LMFDB - Embedded newform 290.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [290,2,Mod(1,290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(290, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 290 = 2 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	290.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:	$2.31566165862$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.14510$ of defining polynomial
Character	$\chi$	$=$	290.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.14510 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.14510 q^{6} -3.89167 q^{7} +1.00000 q^{8} +6.89167 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.14510 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.14510 q^{6} -3.89167 q^{7} +1.00000 q^{8} +6.89167 q^{9} -1.00000 q^{10} -4.29021 q^{11} +3.14510 q^{12} +4.34803 q^{13} -3.89167 q^{14} -3.14510 q^{15} +1.00000 q^{16} +1.60147 q^{17} +6.89167 q^{18} -1.20293 q^{19} -1.00000 q^{20} -12.2397 q^{21} -4.29021 q^{22} -8.34803 q^{23} +3.14510 q^{24} +1.00000 q^{25} +4.34803 q^{26} +12.2397 q^{27} -3.89167 q^{28} -1.00000 q^{29} -3.14510 q^{30} -2.39853 q^{31} +1.00000 q^{32} -13.4931 q^{33} +1.60147 q^{34} +3.89167 q^{35} +6.89167 q^{36} -9.78334 q^{37} -1.20293 q^{38} +13.6750 q^{39} -1.00000 q^{40} +5.78334 q^{41} -12.2397 q^{42} +3.60147 q^{43} -4.29021 q^{44} -6.89167 q^{45} -8.34803 q^{46} +8.58041 q^{47} +3.14510 q^{48} +8.14510 q^{49} +1.00000 q^{50} +5.03677 q^{51} +4.34803 q^{52} +4.80440 q^{53} +12.2397 q^{54} +4.29021 q^{55} -3.89167 q^{56} -3.78334 q^{57} -1.00000 q^{58} -4.05783 q^{59} -3.14510 q^{60} +11.4353 q^{61} -2.39853 q^{62} -26.8201 q^{63} +1.00000 q^{64} -4.34803 q^{65} -13.4931 q^{66} +9.08727 q^{67} +1.60147 q^{68} -26.2554 q^{69} +3.89167 q^{70} -12.0000 q^{71} +6.89167 q^{72} -2.39853 q^{73} -9.78334 q^{74} +3.14510 q^{75} -1.20293 q^{76} +16.6961 q^{77} +13.6750 q^{78} +7.55096 q^{79} -1.00000 q^{80} +17.8201 q^{81} +5.78334 q^{82} +2.79707 q^{83} -12.2397 q^{84} -1.60147 q^{85} +3.60147 q^{86} -3.14510 q^{87} -4.29021 q^{88} -4.29021 q^{89} -6.89167 q^{90} -16.9211 q^{91} -8.34803 q^{92} -7.54364 q^{93} +8.58041 q^{94} +1.20293 q^{95} +3.14510 q^{96} -0.348034 q^{97} +8.14510 q^{98} -29.5667 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} - 3 q^{10} + 3 q^{12} + 3 q^{13} + 3 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 3 q^{20} - 12 q^{21} - 15 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{28} - 3 q^{29} - 3 q^{30} - 9 q^{31} + 3 q^{32} - 24 q^{33} + 3 q^{34} - 3 q^{35} + 6 q^{36} - 3 q^{39} - 3 q^{40} - 12 q^{41} - 12 q^{42} + 9 q^{43} - 6 q^{45} - 15 q^{46} + 3 q^{48} + 18 q^{49} + 3 q^{50} - 6 q^{51} + 3 q^{52} + 9 q^{53} + 12 q^{54} + 3 q^{56} + 18 q^{57} - 3 q^{58} - 15 q^{59} - 3 q^{60} + 15 q^{61} - 9 q^{62} - 30 q^{63} + 3 q^{64} - 3 q^{65} - 24 q^{66} + 18 q^{67} + 3 q^{68} - 9 q^{69} - 3 q^{70} - 36 q^{71} + 6 q^{72} - 9 q^{73} + 3 q^{75} + 30 q^{77} - 3 q^{78} + 9 q^{79} - 3 q^{80} + 3 q^{81} - 12 q^{82} + 12 q^{83} - 12 q^{84} - 3 q^{85} + 9 q^{86} - 3 q^{87} - 6 q^{90} - 24 q^{91} - 15 q^{92} - 18 q^{93} + 3 q^{96} + 9 q^{97} + 18 q^{98} - 30 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 - 3 * q^10 + 3 * q^12 + 3 * q^13 + 3 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 + 6 * q^18 - 3 * q^20 - 12 * q^21 - 15 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^26 + 12 * q^27 + 3 * q^28 - 3 * q^29 - 3 * q^30 - 9 * q^31 + 3 * q^32 - 24 * q^33 + 3 * q^34 - 3 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 - 12 * q^41 - 12 * q^42 + 9 * q^43 - 6 * q^45 - 15 * q^46 + 3 * q^48 + 18 * q^49 + 3 * q^50 - 6 * q^51 + 3 * q^52 + 9 * q^53 + 12 * q^54 + 3 * q^56 + 18 * q^57 - 3 * q^58 - 15 * q^59 - 3 * q^60 + 15 * q^61 - 9 * q^62 - 30 * q^63 + 3 * q^64 - 3 * q^65 - 24 * q^66 + 18 * q^67 + 3 * q^68 - 9 * q^69 - 3 * q^70 - 36 * q^71 + 6 * q^72 - 9 * q^73 + 3 * q^75 + 30 * q^77 - 3 * q^78 + 9 * q^79 - 3 * q^80 + 3 * q^81 - 12 * q^82 + 12 * q^83 - 12 * q^84 - 3 * q^85 + 9 * q^86 - 3 * q^87 - 6 * q^90 - 24 * q^91 - 15 * q^92 - 18 * q^93 + 3 * q^96 + 9 * q^97 + 18 * q^98 - 30 * 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
$3$	3.14510	1.81583	0.907913	−	0.419159i	$-0.137675\pi$
$3$	3.14510	1.81583	0.907913	+	0.419159i	$0.137675\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.14510	1.28398
$7$	−3.89167	−1.47091	−0.735457	−	0.677572i	$-0.763032\pi$
$7$	−3.89167	−1.47091	−0.735457	+	0.677572i	$0.763032\pi$
$8$	1.00000	0.353553
$9$	6.89167	2.29722
$10$	−1.00000	−0.316228
$11$	−4.29021	−1.29355	−0.646773	−	0.762683i	$-0.723882\pi$
$11$	−4.29021	−1.29355	−0.646773	+	0.762683i	$0.723882\pi$
$12$	3.14510	0.907913
$13$	4.34803	1.20593	0.602964	−	0.797769i	$-0.293986\pi$
$13$	4.34803	1.20593	0.602964	+	0.797769i	$0.293986\pi$
$14$	−3.89167	−1.04009
$15$	−3.14510	−0.812062
$16$	1.00000	0.250000
$17$	1.60147	0.388412	0.194206	−	0.980961i	$-0.437787\pi$
$17$	1.60147	0.388412	0.194206	+	0.980961i	$0.437787\pi$
$18$	6.89167	1.62438
$19$	−1.20293	−0.275971	−0.137986	−	0.990434i	$-0.544063\pi$
$19$	−1.20293	−0.275971	−0.137986	+	0.990434i	$0.544063\pi$
$20$	−1.00000	−0.223607
$21$	−12.2397	−2.67092
$22$	−4.29021	−0.914675
$23$	−8.34803	−1.74069	−0.870343	−	0.492447i	$-0.836103\pi$
$23$	−8.34803	−1.74069	−0.870343	+	0.492447i	$0.836103\pi$
$24$	3.14510	0.641991
$25$	1.00000	0.200000
$26$	4.34803	0.852720
$27$	12.2397	2.35553
$28$	−3.89167	−0.735457
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−3.14510	−0.574215
$31$	−2.39853	−0.430790	−0.215395	−	0.976527i	$-0.569104\pi$
$31$	−2.39853	−0.430790	−0.215395	+	0.976527i	$0.569104\pi$
$32$	1.00000	0.176777
$33$	−13.4931	−2.34885
$34$	1.60147	0.274649
$35$	3.89167	0.657812
$36$	6.89167	1.14861
$37$	−9.78334	−1.60837	−0.804186	−	0.594378i	$-0.797398\pi$
$37$	−9.78334	−1.60837	−0.804186	+	0.594378i	$0.797398\pi$
$38$	−1.20293	−0.195141
$39$	13.6750	2.18975
$40$	−1.00000	−0.158114
$41$	5.78334	0.903206	0.451603	−	0.892219i	$-0.350852\pi$
$41$	5.78334	0.903206	0.451603	+	0.892219i	$0.350852\pi$
