LMFDB - Embedded newform 6006.2.a.cf.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6006,2,Mod(1,6006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6006, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 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("6006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6006.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:	$47.9581514540$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.72306708.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - x^{3} + 10x^{2} - 2 $ x^6 - 11x^4 - x^3 + 10x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-3.10887$ of defining polynomial
Character	$\chi$	$=$	6006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.643320 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.643320 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.643320 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +0.643320 q^{15} +1.00000 q^{16} -6.21775 q^{17} +1.00000 q^{18} +8.07709 q^{19} -0.643320 q^{20} -1.00000 q^{21} +1.00000 q^{22} -0.333033 q^{23} -1.00000 q^{24} -4.58614 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.72680 q^{29} +0.643320 q^{30} -9.45914 q^{31} +1.00000 q^{32} -1.00000 q^{33} -6.21775 q^{34} -0.643320 q^{35} +1.00000 q^{36} +7.57443 q^{37} +8.07709 q^{38} +1.00000 q^{39} -0.643320 q^{40} +10.4101 q^{41} -1.00000 q^{42} +7.68155 q^{43} +1.00000 q^{44} -0.643320 q^{45} -0.333033 q^{46} -11.3302 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.58614 q^{50} +6.21775 q^{51} -1.00000 q^{52} +10.2350 q^{53} -1.00000 q^{54} -0.643320 q^{55} +1.00000 q^{56} -8.07709 q^{57} +5.72680 q^{58} +9.90746 q^{59} +0.643320 q^{60} -2.98191 q^{61} -9.45914 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.643320 q^{65} -1.00000 q^{66} -4.75394 q^{67} -6.21775 q^{68} +0.333033 q^{69} -0.643320 q^{70} +11.1941 q^{71} +1.00000 q^{72} -2.17511 q^{73} +7.57443 q^{74} +4.58614 q^{75} +8.07709 q^{76} +1.00000 q^{77} +1.00000 q^{78} -15.2149 q^{79} -0.643320 q^{80} +1.00000 q^{81} +10.4101 q^{82} +10.6407 q^{83} -1.00000 q^{84} +4.00000 q^{85} +7.68155 q^{86} -5.72680 q^{87} +1.00000 q^{88} -15.9049 q^{89} -0.643320 q^{90} -1.00000 q^{91} -0.333033 q^{92} +9.45914 q^{93} -11.3302 q^{94} -5.19615 q^{95} -1.00000 q^{96} +4.52804 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{11} - 6 q^{12} - 6 q^{13} + 6 q^{14} + 6 q^{16} + 6 q^{18} + 2 q^{19} - 6 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 6 q^{26} - 6 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{31} + 6 q^{32} - 6 q^{33} + 6 q^{36} + 12 q^{37} + 2 q^{38} + 6 q^{39} + 4 q^{41} - 6 q^{42} + 4 q^{43} + 6 q^{44} + 10 q^{46} + 4 q^{47} - 6 q^{48} + 6 q^{49} + 10 q^{50} - 6 q^{52} + 18 q^{53} - 6 q^{54} + 6 q^{56} - 2 q^{57} + 6 q^{58} + 14 q^{59} + 2 q^{62} + 6 q^{63} + 6 q^{64} - 6 q^{66} + 4 q^{67} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 2 q^{73} + 12 q^{74} - 10 q^{75} + 2 q^{76} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{81} + 4 q^{82} + 24 q^{83} - 6 q^{84} + 24 q^{85} + 4 q^{86} - 6 q^{87} + 6 q^{88} - 14 q^{89} - 6 q^{91} + 10 q^{92} - 2 q^{93} + 4 q^{94} + 4 q^{95} - 6 q^{96} - 2 q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^11 - 6 * q^12 - 6 * q^13 + 6 * q^14 + 6 * q^16 + 6 * q^18 + 2 * q^19 - 6 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 6 * q^26 - 6 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^31 + 6 * q^32 - 6 * q^33 + 6 * q^36 + 12 * q^37 + 2 * q^38 + 6 * q^39 + 4 * q^41 - 6 * q^42 + 4 * q^43 + 6 * q^44 + 10 * q^46 + 4 * q^47 - 6 * q^48 + 6 * q^49 + 10 * q^50 - 6 * q^52 + 18 * q^53 - 6 * q^54 + 6 * q^56 - 2 * q^57 + 6 * q^58 + 14 * q^59 + 2 * q^62 + 6 * q^63 + 6 * q^64 - 6 * q^66 + 4 * q^67 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 2 * q^73 + 12 * q^74 - 10 * q^75 + 2 * q^76 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^81 + 4 * q^82 + 24 * q^83 - 6 * q^84 + 24 * q^85 + 4 * q^86 - 6 * q^87 + 6 * q^88 - 14 * q^89 - 6 * q^91 + 10 * q^92 - 2 * q^93 + 4 * q^94 + 4 * q^95 - 6 * q^96 - 2 * q^97 + 6 * q^98 + 6 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.643320	−0.287701	−0.143851	−	0.989599i	$-0.545948\pi$
$5$	−0.643320	−0.287701	−0.143851	+	0.989599i	$0.545948\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.643320	−0.203436
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	1.00000	0.267261
$15$	0.643320	0.166104
$16$	1.00000	0.250000
$17$	−6.21775	−1.50803	−0.754013	−	0.656860i	$-0.771884\pi$
$17$	−6.21775	−1.50803	−0.754013	+	0.656860i	$0.771884\pi$
$18$	1.00000	0.235702
$19$	8.07709	1.85301	0.926506	−	0.376280i	$-0.122797\pi$
$19$	8.07709	1.85301	0.926506	+	0.376280i	$0.122797\pi$
$20$	−0.643320	−0.143851
$21$	−1.00000	−0.218218
$22$	1.00000	0.213201
$23$	−0.333033	−0.0694422	−0.0347211	−	0.999397i	$-0.511054\pi$
$23$	−0.333033	−0.0694422	−0.0347211	+	0.999397i	$0.511054\pi$
$24$	−1.00000	−0.204124
$25$	−4.58614	−0.917228
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	5.72680	1.06344	0.531720	−	0.846920i	$-0.321546\pi$
$29$	5.72680	1.06344	0.531720	+	0.846920i	$0.321546\pi$
$30$	0.643320	0.117454
$31$	−9.45914	−1.69891	−0.849456	−	0.527659i	$-0.823070\pi$
$31$	−9.45914	−1.69891	−0.849456	+	0.527659i	$0.823070\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	−6.21775	−1.06634
$35$	−0.643320	−0.108741
$36$	1.00000	0.166667
$37$	7.57443	1.24523	0.622614	−	0.782529i	$-0.286071\pi$
$37$	7.57443	1.24523	0.622614	+	0.782529i	$0.286071\pi$
$38$	8.07709	1.31028
$39$	1.00000	0.160128
$40$	−0.643320	−0.101718
$41$	10.4101	1.62579	0.812894	−	0.582411i	$-0.197891\pi$
$41$	10.4101	1.62579	0.812894	+	0.582411i	$0.197891\pi$
$42$	−1.00000	−0.154303
$43$	7.68155	1.17143	0.585713	−	0.810519i	$-0.300815\pi$
$43$	7.68155	1.17143	0.585713	+	0.810519i	$0.300815\pi$
$44$	1.00000	0.150756
$45$	−0.643320	−0.0959004
$46$	−0.333033	−0.0491030
$47$	−11.3302	−1.65268	−0.826340	−	0.563172i	$-0.809581\pi$
