LMFDB - Embedded newform 8034.2.a.bb.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$1$
Dimension:	$14$
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} - 6 x^{13} - 29 x^{12} + 207 x^{11} + 269 x^{10} - 2601 x^{9} - 847 x^{8} + 14851 x^{7} + \cdots - 2048 $ x^14 - 6x^13 - 29x^12 + 207x^11 + 269x^10 - 2601x^9 - 847x^8 + 14851x^7 + 678x^6 - 39390x^5 - 3280x^4 + 42456x^3 + 10816x^2 - 7296*x - 2048
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.453790$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.453790 q^{5} -1.00000 q^{6} +3.87720 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.453790 q^{5} -1.00000 q^{6} +3.87720 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.453790 q^{10} -1.29295 q^{11} +1.00000 q^{12} -1.00000 q^{13} -3.87720 q^{14} -0.453790 q^{15} +1.00000 q^{16} -0.204049 q^{17} -1.00000 q^{18} -0.475803 q^{19} -0.453790 q^{20} +3.87720 q^{21} +1.29295 q^{22} +1.84848 q^{23} -1.00000 q^{24} -4.79407 q^{25} +1.00000 q^{26} +1.00000 q^{27} +3.87720 q^{28} -5.66720 q^{29} +0.453790 q^{30} -7.72539 q^{31} -1.00000 q^{32} -1.29295 q^{33} +0.204049 q^{34} -1.75943 q^{35} +1.00000 q^{36} +9.68872 q^{37} +0.475803 q^{38} -1.00000 q^{39} +0.453790 q^{40} -7.38884 q^{41} -3.87720 q^{42} -4.47310 q^{43} -1.29295 q^{44} -0.453790 q^{45} -1.84848 q^{46} -3.11558 q^{47} +1.00000 q^{48} +8.03267 q^{49} +4.79407 q^{50} -0.204049 q^{51} -1.00000 q^{52} -2.30074 q^{53} -1.00000 q^{54} +0.586726 q^{55} -3.87720 q^{56} -0.475803 q^{57} +5.66720 q^{58} -13.6380 q^{59} -0.453790 q^{60} -11.4248 q^{61} +7.72539 q^{62} +3.87720 q^{63} +1.00000 q^{64} +0.453790 q^{65} +1.29295 q^{66} +0.678171 q^{67} -0.204049 q^{68} +1.84848 q^{69} +1.75943 q^{70} +5.87504 q^{71} -1.00000 q^{72} -3.56157 q^{73} -9.68872 q^{74} -4.79407 q^{75} -0.475803 q^{76} -5.01301 q^{77} +1.00000 q^{78} +0.0379441 q^{79} -0.453790 q^{80} +1.00000 q^{81} +7.38884 q^{82} -7.81001 q^{83} +3.87720 q^{84} +0.0925952 q^{85} +4.47310 q^{86} -5.66720 q^{87} +1.29295 q^{88} +8.08601 q^{89} +0.453790 q^{90} -3.87720 q^{91} +1.84848 q^{92} -7.72539 q^{93} +3.11558 q^{94} +0.215915 q^{95} -1.00000 q^{96} -2.30097 q^{97} -8.03267 q^{98} -1.29295 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 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 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−0.453790	−0.202941	−0.101471	−	0.994839i	$-0.532355\pi$
$5$	−0.453790	−0.202941	−0.101471	+	0.994839i	$0.532355\pi$
$6$	−1.00000	−0.408248
$7$	3.87720	1.46544	0.732722	−	0.680528i	$-0.238250\pi$
$7$	3.87720	1.46544	0.732722	+	0.680528i	$0.238250\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	0.453790	0.143501
$11$	−1.29295	−0.389838	−0.194919	−	0.980819i	$-0.562444\pi$
$11$	−1.29295	−0.389838	−0.194919	+	0.980819i	$0.562444\pi$
$12$	1.00000	0.288675
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−3.87720	−1.03622
$15$	−0.453790	−0.117168
$16$	1.00000	0.250000
$17$	−0.204049	−0.0494891	−0.0247445	−	0.999694i	$-0.507877\pi$
$17$	−0.204049	−0.0494891	−0.0247445	+	0.999694i	$0.507877\pi$
$18$	−1.00000	−0.235702
$19$	−0.475803	−0.109157	−0.0545784	−	0.998509i	$-0.517381\pi$
$19$	−0.475803	−0.109157	−0.0545784	+	0.998509i	$0.517381\pi$
$20$	−0.453790	−0.101471
$21$	3.87720	0.846074
$22$	1.29295	0.275657
$23$	1.84848	0.385434	0.192717	−	0.981254i	$-0.438270\pi$
$23$	1.84848	0.385434	0.192717	+	0.981254i	$0.438270\pi$
$24$	−1.00000	−0.204124
$25$	−4.79407	−0.958815
$26$	1.00000	0.196116
$27$	1.00000	0.192450
$28$	3.87720	0.732722
$29$	−5.66720	−1.05237	−0.526187	−	0.850369i	$-0.676379\pi$
$29$	−5.66720	−1.05237	−0.526187	+	0.850369i	$0.676379\pi$
$30$	0.453790	0.0828503
$31$	−7.72539	−1.38752	−0.693760	−	0.720206i	$-0.744047\pi$
$31$	−7.72539	−1.38752	−0.693760	+	0.720206i	$0.744047\pi$
$32$	−1.00000	−0.176777
$33$	−1.29295	−0.225073
$34$	0.204049	0.0349941
$35$	−1.75943	−0.297399
$36$	1.00000	0.166667
$37$	9.68872	1.59282	0.796408	−	0.604760i	$-0.206731\pi$
$37$	9.68872	1.59282	0.796408	+	0.604760i	$0.206731\pi$
$38$	0.475803	0.0771855
$39$	−1.00000	−0.160128
$40$	0.453790	0.0717505
$41$	−7.38884	−1.15394	−0.576972	−	0.816764i	$-0.695766\pi$
$41$	−7.38884	−1.15394	−0.576972	+	0.816764i	$0.695766\pi$
$42$	−3.87720	−0.598265
$43$	−4.47310	−0.682142	−0.341071	−	0.940038i	$-0.610790\pi$
$43$	−4.47310	−0.682142	−0.341071	+	0.940038i	$0.610790\pi$
$44$	−1.29295	−0.194919
$45$	−0.453790	−0.0676470
$46$	−1.84848	−0.272543
$47$	−3.11558	−0.454455	−0.227227	−	0.973842i	$-0.572966\pi$
$47$	−3.11558	−0.454455	−0.227227	+	0.973842i	$0.572966\pi$
$48$	1.00000	0.144338
$49$	8.03267	1.14752
$50$	4.79407	0.677985
$51$	−0.204049	−0.0285725
$52$	−1.00000	−0.138675
$53$	−2.30074	−0.316032	−0.158016	−	0.987437i	$-0.550510\pi$
$53$	−2.30074	−0.316032	−0.158016	+	0.987437i	$0.550510\pi$
$54$	−1.00000	−0.136083
$55$	0.586726	0.0791142
$56$	−3.87720	−0.518112
$57$	−0.475803	−0.0630217
$58$	5.66720	0.744140
$59$	−13.6380	−1.77552	−0.887761	−	0.460305i	$-0.847740\pi$
$59$	−13.6380	−1.77552	−0.887761	+	0.460305i	$0.847740\pi$
$60$	−0.453790	−0.0585840
$61$	−11.4248	−1.46280	−0.731400	−	0.681949i	$-0.761133\pi$
$61$	−11.4248	−1.46280	−0.731400	+	0.681949i	$0.761133\pi$
$62$	7.72539	0.981125
$63$	3.87720	0.488481
$64$	1.00000	0.125000
$65$	0.453790	0.0562857
$66$	1.29295	0.159151
$67$	0.678171	0.0828518	0.0414259	−	0.999142i	$-0.486810\pi$
$67$	0.678171	0.0828518	0.0414259	+	0.999142i	$0.486810\pi$
$68$	−0.204049	−0.0247445
$69$	1.84848	0.222530
$70$	1.75943	0.210293
$71$	5.87504	0.697239	0.348620	−	0.937264i	$-0.386650\pi$
$71$	5.87504	0.697239	0.348620	+	0.937264i	$0.386650\pi$
$72$	−1.00000	−0.117851
$73$	−3.56157	−0.416850	−0.208425	−	0.978038i	$-0.566834\pi$
$73$	−3.56157	−0.416850	−0.208425	+	0.978038i	$0.566834\pi$
$74$	−9.68872	−1.12629
$75$	−4.79407	−0.553572
$76$	−0.475803	−0.0545784
$77$	−5.01301	−0.571286
$78$	1.00000	0.113228
