LMFDB - Embedded newform 6019.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49834 q^{2} +2.94692 q^{3} +4.24169 q^{4} -1.72770 q^{5} -7.36239 q^{6} -2.26517 q^{7} -5.60049 q^{8} +5.68431 q^{9} +O(q^{10})$	\(q-2.49834 q^{2} +2.94692 q^{3} +4.24169 q^{4} -1.72770 q^{5} -7.36239 q^{6} -2.26517 q^{7} -5.60049 q^{8} +5.68431 q^{9} +4.31639 q^{10} +0.130457 q^{11} +12.4999 q^{12} +1.00000 q^{13} +5.65915 q^{14} -5.09140 q^{15} +5.50853 q^{16} +4.91538 q^{17} -14.2013 q^{18} +4.17560 q^{19} -7.32838 q^{20} -6.67525 q^{21} -0.325925 q^{22} +8.50929 q^{23} -16.5042 q^{24} -2.01504 q^{25} -2.49834 q^{26} +7.91043 q^{27} -9.60813 q^{28} -0.430750 q^{29} +12.7200 q^{30} -2.02861 q^{31} -2.56119 q^{32} +0.384445 q^{33} -12.2803 q^{34} +3.91354 q^{35} +24.1111 q^{36} +8.95999 q^{37} -10.4321 q^{38} +2.94692 q^{39} +9.67599 q^{40} -5.62911 q^{41} +16.6770 q^{42} -5.42724 q^{43} +0.553357 q^{44} -9.82080 q^{45} -21.2591 q^{46} -5.49783 q^{47} +16.2332 q^{48} -1.86902 q^{49} +5.03424 q^{50} +14.4852 q^{51} +4.24169 q^{52} -4.08388 q^{53} -19.7629 q^{54} -0.225391 q^{55} +12.6860 q^{56} +12.3052 q^{57} +1.07616 q^{58} +11.1583 q^{59} -21.5961 q^{60} +13.9905 q^{61} +5.06816 q^{62} -12.8759 q^{63} -4.61835 q^{64} -1.72770 q^{65} -0.960474 q^{66} +1.90443 q^{67} +20.8495 q^{68} +25.0762 q^{69} -9.77734 q^{70} +4.92812 q^{71} -31.8349 q^{72} -7.70184 q^{73} -22.3851 q^{74} -5.93815 q^{75} +17.7116 q^{76} -0.295507 q^{77} -7.36239 q^{78} +4.29898 q^{79} -9.51711 q^{80} +6.25844 q^{81} +14.0634 q^{82} -7.49122 q^{83} -28.3143 q^{84} -8.49232 q^{85} +13.5591 q^{86} -1.26938 q^{87} -0.730622 q^{88} +0.819726 q^{89} +24.5357 q^{90} -2.26517 q^{91} +36.0937 q^{92} -5.97815 q^{93} +13.7354 q^{94} -7.21421 q^{95} -7.54761 q^{96} -1.49230 q^{97} +4.66944 q^{98} +0.741557 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.49834	−1.76659	−0.883295	−	0.468817i	$-0.844680\pi$
$2$	−2.49834	−1.76659	−0.883295	+	0.468817i	$0.844680\pi$
$3$	2.94692	1.70140	0.850701	−	0.525650i	$-0.176178\pi$
$3$	2.94692	1.70140	0.850701	+	0.525650i	$0.176178\pi$
$4$	4.24169	2.12084
$5$	−1.72770	−0.772653	−0.386326	−	0.922362i	$-0.626256\pi$
$5$	−1.72770	−0.772653	−0.386326	+	0.922362i	$0.626256\pi$
$6$	−7.36239	−3.00568
$7$	−2.26517	−0.856153	−0.428076	−	0.903743i	$-0.640809\pi$
$7$	−2.26517	−0.856153	−0.428076	+	0.903743i	$0.640809\pi$
$8$	−5.60049	−1.98007
$9$	5.68431	1.89477
$10$	4.31639	1.36496
$11$	0.130457	0.0393342	0.0196671	−	0.999807i	$-0.493739\pi$
$11$	0.130457	0.0393342	0.0196671	+	0.999807i	$0.493739\pi$
$12$	12.4999	3.60841
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	5.65915	1.51247
$15$	−5.09140	−1.31459
$16$	5.50853	1.37713
$17$	4.91538	1.19215	0.596077	−	0.802927i	$-0.296725\pi$
$17$	4.91538	1.19215	0.596077	+	0.802927i	$0.296725\pi$
$18$	−14.2013	−3.34728
$19$	4.17560	0.957949	0.478975	−	0.877829i	$-0.341009\pi$
$19$	4.17560	0.957949	0.478975	+	0.877829i	$0.341009\pi$
$20$	−7.32838	−1.63868
$21$	−6.67525	−1.45666
$22$	−0.325925	−0.0694875
$23$	8.50929	1.77431	0.887155	−	0.461472i	$-0.152678\pi$
$23$	8.50929	1.77431	0.887155	+	0.461472i	$0.152678\pi$
$24$	−16.5042	−3.36890
$25$	−2.01504	−0.403008
$26$	−2.49834	−0.489964
$27$	7.91043	1.52236
$28$	−9.60813	−1.81577
$29$	−0.430750	−0.0799883	−0.0399941	−	0.999200i	$-0.512734\pi$
$29$	−0.430750	−0.0799883	−0.0399941	+	0.999200i	$0.512734\pi$
$30$	12.7200	2.32235
$31$	−2.02861	−0.364349	−0.182175	−	0.983266i	$-0.558314\pi$
$31$	−2.02861	−0.364349	−0.182175	+	0.983266i	$0.558314\pi$
$32$	−2.56119	−0.452759
$33$	0.384445	0.0669234
$34$	−12.2803	−2.10605
$35$	3.91354	0.661509
$36$	24.1111	4.01851
$37$	8.95999	1.47301	0.736507	−	0.676430i	$-0.236474\pi$
$37$	8.95999	1.47301	0.736507	+	0.676430i	$0.236474\pi$
$38$	−10.4321	−1.69230
$39$	2.94692	0.471884
$40$	9.67599	1.52991
$41$	−5.62911	−0.879119	−0.439559	−	0.898214i	$-0.644865\pi$
$41$	−5.62911	−0.879119	−0.439559	+	0.898214i	$0.644865\pi$
$42$	16.6770	2.57332
$43$	−5.42724	−0.827646	−0.413823	−	0.910357i	$-0.635807\pi$
$43$	−5.42724	−0.827646	−0.413823	+	0.910357i	$0.635807\pi$
$44$	0.553357	0.0834217
$45$	−9.82080	−1.46400
$46$	−21.2591	−3.13448
$47$	−5.49783	−0.801942	−0.400971	−	0.916091i	$-0.631327\pi$
$47$	−5.49783	−0.801942	−0.400971	+	0.916091i	$0.631327\pi$
$48$	16.2332	2.34306
$49$	−1.86902	−0.267003
$50$	5.03424	0.711950
$51$	14.4852	2.02833
$52$	4.24169	0.588216
$53$	−4.08388	−0.560964	−0.280482	−	0.959859i	$-0.590494\pi$
$53$	−4.08388	−0.560964	−0.280482	+	0.959859i	$0.590494\pi$
$54$	−19.7629	−2.68939
$55$	−0.225391	−0.0303917
$56$	12.6860	1.69524
$57$	12.3052	1.62986
$58$	1.07616	0.141307
$59$	11.1583	1.45268	0.726341	−	0.687334i	$-0.241219\pi$
$59$	11.1583	1.45268	0.726341	+	0.687334i	$0.241219\pi$
$60$	−21.5961	−2.78805
$61$	13.9905	1.79129	0.895647	−	0.444765i	$-0.146713\pi$
$61$	13.9905	1.79129	0.895647	+	0.444765i	$0.146713\pi$
$62$	5.06816	0.643656
$63$	−12.8759	−1.62221
$64$	−4.61835	−0.577293
$65$	−1.72770	−0.214295
$66$	−0.960474	−0.118226
$67$	1.90443	0.232664	0.116332	−	0.993210i	$-0.462886\pi$
$67$	1.90443	0.232664	0.116332	+	0.993210i	$0.462886\pi$
$68$	20.8495	2.52837
$69$	25.0762	3.01881
$70$	−9.77734	−1.16862
$71$	4.92812	0.584860	0.292430	−	0.956287i	$-0.405536\pi$
$71$	4.92812	0.584860	0.292430	+	0.956287i	$0.405536\pi$
$72$	−31.8349	−3.75178
$73$	−7.70184	−0.901432	−0.450716	−	0.892667i	$-0.648831\pi$
$73$	−7.70184	−0.901432	−0.450716	+	0.892667i	$0.648831\pi$
$74$	−22.3851	−2.60221
$75$	−5.93815	−0.685678
