LMFDB - Embedded newform 8034.2.a.ba.1.9

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 44 x^{12} + 36 x^{11} + 722 x^{10} - 451 x^{9} - 5438 x^{8} + 2268 x^{7} + 18441 x^{6} + \cdots - 1492 $ x^14 - x^13 - 44x^12 + 36x^11 + 722x^10 - 451x^9 - 5438x^8 + 2268x^7 + 18441x^6 - 4126x^5 - 22759x^4 + 2997x^3 + 10504x^2 - 506x - 1492
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			1.9
Root			$-0.643572$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.643572 q^{5} +1.00000 q^{6} +1.17705 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.643572 q^{5} +1.00000 q^{6} +1.17705 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.643572 q^{10} -1.62256 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.17705 q^{14} -0.643572 q^{15} +1.00000 q^{16} +1.49860 q^{17} -1.00000 q^{18} +6.90649 q^{19} +0.643572 q^{20} -1.17705 q^{21} +1.62256 q^{22} -6.05927 q^{23} +1.00000 q^{24} -4.58582 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.17705 q^{28} +6.15424 q^{29} +0.643572 q^{30} -2.72186 q^{31} -1.00000 q^{32} +1.62256 q^{33} -1.49860 q^{34} +0.757514 q^{35} +1.00000 q^{36} +9.41176 q^{37} -6.90649 q^{38} +1.00000 q^{39} -0.643572 q^{40} -7.56422 q^{41} +1.17705 q^{42} +8.05306 q^{43} -1.62256 q^{44} +0.643572 q^{45} +6.05927 q^{46} -6.76522 q^{47} -1.00000 q^{48} -5.61456 q^{49} +4.58582 q^{50} -1.49860 q^{51} -1.00000 q^{52} -5.26991 q^{53} +1.00000 q^{54} -1.04423 q^{55} -1.17705 q^{56} -6.90649 q^{57} -6.15424 q^{58} +8.48262 q^{59} -0.643572 q^{60} +12.9422 q^{61} +2.72186 q^{62} +1.17705 q^{63} +1.00000 q^{64} -0.643572 q^{65} -1.62256 q^{66} -3.48887 q^{67} +1.49860 q^{68} +6.05927 q^{69} -0.757514 q^{70} +9.90543 q^{71} -1.00000 q^{72} +2.07783 q^{73} -9.41176 q^{74} +4.58582 q^{75} +6.90649 q^{76} -1.90982 q^{77} -1.00000 q^{78} -0.329478 q^{79} +0.643572 q^{80} +1.00000 q^{81} +7.56422 q^{82} -1.69775 q^{83} -1.17705 q^{84} +0.964456 q^{85} -8.05306 q^{86} -6.15424 q^{87} +1.62256 q^{88} -1.76809 q^{89} -0.643572 q^{90} -1.17705 q^{91} -6.05927 q^{92} +2.72186 q^{93} +6.76522 q^{94} +4.44482 q^{95} +1.00000 q^{96} -15.6706 q^{97} +5.61456 q^{98} -1.62256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	0.643572	0.287814	0.143907	−	0.989591i	$-0.454033\pi$
$5$	0.643572	0.287814	0.143907	+	0.989591i	$0.454033\pi$
$6$	1.00000	0.408248
$7$	1.17705	0.444882	0.222441	−	0.974946i	$-0.428598\pi$
$7$	1.17705	0.444882	0.222441	+	0.974946i	$0.428598\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−0.643572	−0.203515
$11$	−1.62256	−0.489219	−0.244610	−	0.969622i	$-0.578660\pi$
$11$	−1.62256	−0.489219	−0.244610	+	0.969622i	$0.578660\pi$
$12$	−1.00000	−0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.17705	−0.314579
$15$	−0.643572	−0.166169
$16$	1.00000	0.250000
$17$	1.49860	0.363464	0.181732	−	0.983348i	$-0.441830\pi$
$17$	1.49860	0.363464	0.181732	+	0.983348i	$0.441830\pi$
$18$	−1.00000	−0.235702
$19$	6.90649	1.58446	0.792228	−	0.610225i	$-0.208921\pi$
$19$	6.90649	1.58446	0.792228	+	0.610225i	$0.208921\pi$
$20$	0.643572	0.143907
$21$	−1.17705	−0.256853
$22$	1.62256	0.345930
$23$	−6.05927	−1.26345	−0.631723	−	0.775194i	$-0.717652\pi$
$23$	−6.05927	−1.26345	−0.631723	+	0.775194i	$0.717652\pi$
$24$	1.00000	0.204124
$25$	−4.58582	−0.917163
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	1.17705	0.222441
$29$	6.15424	1.14281	0.571407	−	0.820667i	$-0.306398\pi$
$29$	6.15424	1.14281	0.571407	+	0.820667i	$0.306398\pi$
$30$	0.643572	0.117500
$31$	−2.72186	−0.488861	−0.244430	−	0.969667i	$-0.578601\pi$
$31$	−2.72186	−0.488861	−0.244430	+	0.969667i	$0.578601\pi$
$32$	−1.00000	−0.176777
$33$	1.62256	0.282451
$34$	−1.49860	−0.257008
$35$	0.757514	0.128043
$36$	1.00000	0.166667
$37$	9.41176	1.54728	0.773642	−	0.633624i	$-0.218433\pi$
$37$	9.41176	1.54728	0.773642	+	0.633624i	$0.218433\pi$
$38$	−6.90649	−1.12038
$39$	1.00000	0.160128
$40$	−0.643572	−0.101758
$41$	−7.56422	−1.18133	−0.590667	−	0.806916i	$-0.701135\pi$
$41$	−7.56422	−1.18133	−0.590667	+	0.806916i	$0.701135\pi$
$42$	1.17705	0.181622
$43$	8.05306	1.22808	0.614040	−	0.789275i	$-0.289543\pi$
$43$	8.05306	1.22808	0.614040	+	0.789275i	$0.289543\pi$
$44$	−1.62256	−0.244610
$45$	0.643572	0.0959380
$46$	6.05927	0.893391
$47$	−6.76522	−0.986808	−0.493404	−	0.869800i	$-0.664248\pi$
$47$	−6.76522	−0.986808	−0.493404	+	0.869800i	$0.664248\pi$
$48$	−1.00000	−0.144338
$49$	−5.61456	−0.802080
$50$	4.58582	0.648532
$51$	−1.49860	−0.209846
$52$	−1.00000	−0.138675
$53$	−5.26991	−0.723878	−0.361939	−	0.932202i	$-0.617885\pi$
$53$	−5.26991	−0.723878	−0.361939	+	0.932202i	$0.617885\pi$
$54$	1.00000	0.136083
$55$	−1.04423	−0.140804
$56$	−1.17705	−0.157289
$57$	−6.90649	−0.914787
$58$	−6.15424	−0.808091
$59$	8.48262	1.10434	0.552172	−	0.833730i	$-0.313799\pi$
$59$	8.48262	1.10434	0.552172	+	0.833730i	$0.313799\pi$
$60$	−0.643572	−0.0830847
$61$	12.9422	1.65708	0.828540	−	0.559929i	$-0.189172\pi$
$61$	12.9422	1.65708	0.828540	+	0.559929i	$0.189172\pi$
$62$	2.72186	0.345677
$63$	1.17705	0.148294
$64$	1.00000	0.125000
$65$	−0.643572	−0.0798252
$66$	−1.62256	−0.199723
$67$	−3.48887	−0.426233	−0.213117	−	0.977027i	$-0.568361\pi$
$67$	−3.48887	−0.426233	−0.213117	+	0.977027i	$0.568361\pi$
$68$	1.49860	0.181732
$69$	6.05927	0.729451
$70$	−0.757514	−0.0905402
$71$	9.90543	1.17556	0.587779	−	0.809022i	$-0.300002\pi$
$71$	9.90543	1.17556	0.587779	+	0.809022i	$0.300002\pi$
$72$	−1.00000	−0.117851
$73$	2.07783	0.243192	0.121596	−	0.992580i	$-0.461199\pi$
$73$	2.07783	0.243192	0.121596	+	0.992580i	$0.461199\pi$
$74$	−9.41176	−1.09409
$75$	4.58582	0.529524
$76$	6.90649	0.792228
$77$	−1.90982	−0.217645
$78$	−1.00000	−0.113228
$79$	−0.329478	−0.0370692	−0.0185346	−	0.999828i	$-0.505900\pi$
$79$	−0.329478	−0.0370692	−0.0185346	+	0.999828i	$0.505900\pi$
$80$	0.643572	0.0719535
