LMFDB - Embedded newform 6014.2.a.k.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6014,2,Mod(1,6014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6014, 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("6014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6014 = 2 \cdot 31 \cdot 97 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6014.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:	$48.0220317756$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +0.242040 q^{3} +1.00000 q^{4} -4.38700 q^{5} +0.242040 q^{6} +3.95726 q^{7} +1.00000 q^{8} -2.94142 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +0.242040 q^{3} +1.00000 q^{4} -4.38700 q^{5} +0.242040 q^{6} +3.95726 q^{7} +1.00000 q^{8} -2.94142 q^{9} -4.38700 q^{10} -1.54975 q^{11} +0.242040 q^{12} +6.50581 q^{13} +3.95726 q^{14} -1.06183 q^{15} +1.00000 q^{16} -7.22807 q^{17} -2.94142 q^{18} -0.462811 q^{19} -4.38700 q^{20} +0.957815 q^{21} -1.54975 q^{22} +4.63265 q^{23} +0.242040 q^{24} +14.2458 q^{25} +6.50581 q^{26} -1.43806 q^{27} +3.95726 q^{28} -6.10344 q^{29} -1.06183 q^{30} +1.00000 q^{31} +1.00000 q^{32} -0.375101 q^{33} -7.22807 q^{34} -17.3605 q^{35} -2.94142 q^{36} -5.34859 q^{37} -0.462811 q^{38} +1.57467 q^{39} -4.38700 q^{40} +3.21458 q^{41} +0.957815 q^{42} +0.697805 q^{43} -1.54975 q^{44} +12.9040 q^{45} +4.63265 q^{46} +8.48120 q^{47} +0.242040 q^{48} +8.65991 q^{49} +14.2458 q^{50} -1.74948 q^{51} +6.50581 q^{52} -4.59473 q^{53} -1.43806 q^{54} +6.79876 q^{55} +3.95726 q^{56} -0.112019 q^{57} -6.10344 q^{58} +3.45887 q^{59} -1.06183 q^{60} +10.0104 q^{61} +1.00000 q^{62} -11.6400 q^{63} +1.00000 q^{64} -28.5410 q^{65} -0.375101 q^{66} +15.8002 q^{67} -7.22807 q^{68} +1.12129 q^{69} -17.3605 q^{70} -6.77749 q^{71} -2.94142 q^{72} -4.83570 q^{73} -5.34859 q^{74} +3.44806 q^{75} -0.462811 q^{76} -6.13276 q^{77} +1.57467 q^{78} -3.54838 q^{79} -4.38700 q^{80} +8.47618 q^{81} +3.21458 q^{82} -2.81607 q^{83} +0.957815 q^{84} +31.7096 q^{85} +0.697805 q^{86} -1.47728 q^{87} -1.54975 q^{88} -9.32741 q^{89} +12.9040 q^{90} +25.7452 q^{91} +4.63265 q^{92} +0.242040 q^{93} +8.48120 q^{94} +2.03036 q^{95} +0.242040 q^{96} +1.00000 q^{97} +8.65991 q^{98} +4.55846 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) $ 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	0.242040	0.139742	0.0698709	−	0.997556i	$-0.477741\pi$
$3$	0.242040	0.139742	0.0698709	+	0.997556i	$0.477741\pi$
$4$	1.00000	0.500000
$5$	−4.38700	−1.96193	−0.980964	−	0.194190i	$-0.937792\pi$
$5$	−4.38700	−1.96193	−0.980964	+	0.194190i	$0.937792\pi$
$6$	0.242040	0.0988124
$7$	3.95726	1.49570	0.747852	−	0.663866i	$-0.231085\pi$
$7$	3.95726	1.49570	0.747852	+	0.663866i	$0.231085\pi$
$8$	1.00000	0.353553
$9$	−2.94142	−0.980472
$10$	−4.38700	−1.38729
$11$	−1.54975	−0.467267	−0.233633	−	0.972325i	$-0.575062\pi$
$11$	−1.54975	−0.467267	−0.233633	+	0.972325i	$0.575062\pi$
$12$	0.242040	0.0698709
$13$	6.50581	1.80439	0.902194	−	0.431331i	$-0.141956\pi$
$13$	6.50581	1.80439	0.902194	+	0.431331i	$0.141956\pi$
$14$	3.95726	1.05762
$15$	−1.06183	−0.274164
$16$	1.00000	0.250000
$17$	−7.22807	−1.75306	−0.876532	−	0.481344i	$-0.840149\pi$
$17$	−7.22807	−1.75306	−0.876532	+	0.481344i	$0.840149\pi$
$18$	−2.94142	−0.693299
$19$	−0.462811	−0.106176	−0.0530881	−	0.998590i	$-0.516906\pi$
$19$	−0.462811	−0.106176	−0.0530881	+	0.998590i	$0.516906\pi$
$20$	−4.38700	−0.980964
$21$	0.957815	0.209012
$22$	−1.54975	−0.330408
$23$	4.63265	0.965975	0.482988	−	0.875627i	$-0.339552\pi$
$23$	4.63265	0.965975	0.482988	+	0.875627i	$0.339552\pi$
$24$	0.242040	0.0494062
$25$	14.2458	2.84916
$26$	6.50581	1.27589
$27$	−1.43806	−0.276755
$28$	3.95726	0.747852
$29$	−6.10344	−1.13338	−0.566690	−	0.823931i	$-0.691776\pi$
$29$	−6.10344	−1.13338	−0.566690	+	0.823931i	$0.691776\pi$
$30$	−1.06183	−0.193863
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	1.00000	0.176777
$33$	−0.375101	−0.0652968
$34$	−7.22807	−1.23960
$35$	−17.3605	−2.93446
$36$	−2.94142	−0.490236
$37$	−5.34859	−0.879303	−0.439651	−	0.898169i	$-0.644898\pi$
$37$	−5.34859	−0.879303	−0.439651	+	0.898169i	$0.644898\pi$
$38$	−0.462811	−0.0750779
$39$	1.57467	0.252149
$40$	−4.38700	−0.693646
$41$	3.21458	0.502032	0.251016	−	0.967983i	$-0.419235\pi$
$41$	3.21458	0.502032	0.251016	+	0.967983i	$0.419235\pi$
$42$	0.957815	0.147794
$43$	0.697805	0.106414	0.0532072	−	0.998583i	$-0.483056\pi$
$43$	0.697805	0.106414	0.0532072	+	0.998583i	$0.483056\pi$
$44$	−1.54975	−0.233633
$45$	12.9040	1.92362
$46$	4.63265	0.683048
$47$	8.48120	1.23711	0.618555	−	0.785742i	$-0.287718\pi$
$47$	8.48120	1.23711	0.618555	+	0.785742i	$0.287718\pi$
$48$	0.242040	0.0349355
$49$	8.65991	1.23713
$50$	14.2458	2.01466
$51$	−1.74948	−0.244976
$52$	6.50581	0.902194
$53$	−4.59473	−0.631135	−0.315567	−	0.948903i	$-0.602195\pi$
$53$	−4.59473	−0.631135	−0.315567	+	0.948903i	$0.602195\pi$
$54$	−1.43806	−0.195695
$55$	6.79876	0.916744
$56$	3.95726	0.528811
$57$	−0.112019	−0.0148373
$58$	−6.10344	−0.801421
$59$	3.45887	0.450307	0.225153	−	0.974323i	$-0.427712\pi$
$59$	3.45887	0.450307	0.225153	+	0.974323i	$0.427712\pi$
$60$	−1.06183	−0.137082
$61$	10.0104	1.28170	0.640848	−	0.767668i	$-0.278583\pi$
$61$	10.0104	1.28170	0.640848	+	0.767668i	$0.278583\pi$
$62$	1.00000	0.127000
$63$	−11.6400	−1.46650
$64$	1.00000	0.125000
$65$	−28.5410	−3.54008