$76$	17.7116	2.03166
$77$	−0.295507	−0.0336761
$78$	−7.36239	−0.833626
$79$	4.29898	0.483673	0.241836	−	0.970317i	$-0.422250\pi$
$79$	4.29898	0.483673	0.241836	+	0.970317i	$0.422250\pi$
$80$	−9.51711	−1.06405
$81$	6.25844	0.695382
$82$	14.0634	1.55304
$83$	−7.49122	−0.822268	−0.411134	−	0.911575i	$-0.634867\pi$
$83$	−7.49122	−0.822268	−0.411134	+	0.911575i	$0.634867\pi$
$84$	−28.3143	−3.08935
$85$	−8.49232	−0.921121
$86$	13.5591	1.46211
$87$	−1.26938	−0.136092
$88$	−0.730622	−0.0778846
$89$	0.819726	0.0868908	0.0434454	−	0.999056i	$-0.486167\pi$
$89$	0.819726	0.0868908	0.0434454	+	0.999056i	$0.486167\pi$
$90$	24.5357	2.58629
$91$	−2.26517	−0.237454
$92$	36.0937	3.76303
$93$	−5.97815	−0.619905
$94$	13.7354	1.41670
$95$	−7.21421	−0.740162
$96$	−7.54761	−0.770325
$97$	−1.49230	−0.151520	−0.0757601	−	0.997126i	$-0.524138\pi$
$97$	−1.49230	−0.151520	−0.0757601	+	0.997126i	$0.524138\pi$
$98$	4.66944	0.471685
$99$	0.741557	0.0745293
$100$	−8.54716	−0.854716
$101$	4.17402	0.415330	0.207665	−	0.978200i	$-0.433414\pi$
$101$	4.17402	0.415330	0.207665	+	0.978200i	$0.433414\pi$
$102$	−36.1889	−3.58324
$103$	−15.0890	−1.48676	−0.743382	−	0.668868i	$-0.766779\pi$
$103$	−15.0890	−1.48676	−0.743382	+	0.668868i	$0.766779\pi$
$104$	−5.60049	−0.549173
$105$	11.5329	1.12549
$106$	10.2029	0.990994
$107$	5.20676	0.503357	0.251678	−	0.967811i	$-0.419017\pi$
$107$	5.20676	0.503357	0.251678	+	0.967811i	$0.419017\pi$
$108$	33.5536	3.22869
$109$	−2.23208	−0.213795	−0.106897	−	0.994270i	$-0.534092\pi$
$109$	−2.23208	−0.213795	−0.106897	+	0.994270i	$0.534092\pi$
$110$	0.563102	0.0536897
$111$	26.4043	2.50619
$112$	−12.4777	−1.17904
$113$	8.43552	0.793547	0.396773	−	0.917917i	$-0.370130\pi$
$113$	8.43552	0.793547	0.396773	+	0.917917i	$0.370130\pi$
$114$	−30.7424	−2.87929
$115$	−14.7015	−1.37093
$116$	−1.82711	−0.169643
$117$	5.68431	0.525515
$118$	−27.8771	−2.56630
$119$	−11.1341	−1.02067
$120$	28.5143	2.60299
$121$	−10.9830	−0.998453
$122$	−34.9529	−3.16448
$123$	−16.5885	−1.49573
$124$	−8.60474	−0.772728
$125$	12.1199	1.08404
$126$	32.1684	2.86578
$127$	9.72730	0.863158	0.431579	−	0.902075i	$-0.357957\pi$
$127$	9.72730	0.863158	0.431579	+	0.902075i	$0.357957\pi$
$128$	16.6606	1.47260
$129$	−15.9936	−1.40816
$130$	4.31639	0.378572
$131$	−12.1541	−1.06191	−0.530955	−	0.847400i	$-0.678167\pi$
$131$	−12.1541	−1.06191	−0.530955	+	0.847400i	$0.678167\pi$
$132$	1.63070	0.141934
$133$	−9.45844	−0.820151
$134$	−4.75792	−0.411021
$135$	−13.6669	−1.17626
$136$	−27.5285	−2.36055
$137$	−14.2684	−1.21903	−0.609515	−	0.792774i	$-0.708636\pi$
$137$	−14.2684	−1.21903	−0.609515	+	0.792774i	$0.708636\pi$
$138$	−62.6487	−5.33301
$139$	−11.7787	−0.999056	−0.499528	−	0.866298i	$-0.666493\pi$
$139$	−11.7787	−0.999056	−0.499528	+	0.866298i	$0.666493\pi$
$140$	16.6000	1.40296
$141$	−16.2017	−1.36443
$142$	−12.3121	−1.03321
$143$	0.130457	0.0109094
$144$	31.3122	2.60935
$145$	0.744209	0.0618032
$146$	19.2418	1.59246
$147$	−5.50784	−0.454279
$148$	38.0055	3.12403
$149$	−8.49768	−0.696157	−0.348078	−	0.937465i	$-0.613166\pi$
$149$	−8.49768	−0.696157	−0.348078	+	0.937465i	$0.613166\pi$
$150$	14.8355	1.21131
$151$	2.50759	0.204064	0.102032	−	0.994781i	$-0.467466\pi$
$151$	2.50759	0.204064	0.102032	+	0.994781i	$0.467466\pi$
$152$	−23.3854	−1.89681
$153$	27.9405	2.25886
$154$	0.738275	0.0594919
$155$	3.50484	0.281516
$156$	12.4999	1.00079
$157$	−12.0902	−0.964900	−0.482450	−	0.875923i	$-0.660253\pi$
$157$	−12.0902	−0.964900	−0.482450	+	0.875923i	$0.660253\pi$
$158$	−10.7403	−0.854452
$159$	−12.0348	−0.954426
$160$	4.42498	0.349825
$161$	−19.2750	−1.51908
$162$	−15.6357	−1.22846
$163$	15.7118	1.23064	0.615320	−	0.788277i	$-0.289027\pi$
$163$	15.7118	1.23064	0.615320	+	0.788277i	$0.289027\pi$
$164$	−23.8769	−1.86447
$165$	−0.664208	−0.0517085
$166$	18.7156	1.45261
$167$	20.9162	1.61854	0.809272	−	0.587435i	$-0.199862\pi$
$167$	20.9162	1.61854	0.809272	+	0.587435i	$0.199862\pi$
$168$	37.3847	2.88429
$169$	1.00000	0.0769231
$170$	21.2167	1.62724
$171$	23.7354	1.81509
$172$	−23.0207	−1.75531
$173$	22.4269	1.70508	0.852542	−	0.522659i	$-0.175060\pi$
$173$	22.4269	1.70508	0.852542	+	0.522659i	$0.175060\pi$
$174$	3.17135	0.240419
$175$	4.56440	0.345036
$176$	0.718626	0.0541685
$177$	32.8825	2.47160
$178$	−2.04795	−0.153500
$179$	24.2396	1.81175	0.905876	−	0.423542i	$-0.139213\pi$
$179$	24.2396	1.81175	0.905876	+	0.423542i	$0.139213\pi$
$180$	−41.6568	−3.10491
$181$	5.76660	0.428628	0.214314	−	0.976765i	$-0.431248\pi$
$181$	5.76660	0.428628	0.214314	+	0.976765i	$0.431248\pi$
$182$	5.65915	0.419484
$183$	41.2287	3.04771
$184$	−47.6562	−3.51326
$185$	−15.4802	−1.13813
$186$	14.9354	1.09512
$187$	0.641245	0.0468925
$188$	−23.3201	−1.70079
$189$	−17.9184	−1.30338
$190$	18.0235	1.30756
$191$	23.5019	1.70054	0.850270	−	0.526346i	$-0.176438\pi$
$191$	23.5019	1.70054	0.850270	+	0.526346i	$0.176438\pi$
$192$	−13.6099	−0.982208
$193$	−11.8786	−0.855043	−0.427522	−	0.904005i	$-0.640613\pi$
$193$	−11.8786	−0.855043	−0.427522	+	0.904005i	$0.640613\pi$
$194$	3.72827	0.267674
$195$	−5.09140	−0.364603
$196$	−7.92780	−0.566271
$197$	11.9593	0.852066	0.426033	−	0.904708i	$-0.359911\pi$
$197$	11.9593	0.852066	0.426033	+	0.904708i	$0.359911\pi$
$198$	−1.85266	−0.131663
$199$	25.1117	1.78012	0.890062	−	0.455840i	$-0.150661\pi$
$199$	25.1117	1.78012	0.890062	+	0.455840i	$0.150661\pi$
$200$	11.2852	0.797984
$201$	5.61220	0.395854
$202$	−10.4281	−0.733719
$203$	0.975721	0.0684822
