LMFDB - Embedded newform 8034.2.a.o.1.5

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:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 4x^{5} + 14x^{4} + 3x^{3} - 12x^{2} - 3x + 1 $ x^7 - 3x^6 - 4x^5 + 14x^4 + 3x^3 - 12x^2 - 3x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.51101$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.77686 q^{5} +1.00000 q^{6} -3.99413 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.77686 q^{5} +1.00000 q^{6} -3.99413 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.77686 q^{10} -0.580058 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.99413 q^{14} -1.77686 q^{15} +1.00000 q^{16} +6.41168 q^{17} -1.00000 q^{18} -4.99413 q^{19} +1.77686 q^{20} +3.99413 q^{21} +0.580058 q^{22} -6.59303 q^{23} +1.00000 q^{24} -1.84277 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.99413 q^{28} +1.31057 q^{29} +1.77686 q^{30} +6.05760 q^{31} -1.00000 q^{32} +0.580058 q^{33} -6.41168 q^{34} -7.09702 q^{35} +1.00000 q^{36} +6.39448 q^{37} +4.99413 q^{38} -1.00000 q^{39} -1.77686 q^{40} +6.04948 q^{41} -3.99413 q^{42} +11.3839 q^{43} -0.580058 q^{44} +1.77686 q^{45} +6.59303 q^{46} -6.62715 q^{47} -1.00000 q^{48} +8.95309 q^{49} +1.84277 q^{50} -6.41168 q^{51} +1.00000 q^{52} -13.1198 q^{53} +1.00000 q^{54} -1.03068 q^{55} +3.99413 q^{56} +4.99413 q^{57} -1.31057 q^{58} -10.2716 q^{59} -1.77686 q^{60} -12.6576 q^{61} -6.05760 q^{62} -3.99413 q^{63} +1.00000 q^{64} +1.77686 q^{65} -0.580058 q^{66} -2.66759 q^{67} +6.41168 q^{68} +6.59303 q^{69} +7.09702 q^{70} +3.84167 q^{71} -1.00000 q^{72} +12.1465 q^{73} -6.39448 q^{74} +1.84277 q^{75} -4.99413 q^{76} +2.31683 q^{77} +1.00000 q^{78} +2.69447 q^{79} +1.77686 q^{80} +1.00000 q^{81} -6.04948 q^{82} +7.90079 q^{83} +3.99413 q^{84} +11.3927 q^{85} -11.3839 q^{86} -1.31057 q^{87} +0.580058 q^{88} -3.95413 q^{89} -1.77686 q^{90} -3.99413 q^{91} -6.59303 q^{92} -6.05760 q^{93} +6.62715 q^{94} -8.87388 q^{95} +1.00000 q^{96} +8.16221 q^{97} -8.95309 q^{98} -0.580058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	$ 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) $ 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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
$5$	1.77686	0.794636	0.397318	−	0.917681i	$-0.369941\pi$
$5$	1.77686	0.794636	0.397318	+	0.917681i	$0.369941\pi$
$6$	1.00000	0.408248
$7$	−3.99413	−1.50964	−0.754820	−	0.655932i	$-0.772276\pi$
$7$	−3.99413	−1.50964	−0.754820	+	0.655932i	$0.772276\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.77686	−0.561893
$11$	−0.580058	−0.174894	−0.0874470	−	0.996169i	$-0.527871\pi$
$11$	−0.580058	−0.174894	−0.0874470	+	0.996169i	$0.527871\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	3.99413	1.06748
$15$	−1.77686	−0.458783
$16$	1.00000	0.250000
$17$	6.41168	1.55506	0.777531	−	0.628845i	$-0.216472\pi$
$17$	6.41168	1.55506	0.777531	+	0.628845i	$0.216472\pi$
$18$	−1.00000	−0.235702
$19$	−4.99413	−1.14573	−0.572866	−	0.819649i	$-0.694169\pi$
$19$	−4.99413	−1.14573	−0.572866	+	0.819649i	$0.694169\pi$
$20$	1.77686	0.397318
$21$	3.99413	0.871591
$22$	0.580058	0.123669
$23$	−6.59303	−1.37474	−0.687371	−	0.726306i	$-0.741235\pi$
$23$	−6.59303	−1.37474	−0.687371	+	0.726306i	$0.741235\pi$
$24$	1.00000	0.204124
$25$	−1.84277	−0.368553
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−3.99413	−0.754820
$29$	1.31057	0.243367	0.121684	−	0.992569i	$-0.461171\pi$
$29$	1.31057	0.243367	0.121684	+	0.992569i	$0.461171\pi$
$30$	1.77686	0.324409
$31$	6.05760	1.08798	0.543988	−	0.839093i	$-0.316914\pi$
$31$	6.05760	1.08798	0.543988	+	0.839093i	$0.316914\pi$
$32$	−1.00000	−0.176777
$33$	0.580058	0.100975
$34$	−6.41168	−1.09959
$35$	−7.09702	−1.19961
$36$	1.00000	0.166667
$37$	6.39448	1.05125	0.525623	−	0.850718i	$-0.323832\pi$
$37$	6.39448	1.05125	0.525623	+	0.850718i	$0.323832\pi$
$38$	4.99413	0.810155
$39$	−1.00000	−0.160128
$40$	−1.77686	−0.280946
$41$	6.04948	0.944770	0.472385	−	0.881392i	$-0.343393\pi$
$41$	6.04948	0.944770	0.472385	+	0.881392i	$0.343393\pi$
$42$	−3.99413	−0.616308
$43$	11.3839	1.73604	0.868018	−	0.496533i	$-0.165394\pi$
$43$	11.3839	1.73604	0.868018	+	0.496533i	$0.165394\pi$
$44$	−0.580058	−0.0874470
$45$	1.77686	0.264879
$46$	6.59303	0.972090
$47$	−6.62715	−0.966669	−0.483334	−	0.875436i	$-0.660574\pi$
$47$	−6.62715	−0.966669	−0.483334	+	0.875436i	$0.660574\pi$
$48$	−1.00000	−0.144338
$49$	8.95309	1.27901
$50$	1.84277	0.260606
$51$	−6.41168	−0.897815
$52$	1.00000	0.138675
$53$	−13.1198	−1.80214	−0.901070	−	0.433673i	$-0.857217\pi$
$53$	−13.1198	−1.80214	−0.901070	+	0.433673i	$0.857217\pi$
$54$	1.00000	0.136083
$55$	−1.03068	−0.138977
$56$	3.99413	0.533738
$57$	4.99413	0.661489
$58$	−1.31057	−0.172087
$59$	−10.2716	−1.33725	−0.668626	−	0.743599i	$-0.733117\pi$
$59$	−10.2716	−1.33725	−0.668626	+	0.743599i	$0.733117\pi$
$60$	−1.77686	−0.229392
$61$	−12.6576	−1.62064	−0.810318	−	0.585990i	$-0.800706\pi$
$61$	−12.6576	−1.62064	−0.810318	+	0.585990i	$0.800706\pi$
$62$	−6.05760	−0.769316
$63$	−3.99413	−0.503213
$64$	1.00000	0.125000
$65$	1.77686	0.220392
$66$	−0.580058	−0.0714002
$67$	−2.66759	−0.325898	−0.162949	−	0.986634i	$-0.552101\pi$
$67$	−2.66759	−0.325898	−0.162949	+	0.986634i	$0.552101\pi$
$68$	6.41168	0.777531
$69$	6.59303	0.793708
$70$	7.09702	0.848256
$71$	3.84167	0.455923	0.227961	−	0.973670i	$-0.426794\pi$
$71$	3.84167	0.455923	0.227961	+	0.973670i	$0.426794\pi$
$72$	−1.00000	−0.117851
$73$	12.1465	1.42164	0.710818	−	0.703376i	$-0.248325\pi$
$73$	12.1465	1.42164	0.710818	+	0.703376i	$0.248325\pi$
$74$	−6.39448	−0.743343
$75$	1.84277	0.212784
$76$	−4.99413	−0.572866
$77$	2.31683	0.264027
$78$	1.00000	0.113228
$79$	2.69447	0.303152	0.151576	−	0.988446i	$-0.451565\pi$
$79$	2.69447	0.303152	0.151576	+	0.988446i	$0.451565\pi$
