839 q^{25} -5.79120 q^{26} -1.00000 q^{27} +2.09253 q^{28} +0.101311 q^{29} +1.50593 q^{30} -4.63283 q^{31} -5.55970 q^{32} +5.08858 q^{33} +2.01536 q^{34} -2.94196 q^{35} -1.19052 q^{36} -7.78041 q^{37} +3.56345 q^{38} -6.43675 q^{39} +4.80472 q^{40} +1.42586 q^{41} -1.58137 q^{42} -3.65358 q^{43} +6.05808 q^{44} +1.67380 q^{45} -6.94088 q^{46} -7.73754 q^{47} +0.201602 q^{48} -3.91066 q^{49} +1.97791 q^{50} +2.24001 q^{51} -7.66311 q^{52} +1.61074 q^{53} +0.899709 q^{54} -8.51728 q^{55} -5.04542 q^{56} +3.96067 q^{57} -0.0911499 q^{58} -2.46261 q^{59} +1.99270 q^{60} -4.77088 q^{61} +4.16819 q^{62} -1.75765 q^{63} +5.40531 q^{64} +10.7738 q^{65} -4.57824 q^{66} -3.42357 q^{67} +2.66679 q^{68} -7.71459 q^{69} +2.64691 q^{70} -13.1223 q^{71} +2.87054 q^{72} -14.4582 q^{73} +7.00010 q^{74} +2.19839 q^{75} +4.71528 q^{76} +8.94396 q^{77} +5.79120 q^{78} -13.0644 q^{79} -0.337442 q^{80} +1.00000 q^{81} -1.28286 q^{82} -0.423954 q^{83} -2.09253 q^{84} -3.74933 q^{85} +3.28716 q^{86} -0.101311 q^{87} -14.6070 q^{88} +17.1426 q^{89} -1.50593 q^{90} -11.3136 q^{91} -9.18440 q^{92} +4.63283 q^{93} +6.96153 q^{94} -6.62938 q^{95} +5.55970 q^{96} +6.06424 q^{97} +3.51845 q^{98} -5.08858 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9} - 11 q^{10} - 13 q^{11} - 4 q^{12} - q^{13} - 5 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} + 9 q^{21} - 2 q^{22} - 12 q^{23} + 3 q^{24} - q^{25} + 12 q^{26} - 6 q^{27} - 16 q^{28} + 11 q^{30} - 18 q^{31} + 7 q^{32} + 13 q^{33} - 3 q^{34} - 9 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} - 4 q^{44} + 5 q^{45} - 18 q^{46} - 9 q^{47} + 4 q^{48} + 5 q^{49} + 4 q^{50} - 11 q^{51} - 16 q^{52} - 8 q^{53} + 2 q^{54} - 20 q^{55} + 11 q^{56} + 22 q^{57} - 15 q^{58} - 10 q^{59} + q^{60} - 12 q^{61} - 13 q^{62} - 9 q^{63} - 31 q^{64} - 11 q^{65} + 2 q^{66} - 36 q^{67} + 22 q^{68} + 12 q^{69} + q^{70} - 3 q^{71} - 3 q^{72} - 32 q^{73} + 9 q^{74} + q^{75} - 4 q^{76} + 6 q^{77} - 12 q^{78} - q^{79} - 7 q^{80} + 6 q^{81} + 7 q^{82} - 7 q^{83} + 16 q^{84} - 14 q^{85} + 45 q^{86} - 15 q^{88} + 17 q^{89} - 11 q^{90} - 23 q^{91} - 12 q^{92} + 18 q^{93} + 50 q^{94} - 7 q^{96} - 28 q^{97} + 13 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9 - 11 * q^10 - 13 * q^11 - 4 * q^12 - q^13 - 5 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 + 9 * q^21 - 2 * q^22 - 12 * q^23 + 3 * q^24 - q^25 + 12 * q^26 - 6 * q^27 - 16 * q^28 + 11 * q^30 - 18 * q^31 + 7 * q^32 + 13 * q^33 - 3 * q^34 - 9 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 - 4 * q^44 + 5 * q^45 - 18 * q^46 - 9 * q^47 + 4 * q^48 + 5 * q^49 + 4 * q^50 - 11 * q^51 - 16 * q^52 - 8 * q^53 + 2 * q^54 - 20 * q^55 + 11 * q^56 + 22 * q^57 - 15 * q^58 - 10 * q^59 + q^60 - 12 * q^61 - 13 * q^62 - 9 * q^63 - 31 * q^64 - 11 * q^65 + 2 * q^66 - 36 * q^67 + 22 * q^68 + 12 * q^69 + q^70 - 3 * q^71 - 3 * q^72 - 32 * q^73 + 9 * q^74 + q^75 - 4 * q^76 + 6 * q^77 - 12 * q^78 - q^79 - 7 * q^80 + 6 * q^81 + 7 * q^82 - 7 * q^83 + 16 * q^84 - 14 * q^85 + 45 * q^86 - 15 * q^88 + 17 * q^89 - 11 * q^90 - 23 * q^91 - 12 * q^92 + 18 * q^93 + 50 * q^94 - 7 * q^96 - 28 * q^97 + 13 * q^98 - 13 * 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 $

$2$	−0.899709	−0.636190	−0.318095	−	0.948059i	$-0.603043\pi$
$2$	−0.899709	−0.636190	−0.318095	+	0.948059i	$0.603043\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.19052	−0.595262
$5$	1.67380	0.748547	0.374273	−	0.927318i	$-0.377892\pi$
$5$	1.67380	0.748547	0.374273	+	0.927318i	$0.377892\pi$
$6$	0.899709	0.367304
$7$	−1.75765	−0.664330	−0.332165	−	0.943221i	$-0.607779\pi$
$7$	−1.75765	−0.664330	−0.332165	+	0.943221i	$0.607779\pi$
$8$	2.87054	1.01489
$9$	1.00000	0.333333
$10$	−1.50593	−0.476218
$11$	−5.08858	−1.53427	−0.767133	−	0.641488i	$-0.778317\pi$
$11$	−5.08858	−1.53427	−0.767133	+	0.641488i	$0.778317\pi$
$12$	1.19052	0.343675
$13$	6.43675	1.78523	0.892617	−	0.450816i	$-0.148867\pi$
$13$	6.43675	1.78523	0.892617	+	0.450816i	$0.148867\pi$
$14$	1.58137	0.422640
$15$	−1.67380	−0.432174
$16$	−0.201602	−0.0504005
$17$	−2.24001	−0.543283	−0.271641	−	0.962399i	$-0.587566\pi$
$17$	−2.24001	−0.543283	−0.271641	+	0.962399i	$0.587566\pi$
$18$	−0.899709	−0.212063
$19$	−3.96067	−0.908641	−0.454320	−	0.890838i	$-0.650118\pi$
$19$	−3.96067	−0.908641	−0.454320	+	0.890838i	$0.650118\pi$
$20$	−1.99270	−0.445582
$21$	1.75765	0.383551
$22$	4.57824	0.976085
$23$	7.71459	1.60860	0.804301	−	0.594222i	$-0.202540\pi$
$23$	7.71459	1.60860	0.804301	+	0.594222i	$0.202540\pi$
$24$	−2.87054	−0.585947
$25$	−2.19839	−0.439678
$26$	−5.79120	−1.13575
$27$	−1.00000	−0.192450
$28$	2.09253	0.395451
$29$	0.101311	0.0188129	0.00940644	−	0.999956i	$-0.497006\pi$
$29$	0.101311	0.0188129	0.00940644	+	0.999956i	$0.497006\pi$
$30$	1.50593	0.274945
$31$	−4.63283	−0.832080	−0.416040	−	0.909346i	$-0.636582\pi$
$31$	−4.63283	−0.832080	−0.416040	+	0.909346i	$0.636582\pi$
$32$	−5.55970	−0.982826
$33$	5.08858	0.885809
$34$	2.01536	0.345631
$35$	−2.94196	−0.497282
$36$	−1.19052	−0.198421
$37$	−7.78041	−1.27909	−0.639546	−	0.768753i	$-0.720878\pi$
$37$	−7.78041	−1.27909	−0.639546	+	0.768753i	$0.720878\pi$
$38$	3.56345	0.578068
$39$	−6.43675	−1.03071
$40$	4.80472	0.759692
$41$	1.42586	0.222682	0.111341	−	0.993782i	$-0.464485\pi$
$41$	1.42586	0.222682	0.111341	+	0.993782i	$0.464485\pi$
$42$	−1.58137	−0.244011
$43$	−3.65358	−0.557166	−0.278583	−	0.960412i	$-0.589865\pi$
$43$	−3.65358	−0.557166	−0.278583	+	0.960412i	$0.589865\pi$
$44$	6.05808	0.913291
$45$	1.67380	0.249516
$46$	−6.94088	−1.02338
$47$	−7.73754	−1.12864	−0.564318	−	0.825558i	$-0.690861\pi$
$47$	−7.73754	−1.12864	−0.564318	+	0.825558i	$0.690861\pi$
$48$	0.201602	0.0290987
$49$	−3.91066	−0.558665
$50$	1.97791	0.279719
$51$	2.24001	0.313664
$52$	−7.66311	−1.06268
$53$	1.61074	0.221252	0.110626	−	0.993862i	$-0.464715\pi$
$53$	1.61074	0.221252	0.110626	+	0.993862i	$0.464715\pi$
$54$	0.899709	0.122435
$55$	−8.51728	−1.14847
$56$	−5.04542	−0.674222
$57$	3.96067	0.524604
