LMFDB - Embedded newform 8034.2.a.y.1.4

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:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + \cdots - 180 $ x^13 - 5x^12 - 25x^11 + 134x^10 + 196x^9 - 1151x^8 - 801x^7 + 4263x^6 + 2205x^5 - 6840x^4 - 3579x^3 + 3559x^2 + 1839x - 180
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.72356$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.45246 q^{5} -1.00000 q^{6} -1.72356 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.45246 q^{5} -1.00000 q^{6} -1.72356 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.45246 q^{10} -1.08709 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.72356 q^{14} +1.45246 q^{15} +1.00000 q^{16} +6.85068 q^{17} +1.00000 q^{18} +5.87551 q^{19} -1.45246 q^{20} +1.72356 q^{21} -1.08709 q^{22} -3.73717 q^{23} -1.00000 q^{24} -2.89035 q^{25} +1.00000 q^{26} -1.00000 q^{27} -1.72356 q^{28} -5.04062 q^{29} +1.45246 q^{30} +5.87551 q^{31} +1.00000 q^{32} +1.08709 q^{33} +6.85068 q^{34} +2.50341 q^{35} +1.00000 q^{36} -2.76597 q^{37} +5.87551 q^{38} -1.00000 q^{39} -1.45246 q^{40} +5.20035 q^{41} +1.72356 q^{42} +0.243271 q^{43} -1.08709 q^{44} -1.45246 q^{45} -3.73717 q^{46} -10.8042 q^{47} -1.00000 q^{48} -4.02934 q^{49} -2.89035 q^{50} -6.85068 q^{51} +1.00000 q^{52} -3.42652 q^{53} -1.00000 q^{54} +1.57895 q^{55} -1.72356 q^{56} -5.87551 q^{57} -5.04062 q^{58} +12.2262 q^{59} +1.45246 q^{60} -13.3860 q^{61} +5.87551 q^{62} -1.72356 q^{63} +1.00000 q^{64} -1.45246 q^{65} +1.08709 q^{66} +4.14842 q^{67} +6.85068 q^{68} +3.73717 q^{69} +2.50341 q^{70} -1.20168 q^{71} +1.00000 q^{72} +6.43732 q^{73} -2.76597 q^{74} +2.89035 q^{75} +5.87551 q^{76} +1.87366 q^{77} -1.00000 q^{78} +13.4240 q^{79} -1.45246 q^{80} +1.00000 q^{81} +5.20035 q^{82} -16.6762 q^{83} +1.72356 q^{84} -9.95035 q^{85} +0.243271 q^{86} +5.04062 q^{87} -1.08709 q^{88} +4.27223 q^{89} -1.45246 q^{90} -1.72356 q^{91} -3.73717 q^{92} -5.87551 q^{93} -10.8042 q^{94} -8.53396 q^{95} -1.00000 q^{96} +0.783112 q^{97} -4.02934 q^{98} -1.08709 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.45246	−0.649561	−0.324781	−	0.945789i	$-0.605290\pi$
$5$	−1.45246	−0.649561	−0.324781	+	0.945789i	$0.605290\pi$
$6$	−1.00000	−0.408248
$7$	−1.72356	−0.651444	−0.325722	−	0.945466i	$-0.605607\pi$
$7$	−1.72356	−0.651444	−0.325722	+	0.945466i	$0.605607\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.45246	−0.459309
$11$	−1.08709	−0.327769	−0.163885	−	0.986480i	$-0.552402\pi$
$11$	−1.08709	−0.327769	−0.163885	+	0.986480i	$0.552402\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.72356	−0.460640
$15$	1.45246	0.375024
$16$	1.00000	0.250000
$17$	6.85068	1.66153	0.830767	−	0.556621i	$-0.187902\pi$
$17$	6.85068	1.66153	0.830767	+	0.556621i	$0.187902\pi$
$18$	1.00000	0.235702
$19$	5.87551	1.34794	0.673968	−	0.738761i	$-0.264589\pi$
$19$	5.87551	1.34794	0.673968	+	0.738761i	$0.264589\pi$
$20$	−1.45246	−0.324781
$21$	1.72356	0.376111
$22$	−1.08709	−0.231768
$23$	−3.73717	−0.779254	−0.389627	−	0.920973i	$-0.627396\pi$
$23$	−3.73717	−0.779254	−0.389627	+	0.920973i	$0.627396\pi$
$24$	−1.00000	−0.204124
$25$	−2.89035	−0.578070
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−1.72356	−0.325722
$29$	−5.04062	−0.936020	−0.468010	−	0.883723i	$-0.655029\pi$
$29$	−5.04062	−0.936020	−0.468010	+	0.883723i	$0.655029\pi$
$30$	1.45246	0.265182
$31$	5.87551	1.05527	0.527637	−	0.849470i	$-0.323078\pi$
$31$	5.87551	1.05527	0.527637	+	0.849470i	$0.323078\pi$
$32$	1.00000	0.176777
$33$	1.08709	0.189238
$34$	6.85068	1.17488
$35$	2.50341	0.423153
$36$	1.00000	0.166667
$37$	−2.76597	−0.454723	−0.227362	−	0.973810i	$-0.573010\pi$
$37$	−2.76597	−0.454723	−0.227362	+	0.973810i	$0.573010\pi$
$38$	5.87551	0.953134
$39$	−1.00000	−0.160128
$40$	−1.45246	−0.229655
$41$	5.20035	0.812158	0.406079	−	0.913838i	$-0.366896\pi$
$41$	5.20035	0.812158	0.406079	+	0.913838i	$0.366896\pi$
$42$	1.72356	0.265951
$43$	0.243271	0.0370984	0.0185492	−	0.999828i	$-0.494095\pi$
$43$	0.243271	0.0370984	0.0185492	+	0.999828i	$0.494095\pi$
$44$	−1.08709	−0.163885
$45$	−1.45246	−0.216520
$46$	−3.73717	−0.551016
$47$	−10.8042	−1.57596	−0.787978	−	0.615703i	$-0.788872\pi$
$47$	−10.8042	−1.57596	−0.787978	+	0.615703i	$0.788872\pi$
$48$	−1.00000	−0.144338
$49$	−4.02934	−0.575621
$50$	−2.89035	−0.408757
$51$	−6.85068	−0.959287
$52$	1.00000	0.138675
$53$	−3.42652	−0.470669	−0.235335	−	0.971914i	$-0.575619\pi$
$53$	−3.42652	−0.470669	−0.235335	+	0.971914i	$0.575619\pi$
$54$	−1.00000	−0.136083
$55$	1.57895	0.212906
$56$	−1.72356	−0.230320
$57$	−5.87551	−0.778231
$58$	−5.04062	−0.661866
$59$	12.2262	1.59171	0.795856	−	0.605485i	$-0.207021\pi$
$59$	12.2262	1.59171	0.795856	+	0.605485i	$0.207021\pi$
$60$	1.45246	0.187512
$61$	−13.3860	−1.71390	−0.856949	−	0.515400i	$-0.827643\pi$
$61$	−13.3860	−1.71390	−0.856949	+	0.515400i	$0.827643\pi$
$62$	5.87551	0.746191
$63$	−1.72356	−0.217148
$64$	1.00000	0.125000
$65$	−1.45246	−0.180156
$66$	1.08709	0.133811
$67$	4.14842	0.506811	0.253405	−	0.967360i	$-0.418449\pi$
$67$	4.14842	0.506811	0.253405	+	0.967360i	$0.418449\pi$
$68$	6.85068	0.830767
$69$	3.73717	0.449902
$70$	2.50341	0.299214
$71$	−1.20168	−0.142614	−0.0713068	−	0.997454i	$-0.522717\pi$
$71$	−1.20168	−0.142614	−0.0713068	+	0.997454i	$0.522717\pi$
$72$	1.00000	0.117851
$73$	6.43732	0.753432	0.376716	−	0.926329i	$-0.377053\pi$
$73$	6.43732	0.753432	0.376716	+	0.926329i	$0.377053\pi$
$74$	−2.76597	−0.321538
$75$	2.89035	0.333749
$76$	5.87551	0.673968
$77$	1.87366	0.213523
