LMFDB - Embedded newform 6045.2.a.t.1.8

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} + 22x^{6} + 14x^{5} - 52x^{4} - 5x^{3} + 41x^{2} - 4x - 5 $ x^9 - 3x^8 - 7x^7 + 22x^6 + 14x^5 - 52x^4 - 5x^3 + 41x^2 - 4x - 5
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			1.8
Root			$1.66264$ 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)

$f(q)$	$=$	$q+0.662643 q^{2} +1.00000 q^{3} -1.56090 q^{4} +1.00000 q^{5} +0.662643 q^{6} -4.22758 q^{7} -2.35961 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.662643 q^{2} +1.00000 q^{3} -1.56090 q^{4} +1.00000 q^{5} +0.662643 q^{6} -4.22758 q^{7} -2.35961 q^{8} +1.00000 q^{9} +0.662643 q^{10} +4.59002 q^{11} -1.56090 q^{12} +1.00000 q^{13} -2.80138 q^{14} +1.00000 q^{15} +1.55823 q^{16} -4.90512 q^{17} +0.662643 q^{18} +7.00552 q^{19} -1.56090 q^{20} -4.22758 q^{21} +3.04154 q^{22} -8.32362 q^{23} -2.35961 q^{24} +1.00000 q^{25} +0.662643 q^{26} +1.00000 q^{27} +6.59885 q^{28} -4.95501 q^{29} +0.662643 q^{30} +1.00000 q^{31} +5.75177 q^{32} +4.59002 q^{33} -3.25035 q^{34} -4.22758 q^{35} -1.56090 q^{36} +11.0544 q^{37} +4.64216 q^{38} +1.00000 q^{39} -2.35961 q^{40} -5.72418 q^{41} -2.80138 q^{42} -8.48327 q^{43} -7.16458 q^{44} +1.00000 q^{45} -5.51559 q^{46} +3.84272 q^{47} +1.55823 q^{48} +10.8724 q^{49} +0.662643 q^{50} -4.90512 q^{51} -1.56090 q^{52} +1.47534 q^{53} +0.662643 q^{54} +4.59002 q^{55} +9.97543 q^{56} +7.00552 q^{57} -3.28340 q^{58} -12.3669 q^{59} -1.56090 q^{60} -13.1529 q^{61} +0.662643 q^{62} -4.22758 q^{63} +0.694902 q^{64} +1.00000 q^{65} +3.04154 q^{66} +5.06870 q^{67} +7.65643 q^{68} -8.32362 q^{69} -2.80138 q^{70} +5.17385 q^{71} -2.35961 q^{72} +2.12802 q^{73} +7.32514 q^{74} +1.00000 q^{75} -10.9350 q^{76} -19.4047 q^{77} +0.662643 q^{78} +12.7161 q^{79} +1.55823 q^{80} +1.00000 q^{81} -3.79308 q^{82} -15.1608 q^{83} +6.59885 q^{84} -4.90512 q^{85} -5.62138 q^{86} -4.95501 q^{87} -10.8306 q^{88} -12.9317 q^{89} +0.662643 q^{90} -4.22758 q^{91} +12.9924 q^{92} +1.00000 q^{93} +2.54635 q^{94} +7.00552 q^{95} +5.75177 q^{96} -1.01702 q^{97} +7.20454 q^{98} +4.59002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9	\( 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} + 9 q^{13} - 9 q^{14} + 9 q^{15} + 30 q^{16} - 17 q^{17} - 6 q^{18} + 6 q^{19} + 8 q^{20} - 12 q^{21} + 15 q^{22} - 23 q^{23} - 21 q^{24} + 9 q^{25} - 6 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} - 6 q^{30} + 9 q^{31} - 38 q^{32} - 10 q^{33} + 15 q^{34} - 12 q^{35} + 8 q^{36} + 11 q^{37} - 16 q^{38} + 9 q^{39} - 21 q^{40} - 8 q^{41} - 9 q^{42} - 15 q^{43} - q^{44} + 9 q^{45} + 26 q^{46} - 33 q^{47} + 30 q^{48} + 15 q^{49} - 6 q^{50} - 17 q^{51} + 8 q^{52} - 38 q^{53} - 6 q^{54} - 10 q^{55} + 37 q^{56} + 6 q^{57} - 26 q^{58} - 25 q^{59} + 8 q^{60} - 10 q^{61} - 6 q^{62} - 12 q^{63} + 47 q^{64} + 9 q^{65} + 15 q^{66} - 19 q^{67} + 7 q^{68} - 23 q^{69} - 9 q^{70} - 43 q^{71} - 21 q^{72} + q^{73} + 4 q^{74} + 9 q^{75} - 26 q^{76} + 2 q^{77} - 6 q^{78} - 9 q^{79} + 30 q^{80} + 9 q^{81} + 15 q^{82} - 12 q^{83} + 2 q^{84} - 17 q^{85} - 30 q^{86} - 4 q^{87} + q^{88} - 5 q^{89} - 6 q^{90} - 12 q^{91} - 57 q^{92} + 9 q^{93} + 40 q^{94} + 6 q^{95} - 38 q^{96} - 4 q^{97} + 34 q^{98} - 10 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9 - 6 * q^10 - 10 * q^11 + 8 * q^12 + 9 * q^13 - 9 * q^14 + 9 * q^15 + 30 * q^16 - 17 * q^17 - 6 * q^18 + 6 * q^19 + 8 * q^20 - 12 * q^21 + 15 * q^22 - 23 * q^23 - 21 * q^24 + 9 * q^25 - 6 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 - 6 * q^30 + 9 * q^31 - 38 * q^32 - 10 * q^33 + 15 * q^34 - 12 * q^35 + 8 * q^36 + 11 * q^37 - 16 * q^38 + 9 * q^39 - 21 * q^40 - 8 * q^41 - 9 * q^42 - 15 * q^43 - q^44 + 9 * q^45 + 26 * q^46 - 33 * q^47 + 30 * q^48 + 15 * q^49 - 6 * q^50 - 17 * q^51 + 8 * q^52 - 38 * q^53 - 6 * q^54 - 10 * q^55 + 37 * q^56 + 6 * q^57 - 26 * q^58 - 25 * q^59 + 8 * q^60 - 10 * q^61 - 6 * q^62 - 12 * q^63 + 47 * q^64 + 9 * q^65 + 15 * q^66 - 19 * q^67 + 7 * q^68 - 23 * q^69 - 9 * q^70 - 43 * q^71 - 21 * q^72 + q^73 + 4 * q^74 + 9 * q^75 - 26 * q^76 + 2 * q^77 - 6 * q^78 - 9 * q^79 + 30 * q^80 + 9 * q^81 + 15 * q^82 - 12 * q^83 + 2 * q^84 - 17 * q^85 - 30 * q^86 - 4 * q^87 + q^88 - 5 * q^89 - 6 * q^90 - 12 * q^91 - 57 * q^92 + 9 * q^93 + 40 * q^94 + 6 * q^95 - 38 * q^96 - 4 * q^97 + 34 * q^98 - 10 * 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 $

$2$	0.662643	0.468559	0.234280	−	0.972169i	$-0.424727\pi$
$2$	0.662643	0.468559	0.234280	+	0.972169i	$0.424727\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.56090	−0.780452
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.662643	0.270523
$7$	−4.22758	−1.59788	−0.798938	−	0.601414i	$-0.794604\pi$
$7$	−4.22758	−1.59788	−0.798938	+	0.601414i	$0.794604\pi$
$8$	−2.35961	−0.834247
$9$	1.00000	0.333333
$10$	0.662643	0.209546
$11$	4.59002	1.38394	0.691971	−	0.721925i	$-0.256743\pi$
$11$	4.59002	1.38394	0.691971	+	0.721925i	$0.256743\pi$
$12$	−1.56090	−0.450594
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.80138	−0.748699
$15$	1.00000	0.258199
$16$	1.55823	0.389558
$17$	−4.90512	−1.18967	−0.594834	−	0.803849i	$-0.702782\pi$
$17$	−4.90512	−1.18967	−0.594834	+	0.803849i	$0.702782\pi$
$18$	0.662643	0.156186
$19$	7.00552	1.60718	0.803589	−	0.595185i	$-0.202921\pi$
$19$	7.00552	1.60718	0.803589	+	0.595185i	$0.202921\pi$
$20$	−1.56090	−0.349029
$21$	−4.22758	−0.922534
$22$	3.04154	0.648459
$23$	−8.32362	−1.73559	−0.867797	−	0.496918i	$-0.834465\pi$
$23$	−8.32362	−1.73559	−0.867797	+	0.496918i	$0.834465\pi$
$24$	−2.35961	−0.481653
$25$	1.00000	0.200000
$26$	0.662643	0.129955
$27$	1.00000	0.192450
$28$	6.59885	1.24707
$29$	−4.95501	−0.920123	−0.460061	−	0.887887i	$-0.652173\pi$
$29$	−4.95501	−0.920123	−0.460061	+	0.887887i	$0.652173\pi$
$30$	0.662643	0.120981
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	5.75177	1.01678
$33$	4.59002	0.799019
$34$	−3.25035	−0.557430
$35$	−4.22758	−0.714591
$36$	−1.56090	−0.260151
$37$	11.0544	1.81734	0.908668	−	0.417518i	$-0.137100\pi$
$37$	11.0544	1.81734	0.908668	+	0.417518i	$0.137100\pi$
$38$	4.64216	0.753058
