LMFDB - Embedded newform 8034.2.a.w.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} - 8 x^{10} + 94 x^{9} - 7 x^{8} - 580 x^{7} + 180 x^{6} + 1787 x^{5} - 308 x^{4} + \cdots + 768 $ x^12 - 6x^11 - 8x^10 + 94x^9 - 7x^8 - 580x^7 + 180x^6 + 1787x^5 - 308x^4 - 2790x^3 - 352x^2 + 1768*x + 768
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-0.782524$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.21809 q^{5} -1.00000 q^{6} -4.81342 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.21809 q^{5} -1.00000 q^{6} -4.81342 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.21809 q^{10} -4.29400 q^{11} +1.00000 q^{12} +1.00000 q^{13} +4.81342 q^{14} +4.21809 q^{15} +1.00000 q^{16} -2.64843 q^{17} -1.00000 q^{18} +0.655968 q^{19} +4.21809 q^{20} -4.81342 q^{21} +4.29400 q^{22} +1.52610 q^{23} -1.00000 q^{24} +12.7923 q^{25} -1.00000 q^{26} +1.00000 q^{27} -4.81342 q^{28} -0.992673 q^{29} -4.21809 q^{30} +1.93587 q^{31} -1.00000 q^{32} -4.29400 q^{33} +2.64843 q^{34} -20.3034 q^{35} +1.00000 q^{36} -7.13733 q^{37} -0.655968 q^{38} +1.00000 q^{39} -4.21809 q^{40} +7.02108 q^{41} +4.81342 q^{42} -4.82571 q^{43} -4.29400 q^{44} +4.21809 q^{45} -1.52610 q^{46} +1.34179 q^{47} +1.00000 q^{48} +16.1690 q^{49} -12.7923 q^{50} -2.64843 q^{51} +1.00000 q^{52} -1.36163 q^{53} -1.00000 q^{54} -18.1125 q^{55} +4.81342 q^{56} +0.655968 q^{57} +0.992673 q^{58} -14.8662 q^{59} +4.21809 q^{60} -9.04935 q^{61} -1.93587 q^{62} -4.81342 q^{63} +1.00000 q^{64} +4.21809 q^{65} +4.29400 q^{66} +3.79388 q^{67} -2.64843 q^{68} +1.52610 q^{69} +20.3034 q^{70} +4.83297 q^{71} -1.00000 q^{72} +1.21359 q^{73} +7.13733 q^{74} +12.7923 q^{75} +0.655968 q^{76} +20.6688 q^{77} -1.00000 q^{78} -14.6709 q^{79} +4.21809 q^{80} +1.00000 q^{81} -7.02108 q^{82} +8.38742 q^{83} -4.81342 q^{84} -11.1713 q^{85} +4.82571 q^{86} -0.992673 q^{87} +4.29400 q^{88} +12.2086 q^{89} -4.21809 q^{90} -4.81342 q^{91} +1.52610 q^{92} +1.93587 q^{93} -1.34179 q^{94} +2.76693 q^{95} -1.00000 q^{96} +2.87820 q^{97} -16.1690 q^{98} -4.29400 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * 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
$5$	4.21809	1.88639	0.943193	−	0.332244i	$-0.107806\pi$
$5$	4.21809	1.88639	0.943193	+	0.332244i	$0.107806\pi$
$6$	−1.00000	−0.408248
$7$	−4.81342	−1.81930	−0.909651	−	0.415374i	$-0.863651\pi$
$7$	−4.81342	−1.81930	−0.909651	+	0.415374i	$0.863651\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−4.21809	−1.33388
$11$	−4.29400	−1.29469	−0.647345	−	0.762197i	$-0.724121\pi$
$11$	−4.29400	−1.29469	−0.647345	+	0.762197i	$0.724121\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.81342	1.28644
$15$	4.21809	1.08911
$16$	1.00000	0.250000
$17$	−2.64843	−0.642338	−0.321169	−	0.947022i	$-0.604076\pi$
$17$	−2.64843	−0.642338	−0.321169	+	0.947022i	$0.604076\pi$
$18$	−1.00000	−0.235702
$19$	0.655968	0.150489	0.0752446	−	0.997165i	$-0.476026\pi$
$19$	0.655968	0.150489	0.0752446	+	0.997165i	$0.476026\pi$
$20$	4.21809	0.943193
$21$	−4.81342	−1.05037
$22$	4.29400	0.915485
$23$	1.52610	0.318215	0.159107	−	0.987261i	$-0.449138\pi$
$23$	1.52610	0.318215	0.159107	+	0.987261i	$0.449138\pi$
$24$	−1.00000	−0.204124
$25$	12.7923	2.55846
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	−4.81342	−0.909651
$29$	−0.992673	−0.184335	−0.0921674	−	0.995744i	$-0.529379\pi$
$29$	−0.992673	−0.184335	−0.0921674	+	0.995744i	$0.529379\pi$
$30$	−4.21809	−0.770114
$31$	1.93587	0.347692	0.173846	−	0.984773i	$-0.444380\pi$
$31$	1.93587	0.347692	0.173846	+	0.984773i	$0.444380\pi$
$32$	−1.00000	−0.176777
$33$	−4.29400	−0.747490
$34$	2.64843	0.454202
$35$	−20.3034	−3.43191
$36$	1.00000	0.166667
$37$	−7.13733	−1.17337	−0.586685	−	0.809815i	$-0.699567\pi$
$37$	−7.13733	−1.17337	−0.586685	+	0.809815i	$0.699567\pi$
$38$	−0.655968	−0.106412
$39$	1.00000	0.160128
$40$	−4.21809	−0.666938
$41$	7.02108	1.09651	0.548254	−	0.836312i	$-0.315293\pi$
$41$	7.02108	1.09651	0.548254	+	0.836312i	$0.315293\pi$
$42$	4.81342	0.742727
$43$	−4.82571	−0.735913	−0.367957	−	0.929843i	$-0.619943\pi$
$43$	−4.82571	−0.735913	−0.367957	+	0.929843i	$0.619943\pi$
$44$	−4.29400	−0.647345
$45$	4.21809	0.628796
$46$	−1.52610	−0.225012
$47$	1.34179	0.195721	0.0978603	−	0.995200i	$-0.468800\pi$
$47$	1.34179	0.195721	0.0978603	+	0.995200i	$0.468800\pi$
$48$	1.00000	0.144338
$49$	16.1690	2.30986
$50$	−12.7923	−1.80910
$51$	−2.64843	−0.370854
$52$	1.00000	0.138675
$53$	−1.36163	−0.187034	−0.0935168	−	0.995618i	$-0.529811\pi$
$53$	−1.36163	−0.187034	−0.0935168	+	0.995618i	$0.529811\pi$
$54$	−1.00000	−0.136083
$55$	−18.1125	−2.44229
$56$	4.81342	0.643220
$57$	0.655968	0.0868850
$58$	0.992673	0.130344
$59$	−14.8662	−1.93542	−0.967710	−	0.252067i	$-0.918890\pi$
$59$	−14.8662	−1.93542	−0.967710	+	0.252067i	$0.918890\pi$
$60$	4.21809	0.544553
$61$	−9.04935	−1.15865	−0.579325	−	0.815097i	$-0.696684\pi$
$61$	−9.04935	−1.15865	−0.579325	+	0.815097i	$0.696684\pi$
$62$	−1.93587	−0.245856
$63$	−4.81342	−0.606434
$64$	1.00000	0.125000
$65$	4.21809	0.523190
$66$	4.29400	0.528555
$67$	3.79388	0.463496	0.231748	−	0.972776i	$-0.425556\pi$
$67$	3.79388	0.463496	0.231748	+	0.972776i	$0.425556\pi$
$68$	−2.64843	−0.321169
$69$	1.52610	0.183721
$70$	20.3034	2.42672
$71$	4.83297	0.573568	0.286784	−	0.957995i	$-0.407414\pi$
$71$	4.83297	0.573568	0.286784	+	0.957995i	$0.407414\pi$
$72$	−1.00000	−0.117851
$73$	1.21359	0.142040	0.0710199	−	0.997475i	$-0.477375\pi$
$73$	1.21359	0.142040	0.0710199	+	0.997475i	$0.477375\pi$
$74$	7.13733	0.829698
$75$	12.7923	1.47713
$76$	0.655968	0.0752446
$77$	20.6688	2.35543
$78$	−1.00000	−0.113228
$79$	−14.6709	−1.65061	−0.825305	−	0.564688i	$-0.808997\pi$
$79$	−14.6709	−1.65061	−0.825305	+	0.564688i	$0.808997\pi$
$80$	4.21809	0.471597
$81$	1.00000	0.111111