$58$	−0.0911499	−0.0119686
$59$	−2.46261	−0.320604	−0.160302	−	0.987068i	$-0.551247\pi$
$59$	−2.46261	−0.320604	−0.160302	+	0.987068i	$0.551247\pi$
$60$	1.99270	0.257257
$61$	−4.77088	−0.610849	−0.305424	−	0.952216i	$-0.598798\pi$
$61$	−4.77088	−0.610849	−0.305424	+	0.952216i	$0.598798\pi$
$62$	4.16819	0.529361
$63$	−1.75765	−0.221443
$64$	5.40531	0.675664
$65$	10.7738	1.33633
$66$	−4.57824	−0.563543
$67$	−3.42357	−0.418255	−0.209128	−	0.977888i	$-0.567062\pi$
$67$	−3.42357	−0.418255	−0.209128	+	0.977888i	$0.567062\pi$
$68$	2.66679	0.323396
$69$	−7.71459	−0.928727
$70$	2.64691	0.316366
$71$	−13.1223	−1.55733	−0.778665	−	0.627440i	$-0.784103\pi$
$71$	−13.1223	−1.55733	−0.778665	+	0.627440i	$0.784103\pi$
$72$	2.87054	0.338297
$73$	−14.4582	−1.69220	−0.846100	−	0.533025i	$-0.821055\pi$
$73$	−14.4582	−1.69220	−0.846100	+	0.533025i	$0.821055\pi$
$74$	7.00010	0.813745
$75$	2.19839	0.253848
$76$	4.71528	0.540880
$77$	8.94396	1.01926
$78$	5.79120	0.655724
$79$	−13.0644	−1.46986	−0.734930	−	0.678143i	$-0.762785\pi$
$79$	−13.0644	−1.46986	−0.734930	+	0.678143i	$0.762785\pi$
$80$	−0.337442	−0.0377271
$81$	1.00000	0.111111
$82$	−1.28286	−0.141668
$83$	−0.423954	−0.0465350	−0.0232675	−	0.999729i	$-0.507407\pi$
$83$	−0.423954	−0.0465350	−0.0232675	+	0.999729i	$0.507407\pi$
$84$	−2.09253	−0.228314
$85$	−3.74933	−0.406672
$86$	3.28716	0.354463
$87$	−0.101311	−0.0108616
$88$	−14.6070	−1.55711
$89$	17.1426	1.81711	0.908556	−	0.417763i	$-0.137186\pi$
$89$	17.1426	1.81711	0.908556	+	0.417763i	$0.137186\pi$
$90$	−1.50593	−0.158739
$91$	−11.3136	−1.18598
$92$	−9.18440	−0.957540
$93$	4.63283	0.480402
$94$	6.96153	0.718027
$95$	−6.62938	−0.680160
$96$	5.55970	0.567435
$97$	6.06424	0.615730	0.307865	−	0.951430i	$-0.400386\pi$
$97$	6.06424	0.615730	0.307865	+	0.951430i	$0.400386\pi$
$98$	3.51845	0.355417
$99$	−5.08858	−0.511422
$100$	2.61724	0.261724
$101$	10.1166	1.00664	0.503320	−	0.864100i	$-0.332112\pi$
$101$	10.1166	1.00664	0.503320	+	0.864100i	$0.332112\pi$
$102$	−2.01536	−0.199550
$103$	2.53914	0.250189	0.125094	−	0.992145i	$-0.460077\pi$
$103$	2.53914	0.250189	0.125094	+	0.992145i	$0.460077\pi$
$104$	18.4770	1.81182
$105$	2.94196	0.287106
$106$	−1.44919	−0.140758
$107$	9.82497	0.949816	0.474908	−	0.880035i	$-0.342481\pi$
$107$	9.82497	0.949816	0.474908	+	0.880035i	$0.342481\pi$
$108$	1.19052	0.114558
$109$	−15.1110	−1.44738	−0.723688	−	0.690127i	$-0.757555\pi$
$109$	−15.1110	−1.44738	−0.723688	+	0.690127i	$0.757555\pi$
$110$	7.66307	0.730645
$111$	7.78041	0.738484
$112$	0.354346	0.0334826
$113$	2.58916	0.243568	0.121784	−	0.992557i	$-0.461139\pi$
$113$	2.58916	0.243568	0.121784	+	0.992557i	$0.461139\pi$
$114$	−3.56345	−0.333748
$115$	12.9127	1.20411
$116$	−0.120613	−0.0111986
$117$	6.43675	0.595078
$118$	2.21563	0.203965
$119$	3.93716	0.360919
$120$	−4.80472	−0.438609
$121$	14.8937	1.35397
$122$	4.29240	0.388616
$123$	−1.42586	−0.128566
$124$	5.51549	0.495306
$125$	−12.0487	−1.07767
$126$	1.58137	0.140880
$127$	7.24277	0.642692	0.321346	−	0.946962i	$-0.395865\pi$
$127$	7.24277	0.642692	0.321346	+	0.946962i	$0.395865\pi$
$128$	6.25619	0.552975
$129$	3.65358	0.321680
$130$	−9.69332	−0.850160
$131$	2.14842	0.187709	0.0938543	−	0.995586i	$-0.470081\pi$
$131$	2.14842	0.187709	0.0938543	+	0.995586i	$0.470081\pi$
$132$	−6.05808	−0.527289
$133$	6.96149	0.603637
$134$	3.08021	0.266090
$135$	−1.67380	−0.144058
$136$	−6.43005	−0.551372
$137$	6.53872	0.558640	0.279320	−	0.960198i	$-0.409891\pi$
$137$	6.53872	0.558640	0.279320	+	0.960198i	$0.409891\pi$
$138$	6.94088	0.590847
$139$	9.78192	0.829691	0.414846	−	0.909892i	$-0.363836\pi$
$139$	9.78192	0.829691	0.414846	+	0.909892i	$0.363836\pi$
$140$	3.50248	0.296013
$141$	7.73754	0.651618
$142$	11.8062	0.990758
$143$	−32.7540	−2.73902
$144$	−0.201602	−0.0168002
$145$	0.169574	0.0140823
$146$	13.0081	1.07656
$147$	3.91066	0.322546
$148$	9.26277	0.761395
$149$	−12.0860	−0.990120	−0.495060	−	0.868859i	$-0.664854\pi$
$149$	−12.0860	−0.990120	−0.495060	+	0.868859i	$0.664854\pi$
$150$	−1.97791	−0.161496
$151$	12.6923	1.03288	0.516442	−	0.856322i	$-0.327256\pi$
$151$	12.6923	1.03288	0.516442	+	0.856322i	$0.327256\pi$
$152$	−11.3693	−0.922170
$153$	−2.24001	−0.181094
$154$	−8.04696	−0.648442
$155$	−7.75443	−0.622851
$156$	7.66311	0.613540
$157$	−20.3326	−1.62272	−0.811359	−	0.584548i	$-0.801272\pi$
$157$	−20.3326	−1.62272	−0.811359	+	0.584548i	$0.801272\pi$
$158$	11.7542	0.935110
$159$	−1.61074	−0.127740
$160$	−9.30583	−0.735691
$161$	−13.5596	−1.06864
$162$	−0.899709	−0.0706878
$163$	−14.3750	−1.12593	−0.562967	−	0.826480i	$-0.690340\pi$
$163$	−14.3750	−1.12593	−0.562967	+	0.826480i	$0.690340\pi$
$164$	−1.69752	−0.132554
$165$	8.51728	0.663069
$166$	0.381435	0.0296051
$167$	−18.7294	−1.44933	−0.724663	−	0.689103i	$-0.758005\pi$
$167$	−18.7294	−1.44933	−0.724663	+	0.689103i	$0.758005\pi$
$168$	5.04542	0.389262
$169$	28.4318	2.18706
$170$	3.37331	0.258721
$171$	−3.96067	−0.302880
$172$	4.34968	0.331660
$173$	−11.7428	−0.892786	−0.446393	−	0.894837i	$-0.647292\pi$
$173$	−11.7428	−0.892786	−0.446393	+	0.894837i	$0.647292\pi$
$174$	0.0911499	0.00691006
$175$	3.86401	0.292091
$176$	1.02587	0.0773278
$177$	2.46261	0.185101
$178$	−15.4233	−1.15603
$179$	24.5193	1.83266	0.916328	−	0.400429i	$-0.131139\pi$
$179$	24.5193	1.83266	0.916328	+	0.400429i	$0.131139\pi$
$180$	−1.99270	−0.148527
$181$	2.13689	0.158833	0.0794167	−	0.996842i	$-0.474694\pi$
$181$	2.13689	0.158833	0.0794167	+	0.996842i	$0.474694\pi$
$182$	10.1789	0.754512
$183$	4.77088	0.352674
$184$	22.1450	1.63255
$185$	−13.0229	−0.957460
$186$	−4.16819	−0.305627
$187$	11.3985	0.833540
$188$	9.21173	0.671834
$189$	1.75765	0.127850
$190$	5.96451	0.432711
$191$	11.6936	0.846118	0.423059	−	0.906102i	$-0.360956\pi$
$191$	11.6936	0.846118	0.423059	+	0.906102i	$0.360956\pi$
$192$	−5.40531	−0.390095
$193$	2.15548	0.155155	0.0775774	−	0.996986i	$-0.475282\pi$
$193$	2.15548	0.155155	0.0775774	+	0.996986i	$0.475282\pi$
$194$	−5.45605	−0.391721