$39$	1.00000	0.160128
$40$	−2.35961	−0.373087
$41$	−5.72418	−0.893966	−0.446983	−	0.894542i	$-0.647502\pi$
$41$	−5.72418	−0.893966	−0.446983	+	0.894542i	$0.647502\pi$
$42$	−2.80138	−0.432262
$43$	−8.48327	−1.29369	−0.646844	−	0.762623i	$-0.723911\pi$
$43$	−8.48327	−1.29369	−0.646844	+	0.762623i	$0.723911\pi$
$44$	−7.16458	−1.08010
$45$	1.00000	0.149071
$46$	−5.51559	−0.813229
$47$	3.84272	0.560518	0.280259	−	0.959924i	$-0.409580\pi$
$47$	3.84272	0.560518	0.280259	+	0.959924i	$0.409580\pi$
$48$	1.55823	0.224911
$49$	10.8724	1.55320
$50$	0.662643	0.0937118
$51$	−4.90512	−0.686855
$52$	−1.56090	−0.216459
$53$	1.47534	0.202653	0.101327	−	0.994853i	$-0.467691\pi$
$53$	1.47534	0.202653	0.101327	+	0.994853i	$0.467691\pi$
$54$	0.662643	0.0901743
$55$	4.59002	0.618918
$56$	9.97543	1.33302
$57$	7.00552	0.927904
$58$	−3.28340	−0.431132
$59$	−12.3669	−1.61004	−0.805020	−	0.593248i	$-0.797845\pi$
$59$	−12.3669	−1.61004	−0.805020	+	0.593248i	$0.797845\pi$
$60$	−1.56090	−0.201512
$61$	−13.1529	−1.68406	−0.842028	−	0.539435i	$-0.818638\pi$
$61$	−13.1529	−1.68406	−0.842028	+	0.539435i	$0.818638\pi$
$62$	0.662643	0.0841557
$63$	−4.22758	−0.532625
$64$	0.694902	0.0868628
$65$	1.00000	0.124035
$66$	3.04154	0.374388
$67$	5.06870	0.619240	0.309620	−	0.950860i	$-0.399798\pi$
$67$	5.06870	0.619240	0.309620	+	0.950860i	$0.399798\pi$
$68$	7.65643	0.928479
$69$	−8.32362	−1.00205
$70$	−2.80138	−0.334828
$71$	5.17385	0.614023	0.307012	−	0.951706i	$-0.400671\pi$
$71$	5.17385	0.614023	0.307012	+	0.951706i	$0.400671\pi$
$72$	−2.35961	−0.278082
$73$	2.12802	0.249065	0.124533	−	0.992216i	$-0.460257\pi$
$73$	2.12802	0.249065	0.124533	+	0.992216i	$0.460257\pi$
$74$	7.32514	0.851530
$75$	1.00000	0.115470
$76$	−10.9350	−1.25433
$77$	−19.4047	−2.21137
$78$	0.662643	0.0750295
$79$	12.7161	1.43068	0.715338	−	0.698779i	$-0.246273\pi$
$79$	12.7161	1.43068	0.715338	+	0.698779i	$0.246273\pi$
$80$	1.55823	0.174216
$81$	1.00000	0.111111
$82$	−3.79308	−0.418876
$83$	−15.1608	−1.66411	−0.832055	−	0.554693i	$-0.812836\pi$
$83$	−15.1608	−1.66411	−0.832055	+	0.554693i	$0.812836\pi$
$84$	6.59885	0.719993
$85$	−4.90512	−0.532035
$86$	−5.62138	−0.606169
$87$	−4.95501	−0.531233
$88$	−10.8306	−1.15455
$89$	−12.9317	−1.37075	−0.685376	−	0.728189i	$-0.740362\pi$
$89$	−12.9317	−1.37075	−0.685376	+	0.728189i	$0.740362\pi$
$90$	0.662643	0.0698487
$91$	−4.22758	−0.443171
$92$	12.9924	1.35455
$93$	1.00000	0.103695
$94$	2.54635	0.262636
$95$	7.00552	0.718751
$96$	5.75177	0.587037
$97$	−1.01702	−0.103263	−0.0516316	−	0.998666i	$-0.516442\pi$
$97$	−1.01702	−0.103263	−0.0516316	+	0.998666i	$0.516442\pi$
$98$	7.20454	0.727768
$99$	4.59002	0.461314
$100$	−1.56090	−0.156090
$101$	13.7092	1.36411	0.682057	−	0.731299i	$-0.261085\pi$
$101$	13.7092	1.36411	0.682057	+	0.731299i	$0.261085\pi$
$102$	−3.25035	−0.321832
$103$	−19.8806	−1.95890	−0.979448	−	0.201696i	$-0.935355\pi$
$103$	−19.8806	−1.95890	−0.979448	+	0.201696i	$0.935355\pi$
$104$	−2.35961	−0.231379
$105$	−4.22758	−0.412570
$106$	0.977623	0.0949551
$107$	−1.21285	−0.117251	−0.0586253	−	0.998280i	$-0.518672\pi$
$107$	−1.21285	−0.117251	−0.0586253	+	0.998280i	$0.518672\pi$
$108$	−1.56090	−0.150198
$109$	1.23225	0.118028	0.0590141	−	0.998257i	$-0.481204\pi$
$109$	1.23225	0.118028	0.0590141	+	0.998257i	$0.481204\pi$
$110$	3.04154	0.290000
$111$	11.0544	1.04924
$112$	−6.58755	−0.622465
$113$	−14.1485	−1.33098	−0.665488	−	0.746409i	$-0.731777\pi$
$113$	−14.1485	−1.33098	−0.665488	+	0.746409i	$0.731777\pi$
$114$	4.64216	0.434778
$115$	−8.32362	−0.776182
$116$	7.73430	0.718112
$117$	1.00000	0.0924500
$118$	−8.19487	−0.754399
$119$	20.7368	1.90094
$120$	−2.35961	−0.215402
$121$	10.0683	0.915296
$122$	−8.71567	−0.789079
$123$	−5.72418	−0.516132
$124$	−1.56090	−0.140173
$125$	1.00000	0.0894427
$126$	−2.80138	−0.249566
$127$	20.7197	1.83858	0.919288	−	0.393585i	$-0.128765\pi$
$127$	20.7197	1.83858	0.919288	+	0.393585i	$0.128765\pi$
$128$	−11.0431	−0.976078
$129$	−8.48327	−0.746911
$130$	0.662643	0.0581176
$131$	−16.8743	−1.47432	−0.737159	−	0.675719i	$-0.763833\pi$
$131$	−16.8743	−1.47432	−0.737159	+	0.675719i	$0.763833\pi$
$132$	−7.16458	−0.623597
$133$	−29.6164	−2.56807
$134$	3.35874	0.290151
$135$	1.00000	0.0860663
$136$	11.5742	0.992477
$137$	6.54617	0.559277	0.279639	−	0.960105i	$-0.409785\pi$
$137$	6.54617	0.559277	0.279639	+	0.960105i	$0.409785\pi$
$138$	−5.51559	−0.469518
$139$	−15.7282	−1.33405	−0.667024	−	0.745036i	$-0.732432\pi$
$139$	−15.7282	−1.33405	−0.667024	+	0.745036i	$0.732432\pi$
$140$	6.59885	0.557705
$141$	3.84272	0.323615
$142$	3.42841	0.287706
$143$	4.59002	0.383837
$144$	1.55823	0.129853
$145$	−4.95501	−0.411491
$146$	1.41011	0.116702
$147$	10.8724	0.896743
$148$	−17.2549	−1.41834
$149$	16.3697	1.34106	0.670529	−	0.741883i	$-0.266067\pi$
$149$	16.3697	1.34106	0.670529	+	0.741883i	$0.266067\pi$
$150$	0.662643	0.0541046
$151$	−1.32759	−0.108037	−0.0540187	−	0.998540i	$-0.517203\pi$
$151$	−1.32759	−0.108037	−0.0540187	+	0.998540i	$0.517203\pi$
$152$	−16.5303	−1.34078
$153$	−4.90512	−0.396556
$154$	−12.8584	−1.03616
$155$	1.00000	0.0803219
$156$	−1.56090	−0.124972
$157$	−17.6560	−1.40910	−0.704552	−	0.709653i	$-0.748852\pi$
$157$	−17.6560	−1.40910	−0.704552	+	0.709653i	$0.748852\pi$
$158$	8.42625	0.670356
$159$	1.47534	0.117002
$160$	5.75177	0.454717
$161$	35.1888	2.77326
$162$	0.662643	0.0520621
$163$	−4.28386	−0.335538	−0.167769	−	0.985826i	$-0.553656\pi$
$163$	−4.28386	−0.335538	−0.167769	+	0.985826i	$0.553656\pi$
$164$	8.93489	0.697698
$165$	4.59002	0.357332
$166$	−10.0462	−0.779734
$167$	−22.8974	−1.77186	−0.885928	−	0.463822i	$-0.846478\pi$
$167$	−22.8974	−1.77186	−0.885928	+	0.463822i	$0.846478\pi$
$168$	9.97543	0.769621
$169$	1.00000	0.0769231
$170$	−3.25035	−0.249290
$171$	7.00552	0.535726
$172$	13.2416	1.00966
$173$	−11.6003	−0.881952	−0.440976	−	0.897519i	$-0.645368\pi$
$173$	−11.6003	−0.881952	−0.440976	+	0.897519i	$0.645368\pi$
$174$	−3.28340	−0.248914
$175$	−4.22758	−0.319575
$176$	7.15231	0.539126
$177$	−12.3669	−0.929557
$178$	−8.56907	−0.642279
$179$	−4.70277	−0.351502	−0.175751	−	0.984435i	$-0.556235\pi$
