LMFDB - Embedded newform 6042.2.a.bh.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6042,2,Mod(1,6042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6042, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6042 = 2 \cdot 3 \cdot 19 \cdot 53 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6042.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:	$48.2456129013$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 40 x^{11} + 123 x^{10} + 537 x^{9} - 1707 x^{8} - 2914 x^{7} + 9639 x^{6} + \cdots + 1200 $ x^13 - 3x^12 - 40x^11 + 123x^10 + 537x^9 - 1707x^8 - 2914x^7 + 9639x^6 + 6938x^5 - 22200x^4 - 9466x^3 + 16812x^2 + 9304x + 1200
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.23588$ of defining polynomial
Character	$\chi$	$=$	6042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.23588 q^{5} +1.00000 q^{6} +4.85906 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.23588 q^{5} +1.00000 q^{6} +4.85906 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.23588 q^{10} +1.06407 q^{11} +1.00000 q^{12} -2.53960 q^{13} +4.85906 q^{14} +2.23588 q^{15} +1.00000 q^{16} -3.65264 q^{17} +1.00000 q^{18} +1.00000 q^{19} +2.23588 q^{20} +4.85906 q^{21} +1.06407 q^{22} -8.06639 q^{23} +1.00000 q^{24} -0.000837091 q^{25} -2.53960 q^{26} +1.00000 q^{27} +4.85906 q^{28} -0.0513714 q^{29} +2.23588 q^{30} +3.50975 q^{31} +1.00000 q^{32} +1.06407 q^{33} -3.65264 q^{34} +10.8643 q^{35} +1.00000 q^{36} +11.3648 q^{37} +1.00000 q^{38} -2.53960 q^{39} +2.23588 q^{40} -6.26217 q^{41} +4.85906 q^{42} +10.3437 q^{43} +1.06407 q^{44} +2.23588 q^{45} -8.06639 q^{46} -5.04430 q^{47} +1.00000 q^{48} +16.6104 q^{49} -0.000837091 q^{50} -3.65264 q^{51} -2.53960 q^{52} -1.00000 q^{53} +1.00000 q^{54} +2.37914 q^{55} +4.85906 q^{56} +1.00000 q^{57} -0.0513714 q^{58} +1.29839 q^{59} +2.23588 q^{60} +6.47170 q^{61} +3.50975 q^{62} +4.85906 q^{63} +1.00000 q^{64} -5.67824 q^{65} +1.06407 q^{66} +7.68726 q^{67} -3.65264 q^{68} -8.06639 q^{69} +10.8643 q^{70} +1.08680 q^{71} +1.00000 q^{72} -4.88531 q^{73} +11.3648 q^{74} -0.000837091 q^{75} +1.00000 q^{76} +5.17038 q^{77} -2.53960 q^{78} -5.42609 q^{79} +2.23588 q^{80} +1.00000 q^{81} -6.26217 q^{82} +11.8940 q^{83} +4.85906 q^{84} -8.16686 q^{85} +10.3437 q^{86} -0.0513714 q^{87} +1.06407 q^{88} +13.1684 q^{89} +2.23588 q^{90} -12.3401 q^{91} -8.06639 q^{92} +3.50975 q^{93} -5.04430 q^{94} +2.23588 q^{95} +1.00000 q^{96} -16.5336 q^{97} +16.6104 q^{98} +1.06407 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.23588	0.999916	0.499958	−	0.866050i	$-0.333349\pi$
$5$	2.23588	0.999916	0.499958	+	0.866050i	$0.333349\pi$
$6$	1.00000	0.408248
$7$	4.85906	1.83655	0.918276	−	0.395942i	$-0.129582\pi$
$7$	4.85906	1.83655	0.918276	+	0.395942i	$0.129582\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.23588	0.707048
$11$	1.06407	0.320829	0.160415	−	0.987050i	$-0.448717\pi$
$11$	1.06407	0.320829	0.160415	+	0.987050i	$0.448717\pi$
$12$	1.00000	0.288675
$13$	−2.53960	−0.704358	−0.352179	−	0.935933i	$-0.614559\pi$
$13$	−2.53960	−0.704358	−0.352179	+	0.935933i	$0.614559\pi$
$14$	4.85906	1.29864
$15$	2.23588	0.577302
$16$	1.00000	0.250000
$17$	−3.65264	−0.885895	−0.442947	−	0.896548i	$-0.646067\pi$
$17$	−3.65264	−0.885895	−0.442947	+	0.896548i	$0.646067\pi$
$18$	1.00000	0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	2.23588	0.499958
$21$	4.85906	1.06033
$22$	1.06407	0.226861
$23$	−8.06639	−1.68196	−0.840980	−	0.541067i	$-0.818021\pi$
$23$	−8.06639	−1.68196	−0.840980	+	0.541067i	$0.818021\pi$
$24$	1.00000	0.204124
$25$	−0.000837091 0	−0.000167418 0
$26$	−2.53960	−0.498057
$27$	1.00000	0.192450
$28$	4.85906	0.918276
$29$	−0.0513714	−0.00953943	−0.00476972	−	0.999989i	$-0.501518\pi$
$29$	−0.0513714	−0.00953943	−0.00476972	+	0.999989i	$0.501518\pi$
$30$	2.23588	0.408214
$31$	3.50975	0.630370	0.315185	−	0.949030i	$-0.397933\pi$
$31$	3.50975	0.630370	0.315185	+	0.949030i	$0.397933\pi$
$32$	1.00000	0.176777
$33$	1.06407	0.185231
$34$	−3.65264	−0.626422
$35$	10.8643	1.83640
$36$	1.00000	0.166667
$37$	11.3648	1.86836	0.934179	−	0.356804i	$-0.116134\pi$
$37$	11.3648	1.86836	0.934179	+	0.356804i	$0.116134\pi$
$38$	1.00000	0.162221
$39$	−2.53960	−0.406662
$40$	2.23588	0.353524
$41$	−6.26217	−0.977987	−0.488993	−	0.872287i	$-0.662636\pi$
$41$	−6.26217	−0.977987	−0.488993	+	0.872287i	$0.662636\pi$
$42$	4.85906	0.749769
$43$	10.3437	1.57740	0.788699	−	0.614779i	$-0.210755\pi$
$43$	10.3437	1.57740	0.788699	+	0.614779i	$0.210755\pi$
$44$	1.06407	0.160415
$45$	2.23588	0.333305
$46$	−8.06639	−1.18932
$47$	−5.04430	−0.735787	−0.367893	−	0.929868i	$-0.619921\pi$
$47$	−5.04430	−0.735787	−0.367893	+	0.929868i	$0.619921\pi$
$48$	1.00000	0.144338
$49$	16.6104	2.37292
$50$	−0.000837091 0	−0.000118383 0
$51$	−3.65264	−0.511472
$52$	−2.53960	−0.352179
$53$	−1.00000	−0.137361
$53$	−1.00000	−0.137361
$54$	1.00000	0.136083
$55$	2.37914	0.320803
$56$	4.85906	0.649319
$57$	1.00000	0.132453
$58$	−0.0513714	−0.00674540
$59$	1.29839	0.169036	0.0845178	−	0.996422i	$-0.473065\pi$
$59$	1.29839	0.169036	0.0845178	+	0.996422i	$0.473065\pi$
$60$	2.23588	0.288651
$61$	6.47170	0.828616	0.414308	−	0.910137i	$-0.364024\pi$
$61$	6.47170	0.828616	0.414308	+	0.910137i	$0.364024\pi$
$62$	3.50975	0.445739
$63$	4.85906	0.612184
$64$	1.00000	0.125000
$65$	−5.67824	−0.704299
$66$	1.06407	0.130978
$67$	7.68726	0.939148	0.469574	−	0.882893i	$-0.344408\pi$
$67$	7.68726	0.939148	0.469574	+	0.882893i	$0.344408\pi$
$68$	−3.65264	−0.442947
$69$	−8.06639	−0.971080
$70$	10.8643	1.29853
$71$	1.08680	0.128980	0.0644900	−	0.997918i	$-0.479458\pi$
$71$	1.08680	0.128980	0.0644900	+	0.997918i	$0.479458\pi$
$72$	1.00000	0.117851
$73$	−4.88531	−0.571783	−0.285891	−	0.958262i	$-0.592290\pi$
$73$	−4.88531	−0.571783	−0.285891	+	0.958262i	$0.592290\pi$
$74$	11.3648	1.32113
$75$	−0.000837091 0	−9.66590e−5 0
$76$	1.00000	0.114708
$77$	5.17038	0.589220