$195$	−10.7738	−0.771531
$196$	4.65573	0.332552
$197$	6.46675	0.460737	0.230368	−	0.973104i	$-0.426007\pi$
$197$	6.46675	0.460737	0.230368	+	0.973104i	$0.426007\pi$
$198$	4.57824	0.325362
$199$	21.8975	1.55228	0.776138	−	0.630563i	$-0.217176\pi$
$199$	21.8975	1.55228	0.776138	+	0.630563i	$0.217176\pi$
$200$	−6.31057	−0.446225
$201$	3.42357	0.241480
$202$	−9.10200	−0.640415
$203$	−0.178069	−0.0124980
$204$	−2.66679	−0.186713
$205$	2.38661	0.166688
$206$	−2.28449	−0.159168
$207$	7.71459	0.536201
$208$	−1.29766	−0.0899767
$209$	20.1542	1.39410
$210$	−2.64691	−0.182654
$211$	11.2465	0.774243	0.387122	−	0.922029i	$-0.373469\pi$
$211$	11.2465	0.774243	0.387122	+	0.922029i	$0.373469\pi$
$212$	−1.91762	−0.131703
$213$	13.1223	0.899125
$214$	−8.83961	−0.604263
$215$	−6.11537	−0.417065
$216$	−2.87054	−0.195316
$217$	8.14290	0.552776
$218$	13.5955	0.920806
$219$	14.4582	0.976992
$220$	10.1400	0.683641
$221$	−14.4184	−0.969887
$222$	−7.00010	−0.469816
$223$	−19.8849	−1.33159	−0.665797	−	0.746133i	$-0.731908\pi$
$223$	−19.8849	−1.33159	−0.665797	+	0.746133i	$0.731908\pi$
$224$	9.77202	0.652921
$225$	−2.19839	−0.146559
$226$	−2.32949	−0.154955
$227$	−6.20415	−0.411784	−0.205892	−	0.978575i	$-0.566010\pi$
$227$	−6.20415	−0.411784	−0.205892	+	0.978575i	$0.566010\pi$
$228$	−4.71528	−0.312277
$229$	−6.29386	−0.415910	−0.207955	−	0.978138i	$-0.566681\pi$
$229$	−6.29386	−0.415910	−0.207955	+	0.978138i	$0.566681\pi$
$230$	−11.6177	−0.766045
$231$	−8.94396	−0.588470
$232$	0.290816	0.0190930
$233$	−1.37434	−0.0900362	−0.0450181	−	0.998986i	$-0.514335\pi$
$233$	−1.37434	−0.0900362	−0.0450181	+	0.998986i	$0.514335\pi$
$234$	−5.79120	−0.378583
$235$	−12.9511	−0.844836
$236$	2.93179	0.190843
$237$	13.0644	0.848624
$238$	−3.54230	−0.229613
$239$	−1.00000	−0.0646846
$239$	−1.00000	−0.0646846
$240$	0.337442	0.0217818
$241$	−16.6512	−1.07260	−0.536299	−	0.844028i	$-0.680178\pi$
$241$	−16.6512	−1.07260	−0.536299	+	0.844028i	$0.680178\pi$
$242$	−13.4000	−0.861383
$243$	−1.00000	−0.0641500
$244$	5.67985	0.363615
$245$	−6.54566	−0.418187
$246$	1.28286	0.0817921
$247$	−25.4939	−1.62214
$248$	−13.2987	−0.844470
$249$	0.423954	0.0268670
$250$	10.8403	0.685600
$251$	8.70369	0.549372	0.274686	−	0.961534i	$-0.411426\pi$
$251$	8.70369	0.549372	0.274686	+	0.961534i	$0.411426\pi$
$252$	2.09253	0.131817
$253$	−39.2563	−2.46802
$254$	−6.51638	−0.408874
$255$	3.74933	0.234792
$256$	−16.4394	−1.02746
$257$	−17.8087	−1.11087	−0.555437	−	0.831559i	$-0.687449\pi$
$257$	−17.8087	−1.11087	−0.555437	+	0.831559i	$0.687449\pi$
$258$	−3.28716	−0.204650
$259$	13.6753	0.849739
$260$	−12.8265	−0.795467
$261$	0.101311	0.00627096
$262$	−1.93295	−0.119418
$263$	21.2660	1.31132	0.655658	−	0.755058i	$-0.272391\pi$
$263$	21.2660	1.31132	0.655658	+	0.755058i	$0.272391\pi$
$264$	14.6070	0.898998
$265$	2.69605	0.165617
$266$	−6.26331	−0.384028
$267$	−17.1426	−1.04911
$268$	4.07584	0.248971
$269$	−17.1887	−1.04801	−0.524005	−	0.851715i	$-0.675563\pi$
$269$	−17.1887	−1.04801	−0.524005	+	0.851715i	$0.675563\pi$
$270$	1.50593	0.0916482
$271$	19.1030	1.16043	0.580213	−	0.814465i	$-0.302969\pi$
$271$	19.1030	1.16043	0.580213	+	0.814465i	$0.302969\pi$
$272$	0.451591	0.0273817
$273$	11.3136	0.684729
$274$	−5.88294	−0.355401
$275$	11.1867	0.674583
$276$	9.18440	0.552836
$277$	19.3315	1.16152	0.580760	−	0.814075i	$-0.302755\pi$
$277$	19.3315	1.16152	0.580760	+	0.814075i	$0.302755\pi$
$278$	−8.80087	−0.527841
$279$	−4.63283	−0.277360
$280$	−8.44502	−0.504687
$281$	−4.05588	−0.241954	−0.120977	−	0.992655i	$-0.538603\pi$
$281$	−4.05588	−0.241954	−0.120977	+	0.992655i	$0.538603\pi$
$282$	−6.96153	−0.414553
$283$	−10.8007	−0.642035	−0.321018	−	0.947073i	$-0.604025\pi$
$283$	−10.8007	−0.642035	−0.321018	+	0.947073i	$0.604025\pi$
$284$	15.6224	0.927020
$285$	6.62938	0.392691
$286$	29.4690	1.74254
$287$	−2.50617	−0.147934
$288$	−5.55970	−0.327609
$289$	−11.9823	−0.704844
$290$	−0.152567	−0.00895903
$291$	−6.06424	−0.355492
$292$	17.2128	1.00730
$293$	5.01609	0.293043	0.146522	−	0.989207i	$-0.453192\pi$
$293$	5.01609	0.293043	0.146522	+	0.989207i	$0.453192\pi$
$294$	−3.51845	−0.205200
$295$	−4.12191	−0.239987
$296$	−22.3340	−1.29814
$297$	5.08858	0.295270
$298$	10.8738	0.629904
$299$	49.6569	2.87173
$300$	−2.61724	−0.151106
$301$	6.42173	0.370142
$302$	−11.4194	−0.657110
$303$	−10.1166	−0.581184
$304$	0.798480	0.0457959
$305$	−7.98550	−0.457249
$306$	2.01536	0.115210
$307$	−9.70591	−0.553945	−0.276973	−	0.960878i	$-0.589331\pi$
$307$	−9.70591	−0.553945	−0.276973	+	0.960878i	$0.589331\pi$
$308$	−10.6480	−0.606727
$309$	−2.53914	−0.144447
$310$	6.97673	0.396251
$311$	−10.3411	−0.586389	−0.293195	−	0.956053i	$-0.594718\pi$
$311$	−10.3411	−0.586389	−0.293195	+	0.956053i	$0.594718\pi$
$312$	−18.4770	−1.04605
$313$	−23.8987	−1.35084	−0.675418	−	0.737435i	$-0.736037\pi$
$313$	−23.8987	−1.35084	−0.675418	+	0.737435i	$0.736037\pi$
$314$	18.2934	1.03236
$315$	−2.94196	−0.165761
$316$	15.5535	0.874952
$317$	−1.48619	−0.0834729	−0.0417365	−	0.999129i	$-0.513289\pi$
$317$	−1.48619	−0.0834729	−0.0417365	+	0.999129i	$0.513289\pi$
$318$	1.44919	0.0812667
$319$	−0.515527	−0.0288640
$320$	9.04742	0.505766
$321$	−9.82497	−0.548377
$322$	12.1997	0.679860
$323$	8.87196	0.493649
$324$	−1.19052	−0.0661403
$325$	−14.1505	−0.784928
$326$	12.9333	0.716307
$327$	15.1110	0.835643
$328$	4.09299	0.225998
$329$	13.5999	0.749787
$330$	−7.66307	−0.421838
$331$	−17.6038	−0.967593	−0.483797	−	0.875180i	$-0.660743\pi$
$331$	−17.6038	−0.967593	−0.483797	+	0.875180i	$0.660743\pi$
$332$	0.504728	0.0277006
$333$	−7.78041	−0.426364
$334$	16.8510	0.922047
$335$	−5.73037	−0.313083
$336$	−0.354346	−0.0193312
$337$	18.9294	1.03115	0.515576	−	0.856844i	$-0.327578\pi$
$337$	18.9294	1.03115	0.515576	+	0.856844i	$0.327578\pi$
$338$	−25.5803	−1.39139
$339$	−2.58916	−0.140624
$340$	4.46368	0.242077
$341$	23.5745	1.27663
$342$	3.56345	0.192689
$343$	19.1771	1.03547
$344$	−10.4878	−0.565462
$345$	−12.9127	−0.695195
$346$	10.5651	0.567982
