LMFDB - Embedded newform 8034.2.a.z.1.3

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} - 3 x^{13} - 36 x^{12} + 108 x^{11} + 434 x^{10} - 1239 x^{9} - 2404 x^{8} + 6204 x^{7} + \cdots + 1552 $ x^14 - 3x^13 - 36x^12 + 108x^11 + 434x^10 - 1239x^9 - 2404x^8 + 6204x^7 + 6361x^6 - 14618x^5 - 7015x^4 + 15763x^3 + 1118x^2 - 6316*x + 1552
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$3.21497$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.21497 q^{5} +1.00000 q^{6} -1.40491 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.21497 q^{5} +1.00000 q^{6} -1.40491 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.21497 q^{10} -2.53716 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.40491 q^{14} +3.21497 q^{15} +1.00000 q^{16} +7.57385 q^{17} -1.00000 q^{18} +2.48027 q^{19} -3.21497 q^{20} +1.40491 q^{21} +2.53716 q^{22} +7.10176 q^{23} +1.00000 q^{24} +5.33603 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.40491 q^{28} -1.09619 q^{29} -3.21497 q^{30} -2.34857 q^{31} -1.00000 q^{32} +2.53716 q^{33} -7.57385 q^{34} +4.51675 q^{35} +1.00000 q^{36} +5.11651 q^{37} -2.48027 q^{38} -1.00000 q^{39} +3.21497 q^{40} -0.317535 q^{41} -1.40491 q^{42} +9.60063 q^{43} -2.53716 q^{44} -3.21497 q^{45} -7.10176 q^{46} -5.52965 q^{47} -1.00000 q^{48} -5.02622 q^{49} -5.33603 q^{50} -7.57385 q^{51} +1.00000 q^{52} -4.04692 q^{53} +1.00000 q^{54} +8.15690 q^{55} +1.40491 q^{56} -2.48027 q^{57} +1.09619 q^{58} +0.591321 q^{59} +3.21497 q^{60} -0.0491791 q^{61} +2.34857 q^{62} -1.40491 q^{63} +1.00000 q^{64} -3.21497 q^{65} -2.53716 q^{66} -11.1167 q^{67} +7.57385 q^{68} -7.10176 q^{69} -4.51675 q^{70} -16.7385 q^{71} -1.00000 q^{72} +5.34984 q^{73} -5.11651 q^{74} -5.33603 q^{75} +2.48027 q^{76} +3.56449 q^{77} +1.00000 q^{78} +16.3495 q^{79} -3.21497 q^{80} +1.00000 q^{81} +0.317535 q^{82} +3.14585 q^{83} +1.40491 q^{84} -24.3497 q^{85} -9.60063 q^{86} +1.09619 q^{87} +2.53716 q^{88} -4.41812 q^{89} +3.21497 q^{90} -1.40491 q^{91} +7.10176 q^{92} +2.34857 q^{93} +5.52965 q^{94} -7.97401 q^{95} +1.00000 q^{96} -9.59214 q^{97} +5.02622 q^{98} -2.53716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * 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
$5$	−3.21497	−1.43778	−0.718889	−	0.695125i	$-0.755349\pi$
$5$	−3.21497	−1.43778	−0.718889	+	0.695125i	$0.755349\pi$
$6$	1.00000	0.408248
$7$	−1.40491	−0.531007	−0.265503	−	0.964110i	$-0.585538\pi$
$7$	−1.40491	−0.531007	−0.265503	+	0.964110i	$0.585538\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.21497	1.01666
$11$	−2.53716	−0.764983	−0.382492	−	0.923959i	$-0.624934\pi$
$11$	−2.53716	−0.764983	−0.382492	+	0.923959i	$0.624934\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	1.40491	0.375479
$15$	3.21497	0.830102
$16$	1.00000	0.250000
$17$	7.57385	1.83693	0.918464	−	0.395505i	$-0.129430\pi$
$17$	7.57385	1.83693	0.918464	+	0.395505i	$0.129430\pi$
$18$	−1.00000	−0.235702
$19$	2.48027	0.569014	0.284507	−	0.958674i	$-0.408170\pi$
$19$	2.48027	0.569014	0.284507	+	0.958674i	$0.408170\pi$
$20$	−3.21497	−0.718889
$21$	1.40491	0.306577
$22$	2.53716	0.540925
$23$	7.10176	1.48082	0.740410	−	0.672156i	$-0.234631\pi$
$23$	7.10176	1.48082	0.740410	+	0.672156i	$0.234631\pi$
$24$	1.00000	0.204124
$25$	5.33603	1.06721
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	−1.40491	−0.265503
$29$	−1.09619	−0.203558	−0.101779	−	0.994807i	$-0.532453\pi$
$29$	−1.09619	−0.203558	−0.101779	+	0.994807i	$0.532453\pi$
$30$	−3.21497	−0.586970
$31$	−2.34857	−0.421816	−0.210908	−	0.977506i	$-0.567642\pi$
$31$	−2.34857	−0.421816	−0.210908	+	0.977506i	$0.567642\pi$
$32$	−1.00000	−0.176777
$33$	2.53716	0.441663
$34$	−7.57385	−1.29890
$35$	4.51675	0.763470
$36$	1.00000	0.166667
$37$	5.11651	0.841149	0.420574	−	0.907258i	$-0.361829\pi$
$37$	5.11651	0.841149	0.420574	+	0.907258i	$0.361829\pi$
$38$	−2.48027	−0.402354
$39$	−1.00000	−0.160128
$40$	3.21497	0.508331
$41$	−0.317535	−0.0495906	−0.0247953	−	0.999693i	$-0.507893\pi$
$41$	−0.317535	−0.0495906	−0.0247953	+	0.999693i	$0.507893\pi$
$42$	−1.40491	−0.216783
$43$	9.60063	1.46408	0.732041	−	0.681261i	$-0.238568\pi$
$43$	9.60063	1.46408	0.732041	+	0.681261i	$0.238568\pi$
$44$	−2.53716	−0.382492
$45$	−3.21497	−0.479259
$46$	−7.10176	−1.04710
$47$	−5.52965	−0.806583	−0.403292	−	0.915072i	$-0.632134\pi$
$47$	−5.52965	−0.806583	−0.403292	+	0.915072i	$0.632134\pi$
$48$	−1.00000	−0.144338
$49$	−5.02622	−0.718032
$50$	−5.33603	−0.754628
$51$	−7.57385	−1.06055
$52$	1.00000	0.138675
$53$	−4.04692	−0.555887	−0.277944	−	0.960597i	$-0.589653\pi$
$53$	−4.04692	−0.555887	−0.277944	+	0.960597i	$0.589653\pi$
$54$	1.00000	0.136083
$55$	8.15690	1.09988
$56$	1.40491	0.187739
$57$	−2.48027	−0.328520
$58$	1.09619	0.143937
$59$	0.591321	0.0769834	0.0384917	−	0.999259i	$-0.487745\pi$
$59$	0.591321	0.0769834	0.0384917	+	0.999259i	$0.487745\pi$
$60$	3.21497	0.415051
$61$	−0.0491791	−0.00629673	−0.00314837	−	0.999995i	$-0.501002\pi$
$61$	−0.0491791	−0.00629673	−0.00314837	+	0.999995i	$0.501002\pi$
$62$	2.34857	0.298269
$63$	−1.40491	−0.177002
$64$	1.00000	0.125000
$65$	−3.21497	−0.398768
$66$	−2.53716	−0.312303
$67$	−11.1167	−1.35812	−0.679058	−	0.734084i	$-0.737612\pi$
$67$	−11.1167	−1.35812	−0.679058	+	0.734084i	$0.737612\pi$
$68$	7.57385	0.918464
$69$	−7.10176	−0.854952
$70$	−4.51675	−0.539855
$71$	−16.7385	−1.98649	−0.993246	−	0.116031i	$-0.962983\pi$
$71$	−16.7385	−1.98649	−0.993246	+	0.116031i	$0.962983\pi$
$72$	−1.00000	−0.117851
$73$	5.34984	0.626151	0.313075	−	0.949728i	$-0.398641\pi$
$73$	5.34984	0.626151	0.313075	+	0.949728i	$0.398641\pi$
$74$	−5.11651	−0.594782
$75$	−5.33603	−0.616152
$76$	2.48027	0.284507
$77$	3.56449	0.406211
$78$	1.00000	0.113228
$79$	16.3495	1.83946	0.919730	−	0.392552i	$-0.128408\pi$
$79$	16.3495	1.83946	0.919730	+	0.392552i	$0.128408\pi$