$80$	1.77686	0.198659
$81$	1.00000	0.111111
$82$	−6.04948	−0.668054
$83$	7.90079	0.867225	0.433612	−	0.901099i	$-0.357239\pi$
$83$	7.90079	0.867225	0.433612	+	0.901099i	$0.357239\pi$
$84$	3.99413	0.435796
$85$	11.3927	1.23571
$86$	−11.3839	−1.22756
$87$	−1.31057	−0.140508
$88$	0.580058	0.0618344
$89$	−3.95413	−0.419137	−0.209569	−	0.977794i	$-0.567206\pi$
$89$	−3.95413	−0.419137	−0.209569	+	0.977794i	$0.567206\pi$
$90$	−1.77686	−0.187298
$91$	−3.99413	−0.418699
$92$	−6.59303	−0.687371
$93$	−6.05760	−0.628144
$94$	6.62715	0.683538
$95$	−8.87388	−0.910441
$96$	1.00000	0.102062
$97$	8.16221	0.828746	0.414373	−	0.910107i	$-0.364001\pi$
$97$	8.16221	0.828746	0.414373	+	0.910107i	$0.364001\pi$
$98$	−8.95309	−0.904399
$99$	−0.580058	−0.0582980
$100$	−1.84277	−0.184277
$101$	12.4955	1.24334	0.621672	−	0.783278i	$-0.286454\pi$
$101$	12.4955	1.24334	0.621672	+	0.783278i	$0.286454\pi$
$102$	6.41168	0.634851
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	7.09702	0.692598
$106$	13.1198	1.27431
$107$	14.8246	1.43315	0.716573	−	0.697512i	$-0.245710\pi$
$107$	14.8246	1.43315	0.716573	+	0.697512i	$0.245710\pi$
$108$	−1.00000	−0.0962250
$109$	0.449928	0.0430953	0.0215476	−	0.999768i	$-0.493141\pi$
$109$	0.449928	0.0430953	0.0215476	+	0.999768i	$0.493141\pi$
$110$	1.03068	0.0982717
$111$	−6.39448	−0.606937
$112$	−3.99413	−0.377410
$113$	8.60200	0.809208	0.404604	−	0.914492i	$-0.367409\pi$
$113$	8.60200	0.809208	0.404604	+	0.914492i	$0.367409\pi$
$114$	−4.99413	−0.467743
$115$	−11.7149	−1.09242
$116$	1.31057	0.121684
$117$	1.00000	0.0924500
$118$	10.2716	0.945580
$119$	−25.6091	−2.34758
$120$	1.77686	0.162204
$121$	−10.6635	−0.969412
$122$	12.6576	1.14596
$123$	−6.04948	−0.545463
$124$	6.05760	0.543988
$125$	−12.1586	−1.08750
$126$	3.99413	0.355826
$127$	−17.6101	−1.56265	−0.781323	−	0.624126i	$-0.785455\pi$
$127$	−17.6101	−1.56265	−0.781323	+	0.624126i	$0.785455\pi$
$128$	−1.00000	−0.0883883
$129$	−11.3839	−1.00230
$130$	−1.77686	−0.155841
$131$	−6.23844	−0.545055	−0.272527	−	0.962148i	$-0.587860\pi$
$131$	−6.23844	−0.545055	−0.272527	+	0.962148i	$0.587860\pi$
$132$	0.580058	0.0504876
$133$	19.9472	1.72964
$134$	2.66759	0.230445
$135$	−1.77686	−0.152928
$136$	−6.41168	−0.549797
$137$	−16.0387	−1.37028	−0.685140	−	0.728412i	$-0.740259\pi$
$137$	−16.0387	−1.37028	−0.685140	+	0.728412i	$0.740259\pi$
$138$	−6.59303	−0.561236
$139$	5.44497	0.461836	0.230918	−	0.972973i	$-0.425827\pi$
$139$	5.44497	0.461836	0.230918	+	0.972973i	$0.425827\pi$
$140$	−7.09702	−0.599807
$141$	6.62715	0.558106
$142$	−3.84167	−0.322386
$143$	−0.580058	−0.0485069
$144$	1.00000	0.0833333
$145$	2.32870	0.193388
$146$	−12.1465	−1.00525
$147$	−8.95309	−0.738438
$148$	6.39448	0.525623
$149$	7.66917	0.628283	0.314142	−	0.949376i	$-0.398283\pi$
$149$	7.66917	0.628283	0.314142	+	0.949376i	$0.398283\pi$
$150$	−1.84277	−0.150461
$151$	−24.0732	−1.95905	−0.979524	−	0.201329i	$-0.935474\pi$
$151$	−24.0732	−1.95905	−0.979524	+	0.201329i	$0.935474\pi$
$152$	4.99413	0.405078
$153$	6.41168	0.518354
$154$	−2.31683	−0.186695
$155$	10.7635	0.864546
$156$	−1.00000	−0.0800641
$157$	−19.4944	−1.55582	−0.777909	−	0.628377i	$-0.783720\pi$
$157$	−19.4944	−1.55582	−0.777909	+	0.628377i	$0.783720\pi$
$158$	−2.69447	−0.214361
$159$	13.1198	1.04047
$160$	−1.77686	−0.140473
$161$	26.3334	2.07537
$162$	−1.00000	−0.0785674
$163$	23.1065	1.80984	0.904920	−	0.425581i	$-0.139930\pi$
$163$	23.1065	1.80984	0.904920	+	0.425581i	$0.139930\pi$
$164$	6.04948	0.472385
$165$	1.03068	0.0802385
$166$	−7.90079	−0.613221
$167$	9.42071	0.728996	0.364498	−	0.931204i	$-0.381241\pi$
$167$	9.42071	0.728996	0.364498	+	0.931204i	$0.381241\pi$
$168$	−3.99413	−0.308154
$169$	1.00000	0.0769231
$170$	−11.3927	−0.873778
$171$	−4.99413	−0.381911
$172$	11.3839	0.868018
$173$	−22.0526	−1.67663	−0.838315	−	0.545186i	$-0.816459\pi$
$173$	−22.0526	−1.67663	−0.838315	+	0.545186i	$0.816459\pi$
$174$	1.31057	0.0993542
$175$	7.36025	0.556383
$176$	−0.580058	−0.0437235
$177$	10.2716	0.772063
$178$	3.95413	0.296375
$179$	4.54176	0.339467	0.169734	−	0.985490i	$-0.445709\pi$
$179$	4.54176	0.339467	0.169734	+	0.985490i	$0.445709\pi$
$180$	1.77686	0.132439
$181$	15.0371	1.11770	0.558851	−	0.829268i	$-0.311242\pi$
$181$	15.0371	1.11770	0.558851	+	0.829268i	$0.311242\pi$
$182$	3.99413	0.296065
$183$	12.6576	0.935675
$184$	6.59303	0.486045
$185$	11.3621	0.835358
$186$	6.05760	0.444165
$187$	−3.71915	−0.271971
$188$	−6.62715	−0.483334
$189$	3.99413	0.290530
$190$	8.87388	0.643779
$191$	−14.4869	−1.04823	−0.524117	−	0.851646i	$-0.675605\pi$
$191$	−14.4869	−1.04823	−0.524117	+	0.851646i	$0.675605\pi$
$192$	−1.00000	−0.0721688
$193$	4.70533	0.338697	0.169348	−	0.985556i	$-0.445834\pi$
$193$	4.70533	0.338697	0.169348	+	0.985556i	$0.445834\pi$
$194$	−8.16221	−0.586012
$195$	−1.77686	−0.127244
$196$	8.95309	0.639506
$197$	18.9174	1.34781	0.673904	−	0.738819i	$-0.264616\pi$
$197$	18.9174	1.34781	0.673904	+	0.738819i	$0.264616\pi$
$198$	0.580058	0.0412229
$199$	−17.0528	−1.20884	−0.604421	−	0.796665i	$-0.706595\pi$
$199$	−17.0528	−1.20884	−0.604421	+	0.796665i	$0.706595\pi$
$200$	1.84277	0.130303
$201$	2.66759	0.188157
$202$	−12.4955	−0.879177
$203$	−5.23460	−0.367397
$204$	−6.41168	−0.448908
$205$	10.7491	0.750749
$206$	−1.00000	−0.0696733
$207$	−6.59303	−0.458248
$208$	1.00000	0.0693375
$209$	2.89689	0.200382
$210$	−7.09702	−0.489741
$211$	−7.46310	−0.513781	−0.256891	−	0.966440i	$-0.582698\pi$
$211$	−7.46310	−0.513781	−0.256891	+	0.966440i	$0.582698\pi$
$212$	−13.1198	−0.901070
$213$	−3.84167	−0.263227
$214$	−14.8246	−1.01339
$215$	20.2277	1.37952
$216$	1.00000	0.0680414
$217$	−24.1948	−1.64245
$218$	−0.449928	−0.0304730
$219$	−12.1465	−0.820782
$220$	−1.03068	−0.0694886
$221$	6.41168	0.431296
$222$	6.39448	0.429169
