LMFDB - Embedded newform 966.2.a.n.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(1,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("966.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{41}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 10 $ x^2 - x - 10
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.70156$ of defining polynomial
Character	$\chi$	$=$	966.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.70156 q^{10} -4.00000 q^{11} +1.00000 q^{12} -0.701562 q^{13} -1.00000 q^{14} -2.70156 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +7.40312 q^{19} -2.70156 q^{20} +1.00000 q^{21} +4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +2.29844 q^{25} +0.701562 q^{26} +1.00000 q^{27} +1.00000 q^{28} +6.70156 q^{29} +2.70156 q^{30} -2.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -4.00000 q^{34} -2.70156 q^{35} +1.00000 q^{36} +10.7016 q^{37} -7.40312 q^{38} -0.701562 q^{39} +2.70156 q^{40} -6.70156 q^{41} -1.00000 q^{42} +4.70156 q^{43} -4.00000 q^{44} -2.70156 q^{45} -1.00000 q^{46} +8.10469 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.29844 q^{50} +4.00000 q^{51} -0.701562 q^{52} +3.40312 q^{53} -1.00000 q^{54} +10.8062 q^{55} -1.00000 q^{56} +7.40312 q^{57} -6.70156 q^{58} +5.40312 q^{59} -2.70156 q^{60} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.89531 q^{65} +4.00000 q^{66} -10.8062 q^{67} +4.00000 q^{68} +1.00000 q^{69} +2.70156 q^{70} +5.40312 q^{71} -1.00000 q^{72} -11.4031 q^{73} -10.7016 q^{74} +2.29844 q^{75} +7.40312 q^{76} -4.00000 q^{77} +0.701562 q^{78} +8.00000 q^{79} -2.70156 q^{80} +1.00000 q^{81} +6.70156 q^{82} +0.596876 q^{83} +1.00000 q^{84} -10.8062 q^{85} -4.70156 q^{86} +6.70156 q^{87} +4.00000 q^{88} +1.40312 q^{89} +2.70156 q^{90} -0.701562 q^{91} +1.00000 q^{92} -2.00000 q^{93} -8.10469 q^{94} -20.0000 q^{95} -1.00000 q^{96} +12.7016 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} - 8 q^{11} + 2 q^{12} + 5 q^{13} - 2 q^{14} + q^{15} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 2 q^{21} + 8 q^{22} + 2 q^{23} - 2 q^{24} + 11 q^{25} - 5 q^{26} + 2 q^{27} + 2 q^{28} + 7 q^{29} - q^{30} - 4 q^{31} - 2 q^{32} - 8 q^{33} - 8 q^{34} + q^{35} + 2 q^{36} + 15 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} - 7 q^{41} - 2 q^{42} + 3 q^{43} - 8 q^{44} + q^{45} - 2 q^{46} - 3 q^{47} + 2 q^{48} + 2 q^{49} - 11 q^{50} + 8 q^{51} + 5 q^{52} - 6 q^{53} - 2 q^{54} - 4 q^{55} - 2 q^{56} + 2 q^{57} - 7 q^{58} - 2 q^{59} + q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 23 q^{65} + 8 q^{66} + 4 q^{67} + 8 q^{68} + 2 q^{69} - q^{70} - 2 q^{71} - 2 q^{72} - 10 q^{73} - 15 q^{74} + 11 q^{75} + 2 q^{76} - 8 q^{77} - 5 q^{78} + 16 q^{79} + q^{80} + 2 q^{81} + 7 q^{82} + 14 q^{83} + 2 q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 8 q^{88} - 10 q^{89} - q^{90} + 5 q^{91} + 2 q^{92} - 4 q^{93} + 3 q^{94} - 40 q^{95} - 2 q^{96} + 19 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 - 8 * q^11 + 2 * q^12 + 5 * q^13 - 2 * q^14 + q^15 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + q^20 + 2 * q^21 + 8 * q^22 + 2 * q^23 - 2 * q^24 + 11 * q^25 - 5 * q^26 + 2 * q^27 + 2 * q^28 + 7 * q^29 - q^30 - 4 * q^31 - 2 * q^32 - 8 * q^33 - 8 * q^34 + q^35 + 2 * q^36 + 15 * q^37 - 2 * q^38 + 5 * q^39 - q^40 - 7 * q^41 - 2 * q^42 + 3 * q^43 - 8 * q^44 + q^45 - 2 * q^46 - 3 * q^47 + 2 * q^48 + 2 * q^49 - 11 * q^50 + 8 * q^51 + 5 * q^52 - 6 * q^53 - 2 * q^54 - 4 * q^55 - 2 * q^56 + 2 * q^57 - 7 * q^58 - 2 * q^59 + q^60 - 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 23 * q^65 + 8 * q^66 + 4 * q^67 + 8 * q^68 + 2 * q^69 - q^70 - 2 * q^71 - 2 * q^72 - 10 * q^73 - 15 * q^74 + 11 * q^75 + 2 * q^76 - 8 * q^77 - 5 * q^78 + 16 * q^79 + q^80 + 2 * q^81 + 7 * q^82 + 14 * q^83 + 2 * q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 8 * q^88 - 10 * q^89 - q^90 + 5 * q^91 + 2 * q^92 - 4 * q^93 + 3 * q^94 - 40 * q^95 - 2 * q^96 + 19 * q^97 - 2 * q^98 - 8 * 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
$5$	−2.70156	−1.20818	−0.604088	−	0.796918i	$-0.706462\pi$
$5$	−2.70156	−1.20818	−0.604088	+	0.796918i	$0.706462\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.70156	0.854309
$11$	−4.00000	−1.20605	−0.603023	−	0.797724i	$-0.706037\pi$
$11$	−4.00000	−1.20605	−0.603023	+	0.797724i	$0.706037\pi$
$12$	1.00000	0.288675
$13$	−0.701562	−0.194578	−0.0972892	−	0.995256i	$-0.531017\pi$
$13$	−0.701562	−0.194578	−0.0972892	+	0.995256i	$0.531017\pi$
$14$	−1.00000	−0.267261
$15$	−2.70156	−0.697540
$16$	1.00000	0.250000
$17$	4.00000	0.970143	0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000	0.970143	0.485071	+	0.874475i	$0.338794\pi$
$18$	−1.00000	−0.235702
$19$	7.40312	1.69839	0.849197	−	0.528077i	$-0.177087\pi$
$19$	7.40312	1.69839	0.849197	+	0.528077i	$0.177087\pi$
$20$	−2.70156	−0.604088
$21$	1.00000	0.218218
$22$	4.00000	0.852803
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	2.29844	0.459688
$26$	0.701562	0.137588
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	6.70156	1.24445	0.622224	−	0.782839i	$-0.286229\pi$
$29$	6.70156	1.24445	0.622224	+	0.782839i	$0.286229\pi$
$30$	2.70156	0.493236
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	−1.00000	−0.176777
$33$	−4.00000	−0.696311
$34$	−4.00000	−0.685994
$35$	−2.70156	−0.456647
$36$	1.00000	0.166667
$37$	10.7016	1.75933	0.879663	−	0.475598i	$-0.157768\pi$
$37$	10.7016	1.75933	0.879663	+	0.475598i	$0.157768\pi$
$38$	−7.40312	−1.20095
$39$	−0.701562	−0.112340
$40$	2.70156	0.427154
$41$	−6.70156	−1.04661	−0.523304	−	0.852146i	$-0.675301\pi$
$41$	−6.70156	−1.04661	−0.523304	+	0.852146i	$0.675301\pi$
$42$	−1.00000	−0.154303
$43$	4.70156	0.716982	0.358491	−	0.933533i	$-0.383291\pi$
$43$	4.70156	0.716982	0.358491	+	0.933533i	$0.383291\pi$
$44$	−4.00000	−0.603023
$45$	−2.70156	−0.402725
$46$	−1.00000	−0.147442
$47$	8.10469	1.18219	0.591095	−	0.806602i	$-0.298696\pi$
$47$	8.10469	1.18219	0.591095	+	0.806602i	$0.298696\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−2.29844	−0.325048
