LMFDB - Embedded newform 6045.2.a.bg.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:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - 27 x^{14} + 51 x^{13} + 294 x^{12} - 517 x^{11} - 1657 x^{10} + 2678 x^{9} + \cdots - 428 $ x^16 - 2x^15 - 27x^14 + 51x^13 + 294x^12 - 517x^11 - 1657x^10 + 2678x^9 + 5124x^8 - 7583x^7 - 8358x^6 + 11579x^5 + 6027x^4 - 8572x^3 - 780x^2 + 2178*x - 428
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.323092$ 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)

$f(q)$	$=$	$q-0.323092 q^{2} -1.00000 q^{3} -1.89561 q^{4} -1.00000 q^{5} +0.323092 q^{6} +1.90658 q^{7} +1.25864 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.323092 q^{2} -1.00000 q^{3} -1.89561 q^{4} -1.00000 q^{5} +0.323092 q^{6} +1.90658 q^{7} +1.25864 q^{8} +1.00000 q^{9} +0.323092 q^{10} +0.526075 q^{11} +1.89561 q^{12} -1.00000 q^{13} -0.616000 q^{14} +1.00000 q^{15} +3.38456 q^{16} +0.448173 q^{17} -0.323092 q^{18} +1.40537 q^{19} +1.89561 q^{20} -1.90658 q^{21} -0.169971 q^{22} +3.85847 q^{23} -1.25864 q^{24} +1.00000 q^{25} +0.323092 q^{26} -1.00000 q^{27} -3.61413 q^{28} +5.49127 q^{29} -0.323092 q^{30} +1.00000 q^{31} -3.61081 q^{32} -0.526075 q^{33} -0.144801 q^{34} -1.90658 q^{35} -1.89561 q^{36} +2.37259 q^{37} -0.454065 q^{38} +1.00000 q^{39} -1.25864 q^{40} +8.01387 q^{41} +0.616000 q^{42} +0.370441 q^{43} -0.997233 q^{44} -1.00000 q^{45} -1.24664 q^{46} -9.83360 q^{47} -3.38456 q^{48} -3.36497 q^{49} -0.323092 q^{50} -0.448173 q^{51} +1.89561 q^{52} -2.80138 q^{53} +0.323092 q^{54} -0.526075 q^{55} +2.39970 q^{56} -1.40537 q^{57} -1.77419 q^{58} +1.20631 q^{59} -1.89561 q^{60} +1.19712 q^{61} -0.323092 q^{62} +1.90658 q^{63} -5.60250 q^{64} +1.00000 q^{65} +0.169971 q^{66} +13.8123 q^{67} -0.849562 q^{68} -3.85847 q^{69} +0.616000 q^{70} +4.65724 q^{71} +1.25864 q^{72} -5.19975 q^{73} -0.766567 q^{74} -1.00000 q^{75} -2.66404 q^{76} +1.00300 q^{77} -0.323092 q^{78} -8.63157 q^{79} -3.38456 q^{80} +1.00000 q^{81} -2.58922 q^{82} -12.6570 q^{83} +3.61413 q^{84} -0.448173 q^{85} -0.119687 q^{86} -5.49127 q^{87} +0.662140 q^{88} +0.0529458 q^{89} +0.323092 q^{90} -1.90658 q^{91} -7.31415 q^{92} -1.00000 q^{93} +3.17716 q^{94} -1.40537 q^{95} +3.61081 q^{96} -3.83879 q^{97} +1.08719 q^{98} +0.526075 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} - 16 q^{3} + 26 q^{4} - 16 q^{5} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 - 16 * q^3 + 26 * q^4 - 16 * q^5 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q - 2 q^{2} - 16 q^{3} + 26 q^{4} - 16 q^{5} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 16 q^{9} + 2 q^{10} + 3 q^{11} - 26 q^{12} - 16 q^{13} - 5 q^{14} + 16 q^{15} + 38 q^{16} - 13 q^{17} - 2 q^{18} - 26 q^{20} + 2 q^{21} + q^{22} - 15 q^{23} + 9 q^{24} + 16 q^{25} + 2 q^{26} - 16 q^{27} + 8 q^{28} - 4 q^{29} - 2 q^{30} + 16 q^{31} - 30 q^{32} - 3 q^{33} + 29 q^{34} + 2 q^{35} + 26 q^{36} + 12 q^{37} + 16 q^{39} + 9 q^{40} - 12 q^{41} + 5 q^{42} - 7 q^{43} - 13 q^{44} - 16 q^{45} + 14 q^{46} + 17 q^{47} - 38 q^{48} + 16 q^{49} - 2 q^{50} + 13 q^{51} - 26 q^{52} - 36 q^{53} + 2 q^{54} - 3 q^{55} + 41 q^{56} + 16 q^{58} + 53 q^{59} + 26 q^{60} + 34 q^{61} - 2 q^{62} - 2 q^{63} + 79 q^{64} + 16 q^{65} - q^{66} - 13 q^{67} - 39 q^{68} + 15 q^{69} + 5 q^{70} - 11 q^{71} - 9 q^{72} + 34 q^{73} - 12 q^{74} - 16 q^{75} + 86 q^{76} - 32 q^{77} - 2 q^{78} - 7 q^{79} - 38 q^{80} + 16 q^{81} + 27 q^{82} - 28 q^{83} - 8 q^{84} + 13 q^{85} + 38 q^{86} + 4 q^{87} + 23 q^{88} - 8 q^{89} + 2 q^{90} + 2 q^{91} - 71 q^{92} - 16 q^{93} + 66 q^{94} + 30 q^{96} + 4 q^{97} + 22 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 16 * q^3 + 26 * q^4 - 16 * q^5 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 16 * q^9 + 2 * q^10 + 3 * q^11 - 26 * q^12 - 16 * q^13 - 5 * q^14 + 16 * q^15 + 38 * q^16 - 13 * q^17 - 2 * q^18 - 26 * q^20 + 2 * q^21 + q^22 - 15 * q^23 + 9 * q^24 + 16 * q^25 + 2 * q^26 - 16 * q^27 + 8 * q^28 - 4 * q^29 - 2 * q^30 + 16 * q^31 - 30 * q^32 - 3 * q^33 + 29 * q^34 + 2 * q^35 + 26 * q^36 + 12 * q^37 + 16 * q^39 + 9 * q^40 - 12 * q^41 + 5 * q^42 - 7 * q^43 - 13 * q^44 - 16 * q^45 + 14 * q^46 + 17 * q^47 - 38 * q^48 + 16 * q^49 - 2 * q^50 + 13 * q^51 - 26 * q^52 - 36 * q^53 + 2 * q^54 - 3 * q^55 + 41 * q^56 + 16 * q^58 + 53 * q^59 + 26 * q^60 + 34 * q^61 - 2 * q^62 - 2 * q^63 + 79 * q^64 + 16 * q^65 - q^66 - 13 * q^67 - 39 * q^68 + 15 * q^69 + 5 * q^70 - 11 * q^71 - 9 * q^72 + 34 * q^73 - 12 * q^74 - 16 * q^75 + 86 * q^76 - 32 * q^77 - 2 * q^78 - 7 * q^79 - 38 * q^80 + 16 * q^81 + 27 * q^82 - 28 * q^83 - 8 * q^84 + 13 * q^85 + 38 * q^86 + 4 * q^87 + 23 * q^88 - 8 * q^89 + 2 * q^90 + 2 * q^91 - 71 * q^92 - 16 * q^93 + 66 * q^94 + 30 * q^96 + 4 * q^97 + 22 * q^98 + 3 * 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 $

$2$	−0.323092	−0.228461	−0.114230	−	0.993454i	$-0.536440\pi$
$2$	−0.323092	−0.228461	−0.114230	+	0.993454i	$0.536440\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.89561	−0.947806
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.323092	0.131902
$7$	1.90658	0.720618	0.360309	−	0.932833i	$-0.382671\pi$
$7$	1.90658	0.720618	0.360309	+	0.932833i	$0.382671\pi$
$8$	1.25864	0.444997
$9$	1.00000	0.333333
$10$	0.323092	0.102171
$11$	0.526075	0.158618	0.0793088	−	0.996850i	$-0.474729\pi$
$11$	0.526075	0.158618	0.0793088	+	0.996850i	$0.474729\pi$
$12$	1.89561	0.547216
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−0.616000	−0.164633
$15$	1.00000	0.258199
$16$	3.38456	0.846141
$17$	0.448173	0.108698	0.0543489	−	0.998522i	$-0.482692\pi$
$17$	0.448173	0.108698	0.0543489	+	0.998522i	$0.482692\pi$
$18$	−0.323092	−0.0761536
$19$	1.40537	0.322414	0.161207	−	0.986921i	$-0.448461\pi$
$19$	1.40537	0.322414	0.161207	+	0.986921i	$0.448461\pi$
$20$	1.89561	0.423872
$21$	−1.90658	−0.416049
$22$	−0.169971	−0.0362379
$23$	3.85847	0.804546	0.402273	−	0.915520i	$-0.368220\pi$
$23$	3.85847	0.804546	0.402273	+	0.915520i	$0.368220\pi$
$24$	−1.25864	−0.256919
$25$	1.00000	0.200000
$26$	0.323092	0.0633636
$27$	−1.00000	−0.192450
$28$	−3.61413	−0.683006
$29$	5.49127	1.01970	0.509852	−	0.860262i	$-0.329700\pi$
$29$	5.49127	1.01970	0.509852	+	0.860262i	$0.329700\pi$
$30$	−0.323092	−0.0589883
