LMFDB - Embedded newform 5290.2.a.bk.1.6

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			1.6
Root			$-0.687865$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.687865 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.687865 q^{6} +3.00706 q^{7} +1.00000 q^{8} -2.52684 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.687865 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.687865 q^{6} +3.00706 q^{7} +1.00000 q^{8} -2.52684 q^{9} -1.00000 q^{10} +3.24051 q^{11} -0.687865 q^{12} +4.42114 q^{13} +3.00706 q^{14} +0.687865 q^{15} +1.00000 q^{16} +7.05680 q^{17} -2.52684 q^{18} +3.61447 q^{19} -1.00000 q^{20} -2.06845 q^{21} +3.24051 q^{22} -0.687865 q^{24} +1.00000 q^{25} +4.42114 q^{26} +3.80172 q^{27} +3.00706 q^{28} -3.99476 q^{29} +0.687865 q^{30} +1.99276 q^{31} +1.00000 q^{32} -2.22903 q^{33} +7.05680 q^{34} -3.00706 q^{35} -2.52684 q^{36} -10.0427 q^{37} +3.61447 q^{38} -3.04114 q^{39} -1.00000 q^{40} +7.22907 q^{41} -2.06845 q^{42} -11.0826 q^{43} +3.24051 q^{44} +2.52684 q^{45} +6.41451 q^{47} -0.687865 q^{48} +2.04242 q^{49} +1.00000 q^{50} -4.85413 q^{51} +4.42114 q^{52} -13.2329 q^{53} +3.80172 q^{54} -3.24051 q^{55} +3.00706 q^{56} -2.48627 q^{57} -3.99476 q^{58} -7.64606 q^{59} +0.687865 q^{60} -7.00035 q^{61} +1.99276 q^{62} -7.59837 q^{63} +1.00000 q^{64} -4.42114 q^{65} -2.22903 q^{66} +3.21749 q^{67} +7.05680 q^{68} -3.00706 q^{70} +8.14071 q^{71} -2.52684 q^{72} +6.95866 q^{73} -10.0427 q^{74} -0.687865 q^{75} +3.61447 q^{76} +9.74441 q^{77} -3.04114 q^{78} +4.39701 q^{79} -1.00000 q^{80} +4.96546 q^{81} +7.22907 q^{82} +4.45448 q^{83} -2.06845 q^{84} -7.05680 q^{85} -11.0826 q^{86} +2.74786 q^{87} +3.24051 q^{88} -5.09686 q^{89} +2.52684 q^{90} +13.2946 q^{91} -1.37075 q^{93} +6.41451 q^{94} -3.61447 q^{95} -0.687865 q^{96} +4.03052 q^{97} +2.04242 q^{98} -8.18825 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.687865	−0.397139	−0.198569	−	0.980087i	$-0.563630\pi$
$3$	−0.687865	−0.397139	−0.198569	+	0.980087i	$0.563630\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.687865	−0.280820
$7$	3.00706	1.13656	0.568281	−	0.822834i	$-0.307609\pi$
$7$	3.00706	1.13656	0.568281	+	0.822834i	$0.307609\pi$
$8$	1.00000	0.353553
$9$	−2.52684	−0.842281
$10$	−1.00000	−0.316228
$11$	3.24051	0.977050	0.488525	−	0.872550i	$-0.337535\pi$
$11$	3.24051	0.977050	0.488525	+	0.872550i	$0.337535\pi$
$12$	−0.687865	−0.198569
$13$	4.42114	1.22620	0.613101	−	0.790004i	$-0.289922\pi$
$13$	4.42114	1.22620	0.613101	+	0.790004i	$0.289922\pi$
$14$	3.00706	0.803671
$15$	0.687865	0.177606
$16$	1.00000	0.250000
$17$	7.05680	1.71153	0.855763	−	0.517368i	$-0.173088\pi$
$17$	7.05680	1.71153	0.855763	+	0.517368i	$0.173088\pi$
$18$	−2.52684	−0.595582
$19$	3.61447	0.829216	0.414608	−	0.910000i	$-0.363919\pi$
$19$	3.61447	0.829216	0.414608	+	0.910000i	$0.363919\pi$
$20$	−1.00000	−0.223607
$21$	−2.06845	−0.451373
$22$	3.24051	0.690879
$23$	0	0
$23$	0	0
$24$	−0.687865	−0.140410
$25$	1.00000	0.200000
$26$	4.42114	0.867056
$27$	3.80172	0.731641
$28$	3.00706	0.568281
$29$	−3.99476	−0.741809	−0.370904	−	0.928671i	$-0.620952\pi$
$29$	−3.99476	−0.741809	−0.370904	+	0.928671i	$0.620952\pi$
$30$	0.687865	0.125586
$31$	1.99276	0.357910	0.178955	−	0.983857i	$-0.442728\pi$
$31$	1.99276	0.357910	0.178955	+	0.983857i	$0.442728\pi$
$32$	1.00000	0.176777
$33$	−2.22903	−0.388025
$34$	7.05680	1.21023
$35$	−3.00706	−0.508286
$36$	−2.52684	−0.421140
$37$	−10.0427	−1.65101	−0.825504	−	0.564396i	$-0.809109\pi$
$37$	−10.0427	−1.65101	−0.825504	+	0.564396i	$0.809109\pi$
$38$	3.61447	0.586344
$39$	−3.04114	−0.486973
$40$	−1.00000	−0.158114
$41$	7.22907	1.12899	0.564496	−	0.825436i	$-0.309071\pi$
$41$	7.22907	1.12899	0.564496	+	0.825436i	$0.309071\pi$
$42$	−2.06845	−0.319169
$43$	−11.0826	−1.69009	−0.845043	−	0.534698i	$-0.820425\pi$
$43$	−11.0826	−1.69009	−0.845043	+	0.534698i	$0.820425\pi$
$44$	3.24051	0.488525
$45$	2.52684	0.376679
$46$	0	0
$47$	6.41451	0.935652	0.467826	−	0.883821i	$-0.345037\pi$
$47$	6.41451	0.935652	0.467826	+	0.883821i	$0.345037\pi$
$48$	−0.687865	−0.0992847
$49$	2.04242	0.291774
$50$	1.00000	0.141421
$51$	−4.85413	−0.679714
$52$	4.42114	0.613101
$53$	−13.2329	−1.81768	−0.908841	−	0.417144i	$-0.863031\pi$
$53$	−13.2329	−1.81768	−0.908841	+	0.417144i	$0.863031\pi$
$54$	3.80172	0.517349
$55$	−3.24051	−0.436950
$56$	3.00706	0.401836
$57$	−2.48627	−0.329314
$58$	−3.99476	−0.524538
$59$	−7.64606	−0.995432	−0.497716	−	0.867340i	$-0.665828\pi$
$59$	−7.64606	−0.995432	−0.497716	+	0.867340i	$0.665828\pi$
$60$	0.687865	0.0888030
$61$	−7.00035	−0.896303	−0.448152	−	0.893958i	$-0.647918\pi$
$61$	−7.00035	−0.896303	−0.448152	+	0.893958i	$0.647918\pi$
$62$	1.99276	0.253080
$63$	−7.59837	−0.957305
$64$	1.00000	0.125000
$65$	−4.42114	−0.548374
$66$	−2.22903	−0.274375
$67$	3.21749	0.393079	0.196540	−	0.980496i	$-0.437030\pi$
$67$	3.21749	0.393079	0.196540	+	0.980496i	$0.437030\pi$
$68$	7.05680	0.855763
$69$	0	0
$70$	−3.00706	−0.359413
$71$	8.14071	0.966125	0.483063	−	0.875586i	$-0.339524\pi$
$71$	8.14071	0.966125	0.483063	+	0.875586i	$0.339524\pi$
$72$	−2.52684	−0.297791
$73$	6.95866	0.814450	0.407225	−	0.913328i	$-0.366497\pi$
$73$	6.95866	0.814450	0.407225	+	0.913328i	$0.366497\pi$
$74$	−10.0427	−1.16744
$75$	−0.687865	−0.0794278
$76$	3.61447	0.414608
$77$	9.74441	1.11048
$78$	−3.04114	−0.344342
$79$	4.39701	0.494702	0.247351	−	0.968926i	$-0.420440\pi$
$79$	4.39701	0.494702	0.247351	+	0.968926i	$0.420440\pi$