$78$	−1.00000	−0.113228
$79$	13.4240	1.51032	0.755160	−	0.655540i	$-0.227559\pi$
$79$	13.4240	1.51032	0.755160	+	0.655540i	$0.227559\pi$
$80$	−1.45246	−0.162390
$81$	1.00000	0.111111
$82$	5.20035	0.574282
$83$	−16.6762	−1.83046	−0.915228	−	0.402936i	$-0.867990\pi$
$83$	−16.6762	−1.83046	−0.915228	+	0.402936i	$0.867990\pi$
$84$	1.72356	0.188056
$85$	−9.95035	−1.07927
$86$	0.243271	0.0262325
$87$	5.04062	0.540412
$88$	−1.08709	−0.115884
$89$	4.27223	0.452856	0.226428	−	0.974028i	$-0.427295\pi$
$89$	4.27223	0.452856	0.226428	+	0.974028i	$0.427295\pi$
$90$	−1.45246	−0.153103
$91$	−1.72356	−0.180678
$92$	−3.73717	−0.389627
$93$	−5.87551	−0.609262
$94$	−10.8042	−1.11437
$95$	−8.53396	−0.875566
$96$	−1.00000	−0.102062
$97$	0.783112	0.0795130	0.0397565	−	0.999209i	$-0.487342\pi$
$97$	0.783112	0.0795130	0.0397565	+	0.999209i	$0.487342\pi$
$98$	−4.02934	−0.407025
$99$	−1.08709	−0.109256
$100$	−2.89035	−0.289035
$101$	18.8022	1.87089	0.935446	−	0.353469i	$-0.114998\pi$
$101$	18.8022	1.87089	0.935446	+	0.353469i	$0.114998\pi$
$102$	−6.85068	−0.678318
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−2.50341	−0.244307
$106$	−3.42652	−0.332813
$107$	−14.8030	−1.43106	−0.715532	−	0.698580i	$-0.753815\pi$
$107$	−14.8030	−1.43106	−0.715532	+	0.698580i	$0.753815\pi$
$108$	−1.00000	−0.0962250
$109$	17.2028	1.64773	0.823863	−	0.566789i	$-0.191815\pi$
$109$	17.2028	1.64773	0.823863	+	0.566789i	$0.191815\pi$
$110$	1.57895	0.150547
$111$	2.76597	0.262535
$112$	−1.72356	−0.162861
$113$	−4.27985	−0.402614	−0.201307	−	0.979528i	$-0.564519\pi$
$113$	−4.27985	−0.402614	−0.201307	+	0.979528i	$0.564519\pi$
$114$	−5.87551	−0.550292
$115$	5.42810	0.506173
$116$	−5.04062	−0.468010
$117$	1.00000	0.0924500
$118$	12.2262	1.12551
$119$	−11.8075	−1.08240
$120$	1.45246	0.132591
$121$	−9.81824	−0.892567
$122$	−13.3860	−1.21191
$123$	−5.20035	−0.468899
$124$	5.87551	0.527637
$125$	11.4604	1.02505
$126$	−1.72356	−0.153547
$127$	−16.6757	−1.47973	−0.739865	−	0.672756i	$-0.765110\pi$
$127$	−16.6757	−1.47973	−0.739865	+	0.672756i	$0.765110\pi$
$128$	1.00000	0.0883883
$129$	−0.243271	−0.0214188
$130$	−1.45246	−0.127389
$131$	20.0092	1.74821	0.874104	−	0.485738i	$-0.161449\pi$
$131$	20.0092	1.74821	0.874104	+	0.485738i	$0.161449\pi$
$132$	1.08709	0.0946189
$133$	−10.1268	−0.878104
$134$	4.14842	0.358369
$135$	1.45246	0.125008
$136$	6.85068	0.587441
$137$	14.1790	1.21139	0.605696	−	0.795696i	$-0.292895\pi$
$137$	14.1790	1.21139	0.605696	+	0.795696i	$0.292895\pi$
$138$	3.73717	0.318129
$139$	17.8457	1.51365	0.756824	−	0.653618i	$-0.226750\pi$
$139$	17.8457	1.51365	0.756824	+	0.653618i	$0.226750\pi$
$140$	2.50341	0.211576
$141$	10.8042	0.909879
$142$	−1.20168	−0.100843
$143$	−1.08709	−0.0909069
$144$	1.00000	0.0833333
$145$	7.32132	0.608002
$146$	6.43732	0.532757
$147$	4.02934	0.332335
$148$	−2.76597	−0.227362
$149$	−17.3689	−1.42291	−0.711457	−	0.702729i	$-0.751965\pi$
$149$	−17.3689	−1.42291	−0.711457	+	0.702729i	$0.751965\pi$
$150$	2.89035	0.235996
$151$	10.4241	0.848302	0.424151	−	0.905592i	$-0.360573\pi$
$151$	10.4241	0.848302	0.424151	+	0.905592i	$0.360573\pi$
$152$	5.87551	0.476567
$153$	6.85068	0.553844
$154$	1.87366	0.150984
$155$	−8.53396	−0.685464
$156$	−1.00000	−0.0800641
$157$	15.8243	1.26291	0.631456	−	0.775411i	$-0.282457\pi$
$157$	15.8243	1.26291	0.631456	+	0.775411i	$0.282457\pi$
$158$	13.4240	1.06796
$159$	3.42652	0.271741
$160$	−1.45246	−0.114827
$161$	6.44123	0.507640
$162$	1.00000	0.0785674
$163$	21.3787	1.67451	0.837254	−	0.546814i	$-0.184160\pi$
$163$	21.3787	1.67451	0.837254	+	0.546814i	$0.184160\pi$
$164$	5.20035	0.406079
$165$	−1.57895	−0.122921
$166$	−16.6762	−1.29433
$167$	7.99844	0.618938	0.309469	−	0.950910i	$-0.399849\pi$
$167$	7.99844	0.618938	0.309469	+	0.950910i	$0.399849\pi$
$168$	1.72356	0.132975
$169$	1.00000	0.0769231
$170$	−9.95035	−0.763157
$171$	5.87551	0.449312
$172$	0.243271	0.0185492
$173$	18.0726	1.37403	0.687017	−	0.726642i	$-0.258920\pi$
$173$	18.0726	1.37403	0.687017	+	0.726642i	$0.258920\pi$
$174$	5.04062	0.382129
$175$	4.98169	0.376580
$176$	−1.08709	−0.0819423
$177$	−12.2262	−0.918976
$178$	4.27223	0.320218
$179$	−4.70667	−0.351793	−0.175897	−	0.984409i	$-0.556282\pi$
$179$	−4.70667	−0.351793	−0.175897	+	0.984409i	$0.556282\pi$
$180$	−1.45246	−0.108260
$181$	7.31360	0.543615	0.271808	−	0.962352i	$-0.412379\pi$
$181$	7.31360	0.543615	0.271808	+	0.962352i	$0.412379\pi$
$182$	−1.72356	−0.127759
$183$	13.3860	0.989520
$184$	−3.73717	−0.275508
$185$	4.01747	0.295371
$186$	−5.87551	−0.430813
$187$	−7.44729	−0.544600
$188$	−10.8042	−0.787978
$189$	1.72356	0.125370
$190$	−8.53396	−0.619119
$191$	14.8166	1.07209	0.536044	−	0.844190i	$-0.319918\pi$
$191$	14.8166	1.07209	0.536044	+	0.844190i	$0.319918\pi$
$192$	−1.00000	−0.0721688
$193$	−0.0984871	−0.00708926	−0.00354463	−	0.999994i	$-0.501128\pi$
$193$	−0.0984871	−0.00708926	−0.00354463	+	0.999994i	$0.501128\pi$
$194$	0.783112	0.0562242
$195$	1.45246	0.104013
$196$	−4.02934	−0.287810
$197$	12.2026	0.869401	0.434700	−	0.900575i	$-0.356854\pi$
$197$	12.2026	0.869401	0.434700	+	0.900575i	$0.356854\pi$
$198$	−1.08709	−0.0772560
$199$	12.0042	0.850959	0.425479	−	0.904968i	$-0.360106\pi$
$199$	12.0042	0.850959	0.425479	+	0.904968i	$0.360106\pi$
$200$	−2.89035	−0.204379
$201$	−4.14842	−0.292607
$202$	18.8022	1.32292
$203$	8.68781	0.609765
$204$	−6.85068	−0.479643
$205$	−7.55331	−0.527546
$206$	1.00000	0.0696733
$207$	−3.73717	−0.259751
$208$	1.00000	0.0693375
$209$	−6.38720	−0.441812
$210$	−2.50341	−0.172751