$51$	4.00000	0.560112
$52$	−0.701562	−0.0972892
$53$	3.40312	0.467455	0.233728	−	0.972302i	$-0.424908\pi$
$53$	3.40312	0.467455	0.233728	+	0.972302i	$0.424908\pi$
$54$	−1.00000	−0.136083
$55$	10.8062	1.45711
$56$	−1.00000	−0.133631
$57$	7.40312	0.980568
$58$	−6.70156	−0.879958
$59$	5.40312	0.703427	0.351713	−	0.936108i	$-0.385599\pi$
$59$	5.40312	0.703427	0.351713	+	0.936108i	$0.385599\pi$
$60$	−2.70156	−0.348770
$61$	−2.00000	−0.256074	−0.128037	−	0.991769i	$-0.540868\pi$
$61$	−2.00000	−0.256074	−0.128037	+	0.991769i	$0.540868\pi$
$62$	2.00000	0.254000
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	1.89531	0.235085
$66$	4.00000	0.492366
$67$	−10.8062	−1.32019	−0.660097	−	0.751181i	$-0.729485\pi$
$67$	−10.8062	−1.32019	−0.660097	+	0.751181i	$0.729485\pi$
$68$	4.00000	0.485071
$69$	1.00000	0.120386
$70$	2.70156	0.322898
$71$	5.40312	0.641233	0.320616	−	0.947209i	$-0.396110\pi$
$71$	5.40312	0.641233	0.320616	+	0.947209i	$0.396110\pi$
$72$	−1.00000	−0.117851
$73$	−11.4031	−1.33463	−0.667317	−	0.744773i	$-0.732558\pi$
$73$	−11.4031	−1.33463	−0.667317	+	0.744773i	$0.732558\pi$
$74$	−10.7016	−1.24403
$75$	2.29844	0.265401
$76$	7.40312	0.849197
$77$	−4.00000	−0.455842
$78$	0.701562	0.0794363
$79$	8.00000	0.900070	0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000	0.900070	0.450035	+	0.893011i	$0.351411\pi$
$80$	−2.70156	−0.302044
$81$	1.00000	0.111111
$82$	6.70156	0.740064
$83$	0.596876	0.0655156	0.0327578	−	0.999463i	$-0.489571\pi$
$83$	0.596876	0.0655156	0.0327578	+	0.999463i	$0.489571\pi$
$84$	1.00000	0.109109
$85$	−10.8062	−1.17210
$86$	−4.70156	−0.506982
$87$	6.70156	0.718483
$88$	4.00000	0.426401
$89$	1.40312	0.148731	0.0743654	−	0.997231i	$-0.476307\pi$
$89$	1.40312	0.148731	0.0743654	+	0.997231i	$0.476307\pi$
$90$	2.70156	0.284770
$91$	−0.701562	−0.0735437
$92$	1.00000	0.104257
$93$	−2.00000	−0.207390
$94$	−8.10469	−0.835935
$95$	−20.0000	−2.05196
$96$	−1.00000	−0.102062
$97$	12.7016	1.28965	0.644824	−	0.764331i	$-0.276931\pi$
$97$	12.7016	1.28965	0.644824	+	0.764331i	$0.276931\pi$
$98$	−1.00000	−0.101015
$99$	−4.00000	−0.402015
$100$	2.29844	0.229844
$101$	9.40312	0.935646	0.467823	−	0.883822i	$-0.345039\pi$
$101$	9.40312	0.935646	0.467823	+	0.883822i	$0.345039\pi$
$102$	−4.00000	−0.396059
$103$	8.70156	0.857390	0.428695	−	0.903449i	$-0.358973\pi$
$103$	8.70156	0.857390	0.428695	+	0.903449i	$0.358973\pi$
$104$	0.701562	0.0687938
$105$	−2.70156	−0.263645
$106$	−3.40312	−0.330541
$107$	−6.80625	−0.657985	−0.328992	−	0.944333i	$-0.606709\pi$
$107$	−6.80625	−0.657985	−0.328992	+	0.944333i	$0.606709\pi$
$108$	1.00000	0.0962250
$109$	−1.29844	−0.124368	−0.0621839	−	0.998065i	$-0.519807\pi$
$109$	−1.29844	−0.124368	−0.0621839	+	0.998065i	$0.519807\pi$
$110$	−10.8062	−1.03034
$111$	10.7016	1.01575
$112$	1.00000	0.0944911
$113$	−12.1047	−1.13871	−0.569357	−	0.822091i	$-0.692808\pi$
$113$	−12.1047	−1.13871	−0.569357	+	0.822091i	$0.692808\pi$
$114$	−7.40312	−0.693366
$115$	−2.70156	−0.251922
$116$	6.70156	0.622224
$117$	−0.701562	−0.0648594
$118$	−5.40312	−0.497398
$119$	4.00000	0.366679
$120$	2.70156	0.246618
$121$	5.00000	0.454545
$122$	2.00000	0.181071
$123$	−6.70156	−0.604260
$124$	−2.00000	−0.179605
$125$	7.29844	0.652792
$126$	−1.00000	−0.0890871
$127$	0.701562	0.0622536	0.0311268	−	0.999515i	$-0.490090\pi$
$127$	0.701562	0.0622536	0.0311268	+	0.999515i	$0.490090\pi$
$128$	−1.00000	−0.0883883
$129$	4.70156	0.413949
$130$	−1.89531	−0.166230
$131$	5.40312	0.472073	0.236037	−	0.971744i	$-0.424151\pi$
$131$	5.40312	0.472073	0.236037	+	0.971744i	$0.424151\pi$
$132$	−4.00000	−0.348155
$133$	7.40312	0.641932
$134$	10.8062	0.933518
$135$	−2.70156	−0.232513
$136$	−4.00000	−0.342997
$137$	−13.2984	−1.13616	−0.568081	−	0.822973i	$-0.692314\pi$
$137$	−13.2984	−1.13616	−0.568081	+	0.822973i	$0.692314\pi$
$138$	−1.00000	−0.0851257
$139$	11.2984	0.958321	0.479160	−	0.877727i	$-0.340941\pi$
$139$	11.2984	0.958321	0.479160	+	0.877727i	$0.340941\pi$
$140$	−2.70156	−0.228324
$141$	8.10469	0.682538
$142$	−5.40312	−0.453420
$143$	2.80625	0.234670
$144$	1.00000	0.0833333
$145$	−18.1047	−1.50351
$146$	11.4031	0.943729
$147$	1.00000	0.0824786
$148$	10.7016	0.879663
$149$	18.2094	1.49177	0.745885	−	0.666075i	$-0.232027\pi$
$149$	18.2094	1.49177	0.745885	+	0.666075i	$0.232027\pi$
$150$	−2.29844	−0.187667
$151$	−20.9109	−1.70171	−0.850854	−	0.525402i	$-0.823915\pi$
$151$	−20.9109	−1.70171	−0.850854	+	0.525402i	$0.823915\pi$
$152$	−7.40312	−0.600473
$153$	4.00000	0.323381
$154$	4.00000	0.322329
$155$	5.40312	0.433989
$156$	−0.701562	−0.0561699
$157$	11.4031	0.910068	0.455034	−	0.890474i	$-0.349627\pi$
$157$	11.4031	0.910068	0.455034	+	0.890474i	$0.349627\pi$
$158$	−8.00000	−0.636446
$159$	3.40312	0.269885
$160$	2.70156	0.213577
$161$	1.00000	0.0788110
$162$	−1.00000	−0.0785674
$163$	14.8062	1.15971	0.579857	−	0.814718i	$-0.303108\pi$
$163$	14.8062	1.15971	0.579857	+	0.814718i	$0.303108\pi$
$164$	−6.70156	−0.523304
$165$	10.8062	0.841265
$166$	−0.596876	−0.0463265
$167$	−0.596876	−0.0461876	−0.0230938	−	0.999733i	$-0.507352\pi$
$167$	−0.596876	−0.0461876	−0.0230938	+	0.999733i	$0.507352\pi$
$168$	−1.00000	−0.0771517
$169$	−12.5078	−0.962139
$170$	10.8062	0.828801
$171$	7.40312	0.566131
$172$	4.70156	0.358491
$173$	6.59688	0.501551	0.250776	−	0.968045i	$-0.419314\pi$
$173$	6.59688	0.501551	0.250776	+	0.968045i	$0.419314\pi$
$174$	−6.70156	−0.508044
$175$	2.29844	0.173746
$176$	−4.00000	−0.301511
$177$	5.40312	0.406124
$178$	−1.40312	−0.105169
$179$	−5.89531	−0.440636	−0.220318	−	0.975428i	$-0.570710\pi$
$179$	−5.89531	−0.440636	−0.220318	+	0.975428i	$0.570710\pi$
$180$	−2.70156	−0.201363
$181$	8.80625	0.654563	0.327282	−	0.944927i	$-0.393867\pi$
$181$	8.80625	0.654563	0.327282	+	0.944927i	$0.393867\pi$
$182$	0.701562	0.0520032
$183$	−2.00000	−0.147844
$184$	−1.00000	−0.0737210
$185$	−28.9109	−2.12557
$186$	2.00000	0.146647
$187$	−16.0000	−1.17004
$188$	8.10469	0.591095
$189$	1.00000	0.0727393
$190$	20.0000	1.45095