$81$	1.00000	0.111111
$82$	7.56422	0.835329
$83$	−1.69775	−0.186353	−0.0931764	−	0.995650i	$-0.529702\pi$
$83$	−1.69775	−0.186353	−0.0931764	+	0.995650i	$0.529702\pi$
$84$	−1.17705	−0.128426
$85$	0.964456	0.104610
$86$	−8.05306	−0.868384
$87$	−6.15424	−0.659804
$88$	1.62256	0.172965
$89$	−1.76809	−0.187417	−0.0937083	−	0.995600i	$-0.529872\pi$
$89$	−1.76809	−0.187417	−0.0937083	+	0.995600i	$0.529872\pi$
$90$	−0.643572	−0.0678384
$91$	−1.17705	−0.123388
$92$	−6.05927	−0.631723
$93$	2.72186	0.282244
$94$	6.76522	0.697779
$95$	4.44482	0.456029
$96$	1.00000	0.102062
$97$	−15.6706	−1.59111	−0.795556	−	0.605881i	$-0.792821\pi$
$97$	−15.6706	−1.59111	−0.795556	+	0.605881i	$0.792821\pi$
$98$	5.61456	0.567156
$99$	−1.62256	−0.163073
$100$	−4.58582	−0.458582
$101$	−5.93932	−0.590985	−0.295492	−	0.955345i	$-0.595484\pi$
$101$	−5.93932	−0.590985	−0.295492	+	0.955345i	$0.595484\pi$
$102$	1.49860	0.148383
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−0.757514	−0.0739258
$106$	5.26991	0.511859
$107$	9.16659	0.886168	0.443084	−	0.896480i	$-0.353884\pi$
$107$	9.16659	0.886168	0.443084	+	0.896480i	$0.353884\pi$
$108$	−1.00000	−0.0962250
$109$	−0.979696	−0.0938379	−0.0469189	−	0.998899i	$-0.514940\pi$
$109$	−0.979696	−0.0938379	−0.0469189	+	0.998899i	$0.514940\pi$
$110$	1.04423	0.0995636
$111$	−9.41176	−0.893324
$112$	1.17705	0.111220
$113$	13.0922	1.23161	0.615807	−	0.787897i	$-0.288830\pi$
$113$	13.0922	1.23161	0.615807	+	0.787897i	$0.288830\pi$
$114$	6.90649	0.646852
$115$	−3.89957	−0.363637
$116$	6.15424	0.571407
$117$	−1.00000	−0.0924500
$118$	−8.48262	−0.780889
$119$	1.76392	0.161698
$120$	0.643572	0.0587498
$121$	−8.36731	−0.760665
$122$	−12.9422	−1.17173
$123$	7.56422	0.682043
$124$	−2.72186	−0.244430
$125$	−6.16916	−0.551786
$126$	−1.17705	−0.104860
$127$	4.42014	0.392224	0.196112	−	0.980582i	$-0.437168\pi$
$127$	4.42014	0.392224	0.196112	+	0.980582i	$0.437168\pi$
$128$	−1.00000	−0.0883883
$129$	−8.05306	−0.709032
$130$	0.643572	0.0564450
$131$	3.53496	0.308850	0.154425	−	0.988004i	$-0.450647\pi$
$131$	3.53496	0.308850	0.154425	+	0.988004i	$0.450647\pi$
$132$	1.62256	0.141225
$133$	8.12926	0.704896
$134$	3.48887	0.301392
$135$	−0.643572	−0.0553898
$136$	−1.49860	−0.128504
$137$	14.5896	1.24647	0.623235	−	0.782034i	$-0.285818\pi$
$137$	14.5896	1.24647	0.623235	+	0.782034i	$0.285818\pi$
$138$	−6.05927	−0.515799
$139$	−0.829863	−0.0703881	−0.0351940	−	0.999380i	$-0.511205\pi$
$139$	−0.829863	−0.0703881	−0.0351940	+	0.999380i	$0.511205\pi$
$140$	0.757514	0.0640216
$141$	6.76522	0.569734
$142$	−9.90543	−0.831245
$143$	1.62256	0.135685
$144$	1.00000	0.0833333
$145$	3.96069	0.328918
$146$	−2.07783	−0.171962
$147$	5.61456	0.463081
$148$	9.41176	0.773642
$149$	7.83483	0.641854	0.320927	−	0.947104i	$-0.396006\pi$
$149$	7.83483	0.641854	0.320927	+	0.947104i	$0.396006\pi$
$150$	−4.58582	−0.374430
$151$	4.95195	0.402984	0.201492	−	0.979490i	$-0.435421\pi$
$151$	4.95195	0.402984	0.201492	+	0.979490i	$0.435421\pi$
$152$	−6.90649	−0.560190
$153$	1.49860	0.121155
$154$	1.90982	0.153898
$155$	−1.75171	−0.140701
$156$	1.00000	0.0800641
$157$	4.49425	0.358680	0.179340	−	0.983787i	$-0.442604\pi$
$157$	4.49425	0.358680	0.179340	+	0.983787i	$0.442604\pi$
$158$	0.329478	0.0262119
$159$	5.26991	0.417931
$160$	−0.643572	−0.0508788
$161$	−7.13205	−0.562084
$162$	−1.00000	−0.0785674
$163$	13.0819	1.02466	0.512328	−	0.858790i	$-0.328783\pi$
$163$	13.0819	1.02466	0.512328	+	0.858790i	$0.328783\pi$
$164$	−7.56422	−0.590667
$165$	1.04423	0.0812933
$166$	1.69775	0.131771
$167$	−0.842027	−0.0651580	−0.0325790	−	0.999469i	$-0.510372\pi$
$167$	−0.842027	−0.0651580	−0.0325790	+	0.999469i	$0.510372\pi$
$168$	1.17705	0.0908111
$169$	1.00000	0.0769231
$170$	−0.964456	−0.0739704
$171$	6.90649	0.528152
$172$	8.05306	0.614040
$173$	−12.9042	−0.981084	−0.490542	−	0.871417i	$-0.663201\pi$
$173$	−12.9042	−0.981084	−0.490542	+	0.871417i	$0.663201\pi$
$174$	6.15424	0.466552
$175$	−5.39772	−0.408029
$176$	−1.62256	−0.122305
$177$	−8.48262	−0.637593
$178$	1.76809	0.132524
$179$	2.76289	0.206508	0.103254	−	0.994655i	$-0.467075\pi$
$179$	2.76289	0.206508	0.103254	+	0.994655i	$0.467075\pi$
$180$	0.643572	0.0479690
$181$	8.64089	0.642273	0.321136	−	0.947033i	$-0.395935\pi$
$181$	8.64089	0.642273	0.321136	+	0.947033i	$0.395935\pi$
$182$	1.17705	0.0872485
$183$	−12.9422	−0.956716
$184$	6.05927	0.446695
$185$	6.05714	0.445330
$186$	−2.72186	−0.199577
$187$	−2.43156	−0.177813
$188$	−6.76522	−0.493404
$189$	−1.17705	−0.0856175
$190$	−4.44482	−0.322461
$191$	−1.08471	−0.0784870	−0.0392435	−	0.999230i	$-0.512495\pi$
$191$	−1.08471	−0.0784870	−0.0392435	+	0.999230i	$0.512495\pi$
$192$	−1.00000	−0.0721688
$193$	18.1254	1.30469	0.652347	−	0.757921i	$-0.273785\pi$
$193$	18.1254	1.30469	0.652347	+	0.757921i	$0.273785\pi$
$194$	15.6706	1.12509
$195$	0.643572	0.0460871
$196$	−5.61456	−0.401040
$197$	−19.3889	−1.38140	−0.690702	−	0.723139i	$-0.742698\pi$
$197$	−19.3889	−1.38140	−0.690702	+	0.723139i	$0.742698\pi$
$198$	1.62256	0.115310
$199$	13.7592	0.975367	0.487684	−	0.873020i	$-0.337842\pi$
$199$	13.7592	0.975367	0.487684	+	0.873020i	$0.337842\pi$
$200$	4.58582	0.324266
$201$	3.48887	0.246086
$202$	5.93932	0.417889
$203$	7.24383	0.508417
$204$	−1.49860	−0.104923
$205$	−4.86812	−0.340004
$206$	−1.00000	−0.0696733
$207$	−6.05927	−0.421148
$208$	−1.00000	−0.0693375
$209$	−11.2062	−0.775147
$210$	0.757514	0.0522734
$211$	28.7921	1.98213	0.991063	−	0.133392i	$-0.0425870\pi$
$211$	28.7921	1.98213	0.991063	+	0.133392i	$0.0425870\pi$
$212$	−5.26991	−0.361939
$213$	−9.90543	−0.678709
$214$	−9.16659	−0.626615
$215$	5.18272	0.353459
$216$	1.00000	0.0680414
$217$	−3.20376	−0.217485
$218$	0.979696	0.0663534
$219$	−2.07783	−0.140407
$220$	−1.04423	−0.0704021
$221$	−1.49860	−0.100807
$222$	9.41176	0.631676