$223$	−14.0884	−0.943428	−0.471714	−	0.881752i	$-0.656365\pi$
$223$	−14.0884	−0.943428	−0.471714	+	0.881752i	$0.656365\pi$
$224$	3.99413	0.266869
$225$	−1.84277	−0.122851
$226$	−8.60200	−0.572197
$227$	11.7368	0.779000	0.389500	−	0.921026i	$-0.372648\pi$
$227$	11.7368	0.779000	0.389500	+	0.921026i	$0.372648\pi$
$228$	4.99413	0.330744
$229$	−22.2214	−1.46843	−0.734215	−	0.678917i	$-0.762450\pi$
$229$	−22.2214	−1.46843	−0.734215	+	0.678917i	$0.762450\pi$
$230$	11.7149	0.772458
$231$	−2.31683	−0.152436
$232$	−1.31057	−0.0860433
$233$	−2.45597	−0.160896	−0.0804480	−	0.996759i	$-0.525635\pi$
$233$	−2.45597	−0.160896	−0.0804480	+	0.996759i	$0.525635\pi$
$234$	−1.00000	−0.0653720
$235$	−11.7755	−0.768150
$236$	−10.2716	−0.668626
$237$	−2.69447	−0.175025
$238$	25.6091	1.65999
$239$	0.439459	0.0284262	0.0142131	−	0.999899i	$-0.495476\pi$
$239$	0.439459	0.0284262	0.0142131	+	0.999899i	$0.495476\pi$
$240$	−1.77686	−0.114696
$241$	−25.8545	−1.66543	−0.832717	−	0.553699i	$-0.813216\pi$
$241$	−25.8545	−1.66543	−0.832717	+	0.553699i	$0.813216\pi$
$242$	10.6635	0.685478
$243$	−1.00000	−0.0641500
$244$	−12.6576	−0.810318
$245$	15.9084	1.01635
$246$	6.04948	0.385701
$247$	−4.99413	−0.317769
$248$	−6.05760	−0.384658
$249$	−7.90079	−0.500692
$250$	12.1586	0.768980
$251$	−22.2828	−1.40648	−0.703240	−	0.710952i	$-0.748264\pi$
$251$	−22.2828	−1.40648	−0.703240	+	0.710952i	$0.748264\pi$
$252$	−3.99413	−0.251607
$253$	3.82434	0.240434
$254$	17.6101	1.10496
$255$	−11.3927	−0.713436
$256$	1.00000	0.0625000
$257$	21.2192	1.32362	0.661809	−	0.749672i	$-0.269789\pi$
$257$	21.2192	1.32362	0.661809	+	0.749672i	$0.269789\pi$
$258$	11.3839	0.708733
$259$	−25.5404	−1.58700
$260$	1.77686	0.110196
$261$	1.31057	0.0811224
$262$	6.23844	0.385412
$263$	−30.7091	−1.89360	−0.946802	−	0.321816i	$-0.895707\pi$
$263$	−30.7091	−1.89360	−0.946802	+	0.321816i	$0.895707\pi$
$264$	−0.580058	−0.0357001
$265$	−23.3120	−1.43205
$266$	−19.9472	−1.22304
$267$	3.95413	0.241989
$268$	−2.66759	−0.162949
$269$	−5.25791	−0.320580	−0.160290	−	0.987070i	$-0.551243\pi$
$269$	−5.25791	−0.320580	−0.160290	+	0.987070i	$0.551243\pi$
$270$	1.77686	0.108136
$271$	8.79084	0.534006	0.267003	−	0.963696i	$-0.413967\pi$
$271$	8.79084	0.534006	0.267003	+	0.963696i	$0.413967\pi$
$272$	6.41168	0.388765
$273$	3.99413	0.241736
$274$	16.0387	0.968934
$275$	1.06891	0.0644578
$276$	6.59303	0.396854
$277$	−22.0601	−1.32547	−0.662733	−	0.748856i	$-0.730604\pi$
$277$	−22.0601	−1.32547	−0.662733	+	0.748856i	$0.730604\pi$
$278$	−5.44497	−0.326567
$279$	6.05760	0.362659
$280$	7.09702	0.424128
$281$	−2.69154	−0.160564	−0.0802820	−	0.996772i	$-0.525582\pi$
$281$	−2.69154	−0.160564	−0.0802820	+	0.996772i	$0.525582\pi$
$282$	−6.62715	−0.394641
$283$	1.11537	0.0663018	0.0331509	−	0.999450i	$-0.489446\pi$
$283$	1.11537	0.0663018	0.0331509	+	0.999450i	$0.489446\pi$
$284$	3.84167	0.227961
$285$	8.87388	0.525643
$286$	0.580058	0.0342995
$287$	−24.1624	−1.42626
$288$	−1.00000	−0.0589256
$289$	24.1097	1.41822
$290$	−2.32870	−0.136746
$291$	−8.16221	−0.478477
$292$	12.1465	0.710818
$293$	23.8587	1.39384	0.696919	−	0.717149i	$-0.254553\pi$
$293$	23.8587	1.39384	0.696919	+	0.717149i	$0.254553\pi$
$294$	8.95309	0.522155
$295$	−18.2513	−1.06263
$296$	−6.39448	−0.371672
$297$	0.580058	0.0336584
$298$	−7.66917	−0.444263
$299$	−6.59303	−0.381285
$300$	1.84277	0.106392
$301$	−45.4690	−2.62079
$302$	24.0732	1.38526
$303$	−12.4955	−0.717845
$304$	−4.99413	−0.286433
$305$	−22.4907	−1.28782
$306$	−6.41168	−0.366531
$307$	18.1999	1.03873	0.519363	−	0.854554i	$-0.326169\pi$
$307$	18.1999	1.03873	0.519363	+	0.854554i	$0.326169\pi$
$308$	2.31683	0.132014
$309$	−1.00000	−0.0568880
$310$	−10.7635	−0.611326
$311$	16.7588	0.950305	0.475153	−	0.879903i	$-0.342393\pi$
$311$	16.7588	0.950305	0.475153	+	0.879903i	$0.342393\pi$
$312$	1.00000	0.0566139
$313$	15.1054	0.853809	0.426904	−	0.904297i	$-0.359604\pi$
$313$	15.1054	0.853809	0.426904	+	0.904297i	$0.359604\pi$
$314$	19.4944	1.10013
$315$	−7.09702	−0.399872
$316$	2.69447	0.151576
$317$	26.7194	1.50071	0.750355	−	0.661035i	$-0.229882\pi$
$317$	26.7194	1.50071	0.750355	+	0.661035i	$0.229882\pi$
$318$	−13.1198	−0.735721
$319$	−0.760208	−0.0425635
$320$	1.77686	0.0993295
$321$	−14.8246	−0.827427
$322$	−26.3334	−1.46751
$323$	−32.0208	−1.78168
$324$	1.00000	0.0555556
$325$	−1.84277	−0.102218
$326$	−23.1065	−1.27975
$327$	−0.449928	−0.0248811
$328$	−6.04948	−0.334027
$329$	26.4697	1.45932
$330$	−1.03068	−0.0567372
$331$	−30.1515	−1.65728	−0.828638	−	0.559784i	$-0.810884\pi$
$331$	−30.1515	−1.65728	−0.828638	+	0.559784i	$0.810884\pi$
$332$	7.90079	0.433612
$333$	6.39448	0.350415
$334$	−9.42071	−0.515478
$335$	−4.73994	−0.258971
$336$	3.99413	0.217898
$337$	−2.90829	−0.158425	−0.0792123	−	0.996858i	$-0.525241\pi$
$337$	−2.90829	−0.158425	−0.0792123	+	0.996858i	$0.525241\pi$
$338$	−1.00000	−0.0543928
$339$	−8.60200	−0.467197
$340$	11.3927	0.617854
$341$	−3.51376	−0.190281
$342$	4.99413	0.270052
$343$	−7.80090	−0.421209
$344$	−11.3839	−0.613781
$345$	11.7149	0.630709
$346$	22.0526	1.18556
$347$	−26.1265	−1.40255	−0.701273	−	0.712893i	$-0.747385\pi$
$347$	−26.1265	−1.40255	−0.701273	+	0.712893i	$0.747385\pi$
$348$	−1.31057	−0.0702541
$349$	−19.4604	−1.04169	−0.520846	−	0.853651i	$-0.674383\pi$
$349$	−19.4604	−1.04169	−0.520846	+	0.853651i	$0.674383\pi$
$350$	−7.36025	−0.393422
$351$	−1.00000	−0.0533761
$352$	0.580058	0.0309172
$353$	14.8833	0.792158	0.396079	−	0.918216i	$-0.370371\pi$
$353$	14.8833	0.792158	0.396079	+	0.918216i	$0.370371\pi$
$354$	−10.2716	−0.545931
$355$	6.82612	0.362293
$356$	−3.95413	−0.209569
$357$	25.6091	1.35538
$358$	−4.54176	−0.240040
$359$	−6.94723	−0.366661	−0.183330	−	0.983051i	$-0.558688\pi$
$359$	−6.94723	−0.366661	−0.183330	+	0.983051i	$0.558688\pi$