$179$	−4.70277	−0.351502	−0.175751	+	0.984435i	$0.556235\pi$
$180$	−1.56090	−0.116343
$181$	−16.7653	−1.24615	−0.623077	−	0.782160i	$-0.714118\pi$
$181$	−16.7653	−1.24615	−0.623077	+	0.782160i	$0.714118\pi$
$182$	−2.80138	−0.207652
$183$	−13.1529	−0.972290
$184$	19.6405	1.44792
$185$	11.0544	0.812738
$186$	0.662643	0.0485873
$187$	−22.5146	−1.64643
$188$	−5.99812	−0.437458
$189$	−4.22758	−0.307511
$190$	4.64216	0.336778
$191$	−23.2952	−1.68558	−0.842790	−	0.538242i	$-0.819089\pi$
$191$	−23.2952	−1.68558	−0.842790	+	0.538242i	$0.819089\pi$
$192$	0.694902	0.0501502
$193$	−6.38654	−0.459713	−0.229856	−	0.973225i	$-0.573826\pi$
$193$	−6.38654	−0.459713	−0.229856	+	0.973225i	$0.573826\pi$
$194$	−0.673924	−0.0483849
$195$	1.00000	0.0716115
$196$	−16.9708	−1.21220
$197$	13.9790	0.995965	0.497983	−	0.867187i	$-0.334074\pi$
$197$	13.9790	0.995965	0.497983	+	0.867187i	$0.334074\pi$
$198$	3.04154	0.216153
$199$	−11.5254	−0.817012	−0.408506	−	0.912756i	$-0.633950\pi$
$199$	−11.5254	−0.817012	−0.408506	+	0.912756i	$0.633950\pi$
$200$	−2.35961	−0.166849
$201$	5.06870	0.357518
$202$	9.08429	0.639168
$203$	20.9477	1.47024
$204$	7.65643	0.536057
$205$	−5.72418	−0.399794
$206$	−13.1738	−0.917859
$207$	−8.32362	−0.578532
$208$	1.55823	0.108044
$209$	32.1555	2.22424
$210$	−2.80138	−0.193313
$211$	0.00839042	0.000577621 0	0.000288810	−	1.00000i	$-0.499908\pi$
$211$	0.00839042	0.000577621 0	0.000288810		1.00000i	$0.499908\pi$
$212$	−2.30286	−0.158161
$213$	5.17385	0.354506
$214$	−0.803686	−0.0549388
$215$	−8.48327	−0.578555
$216$	−2.35961	−0.160551
$217$	−4.22758	−0.286987
$218$	0.816542	0.0553032
$219$	2.12802	0.143798
$220$	−7.16458	−0.483036
$221$	−4.90512	−0.329954
$222$	7.32514	0.491631
$223$	−12.7020	−0.850586	−0.425293	−	0.905056i	$-0.639829\pi$
$223$	−12.7020	−0.850586	−0.425293	+	0.905056i	$0.639829\pi$
$224$	−24.3161	−1.62468
$225$	1.00000	0.0666667
$226$	−9.37538	−0.623641
$227$	20.4588	1.35790	0.678950	−	0.734185i	$-0.262435\pi$
$227$	20.4588	1.35790	0.678950	+	0.734185i	$0.262435\pi$
$228$	−10.9350	−0.724185
$229$	3.92803	0.259571	0.129786	−	0.991542i	$-0.458571\pi$
$229$	3.92803	0.259571	0.129786	+	0.991542i	$0.458571\pi$
$230$	−5.51559	−0.363687
$231$	−19.4047	−1.27673
$232$	11.6919	0.767610
$233$	−14.8976	−0.975977	−0.487988	−	0.872850i	$-0.662269\pi$
$233$	−14.8976	−0.975977	−0.487988	+	0.872850i	$0.662269\pi$
$234$	0.662643	0.0433183
$235$	3.84272	0.250671
$236$	19.3036	1.25656
$237$	12.7161	0.826001
$238$	13.7411	0.890703
$239$	19.7470	1.27732	0.638662	−	0.769487i	$-0.279488\pi$
$239$	19.7470	1.27732	0.638662	+	0.769487i	$0.279488\pi$
$240$	1.55823	0.100583
$241$	19.4344	1.25188	0.625940	−	0.779871i	$-0.284715\pi$
$241$	19.4344	1.25188	0.625940	+	0.779871i	$0.284715\pi$
$242$	6.67166	0.428871
$243$	1.00000	0.0641500
$244$	20.5304	1.31432
$245$	10.8724	0.694614
$246$	−3.79308	−0.241838
$247$	7.00552	0.445751
$248$	−2.35961	−0.149835
$249$	−15.1608	−0.960775
$250$	0.662643	0.0419092
$251$	−17.3755	−1.09673	−0.548365	−	0.836239i	$-0.684750\pi$
$251$	−17.3755	−1.09673	−0.548365	+	0.836239i	$0.684750\pi$
$252$	6.59885	0.415688
$253$	−38.2056	−2.40196
$254$	13.7298	0.861482
$255$	−4.90512	−0.307171
$256$	−8.70741	−0.544213
$257$	−17.2250	−1.07447	−0.537234	−	0.843433i	$-0.680531\pi$
$257$	−17.2250	−1.07447	−0.537234	+	0.843433i	$0.680531\pi$
$258$	−5.62138	−0.349972
$259$	−46.7335	−2.90388
$260$	−1.56090	−0.0968032
$261$	−4.95501	−0.306708
$262$	−11.1817	−0.690805
$263$	10.0046	0.616912	0.308456	−	0.951239i	$-0.400188\pi$
$263$	10.0046	0.616912	0.308456	+	0.951239i	$0.400188\pi$
$264$	−10.8306	−0.666580
$265$	1.47534	0.0906294
$266$	−19.6251	−1.20329
$267$	−12.9317	−0.791404
$268$	−7.91175	−0.483287
$269$	−5.54820	−0.338280	−0.169140	−	0.985592i	$-0.554099\pi$
$269$	−5.54820	−0.338280	−0.169140	+	0.985592i	$0.554099\pi$
$270$	0.662643	0.0403272
$271$	12.9364	0.785831	0.392916	−	0.919575i	$-0.371466\pi$
$271$	12.9364	0.785831	0.392916	+	0.919575i	$0.371466\pi$
$272$	−7.64332	−0.463444
$273$	−4.22758	−0.255865
$274$	4.33778	0.262055
$275$	4.59002	0.276788
$276$	12.9924	0.782049
$277$	−28.2323	−1.69631	−0.848157	−	0.529746i	$-0.822287\pi$
$277$	−28.2323	−1.69631	−0.848157	+	0.529746i	$0.822287\pi$
$278$	−10.4222	−0.625081
$279$	1.00000	0.0598684
$280$	9.97543	0.596146
$281$	−32.1093	−1.91548	−0.957741	−	0.287633i	$-0.907132\pi$
$281$	−32.1093	−1.91548	−0.957741	+	0.287633i	$0.907132\pi$
$282$	2.54635	0.151633
$283$	−14.6117	−0.868578	−0.434289	−	0.900774i	$-0.643000\pi$
$283$	−14.6117	−0.868578	−0.434289	+	0.900774i	$0.643000\pi$
$284$	−8.07589	−0.479216
$285$	7.00552	0.414971
$286$	3.04154	0.179850
$287$	24.1994	1.42845
$288$	5.75177	0.338926
$289$	7.06024	0.415308
$290$	−3.28340	−0.192808
$291$	−1.01702	−0.0596191
$292$	−3.32163	−0.194384
$293$	−19.5729	−1.14346	−0.571730	−	0.820442i	$-0.693728\pi$
$293$	−19.5729	−1.14346	−0.571730	+	0.820442i	$0.693728\pi$
$294$	7.20454	0.420177
$295$	−12.3669	−0.720031
$296$	−26.0841	−1.51611
$297$	4.59002	0.266340
$298$	10.8473	0.628365
$299$	−8.32362	−0.481367
$300$	−1.56090	−0.0901189
$301$	35.8637	2.06715
$302$	−0.879715	−0.0506219
$303$	13.7092	0.787572
$304$	10.9162	0.626089
$305$	−13.1529	−0.753132
$306$	−3.25035	−0.185810
$307$	−8.70365	−0.496744	−0.248372	−	0.968665i	$-0.579896\pi$
$307$	−8.70365	−0.496744	−0.248372	+	0.968665i	$0.579896\pi$
$308$	30.2888	1.72587
$309$	−19.8806	−1.13097
$310$	0.662643	0.0376356
$311$	11.9091	0.675304	0.337652	−	0.941271i	$-0.390367\pi$
$311$	11.9091	0.675304	0.337652	+	0.941271i	$0.390367\pi$
$312$	−2.35961	−0.133586
$313$	−11.4549	−0.647472	−0.323736	−	0.946147i	$-0.604939\pi$
$313$	−11.4549	−0.647472	−0.323736	+	0.946147i	$0.604939\pi$
$314$	−11.6996	−0.660248
$315$	−4.22758	−0.238197
$316$	−19.8487	−1.11657
$317$	−10.8349	−0.608547	−0.304273	−	0.952585i	$-0.598414\pi$
$317$	−10.8349	−0.608547	−0.304273	+	0.952585i	$0.598414\pi$
$318$	0.977623	0.0548224
$319$	−22.7436	−1.27340
$320$	0.694902	0.0388462
$321$	−1.21285	−0.0676946
$322$	23.3176	1.29944
$323$	−34.3630	−1.91201
$324$	−1.56090	−0.0867169
$325$	1.00000	0.0554700
$326$	−2.83867	−0.157219
$327$	1.23225	0.0681437