$211$	−5.33439	−0.367235	−0.183617	−	0.982998i	$-0.558781\pi$
$211$	−5.33439	−0.367235	−0.183617	+	0.982998i	$0.558781\pi$
$212$	−3.42652	−0.235335
$213$	1.20168	0.0823380
$214$	−14.8030	−1.01191
$215$	−0.353342	−0.0240977
$216$	−1.00000	−0.0680414
$217$	−10.1268	−0.687451
$218$	17.2028	1.16512
$219$	−6.43732	−0.434994
$220$	1.57895	0.106453
$221$	6.85068	0.460826
$222$	2.76597	0.185640
$223$	−17.6229	−1.18012	−0.590058	−	0.807361i	$-0.700895\pi$
$223$	−17.6229	−1.18012	−0.590058	+	0.807361i	$0.700895\pi$
$224$	−1.72356	−0.115160
$225$	−2.89035	−0.192690
$226$	−4.27985	−0.284691
$227$	−7.67048	−0.509108	−0.254554	−	0.967059i	$-0.581929\pi$
$227$	−7.67048	−0.509108	−0.254554	+	0.967059i	$0.581929\pi$
$228$	−5.87551	−0.389115
$229$	−3.27629	−0.216503	−0.108252	−	0.994124i	$-0.534525\pi$
$229$	−3.27629	−0.216503	−0.108252	+	0.994124i	$0.534525\pi$
$230$	5.42810	0.357918
$231$	−1.87366	−0.123278
$232$	−5.04062	−0.330933
$233$	20.6323	1.35167	0.675835	−	0.737053i	$-0.263783\pi$
$233$	20.6323	1.35167	0.675835	+	0.737053i	$0.263783\pi$
$234$	1.00000	0.0653720
$235$	15.6927	1.02368
$236$	12.2262	0.795856
$237$	−13.4240	−0.871984
$238$	−11.8075	−0.765370
$239$	3.99774	0.258592	0.129296	−	0.991606i	$-0.458728\pi$
$239$	3.99774	0.258592	0.129296	+	0.991606i	$0.458728\pi$
$240$	1.45246	0.0937561
$241$	25.8910	1.66779	0.833893	−	0.551926i	$-0.186107\pi$
$241$	25.8910	1.66779	0.833893	+	0.551926i	$0.186107\pi$
$242$	−9.81824	−0.631140
$243$	−1.00000	−0.0641500
$244$	−13.3860	−0.856949
$245$	5.85247	0.373901
$246$	−5.20035	−0.331562
$247$	5.87551	0.373850
$248$	5.87551	0.373095
$249$	16.6762	1.05681
$250$	11.4604	0.724822
$251$	0.207349	0.0130877	0.00654387	−	0.999979i	$-0.497917\pi$
$251$	0.207349	0.0130877	0.00654387	+	0.999979i	$0.497917\pi$
$252$	−1.72356	−0.108574
$253$	4.06263	0.255416
$254$	−16.6757	−1.04633
$255$	9.95035	0.623115
$256$	1.00000	0.0625000
$257$	−12.6839	−0.791198	−0.395599	−	0.918423i	$-0.629463\pi$
$257$	−12.6839	−0.791198	−0.395599	+	0.918423i	$0.629463\pi$
$258$	−0.243271	−0.0151454
$259$	4.76732	0.296227
$260$	−1.45246	−0.0900779
$261$	−5.04062	−0.312007
$262$	20.0092	1.23617
$263$	−23.8330	−1.46961	−0.734803	−	0.678281i	$-0.762725\pi$
$263$	−23.8330	−1.46961	−0.734803	+	0.678281i	$0.762725\pi$
$264$	1.08709	0.0669056
$265$	4.97690	0.305728
$266$	−10.1268	−0.620913
$267$	−4.27223	−0.261457
$268$	4.14842	0.253405
$269$	19.9757	1.21794	0.608969	−	0.793194i	$-0.291583\pi$
$269$	19.9757	1.21794	0.608969	+	0.793194i	$0.291583\pi$
$270$	1.45246	0.0883941
$271$	−19.6972	−1.19652	−0.598260	−	0.801302i	$-0.704141\pi$
$271$	−19.6972	−1.19652	−0.598260	+	0.801302i	$0.704141\pi$
$272$	6.85068	0.415383
$273$	1.72356	0.104315
$274$	14.1790	0.856584
$275$	3.14207	0.189474
$276$	3.73717	0.224951
$277$	19.2254	1.15514	0.577572	−	0.816340i	$-0.304000\pi$
$277$	19.2254	1.15514	0.577572	+	0.816340i	$0.304000\pi$
$278$	17.8457	1.07031
$279$	5.87551	0.351758
$280$	2.50341	0.149607
$281$	8.85431	0.528204	0.264102	−	0.964495i	$-0.414924\pi$
$281$	8.85431	0.528204	0.264102	+	0.964495i	$0.414924\pi$
$282$	10.8042	0.643382
$283$	−14.3114	−0.850723	−0.425361	−	0.905024i	$-0.639853\pi$
$283$	−14.3114	−0.850723	−0.425361	+	0.905024i	$0.639853\pi$
$284$	−1.20168	−0.0713068
$285$	8.53396	0.505508
$286$	−1.08709	−0.0642809
$287$	−8.96310	−0.529075
$288$	1.00000	0.0589256
$289$	29.9318	1.76069
$290$	7.32132	0.429923
$291$	−0.783112	−0.0459068
$292$	6.43732	0.376716
$293$	0.776075	0.0453388	0.0226694	−	0.999743i	$-0.492783\pi$
$293$	0.776075	0.0453388	0.0226694	+	0.999743i	$0.492783\pi$
$294$	4.02934	0.234996
$295$	−17.7581	−1.03391
$296$	−2.76597	−0.160769
$297$	1.08709	0.0630792
$298$	−17.3689	−1.00615
$299$	−3.73717	−0.216126
$300$	2.89035	0.166875
$301$	−0.419291	−0.0241675
$302$	10.4241	0.599840
$303$	−18.8022	−1.08016
$304$	5.87551	0.336984
$305$	19.4426	1.11328
$306$	6.85068	0.391627
$307$	29.9498	1.70933	0.854664	−	0.519182i	$-0.173763\pi$
$307$	29.9498	1.70933	0.854664	+	0.519182i	$0.173763\pi$
$308$	1.87366	0.106762
$309$	−1.00000	−0.0568880
$310$	−8.53396	−0.484697
$311$	−4.39195	−0.249045	−0.124522	−	0.992217i	$-0.539740\pi$
$311$	−4.39195	−0.249045	−0.124522	+	0.992217i	$0.539740\pi$
$312$	−1.00000	−0.0566139
$313$	17.8325	1.00795	0.503976	−	0.863718i	$-0.331870\pi$
$313$	17.8325	1.00795	0.503976	+	0.863718i	$0.331870\pi$
$314$	15.8243	0.893014
$315$	2.50341	0.141051
$316$	13.4240	0.755160
$317$	−15.0694	−0.846383	−0.423192	−	0.906040i	$-0.639090\pi$
$317$	−15.0694	−0.846383	−0.423192	+	0.906040i	$0.639090\pi$
$318$	3.42652	0.192150
$319$	5.47960	0.306799
$320$	−1.45246	−0.0811951
$321$	14.8030	0.826225
$322$	6.44123	0.358956
$323$	40.2512	2.23964
$324$	1.00000	0.0555556
$325$	−2.89035	−0.160328
$326$	21.3787	1.18406
$327$	−17.2028	−0.951315
$328$	5.20035	0.287141
$329$	18.6217	1.02665
$330$	−1.57895	−0.0869186
$331$	−6.92352	−0.380551	−0.190276	−	0.981731i	$-0.560938\pi$
$331$	−6.92352	−0.380551	−0.190276	+	0.981731i	$0.560938\pi$
$332$	−16.6762	−0.915228
$333$	−2.76597	−0.151574
$334$	7.99844	0.437655
$335$	−6.02543	−0.329204
$336$	1.72356	0.0940278
$337$	−7.35657	−0.400738	−0.200369	−	0.979721i	$-0.564214\pi$
$337$	−7.35657	−0.400738	−0.200369	+	0.979721i	$0.564214\pi$
$338$	1.00000	0.0543928
$339$	4.27985	0.232449
$340$	−9.95035	−0.539634
$341$	−6.38720	−0.345886
$342$	5.87551	0.317711
$343$	19.0097	1.02643
$344$	0.243271	0.0131163
$345$	−5.42810	−0.292239
$346$	18.0726	0.971588
$347$	13.9261	0.747592	0.373796	−	0.927511i	$-0.378056\pi$