$191$	−2.80625	−0.203053	−0.101527	−	0.994833i	$-0.532373\pi$
$191$	−2.80625	−0.203053	−0.101527	+	0.994833i	$0.532373\pi$
$192$	1.00000	0.0721688
$193$	−3.89531	−0.280391	−0.140195	−	0.990124i	$-0.544773\pi$
$193$	−3.89531	−0.280391	−0.140195	+	0.990124i	$0.544773\pi$
$194$	−12.7016	−0.911919
$195$	1.89531	0.135726
$196$	1.00000	0.0714286
$197$	−9.50781	−0.677403	−0.338702	−	0.940894i	$-0.609988\pi$
$197$	−9.50781	−0.677403	−0.338702	+	0.940894i	$0.609988\pi$
$198$	4.00000	0.284268
$199$	−8.70156	−0.616837	−0.308419	−	0.951251i	$-0.599800\pi$
$199$	−8.70156	−0.616837	−0.308419	+	0.951251i	$0.599800\pi$
$200$	−2.29844	−0.162524
$201$	−10.8062	−0.762214
$202$	−9.40312	−0.661602
$203$	6.70156	0.470357
$204$	4.00000	0.280056
$205$	18.1047	1.26449
$206$	−8.70156	−0.606267
$207$	1.00000	0.0695048
$208$	−0.701562	−0.0486446
$209$	−29.6125	−2.04834
$210$	2.70156	0.186425
$211$	−14.8062	−1.01930	−0.509652	−	0.860381i	$-0.670226\pi$
$211$	−14.8062	−1.01930	−0.509652	+	0.860381i	$0.670226\pi$
$212$	3.40312	0.233728
$213$	5.40312	0.370216
$214$	6.80625	0.465266
$215$	−12.7016	−0.866239
$216$	−1.00000	−0.0680414
$217$	−2.00000	−0.135769
$218$	1.29844	0.0879413
$219$	−11.4031	−0.770552
$220$	10.8062	0.728557
$221$	−2.80625	−0.188769
$222$	−10.7016	−0.718242
$223$	−22.0000	−1.47323	−0.736614	−	0.676313i	$-0.763577\pi$
$223$	−22.0000	−1.47323	−0.736614	+	0.676313i	$0.763577\pi$
$224$	−1.00000	−0.0668153
$225$	2.29844	0.153229
$226$	12.1047	0.805192
$227$	−3.89531	−0.258541	−0.129271	−	0.991609i	$-0.541264\pi$
$227$	−3.89531	−0.258541	−0.129271	+	0.991609i	$0.541264\pi$
$228$	7.40312	0.490284
$229$	−27.4031	−1.81085	−0.905425	−	0.424507i	$-0.860447\pi$
$229$	−27.4031	−1.81085	−0.905425	+	0.424507i	$0.860447\pi$
$230$	2.70156	0.178136
$231$	−4.00000	−0.263181
$232$	−6.70156	−0.439979
$233$	−26.0000	−1.70332	−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000	−1.70332	−0.851658	+	0.524097i	$0.824403\pi$
$234$	0.701562	0.0458626
$235$	−21.8953	−1.42829
$236$	5.40312	0.351713
$237$	8.00000	0.519656
$238$	−4.00000	−0.259281
$239$	−14.8062	−0.957737	−0.478868	−	0.877887i	$-0.658953\pi$
$239$	−14.8062	−0.957737	−0.478868	+	0.877887i	$0.658953\pi$
$240$	−2.70156	−0.174385
$241$	28.9109	1.86232	0.931159	−	0.364615i	$-0.118799\pi$
$241$	28.9109	1.86232	0.931159	+	0.364615i	$0.118799\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	−2.00000	−0.128037
$245$	−2.70156	−0.172596
$246$	6.70156	0.427276
$247$	−5.19375	−0.330470
$248$	2.00000	0.127000
$249$	0.596876	0.0378255
$250$	−7.29844	−0.461594
$251$	13.2984	0.839390	0.419695	−	0.907665i	$-0.362137\pi$
$251$	13.2984	0.839390	0.419695	+	0.907665i	$0.362137\pi$
$252$	1.00000	0.0629941
$253$	−4.00000	−0.251478
$254$	−0.701562	−0.0440199
$255$	−10.8062	−0.676714
$256$	1.00000	0.0625000
$257$	2.00000	0.124757	0.0623783	−	0.998053i	$-0.480131\pi$
$257$	2.00000	0.124757	0.0623783	+	0.998053i	$0.480131\pi$
$258$	−4.70156	−0.292706
$259$	10.7016	0.664963
$260$	1.89531	0.117542
$261$	6.70156	0.414816
$262$	−5.40312	−0.333806
$263$	3.29844	0.203390	0.101695	−	0.994816i	$-0.467573\pi$
$263$	3.29844	0.203390	0.101695	+	0.994816i	$0.467573\pi$
$264$	4.00000	0.246183
$265$	−9.19375	−0.564768
$266$	−7.40312	−0.453915
$267$	1.40312	0.0858698
$268$	−10.8062	−0.660097
$269$	28.2094	1.71996	0.859978	−	0.510331i	$-0.170477\pi$
$269$	28.2094	1.71996	0.859978	+	0.510331i	$0.170477\pi$
$270$	2.70156	0.164412
$271$	−11.4031	−0.692690	−0.346345	−	0.938107i	$-0.612577\pi$
$271$	−11.4031	−0.692690	−0.346345	+	0.938107i	$0.612577\pi$
$272$	4.00000	0.242536
$273$	−0.701562	−0.0424605
$274$	13.2984	0.803388
$275$	−9.19375	−0.554404
$276$	1.00000	0.0601929
$277$	−8.59688	−0.516536	−0.258268	−	0.966073i	$-0.583152\pi$
$277$	−8.59688	−0.516536	−0.258268	+	0.966073i	$0.583152\pi$
$278$	−11.2984	−0.677635
$279$	−2.00000	−0.119737
$280$	2.70156	0.161449
$281$	−17.5078	−1.04443	−0.522214	−	0.852814i	$-0.674894\pi$
$281$	−17.5078	−1.04443	−0.522214	+	0.852814i	$0.674894\pi$
$282$	−8.10469	−0.482627
$283$	−20.8062	−1.23680	−0.618402	−	0.785862i	$-0.712219\pi$
$283$	−20.8062	−1.23680	−0.618402	+	0.785862i	$0.712219\pi$
$284$	5.40312	0.320616
$285$	−20.0000	−1.18470
$286$	−2.80625	−0.165937
$287$	−6.70156	−0.395581
$288$	−1.00000	−0.0589256
$289$	−1.00000	−0.0588235
$290$	18.1047	1.06314
$291$	12.7016	0.744579
$292$	−11.4031	−0.667317
$293$	4.80625	0.280784	0.140392	−	0.990096i	$-0.455164\pi$
$293$	4.80625	0.280784	0.140392	+	0.990096i	$0.455164\pi$
$294$	−1.00000	−0.0583212
$295$	−14.5969	−0.849863
$296$	−10.7016	−0.622016
$297$	−4.00000	−0.232104
$298$	−18.2094	−1.05484
$299$	−0.701562	−0.0405724
$300$	2.29844	0.132700
$301$	4.70156	0.270994
$302$	20.9109	1.20329
$303$	9.40312	0.540195
$304$	7.40312	0.424598
$305$	5.40312	0.309382
$306$	−4.00000	−0.228665
$307$	−32.9109	−1.87833	−0.939163	−	0.343471i	$-0.888397\pi$
$307$	−32.9109	−1.87833	−0.939163	+	0.343471i	$0.888397\pi$
$308$	−4.00000	−0.227921
$309$	8.70156	0.495015
$310$	−5.40312	−0.306877
$311$	0.596876	0.0338457	0.0169229	−	0.999857i	$-0.494613\pi$
$311$	0.596876	0.0338457	0.0169229	+	0.999857i	$0.494613\pi$
$312$	0.701562	0.0397181
$313$	32.2094	1.82058	0.910291	−	0.413970i	$-0.135858\pi$
$313$	32.2094	1.82058	0.910291	+	0.413970i	$0.135858\pi$
$314$	−11.4031	−0.643516
$315$	−2.70156	−0.152216
$316$	8.00000	0.450035
$317$	−14.7016	−0.825722	−0.412861	−	0.910794i	$-0.635470\pi$
$317$	−14.7016	−0.825722	−0.412861	+	0.910794i	$0.635470\pi$
$318$	−3.40312	−0.190838
$319$	−26.8062	−1.50086
$320$	−2.70156	−0.151022
$321$	−6.80625	−0.379888
$322$	−1.00000	−0.0557278
$323$	29.6125	1.64768
$324$	1.00000	0.0555556
$325$	−1.61250	−0.0894452
$326$	−14.8062	−0.820042
$327$	−1.29844	−0.0718038
$328$	6.70156	0.370032
$329$	8.10469	0.446826
$330$	−10.8062	−0.594864
$331$	−20.0000	−1.09930	−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000	−1.09930	−0.549650	+	0.835395i	$0.685239\pi$
$332$	0.596876	0.0327578
$333$	10.7016	0.586442
$334$	0.596876	0.0326596
$335$	29.1938	1.59503
$336$	1.00000	0.0545545