$42$	−12.2397	−1.88863
$43$	3.60147	0.549218	0.274609	−	0.961556i	$-0.411452\pi$
$43$	3.60147	0.549218	0.274609	+	0.961556i	$0.411452\pi$
$44$	−4.29021	−0.646773
$45$	−6.89167	−1.02735
$46$	−8.34803	−1.23085
$47$	8.58041	1.25158	0.625791	−	0.779991i	$-0.284776\pi$
$47$	8.58041	1.25158	0.625791	+	0.779991i	$0.284776\pi$
$48$	3.14510	0.453956
$49$	8.14510	1.16359
$50$	1.00000	0.141421
$51$	5.03677	0.705289
$52$	4.34803	0.602964
$53$	4.80440	0.659935	0.329967	−	0.943992i	$-0.392962\pi$
$53$	4.80440	0.659935	0.329967	+	0.943992i	$0.392962\pi$
$54$	12.2397	1.66561
$55$	4.29021	0.578491
$56$	−3.89167	−0.520046
$57$	−3.78334	−0.501116
$58$	−1.00000	−0.131306
$59$	−4.05783	−0.528284	−0.264142	−	0.964484i	$-0.585089\pi$
$59$	−4.05783	−0.528284	−0.264142	+	0.964484i	$0.585089\pi$
$60$	−3.14510	−0.406031
$61$	11.4353	1.46414	0.732071	−	0.681229i	$-0.238554\pi$
$61$	11.4353	1.46414	0.732071	+	0.681229i	$0.238554\pi$
$62$	−2.39853	−0.304614
$63$	−26.8201	−3.37902
$64$	1.00000	0.125000
$65$	−4.34803	−0.539307
$66$	−13.4931	−1.66089
$67$	9.08727	1.11019	0.555094	−	0.831788i	$-0.312682\pi$
$67$	9.08727	1.11019	0.555094	+	0.831788i	$0.312682\pi$
$68$	1.60147	0.194206
$69$	−26.2554	−3.16078
$70$	3.89167	0.465144
$71$	−12.0000	−1.42414	−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000	−1.42414	−0.712069	+	0.702109i	$0.752242\pi$
$72$	6.89167	0.812191
$73$	−2.39853	−0.280727	−0.140364	−	0.990100i	$-0.544827\pi$
$73$	−2.39853	−0.280727	−0.140364	+	0.990100i	$0.544827\pi$
$74$	−9.78334	−1.13729
$75$	3.14510	0.363165
$76$	−1.20293	−0.137986
$77$	16.6961	1.90269
$78$	13.6750	1.54839
$79$	7.55096	0.849550	0.424775	−	0.905299i	$-0.360353\pi$
$79$	7.55096	0.849550	0.424775	+	0.905299i	$0.360353\pi$
$80$	−1.00000	−0.111803
$81$	17.8201	1.98001
$82$	5.78334	0.638663
$83$	2.79707	0.307018	0.153509	−	0.988147i	$-0.450943\pi$
$83$	2.79707	0.307018	0.153509	+	0.988147i	$0.450943\pi$
$84$	−12.2397	−1.33546
$85$	−1.60147	−0.173703
$86$	3.60147	0.388356
$87$	−3.14510	−0.337190
$88$	−4.29021	−0.457337
$89$	−4.29021	−0.454761	−0.227380	−	0.973806i	$-0.573016\pi$
$89$	−4.29021	−0.454761	−0.227380	+	0.973806i	$0.573016\pi$
$90$	−6.89167	−0.726446
$91$	−16.9211	−1.77382
$92$	−8.34803	−0.870343
$93$	−7.54364	−0.782239
$94$	8.58041	0.885002
$95$	1.20293	0.123418
$96$	3.14510	0.320996
$97$	−0.348034	−0.0353375	−0.0176687	−	0.999844i	$-0.505624\pi$
$97$	−0.348034	−0.0353375	−0.0176687	+	0.999844i	$0.505624\pi$
$98$	8.14510	0.822780
$99$	−29.5667	−2.97156
$100$	1.00000	0.100000
$101$	−18.4216	−1.83302	−0.916508	−	0.400017i	$-0.869004\pi$
$101$	−18.4216	−1.83302	−0.916508	+	0.400017i	$0.869004\pi$
$102$	5.03677	0.498715
$103$	12.0735	1.18964	0.594821	−	0.803858i	$-0.297223\pi$
$103$	12.0735	1.18964	0.594821	+	0.803858i	$0.297223\pi$
$104$	4.34803	0.426360
$105$	12.2397	1.19447
$106$	4.80440	0.466644
$107$	−5.78334	−0.559097	−0.279548	−	0.960132i	$-0.590185\pi$
$107$	−5.78334	−0.559097	−0.279548	+	0.960132i	$0.590185\pi$
$108$	12.2397	1.17777
$109$	10.7971	1.03417	0.517086	−	0.855934i	$-0.327017\pi$
$109$	10.7971	1.03417	0.517086	+	0.855934i	$0.327017\pi$
$110$	4.29021	0.409055
$111$	−30.7696	−2.92052
$112$	−3.89167	−0.367728
$113$	12.2324	1.15073	0.575363	−	0.817898i	$-0.304861\pi$
$113$	12.2324	1.15073	0.575363	+	0.817898i	$0.304861\pi$
$114$	−3.78334	−0.354342
$115$	8.34803	0.778458
$116$	−1.00000	−0.0928477
$117$	29.9652	2.77029
$118$	−4.05783	−0.373553
$119$	−6.23238	−0.571321
$120$	−3.14510	−0.287107
$121$	7.40586	0.673260
$122$	11.4353	1.03530
$123$	18.1892	1.64007
$124$	−2.39853	−0.215395
$125$	−1.00000	−0.0894427
$126$	−26.8201	−2.38933
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	1.00000	0.0883883
$129$	11.3270	0.997285
$130$	−4.34803	−0.381348
$131$	−20.9863	−1.83358	−0.916790	−	0.399371i	$-0.869229\pi$
$131$	−20.9863	−1.83358	−0.916790	+	0.399371i	$0.869229\pi$
$132$	−13.4931	−1.17443
$133$	4.68141	0.405930
$134$	9.08727	0.785021
$135$	−12.2397	−1.05343
$136$	1.60147	0.137325
$137$	3.65197	0.312009	0.156004	−	0.987756i	$-0.450139\pi$
$137$	3.65197	0.312009	0.156004	+	0.987756i	$0.450139\pi$
$138$	−26.2554	−2.23501
$139$	13.6750	1.15990	0.579950	−	0.814652i	$-0.303072\pi$
$139$	13.6750	1.15990	0.579950	+	0.814652i	$0.303072\pi$
$140$	3.89167	0.328906
$141$	26.9863	2.27265
$142$	−12.0000	−1.00702
$143$	−18.6540	−1.55992
$144$	6.89167	0.574306
$145$	1.00000	0.0830455
$146$	−2.39853	−0.198504
$147$	25.6172	2.11287
$148$	−9.78334	−0.804186
$149$	7.27648	0.596112	0.298056	−	0.954548i	$-0.403662\pi$
$149$	7.27648	0.596112	0.298056	+	0.954548i	$0.403662\pi$
$150$	3.14510	0.256797
$151$	−8.69607	−0.707676	−0.353838	−	0.935307i	$-0.615124\pi$
$151$	−8.69607	−0.707676	−0.353838	+	0.935307i	$0.615124\pi$
$152$	−1.20293	−0.0975706
$153$	11.0368	0.892270
$154$	16.6961	1.34541
$155$	2.39853	0.192655
$156$	13.6750	1.09488
$157$	−10.0000	−0.798087	−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000	−0.798087	−0.399043	+	0.916932i	$0.630658\pi$
$158$	7.55096	0.600723
$159$	15.1103	1.19833
$160$	−1.00000	−0.0790569
$161$	32.4878	2.56040
$162$	17.8201	1.40008
$163$	−0.580411	−0.0454613	−0.0227306	−	0.999742i	$-0.507236\pi$
$163$	−0.580411	−0.0454613	−0.0227306	+	0.999742i	$0.507236\pi$
$164$	5.78334	0.451603
$165$	13.4931	1.05044
$166$	2.79707	0.217095
$167$	20.2554	1.56741	0.783706	−	0.621132i	$-0.213327\pi$
$167$	20.2554	1.56741	0.783706	+	0.621132i	$0.213327\pi$
$168$	−12.2397	−0.944314
$169$	5.90540	0.454261
$170$	−1.60147	−0.122827
$171$	−8.29021	−0.633968
$172$	3.60147	0.274609
$173$	−1.94217	−0.147661	−0.0738303	−	0.997271i	$-0.523522\pi$
$173$	−1.94217	−0.147661	−0.0738303	+	0.997271i	$0.523522\pi$
$174$	−3.14510	−0.238430
$175$	−3.89167	−0.294183
$176$	−4.29021	−0.323386
$177$	−12.7623	−0.959272
$178$	−4.29021	−0.321564
$179$	−10.9284	−0.816830	−0.408415	−	0.912796i	$-0.633918\pi$
$179$	−10.9284	−0.816830	−0.408415	+	0.912796i	$0.633918\pi$
$180$	−6.89167	−0.513675
$181$	−1.20293	−0.0894132	−0.0447066	−	0.999000i	$-0.514235\pi$
$181$	−1.20293	−0.0894132	−0.0447066	+	0.999000i	$0.514235\pi$