$347$	13.9261	0.747592	0.373796	+	0.927511i	$0.378056\pi$
$348$	5.04062	0.270206
$349$	0.757056	0.0405243	0.0202621	−	0.999795i	$-0.493550\pi$
$349$	0.757056	0.0405243	0.0202621	+	0.999795i	$0.493550\pi$
$350$	4.98169	0.266283
$351$	−1.00000	−0.0533761
$352$	−1.08709	−0.0579420
$353$	18.7786	0.999484	0.499742	−	0.866174i	$-0.333428\pi$
$353$	18.7786	0.999484	0.499742	+	0.866174i	$0.333428\pi$
$354$	−12.2262	−0.649814
$355$	1.74540	0.0926363
$356$	4.27223	0.226428
$357$	11.8075	0.624922
$358$	−4.70667	−0.248755
$359$	2.04881	0.108132	0.0540661	−	0.998537i	$-0.482782\pi$
$359$	2.04881	0.108132	0.0540661	+	0.998537i	$0.482782\pi$
$360$	−1.45246	−0.0765515
$361$	15.5216	0.816929
$362$	7.31360	0.384394
$363$	9.81824	0.515324
$364$	−1.72356	−0.0903390
$365$	−9.34997	−0.489400
$366$	13.3860	0.699696
$367$	−31.4980	−1.64418	−0.822091	−	0.569356i	$-0.807193\pi$
$367$	−31.4980	−1.64418	−0.822091	+	0.569356i	$0.807193\pi$
$368$	−3.73717	−0.194813
$369$	5.20035	0.270719
$370$	4.01747	0.208859
$371$	5.90581	0.306615
$372$	−5.87551	−0.304631
$373$	19.7812	1.02423	0.512115	−	0.858917i	$-0.328862\pi$
$373$	19.7812	1.02423	0.512115	+	0.858917i	$0.328862\pi$
$374$	−7.44729	−0.385090
$375$	−11.4604	−0.591815
$376$	−10.8042	−0.557185
$377$	−5.04062	−0.259605
$378$	1.72356	0.0886503
$379$	−4.52169	−0.232264	−0.116132	−	0.993234i	$-0.537050\pi$
$379$	−4.52169	−0.232264	−0.116132	+	0.993234i	$0.537050\pi$
$380$	−8.53396	−0.437783
$381$	16.6757	0.854322
$382$	14.8166	0.758081
$383$	−11.7275	−0.599245	−0.299622	−	0.954058i	$-0.596861\pi$
$383$	−11.7275	−0.599245	−0.299622	+	0.954058i	$0.596861\pi$
$384$	−1.00000	−0.0510310
$385$	−2.72142	−0.138696
$386$	−0.0984871	−0.00501286
$387$	0.243271	0.0123661
$388$	0.783112	0.0397565
$389$	6.00256	0.304342	0.152171	−	0.988354i	$-0.451374\pi$
$389$	6.00256	0.304342	0.152171	+	0.988354i	$0.451374\pi$
$390$	1.45246	0.0735483
$391$	−25.6021	−1.29476
$392$	−4.02934	−0.203513
$393$	−20.0092	−1.00933
$394$	12.2026	0.614759
$395$	−19.4979	−0.981046
$396$	−1.08709	−0.0546282
$397$	8.02979	0.403004	0.201502	−	0.979488i	$-0.435418\pi$
$397$	8.02979	0.403004	0.201502	+	0.979488i	$0.435418\pi$
$398$	12.0042	0.601719
$399$	10.1268	0.506974
$400$	−2.89035	−0.144518
$401$	0.201450	0.0100600	0.00502998	−	0.999987i	$-0.498399\pi$
$401$	0.201450	0.0100600	0.00502998	+	0.999987i	$0.498399\pi$
$402$	−4.14842	−0.206905
$403$	5.87551	0.292680
$404$	18.8022	0.935446
$405$	−1.45246	−0.0721735
$406$	8.68781	0.431169
$407$	3.00686	0.149044
$408$	−6.85068	−0.339159
$409$	32.3410	1.59916	0.799579	−	0.600561i	$-0.205056\pi$
$409$	32.3410	1.59916	0.799579	+	0.600561i	$0.205056\pi$
$410$	−7.55331	−0.373031
$411$	−14.1790	−0.699398
$412$	1.00000	0.0492665
$413$	−21.0725	−1.03691
$414$	−3.73717	−0.183672
$415$	24.2216	1.18899
$416$	1.00000	0.0490290
$417$	−17.8457	−0.873905
$418$	−6.38720	−0.312408
$419$	−32.9225	−1.60837	−0.804184	−	0.594380i	$-0.797398\pi$
$419$	−32.9225	−1.60837	−0.804184	+	0.594380i	$0.797398\pi$
$420$	−2.50341	−0.122154
$421$	−8.78959	−0.428378	−0.214189	−	0.976792i	$-0.568711\pi$
$421$	−8.78959	−0.428378	−0.214189	+	0.976792i	$0.568711\pi$
$422$	−5.33439	−0.259674
$423$	−10.8042	−0.525319
$424$	−3.42652	−0.166407
$425$	−19.8009	−0.960483
$426$	1.20168	0.0582218
$427$	23.0715	1.11651
$428$	−14.8030	−0.715532
$429$	1.08709	0.0524851
$430$	−0.353342	−0.0170396
$431$	−20.0888	−0.967643	−0.483821	−	0.875167i	$-0.660752\pi$
$431$	−20.0888	−0.967643	−0.483821	+	0.875167i	$0.660752\pi$
$432$	−1.00000	−0.0481125
$433$	28.8078	1.38442	0.692208	−	0.721698i	$-0.256638\pi$
$433$	28.8078	1.38442	0.692208	+	0.721698i	$0.256638\pi$
$434$	−10.1268	−0.486102
$435$	−7.32132	−0.351030
$436$	17.2028	0.823863
$437$	−21.9578	−1.05038
$438$	−6.43732	−0.307587
$439$	−35.9955	−1.71797	−0.858986	−	0.512000i	$-0.828905\pi$
$439$	−35.9955	−1.71797	−0.858986	+	0.512000i	$0.828905\pi$
$440$	1.57895	0.0752737
$441$	−4.02934	−0.191874
$442$	6.85068	0.325854
$443$	34.1600	1.62299	0.811495	−	0.584359i	$-0.198654\pi$
$443$	34.1600	1.62299	0.811495	+	0.584359i	$0.198654\pi$
$444$	2.76597	0.131267
$445$	−6.20526	−0.294158
$446$	−17.6229	−0.834467
$447$	17.3689	0.821520
$448$	−1.72356	−0.0814305
$449$	−25.2978	−1.19388	−0.596939	−	0.802286i	$-0.703617\pi$
$449$	−25.2978	−1.19388	−0.596939	+	0.802286i	$0.703617\pi$
$450$	−2.89035	−0.136252
$451$	−5.65323	−0.266200
$452$	−4.27985	−0.201307
$453$	−10.4241	−0.489767
$454$	−7.67048	−0.359993
$455$	2.50341	0.117361
$456$	−5.87551	−0.275146
$457$	−24.2417	−1.13398	−0.566989	−	0.823725i	$-0.691892\pi$
$457$	−24.2417	−1.13398	−0.566989	+	0.823725i	$0.691892\pi$
$458$	−3.27629	−0.153091
$459$	−6.85068	−0.319762
$460$	5.42810	0.253087
$461$	−6.96065	−0.324190	−0.162095	−	0.986775i	$-0.551825\pi$
$461$	−6.96065	−0.324190	−0.162095	+	0.986775i	$0.551825\pi$
$462$	−1.87366	−0.0871706
$463$	−11.3983	−0.529724	−0.264862	−	0.964286i	$-0.585326\pi$
$463$	−11.3983	−0.529724	−0.264862	+	0.964286i	$0.585326\pi$
$464$	−5.04062	−0.234005
$465$	8.53396	0.395753
$466$	20.6323	0.955775
$467$	−8.64827	−0.400194	−0.200097	−	0.979776i	$-0.564126\pi$
$467$	−8.64827	−0.400194	−0.200097	+	0.979776i	$0.564126\pi$
$468$	1.00000	0.0462250
$469$	−7.15005	−0.330159
$470$	15.6927	0.723851
$471$	−15.8243	−0.729143
$472$	12.2262	0.562755
$473$	−0.264457	−0.0121597
$474$	−13.4240	−0.616586
$475$	−16.9823	−0.779201
$476$	−11.8075	−0.541198
$477$	−3.42652	−0.156890
$478$	3.99774	0.182852
$479$	−19.6355	−0.897167	−0.448584	−	0.893741i	$-0.648071\pi$
$479$	−19.6355	−0.897167	−0.448584	+	0.893741i	$0.648071\pi$