$79$	0.0379441	0.00426905	0.00213452	−	0.999998i	$-0.499321\pi$
$79$	0.0379441	0.00426905	0.00213452	+	0.999998i	$0.499321\pi$
$80$	−0.453790	−0.0507353
$81$	1.00000	0.111111
$82$	7.38884	0.815961
$83$	−7.81001	−0.857260	−0.428630	−	0.903480i	$-0.641004\pi$
$83$	−7.81001	−0.857260	−0.428630	+	0.903480i	$0.641004\pi$
$84$	3.87720	0.423037
$85$	0.0925952	0.0100434
$86$	4.47310	0.482347
$87$	−5.66720	−0.607588
$88$	1.29295	0.137829
$89$	8.08601	0.857115	0.428558	−	0.903514i	$-0.359022\pi$
$89$	8.08601	0.857115	0.428558	+	0.903514i	$0.359022\pi$
$90$	0.453790	0.0478337
$91$	−3.87720	−0.406441
$92$	1.84848	0.192717
$93$	−7.72539	−0.801085
$94$	3.11558	0.321348
$95$	0.215915	0.0221524
$96$	−1.00000	−0.102062
$97$	−2.30097	−0.233628	−0.116814	−	0.993154i	$-0.537268\pi$
$97$	−2.30097	−0.233628	−0.116814	+	0.993154i	$0.537268\pi$
$98$	−8.03267	−0.811422
$99$	−1.29295	−0.129946
$100$	−4.79407	−0.479407
$101$	−3.28191	−0.326562	−0.163281	−	0.986580i	$-0.552208\pi$
$101$	−3.28191	−0.326562	−0.163281	+	0.986580i	$0.552208\pi$
$102$	0.204049	0.0202038
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	−1.75943	−0.171703
$106$	2.30074	0.223468
$107$	−13.4166	−1.29703	−0.648515	−	0.761202i	$-0.724610\pi$
$107$	−13.4166	−1.29703	−0.648515	+	0.761202i	$0.724610\pi$
$108$	1.00000	0.0962250
$109$	13.6736	1.30969	0.654845	−	0.755763i	$-0.272734\pi$
$109$	13.6736	1.30969	0.654845	+	0.755763i	$0.272734\pi$
$110$	−0.586726	−0.0559422
$111$	9.68872	0.919612
$112$	3.87720	0.366361
$113$	−5.72283	−0.538359	−0.269179	−	0.963090i	$-0.586752\pi$
$113$	−5.72283	−0.538359	−0.269179	+	0.963090i	$0.586752\pi$
$114$	0.475803	0.0445631
$115$	−0.838820	−0.0782204
$116$	−5.66720	−0.526187
$117$	−1.00000	−0.0924500
$118$	13.6380	1.25548
$119$	−0.791137	−0.0725234
$120$	0.453790	0.0414252
$121$	−9.32829	−0.848026
$122$	11.4248	1.03436
$123$	−7.38884	−0.666230
$124$	−7.72539	−0.693760
$125$	4.44445	0.397524
$126$	−3.87720	−0.345408
$127$	5.32461	0.472483	0.236241	−	0.971694i	$-0.424084\pi$
$127$	5.32461	0.472483	0.236241	+	0.971694i	$0.424084\pi$
$128$	−1.00000	−0.0883883
$129$	−4.47310	−0.393835
$130$	−0.453790	−0.0398000
$131$	−5.11582	−0.446971	−0.223486	−	0.974707i	$-0.571744\pi$
$131$	−5.11582	−0.446971	−0.223486	+	0.974707i	$0.571744\pi$
$132$	−1.29295	−0.112537
$133$	−1.84478	−0.159963
$134$	−0.678171	−0.0585851
$135$	−0.453790	−0.0390560
$136$	0.204049	0.0174970
$137$	−17.4572	−1.49147	−0.745736	−	0.666241i	$-0.767902\pi$
$137$	−17.4572	−1.49147	−0.745736	+	0.666241i	$0.767902\pi$
$138$	−1.84848	−0.157353
$139$	15.5994	1.32312	0.661560	−	0.749892i	$-0.269895\pi$
$139$	15.5994	1.32312	0.661560	+	0.749892i	$0.269895\pi$
$140$	−1.75943	−0.148699
$141$	−3.11558	−0.262379
$142$	−5.87504	−0.493023
$143$	1.29295	0.108122
$144$	1.00000	0.0833333
$145$	2.57172	0.213570
$146$	3.56157	0.294758
$147$	8.03267	0.662523
$148$	9.68872	0.796408
$149$	−6.75794	−0.553632	−0.276816	−	0.960923i	$-0.589279\pi$
$149$	−6.75794	−0.553632	−0.276816	+	0.960923i	$0.589279\pi$
$150$	4.79407	0.391435
$151$	6.66373	0.542287	0.271143	−	0.962539i	$-0.412598\pi$
$151$	6.66373	0.542287	0.271143	+	0.962539i	$0.412598\pi$
$152$	0.475803	0.0385927
$153$	−0.204049	−0.0164964
$154$	5.01301	0.403960
$155$	3.50570	0.281585
$156$	−1.00000	−0.0800641
$157$	−13.6895	−1.09254	−0.546271	−	0.837608i	$-0.683953\pi$
$157$	−13.6895	−1.09254	−0.546271	+	0.837608i	$0.683953\pi$
$158$	−0.0379441	−0.00301867
$159$	−2.30074	−0.182461
$160$	0.453790	0.0358753
$161$	7.16691	0.564832
$162$	−1.00000	−0.0785674
$163$	−3.83818	−0.300630	−0.150315	−	0.988638i	$-0.548029\pi$
$163$	−3.83818	−0.300630	−0.150315	+	0.988638i	$0.548029\pi$
$164$	−7.38884	−0.576972
$165$	0.586726	0.0456766
$166$	7.81001	0.606174
$167$	−20.6485	−1.59783	−0.798913	−	0.601446i	$-0.794591\pi$
$167$	−20.6485	−1.59783	−0.798913	+	0.601446i	$0.794591\pi$
$168$	−3.87720	−0.299132
$169$	1.00000	0.0769231
$170$	−0.0925952	−0.00710173
$171$	−0.475803	−0.0363856
$172$	−4.47310	−0.341071
$173$	−5.28951	−0.402154	−0.201077	−	0.979575i	$-0.564444\pi$
$173$	−5.28951	−0.402154	−0.201077	+	0.979575i	$0.564444\pi$
$174$	5.66720	0.429630
$175$	−18.5876	−1.40509
$176$	−1.29295	−0.0974595
$177$	−13.6380	−1.02510
$178$	−8.08601	−0.606072
$179$	15.5884	1.16513	0.582567	−	0.812783i	$-0.302049\pi$
$179$	15.5884	1.16513	0.582567	+	0.812783i	$0.302049\pi$
$180$	−0.453790	−0.0338235
$181$	25.5435	1.89863	0.949315	−	0.314327i	$-0.101779\pi$
$181$	25.5435	1.89863	0.949315	+	0.314327i	$0.101779\pi$
$182$	3.87720	0.287397
$183$	−11.4248	−0.844547
$184$	−1.84848	−0.136272
$185$	−4.39664	−0.323248
$186$	7.72539	0.566453
$187$	0.263824	0.0192927
$188$	−3.11558	−0.227227
$189$	3.87720	0.282025
$190$	−0.215915	−0.0156641
$191$	−2.83614	−0.205216	−0.102608	−	0.994722i	$-0.532719\pi$
$191$	−2.83614	−0.205216	−0.102608	+	0.994722i	$0.532719\pi$
$192$	1.00000	0.0721688
$193$	−21.2934	−1.53274	−0.766368	−	0.642402i	$-0.777938\pi$
$193$	−21.2934	−1.53274	−0.766368	+	0.642402i	$0.777938\pi$
$194$	2.30097	0.165200
$195$	0.453790	0.0324966
$196$	8.03267	0.573762
$197$	11.3818	0.810919	0.405459	−	0.914113i	$-0.367112\pi$
$197$	11.3818	0.810919	0.405459	+	0.914113i	$0.367112\pi$
$198$	1.29295	0.0918857
$199$	16.0284	1.13622	0.568112	−	0.822951i	$-0.307674\pi$
$199$	16.0284	1.13622	0.568112	+	0.822951i	$0.307674\pi$
$200$	4.79407	0.338992
$201$	0.678171	0.0478345
$202$	3.28191	0.230914
$203$	−21.9729	−1.54219
$204$	−0.204049	−0.0142863
$205$	3.35298	0.234183
$206$	−1.00000	−0.0696733
$207$	1.84848	0.128478
$208$	−1.00000	−0.0693375
$209$	0.615188	0.0425535
$210$	1.75943	0.121412
$211$	18.2423	1.25585	0.627927	−	0.778273i	$-0.283904\pi$
$211$	18.2423	1.25585	0.627927	+	0.778273i	$0.283904\pi$
$212$	−2.30074	−0.158016
$213$	5.87504	0.402551
$214$	13.4166	0.917139
$215$	2.02985	0.138435
$216$	−1.00000	−0.0680414
$217$	−29.9529	−2.03333
$218$	−13.6736	−0.926090