$204$	61.4417	4.30178
$205$	9.72543	0.679254
$206$	37.6974	2.62650
$207$	48.3694	3.36191
$208$	5.50853	0.381948
$209$	0.544736	0.0376802
$210$	−28.8130	−1.98828
$211$	−7.61366	−0.524146	−0.262073	−	0.965048i	$-0.584406\pi$
$211$	−7.61366	−0.524146	−0.262073	+	0.965048i	$0.584406\pi$
$212$	−17.3225	−1.18972
$213$	14.5227	0.995082
$214$	−13.0082	−0.889225
$215$	9.37667	0.639483
$216$	−44.3023	−3.01439
$217$	4.59514	0.311939
$218$	5.57650	0.377688
$219$	−22.6967	−1.53370
$220$	−0.956038	−0.0644560
$221$	4.91538	0.330644
$222$	−65.9669	−4.42741
$223$	17.4489	1.16846	0.584231	−	0.811587i	$-0.301396\pi$
$223$	17.4489	1.16846	0.584231	+	0.811587i	$0.301396\pi$
$224$	5.80152	0.387630
$225$	−11.4541	−0.763607
$226$	−21.0748	−1.40187
$227$	14.2992	0.949071	0.474535	−	0.880236i	$-0.342616\pi$
$227$	14.2992	0.949071	0.474535	+	0.880236i	$0.342616\pi$
$228$	52.1946	3.45667
$229$	−9.30746	−0.615054	−0.307527	−	0.951539i	$-0.599501\pi$
$229$	−9.30746	−0.615054	−0.307527	+	0.951539i	$0.599501\pi$
$230$	36.7294	2.42186
$231$	−0.870833	−0.0572966
$232$	2.41241	0.158383
$233$	19.9200	1.30500	0.652502	−	0.757787i	$-0.273719\pi$
$233$	19.9200	1.30500	0.652502	+	0.757787i	$0.273719\pi$
$234$	−14.2013	−0.928369
$235$	9.49863	0.619622
$236$	47.3299	3.08091
$237$	12.6687	0.822922
$238$	27.8169	1.80310
$239$	−13.4366	−0.869138	−0.434569	−	0.900638i	$-0.643099\pi$
$239$	−13.4366	−0.869138	−0.434569	+	0.900638i	$0.643099\pi$
$240$	−28.0461	−1.81037
$241$	−12.5793	−0.810303	−0.405152	−	0.914250i	$-0.632781\pi$
$241$	−12.5793	−0.810303	−0.405152	+	0.914250i	$0.632781\pi$
$242$	27.4392	1.76386
$243$	−5.28820	−0.339238
$244$	59.3431	3.79905
$245$	3.22911	0.206301
$246$	41.4437	2.64235
$247$	4.17560	0.265687
$248$	11.3612	0.721438
$249$	−22.0760	−1.39901
$250$	−30.2796	−1.91505
$251$	4.09179	0.258271	0.129136	−	0.991627i	$-0.458780\pi$
$251$	4.09179	0.258271	0.129136	+	0.991627i	$0.458780\pi$
$252$	−54.6156	−3.44046
$253$	1.11010	0.0697911
$254$	−24.3021	−1.52485
$255$	−25.0261	−1.56720
$256$	−32.3870	−2.02419
$257$	25.7268	1.60479	0.802395	−	0.596793i	$-0.203559\pi$
$257$	25.7268	1.60479	0.802395	+	0.596793i	$0.203559\pi$
$258$	39.9574	2.48764
$259$	−20.2959	−1.26112
$260$	−7.32838	−0.454487
$261$	−2.44852	−0.151559
$262$	30.3651	1.87596
$263$	−29.4617	−1.81669	−0.908344	−	0.418223i	$-0.862653\pi$
$263$	−29.4617	−1.81669	−0.908344	+	0.418223i	$0.862653\pi$
$264$	−2.15308	−0.132513
$265$	7.05574	0.433430
$266$	23.6304	1.44887
$267$	2.41566	0.147836
$268$	8.07801	0.493443
$269$	27.1076	1.65278	0.826388	−	0.563101i	$-0.190392\pi$
$269$	27.1076	1.65278	0.826388	+	0.563101i	$0.190392\pi$
$270$	34.1445	2.07797
$271$	10.2219	0.620939	0.310469	−	0.950583i	$-0.399514\pi$
$271$	10.2219	0.620939	0.310469	+	0.950583i	$0.399514\pi$
$272$	27.0765	1.64175
$273$	−6.67525	−0.404005
$274$	35.6472	2.15353
$275$	−0.262876	−0.0158520
$276$	106.365	6.40243
$277$	−0.0738779	−0.00443889	−0.00221945	−	0.999998i	$-0.500706\pi$
$277$	−0.0738779	−0.00443889	−0.00221945	+	0.999998i	$0.500706\pi$
$278$	29.4271	1.76492
$279$	−11.5313	−0.690358
$280$	−21.9177	−1.30983
$281$	10.5556	0.629693	0.314847	−	0.949143i	$-0.398047\pi$
$281$	10.5556	0.629693	0.314847	+	0.949143i	$0.398047\pi$
$282$	40.4772	2.41038
$283$	−9.98460	−0.593523	−0.296762	−	0.954952i	$-0.595907\pi$
$283$	−9.98460	−0.593523	−0.296762	+	0.954952i	$0.595907\pi$
$284$	20.9035	1.24040
$285$	−21.2597	−1.25931
$286$	−0.325925	−0.0192724
$287$	12.7509	0.752660
$288$	−14.5586	−0.857873
$289$	7.16094	0.421231
$290$	−1.85928	−0.109181
$291$	−4.39768	−0.257797
$292$	−32.6688	−1.91180
$293$	11.1580	0.651856	0.325928	−	0.945395i	$-0.394323\pi$
$293$	11.1580	0.651856	0.325928	+	0.945395i	$0.394323\pi$
$294$	13.7604	0.802526
$295$	−19.2782	−1.12242
$296$	−50.1803	−2.91667
$297$	1.03197	0.0598810
$298$	21.2301	1.22982
$299$	8.50929	0.492105
$300$	−25.1878	−1.45422
$301$	12.2936	0.708592
$302$	−6.26480	−0.360498
$303$	12.3005	0.706644
$304$	23.0014	1.31922
$305$	−24.1714	−1.38405
$306$	−69.8048	−3.99048
$307$	2.69690	0.153920	0.0769600	−	0.997034i	$-0.475479\pi$
$307$	2.69690	0.153920	0.0769600	+	0.997034i	$0.475479\pi$
$308$	−1.25345	−0.0714217
$309$	−44.4660	−2.52958
$310$	−8.75627	−0.497323
$311$	6.29006	0.356676	0.178338	−	0.983969i	$-0.442928\pi$
$311$	6.29006	0.356676	0.178338	+	0.983969i	$0.442928\pi$
$312$	−16.5042	−0.934364
$313$	2.72420	0.153981	0.0769905	−	0.997032i	$-0.475469\pi$
$313$	2.72420	0.153981	0.0769905	+	0.997032i	$0.475469\pi$
$314$	30.2053	1.70458
$315$	22.2458	1.25341
$316$	18.2349	1.02579
$317$	18.1908	1.02170	0.510850	−	0.859670i	$-0.329331\pi$
$317$	18.1908	1.02170	0.510850	+	0.859670i	$0.329331\pi$
$318$	30.0671	1.68608
$319$	−0.0561943	−0.00314628
$320$	7.97914	0.446047
$321$	15.3439	0.856412
$322$	48.1553	2.68359
$323$	20.5247	1.14202
$324$	26.5463	1.47480
$325$	−2.01504	−0.111774
$326$	−39.2533	−2.17404
$327$	−6.57776	−0.363751
$328$	31.5257	1.74072
$329$	12.4535	0.686584
$330$	1.65942	0.0913478
$331$	23.9816	1.31815	0.659075	−	0.752077i	$-0.270948\pi$
$331$	23.9816	1.31815	0.659075	+	0.752077i	$0.270948\pi$
$332$	−31.7754	−1.74390
$333$	50.9314	2.79102
$334$	−52.2557	−2.85930
$335$	−3.29030	−0.179768
$336$	−36.7708	−2.00601
$337$	3.37852	0.184040	0.0920199	−	0.995757i	$-0.470668\pi$
$337$	3.37852	0.184040	0.0920199	+	0.995757i	$0.470668\pi$
$338$	−2.49834	−0.135892
$339$	24.8588	1.35014
$340$	−36.0218	−1.95355
$341$	−0.264646	−0.0143314
$342$	−59.2991	−3.20653
$343$	20.0898	1.08475
$344$	30.3952	1.63880
