LMFDB - Embedded newform 8034.2.a.x.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - x^{12} - 40 x^{11} + 34 x^{10} + 604 x^{9} - 381 x^{8} - 4352 x^{7} + 1474 x^{6} + 15809 x^{5} + \cdots + 8832 $ x^13 - x^12 - 40x^11 + 34x^10 + 604x^9 - 381x^8 - 4352x^7 + 1474x^6 + 15809x^5 - 368x^4 - 27369x^3 - 7621x^2 + 17300*x + 8832
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-2.01149$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.01149 q^{5} -1.00000 q^{6} +0.821182 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.01149 q^{5} -1.00000 q^{6} +0.821182 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.01149 q^{10} -4.01401 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.821182 q^{14} -2.01149 q^{15} +1.00000 q^{16} +5.69670 q^{17} -1.00000 q^{18} -7.47060 q^{19} -2.01149 q^{20} +0.821182 q^{21} +4.01401 q^{22} +6.57569 q^{23} -1.00000 q^{24} -0.953907 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.821182 q^{28} +6.26676 q^{29} +2.01149 q^{30} +3.73369 q^{31} -1.00000 q^{32} -4.01401 q^{33} -5.69670 q^{34} -1.65180 q^{35} +1.00000 q^{36} +5.38725 q^{37} +7.47060 q^{38} +1.00000 q^{39} +2.01149 q^{40} +10.3207 q^{41} -0.821182 q^{42} -6.06943 q^{43} -4.01401 q^{44} -2.01149 q^{45} -6.57569 q^{46} -6.22769 q^{47} +1.00000 q^{48} -6.32566 q^{49} +0.953907 q^{50} +5.69670 q^{51} +1.00000 q^{52} -7.76530 q^{53} -1.00000 q^{54} +8.07413 q^{55} -0.821182 q^{56} -7.47060 q^{57} -6.26676 q^{58} +1.22066 q^{59} -2.01149 q^{60} -12.6859 q^{61} -3.73369 q^{62} +0.821182 q^{63} +1.00000 q^{64} -2.01149 q^{65} +4.01401 q^{66} +13.8320 q^{67} +5.69670 q^{68} +6.57569 q^{69} +1.65180 q^{70} -12.0421 q^{71} -1.00000 q^{72} -1.91417 q^{73} -5.38725 q^{74} -0.953907 q^{75} -7.47060 q^{76} -3.29623 q^{77} -1.00000 q^{78} -4.90081 q^{79} -2.01149 q^{80} +1.00000 q^{81} -10.3207 q^{82} -8.34909 q^{83} +0.821182 q^{84} -11.4589 q^{85} +6.06943 q^{86} +6.26676 q^{87} +4.01401 q^{88} +6.85911 q^{89} +2.01149 q^{90} +0.821182 q^{91} +6.57569 q^{92} +3.73369 q^{93} +6.22769 q^{94} +15.0270 q^{95} -1.00000 q^{96} -6.26340 q^{97} +6.32566 q^{98} -4.01401 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * 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
$5$	−2.01149	−0.899566	−0.449783	−	0.893138i	$-0.648499\pi$
$5$	−2.01149	−0.899566	−0.449783	+	0.893138i	$0.648499\pi$
$6$	−1.00000	−0.408248
$7$	0.821182	0.310377	0.155189	−	0.987885i	$-0.450401\pi$
$7$	0.821182	0.310377	0.155189	+	0.987885i	$0.450401\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.01149	0.636089
$11$	−4.01401	−1.21027	−0.605134	−	0.796123i	$-0.706881\pi$
$11$	−4.01401	−1.21027	−0.605134	+	0.796123i	$0.706881\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.821182	−0.219470
$15$	−2.01149	−0.519365
$16$	1.00000	0.250000
$17$	5.69670	1.38165	0.690826	−	0.723021i	$-0.257247\pi$
$17$	5.69670	1.38165	0.690826	+	0.723021i	$0.257247\pi$
$18$	−1.00000	−0.235702
$19$	−7.47060	−1.71387	−0.856937	−	0.515422i	$-0.827635\pi$
$19$	−7.47060	−1.71387	−0.856937	+	0.515422i	$0.827635\pi$
$20$	−2.01149	−0.449783
$21$	0.821182	0.179196
$22$	4.01401	0.855789
$23$	6.57569	1.37113	0.685563	−	0.728013i	$-0.259556\pi$
$23$	6.57569	1.37113	0.685563	+	0.728013i	$0.259556\pi$
$24$	−1.00000	−0.204124
$25$	−0.953907	−0.190781
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	0.821182	0.155189
$29$	6.26676	1.16371	0.581854	−	0.813293i	$-0.302327\pi$
$29$	6.26676	1.16371	0.581854	+	0.813293i	$0.302327\pi$
$30$	2.01149	0.367246
$31$	3.73369	0.670591	0.335296	−	0.942113i	$-0.391164\pi$
$31$	3.73369	0.670591	0.335296	+	0.942113i	$0.391164\pi$
$32$	−1.00000	−0.176777
$33$	−4.01401	−0.698749
$34$	−5.69670	−0.976976
$35$	−1.65180	−0.279205
$36$	1.00000	0.166667
$37$	5.38725	0.885659	0.442830	−	0.896606i	$-0.353975\pi$
$37$	5.38725	0.885659	0.442830	+	0.896606i	$0.353975\pi$
$38$	7.47060	1.21189
$39$	1.00000	0.160128
$40$	2.01149	0.318045
$41$	10.3207	1.61183	0.805913	−	0.592034i	$-0.201675\pi$
$41$	10.3207	1.61183	0.805913	+	0.592034i	$0.201675\pi$
$42$	−0.821182	−0.126711
$43$	−6.06943	−0.925579	−0.462790	−	0.886468i	$-0.653151\pi$
$43$	−6.06943	−0.925579	−0.462790	+	0.886468i	$0.653151\pi$
$44$	−4.01401	−0.605134
$45$	−2.01149	−0.299855
$46$	−6.57569	−0.969532
$47$	−6.22769	−0.908402	−0.454201	−	0.890899i	$-0.650075\pi$
$47$	−6.22769	−0.908402	−0.454201	+	0.890899i	$0.650075\pi$
$48$	1.00000	0.144338
$49$	−6.32566	−0.903666
$50$	0.953907	0.134903
$51$	5.69670	0.797698
$52$	1.00000	0.138675
$53$	−7.76530	−1.06665	−0.533323	−	0.845912i	$-0.679057\pi$
$53$	−7.76530	−1.06665	−0.533323	+	0.845912i	$0.679057\pi$
$54$	−1.00000	−0.136083
$55$	8.07413	1.08872
$56$	−0.821182	−0.109735
$57$	−7.47060	−0.989505
$58$	−6.26676	−0.822866
$59$	1.22066	0.158917	0.0794585	−	0.996838i	$-0.474681\pi$
$59$	1.22066	0.158917	0.0794585	+	0.996838i	$0.474681\pi$
$60$	−2.01149	−0.259682
$61$	−12.6859	−1.62427	−0.812134	−	0.583471i	$-0.801694\pi$
$61$	−12.6859	−1.62427	−0.812134	+	0.583471i	$0.801694\pi$
$62$	−3.73369	−0.474180
$63$	0.821182	0.103459
$64$	1.00000	0.125000
$65$	−2.01149	−0.249495
$66$	4.01401	0.494090
$67$	13.8320	1.68985	0.844924	−	0.534886i	$-0.179645\pi$
$67$	13.8320	1.68985	0.844924	+	0.534886i	$0.179645\pi$
$68$	5.69670	0.690826
$69$	6.57569	0.791620
$70$	1.65180	0.197428
$71$	−12.0421	−1.42913	−0.714567	−	0.699567i	$-0.753376\pi$
$71$	−12.0421	−1.42913	−0.714567	+	0.699567i	$0.753376\pi$
$72$	−1.00000	−0.117851
$73$	−1.91417	−0.224037	−0.112018	−	0.993706i	$-0.535732\pi$