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−3.61081	−0.638307
$33$	−0.526075	−0.0915779
$34$	−0.144801	−0.0248332
$35$	−1.90658	−0.322270
$36$	−1.89561	−0.315935
$37$	2.37259	0.390052	0.195026	−	0.980798i	$-0.437521\pi$
$37$	2.37259	0.390052	0.195026	+	0.980798i	$0.437521\pi$
$38$	−0.454065	−0.0736591
$39$	1.00000	0.160128
$40$	−1.25864	−0.199009
$41$	8.01387	1.25156	0.625778	−	0.780001i	$-0.284781\pi$
$41$	8.01387	1.25156	0.625778	+	0.780001i	$0.284781\pi$
$42$	0.616000	0.0950509
$43$	0.370441	0.0564917	0.0282459	−	0.999601i	$-0.491008\pi$
$43$	0.370441	0.0564917	0.0282459	+	0.999601i	$0.491008\pi$
$44$	−0.997233	−0.150339
$45$	−1.00000	−0.149071
$46$	−1.24664	−0.183807
$47$	−9.83360	−1.43438	−0.717189	−	0.696879i	$-0.754572\pi$
$47$	−9.83360	−1.43438	−0.717189	+	0.696879i	$0.754572\pi$
$48$	−3.38456	−0.488520
$49$	−3.36497	−0.480709
$50$	−0.323092	−0.0456922
$51$	−0.448173	−0.0627568
$52$	1.89561	0.262874
$53$	−2.80138	−0.384799	−0.192399	−	0.981317i	$-0.561627\pi$
$53$	−2.80138	−0.384799	−0.192399	+	0.981317i	$0.561627\pi$
$54$	0.323092	0.0439673
$55$	−0.526075	−0.0709359
$56$	2.39970	0.320673
$57$	−1.40537	−0.186146
$58$	−1.77419	−0.232962
$59$	1.20631	0.157049	0.0785244	−	0.996912i	$-0.474979\pi$
$59$	1.20631	0.157049	0.0785244	+	0.996912i	$0.474979\pi$
$60$	−1.89561	−0.244722
$61$	1.19712	0.153275	0.0766375	−	0.997059i	$-0.475582\pi$
$61$	1.19712	0.153275	0.0766375	+	0.997059i	$0.475582\pi$
$62$	−0.323092	−0.0410328
$63$	1.90658	0.240206
$64$	−5.60250	−0.700313
$65$	1.00000	0.124035
$66$	0.169971	0.0209220
$67$	13.8123	1.68744	0.843722	−	0.536781i	$-0.180360\pi$
$67$	13.8123	1.68744	0.843722	+	0.536781i	$0.180360\pi$
$68$	−0.849562	−0.103024
$69$	−3.85847	−0.464505
$70$	0.616000	0.0736261
$71$	4.65724	0.552713	0.276356	−	0.961055i	$-0.410873\pi$
$71$	4.65724	0.552713	0.276356	+	0.961055i	$0.410873\pi$
$72$	1.25864	0.148332
$73$	−5.19975	−0.608585	−0.304293	−	0.952579i	$-0.598420\pi$
$73$	−5.19975	−0.608585	−0.304293	+	0.952579i	$0.598420\pi$
$74$	−0.766567	−0.0891116
$75$	−1.00000	−0.115470
$76$	−2.66404	−0.305586
$77$	1.00300	0.114303
$78$	−0.323092	−0.0365830
$79$	−8.63157	−0.971128	−0.485564	−	0.874201i	$-0.661386\pi$
$79$	−8.63157	−0.971128	−0.485564	+	0.874201i	$0.661386\pi$
$80$	−3.38456	−0.378406
$81$	1.00000	0.111111
$82$	−2.58922	−0.285932
$83$	−12.6570	−1.38928	−0.694641	−	0.719357i	$-0.744437\pi$
$83$	−12.6570	−1.38928	−0.694641	+	0.719357i	$0.744437\pi$
$84$	3.61413	0.394334
$85$	−0.448173	−0.0486112
$86$	−0.119687	−0.0129061
$87$	−5.49127	−0.588726
$88$	0.662140	0.0705844
$89$	0.0529458	0.00561225	0.00280612	−	0.999996i	$-0.499107\pi$
$89$	0.0529458	0.00561225	0.00280612	+	0.999996i	$0.499107\pi$
$90$	0.323092	0.0340569
$91$	−1.90658	−0.199864
$92$	−7.31415	−0.762553
$93$	−1.00000	−0.103695
$94$	3.17716	0.327699
$95$	−1.40537	−0.144188
$96$	3.61081	0.368527
$97$	−3.83879	−0.389770	−0.194885	−	0.980826i	$-0.562433\pi$
$97$	−3.83879	−0.389770	−0.194885	+	0.980826i	$0.562433\pi$
$98$	1.08719	0.109823
$99$	0.526075	0.0528725
$100$	−1.89561	−0.189561
$101$	−9.23464	−0.918881	−0.459440	−	0.888209i	$-0.651950\pi$
$101$	−9.23464	−0.918881	−0.459440	+	0.888209i	$0.651950\pi$
$102$	0.144801	0.0143375
$103$	16.9724	1.67234	0.836170	−	0.548470i	$-0.184790\pi$
$103$	16.9724	1.67234	0.836170	+	0.548470i	$0.184790\pi$
$104$	−1.25864	−0.123420
$105$	1.90658	0.186063
$106$	0.905103	0.0879114
$107$	−0.0766773	−0.00741268	−0.00370634	−	0.999993i	$-0.501180\pi$
$107$	−0.0766773	−0.00741268	−0.00370634	+	0.999993i	$0.501180\pi$
$108$	1.89561	0.182405
$109$	4.33805	0.415510	0.207755	−	0.978181i	$-0.433384\pi$
$109$	4.33805	0.415510	0.207755	+	0.978181i	$0.433384\pi$
$110$	0.169971	0.0162061
$111$	−2.37259	−0.225197
$112$	6.45293	0.609745
$113$	1.65778	0.155951	0.0779753	−	0.996955i	$-0.475154\pi$
$113$	1.65778	0.155951	0.0779753	+	0.996955i	$0.475154\pi$
$114$	0.454065	0.0425271
$115$	−3.85847	−0.359804
$116$	−10.4093	−0.966481
$117$	−1.00000	−0.0924500
$118$	−0.389751	−0.0358795
$119$	0.854476	0.0783297
$120$	1.25864	0.114898
$121$	−10.7232	−0.974840
$122$	−0.386779	−0.0350173
$123$	−8.01387	−0.722587
$124$	−1.89561	−0.170231
$125$	−1.00000	−0.0894427
$126$	−0.616000	−0.0548777
$127$	5.58395	0.495495	0.247748	−	0.968825i	$-0.420310\pi$
$127$	5.58395	0.495495	0.247748	+	0.968825i	$0.420310\pi$
$128$	9.03175	0.798301
$129$	−0.370441	−0.0326155
$130$	−0.323092	−0.0283371
$131$	4.18116	0.365309	0.182655	−	0.983177i	$-0.441531\pi$
$131$	4.18116	0.365309	0.182655	+	0.983177i	$0.441531\pi$
$132$	0.997233	0.0867980
$133$	2.67945	0.232338
$134$	−4.46266	−0.385515
$135$	1.00000	0.0860663
$136$	0.564089	0.0483703
$137$	7.54899	0.644953	0.322477	−	0.946577i	$-0.395485\pi$
$137$	7.54899	0.644953	0.322477	+	0.946577i	$0.395485\pi$
$138$	1.24664	0.106121
$139$	−9.32559	−0.790986	−0.395493	−	0.918469i	$-0.629426\pi$
$139$	−9.32559	−0.790986	−0.395493	+	0.918469i	$0.629426\pi$
$140$	3.61413	0.305450
$141$	9.83360	0.828138
$142$	−1.50472	−0.126273
$143$	−0.526075	−0.0439926
$144$	3.38456	0.282047
$145$	−5.49127	−0.456025
$146$	1.68000	0.139038
$147$	3.36497	0.277538
$148$	−4.49752	−0.369694
$149$	−15.6383	−1.28114	−0.640569	−	0.767901i	$-0.721301\pi$
$149$	−15.6383	−1.28114	−0.640569	+	0.767901i	$0.721301\pi$
$150$	0.323092	0.0263804
$151$	3.80954	0.310016	0.155008	−	0.987913i	$-0.450460\pi$
$151$	3.80954	0.310016	0.155008	+	0.987913i	$0.450460\pi$
$152$	1.76886	0.143474
$153$	0.448173	0.0362326
$154$	−0.324062	−0.0261137
$155$	−1.00000	−0.0803219
$156$	−1.89561	−0.151770
$157$	19.3792	1.54663	0.773315	−	0.634022i	$-0.218597\pi$
$157$	19.3792	1.54663	0.773315	+	0.634022i	$0.218597\pi$
$158$	2.78880	0.221865
$159$	2.80138	0.222164
$160$	3.61081	0.285460
$161$	7.35646	0.579770
$162$	−0.323092	−0.0253845
$163$	−8.60080	−0.673667	−0.336833	−	0.941564i	$-0.609356\pi$
$163$	−8.60080	−0.673667	−0.336833	+	0.941564i	$0.609356\pi$
$164$	−15.1912	−1.18623
$165$	0.526075	0.0409549
$166$	4.08937	0.317396
$167$	−6.78853	−0.525313	−0.262656	−	0.964889i	$-0.584599\pi$
$167$	−6.78853	−0.525313	−0.262656	+	0.964889i	$0.584599\pi$
$168$	−2.39970	−0.185141
$169$	1.00000	0.0769231
$170$	0.144801	0.0111057
$171$	1.40537	0.107471
$172$	−0.702212	−0.0535432
$173$	4.16551	0.316698	0.158349	−	0.987383i	$-0.449383\pi$