$47$	−11.3302	−1.65268	−0.826340	+	0.563172i	$0.809581\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−4.58614	−0.648578
$51$	6.21775	0.870659
$52$	−1.00000	−0.138675
$53$	10.2350	1.40589	0.702944	−	0.711246i	$-0.251869\pi$
$53$	10.2350	1.40589	0.702944	+	0.711246i	$0.251869\pi$
$54$	−1.00000	−0.136083
$55$	−0.643320	−0.0867452
$56$	1.00000	0.133631
$57$	−8.07709	−1.06984
$58$	5.72680	0.751965
$59$	9.90746	1.28984	0.644921	−	0.764249i	$-0.276890\pi$
$59$	9.90746	1.28984	0.644921	+	0.764249i	$0.276890\pi$
$60$	0.643320	0.0830522
$61$	−2.98191	−0.381794	−0.190897	−	0.981610i	$-0.561140\pi$
$61$	−2.98191	−0.381794	−0.190897	+	0.981610i	$0.561140\pi$
$62$	−9.45914	−1.20131
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0.643320	0.0797940
$66$	−1.00000	−0.123091
$67$	−4.75394	−0.580787	−0.290393	−	0.956907i	$-0.593786\pi$
$67$	−4.75394	−0.580787	−0.290393	+	0.956907i	$0.593786\pi$
$68$	−6.21775	−0.754013
$69$	0.333033	0.0400925
$70$	−0.643320	−0.0768914
$71$	11.1941	1.32850	0.664248	−	0.747513i	$-0.268752\pi$
$71$	11.1941	1.32850	0.664248	+	0.747513i	$0.268752\pi$
$72$	1.00000	0.117851
$73$	−2.17511	−0.254578	−0.127289	−	0.991866i	$-0.540628\pi$
$73$	−2.17511	−0.254578	−0.127289	+	0.991866i	$0.540628\pi$
$74$	7.57443	0.880509
$75$	4.58614	0.529562
$76$	8.07709	0.926506
$77$	1.00000	0.113961
$78$	1.00000	0.113228
$79$	−15.2149	−1.71181	−0.855906	−	0.517132i	$-0.827000\pi$
$79$	−15.2149	−1.71181	−0.855906	+	0.517132i	$0.827000\pi$
$80$	−0.643320	−0.0719253
$81$	1.00000	0.111111
$82$	10.4101	1.14961
$83$	10.6407	1.16797	0.583985	−	0.811765i	$-0.301493\pi$
$83$	10.6407	1.16797	0.583985	+	0.811765i	$0.301493\pi$
$84$	−1.00000	−0.109109
$85$	4.00000	0.433861
$86$	7.68155	0.828323
$87$	−5.72680	−0.613977
$88$	1.00000	0.106600
$89$	−15.9049	−1.68591	−0.842956	−	0.537983i	$-0.819186\pi$
$89$	−15.9049	−1.68591	−0.842956	+	0.537983i	$0.819186\pi$
$90$	−0.643320	−0.0678118
$91$	−1.00000	−0.104828
$92$	−0.333033	−0.0347211
$93$	9.45914	0.980868
$94$	−11.3302	−1.16862
$95$	−5.19615	−0.533114
$96$	−1.00000	−0.102062
$97$	4.52804	0.459752	0.229876	−	0.973220i	$-0.426168\pi$
$97$	4.52804	0.459752	0.229876	+	0.973220i	$0.426168\pi$
$98$	1.00000	0.101015
$99$	1.00000	0.100504
$100$	−4.58614	−0.458614
$101$	15.3295	1.52534	0.762672	−	0.646785i	$-0.223887\pi$
$101$	15.3295	1.52534	0.762672	+	0.646785i	$0.223887\pi$
$102$	6.21775	0.615649
$103$	11.3302	1.11640	0.558199	−	0.829707i	$-0.311493\pi$
$103$	11.3302	1.11640	0.558199	+	0.829707i	$0.311493\pi$
$104$	−1.00000	−0.0980581
$105$	0.643320	0.0627816
$106$	10.2350	0.994112
$107$	−1.83392	−0.177292	−0.0886458	−	0.996063i	$-0.528254\pi$
$107$	−1.83392	−0.177292	−0.0886458	+	0.996063i	$0.528254\pi$
$108$	−1.00000	−0.0962250
$109$	−16.9183	−1.62048	−0.810239	−	0.586099i	$-0.800663\pi$
$109$	−16.9183	−1.62048	−0.810239	+	0.586099i	$0.800663\pi$
$110$	−0.643320	−0.0613381
$111$	−7.57443	−0.718933
$112$	1.00000	0.0944911
$113$	14.7748	1.38989	0.694946	−	0.719062i	$-0.255428\pi$
$113$	14.7748	1.38989	0.694946	+	0.719062i	$0.255428\pi$
$114$	−8.07709	−0.756489
$115$	0.214247	0.0199786
$116$	5.72680	0.531720
$117$	−1.00000	−0.0924500
$118$	9.90746	0.912056
$119$	−6.21775	−0.569980
$120$	0.643320	0.0587268
$121$	1.00000	0.0909091
$122$	−2.98191	−0.269969
$123$	−10.4101	−0.938649
$124$	−9.45914	−0.849456
$125$	6.16695	0.551589
$126$	1.00000	0.0890871
$127$	5.24400	0.465330	0.232665	−	0.972557i	$-0.425255\pi$
$127$	5.24400	0.465330	0.232665	+	0.972557i	$0.425255\pi$
$128$	1.00000	0.0883883
$129$	−7.68155	−0.676323
$130$	0.643320	0.0564229
$131$	−10.4218	−0.910560	−0.455280	−	0.890348i	$-0.650461\pi$
$131$	−10.4218	−0.910560	−0.455280	+	0.890348i	$0.650461\pi$
$132$	−1.00000	−0.0870388
$133$	8.07709	0.700373
$134$	−4.75394	−0.410678
$135$	0.643320	0.0553681
$136$	−6.21775	−0.533168
$137$	5.10597	0.436233	0.218116	−	0.975923i	$-0.430009\pi$
$137$	5.10597	0.436233	0.218116	+	0.975923i	$0.430009\pi$
$138$	0.333033	0.0283497
$139$	−8.57420	−0.727254	−0.363627	−	0.931545i	$-0.618462\pi$
$139$	−8.57420	−0.727254	−0.363627	+	0.931545i	$0.618462\pi$
$140$	−0.643320	−0.0543704
$141$	11.3302	0.954175
$142$	11.1941	0.939388
$143$	−1.00000	−0.0836242
$144$	1.00000	0.0833333
$145$	−3.68416	−0.305953
$146$	−2.17511	−0.180014
$147$	−1.00000	−0.0824786
$148$	7.57443	0.622614
$149$	13.4461	1.10154	0.550772	−	0.834656i	$-0.314333\pi$
$149$	13.4461	1.10154	0.550772	+	0.834656i	$0.314333\pi$
$150$	4.58614	0.374457
$151$	−21.2178	−1.72668	−0.863340	−	0.504623i	$-0.831631\pi$
$151$	−21.2178	−1.72668	−0.863340	+	0.504623i	$0.831631\pi$
$152$	8.07709	0.655139
$153$	−6.21775	−0.502675
$154$	1.00000	0.0805823
$155$	6.08525	0.488779
$156$	1.00000	0.0800641
$157$	−12.0436	−0.961181	−0.480590	−	0.876945i	$-0.659578\pi$
$157$	−12.0436	−0.961181	−0.480590	+	0.876945i	$0.659578\pi$
$158$	−15.2149	−1.21043
$159$	−10.2350	−0.811689
$160$	−0.643320	−0.0508589
$161$	−0.333033	−0.0262467
$162$	1.00000	0.0785674
$163$	25.1224	1.96774	0.983868	−	0.178895i	$-0.0572521\pi$
$163$	25.1224	1.96774	0.983868	+	0.178895i	$0.0572521\pi$
$164$	10.4101	0.812894
$165$	0.643320	0.0500824
$166$	10.6407	0.825879
$167$	2.89665	0.224150	0.112075	−	0.993700i	$-0.464250\pi$
$167$	2.89665	0.224150	0.112075	+	0.993700i	$0.464250\pi$
$168$	−1.00000	−0.0771517
$169$	1.00000	0.0769231
$170$	4.00000	0.306786
$171$	8.07709	0.617671
$172$	7.68155	0.585713
$173$	1.98629	0.151015	0.0755073	−	0.997145i	$-0.475942\pi$
$173$	1.98629	0.151015	0.0755073	+	0.997145i	$0.475942\pi$
$174$	−5.72680	−0.434147
$175$	−4.58614	−0.346680
$176$	1.00000	0.0753778
$177$	−9.90746	−0.744690
$178$	−15.9049	−1.19212
$179$	3.89087	0.290818	0.145409	−	0.989372i	$-0.453550\pi$
$179$	3.89087	0.290818	0.145409	+	0.989372i	$0.453550\pi$
$180$	−0.643320	−0.0479502
$181$	11.6968	0.869414	0.434707	−	0.900572i	$-0.356852\pi$
$181$	11.6968	0.869414	0.434707	+	0.900572i	$0.356852\pi$
$182$	−1.00000	−0.0741249
$183$	2.98191	0.220429
$184$	−0.333033	−0.0245515
$185$	−4.87278	−0.358254
$186$	9.45914	0.693578
$187$	−6.21775	−0.454687
$188$	−11.3302	−0.826340