$80$	−1.00000	−0.111803
$81$	4.96546	0.551717
$82$	7.22907	0.798317
$83$	4.45448	0.488942	0.244471	−	0.969657i	$-0.421386\pi$
$83$	4.45448	0.488942	0.244471	+	0.969657i	$0.421386\pi$
$84$	−2.06845	−0.225687
$85$	−7.05680	−0.765418
$86$	−11.0826	−1.19507
$87$	2.74786	0.294601
$88$	3.24051	0.345439
$89$	−5.09686	−0.540266	−0.270133	−	0.962823i	$-0.587068\pi$
$89$	−5.09686	−0.540266	−0.270133	+	0.962823i	$0.587068\pi$
$90$	2.52684	0.266353
$91$	13.2946	1.39366
$92$	0	0
$93$	−1.37075	−0.142140
$94$	6.41451	0.661606
$95$	−3.61447	−0.370837
$96$	−0.687865	−0.0702049
$97$	4.03052	0.409238	0.204619	−	0.978842i	$-0.434405\pi$
$97$	4.03052	0.409238	0.204619	+	0.978842i	$0.434405\pi$
$98$	2.04242	0.206316
$99$	−8.18825	−0.822951
$100$	1.00000	0.100000
$101$	11.5235	1.14663	0.573317	−	0.819334i	$-0.305656\pi$
$101$	11.5235	1.14663	0.573317	+	0.819334i	$0.305656\pi$
$102$	−4.85413	−0.480630
$103$	15.0440	1.48233	0.741164	−	0.671324i	$-0.234274\pi$
$103$	15.0440	1.48233	0.741164	+	0.671324i	$0.234274\pi$
$104$	4.42114	0.433528
$105$	2.06845	0.201860
$106$	−13.2329	−1.28529
$107$	−14.4599	−1.39789	−0.698944	−	0.715176i	$-0.746346\pi$
$107$	−14.4599	−1.39789	−0.698944	+	0.715176i	$0.746346\pi$
$108$	3.80172	0.365821
$109$	12.1963	1.16819	0.584095	−	0.811685i	$-0.301450\pi$
$109$	12.1963	1.16819	0.584095	+	0.811685i	$0.301450\pi$
$110$	−3.24051	−0.308970
$111$	6.90801	0.655680
$112$	3.00706	0.284141
$113$	5.74348	0.540301	0.270151	−	0.962818i	$-0.412926\pi$
$113$	5.74348	0.540301	0.270151	+	0.962818i	$0.412926\pi$
$114$	−2.48627	−0.232860
$115$	0	0
$116$	−3.99476	−0.370904
$117$	−11.1715	−1.03281
$118$	−7.64606	−0.703876
$119$	21.2202	1.94526
$120$	0.687865	0.0627932
$121$	−0.499101	−0.0453728
$122$	−7.00035	−0.633782
$123$	−4.97262	−0.448366
$124$	1.99276	0.178955
$125$	−1.00000	−0.0894427
$126$	−7.59837	−0.676917
$127$	−2.01342	−0.178662	−0.0893311	−	0.996002i	$-0.528473\pi$
$127$	−2.01342	−0.178662	−0.0893311	+	0.996002i	$0.528473\pi$
$128$	1.00000	0.0883883
$129$	7.62336	0.671199
$130$	−4.42114	−0.387759
$131$	21.4548	1.87452	0.937258	−	0.348637i	$-0.113355\pi$
$131$	21.4548	1.87452	0.937258	+	0.348637i	$0.113355\pi$
$132$	−2.22903	−0.194012
$133$	10.8689	0.942456
$134$	3.21749	0.277949
$135$	−3.80172	−0.327200
$136$	7.05680	0.605116
$137$	−2.35751	−0.201416	−0.100708	−	0.994916i	$-0.532111\pi$
$137$	−2.35751	−0.201416	−0.100708	+	0.994916i	$0.532111\pi$
$138$	0	0
$139$	4.72632	0.400881	0.200441	−	0.979706i	$-0.435763\pi$
$139$	4.72632	0.400881	0.200441	+	0.979706i	$0.435763\pi$
$140$	−3.00706	−0.254143
$141$	−4.41231	−0.371584
$142$	8.14071	0.683154
$143$	14.3267	1.19806
$144$	−2.52684	−0.210570
$145$	3.99476	0.331747
$146$	6.95866	0.575903
$147$	−1.40491	−0.115875
$148$	−10.0427	−0.825504
$149$	−12.2296	−1.00189	−0.500945	−	0.865479i	$-0.667014\pi$
$149$	−12.2296	−1.00189	−0.500945	+	0.865479i	$0.667014\pi$
$150$	−0.687865	−0.0561639
$151$	−0.0384797	−0.00313143	−0.00156572	−	0.999999i	$-0.500498\pi$
$151$	−0.0384797	−0.00313143	−0.00156572	+	0.999999i	$0.500498\pi$
$152$	3.61447	0.293172
$153$	−17.8314	−1.44159
$154$	9.74441	0.785227
$155$	−1.99276	−0.160062
$156$	−3.04114	−0.243486
$157$	20.7487	1.65593	0.827964	−	0.560781i	$-0.189499\pi$
$157$	20.7487	1.65593	0.827964	+	0.560781i	$0.189499\pi$
$158$	4.39701	0.349807
$159$	9.10246	0.721872
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	4.96546	0.390123
$163$	−7.23879	−0.566986	−0.283493	−	0.958974i	$-0.591493\pi$
$163$	−7.23879	−0.566986	−0.283493	+	0.958974i	$0.591493\pi$
$164$	7.22907	0.564496
$165$	2.22903	0.173530
$166$	4.45448	0.345734
$167$	−12.4771	−0.965504	−0.482752	−	0.875757i	$-0.660363\pi$
$167$	−12.4771	−0.965504	−0.482752	+	0.875757i	$0.660363\pi$
$168$	−2.06845	−0.159585
$169$	6.54644	0.503572
$170$	−7.05680	−0.541232
$171$	−9.13319	−0.698433
$172$	−11.0826	−0.845043
$173$	−3.40711	−0.259038	−0.129519	−	0.991577i	$-0.541343\pi$
$173$	−3.40711	−0.259038	−0.129519	+	0.991577i	$0.541343\pi$
$174$	2.74786	0.208314
$175$	3.00706	0.227313
$176$	3.24051	0.244263
$177$	5.25945	0.395325
$178$	−5.09686	−0.382026
$179$	18.1315	1.35521	0.677606	−	0.735426i	$-0.263018\pi$
$179$	18.1315	1.35521	0.677606	+	0.735426i	$0.263018\pi$
$180$	2.52684	0.188340
$181$	−10.7644	−0.800113	−0.400056	−	0.916491i	$-0.631009\pi$
$181$	−10.7644	−0.800113	−0.400056	+	0.916491i	$0.631009\pi$
$182$	13.2946	0.985463
$183$	4.81530	0.355957
$184$	0	0
$185$	10.0427	0.738353
$186$	−1.37075	−0.100508
$187$	22.8676	1.67225
$188$	6.41451	0.467826
$189$	11.4320	0.831556
$190$	−3.61447	−0.262221
$191$	15.3586	1.11131	0.555654	−	0.831414i	$-0.312468\pi$
$191$	15.3586	1.11131	0.555654	+	0.831414i	$0.312468\pi$
$192$	−0.687865	−0.0496424
$193$	−20.1852	−1.45296	−0.726480	−	0.687187i	$-0.758845\pi$
$193$	−20.1852	−1.45296	−0.726480	+	0.687187i	$0.758845\pi$
$194$	4.03052	0.289375
$195$	3.04114	0.217781
$196$	2.04242	0.145887
$197$	15.8568	1.12975	0.564875	−	0.825176i	$-0.308924\pi$
$197$	15.8568	1.12975	0.564875	+	0.825176i	$0.308924\pi$
$198$	−8.18825	−0.581914
$199$	4.50450	0.319315	0.159658	−	0.987172i	$-0.448961\pi$
$199$	4.50450	0.319315	0.159658	+	0.987172i	$0.448961\pi$
$200$	1.00000	0.0707107
$201$	−2.21320	−0.156107
$202$	11.5235	0.810792
$203$	−12.0125	−0.843112
$204$	−4.85413	−0.339857
$205$	−7.22907	−0.504900
$206$	15.0440	1.04816
$207$	0	0
$208$	4.42114	0.306551
$209$	11.7127	0.810186
$210$	2.06845	0.142737
$211$	0.303976	0.0209266	0.0104633	−	0.999945i	$-0.496669\pi$
