LMFDB - Embedded newform 6045.2.a.u.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 7x^{7} + 20x^{6} + 20x^{5} - 38x^{4} - 27x^{3} + 13x^{2} + 6x - 1 $ x^9 - 3x^8 - 7x^7 + 20x^6 + 20x^5 - 38x^4 - 27x^3 + 13x^2 + 6x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-1.69393$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.69393 q^{2} +1.00000 q^{3} +0.869413 q^{4} +1.00000 q^{5} +1.69393 q^{6} -0.954273 q^{7} -1.91514 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.69393 q^{2} +1.00000 q^{3} +0.869413 q^{4} +1.00000 q^{5} +1.69393 q^{6} -0.954273 q^{7} -1.91514 q^{8} +1.00000 q^{9} +1.69393 q^{10} -1.41022 q^{11} +0.869413 q^{12} -1.00000 q^{13} -1.61648 q^{14} +1.00000 q^{15} -4.98295 q^{16} +5.16741 q^{17} +1.69393 q^{18} -6.95247 q^{19} +0.869413 q^{20} -0.954273 q^{21} -2.38883 q^{22} -0.856309 q^{23} -1.91514 q^{24} +1.00000 q^{25} -1.69393 q^{26} +1.00000 q^{27} -0.829657 q^{28} -9.66162 q^{29} +1.69393 q^{30} -1.00000 q^{31} -4.61050 q^{32} -1.41022 q^{33} +8.75325 q^{34} -0.954273 q^{35} +0.869413 q^{36} -11.2061 q^{37} -11.7770 q^{38} -1.00000 q^{39} -1.91514 q^{40} +12.3923 q^{41} -1.61648 q^{42} -6.52173 q^{43} -1.22607 q^{44} +1.00000 q^{45} -1.45053 q^{46} -6.20415 q^{47} -4.98295 q^{48} -6.08936 q^{49} +1.69393 q^{50} +5.16741 q^{51} -0.869413 q^{52} +5.25758 q^{53} +1.69393 q^{54} -1.41022 q^{55} +1.82757 q^{56} -6.95247 q^{57} -16.3662 q^{58} -4.02966 q^{59} +0.869413 q^{60} -15.4237 q^{61} -1.69393 q^{62} -0.954273 q^{63} +2.15600 q^{64} -1.00000 q^{65} -2.38883 q^{66} +5.94986 q^{67} +4.49261 q^{68} -0.856309 q^{69} -1.61648 q^{70} +8.50938 q^{71} -1.91514 q^{72} +5.49518 q^{73} -18.9823 q^{74} +1.00000 q^{75} -6.04457 q^{76} +1.34574 q^{77} -1.69393 q^{78} +14.0251 q^{79} -4.98295 q^{80} +1.00000 q^{81} +20.9918 q^{82} +10.4007 q^{83} -0.829657 q^{84} +5.16741 q^{85} -11.0474 q^{86} -9.66162 q^{87} +2.70078 q^{88} -1.70701 q^{89} +1.69393 q^{90} +0.954273 q^{91} -0.744486 q^{92} -1.00000 q^{93} -10.5094 q^{94} -6.95247 q^{95} -4.61050 q^{96} -11.6081 q^{97} -10.3150 q^{98} -1.41022 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9	\( 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9} - 3 q^{10} + 5 q^{12} - 9 q^{13} + 11 q^{14} + 9 q^{15} + 9 q^{16} - 5 q^{17} - 3 q^{18} - 12 q^{19} + 5 q^{20} - 5 q^{21} - 17 q^{22} - 21 q^{23} - 18 q^{24} + 9 q^{25} + 3 q^{26} + 9 q^{27} - 8 q^{28} - 15 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} + 9 q^{34} - 5 q^{35} + 5 q^{36} - 13 q^{37} - 24 q^{38} - 9 q^{39} - 18 q^{40} - 11 q^{41} + 11 q^{42} - 26 q^{43} + 5 q^{44} + 9 q^{45} + 14 q^{46} - 21 q^{47} + 9 q^{48} - 26 q^{49} - 3 q^{50} - 5 q^{51} - 5 q^{52} + 18 q^{53} - 3 q^{54} - 19 q^{56} - 12 q^{57} - 16 q^{58} - 24 q^{59} + 5 q^{60} - 4 q^{61} + 3 q^{62} - 5 q^{63} + 2 q^{64} - 9 q^{65} - 17 q^{66} - 20 q^{67} - 19 q^{68} - 21 q^{69} + 11 q^{70} - 13 q^{71} - 18 q^{72} + 15 q^{73} + 12 q^{74} + 9 q^{75} + 54 q^{76} - 28 q^{77} + 3 q^{78} - 15 q^{79} + 9 q^{80} + 9 q^{81} - 21 q^{82} - 5 q^{83} - 8 q^{84} - 5 q^{85} + 36 q^{86} - 15 q^{87} + 23 q^{88} + 31 q^{89} - 3 q^{90} + 5 q^{91} - 7 q^{92} - 9 q^{93} - 12 q^{95} - 9 q^{96} - 11 q^{97} - 23 q^{98}+O(q^{100}) \) 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9 - 3 * q^10 + 5 * q^12 - 9 * q^13 + 11 * q^14 + 9 * q^15 + 9 * q^16 - 5 * q^17 - 3 * q^18 - 12 * q^19 + 5 * q^20 - 5 * q^21 - 17 * q^22 - 21 * q^23 - 18 * q^24 + 9 * q^25 + 3 * q^26 + 9 * q^27 - 8 * q^28 - 15 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 + 9 * q^34 - 5 * q^35 + 5 * q^36 - 13 * q^37 - 24 * q^38 - 9 * q^39 - 18 * q^40 - 11 * q^41 + 11 * q^42 - 26 * q^43 + 5 * q^44 + 9 * q^45 + 14 * q^46 - 21 * q^47 + 9 * q^48 - 26 * q^49 - 3 * q^50 - 5 * q^51 - 5 * q^52 + 18 * q^53 - 3 * q^54 - 19 * q^56 - 12 * q^57 - 16 * q^58 - 24 * q^59 + 5 * q^60 - 4 * q^61 + 3 * q^62 - 5 * q^63 + 2 * q^64 - 9 * q^65 - 17 * q^66 - 20 * q^67 - 19 * q^68 - 21 * q^69 + 11 * q^70 - 13 * q^71 - 18 * q^72 + 15 * q^73 + 12 * q^74 + 9 * q^75 + 54 * q^76 - 28 * q^77 + 3 * q^78 - 15 * q^79 + 9 * q^80 + 9 * q^81 - 21 * q^82 - 5 * q^83 - 8 * q^84 - 5 * q^85 + 36 * q^86 - 15 * q^87 + 23 * q^88 + 31 * q^89 - 3 * q^90 + 5 * q^91 - 7 * q^92 - 9 * q^93 - 12 * q^95 - 9 * q^96 - 11 * q^97 - 23 * q^98

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 $

$2$	1.69393	1.19779	0.598896	−	0.800827i	$-0.295606\pi$
$2$	1.69393	1.19779	0.598896	+	0.800827i	$0.295606\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.869413	0.434706
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.69393	0.691546
$7$	−0.954273	−0.360681	−0.180341	−	0.983604i	$-0.557720\pi$
$7$	−0.954273	−0.360681	−0.180341	+	0.983604i	$0.557720\pi$
$8$	−1.91514	−0.677104
$9$	1.00000	0.333333
$10$	1.69393	0.535669
$11$	−1.41022	−0.425199	−0.212599	−	0.977139i	$-0.568193\pi$
$11$	−1.41022	−0.425199	−0.212599	+	0.977139i	$0.568193\pi$
$12$	0.869413	0.250978
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.61648	−0.432021
$15$	1.00000	0.258199
$16$	−4.98295	−1.24574
$17$	5.16741	1.25328	0.626640	−	0.779309i	$-0.284430\pi$
$17$	5.16741	1.25328	0.626640	+	0.779309i	$0.284430\pi$
$18$	1.69393	0.399264
$19$	−6.95247	−1.59501	−0.797503	−	0.603315i	$-0.793846\pi$
$19$	−6.95247	−1.59501	−0.797503	+	0.603315i	$0.793846\pi$
$20$	0.869413	0.194407
$21$	−0.954273	−0.208239
$22$	−2.38883	−0.509300
$23$	−0.856309	−0.178553	−0.0892764	−	0.996007i	$-0.528455\pi$
$23$	−0.856309	−0.178553	−0.0892764	+	0.996007i	$0.528455\pi$
$24$	−1.91514	−0.390926
$25$	1.00000	0.200000
$26$	−1.69393	−0.332208
$27$	1.00000	0.192450
$28$	−0.829657	−0.156790
$29$	−9.66162	−1.79412	−0.897059	−	0.441910i	$-0.854301\pi$
$29$	−9.66162	−1.79412	−0.897059	+	0.441910i	$0.854301\pi$
$30$	1.69393	0.309269
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−4.61050	−0.815030
$33$	−1.41022	−0.245489
$34$	8.75325	1.50117
$35$	−0.954273	−0.161302
$36$	0.869413	0.144902
$37$	−11.2061	−1.84227	−0.921133	−	0.389248i	$-0.872735\pi$
$37$	−11.2061	−1.84227	−0.921133	+	0.389248i	$0.872735\pi$
$38$	−11.7770	−1.91049
$39$	−1.00000	−0.160128
$40$	−1.91514	−0.302810