$189$	−1.00000	−0.0727393
$190$	−5.19615	−0.376969
$191$	15.1206	1.09409	0.547043	−	0.837105i	$-0.315754\pi$
$191$	15.1206	1.09409	0.547043	+	0.837105i	$0.315754\pi$
$192$	−1.00000	−0.0721688
$193$	14.0790	1.01343	0.506716	−	0.862113i	$-0.330859\pi$
$193$	14.0790	1.01343	0.506716	+	0.862113i	$0.330859\pi$
$194$	4.52804	0.325094
$195$	−0.643320	−0.0460691
$196$	1.00000	0.0714286
$197$	−3.82016	−0.272175	−0.136087	−	0.990697i	$-0.543453\pi$
$197$	−3.82016	−0.272175	−0.136087	+	0.990697i	$0.543453\pi$
$198$	1.00000	0.0710669
$199$	26.8404	1.90266	0.951332	−	0.308167i	$-0.0997154\pi$
$199$	26.8404	1.90266	0.951332	+	0.308167i	$0.0997154\pi$
$200$	−4.58614	−0.324289
$201$	4.75394	0.335317
$202$	15.3295	1.07858
$203$	5.72680	0.401942
$204$	6.21775	0.435329
$205$	−6.69704	−0.467741
$206$	11.3302	0.789412
$207$	−0.333033	−0.0231474
$208$	−1.00000	−0.0693375
$209$	8.07709	0.558704
$210$	0.643320	0.0443933
$211$	11.1860	0.770076	0.385038	−	0.922901i	$-0.374188\pi$
$211$	11.1860	0.770076	0.385038	+	0.922901i	$0.374188\pi$
$212$	10.2350	0.702944
$213$	−11.1941	−0.767007
$214$	−1.83392	−0.125364
$215$	−4.94169	−0.337021
$216$	−1.00000	−0.0680414
$217$	−9.45914	−0.642129
$218$	−16.9183	−1.14585
$219$	2.17511	0.146981
$220$	−0.643320	−0.0433726
$221$	6.21775	0.418251
$222$	−7.57443	−0.508362
$223$	−2.28687	−0.153140	−0.0765699	−	0.997064i	$-0.524397\pi$
$223$	−2.28687	−0.153140	−0.0765699	+	0.997064i	$0.524397\pi$
$224$	1.00000	0.0668153
$225$	−4.58614	−0.305743
$226$	14.7748	0.982802
$227$	6.62961	0.440022	0.220011	−	0.975497i	$-0.429391\pi$
$227$	6.62961	0.440022	0.220011	+	0.975497i	$0.429391\pi$
$228$	−8.07709	−0.534919
$229$	22.6959	1.49979	0.749893	−	0.661559i	$-0.230105\pi$
$229$	22.6959	1.49979	0.749893	+	0.661559i	$0.230105\pi$
$230$	0.214247	0.0141270
$231$	−1.00000	−0.0657952
$232$	5.72680	0.375983
$233$	−11.8313	−0.775095	−0.387547	−	0.921850i	$-0.626678\pi$
$233$	−11.8313	−0.775095	−0.387547	+	0.921850i	$0.626678\pi$
$234$	−1.00000	−0.0653720
$235$	7.28894	0.475478
$236$	9.90746	0.644921
$237$	15.2149	0.988315
$238$	−6.21775	−0.403037
$239$	15.5937	1.00867	0.504335	−	0.863508i	$-0.331738\pi$
$239$	15.5937	1.00867	0.504335	+	0.863508i	$0.331738\pi$
$240$	0.643320	0.0415261
$241$	18.1588	1.16971	0.584855	−	0.811138i	$-0.301151\pi$
$241$	18.1588	1.16971	0.584855	+	0.811138i	$0.301151\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	−2.98191	−0.190897
$245$	−0.643320	−0.0411002
$246$	−10.4101	−0.663725
$247$	−8.07709	−0.513933
$248$	−9.45914	−0.600656
$249$	−10.6407	−0.674328
$250$	6.16695	0.390032
$251$	9.97613	0.629688	0.314844	−	0.949144i	$-0.398048\pi$
$251$	9.97613	0.629688	0.314844	+	0.949144i	$0.398048\pi$
$252$	1.00000	0.0629941
$253$	−0.333033	−0.0209376
$254$	5.24400	0.329038
$255$	−4.00000	−0.250490
$256$	1.00000	0.0625000
$257$	17.9399	1.11906	0.559531	−	0.828809i	$-0.310981\pi$
$257$	17.9399	1.11906	0.559531	+	0.828809i	$0.310981\pi$
$258$	−7.68155	−0.478233
$259$	7.57443	0.470652
$260$	0.643320	0.0398970
$261$	5.72680	0.354480
$262$	−10.4218	−0.643863
$263$	−29.8311	−1.83946	−0.919732	−	0.392548i	$-0.871594\pi$
$263$	−29.8311	−1.83946	−0.919732	+	0.392548i	$0.871594\pi$
$264$	−1.00000	−0.0615457
$265$	−6.58438	−0.404476
$266$	8.07709	0.495238
$267$	15.9049	0.973361
$268$	−4.75394	−0.290393
$269$	8.78292	0.535504	0.267752	−	0.963488i	$-0.413719\pi$
$269$	8.78292	0.535504	0.267752	+	0.963488i	$0.413719\pi$
$270$	0.643320	0.0391512
$271$	−31.1891	−1.89461	−0.947303	−	0.320340i	$-0.896203\pi$
$271$	−31.1891	−1.89461	−0.947303	+	0.320340i	$0.896203\pi$
$272$	−6.21775	−0.377006
$273$	1.00000	0.0605228
$274$	5.10597	0.308463
$275$	−4.58614	−0.276555
$276$	0.333033	0.0200462
$277$	2.39025	0.143616	0.0718082	−	0.997418i	$-0.477123\pi$
$277$	2.39025	0.143616	0.0718082	+	0.997418i	$0.477123\pi$
$278$	−8.57420	−0.514247
$279$	−9.45914	−0.566304
$280$	−0.643320	−0.0384457
$281$	21.9054	1.30677	0.653384	−	0.757027i	$-0.273349\pi$
$281$	21.9054	1.30677	0.653384	+	0.757027i	$0.273349\pi$
$282$	11.3302	0.674704
$283$	12.8666	0.764841	0.382421	−	0.923988i	$-0.375091\pi$
$283$	12.8666	0.764841	0.382421	+	0.923988i	$0.375091\pi$
$284$	11.1941	0.664248
$285$	5.19615	0.307794
$286$	−1.00000	−0.0591312
$287$	10.4101	0.614490
$288$	1.00000	0.0589256
$289$	21.6604	1.27414
$290$	−3.68416	−0.216341
$291$	−4.52804	−0.265438
$292$	−2.17511	−0.127289
$293$	−22.7298	−1.32789	−0.663944	−	0.747783i	$-0.731118\pi$
$293$	−22.7298	−1.32789	−0.663944	+	0.747783i	$0.731118\pi$
$294$	−1.00000	−0.0583212
$295$	−6.37367	−0.371089
$296$	7.57443	0.440255
$297$	−1.00000	−0.0580259
$298$	13.4461	0.778909
$299$	0.333033	0.0192598
$300$	4.58614	0.264781
$301$	7.68155	0.442757
$302$	−21.2178	−1.22095
$303$	−15.3295	−0.880658
$304$	8.07709	0.463253
$305$	1.91832	0.109843
$306$	−6.21775	−0.355445
$307$	15.0192	0.857193	0.428597	−	0.903496i	$-0.359008\pi$
$307$	15.0192	0.857193	0.428597	+	0.903496i	$0.359008\pi$
$308$	1.00000	0.0569803
$309$	−11.3302	−0.644553
$310$	6.08525	0.345619
$311$	18.5178	1.05005	0.525025	−	0.851087i	$-0.324056\pi$
$311$	18.5178	1.05005	0.525025	+	0.851087i	$0.324056\pi$
$312$	1.00000	0.0566139
$313$	−20.7771	−1.17439	−0.587194	−	0.809446i	$-0.699768\pi$
$313$	−20.7771	−1.17439	−0.587194	+	0.809446i	$0.699768\pi$
$314$	−12.0436	−0.679657
$315$	−0.643320	−0.0362470
$316$	−15.2149	−0.855906
$317$	−10.2202	−0.574026	−0.287013	−	0.957927i	$-0.592662\pi$
$317$	−10.2202	−0.574026	−0.287013	+	0.957927i	$0.592662\pi$
$318$	−10.2350	−0.573951
$319$	5.72680	0.320639
$320$	−0.643320	−0.0359627
$321$	1.83392	0.102359
$322$	−0.333033	−0.0185592
$323$	−50.2213	−2.79439
$324$	1.00000	0.0555556
$325$	4.58614	0.254393
$326$	25.1224	1.39140
$327$	16.9183	0.935584
$328$	10.4101	0.574803
$329$	−11.3302	−0.624654
$330$	0.643320	0.0354136
$331$	−14.7797	−0.812364	−0.406182	−	0.913792i	$-0.633140\pi$
$331$	−14.7797	−0.812364	−0.406182	+	0.913792i	$0.633140\pi$
$332$	10.6407	0.583985
$333$	7.57443	0.415076
$334$	2.89665	0.158498