$480$	1.45246	0.0662956
$481$	−2.76597	−0.126118
$482$	25.8910	1.17930
$483$	−6.44123	−0.293086
$484$	−9.81824	−0.446284
$485$	−1.13744	−0.0516485
$486$	−1.00000	−0.0453609
$487$	14.0046	0.634608	0.317304	−	0.948324i	$-0.397223\pi$
$487$	14.0046	0.634608	0.317304	+	0.948324i	$0.397223\pi$
$488$	−13.3860	−0.605955
$489$	−21.3787	−0.966778
$490$	5.85247	0.264388
$491$	−10.5709	−0.477059	−0.238529	−	0.971135i	$-0.576665\pi$
$491$	−10.5709	−0.477059	−0.238529	+	0.971135i	$0.576665\pi$
$492$	−5.20035	−0.234450
$493$	−34.5317	−1.55523
$494$	5.87551	0.264352
$495$	1.57895	0.0709687
$496$	5.87551	0.263818
$497$	2.07117	0.0929048
$498$	16.6762	0.747281
$499$	26.0529	1.16629	0.583144	−	0.812369i	$-0.301822\pi$
$499$	26.0529	1.16629	0.583144	+	0.812369i	$0.301822\pi$
$500$	11.4604	0.512527
$501$	−7.99844	−0.357344
$502$	0.207349	0.00925444
$503$	−23.5628	−1.05061	−0.525306	−	0.850914i	$-0.676049\pi$
$503$	−23.5628	−1.05061	−0.525306	+	0.850914i	$0.676049\pi$
$504$	−1.72356	−0.0767734
$505$	−27.3095	−1.21526
$506$	4.06263	0.180606
$507$	−1.00000	−0.0444116
$508$	−16.6757	−0.739865
$509$	−34.0392	−1.50876	−0.754380	−	0.656438i	$-0.772062\pi$
$509$	−34.0392	−1.50876	−0.754380	+	0.656438i	$0.772062\pi$
$510$	9.95035	0.440609
$511$	−11.0951	−0.490819
$512$	1.00000	0.0441942
$513$	−5.87551	−0.259410
$514$	−12.6839	−0.559461
$515$	−1.45246	−0.0640032
$516$	−0.243271	−0.0107094
$517$	11.7451	0.516550
$518$	4.76732	0.209464
$519$	−18.0726	−0.793299
$520$	−1.45246	−0.0636947
$521$	21.5854	0.945673	0.472836	−	0.881150i	$-0.343230\pi$
$521$	21.5854	0.945673	0.472836	+	0.881150i	$0.343230\pi$
$522$	−5.04062	−0.220622
$523$	20.9817	0.917464	0.458732	−	0.888575i	$-0.348304\pi$
$523$	20.9817	0.917464	0.458732	+	0.888575i	$0.348304\pi$
$524$	20.0092	0.874104
$525$	−4.98169	−0.217419
$526$	−23.8330	−1.03917
$527$	40.2512	1.75337
$528$	1.08709	0.0473094
$529$	−9.03356	−0.392763
$530$	4.97690	0.216183
$531$	12.2262	0.530571
$532$	−10.1268	−0.439052
$533$	5.20035	0.225252
$534$	−4.27223	−0.184878
$535$	21.5009	0.929563
$536$	4.14842	0.179185
$537$	4.70667	0.203108
$538$	19.9757	0.861213
$539$	4.38025	0.188671
$540$	1.45246	0.0625040
$541$	4.34518	0.186814	0.0934068	−	0.995628i	$-0.470224\pi$
$541$	4.34518	0.186814	0.0934068	+	0.995628i	$0.470224\pi$
$542$	−19.6972	−0.846067
$543$	−7.31360	−0.313856
$544$	6.85068	0.293720
$545$	−24.9864	−1.07030
$546$	1.72356	0.0737615
$547$	31.2177	1.33477	0.667387	−	0.744711i	$-0.267413\pi$
$547$	31.2177	1.33477	0.667387	+	0.744711i	$0.267413\pi$
$548$	14.1790	0.605696
$549$	−13.3860	−0.571300
$550$	3.14207	0.133978
$551$	−29.6162	−1.26169
$552$	3.73717	0.159065
$553$	−23.1371	−0.983889
$554$	19.2254	0.816811
$555$	−4.01747	−0.170532
$556$	17.8457	0.756824
$557$	41.3998	1.75417	0.877083	−	0.480338i	$-0.159486\pi$
$557$	41.3998	1.75417	0.877083	+	0.480338i	$0.159486\pi$
$558$	5.87551	0.248730
$559$	0.243271	0.0102893
$560$	2.50341	0.105788
$561$	7.44729	0.314425
$562$	8.85431	0.373497
$563$	−16.8853	−0.711632	−0.355816	−	0.934556i	$-0.615797\pi$
$563$	−16.8853	−0.711632	−0.355816	+	0.934556i	$0.615797\pi$
$564$	10.8042	0.454939
$565$	6.21632	0.261523
$566$	−14.3114	−0.601552
$567$	−1.72356	−0.0723827
$568$	−1.20168	−0.0504215
$569$	45.2884	1.89859	0.949295	−	0.314386i	$-0.101799\pi$
$569$	45.2884	1.89859	0.949295	+	0.314386i	$0.101799\pi$
$570$	8.53396	0.357448
$571$	−11.5457	−0.483174	−0.241587	−	0.970379i	$-0.577668\pi$
$571$	−11.5457	−0.483174	−0.241587	+	0.970379i	$0.577668\pi$
$572$	−1.08709	−0.0454534
$573$	−14.8166	−0.618970
$574$	−8.96310	−0.374113
$575$	10.8017	0.450464
$576$	1.00000	0.0416667
$577$	−19.5396	−0.813446	−0.406723	−	0.913552i	$-0.633329\pi$
$577$	−19.5396	−0.813446	−0.406723	+	0.913552i	$0.633329\pi$
$578$	29.9318	1.24500
$579$	0.0984871	0.00409298
$580$	7.32132	0.304001
$581$	28.7425	1.19244
$582$	−0.783112	−0.0324610
$583$	3.72493	0.154271
$584$	6.43732	0.266378
$585$	−1.45246	−0.0600519
$586$	0.776075	0.0320594
$587$	−2.85236	−0.117730	−0.0588648	−	0.998266i	$-0.518748\pi$
$587$	−2.85236	−0.117730	−0.0588648	+	0.998266i	$0.518748\pi$
$588$	4.02934	0.166167
$589$	34.5216	1.42244
$590$	−17.7581	−0.731088
$591$	−12.2026	−0.501949
$592$	−2.76597	−0.113681
$593$	−16.8061	−0.690142	−0.345071	−	0.938577i	$-0.612145\pi$
$593$	−16.8061	−0.690142	−0.345071	+	0.938577i	$0.612145\pi$
$594$	1.08709	0.0446038
$595$	17.1500	0.703082
$596$	−17.3689	−0.711457
$597$	−12.0042	−0.491301
$598$	−3.73717	−0.152824
$599$	28.5549	1.16672	0.583361	−	0.812213i	$-0.301737\pi$
$599$	28.5549	1.16672	0.583361	+	0.812213i	$0.301737\pi$
$600$	2.89035	0.117998
$601$	45.4413	1.85359	0.926795	−	0.375567i	$-0.122552\pi$
$601$	45.4413	1.85359	0.926795	+	0.375567i	$0.122552\pi$
$602$	−0.419291	−0.0170890
$603$	4.14842	0.168937
$604$	10.4241	0.424151
$605$	14.2606	0.579777
$606$	−18.8022	−0.763789
$607$	19.8887	0.807256	0.403628	−	0.914923i	$-0.367749\pi$
$607$	19.8887	0.807256	0.403628	+	0.914923i	$0.367749\pi$
$608$	5.87551	0.238283
$609$	−8.68781	−0.352048
$610$	19.4426	0.787209
$611$	−10.8042	−0.437092
$612$	6.85068	0.276922
$613$	−10.8461	−0.438070	−0.219035	−	0.975717i	$-0.570291\pi$
$613$	−10.8461	−0.438070	−0.219035	+	0.975717i	$0.570291\pi$
$614$	29.9498	1.20868
$615$	7.55331	0.304579
$616$	1.87366	0.0754919
$617$	−23.2002	−0.934004	−0.467002	−	0.884256i	$-0.654666\pi$
$617$	−23.2002	−0.934004	−0.467002	+	0.884256i	$0.654666\pi$
$618$	−1.00000	−0.0402259
$619$	−8.66059	−0.348099	−0.174049	−	0.984737i	$-0.555685\pi$