$82$	−7.02108	−0.775348
$83$	8.38742	0.920639	0.460319	−	0.887753i	$-0.347735\pi$
$83$	8.38742	0.920639	0.460319	+	0.887753i	$0.347735\pi$
$84$	−4.81342	−0.525187
$85$	−11.1713	−1.21170
$86$	4.82571	0.520369
$87$	−0.992673	−0.106426
$88$	4.29400	0.457742
$89$	12.2086	1.29410	0.647052	−	0.762446i	$-0.276002\pi$
$89$	12.2086	1.29410	0.647052	+	0.762446i	$0.276002\pi$
$90$	−4.21809	−0.444626
$91$	−4.81342	−0.504584
$92$	1.52610	0.159107
$93$	1.93587	0.200740
$94$	−1.34179	−0.138395
$95$	2.76693	0.283881
$96$	−1.00000	−0.102062
$97$	2.87820	0.292237	0.146118	−	0.989267i	$-0.453322\pi$
$97$	2.87820	0.292237	0.146118	+	0.989267i	$0.453322\pi$
$98$	−16.1690	−1.63332
$99$	−4.29400	−0.431564
$100$	12.7923	1.27923
$101$	−14.6408	−1.45681	−0.728405	−	0.685147i	$-0.759738\pi$
$101$	−14.6408	−1.45681	−0.728405	+	0.685147i	$0.759738\pi$
$102$	2.64843	0.262233
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−20.3034	−1.98141
$106$	1.36163	0.132253
$107$	−13.4887	−1.30401	−0.652003	−	0.758216i	$-0.726071\pi$
$107$	−13.4887	−1.30401	−0.652003	+	0.758216i	$0.726071\pi$
$108$	1.00000	0.0962250
$109$	−2.10949	−0.202052	−0.101026	−	0.994884i	$-0.532213\pi$
$109$	−2.10949	−0.202052	−0.101026	+	0.994884i	$0.532213\pi$
$110$	18.1125	1.72696
$111$	−7.13733	−0.677446
$112$	−4.81342	−0.454825
$113$	−3.48546	−0.327884	−0.163942	−	0.986470i	$-0.552421\pi$
$113$	−3.48546	−0.327884	−0.163942	+	0.986470i	$0.552421\pi$
$114$	−0.655968	−0.0614370
$115$	6.43724	0.600276
$116$	−0.992673	−0.0921674
$117$	1.00000	0.0924500
$118$	14.8662	1.36855
$119$	12.7480	1.16861
$120$	−4.21809	−0.385057
$121$	7.43847	0.676225
$122$	9.04935	0.819289
$123$	7.02108	0.633069
$124$	1.93587	0.173846
$125$	32.8685	2.93985
$126$	4.81342	0.428814
$127$	−18.7851	−1.66691	−0.833456	−	0.552585i	$-0.813641\pi$
$127$	−18.7851	−1.66691	−0.833456	+	0.552585i	$0.813641\pi$
$128$	−1.00000	−0.0883883
$129$	−4.82571	−0.424880
$130$	−4.21809	−0.369951
$131$	−2.17667	−0.190176	−0.0950881	−	0.995469i	$-0.530313\pi$
$131$	−2.17667	−0.190176	−0.0950881	+	0.995469i	$0.530313\pi$
$132$	−4.29400	−0.373745
$133$	−3.15745	−0.273785
$134$	−3.79388	−0.327741
$135$	4.21809	0.363035
$136$	2.64843	0.227101
$137$	10.6655	0.911213	0.455606	−	0.890181i	$-0.349422\pi$
$137$	10.6655	0.911213	0.455606	+	0.890181i	$0.349422\pi$
$138$	−1.52610	−0.129911
$139$	−7.36838	−0.624978	−0.312489	−	0.949921i	$-0.601163\pi$
$139$	−7.36838	−0.624978	−0.312489	+	0.949921i	$0.601163\pi$
$140$	−20.3034	−1.71595
$141$	1.34179	0.112999
$142$	−4.83297	−0.405574
$143$	−4.29400	−0.359083
$144$	1.00000	0.0833333
$145$	−4.18718	−0.347727
$146$	−1.21359	−0.100437
$147$	16.1690	1.33360
$148$	−7.13733	−0.586685
$149$	−4.93093	−0.403958	−0.201979	−	0.979390i	$-0.564737\pi$
$149$	−4.93093	−0.403958	−0.201979	+	0.979390i	$0.564737\pi$
$150$	−12.7923	−1.04449
$151$	−9.49514	−0.772703	−0.386352	−	0.922352i	$-0.626265\pi$
$151$	−9.49514	−0.772703	−0.386352	+	0.922352i	$0.626265\pi$
$152$	−0.655968	−0.0532060
$153$	−2.64843	−0.214113
$154$	−20.6688	−1.66554
$155$	8.16567	0.655882
$156$	1.00000	0.0800641
$157$	12.2902	0.980861	0.490430	−	0.871480i	$-0.336840\pi$
$157$	12.2902	0.980861	0.490430	+	0.871480i	$0.336840\pi$
$158$	14.6709	1.16716
$159$	−1.36163	−0.107984
$160$	−4.21809	−0.333469
$161$	−7.34578	−0.578928
$162$	−1.00000	−0.0785674
$163$	4.10109	0.321223	0.160611	−	0.987018i	$-0.448653\pi$
$163$	4.10109	0.321223	0.160611	+	0.987018i	$0.448653\pi$
$164$	7.02108	0.548254
$165$	−18.1125	−1.41006
$166$	−8.38742	−0.650990
$167$	−7.18868	−0.556277	−0.278139	−	0.960541i	$-0.589717\pi$
$167$	−7.18868	−0.556277	−0.278139	+	0.960541i	$0.589717\pi$
$168$	4.81342	0.371363
$169$	1.00000	0.0769231
$170$	11.1713	0.856800
$171$	0.655968	0.0501631
$172$	−4.82571	−0.367957
$173$	−14.0660	−1.06942	−0.534709	−	0.845036i	$-0.679579\pi$
$173$	−14.0660	−1.06942	−0.534709	+	0.845036i	$0.679579\pi$
$174$	0.992673	0.0752543
$175$	−61.5746	−4.65460
$176$	−4.29400	−0.323673
$177$	−14.8662	−1.11742
$178$	−12.2086	−0.915070
$179$	−21.1002	−1.57710	−0.788551	−	0.614969i	$-0.789169\pi$
$179$	−21.1002	−1.57710	−0.788551	+	0.614969i	$0.789169\pi$
$180$	4.21809	0.314398
$181$	−18.8679	−1.40244	−0.701219	−	0.712946i	$-0.747360\pi$
$181$	−18.8679	−1.40244	−0.701219	+	0.712946i	$0.747360\pi$
$182$	4.81342	0.356794
$183$	−9.04935	−0.668947
$184$	−1.52610	−0.112506
$185$	−30.1059	−2.21343
$186$	−1.93587	−0.141945
$187$	11.3724	0.831629
$188$	1.34179	0.0978603
$189$	−4.81342	−0.350125
$190$	−2.76693	−0.200734
$191$	−1.99582	−0.144412	−0.0722062	−	0.997390i	$-0.523004\pi$
$191$	−1.99582	−0.144412	−0.0722062	+	0.997390i	$0.523004\pi$
$192$	1.00000	0.0721688
$193$	−14.0177	−1.00902	−0.504508	−	0.863407i	$-0.668326\pi$
$193$	−14.0177	−1.00902	−0.504508	+	0.863407i	$0.668326\pi$
$194$	−2.87820	−0.206643
$195$	4.21809	0.302064
$196$	16.1690	1.15493
$197$	0.236467	0.0168476	0.00842378	−	0.999965i	$-0.497319\pi$
$197$	0.236467	0.0168476	0.00842378	+	0.999965i	$0.497319\pi$
$198$	4.29400	0.305162
$199$	−21.3648	−1.51451	−0.757255	−	0.653119i	$-0.773460\pi$
$199$	−21.3648	−1.51451	−0.757255	+	0.653119i	$0.773460\pi$
$200$	−12.7923	−0.904551
$201$	3.79388	0.267599
$202$	14.6408	1.03012
$203$	4.77815	0.335361
$204$	−2.64843	−0.185427
$205$	29.6155	2.06844
$206$	1.00000	0.0696733
$207$	1.52610	0.106072
$208$	1.00000	0.0693375
$209$	−2.81673	−0.194837
$210$	20.3034	1.40107
$211$	−8.26635	−0.569079	−0.284539	−	0.958664i	$-0.591841\pi$
$211$	−8.26635	−0.569079	−0.284539	+	0.958664i	$0.591841\pi$
$212$	−1.36163	−0.0935168
$213$	4.83297	0.331150
$214$	13.4887	0.922072
$215$	−20.3553	−1.38822
$216$	−1.00000	−0.0680414
$217$	−9.31815	−0.632557
$218$	2.10949	0.142872
$219$	1.21359	0.0820067
$220$	−18.1125	−1.22114
$221$	−2.64843	−0.178153
$222$	7.13733	0.479026