$41$	12.3923	1.93536	0.967680	−	0.252183i	$-0.0811484\pi$
$41$	12.3923	1.93536	0.967680	+	0.252183i	$0.0811484\pi$
$42$	−1.61648	−0.249428
$43$	−6.52173	−0.994554	−0.497277	−	0.867592i	$-0.665667\pi$
$43$	−6.52173	−0.994554	−0.497277	+	0.867592i	$0.665667\pi$
$44$	−1.22607	−0.184837
$45$	1.00000	0.149071
$46$	−1.45053	−0.213869
$47$	−6.20415	−0.904969	−0.452484	−	0.891772i	$-0.649462\pi$
$47$	−6.20415	−0.904969	−0.452484	+	0.891772i	$0.649462\pi$
$48$	−4.98295	−0.719226
$49$	−6.08936	−0.869909
$50$	1.69393	0.239558
$51$	5.16741	0.723582
$52$	−0.869413	−0.120566
$53$	5.25758	0.722184	0.361092	−	0.932530i	$-0.382404\pi$
$53$	5.25758	0.722184	0.361092	+	0.932530i	$0.382404\pi$
$54$	1.69393	0.230515
$55$	−1.41022	−0.190155
$56$	1.82757	0.244219
$57$	−6.95247	−0.920877
$58$	−16.3662	−2.14898
$59$	−4.02966	−0.524617	−0.262308	−	0.964984i	$-0.584484\pi$
$59$	−4.02966	−0.524617	−0.262308	+	0.964984i	$0.584484\pi$
$60$	0.869413	0.112241
$61$	−15.4237	−1.97480	−0.987399	−	0.158252i	$-0.949414\pi$
$61$	−15.4237	−1.97480	−0.987399	+	0.158252i	$0.949414\pi$
$62$	−1.69393	−0.215130
$63$	−0.954273	−0.120227
$64$	2.15600	0.269500
$65$	−1.00000	−0.124035
$66$	−2.38883	−0.294044
$67$	5.94986	0.726891	0.363446	−	0.931615i	$-0.381600\pi$
$67$	5.94986	0.726891	0.363446	+	0.931615i	$0.381600\pi$
$68$	4.49261	0.544809
$69$	−0.856309	−0.103087
$70$	−1.61648	−0.193206
$71$	8.50938	1.00988	0.504939	−	0.863155i	$-0.331515\pi$
$71$	8.50938	1.00988	0.504939	+	0.863155i	$0.331515\pi$
$72$	−1.91514	−0.225701
$73$	5.49518	0.643162	0.321581	−	0.946882i	$-0.395786\pi$
$73$	5.49518	0.643162	0.321581	+	0.946882i	$0.395786\pi$
$74$	−18.9823	−2.20665
$75$	1.00000	0.115470
$76$	−6.04457	−0.693359
$77$	1.34574	0.153361
$78$	−1.69393	−0.191800
$79$	14.0251	1.57794	0.788971	−	0.614431i	$-0.210614\pi$
$79$	14.0251	1.57794	0.788971	+	0.614431i	$0.210614\pi$
$80$	−4.98295	−0.557110
$81$	1.00000	0.111111
$82$	20.9918	2.31816
$83$	10.4007	1.14163	0.570814	−	0.821079i	$-0.306628\pi$
$83$	10.4007	1.14163	0.570814	+	0.821079i	$0.306628\pi$
$84$	−0.829657	−0.0905230
$85$	5.16741	0.560484
$86$	−11.0474	−1.19127
$87$	−9.66162	−1.03583
$88$	2.70078	0.287904
$89$	−1.70701	−0.180943	−0.0904715	−	0.995899i	$-0.528837\pi$
$89$	−1.70701	−0.180943	−0.0904715	+	0.995899i	$0.528837\pi$
$90$	1.69393	0.178556
$91$	0.954273	0.100035
$92$	−0.744486	−0.0776181
$93$	−1.00000	−0.103695
$94$	−10.5094	−1.08396
$95$	−6.95247	−0.713308
$96$	−4.61050	−0.470558
$97$	−11.6081	−1.17862	−0.589310	−	0.807907i	$-0.700601\pi$
$97$	−11.6081	−1.17862	−0.589310	+	0.807907i	$0.700601\pi$
$98$	−10.3150	−1.04197
$99$	−1.41022	−0.141733
$100$	0.869413	0.0869413
$101$	7.60442	0.756668	0.378334	−	0.925669i	$-0.376497\pi$
$101$	7.60442	0.756668	0.378334	+	0.925669i	$0.376497\pi$
$102$	8.75325	0.866701
$103$	5.14872	0.507318	0.253659	−	0.967294i	$-0.418366\pi$
$103$	5.14872	0.507318	0.253659	+	0.967294i	$0.418366\pi$
$104$	1.91514	0.187795
$105$	−0.954273	−0.0931275
$106$	8.90599	0.865026
$107$	−4.37557	−0.423002	−0.211501	−	0.977378i	$-0.567835\pi$
$107$	−4.37557	−0.423002	−0.211501	+	0.977378i	$0.567835\pi$
$108$	0.869413	0.0836593
$109$	−20.6437	−1.97731	−0.988653	−	0.150215i	$-0.952003\pi$
$109$	−20.6437	−1.97731	−0.988653	+	0.150215i	$0.952003\pi$
$110$	−2.38883	−0.227766
$111$	−11.2061	−1.06363
$112$	4.75509	0.449314
$113$	−9.83360	−0.925067	−0.462534	−	0.886602i	$-0.653060\pi$
$113$	−9.83360	−0.925067	−0.462534	+	0.886602i	$0.653060\pi$
$114$	−11.7770	−1.10302
$115$	−0.856309	−0.0798512
$116$	−8.39994	−0.779915
$117$	−1.00000	−0.0924500
$118$	−6.82598	−0.628382
$119$	−4.93112	−0.452035
$120$	−1.91514	−0.174828
$121$	−9.01127	−0.819206
$122$	−26.1267	−2.36540
$123$	12.3923	1.11738
$124$	−0.869413	−0.0780756
$125$	1.00000	0.0894427
$126$	−1.61648	−0.144007
$127$	4.66306	0.413780	0.206890	−	0.978364i	$-0.433666\pi$
$127$	4.66306	0.413780	0.206890	+	0.978364i	$0.433666\pi$
$128$	12.8731	1.13784
$129$	−6.52173	−0.574206
$130$	−1.69393	−0.148568
$131$	−15.9217	−1.39109	−0.695543	−	0.718485i	$-0.744836\pi$
$131$	−15.9217	−1.39109	−0.695543	+	0.718485i	$0.744836\pi$
$132$	−1.22607	−0.106716
$133$	6.63455	0.575289
$134$	10.0787	0.870665
$135$	1.00000	0.0860663
$136$	−9.89631	−0.848601
$137$	0.910593	0.0777972	0.0388986	−	0.999243i	$-0.487615\pi$
$137$	0.910593	0.0777972	0.0388986	+	0.999243i	$0.487615\pi$
$138$	−1.45053	−0.123477
$139$	−6.00865	−0.509647	−0.254823	−	0.966988i	$-0.582017\pi$
$139$	−6.00865	−0.509647	−0.254823	+	0.966988i	$0.582017\pi$
$140$	−0.829657	−0.0701188
$141$	−6.20415	−0.522484
$142$	14.4143	1.20962
$143$	1.41022	0.117929
$144$	−4.98295	−0.415246
$145$	−9.66162	−0.802354
$146$	9.30847	0.770375
$147$	−6.08936	−0.502242
$148$	−9.74270	−0.800845
$149$	20.3892	1.67035	0.835175	−	0.549984i	$-0.185366\pi$
$149$	20.3892	1.67035	0.835175	+	0.549984i	$0.185366\pi$
$150$	1.69393	0.138309
$151$	−0.410297	−0.0333895	−0.0166948	−	0.999861i	$-0.505314\pi$
$151$	−0.410297	−0.0333895	−0.0166948	+	0.999861i	$0.505314\pi$
$152$	13.3149	1.07998
$153$	5.16741	0.417760
$154$	2.27959	0.183695
$155$	−1.00000	−0.0803219
$156$	−0.869413	−0.0696087
$157$	18.5151	1.47766	0.738832	−	0.673890i	$-0.235378\pi$
$157$	18.5151	1.47766	0.738832	+	0.673890i	$0.235378\pi$
$158$	23.7575	1.89005
$159$	5.25758	0.416953
$160$	−4.61050	−0.364492
$161$	0.817153	0.0644006
$162$	1.69393	0.133088
$163$	−10.2035	−0.799202	−0.399601	−	0.916689i	$-0.630851\pi$
$163$	−10.2035	−0.799202	−0.399601	+	0.916689i	$0.630851\pi$
$164$	10.7741	0.841313
$165$	−1.41022	−0.109786
$166$	17.6181	1.36743
$167$	−14.2000	−1.09883	−0.549415	−	0.835550i	$-0.685149\pi$
$167$	−14.2000	−1.09883	−0.549415	+	0.835550i	$0.685149\pi$
$168$	1.82757	0.141000
$169$	1.00000	0.0769231
$170$	8.75325	0.671343
$171$	−6.95247	−0.531668
$172$	−5.67008	−0.432339
$173$	20.5144	1.55968	0.779840	−	0.625979i	$-0.215300\pi$
$173$	20.5144	1.55968	0.779840	+	0.625979i	$0.215300\pi$
$174$	−16.3662	−1.24071
$175$	−0.954273	−0.0721363
$176$	7.02708	0.529686
$177$	−4.02966	−0.302888
$178$	−2.89157	−0.216732
$179$	−21.4343	−1.60208	−0.801039	−	0.598612i	$-0.795719\pi$