$80$	−3.21497	−0.359445
$81$	1.00000	0.111111
$82$	0.317535	0.0350658
$83$	3.14585	0.345302	0.172651	−	0.984983i	$-0.444767\pi$
$83$	3.14585	0.345302	0.172651	+	0.984983i	$0.444767\pi$
$84$	1.40491	0.153289
$85$	−24.3497	−2.64109
$86$	−9.60063	−1.03526
$87$	1.09619	0.117524
$88$	2.53716	0.270462
$89$	−4.41812	−0.468319	−0.234160	−	0.972198i	$-0.575234\pi$
$89$	−4.41812	−0.468319	−0.234160	+	0.972198i	$0.575234\pi$
$90$	3.21497	0.338888
$91$	−1.40491	−0.147275
$92$	7.10176	0.740410
$93$	2.34857	0.243536
$94$	5.52965	0.570340
$95$	−7.97401	−0.818116
$96$	1.00000	0.102062
$97$	−9.59214	−0.973934	−0.486967	−	0.873420i	$-0.661897\pi$
$97$	−9.59214	−0.973934	−0.486967	+	0.873420i	$0.661897\pi$
$98$	5.02622	0.507725
$99$	−2.53716	−0.254994
$100$	5.33603	0.533603
$101$	−13.2784	−1.32125	−0.660626	−	0.750715i	$-0.729709\pi$
$101$	−13.2784	−1.32125	−0.660626	+	0.750715i	$0.729709\pi$
$102$	7.57385	0.749923
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.00000	−0.0980581
$105$	−4.51675	−0.440790
$106$	4.04692	0.393072
$107$	−5.70699	−0.551715	−0.275858	−	0.961198i	$-0.588962\pi$
$107$	−5.70699	−0.551715	−0.275858	+	0.961198i	$0.588962\pi$
$108$	−1.00000	−0.0962250
$109$	0.714942	0.0684791	0.0342395	−	0.999414i	$-0.489099\pi$
$109$	0.714942	0.0684791	0.0342395	+	0.999414i	$0.489099\pi$
$110$	−8.15690	−0.777730
$111$	−5.11651	−0.485637
$112$	−1.40491	−0.132752
$113$	0.0112939	0.00106244	0.000531219	−	1.00000i	$-0.499831\pi$
$113$	0.0112939	0.00106244	0.000531219		1.00000i	$0.499831\pi$
$114$	2.48027	0.232299
$115$	−22.8320	−2.12909
$116$	−1.09619	−0.101779
$117$	1.00000	0.0924500
$118$	−0.591321	−0.0544355
$119$	−10.6406	−0.975421
$120$	−3.21497	−0.293485
$121$	−4.56281	−0.414800
$122$	0.0491791	0.00445246
$123$	0.317535	0.0286311
$124$	−2.34857	−0.210908
$125$	−1.08032	−0.0966269
$126$	1.40491	0.125160
$127$	9.16672	0.813415	0.406708	−	0.913558i	$-0.366677\pi$
$127$	9.16672	0.813415	0.406708	+	0.913558i	$0.366677\pi$
$128$	−1.00000	−0.0883883
$129$	−9.60063	−0.845288
$130$	3.21497	0.281971
$131$	6.04237	0.527925	0.263962	−	0.964533i	$-0.414971\pi$
$131$	6.04237	0.527925	0.263962	+	0.964533i	$0.414971\pi$
$132$	2.53716	0.220832
$133$	−3.48457	−0.302150
$134$	11.1167	0.960333
$135$	3.21497	0.276701
$136$	−7.57385	−0.649452
$137$	−19.2977	−1.64871	−0.824356	−	0.566072i	$-0.808462\pi$
$137$	−19.2977	−1.64871	−0.824356	+	0.566072i	$0.808462\pi$
$138$	7.10176	0.604542
$139$	−4.39044	−0.372392	−0.186196	−	0.982513i	$-0.559616\pi$
$139$	−4.39044	−0.372392	−0.186196	+	0.982513i	$0.559616\pi$
$140$	4.51675	0.381735
$141$	5.52965	0.465681
$142$	16.7385	1.40466
$143$	−2.53716	−0.212168
$144$	1.00000	0.0833333
$145$	3.52423	0.292672
$146$	−5.34984	−0.442756
$147$	5.02622	0.414556
$148$	5.11651	0.420574
$149$	5.11066	0.418682	0.209341	−	0.977843i	$-0.432868\pi$
$149$	5.11066	0.418682	0.209341	+	0.977843i	$0.432868\pi$
$150$	5.33603	0.435685
$151$	10.3452	0.841879	0.420940	−	0.907089i	$-0.361700\pi$
$151$	10.3452	0.841879	0.420940	+	0.907089i	$0.361700\pi$
$152$	−2.48027	−0.201177
$153$	7.57385	0.612309
$154$	−3.56449	−0.287235
$155$	7.55060	0.606478
$156$	−1.00000	−0.0800641
$157$	19.2837	1.53900	0.769502	−	0.638645i	$-0.220505\pi$
$157$	19.2837	1.53900	0.769502	+	0.638645i	$0.220505\pi$
$158$	−16.3495	−1.30069
$159$	4.04692	0.320942
$160$	3.21497	0.254166
$161$	−9.97735	−0.786326
$162$	−1.00000	−0.0785674
$163$	24.1659	1.89282	0.946408	−	0.322972i	$-0.104682\pi$
$163$	24.1659	1.89282	0.946408	+	0.322972i	$0.104682\pi$
$164$	−0.317535	−0.0247953
$165$	−8.15690	−0.635014
$166$	−3.14585	−0.244165
$167$	16.6964	1.29200	0.646001	−	0.763336i	$-0.276440\pi$
$167$	16.6964	1.29200	0.646001	+	0.763336i	$0.276440\pi$
$168$	−1.40491	−0.108391
$169$	1.00000	0.0769231
$170$	24.3497	1.86754
$171$	2.48027	0.189671
$172$	9.60063	0.732041
$173$	−15.7177	−1.19499	−0.597496	−	0.801872i	$-0.703838\pi$
$173$	−15.7177	−1.19499	−0.597496	+	0.801872i	$0.703838\pi$
$174$	−1.09619	−0.0831023
$175$	−7.49665	−0.566694
$176$	−2.53716	−0.191246
$177$	−0.591321	−0.0444464
$178$	4.41812	0.331152
$179$	15.1298	1.13085	0.565426	−	0.824799i	$-0.308712\pi$
$179$	15.1298	1.13085	0.565426	+	0.824799i	$0.308712\pi$
$180$	−3.21497	−0.239630
$181$	7.66911	0.570040	0.285020	−	0.958522i	$-0.408000\pi$
$181$	7.66911	0.570040	0.285020	+	0.958522i	$0.408000\pi$
$182$	1.40491	0.104139
$183$	0.0491791	0.00363542
$184$	−7.10176	−0.523549
$185$	−16.4494	−1.20939
$186$	−2.34857	−0.172206
$187$	−19.2161	−1.40522
$188$	−5.52965	−0.403292
$189$	1.40491	0.102192
$190$	7.97401	0.578495
$191$	−16.0169	−1.15894	−0.579469	−	0.814994i	$-0.696740\pi$
$191$	−16.0169	−1.15894	−0.579469	+	0.814994i	$0.696740\pi$
$192$	−1.00000	−0.0721688
$193$	6.03418	0.434350	0.217175	−	0.976133i	$-0.430316\pi$
$193$	6.03418	0.434350	0.217175	+	0.976133i	$0.430316\pi$
$194$	9.59214	0.688676
$195$	3.21497	0.230229
$196$	−5.02622	−0.359016
$197$	−14.6922	−1.04677	−0.523387	−	0.852095i	$-0.675332\pi$
$197$	−14.6922	−1.04677	−0.523387	+	0.852095i	$0.675332\pi$
$198$	2.53716	0.180308
$199$	9.27945	0.657803	0.328901	−	0.944364i	$-0.393322\pi$
$199$	9.27945	0.657803	0.328901	+	0.944364i	$0.393322\pi$
$200$	−5.33603	−0.377314
$201$	11.1167	0.784109
$202$	13.2784	0.934266
$203$	1.54006	0.108091
$204$	−7.57385	−0.530275
$205$	1.02086	0.0713002
$206$	1.00000	0.0696733
$207$	7.10176	0.493607
$208$	1.00000	0.0693375
$209$	−6.29286	−0.435286
$210$	4.51675	0.311685
$211$	−23.6370	−1.62724	−0.813618	−	0.581400i	$-0.802505\pi$
$211$	−23.6370	−1.62724	−0.813618	+	0.581400i	$0.802505\pi$
$212$	−4.04692	−0.277944
$213$	16.7385	1.14690
$214$	5.70699	0.390122
$215$	−30.8657	−2.10503
$216$	1.00000	0.0680414
$217$	3.29954	0.223987
$218$	−0.714942	−0.0484220
$219$	−5.34984	−0.361508
$220$	8.15690	0.549938
$221$	7.57385	0.509472
$222$	5.11651	0.343398