$223$	−2.67211	−0.178938	−0.0894689	−	0.995990i	$-0.528517\pi$
$223$	−2.67211	−0.178938	−0.0894689	+	0.995990i	$0.528517\pi$
$224$	4.81342	0.321610
$225$	12.7923	0.852819
$226$	3.48546	0.231849
$227$	12.4207	0.824392	0.412196	−	0.911095i	$-0.364762\pi$
$227$	12.4207	0.824392	0.412196	+	0.911095i	$0.364762\pi$
$228$	0.655968	0.0434425
$229$	−24.6135	−1.62651	−0.813253	−	0.581911i	$-0.802305\pi$
$229$	−24.6135	−1.62651	−0.813253	+	0.581911i	$0.802305\pi$
$230$	−6.43724	−0.424459
$231$	20.6688	1.35991
$232$	0.992673	0.0651722
$233$	5.52696	0.362083	0.181042	−	0.983475i	$-0.442053\pi$
$233$	5.52696	0.362083	0.181042	+	0.983475i	$0.442053\pi$
$234$	−1.00000	−0.0653720
$235$	5.65980	0.369205
$236$	−14.8662	−0.967710
$237$	−14.6709	−0.952980
$238$	−12.7480	−0.826330
$239$	14.7857	0.956410	0.478205	−	0.878248i	$-0.341288\pi$
$239$	14.7857	0.956410	0.478205	+	0.878248i	$0.341288\pi$
$240$	4.21809	0.272276
$241$	−15.9625	−1.02823	−0.514117	−	0.857720i	$-0.671880\pi$
$241$	−15.9625	−1.02823	−0.514117	+	0.857720i	$0.671880\pi$
$242$	−7.43847	−0.478163
$243$	1.00000	0.0641500
$244$	−9.04935	−0.579325
$245$	68.2023	4.35729
$246$	−7.02108	−0.447647
$247$	0.655968	0.0417382
$248$	−1.93587	−0.122928
$249$	8.38742	0.531531
$250$	−32.8685	−2.07879
$251$	−7.52069	−0.474702	−0.237351	−	0.971424i	$-0.576279\pi$
$251$	−7.52069	−0.474702	−0.237351	+	0.971424i	$0.576279\pi$
$252$	−4.81342	−0.303217
$253$	−6.55309	−0.411990
$254$	18.7851	1.17869
$255$	−11.1713	−0.699574
$256$	1.00000	0.0625000
$257$	−27.5314	−1.71736	−0.858681	−	0.512511i	$-0.828715\pi$
$257$	−27.5314	−1.71736	−0.858681	+	0.512511i	$0.828715\pi$
$258$	4.82571	0.300435
$259$	34.3550	2.13471
$260$	4.21809	0.261595
$261$	−0.992673	−0.0614449
$262$	2.17667	0.134475
$263$	−4.79598	−0.295733	−0.147866	−	0.989007i	$-0.547241\pi$
$263$	−4.79598	−0.295733	−0.147866	+	0.989007i	$0.547241\pi$
$264$	4.29400	0.264278
$265$	−5.74346	−0.352818
$266$	3.15745	0.193596
$267$	12.2086	0.747151
$268$	3.79388	0.231748
$269$	−18.4173	−1.12292	−0.561462	−	0.827503i	$-0.689761\pi$
$269$	−18.4173	−1.12292	−0.561462	+	0.827503i	$0.689761\pi$
$270$	−4.21809	−0.256705
$271$	27.1420	1.64876	0.824380	−	0.566037i	$-0.191524\pi$
$271$	27.1420	1.64876	0.824380	+	0.566037i	$0.191524\pi$
$272$	−2.64843	−0.160585
$273$	−4.81342	−0.291321
$274$	−10.6655	−0.644325
$275$	−54.9301	−3.31241
$276$	1.52610	0.0918606
$277$	30.3796	1.82533	0.912667	−	0.408704i	$-0.134019\pi$
$277$	30.3796	1.82533	0.912667	+	0.408704i	$0.134019\pi$
$278$	7.36838	0.441926
$279$	1.93587	0.115897
$280$	20.3034	1.21336
$281$	−22.8883	−1.36540	−0.682700	−	0.730698i	$-0.739195\pi$
$281$	−22.8883	−1.36540	−0.682700	+	0.730698i	$0.739195\pi$
$282$	−1.34179	−0.0799026
$283$	17.8384	1.06038	0.530192	−	0.847877i	$-0.322120\pi$
$283$	17.8384	1.06038	0.530192	+	0.847877i	$0.322120\pi$
$284$	4.83297	0.286784
$285$	2.76693	0.163899
$286$	4.29400	0.253910
$287$	−33.7954	−1.99488
$288$	−1.00000	−0.0589256
$289$	−9.98583	−0.587402
$290$	4.18718	0.245880
$291$	2.87820	0.168723
$292$	1.21359	0.0710199
$293$	−15.8528	−0.926131	−0.463065	−	0.886324i	$-0.653251\pi$
$293$	−15.8528	−0.926131	−0.463065	+	0.886324i	$0.653251\pi$
$294$	−16.1690	−0.942996
$295$	−62.7071	−3.65095
$296$	7.13733	0.414849
$297$	−4.29400	−0.249163
$298$	4.93093	0.285641
$299$	1.52610	0.0882568
$300$	12.7923	0.738563
$301$	23.2282	1.33885
$302$	9.49514	0.546384
$303$	−14.6408	−0.841089
$304$	0.655968	0.0376223
$305$	−38.1710	−2.18566
$306$	2.64843	0.151401
$307$	28.0252	1.59948	0.799742	−	0.600343i	$-0.204969\pi$
$307$	28.0252	1.59948	0.799742	+	0.600343i	$0.204969\pi$
$308$	20.6688	1.17772
$309$	−1.00000	−0.0568880
$310$	−8.16567	−0.463779
$311$	−10.6744	−0.605288	−0.302644	−	0.953104i	$-0.597869\pi$
$311$	−10.6744	−0.605288	−0.302644	+	0.953104i	$0.597869\pi$
$312$	−1.00000	−0.0566139
$313$	15.8503	0.895912	0.447956	−	0.894056i	$-0.352152\pi$
$313$	15.8503	0.895912	0.447956	+	0.894056i	$0.352152\pi$
$314$	−12.2902	−0.693573
$315$	−20.3034	−1.14397
$316$	−14.6709	−0.825305
$317$	22.0671	1.23941	0.619705	−	0.784835i	$-0.287252\pi$
$317$	22.0671	1.23941	0.619705	+	0.784835i	$0.287252\pi$
$318$	1.36163	0.0763561
$319$	4.26254	0.238657
$320$	4.21809	0.235798
$321$	−13.4887	−0.752868
$322$	7.34578	0.409364
$323$	−1.73728	−0.0966650
$324$	1.00000	0.0555556
$325$	12.7923	0.709588
$326$	−4.10109	−0.227139
$327$	−2.10949	−0.116655
$328$	−7.02108	−0.387674
$329$	−6.45861	−0.356075
$330$	18.1125	0.997060
$331$	−5.84180	−0.321095	−0.160547	−	0.987028i	$-0.551326\pi$
$331$	−5.84180	−0.321095	−0.160547	+	0.987028i	$0.551326\pi$
$332$	8.38742	0.460319
$333$	−7.13733	−0.391123
$334$	7.18868	0.393347
$335$	16.0029	0.874332
$336$	−4.81342	−0.262594
$337$	6.31009	0.343732	0.171866	−	0.985120i	$-0.445020\pi$
$337$	6.31009	0.343732	0.171866	+	0.985120i	$0.445020\pi$
$338$	−1.00000	−0.0543928
$339$	−3.48546	−0.189304
$340$	−11.1713	−0.605849
$341$	−8.31263	−0.450154
$342$	−0.655968	−0.0354707
$343$	−44.1343	−2.38303
$344$	4.82571	0.260185
$345$	6.43724	0.346569
$346$	14.0660	0.756193
$347$	11.8496	0.636122	0.318061	−	0.948070i	$-0.396968\pi$
$347$	11.8496	0.636122	0.318061	+	0.948070i	$0.396968\pi$
$348$	−0.992673	−0.0532129
$349$	2.98569	0.159820	0.0799102	−	0.996802i	$-0.474537\pi$
$349$	2.98569	0.159820	0.0799102	+	0.996802i	$0.474537\pi$
$350$	61.5746	3.29130
$351$	1.00000	0.0533761
$352$	4.29400	0.228871
$353$	−33.7345	−1.79550	−0.897752	−	0.440501i	$-0.854801\pi$
$353$	−33.7345	−1.79550	−0.897752	+	0.440501i	$0.854801\pi$
$354$	14.8662	0.790132
$355$	20.3859	1.08197
$356$	12.2086	0.647052
$357$	12.7480	0.674696
$358$	21.1002	1.11518
$359$	−6.51521	−0.343860	−0.171930	−	0.985109i	$-0.555000\pi$
$359$	−6.51521	−0.343860	−0.171930	+	0.985109i	$0.555000\pi$
$360$	−4.21809	−0.222313