$182$	−16.9211	−1.25428
$183$	35.9652	2.65863
$184$	−8.34803	−0.615425
$185$	9.78334	0.719286
$186$	−7.54364	−0.553126
$187$	−6.87062	−0.502429
$188$	8.58041	0.625791
$189$	−47.6329	−3.46478
$190$	1.20293	0.0872698
$191$	−15.7760	−1.14151	−0.570756	−	0.821120i	$-0.693350\pi$
$191$	−15.7760	−1.14151	−0.570756	+	0.821120i	$0.693350\pi$
$192$	3.14510	0.226978
$193$	9.94217	0.715653	0.357827	−	0.933788i	$-0.383518\pi$
$193$	9.94217	0.715653	0.357827	+	0.933788i	$0.383518\pi$
$194$	−0.348034	−0.0249874
$195$	−13.6750	−0.979288
$196$	8.14510	0.581793
$197$	−25.1681	−1.79316	−0.896578	−	0.442885i	$-0.853955\pi$
$197$	−25.1681	−1.79316	−0.896578	+	0.442885i	$0.853955\pi$
$198$	−29.5667	−2.10121
$199$	−18.7696	−1.33054	−0.665271	−	0.746602i	$-0.731684\pi$
$199$	−18.7696	−1.33054	−0.665271	+	0.746602i	$0.731684\pi$
$200$	1.00000	0.0707107
$201$	28.5804	2.01591
$202$	−18.4216	−1.29614
$203$	3.89167	0.273142
$204$	5.03677	0.352645
$205$	−5.78334	−0.403926
$206$	12.0735	0.841204
$207$	−57.5319	−3.99874
$208$	4.34803	0.301482
$209$	5.16082	0.356981
$210$	12.2397	0.844620
$211$	12.2902	0.846093	0.423046	−	0.906108i	$-0.360961\pi$
$211$	12.2902	0.846093	0.423046	+	0.906108i	$0.360961\pi$
$212$	4.80440	0.329967
$213$	−37.7412	−2.58599
$214$	−5.78334	−0.395341
$215$	−3.60147	−0.245618
$216$	12.2397	0.832806
$217$	9.33431	0.633654
$218$	10.7971	0.731270
$219$	−7.54364	−0.509752
$220$	4.29021	0.289246
$221$	6.96323	0.468397
$222$	−30.7696	−2.06512
$223$	20.2324	1.35486	0.677430	−	0.735587i	$-0.263094\pi$
$223$	20.2324	1.35486	0.677430	+	0.735587i	$0.263094\pi$
$224$	−3.89167	−0.260023
$225$	6.89167	0.459445
$226$	12.2324	0.813686
$227$	8.98627	0.596440	0.298220	−	0.954497i	$-0.403607\pi$
$227$	8.98627	0.596440	0.298220	+	0.954497i	$0.403607\pi$
$228$	−3.78334	−0.250558
$229$	−21.2692	−1.40551	−0.702753	−	0.711434i	$-0.748046\pi$
$229$	−21.2692	−1.40551	−0.702753	+	0.711434i	$0.748046\pi$
$230$	8.34803	0.550453
$231$	52.5108	3.45496
$232$	−1.00000	−0.0656532
$233$	11.1608	0.731170	0.365585	−	0.930778i	$-0.380869\pi$
$233$	11.1608	0.731170	0.365585	+	0.930778i	$0.380869\pi$
$234$	29.9652	1.95889
$235$	−8.58041	−0.559724
$236$	−4.05783	−0.264142
$237$	23.7486	1.54263
$238$	−6.23238	−0.403985
$239$	−1.92645	−0.124612	−0.0623059	−	0.998057i	$-0.519845\pi$
$239$	−1.92645	−0.124612	−0.0623059	+	0.998057i	$0.519845\pi$
$240$	−3.14510	−0.203016
$241$	−17.7255	−1.14180	−0.570900	−	0.821019i	$-0.693406\pi$
$241$	−17.7255	−1.14180	−0.570900	+	0.821019i	$0.693406\pi$
$242$	7.40586	0.476067
$243$	19.3270	1.23983
$244$	11.4353	0.732071
$245$	−8.14510	−0.520372
$246$	18.1892	1.15970
$247$	−5.23039	−0.332801
$248$	−2.39853	−0.152307
$249$	8.79707	0.557492
$250$	−1.00000	−0.0632456
$251$	−14.3638	−0.906632	−0.453316	−	0.891350i	$-0.649759\pi$
$251$	−14.3638	−0.906632	−0.453316	+	0.891350i	$0.649759\pi$
$252$	−26.8201	−1.68951
$253$	35.8148	2.25166
$254$	8.00000	0.501965
$255$	−5.03677	−0.315415
$256$	1.00000	0.0625000
$257$	−14.3638	−0.895986	−0.447993	−	0.894037i	$-0.647861\pi$
$257$	−14.3638	−0.895986	−0.447993	+	0.894037i	$0.647861\pi$
$258$	11.3270	0.705187
$259$	38.0735	2.36578
$260$	−4.34803	−0.269654
$261$	−6.89167	−0.426584
$262$	−20.9863	−1.29654
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	−13.4931	−0.830445
$265$	−4.80440	−0.295132
$266$	4.68141	0.287036
$267$	−13.4931	−0.825767
$268$	9.08727	0.555094
$269$	−12.1083	−0.738258	−0.369129	−	0.929378i	$-0.620344\pi$
$269$	−12.1083	−0.738258	−0.369129	+	0.929378i	$0.620344\pi$
$270$	−12.2397	−0.744885
$271$	3.49314	0.212193	0.106096	−	0.994356i	$-0.466165\pi$
$271$	3.49314	0.212193	0.106096	+	0.994356i	$0.466165\pi$
$272$	1.60147	0.0971031
$273$	−53.2186	−3.22094
$274$	3.65197	0.220623
$275$	−4.29021	−0.258709
$276$	−26.2554	−1.58039
$277$	22.1471	1.33069	0.665345	−	0.746536i	$-0.268284\pi$
$277$	22.1471	1.33069	0.665345	+	0.746536i	$0.268284\pi$
$278$	13.6750	0.820173
$279$	−16.5299	−0.989620
$280$	3.89167	0.232572
$281$	−14.8779	−0.887544	−0.443772	−	0.896140i	$-0.646360\pi$
$281$	−14.8779	−0.887544	−0.443772	+	0.896140i	$0.646360\pi$
$282$	26.9863	1.60701
$283$	5.20293	0.309282	0.154641	−	0.987971i	$-0.450578\pi$
$283$	5.20293	0.309282	0.154641	+	0.987971i	$0.450578\pi$
$284$	−12.0000	−0.712069
$285$	3.78334	0.224106
$286$	−18.6540	−1.10303
$287$	−22.5069	−1.32854
$288$	6.89167	0.406096
$289$	−14.4353	−0.849136
$290$	1.00000	0.0587220
$291$	−1.09460	−0.0641667
$292$	−2.39853	−0.140364
$293$	17.7833	1.03891	0.519457	−	0.854497i	$-0.326134\pi$
$293$	17.7833	1.03891	0.519457	+	0.854497i	$0.326134\pi$
$294$	25.6172	1.49402
$295$	4.05783	0.236256
$296$	−9.78334	−0.568645
$297$	−52.5108	−3.04699
$298$	7.27648	0.421515
$299$	−36.2975	−2.09914
$300$	3.14510	0.181583
$301$	−14.0157	−0.807853
$302$	−8.69607	−0.500402
$303$	−57.9378	−3.32844
$304$	−1.20293	−0.0689928
$305$	−11.4353	−0.654784
$306$	11.0368	0.630930
$307$	2.40586	0.137310	0.0686549	−	0.997640i	$-0.478129\pi$
$307$	2.40586	0.137310	0.0686549	+	0.997640i	$0.478129\pi$
$308$	16.6961	0.951347
$309$	37.9725	2.16018
$310$	2.39853	0.136228
$311$	16.2470	0.921285	0.460642	−	0.887586i	$-0.347619\pi$
$311$	16.2470	0.921285	0.460642	+	0.887586i	$0.347619\pi$
$312$	13.6750	0.774195
$313$	−12.1745	−0.688146	−0.344073	−	0.938943i	$-0.611807\pi$
$313$	−12.1745	−0.688146	−0.344073	+	0.938943i	$0.611807\pi$
$314$	−10.0000	−0.564333
$315$	26.8201	1.51114
$316$	7.55096	0.424775
$317$	−13.6823	−0.768477	−0.384238	−	0.923234i	$-0.625536\pi$
$317$	−13.6823	−0.768477	−0.384238	+	0.923234i	$0.625536\pi$
$318$	15.1103	0.847345
$319$	4.29021	0.240205
$320$	−1.00000	−0.0559017
$321$	−18.1892	−1.01522
$322$	32.4878	1.81047
$323$	−1.92645	−0.107191
$324$	17.8201	0.990006
$325$	4.34803	0.241186
$326$	−0.580411	−0.0321460
$327$	33.9579	1.87788
$328$	5.78334	0.319332
$329$	−33.3921	−1.84097
$330$	13.4931	0.742773
$331$	8.87062	0.487573	0.243787	−	0.969829i	$-0.421610\pi$
$331$	8.87062	0.487573	0.243787	+	0.969829i	$0.421610\pi$
$332$	2.79707	0.153509
$333$	−67.4236	−3.69479
$334$	20.2554	1.10833
$335$	−9.08727	−0.496491
$336$	−12.2397	−0.667731