$360$	−1.77686	−0.0936488
$361$	5.94135	0.312703
$362$	−15.0371	−0.790335
$363$	10.6635	0.559690
$364$	−3.99413	−0.209349
$365$	21.5826	1.12968
$366$	−12.6576	−0.661622
$367$	−16.9537	−0.884978	−0.442489	−	0.896774i	$-0.645904\pi$
$367$	−16.9537	−0.884978	−0.442489	+	0.896774i	$0.645904\pi$
$368$	−6.59303	−0.343686
$369$	6.04948	0.314923
$370$	−11.3621	−0.590687
$371$	52.4021	2.72058
$372$	−6.05760	−0.314072
$373$	−13.4320	−0.695484	−0.347742	−	0.937590i	$-0.613051\pi$
$373$	−13.4320	−0.695484	−0.347742	+	0.937590i	$0.613051\pi$
$374$	3.71915	0.192313
$375$	12.1586	0.627870
$376$	6.62715	0.341769
$377$	1.31057	0.0674979
$378$	−3.99413	−0.205436
$379$	22.2036	1.14052	0.570260	−	0.821464i	$-0.306842\pi$
$379$	22.2036	1.14052	0.570260	+	0.821464i	$0.306842\pi$
$380$	−8.87388	−0.455220
$381$	17.6101	0.902195
$382$	14.4869	0.741214
$383$	32.3119	1.65106	0.825530	−	0.564358i	$-0.190876\pi$
$383$	32.3119	1.65106	0.825530	+	0.564358i	$0.190876\pi$
$384$	1.00000	0.0510310
$385$	4.11668	0.209805
$386$	−4.70533	−0.239495
$387$	11.3839	0.578678
$388$	8.16221	0.414373
$389$	6.20757	0.314736	0.157368	−	0.987540i	$-0.449699\pi$
$389$	6.20757	0.314736	0.157368	+	0.987540i	$0.449699\pi$
$390$	1.77686	0.0899748
$391$	−42.2724	−2.13781
$392$	−8.95309	−0.452199
$393$	6.23844	0.314687
$394$	−18.9174	−0.953044
$395$	4.78770	0.240895
$396$	−0.580058	−0.0291490
$397$	−31.7721	−1.59460	−0.797298	−	0.603586i	$-0.793738\pi$
$397$	−31.7721	−1.59460	−0.797298	+	0.603586i	$0.793738\pi$
$398$	17.0528	0.854780
$399$	−19.9472	−0.998610
$400$	−1.84277	−0.0921383
$401$	−1.07631	−0.0537483	−0.0268742	−	0.999639i	$-0.508555\pi$
$401$	−1.07631	−0.0537483	−0.0268742	+	0.999639i	$0.508555\pi$
$402$	−2.66759	−0.133047
$403$	6.05760	0.301750
$404$	12.4955	0.621672
$405$	1.77686	0.0882929
$406$	5.23460	0.259789
$407$	−3.70917	−0.183857
$408$	6.41168	0.317426
$409$	−9.73909	−0.481567	−0.240783	−	0.970579i	$-0.577404\pi$
$409$	−9.73909	−0.481567	−0.240783	+	0.970579i	$0.577404\pi$
$410$	−10.7491	−0.530860
$411$	16.0387	0.791131
$412$	1.00000	0.0492665
$413$	41.0262	2.01877
$414$	6.59303	0.324030
$415$	14.0386	0.689128
$416$	−1.00000	−0.0490290
$417$	−5.44497	−0.266641
$418$	−2.89689	−0.141691
$419$	15.8585	0.774740	0.387370	−	0.921924i	$-0.373384\pi$
$419$	15.8585	0.774740	0.387370	+	0.921924i	$0.373384\pi$
$420$	7.09702	0.346299
$421$	7.52106	0.366554	0.183277	−	0.983061i	$-0.441329\pi$
$421$	7.52106	0.366554	0.183277	+	0.983061i	$0.441329\pi$
$422$	7.46310	0.363298
$423$	−6.62715	−0.322223
$424$	13.1198	0.637153
$425$	−11.8152	−0.573123
$426$	3.84167	0.186130
$427$	50.5560	2.44658
$428$	14.8246	0.716573
$429$	0.580058	0.0280055
$430$	−20.2277	−0.975466
$431$	−2.73677	−0.131826	−0.0659129	−	0.997825i	$-0.520996\pi$
$431$	−2.73677	−0.131826	−0.0659129	+	0.997825i	$0.520996\pi$
$432$	−1.00000	−0.0481125
$433$	−12.6570	−0.608259	−0.304129	−	0.952631i	$-0.598365\pi$
$433$	−12.6570	−0.608259	−0.304129	+	0.952631i	$0.598365\pi$
$434$	24.1948	1.16139
$435$	−2.32870	−0.111653
$436$	0.449928	0.0215476
$437$	32.9265	1.57509
$438$	12.1465	0.580380
$439$	26.3495	1.25759	0.628795	−	0.777571i	$-0.283548\pi$
$439$	26.3495	1.25759	0.628795	+	0.777571i	$0.283548\pi$
$440$	1.03068	0.0491358
$441$	8.95309	0.426338
$442$	−6.41168	−0.304973
$443$	−1.36156	−0.0646897	−0.0323448	−	0.999477i	$-0.510297\pi$
$443$	−1.36156	−0.0646897	−0.0323448	+	0.999477i	$0.510297\pi$
$444$	−6.39448	−0.303469
$445$	−7.02594	−0.333062
$446$	14.0884	0.667104
$447$	−7.66917	−0.362740
$448$	−3.99413	−0.188705
$449$	−8.70559	−0.410842	−0.205421	−	0.978674i	$-0.565856\pi$
$449$	−8.70559	−0.410842	−0.205421	+	0.978674i	$0.565856\pi$
$450$	1.84277	0.0868688
$451$	−3.50905	−0.165235
$452$	8.60200	0.404604
$453$	24.0732	1.13106
$454$	−11.7368	−0.550836
$455$	−7.09702	−0.332713
$456$	−4.99413	−0.233872
$457$	35.5594	1.66340	0.831700	−	0.555225i	$-0.187368\pi$
$457$	35.5594	1.66340	0.831700	+	0.555225i	$0.187368\pi$
$458$	22.2214	1.03834
$459$	−6.41168	−0.299272
$460$	−11.7149	−0.546210
$461$	−28.8532	−1.34383	−0.671913	−	0.740630i	$-0.734527\pi$
$461$	−28.8532	−1.34383	−0.671913	+	0.740630i	$0.734527\pi$
$462$	2.31683	0.107789
$463$	28.1865	1.30994	0.654970	−	0.755655i	$-0.272681\pi$
$463$	28.1865	1.30994	0.654970	+	0.755655i	$0.272681\pi$
$464$	1.31057	0.0608418
$465$	−10.7635	−0.499146
$466$	2.45597	0.113771
$467$	−24.3804	−1.12819	−0.564095	−	0.825710i	$-0.690775\pi$
$467$	−24.3804	−1.12819	−0.564095	+	0.825710i	$0.690775\pi$
$468$	1.00000	0.0462250
$469$	10.6547	0.491989
$470$	11.7755	0.543164
$471$	19.4944	0.898252
$472$	10.2716	0.472790
$473$	−6.60335	−0.303622
$474$	2.69447	0.123761
$475$	9.20301	0.422263
$476$	−25.6091	−1.17379
$477$	−13.1198	−0.600713
$478$	−0.439459	−0.0201004
$479$	3.35175	0.153145	0.0765727	−	0.997064i	$-0.475602\pi$
$479$	3.35175	0.153145	0.0765727	+	0.997064i	$0.475602\pi$
$480$	1.77686	0.0811022
$481$	6.39448	0.291563
$482$	25.8545	1.17764
$483$	−26.3334	−1.19821
$484$	−10.6635	−0.484706
$485$	14.5031	0.658552
$486$	1.00000	0.0453609
$487$	−27.2724	−1.23583	−0.617915	−	0.786245i	$-0.712022\pi$
$487$	−27.2724	−1.23583	−0.617915	+	0.786245i	$0.712022\pi$
$488$	12.6576	0.572981
$489$	−23.1065	−1.04491
$490$	−15.9084	−0.718668
$491$	−8.42210	−0.380084	−0.190042	−	0.981776i	$-0.560862\pi$
$491$	−8.42210	−0.380084	−0.190042	+	0.981776i	$0.560862\pi$
$492$	−6.04948	−0.272732
$493$	8.40297	0.378451
$494$	4.99413	0.224697
$495$	−1.03068	−0.0463257
$496$	6.05760	0.271994
$497$	−15.3441	−0.688279
$498$	7.90079	0.354043
$499$	−9.31527	−0.417009	−0.208504	−	0.978021i	$-0.566860\pi$
$499$	−9.31527	−0.417009	−0.208504	+	0.978021i	$0.566860\pi$
$500$	−12.1586	−0.543751
$501$	−9.42071	−0.420886
$502$	22.2828	0.994532
$503$	−24.8290	−1.10707	−0.553534	−	0.832826i	$-0.686721\pi$