$361$	−18.5697	−0.977353
$362$	18.8679	0.991673
$363$	7.43847	0.390418
$364$	−4.81342	−0.252292
$365$	5.11902	0.267942
$366$	9.04935	0.473017
$367$	25.6512	1.33898	0.669490	−	0.742821i	$-0.266513\pi$
$367$	25.6512	1.33898	0.669490	+	0.742821i	$0.266513\pi$
$368$	1.52610	0.0795536
$369$	7.02108	0.365503
$370$	30.1059	1.56513
$371$	6.55407	0.340271
$372$	1.93587	0.100370
$373$	−14.8679	−0.769830	−0.384915	−	0.922952i	$-0.625769\pi$
$373$	−14.8679	−0.769830	−0.384915	+	0.922952i	$0.625769\pi$
$374$	−11.3724	−0.588051
$375$	32.8685	1.69732
$376$	−1.34179	−0.0691977
$377$	−0.992673	−0.0511253
$378$	4.81342	0.247576
$379$	−8.72164	−0.448001	−0.224000	−	0.974589i	$-0.571912\pi$
$379$	−8.72164	−0.448001	−0.224000	+	0.974589i	$0.571912\pi$
$380$	2.76693	0.141940
$381$	−18.7851	−0.962392
$382$	1.99582	0.102115
$383$	−4.66833	−0.238541	−0.119270	−	0.992862i	$-0.538055\pi$
$383$	−4.66833	−0.238541	−0.119270	+	0.992862i	$0.538055\pi$
$384$	−1.00000	−0.0510310
$385$	87.1830	4.44326
$386$	14.0177	0.713481
$387$	−4.82571	−0.245304
$388$	2.87820	0.146118
$389$	−19.0163	−0.964166	−0.482083	−	0.876126i	$-0.660120\pi$
$389$	−19.0163	−0.964166	−0.482083	+	0.876126i	$0.660120\pi$
$390$	−4.21809	−0.213591
$391$	−4.04178	−0.204401
$392$	−16.1690	−0.816658
$393$	−2.17667	−0.109798
$394$	−0.236467	−0.0119130
$395$	−61.8833	−3.11369
$396$	−4.29400	−0.215782
$397$	12.2106	0.612833	0.306416	−	0.951898i	$-0.400870\pi$
$397$	12.2106	0.612833	0.306416	+	0.951898i	$0.400870\pi$
$398$	21.3648	1.07092
$399$	−3.15745	−0.158070
$400$	12.7923	0.639614
$401$	25.4544	1.27113	0.635567	−	0.772046i	$-0.280767\pi$
$401$	25.4544	1.27113	0.635567	+	0.772046i	$0.280767\pi$
$402$	−3.79388	−0.189221
$403$	1.93587	0.0964325
$404$	−14.6408	−0.728405
$405$	4.21809	0.209599
$406$	−4.77815	−0.237136
$407$	30.6477	1.51915
$408$	2.64843	0.131117
$409$	−17.5734	−0.868951	−0.434475	−	0.900684i	$-0.643066\pi$
$409$	−17.5734	−0.868951	−0.434475	+	0.900684i	$0.643066\pi$
$410$	−29.6155	−1.46261
$411$	10.6655	0.526089
$412$	−1.00000	−0.0492665
$413$	71.5575	3.52111
$414$	−1.52610	−0.0750039
$415$	35.3789	1.73668
$416$	−1.00000	−0.0490290
$417$	−7.36838	−0.360831
$418$	2.81673	0.137771
$419$	25.0377	1.22317	0.611585	−	0.791179i	$-0.290532\pi$
$419$	25.0377	1.22317	0.611585	+	0.791179i	$0.290532\pi$
$420$	−20.3034	−0.990706
$421$	37.5028	1.82778	0.913888	−	0.405966i	$-0.133065\pi$
$421$	37.5028	1.82778	0.913888	+	0.405966i	$0.133065\pi$
$422$	8.26635	0.402400
$423$	1.34179	0.0652402
$424$	1.36163	0.0661264
$425$	−33.8794	−1.64339
$426$	−4.83297	−0.234158
$427$	43.5583	2.10793
$428$	−13.4887	−0.652003
$429$	−4.29400	−0.207316
$430$	20.3553	0.981618
$431$	−9.35222	−0.450480	−0.225240	−	0.974303i	$-0.572317\pi$
$431$	−9.35222	−0.450480	−0.225240	+	0.974303i	$0.572317\pi$
$432$	1.00000	0.0481125
$433$	−1.48956	−0.0715835	−0.0357917	−	0.999359i	$-0.511395\pi$
$433$	−1.48956	−0.0715835	−0.0357917	+	0.999359i	$0.511395\pi$
$434$	9.31815	0.447285
$435$	−4.18718	−0.200760
$436$	−2.10949	−0.101026
$437$	1.00107	0.0478879
$438$	−1.21359	−0.0579875
$439$	35.5882	1.69853	0.849265	−	0.527967i	$-0.177045\pi$
$439$	35.5882	1.69853	0.849265	+	0.527967i	$0.177045\pi$
$440$	18.1125	0.863479
$441$	16.1690	0.769953
$442$	2.64843	0.125973
$443$	−3.05759	−0.145270	−0.0726352	−	0.997359i	$-0.523141\pi$
$443$	−3.05759	−0.145270	−0.0726352	+	0.997359i	$0.523141\pi$
$444$	−7.13733	−0.338723
$445$	51.4968	2.44118
$446$	2.67211	0.126528
$447$	−4.93093	−0.233225
$448$	−4.81342	−0.227413
$449$	−5.76893	−0.272253	−0.136126	−	0.990691i	$-0.543465\pi$
$449$	−5.76893	−0.272253	−0.136126	+	0.990691i	$0.543465\pi$
$450$	−12.7923	−0.603034
$451$	−30.1485	−1.41964
$452$	−3.48546	−0.163942
$453$	−9.49514	−0.446120
$454$	−12.4207	−0.582933
$455$	−20.3034	−0.951840
$456$	−0.655968	−0.0307185
$457$	28.6429	1.33986	0.669929	−	0.742425i	$-0.266324\pi$
$457$	28.6429	1.33986	0.669929	+	0.742425i	$0.266324\pi$
$458$	24.6135	1.15011
$459$	−2.64843	−0.123618
$460$	6.43724	0.300138
$461$	8.15612	0.379868	0.189934	−	0.981797i	$-0.439173\pi$
$461$	8.15612	0.379868	0.189934	+	0.981797i	$0.439173\pi$
$462$	−20.6688	−0.961602
$463$	−10.4360	−0.485001	−0.242501	−	0.970151i	$-0.577968\pi$
$463$	−10.4360	−0.485001	−0.242501	+	0.970151i	$0.577968\pi$
$464$	−0.992673	−0.0460837
$465$	8.16567	0.378674
$466$	−5.52696	−0.256031
$467$	−29.0299	−1.34334	−0.671671	−	0.740850i	$-0.734423\pi$
$467$	−29.0299	−1.34334	−0.671671	+	0.740850i	$0.734423\pi$
$468$	1.00000	0.0462250
$469$	−18.2615	−0.843239
$470$	−5.65980	−0.261067
$471$	12.2902	0.566300
$472$	14.8662	0.684274
$473$	20.7216	0.952780
$474$	14.6709	0.673858
$475$	8.39132	0.385020
$476$	12.7480	0.584303
$477$	−1.36163	−0.0623445
$478$	−14.7857	−0.676284
$479$	12.8742	0.588238	0.294119	−	0.955769i	$-0.404974\pi$
$479$	12.8742	0.588238	0.294119	+	0.955769i	$0.404974\pi$
$480$	−4.21809	−0.192529
$481$	−7.13733	−0.325434
$482$	15.9625	0.727071
$483$	−7.34578	−0.334244
$484$	7.43847	0.338112
$485$	12.1405	0.551272
$486$	−1.00000	−0.0453609
$487$	1.48082	0.0671023	0.0335511	−	0.999437i	$-0.489318\pi$
$487$	1.48082	0.0671023	0.0335511	+	0.999437i	$0.489318\pi$
$488$	9.04935	0.409645
$489$	4.10109	0.185458
$490$	−68.2023	−3.08107
$491$	11.9383	0.538769	0.269384	−	0.963033i	$-0.413180\pi$
$491$	11.9383	0.538769	0.269384	+	0.963033i	$0.413180\pi$
$492$	7.02108	0.316535
$493$	2.62902	0.118405
$494$	−0.655968	−0.0295134
$495$	−18.1125	−0.814096
$496$	1.93587	0.0869231
$497$	−23.2631	−1.04349
$498$	−8.38742	−0.375849
$499$	−41.2431	−1.84629	−0.923147	−	0.384447i	$-0.874392\pi$
$499$	−41.2431	−1.84629	−0.923147	+	0.384447i	$0.874392\pi$
$500$	32.8685	1.46993
$501$	−7.18868	−0.321167
$502$	7.52069	0.335665
$503$	−13.4839	−0.601217	−0.300608	−	0.953748i	$-0.597190\pi$