$337$	−14.1819	−0.772536	−0.386268	−	0.922387i	$-0.626236\pi$
$337$	−14.1819	−0.772536	−0.386268	+	0.922387i	$0.626236\pi$
$338$	5.90540	0.321211
$339$	38.4721	2.08952
$340$	−1.60147	−0.0868517
$341$	10.2902	0.557246
$342$	−8.29021	−0.448283
$343$	−4.45636	−0.240621
$344$	3.60147	0.194178
$345$	26.2554	1.41354
$346$	−1.94217	−0.104412
$347$	−27.1755	−1.45886	−0.729428	−	0.684058i	$-0.760214\pi$
$347$	−27.1755	−1.45886	−0.729428	+	0.684058i	$0.760214\pi$
$348$	−3.14510	−0.168595
$349$	1.31859	0.0705824	0.0352912	−	0.999377i	$-0.488764\pi$
$349$	1.31859	0.0705824	0.0352912	+	0.999377i	$0.488764\pi$
$350$	−3.89167	−0.208019
$351$	53.2186	2.84060
$352$	−4.29021	−0.228669
$353$	13.8990	0.739769	0.369885	−	0.929078i	$-0.379397\pi$
$353$	13.8990	0.739769	0.369885	+	0.929078i	$0.379397\pi$
$354$	−12.7623	−0.678308
$355$	12.0000	0.636894
$356$	−4.29021	−0.227380
$357$	−19.6015	−1.03742
$358$	−10.9284	−0.577586
$359$	1.26076	0.0665403	0.0332702	−	0.999446i	$-0.489408\pi$
$359$	1.26076	0.0665403	0.0332702	+	0.999446i	$0.489408\pi$
$360$	−6.89167	−0.363223
$361$	−17.5530	−0.923840
$362$	−1.20293	−0.0632247
$363$	23.2922	1.22252
$364$	−16.9211	−0.886908
$365$	2.39853	0.125545
$366$	35.9652	1.87993
$367$	−17.2765	−0.901825	−0.450912	−	0.892568i	$-0.648901\pi$
$367$	−17.2765	−0.901825	−0.450912	+	0.892568i	$0.648901\pi$
$368$	−8.34803	−0.435171
$369$	39.8569	2.07487
$370$	9.78334	0.508612
$371$	−18.6971	−0.970707
$372$	−7.54364	−0.391119
$373$	32.9515	1.70616	0.853082	−	0.521777i	$-0.174731\pi$
$373$	32.9515	1.70616	0.853082	+	0.521777i	$0.174731\pi$
$374$	−6.87062	−0.355271
$375$	−3.14510	−0.162412
$376$	8.58041	0.442501
$377$	−4.34803	−0.223935
$378$	−47.6329	−2.44997
$379$	−4.87062	−0.250187	−0.125093	−	0.992145i	$-0.539923\pi$
$379$	−4.87062	−0.250187	−0.125093	+	0.992145i	$0.539923\pi$
$380$	1.20293	0.0617091
$381$	25.1608	1.28903
$382$	−15.7760	−0.807171
$383$	−2.06622	−0.105579	−0.0527894	−	0.998606i	$-0.516811\pi$
$383$	−2.06622	−0.105579	−0.0527894	+	0.998606i	$0.516811\pi$
$384$	3.14510	0.160498
$385$	−16.6961	−0.850910
$386$	9.94217	0.506043
$387$	24.8201	1.26168
$388$	−0.348034	−0.0176687
$389$	23.9725	1.21546	0.607728	−	0.794145i	$-0.292081\pi$
$389$	23.9725	1.21546	0.607728	+	0.794145i	$0.292081\pi$
$390$	−13.6750	−0.692461
$391$	−13.3691	−0.676104
$392$	8.14510	0.411390
$393$	−66.0040	−3.32946
$394$	−25.1681	−1.26795
$395$	−7.55096	−0.379930
$396$	−29.5667	−1.48578
$397$	24.1544	1.21228	0.606138	−	0.795360i	$-0.292718\pi$
$397$	24.1544	1.21228	0.606138	+	0.795360i	$0.292718\pi$
$398$	−18.7696	−0.940836
$399$	14.7235	0.737098
$400$	1.00000	0.0500000
$401$	16.2470	0.811338	0.405669	−	0.914020i	$-0.367039\pi$
$401$	16.2470	0.811338	0.405669	+	0.914020i	$0.367039\pi$
$402$	28.5804	1.42546
$403$	−10.4289	−0.519501
$404$	−18.4216	−0.916508
$405$	−17.8201	−0.885489
$406$	3.89167	0.193140
$407$	41.9725	2.08050
$408$	5.03677	0.249357
$409$	9.08727	0.449337	0.224668	−	0.974435i	$-0.427870\pi$
$409$	9.08727	0.449337	0.224668	+	0.974435i	$0.427870\pi$
$410$	−5.78334	−0.285619
$411$	11.4858	0.566553
$412$	12.0735	0.594821
$413$	15.7917	0.777060
$414$	−57.5319	−2.82754
$415$	−2.79707	−0.137303
$416$	4.34803	0.213180
$417$	43.0093	2.10618
$418$	5.16082	0.252424
$419$	32.4446	1.58502	0.792512	−	0.609856i	$-0.208773\pi$
$419$	32.4446	1.58502	0.792512	+	0.609856i	$0.208773\pi$
$420$	12.2397	0.597236
$421$	25.5667	1.24604	0.623022	−	0.782204i	$-0.285905\pi$
$421$	25.5667	1.24604	0.623022	+	0.782204i	$0.285905\pi$
$422$	12.2902	0.598278
$423$	59.1334	2.87516
$424$	4.80440	0.233322
$425$	1.60147	0.0776825
$426$	−37.7412	−1.82857
$427$	−44.5025	−2.15362
$428$	−5.78334	−0.279548
$429$	−58.6686	−2.83255
$430$	−3.60147	−0.173678
$431$	−1.70979	−0.0823579	−0.0411790	−	0.999152i	$-0.513111\pi$
$431$	−1.70979	−0.0823579	−0.0411790	+	0.999152i	$0.513111\pi$
$432$	12.2397	0.588883
$433$	−23.7412	−1.14093	−0.570465	−	0.821322i	$-0.693237\pi$
$433$	−23.7412	−1.14093	−0.570465	+	0.821322i	$0.693237\pi$
$434$	9.33431	0.448061
$435$	3.14510	0.150796
$436$	10.7971	0.517086
$437$	10.0421	0.480379
$438$	−7.54364	−0.360449
$439$	−8.47941	−0.404700	−0.202350	−	0.979313i	$-0.564858\pi$
$439$	−8.47941	−0.404700	−0.202350	+	0.979313i	$0.564858\pi$
$440$	4.29021	0.204528
$441$	56.1334	2.67302
$442$	6.96323	0.331207
$443$	18.4490	0.876540	0.438270	−	0.898843i	$-0.355591\pi$
$443$	18.4490	0.876540	0.438270	+	0.898843i	$0.355591\pi$
$444$	−30.7696	−1.46026
$445$	4.29021	0.203375
$446$	20.2324	0.958031
$447$	22.8853	1.08244
$448$	−3.89167	−0.183864
$449$	−11.3775	−0.536936	−0.268468	−	0.963289i	$-0.586517\pi$
$449$	−11.3775	−0.536936	−0.268468	+	0.963289i	$0.586517\pi$
$450$	6.89167	0.324876
$451$	−24.8117	−1.16834
$452$	12.2324	0.575363
$453$	−27.3500	−1.28502
$454$	8.98627	0.421747
$455$	16.9211	0.793274
$456$	−3.78334	−0.177171
$457$	−4.40586	−0.206098	−0.103049	−	0.994676i	$-0.532860\pi$
$457$	−4.40586	−0.206098	−0.103049	+	0.994676i	$0.532860\pi$
$458$	−21.2692	−0.993842
$459$	19.6015	0.914918
$460$	8.34803	0.389229
$461$	15.3113	0.713116	0.356558	−	0.934273i	$-0.383950\pi$
$461$	15.3113	0.713116	0.356558	+	0.934273i	$0.383950\pi$
$462$	52.5108	2.44303
$463$	−17.0873	−0.794113	−0.397056	−	0.917794i	$-0.629968\pi$
$463$	−17.0873	−0.794113	−0.397056	+	0.917794i	$0.629968\pi$
$464$	−1.00000	−0.0464238
$465$	7.54364	0.349828
$466$	11.1608	0.517015
$467$	−22.3711	−1.03521	−0.517605	−	0.855620i	$-0.673176\pi$
$467$	−22.3711	−1.03521	−0.517605	+	0.855620i	$0.673176\pi$
$468$	29.9652	1.38514
$469$	−35.3647	−1.63299
$470$	−8.58041	−0.395785
$471$	−31.4510	−1.44919
$472$	−4.05783	−0.186777
$473$	−15.4510	−0.710439
$474$	23.7486	1.09081
$475$	−1.20293	−0.0551943
$476$	−6.23238	−0.285661
$477$	33.1103	1.51602
$478$	−1.92645	−0.0881139
$479$	−8.00733	−0.365864	−0.182932	−	0.983126i	$-0.558559\pi$
$479$	−8.00733	−0.365864	−0.182932	+	0.983126i	$0.558559\pi$
$480$	−3.14510	−0.143554
$481$	−42.5383	−1.93958
$482$	−17.7255	−0.807375
$483$	102.177	4.64924
$484$	7.40586	0.336630
$485$	0.348034	0.0158034
$486$	19.3270	0.876690