$66$	−0.375101	−0.0461718
$67$	15.8002	1.93030	0.965152	−	0.261690i	$-0.0842798\pi$
$67$	15.8002	1.93030	0.965152	+	0.261690i	$0.0842798\pi$
$68$	−7.22807	−0.876532
$69$	1.12129	0.134987
$70$	−17.3605	−2.07498
$71$	−6.77749	−0.804340	−0.402170	−	0.915565i	$-0.631744\pi$
$71$	−6.77749	−0.804340	−0.402170	+	0.915565i	$0.631744\pi$
$72$	−2.94142	−0.346649
$73$	−4.83570	−0.565975	−0.282988	−	0.959124i	$-0.591326\pi$
$73$	−4.83570	−0.565975	−0.282988	+	0.959124i	$0.591326\pi$
$74$	−5.34859	−0.621761
$75$	3.44806	0.398147
$76$	−0.462811	−0.0530881
$77$	−6.13276	−0.698893
$78$	1.57467	0.178296
$79$	−3.54838	−0.399224	−0.199612	−	0.979875i	$-0.563968\pi$
$79$	−3.54838	−0.399224	−0.199612	+	0.979875i	$0.563968\pi$
$80$	−4.38700	−0.490482
$81$	8.47618	0.941798
$82$	3.21458	0.354990
$83$	−2.81607	−0.309104	−0.154552	−	0.987985i	$-0.549393\pi$
$83$	−2.81607	−0.309104	−0.154552	+	0.987985i	$0.549393\pi$
$84$	0.957815	0.104506
$85$	31.7096	3.43938
$86$	0.697805	0.0752463
$87$	−1.47728	−0.158381
$88$	−1.54975	−0.165204
$89$	−9.32741	−0.988704	−0.494352	−	0.869262i	$-0.664595\pi$
$89$	−9.32741	−0.988704	−0.494352	+	0.869262i	$0.664595\pi$
$90$	12.9040	1.36020
$91$	25.7452	2.69883
$92$	4.63265	0.482988
$93$	0.242040	0.0250984
$94$	8.48120	0.874769
$95$	2.03036	0.208310
$96$	0.242040	0.0247031
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	8.65991	0.874783
$99$	4.55846	0.458142
$100$	14.2458	1.42458
$101$	14.6711	1.45983	0.729913	−	0.683540i	$-0.239561\pi$
$101$	14.6711	1.45983	0.729913	+	0.683540i	$0.239561\pi$
$102$	−1.74948	−0.173225
$103$	−1.89207	−0.186431	−0.0932157	−	0.995646i	$-0.529715\pi$
$103$	−1.89207	−0.186431	−0.0932157	+	0.995646i	$0.529715\pi$
$104$	6.50581	0.637947
$105$	−4.20194	−0.410067
$106$	−4.59473	−0.446280
$107$	17.1423	1.65721	0.828605	−	0.559834i	$-0.189135\pi$
$107$	17.1423	1.65721	0.828605	+	0.559834i	$0.189135\pi$
$108$	−1.43806	−0.138377
$109$	2.85392	0.273356	0.136678	−	0.990616i	$-0.456357\pi$
$109$	2.85392	0.273356	0.136678	+	0.990616i	$0.456357\pi$
$110$	6.79876	0.648236
$111$	−1.29457	−0.122875
$112$	3.95726	0.373926
$113$	9.47268	0.891115	0.445557	−	0.895253i	$-0.353006\pi$
$113$	9.47268	0.891115	0.445557	+	0.895253i	$0.353006\pi$
$114$	−0.112019	−0.0104915
$115$	−20.3235	−1.89517
$116$	−6.10344	−0.566690
$117$	−19.1363	−1.76915
$118$	3.45887	0.318415
$119$	−28.6033	−2.62206
$120$	−1.06183	−0.0969314
$121$	−8.59828	−0.781662
$122$	10.0104	0.906296
$123$	0.778056	0.0701549
$124$	1.00000	0.0898027
$125$	−40.5614	−3.62792
$126$	−11.6400	−1.03697
$127$	16.5949	1.47256	0.736279	−	0.676678i	$-0.236581\pi$
$127$	16.5949	1.47256	0.736279	+	0.676678i	$0.236581\pi$
$128$	1.00000	0.0883883
$129$	0.168897	0.0148705
$130$	−28.5410	−2.50321
$131$	22.7008	1.98338	0.991689	−	0.128655i	$-0.0410659\pi$
$131$	22.7008	1.98338	0.991689	+	0.128655i	$0.0410659\pi$
$132$	−0.375101	−0.0326484
$133$	−1.83146	−0.158808
$134$	15.8002	1.36493
$135$	6.30878	0.542973
$136$	−7.22807	−0.619802
$137$	−4.17354	−0.356569	−0.178285	−	0.983979i	$-0.557055\pi$
$137$	−4.17354	−0.356569	−0.178285	+	0.983979i	$0.557055\pi$
$138$	1.12129	0.0954504
$139$	−14.9115	−1.26478	−0.632389	−	0.774651i	$-0.717926\pi$
$139$	−14.9115	−1.26478	−0.632389	+	0.774651i	$0.717926\pi$
$140$	−17.3605	−1.46723
$141$	2.05279	0.172876
$142$	−6.77749	−0.568755
$143$	−10.0824	−0.843131
$144$	−2.94142	−0.245118
$145$	26.7758	2.22361
$146$	−4.83570	−0.400205
$147$	2.09604	0.172879
$148$	−5.34859	−0.439651
$149$	19.1956	1.57257	0.786283	−	0.617867i	$-0.212003\pi$
$149$	19.1956	1.57257	0.786283	+	0.617867i	$0.212003\pi$
$150$	3.44806	0.281533
$151$	−8.82639	−0.718281	−0.359141	−	0.933284i	$-0.616930\pi$
$151$	−8.82639	−0.718281	−0.359141	+	0.933284i	$0.616930\pi$
$152$	−0.462811	−0.0375390
$153$	21.2608	1.71883
$154$	−6.13276	−0.494192
$155$	−4.38700	−0.352373
$156$	1.57467	0.126074
$157$	−4.65422	−0.371447	−0.185724	−	0.982602i	$-0.559463\pi$
$157$	−4.65422	−0.371447	−0.185724	+	0.982602i	$0.559463\pi$
$158$	−3.54838	−0.282294
$159$	−1.11211	−0.0881960
$160$	−4.38700	−0.346823
$161$	18.3326	1.44481
$162$	8.47618	0.665952
$163$	9.70690	0.760303	0.380151	−	0.924924i	$-0.375872\pi$
$163$	9.70690	0.760303	0.380151	+	0.924924i	$0.375872\pi$
$164$	3.21458	0.251016
$165$	1.64557	0.128108
$166$	−2.81607	−0.218569
$167$	10.1581	0.786056	0.393028	−	0.919527i	$-0.371428\pi$
$167$	10.1581	0.786056	0.393028	+	0.919527i	$0.371428\pi$
$168$	0.957815	0.0738971
$169$	29.3256	2.25582
$170$	31.7096	2.43201
$171$	1.36132	0.104103
$172$	0.697805	0.0532072
$173$	8.16970	0.621131	0.310565	−	0.950552i	$-0.399482\pi$
$173$	8.16970	0.621131	0.310565	+	0.950552i	$0.399482\pi$
$174$	−1.47728	−0.111992
$175$	56.3744	4.26150
$176$	−1.54975	−0.116817
$177$	0.837186	0.0629267
$178$	−9.32741	−0.699119
$179$	13.2670	0.991621	0.495810	−	0.868431i	$-0.334871\pi$
$179$	13.2670	0.991621	0.495810	+	0.868431i	$0.334871\pi$
$180$	12.9040	0.961808
$181$	19.0812	1.41829	0.709147	−	0.705061i	$-0.249080\pi$
$181$	19.0812	1.41829	0.709147	+	0.705061i	$0.249080\pi$
$182$	25.7452	1.90836
$183$	2.42291	0.179107
$184$	4.63265	0.341524
$185$	23.4643	1.72513
$186$	0.242040	0.0177472
$187$	11.2017	0.819149
$188$	8.48120	0.618555
$189$	−5.69078	−0.413943
$190$	2.03036	0.147297
$191$	−11.5892	−0.838568	−0.419284	−	0.907855i	$-0.637719\pi$
$191$	−11.5892	−0.838568	−0.419284	+	0.907855i	$0.637719\pi$