$503$	−24.8290	−1.10707	−0.553534	+	0.832826i	$0.686721\pi$
$504$	3.99413	0.177913
$505$	22.2027	0.988006
$506$	−3.82434	−0.170013
$507$	−1.00000	−0.0444116
$508$	−17.6101	−0.781323
$509$	−25.2050	−1.11719	−0.558595	−	0.829440i	$-0.688660\pi$
$509$	−25.2050	−1.11719	−0.558595	+	0.829440i	$0.688660\pi$
$510$	11.3927	0.504476
$511$	−48.5146	−2.14616
$512$	−1.00000	−0.0441942
$513$	4.99413	0.220496
$514$	−21.2192	−0.935939
$515$	1.77686	0.0782978
$516$	−11.3839	−0.501150
$517$	3.84413	0.169065
$518$	25.5404	1.12218
$519$	22.0526	0.968003
$520$	−1.77686	−0.0779205
$521$	−31.4155	−1.37634	−0.688169	−	0.725551i	$-0.741585\pi$
$521$	−31.4155	−1.37634	−0.688169	+	0.725551i	$0.741585\pi$
$522$	−1.31057	−0.0573622
$523$	−23.4078	−1.02355	−0.511775	−	0.859119i	$-0.671012\pi$
$523$	−23.4078	−1.02355	−0.511775	+	0.859119i	$0.671012\pi$
$524$	−6.23844	−0.272527
$525$	−7.36025	−0.321228
$526$	30.7091	1.33898
$527$	38.8394	1.69187
$528$	0.580058	0.0252438
$529$	20.4681	0.889917
$530$	23.3120	1.01261
$531$	−10.2716	−0.445751
$532$	19.9472	0.864822
$533$	6.04948	0.262032
$534$	−3.95413	−0.171112
$535$	26.3412	1.13883
$536$	2.66759	0.115222
$537$	−4.54176	−0.195992
$538$	5.25791	0.226684
$539$	−5.19331	−0.223692
$540$	−1.77686	−0.0764639
$541$	−19.2659	−0.828307	−0.414153	−	0.910207i	$-0.635922\pi$
$541$	−19.2659	−0.828307	−0.414153	+	0.910207i	$0.635922\pi$
$542$	−8.79084	−0.377599
$543$	−15.0371	−0.645306
$544$	−6.41168	−0.274899
$545$	0.799460	0.0342451
$546$	−3.99413	−0.170933
$547$	−18.6484	−0.797350	−0.398675	−	0.917092i	$-0.630530\pi$
$547$	−18.6484	−0.797350	−0.398675	+	0.917092i	$0.630530\pi$
$548$	−16.0387	−0.685140
$549$	−12.6576	−0.540212
$550$	−1.06891	−0.0455785
$551$	−6.54517	−0.278834
$552$	−6.59303	−0.280618
$553$	−10.7621	−0.457650
$554$	22.0601	0.937246
$555$	−11.3621	−0.482294
$556$	5.44497	0.230918
$557$	−28.1898	−1.19444	−0.597219	−	0.802078i	$-0.703728\pi$
$557$	−28.1898	−1.19444	−0.597219	+	0.802078i	$0.703728\pi$
$558$	−6.05760	−0.256439
$559$	11.3839	0.481490
$560$	−7.09702	−0.299904
$561$	3.71915	0.157023
$562$	2.69154	0.113536
$563$	−20.6201	−0.869036	−0.434518	−	0.900663i	$-0.643081\pi$
$563$	−20.6201	−0.869036	−0.434518	+	0.900663i	$0.643081\pi$
$564$	6.62715	0.279053
$565$	15.2846	0.643026
$566$	−1.11537	−0.0468825
$567$	−3.99413	−0.167738
$568$	−3.84167	−0.161193
$569$	−20.5789	−0.862711	−0.431356	−	0.902182i	$-0.641965\pi$
$569$	−20.5789	−0.862711	−0.431356	+	0.902182i	$0.641965\pi$
$570$	−8.87388	−0.371686
$571$	−12.2975	−0.514634	−0.257317	−	0.966327i	$-0.582839\pi$
$571$	−12.2975	−0.514634	−0.257317	+	0.966327i	$0.582839\pi$
$572$	−0.580058	−0.0242534
$573$	14.4869	0.605199
$574$	24.1624	1.00852
$575$	12.1494	0.506666
$576$	1.00000	0.0416667
$577$	−35.7752	−1.48934	−0.744670	−	0.667433i	$-0.767393\pi$
$577$	−35.7752	−1.48934	−0.744670	+	0.667433i	$0.767393\pi$
$578$	−24.1097	−1.00283
$579$	−4.70533	−0.195547
$580$	2.32870	0.0966942
$581$	−31.5568	−1.30920
$582$	8.16221	0.338334
$583$	7.61023	0.315184
$584$	−12.1465	−0.502624
$585$	1.77686	0.0734642
$586$	−23.8587	−0.985593
$587$	11.6995	0.482891	0.241445	−	0.970414i	$-0.422379\pi$
$587$	11.6995	0.482891	0.241445	+	0.970414i	$0.422379\pi$
$588$	−8.95309	−0.369219
$589$	−30.2524	−1.24653
$590$	18.2513	0.751392
$591$	−18.9174	−0.778157
$592$	6.39448	0.262811
$593$	13.9057	0.571037	0.285519	−	0.958373i	$-0.407834\pi$
$593$	13.9057	0.571037	0.285519	+	0.958373i	$0.407834\pi$
$594$	−0.580058	−0.0238001
$595$	−45.5038	−1.86547
$596$	7.66917	0.314142
$597$	17.0528	0.697925
$598$	6.59303	0.269609
$599$	−7.48070	−0.305653	−0.152827	−	0.988253i	$-0.548838\pi$
$599$	−7.48070	−0.305653	−0.152827	+	0.988253i	$0.548838\pi$
$600$	−1.84277	−0.0752306
$601$	−42.2169	−1.72206	−0.861031	−	0.508552i	$-0.830181\pi$
$601$	−42.2169	−1.72206	−0.861031	+	0.508552i	$0.830181\pi$
$602$	45.4690	1.85318
$603$	−2.66759	−0.108633
$604$	−24.0732	−0.979524
$605$	−18.9476	−0.770330
$606$	12.4955	0.507593
$607$	−10.4445	−0.423930	−0.211965	−	0.977277i	$-0.567986\pi$
$607$	−10.4445	−0.423930	−0.211965	+	0.977277i	$0.567986\pi$
$608$	4.99413	0.202539
$609$	5.23460	0.212117
$610$	22.4907	0.910624
$611$	−6.62715	−0.268106
$612$	6.41168	0.259177
$613$	13.2739	0.536128	0.268064	−	0.963401i	$-0.413616\pi$
$613$	13.2739	0.536128	0.268064	+	0.963401i	$0.413616\pi$
$614$	−18.1999	−0.734490
$615$	−10.7491	−0.433445
$616$	−2.31683	−0.0933477
$617$	−33.9656	−1.36741	−0.683703	−	0.729761i	$-0.739631\pi$
$617$	−33.9656	−1.36741	−0.683703	+	0.729761i	$0.739631\pi$
$618$	1.00000	0.0402259
$619$	32.9674	1.32507	0.662536	−	0.749030i	$-0.269480\pi$
$619$	32.9674	1.32507	0.662536	+	0.749030i	$0.269480\pi$
$620$	10.7635	0.432273
$621$	6.59303	0.264569
$622$	−16.7588	−0.671967
$623$	15.7933	0.632746
$624$	−1.00000	−0.0400320
$625$	−12.3904	−0.495615
$626$	−15.1054	−0.603734
$627$	−2.89689	−0.115690
$628$	−19.4944	−0.777909
$629$	40.9994	1.63475
$630$	7.09702	0.282752
$631$	15.2257	0.606124	0.303062	−	0.952971i	$-0.401991\pi$
$631$	15.2257	0.606124	0.303062	+	0.952971i	$0.401991\pi$
$632$	−2.69447	−0.107180
$633$	7.46310	0.296632
$634$	−26.7194	−1.06116
$635$	−31.2908	−1.24174
$636$	13.1198	0.520233
$637$	8.95309	0.354734
$638$	0.760208	0.0300969
$639$	3.84167	0.151974
$640$	−1.77686	−0.0702366
$641$	13.3374	0.526796	0.263398	−	0.964687i	$-0.415157\pi$
$641$	13.3374	0.526796	0.263398	+	0.964687i	$0.415157\pi$
$642$	14.8246	0.585079
$643$	−22.2996	−0.879410	−0.439705	−	0.898142i	$-0.644917\pi$
$643$	−22.2996	−0.879410	−0.439705	+	0.898142i	$0.644917\pi$
$644$	26.3334	1.03768
$645$	−20.2277	−0.796464
$646$	32.0208	1.25984
$647$	−30.3519	−1.19326	−0.596629	−	0.802517i	$-0.703493\pi$
$647$	−30.3519	−1.19326	−0.596629	+	0.802517i	$0.703493\pi$
$648$	−1.00000	−0.0392837
$649$	5.95814	0.233877
$650$	1.84277	0.0722792