$223$	−12.7364	−0.852892	−0.426446	−	0.904513i	$-0.640235\pi$
$223$	−12.7364	−0.852892	−0.426446	+	0.904513i	$0.640235\pi$
$224$	−1.17705	−0.0786447
$225$	−4.58582	−0.305721
$226$	−13.0922	−0.870883
$227$	−22.9067	−1.52037	−0.760185	−	0.649706i	$-0.774892\pi$
$227$	−22.9067	−1.52037	−0.760185	+	0.649706i	$0.774892\pi$
$228$	−6.90649	−0.457393
$229$	10.6201	0.701794	0.350897	−	0.936414i	$-0.385877\pi$
$229$	10.6201	0.701794	0.350897	+	0.936414i	$0.385877\pi$
$230$	3.89957	0.257130
$231$	1.90982	0.125657
$232$	−6.15424	−0.404046
$233$	6.61868	0.433604	0.216802	−	0.976216i	$-0.430437\pi$
$233$	6.61868	0.433604	0.216802	+	0.976216i	$0.430437\pi$
$234$	1.00000	0.0653720
$235$	−4.35390	−0.284017
$236$	8.48262	0.552172
$237$	0.329478	0.0214019
$238$	−1.76392	−0.114338
$239$	−16.6591	−1.07759	−0.538794	−	0.842438i	$-0.681120\pi$
$239$	−16.6591	−1.07759	−0.538794	+	0.842438i	$0.681120\pi$
$240$	−0.643572	−0.0415424
$241$	−13.5837	−0.875000	−0.437500	−	0.899218i	$-0.644136\pi$
$241$	−13.5837	−0.875000	−0.437500	+	0.899218i	$0.644136\pi$
$242$	8.36731	0.537871
$243$	−1.00000	−0.0641500
$244$	12.9422	0.828540
$245$	−3.61337	−0.230850
$246$	−7.56422	−0.482277
$247$	−6.90649	−0.439449
$248$	2.72186	0.172838
$249$	1.69775	0.107591
$250$	6.16916	0.390172
$251$	23.5935	1.48921	0.744603	−	0.667508i	$-0.232639\pi$
$251$	23.5935	1.48921	0.744603	+	0.667508i	$0.232639\pi$
$252$	1.17705	0.0741470
$253$	9.83151	0.618102
$254$	−4.42014	−0.277344
$255$	−0.964456	−0.0603966
$256$	1.00000	0.0625000
$257$	0.0762573	0.00475680	0.00237840	−	0.999997i	$-0.499243\pi$
$257$	0.0762573	0.00475680	0.00237840	+	0.999997i	$0.499243\pi$
$258$	8.05306	0.501362
$259$	11.0781	0.688358
$260$	−0.643572	−0.0399126
$261$	6.15424	0.380938
$262$	−3.53496	−0.218390
$263$	−26.4812	−1.63290	−0.816451	−	0.577414i	$-0.804062\pi$
$263$	−26.4812	−1.63290	−0.816451	+	0.577414i	$0.804062\pi$
$264$	−1.62256	−0.0998615
$265$	−3.39157	−0.208342
$266$	−8.12926	−0.498437
$267$	1.76809	0.108205
$268$	−3.48887	−0.213117
$269$	−23.4459	−1.42952	−0.714761	−	0.699368i	$-0.753465\pi$
$269$	−23.4459	−1.42952	−0.714761	+	0.699368i	$0.753465\pi$
$270$	0.643572	0.0391665
$271$	19.3142	1.17325	0.586626	−	0.809858i	$-0.300456\pi$
$271$	19.3142	1.17325	0.586626	+	0.809858i	$0.300456\pi$
$272$	1.49860	0.0908659
$273$	1.17705	0.0712381
$274$	−14.5896	−0.881388
$275$	7.44075	0.448694
$276$	6.05927	0.364725
$277$	17.3607	1.04311	0.521553	−	0.853219i	$-0.325353\pi$
$277$	17.3607	1.04311	0.521553	+	0.853219i	$0.325353\pi$
$278$	0.829863	0.0497719
$279$	−2.72186	−0.162954
$280$	−0.757514	−0.0452701
$281$	−16.4966	−0.984106	−0.492053	−	0.870565i	$-0.663753\pi$
$281$	−16.4966	−0.984106	−0.492053	+	0.870565i	$0.663753\pi$
$282$	−6.76522	−0.402863
$283$	−17.2117	−1.02313	−0.511564	−	0.859245i	$-0.670934\pi$
$283$	−17.2117	−1.02313	−0.511564	+	0.859245i	$0.670934\pi$
$284$	9.90543	0.587779
$285$	−4.44482	−0.263288
$286$	−1.62256	−0.0959438
$287$	−8.90344	−0.525554
$288$	−1.00000	−0.0589256
$289$	−14.7542	−0.867894
$290$	−3.96069	−0.232580
$291$	15.6706	0.918628
$292$	2.07783	0.121596
$293$	4.91838	0.287335	0.143667	−	0.989626i	$-0.454110\pi$
$293$	4.91838	0.287335	0.143667	+	0.989626i	$0.454110\pi$
$294$	−5.61456	−0.327448
$295$	5.45918	0.317845
$296$	−9.41176	−0.547047
$297$	1.62256	0.0941503
$298$	−7.83483	−0.453860
$299$	6.05927	0.350417
$300$	4.58582	0.264762
$301$	9.47883	0.546350
$302$	−4.95195	−0.284952
$303$	5.93932	0.341205
$304$	6.90649	0.396114
$305$	8.32924	0.476931
$306$	−1.49860	−0.0856692
$307$	−3.35221	−0.191321	−0.0956603	−	0.995414i	$-0.530496\pi$
$307$	−3.35221	−0.191321	−0.0956603	+	0.995414i	$0.530496\pi$
$308$	−1.90982	−0.108822
$309$	−1.00000	−0.0568880
$310$	1.75171	0.0994906
$311$	28.2832	1.60379	0.801897	−	0.597462i	$-0.203824\pi$
$311$	28.2832	1.60379	0.801897	+	0.597462i	$0.203824\pi$
$312$	−1.00000	−0.0566139
$313$	22.0633	1.24709	0.623547	−	0.781786i	$-0.285691\pi$
$313$	22.0633	1.24709	0.623547	+	0.781786i	$0.285691\pi$
$314$	−4.49425	−0.253625
$315$	0.757514	0.0426811
$316$	−0.329478	−0.0185346
$317$	6.69370	0.375956	0.187978	−	0.982173i	$-0.439807\pi$
$317$	6.69370	0.375956	0.187978	+	0.982173i	$0.439807\pi$
$318$	−5.26991	−0.295522
$319$	−9.98560	−0.559086
$320$	0.643572	0.0359767
$321$	−9.16659	−0.511629
$322$	7.13205	0.397453
$323$	10.3501	0.575892
$324$	1.00000	0.0555556
$325$	4.58582	0.254375
$326$	−13.0819	−0.724542
$327$	0.979696	0.0541773
$328$	7.56422	0.417664
$329$	−7.96298	−0.439013
$330$	−1.04423	−0.0574830
$331$	15.8048	0.868710	0.434355	−	0.900742i	$-0.356976\pi$
$331$	15.8048	0.868710	0.434355	+	0.900742i	$0.356976\pi$
$332$	−1.69775	−0.0931764
$333$	9.41176	0.515761
$334$	0.842027	0.0460737
$335$	−2.24534	−0.122676
$336$	−1.17705	−0.0642132
$337$	−28.1213	−1.53187	−0.765934	−	0.642919i	$-0.777723\pi$
$337$	−28.1213	−1.53187	−0.765934	+	0.642919i	$0.777723\pi$
$338$	−1.00000	−0.0543928
$339$	−13.0922	−0.711073
$340$	0.964456	0.0523050
$341$	4.41637	0.239160
$342$	−6.90649	−0.373460
$343$	−14.8479	−0.801713
$344$	−8.05306	−0.434192
$345$	3.89957	0.209946
$346$	12.9042	0.693731
$347$	10.8696	0.583509	0.291755	−	0.956493i	$-0.405761\pi$
$347$	10.8696	0.583509	0.291755	+	0.956493i	$0.405761\pi$
$348$	−6.15424	−0.329902
$349$	−21.7245	−1.16289	−0.581443	−	0.813587i	$-0.697512\pi$
$349$	−21.7245	−1.16289	−0.581443	+	0.813587i	$0.697512\pi$
$350$	5.39772	0.288520
$351$	1.00000	0.0533761
$352$	1.62256	0.0864826
$353$	17.5463	0.933894	0.466947	−	0.884285i	$-0.345354\pi$
$353$	17.5463	0.933894	0.466947	+	0.884285i	$0.345354\pi$
$354$	8.48262	0.450846
$355$	6.37485	0.338342
$356$	−1.76809	−0.0937083
$357$	−1.76392	−0.0933566
$358$	−2.76289	−0.146023
$359$	25.6817	1.35543	0.677713	−	0.735326i	$-0.262971\pi$
$359$	25.6817	1.35543	0.677713	+	0.735326i	$0.262971\pi$
$360$	−0.643572	−0.0339192