$223$	21.0616	1.41039	0.705195	−	0.709013i	$-0.250859\pi$
$223$	21.0616	1.41039	0.705195	+	0.709013i	$0.250859\pi$
$224$	1.40491	0.0938697
$225$	5.33603	0.355735
$226$	−0.0112939	−0.000751258 0
$227$	−11.7708	−0.781254	−0.390627	−	0.920549i	$-0.627742\pi$
$227$	−11.7708	−0.781254	−0.390627	+	0.920549i	$0.627742\pi$
$228$	−2.48027	−0.164260
$229$	12.9373	0.854919	0.427460	−	0.904034i	$-0.359409\pi$
$229$	12.9373	0.854919	0.427460	+	0.904034i	$0.359409\pi$
$230$	22.8320	1.50549
$231$	−3.56449	−0.234526
$232$	1.09619	0.0719687
$233$	−14.2591	−0.934141	−0.467071	−	0.884220i	$-0.654691\pi$
$233$	−14.2591	−0.934141	−0.467071	+	0.884220i	$0.654691\pi$
$234$	−1.00000	−0.0653720
$235$	17.7777	1.15969
$236$	0.591321	0.0384917
$237$	−16.3495	−1.06201
$238$	10.6406	0.689727
$239$	7.67833	0.496670	0.248335	−	0.968674i	$-0.420117\pi$
$239$	7.67833	0.496670	0.248335	+	0.968674i	$0.420117\pi$
$240$	3.21497	0.207525
$241$	17.8173	1.14771	0.573857	−	0.818955i	$-0.305446\pi$
$241$	17.8173	1.14771	0.573857	+	0.818955i	$0.305446\pi$
$242$	4.56281	0.293308
$243$	−1.00000	−0.0641500
$244$	−0.0491791	−0.00314837
$245$	16.1591	1.03237
$246$	−0.317535	−0.0202453
$247$	2.48027	0.157816
$248$	2.34857	0.149135
$249$	−3.14585	−0.199360
$250$	1.08032	0.0683256
$251$	11.4843	0.724883	0.362442	−	0.932006i	$-0.381943\pi$
$251$	11.4843	0.724883	0.362442	+	0.932006i	$0.381943\pi$
$252$	−1.40491	−0.0885012
$253$	−18.0183	−1.13280
$254$	−9.16672	−0.575171
$255$	24.3497	1.52484
$256$	1.00000	0.0625000
$257$	−0.559098	−0.0348756	−0.0174378	−	0.999848i	$-0.505551\pi$
$257$	−0.559098	−0.0348756	−0.0174378	+	0.999848i	$0.505551\pi$
$258$	9.60063	0.597709
$259$	−7.18825	−0.446656
$260$	−3.21497	−0.199384
$261$	−1.09619	−0.0678527
$262$	−6.04237	−0.373299
$263$	25.6348	1.58071	0.790354	−	0.612651i	$-0.209897\pi$
$263$	25.6348	1.58071	0.790354	+	0.612651i	$0.209897\pi$
$264$	−2.53716	−0.156152
$265$	13.0107	0.799243
$266$	3.48457	0.213653
$267$	4.41812	0.270384
$268$	−11.1167	−0.679058
$269$	−8.75155	−0.533591	−0.266796	−	0.963753i	$-0.585965\pi$
$269$	−8.75155	−0.533591	−0.266796	+	0.963753i	$0.585965\pi$
$270$	−3.21497	−0.195657
$271$	20.9500	1.27262	0.636311	−	0.771432i	$-0.280459\pi$
$271$	20.9500	1.27262	0.636311	+	0.771432i	$0.280459\pi$
$272$	7.57385	0.459232
$273$	1.40491	0.0850292
$274$	19.2977	1.16581
$275$	−13.5384	−0.816395
$276$	−7.10176	−0.427476
$277$	27.0963	1.62806	0.814030	−	0.580823i	$-0.197269\pi$
$277$	27.0963	1.62806	0.814030	+	0.580823i	$0.197269\pi$
$278$	4.39044	0.263321
$279$	−2.34857	−0.140605
$280$	−4.51675	−0.269927
$281$	22.0661	1.31635	0.658175	−	0.752865i	$-0.271329\pi$
$281$	22.0661	1.31635	0.658175	+	0.752865i	$0.271329\pi$
$282$	−5.52965	−0.329286
$283$	−20.6144	−1.22540	−0.612701	−	0.790315i	$-0.709917\pi$
$283$	−20.6144	−1.22540	−0.612701	+	0.790315i	$0.709917\pi$
$284$	−16.7385	−0.993246
$285$	7.97401	0.472339
$286$	2.53716	0.150026
$287$	0.446108	0.0263329
$288$	−1.00000	−0.0589256
$289$	40.3631	2.37430
$290$	−3.52423	−0.206950
$291$	9.59214	0.562301
$292$	5.34984	0.313075
$293$	−15.5930	−0.910950	−0.455475	−	0.890249i	$-0.650531\pi$
$293$	−15.5930	−0.910950	−0.455475	+	0.890249i	$0.650531\pi$
$294$	−5.02622	−0.293135
$295$	−1.90108	−0.110685
$296$	−5.11651	−0.297391
$297$	2.53716	0.147221
$298$	−5.11066	−0.296053
$299$	7.10176	0.410706
$300$	−5.33603	−0.308076
$301$	−13.4880	−0.777438
$302$	−10.3452	−0.595298
$303$	13.2784	0.762825
$304$	2.48027	0.142254
$305$	0.158109	0.00905331
$306$	−7.57385	−0.432968
$307$	−13.8308	−0.789366	−0.394683	−	0.918817i	$-0.629146\pi$
$307$	−13.8308	−0.789366	−0.394683	+	0.918817i	$0.629146\pi$
$308$	3.56449	0.203106
$309$	1.00000	0.0568880
$310$	−7.55060	−0.428845
$311$	−21.7094	−1.23103	−0.615515	−	0.788126i	$-0.711052\pi$
$311$	−21.7094	−1.23103	−0.615515	+	0.788126i	$0.711052\pi$
$312$	1.00000	0.0566139
$313$	−7.64960	−0.432381	−0.216190	−	0.976351i	$-0.569363\pi$
$313$	−7.64960	−0.432381	−0.216190	+	0.976351i	$0.569363\pi$
$314$	−19.2837	−1.08824
$315$	4.51675	0.254490
$316$	16.3495	0.919730
$317$	7.63340	0.428735	0.214367	−	0.976753i	$-0.431231\pi$
$317$	7.63340	0.428735	0.214367	+	0.976753i	$0.431231\pi$
$318$	−4.04692	−0.226940
$319$	2.78122	0.155719
$320$	−3.21497	−0.179722
$321$	5.70699	0.318533
$322$	9.97735	0.556016
$323$	18.7852	1.04524
$324$	1.00000	0.0555556
$325$	5.33603	0.295990
$326$	−24.1659	−1.33842
$327$	−0.714942	−0.0395364
$328$	0.317535	0.0175329
$329$	7.76868	0.428301
$330$	8.15690	0.449023
$331$	−6.12990	−0.336930	−0.168465	−	0.985708i	$-0.553881\pi$
$331$	−6.12990	−0.336930	−0.168465	+	0.985708i	$0.553881\pi$
$332$	3.14585	0.172651
$333$	5.11651	0.280383
$334$	−16.6964	−0.913584
$335$	35.7397	1.95267
$336$	1.40491	0.0766443
$337$	−20.2018	−1.10046	−0.550230	−	0.835013i	$-0.685460\pi$
$337$	−20.2018	−1.10046	−0.550230	+	0.835013i	$0.685460\pi$
$338$	−1.00000	−0.0543928
$339$	−0.0112939	−0.000613399 0
$340$	−24.3497	−1.32055
$341$	5.95872	0.322683
$342$	−2.48027	−0.134118
$343$	16.8958	0.912287
$344$	−9.60063	−0.517631
$345$	22.8320	1.22923
$346$	15.7177	0.844987
$347$	−29.8190	−1.60077	−0.800385	−	0.599486i	$-0.795372\pi$
$347$	−29.8190	−1.60077	−0.800385	+	0.599486i	$0.795372\pi$
$348$	1.09619	0.0587622
$349$	−15.6189	−0.836061	−0.418031	−	0.908433i	$-0.637279\pi$
$349$	−15.6189	−0.836061	−0.418031	+	0.908433i	$0.637279\pi$
$350$	7.49665	0.400713
$351$	−1.00000	−0.0533761
$352$	2.53716	0.135231
$353$	−26.9240	−1.43302	−0.716510	−	0.697577i	$-0.754262\pi$
$353$	−26.9240	−1.43302	−0.716510	+	0.697577i	$0.754262\pi$
$354$	0.591321	0.0314283
$355$	53.8137	2.85613
$356$	−4.41812	−0.234160
$357$	10.6406	0.563160
$358$	−15.1298	−0.799633
$359$	6.70826	0.354048	0.177024	−	0.984206i	$-0.443353\pi$
$359$	6.70826	0.354048	0.177024	+	0.984206i	$0.443353\pi$
$360$	3.21497	0.169444
$361$	−12.8482	−0.676223
$362$	−7.66911	−0.403079