$328$	13.5068	0.745789
$329$	−16.2454	−0.895638
$330$	3.04154	0.167431
$331$	17.1735	0.943939	0.471970	−	0.881615i	$-0.343543\pi$
$331$	17.1735	0.943939	0.471970	+	0.881615i	$0.343543\pi$
$332$	23.6645	1.29876
$333$	11.0544	0.605779
$334$	−15.1728	−0.830220
$335$	5.06870	0.276933
$336$	−6.58755	−0.359380
$337$	19.2930	1.05096	0.525479	−	0.850806i	$-0.323886\pi$
$337$	19.2930	1.05096	0.525479	+	0.850806i	$0.323886\pi$
$338$	0.662643	0.0360430
$339$	−14.1485	−0.768439
$340$	7.65643	0.415228
$341$	4.59002	0.248563
$342$	4.64216	0.251019
$343$	−16.3710	−0.883953
$344$	20.0172	1.07926
$345$	−8.32362	−0.448129
$346$	−7.68684	−0.413247
$347$	7.23114	0.388188	0.194094	−	0.980983i	$-0.437823\pi$
$347$	7.23114	0.388188	0.194094	+	0.980983i	$0.437823\pi$
$348$	7.73430	0.414602
$349$	3.29761	0.176517	0.0882585	−	0.996098i	$-0.471870\pi$
$349$	3.29761	0.176517	0.0882585	+	0.996098i	$0.471870\pi$
$350$	−2.80138	−0.149740
$351$	1.00000	0.0533761
$352$	26.4007	1.40716
$353$	10.5967	0.564004	0.282002	−	0.959414i	$-0.409001\pi$
$353$	10.5967	0.564004	0.282002	+	0.959414i	$0.409001\pi$
$354$	−8.19487	−0.435552
$355$	5.17385	0.274599
$356$	20.1851	1.06981
$357$	20.7368	1.09751
$358$	−3.11626	−0.164699
$359$	12.9334	0.682598	0.341299	−	0.939955i	$-0.389133\pi$
$359$	12.9334	0.682598	0.341299	+	0.939955i	$0.389133\pi$
$360$	−2.35961	−0.124362
$361$	30.0773	1.58302
$362$	−11.1094	−0.583897
$363$	10.0683	0.528447
$364$	6.59885	0.345874
$365$	2.12802	0.111385
$366$	−8.71567	−0.455575
$367$	−13.2797	−0.693192	−0.346596	−	0.938014i	$-0.612663\pi$
$367$	−13.2797	−0.693192	−0.346596	+	0.938014i	$0.612663\pi$
$368$	−12.9701	−0.676115
$369$	−5.72418	−0.297989
$370$	7.32514	0.380816
$371$	−6.23712	−0.323815
$372$	−1.56090	−0.0809291
$373$	31.8510	1.64918	0.824591	−	0.565729i	$-0.191405\pi$
$373$	31.8510	1.64918	0.824591	+	0.565729i	$0.191405\pi$
$374$	−14.9191	−0.771450
$375$	1.00000	0.0516398
$376$	−9.06731	−0.467611
$377$	−4.95501	−0.255196
$378$	−2.80138	−0.144087
$379$	7.24939	0.372376	0.186188	−	0.982514i	$-0.440387\pi$
$379$	7.24939	0.372376	0.186188	+	0.982514i	$0.440387\pi$
$380$	−10.9350	−0.560951
$381$	20.7197	1.06150
$382$	−15.4364	−0.789794
$383$	−1.55026	−0.0792147	−0.0396073	−	0.999215i	$-0.512611\pi$
$383$	−1.55026	−0.0792147	−0.0396073	+	0.999215i	$0.512611\pi$
$384$	−11.0431	−0.563539
$385$	−19.4047	−0.988953
$386$	−4.23199	−0.215403
$387$	−8.48327	−0.431229
$388$	1.58748	0.0805920
$389$	−14.3774	−0.728963	−0.364482	−	0.931211i	$-0.618754\pi$
$389$	−14.3774	−0.728963	−0.364482	+	0.931211i	$0.618754\pi$
$390$	0.662643	0.0335542
$391$	40.8284	2.06478
$392$	−25.6547	−1.29576
$393$	−16.8743	−0.851198
$394$	9.26311	0.466669
$395$	12.7161	0.639818
$396$	−7.16458	−0.360034
$397$	−8.33072	−0.418107	−0.209053	−	0.977904i	$-0.567038\pi$
$397$	−8.33072	−0.418107	−0.209053	+	0.977904i	$0.567038\pi$
$398$	−7.63720	−0.382818
$399$	−29.6164	−1.48267
$400$	1.55823	0.0779116
$401$	−13.1650	−0.657430	−0.328715	−	0.944429i	$-0.606615\pi$
$401$	−13.1650	−0.657430	−0.328715	+	0.944429i	$0.606615\pi$
$402$	3.35874	0.167519
$403$	1.00000	0.0498135
$404$	−21.3987	−1.06463
$405$	1.00000	0.0496904
$406$	13.8809	0.688895
$407$	50.7400	2.51509
$408$	11.5742	0.573007
$409$	6.71778	0.332173	0.166086	−	0.986111i	$-0.446887\pi$
$409$	6.71778	0.332173	0.166086	+	0.986111i	$0.446887\pi$
$410$	−3.79308	−0.187327
$411$	6.54617	0.322899
$412$	31.0318	1.52883
$413$	52.2823	2.57264
$414$	−5.51559	−0.271076
$415$	−15.1608	−0.744213
$416$	5.75177	0.282004
$417$	−15.7282	−0.770213
$418$	21.3076	1.04219
$419$	33.7905	1.65077	0.825387	−	0.564568i	$-0.190957\pi$
$419$	33.7905	1.65077	0.825387	+	0.564568i	$0.190957\pi$
$420$	6.59885	0.321991
$421$	38.0946	1.85662	0.928308	−	0.371812i	$-0.121263\pi$
$421$	38.0946	1.85662	0.928308	+	0.371812i	$0.121263\pi$
$422$	0.00555985	0.000270649 0
$423$	3.84272	0.186839
$424$	−3.48122	−0.169063
$425$	−4.90512	−0.237933
$426$	3.42841	0.166107
$427$	55.6049	2.69091
$428$	1.89314	0.0915085
$429$	4.59002	0.221608
$430$	−5.62138	−0.271087
$431$	7.41991	0.357404	0.178702	−	0.983903i	$-0.442810\pi$
$431$	7.41991	0.357404	0.178702	+	0.983903i	$0.442810\pi$
$432$	1.55823	0.0749705
$433$	9.33436	0.448581	0.224290	−	0.974522i	$-0.427994\pi$
$433$	9.33436	0.448581	0.224290	+	0.974522i	$0.427994\pi$
$434$	−2.80138	−0.134470
$435$	−4.95501	−0.237575
$436$	−1.92343	−0.0921154
$437$	−58.3113	−2.78941
$438$	1.41011	0.0673779
$439$	−0.383962	−0.0183255	−0.00916276	−	0.999958i	$-0.502917\pi$
$439$	−0.383962	−0.0183255	−0.00916276	+	0.999958i	$0.502917\pi$
$440$	−10.8306	−0.516331
$441$	10.8724	0.517735
$442$	−3.25035	−0.154603
$443$	−3.78627	−0.179891	−0.0899457	−	0.995947i	$-0.528669\pi$
$443$	−3.78627	−0.179891	−0.0899457	+	0.995947i	$0.528669\pi$
$444$	−17.2549	−0.818882
$445$	−12.9317	−0.613019
$446$	−8.41686	−0.398550
$447$	16.3697	0.774260
$448$	−2.93776	−0.138796
$449$	−1.48090	−0.0698878	−0.0349439	−	0.999389i	$-0.511125\pi$
$449$	−1.48090	−0.0698878	−0.0349439	+	0.999389i	$0.511125\pi$
$450$	0.662643	0.0312373
$451$	−26.2741	−1.23720
$452$	22.0844	1.03876
$453$	−1.32759	−0.0623754
$454$	13.5569	0.636256
$455$	−4.22758	−0.198192
$456$	−16.5303	−0.774102
$457$	2.53866	0.118754	0.0593768	−	0.998236i	$-0.481089\pi$
$457$	2.53866	0.118754	0.0593768	+	0.998236i	$0.481089\pi$
$458$	2.60288	0.121625
$459$	−4.90512	−0.228952
$460$	12.9924	0.605773
$461$	−10.1976	−0.474948	−0.237474	−	0.971394i	$-0.576319\pi$
$461$	−10.1976	−0.474948	−0.237474	+	0.971394i	$0.576319\pi$
$462$	−12.8584	−0.598225
$463$	33.3096	1.54803	0.774013	−	0.633169i	$-0.218246\pi$
$463$	33.3096	1.54803	0.774013	+	0.633169i	$0.218246\pi$
$464$	−7.72106	−0.358441
$465$	1.00000	0.0463739
$466$	−9.87181	−0.457303
$467$	−0.738595	−0.0341781	−0.0170891	−	0.999854i	$-0.505440\pi$
$467$	−0.738595	−0.0341781	−0.0170891	+	0.999854i	$0.505440\pi$
$468$	−1.56090	−0.0721528
$469$	−21.4283	−0.989468
$470$	2.54635	0.117454
$471$	−17.6560	−0.813546
$472$	29.1811	1.34317
$473$	−38.9384	−1.79039
$474$	8.42625	0.387030
$475$	7.00552	0.321435
$476$	−32.3682	−1.48359
$477$	1.47534	0.0675511
$478$	13.0852	0.598502