$503$	−13.4839	−0.601217	−0.300608	+	0.953748i	$0.597190\pi$
$504$	4.81342	0.214407
$505$	−61.7560	−2.74811
$506$	6.55309	0.291321
$507$	1.00000	0.0444116
$508$	−18.7851	−0.833456
$509$	16.7375	0.741877	0.370939	−	0.928657i	$-0.379036\pi$
$509$	16.7375	0.741877	0.370939	+	0.928657i	$0.379036\pi$
$510$	11.1713	0.494674
$511$	−5.84151	−0.258413
$512$	−1.00000	−0.0441942
$513$	0.655968	0.0289617
$514$	27.5314	1.21436
$515$	−4.21809	−0.185871
$516$	−4.82571	−0.212440
$517$	−5.76166	−0.253398
$518$	−34.3550	−1.50947
$519$	−14.0660	−0.617429
$520$	−4.21809	−0.184975
$521$	30.8017	1.34945	0.674723	−	0.738071i	$-0.264263\pi$
$521$	30.8017	1.34945	0.674723	+	0.738071i	$0.264263\pi$
$522$	0.992673	0.0434481
$523$	7.33470	0.320724	0.160362	−	0.987058i	$-0.448734\pi$
$523$	7.33470	0.320724	0.160362	+	0.987058i	$0.448734\pi$
$524$	−2.17667	−0.0950881
$525$	−61.5746	−2.68734
$526$	4.79598	0.209115
$527$	−5.12701	−0.223336
$528$	−4.29400	−0.186873
$529$	−20.6710	−0.898739
$530$	5.74346	0.249480
$531$	−14.8662	−0.645140
$532$	−3.15745	−0.136893
$533$	7.02108	0.304117
$534$	−12.2086	−0.528316
$535$	−56.8967	−2.45986
$536$	−3.79388	−0.163870
$537$	−21.1002	−0.910541
$538$	18.4173	0.794026
$539$	−69.4298	−2.99055
$540$	4.21809	0.181518
$541$	15.0975	0.649091	0.324545	−	0.945870i	$-0.394789\pi$
$541$	15.0975	0.649091	0.324545	+	0.945870i	$0.394789\pi$
$542$	−27.1420	−1.16585
$543$	−18.8679	−0.809698
$544$	2.64843	0.113550
$545$	−8.89800	−0.381149
$546$	4.81342	0.205995
$547$	−9.07339	−0.387950	−0.193975	−	0.981006i	$-0.562138\pi$
$547$	−9.07339	−0.387950	−0.193975	+	0.981006i	$0.562138\pi$
$548$	10.6655	0.455606
$549$	−9.04935	−0.386217
$550$	54.9301	2.34223
$551$	−0.651161	−0.0277404
$552$	−1.52610	−0.0649553
$553$	70.6174	3.00296
$554$	−30.3796	−1.29071
$555$	−30.1059	−1.27792
$556$	−7.36838	−0.312489
$557$	25.0527	1.06152	0.530758	−	0.847523i	$-0.321907\pi$
$557$	25.0527	1.06152	0.530758	+	0.847523i	$0.321907\pi$
$558$	−1.93587	−0.0819518
$559$	−4.82571	−0.204106
$560$	−20.3034	−0.857977
$561$	11.3724	0.480141
$562$	22.8883	0.965484
$563$	27.3887	1.15430	0.577149	−	0.816639i	$-0.304165\pi$
$563$	27.3887	1.15430	0.577149	+	0.816639i	$0.304165\pi$
$564$	1.34179	0.0564997
$565$	−14.7020	−0.618516
$566$	−17.8384	−0.749805
$567$	−4.81342	−0.202145
$568$	−4.83297	−0.202787
$569$	7.91850	0.331961	0.165980	−	0.986129i	$-0.446921\pi$
$569$	7.91850	0.331961	0.165980	+	0.986129i	$0.446921\pi$
$570$	−2.76693	−0.115894
$571$	19.1442	0.801161	0.400581	−	0.916262i	$-0.368808\pi$
$571$	19.1442	0.801161	0.400581	+	0.916262i	$0.368808\pi$
$572$	−4.29400	−0.179541
$573$	−1.99582	−0.0833766
$574$	33.7954	1.41059
$575$	19.5223	0.814138
$576$	1.00000	0.0416667
$577$	35.7241	1.48721	0.743607	−	0.668617i	$-0.233113\pi$
$577$	35.7241	1.48721	0.743607	+	0.668617i	$0.233113\pi$
$578$	9.98583	0.415356
$579$	−14.0177	−0.582555
$580$	−4.18718	−0.173863
$581$	−40.3722	−1.67492
$582$	−2.87820	−0.119305
$583$	5.84682	0.242151
$584$	−1.21359	−0.0502186
$585$	4.21809	0.174397
$586$	15.8528	0.654873
$587$	−29.4458	−1.21536	−0.607680	−	0.794182i	$-0.707900\pi$
$587$	−29.4458	−1.21536	−0.607680	+	0.794182i	$0.707900\pi$
$588$	16.1690	0.666799
$589$	1.26987	0.0523239
$590$	62.7071	2.58161
$591$	0.236467	0.00972694
$592$	−7.13733	−0.293343
$593$	−43.7704	−1.79743	−0.898717	−	0.438528i	$-0.855500\pi$
$593$	−43.7704	−1.79743	−0.898717	+	0.438528i	$0.855500\pi$
$594$	4.29400	0.176185
$595$	53.7722	2.20444
$596$	−4.93093	−0.201979
$597$	−21.3648	−0.874403
$598$	−1.52610	−0.0624070
$599$	−37.2570	−1.52228	−0.761140	−	0.648588i	$-0.775360\pi$
$599$	−37.2570	−1.52228	−0.761140	+	0.648588i	$0.775360\pi$
$600$	−12.7923	−0.522243
$601$	27.2474	1.11145	0.555723	−	0.831368i	$-0.312442\pi$
$601$	27.2474	1.11145	0.555723	+	0.831368i	$0.312442\pi$
$602$	−23.2282	−0.946709
$603$	3.79388	0.154499
$604$	−9.49514	−0.386352
$605$	31.3761	1.27562
$606$	14.6408	0.594740
$607$	5.08465	0.206380	0.103190	−	0.994662i	$-0.467095\pi$
$607$	5.08465	0.206380	0.103190	+	0.994662i	$0.467095\pi$
$608$	−0.655968	−0.0266030
$609$	4.77815	0.193620
$610$	38.1710	1.54550
$611$	1.34179	0.0542831
$612$	−2.64843	−0.107056
$613$	38.3291	1.54810	0.774048	−	0.633127i	$-0.218229\pi$
$613$	38.3291	1.54810	0.774048	+	0.633127i	$0.218229\pi$
$614$	−28.0252	−1.13101
$615$	29.6155	1.19421
$616$	−20.6688	−0.832772
$617$	13.7858	0.554996	0.277498	−	0.960726i	$-0.410495\pi$
$617$	13.7858	0.554996	0.277498	+	0.960726i	$0.410495\pi$
$618$	1.00000	0.0402259
$619$	35.3882	1.42237	0.711187	−	0.703003i	$-0.248158\pi$
$619$	35.3882	1.42237	0.711187	+	0.703003i	$0.248158\pi$
$620$	8.16567	0.327941
$621$	1.52610	0.0612404
$622$	10.6744	0.428004
$623$	−58.7649	−2.35437
$624$	1.00000	0.0400320
$625$	74.6810	2.98724
$626$	−15.8503	−0.633505
$627$	−2.81673	−0.112489
$628$	12.2902	0.490430
$629$	18.9027	0.753701
$630$	20.3034	0.808908
$631$	13.8617	0.551827	0.275914	−	0.961182i	$-0.411020\pi$
$631$	13.8617	0.551827	0.275914	+	0.961182i	$0.411020\pi$
$632$	14.6709	0.583578
$633$	−8.26635	−0.328558
$634$	−22.0671	−0.876395
$635$	−79.2374	−3.14444
$636$	−1.36163	−0.0539919
$637$	16.1690	0.640640
$638$	−4.26254	−0.168756
$639$	4.83297	0.191189
$640$	−4.21809	−0.166735
$641$	39.4048	1.55640	0.778198	−	0.628019i	$-0.216134\pi$
$641$	39.4048	1.55640	0.778198	+	0.628019i	$0.216134\pi$
$642$	13.4887	0.532358
$643$	15.6956	0.618975	0.309488	−	0.950903i	$-0.399842\pi$
$643$	15.6956	0.618975	0.309488	+	0.950903i	$0.399842\pi$
$644$	−7.34578	−0.289464
$645$	−20.3553	−0.801488
$646$	1.73728	0.0683525
$647$	4.10390	0.161341	0.0806705	−	0.996741i	$-0.474294\pi$
$647$	4.10390	0.161341	0.0806705	+	0.996741i	$0.474294\pi$
$648$	−1.00000	−0.0392837
$649$	63.8357	2.50577
$650$	−12.7923	−0.501754
$651$	−9.31815	−0.365207
$652$	4.10109	0.160611