$335$	3.05831	0.167093
$336$	−1.00000	−0.0545545
$337$	−9.27387	−0.505180	−0.252590	−	0.967573i	$-0.581282\pi$
$337$	−9.27387	−0.505180	−0.252590	+	0.967573i	$0.581282\pi$
$338$	1.00000	0.0543928
$339$	−14.7748	−0.802455
$340$	4.00000	0.216930
$341$	−9.45914	−0.512241
$342$	8.07709	0.436759
$343$	1.00000	0.0539949
$344$	7.68155	0.414162
$345$	−0.214247	−0.0115347
$346$	1.98629	0.106783
$347$	20.7920	1.11617	0.558085	−	0.829784i	$-0.311536\pi$
$347$	20.7920	1.11617	0.558085	+	0.829784i	$0.311536\pi$
$348$	−5.72680	−0.306988
$349$	2.46460	0.131927	0.0659636	−	0.997822i	$-0.478988\pi$
$349$	2.46460	0.131927	0.0659636	+	0.997822i	$0.478988\pi$
$350$	−4.58614	−0.245139
$351$	1.00000	0.0533761
$352$	1.00000	0.0533002
$353$	−18.2873	−0.973335	−0.486668	−	0.873587i	$-0.661788\pi$
$353$	−18.2873	−0.973335	−0.486668	+	0.873587i	$0.661788\pi$
$354$	−9.90746	−0.526576
$355$	−7.20139	−0.382210
$356$	−15.9049	−0.842956
$357$	6.21775	0.329078
$358$	3.89087	0.205639
$359$	8.84593	0.466870	0.233435	−	0.972372i	$-0.425003\pi$
$359$	8.84593	0.466870	0.233435	+	0.972372i	$0.425003\pi$
$360$	−0.643320	−0.0339059
$361$	46.2394	2.43365
$362$	11.6968	0.614768
$363$	−1.00000	−0.0524864
$364$	−1.00000	−0.0524142
$365$	1.39929	0.0732423
$366$	2.98191	0.155867
$367$	−21.1194	−1.10242	−0.551212	−	0.834365i	$-0.685834\pi$
$367$	−21.1194	−1.10242	−0.551212	+	0.834365i	$0.685834\pi$
$368$	−0.333033	−0.0173605
$369$	10.4101	0.541930
$370$	−4.87278	−0.253324
$371$	10.2350	0.531375
$372$	9.45914	0.490434
$373$	−15.4861	−0.801838	−0.400919	−	0.916113i	$-0.631309\pi$
$373$	−15.4861	−0.801838	−0.400919	+	0.916113i	$0.631309\pi$
$374$	−6.21775	−0.321512
$375$	−6.16695	−0.318460
$376$	−11.3302	−0.584310
$377$	−5.72680	−0.294945
$378$	−1.00000	−0.0514344
$379$	16.7214	0.858921	0.429461	−	0.903086i	$-0.358704\pi$
$379$	16.7214	0.858921	0.429461	+	0.903086i	$0.358704\pi$
$380$	−5.19615	−0.266557
$381$	−5.24400	−0.268658
$382$	15.1206	0.773635
$383$	−34.1814	−1.74659	−0.873295	−	0.487193i	$-0.838021\pi$
$383$	−34.1814	−1.74659	−0.873295	+	0.487193i	$0.838021\pi$
$384$	−1.00000	−0.0510310
$385$	−0.643320	−0.0327866
$386$	14.0790	0.716604
$387$	7.68155	0.390475
$388$	4.52804	0.229876
$389$	39.0314	1.97897	0.989485	−	0.144632i	$-0.0461999\pi$
$389$	39.0314	1.97897	0.989485	+	0.144632i	$0.0461999\pi$
$390$	−0.643320	−0.0325758
$391$	2.07072	0.104721
$392$	1.00000	0.0505076
$393$	10.4218	0.525712
$394$	−3.82016	−0.192457
$395$	9.78805	0.492490
$396$	1.00000	0.0502519
$397$	−24.3603	−1.22261	−0.611303	−	0.791396i	$-0.709355\pi$
$397$	−24.3603	−1.22261	−0.611303	+	0.791396i	$0.709355\pi$
$398$	26.8404	1.34539
$399$	−8.07709	−0.404360
$400$	−4.58614	−0.229307
$401$	10.0137	0.500061	0.250031	−	0.968238i	$-0.419559\pi$
$401$	10.0137	0.500061	0.250031	+	0.968238i	$0.419559\pi$
$402$	4.75394	0.237105
$403$	9.45914	0.471194
$404$	15.3295	0.762672
$405$	−0.643320	−0.0319668
$406$	5.72680	0.284216
$407$	7.57443	0.375451
$408$	6.21775	0.307824
$409$	−16.3186	−0.806905	−0.403453	−	0.915001i	$-0.632190\pi$
$409$	−16.3186	−0.806905	−0.403453	+	0.915001i	$0.632190\pi$
$410$	−6.69704	−0.330743
$411$	−5.10597	−0.251859
$412$	11.3302	0.558199
$413$	9.90746	0.487514
$414$	−0.333033	−0.0163677
$415$	−6.84538	−0.336026
$416$	−1.00000	−0.0490290
$417$	8.57420	0.419881
$418$	8.07709	0.395064
$419$	2.21195	0.108061	0.0540303	−	0.998539i	$-0.482793\pi$
$419$	2.21195	0.108061	0.0540303	+	0.998539i	$0.482793\pi$
$420$	0.643320	0.0313908
$421$	9.95963	0.485403	0.242701	−	0.970101i	$-0.421966\pi$
$421$	9.95963	0.485403	0.242701	+	0.970101i	$0.421966\pi$
$422$	11.1860	0.544526
$423$	−11.3302	−0.550893
$424$	10.2350	0.497056
$425$	28.5155	1.38320
$426$	−11.1941	−0.542356
$427$	−2.98191	−0.144305
$428$	−1.83392	−0.0886458
$429$	1.00000	0.0482805
$430$	−4.94169	−0.238310
$431$	21.8093	1.05051	0.525257	−	0.850943i	$-0.323969\pi$
$431$	21.8093	1.05051	0.525257	+	0.850943i	$0.323969\pi$
$432$	−1.00000	−0.0481125
$433$	−21.8833	−1.05165	−0.525823	−	0.850594i	$-0.676243\pi$
$433$	−21.8833	−1.05165	−0.525823	+	0.850594i	$0.676243\pi$
$434$	−9.45914	−0.454053
$435$	3.68416	0.176642
$436$	−16.9183	−0.810239
$437$	−2.68994	−0.128677
$438$	2.17511	0.103931
$439$	32.2421	1.53883	0.769415	−	0.638749i	$-0.220548\pi$
$439$	32.2421	1.53883	0.769415	+	0.638749i	$0.220548\pi$
$440$	−0.643320	−0.0306691
$441$	1.00000	0.0476190
$442$	6.21775	0.295748
$443$	−16.4862	−0.783285	−0.391642	−	0.920117i	$-0.628093\pi$
$443$	−16.4862	−0.783285	−0.391642	+	0.920117i	$0.628093\pi$
$444$	−7.57443	−0.359466
$445$	10.2319	0.485039
$446$	−2.28687	−0.108286
$447$	−13.4461	−0.635977
$448$	1.00000	0.0472456
$449$	12.9302	0.610215	0.305107	−	0.952318i	$-0.401308\pi$
$449$	12.9302	0.610215	0.305107	+	0.952318i	$0.401308\pi$
$450$	−4.58614	−0.216193
$451$	10.4101	0.490194
$452$	14.7748	0.694946
$453$	21.2178	0.996899
$454$	6.62961	0.311143
$455$	0.643320	0.0301593
$456$	−8.07709	−0.378245
$457$	−35.8230	−1.67573	−0.837865	−	0.545877i	$-0.816196\pi$
$457$	−35.8230	−1.67573	−0.837865	+	0.545877i	$0.816196\pi$
$458$	22.6959	1.06051
$459$	6.21775	0.290220
$460$	0.214247	0.00998931
$461$	−13.9837	−0.651285	−0.325642	−	0.945493i	$-0.605581\pi$
$461$	−13.9837	−0.651285	−0.325642	+	0.945493i	$0.605581\pi$
$462$	−1.00000	−0.0465242
$463$	8.90575	0.413886	0.206943	−	0.978353i	$-0.433649\pi$
$463$	8.90575	0.413886	0.206943	+	0.978353i	$0.433649\pi$
$464$	5.72680	0.265860
$465$	−6.08525	−0.282197
$466$	−11.8313	−0.548075
$467$	15.0252	0.695283	0.347642	−	0.937628i	$-0.386983\pi$
$467$	15.0252	0.695283	0.347642	+	0.937628i	$0.386983\pi$
$468$	−1.00000	−0.0462250
$469$	−4.75394	−0.219517
$470$	7.28894	0.336214
$471$	12.0436	0.554938
$472$	9.90746	0.456028
$473$	7.68155	0.353198
$474$	15.2149	0.698844
$475$	−37.0427	−1.69963
$476$	−6.21775	−0.284990
$477$	10.2350	0.468629
$478$	15.5937	0.713238
$479$	−4.11966	−0.188232	−0.0941160	−	0.995561i	$-0.530002\pi$
$479$	−4.11966	−0.188232	−0.0941160	+	0.995561i	$0.530002\pi$
$480$	0.643320	0.0293634
$481$	−7.57443	−0.345364