$78$	−2.53960	−0.287553
$79$	−5.42609	−0.610483	−0.305241	−	0.952275i	$-0.598737\pi$
$79$	−5.42609	−0.610483	−0.305241	+	0.952275i	$0.598737\pi$
$80$	2.23588	0.249979
$81$	1.00000	0.111111
$82$	−6.26217	−0.691541
$83$	11.8940	1.30554	0.652770	−	0.757556i	$-0.273607\pi$
$83$	11.8940	1.30554	0.652770	+	0.757556i	$0.273607\pi$
$84$	4.85906	0.530167
$85$	−8.16686	−0.885821
$86$	10.3437	1.11539
$87$	−0.0513714	−0.00550759
$88$	1.06407	0.113430
$89$	13.1684	1.39585	0.697925	−	0.716171i	$-0.254107\pi$
$89$	13.1684	1.39585	0.697925	+	0.716171i	$0.254107\pi$
$90$	2.23588	0.235683
$91$	−12.3401	−1.29359
$92$	−8.06639	−0.840980
$93$	3.50975	0.363944
$94$	−5.04430	−0.520280
$95$	2.23588	0.229397
$96$	1.00000	0.102062
$97$	−16.5336	−1.67873	−0.839365	−	0.543568i	$-0.817073\pi$
$97$	−16.5336	−1.67873	−0.839365	+	0.543568i	$0.817073\pi$
$98$	16.6104	1.67791
$99$	1.06407	0.106943
$100$	−0.000837091 0	−8.37091e−5 0
$101$	6.11117	0.608084	0.304042	−	0.952659i	$-0.401664\pi$
$101$	6.11117	0.608084	0.304042	+	0.952659i	$0.401664\pi$
$102$	−3.65264	−0.361665
$103$	4.78335	0.471318	0.235659	−	0.971836i	$-0.424275\pi$
$103$	4.78335	0.471318	0.235659	+	0.971836i	$0.424275\pi$
$104$	−2.53960	−0.249028
$105$	10.8643	1.06024
$106$	−1.00000	−0.0971286
$107$	10.7437	1.03864	0.519318	−	0.854581i	$-0.326186\pi$
$107$	10.7437	1.03864	0.519318	+	0.854581i	$0.326186\pi$
$108$	1.00000	0.0962250
$109$	11.2034	1.07309	0.536547	−	0.843871i	$-0.319729\pi$
$109$	11.2034	1.07309	0.536547	+	0.843871i	$0.319729\pi$
$110$	2.37914	0.226842
$111$	11.3648	1.07870
$112$	4.85906	0.459138
$113$	−15.6355	−1.47087	−0.735433	−	0.677597i	$-0.763021\pi$
$113$	−15.6355	−1.47087	−0.735433	+	0.677597i	$0.763021\pi$
$114$	1.00000	0.0936586
$115$	−18.0355	−1.68182
$116$	−0.0513714	−0.00476972
$117$	−2.53960	−0.234786
$118$	1.29839	0.119526
$119$	−17.7484	−1.62699
$120$	2.23588	0.204107
$121$	−9.86775	−0.897068
$122$	6.47170	0.585920
$123$	−6.26217	−0.564641
$124$	3.50975	0.315185
$125$	−11.1813	−1.00008
$126$	4.85906	0.432879
$127$	−8.03040	−0.712583	−0.356292	−	0.934375i	$-0.615959\pi$
$127$	−8.03040	−0.712583	−0.356292	+	0.934375i	$0.615959\pi$
$128$	1.00000	0.0883883
$129$	10.3437	0.910711
$130$	−5.67824	−0.498015
$131$	6.91097	0.603814	0.301907	−	0.953337i	$-0.402377\pi$
$131$	6.91097	0.603814	0.301907	+	0.953337i	$0.402377\pi$
$132$	1.06407	0.0926155
$133$	4.85906	0.421334
$134$	7.68726	0.664078
$135$	2.23588	0.192434
$136$	−3.65264	−0.313211
$137$	−10.8110	−0.923647	−0.461823	−	0.886972i	$-0.652805\pi$
$137$	−10.8110	−0.923647	−0.461823	+	0.886972i	$0.652805\pi$
$138$	−8.06639	−0.686657
$139$	−20.3171	−1.72327	−0.861636	−	0.507527i	$-0.830560\pi$
$139$	−20.3171	−1.72327	−0.861636	+	0.507527i	$0.830560\pi$
$140$	10.8643	0.918199
$141$	−5.04430	−0.424807
$142$	1.08680	0.0912026
$143$	−2.70232	−0.225979
$144$	1.00000	0.0833333
$145$	−0.114860	−0.00953863
$146$	−4.88531	−0.404311
$147$	16.6104	1.37001
$148$	11.3648	0.934179
$149$	−4.03479	−0.330543	−0.165272	−	0.986248i	$-0.552850\pi$
$149$	−4.03479	−0.330543	−0.165272	+	0.986248i	$0.552850\pi$
$150$	−0.000837091 0	−6.83482e−5 0
$151$	11.0224	0.896989	0.448494	−	0.893786i	$-0.351960\pi$
$151$	11.0224	0.896989	0.448494	+	0.893786i	$0.351960\pi$
$152$	1.00000	0.0811107
$153$	−3.65264	−0.295298
$154$	5.17038	0.416641
$155$	7.84738	0.630317
$156$	−2.53960	−0.203331
$157$	5.89391	0.470385	0.235193	−	0.971949i	$-0.424428\pi$
$157$	5.89391	0.470385	0.235193	+	0.971949i	$0.424428\pi$
$158$	−5.42609	−0.431676
$159$	−1.00000	−0.0793052
$160$	2.23588	0.176762
$161$	−39.1951	−3.08900
$162$	1.00000	0.0785674
$163$	−6.87088	−0.538169	−0.269084	−	0.963117i	$-0.586721\pi$
$163$	−6.87088	−0.538169	−0.269084	+	0.963117i	$0.586721\pi$
$164$	−6.26217	−0.488993
$165$	2.37914	0.185215
$166$	11.8940	0.923156
$167$	−15.3972	−1.19147	−0.595736	−	0.803180i	$-0.703140\pi$
$167$	−15.3972	−1.19147	−0.595736	+	0.803180i	$0.703140\pi$
$168$	4.85906	0.374884
$169$	−6.55043	−0.503879
$170$	−8.16686	−0.626370
$171$	1.00000	0.0764719
$172$	10.3437	0.788699
$173$	−6.95267	−0.528602	−0.264301	−	0.964440i	$-0.585141\pi$
$173$	−6.95267	−0.528602	−0.264301	+	0.964440i	$0.585141\pi$
$174$	−0.0513714	−0.00389446
$175$	−0.00406748	−0.000307472 0
$176$	1.06407	0.0802074
$177$	1.29839	0.0975928
$178$	13.1684	0.987015
$179$	−1.36082	−0.101712	−0.0508562	−	0.998706i	$-0.516195\pi$
$179$	−1.36082	−0.101712	−0.0508562	+	0.998706i	$0.516195\pi$
$180$	2.23588	0.166653
$181$	−9.29349	−0.690780	−0.345390	−	0.938459i	$-0.612253\pi$
$181$	−9.29349	−0.690780	−0.345390	+	0.938459i	$0.612253\pi$
$182$	−12.3401	−0.914707
$183$	6.47170	0.478402
$184$	−8.06639	−0.594662
$185$	25.4103	1.86820
$186$	3.50975	0.257347
$187$	−3.88667	−0.284221
$188$	−5.04430	−0.367893
$189$	4.85906	0.353444
$190$	2.23588	0.162208
$191$	−22.4262	−1.62270	−0.811350	−	0.584561i	$-0.801267\pi$
$191$	−22.4262	−1.62270	−0.811350	+	0.584561i	$0.801267\pi$
$192$	1.00000	0.0721688
$193$	−8.66625	−0.623810	−0.311905	−	0.950113i	$-0.600967\pi$
$193$	−8.66625	−0.623810	−0.311905	+	0.950113i	$0.600967\pi$
$194$	−16.5336	−1.18704
$195$	−5.67824	−0.406628
$196$	16.6104	1.18646
$197$	−9.64356	−0.687075	−0.343537	−	0.939139i	$-0.611625\pi$
$197$	−9.64356	−0.687075	−0.343537	+	0.939139i	$0.611625\pi$
$198$	1.06407	0.0756202
$199$	21.2489	1.50629	0.753147	−	0.657852i	$-0.228535\pi$
$199$	21.2489	1.50629	0.753147	+	0.657852i	$0.228535\pi$
$200$	−0.000837091 0	−5.91913e−5 0
$201$	7.68726	0.542217
$202$	6.11117	0.429981
$203$	−0.249617	−0.0175197
$204$	−3.65264	−0.255736
$205$	−14.0015	−0.977905
$206$	4.78335	0.333272
$207$	−8.06639	−0.560653
$208$	−2.53960	−0.176090
$209$	1.06407	0.0736033
$210$	10.8643	0.749706
$211$	−0.701469	−0.0482911	−0.0241455	−	0.999708i	$-0.507687\pi$
$211$	−0.701469	−0.0482911	−0.0241455	+	0.999708i	$0.507687\pi$
$212$	−1.00000	−0.0686803
$213$	1.08680	0.0744666
$214$	10.7437	0.734427
$215$	23.1273	1.57727
$216$	1.00000	0.0680414