$347$	−1.63077	−0.0875444	−0.0437722	−	0.999042i	$-0.513938\pi$
$347$	−1.63077	−0.0875444	−0.0437722	+	0.999042i	$0.513938\pi$
$348$	0.120613	0.00646552
$349$	8.00213	0.428344	0.214172	−	0.976796i	$-0.431295\pi$
$349$	8.00213	0.428344	0.214172	+	0.976796i	$0.431295\pi$
$350$	−3.47648	−0.185826
$351$	−6.43675	−0.343568
$352$	28.2910	1.50792
$353$	9.60124	0.511022	0.255511	−	0.966806i	$-0.417756\pi$
$353$	9.60124	0.511022	0.255511	+	0.966806i	$0.417756\pi$
$354$	−2.21563	−0.117759
$355$	−21.9641	−1.16573
$356$	−20.4087	−1.08166
$357$	−3.93716	−0.208377
$358$	−22.0602	−1.16592
$359$	−31.4338	−1.65901	−0.829506	−	0.558498i	$-0.811378\pi$
$359$	−31.4338	−1.65901	−0.829506	+	0.558498i	$0.811378\pi$
$360$	4.80472	0.253231
$361$	−3.31307	−0.174372
$362$	−1.92257	−0.101048
$363$	−14.8937	−0.781716
$364$	13.4691	0.705972
$365$	−24.2001	−1.26669
$366$	−4.29240	−0.224367
$367$	−9.76744	−0.509856	−0.254928	−	0.966960i	$-0.582052\pi$
$367$	−9.76744	−0.509856	−0.254928	+	0.966960i	$0.582052\pi$
$368$	−1.55528	−0.0810744
$369$	1.42586	0.0742273
$370$	11.7168	0.609126
$371$	−2.83111	−0.146984
$372$	−5.51549	−0.285965
$373$	18.4876	0.957252	0.478626	−	0.878019i	$-0.341135\pi$
$373$	18.4876	0.957252	0.478626	+	0.878019i	$0.341135\pi$
$374$	−10.2553	−0.530290
$375$	12.0487	0.622191
$376$	−22.2109	−1.14544
$377$	0.652111	0.0335854
$378$	−1.58137	−0.0813371
$379$	−1.80626	−0.0927813	−0.0463907	−	0.998923i	$-0.514772\pi$
$379$	−1.80626	−0.0927813	−0.0463907	+	0.998923i	$0.514772\pi$
$380$	7.89244	0.404874
$381$	−7.24277	−0.371058
$382$	−10.5208	−0.538292
$383$	−25.2177	−1.28856	−0.644281	−	0.764789i	$-0.722843\pi$
$383$	−25.2177	−1.28856	−0.644281	+	0.764789i	$0.722843\pi$
$384$	−6.25619	−0.319260
$385$	14.9704	0.762963
$386$	−1.93930	−0.0987079
$387$	−3.65358	−0.185722
$388$	−7.21962	−0.366521
$389$	29.1698	1.47897	0.739485	−	0.673173i	$-0.235069\pi$
$389$	29.1698	1.47897	0.739485	+	0.673173i	$0.235069\pi$
$390$	9.69332	0.490840
$391$	−17.2808	−0.873926
$392$	−11.2257	−0.566984
$393$	−2.14842	−0.108374
$394$	−5.81819	−0.293116
$395$	−21.8672	−1.10026
$396$	6.05808	0.304430
$397$	37.3463	1.87435	0.937177	−	0.348853i	$-0.113429\pi$
$397$	37.3463	1.87435	0.937177	+	0.348853i	$0.113429\pi$
$398$	−19.7014	−0.987542
$399$	−6.96149	−0.348510
$400$	0.443200	0.0221600
$401$	5.50916	0.275114	0.137557	−	0.990494i	$-0.456075\pi$
$401$	5.50916	0.275114	0.137557	+	0.990494i	$0.456075\pi$
$402$	−3.08021	−0.153627
$403$	−29.8204	−1.48546
$404$	−12.0441	−0.599215
$405$	1.67380	0.0831718
$406$	0.160210	0.00795108
$407$	39.5913	1.96247
$408$	6.43005	0.318335
$409$	−28.2723	−1.39797	−0.698987	−	0.715134i	$-0.746366\pi$
$409$	−28.2723	−1.39797	−0.698987	+	0.715134i	$0.746366\pi$
$410$	−2.14725	−0.106045
$411$	−6.53872	−0.322531
$412$	−3.02291	−0.148928
$413$	4.32840	0.212987
$414$	−6.94088	−0.341126
$415$	−0.709615	−0.0348337
$416$	−35.7864	−1.75457
$417$	−9.78192	−0.479023
$418$	−18.1329	−0.886910
$419$	12.0357	0.587983	0.293992	−	0.955808i	$-0.405016\pi$
$419$	12.0357	0.587983	0.293992	+	0.955808i	$0.405016\pi$
$420$	−3.50248	−0.170903
$421$	−29.9983	−1.46203	−0.731015	−	0.682362i	$-0.760953\pi$
$421$	−29.9983	−1.46203	−0.731015	+	0.682362i	$0.760953\pi$
$422$	−10.1186	−0.492566
$423$	−7.73754	−0.376212
$424$	4.62368	0.224546
$425$	4.92442	0.238869
$426$	−11.8062	−0.572014
$427$	8.38555	0.405805
$428$	−11.6969	−0.565390
$429$	32.7540	1.58138
$430$	5.50205	0.265332
$431$	−17.8098	−0.857870	−0.428935	−	0.903335i	$-0.641111\pi$
$431$	−17.8098	−0.857870	−0.428935	+	0.903335i	$0.641111\pi$
$432$	0.201602	0.00969958
$433$	20.2488	0.973094	0.486547	−	0.873654i	$-0.338256\pi$
$433$	20.2488	0.973094	0.486547	+	0.873654i	$0.338256\pi$
$434$	−7.32623	−0.351670
$435$	−0.169574	−0.00813043
$436$	17.9901	0.861568
$437$	−30.5550	−1.46164
$438$	−13.0081	−0.621552
$439$	−34.7608	−1.65904	−0.829521	−	0.558475i	$-0.811387\pi$
$439$	−34.7608	−1.65904	−0.829521	+	0.558475i	$0.811387\pi$
$440$	−24.4492	−1.16557
$441$	−3.91066	−0.186222
$442$	12.9724	0.617032
$443$	−25.7595	−1.22387	−0.611935	−	0.790908i	$-0.709608\pi$
$443$	−25.7595	−1.22387	−0.611935	+	0.790908i	$0.709608\pi$
$444$	−9.26277	−0.439592
$445$	28.6933	1.36019
$446$	17.8907	0.847147
$447$	12.0860	0.571646
$448$	−9.50066	−0.448864
$449$	−30.2122	−1.42580	−0.712901	−	0.701265i	$-0.752619\pi$
$449$	−30.2122	−1.42580	−0.712901	+	0.701265i	$0.752619\pi$
$450$	1.97791	0.0932396
$451$	−7.25561	−0.341653
$452$	−3.08246	−0.144987
$453$	−12.6923	−0.596336
$454$	5.58193	0.261973
$455$	−18.9367	−0.887765
$456$	11.3693	0.532415
$457$	1.33578	0.0624850	0.0312425	−	0.999512i	$-0.490054\pi$
$457$	1.33578	0.0624850	0.0312425	+	0.999512i	$0.490054\pi$
$458$	5.66264	0.264598
$459$	2.24001	0.104555
$460$	−15.3729	−0.716764
$461$	16.6243	0.774272	0.387136	−	0.922023i	$-0.373464\pi$
$461$	16.6243	0.774272	0.387136	+	0.922023i	$0.373464\pi$
$462$	8.04696	0.374378
$463$	29.4246	1.36748	0.683739	−	0.729726i	$-0.260353\pi$
$463$	29.4246	1.36748	0.683739	+	0.729726i	$0.260353\pi$
$464$	−0.0204244	−0.000948179 0
$465$	7.75443	0.359603
$466$	1.23651	0.0572801
$467$	−2.53660	−0.117380	−0.0586899	−	0.998276i	$-0.518692\pi$
$467$	−2.53660	−0.117380	−0.0586899	+	0.998276i	$0.518692\pi$
$468$	−7.66311	−0.354228
$469$	6.01744	0.277859
$470$	11.6522	0.537476
$471$	20.3326	0.936876
$472$	−7.06901	−0.325378
$473$	18.5916	0.854841
$474$	−11.7542	−0.539886
$475$	8.70710	0.399509
$476$	−4.68729	−0.214842
$477$	1.61074	0.0737505
$478$	0.899709	0.0411517
$479$	38.6620	1.76651	0.883255	−	0.468893i	$-0.155347\pi$
$479$	38.6620	1.76651	0.883255	+	0.468893i	$0.155347\pi$
$480$	9.30583	0.424751
$481$	−50.0806	−2.28348
$482$	14.9812	0.682376
$483$	13.5596	0.616981
$484$	−17.7313	−0.805968
$485$	10.1503	0.460903
$486$	0.899709	0.0408116
$487$	9.29522	0.421207	0.210603	−	0.977572i	$-0.432457\pi$
$487$	9.29522	0.421207	0.210603	+	0.977572i	$0.432457\pi$
$488$	−13.6950	−0.619944
$489$	14.3750	0.650058
$490$	5.88919	0.266046
$491$	11.3475	0.512105	0.256052	−	0.966663i	$-0.417578\pi$