$192$	0.242040	0.0174677
$193$	−2.45769	−0.176909	−0.0884543	−	0.996080i	$-0.528193\pi$
$193$	−2.45769	−0.176909	−0.0884543	+	0.996080i	$0.528193\pi$
$194$	1.00000	0.0717958
$195$	−6.90807	−0.494697
$196$	8.65991	0.618565
$197$	6.20088	0.441794	0.220897	−	0.975297i	$-0.429101\pi$
$197$	6.20088	0.441794	0.220897	+	0.975297i	$0.429101\pi$
$198$	4.55846	0.323955
$199$	−18.6781	−1.32405	−0.662027	−	0.749480i	$-0.730304\pi$
$199$	−18.6781	−1.32405	−0.662027	+	0.749480i	$0.730304\pi$
$200$	14.2458	1.00733
$201$	3.82429	0.269744
$202$	14.6711	1.03225
$203$	−24.1529	−1.69520
$204$	−1.74948	−0.122488
$205$	−14.1024	−0.984951
$206$	−1.89207	−0.131827
$207$	−13.6266	−0.947112
$208$	6.50581	0.451097
$209$	0.717241	0.0496126
$210$	−4.20194	−0.289961
$211$	−13.4125	−0.923355	−0.461678	−	0.887048i	$-0.652752\pi$
$211$	−13.4125	−0.923355	−0.461678	+	0.887048i	$0.652752\pi$
$212$	−4.59473	−0.315567
$213$	−1.64042	−0.112400
$214$	17.1423	1.17182
$215$	−3.06128	−0.208777
$216$	−1.43806	−0.0978476
$217$	3.95726	0.268636
$218$	2.85392	0.193292
$219$	−1.17043	−0.0790905
$220$	6.79876	0.458372
$221$	−47.0245	−3.16321
$222$	−1.29457	−0.0868860
$223$	7.11831	0.476677	0.238339	−	0.971182i	$-0.423397\pi$
$223$	7.11831	0.476677	0.238339	+	0.971182i	$0.423397\pi$
$224$	3.95726	0.264406
$225$	−41.9028	−2.79352
$226$	9.47268	0.630113
$227$	10.2209	0.678388	0.339194	−	0.940716i	$-0.389846\pi$
$227$	10.2209	0.678388	0.339194	+	0.940716i	$0.389846\pi$
$228$	−0.112019	−0.00741863
$229$	22.2447	1.46997	0.734987	−	0.678081i	$-0.237188\pi$
$229$	22.2447	1.46997	0.734987	+	0.678081i	$0.237188\pi$
$230$	−20.3235	−1.34009
$231$	−1.48437	−0.0976646
$232$	−6.10344	−0.400711
$233$	14.0647	0.921408	0.460704	−	0.887554i	$-0.347597\pi$
$233$	14.0647	0.921408	0.460704	+	0.887554i	$0.347597\pi$
$234$	−19.1363	−1.25098
$235$	−37.2070	−2.42712
$236$	3.45887	0.225153
$237$	−0.858851	−0.0557884
$238$	−28.6033	−1.85408
$239$	−1.95645	−0.126553	−0.0632763	−	0.997996i	$-0.520155\pi$
$239$	−1.95645	−0.126553	−0.0632763	+	0.997996i	$0.520155\pi$
$240$	−1.06183	−0.0685409
$241$	16.0423	1.03337	0.516687	−	0.856174i	$-0.327165\pi$
$241$	16.0423	1.03337	0.516687	+	0.856174i	$0.327165\pi$
$242$	−8.59828	−0.552718
$243$	6.36576	0.408364
$244$	10.0104	0.640848
$245$	−37.9911	−2.42716
$246$	0.778056	0.0496070
$247$	−3.01096	−0.191583
$248$	1.00000	0.0635001
$249$	−0.681602	−0.0431947
$250$	−40.5614	−2.56533
$251$	3.44442	0.217410	0.108705	−	0.994074i	$-0.465330\pi$
$251$	3.44442	0.217410	0.108705	+	0.994074i	$0.465330\pi$
$252$	−11.6400	−0.733248
$253$	−7.17945	−0.451368
$254$	16.5949	1.04126
$255$	7.67498	0.480626
$256$	1.00000	0.0625000
$257$	19.8530	1.23840	0.619198	−	0.785235i	$-0.287458\pi$
$257$	19.8530	1.23840	0.619198	+	0.785235i	$0.287458\pi$
$258$	0.168897	0.0105151
$259$	−21.1658	−1.31518
$260$	−28.5410	−1.77004
$261$	17.9528	1.11125
$262$	22.7008	1.40246
$263$	−29.2864	−1.80588	−0.902939	−	0.429769i	$-0.858595\pi$
$263$	−29.2864	−1.80588	−0.902939	+	0.429769i	$0.858595\pi$
$264$	−0.375101	−0.0230859
$265$	20.1571	1.23824
$266$	−1.83146	−0.112294
$267$	−2.25761	−0.138163
$268$	15.8002	0.965152
$269$	−3.65686	−0.222963	−0.111481	−	0.993767i	$-0.535560\pi$
$269$	−3.65686	−0.222963	−0.111481	+	0.993767i	$0.535560\pi$
$270$	6.30878	0.383940
$271$	7.71252	0.468502	0.234251	−	0.972176i	$-0.424736\pi$
$271$	7.71252	0.468502	0.234251	+	0.972176i	$0.424736\pi$
$272$	−7.22807	−0.438266
$273$	6.23137	0.377140
$274$	−4.17354	−0.252133
$275$	−22.0774	−1.33132
$276$	1.12129	0.0674936
$277$	−16.3001	−0.979380	−0.489690	−	0.871897i	$-0.662890\pi$
$277$	−16.3001	−0.979380	−0.489690	+	0.871897i	$0.662890\pi$
$278$	−14.9115	−0.894334
$279$	−2.94142	−0.176098
$280$	−17.3605	−1.03749
$281$	12.4647	0.743583	0.371792	−	0.928316i	$-0.378744\pi$
$281$	12.4647	0.743583	0.371792	+	0.928316i	$0.378744\pi$
$282$	2.05279	0.122242
$283$	−22.3527	−1.32873	−0.664365	−	0.747408i	$-0.731298\pi$
$283$	−22.3527	−1.32873	−0.664365	+	0.747408i	$0.731298\pi$
$284$	−6.77749	−0.402170
$285$	0.491427	0.0291096
$286$	−10.0824	−0.596183
$287$	12.7209	0.750892
$288$	−2.94142	−0.173325
$289$	35.2450	2.07323
$290$	26.7758	1.57233
$291$	0.242040	0.0141886
$292$	−4.83570	−0.282988
$293$	8.76974	0.512334	0.256167	−	0.966633i	$-0.417540\pi$
$293$	8.76974	0.512334	0.256167	+	0.966633i	$0.417540\pi$
$294$	2.09604	0.122244
$295$	−15.1741	−0.883470
$296$	−5.34859	−0.310880
$297$	2.22863	0.129318
$298$	19.1956	1.11197
$299$	30.1392	1.74299
$300$	3.44806	0.199074
$301$	2.76140	0.159164
$302$	−8.82639	−0.507901
$303$	3.55099	0.203999
$304$	−0.462811	−0.0265441
$305$	−43.9155	−2.51460
$306$	21.2608	1.21540
$307$	−7.21882	−0.412000	−0.206000	−	0.978552i	$-0.566045\pi$
$307$	−7.21882	−0.412000	−0.206000	+	0.978552i	$0.566045\pi$
$308$	−6.13276	−0.349446
$309$	−0.457957	−0.0260523
$310$	−4.38700	−0.249165
$311$	−5.52367	−0.313219	−0.156609	−	0.987661i	$-0.550056\pi$
$311$	−5.52367	−0.313219	−0.156609	+	0.987661i	$0.550056\pi$
$312$	1.57467	0.0891480
$313$	−10.7035	−0.604998	−0.302499	−	0.953150i	$-0.597821\pi$
$313$	−10.7035	−0.604998	−0.302499	+	0.953150i	$0.597821\pi$
$314$	−4.65422	−0.262653
$315$	51.0645	2.87716
$316$	−3.54838	−0.199612
$317$	26.9944	1.51616	0.758078	−	0.652164i	$-0.226139\pi$
$317$	26.9944	1.51616	0.758078	+	0.652164i	$0.226139\pi$
$318$	−1.11211	−0.0623640
$319$	9.45881	0.529591