$219$	−3.56157	−0.240669
$220$	0.586726	0.0395571
$221$	0.204049	0.0137258
$222$	−9.68872	−0.650264
$223$	−15.8632	−1.06228	−0.531140	−	0.847284i	$-0.678236\pi$
$223$	−15.8632	−1.06228	−0.531140	+	0.847284i	$0.678236\pi$
$224$	−3.87720	−0.259056
$225$	−4.79407	−0.319605
$226$	5.72283	0.380677
$227$	5.41706	0.359543	0.179772	−	0.983708i	$-0.442464\pi$
$227$	5.41706	0.359543	0.179772	+	0.983708i	$0.442464\pi$
$228$	−0.475803	−0.0315108
$229$	17.2160	1.13767	0.568833	−	0.822453i	$-0.307395\pi$
$229$	17.2160	1.13767	0.568833	+	0.822453i	$0.307395\pi$
$230$	0.838820	0.0553102
$231$	−5.01301	−0.329832
$232$	5.66720	0.372070
$233$	−2.06406	−0.135221	−0.0676105	−	0.997712i	$-0.521538\pi$
$233$	−2.06406	−0.135221	−0.0676105	+	0.997712i	$0.521538\pi$
$234$	1.00000	0.0653720
$235$	1.41382	0.0922275
$236$	−13.6380	−0.887761
$237$	0.0379441	0.00246474
$238$	0.791137	0.0512818
$239$	−8.92571	−0.577356	−0.288678	−	0.957426i	$-0.593216\pi$
$239$	−8.92571	−0.577356	−0.288678	+	0.957426i	$0.593216\pi$
$240$	−0.453790	−0.0292920
$241$	9.50540	0.612296	0.306148	−	0.951984i	$-0.400960\pi$
$241$	9.50540	0.612296	0.306148	+	0.951984i	$0.400960\pi$
$242$	9.32829	0.599645
$243$	1.00000	0.0641500
$244$	−11.4248	−0.731400
$245$	−3.64515	−0.232880
$246$	7.38884	0.471095
$247$	0.475803	0.0302746
$248$	7.72539	0.490563
$249$	−7.81001	−0.494939
$250$	−4.44445	−0.281092
$251$	−0.527595	−0.0333015	−0.0166508	−	0.999861i	$-0.505300\pi$
$251$	−0.527595	−0.0333015	−0.0166508	+	0.999861i	$0.505300\pi$
$252$	3.87720	0.244241
$253$	−2.38998	−0.150257
$254$	−5.32461	−0.334096
$255$	0.0925952	0.00579854
$256$	1.00000	0.0625000
$257$	−18.6801	−1.16523	−0.582617	−	0.812747i	$-0.697971\pi$
$257$	−18.6801	−1.16523	−0.582617	+	0.812747i	$0.697971\pi$
$258$	4.47310	0.278483
$259$	37.5651	2.33418
$260$	0.453790	0.0281429
$261$	−5.66720	−0.350791
$262$	5.11582	0.316056
$263$	15.6935	0.967703	0.483852	−	0.875150i	$-0.339237\pi$
$263$	15.6935	0.967703	0.483852	+	0.875150i	$0.339237\pi$
$264$	1.29295	0.0795754
$265$	1.04406	0.0641358
$266$	1.84478	0.113111
$267$	8.08601	0.494856
$268$	0.678171	0.0414259
$269$	7.28894	0.444415	0.222207	−	0.974999i	$-0.428674\pi$
$269$	7.28894	0.444415	0.222207	+	0.974999i	$0.428674\pi$
$270$	0.453790	0.0276168
$271$	−11.6259	−0.706220	−0.353110	−	0.935582i	$-0.614876\pi$
$271$	−11.6259	−0.706220	−0.353110	+	0.935582i	$0.614876\pi$
$272$	−0.204049	−0.0123723
$273$	−3.87720	−0.234659
$274$	17.4572	1.05463
$275$	6.19848	0.373783
$276$	1.84848	0.111265
$277$	19.8613	1.19335	0.596674	−	0.802484i	$-0.296489\pi$
$277$	19.8613	1.19335	0.596674	+	0.802484i	$0.296489\pi$
$278$	−15.5994	−0.935588
$279$	−7.72539	−0.462507
$280$	1.75943	0.105146
$281$	−8.32906	−0.496870	−0.248435	−	0.968649i	$-0.579916\pi$
$281$	−8.32906	−0.496870	−0.248435	+	0.968649i	$0.579916\pi$
$282$	3.11558	0.185530
$283$	10.7185	0.637148	0.318574	−	0.947898i	$-0.396796\pi$
$283$	10.7185	0.637148	0.318574	+	0.947898i	$0.396796\pi$
$284$	5.87504	0.348620
$285$	0.215915	0.0127897
$286$	−1.29295	−0.0764535
$287$	−28.6480	−1.69104
$288$	−1.00000	−0.0589256
$289$	−16.9584	−0.997551
$290$	−2.57172	−0.151017
$291$	−2.30097	−0.134885
$292$	−3.56157	−0.208425
$293$	4.33001	0.252962	0.126481	−	0.991969i	$-0.459632\pi$
$293$	4.33001	0.252962	0.126481	+	0.991969i	$0.459632\pi$
$294$	−8.03267	−0.468475
$295$	6.18881	0.360326
$296$	−9.68872	−0.563145
$297$	−1.29295	−0.0750244
$298$	6.75794	0.391477
$299$	−1.84848	−0.106900
$300$	−4.79407	−0.276786
$301$	−17.3431	−0.999640
$302$	−6.66373	−0.383455
$303$	−3.28191	−0.188541
$304$	−0.475803	−0.0272892
$305$	5.18447	0.296862
$306$	0.204049	0.0116647
$307$	21.3696	1.21963	0.609813	−	0.792545i	$-0.291245\pi$
$307$	21.3696	1.21963	0.609813	+	0.792545i	$0.291245\pi$
$308$	−5.01301	−0.285643
$309$	1.00000	0.0568880
$310$	−3.50570	−0.199111
$311$	19.9313	1.13020	0.565099	−	0.825023i	$-0.308838\pi$
$311$	19.9313	1.13020	0.565099	+	0.825023i	$0.308838\pi$
$312$	1.00000	0.0566139
$313$	18.7275	1.05854	0.529269	−	0.848454i	$-0.322466\pi$
$313$	18.7275	1.05854	0.529269	+	0.848454i	$0.322466\pi$
$314$	13.6895	0.772544
$315$	−1.75943	−0.0991329
$316$	0.0379441	0.00213452
$317$	−29.4087	−1.65176	−0.825879	−	0.563848i	$-0.809321\pi$
$317$	−29.4087	−1.65176	−0.825879	+	0.563848i	$0.809321\pi$
$318$	2.30074	0.129019
$319$	7.32739	0.410255
$320$	−0.453790	−0.0253676
$321$	−13.4166	−0.748841
$322$	−7.16691	−0.399396
$323$	0.0970870	0.00540207
$324$	1.00000	0.0555556
$325$	4.79407	0.265927
$326$	3.83818	0.212577
$327$	13.6736	0.756150
$328$	7.38884	0.407981
$329$	−12.0797	−0.665977
$330$	−0.586726	−0.0322982
$331$	−15.8151	−0.869279	−0.434639	−	0.900605i	$-0.643124\pi$
$331$	−15.8151	−0.869279	−0.434639	+	0.900605i	$0.643124\pi$
$332$	−7.81001	−0.428630
$333$	9.68872	0.530938
$334$	20.6485	1.12983
$335$	−0.307747	−0.0168140
$336$	3.87720	0.211519
$337$	14.2786	0.777803	0.388902	−	0.921279i	$-0.372855\pi$
$337$	14.2786	0.777803	0.388902	+	0.921279i	$0.372855\pi$
$338$	−1.00000	−0.0543928
$339$	−5.72283	−0.310822
$340$	0.0925952	0.00502168
$341$	9.98851	0.540908
$342$	0.475803	0.0257285
$343$	4.00386	0.216188
$344$	4.47310	0.241174
$345$	−0.838820	−0.0451606
$346$	5.28951	0.284366
$347$	1.58327	0.0849945	0.0424973	−	0.999097i	$-0.486469\pi$
$347$	1.58327	0.0849945	0.0424973	+	0.999097i	$0.486469\pi$
$348$	−5.66720	−0.303794
$349$	−22.0059	−1.17795	−0.588976	−	0.808151i	$-0.700469\pi$
$349$	−22.0059	−1.17795	−0.588976	+	0.808151i	$0.700469\pi$
$350$	18.5876	0.993548
$351$	−1.00000	−0.0533761
$352$	1.29295	0.0689143
$353$	14.1320	0.752171	0.376086	−	0.926585i	$-0.377270\pi$
$353$	14.1320	0.752171	0.376086	+	0.926585i	$0.377270\pi$
$354$	13.6380	0.724854
$355$	−2.66604	−0.141499
$356$	8.08601	0.428558
$357$	−0.791137	−0.0418714
$358$	−15.5884	−0.823873
$359$	−7.97890	−0.421110	−0.210555	−	0.977582i	$-0.567527\pi$
