LMFDB - Embedded newform 6015.2.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.967785 q^{2} -1.00000 q^{3} -1.06339 q^{4} +1.00000 q^{5} +0.967785 q^{6} +0.0385606 q^{7} +2.96471 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.967785 q^{2} -1.00000 q^{3} -1.06339 q^{4} +1.00000 q^{5} +0.967785 q^{6} +0.0385606 q^{7} +2.96471 q^{8} +1.00000 q^{9} -0.967785 q^{10} +1.36875 q^{11} +1.06339 q^{12} -5.05948 q^{13} -0.0373184 q^{14} -1.00000 q^{15} -0.742415 q^{16} -8.03313 q^{17} -0.967785 q^{18} -6.83775 q^{19} -1.06339 q^{20} -0.0385606 q^{21} -1.32466 q^{22} -6.37430 q^{23} -2.96471 q^{24} +1.00000 q^{25} +4.89649 q^{26} -1.00000 q^{27} -0.0410050 q^{28} -1.62732 q^{29} +0.967785 q^{30} +8.44011 q^{31} -5.21091 q^{32} -1.36875 q^{33} +7.77435 q^{34} +0.0385606 q^{35} -1.06339 q^{36} -1.79390 q^{37} +6.61748 q^{38} +5.05948 q^{39} +2.96471 q^{40} +4.66765 q^{41} +0.0373184 q^{42} -8.81842 q^{43} -1.45552 q^{44} +1.00000 q^{45} +6.16895 q^{46} -0.604374 q^{47} +0.742415 q^{48} -6.99851 q^{49} -0.967785 q^{50} +8.03313 q^{51} +5.38021 q^{52} +5.09145 q^{53} +0.967785 q^{54} +1.36875 q^{55} +0.114321 q^{56} +6.83775 q^{57} +1.57490 q^{58} -7.44460 q^{59} +1.06339 q^{60} -0.111101 q^{61} -8.16821 q^{62} +0.0385606 q^{63} +6.52787 q^{64} -5.05948 q^{65} +1.32466 q^{66} -1.06922 q^{67} +8.54237 q^{68} +6.37430 q^{69} -0.0373184 q^{70} -0.673783 q^{71} +2.96471 q^{72} +7.61044 q^{73} +1.73611 q^{74} -1.00000 q^{75} +7.27121 q^{76} +0.0527798 q^{77} -4.89649 q^{78} +14.5655 q^{79} -0.742415 q^{80} +1.00000 q^{81} -4.51728 q^{82} -3.68963 q^{83} +0.0410050 q^{84} -8.03313 q^{85} +8.53433 q^{86} +1.62732 q^{87} +4.05794 q^{88} -0.405325 q^{89} -0.967785 q^{90} -0.195097 q^{91} +6.77838 q^{92} -8.44011 q^{93} +0.584904 q^{94} -6.83775 q^{95} +5.21091 q^{96} +2.63073 q^{97} +6.77306 q^{98} +1.36875 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) $ 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.967785	−0.684328	−0.342164	−	0.939640i	$-0.611160\pi$
$2$	−0.967785	−0.684328	−0.342164	+	0.939640i	$0.611160\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.06339	−0.531696
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.967785	0.395097
$7$	0.0385606	0.0145745	0.00728726	−	0.999973i	$-0.497680\pi$
$7$	0.0385606	0.0145745	0.00728726	+	0.999973i	$0.497680\pi$
$8$	2.96471	1.04818
$9$	1.00000	0.333333
$10$	−0.967785	−0.306041
$11$	1.36875	0.412694	0.206347	−	0.978479i	$-0.433842\pi$
$11$	1.36875	0.412694	0.206347	+	0.978479i	$0.433842\pi$
$12$	1.06339	0.306975
$13$	−5.05948	−1.40325	−0.701624	−	0.712547i	$-0.747541\pi$
$13$	−5.05948	−1.40325	−0.701624	+	0.712547i	$0.747541\pi$
$14$	−0.0373184	−0.00997375
$15$	−1.00000	−0.258199
$16$	−0.742415	−0.185604
$17$	−8.03313	−1.94832	−0.974160	−	0.225858i	$-0.927482\pi$
$17$	−8.03313	−1.94832	−0.974160	+	0.225858i	$0.927482\pi$
$18$	−0.967785	−0.228109
$19$	−6.83775	−1.56869	−0.784344	−	0.620326i	$-0.787000\pi$
$19$	−6.83775	−1.56869	−0.784344	+	0.620326i	$0.787000\pi$
$20$	−1.06339	−0.237782
$21$	−0.0385606	−0.00841461
$22$	−1.32466	−0.282418
$23$	−6.37430	−1.32913	−0.664566	−	0.747229i	$-0.731384\pi$
$23$	−6.37430	−1.32913	−0.664566	+	0.747229i	$0.731384\pi$
$24$	−2.96471	−0.605168
$25$	1.00000	0.200000
$26$	4.89649	0.960281
$27$	−1.00000	−0.192450
$28$	−0.0410050	−0.00774922
$29$	−1.62732	−0.302186	−0.151093	−	0.988520i	$-0.548279\pi$
$29$	−1.62732	−0.302186	−0.151093	+	0.988520i	$0.548279\pi$
$30$	0.967785	0.176693
$31$	8.44011	1.51589	0.757944	−	0.652319i	$-0.226204\pi$
$31$	8.44011	1.51589	0.757944	+	0.652319i	$0.226204\pi$
$32$	−5.21091	−0.921168
$33$	−1.36875	−0.238269
$34$	7.77435	1.33329
$35$	0.0385606	0.00651793
$36$	−1.06339	−0.177232
$37$	−1.79390	−0.294915	−0.147458	−	0.989068i	$-0.547109\pi$
$37$	−1.79390	−0.294915	−0.147458	+	0.989068i	$0.547109\pi$
$38$	6.61748	1.07350
$39$	5.05948	0.810166
$40$	2.96471	0.468761
$41$	4.66765	0.728964	0.364482	−	0.931210i	$-0.381246\pi$
$41$	4.66765	0.728964	0.364482	+	0.931210i	$0.381246\pi$
$42$	0.0373184	0.00575835
$43$	−8.81842	−1.34480	−0.672398	−	0.740190i	$-0.734736\pi$
$43$	−8.81842	−1.34480	−0.672398	+	0.740190i	$0.734736\pi$
$44$	−1.45552	−0.219428
$45$	1.00000	0.149071
$46$	6.16895	0.909562
$47$	−0.604374	−0.0881570	−0.0440785	−	0.999028i	$-0.514035\pi$
$47$	−0.604374	−0.0881570	−0.0440785	+	0.999028i	$0.514035\pi$
$48$	0.742415	0.107158
$49$	−6.99851	−0.999788
$50$	−0.967785	−0.136866
$51$	8.03313	1.12486
$52$	5.38021	0.746101
$53$	5.09145	0.699365	0.349682	−	0.936868i	$-0.386290\pi$
$53$	5.09145	0.699365	0.349682	+	0.936868i	$0.386290\pi$
$54$	0.967785	0.131699
$55$	1.36875	0.184562
$56$	0.114321	0.0152768
$57$	6.83775	0.905683
$58$	1.57490	0.206794
$59$	−7.44460	−0.969204	−0.484602	−	0.874735i	$-0.661036\pi$
$59$	−7.44460	−0.969204	−0.484602	+	0.874735i	$0.661036\pi$
$60$	1.06339	0.137283
$61$	−0.111101	−0.0142251	−0.00711254	−	0.999975i	$-0.502264\pi$
$61$	−0.111101	−0.0142251	−0.00711254	+	0.999975i	$0.502264\pi$
$62$	−8.16821	−1.03736
$63$	0.0385606	0.00485818
$64$	6.52787	0.815984
$65$	−5.05948	−0.627552
$66$	1.32466	0.163054
$67$	−1.06922	−0.130626	−0.0653130	−	0.997865i	$-0.520805\pi$
$67$	−1.06922	−0.130626	−0.0653130	+	0.997865i	$0.520805\pi$
$68$	8.54237	1.03591
$69$	6.37430	0.767375
$70$	−0.0373184	−0.00446040
$71$	−0.673783	−0.0799634	−0.0399817	−	0.999200i	$-0.512730\pi$
$71$	−0.673783	−0.0799634	−0.0399817	+	0.999200i	$0.512730\pi$
$72$	2.96471	0.349394
$73$	7.61044	0.890735	0.445367	−	0.895348i	$-0.353073\pi$
$73$	7.61044	0.890735	0.445367	+	0.895348i	$0.353073\pi$
$74$	1.73611	0.201819
$75$	−1.00000	−0.115470
$76$	7.27121	0.834065
$77$	0.0527798	0.00601482
$78$	−4.89649	−0.554419
$79$	14.5655	1.63875	0.819373	−	0.573261i	$-0.194322\pi$
$79$	14.5655	1.63875	0.819373	+	0.573261i	$0.194322\pi$
$80$	−0.742415	−0.0830045
$81$	1.00000	0.111111
$82$	−4.51728	−0.498850
