LMFDB - Embedded newform 5290.2.a.bk.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5290,2,Mod(1,5290)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5290, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5290.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5290 = 2 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5290.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:	$42.2408626693$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 5 x^{14} - 24 x^{13} + 142 x^{12} + 184 x^{11} - 1488 x^{10} - 426 x^{9} + 7165 x^{8} + \cdots - 32 $ x^15 - 5x^14 - 24x^13 + 142x^12 + 184x^11 - 1488x^10 - 426x^9 + 7165x^8 - 206x^7 - 16453x^6 + 637x^5 + 16290x^4 + 1068x^3 - 4992x^2 - 848x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 230)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$1.31120$ of defining polynomial
Character	$\chi$	$=$	5290.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.31120 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.31120 q^{6} -3.61614 q^{7} +1.00000 q^{8} -1.28075 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.31120 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.31120 q^{6} -3.61614 q^{7} +1.00000 q^{8} -1.28075 q^{9} -1.00000 q^{10} -3.14951 q^{11} +1.31120 q^{12} +3.52217 q^{13} -3.61614 q^{14} -1.31120 q^{15} +1.00000 q^{16} +4.96756 q^{17} -1.28075 q^{18} -1.16157 q^{19} -1.00000 q^{20} -4.74149 q^{21} -3.14951 q^{22} +1.31120 q^{24} +1.00000 q^{25} +3.52217 q^{26} -5.61293 q^{27} -3.61614 q^{28} +5.04510 q^{29} -1.31120 q^{30} +6.15794 q^{31} +1.00000 q^{32} -4.12963 q^{33} +4.96756 q^{34} +3.61614 q^{35} -1.28075 q^{36} -0.957846 q^{37} -1.16157 q^{38} +4.61827 q^{39} -1.00000 q^{40} +2.20177 q^{41} -4.74149 q^{42} +8.45052 q^{43} -3.14951 q^{44} +1.28075 q^{45} -6.16026 q^{47} +1.31120 q^{48} +6.07649 q^{49} +1.00000 q^{50} +6.51347 q^{51} +3.52217 q^{52} +12.3701 q^{53} -5.61293 q^{54} +3.14951 q^{55} -3.61614 q^{56} -1.52305 q^{57} +5.04510 q^{58} +7.95193 q^{59} -1.31120 q^{60} -8.77820 q^{61} +6.15794 q^{62} +4.63139 q^{63} +1.00000 q^{64} -3.52217 q^{65} -4.12963 q^{66} +15.5122 q^{67} +4.96756 q^{68} +3.61614 q^{70} +1.07941 q^{71} -1.28075 q^{72} -2.34692 q^{73} -0.957846 q^{74} +1.31120 q^{75} -1.16157 q^{76} +11.3891 q^{77} +4.61827 q^{78} +7.30901 q^{79} -1.00000 q^{80} -3.51741 q^{81} +2.20177 q^{82} -14.6609 q^{83} -4.74149 q^{84} -4.96756 q^{85} +8.45052 q^{86} +6.61514 q^{87} -3.14951 q^{88} +1.58594 q^{89} +1.28075 q^{90} -12.7367 q^{91} +8.07430 q^{93} -6.16026 q^{94} +1.16157 q^{95} +1.31120 q^{96} -0.135127 q^{97} +6.07649 q^{98} +4.03374 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * 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
$3$	1.31120	0.757022	0.378511	−	0.925597i	$-0.376436\pi$
$3$	1.31120	0.757022	0.378511	+	0.925597i	$0.376436\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.31120	0.535295
$7$	−3.61614	−1.36677	−0.683387	−	0.730056i	$-0.739494\pi$
$7$	−3.61614	−1.36677	−0.683387	+	0.730056i	$0.739494\pi$
$8$	1.00000	0.353553
$9$	−1.28075	−0.426918
$10$	−1.00000	−0.316228
$11$	−3.14951	−0.949612	−0.474806	−	0.880091i	$-0.657482\pi$
$11$	−3.14951	−0.949612	−0.474806	+	0.880091i	$0.657482\pi$
$12$	1.31120	0.378511
$13$	3.52217	0.976874	0.488437	−	0.872599i	$-0.337567\pi$
$13$	3.52217	0.976874	0.488437	+	0.872599i	$0.337567\pi$
$14$	−3.61614	−0.966455
$15$	−1.31120	−0.338550
$16$	1.00000	0.250000
$17$	4.96756	1.20481	0.602405	−	0.798190i	$-0.294209\pi$
$17$	4.96756	1.20481	0.602405	+	0.798190i	$0.294209\pi$
$18$	−1.28075	−0.301877
$19$	−1.16157	−0.266482	−0.133241	−	0.991084i	$-0.542538\pi$
$19$	−1.16157	−0.266482	−0.133241	+	0.991084i	$0.542538\pi$
$20$	−1.00000	−0.223607
$21$	−4.74149	−1.03468
$22$	−3.14951	−0.671477
$23$	0	0
$23$	0	0
$24$	1.31120	0.267648
$25$	1.00000	0.200000
$26$	3.52217	0.690754
$27$	−5.61293	−1.08021
$28$	−3.61614	−0.683387
$29$	5.04510	0.936852	0.468426	−	0.883503i	$-0.344821\pi$
$29$	5.04510	0.936852	0.468426	+	0.883503i	$0.344821\pi$
$30$	−1.31120	−0.239391
$31$	6.15794	1.10600	0.553000	−	0.833181i	$-0.313483\pi$
$31$	6.15794	1.10600	0.553000	+	0.833181i	$0.313483\pi$
$32$	1.00000	0.176777
$33$	−4.12963	−0.718877
$34$	4.96756	0.851930
$35$	3.61614	0.611240
$36$	−1.28075	−0.213459
$37$	−0.957846	−0.157469	−0.0787344	−	0.996896i	$-0.525088\pi$
$37$	−0.957846	−0.157469	−0.0787344	+	0.996896i	$0.525088\pi$
$38$	−1.16157	−0.188431
$39$	4.61827	0.739515
$40$	−1.00000	−0.158114
$41$	2.20177	0.343859	0.171930	−	0.985109i	$-0.445000\pi$
$41$	2.20177	0.343859	0.171930	+	0.985109i	$0.445000\pi$
$42$	−4.74149	−0.731628
$43$	8.45052	1.28869	0.644346	−	0.764734i	$-0.277130\pi$
$43$	8.45052	1.28869	0.644346	+	0.764734i	$0.277130\pi$
$44$	−3.14951	−0.474806
$45$	1.28075	0.190923
$46$	0	0
$47$	−6.16026	−0.898567	−0.449283	−	0.893389i	$-0.648321\pi$
$47$	−6.16026	−0.898567	−0.449283	+	0.893389i	$0.648321\pi$
$48$	1.31120	0.189255
$49$	6.07649	0.868071
$50$	1.00000	0.141421
$51$	6.51347	0.912068
$52$	3.52217	0.488437
$53$	12.3701	1.69916	0.849579	−	0.527461i	$-0.176856\pi$
$53$	12.3701	1.69916	0.849579	+	0.527461i	$0.176856\pi$
$54$	−5.61293	−0.763822
$55$	3.14951	0.424679
$56$	−3.61614	−0.483228
$57$	−1.52305	−0.201733
$58$	5.04510	0.662455
$59$	7.95193	1.03525	0.517626	−	0.855607i	$-0.326816\pi$
$59$	7.95193	1.03525	0.517626	+	0.855607i	$0.326816\pi$
$60$	−1.31120	−0.169275
$61$	−8.77820	−1.12393	−0.561967	−	0.827160i	$-0.689955\pi$
$61$	−8.77820	−1.12393	−0.561967	+	0.827160i	$0.689955\pi$
$62$	6.15794	0.782060
$63$	4.63139	0.583500
$64$	1.00000	0.125000
$65$	−3.52217	−0.436871
$66$	−4.12963	−0.508323
$67$	15.5122	1.89512	0.947561	−	0.319575i	$-0.103540\pi$
$67$	15.5122	1.89512	0.947561	+	0.319575i	$0.103540\pi$
$68$	4.96756	0.602405
$69$	0	0
$70$	3.61614	0.432212
$71$	1.07941	0.128102	0.0640510	−	0.997947i	$-0.479598\pi$