$337$	34.2094	1.86350	0.931752	−	0.363096i	$-0.118280\pi$
$337$	34.2094	1.86350	0.931752	+	0.363096i	$0.118280\pi$
$338$	12.5078	0.680335
$339$	−12.1047	−0.657436
$340$	−10.8062	−0.586051
$341$	8.00000	0.433224
$342$	−7.40312	−0.400315
$343$	1.00000	0.0539949
$344$	−4.70156	−0.253491
$345$	−2.70156	−0.145447
$346$	−6.59688	−0.354650
$347$	−16.7016	−0.896587	−0.448293	−	0.893886i	$-0.647968\pi$
$347$	−16.7016	−0.896587	−0.448293	+	0.893886i	$0.647968\pi$
$348$	6.70156	0.359241
$349$	25.4031	1.35980	0.679899	−	0.733306i	$-0.262024\pi$
$349$	25.4031	1.35980	0.679899	+	0.733306i	$0.262024\pi$
$350$	−2.29844	−0.122857
$351$	−0.701562	−0.0374466
$352$	4.00000	0.213201
$353$	10.7016	0.569587	0.284793	−	0.958589i	$-0.408075\pi$
$353$	10.7016	0.569587	0.284793	+	0.958589i	$0.408075\pi$
$354$	−5.40312	−0.287173
$355$	−14.5969	−0.774722
$356$	1.40312	0.0743654
$357$	4.00000	0.211702
$358$	5.89531	0.311577
$359$	−22.1047	−1.16664	−0.583320	−	0.812242i	$-0.698247\pi$
$359$	−22.1047	−1.16664	−0.583320	+	0.812242i	$0.698247\pi$
$360$	2.70156	0.142385
$361$	35.8062	1.88454
$362$	−8.80625	−0.462846
$363$	5.00000	0.262432
$364$	−0.701562	−0.0367718
$365$	30.8062	1.61247
$366$	2.00000	0.104542
$367$	2.10469	0.109864	0.0549319	−	0.998490i	$-0.482506\pi$
$367$	2.10469	0.109864	0.0549319	+	0.998490i	$0.482506\pi$
$368$	1.00000	0.0521286
$369$	−6.70156	−0.348869
$370$	28.9109	1.50301
$371$	3.40312	0.176681
$372$	−2.00000	−0.103695
$373$	24.8062	1.28442	0.642209	−	0.766529i	$-0.278018\pi$
$373$	24.8062	1.28442	0.642209	+	0.766529i	$0.278018\pi$
$374$	16.0000	0.827340
$375$	7.29844	0.376890
$376$	−8.10469	−0.417967
$377$	−4.70156	−0.242143
$378$	−1.00000	−0.0514344
$379$	7.29844	0.374896	0.187448	−	0.982275i	$-0.439978\pi$
$379$	7.29844	0.374896	0.187448	+	0.982275i	$0.439978\pi$
$380$	−20.0000	−1.02598
$381$	0.701562	0.0359421
$382$	2.80625	0.143580
$383$	−21.6125	−1.10435	−0.552174	−	0.833729i	$-0.686201\pi$
$383$	−21.6125	−1.10435	−0.552174	+	0.833729i	$0.686201\pi$
$384$	−1.00000	−0.0510310
$385$	10.8062	0.550737
$386$	3.89531	0.198266
$387$	4.70156	0.238994
$388$	12.7016	0.644824
$389$	−6.00000	−0.304212	−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000	−0.304212	−0.152106	+	0.988364i	$0.548606\pi$
$390$	−1.89531	−0.0959729
$391$	4.00000	0.202289
$392$	−1.00000	−0.0505076
$393$	5.40312	0.272552
$394$	9.50781	0.478997
$395$	−21.6125	−1.08744
$396$	−4.00000	−0.201008
$397$	21.4031	1.07419	0.537096	−	0.843521i	$-0.319521\pi$
$397$	21.4031	1.07419	0.537096	+	0.843521i	$0.319521\pi$
$398$	8.70156	0.436170
$399$	7.40312	0.370620
$400$	2.29844	0.114922
$401$	30.0000	1.49813	0.749064	−	0.662497i	$-0.230503\pi$
$401$	30.0000	1.49813	0.749064	+	0.662497i	$0.230503\pi$
$402$	10.8062	0.538967
$403$	1.40312	0.0698946
$404$	9.40312	0.467823
$405$	−2.70156	−0.134242
$406$	−6.70156	−0.332593
$407$	−42.8062	−2.12183
$408$	−4.00000	−0.198030
$409$	−7.40312	−0.366061	−0.183030	−	0.983107i	$-0.558591\pi$
$409$	−7.40312	−0.366061	−0.183030	+	0.983107i	$0.558591\pi$
$410$	−18.1047	−0.894127
$411$	−13.2984	−0.655964
$412$	8.70156	0.428695
$413$	5.40312	0.265870
$414$	−1.00000	−0.0491473
$415$	−1.61250	−0.0791544
$416$	0.701562	0.0343969
$417$	11.2984	0.553287
$418$	29.6125	1.44839
$419$	38.2094	1.86665	0.933325	−	0.359033i	$-0.116893\pi$
$419$	38.2094	1.86665	0.933325	+	0.359033i	$0.116893\pi$
$420$	−2.70156	−0.131823
$421$	−9.29844	−0.453178	−0.226589	−	0.973990i	$-0.572757\pi$
$421$	−9.29844	−0.453178	−0.226589	+	0.973990i	$0.572757\pi$
$422$	14.8062	0.720757
$423$	8.10469	0.394063
$424$	−3.40312	−0.165270
$425$	9.19375	0.445962
$426$	−5.40312	−0.261782
$427$	−2.00000	−0.0967868
$428$	−6.80625	−0.328992
$429$	2.80625	0.135487
$430$	12.7016	0.612524
$431$	40.9109	1.97061	0.985305	−	0.170803i	$-0.0546362\pi$
$431$	40.9109	1.97061	0.985305	+	0.170803i	$0.0546362\pi$
$432$	1.00000	0.0481125
$433$	−26.3141	−1.26457	−0.632286	−	0.774735i	$-0.717883\pi$
$433$	−26.3141	−1.26457	−0.632286	+	0.774735i	$0.717883\pi$
$434$	2.00000	0.0960031
$435$	−18.1047	−0.868053
$436$	−1.29844	−0.0621839
$437$	7.40312	0.354139
$438$	11.4031	0.544862
$439$	−22.0000	−1.05000	−0.525001	−	0.851101i	$-0.675935\pi$
$439$	−22.0000	−1.05000	−0.525001	+	0.851101i	$0.675935\pi$
$440$	−10.8062	−0.515168
$441$	1.00000	0.0476190
$442$	2.80625	0.133480
$443$	−7.29844	−0.346759	−0.173380	−	0.984855i	$-0.555469\pi$
$443$	−7.29844	−0.346759	−0.173380	+	0.984855i	$0.555469\pi$
$444$	10.7016	0.507874
$445$	−3.79063	−0.179693
$446$	22.0000	1.04173
$447$	18.2094	0.861274
$448$	1.00000	0.0472456
$449$	38.4187	1.81309	0.906546	−	0.422106i	$-0.138709\pi$
$449$	38.4187	1.81309	0.906546	+	0.422106i	$0.138709\pi$
$450$	−2.29844	−0.108349
$451$	26.8062	1.26226
$452$	−12.1047	−0.569357
$453$	−20.9109	−0.982481
$454$	3.89531	0.182816
$455$	1.89531	0.0888537
$456$	−7.40312	−0.346683
$457$	−10.2094	−0.477574	−0.238787	−	0.971072i	$-0.576750\pi$
$457$	−10.2094	−0.477574	−0.238787	+	0.971072i	$0.576750\pi$
$458$	27.4031	1.28046
$459$	4.00000	0.186704
$460$	−2.70156	−0.125961
$461$	36.2094	1.68644	0.843219	−	0.537570i	$-0.180658\pi$
$461$	36.2094	1.68644	0.843219	+	0.537570i	$0.180658\pi$
$462$	4.00000	0.186097
$463$	−28.7016	−1.33387	−0.666937	−	0.745114i	$-0.732395\pi$
$463$	−28.7016	−1.33387	−0.666937	+	0.745114i	$0.732395\pi$
$464$	6.70156	0.311112
$465$	5.40312	0.250564
$466$	26.0000	1.20443
$467$	2.70156	0.125013	0.0625067	−	0.998045i	$-0.480091\pi$
$467$	2.70156	0.125013	0.0625067	+	0.998045i	$0.480091\pi$
$468$	−0.701562	−0.0324297
$469$	−10.8062	−0.498986
$470$	21.8953	1.00996
$471$	11.4031	0.525428
$472$	−5.40312	−0.248699
$473$	−18.8062	−0.864712
$474$	−8.00000	−0.367452
$475$	17.0156	0.780730
$476$	4.00000	0.183340
$477$	3.40312	0.155818
$478$	14.8062	0.677222
$479$	29.4031	1.34346	0.671732	−	0.740795i	$-0.265551\pi$
$479$	29.4031	1.34346	0.671732	+	0.740795i	$0.265551\pi$
$480$	2.70156	0.123309
$481$	−7.50781	−0.342327
$482$	−28.9109	−1.31686
$483$	1.00000	0.0455016
$484$	5.00000	0.227273
$485$	−34.3141	−1.55812
$486$	−1.00000	−0.0453609