$83$	−3.68963	−0.404990	−0.202495	−	0.979283i	$-0.564905\pi$
$83$	−3.68963	−0.404990	−0.202495	+	0.979283i	$0.564905\pi$
$84$	0.0410050	0.00447401
$85$	−8.03313	−0.871315
$86$	8.53433	0.920281
$87$	1.62732	0.174467
$88$	4.05794	0.432578
$89$	−0.405325	−0.0429644	−0.0214822	−	0.999769i	$-0.506839\pi$
$89$	−0.405325	−0.0429644	−0.0214822	+	0.999769i	$0.506839\pi$
$90$	−0.967785	−0.102014
$91$	−0.195097	−0.0204517
$92$	6.77838	0.706695
$93$	−8.44011	−0.875199
$94$	0.584904	0.0603282
$95$	−6.83775	−0.701539
$96$	5.21091	0.531837
$97$	2.63073	0.267110	0.133555	−	0.991041i	$-0.457361\pi$
$97$	2.63073	0.267110	0.133555	+	0.991041i	$0.457361\pi$
$98$	6.77306	0.684182
$99$	1.36875	0.137565
$100$	−1.06339	−0.106339
$101$	17.6585	1.75709	0.878543	−	0.477663i	$-0.158516\pi$
$101$	17.6585	1.75709	0.878543	+	0.477663i	$0.158516\pi$
$102$	−7.77435	−0.769775
$103$	14.4359	1.42241	0.711204	−	0.702986i	$-0.248150\pi$
$103$	14.4359	1.42241	0.711204	+	0.702986i	$0.248150\pi$
$104$	−14.9999	−1.47086
$105$	−0.0385606	−0.00376313
$106$	−4.92743	−0.478595
$107$	−3.96813	−0.383614	−0.191807	−	0.981433i	$-0.561435\pi$
$107$	−3.96813	−0.383614	−0.191807	+	0.981433i	$0.561435\pi$
$108$	1.06339	0.102325
$109$	5.31476	0.509062	0.254531	−	0.967065i	$-0.418079\pi$
$109$	5.31476	0.509062	0.254531	+	0.967065i	$0.418079\pi$
$110$	−1.32466	−0.126301
$111$	1.79390	0.170270
$112$	−0.0286279	−0.00270509
$113$	−11.8829	−1.11785	−0.558926	−	0.829218i	$-0.688786\pi$
$113$	−11.8829	−1.11785	−0.558926	+	0.829218i	$0.688786\pi$
$114$	−6.61748	−0.619784
$115$	−6.37430	−0.594406
$116$	1.73048	0.160671
$117$	−5.05948	−0.467749
$118$	7.20477	0.663253
$119$	−0.309762	−0.0283959
$120$	−2.96471	−0.270639
$121$	−9.12652	−0.829684
$122$	0.107522	0.00973461
$123$	−4.66765	−0.420868
$124$	−8.97514	−0.805992
$125$	1.00000	0.0894427
$126$	−0.0373184	−0.00332458
$127$	2.89743	0.257105	0.128553	−	0.991703i	$-0.458967\pi$
$127$	2.89743	0.257105	0.128553	+	0.991703i	$0.458967\pi$
$128$	4.10425	0.362768
$129$	8.81842	0.776418
$130$	4.89649	0.429451
$131$	−2.67293	−0.233535	−0.116767	−	0.993159i	$-0.537253\pi$
$131$	−2.67293	−0.233535	−0.116767	+	0.993159i	$0.537253\pi$
$132$	1.45552	0.126687
$133$	−0.263668	−0.0228629
$134$	1.03477	0.0893909
$135$	−1.00000	−0.0860663
$136$	−23.8159	−2.04219
$137$	1.27640	0.109050	0.0545251	−	0.998512i	$-0.482635\pi$
$137$	1.27640	0.109050	0.0545251	+	0.998512i	$0.482635\pi$
$138$	−6.16895	−0.525136
$139$	7.43582	0.630698	0.315349	−	0.948976i	$-0.397878\pi$
$139$	7.43582	0.630698	0.315349	+	0.948976i	$0.397878\pi$
$140$	−0.0410050	−0.00346555
$141$	0.604374	0.0508974
$142$	0.652078	0.0547211
$143$	−6.92517	−0.579112
$144$	−0.742415	−0.0618679
$145$	−1.62732	−0.135142
$146$	−7.36527	−0.609554
$147$	6.99851	0.577228
$148$	1.90762	0.156805
$149$	−11.9384	−0.978030	−0.489015	−	0.872275i	$-0.662644\pi$
$149$	−11.9384	−0.978030	−0.489015	+	0.872275i	$0.662644\pi$
$150$	0.967785	0.0790193
$151$	−10.0894	−0.821066	−0.410533	−	0.911846i	$-0.634657\pi$
$151$	−10.0894	−0.821066	−0.410533	+	0.911846i	$0.634657\pi$
$152$	−20.2719	−1.64427
$153$	−8.03313	−0.649440
$154$	−0.0510795	−0.00411610
$155$	8.44011	0.677926
$156$	−5.38021	−0.430762
$157$	−10.4824	−0.836590	−0.418295	−	0.908311i	$-0.637372\pi$
$157$	−10.4824	−0.836590	−0.418295	+	0.908311i	$0.637372\pi$
$158$	−14.0963	−1.12144
$159$	−5.09145	−0.403778
$160$	−5.21091	−0.411959
$161$	−0.245797	−0.0193715
$162$	−0.967785	−0.0760364
$163$	−12.4915	−0.978411	−0.489205	−	0.872169i	$-0.662713\pi$
$163$	−12.4915	−0.978411	−0.489205	+	0.872169i	$0.662713\pi$
$164$	−4.96354	−0.387587
$165$	−1.36875	−0.106557
$166$	3.57077	0.277146
$167$	10.5628	0.817371	0.408685	−	0.912675i	$-0.365987\pi$
$167$	10.5628	0.817371	0.408685	+	0.912675i	$0.365987\pi$
$168$	−0.114321	−0.00882004
$169$	12.5984	0.969105
$170$	7.77435	0.596265
$171$	−6.83775	−0.522896
$172$	9.37743	0.715023
$173$	5.60816	0.426380	0.213190	−	0.977011i	$-0.431615\pi$
$173$	5.60816	0.426380	0.213190	+	0.977011i	$0.431615\pi$
$174$	−1.57490	−0.119393
$175$	0.0385606	0.00291491
$176$	−1.01618	−0.0765975
$177$	7.44460	0.559570
$178$	0.392267	0.0294017
$179$	−22.5854	−1.68811	−0.844056	−	0.536255i	$-0.819838\pi$
$179$	−22.5854	−1.68811	−0.844056	+	0.536255i	$0.819838\pi$
$180$	−1.06339	−0.0792605
$181$	−12.4724	−0.927064	−0.463532	−	0.886080i	$-0.653418\pi$
$181$	−12.4724	−0.927064	−0.463532	+	0.886080i	$0.653418\pi$
$182$	0.188812	0.0139956
$183$	0.111101	0.00821285
$184$	−18.8979	−1.39317
$185$	−1.79390	−0.131890
$186$	8.16821	0.598922
$187$	−10.9954	−0.804060
$188$	0.642686	0.0468727
$189$	−0.0385606	−0.00280487
$190$	6.61748	0.480082
$191$	7.73996	0.560044	0.280022	−	0.959994i	$-0.409658\pi$
$191$	7.73996	0.560044	0.280022	+	0.959994i	$0.409658\pi$
$192$	−6.52787	−0.471109
$193$	−18.1909	−1.30941	−0.654706	−	0.755884i	$-0.727208\pi$
$193$	−18.1909	−1.30941	−0.654706	+	0.755884i	$0.727208\pi$
$194$	−2.54598	−0.182791
$195$	5.05948	0.362317
$196$	7.44216	0.531583
$197$	8.92935	0.636190	0.318095	−	0.948059i	$-0.396957\pi$
$197$	8.92935	0.636190	0.318095	+	0.948059i	$0.396957\pi$
$198$	−1.32466	−0.0941392
$199$	17.1379	1.21487	0.607436	−	0.794369i	$-0.292198\pi$
$199$	17.1379	1.21487	0.607436	+	0.794369i	$0.292198\pi$
$200$	2.96471	0.209636
$201$	1.06922	0.0754169
$202$	−17.0896	−1.20242
$203$	−0.0627505	−0.00440422
$204$	−8.54237	−0.598085
$205$	4.66765	0.326003
$206$	−13.9708	−0.973392
$207$	−6.37430	−0.443044
$208$	3.75623	0.260448
$209$	−9.35918	−0.647388
$210$	0.0373184	0.00257521
$211$	12.5548	0.864309	0.432155	−	0.901800i	$-0.357753\pi$
$211$	12.5548	0.864309	0.432155	+	0.901800i	$0.357753\pi$
$212$	−5.41421	−0.371849
$213$	0.673783	0.0461669
$214$	3.84030	0.262518
$215$	−8.81842	−0.601411
$216$	−2.96471	−0.201723
$217$	0.325455	0.0220934
$218$	−5.14355	−0.348365
$219$	−7.61044	−0.514266
$220$	−1.45552	−0.0981310