$71$	1.07941	0.128102	0.0640510	+	0.997947i	$0.479598\pi$
$72$	−1.28075	−0.150938
$73$	−2.34692	−0.274686	−0.137343	−	0.990524i	$-0.543856\pi$
$73$	−2.34692	−0.274686	−0.137343	+	0.990524i	$0.543856\pi$
$74$	−0.957846	−0.111347
$75$	1.31120	0.151404
$76$	−1.16157	−0.133241
$77$	11.3891	1.29790
$78$	4.61827	0.522916
$79$	7.30901	0.822328	0.411164	−	0.911561i	$-0.365122\pi$
$79$	7.30901	0.822328	0.411164	+	0.911561i	$0.365122\pi$
$80$	−1.00000	−0.111803
$81$	−3.51741	−0.390823
$82$	2.20177	0.243145
$83$	−14.6609	−1.60924	−0.804622	−	0.593788i	$-0.797632\pi$
$83$	−14.6609	−1.60924	−0.804622	+	0.593788i	$0.797632\pi$
$84$	−4.74149	−0.517339
$85$	−4.96756	−0.538808
$86$	8.45052	0.911243
$87$	6.61514	0.709218
$88$	−3.14951	−0.335738
$89$	1.58594	0.168109	0.0840546	−	0.996461i	$-0.473213\pi$
$89$	1.58594	0.168109	0.0840546	+	0.996461i	$0.473213\pi$
$90$	1.28075	0.135003
$91$	−12.7367	−1.33517
$92$	0	0
$93$	8.07430	0.837266
$94$	−6.16026	−0.635383
$95$	1.16157	0.119174
$96$	1.31120	0.133824
$97$	−0.135127	−0.0137200	−0.00686002	−	0.999976i	$-0.502184\pi$
$97$	−0.135127	−0.0137200	−0.00686002	+	0.999976i	$0.502184\pi$
$98$	6.07649	0.613819
$99$	4.03374	0.405406
$100$	1.00000	0.100000
$101$	12.9048	1.28407	0.642036	−	0.766675i	$-0.278090\pi$
$101$	12.9048	1.28407	0.642036	+	0.766675i	$0.278090\pi$
$102$	6.51347	0.644930
$103$	−6.73469	−0.663588	−0.331794	−	0.943352i	$-0.607654\pi$
$103$	−6.73469	−0.663588	−0.331794	+	0.943352i	$0.607654\pi$
$104$	3.52217	0.345377
$105$	4.74149	0.462722
$106$	12.3701	1.20149
$107$	−15.0699	−1.45686	−0.728432	−	0.685118i	$-0.759750\pi$
$107$	−15.0699	−1.45686	−0.728432	+	0.685118i	$0.759750\pi$
$108$	−5.61293	−0.540104
$109$	12.7003	1.21646	0.608232	−	0.793759i	$-0.291879\pi$
$109$	12.7003	1.21646	0.608232	+	0.793759i	$0.291879\pi$
$110$	3.14951	0.300294
$111$	−1.25593	−0.119207
$112$	−3.61614	−0.341693
$113$	14.0869	1.32518	0.662592	−	0.748980i	$-0.269456\pi$
$113$	14.0869	1.32518	0.662592	+	0.748980i	$0.269456\pi$
$114$	−1.52305	−0.142646
$115$	0	0
$116$	5.04510	0.468426
$117$	−4.51103	−0.417045
$118$	7.95193	0.732034
$119$	−17.9634	−1.64670
$120$	−1.31120	−0.119696
$121$	−1.08061	−0.0982374
$122$	−8.77820	−0.794741
$123$	2.88697	0.260309
$124$	6.15794	0.553000
$125$	−1.00000	−0.0894427
$126$	4.63139	0.412597
$127$	−3.35646	−0.297838	−0.148919	−	0.988849i	$-0.547579\pi$
$127$	−3.35646	−0.297838	−0.148919	+	0.988849i	$0.547579\pi$
$128$	1.00000	0.0883883
$129$	11.0803	0.975568
$130$	−3.52217	−0.308915
$131$	16.9660	1.48233	0.741163	−	0.671325i	$-0.234275\pi$
$131$	16.9660	1.48233	0.741163	+	0.671325i	$0.234275\pi$
$132$	−4.12963	−0.359438
$133$	4.20039	0.364220
$134$	15.5122	1.34005
$135$	5.61293	0.483084
$136$	4.96756	0.425965
$137$	14.4268	1.23257	0.616284	−	0.787524i	$-0.288637\pi$
$137$	14.4268	1.23257	0.616284	+	0.787524i	$0.288637\pi$
$138$	0	0
$139$	11.0105	0.933901	0.466950	−	0.884283i	$-0.345353\pi$
$139$	11.0105	0.933901	0.466950	+	0.884283i	$0.345353\pi$
$140$	3.61614	0.305620
$141$	−8.07734	−0.680235
$142$	1.07941	0.0905818
$143$	−11.0931	−0.927651
$144$	−1.28075	−0.106729
$145$	−5.04510	−0.418973
$146$	−2.34692	−0.194233
$147$	7.96750	0.657148
$148$	−0.957846	−0.0787344
$149$	1.23855	0.101466	0.0507331	−	0.998712i	$-0.483844\pi$
$149$	1.23855	0.101466	0.0507331	+	0.998712i	$0.483844\pi$
$150$	1.31120	0.107059
$151$	−22.7286	−1.84963	−0.924813	−	0.380422i	$-0.875779\pi$
$151$	−22.7286	−1.84963	−0.924813	+	0.380422i	$0.875779\pi$
$152$	−1.16157	−0.0942156
$153$	−6.36222	−0.514355
$154$	11.3891	0.917757
$155$	−6.15794	−0.494618
$156$	4.61827	0.369757
$157$	16.1780	1.29114	0.645571	−	0.763700i	$-0.276619\pi$
$157$	16.1780	1.29114	0.645571	+	0.763700i	$0.276619\pi$
$158$	7.30901	0.581474
$159$	16.2196	1.28630
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−3.51741	−0.276354
$163$	−11.6751	−0.914466	−0.457233	−	0.889347i	$-0.651159\pi$
$163$	−11.6751	−0.914466	−0.457233	+	0.889347i	$0.651159\pi$
$164$	2.20177	0.171930
$165$	4.12963	0.321492
$166$	−14.6609	−1.13791
$167$	6.79041	0.525457	0.262729	−	0.964870i	$-0.415378\pi$
$167$	6.79041	0.525457	0.262729	+	0.964870i	$0.415378\pi$
$168$	−4.74149	−0.365814
$169$	−0.594330	−0.0457177
$170$	−4.96756	−0.380995
$171$	1.48768	0.113766
$172$	8.45052	0.644346
$173$	−3.77075	−0.286685	−0.143342	−	0.989673i	$-0.545785\pi$
$173$	−3.77075	−0.286685	−0.143342	+	0.989673i	$0.545785\pi$
$174$	6.61514	0.501493
$175$	−3.61614	−0.273355
$176$	−3.14951	−0.237403
$177$	10.4266	0.783709
$178$	1.58594	0.118871
$179$	11.5561	0.863741	0.431871	−	0.901936i	$-0.357854\pi$
$179$	11.5561	0.863741	0.431871	+	0.901936i	$0.357854\pi$
$180$	1.28075	0.0954617
$181$	16.2020	1.20428	0.602142	−	0.798389i	$-0.294314\pi$
$181$	16.2020	1.20428	0.602142	+	0.798389i	$0.294314\pi$
$182$	−12.7367	−0.944105
$183$	−11.5100	−0.850842
$184$	0	0
$185$	0.957846	0.0704222
$186$	8.07430	0.592036
$187$	−15.6454	−1.14410
$188$	−6.16026	−0.449283
$189$	20.2971	1.47640
$190$	1.16157	0.0842690
$191$	−3.85033	−0.278600	−0.139300	−	0.990250i	$-0.544485\pi$
$191$	−3.85033	−0.278600	−0.139300	+	0.990250i	$0.544485\pi$
$192$	1.31120	0.0946277
$193$	17.6774	1.27245	0.636225	−	0.771504i	$-0.280495\pi$
$193$	17.6774	1.27245	0.636225	+	0.771504i	$0.280495\pi$
$194$	−0.135127	−0.00970154
$195$	−4.61827	−0.330721
$196$	6.07649	0.434035
$197$	−26.5330	−1.89040	−0.945200	−	0.326491i	$-0.894134\pi$
$197$	−26.5330	−1.89040	−0.945200	+	0.326491i	$0.894134\pi$
$198$	4.03374	0.286666
$199$	8.64754	0.613008	0.306504	−	0.951869i	$-0.400841\pi$
$199$	8.64754	0.613008	0.306504	+	0.951869i	$0.400841\pi$
$200$	1.00000	0.0707107
$201$	20.3397	1.43465
$202$	12.9048	0.907976
$203$	−18.2438	−1.28047
$204$	6.51347	0.456034
$205$	−2.20177	−0.153779
$206$	−6.73469	−0.469228
$207$	0	0
$208$	3.52217	0.244218
$209$	3.65836	0.253054
$210$	4.74149	0.327194