$487$	−12.7016	−0.575563	−0.287781	−	0.957696i	$-0.592918\pi$
$487$	−12.7016	−0.575563	−0.287781	+	0.957696i	$0.592918\pi$
$488$	2.00000	0.0905357
$489$	14.8062	0.669562
$490$	2.70156	0.122044
$491$	41.6125	1.87795	0.938973	−	0.343991i	$-0.111779\pi$
$491$	41.6125	1.87795	0.938973	+	0.343991i	$0.111779\pi$
$492$	−6.70156	−0.302130
$493$	26.8062	1.20729
$494$	5.19375	0.233678
$495$	10.8062	0.485705
$496$	−2.00000	−0.0898027
$497$	5.40312	0.242363
$498$	−0.596876	−0.0267466
$499$	−10.5969	−0.474381	−0.237191	−	0.971463i	$-0.576227\pi$
$499$	−10.5969	−0.474381	−0.237191	+	0.971463i	$0.576227\pi$
$500$	7.29844	0.326396
$501$	−0.596876	−0.0266664
$502$	−13.2984	−0.593538
$503$	17.4031	0.775967	0.387983	−	0.921666i	$-0.373172\pi$
$503$	17.4031	0.775967	0.387983	+	0.921666i	$0.373172\pi$
$504$	−1.00000	−0.0445435
$505$	−25.4031	−1.13042
$506$	4.00000	0.177822
$507$	−12.5078	−0.555491
$508$	0.701562	0.0311268
$509$	−13.6125	−0.603363	−0.301682	−	0.953409i	$-0.597548\pi$
$509$	−13.6125	−0.603363	−0.301682	+	0.953409i	$0.597548\pi$
$510$	10.8062	0.478509
$511$	−11.4031	−0.504445
$512$	−1.00000	−0.0441942
$513$	7.40312	0.326856
$514$	−2.00000	−0.0882162
$515$	−23.5078	−1.03588
$516$	4.70156	0.206975
$517$	−32.4187	−1.42577
$518$	−10.7016	−0.470200
$519$	6.59688	0.289571
$520$	−1.89531	−0.0831150
$521$	−33.4031	−1.46342	−0.731709	−	0.681617i	$-0.761277\pi$
$521$	−33.4031	−1.46342	−0.731709	+	0.681617i	$0.761277\pi$
$522$	−6.70156	−0.293319
$523$	−4.80625	−0.210163	−0.105081	−	0.994464i	$-0.533510\pi$
$523$	−4.80625	−0.210163	−0.105081	+	0.994464i	$0.533510\pi$
$524$	5.40312	0.236037
$525$	2.29844	0.100312
$526$	−3.29844	−0.143819
$527$	−8.00000	−0.348485
$528$	−4.00000	−0.174078
$529$	1.00000	0.0434783
$530$	9.19375	0.399351
$531$	5.40312	0.234476
$532$	7.40312	0.320966
$533$	4.70156	0.203647
$534$	−1.40312	−0.0607191
$535$	18.3875	0.794961
$536$	10.8062	0.466759
$537$	−5.89531	−0.254402
$538$	−28.2094	−1.21619
$539$	−4.00000	−0.172292
$540$	−2.70156	−0.116257
$541$	20.5969	0.885529	0.442764	−	0.896638i	$-0.353998\pi$
$541$	20.5969	0.885529	0.442764	+	0.896638i	$0.353998\pi$
$542$	11.4031	0.489806
$543$	8.80625	0.377912
$544$	−4.00000	−0.171499
$545$	3.50781	0.150258
$546$	0.701562	0.0300241
$547$	−35.0156	−1.49716	−0.748580	−	0.663045i	$-0.769264\pi$
$547$	−35.0156	−1.49716	−0.748580	+	0.663045i	$0.769264\pi$
$548$	−13.2984	−0.568081
$549$	−2.00000	−0.0853579
$550$	9.19375	0.392023
$551$	49.6125	2.11356
$552$	−1.00000	−0.0425628
$553$	8.00000	0.340195
$554$	8.59688	0.365246
$555$	−28.9109	−1.22720
$556$	11.2984	0.479160
$557$	−24.5969	−1.04220	−0.521102	−	0.853495i	$-0.674479\pi$
$557$	−24.5969	−1.04220	−0.521102	+	0.853495i	$0.674479\pi$
$558$	2.00000	0.0846668
$559$	−3.29844	−0.139509
$560$	−2.70156	−0.114162
$561$	−16.0000	−0.675521
$562$	17.5078	0.738522
$563$	16.1047	0.678732	0.339366	−	0.940654i	$-0.389788\pi$
$563$	16.1047	0.678732	0.339366	+	0.940654i	$0.389788\pi$
$564$	8.10469	0.341269
$565$	32.7016	1.37577
$566$	20.8062	0.874552
$567$	1.00000	0.0419961
$568$	−5.40312	−0.226710
$569$	25.2984	1.06057	0.530283	−	0.847821i	$-0.322086\pi$
$569$	25.2984	1.06057	0.530283	+	0.847821i	$0.322086\pi$
$570$	20.0000	0.837708
$571$	10.8062	0.452227	0.226114	−	0.974101i	$-0.427398\pi$
$571$	10.8062	0.452227	0.226114	+	0.974101i	$0.427398\pi$
$572$	2.80625	0.117335
$573$	−2.80625	−0.117233
$574$	6.70156	0.279718
$575$	2.29844	0.0958515
$576$	1.00000	0.0416667
$577$	−10.0000	−0.416305	−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000	−0.416305	−0.208153	+	0.978096i	$0.566745\pi$
$578$	1.00000	0.0415945
$579$	−3.89531	−0.161884
$580$	−18.1047	−0.751756
$581$	0.596876	0.0247626
$582$	−12.7016	−0.526497
$583$	−13.6125	−0.563772
$584$	11.4031	0.471865
$585$	1.89531	0.0783616
$586$	−4.80625	−0.198544
$587$	−10.8062	−0.446022	−0.223011	−	0.974816i	$-0.571589\pi$
$587$	−10.8062	−0.446022	−0.223011	+	0.974816i	$0.571589\pi$
$588$	1.00000	0.0412393
$589$	−14.8062	−0.610081
$590$	14.5969	0.600944
$591$	−9.50781	−0.391099
$592$	10.7016	0.439831
$593$	37.2984	1.53166	0.765832	−	0.643041i	$-0.222328\pi$
$593$	37.2984	1.53166	0.765832	+	0.643041i	$0.222328\pi$
$594$	4.00000	0.164122
$595$	−10.8062	−0.443013
$596$	18.2094	0.745885
$597$	−8.70156	−0.356131
$598$	0.701562	0.0286890
$599$	−37.6125	−1.53680	−0.768402	−	0.639967i	$-0.778948\pi$
$599$	−37.6125	−1.53680	−0.768402	+	0.639967i	$0.778948\pi$
$600$	−2.29844	−0.0938333
$601$	−0.596876	−0.0243471	−0.0121735	−	0.999926i	$-0.503875\pi$
$601$	−0.596876	−0.0243471	−0.0121735	+	0.999926i	$0.503875\pi$
$602$	−4.70156	−0.191621
$603$	−10.8062	−0.440064
$604$	−20.9109	−0.850854
$605$	−13.5078	−0.549171
$606$	−9.40312	−0.381976
$607$	11.6125	0.471337	0.235668	−	0.971834i	$-0.424272\pi$
$607$	11.6125	0.471337	0.235668	+	0.971834i	$0.424272\pi$
$608$	−7.40312	−0.300236
$609$	6.70156	0.271561
$610$	−5.40312	−0.218766
$611$	−5.68594	−0.230029
$612$	4.00000	0.161690
$613$	−2.70156	−0.109115	−0.0545575	−	0.998511i	$-0.517375\pi$
$613$	−2.70156	−0.109115	−0.0545575	+	0.998511i	$0.517375\pi$
$614$	32.9109	1.32818
$615$	18.1047	0.730051
$616$	4.00000	0.161165
$617$	−44.8062	−1.80383	−0.901916	−	0.431912i	$-0.857839\pi$
$617$	−44.8062	−1.80383	−0.901916	+	0.431912i	$0.857839\pi$
$618$	−8.70156	−0.350028
$619$	−32.8062	−1.31859	−0.659297	−	0.751882i	$-0.729146\pi$
$619$	−32.8062	−1.31859	−0.659297	+	0.751882i	$0.729146\pi$
$620$	5.40312	0.216995
$621$	1.00000	0.0401286
$622$	−0.596876	−0.0239325
$623$	1.40312	0.0562150
$624$	−0.701562	−0.0280850
$625$	−31.2094	−1.24837
$626$	−32.2094	−1.28735
$627$	−29.6125	−1.18261
$628$	11.4031	0.455034
$629$	42.8062	1.70680
$630$	2.70156	0.107633
$631$	21.6125	0.860380	0.430190	−	0.902738i	$-0.358447\pi$
$631$	21.6125	0.860380	0.430190	+	0.902738i	$0.358447\pi$
$632$	−8.00000	−0.318223
$633$	−14.8062	−0.588496
$634$	14.7016	0.583874
$635$	−1.89531	−0.0752132
$636$	3.40312	0.134943
$637$	−0.701562	−0.0277969
$638$	26.8062	1.06127
$639$	5.40312	0.213744
$640$	2.70156	0.106789