$217$	17.0541	1.15771
$218$	11.2034	0.758792
$219$	−4.88531	−0.330119
$220$	2.37914	0.160401
$221$	9.27624	0.623987
$222$	11.3648	0.762754
$223$	14.8513	0.994514	0.497257	−	0.867603i	$-0.334341\pi$
$223$	14.8513	0.994514	0.497257	+	0.867603i	$0.334341\pi$
$224$	4.85906	0.324659
$225$	−0.000837091 0	−5.58061e−5 0
$226$	−15.6355	−1.04006
$227$	−9.72397	−0.645402	−0.322701	−	0.946501i	$-0.604591\pi$
$227$	−9.72397	−0.645402	−0.322701	+	0.946501i	$0.604591\pi$
$228$	1.00000	0.0662266
$229$	−25.8189	−1.70616	−0.853079	−	0.521782i	$-0.825268\pi$
$229$	−25.8189	−1.70616	−0.853079	+	0.521782i	$0.825268\pi$
$230$	−18.0355	−1.18923
$231$	5.17038	0.340186
$232$	−0.0513714	−0.00337270
$233$	−6.71392	−0.439843	−0.219922	−	0.975518i	$-0.570580\pi$
$233$	−6.71392	−0.439843	−0.219922	+	0.975518i	$0.570580\pi$
$234$	−2.53960	−0.166019
$235$	−11.2785	−0.735725
$236$	1.29839	0.0845178
$237$	−5.42609	−0.352462
$238$	−17.7484	−1.15046
$239$	−7.39819	−0.478549	−0.239274	−	0.970952i	$-0.576910\pi$
$239$	−7.39819	−0.478549	−0.239274	+	0.970952i	$0.576910\pi$
$240$	2.23588	0.144325
$241$	−23.2465	−1.49744	−0.748720	−	0.662886i	$-0.769331\pi$
$241$	−23.2465	−1.49744	−0.748720	+	0.662886i	$0.769331\pi$
$242$	−9.86775	−0.634323
$243$	1.00000	0.0641500
$244$	6.47170	0.414308
$245$	37.1390	2.37272
$246$	−6.26217	−0.399261
$247$	−2.53960	−0.161591
$248$	3.50975	0.222869
$249$	11.8940	0.753754
$250$	−11.1813	−0.707166
$251$	16.9072	1.06717	0.533586	−	0.845746i	$-0.320844\pi$
$251$	16.9072	1.06717	0.533586	+	0.845746i	$0.320844\pi$
$252$	4.85906	0.306092
$253$	−8.58321	−0.539622
$254$	−8.03040	−0.503872
$255$	−8.16686	−0.511429
$256$	1.00000	0.0625000
$257$	14.3681	0.896257	0.448129	−	0.893969i	$-0.352091\pi$
$257$	14.3681	0.896257	0.448129	+	0.893969i	$0.352091\pi$
$258$	10.3437	0.643970
$259$	55.2221	3.43134
$260$	−5.67824	−0.352150
$261$	−0.0513714	−0.00317981
$262$	6.91097	0.426961
$263$	−7.56276	−0.466340	−0.233170	−	0.972436i	$-0.574910\pi$
$263$	−7.56276	−0.466340	−0.233170	+	0.972436i	$0.574910\pi$
$264$	1.06407	0.0654890
$265$	−2.23588	−0.137349
$266$	4.85906	0.297928
$267$	13.1684	0.805894
$268$	7.68726	0.469574
$269$	26.5234	1.61716	0.808580	−	0.588386i	$-0.200236\pi$
$269$	26.5234	1.61716	0.808580	+	0.588386i	$0.200236\pi$
$270$	2.23588	0.136071
$271$	−17.8970	−1.08717	−0.543583	−	0.839355i	$-0.682933\pi$
$271$	−17.8970	−1.08717	−0.543583	+	0.839355i	$0.682933\pi$
$272$	−3.65264	−0.221474
$273$	−12.3401	−0.746855
$274$	−10.8110	−0.653117
$275$	−0.000890725 0	−5.37127e−5 0
$276$	−8.06639	−0.485540
$277$	−11.7267	−0.704592	−0.352296	−	0.935889i	$-0.614599\pi$
$277$	−11.7267	−0.704592	−0.352296	+	0.935889i	$0.614599\pi$
$278$	−20.3171	−1.21854
$279$	3.50975	0.210123
$280$	10.8643	0.649265
$281$	−25.6489	−1.53008	−0.765042	−	0.643980i	$-0.777282\pi$
$281$	−25.6489	−1.53008	−0.765042	+	0.643980i	$0.777282\pi$
$282$	−5.04430	−0.300384
$283$	26.2814	1.56227	0.781133	−	0.624364i	$-0.214642\pi$
$283$	26.2814	1.56227	0.781133	+	0.624364i	$0.214642\pi$
$284$	1.08680	0.0644900
$285$	2.23588	0.132442
$286$	−2.70232	−0.159791
$287$	−30.4283	−1.79612
$288$	1.00000	0.0589256
$289$	−3.65824	−0.215191
$290$	−0.114860	−0.00674483
$291$	−16.5336	−0.969215
$292$	−4.88531	−0.285891
$293$	24.5815	1.43607	0.718034	−	0.696008i	$-0.245042\pi$
$293$	24.5815	1.43607	0.718034	+	0.696008i	$0.245042\pi$
$294$	16.6104	0.968741
$295$	2.90304	0.169022
$296$	11.3648	0.660564
$297$	1.06407	0.0617437
$298$	−4.03479	−0.233729
$299$	20.4854	1.18470
$300$	−0.000837091 0	−4.83295e−5 0
$301$	50.2606	2.89697
$302$	11.0224	0.634267
$303$	6.11117	0.351078
$304$	1.00000	0.0573539
$305$	14.4699	0.828546
$306$	−3.65264	−0.208807
$307$	−0.226648	−0.0129355	−0.00646775	−	0.999979i	$-0.502059\pi$
$307$	−0.226648	−0.0129355	−0.00646775	+	0.999979i	$0.502059\pi$
$308$	5.17038	0.294610
$309$	4.78335	0.272115
$310$	7.84738	0.445701
$311$	−24.9700	−1.41592	−0.707960	−	0.706253i	$-0.750384\pi$
$311$	−24.9700	−1.41592	−0.707960	+	0.706253i	$0.750384\pi$
$312$	−2.53960	−0.143777
$313$	5.47278	0.309340	0.154670	−	0.987966i	$-0.450569\pi$
$313$	5.47278	0.309340	0.154670	+	0.987966i	$0.450569\pi$
$314$	5.89391	0.332612
$315$	10.8643	0.612133
$316$	−5.42609	−0.305241
$317$	−15.5232	−0.871870	−0.435935	−	0.899978i	$-0.643582\pi$
$317$	−15.5232	−0.871870	−0.435935	+	0.899978i	$0.643582\pi$
$318$	−1.00000	−0.0560772
$319$	−0.0546628	−0.00306053
$320$	2.23588	0.124990
$321$	10.7437	0.599657
$322$	−39.1951	−2.18426
$323$	−3.65264	−0.203238
$324$	1.00000	0.0555556
$325$	0.00212588	0.000117922 0
$326$	−6.87088	−0.380543
$327$	11.2034	0.619551
$328$	−6.26217	−0.345771
$329$	−24.5105	−1.35131
$330$	2.37914	0.130967
$331$	−23.9671	−1.31735	−0.658675	−	0.752427i	$-0.728883\pi$
$331$	−23.9671	−1.31735	−0.658675	+	0.752427i	$0.728883\pi$
$332$	11.8940	0.652770
$333$	11.3648	0.622786
$334$	−15.3972	−0.842498
$335$	17.1878	0.939069
$336$	4.85906	0.265083
$337$	0.0592164	0.00322573	0.00161286	−	0.999999i	$-0.499487\pi$
$337$	0.0592164	0.00322573	0.00161286	+	0.999999i	$0.499487\pi$
$338$	−6.55043	−0.356296
$339$	−15.6355	−0.849205
$340$	−8.16686	−0.442910
$341$	3.73462	0.202241
$342$	1.00000	0.0540738
$343$	46.6977	2.52144
$344$	10.3437	0.557695
$345$	−18.0355	−0.970998
$346$	−6.95267	−0.373778
$347$	19.9759	1.07237	0.536183	−	0.844102i	$-0.319866\pi$
$347$	19.9759	1.07237	0.536183	+	0.844102i	$0.319866\pi$
$348$	−0.0513714	−0.00275380
$349$	−17.6321	−0.943822	−0.471911	−	0.881646i	$-0.656436\pi$
$349$	−17.6321	−0.943822	−0.471911	+	0.881646i	$0.656436\pi$
$350$	−0.00406748	−0.000217416 0
$351$	−2.53960	−0.135554
$352$	1.06407	0.0567152
$353$	−27.4761	−1.46241	−0.731203	−	0.682160i	$-0.761041\pi$
$353$	−27.4761	−1.46241	−0.731203	+	0.682160i	$0.761041\pi$
$354$	1.29839	0.0690085
$355$	2.42996	0.128969
$356$	13.1684	0.697925
$357$	−17.7484	−0.939344
$358$	−1.36082	−0.0719215
$359$	−17.4748	−0.922285	−0.461142	−	0.887326i	$-0.652560\pi$