$211$	−0.497276	−0.0342339	−0.0171170	−	0.999853i	$-0.505449\pi$
$211$	−0.497276	−0.0342339	−0.0171170	+	0.999853i	$0.505449\pi$
$212$	12.3701	0.849579
$213$	1.41532	0.0969760
$214$	−15.0699	−1.03016
$215$	−8.45052	−0.576321
$216$	−5.61293	−0.381911
$217$	−22.2680	−1.51165
$218$	12.7003	0.860170
$219$	−3.07728	−0.207944
$220$	3.14951	0.212340
$221$	17.4966	1.17695
$222$	−1.25593	−0.0842924
$223$	−3.53102	−0.236454	−0.118227	−	0.992987i	$-0.537721\pi$
$223$	−3.53102	−0.236454	−0.118227	+	0.992987i	$0.537721\pi$
$224$	−3.61614	−0.241614
$225$	−1.28075	−0.0853836
$226$	14.0869	0.937047
$227$	−12.8244	−0.851183	−0.425592	−	0.904915i	$-0.639934\pi$
$227$	−12.8244	−0.851183	−0.425592	+	0.904915i	$0.639934\pi$
$228$	−1.52305	−0.100866
$229$	−13.3800	−0.884178	−0.442089	−	0.896971i	$-0.645762\pi$
$229$	−13.3800	−0.884178	−0.442089	+	0.896971i	$0.645762\pi$
$230$	0	0
$231$	14.9333	0.982542
$232$	5.04510	0.331227
$233$	28.4249	1.86218	0.931090	−	0.364791i	$-0.118859\pi$
$233$	28.4249	1.86218	0.931090	+	0.364791i	$0.118859\pi$
$234$	−4.51103	−0.294895
$235$	6.16026	0.401851
$236$	7.95193	0.517626
$237$	9.58358	0.622520
$238$	−17.9634	−1.16440
$239$	14.6017	0.944503	0.472251	−	0.881464i	$-0.343442\pi$
$239$	14.6017	0.944503	0.472251	+	0.881464i	$0.343442\pi$
$240$	−1.31120	−0.0846376
$241$	21.3303	1.37400	0.687002	−	0.726655i	$-0.258926\pi$
$241$	21.3303	1.37400	0.687002	+	0.726655i	$0.258926\pi$
$242$	−1.08061	−0.0694643
$243$	12.2267	0.784346
$244$	−8.77820	−0.561967
$245$	−6.07649	−0.388213
$246$	2.88697	0.184066
$247$	−4.09124	−0.260319
$248$	6.15794	0.391030
$249$	−19.2234	−1.21823
$250$	−1.00000	−0.0632456
$251$	−17.0976	−1.07919	−0.539594	−	0.841925i	$-0.681422\pi$
$251$	−17.0976	−1.07919	−0.539594	+	0.841925i	$0.681422\pi$
$252$	4.63139	0.291750
$253$	0	0
$254$	−3.35646	−0.210603
$255$	−6.51347	−0.407889
$256$	1.00000	0.0625000
$257$	−29.9543	−1.86850	−0.934248	−	0.356623i	$-0.883928\pi$
$257$	−29.9543	−1.86850	−0.934248	+	0.356623i	$0.883928\pi$
$258$	11.0803	0.689831
$259$	3.46371	0.215224
$260$	−3.52217	−0.218436
$261$	−6.46154	−0.399959
$262$	16.9660	1.04816
$263$	−2.46654	−0.152093	−0.0760467	−	0.997104i	$-0.524230\pi$
$263$	−2.46654	−0.152093	−0.0760467	+	0.997104i	$0.524230\pi$
$264$	−4.12963	−0.254161
$265$	−12.3701	−0.759887
$266$	4.20039	0.257543
$267$	2.07948	0.127262
$268$	15.5122	0.947561
$269$	4.08349	0.248975	0.124487	−	0.992221i	$-0.460271\pi$
$269$	4.08349	0.248975	0.124487	+	0.992221i	$0.460271\pi$
$270$	5.61293	0.341592
$271$	12.9062	0.783999	0.391999	−	0.919965i	$-0.371784\pi$
$271$	12.9062	0.783999	0.391999	+	0.919965i	$0.371784\pi$
$272$	4.96756	0.301203
$273$	−16.7003	−1.01075
$274$	14.4268	0.871557
$275$	−3.14951	−0.189922
$276$	0	0
$277$	14.8828	0.894218	0.447109	−	0.894479i	$-0.352454\pi$
$277$	14.8828	0.894218	0.447109	+	0.894479i	$0.352454\pi$
$278$	11.0105	0.660368
$279$	−7.88681	−0.472171
$280$	3.61614	0.216106
$281$	−18.4841	−1.10267	−0.551335	−	0.834284i	$-0.685882\pi$
$281$	−18.4841	−1.10267	−0.551335	+	0.834284i	$0.685882\pi$
$282$	−8.07734	−0.480999
$283$	−12.8751	−0.765344	−0.382672	−	0.923884i	$-0.624996\pi$
$283$	−12.8751	−0.765344	−0.382672	+	0.923884i	$0.624996\pi$
$284$	1.07941	0.0640510
$285$	1.52305	0.0902176
$286$	−11.0931	−0.655948
$287$	−7.96193	−0.469978
$288$	−1.28075	−0.0754691
$289$	7.67668	0.451569
$290$	−5.04510	−0.296259
$291$	−0.177178	−0.0103864
$292$	−2.34692	−0.137343
$293$	16.7824	0.980437	0.490218	−	0.871600i	$-0.336917\pi$
$293$	16.7824	0.980437	0.490218	+	0.871600i	$0.336917\pi$
$294$	7.96750	0.464674
$295$	−7.95193	−0.462979
$296$	−0.957846	−0.0556737
$297$	17.6779	1.02578
$298$	1.23855	0.0717474
$299$	0	0
$300$	1.31120	0.0757022
$301$	−30.5583	−1.76135
$302$	−22.7286	−1.30788
$303$	16.9207	0.972070
$304$	−1.16157	−0.0666205
$305$	8.77820	0.502638
$306$	−6.36222	−0.363704
$307$	0.364016	0.0207755	0.0103877	−	0.999946i	$-0.496693\pi$
$307$	0.364016	0.0207755	0.0103877	+	0.999946i	$0.496693\pi$
$308$	11.3891	0.648952
$309$	−8.83052	−0.502351
$310$	−6.15794	−0.349748
$311$	−7.29349	−0.413576	−0.206788	−	0.978386i	$-0.566301\pi$
$311$	−7.29349	−0.413576	−0.206788	+	0.978386i	$0.566301\pi$
$312$	4.61827	0.261458
$313$	−25.9726	−1.46806	−0.734030	−	0.679117i	$-0.762363\pi$
$313$	−25.9726	−1.46806	−0.734030	+	0.679117i	$0.762363\pi$
$314$	16.1780	0.912976
$315$	−4.63139	−0.260949
$316$	7.30901	0.411164
$317$	−10.0369	−0.563726	−0.281863	−	0.959455i	$-0.590952\pi$
$317$	−10.0369	−0.563726	−0.281863	+	0.959455i	$0.590952\pi$
$318$	16.2196	0.909551
$319$	−15.8896	−0.889646
$320$	−1.00000	−0.0559017
$321$	−19.7597	−1.10288
$322$	0	0
$323$	−5.77016	−0.321060
$324$	−3.51741	−0.195412
$325$	3.52217	0.195375
$326$	−11.6751	−0.646625
$327$	16.6526	0.920890
$328$	2.20177	0.121573
$329$	22.2764	1.22814
$330$	4.12963	0.227329
$331$	−28.1837	−1.54912	−0.774558	−	0.632502i	$-0.782028\pi$
$331$	−28.1837	−1.54912	−0.774558	+	0.632502i	$0.782028\pi$
$332$	−14.6609	−0.804622
$333$	1.22676	0.0672263
$334$	6.79041	0.371554
$335$	−15.5122	−0.847524
$336$	−4.74149	−0.258669
$337$	−22.5355	−1.22759	−0.613793	−	0.789467i	$-0.710357\pi$
$337$	−22.5355	−1.22759	−0.613793	+	0.789467i	$0.710357\pi$
$338$	−0.594330	−0.0323273
$339$	18.4708	1.00319
$340$	−4.96756	−0.269404
$341$	−19.3945	−1.05027
$342$	1.48768	0.0804446
$343$	3.33953	0.180318
$344$	8.45052	0.455622
$345$	0	0
$346$	−3.77075	−0.202717
$347$	15.9837	0.858050	0.429025	−	0.903293i	$-0.358857\pi$
$347$	15.9837	0.858050	0.429025	+	0.903293i	$0.358857\pi$
$348$	6.61514	0.354609
$349$	−20.6925	−1.10765	−0.553823	−	0.832635i	$-0.686831\pi$
$349$	−20.6925	−1.10765	−0.553823	+	0.832635i	$0.686831\pi$
$350$	−3.61614	−0.193291
$351$	−19.7697	−1.05523
$352$	−3.14951	−0.167869
$353$	10.7261	0.570893	0.285447	−	0.958395i	$-0.407858\pi$
$353$	10.7261	0.570893	0.285447	+	0.958395i	$0.407858\pi$