$363$	4.56281	0.239485
$364$	−1.40491	−0.0736374
$365$	−17.1996	−0.900266
$366$	−0.0491791	−0.00257063
$367$	23.3923	1.22107	0.610535	−	0.791989i	$-0.290955\pi$
$367$	23.3923	1.22107	0.610535	+	0.791989i	$0.290955\pi$
$368$	7.10176	0.370205
$369$	−0.317535	−0.0165302
$370$	16.4494	0.855164
$371$	5.68557	0.295180
$372$	2.34857	0.121768
$373$	−33.8963	−1.75508	−0.877541	−	0.479501i	$-0.840818\pi$
$373$	−33.8963	−1.75508	−0.877541	+	0.479501i	$0.840818\pi$
$374$	19.2161	0.993640
$375$	1.08032	0.0557876
$376$	5.52965	0.285170
$377$	−1.09619	−0.0564569
$378$	−1.40491	−0.0722609
$379$	−23.2303	−1.19326	−0.596631	−	0.802516i	$-0.703494\pi$
$379$	−23.2303	−1.19326	−0.596631	+	0.802516i	$0.703494\pi$
$380$	−7.97401	−0.409058
$381$	−9.16672	−0.469625
$382$	16.0169	0.819493
$383$	0.229743	0.0117393	0.00586965	−	0.999983i	$-0.498132\pi$
$383$	0.229743	0.0117393	0.00586965	+	0.999983i	$0.498132\pi$
$384$	1.00000	0.0510310
$385$	−11.4597	−0.584042
$386$	−6.03418	−0.307132
$387$	9.60063	0.488027
$388$	−9.59214	−0.486967
$389$	31.6902	1.60676	0.803379	−	0.595468i	$-0.203033\pi$
$389$	31.6902	1.60676	0.803379	+	0.595468i	$0.203033\pi$
$390$	−3.21497	−0.162796
$391$	53.7877	2.72016
$392$	5.02622	0.253863
$393$	−6.04237	−0.304797
$394$	14.6922	0.740182
$395$	−52.5631	−2.64473
$396$	−2.53716	−0.127497
$397$	−3.56877	−0.179111	−0.0895556	−	0.995982i	$-0.528545\pi$
$397$	−3.56877	−0.179111	−0.0895556	+	0.995982i	$0.528545\pi$
$398$	−9.27945	−0.465137
$399$	3.48457	0.174447
$400$	5.33603	0.266801
$401$	34.3052	1.71312	0.856560	−	0.516047i	$-0.172597\pi$
$401$	34.3052	1.71312	0.856560	+	0.516047i	$0.172597\pi$
$402$	−11.1167	−0.554449
$403$	−2.34857	−0.116991
$404$	−13.2784	−0.660626
$405$	−3.21497	−0.159753
$406$	−1.54006	−0.0764318
$407$	−12.9814	−0.643465
$408$	7.57385	0.374961
$409$	−21.3744	−1.05689	−0.528447	−	0.848966i	$-0.677225\pi$
$409$	−21.3744	−1.05689	−0.528447	+	0.848966i	$0.677225\pi$
$410$	−1.02086	−0.0504169
$411$	19.2977	0.951884
$412$	−1.00000	−0.0492665
$413$	−0.830754	−0.0408787
$414$	−7.10176	−0.349033
$415$	−10.1138	−0.496467
$416$	−1.00000	−0.0490290
$417$	4.39044	0.215001
$418$	6.29286	0.307794
$419$	7.08545	0.346147	0.173073	−	0.984909i	$-0.444630\pi$
$419$	7.08545	0.346147	0.173073	+	0.984909i	$0.444630\pi$
$420$	−4.51675	−0.220395
$421$	7.09461	0.345770	0.172885	−	0.984942i	$-0.444691\pi$
$421$	7.09461	0.345770	0.172885	+	0.984942i	$0.444691\pi$
$422$	23.6370	1.15063
$423$	−5.52965	−0.268861
$424$	4.04692	0.196536
$425$	40.4143	1.96038
$426$	−16.7385	−0.810982
$427$	0.0690923	0.00334361
$428$	−5.70699	−0.275858
$429$	2.53716	0.122495
$430$	30.8657	1.48848
$431$	22.5540	1.08639	0.543194	−	0.839607i	$-0.317215\pi$
$431$	22.5540	1.08639	0.543194	+	0.839607i	$0.317215\pi$
$432$	−1.00000	−0.0481125
$433$	1.25553	0.0603372	0.0301686	−	0.999545i	$-0.490396\pi$
$433$	1.25553	0.0603372	0.0301686	+	0.999545i	$0.490396\pi$
$434$	−3.29954	−0.158383
$435$	−3.52423	−0.168974
$436$	0.714942	0.0342395
$437$	17.6143	0.842607
$438$	5.34984	0.255625
$439$	−8.79229	−0.419633	−0.209817	−	0.977741i	$-0.567287\pi$
$439$	−8.79229	−0.419633	−0.209817	+	0.977741i	$0.567287\pi$
$440$	−8.15690	−0.388865
$441$	−5.02622	−0.239344
$442$	−7.57385	−0.360251
$443$	11.5561	0.549045	0.274522	−	0.961581i	$-0.411480\pi$
$443$	11.5561	0.549045	0.274522	+	0.961581i	$0.411480\pi$
$444$	−5.11651	−0.242819
$445$	14.2041	0.673339
$446$	−21.0616	−0.997297
$447$	−5.11066	−0.241726
$448$	−1.40491	−0.0663759
$449$	26.2196	1.23738	0.618689	−	0.785636i	$-0.287664\pi$
$449$	26.2196	1.23738	0.618689	+	0.785636i	$0.287664\pi$
$450$	−5.33603	−0.251543
$451$	0.805637	0.0379360
$452$	0.0112939	0.000531219 0
$453$	−10.3452	−0.486059
$454$	11.7708	0.552430
$455$	4.51675	0.211749
$456$	2.48027	0.116150
$457$	−26.1019	−1.22100	−0.610499	−	0.792017i	$-0.709031\pi$
$457$	−26.1019	−1.22100	−0.610499	+	0.792017i	$0.709031\pi$
$458$	−12.9373	−0.604519
$459$	−7.57385	−0.353517
$460$	−22.8320	−1.06455
$461$	−29.0448	−1.35275	−0.676376	−	0.736556i	$-0.736451\pi$
$461$	−29.0448	−1.35275	−0.676376	+	0.736556i	$0.736451\pi$
$462$	3.56449	0.165835
$463$	13.2014	0.613522	0.306761	−	0.951787i	$-0.400755\pi$
$463$	13.2014	0.613522	0.306761	+	0.951787i	$0.400755\pi$
$464$	−1.09619	−0.0508896
$465$	−7.55060	−0.350151
$466$	14.2591	0.660538
$467$	−8.32279	−0.385133	−0.192567	−	0.981284i	$-0.561681\pi$
$467$	−8.32279	−0.385133	−0.192567	+	0.981284i	$0.561681\pi$
$468$	1.00000	0.0462250
$469$	15.6179	0.721169
$470$	−17.7777	−0.820023
$471$	−19.2837	−0.888544
$472$	−0.591321	−0.0272177
$473$	−24.3584	−1.12000
$474$	16.3495	0.750956
$475$	13.2348	0.607255
$476$	−10.6406	−0.487711
$477$	−4.04692	−0.185296
$478$	−7.67833	−0.351198
$479$	−31.2476	−1.42774	−0.713869	−	0.700279i	$-0.753059\pi$
$479$	−31.2476	−1.42774	−0.713869	+	0.700279i	$0.753059\pi$
$480$	−3.21497	−0.146743
$481$	5.11651	0.233293
$482$	−17.8173	−0.811557
$483$	9.97735	0.453985
$484$	−4.56281	−0.207400
$485$	30.8384	1.40030
$486$	1.00000	0.0453609
$487$	33.0131	1.49596	0.747982	−	0.663718i	$-0.231023\pi$
$487$	33.0131	1.49596	0.747982	+	0.663718i	$0.231023\pi$
$488$	0.0491791	0.00222623
$489$	−24.1659	−1.09282
$490$	−16.1591	−0.729996
$491$	22.0882	0.996828	0.498414	−	0.866939i	$-0.333916\pi$
$491$	22.0882	0.996828	0.498414	+	0.866939i	$0.333916\pi$
$492$	0.317535	0.0143156
$493$	−8.30241	−0.373922
$494$	−2.48027	−0.111593
$495$	8.15690	0.366625
$496$	−2.34857	−0.105454
$497$	23.5161	1.05484
$498$	3.14585	0.140969
$499$	−34.2370	−1.53266	−0.766330	−	0.642448i	$-0.777919\pi$
$499$	−34.2370	−1.53266	−0.766330	+	0.642448i	$0.777919\pi$
$500$	−1.08032	−0.0483135
$501$	−16.6964	−0.745938
$502$	−11.4843	−0.512570
$503$	34.8724	1.55488	0.777442	−	0.628955i	$-0.216517\pi$
$503$	34.8724	1.55488	0.777442	+	0.628955i	$0.216517\pi$
$504$	1.40491	0.0625798
$505$	42.6897	1.89967