$487$	−17.0441	−0.772342	−0.386171	−	0.922427i	$-0.626203\pi$
$487$	−17.0441	−0.772342	−0.386171	+	0.922427i	$0.626203\pi$
$488$	11.4353	0.517652
$489$	−1.82545	−0.0825498
$490$	−8.14510	−0.367958
$491$	37.0873	1.67373	0.836863	−	0.547413i	$-0.184387\pi$
$491$	37.0873	1.67373	0.836863	+	0.547413i	$0.184387\pi$
$492$	18.1892	0.820033
$493$	−1.60147	−0.0721264
$494$	−5.23039	−0.235326
$495$	29.5667	1.32892
$496$	−2.39853	−0.107697
$497$	46.7001	2.09478
$498$	8.79707	0.394206
$499$	−23.5089	−1.05240	−0.526200	−	0.850361i	$-0.676384\pi$
$499$	−23.5089	−1.05240	−0.526200	+	0.850361i	$0.676384\pi$
$500$	−1.00000	−0.0447214
$501$	63.7054	2.84615
$502$	−14.3638	−0.641086
$503$	17.1608	0.765163	0.382582	−	0.923922i	$-0.375035\pi$
$503$	17.1608	0.765163	0.382582	+	0.923922i	$0.375035\pi$
$504$	−26.8201	−1.19466
$505$	18.4216	0.819750
$506$	35.8148	1.59216
$507$	18.5731	0.824860
$508$	8.00000	0.354943
$509$	−14.3638	−0.636662	−0.318331	−	0.947980i	$-0.603122\pi$
$509$	−14.3638	−0.636662	−0.318331	+	0.947980i	$0.603122\pi$
$510$	−5.03677	−0.223032
$511$	9.33431	0.412925
$512$	1.00000	0.0441942
$513$	−14.7235	−0.650059
$514$	−14.3638	−0.633558
$515$	−12.0735	−0.532024
$516$	11.3270	0.498642
$517$	−36.8117	−1.61898
$518$	38.0735	1.67286
$519$	−6.10833	−0.268126
$520$	−4.34803	−0.190674
$521$	−32.0388	−1.40364	−0.701822	−	0.712352i	$-0.747630\pi$
$521$	−32.0388	−1.40364	−0.701822	+	0.712352i	$0.747630\pi$
$522$	−6.89167	−0.301640
$523$	−26.9442	−1.17819	−0.589093	−	0.808065i	$-0.700515\pi$
$523$	−26.9442	−1.17819	−0.589093	+	0.808065i	$0.700515\pi$
$524$	−20.9863	−0.916790
$525$	−12.2397	−0.534185
$526$	−12.0000	−0.523225
$527$	−3.84117	−0.167324
$528$	−13.4931	−0.587213
$529$	46.6897	2.02999
$530$	−4.80440	−0.208690
$531$	−27.9652	−1.21359
$532$	4.68141	0.202965
$533$	25.1462	1.08920
$534$	−13.4931	−0.583905
$535$	5.78334	0.250036
$536$	9.08727	0.392510
$537$	−34.3711	−1.48322
$538$	−12.1083	−0.522027
$539$	−34.9442	−1.50515
$540$	−12.2397	−0.526713
$541$	−13.5005	−0.580430	−0.290215	−	0.956961i	$-0.593727\pi$
$541$	−13.5005	−0.580430	−0.290215	+	0.956961i	$0.593727\pi$
$542$	3.49314	0.150043
$543$	−3.78334	−0.162359
$544$	1.60147	0.0686623
$545$	−10.7971	−0.462496
$546$	−53.2186	−2.27755
$547$	35.1755	1.50399	0.751997	−	0.659166i	$-0.229091\pi$
$547$	35.1755	1.50399	0.751997	+	0.659166i	$0.229091\pi$
$548$	3.65197	0.156004
$549$	78.8084	3.36346
$550$	−4.29021	−0.182935
$551$	1.20293	0.0512466
$552$	−26.2554	−1.11751
$553$	−29.3859	−1.24961
$554$	22.1471	0.940940
$555$	30.7696	1.30610
$556$	13.6750	0.579950
$557$	18.6382	0.789728	0.394864	−	0.918740i	$-0.370792\pi$
$557$	18.6382	0.789728	0.394864	+	0.918740i	$0.370792\pi$
$558$	−16.5299	−0.699767
$559$	15.6593	0.662318
$560$	3.89167	0.164453
$561$	−21.6088	−0.912324
$562$	−14.8779	−0.627588
$563$	−0.421581	−0.0177675	−0.00888376	−	0.999961i	$-0.502828\pi$
$563$	−0.421581	−0.0177675	−0.00888376	+	0.999961i	$0.502828\pi$
$564$	26.9863	1.13633
$565$	−12.2324	−0.514620
$566$	5.20293	0.218696
$567$	−69.3500	−2.91243
$568$	−12.0000	−0.503509
$569$	7.49314	0.314129	0.157064	−	0.987588i	$-0.449797\pi$
$569$	7.49314	0.314129	0.157064	+	0.987588i	$0.449797\pi$
$570$	3.78334	0.158467
$571$	6.46369	0.270497	0.135249	−	0.990812i	$-0.456817\pi$
$571$	6.46369	0.270497	0.135249	+	0.990812i	$0.456817\pi$
$572$	−18.6540	−0.779961
$573$	−49.6172	−2.07279
$574$	−22.5069	−0.939418
$575$	−8.34803	−0.348137
$576$	6.89167	0.287153
$577$	−31.5594	−1.31383	−0.656917	−	0.753963i	$-0.728140\pi$
$577$	−31.5594	−1.31383	−0.656917	+	0.753963i	$0.728140\pi$
$578$	−14.4353	−0.600430
$579$	31.2692	1.29950
$580$	1.00000	0.0415227
$581$	−10.8853	−0.451597
$582$	−1.09460	−0.0453727
$583$	−20.6118	−0.853656
$584$	−2.39853	−0.0992521
$585$	−29.9652	−1.23891
$586$	17.7833	0.734623
$587$	−11.5941	−0.478541	−0.239271	−	0.970953i	$-0.576908\pi$
$587$	−11.5941	−0.478541	−0.239271	+	0.970953i	$0.576908\pi$
$588$	25.6172	1.05643
$589$	2.88527	0.118886
$590$	4.05783	0.167058
$591$	−79.1564	−3.25606
$592$	−9.78334	−0.402093
$593$	−18.4648	−0.758257	−0.379128	−	0.925344i	$-0.623776\pi$
$593$	−18.4648	−0.758257	−0.379128	+	0.925344i	$0.623776\pi$
$594$	−52.5108	−2.15455
$595$	6.23238	0.255503
$596$	7.27648	0.298056
$597$	−59.0324	−2.41603
$598$	−36.2975	−1.48432
$599$	−28.3711	−1.15921	−0.579605	−	0.814897i	$-0.696793\pi$
$599$	−28.3711	−1.15921	−0.579605	+	0.814897i	$0.696793\pi$
$600$	3.14510	0.128398
$601$	−34.4648	−1.40585	−0.702923	−	0.711266i	$-0.748122\pi$
$601$	−34.4648	−1.40585	−0.702923	+	0.711266i	$0.748122\pi$
$602$	−14.0157	−0.571238
$603$	62.6265	2.55035
$604$	−8.69607	−0.353838
$605$	−7.40586	−0.301091
$606$	−57.9378	−2.35356
$607$	36.7275	1.49072	0.745362	−	0.666660i	$-0.232277\pi$
$607$	36.7275	1.49072	0.745362	+	0.666660i	$0.232277\pi$
$608$	−1.20293	−0.0487853
$609$	12.2397	0.495978
$610$	−11.4353	−0.463002
$611$	37.3079	1.50932
$612$	11.0368	0.446135
$613$	8.95149	0.361547	0.180774	−	0.983525i	$-0.442140\pi$
$613$	8.95149	0.361547	0.180774	+	0.983525i	$0.442140\pi$
$614$	2.40586	0.0970927
$615$	−18.1892	−0.733460
$616$	16.6961	0.672704
$617$	22.3985	0.901731	0.450866	−	0.892592i	$-0.351115\pi$
$617$	22.3985	0.901731	0.450866	+	0.892592i	$0.351115\pi$
$618$	37.9725	1.52748
$619$	31.5392	1.26767	0.633834	−	0.773469i	$-0.281480\pi$
$619$	31.5392	1.26767	0.633834	+	0.773469i	$0.281480\pi$
$620$	2.39853	0.0963275
$621$	−102.177	−4.10024
$622$	16.2470	0.651447
$623$	16.6961	0.668914
$624$	13.6750	0.547439
$625$	1.00000	0.0400000
$626$	−12.1745	−0.486593
$627$	16.2313	0.648216
$628$	−10.0000	−0.399043
$629$	−15.6677	−0.624712
$630$	26.8201	1.06854
$631$	−41.0598	−1.63457	−0.817283	−	0.576237i	$-0.804521\pi$
$631$	−41.0598	−1.63457	−0.817283	+	0.576237i	$0.804521\pi$
$632$	7.55096	0.300361
$633$	38.6540	1.53636
$634$	−13.6823	−0.543395
$635$	−8.00000	−0.317470
$636$	15.1103	0.599163
$637$	35.4152	1.40320
$638$	4.29021	0.169851
$639$	−82.7001	−3.27156
$640$	−1.00000	−0.0395285
$641$	40.5383	1.60117	0.800583	−	0.599221i	$-0.204523\pi$
$641$	40.5383	1.60117	0.800583	+	0.599221i	$0.204523\pi$