$354$	10.4266	0.554166
$355$	−1.07941	−0.0572890
$356$	1.58594	0.0840546
$357$	−23.5536	−1.24659
$358$	11.5561	0.610757
$359$	−15.2290	−0.803756	−0.401878	−	0.915693i	$-0.631642\pi$
$359$	−15.2290	−0.803756	−0.401878	+	0.915693i	$0.631642\pi$
$360$	1.28075	0.0675016
$361$	−17.6508	−0.928987
$362$	16.2020	0.851557
$363$	−1.41690	−0.0743679
$364$	−12.7367	−0.667583
$365$	2.34692	0.122843
$366$	−11.5100	−0.601636
$367$	15.5272	0.810516	0.405258	−	0.914202i	$-0.367182\pi$
$367$	15.5272	0.810516	0.405258	+	0.914202i	$0.367182\pi$
$368$	0	0
$369$	−2.81993	−0.146800
$370$	0.957846	0.0497960
$371$	−44.7319	−2.32236
$372$	8.07430	0.418633
$373$	20.7074	1.07219	0.536094	−	0.844159i	$-0.319899\pi$
$373$	20.7074	1.07219	0.536094	+	0.844159i	$0.319899\pi$
$374$	−15.6454	−0.809003
$375$	−1.31120	−0.0677101
$376$	−6.16026	−0.317691
$377$	17.7697	0.915186
$378$	20.2971	1.04397
$379$	5.07433	0.260651	0.130325	−	0.991471i	$-0.458398\pi$
$379$	5.07433	0.260651	0.130325	+	0.991471i	$0.458398\pi$
$380$	1.16157	0.0595872
$381$	−4.40100	−0.225470
$382$	−3.85033	−0.197000
$383$	−1.77390	−0.0906422	−0.0453211	−	0.998972i	$-0.514431\pi$
$383$	−1.77390	−0.0906422	−0.0453211	+	0.998972i	$0.514431\pi$
$384$	1.31120	0.0669119
$385$	−11.3891	−0.580441
$386$	17.6774	0.899757
$387$	−10.8230	−0.550166
$388$	−0.135127	−0.00686002
$389$	−5.06064	−0.256585	−0.128292	−	0.991736i	$-0.540950\pi$
$389$	−5.06064	−0.256585	−0.128292	+	0.991736i	$0.540950\pi$
$390$	−4.61827	−0.233855
$391$	0	0
$392$	6.07649	0.306909
$393$	22.2458	1.12215
$394$	−26.5330	−1.33672
$395$	−7.30901	−0.367756
$396$	4.03374	0.202703
$397$	−2.38213	−0.119556	−0.0597779	−	0.998212i	$-0.519039\pi$
$397$	−2.38213	−0.119556	−0.0597779	+	0.998212i	$0.519039\pi$
$398$	8.64754	0.433462
$399$	5.50756	0.275723
$400$	1.00000	0.0500000
$401$	−16.3779	−0.817876	−0.408938	−	0.912562i	$-0.634101\pi$
$401$	−16.3779	−0.817876	−0.408938	+	0.912562i	$0.634101\pi$
$402$	20.3397	1.01445
$403$	21.6893	1.08042
$404$	12.9048	0.642036
$405$	3.51741	0.174781
$406$	−18.2438	−0.905426
$407$	3.01674	0.149534
$408$	6.51347	0.322465
$409$	−40.0872	−1.98218	−0.991092	−	0.133176i	$-0.957483\pi$
$409$	−40.0872	−1.98218	−0.991092	+	0.133176i	$0.957483\pi$
$410$	−2.20177	−0.108738
$411$	18.9165	0.933081
$412$	−6.73469	−0.331794
$413$	−28.7553	−1.41496
$414$	0	0
$415$	14.6609	0.719676
$416$	3.52217	0.172689
$417$	14.4370	0.706983
$418$	3.65836	0.178936
$419$	27.3306	1.33519	0.667595	−	0.744525i	$-0.267324\pi$
$419$	27.3306	1.33519	0.667595	+	0.744525i	$0.267324\pi$
$420$	4.74149	0.231361
$421$	−29.9565	−1.45999	−0.729996	−	0.683451i	$-0.760478\pi$
$421$	−29.9565	−1.45999	−0.729996	+	0.683451i	$0.760478\pi$
$422$	−0.497276	−0.0242070
$423$	7.88978	0.383614
$424$	12.3701	0.600743
$425$	4.96756	0.240962
$426$	1.41532	0.0685724
$427$	31.7432	1.53616
$428$	−15.0699	−0.728432
$429$	−14.5453	−0.702252
$430$	−8.45052	−0.407520
$431$	−11.1446	−0.536814	−0.268407	−	0.963306i	$-0.586497\pi$
$431$	−11.1446	−0.536814	−0.268407	+	0.963306i	$0.586497\pi$
$432$	−5.61293	−0.270052
$433$	15.9555	0.766771	0.383386	−	0.923588i	$-0.374758\pi$
$433$	15.9555	0.766771	0.383386	+	0.923588i	$0.374758\pi$
$434$	−22.2680	−1.06890
$435$	−6.61514	−0.317172
$436$	12.7003	0.608232
$437$	0	0
$438$	−3.07728	−0.147038
$439$	−19.6094	−0.935903	−0.467952	−	0.883754i	$-0.655008\pi$
$439$	−19.6094	−0.935903	−0.467952	+	0.883754i	$0.655008\pi$
$440$	3.14951	0.150147
$441$	−7.78249	−0.370595
$442$	17.4966	0.832228
$443$	−21.8222	−1.03680	−0.518401	−	0.855138i	$-0.673472\pi$
$443$	−21.8222	−1.03680	−0.518401	+	0.855138i	$0.673472\pi$
$444$	−1.25593	−0.0596037
$445$	−1.58594	−0.0751808
$446$	−3.53102	−0.167198
$447$	1.62399	0.0768121
$448$	−3.61614	−0.170847
$449$	−10.8162	−0.510449	−0.255225	−	0.966882i	$-0.582149\pi$
$449$	−10.8162	−0.510449	−0.255225	+	0.966882i	$0.582149\pi$
$450$	−1.28075	−0.0603753
$451$	−6.93450	−0.326533
$452$	14.0869	0.662592
$453$	−29.8017	−1.40021
$454$	−12.8244	−0.601878
$455$	12.7367	0.597104
$456$	−1.52305	−0.0713232
$457$	21.9582	1.02716	0.513581	−	0.858041i	$-0.328319\pi$
$457$	21.9582	1.02716	0.513581	+	0.858041i	$0.328319\pi$
$458$	−13.3800	−0.625208
$459$	−27.8826	−1.30145
$460$	0	0
$461$	37.0763	1.72682	0.863408	−	0.504507i	$-0.168326\pi$
$461$	37.0763	1.72682	0.863408	+	0.504507i	$0.168326\pi$
$462$	14.9333	0.694762
$463$	−28.3719	−1.31855	−0.659277	−	0.751900i	$-0.729137\pi$
$463$	−28.3719	−1.31855	−0.659277	+	0.751900i	$0.729137\pi$
$464$	5.04510	0.234213
$465$	−8.07430	−0.374437
$466$	28.4249	1.31676
$467$	9.50192	0.439696	0.219848	−	0.975534i	$-0.429444\pi$
$467$	9.50192	0.439696	0.219848	+	0.975534i	$0.429444\pi$
$468$	−4.51103	−0.208522
$469$	−56.0945	−2.59020
$470$	6.16026	0.284152
$471$	21.2126	0.977423
$472$	7.95193	0.366017
$473$	−26.6150	−1.22376
$474$	9.58358	0.440188
$475$	−1.16157	−0.0532964
$476$	−17.9634	−0.823352
$477$	−15.8430	−0.725401
$478$	14.6017	0.667864
$479$	5.70246	0.260552	0.130276	−	0.991478i	$-0.458414\pi$
$479$	5.70246	0.260552	0.130276	+	0.991478i	$0.458414\pi$
$480$	−1.31120	−0.0598478
$481$	−3.37369	−0.153827
$482$	21.3303	0.971568
$483$	0	0
$484$	−1.08061	−0.0491187
$485$	0.135127	0.00613579
$486$	12.2267	0.554617
$487$	18.9032	0.856584	0.428292	−	0.903640i	$-0.359115\pi$
$487$	18.9032	0.856584	0.428292	+	0.903640i	$0.359115\pi$
$488$	−8.77820	−0.397371
$489$	−15.3084	−0.692271
$490$	−6.07649	−0.274508
$491$	7.56954	0.341609	0.170804	−	0.985305i	$-0.445363\pi$
$491$	7.56954	0.341609	0.170804	+	0.985305i	$0.445363\pi$
$492$	2.88697	0.130154
$493$	25.0619	1.12873
$494$	−4.09124	−0.184073
$495$	−4.03374	−0.181303
$496$	6.15794	0.276500
$497$	−3.90329	−0.175086
$498$	−19.2234	−0.861420
$499$	21.0387	0.941823	0.470911	−	0.882181i	$-0.343925\pi$
$499$	21.0387	0.941823	0.470911	+	0.882181i	$0.343925\pi$