$73$	−1.91417	−0.224037	−0.112018	+	0.993706i	$0.535732\pi$
$74$	−5.38725	−0.626256
$75$	−0.953907	−0.110148
$76$	−7.47060	−0.856937
$77$	−3.29623	−0.375640
$78$	−1.00000	−0.113228
$79$	−4.90081	−0.551384	−0.275692	−	0.961246i	$-0.588907\pi$
$79$	−4.90081	−0.551384	−0.275692	+	0.961246i	$0.588907\pi$
$80$	−2.01149	−0.224891
$81$	1.00000	0.111111
$82$	−10.3207	−1.13973
$83$	−8.34909	−0.916432	−0.458216	−	0.888841i	$-0.651511\pi$
$83$	−8.34909	−0.916432	−0.458216	+	0.888841i	$0.651511\pi$
$84$	0.821182	0.0895982
$85$	−11.4589	−1.24289
$86$	6.06943	0.654483
$87$	6.26676	0.671867
$88$	4.01401	0.427895
$89$	6.85911	0.727064	0.363532	−	0.931582i	$-0.381571\pi$
$89$	6.85911	0.727064	0.363532	+	0.931582i	$0.381571\pi$
$90$	2.01149	0.212030
$91$	0.821182	0.0860832
$92$	6.57569	0.685563
$93$	3.73369	0.387166
$94$	6.22769	0.642337
$95$	15.0270	1.54174
$96$	−1.00000	−0.102062
$97$	−6.26340	−0.635952	−0.317976	−	0.948099i	$-0.603003\pi$
$97$	−6.26340	−0.635952	−0.317976	+	0.948099i	$0.603003\pi$
$98$	6.32566	0.638988
$99$	−4.01401	−0.403423
$100$	−0.953907	−0.0953907
$101$	3.28354	0.326724	0.163362	−	0.986566i	$-0.447766\pi$
$101$	3.28354	0.326724	0.163362	+	0.986566i	$0.447766\pi$
$102$	−5.69670	−0.564057
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	−1.65180	−0.161199
$106$	7.76530	0.754233
$107$	15.0879	1.45860	0.729301	−	0.684193i	$-0.239845\pi$
$107$	15.0879	1.45860	0.729301	+	0.684193i	$0.239845\pi$
$108$	1.00000	0.0962250
$109$	−16.0197	−1.53441	−0.767203	−	0.641404i	$-0.778352\pi$
$109$	−16.0197	−1.53441	−0.767203	+	0.641404i	$0.778352\pi$
$110$	−8.07413	−0.769838
$111$	5.38725	0.511336
$112$	0.821182	0.0775944
$113$	15.9007	1.49581	0.747906	−	0.663805i	$-0.231059\pi$
$113$	15.9007	1.49581	0.747906	+	0.663805i	$0.231059\pi$
$114$	7.47060	0.699686
$115$	−13.2269	−1.23342
$116$	6.26676	0.581854
$117$	1.00000	0.0924500
$118$	−1.22066	−0.112371
$119$	4.67803	0.428834
$120$	2.01149	0.183623
$121$	5.11225	0.464750
$122$	12.6859	1.14853
$123$	10.3207	0.930588
$124$	3.73369	0.335296
$125$	11.9762	1.07119
$126$	−0.821182	−0.0731567
$127$	19.2220	1.70567	0.852837	−	0.522178i	$-0.174880\pi$
$127$	19.2220	1.70567	0.852837	+	0.522178i	$0.174880\pi$
$128$	−1.00000	−0.0883883
$129$	−6.06943	−0.534383
$130$	2.01149	0.176419
$131$	9.75872	0.852623	0.426312	−	0.904576i	$-0.359813\pi$
$131$	9.75872	0.852623	0.426312	+	0.904576i	$0.359813\pi$
$132$	−4.01401	−0.349374
$133$	−6.13472	−0.531948
$134$	−13.8320	−1.19490
$135$	−2.01149	−0.173122
$136$	−5.69670	−0.488488
$137$	4.57148	0.390568	0.195284	−	0.980747i	$-0.437437\pi$
$137$	4.57148	0.390568	0.195284	+	0.980747i	$0.437437\pi$
$138$	−6.57569	−0.559760
$139$	−1.30551	−0.110732	−0.0553661	−	0.998466i	$-0.517633\pi$
$139$	−1.30551	−0.110732	−0.0553661	+	0.998466i	$0.517633\pi$
$140$	−1.65180	−0.139602
$141$	−6.22769	−0.524466
$142$	12.0421	1.01055
$143$	−4.01401	−0.335668
$144$	1.00000	0.0833333
$145$	−12.6055	−1.04683
$146$	1.91417	0.158418
$147$	−6.32566	−0.521732
$148$	5.38725	0.442830
$149$	−23.6104	−1.93424	−0.967120	−	0.254319i	$-0.918149\pi$
$149$	−23.6104	−1.93424	−0.967120	+	0.254319i	$0.918149\pi$
$150$	0.953907	0.0778862
$151$	8.00670	0.651576	0.325788	−	0.945443i	$-0.394370\pi$
$151$	8.00670	0.651576	0.325788	+	0.945443i	$0.394370\pi$
$152$	7.47060	0.605946
$153$	5.69670	0.460551
$154$	3.29623	0.265618
$155$	−7.51029	−0.603241
$156$	1.00000	0.0800641
$157$	0.407820	0.0325476	0.0162738	−	0.999868i	$-0.494820\pi$
$157$	0.407820	0.0325476	0.0162738	+	0.999868i	$0.494820\pi$
$158$	4.90081	0.389887
$159$	−7.76530	−0.615828
$160$	2.01149	0.159022
$161$	5.39983	0.425567
$162$	−1.00000	−0.0785674
$163$	5.20987	0.408069	0.204034	−	0.978964i	$-0.434595\pi$
$163$	5.20987	0.408069	0.204034	+	0.978964i	$0.434595\pi$
$164$	10.3207	0.805913
$165$	8.07413	0.628570
$166$	8.34909	0.648015
$167$	17.3628	1.34357	0.671787	−	0.740744i	$-0.265527\pi$
$167$	17.3628	1.34357	0.671787	+	0.740744i	$0.265527\pi$
$168$	−0.821182	−0.0633555
$169$	1.00000	0.0769231
$170$	11.4589	0.878854
$171$	−7.47060	−0.571291
$172$	−6.06943	−0.462790
$173$	6.21001	0.472138	0.236069	−	0.971736i	$-0.424141\pi$
$173$	6.21001	0.472138	0.236069	+	0.971736i	$0.424141\pi$
$174$	−6.26676	−0.475082
$175$	−0.783331	−0.0592143
$176$	−4.01401	−0.302567
$177$	1.22066	0.0917508
$178$	−6.85911	−0.514112
$179$	8.59574	0.642476	0.321238	−	0.946999i	$-0.395901\pi$
$179$	8.59574	0.642476	0.321238	+	0.946999i	$0.395901\pi$
$180$	−2.01149	−0.149928
$181$	−8.60169	−0.639358	−0.319679	−	0.947526i	$-0.603575\pi$
$181$	−8.60169	−0.639358	−0.319679	+	0.947526i	$0.603575\pi$
$182$	−0.821182	−0.0608700
$183$	−12.6859	−0.937771
$184$	−6.57569	−0.484766
$185$	−10.8364	−0.796709
$186$	−3.73369	−0.273768
$187$	−22.8666	−1.67217
$188$	−6.22769	−0.454201
$189$	0.821182	0.0597322
$190$	−15.0270	−1.09018
$191$	18.0101	1.30316	0.651581	−	0.758579i	$-0.274106\pi$
$191$	18.0101	1.30316	0.651581	+	0.758579i	$0.274106\pi$
$192$	1.00000	0.0721688
$193$	13.9209	1.00205	0.501025	−	0.865433i	$-0.332956\pi$
$193$	13.9209	1.00205	0.501025	+	0.865433i	$0.332956\pi$
$194$	6.26340	0.449686
$195$	−2.01149	−0.144046
$196$	−6.32566	−0.451833
$197$	6.73733	0.480015	0.240007	−	0.970771i	$-0.422850\pi$
$197$	6.73733	0.480015	0.240007	+	0.970771i	$0.422850\pi$
$198$	4.01401	0.285263
$199$	15.6727	1.11100	0.555502	−	0.831515i	$-0.312526\pi$
$199$	15.6727	1.11100	0.555502	+	0.831515i	$0.312526\pi$
$200$	0.953907	0.0674514
$201$	13.8320	0.975635
$202$	−3.28354	−0.231029
$203$	5.14615	0.361189
$204$	5.69670	0.398849