$320$	−4.38700	−0.245241
$321$	4.14913	0.231582
$322$	18.3326	1.02164
$323$	3.34523	0.186134
$324$	8.47618	0.470899
$325$	92.6805	5.14099
$326$	9.70690	0.537615
$327$	0.690764	0.0381993
$328$	3.21458	0.177495
$329$	33.5623	1.85035
$330$	1.64557	0.0905857
$331$	15.0297	0.826108	0.413054	−	0.910707i	$-0.364462\pi$
$331$	15.0297	0.826108	0.413054	+	0.910707i	$0.364462\pi$
$332$	−2.81607	−0.154552
$333$	15.7324	0.862132
$334$	10.1581	0.555825
$335$	−69.3156	−3.78712
$336$	0.957815	0.0522531
$337$	32.0808	1.74755	0.873776	−	0.486329i	$-0.161664\pi$
$337$	32.0808	1.74755	0.873776	+	0.486329i	$0.161664\pi$
$338$	29.3256	1.59510
$339$	2.29277	0.124526
$340$	31.7096	1.71969
$341$	−1.54975	−0.0839236
$342$	1.36132	0.0736118
$343$	6.56869	0.354676
$344$	0.697805	0.0376231
$345$	−4.91909	−0.264835
$346$	8.16970	0.439206
$347$	13.6548	0.733028	0.366514	−	0.930413i	$-0.380551\pi$
$347$	13.6548	0.733028	0.366514	+	0.930413i	$0.380551\pi$
$348$	−1.47728	−0.0791904
$349$	−30.2984	−1.62183	−0.810917	−	0.585161i	$-0.801031\pi$
$349$	−30.2984	−1.62183	−0.810917	+	0.585161i	$0.801031\pi$
$350$	56.3744	3.01334
$351$	−9.35575	−0.499373
$352$	−1.54975	−0.0826019
$353$	2.02467	0.107762	0.0538811	−	0.998547i	$-0.482841\pi$
$353$	2.02467	0.107762	0.0538811	+	0.998547i	$0.482841\pi$
$354$	0.837186	0.0444959
$355$	29.7329	1.57806
$356$	−9.32741	−0.494352
$357$	−6.92316	−0.366412
$358$	13.2670	0.701182
$359$	−32.1285	−1.69568	−0.847838	−	0.530256i	$-0.822096\pi$
$359$	−32.1285	−1.69568	−0.847838	+	0.530256i	$0.822096\pi$
$360$	12.9040	0.680101
$361$	−18.7858	−0.988727
$362$	19.0812	1.00289
$363$	−2.08113	−0.109231
$364$	25.7452	1.34941
$365$	21.2142	1.11040
$366$	2.42291	0.126648
$367$	−17.3453	−0.905416	−0.452708	−	0.891659i	$-0.649542\pi$
$367$	−17.3453	−0.905416	−0.452708	+	0.891659i	$0.649542\pi$
$368$	4.63265	0.241494
$369$	−9.45540	−0.492229
$370$	23.4643	1.21985
$371$	−18.1825	−0.943991
$372$	0.242040	0.0125492
$373$	13.6727	0.707947	0.353973	−	0.935255i	$-0.384830\pi$
$373$	13.6727	0.707947	0.353973	+	0.935255i	$0.384830\pi$
$374$	11.2017	0.579226
$375$	−9.81748	−0.506972
$376$	8.48120	0.437384
$377$	−39.7079	−2.04506
$378$	−5.69078	−0.292702
$379$	−4.04847	−0.207956	−0.103978	−	0.994580i	$-0.533157\pi$
$379$	−4.04847	−0.207956	−0.103978	+	0.994580i	$0.533157\pi$
$380$	2.03036	0.104155
$381$	4.01663	0.205778
$382$	−11.5892	−0.592957
$383$	10.9128	0.557620	0.278810	−	0.960346i	$-0.410060\pi$
$383$	10.9128	0.557620	0.278810	+	0.960346i	$0.410060\pi$
$384$	0.242040	0.0123516
$385$	26.9044	1.37118
$386$	−2.45769	−0.125093
$387$	−2.05254	−0.104336
$388$	1.00000	0.0507673
$389$	−26.6262	−1.35000	−0.675001	−	0.737817i	$-0.735857\pi$
$389$	−26.6262	−1.35000	−0.675001	+	0.737817i	$0.735857\pi$
$390$	−6.90807	−0.349804
$391$	−33.4851	−1.69342
$392$	8.65991	0.437391
$393$	5.49451	0.277161
$394$	6.20088	0.312396
$395$	15.5668	0.783250
$396$	4.55846	0.229071
$397$	31.7320	1.59259	0.796293	−	0.604911i	$-0.206791\pi$
$397$	31.7320	1.59259	0.796293	+	0.604911i	$0.206791\pi$
$398$	−18.6781	−0.936248
$399$	−0.443288	−0.0221922
$400$	14.2458	0.712290
$401$	16.8848	0.843184	0.421592	−	0.906786i	$-0.361471\pi$
$401$	16.8848	0.843184	0.421592	+	0.906786i	$0.361471\pi$
$402$	3.82429	0.190738
$403$	6.50581	0.324078
$404$	14.6711	0.729913
$405$	−37.1850	−1.84774
$406$	−24.1529	−1.19869
$407$	8.28897	0.410869
$408$	−1.74948	−0.0866123
$409$	−3.88941	−0.192319	−0.0961595	−	0.995366i	$-0.530656\pi$
$409$	−3.88941	−0.192319	−0.0961595	+	0.995366i	$0.530656\pi$
$410$	−14.1024	−0.696466
$411$	−1.01016	−0.0498277
$412$	−1.89207	−0.0932157
$413$	13.6877	0.673526
$414$	−13.6266	−0.669709
$415$	12.3541	0.606439
$416$	6.50581	0.318974
$417$	−3.60919	−0.176743
$418$	0.717241	0.0350814
$419$	18.9011	0.923381	0.461691	−	0.887041i	$-0.347243\pi$
$419$	18.9011	0.923381	0.461691	+	0.887041i	$0.347243\pi$
$420$	−4.20194	−0.205034
$421$	−8.96630	−0.436991	−0.218495	−	0.975838i	$-0.570115\pi$
$421$	−8.96630	−0.436991	−0.218495	+	0.975838i	$0.570115\pi$
$422$	−13.4125	−0.652911
$423$	−24.9467	−1.21295
$424$	−4.59473	−0.223140
$425$	−102.970	−4.99476
$426$	−1.64042	−0.0794788
$427$	39.6136	1.91704
$428$	17.1423	0.828605
$429$	−2.44034	−0.117821
$430$	−3.06128	−0.147628
$431$	−18.6328	−0.897511	−0.448755	−	0.893655i	$-0.648133\pi$
$431$	−18.6328	−0.897511	−0.448755	+	0.893655i	$0.648133\pi$
$432$	−1.43806	−0.0691887
$433$	−17.9403	−0.862158	−0.431079	−	0.902314i	$-0.641867\pi$
$433$	−17.9403	−0.862158	−0.431079	+	0.902314i	$0.641867\pi$
$434$	3.95726	0.189955
$435$	6.48082	0.310732
$436$	2.85392	0.136678
$437$	−2.14404	−0.102564
$438$	−1.17043	−0.0559254
$439$	−5.92756	−0.282907	−0.141454	−	0.989945i	$-0.545178\pi$
$439$	−5.92756	−0.282907	−0.141454	+	0.989945i	$0.545178\pi$
$440$	6.79876	0.324118
$441$	−25.4724	−1.21297
$442$	−47.0245	−2.23673
$443$	18.3772	0.873126	0.436563	−	0.899674i	$-0.356196\pi$
$443$	18.3772	0.873126	0.436563	+	0.899674i	$0.356196\pi$
$444$	−1.29457	−0.0614377
$445$	40.9194	1.93977
$446$	7.11831	0.337062
$447$	4.64611	0.219753
$448$	3.95726	0.186963
$449$	30.6029	1.44424	0.722121	−	0.691767i	$-0.243167\pi$
$449$	30.6029	1.44424	0.722121	+	0.691767i	$0.243167\pi$
$450$	−41.9028	−1.97532
$451$	−4.98179	−0.234583
$452$	9.47268	0.445557
$453$	−2.13634	−0.100374
$454$	10.2209	0.479693
$455$	−112.944	−5.29491
$456$	−0.112019	−0.00524576