$211$	0.303976	0.0209266	0.0104633	+	0.999945i	$0.496669\pi$
$212$	−13.2329	−0.908841
$213$	−5.59971	−0.383686
$214$	−14.4599	−0.988457
$215$	11.0826	0.755830
$216$	3.80172	0.258674
$217$	5.99234	0.406787
$218$	12.1963	0.826035
$219$	−4.78662	−0.323450
$220$	−3.24051	−0.218475
$221$	31.1991	2.09868
$222$	6.90801	0.463636
$223$	−3.69023	−0.247116	−0.123558	−	0.992337i	$-0.539431\pi$
$223$	−3.69023	−0.247116	−0.123558	+	0.992337i	$0.539431\pi$
$224$	3.00706	0.200918
$225$	−2.52684	−0.168456
$226$	5.74348	0.382051
$227$	−6.07432	−0.403167	−0.201583	−	0.979471i	$-0.564609\pi$
$227$	−6.07432	−0.403167	−0.201583	+	0.979471i	$0.564609\pi$
$228$	−2.48627	−0.164657
$229$	−6.76155	−0.446815	−0.223408	−	0.974725i	$-0.571718\pi$
$229$	−6.76155	−0.446815	−0.223408	+	0.974725i	$0.571718\pi$
$230$	0	0
$231$	−6.70284	−0.441014
$232$	−3.99476	−0.262269
$233$	0.183316	0.0120094	0.00600472	−	0.999982i	$-0.498089\pi$
$233$	0.183316	0.0120094	0.00600472	+	0.999982i	$0.498089\pi$
$234$	−11.1715	−0.730305
$235$	−6.41451	−0.418436
$236$	−7.64606	−0.497716
$237$	−3.02455	−0.196466
$238$	21.2202	1.37550
$239$	−16.0127	−1.03578	−0.517888	−	0.855448i	$-0.673282\pi$
$239$	−16.0127	−1.03578	−0.517888	+	0.855448i	$0.673282\pi$
$240$	0.687865	0.0444015
$241$	−19.2723	−1.24144	−0.620720	−	0.784032i	$-0.713160\pi$
$241$	−19.2723	−1.24144	−0.620720	+	0.784032i	$0.713160\pi$
$242$	−0.499101	−0.0320834
$243$	−14.8207	−0.950750
$244$	−7.00035	−0.448152
$245$	−2.04242	−0.130485
$246$	−4.97262	−0.317043
$247$	15.9801	1.01679
$248$	1.99276	0.126540
$249$	−3.06408	−0.194178
$250$	−1.00000	−0.0632456
$251$	6.23430	0.393505	0.196753	−	0.980453i	$-0.436960\pi$
$251$	6.23430	0.393505	0.196753	+	0.980453i	$0.436960\pi$
$252$	−7.59837	−0.478652
$253$	0	0
$254$	−2.01342	−0.126333
$255$	4.85413	0.303977
$256$	1.00000	0.0625000
$257$	3.11681	0.194421	0.0972107	−	0.995264i	$-0.469008\pi$
$257$	3.11681	0.194421	0.0972107	+	0.995264i	$0.469008\pi$
$258$	7.62336	0.474609
$259$	−30.1990	−1.87647
$260$	−4.42114	−0.274187
$261$	10.0941	0.624811
$262$	21.4548	1.32548
$263$	17.0419	1.05085	0.525426	−	0.850840i	$-0.323906\pi$
$263$	17.0419	1.05085	0.525426	+	0.850840i	$0.323906\pi$
$264$	−2.22903	−0.137187
$265$	13.2329	0.812892
$266$	10.8689	0.666417
$267$	3.50595	0.214561
$268$	3.21749	0.196540
$269$	−13.0472	−0.795501	−0.397751	−	0.917494i	$-0.630209\pi$
$269$	−13.0472	−0.795501	−0.397751	+	0.917494i	$0.630209\pi$
$270$	−3.80172	−0.231365
$271$	20.4629	1.24303	0.621516	−	0.783402i	$-0.286517\pi$
$271$	20.4629	1.24303	0.621516	+	0.783402i	$0.286517\pi$
$272$	7.05680	0.427882
$273$	−9.14491	−0.553475
$274$	−2.35751	−0.142422
$275$	3.24051	0.195410
$276$	0	0
$277$	7.62194	0.457958	0.228979	−	0.973431i	$-0.426461\pi$
$277$	7.62194	0.457958	0.228979	+	0.973431i	$0.426461\pi$
$278$	4.72632	0.283466
$279$	−5.03538	−0.301460
$280$	−3.00706	−0.179706
$281$	−30.6641	−1.82927	−0.914634	−	0.404284i	$-0.867521\pi$
$281$	−30.6641	−1.82927	−0.914634	+	0.404284i	$0.867521\pi$
$282$	−4.41231	−0.262749
$283$	−4.20804	−0.250142	−0.125071	−	0.992148i	$-0.539916\pi$
$283$	−4.20804	−0.250142	−0.125071	+	0.992148i	$0.539916\pi$
$284$	8.14071	0.483063
$285$	2.48627	0.147274
$286$	14.3267	0.847157
$287$	21.7383	1.28317
$288$	−2.52684	−0.148896
$289$	32.7985	1.92932
$290$	3.99476	0.234580
$291$	−2.77245	−0.162524
$292$	6.95866	0.407225
$293$	−13.3949	−0.782538	−0.391269	−	0.920276i	$-0.627964\pi$
$293$	−13.3949	−0.782538	−0.391269	+	0.920276i	$0.627964\pi$
$294$	−1.40491	−0.0819360
$295$	7.64606	0.445171
$296$	−10.0427	−0.583720
$297$	12.3195	0.714850
$298$	−12.2296	−0.708443
$299$	0	0
$300$	−0.687865	−0.0397139
$301$	−33.3262	−1.92089
$302$	−0.0384797	−0.00221426
$303$	−7.92663	−0.455373
$304$	3.61447	0.207304
$305$	7.00035	0.400839
$306$	−17.8314	−1.01935
$307$	−27.6037	−1.57543	−0.787714	−	0.616041i	$-0.788736\pi$
$307$	−27.6037	−1.57543	−0.787714	+	0.616041i	$0.788736\pi$
$308$	9.74441	0.555239
$309$	−10.3482	−0.588690
$310$	−1.99276	−0.113181
$311$	5.16786	0.293042	0.146521	−	0.989208i	$-0.453192\pi$
$311$	5.16786	0.293042	0.146521	+	0.989208i	$0.453192\pi$
$312$	−3.04114	−0.172171
$313$	−17.8087	−1.00661	−0.503304	−	0.864109i	$-0.667882\pi$
$313$	−17.8087	−1.00661	−0.503304	+	0.864109i	$0.667882\pi$
$314$	20.7487	1.17092
$315$	7.59837	0.428120
$316$	4.39701	0.247351
$317$	10.0607	0.565067	0.282533	−	0.959257i	$-0.408825\pi$
$317$	10.0607	0.565067	0.282533	+	0.959257i	$0.408825\pi$
$318$	9.10246	0.510441
$319$	−12.9451	−0.724784
$320$	−1.00000	−0.0559017
$321$	9.94644	0.555156
$322$	0	0
$323$	25.5066	1.41923
$324$	4.96546	0.275859
$325$	4.42114	0.245240
$326$	−7.23879	−0.400920
$327$	−8.38938	−0.463934
$328$	7.22907	0.399159
$329$	19.2888	1.06343
$330$	2.22903	0.122704
$331$	−17.8193	−0.979436	−0.489718	−	0.871881i	$-0.662900\pi$
$331$	−17.8193	−0.979436	−0.489718	+	0.871881i	$0.662900\pi$
$332$	4.45448	0.244471
$333$	25.3763	1.39061
$334$	−12.4771	−0.682714
$335$	−3.21749	−0.175790
$336$	−2.06845	−0.112843
$337$	−9.41639	−0.512944	−0.256472	−	0.966552i	$-0.582560\pi$
$337$	−9.41639	−0.512944	−0.256472	+	0.966552i	$0.582560\pi$
$338$	6.54644	0.356079
$339$	−3.95074	−0.214575
$340$	−7.05680	−0.382709
$341$	6.45754	0.349696
$342$	−9.13319	−0.493867
$343$	−14.9077	−0.804943
$344$	−11.0826	−0.597536
$345$	0	0
$346$	−3.40711	−0.183167
$347$	4.29239	0.230427	0.115214	−	0.993341i	$-0.463245\pi$
$347$	4.29239	0.230427	0.115214	+	0.993341i	$0.463245\pi$
$348$	2.74786	0.147301