$179$	−21.4343	−1.60208	−0.801039	+	0.598612i	$0.795719\pi$
$180$	0.869413	0.0648022
$181$	−6.35553	−0.472403	−0.236201	−	0.971704i	$-0.575902\pi$
$181$	−6.35553	−0.472403	−0.236201	+	0.971704i	$0.575902\pi$
$182$	1.61648	0.119821
$183$	−15.4237	−1.14015
$184$	1.63995	0.120899
$185$	−11.2061	−0.823887
$186$	−1.69393	−0.124205
$187$	−7.28721	−0.532893
$188$	−5.39397	−0.393396
$189$	−0.954273	−0.0694131
$190$	−11.7770	−0.854395
$191$	2.62622	0.190027	0.0950135	−	0.995476i	$-0.469711\pi$
$191$	2.62622	0.190027	0.0950135	+	0.995476i	$0.469711\pi$
$192$	2.15600	0.155596
$193$	−14.7338	−1.06056	−0.530280	−	0.847822i	$-0.677913\pi$
$193$	−14.7338	−1.06056	−0.530280	+	0.847822i	$0.677913\pi$
$194$	−19.6633	−1.41174
$195$	−1.00000	−0.0716115
$196$	−5.29417	−0.378155
$197$	−22.8321	−1.62672	−0.813360	−	0.581761i	$-0.802364\pi$
$197$	−22.8321	−1.62672	−0.813360	+	0.581761i	$0.802364\pi$
$198$	−2.38883	−0.169767
$199$	−19.5782	−1.38786	−0.693931	−	0.720041i	$-0.744123\pi$
$199$	−19.5782	−1.38786	−0.693931	+	0.720041i	$0.744123\pi$
$200$	−1.91514	−0.135421
$201$	5.94986	0.419671
$202$	12.8814	0.906331
$203$	9.21983	0.647105
$204$	4.49261	0.314546
$205$	12.3923	0.865519
$206$	8.72159	0.607662
$207$	−0.856309	−0.0595176
$208$	4.98295	0.345505
$209$	9.80454	0.678194
$210$	−1.61648	−0.111547
$211$	−19.4522	−1.33915	−0.669573	−	0.742747i	$-0.733523\pi$
$211$	−19.4522	−1.33915	−0.669573	+	0.742747i	$0.733523\pi$
$212$	4.57101	0.313938
$213$	8.50938	0.583053
$214$	−7.41192	−0.506668
$215$	−6.52173	−0.444778
$216$	−1.91514	−0.130309
$217$	0.954273	0.0647803
$218$	−34.9690	−2.36840
$219$	5.49518	0.371330
$220$	−1.22607	−0.0826615
$221$	−5.16741	−0.347597
$222$	−18.9823	−1.27401
$223$	28.4537	1.90540	0.952699	−	0.303914i	$-0.0982936\pi$
$223$	28.4537	1.90540	0.952699	+	0.303914i	$0.0982936\pi$
$224$	4.39968	0.293966
$225$	1.00000	0.0666667
$226$	−16.6575	−1.10804
$227$	20.6041	1.36754	0.683770	−	0.729697i	$-0.260339\pi$
$227$	20.6041	1.36754	0.683770	+	0.729697i	$0.260339\pi$
$228$	−6.04457	−0.400311
$229$	−0.299236	−0.0197741	−0.00988704	−	0.999951i	$-0.503147\pi$
$229$	−0.299236	−0.0197741	−0.00988704	+	0.999951i	$0.503147\pi$
$230$	−1.45053	−0.0956452
$231$	1.34574	0.0885432
$232$	18.5034	1.21481
$233$	18.6763	1.22353	0.611763	−	0.791041i	$-0.290461\pi$
$233$	18.6763	1.22353	0.611763	+	0.791041i	$0.290461\pi$
$234$	−1.69393	−0.110736
$235$	−6.20415	−0.404714
$236$	−3.50344	−0.228054
$237$	14.0251	0.911025
$238$	−8.35299	−0.541444
$239$	−19.3435	−1.25122	−0.625612	−	0.780134i	$-0.715151\pi$
$239$	−19.3435	−1.25122	−0.625612	+	0.780134i	$0.715151\pi$
$240$	−4.98295	−0.321648
$241$	25.2572	1.62696	0.813480	−	0.581593i	$-0.197570\pi$
$241$	25.2572	1.62696	0.813480	+	0.581593i	$0.197570\pi$
$242$	−15.2645	−0.981239
$243$	1.00000	0.0641500
$244$	−13.4095	−0.858457
$245$	−6.08936	−0.389035
$246$	20.9918	1.33839
$247$	6.95247	0.442375
$248$	1.91514	0.121612
$249$	10.4007	0.659119
$250$	1.69393	0.107134
$251$	−2.20775	−0.139352	−0.0696759	−	0.997570i	$-0.522197\pi$
$251$	−2.20775	−0.139352	−0.0696759	+	0.997570i	$0.522197\pi$
$252$	−0.829657	−0.0522635
$253$	1.20759	0.0759204
$254$	7.89891	0.495622
$255$	5.16741	0.323596
$256$	17.4942	1.09339
$257$	0.947697	0.0591157	0.0295578	−	0.999563i	$-0.490590\pi$
$257$	0.947697	0.0591157	0.0295578	+	0.999563i	$0.490590\pi$
$258$	−11.0474	−0.687780
$259$	10.6936	0.664471
$260$	−0.869413	−0.0539187
$261$	−9.66162	−0.598039
$262$	−26.9703	−1.66623
$263$	−13.6015	−0.838703	−0.419352	−	0.907824i	$-0.637743\pi$
$263$	−13.6015	−0.838703	−0.419352	+	0.907824i	$0.637743\pi$
$264$	2.70078	0.166221
$265$	5.25758	0.322970
$266$	11.2385	0.689076
$267$	−1.70701	−0.104467
$268$	5.17289	0.315984
$269$	10.5878	0.645549	0.322775	−	0.946476i	$-0.395384\pi$
$269$	10.5878	0.645549	0.322775	+	0.946476i	$0.395384\pi$
$270$	1.69393	0.103090
$271$	23.6884	1.43897	0.719485	−	0.694508i	$-0.244378\pi$
$271$	23.6884	1.43897	0.719485	+	0.694508i	$0.244378\pi$
$272$	−25.7489	−1.56126
$273$	0.954273	0.0577552
$274$	1.54249	0.0931849
$275$	−1.41022	−0.0850398
$276$	−0.744486	−0.0448128
$277$	1.75768	0.105609	0.0528043	−	0.998605i	$-0.483184\pi$
$277$	1.75768	0.105609	0.0528043	+	0.998605i	$0.483184\pi$
$278$	−10.1783	−0.610451
$279$	−1.00000	−0.0598684
$280$	1.82757	0.109218
$281$	−10.5481	−0.629247	−0.314623	−	0.949217i	$-0.601878\pi$
$281$	−10.5481	−0.629247	−0.314623	+	0.949217i	$0.601878\pi$
$282$	−10.5094	−0.625827
$283$	−27.3519	−1.62590	−0.812951	−	0.582333i	$-0.802140\pi$
$283$	−27.3519	−1.62590	−0.812951	+	0.582333i	$0.802140\pi$
$284$	7.39816	0.439000
$285$	−6.95247	−0.411829
$286$	2.38883	0.141254
$287$	−11.8257	−0.698048
$288$	−4.61050	−0.271677
$289$	9.70209	0.570711
$290$	−16.3662	−0.961054
$291$	−11.6081	−0.680477
$292$	4.77758	0.279587
$293$	2.32088	0.135587	0.0677936	−	0.997699i	$-0.478404\pi$
$293$	2.32088	0.135587	0.0677936	+	0.997699i	$0.478404\pi$
$294$	−10.3150	−0.601582
$295$	−4.02966	−0.234616
$296$	21.4612	1.24741
$297$	−1.41022	−0.0818296
$298$	34.5380	2.00073
$299$	0.856309	0.0495216
$300$	0.869413	0.0501956
$301$	6.22351	0.358717
$302$	−0.695017	−0.0399937
$303$	7.60442	0.436863
$304$	34.6438	1.98696
$305$	−15.4237	−0.883156
$306$	8.75325	0.500390
$307$	−8.84820	−0.504994	−0.252497	−	0.967598i	$-0.581252\pi$
$307$	−8.84820	−0.504994	−0.252497	+	0.967598i	$0.581252\pi$
$308$	1.17000	0.0666671
$309$	5.14872	0.292900
$310$	−1.69393	−0.0962090
$311$	−10.6983	−0.606646	−0.303323	−	0.952888i	$-0.598096\pi$
$311$	−10.6983	−0.606646	−0.303323	+	0.952888i	$0.598096\pi$
$312$	1.91514	0.108423
$313$	2.95065	0.166781	0.0833903	−	0.996517i	$-0.473425\pi$
$313$	2.95065	0.166781	0.0833903	+	0.996517i	$0.473425\pi$
$314$	31.3633	1.76993
$315$	−0.954273	−0.0537672
$316$	12.1936	0.685941
$317$	14.7256	0.827074	0.413537	−	0.910487i	$-0.364293\pi$
$317$	14.7256	0.827074	0.413537	+	0.910487i	$0.364293\pi$
$318$	8.90599	0.499423
$319$	13.6251	0.762857
$320$	2.15600	0.120524
$321$	−4.37557	−0.244220
$322$	1.38420	0.0771386
$323$	−35.9262	−1.99899
$324$	0.869413	0.0483007
$325$	−1.00000	−0.0554700
$326$	−17.2841	−0.957278
$327$	−20.6437	−1.14160