$479$	19.4480	0.888602	0.444301	−	0.895877i	$-0.353452\pi$
$479$	19.4480	0.888602	0.444301	+	0.895877i	$0.353452\pi$
$480$	5.75177	0.262531
$481$	11.0544	0.504039
$482$	12.8781	0.586580
$483$	35.1888	1.60114
$484$	−15.7156	−0.714345
$485$	−1.01702	−0.0461807
$486$	0.662643	0.0300581
$487$	20.8170	0.943309	0.471655	−	0.881783i	$-0.343657\pi$
$487$	20.8170	0.943309	0.471655	+	0.881783i	$0.343657\pi$
$488$	31.0357	1.40492
$489$	−4.28386	−0.193723
$490$	7.20454	0.325468
$491$	33.3790	1.50637	0.753187	−	0.657807i	$-0.228516\pi$
$491$	33.3790	1.50637	0.753187	+	0.657807i	$0.228516\pi$
$492$	8.93489	0.402816
$493$	24.3050	1.09464
$494$	4.64216	0.208861
$495$	4.59002	0.206306
$496$	1.55823	0.0699667
$497$	−21.8729	−0.981132
$498$	−10.0462	−0.450180
$499$	−12.9614	−0.580233	−0.290117	−	0.956991i	$-0.593694\pi$
$499$	−12.9614	−0.580233	−0.290117	+	0.956991i	$0.593694\pi$
$500$	−1.56090	−0.0698058
$501$	−22.8974	−1.02298
$502$	−11.5137	−0.513883
$503$	9.04377	0.403242	0.201621	−	0.979464i	$-0.435379\pi$
$503$	9.04377	0.403242	0.201621	+	0.979464i	$0.435379\pi$
$504$	9.97543	0.444341
$505$	13.7092	0.610051
$506$	−25.3166	−1.12546
$507$	1.00000	0.0444116
$508$	−32.3415	−1.43492
$509$	17.2478	0.764493	0.382247	−	0.924060i	$-0.375150\pi$
$509$	17.2478	0.764493	0.382247	+	0.924060i	$0.375150\pi$
$510$	−3.25035	−0.143928
$511$	−8.99636	−0.397975
$512$	16.3162	0.721082
$513$	7.00552	0.309301
$514$	−11.4141	−0.503452
$515$	−19.8806	−0.876045
$516$	13.2416	0.582928
$517$	17.6382	0.775725
$518$	−30.9676	−1.36064
$519$	−11.6003	−0.509196
$520$	−2.35961	−0.103476
$521$	17.0113	0.745276	0.372638	−	0.927977i	$-0.378453\pi$
$521$	17.0113	0.745276	0.372638	+	0.927977i	$0.378453\pi$
$522$	−3.28340	−0.143711
$523$	2.85221	0.124719	0.0623593	−	0.998054i	$-0.480138\pi$
$523$	2.85221	0.124719	0.0623593	+	0.998054i	$0.480138\pi$
$524$	26.3392	1.15063
$525$	−4.22758	−0.184507
$526$	6.62949	0.289060
$527$	−4.90512	−0.213671
$528$	7.15231	0.311264
$529$	46.2827	2.01229
$530$	0.977623	0.0424652
$531$	−12.3669	−0.536680
$532$	46.2284	2.00425
$533$	−5.72418	−0.247942
$534$	−8.56907	−0.370820
$535$	−1.21285	−0.0524360
$536$	−11.9601	−0.516599
$537$	−4.70277	−0.202940
$538$	−3.67647	−0.158504
$539$	49.9047	2.14955
$540$	−1.56090	−0.0671706
$541$	17.1271	0.736350	0.368175	−	0.929757i	$-0.379983\pi$
$541$	17.1271	0.736350	0.368175	+	0.929757i	$0.379983\pi$
$542$	8.57222	0.368209
$543$	−16.7653	−0.719468
$544$	−28.2131	−1.20963
$545$	1.23225	0.0527838
$546$	−2.80138	−0.119888
$547$	−13.7340	−0.587225	−0.293613	−	0.955924i	$-0.594858\pi$
$547$	−13.7340	−0.587225	−0.293613	+	0.955924i	$0.594858\pi$
$548$	−10.2180	−0.436489
$549$	−13.1529	−0.561352
$550$	3.04154	0.129692
$551$	−34.7125	−1.47880
$552$	19.6405	0.835954
$553$	−53.7584	−2.28604
$554$	−18.7079	−0.794823
$555$	11.0544	0.469234
$556$	24.5502	1.04116
$557$	−10.0194	−0.424535	−0.212267	−	0.977212i	$-0.568085\pi$
$557$	−10.0194	−0.424535	−0.212267	+	0.977212i	$0.568085\pi$
$558$	0.662643	0.0280519
$559$	−8.48327	−0.358804
$560$	−6.58755	−0.278375
$561$	−22.5146	−0.950567
$562$	−21.2770	−0.897516
$563$	1.06191	0.0447541	0.0223771	−	0.999750i	$-0.492877\pi$
$563$	1.06191	0.0447541	0.0223771	+	0.999750i	$0.492877\pi$
$564$	−5.99812	−0.252566
$565$	−14.1485	−0.595231
$566$	−9.68237	−0.406980
$567$	−4.22758	−0.177542
$568$	−12.2083	−0.512247
$569$	−16.5539	−0.693975	−0.346988	−	0.937870i	$-0.612795\pi$
$569$	−16.5539	−0.693975	−0.346988	+	0.937870i	$0.612795\pi$
$570$	4.64216	0.194439
$571$	−28.3466	−1.18627	−0.593135	−	0.805103i	$-0.702110\pi$
$571$	−28.3466	−1.18627	−0.593135	+	0.805103i	$0.702110\pi$
$572$	−7.16458	−0.299566
$573$	−23.2952	−0.973170
$574$	16.0356	0.669312
$575$	−8.32362	−0.347119
$576$	0.694902	0.0289543
$577$	−21.4687	−0.893752	−0.446876	−	0.894596i	$-0.647464\pi$
$577$	−21.4687	−0.893752	−0.446876	+	0.894596i	$0.647464\pi$
$578$	4.67842	0.194597
$579$	−6.38654	−0.265415
$580$	7.73430	0.321149
$581$	64.0934	2.65904
$582$	−0.673924	−0.0279351
$583$	6.77183	0.280461
$584$	−5.02128	−0.207782
$585$	1.00000	0.0413449
$586$	−12.9698	−0.535779
$587$	−1.75440	−0.0724118	−0.0362059	−	0.999344i	$-0.511527\pi$
$587$	−1.75440	−0.0724118	−0.0362059	+	0.999344i	$0.511527\pi$
$588$	−16.9708	−0.699865
$589$	7.00552	0.288658
$590$	−8.19487	−0.337377
$591$	13.9790	0.575021
$592$	17.2254	0.707958
$593$	−4.88329	−0.200533	−0.100266	−	0.994961i	$-0.531969\pi$
$593$	−4.88329	−0.200533	−0.100266	+	0.994961i	$0.531969\pi$
$594$	3.04154	0.124796
$595$	20.7368	0.850126
$596$	−25.5515	−1.04663
$597$	−11.5254	−0.471702
$598$	−5.51559	−0.225549
$599$	−25.9911	−1.06197	−0.530983	−	0.847382i	$-0.678177\pi$
$599$	−25.9911	−1.06197	−0.530983	+	0.847382i	$0.678177\pi$
$600$	−2.35961	−0.0963306
$601$	39.8697	1.62632	0.813159	−	0.582041i	$-0.197746\pi$
$601$	39.8697	1.62632	0.813159	+	0.582041i	$0.197746\pi$
$602$	23.7648	0.968582
$603$	5.06870	0.206413
$604$	2.07223	0.0843180
$605$	10.0683	0.409333
$606$	9.08429	0.369024
$607$	4.85029	0.196867	0.0984335	−	0.995144i	$-0.468617\pi$
$607$	4.85029	0.196867	0.0984335	+	0.995144i	$0.468617\pi$
$608$	40.2941	1.63414
$609$	20.9477	0.848844
$610$	−8.71567	−0.352887
$611$	3.84272	0.155460
$612$	7.65643	0.309493
$613$	24.6186	0.994336	0.497168	−	0.867654i	$-0.334373\pi$
$613$	24.6186	0.994336	0.497168	+	0.867654i	$0.334373\pi$
$614$	−5.76741	−0.232754
$615$	−5.72418	−0.230821
$616$	45.7874	1.84483
$617$	−16.9849	−0.683787	−0.341893	−	0.939739i	$-0.611068\pi$
$617$	−16.9849	−0.683787	−0.341893	+	0.939739i	$0.611068\pi$
$618$	−13.1738	−0.529926
$619$	34.3300	1.37984	0.689920	−	0.723886i	$-0.257646\pi$
$619$	34.3300	1.37984	0.689920	+	0.723886i	$0.257646\pi$
$620$	−1.56090	−0.0626874
$621$	−8.32362	−0.334015
$622$	7.89149	0.316420
$623$	54.6696	2.19029
$624$	1.55823	0.0623792
$625$	1.00000	0.0400000
$626$	−7.59054	−0.303379
$627$	32.1555	1.28417
$628$	27.5593	1.09974
$629$	−54.2233	−2.16203
$630$	−2.80138	−0.111609
$631$	−32.3409	−1.28747	−0.643736	−	0.765247i	$-0.722617\pi$
$631$	−32.3409	−1.28747	−0.643736	+	0.765247i	$0.722617\pi$
$632$	−30.0051	−1.19354
$633$	0.00839042	0.000333489 0
$634$	−7.17965	−0.285140