$506$	18.0183	0.801012
$507$	−1.00000	−0.0444116
$508$	9.16672	0.406708
$509$	33.8685	1.50120	0.750598	−	0.660759i	$-0.229766\pi$
$509$	33.8685	1.50120	0.750598	+	0.660759i	$0.229766\pi$
$510$	−24.3497	−1.07822
$511$	−7.51605	−0.332490
$512$	−1.00000	−0.0441942
$513$	−2.48027	−0.109507
$514$	0.559098	0.0246607
$515$	3.21497	0.141668
$516$	−9.60063	−0.422644
$517$	14.0296	0.617023
$518$	7.18825	0.315833
$519$	15.7177	0.689929
$520$	3.21497	0.140986
$521$	10.6760	0.467726	0.233863	−	0.972270i	$-0.424863\pi$
$521$	10.6760	0.467726	0.233863	+	0.972270i	$0.424863\pi$
$522$	1.09619	0.0479791
$523$	14.0032	0.612315	0.306157	−	0.951981i	$-0.400957\pi$
$523$	14.0032	0.612315	0.306157	+	0.951981i	$0.400957\pi$
$524$	6.04237	0.263962
$525$	7.49665	0.327181
$526$	−25.6348	−1.11773
$527$	−17.7877	−0.774846
$528$	2.53716	0.110416
$529$	27.4350	1.19283
$530$	−13.0107	−0.565150
$531$	0.591321	0.0256611
$532$	−3.48457	−0.151075
$533$	−0.317535	−0.0137540
$534$	−4.41812	−0.191191
$535$	18.3478	0.793244
$536$	11.1167	0.480167
$537$	−15.1298	−0.652898
$538$	8.75155	0.377306
$539$	12.7523	0.549282
$540$	3.21497	0.138350
$541$	−13.8044	−0.593496	−0.296748	−	0.954956i	$-0.595902\pi$
$541$	−13.8044	−0.593496	−0.296748	+	0.954956i	$0.595902\pi$
$542$	−20.9500	−0.899880
$543$	−7.66911	−0.329113
$544$	−7.57385	−0.324726
$545$	−2.29852	−0.0984577
$546$	−1.40491	−0.0601247
$547$	−5.72499	−0.244783	−0.122391	−	0.992482i	$-0.539056\pi$
$547$	−5.72499	−0.244783	−0.122391	+	0.992482i	$0.539056\pi$
$548$	−19.2977	−0.824356
$549$	−0.0491791	−0.00209891
$550$	13.5384	0.577278
$551$	−2.71886	−0.115828
$552$	7.10176	0.302271
$553$	−22.9696	−0.976766
$554$	−27.0963	−1.15121
$555$	16.4494	0.698239
$556$	−4.39044	−0.186196
$557$	−13.2383	−0.560926	−0.280463	−	0.959865i	$-0.590488\pi$
$557$	−13.2383	−0.560926	−0.280463	+	0.959865i	$0.590488\pi$
$558$	2.34857	0.0994231
$559$	9.60063	0.406063
$560$	4.51675	0.190868
$561$	19.2161	0.811304
$562$	−22.0661	−0.930800
$563$	−16.4880	−0.694887	−0.347444	−	0.937701i	$-0.612950\pi$
$563$	−16.4880	−0.694887	−0.347444	+	0.937701i	$0.612950\pi$
$564$	5.52965	0.232840
$565$	−0.0363095	−0.00152755
$566$	20.6144	0.866490
$567$	−1.40491	−0.0590008
$568$	16.7385	0.702331
$569$	6.88126	0.288478	0.144239	−	0.989543i	$-0.453927\pi$
$569$	6.88126	0.288478	0.144239	+	0.989543i	$0.453927\pi$
$570$	−7.97401	−0.333994
$571$	−22.0933	−0.924576	−0.462288	−	0.886730i	$-0.652971\pi$
$571$	−22.0933	−0.924576	−0.462288	+	0.886730i	$0.652971\pi$
$572$	−2.53716	−0.106084
$573$	16.0169	0.669114
$574$	−0.446108	−0.0186202
$575$	37.8952	1.58034
$576$	1.00000	0.0416667
$577$	23.0450	0.959376	0.479688	−	0.877439i	$-0.340750\pi$
$577$	23.0450	0.959376	0.479688	+	0.877439i	$0.340750\pi$
$578$	−40.3631	−1.67889
$579$	−6.03418	−0.250772
$580$	3.52423	0.146336
$581$	−4.41964	−0.183358
$582$	−9.59214	−0.397607
$583$	10.2677	0.425245
$584$	−5.34984	−0.221378
$585$	−3.21497	−0.132923
$586$	15.5930	0.644139
$587$	−30.2929	−1.25032	−0.625162	−	0.780495i	$-0.714967\pi$
$587$	−30.2929	−1.25032	−0.625162	+	0.780495i	$0.714967\pi$
$588$	5.02622	0.207278
$589$	−5.82511	−0.240020
$590$	1.90108	0.0782661
$591$	14.6922	0.604356
$592$	5.11651	0.210287
$593$	48.2902	1.98304	0.991521	−	0.129948i	$-0.0414811\pi$
$593$	48.2902	1.98304	0.991521	+	0.129948i	$0.0414811\pi$
$594$	−2.53716	−0.104101
$595$	34.2092	1.40244
$596$	5.11066	0.209341
$597$	−9.27945	−0.379783
$598$	−7.10176	−0.290413
$599$	26.3791	1.07782	0.538911	−	0.842363i	$-0.318836\pi$
$599$	26.3791	1.07782	0.538911	+	0.842363i	$0.318836\pi$
$600$	5.33603	0.217842
$601$	−17.8024	−0.726174	−0.363087	−	0.931755i	$-0.618277\pi$
$601$	−17.8024	−0.726174	−0.363087	+	0.931755i	$0.618277\pi$
$602$	13.4880	0.549732
$603$	−11.1167	−0.452705
$604$	10.3452	0.420940
$605$	14.6693	0.596391
$606$	−13.2784	−0.539399
$607$	−13.3337	−0.541200	−0.270600	−	0.962692i	$-0.587222\pi$
$607$	−13.3337	−0.541200	−0.270600	+	0.962692i	$0.587222\pi$
$608$	−2.48027	−0.100588
$609$	−1.54006	−0.0624063
$610$	−0.158109	−0.00640165
$611$	−5.52965	−0.223706
$612$	7.57385	0.306155
$613$	11.4072	0.460733	0.230367	−	0.973104i	$-0.426007\pi$
$613$	11.4072	0.460733	0.230367	+	0.973104i	$0.426007\pi$
$614$	13.8308	0.558166
$615$	−1.02086	−0.0411652
$616$	−3.56449	−0.143617
$617$	18.7919	0.756534	0.378267	−	0.925697i	$-0.376520\pi$
$617$	18.7919	0.756534	0.378267	+	0.925697i	$0.376520\pi$
$618$	−1.00000	−0.0402259
$619$	−5.95938	−0.239528	−0.119764	−	0.992802i	$-0.538214\pi$
$619$	−5.95938	−0.239528	−0.119764	+	0.992802i	$0.538214\pi$
$620$	7.55060	0.303239
$621$	−7.10176	−0.284984
$622$	21.7094	0.870469
$623$	6.20706	0.248681
$624$	−1.00000	−0.0400320
$625$	−23.2069	−0.928278
$626$	7.64960	0.305739
$627$	6.29286	0.251313
$628$	19.2837	0.769502
$629$	38.7516	1.54513
$630$	−4.51675	−0.179952
$631$	47.0677	1.87374	0.936868	−	0.349683i	$-0.113711\pi$
$631$	47.0677	1.87374	0.936868	+	0.349683i	$0.113711\pi$
$632$	−16.3495	−0.650347
$633$	23.6370	0.939485
$634$	−7.63340	−0.303161
$635$	−29.4707	−1.16951
$636$	4.04692	0.160471
$637$	−5.02622	−0.199146
$638$	−2.78122	−0.110110
$639$	−16.7385	−0.662164
$640$	3.21497	0.127083
$641$	41.9763	1.65796	0.828981	−	0.559276i	$-0.188921\pi$
$641$	41.9763	1.65796	0.828981	+	0.559276i	$0.188921\pi$
$642$	−5.70699	−0.225237
$643$	28.9315	1.14095	0.570474	−	0.821316i	$-0.306759\pi$
$643$	28.9315	1.14095	0.570474	+	0.821316i	$0.306759\pi$
$644$	−9.97735	−0.393163
$645$	30.8657	1.21534
$646$	−18.7852	−0.739095
$647$	6.43859	0.253127	0.126563	−	0.991959i	$-0.459605\pi$
$647$	6.43859	0.253127	0.126563	+	0.991959i	$0.459605\pi$
$648$	−1.00000	−0.0392837
$649$	−1.50028	−0.0588910
$650$	−5.33603	−0.209296
$651$	−3.29954	−0.129319
$652$	24.1659	0.946408
$653$	−2.80854	−0.109907	−0.0549534	−	0.998489i	$-0.517501\pi$
$653$	−2.80854	−0.109907	−0.0549534	+	0.998489i	$0.517501\pi$