$653$	34.4890	1.34966	0.674830	−	0.737973i	$-0.264217\pi$
$653$	34.4890	1.34966	0.674830	+	0.737973i	$0.264217\pi$
$654$	2.10949	0.0824875
$655$	−9.18137	−0.358746
$656$	7.02108	0.274127
$657$	1.21359	0.0473466
$658$	6.45861	0.251783
$659$	3.43753	0.133907	0.0669535	−	0.997756i	$-0.478672\pi$
$659$	3.43753	0.133907	0.0669535	+	0.997756i	$0.478672\pi$
$660$	−18.1125	−0.705028
$661$	−21.8422	−0.849565	−0.424782	−	0.905296i	$-0.639649\pi$
$661$	−21.8422	−0.849565	−0.424782	+	0.905296i	$0.639649\pi$
$662$	5.84180	0.227048
$663$	−2.64843	−0.102856
$664$	−8.38742	−0.325495
$665$	−13.3184	−0.516465
$666$	7.13733	0.276566
$667$	−1.51492	−0.0586580
$668$	−7.18868	−0.278139
$669$	−2.67211	−0.103310
$670$	−16.0029	−0.618246
$671$	38.8579	1.50009
$672$	4.81342	0.185682
$673$	−29.9645	−1.15505	−0.577523	−	0.816374i	$-0.695981\pi$
$673$	−29.9645	−1.15505	−0.577523	+	0.816374i	$0.695981\pi$
$674$	−6.31009	−0.243055
$675$	12.7923	0.492375
$676$	1.00000	0.0384615
$677$	−32.0957	−1.23354	−0.616770	−	0.787144i	$-0.711559\pi$
$677$	−32.0957	−1.23354	−0.616770	+	0.787144i	$0.711559\pi$
$678$	3.48546	0.133858
$679$	−13.8540	−0.531667
$680$	11.1713	0.428400
$681$	12.4207	0.475963
$682$	8.31263	0.318307
$683$	−48.1248	−1.84144	−0.920722	−	0.390218i	$-0.872400\pi$
$683$	−48.1248	−1.84144	−0.920722	+	0.390218i	$0.872400\pi$
$684$	0.655968	0.0250815
$685$	44.9879	1.71890
$686$	44.1343	1.68506
$687$	−24.6135	−0.939063
$688$	−4.82571	−0.183978
$689$	−1.36163	−0.0518738
$690$	−6.43724	−0.245062
$691$	35.3486	1.34472	0.672362	−	0.740222i	$-0.265280\pi$
$691$	35.3486	1.34472	0.672362	+	0.740222i	$0.265280\pi$
$692$	−14.0660	−0.534709
$693$	20.6688	0.785145
$694$	−11.8496	−0.449806
$695$	−31.0805	−1.17895
$696$	0.992673	0.0376272
$697$	−18.5948	−0.704329
$698$	−2.98569	−0.113010
$699$	5.52696	0.209049
$700$	−61.5746	−2.32730
$701$	−14.7957	−0.558826	−0.279413	−	0.960171i	$-0.590140\pi$
$701$	−14.7957	−0.558826	−0.279413	+	0.960171i	$0.590140\pi$
$702$	−1.00000	−0.0377426
$703$	−4.68186	−0.176580
$704$	−4.29400	−0.161836
$705$	5.65980	0.213160
$706$	33.7345	1.26961
$707$	70.4721	2.65038
$708$	−14.8662	−0.558708
$709$	28.9327	1.08659	0.543296	−	0.839541i	$-0.317176\pi$
$709$	28.9327	1.08659	0.543296	+	0.839541i	$0.317176\pi$
$710$	−20.3859	−0.765070
$711$	−14.6709	−0.550203
$712$	−12.2086	−0.457535
$713$	2.95434	0.110641
$714$	−12.7480	−0.477082
$715$	−18.1125	−0.677369
$716$	−21.1002	−0.788551
$717$	14.7857	0.552184
$718$	6.51521	0.243146
$719$	−38.8020	−1.44707	−0.723534	−	0.690288i	$-0.757484\pi$
$719$	−38.8020	−1.44707	−0.723534	+	0.690288i	$0.757484\pi$
$720$	4.21809	0.157199
$721$	4.81342	0.179261
$722$	18.5697	0.691093
$723$	−15.9625	−0.593651
$724$	−18.8679	−0.701219
$725$	−12.6985	−0.471612
$726$	−7.43847	−0.276068
$727$	16.6426	0.617238	0.308619	−	0.951186i	$-0.400133\pi$
$727$	16.6426	0.617238	0.308619	+	0.951186i	$0.400133\pi$
$728$	4.81342	0.178397
$729$	1.00000	0.0370370
$730$	−5.11902	−0.189464
$731$	12.7805	0.472705
$732$	−9.04935	−0.334473
$733$	−40.2474	−1.48657	−0.743285	−	0.668975i	$-0.766733\pi$
$733$	−40.2474	−1.48657	−0.743285	+	0.668975i	$0.766733\pi$
$734$	−25.6512	−0.946802
$735$	68.2023	2.51568
$736$	−1.52610	−0.0562529
$737$	−16.2909	−0.600084
$738$	−7.02108	−0.258449
$739$	−40.9021	−1.50461	−0.752305	−	0.658815i	$-0.771058\pi$
$739$	−40.9021	−1.50461	−0.752305	+	0.658815i	$0.771058\pi$
$740$	−30.1059	−1.10672
$741$	0.655968	0.0240976
$742$	−6.55407	−0.240608
$743$	−10.1196	−0.371253	−0.185627	−	0.982620i	$-0.559432\pi$
$743$	−10.1196	−0.371253	−0.185627	+	0.982620i	$0.559432\pi$
$744$	−1.93587	−0.0709724
$745$	−20.7991	−0.762020
$746$	14.8679	0.544352
$747$	8.38742	0.306880
$748$	11.3724	0.415815
$749$	64.9270	2.37238
$750$	−32.8685	−1.20019
$751$	2.57695	0.0940342	0.0470171	−	0.998894i	$-0.485028\pi$
$751$	2.57695	0.0940342	0.0470171	+	0.998894i	$0.485028\pi$
$752$	1.34179	0.0489302
$753$	−7.52069	−0.274069
$754$	0.992673	0.0361510
$755$	−40.0513	−1.45762
$756$	−4.81342	−0.175062
$757$	39.8064	1.44679	0.723394	−	0.690435i	$-0.242581\pi$
$757$	39.8064	1.44679	0.723394	+	0.690435i	$0.242581\pi$
$758$	8.72164	0.316784
$759$	−6.55309	−0.237862
$760$	−2.76693	−0.100367
$761$	43.5365	1.57820	0.789098	−	0.614267i	$-0.210548\pi$
$761$	43.5365	1.57820	0.789098	+	0.614267i	$0.210548\pi$
$762$	18.7851	0.680514
$763$	10.1538	0.367594
$764$	−1.99582	−0.0722062
$765$	−11.1713	−0.403899
$766$	4.66833	0.168674
$767$	−14.8662	−0.536789
$768$	1.00000	0.0360844
$769$	3.22205	0.116190	0.0580950	−	0.998311i	$-0.481497\pi$
$769$	3.22205	0.116190	0.0580950	+	0.998311i	$0.481497\pi$
$770$	−87.1830	−3.14186
$771$	−27.5314	−0.991519
$772$	−14.0177	−0.504508
$773$	31.7493	1.14194	0.570971	−	0.820970i	$-0.306567\pi$
$773$	31.7493	1.14194	0.570971	+	0.820970i	$0.306567\pi$
$774$	4.82571	0.173456
$775$	24.7642	0.889555
$776$	−2.87820	−0.103321
$777$	34.3550	1.23248
$778$	19.0163	0.681768
$779$	4.60560	0.165013
$780$	4.21809	0.151032
$781$	−20.7528	−0.742594
$782$	4.04178	0.144534
$783$	−0.992673	−0.0354752
$784$	16.1690	0.577465
$785$	51.8410	1.85028
$786$	2.17667	0.0776391
$787$	−20.9982	−0.748504	−0.374252	−	0.927327i	$-0.622101\pi$
$787$	−20.9982	−0.748504	−0.374252	+	0.927327i	$0.622101\pi$
$788$	0.236467	0.00842378
$789$	−4.79598	−0.170741
$790$	61.8833	2.20171
$791$	16.7770	0.596520
$792$	4.29400	0.152581
$793$	−9.04935	−0.321352
$794$	−12.2106	−0.433338
$795$	−5.74346	−0.203699
$796$	−21.3648	−0.757255
$797$	31.6900	1.12252	0.561258	−	0.827641i	$-0.310318\pi$
$797$	31.6900	1.12252	0.561258	+	0.827641i	$0.310318\pi$
$798$	3.15745	0.111772
$799$	−3.55364	−0.125719
$800$	−12.7923	−0.452275
$801$	12.2086	0.431368
$802$	−25.4544	−0.898827
$803$	−5.21115	−0.183898
$804$	3.79388	0.133800
$805$	−30.9851	−1.09208
$806$	−1.93587	−0.0681881