$359$	−7.97890	−0.421110	−0.210555	+	0.977582i	$0.567527\pi$
$360$	0.453790	0.0239168
$361$	−18.7736	−0.988085
$362$	−25.5435	−1.34253
$363$	−9.32829	−0.489608
$364$	−3.87720	−0.203220
$365$	1.61620	0.0845960
$366$	11.4248	0.597185
$367$	21.7801	1.13691	0.568455	−	0.822714i	$-0.307541\pi$
$367$	21.7801	1.13691	0.568455	+	0.822714i	$0.307541\pi$
$368$	1.84848	0.0963585
$369$	−7.38884	−0.384648
$370$	4.39664	0.228571
$371$	−8.92044	−0.463126
$372$	−7.72539	−0.400543
$373$	−22.1999	−1.14947	−0.574733	−	0.818341i	$-0.694894\pi$
$373$	−22.1999	−1.14947	−0.574733	+	0.818341i	$0.694894\pi$
$374$	−0.263824	−0.0136420
$375$	4.44445	0.229511
$376$	3.11558	0.160674
$377$	5.66720	0.291876
$378$	−3.87720	−0.199422
$379$	14.0417	0.721271	0.360636	−	0.932707i	$-0.382560\pi$
$379$	14.0417	0.721271	0.360636	+	0.932707i	$0.382560\pi$
$380$	0.215915	0.0110762
$381$	5.32461	0.272788
$382$	2.83614	0.145109
$383$	25.5397	1.30502	0.652508	−	0.757782i	$-0.273717\pi$
$383$	25.5397	1.30502	0.652508	+	0.757782i	$0.273717\pi$
$384$	−1.00000	−0.0510310
$385$	2.27485	0.115937
$386$	21.2934	1.08381
$387$	−4.47310	−0.227381
$388$	−2.30097	−0.116814
$389$	19.7650	1.00212	0.501062	−	0.865411i	$-0.332943\pi$
$389$	19.7650	1.00212	0.501062	+	0.865411i	$0.332943\pi$
$390$	−0.453790	−0.0229786
$391$	−0.377179	−0.0190748
$392$	−8.03267	−0.405711
$393$	−5.11582	−0.258059
$394$	−11.3818	−0.573406
$395$	−0.0172187	−0.000866365 0
$396$	−1.29295	−0.0649730
$397$	20.1910	1.01336	0.506680	−	0.862134i	$-0.330873\pi$
$397$	20.1910	1.01336	0.506680	+	0.862134i	$0.330873\pi$
$398$	−16.0284	−0.803432
$399$	−1.84478	−0.0923547
$400$	−4.79407	−0.239704
$401$	12.9075	0.644568	0.322284	−	0.946643i	$-0.395549\pi$
$401$	12.9075	0.644568	0.322284	+	0.946643i	$0.395549\pi$
$402$	−0.678171	−0.0338241
$403$	7.72539	0.384829
$404$	−3.28191	−0.163281
$405$	−0.453790	−0.0225490
$406$	21.9729	1.09050
$407$	−12.5270	−0.620940
$408$	0.204049	0.0101019
$409$	20.8045	1.02872	0.514358	−	0.857576i	$-0.328030\pi$
$409$	20.8045	1.02872	0.514358	+	0.857576i	$0.328030\pi$
$410$	−3.35298	−0.165592
$411$	−17.4572	−0.861102
$412$	1.00000	0.0492665
$413$	−52.8774	−2.60193
$414$	−1.84848	−0.0908477
$415$	3.54410	0.173973
$416$	1.00000	0.0490290
$417$	15.5994	0.763904
$418$	−0.615188	−0.0300898
$419$	−1.39954	−0.0683720	−0.0341860	−	0.999415i	$-0.510884\pi$
$419$	−1.39954	−0.0683720	−0.0341860	+	0.999415i	$0.510884\pi$
$420$	−1.75943	−0.0858516
$421$	−25.4738	−1.24152	−0.620758	−	0.784002i	$-0.713175\pi$
$421$	−25.4738	−1.24152	−0.620758	+	0.784002i	$0.713175\pi$
$422$	−18.2423	−0.888022
$423$	−3.11558	−0.151485
$424$	2.30074	0.111734
$425$	0.978224	0.0474509
$426$	−5.87504	−0.284647
$427$	−44.2963	−2.14365
$428$	−13.4166	−0.648515
$429$	1.29295	0.0624241
$430$	−2.02985	−0.0978881
$431$	−11.2527	−0.542023	−0.271012	−	0.962576i	$-0.587358\pi$
$431$	−11.2527	−0.542023	−0.271012	+	0.962576i	$0.587358\pi$
$432$	1.00000	0.0481125
$433$	−0.443161	−0.0212969	−0.0106485	−	0.999943i	$-0.503390\pi$
$433$	−0.443161	−0.0212969	−0.0106485	+	0.999943i	$0.503390\pi$
$434$	29.9529	1.43778
$435$	2.57172	0.123305
$436$	13.6736	0.654845
$437$	−0.879511	−0.0420727
$438$	3.56157	0.170178
$439$	−18.9244	−0.903212	−0.451606	−	0.892218i	$-0.649149\pi$
$439$	−18.9244	−0.903212	−0.451606	+	0.892218i	$0.649149\pi$
$440$	−0.586726	−0.0279711
$441$	8.03267	0.382508
$442$	−0.204049	−0.00970560
$443$	4.55574	0.216450	0.108225	−	0.994126i	$-0.465483\pi$
$443$	4.55574	0.216450	0.108225	+	0.994126i	$0.465483\pi$
$444$	9.68872	0.459806
$445$	−3.66935	−0.173944
$446$	15.8632	0.751145
$447$	−6.75794	−0.319640
$448$	3.87720	0.183180
$449$	−5.07426	−0.239469	−0.119735	−	0.992806i	$-0.538204\pi$
$449$	−5.07426	−0.239469	−0.119735	+	0.992806i	$0.538204\pi$
$450$	4.79407	0.225995
$451$	9.55338	0.449851
$452$	−5.72283	−0.269179
$453$	6.66373	0.313089
$454$	−5.41706	−0.254235
$455$	1.75943	0.0824835
$456$	0.475803	0.0222815
$457$	−5.60898	−0.262377	−0.131189	−	0.991357i	$-0.541879\pi$
$457$	−5.60898	−0.262377	−0.131189	+	0.991357i	$0.541879\pi$
$458$	−17.2160	−0.804451
$459$	−0.204049	−0.00952417
$460$	−0.838820	−0.0391102
$461$	9.52366	0.443561	0.221781	−	0.975097i	$-0.428813\pi$
$461$	9.52366	0.443561	0.221781	+	0.975097i	$0.428813\pi$
$462$	5.01301	0.233226
$463$	−12.1793	−0.566021	−0.283011	−	0.959117i	$-0.591333\pi$
$463$	−12.1793	−0.566021	−0.283011	+	0.959117i	$0.591333\pi$
$464$	−5.66720	−0.263093
$465$	3.50570	0.162573
$466$	2.06406	0.0956157
$467$	−5.89842	−0.272946	−0.136473	−	0.990644i	$-0.543577\pi$
$467$	−5.89842	−0.272946	−0.136473	+	0.990644i	$0.543577\pi$
$468$	−1.00000	−0.0462250
$469$	2.62940	0.121415
$470$	−1.41382	−0.0652147
$471$	−13.6895	−0.630779
$472$	13.6380	0.627742
$473$	5.78349	0.265925
$474$	−0.0379441	−0.00174283
$475$	2.28104	0.104661
$476$	−0.791137	−0.0362617
$477$	−2.30074	−0.105344
$478$	8.92571	0.408252
$479$	0.166160	0.00759207	0.00379603	−	0.999993i	$-0.498792\pi$
$479$	0.166160	0.00759207	0.00379603	+	0.999993i	$0.498792\pi$
$480$	0.453790	0.0207126
$481$	−9.68872	−0.441768
$482$	−9.50540	−0.432959
$483$	7.16691	0.326106
$484$	−9.32829	−0.424013
$485$	1.04416	0.0474128
$486$	−1.00000	−0.0453609
$487$	−31.8793	−1.44459	−0.722293	−	0.691587i	$-0.756912\pi$
$487$	−31.8793	−1.44459	−0.722293	+	0.691587i	$0.756912\pi$
$488$	11.4248	0.517178
$489$	−3.83818	−0.173569
$490$	3.64515	0.164671
$491$	35.7593	1.61380	0.806898	−	0.590691i	$-0.201145\pi$
$491$	35.7593	1.61380	0.806898	+	0.590691i	$0.201145\pi$
$492$	−7.38884	−0.333115
$493$	1.15639	0.0520810
$494$	−0.475803	−0.0214074
$495$	0.586726	0.0263714
$496$	−7.72539	−0.346880
$497$	22.7787	1.02176
$498$	7.81001	0.349975
$499$	23.4178	1.04832	0.524162	−	0.851619i	$-0.324379\pi$
$499$	23.4178	1.04832	0.524162	+	0.851619i	$0.324379\pi$
$500$	4.44445	0.198762
$501$	−20.6485	−0.922506
$502$	0.527595	0.0235477
$503$	2.64065	0.117741	0.0588703	−	0.998266i	$-0.481250\pi$