$205$	−20.7600	−1.44994
$206$	−1.00000	−0.0696733
$207$	6.57569	0.457042
$208$	1.00000	0.0693375
$209$	29.9870	2.07425
$210$	1.65180	0.113985
$211$	18.4088	1.26731	0.633656	−	0.773615i	$-0.281554\pi$
$211$	18.4088	1.26731	0.633656	+	0.773615i	$0.281554\pi$
$212$	−7.76530	−0.533323
$213$	−12.0421	−0.825111
$214$	−15.0879	−1.03139
$215$	12.2086	0.832619
$216$	−1.00000	−0.0680414
$217$	3.06604	0.208136
$218$	16.0197	1.08499
$219$	−1.91417	−0.129348
$220$	8.07413	0.544358
$221$	5.69670	0.383202
$222$	−5.38725	−0.361569
$223$	−1.01683	−0.0680918	−0.0340459	−	0.999420i	$-0.510839\pi$
$223$	−1.01683	−0.0680918	−0.0340459	+	0.999420i	$0.510839\pi$
$224$	−0.821182	−0.0548675
$225$	−0.953907	−0.0635938
$226$	−15.9007	−1.05770
$227$	26.7748	1.77711	0.888554	−	0.458773i	$-0.151711\pi$
$227$	26.7748	1.77711	0.888554	+	0.458773i	$0.151711\pi$
$228$	−7.47060	−0.494753
$229$	−8.56176	−0.565777	−0.282888	−	0.959153i	$-0.591293\pi$
$229$	−8.56176	−0.565777	−0.282888	+	0.959153i	$0.591293\pi$
$230$	13.2269	0.872158
$231$	−3.29623	−0.216876
$232$	−6.26676	−0.411433
$233$	13.4090	0.878452	0.439226	−	0.898377i	$-0.355253\pi$
$233$	13.4090	0.878452	0.439226	+	0.898377i	$0.355253\pi$
$234$	−1.00000	−0.0653720
$235$	12.5269	0.817168
$236$	1.22066	0.0794585
$237$	−4.90081	−0.318341
$238$	−4.67803	−0.303231
$239$	21.1664	1.36914	0.684572	−	0.728945i	$-0.259989\pi$
$239$	21.1664	1.36914	0.684572	+	0.728945i	$0.259989\pi$
$240$	−2.01149	−0.129841
$241$	−29.8935	−1.92561	−0.962805	−	0.270197i	$-0.912911\pi$
$241$	−29.8935	−1.92561	−0.962805	+	0.270197i	$0.912911\pi$
$242$	−5.11225	−0.328628
$243$	1.00000	0.0641500
$244$	−12.6859	−0.812134
$245$	12.7240	0.812907
$246$	−10.3207	−0.658025
$247$	−7.47060	−0.475343
$248$	−3.73369	−0.237090
$249$	−8.34909	−0.529102
$250$	−11.9762	−0.757443
$251$	2.06160	0.130127	0.0650635	−	0.997881i	$-0.479275\pi$
$251$	2.06160	0.130127	0.0650635	+	0.997881i	$0.479275\pi$
$252$	0.821182	0.0517296
$253$	−26.3949	−1.65943
$254$	−19.2220	−1.20609
$255$	−11.4589	−0.717581
$256$	1.00000	0.0625000
$257$	−24.9650	−1.55727	−0.778635	−	0.627477i	$-0.784088\pi$
$257$	−24.9650	−1.55727	−0.778635	+	0.627477i	$0.784088\pi$
$258$	6.06943	0.377866
$259$	4.42391	0.274889
$260$	−2.01149	−0.124747
$261$	6.26676	0.387903
$262$	−9.75872	−0.602896
$263$	2.46409	0.151942	0.0759712	−	0.997110i	$-0.475794\pi$
$263$	2.46409	0.151942	0.0759712	+	0.997110i	$0.475794\pi$
$264$	4.01401	0.247045
$265$	15.6198	0.959518
$266$	6.13472	0.376144
$267$	6.85911	0.419771
$268$	13.8320	0.844924
$269$	−11.8675	−0.723574	−0.361787	−	0.932261i	$-0.617833\pi$
$269$	−11.8675	−0.723574	−0.361787	+	0.932261i	$0.617833\pi$
$270$	2.01149	0.122415
$271$	−22.9744	−1.39560	−0.697798	−	0.716295i	$-0.745837\pi$
$271$	−22.9744	−1.39560	−0.697798	+	0.716295i	$0.745837\pi$
$272$	5.69670	0.345413
$273$	0.821182	0.0497002
$274$	−4.57148	−0.276173
$275$	3.82899	0.230897
$276$	6.57569	0.395810
$277$	27.0376	1.62453	0.812265	−	0.583288i	$-0.198234\pi$
$277$	27.0376	1.62453	0.812265	+	0.583288i	$0.198234\pi$
$278$	1.30551	0.0782994
$279$	3.73369	0.223530
$280$	1.65180	0.0987138
$281$	−25.3000	−1.50927	−0.754636	−	0.656143i	$-0.772187\pi$
$281$	−25.3000	−1.50927	−0.754636	+	0.656143i	$0.772187\pi$
$282$	6.22769	0.370854
$283$	24.2173	1.43957	0.719785	−	0.694197i	$-0.244240\pi$
$283$	24.2173	1.43957	0.719785	+	0.694197i	$0.244240\pi$
$284$	−12.0421	−0.714567
$285$	15.0270	0.890125
$286$	4.01401	0.237353
$287$	8.47518	0.500274
$288$	−1.00000	−0.0589256
$289$	15.4524	0.908965
$290$	12.6055	0.740222
$291$	−6.26340	−0.367167
$292$	−1.91417	−0.112018
$293$	23.4317	1.36889	0.684447	−	0.729062i	$-0.260044\pi$
$293$	23.4317	1.36889	0.684447	+	0.729062i	$0.260044\pi$
$294$	6.32566	0.368920
$295$	−2.45535	−0.142956
$296$	−5.38725	−0.313128
$297$	−4.01401	−0.232916
$298$	23.6104	1.36771
$299$	6.57569	0.380282
$300$	−0.953907	−0.0550739
$301$	−4.98410	−0.287279
$302$	−8.00670	−0.460734
$303$	3.28354	0.188634
$304$	−7.47060	−0.428468
$305$	25.5176	1.46114
$306$	−5.69670	−0.325659
$307$	2.15165	0.122801	0.0614005	−	0.998113i	$-0.480443\pi$
$307$	2.15165	0.122801	0.0614005	+	0.998113i	$0.480443\pi$
$308$	−3.29623	−0.187820
$309$	1.00000	0.0568880
$310$	7.51029	0.426556
$311$	19.1059	1.08340	0.541699	−	0.840572i	$-0.317781\pi$
$311$	19.1059	1.08340	0.541699	+	0.840572i	$0.317781\pi$
$312$	−1.00000	−0.0566139
$313$	−27.6660	−1.56377	−0.781887	−	0.623420i	$-0.785743\pi$
$313$	−27.6660	−1.56377	−0.781887	+	0.623420i	$0.785743\pi$
$314$	−0.407820	−0.0230146
$315$	−1.65180	−0.0930683
$316$	−4.90081	−0.275692
$317$	10.6778	0.599728	0.299864	−	0.953982i	$-0.403059\pi$
$317$	10.6778	0.599728	0.299864	+	0.953982i	$0.403059\pi$
$318$	7.76530	0.435456
$319$	−25.1548	−1.40840
$320$	−2.01149	−0.112446
$321$	15.0879	0.842124
$322$	−5.39983	−0.300921
$323$	−42.5578	−2.36798
$324$	1.00000	0.0555556
$325$	−0.953907	−0.0529133
$326$	−5.20987	−0.288548
$327$	−16.0197	−0.885890
$328$	−10.3207	−0.569866
$329$	−5.11407	−0.281948
$330$	−8.07413	−0.444466
$331$	24.0514	1.32199	0.660993	−	0.750392i	$-0.270135\pi$
$331$	24.0514	1.32199	0.660993	+	0.750392i	$0.270135\pi$
$332$	−8.34909	−0.458216
$333$	5.38725	0.295220
$334$	−17.3628	−0.950051
$335$	−27.8230	−1.52013
$336$	0.821182	0.0447991
$337$	26.1298	1.42338	0.711690	−	0.702494i	$-0.247930\pi$
$337$	26.1298	1.42338	0.711690	+	0.702494i	$0.247930\pi$
$338$	−1.00000	−0.0543928
$339$	15.9007	0.863608
$340$	−11.4589	−0.621444
$341$	−14.9871	−0.811596
$342$	7.47060	0.403964
$343$	−10.9428	−0.590855