$328$	−23.7331	−1.31044
$329$	5.92045	0.326405
$330$	−2.38883	−0.131501
$331$	26.6335	1.46391	0.731955	−	0.681353i	$-0.238608\pi$
$331$	26.6335	1.46391	0.731955	+	0.681353i	$0.238608\pi$
$332$	9.04253	0.496273
$333$	−11.2061	−0.614089
$334$	−24.0539	−1.31617
$335$	5.94986	0.325076
$336$	4.75509	0.259411
$337$	−5.92767	−0.322901	−0.161450	−	0.986881i	$-0.551617\pi$
$337$	−5.92767	−0.322901	−0.161450	+	0.986881i	$0.551617\pi$
$338$	1.69393	0.0921379
$339$	−9.83360	−0.534088
$340$	4.49261	0.243646
$341$	1.41022	0.0763680
$342$	−11.7770	−0.636828
$343$	12.4908	0.674441
$344$	12.4900	0.673417
$345$	−0.856309	−0.0461021
$346$	34.7500	1.86817
$347$	−3.34382	−0.179506	−0.0897528	−	0.995964i	$-0.528608\pi$
$347$	−3.34382	−0.179506	−0.0897528	+	0.995964i	$0.528608\pi$
$348$	−8.39994	−0.450284
$349$	14.6111	0.782112	0.391056	−	0.920367i	$-0.372110\pi$
$349$	14.6111	0.782112	0.391056	+	0.920367i	$0.372110\pi$
$350$	−1.61648	−0.0864042
$351$	−1.00000	−0.0533761
$352$	6.50185	0.346550
$353$	14.8628	0.791065	0.395533	−	0.918452i	$-0.370560\pi$
$353$	14.8628	0.791065	0.395533	+	0.918452i	$0.370560\pi$
$354$	−6.82598	−0.362797
$355$	8.50938	0.451631
$356$	−1.48410	−0.0786571
$357$	−4.93112	−0.260982
$358$	−36.3084	−1.91896
$359$	36.0695	1.90367	0.951837	−	0.306605i	$-0.0991932\pi$
$359$	36.0695	1.90367	0.951837	+	0.306605i	$0.0991932\pi$
$360$	−1.91514	−0.100937
$361$	29.3368	1.54404
$362$	−10.7658	−0.565840
$363$	−9.01127	−0.472969
$364$	0.829657	0.0434859
$365$	5.49518	0.287631
$366$	−26.1267	−1.36566
$367$	1.21421	0.0633815	0.0316907	−	0.999498i	$-0.489911\pi$
$367$	1.21421	0.0633815	0.0316907	+	0.999498i	$0.489911\pi$
$368$	4.26694	0.222430
$369$	12.3923	0.645120
$370$	−18.9823	−0.986845
$371$	−5.01716	−0.260478
$372$	−0.869413	−0.0450770
$373$	−0.669467	−0.0346637	−0.0173318	−	0.999850i	$-0.505517\pi$
$373$	−0.669467	−0.0346637	−0.0173318	+	0.999850i	$0.505517\pi$
$374$	−12.3440	−0.638295
$375$	1.00000	0.0516398
$376$	11.8818	0.612758
$377$	9.66162	0.497599
$378$	−1.61648	−0.0831425
$379$	−35.0648	−1.80116	−0.900578	−	0.434695i	$-0.856856\pi$
$379$	−35.0648	−1.80116	−0.900578	+	0.434695i	$0.856856\pi$
$380$	−6.04457	−0.310080
$381$	4.66306	0.238896
$382$	4.44865	0.227613
$383$	−2.10909	−0.107770	−0.0538848	−	0.998547i	$-0.517160\pi$
$383$	−2.10909	−0.107770	−0.0538848	+	0.998547i	$0.517160\pi$
$384$	12.8731	0.656929
$385$	1.34574	0.0685852
$386$	−24.9581	−1.27033
$387$	−6.52173	−0.331518
$388$	−10.0922	−0.512354
$389$	1.34603	0.0682462	0.0341231	−	0.999418i	$-0.489136\pi$
$389$	1.34603	0.0682462	0.0341231	+	0.999418i	$0.489136\pi$
$390$	−1.69393	−0.0857757
$391$	−4.42490	−0.223777
$392$	11.6620	0.589019
$393$	−15.9217	−0.803144
$394$	−38.6761	−1.94847
$395$	14.0251	0.705677
$396$	−1.22607	−0.0616122
$397$	8.20218	0.411656	0.205828	−	0.978588i	$-0.434011\pi$
$397$	8.20218	0.411656	0.205828	+	0.978588i	$0.434011\pi$
$398$	−33.1642	−1.66237
$399$	6.63455	0.332143
$400$	−4.98295	−0.249147
$401$	19.9915	0.998330	0.499165	−	0.866507i	$-0.333640\pi$
$401$	19.9915	0.998330	0.499165	+	0.866507i	$0.333640\pi$
$402$	10.0787	0.502678
$403$	1.00000	0.0498135
$404$	6.61138	0.328928
$405$	1.00000	0.0496904
$406$	15.6178	0.775097
$407$	15.8031	0.783329
$408$	−9.89631	−0.489940
$409$	−1.52586	−0.0754490	−0.0377245	−	0.999288i	$-0.512011\pi$
$409$	−1.52586	−0.0754490	−0.0377245	+	0.999288i	$0.512011\pi$
$410$	20.9918	1.03671
$411$	0.910593	0.0449163
$412$	4.47636	0.220534
$413$	3.84539	0.189219
$414$	−1.45053	−0.0712897
$415$	10.4007	0.510552
$416$	4.61050	0.226049
$417$	−6.00865	−0.294245
$418$	16.6083	0.812336
$419$	−6.05110	−0.295615	−0.147808	−	0.989016i	$-0.547222\pi$
$419$	−6.05110	−0.295615	−0.147808	+	0.989016i	$0.547222\pi$
$420$	−0.829657	−0.0404831
$421$	−12.7845	−0.623077	−0.311538	−	0.950234i	$-0.600844\pi$
$421$	−12.7845	−0.623077	−0.311538	+	0.950234i	$0.600844\pi$
$422$	−32.9508	−1.60402
$423$	−6.20415	−0.301656
$424$	−10.0690	−0.488994
$425$	5.16741	0.250656
$426$	14.4143	0.698376
$427$	14.7184	0.712272
$428$	−3.80417	−0.183882
$429$	1.41022	0.0680863
$430$	−11.0474	−0.532752
$431$	0.568587	0.0273879	0.0136939	−	0.999906i	$-0.495641\pi$
$431$	0.568587	0.0273879	0.0136939	+	0.999906i	$0.495641\pi$
$432$	−4.98295	−0.239742
$433$	26.9367	1.29449	0.647247	−	0.762280i	$-0.275920\pi$
$433$	26.9367	1.29449	0.647247	+	0.762280i	$0.275920\pi$
$434$	1.61648	0.0775933
$435$	−9.66162	−0.463239
$436$	−17.9479	−0.859548
$437$	5.95346	0.284793
$438$	9.30847	0.444776
$439$	−17.6074	−0.840355	−0.420178	−	0.907442i	$-0.638032\pi$
$439$	−17.6074	−0.840355	−0.420178	+	0.907442i	$0.638032\pi$
$440$	2.70078	0.128755
$441$	−6.08936	−0.289970
$442$	−8.75325	−0.416349
$443$	−28.0445	−1.33243	−0.666217	−	0.745757i	$-0.732088\pi$
$443$	−28.0445	−1.33243	−0.666217	+	0.745757i	$0.732088\pi$
$444$	−9.74270	−0.462368
$445$	−1.70701	−0.0809202
$446$	48.1986	2.28227
$447$	20.3892	0.964377
$448$	−2.05742	−0.0972038
$449$	5.20295	0.245542	0.122771	−	0.992435i	$-0.460822\pi$
$449$	5.20295	0.245542	0.122771	+	0.992435i	$0.460822\pi$
$450$	1.69393	0.0798528
$451$	−17.4760	−0.822912
$452$	−8.54946	−0.402133
$453$	−0.410297	−0.0192775
$454$	34.9019	1.63803
$455$	0.954273	0.0447370
$456$	13.3149	0.623530
$457$	−26.0935	−1.22060	−0.610302	−	0.792169i	$-0.708952\pi$
$457$	−26.0935	−1.22060	−0.610302	+	0.792169i	$0.708952\pi$
$458$	−0.506886	−0.0236852
$459$	5.16741	0.241194
$460$	−0.744486	−0.0347118
$461$	9.34210	0.435105	0.217552	−	0.976049i	$-0.430193\pi$
$461$	9.34210	0.435105	0.217552	+	0.976049i	$0.430193\pi$
$462$	2.27959	0.106056
$463$	−9.57953	−0.445199	−0.222599	−	0.974910i	$-0.571454\pi$
$463$	−9.57953	−0.445199	−0.222599	+	0.974910i	$0.571454\pi$
$464$	48.1434	2.23500
$465$	−1.00000	−0.0463739
$466$	31.6364	1.46553
$467$	2.94976	0.136498	0.0682492	−	0.997668i	$-0.478259\pi$
$467$	2.94976	0.136498	0.0682492	+	0.997668i	$0.478259\pi$
$468$	−0.869413	−0.0401886
$469$	−5.67779	−0.262176
$470$	−10.5094	−0.484764
$471$	18.5151	0.853129
$472$	7.71736	0.355220
$473$	9.19711	0.422883
$474$	23.7575	1.09122
$475$	−6.95247	−0.319001
$476$	−4.28718	−0.196502
$477$	5.25758	0.240728