$173$	4.16551	0.316698	0.158349	+	0.987383i	$0.449383\pi$
$174$	1.77419	0.134501
$175$	1.90658	0.144124
$176$	1.78053	0.134213
$177$	−1.20631	−0.0906721
$178$	−0.0171064	−0.00128218
$179$	4.84454	0.362098	0.181049	−	0.983474i	$-0.442051\pi$
$179$	4.84454	0.362098	0.181049	+	0.983474i	$0.442051\pi$
$180$	1.89561	0.141291
$181$	18.8758	1.40303	0.701513	−	0.712657i	$-0.252508\pi$
$181$	18.8758	1.40303	0.701513	+	0.712657i	$0.252508\pi$
$182$	0.616000	0.0456610
$183$	−1.19712	−0.0884934
$184$	4.85643	0.358021
$185$	−2.37259	−0.174437
$186$	0.323092	0.0236903
$187$	0.235772	0.0172414
$188$	18.6407	1.35951
$189$	−1.90658	−0.138683
$190$	0.454065	0.0329413
$191$	2.49898	0.180820	0.0904100	−	0.995905i	$-0.471182\pi$
$191$	2.49898	0.180820	0.0904100	+	0.995905i	$0.471182\pi$
$192$	5.60250	0.404326
$193$	−14.5751	−1.04914	−0.524568	−	0.851368i	$-0.675773\pi$
$193$	−14.5751	−1.04914	−0.524568	+	0.851368i	$0.675773\pi$
$194$	1.24028	0.0890472
$195$	−1.00000	−0.0716115
$196$	6.37867	0.455619
$197$	−22.7595	−1.62154	−0.810772	−	0.585362i	$-0.800953\pi$
$197$	−22.7595	−1.62154	−0.810772	+	0.585362i	$0.800953\pi$
$198$	−0.169971	−0.0120793
$199$	2.59312	0.183821	0.0919105	−	0.995767i	$-0.470703\pi$
$199$	2.59312	0.183821	0.0919105	+	0.995767i	$0.470703\pi$
$200$	1.25864	0.0889995
$201$	−13.8123	−0.974246
$202$	2.98364	0.209928
$203$	10.4695	0.734817
$204$	0.849562	0.0594812
$205$	−8.01387	−0.559713
$206$	−5.48365	−0.382064
$207$	3.85847	0.268182
$208$	−3.38456	−0.234677
$209$	0.739331	0.0511406
$210$	−0.616000	−0.0425081
$211$	−11.8926	−0.818720	−0.409360	−	0.912373i	$-0.634248\pi$
$211$	−11.8926	−0.818720	−0.409360	+	0.912373i	$0.634248\pi$
$212$	5.31032	0.364714
$213$	−4.65724	−0.319109
$214$	0.0247739	0.00169351
$215$	−0.370441	−0.0252639
$216$	−1.25864	−0.0856398
$217$	1.90658	0.129427
$218$	−1.40159	−0.0949277
$219$	5.19975	0.351367
$220$	0.997233	0.0672335
$221$	−0.448173	−0.0301474
$222$	0.766567	0.0514486
$223$	0.642144	0.0430011	0.0215006	−	0.999769i	$-0.493156\pi$
$223$	0.642144	0.0430011	0.0215006	+	0.999769i	$0.493156\pi$
$224$	−6.88429	−0.459976
$225$	1.00000	0.0666667
$226$	−0.535615	−0.0356286
$227$	4.11556	0.273159	0.136580	−	0.990629i	$-0.456389\pi$
$227$	4.11556	0.273159	0.136580	+	0.990629i	$0.456389\pi$
$228$	2.66404	0.176430
$229$	−0.914957	−0.0604620	−0.0302310	−	0.999543i	$-0.509624\pi$
$229$	−0.914957	−0.0604620	−0.0302310	+	0.999543i	$0.509624\pi$
$230$	1.24664	0.0822011
$231$	−1.00300	−0.0659927
$232$	6.91155	0.453765
$233$	9.06264	0.593713	0.296857	−	0.954922i	$-0.404062\pi$
$233$	9.06264	0.593713	0.296857	+	0.954922i	$0.404062\pi$
$234$	0.323092	0.0211212
$235$	9.83360	0.641473
$236$	−2.28670	−0.148852
$237$	8.63157	0.560681
$238$	−0.276075	−0.0178953
$239$	−22.5243	−1.45698	−0.728488	−	0.685059i	$-0.759776\pi$
$239$	−22.5243	−1.45698	−0.728488	+	0.685059i	$0.759776\pi$
$240$	3.38456	0.218473
$241$	25.3339	1.63190	0.815951	−	0.578122i	$-0.196214\pi$
$241$	25.3339	1.63190	0.815951	+	0.578122i	$0.196214\pi$
$242$	3.46460	0.222713
$243$	−1.00000	−0.0641500
$244$	−2.26927	−0.145275
$245$	3.36497	0.214980
$246$	2.58922	0.165083
$247$	−1.40537	−0.0894217
$248$	1.25864	0.0799239
$249$	12.6570	0.802102
$250$	0.323092	0.0204342
$251$	28.4128	1.79340	0.896699	−	0.442641i	$-0.145958\pi$
$251$	28.4128	1.79340	0.896699	+	0.442641i	$0.145958\pi$
$252$	−3.61413	−0.227669
$253$	2.02984	0.127615
$254$	−1.80413	−0.113201
$255$	0.448173	0.0280657
$256$	8.28692	0.517932
$257$	17.6055	1.09820	0.549100	−	0.835757i	$-0.314971\pi$
$257$	17.6055	1.09820	0.549100	+	0.835757i	$0.314971\pi$
$258$	0.119687	0.00745137
$259$	4.52353	0.281079
$260$	−1.89561	−0.117561
$261$	5.49127	0.339901
$262$	−1.35090	−0.0834589
$263$	−29.5180	−1.82016	−0.910079	−	0.414435i	$-0.863979\pi$
$263$	−29.5180	−1.82016	−0.910079	+	0.414435i	$0.863979\pi$
$264$	−0.662140	−0.0407519
$265$	2.80138	0.172087
$266$	−0.865710	−0.0530801
$267$	−0.0529458	−0.00324023
$268$	−26.1828	−1.59937
$269$	23.8940	1.45684	0.728421	−	0.685130i	$-0.240255\pi$
$269$	23.8940	1.45684	0.728421	+	0.685130i	$0.240255\pi$
$270$	−0.323092	−0.0196628
$271$	28.8605	1.75315	0.876575	−	0.481264i	$-0.159822\pi$
$271$	28.8605	1.75315	0.876575	+	0.481264i	$0.159822\pi$
$272$	1.51687	0.0919738
$273$	1.90658	0.115391
$274$	−2.43902	−0.147347
$275$	0.526075	0.0317235
$276$	7.31415	0.440260
$277$	22.7807	1.36876	0.684380	−	0.729125i	$-0.260073\pi$
$277$	22.7807	1.36876	0.684380	+	0.729125i	$0.260073\pi$
$278$	3.01303	0.180709
$279$	1.00000	0.0598684
$280$	−2.39970	−0.143409
$281$	−7.19792	−0.429392	−0.214696	−	0.976681i	$-0.568876\pi$
$281$	−7.19792	−0.429392	−0.214696	+	0.976681i	$0.568876\pi$
$282$	−3.17716	−0.189197
$283$	19.0325	1.13137	0.565684	−	0.824622i	$-0.308612\pi$
$283$	19.0325	1.13137	0.565684	+	0.824622i	$0.308612\pi$
$284$	−8.82832	−0.523864
$285$	1.40537	0.0832471
$286$	0.169971	0.0100506
$287$	15.2791	0.901894
$288$	−3.61081	−0.212769
$289$	−16.7991	−0.988185
$290$	1.77419	0.104184
$291$	3.83879	0.225034
$292$	9.85671	0.576820
$293$	9.76271	0.570344	0.285172	−	0.958476i	$-0.407949\pi$
$293$	9.76271	0.570344	0.285172	+	0.958476i	$0.407949\pi$
$294$	−1.08719	−0.0634065
$295$	−1.20631	−0.0702343
$296$	2.98625	0.173572
$297$	−0.526075	−0.0305260
$298$	5.05261	0.292690
$299$	−3.85847	−0.223141
$300$	1.89561	0.109443
$301$	0.706274	0.0407090
$302$	−1.23083	−0.0708265
$303$	9.23464	0.530516
$304$	4.75657	0.272808
$305$	−1.19712	−0.0685467
$306$	−0.144801	−0.00827774
$307$	17.3835	0.992131	0.496066	−	0.868285i	$-0.334777\pi$
$307$	17.3835	0.992131	0.496066	+	0.868285i	$0.334777\pi$
$308$	−1.90130	−0.108337
$309$	−16.9724	−0.965526
$310$	0.323092	0.0183504
$311$	6.36654	0.361013	0.180507	−	0.983574i	$-0.442226\pi$
$311$	6.36654	0.361013	0.180507	+	0.983574i	$0.442226\pi$
$312$	1.25864	0.0712566
$313$	−24.2427	−1.37028	−0.685140	−	0.728411i	$-0.740259\pi$
$313$	−24.2427	−1.37028	−0.685140	+	0.728411i	$0.740259\pi$
$314$	−6.26128	−0.353344
$315$	−1.90658	−0.107423
$316$	16.3621	0.920440
$317$	17.5038	0.983109	0.491555	−	0.870847i	$-0.336429\pi$
$317$	17.5038	0.983109	0.491555	+	0.870847i	$0.336429\pi$
$318$	−0.905103	−0.0507557
$319$	2.88882	0.161743
$320$	5.60250	0.313189
$321$	0.0766773	0.00427971
$322$	−2.37682	−0.132455
$323$	0.629850	0.0350458