$635$	20.7197	0.822236
$636$	−2.30286	−0.0913145
$637$	10.8724	0.430782
$638$	−15.0709	−0.596662
$639$	5.17385	0.204674
$640$	−11.0431	−0.436515
$641$	45.4947	1.79693	0.898466	−	0.439043i	$-0.144683\pi$
$641$	45.4947	1.79693	0.898466	+	0.439043i	$0.144683\pi$
$642$	−0.803686	−0.0317189
$643$	28.6207	1.12869	0.564346	−	0.825539i	$-0.309129\pi$
$643$	28.6207	1.12869	0.564346	+	0.825539i	$0.309129\pi$
$644$	−54.9263	−2.16440
$645$	−8.48327	−0.334029
$646$	−22.7704	−0.895888
$647$	−36.0024	−1.41540	−0.707699	−	0.706514i	$-0.750267\pi$
$647$	−36.0024	−1.41540	−0.707699	+	0.706514i	$0.750267\pi$
$648$	−2.35961	−0.0926941
$649$	−56.7645	−2.22820
$650$	0.662643	0.0259910
$651$	−4.22758	−0.165692
$652$	6.68670	0.261872
$653$	10.2469	0.400992	0.200496	−	0.979695i	$-0.435745\pi$
$653$	10.2469	0.400992	0.200496	+	0.979695i	$0.435745\pi$
$654$	0.816542	0.0319293
$655$	−16.8743	−0.659335
$656$	−8.91960	−0.348252
$657$	2.12802	0.0830218
$658$	−10.7649	−0.419660
$659$	−7.07252	−0.275506	−0.137753	−	0.990467i	$-0.543988\pi$
$659$	−7.07252	−0.275506	−0.137753	+	0.990467i	$0.543988\pi$
$660$	−7.16458	−0.278881
$661$	−30.0701	−1.16959	−0.584795	−	0.811181i	$-0.698825\pi$
$661$	−30.0701	−1.16959	−0.584795	+	0.811181i	$0.698825\pi$
$662$	11.3799	0.442291
$663$	−4.90512	−0.190499
$664$	35.7735	1.38828
$665$	−29.6164	−1.14848
$666$	7.32514	0.283843
$667$	41.2436	1.59696
$668$	35.7407	1.38285
$669$	−12.7020	−0.491086
$670$	3.35874	0.129759
$671$	−60.3720	−2.33064
$672$	−24.3161	−0.938012
$673$	−33.0656	−1.27459	−0.637293	−	0.770622i	$-0.719946\pi$
$673$	−33.0656	−1.27459	−0.637293	+	0.770622i	$0.719946\pi$
$674$	12.7844	0.492436
$675$	1.00000	0.0384900
$676$	−1.56090	−0.0600348
$677$	−2.17907	−0.0837486	−0.0418743	−	0.999123i	$-0.513333\pi$
$677$	−2.17907	−0.0837486	−0.0418743	+	0.999123i	$0.513333\pi$
$678$	−9.37538	−0.360059
$679$	4.29955	0.165002
$680$	11.5742	0.443849
$681$	20.4588	0.783984
$682$	3.04154	0.116467
$683$	−8.94286	−0.342189	−0.171095	−	0.985255i	$-0.554730\pi$
$683$	−8.94286	−0.342189	−0.171095	+	0.985255i	$0.554730\pi$
$684$	−10.9350	−0.418108
$685$	6.54617	0.250116
$686$	−10.8481	−0.414184
$687$	3.92803	0.149864
$688$	−13.2189	−0.503966
$689$	1.47534	0.0562060
$690$	−5.51559	−0.209975
$691$	−29.1592	−1.10927	−0.554634	−	0.832094i	$-0.687142\pi$
$691$	−29.1592	−1.10927	−0.554634	+	0.832094i	$0.687142\pi$
$692$	18.1069	0.688322
$693$	−19.4047	−0.737122
$694$	4.79166	0.181889
$695$	−15.7282	−0.596605
$696$	11.6919	0.443180
$697$	28.0778	1.06352
$698$	2.18514	0.0827087
$699$	−14.8976	−0.563480
$700$	6.59885	0.249413
$701$	29.9733	1.13208	0.566039	−	0.824379i	$-0.308475\pi$
$701$	29.9733	1.13208	0.566039	+	0.824379i	$0.308475\pi$
$702$	0.662643	0.0250098
$703$	77.4421	2.92078
$704$	3.18961	0.120213
$705$	3.84272	0.144725
$706$	7.02181	0.264269
$707$	−57.9567	−2.17968
$708$	19.3036	0.725475
$709$	−0.775800	−0.0291358	−0.0145679	−	0.999894i	$-0.504637\pi$
$709$	−0.775800	−0.0291358	−0.0145679	+	0.999894i	$0.504637\pi$
$710$	3.42841	0.128666
$711$	12.7161	0.476892
$712$	30.5136	1.14355
$713$	−8.32362	−0.311722
$714$	13.7411	0.514248
$715$	4.59002	0.171657
$716$	7.34058	0.274330
$717$	19.7470	0.737463
$718$	8.57021	0.319837
$719$	12.5129	0.466654	0.233327	−	0.972398i	$-0.425039\pi$
$719$	12.5129	0.466654	0.233327	+	0.972398i	$0.425039\pi$
$720$	1.55823	0.0580719
$721$	84.0469	3.13007
$722$	19.9305	0.741738
$723$	19.4344	0.722773
$724$	26.1690	0.972564
$725$	−4.95501	−0.184025
$726$	6.67166	0.247609
$727$	−23.1051	−0.856921	−0.428460	−	0.903561i	$-0.640944\pi$
$727$	−23.1051	−0.856921	−0.428460	+	0.903561i	$0.640944\pi$
$728$	9.97543	0.369714
$729$	1.00000	0.0370370
$730$	1.41011	0.0521907
$731$	41.6115	1.53906
$732$	20.5304	0.758826
$733$	4.88460	0.180417	0.0902083	−	0.995923i	$-0.471247\pi$
$733$	4.88460	0.180417	0.0902083	+	0.995923i	$0.471247\pi$
$734$	−8.79967	−0.324802
$735$	10.8724	0.401036
$736$	−47.8755	−1.76472
$737$	23.2654	0.856992
$738$	−3.79308	−0.139625
$739$	−3.52336	−0.129609	−0.0648044	−	0.997898i	$-0.520642\pi$
$739$	−3.52336	−0.129609	−0.0648044	+	0.997898i	$0.520642\pi$
$740$	−17.2549	−0.634303
$741$	7.00552	0.257354
$742$	−4.13298	−0.151726
$743$	2.07995	0.0763059	0.0381529	−	0.999272i	$-0.487853\pi$
$743$	2.07995	0.0763059	0.0381529	+	0.999272i	$0.487853\pi$
$744$	−2.35961	−0.0865074
$745$	16.3697	0.599740
$746$	21.1058	0.772740
$747$	−15.1608	−0.554703
$748$	35.1432	1.28496
$749$	5.12742	0.187352
$750$	0.662643	0.0241963
$751$	−26.6247	−0.971551	−0.485775	−	0.874084i	$-0.661463\pi$
$751$	−26.6247	−0.971551	−0.485775	+	0.874084i	$0.661463\pi$
$752$	5.98785	0.218354
$753$	−17.3755	−0.633198
$754$	−3.28340	−0.119574
$755$	−1.32759	−0.0483158
$756$	6.59885	0.239998
$757$	−8.96771	−0.325937	−0.162968	−	0.986631i	$-0.552107\pi$
$757$	−8.96771	−0.325937	−0.162968	+	0.986631i	$0.552107\pi$
$758$	4.80376	0.174480
$759$	−38.2056	−1.38677
$760$	−16.5303	−0.599616
$761$	10.1319	0.367281	0.183640	−	0.982993i	$-0.441212\pi$
$761$	10.1319	0.367281	0.183640	+	0.982993i	$0.441212\pi$
$762$	13.7298	0.497377
$763$	−5.20944	−0.188594
$764$	36.3616	1.31552
$765$	−4.90512	−0.177345
$766$	−1.02727	−0.0371168
$767$	−12.3669	−0.446545
$768$	−8.70741	−0.314202
$769$	33.2651	1.19957	0.599784	−	0.800162i	$-0.295253\pi$
$769$	33.2651	1.19957	0.599784	+	0.800162i	$0.295253\pi$
$770$	−12.8584	−0.463383
$771$	−17.2250	−0.620345
$772$	9.96877	0.358784
$773$	29.2568	1.05229	0.526147	−	0.850394i	$-0.323636\pi$
$773$	29.2568	1.05229	0.526147	+	0.850394i	$0.323636\pi$
$774$	−5.62138	−0.202056
$775$	1.00000	0.0359211
$776$	2.39978	0.0861471
$777$	−46.7335	−1.67655
$778$	−9.52708	−0.341562
$779$	−40.1008	−1.43676
$780$	−1.56090	−0.0558893
$781$	23.7481	0.849773
$782$	27.0546	0.967472
$783$	−4.95501	−0.177078
$784$	16.9418	0.605063
$785$	−17.6560	−0.630170
$786$	−11.1817	−0.398837
$787$	8.64229	0.308064	0.154032	−	0.988066i	$-0.450774\pi$
$787$	8.64229	0.308064	0.154032	+	0.988066i	$0.450774\pi$
$788$	−21.8199	−0.777303
$789$	10.0046	0.356174
$790$	8.42625	0.299792
$791$	59.8138	2.12673
$792$	−10.8306	−0.384850
$793$	−13.1529	−0.467073
$794$	−5.52029	−0.195908