$359$	−17.4748	−0.922285	−0.461142	+	0.887326i	$0.652560\pi$
$360$	2.23588	0.117841
$361$	1.00000	0.0526316
$362$	−9.29349	−0.488455
$363$	−9.86775	−0.517923
$364$	−12.3401	−0.646795
$365$	−10.9230	−0.571735
$366$	6.47170	0.338281
$367$	−25.0135	−1.30570	−0.652848	−	0.757489i	$-0.726426\pi$
$367$	−25.0135	−1.30570	−0.652848	+	0.757489i	$0.726426\pi$
$368$	−8.06639	−0.420490
$369$	−6.26217	−0.325996
$370$	25.4103	1.32102
$371$	−4.85906	−0.252270
$372$	3.50975	0.181972
$373$	1.12241	0.0581161	0.0290580	−	0.999578i	$-0.490749\pi$
$373$	1.12241	0.0581161	0.0290580	+	0.999578i	$0.490749\pi$
$374$	−3.88667	−0.200975
$375$	−11.1813	−0.577399
$376$	−5.04430	−0.260140
$377$	0.130463	0.00671918
$378$	4.85906	0.249923
$379$	18.3685	0.943527	0.471763	−	0.881725i	$-0.343618\pi$
$379$	18.3685	0.943527	0.471763	+	0.881725i	$0.343618\pi$
$380$	2.23588	0.114698
$381$	−8.03040	−0.411410
$382$	−22.4262	−1.14742
$383$	9.68991	0.495131	0.247566	−	0.968871i	$-0.420369\pi$
$383$	9.68991	0.495131	0.247566	+	0.968871i	$0.420369\pi$
$384$	1.00000	0.0510310
$385$	11.5604	0.589171
$386$	−8.66625	−0.441101
$387$	10.3437	0.525799
$388$	−16.5336	−0.839365
$389$	−9.22117	−0.467532	−0.233766	−	0.972293i	$-0.575105\pi$
$389$	−9.22117	−0.467532	−0.233766	+	0.972293i	$0.575105\pi$
$390$	−5.67824	−0.287529
$391$	29.4636	1.49004
$392$	16.6104	0.838954
$393$	6.91097	0.348612
$394$	−9.64356	−0.485835
$395$	−12.1321	−0.610431
$396$	1.06407	0.0534716
$397$	17.1401	0.860239	0.430120	−	0.902772i	$-0.358471\pi$
$397$	17.1401	0.860239	0.430120	+	0.902772i	$0.358471\pi$
$398$	21.2489	1.06511
$399$	4.85906	0.243257
$400$	−0.000837091 0	−4.18546e−5 0
$401$	20.6897	1.03319	0.516596	−	0.856229i	$-0.327199\pi$
$401$	20.6897	1.03319	0.516596	+	0.856229i	$0.327199\pi$
$402$	7.68726	0.383406
$403$	−8.91336	−0.444006
$404$	6.11117	0.304042
$405$	2.23588	0.111102
$406$	−0.249617	−0.0123883
$407$	12.0929	0.599424
$408$	−3.65264	−0.180832
$409$	−28.0306	−1.38602	−0.693012	−	0.720926i	$-0.743717\pi$
$409$	−28.0306	−1.38602	−0.693012	+	0.720926i	$0.743717\pi$
$410$	−14.0015	−0.691483
$411$	−10.8110	−0.533268
$412$	4.78335	0.235659
$413$	6.30894	0.310443
$414$	−8.06639	−0.396442
$415$	26.5936	1.30543
$416$	−2.53960	−0.124514
$417$	−20.3171	−0.994931
$418$	1.06407	0.0520454
$419$	−1.76135	−0.0860477	−0.0430239	−	0.999074i	$-0.513699\pi$
$419$	−1.76135	−0.0860477	−0.0430239	+	0.999074i	$0.513699\pi$
$420$	10.8643	0.530122
$421$	−16.9847	−0.827785	−0.413893	−	0.910326i	$-0.635831\pi$
$421$	−16.9847	−0.827785	−0.413893	+	0.910326i	$0.635831\pi$
$422$	−0.701469	−0.0341470
$423$	−5.04430	−0.245262
$424$	−1.00000	−0.0485643
$425$	0.00305759	0.000148315 0
$426$	1.08680	0.0526558
$427$	31.4464	1.52180
$428$	10.7437	0.519318
$429$	−2.70232	−0.130469
$430$	23.1273	1.11530
$431$	−19.3369	−0.931427	−0.465714	−	0.884935i	$-0.654202\pi$
$431$	−19.3369	−0.931427	−0.465714	+	0.884935i	$0.654202\pi$
$432$	1.00000	0.0481125
$433$	−8.38376	−0.402898	−0.201449	−	0.979499i	$-0.564565\pi$
$433$	−8.38376	−0.402898	−0.201449	+	0.979499i	$0.564565\pi$
$434$	17.0541	0.818622
$435$	−0.114860	−0.00550713
$436$	11.2034	0.536547
$437$	−8.06639	−0.385868
$438$	−4.88531	−0.233429
$439$	−4.81791	−0.229946	−0.114973	−	0.993369i	$-0.536678\pi$
$439$	−4.81791	−0.229946	−0.114973	+	0.993369i	$0.536678\pi$
$440$	2.37914	0.113421
$441$	16.6104	0.790974
$442$	9.27624	0.441226
$443$	9.88205	0.469510	0.234755	−	0.972055i	$-0.424571\pi$
$443$	9.88205	0.469510	0.234755	+	0.972055i	$0.424571\pi$
$444$	11.3648	0.539349
$445$	29.4430	1.39573
$446$	14.8513	0.703227
$447$	−4.03479	−0.190839
$448$	4.85906	0.229569
$449$	17.7645	0.838356	0.419178	−	0.907904i	$-0.362318\pi$
$449$	17.7645	0.838356	0.419178	+	0.907904i	$0.362318\pi$
$450$	−0.000837091 0	−3.94609e−5 0
$451$	−6.66340	−0.313767
$452$	−15.6355	−0.735433
$453$	11.0224	0.517877
$454$	−9.72397	−0.456368
$455$	−27.5909	−1.29348
$456$	1.00000	0.0468293
$457$	20.7090	0.968724	0.484362	−	0.874868i	$-0.339052\pi$
$457$	20.7090	0.968724	0.484362	+	0.874868i	$0.339052\pi$
$458$	−25.8189	−1.20644
$459$	−3.65264	−0.170491
$460$	−18.0355	−0.840909
$461$	23.1568	1.07852	0.539260	−	0.842139i	$-0.318704\pi$
$461$	23.1568	1.07852	0.539260	+	0.842139i	$0.318704\pi$
$462$	5.17038	0.240548
$463$	30.8927	1.43570	0.717852	−	0.696195i	$-0.245125\pi$
$463$	30.8927	1.43570	0.717852	+	0.696195i	$0.245125\pi$
$464$	−0.0513714	−0.00238486
$465$	7.84738	0.363914
$466$	−6.71392	−0.311016
$467$	−26.3616	−1.21987	−0.609934	−	0.792452i	$-0.708804\pi$
$467$	−26.3616	−1.21987	−0.609934	+	0.792452i	$0.708804\pi$
$468$	−2.53960	−0.117393
$469$	37.3528	1.72479
$470$	−11.2785	−0.520236
$471$	5.89391	0.271577
$472$	1.29839	0.0597631
$473$	11.0064	0.506076
$474$	−5.42609	−0.249228
$475$	−0.000837091 0	−3.84084e−5 0
$476$	−17.7484	−0.813496
$477$	−1.00000	−0.0457869
$478$	−7.39819	−0.338385
$479$	21.2464	0.970773	0.485387	−	0.874300i	$-0.338679\pi$
$479$	21.2464	0.970773	0.485387	+	0.874300i	$0.338679\pi$
$480$	2.23588	0.102054
$481$	−28.8620	−1.31599
$482$	−23.2465	−1.05885
$483$	−39.1951	−1.78344
$484$	−9.86775	−0.448534
$485$	−36.9671	−1.67859
$486$	1.00000	0.0453609
$487$	−7.54046	−0.341691	−0.170845	−	0.985298i	$-0.554650\pi$
$487$	−7.54046	−0.341691	−0.170845	+	0.985298i	$0.554650\pi$
$488$	6.47170	0.292960
$489$	−6.87088	−0.310712
$490$	37.1390	1.67777
$491$	15.6285	0.705302	0.352651	−	0.935755i	$-0.385280\pi$
$491$	15.6285	0.705302	0.352651	+	0.935755i	$0.385280\pi$
$492$	−6.26217	−0.282320
$493$	0.187641	0.00845093
$494$	−2.53960	−0.114262
$495$	2.37914	0.106934
$496$	3.50975	0.157592
$497$	5.28084	0.236878
$498$	11.8940	0.532985
$499$	18.4390	0.825444	0.412722	−	0.910857i	$-0.364578\pi$
$499$	18.4390	0.825444	0.412722	+	0.910857i	$0.364578\pi$
$500$	−11.1813	−0.500042
$501$	−15.3972	−0.687897
$502$	16.9072	0.754604
$503$	2.48547	0.110822	0.0554108	−	0.998464i	$-0.482353\pi$