$491$	11.3475	0.512105	0.256052	+	0.966663i	$0.417578\pi$
$492$	1.69752	0.0765302
$493$	−0.226937	−0.0102207
$494$	22.9371	1.03199
$495$	−8.51728	−0.382823
$496$	0.933987	0.0419372
$497$	23.0644	1.03458
$498$	−0.381435	−0.0170925
$499$	24.8745	1.11353	0.556767	−	0.830669i	$-0.312042\pi$
$499$	24.8745	1.11353	0.556767	+	0.830669i	$0.312042\pi$
$500$	14.3442	0.641494
$501$	18.7294	0.836769
$502$	−7.83078	−0.349505
$503$	13.2786	0.592064	0.296032	−	0.955178i	$-0.404337\pi$
$503$	13.2786	0.592064	0.296032	+	0.955178i	$0.404337\pi$
$504$	−5.04542	−0.224741
$505$	16.9332	0.753517
$506$	35.3192	1.57013
$507$	−28.4318	−1.26270
$508$	−8.62270	−0.382570
$509$	33.4053	1.48067	0.740333	−	0.672241i	$-0.234668\pi$
$509$	33.4053	1.48067	0.740333	+	0.672241i	$0.234668\pi$
$510$	−3.37331	−0.149373
$511$	25.4124	1.12418
$512$	2.27826	0.100686
$513$	3.96067	0.174868
$514$	16.0226	0.706727
$515$	4.25001	0.187278
$516$	−4.34968	−0.191484
$517$	39.3731	1.73163
$518$	−12.3037	−0.540596
$519$	11.7428	0.515451
$520$	30.9268	1.35623
$521$	33.4430	1.46516	0.732582	−	0.680678i	$-0.238315\pi$
$521$	33.4430	1.46516	0.732582	+	0.680678i	$0.238315\pi$
$522$	−0.0911499	−0.00398952
$523$	−25.7941	−1.12790	−0.563948	−	0.825810i	$-0.690718\pi$
$523$	−25.7941	−1.12790	−0.563948	+	0.825810i	$0.690718\pi$
$524$	−2.55775	−0.111736
$525$	−3.86401	−0.168639
$526$	−19.1332	−0.834246
$527$	10.3776	0.452055
$528$	−1.02587	−0.0446452
$529$	36.5148	1.58760
$530$	−2.42566	−0.105364
$531$	−2.46261	−0.106868
$532$	−8.28782	−0.359323
$533$	9.17791	0.397540
$534$	15.4233	0.667433
$535$	16.4451	0.710982
$536$	−9.82749	−0.424483
$537$	−24.5193	−1.05808
$538$	15.4648	0.666734
$539$	19.8997	0.857141
$540$	1.99270	0.0857522
$541$	4.49430	0.193225	0.0966126	−	0.995322i	$-0.469199\pi$
$541$	4.49430	0.193225	0.0966126	+	0.995322i	$0.469199\pi$
$542$	−17.1871	−0.738251
$543$	−2.13689	−0.0917025
$544$	12.4538	0.533952
$545$	−25.2929	−1.08343
$546$	−10.1789	−0.435618
$547$	−24.5160	−1.04823	−0.524114	−	0.851648i	$-0.675603\pi$
$547$	−24.5160	−1.04823	−0.524114	+	0.851648i	$0.675603\pi$
$548$	−7.78450	−0.332537
$549$	−4.77088	−0.203616
$550$	−10.0648	−0.429163
$551$	−0.401258	−0.0170942
$552$	−22.1450	−0.942556
$553$	22.9627	0.976472
$554$	−17.3928	−0.738947
$555$	13.0229	0.552790
$556$	−11.6456	−0.493884
$557$	25.5502	1.08260	0.541299	−	0.840830i	$-0.317933\pi$
$557$	25.5502	1.08260	0.541299	+	0.840830i	$0.317933\pi$
$558$	4.16819	0.176454
$559$	−23.5172	−0.994672
$560$	0.593105	0.0250633
$561$	−11.3985	−0.481245
$562$	3.64911	0.153929
$563$	−13.4776	−0.568011	−0.284006	−	0.958823i	$-0.591663\pi$
$563$	−13.4776	−0.568011	−0.284006	+	0.958823i	$0.591663\pi$
$564$	−9.21173	−0.387884
$565$	4.33374	0.182322
$566$	9.71749	0.408456
$567$	−1.75765	−0.0738145
$568$	−37.6681	−1.58052
$569$	−6.39428	−0.268062	−0.134031	−	0.990977i	$-0.542792\pi$
$569$	−6.39428	−0.268062	−0.134031	+	0.990977i	$0.542792\pi$
$570$	−5.96451	−0.249826
$571$	−17.9506	−0.751210	−0.375605	−	0.926780i	$-0.622565\pi$
$571$	−17.9506	−0.751210	−0.375605	+	0.926780i	$0.622565\pi$
$572$	38.9944	1.63044
$573$	−11.6936	−0.488506
$574$	2.25482	0.0941144
$575$	−16.9597	−0.707267
$576$	5.40531	0.225221
$577$	−37.1291	−1.54571	−0.772853	−	0.634585i	$-0.781171\pi$
$577$	−37.1291	−1.54571	−0.772853	+	0.634585i	$0.781171\pi$
$578$	10.7806	0.448415
$579$	−2.15548	−0.0895787
$580$	−0.201882	−0.00838268
$581$	0.745165	0.0309146
$582$	5.45605	0.226160
$583$	−8.19636	−0.339459
$584$	−41.5027	−1.71740
$585$	10.7738	0.445444
$586$	−4.51302	−0.186431
$587$	−36.6232	−1.51160	−0.755800	−	0.654803i	$-0.772752\pi$
$587$	−36.6232	−1.51160	−0.755800	+	0.654803i	$0.772752\pi$
$588$	−4.65573	−0.191999
$589$	18.3491	0.756062
$590$	3.70852	0.152677
$591$	−6.46675	−0.266006
$592$	1.56855	0.0644669
$593$	38.1568	1.56691	0.783456	−	0.621447i	$-0.213455\pi$
$593$	38.1568	1.56691	0.783456	+	0.621447i	$0.213455\pi$
$594$	−4.57824	−0.187848
$595$	6.59003	0.270165
$596$	14.3886	0.589381
$597$	−21.8975	−0.896207
$598$	−44.6767	−1.82697
$599$	48.4161	1.97823	0.989115	−	0.147148i	$-0.0470092\pi$
$599$	48.4161	1.97823	0.989115	+	0.147148i	$0.0470092\pi$
$600$	6.31057	0.257628
$601$	22.2469	0.907472	0.453736	−	0.891136i	$-0.350091\pi$
$601$	22.2469	0.907472	0.453736	+	0.891136i	$0.350091\pi$
$602$	−5.77768	−0.235481
$603$	−3.42357	−0.139418
$604$	−15.1105	−0.614837
$605$	24.9291	1.01351
$606$	9.10200	0.369744
$607$	40.3888	1.63933	0.819665	−	0.572842i	$-0.194159\pi$
$607$	40.3888	1.63933	0.819665	+	0.572842i	$0.194159\pi$
$608$	22.0202	0.893035
$609$	0.178069	0.00721571
$610$	7.18463	0.290897
$611$	−49.8046	−2.01488
$612$	2.66679	0.107799
$613$	−16.3156	−0.658979	−0.329490	−	0.944159i	$-0.606877\pi$
$613$	−16.3156	−0.658979	−0.329490	+	0.944159i	$0.606877\pi$
$614$	8.73249	0.352415
$615$	−2.38661	−0.0962373
$616$	25.6740	1.03444
$617$	5.46752	0.220114	0.110057	−	0.993925i	$-0.464897\pi$
$617$	5.46752	0.220114	0.110057	+	0.993925i	$0.464897\pi$
$618$	2.28449	0.0918955
$619$	43.6271	1.75352	0.876761	−	0.480926i	$-0.159700\pi$
$619$	43.6271	1.75352	0.876761	+	0.480926i	$0.159700\pi$
$620$	9.23184	0.370760
$621$	−7.71459	−0.309576
$622$	9.30397	0.373055
$623$	−30.1307	−1.20716
$624$	1.29766	0.0519481
$625$	−9.17513	−0.367005
$626$	21.5019	0.859389
$627$	−20.1542	−0.804882
$628$	24.2065	0.965943
$629$	17.4282	0.694908
$630$	2.64691	0.105455
$631$	25.7573	1.02538	0.512692	−	0.858573i	$-0.328648\pi$
$631$	25.7573	1.02538	0.512692	+	0.858573i	$0.328648\pi$
$632$	−37.5019	−1.49175
$633$	−11.2465	−0.447010
$634$	1.33714	0.0531046
$635$	12.1230	0.481085
$636$	1.91762	0.0760386
$637$	−25.1719	−0.997349
$638$	0.463824	0.0183630
$639$	−13.1223	−0.519110
$640$	10.4716	0.413927
$641$	2.85693	0.112842	0.0564210	−	0.998407i	$-0.482031\pi$
$641$	2.85693	0.112842	0.0564210	+	0.998407i	$0.482031\pi$
$642$	8.83961	0.348872
$643$	10.7053	0.422176	0.211088	−	0.977467i	$-0.432299\pi$
$643$	10.7053	0.422176	0.211088	+	0.977467i	$0.432299\pi$