$482$	18.1588	0.827110
$483$	0.333033	0.0151535
$484$	1.00000	0.0454545
$485$	−2.91297	−0.132271
$486$	−1.00000	−0.0453609
$487$	−9.56472	−0.433419	−0.216709	−	0.976236i	$-0.569532\pi$
$487$	−9.56472	−0.433419	−0.216709	+	0.976236i	$0.569532\pi$
$488$	−2.98191	−0.134985
$489$	−25.1224	−1.13607
$490$	−0.643320	−0.0290622
$491$	40.1662	1.81267	0.906337	−	0.422556i	$-0.138867\pi$
$491$	40.1662	1.81267	0.906337	+	0.422556i	$0.138867\pi$
$492$	−10.4101	−0.469325
$493$	−35.6078	−1.60369
$494$	−8.07709	−0.363406
$495$	−0.643320	−0.0289151
$496$	−9.45914	−0.424728
$497$	11.1941	0.502124
$498$	−10.6407	−0.476822
$499$	4.73773	0.212090	0.106045	−	0.994361i	$-0.466181\pi$
$499$	4.73773	0.212090	0.106045	+	0.994361i	$0.466181\pi$
$500$	6.16695	0.275794
$501$	−2.89665	−0.129413
$502$	9.97613	0.445256
$503$	−4.74433	−0.211539	−0.105770	−	0.994391i	$-0.533731\pi$
$503$	−4.74433	−0.211539	−0.105770	+	0.994391i	$0.533731\pi$
$504$	1.00000	0.0445435
$505$	−9.86178	−0.438844
$506$	−0.333033	−0.0148051
$507$	−1.00000	−0.0444116
$508$	5.24400	0.232665
$509$	−16.0339	−0.710688	−0.355344	−	0.934736i	$-0.615636\pi$
$509$	−16.0339	−0.710688	−0.355344	+	0.934736i	$0.615636\pi$
$510$	−4.00000	−0.177123
$511$	−2.17511	−0.0962213
$512$	1.00000	0.0441942
$513$	−8.07709	−0.356612
$514$	17.9399	0.791297
$515$	−7.28894	−0.321189
$516$	−7.68155	−0.338161
$517$	−11.3302	−0.498302
$518$	7.57443	0.332801
$519$	−1.98629	−0.0871883
$520$	0.643320	0.0282114
$521$	−35.6855	−1.56341	−0.781705	−	0.623648i	$-0.785650\pi$
$521$	−35.6855	−1.56341	−0.781705	+	0.623648i	$0.785650\pi$
$522$	5.72680	0.250655
$523$	17.5093	0.765627	0.382813	−	0.923826i	$-0.374955\pi$
$523$	17.5093	0.765627	0.382813	+	0.923826i	$0.374955\pi$
$524$	−10.4218	−0.455280
$525$	4.58614	0.200156
$526$	−29.8311	−1.30070
$527$	58.8146	2.56200
$528$	−1.00000	−0.0435194
$529$	−22.8891	−0.995178
$530$	−6.58438	−0.286007
$531$	9.90746	0.429947
$532$	8.07709	0.350186
$533$	−10.4101	−0.450913
$534$	15.9049	0.688270
$535$	1.17980	0.0510070
$536$	−4.75394	−0.205339
$537$	−3.89087	−0.167904
$538$	8.78292	0.378659
$539$	1.00000	0.0430730
$540$	0.643320	0.0276841
$541$	−13.4465	−0.578110	−0.289055	−	0.957313i	$-0.593341\pi$
$541$	−13.4465	−0.578110	−0.289055	+	0.957313i	$0.593341\pi$
$542$	−31.1891	−1.33969
$543$	−11.6968	−0.501956
$544$	−6.21775	−0.266584
$545$	10.8839	0.466214
$546$	1.00000	0.0427960
$547$	6.59409	0.281943	0.140972	−	0.990014i	$-0.454977\pi$
$547$	6.59409	0.281943	0.140972	+	0.990014i	$0.454977\pi$
$548$	5.10597	0.218116
$549$	−2.98191	−0.127265
$550$	−4.58614	−0.195554
$551$	46.2559	1.97057
$552$	0.333033	0.0141748
$553$	−15.2149	−0.647004
$554$	2.39025	0.101552
$555$	4.87278	0.206838
$556$	−8.57420	−0.363627
$557$	−10.4793	−0.444024	−0.222012	−	0.975044i	$-0.571262\pi$
$557$	−10.4793	−0.444024	−0.222012	+	0.975044i	$0.571262\pi$
$558$	−9.45914	−0.400438
$559$	−7.68155	−0.324895
$560$	−0.643320	−0.0271852
$561$	6.21775	0.262514
$562$	21.9054	0.924024
$563$	7.21867	0.304231	0.152115	−	0.988363i	$-0.451392\pi$
$563$	7.21867	0.304231	0.152115	+	0.988363i	$0.451392\pi$
$564$	11.3302	0.477087
$565$	−9.50489	−0.399874
$566$	12.8666	0.540824
$567$	1.00000	0.0419961
$568$	11.1941	0.469694
$569$	−2.75492	−0.115492	−0.0577462	−	0.998331i	$-0.518391\pi$
$569$	−2.75492	−0.115492	−0.0577462	+	0.998331i	$0.518391\pi$
$570$	5.19615	0.217643
$571$	28.3587	1.18678	0.593388	−	0.804917i	$-0.297790\pi$
$571$	28.3587	1.18678	0.593388	+	0.804917i	$0.297790\pi$
$572$	−1.00000	−0.0418121
$573$	−15.1206	−0.631670
$574$	10.4101	0.434510
$575$	1.52734	0.0636943
$576$	1.00000	0.0416667
$577$	−18.4807	−0.769363	−0.384682	−	0.923049i	$-0.625689\pi$
$577$	−18.4807	−0.769363	−0.384682	+	0.923049i	$0.625689\pi$
$578$	21.6604	0.900954
$579$	−14.0790	−0.585105
$580$	−3.68416	−0.152976
$581$	10.6407	0.441451
$582$	−4.52804	−0.187693
$583$	10.2350	0.423891
$584$	−2.17511	−0.0900068
$585$	0.643320	0.0265980
$586$	−22.7298	−0.938958
$587$	−3.97818	−0.164197	−0.0820985	−	0.996624i	$-0.526162\pi$
$587$	−3.97818	−0.164197	−0.0820985	+	0.996624i	$0.526162\pi$
$588$	−1.00000	−0.0412393
$589$	−76.4024	−3.14811
$590$	−6.37367	−0.262400
$591$	3.82016	0.157140
$592$	7.57443	0.311307
$593$	−22.4171	−0.920561	−0.460281	−	0.887773i	$-0.652251\pi$
$593$	−22.4171	−0.920561	−0.460281	+	0.887773i	$0.652251\pi$
$594$	−1.00000	−0.0410305
$595$	4.00000	0.163984
$596$	13.4461	0.550772
$597$	−26.8404	−1.09850
$598$	0.333033	0.0136187
$599$	27.3984	1.11947	0.559734	−	0.828672i	$-0.310903\pi$
$599$	27.3984	1.11947	0.559734	+	0.828672i	$0.310903\pi$
$600$	4.58614	0.187228
$601$	−13.1997	−0.538426	−0.269213	−	0.963081i	$-0.586764\pi$
$601$	−13.1997	−0.538426	−0.269213	+	0.963081i	$0.586764\pi$
$602$	7.68155	0.313077
$603$	−4.75394	−0.193596
$604$	−21.2178	−0.863340
$605$	−0.643320	−0.0261547
$606$	−15.3295	−0.622719
$607$	37.1131	1.50637	0.753186	−	0.657807i	$-0.228516\pi$
$607$	37.1131	1.50637	0.753186	+	0.657807i	$0.228516\pi$
$608$	8.07709	0.327569
$609$	−5.72680	−0.232061
$610$	1.91832	0.0776705
$611$	11.3302	0.458371
$612$	−6.21775	−0.251338
$613$	−27.1962	−1.09844	−0.549221	−	0.835677i	$-0.685076\pi$
$613$	−27.1962	−1.09844	−0.549221	+	0.835677i	$0.685076\pi$
$614$	15.0192	0.606127
$615$	6.69704	0.270051
$616$	1.00000	0.0402911
$617$	8.35528	0.336371	0.168185	−	0.985755i	$-0.446209\pi$
$617$	8.35528	0.336371	0.168185	+	0.985755i	$0.446209\pi$
$618$	−11.3302	−0.455767
$619$	−24.3369	−0.978183	−0.489091	−	0.872233i	$-0.662672\pi$
$619$	−24.3369	−0.978183	−0.489091	+	0.872233i	$0.662672\pi$
$620$	6.08525	0.244390
$621$	0.333033	0.0133642
$622$	18.5178	0.742497
$623$	−15.9049	−0.637215
$624$	1.00000	0.0400320
$625$	18.9634	0.758535
$626$	−20.7771	−0.830418
$627$	−8.07709	−0.322568
$628$	−12.0436	−0.480590
$629$	−47.0959	−1.87784
$630$	−0.643320	−0.0256305
$631$	−40.7511	−1.62228	−0.811138	−	0.584855i	$-0.801151\pi$
$631$	−40.7511	−1.62228	−0.811138	+	0.584855i	$0.801151\pi$
$632$	−15.2149	−0.605217
$633$	−11.1860	−0.444603