$651$	24.1948	0.948271
$652$	23.1065	0.904920
$653$	45.5866	1.78394	0.891972	−	0.452091i	$-0.149322\pi$
$653$	45.5866	1.78394	0.891972	+	0.452091i	$0.149322\pi$
$654$	0.449928	0.0175936
$655$	−11.0848	−0.433120
$656$	6.04948	0.236193
$657$	12.1465	0.473879
$658$	−26.4697	−1.03190
$659$	13.9845	0.544758	0.272379	−	0.962190i	$-0.412190\pi$
$659$	13.9845	0.544758	0.272379	+	0.962190i	$0.412190\pi$
$660$	1.03068	0.0401193
$661$	18.5805	0.722698	0.361349	−	0.932431i	$-0.382316\pi$
$661$	18.5805	0.722698	0.361349	+	0.932431i	$0.382316\pi$
$662$	30.1515	1.17187
$663$	−6.41168	−0.249009
$664$	−7.90079	−0.306610
$665$	35.4434	1.37444
$666$	−6.39448	−0.247781
$667$	−8.64065	−0.334567
$668$	9.42071	0.364498
$669$	14.0884	0.544688
$670$	4.73994	0.183120
$671$	7.34213	0.283440
$672$	−3.99413	−0.154077
$673$	−15.7021	−0.605272	−0.302636	−	0.953106i	$-0.597867\pi$
$673$	−15.7021	−0.605272	−0.302636	+	0.953106i	$0.597867\pi$
$674$	2.90829	0.112023
$675$	1.84277	0.0709281
$676$	1.00000	0.0384615
$677$	−24.4464	−0.939553	−0.469777	−	0.882785i	$-0.655666\pi$
$677$	−24.4464	−0.939553	−0.469777	+	0.882785i	$0.655666\pi$
$678$	8.60200	0.330358
$679$	−32.6009	−1.25111
$680$	−11.3927	−0.436889
$681$	−11.7368	−0.449756
$682$	3.51376	0.134549
$683$	41.5076	1.58824	0.794122	−	0.607759i	$-0.207931\pi$
$683$	41.5076	1.58824	0.794122	+	0.607759i	$0.207931\pi$
$684$	−4.99413	−0.190955
$685$	−28.4986	−1.08887
$686$	7.80090	0.297840
$687$	22.2214	0.847798
$688$	11.3839	0.434009
$689$	−13.1198	−0.499824
$690$	−11.7149	−0.445979
$691$	−9.63399	−0.366494	−0.183247	−	0.983067i	$-0.558661\pi$
$691$	−9.63399	−0.366494	−0.183247	+	0.983067i	$0.558661\pi$
$692$	−22.0526	−0.838315
$693$	2.31683	0.0880090
$694$	26.1265	0.991750
$695$	9.67495	0.366992
$696$	1.31057	0.0496771
$697$	38.7874	1.46918
$698$	19.4604	0.736587
$699$	2.45597	0.0928933
$700$	7.36025	0.278191
$701$	8.61709	0.325463	0.162732	−	0.986670i	$-0.447970\pi$
$701$	8.61709	0.325463	0.162732	+	0.986670i	$0.447970\pi$
$702$	1.00000	0.0377426
$703$	−31.9349	−1.20445
$704$	−0.580058	−0.0218618
$705$	11.7755	0.443492
$706$	−14.8833	−0.560141
$707$	−49.9085	−1.87700
$708$	10.2716	0.386032
$709$	−41.2159	−1.54790	−0.773949	−	0.633248i	$-0.781721\pi$
$709$	−41.2159	−1.54790	−0.773949	+	0.633248i	$0.781721\pi$
$710$	−6.82612	−0.256180
$711$	2.69447	0.101051
$712$	3.95413	0.148187
$713$	−39.9380	−1.49569
$714$	−25.6091	−0.958397
$715$	−1.03068	−0.0385453
$716$	4.54176	0.169734
$717$	−0.439459	−0.0164119
$718$	6.94723	0.259268
$719$	12.5409	0.467697	0.233849	−	0.972273i	$-0.424868\pi$
$719$	12.5409	0.467697	0.233849	+	0.972273i	$0.424868\pi$
$720$	1.77686	0.0662197
$721$	−3.99413	−0.148749
$722$	−5.94135	−0.221114
$723$	25.8545	0.961538
$724$	15.0371	0.558851
$725$	−2.41508	−0.0896938
$726$	−10.6635	−0.395761
$727$	−15.0778	−0.559204	−0.279602	−	0.960116i	$-0.590202\pi$
$727$	−15.0778	−0.559204	−0.279602	+	0.960116i	$0.590202\pi$
$728$	3.99413	0.148032
$729$	1.00000	0.0370370
$730$	−21.5826	−0.798807
$731$	72.9902	2.69964
$732$	12.6576	0.467837
$733$	22.3904	0.827007	0.413504	−	0.910503i	$-0.364305\pi$
$733$	22.3904	0.827007	0.413504	+	0.910503i	$0.364305\pi$
$734$	16.9537	0.625774
$735$	−15.9084	−0.586790
$736$	6.59303	0.243022
$737$	1.54736	0.0569977
$738$	−6.04948	−0.222685
$739$	−51.4528	−1.89272	−0.946360	−	0.323113i	$-0.895271\pi$
$739$	−51.4528	−1.89272	−0.946360	+	0.323113i	$0.895271\pi$
$740$	11.3621	0.417679
$741$	4.99413	0.183464
$742$	−52.4021	−1.92374
$743$	5.34412	0.196057	0.0980283	−	0.995184i	$-0.468746\pi$
$743$	5.34412	0.196057	0.0980283	+	0.995184i	$0.468746\pi$
$744$	6.05760	0.222082
$745$	13.6271	0.499257
$746$	13.4320	0.491781
$747$	7.90079	0.289075
$748$	−3.71915	−0.135985
$749$	−59.2113	−2.16353
$750$	−12.1586	−0.443971
$751$	24.3927	0.890102	0.445051	−	0.895505i	$-0.353186\pi$
$751$	24.3927	0.890102	0.445051	+	0.895505i	$0.353186\pi$
$752$	−6.62715	−0.241667
$753$	22.2828	0.812032
$754$	−1.31057	−0.0477282
$755$	−42.7747	−1.55673
$756$	3.99413	0.145265
$757$	−24.3390	−0.884615	−0.442307	−	0.896864i	$-0.645840\pi$
$757$	−24.3390	−0.884615	−0.442307	+	0.896864i	$0.645840\pi$
$758$	−22.2036	−0.806470
$759$	−3.82434	−0.138815
$760$	8.87388	0.321889
$761$	−22.6685	−0.821734	−0.410867	−	0.911695i	$-0.634774\pi$
$761$	−22.6685	−0.821734	−0.410867	+	0.911695i	$0.634774\pi$
$762$	−17.6101	−0.637948
$763$	−1.79707	−0.0650584
$764$	−14.4869	−0.524117
$765$	11.3927	0.411903
$766$	−32.3119	−1.16748
$767$	−10.2716	−0.370887
$768$	−1.00000	−0.0360844
$769$	−39.2405	−1.41505	−0.707525	−	0.706688i	$-0.750188\pi$
$769$	−39.2405	−1.41505	−0.707525	+	0.706688i	$0.750188\pi$
$770$	−4.11668	−0.148355
$771$	−21.2192	−0.764191
$772$	4.70533	0.169348
$773$	−36.1583	−1.30052	−0.650262	−	0.759710i	$-0.725341\pi$
$773$	−36.1583	−1.30052	−0.650262	+	0.759710i	$0.725341\pi$
$774$	−11.3839	−0.409187
$775$	−11.1627	−0.400977
$776$	−8.16221	−0.293006
$777$	25.5404	0.916256
$778$	−6.20757	−0.222552
$779$	−30.2119	−1.08245
$780$	−1.77686	−0.0636218
$781$	−2.22839	−0.0797382
$782$	42.2724	1.51166
$783$	−1.31057	−0.0468360
$784$	8.95309	0.319753
$785$	−34.6387	−1.23631
$786$	−6.23844	−0.222518
$787$	−13.0837	−0.466383	−0.233192	−	0.972431i	$-0.574917\pi$
$787$	−13.0837	−0.466383	−0.233192	+	0.972431i	$0.574917\pi$
$788$	18.9174	0.673904
$789$	30.7091	1.09327
$790$	−4.78770	−0.170339
$791$	−34.3575	−1.22161
$792$	0.580058	0.0206115
$793$	−12.6576	−0.449484
$794$	31.7721	1.12755
$795$	23.3120	0.826792
$796$	−17.0528	−0.604421
$797$	−18.0958	−0.640986	−0.320493	−	0.947251i	$-0.603849\pi$
$797$	−18.0958	−0.640986	−0.320493	+	0.947251i	$0.603849\pi$
$798$	19.9472	0.706124
$799$	−42.4912	−1.50323
$800$	1.84277	0.0651516
$801$	−3.95413	−0.139712
$802$	1.07631	0.0380058
$803$	−7.04565	−0.248636
$804$	2.66759	0.0940787