$349$	3.59399	0.192382	0.0961909	−	0.995363i	$-0.469334\pi$
$349$	3.59399	0.192382	0.0961909	+	0.995363i	$0.469334\pi$
$350$	3.00706	0.160734
$351$	16.8079	0.897140
$352$	3.24051	0.172720
$353$	32.8570	1.74880	0.874400	−	0.485205i	$-0.161255\pi$
$353$	32.8570	1.74880	0.874400	+	0.485205i	$0.161255\pi$
$354$	5.25945	0.279537
$355$	−8.14071	−0.432064
$356$	−5.09686	−0.270133
$357$	−14.5967	−0.772537
$358$	18.1315	0.958279
$359$	−13.4752	−0.711194	−0.355597	−	0.934639i	$-0.615722\pi$
$359$	−13.4752	−0.711194	−0.355597	+	0.934639i	$0.615722\pi$
$360$	2.52684	0.133176
$361$	−5.93561	−0.312400
$362$	−10.7644	−0.565765
$363$	0.343314	0.0180193
$364$	13.2946	0.696828
$365$	−6.95866	−0.364233
$366$	4.81530	0.251700
$367$	25.1845	1.31462	0.657310	−	0.753620i	$-0.271694\pi$
$367$	25.1845	1.31462	0.657310	+	0.753620i	$0.271694\pi$
$368$	0	0
$369$	−18.2667	−0.950928
$370$	10.0427	0.522095
$371$	−39.7922	−2.06591
$372$	−1.37075	−0.0710699
$373$	−13.0191	−0.674103	−0.337051	−	0.941486i	$-0.609430\pi$
$373$	−13.0191	−0.674103	−0.337051	+	0.941486i	$0.609430\pi$
$374$	22.8676	1.18246
$375$	0.687865	0.0355212
$376$	6.41451	0.330803
$377$	−17.6614	−0.909608
$378$	11.4320	0.587999
$379$	−4.98084	−0.255849	−0.127924	−	0.991784i	$-0.540831\pi$
$379$	−4.98084	−0.255849	−0.127924	+	0.991784i	$0.540831\pi$
$380$	−3.61447	−0.185418
$381$	1.38496	0.0709537
$382$	15.3586	0.785813
$383$	6.43033	0.328575	0.164287	−	0.986413i	$-0.447468\pi$
$383$	6.43033	0.328575	0.164287	+	0.986413i	$0.447468\pi$
$384$	−0.687865	−0.0351025
$385$	−9.74441	−0.496621
$386$	−20.1852	−1.02740
$387$	28.0041	1.42353
$388$	4.03052	0.204619
$389$	−17.9814	−0.911693	−0.455847	−	0.890058i	$-0.650663\pi$
$389$	−17.9814	−0.911693	−0.455847	+	0.890058i	$0.650663\pi$
$390$	3.04114	0.153994
$391$	0	0
$392$	2.04242	0.103158
$393$	−14.7580	−0.744443
$394$	15.8568	0.798854
$395$	−4.39701	−0.221238
$396$	−8.18825	−0.411475
$397$	8.60381	0.431813	0.215906	−	0.976414i	$-0.430729\pi$
$397$	8.60381	0.431813	0.215906	+	0.976414i	$0.430729\pi$
$398$	4.50450	0.225790
$399$	−7.47636	−0.374286
$400$	1.00000	0.0500000
$401$	28.0514	1.40082	0.700409	−	0.713741i	$-0.253001\pi$
$401$	28.0514	1.40082	0.700409	+	0.713741i	$0.253001\pi$
$402$	−2.21320	−0.110384
$403$	8.81025	0.438870
$404$	11.5235	0.573317
$405$	−4.96546	−0.246736
$406$	−12.0125	−0.596170
$407$	−32.5434	−1.61312
$408$	−4.85413	−0.240315
$409$	−7.73500	−0.382471	−0.191236	−	0.981544i	$-0.561249\pi$
$409$	−7.73500	−0.382471	−0.191236	+	0.981544i	$0.561249\pi$
$410$	−7.22907	−0.357018
$411$	1.62165	0.0799901
$412$	15.0440	0.741164
$413$	−22.9922	−1.13137
$414$	0	0
$415$	−4.45448	−0.218662
$416$	4.42114	0.216764
$417$	−3.25107	−0.159206
$418$	11.7127	0.572888
$419$	−15.1663	−0.740920	−0.370460	−	0.928848i	$-0.620800\pi$
$419$	−15.1663	−0.740920	−0.370460	+	0.928848i	$0.620800\pi$
$420$	2.06845	0.100930
$421$	−9.52120	−0.464035	−0.232017	−	0.972712i	$-0.574533\pi$
$421$	−9.52120	−0.464035	−0.232017	+	0.972712i	$0.574533\pi$
$422$	0.303976	0.0147973
$423$	−16.2084	−0.788082
$424$	−13.2329	−0.642647
$425$	7.05680	0.342305
$426$	−5.59971	−0.271307
$427$	−21.0505	−1.01870
$428$	−14.4599	−0.698944
$429$	−9.85485	−0.475797
$430$	11.0826	0.534452
$431$	0.185120	0.00891690	0.00445845	−	0.999990i	$-0.498581\pi$
$431$	0.185120	0.00891690	0.00445845	+	0.999990i	$0.498581\pi$
$432$	3.80172	0.182910
$433$	9.91090	0.476288	0.238144	−	0.971230i	$-0.423461\pi$
$433$	9.91090	0.476288	0.238144	+	0.971230i	$0.423461\pi$
$434$	5.99234	0.287642
$435$	−2.74786	−0.131750
$436$	12.1963	0.584095
$437$	0	0
$438$	−4.78662	−0.228713
$439$	−37.5453	−1.79194	−0.895971	−	0.444113i	$-0.853519\pi$
$439$	−37.5453	−1.79194	−0.895971	+	0.444113i	$0.853519\pi$
$440$	−3.24051	−0.154485
$441$	−5.16087	−0.245756
$442$	31.1991	1.48399
$443$	12.4666	0.592305	0.296153	−	0.955141i	$-0.404296\pi$
$443$	12.4666	0.592305	0.296153	+	0.955141i	$0.404296\pi$
$444$	6.90801	0.327840
$445$	5.09686	0.241614
$446$	−3.69023	−0.174737
$447$	8.41232	0.397889
$448$	3.00706	0.142070
$449$	−15.7584	−0.743684	−0.371842	−	0.928296i	$-0.621274\pi$
$449$	−15.7584	−0.743684	−0.371842	+	0.928296i	$0.621274\pi$
$450$	−2.52684	−0.119116
$451$	23.4259	1.10308
$452$	5.74348	0.270151
$453$	0.0264688	0.00124361
$454$	−6.07432	−0.285082
$455$	−13.2946	−0.623262
$456$	−2.48627	−0.116430
$457$	9.77158	0.457095	0.228548	−	0.973533i	$-0.426602\pi$
$457$	9.77158	0.457095	0.228548	+	0.973533i	$0.426602\pi$
$458$	−6.76155	−0.315946
$459$	26.8280	1.25222
$460$	0	0
$461$	4.93513	0.229852	0.114926	−	0.993374i	$-0.463337\pi$
$461$	4.93513	0.229852	0.114926	+	0.993374i	$0.463337\pi$
$462$	−6.70284	−0.311844
$463$	11.4617	0.532672	0.266336	−	0.963880i	$-0.414187\pi$
$463$	11.4617	0.532672	0.266336	+	0.963880i	$0.414187\pi$
$464$	−3.99476	−0.185452
$465$	1.37075	0.0635669
$466$	0.183316	0.00849196
$467$	−20.7077	−0.958240	−0.479120	−	0.877749i	$-0.659044\pi$
$467$	−20.7077	−0.958240	−0.479120	+	0.877749i	$0.659044\pi$
$468$	−11.1715	−0.516403
$469$	9.67520	0.446759
$470$	−6.41451	−0.295879
$471$	−14.2723	−0.657634
$472$	−7.64606	−0.351938
$473$	−35.9134	−1.65130
$474$	−3.02455	−0.138922
$475$	3.61447	0.165843
$476$	21.2202	0.972628
$477$	33.4375	1.53100
$478$	−16.0127	−0.732405
$479$	13.1882	0.602585	0.301292	−	0.953532i	$-0.402582\pi$
$479$	13.1882	0.602585	0.301292	+	0.953532i	$0.402582\pi$
$480$	0.687865	0.0313966
$481$	−44.4001	−2.02447
$482$	−19.2723	−0.877831
$483$	0	0
$484$	−0.499101	−0.0226864
$485$	−4.03052	−0.183017