$500$	−1.00000	−0.0447214
$501$	8.90358	0.397783
$502$	−17.0976	−0.763102
$503$	11.1353	0.496497	0.248249	−	0.968696i	$-0.420145\pi$
$503$	11.1353	0.496497	0.248249	+	0.968696i	$0.420145\pi$
$504$	4.63139	0.206298
$505$	−12.9048	−0.574254
$506$	0	0
$507$	−0.779286	−0.0346093
$508$	−3.35646	−0.148919
$509$	37.7982	1.67537	0.837687	−	0.546150i	$-0.183907\pi$
$509$	37.7982	1.67537	0.837687	+	0.546150i	$0.183907\pi$
$510$	−6.51347	−0.288421
$511$	8.48680	0.375434
$512$	1.00000	0.0441942
$513$	6.51979	0.287856
$514$	−29.9543	−1.32123
$515$	6.73469	0.296766
$516$	11.0803	0.487784
$517$	19.4018	0.853290
$518$	3.46371	0.152187
$519$	−4.94421	−0.217027
$520$	−3.52217	−0.154457
$521$	37.2834	1.63342	0.816708	−	0.577051i	$-0.195797\pi$
$521$	37.2834	1.63342	0.816708	+	0.577051i	$0.195797\pi$
$522$	−6.46154	−0.282814
$523$	−3.08580	−0.134932	−0.0674662	−	0.997722i	$-0.521491\pi$
$523$	−3.08580	−0.134932	−0.0674662	+	0.997722i	$0.521491\pi$
$524$	16.9660	0.741163
$525$	−4.74149	−0.206936
$526$	−2.46654	−0.107546
$527$	30.5900	1.33252
$528$	−4.12963	−0.179719
$529$	0	0
$530$	−12.3701	−0.537321
$531$	−10.1845	−0.441968
$532$	4.20039	0.182110
$533$	7.75502	0.335907
$534$	2.07948	0.0899881
$535$	15.0699	0.651529
$536$	15.5122	0.670027
$537$	15.1523	0.653871
$538$	4.08349	0.176052
$539$	−19.1380	−0.824330
$540$	5.61293	0.241542
$541$	25.1062	1.07940	0.539700	−	0.841857i	$-0.318537\pi$
$541$	25.1062	1.07940	0.539700	+	0.841857i	$0.318537\pi$
$542$	12.9062	0.554371
$543$	21.2440	0.911669
$544$	4.96756	0.212982
$545$	−12.7003	−0.544019
$546$	−16.7003	−0.714708
$547$	−27.9394	−1.19460	−0.597301	−	0.802017i	$-0.703760\pi$
$547$	−27.9394	−1.19460	−0.597301	+	0.802017i	$0.703760\pi$
$548$	14.4268	0.616284
$549$	11.2427	0.479827
$550$	−3.14951	−0.134295
$551$	−5.86023	−0.249654
$552$	0	0
$553$	−26.4304	−1.12394
$554$	14.8828	0.632308
$555$	1.25593	0.0533112
$556$	11.0105	0.466950
$557$	6.99671	0.296460	0.148230	−	0.988953i	$-0.452642\pi$
$557$	6.99671	0.296460	0.148230	+	0.988953i	$0.452642\pi$
$558$	−7.88681	−0.333875
$559$	29.7642	1.25889
$560$	3.61614	0.152810
$561$	−20.5142	−0.866111
$562$	−18.4841	−0.779706
$563$	−20.4404	−0.861460	−0.430730	−	0.902481i	$-0.641744\pi$
$563$	−20.4404	−0.861460	−0.430730	+	0.902481i	$0.641744\pi$
$564$	−8.07734	−0.340117
$565$	−14.0869	−0.592640
$566$	−12.8751	−0.541180
$567$	12.7195	0.534167
$568$	1.07941	0.0452909
$569$	−5.96631	−0.250121	−0.125060	−	0.992149i	$-0.539912\pi$
$569$	−5.96631	−0.250121	−0.125060	+	0.992149i	$0.539912\pi$
$570$	1.52305	0.0637934
$571$	−6.74153	−0.282124	−0.141062	−	0.990001i	$-0.545052\pi$
$571$	−6.74153	−0.282124	−0.141062	+	0.990001i	$0.545052\pi$
$572$	−11.0931	−0.463825
$573$	−5.04855	−0.210906
$574$	−7.96193	−0.332324
$575$	0	0
$576$	−1.28075	−0.0533647
$577$	36.2809	1.51039	0.755196	−	0.655499i	$-0.227541\pi$
$577$	36.2809	1.51039	0.755196	+	0.655499i	$0.227541\pi$
$578$	7.67668	0.319308
$579$	23.1786	0.963272
$580$	−5.04510	−0.209487
$581$	53.0159	2.19947
$582$	−0.177178	−0.00734427
$583$	−38.9596	−1.61354
$584$	−2.34692	−0.0971163
$585$	4.51103	0.186508
$586$	16.7824	0.693274
$587$	−27.0407	−1.11609	−0.558045	−	0.829811i	$-0.688448\pi$
$587$	−27.0407	−1.11609	−0.558045	+	0.829811i	$0.688448\pi$
$588$	7.96750	0.328574
$589$	−7.15287	−0.294729
$590$	−7.95193	−0.327376
$591$	−34.7901	−1.43107
$592$	−0.957846	−0.0393672
$593$	−22.3090	−0.916120	−0.458060	−	0.888921i	$-0.651455\pi$
$593$	−22.3090	−0.916120	−0.458060	+	0.888921i	$0.651455\pi$
$594$	17.6779	0.725335
$595$	17.9634	0.736428
$596$	1.23855	0.0507331
$597$	11.3387	0.464060
$598$	0	0
$599$	23.9530	0.978693	0.489347	−	0.872089i	$-0.337235\pi$
$599$	23.9530	0.978693	0.489347	+	0.872089i	$0.337235\pi$
$600$	1.31120	0.0535295
$601$	0.908172	0.0370451	0.0185226	−	0.999828i	$-0.494104\pi$
$601$	0.908172	0.0370451	0.0185226	+	0.999828i	$0.494104\pi$
$602$	−30.5583	−1.24546
$603$	−19.8674	−0.809061
$604$	−22.7286	−0.924813
$605$	1.08061	0.0439331
$606$	16.9207	0.687357
$607$	31.1358	1.26376	0.631882	−	0.775065i	$-0.282283\pi$
$607$	31.1358	1.26376	0.631882	+	0.775065i	$0.282283\pi$
$608$	−1.16157	−0.0471078
$609$	−23.9213	−0.969340
$610$	8.77820	0.355419
$611$	−21.6975	−0.877786
$612$	−6.36222	−0.257178
$613$	−16.0906	−0.649895	−0.324948	−	0.945732i	$-0.605347\pi$
$613$	−16.0906	−0.649895	−0.324948	+	0.945732i	$0.605347\pi$
$614$	0.364016	0.0146905
$615$	−2.88697	−0.116414
$616$	11.3891	0.458879
$617$	22.3451	0.899580	0.449790	−	0.893134i	$-0.351499\pi$
$617$	22.3451	0.899580	0.449790	+	0.893134i	$0.351499\pi$
$618$	−8.83052	−0.355216
$619$	−13.2003	−0.530564	−0.265282	−	0.964171i	$-0.585465\pi$
$619$	−13.2003	−0.530564	−0.265282	+	0.964171i	$0.585465\pi$
$620$	−6.15794	−0.247309
$621$	0	0
$622$	−7.29349	−0.292442
$623$	−5.73499	−0.229767
$624$	4.61827	0.184879
$625$	1.00000	0.0400000
$626$	−25.9726	−1.03808
$627$	4.79685	0.191568
$628$	16.1780	0.645571
$629$	−4.75816	−0.189720
$630$	−4.63139	−0.184519
$631$	−27.8956	−1.11051	−0.555253	−	0.831682i	$-0.687378\pi$
$631$	−27.8956	−1.11051	−0.555253	+	0.831682i	$0.687378\pi$
$632$	7.30901	0.290737
$633$	−0.652029	−0.0259158
$634$	−10.0369	−0.398614
$635$	3.35646	0.133197
$636$	16.2196	0.643150
$637$	21.4024	0.847995
$638$	−15.8896	−0.629075
$639$	−1.38245	−0.0546890
$640$	−1.00000	−0.0395285
$641$	−15.9297	−0.629185	−0.314593	−	0.949227i	$-0.601868\pi$
$641$	−15.9297	−0.629185	−0.314593	+	0.949227i	$0.601868\pi$
$642$	−19.7597	−0.779852
$643$	−21.7301	−0.856952	−0.428476	−	0.903553i	$-0.640949\pi$
$643$	−21.7301	−0.856952	−0.428476	+	0.903553i	$0.640949\pi$
$644$	0	0
$645$	−11.0803	−0.436287
$646$	−5.77016	−0.227024
$647$	−19.8277	−0.779507	−0.389753	−	0.920919i	$-0.627440\pi$
$647$	−19.8277	−0.779507	−0.389753	+	0.920919i	$0.627440\pi$
$648$	−3.51741	−0.138177
$649$	−25.0446	−0.983088
$650$	3.52217	0.138151
$651$	−29.1978	−1.14435