$503$	2.64065	0.117741	0.0588703	+	0.998266i	$0.481250\pi$
$504$	−3.87720	−0.172704
$505$	1.48930	0.0662729
$506$	2.38998	0.106248
$507$	1.00000	0.0444116
$508$	5.32461	0.236241
$509$	23.2141	1.02895	0.514474	−	0.857506i	$-0.327987\pi$
$509$	23.2141	1.02895	0.514474	+	0.857506i	$0.327987\pi$
$510$	−0.0925952	−0.00410019
$511$	−13.8089	−0.610870
$512$	−1.00000	−0.0441942
$513$	−0.475803	−0.0210072
$514$	18.6801	0.823945
$515$	−0.453790	−0.0199964
$516$	−4.47310	−0.196917
$517$	4.02828	0.177164
$518$	−37.5651	−1.65052
$519$	−5.28951	−0.232184
$520$	−0.453790	−0.0199000
$521$	−18.1187	−0.793793	−0.396897	−	0.917863i	$-0.629913\pi$
$521$	−18.1187	−0.793793	−0.396897	+	0.917863i	$0.629913\pi$
$522$	5.66720	0.248047
$523$	−31.7767	−1.38950	−0.694749	−	0.719252i	$-0.744485\pi$
$523$	−31.7767	−1.38950	−0.694749	+	0.719252i	$0.744485\pi$
$524$	−5.11582	−0.223486
$525$	−18.5876	−0.811228
$526$	−15.6935	−0.684269
$527$	1.57635	0.0686671
$528$	−1.29295	−0.0562683
$529$	−19.5831	−0.851441
$530$	−1.04406	−0.0453509
$531$	−13.6380	−0.591840
$532$	−1.84478	−0.0799815
$533$	7.38884	0.320046
$534$	−8.08601	−0.349916
$535$	6.08831	0.263221
$536$	−0.678171	−0.0292925
$537$	15.5884	0.672690
$538$	−7.28894	−0.314249
$539$	−10.3858	−0.447349
$540$	−0.453790	−0.0195280
$541$	−15.8913	−0.683219	−0.341610	−	0.939842i	$-0.610972\pi$
$541$	−15.8913	−0.683219	−0.341610	+	0.939842i	$0.610972\pi$
$542$	11.6259	0.499373
$543$	25.5435	1.09617
$544$	0.204049	0.00874851
$545$	−6.20493	−0.265790
$546$	3.87720	0.165929
$547$	−17.3725	−0.742793	−0.371397	−	0.928474i	$-0.621121\pi$
$547$	−17.3725	−0.742793	−0.371397	+	0.928474i	$0.621121\pi$
$548$	−17.4572	−0.745736
$549$	−11.4248	−0.487600
$550$	−6.19848	−0.264304
$551$	2.69647	0.114874
$552$	−1.84848	−0.0786764
$553$	0.147117	0.00625605
$554$	−19.8613	−0.843824
$555$	−4.39664	−0.186627
$556$	15.5994	0.661560
$557$	−29.2274	−1.23840	−0.619202	−	0.785232i	$-0.712544\pi$
$557$	−29.2274	−1.23840	−0.619202	+	0.785232i	$0.712544\pi$
$558$	7.72539	0.327042
$559$	4.47310	0.189192
$560$	−1.75943	−0.0743497
$561$	0.263824	0.0111387
$562$	8.32906	0.351340
$563$	−2.17941	−0.0918511	−0.0459255	−	0.998945i	$-0.514624\pi$
$563$	−2.17941	−0.0918511	−0.0459255	+	0.998945i	$0.514624\pi$
$564$	−3.11558	−0.131190
$565$	2.59696	0.109255
$566$	−10.7185	−0.450532
$567$	3.87720	0.162827
$568$	−5.87504	−0.246511
$569$	−45.1866	−1.89432	−0.947161	−	0.320760i	$-0.896062\pi$
$569$	−45.1866	−1.89432	−0.947161	+	0.320760i	$0.896062\pi$
$570$	−0.215915	−0.00904368
$571$	−35.1769	−1.47211	−0.736054	−	0.676923i	$-0.763313\pi$
$571$	−35.1769	−1.47211	−0.736054	+	0.676923i	$0.763313\pi$
$572$	1.29295	0.0540608
$573$	−2.83614	−0.118481
$574$	28.6480	1.19575
$575$	−8.86174	−0.369560
$576$	1.00000	0.0416667
$577$	−28.6385	−1.19224	−0.596118	−	0.802897i	$-0.703291\pi$
$577$	−28.6385	−1.19224	−0.596118	+	0.802897i	$0.703291\pi$
$578$	16.9584	0.705375
$579$	−21.2934	−0.884925
$580$	2.57172	0.106785
$581$	−30.2810	−1.25627
$582$	2.30097	0.0953784
$583$	2.97474	0.123201
$584$	3.56157	0.147379
$585$	0.453790	0.0187619
$586$	−4.33001	−0.178871
$587$	−16.6147	−0.685761	−0.342881	−	0.939379i	$-0.611403\pi$
$587$	−16.6147	−0.685761	−0.342881	+	0.939379i	$0.611403\pi$
$588$	8.03267	0.331262
$589$	3.67576	0.151457
$590$	−6.18881	−0.254789
$591$	11.3818	0.468184
$592$	9.68872	0.398204
$593$	44.3734	1.82220	0.911099	−	0.412189i	$-0.135236\pi$
$593$	44.3734	1.82220	0.911099	+	0.412189i	$0.135236\pi$
$594$	1.29295	0.0530502
$595$	0.359010	0.0147180
$596$	−6.75794	−0.276816
$597$	16.0284	0.655999
$598$	1.84848	0.0755898
$599$	11.1662	0.456239	0.228119	−	0.973633i	$-0.426742\pi$
$599$	11.1662	0.456239	0.228119	+	0.973633i	$0.426742\pi$
$600$	4.79407	0.195717
$601$	−33.4940	−1.36625	−0.683124	−	0.730302i	$-0.739379\pi$
$601$	−33.4940	−1.36625	−0.683124	+	0.730302i	$0.739379\pi$
$602$	17.3431	0.706853
$603$	0.678171	0.0276173
$604$	6.66373	0.271143
$605$	4.23308	0.172099
$606$	3.28191	0.133318
$607$	14.4014	0.584533	0.292267	−	0.956337i	$-0.405591\pi$
$607$	14.4014	0.584533	0.292267	+	0.956337i	$0.405591\pi$
$608$	0.475803	0.0192964
$609$	−21.9729	−0.890386
$610$	−5.18447	−0.209913
$611$	3.11558	0.126043
$612$	−0.204049	−0.00824818
$613$	−22.7741	−0.919836	−0.459918	−	0.887961i	$-0.652121\pi$
$613$	−22.7741	−0.919836	−0.459918	+	0.887961i	$0.652121\pi$
$614$	−21.3696	−0.862406
$615$	3.35298	0.135205
$616$	5.01301	0.201980
$617$	36.7666	1.48017	0.740084	−	0.672514i	$-0.234786\pi$
$617$	36.7666	1.48017	0.740084	+	0.672514i	$0.234786\pi$
$618$	−1.00000	−0.0402259
$619$	22.8495	0.918398	0.459199	−	0.888333i	$-0.348136\pi$
$619$	22.8495	0.918398	0.459199	+	0.888333i	$0.348136\pi$
$620$	3.50570	0.140792
$621$	1.84848	0.0741768
$622$	−19.9313	−0.799171
$623$	31.3511	1.25605
$624$	−1.00000	−0.0400320
$625$	21.9535	0.878141
$626$	−18.7275	−0.748500
$627$	0.615188	0.0245683
$628$	−13.6895	−0.546271
$629$	−1.97697	−0.0788269
$630$	1.75943	0.0700975
$631$	6.03358	0.240193	0.120097	−	0.992762i	$-0.461680\pi$
$631$	6.03358	0.240193	0.120097	+	0.992762i	$0.461680\pi$
$632$	−0.0379441	−0.00150934
$633$	18.2423	0.725067
$634$	29.4087	1.16797
$635$	−2.41626	−0.0958862
$636$	−2.30074	−0.0912305
$637$	−8.03267	−0.318266
$638$	−7.32739	−0.290094
$639$	5.87504	0.232413
$640$	0.453790	0.0179376
$641$	−18.5836	−0.734006	−0.367003	−	0.930220i	$-0.619616\pi$
$641$	−18.5836	−0.734006	−0.367003	+	0.930220i	$0.619616\pi$
$642$	13.4166	0.529511
$643$	25.8742	1.02038	0.510190	−	0.860062i	$-0.329575\pi$
$643$	25.8742	1.02038	0.510190	+	0.860062i	$0.329575\pi$
$644$	7.16691	0.282416
$645$	2.02985	0.0799253
$646$	−0.0970870	−0.00381984
$647$	7.09152	0.278797	0.139398	−	0.990236i	$-0.455483\pi$
$647$	7.09152	0.278797	0.139398	+	0.990236i	$0.455483\pi$
$648$	−1.00000	−0.0392837
$649$	17.6333	0.692166
$650$	−4.79407	−0.188039
$651$	−29.9529	−1.17395