$807$	−18.4173	−0.648320
$808$	14.6408	0.515060
$809$	−15.3005	−0.537937	−0.268969	−	0.963149i	$-0.586683\pi$
$809$	−15.3005	−0.537937	−0.268969	+	0.963149i	$0.586683\pi$
$810$	−4.21809	−0.148209
$811$	35.3356	1.24080	0.620400	−	0.784286i	$-0.286970\pi$
$811$	35.3356	1.24080	0.620400	+	0.784286i	$0.286970\pi$
$812$	4.77815	0.167680
$813$	27.1420	0.951912
$814$	−30.6477	−1.07420
$815$	17.2988	0.605950
$816$	−2.64843	−0.0927135
$817$	−3.16551	−0.110747
$818$	17.5734	0.614441
$819$	−4.81342	−0.168195
$820$	29.6155	1.03422
$821$	−47.5746	−1.66037	−0.830183	−	0.557491i	$-0.811764\pi$
$821$	−47.5746	−1.66037	−0.830183	+	0.557491i	$0.811764\pi$
$822$	−10.6655	−0.372001
$823$	−33.6003	−1.17123	−0.585616	−	0.810589i	$-0.699147\pi$
$823$	−33.6003	−1.17123	−0.585616	+	0.810589i	$0.699147\pi$
$824$	1.00000	0.0348367
$825$	−54.9301	−1.91242
$826$	−71.5575	−2.48980
$827$	45.2481	1.57343	0.786715	−	0.617316i	$-0.211780\pi$
$827$	45.2481	1.57343	0.786715	+	0.617316i	$0.211780\pi$
$828$	1.52610	0.0530358
$829$	2.31906	0.0805443	0.0402721	−	0.999189i	$-0.487178\pi$
$829$	2.31906	0.0805443	0.0402721	+	0.999189i	$0.487178\pi$
$830$	−35.3789	−1.22802
$831$	30.3796	1.05386
$832$	1.00000	0.0346688
$833$	−42.8225	−1.48371
$834$	7.36838	0.255146
$835$	−30.3225	−1.04935
$836$	−2.81673	−0.0974185
$837$	1.93587	0.0669134
$838$	−25.0377	−0.864911
$839$	−15.1801	−0.524076	−0.262038	−	0.965058i	$-0.584395\pi$
$839$	−15.1801	−0.524076	−0.262038	+	0.965058i	$0.584395\pi$
$840$	20.3034	0.700535
$841$	−28.0146	−0.966021
$842$	−37.5028	−1.29243
$843$	−22.8883	−0.788315
$844$	−8.26635	−0.284539
$845$	4.21809	0.145107
$846$	−1.34179	−0.0461318
$847$	−35.8045	−1.23026
$848$	−1.36163	−0.0467584
$849$	17.8384	0.612213
$850$	33.8794	1.16205
$851$	−10.8923	−0.373384
$852$	4.83297	0.165575
$853$	7.81605	0.267617	0.133808	−	0.991007i	$-0.457279\pi$
$853$	7.81605	0.267617	0.133808	+	0.991007i	$0.457279\pi$
$854$	−43.5583	−1.49053
$855$	2.76693	0.0946270
$856$	13.4887	0.461036
$857$	−49.9702	−1.70695	−0.853475	−	0.521134i	$-0.825509\pi$
$857$	−49.9702	−1.70695	−0.853475	+	0.521134i	$0.825509\pi$
$858$	4.29400	0.146595
$859$	−28.9793	−0.988761	−0.494380	−	0.869246i	$-0.664605\pi$
$859$	−28.9793	−0.988761	−0.494380	+	0.869246i	$0.664605\pi$
$860$	−20.3553	−0.694109
$861$	−33.7954	−1.15174
$862$	9.35222	0.318538
$863$	−40.7436	−1.38693	−0.693463	−	0.720492i	$-0.743916\pi$
$863$	−40.7436	−1.38693	−0.693463	+	0.720492i	$0.743916\pi$
$864$	−1.00000	−0.0340207
$865$	−59.3317	−2.01734
$866$	1.48956	0.0506172
$867$	−9.98583	−0.339137
$868$	−9.31815	−0.316279
$869$	62.9971	2.13703
$870$	4.18718	0.141959
$871$	3.79388	0.128551
$872$	2.10949	0.0714362
$873$	2.87820	0.0974123
$874$	−1.00107	−0.0338618
$875$	−158.210	−5.34847
$876$	1.21359	0.0410034
$877$	−42.0415	−1.41964	−0.709820	−	0.704384i	$-0.751224\pi$
$877$	−42.0415	−1.41964	−0.709820	+	0.704384i	$0.751224\pi$
$878$	−35.5882	−1.20104
$879$	−15.8528	−0.534702
$880$	−18.1125	−0.610572
$881$	−24.3898	−0.821714	−0.410857	−	0.911700i	$-0.634770\pi$
$881$	−24.3898	−0.821714	−0.410857	+	0.911700i	$0.634770\pi$
$882$	−16.1690	−0.544439
$883$	12.4278	0.418230	0.209115	−	0.977891i	$-0.432942\pi$
$883$	12.4278	0.418230	0.209115	+	0.977891i	$0.432942\pi$
$884$	−2.64843	−0.0890763
$885$	−62.7071	−2.10788
$886$	3.05759	0.102722
$887$	2.20287	0.0739651	0.0369826	−	0.999316i	$-0.488225\pi$
$887$	2.20287	0.0739651	0.0369826	+	0.999316i	$0.488225\pi$
$888$	7.13733	0.239513
$889$	90.4208	3.03262
$890$	−51.4968	−1.72618
$891$	−4.29400	−0.143855
$892$	−2.67211	−0.0894689
$893$	0.880173	0.0294539
$894$	4.93093	0.164915
$895$	−89.0025	−2.97503
$896$	4.81342	0.160805
$897$	1.52610	0.0509551
$898$	5.76893	0.192512
$899$	−1.92168	−0.0640918
$900$	12.7923	0.426409
$901$	3.60617	0.120139
$902$	30.1485	1.00384
$903$	23.2282	0.772984
$904$	3.48546	0.115925
$905$	−79.5864	−2.64554
$906$	9.49514	0.315455
$907$	18.8620	0.626303	0.313152	−	0.949703i	$-0.398615\pi$
$907$	18.8620	0.626303	0.313152	+	0.949703i	$0.398615\pi$
$908$	12.4207	0.412196
$909$	−14.6408	−0.485603
$910$	20.3034	0.673052
$911$	7.57458	0.250957	0.125479	−	0.992096i	$-0.459953\pi$
$911$	7.57458	0.250957	0.125479	+	0.992096i	$0.459953\pi$
$912$	0.655968	0.0217213
$913$	−36.0156	−1.19194
$914$	−28.6429	−0.947423
$915$	−38.1710	−1.26189
$916$	−24.6135	−0.813253
$917$	10.4772	0.345988
$918$	2.64843	0.0874111
$919$	−35.9284	−1.18517	−0.592584	−	0.805508i	$-0.701892\pi$
$919$	−35.9284	−1.18517	−0.592584	+	0.805508i	$0.701892\pi$
$920$	−6.43724	−0.212230
$921$	28.0252	0.923463
$922$	−8.15612	−0.268607
$923$	4.83297	0.159079
$924$	20.6688	0.679955
$925$	−91.3028	−3.00202
$926$	10.4360	0.342948
$927$	−1.00000	−0.0328443
$928$	0.992673	0.0325861
$929$	−16.4262	−0.538927	−0.269464	−	0.963011i	$-0.586846\pi$
$929$	−16.4262	−0.538927	−0.269464	+	0.963011i	$0.586846\pi$
$930$	−8.16567	−0.267763
$931$	10.6063	0.347609
$932$	5.52696	0.181042
$933$	−10.6744	−0.349463
$934$	29.0299	0.949886
$935$	47.9696	1.56877
$936$	−1.00000	−0.0326860
$937$	51.2234	1.67340	0.836698	−	0.547665i	$-0.184483\pi$
$937$	51.2234	1.67340	0.836698	+	0.547665i	$0.184483\pi$
$938$	18.2615	0.596260
$939$	15.8503	0.517255
$940$	5.65980	0.184602
$941$	22.0325	0.718238	0.359119	−	0.933292i	$-0.383077\pi$
$941$	22.0325	0.718238	0.359119	+	0.933292i	$0.383077\pi$
$942$	−12.2902	−0.400435
$943$	10.7149	0.348925
$944$	−14.8662	−0.483855
$945$	−20.3034	−0.660471
$946$	−20.7216	−0.673717
$947$	−36.1189	−1.17371	−0.586854	−	0.809693i	$-0.699634\pi$
$947$	−36.1189	−1.17371	−0.586854	+	0.809693i	$0.699634\pi$
$948$	−14.6709	−0.476490
$949$	1.21359	0.0393947
$950$	−8.39132	−0.272250
$951$	22.0671	0.715574
$952$	−12.7480	−0.413165
$953$	−25.1622	−0.815083	−0.407541	−	0.913187i	$-0.633614\pi$
$953$	−25.1622	−0.815083	−0.407541	+	0.913187i	$0.633614\pi$