$642$	−18.1892	−0.717871
$643$	−35.2765	−1.39117	−0.695584	−	0.718445i	$-0.744854\pi$
$643$	−35.2765	−1.39117	−0.695584	+	0.718445i	$0.744854\pi$
$644$	32.4878	1.28020
$645$	−11.3270	−0.445999
$646$	−1.92645	−0.0757953
$647$	−3.69514	−0.145271	−0.0726355	−	0.997359i	$-0.523141\pi$
$647$	−3.69514	−0.145271	−0.0726355	+	0.997359i	$0.523141\pi$
$648$	17.8201	0.700040
$649$	17.4089	0.683360
$650$	4.34803	0.170544
$651$	29.3574	1.15061
$652$	−0.580411	−0.0227306
$653$	−8.52152	−0.333473	−0.166736	−	0.986002i	$-0.553323\pi$
$653$	−8.52152	−0.333473	−0.166736	+	0.986002i	$0.553323\pi$
$654$	33.9579	1.32786
$655$	20.9863	0.820002
$656$	5.78334	0.225802
$657$	−16.5299	−0.644893
$658$	−33.3921	−1.30176
$659$	−5.10193	−0.198743	−0.0993715	−	0.995050i	$-0.531683\pi$
$659$	−5.10193	−0.198743	−0.0993715	+	0.995050i	$0.531683\pi$
$660$	13.4931	0.525220
$661$	−14.6961	−0.571611	−0.285805	−	0.958288i	$-0.592261\pi$
$661$	−14.6961	−0.571611	−0.285805	+	0.958288i	$0.592261\pi$
$662$	8.87062	0.344766
$663$	21.9001	0.850528
$664$	2.79707	0.108547
$665$	−4.68141	−0.181537
$666$	−67.4236	−2.61261
$667$	8.34803	0.323237
$668$	20.2554	0.783706
$669$	63.6329	2.46019
$670$	−9.08727	−0.351072
$671$	−49.0598	−1.89393
$672$	−12.2397	−0.472157
$673$	−25.5813	−0.986088	−0.493044	−	0.870004i	$-0.664116\pi$
$673$	−25.5813	−0.986088	−0.493044	+	0.870004i	$0.664116\pi$
$674$	−14.1819	−0.546265
$675$	12.2397	0.471106
$676$	5.90540	0.227131
$677$	−21.2344	−0.816103	−0.408052	−	0.912959i	$-0.633792\pi$
$677$	−21.2344	−0.816103	−0.408052	+	0.912959i	$0.633792\pi$
$678$	38.4721	1.47751
$679$	1.35443	0.0519784
$680$	−1.60147	−0.0614134
$681$	28.2628	1.08303
$682$	10.2902	0.394032
$683$	−22.1324	−0.846874	−0.423437	−	0.905925i	$-0.639177\pi$
$683$	−22.1324	−0.846874	−0.423437	+	0.905925i	$0.639177\pi$
$684$	−8.29021	−0.316984
$685$	−3.65197	−0.139534
$686$	−4.45636	−0.170145
$687$	−66.8937	−2.55215
$688$	3.60147	0.137305
$689$	20.8897	0.795833
$690$	26.2554	0.999527
$691$	8.08088	0.307411	0.153705	−	0.988117i	$-0.450879\pi$
$691$	8.08088	0.307411	0.153705	+	0.988117i	$0.450879\pi$
$692$	−1.94217	−0.0738303
$693$	115.064	4.37091
$694$	−27.1755	−1.03157
$695$	−13.6750	−0.518723
$696$	−3.14510	−0.119215
$697$	9.26182	0.350817
$698$	1.31859	0.0499093
$699$	35.1019	1.32768
$700$	−3.89167	−0.147091
$701$	28.2902	1.06851	0.534253	−	0.845325i	$-0.320593\pi$
$701$	28.2902	1.06851	0.534253	+	0.845325i	$0.320593\pi$
$702$	53.2186	2.00861
$703$	11.7687	0.443864
$704$	−4.29021	−0.161693
$705$	−26.9863	−1.01636
$706$	13.8990	0.523096
$707$	71.6907	2.69621
$708$	−12.7623	−0.479636
$709$	52.2060	1.96064	0.980318	−	0.197423i	$-0.0632571\pi$
$709$	52.2060	1.96064	0.980318	+	0.197423i	$0.0632571\pi$
$710$	12.0000	0.450352
$711$	52.0388	1.95161
$712$	−4.29021	−0.160782
$713$	20.0230	0.749869
$714$	−19.6015	−0.733566
$715$	18.6540	0.697618
$716$	−10.9284	−0.408415
$717$	−6.05889	−0.226273
$718$	1.26076	0.0470511
$719$	27.0177	1.00759	0.503795	−	0.863823i	$-0.331937\pi$
$719$	27.0177	1.00759	0.503795	+	0.863823i	$0.331937\pi$
$720$	−6.89167	−0.256837
$721$	−46.9863	−1.74986
$722$	−17.5530	−0.653253
$723$	−55.7486	−2.07331
$724$	−1.20293	−0.0447066
$725$	−1.00000	−0.0371391
$726$	23.2922	0.864455
$727$	−33.7559	−1.25194	−0.625968	−	0.779849i	$-0.715296\pi$
$727$	−33.7559	−1.25194	−0.625968	+	0.779849i	$0.715296\pi$
$728$	−16.9211	−0.627138
$729$	7.32499	0.271296
$730$	2.39853	0.0887737
$731$	5.76762	0.213323
$732$	35.9652	1.32931
$733$	9.52059	0.351651	0.175826	−	0.984421i	$-0.443741\pi$
$733$	9.52059	0.351651	0.175826	+	0.984421i	$0.443741\pi$
$734$	−17.2765	−0.637686
$735$	−25.6172	−0.944904
$736$	−8.34803	−0.307713
$737$	−38.9863	−1.43608
$738$	39.8569	1.46715
$739$	0.0735473	0.00270548	0.00135274	−	0.999999i	$-0.499569\pi$
$739$	0.0735473	0.00270548	0.00135274	+	0.999999i	$0.499569\pi$
$740$	9.78334	0.359643
$741$	−16.4501	−0.604309
$742$	−18.6971	−0.686393
$743$	27.4196	1.00593	0.502964	−	0.864308i	$-0.332243\pi$
$743$	27.4196	1.00593	0.502964	+	0.864308i	$0.332243\pi$
$744$	−7.54364	−0.276563
$745$	−7.27648	−0.266590
$746$	32.9515	1.20644
$747$	19.2765	0.705289
$748$	−6.87062	−0.251215
$749$	22.5069	0.822383
$750$	−3.14510	−0.114843
$751$	−17.0873	−0.623523	−0.311762	−	0.950160i	$-0.600919\pi$
$751$	−17.0873	−0.623523	−0.311762	+	0.950160i	$0.600919\pi$
$752$	8.58041	0.312895
$753$	−45.1755	−1.64629
$754$	−4.34803	−0.158346
$755$	8.69607	0.316482
$756$	−47.6329	−1.73239
$757$	25.7833	0.937111	0.468556	−	0.883434i	$-0.344775\pi$
$757$	25.7833	0.937111	0.468556	+	0.883434i	$0.344775\pi$
$758$	−4.87062	−0.176909
$759$	112.641	4.08862
$760$	1.20293	0.0436349
$761$	9.28381	0.336538	0.168269	−	0.985741i	$-0.446182\pi$
$761$	9.28381	0.336538	0.168269	+	0.985741i	$0.446182\pi$
$762$	25.1608	0.911480
$763$	−42.0186	−1.52118
$764$	−15.7760	−0.570756
$765$	−11.0368	−0.399035
$766$	−2.06622	−0.0746555
$767$	−17.6436	−0.637073
$768$	3.14510	0.113489
$769$	−33.1019	−1.19369	−0.596843	−	0.802358i	$-0.703579\pi$
$769$	−33.1019	−1.19369	−0.596843	+	0.802358i	$0.703579\pi$
$770$	−16.6961	−0.601685
$771$	−45.1755	−1.62696
$772$	9.94217	0.357827
$773$	25.7687	0.926835	0.463418	−	0.886140i	$-0.346623\pi$
$773$	25.7687	0.926835	0.463418	+	0.886140i	$0.346623\pi$
$774$	24.8201	0.892141
$775$	−2.39853	−0.0861579
$776$	−0.348034	−0.0124937
$777$	119.745	4.29584
$778$	23.9725	0.859457
$779$	−6.95696	−0.249259
$780$	−13.6750	−0.489644
$781$	51.4825	1.84219
$782$	−13.3691	−0.478078
$783$	−12.2397	−0.437411
$784$	8.14510	0.290897
$785$	10.0000	0.356915
$786$	−66.0040	−2.35428
$787$	−33.3500	−1.18880	−0.594400	−	0.804170i	$-0.702610\pi$
$787$	−33.3500	−1.18880	−0.594400	+	0.804170i	$0.702610\pi$
$788$	−25.1681	−0.896578
$789$	−37.7412	−1.34362
$790$	−7.55096	−0.268651
$791$	−47.6044	−1.69262
$792$	−29.5667	−1.05061
$793$	49.7211	1.76565
$794$	24.1544	0.857208
$795$	−15.1103	−0.535908
$796$	−18.7696	−0.665271
$797$	−7.05982	−0.250072	−0.125036	−	0.992152i	$-0.539905\pi$
$797$	−7.05982	−0.250072	−0.125036	+	0.992152i	$0.539905\pi$
$798$	14.7235	0.521207