$652$	−3.83818	−0.150315
$653$	19.5477	0.764962	0.382481	−	0.923963i	$-0.375070\pi$
$653$	19.5477	0.764962	0.382481	+	0.923963i	$0.375070\pi$
$654$	−13.6736	−0.534679
$655$	2.32151	0.0907088
$656$	−7.38884	−0.288486
$657$	−3.56157	−0.138950
$658$	12.0797	0.470917
$659$	−42.0542	−1.63820	−0.819099	−	0.573653i	$-0.805526\pi$
$659$	−42.0542	−1.63820	−0.819099	+	0.573653i	$0.805526\pi$
$660$	0.586726	0.0228383
$661$	−19.6058	−0.762576	−0.381288	−	0.924456i	$-0.624519\pi$
$661$	−19.6058	−0.762576	−0.381288	+	0.924456i	$0.624519\pi$
$662$	15.8151	0.614673
$663$	0.204049	0.00792459
$664$	7.81001	0.303087
$665$	0.837145	0.0324631
$666$	−9.68872	−0.375430
$667$	−10.4757	−0.405621
$668$	−20.6485	−0.798913
$669$	−15.8632	−0.613307
$670$	0.307747	0.0118893
$671$	14.7717	0.570255
$672$	−3.87720	−0.149566
$673$	−2.51438	−0.0969222	−0.0484611	−	0.998825i	$-0.515432\pi$
$673$	−2.51438	−0.0969222	−0.0484611	+	0.998825i	$0.515432\pi$
$674$	−14.2786	−0.549990
$675$	−4.79407	−0.184524
$676$	1.00000	0.0384615
$677$	3.82779	0.147114	0.0735569	−	0.997291i	$-0.476565\pi$
$677$	3.82779	0.147114	0.0735569	+	0.997291i	$0.476565\pi$
$678$	5.72283	0.219784
$679$	−8.92133	−0.342369
$680$	−0.0925952	−0.00355087
$681$	5.41706	0.207582
$682$	−9.98851	−0.382480
$683$	5.50265	0.210553	0.105276	−	0.994443i	$-0.466427\pi$
$683$	5.50265	0.210553	0.105276	+	0.994443i	$0.466427\pi$
$684$	−0.475803	−0.0181928
$685$	7.92192	0.302681
$686$	−4.00386	−0.152868
$687$	17.2160	0.656831
$688$	−4.47310	−0.170536
$689$	2.30074	0.0876514
$690$	0.838820	0.0319333
$691$	−20.1534	−0.766670	−0.383335	−	0.923609i	$-0.625224\pi$
$691$	−20.1534	−0.766670	−0.383335	+	0.923609i	$0.625224\pi$
$692$	−5.28951	−0.201077
$693$	−5.01301	−0.190429
$694$	−1.58327	−0.0601002
$695$	−7.07884	−0.268516
$696$	5.66720	0.214815
$697$	1.50768	0.0571076
$698$	22.0059	0.832937
$699$	−2.06406	−0.0780699
$700$	−18.5876	−0.702544
$701$	−25.0943	−0.947798	−0.473899	−	0.880579i	$-0.657154\pi$
$701$	−25.0943	−0.947798	−0.473899	+	0.880579i	$0.657154\pi$
$702$	1.00000	0.0377426
$703$	−4.60992	−0.173867
$704$	−1.29295	−0.0487298
$705$	1.41382	0.0532476
$706$	−14.1320	−0.531865
$707$	−12.7246	−0.478558
$708$	−13.6380	−0.512549
$709$	−2.53504	−0.0952053	−0.0476026	−	0.998866i	$-0.515158\pi$
$709$	−2.53504	−0.0952053	−0.0476026	+	0.998866i	$0.515158\pi$
$710$	2.66604	0.100055
$711$	0.0379441	0.00142302
$712$	−8.08601	−0.303036
$713$	−14.2802	−0.534798
$714$	0.791137	0.0296076
$715$	−0.586726	−0.0219423
$716$	15.5884	0.582567
$717$	−8.92571	−0.333337
$718$	7.97890	0.297770
$719$	4.04303	0.150780	0.0753899	−	0.997154i	$-0.475980\pi$
$719$	4.04303	0.150780	0.0753899	+	0.997154i	$0.475980\pi$
$720$	−0.453790	−0.0169118
$721$	3.87720	0.144394
$722$	18.7736	0.698681
$723$	9.50540	0.353509
$724$	25.5435	0.949315
$725$	27.1690	1.00903
$726$	9.32829	0.346205
$727$	2.60500	0.0966140	0.0483070	−	0.998833i	$-0.484617\pi$
$727$	2.60500	0.0966140	0.0483070	+	0.998833i	$0.484617\pi$
$728$	3.87720	0.143699
$729$	1.00000	0.0370370
$730$	−1.61620	−0.0598184
$731$	0.912731	0.0337586
$732$	−11.4248	−0.422274
$733$	−19.9473	−0.736772	−0.368386	−	0.929673i	$-0.620089\pi$
$733$	−19.9473	−0.736772	−0.368386	+	0.929673i	$0.620089\pi$
$734$	−21.7801	−0.803917
$735$	−3.64515	−0.134453
$736$	−1.84848	−0.0681358
$737$	−0.876839	−0.0322988
$738$	7.38884	0.271987
$739$	−51.6136	−1.89864	−0.949318	−	0.314316i	$-0.898225\pi$
$739$	−51.6136	−1.89864	−0.949318	+	0.314316i	$0.898225\pi$
$740$	−4.39664	−0.161624
$741$	0.475803	0.0174791
$742$	8.92044	0.327480
$743$	21.7795	0.799012	0.399506	−	0.916730i	$-0.369182\pi$
$743$	21.7795	0.799012	0.399506	+	0.916730i	$0.369182\pi$
$744$	7.72539	0.283226
$745$	3.06669	0.112355
$746$	22.1999	0.812795
$747$	−7.81001	−0.285753
$748$	0.263824	0.00964636
$749$	−52.0188	−1.90072
$750$	−4.44445	−0.162288
$751$	11.1206	0.405795	0.202898	−	0.979200i	$-0.434964\pi$
$751$	11.1206	0.405795	0.202898	+	0.979200i	$0.434964\pi$
$752$	−3.11558	−0.113614
$753$	−0.527595	−0.0192266
$754$	−5.66720	−0.206387
$755$	−3.02394	−0.110052
$756$	3.87720	0.141012
$757$	36.0724	1.31107	0.655537	−	0.755163i	$-0.272442\pi$
$757$	36.0724	1.31107	0.655537	+	0.755163i	$0.272442\pi$
$758$	−14.0417	−0.510016
$759$	−2.38998	−0.0867508
$760$	−0.215915	−0.00783205
$761$	−9.66051	−0.350193	−0.175097	−	0.984551i	$-0.556024\pi$
$761$	−9.66051	−0.350193	−0.175097	+	0.984551i	$0.556024\pi$
$762$	−5.32461	−0.192890
$763$	53.0151	1.91928
$764$	−2.83614	−0.102608
$765$	0.0925952	0.00334779
$766$	−25.5397	−0.922785
$767$	13.6380	0.492441
$768$	1.00000	0.0360844
$769$	20.1651	0.727172	0.363586	−	0.931561i	$-0.381552\pi$
$769$	20.1651	0.727172	0.363586	+	0.931561i	$0.381552\pi$
$770$	−2.27485	−0.0819801
$771$	−18.6801	−0.672748
$772$	−21.2934	−0.766368
$773$	32.0968	1.15444	0.577221	−	0.816588i	$-0.304137\pi$
$773$	32.0968	1.15444	0.577221	+	0.816588i	$0.304137\pi$
$774$	4.47310	0.160782
$775$	37.0361	1.33038
$776$	2.30097	0.0826001
$777$	37.5651	1.34764
$778$	−19.7650	−0.708609
$779$	3.51564	0.125961
$780$	0.453790	0.0162483
$781$	−7.59612	−0.271810
$782$	0.377179	0.0134879
$783$	−5.66720	−0.202529
$784$	8.03267	0.286881
$785$	6.21216	0.221722
$786$	5.11582	0.182475
$787$	−23.4264	−0.835060	−0.417530	−	0.908663i	$-0.637104\pi$
$787$	−23.4264	−0.835060	−0.417530	+	0.908663i	$0.637104\pi$
$788$	11.3818	0.405459
$789$	15.6935	0.558704
$790$	0.0172187	0.000612613 0
$791$	−22.1886	−0.788934
$792$	1.29295	0.0459429
$793$	11.4248	0.405707
$794$	−20.1910	−0.716553
$795$	1.04406	0.0370288
$796$	16.0284	0.568112
$797$	−37.8892	−1.34210	−0.671052	−	0.741410i	$-0.734157\pi$
$797$	−37.8892	−1.34210	−0.671052	+	0.741410i	$0.734157\pi$
$798$	1.84478	0.0653046
$799$	0.635730	0.0224905
$800$	4.79407	0.169496
$801$	8.08601	0.285705
$802$	−12.9075	−0.455778
$803$	4.60492	0.162504
$804$	0.678171	0.0239172
$805$	−3.25227	−0.114628