$457$	−8.15889	−0.381657	−0.190828	−	0.981623i	$-0.561117\pi$
$457$	−8.15889	−0.381657	−0.190828	+	0.981623i	$0.561117\pi$
$458$	22.2447	1.03943
$459$	10.3944	0.485169
$460$	−20.3235	−0.947587
$461$	13.6469	0.635600	0.317800	−	0.948158i	$-0.397056\pi$
$461$	13.6469	0.635600	0.317800	+	0.948158i	$0.397056\pi$
$462$	−1.48437	−0.0690593
$463$	−35.1657	−1.63429	−0.817145	−	0.576433i	$-0.804444\pi$
$463$	−35.1657	−1.63429	−0.817145	+	0.576433i	$0.804444\pi$
$464$	−6.10344	−0.283345
$465$	−1.06183	−0.0492412
$466$	14.0647	0.651534
$467$	36.2345	1.67673	0.838366	−	0.545108i	$-0.183511\pi$
$467$	36.2345	1.67673	0.838366	+	0.545108i	$0.183511\pi$
$468$	−19.1363	−0.884576
$469$	62.5256	2.88716
$470$	−37.2070	−1.71623
$471$	−1.12651	−0.0519067
$472$	3.45887	0.159208
$473$	−1.08142	−0.0497239
$474$	−0.858851	−0.0394483
$475$	−6.59312	−0.302513
$476$	−28.6033	−1.31103
$477$	13.5150	0.618810
$478$	−1.95645	−0.0894861
$479$	−26.7183	−1.22079	−0.610396	−	0.792097i	$-0.708990\pi$
$479$	−26.7183	−1.22079	−0.610396	+	0.792097i	$0.708990\pi$
$480$	−1.06183	−0.0484657
$481$	−34.7969	−1.58660
$482$	16.0423	0.730706
$483$	4.43723	0.201901
$484$	−8.59828	−0.390831
$485$	−4.38700	−0.199204
$486$	6.36576	0.288757
$487$	30.7412	1.39302	0.696508	−	0.717549i	$-0.254736\pi$
$487$	30.7412	1.39302	0.696508	+	0.717549i	$0.254736\pi$
$488$	10.0104	0.453148
$489$	2.34946	0.106246
$490$	−37.9911	−1.71626
$491$	−10.8516	−0.489726	−0.244863	−	0.969558i	$-0.578743\pi$
$491$	−10.8516	−0.489726	−0.244863	+	0.969558i	$0.578743\pi$
$492$	0.778056	0.0350775
$493$	44.1161	1.98689
$494$	−3.01096	−0.135470
$495$	−19.9980	−0.898842
$496$	1.00000	0.0449013
$497$	−26.8203	−1.20305
$498$	−0.681602	−0.0305433
$499$	−20.4422	−0.915117	−0.457559	−	0.889179i	$-0.651276\pi$
$499$	−20.4422	−0.915117	−0.457559	+	0.889179i	$0.651276\pi$
$500$	−40.5614	−1.81396
$501$	2.45866	0.109845
$502$	3.44442	0.153732
$503$	20.7770	0.926401	0.463201	−	0.886253i	$-0.346701\pi$
$503$	20.7770	0.926401	0.463201	+	0.886253i	$0.346701\pi$
$504$	−11.6400	−0.518485
$505$	−64.3620	−2.86407
$506$	−7.17945	−0.319166
$507$	7.09797	0.315232
$508$	16.5949	0.736279
$509$	7.27586	0.322497	0.161248	−	0.986914i	$-0.448448\pi$
$509$	7.27586	0.322497	0.161248	+	0.986914i	$0.448448\pi$
$510$	7.67498	0.339854
$511$	−19.1361	−0.846531
$512$	1.00000	0.0441942
$513$	0.665551	0.0293848
$514$	19.8530	0.875678
$515$	8.30053	0.365765
$516$	0.168897	0.00743527
$517$	−13.1437	−0.578060
$518$	−21.1658	−0.929970
$519$	1.97739	0.0867980
$520$	−28.5410	−1.25161
$521$	−24.4470	−1.07104	−0.535522	−	0.844521i	$-0.679885\pi$
$521$	−24.4470	−1.07104	−0.535522	+	0.844521i	$0.679885\pi$
$522$	17.9528	0.785771
$523$	−5.56124	−0.243176	−0.121588	−	0.992581i	$-0.538799\pi$
$523$	−5.56124	−0.243176	−0.121588	+	0.992581i	$0.538799\pi$
$524$	22.7008	0.991689
$525$	13.6449	0.595510
$526$	−29.2864	−1.27695
$527$	−7.22807	−0.314860
$528$	−0.375101	−0.0163242
$529$	−1.53851	−0.0668920
$530$	20.1571	0.875569
$531$	−10.1740	−0.441513
$532$	−1.83146	−0.0794041
$533$	20.9134	0.905861
$534$	−2.25761	−0.0976962
$535$	−75.2034	−3.25133
$536$	15.8002	0.682465
$537$	3.21114	0.138571
$538$	−3.65686	−0.157658
$539$	−13.4207	−0.578070
$540$	6.30878	0.271487
$541$	−30.8736	−1.32736	−0.663680	−	0.748017i	$-0.731006\pi$
$541$	−30.8736	−1.32736	−0.663680	+	0.748017i	$0.731006\pi$
$542$	7.71252	0.331281
$543$	4.61841	0.198195
$544$	−7.22807	−0.309901
$545$	−12.5202	−0.536305
$546$	6.23137	0.266678
$547$	−7.46732	−0.319280	−0.159640	−	0.987175i	$-0.551033\pi$
$547$	−7.46732	−0.319280	−0.159640	+	0.987175i	$0.551033\pi$
$548$	−4.17354	−0.178285
$549$	−29.4447	−1.25667
$550$	−22.0774	−0.941385
$551$	2.82474	0.120338
$552$	1.12129	0.0477252
$553$	−14.0419	−0.597122
$554$	−16.3001	−0.692526
$555$	5.67930	0.241073
$556$	−14.9115	−0.632389
$557$	−35.1197	−1.48807	−0.744035	−	0.668140i	$-0.767091\pi$
$557$	−35.1197	−1.48807	−0.744035	+	0.668140i	$0.767091\pi$
$558$	−2.94142	−0.124520
$559$	4.53979	0.192013
$560$	−17.3605	−0.733616
$561$	2.71126	0.114469
$562$	12.4647	0.525793
$563$	40.4229	1.70362	0.851811	−	0.523849i	$-0.175504\pi$
$563$	40.4229	1.70362	0.851811	+	0.523849i	$0.175504\pi$
$564$	2.05279	0.0864380
$565$	−41.5567	−1.74830
$566$	−22.3527	−0.939554
$567$	33.5425	1.40865
$568$	−6.77749	−0.284377
$569$	29.7443	1.24694	0.623472	−	0.781846i	$-0.285721\pi$
$569$	29.7443	1.24694	0.623472	+	0.781846i	$0.285721\pi$
$570$	0.491427	0.0205836
$571$	−42.7440	−1.78878	−0.894391	−	0.447286i	$-0.852391\pi$
$571$	−42.7440	−1.78878	−0.894391	+	0.447286i	$0.852391\pi$
$572$	−10.0824	−0.421565
$573$	−2.80506	−0.117183
$574$	12.7209	0.530961
$575$	65.9959	2.75222
$576$	−2.94142	−0.122559
$577$	−9.20061	−0.383027	−0.191513	−	0.981490i	$-0.561340\pi$
$577$	−9.20061	−0.383027	−0.191513	+	0.981490i	$0.561340\pi$
$578$	35.2450	1.46600
$579$	−0.594860	−0.0247215
$580$	26.7758	1.11181
$581$	−11.1439	−0.462328
$582$	0.242040	0.0100329
$583$	7.12068	0.294908
$584$	−4.83570	−0.200102
$585$	83.9510	3.47095
$586$	8.76974	0.362275
$587$	−5.29458	−0.218531	−0.109265	−	0.994013i	$-0.534850\pi$
$587$	−5.29458	−0.218531	−0.109265	+	0.994013i	$0.534850\pi$
$588$	2.09604	0.0864394
$589$	−0.462811	−0.0190698
$590$	−15.1741	−0.624707
$591$	1.50086	0.0617372
$592$	−5.34859	−0.219826
$593$	−7.15011	−0.293620	−0.146810	−	0.989165i	$-0.546901\pi$