$619$	−8.66059	−0.348099	−0.174049	+	0.984737i	$0.555685\pi$
$620$	−8.53396	−0.342732
$621$	3.73717	0.149967
$622$	−4.39195	−0.176101
$623$	−7.36345	−0.295010
$624$	−1.00000	−0.0400320
$625$	−2.19411	−0.0877643
$626$	17.8325	0.712729
$627$	6.38720	0.255080
$628$	15.8243	0.631456
$629$	−18.9488	−0.755538
$630$	2.50341	0.0997381
$631$	−24.7463	−0.985134	−0.492567	−	0.870275i	$-0.663941\pi$
$631$	−24.7463	−0.985134	−0.492567	+	0.870275i	$0.663941\pi$
$632$	13.4240	0.533979
$633$	5.33439	0.212023
$634$	−15.0694	−0.598483
$635$	24.2208	0.961175
$636$	3.42652	0.135870
$637$	−4.02934	−0.159648
$638$	5.47960	0.216939
$639$	−1.20168	−0.0475379
$640$	−1.45246	−0.0574136
$641$	−11.8534	−0.468182	−0.234091	−	0.972215i	$-0.575211\pi$
$641$	−11.8534	−0.468182	−0.234091	+	0.972215i	$0.575211\pi$
$642$	14.8030	0.584229
$643$	4.66636	0.184023	0.0920117	−	0.995758i	$-0.470670\pi$
$643$	4.66636	0.184023	0.0920117	+	0.995758i	$0.470670\pi$
$644$	6.44123	0.253820
$645$	0.353342	0.0139128
$646$	40.2512	1.58366
$647$	2.78194	0.109369	0.0546847	−	0.998504i	$-0.482585\pi$
$647$	2.78194	0.109369	0.0546847	+	0.998504i	$0.482585\pi$
$648$	1.00000	0.0392837
$649$	−13.2909	−0.521715
$650$	−2.89035	−0.113369
$651$	10.1268	0.396900
$652$	21.3787	0.837254
$653$	−34.4145	−1.34674	−0.673371	−	0.739305i	$-0.735154\pi$
$653$	−34.4145	−1.34674	−0.673371	+	0.739305i	$0.735154\pi$
$654$	−17.2028	−0.672681
$655$	−29.0626	−1.13557
$656$	5.20035	0.203039
$657$	6.43732	0.251144
$658$	18.6217	0.725949
$659$	−22.0698	−0.859719	−0.429859	−	0.902896i	$-0.641437\pi$
$659$	−22.0698	−0.859719	−0.429859	+	0.902896i	$0.641437\pi$
$660$	−1.57895	−0.0614607
$661$	0.155198	0.00603652	0.00301826	−	0.999995i	$-0.499039\pi$
$661$	0.155198	0.00603652	0.00301826	+	0.999995i	$0.499039\pi$
$662$	−6.92352	−0.269090
$663$	−6.85068	−0.266058
$664$	−16.6762	−0.647164
$665$	14.7088	0.570382
$666$	−2.76597	−0.107179
$667$	18.8377	0.729397
$668$	7.99844	0.309469
$669$	17.6229	0.681340
$670$	−6.02543	−0.232783
$671$	14.5517	0.561764
$672$	1.72356	0.0664877
$673$	23.8498	0.919344	0.459672	−	0.888089i	$-0.347967\pi$
$673$	23.8498	0.919344	0.459672	+	0.888089i	$0.347967\pi$
$674$	−7.35657	−0.283364
$675$	2.89035	0.111250
$676$	1.00000	0.0384615
$677$	−23.1360	−0.889189	−0.444595	−	0.895732i	$-0.646652\pi$
$677$	−23.1360	−0.889189	−0.444595	+	0.895732i	$0.646652\pi$
$678$	4.27985	0.164367
$679$	−1.34974	−0.0517983
$680$	−9.95035	−0.381579
$681$	7.67048	0.293933
$682$	−6.38720	−0.244578
$683$	44.4789	1.70194	0.850969	−	0.525216i	$-0.176016\pi$
$683$	44.4789	1.70194	0.850969	+	0.525216i	$0.176016\pi$
$684$	5.87551	0.224656
$685$	−20.5944	−0.786873
$686$	19.0097	0.725795
$687$	3.27629	0.124998
$688$	0.243271	0.00927461
$689$	−3.42652	−0.130540
$690$	−5.42810	−0.206644
$691$	−33.1588	−1.26142	−0.630710	−	0.776018i	$-0.717236\pi$
$691$	−33.1588	−1.26142	−0.630710	+	0.776018i	$0.717236\pi$
$692$	18.0726	0.687017
$693$	1.87366	0.0711745
$694$	13.9261	0.528627
$695$	−25.9201	−0.983207
$696$	5.04062	0.191064
$697$	35.6259	1.34943
$698$	0.757056	0.0286550
$699$	−20.6323	−0.780387
$700$	4.98169	0.188290
$701$	15.8833	0.599904	0.299952	−	0.953954i	$-0.403029\pi$
$701$	15.8833	0.599904	0.299952	+	0.953954i	$0.403029\pi$
$702$	−1.00000	−0.0377426
$703$	−16.2515	−0.612937
$704$	−1.08709	−0.0409712
$705$	−15.6927	−0.591022
$706$	18.7786	0.706742
$707$	−32.4068	−1.21878
$708$	−12.2262	−0.459488
$709$	−38.6870	−1.45292	−0.726461	−	0.687208i	$-0.758836\pi$
$709$	−38.6870	−1.45292	−0.726461	+	0.687208i	$0.758836\pi$
$710$	1.74540	0.0655037
$711$	13.4240	0.503440
$712$	4.27223	0.160109
$713$	−21.9578	−0.822326
$714$	11.8075	0.441886
$715$	1.57895	0.0590496
$716$	−4.70667	−0.175897
$717$	−3.99774	−0.149298
$718$	2.04881	0.0764610
$719$	34.2491	1.27728	0.638638	−	0.769508i	$-0.279498\pi$
$719$	34.2491	1.27728	0.638638	+	0.769508i	$0.279498\pi$
$720$	−1.45246	−0.0541301
$721$	−1.72356	−0.0641887
$722$	15.5216	0.577656
$723$	−25.8910	−0.962897
$724$	7.31360	0.271808
$725$	14.5692	0.541086
$726$	9.81824	0.364389
$727$	35.1224	1.30262	0.651308	−	0.758813i	$-0.274221\pi$
$727$	35.1224	1.30262	0.651308	+	0.758813i	$0.274221\pi$
$728$	−1.72356	−0.0638793
$729$	1.00000	0.0370370
$730$	−9.34997	−0.346058
$731$	1.66657	0.0616403
$732$	13.3860	0.494760
$733$	31.7500	1.17271	0.586357	−	0.810053i	$-0.300562\pi$
$733$	31.7500	1.17271	0.586357	+	0.810053i	$0.300562\pi$
$734$	−31.4980	−1.16261
$735$	−5.85247	−0.215872
$736$	−3.73717	−0.137754
$737$	−4.50970	−0.166117
$738$	5.20035	0.191427
$739$	−3.79938	−0.139763	−0.0698813	−	0.997555i	$-0.522262\pi$
$739$	−3.79938	−0.139763	−0.0698813	+	0.997555i	$0.522262\pi$
$740$	4.01747	0.147685
$741$	−5.87551	−0.215842
$742$	5.90581	0.216809
$743$	−22.3055	−0.818308	−0.409154	−	0.912465i	$-0.634176\pi$
$743$	−22.3055	−0.818308	−0.409154	+	0.912465i	$0.634176\pi$
$744$	−5.87551	−0.215407
$745$	25.2277	0.924270
$746$	19.7812	0.724240
$747$	−16.6762	−0.610152
$748$	−7.44729	−0.272300
$749$	25.5139	0.932258
$750$	−11.4604	−0.418476
$751$	20.9148	0.763191	0.381596	−	0.924329i	$-0.375375\pi$
$751$	20.9148	0.763191	0.381596	+	0.924329i	$0.375375\pi$
$752$	−10.8042	−0.393989
$753$	−0.207349	−0.00755622
$754$	−5.04062	−0.183569
$755$	−15.1406	−0.551024
$756$	1.72356	0.0626852
$757$	43.2715	1.57273	0.786365	−	0.617762i	$-0.211961\pi$
$757$	43.2715	1.57273	0.786365	+	0.617762i	$0.211961\pi$
$758$	−4.52169	−0.164235
$759$	−4.06263	−0.147464
$760$	−8.53396	−0.309559
$761$	−34.0402	−1.23395	−0.616977	−	0.786981i	$-0.711643\pi$