$805$	46.7909	1.64916
$806$	−6.05760	−0.213370
$807$	5.25791	0.185087
$808$	−12.4955	−0.439589
$809$	−25.8625	−0.909279	−0.454639	−	0.890676i	$-0.650232\pi$
$809$	−25.8625	−0.909279	−0.454639	+	0.890676i	$0.650232\pi$
$810$	−1.77686	−0.0624325
$811$	29.4105	1.03274	0.516372	−	0.856365i	$-0.327282\pi$
$811$	29.4105	1.03274	0.516372	+	0.856365i	$0.327282\pi$
$812$	−5.23460	−0.183698
$813$	−8.79084	−0.308308
$814$	3.70917	0.130006
$815$	41.0570	1.43816
$816$	−6.41168	−0.224454
$817$	−56.8529	−1.98903
$818$	9.73909	0.340519
$819$	−3.99413	−0.139566
$820$	10.7491	0.375374
$821$	−36.3972	−1.27027	−0.635136	−	0.772401i	$-0.719056\pi$
$821$	−36.3972	−1.27027	−0.635136	+	0.772401i	$0.719056\pi$
$822$	−16.0387	−0.559414
$823$	0.996537	0.0347371	0.0173686	−	0.999849i	$-0.494471\pi$
$823$	0.996537	0.0347371	0.0173686	+	0.999849i	$0.494471\pi$
$824$	−1.00000	−0.0348367
$825$	−1.06891	−0.0372147
$826$	−41.0262	−1.42749
$827$	−50.7933	−1.76626	−0.883129	−	0.469131i	$-0.844567\pi$
$827$	−50.7933	−1.76626	−0.883129	+	0.469131i	$0.844567\pi$
$828$	−6.59303	−0.229124
$829$	−4.46349	−0.155023	−0.0775116	−	0.996991i	$-0.524697\pi$
$829$	−4.46349	−0.155023	−0.0775116	+	0.996991i	$0.524697\pi$
$830$	−14.0386	−0.487287
$831$	22.0601	0.765258
$832$	1.00000	0.0346688
$833$	57.4044	1.98894
$834$	5.44497	0.188544
$835$	16.7393	0.579287
$836$	2.89689	0.100191
$837$	−6.05760	−0.209381
$838$	−15.8585	−0.547824
$839$	−34.3485	−1.18584	−0.592921	−	0.805261i	$-0.702025\pi$
$839$	−34.3485	−1.18584	−0.592921	+	0.805261i	$0.702025\pi$
$840$	−7.09702	−0.244870
$841$	−27.2824	−0.940772
$842$	−7.52106	−0.259193
$843$	2.69154	0.0927017
$844$	−7.46310	−0.256891
$845$	1.77686	0.0611259
$846$	6.62715	0.227846
$847$	42.5916	1.46346
$848$	−13.1198	−0.450535
$849$	−1.11537	−0.0382794
$850$	11.8152	0.405259
$851$	−42.1590	−1.44519
$852$	−3.84167	−0.131614
$853$	−2.70374	−0.0925743	−0.0462872	−	0.998928i	$-0.514739\pi$
$853$	−2.70374	−0.0925743	−0.0462872	+	0.998928i	$0.514739\pi$
$854$	−50.5560	−1.72999
$855$	−8.87388	−0.303480
$856$	−14.8246	−0.506694
$857$	−8.73255	−0.298298	−0.149149	−	0.988815i	$-0.547653\pi$
$857$	−8.73255	−0.298298	−0.149149	+	0.988815i	$0.547653\pi$
$858$	−0.580058	−0.0198029
$859$	−31.1071	−1.06136	−0.530681	−	0.847572i	$-0.678064\pi$
$859$	−31.1071	−1.06136	−0.530681	+	0.847572i	$0.678064\pi$
$860$	20.2277	0.689758
$861$	24.1624	0.823453
$862$	2.73677	0.0932149
$863$	−21.0751	−0.717405	−0.358702	−	0.933452i	$-0.616781\pi$
$863$	−21.0751	−0.717405	−0.358702	+	0.933452i	$0.616781\pi$
$864$	1.00000	0.0340207
$865$	−39.1844	−1.33231
$866$	12.6570	0.430104
$867$	−24.1097	−0.818807
$868$	−24.1948	−0.821227
$869$	−1.56295	−0.0530194
$870$	2.32870	0.0789505
$871$	−2.66759	−0.0903879
$872$	−0.449928	−0.0152365
$873$	8.16221	0.276249
$874$	−32.9265	−1.11375
$875$	48.5632	1.64174
$876$	−12.1465	−0.410391
$877$	41.3978	1.39790	0.698952	−	0.715168i	$-0.253650\pi$
$877$	41.3978	1.39790	0.698952	+	0.715168i	$0.253650\pi$
$878$	−26.3495	−0.889251
$879$	−23.8587	−0.804733
$880$	−1.03068	−0.0347443
$881$	45.4935	1.53272	0.766358	−	0.642414i	$-0.222067\pi$
$881$	45.4935	1.53272	0.766358	+	0.642414i	$0.222067\pi$
$882$	−8.95309	−0.301466
$883$	−3.89717	−0.131150	−0.0655751	−	0.997848i	$-0.520888\pi$
$883$	−3.89717	−0.131150	−0.0655751	+	0.997848i	$0.520888\pi$
$884$	6.41168	0.215648
$885$	18.2513	0.613509
$886$	1.36156	0.0457425
$887$	30.0627	1.00941	0.504703	−	0.863293i	$-0.331602\pi$
$887$	30.0627	1.00941	0.504703	+	0.863293i	$0.331602\pi$
$888$	6.39448	0.214585
$889$	70.3372	2.35903
$890$	7.02594	0.235510
$891$	−0.580058	−0.0194327
$892$	−14.0884	−0.471714
$893$	33.0968	1.10754
$894$	7.66917	0.256496
$895$	8.07008	0.269753
$896$	3.99413	0.133435
$897$	6.59303	0.220135
$898$	8.70559	0.290509
$899$	7.93892	0.264778
$900$	−1.84277	−0.0614255
$901$	−84.1199	−2.80244
$902$	3.50905	0.116839
$903$	45.4690	1.51311
$904$	−8.60200	−0.286098
$905$	26.7189	0.888167
$906$	−24.0732	−0.799778
$907$	−18.6460	−0.619131	−0.309565	−	0.950878i	$-0.600184\pi$
$907$	−18.6460	−0.619131	−0.309565	+	0.950878i	$0.600184\pi$
$908$	11.7368	0.389500
$909$	12.4955	0.414448
$910$	7.09702	0.235264
$911$	9.08947	0.301148	0.150574	−	0.988599i	$-0.451888\pi$
$911$	9.08947	0.301148	0.150574	+	0.988599i	$0.451888\pi$
$912$	4.99413	0.165372
$913$	−4.58292	−0.151672
$914$	−35.5594	−1.17620
$915$	22.4907	0.743521
$916$	−22.2214	−0.734215
$917$	24.9171	0.822836
$918$	6.41168	0.211617
$919$	−38.1617	−1.25884	−0.629420	−	0.777066i	$-0.716707\pi$
$919$	−38.1617	−1.25884	−0.629420	+	0.777066i	$0.716707\pi$
$920$	11.7149	0.386229
$921$	−18.1999	−0.599708
$922$	28.8532	0.950228
$923$	3.84167	0.126450
$924$	−2.31683	−0.0762180
$925$	−11.7835	−0.387440
$926$	−28.1865	−0.926267
$927$	1.00000	0.0328443
$928$	−1.31057	−0.0430217
$929$	30.0092	0.984569	0.492284	−	0.870434i	$-0.336162\pi$
$929$	30.0092	0.984569	0.492284	+	0.870434i	$0.336162\pi$
$930$	10.7635	0.352949
$931$	−44.7129	−1.46541
$932$	−2.45597	−0.0804480
$933$	−16.7588	−0.548659
$934$	24.3804	0.797751
$935$	−6.60841	−0.216118
$936$	−1.00000	−0.0326860
$937$	−8.65798	−0.282844	−0.141422	−	0.989949i	$-0.545167\pi$
$937$	−8.65798	−0.282844	−0.141422	+	0.989949i	$0.545167\pi$
$938$	−10.6547	−0.347889
$939$	−15.1054	−0.492947
$940$	−11.7755	−0.384075
$941$	−47.0434	−1.53357	−0.766786	−	0.641903i	$-0.778145\pi$
$941$	−47.0434	−1.53357	−0.766786	+	0.641903i	$0.778145\pi$
$942$	−19.4944	−0.635160
$943$	−39.8844	−1.29882
$944$	−10.2716	−0.334313
$945$	7.09702	0.230866
$946$	6.60335	0.214693
$947$	37.1553	1.20739	0.603693	−	0.797217i	$-0.293695\pi$
$947$	37.1553	1.20739	0.603693	+	0.797217i	$0.293695\pi$
$948$	−2.69447	−0.0875124
$949$	12.1465	0.394291
$950$	−9.20301	−0.298585
$951$	−26.7194	−0.866436
$952$	25.6091	0.829996