$593$	−7.15011	−0.293620	−0.146810	+	0.989165i	$0.546901\pi$
$594$	2.22863	0.0914419
$595$	125.483	5.14430
$596$	19.1956	0.786283
$597$	−4.52085	−0.185026
$598$	30.1392	1.23248
$599$	−18.7973	−0.768039	−0.384019	−	0.923325i	$-0.625460\pi$
$599$	−18.7973	−0.768039	−0.384019	+	0.923325i	$0.625460\pi$
$600$	3.44806	0.140766
$601$	−11.9635	−0.488002	−0.244001	−	0.969775i	$-0.578460\pi$
$601$	−11.9635	−0.488002	−0.244001	+	0.969775i	$0.578460\pi$
$602$	2.76140	0.112546
$603$	−46.4750	−1.89261
$604$	−8.82639	−0.359141
$605$	37.7207	1.53356
$606$	3.55099	0.144249
$607$	2.72328	0.110535	0.0552673	−	0.998472i	$-0.482399\pi$
$607$	2.72328	0.110535	0.0552673	+	0.998472i	$0.482399\pi$
$608$	−0.462811	−0.0187695
$609$	−5.84597	−0.236891
$610$	−43.9155	−1.77809
$611$	55.1771	2.23223
$612$	21.2608	0.859415
$613$	−5.69205	−0.229900	−0.114950	−	0.993371i	$-0.536671\pi$
$613$	−5.69205	−0.229900	−0.114950	+	0.993371i	$0.536671\pi$
$614$	−7.21882	−0.291328
$615$	−3.41333	−0.137639
$616$	−6.13276	−0.247096
$617$	6.64045	0.267334	0.133667	−	0.991026i	$-0.457325\pi$
$617$	6.64045	0.267334	0.133667	+	0.991026i	$0.457325\pi$
$618$	−0.457957	−0.0184217
$619$	−26.6157	−1.06978	−0.534888	−	0.844923i	$-0.679646\pi$
$619$	−26.6157	−1.06978	−0.534888	+	0.844923i	$0.679646\pi$
$620$	−4.38700	−0.176186
$621$	−6.66204	−0.267338
$622$	−5.52367	−0.221479
$623$	−36.9110	−1.47881
$624$	1.57467	0.0630371
$625$	106.714	4.26856
$626$	−10.7035	−0.427798
$627$	0.173601	0.00693296
$628$	−4.65422	−0.185724
$629$	38.6600	1.54147
$630$	51.0645	2.03446
$631$	14.7191	0.585958	0.292979	−	0.956119i	$-0.405353\pi$
$631$	14.7191	0.585958	0.292979	+	0.956119i	$0.405353\pi$
$632$	−3.54838	−0.141147
$633$	−3.24636	−0.129031
$634$	26.9944	1.07208
$635$	−72.8018	−2.88905
$636$	−1.11211	−0.0440980
$637$	56.3397	2.23226
$638$	9.45881	0.374478
$639$	19.9354	0.788633
$640$	−4.38700	−0.173412
$641$	−23.1306	−0.913604	−0.456802	−	0.889568i	$-0.651005\pi$
$641$	−23.1306	−0.913604	−0.456802	+	0.889568i	$0.651005\pi$
$642$	4.14913	0.163753
$643$	−1.59692	−0.0629765	−0.0314883	−	0.999504i	$-0.510025\pi$
$643$	−1.59692	−0.0629765	−0.0314883	+	0.999504i	$0.510025\pi$
$644$	18.3326	0.722406
$645$	−0.740951	−0.0291749
$646$	3.34523	0.131616
$647$	22.3371	0.878164	0.439082	−	0.898447i	$-0.355304\pi$
$647$	22.3371	0.878164	0.439082	+	0.898447i	$0.355304\pi$
$648$	8.47618	0.332976
$649$	−5.36039	−0.210414
$650$	92.6805	3.63523
$651$	0.957815	0.0375397
$652$	9.70690	0.380151
$653$	−46.2956	−1.81169	−0.905843	−	0.423614i	$-0.860761\pi$
$653$	−46.2956	−1.81169	−0.905843	+	0.423614i	$0.860761\pi$
$654$	0.690764	0.0270110
$655$	−99.5885	−3.89125
$656$	3.21458	0.125508
$657$	14.2238	0.554923
$658$	33.5623	1.30839
$659$	−42.1019	−1.64006	−0.820029	−	0.572322i	$-0.806043\pi$
$659$	−42.1019	−1.64006	−0.820029	+	0.572322i	$0.806043\pi$
$660$	1.64557	0.0640538
$661$	33.9077	1.31886	0.659429	−	0.751767i	$-0.270798\pi$
$661$	33.9077	1.31886	0.659429	+	0.751767i	$0.270798\pi$
$662$	15.0297	0.584146
$663$	−11.3818	−0.442033
$664$	−2.81607	−0.109285
$665$	8.03464	0.311570
$666$	15.7324	0.609619
$667$	−28.2751	−1.09482
$668$	10.1581	0.393028
$669$	1.72292	0.0666118
$670$	−69.3156	−2.67790
$671$	−15.5136	−0.598894
$672$	0.957815	0.0369485
$673$	−40.2826	−1.55278	−0.776391	−	0.630252i	$-0.782952\pi$
$673$	−40.2826	−1.55278	−0.776391	+	0.630252i	$0.782952\pi$
$674$	32.0808	1.23571
$675$	−20.4863	−0.788519
$676$	29.3256	1.12791
$677$	−4.33541	−0.166623	−0.0833117	−	0.996524i	$-0.526550\pi$
$677$	−4.33541	−0.166623	−0.0833117	+	0.996524i	$0.526550\pi$
$678$	2.29277	0.0880532
$679$	3.95726	0.151866
$680$	31.7096	1.21601
$681$	2.47388	0.0947992
$682$	−1.54975	−0.0593430
$683$	−40.5642	−1.55214	−0.776072	−	0.630644i	$-0.782791\pi$
$683$	−40.5642	−1.55214	−0.776072	+	0.630644i	$0.782791\pi$
$684$	1.36132	0.0520514
$685$	18.3093	0.699563
$686$	6.56869	0.250794
$687$	5.38412	0.205417
$688$	0.697805	0.0266036
$689$	−29.8925	−1.13881
$690$	−4.91909	−0.187267
$691$	−36.9194	−1.40448	−0.702241	−	0.711940i	$-0.747817\pi$
$691$	−36.9194	−1.40448	−0.702241	+	0.711940i	$0.747817\pi$
$692$	8.16970	0.310565
$693$	18.0390	0.685245
$694$	13.6548	0.518329
$695$	65.4169	2.48141
$696$	−1.47728	−0.0559961
$697$	−23.2352	−0.880095
$698$	−30.2984	−1.14681
$699$	3.40421	0.128759
$700$	56.3744	2.13075
$701$	6.02839	0.227689	0.113845	−	0.993499i	$-0.463683\pi$
$701$	6.02839	0.227689	0.113845	+	0.993499i	$0.463683\pi$
$702$	−9.35575	−0.353110
$703$	2.47539	0.0933610
$704$	−1.54975	−0.0584084
$705$	−9.00559	−0.339170
$706$	2.02467	0.0761994
$707$	58.0572	2.18347
$708$	0.837186	0.0314634
$709$	−29.6624	−1.11400	−0.556998	−	0.830514i	$-0.688047\pi$
$709$	−29.6624	−1.11400	−0.556998	+	0.830514i	$0.688047\pi$
$710$	29.7329	1.11586
$711$	10.4373	0.391429
$712$	−9.32741	−0.349560
$713$	4.63265	0.173494
$714$	−6.92316	−0.259093
$715$	44.2314	1.65416
$716$	13.2670	0.495810
$717$	−0.473540	−0.0176847
$718$	−32.1285	−1.19902
$719$	−1.69077	−0.0630550	−0.0315275	−	0.999503i	$-0.510037\pi$
$719$	−1.69077	−0.0630550	−0.0315275	+	0.999503i	$0.510037\pi$
$720$	12.9040	0.480904
$721$	−7.48742	−0.278846
$722$	−18.7858	−0.699135
$723$	3.88287	0.144406
$724$	19.0812	0.709147
$725$	−86.9485	−3.22918
$726$	−2.08113	−0.0772379
$727$	29.9519	1.11086	0.555428	−	0.831565i	$-0.312555\pi$
$727$	29.9519	1.11086	0.555428	+	0.831565i	$0.312555\pi$
$728$	25.7452	0.954180