$634$	−10.2202	−0.405898
$635$	−3.37357	−0.133876
$636$	−10.2350	−0.405845
$637$	−1.00000	−0.0396214
$638$	5.72680	0.226726
$639$	11.1941	0.442832
$640$	−0.643320	−0.0254294
$641$	−40.8675	−1.61417	−0.807086	−	0.590435i	$-0.798956\pi$
$641$	−40.8675	−1.61417	−0.807086	+	0.590435i	$0.798956\pi$
$642$	1.83392	0.0723790
$643$	−10.4747	−0.413081	−0.206541	−	0.978438i	$-0.566221\pi$
$643$	−10.4747	−0.413081	−0.206541	+	0.978438i	$0.566221\pi$
$644$	−0.333033	−0.0131233
$645$	4.94169	0.194579
$646$	−50.2213	−1.97593
$647$	1.75027	0.0688102	0.0344051	−	0.999408i	$-0.489046\pi$
$647$	1.75027	0.0688102	0.0344051	+	0.999408i	$0.489046\pi$
$648$	1.00000	0.0392837
$649$	9.90746	0.388902
$650$	4.58614	0.179883
$651$	9.45914	0.370733
$652$	25.1224	0.983868
$653$	30.3529	1.18780	0.593900	−	0.804539i	$-0.297587\pi$
$653$	30.3529	1.18780	0.593900	+	0.804539i	$0.297587\pi$
$654$	16.9183	0.661557
$655$	6.70457	0.261969
$656$	10.4101	0.406447
$657$	−2.17511	−0.0848593
$658$	−11.3302	−0.441697
$659$	−35.2654	−1.37375	−0.686873	−	0.726777i	$-0.741017\pi$
$659$	−35.2654	−1.37375	−0.686873	+	0.726777i	$0.741017\pi$
$660$	0.643320	0.0250412
$661$	26.7485	1.04040	0.520198	−	0.854046i	$-0.325858\pi$
$661$	26.7485	1.04040	0.520198	+	0.854046i	$0.325858\pi$
$662$	−14.7797	−0.574428
$663$	−6.21775	−0.241477
$664$	10.6407	0.412940
$665$	−5.19615	−0.201498
$666$	7.57443	0.293503
$667$	−1.90721	−0.0738476
$668$	2.89665	0.112075
$669$	2.28687	0.0884153
$670$	3.05831	0.118153
$671$	−2.98191	−0.115115
$672$	−1.00000	−0.0385758
$673$	42.1409	1.62441	0.812205	−	0.583372i	$-0.198267\pi$
$673$	42.1409	1.62441	0.812205	+	0.583372i	$0.198267\pi$
$674$	−9.27387	−0.357216
$675$	4.58614	0.176521
$676$	1.00000	0.0384615
$677$	5.73240	0.220314	0.110157	−	0.993914i	$-0.464865\pi$
$677$	5.73240	0.220314	0.110157	+	0.993914i	$0.464865\pi$
$678$	−14.7748	−0.567421
$679$	4.52804	0.173770
$680$	4.00000	0.153393
$681$	−6.62961	−0.254047
$682$	−9.45914	−0.362209
$683$	17.6275	0.674499	0.337250	−	0.941415i	$-0.390503\pi$
$683$	17.6275	0.674499	0.337250	+	0.941415i	$0.390503\pi$
$684$	8.07709	0.308835
$685$	−3.28477	−0.125505
$686$	1.00000	0.0381802
$687$	−22.6959	−0.865902
$688$	7.68155	0.292856
$689$	−10.2350	−0.389923
$690$	−0.214247	−0.00815623
$691$	−40.5145	−1.54124	−0.770622	−	0.637292i	$-0.780054\pi$
$691$	−40.5145	−1.54124	−0.770622	+	0.637292i	$0.780054\pi$
$692$	1.98629	0.0755073
$693$	1.00000	0.0379869
$694$	20.7920	0.789252
$695$	5.51595	0.209232
$696$	−5.72680	−0.217074
$697$	−64.7275	−2.45173
$698$	2.46460	0.0932866
$699$	11.8313	0.447501
$700$	−4.58614	−0.173340
$701$	−50.7299	−1.91604	−0.958021	−	0.286698i	$-0.907442\pi$
$701$	−50.7299	−1.91604	−0.958021	+	0.286698i	$0.907442\pi$
$702$	1.00000	0.0377426
$703$	61.1794	2.30742
$704$	1.00000	0.0376889
$705$	−7.28894	−0.274517
$706$	−18.2873	−0.688252
$707$	15.3295	0.576526
$708$	−9.90746	−0.372345
$709$	15.0280	0.564389	0.282195	−	0.959357i	$-0.408938\pi$
$709$	15.0280	0.564389	0.282195	+	0.959357i	$0.408938\pi$
$710$	−7.20139	−0.270263
$711$	−15.2149	−0.570604
$712$	−15.9049	−0.596060
$713$	3.15021	0.117976
$714$	6.21775	0.232693
$715$	0.643320	0.0240588
$716$	3.89087	0.145409
$717$	−15.5937	−0.582356
$718$	8.84593	0.330127
$719$	−36.5360	−1.36256	−0.681282	−	0.732021i	$-0.738577\pi$
$719$	−36.5360	−1.36256	−0.681282	+	0.732021i	$0.738577\pi$
$720$	−0.643320	−0.0239751
$721$	11.3302	0.421959
$722$	46.2394	1.72085
$723$	−18.1588	−0.675333
$724$	11.6968	0.434707
$725$	−26.2639	−0.975416
$726$	−1.00000	−0.0371135
$727$	6.41536	0.237932	0.118966	−	0.992898i	$-0.462042\pi$
$727$	6.41536	0.237932	0.118966	+	0.992898i	$0.462042\pi$
$728$	−1.00000	−0.0370625
$729$	1.00000	0.0370370
$730$	1.39929	0.0517902
$731$	−47.7620	−1.76654
$732$	2.98191	0.110214
$733$	3.21204	0.118639	0.0593197	−	0.998239i	$-0.481107\pi$
$733$	3.21204	0.118639	0.0593197	+	0.998239i	$0.481107\pi$
$734$	−21.1194	−0.779531
$735$	0.643320	0.0237292
$736$	−0.333033	−0.0122758
$737$	−4.75394	−0.175114
$738$	10.4101	0.383202
$739$	13.2274	0.486580	0.243290	−	0.969954i	$-0.421773\pi$
$739$	13.2274	0.486580	0.243290	+	0.969954i	$0.421773\pi$
$740$	−4.87278	−0.179127
$741$	8.07709	0.296719
$742$	10.2350	0.375739
$743$	46.5861	1.70908	0.854540	−	0.519386i	$-0.173839\pi$
$743$	46.5861	1.70908	0.854540	+	0.519386i	$0.173839\pi$
$744$	9.45914	0.346789
$745$	−8.65011	−0.316916
$746$	−15.4861	−0.566985
$747$	10.6407	0.389323
$748$	−6.21775	−0.227343
$749$	−1.83392	−0.0670099
$750$	−6.16695	−0.225185
$751$	−19.2885	−0.703848	−0.351924	−	0.936029i	$-0.614472\pi$
$751$	−19.2885	−0.703848	−0.351924	+	0.936029i	$0.614472\pi$
$752$	−11.3302	−0.413170
$753$	−9.97613	−0.363550
$754$	−5.72680	−0.208558
$755$	13.6498	0.496768
$756$	−1.00000	−0.0363696
$757$	−10.5208	−0.382384	−0.191192	−	0.981553i	$-0.561235\pi$
$757$	−10.5208	−0.382384	−0.191192	+	0.981553i	$0.561235\pi$
$758$	16.7214	0.607349
$759$	0.333033	0.0120883
$760$	−5.19615	−0.188484
$761$	−44.7854	−1.62347	−0.811735	−	0.584025i	$-0.801477\pi$
$761$	−44.7854	−1.62347	−0.811735	+	0.584025i	$0.801477\pi$
$762$	−5.24400	−0.189970
$763$	−16.9183	−0.612483
$764$	15.1206	0.547043
$765$	4.00000	0.144620
$766$	−34.1814	−1.23503
$767$	−9.90746	−0.357738
$768$	−1.00000	−0.0360844
$769$	18.9915	0.684851	0.342425	−	0.939545i	$-0.388752\pi$
$769$	18.9915	0.684851	0.342425	+	0.939545i	$0.388752\pi$
$770$	−0.643320	−0.0231836
$771$	−17.9399	−0.646091
$772$	14.0790	0.506716
$773$	−8.20782	−0.295215	−0.147607	−	0.989046i	$-0.547157\pi$
$773$	−8.20782	−0.295215	−0.147607	+	0.989046i	$0.547157\pi$
$774$	7.68155	0.276108
$775$	43.3810	1.55829
$776$	4.52804	0.162547
$777$	−7.57443	−0.271731
$778$	39.0314	1.39934
$779$	84.0836	3.01261
$780$	−0.643320	−0.0230345
$781$	11.1941	0.400556
$782$	2.07072	0.0740487
$783$	−5.72680	−0.204659
$784$	1.00000	0.0357143
$785$	7.74786	0.276533
$786$	10.4218	0.371735
$787$	3.99539	0.142420	0.0712102	−	0.997461i	$-0.477314\pi$
$787$	3.99539	0.142420	0.0712102	+	0.997461i	$0.477314\pi$
$788$	−3.82016	−0.136087