$644$	16.1430	0.636123
$645$	6.11537	0.240792
$646$	−7.98217	−0.314054
$647$	10.9862	0.431913	0.215956	−	0.976403i	$-0.430713\pi$
$647$	10.9862	0.431913	0.215956	+	0.976403i	$0.430713\pi$
$648$	2.87054	0.112766
$649$	12.5312	0.491892
$650$	12.7313	0.499363
$651$	−8.14290	−0.319145
$652$	17.1137	0.670226
$653$	−41.1768	−1.61137	−0.805687	−	0.592342i	$-0.798203\pi$
$653$	−41.1768	−1.61137	−0.805687	+	0.592342i	$0.798203\pi$
$654$	−13.5955	−0.531628
$655$	3.59603	0.140509
$656$	−0.287456	−0.0112233
$657$	−14.4582	−0.564066
$658$	−12.2359	−0.477007
$659$	1.39962	0.0545216	0.0272608	−	0.999628i	$-0.491322\pi$
$659$	1.39962	0.0545216	0.0272608	+	0.999628i	$0.491322\pi$
$660$	−10.1400	−0.394700
$661$	26.9112	1.04673	0.523363	−	0.852110i	$-0.324677\pi$
$661$	26.9112	1.04673	0.523363	+	0.852110i	$0.324677\pi$
$662$	15.8383	0.615573
$663$	14.4184	0.559964
$664$	−1.21698	−0.0472280
$665$	11.6521	0.451851
$666$	7.00010	0.271248
$667$	0.781569	0.0302625
$668$	22.2978	0.862729
$669$	19.8849	0.768797
$670$	5.15566	0.199181
$671$	24.2770	0.937204
$672$	−9.77202	−0.376964
$673$	35.4943	1.36821	0.684103	−	0.729386i	$-0.260194\pi$
$673$	35.4943	1.36821	0.684103	+	0.729386i	$0.260194\pi$
$674$	−17.0310	−0.656009
$675$	2.19839	0.0846161
$676$	−33.8487	−1.30187
$677$	7.66192	0.294471	0.147236	−	0.989101i	$-0.452962\pi$
$677$	7.66192	0.294471	0.147236	+	0.989101i	$0.452962\pi$
$678$	2.32949	0.0894635
$679$	−10.6588	−0.409048
$680$	−10.7626	−0.412728
$681$	6.20415	0.237744
$682$	−21.2102	−0.812180
$683$	−11.5533	−0.442074	−0.221037	−	0.975265i	$-0.570944\pi$
$683$	−11.5533	−0.442074	−0.221037	+	0.975265i	$0.570944\pi$
$684$	4.71528	0.180293
$685$	10.9445	0.418168
$686$	−17.2538	−0.658755
$687$	6.29386	0.240126
$688$	0.736569	0.0280814
$689$	10.3679	0.394986
$690$	11.6177	0.442276
$691$	9.48943	0.360995	0.180498	−	0.983575i	$-0.442229\pi$
$691$	9.48943	0.360995	0.180498	+	0.983575i	$0.442229\pi$
$692$	13.9801	0.531442
$693$	8.94396	0.339753
$694$	1.46722	0.0556949
$695$	16.3730	0.621063
$696$	−0.290816	−0.0110234
$697$	−3.19395	−0.120979
$698$	−7.19959	−0.272508
$699$	1.37434	0.0519824
$700$	−4.60019	−0.173871
$701$	−33.6461	−1.27079	−0.635397	−	0.772186i	$-0.719164\pi$
$701$	−33.6461	−1.27079	−0.635397	+	0.772186i	$0.719164\pi$
$702$	5.79120	0.218575
$703$	30.8157	1.16223
$704$	−27.5054	−1.03665
$705$	12.9511	0.487766
$706$	−8.63831	−0.325107
$707$	−17.7815	−0.668742
$708$	−2.93179	−0.110183
$709$	−27.7519	−1.04224	−0.521122	−	0.853482i	$-0.674486\pi$
$709$	−27.7519	−1.04224	−0.521122	+	0.853482i	$0.674486\pi$
$710$	19.7613	0.741629
$711$	−13.0644	−0.489953
$712$	49.2085	1.84417
$713$	−35.7403	−1.33849
$714$	3.54230	0.132567
$715$	−54.8236	−2.05029
$716$	−29.1908	−1.09091
$717$	1.00000	0.0373457
$718$	28.2812	1.05545
$719$	−28.9767	−1.08065	−0.540324	−	0.841457i	$-0.681698\pi$
$719$	−28.9767	−1.08065	−0.540324	+	0.841457i	$0.681698\pi$
$720$	−0.337442	−0.0125757
$721$	−4.46292	−0.166208
$722$	2.98080	0.110934
$723$	16.6512	0.619265
$724$	−2.54402	−0.0945476
$725$	−0.222720	−0.00827161
$726$	13.4000	0.497320
$727$	−17.6229	−0.653599	−0.326799	−	0.945094i	$-0.605970\pi$
$727$	−17.6229	−0.653599	−0.326799	+	0.945094i	$0.605970\pi$
$728$	−32.4761	−1.20364
$729$	1.00000	0.0370370
$730$	21.7730	0.805855
$731$	8.18407	0.302699
$732$	−5.67985	−0.209933
$733$	10.2978	0.380359	0.190180	−	0.981749i	$-0.439093\pi$
$733$	10.2978	0.380359	0.190180	+	0.981749i	$0.439093\pi$
$734$	8.78785	0.324366
$735$	6.54566	0.241440
$736$	−42.8908	−1.58098
$737$	17.4211	0.641714
$738$	−1.28286	−0.0472227
$739$	13.2229	0.486411	0.243206	−	0.969975i	$-0.421801\pi$
$739$	13.2229	0.486411	0.243206	+	0.969975i	$0.421801\pi$
$740$	15.5040	0.569940
$741$	25.4939	0.936541
$742$	2.54718	0.0935098
$743$	7.80394	0.286299	0.143149	−	0.989701i	$-0.454277\pi$
$743$	7.80394	0.286299	0.143149	+	0.989701i	$0.454277\pi$
$744$	13.2987	0.487555
$745$	−20.2295	−0.741151
$746$	−16.6335	−0.608994
$747$	−0.423954	−0.0155117
$748$	−13.5702	−0.496175
$749$	−17.2689	−0.630991
$750$	−10.8403	−0.395832
$751$	50.3886	1.83871	0.919353	−	0.393435i	$-0.128713\pi$
$751$	50.3886	1.83871	0.919353	+	0.393435i	$0.128713\pi$
$752$	1.55990	0.0568838
$753$	−8.70369	−0.317180
$754$	−0.586710	−0.0213667
$755$	21.2444	0.773162
$756$	−2.09253	−0.0761045
$757$	−46.6796	−1.69660	−0.848299	−	0.529517i	$-0.822373\pi$
$757$	−46.6796	−1.69660	−0.848299	+	0.529517i	$0.822373\pi$
$758$	1.62511	0.0590265
$759$	39.2563	1.42491
$760$	−19.0299	−0.690287
$761$	24.2370	0.878591	0.439296	−	0.898343i	$-0.355228\pi$
$761$	24.2370	0.878591	0.439296	+	0.898343i	$0.355228\pi$
$762$	6.51638	0.236064
$763$	26.5600	0.961536
$764$	−13.9215	−0.503662
$765$	−3.74933	−0.135557
$766$	22.6886	0.819771
$767$	−15.8512	−0.572353
$768$	16.4394	0.593205
$769$	23.9656	0.864222	0.432111	−	0.901820i	$-0.357769\pi$
$769$	23.9656	0.864222	0.432111	+	0.901820i	$0.357769\pi$
$770$	−13.4690	−0.485389
$771$	17.8087	0.641363
$772$	−2.56615	−0.0923578
$773$	1.40235	0.0504391	0.0252195	−	0.999682i	$-0.491972\pi$
$773$	1.40235	0.0504391	0.0252195	+	0.999682i	$0.491972\pi$
$774$	3.28716	0.118154
$775$	10.1848	0.365847
$776$	17.4076	0.624898
$777$	−13.6753	−0.490597
$778$	−26.2444	−0.940906
$779$	−5.64737	−0.202338
$780$	12.8265	0.459263
$781$	66.7739	2.38936
$782$	15.5477	0.555983
$783$	−0.101311	−0.00362054
$784$	0.788396	0.0281570
$785$	−34.0327	−1.21468
$786$	1.93295	0.0689462
$787$	−22.5141	−0.802540	−0.401270	−	0.915960i	$-0.631431\pi$
$787$	−22.5141	−0.802540	−0.401270	+	0.915960i	$0.631431\pi$
$788$	−7.69882	−0.274259
$789$	−21.2660	−0.757089
$790$	19.6741	0.699974
$791$	−4.55085	−0.161809
$792$	−14.6070	−0.519037
$793$	−30.7090	−1.09051
$794$	−33.6007	−1.19245
$795$	−2.69605	−0.0956191
$796$	−26.0696	−0.924011
$797$	−35.7937	−1.26788	−0.633939	−	0.773383i	$-0.718563\pi$
$797$	−35.7937	−1.26788	−0.633939	+	0.773383i	$0.718563\pi$
$798$	6.26331	0.221719
$799$	17.3322	0.613168
$800$	12.2224	0.432127
$801$	17.1426	0.605704
$802$	−4.95664	−0.175025