$344$	6.06943	0.327242
$345$	−13.2269	−0.712114
$346$	−6.21001	−0.333852
$347$	−19.0549	−1.02292	−0.511460	−	0.859307i	$-0.670895\pi$
$347$	−19.0549	−1.02292	−0.511460	+	0.859307i	$0.670895\pi$
$348$	6.26676	0.335934
$349$	21.8543	1.16984	0.584918	−	0.811093i	$-0.301127\pi$
$349$	21.8543	1.16984	0.584918	+	0.811093i	$0.301127\pi$
$350$	0.783331	0.0418708
$351$	1.00000	0.0533761
$352$	4.01401	0.213947
$353$	−23.2775	−1.23893	−0.619467	−	0.785023i	$-0.712651\pi$
$353$	−23.2775	−1.23893	−0.619467	+	0.785023i	$0.712651\pi$
$354$	−1.22066	−0.0648776
$355$	24.2226	1.28560
$356$	6.85911	0.363532
$357$	4.67803	0.247587
$358$	−8.59574	−0.454299
$359$	15.2346	0.804054	0.402027	−	0.915628i	$-0.368306\pi$
$359$	15.2346	0.804054	0.402027	+	0.915628i	$0.368306\pi$
$360$	2.01149	0.106015
$361$	36.8099	1.93736
$362$	8.60169	0.452095
$363$	5.11225	0.268323
$364$	0.821182	0.0430416
$365$	3.85033	0.201536
$366$	12.6859	0.663105
$367$	31.9213	1.66628	0.833140	−	0.553062i	$-0.186541\pi$
$367$	31.9213	1.66628	0.833140	+	0.553062i	$0.186541\pi$
$368$	6.57569	0.342781
$369$	10.3207	0.537275
$370$	10.8364	0.563358
$371$	−6.37672	−0.331063
$372$	3.73369	0.193583
$373$	−11.8576	−0.613964	−0.306982	−	0.951715i	$-0.599319\pi$
$373$	−11.8576	−0.613964	−0.306982	+	0.951715i	$0.599319\pi$
$374$	22.8666	1.18240
$375$	11.9762	0.618450
$376$	6.22769	0.321169
$377$	6.26676	0.322755
$378$	−0.821182	−0.0422370
$379$	10.7364	0.551492	0.275746	−	0.961231i	$-0.411075\pi$
$379$	10.7364	0.551492	0.275746	+	0.961231i	$0.411075\pi$
$380$	15.0270	0.770871
$381$	19.2220	0.984771
$382$	−18.0101	−0.921475
$383$	33.6911	1.72154	0.860768	−	0.508997i	$-0.169984\pi$
$383$	33.6911	1.72154	0.860768	+	0.508997i	$0.169984\pi$
$384$	−1.00000	−0.0510310
$385$	6.63033	0.337913
$386$	−13.9209	−0.708557
$387$	−6.06943	−0.308526
$388$	−6.26340	−0.317976
$389$	−8.50993	−0.431470	−0.215735	−	0.976452i	$-0.569215\pi$
$389$	−8.50993	−0.431470	−0.215735	+	0.976452i	$0.569215\pi$
$390$	2.01149	0.101856
$391$	37.4597	1.89442
$392$	6.32566	0.319494
$393$	9.75872	0.492262
$394$	−6.73733	−0.339422
$395$	9.85792	0.496006
$396$	−4.01401	−0.201711
$397$	16.6267	0.834471	0.417236	−	0.908798i	$-0.362999\pi$
$397$	16.6267	0.834471	0.417236	+	0.908798i	$0.362999\pi$
$398$	−15.6727	−0.785599
$399$	−6.13472	−0.307120
$400$	−0.953907	−0.0476954
$401$	7.17142	0.358124	0.179062	−	0.983838i	$-0.442694\pi$
$401$	7.17142	0.358124	0.179062	+	0.983838i	$0.442694\pi$
$402$	−13.8320	−0.689878
$403$	3.73369	0.185989
$404$	3.28354	0.163362
$405$	−2.01149	−0.0999517
$406$	−5.14615	−0.255399
$407$	−21.6245	−1.07189
$408$	−5.69670	−0.282029
$409$	4.06328	0.200917	0.100458	−	0.994941i	$-0.467969\pi$
$409$	4.06328	0.200917	0.100458	+	0.994941i	$0.467969\pi$
$410$	20.7600	1.02526
$411$	4.57148	0.225495
$412$	1.00000	0.0492665
$413$	1.00239	0.0493243
$414$	−6.57569	−0.323177
$415$	16.7941	0.824391
$416$	−1.00000	−0.0490290
$417$	−1.30551	−0.0639312
$418$	−29.9870	−1.46671
$419$	−7.30228	−0.356740	−0.178370	−	0.983963i	$-0.557082\pi$
$419$	−7.30228	−0.356740	−0.178370	+	0.983963i	$0.557082\pi$
$420$	−1.65180	−0.0805995
$421$	−15.4170	−0.751377	−0.375689	−	0.926746i	$-0.622594\pi$
$421$	−15.4170	−0.751377	−0.375689	+	0.926746i	$0.622594\pi$
$422$	−18.4088	−0.896125
$423$	−6.22769	−0.302801
$424$	7.76530	0.377116
$425$	−5.43413	−0.263594
$426$	12.0421	0.583442
$427$	−10.4175	−0.504136
$428$	15.0879	0.729301
$429$	−4.01401	−0.193798
$430$	−12.2086	−0.588751
$431$	−0.830936	−0.0400248	−0.0200124	−	0.999800i	$-0.506371\pi$
$431$	−0.830936	−0.0400248	−0.0200124	+	0.999800i	$0.506371\pi$
$432$	1.00000	0.0481125
$433$	19.8022	0.951632	0.475816	−	0.879545i	$-0.342153\pi$
$433$	19.8022	0.951632	0.475816	+	0.879545i	$0.342153\pi$
$434$	−3.06604	−0.147175
$435$	−12.6055	−0.604389
$436$	−16.0197	−0.767203
$437$	−49.1243	−2.34994
$438$	1.91417	0.0914626
$439$	−25.7568	−1.22930	−0.614652	−	0.788798i	$-0.710704\pi$
$439$	−25.7568	−1.22930	−0.614652	+	0.788798i	$0.710704\pi$
$440$	−8.07413	−0.384919
$441$	−6.32566	−0.301222
$442$	−5.69670	−0.270964
$443$	16.7571	0.796155	0.398077	−	0.917352i	$-0.369678\pi$
$443$	16.7571	0.796155	0.398077	+	0.917352i	$0.369678\pi$
$444$	5.38725	0.255668
$445$	−13.7970	−0.654042
$446$	1.01683	0.0481481
$447$	−23.6104	−1.11673
$448$	0.821182	0.0387972
$449$	5.18535	0.244712	0.122356	−	0.992486i	$-0.460955\pi$
$449$	5.18535	0.244712	0.122356	+	0.992486i	$0.460955\pi$
$450$	0.953907	0.0449676
$451$	−41.4274	−1.95074
$452$	15.9007	0.747906
$453$	8.00670	0.376187
$454$	−26.7748	−1.25660
$455$	−1.65180	−0.0774375
$456$	7.47060	0.349843
$457$	19.8473	0.928417	0.464209	−	0.885726i	$-0.346339\pi$
$457$	19.8473	0.928417	0.464209	+	0.885726i	$0.346339\pi$
$458$	8.56176	0.400065
$459$	5.69670	0.265899
$460$	−13.2269	−0.616709
$461$	31.6441	1.47381	0.736907	−	0.675994i	$-0.236285\pi$
$461$	31.6441	1.47381	0.736907	+	0.675994i	$0.236285\pi$
$462$	3.29623	0.153354
$463$	10.9116	0.507104	0.253552	−	0.967322i	$-0.418401\pi$
$463$	10.9116	0.507104	0.253552	+	0.967322i	$0.418401\pi$
$464$	6.26676	0.290927
$465$	−7.51029	−0.348281
$466$	−13.4090	−0.621159
$467$	20.1662	0.933178	0.466589	−	0.884474i	$-0.345483\pi$
$467$	20.1662	0.933178	0.466589	+	0.884474i	$0.345483\pi$
$468$	1.00000	0.0462250
$469$	11.3586	0.524491
$470$	−12.5269	−0.577825
$471$	0.407820	0.0187914
$472$	−1.22066	−0.0561856
$473$	24.3627	1.12020
$474$	4.90081	0.225101
$475$	7.12626	0.326975
$476$	4.67803	0.214417
$477$	−7.76530	−0.355549
$478$	−21.1664	−0.968131