$221$	40.6435	2.73398
$222$	−1.73611	−0.116520
$223$	14.4042	0.964579	0.482289	−	0.876012i	$-0.339805\pi$
$223$	14.4042	0.964579	0.482289	+	0.876012i	$0.339805\pi$
$224$	−0.200936	−0.0134256
$225$	1.00000	0.0666667
$226$	11.5001	0.764977
$227$	−14.6402	−0.971704	−0.485852	−	0.874041i	$-0.661491\pi$
$227$	−14.6402	−0.971704	−0.485852	+	0.874041i	$0.661491\pi$
$228$	−7.27121	−0.481548
$229$	−5.76676	−0.381078	−0.190539	−	0.981680i	$-0.561024\pi$
$229$	−5.76676	−0.381078	−0.190539	+	0.981680i	$0.561024\pi$
$230$	6.16895	0.406769
$231$	−0.0527798	−0.00347266
$232$	−4.82453	−0.316746
$233$	12.6733	0.830253	0.415126	−	0.909764i	$-0.363737\pi$
$233$	12.6733	0.830253	0.415126	+	0.909764i	$0.363737\pi$
$234$	4.89649	0.320094
$235$	−0.604374	−0.0394250
$236$	7.91653	0.515322
$237$	−14.5655	−0.946130
$238$	0.299783	0.0194321
$239$	8.19736	0.530243	0.265122	−	0.964215i	$-0.414588\pi$
$239$	8.19736	0.530243	0.265122	+	0.964215i	$0.414588\pi$
$240$	0.742415	0.0479227
$241$	−6.49970	−0.418682	−0.209341	−	0.977843i	$-0.567132\pi$
$241$	−6.49970	−0.418682	−0.209341	+	0.977843i	$0.567132\pi$
$242$	8.83251	0.567775
$243$	−1.00000	−0.0641500
$244$	0.118144	0.00756341
$245$	−6.99851	−0.447119
$246$	4.51728	0.288011
$247$	34.5955	2.20126
$248$	25.0224	1.58893
$249$	3.68963	0.233821
$250$	−0.967785	−0.0612081
$251$	10.7851	0.680747	0.340374	−	0.940290i	$-0.389446\pi$
$251$	10.7851	0.680747	0.340374	+	0.940290i	$0.389446\pi$
$252$	−0.0410050	−0.00258307
$253$	−8.72482	−0.548525
$254$	−2.80409	−0.175944
$255$	8.03313	0.503054
$256$	−17.0278	−1.06424
$257$	22.1505	1.38171	0.690854	−	0.722994i	$-0.257235\pi$
$257$	22.1505	1.38171	0.690854	+	0.722994i	$0.257235\pi$
$258$	−8.53433	−0.531324
$259$	−0.0691738	−0.00429825
$260$	5.38021	0.333667
$261$	−1.62732	−0.100729
$262$	2.58682	0.159814
$263$	11.7446	0.724206	0.362103	−	0.932138i	$-0.382059\pi$
$263$	11.7446	0.724206	0.362103	+	0.932138i	$0.382059\pi$
$264$	−4.05794	−0.249749
$265$	5.09145	0.312765
$266$	0.255174	0.0156457
$267$	0.405325	0.0248055
$268$	1.13700	0.0694533
$269$	−0.113807	−0.00693896	−0.00346948	−	0.999994i	$-0.501104\pi$
$269$	−0.113807	−0.00693896	−0.00346948	+	0.999994i	$0.501104\pi$
$270$	0.967785	0.0588975
$271$	−15.0048	−0.911475	−0.455737	−	0.890114i	$-0.650624\pi$
$271$	−15.0048	−0.911475	−0.455737	+	0.890114i	$0.650624\pi$
$272$	5.96391	0.361615
$273$	0.195097	0.0118078
$274$	−1.23528	−0.0746261
$275$	1.36875	0.0825388
$276$	−6.77838	−0.408010
$277$	26.4564	1.58961	0.794807	−	0.606862i	$-0.207572\pi$
$277$	26.4564	1.58961	0.794807	+	0.606862i	$0.207572\pi$
$278$	−7.19627	−0.431604
$279$	8.44011	0.505296
$280$	0.114321	0.00683197
$281$	−11.1225	−0.663512	−0.331756	−	0.943365i	$-0.607641\pi$
$281$	−11.1225	−0.663512	−0.331756	+	0.943365i	$0.607641\pi$
$282$	−0.584904	−0.0348305
$283$	2.44231	0.145180	0.0725902	−	0.997362i	$-0.476873\pi$
$283$	2.44231	0.145180	0.0725902	+	0.997362i	$0.476873\pi$
$284$	0.716496	0.0425162
$285$	6.83775	0.405034
$286$	6.70208	0.396302
$287$	0.179987	0.0106243
$288$	−5.21091	−0.307056
$289$	47.5312	2.79595
$290$	1.57490	0.0924812
$291$	−2.63073	−0.154216
$292$	−8.09288	−0.473600
$293$	17.6630	1.03188	0.515941	−	0.856624i	$-0.327442\pi$
$293$	17.6630	1.03188	0.515941	+	0.856624i	$0.327442\pi$
$294$	−6.77306	−0.395013
$295$	−7.44460	−0.433441
$296$	−5.31839	−0.309125
$297$	−1.36875	−0.0794230
$298$	11.5538	0.669293
$299$	32.2506	1.86510
$300$	1.06339	0.0613950
$301$	−0.340043	−0.0195998
$302$	9.76440	0.561878
$303$	−17.6585	−1.01445
$304$	5.07645	0.291154
$305$	−0.111101	−0.00636165
$306$	7.77435	0.444430
$307$	−23.8955	−1.36379	−0.681895	−	0.731450i	$-0.738844\pi$
$307$	−23.8955	−1.36379	−0.681895	+	0.731450i	$0.738844\pi$
$308$	−0.0561256	−0.00319805
$309$	−14.4359	−0.821227
$310$	−8.16821	−0.463923
$311$	−4.84878	−0.274949	−0.137475	−	0.990505i	$-0.543899\pi$
$311$	−4.84878	−0.274949	−0.137475	+	0.990505i	$0.543899\pi$
$312$	14.9999	0.849201
$313$	5.56942	0.314802	0.157401	−	0.987535i	$-0.449688\pi$
$313$	5.56942	0.314802	0.157401	+	0.987535i	$0.449688\pi$
$314$	10.1448	0.572502
$315$	0.0385606	0.00217264
$316$	−15.4888	−0.871314
$317$	21.7365	1.22084	0.610421	−	0.792077i	$-0.291000\pi$
$317$	21.7365	1.22084	0.610421	+	0.792077i	$0.291000\pi$
$318$	4.92743	0.276317
$319$	−2.22740	−0.124710
$320$	6.52787	0.364919
$321$	3.96813	0.221480
$322$	0.237878	0.0132564
$323$	54.9286	3.05631
$324$	−1.06339	−0.0590773
$325$	−5.05948	−0.280650
$326$	12.0891	0.669553
$327$	−5.31476	−0.293907
$328$	13.8382	0.764087
$329$	−0.0233050	−0.00128485
$330$	1.32466	0.0729199
$331$	1.22492	0.0673278	0.0336639	−	0.999433i	$-0.489282\pi$
$331$	1.22492	0.0673278	0.0336639	+	0.999433i	$0.489282\pi$
$332$	3.92353	0.215331
$333$	−1.79390	−0.0983052
$334$	−10.2225	−0.559349
$335$	−1.06922	−0.0584177
$336$	0.0286279	0.00156178
$337$	−9.00251	−0.490398	−0.245199	−	0.969473i	$-0.578853\pi$
$337$	−9.00251	−0.490398	−0.245199	+	0.969473i	$0.578853\pi$
$338$	−12.1925	−0.663185
$339$	11.8829	0.645392
$340$	8.54237	0.463275
$341$	11.5524	0.625598
$342$	6.61748	0.357832
$343$	−0.539791	−0.0291460
$344$	−26.1440	−1.40959
$345$	6.37430	0.343181
$346$	−5.42749	−0.291784
$347$	23.4297	1.25777	0.628887	−	0.777497i	$-0.283511\pi$
$347$	23.4297	1.25777	0.628887	+	0.777497i	$0.283511\pi$
$348$	−1.73048	−0.0927635
$349$	0.493229	0.0264020	0.0132010	−	0.999913i	$-0.495798\pi$
$349$	0.493229	0.0264020	0.0132010	+	0.999913i	$0.495798\pi$
$350$	−0.0373184	−0.00199475
$351$	5.05948	0.270055
$352$	−7.13244	−0.380160
$353$	−9.74792	−0.518829	−0.259415	−	0.965766i	$-0.583530\pi$
$353$	−9.74792	−0.518829	−0.259415	+	0.965766i	$0.583530\pi$
$354$	−7.20477	−0.382929
$355$	−0.673783	−0.0357607
$356$	0.431019	0.0228440
$357$	0.309762	0.0163944
$358$	21.8578	1.15522
$359$	37.3762	1.97264	0.986321	−	0.164837i	$-0.0527098\pi$
$359$	37.3762	1.97264	0.986321	+	0.164837i	$0.0527098\pi$