$652$	−11.6751	−0.457233
$653$	6.98897	0.273500	0.136750	−	0.990606i	$-0.456334\pi$
$653$	6.98897	0.273500	0.136750	+	0.990606i	$0.456334\pi$
$654$	16.6526	0.651168
$655$	−16.9660	−0.662916
$656$	2.20177	0.0859648
$657$	3.00583	0.117268
$658$	22.2764	0.868424
$659$	16.7329	0.651820	0.325910	−	0.945401i	$-0.394329\pi$
$659$	16.7329	0.651820	0.325910	+	0.945401i	$0.394329\pi$
$660$	4.12963	0.160746
$661$	1.88913	0.0734786	0.0367393	−	0.999325i	$-0.488303\pi$
$661$	1.88913	0.0734786	0.0367393	+	0.999325i	$0.488303\pi$
$662$	−28.1837	−1.09539
$663$	22.9415	0.890975
$664$	−14.6609	−0.568953
$665$	−4.20039	−0.162884
$666$	1.22676	0.0475362
$667$	0	0
$668$	6.79041	0.262729
$669$	−4.62987	−0.179001
$670$	−15.5122	−0.599290
$671$	27.6470	1.06730
$672$	−4.74149	−0.182907
$673$	34.6587	1.33600	0.667998	−	0.744163i	$-0.267152\pi$
$673$	34.6587	1.33600	0.667998	+	0.744163i	$0.267152\pi$
$674$	−22.5355	−0.868034
$675$	−5.61293	−0.216042
$676$	−0.594330	−0.0228589
$677$	24.6522	0.947460	0.473730	−	0.880670i	$-0.342907\pi$
$677$	24.6522	0.947460	0.473730	+	0.880670i	$0.342907\pi$
$678$	18.4708	0.709365
$679$	0.488638	0.0187522
$680$	−4.96756	−0.190497
$681$	−16.8153	−0.644364
$682$	−19.3945	−0.742653
$683$	17.8802	0.684169	0.342084	−	0.939669i	$-0.388867\pi$
$683$	17.8802	0.684169	0.342084	+	0.939669i	$0.388867\pi$
$684$	1.48768	0.0568829
$685$	−14.4268	−0.551221
$686$	3.33953	0.127504
$687$	−17.5439	−0.669342
$688$	8.45052	0.322173
$689$	43.5694	1.65986
$690$	0	0
$691$	−17.8803	−0.680197	−0.340099	−	0.940390i	$-0.610460\pi$
$691$	−17.8803	−0.680197	−0.340099	+	0.940390i	$0.610460\pi$
$692$	−3.77075	−0.143342
$693$	−14.5866	−0.554099
$694$	15.9837	0.606733
$695$	−11.0105	−0.417653
$696$	6.61514	0.250746
$697$	10.9374	0.414285
$698$	−20.6925	−0.783223
$699$	37.2708	1.40971
$700$	−3.61614	−0.136677
$701$	−41.4364	−1.56503	−0.782516	−	0.622631i	$-0.786064\pi$
$701$	−41.4364	−1.56503	−0.782516	+	0.622631i	$0.786064\pi$
$702$	−19.7697	−0.746158
$703$	1.11260	0.0419626
$704$	−3.14951	−0.118701
$705$	8.07734	0.304210
$706$	10.7261	0.403683
$707$	−46.6655	−1.75504
$708$	10.4266	0.391854
$709$	38.3664	1.44088	0.720440	−	0.693517i	$-0.243940\pi$
$709$	38.3664	1.44088	0.720440	+	0.693517i	$0.243940\pi$
$710$	−1.07941	−0.0405094
$711$	−9.36104	−0.351066
$712$	1.58594	0.0594356
$713$	0	0
$714$	−23.5536	−0.881473
$715$	11.0931	0.414858
$716$	11.5561	0.431871
$717$	19.1457	0.715009
$718$	−15.2290	−0.568341
$719$	−2.34937	−0.0876167	−0.0438084	−	0.999040i	$-0.513949\pi$
$719$	−2.34937	−0.0876167	−0.0438084	+	0.999040i	$0.513949\pi$
$720$	1.28075	0.0477309
$721$	24.3536	0.906975
$722$	−17.6508	−0.656893
$723$	27.9683	1.04015
$724$	16.2020	0.602142
$725$	5.04510	0.187370
$726$	−1.41690	−0.0525860
$727$	49.7210	1.84405	0.922024	−	0.387132i	$-0.126534\pi$
$727$	49.7210	1.84405	0.922024	+	0.387132i	$0.126534\pi$
$728$	−12.7367	−0.472052
$729$	26.5839	0.984591
$730$	2.34692	0.0868634
$731$	41.9785	1.55263
$732$	−11.5100	−0.425421
$733$	−41.8260	−1.54488	−0.772439	−	0.635089i	$-0.780964\pi$
$733$	−41.8260	−1.54488	−0.772439	+	0.635089i	$0.780964\pi$
$734$	15.5272	0.573121
$735$	−7.96750	−0.293886
$736$	0	0
$737$	−48.8559	−1.79963
$738$	−2.81993	−0.103803
$739$	−5.30005	−0.194966	−0.0974828	−	0.995237i	$-0.531079\pi$
$739$	−5.30005	−0.194966	−0.0974828	+	0.995237i	$0.531079\pi$
$740$	0.957846	0.0352111
$741$	−5.36443	−0.197067
$742$	−44.7319	−1.64216
$743$	49.2260	1.80593	0.902963	−	0.429718i	$-0.141387\pi$
$743$	49.2260	1.80593	0.902963	+	0.429718i	$0.141387\pi$
$744$	8.07430	0.296018
$745$	−1.23855	−0.0453770
$746$	20.7074	0.758151
$747$	18.7770	0.687015
$748$	−15.6454	−0.572051
$749$	54.4950	1.99120
$750$	−1.31120	−0.0478783
$751$	40.0566	1.46169	0.730844	−	0.682545i	$-0.239127\pi$
$751$	40.0566	1.46169	0.730844	+	0.682545i	$0.239127\pi$
$752$	−6.16026	−0.224642
$753$	−22.4183	−0.816969
$754$	17.7697	0.647135
$755$	22.7286	0.827178
$756$	20.2971	0.738200
$757$	41.0244	1.49106	0.745529	−	0.666473i	$-0.232197\pi$
$757$	41.0244	1.49106	0.745529	+	0.666473i	$0.232197\pi$
$758$	5.07433	0.184308
$759$	0	0
$760$	1.16157	0.0421345
$761$	−46.3560	−1.68040	−0.840202	−	0.542273i	$-0.817564\pi$
$761$	−46.3560	−1.68040	−0.840202	+	0.542273i	$0.817564\pi$
$762$	−4.40100	−0.159431
$763$	−45.9260	−1.66263
$764$	−3.85033	−0.139300
$765$	6.36222	0.230027
$766$	−1.77390	−0.0640937
$767$	28.0080	1.01131
$768$	1.31120	0.0473139
$769$	−19.0095	−0.685500	−0.342750	−	0.939427i	$-0.611358\pi$
$769$	−19.0095	−0.685500	−0.342750	+	0.939427i	$0.611358\pi$
$770$	−11.3891	−0.410433
$771$	−39.2761	−1.41449
$772$	17.6774	0.636225
$773$	−23.9067	−0.859864	−0.429932	−	0.902861i	$-0.641462\pi$
$773$	−23.9067	−0.859864	−0.429932	+	0.902861i	$0.641462\pi$
$774$	−10.8230	−0.389026
$775$	6.15794	0.221200
$776$	−0.135127	−0.00485077
$777$	4.54162	0.162930
$778$	−5.06064	−0.181433
$779$	−2.55751	−0.0916322
$780$	−4.61827	−0.165361
$781$	−3.39960	−0.121647
$782$	0	0
$783$	−28.3178	−1.01200
$784$	6.07649	0.217018
$785$	−16.1780	−0.577417
$786$	22.2458	0.793482
$787$	27.9989	0.998054	0.499027	−	0.866586i	$-0.333691\pi$
$787$	27.9989	0.998054	0.499027	+	0.866586i	$0.333691\pi$
$788$	−26.5330	−0.945200
$789$	−3.23413	−0.115138
$790$	−7.30901	−0.260043
$791$	−50.9403	−1.81123
$792$	4.03374	0.143333
$793$	−30.9183	−1.09794
$794$	−2.38213	−0.0845387
$795$	−16.2196	−0.575251
$796$	8.64754	0.306504
$797$	−2.48986	−0.0881954	−0.0440977	−	0.999027i	$-0.514041\pi$
$797$	−2.48986	−0.0881954	−0.0440977	+	0.999027i	$0.514041\pi$
$798$	5.50756	0.194965
$799$	−30.6015	−1.08260
$800$	1.00000	0.0353553
$801$	−2.03120	−0.0717689
$802$	−16.3779	−0.578325
$803$	7.39164	0.260845
$804$	20.3397	0.717324
$805$	0	0
$806$	21.6893	0.763973
$807$	5.35427	0.188479
$808$	12.9048	0.453988
$809$	−32.5826	−1.14554	−0.572771	−	0.819715i	$-0.694132\pi$