$486$	−14.8207	−0.672282
$487$	−33.7045	−1.52730	−0.763649	−	0.645631i	$-0.776594\pi$
$487$	−33.7045	−1.52730	−0.763649	+	0.645631i	$0.776594\pi$
$488$	−7.00035	−0.316891
$489$	4.97931	0.225172
$490$	−2.04242	−0.0922672
$491$	29.4087	1.32720	0.663598	−	0.748090i	$-0.269029\pi$
$491$	29.4087	1.32720	0.663598	+	0.748090i	$0.269029\pi$
$492$	−4.97262	−0.224183
$493$	−28.1902	−1.26962
$494$	15.9801	0.718977
$495$	8.18825	0.368035
$496$	1.99276	0.0894774
$497$	24.4796	1.09806
$498$	−3.06408	−0.137305
$499$	39.7987	1.78164	0.890818	−	0.454360i	$-0.150132\pi$
$499$	39.7987	1.78164	0.890818	+	0.454360i	$0.150132\pi$
$500$	−1.00000	−0.0447214
$501$	8.58253	0.383439
$502$	6.23430	0.278250
$503$	−6.32803	−0.282153	−0.141076	−	0.989999i	$-0.545056\pi$
$503$	−6.32803	−0.282153	−0.141076	+	0.989999i	$0.545056\pi$
$504$	−7.59837	−0.338458
$505$	−11.5235	−0.512790
$506$	0	0
$507$	−4.50307	−0.199988
$508$	−2.01342	−0.0893311
$509$	32.2461	1.42928	0.714642	−	0.699490i	$-0.246589\pi$
$509$	32.2461	1.42928	0.714642	+	0.699490i	$0.246589\pi$
$510$	4.85413	0.214944
$511$	20.9251	0.925673
$512$	1.00000	0.0441942
$513$	13.7412	0.606689
$514$	3.11681	0.137477
$515$	−15.0440	−0.662918
$516$	7.62336	0.335600
$517$	20.7863	0.914179
$518$	−30.1990	−1.32687
$519$	2.34363	0.102874
$520$	−4.42114	−0.193880
$521$	0.599361	0.0262585	0.0131292	−	0.999914i	$-0.495821\pi$
$521$	0.599361	0.0262585	0.0131292	+	0.999914i	$0.495821\pi$
$522$	10.0941	0.441808
$523$	19.9511	0.872399	0.436200	−	0.899850i	$-0.356324\pi$
$523$	19.9511	0.872399	0.436200	+	0.899850i	$0.356324\pi$
$524$	21.4548	0.937258
$525$	−2.06845	−0.0902746
$526$	17.0419	0.743064
$527$	14.0625	0.612572
$528$	−2.22903	−0.0970062
$529$	0	0
$530$	13.2329	0.574801
$531$	19.3204	0.838433
$532$	10.8689	0.471228
$533$	31.9607	1.38437
$534$	3.50595	0.151717
$535$	14.4599	0.625155
$536$	3.21749	0.138975
$537$	−12.4720	−0.538207
$538$	−13.0472	−0.562504
$539$	6.61848	0.285078
$540$	−3.80172	−0.163600
$541$	32.5082	1.39764	0.698819	−	0.715299i	$-0.253709\pi$
$541$	32.5082	1.39764	0.698819	+	0.715299i	$0.253709\pi$
$542$	20.4629	0.878956
$543$	7.40446	0.317756
$544$	7.05680	0.302558
$545$	−12.1963	−0.522430
$546$	−9.14491	−0.391366
$547$	13.0757	0.559075	0.279537	−	0.960135i	$-0.409819\pi$
$547$	13.0757	0.559075	0.279537	+	0.960135i	$0.409819\pi$
$548$	−2.35751	−0.100708
$549$	17.6888	0.754939
$550$	3.24051	0.138176
$551$	−14.4389	−0.615120
$552$	0	0
$553$	13.2221	0.562260
$554$	7.62194	0.323825
$555$	−6.90801	−0.293229
$556$	4.72632	0.200441
$557$	35.6049	1.50863	0.754315	−	0.656513i	$-0.227969\pi$
$557$	35.6049	1.50863	0.754315	+	0.656513i	$0.227969\pi$
$558$	−5.03538	−0.213165
$559$	−48.9978	−2.07239
$560$	−3.00706	−0.127072
$561$	−15.7298	−0.664114
$562$	−30.6641	−1.29349
$563$	−25.5432	−1.07652	−0.538260	−	0.842779i	$-0.680918\pi$
$563$	−25.5432	−1.07652	−0.538260	+	0.842779i	$0.680918\pi$
$564$	−4.41231	−0.185792
$565$	−5.74348	−0.241630
$566$	−4.20804	−0.176877
$567$	14.9314	0.627061
$568$	8.14071	0.341577
$569$	−8.54974	−0.358424	−0.179212	−	0.983811i	$-0.557355\pi$
$569$	−8.54974	−0.358424	−0.179212	+	0.983811i	$0.557355\pi$
$570$	2.48627	0.104138
$571$	−44.2257	−1.85079	−0.925393	−	0.379008i	$-0.876265\pi$
$571$	−44.2257	−1.85079	−0.925393	+	0.379008i	$0.876265\pi$
$572$	14.3267	0.599031
$573$	−10.5646	−0.441344
$574$	21.7383	0.907338
$575$	0	0
$576$	−2.52684	−0.105285
$577$	14.7969	0.616002	0.308001	−	0.951386i	$-0.400340\pi$
$577$	14.7969	0.616002	0.308001	+	0.951386i	$0.400340\pi$
$578$	32.7985	1.36424
$579$	13.8847	0.577027
$580$	3.99476	0.165873
$581$	13.3949	0.555714
$582$	−2.77245	−0.114922
$583$	−42.8814	−1.77597
$584$	6.95866	0.287951
$585$	11.1715	0.461885
$586$	−13.3949	−0.553338
$587$	−7.75421	−0.320050	−0.160025	−	0.987113i	$-0.551158\pi$
$587$	−7.75421	−0.320050	−0.160025	+	0.987113i	$0.551158\pi$
$588$	−1.40491	−0.0579375
$589$	7.20276	0.296784
$590$	7.64606	0.314783
$591$	−10.9073	−0.448668
$592$	−10.0427	−0.412752
$593$	43.2717	1.77696	0.888479	−	0.458918i	$-0.151763\pi$
$593$	43.2717	1.77696	0.888479	+	0.458918i	$0.151763\pi$
$594$	12.3195	0.505476
$595$	−21.2202	−0.869945
$596$	−12.2296	−0.500945
$597$	−3.09849	−0.126813
$598$	0	0
$599$	14.4615	0.590880	0.295440	−	0.955361i	$-0.404534\pi$
$599$	14.4615	0.590880	0.295440	+	0.955361i	$0.404534\pi$
$600$	−0.687865	−0.0280820
$601$	−38.3829	−1.56567	−0.782835	−	0.622230i	$-0.786227\pi$
$601$	−38.3829	−1.56567	−0.782835	+	0.622230i	$0.786227\pi$
$602$	−33.3262	−1.35827
$603$	−8.13010	−0.331083
$604$	−0.0384797	−0.00156572
$605$	0.499101	0.0202913
$606$	−7.92663	−0.321997
$607$	8.49676	0.344873	0.172436	−	0.985021i	$-0.444836\pi$
$607$	8.49676	0.344873	0.172436	+	0.985021i	$0.444836\pi$
$608$	3.61447	0.146586
$609$	8.26297	0.334833
$610$	7.00035	0.283436
$611$	28.3594	1.14730
$612$	−17.8314	−0.720793
$613$	12.9136	0.521574	0.260787	−	0.965396i	$-0.416018\pi$
$613$	12.9136	0.521574	0.260787	+	0.965396i	$0.416018\pi$
$614$	−27.6037	−1.11400
$615$	4.97262	0.200516
$616$	9.74441	0.392614
$617$	−2.64777	−0.106595	−0.0532975	−	0.998579i	$-0.516973\pi$
$617$	−2.64777	−0.106595	−0.0532975	+	0.998579i	$0.516973\pi$
$618$	−10.3482	−0.416267
$619$	0.535543	0.0215253	0.0107626	−	0.999942i	$-0.496574\pi$
$619$	0.535543	0.0215253	0.0107626	+	0.999942i	$0.496574\pi$
$620$	−1.99276	−0.0800310
$621$	0	0
$622$	5.16786	0.207212
$623$	−15.3266	−0.614046
$624$	−3.04114	−0.121743
$625$	1.00000	0.0400000
$626$	−17.8087	−0.711779
$627$	−8.05677	−0.321756