$345$	−43.3242	−2.33250
$346$	−56.0299	−3.01219
$347$	−20.1201	−1.08010	−0.540052	−	0.841632i	$-0.681595\pi$
$347$	−20.1201	−1.08010	−0.540052	+	0.841632i	$0.681595\pi$
$348$	−5.38433	−0.288630
$349$	−25.9760	−1.39046	−0.695231	−	0.718787i	$-0.744698\pi$
$349$	−25.9760	−1.39046	−0.695231	+	0.718787i	$0.744698\pi$
$350$	−11.4034	−0.609537
$351$	7.91043	0.422228
$352$	−0.334125	−0.0178089
$353$	2.57521	0.137065	0.0685323	−	0.997649i	$-0.478168\pi$
$353$	2.57521	0.137065	0.0685323	+	0.997649i	$0.478168\pi$
$354$	−82.1515	−4.36630
$355$	−8.51433	−0.451893
$356$	3.47702	0.184282
$357$	−32.8114	−1.73656
$358$	−60.5587	−3.20063
$359$	3.27688	0.172947	0.0864736	−	0.996254i	$-0.472440\pi$
$359$	3.27688	0.172947	0.0864736	+	0.996254i	$0.472440\pi$
$360$	55.0013	2.89882
$361$	−1.56433	−0.0823330
$362$	−14.4069	−0.757210
$363$	−32.3659	−1.69877
$364$	−9.60813	−0.503603
$365$	13.3065	0.696494
$366$	−103.003	−5.38406
$367$	6.55794	0.342322	0.171161	−	0.985243i	$-0.445248\pi$
$367$	6.55794	0.342322	0.171161	+	0.985243i	$0.445248\pi$
$368$	46.8737	2.44346
$369$	−31.9976	−1.66573
$370$	38.6748	2.01061
$371$	9.25067	0.480271
$372$	−25.3574	−1.31472
$373$	−16.7743	−0.868539	−0.434269	−	0.900783i	$-0.642993\pi$
$373$	−16.7743	−0.868539	−0.434269	+	0.900783i	$0.642993\pi$
$374$	−1.60205	−0.0828398
$375$	35.7163	1.84438
$376$	30.7906	1.58790
$377$	−0.430750	−0.0221848
$378$	44.7663	2.30253
$379$	−5.81728	−0.298813	−0.149407	−	0.988776i	$-0.547736\pi$
$379$	−5.81728	−0.298813	−0.149407	+	0.988776i	$0.547736\pi$
$380$	−30.6004	−1.56977
$381$	28.6655	1.46858
$382$	−58.7158	−3.00416
$383$	35.3957	1.80863	0.904317	−	0.426862i	$-0.140381\pi$
$383$	35.3957	1.80863	0.904317	+	0.426862i	$0.140381\pi$
$384$	49.0973	2.50548
$385$	0.510548	0.0260199
$386$	29.6769	1.51051
$387$	−30.8501	−1.56820
$388$	−6.32987	−0.321351
$389$	−15.8690	−0.804591	−0.402296	−	0.915510i	$-0.631788\pi$
$389$	−15.8690	−0.804591	−0.402296	+	0.915510i	$0.631788\pi$
$390$	12.7200	0.644104
$391$	41.8264	2.11525
$392$	10.4674	0.528685
$393$	−35.8172	−1.80674
$394$	−29.8784	−1.50525
$395$	−7.42736	−0.373711
$396$	3.14545	0.158065
$397$	6.85771	0.344178	0.172089	−	0.985081i	$-0.444948\pi$
$397$	6.85771	0.344178	0.172089	+	0.985081i	$0.444948\pi$
$398$	−62.7376	−3.14475
$399$	−27.8732	−1.39541
$400$	−11.0999	−0.554995
$401$	23.2843	1.16276	0.581380	−	0.813632i	$-0.302513\pi$
$401$	23.2843	1.16276	0.581380	+	0.813632i	$0.302513\pi$
$402$	−14.0212	−0.699313
$403$	−2.02861	−0.101052
$404$	17.7049	0.880851
$405$	−10.8127	−0.537289
$406$	−2.43768	−0.120980
$407$	1.16889	0.0579399
$408$	−81.1242	−4.01625
$409$	28.9970	1.43381	0.716905	−	0.697170i	$-0.245558\pi$
$409$	28.9970	1.43381	0.716905	+	0.697170i	$0.245558\pi$
$410$	−24.2974	−1.19996
$411$	−42.0477	−2.07406
$412$	−64.0028	−3.15319
$413$	−25.2753	−1.24372
$414$	−120.843	−5.93912
$415$	12.9426	0.635328
$416$	−2.56119	−0.125573
$417$	−34.7108	−1.69980
$418$	−1.36093	−0.0665655
$419$	−34.2825	−1.67481	−0.837404	−	0.546585i	$-0.815928\pi$
$419$	−34.2825	−1.67481	−0.837404	+	0.546585i	$0.815928\pi$
$420$	48.9188	2.38699
$421$	0.421451	0.0205403	0.0102701	−	0.999947i	$-0.496731\pi$
$421$	0.421451	0.0205403	0.0102701	+	0.999947i	$0.496731\pi$
$422$	19.0215	0.925951
$423$	−31.2514	−1.51949
$424$	22.8717	1.11075
$425$	−9.90467	−0.480447
$426$	−36.2827	−1.75790
$427$	−31.6907	−1.53362
$428$	22.0855	1.06754
$429$	0.384445	0.0185612
$430$	−23.4261	−1.12971
$431$	15.9137	0.766534	0.383267	−	0.923638i	$-0.374799\pi$
$431$	15.9137	0.766534	0.383267	+	0.923638i	$0.374799\pi$
$432$	43.5749	2.09650
$433$	29.2901	1.40759	0.703796	−	0.710402i	$-0.251487\pi$
$433$	29.2901	1.40759	0.703796	+	0.710402i	$0.251487\pi$
$434$	−11.4802	−0.551068
$435$	2.19312	0.105152
$436$	−9.46780	−0.453425
$437$	35.5314	1.69970
$438$	56.7039	2.70942
$439$	−23.4744	−1.12037	−0.560186	−	0.828367i	$-0.689270\pi$
$439$	−23.4744	−1.12037	−0.560186	+	0.828367i	$0.689270\pi$
$440$	1.26230	0.0601777
$441$	−10.6241	−0.505909
$442$	−12.2803	−0.584113
$443$	−20.3333	−0.966064	−0.483032	−	0.875603i	$-0.660464\pi$
$443$	−20.3333	−0.966064	−0.483032	+	0.875603i	$0.660464\pi$
$444$	111.999	5.31523
$445$	−1.41624	−0.0671364
$446$	−43.5932	−2.06420
$447$	−25.0419	−1.18444
$448$	10.4613	0.494251
$449$	22.3421	1.05439	0.527195	−	0.849744i	$-0.323244\pi$
$449$	22.3421	1.05439	0.527195	+	0.849744i	$0.323244\pi$
$450$	28.6162	1.34898
$451$	−0.734356	−0.0345795
$452$	35.7808	1.68299
$453$	7.38964	0.347196
$454$	−35.7242	−1.67662
$455$	3.91354	0.183469
$456$	−68.9149	−3.22723
$457$	−12.4139	−0.580698	−0.290349	−	0.956921i	$-0.593771\pi$
$457$	−12.4139	−0.580698	−0.290349	+	0.956921i	$0.593771\pi$
$458$	23.2532	1.08655
$459$	38.8828	1.81489
$460$	−62.3593	−2.90752
$461$	−16.4253	−0.765002	−0.382501	−	0.923955i	$-0.624937\pi$
$461$	−16.4253	−0.765002	−0.382501	+	0.923955i	$0.624937\pi$
$462$	2.17563	0.101220
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	−2.37280	−0.110154
$465$	10.3285	0.478971
$466$	−49.7669	−2.30541
$467$	−10.8028	−0.499894	−0.249947	−	0.968260i	$-0.580413\pi$
$467$	−10.8028	−0.499894	−0.249947	+	0.968260i	$0.580413\pi$
$468$	24.1111	1.11453
$469$	−4.31386	−0.199196
$470$	−23.7308	−1.09462
$471$	−35.6287	−1.64168
$472$	−62.4917	−2.87642
$473$	−0.708021	−0.0325548
$474$	−31.6507	−1.45377
$475$	−8.41400	−0.386061
$476$	−47.2276	−2.16467
$477$	−23.2140	−1.06290
$478$	33.5690	1.53541
$479$	17.9702	0.821081	0.410540	−	0.911842i	$-0.365340\pi$