$809$	−32.5826	−1.14554	−0.572771	+	0.819715i	$0.694132\pi$
$810$	3.51741	0.123589
$811$	19.2096	0.674540	0.337270	−	0.941408i	$-0.390496\pi$
$811$	19.2096	0.674540	0.337270	+	0.941408i	$0.390496\pi$
$812$	−18.2438	−0.640233
$813$	16.9227	0.593504
$814$	3.01674	0.105737
$815$	11.6751	0.408962
$816$	6.51347	0.228017
$817$	−9.81585	−0.343413
$818$	−40.0872	−1.40162
$819$	16.3125	0.570006
$820$	−2.20177	−0.0768893
$821$	−34.4281	−1.20155	−0.600774	−	0.799419i	$-0.705141\pi$
$821$	−34.4281	−1.20155	−0.600774	+	0.799419i	$0.705141\pi$
$822$	18.9165	0.659788
$823$	−56.5034	−1.96959	−0.984793	−	0.173732i	$-0.944417\pi$
$823$	−56.5034	−1.96959	−0.984793	+	0.173732i	$0.944417\pi$
$824$	−6.73469	−0.234614
$825$	−4.12963	−0.143775
$826$	−28.7553	−1.00053
$827$	33.4116	1.16184	0.580918	−	0.813962i	$-0.302694\pi$
$827$	33.4116	1.16184	0.580918	+	0.813962i	$0.302694\pi$
$828$	0	0
$829$	−45.4187	−1.57746	−0.788728	−	0.614742i	$-0.789260\pi$
$829$	−45.4187	−1.57746	−0.788728	+	0.614742i	$0.789260\pi$
$830$	14.6609	0.508887
$831$	19.5143	0.676943
$832$	3.52217	0.122109
$833$	30.1854	1.04586
$834$	14.4370	0.499913
$835$	−6.79041	−0.234992
$836$	3.65836	0.126527
$837$	−34.5641	−1.19471
$838$	27.3306	0.944122
$839$	21.0551	0.726901	0.363451	−	0.931613i	$-0.381599\pi$
$839$	21.0551	0.726901	0.363451	+	0.931613i	$0.381599\pi$
$840$	4.74149	0.163597
$841$	−3.54692	−0.122308
$842$	−29.9565	−1.03237
$843$	−24.2364	−0.834746
$844$	−0.497276	−0.0171170
$845$	0.594330	0.0204456
$846$	7.88978	0.271256
$847$	3.90765	0.134268
$848$	12.3701	0.424790
$849$	−16.8818	−0.579382
$850$	4.96756	0.170386
$851$	0	0
$852$	1.41532	0.0484880
$853$	7.65046	0.261947	0.130973	−	0.991386i	$-0.458190\pi$
$853$	7.65046	0.261947	0.130973	+	0.991386i	$0.458190\pi$
$854$	31.7432	1.08623
$855$	−1.48768	−0.0508776
$856$	−15.0699	−0.515079
$857$	−12.5359	−0.428219	−0.214110	−	0.976810i	$-0.568685\pi$
$857$	−12.5359	−0.428219	−0.214110	+	0.976810i	$0.568685\pi$
$858$	−14.5453	−0.496567
$859$	42.6589	1.45550	0.727751	−	0.685842i	$-0.240566\pi$
$859$	42.6589	1.45550	0.727751	+	0.685842i	$0.240566\pi$
$860$	−8.45052	−0.288160
$861$	−10.4397	−0.355783
$862$	−11.1446	−0.379585
$863$	44.3134	1.50844	0.754222	−	0.656619i	$-0.228014\pi$
$863$	44.3134	1.50844	0.754222	+	0.656619i	$0.228014\pi$
$864$	−5.61293	−0.190956
$865$	3.77075	0.128209
$866$	15.9555	0.542189
$867$	10.0657	0.341848
$868$	−22.2680	−0.755825
$869$	−23.0198	−0.780892
$870$	−6.61514	−0.224274
$871$	54.6367	1.85129
$872$	12.7003	0.430085
$873$	0.173064	0.00585733
$874$	0	0
$875$	3.61614	0.122248
$876$	−3.07728	−0.103972
$877$	47.3057	1.59740	0.798701	−	0.601729i	$-0.205521\pi$
$877$	47.3057	1.59740	0.798701	+	0.601729i	$0.205521\pi$
$878$	−19.6094	−0.661784
$879$	22.0051	0.742212
$880$	3.14951	0.106170
$881$	48.0057	1.61735	0.808676	−	0.588254i	$-0.200185\pi$
$881$	48.0057	1.61735	0.808676	+	0.588254i	$0.200185\pi$
$882$	−7.78249	−0.262050
$883$	−40.9247	−1.37723	−0.688613	−	0.725129i	$-0.741780\pi$
$883$	−40.9247	−1.37723	−0.688613	+	0.725129i	$0.741780\pi$
$884$	17.4966	0.588474
$885$	−10.4266	−0.350485
$886$	−21.8222	−0.733130
$887$	−44.1551	−1.48258	−0.741292	−	0.671183i	$-0.765787\pi$
$887$	−44.1551	−1.48258	−0.741292	+	0.671183i	$0.765787\pi$
$888$	−1.25593	−0.0421462
$889$	12.1375	0.407077
$890$	−1.58594	−0.0531608
$891$	11.0781	0.371130
$892$	−3.53102	−0.118227
$893$	7.15556	0.239452
$894$	1.62399	0.0543143
$895$	−11.5561	−0.386277
$896$	−3.61614	−0.120807
$897$	0	0
$898$	−10.8162	−0.360942
$899$	31.0675	1.03616
$900$	−1.28075	−0.0426918
$901$	61.4490	2.04716
$902$	−6.93450	−0.230894
$903$	−40.0681	−1.33338
$904$	14.0869	0.468523
$905$	−16.2020	−0.538572
$906$	−29.8017	−0.990096
$907$	−0.832231	−0.0276338	−0.0138169	−	0.999905i	$-0.504398\pi$
$907$	−0.832231	−0.0276338	−0.0138169	+	0.999905i	$0.504398\pi$
$908$	−12.8244	−0.425592
$909$	−16.5278	−0.548193
$910$	12.7367	0.422216
$911$	26.3756	0.873862	0.436931	−	0.899495i	$-0.356065\pi$
$911$	26.3756	0.873862	0.436931	+	0.899495i	$0.356065\pi$
$912$	−1.52305	−0.0504331
$913$	46.1746	1.52816
$914$	21.9582	0.726313
$915$	11.5100	0.380508
$916$	−13.3800	−0.442089
$917$	−61.3515	−2.02600
$918$	−27.8826	−0.920262
$919$	14.7025	0.484990	0.242495	−	0.970153i	$-0.422034\pi$
$919$	14.7025	0.484990	0.242495	+	0.970153i	$0.422034\pi$
$920$	0	0
$921$	0.477298	0.0157275
$922$	37.0763	1.22104
$923$	3.80185	0.125140
$924$	14.9333	0.491271
$925$	−0.957846	−0.0314938
$926$	−28.3719	−0.932358
$927$	8.62547	0.283298
$928$	5.04510	0.165614
$929$	−9.14220	−0.299946	−0.149973	−	0.988690i	$-0.547919\pi$
$929$	−9.14220	−0.299946	−0.149973	+	0.988690i	$0.547919\pi$
$930$	−8.07430	−0.264767
$931$	−7.05826	−0.231325
$932$	28.4249	0.931090
$933$	−9.56323	−0.313086
$934$	9.50192	0.310912
$935$	15.6454	0.511658
$936$	−4.51103	−0.147448
$937$	16.8071	0.549065	0.274532	−	0.961578i	$-0.411477\pi$
$937$	16.8071	0.549065	0.274532	+	0.961578i	$0.411477\pi$
$938$	−56.0945	−1.83155
$939$	−34.0553	−1.11135
$940$	6.16026	0.200926
$941$	19.2847	0.628664	0.314332	−	0.949313i	$-0.398220\pi$
$941$	19.2847	0.628664	0.314332	+	0.949313i	$0.398220\pi$
$942$	21.2126	0.691143
$943$	0	0
$944$	7.95193	0.258813
$945$	−20.2971	−0.660266
$946$	−26.6150	−0.865327
$947$	45.1096	1.46586	0.732932	−	0.680302i	$-0.238151\pi$
$947$	45.1096	1.46586	0.732932	+	0.680302i	$0.238151\pi$
$948$	9.58358	0.311260
$949$	−8.26625	−0.268334
$950$	−1.16157	−0.0376862
$951$	−13.1603	−0.426753
$952$	−17.9634	−0.582198
$953$	−26.5479	−0.859970	−0.429985	−	0.902836i	$-0.641481\pi$
$953$	−26.5479	−0.859970	−0.429985	+	0.902836i	$0.641481\pi$
$954$	−15.8430	−0.512936
$955$	3.85033	0.124594
$956$	14.6017	0.472251
$957$	−20.8344	−0.673482
$958$	5.70246	0.184238
$959$	−52.1695	−1.68464
$960$	−1.31120	−0.0423188
$961$	6.92026	0.223234
$962$	−3.37369	−0.108772
$963$	19.3008	0.621961