$803$	73.5715	2.59628
$804$	−4.07584	−0.143744
$805$	−22.6960	−0.799929
$806$	26.8296	0.945033
$807$	17.1887	0.605069
$808$	29.0402	1.02163
$809$	−22.3480	−0.785712	−0.392856	−	0.919600i	$-0.628513\pi$
$809$	−22.3480	−0.785712	−0.392856	+	0.919600i	$0.628513\pi$
$810$	−1.50593	−0.0529131
$811$	12.5070	0.439182	0.219591	−	0.975592i	$-0.429528\pi$
$811$	12.5070	0.439182	0.219591	+	0.975592i	$0.429528\pi$
$812$	0.211995	0.00743957
$813$	−19.1030	−0.669972
$814$	−35.6206	−1.24850
$815$	−24.0608	−0.842813
$816$	−0.451591	−0.0158088
$817$	14.4706	0.506264
$818$	25.4368	0.889377
$819$	−11.3136	−0.395328
$820$	−2.84131	−0.0992230
$821$	−38.7711	−1.35312	−0.676560	−	0.736387i	$-0.736530\pi$
$821$	−38.7711	−1.35312	−0.676560	+	0.736387i	$0.736530\pi$
$822$	5.88294	0.205191
$823$	51.3284	1.78920	0.894598	−	0.446872i	$-0.147462\pi$
$823$	51.3284	1.78920	0.894598	+	0.446872i	$0.147462\pi$
$824$	7.28871	0.253914
$825$	−11.1867	−0.389471
$826$	−3.89430	−0.135500
$827$	−15.0423	−0.523072	−0.261536	−	0.965194i	$-0.584229\pi$
$827$	−15.0423	−0.523072	−0.261536	+	0.965194i	$0.584229\pi$
$828$	−9.18440	−0.319180
$829$	−24.9052	−0.864992	−0.432496	−	0.901636i	$-0.642367\pi$
$829$	−24.9052	−0.864992	−0.432496	+	0.901636i	$0.642367\pi$
$830$	0.638447	0.0221608
$831$	−19.3315	−0.670604
$832$	34.7927	1.20622
$833$	8.75992	0.303513
$834$	8.80087	0.304749
$835$	−31.3493	−1.08489
$836$	−23.9941	−0.829853
$837$	4.63283	0.160134
$838$	−10.8286	−0.374069
$839$	14.5488	0.502279	0.251139	−	0.967951i	$-0.419195\pi$
$839$	14.5488	0.502279	0.251139	+	0.967951i	$0.419195\pi$
$840$	8.44502	0.291381
$841$	−28.9897	−0.999646
$842$	26.9898	0.930129
$843$	4.05588	0.139692
$844$	−13.3893	−0.460878
$845$	47.5892	1.63712
$846$	6.96153	0.239342
$847$	−26.1779	−0.899484
$848$	−0.324727	−0.0111512
$849$	10.8007	0.370679
$850$	−4.43054	−0.151966
$851$	−60.0226	−2.05755
$852$	−15.6224	−0.535215
$853$	−33.7550	−1.15575	−0.577875	−	0.816125i	$-0.696118\pi$
$853$	−33.7550	−1.15575	−0.577875	+	0.816125i	$0.696118\pi$
$854$	−7.54455	−0.258169
$855$	−6.62938	−0.226720
$856$	28.2030	0.963959
$857$	47.0497	1.60719	0.803593	−	0.595179i	$-0.202919\pi$
$857$	47.0497	1.60719	0.803593	+	0.595179i	$0.202919\pi$
$858$	−29.4690	−1.00606
$859$	−47.7888	−1.63053	−0.815267	−	0.579085i	$-0.803410\pi$
$859$	−47.7888	−1.63053	−0.815267	+	0.579085i	$0.803410\pi$
$860$	7.28050	0.248263
$861$	2.50617	0.0854100
$862$	16.0237	0.545768
$863$	30.8008	1.04847	0.524236	−	0.851573i	$-0.324351\pi$
$863$	30.8008	1.04847	0.524236	+	0.851573i	$0.324351\pi$
$864$	5.55970	0.189145
$865$	−19.6551	−0.668292
$866$	−18.2180	−0.619072
$867$	11.9823	0.406942
$868$	−9.69432	−0.329047
$869$	66.4793	2.25516
$870$	0.152567	0.00517250
$871$	−22.0366	−0.746683
$872$	−43.3769	−1.46893
$873$	6.06424	0.205243
$874$	27.4906	0.929882
$875$	21.1774	0.715926
$876$	−17.2128	−0.581566
$877$	−43.0660	−1.45424	−0.727118	−	0.686512i	$-0.759141\pi$
$877$	−43.0660	−1.45424	−0.727118	+	0.686512i	$0.759141\pi$
$878$	31.2746	1.05547
$879$	−5.01609	−0.169189
$880$	1.71710	0.0578834
$881$	30.2543	1.01929	0.509647	−	0.860384i	$-0.329776\pi$
$881$	30.2543	1.01929	0.509647	+	0.860384i	$0.329776\pi$
$882$	3.51845	0.118472
$883$	33.4773	1.12660	0.563300	−	0.826252i	$-0.309531\pi$
$883$	33.4773	1.12660	0.563300	+	0.826252i	$0.309531\pi$
$884$	17.1655	0.577337
$885$	4.12191	0.138557
$886$	23.1760	0.778613
$887$	−34.7429	−1.16655	−0.583277	−	0.812274i	$-0.698230\pi$
$887$	−34.7429	−1.16655	−0.583277	+	0.812274i	$0.698230\pi$
$888$	22.3340	0.749480
$889$	−12.7303	−0.426960
$890$	−25.8156	−0.865341
$891$	−5.08858	−0.170474
$892$	23.6735	0.792648
$893$	30.6458	1.02552
$894$	−10.8738	−0.363676
$895$	41.0404	1.37183
$896$	−10.9962	−0.367358
$897$	−49.6569	−1.65800
$898$	27.1822	0.907081
$899$	−0.469354	−0.0156538
$900$	2.61724	0.0872412
$901$	−3.60807	−0.120202
$902$	6.52794	0.217356
$903$	−6.42173	−0.213702
$904$	7.43230	0.247194
$905$	3.57672	0.118894
$906$	11.4194	0.379383
$907$	−18.9277	−0.628484	−0.314242	−	0.949343i	$-0.601750\pi$
$907$	−18.9277	−0.628484	−0.314242	+	0.949343i	$0.601750\pi$
$908$	7.38620	0.245120
$909$	10.1166	0.335547
$910$	17.0375	0.564787
$911$	−53.6024	−1.77593	−0.887964	−	0.459914i	$-0.847880\pi$
$911$	−53.6024	−1.77593	−0.887964	+	0.459914i	$0.847880\pi$
$912$	−0.798480	−0.0264403
$913$	2.15733	0.0713971
$914$	−1.20181	−0.0397524
$915$	7.98550	0.263993
$916$	7.49300	0.247576
$917$	−3.77618	−0.124701
$918$	−2.01536	−0.0665167
$919$	−38.1249	−1.25762	−0.628812	−	0.777558i	$-0.716458\pi$
$919$	−38.1249	−1.25762	−0.628812	+	0.777558i	$0.716458\pi$
$920$	37.0664	1.22204
$921$	9.70591	0.319821
$922$	−14.9571	−0.492584
$923$	−84.4650	−2.78020
$924$	10.6480	0.350294
$925$	17.1044	0.562388
$926$	−26.4736	−0.869976
$927$	2.53914	0.0833963
$928$	−0.563256	−0.0184898
$929$	23.1631	0.759957	0.379978	−	0.924995i	$-0.375931\pi$
$929$	23.1631	0.759957	0.379978	+	0.924995i	$0.375931\pi$
$930$	−6.97673	−0.228776
$931$	15.4888	0.507626
$932$	1.63619	0.0535952
$933$	10.3411	0.338552
$934$	2.28220	0.0746758
$935$	19.0788	0.623944
$936$	18.4770	0.603939
$937$	3.99000	0.130348	0.0651738	−	0.997874i	$-0.479240\pi$
$937$	3.99000	0.130348	0.0651738	+	0.997874i	$0.479240\pi$
$938$	−5.41394	−0.176771
$939$	23.8987	0.779906
$940$	15.4186	0.502899
$941$	15.0860	0.491790	0.245895	−	0.969296i	$-0.420918\pi$
$941$	15.0860	0.491790	0.245895	+	0.969296i	$0.420918\pi$
$942$	−18.2934	−0.596031
$943$	10.9999	0.358207
$944$	0.496466	0.0161586
$945$	2.94196	0.0957020
$946$	−16.7270	−0.543841
$947$	−55.4188	−1.80087	−0.900435	−	0.434991i	$-0.856752\pi$
$947$	−55.4188	−1.80087	−0.900435	+	0.434991i	$0.856752\pi$
$948$	−15.5535	−0.505154
$949$	−93.0636	−3.02097
$950$	−7.83385	−0.254164
$951$	1.48619	0.0481931
$952$	11.3018	0.366293
$953$	−46.8160	−1.51652	−0.758259	−	0.651953i	$-0.773950\pi$
$953$	−46.8160	−1.51652	−0.758259	+	0.651953i	$0.773950\pi$
$954$	−1.44919	−0.0469193
$955$	19.5727	0.633359
$956$	1.19052	0.0385043