$806$	−7.72539	−0.272115
$807$	7.28894	0.256583
$808$	3.28191	0.115457
$809$	−26.5488	−0.933407	−0.466703	−	0.884414i	$-0.654558\pi$
$809$	−26.5488	−0.933407	−0.466703	+	0.884414i	$0.654558\pi$
$810$	0.453790	0.0159446
$811$	25.8198	0.906656	0.453328	−	0.891344i	$-0.350237\pi$
$811$	25.8198	0.906656	0.453328	+	0.891344i	$0.350237\pi$
$812$	−21.9729	−0.771097
$813$	−11.6259	−0.407737
$814$	12.5270	0.439071
$815$	1.74173	0.0610101
$816$	−0.204049	−0.00714313
$817$	2.12832	0.0744604
$818$	−20.8045	−0.727412
$819$	−3.87720	−0.135480
$820$	3.35298	0.117091
$821$	−24.6861	−0.861552	−0.430776	−	0.902459i	$-0.641760\pi$
$821$	−24.6861	−0.861552	−0.430776	+	0.902459i	$0.641760\pi$
$822$	17.4572	0.608891
$823$	−18.5367	−0.646150	−0.323075	−	0.946373i	$-0.604717\pi$
$823$	−18.5367	−0.646150	−0.323075	+	0.946373i	$0.604717\pi$
$824$	−1.00000	−0.0348367
$825$	6.19848	0.215803
$826$	52.8774	1.83984
$827$	14.6031	0.507799	0.253900	−	0.967231i	$-0.418287\pi$
$827$	14.6031	0.507799	0.253900	+	0.967231i	$0.418287\pi$
$828$	1.84848	0.0642390
$829$	51.1255	1.77566	0.887832	−	0.460168i	$-0.152211\pi$
$829$	51.1255	1.77566	0.887832	+	0.460168i	$0.152211\pi$
$830$	−3.54410	−0.123018
$831$	19.8613	0.688979
$832$	−1.00000	−0.0346688
$833$	−1.63906	−0.0567899
$834$	−15.5994	−0.540162
$835$	9.37007	0.324265
$836$	0.615188	0.0212767
$837$	−7.72539	−0.267028
$838$	1.39954	0.0483463
$839$	15.5369	0.536394	0.268197	−	0.963364i	$-0.413572\pi$
$839$	15.5369	0.536394	0.268197	+	0.963364i	$0.413572\pi$
$840$	1.75943	0.0607062
$841$	3.11720	0.107490
$842$	25.4738	0.877885
$843$	−8.32906	−0.286868
$844$	18.2423	0.627927
$845$	−0.453790	−0.0156109
$846$	3.11558	0.107116
$847$	−36.1676	−1.24273
$848$	−2.30074	−0.0790079
$849$	10.7185	0.367858
$850$	−0.978224	−0.0335528
$851$	17.9094	0.613925
$852$	5.87504	0.201276
$853$	41.9137	1.43510	0.717548	−	0.696509i	$-0.245264\pi$
$853$	41.9137	1.43510	0.717548	+	0.696509i	$0.245264\pi$
$854$	44.2963	1.51579
$855$	0.215915	0.00738413
$856$	13.4166	0.458570
$857$	26.2430	0.896443	0.448222	−	0.893922i	$-0.352058\pi$
$857$	26.2430	0.896443	0.448222	+	0.893922i	$0.352058\pi$
$858$	−1.29295	−0.0441405
$859$	37.8711	1.29215	0.646073	−	0.763276i	$-0.276410\pi$
$859$	37.8711	1.29215	0.646073	+	0.763276i	$0.276410\pi$
$860$	2.02985	0.0692173
$861$	−28.6480	−0.976322
$862$	11.2527	0.383268
$863$	−47.3270	−1.61103	−0.805515	−	0.592575i	$-0.798111\pi$
$863$	−47.3270	−1.61103	−0.805515	+	0.592575i	$0.798111\pi$
$864$	−1.00000	−0.0340207
$865$	2.40033	0.0816135
$866$	0.443161	0.0150592
$867$	−16.9584	−0.575936
$868$	−29.9529	−1.01667
$869$	−0.0490597	−0.00166424
$870$	−2.57172	−0.0871895
$871$	−0.678171	−0.0229789
$872$	−13.6736	−0.463045
$873$	−2.30097	−0.0778761
$874$	0.879511	0.0297499
$875$	17.2320	0.582549
$876$	−3.56157	−0.120334
$877$	−20.0068	−0.675580	−0.337790	−	0.941222i	$-0.609679\pi$
$877$	−20.0068	−0.675580	−0.337790	+	0.941222i	$0.609679\pi$
$878$	18.9244	0.638667
$879$	4.33001	0.146048
$880$	0.586726	0.0197785
$881$	31.5624	1.06336	0.531682	−	0.846944i	$-0.321560\pi$
$881$	31.5624	1.06336	0.531682	+	0.846944i	$0.321560\pi$
$882$	−8.03267	−0.270474
$883$	−2.71537	−0.0913795	−0.0456898	−	0.998956i	$-0.514549\pi$
$883$	−2.71537	−0.0913795	−0.0456898	+	0.998956i	$0.514549\pi$
$884$	0.204049	0.00686290
$885$	6.18881	0.208034
$886$	−4.55574	−0.153053
$887$	43.4841	1.46005	0.730026	−	0.683419i	$-0.239508\pi$
$887$	43.4841	1.46005	0.730026	+	0.683419i	$0.239508\pi$
$888$	−9.68872	−0.325132
$889$	20.6446	0.692397
$890$	3.66935	0.122997
$891$	−1.29295	−0.0433153
$892$	−15.8632	−0.531140
$893$	1.48240	0.0496068
$894$	6.75794	0.226019
$895$	−7.07387	−0.236453
$896$	−3.87720	−0.129528
$897$	−1.84848	−0.0617188
$898$	5.07426	0.169330
$899$	43.7813	1.46019
$900$	−4.79407	−0.159802
$901$	0.469464	0.0156401
$902$	−9.55338	−0.318093
$903$	−17.3431	−0.577143
$904$	5.72283	0.190339
$905$	−11.5914	−0.385310
$906$	−6.66373	−0.221388
$907$	23.9681	0.795847	0.397923	−	0.917419i	$-0.369731\pi$
$907$	23.9681	0.795847	0.397923	+	0.917419i	$0.369731\pi$
$908$	5.41706	0.179772
$909$	−3.28191	−0.108854
$910$	−1.75943	−0.0583247
$911$	−4.28155	−0.141854	−0.0709271	−	0.997482i	$-0.522596\pi$
$911$	−4.28155	−0.141854	−0.0709271	+	0.997482i	$0.522596\pi$
$912$	−0.475803	−0.0157554
$913$	10.0979	0.334193
$914$	5.60898	0.185529
$915$	5.18447	0.171393
$916$	17.2160	0.568833
$917$	−19.8350	−0.655011
$918$	0.204049	0.00673461
$919$	−59.3392	−1.95742	−0.978709	−	0.205252i	$-0.934198\pi$
$919$	−59.3392	−1.95742	−0.978709	+	0.205252i	$0.934198\pi$
$920$	0.838820	0.0276551
$921$	21.3696	0.704151
$922$	−9.52366	−0.313645
$923$	−5.87504	−0.193379
$924$	−5.01301	−0.164916
$925$	−46.4484	−1.52722
$926$	12.1793	0.400237
$927$	1.00000	0.0328443
$928$	5.66720	0.186035
$929$	−49.2330	−1.61528	−0.807641	−	0.589674i	$-0.799256\pi$
$929$	−49.2330	−1.61528	−0.807641	+	0.589674i	$0.799256\pi$
$930$	−3.50570	−0.114957
$931$	−3.82197	−0.125260
$932$	−2.06406	−0.0676105
$933$	19.9313	0.652520
$934$	5.89842	0.193002
$935$	−0.119721	−0.00391529
$936$	1.00000	0.0326860
$937$	20.1812	0.659292	0.329646	−	0.944105i	$-0.393071\pi$
$937$	20.1812	0.659292	0.329646	+	0.944105i	$0.393071\pi$
$938$	−2.62940	−0.0858531
$939$	18.7275	0.611148
$940$	1.41382	0.0461137
$941$	−1.28784	−0.0419823	−0.0209911	−	0.999780i	$-0.506682\pi$
$941$	−1.28784	−0.0419823	−0.0209911	+	0.999780i	$0.506682\pi$
$942$	13.6895	0.446028
$943$	−13.6581	−0.444769
$944$	−13.6380	−0.443880
$945$	−1.75943	−0.0572344
$946$	−5.78349	−0.188037
$947$	−11.7884	−0.383071	−0.191535	−	0.981486i	$-0.561347\pi$
$947$	−11.7884	−0.383071	−0.191535	+	0.981486i	$0.561347\pi$
$948$	0.0379441	0.00123237
$949$	3.56157	0.115613
$950$	−2.28104	−0.0740066
$951$	−29.4087	−0.953643
$952$	0.791137	0.0256409
$953$	1.24913	0.0404632	0.0202316	−	0.999795i	$-0.493560\pi$
$953$	1.24913	0.0404632	0.0202316	+	0.999795i	$0.493560\pi$