$628$	20.7487	0.827964
$629$	−70.8693	−2.82574
$630$	7.59837	0.302726
$631$	45.3759	1.80639	0.903194	−	0.429233i	$-0.141216\pi$
$631$	45.3759	1.80639	0.903194	+	0.429233i	$0.141216\pi$
$632$	4.39701	0.174904
$633$	−0.209094	−0.00831076
$634$	10.0607	0.399563
$635$	2.01342	0.0799001
$636$	9.10246	0.360936
$637$	9.02982	0.357774
$638$	−12.9451	−0.512500
$639$	−20.5703	−0.813748
$640$	−1.00000	−0.0395285
$641$	2.33116	0.0920754	0.0460377	−	0.998940i	$-0.485341\pi$
$641$	2.33116	0.0920754	0.0460377	+	0.998940i	$0.485341\pi$
$642$	9.94644	0.392555
$643$	−12.3892	−0.488582	−0.244291	−	0.969702i	$-0.578555\pi$
$643$	−12.3892	−0.488582	−0.244291	+	0.969702i	$0.578555\pi$
$644$	0	0
$645$	−7.62336	−0.300169
$646$	25.5066	1.00354
$647$	33.8137	1.32936	0.664678	−	0.747130i	$-0.268569\pi$
$647$	33.8137	1.32936	0.664678	+	0.747130i	$0.268569\pi$
$648$	4.96546	0.195062
$649$	−24.7771	−0.972587
$650$	4.42114	0.173411
$651$	−4.12192	−0.161551
$652$	−7.23879	−0.283493
$653$	10.1269	0.396297	0.198148	−	0.980172i	$-0.436507\pi$
$653$	10.1269	0.396297	0.198148	+	0.980172i	$0.436507\pi$
$654$	−8.38938	−0.328051
$655$	−21.4548	−0.838309
$656$	7.22907	0.282248
$657$	−17.5834	−0.685995
$658$	19.2888	0.751956
$659$	−42.5658	−1.65813	−0.829065	−	0.559153i	$-0.811127\pi$
$659$	−42.5658	−1.65813	−0.829065	+	0.559153i	$0.811127\pi$
$660$	2.22903	0.0867650
$661$	−44.2466	−1.72099	−0.860496	−	0.509457i	$-0.829846\pi$
$661$	−44.2466	−1.72099	−0.860496	+	0.509457i	$0.829846\pi$
$662$	−17.8193	−0.692566
$663$	−21.4608	−0.833467
$664$	4.45448	0.172867
$665$	−10.8689	−0.421479
$666$	25.3763	0.983311
$667$	0	0
$668$	−12.4771	−0.482752
$669$	2.53838	0.0981394
$670$	−3.21749	−0.124303
$671$	−22.6847	−0.875733
$672$	−2.06845	−0.0797923
$673$	−32.2231	−1.24211	−0.621054	−	0.783768i	$-0.713295\pi$
$673$	−32.2231	−1.24211	−0.621054	+	0.783768i	$0.713295\pi$
$674$	−9.41639	−0.362706
$675$	3.80172	0.146328
$676$	6.54644	0.251786
$677$	23.4688	0.901979	0.450990	−	0.892529i	$-0.351071\pi$
$677$	23.4688	0.901979	0.450990	+	0.892529i	$0.351071\pi$
$678$	−3.95074	−0.151727
$679$	12.1200	0.465124
$680$	−7.05680	−0.270616
$681$	4.17831	0.160113
$682$	6.45754	0.247272
$683$	−3.49348	−0.133674	−0.0668372	−	0.997764i	$-0.521291\pi$
$683$	−3.49348	−0.133674	−0.0668372	+	0.997764i	$0.521291\pi$
$684$	−9.13319	−0.349216
$685$	2.35751	0.0900759
$686$	−14.9077	−0.569180
$687$	4.65103	0.177448
$688$	−11.0826	−0.422522
$689$	−58.5045	−2.22884
$690$	0	0
$691$	10.5647	0.401899	0.200950	−	0.979602i	$-0.435597\pi$
$691$	10.5647	0.401899	0.200950	+	0.979602i	$0.435597\pi$
$692$	−3.40711	−0.129519
$693$	−24.6226	−0.935335
$694$	4.29239	0.162937
$695$	−4.72632	−0.179280
$696$	2.74786	0.104157
$697$	51.0141	1.93230
$698$	3.59399	0.136034
$699$	−0.126097	−0.00476942
$700$	3.00706	0.113656
$701$	−17.9562	−0.678196	−0.339098	−	0.940751i	$-0.610122\pi$
$701$	−17.9562	−0.678196	−0.339098	+	0.940751i	$0.610122\pi$
$702$	16.8079	0.634374
$703$	−36.2990	−1.36904
$704$	3.24051	0.122131
$705$	4.41231	0.166177
$706$	32.8570	1.23659
$707$	34.6519	1.30322
$708$	5.25945	0.197662
$709$	−51.7367	−1.94301	−0.971507	−	0.237012i	$-0.923832\pi$
$709$	−51.7367	−1.94301	−0.971507	+	0.237012i	$0.923832\pi$
$710$	−8.14071	−0.305516
$711$	−11.1106	−0.416678
$712$	−5.09686	−0.191013
$713$	0	0
$714$	−14.5967	−0.546266
$715$	−14.3267	−0.535789
$716$	18.1315	0.677606
$717$	11.0146	0.411347
$718$	−13.4752	−0.502890
$719$	−12.3012	−0.458757	−0.229378	−	0.973337i	$-0.573669\pi$
$719$	−12.3012	−0.458757	−0.229378	+	0.973337i	$0.573669\pi$
$720$	2.52684	0.0941698
$721$	45.2382	1.68476
$722$	−5.93561	−0.220900
$723$	13.2568	0.493024
$724$	−10.7644	−0.400056
$725$	−3.99476	−0.148362
$726$	0.343314	0.0127416
$727$	−23.8666	−0.885163	−0.442582	−	0.896728i	$-0.645937\pi$
$727$	−23.8666	−0.885163	−0.442582	+	0.896728i	$0.645937\pi$
$728$	13.2946	0.492732
$729$	−4.70172	−0.174138
$730$	−6.95866	−0.257552
$731$	−78.2080	−2.89263
$732$	4.81530	0.177978
$733$	−26.8902	−0.993213	−0.496606	−	0.867976i	$-0.665421\pi$
$733$	−26.8902	−0.993213	−0.496606	+	0.867976i	$0.665421\pi$
$734$	25.1845	0.929577
$735$	1.40491	0.0518209
$736$	0	0
$737$	10.4263	0.384058
$738$	−18.2667	−0.672407
$739$	−14.6105	−0.537457	−0.268729	−	0.963216i	$-0.586603\pi$
$739$	−14.6105	−0.537457	−0.268729	+	0.963216i	$0.586603\pi$
$740$	10.0427	0.369177
$741$	−10.9921	−0.403806
$742$	−39.7922	−1.46082
$743$	40.3251	1.47938	0.739692	−	0.672945i	$-0.234971\pi$
$743$	40.3251	1.47938	0.739692	+	0.672945i	$0.234971\pi$
$744$	−1.37075	−0.0502540
$745$	12.2296	0.448058
$746$	−13.0191	−0.476663
$747$	−11.2558	−0.411827
$748$	22.8676	0.836124
$749$	−43.4817	−1.58879
$750$	0.687865	0.0251173
$751$	−26.1441	−0.954011	−0.477006	−	0.878900i	$-0.658278\pi$
$751$	−26.1441	−0.954011	−0.477006	+	0.878900i	$0.658278\pi$
$752$	6.41451	0.233913
$753$	−4.28835	−0.156276
$754$	−17.6614	−0.643190
$755$	0.0384797	0.00140042
$756$	11.4320	0.415778
$757$	−0.863652	−0.0313899	−0.0156950	−	0.999877i	$-0.504996\pi$
$757$	−0.863652	−0.0313899	−0.0156950	+	0.999877i	$0.504996\pi$
$758$	−4.98084	−0.180912
$759$	0	0
$760$	−3.61447	−0.131111
$761$	21.7751	0.789347	0.394673	−	0.918821i	$-0.370858\pi$
$761$	21.7751	0.789347	0.394673	+	0.918821i	$0.370858\pi$
$762$	1.38496	0.0501718
$763$	36.6749	1.32772
$764$	15.3586	0.555654
$765$	17.8314	0.644697
$766$	6.43033	0.232337
$767$	−33.8043	−1.22060
$768$	−0.687865	−0.0248212
$769$	−18.3649	−0.662257	−0.331129	−	0.943586i	$-0.607429\pi$