$953$	−3.14924	−0.102014	−0.0510070	−	0.998698i	$-0.516243\pi$
$953$	−3.14924	−0.102014	−0.0510070	+	0.998698i	$0.516243\pi$
$954$	13.1198	0.424769
$955$	−25.7412	−0.832965
$956$	0.439459	0.0142131
$957$	0.760208	0.0245740
$958$	−3.35175	−0.108290
$959$	64.0607	2.06863
$960$	−1.77686	−0.0573479
$961$	5.69450	0.183693
$962$	−6.39448	−0.206166
$963$	14.8246	0.477715
$964$	−25.8545	−0.832717
$965$	8.36071	0.269141
$966$	26.3334	0.847265
$967$	12.7204	0.409059	0.204529	−	0.978860i	$-0.434434\pi$
$967$	12.7204	0.409059	0.204529	+	0.978860i	$0.434434\pi$
$968$	10.6635	0.342739
$969$	32.0208	1.02866
$970$	−14.5031	−0.465667
$971$	53.9868	1.73252	0.866259	−	0.499595i	$-0.166518\pi$
$971$	53.9868	1.73252	0.866259	+	0.499595i	$0.166518\pi$
$972$	−1.00000	−0.0320750
$973$	−21.7479	−0.697206
$974$	27.2724	0.873864
$975$	1.84277	0.0590157
$976$	−12.6576	−0.405159
$977$	41.5695	1.32993	0.664963	−	0.746877i	$-0.268447\pi$
$977$	41.5695	1.32993	0.664963	+	0.746877i	$0.268447\pi$
$978$	23.1065	0.738864
$979$	2.29363	0.0733046
$980$	15.9084	0.508175
$981$	0.449928	0.0143651
$982$	8.42210	0.268760
$983$	−30.8874	−0.985156	−0.492578	−	0.870268i	$-0.663945\pi$
$983$	−30.8874	−0.985156	−0.492578	+	0.870268i	$0.663945\pi$
$984$	6.04948	0.192850
$985$	33.6136	1.07102
$986$	−8.40297	−0.267605
$987$	−26.4697	−0.842540
$988$	−4.99413	−0.158885
$989$	−75.0547	−2.38660
$990$	1.03068	0.0327572
$991$	30.8564	0.980185	0.490092	−	0.871670i	$-0.336963\pi$
$991$	30.8564	0.980185	0.490092	+	0.871670i	$0.336963\pi$
$992$	−6.05760	−0.192329
$993$	30.1515	0.956829
$994$	15.3441	0.486687
$995$	−30.3005	−0.960589
$996$	−7.90079	−0.250346
$997$	−18.2690	−0.578584	−0.289292	−	0.957241i	$-0.593420\pi$
$997$	−18.2690	−0.578584	−0.289292	+	0.957241i	$0.593420\pi$
$998$	9.31527	0.294870
$999$	−6.39448	−0.202312

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.o.1.5	✓	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.o.1.5	✓	7	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.77686 q^{5} +1.00000 q^{6} -3.99413 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.77686 q^{5} +1.00000 q^{6} -3.99413 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.77686 q^{10} -0.580058 q^{11} -1.00000 q^{12} +1.00000 q^{13} +3.99413 q^{14} -1.77686 q^{15} +1.00000 q^{16} +6.41168 q^{17} -1.00000 q^{18} -4.99413 q^{19} +1.77686 q^{20} +3.99413 q^{21} +0.580058 q^{22} -6.59303 q^{23} +1.00000 q^{24} -1.84277 q^{25} -1.00000 q^{26} -1.00000 q^{27} -3.99413 q^{28} +1.31057 q^{29} +1.77686 q^{30} +6.05760 q^{31} -1.00000 q^{32} +0.580058 q^{33} -6.41168 q^{34} -7.09702 q^{35} +1.00000 q^{36} +6.39448 q^{37} +4.99413 q^{38} -1.00000 q^{39} -1.77686 q^{40} +6.04948 q^{41} -3.99413 q^{42} +11.3839 q^{43} -0.580058 q^{44} +1.77686 q^{45} +6.59303 q^{46} -6.62715 q^{47} -1.00000 q^{48} +8.95309 q^{49} +1.84277 q^{50} -6.41168 q^{51} +1.00000 q^{52} -13.1198 q^{53} +1.00000 q^{54} -1.03068 q^{55} +3.99413 q^{56} +4.99413 q^{57} -1.31057 q^{58} -10.2716 q^{59} -1.77686 q^{60} -12.6576 q^{61} -6.05760 q^{62} -3.99413 q^{63} +1.00000 q^{64} +1.77686 q^{65} -0.580058 q^{66} -2.66759 q^{67} +6.41168 q^{68} +6.59303 q^{69} +7.09702 q^{70} +3.84167 q^{71} -1.00000 q^{72} +12.1465 q^{73} -6.39448 q^{74} +1.84277 q^{75} -4.99413 q^{76} +2.31683 q^{77} +1.00000 q^{78} +2.69447 q^{79} +1.77686 q^{80} +1.00000 q^{81} -6.04948 q^{82} +7.90079 q^{83} +3.99413 q^{84} +11.3927 q^{85} -11.3839 q^{86} -1.31057 q^{87} +0.580058 q^{88} -3.95413 q^{89} -1.77686 q^{90} -3.99413 q^{91} -6.59303 q^{92} -6.05760 q^{93} +6.62715 q^{94} -8.87388 q^{95} +1.00000 q^{96} +8.16221 q^{97} -8.95309 q^{98} -0.580058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9	\( 7 q - 7 q^{2} - 7 q^{3} + 7 q^{4} + 2 q^{5} + 7 q^{6} - 9 q^{7} - 7 q^{8} + 7 q^{9} - 2 q^{10} - 7 q^{12} + 7 q^{13} + 9 q^{14} - 2 q^{15} + 7 q^{16} + 3 q^{17} - 7 q^{18} - 16 q^{19} + 2 q^{20} + 9 q^{21} + 6 q^{23} + 7 q^{24} + 15 q^{25} - 7 q^{26} - 7 q^{27} - 9 q^{28} - 5 q^{29} + 2 q^{30} - 16 q^{31} - 7 q^{32} - 3 q^{34} - 10 q^{35} + 7 q^{36} + 17 q^{37} + 16 q^{38} - 7 q^{39} - 2 q^{40} + 12 q^{41} - 9 q^{42} - 22 q^{43} + 2 q^{45} - 6 q^{46} - 7 q^{48} - 2 q^{49} - 15 q^{50} - 3 q^{51} + 7 q^{52} + 2 q^{53} + 7 q^{54} - 16 q^{55} + 9 q^{56} + 16 q^{57} + 5 q^{58} - 3 q^{59} - 2 q^{60} - 6 q^{61} + 16 q^{62} - 9 q^{63} + 7 q^{64} + 2 q^{65} + q^{67} + 3 q^{68} - 6 q^{69} + 10 q^{70} + 15 q^{71} - 7 q^{72} + 17 q^{73} - 17 q^{74} - 15 q^{75} - 16 q^{76} - 10 q^{77} + 7 q^{78} - 27 q^{79} + 2 q^{80} + 7 q^{81} - 12 q^{82} + 12 q^{83} + 9 q^{84} + 15 q^{85} + 22 q^{86} + 5 q^{87} - 9 q^{89} - 2 q^{90} - 9 q^{91} + 6 q^{92} + 16 q^{93} - 12 q^{95} + 7 q^{96} - 3 q^{97} + 2 q^{98}+O(q^{100}) \) 7 * q - 7 * q^2 - 7 * q^3 + 7 * q^4 + 2 * q^5 + 7 * q^6 - 9 * q^7 - 7 * q^8 + 7 * q^9 - 2 * q^10 - 7 * q^12 + 7 * q^13 + 9 * q^14 - 2 * q^15 + 7 * q^16 + 3 * q^17 - 7 * q^18 - 16 * q^19 + 2 * q^20 + 9 * q^21 + 6 * q^23 + 7 * q^24 + 15 * q^25 - 7 * q^26 - 7 * q^27 - 9 * q^28 - 5 * q^29 + 2 * q^30 - 16 * q^31 - 7 * q^32 - 3 * q^34 - 10 * q^35 + 7 * q^36 + 17 * q^37 + 16 * q^38 - 7 * q^39 - 2 * q^40 + 12 * q^41 - 9 * q^42 - 22 * q^43 + 2 * q^45 - 6 * q^46 - 7 * q^48 - 2 * q^49 - 15 * q^50 - 3 * q^51 + 7 * q^52 + 2 * q^53 + 7 * q^54 - 16 * q^55 + 9 * q^56 + 16 * q^57 + 5 * q^58 - 3 * q^59 - 2 * q^60 - 6 * q^61 + 16 * q^62 - 9 * q^63 + 7 * q^64 + 2 * q^65 + q^67 + 3 * q^68 - 6 * q^69 + 10 * q^70 + 15 * q^71 - 7 * q^72 + 17 * q^73 - 17 * q^74 - 15 * q^75 - 16 * q^76 - 10 * q^77 + 7 * q^78 - 27 * q^79 + 2 * q^80 + 7 * q^81 - 12 * q^82 + 12 * q^83 + 9 * q^84 + 15 * q^85 + 22 * q^86 + 5 * q^87 - 9 * q^89 - 2 * q^90 - 9 * q^91 + 6 * q^92 + 16 * q^93 - 12 * q^95 + 7 * q^96 - 3 * q^97 + 2 * q^98

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