$478$	−32.7666	−1.49871
$479$	28.1049	1.28415	0.642073	−	0.766644i	$-0.278075\pi$
$479$	28.1049	1.28415	0.642073	+	0.766644i	$0.278075\pi$
$480$	−4.61050	−0.210440
$481$	11.2061	0.510953
$482$	42.7841	1.94876
$483$	0.817153	0.0371817
$484$	−7.83451	−0.356114
$485$	−11.6081	−0.527095
$486$	1.69393	0.0768384
$487$	15.1680	0.687327	0.343664	−	0.939093i	$-0.388332\pi$
$487$	15.1680	0.687327	0.343664	+	0.939093i	$0.388332\pi$
$488$	29.5385	1.33714
$489$	−10.2035	−0.461420
$490$	−10.3150	−0.465983
$491$	−4.70423	−0.212299	−0.106149	−	0.994350i	$-0.533852\pi$
$491$	−4.70423	−0.212299	−0.106149	+	0.994350i	$0.533852\pi$
$492$	10.7741	0.485732
$493$	−49.9255	−2.24853
$494$	11.7770	0.529873
$495$	−1.41022	−0.0633849
$496$	4.98295	0.223741
$497$	−8.12027	−0.364244
$498$	17.6181	0.789488
$499$	−15.7829	−0.706542	−0.353271	−	0.935521i	$-0.614931\pi$
$499$	−15.7829	−0.706542	−0.353271	+	0.935521i	$0.614931\pi$
$500$	0.869413	0.0388813
$501$	−14.2000	−0.634410
$502$	−3.73978	−0.166915
$503$	−17.3665	−0.774332	−0.387166	−	0.922010i	$-0.626546\pi$
$503$	−17.3665	−0.774332	−0.387166	+	0.922010i	$0.626546\pi$
$504$	1.82757	0.0814063
$505$	7.60442	0.338392
$506$	2.04558	0.0909369
$507$	1.00000	0.0444116
$508$	4.05412	0.179873
$509$	−1.22560	−0.0543236	−0.0271618	−	0.999631i	$-0.508647\pi$
$509$	−1.22560	−0.0543236	−0.0271618	+	0.999631i	$0.508647\pi$
$510$	8.75325	0.387600
$511$	−5.24390	−0.231976
$512$	3.88781	0.171819
$513$	−6.95247	−0.306959
$514$	1.60534	0.0708083
$515$	5.14872	0.226880
$516$	−5.67008	−0.249611
$517$	8.74925	0.384792
$518$	18.1143	0.795898
$519$	20.5144	0.900481
$520$	1.91514	0.0839844
$521$	−1.16000	−0.0508205	−0.0254103	−	0.999677i	$-0.508089\pi$
$521$	−1.16000	−0.0508205	−0.0254103	+	0.999677i	$0.508089\pi$
$522$	−16.3662	−0.716327
$523$	−3.56411	−0.155848	−0.0779238	−	0.996959i	$-0.524829\pi$
$523$	−3.56411	−0.155848	−0.0779238	+	0.996959i	$0.524829\pi$
$524$	−13.8425	−0.604714
$525$	−0.954273	−0.0416479
$526$	−23.0400	−1.00459
$527$	−5.16741	−0.225096
$528$	7.02708	0.305814
$529$	−22.2667	−0.968119
$530$	8.90599	0.386851
$531$	−4.02966	−0.174872
$532$	5.76816	0.250082
$533$	−12.3923	−0.536772
$534$	−2.89157	−0.125130
$535$	−4.37557	−0.189172
$536$	−11.3948	−0.492181
$537$	−21.4343	−0.924960
$538$	17.9350	0.773234
$539$	8.58737	0.369884
$540$	0.869413	0.0374136
$541$	37.2258	1.60046	0.800231	−	0.599692i	$-0.204710\pi$
$541$	37.2258	1.60046	0.800231	+	0.599692i	$0.204710\pi$
$542$	40.1266	1.72359
$543$	−6.35553	−0.272742
$544$	−23.8243	−1.02146
$545$	−20.6437	−0.884278
$546$	1.61648	0.0691788
$547$	−10.6704	−0.456232	−0.228116	−	0.973634i	$-0.573257\pi$
$547$	−10.6704	−0.456232	−0.228116	+	0.973634i	$0.573257\pi$
$548$	0.791682	0.0338190
$549$	−15.4237	−0.658266
$550$	−2.38883	−0.101860
$551$	67.1721	2.86163
$552$	1.63995	0.0698010
$553$	−13.3837	−0.569134
$554$	2.97739	0.126497
$555$	−11.2061	−0.475671
$556$	−5.22400	−0.221547
$557$	37.0903	1.57157	0.785784	−	0.618501i	$-0.212260\pi$
$557$	37.0903	1.57157	0.785784	+	0.618501i	$0.212260\pi$
$558$	−1.69393	−0.0717100
$559$	6.52173	0.275840
$560$	4.75509	0.200939
$561$	−7.28721	−0.307666
$562$	−17.8678	−0.753707
$563$	24.5471	1.03454	0.517268	−	0.855823i	$-0.326949\pi$
$563$	24.5471	1.03454	0.517268	+	0.855823i	$0.326949\pi$
$564$	−5.39397	−0.227127
$565$	−9.83360	−0.413703
$566$	−46.3323	−1.94749
$567$	−0.954273	−0.0400757
$568$	−16.2966	−0.683792
$569$	25.3201	1.06147	0.530736	−	0.847537i	$-0.321915\pi$
$569$	25.3201	1.06147	0.530736	+	0.847537i	$0.321915\pi$
$570$	−11.7770	−0.493285
$571$	−38.0298	−1.59150	−0.795748	−	0.605628i	$-0.792922\pi$
$571$	−38.0298	−1.59150	−0.795748	+	0.605628i	$0.792922\pi$
$572$	1.22607	0.0512645
$573$	2.62622	0.109712
$574$	−20.0319	−0.836116
$575$	−0.856309	−0.0357106
$576$	2.15600	0.0898335
$577$	26.5774	1.10643	0.553215	−	0.833038i	$-0.313401\pi$
$577$	26.5774	1.10643	0.553215	+	0.833038i	$0.313401\pi$
$578$	16.4347	0.683593
$579$	−14.7338	−0.612315
$580$	−8.39994	−0.348789
$581$	−9.92513	−0.411764
$582$	−19.6633	−0.815070
$583$	−7.41437	−0.307072
$584$	−10.5240	−0.435488
$585$	−1.00000	−0.0413449
$586$	3.93142	0.162405
$587$	20.3016	0.837938	0.418969	−	0.908001i	$-0.362392\pi$
$587$	20.3016	0.837938	0.418969	+	0.908001i	$0.362392\pi$
$588$	−5.29417	−0.218328
$589$	6.95247	0.286471
$590$	−6.82598	−0.281021
$591$	−22.8321	−0.939187
$592$	55.8392	2.29498
$593$	35.8197	1.47094	0.735470	−	0.677558i	$-0.236962\pi$
$593$	35.8197	1.47094	0.735470	+	0.677558i	$0.236962\pi$
$594$	−2.38883	−0.0980148
$595$	−4.93112	−0.202156
$596$	17.7266	0.726112
$597$	−19.5782	−0.801283
$598$	1.45053	0.0593166
$599$	−8.21382	−0.335608	−0.167804	−	0.985820i	$-0.553668\pi$
$599$	−8.21382	−0.335608	−0.167804	+	0.985820i	$0.553668\pi$
$600$	−1.91514	−0.0781853
$601$	−6.35691	−0.259304	−0.129652	−	0.991560i	$-0.541386\pi$
$601$	−6.35691	−0.259304	−0.129652	+	0.991560i	$0.541386\pi$
$602$	10.5422	0.429669
$603$	5.94986	0.242297
$604$	−0.356718	−0.0145146
$605$	−9.01127	−0.366360
$606$	12.8814	0.523271
$607$	31.8818	1.29404	0.647021	−	0.762472i	$-0.276015\pi$
$607$	31.8818	1.29404	0.647021	+	0.762472i	$0.276015\pi$
$608$	32.0544	1.29998
$609$	9.21983	0.373606
$610$	−26.1267	−1.05784
$611$	6.20415	0.250993
$612$	4.49261	0.181603
$613$	32.0969	1.29638	0.648191	−	0.761478i	$-0.275526\pi$
$613$	32.0969	1.29638	0.648191	+	0.761478i	$0.275526\pi$
$614$	−14.9883	−0.604877
$615$	12.3923	0.499708
$616$	−2.57728	−0.103842
$617$	−48.5060	−1.95278	−0.976389	−	0.216022i	$-0.930692\pi$
$617$	−48.5060	−1.95278	−0.976389	+	0.216022i	$0.930692\pi$
$618$	8.72159	0.350834
$619$	1.83438	0.0737298	0.0368649	−	0.999320i	$-0.488263\pi$
$619$	1.83438	0.0737298	0.0368649	+	0.999320i	$0.488263\pi$
$620$	−0.869413	−0.0349165
$621$	−0.856309	−0.0343625
$622$	−18.1223	−0.726636
$623$	1.62896	0.0652627
$624$	4.98295	0.199478
$625$	1.00000	0.0400000
$626$	4.99821	0.199768
$627$	9.80454	0.391556
$628$	16.0972	0.642350
$629$	−57.9063	−2.30888
$630$	−1.61648	−0.0644019
$631$	30.9485	1.23204	0.616020	−	0.787731i	$-0.288744\pi$
$631$	30.9485	1.23204	0.616020	+	0.787731i	$0.288744\pi$
$632$	−26.8599	−1.06843