$799$	13.7412	0.486130
$800$	1.00000	0.0353553
$801$	−29.5667	−1.04469
$802$	16.2470	0.573703
$803$	10.2902	0.363133
$804$	28.5804	1.00795
$805$	−32.4878	−1.14504
$806$	−10.4289	−0.367343
$807$	−38.0819	−1.34055
$808$	−18.4216	−0.648069
$809$	18.6814	0.656803	0.328402	−	0.944538i	$-0.393490\pi$
$809$	18.6814	0.656803	0.328402	+	0.944538i	$0.393490\pi$
$810$	−17.8201	−0.626135
$811$	36.2133	1.27162	0.635811	−	0.771845i	$-0.280666\pi$
$811$	36.2133	1.27162	0.635811	+	0.771845i	$0.280666\pi$
$812$	3.89167	0.136571
$813$	10.9863	0.385305
$814$	41.9725	1.47114
$815$	0.580411	0.0203309
$816$	5.03677	0.176322
$817$	−4.33231	−0.151569
$818$	9.08727	0.317729
$819$	−116.615	−4.07485
$820$	−5.78334	−0.201963
$821$	−36.8706	−1.28679	−0.643397	−	0.765533i	$-0.722475\pi$
$821$	−36.8706	−1.28679	−0.643397	+	0.765533i	$0.722475\pi$
$822$	11.4858	0.400614
$823$	39.0324	1.36058	0.680291	−	0.732942i	$-0.261853\pi$
$823$	39.0324	1.36058	0.680291	+	0.732942i	$0.261853\pi$
$824$	12.0735	0.420602
$825$	−13.4931	−0.469771
$826$	15.7917	0.549465
$827$	17.2103	0.598459	0.299230	−	0.954181i	$-0.403270\pi$
$827$	17.2103	0.598459	0.299230	+	0.954181i	$0.403270\pi$
$828$	−57.5319	−1.99937
$829$	32.7034	1.13584	0.567918	−	0.823085i	$-0.307749\pi$
$829$	32.7034	1.13584	0.567918	+	0.823085i	$0.307749\pi$
$830$	−2.79707	−0.0970877
$831$	69.6549	2.41630
$832$	4.34803	0.150741
$833$	13.0441	0.451951
$834$	43.0093	1.48929
$835$	−20.2554	−0.700968
$836$	5.16082	0.178491
$837$	−29.3574	−1.01474
$838$	32.4446	1.12078
$839$	−32.3049	−1.11529	−0.557644	−	0.830080i	$-0.688294\pi$
$839$	−32.3049	−1.11529	−0.557644	+	0.830080i	$0.688294\pi$
$840$	12.2397	0.422310
$841$	1.00000	0.0344828
$842$	25.5667	0.881086
$843$	−46.7927	−1.61162
$844$	12.2902	0.423046
$845$	−5.90540	−0.203152
$846$	59.1334	2.03305
$847$	−28.8212	−0.990307
$848$	4.80440	0.164984
$849$	16.3638	0.561603
$850$	1.60147	0.0549298
$851$	81.6717	2.79967
$852$	−37.7412	−1.29299
$853$	46.7422	1.60042	0.800211	−	0.599719i	$-0.204721\pi$
$853$	46.7422	1.60042	0.800211	+	0.599719i	$0.204721\pi$
$854$	−44.5025	−1.52284
$855$	8.29021	0.283519
$856$	−5.78334	−0.197671
$857$	30.4648	1.04066	0.520328	−	0.853966i	$-0.325810\pi$
$857$	30.4648	1.04066	0.520328	+	0.853966i	$0.325810\pi$
$858$	−58.6686	−2.00291
$859$	−30.7971	−1.05078	−0.525391	−	0.850861i	$-0.676081\pi$
$859$	−30.7971	−1.05078	−0.525391	+	0.850861i	$0.676081\pi$
$860$	−3.60147	−0.122809
$861$	−70.7864	−2.41239
$862$	−1.70979	−0.0582358
$863$	34.9010	1.18804	0.594022	−	0.804449i	$-0.297539\pi$
$863$	34.9010	1.18804	0.594022	+	0.804449i	$0.297539\pi$
$864$	12.2397	0.416403
$865$	1.94217	0.0660358
$866$	−23.7412	−0.806760
$867$	−45.4005	−1.54188
$868$	9.33431	0.316827
$869$	−32.3952	−1.09893
$870$	3.14510	0.106629
$871$	39.5118	1.33881
$872$	10.7971	0.365635
$873$	−2.39853	−0.0811781
$874$	10.0421	0.339679
$875$	3.89167	0.131562
$876$	−7.54364	−0.254876
$877$	36.9599	1.24805	0.624023	−	0.781406i	$-0.285497\pi$
$877$	36.9599	1.24805	0.624023	+	0.781406i	$0.285497\pi$
$878$	−8.47941	−0.286166
$879$	55.9304	1.88649
$880$	4.29021	0.144623
$881$	25.0009	0.842303	0.421151	−	0.906990i	$-0.361626\pi$
$881$	25.0009	0.842303	0.421151	+	0.906990i	$0.361626\pi$
$882$	56.1334	1.89011
$883$	52.7696	1.77584	0.887919	−	0.459999i	$-0.152150\pi$
$883$	52.7696	1.77584	0.887919	+	0.459999i	$0.152150\pi$
$884$	6.96323	0.234199
$885$	12.7623	0.429000
$886$	18.4490	0.619807
$887$	−23.5667	−0.791292	−0.395646	−	0.918403i	$-0.629479\pi$
$887$	−23.5667	−0.791292	−0.395646	+	0.918403i	$0.629479\pi$
$888$	−30.7696	−1.03256
$889$	−31.1334	−1.04418
$890$	4.29021	0.143808
$891$	−76.4520	−2.56124
$892$	20.2324	0.677430
$893$	−10.3216	−0.345401
$894$	22.8853	0.765398
$895$	10.9284	0.365298
$896$	−3.89167	−0.130012
$897$	−114.159	−3.81167
$898$	−11.3775	−0.379671
$899$	2.39853	0.0799956
$900$	6.89167	0.229722
$901$	7.69408	0.256327
$902$	−24.8117	−0.826140
$903$	−44.0809	−1.46692
$904$	12.2324	0.406843
$905$	1.20293	0.0399868
$906$	−27.3500	−0.908644
$907$	25.2103	0.837093	0.418546	−	0.908195i	$-0.362540\pi$
$907$	25.2103	0.837093	0.418546	+	0.908195i	$0.362540\pi$
$908$	8.98627	0.298220
$909$	−126.955	−4.21085
$910$	16.9211	0.560930
$911$	32.5961	1.07996	0.539979	−	0.841679i	$-0.318432\pi$
$911$	32.5961	1.07996	0.539979	+	0.841679i	$0.318432\pi$
$912$	−3.78334	−0.125279
$913$	−12.0000	−0.397142
$914$	−4.40586	−0.145733
$915$	−35.9652	−1.18897
$916$	−21.2692	−0.702753
$917$	81.6717	2.69704
$918$	19.6015	0.646945
$919$	44.0000	1.45143	0.725713	−	0.687998i	$-0.241510\pi$
$919$	44.0000	1.45143	0.725713	+	0.687998i	$0.241510\pi$
$920$	8.34803	0.275227
$921$	7.56668	0.249331
$922$	15.3113	0.504249
$923$	−52.1764	−1.71741
$924$	52.5108	1.72748
$925$	−9.78334	−0.321674
$926$	−17.0873	−0.561523
$927$	83.2069	2.73287
$928$	−1.00000	−0.0328266
$929$	5.05249	0.165767	0.0828835	−	0.996559i	$-0.473587\pi$
$929$	5.05249	0.165767	0.0828835	+	0.996559i	$0.473587\pi$
$930$	7.54364	0.247366
$931$	−9.79800	−0.321116
$932$	11.1608	0.365585
$933$	51.0986	1.67289
$934$	−22.3711	−0.732004
$935$	6.87062	0.224693
$936$	29.9652	0.979444
$937$	−19.6088	−0.640591	−0.320296	−	0.947318i	$-0.603782\pi$
$937$	−19.6088	−0.640591	−0.320296	+	0.947318i	$0.603782\pi$
$938$	−35.3647	−1.15470
$939$	−38.2902	−1.24955
$940$	−8.58041	−0.279862
$941$	6.68141	0.217808	0.108904	−	0.994052i	$-0.465266\pi$
$941$	6.68141	0.217808	0.108904	+	0.994052i	$0.465266\pi$
$942$	−31.4510	−1.02473
$943$	−48.2795	−1.57220
$944$	−4.05783	−0.132071
$945$	47.6329	1.54950
$946$	−15.4510	−0.502356
$947$	33.4667	1.08752	0.543762	−	0.839240i	$-0.317000\pi$
$947$	33.4667	1.08752	0.543762	+	0.839240i	$0.317000\pi$
$948$	23.7486	0.771317
$949$	−10.4289	−0.338537
$950$	−1.20293	−0.0390282
$951$	−43.0324	−1.39542
$952$	−6.23238	−0.201992
$953$	−43.7412	−1.41692	−0.708459	−	0.705752i	$-0.750609\pi$
$953$	−43.7412	−1.41692	−0.708459	+	0.705752i	$0.750609\pi$
$954$	33.1103	1.07199
$955$	15.7760	0.510500
$956$	−1.92645	−0.0623059
$957$	13.4931	0.436171
$958$	−8.00733	−0.258705
$959$	−14.2123	−0.458938