$479$	−36.9149	−1.68668	−0.843342	−	0.537377i	$-0.819415\pi$
$479$	−36.9149	−1.68668	−0.843342	+	0.537377i	$0.819415\pi$
$480$	2.01149	0.0918115
$481$	5.38725	0.245638
$482$	29.8935	1.36161
$483$	5.39983	0.245701
$484$	5.11225	0.232375
$485$	12.5988	0.572081
$486$	−1.00000	−0.0453609
$487$	−11.2473	−0.509666	−0.254833	−	0.966985i	$-0.582020\pi$
$487$	−11.2473	−0.509666	−0.254833	+	0.966985i	$0.582020\pi$
$488$	12.6859	0.574265
$489$	5.20987	0.235599
$490$	−12.7240	−0.574812
$491$	−11.0305	−0.497800	−0.248900	−	0.968529i	$-0.580069\pi$
$491$	−11.0305	−0.497800	−0.248900	+	0.968529i	$0.580069\pi$
$492$	10.3207	0.465294
$493$	35.6999	1.60784
$494$	7.47060	0.336118
$495$	8.07413	0.362905
$496$	3.73369	0.167648
$497$	−9.88875	−0.443571
$498$	8.34909	0.374132
$499$	−34.3363	−1.53711	−0.768553	−	0.639787i	$-0.779023\pi$
$499$	−34.3363	−1.53711	−0.768553	+	0.639787i	$0.779023\pi$
$500$	11.9762	0.535593
$501$	17.3628	0.775713
$502$	−2.06160	−0.0920137
$503$	−3.83250	−0.170883	−0.0854414	−	0.996343i	$-0.527230\pi$
$503$	−3.83250	−0.170883	−0.0854414	+	0.996343i	$0.527230\pi$
$504$	−0.821182	−0.0365783
$505$	−6.60480	−0.293910
$506$	26.3949	1.17339
$507$	1.00000	0.0444116
$508$	19.2220	0.852837
$509$	−34.8620	−1.54523	−0.772615	−	0.634875i	$-0.781052\pi$
$509$	−34.8620	−1.54523	−0.772615	+	0.634875i	$0.781052\pi$
$510$	11.4589	0.507407
$511$	−1.57188	−0.0695359
$512$	−1.00000	−0.0441942
$513$	−7.47060	−0.329835
$514$	24.9650	1.10116
$515$	−2.01149	−0.0886368
$516$	−6.06943	−0.267192
$517$	24.9980	1.09941
$518$	−4.42391	−0.194376
$519$	6.21001	0.272589
$520$	2.01149	0.0882097
$521$	−7.20890	−0.315828	−0.157914	−	0.987453i	$-0.550477\pi$
$521$	−7.20890	−0.315828	−0.157914	+	0.987453i	$0.550477\pi$
$522$	−6.26676	−0.274289
$523$	2.41099	0.105425	0.0527127	−	0.998610i	$-0.483213\pi$
$523$	2.41099	0.105425	0.0527127	+	0.998610i	$0.483213\pi$
$524$	9.75872	0.426312
$525$	−0.783331	−0.0341874
$526$	−2.46409	−0.107440
$527$	21.2697	0.926525
$528$	−4.01401	−0.174687
$529$	20.2397	0.879986
$530$	−15.6198	−0.678482
$531$	1.22066	0.0529723
$532$	−6.13472	−0.265974
$533$	10.3207	0.447040
$534$	−6.85911	−0.296823
$535$	−30.3491	−1.31211
$536$	−13.8320	−0.597452
$537$	8.59574	0.370934
$538$	11.8675	0.511644
$539$	25.3912	1.09368
$540$	−2.01149	−0.0865608
$541$	−3.53906	−0.152156	−0.0760781	−	0.997102i	$-0.524240\pi$
$541$	−3.53906	−0.152156	−0.0760781	+	0.997102i	$0.524240\pi$
$542$	22.9744	0.986835
$543$	−8.60169	−0.369134
$544$	−5.69670	−0.244244
$545$	32.2234	1.38030
$546$	−0.821182	−0.0351433
$547$	−17.8808	−0.764528	−0.382264	−	0.924053i	$-0.624856\pi$
$547$	−17.8808	−0.764528	−0.382264	+	0.924053i	$0.624856\pi$
$548$	4.57148	0.195284
$549$	−12.6859	−0.541423
$550$	−3.82899	−0.163269
$551$	−46.8165	−1.99445
$552$	−6.57569	−0.279880
$553$	−4.02445	−0.171137
$554$	−27.0376	−1.14872
$555$	−10.8364	−0.459980
$556$	−1.30551	−0.0553661
$557$	−28.3208	−1.19999	−0.599996	−	0.800003i	$-0.704831\pi$
$557$	−28.3208	−1.19999	−0.599996	+	0.800003i	$0.704831\pi$
$558$	−3.73369	−0.158060
$559$	−6.06943	−0.256710
$560$	−1.65180	−0.0698012
$561$	−22.8666	−0.965428
$562$	25.3000	1.06722
$563$	32.1109	1.35332	0.676658	−	0.736298i	$-0.263428\pi$
$563$	32.1109	1.35332	0.676658	+	0.736298i	$0.263428\pi$
$564$	−6.22769	−0.262233
$565$	−31.9841	−1.34558
$566$	−24.2173	−1.01793
$567$	0.821182	0.0344864
$568$	12.0421	0.505275
$569$	−4.03551	−0.169177	−0.0845886	−	0.996416i	$-0.526958\pi$
$569$	−4.03551	−0.169177	−0.0845886	+	0.996416i	$0.526958\pi$
$570$	−15.0270	−0.629413
$571$	−2.62690	−0.109932	−0.0549662	−	0.998488i	$-0.517505\pi$
$571$	−2.62690	−0.109932	−0.0549662	+	0.998488i	$0.517505\pi$
$572$	−4.01401	−0.167834
$573$	18.0101	0.752381
$574$	−8.47518	−0.353747
$575$	−6.27260	−0.261585
$576$	1.00000	0.0416667
$577$	32.0620	1.33476	0.667379	−	0.744718i	$-0.267416\pi$
$577$	32.0620	1.33476	0.667379	+	0.744718i	$0.267416\pi$
$578$	−15.4524	−0.642735
$579$	13.9209	0.578534
$580$	−12.6055	−0.523416
$581$	−6.85612	−0.284440
$582$	6.26340	0.259626
$583$	31.1700	1.29093
$584$	1.91417	0.0792089
$585$	−2.01149	−0.0831649
$586$	−23.4317	−0.967955
$587$	12.1537	0.501635	0.250817	−	0.968034i	$-0.419301\pi$
$587$	12.1537	0.501635	0.250817	+	0.968034i	$0.419301\pi$
$588$	−6.32566	−0.260866
$589$	−27.8929	−1.14931
$590$	2.45535	0.101085
$591$	6.73733	0.277137
$592$	5.38725	0.221415
$593$	−20.1653	−0.828090	−0.414045	−	0.910256i	$-0.635884\pi$
$593$	−20.1653	−0.828090	−0.414045	+	0.910256i	$0.635884\pi$
$594$	4.01401	0.164697
$595$	−9.40980	−0.385764
$596$	−23.6104	−0.967120
$597$	15.6727	0.641439
$598$	−6.57569	−0.268900
$599$	33.5223	1.36968	0.684841	−	0.728692i	$-0.259871\pi$
$599$	33.5223	1.36968	0.684841	+	0.728692i	$0.259871\pi$
$600$	0.953907	0.0389431
$601$	17.1442	0.699326	0.349663	−	0.936875i	$-0.386296\pi$
$601$	17.1442	0.699326	0.349663	+	0.936875i	$0.386296\pi$
$602$	4.98410	0.203137
$603$	13.8320	0.563283
$604$	8.00670	0.325788
$605$	−10.2832	−0.418073
$606$	−3.28354	−0.133385
$607$	28.2778	1.14776	0.573881	−	0.818939i	$-0.305437\pi$
$607$	28.2778	1.14776	0.573881	+	0.818939i	$0.305437\pi$
$608$	7.47060	0.302973
$609$	5.14615	0.208532
$610$	−25.5176	−1.03318
$611$	−6.22769	−0.251945
$612$	5.69670	0.230275
$613$	48.8247	1.97201	0.986006	−	0.166708i	$-0.0533137\pi$
$613$	48.8247	1.97201	0.986006	+	0.166708i	$0.0533137\pi$
$614$	−2.15165	−0.0868334
$615$	−20.7600	−0.837125
$616$	3.29623	0.132809
$617$	2.29370	0.0923410	0.0461705	−	0.998934i	$-0.485298\pi$
$617$	2.29370	0.0923410	0.0461705	+	0.998934i	$0.485298\pi$