$361$	28.6996	1.51050
$362$	−8.64089	−0.454155
$363$	8.36731	0.439170
$364$	−1.17705	−0.0616940
$365$	1.33723	0.0699939
$366$	12.9422	0.676500
$367$	−31.1996	−1.62861	−0.814304	−	0.580439i	$-0.802881\pi$
$367$	−31.1996	−1.62861	−0.814304	+	0.580439i	$0.802881\pi$
$368$	−6.05927	−0.315861
$369$	−7.56422	−0.393778
$370$	−6.05714	−0.314896
$371$	−6.20293	−0.322040
$372$	2.72186	0.141122
$373$	14.9563	0.774407	0.387204	−	0.921994i	$-0.373441\pi$
$373$	14.9563	0.774407	0.387204	+	0.921994i	$0.373441\pi$
$374$	2.43156	0.125733
$375$	6.16916	0.318574
$376$	6.76522	0.348889
$377$	−6.15424	−0.316959
$378$	1.17705	0.0605407
$379$	15.4787	0.795085	0.397543	−	0.917584i	$-0.369863\pi$
$379$	15.4787	0.795085	0.397543	+	0.917584i	$0.369863\pi$
$380$	4.44482	0.228014
$381$	−4.42014	−0.226450
$382$	1.08471	0.0554987
$383$	2.23651	0.114280	0.0571402	−	0.998366i	$-0.481802\pi$
$383$	2.23651	0.114280	0.0571402	+	0.998366i	$0.481802\pi$
$384$	1.00000	0.0510310
$385$	−1.22911	−0.0626412
$386$	−18.1254	−0.922557
$387$	8.05306	0.409360
$388$	−15.6706	−0.795556
$389$	−12.8220	−0.650102	−0.325051	−	0.945697i	$-0.605381\pi$
$389$	−12.8220	−0.650102	−0.325051	+	0.945697i	$0.605381\pi$
$390$	−0.643572	−0.0325885
$391$	−9.08042	−0.459216
$392$	5.61456	0.283578
$393$	−3.53496	−0.178315
$394$	19.3889	0.976801
$395$	−0.212043	−0.0106690
$396$	−1.62256	−0.0815365
$397$	20.6229	1.03503	0.517516	−	0.855674i	$-0.326857\pi$
$397$	20.6229	1.03503	0.517516	+	0.855674i	$0.326857\pi$
$398$	−13.7592	−0.689689
$399$	−8.12926	−0.406972
$400$	−4.58582	−0.229291
$401$	−3.88998	−0.194256	−0.0971282	−	0.995272i	$-0.530966\pi$
$401$	−3.88998	−0.194256	−0.0971282	+	0.995272i	$0.530966\pi$
$402$	−3.48887	−0.174009
$403$	2.72186	0.135586
$404$	−5.93932	−0.295492
$405$	0.643572	0.0319793
$406$	−7.24383	−0.359505
$407$	−15.2711	−0.756961
$408$	1.49860	0.0741917
$409$	12.0257	0.594631	0.297315	−	0.954779i	$-0.403909\pi$
$409$	12.0257	0.594631	0.297315	+	0.954779i	$0.403909\pi$
$410$	4.86812	0.240419
$411$	−14.5896	−0.719650
$412$	1.00000	0.0492665
$413$	9.98444	0.491302
$414$	6.05927	0.297797
$415$	−1.09263	−0.0536349
$416$	1.00000	0.0490290
$417$	0.829863	0.0406386
$418$	11.2062	0.548112
$419$	−9.30539	−0.454598	−0.227299	−	0.973825i	$-0.572989\pi$
$419$	−9.30539	−0.454598	−0.227299	+	0.973825i	$0.572989\pi$
$420$	−0.757514	−0.0369629
$421$	37.1227	1.80925	0.904624	−	0.426210i	$-0.140152\pi$
$421$	37.1227	1.80925	0.904624	+	0.426210i	$0.140152\pi$
$422$	−28.7921	−1.40158
$423$	−6.76522	−0.328936
$424$	5.26991	0.255930
$425$	−6.87230	−0.333355
$426$	9.90543	0.479919
$427$	15.2336	0.737205
$428$	9.16659	0.443084
$429$	−1.62256	−0.0783378
$430$	−5.18272	−0.249933
$431$	−4.29157	−0.206718	−0.103359	−	0.994644i	$-0.532959\pi$
$431$	−4.29157	−0.206718	−0.103359	+	0.994644i	$0.532959\pi$
$432$	−1.00000	−0.0481125
$433$	9.74101	0.468123	0.234062	−	0.972222i	$-0.424798\pi$
$433$	9.74101	0.468123	0.234062	+	0.972222i	$0.424798\pi$
$434$	3.20376	0.153785
$435$	−3.96069	−0.189901
$436$	−0.979696	−0.0469189
$437$	−41.8483	−2.00187
$438$	2.07783	0.0992826
$439$	13.6511	0.651532	0.325766	−	0.945450i	$-0.394378\pi$
$439$	13.6511	0.651532	0.325766	+	0.945450i	$0.394378\pi$
$440$	1.04423	0.0497818
$441$	−5.61456	−0.267360
$442$	1.49860	0.0712811
$443$	−22.2391	−1.05661	−0.528306	−	0.849054i	$-0.677173\pi$
$443$	−22.2391	−1.05661	−0.528306	+	0.849054i	$0.677173\pi$
$444$	−9.41176	−0.446662
$445$	−1.13789	−0.0539411
$446$	12.7364	0.603086
$447$	−7.83483	−0.370575
$448$	1.17705	0.0556102
$449$	−19.2668	−0.909259	−0.454629	−	0.890681i	$-0.650228\pi$
$449$	−19.2668	−0.909259	−0.454629	+	0.890681i	$0.650228\pi$
$450$	4.58582	0.216177
$451$	12.2734	0.577931
$452$	13.0922	0.615807
$453$	−4.95195	−0.232663
$454$	22.9067	1.07506
$455$	−0.757514	−0.0355128
$456$	6.90649	0.323426
$457$	−40.3189	−1.88604	−0.943019	−	0.332739i	$-0.892027\pi$
$457$	−40.3189	−1.88604	−0.943019	+	0.332739i	$0.892027\pi$
$458$	−10.6201	−0.496243
$459$	−1.49860	−0.0699486
$460$	−3.89957	−0.181819
$461$	−9.53646	−0.444157	−0.222079	−	0.975029i	$-0.571284\pi$
$461$	−9.53646	−0.444157	−0.222079	+	0.975029i	$0.571284\pi$
$462$	−1.90982	−0.0888531
$463$	21.8752	1.01663	0.508313	−	0.861172i	$-0.330269\pi$
$463$	21.8752	1.01663	0.508313	+	0.861172i	$0.330269\pi$
$464$	6.15424	0.285703
$465$	1.75171	0.0812337
$466$	−6.61868	−0.306605
$467$	41.0475	1.89945	0.949726	−	0.313083i	$-0.101362\pi$
$467$	41.0475	1.89945	0.949726	+	0.313083i	$0.101362\pi$
$468$	−1.00000	−0.0462250
$469$	−4.10656	−0.189623
$470$	4.35390	0.200831
$471$	−4.49425	−0.207084
$472$	−8.48262	−0.390444
$473$	−13.0665	−0.600800
$474$	−0.329478	−0.0151334
$475$	−31.6719	−1.45321
$476$	1.76392	0.0808492
$477$	−5.26991	−0.241293
$478$	16.6591	0.761970
$479$	13.1109	0.599051	0.299526	−	0.954088i	$-0.403172\pi$
$479$	13.1109	0.599051	0.299526	+	0.954088i	$0.403172\pi$
$480$	0.643572	0.0293749
$481$	−9.41176	−0.429139
$482$	13.5837	0.618719
$483$	7.13205	0.324519
$484$	−8.36731	−0.380332
$485$	−10.0852	−0.457944
$486$	1.00000	0.0453609
$487$	−9.34915	−0.423650	−0.211825	−	0.977308i	$-0.567941\pi$
$487$	−9.34915	−0.423650	−0.211825	+	0.977308i	$0.567941\pi$
$488$	−12.9422	−0.585867
$489$	−13.0819	−0.591586
$490$	3.61337	0.163236
$491$	−3.89868	−0.175945	−0.0879726	−	0.996123i	$-0.528039\pi$
$491$	−3.89868	−0.175945	−0.0879726	+	0.996123i	$0.528039\pi$
$492$	7.56422	0.341022
$493$	9.22274	0.415371
$494$	6.90649	0.310738
$495$	−1.04423	−0.0469347
$496$	−2.72186	−0.122215
$497$	11.6591	0.522984
$498$	−1.69775	−0.0760782
$499$	−25.0610	−1.12188	−0.560942	−	0.827855i	$-0.689561\pi$
$499$	−25.0610	−1.12188	−0.560942	+	0.827855i	$0.689561\pi$
$500$	−6.16916	−0.275893
$501$	0.842027	0.0376190
$502$	−23.5935	−1.05303
$503$	18.4213	0.821364	0.410682	−	0.911779i	$-0.365291\pi$