$360$	2.96471	0.156254
$361$	27.7549	1.46078
$362$	12.0706	0.634415
$363$	9.12652	0.479018
$364$	0.207464	0.0108741
$365$	7.61044	0.398349
$366$	−0.107522	−0.00562028
$367$	−0.444171	−0.0231856	−0.0115928	−	0.999933i	$-0.503690\pi$
$367$	−0.444171	−0.0231856	−0.0115928	+	0.999933i	$0.503690\pi$
$368$	4.73237	0.246692
$369$	4.66765	0.242988
$370$	1.73611	0.0902561
$371$	0.196329	0.0101929
$372$	8.97514	0.465339
$373$	−37.1844	−1.92533	−0.962667	−	0.270687i	$-0.912749\pi$
$373$	−37.1844	−1.92533	−0.962667	+	0.270687i	$0.912749\pi$
$374$	10.6411	0.550240
$375$	−1.00000	−0.0516398
$376$	−1.79179	−0.0924045
$377$	8.23341	0.424042
$378$	0.0373184	0.00191945
$379$	−19.9653	−1.02555	−0.512774	−	0.858523i	$-0.671382\pi$
$379$	−19.9653	−1.02555	−0.512774	+	0.858523i	$0.671382\pi$
$380$	7.27121	0.373005
$381$	−2.89743	−0.148440
$382$	−7.49062	−0.383253
$383$	12.2584	0.626375	0.313188	−	0.949691i	$-0.398603\pi$
$383$	12.2584	0.626375	0.313188	+	0.949691i	$0.398603\pi$
$384$	−4.10425	−0.209444
$385$	0.0527798	0.00268991
$386$	17.6049	0.896067
$387$	−8.81842	−0.448265
$388$	−2.79749	−0.142021
$389$	9.86612	0.500232	0.250116	−	0.968216i	$-0.419531\pi$
$389$	9.86612	0.500232	0.250116	+	0.968216i	$0.419531\pi$
$390$	−4.89649	−0.247944
$391$	51.2056	2.58958
$392$	−20.7485	−1.04796
$393$	2.67293	0.134831
$394$	−8.64170	−0.435362
$395$	14.5655	0.732869
$396$	−1.45552	−0.0731425
$397$	−9.36617	−0.470074	−0.235037	−	0.971986i	$-0.575521\pi$
$397$	−9.36617	−0.470074	−0.235037	+	0.971986i	$0.575521\pi$
$398$	−16.5858	−0.831370
$399$	0.263668	0.0131999
$400$	−0.742415	−0.0371207
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−1.03477	−0.0516099
$403$	−42.7026	−2.12717
$404$	−18.7779	−0.934235
$405$	1.00000	0.0496904
$406$	0.0607290	0.00301393
$407$	−2.45540	−0.121710
$408$	23.8159	1.17906
$409$	−25.2300	−1.24754	−0.623772	−	0.781606i	$-0.714401\pi$
$409$	−25.2300	−1.24754	−0.623772	+	0.781606i	$0.714401\pi$
$410$	−4.51728	−0.223093
$411$	−1.27640	−0.0629602
$412$	−15.3510	−0.756288
$413$	−0.287068	−0.0141257
$414$	6.16895	0.303187
$415$	−3.68963	−0.181117
$416$	26.3645	1.29263
$417$	−7.43582	−0.364134
$418$	9.05767	0.443025
$419$	−7.82024	−0.382044	−0.191022	−	0.981586i	$-0.561180\pi$
$419$	−7.82024	−0.382044	−0.191022	+	0.981586i	$0.561180\pi$
$420$	0.0410050	0.00200084
$421$	35.5512	1.73266	0.866329	−	0.499474i	$-0.166473\pi$
$421$	35.5512	1.73266	0.866329	+	0.499474i	$0.166473\pi$
$422$	−12.1504	−0.591471
$423$	−0.604374	−0.0293857
$424$	15.0947	0.733061
$425$	−8.03313	−0.389664
$426$	−0.652078	−0.0315933
$427$	−0.00428413	−0.000207324 0
$428$	4.21968	0.203966
$429$	6.92517	0.334350
$430$	8.53433	0.411562
$431$	37.1996	1.79184	0.895921	−	0.444213i	$-0.146517\pi$
$431$	37.1996	1.79184	0.895921	+	0.444213i	$0.146517\pi$
$432$	0.742415	0.0357194
$433$	−12.8537	−0.617707	−0.308854	−	0.951110i	$-0.599945\pi$
$433$	−12.8537	−0.617707	−0.308854	+	0.951110i	$0.599945\pi$
$434$	−0.314971	−0.0151191
$435$	1.62732	0.0780241
$436$	−5.65168	−0.270666
$437$	43.5859	2.08500
$438$	7.36527	0.351926
$439$	−19.6397	−0.937353	−0.468677	−	0.883370i	$-0.655269\pi$
$439$	−19.6397	−0.937353	−0.468677	+	0.883370i	$0.655269\pi$
$440$	4.05794	0.193455
$441$	−6.99851	−0.333263
$442$	−39.3342	−1.87094
$443$	9.70662	0.461176	0.230588	−	0.973052i	$-0.425935\pi$
$443$	9.70662	0.461176	0.230588	+	0.973052i	$0.425935\pi$
$444$	−1.90762	−0.0905316
$445$	−0.405325	−0.0192142
$446$	−13.9402	−0.660088
$447$	11.9384	0.564666
$448$	0.251719	0.0118926
$449$	−6.59488	−0.311232	−0.155616	−	0.987818i	$-0.549736\pi$
$449$	−6.59488	−0.311232	−0.155616	+	0.987818i	$0.549736\pi$
$450$	−0.967785	−0.0456218
$451$	6.38885	0.300839
$452$	12.6362	0.594357
$453$	10.0894	0.474043
$454$	14.1686	0.664964
$455$	−0.195097	−0.00914627
$456$	20.2719	0.949320
$457$	7.61680	0.356299	0.178149	−	0.984003i	$-0.442989\pi$
$457$	7.61680	0.356299	0.178149	+	0.984003i	$0.442989\pi$
$458$	5.58098	0.260782
$459$	8.03313	0.374954
$460$	6.77838	0.316043
$461$	6.12394	0.285220	0.142610	−	0.989779i	$-0.454450\pi$
$461$	6.12394	0.285220	0.142610	+	0.989779i	$0.454450\pi$
$462$	0.0510795	0.00237643
$463$	−29.7973	−1.38480	−0.692398	−	0.721516i	$-0.743446\pi$
$463$	−29.7973	−1.38480	−0.692398	+	0.721516i	$0.743446\pi$
$464$	1.20815	0.0560869
$465$	−8.44011	−0.391401
$466$	−12.2650	−0.568165
$467$	−15.6821	−0.725680	−0.362840	−	0.931851i	$-0.618193\pi$
$467$	−15.6821	−0.725680	−0.362840	+	0.931851i	$0.618193\pi$
$468$	5.38021	0.248700
$469$	−0.0412297	−0.00190381
$470$	0.584904	0.0269796
$471$	10.4824	0.483006
$472$	−22.0710	−1.01590
$473$	−12.0702	−0.554989
$474$	14.0963	0.647463
$475$	−6.83775	−0.313738
$476$	0.329399	0.0150980
$477$	5.09145	0.233122
$478$	−7.93329	−0.362860
$479$	1.30973	0.0598433	0.0299217	−	0.999552i	$-0.490474\pi$
$479$	1.30973	0.0598433	0.0299217	+	0.999552i	$0.490474\pi$
$480$	5.21091	0.237845
$481$	9.07621	0.413840
$482$	6.29031	0.286516
$483$	0.245797	0.0111841
$484$	9.70507	0.441139
$485$	2.63073	0.119455
$486$	0.967785	0.0438996
$487$	12.9191	0.585421	0.292711	−	0.956201i	$-0.405443\pi$
$487$	12.9191	0.585421	0.292711	+	0.956201i	$0.405443\pi$
$488$	−0.329383	−0.0149105
$489$	12.4915	0.564886
$490$	6.77306	0.305976
$491$	30.6236	1.38202	0.691011	−	0.722844i	$-0.257166\pi$
$491$	30.6236	1.38202	0.691011	+	0.722844i	$0.257166\pi$
$492$	4.96354	0.223774
$493$	13.0725	0.588756
$494$	−33.4810	−1.50638
$495$	1.36875	0.0615208
$496$	−6.26606	−0.281354
$497$	−0.0259815	−0.00116543
$498$	−3.57077	−0.160010
$499$	−16.5227	−0.739658	−0.369829	−	0.929100i	$-0.620584\pi$
$499$	−16.5227	−0.739658	−0.369829	+	0.929100i	$0.620584\pi$
$500$	−1.06339	−0.0475563
$501$	−10.5628	−0.471909
$502$	−10.4376	−0.465854
$503$	18.1210	0.807973	0.403987	−	0.914765i	$-0.367624\pi$
$503$	18.1210	0.807973	0.403987	+	0.914765i	$0.367624\pi$
$504$	0.114321	0.00509225