$479$	17.9702	0.821081	0.410540	+	0.911842i	$0.365340\pi$
$480$	13.0400	0.595193
$481$	8.95999	0.408540
$482$	31.4273	1.43147
$483$	−56.8017	−2.58457
$484$	−46.5864	−2.11756
$485$	2.57825	0.117073
$486$	13.2117	0.599295
$487$	−7.89442	−0.357731	−0.178865	−	0.983874i	$-0.557243\pi$
$487$	−7.89442	−0.357731	−0.178865	+	0.983874i	$0.557243\pi$
$488$	−78.3534	−3.54689
$489$	46.3013	2.09382
$490$	−8.06741	−0.364449
$491$	31.3841	1.41634	0.708172	−	0.706040i	$-0.249520\pi$
$491$	31.3841	1.41634	0.708172	+	0.706040i	$0.249520\pi$
$492$	−70.3632	−3.17222
$493$	−2.11730	−0.0953584
$494$	−10.4321	−0.469361
$495$	−1.28119	−0.0575853
$496$	−11.1747	−0.501758
$497$	−11.1630	−0.500729
$498$	55.1532	2.47148
$499$	−20.3396	−0.910526	−0.455263	−	0.890357i	$-0.650455\pi$
$499$	−20.3396	−0.910526	−0.455263	+	0.890357i	$0.650455\pi$
$500$	51.4089	2.29907
$501$	61.6382	2.75379
$502$	−10.2227	−0.456260
$503$	−36.4262	−1.62416	−0.812082	−	0.583543i	$-0.801666\pi$
$503$	−36.4262	−1.62416	−0.812082	+	0.583543i	$0.801666\pi$
$504$	72.1114	3.21210
$505$	−7.21147	−0.320906
$506$	−2.77339	−0.123292
$507$	2.94692	0.130877
$508$	41.2602	1.83062
$509$	18.9269	0.838922	0.419461	−	0.907773i	$-0.362219\pi$
$509$	18.9269	0.838922	0.419461	+	0.907773i	$0.362219\pi$
$510$	62.5237	2.76860
$511$	17.4460	0.771764
$512$	47.5925	2.10331
$513$	33.0308	1.45835
$514$	−64.2741	−2.83501
$515$	26.0693	1.14875
$516$	−67.8399	−2.98649
$517$	−0.717230	−0.0315438
$518$	50.7059	2.22789
$519$	66.0901	2.90103
$520$	9.67599	0.424320
$521$	26.8067	1.17442	0.587210	−	0.809434i	$-0.300226\pi$
$521$	26.8067	1.17442	0.587210	+	0.809434i	$0.300226\pi$
$522$	6.11722	0.267743
$523$	−5.88152	−0.257181	−0.128590	−	0.991698i	$-0.541045\pi$
$523$	−5.88152	−0.257181	−0.128590	+	0.991698i	$0.541045\pi$
$524$	−51.5540	−2.25215
$525$	13.4509	0.587045
$526$	73.6053	3.20935
$527$	−9.97139	−0.434361
$528$	2.11773	0.0921623
$529$	49.4080	2.14818
$530$	−17.6276	−0.765694
$531$	63.4271	2.75250
$532$	−40.1197	−1.73941
$533$	−5.62911	−0.243824
$534$	−6.03514	−0.261166
$535$	−8.99575	−0.388920
$536$	−10.6658	−0.460690
$537$	71.4320	3.08252
$538$	−67.7238	−2.91978
$539$	−0.243827	−0.0105024
$540$	−57.9706	−2.49466
$541$	−10.4014	−0.447193	−0.223596	−	0.974682i	$-0.571780\pi$
$541$	−10.4014	−0.447193	−0.223596	+	0.974682i	$0.571780\pi$
$542$	−25.5379	−1.09695
$543$	16.9937	0.729269
$544$	−12.5892	−0.539758
$545$	3.85638	0.165189
$546$	16.6770	0.713711
$547$	−32.5132	−1.39016	−0.695081	−	0.718931i	$-0.744632\pi$
$547$	−32.5132	−1.39016	−0.695081	+	0.718931i	$0.744632\pi$
$548$	−60.5220	−2.58537
$549$	79.5261	3.39409
$550$	0.656752	0.0280040
$551$	−1.79864	−0.0766247
$552$	−140.439	−5.97747
$553$	−9.73790	−0.414098
$554$	0.184572	0.00784171
$555$	−45.6189	−1.93641
$556$	−49.9615	−2.11884
$557$	9.22851	0.391025	0.195512	−	0.980701i	$-0.437363\pi$
$557$	9.22851	0.391025	0.195512	+	0.980701i	$0.437363\pi$
$558$	28.8090	1.21958
$559$	−5.42724	−0.229548
$560$	21.5578	0.910985
$561$	1.88969	0.0797830
$562$	−26.3714	−1.11241
$563$	−32.5875	−1.37340	−0.686700	−	0.726941i	$-0.740941\pi$
$563$	−32.5875	−1.37340	−0.686700	+	0.726941i	$0.740941\pi$
$564$	−68.7223	−2.89373
$565$	−14.5741	−0.613136
$566$	24.9449	1.04851
$567$	−14.1764	−0.595353
$568$	−27.5998	−1.15806
$569$	4.48331	0.187950	0.0939751	−	0.995575i	$-0.470043\pi$
$569$	4.48331	0.187950	0.0939751	+	0.995575i	$0.470043\pi$
$570$	53.1138	2.22469
$571$	−22.2268	−0.930163	−0.465081	−	0.885268i	$-0.653975\pi$
$571$	−22.2268	−0.930163	−0.465081	+	0.885268i	$0.653975\pi$
$572$	0.553357	0.0231370
$573$	69.2582	2.89330
$574$	−31.8560	−1.32964
$575$	−17.1465	−0.715060
$576$	−26.2521	−1.09384
$577$	−29.4221	−1.22486	−0.612429	−	0.790525i	$-0.709808\pi$
$577$	−29.4221	−1.22486	−0.612429	+	0.790525i	$0.709808\pi$
$578$	−17.8904	−0.744144
$579$	−35.0054	−1.45477
$580$	3.15670	0.131075
$581$	16.9689	0.703987
$582$	10.9869	0.455421
$583$	−0.532770	−0.0220651
$584$	43.1341	1.78490
$585$	−9.82080	−0.406040
$586$	−27.8764	−1.15156
$587$	3.05337	0.126026	0.0630131	−	0.998013i	$-0.479929\pi$
$587$	3.05337	0.126026	0.0630131	+	0.998013i	$0.479929\pi$
$588$	−23.3625	−0.963455
$589$	−8.47068	−0.349028
$590$	48.1634	1.98286
$591$	35.2431	1.44971
$592$	49.3564	2.02854
$593$	−29.6773	−1.21870	−0.609351	−	0.792901i	$-0.708570\pi$
$593$	−29.6773	−1.21870	−0.609351	+	0.792901i	$0.708570\pi$
$594$	−2.57821	−0.105785
$595$	19.2365	0.788620
$596$	−36.0445	−1.47644
$597$	74.0021	3.02871
$598$	−21.2591	−0.869348
$599$	38.8549	1.58757	0.793784	−	0.608200i	$-0.208108\pi$
$599$	38.8549	1.58757	0.793784	+	0.608200i	$0.208108\pi$
$600$	33.2565	1.35769
$601$	−10.6583	−0.434761	−0.217380	−	0.976087i	$-0.569751\pi$
$601$	−10.6583	−0.434761	−0.217380	+	0.976087i	$0.569751\pi$
$602$	−30.7136	−1.25179
$603$	10.8254	0.440844
$604$	10.6364	0.432789
$605$	18.9753	0.771457
$606$	−30.7307	−1.24835
$607$	3.13909	0.127412	0.0637059	−	0.997969i	$-0.479708\pi$
$607$	3.13909	0.127412	0.0637059	+	0.997969i	$0.479708\pi$
$608$	−10.6945	−0.433720
$609$	2.87537	0.116516
$610$	60.3882	2.44505
$611$	−5.49783	−0.222419
$612$	118.515	4.79068
$613$	−8.70071	−0.351418	−0.175709	−	0.984442i	$-0.556222\pi$
$613$	−8.70071	−0.351418	−0.175709	+	0.984442i	$0.556222\pi$
$614$	−6.73775	−0.271914
$615$	28.6600	1.15568
$616$	1.65498	0.0666811
$617$	−28.5225	−1.14827	−0.574136	−	0.818760i	$-0.694662\pi$
$617$	−28.5225	−1.14827	−0.574136	+	0.818760i	$0.694662\pi$
$618$	111.091	4.46874
$619$	8.70986	0.350079	0.175039	−	0.984561i	$-0.443995\pi$