$795$	1.47534	0.0523249
$796$	17.9900	0.637639
$797$	23.1816	0.821134	0.410567	−	0.911830i	$-0.365331\pi$
$797$	23.1816	0.821134	0.410567	+	0.911830i	$0.365331\pi$
$798$	−19.6251	−0.694721
$799$	−18.8490	−0.666830
$800$	5.75177	0.203356
$801$	−12.9317	−0.456918
$802$	−8.72370	−0.308045
$803$	9.76763	0.344692
$804$	−7.91175	−0.279026
$805$	35.1888	1.24024
$806$	0.662643	0.0233406
$807$	−5.54820	−0.195306
$808$	−32.3483	−1.13801
$809$	12.0073	0.422153	0.211077	−	0.977470i	$-0.432303\pi$
$809$	12.0073	0.422153	0.211077	+	0.977470i	$0.432303\pi$
$810$	0.662643	0.0232829
$811$	−35.2415	−1.23750	−0.618748	−	0.785590i	$-0.712360\pi$
$811$	−35.2415	−1.23750	−0.618748	+	0.785590i	$0.712360\pi$
$812$	−32.6974	−1.14745
$813$	12.9364	0.453700
$814$	33.6225	1.17847
$815$	−4.28386	−0.150057
$816$	−7.64332	−0.267570
$817$	−59.4298	−2.07918
$818$	4.45149	0.155643
$819$	−4.22758	−0.147724
$820$	8.93489	0.312020
$821$	3.88947	0.135743	0.0678717	−	0.997694i	$-0.478379\pi$
$821$	3.88947	0.135743	0.0678717	+	0.997694i	$0.478379\pi$
$822$	4.33778	0.151297
$823$	−35.0023	−1.22010	−0.610051	−	0.792362i	$-0.708851\pi$
$823$	−35.0023	−1.22010	−0.610051	+	0.792362i	$0.708851\pi$
$824$	46.9105	1.63420
$825$	4.59002	0.159804
$826$	34.6445	1.20543
$827$	−27.4740	−0.955365	−0.477683	−	0.878532i	$-0.658523\pi$
$827$	−27.4740	−0.955365	−0.477683	+	0.878532i	$0.658523\pi$
$828$	12.9924	0.451516
$829$	21.7529	0.755510	0.377755	−	0.925906i	$-0.376696\pi$
$829$	21.7529	0.755510	0.377755	+	0.925906i	$0.376696\pi$
$830$	−10.0462	−0.348708
$831$	−28.2323	−0.979367
$832$	0.694902	0.0240914
$833$	−53.3306	−1.84780
$834$	−10.4222	−0.360891
$835$	−22.8974	−0.792398
$836$	−50.1916	−1.73591
$837$	1.00000	0.0345651
$838$	22.3910	0.773485
$839$	−21.7299	−0.750198	−0.375099	−	0.926985i	$-0.622391\pi$
$839$	−21.7299	−0.750198	−0.375099	+	0.926985i	$0.622391\pi$
$840$	9.97543	0.344185
$841$	−4.44785	−0.153374
$842$	25.2431	0.869935
$843$	−32.1093	−1.10590
$844$	−0.0130967	−0.000450805 0
$845$	1.00000	0.0344010
$846$	2.54635	0.0875454
$847$	−42.5644	−1.46253
$848$	2.29892	0.0789453
$849$	−14.6117	−0.501474
$850$	−3.25035	−0.111486
$851$	−92.0129	−3.15416
$852$	−8.07589	−0.276675
$853$	8.23128	0.281834	0.140917	−	0.990021i	$-0.454995\pi$
$853$	8.23128	0.281834	0.140917	+	0.990021i	$0.454995\pi$
$854$	36.8462	1.26085
$855$	7.00552	0.239584
$856$	2.86185	0.0978160
$857$	−43.1542	−1.47412	−0.737060	−	0.675827i	$-0.763787\pi$
$857$	−43.1542	−1.47412	−0.737060	+	0.675827i	$0.763787\pi$
$858$	3.04154	0.103837
$859$	−57.5737	−1.96439	−0.982195	−	0.187862i	$-0.939844\pi$
$859$	−57.5737	−1.96439	−0.982195	+	0.187862i	$0.939844\pi$
$860$	13.2416	0.451534
$861$	24.1994	0.824714
$862$	4.91675	0.167465
$863$	−22.8562	−0.778032	−0.389016	−	0.921231i	$-0.627185\pi$
$863$	−22.8562	−0.778032	−0.389016	+	0.921231i	$0.627185\pi$
$864$	5.75177	0.195679
$865$	−11.6003	−0.394421
$866$	6.18535	0.210187
$867$	7.06024	0.239778
$868$	6.59885	0.223980
$869$	58.3672	1.97997
$870$	−3.28340	−0.111318
$871$	5.06870	0.171746
$872$	−2.90763	−0.0984648
$873$	−1.01702	−0.0344211
$874$	−38.6396	−1.30700
$875$	−4.22758	−0.142918
$876$	−3.32163	−0.112227
$877$	8.69302	0.293542	0.146771	−	0.989170i	$-0.453112\pi$
$877$	8.69302	0.293542	0.146771	+	0.989170i	$0.453112\pi$
$878$	−0.254430	−0.00858659
$879$	−19.5729	−0.660177
$880$	7.15231	0.241104
$881$	15.4447	0.520345	0.260173	−	0.965562i	$-0.416221\pi$
$881$	15.4447	0.520345	0.260173	+	0.965562i	$0.416221\pi$
$882$	7.20454	0.242589
$883$	−45.9789	−1.54731	−0.773656	−	0.633606i	$-0.781574\pi$
$883$	−45.9789	−1.54731	−0.773656	+	0.633606i	$0.781574\pi$
$884$	7.65643	0.257514
$885$	−12.3669	−0.415710
$886$	−2.50895	−0.0842897
$887$	33.0352	1.10921	0.554607	−	0.832112i	$-0.312869\pi$
$887$	33.0352	1.10921	0.554607	+	0.832112i	$0.312869\pi$
$888$	−26.0841	−0.875326
$889$	−87.5942	−2.93782
$890$	−8.56907	−0.287236
$891$	4.59002	0.153771
$892$	19.8265	0.663842
$893$	26.9203	0.900852
$894$	10.8473	0.362787
$895$	−4.70277	−0.157196
$896$	46.6854	1.55965
$897$	−8.32362	−0.277918
$898$	−0.981305	−0.0327466
$899$	−4.95501	−0.165259
$900$	−1.56090	−0.0520302
$901$	−7.23672	−0.241090
$902$	−17.4103	−0.579700
$903$	35.8637	1.19347
$904$	33.3848	1.11036
$905$	−16.7653	−0.557297
$906$	−0.879715	−0.0292266
$907$	7.94128	0.263686	0.131843	−	0.991271i	$-0.457911\pi$
$907$	7.94128	0.263686	0.131843	+	0.991271i	$0.457911\pi$
$908$	−31.9343	−1.05978
$909$	13.7092	0.454705
$910$	−2.80138	−0.0928647
$911$	27.8316	0.922102	0.461051	−	0.887374i	$-0.347473\pi$
$911$	27.8316	0.922102	0.461051	+	0.887374i	$0.347473\pi$
$912$	10.9162	0.361473
$913$	−69.5882	−2.30303
$914$	1.68223	0.0556431
$915$	−13.1529	−0.434821
$916$	−6.13128	−0.202583
$917$	71.3376	2.35578
$918$	−3.25035	−0.107277
$919$	21.6286	0.713462	0.356731	−	0.934207i	$-0.383891\pi$
$919$	21.6286	0.713462	0.356731	+	0.934207i	$0.383891\pi$
$920$	19.6405	0.647527
$921$	−8.70365	−0.286795
$922$	−6.75734	−0.222541
$923$	5.17385	0.170299
$924$	30.2888	0.996429
$925$	11.0544	0.363467
$926$	22.0723	0.725342
$927$	−19.8806	−0.652965
$928$	−28.5001	−0.935561
$929$	−22.6412	−0.742834	−0.371417	−	0.928466i	$-0.621128\pi$
$929$	−22.6412	−0.742834	−0.371417	+	0.928466i	$0.621128\pi$
$930$	0.662643	0.0217289
$931$	76.1671	2.49628
$932$	23.2538	0.761703
$933$	11.9091	0.389887
$934$	−0.489425	−0.0160145
$935$	−22.5146	−0.736306
$936$	−2.35961	−0.0771262
$937$	−13.3693	−0.436756	−0.218378	−	0.975864i	$-0.570077\pi$
$937$	−13.3693	−0.436756	−0.218378	+	0.975864i	$0.570077\pi$
$938$	−14.1993	−0.463624
$939$	−11.4549	−0.373818
$940$	−5.99812	−0.195637
$941$	36.7843	1.19914	0.599568	−	0.800324i	$-0.295339\pi$
$941$	36.7843	1.19914	0.599568	+	0.800324i	$0.295339\pi$
$942$	−11.6996	−0.381195
$943$	47.6459	1.55156
$944$	−19.2706	−0.627204
$945$	−4.22758	−0.137523
$946$	−25.8022	−0.838903
$947$	−28.5044	−0.926270	−0.463135	−	0.886288i	$-0.653275\pi$
$947$	−28.5044	−0.926270	−0.463135	+	0.886288i	$0.653275\pi$
$948$	−19.8487	−0.644654
$949$	2.12802	0.0690783
$950$	4.64216	0.150612
$951$	−10.8349	−0.351345
$952$	−48.9307	−1.58585