$960$	−3.14510	−0.101508
$961$	−25.2470	−0.814420
$962$	−42.5383	−1.37149
$963$	−39.8569	−1.28437
$964$	−17.7255	−0.570900
$965$	−9.94217	−0.320050
$966$	102.177	3.28751
$967$	−35.9304	−1.15544	−0.577722	−	0.816233i	$-0.696058\pi$
$967$	−35.9304	−1.15544	−0.577722	+	0.816233i	$0.696058\pi$
$968$	7.40586	0.238033
$969$	−6.05889	−0.194640
$970$	0.348034	0.0111747
$971$	26.7971	0.859959	0.429979	−	0.902839i	$-0.358521\pi$
$971$	26.7971	0.859959	0.429979	+	0.902839i	$0.358521\pi$
$972$	19.3270	0.619913
$973$	−53.2186	−1.70611
$974$	−17.0441	−0.546128
$975$	13.6750	0.437951
$976$	11.4353	0.366035
$977$	−21.4510	−0.686279	−0.343140	−	0.939284i	$-0.611490\pi$
$977$	−21.4510	−0.686279	−0.343140	+	0.939284i	$0.611490\pi$
$978$	−1.82545	−0.0583715
$979$	18.4059	0.588254
$980$	−8.14510	−0.260186
$981$	74.4098	2.37572
$982$	37.0873	1.18350
$983$	49.8715	1.59066	0.795328	−	0.606180i	$-0.207299\pi$
$983$	49.8715	1.59066	0.795328	+	0.606180i	$0.207299\pi$
$984$	18.1892	0.579851
$985$	25.1681	0.801924
$986$	−1.60147	−0.0510011
$987$	−105.022	−3.34288
$988$	−5.23039	−0.166401
$989$	−30.0652	−0.956016
$990$	29.5667	0.939691
$991$	−16.2167	−0.515139	−0.257570	−	0.966260i	$-0.582922\pi$
$991$	−16.2167	−0.515139	−0.257570	+	0.966260i	$0.582922\pi$
$992$	−2.39853	−0.0761535
$993$	27.8990	0.885348
$994$	46.7001	1.48124
$995$	18.7696	0.595037
$996$	8.79707	0.278746
$997$	6.31766	0.200082	0.100041	−	0.994983i	$-0.468103\pi$
$997$	6.31766	0.200082	0.100041	+	0.994983i	$0.468103\pi$
$998$	−23.5089	−0.744160
$999$	−119.745	−3.78857

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	290.2.a.e.1.3	✓	3
3.2	odd	2		2610.2.a.x.1.1		3
4.3	odd	2		2320.2.a.l.1.1		3
5.2	odd	4		1450.2.b.l.349.4		6
5.3	odd	4		1450.2.b.l.349.3		6
5.4	even	2		1450.2.a.p.1.1		3
8.3	odd	2		9280.2.a.by.1.3		3
8.5	even	2		9280.2.a.bf.1.1		3
29.28	even	2		8410.2.a.v.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.a.e.1.3	✓	3	1.1	even	1	trivial
1450.2.a.p.1.1		3	5.4	even	2
1450.2.b.l.349.3		6	5.3	odd	4
1450.2.b.l.349.4		6	5.2	odd	4
2320.2.a.l.1.1		3	4.3	odd	2
2610.2.a.x.1.1		3	3.2	odd	2
8410.2.a.v.1.1		3	29.28	even	2
9280.2.a.bf.1.1		3	8.5	even	2
9280.2.a.by.1.3		3	8.3	odd	2

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:	\( N \)	\(=\)	\( 290 = 2 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.14510 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.14510 q^{6} -3.89167 q^{7} +1.00000 q^{8} +6.89167 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.14510 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.14510 q^{6} -3.89167 q^{7} +1.00000 q^{8} +6.89167 q^{9} -1.00000 q^{10} -4.29021 q^{11} +3.14510 q^{12} +4.34803 q^{13} -3.89167 q^{14} -3.14510 q^{15} +1.00000 q^{16} +1.60147 q^{17} +6.89167 q^{18} -1.20293 q^{19} -1.00000 q^{20} -12.2397 q^{21} -4.29021 q^{22} -8.34803 q^{23} +3.14510 q^{24} +1.00000 q^{25} +4.34803 q^{26} +12.2397 q^{27} -3.89167 q^{28} -1.00000 q^{29} -3.14510 q^{30} -2.39853 q^{31} +1.00000 q^{32} -13.4931 q^{33} +1.60147 q^{34} +3.89167 q^{35} +6.89167 q^{36} -9.78334 q^{37} -1.20293 q^{38} +13.6750 q^{39} -1.00000 q^{40} +5.78334 q^{41} -12.2397 q^{42} +3.60147 q^{43} -4.29021 q^{44} -6.89167 q^{45} -8.34803 q^{46} +8.58041 q^{47} +3.14510 q^{48} +8.14510 q^{49} +1.00000 q^{50} +5.03677 q^{51} +4.34803 q^{52} +4.80440 q^{53} +12.2397 q^{54} +4.29021 q^{55} -3.89167 q^{56} -3.78334 q^{57} -1.00000 q^{58} -4.05783 q^{59} -3.14510 q^{60} +11.4353 q^{61} -2.39853 q^{62} -26.8201 q^{63} +1.00000 q^{64} -4.34803 q^{65} -13.4931 q^{66} +9.08727 q^{67} +1.60147 q^{68} -26.2554 q^{69} +3.89167 q^{70} -12.0000 q^{71} +6.89167 q^{72} -2.39853 q^{73} -9.78334 q^{74} +3.14510 q^{75} -1.20293 q^{76} +16.6961 q^{77} +13.6750 q^{78} +7.55096 q^{79} -1.00000 q^{80} +17.8201 q^{81} +5.78334 q^{82} +2.79707 q^{83} -12.2397 q^{84} -1.60147 q^{85} +3.60147 q^{86} -3.14510 q^{87} -4.29021 q^{88} -4.29021 q^{89} -6.89167 q^{90} -16.9211 q^{91} -8.34803 q^{92} -7.54364 q^{93} +8.58041 q^{94} +1.20293 q^{95} +3.14510 q^{96} -0.348034 q^{97} +8.14510 q^{98} -29.5667 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} + 3 q^{8} + 6 q^{9} - 3 q^{10} + 3 q^{12} + 3 q^{13} + 3 q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 3 q^{20} - 12 q^{21} - 15 q^{23} + 3 q^{24} + 3 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{28} - 3 q^{29} - 3 q^{30} - 9 q^{31} + 3 q^{32} - 24 q^{33} + 3 q^{34} - 3 q^{35} + 6 q^{36} - 3 q^{39} - 3 q^{40} - 12 q^{41} - 12 q^{42} + 9 q^{43} - 6 q^{45} - 15 q^{46} + 3 q^{48} + 18 q^{49} + 3 q^{50} - 6 q^{51} + 3 q^{52} + 9 q^{53} + 12 q^{54} + 3 q^{56} + 18 q^{57} - 3 q^{58} - 15 q^{59} - 3 q^{60} + 15 q^{61} - 9 q^{62} - 30 q^{63} + 3 q^{64} - 3 q^{65} - 24 q^{66} + 18 q^{67} + 3 q^{68} - 9 q^{69} - 3 q^{70} - 36 q^{71} + 6 q^{72} - 9 q^{73} + 3 q^{75} + 30 q^{77} - 3 q^{78} + 9 q^{79} - 3 q^{80} + 3 q^{81} - 12 q^{82} + 12 q^{83} - 12 q^{84} - 3 q^{85} + 9 q^{86} - 3 q^{87} - 6 q^{90} - 24 q^{91} - 15 q^{92} - 18 q^{93} + 3 q^{96} + 9 q^{97} + 18 q^{98} - 30 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + 3 * q^7 + 3 * q^8 + 6 * q^9 - 3 * q^10 + 3 * q^12 + 3 * q^13 + 3 * q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 + 6 * q^18 - 3 * q^20 - 12 * q^21 - 15 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^26 + 12 * q^27 + 3 * q^28 - 3 * q^29 - 3 * q^30 - 9 * q^31 + 3 * q^32 - 24 * q^33 + 3 * q^34 - 3 * q^35 + 6 * q^36 - 3 * q^39 - 3 * q^40 - 12 * q^41 - 12 * q^42 + 9 * q^43 - 6 * q^45 - 15 * q^46 + 3 * q^48 + 18 * q^49 + 3 * q^50 - 6 * q^51 + 3 * q^52 + 9 * q^53 + 12 * q^54 + 3 * q^56 + 18 * q^57 - 3 * q^58 - 15 * q^59 - 3 * q^60 + 15 * q^61 - 9 * q^62 - 30 * q^63 + 3 * q^64 - 3 * q^65 - 24 * q^66 + 18 * q^67 + 3 * q^68 - 9 * q^69 - 3 * q^70 - 36 * q^71 + 6 * q^72 - 9 * q^73 + 3 * q^75 + 30 * q^77 - 3 * q^78 + 9 * q^79 - 3 * q^80 + 3 * q^81 - 12 * q^82 + 12 * q^83 - 12 * q^84 - 3 * q^85 + 9 * q^86 - 3 * q^87 - 6 * q^90 - 24 * q^91 - 15 * q^92 - 18 * q^93 + 3 * q^96 + 9 * q^97 + 18 * q^98 - 30 * q^99

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