$633$	−19.4522	−0.773156
$634$	24.9442	0.990662
$635$	4.66306	0.185048
$636$	4.57101	0.181252
$637$	6.08936	0.241269
$638$	23.0800	0.913744
$639$	8.50938	0.336626
$640$	12.8731	0.508855
$641$	10.3199	0.407611	0.203806	−	0.979011i	$-0.434669\pi$
$641$	10.3199	0.407611	0.203806	+	0.979011i	$0.434669\pi$
$642$	−7.41192	−0.292525
$643$	−17.0913	−0.674014	−0.337007	−	0.941502i	$-0.609415\pi$
$643$	−17.0913	−0.674014	−0.337007	+	0.941502i	$0.609415\pi$
$644$	0.710443	0.0279954
$645$	−6.52173	−0.256793
$646$	−60.8567	−2.39437
$647$	−10.3270	−0.405997	−0.202999	−	0.979179i	$-0.565069\pi$
$647$	−10.3270	−0.405997	−0.202999	+	0.979179i	$0.565069\pi$
$648$	−1.91514	−0.0752338
$649$	5.68272	0.223066
$650$	−1.69393	−0.0664416
$651$	0.954273	0.0374009
$652$	−8.87108	−0.347418
$653$	33.7487	1.32069	0.660344	−	0.750963i	$-0.270410\pi$
$653$	33.7487	1.32069	0.660344	+	0.750963i	$0.270410\pi$
$654$	−34.9690	−1.36740
$655$	−15.9217	−0.622112
$656$	−61.7504	−2.41095
$657$	5.49518	0.214387
$658$	10.0289	0.390966
$659$	−48.0386	−1.87132	−0.935659	−	0.352905i	$-0.885194\pi$
$659$	−48.0386	−1.87132	−0.935659	+	0.352905i	$0.885194\pi$
$660$	−1.22607	−0.0477246
$661$	−12.0365	−0.468164	−0.234082	−	0.972217i	$-0.575208\pi$
$661$	−12.0365	−0.468164	−0.234082	+	0.972217i	$0.575208\pi$
$662$	45.1154	1.75346
$663$	−5.16741	−0.200685
$664$	−19.9188	−0.773001
$665$	6.63455	0.257277
$666$	−18.9823	−0.735551
$667$	8.27334	0.320345
$668$	−12.3457	−0.477668
$669$	28.4537	1.10008
$670$	10.0787	0.389373
$671$	21.7508	0.839682
$672$	4.39968	0.169721
$673$	−26.3329	−1.01506	−0.507530	−	0.861634i	$-0.669441\pi$
$673$	−26.3329	−1.01506	−0.507530	+	0.861634i	$0.669441\pi$
$674$	−10.0411	−0.386768
$675$	1.00000	0.0384900
$676$	0.869413	0.0334390
$677$	−13.9284	−0.535311	−0.267656	−	0.963515i	$-0.586249\pi$
$677$	−13.9284	−0.535311	−0.267656	+	0.963515i	$0.586249\pi$
$678$	−16.6575	−0.639726
$679$	11.0773	0.425106
$680$	−9.89631	−0.379506
$681$	20.6041	0.789550
$682$	2.38883	0.0914730
$683$	−18.1170	−0.693230	−0.346615	−	0.938008i	$-0.612669\pi$
$683$	−18.1170	−0.693230	−0.346615	+	0.938008i	$0.612669\pi$
$684$	−6.04457	−0.231120
$685$	0.910593	0.0347920
$686$	21.1586	0.807840
$687$	−0.299236	−0.0114166
$688$	32.4974	1.23895
$689$	−5.25758	−0.200298
$690$	−1.45053	−0.0552208
$691$	−46.4810	−1.76822	−0.884111	−	0.467277i	$-0.845235\pi$
$691$	−46.4810	−1.76822	−0.884111	+	0.467277i	$0.845235\pi$
$692$	17.8355	0.678003
$693$	1.34574	0.0511204
$694$	−5.66421	−0.215010
$695$	−6.00865	−0.227921
$696$	18.5034	0.701368
$697$	64.0363	2.42555
$698$	24.7502	0.936808
$699$	18.6763	0.706403
$700$	−0.829657	−0.0313581
$701$	−0.103791	−0.00392013	−0.00196006	−	0.999998i	$-0.500624\pi$
$701$	−0.103791	−0.00392013	−0.00196006	+	0.999998i	$0.500624\pi$
$702$	−1.69393	−0.0639334
$703$	77.9098	2.93842
$704$	−3.04045	−0.114591
$705$	−6.20415	−0.233662
$706$	25.1765	0.947532
$707$	−7.25669	−0.272916
$708$	−3.50344	−0.131667
$709$	26.3702	0.990355	0.495178	−	0.868792i	$-0.335103\pi$
$709$	26.3702	0.990355	0.495178	+	0.868792i	$0.335103\pi$
$710$	14.4143	0.540960
$711$	14.0251	0.525981
$712$	3.26917	0.122517
$713$	0.856309	0.0320690
$714$	−8.35299	−0.312603
$715$	1.41022	0.0527394
$716$	−18.6353	−0.696434
$717$	−19.3435	−0.722395
$718$	61.0993	2.28021
$719$	17.8007	0.663854	0.331927	−	0.943305i	$-0.392301\pi$
$719$	17.8007	0.663854	0.331927	+	0.943305i	$0.392301\pi$
$720$	−4.98295	−0.185703
$721$	−4.91328	−0.182980
$722$	49.6946	1.84944
$723$	25.2572	0.939326
$724$	−5.52558	−0.205356
$725$	−9.66162	−0.358824
$726$	−15.2645	−0.566518
$727$	39.7619	1.47469	0.737344	−	0.675517i	$-0.236080\pi$
$727$	39.7619	1.47469	0.737344	+	0.675517i	$0.236080\pi$
$728$	−1.82757	−0.0677341
$729$	1.00000	0.0370370
$730$	9.30847	0.344522
$731$	−33.7004	−1.24646
$732$	−13.4095	−0.495630
$733$	23.8136	0.879576	0.439788	−	0.898102i	$-0.355054\pi$
$733$	23.8136	0.879576	0.439788	+	0.898102i	$0.355054\pi$
$734$	2.05680	0.0759179
$735$	−6.08936	−0.224610
$736$	3.94802	0.145526
$737$	−8.39064	−0.309073
$738$	20.9918	0.772720
$739$	−40.0175	−1.47207	−0.736034	−	0.676944i	$-0.763304\pi$
$739$	−40.0175	−1.47207	−0.736034	+	0.676944i	$0.763304\pi$
$740$	−9.74270	−0.358149
$741$	6.95247	0.255405
$742$	−8.49874	−0.311999
$743$	−23.0386	−0.845206	−0.422603	−	0.906315i	$-0.638883\pi$
$743$	−23.0386	−0.845206	−0.422603	+	0.906315i	$0.638883\pi$
$744$	1.91514	0.0702124
$745$	20.3892	0.747003
$746$	−1.13403	−0.0415199
$747$	10.4007	0.380543
$748$	−6.33559	−0.231652
$749$	4.17548	0.152569
$750$	1.69393	0.0618537
$751$	−31.7878	−1.15995	−0.579977	−	0.814633i	$-0.696938\pi$
$751$	−31.7878	−1.15995	−0.579977	+	0.814633i	$0.696938\pi$
$752$	30.9150	1.12735
$753$	−2.20775	−0.0804548
$754$	16.3662	0.596020
$755$	−0.410297	−0.0149322
$756$	−0.829657	−0.0301743
$757$	14.4469	0.525083	0.262542	−	0.964921i	$-0.415439\pi$
$757$	14.4469	0.525083	0.262542	+	0.964921i	$0.415439\pi$
$758$	−59.3974	−2.15741
$759$	1.20759	0.0438327
$760$	13.3149	0.482984
$761$	−1.16221	−0.0421300	−0.0210650	−	0.999778i	$-0.506706\pi$
$761$	−1.16221	−0.0421300	−0.0210650	+	0.999778i	$0.506706\pi$
$762$	7.89891	0.286147
$763$	19.6997	0.713177
$764$	2.28327	0.0826059
$765$	5.16741	0.186828
$766$	−3.57266	−0.129086
$767$	4.02966	0.145503
$768$	17.4942	0.631269
$769$	−32.2228	−1.16198	−0.580992	−	0.813909i	$-0.697335\pi$
$769$	−32.2228	−1.16198	−0.580992	+	0.813909i	$0.697335\pi$
$770$	2.27959	0.0821509
$771$	0.947697	0.0341305
$772$	−12.8097	−0.461033
$773$	−49.3901	−1.77644	−0.888219	−	0.459420i	$-0.848057\pi$
$773$	−49.3901	−1.77644	−0.888219	+	0.459420i	$0.848057\pi$
$774$	−11.0474	−0.397090
$775$	−1.00000	−0.0359211
$776$	22.2311	0.798049
$777$	10.6936	0.383632
$778$	2.28008	0.0817448
$779$	−86.1574	−3.08691
$780$	−0.869413	−0.0311300
$781$	−12.0001	−0.429399
$782$	−7.49548	−0.268038
$783$	−9.66162	−0.345278
$784$	30.3430	1.08368
$785$	18.5151	0.660831
$786$	−26.9703	−0.961999
$787$	−19.7427	−0.703752	−0.351876	−	0.936047i	$-0.614456\pi$
$787$	−19.7427	−0.703752	−0.351876	+	0.936047i	$0.614456\pi$
$788$	−19.8505	−0.707146
$789$	−13.6015	−0.484226
$790$	23.7575	0.845254