$505$	17.6585	0.785793
$506$	8.44375	0.375371
$507$	−12.5984	−0.559513
$508$	−3.08110	−0.136702
$509$	22.2253	0.985121	0.492560	−	0.870278i	$-0.336061\pi$
$509$	22.2253	0.985121	0.492560	+	0.870278i	$0.336061\pi$
$510$	−7.77435	−0.344254
$511$	0.293463	0.0129820
$512$	8.27074	0.365518
$513$	6.83775	0.301894
$514$	−21.4369	−0.945541
$515$	14.4359	0.636120
$516$	−9.37743	−0.412818
$517$	−0.827237	−0.0363818
$518$	0.0669454	0.00294141
$519$	−5.60816	−0.246171
$520$	−14.9999	−0.657788
$521$	−1.84094	−0.0806532	−0.0403266	−	0.999187i	$-0.512840\pi$
$521$	−1.84094	−0.0806532	−0.0403266	+	0.999187i	$0.512840\pi$
$522$	1.57490	0.0689314
$523$	−29.9741	−1.31068	−0.655338	−	0.755336i	$-0.727474\pi$
$523$	−29.9741	−1.31068	−0.655338	+	0.755336i	$0.727474\pi$
$524$	2.84237	0.124170
$525$	−0.0385606	−0.00168292
$526$	−11.3663	−0.495594
$527$	−67.8005	−2.95344
$528$	1.01618	0.0442236
$529$	17.6317	0.766595
$530$	−4.92743	−0.214034
$531$	−7.44460	−0.323068
$532$	0.280382	0.0121561
$533$	−23.6159	−1.02292
$534$	−0.392267	−0.0169751
$535$	−3.96813	−0.171557
$536$	−3.16992	−0.136920
$537$	22.5854	0.974632
$538$	0.110141	0.00474852
$539$	−9.57922	−0.412606
$540$	1.06339	0.0457611
$541$	9.71029	0.417478	0.208739	−	0.977971i	$-0.433064\pi$
$541$	9.71029	0.417478	0.208739	+	0.977971i	$0.433064\pi$
$542$	14.5214	0.623747
$543$	12.4724	0.535241
$544$	41.8599	1.79473
$545$	5.31476	0.227659
$546$	−0.188812	−0.00808039
$547$	3.08610	0.131952	0.0659761	−	0.997821i	$-0.478984\pi$
$547$	3.08610	0.131952	0.0659761	+	0.997821i	$0.478984\pi$
$548$	−1.35731	−0.0579816
$549$	−0.111101	−0.00474169
$550$	−1.32466	−0.0564835
$551$	11.1272	0.474036
$552$	18.8979	0.804349
$553$	0.561654	0.0238839
$554$	−25.6042	−1.08782
$555$	1.79390	0.0761468
$556$	−7.90719	−0.335339
$557$	−38.9505	−1.65039	−0.825193	−	0.564851i	$-0.808933\pi$
$557$	−38.9505	−1.65039	−0.825193	+	0.564851i	$0.808933\pi$
$558$	−8.16821	−0.345788
$559$	44.6166	1.88708
$560$	−0.0286279	−0.00120975
$561$	10.9954	0.464224
$562$	10.7642	0.454060
$563$	12.6720	0.534062	0.267031	−	0.963688i	$-0.413957\pi$
$563$	12.6720	0.534062	0.267031	+	0.963688i	$0.413957\pi$
$564$	−0.642686	−0.0270620
$565$	−11.8829	−0.499918
$566$	−2.36363	−0.0993509
$567$	0.0385606	0.00161939
$568$	−1.99757	−0.0838161
$569$	39.1171	1.63988	0.819938	−	0.572452i	$-0.194008\pi$
$569$	39.1171	1.63988	0.819938	+	0.572452i	$0.194008\pi$
$570$	−6.61748	−0.277176
$571$	28.5486	1.19472	0.597361	−	0.801973i	$-0.296216\pi$
$571$	28.5486	1.19472	0.597361	+	0.801973i	$0.296216\pi$
$572$	7.36417	0.307911
$573$	−7.73996	−0.323342
$574$	−0.174189	−0.00727051
$575$	−6.37430	−0.265827
$576$	6.52787	0.271995
$577$	−12.6803	−0.527889	−0.263945	−	0.964538i	$-0.585024\pi$
$577$	−12.6803	−0.527889	−0.263945	+	0.964538i	$0.585024\pi$
$578$	−46.0000	−1.91335
$579$	18.1909	0.755989
$580$	1.73048	0.0718543
$581$	−0.142274	−0.00590254
$582$	2.54598	0.105534
$583$	6.96893	0.288623
$584$	22.5627	0.933652
$585$	−5.05948	−0.209184
$586$	−17.0940	−0.706145
$587$	−28.5197	−1.17713	−0.588567	−	0.808448i	$-0.700308\pi$
$587$	−28.5197	−1.17713	−0.588567	+	0.808448i	$0.700308\pi$
$588$	−7.44216	−0.306910
$589$	−57.7114	−2.37796
$590$	7.20477	0.296616
$591$	−8.92935	−0.367305
$592$	1.33182	0.0547374
$593$	34.5371	1.41827	0.709135	−	0.705072i	$-0.249086\pi$
$593$	34.5371	1.41827	0.709135	+	0.705072i	$0.249086\pi$
$594$	1.32466	0.0543513
$595$	−0.309762	−0.0126990
$596$	12.6952	0.520014
$597$	−17.1379	−0.701407
$598$	−31.2117	−1.27634
$599$	−5.69013	−0.232493	−0.116246	−	0.993220i	$-0.537086\pi$
$599$	−5.69013	−0.232493	−0.116246	+	0.993220i	$0.537086\pi$
$600$	−2.96471	−0.121034
$601$	8.39230	0.342329	0.171165	−	0.985242i	$-0.445247\pi$
$601$	8.39230	0.342329	0.171165	+	0.985242i	$0.445247\pi$
$602$	0.329089	0.0134127
$603$	−1.06922	−0.0435420
$604$	10.7290	0.436558
$605$	−9.12652	−0.371046
$606$	17.0896	0.694219
$607$	−27.6619	−1.12276	−0.561381	−	0.827557i	$-0.689730\pi$
$607$	−27.6619	−1.12276	−0.561381	+	0.827557i	$0.689730\pi$
$608$	35.6309	1.44503
$609$	0.0627505	0.00254278
$610$	0.107522	0.00435345
$611$	3.05782	0.123706
$612$	8.54237	0.345305
$613$	39.0903	1.57884	0.789421	−	0.613853i	$-0.210381\pi$
$613$	39.0903	1.57884	0.789421	+	0.613853i	$0.210381\pi$
$614$	23.1258	0.933280
$615$	−4.66765	−0.188218
$616$	0.156477	0.00630462
$617$	−10.4255	−0.419714	−0.209857	−	0.977732i	$-0.567300\pi$
$617$	−10.4255	−0.419714	−0.209857	+	0.977732i	$0.567300\pi$
$618$	13.9708	0.561988
$619$	20.5403	0.825584	0.412792	−	0.910825i	$-0.364554\pi$
$619$	20.5403	0.825584	0.412792	+	0.910825i	$0.364554\pi$
$620$	−8.97514	−0.360450
$621$	6.37430	0.255792
$622$	4.69258	0.188155
$623$	−0.0156296	−0.000626185 0
$624$	−3.75623	−0.150370
$625$	1.00000	0.0400000
$626$	−5.39000	−0.215428
$627$	9.35918	0.373770
$628$	11.1469	0.444812
$629$	14.4106	0.574590
$630$	−0.0373184	−0.00148680
$631$	19.1135	0.760895	0.380447	−	0.924803i	$-0.375770\pi$
$631$	19.1135	0.760895	0.380447	+	0.924803i	$0.375770\pi$
$632$	43.1824	1.71770
$633$	−12.5548	−0.499009
$634$	−21.0362	−0.835455
$635$	2.89743	0.114981
$636$	5.41421	0.214687
$637$	35.4089	1.40295
$638$	2.15564	0.0853427
$639$	−0.673783	−0.0266545
$640$	4.10425	0.162235
$641$	13.3984	0.529204	0.264602	−	0.964358i	$-0.414759\pi$
$641$	13.3984	0.529204	0.264602	+	0.964358i	$0.414759\pi$
$642$	−3.84030	−0.151565
$643$	21.2359	0.837462	0.418731	−	0.908110i	$-0.362475\pi$
$643$	21.2359	0.837462	0.418731	+	0.908110i	$0.362475\pi$
$644$	0.261378	0.0102997
$645$	8.81842	0.347225
$646$	−53.1591	−2.09152
$647$	−12.1837	−0.478990	−0.239495	−	0.970898i	$-0.576982\pi$
$647$	−12.1837	−0.478990	−0.239495	+	0.970898i	$0.576982\pi$
$648$	2.96471	0.116465
$649$	−10.1898	−0.399985
$650$	4.89649	0.192056
$651$	−0.325455	−0.0127556
$652$	13.2834	0.520217
$653$	−3.21977	−0.125999	−0.0629996	−	0.998014i	$-0.520067\pi$