$503$	18.4213	0.821364	0.410682	+	0.911779i	$0.365291\pi$
$504$	−1.17705	−0.0524298
$505$	−3.82238	−0.170094
$506$	−9.83151	−0.437064
$507$	−1.00000	−0.0444116
$508$	4.42014	0.196112
$509$	42.1686	1.86909	0.934546	−	0.355842i	$-0.115806\pi$
$509$	42.1686	1.86909	0.934546	+	0.355842i	$0.115806\pi$
$510$	0.964456	0.0427068
$511$	2.44570	0.108192
$512$	−1.00000	−0.0441942
$513$	−6.90649	−0.304929
$514$	−0.0762573	−0.00336356
$515$	0.643572	0.0283592
$516$	−8.05306	−0.354516
$517$	10.9769	0.482766
$518$	−11.0781	−0.486743
$519$	12.9042	0.566429
$520$	0.643572	0.0282225
$521$	−4.06054	−0.177895	−0.0889477	−	0.996036i	$-0.528350\pi$
$521$	−4.06054	−0.177895	−0.0889477	+	0.996036i	$0.528350\pi$
$522$	−6.15424	−0.269364
$523$	−38.7979	−1.69651	−0.848256	−	0.529587i	$-0.822347\pi$
$523$	−38.7979	−1.69651	−0.848256	+	0.529587i	$0.822347\pi$
$524$	3.53496	0.154425
$525$	5.39772	0.235576
$526$	26.4812	1.15464
$527$	−4.07898	−0.177683
$528$	1.62256	0.0706127
$529$	13.7148	0.596294
$530$	3.39157	0.147320
$531$	8.48262	0.368114
$532$	8.12926	0.352448
$533$	7.56422	0.327643
$534$	−1.76809	−0.0765125
$535$	5.89936	0.255051
$536$	3.48887	0.150696
$537$	−2.76289	−0.119227
$538$	23.4459	1.01083
$539$	9.10994	0.392393
$540$	−0.643572	−0.0276949
$541$	18.9115	0.813067	0.406534	−	0.913636i	$-0.366737\pi$
$541$	18.9115	0.813067	0.406534	+	0.913636i	$0.366737\pi$
$542$	−19.3142	−0.829614
$543$	−8.64089	−0.370816
$544$	−1.49860	−0.0642519
$545$	−0.630505	−0.0270079
$546$	−1.17705	−0.0503729
$547$	−2.99158	−0.127911	−0.0639554	−	0.997953i	$-0.520372\pi$
$547$	−2.99158	−0.127911	−0.0639554	+	0.997953i	$0.520372\pi$
$548$	14.5896	0.623235
$549$	12.9422	0.552360
$550$	−7.44075	−0.317274
$551$	42.5042	1.81074
$552$	−6.05927	−0.257900
$553$	−0.387811	−0.0164914
$554$	−17.3607	−0.737587
$555$	−6.05714	−0.257111
$556$	−0.829863	−0.0351940
$557$	20.2906	0.859739	0.429870	−	0.902891i	$-0.358560\pi$
$557$	20.2906	0.859739	0.429870	+	0.902891i	$0.358560\pi$
$558$	2.72186	0.115226
$559$	−8.05306	−0.340608
$560$	0.757514	0.0320108
$561$	2.43156	0.102661
$562$	16.4966	0.695868
$563$	17.4691	0.736237	0.368118	−	0.929779i	$-0.380002\pi$
$563$	17.4691	0.736237	0.368118	+	0.929779i	$0.380002\pi$
$564$	6.76522	0.284867
$565$	8.42579	0.354476
$566$	17.2117	0.723460
$567$	1.17705	0.0494313
$568$	−9.90543	−0.415622
$569$	−2.10370	−0.0881918	−0.0440959	−	0.999027i	$-0.514041\pi$
$569$	−2.10370	−0.0881918	−0.0440959	+	0.999027i	$0.514041\pi$
$570$	4.44482	0.186173
$571$	32.1980	1.34744	0.673721	−	0.738985i	$-0.264695\pi$
$571$	32.1980	1.34744	0.673721	+	0.738985i	$0.264695\pi$
$572$	1.62256	0.0678425
$573$	1.08471	0.0453145
$574$	8.90344	0.371623
$575$	27.7867	1.15879
$576$	1.00000	0.0416667
$577$	37.6482	1.56731	0.783657	−	0.621194i	$-0.213352\pi$
$577$	37.6482	1.56731	0.783657	+	0.621194i	$0.213352\pi$
$578$	14.7542	0.613694
$579$	−18.1254	−0.753265
$580$	3.96069	0.164459
$581$	−1.99834	−0.0829050
$582$	−15.6706	−0.649568
$583$	8.55073	0.354135
$584$	−2.07783	−0.0859812
$585$	−0.643572	−0.0266084
$586$	−4.91838	−0.203176
$587$	36.8823	1.52230	0.761148	−	0.648578i	$-0.224636\pi$
$587$	36.8823	1.52230	0.761148	+	0.648578i	$0.224636\pi$
$588$	5.61456	0.231541
$589$	−18.7985	−0.774579
$590$	−5.45918	−0.224751
$591$	19.3889	0.797554
$592$	9.41176	0.386821
$593$	38.8654	1.59601	0.798004	−	0.602652i	$-0.205889\pi$
$593$	38.8654	1.59601	0.798004	+	0.602652i	$0.205889\pi$
$594$	−1.62256	−0.0665743
$595$	1.13521	0.0465390
$596$	7.83483	0.320927
$597$	−13.7592	−0.563129
$598$	−6.05927	−0.247782
$599$	2.56135	0.104654	0.0523270	−	0.998630i	$-0.483336\pi$
$599$	2.56135	0.104654	0.0523270	+	0.998630i	$0.483336\pi$
$600$	−4.58582	−0.187215
$601$	38.8543	1.58490	0.792451	−	0.609936i	$-0.208805\pi$
$601$	38.8543	1.58490	0.792451	+	0.609936i	$0.208805\pi$
$602$	−9.47883	−0.386328
$603$	−3.48887	−0.142078
$604$	4.95195	0.201492
$605$	−5.38496	−0.218930
$606$	−5.93932	−0.241269
$607$	−0.129186	−0.00524350	−0.00262175	−	0.999997i	$-0.500835\pi$
$607$	−0.129186	−0.00524350	−0.00262175	+	0.999997i	$0.500835\pi$
$608$	−6.90649	−0.280095
$609$	−7.24383	−0.293535
$610$	−8.32924	−0.337241
$611$	6.76522	0.273691
$612$	1.49860	0.0605773
$613$	1.47528	0.0595858	0.0297929	−	0.999556i	$-0.490515\pi$
$613$	1.47528	0.0595858	0.0297929	+	0.999556i	$0.490515\pi$
$614$	3.35221	0.135284
$615$	4.86812	0.196302
$616$	1.90982	0.0769490
$617$	−10.5489	−0.424684	−0.212342	−	0.977195i	$-0.568109\pi$
$617$	−10.5489	−0.424684	−0.212342	+	0.977195i	$0.568109\pi$
$618$	1.00000	0.0402259
$619$	25.3604	1.01932	0.509660	−	0.860376i	$-0.329771\pi$
$619$	25.3604	1.01932	0.509660	+	0.860376i	$0.329771\pi$
$620$	−1.75171	−0.0703505
$621$	6.05927	0.243150
$622$	−28.2832	−1.13405
$623$	−2.08112	−0.0833783
$624$	1.00000	0.0400320
$625$	18.9588	0.758351
$626$	−22.0633	−0.881829
$627$	11.2062	0.447531
$628$	4.49425	0.179340
$629$	14.1044	0.562381
$630$	−0.757514	−0.0301801
$631$	28.5992	1.13852	0.569258	−	0.822159i	$-0.307231\pi$
$631$	28.5992	1.13852	0.569258	+	0.822159i	$0.307231\pi$
$632$	0.329478	0.0131059
$633$	−28.7921	−1.14438
$634$	−6.69370	−0.265841
$635$	2.84467	0.112887
$636$	5.26991	0.208966
$637$	5.61456	0.222457
$638$	9.98560	0.395334
$639$	9.90543	0.391853
$640$	−0.643572	−0.0254394
$641$	−29.4248	−1.16221	−0.581106	−	0.813828i	$-0.697380\pi$
$641$	−29.4248	−1.16221	−0.581106	+	0.813828i	$0.697380\pi$
$642$	9.16659	0.361776
$643$	21.1208	0.832923	0.416461	−	0.909153i	$-0.363270\pi$
$643$	21.1208	0.832923	0.416461	+	0.909153i	$0.363270\pi$
$644$	−7.13205	−0.281042
$645$	−5.18272	−0.204069
$646$	−10.3501	−0.407217
$647$	−13.6705	−0.537443	−0.268722	−	0.963218i	$-0.586601\pi$
$647$	−13.6705	−0.537443	−0.268722	+	0.963218i	$0.586601\pi$
$648$	−1.00000	−0.0392837
$649$	−13.7635	−0.540266
$650$	−4.58582	−0.179870
$651$	3.20376	0.125565