$954$	1.36163	0.0440842
$955$	−8.41855	−0.272418
$956$	14.7857	0.478205
$957$	4.26254	0.137788
$958$	−12.8742	−0.415947
$959$	−51.3374	−1.65777
$960$	4.21809	0.136138
$961$	−27.2524	−0.879110
$962$	7.13733	0.230117
$963$	−13.4887	−0.434669
$964$	−15.9625	−0.514117
$965$	−59.1279	−1.90339
$966$	7.34578	0.236347
$967$	−1.46713	−0.0471797	−0.0235898	−	0.999722i	$-0.507510\pi$
$967$	−1.46713	−0.0471797	−0.0235898	+	0.999722i	$0.507510\pi$
$968$	−7.43847	−0.239082
$969$	−1.73728	−0.0558096
$970$	−12.1405	−0.389808
$971$	40.7250	1.30693	0.653464	−	0.756957i	$-0.273315\pi$
$971$	40.7250	1.30693	0.653464	+	0.756957i	$0.273315\pi$
$972$	1.00000	0.0320750
$973$	35.4671	1.13702
$974$	−1.48082	−0.0474485
$975$	12.7923	0.409681
$976$	−9.04935	−0.289663
$977$	−15.3214	−0.490176	−0.245088	−	0.969501i	$-0.578817\pi$
$977$	−15.3214	−0.490176	−0.245088	+	0.969501i	$0.578817\pi$
$978$	−4.10109	−0.131139
$979$	−52.4236	−1.67547
$980$	68.2023	2.17864
$981$	−2.10949	−0.0673507
$982$	−11.9383	−0.380967
$983$	15.3087	0.488272	0.244136	−	0.969741i	$-0.421496\pi$
$983$	15.3087	0.488272	0.244136	+	0.969741i	$0.421496\pi$
$984$	−7.02108	−0.223824
$985$	0.997438	0.0317810
$986$	−2.62902	−0.0837251
$987$	−6.45861	−0.205580
$988$	0.655968	0.0208691
$989$	−7.36453	−0.234178
$990$	18.1125	0.575653
$991$	56.9074	1.80772	0.903862	−	0.427825i	$-0.140720\pi$
$991$	56.9074	1.80772	0.903862	+	0.427825i	$0.140720\pi$
$992$	−1.93587	−0.0614639
$993$	−5.84180	−0.185384
$994$	23.2631	0.737862
$995$	−90.1186	−2.85695
$996$	8.38742	0.265766
$997$	58.7078	1.85930	0.929648	−	0.368449i	$-0.120111\pi$
$997$	58.7078	1.85930	0.929648	+	0.368449i	$0.120111\pi$
$998$	41.2431	1.30553
$999$	−7.13733	−0.225815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.w.1.12	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.w.1.12	✓	12	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.21809 q^{5} -1.00000 q^{6} -4.81342 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +4.21809 q^{5} -1.00000 q^{6} -4.81342 q^{7} -1.00000 q^{8} +1.00000 q^{9} -4.21809 q^{10} -4.29400 q^{11} +1.00000 q^{12} +1.00000 q^{13} +4.81342 q^{14} +4.21809 q^{15} +1.00000 q^{16} -2.64843 q^{17} -1.00000 q^{18} +0.655968 q^{19} +4.21809 q^{20} -4.81342 q^{21} +4.29400 q^{22} +1.52610 q^{23} -1.00000 q^{24} +12.7923 q^{25} -1.00000 q^{26} +1.00000 q^{27} -4.81342 q^{28} -0.992673 q^{29} -4.21809 q^{30} +1.93587 q^{31} -1.00000 q^{32} -4.29400 q^{33} +2.64843 q^{34} -20.3034 q^{35} +1.00000 q^{36} -7.13733 q^{37} -0.655968 q^{38} +1.00000 q^{39} -4.21809 q^{40} +7.02108 q^{41} +4.81342 q^{42} -4.82571 q^{43} -4.29400 q^{44} +4.21809 q^{45} -1.52610 q^{46} +1.34179 q^{47} +1.00000 q^{48} +16.1690 q^{49} -12.7923 q^{50} -2.64843 q^{51} +1.00000 q^{52} -1.36163 q^{53} -1.00000 q^{54} -18.1125 q^{55} +4.81342 q^{56} +0.655968 q^{57} +0.992673 q^{58} -14.8662 q^{59} +4.21809 q^{60} -9.04935 q^{61} -1.93587 q^{62} -4.81342 q^{63} +1.00000 q^{64} +4.21809 q^{65} +4.29400 q^{66} +3.79388 q^{67} -2.64843 q^{68} +1.52610 q^{69} +20.3034 q^{70} +4.83297 q^{71} -1.00000 q^{72} +1.21359 q^{73} +7.13733 q^{74} +12.7923 q^{75} +0.655968 q^{76} +20.6688 q^{77} -1.00000 q^{78} -14.6709 q^{79} +4.21809 q^{80} +1.00000 q^{81} -7.02108 q^{82} +8.38742 q^{83} -4.81342 q^{84} -11.1713 q^{85} +4.82571 q^{86} -0.992673 q^{87} +4.29400 q^{88} +12.2086 q^{89} -4.21809 q^{90} -4.81342 q^{91} +1.52610 q^{92} +1.93587 q^{93} -1.34179 q^{94} +2.76693 q^{95} -1.00000 q^{96} +2.87820 q^{97} -16.1690 q^{98} -4.29400 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9	\( 12 q - 12 q^{2} + 12 q^{3} + 12 q^{4} - 4 q^{5} - 12 q^{6} - 12 q^{8} + 12 q^{9} + 4 q^{10} - 9 q^{11} + 12 q^{12} + 12 q^{13} - 4 q^{15} + 12 q^{16} - 20 q^{17} - 12 q^{18} + 4 q^{19} - 4 q^{20} + 9 q^{22} - 30 q^{23} - 12 q^{24} + 14 q^{25} - 12 q^{26} + 12 q^{27} - 29 q^{29} + 4 q^{30} + 6 q^{31} - 12 q^{32} - 9 q^{33} + 20 q^{34} - 22 q^{35} + 12 q^{36} + 7 q^{37} - 4 q^{38} + 12 q^{39} + 4 q^{40} - 8 q^{41} - 8 q^{43} - 9 q^{44} - 4 q^{45} + 30 q^{46} - 16 q^{47} + 12 q^{48} + 10 q^{49} - 14 q^{50} - 20 q^{51} + 12 q^{52} - 9 q^{53} - 12 q^{54} - 20 q^{55} + 4 q^{57} + 29 q^{58} - 29 q^{59} - 4 q^{60} - 26 q^{61} - 6 q^{62} + 12 q^{64} - 4 q^{65} + 9 q^{66} + 12 q^{67} - 20 q^{68} - 30 q^{69} + 22 q^{70} - 35 q^{71} - 12 q^{72} + 18 q^{73} - 7 q^{74} + 14 q^{75} + 4 q^{76} - 25 q^{77} - 12 q^{78} - 37 q^{79} - 4 q^{80} + 12 q^{81} + 8 q^{82} - 24 q^{83} - 17 q^{85} + 8 q^{86} - 29 q^{87} + 9 q^{88} + 15 q^{89} + 4 q^{90} - 30 q^{92} + 6 q^{93} + 16 q^{94} - 54 q^{95} - 12 q^{96} - 11 q^{97} - 10 q^{98} - 9 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 12 * q^3 + 12 * q^4 - 4 * q^5 - 12 * q^6 - 12 * q^8 + 12 * q^9 + 4 * q^10 - 9 * q^11 + 12 * q^12 + 12 * q^13 - 4 * q^15 + 12 * q^16 - 20 * q^17 - 12 * q^18 + 4 * q^19 - 4 * q^20 + 9 * q^22 - 30 * q^23 - 12 * q^24 + 14 * q^25 - 12 * q^26 + 12 * q^27 - 29 * q^29 + 4 * q^30 + 6 * q^31 - 12 * q^32 - 9 * q^33 + 20 * q^34 - 22 * q^35 + 12 * q^36 + 7 * q^37 - 4 * q^38 + 12 * q^39 + 4 * q^40 - 8 * q^41 - 8 * q^43 - 9 * q^44 - 4 * q^45 + 30 * q^46 - 16 * q^47 + 12 * q^48 + 10 * q^49 - 14 * q^50 - 20 * q^51 + 12 * q^52 - 9 * q^53 - 12 * q^54 - 20 * q^55 + 4 * q^57 + 29 * q^58 - 29 * q^59 - 4 * q^60 - 26 * q^61 - 6 * q^62 + 12 * q^64 - 4 * q^65 + 9 * q^66 + 12 * q^67 - 20 * q^68 - 30 * q^69 + 22 * q^70 - 35 * q^71 - 12 * q^72 + 18 * q^73 - 7 * q^74 + 14 * q^75 + 4 * q^76 - 25 * q^77 - 12 * q^78 - 37 * q^79 - 4 * q^80 + 12 * q^81 + 8 * q^82 - 24 * q^83 - 17 * q^85 + 8 * q^86 - 29 * q^87 + 9 * q^88 + 15 * q^89 + 4 * q^90 - 30 * q^92 + 6 * q^93 + 16 * q^94 - 54 * q^95 - 12 * q^96 - 11 * q^97 - 10 * q^98 - 9 * q^99

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