$761$	−34.0402	−1.23395	−0.616977	+	0.786981i	$0.711643\pi$
$762$	16.6757	0.604097
$763$	−29.6500	−1.07340
$764$	14.8166	0.536044
$765$	−9.95035	−0.359756
$766$	−11.7275	−0.423730
$767$	12.2262	0.441462
$768$	−1.00000	−0.0360844
$769$	50.6771	1.82746	0.913732	−	0.406318i	$-0.133187\pi$
$769$	50.6771	1.82746	0.913732	+	0.406318i	$0.133187\pi$
$770$	−2.72142	−0.0980732
$771$	12.6839	0.456798
$772$	−0.0984871	−0.00354463
$773$	26.6999	0.960329	0.480164	−	0.877179i	$-0.340577\pi$
$773$	26.6999	0.960329	0.480164	+	0.877179i	$0.340577\pi$
$774$	0.243271	0.00874418
$775$	−16.9823	−0.610022
$776$	0.783112	0.0281121
$777$	−4.76732	−0.171027
$778$	6.00256	0.215202
$779$	30.5547	1.09474
$780$	1.45246	0.0520065
$781$	1.30634	0.0467444
$782$	−25.6021	−0.915531
$783$	5.04062	0.180137
$784$	−4.02934	−0.143905
$785$	−22.9841	−0.820339
$786$	−20.0092	−0.713703
$787$	17.1710	0.612078	0.306039	−	0.952019i	$-0.400996\pi$
$787$	17.1710	0.612078	0.306039	+	0.952019i	$0.400996\pi$
$788$	12.2026	0.434700
$789$	23.8330	0.848477
$790$	−19.4979	−0.693704
$791$	7.37657	0.262281
$792$	−1.08709	−0.0386280
$793$	−13.3860	−0.475350
$794$	8.02979	0.284967
$795$	−4.97690	−0.176512
$796$	12.0042	0.425479
$797$	−4.51189	−0.159819	−0.0799096	−	0.996802i	$-0.525463\pi$
$797$	−4.51189	−0.159819	−0.0799096	+	0.996802i	$0.525463\pi$
$798$	10.1268	0.358485
$799$	−74.0162	−2.61850
$800$	−2.89035	−0.102189
$801$	4.27223	0.150952
$802$	0.201450	0.00711346
$803$	−6.99794	−0.246952
$804$	−4.14842	−0.146304
$805$	−9.35565	−0.329743
$806$	5.87551	0.206956
$807$	−19.9757	−0.703177
$808$	18.8022	0.661460
$809$	36.9290	1.29835	0.649177	−	0.760637i	$-0.275113\pi$
$809$	36.9290	1.29835	0.649177	+	0.760637i	$0.275113\pi$
$810$	−1.45246	−0.0510343
$811$	5.86584	0.205977	0.102989	−	0.994683i	$-0.467159\pi$
$811$	5.86584	0.205977	0.102989	+	0.994683i	$0.467159\pi$
$812$	8.68781	0.304882
$813$	19.6972	0.690811
$814$	3.00686	0.105390
$815$	−31.0518	−1.08770
$816$	−6.85068	−0.239822
$817$	1.42934	0.0500063
$818$	32.3410	1.13078
$819$	−1.72356	−0.0602260
$820$	−7.55331	−0.263773
$821$	3.60205	0.125712	0.0628562	−	0.998023i	$-0.479979\pi$
$821$	3.60205	0.125712	0.0628562	+	0.998023i	$0.479979\pi$
$822$	−14.1790	−0.494549
$823$	28.3858	0.989467	0.494734	−	0.869045i	$-0.335266\pi$
$823$	28.3858	0.989467	0.494734	+	0.869045i	$0.335266\pi$
$824$	1.00000	0.0348367
$825$	−3.14207	−0.109393
$826$	−21.0725	−0.733207
$827$	−26.3975	−0.917930	−0.458965	−	0.888454i	$-0.651780\pi$
$827$	−26.3975	−0.917930	−0.458965	+	0.888454i	$0.651780\pi$
$828$	−3.73717	−0.129876
$829$	12.2479	0.425386	0.212693	−	0.977119i	$-0.431777\pi$
$829$	12.2479	0.425386	0.212693	+	0.977119i	$0.431777\pi$
$830$	24.2216	0.840745
$831$	−19.2254	−0.666923
$832$	1.00000	0.0346688
$833$	−27.6037	−0.956413
$834$	−17.8457	−0.617944
$835$	−11.6174	−0.402038
$836$	−6.38720	−0.220906
$837$	−5.87551	−0.203087
$838$	−32.9225	−1.13729
$839$	−33.3812	−1.15245	−0.576223	−	0.817292i	$-0.695474\pi$
$839$	−33.3812	−1.15245	−0.576223	+	0.817292i	$0.695474\pi$
$840$	−2.50341	−0.0863757
$841$	−3.59211	−0.123866
$842$	−8.78959	−0.302909
$843$	−8.85431	−0.304959
$844$	−5.33439	−0.183617
$845$	−1.45246	−0.0499662
$846$	−10.8042	−0.371457
$847$	16.9223	0.581458
$848$	−3.42652	−0.117667
$849$	14.3114	0.491165
$850$	−19.8009	−0.679164
$851$	10.3369	0.354345
$852$	1.20168	0.0411690
$853$	1.11322	0.0381159	0.0190579	−	0.999818i	$-0.493933\pi$
$853$	1.11322	0.0381159	0.0190579	+	0.999818i	$0.493933\pi$
$854$	23.0715	0.789491
$855$	−8.53396	−0.291855
$856$	−14.8030	−0.505957
$857$	−39.9628	−1.36510	−0.682552	−	0.730837i	$-0.739130\pi$
$857$	−39.9628	−1.36510	−0.682552	+	0.730837i	$0.739130\pi$
$858$	1.08709	0.0371126
$859$	39.2156	1.33802	0.669010	−	0.743254i	$-0.266718\pi$
$859$	39.2156	1.33802	0.669010	+	0.743254i	$0.266718\pi$
$860$	−0.353342	−0.0120488
$861$	8.96310	0.305462
$862$	−20.0888	−0.684227
$863$	5.20896	0.177315	0.0886576	−	0.996062i	$-0.471742\pi$
$863$	5.20896	0.177315	0.0886576	+	0.996062i	$0.471742\pi$
$864$	−1.00000	−0.0340207
$865$	−26.2498	−0.892519
$866$	28.8078	0.978930
$867$	−29.9318	−1.01654
$868$	−10.1268	−0.343726
$869$	−14.5931	−0.495037
$870$	−7.32132	−0.248216
$871$	4.14842	0.140564
$872$	17.2028	0.582559
$873$	0.783112	0.0265043
$874$	−21.9578	−0.742733
$875$	−19.7527	−0.667765
$876$	−6.43732	−0.217497
$877$	−3.37722	−0.114041	−0.0570203	−	0.998373i	$-0.518160\pi$
$877$	−3.37722	−0.114041	−0.0570203	+	0.998373i	$0.518160\pi$
$878$	−35.9955	−1.21479
$879$	−0.776075	−0.0261764
$880$	1.57895	0.0532266
$881$	−2.23545	−0.0753144	−0.0376572	−	0.999291i	$-0.511989\pi$
$881$	−2.23545	−0.0753144	−0.0376572	+	0.999291i	$0.511989\pi$
$882$	−4.02934	−0.135675
$883$	−22.5183	−0.757803	−0.378901	−	0.925437i	$-0.623698\pi$
$883$	−22.5183	−0.757803	−0.378901	+	0.925437i	$0.623698\pi$
$884$	6.85068	0.230413
$885$	17.7581	0.596931
$886$	34.1600	1.14763
$887$	40.4057	1.35669	0.678345	−	0.734744i	$-0.262698\pi$
$887$	40.4057	1.35669	0.678345	+	0.734744i	$0.262698\pi$
$888$	2.76597	0.0928200
$889$	28.7416	0.963961
$890$	−6.20526	−0.208001
$891$	−1.08709	−0.0364188
$892$	−17.6229	−0.590058
$893$	−63.4803	−2.12429
$894$	17.3689	0.580903
$895$	6.83627	0.228511
$896$	−1.72356	−0.0575801
$897$	3.73717	0.124780
$898$	−25.2978	−0.844200
$899$	−29.6162	−0.987757
$900$	−2.89035	−0.0963451
$901$	−23.4740	−0.782032
$902$	−5.65323	−0.188232
$903$	0.419291	0.0139531
$904$	−4.27985	−0.142346
$905$	−10.6227	−0.353111
$906$	−10.4241	−0.346318
$907$	11.5295	0.382832	0.191416	−	0.981509i	$-0.438692\pi$