$324$	−1.89561	−0.105312
$325$	−1.00000	−0.0554700
$326$	2.77885	0.153906
$327$	−4.33805	−0.239895
$328$	10.0866	0.556939
$329$	−18.7485	−1.03364
$330$	−0.169971	−0.00935658
$331$	30.1459	1.65697	0.828484	−	0.560013i	$-0.189204\pi$
$331$	30.1459	1.65697	0.828484	+	0.560013i	$0.189204\pi$
$332$	23.9927	1.31677
$333$	2.37259	0.130017
$334$	2.19332	0.120013
$335$	−13.8123	−0.754648
$336$	−6.45293	−0.352036
$337$	−12.0709	−0.657545	−0.328773	−	0.944409i	$-0.606635\pi$
$337$	−12.0709	−0.657545	−0.328773	+	0.944409i	$0.606635\pi$
$338$	−0.323092	−0.0175739
$339$	−1.65778	−0.0900381
$340$	0.849562	0.0460739
$341$	0.526075	0.0284885
$342$	−0.454065	−0.0245530
$343$	−19.7616	−1.06703
$344$	0.466253	0.0251387
$345$	3.85847	0.207733
$346$	−1.34584	−0.0723531
$347$	−14.0209	−0.752680	−0.376340	−	0.926482i	$-0.622817\pi$
$347$	−14.0209	−0.752680	−0.376340	+	0.926482i	$0.622817\pi$
$348$	10.4093	0.557998
$349$	29.5944	1.58415	0.792075	−	0.610423i	$-0.209001\pi$
$349$	29.5944	1.58415	0.792075	+	0.610423i	$0.209001\pi$
$350$	−0.616000	−0.0329266
$351$	1.00000	0.0533761
$352$	−1.89956	−0.101247
$353$	21.7275	1.15644	0.578220	−	0.815881i	$-0.303747\pi$
$353$	21.7275	1.15644	0.578220	+	0.815881i	$0.303747\pi$
$354$	0.389751	0.0207150
$355$	−4.65724	−0.247181
$356$	−0.100365	−0.00531932
$357$	−0.854476	−0.0452237
$358$	−1.56524	−0.0827252
$359$	17.6826	0.933251	0.466625	−	0.884455i	$-0.345470\pi$
$359$	17.6826	0.933251	0.466625	+	0.884455i	$0.345470\pi$
$360$	−1.25864	−0.0663363
$361$	−17.0249	−0.896049
$362$	−6.09862	−0.320536
$363$	10.7232	0.562824
$364$	3.61413	0.189432
$365$	5.19975	0.272168
$366$	0.386779	0.0202173
$367$	−0.378665	−0.0197662	−0.00988309	−	0.999951i	$-0.503146\pi$
$367$	−0.378665	−0.0197662	−0.00988309	+	0.999951i	$0.503146\pi$
$368$	13.0592	0.680759
$369$	8.01387	0.417186
$370$	0.766567	0.0398519
$371$	−5.34104	−0.277293
$372$	1.89561	0.0982829
$373$	−22.5447	−1.16732	−0.583660	−	0.811998i	$-0.698380\pi$
$373$	−22.5447	−1.16732	−0.583660	+	0.811998i	$0.698380\pi$
$374$	−0.0761763	−0.00393898
$375$	1.00000	0.0516398
$376$	−12.3770	−0.638294
$377$	−5.49127	−0.282815
$378$	0.616000	0.0316836
$379$	−3.16724	−0.162690	−0.0813452	−	0.996686i	$-0.525922\pi$
$379$	−3.16724	−0.162690	−0.0813452	+	0.996686i	$0.525922\pi$
$380$	2.66404	0.136662
$381$	−5.58395	−0.286074
$382$	−0.807402	−0.0413103
$383$	−28.7246	−1.46776	−0.733878	−	0.679281i	$-0.762292\pi$
$383$	−28.7246	−1.46776	−0.733878	+	0.679281i	$0.762292\pi$
$384$	−9.03175	−0.460900
$385$	−1.00300	−0.0511177
$386$	4.70910	0.239687
$387$	0.370441	0.0188306
$388$	7.27685	0.369426
$389$	7.08484	0.359216	0.179608	−	0.983738i	$-0.442517\pi$
$389$	7.08484	0.359216	0.179608	+	0.983738i	$0.442517\pi$
$390$	0.323092	0.0163604
$391$	1.72926	0.0874524
$392$	−4.23529	−0.213914
$393$	−4.18116	−0.210912
$394$	7.35341	0.370459
$395$	8.63157	0.434302
$396$	−0.997233	−0.0501129
$397$	33.7296	1.69284	0.846420	−	0.532517i	$-0.178754\pi$
$397$	33.7296	1.69284	0.846420	+	0.532517i	$0.178754\pi$
$398$	−0.837816	−0.0419959
$399$	−2.67945	−0.134140
$400$	3.38456	0.169228
$401$	21.5941	1.07836	0.539179	−	0.842191i	$-0.318735\pi$
$401$	21.5941	1.07836	0.539179	+	0.842191i	$0.318735\pi$
$402$	4.46266	0.222577
$403$	−1.00000	−0.0498135
$404$	17.5053	0.870921
$405$	−1.00000	−0.0496904
$406$	−3.38263	−0.167877
$407$	1.24816	0.0618691
$408$	−0.564089	−0.0279266
$409$	21.3699	1.05667	0.528337	−	0.849035i	$-0.322816\pi$
$409$	21.3699	1.05667	0.528337	+	0.849035i	$0.322816\pi$
$410$	2.58922	0.127873
$411$	−7.54899	−0.372364
$412$	−32.1731	−1.58505
$413$	2.29993	0.113172
$414$	−1.24664	−0.0612690
$415$	12.6570	0.621306
$416$	3.61081	0.177035
$417$	9.32559	0.456676
$418$	−0.238872	−0.0116836
$419$	−0.178757	−0.00873287	−0.00436644	−	0.999990i	$-0.501390\pi$
$419$	−0.178757	−0.00873287	−0.00436644	+	0.999990i	$0.501390\pi$
$420$	−3.61413	−0.176351
$421$	−0.264546	−0.0128932	−0.00644659	−	0.999979i	$-0.502052\pi$
$421$	−0.264546	−0.0128932	−0.00644659	+	0.999979i	$0.502052\pi$
$422$	3.84240	0.187045
$423$	−9.83360	−0.478126
$424$	−3.52593	−0.171234
$425$	0.448173	0.0217396
$426$	1.50472	0.0729039
$427$	2.28239	0.110453
$428$	0.145350	0.00702578
$429$	0.526075	0.0253991
$430$	0.119687	0.00577180
$431$	20.2712	0.976431	0.488215	−	0.872723i	$-0.337648\pi$
$431$	20.2712	0.976431	0.488215	+	0.872723i	$0.337648\pi$
$432$	−3.38456	−0.162840
$433$	36.1236	1.73599	0.867995	−	0.496573i	$-0.165408\pi$
$433$	36.1236	1.73599	0.867995	+	0.496573i	$0.165408\pi$
$434$	−0.616000	−0.0295690
$435$	5.49127	0.263286
$436$	−8.22326	−0.393823
$437$	5.42258	0.259397
$438$	−1.68000	−0.0802735
$439$	34.2892	1.63654	0.818268	−	0.574837i	$-0.194935\pi$
$439$	34.2892	1.63654	0.818268	+	0.574837i	$0.194935\pi$
$440$	−0.662140	−0.0315663
$441$	−3.36497	−0.160236
$442$	0.144801	0.00688749
$443$	23.3021	1.10712	0.553558	−	0.832811i	$-0.313270\pi$
$443$	23.3021	1.10712	0.553558	+	0.832811i	$0.313270\pi$
$444$	4.49752	0.213443
$445$	−0.0529458	−0.00250987
$446$	−0.207472	−0.00982407
$447$	15.6383	0.739665
$448$	−10.6816	−0.504658
$449$	28.4998	1.34499	0.672495	−	0.740101i	$-0.265223\pi$
$449$	28.4998	1.34499	0.672495	+	0.740101i	$0.265223\pi$
$450$	−0.323092	−0.0152307
$451$	4.21590	0.198519
$452$	−3.14250	−0.147811
$453$	−3.80954	−0.178988
$454$	−1.32971	−0.0624062
$455$	1.90658	0.0893817
$456$	−1.76886	−0.0828345
$457$	−19.5796	−0.915897	−0.457949	−	0.888979i	$-0.651416\pi$
$457$	−19.5796	−0.915897	−0.457949	+	0.888979i	$0.651416\pi$
$458$	0.295616	0.0138132
$459$	−0.448173	−0.0209189
$460$	7.31415	0.341024
$461$	9.85306	0.458903	0.229451	−	0.973320i	$-0.426307\pi$
$461$	9.85306	0.458903	0.229451	+	0.973320i	$0.426307\pi$
$462$	0.324062	0.0150767
$463$	34.2813	1.59319	0.796594	−	0.604515i	$-0.206633\pi$
$463$	34.2813	1.59319	0.796594	+	0.604515i	$0.206633\pi$
$464$	18.5856	0.862813
$465$	1.00000	0.0463739
$466$	−2.92807	−0.135640
$467$	18.9179	0.875415	0.437707	−	0.899117i	$-0.355791\pi$
$467$	18.9179	0.875415	0.437707	+	0.899117i	$0.355791\pi$
$468$	1.89561	0.0876247
$469$	26.3342	1.21600
$470$	−3.17716	−0.146552
$471$	−19.3792	−0.892947
$472$	1.51832	0.0698862
$473$	0.194880	0.00896058
$474$	−2.78880	−0.128094
$475$	1.40537	0.0644829
$476$	−1.61975	−0.0742413
$477$	−2.80138	−0.128266