$653$	−3.21977	−0.125999	−0.0629996	+	0.998014i	$0.520067\pi$
$654$	5.14355	0.201129
$655$	−2.67293	−0.104440
$656$	−3.46533	−0.135298
$657$	7.61044	0.296912
$658$	0.0225542	0.000879255 0
$659$	−22.0734	−0.859857	−0.429929	−	0.902863i	$-0.641461\pi$
$659$	−22.0734	−0.859857	−0.429929	+	0.902863i	$0.641461\pi$
$660$	1.45552	0.0566560
$661$	34.1496	1.32827	0.664134	−	0.747614i	$-0.268801\pi$
$661$	34.1496	1.32827	0.664134	+	0.747614i	$0.268801\pi$
$662$	−1.18546	−0.0460743
$663$	−40.6435	−1.57846
$664$	−10.9387	−0.424503
$665$	−0.263668	−0.0102246
$666$	1.73611	0.0672729
$667$	10.3730	0.401646
$668$	−11.2324	−0.434593
$669$	−14.4042	−0.556900
$670$	1.03477	0.0399768
$671$	−0.152070	−0.00587060
$672$	0.200936	0.00775127
$673$	−1.20779	−0.0465568	−0.0232784	−	0.999729i	$-0.507410\pi$
$673$	−1.20779	−0.0465568	−0.0232784	+	0.999729i	$0.507410\pi$
$674$	8.71249	0.335593
$675$	−1.00000	−0.0384900
$676$	−13.3970	−0.515269
$677$	36.9838	1.42140	0.710701	−	0.703494i	$-0.248378\pi$
$677$	36.9838	1.42140	0.710701	+	0.703494i	$0.248378\pi$
$678$	−11.5001	−0.441659
$679$	0.101442	0.00389300
$680$	−23.8159	−0.913297
$681$	14.6402	0.561014
$682$	−11.1802	−0.428114
$683$	−42.1436	−1.61258	−0.806291	−	0.591520i	$-0.798528\pi$
$683$	−42.1436	−1.61258	−0.806291	+	0.591520i	$0.798528\pi$
$684$	7.27121	0.278022
$685$	1.27640	0.0487688
$686$	0.522401	0.0199454
$687$	5.76676	0.220016
$688$	6.54692	0.249599
$689$	−25.7601	−0.981382
$690$	−6.16895	−0.234848
$691$	−44.7550	−1.70256	−0.851279	−	0.524713i	$-0.824173\pi$
$691$	−44.7550	−1.70256	−0.851279	+	0.524713i	$0.824173\pi$
$692$	−5.96367	−0.226705
$693$	0.0527798	0.00200494
$694$	−22.6750	−0.860730
$695$	7.43582	0.282057
$696$	4.82453	0.182873
$697$	−37.4958	−1.42026
$698$	−0.477340	−0.0180676
$699$	−12.6733	−0.479347
$700$	−0.0410050	−0.00154984
$701$	−4.44484	−0.167879	−0.0839397	−	0.996471i	$-0.526750\pi$
$701$	−4.44484	−0.167879	−0.0839397	+	0.996471i	$0.526750\pi$
$702$	−4.89649	−0.184806
$703$	12.2663	0.462630
$704$	8.93503	0.336752
$705$	0.604374	0.0227620
$706$	9.43389	0.355049
$707$	0.680922	0.0256087
$708$	−7.91653	−0.297521
$709$	21.6999	0.814956	0.407478	−	0.913215i	$-0.366408\pi$
$709$	21.6999	0.814956	0.407478	+	0.913215i	$0.366408\pi$
$710$	0.652078	0.0244720
$711$	14.5655	0.546249
$712$	−1.20167	−0.0450344
$713$	−53.7998	−2.01482
$714$	−0.299783	−0.0112191
$715$	−6.92517	−0.258987
$716$	24.0171	0.897562
$717$	−8.19736	−0.306136
$718$	−36.1722	−1.34993
$719$	−25.0275	−0.933367	−0.466683	−	0.884424i	$-0.654551\pi$
$719$	−25.0275	−0.933367	−0.466683	+	0.884424i	$0.654551\pi$
$720$	−0.742415	−0.0276682
$721$	0.556655	0.0207309
$722$	−26.8608	−0.999654
$723$	6.49970	0.241726
$724$	13.2630	0.492916
$725$	−1.62732	−0.0604372
$726$	−8.83251	−0.327805
$727$	−26.7346	−0.991532	−0.495766	−	0.868456i	$-0.665113\pi$
$727$	−26.7346	−0.991532	−0.495766	+	0.868456i	$0.665113\pi$
$728$	−0.578404	−0.0214371
$729$	1.00000	0.0370370
$730$	−7.36527	−0.272601
$731$	70.8395	2.62009
$732$	−0.118144	−0.00436674
$733$	50.8026	1.87644	0.938218	−	0.346046i	$-0.112476\pi$
$733$	50.8026	1.87644	0.938218	+	0.346046i	$0.112476\pi$
$734$	0.429862	0.0158665
$735$	6.99851	0.258144
$736$	33.2159	1.22435
$737$	−1.46349	−0.0539085
$738$	−4.51728	−0.166283
$739$	−28.6235	−1.05293	−0.526466	−	0.850196i	$-0.676483\pi$
$739$	−28.6235	−1.05293	−0.526466	+	0.850196i	$0.676483\pi$
$740$	1.90762	0.0701255
$741$	−34.5955	−1.27090
$742$	−0.190005	−0.00697529
$743$	5.66029	0.207656	0.103828	−	0.994595i	$-0.466891\pi$
$743$	5.66029	0.207656	0.103828	+	0.994595i	$0.466891\pi$
$744$	−25.0224	−0.917367
$745$	−11.9384	−0.437388
$746$	35.9865	1.31756
$747$	−3.68963	−0.134997
$748$	11.6924	0.427515
$749$	−0.153013	−0.00559099
$750$	0.967785	0.0353385
$751$	−35.5275	−1.29642	−0.648209	−	0.761463i	$-0.724482\pi$
$751$	−35.5275	−1.29642	−0.648209	+	0.761463i	$0.724482\pi$
$752$	0.448696	0.0163623
$753$	−10.7851	−0.393030
$754$	−7.96817	−0.290184
$755$	−10.0894	−0.367192
$756$	0.0410050	0.00149134
$757$	−23.2492	−0.845005	−0.422503	−	0.906362i	$-0.638848\pi$
$757$	−23.2492	−0.845005	−0.422503	+	0.906362i	$0.638848\pi$
$758$	19.3221	0.701811
$759$	8.72482	0.316691
$760$	−20.2719	−0.735340
$761$	25.7294	0.932690	0.466345	−	0.884603i	$-0.345571\pi$
$761$	25.7294	0.932690	0.466345	+	0.884603i	$0.345571\pi$
$762$	2.80409	0.101581
$763$	0.204940	0.00741934
$764$	−8.23061	−0.297773
$765$	−8.03313	−0.290438
$766$	−11.8635	−0.428646
$767$	37.6658	1.36003
$768$	17.0278	0.614437
$769$	19.8048	0.714180	0.357090	−	0.934070i	$-0.383769\pi$
$769$	19.8048	0.714180	0.357090	+	0.934070i	$0.383769\pi$
$770$	−0.0510795	−0.00184078
$771$	−22.1505	−0.797730
$772$	19.3441	0.696209
$773$	−36.5886	−1.31600	−0.658000	−	0.753018i	$-0.728597\pi$
$773$	−36.5886	−1.31600	−0.658000	+	0.753018i	$0.728597\pi$
$774$	8.53433	0.306760
$775$	8.44011	0.303178
$776$	7.79933	0.279980
$777$	0.0691738	0.00248160
$778$	−9.54829	−0.342323
$779$	−31.9162	−1.14352
$780$	−5.38021	−0.192642
$781$	−0.922241	−0.0330004
$782$	−49.5560	−1.77212
$783$	1.62732	0.0581558
$784$	5.19580	0.185564
$785$	−10.4824	−0.374135
$786$	−2.58682	−0.0922689
$787$	20.5456	0.732372	0.366186	−	0.930542i	$-0.380663\pi$
$787$	20.5456	0.732372	0.366186	+	0.930542i	$0.380663\pi$
$788$	−9.49540	−0.338260
$789$	−11.7446	−0.418120
$790$	−14.0963	−0.501523
$791$	−0.458212	−0.0162922
$792$	4.05794	0.144193
$793$	0.562116	0.0199613
$794$	9.06444	0.321685
$795$	−5.09145	−0.180575
$796$	−18.2243	−0.645943
$797$	8.49036	0.300744	0.150372	−	0.988629i	$-0.451953\pi$
$797$	8.49036	0.300744	0.150372	+	0.988629i	$0.451953\pi$
$798$	−0.255174	−0.00903305
$799$	4.85501	0.171758
$800$	−5.21091	−0.184234
$801$	−0.405325	−0.0143215
$802$	0.967785	0.0341737
$803$	10.4168	0.367601
$804$	−1.13700	−0.0400989
$805$	−0.245797	−0.00866319
$806$	41.3269	1.45568
$807$	0.113807	0.00400621
$808$	52.3522	1.84175