$641$	49.7172	1.96371	0.981855	−	0.189631i	$-0.0607293\pi$
$641$	49.7172	1.96371	0.981855	+	0.189631i	$0.0607293\pi$
$642$	6.80625	0.268621
$643$	−24.8062	−0.978263	−0.489131	−	0.872210i	$-0.662686\pi$
$643$	−24.8062	−0.978263	−0.489131	+	0.872210i	$0.662686\pi$
$644$	1.00000	0.0394055
$645$	−12.7016	−0.500124
$646$	−29.6125	−1.16509
$647$	−19.4031	−0.762816	−0.381408	−	0.924407i	$-0.624561\pi$
$647$	−19.4031	−0.762816	−0.381408	+	0.924407i	$0.624561\pi$
$648$	−1.00000	−0.0392837
$649$	−21.6125	−0.848365
$650$	1.61250	0.0632473
$651$	−2.00000	−0.0783862
$652$	14.8062	0.579857
$653$	−12.1047	−0.473693	−0.236846	−	0.971547i	$-0.576114\pi$
$653$	−12.1047	−0.473693	−0.236846	+	0.971547i	$0.576114\pi$
$654$	1.29844	0.0507729
$655$	−14.5969	−0.570347
$656$	−6.70156	−0.261652
$657$	−11.4031	−0.444878
$658$	−8.10469	−0.315954
$659$	8.00000	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$659$	8.00000	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$660$	10.8062	0.420633
$661$	−34.4187	−1.33873	−0.669367	−	0.742932i	$-0.733435\pi$
$661$	−34.4187	−1.33873	−0.669367	+	0.742932i	$0.733435\pi$
$662$	20.0000	0.777322
$663$	−2.80625	−0.108986
$664$	−0.596876	−0.0231633
$665$	−20.0000	−0.775567
$666$	−10.7016	−0.414677
$667$	6.70156	0.259486
$668$	−0.596876	−0.0230938
$669$	−22.0000	−0.850569
$670$	−29.1938	−1.12785
$671$	8.00000	0.308837
$672$	−1.00000	−0.0385758
$673$	1.29844	0.0500511	0.0250256	−	0.999687i	$-0.492033\pi$
$673$	1.29844	0.0500511	0.0250256	+	0.999687i	$0.492033\pi$
$674$	−34.2094	−1.31770
$675$	2.29844	0.0884669
$676$	−12.5078	−0.481070
$677$	26.4187	1.01535	0.507677	−	0.861547i	$-0.330504\pi$
$677$	26.4187	1.01535	0.507677	+	0.861547i	$0.330504\pi$
$678$	12.1047	0.464878
$679$	12.7016	0.487441
$680$	10.8062	0.414401
$681$	−3.89531	−0.149269
$682$	−8.00000	−0.306336
$683$	−17.6125	−0.673923	−0.336962	−	0.941518i	$-0.609399\pi$
$683$	−17.6125	−0.673923	−0.336962	+	0.941518i	$0.609399\pi$
$684$	7.40312	0.283066
$685$	35.9266	1.37268
$686$	−1.00000	−0.0381802
$687$	−27.4031	−1.04549
$688$	4.70156	0.179245
$689$	−2.38750	−0.0909566
$690$	2.70156	0.102847
$691$	31.5078	1.19861	0.599307	−	0.800519i	$-0.295443\pi$
$691$	31.5078	1.19861	0.599307	+	0.800519i	$0.295443\pi$
$692$	6.59688	0.250776
$693$	−4.00000	−0.151947
$694$	16.7016	0.633983
$695$	−30.5234	−1.15782
$696$	−6.70156	−0.254022
$697$	−26.8062	−1.01536
$698$	−25.4031	−0.961522
$699$	−26.0000	−0.983410
$700$	2.29844	0.0868728
$701$	−17.0156	−0.642671	−0.321336	−	0.946965i	$-0.604132\pi$
$701$	−17.0156	−0.642671	−0.321336	+	0.946965i	$0.604132\pi$
$702$	0.701562	0.0264788
$703$	79.2250	2.98803
$704$	−4.00000	−0.150756
$705$	−21.8953	−0.824625
$706$	−10.7016	−0.402759
$707$	9.40312	0.353641
$708$	5.40312	0.203062
$709$	48.8062	1.83296	0.916479	−	0.400084i	$-0.131019\pi$
$709$	48.8062	1.83296	0.916479	+	0.400084i	$0.131019\pi$
$710$	14.5969	0.547811
$711$	8.00000	0.300023
$712$	−1.40312	−0.0525843
$713$	−2.00000	−0.0749006
$714$	−4.00000	−0.149696
$715$	−7.58125	−0.283523
$716$	−5.89531	−0.220318
$717$	−14.8062	−0.552949
$718$	22.1047	0.824940
$719$	38.9109	1.45113	0.725567	−	0.688152i	$-0.241578\pi$
$719$	38.9109	1.45113	0.725567	+	0.688152i	$0.241578\pi$
$720$	−2.70156	−0.100681
$721$	8.70156	0.324063
$722$	−35.8062	−1.33257
$723$	28.9109	1.07521
$724$	8.80625	0.327282
$725$	15.4031	0.572058
$726$	−5.00000	−0.185567
$727$	−12.0000	−0.445055	−0.222528	−	0.974926i	$-0.571431\pi$
$727$	−12.0000	−0.445055	−0.222528	+	0.974926i	$0.571431\pi$
$728$	0.701562	0.0260016
$729$	1.00000	0.0370370
$730$	−30.8062	−1.14019
$731$	18.8062	0.695574
$732$	−2.00000	−0.0739221
$733$	13.7906	0.509368	0.254684	−	0.967024i	$-0.418028\pi$
$733$	13.7906	0.509368	0.254684	+	0.967024i	$0.418028\pi$
$734$	−2.10469	−0.0776854
$735$	−2.70156	−0.0996486
$736$	−1.00000	−0.0368605
$737$	43.2250	1.59221
$738$	6.70156	0.246688
$739$	35.0156	1.28807	0.644035	−	0.764996i	$-0.277259\pi$
$739$	35.0156	1.28807	0.644035	+	0.764996i	$0.277259\pi$
$740$	−28.9109	−1.06279
$741$	−5.19375	−0.190797
$742$	−3.40312	−0.124933
$743$	32.0000	1.17397	0.586983	−	0.809599i	$-0.300316\pi$
$743$	32.0000	1.17397	0.586983	+	0.809599i	$0.300316\pi$
$744$	2.00000	0.0733236
$745$	−49.1938	−1.80232
$746$	−24.8062	−0.908221
$747$	0.596876	0.0218385
$748$	−16.0000	−0.585018
$749$	−6.80625	−0.248695
$750$	−7.29844	−0.266501
$751$	−21.6125	−0.788651	−0.394326	−	0.918971i	$-0.629022\pi$
$751$	−21.6125	−0.788651	−0.394326	+	0.918971i	$0.629022\pi$
$752$	8.10469	0.295548
$753$	13.2984	0.484622
$754$	4.70156	0.171221
$755$	56.4922	2.05596
$756$	1.00000	0.0363696
$757$	50.4187	1.83250	0.916250	−	0.400606i	$-0.131201\pi$
$757$	50.4187	1.83250	0.916250	+	0.400606i	$0.131201\pi$
$758$	−7.29844	−0.265091
$759$	−4.00000	−0.145191
$760$	20.0000	0.725476
$761$	15.6125	0.565953	0.282976	−	0.959127i	$-0.408678\pi$
$761$	15.6125	0.565953	0.282976	+	0.959127i	$0.408678\pi$
$762$	−0.701562	−0.0254149
$763$	−1.29844	−0.0470066
$764$	−2.80625	−0.101527
$765$	−10.8062	−0.390701
$766$	21.6125	0.780891
$767$	−3.79063	−0.136872
$768$	1.00000	0.0360844
$769$	−28.9109	−1.04255	−0.521277	−	0.853387i	$-0.674544\pi$
$769$	−28.9109	−1.04255	−0.521277	+	0.853387i	$0.674544\pi$
$770$	−10.8062	−0.389430
$771$	2.00000	0.0720282
$772$	−3.89531	−0.140195
$773$	12.1047	0.435375	0.217688	−	0.976018i	$-0.430149\pi$
$773$	12.1047	0.435375	0.217688	+	0.976018i	$0.430149\pi$
$774$	−4.70156	−0.168994
$775$	−4.59688	−0.165125
$776$	−12.7016	−0.455960
$777$	10.7016	0.383916
$778$	6.00000	0.215110
$779$	−49.6125	−1.77755
$780$	1.89531	0.0678631
$781$	−21.6125	−0.773356
$782$	−4.00000	−0.143040
$783$	6.70156	0.239494
$784$	1.00000	0.0357143
$785$	−30.8062	−1.09952
$786$	−5.40312	−0.192723
$787$	−31.4031	−1.11940	−0.559700	−	0.828695i	$-0.689084\pi$
$787$	−31.4031	−1.11940	−0.559700	+	0.828695i	$0.689084\pi$
$788$	−9.50781	−0.338702
$789$	3.29844	0.117427
$790$	21.6125	0.768938
$791$	−12.1047	−0.430393
$792$	4.00000	0.142134
$793$	1.40312	0.0498264
$794$	−21.4031	−0.759568
$795$	−9.19375	−0.326069