$619$	8.70986	0.350079	0.175039	+	0.984561i	$0.443995\pi$
$620$	14.8664	0.597051
$621$	67.3122	2.70114
$622$	−15.7147	−0.630101
$623$	−1.85682	−0.0743917
$624$	16.2332	0.649847
$625$	−10.8644	−0.434577
$626$	−6.80597	−0.272021
$627$	1.60529	0.0641092
$628$	−51.2827	−2.04640
$629$	44.0417	1.75606
$630$	−55.5774	−2.21426
$631$	32.9150	1.31033	0.655164	−	0.755487i	$-0.272600\pi$
$631$	32.9150	1.31033	0.655164	+	0.755487i	$0.272600\pi$
$632$	−24.0764	−0.957706
$633$	−22.4368	−0.891783
$634$	−45.4468	−1.80492
$635$	−16.8059	−0.666922
$636$	−51.0481	−2.02419
$637$	−1.86902	−0.0740533
$638$	0.140392	0.00555819
$639$	28.0129	1.10817
$640$	−28.7845	−1.13781
$641$	12.4542	0.491912	0.245956	−	0.969281i	$-0.420898\pi$
$641$	12.4542	0.491912	0.245956	+	0.969281i	$0.420898\pi$
$642$	−38.3342	−1.51293
$643$	10.7915	0.425577	0.212788	−	0.977098i	$-0.431746\pi$
$643$	10.7915	0.425577	0.212788	+	0.977098i	$0.431746\pi$
$644$	−81.7583	−3.22173
$645$	27.6322	1.08802
$646$	−51.2775	−2.01749
$647$	−1.52932	−0.0601239	−0.0300619	−	0.999548i	$-0.509570\pi$
$647$	−1.52932	−0.0601239	−0.0300619	+	0.999548i	$0.509570\pi$
$648$	−35.0503	−1.37691
$649$	1.45567	0.0571402
$650$	5.03424	0.197459
$651$	13.5415	0.530733
$652$	66.6444	2.61000
$653$	−15.0667	−0.589604	−0.294802	−	0.955558i	$-0.595254\pi$
$653$	−15.0667	−0.589604	−0.294802	+	0.955558i	$0.595254\pi$
$654$	16.4335	0.642599
$655$	20.9987	0.820488
$656$	−31.0081	−1.21066
$657$	−43.7796	−1.70801
$658$	−31.1131	−1.21291
$659$	−41.8521	−1.63033	−0.815163	−	0.579231i	$-0.803353\pi$
$659$	−41.8521	−1.63033	−0.815163	+	0.579231i	$0.803353\pi$
$660$	−2.81736	−0.109666
$661$	−15.6862	−0.610123	−0.305062	−	0.952333i	$-0.598677\pi$
$661$	−15.6862	−0.610123	−0.305062	+	0.952333i	$0.598677\pi$
$662$	−59.9142	−2.32863
$663$	14.4852	0.562559
$664$	41.9545	1.62815
$665$	16.3414	0.633692
$666$	−127.244	−4.93059
$667$	−3.66538	−0.141924
$668$	88.7199	3.43268
$669$	51.4204	1.98803
$670$	8.22027	0.317577
$671$	1.82515	0.0704592
$672$	17.0966	0.659515
$673$	50.9816	1.96520	0.982598	−	0.185743i	$-0.0594693\pi$
$673$	50.9816	1.96520	0.982598	+	0.185743i	$0.0594693\pi$
$674$	−8.44068	−0.325123
$675$	−15.9398	−0.613524
$676$	4.24169	0.163142
$677$	−26.5067	−1.01873	−0.509367	−	0.860549i	$-0.670121\pi$
$677$	−26.5067	−1.01873	−0.509367	+	0.860549i	$0.670121\pi$
$678$	−62.1055	−2.38515
$679$	3.38031	0.129724
$680$	47.5611	1.82389
$681$	42.1385	1.61475
$682$	0.661176	0.0253177
$683$	31.3508	1.19960	0.599802	−	0.800149i	$-0.295246\pi$
$683$	31.3508	1.19960	0.599802	+	0.800149i	$0.295246\pi$
$684$	100.678	3.84953
$685$	24.6516	0.941887
$686$	−50.1911	−1.91631
$687$	−27.4283	−1.04645
$688$	−29.8961	−1.13978
$689$	−4.08388	−0.155583
$690$	108.238	4.12057
$691$	−32.2076	−1.22524	−0.612618	−	0.790379i	$-0.709884\pi$
$691$	−32.2076	−1.22524	−0.612618	+	0.790379i	$0.709884\pi$
$692$	95.1278	3.61622
$693$	−1.67975	−0.0638085
$694$	50.2668	1.90810
$695$	20.3501	0.771923
$696$	7.10917	0.269472
$697$	−27.6692	−1.04805
$698$	64.8967	2.45638
$699$	58.7026	2.22034
$700$	19.3607	0.731767
$701$	7.92718	0.299405	0.149703	−	0.988731i	$-0.452168\pi$
$701$	7.92718	0.299405	0.149703	+	0.988731i	$0.452168\pi$
$702$	−19.7629	−0.745903
$703$	37.4134	1.41107
$704$	−0.602495	−0.0227074
$705$	27.9917	1.05423
$706$	−6.43374	−0.242137
$707$	−9.45485	−0.355586
$708$	139.477	5.24187
$709$	37.3990	1.40455	0.702275	−	0.711906i	$-0.252168\pi$
$709$	37.3990	1.40455	0.702275	+	0.711906i	$0.252168\pi$
$710$	21.2717	0.798311
$711$	24.4367	0.916448
$712$	−4.59086	−0.172050
$713$	−17.2620	−0.646469
$714$	81.9739	3.06780
$715$	−0.225391	−0.00842914
$716$	102.817	3.84244
$717$	−39.5964	−1.47875
$718$	−8.18676	−0.305527
$719$	1.98211	0.0739202	0.0369601	−	0.999317i	$-0.488233\pi$
$719$	1.98211	0.0739202	0.0369601	+	0.999317i	$0.488233\pi$
$720$	−54.0982	−2.01612
$721$	34.1791	1.27290
$722$	3.90821	0.145449
$723$	−37.0701	−1.37865
$724$	24.4601	0.909053
$725$	0.867978	0.0322359
$726$	80.8609	3.00103
$727$	−2.50479	−0.0928975	−0.0464487	−	0.998921i	$-0.514790\pi$
$727$	−2.50479	−0.0928975	−0.0464487	+	0.998921i	$0.514790\pi$
$728$	12.6860	0.470176
$729$	−34.3592	−1.27256
$730$	−33.2441	−1.23042
$731$	−26.6769	−0.986682
$732$	174.879	6.46372
$733$	−11.6749	−0.431222	−0.215611	−	0.976479i	$-0.569174\pi$
$733$	−11.6749	−0.431222	−0.215611	+	0.976479i	$0.569174\pi$
$734$	−16.3839	−0.604742
$735$	9.51592	0.351000
$736$	−21.7939	−0.803334
$737$	0.248446	0.00915164
$738$	79.9407	2.94266
$739$	16.8163	0.618596	0.309298	−	0.950965i	$-0.399906\pi$
$739$	16.8163	0.618596	0.309298	+	0.950965i	$0.399906\pi$
$740$	−65.6622	−2.41379
$741$	12.3052	0.452041
$742$	−23.1113	−0.848442
$743$	−7.90480	−0.289999	−0.145000	−	0.989432i	$-0.546318\pi$
$743$	−7.90480	−0.289999	−0.145000	+	0.989432i	$0.546318\pi$
$744$	33.4805	1.22746
$745$	14.6815	0.537888
$746$	41.9078	1.53435
$747$	−42.5824	−1.55801
$748$	2.71996	0.0994516
$749$	−11.7942	−0.430950
$750$	−89.2315	−3.25827
$751$	36.0110	1.31406	0.657030	−	0.753864i	$-0.271812\pi$
$751$	36.0110	1.31406	0.657030	+	0.753864i	$0.271812\pi$
$752$	−30.2850	−1.10438
$753$	12.0582	0.439424
$754$	1.07616	0.0391914
$755$	−4.33237	−0.157671
$756$	−76.0044	−2.76425
$757$	−3.73581	−0.135780	−0.0678902	−	0.997693i	$-0.521627\pi$
$757$	−3.73581	−0.135780	−0.0678902	+	0.997693i	$0.521627\pi$
$758$	14.5335	0.527881
$759$	3.27136	0.118743
$760$	40.4031	1.46557
$761$	−7.91105	−0.286775	−0.143388	−	0.989667i	$-0.545800\pi$