$954$	2.30074	0.0744894
$955$	1.28701	0.0416467
$956$	−8.92571	−0.288678
$957$	7.32739	0.236861
$958$	−0.166160	−0.00536840
$959$	−67.6852	−2.18567
$960$	−0.453790	−0.0146460
$961$	28.6816	0.925213
$962$	9.68872	0.312377
$963$	−13.4166	−0.432344
$964$	9.50540	0.306148
$965$	9.66275	0.311055
$966$	−7.16691	−0.230592
$967$	−52.6500	−1.69311	−0.846556	−	0.532300i	$-0.821328\pi$
$967$	−52.6500	−1.69311	−0.846556	+	0.532300i	$0.821328\pi$
$968$	9.32829	0.299823
$969$	0.0970870	0.00311888
$970$	−1.04416	−0.0335259
$971$	−25.1840	−0.808193	−0.404096	−	0.914716i	$-0.632414\pi$
$971$	−25.1840	−0.808193	−0.404096	+	0.914716i	$0.632414\pi$
$972$	1.00000	0.0320750
$973$	60.4818	1.93896
$974$	31.8793	1.02148
$975$	4.79407	0.153533
$976$	−11.4248	−0.365700
$977$	−19.2605	−0.616197	−0.308098	−	0.951354i	$-0.599693\pi$
$977$	−19.2605	−0.616197	−0.308098	+	0.951354i	$0.599693\pi$
$978$	3.83818	0.122732
$979$	−10.4548	−0.334136
$980$	−3.64515	−0.116440
$981$	13.6736	0.436563
$982$	−35.7593	−1.14113
$983$	−50.5635	−1.61273	−0.806363	−	0.591421i	$-0.798567\pi$
$983$	−50.5635	−1.61273	−0.806363	+	0.591421i	$0.798567\pi$
$984$	7.38884	0.235548
$985$	−5.16494	−0.164569
$986$	−1.15639	−0.0368268
$987$	−12.0797	−0.384502
$988$	0.475803	0.0151373
$989$	−8.26843	−0.262921
$990$	−0.586726	−0.0186474
$991$	56.3374	1.78962	0.894808	−	0.446450i	$-0.147312\pi$
$991$	56.3374	1.78962	0.894808	+	0.446450i	$0.147312\pi$
$992$	7.72539	0.245281
$993$	−15.8151	−0.501878
$994$	−22.7787	−0.722497
$995$	−7.27353	−0.230587
$996$	−7.81001	−0.247470
$997$	18.3016	0.579616	0.289808	−	0.957085i	$-0.406409\pi$
$997$	18.3016	0.579616	0.289808	+	0.957085i	$0.406409\pi$
$998$	−23.4178	−0.741277
$999$	9.68872	0.306537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.bb.1.7	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.bb.1.7	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.453790 q^{5} -1.00000 q^{6} +3.87720 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -0.453790 q^{5} -1.00000 q^{6} +3.87720 q^{7} -1.00000 q^{8} +1.00000 q^{9} +0.453790 q^{10} -1.29295 q^{11} +1.00000 q^{12} -1.00000 q^{13} -3.87720 q^{14} -0.453790 q^{15} +1.00000 q^{16} -0.204049 q^{17} -1.00000 q^{18} -0.475803 q^{19} -0.453790 q^{20} +3.87720 q^{21} +1.29295 q^{22} +1.84848 q^{23} -1.00000 q^{24} -4.79407 q^{25} +1.00000 q^{26} +1.00000 q^{27} +3.87720 q^{28} -5.66720 q^{29} +0.453790 q^{30} -7.72539 q^{31} -1.00000 q^{32} -1.29295 q^{33} +0.204049 q^{34} -1.75943 q^{35} +1.00000 q^{36} +9.68872 q^{37} +0.475803 q^{38} -1.00000 q^{39} +0.453790 q^{40} -7.38884 q^{41} -3.87720 q^{42} -4.47310 q^{43} -1.29295 q^{44} -0.453790 q^{45} -1.84848 q^{46} -3.11558 q^{47} +1.00000 q^{48} +8.03267 q^{49} +4.79407 q^{50} -0.204049 q^{51} -1.00000 q^{52} -2.30074 q^{53} -1.00000 q^{54} +0.586726 q^{55} -3.87720 q^{56} -0.475803 q^{57} +5.66720 q^{58} -13.6380 q^{59} -0.453790 q^{60} -11.4248 q^{61} +7.72539 q^{62} +3.87720 q^{63} +1.00000 q^{64} +0.453790 q^{65} +1.29295 q^{66} +0.678171 q^{67} -0.204049 q^{68} +1.84848 q^{69} +1.75943 q^{70} +5.87504 q^{71} -1.00000 q^{72} -3.56157 q^{73} -9.68872 q^{74} -4.79407 q^{75} -0.475803 q^{76} -5.01301 q^{77} +1.00000 q^{78} +0.0379441 q^{79} -0.453790 q^{80} +1.00000 q^{81} +7.38884 q^{82} -7.81001 q^{83} +3.87720 q^{84} +0.0925952 q^{85} +4.47310 q^{86} -5.66720 q^{87} +1.29295 q^{88} +8.08601 q^{89} +0.453790 q^{90} -3.87720 q^{91} +1.84848 q^{92} -7.72539 q^{93} +3.11558 q^{94} +0.215915 q^{95} -1.00000 q^{96} -2.30097 q^{97} -8.03267 q^{98} -1.29295 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9	\( 14 q - 14 q^{2} + 14 q^{3} + 14 q^{4} - 6 q^{5} - 14 q^{6} - 4 q^{7} - 14 q^{8} + 14 q^{9} + 6 q^{10} - 8 q^{11} + 14 q^{12} - 14 q^{13} + 4 q^{14} - 6 q^{15} + 14 q^{16} - 4 q^{17} - 14 q^{18} - q^{19} - 6 q^{20} - 4 q^{21} + 8 q^{22} - 9 q^{23} - 14 q^{24} + 24 q^{25} + 14 q^{26} + 14 q^{27} - 4 q^{28} - 10 q^{29} + 6 q^{30} - 5 q^{31} - 14 q^{32} - 8 q^{33} + 4 q^{34} - 16 q^{35} + 14 q^{36} - 4 q^{37} + q^{38} - 14 q^{39} + 6 q^{40} - 24 q^{41} + 4 q^{42} - 8 q^{44} - 6 q^{45} + 9 q^{46} - 32 q^{47} + 14 q^{48} + 24 q^{49} - 24 q^{50} - 4 q^{51} - 14 q^{52} - 5 q^{53} - 14 q^{54} - 8 q^{55} + 4 q^{56} - q^{57} + 10 q^{58} - 13 q^{59} - 6 q^{60} + 2 q^{61} + 5 q^{62} - 4 q^{63} + 14 q^{64} + 6 q^{65} + 8 q^{66} - 16 q^{67} - 4 q^{68} - 9 q^{69} + 16 q^{70} - 29 q^{71} - 14 q^{72} + 4 q^{74} + 24 q^{75} - q^{76} - 9 q^{77} + 14 q^{78} - 21 q^{79} - 6 q^{80} + 14 q^{81} + 24 q^{82} - 40 q^{83} - 4 q^{84} - 7 q^{85} - 10 q^{87} + 8 q^{88} - 48 q^{89} + 6 q^{90} + 4 q^{91} - 9 q^{92} - 5 q^{93} + 32 q^{94} - 26 q^{95} - 14 q^{96} + 18 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 14 * q - 14 * q^2 + 14 * q^3 + 14 * q^4 - 6 * q^5 - 14 * q^6 - 4 * q^7 - 14 * q^8 + 14 * q^9 + 6 * q^10 - 8 * q^11 + 14 * q^12 - 14 * q^13 + 4 * q^14 - 6 * q^15 + 14 * q^16 - 4 * q^17 - 14 * q^18 - q^19 - 6 * q^20 - 4 * q^21 + 8 * q^22 - 9 * q^23 - 14 * q^24 + 24 * q^25 + 14 * q^26 + 14 * q^27 - 4 * q^28 - 10 * q^29 + 6 * q^30 - 5 * q^31 - 14 * q^32 - 8 * q^33 + 4 * q^34 - 16 * q^35 + 14 * q^36 - 4 * q^37 + q^38 - 14 * q^39 + 6 * q^40 - 24 * q^41 + 4 * q^42 - 8 * q^44 - 6 * q^45 + 9 * q^46 - 32 * q^47 + 14 * q^48 + 24 * q^49 - 24 * q^50 - 4 * q^51 - 14 * q^52 - 5 * q^53 - 14 * q^54 - 8 * q^55 + 4 * q^56 - q^57 + 10 * q^58 - 13 * q^59 - 6 * q^60 + 2 * q^61 + 5 * q^62 - 4 * q^63 + 14 * q^64 + 6 * q^65 + 8 * q^66 - 16 * q^67 - 4 * q^68 - 9 * q^69 + 16 * q^70 - 29 * q^71 - 14 * q^72 + 4 * q^74 + 24 * q^75 - q^76 - 9 * q^77 + 14 * q^78 - 21 * q^79 - 6 * q^80 + 14 * q^81 + 24 * q^82 - 40 * q^83 - 4 * q^84 - 7 * q^85 - 10 * q^87 + 8 * q^88 - 48 * q^89 + 6 * q^90 + 4 * q^91 - 9 * q^92 - 5 * q^93 + 32 * q^94 - 26 * q^95 - 14 * q^96 + 18 * q^97 - 24 * q^98 - 8 * q^99

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