$769$	−18.3649	−0.662257	−0.331129	+	0.943586i	$0.607429\pi$
$770$	−9.74441	−0.351164
$771$	−2.14395	−0.0772123
$772$	−20.1852	−0.726480
$773$	18.8611	0.678388	0.339194	−	0.940716i	$-0.389846\pi$
$773$	18.8611	0.678388	0.339194	+	0.940716i	$0.389846\pi$
$774$	28.0041	1.00659
$775$	1.99276	0.0715819
$776$	4.03052	0.144687
$777$	20.7728	0.745221
$778$	−17.9814	−0.644664
$779$	26.1293	0.936178
$780$	3.04114	0.108890
$781$	26.3801	0.943953
$782$	0	0
$783$	−15.1870	−0.542738
$784$	2.04242	0.0729436
$785$	−20.7487	−0.740554
$786$	−14.7580	−0.526401
$787$	−15.9578	−0.568834	−0.284417	−	0.958701i	$-0.591800\pi$
$787$	−15.9578	−0.568834	−0.284417	+	0.958701i	$0.591800\pi$
$788$	15.8568	0.564875
$789$	−11.7226	−0.417334
$790$	−4.39701	−0.156439
$791$	17.2710	0.614086
$792$	−8.18825	−0.290957
$793$	−30.9495	−1.09905
$794$	8.60381	0.305338
$795$	−9.10246	−0.322831
$796$	4.50450	0.159658
$797$	12.4599	0.441352	0.220676	−	0.975347i	$-0.429174\pi$
$797$	12.4599	0.441352	0.220676	+	0.975347i	$0.429174\pi$
$798$	−7.47636	−0.264660
$799$	45.2659	1.60139
$800$	1.00000	0.0353553
$801$	12.8790	0.455056
$802$	28.0514	0.990528
$803$	22.5496	0.795758
$804$	−2.21320	−0.0780536
$805$	0	0
$806$	8.81025	0.310328
$807$	8.97470	0.315925
$808$	11.5235	0.405396
$809$	−25.0683	−0.881355	−0.440678	−	0.897665i	$-0.645262\pi$
$809$	−25.0683	−0.881355	−0.440678	+	0.897665i	$0.645262\pi$
$810$	−4.96546	−0.174468
$811$	−51.4556	−1.80685	−0.903426	−	0.428745i	$-0.858956\pi$
$811$	−51.4556	−1.80685	−0.903426	+	0.428745i	$0.858956\pi$
$812$	−12.0125	−0.421556
$813$	−14.0757	−0.493656
$814$	−32.5434	−1.14065
$815$	7.23879	0.253564
$816$	−4.85413	−0.169928
$817$	−40.0579	−1.40145
$818$	−7.73500	−0.270448
$819$	−33.5934	−1.17385
$820$	−7.22907	−0.252450
$821$	−15.1637	−0.529218	−0.264609	−	0.964356i	$-0.585243\pi$
$821$	−15.1637	−0.529218	−0.264609	+	0.964356i	$0.585243\pi$
$822$	1.62165	0.0565615
$823$	−47.0601	−1.64041	−0.820205	−	0.572069i	$-0.806141\pi$
$823$	−47.0601	−1.64041	−0.820205	+	0.572069i	$0.806141\pi$
$824$	15.0440	0.524082
$825$	−2.22903	−0.0776049
$826$	−22.9922	−0.800000
$827$	8.29138	0.288319	0.144160	−	0.989554i	$-0.453952\pi$
$827$	8.29138	0.288319	0.144160	+	0.989554i	$0.453952\pi$
$828$	0	0
$829$	20.2564	0.703533	0.351767	−	0.936088i	$-0.385581\pi$
$829$	20.2564	0.703533	0.351767	+	0.936088i	$0.385581\pi$
$830$	−4.45448	−0.154617
$831$	−5.24286	−0.181873
$832$	4.42114	0.153275
$833$	14.4130	0.499379
$834$	−3.25107	−0.112575
$835$	12.4771	0.431786
$836$	11.7127	0.405093
$837$	7.57590	0.261861
$838$	−15.1663	−0.523910
$839$	10.7918	0.372575	0.186288	−	0.982495i	$-0.440354\pi$
$839$	10.7918	0.372575	0.186288	+	0.982495i	$0.440354\pi$
$840$	2.06845	0.0713684
$841$	−13.0419	−0.449720
$842$	−9.52120	−0.328122
$843$	21.0928	0.726473
$844$	0.303976	0.0104633
$845$	−6.54644	−0.225204
$846$	−16.2084	−0.557258
$847$	−1.50083	−0.0515690
$848$	−13.2329	−0.454420
$849$	2.89456	0.0993411
$850$	7.05680	0.242046
$851$	0	0
$852$	−5.59971	−0.191843
$853$	22.7371	0.778504	0.389252	−	0.921131i	$-0.372733\pi$
$853$	22.7371	0.778504	0.389252	+	0.921131i	$0.372733\pi$
$854$	−21.0505	−0.720333
$855$	9.13319	0.312349
$856$	−14.4599	−0.494228
$857$	37.5978	1.28432	0.642158	−	0.766572i	$-0.278039\pi$
$857$	37.5978	1.28432	0.642158	+	0.766572i	$0.278039\pi$
$858$	−9.85485	−0.336439
$859$	5.45752	0.186208	0.0931040	−	0.995656i	$-0.470321\pi$
$859$	5.45752	0.186208	0.0931040	+	0.995656i	$0.470321\pi$
$860$	11.0826	0.377915
$861$	−14.9530	−0.509596
$862$	0.185120	0.00630520
$863$	−44.1692	−1.50354	−0.751768	−	0.659428i	$-0.770799\pi$
$863$	−44.1692	−1.50354	−0.751768	+	0.659428i	$0.770799\pi$
$864$	3.80172	0.129337
$865$	3.40711	0.115845
$866$	9.91090	0.336786
$867$	−22.5609	−0.766209
$868$	5.99234	0.203393
$869$	14.2486	0.483349
$870$	−2.74786	−0.0931610
$871$	14.2250	0.481995
$872$	12.1963	0.413017
$873$	−10.1845	−0.344693
$874$	0	0
$875$	−3.00706	−0.101657
$876$	−4.78662	−0.161725
$877$	−6.59200	−0.222596	−0.111298	−	0.993787i	$-0.535501\pi$
$877$	−6.59200	−0.222596	−0.111298	+	0.993787i	$0.535501\pi$
$878$	−37.5453	−1.26709
$879$	9.21387	0.310776
$880$	−3.24051	−0.109238
$881$	−18.0183	−0.607051	−0.303526	−	0.952823i	$-0.598164\pi$
$881$	−18.0183	−0.607051	−0.303526	+	0.952823i	$0.598164\pi$
$882$	−5.16087	−0.173776
$883$	−11.8896	−0.400119	−0.200059	−	0.979784i	$-0.564113\pi$
$883$	−11.8896	−0.400119	−0.200059	+	0.979784i	$0.564113\pi$
$884$	31.1991	1.04934
$885$	−5.25945	−0.176795
$886$	12.4666	0.418823
$887$	57.6454	1.93554	0.967772	−	0.251827i	$-0.0810314\pi$
$887$	57.6454	1.93554	0.967772	+	0.251827i	$0.0810314\pi$
$888$	6.90801	0.231818
$889$	−6.05448	−0.203061
$890$	5.09686	0.170847
$891$	16.0906	0.539056
$892$	−3.69023	−0.123558
$893$	23.1850	0.775858
$894$	8.41232	0.281350
$895$	−18.1315	−0.606069
$896$	3.00706	0.100459
$897$	0	0
$898$	−15.7584	−0.525864
$899$	−7.96059	−0.265500
$900$	−2.52684	−0.0842281
$901$	−93.3821	−3.11101
$902$	23.4259	0.779996
$903$	22.9239	0.762860
$904$	5.74348	0.191025
$905$	10.7644	0.357821
$906$	0.0264688	0.000879368 0
$907$	−23.3487	−0.775280	−0.387640	−	0.921811i	$-0.626710\pi$
$907$	−23.3487	−0.775280	−0.387640	+	0.921811i	$0.626710\pi$
$908$	−6.07432	−0.201583
$909$	−29.1181	−0.965787
$910$	−13.2946	−0.440713
$911$	11.6184	0.384935	0.192467	−	0.981303i	$-0.438351\pi$
$911$	11.6184	0.384935	0.192467	+	0.981303i	$0.438351\pi$
$912$	−2.48627	−0.0823285
$913$	14.4348	0.477721
$914$	9.77158	0.323215
$915$	−4.81530	−0.159189