$729$	−23.8878	−0.884732
$730$	21.2142	0.785173
$731$	−5.04378	−0.186551
$732$	2.42291	0.0895533
$733$	26.3544	0.973422	0.486711	−	0.873563i	$-0.338196\pi$
$733$	26.3544	0.973422	0.486711	+	0.873563i	$0.338196\pi$
$734$	−17.3453	−0.640226
$735$	−9.19536	−0.339176
$736$	4.63265	0.170762
$737$	−24.4864	−0.901967
$738$	−9.45540	−0.348058
$739$	35.7897	1.31654	0.658272	−	0.752780i	$-0.271288\pi$
$739$	35.7897	1.31654	0.658272	+	0.752780i	$0.271288\pi$
$740$	23.4643	0.862564
$741$	−0.728774	−0.0267722
$742$	−18.1825	−0.667502
$743$	3.34454	0.122699	0.0613496	−	0.998116i	$-0.480460\pi$
$743$	3.34454	0.122699	0.0613496	+	0.998116i	$0.480460\pi$
$744$	0.242040	0.00887362
$745$	−84.2112	−3.08526
$746$	13.6727	0.500594
$747$	8.28323	0.303068
$748$	11.2017	0.409574
$749$	67.8366	2.47869
$750$	−9.81748	−0.358484
$751$	7.78331	0.284017	0.142009	−	0.989865i	$-0.454644\pi$
$751$	7.78331	0.284017	0.142009	+	0.989865i	$0.454644\pi$
$752$	8.48120	0.309277
$753$	0.833689	0.0303813
$754$	−39.7079	−1.44607
$755$	38.7214	1.40922
$756$	−5.69078	−0.206972
$757$	−12.0327	−0.437338	−0.218669	−	0.975799i	$-0.570171\pi$
$757$	−12.0327	−0.437338	−0.218669	+	0.975799i	$0.570171\pi$
$758$	−4.04847	−0.147047
$759$	−1.73771	−0.0630751
$760$	2.03036	0.0736487
$761$	−38.9938	−1.41352	−0.706762	−	0.707452i	$-0.749845\pi$
$761$	−38.9938	−1.41352	−0.706762	+	0.707452i	$0.749845\pi$
$762$	4.01663	0.145507
$763$	11.2937	0.408860
$764$	−11.5892	−0.419284
$765$	−93.2710	−3.37222
$766$	10.9128	0.394297
$767$	22.5028	0.812528
$768$	0.242040	0.00873387
$769$	26.5813	0.958547	0.479274	−	0.877666i	$-0.340900\pi$
$769$	26.5813	0.958547	0.479274	+	0.877666i	$0.340900\pi$
$770$	26.9044	0.969569
$771$	4.80522	0.173056
$772$	−2.45769	−0.0884543
$773$	−28.0617	−1.00931	−0.504655	−	0.863321i	$-0.668380\pi$
$773$	−28.0617	−1.00931	−0.504655	+	0.863321i	$0.668380\pi$
$774$	−2.05254	−0.0737769
$775$	14.2458	0.511724
$776$	1.00000	0.0358979
$777$	−5.12296	−0.183785
$778$	−26.6262	−0.954596
$779$	−1.48774	−0.0533039
$780$	−6.90807	−0.247349
$781$	10.5034	0.375842
$782$	−33.4851	−1.19743
$783$	8.77712	0.313669
$784$	8.65991	0.309282
$785$	20.4181	0.728753
$786$	5.49451	0.195983
$787$	−4.27614	−0.152428	−0.0762140	−	0.997091i	$-0.524283\pi$
$787$	−4.27614	−0.152428	−0.0762140	+	0.997091i	$0.524283\pi$
$788$	6.20088	0.220897
$789$	−7.08849	−0.252357
$790$	15.5668	0.553841
$791$	37.4858	1.33284
$792$	4.55846	0.161978
$793$	65.1256	2.31268
$794$	31.7320	1.12613
$795$	4.87883	0.173034
$796$	−18.6781	−0.662027
$797$	15.4472	0.547167	0.273584	−	0.961848i	$-0.411791\pi$
$797$	15.4472	0.547167	0.273584	+	0.961848i	$0.411791\pi$
$798$	−0.443288	−0.0156922
$799$	−61.3027	−2.16873
$800$	14.2458	0.503665
$801$	27.4358	0.969397
$802$	16.8848	0.596221
$803$	7.49411	0.264462
$804$	3.82429	0.134872
$805$	−80.4253	−2.83462
$806$	6.50581	0.229157
$807$	−0.885106	−0.0311572
$808$	14.6711	0.516126
$809$	−17.2200	−0.605423	−0.302711	−	0.953082i	$-0.597892\pi$
$809$	−17.2200	−0.605423	−0.302711	+	0.953082i	$0.597892\pi$
$810$	−37.1850	−1.30655
$811$	−43.8957	−1.54139	−0.770694	−	0.637206i	$-0.780090\pi$
$811$	−43.8957	−1.54139	−0.770694	+	0.637206i	$0.780090\pi$
$812$	−24.1529	−0.847601
$813$	1.86674	0.0654694
$814$	8.28897	0.290528
$815$	−42.5842	−1.49166
$816$	−1.74948	−0.0612441
$817$	−0.322952	−0.0112987
$818$	−3.88941	−0.135990
$819$	−75.7273	−2.64613
$820$	−14.1024	−0.492476
$821$	−17.4951	−0.610584	−0.305292	−	0.952259i	$-0.598754\pi$
$821$	−17.4951	−0.610584	−0.305292	+	0.952259i	$0.598754\pi$
$822$	−1.01016	−0.0352335
$823$	23.3403	0.813591	0.406795	−	0.913519i	$-0.366646\pi$
$823$	23.3403	0.813591	0.406795	+	0.913519i	$0.366646\pi$
$824$	−1.89207	−0.0659134
$825$	−5.34362	−0.186041
$826$	13.6877	0.476255
$827$	1.61669	0.0562177	0.0281089	−	0.999605i	$-0.491051\pi$
$827$	1.61669	0.0562177	0.0281089	+	0.999605i	$0.491051\pi$
$828$	−13.6266	−0.473556
$829$	15.4460	0.536461	0.268230	−	0.963355i	$-0.413561\pi$
$829$	15.4460	0.536461	0.268230	+	0.963355i	$0.413561\pi$
$830$	12.3541	0.428817
$831$	−3.94529	−0.136860
$832$	6.50581	0.225548
$833$	−62.5944	−2.16877
$834$	−3.60919	−0.124976
$835$	−44.5635	−1.54218
$836$	0.717241	0.0248063
$837$	−1.43806	−0.0497067
$838$	18.9011	0.652929
$839$	−18.1990	−0.628298	−0.314149	−	0.949374i	$-0.601719\pi$
$839$	−18.1990	−0.628298	−0.314149	+	0.949374i	$0.601719\pi$
$840$	−4.20194	−0.144981
$841$	8.25202	0.284552
$842$	−8.96630	−0.308999
$843$	3.01696	0.103910
$844$	−13.4125	−0.461678
$845$	−128.652	−4.42575
$846$	−24.9467	−0.857686
$847$	−34.0256	−1.16913
$848$	−4.59473	−0.157784
$849$	−5.41025	−0.185679
$850$	−102.970	−3.53183
$851$	−24.7782	−0.849385
$852$	−1.64042	−0.0562000
$853$	28.6552	0.981136	0.490568	−	0.871403i	$-0.336789\pi$
$853$	28.6552	0.981136	0.490568	+	0.871403i	$0.336789\pi$
$854$	39.6136	1.35555
$855$	−5.97212	−0.204242
$856$	17.1423	0.585912
$857$	−55.5756	−1.89843	−0.949213	−	0.314634i	$-0.898118\pi$
$857$	−55.5756	−1.89843	−0.949213	+	0.314634i	$0.898118\pi$
$858$	−2.44034	−0.0833118
$859$	40.8386	1.39339	0.696697	−	0.717365i	$-0.254652\pi$
$859$	40.8386	1.39339	0.696697	+	0.717365i	$0.254652\pi$
$860$	−3.06128	−0.104389
$861$	3.07897	0.104931
$862$	−18.6328	−0.634636
$863$	58.2276	1.98209	0.991045	−	0.133528i	$-0.0426305\pi$
$863$	58.2276	1.98209	0.991045	+	0.133528i	$0.0426305\pi$
$864$	−1.43806	−0.0489238