$796$	−8.70156	−0.308419
$797$	9.29844	0.329368	0.164684	−	0.986346i	$-0.447340\pi$
$797$	9.29844	0.329368	0.164684	+	0.986346i	$0.447340\pi$
$798$	−7.40312	−0.262068
$799$	32.4187	1.14689
$800$	−2.29844	−0.0812621
$801$	1.40312	0.0495770
$802$	−30.0000	−1.05934
$803$	45.6125	1.60963
$804$	−10.8062	−0.381107
$805$	−2.70156	−0.0952176
$806$	−1.40312	−0.0494229
$807$	28.2094	0.993017
$808$	−9.40312	−0.330801
$809$	−33.0156	−1.16077	−0.580384	−	0.814343i	$-0.697097\pi$
$809$	−33.0156	−1.16077	−0.580384	+	0.814343i	$0.697097\pi$
$810$	2.70156	0.0949232
$811$	20.4922	0.719578	0.359789	−	0.933034i	$-0.382849\pi$
$811$	20.4922	0.719578	0.359789	+	0.933034i	$0.382849\pi$
$812$	6.70156	0.235179
$813$	−11.4031	−0.399925
$814$	42.8062	1.50036
$815$	−40.0000	−1.40114
$816$	4.00000	0.140028
$817$	34.8062	1.21772
$818$	7.40312	0.258844
$819$	−0.701562	−0.0245146
$820$	18.1047	0.632243
$821$	−23.6125	−0.824082	−0.412041	−	0.911165i	$-0.635184\pi$
$821$	−23.6125	−0.824082	−0.412041	+	0.911165i	$0.635184\pi$
$822$	13.2984	0.463836
$823$	−7.29844	−0.254408	−0.127204	−	0.991877i	$-0.540600\pi$
$823$	−7.29844	−0.254408	−0.127204	+	0.991877i	$0.540600\pi$
$824$	−8.70156	−0.303133
$825$	−9.19375	−0.320085
$826$	−5.40312	−0.187999
$827$	−34.5969	−1.20305	−0.601526	−	0.798854i	$-0.705440\pi$
$827$	−34.5969	−1.20305	−0.601526	+	0.798854i	$0.705440\pi$
$828$	1.00000	0.0347524
$829$	42.5969	1.47945	0.739725	−	0.672909i	$-0.234955\pi$
$829$	42.5969	1.47945	0.739725	+	0.672909i	$0.234955\pi$
$830$	1.61250	0.0559706
$831$	−8.59688	−0.298222
$832$	−0.701562	−0.0243223
$833$	4.00000	0.138592
$834$	−11.2984	−0.391233
$835$	1.61250	0.0558028
$836$	−29.6125	−1.02417
$837$	−2.00000	−0.0691301
$838$	−38.2094	−1.31992
$839$	3.79063	0.130867	0.0654335	−	0.997857i	$-0.479157\pi$
$839$	3.79063	0.130867	0.0654335	+	0.997857i	$0.479157\pi$
$840$	2.70156	0.0932127
$841$	15.9109	0.548653
$842$	9.29844	0.320445
$843$	−17.5078	−0.603001
$844$	−14.8062	−0.509652
$845$	33.7906	1.16243
$846$	−8.10469	−0.278645
$847$	5.00000	0.171802
$848$	3.40312	0.116864
$849$	−20.8062	−0.714069
$850$	−9.19375	−0.315343
$851$	10.7016	0.366845
$852$	5.40312	0.185108
$853$	−10.1047	−0.345978	−0.172989	−	0.984924i	$-0.555342\pi$
$853$	−10.1047	−0.345978	−0.172989	+	0.984924i	$0.555342\pi$
$854$	2.00000	0.0684386
$855$	−20.0000	−0.683986
$856$	6.80625	0.232633
$857$	−6.70156	−0.228921	−0.114461	−	0.993428i	$-0.536514\pi$
$857$	−6.70156	−0.228921	−0.114461	+	0.993428i	$0.536514\pi$
$858$	−2.80625	−0.0958037
$859$	−47.5078	−1.62095	−0.810473	−	0.585776i	$-0.800790\pi$
$859$	−47.5078	−1.62095	−0.810473	+	0.585776i	$0.800790\pi$
$860$	−12.7016	−0.433120
$861$	−6.70156	−0.228389
$862$	−40.9109	−1.39343
$863$	−57.6125	−1.96115	−0.980576	−	0.196139i	$-0.937160\pi$
$863$	−57.6125	−1.96115	−0.980576	+	0.196139i	$0.937160\pi$
$864$	−1.00000	−0.0340207
$865$	−17.8219	−0.605962
$866$	26.3141	0.894188
$867$	−1.00000	−0.0339618
$868$	−2.00000	−0.0678844
$869$	−32.0000	−1.08553
$870$	18.1047	0.613806
$871$	7.58125	0.256881
$872$	1.29844	0.0439707
$873$	12.7016	0.429883
$874$	−7.40312	−0.250414
$875$	7.29844	0.246732
$876$	−11.4031	−0.385276
$877$	−4.59688	−0.155225	−0.0776127	−	0.996984i	$-0.524730\pi$
$877$	−4.59688	−0.155225	−0.0776127	+	0.996984i	$0.524730\pi$
$878$	22.0000	0.742464
$879$	4.80625	0.162111
$880$	10.8062	0.364279
$881$	−32.2094	−1.08516	−0.542581	−	0.840004i	$-0.682553\pi$
$881$	−32.2094	−1.08516	−0.542581	+	0.840004i	$0.682553\pi$
$882$	−1.00000	−0.0336718
$883$	−37.4031	−1.25872	−0.629358	−	0.777116i	$-0.716682\pi$
$883$	−37.4031	−1.25872	−0.629358	+	0.777116i	$0.716682\pi$
$884$	−2.80625	−0.0943844
$885$	−14.5969	−0.490669
$886$	7.29844	0.245196
$887$	10.2094	0.342797	0.171399	−	0.985202i	$-0.445171\pi$
$887$	10.2094	0.342797	0.171399	+	0.985202i	$0.445171\pi$
$888$	−10.7016	−0.359121
$889$	0.701562	0.0235296
$890$	3.79063	0.127062
$891$	−4.00000	−0.134005
$892$	−22.0000	−0.736614
$893$	60.0000	2.00782
$894$	−18.2094	−0.609013
$895$	15.9266	0.532366
$896$	−1.00000	−0.0334077
$897$	−0.701562	−0.0234245
$898$	−38.4187	−1.28205
$899$	−13.4031	−0.447019
$900$	2.29844	0.0766146
$901$	13.6125	0.453498
$902$	−26.8062	−0.892550
$903$	4.70156	0.156458
$904$	12.1047	0.402596
$905$	−23.7906	−0.790827
$906$	20.9109	0.694719
$907$	−11.5078	−0.382111	−0.191055	−	0.981579i	$-0.561191\pi$
$907$	−11.5078	−0.382111	−0.191055	+	0.981579i	$0.561191\pi$
$908$	−3.89531	−0.129271
$909$	9.40312	0.311882
$910$	−1.89531	−0.0628290
$911$	33.8953	1.12300	0.561501	−	0.827476i	$-0.310224\pi$
$911$	33.8953	1.12300	0.561501	+	0.827476i	$0.310224\pi$
$912$	7.40312	0.245142
$913$	−2.38750	−0.0790148
$914$	10.2094	0.337696
$915$	5.40312	0.178622
$916$	−27.4031	−0.905425
$917$	5.40312	0.178427
$918$	−4.00000	−0.132020
$919$	24.4187	0.805500	0.402750	−	0.915310i	$-0.368054\pi$
$919$	24.4187	0.805500	0.402750	+	0.915310i	$0.368054\pi$
$920$	2.70156	0.0890679
$921$	−32.9109	−1.08445
$922$	−36.2094	−1.19249
$923$	−3.79063	−0.124770
$924$	−4.00000	−0.131590
$925$	24.5969	0.808740
$926$	28.7016	0.943192
$927$	8.70156	0.285797
$928$	−6.70156	−0.219990
$929$	−1.08907	−0.0357311	−0.0178655	−	0.999840i	$-0.505687\pi$
$929$	−1.08907	−0.0357311	−0.0178655	+	0.999840i	$0.505687\pi$
$930$	−5.40312	−0.177175
$931$	7.40312	0.242628
$932$	−26.0000	−0.851658
$933$	0.596876	0.0195408
$934$	−2.70156	−0.0883978
$935$	43.2250	1.41361
$936$	0.701562	0.0229313
$937$	5.89531	0.192592	0.0962958	−	0.995353i	$-0.469301\pi$
$937$	5.89531	0.192592	0.0962958	+	0.995353i	$0.469301\pi$
$938$	10.8062	0.352837
$939$	32.2094	1.05111
$940$	−21.8953	−0.714146
$941$	−32.3141	−1.05341	−0.526704	−	0.850049i	$-0.676572\pi$
$941$	−32.3141	−1.05341	−0.526704	+	0.850049i	$0.676572\pi$
$942$	−11.4031	−0.371534
$943$	−6.70156	−0.218233
$944$	5.40312	0.175857
$945$	−2.70156	−0.0878818
$946$	18.8062	0.611444
$947$	−28.9109	−0.939479	−0.469740	−	0.882805i	$-0.655652\pi$
$947$	−28.9109	−0.939479	−0.469740	+	0.882805i	$0.655652\pi$
$948$	8.00000	0.259828
$949$	8.00000	0.259691