$957$	0.515527	0.0166646
$958$	−34.7845	−1.12384
$959$	−11.4928	−0.371122
$960$	−9.04742	−0.292004
$961$	−9.53693	−0.307643
$962$	45.0579	1.45273
$963$	9.82497	0.316605
$964$	19.8237	0.638477
$965$	3.60784	0.116141
$966$	−12.1997	−0.392517
$967$	−32.6031	−1.04844	−0.524222	−	0.851582i	$-0.675644\pi$
$967$	−32.6031	−1.04844	−0.524222	+	0.851582i	$0.675644\pi$
$968$	42.7530	1.37413
$969$	−8.87196	−0.285008
$970$	−9.13233	−0.293222
$971$	−22.8194	−0.732310	−0.366155	−	0.930554i	$-0.619326\pi$
$971$	−22.8194	−0.732310	−0.366155	+	0.930554i	$0.619326\pi$
$972$	1.19052	0.0381861
$973$	−17.1932	−0.551189
$974$	−8.36299	−0.267967
$975$	14.1505	0.453178
$976$	0.961819	0.0307871
$977$	−13.1827	−0.421751	−0.210875	−	0.977513i	$-0.567631\pi$
$977$	−13.1827	−0.421751	−0.210875	+	0.977513i	$0.567631\pi$
$978$	−12.9333	−0.413560
$979$	−87.2315	−2.78793
$980$	7.79277	0.248931
$981$	−15.1110	−0.482459
$982$	−10.2094	−0.325796
$983$	−26.5649	−0.847290	−0.423645	−	0.905828i	$-0.639250\pi$
$983$	−26.5649	−0.847290	−0.423645	+	0.905828i	$0.639250\pi$
$984$	−4.09299	−0.130480
$985$	10.8240	0.344883
$986$	0.204177	0.00650232
$987$	−13.5999	−0.432890
$988$	30.3511	0.965597
$989$	−28.1859	−0.896259
$990$	7.66307	0.243548
$991$	29.8250	0.947423	0.473711	−	0.880680i	$-0.342914\pi$
$991$	29.8250	0.947423	0.473711	+	0.880680i	$0.342914\pi$
$992$	25.7571	0.817790
$993$	17.6038	0.558640
$994$	−20.7513	−0.658191
$995$	36.6521	1.16195
$996$	−0.504728	−0.0159929
$997$	21.3442	0.675976	0.337988	−	0.941150i	$-0.390254\pi$
$997$	21.3442	0.675976	0.337988	+	0.941150i	$0.390254\pi$
$998$	−22.3798	−0.708419
$999$	7.78041	0.246161

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	717.2.a.d.1.3	✓	6
3.2	odd	2		2151.2.a.e.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
717.2.a.d.1.3	✓	6	1.1	even	1	trivial
2151.2.a.e.1.4		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 717 = 3 \cdot 239 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	717.a (trivial)

\(f(q)\)	\(=\)	\(q-0.899709 q^{2} -1.00000 q^{3} -1.19052 q^{4} +1.67380 q^{5} +0.899709 q^{6} -1.75765 q^{7} +2.87054 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.899709 q^{2} -1.00000 q^{3} -1.19052 q^{4} +1.67380 q^{5} +0.899709 q^{6} -1.75765 q^{7} +2.87054 q^{8} +1.00000 q^{9} -1.50593 q^{10} -5.08858 q^{11} +1.19052 q^{12} +6.43675 q^{13} +1.58137 q^{14} -1.67380 q^{15} -0.201602 q^{16} -2.24001 q^{17} -0.899709 q^{18} -3.96067 q^{19} -1.99270 q^{20} +1.75765 q^{21} +4.57824 q^{22} +7.71459 q^{23} -2.87054 q^{24} -2.19839 q^{25} -5.79120 q^{26} -1.00000 q^{27} +2.09253 q^{28} +0.101311 q^{29} +1.50593 q^{30} -4.63283 q^{31} -5.55970 q^{32} +5.08858 q^{33} +2.01536 q^{34} -2.94196 q^{35} -1.19052 q^{36} -7.78041 q^{37} +3.56345 q^{38} -6.43675 q^{39} +4.80472 q^{40} +1.42586 q^{41} -1.58137 q^{42} -3.65358 q^{43} +6.05808 q^{44} +1.67380 q^{45} -6.94088 q^{46} -7.73754 q^{47} +0.201602 q^{48} -3.91066 q^{49} +1.97791 q^{50} +2.24001 q^{51} -7.66311 q^{52} +1.61074 q^{53} +0.899709 q^{54} -8.51728 q^{55} -5.04542 q^{56} +3.96067 q^{57} -0.0911499 q^{58} -2.46261 q^{59} +1.99270 q^{60} -4.77088 q^{61} +4.16819 q^{62} -1.75765 q^{63} +5.40531 q^{64} +10.7738 q^{65} -4.57824 q^{66} -3.42357 q^{67} +2.66679 q^{68} -7.71459 q^{69} +2.64691 q^{70} -13.1223 q^{71} +2.87054 q^{72} -14.4582 q^{73} +7.00010 q^{74} +2.19839 q^{75} +4.71528 q^{76} +8.94396 q^{77} +5.79120 q^{78} -13.0644 q^{79} -0.337442 q^{80} +1.00000 q^{81} -1.28286 q^{82} -0.423954 q^{83} -2.09253 q^{84} -3.74933 q^{85} +3.28716 q^{86} -0.101311 q^{87} -14.6070 q^{88} +17.1426 q^{89} -1.50593 q^{90} -11.3136 q^{91} -9.18440 q^{92} +4.63283 q^{93} +6.96153 q^{94} -6.62938 q^{95} +5.55970 q^{96} +6.06424 q^{97} +3.51845 q^{98} -5.08858 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9	\( 6 q - 2 q^{2} - 6 q^{3} + 4 q^{4} + 5 q^{5} + 2 q^{6} - 9 q^{7} - 3 q^{8} + 6 q^{9} - 11 q^{10} - 13 q^{11} - 4 q^{12} - q^{13} - 5 q^{15} - 4 q^{16} + 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} + 9 q^{21} - 2 q^{22} - 12 q^{23} + 3 q^{24} - q^{25} + 12 q^{26} - 6 q^{27} - 16 q^{28} + 11 q^{30} - 18 q^{31} + 7 q^{32} + 13 q^{33} - 3 q^{34} - 9 q^{35} + 4 q^{36} - 8 q^{37} - 5 q^{38} + q^{39} - 11 q^{40} + 10 q^{41} - 14 q^{43} - 4 q^{44} + 5 q^{45} - 18 q^{46} - 9 q^{47} + 4 q^{48} + 5 q^{49} + 4 q^{50} - 11 q^{51} - 16 q^{52} - 8 q^{53} + 2 q^{54} - 20 q^{55} + 11 q^{56} + 22 q^{57} - 15 q^{58} - 10 q^{59} + q^{60} - 12 q^{61} - 13 q^{62} - 9 q^{63} - 31 q^{64} - 11 q^{65} + 2 q^{66} - 36 q^{67} + 22 q^{68} + 12 q^{69} + q^{70} - 3 q^{71} - 3 q^{72} - 32 q^{73} + 9 q^{74} + q^{75} - 4 q^{76} + 6 q^{77} - 12 q^{78} - q^{79} - 7 q^{80} + 6 q^{81} + 7 q^{82} - 7 q^{83} + 16 q^{84} - 14 q^{85} + 45 q^{86} - 15 q^{88} + 17 q^{89} - 11 q^{90} - 23 q^{91} - 12 q^{92} + 18 q^{93} + 50 q^{94} - 7 q^{96} - 28 q^{97} + 13 q^{98} - 13 q^{99}+O(q^{100}) \) 6 * q - 2 * q^2 - 6 * q^3 + 4 * q^4 + 5 * q^5 + 2 * q^6 - 9 * q^7 - 3 * q^8 + 6 * q^9 - 11 * q^10 - 13 * q^11 - 4 * q^12 - q^13 - 5 * q^15 - 4 * q^16 + 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 + 9 * q^21 - 2 * q^22 - 12 * q^23 + 3 * q^24 - q^25 + 12 * q^26 - 6 * q^27 - 16 * q^28 + 11 * q^30 - 18 * q^31 + 7 * q^32 + 13 * q^33 - 3 * q^34 - 9 * q^35 + 4 * q^36 - 8 * q^37 - 5 * q^38 + q^39 - 11 * q^40 + 10 * q^41 - 14 * q^43 - 4 * q^44 + 5 * q^45 - 18 * q^46 - 9 * q^47 + 4 * q^48 + 5 * q^49 + 4 * q^50 - 11 * q^51 - 16 * q^52 - 8 * q^53 + 2 * q^54 - 20 * q^55 + 11 * q^56 + 22 * q^57 - 15 * q^58 - 10 * q^59 + q^60 - 12 * q^61 - 13 * q^62 - 9 * q^63 - 31 * q^64 - 11 * q^65 + 2 * q^66 - 36 * q^67 + 22 * q^68 + 12 * q^69 + q^70 - 3 * q^71 - 3 * q^72 - 32 * q^73 + 9 * q^74 + q^75 - 4 * q^76 + 6 * q^77 - 12 * q^78 - q^79 - 7 * q^80 + 6 * q^81 + 7 * q^82 - 7 * q^83 + 16 * q^84 - 14 * q^85 + 45 * q^86 - 15 * q^88 + 17 * q^89 - 11 * q^90 - 23 * q^91 - 12 * q^92 + 18 * q^93 + 50 * q^94 - 7 * q^96 - 28 * q^97 + 13 * q^98 - 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more