$503$	2.48547	0.110822	0.0554108	+	0.998464i	$0.482353\pi$
$504$	4.85906	0.216440
$505$	13.6639	0.608033
$506$	−8.58321	−0.381570
$507$	−6.55043	−0.290915
$508$	−8.03040	−0.356292
$509$	3.73574	0.165584	0.0827919	−	0.996567i	$-0.473616\pi$
$509$	3.73574	0.165584	0.0827919	+	0.996567i	$0.473616\pi$
$510$	−8.16686	−0.361635
$511$	−23.7380	−1.05011
$512$	1.00000	0.0441942
$513$	1.00000	0.0441511
$514$	14.3681	0.633750
$515$	10.6950	0.471278
$516$	10.3437	0.455356
$517$	−5.36749	−0.236062
$518$	55.2221	2.42632
$519$	−6.95267	−0.305188
$520$	−5.67824	−0.249007
$521$	−7.01312	−0.307250	−0.153625	−	0.988129i	$-0.549095\pi$
$521$	−7.01312	−0.307250	−0.153625	+	0.988129i	$0.549095\pi$
$522$	−0.0513714	−0.00224847
$523$	40.9483	1.79054	0.895271	−	0.445522i	$-0.146982\pi$
$523$	40.9483	1.79054	0.895271	+	0.445522i	$0.146982\pi$
$524$	6.91097	0.301907
$525$	−0.00406748	−0.000177519 0
$526$	−7.56276	−0.329752
$527$	−12.8198	−0.558441
$528$	1.06407	0.0463077
$529$	42.0667	1.82899
$530$	−2.23588	−0.0971205
$531$	1.29839	0.0563452
$532$	4.85906	0.210667
$533$	15.9034	0.688853
$534$	13.1684	0.569853
$535$	24.0217	1.03855
$536$	7.68726	0.332039
$537$	−1.36082	−0.0587237
$538$	26.5234	1.14351
$539$	17.6747	0.761303
$540$	2.23588	0.0962170
$541$	11.1803	0.480677	0.240339	−	0.970689i	$-0.422742\pi$
$541$	11.1803	0.480677	0.240339	+	0.970689i	$0.422742\pi$
$542$	−17.8970	−0.768743
$543$	−9.29349	−0.398822
$544$	−3.65264	−0.156606
$545$	25.0495	1.07300
$546$	−12.3401	−0.528106
$547$	−29.5415	−1.26310	−0.631551	−	0.775334i	$-0.717581\pi$
$547$	−29.5415	−1.26310	−0.631551	+	0.775334i	$0.717581\pi$
$548$	−10.8110	−0.461823
$549$	6.47170	0.276205
$550$	−0.000890725 0	−3.79806e−5 0
$551$	−0.0513714	−0.00218850
$552$	−8.06639	−0.343328
$553$	−26.3657	−1.12118
$554$	−11.7267	−0.498221
$555$	25.4103	1.07861
$556$	−20.3171	−0.861636
$557$	−28.7161	−1.21674	−0.608370	−	0.793654i	$-0.708176\pi$
$557$	−28.7161	−1.21674	−0.608370	+	0.793654i	$0.708176\pi$
$558$	3.50975	0.148580
$559$	−26.2688	−1.11105
$560$	10.8643	0.459099
$561$	−3.88667	−0.164095
$562$	−25.6489	−1.08193
$563$	−7.17826	−0.302528	−0.151264	−	0.988493i	$-0.548334\pi$
$563$	−7.17826	−0.302528	−0.151264	+	0.988493i	$0.548334\pi$
$564$	−5.04430	−0.212403
$565$	−34.9592	−1.47074
$566$	26.2814	1.10469
$567$	4.85906	0.204061
$568$	1.08680	0.0456013
$569$	6.62618	0.277784	0.138892	−	0.990308i	$-0.455646\pi$
$569$	6.62618	0.277784	0.138892	+	0.990308i	$0.455646\pi$
$570$	2.23588	0.0936507
$571$	−28.8039	−1.20541	−0.602703	−	0.797965i	$-0.705910\pi$
$571$	−28.8039	−1.20541	−0.602703	+	0.797965i	$0.705910\pi$
$572$	−2.70232	−0.112989
$573$	−22.4262	−0.936866
$574$	−30.4283	−1.27005
$575$	0.00675231	0.000281591 0
$576$	1.00000	0.0416667
$577$	40.8738	1.70160	0.850799	−	0.525492i	$-0.176119\pi$
$577$	40.8738	1.70160	0.850799	+	0.525492i	$0.176119\pi$
$578$	−3.65824	−0.152163
$579$	−8.66625	−0.360157
$580$	−0.114860	−0.00476932
$581$	57.7938	2.39769
$582$	−16.5336	−0.685339
$583$	−1.06407	−0.0440693
$584$	−4.88531	−0.202156
$585$	−5.67824	−0.234766
$586$	24.5815	1.01545
$587$	−15.7361	−0.649498	−0.324749	−	0.945800i	$-0.605280\pi$
$587$	−15.7361	−0.649498	−0.324749	+	0.945800i	$0.605280\pi$
$588$	16.6104	0.685003
$589$	3.50975	0.144617
$590$	2.90304	0.119516
$591$	−9.64356	−0.396683
$592$	11.3648	0.467090
$593$	−8.58645	−0.352603	−0.176302	−	0.984336i	$-0.556413\pi$
$593$	−8.58645	−0.352603	−0.176302	+	0.984336i	$0.556413\pi$
$594$	1.06407	0.0436594
$595$	−39.6833	−1.62685
$596$	−4.03479	−0.165272
$597$	21.2489	0.869660
$598$	20.4854	0.837711
$599$	8.36467	0.341771	0.170886	−	0.985291i	$-0.445337\pi$
$599$	8.36467	0.341771	0.170886	+	0.985291i	$0.445337\pi$
$600$	−0.000837091 0	−3.41741e−5 0
$601$	−6.10638	−0.249084	−0.124542	−	0.992214i	$-0.539746\pi$
$601$	−6.10638	−0.249084	−0.124542	+	0.992214i	$0.539746\pi$
$602$	50.2606	2.04847
$603$	7.68726	0.313049
$604$	11.0224	0.448494
$605$	−22.0631	−0.896993
$606$	6.11117	0.248249
$607$	18.9633	0.769695	0.384848	−	0.922980i	$-0.374254\pi$
$607$	18.9633	0.769695	0.384848	+	0.922980i	$0.374254\pi$
$608$	1.00000	0.0405554
$609$	−0.249617	−0.0101150
$610$	14.4699	0.585871
$611$	12.8105	0.518258
$612$	−3.65264	−0.147649
$613$	14.4752	0.584648	0.292324	−	0.956319i	$-0.405571\pi$
$613$	14.4752	0.584648	0.292324	+	0.956319i	$0.405571\pi$
$614$	−0.226648	−0.00914678
$615$	−14.0015	−0.564594
$616$	5.17038	0.208321
$617$	14.8985	0.599793	0.299896	−	0.953972i	$-0.403048\pi$
$617$	14.8985	0.599793	0.299896	+	0.953972i	$0.403048\pi$
$618$	4.78335	0.192415
$619$	−28.8458	−1.15941	−0.579705	−	0.814826i	$-0.696832\pi$
$619$	−28.8458	−1.15941	−0.579705	+	0.814826i	$0.696832\pi$
$620$	7.84738	0.315158
$621$	−8.06639	−0.323693
$622$	−24.9700	−1.00121
$623$	63.9861	2.56355
$624$	−2.53960	−0.101665
$625$	−24.9958	−0.999833
$626$	5.47278	0.218736
$627$	1.06407	0.0424949
$628$	5.89391	0.235193
$629$	−41.5114	−1.65517
$630$	10.8643	0.432843
$631$	−16.3567	−0.651151	−0.325575	−	0.945516i	$-0.605558\pi$
$631$	−16.3567	−0.651151	−0.325575	+	0.945516i	$0.605558\pi$
$632$	−5.42609	−0.215838
$633$	−0.701469	−0.0278809
$634$	−15.5232	−0.616505
$635$	−17.9550	−0.712524
$636$	−1.00000	−0.0396526
$637$	−42.1839	−1.67139
$638$	−0.0546628	−0.00216412
$639$	1.08680	0.0429933
$640$	2.23588	0.0883809
$641$	42.5514	1.68068	0.840340	−	0.542060i	$-0.182355\pi$
$641$	42.5514	1.68068	0.840340	+	0.542060i	$0.182355\pi$
$642$	10.7437	0.424022
$643$	−23.7056	−0.934857	−0.467429	−	0.884031i	$-0.654820\pi$
$643$	−23.7056	−0.934857	−0.467429	+	0.884031i	$0.654820\pi$
$644$	−39.1951	−1.54450
$645$	23.1273	0.910635
$646$	−3.65264	−0.143711
$647$	−18.9433	−0.744736	−0.372368	−	0.928085i	$-0.621454\pi$
$647$	−18.9433	−0.744736	−0.372368	+	0.928085i	$0.621454\pi$
$648$	1.00000	0.0392837
$649$	1.38158	0.0542316
$650$	0.00212588	8.33838e−5 0
$651$	17.0541	0.668402
$652$	−6.87088	−0.269084
$653$	−10.6473	−0.416661	−0.208330	−	0.978059i	$-0.566803\pi$