$654$	0.714942	0.0279565
$655$	−19.4261	−0.759039
$656$	−0.317535	−0.0123976
$657$	5.34984	0.208717
$658$	−7.76868	−0.302855
$659$	−35.7289	−1.39180	−0.695901	−	0.718138i	$-0.744995\pi$
$659$	−35.7289	−1.39180	−0.695901	+	0.718138i	$0.744995\pi$
$660$	−8.15690	−0.317507
$661$	10.0657	0.391510	0.195755	−	0.980653i	$-0.437284\pi$
$661$	10.0657	0.391510	0.195755	+	0.980653i	$0.437284\pi$
$662$	6.12990	0.238245
$663$	−7.57385	−0.294144
$664$	−3.14585	−0.122083
$665$	11.2028	0.434425
$666$	−5.11651	−0.198261
$667$	−7.78491	−0.301433
$668$	16.6964	0.646001
$669$	−21.0616	−0.814289
$670$	−35.7397	−1.38075
$671$	0.124775	0.00481690
$672$	−1.40491	−0.0541957
$673$	−10.9942	−0.423795	−0.211898	−	0.977292i	$-0.567964\pi$
$673$	−10.9942	−0.423795	−0.211898	+	0.977292i	$0.567964\pi$
$674$	20.2018	0.778143
$675$	−5.33603	−0.205384
$676$	1.00000	0.0384615
$677$	21.7987	0.837790	0.418895	−	0.908035i	$-0.362417\pi$
$677$	21.7987	0.837790	0.418895	+	0.908035i	$0.362417\pi$
$678$	0.0112939	0.000433739 0
$679$	13.4761	0.517166
$680$	24.3497	0.933768
$681$	11.7708	0.451057
$682$	−5.95872	−0.228171
$683$	−12.0227	−0.460037	−0.230019	−	0.973186i	$-0.573879\pi$
$683$	−12.0227	−0.460037	−0.230019	+	0.973186i	$0.573879\pi$
$684$	2.48027	0.0948357
$685$	62.0414	2.37048
$686$	−16.8958	−0.645084
$687$	−12.9373	−0.493588
$688$	9.60063	0.366021
$689$	−4.04692	−0.154175
$690$	−22.8320	−0.869197
$691$	41.0374	1.56114	0.780568	−	0.625071i	$-0.214930\pi$
$691$	41.0374	1.56114	0.780568	+	0.625071i	$0.214930\pi$
$692$	−15.7177	−0.597496
$693$	3.56449	0.135404
$694$	29.8190	1.13192
$695$	14.1151	0.535417
$696$	−1.09619	−0.0415512
$697$	−2.40496	−0.0910943
$698$	15.6189	0.591184
$699$	14.2591	0.539327
$700$	−7.49665	−0.283347
$701$	−48.9662	−1.84943	−0.924715	−	0.380661i	$-0.875696\pi$
$701$	−48.9662	−1.84943	−0.924715	+	0.380661i	$0.875696\pi$
$702$	1.00000	0.0377426
$703$	12.6903	0.478625
$704$	−2.53716	−0.0956229
$705$	−17.7777	−0.669546
$706$	26.9240	1.01330
$707$	18.6550	0.701594
$708$	−0.591321	−0.0222232
$709$	−19.0876	−0.716850	−0.358425	−	0.933559i	$-0.616686\pi$
$709$	−19.0876	−0.716850	−0.358425	+	0.933559i	$0.616686\pi$
$710$	−53.8137	−2.01959
$711$	16.3495	0.613153
$712$	4.41812	0.165576
$713$	−16.6790	−0.624634
$714$	−10.6406	−0.398214
$715$	8.15690	0.305051
$716$	15.1298	0.565426
$717$	−7.67833	−0.286752
$718$	−6.70826	−0.250350
$719$	13.0914	0.488227	0.244114	−	0.969747i	$-0.421503\pi$
$719$	13.0914	0.488227	0.244114	+	0.969747i	$0.421503\pi$
$720$	−3.21497	−0.119815
$721$	1.40491	0.0523217
$722$	12.8482	0.478162
$723$	−17.8173	−0.662633
$724$	7.66911	0.285020
$725$	−5.84933	−0.217239
$726$	−4.56281	−0.169342
$727$	−36.6764	−1.36025	−0.680126	−	0.733095i	$-0.738075\pi$
$727$	−36.6764	−1.36025	−0.680126	+	0.733095i	$0.738075\pi$
$728$	1.40491	0.0520695
$729$	1.00000	0.0370370
$730$	17.1996	0.636584
$731$	72.7137	2.68941
$732$	0.0491791	0.00181771
$733$	−19.8895	−0.734635	−0.367317	−	0.930096i	$-0.619724\pi$
$733$	−19.8895	−0.734635	−0.367317	+	0.930096i	$0.619724\pi$
$734$	−23.3923	−0.863426
$735$	−16.1591	−0.596039
$736$	−7.10176	−0.261774
$737$	28.2048	1.03894
$738$	0.317535	0.0116886
$739$	0.682756	0.0251156	0.0125578	−	0.999921i	$-0.496003\pi$
$739$	0.682756	0.0251156	0.0125578	+	0.999921i	$0.496003\pi$
$740$	−16.4494	−0.604693
$741$	−2.48027	−0.0911152
$742$	−5.68557	−0.208724
$743$	7.08974	0.260097	0.130049	−	0.991508i	$-0.458487\pi$
$743$	7.08974	0.260097	0.130049	+	0.991508i	$0.458487\pi$
$744$	−2.34857	−0.0861029
$745$	−16.4306	−0.601971
$746$	33.8963	1.24103
$747$	3.14585	0.115101
$748$	−19.2161	−0.702610
$749$	8.01782	0.292965
$750$	−1.08032	−0.0394478
$751$	19.9492	0.727956	0.363978	−	0.931408i	$-0.381418\pi$
$751$	19.9492	0.727956	0.363978	+	0.931408i	$0.381418\pi$
$752$	−5.52965	−0.201646
$753$	−11.4843	−0.418512
$754$	1.09619	0.0399211
$755$	−33.2595	−1.21044
$756$	1.40491	0.0510962
$757$	−36.2103	−1.31609	−0.658043	−	0.752980i	$-0.728615\pi$
$757$	−36.2103	−1.31609	−0.658043	+	0.752980i	$0.728615\pi$
$758$	23.2303	0.843763
$759$	18.0183	0.654024
$760$	7.97401	0.289248
$761$	−39.1506	−1.41921	−0.709603	−	0.704602i	$-0.751126\pi$
$761$	−39.1506	−1.41921	−0.709603	+	0.704602i	$0.751126\pi$
$762$	9.16672	0.332075
$763$	−1.00443	−0.0363629
$764$	−16.0169	−0.579469
$765$	−24.3497	−0.880365
$766$	−0.229743	−0.00830094
$767$	0.591321	0.0213514
$768$	−1.00000	−0.0360844
$769$	−21.2933	−0.767855	−0.383928	−	0.923363i	$-0.625429\pi$
$769$	−21.2933	−0.767855	−0.383928	+	0.923363i	$0.625429\pi$
$770$	11.4597	0.412980
$771$	0.559098	0.0201354
$772$	6.03418	0.217175
$773$	28.5594	1.02721	0.513605	−	0.858027i	$-0.328310\pi$
$773$	28.5594	1.02721	0.513605	+	0.858027i	$0.328310\pi$
$774$	−9.60063	−0.345087
$775$	−12.5321	−0.450165
$776$	9.59214	0.344338
$777$	7.18825	0.257877
$778$	−31.6902	−1.13615
$779$	−0.787573	−0.0282177
$780$	3.21497	0.115114
$781$	42.4682	1.51963
$782$	−53.7877	−1.92344
$783$	1.09619	0.0391748
$784$	−5.02622	−0.179508
$785$	−61.9964	−2.21275
$786$	6.04237	0.215524
$787$	30.6319	1.09191	0.545955	−	0.837814i	$-0.316167\pi$
$787$	30.6319	1.09191	0.545955	+	0.837814i	$0.316167\pi$
$788$	−14.6922	−0.523387
$789$	−25.6348	−0.912622
$790$	52.5631	1.87011
$791$	−0.0158669	−0.000564162 0
$792$	2.53716	0.0901542
$793$	−0.0491791	−0.00174640
$794$	3.56877	0.126651
$795$	−13.0107	−0.461443
$796$	9.27945	0.328901
$797$	−33.3366	−1.18084	−0.590421	−	0.807095i	$-0.701038\pi$
$797$	−33.3366	−1.18084	−0.590421	+	0.807095i	$0.701038\pi$
$798$	−3.48457	−0.123352
$799$	−41.8808	−1.48163
$800$	−5.33603	−0.188657
$801$	−4.41812	−0.156106
$802$	−34.3052	−1.21136
$803$	−13.5734	−0.478995
$804$	11.1167	0.392054
$805$	32.0769	1.13056
$806$	2.34857	0.0827250
$807$	8.75155	0.308069
$808$	13.2784	0.467133
$809$	37.0003	1.30086	0.650431	−	0.759566i	$-0.274588\pi$