$950$	−17.0156	−0.552060
$951$	−14.7016	−0.476731
$952$	−4.00000	−0.129641
$953$	−41.2250	−1.33541	−0.667704	−	0.744427i	$-0.732723\pi$
$953$	−41.2250	−1.33541	−0.667704	+	0.744427i	$0.732723\pi$
$954$	−3.40312	−0.110180
$955$	7.58125	0.245324
$956$	−14.8062	−0.478868
$957$	−26.8062	−0.866523
$958$	−29.4031	−0.949972
$959$	−13.2984	−0.429429
$960$	−2.70156	−0.0871925
$961$	−27.0000	−0.870968
$962$	7.50781	0.242062
$963$	−6.80625	−0.219328
$964$	28.9109	0.931159
$965$	10.5234	0.338761
$966$	−1.00000	−0.0321745
$967$	10.8062	0.347506	0.173753	−	0.984789i	$-0.444411\pi$
$967$	10.8062	0.347506	0.173753	+	0.984789i	$0.444411\pi$
$968$	−5.00000	−0.160706
$969$	29.6125	0.951290
$970$	34.3141	1.10176
$971$	−39.8219	−1.27794	−0.638972	−	0.769230i	$-0.720640\pi$
$971$	−39.8219	−1.27794	−0.638972	+	0.769230i	$0.720640\pi$
$972$	1.00000	0.0320750
$973$	11.2984	0.362211
$974$	12.7016	0.406984
$975$	−1.61250	−0.0516412
$976$	−2.00000	−0.0640184
$977$	−53.7172	−1.71856	−0.859282	−	0.511501i	$-0.829090\pi$
$977$	−53.7172	−1.71856	−0.859282	+	0.511501i	$0.829090\pi$
$978$	−14.8062	−0.473452
$979$	−5.61250	−0.179376
$980$	−2.70156	−0.0862982
$981$	−1.29844	−0.0414559
$982$	−41.6125	−1.32791
$983$	3.79063	0.120902	0.0604511	−	0.998171i	$-0.480746\pi$
$983$	3.79063	0.120902	0.0604511	+	0.998171i	$0.480746\pi$
$984$	6.70156	0.213638
$985$	25.6859	0.818422
$986$	−26.8062	−0.853685
$987$	8.10469	0.257975
$988$	−5.19375	−0.165235
$989$	4.70156	0.149501
$990$	−10.8062	−0.343445
$991$	28.0000	0.889449	0.444725	−	0.895667i	$-0.353302\pi$
$991$	28.0000	0.889449	0.444725	+	0.895667i	$0.353302\pi$
$992$	2.00000	0.0635001
$993$	−20.0000	−0.634681
$994$	−5.40312	−0.171377
$995$	23.5078	0.745248
$996$	0.596876	0.0189127
$997$	−10.5969	−0.335606	−0.167803	−	0.985821i	$-0.553667\pi$
$997$	−10.5969	−0.335606	−0.167803	+	0.985821i	$0.553667\pi$
$998$	10.5969	0.335438
$999$	10.7016	0.338582

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.a.n.1.1	✓	2
3.2	odd	2		2898.2.a.bb.1.2		2
4.3	odd	2		7728.2.a.bc.1.1		2
7.6	odd	2		6762.2.a.bo.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.a.n.1.1	✓	2	1.1	even	1	trivial
2898.2.a.bb.1.2		2	3.2	odd	2
6762.2.a.bo.1.2		2	7.6	odd	2
7728.2.a.bc.1.1		2	4.3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.70156 q^{5} -1.00000 q^{6} +1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.70156 q^{10} -4.00000 q^{11} +1.00000 q^{12} -0.701562 q^{13} -1.00000 q^{14} -2.70156 q^{15} +1.00000 q^{16} +4.00000 q^{17} -1.00000 q^{18} +7.40312 q^{19} -2.70156 q^{20} +1.00000 q^{21} +4.00000 q^{22} +1.00000 q^{23} -1.00000 q^{24} +2.29844 q^{25} +0.701562 q^{26} +1.00000 q^{27} +1.00000 q^{28} +6.70156 q^{29} +2.70156 q^{30} -2.00000 q^{31} -1.00000 q^{32} -4.00000 q^{33} -4.00000 q^{34} -2.70156 q^{35} +1.00000 q^{36} +10.7016 q^{37} -7.40312 q^{38} -0.701562 q^{39} +2.70156 q^{40} -6.70156 q^{41} -1.00000 q^{42} +4.70156 q^{43} -4.00000 q^{44} -2.70156 q^{45} -1.00000 q^{46} +8.10469 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.29844 q^{50} +4.00000 q^{51} -0.701562 q^{52} +3.40312 q^{53} -1.00000 q^{54} +10.8062 q^{55} -1.00000 q^{56} +7.40312 q^{57} -6.70156 q^{58} +5.40312 q^{59} -2.70156 q^{60} -2.00000 q^{61} +2.00000 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.89531 q^{65} +4.00000 q^{66} -10.8062 q^{67} +4.00000 q^{68} +1.00000 q^{69} +2.70156 q^{70} +5.40312 q^{71} -1.00000 q^{72} -11.4031 q^{73} -10.7016 q^{74} +2.29844 q^{75} +7.40312 q^{76} -4.00000 q^{77} +0.701562 q^{78} +8.00000 q^{79} -2.70156 q^{80} +1.00000 q^{81} +6.70156 q^{82} +0.596876 q^{83} +1.00000 q^{84} -10.8062 q^{85} -4.70156 q^{86} +6.70156 q^{87} +4.00000 q^{88} +1.40312 q^{89} +2.70156 q^{90} -0.701562 q^{91} +1.00000 q^{92} -2.00000 q^{93} -8.10469 q^{94} -20.0000 q^{95} -1.00000 q^{96} +12.7016 q^{97} -1.00000 q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} + 2 q^{7} - 2 q^{8} + 2 q^{9} - q^{10} - 8 q^{11} + 2 q^{12} + 5 q^{13} - 2 q^{14} + q^{15} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + q^{20} + 2 q^{21} + 8 q^{22} + 2 q^{23} - 2 q^{24} + 11 q^{25} - 5 q^{26} + 2 q^{27} + 2 q^{28} + 7 q^{29} - q^{30} - 4 q^{31} - 2 q^{32} - 8 q^{33} - 8 q^{34} + q^{35} + 2 q^{36} + 15 q^{37} - 2 q^{38} + 5 q^{39} - q^{40} - 7 q^{41} - 2 q^{42} + 3 q^{43} - 8 q^{44} + q^{45} - 2 q^{46} - 3 q^{47} + 2 q^{48} + 2 q^{49} - 11 q^{50} + 8 q^{51} + 5 q^{52} - 6 q^{53} - 2 q^{54} - 4 q^{55} - 2 q^{56} + 2 q^{57} - 7 q^{58} - 2 q^{59} + q^{60} - 4 q^{61} + 4 q^{62} + 2 q^{63} + 2 q^{64} + 23 q^{65} + 8 q^{66} + 4 q^{67} + 8 q^{68} + 2 q^{69} - q^{70} - 2 q^{71} - 2 q^{72} - 10 q^{73} - 15 q^{74} + 11 q^{75} + 2 q^{76} - 8 q^{77} - 5 q^{78} + 16 q^{79} + q^{80} + 2 q^{81} + 7 q^{82} + 14 q^{83} + 2 q^{84} + 4 q^{85} - 3 q^{86} + 7 q^{87} + 8 q^{88} - 10 q^{89} - q^{90} + 5 q^{91} + 2 q^{92} - 4 q^{93} + 3 q^{94} - 40 q^{95} - 2 q^{96} + 19 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 + q^5 - 2 * q^6 + 2 * q^7 - 2 * q^8 + 2 * q^9 - q^10 - 8 * q^11 + 2 * q^12 + 5 * q^13 - 2 * q^14 + q^15 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + q^20 + 2 * q^21 + 8 * q^22 + 2 * q^23 - 2 * q^24 + 11 * q^25 - 5 * q^26 + 2 * q^27 + 2 * q^28 + 7 * q^29 - q^30 - 4 * q^31 - 2 * q^32 - 8 * q^33 - 8 * q^34 + q^35 + 2 * q^36 + 15 * q^37 - 2 * q^38 + 5 * q^39 - q^40 - 7 * q^41 - 2 * q^42 + 3 * q^43 - 8 * q^44 + q^45 - 2 * q^46 - 3 * q^47 + 2 * q^48 + 2 * q^49 - 11 * q^50 + 8 * q^51 + 5 * q^52 - 6 * q^53 - 2 * q^54 - 4 * q^55 - 2 * q^56 + 2 * q^57 - 7 * q^58 - 2 * q^59 + q^60 - 4 * q^61 + 4 * q^62 + 2 * q^63 + 2 * q^64 + 23 * q^65 + 8 * q^66 + 4 * q^67 + 8 * q^68 + 2 * q^69 - q^70 - 2 * q^71 - 2 * q^72 - 10 * q^73 - 15 * q^74 + 11 * q^75 + 2 * q^76 - 8 * q^77 - 5 * q^78 + 16 * q^79 + q^80 + 2 * q^81 + 7 * q^82 + 14 * q^83 + 2 * q^84 + 4 * q^85 - 3 * q^86 + 7 * q^87 + 8 * q^88 - 10 * q^89 - q^90 + 5 * q^91 + 2 * q^92 - 4 * q^93 + 3 * q^94 - 40 * q^95 - 2 * q^96 + 19 * q^97 - 2 * q^98 - 8 * q^99

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