$618$	−1.00000	−0.0402259
$619$	37.9217	1.52420	0.762101	−	0.647458i	$-0.224168\pi$
$619$	37.9217	1.52420	0.762101	+	0.647458i	$0.224168\pi$
$620$	−7.51029	−0.301621
$621$	6.57569	0.263873
$622$	−19.1059	−0.766079
$623$	5.63257	0.225664
$624$	1.00000	0.0400320
$625$	−19.3205	−0.772821
$626$	27.6660	1.10576
$627$	29.9870	1.19757
$628$	0.407820	0.0162738
$629$	30.6896	1.22367
$630$	1.65180	0.0658092
$631$	−22.0966	−0.879650	−0.439825	−	0.898084i	$-0.644960\pi$
$631$	−22.0966	−0.879650	−0.439825	+	0.898084i	$0.644960\pi$
$632$	4.90081	0.194944
$633$	18.4088	0.731683
$634$	−10.6778	−0.424071
$635$	−38.6648	−1.53437
$636$	−7.76530	−0.307914
$637$	−6.32566	−0.250632
$638$	25.1548	0.995889
$639$	−12.0421	−0.476378
$640$	2.01149	0.0795111
$641$	−31.3741	−1.23920	−0.619601	−	0.784917i	$-0.712706\pi$
$641$	−31.3741	−1.23920	−0.619601	+	0.784917i	$0.712706\pi$
$642$	−15.0879	−0.595472
$643$	−43.1178	−1.70040	−0.850201	−	0.526459i	$-0.823519\pi$
$643$	−43.1178	−1.70040	−0.850201	+	0.526459i	$0.823519\pi$
$644$	5.39983	0.212783
$645$	12.2086	0.480713
$646$	42.5578	1.67441
$647$	43.9051	1.72609	0.863043	−	0.505131i	$-0.168556\pi$
$647$	43.9051	1.72609	0.863043	+	0.505131i	$0.168556\pi$
$648$	−1.00000	−0.0392837
$649$	−4.89976	−0.192332
$650$	0.953907	0.0374153
$651$	3.06604	0.120168
$652$	5.20987	0.204034
$653$	−15.9181	−0.622924	−0.311462	−	0.950259i	$-0.600819\pi$
$653$	−15.9181	−0.622924	−0.311462	+	0.950259i	$0.600819\pi$
$654$	16.0197	0.626419
$655$	−19.6296	−0.766991
$656$	10.3207	0.402956
$657$	−1.91417	−0.0746789
$658$	5.11407	0.199367
$659$	−10.7692	−0.419509	−0.209755	−	0.977754i	$-0.567267\pi$
$659$	−10.7692	−0.419509	−0.209755	+	0.977754i	$0.567267\pi$
$660$	8.07413	0.314285
$661$	−36.4957	−1.41952	−0.709759	−	0.704445i	$-0.751196\pi$
$661$	−36.4957	−1.41952	−0.709759	+	0.704445i	$0.751196\pi$
$662$	−24.0514	−0.934786
$663$	5.69670	0.221242
$664$	8.34909	0.324008
$665$	12.3399	0.478522
$666$	−5.38725	−0.208752
$667$	41.2083	1.59559
$668$	17.3628	0.671787
$669$	−1.01683	−0.0393128
$670$	27.8230	1.07489
$671$	50.9214	1.96580
$672$	−0.821182	−0.0316778
$673$	0.138495	0.00533857	0.00266929	−	0.999996i	$-0.499150\pi$
$673$	0.138495	0.00533857	0.00266929	+	0.999996i	$0.499150\pi$
$674$	−26.1298	−1.00648
$675$	−0.953907	−0.0367159
$676$	1.00000	0.0384615
$677$	11.5750	0.444862	0.222431	−	0.974948i	$-0.428601\pi$
$677$	11.5750	0.444862	0.222431	+	0.974948i	$0.428601\pi$
$678$	−15.9007	−0.610663
$679$	−5.14339	−0.197385
$680$	11.4589	0.439427
$681$	26.7748	1.02601
$682$	14.9871	0.573885
$683$	−46.4837	−1.77865	−0.889324	−	0.457277i	$-0.848825\pi$
$683$	−46.4837	−1.77865	−0.889324	+	0.457277i	$0.848825\pi$
$684$	−7.47060	−0.285646
$685$	−9.19550	−0.351342
$686$	10.9428	0.417798
$687$	−8.56176	−0.326651
$688$	−6.06943	−0.231395
$689$	−7.76530	−0.295834
$690$	13.2269	0.503541
$691$	21.4389	0.815575	0.407787	−	0.913077i	$-0.366300\pi$
$691$	21.4389	0.815575	0.407787	+	0.913077i	$0.366300\pi$
$692$	6.21001	0.236069
$693$	−3.29623	−0.125213
$694$	19.0549	0.723314
$695$	2.62603	0.0996108
$696$	−6.26676	−0.237541
$697$	58.7940	2.22698
$698$	−21.8543	−0.827199
$699$	13.4090	0.507174
$700$	−0.783331	−0.0296071
$701$	−6.42587	−0.242702	−0.121351	−	0.992610i	$-0.538723\pi$
$701$	−6.42587	−0.242702	−0.121351	+	0.992610i	$0.538723\pi$
$702$	−1.00000	−0.0377426
$703$	−40.2460	−1.51791
$704$	−4.01401	−0.151284
$705$	12.5269	0.471792
$706$	23.2775	0.876059
$707$	2.69638	0.101408
$708$	1.22066	0.0458754
$709$	13.6364	0.512125	0.256062	−	0.966660i	$-0.417575\pi$
$709$	13.6364	0.512125	0.256062	+	0.966660i	$0.417575\pi$
$710$	−24.2226	−0.909057
$711$	−4.90081	−0.183795
$712$	−6.85911	−0.257056
$713$	24.5516	0.919465
$714$	−4.67803	−0.175071
$715$	8.07413	0.301955
$716$	8.59574	0.321238
$717$	21.1664	0.790475
$718$	−15.2346	−0.568552
$719$	15.5265	0.579040	0.289520	−	0.957172i	$-0.406504\pi$
$719$	15.5265	0.579040	0.289520	+	0.957172i	$0.406504\pi$
$720$	−2.01149	−0.0749638
$721$	0.821182	0.0305824
$722$	−36.8099	−1.36992
$723$	−29.8935	−1.11175
$724$	−8.60169	−0.319679
$725$	−5.97791	−0.222014
$726$	−5.11225	−0.189733
$727$	38.4042	1.42433	0.712166	−	0.702011i	$-0.247714\pi$
$727$	38.4042	1.42433	0.712166	+	0.702011i	$0.247714\pi$
$728$	−0.821182	−0.0304350
$729$	1.00000	0.0370370
$730$	−3.85033	−0.142507
$731$	−34.5757	−1.27883
$732$	−12.6859	−0.468886
$733$	−42.7364	−1.57851	−0.789253	−	0.614068i	$-0.789532\pi$
$733$	−42.7364	−1.57851	−0.789253	+	0.614068i	$0.789532\pi$
$734$	−31.9213	−1.17824
$735$	12.7240	0.469332
$736$	−6.57569	−0.242383
$737$	−55.5218	−2.04517
$738$	−10.3207	−0.379911
$739$	−35.3258	−1.29948	−0.649740	−	0.760156i	$-0.725122\pi$
$739$	−35.3258	−1.29948	−0.649740	+	0.760156i	$0.725122\pi$
$740$	−10.8364	−0.398354
$741$	−7.47060	−0.274439
$742$	6.37672	0.234097
$743$	5.42658	0.199082	0.0995409	−	0.995033i	$-0.468263\pi$
$743$	5.42658	0.199082	0.0995409	+	0.995033i	$0.468263\pi$
$744$	−3.73369	−0.136884
$745$	47.4921	1.73998
$746$	11.8576	0.434138
$747$	−8.34909	−0.305477
$748$	−22.8666	−0.836085
$749$	12.3899	0.452717
$750$	−11.9762	−0.437310
$751$	−11.9136	−0.434732	−0.217366	−	0.976090i	$-0.569747\pi$
$751$	−11.9136	−0.434732	−0.217366	+	0.976090i	$0.569747\pi$
$752$	−6.22769	−0.227101
$753$	2.06160	0.0751289
$754$	−6.26676	−0.228222
$755$	−16.1054	−0.586135
$756$	0.821182	0.0298661
$757$	−16.2461	−0.590476	−0.295238	−	0.955424i	$-0.595399\pi$
$757$	−16.2461	−0.590476	−0.295238	+	0.955424i	$0.595399\pi$
$758$	−10.7364	−0.389963