$652$	13.0819	0.512328
$653$	21.2825	0.832847	0.416424	−	0.909171i	$-0.363283\pi$
$653$	21.2825	0.832847	0.416424	+	0.909171i	$0.363283\pi$
$654$	−0.979696	−0.0383092
$655$	2.27500	0.0888915
$656$	−7.56422	−0.295333
$657$	2.07783	0.0810639
$658$	7.96298	0.310429
$659$	6.56859	0.255876	0.127938	−	0.991782i	$-0.459164\pi$
$659$	6.56859	0.255876	0.127938	+	0.991782i	$0.459164\pi$
$660$	1.04423	0.0406466
$661$	−20.1598	−0.784124	−0.392062	−	0.919939i	$-0.628238\pi$
$661$	−20.1598	−0.784124	−0.392062	+	0.919939i	$0.628238\pi$
$662$	−15.8048	−0.614270
$663$	1.49860	0.0582008
$664$	1.69775	0.0658857
$665$	5.23176	0.202879
$666$	−9.41176	−0.364698
$667$	−37.2902	−1.44388
$668$	−0.842027	−0.0325790
$669$	12.7364	0.492417
$670$	2.24534	0.0867449
$671$	−20.9995	−0.810676
$672$	1.17705	0.0454056
$673$	33.0805	1.27516	0.637579	−	0.770385i	$-0.279936\pi$
$673$	33.0805	1.27516	0.637579	+	0.770385i	$0.279936\pi$
$674$	28.1213	1.08319
$675$	4.58582	0.176508
$676$	1.00000	0.0384615
$677$	−3.63576	−0.139734	−0.0698668	−	0.997556i	$-0.522257\pi$
$677$	−3.63576	−0.139734	−0.0698668	+	0.997556i	$0.522257\pi$
$678$	13.0922	0.502804
$679$	−18.4451	−0.707856
$680$	−0.964456	−0.0369852
$681$	22.9067	0.877786
$682$	−4.41637	−0.169112
$683$	23.9793	0.917542	0.458771	−	0.888555i	$-0.348290\pi$
$683$	23.9793	0.917542	0.458771	+	0.888555i	$0.348290\pi$
$684$	6.90649	0.264076
$685$	9.38943	0.358752
$686$	14.8479	0.566897
$687$	−10.6201	−0.405181
$688$	8.05306	0.307020
$689$	5.26991	0.200768
$690$	−3.89957	−0.148454
$691$	10.4362	0.397010	0.198505	−	0.980100i	$-0.436391\pi$
$691$	10.4362	0.397010	0.198505	+	0.980100i	$0.436391\pi$
$692$	−12.9042	−0.490542
$693$	−1.90982	−0.0725482
$694$	−10.8696	−0.412603
$695$	−0.534076	−0.0202587
$696$	6.15424	0.233276
$697$	−11.3357	−0.429372
$698$	21.7245	0.822285
$699$	−6.61868	−0.250342
$700$	−5.39772	−0.204015
$701$	−10.1995	−0.385230	−0.192615	−	0.981274i	$-0.561697\pi$
$701$	−10.1995	−0.385230	−0.192615	+	0.981274i	$0.561697\pi$
$702$	−1.00000	−0.0377426
$703$	65.0022	2.45160
$704$	−1.62256	−0.0611524
$705$	4.35390	0.163977
$706$	−17.5463	−0.660363
$707$	−6.99086	−0.262918
$708$	−8.48262	−0.318796
$709$	34.4092	1.29226	0.646132	−	0.763226i	$-0.276386\pi$
$709$	34.4092	1.29226	0.646132	+	0.763226i	$0.276386\pi$
$710$	−6.37485	−0.239244
$711$	−0.329478	−0.0123564
$712$	1.76809	0.0662618
$713$	16.4925	0.617649
$714$	1.76392	0.0660131
$715$	1.04423	0.0390520
$716$	2.76289	0.103254
$717$	16.6591	0.622146
$718$	−25.6817	−0.958431
$719$	41.7873	1.55840	0.779202	−	0.626773i	$-0.215625\pi$
$719$	41.7873	1.55840	0.779202	+	0.626773i	$0.215625\pi$
$720$	0.643572	0.0239845
$721$	1.17705	0.0438355
$722$	−28.6996	−1.06809
$723$	13.5837	0.505182
$724$	8.64089	0.321136
$725$	−28.2222	−1.04815
$726$	−8.36731	−0.310540
$727$	11.9237	0.442224	0.221112	−	0.975248i	$-0.429031\pi$
$727$	11.9237	0.442224	0.221112	+	0.975248i	$0.429031\pi$
$728$	1.17705	0.0436243
$729$	1.00000	0.0370370
$730$	−1.33723	−0.0494932
$731$	12.0683	0.446362
$732$	−12.9422	−0.478358
$733$	46.1861	1.70592	0.852962	−	0.521974i	$-0.174804\pi$
$733$	46.1861	1.70592	0.852962	+	0.521974i	$0.174804\pi$
$734$	31.1996	1.15160
$735$	3.61337	0.133281
$736$	6.05927	0.223348
$737$	5.66089	0.208521
$738$	7.56422	0.278443
$739$	10.1331	0.372752	0.186376	−	0.982479i	$-0.440326\pi$
$739$	10.1331	0.372752	0.186376	+	0.982479i	$0.440326\pi$
$740$	6.05714	0.222665
$741$	6.90649	0.253716
$742$	6.20293	0.227717
$743$	20.5959	0.755589	0.377795	−	0.925889i	$-0.376683\pi$
$743$	20.5959	0.755589	0.377795	+	0.925889i	$0.376683\pi$
$744$	−2.72186	−0.0997883
$745$	5.04228	0.184735
$746$	−14.9563	−0.547589
$747$	−1.69775	−0.0621176
$748$	−2.43156	−0.0889067
$749$	10.7895	0.394240
$750$	−6.16916	−0.225266
$751$	33.3868	1.21830	0.609150	−	0.793055i	$-0.291511\pi$
$751$	33.3868	1.21830	0.609150	+	0.793055i	$0.291511\pi$
$752$	−6.76522	−0.246702
$753$	−23.5935	−0.859793
$754$	6.15424	0.224124
$755$	3.18693	0.115984
$756$	−1.17705	−0.0428088
$757$	19.0021	0.690643	0.345321	−	0.938484i	$-0.387770\pi$
$757$	19.0021	0.690643	0.345321	+	0.938484i	$0.387770\pi$
$758$	−15.4787	−0.562210
$759$	−9.83151	−0.356861
$760$	−4.44482	−0.161231
$761$	−12.9138	−0.468126	−0.234063	−	0.972221i	$-0.575202\pi$
$761$	−12.9138	−0.468126	−0.234063	+	0.972221i	$0.575202\pi$
$762$	4.42014	0.160125
$763$	−1.15315	−0.0417468
$764$	−1.08471	−0.0392435
$765$	0.964456	0.0348700
$766$	−2.23651	−0.0808084
$767$	−8.48262	−0.306290
$768$	−1.00000	−0.0360844
$769$	23.2573	0.838681	0.419341	−	0.907829i	$-0.362261\pi$
$769$	23.2573	0.838681	0.419341	+	0.907829i	$0.362261\pi$
$770$	1.22911	0.0442940
$771$	−0.0762573	−0.00274634
$772$	18.1254	0.652347
$773$	−36.7853	−1.32307	−0.661537	−	0.749912i	$-0.730096\pi$
$773$	−36.7853	−1.32307	−0.661537	+	0.749912i	$0.730096\pi$
$774$	−8.05306	−0.289461
$775$	12.4820	0.448365
$776$	15.6706	0.562543
$777$	−11.0781	−0.397424
$778$	12.8220	0.459691
$779$	−52.2422	−1.87177
$780$	0.643572	0.0230436
$781$	−16.0721	−0.575105
$782$	9.08042	0.324715
$783$	−6.15424	−0.219935
$784$	−5.61456	−0.200520
$785$	2.89237	0.103233
$786$	3.53496	0.126088
$787$	−5.48590	−0.195551	−0.0977756	−	0.995208i	$-0.531173\pi$
$787$	−5.48590	−0.195551	−0.0977756	+	0.995208i	$0.531173\pi$
$788$	−19.3889	−0.690702
$789$	26.4812	0.942757
$790$	0.212043	0.00754415
$791$	15.4102	0.547923
$792$	1.62256	0.0576550
$793$	−12.9422	−0.459592
$794$	−20.6229	−0.731878
$795$	3.39157	0.120286
$796$	13.7592	0.487684
$797$	−47.6326	−1.68723	−0.843617	−	0.536946i	$-0.819578\pi$
$797$	−47.6326	−1.68723	−0.843617	+	0.536946i	$0.819578\pi$
$798$	8.12926	0.287773
$799$	−10.1383	−0.358669
$800$	4.58582	0.162133
$801$	−1.76809	−0.0624722
$802$	3.88998	0.137360
$803$	−3.37140	−0.118974
$804$	3.48887	0.123043
$805$	−4.58998	−0.161776