$478$	7.27743	0.332862
$479$	−14.5927	−0.666756	−0.333378	−	0.942793i	$-0.608189\pi$
$479$	−14.5927	−0.666756	−0.333378	+	0.942793i	$0.608189\pi$
$480$	−3.61081	−0.164810
$481$	−2.37259	−0.108181
$482$	−8.18520	−0.372826
$483$	−7.35646	−0.334730
$484$	20.3271	0.923959
$485$	3.83879	0.174310
$486$	0.323092	0.0146558
$487$	12.6047	0.571173	0.285587	−	0.958353i	$-0.407812\pi$
$487$	12.6047	0.571173	0.285587	+	0.958353i	$0.407812\pi$
$488$	1.50674	0.0682070
$489$	8.60080	0.388942
$490$	−1.08719	−0.0491145
$491$	−18.9474	−0.855084	−0.427542	−	0.903995i	$-0.640620\pi$
$491$	−18.9474	−0.855084	−0.427542	+	0.903995i	$0.640620\pi$
$492$	15.1912	0.684872
$493$	2.46104	0.110840
$494$	0.454065	0.0204293
$495$	−0.526075	−0.0236453
$496$	3.38456	0.151971
$497$	8.87938	0.398295
$498$	−4.08937	−0.183249
$499$	37.1660	1.66378	0.831890	−	0.554940i	$-0.187259\pi$
$499$	37.1660	1.66378	0.831890	+	0.554940i	$0.187259\pi$
$500$	1.89561	0.0847743
$501$	6.78853	0.303289
$502$	−9.17995	−0.409721
$503$	−39.9856	−1.78287	−0.891435	−	0.453149i	$-0.850301\pi$
$503$	−39.9856	−1.78287	−0.891435	+	0.453149i	$0.850301\pi$
$504$	2.39970	0.106891
$505$	9.23464	0.410936
$506$	−0.655826	−0.0291550
$507$	−1.00000	−0.0444116
$508$	−10.5850	−0.469633
$509$	−35.2765	−1.56360	−0.781802	−	0.623527i	$-0.785699\pi$
$509$	−35.2765	−1.56360	−0.781802	+	0.623527i	$0.785699\pi$
$510$	−0.144801	−0.00641191
$511$	−9.91373	−0.438558
$512$	−20.7409	−0.916629
$513$	−1.40537	−0.0620487
$514$	−5.68820	−0.250896
$515$	−16.9724	−0.747893
$516$	0.702212	0.0309132
$517$	−5.17321	−0.227517
$518$	−1.46152	−0.0642154
$519$	−4.16551	−0.182846
$520$	1.25864	0.0551951
$521$	33.0504	1.44796	0.723982	−	0.689819i	$-0.242310\pi$
$521$	33.0504	1.44796	0.723982	+	0.689819i	$0.242310\pi$
$522$	−1.77419	−0.0776541
$523$	−22.6837	−0.991890	−0.495945	−	0.868354i	$-0.665178\pi$
$523$	−22.6837	−0.991890	−0.495945	+	0.868354i	$0.665178\pi$
$524$	−7.92585	−0.346242
$525$	−1.90658	−0.0832098
$526$	9.53704	0.415835
$527$	0.448173	0.0195227
$528$	−1.78053	−0.0774878
$529$	−8.11225	−0.352706
$530$	−0.905103	−0.0393152
$531$	1.20631	0.0523496
$532$	−5.07919	−0.220211
$533$	−8.01387	−0.347119
$534$	0.0171064	0.000740266 0
$535$	0.0766773	0.00331505
$536$	17.3848	0.750908
$537$	−4.84454	−0.209057
$538$	−7.71996	−0.332831
$539$	−1.77022	−0.0762489
$540$	−1.89561	−0.0815741
$541$	12.9222	0.555570	0.277785	−	0.960643i	$-0.410400\pi$
$541$	12.9222	0.555570	0.277785	+	0.960643i	$0.410400\pi$
$542$	−9.32461	−0.400526
$543$	−18.8758	−0.810037
$544$	−1.61827	−0.0693827
$545$	−4.33805	−0.185822
$546$	−0.616000	−0.0263624
$547$	20.0212	0.856046	0.428023	−	0.903768i	$-0.359210\pi$
$547$	20.0212	0.856046	0.428023	+	0.903768i	$0.359210\pi$
$548$	−14.3099	−0.611291
$549$	1.19712	0.0510917
$550$	−0.169971	−0.00724758
$551$	7.71728	0.328767
$552$	−4.85643	−0.206703
$553$	−16.4568	−0.699812
$554$	−7.36028	−0.312708
$555$	2.37259	0.100711
$556$	17.6777	0.749701
$557$	7.33808	0.310924	0.155462	−	0.987842i	$-0.450313\pi$
$557$	7.33808	0.310924	0.155462	+	0.987842i	$0.450313\pi$
$558$	−0.323092	−0.0136776
$559$	−0.370441	−0.0156680
$560$	−6.45293	−0.272686
$561$	−0.235772	−0.00995432
$562$	2.32559	0.0980993
$563$	−14.7688	−0.622429	−0.311215	−	0.950340i	$-0.600736\pi$
$563$	−14.7688	−0.622429	−0.311215	+	0.950340i	$0.600736\pi$
$564$	−18.6407	−0.784914
$565$	−1.65778	−0.0697432
$566$	−6.14927	−0.258473
$567$	1.90658	0.0800687
$568$	5.86180	0.245956
$569$	−16.1891	−0.678682	−0.339341	−	0.940663i	$-0.610204\pi$
$569$	−16.1891	−0.678682	−0.339341	+	0.940663i	$0.610204\pi$
$570$	−0.454065	−0.0190187
$571$	19.9485	0.834819	0.417410	−	0.908718i	$-0.362938\pi$
$571$	19.9485	0.834819	0.417410	+	0.908718i	$0.362938\pi$
$572$	0.997233	0.0416964
$573$	−2.49898	−0.104396
$574$	−4.93655	−0.206048
$575$	3.85847	0.160909
$576$	−5.60250	−0.233438
$577$	32.0707	1.33512	0.667560	−	0.744556i	$-0.267339\pi$
$577$	32.0707	1.33512	0.667560	+	0.744556i	$0.267339\pi$
$578$	5.42767	0.225762
$579$	14.5751	0.605720
$580$	10.4093	0.432223
$581$	−24.1315	−1.00114
$582$	−1.24028	−0.0514114
$583$	−1.47373	−0.0610358
$584$	−6.54463	−0.270819
$585$	1.00000	0.0413449
$586$	−3.15426	−0.130301
$587$	−37.6213	−1.55280	−0.776398	−	0.630243i	$-0.782955\pi$
$587$	−37.6213	−1.55280	−0.776398	+	0.630243i	$0.782955\pi$
$588$	−6.37867	−0.263052
$589$	1.40537	0.0579073
$590$	0.389751	0.0160458
$591$	22.7595	0.936199
$592$	8.03020	0.330039
$593$	−21.4007	−0.878821	−0.439411	−	0.898286i	$-0.644813\pi$
$593$	−21.4007	−0.878821	−0.439411	+	0.898286i	$0.644813\pi$
$594$	0.169971	0.00697398
$595$	−0.854476	−0.0350301
$596$	29.6441	1.21427
$597$	−2.59312	−0.106129
$598$	1.24664	0.0509789
$599$	−3.71774	−0.151903	−0.0759513	−	0.997112i	$-0.524199\pi$
$599$	−3.71774	−0.151903	−0.0759513	+	0.997112i	$0.524199\pi$
$600$	−1.25864	−0.0513839
$601$	22.7657	0.928633	0.464317	−	0.885669i	$-0.346300\pi$
$601$	22.7657	0.928633	0.464317	+	0.885669i	$0.346300\pi$
$602$	−0.228192	−0.00930040
$603$	13.8123	0.562481
$604$	−7.22141	−0.293835
$605$	10.7232	0.435962
$606$	−2.98364	−0.121202
$607$	−32.6707	−1.32606	−0.663031	−	0.748592i	$-0.730730\pi$
$607$	−32.6707	−1.32606	−0.663031	+	0.748592i	$0.730730\pi$
$608$	−5.07453	−0.205800
$609$	−10.4695	−0.424247
$610$	0.386779	0.0156602
$611$	9.83360	0.397825
$612$	−0.849562	−0.0343415
$613$	16.3102	0.658764	0.329382	−	0.944197i	$-0.393160\pi$
$613$	16.3102	0.658764	0.329382	+	0.944197i	$0.393160\pi$
$614$	−5.61649	−0.226663
$615$	8.01387	0.323151
$616$	1.26242	0.0508644
$617$	−0.165329	−0.00665588	−0.00332794	−	0.999994i	$-0.501059\pi$
$617$	−0.165329	−0.00665588	−0.00332794	+	0.999994i	$0.501059\pi$
$618$	5.48365	0.220585
$619$	−20.6520	−0.830072	−0.415036	−	0.909805i	$-0.636231\pi$
$619$	−20.6520	−0.830072	−0.415036	+	0.909805i	$0.636231\pi$
$620$	1.89561	0.0761296
$621$	−3.85847	−0.154835
$622$	−2.05698	−0.0824774
$623$	0.100945	0.00404429
$624$	3.38456	0.135491
$625$	1.00000	0.0400000
$626$	7.83264	0.313055
$627$	−0.739331	−0.0295260
$628$	−36.7355	−1.46590
$629$	1.06333	0.0423978
$630$	0.616000	0.0245420
$631$	−19.3765	−0.771366	−0.385683	−	0.922631i	$-0.626034\pi$
$631$	−19.3765	−0.771366	−0.385683	+	0.922631i	$0.626034\pi$
$632$	−10.8641	−0.432149
$633$	11.8926	0.472688
$634$	−5.65533	−0.224602