$964$	21.3303	0.687002
$965$	−17.6774	−0.569056
$966$	0	0
$967$	0.555100	0.0178508	0.00892541	−	0.999960i	$-0.497159\pi$
$967$	0.555100	0.0178508	0.00892541	+	0.999960i	$0.497159\pi$
$968$	−1.08061	−0.0347322
$969$	−7.56583	−0.243050
$970$	0.135127	0.00433866
$971$	−36.1945	−1.16154	−0.580768	−	0.814069i	$-0.697248\pi$
$971$	−36.1945	−1.16154	−0.580768	+	0.814069i	$0.697248\pi$
$972$	12.2267	0.392173
$973$	−39.8157	−1.27643
$974$	18.9032	0.605697
$975$	4.61827	0.147903
$976$	−8.77820	−0.280983
$977$	−19.5359	−0.625010	−0.312505	−	0.949916i	$-0.601168\pi$
$977$	−19.5359	−0.625010	−0.312505	+	0.949916i	$0.601168\pi$
$978$	−15.3084	−0.489509
$979$	−4.99493	−0.159639
$980$	−6.07649	−0.194106
$981$	−16.2659	−0.519330
$982$	7.56954	0.241554
$983$	12.1376	0.387129	0.193565	−	0.981088i	$-0.437995\pi$
$983$	12.1376	0.387129	0.193565	+	0.981088i	$0.437995\pi$
$984$	2.88697	0.0920331
$985$	26.5330	0.845413
$986$	25.0619	0.798133
$987$	29.2088	0.929727
$988$	−4.09124	−0.130160
$989$	0	0
$990$	−4.03374	−0.128201
$991$	16.6514	0.528950	0.264475	−	0.964393i	$-0.414801\pi$
$991$	16.6514	0.528950	0.264475	+	0.964393i	$0.414801\pi$
$992$	6.15794	0.195515
$993$	−36.9545	−1.17272
$994$	−3.90329	−0.123805
$995$	−8.64754	−0.274146
$996$	−19.2234	−0.609116
$997$	20.4518	0.647714	0.323857	−	0.946106i	$-0.395020\pi$
$997$	20.4518	0.647714	0.323857	+	0.946106i	$0.395020\pi$
$998$	21.0387	0.665969
$999$	5.37632	0.170099

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bk.1.10		15
23.3	even	11		230.2.g.d.101.2	yes	30
23.8	even	11		230.2.g.d.41.2	✓	30
23.22	odd	2		5290.2.a.bl.1.10		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.41.2	✓	30	23.8	even	11
230.2.g.d.101.2	yes	30	23.3	even	11
5290.2.a.bk.1.10		15	1.1	even	1	trivial
5290.2.a.bl.1.10		15	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5290 = 2 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5290.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.31120 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.31120 q^{6} -3.61614 q^{7} +1.00000 q^{8} -1.28075 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.31120 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.31120 q^{6} -3.61614 q^{7} +1.00000 q^{8} -1.28075 q^{9} -1.00000 q^{10} -3.14951 q^{11} +1.31120 q^{12} +3.52217 q^{13} -3.61614 q^{14} -1.31120 q^{15} +1.00000 q^{16} +4.96756 q^{17} -1.28075 q^{18} -1.16157 q^{19} -1.00000 q^{20} -4.74149 q^{21} -3.14951 q^{22} +1.31120 q^{24} +1.00000 q^{25} +3.52217 q^{26} -5.61293 q^{27} -3.61614 q^{28} +5.04510 q^{29} -1.31120 q^{30} +6.15794 q^{31} +1.00000 q^{32} -4.12963 q^{33} +4.96756 q^{34} +3.61614 q^{35} -1.28075 q^{36} -0.957846 q^{37} -1.16157 q^{38} +4.61827 q^{39} -1.00000 q^{40} +2.20177 q^{41} -4.74149 q^{42} +8.45052 q^{43} -3.14951 q^{44} +1.28075 q^{45} -6.16026 q^{47} +1.31120 q^{48} +6.07649 q^{49} +1.00000 q^{50} +6.51347 q^{51} +3.52217 q^{52} +12.3701 q^{53} -5.61293 q^{54} +3.14951 q^{55} -3.61614 q^{56} -1.52305 q^{57} +5.04510 q^{58} +7.95193 q^{59} -1.31120 q^{60} -8.77820 q^{61} +6.15794 q^{62} +4.63139 q^{63} +1.00000 q^{64} -3.52217 q^{65} -4.12963 q^{66} +15.5122 q^{67} +4.96756 q^{68} +3.61614 q^{70} +1.07941 q^{71} -1.28075 q^{72} -2.34692 q^{73} -0.957846 q^{74} +1.31120 q^{75} -1.16157 q^{76} +11.3891 q^{77} +4.61827 q^{78} +7.30901 q^{79} -1.00000 q^{80} -3.51741 q^{81} +2.20177 q^{82} -14.6609 q^{83} -4.74149 q^{84} -4.96756 q^{85} +8.45052 q^{86} +6.61514 q^{87} -3.14951 q^{88} +1.58594 q^{89} +1.28075 q^{90} -12.7367 q^{91} +8.07430 q^{93} -6.16026 q^{94} +1.16157 q^{95} +1.31120 q^{96} -0.135127 q^{97} +6.07649 q^{98} +4.03374 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9} - 15 q^{10} - 7 q^{11} + 5 q^{12} + 17 q^{13} + 4 q^{14} - 5 q^{15} + 15 q^{16} - 2 q^{17} + 28 q^{18} - 18 q^{19} - 15 q^{20} - 7 q^{22} + 5 q^{24} + 15 q^{25} + 17 q^{26} + 29 q^{27} + 4 q^{28} + 35 q^{29} - 5 q^{30} + 19 q^{31} + 15 q^{32} + 21 q^{33} - 2 q^{34} - 4 q^{35} + 28 q^{36} + 12 q^{37} - 18 q^{38} + 26 q^{39} - 15 q^{40} + 27 q^{41} - 12 q^{43} - 7 q^{44} - 28 q^{45} + 40 q^{47} + 5 q^{48} + 29 q^{49} + 15 q^{50} + 27 q^{51} + 17 q^{52} + 20 q^{53} + 29 q^{54} + 7 q^{55} + 4 q^{56} + 11 q^{57} + 35 q^{58} + 15 q^{59} - 5 q^{60} - 28 q^{61} + 19 q^{62} + 51 q^{63} + 15 q^{64} - 17 q^{65} + 21 q^{66} - 4 q^{67} - 2 q^{68} - 4 q^{70} + 22 q^{71} + 28 q^{72} + 48 q^{73} + 12 q^{74} + 5 q^{75} - 18 q^{76} + 45 q^{77} + 26 q^{78} + 2 q^{79} - 15 q^{80} + 79 q^{81} + 27 q^{82} + 29 q^{83} + 2 q^{85} - 12 q^{86} - 7 q^{87} - 7 q^{88} - 20 q^{89} - 28 q^{90} - 6 q^{91} + 63 q^{93} + 40 q^{94} + 18 q^{95} + 5 q^{96} + 22 q^{97} + 29 q^{98} - 23 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 5 * q^3 + 15 * q^4 - 15 * q^5 + 5 * q^6 + 4 * q^7 + 15 * q^8 + 28 * q^9 - 15 * q^10 - 7 * q^11 + 5 * q^12 + 17 * q^13 + 4 * q^14 - 5 * q^15 + 15 * q^16 - 2 * q^17 + 28 * q^18 - 18 * q^19 - 15 * q^20 - 7 * q^22 + 5 * q^24 + 15 * q^25 + 17 * q^26 + 29 * q^27 + 4 * q^28 + 35 * q^29 - 5 * q^30 + 19 * q^31 + 15 * q^32 + 21 * q^33 - 2 * q^34 - 4 * q^35 + 28 * q^36 + 12 * q^37 - 18 * q^38 + 26 * q^39 - 15 * q^40 + 27 * q^41 - 12 * q^43 - 7 * q^44 - 28 * q^45 + 40 * q^47 + 5 * q^48 + 29 * q^49 + 15 * q^50 + 27 * q^51 + 17 * q^52 + 20 * q^53 + 29 * q^54 + 7 * q^55 + 4 * q^56 + 11 * q^57 + 35 * q^58 + 15 * q^59 - 5 * q^60 - 28 * q^61 + 19 * q^62 + 51 * q^63 + 15 * q^64 - 17 * q^65 + 21 * q^66 - 4 * q^67 - 2 * q^68 - 4 * q^70 + 22 * q^71 + 28 * q^72 + 48 * q^73 + 12 * q^74 + 5 * q^75 - 18 * q^76 + 45 * q^77 + 26 * q^78 + 2 * q^79 - 15 * q^80 + 79 * q^81 + 27 * q^82 + 29 * q^83 + 2 * q^85 - 12 * q^86 - 7 * q^87 - 7 * q^88 - 20 * q^89 - 28 * q^90 - 6 * q^91 + 63 * q^93 + 40 * q^94 + 18 * q^95 + 5 * q^96 + 22 * q^97 + 29 * q^98 - 23 * q^99

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