$653$	−10.6473	−0.416661	−0.208330	+	0.978059i	$0.566803\pi$
$654$	11.2034	0.438089
$655$	15.4521	0.603764
$656$	−6.26217	−0.244497
$657$	−4.88531	−0.190594
$658$	−24.5105	−0.955521
$659$	−25.2086	−0.981986	−0.490993	−	0.871163i	$-0.663366\pi$
$659$	−25.2086	−0.981986	−0.490993	+	0.871163i	$0.663366\pi$
$660$	2.37914	0.0926077
$661$	−23.8874	−0.929113	−0.464556	−	0.885544i	$-0.653786\pi$
$661$	−23.8874	−0.929113	−0.464556	+	0.885544i	$0.653786\pi$
$662$	−23.9671	−0.931508
$663$	9.27624	0.360259
$664$	11.8940	0.461578
$665$	10.8643	0.421298
$666$	11.3648	0.440376
$667$	0.414382	0.0160449
$668$	−15.3972	−0.595736
$669$	14.8513	0.574183
$670$	17.1878	0.664022
$671$	6.88635	0.265844
$672$	4.85906	0.187442
$673$	18.5568	0.715313	0.357656	−	0.933853i	$-0.383576\pi$
$673$	18.5568	0.715313	0.357656	+	0.933853i	$0.383576\pi$
$674$	0.0592164	0.00228093
$675$	−0.000837091 0	−3.22197e−5 0
$676$	−6.55043	−0.251940
$677$	10.5724	0.406331	0.203165	−	0.979144i	$-0.434877\pi$
$677$	10.5724	0.406331	0.203165	+	0.979144i	$0.434877\pi$
$678$	−15.6355	−0.600479
$679$	−80.3376	−3.08307
$680$	−8.16686	−0.313185
$681$	−9.72397	−0.372623
$682$	3.73462	0.143006
$683$	14.6763	0.561575	0.280787	−	0.959770i	$-0.409404\pi$
$683$	14.6763	0.561575	0.280787	+	0.959770i	$0.409404\pi$
$684$	1.00000	0.0382360
$685$	−24.1721	−0.923569
$686$	46.6977	1.78293
$687$	−25.8189	−0.985051
$688$	10.3437	0.394350
$689$	2.53960	0.0967511
$690$	−18.0355	−0.686599
$691$	29.9587	1.13968	0.569841	−	0.821755i	$-0.307005\pi$
$691$	29.9587	1.13968	0.569841	+	0.821755i	$0.307005\pi$
$692$	−6.95267	−0.264301
$693$	5.17038	0.196407
$694$	19.9759	0.758277
$695$	−45.4266	−1.72313
$696$	−0.0513714	−0.00194723
$697$	22.8734	0.866393
$698$	−17.6321	−0.667383
$699$	−6.71392	−0.253944
$700$	−0.00406748	−0.000153736 0
$701$	−44.2120	−1.66987	−0.834933	−	0.550352i	$-0.814494\pi$
$701$	−44.2120	−1.66987	−0.834933	+	0.550352i	$0.814494\pi$
$702$	−2.53960	−0.0958510
$703$	11.3648	0.428631
$704$	1.06407	0.0401037
$705$	−11.2785	−0.424771
$706$	−27.4761	−1.03408
$707$	29.6945	1.11678
$708$	1.29839	0.0487964
$709$	−42.2113	−1.58528	−0.792639	−	0.609691i	$-0.791294\pi$
$709$	−42.2113	−1.58528	−0.792639	+	0.609691i	$0.791294\pi$
$710$	2.42996	0.0911950
$711$	−5.42609	−0.203494
$712$	13.1684	0.493507
$713$	−28.3110	−1.06026
$714$	−17.7484	−0.664216
$715$	−6.04206	−0.225960
$716$	−1.36082	−0.0508562
$717$	−7.39819	−0.276290
$718$	−17.4748	−0.652154
$719$	−20.3006	−0.757084	−0.378542	−	0.925584i	$-0.623574\pi$
$719$	−20.3006	−0.757084	−0.378542	+	0.925584i	$0.623574\pi$
$720$	2.23588	0.0833264
$721$	23.2426	0.865599
$722$	1.00000	0.0372161
$723$	−23.2465	−0.864548
$724$	−9.29349	−0.345390
$725$	4.30026e−5 0	1.59707e−6 0
$726$	−9.86775	−0.366227
$727$	−48.2163	−1.78824	−0.894121	−	0.447826i	$-0.852199\pi$
$727$	−48.2163	−1.78824	−0.894121	+	0.447826i	$0.852199\pi$
$728$	−12.3401	−0.457353
$729$	1.00000	0.0370370
$730$	−10.9230	−0.404278
$731$	−37.7818	−1.39741
$732$	6.47170	0.239201
$733$	22.6801	0.837707	0.418853	−	0.908054i	$-0.362432\pi$
$733$	22.6801	0.837707	0.418853	+	0.908054i	$0.362432\pi$
$734$	−25.0135	−0.923267
$735$	37.1390	1.36989
$736$	−8.06639	−0.297331
$737$	8.17979	0.301306
$738$	−6.26217	−0.230514
$739$	−16.2510	−0.597803	−0.298902	−	0.954284i	$-0.596620\pi$
$739$	−16.2510	−0.597803	−0.298902	+	0.954284i	$0.596620\pi$
$740$	25.4103	0.934101
$741$	−2.53960	−0.0932946
$742$	−4.85906	−0.178382
$743$	−2.82925	−0.103795	−0.0518976	−	0.998652i	$-0.516527\pi$
$743$	−2.82925	−0.103795	−0.0518976	+	0.998652i	$0.516527\pi$
$744$	3.50975	0.128674
$745$	−9.02131	−0.330515
$746$	1.12241	0.0410943
$747$	11.8940	0.435180
$748$	−3.88667	−0.142111
$749$	52.2045	1.90751
$750$	−11.1813	−0.408282
$751$	35.0149	1.27771	0.638856	−	0.769327i	$-0.279408\pi$
$751$	35.0149	1.27771	0.638856	+	0.769327i	$0.279408\pi$
$752$	−5.04430	−0.183947
$753$	16.9072	0.616132
$754$	0.130463	0.00475118
$755$	24.6447	0.896914
$756$	4.85906	0.176722
$757$	3.44885	0.125351	0.0626753	−	0.998034i	$-0.480037\pi$
$757$	3.44885	0.125351	0.0626753	+	0.998034i	$0.480037\pi$
$758$	18.3685	0.667174
$759$	−8.58321	−0.311551
$760$	2.23588	0.0811039
$761$	35.2345	1.27725	0.638626	−	0.769518i	$-0.279503\pi$
$761$	35.2345	1.27725	0.638626	+	0.769518i	$0.279503\pi$
$762$	−8.03040	−0.290911
$763$	54.4381	1.97079
$764$	−22.4262	−0.811350
$765$	−8.16686	−0.295274
$766$	9.68991	0.350111
$767$	−3.29739	−0.119062
$768$	1.00000	0.0360844
$769$	35.7926	1.29071	0.645357	−	0.763881i	$-0.276709\pi$
$769$	35.7926	1.29071	0.645357	+	0.763881i	$0.276709\pi$
$770$	11.5604	0.416606
$771$	14.3681	0.517454
$772$	−8.66625	−0.311905
$773$	30.6102	1.10097	0.550487	−	0.834844i	$-0.314442\pi$
$773$	30.6102	1.10097	0.550487	+	0.834844i	$0.314442\pi$
$774$	10.3437	0.371796
$775$	−0.00293798	−0.000105535 0
$776$	−16.5336	−0.593521
$777$	55.2221	1.98108
$778$	−9.22117	−0.330595
$779$	−6.26217	−0.224366
$780$	−5.67824	−0.203314
$781$	1.15644	0.0413806
$782$	29.4636	1.05362
$783$	−0.0513714	−0.00183586
$784$	16.6104	0.593230
$785$	13.1781	0.470346
$786$	6.91097	0.246506
$787$	−9.11265	−0.324831	−0.162416	−	0.986722i	$-0.551928\pi$
$787$	−9.11265	−0.324831	−0.162416	+	0.986722i	$0.551928\pi$
$788$	−9.64356	−0.343537
$789$	−7.56276	−0.269241
$790$	−12.1321	−0.431640
$791$	−75.9739	−2.70132
$792$	1.06407	0.0378101
$793$	−16.4355	−0.583643
$794$	17.1401	0.608281
$795$	−2.23588	−0.0792985
$796$	21.2489	0.753147
$797$	43.9610	1.55718	0.778589	−	0.627535i	$-0.215936\pi$
$797$	43.9610	1.55718	0.778589	+	0.627535i	$0.215936\pi$
$798$	4.85906	0.172009
$799$	18.4250	0.651830
$800$	−0.000837091 0	−2.95956e−5 0
$801$	13.1684	0.465283
$802$	20.6897	0.730578
$803$	−5.19832	−0.183445
$804$	7.68726	0.271109
$805$	−87.6355	−3.08875
$806$	−8.91336	−0.313960
$807$	26.5234	0.933668
$808$	6.11117	0.214990
$809$	−27.9893	−0.984052	−0.492026	−	0.870581i	$-0.663743\pi$