$791$	9.38394	0.333654
$792$	2.70078	0.0959680
$793$	15.4237	0.547710
$794$	13.8940	0.493078
$795$	5.25758	0.186467
$796$	−17.0215	−0.603313
$797$	−20.2060	−0.715734	−0.357867	−	0.933773i	$-0.616496\pi$
$797$	−20.2060	−0.715734	−0.357867	+	0.933773i	$0.616496\pi$
$798$	11.2385	0.397838
$799$	−32.0594	−1.13418
$800$	−4.61050	−0.163006
$801$	−1.70701	−0.0603143
$802$	33.8644	1.19579
$803$	−7.74944	−0.273472
$804$	5.17289	0.182434
$805$	0.817153	0.0288008
$806$	1.69393	0.0596663
$807$	10.5878	0.372708
$808$	−14.5635	−0.512343
$809$	−42.8344	−1.50598	−0.752988	−	0.658034i	$-0.771388\pi$
$809$	−42.8344	−1.50598	−0.752988	+	0.658034i	$0.771388\pi$
$810$	1.69393	0.0595188
$811$	27.8372	0.977497	0.488748	−	0.872425i	$-0.337454\pi$
$811$	27.8372	0.977497	0.488748	+	0.872425i	$0.337454\pi$
$812$	8.01584	0.281301
$813$	23.6884	0.830789
$814$	26.7694	0.938266
$815$	−10.2035	−0.357414
$816$	−25.7489	−0.901392
$817$	45.3421	1.58632
$818$	−2.58471	−0.0903723
$819$	0.954273	0.0333450
$820$	10.7741	0.376247
$821$	26.5203	0.925565	0.462782	−	0.886472i	$-0.346851\pi$
$821$	26.5203	0.925565	0.462782	+	0.886472i	$0.346851\pi$
$822$	1.54249	0.0538003
$823$	−9.95025	−0.346844	−0.173422	−	0.984848i	$-0.555482\pi$
$823$	−9.95025	−0.346844	−0.173422	+	0.984848i	$0.555482\pi$
$824$	−9.86051	−0.343507
$825$	−1.41022	−0.0490977
$826$	6.51384	0.226646
$827$	2.37997	0.0827598	0.0413799	−	0.999143i	$-0.486825\pi$
$827$	2.37997	0.0827598	0.0413799	+	0.999143i	$0.486825\pi$
$828$	−0.744486	−0.0258727
$829$	−8.44026	−0.293142	−0.146571	−	0.989200i	$-0.546824\pi$
$829$	−8.44026	−0.293142	−0.146571	+	0.989200i	$0.546824\pi$
$830$	17.6181	0.611535
$831$	1.75768	0.0609731
$832$	−2.15600	−0.0747460
$833$	−31.4662	−1.09024
$834$	−10.1783	−0.352444
$835$	−14.2000	−0.491412
$836$	8.52420	0.294816
$837$	−1.00000	−0.0345651
$838$	−10.2502	−0.354086
$839$	46.7070	1.61251	0.806253	−	0.591571i	$-0.201492\pi$
$839$	46.7070	1.61251	0.806253	+	0.591571i	$0.201492\pi$
$840$	1.82757	0.0630570
$841$	64.3470	2.21886
$842$	−21.6560	−0.746316
$843$	−10.5481	−0.363296
$844$	−16.9120	−0.582135
$845$	1.00000	0.0344010
$846$	−10.5094	−0.361322
$847$	8.59921	0.295472
$848$	−26.1982	−0.899651
$849$	−27.3519	−0.938714
$850$	8.75325	0.300234
$851$	9.59586	0.328942
$852$	7.39816	0.253457
$853$	−48.9537	−1.67614	−0.838071	−	0.545561i	$-0.816317\pi$
$853$	−48.9537	−1.67614	−0.838071	+	0.545561i	$0.816317\pi$
$854$	24.9320	0.853154
$855$	−6.95247	−0.237769
$856$	8.37982	0.286416
$857$	−11.3912	−0.389115	−0.194558	−	0.980891i	$-0.562327\pi$
$857$	−11.3912	−0.389115	−0.194558	+	0.980891i	$0.562327\pi$
$858$	2.38883	0.0815532
$859$	−25.3832	−0.866063	−0.433032	−	0.901379i	$-0.642556\pi$
$859$	−25.3832	−0.866063	−0.433032	+	0.901379i	$0.642556\pi$
$860$	−5.67008	−0.193348
$861$	−11.8257	−0.403018
$862$	0.963148	0.0328050
$863$	−6.14502	−0.209179	−0.104589	−	0.994515i	$-0.533353\pi$
$863$	−6.14502	−0.209179	−0.104589	+	0.994515i	$0.533353\pi$
$864$	−4.61050	−0.156853
$865$	20.5144	0.697510
$866$	45.6290	1.55054
$867$	9.70209	0.329500
$868$	0.829657	0.0281604
$869$	−19.7785	−0.670939
$870$	−16.3662	−0.554865
$871$	−5.94986	−0.201603
$872$	39.5356	1.33884
$873$	−11.6081	−0.392874
$874$	10.0848	0.341122
$875$	−0.954273	−0.0322603
$876$	4.77758	0.161419
$877$	−24.4876	−0.826887	−0.413444	−	0.910530i	$-0.635674\pi$
$877$	−24.4876	−0.826887	−0.413444	+	0.910530i	$0.635674\pi$
$878$	−29.8258	−1.00657
$879$	2.32088	0.0782814
$880$	7.02708	0.236883
$881$	31.4605	1.05993	0.529966	−	0.848019i	$-0.322205\pi$
$881$	31.4605	1.05993	0.529966	+	0.848019i	$0.322205\pi$
$882$	−10.3150	−0.347323
$883$	6.16411	0.207439	0.103719	−	0.994607i	$-0.466926\pi$
$883$	6.16411	0.207439	0.103719	+	0.994607i	$0.466926\pi$
$884$	−4.49261	−0.151103
$885$	−4.02966	−0.135455
$886$	−47.5056	−1.59598
$887$	−37.8389	−1.27051	−0.635253	−	0.772304i	$-0.719104\pi$
$887$	−37.8389	−1.27051	−0.635253	+	0.772304i	$0.719104\pi$
$888$	21.4612	0.720190
$889$	−4.44983	−0.149243
$890$	−2.89157	−0.0969256
$891$	−1.41022	−0.0472443
$892$	24.7380	0.828289
$893$	43.1342	1.44343
$894$	34.5380	1.15512
$895$	−21.4343	−0.716471
$896$	−12.2845	−0.410396
$897$	0.856309	0.0285913
$898$	8.81345	0.294109
$899$	9.66162	0.322233
$900$	0.869413	0.0289804
$901$	27.1680	0.905099
$902$	−29.6032	−0.985678
$903$	6.22351	0.207105
$904$	18.8327	0.626367
$905$	−6.35553	−0.211265
$906$	−0.695017	−0.0230904
$907$	−38.8583	−1.29027	−0.645134	−	0.764070i	$-0.723198\pi$
$907$	−38.8583	−1.29027	−0.645134	+	0.764070i	$0.723198\pi$
$908$	17.9135	0.594479
$909$	7.60442	0.252223
$910$	1.61648	0.0535856
$911$	33.0347	1.09449	0.547244	−	0.836973i	$-0.315677\pi$
$911$	33.0347	1.09449	0.547244	+	0.836973i	$0.315677\pi$
$912$	34.6438	1.14717
$913$	−14.6674	−0.485419
$914$	−44.2007	−1.46203
$915$	−15.4237	−0.509890
$916$	−0.260160	−0.00859592
$917$	15.1936	0.501738
$918$	8.75325	0.288900
$919$	−24.5281	−0.809108	−0.404554	−	0.914514i	$-0.632573\pi$
$919$	−24.5281	−0.809108	−0.404554	+	0.914514i	$0.632573\pi$
$920$	1.63995	0.0540676
$921$	−8.84820	−0.291558
$922$	15.8249	0.521165
$923$	−8.50938	−0.280090
$924$	1.17000	0.0384903
$925$	−11.2061	−0.368453
$926$	−16.2271	−0.533256
$927$	5.14872	0.169106
$928$	44.5450	1.46226
$929$	−9.66252	−0.317017	−0.158509	−	0.987358i	$-0.550669\pi$
$929$	−9.66252	−0.317017	−0.158509	+	0.987358i	$0.550669\pi$
$930$	−1.69393	−0.0555463
$931$	42.3361	1.38751
$932$	16.2374	0.531874
$933$	−10.6983	−0.350247
$934$	4.99669	0.163497
$935$	−7.28721	−0.238317
$936$	1.91514	0.0625983
$937$	49.8373	1.62811	0.814057	−	0.580785i	$-0.197254\pi$
$937$	49.8373	1.62811	0.814057	+	0.580785i	$0.197254\pi$
$938$	−9.61780	−0.314032
$939$	2.95065	0.0962908
$940$	−5.39397	−0.175932
$941$	6.01308	0.196021	0.0980103	−	0.995185i	$-0.468752\pi$
$941$	6.01308	0.196021	0.0980103	+	0.995185i	$0.468752\pi$
$942$	31.3633	1.02187
$943$	−10.6117	−0.345564
$944$	20.0796	0.653534
$945$	−0.954273	−0.0310425
$946$	15.5793	0.506526
$947$	−26.7809	−0.870261	−0.435131	−	0.900367i	$-0.643298\pi$
$947$	−26.7809	−0.870261	−0.435131	+	0.900367i	$0.643298\pi$
$948$	12.1936	0.396028