$806$	−2.72186	−0.0958735
$807$	23.4459	0.825335
$808$	5.93932	0.208945
$809$	−38.1522	−1.34136	−0.670679	−	0.741747i	$-0.733997\pi$
$809$	−38.1522	−1.34136	−0.670679	+	0.741747i	$0.733997\pi$
$810$	−0.643572	−0.0226128
$811$	−16.4021	−0.575957	−0.287978	−	0.957637i	$-0.592983\pi$
$811$	−16.4021	−0.575957	−0.287978	+	0.957637i	$0.592983\pi$
$812$	7.24383	0.254208
$813$	−19.3142	−0.677377
$814$	15.2711	0.535252
$815$	8.41916	0.294910
$816$	−1.49860	−0.0524614
$817$	55.6184	1.94584
$818$	−12.0257	−0.420468
$819$	−1.17705	−0.0411293
$820$	−4.86812	−0.170002
$821$	28.5588	0.996710	0.498355	−	0.866973i	$-0.333938\pi$
$821$	28.5588	0.996710	0.498355	+	0.866973i	$0.333938\pi$
$822$	14.5896	0.508870
$823$	27.8798	0.971829	0.485915	−	0.874006i	$-0.338487\pi$
$823$	27.8798	0.971829	0.485915	+	0.874006i	$0.338487\pi$
$824$	−1.00000	−0.0348367
$825$	−7.44075	−0.259053
$826$	−9.98444	−0.347403
$827$	29.5089	1.02613	0.513063	−	0.858351i	$-0.328511\pi$
$827$	29.5089	1.02613	0.513063	+	0.858351i	$0.328511\pi$
$828$	−6.05927	−0.210574
$829$	11.4832	0.398829	0.199415	−	0.979915i	$-0.436096\pi$
$829$	11.4832	0.398829	0.199415	+	0.979915i	$0.436096\pi$
$830$	1.09263	0.0379256
$831$	−17.3607	−0.602237
$832$	−1.00000	−0.0346688
$833$	−8.41397	−0.291527
$834$	−0.829863	−0.0287358
$835$	−0.541905	−0.0187534
$836$	−11.2062	−0.387573
$837$	2.72186	0.0940813
$838$	9.30539	0.321449
$839$	34.7745	1.20055	0.600274	−	0.799795i	$-0.295058\pi$
$839$	34.7745	1.20055	0.600274	+	0.799795i	$0.295058\pi$
$840$	0.757514	0.0261367
$841$	8.87466	0.306023
$842$	−37.1227	−1.27933
$843$	16.4966	0.568174
$844$	28.7921	0.991063
$845$	0.643572	0.0221395
$846$	6.76522	0.232593
$847$	−9.84871	−0.338406
$848$	−5.26991	−0.180970
$849$	17.2117	0.590703
$850$	6.87230	0.235718
$851$	−57.0284	−1.95491
$852$	−9.90543	−0.339354
$853$	−33.8518	−1.15906	−0.579532	−	0.814950i	$-0.696765\pi$
$853$	−33.8518	−1.15906	−0.579532	+	0.814950i	$0.696765\pi$
$854$	−15.2336	−0.521283
$855$	4.44482	0.152010
$856$	−9.16659	−0.313308
$857$	0.260357	0.00889363	0.00444682	−	0.999990i	$-0.498585\pi$
$857$	0.260357	0.00889363	0.00444682	+	0.999990i	$0.498585\pi$
$858$	1.62256	0.0553932
$859$	19.4697	0.664297	0.332149	−	0.943227i	$-0.392226\pi$
$859$	19.4697	0.664297	0.332149	+	0.943227i	$0.392226\pi$
$860$	5.18272	0.176729
$861$	8.90344	0.303429
$862$	4.29157	0.146171
$863$	37.6400	1.28128	0.640641	−	0.767841i	$-0.278669\pi$
$863$	37.6400	1.28128	0.640641	+	0.767841i	$0.278669\pi$
$864$	1.00000	0.0340207
$865$	−8.30475	−0.282370
$866$	−9.74101	−0.331013
$867$	14.7542	0.501079
$868$	−3.20376	−0.108743
$869$	0.534597	0.0181350
$870$	3.96069	0.134280
$871$	3.48887	0.118216
$872$	0.979696	0.0331767
$873$	−15.6706	−0.530370
$874$	41.8483	1.41554
$875$	−7.26139	−0.245480
$876$	−2.07783	−0.0702034
$877$	−10.7653	−0.363518	−0.181759	−	0.983343i	$-0.558179\pi$
$877$	−10.7653	−0.363518	−0.181759	+	0.983343i	$0.558179\pi$
$878$	−13.6511	−0.460703
$879$	−4.91838	−0.165893
$880$	−1.04423	−0.0352010
$881$	0.252673	0.00851276	0.00425638	−	0.999991i	$-0.498645\pi$
$881$	0.252673	0.00851276	0.00425638	+	0.999991i	$0.498645\pi$
$882$	5.61456	0.189052
$883$	23.2546	0.782579	0.391289	−	0.920268i	$-0.372029\pi$
$883$	23.2546	0.782579	0.391289	+	0.920268i	$0.372029\pi$
$884$	−1.49860	−0.0504033
$885$	−5.45918	−0.183508
$886$	22.2391	0.747138
$887$	4.32823	0.145328	0.0726639	−	0.997356i	$-0.476850\pi$
$887$	4.32823	0.145328	0.0726639	+	0.997356i	$0.476850\pi$
$888$	9.41176	0.315838
$889$	5.20271	0.174493
$890$	1.13789	0.0381421
$891$	−1.62256	−0.0543577
$892$	−12.7364	−0.426446
$893$	−46.7239	−1.56356
$894$	7.83483	0.262036
$895$	1.77812	0.0594359
$896$	−1.17705	−0.0393224
$897$	−6.05927	−0.202313
$898$	19.2668	0.642943
$899$	−16.7510	−0.558677
$900$	−4.58582	−0.152861
$901$	−7.89749	−0.263103
$902$	−12.2734	−0.408659
$903$	−9.47883	−0.315436
$904$	−13.0922	−0.435441
$905$	5.56103	0.184855
$906$	4.95195	0.164517
$907$	21.2902	0.706928	0.353464	−	0.935448i	$-0.385004\pi$
$907$	21.2902	0.706928	0.353464	+	0.935448i	$0.385004\pi$
$908$	−22.9067	−0.760185
$909$	−5.93932	−0.196995
$910$	0.757514	0.0251113
$911$	0.346872	0.0114924	0.00574619	−	0.999983i	$-0.498171\pi$
$911$	0.346872	0.0114924	0.00574619	+	0.999983i	$0.498171\pi$
$912$	−6.90649	−0.228697
$913$	2.75470	0.0911674
$914$	40.3189	1.33363
$915$	−8.32924	−0.275356
$916$	10.6201	0.350897
$917$	4.16081	0.137402
$918$	1.49860	0.0494611
$919$	−16.6945	−0.550700	−0.275350	−	0.961344i	$-0.588794\pi$
$919$	−16.6945	−0.550700	−0.275350	+	0.961344i	$0.588794\pi$
$920$	3.89957	0.128565
$921$	3.35221	0.110459
$922$	9.53646	0.314066
$923$	−9.90543	−0.326041
$924$	1.90982	0.0628286
$925$	−43.1606	−1.41911
$926$	−21.8752	−0.718863
$927$	1.00000	0.0328443
$928$	−6.15424	−0.202023
$929$	−37.0289	−1.21488	−0.607439	−	0.794366i	$-0.707803\pi$
$929$	−37.0289	−1.21488	−0.607439	+	0.794366i	$0.707803\pi$
$930$	−1.75171	−0.0574409
$931$	−38.7769	−1.27086
$932$	6.61868	0.216802
$933$	−28.2832	−0.925951
$934$	−41.0475	−1.34311
$935$	−1.56488	−0.0511772
$936$	1.00000	0.0326860
$937$	29.0955	0.950507	0.475254	−	0.879849i	$-0.342356\pi$
$937$	29.0955	0.950507	0.475254	+	0.879849i	$0.342356\pi$
$938$	4.10656	0.134084
$939$	−22.0633	−0.720010
$940$	−4.35390	−0.142009
$941$	3.95886	0.129055	0.0645276	−	0.997916i	$-0.479446\pi$
$941$	3.95886	0.129055	0.0645276	+	0.997916i	$0.479446\pi$
$942$	4.49425	0.146431
$943$	45.8337	1.49255
$944$	8.48262	0.276086
$945$	−0.757514	−0.0246419
$946$	13.0665	0.424830
$947$	−9.69321	−0.314987	−0.157493	−	0.987520i	$-0.550341\pi$
$947$	−9.69321	−0.314987	−0.157493	+	0.987520i	$0.550341\pi$
$948$	0.329478	0.0107010
$949$	−2.07783	−0.0674492
$950$	31.6719	1.02757
$951$	−6.69370	−0.217058
$952$	−1.76392	−0.0571690
$953$	−37.8939	−1.22750	−0.613752	−	0.789499i	$-0.710341\pi$