$907$	11.5295	0.382832	0.191416	+	0.981509i	$0.438692\pi$
$908$	−7.67048	−0.254554
$909$	18.8022	0.623631
$910$	2.50341	0.0829871
$911$	7.17269	0.237642	0.118821	−	0.992916i	$-0.462089\pi$
$911$	7.17269	0.237642	0.118821	+	0.992916i	$0.462089\pi$
$912$	−5.87551	−0.194558
$913$	18.1285	0.599967
$914$	−24.2417	−0.801844
$915$	−19.4426	−0.642754
$916$	−3.27629	−0.108252
$917$	−34.4870	−1.13886
$918$	−6.85068	−0.226106
$919$	15.3843	0.507483	0.253741	−	0.967272i	$-0.418339\pi$
$919$	15.3843	0.507483	0.253741	+	0.967272i	$0.418339\pi$
$920$	5.42810	0.178959
$921$	−29.9498	−0.986881
$922$	−6.96065	−0.229237
$923$	−1.20168	−0.0395539
$924$	−1.87366	−0.0616389
$925$	7.99464	0.262862
$926$	−11.3983	−0.374571
$927$	1.00000	0.0328443
$928$	−5.04062	−0.165467
$929$	13.0607	0.428507	0.214254	−	0.976778i	$-0.431268\pi$
$929$	13.0607	0.428507	0.214254	+	0.976778i	$0.431268\pi$
$930$	8.53396	0.279840
$931$	−23.6745	−0.775899
$932$	20.6323	0.675835
$933$	4.39195	0.143786
$934$	−8.64827	−0.282980
$935$	10.8169	0.353751
$936$	1.00000	0.0326860
$937$	8.43383	0.275521	0.137761	−	0.990466i	$-0.456010\pi$
$937$	8.43383	0.275521	0.137761	+	0.990466i	$0.456010\pi$
$938$	−7.15005	−0.233457
$939$	−17.8325	−0.581941
$940$	15.6927	0.511840
$941$	16.1764	0.527337	0.263668	−	0.964613i	$-0.415068\pi$
$941$	16.1764	0.527337	0.263668	+	0.964613i	$0.415068\pi$
$942$	−15.8243	−0.515582
$943$	−19.4346	−0.632877
$944$	12.2262	0.397928
$945$	−2.50341	−0.0814358
$946$	−0.264457	−0.00859823
$947$	−19.1199	−0.621314	−0.310657	−	0.950522i	$-0.600549\pi$
$947$	−19.1199	−0.621314	−0.310657	+	0.950522i	$0.600549\pi$
$948$	−13.4240	−0.435992
$949$	6.43732	0.208964
$950$	−16.9823	−0.550978
$951$	15.0694	0.488660
$952$	−11.8075	−0.382685
$953$	−4.74034	−0.153555	−0.0767773	−	0.997048i	$-0.524463\pi$
$953$	−4.74034	−0.153555	−0.0767773	+	0.997048i	$0.524463\pi$
$954$	−3.42652	−0.110938
$955$	−21.5205	−0.696387
$956$	3.99774	0.129296
$957$	−5.47960	−0.177130
$958$	−19.6355	−0.634393
$959$	−24.4383	−0.789154
$960$	1.45246	0.0468780
$961$	3.52165	0.113602
$962$	−2.76597	−0.0891786
$963$	−14.8030	−0.477021
$964$	25.8910	0.833893
$965$	0.143049	0.00460491
$966$	−6.44123	−0.207243
$967$	−25.9667	−0.835032	−0.417516	−	0.908670i	$-0.637099\pi$
$967$	−25.9667	−0.835032	−0.417516	+	0.908670i	$0.637099\pi$
$968$	−9.81824	−0.315570
$969$	−40.2512	−1.29306
$970$	−1.13744	−0.0365210
$971$	−11.3197	−0.363265	−0.181633	−	0.983366i	$-0.558138\pi$
$971$	−11.3197	−0.363265	−0.181633	+	0.983366i	$0.558138\pi$
$972$	−1.00000	−0.0320750
$973$	−30.7580	−0.986057
$974$	14.0046	0.448735
$975$	2.89035	0.0925653
$976$	−13.3860	−0.428475
$977$	26.2961	0.841288	0.420644	−	0.907226i	$-0.361804\pi$
$977$	26.2961	0.841288	0.420644	+	0.907226i	$0.361804\pi$
$978$	−21.3787	−0.683615
$979$	−4.64430	−0.148432
$980$	5.85247	0.186950
$981$	17.2028	0.549242
$982$	−10.5709	−0.337331
$983$	−42.2251	−1.34677	−0.673386	−	0.739291i	$-0.735161\pi$
$983$	−42.2251	−1.34677	−0.673386	+	0.739291i	$0.735161\pi$
$984$	−5.20035	−0.165781
$985$	−17.7239	−0.564729
$986$	−34.5317	−1.09971
$987$	−18.6217	−0.592735
$988$	5.87551	0.186925
$989$	−0.909144	−0.0289091
$990$	1.57895	0.0501825
$991$	55.0214	1.74781	0.873906	−	0.486094i	$-0.161579\pi$
$991$	55.0214	1.74781	0.873906	+	0.486094i	$0.161579\pi$
$992$	5.87551	0.186548
$993$	6.92352	0.219711
$994$	2.07117	0.0656936
$995$	−17.4357	−0.552750
$996$	16.6762	0.528407
$997$	−26.7654	−0.847669	−0.423834	−	0.905740i	$-0.639316\pi$
$997$	−26.7654	−0.847669	−0.423834	+	0.905740i	$0.639316\pi$
$998$	26.0529	0.824690
$999$	2.76597	0.0875115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.y.1.4	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.y.1.4	✓	13	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.45246 q^{5} -1.00000 q^{6} -1.72356 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.45246 q^{5} -1.00000 q^{6} -1.72356 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.45246 q^{10} -1.08709 q^{11} -1.00000 q^{12} +1.00000 q^{13} -1.72356 q^{14} +1.45246 q^{15} +1.00000 q^{16} +6.85068 q^{17} +1.00000 q^{18} +5.87551 q^{19} -1.45246 q^{20} +1.72356 q^{21} -1.08709 q^{22} -3.73717 q^{23} -1.00000 q^{24} -2.89035 q^{25} +1.00000 q^{26} -1.00000 q^{27} -1.72356 q^{28} -5.04062 q^{29} +1.45246 q^{30} +5.87551 q^{31} +1.00000 q^{32} +1.08709 q^{33} +6.85068 q^{34} +2.50341 q^{35} +1.00000 q^{36} -2.76597 q^{37} +5.87551 q^{38} -1.00000 q^{39} -1.45246 q^{40} +5.20035 q^{41} +1.72356 q^{42} +0.243271 q^{43} -1.08709 q^{44} -1.45246 q^{45} -3.73717 q^{46} -10.8042 q^{47} -1.00000 q^{48} -4.02934 q^{49} -2.89035 q^{50} -6.85068 q^{51} +1.00000 q^{52} -3.42652 q^{53} -1.00000 q^{54} +1.57895 q^{55} -1.72356 q^{56} -5.87551 q^{57} -5.04062 q^{58} +12.2262 q^{59} +1.45246 q^{60} -13.3860 q^{61} +5.87551 q^{62} -1.72356 q^{63} +1.00000 q^{64} -1.45246 q^{65} +1.08709 q^{66} +4.14842 q^{67} +6.85068 q^{68} +3.73717 q^{69} +2.50341 q^{70} -1.20168 q^{71} +1.00000 q^{72} +6.43732 q^{73} -2.76597 q^{74} +2.89035 q^{75} +5.87551 q^{76} +1.87366 q^{77} -1.00000 q^{78} +13.4240 q^{79} -1.45246 q^{80} +1.00000 q^{81} +5.20035 q^{82} -16.6762 q^{83} +1.72356 q^{84} -9.95035 q^{85} +0.243271 q^{86} +5.04062 q^{87} -1.08709 q^{88} +4.27223 q^{89} -1.45246 q^{90} -1.72356 q^{91} -3.73717 q^{92} -5.87551 q^{93} -10.8042 q^{94} -8.53396 q^{95} -1.00000 q^{96} +0.783112 q^{97} -4.02934 q^{98} -1.08709 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

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