$953$	31.7760	1.02933	0.514663	−	0.857393i	$-0.327917\pi$
$953$	31.7760	1.02933	0.514663	+	0.857393i	$0.327917\pi$
$954$	0.977623	0.0316517
$955$	−23.2952	−0.753814
$956$	−30.8231	−0.996890
$957$	−22.7436	−0.735196
$958$	12.8871	0.416363
$959$	−27.6745	−0.893656
$960$	0.694902	0.0224279
$961$	1.00000	0.0322581
$962$	7.32514	0.236172
$963$	−1.21285	−0.0390835
$964$	−30.3352	−0.977033
$965$	−6.38654	−0.205590
$966$	23.3176	0.750231
$967$	−51.8642	−1.66784	−0.833921	−	0.551884i	$-0.813909\pi$
$967$	−51.8642	−1.66784	−0.833921	+	0.551884i	$0.813909\pi$
$968$	−23.7571	−0.763583
$969$	−34.3630	−1.10390
$970$	−0.673924	−0.0216384
$971$	−34.4614	−1.10592	−0.552959	−	0.833208i	$-0.686502\pi$
$971$	−34.4614	−1.10592	−0.552959	+	0.833208i	$0.686502\pi$
$972$	−1.56090	−0.0500660
$973$	66.4922	2.13164
$974$	13.7942	0.441996
$975$	1.00000	0.0320256
$976$	−20.4953	−0.656037
$977$	2.39575	0.0766469	0.0383234	−	0.999265i	$-0.487798\pi$
$977$	2.39575	0.0766469	0.0383234	+	0.999265i	$0.487798\pi$
$978$	−2.83867	−0.0907707
$979$	−59.3565	−1.89704
$980$	−16.9708	−0.542113
$981$	1.23225	0.0393428
$982$	22.1184	0.705825
$983$	1.31377	0.0419029	0.0209515	−	0.999780i	$-0.493330\pi$
$983$	1.31377	0.0419029	0.0209515	+	0.999780i	$0.493330\pi$
$984$	13.5068	0.430581
$985$	13.9790	0.445409
$986$	16.1055	0.512904
$987$	−16.2454	−0.517097
$988$	−10.9350	−0.347887
$989$	70.6116	2.24532
$990$	3.04154	0.0966665
$991$	26.2665	0.834383	0.417191	−	0.908819i	$-0.363014\pi$
$991$	26.2665	0.834383	0.417191	+	0.908819i	$0.363014\pi$
$992$	5.75177	0.182619
$993$	17.1735	0.544983
$994$	−14.4939	−0.459719
$995$	−11.5254	−0.365379
$996$	23.6645	0.749839
$997$	28.5067	0.902815	0.451408	−	0.892318i	$-0.350922\pi$
$997$	28.5067	0.902815	0.451408	+	0.892318i	$0.350922\pi$
$998$	−8.58880	−0.271874
$999$	11.0544	0.349747

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.t.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.t.1.8	✓	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)

\(f(q)\)	\(=\)	\(q+0.662643 q^{2} +1.00000 q^{3} -1.56090 q^{4} +1.00000 q^{5} +0.662643 q^{6} -4.22758 q^{7} -2.35961 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.662643 q^{2} +1.00000 q^{3} -1.56090 q^{4} +1.00000 q^{5} +0.662643 q^{6} -4.22758 q^{7} -2.35961 q^{8} +1.00000 q^{9} +0.662643 q^{10} +4.59002 q^{11} -1.56090 q^{12} +1.00000 q^{13} -2.80138 q^{14} +1.00000 q^{15} +1.55823 q^{16} -4.90512 q^{17} +0.662643 q^{18} +7.00552 q^{19} -1.56090 q^{20} -4.22758 q^{21} +3.04154 q^{22} -8.32362 q^{23} -2.35961 q^{24} +1.00000 q^{25} +0.662643 q^{26} +1.00000 q^{27} +6.59885 q^{28} -4.95501 q^{29} +0.662643 q^{30} +1.00000 q^{31} +5.75177 q^{32} +4.59002 q^{33} -3.25035 q^{34} -4.22758 q^{35} -1.56090 q^{36} +11.0544 q^{37} +4.64216 q^{38} +1.00000 q^{39} -2.35961 q^{40} -5.72418 q^{41} -2.80138 q^{42} -8.48327 q^{43} -7.16458 q^{44} +1.00000 q^{45} -5.51559 q^{46} +3.84272 q^{47} +1.55823 q^{48} +10.8724 q^{49} +0.662643 q^{50} -4.90512 q^{51} -1.56090 q^{52} +1.47534 q^{53} +0.662643 q^{54} +4.59002 q^{55} +9.97543 q^{56} +7.00552 q^{57} -3.28340 q^{58} -12.3669 q^{59} -1.56090 q^{60} -13.1529 q^{61} +0.662643 q^{62} -4.22758 q^{63} +0.694902 q^{64} +1.00000 q^{65} +3.04154 q^{66} +5.06870 q^{67} +7.65643 q^{68} -8.32362 q^{69} -2.80138 q^{70} +5.17385 q^{71} -2.35961 q^{72} +2.12802 q^{73} +7.32514 q^{74} +1.00000 q^{75} -10.9350 q^{76} -19.4047 q^{77} +0.662643 q^{78} +12.7161 q^{79} +1.55823 q^{80} +1.00000 q^{81} -3.79308 q^{82} -15.1608 q^{83} +6.59885 q^{84} -4.90512 q^{85} -5.62138 q^{86} -4.95501 q^{87} -10.8306 q^{88} -12.9317 q^{89} +0.662643 q^{90} -4.22758 q^{91} +12.9924 q^{92} +1.00000 q^{93} +2.54635 q^{94} +7.00552 q^{95} +5.75177 q^{96} -1.01702 q^{97} +7.20454 q^{98} +4.59002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9	\( 9 q - 6 q^{2} + 9 q^{3} + 8 q^{4} + 9 q^{5} - 6 q^{6} - 12 q^{7} - 21 q^{8} + 9 q^{9} - 6 q^{10} - 10 q^{11} + 8 q^{12} + 9 q^{13} - 9 q^{14} + 9 q^{15} + 30 q^{16} - 17 q^{17} - 6 q^{18} + 6 q^{19} + 8 q^{20} - 12 q^{21} + 15 q^{22} - 23 q^{23} - 21 q^{24} + 9 q^{25} - 6 q^{26} + 9 q^{27} + 2 q^{28} - 4 q^{29} - 6 q^{30} + 9 q^{31} - 38 q^{32} - 10 q^{33} + 15 q^{34} - 12 q^{35} + 8 q^{36} + 11 q^{37} - 16 q^{38} + 9 q^{39} - 21 q^{40} - 8 q^{41} - 9 q^{42} - 15 q^{43} - q^{44} + 9 q^{45} + 26 q^{46} - 33 q^{47} + 30 q^{48} + 15 q^{49} - 6 q^{50} - 17 q^{51} + 8 q^{52} - 38 q^{53} - 6 q^{54} - 10 q^{55} + 37 q^{56} + 6 q^{57} - 26 q^{58} - 25 q^{59} + 8 q^{60} - 10 q^{61} - 6 q^{62} - 12 q^{63} + 47 q^{64} + 9 q^{65} + 15 q^{66} - 19 q^{67} + 7 q^{68} - 23 q^{69} - 9 q^{70} - 43 q^{71} - 21 q^{72} + q^{73} + 4 q^{74} + 9 q^{75} - 26 q^{76} + 2 q^{77} - 6 q^{78} - 9 q^{79} + 30 q^{80} + 9 q^{81} + 15 q^{82} - 12 q^{83} + 2 q^{84} - 17 q^{85} - 30 q^{86} - 4 q^{87} + q^{88} - 5 q^{89} - 6 q^{90} - 12 q^{91} - 57 q^{92} + 9 q^{93} + 40 q^{94} + 6 q^{95} - 38 q^{96} - 4 q^{97} + 34 q^{98} - 10 q^{99}+O(q^{100}) \) 9 * q - 6 * q^2 + 9 * q^3 + 8 * q^4 + 9 * q^5 - 6 * q^6 - 12 * q^7 - 21 * q^8 + 9 * q^9 - 6 * q^10 - 10 * q^11 + 8 * q^12 + 9 * q^13 - 9 * q^14 + 9 * q^15 + 30 * q^16 - 17 * q^17 - 6 * q^18 + 6 * q^19 + 8 * q^20 - 12 * q^21 + 15 * q^22 - 23 * q^23 - 21 * q^24 + 9 * q^25 - 6 * q^26 + 9 * q^27 + 2 * q^28 - 4 * q^29 - 6 * q^30 + 9 * q^31 - 38 * q^32 - 10 * q^33 + 15 * q^34 - 12 * q^35 + 8 * q^36 + 11 * q^37 - 16 * q^38 + 9 * q^39 - 21 * q^40 - 8 * q^41 - 9 * q^42 - 15 * q^43 - q^44 + 9 * q^45 + 26 * q^46 - 33 * q^47 + 30 * q^48 + 15 * q^49 - 6 * q^50 - 17 * q^51 + 8 * q^52 - 38 * q^53 - 6 * q^54 - 10 * q^55 + 37 * q^56 + 6 * q^57 - 26 * q^58 - 25 * q^59 + 8 * q^60 - 10 * q^61 - 6 * q^62 - 12 * q^63 + 47 * q^64 + 9 * q^65 + 15 * q^66 - 19 * q^67 + 7 * q^68 - 23 * q^69 - 9 * q^70 - 43 * q^71 - 21 * q^72 + q^73 + 4 * q^74 + 9 * q^75 - 26 * q^76 + 2 * q^77 - 6 * q^78 - 9 * q^79 + 30 * q^80 + 9 * q^81 + 15 * q^82 - 12 * q^83 + 2 * q^84 - 17 * q^85 - 30 * q^86 - 4 * q^87 + q^88 - 5 * q^89 - 6 * q^90 - 12 * q^91 - 57 * q^92 + 9 * q^93 + 40 * q^94 + 6 * q^95 - 38 * q^96 - 4 * q^97 + 34 * q^98 - 10 * q^99

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