$809$	37.0003	1.30086	0.650431	+	0.759566i	$0.274588\pi$
$810$	3.21497	0.112963
$811$	52.9625	1.85977	0.929883	−	0.367856i	$-0.119908\pi$
$811$	52.9625	1.85977	0.929883	+	0.367856i	$0.119908\pi$
$812$	1.54006	0.0540454
$813$	−20.9500	−0.734749
$814$	12.9814	0.454998
$815$	−77.6925	−2.72145
$816$	−7.57385	−0.265138
$817$	23.8122	0.833083
$818$	21.3744	0.747337
$819$	−1.40491	−0.0490916
$820$	1.02086	0.0356501
$821$	−4.57433	−0.159645	−0.0798226	−	0.996809i	$-0.525435\pi$
$821$	−4.57433	−0.159645	−0.0798226	+	0.996809i	$0.525435\pi$
$822$	−19.2977	−0.673084
$823$	33.7222	1.17548	0.587741	−	0.809049i	$-0.300017\pi$
$823$	33.7222	1.17548	0.587741	+	0.809049i	$0.300017\pi$
$824$	1.00000	0.0348367
$825$	13.5384	0.471346
$826$	0.830754	0.0289056
$827$	16.9998	0.591142	0.295571	−	0.955321i	$-0.404490\pi$
$827$	16.9998	0.591142	0.295571	+	0.955321i	$0.404490\pi$
$828$	7.10176	0.246803
$829$	21.0052	0.729541	0.364770	−	0.931097i	$-0.381147\pi$
$829$	21.0052	0.729541	0.364770	+	0.931097i	$0.381147\pi$
$830$	10.1138	0.351055
$831$	−27.0963	−0.939960
$832$	1.00000	0.0346688
$833$	−38.0678	−1.31897
$834$	−4.39044	−0.152028
$835$	−53.6783	−1.85761
$836$	−6.29286	−0.217643
$837$	2.34857	0.0811786
$838$	−7.08545	−0.244763
$839$	34.1811	1.18006	0.590031	−	0.807380i	$-0.299115\pi$
$839$	34.1811	1.18006	0.590031	+	0.807380i	$0.299115\pi$
$840$	4.51675	0.155843
$841$	−27.7984	−0.958564
$842$	−7.09461	−0.244496
$843$	−22.0661	−0.759995
$844$	−23.6370	−0.813618
$845$	−3.21497	−0.110598
$846$	5.52965	0.190113
$847$	6.41034	0.220262
$848$	−4.04692	−0.138972
$849$	20.6144	0.707486
$850$	−40.4143	−1.38620
$851$	36.3362	1.24559
$852$	16.7385	0.573451
$853$	43.2603	1.48120	0.740602	−	0.671944i	$-0.234540\pi$
$853$	43.2603	1.48120	0.740602	+	0.671944i	$0.234540\pi$
$854$	−0.0690923	−0.00236429
$855$	−7.97401	−0.272705
$856$	5.70699	0.195061
$857$	31.1550	1.06423	0.532117	−	0.846671i	$-0.321396\pi$
$857$	31.1550	1.06423	0.532117	+	0.846671i	$0.321396\pi$
$858$	−2.53716	−0.0866173
$859$	−16.3331	−0.557279	−0.278640	−	0.960396i	$-0.589884\pi$
$859$	−16.3331	−0.557279	−0.278640	+	0.960396i	$0.589884\pi$
$860$	−30.8657	−1.05251
$861$	−0.446108	−0.0152033
$862$	−22.5540	−0.768192
$863$	−35.1370	−1.19608	−0.598038	−	0.801468i	$-0.704053\pi$
$863$	−35.1370	−1.19608	−0.598038	+	0.801468i	$0.704053\pi$
$864$	1.00000	0.0340207
$865$	50.5318	1.71813
$866$	−1.25553	−0.0426648
$867$	−40.3631	−1.37080
$868$	3.29954	0.111994
$869$	−41.4813	−1.40716
$870$	3.52423	0.119483
$871$	−11.1167	−0.376674
$872$	−0.714942	−0.0242110
$873$	−9.59214	−0.324645
$874$	−17.6143	−0.595813
$875$	1.51776	0.0513096
$876$	−5.34984	−0.180754
$877$	18.6302	0.629098	0.314549	−	0.949241i	$-0.398147\pi$
$877$	18.6302	0.629098	0.314549	+	0.949241i	$0.398147\pi$
$878$	8.79229	0.296725
$879$	15.5930	0.525937
$880$	8.15690	0.274969
$881$	35.4645	1.19483	0.597414	−	0.801933i	$-0.296195\pi$
$881$	35.4645	1.19483	0.597414	+	0.801933i	$0.296195\pi$
$882$	5.02622	0.169242
$883$	−13.8411	−0.465791	−0.232896	−	0.972502i	$-0.574820\pi$
$883$	−13.8411	−0.465791	−0.232896	+	0.972502i	$0.574820\pi$
$884$	7.57385	0.254736
$885$	1.90108	0.0639040
$886$	−11.5561	−0.388233
$887$	−13.0912	−0.439559	−0.219779	−	0.975550i	$-0.570534\pi$
$887$	−13.0912	−0.439559	−0.219779	+	0.975550i	$0.570534\pi$
$888$	5.11651	0.171699
$889$	−12.8784	−0.431929
$890$	−14.2041	−0.476123
$891$	−2.53716	−0.0849982
$892$	21.0616	0.705195
$893$	−13.7151	−0.458957
$894$	5.11066	0.170926
$895$	−48.6417	−1.62591
$896$	1.40491	0.0469348
$897$	−7.10176	−0.237121
$898$	−26.2196	−0.874959
$899$	2.57450	0.0858642
$900$	5.33603	0.177868
$901$	−30.6508	−1.02112
$902$	−0.805637	−0.0268248
$903$	13.4880	0.448854
$904$	−0.0112939	−0.000375629 0
$905$	−24.6559	−0.819591
$906$	10.3452	0.343696
$907$	6.36080	0.211207	0.105603	−	0.994408i	$-0.466323\pi$
$907$	6.36080	0.211207	0.105603	+	0.994408i	$0.466323\pi$
$908$	−11.7708	−0.390627
$909$	−13.2784	−0.440417
$910$	−4.51675	−0.149729
$911$	44.6319	1.47872	0.739361	−	0.673309i	$-0.235128\pi$
$911$	44.6319	1.47872	0.739361	+	0.673309i	$0.235128\pi$
$912$	−2.48027	−0.0821301
$913$	−7.98153	−0.264150
$914$	26.1019	0.863375
$915$	−0.158109	−0.00522693
$916$	12.9373	0.427460
$917$	−8.48901	−0.280332
$918$	7.57385	0.249974
$919$	11.4655	0.378213	0.189106	−	0.981957i	$-0.439441\pi$
$919$	11.4655	0.378213	0.189106	+	0.981957i	$0.439441\pi$
$920$	22.8320	0.752747
$921$	13.8308	0.455741
$922$	29.0448	0.956541
$923$	−16.7385	−0.550954
$924$	−3.56449	−0.117263
$925$	27.3018	0.897679
$926$	−13.2014	−0.433825
$927$	−1.00000	−0.0328443
$928$	1.09619	0.0359844
$929$	−46.9608	−1.54073	−0.770367	−	0.637601i	$-0.779927\pi$
$929$	−46.9608	−1.54073	−0.770367	+	0.637601i	$0.779927\pi$
$930$	7.55060	0.247594
$931$	−12.4664	−0.408570
$932$	−14.2591	−0.467071
$933$	21.7094	0.710735
$934$	8.32279	0.272330
$935$	61.7791	2.02039
$936$	−1.00000	−0.0326860
$937$	−56.9779	−1.86139	−0.930694	−	0.365800i	$-0.880796\pi$
$937$	−56.9779	−1.86139	−0.930694	+	0.365800i	$0.880796\pi$
$938$	−15.6179	−0.509944
$939$	7.64960	0.249635
$940$	17.7777	0.579844
$941$	12.4270	0.405110	0.202555	−	0.979271i	$-0.435076\pi$
$941$	12.4270	0.405110	0.202555	+	0.979271i	$0.435076\pi$
$942$	19.2837	0.628296
$943$	−2.25506	−0.0734347
$944$	0.591321	0.0192458
$945$	−4.51675	−0.146930
$946$	24.3584	0.791958
$947$	−60.7311	−1.97349	−0.986747	−	0.162266i	$-0.948120\pi$
$947$	−60.7311	−1.97349	−0.986747	+	0.162266i	$0.948120\pi$
$948$	−16.3495	−0.531006
$949$	5.34984	0.173663
$950$	−13.2348	−0.429394
$951$	−7.63340	−0.247530
$952$	10.6406	0.344864
$953$	39.4367	1.27748	0.638741	−	0.769422i	$-0.279456\pi$
$953$	39.4367	1.27748	0.638741	+	0.769422i	$0.279456\pi$
$954$	4.04692	0.131024
$955$	51.4937	1.66630
$956$	7.67833	0.248335
$957$	−2.78122	−0.0899042
$958$	31.2476	1.00956