$635$	−5.58395	−0.221592
$636$	−5.31032	−0.210568
$637$	3.36497	0.133325
$638$	−0.933356	−0.0369519
$639$	4.65724	0.184238
$640$	−9.03175	−0.357011
$641$	−17.0771	−0.674507	−0.337253	−	0.941414i	$-0.609498\pi$
$641$	−17.0771	−0.674507	−0.337253	+	0.941414i	$0.609498\pi$
$642$	−0.0247739	−0.000977746 0
$643$	−0.106014	−0.00418080	−0.00209040	−	0.999998i	$-0.500665\pi$
$643$	−0.106014	−0.00418080	−0.00209040	+	0.999998i	$0.500665\pi$
$644$	−13.9450	−0.549509
$645$	0.370441	0.0145861
$646$	−0.203500	−0.00800658
$647$	14.2044	0.558434	0.279217	−	0.960228i	$-0.409925\pi$
$647$	14.2044	0.558434	0.279217	+	0.960228i	$0.409925\pi$
$648$	1.25864	0.0494441
$649$	0.634611	0.0249107
$650$	0.323092	0.0126727
$651$	−1.90658	−0.0747246
$652$	16.3038	0.638505
$653$	−47.8150	−1.87115	−0.935573	−	0.353134i	$-0.885116\pi$
$653$	−47.8150	−1.87115	−0.935573	+	0.353134i	$0.885116\pi$
$654$	1.40159	0.0548065
$655$	−4.18116	−0.163371
$656$	27.1235	1.05899
$657$	−5.19975	−0.202862
$658$	6.05750	0.236146
$659$	3.57206	0.139148	0.0695739	−	0.997577i	$-0.477836\pi$
$659$	3.57206	0.139148	0.0695739	+	0.997577i	$0.477836\pi$
$660$	−0.997233	−0.0388173
$661$	−24.8222	−0.965472	−0.482736	−	0.875766i	$-0.660357\pi$
$661$	−24.8222	−0.965472	−0.482736	+	0.875766i	$0.660357\pi$
$662$	−9.73990	−0.378552
$663$	0.448173	0.0174056
$664$	−15.9306	−0.618227
$665$	−2.67945	−0.103905
$666$	−0.766567	−0.0297039
$667$	21.1879	0.820398
$668$	12.8684	0.497894
$669$	−0.642144	−0.0248267
$670$	4.46266	0.172407
$671$	0.629772	0.0243121
$672$	6.88429	0.265567
$673$	24.6544	0.950356	0.475178	−	0.879890i	$-0.342384\pi$
$673$	24.6544	0.950356	0.475178	+	0.879890i	$0.342384\pi$
$674$	3.90002	0.150223
$675$	−1.00000	−0.0384900
$676$	−1.89561	−0.0729081
$677$	−3.05205	−0.117300	−0.0586498	−	0.998279i	$-0.518680\pi$
$677$	−3.05205	−0.117300	−0.0586498	+	0.998279i	$0.518680\pi$
$678$	0.535615	0.0205702
$679$	−7.31895	−0.280875
$680$	−0.564089	−0.0216318
$681$	−4.11556	−0.157709
$682$	−0.169971	−0.00650852
$683$	12.4465	0.476251	0.238125	−	0.971234i	$-0.423467\pi$
$683$	12.4465	0.476251	0.238125	+	0.971234i	$0.423467\pi$
$684$	−2.66404	−0.101862
$685$	−7.54899	−0.288432
$686$	6.38482	0.243774
$687$	0.914957	0.0349078
$688$	1.25378	0.0478000
$689$	2.80138	0.106724
$690$	−1.24664	−0.0474588
$691$	−39.6099	−1.50683	−0.753416	−	0.657544i	$-0.771595\pi$
$691$	−39.6099	−1.50683	−0.753416	+	0.657544i	$0.771595\pi$
$692$	−7.89619	−0.300168
$693$	1.00300	0.0381009
$694$	4.53004	0.171958
$695$	9.32559	0.353740
$696$	−6.91155	−0.261982
$697$	3.59160	0.136042
$698$	−9.56172	−0.361916
$699$	−9.06264	−0.342780
$700$	−3.61413	−0.136601
$701$	−26.7027	−1.00855	−0.504273	−	0.863544i	$-0.668240\pi$
$701$	−26.7027	−1.00855	−0.504273	+	0.863544i	$0.668240\pi$
$702$	−0.323092	−0.0121943
$703$	3.33438	0.125758
$704$	−2.94734	−0.111082
$705$	−9.83360	−0.370355
$706$	−7.02001	−0.264201
$707$	−17.6065	−0.662162
$708$	2.28670	0.0859395
$709$	24.6538	0.925894	0.462947	−	0.886386i	$-0.346792\pi$
$709$	24.6538	0.925894	0.462947	+	0.886386i	$0.346792\pi$
$710$	1.50472	0.0564711
$711$	−8.63157	−0.323709
$712$	0.0666398	0.00249743
$713$	3.85847	0.144501
$714$	0.276075	0.0103318
$715$	0.526075	0.0196741
$716$	−9.18337	−0.343199
$717$	22.5243	0.841185
$718$	−5.71311	−0.213211
$719$	1.62404	0.0605666	0.0302833	−	0.999541i	$-0.490359\pi$
$719$	1.62404	0.0605666	0.0302833	+	0.999541i	$0.490359\pi$
$720$	−3.38456	−0.126135
$721$	32.3592	1.20512
$722$	5.50063	0.204712
$723$	−25.3339	−0.942179
$724$	−35.7811	−1.32980
$725$	5.49127	0.203941
$726$	−3.46460	−0.128583
$727$	15.5448	0.576524	0.288262	−	0.957552i	$-0.406923\pi$
$727$	15.5448	0.576524	0.288262	+	0.957552i	$0.406923\pi$
$728$	−2.39970	−0.0889387
$729$	1.00000	0.0370370
$730$	−1.68000	−0.0621796
$731$	0.166022	0.00614053
$732$	2.26927	0.0838745
$733$	−17.8135	−0.657958	−0.328979	−	0.944337i	$-0.606705\pi$
$733$	−17.8135	−0.657958	−0.328979	+	0.944337i	$0.606705\pi$
$734$	0.122344	0.00451580
$735$	−3.36497	−0.124119
$736$	−13.9322	−0.513547
$737$	7.26631	0.267658
$738$	−2.58922	−0.0953105
$739$	−17.2831	−0.635771	−0.317885	−	0.948129i	$-0.602973\pi$
$739$	−17.2831	−0.635771	−0.317885	+	0.948129i	$0.602973\pi$
$740$	4.49752	0.165332
$741$	1.40537	0.0516276
$742$	1.72565	0.0633506
$743$	19.1320	0.701884	0.350942	−	0.936397i	$-0.385862\pi$
$743$	19.1320	0.701884	0.350942	+	0.936397i	$0.385862\pi$
$744$	−1.25864	−0.0461441
$745$	15.6383	0.572942
$746$	7.28402	0.266687
$747$	−12.6570	−0.463094
$748$	−0.446933	−0.0163415
$749$	−0.146191	−0.00534171
$750$	−0.323092	−0.0117977
$751$	18.5757	0.677837	0.338918	−	0.940816i	$-0.389939\pi$
$751$	18.5757	0.677837	0.338918	+	0.940816i	$0.389939\pi$
$752$	−33.2825	−1.21369
$753$	−28.4128	−1.03542
$754$	1.77419	0.0646121
$755$	−3.80954	−0.138643
$756$	3.61413	0.131445
$757$	5.47669	0.199054	0.0995268	−	0.995035i	$-0.468267\pi$
$757$	5.47669	0.199054	0.0995268	+	0.995035i	$0.468267\pi$
$758$	1.02331	0.0371684
$759$	−2.02984	−0.0736786
$760$	−1.76886	−0.0641633
$761$	−12.1764	−0.441392	−0.220696	−	0.975343i	$-0.570833\pi$
$761$	−12.1764	−0.441392	−0.220696	+	0.975343i	$0.570833\pi$
$762$	1.80413	0.0653568
$763$	8.27082	0.299424
$764$	−4.73710	−0.171382
$765$	−0.448173	−0.0162037
$766$	9.28068	0.335325
$767$	−1.20631	−0.0435575
$768$	−8.28692	−0.299028
$769$	−21.1650	−0.763228	−0.381614	−	0.924322i	$-0.624632\pi$
$769$	−21.1650	−0.763228	−0.381614	+	0.924322i	$0.624632\pi$
$770$	0.324062	0.0116784
$771$	−17.6055	−0.634046
$772$	27.6287	0.994378
$773$	6.59048	0.237043	0.118522	−	0.992951i	$-0.462185\pi$
$773$	6.59048	0.237043	0.118522	+	0.992951i	$0.462185\pi$
$774$	−0.119687	−0.00430205
$775$	1.00000	0.0359211
$776$	−4.83166	−0.173447
$777$	−4.52353	−0.162281
$778$	−2.28906	−0.0820667
$779$	11.2625	0.403520
$780$	1.89561	0.0678738
$781$	2.45006	0.0876699
$782$	−0.558711	−0.0199794
$783$	−5.49127	−0.196242
$784$	−11.3889	−0.406748
$785$	−19.3792	−0.691674
$786$	1.35090	0.0481850
$787$	7.01490	0.250054	0.125027	−	0.992153i	$-0.460098\pi$
$787$	7.01490	0.250054	0.125027	+	0.992153i	$0.460098\pi$
$788$	43.1431	1.53691
$789$	29.5180	1.05087
$790$	−2.78880	−0.0992209
$791$	3.16068	0.112381
$792$	0.662140	0.0235281
$793$	−1.19712	−0.0425108
$794$	−10.8978	−0.386747
$795$	−2.80138	−0.0993546