$809$	−27.9893	−0.984052	−0.492026	+	0.870581i	$0.663743\pi$
$810$	2.23588	0.0785608
$811$	1.20043	0.0421527	0.0210763	−	0.999778i	$-0.493291\pi$
$811$	1.20043	0.0421527	0.0210763	+	0.999778i	$0.493291\pi$
$812$	−0.249617	−0.00875983
$813$	−17.8970	−0.627676
$814$	12.0929	0.423857
$815$	−15.3625	−0.538123
$816$	−3.65264	−0.127868
$817$	10.3437	0.361880
$818$	−28.0306	−0.980067
$819$	−12.3401	−0.431197
$820$	−14.0015	−0.488953
$821$	−26.8414	−0.936772	−0.468386	−	0.883524i	$-0.655164\pi$
$821$	−26.8414	−0.936772	−0.468386	+	0.883524i	$0.655164\pi$
$822$	−10.8110	−0.377077
$823$	0.634936	0.0221325	0.0110662	−	0.999939i	$-0.496477\pi$
$823$	0.634936	0.0221325	0.0110662	+	0.999939i	$0.496477\pi$
$824$	4.78335	0.166636
$825$	−0.000890725 0	−3.10111e−5 0
$826$	6.30894	0.219516
$827$	13.8713	0.482352	0.241176	−	0.970481i	$-0.422467\pi$
$827$	13.8713	0.482352	0.241176	+	0.970481i	$0.422467\pi$
$828$	−8.06639	−0.280327
$829$	39.9549	1.38769	0.693845	−	0.720124i	$-0.255915\pi$
$829$	39.9549	1.38769	0.693845	+	0.720124i	$0.255915\pi$
$830$	26.5936	0.923079
$831$	−11.7267	−0.406796
$832$	−2.53960	−0.0880448
$833$	−60.6719	−2.10216
$834$	−20.3171	−0.703523
$835$	−34.4263	−1.19137
$836$	1.06407	0.0368017
$837$	3.50975	0.121315
$838$	−1.76135	−0.0608449
$839$	−14.6037	−0.504176	−0.252088	−	0.967704i	$-0.581117\pi$
$839$	−14.6037	−0.504176	−0.252088	+	0.967704i	$0.581117\pi$
$840$	10.8643	0.374853
$841$	−28.9974	−0.999909
$842$	−16.9847	−0.585332
$843$	−25.6489	−0.883395
$844$	−0.701469	−0.0241455
$845$	−14.6460	−0.503837
$846$	−5.04430	−0.173427
$847$	−47.9480	−1.64751
$848$	−1.00000	−0.0343401
$849$	26.2814	0.901975
$850$	0.00305759	0.000104875 0
$851$	−91.6728	−3.14250
$852$	1.08680	0.0372333
$853$	18.5388	0.634756	0.317378	−	0.948299i	$-0.397198\pi$
$853$	18.5388	0.634756	0.317378	+	0.948299i	$0.397198\pi$
$854$	31.4464	1.07607
$855$	2.23588	0.0764655
$856$	10.7437	0.367214
$857$	−3.36019	−0.114782	−0.0573909	−	0.998352i	$-0.518278\pi$
$857$	−3.36019	−0.114782	−0.0573909	+	0.998352i	$0.518278\pi$
$858$	−2.70232	−0.0922555
$859$	39.8155	1.35849	0.679243	−	0.733913i	$-0.262308\pi$
$859$	39.8155	1.35849	0.679243	+	0.733913i	$0.262308\pi$
$860$	23.1273	0.788633
$861$	−30.4283	−1.03699
$862$	−19.3369	−0.658619
$863$	−37.8388	−1.28805	−0.644023	−	0.765006i	$-0.722736\pi$
$863$	−37.8388	−1.28805	−0.644023	+	0.765006i	$0.722736\pi$
$864$	1.00000	0.0340207
$865$	−15.5453	−0.528558
$866$	−8.38376	−0.284892
$867$	−3.65824	−0.124240
$868$	17.0541	0.578853
$869$	−5.77374	−0.195861
$870$	−0.114860	−0.00389413
$871$	−19.5226	−0.661497
$872$	11.2034	0.379396
$873$	−16.5336	−0.559577
$874$	−8.06639	−0.272850
$875$	−54.3305	−1.83671
$876$	−4.88531	−0.165059
$877$	9.55160	0.322534	0.161267	−	0.986911i	$-0.448442\pi$
$877$	9.55160	0.322534	0.161267	+	0.986911i	$0.448442\pi$
$878$	−4.81791	−0.162597
$879$	24.5815	0.829115
$880$	2.37914	0.0802007
$881$	3.14837	0.106071	0.0530356	−	0.998593i	$-0.483110\pi$
$881$	3.14837	0.106071	0.0530356	+	0.998593i	$0.483110\pi$
$882$	16.6104	0.559303
$883$	46.9114	1.57870	0.789348	−	0.613946i	$-0.210419\pi$
$883$	46.9114	1.57870	0.789348	+	0.613946i	$0.210419\pi$
$884$	9.27624	0.311994
$885$	2.90304	0.0975846
$886$	9.88205	0.331994
$887$	−0.877053	−0.0294486	−0.0147243	−	0.999892i	$-0.504687\pi$
$887$	−0.877053	−0.0294486	−0.0147243	+	0.999892i	$0.504687\pi$
$888$	11.3648	0.381377
$889$	−39.0202	−1.30870
$890$	29.4430	0.986932
$891$	1.06407	0.0356477
$892$	14.8513	0.497257
$893$	−5.04430	−0.168801
$894$	−4.03479	−0.134944
$895$	−3.04263	−0.101704
$896$	4.85906	0.162330
$897$	20.4854	0.683988
$898$	17.7645	0.592808
$899$	−0.180301	−0.00601337
$900$	−0.000837091 0	−2.79030e−5 0
$901$	3.65264	0.121687
$902$	−6.66340	−0.221867
$903$	50.2606	1.67257
$904$	−15.6355	−0.520030
$905$	−20.7791	−0.690722
$906$	11.0224	0.366194
$907$	38.9350	1.29281	0.646407	−	0.762993i	$-0.276271\pi$
$907$	38.9350	1.29281	0.646407	+	0.762993i	$0.276271\pi$
$908$	−9.72397	−0.322701
$909$	6.11117	0.202695
$910$	−27.5909	−0.914630
$911$	−11.1261	−0.368623	−0.184312	−	0.982868i	$-0.559006\pi$
$911$	−11.1261	−0.368623	−0.184312	+	0.982868i	$0.559006\pi$
$912$	1.00000	0.0331133
$913$	12.6561	0.418856
$914$	20.7090	0.684991
$915$	14.4699	0.478362
$916$	−25.8189	−0.853079
$917$	33.5808	1.10894
$918$	−3.65264	−0.120555
$919$	7.07942	0.233529	0.116764	−	0.993160i	$-0.462748\pi$
$919$	7.07942	0.233529	0.116764	+	0.993160i	$0.462748\pi$
$920$	−18.0355	−0.594613
$921$	−0.226648	−0.00746831
$922$	23.1568	0.762629
$923$	−2.76005	−0.0908481
$924$	5.17038	0.170093
$925$	−0.00951336	−0.000312797 0
$926$	30.8927	1.01520
$927$	4.78335	0.157106
$928$	−0.0513714	−0.00168635
$929$	3.24594	0.106496	0.0532480	−	0.998581i	$-0.483043\pi$
$929$	3.24594	0.106496	0.0532480	+	0.998581i	$0.483043\pi$
$930$	7.84738	0.257326
$931$	16.6104	0.544385
$932$	−6.71392	−0.219922
$933$	−24.9700	−0.817482
$934$	−26.3616	−0.862577
$935$	−8.69012	−0.284197
$936$	−2.53960	−0.0830094
$937$	−26.8783	−0.878075	−0.439037	−	0.898469i	$-0.644680\pi$
$937$	−26.8783	−0.878075	−0.439037	+	0.898469i	$0.644680\pi$
$938$	37.3528	1.21961
$939$	5.47278	0.178598
$940$	−11.2785	−0.367863
$941$	23.8370	0.777065	0.388532	−	0.921435i	$-0.372982\pi$
$941$	23.8370	0.777065	0.388532	+	0.921435i	$0.372982\pi$
$942$	5.89391	0.192034
$943$	50.5131	1.64493
$944$	1.29839	0.0422589
$945$	10.8643	0.353415
$946$	11.0064	0.357850
$947$	14.6104	0.474775	0.237388	−	0.971415i	$-0.423709\pi$
$947$	14.6104	0.474775	0.237388	+	0.971415i	$0.423709\pi$
$948$	−5.42609	−0.176231
$949$	12.4067	0.402740
$950$	−0.000837091 0	−2.71588e−5 0
$951$	−15.5232	−0.503374
$952$	−17.7484	−0.575228
$953$	25.9357	0.840139	0.420070	−	0.907492i	$-0.362006\pi$
$953$	25.9357	0.840139	0.420070	+	0.907492i	$0.362006\pi$
$954$	−1.00000	−0.0323762
$955$	−50.1422	−1.62256
$956$	−7.39819	−0.239274
$957$	−0.0546628	−0.00176700
$958$	21.2464	0.686440
$959$	−52.5313	−1.69632