$809$	14.8207	0.521067	0.260533	−	0.965465i	$-0.416102\pi$
$809$	14.8207	0.521067	0.260533	+	0.965465i	$0.416102\pi$
$810$	−0.967785	−0.0340045
$811$	39.4537	1.38541	0.692703	−	0.721223i	$-0.256420\pi$
$811$	39.4537	1.38541	0.692703	+	0.721223i	$0.256420\pi$
$812$	0.0667284	0.00234171
$813$	15.0048	0.526240
$814$	2.37630	0.0832893
$815$	−12.4915	−0.437559
$816$	−5.96391	−0.208779
$817$	60.2982	2.10957
$818$	24.4172	0.853729
$819$	−0.195097	−0.00681723
$820$	−4.96354	−0.173334
$821$	22.8723	0.798247	0.399124	−	0.916897i	$-0.369314\pi$
$821$	22.8723	0.798247	0.399124	+	0.916897i	$0.369314\pi$
$822$	1.23528	0.0430854
$823$	16.5273	0.576104	0.288052	−	0.957615i	$-0.406992\pi$
$823$	16.5273	0.576104	0.288052	+	0.957615i	$0.406992\pi$
$824$	42.7981	1.49094
$825$	−1.36875	−0.0476538
$826$	0.277820	0.00966660
$827$	−2.90100	−0.100878	−0.0504388	−	0.998727i	$-0.516062\pi$
$827$	−2.90100	−0.100878	−0.0504388	+	0.998727i	$0.516062\pi$
$828$	6.77838	0.235565
$829$	−55.5957	−1.93092	−0.965460	−	0.260552i	$-0.916095\pi$
$829$	−55.5957	−1.93092	−0.965460	+	0.260552i	$0.916095\pi$
$830$	3.57077	0.123943
$831$	−26.4564	−0.917764
$832$	−33.0277	−1.14503
$833$	56.2200	1.94791
$834$	7.19627	0.249187
$835$	10.5628	0.365539
$836$	9.95247	0.344213
$837$	−8.44011	−0.291733
$838$	7.56831	0.261443
$839$	−32.6375	−1.12677	−0.563386	−	0.826194i	$-0.690501\pi$
$839$	−32.6375	−1.12677	−0.563386	+	0.826194i	$0.690501\pi$
$840$	−0.114321	−0.00394444
$841$	−26.3518	−0.908683
$842$	−34.4059	−1.18571
$843$	11.1225	0.383079
$844$	−13.3507	−0.459550
$845$	12.5984	0.433397
$846$	0.584904	0.0201094
$847$	−0.351924	−0.0120922
$848$	−3.77997	−0.129805
$849$	−2.44231	−0.0838199
$850$	7.77435	0.266658
$851$	11.4349	0.391982
$852$	−0.716496	−0.0245467
$853$	−18.7331	−0.641410	−0.320705	−	0.947179i	$-0.603920\pi$
$853$	−18.7331	−0.641410	−0.320705	+	0.947179i	$0.603920\pi$
$854$	0.00414612	0.000141877 0
$855$	−6.83775	−0.233846
$856$	−11.7643	−0.402097
$857$	8.10761	0.276951	0.138475	−	0.990366i	$-0.455780\pi$
$857$	8.10761	0.276951	0.138475	+	0.990366i	$0.455780\pi$
$858$	−6.70208	−0.228805
$859$	3.92528	0.133929	0.0669644	−	0.997755i	$-0.478669\pi$
$859$	3.92528	0.133929	0.0669644	+	0.997755i	$0.478669\pi$
$860$	9.37743	0.319768
$861$	−0.179987	−0.00613395
$862$	−36.0012	−1.22621
$863$	45.3277	1.54297	0.771486	−	0.636246i	$-0.219514\pi$
$863$	45.3277	1.54297	0.771486	+	0.636246i	$0.219514\pi$
$864$	5.21091	0.177279
$865$	5.60816	0.190683
$866$	12.4396	0.422714
$867$	−47.5312	−1.61424
$868$	−0.346087	−0.0117469
$869$	19.9365	0.676300
$870$	−1.57490	−0.0533941
$871$	5.40970	0.183301
$872$	15.7567	0.533589
$873$	2.63073	0.0890366
$874$	−42.1818	−1.42682
$875$	0.0385606	0.00130359
$876$	8.09288	0.273433
$877$	−5.95092	−0.200948	−0.100474	−	0.994940i	$-0.532036\pi$
$877$	−5.95092	−0.200948	−0.100474	+	0.994940i	$0.532036\pi$
$878$	19.0070	0.641456
$879$	−17.6630	−0.595757
$880$	−1.01618	−0.0342554
$881$	23.3372	0.786251	0.393126	−	0.919485i	$-0.371394\pi$
$881$	23.3372	0.786251	0.393126	+	0.919485i	$0.371394\pi$
$882$	6.77306	0.228061
$883$	−54.8408	−1.84554	−0.922770	−	0.385352i	$-0.874080\pi$
$883$	−54.8408	−1.84554	−0.922770	+	0.385352i	$0.874080\pi$
$884$	−43.2200	−1.45364
$885$	7.44460	0.250248
$886$	−9.39393	−0.315595
$887$	35.2924	1.18500	0.592502	−	0.805569i	$-0.298140\pi$
$887$	35.2924	1.18500	0.592502	+	0.805569i	$0.298140\pi$
$888$	5.31839	0.178473
$889$	0.111726	0.00374718
$890$	0.392267	0.0131488
$891$	1.36875	0.0458549
$892$	−15.3173	−0.512862
$893$	4.13256	0.138291
$894$	−11.5538	−0.386416
$895$	−22.5854	−0.754947
$896$	0.158262	0.00528716
$897$	−32.2506	−1.07682
$898$	6.38243	0.212984
$899$	−13.7348	−0.458081
$900$	−1.06339	−0.0354464
$901$	−40.9003	−1.36259
$902$	−6.18303	−0.205872
$903$	0.340043	0.0113159
$904$	−35.2294	−1.17171
$905$	−12.4724	−0.414596
$906$	−9.76440	−0.324401
$907$	−40.4879	−1.34438	−0.672189	−	0.740379i	$-0.734646\pi$
$907$	−40.4879	−1.34438	−0.672189	+	0.740379i	$0.734646\pi$
$908$	15.5683	0.516651
$909$	17.6585	0.585695
$910$	0.188812	0.00625904
$911$	−54.5565	−1.80754	−0.903768	−	0.428022i	$-0.859211\pi$
$911$	−54.5565	−1.80754	−0.903768	+	0.428022i	$0.859211\pi$
$912$	−5.07645	−0.168098
$913$	−5.05019	−0.167137
$914$	−7.37143	−0.243825
$915$	0.111101	0.00367290
$916$	6.13232	0.202618
$917$	−0.103070	−0.00340366
$918$	−7.77435	−0.256592
$919$	16.7567	0.552751	0.276376	−	0.961050i	$-0.410867\pi$
$919$	16.7567	0.552751	0.276376	+	0.961050i	$0.410867\pi$
$920$	−18.8979	−0.623046
$921$	23.8955	0.787385
$922$	−5.92666	−0.195184
$923$	3.40899	0.112208
$924$	0.0561256	0.00184640
$925$	−1.79390	−0.0589831
$926$	28.8373	0.947654
$927$	14.4359	0.474136
$928$	8.47984	0.278364
$929$	31.2342	1.02476	0.512381	−	0.858758i	$-0.328764\pi$
$929$	31.2342	1.02476	0.512381	+	0.858758i	$0.328764\pi$
$930$	8.16821	0.267846
$931$	47.8541	1.56836
$932$	−13.4766	−0.441442
$933$	4.84878	0.158742
$934$	15.1769	0.496603
$935$	−10.9954	−0.359586
$936$	−14.9999	−0.490286
$937$	43.6996	1.42760	0.713802	−	0.700348i	$-0.246972\pi$
$937$	43.6996	1.42760	0.713802	+	0.700348i	$0.246972\pi$
$938$	0.0399015	0.00130283
$939$	−5.56942	−0.181751
$940$	0.642686	0.0209621
$941$	29.5721	0.964023	0.482012	−	0.876165i	$-0.339906\pi$
$941$	29.5721	0.964023	0.482012	+	0.876165i	$0.339906\pi$
$942$	−10.1448	−0.330534
$943$	−29.7530	−0.968890
$944$	5.52698	0.179888
$945$	−0.0385606	−0.00125438
$946$	11.6814	0.379794
$947$	−7.56250	−0.245748	−0.122874	−	0.992422i	$-0.539211\pi$
$947$	−7.56250	−0.245748	−0.122874	+	0.992422i	$0.539211\pi$
$948$	15.4888	0.503054
$949$	−38.5049	−1.24992
$950$	6.61748	0.214699
$951$	−21.7365	−0.704853
$952$	−0.918354	−0.0297640
$953$	−46.1077	−1.49358	−0.746788	−	0.665062i	$-0.768405\pi$
$953$	−46.1077	−1.49358	−0.746788	+	0.665062i	$0.768405\pi$
$954$	−4.92743	−0.159532
$955$	7.73996	0.250459
$956$	−8.71701	−0.281928