$796$	−4.91554	−0.174227
$797$	−14.6449	−0.518749	−0.259374	−	0.965777i	$-0.583516\pi$
$797$	−14.6449	−0.518749	−0.259374	+	0.965777i	$0.583516\pi$
$798$	0.865710	0.0306458
$799$	−4.40715	−0.155914
$800$	−3.61081	−0.127661
$801$	0.0529458	0.00187075
$802$	−6.97689	−0.246363
$803$	−2.73546	−0.0965322
$804$	26.1828	0.923396
$805$	−7.35646	−0.259281
$806$	0.323092	0.0113804
$807$	−23.8940	−0.841108
$808$	−11.6231	−0.408900
$809$	−36.3824	−1.27914	−0.639568	−	0.768735i	$-0.720887\pi$
$809$	−36.3824	−1.27914	−0.639568	+	0.768735i	$0.720887\pi$
$810$	0.323092	0.0113523
$811$	53.1139	1.86508	0.932540	−	0.361066i	$-0.117587\pi$
$811$	53.1139	1.86508	0.932540	+	0.361066i	$0.117587\pi$
$812$	−19.8462	−0.696464
$813$	−28.8605	−1.01218
$814$	−0.403272	−0.0141347
$815$	8.60080	0.301273
$816$	−1.51687	−0.0531011
$817$	0.520607	0.0182137
$818$	−6.90445	−0.241409
$819$	−1.90658	−0.0666212
$820$	15.1912	0.530499
$821$	−46.0351	−1.60664	−0.803318	−	0.595550i	$-0.796934\pi$
$821$	−46.0351	−1.60664	−0.803318	+	0.595550i	$0.796934\pi$
$822$	2.43902	0.0850706
$823$	−26.2525	−0.915103	−0.457552	−	0.889183i	$-0.651273\pi$
$823$	−26.2525	−0.915103	−0.457552	+	0.889183i	$0.651273\pi$
$824$	21.3622	0.744187
$825$	−0.526075	−0.0183156
$826$	−0.743090	−0.0258554
$827$	−53.2892	−1.85305	−0.926524	−	0.376236i	$-0.877218\pi$
$827$	−53.2892	−1.85305	−0.926524	+	0.376236i	$0.877218\pi$
$828$	−7.31415	−0.254184
$829$	53.5867	1.86114	0.930571	−	0.366112i	$-0.119311\pi$
$829$	53.5867	1.86114	0.930571	+	0.366112i	$0.119311\pi$
$830$	−4.08937	−0.141944
$831$	−22.7807	−0.790254
$832$	5.60250	0.194232
$833$	−1.50809	−0.0522521
$834$	−3.01303	−0.104333
$835$	6.78853	0.234927
$836$	−1.40148	−0.0484713
$837$	−1.00000	−0.0345651
$838$	0.0577552	0.00199512
$839$	8.56642	0.295746	0.147873	−	0.989006i	$-0.452757\pi$
$839$	8.56642	0.295746	0.147873	+	0.989006i	$0.452757\pi$
$840$	2.39970	0.0827974
$841$	1.15408	0.0397959
$842$	0.0854727	0.00294558
$843$	7.19792	0.247910
$844$	22.5437	0.775987
$845$	−1.00000	−0.0344010
$846$	3.17716	0.109233
$847$	−20.4447	−0.702488
$848$	−9.48144	−0.325594
$849$	−19.0325	−0.653195
$850$	−0.144801	−0.00496664
$851$	9.15457	0.313815
$852$	8.82832	0.302453
$853$	−1.14065	−0.0390553	−0.0195276	−	0.999809i	$-0.506216\pi$
$853$	−1.14065	−0.0390553	−0.0195276	+	0.999809i	$0.506216\pi$
$854$	−0.737424	−0.0252341
$855$	−1.40537	−0.0480627
$856$	−0.0965093	−0.00329862
$857$	−3.23059	−0.110355	−0.0551773	−	0.998477i	$-0.517572\pi$
$857$	−3.23059	−0.110355	−0.0551773	+	0.998477i	$0.517572\pi$
$858$	−0.169971	−0.00580271
$859$	21.8452	0.745350	0.372675	−	0.927962i	$-0.378441\pi$
$859$	21.8452	0.745350	0.372675	+	0.927962i	$0.378441\pi$
$860$	0.702212	0.0239452
$861$	−15.2791	−0.520709
$862$	−6.54948	−0.223076
$863$	−32.2303	−1.09713	−0.548565	−	0.836108i	$-0.684826\pi$
$863$	−32.2303	−1.09713	−0.548565	+	0.836108i	$0.684826\pi$
$864$	3.61081	0.122842
$865$	−4.16551	−0.141632
$866$	−11.6713	−0.396606
$867$	16.7991	0.570529
$868$	−3.61413	−0.122672
$869$	−4.54085	−0.154038
$870$	−1.77419	−0.0601506
$871$	−13.8123	−0.468013
$872$	5.46005	0.184901
$873$	−3.83879	−0.129923
$874$	−1.75199	−0.0592621
$875$	−1.90658	−0.0644541
$876$	−9.85671	−0.333027
$877$	−2.05558	−0.0694120	−0.0347060	−	0.999398i	$-0.511049\pi$
$877$	−2.05558	−0.0694120	−0.0347060	+	0.999398i	$0.511049\pi$
$878$	−11.0786	−0.373884
$879$	−9.76271	−0.329288
$880$	−1.78053	−0.0600218
$881$	51.8353	1.74637	0.873187	−	0.487385i	$-0.162049\pi$
$881$	51.8353	1.74637	0.873187	+	0.487385i	$0.162049\pi$
$882$	1.08719	0.0366078
$883$	−53.6198	−1.80445	−0.902225	−	0.431265i	$-0.858067\pi$
$883$	−53.6198	−1.80445	−0.902225	+	0.431265i	$0.858067\pi$
$884$	0.849562	0.0285738
$885$	1.20631	0.0405498
$886$	−7.52873	−0.252932
$887$	−27.3927	−0.919758	−0.459879	−	0.887982i	$-0.652107\pi$
$887$	−27.3927	−0.919758	−0.459879	+	0.887982i	$0.652107\pi$
$888$	−2.98625	−0.100212
$889$	10.6462	0.357063
$890$	0.0171064	0.000573408 0
$891$	0.526075	0.0176242
$892$	−1.21725	−0.0407567
$893$	−13.8199	−0.462464
$894$	−5.05261	−0.168985
$895$	−4.84454	−0.161935
$896$	17.2197	0.575271
$897$	3.85847	0.128830
$898$	−9.20808	−0.307278
$899$	5.49127	0.183144
$900$	−1.89561	−0.0631870
$901$	−1.25550	−0.0418268
$902$	−1.36212	−0.0453538
$903$	−0.706274	−0.0235033
$904$	2.08655	0.0693976
$905$	−18.8758	−0.627452
$906$	1.23083	0.0408917
$907$	46.9153	1.55780	0.778898	−	0.627151i	$-0.215779\pi$
$907$	46.9153	1.55780	0.778898	+	0.627151i	$0.215779\pi$
$908$	−7.80151	−0.258902
$909$	−9.23464	−0.306294
$910$	−0.616000	−0.0204202
$911$	−12.7546	−0.422579	−0.211290	−	0.977423i	$-0.567766\pi$
$911$	−12.7546	−0.422579	−0.211290	+	0.977423i	$0.567766\pi$
$912$	−4.75657	−0.157506
$913$	−6.65851	−0.220364
$914$	6.32604	0.209247
$915$	1.19712	0.0395754
$916$	1.73440	0.0573063
$917$	7.97170	0.263249
$918$	0.144801	0.00477915
$919$	−11.6249	−0.383470	−0.191735	−	0.981447i	$-0.561411\pi$
$919$	−11.6249	−0.383470	−0.191735	+	0.981447i	$0.561411\pi$
$920$	−4.85643	−0.160112
$921$	−17.3835	−0.572807
$922$	−3.18345	−0.104841
$923$	−4.65724	−0.153295
$924$	1.90130	0.0625482
$925$	2.37259	0.0780104
$926$	−11.0760	−0.363981
$927$	16.9724	0.557447
$928$	−19.8280	−0.650884
$929$	13.2818	0.435762	0.217881	−	0.975975i	$-0.430085\pi$
$929$	13.2818	0.435762	0.217881	+	0.975975i	$0.430085\pi$
$930$	−0.323092	−0.0105946
$931$	−4.72903	−0.154988
$932$	−17.1792	−0.562725
$933$	−6.36654	−0.208431
$934$	−6.11222	−0.199998
$935$	−0.235772	−0.00771058
$936$	−1.25864	−0.0411400
$937$	−41.3794	−1.35181	−0.675903	−	0.736990i	$-0.736246\pi$
$937$	−41.3794	−1.35181	−0.675903	+	0.736990i	$0.736246\pi$
$938$	−8.50839	−0.277809
$939$	24.2427	0.791132
$940$	−18.6407	−0.607992
$941$	−2.26516	−0.0738421	−0.0369210	−	0.999318i	$-0.511755\pi$
$941$	−2.26516	−0.0738421	−0.0369210	+	0.999318i	$0.511755\pi$
$942$	6.26128	0.204003
$943$	30.9212	1.00693
$944$	4.08285	0.132885
$945$	1.90658	0.0620209
$946$	−0.0629641	−0.00204714
$947$	4.98852	0.162105	0.0810526	−	0.996710i	$-0.474172\pi$
$947$	4.98852	0.162105	0.0810526	+	0.996710i	$0.474172\pi$
$948$	−16.3621	−0.531416
$949$	5.19975	0.168791
$950$	−0.454065	−0.0147318
$951$	−17.5038	−0.567598
$952$	1.07548	0.0348565
$953$	−39.7539	−1.28776	−0.643878	−	0.765128i	$-0.722675\pi$