$789$	29.8311	1.06201
$790$	9.78805	0.348243
$791$	14.7748	0.525330
$792$	1.00000	0.0355335
$793$	2.98191	0.105891
$794$	−24.3603	−0.864514
$795$	6.58438	0.233524
$796$	26.8404	0.951332
$797$	−22.9153	−0.811703	−0.405852	−	0.913939i	$-0.633025\pi$
$797$	−22.9153	−0.811703	−0.405852	+	0.913939i	$0.633025\pi$
$798$	−8.07709	−0.285926
$799$	70.4483	2.49228
$800$	−4.58614	−0.162145
$801$	−15.9049	−0.561970
$802$	10.0137	0.353597
$803$	−2.17511	−0.0767581
$804$	4.75394	0.167659
$805$	0.214247	0.00755121
$806$	9.45914	0.333184
$807$	−8.78292	−0.309173
$808$	15.3295	0.539291
$809$	−41.9727	−1.47568	−0.737841	−	0.674974i	$-0.764155\pi$
$809$	−41.9727	−1.47568	−0.737841	+	0.674974i	$0.764155\pi$
$810$	−0.643320	−0.0226039
$811$	−7.99139	−0.280616	−0.140308	−	0.990108i	$-0.544809\pi$
$811$	−7.99139	−0.280616	−0.140308	+	0.990108i	$0.544809\pi$
$812$	5.72680	0.200971
$813$	31.1891	1.09385
$814$	7.57443	0.265484
$815$	−16.1617	−0.566120
$816$	6.21775	0.217665
$817$	62.0446	2.17067
$818$	−16.3186	−0.570568
$819$	−1.00000	−0.0349428
$820$	−6.69704	−0.233871
$821$	21.6136	0.754321	0.377160	−	0.926148i	$-0.376901\pi$
$821$	21.6136	0.754321	0.377160	+	0.926148i	$0.376901\pi$
$822$	−5.10597	−0.178091
$823$	−35.9399	−1.25279	−0.626394	−	0.779507i	$-0.715470\pi$
$823$	−35.9399	−1.25279	−0.626394	+	0.779507i	$0.715470\pi$
$824$	11.3302	0.394706
$825$	4.58614	0.159669
$826$	9.90746	0.344725
$827$	−27.2306	−0.946899	−0.473450	−	0.880821i	$-0.656991\pi$
$827$	−27.2306	−0.946899	−0.473450	+	0.880821i	$0.656991\pi$
$828$	−0.333033	−0.0115737
$829$	−32.5457	−1.13036	−0.565179	−	0.824968i	$-0.691193\pi$
$829$	−32.5457	−1.13036	−0.565179	+	0.824968i	$0.691193\pi$
$830$	−6.84538	−0.237607
$831$	−2.39025	−0.0829170
$832$	−1.00000	−0.0346688
$833$	−6.21775	−0.215432
$834$	8.57420	0.296900
$835$	−1.86347	−0.0644882
$836$	8.07709	0.279352
$837$	9.45914	0.326956
$838$	2.21195	0.0764104
$839$	21.4464	0.740412	0.370206	−	0.928950i	$-0.379287\pi$
$839$	21.4464	0.740412	0.370206	+	0.928950i	$0.379287\pi$
$840$	0.643320	0.0221966
$841$	3.79619	0.130903
$842$	9.95963	0.343232
$843$	−21.9054	−0.754462
$844$	11.1860	0.385038
$845$	−0.643320	−0.0221309
$846$	−11.3302	−0.389540
$847$	1.00000	0.0343604
$848$	10.2350	0.351472
$849$	−12.8666	−0.441581
$850$	28.5155	0.978072
$851$	−2.52254	−0.0864714
$852$	−11.1941	−0.383504
$853$	3.07061	0.105136	0.0525678	−	0.998617i	$-0.483259\pi$
$853$	3.07061	0.105136	0.0525678	+	0.998617i	$0.483259\pi$
$854$	−2.98191	−0.102039
$855$	−5.19615	−0.177705
$856$	−1.83392	−0.0626821
$857$	−32.4893	−1.10981	−0.554907	−	0.831913i	$-0.687246\pi$
$857$	−32.4893	−1.10981	−0.554907	+	0.831913i	$0.687246\pi$
$858$	1.00000	0.0341394
$859$	16.0724	0.548383	0.274191	−	0.961675i	$-0.411590\pi$
$859$	16.0724	0.548383	0.274191	+	0.961675i	$0.411590\pi$
$860$	−4.94169	−0.168510
$861$	−10.4101	−0.354776
$862$	21.8093	0.742826
$863$	−5.47375	−0.186329	−0.0931644	−	0.995651i	$-0.529698\pi$
$863$	−5.47375	−0.186329	−0.0931644	+	0.995651i	$0.529698\pi$
$864$	−1.00000	−0.0340207
$865$	−1.27782	−0.0434471
$866$	−21.8833	−0.743626
$867$	−21.6604	−0.735626
$868$	−9.45914	−0.321064
$869$	−15.2149	−0.516131
$870$	3.68416	0.124905
$871$	4.75394	0.161081
$872$	−16.9183	−0.572926
$873$	4.52804	0.153251
$874$	−2.68994	−0.0909885
$875$	6.16695	0.208481
$876$	2.17511	0.0734903
$877$	−39.7952	−1.34379	−0.671893	−	0.740648i	$-0.734519\pi$
$877$	−39.7952	−1.34379	−0.671893	+	0.740648i	$0.734519\pi$
$878$	32.2421	1.08812
$879$	22.7298	0.766656
$880$	−0.643320	−0.0216863
$881$	7.11789	0.239808	0.119904	−	0.992786i	$-0.461741\pi$
$881$	7.11789	0.239808	0.119904	+	0.992786i	$0.461741\pi$
$882$	1.00000	0.0336718
$883$	−35.9528	−1.20991	−0.604954	−	0.796261i	$-0.706808\pi$
$883$	−35.9528	−1.20991	−0.604954	+	0.796261i	$0.706808\pi$
$884$	6.21775	0.209126
$885$	6.37367	0.214248
$886$	−16.4862	−0.553866
$887$	−49.4210	−1.65940	−0.829698	−	0.558212i	$-0.811487\pi$
$887$	−49.4210	−1.65940	−0.829698	+	0.558212i	$0.811487\pi$
$888$	−7.57443	−0.254181
$889$	5.24400	0.175878
$890$	10.2319	0.342974
$891$	1.00000	0.0335013
$892$	−2.28687	−0.0765699
$893$	−91.5151	−3.06244
$894$	−13.4461	−0.449703
$895$	−2.50308	−0.0836686
$896$	1.00000	0.0334077
$897$	−0.333033	−0.0111197
$898$	12.9302	0.431487
$899$	−54.1706	−1.80669
$900$	−4.58614	−0.152871
$901$	−63.6387	−2.12011
$902$	10.4101	0.346619
$903$	−7.68155	−0.255626
$904$	14.7748	0.491401
$905$	−7.52476	−0.250131
$906$	21.2178	0.704914
$907$	−28.7063	−0.953178	−0.476589	−	0.879126i	$-0.658127\pi$
$907$	−28.7063	−0.953178	−0.476589	+	0.879126i	$0.658127\pi$
$908$	6.62961	0.220011
$909$	15.3295	0.508448
$910$	0.643320	0.0213258
$911$	33.1312	1.09769	0.548843	−	0.835925i	$-0.315068\pi$
$911$	33.1312	1.09769	0.548843	+	0.835925i	$0.315068\pi$
$912$	−8.07709	−0.267459
$913$	10.6407	0.352156
$914$	−35.8230	−1.18492
$915$	−1.91832	−0.0634177
$916$	22.6959	0.749893
$917$	−10.4218	−0.344159
$918$	6.21775	0.205216
$919$	−13.1879	−0.435030	−0.217515	−	0.976057i	$-0.569795\pi$
$919$	−13.1879	−0.435030	−0.217515	+	0.976057i	$0.569795\pi$
$920$	0.214247	0.00706351
$921$	−15.0192	−0.494901
$922$	−13.9837	−0.460528
$923$	−11.1941	−0.368458
$924$	−1.00000	−0.0328976
$925$	−34.7374	−1.14216
$926$	8.90575	0.292661
$927$	11.3302	0.372133
$928$	5.72680	0.187991
$929$	7.54363	0.247498	0.123749	−	0.992314i	$-0.460508\pi$
$929$	7.54363	0.247498	0.123749	+	0.992314i	$0.460508\pi$
$930$	−6.08525	−0.199543
$931$	8.07709	0.264716
$932$	−11.8313	−0.387547
$933$	−18.5178	−0.606246
$934$	15.0252	0.491639
$935$	4.00000	0.130814
$936$	−1.00000	−0.0326860
$937$	−22.7442	−0.743021	−0.371511	−	0.928429i	$-0.621160\pi$
$937$	−22.7442	−0.743021	−0.371511	+	0.928429i	$0.621160\pi$
$938$	−4.75394	−0.155222
$939$	20.7771	0.678034
$940$	7.28894	0.237739
$941$	−10.8569	−0.353925	−0.176962	−	0.984218i	$-0.556627\pi$
$941$	−10.8569	−0.353925	−0.176962	+	0.984218i	$0.556627\pi$
$942$	12.0436	0.392400
$943$	−3.46692	−0.112898
$944$	9.90746	0.322460
$945$	0.643320	0.0209272