$960$	2.23588	0.0721627
$961$	−18.6817	−0.602634
$962$	−28.8620	−0.930548
$963$	10.7437	0.346212
$964$	−23.2465	−0.748720
$965$	−19.3767	−0.623758
$966$	−39.1951	−1.26108
$967$	60.0163	1.92999	0.964997	−	0.262260i	$-0.0844678\pi$
$967$	60.0163	1.92999	0.964997	+	0.262260i	$0.0844678\pi$
$968$	−9.86775	−0.317162
$969$	−3.65264	−0.117340
$970$	−36.9671	−1.18694
$971$	−58.5907	−1.88026	−0.940132	−	0.340810i	$-0.889299\pi$
$971$	−58.5907	−1.88026	−0.940132	+	0.340810i	$0.889299\pi$
$972$	1.00000	0.0320750
$973$	−98.7218	−3.16488
$974$	−7.54046	−0.241612
$975$	0.00212588	6.80826e−5 0
$976$	6.47170	0.207154
$977$	32.7691	1.04837	0.524187	−	0.851603i	$-0.324369\pi$
$977$	32.7691	1.04837	0.524187	+	0.851603i	$0.324369\pi$
$978$	−6.87088	−0.219706
$979$	14.0121	0.447830
$980$	37.1390	1.18636
$981$	11.2034	0.357698
$982$	15.6285	0.498724
$983$	2.55164	0.0813845	0.0406923	−	0.999172i	$-0.487044\pi$
$983$	2.55164	0.0813845	0.0406923	+	0.999172i	$0.487044\pi$
$984$	−6.26217	−0.199631
$985$	−21.5618	−0.687017
$986$	0.187641	0.00597571
$987$	−24.5105	−0.780179
$988$	−2.53960	−0.0807955
$989$	−83.4363	−2.65312
$990$	2.37914	0.0756139
$991$	−37.3938	−1.18785	−0.593927	−	0.804519i	$-0.702423\pi$
$991$	−37.3938	−1.18785	−0.593927	+	0.804519i	$0.702423\pi$
$992$	3.50975	0.111435
$993$	−23.9671	−0.760573
$994$	5.28084	0.167498
$995$	47.5100	1.50617
$996$	11.8940	0.376877
$997$	−27.4129	−0.868177	−0.434088	−	0.900870i	$-0.642929\pi$
$997$	−27.4129	−0.868177	−0.434088	+	0.900870i	$0.642929\pi$
$998$	18.4390	0.583677
$999$	11.3648	0.359566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6042.2.a.bh.1.10	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6042.2.a.bh.1.10	✓	13	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6042.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.23588 q^{5} +1.00000 q^{6} +4.85906 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.23588 q^{5} +1.00000 q^{6} +4.85906 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.23588 q^{10} +1.06407 q^{11} +1.00000 q^{12} -2.53960 q^{13} +4.85906 q^{14} +2.23588 q^{15} +1.00000 q^{16} -3.65264 q^{17} +1.00000 q^{18} +1.00000 q^{19} +2.23588 q^{20} +4.85906 q^{21} +1.06407 q^{22} -8.06639 q^{23} +1.00000 q^{24} -0.000837091 q^{25} -2.53960 q^{26} +1.00000 q^{27} +4.85906 q^{28} -0.0513714 q^{29} +2.23588 q^{30} +3.50975 q^{31} +1.00000 q^{32} +1.06407 q^{33} -3.65264 q^{34} +10.8643 q^{35} +1.00000 q^{36} +11.3648 q^{37} +1.00000 q^{38} -2.53960 q^{39} +2.23588 q^{40} -6.26217 q^{41} +4.85906 q^{42} +10.3437 q^{43} +1.06407 q^{44} +2.23588 q^{45} -8.06639 q^{46} -5.04430 q^{47} +1.00000 q^{48} +16.6104 q^{49} -0.000837091 q^{50} -3.65264 q^{51} -2.53960 q^{52} -1.00000 q^{53} +1.00000 q^{54} +2.37914 q^{55} +4.85906 q^{56} +1.00000 q^{57} -0.0513714 q^{58} +1.29839 q^{59} +2.23588 q^{60} +6.47170 q^{61} +3.50975 q^{62} +4.85906 q^{63} +1.00000 q^{64} -5.67824 q^{65} +1.06407 q^{66} +7.68726 q^{67} -3.65264 q^{68} -8.06639 q^{69} +10.8643 q^{70} +1.08680 q^{71} +1.00000 q^{72} -4.88531 q^{73} +11.3648 q^{74} -0.000837091 q^{75} +1.00000 q^{76} +5.17038 q^{77} -2.53960 q^{78} -5.42609 q^{79} +2.23588 q^{80} +1.00000 q^{81} -6.26217 q^{82} +11.8940 q^{83} +4.85906 q^{84} -8.16686 q^{85} +10.3437 q^{86} -0.0513714 q^{87} +1.06407 q^{88} +13.1684 q^{89} +2.23588 q^{90} -12.3401 q^{91} -8.06639 q^{92} +3.50975 q^{93} -5.04430 q^{94} +2.23588 q^{95} +1.00000 q^{96} -16.5336 q^{97} +16.6104 q^{98} +1.06407 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} + 13 q^{3} + 13 q^{4} + 3 q^{5} + 13 q^{6} + 12 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 4 q^{11} + 13 q^{12} + 18 q^{13} + 12 q^{14} + 3 q^{15} + 13 q^{16} + 3 q^{17} + 13 q^{18} + 13 q^{19} + 3 q^{20} + 12 q^{21} + 4 q^{22} + 8 q^{23} + 13 q^{24} + 24 q^{25} + 18 q^{26} + 13 q^{27} + 12 q^{28} + 11 q^{29} + 3 q^{30} + 2 q^{31} + 13 q^{32} + 4 q^{33} + 3 q^{34} - 6 q^{35} + 13 q^{36} + 26 q^{37} + 13 q^{38} + 18 q^{39} + 3 q^{40} + 3 q^{41} + 12 q^{42} + 24 q^{43} + 4 q^{44} + 3 q^{45} + 8 q^{46} + 4 q^{47} + 13 q^{48} + 41 q^{49} + 24 q^{50} + 3 q^{51} + 18 q^{52} - 13 q^{53} + 13 q^{54} + 23 q^{55} + 12 q^{56} + 13 q^{57} + 11 q^{58} + 8 q^{59} + 3 q^{60} + 29 q^{61} + 2 q^{62} + 12 q^{63} + 13 q^{64} + 13 q^{65} + 4 q^{66} - 5 q^{67} + 3 q^{68} + 8 q^{69} - 6 q^{70} + 29 q^{71} + 13 q^{72} + 15 q^{73} + 26 q^{74} + 24 q^{75} + 13 q^{76} + 3 q^{77} + 18 q^{78} + 15 q^{79} + 3 q^{80} + 13 q^{81} + 3 q^{82} + 4 q^{83} + 12 q^{84} - q^{85} + 24 q^{86} + 11 q^{87} + 4 q^{88} + 3 q^{89} + 3 q^{90} - 29 q^{91} + 8 q^{92} + 2 q^{93} + 4 q^{94} + 3 q^{95} + 13 q^{96} + 50 q^{97} + 41 q^{98} + 4 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 + 13 * q^3 + 13 * q^4 + 3 * q^5 + 13 * q^6 + 12 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 4 * q^11 + 13 * q^12 + 18 * q^13 + 12 * q^14 + 3 * q^15 + 13 * q^16 + 3 * q^17 + 13 * q^18 + 13 * q^19 + 3 * q^20 + 12 * q^21 + 4 * q^22 + 8 * q^23 + 13 * q^24 + 24 * q^25 + 18 * q^26 + 13 * q^27 + 12 * q^28 + 11 * q^29 + 3 * q^30 + 2 * q^31 + 13 * q^32 + 4 * q^33 + 3 * q^34 - 6 * q^35 + 13 * q^36 + 26 * q^37 + 13 * q^38 + 18 * q^39 + 3 * q^40 + 3 * q^41 + 12 * q^42 + 24 * q^43 + 4 * q^44 + 3 * q^45 + 8 * q^46 + 4 * q^47 + 13 * q^48 + 41 * q^49 + 24 * q^50 + 3 * q^51 + 18 * q^52 - 13 * q^53 + 13 * q^54 + 23 * q^55 + 12 * q^56 + 13 * q^57 + 11 * q^58 + 8 * q^59 + 3 * q^60 + 29 * q^61 + 2 * q^62 + 12 * q^63 + 13 * q^64 + 13 * q^65 + 4 * q^66 - 5 * q^67 + 3 * q^68 + 8 * q^69 - 6 * q^70 + 29 * q^71 + 13 * q^72 + 15 * q^73 + 26 * q^74 + 24 * q^75 + 13 * q^76 + 3 * q^77 + 18 * q^78 + 15 * q^79 + 3 * q^80 + 13 * q^81 + 3 * q^82 + 4 * q^83 + 12 * q^84 - q^85 + 24 * q^86 + 11 * q^87 + 4 * q^88 + 3 * q^89 + 3 * q^90 - 29 * q^91 + 8 * q^92 + 2 * q^93 + 4 * q^94 + 3 * q^95 + 13 * q^96 + 50 * q^97 + 41 * q^98 + 4 * q^99

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