$953$	−39.7539	−1.28776	−0.643878	+	0.765128i	$0.722675\pi$
$954$	0.905103	0.0293038
$955$	−2.49898	−0.0808652
$956$	42.6973	1.38093
$957$	−2.88882	−0.0933823
$958$	4.71478	0.152328
$959$	14.3927	0.464765
$960$	−5.60250	−0.180820
$961$	1.00000	0.0322581
$962$	0.766567	0.0247151
$963$	−0.0766773	−0.00247089
$964$	−48.0233	−1.54673
$965$	14.5751	0.469188
$966$	2.37682	0.0764728
$967$	−9.78691	−0.314726	−0.157363	−	0.987541i	$-0.550299\pi$
$967$	−9.78691	−0.314726	−0.157363	+	0.987541i	$0.550299\pi$
$968$	−13.4967	−0.433801
$969$	−0.629850	−0.0202337
$970$	−1.24028	−0.0398231
$971$	15.0141	0.481826	0.240913	−	0.970547i	$-0.422553\pi$
$971$	15.0141	0.481826	0.240913	+	0.970547i	$0.422553\pi$
$972$	1.89561	0.0608018
$973$	−17.7800	−0.569999
$974$	−4.07248	−0.130491
$975$	1.00000	0.0320256
$976$	4.05172	0.129692
$977$	8.01930	0.256560	0.128280	−	0.991738i	$-0.459054\pi$
$977$	8.01930	0.256560	0.128280	+	0.991738i	$0.459054\pi$
$978$	−2.77885	−0.0888579
$979$	0.0278535	0.000890200 0
$980$	−6.37867	−0.203759
$981$	4.33805	0.138503
$982$	6.12176	0.195353
$983$	11.5263	0.367632	0.183816	−	0.982961i	$-0.441155\pi$
$983$	11.5263	0.367632	0.183816	+	0.982961i	$0.441155\pi$
$984$	−10.0866	−0.321549
$985$	22.7595	0.725177
$986$	−0.795143	−0.0253225
$987$	18.7485	0.596772
$988$	2.66404	0.0847544
$989$	1.42933	0.0454502
$990$	0.169971	0.00540202
$991$	−3.67496	−0.116739	−0.0583695	−	0.998295i	$-0.518590\pi$
$991$	−3.67496	−0.116739	−0.0583695	+	0.998295i	$0.518590\pi$
$992$	−3.61081	−0.114643
$993$	−30.1459	−0.956650
$994$	−2.86886	−0.0909948
$995$	−2.59312	−0.0822073
$996$	−23.9927	−0.760237
$997$	16.2794	0.515574	0.257787	−	0.966202i	$-0.417007\pi$
$997$	16.2794	0.515574	0.257787	+	0.966202i	$0.417007\pi$
$998$	−12.0081	−0.380109
$999$	−2.37259	−0.0750655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bg.1.9	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bg.1.9	✓	16	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)

\(f(q)\)	\(=\)	\(q-0.323092 q^{2} -1.00000 q^{3} -1.89561 q^{4} -1.00000 q^{5} +0.323092 q^{6} +1.90658 q^{7} +1.25864 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.323092 q^{2} -1.00000 q^{3} -1.89561 q^{4} -1.00000 q^{5} +0.323092 q^{6} +1.90658 q^{7} +1.25864 q^{8} +1.00000 q^{9} +0.323092 q^{10} +0.526075 q^{11} +1.89561 q^{12} -1.00000 q^{13} -0.616000 q^{14} +1.00000 q^{15} +3.38456 q^{16} +0.448173 q^{17} -0.323092 q^{18} +1.40537 q^{19} +1.89561 q^{20} -1.90658 q^{21} -0.169971 q^{22} +3.85847 q^{23} -1.25864 q^{24} +1.00000 q^{25} +0.323092 q^{26} -1.00000 q^{27} -3.61413 q^{28} +5.49127 q^{29} -0.323092 q^{30} +1.00000 q^{31} -3.61081 q^{32} -0.526075 q^{33} -0.144801 q^{34} -1.90658 q^{35} -1.89561 q^{36} +2.37259 q^{37} -0.454065 q^{38} +1.00000 q^{39} -1.25864 q^{40} +8.01387 q^{41} +0.616000 q^{42} +0.370441 q^{43} -0.997233 q^{44} -1.00000 q^{45} -1.24664 q^{46} -9.83360 q^{47} -3.38456 q^{48} -3.36497 q^{49} -0.323092 q^{50} -0.448173 q^{51} +1.89561 q^{52} -2.80138 q^{53} +0.323092 q^{54} -0.526075 q^{55} +2.39970 q^{56} -1.40537 q^{57} -1.77419 q^{58} +1.20631 q^{59} -1.89561 q^{60} +1.19712 q^{61} -0.323092 q^{62} +1.90658 q^{63} -5.60250 q^{64} +1.00000 q^{65} +0.169971 q^{66} +13.8123 q^{67} -0.849562 q^{68} -3.85847 q^{69} +0.616000 q^{70} +4.65724 q^{71} +1.25864 q^{72} -5.19975 q^{73} -0.766567 q^{74} -1.00000 q^{75} -2.66404 q^{76} +1.00300 q^{77} -0.323092 q^{78} -8.63157 q^{79} -3.38456 q^{80} +1.00000 q^{81} -2.58922 q^{82} -12.6570 q^{83} +3.61413 q^{84} -0.448173 q^{85} -0.119687 q^{86} -5.49127 q^{87} +0.662140 q^{88} +0.0529458 q^{89} +0.323092 q^{90} -1.90658 q^{91} -7.31415 q^{92} -1.00000 q^{93} +3.17716 q^{94} -1.40537 q^{95} +3.61081 q^{96} -3.83879 q^{97} +1.08719 q^{98} +0.526075 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} - 16 q^{3} + 26 q^{4} - 16 q^{5} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 - 16 * q^3 + 26 * q^4 - 16 * q^5 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 16 * q^9	\( 16 q - 2 q^{2} - 16 q^{3} + 26 q^{4} - 16 q^{5} + 2 q^{6} - 2 q^{7} - 9 q^{8} + 16 q^{9} + 2 q^{10} + 3 q^{11} - 26 q^{12} - 16 q^{13} - 5 q^{14} + 16 q^{15} + 38 q^{16} - 13 q^{17} - 2 q^{18} - 26 q^{20} + 2 q^{21} + q^{22} - 15 q^{23} + 9 q^{24} + 16 q^{25} + 2 q^{26} - 16 q^{27} + 8 q^{28} - 4 q^{29} - 2 q^{30} + 16 q^{31} - 30 q^{32} - 3 q^{33} + 29 q^{34} + 2 q^{35} + 26 q^{36} + 12 q^{37} + 16 q^{39} + 9 q^{40} - 12 q^{41} + 5 q^{42} - 7 q^{43} - 13 q^{44} - 16 q^{45} + 14 q^{46} + 17 q^{47} - 38 q^{48} + 16 q^{49} - 2 q^{50} + 13 q^{51} - 26 q^{52} - 36 q^{53} + 2 q^{54} - 3 q^{55} + 41 q^{56} + 16 q^{58} + 53 q^{59} + 26 q^{60} + 34 q^{61} - 2 q^{62} - 2 q^{63} + 79 q^{64} + 16 q^{65} - q^{66} - 13 q^{67} - 39 q^{68} + 15 q^{69} + 5 q^{70} - 11 q^{71} - 9 q^{72} + 34 q^{73} - 12 q^{74} - 16 q^{75} + 86 q^{76} - 32 q^{77} - 2 q^{78} - 7 q^{79} - 38 q^{80} + 16 q^{81} + 27 q^{82} - 28 q^{83} - 8 q^{84} + 13 q^{85} + 38 q^{86} + 4 q^{87} + 23 q^{88} - 8 q^{89} + 2 q^{90} + 2 q^{91} - 71 q^{92} - 16 q^{93} + 66 q^{94} + 30 q^{96} + 4 q^{97} + 22 q^{98} + 3 q^{99}+O(q^{100}) \) 16 * q - 2 * q^2 - 16 * q^3 + 26 * q^4 - 16 * q^5 + 2 * q^6 - 2 * q^7 - 9 * q^8 + 16 * q^9 + 2 * q^10 + 3 * q^11 - 26 * q^12 - 16 * q^13 - 5 * q^14 + 16 * q^15 + 38 * q^16 - 13 * q^17 - 2 * q^18 - 26 * q^20 + 2 * q^21 + q^22 - 15 * q^23 + 9 * q^24 + 16 * q^25 + 2 * q^26 - 16 * q^27 + 8 * q^28 - 4 * q^29 - 2 * q^30 + 16 * q^31 - 30 * q^32 - 3 * q^33 + 29 * q^34 + 2 * q^35 + 26 * q^36 + 12 * q^37 + 16 * q^39 + 9 * q^40 - 12 * q^41 + 5 * q^42 - 7 * q^43 - 13 * q^44 - 16 * q^45 + 14 * q^46 + 17 * q^47 - 38 * q^48 + 16 * q^49 - 2 * q^50 + 13 * q^51 - 26 * q^52 - 36 * q^53 + 2 * q^54 - 3 * q^55 + 41 * q^56 + 16 * q^58 + 53 * q^59 + 26 * q^60 + 34 * q^61 - 2 * q^62 - 2 * q^63 + 79 * q^64 + 16 * q^65 - q^66 - 13 * q^67 - 39 * q^68 + 15 * q^69 + 5 * q^70 - 11 * q^71 - 9 * q^72 + 34 * q^73 - 12 * q^74 - 16 * q^75 + 86 * q^76 - 32 * q^77 - 2 * q^78 - 7 * q^79 - 38 * q^80 + 16 * q^81 + 27 * q^82 - 28 * q^83 - 8 * q^84 + 13 * q^85 + 38 * q^86 + 4 * q^87 + 23 * q^88 - 8 * q^89 + 2 * q^90 + 2 * q^91 - 71 * q^92 - 16 * q^93 + 66 * q^94 + 30 * q^96 + 4 * q^97 + 22 * q^98 + 3 * q^99

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