$761$	−7.91105	−0.286775	−0.143388	+	0.989667i	$0.545800\pi$
$762$	−71.6162	−2.59438
$763$	5.05604	0.183041
$764$	99.6879	3.60658
$765$	−48.2730	−1.74531
$766$	−88.4303	−3.19512
$767$	11.1583	0.402902
$768$	−95.4418	−3.44396
$769$	−20.4779	−0.738453	−0.369227	−	0.929339i	$-0.620377\pi$
$769$	−20.4779	−0.738453	−0.369227	+	0.929339i	$0.620377\pi$
$770$	−1.27552	−0.0459666
$771$	75.8146	2.73039
$772$	−50.3855	−1.81341
$773$	−6.06885	−0.218281	−0.109141	−	0.994026i	$-0.534810\pi$
$773$	−6.06885	−0.218281	−0.109141	+	0.994026i	$0.534810\pi$
$774$	77.0740	2.77037
$775$	4.08773	0.146836
$776$	8.35761	0.300021
$777$	−59.8102	−2.14568
$778$	39.6462	1.42138
$779$	−23.5049	−0.842151
$780$	−21.5961	−0.773265
$781$	0.642907	0.0230050
$782$	−104.496	−3.73678
$783$	−3.40742	−0.121771
$784$	−10.2956	−0.367698
$785$	20.8882	0.745533
$786$	89.4834	3.19177
$787$	12.7829	0.455662	0.227831	−	0.973701i	$-0.426837\pi$
$787$	12.7829	0.455662	0.227831	+	0.973701i	$0.426837\pi$
$788$	50.7277	1.80710
$789$	−86.8212	−3.09092
$790$	18.5560	0.660194
$791$	−19.1078	−0.679397
$792$	−4.15308	−0.147573
$793$	13.9905	0.496816
$794$	−17.1329	−0.608023
$795$	20.7927	0.737440
$796$	106.516	3.77536
$797$	−12.7518	−0.451693	−0.225847	−	0.974163i	$-0.572515\pi$
$797$	−12.7518	−0.451693	−0.225847	+	0.974163i	$0.572515\pi$
$798$	69.6367	2.46511
$799$	−27.0239	−0.956038
$800$	5.16089	0.182465
$801$	4.65957	0.164638
$802$	−58.1719	−2.05412
$803$	−1.00476	−0.0354571
$804$	23.8052	0.839545
$805$	33.3014	1.17372
$806$	5.06816	0.178518
$807$	79.8837	2.81204
$808$	−23.3765	−0.822384
$809$	11.7446	0.412920	0.206460	−	0.978455i	$-0.433806\pi$
$809$	11.7446	0.412920	0.206460	+	0.978455i	$0.433806\pi$
$810$	27.0139	0.949170
$811$	41.6297	1.46182	0.730909	−	0.682475i	$-0.239096\pi$
$811$	41.6297	1.46182	0.730909	+	0.682475i	$0.239096\pi$
$812$	4.13870	0.145240
$813$	30.1232	1.05647
$814$	−2.92029	−0.102356
$815$	−27.1453	−0.950858
$816$	79.7922	2.79328
$817$	−22.6620	−0.792843
$818$	−72.4444	−2.53296
$819$	−12.8759	−0.449921
$820$	41.2522	1.44059
$821$	23.8836	0.833544	0.416772	−	0.909011i	$-0.363161\pi$
$821$	23.8836	0.833544	0.416772	+	0.909011i	$0.363161\pi$
$822$	105.049	3.66402
$823$	1.84776	0.0644090	0.0322045	−	0.999481i	$-0.489747\pi$
$823$	1.84776	0.0644090	0.0322045	+	0.999481i	$0.489747\pi$
$824$	84.5058	2.94390
$825$	−0.774672	−0.0269706
$826$	63.1463	2.19714
$827$	−23.5130	−0.817628	−0.408814	−	0.912618i	$-0.634057\pi$
$827$	−23.5130	−0.817628	−0.408814	+	0.912618i	$0.634057\pi$
$828$	205.168	7.13008
$829$	−9.35975	−0.325078	−0.162539	−	0.986702i	$-0.551968\pi$
$829$	−9.35975	−0.325078	−0.162539	+	0.986702i	$0.551968\pi$
$830$	−32.3350	−1.12236
$831$	−0.217712	−0.00755234
$832$	−4.61835	−0.160112
$833$	−9.18694	−0.318309
$834$	86.7193	3.00284
$835$	−36.1370	−1.25057
$836$	2.31060	0.0799138
$837$	−16.0472	−0.554672
$838$	85.6491	2.95870
$839$	−25.2619	−0.872137	−0.436069	−	0.899913i	$-0.643630\pi$
$839$	−25.2619	−0.872137	−0.436069	+	0.899913i	$0.643630\pi$
$840$	−64.5897	−2.22856
$841$	−28.8145	−0.993602
$842$	−1.05293	−0.0362862
$843$	31.1064	1.07136
$844$	−32.2947	−1.11163
$845$	−1.72770	−0.0594348
$846$	78.0765	2.68433
$847$	24.8783	0.854828
$848$	−22.4962	−0.772522
$849$	−29.4238	−1.00982
$850$	24.7452	0.848754
$851$	76.2432	2.61358
$852$	61.6009	2.11041
$853$	10.7693	0.368734	0.184367	−	0.982857i	$-0.440976\pi$
$853$	10.7693	0.368734	0.184367	+	0.982857i	$0.440976\pi$
$854$	79.1741	2.70928
$855$	−41.0078	−1.40244
$856$	−29.1604	−0.996682
$857$	−5.75627	−0.196630	−0.0983152	−	0.995155i	$-0.531345\pi$
$857$	−5.75627	−0.196630	−0.0983152	+	0.995155i	$0.531345\pi$
$858$	−0.960474	−0.0327900
$859$	−33.4592	−1.14161	−0.570806	−	0.821085i	$-0.693369\pi$
$859$	−33.4592	−1.14161	−0.570806	+	0.821085i	$0.693369\pi$
$860$	39.7729	1.35624
$861$	37.5757	1.28058
$862$	−39.7577	−1.35415
$863$	−2.34397	−0.0797898	−0.0398949	−	0.999204i	$-0.512702\pi$
$863$	−2.34397	−0.0797898	−0.0398949	+	0.999204i	$0.512702\pi$
$864$	−20.2601	−0.689263
$865$	−38.7470	−1.31744
$866$	−73.1765	−2.48664
$867$	21.1027	0.716684
$868$	19.4912	0.661573
$869$	0.560831	0.0190249
$870$	−5.47915	−0.185761
$871$	1.90443	0.0645293
$872$	12.5008	0.423329
$873$	−8.48270	−0.287096
$874$	−88.7695	−3.00267
$875$	−27.4536	−0.928102
$876$	−96.2722	−3.25274
$877$	−28.3108	−0.955987	−0.477994	−	0.878363i	$-0.658636\pi$
$877$	−28.3108	−0.955987	−0.477994	+	0.878363i	$0.658636\pi$
$878$	58.6470	1.97924
$879$	32.8816	1.10907
$880$	−1.24157	−0.0418534
$881$	29.5188	0.994514	0.497257	−	0.867603i	$-0.334341\pi$
$881$	29.5188	0.994514	0.497257	+	0.867603i	$0.334341\pi$
$882$	26.5425	0.893734
$883$	−9.82967	−0.330795	−0.165397	−	0.986227i	$-0.552891\pi$
$883$	−9.82967	−0.330795	−0.165397	+	0.986227i	$0.552891\pi$
$884$	20.8495	0.701244
$885$	−56.8112	−1.90969
$886$	50.7994	1.70664
$887$	8.40669	0.282269	0.141134	−	0.989990i	$-0.454925\pi$
$887$	8.40669	0.282269	0.141134	+	0.989990i	$0.454925\pi$
$888$	−147.877	−4.96243
$889$	−22.0340	−0.738995
$890$	3.53825	0.118603
$891$	0.816457	0.0273523
$892$	74.0126	2.47813
$893$	−22.9568	−0.768219
$894$	62.5632	2.09243
$895$	−41.8789	−1.39986
$896$	−37.7390	−1.26077
$897$	25.0762	0.837269
$898$	−55.8182	−1.86268
$899$	0.873825	0.0291437
$900$	−48.5847	−1.61949
$901$	−20.0738	−0.668756
$902$	1.83467	0.0610878
$903$	36.2282	1.20560
$904$	−47.2430	−1.57128
$905$	−9.96298	−0.331181
$906$	−18.4618	−0.613353
$907$	39.5684	1.31385	0.656924	−	0.753957i	$-0.271857\pi$