$759$	−26.3949	−0.958073
$760$	−15.0270	−0.545088
$761$	53.9409	1.95535	0.977677	−	0.210112i	$-0.0673829\pi$
$761$	53.9409	1.95535	0.977677	+	0.210112i	$0.0673829\pi$
$762$	−19.2220	−0.696338
$763$	−13.1551	−0.476245
$764$	18.0101	0.651581
$765$	−11.4589	−0.414296
$766$	−33.6911	−1.21731
$767$	1.22066	0.0440756
$768$	1.00000	0.0360844
$769$	0.947837	0.0341799	0.0170899	−	0.999854i	$-0.494560\pi$
$769$	0.947837	0.0341799	0.0170899	+	0.999854i	$0.494560\pi$
$770$	−6.63033	−0.238940
$771$	−24.9650	−0.899091
$772$	13.9209	0.501025
$773$	40.5513	1.45853	0.729264	−	0.684232i	$-0.239862\pi$
$773$	40.5513	1.45853	0.729264	+	0.684232i	$0.239862\pi$
$774$	6.06943	0.218161
$775$	−3.56160	−0.127936
$776$	6.26340	0.224843
$777$	4.42391	0.158707
$778$	8.50993	0.305096
$779$	−77.1020	−2.76246
$780$	−2.01149	−0.0720229
$781$	48.3371	1.72964
$782$	−37.4597	−1.33956
$783$	6.26676	0.223956
$784$	−6.32566	−0.225916
$785$	−0.820327	−0.0292787
$786$	−9.75872	−0.348082
$787$	−34.8549	−1.24244	−0.621221	−	0.783635i	$-0.713363\pi$
$787$	−34.8549	−1.24244	−0.621221	+	0.783635i	$0.713363\pi$
$788$	6.73733	0.240007
$789$	2.46409	0.0877240
$790$	−9.85792	−0.350729
$791$	13.0574	0.464266
$792$	4.01401	0.142632
$793$	−12.6859	−0.450491
$794$	−16.6267	−0.590060
$795$	15.6198	0.553978
$796$	15.6727	0.555502
$797$	−48.2392	−1.70872	−0.854360	−	0.519682i	$-0.826050\pi$
$797$	−48.2392	−1.70872	−0.854360	+	0.519682i	$0.826050\pi$
$798$	6.13472	0.217167
$799$	−35.4773	−1.25510
$800$	0.953907	0.0337257
$801$	6.85911	0.242355
$802$	−7.17142	−0.253232
$803$	7.68349	0.271145
$804$	13.8320	0.487817
$805$	−10.8617	−0.382825
$806$	−3.73369	−0.131514
$807$	−11.8675	−0.417756
$808$	−3.28354	−0.115514
$809$	13.0726	0.459609	0.229804	−	0.973237i	$-0.426191\pi$
$809$	13.0726	0.459609	0.229804	+	0.973237i	$0.426191\pi$
$810$	2.01149	0.0706766
$811$	5.68374	0.199583	0.0997916	−	0.995008i	$-0.468182\pi$
$811$	5.68374	0.199583	0.0997916	+	0.995008i	$0.468182\pi$
$812$	5.14615	0.180594
$813$	−22.9744	−0.805747
$814$	21.6245	0.757937
$815$	−10.4796	−0.367085
$816$	5.69670	0.199424
$817$	45.3423	1.58633
$818$	−4.06328	−0.142069
$819$	0.821182	0.0286944
$820$	−20.7600	−0.724971
$821$	48.7601	1.70174	0.850869	−	0.525377i	$-0.176076\pi$
$821$	48.7601	1.70174	0.850869	+	0.525377i	$0.176076\pi$
$822$	−4.57148	−0.159449
$823$	−9.01671	−0.314303	−0.157151	−	0.987575i	$-0.550231\pi$
$823$	−9.01671	−0.314303	−0.157151	+	0.987575i	$0.550231\pi$
$824$	−1.00000	−0.0348367
$825$	3.82899	0.133308
$826$	−1.00239	−0.0348775
$827$	−41.3831	−1.43903	−0.719515	−	0.694477i	$-0.755636\pi$
$827$	−41.3831	−1.43903	−0.719515	+	0.694477i	$0.755636\pi$
$828$	6.57569	0.228521
$829$	−26.1452	−0.908062	−0.454031	−	0.890986i	$-0.650014\pi$
$829$	−26.1452	−0.908062	−0.454031	+	0.890986i	$0.650014\pi$
$830$	−16.7941	−0.582932
$831$	27.0376	0.937923
$832$	1.00000	0.0346688
$833$	−36.0354	−1.24855
$834$	1.30551	0.0452062
$835$	−34.9251	−1.20863
$836$	29.9870	1.03712
$837$	3.73369	0.129055
$838$	7.30228	0.252253
$839$	−29.9128	−1.03270	−0.516352	−	0.856376i	$-0.672710\pi$
$839$	−29.9128	−1.03270	−0.516352	+	0.856376i	$0.672710\pi$
$840$	1.65180	0.0569925
$841$	10.2723	0.354217
$842$	15.4170	0.531304
$843$	−25.3000	−0.871379
$844$	18.4088	0.633656
$845$	−2.01149	−0.0691974
$846$	6.22769	0.214112
$847$	4.19808	0.144248
$848$	−7.76530	−0.266661
$849$	24.2173	0.831136
$850$	5.43413	0.186389
$851$	35.4249	1.21435
$852$	−12.0421	−0.412556
$853$	−23.6707	−0.810470	−0.405235	−	0.914213i	$-0.632810\pi$
$853$	−23.6707	−0.810470	−0.405235	+	0.914213i	$0.632810\pi$
$854$	10.4175	0.356478
$855$	15.0270	0.513914
$856$	−15.0879	−0.515694
$857$	−32.0261	−1.09399	−0.546996	−	0.837135i	$-0.684229\pi$
$857$	−32.0261	−1.09399	−0.546996	+	0.837135i	$0.684229\pi$
$858$	4.01401	0.137036
$859$	31.7896	1.08465	0.542323	−	0.840170i	$-0.317545\pi$
$859$	31.7896	1.08465	0.542323	+	0.840170i	$0.317545\pi$
$860$	12.2086	0.416310
$861$	8.47518	0.288833
$862$	0.830936	0.0283018
$863$	30.8405	1.04982	0.524912	−	0.851157i	$-0.324098\pi$
$863$	30.8405	1.04982	0.524912	+	0.851157i	$0.324098\pi$
$864$	−1.00000	−0.0340207
$865$	−12.4914	−0.424719
$866$	−19.8022	−0.672905
$867$	15.4524	0.524791
$868$	3.06604	0.104068
$869$	19.6719	0.667322
$870$	12.6055	0.427367
$871$	13.8320	0.468680
$872$	16.0197	0.542495
$873$	−6.26340	−0.211984
$874$	49.1243	1.66166
$875$	9.83466	0.332472
$876$	−1.91417	−0.0646738
$877$	31.1326	1.05127	0.525637	−	0.850709i	$-0.323827\pi$
$877$	31.1326	1.05127	0.525637	+	0.850709i	$0.323827\pi$
$878$	25.7568	0.869249
$879$	23.4317	0.790332
$880$	8.07413	0.272179
$881$	39.6063	1.33437	0.667185	−	0.744892i	$-0.267499\pi$
$881$	39.6063	1.33437	0.667185	+	0.744892i	$0.267499\pi$
$882$	6.32566	0.212996
$883$	18.5849	0.625433	0.312716	−	0.949847i	$-0.398761\pi$
$883$	18.5849	0.625433	0.312716	+	0.949847i	$0.398761\pi$
$884$	5.69670	0.191601
$885$	−2.45535	−0.0825359
$886$	−16.7571	−0.562966
$887$	3.40170	0.114218	0.0571090	−	0.998368i	$-0.481812\pi$
$887$	3.40170	0.114218	0.0571090	+	0.998368i	$0.481812\pi$
$888$	−5.38725	−0.180784
$889$	15.7847	0.529402
$890$	13.7970	0.462478
$891$	−4.01401	−0.134474
$892$	−1.01683	−0.0340459
$893$	46.5246	1.55689
$894$	23.6104	0.789650
$895$	−17.2902	−0.577949
$896$	−0.821182	−0.0274337
$897$	6.57569	0.219556
$898$	−5.18535	−0.173037
$899$	23.3982	0.780373
$900$	−0.953907	−0.0317969
$901$	−44.2366	−1.47373
$902$	41.4274	1.37938
$903$	−4.98410	−0.165861
$904$	−15.9007	−0.528849
$905$	17.3022	0.575145
$906$	−8.00670	−0.266005