$953$	−37.8939	−1.22750	−0.613752	+	0.789499i	$0.710341\pi$
$954$	5.26991	0.170620
$955$	−0.698090	−0.0225897
$956$	−16.6591	−0.538794
$957$	9.98560	0.322789
$958$	−13.1109	−0.423593
$959$	17.1726	0.554532
$960$	−0.643572	−0.0207712
$961$	−23.5915	−0.761015
$962$	9.41176	0.303447
$963$	9.16659	0.295389
$964$	−13.5837	−0.437500
$965$	11.6650	0.375509
$966$	−7.13205	−0.229470
$967$	−20.9496	−0.673695	−0.336847	−	0.941559i	$-0.609361\pi$
$967$	−20.9496	−0.673695	−0.336847	+	0.941559i	$0.609361\pi$
$968$	8.36731	0.268936
$969$	−10.3501	−0.332492
$970$	10.0852	0.323815
$971$	−31.2211	−1.00193	−0.500966	−	0.865467i	$-0.667022\pi$
$971$	−31.2211	−1.00193	−0.500966	+	0.865467i	$0.667022\pi$
$972$	−1.00000	−0.0320750
$973$	−0.976788	−0.0313144
$974$	9.34915	0.299566
$975$	−4.58582	−0.146864
$976$	12.9422	0.414270
$977$	31.4890	1.00742	0.503711	−	0.863872i	$-0.331967\pi$
$977$	31.4890	1.00742	0.503711	+	0.863872i	$0.331967\pi$
$978$	13.0819	0.418314
$979$	2.86882	0.0916878
$980$	−3.61337	−0.115425
$981$	−0.979696	−0.0312793
$982$	3.89868	0.124412
$983$	−45.3072	−1.44507	−0.722537	−	0.691332i	$-0.757024\pi$
$983$	−45.3072	−1.44507	−0.722537	+	0.691332i	$0.757024\pi$
$984$	−7.56422	−0.241139
$985$	−12.4782	−0.397588
$986$	−9.22274	−0.293712
$987$	7.96298	0.253464
$988$	−6.90649	−0.219725
$989$	−48.7957	−1.55161
$990$	1.04423	0.0331879
$991$	−2.35314	−0.0747498	−0.0373749	−	0.999301i	$-0.511900\pi$
$991$	−2.35314	−0.0747498	−0.0373749	+	0.999301i	$0.511900\pi$
$992$	2.72186	0.0864192
$993$	−15.8048	−0.501550
$994$	−11.6591	−0.369806
$995$	8.85506	0.280724
$996$	1.69775	0.0537954
$997$	45.3234	1.43541	0.717703	−	0.696349i	$-0.245193\pi$
$997$	45.3234	1.43541	0.717703	+	0.696349i	$0.245193\pi$
$998$	25.0610	0.793292
$999$	−9.41176	−0.297775

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.ba.1.9	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.ba.1.9	✓	14	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.643572 q^{5} +1.00000 q^{6} +1.17705 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +0.643572 q^{5} +1.00000 q^{6} +1.17705 q^{7} -1.00000 q^{8} +1.00000 q^{9} -0.643572 q^{10} -1.62256 q^{11} -1.00000 q^{12} -1.00000 q^{13} -1.17705 q^{14} -0.643572 q^{15} +1.00000 q^{16} +1.49860 q^{17} -1.00000 q^{18} +6.90649 q^{19} +0.643572 q^{20} -1.17705 q^{21} +1.62256 q^{22} -6.05927 q^{23} +1.00000 q^{24} -4.58582 q^{25} +1.00000 q^{26} -1.00000 q^{27} +1.17705 q^{28} +6.15424 q^{29} +0.643572 q^{30} -2.72186 q^{31} -1.00000 q^{32} +1.62256 q^{33} -1.49860 q^{34} +0.757514 q^{35} +1.00000 q^{36} +9.41176 q^{37} -6.90649 q^{38} +1.00000 q^{39} -0.643572 q^{40} -7.56422 q^{41} +1.17705 q^{42} +8.05306 q^{43} -1.62256 q^{44} +0.643572 q^{45} +6.05927 q^{46} -6.76522 q^{47} -1.00000 q^{48} -5.61456 q^{49} +4.58582 q^{50} -1.49860 q^{51} -1.00000 q^{52} -5.26991 q^{53} +1.00000 q^{54} -1.04423 q^{55} -1.17705 q^{56} -6.90649 q^{57} -6.15424 q^{58} +8.48262 q^{59} -0.643572 q^{60} +12.9422 q^{61} +2.72186 q^{62} +1.17705 q^{63} +1.00000 q^{64} -0.643572 q^{65} -1.62256 q^{66} -3.48887 q^{67} +1.49860 q^{68} +6.05927 q^{69} -0.757514 q^{70} +9.90543 q^{71} -1.00000 q^{72} +2.07783 q^{73} -9.41176 q^{74} +4.58582 q^{75} +6.90649 q^{76} -1.90982 q^{77} -1.00000 q^{78} -0.329478 q^{79} +0.643572 q^{80} +1.00000 q^{81} +7.56422 q^{82} -1.69775 q^{83} -1.17705 q^{84} +0.964456 q^{85} -8.05306 q^{86} -6.15424 q^{87} +1.62256 q^{88} -1.76809 q^{89} -0.643572 q^{90} -1.17705 q^{91} -6.05927 q^{92} +2.72186 q^{93} +6.76522 q^{94} +4.44482 q^{95} +1.00000 q^{96} -15.6706 q^{97} +5.61456 q^{98} -1.62256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - q^{5} + 14 q^{6} + 5 q^{7} - 14 q^{8} + 14 q^{9} + q^{10} - q^{11} - 14 q^{12} - 14 q^{13} - 5 q^{14} + q^{15} + 14 q^{16} - 12 q^{17} - 14 q^{18} + 10 q^{19} - q^{20} - 5 q^{21} + q^{22} - q^{23} + 14 q^{24} + 19 q^{25} + 14 q^{26} - 14 q^{27} + 5 q^{28} + 6 q^{29} - q^{30} + 20 q^{31} - 14 q^{32} + q^{33} + 12 q^{34} - 16 q^{35} + 14 q^{36} - 3 q^{37} - 10 q^{38} + 14 q^{39} + q^{40} + q^{41} + 5 q^{42} + 6 q^{43} - q^{44} - q^{45} + q^{46} - 13 q^{47} - 14 q^{48} + 9 q^{49} - 19 q^{50} + 12 q^{51} - 14 q^{52} - 27 q^{53} + 14 q^{54} + 10 q^{55} - 5 q^{56} - 10 q^{57} - 6 q^{58} - 6 q^{59} + q^{60} - 4 q^{61} - 20 q^{62} + 5 q^{63} + 14 q^{64} + q^{65} - q^{66} + 13 q^{67} - 12 q^{68} + q^{69} + 16 q^{70} + 18 q^{71} - 14 q^{72} + 11 q^{73} + 3 q^{74} - 19 q^{75} + 10 q^{76} - 15 q^{77} - 14 q^{78} + 33 q^{79} - q^{80} + 14 q^{81} - q^{82} - 25 q^{83} - 5 q^{84} + 25 q^{85} - 6 q^{86} - 6 q^{87} + q^{88} + 3 q^{89} + q^{90} - 5 q^{91} - q^{92} - 20 q^{93} + 13 q^{94} + 30 q^{95} + 14 q^{96} + 11 q^{97} - 9 q^{98} - q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - q^5 + 14 * q^6 + 5 * q^7 - 14 * q^8 + 14 * q^9 + q^10 - q^11 - 14 * q^12 - 14 * q^13 - 5 * q^14 + q^15 + 14 * q^16 - 12 * q^17 - 14 * q^18 + 10 * q^19 - q^20 - 5 * q^21 + q^22 - q^23 + 14 * q^24 + 19 * q^25 + 14 * q^26 - 14 * q^27 + 5 * q^28 + 6 * q^29 - q^30 + 20 * q^31 - 14 * q^32 + q^33 + 12 * q^34 - 16 * q^35 + 14 * q^36 - 3 * q^37 - 10 * q^38 + 14 * q^39 + q^40 + q^41 + 5 * q^42 + 6 * q^43 - q^44 - q^45 + q^46 - 13 * q^47 - 14 * q^48 + 9 * q^49 - 19 * q^50 + 12 * q^51 - 14 * q^52 - 27 * q^53 + 14 * q^54 + 10 * q^55 - 5 * q^56 - 10 * q^57 - 6 * q^58 - 6 * q^59 + q^60 - 4 * q^61 - 20 * q^62 + 5 * q^63 + 14 * q^64 + q^65 - q^66 + 13 * q^67 - 12 * q^68 + q^69 + 16 * q^70 + 18 * q^71 - 14 * q^72 + 11 * q^73 + 3 * q^74 - 19 * q^75 + 10 * q^76 - 15 * q^77 - 14 * q^78 + 33 * q^79 - q^80 + 14 * q^81 - q^82 - 25 * q^83 - 5 * q^84 + 25 * q^85 - 6 * q^86 - 6 * q^87 + q^88 + 3 * q^89 + q^90 - 5 * q^91 - q^92 - 20 * q^93 + 13 * q^94 + 30 * q^95 + 14 * q^96 + 11 * q^97 - 9 * q^98 - q^99

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