$916$	−6.76155	−0.223408
$917$	64.5159	2.13050
$918$	26.8280	0.885456
$919$	−33.3193	−1.09910	−0.549552	−	0.835460i	$-0.685201\pi$
$919$	−33.3193	−1.09910	−0.549552	+	0.835460i	$0.685201\pi$
$920$	0	0
$921$	18.9876	0.625664
$922$	4.93513	0.162530
$923$	35.9912	1.18466
$924$	−6.70284	−0.220507
$925$	−10.0427	−0.330202
$926$	11.4617	0.376656
$927$	−38.0138	−1.24854
$928$	−3.99476	−0.131134
$929$	34.9723	1.14741	0.573703	−	0.819064i	$-0.305507\pi$
$929$	34.9723	1.14741	0.573703	+	0.819064i	$0.305507\pi$
$930$	1.37075	0.0449486
$931$	7.38227	0.241944
$932$	0.183316	0.00600472
$933$	−3.55479	−0.116379
$934$	−20.7077	−0.677578
$935$	−22.8676	−0.747852
$936$	−11.1715	−0.365152
$937$	48.9021	1.59756	0.798781	−	0.601622i	$-0.205478\pi$
$937$	48.9021	1.59756	0.798781	+	0.601622i	$0.205478\pi$
$938$	9.67520	0.315907
$939$	12.2500	0.399763
$940$	−6.41451	−0.209218
$941$	11.5317	0.375922	0.187961	−	0.982176i	$-0.439812\pi$
$941$	11.5317	0.375922	0.187961	+	0.982176i	$0.439812\pi$
$942$	−14.2723	−0.465017
$943$	0	0
$944$	−7.64606	−0.248858
$945$	−11.4320	−0.371883
$946$	−35.9134	−1.16764
$947$	56.7577	1.84438	0.922189	−	0.386740i	$-0.126399\pi$
$947$	56.7577	1.84438	0.922189	+	0.386740i	$0.126399\pi$
$948$	−3.02455	−0.0982328
$949$	30.7652	0.998680
$950$	3.61447	0.117269
$951$	−6.92042	−0.224410
$952$	21.2202	0.687752
$953$	−25.6080	−0.829526	−0.414763	−	0.909930i	$-0.636135\pi$
$953$	−25.6080	−0.829526	−0.414763	+	0.909930i	$0.636135\pi$
$954$	33.4375	1.08258
$955$	−15.3586	−0.496992
$956$	−16.0127	−0.517888
$957$	8.90445	0.287840
$958$	13.1882	0.426092
$959$	−7.08918	−0.228922
$960$	0.687865	0.0222007
$961$	−27.0289	−0.871901
$962$	−44.4001	−1.43152
$963$	36.5378	1.17741
$964$	−19.2723	−0.620720
$965$	20.1852	0.649784
$966$	0	0
$967$	−28.6360	−0.920871	−0.460436	−	0.887693i	$-0.652307\pi$
$967$	−28.6360	−0.920871	−0.460436	+	0.887693i	$0.652307\pi$
$968$	−0.499101	−0.0160417
$969$	−17.5451	−0.563630
$970$	−4.03052	−0.129412
$971$	−7.91842	−0.254114	−0.127057	−	0.991895i	$-0.540553\pi$
$971$	−7.91842	−0.254114	−0.127057	+	0.991895i	$0.540553\pi$
$972$	−14.8207	−0.475375
$973$	14.2123	0.455627
$974$	−33.7045	−1.07996
$975$	−3.04114	−0.0973945
$976$	−7.00035	−0.224076
$977$	55.8545	1.78694	0.893471	−	0.449120i	$-0.148262\pi$
$977$	55.8545	1.78694	0.893471	+	0.449120i	$0.148262\pi$
$978$	4.97931	0.159221
$979$	−16.5164	−0.527867
$980$	−2.04242	−0.0652427
$981$	−30.8180	−0.983944
$982$	29.4087	0.938469
$983$	−46.5564	−1.48492	−0.742459	−	0.669892i	$-0.766340\pi$
$983$	−46.5564	−1.48492	−0.742459	+	0.669892i	$0.766340\pi$
$984$	−4.97262	−0.158521
$985$	−15.8568	−0.505240
$986$	−28.1902	−0.897760
$987$	−13.2681	−0.422328
$988$	15.9801	0.508394
$989$	0	0
$990$	8.18825	0.260240
$991$	39.8747	1.26666	0.633331	−	0.773881i	$-0.281687\pi$
$991$	39.8747	1.26666	0.633331	+	0.773881i	$0.281687\pi$
$992$	1.99276	0.0632701
$993$	12.2573	0.388972
$994$	24.4796	0.776447
$995$	−4.50450	−0.142802
$996$	−3.06408	−0.0970890
$997$	−45.6111	−1.44452	−0.722259	−	0.691622i	$-0.756896\pi$
$997$	−45.6111	−1.44452	−0.722259	+	0.691622i	$0.756896\pi$
$998$	39.7987	1.25981
$999$	−38.1795	−1.20795

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5290.2.a.bk.1.6		15
23.4	even	11		230.2.g.d.131.2	✓	30
23.6	even	11		230.2.g.d.151.2	yes	30
23.22	odd	2		5290.2.a.bl.1.6		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.131.2	✓	30	23.4	even	11
230.2.g.d.151.2	yes	30	23.6	even	11
5290.2.a.bk.1.6		15	1.1	even	1	trivial
5290.2.a.bl.1.6		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.687865 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.687865 q^{6} +3.00706 q^{7} +1.00000 q^{8} -2.52684 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.687865 q^{3} +1.00000 q^{4} -1.00000 q^{5} -0.687865 q^{6} +3.00706 q^{7} +1.00000 q^{8} -2.52684 q^{9} -1.00000 q^{10} +3.24051 q^{11} -0.687865 q^{12} +4.42114 q^{13} +3.00706 q^{14} +0.687865 q^{15} +1.00000 q^{16} +7.05680 q^{17} -2.52684 q^{18} +3.61447 q^{19} -1.00000 q^{20} -2.06845 q^{21} +3.24051 q^{22} -0.687865 q^{24} +1.00000 q^{25} +4.42114 q^{26} +3.80172 q^{27} +3.00706 q^{28} -3.99476 q^{29} +0.687865 q^{30} +1.99276 q^{31} +1.00000 q^{32} -2.22903 q^{33} +7.05680 q^{34} -3.00706 q^{35} -2.52684 q^{36} -10.0427 q^{37} +3.61447 q^{38} -3.04114 q^{39} -1.00000 q^{40} +7.22907 q^{41} -2.06845 q^{42} -11.0826 q^{43} +3.24051 q^{44} +2.52684 q^{45} +6.41451 q^{47} -0.687865 q^{48} +2.04242 q^{49} +1.00000 q^{50} -4.85413 q^{51} +4.42114 q^{52} -13.2329 q^{53} +3.80172 q^{54} -3.24051 q^{55} +3.00706 q^{56} -2.48627 q^{57} -3.99476 q^{58} -7.64606 q^{59} +0.687865 q^{60} -7.00035 q^{61} +1.99276 q^{62} -7.59837 q^{63} +1.00000 q^{64} -4.42114 q^{65} -2.22903 q^{66} +3.21749 q^{67} +7.05680 q^{68} -3.00706 q^{70} +8.14071 q^{71} -2.52684 q^{72} +6.95866 q^{73} -10.0427 q^{74} -0.687865 q^{75} +3.61447 q^{76} +9.74441 q^{77} -3.04114 q^{78} +4.39701 q^{79} -1.00000 q^{80} +4.96546 q^{81} +7.22907 q^{82} +4.45448 q^{83} -2.06845 q^{84} -7.05680 q^{85} -11.0826 q^{86} +2.74786 q^{87} +3.24051 q^{88} -5.09686 q^{89} +2.52684 q^{90} +13.2946 q^{91} -1.37075 q^{93} +6.41451 q^{94} -3.61447 q^{95} -0.687865 q^{96} +4.03052 q^{97} +2.04242 q^{98} -8.18825 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 5 q^{3} + 15 q^{4} - 15 q^{5} + 5 q^{6} + 4 q^{7} + 15 q^{8} + 28 q^{9}+O(q^{10}) \) 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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