$946$	7.68155	0.249749
$947$	−32.6820	−1.06202	−0.531011	−	0.847365i	$-0.678188\pi$
$947$	−32.6820	−1.06202	−0.531011	+	0.847365i	$0.678188\pi$
$948$	15.2149	0.494157
$949$	2.17511	0.0706072
$950$	−37.0427	−1.20182
$951$	10.2202	0.331414
$952$	−6.21775	−0.201518
$953$	−16.9474	−0.548980	−0.274490	−	0.961590i	$-0.588509\pi$
$953$	−16.9474	−0.548980	−0.274490	+	0.961590i	$0.588509\pi$
$954$	10.2350	0.331371
$955$	−9.72735	−0.314770
$956$	15.5937	0.504335
$957$	−5.72680	−0.185121
$958$	−4.11966	−0.133100
$959$	5.10597	0.164880
$960$	0.643320	0.0207631
$961$	58.4754	1.88630
$962$	−7.57443	−0.244209
$963$	−1.83392	−0.0590972
$964$	18.1588	0.584855
$965$	−9.05733	−0.291566
$966$	0.333033	0.0107152
$967$	4.29063	0.137977	0.0689887	−	0.997617i	$-0.478023\pi$
$967$	4.29063	0.137977	0.0689887	+	0.997617i	$0.478023\pi$
$968$	1.00000	0.0321412
$969$	50.2213	1.61334
$970$	−2.91297	−0.0935300
$971$	33.2720	1.06775	0.533874	−	0.845564i	$-0.320736\pi$
$971$	33.2720	1.06775	0.533874	+	0.845564i	$0.320736\pi$
$972$	−1.00000	−0.0320750
$973$	−8.57420	−0.274876
$974$	−9.56472	−0.306473
$975$	−4.58614	−0.146874
$976$	−2.98191	−0.0954485
$977$	−19.1720	−0.613366	−0.306683	−	0.951812i	$-0.599219\pi$
$977$	−19.1720	−0.613366	−0.306683	+	0.951812i	$0.599219\pi$
$978$	−25.1224	−0.803325
$979$	−15.9049	−0.508321
$980$	−0.643320	−0.0205501
$981$	−16.9183	−0.540159
$982$	40.1662	1.28175
$983$	17.1181	0.545984	0.272992	−	0.962016i	$-0.411987\pi$
$983$	17.1181	0.545984	0.272992	+	0.962016i	$0.411987\pi$
$984$	−10.4101	−0.331863
$985$	2.45758	0.0783051
$986$	−35.6078	−1.13398
$987$	11.3302	0.360644
$988$	−8.07709	−0.256967
$989$	−2.55821	−0.0813464
$990$	−0.643320	−0.0204460
$991$	−18.5280	−0.588560	−0.294280	−	0.955719i	$-0.595080\pi$
$991$	−18.5280	−0.588560	−0.294280	+	0.955719i	$0.595080\pi$
$992$	−9.45914	−0.300328
$993$	14.7797	0.469019
$994$	11.1941	0.355055
$995$	−17.2670	−0.547399
$996$	−10.6407	−0.337164
$997$	24.5822	0.778525	0.389263	−	0.921127i	$-0.372730\pi$
$997$	24.5822	0.778525	0.389263	+	0.921127i	$0.372730\pi$
$998$	4.73773	0.149970
$999$	−7.57443	−0.239644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6006.2.a.cf.1.3	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6006.2.a.cf.1.3	✓	6	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6006 = 2 \cdot 3 \cdot 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6006.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.643320 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.643320 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -0.643320 q^{10} +1.00000 q^{11} -1.00000 q^{12} -1.00000 q^{13} +1.00000 q^{14} +0.643320 q^{15} +1.00000 q^{16} -6.21775 q^{17} +1.00000 q^{18} +8.07709 q^{19} -0.643320 q^{20} -1.00000 q^{21} +1.00000 q^{22} -0.333033 q^{23} -1.00000 q^{24} -4.58614 q^{25} -1.00000 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.72680 q^{29} +0.643320 q^{30} -9.45914 q^{31} +1.00000 q^{32} -1.00000 q^{33} -6.21775 q^{34} -0.643320 q^{35} +1.00000 q^{36} +7.57443 q^{37} +8.07709 q^{38} +1.00000 q^{39} -0.643320 q^{40} +10.4101 q^{41} -1.00000 q^{42} +7.68155 q^{43} +1.00000 q^{44} -0.643320 q^{45} -0.333033 q^{46} -11.3302 q^{47} -1.00000 q^{48} +1.00000 q^{49} -4.58614 q^{50} +6.21775 q^{51} -1.00000 q^{52} +10.2350 q^{53} -1.00000 q^{54} -0.643320 q^{55} +1.00000 q^{56} -8.07709 q^{57} +5.72680 q^{58} +9.90746 q^{59} +0.643320 q^{60} -2.98191 q^{61} -9.45914 q^{62} +1.00000 q^{63} +1.00000 q^{64} +0.643320 q^{65} -1.00000 q^{66} -4.75394 q^{67} -6.21775 q^{68} +0.333033 q^{69} -0.643320 q^{70} +11.1941 q^{71} +1.00000 q^{72} -2.17511 q^{73} +7.57443 q^{74} +4.58614 q^{75} +8.07709 q^{76} +1.00000 q^{77} +1.00000 q^{78} -15.2149 q^{79} -0.643320 q^{80} +1.00000 q^{81} +10.4101 q^{82} +10.6407 q^{83} -1.00000 q^{84} +4.00000 q^{85} +7.68155 q^{86} -5.72680 q^{87} +1.00000 q^{88} -15.9049 q^{89} -0.643320 q^{90} -1.00000 q^{91} -0.333033 q^{92} +9.45914 q^{93} -11.3302 q^{94} -5.19615 q^{95} -1.00000 q^{96} +4.52804 q^{97} +1.00000 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} - 6 q^{3} + 6 q^{4} - 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 6 q^{11} - 6 q^{12} - 6 q^{13} + 6 q^{14} + 6 q^{16} + 6 q^{18} + 2 q^{19} - 6 q^{21} + 6 q^{22} + 10 q^{23} - 6 q^{24} + 10 q^{25} - 6 q^{26} - 6 q^{27} + 6 q^{28} + 6 q^{29} + 2 q^{31} + 6 q^{32} - 6 q^{33} + 6 q^{36} + 12 q^{37} + 2 q^{38} + 6 q^{39} + 4 q^{41} - 6 q^{42} + 4 q^{43} + 6 q^{44} + 10 q^{46} + 4 q^{47} - 6 q^{48} + 6 q^{49} + 10 q^{50} - 6 q^{52} + 18 q^{53} - 6 q^{54} + 6 q^{56} - 2 q^{57} + 6 q^{58} + 14 q^{59} + 2 q^{62} + 6 q^{63} + 6 q^{64} - 6 q^{66} + 4 q^{67} - 10 q^{69} + 14 q^{71} + 6 q^{72} + 2 q^{73} + 12 q^{74} - 10 q^{75} + 2 q^{76} + 6 q^{77} + 6 q^{78} + 6 q^{79} + 6 q^{81} + 4 q^{82} + 24 q^{83} - 6 q^{84} + 24 q^{85} + 4 q^{86} - 6 q^{87} + 6 q^{88} - 14 q^{89} - 6 q^{91} + 10 q^{92} - 2 q^{93} + 4 q^{94} + 4 q^{95} - 6 q^{96} - 2 q^{97} + 6 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 - 6 * q^3 + 6 * q^4 - 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 6 * q^11 - 6 * q^12 - 6 * q^13 + 6 * q^14 + 6 * q^16 + 6 * q^18 + 2 * q^19 - 6 * q^21 + 6 * q^22 + 10 * q^23 - 6 * q^24 + 10 * q^25 - 6 * q^26 - 6 * q^27 + 6 * q^28 + 6 * q^29 + 2 * q^31 + 6 * q^32 - 6 * q^33 + 6 * q^36 + 12 * q^37 + 2 * q^38 + 6 * q^39 + 4 * q^41 - 6 * q^42 + 4 * q^43 + 6 * q^44 + 10 * q^46 + 4 * q^47 - 6 * q^48 + 6 * q^49 + 10 * q^50 - 6 * q^52 + 18 * q^53 - 6 * q^54 + 6 * q^56 - 2 * q^57 + 6 * q^58 + 14 * q^59 + 2 * q^62 + 6 * q^63 + 6 * q^64 - 6 * q^66 + 4 * q^67 - 10 * q^69 + 14 * q^71 + 6 * q^72 + 2 * q^73 + 12 * q^74 - 10 * q^75 + 2 * q^76 + 6 * q^77 + 6 * q^78 + 6 * q^79 + 6 * q^81 + 4 * q^82 + 24 * q^83 - 6 * q^84 + 24 * q^85 + 4 * q^86 - 6 * q^87 + 6 * q^88 - 14 * q^89 - 6 * q^91 + 10 * q^92 - 2 * q^93 + 4 * q^94 + 4 * q^95 - 6 * q^96 - 2 * q^97 + 6 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

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