$907$	22.1189	0.734446	0.367223	−	0.930133i	$-0.380309\pi$
$907$	22.1189	0.734446	0.367223	+	0.930133i	$0.380309\pi$
$908$	26.7748	0.888554
$909$	3.28354	0.108908
$910$	1.65180	0.0547566
$911$	−11.2789	−0.373685	−0.186843	−	0.982390i	$-0.559825\pi$
$911$	−11.2789	−0.373685	−0.186843	+	0.982390i	$0.559825\pi$
$912$	−7.47060	−0.247376
$913$	33.5133	1.10913
$914$	−19.8473	−0.656490
$915$	25.5176	0.843587
$916$	−8.56176	−0.282888
$917$	8.01368	0.264635
$918$	−5.69670	−0.188019
$919$	−25.8227	−0.851812	−0.425906	−	0.904767i	$-0.640045\pi$
$919$	−25.8227	−0.851812	−0.425906	+	0.904767i	$0.640045\pi$
$920$	13.2269	0.436079
$921$	2.15165	0.0708991
$922$	−31.6441	−1.04214
$923$	−12.0421	−0.396371
$924$	−3.29623	−0.108438
$925$	−5.13894	−0.168967
$926$	−10.9116	−0.358577
$927$	1.00000	0.0328443
$928$	−6.26676	−0.205716
$929$	−26.4612	−0.868165	−0.434083	−	0.900873i	$-0.642927\pi$
$929$	−26.4612	−0.868165	−0.434083	+	0.900873i	$0.642927\pi$
$930$	7.51029	0.246272
$931$	47.2565	1.54877
$932$	13.4090	0.439226
$933$	19.1059	0.625501
$934$	−20.1662	−0.659857
$935$	45.9959	1.50423
$936$	−1.00000	−0.0326860
$937$	2.10349	0.0687179	0.0343590	−	0.999410i	$-0.489061\pi$
$937$	2.10349	0.0687179	0.0343590	+	0.999410i	$0.489061\pi$
$938$	−11.3586	−0.370871
$939$	−27.6660	−0.902846
$940$	12.5269	0.408584
$941$	−13.3003	−0.433578	−0.216789	−	0.976219i	$-0.569558\pi$
$941$	−13.3003	−0.433578	−0.216789	+	0.976219i	$0.569558\pi$
$942$	−0.407820	−0.0132875
$943$	67.8658	2.21002
$944$	1.22066	0.0397293
$945$	−1.65180	−0.0537330
$946$	−24.3627	−0.792101
$947$	28.6455	0.930853	0.465427	−	0.885086i	$-0.345901\pi$
$947$	28.6455	0.930853	0.465427	+	0.885086i	$0.345901\pi$
$948$	−4.90081	−0.159171
$949$	−1.91417	−0.0621366
$950$	−7.12626	−0.231206
$951$	10.6778	0.346253
$952$	−4.67803	−0.151616
$953$	47.5087	1.53896	0.769479	−	0.638672i	$-0.220516\pi$
$953$	47.5087	1.53896	0.769479	+	0.638672i	$0.220516\pi$
$954$	7.76530	0.251411
$955$	−36.2271	−1.17228
$956$	21.1664	0.684572
$957$	−25.1548	−0.813140
$958$	36.9149	1.19267
$959$	3.75402	0.121224
$960$	−2.01149	−0.0649206
$961$	−17.0595	−0.550307
$962$	−5.38725	−0.173692
$963$	15.0879	0.486201
$964$	−29.8935	−0.962805
$965$	−28.0018	−0.901411
$966$	−5.39983	−0.173737
$967$	18.1691	0.584279	0.292139	−	0.956376i	$-0.405633\pi$
$967$	18.1691	0.584279	0.292139	+	0.956376i	$0.405633\pi$
$968$	−5.11225	−0.164314
$969$	−42.5578	−1.36715
$970$	−12.5988	−0.404522
$971$	−25.7719	−0.827060	−0.413530	−	0.910490i	$-0.635704\pi$
$971$	−25.7719	−0.827060	−0.413530	+	0.910490i	$0.635704\pi$
$972$	1.00000	0.0320750
$973$	−1.07206	−0.0343688
$974$	11.2473	0.360388
$975$	−0.953907	−0.0305495
$976$	−12.6859	−0.406067
$977$	11.8192	0.378130	0.189065	−	0.981965i	$-0.439454\pi$
$977$	11.8192	0.378130	0.189065	+	0.981965i	$0.439454\pi$
$978$	−5.20987	−0.166593
$979$	−27.5325	−0.879943
$980$	12.7240	0.406453
$981$	−16.0197	−0.511469
$982$	11.0305	0.351998
$983$	52.4108	1.67164	0.835822	−	0.549000i	$-0.184991\pi$
$983$	52.4108	1.67164	0.835822	+	0.549000i	$0.184991\pi$
$984$	−10.3207	−0.329013
$985$	−13.5521	−0.431805
$986$	−35.6999	−1.13692
$987$	−5.11407	−0.162783
$988$	−7.47060	−0.237671
$989$	−39.9107	−1.26909
$990$	−8.07413	−0.256613
$991$	−45.7082	−1.45197	−0.725984	−	0.687712i	$-0.758615\pi$
$991$	−45.7082	−1.45197	−0.725984	+	0.687712i	$0.758615\pi$
$992$	−3.73369	−0.118545
$993$	24.0514	0.763249
$994$	9.88875	0.313652
$995$	−31.5254	−0.999422
$996$	−8.34909	−0.264551
$997$	−8.39324	−0.265816	−0.132908	−	0.991128i	$-0.542432\pi$
$997$	−8.39324	−0.265816	−0.132908	+	0.991128i	$0.542432\pi$
$998$	34.3363	1.08690
$999$	5.38725	0.170445

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.x.1.4	✓	13	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.01149 q^{5} -1.00000 q^{6} +0.821182 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.01149 q^{5} -1.00000 q^{6} +0.821182 q^{7} -1.00000 q^{8} +1.00000 q^{9} +2.01149 q^{10} -4.01401 q^{11} +1.00000 q^{12} +1.00000 q^{13} -0.821182 q^{14} -2.01149 q^{15} +1.00000 q^{16} +5.69670 q^{17} -1.00000 q^{18} -7.47060 q^{19} -2.01149 q^{20} +0.821182 q^{21} +4.01401 q^{22} +6.57569 q^{23} -1.00000 q^{24} -0.953907 q^{25} -1.00000 q^{26} +1.00000 q^{27} +0.821182 q^{28} +6.26676 q^{29} +2.01149 q^{30} +3.73369 q^{31} -1.00000 q^{32} -4.01401 q^{33} -5.69670 q^{34} -1.65180 q^{35} +1.00000 q^{36} +5.38725 q^{37} +7.47060 q^{38} +1.00000 q^{39} +2.01149 q^{40} +10.3207 q^{41} -0.821182 q^{42} -6.06943 q^{43} -4.01401 q^{44} -2.01149 q^{45} -6.57569 q^{46} -6.22769 q^{47} +1.00000 q^{48} -6.32566 q^{49} +0.953907 q^{50} +5.69670 q^{51} +1.00000 q^{52} -7.76530 q^{53} -1.00000 q^{54} +8.07413 q^{55} -0.821182 q^{56} -7.47060 q^{57} -6.26676 q^{58} +1.22066 q^{59} -2.01149 q^{60} -12.6859 q^{61} -3.73369 q^{62} +0.821182 q^{63} +1.00000 q^{64} -2.01149 q^{65} +4.01401 q^{66} +13.8320 q^{67} +5.69670 q^{68} +6.57569 q^{69} +1.65180 q^{70} -12.0421 q^{71} -1.00000 q^{72} -1.91417 q^{73} -5.38725 q^{74} -0.953907 q^{75} -7.47060 q^{76} -3.29623 q^{77} -1.00000 q^{78} -4.90081 q^{79} -2.01149 q^{80} +1.00000 q^{81} -10.3207 q^{82} -8.34909 q^{83} +0.821182 q^{84} -11.4589 q^{85} +6.06943 q^{86} +6.26676 q^{87} +4.01401 q^{88} +6.85911 q^{89} +2.01149 q^{90} +0.821182 q^{91} +6.57569 q^{92} +3.73369 q^{93} +6.22769 q^{94} +15.0270 q^{95} -1.00000 q^{96} -6.26340 q^{97} +6.32566 q^{98} -4.01401 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * q^99

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