$907$	39.5684	1.31385	0.656924	+	0.753957i	$0.271857\pi$
$908$	60.6527	2.01283
$909$	23.7264	0.786955
$910$	−9.77734	−0.324116
$911$	−35.4345	−1.17400	−0.586999	−	0.809588i	$-0.699691\pi$
$911$	−35.4345	−1.17400	−0.586999	+	0.809588i	$0.699691\pi$
$912$	67.7833	2.24453
$913$	−0.977281	−0.0323433
$914$	31.0141	1.02585
$915$	−71.2310	−2.35482
$916$	−39.4793	−1.30443
$917$	27.5311	0.909158
$918$	−97.1422	−3.20617
$919$	53.5926	1.76786	0.883928	−	0.467623i	$-0.154890\pi$
$919$	53.5926	1.76786	0.883928	+	0.467623i	$0.154890\pi$
$920$	82.3358	2.71453
$921$	7.94752	0.261880
$922$	41.0359	1.35145
$923$	4.92812	0.162211
$924$	−3.69380	−0.121517
$925$	−18.0547	−0.593636
$926$	2.49834	0.0821004
$927$	−85.7705	−2.81707
$928$	1.10323	0.0362154
$929$	35.9021	1.17791	0.588955	−	0.808166i	$-0.299540\pi$
$929$	35.9021	1.17791	0.588955	+	0.808166i	$0.299540\pi$
$930$	−25.8040	−0.846146
$931$	−7.80429	−0.255775
$932$	84.4945	2.76771
$933$	18.5363	0.606850
$934$	26.9890	0.883108
$935$	−1.10788	−0.0362316
$936$	−31.8349	−1.04056
$937$	−46.4989	−1.51905	−0.759526	−	0.650477i	$-0.774569\pi$
$937$	−46.4989	−1.51905	−0.759526	+	0.650477i	$0.774569\pi$
$938$	10.7775	0.351897
$939$	8.02799	0.261984
$940$	40.2902	1.31412
$941$	−31.5894	−1.02978	−0.514892	−	0.857255i	$-0.672168\pi$
$941$	−31.5894	−1.02978	−0.514892	+	0.857255i	$0.672168\pi$
$942$	89.0125	2.90018
$943$	−47.8997	−1.55983
$944$	61.4657	2.00054
$945$	30.9578	1.00706
$946$	1.76887	0.0575111
$947$	−44.9265	−1.45992	−0.729958	−	0.683492i	$-0.760460\pi$
$947$	−44.9265	−1.45992	−0.729958	+	0.683492i	$0.760460\pi$
$948$	53.7367	1.74529
$949$	−7.70184	−0.250012
$950$	21.0210	0.682012
$951$	53.6069	1.73832
$952$	62.3567	2.02099
$953$	6.54411	0.211984	0.105992	−	0.994367i	$-0.466198\pi$
$953$	6.54411	0.211984	0.105992	+	0.994367i	$0.466198\pi$
$954$	57.9965	1.87771
$955$	−40.6044	−1.31393
$956$	−56.9936	−1.84331
$957$	−0.165600	−0.00535308
$958$	−44.8957	−1.45051
$959$	32.3203	1.04368
$960$	23.5138	0.758906
$961$	−26.8847	−0.867249
$962$	−22.3851	−0.721724
$963$	29.5968	0.953745
$964$	−53.3574	−1.71853
$965$	20.5228	0.660652
$966$	141.910	4.56587
$967$	−30.2761	−0.973615	−0.486808	−	0.873509i	$-0.661839\pi$
$967$	−30.2761	−0.973615	−0.486808	+	0.873509i	$0.661839\pi$
$968$	61.5100	1.97701
$969$	60.4845	1.94304
$970$	−6.44135	−0.206819
$971$	−9.95621	−0.319510	−0.159755	−	0.987157i	$-0.551070\pi$
$971$	−9.95621	−0.319510	−0.159755	+	0.987157i	$0.551070\pi$
$972$	−22.4309	−0.719470
$973$	26.6807	0.855344
$974$	19.7229	0.631963
$975$	−5.93815	−0.190173
$976$	77.0669	2.46685
$977$	22.4785	0.719150	0.359575	−	0.933116i	$-0.382922\pi$
$977$	22.4785	0.719150	0.359575	+	0.933116i	$0.382922\pi$
$978$	−115.676	−3.69891
$979$	0.106939	0.00341778
$980$	13.6969	0.437531
$981$	−12.6879	−0.405092
$982$	−78.4080	−2.50210
$983$	−57.8743	−1.84590	−0.922951	−	0.384917i	$-0.874230\pi$
$983$	−57.8743	−1.84590	−0.922951	+	0.384917i	$0.874230\pi$
$984$	92.9037	2.96166
$985$	−20.6622	−0.658351
$986$	5.28973	0.168459
$987$	36.6994	1.16816
$988$	17.7116	0.563481
$989$	−46.1820	−1.46850
$990$	3.20085	0.101730
$991$	38.3613	1.21859	0.609293	−	0.792945i	$-0.291453\pi$
$991$	38.3613	1.21859	0.609293	+	0.792945i	$0.291453\pi$
$992$	5.19566	0.164962
$993$	70.6718	2.24270
$994$	27.8889	0.884583
$995$	−43.3856	−1.37542
$996$	−93.6394	−2.96708
$997$	12.5616	0.397830	0.198915	−	0.980017i	$-0.436258\pi$
$997$	12.5616	0.397830	0.198915	+	0.980017i	$0.436258\pi$
$998$	50.8152	1.60853
$999$	70.8774	2.24246

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.11	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.11	✓	130	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.49834 q^{2} +2.94692 q^{3} +4.24169 q^{4} -1.72770 q^{5} -7.36239 q^{6} -2.26517 q^{7} -5.60049 q^{8} +5.68431 q^{9} +O(q^{10})\)	\(q-2.49834 q^{2} +2.94692 q^{3} +4.24169 q^{4} -1.72770 q^{5} -7.36239 q^{6} -2.26517 q^{7} -5.60049 q^{8} +5.68431 q^{9} +4.31639 q^{10} +0.130457 q^{11} +12.4999 q^{12} +1.00000 q^{13} +5.65915 q^{14} -5.09140 q^{15} +5.50853 q^{16} +4.91538 q^{17} -14.2013 q^{18} +4.17560 q^{19} -7.32838 q^{20} -6.67525 q^{21} -0.325925 q^{22} +8.50929 q^{23} -16.5042 q^{24} -2.01504 q^{25} -2.49834 q^{26} +7.91043 q^{27} -9.60813 q^{28} -0.430750 q^{29} +12.7200 q^{30} -2.02861 q^{31} -2.56119 q^{32} +0.384445 q^{33} -12.2803 q^{34} +3.91354 q^{35} +24.1111 q^{36} +8.95999 q^{37} -10.4321 q^{38} +2.94692 q^{39} +9.67599 q^{40} -5.62911 q^{41} +16.6770 q^{42} -5.42724 q^{43} +0.553357 q^{44} -9.82080 q^{45} -21.2591 q^{46} -5.49783 q^{47} +16.2332 q^{48} -1.86902 q^{49} +5.03424 q^{50} +14.4852 q^{51} +4.24169 q^{52} -4.08388 q^{53} -19.7629 q^{54} -0.225391 q^{55} +12.6860 q^{56} +12.3052 q^{57} +1.07616 q^{58} +11.1583 q^{59} -21.5961 q^{60} +13.9905 q^{61} +5.06816 q^{62} -12.8759 q^{63} -4.61835 q^{64} -1.72770 q^{65} -0.960474 q^{66} +1.90443 q^{67} +20.8495 q^{68} +25.0762 q^{69} -9.77734 q^{70} +4.92812 q^{71} -31.8349 q^{72} -7.70184 q^{73} -22.3851 q^{74} -5.93815 q^{75} +17.7116 q^{76} -0.295507 q^{77} -7.36239 q^{78} +4.29898 q^{79} -9.51711 q^{80} +6.25844 q^{81} +14.0634 q^{82} -7.49122 q^{83} -28.3143 q^{84} -8.49232 q^{85} +13.5591 q^{86} -1.26938 q^{87} -0.730622 q^{88} +0.819726 q^{89} +24.5357 q^{90} -2.26517 q^{91} +36.0937 q^{92} -5.97815 q^{93} +13.7354 q^{94} -7.21421 q^{95} -7.54761 q^{96} -1.49230 q^{97} +4.66944 q^{98} +0.741557 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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