$959$	27.1115	0.875477
$960$	3.21497	0.103763
$961$	−25.4842	−0.822071
$962$	−5.11651	−0.164963
$963$	−5.70699	−0.183905
$964$	17.8173	0.573857
$965$	−19.3997	−0.624498
$966$	−9.97735	−0.321016
$967$	18.1825	0.584710	0.292355	−	0.956310i	$-0.405561\pi$
$967$	18.1825	0.584710	0.292355	+	0.956310i	$0.405561\pi$
$968$	4.56281	0.146654
$969$	−18.7852	−0.603468
$970$	−30.8384	−0.990163
$971$	41.6240	1.33578	0.667889	−	0.744261i	$-0.267198\pi$
$971$	41.6240	1.33578	0.667889	+	0.744261i	$0.267198\pi$
$972$	−1.00000	−0.0320750
$973$	6.16818	0.197743
$974$	−33.0131	−1.05781
$975$	−5.33603	−0.170890
$976$	−0.0491791	−0.00157418
$977$	20.3397	0.650724	0.325362	−	0.945590i	$-0.394514\pi$
$977$	20.3397	0.650724	0.325362	+	0.945590i	$0.394514\pi$
$978$	24.1659	0.772739
$979$	11.2095	0.358256
$980$	16.1591	0.516185
$981$	0.714942	0.0228264
$982$	−22.0882	−0.704864
$983$	5.83910	0.186239	0.0931193	−	0.995655i	$-0.470316\pi$
$983$	5.83910	0.186239	0.0931193	+	0.995655i	$0.470316\pi$
$984$	−0.317535	−0.0101226
$985$	47.2349	1.50503
$986$	8.30241	0.264403
$987$	−7.76868	−0.247280
$988$	2.48027	0.0789081
$989$	68.1814	2.16804
$990$	−8.15690	−0.259243
$991$	−23.5945	−0.749505	−0.374753	−	0.927125i	$-0.622272\pi$
$991$	−23.5945	−0.749505	−0.374753	+	0.927125i	$0.622272\pi$
$992$	2.34857	0.0745673
$993$	6.12990	0.194527
$994$	−23.5161	−0.745885
$995$	−29.8331	−0.945774
$996$	−3.14585	−0.0996800
$997$	−20.6271	−0.653266	−0.326633	−	0.945151i	$-0.605914\pi$
$997$	−20.6271	−0.653266	−0.326633	+	0.945151i	$0.605914\pi$
$998$	34.2370	1.08375
$999$	−5.11651	−0.161879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.z.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.z.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.21497 q^{5} +1.00000 q^{6} -1.40491 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.21497 q^{5} +1.00000 q^{6} -1.40491 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.21497 q^{10} -2.53716 q^{11} -1.00000 q^{12} +1.00000 q^{13} +1.40491 q^{14} +3.21497 q^{15} +1.00000 q^{16} +7.57385 q^{17} -1.00000 q^{18} +2.48027 q^{19} -3.21497 q^{20} +1.40491 q^{21} +2.53716 q^{22} +7.10176 q^{23} +1.00000 q^{24} +5.33603 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.40491 q^{28} -1.09619 q^{29} -3.21497 q^{30} -2.34857 q^{31} -1.00000 q^{32} +2.53716 q^{33} -7.57385 q^{34} +4.51675 q^{35} +1.00000 q^{36} +5.11651 q^{37} -2.48027 q^{38} -1.00000 q^{39} +3.21497 q^{40} -0.317535 q^{41} -1.40491 q^{42} +9.60063 q^{43} -2.53716 q^{44} -3.21497 q^{45} -7.10176 q^{46} -5.52965 q^{47} -1.00000 q^{48} -5.02622 q^{49} -5.33603 q^{50} -7.57385 q^{51} +1.00000 q^{52} -4.04692 q^{53} +1.00000 q^{54} +8.15690 q^{55} +1.40491 q^{56} -2.48027 q^{57} +1.09619 q^{58} +0.591321 q^{59} +3.21497 q^{60} -0.0491791 q^{61} +2.34857 q^{62} -1.40491 q^{63} +1.00000 q^{64} -3.21497 q^{65} -2.53716 q^{66} -11.1167 q^{67} +7.57385 q^{68} -7.10176 q^{69} -4.51675 q^{70} -16.7385 q^{71} -1.00000 q^{72} +5.34984 q^{73} -5.11651 q^{74} -5.33603 q^{75} +2.48027 q^{76} +3.56449 q^{77} +1.00000 q^{78} +16.3495 q^{79} -3.21497 q^{80} +1.00000 q^{81} +0.317535 q^{82} +3.14585 q^{83} +1.40491 q^{84} -24.3497 q^{85} -9.60063 q^{86} +1.09619 q^{87} +2.53716 q^{88} -4.41812 q^{89} +3.21497 q^{90} -1.40491 q^{91} +7.10176 q^{92} +2.34857 q^{93} +5.52965 q^{94} -7.97401 q^{95} +1.00000 q^{96} -9.59214 q^{97} +5.02622 q^{98} -2.53716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} - 14 q^{3} + 14 q^{4} - 3 q^{5} + 14 q^{6} + 4 q^{7} - 14 q^{8} + 14 q^{9} + 3 q^{10} + 5 q^{11} - 14 q^{12} + 14 q^{13} - 4 q^{14} + 3 q^{15} + 14 q^{16} - 7 q^{17} - 14 q^{18} + 31 q^{19} - 3 q^{20} - 4 q^{21} - 5 q^{22} + 14 q^{23} + 14 q^{24} + 11 q^{25} - 14 q^{26} - 14 q^{27} + 4 q^{28} + 9 q^{29} - 3 q^{30} + 23 q^{31} - 14 q^{32} - 5 q^{33} + 7 q^{34} - 2 q^{35} + 14 q^{36} + 12 q^{37} - 31 q^{38} - 14 q^{39} + 3 q^{40} - 5 q^{41} + 4 q^{42} - 2 q^{43} + 5 q^{44} - 3 q^{45} - 14 q^{46} - 11 q^{47} - 14 q^{48} + 52 q^{49} - 11 q^{50} + 7 q^{51} + 14 q^{52} + 6 q^{53} + 14 q^{54} + 30 q^{55} - 4 q^{56} - 31 q^{57} - 9 q^{58} - 4 q^{59} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 4 q^{63} + 14 q^{64} - 3 q^{65} + 5 q^{66} + 24 q^{67} - 7 q^{68} - 14 q^{69} + 2 q^{70} + 20 q^{71} - 14 q^{72} + 2 q^{73} - 12 q^{74} - 11 q^{75} + 31 q^{76} - 28 q^{77} + 14 q^{78} + 59 q^{79} - 3 q^{80} + 14 q^{81} + 5 q^{82} + q^{83} - 4 q^{84} - 29 q^{85} + 2 q^{86} - 9 q^{87} - 5 q^{88} + 6 q^{89} + 3 q^{90} + 4 q^{91} + 14 q^{92} - 23 q^{93} + 11 q^{94} - 58 q^{95} + 14 q^{96} - 6 q^{97} - 52 q^{98} + 5 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 - 14 * q^3 + 14 * q^4 - 3 * q^5 + 14 * q^6 + 4 * q^7 - 14 * q^8 + 14 * q^9 + 3 * q^10 + 5 * q^11 - 14 * q^12 + 14 * q^13 - 4 * q^14 + 3 * q^15 + 14 * q^16 - 7 * q^17 - 14 * q^18 + 31 * q^19 - 3 * q^20 - 4 * q^21 - 5 * q^22 + 14 * q^23 + 14 * q^24 + 11 * q^25 - 14 * q^26 - 14 * q^27 + 4 * q^28 + 9 * q^29 - 3 * q^30 + 23 * q^31 - 14 * q^32 - 5 * q^33 + 7 * q^34 - 2 * q^35 + 14 * q^36 + 12 * q^37 - 31 * q^38 - 14 * q^39 + 3 * q^40 - 5 * q^41 + 4 * q^42 - 2 * q^43 + 5 * q^44 - 3 * q^45 - 14 * q^46 - 11 * q^47 - 14 * q^48 + 52 * q^49 - 11 * q^50 + 7 * q^51 + 14 * q^52 + 6 * q^53 + 14 * q^54 + 30 * q^55 - 4 * q^56 - 31 * q^57 - 9 * q^58 - 4 * q^59 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 4 * q^63 + 14 * q^64 - 3 * q^65 + 5 * q^66 + 24 * q^67 - 7 * q^68 - 14 * q^69 + 2 * q^70 + 20 * q^71 - 14 * q^72 + 2 * q^73 - 12 * q^74 - 11 * q^75 + 31 * q^76 - 28 * q^77 + 14 * q^78 + 59 * q^79 - 3 * q^80 + 14 * q^81 + 5 * q^82 + q^83 - 4 * q^84 - 29 * q^85 + 2 * q^86 - 9 * q^87 - 5 * q^88 + 6 * q^89 + 3 * q^90 + 4 * q^91 + 14 * q^92 - 23 * q^93 + 11 * q^94 - 58 * q^95 + 14 * q^96 - 6 * q^97 - 52 * q^98 + 5 * q^99

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