$957$	2.22740	0.0720016
$958$	−1.26754	−0.0409524
$959$	0.0492187	0.00158936
$960$	−6.52787	−0.210686
$961$	40.2354	1.29792
$962$	−8.78382	−0.283202
$963$	−3.96813	−0.127871
$964$	6.91173	0.222612
$965$	−18.1909	−0.585587
$966$	−0.237878	−0.00765361
$967$	−29.4897	−0.948324	−0.474162	−	0.880438i	$-0.657249\pi$
$967$	−29.4897	−0.948324	−0.474162	+	0.880438i	$0.657249\pi$
$968$	−27.0574	−0.869659
$969$	−54.9286	−1.76456
$970$	−2.54598	−0.0817464
$971$	26.3693	0.846231	0.423116	−	0.906076i	$-0.360936\pi$
$971$	26.3693	0.846231	0.423116	+	0.906076i	$0.360936\pi$
$972$	1.06339	0.0341083
$973$	0.286729	0.00919212
$974$	−12.5029	−0.400620
$975$	5.05948	0.162033
$976$	0.0824833	0.00264023
$977$	−53.4257	−1.70924	−0.854619	−	0.519255i	$-0.826209\pi$
$977$	−53.4257	−1.70924	−0.854619	+	0.519255i	$0.826209\pi$
$978$	−12.0891	−0.386567
$979$	−0.554789	−0.0177311
$980$	7.44216	0.237731
$981$	5.31476	0.169687
$982$	−29.6370	−0.945755
$983$	−25.3433	−0.808325	−0.404162	−	0.914687i	$-0.632437\pi$
$983$	−25.3433	−0.808325	−0.404162	+	0.914687i	$0.632437\pi$
$984$	−13.8382	−0.441146
$985$	8.92935	0.284513
$986$	−12.6514	−0.402902
$987$	0.0233050	0.000741806 0
$988$	−36.7886	−1.17040
$989$	56.2112	1.78741
$990$	−1.32466	−0.0421003
$991$	−30.0966	−0.956050	−0.478025	−	0.878346i	$-0.658647\pi$
$991$	−30.0966	−0.956050	−0.478025	+	0.878346i	$0.658647\pi$
$992$	−43.9807	−1.39639
$993$	−1.22492	−0.0388717
$994$	0.0251445	0.000797535 0
$995$	17.1379	0.543307
$996$	−3.92353	−0.124322
$997$	58.6677	1.85803	0.929013	−	0.370048i	$-0.120659\pi$
$997$	58.6677	1.85803	0.929013	+	0.370048i	$0.120659\pi$
$998$	15.9904	0.506169
$999$	1.79390	0.0567565

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.g.1.12	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.g.1.12	✓	36	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.967785 q^{2} -1.00000 q^{3} -1.06339 q^{4} +1.00000 q^{5} +0.967785 q^{6} +0.0385606 q^{7} +2.96471 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.967785 q^{2} -1.00000 q^{3} -1.06339 q^{4} +1.00000 q^{5} +0.967785 q^{6} +0.0385606 q^{7} +2.96471 q^{8} +1.00000 q^{9} -0.967785 q^{10} +1.36875 q^{11} +1.06339 q^{12} -5.05948 q^{13} -0.0373184 q^{14} -1.00000 q^{15} -0.742415 q^{16} -8.03313 q^{17} -0.967785 q^{18} -6.83775 q^{19} -1.06339 q^{20} -0.0385606 q^{21} -1.32466 q^{22} -6.37430 q^{23} -2.96471 q^{24} +1.00000 q^{25} +4.89649 q^{26} -1.00000 q^{27} -0.0410050 q^{28} -1.62732 q^{29} +0.967785 q^{30} +8.44011 q^{31} -5.21091 q^{32} -1.36875 q^{33} +7.77435 q^{34} +0.0385606 q^{35} -1.06339 q^{36} -1.79390 q^{37} +6.61748 q^{38} +5.05948 q^{39} +2.96471 q^{40} +4.66765 q^{41} +0.0373184 q^{42} -8.81842 q^{43} -1.45552 q^{44} +1.00000 q^{45} +6.16895 q^{46} -0.604374 q^{47} +0.742415 q^{48} -6.99851 q^{49} -0.967785 q^{50} +8.03313 q^{51} +5.38021 q^{52} +5.09145 q^{53} +0.967785 q^{54} +1.36875 q^{55} +0.114321 q^{56} +6.83775 q^{57} +1.57490 q^{58} -7.44460 q^{59} +1.06339 q^{60} -0.111101 q^{61} -8.16821 q^{62} +0.0385606 q^{63} +6.52787 q^{64} -5.05948 q^{65} +1.32466 q^{66} -1.06922 q^{67} +8.54237 q^{68} +6.37430 q^{69} -0.0373184 q^{70} -0.673783 q^{71} +2.96471 q^{72} +7.61044 q^{73} +1.73611 q^{74} -1.00000 q^{75} +7.27121 q^{76} +0.0527798 q^{77} -4.89649 q^{78} +14.5655 q^{79} -0.742415 q^{80} +1.00000 q^{81} -4.51728 q^{82} -3.68963 q^{83} +0.0410050 q^{84} -8.03313 q^{85} +8.53433 q^{86} +1.62732 q^{87} +4.05794 q^{88} -0.405325 q^{89} -0.967785 q^{90} -0.195097 q^{91} +6.77838 q^{92} -8.44011 q^{93} +0.584904 q^{94} -6.83775 q^{95} +5.21091 q^{96} +2.63073 q^{97} +6.77306 q^{98} +1.36875 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9}+O(q^{10}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9	\( 36 q - 36 q^{3} + 36 q^{4} + 36 q^{5} - 4 q^{7} - 3 q^{8} + 36 q^{9} + 15 q^{11} - 36 q^{12} + 8 q^{13} + 10 q^{14} - 36 q^{15} + 36 q^{16} + 32 q^{17} + 5 q^{19} + 36 q^{20} + 4 q^{21} + q^{22} - 10 q^{23} + 3 q^{24} + 36 q^{25} + 22 q^{26} - 36 q^{27} + 61 q^{29} + 15 q^{31} - q^{32} - 15 q^{33} + 26 q^{34} - 4 q^{35} + 36 q^{36} + 16 q^{37} + 20 q^{38} - 8 q^{39} - 3 q^{40} + 61 q^{41} - 10 q^{42} - 35 q^{43} + 39 q^{44} + 36 q^{45} + 11 q^{46} - 28 q^{47} - 36 q^{48} + 68 q^{49} - 32 q^{51} + 4 q^{52} + 33 q^{53} + 15 q^{55} + 23 q^{56} - 5 q^{57} + 6 q^{58} + 35 q^{59} - 36 q^{60} + 55 q^{61} + q^{62} - 4 q^{63} + 15 q^{64} + 8 q^{65} - q^{66} - 34 q^{67} + 60 q^{68} + 10 q^{69} + 10 q^{70} + 42 q^{71} - 3 q^{72} + 53 q^{73} + 54 q^{74} - 36 q^{75} + 20 q^{76} + 20 q^{77} - 22 q^{78} + 25 q^{79} + 36 q^{80} + 36 q^{81} - 15 q^{82} - 11 q^{83} + 32 q^{85} + 53 q^{86} - 61 q^{87} + 27 q^{88} + 81 q^{89} + 15 q^{91} - 7 q^{92} - 15 q^{93} + 56 q^{94} + 5 q^{95} + q^{96} + 47 q^{97} - 3 q^{98} + 15 q^{99}+O(q^{100}) \) 36 * q - 36 * q^3 + 36 * q^4 + 36 * q^5 - 4 * q^7 - 3 * q^8 + 36 * q^9 + 15 * q^11 - 36 * q^12 + 8 * q^13 + 10 * q^14 - 36 * q^15 + 36 * q^16 + 32 * q^17 + 5 * q^19 + 36 * q^20 + 4 * q^21 + q^22 - 10 * q^23 + 3 * q^24 + 36 * q^25 + 22 * q^26 - 36 * q^27 + 61 * q^29 + 15 * q^31 - q^32 - 15 * q^33 + 26 * q^34 - 4 * q^35 + 36 * q^36 + 16 * q^37 + 20 * q^38 - 8 * q^39 - 3 * q^40 + 61 * q^41 - 10 * q^42 - 35 * q^43 + 39 * q^44 + 36 * q^45 + 11 * q^46 - 28 * q^47 - 36 * q^48 + 68 * q^49 - 32 * q^51 + 4 * q^52 + 33 * q^53 + 15 * q^55 + 23 * q^56 - 5 * q^57 + 6 * q^58 + 35 * q^59 - 36 * q^60 + 55 * q^61 + q^62 - 4 * q^63 + 15 * q^64 + 8 * q^65 - q^66 - 34 * q^67 + 60 * q^68 + 10 * q^69 + 10 * q^70 + 42 * q^71 - 3 * q^72 + 53 * q^73 + 54 * q^74 - 36 * q^75 + 20 * q^76 + 20 * q^77 - 22 * q^78 + 25 * q^79 + 36 * q^80 + 36 * q^81 - 15 * q^82 - 11 * q^83 + 32 * q^85 + 53 * q^86 - 61 * q^87 + 27 * q^88 + 81 * q^89 + 15 * q^91 - 7 * q^92 - 15 * q^93 + 56 * q^94 + 5 * q^95 + q^96 + 47 * q^97 - 3 * q^98 + 15 * q^99

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