$949$	−5.49518	−0.178381
$950$	−11.7770	−0.382097
$951$	14.7256	0.477511
$952$	9.44378	0.306075
$953$	−52.7778	−1.70964	−0.854820	−	0.518925i	$-0.826332\pi$
$953$	−52.7778	−1.70964	−0.854820	+	0.518925i	$0.826332\pi$
$954$	8.90599	0.288342
$955$	2.62622	0.0849826
$956$	−16.8175	−0.543916
$957$	13.6251	0.440436
$958$	47.6078	1.53814
$959$	−0.868955	−0.0280600
$960$	2.15600	0.0695847
$961$	1.00000	0.0322581
$962$	18.9823	0.612015
$963$	−4.37557	−0.141001
$964$	21.9589	0.707250
$965$	−14.7338	−0.474297
$966$	1.38420	0.0445360
$967$	−24.5205	−0.788527	−0.394264	−	0.918997i	$-0.629000\pi$
$967$	−24.5205	−0.788527	−0.394264	+	0.918997i	$0.629000\pi$
$968$	17.2578	0.554688
$969$	−35.9262	−1.15412
$970$	−19.6633	−0.631351
$971$	45.8173	1.47035	0.735174	−	0.677879i	$-0.237101\pi$
$971$	45.8173	1.47035	0.735174	+	0.677879i	$0.237101\pi$
$972$	0.869413	0.0278864
$973$	5.73389	0.183820
$974$	25.6936	0.823275
$975$	−1.00000	−0.0320256
$976$	76.8553	2.46008
$977$	9.17923	0.293670	0.146835	−	0.989161i	$-0.453091\pi$
$977$	9.17923	0.293670	0.146835	+	0.989161i	$0.453091\pi$
$978$	−17.2841	−0.552685
$979$	2.40727	0.0769367
$980$	−5.29417	−0.169116
$981$	−20.6437	−0.659102
$982$	−7.96865	−0.254290
$983$	17.8229	0.568461	0.284231	−	0.958756i	$-0.408262\pi$
$983$	17.8229	0.568461	0.284231	+	0.958756i	$0.408262\pi$
$984$	−23.7331	−0.756583
$985$	−22.8321	−0.727491
$986$	−84.5706	−2.69328
$987$	5.92045	0.188450
$988$	6.04457	0.192303
$989$	5.58462	0.177580
$990$	−2.38883	−0.0759219
$991$	17.0891	0.542852	0.271426	−	0.962459i	$-0.412505\pi$
$991$	17.0891	0.542852	0.271426	+	0.962459i	$0.412505\pi$
$992$	4.61050	0.146384
$993$	26.6335	0.845189
$994$	−13.7552	−0.436288
$995$	−19.5782	−0.620671
$996$	9.04253	0.286523
$997$	18.4306	0.583703	0.291851	−	0.956464i	$-0.405729\pi$
$997$	18.4306	0.583703	0.291851	+	0.956464i	$0.405729\pi$
$998$	−26.7353	−0.846290
$999$	−11.2061	−0.354544

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.u.1.9	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.u.1.9	✓	9	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q+1.69393 q^{2} +1.00000 q^{3} +0.869413 q^{4} +1.00000 q^{5} +1.69393 q^{6} -0.954273 q^{7} -1.91514 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.69393 q^{2} +1.00000 q^{3} +0.869413 q^{4} +1.00000 q^{5} +1.69393 q^{6} -0.954273 q^{7} -1.91514 q^{8} +1.00000 q^{9} +1.69393 q^{10} -1.41022 q^{11} +0.869413 q^{12} -1.00000 q^{13} -1.61648 q^{14} +1.00000 q^{15} -4.98295 q^{16} +5.16741 q^{17} +1.69393 q^{18} -6.95247 q^{19} +0.869413 q^{20} -0.954273 q^{21} -2.38883 q^{22} -0.856309 q^{23} -1.91514 q^{24} +1.00000 q^{25} -1.69393 q^{26} +1.00000 q^{27} -0.829657 q^{28} -9.66162 q^{29} +1.69393 q^{30} -1.00000 q^{31} -4.61050 q^{32} -1.41022 q^{33} +8.75325 q^{34} -0.954273 q^{35} +0.869413 q^{36} -11.2061 q^{37} -11.7770 q^{38} -1.00000 q^{39} -1.91514 q^{40} +12.3923 q^{41} -1.61648 q^{42} -6.52173 q^{43} -1.22607 q^{44} +1.00000 q^{45} -1.45053 q^{46} -6.20415 q^{47} -4.98295 q^{48} -6.08936 q^{49} +1.69393 q^{50} +5.16741 q^{51} -0.869413 q^{52} +5.25758 q^{53} +1.69393 q^{54} -1.41022 q^{55} +1.82757 q^{56} -6.95247 q^{57} -16.3662 q^{58} -4.02966 q^{59} +0.869413 q^{60} -15.4237 q^{61} -1.69393 q^{62} -0.954273 q^{63} +2.15600 q^{64} -1.00000 q^{65} -2.38883 q^{66} +5.94986 q^{67} +4.49261 q^{68} -0.856309 q^{69} -1.61648 q^{70} +8.50938 q^{71} -1.91514 q^{72} +5.49518 q^{73} -18.9823 q^{74} +1.00000 q^{75} -6.04457 q^{76} +1.34574 q^{77} -1.69393 q^{78} +14.0251 q^{79} -4.98295 q^{80} +1.00000 q^{81} +20.9918 q^{82} +10.4007 q^{83} -0.829657 q^{84} +5.16741 q^{85} -11.0474 q^{86} -9.66162 q^{87} +2.70078 q^{88} -1.70701 q^{89} +1.69393 q^{90} +0.954273 q^{91} -0.744486 q^{92} -1.00000 q^{93} -10.5094 q^{94} -6.95247 q^{95} -4.61050 q^{96} -11.6081 q^{97} -10.3150 q^{98} -1.41022 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9	\( 9 q - 3 q^{2} + 9 q^{3} + 5 q^{4} + 9 q^{5} - 3 q^{6} - 5 q^{7} - 18 q^{8} + 9 q^{9} - 3 q^{10} + 5 q^{12} - 9 q^{13} + 11 q^{14} + 9 q^{15} + 9 q^{16} - 5 q^{17} - 3 q^{18} - 12 q^{19} + 5 q^{20} - 5 q^{21} - 17 q^{22} - 21 q^{23} - 18 q^{24} + 9 q^{25} + 3 q^{26} + 9 q^{27} - 8 q^{28} - 15 q^{29} - 3 q^{30} - 9 q^{31} - 9 q^{32} + 9 q^{34} - 5 q^{35} + 5 q^{36} - 13 q^{37} - 24 q^{38} - 9 q^{39} - 18 q^{40} - 11 q^{41} + 11 q^{42} - 26 q^{43} + 5 q^{44} + 9 q^{45} + 14 q^{46} - 21 q^{47} + 9 q^{48} - 26 q^{49} - 3 q^{50} - 5 q^{51} - 5 q^{52} + 18 q^{53} - 3 q^{54} - 19 q^{56} - 12 q^{57} - 16 q^{58} - 24 q^{59} + 5 q^{60} - 4 q^{61} + 3 q^{62} - 5 q^{63} + 2 q^{64} - 9 q^{65} - 17 q^{66} - 20 q^{67} - 19 q^{68} - 21 q^{69} + 11 q^{70} - 13 q^{71} - 18 q^{72} + 15 q^{73} + 12 q^{74} + 9 q^{75} + 54 q^{76} - 28 q^{77} + 3 q^{78} - 15 q^{79} + 9 q^{80} + 9 q^{81} - 21 q^{82} - 5 q^{83} - 8 q^{84} - 5 q^{85} + 36 q^{86} - 15 q^{87} + 23 q^{88} + 31 q^{89} - 3 q^{90} + 5 q^{91} - 7 q^{92} - 9 q^{93} - 12 q^{95} - 9 q^{96} - 11 q^{97} - 23 q^{98}+O(q^{100}) \) 9 * q - 3 * q^2 + 9 * q^3 + 5 * q^4 + 9 * q^5 - 3 * q^6 - 5 * q^7 - 18 * q^8 + 9 * q^9 - 3 * q^10 + 5 * q^12 - 9 * q^13 + 11 * q^14 + 9 * q^15 + 9 * q^16 - 5 * q^17 - 3 * q^18 - 12 * q^19 + 5 * q^20 - 5 * q^21 - 17 * q^22 - 21 * q^23 - 18 * q^24 + 9 * q^25 + 3 * q^26 + 9 * q^27 - 8 * q^28 - 15 * q^29 - 3 * q^30 - 9 * q^31 - 9 * q^32 + 9 * q^34 - 5 * q^35 + 5 * q^36 - 13 * q^37 - 24 * q^38 - 9 * q^39 - 18 * q^40 - 11 * q^41 + 11 * q^42 - 26 * q^43 + 5 * q^44 + 9 * q^45 + 14 * q^46 - 21 * q^47 + 9 * q^48 - 26 * q^49 - 3 * q^50 - 5 * q^51 - 5 * q^52 + 18 * q^53 - 3 * q^54 - 19 * q^56 - 12 * q^57 - 16 * q^58 - 24 * q^59 + 5 * q^60 - 4 * q^61 + 3 * q^62 - 5 * q^63 + 2 * q^64 - 9 * q^65 - 17 * q^66 - 20 * q^67 - 19 * q^68 - 21 * q^69 + 11 * q^70 - 13 * q^71 - 18 * q^72 + 15 * q^73 + 12 * q^74 + 9 * q^75 + 54 * q^76 - 28 * q^77 + 3 * q^78 - 15 * q^79 + 9 * q^80 + 9 * q^81 - 21 * q^82 - 5 * q^83 - 8 * q^84 - 5 * q^85 + 36 * q^86 - 15 * q^87 + 23 * q^88 + 31 * q^89 - 3 * q^90 + 5 * q^91 - 7 * q^92 - 9 * q^93 - 12 * q^95 - 9 * q^96 - 11 * q^97 - 23 * q^98

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