$865$	−35.8405	−1.21861
$866$	−17.9403	−0.609638
$867$	8.53069	0.289718
$868$	3.95726	0.134318
$869$	5.49911	0.186544
$870$	6.48082	0.219720
$871$	102.793	3.48302
$872$	2.85392	0.0966460
$873$	−2.94142	−0.0995519
$874$	−2.14404	−0.0725234
$875$	−160.512	−5.42629
$876$	−1.17043	−0.0395452
$877$	8.09693	0.273414	0.136707	−	0.990612i	$-0.456348\pi$
$877$	8.09693	0.273414	0.136707	+	0.990612i	$0.456348\pi$
$878$	−5.92756	−0.200046
$879$	2.12263	0.0715945
$880$	6.79876	0.229186
$881$	1.38815	0.0467680	0.0233840	−	0.999727i	$-0.492556\pi$
$881$	1.38815	0.0467680	0.0233840	+	0.999727i	$0.492556\pi$
$882$	−25.4724	−0.857700
$883$	10.1613	0.341953	0.170977	−	0.985275i	$-0.445308\pi$
$883$	10.1613	0.341953	0.170977	+	0.985275i	$0.445308\pi$
$884$	−47.0245	−1.58160
$885$	−3.67274	−0.123458
$886$	18.3772	0.617393
$887$	15.0877	0.506595	0.253298	−	0.967388i	$-0.418485\pi$
$887$	15.0877	0.506595	0.253298	+	0.967388i	$0.418485\pi$
$888$	−1.29457	−0.0434430
$889$	65.6703	2.20251
$890$	40.9194	1.37162
$891$	−13.1360	−0.440071
$892$	7.11831	0.238339
$893$	−3.92519	−0.131352
$894$	4.64611	0.155389
$895$	−58.2023	−1.94549
$896$	3.95726	0.132203
$897$	7.29489	0.243569
$898$	30.6029	1.02123
$899$	−6.10344	−0.203561
$900$	−41.9028	−1.39676
$901$	33.2110	1.10642
$902$	−4.98179	−0.165875
$903$	0.668369	0.0222419
$904$	9.47268	0.315057
$905$	−83.7093	−2.78259
$906$	−2.13634	−0.0709751
$907$	−40.2508	−1.33651	−0.668254	−	0.743933i	$-0.732958\pi$
$907$	−40.2508	−1.33651	−0.668254	+	0.743933i	$0.732958\pi$
$908$	10.2209	0.339194
$909$	−43.1537	−1.43132
$910$	−112.944	−3.74407
$911$	−38.9095	−1.28913	−0.644565	−	0.764549i	$-0.722962\pi$
$911$	−38.9095	−1.28913	−0.644565	+	0.764549i	$0.722962\pi$
$912$	−0.112019	−0.00370932
$913$	4.36420	0.144434
$914$	−8.15889	−0.269872
$915$	−10.6293	−0.351394
$916$	22.2447	0.734987
$917$	89.8330	2.96655
$918$	10.3944	0.343066
$919$	−2.66143	−0.0877925	−0.0438963	−	0.999036i	$-0.513977\pi$
$919$	−2.66143	−0.0877925	−0.0438963	+	0.999036i	$0.513977\pi$
$920$	−20.3235	−0.670045
$921$	−1.74724	−0.0575736
$922$	13.6469	0.449437
$923$	−44.0931	−1.45134
$924$	−1.48437	−0.0488323
$925$	−76.1950	−2.50527
$926$	−35.1657	−1.15562
$927$	5.56537	0.182791
$928$	−6.10344	−0.200355
$929$	−26.4998	−0.869430	−0.434715	−	0.900568i	$-0.643151\pi$
$929$	−26.4998	−0.869430	−0.434715	+	0.900568i	$0.643151\pi$
$930$	−1.06183	−0.0348188
$931$	−4.00790	−0.131354
$932$	14.0647	0.460704
$933$	−1.33695	−0.0437698
$934$	36.2345	1.18563
$935$	−49.1419	−1.60711
$936$	−19.1363	−0.625490
$937$	39.1628	1.27939	0.639696	−	0.768628i	$-0.279060\pi$
$937$	39.1628	1.27939	0.639696	+	0.768628i	$0.279060\pi$
$938$	62.5256	2.04153
$939$	−2.59068	−0.0845435
$940$	−37.2070	−1.21356
$941$	38.8880	1.26771	0.633857	−	0.773450i	$-0.281471\pi$
$941$	38.8880	1.26771	0.633857	+	0.773450i	$0.281471\pi$
$942$	−1.12651	−0.0367036
$943$	14.8920	0.484951
$944$	3.45887	0.112577
$945$	24.9655	0.812127
$946$	−1.08142	−0.0351601
$947$	24.8251	0.806707	0.403354	−	0.915044i	$-0.367844\pi$
$947$	24.8251	0.806707	0.403354	+	0.915044i	$0.367844\pi$
$948$	−0.858851	−0.0278942
$949$	−31.4601	−1.02124
$950$	−6.59312	−0.213909
$951$	6.53372	0.211870
$952$	−28.6033	−0.927040
$953$	−5.85132	−0.189543	−0.0947714	−	0.995499i	$-0.530212\pi$
$953$	−5.85132	−0.189543	−0.0947714	+	0.995499i	$0.530212\pi$
$954$	13.5150	0.437565
$955$	50.8420	1.64521
$956$	−1.95645	−0.0632763
$957$	2.28941	0.0740061
$958$	−26.7183	−0.863230
$959$	−16.5158	−0.533322
$960$	−1.06183	−0.0342704
$961$	1.00000	0.0322581
$962$	−34.7969	−1.12190
$963$	−50.4227	−1.62485
$964$	16.0423	0.516687
$965$	10.7819	0.347082
$966$	4.43723	0.142765
$967$	37.8480	1.21711	0.608554	−	0.793512i	$-0.291750\pi$
$967$	37.8480	1.21711	0.608554	+	0.793512i	$0.291750\pi$
$968$	−8.59828	−0.276359
$969$	0.809680	0.0260107
$970$	−4.38700	−0.140858
$971$	3.59883	0.115492	0.0577460	−	0.998331i	$-0.481609\pi$
$971$	3.59883	0.115492	0.0577460	+	0.998331i	$0.481609\pi$
$972$	6.36576	0.204182
$973$	−59.0088	−1.89173
$974$	30.7412	0.985011
$975$	22.4324	0.718412
$976$	10.0104	0.320424
$977$	26.0290	0.832740	0.416370	−	0.909195i	$-0.363302\pi$
$977$	26.0290	0.832740	0.416370	+	0.909195i	$0.363302\pi$
$978$	2.34946	0.0751274
$979$	14.4551	0.461989
$980$	−37.9911	−1.21358
$981$	−8.39458	−0.268018
$982$	−10.8516	−0.346288
$983$	15.4050	0.491344	0.245672	−	0.969353i	$-0.420991\pi$
$983$	15.4050	0.491344	0.245672	+	0.969353i	$0.420991\pi$
$984$	0.778056	0.0248035
$985$	−27.2033	−0.866768
$986$	44.1161	1.40494
$987$	8.12342	0.258571
$988$	−3.01096	−0.0957915
$989$	3.23269	0.102794
$990$	−19.9980	−0.635577
$991$	−8.31048	−0.263991	−0.131996	−	0.991250i	$-0.542138\pi$
$991$	−8.31048	−0.263991	−0.131996	+	0.991250i	$0.542138\pi$
$992$	1.00000	0.0317500
$993$	3.63779	0.115442
$994$	−26.8203	−0.850688
$995$	81.9409	2.59770
$996$	−0.681602	−0.0215974
$997$	42.8991	1.35863	0.679314	−	0.733848i	$-0.262277\pi$
$997$	42.8991	1.35863	0.679314	+	0.733848i	$0.262277\pi$
$998$	−20.4422	−0.647086
$999$	7.69160	0.243351

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.k.1.18	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.k.1.18	✓	37	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:	\( N \)	\(=\)	\( 6014 = 2 \cdot 31 \cdot 97 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +0.242040 q^{3} +1.00000 q^{4} -4.38700 q^{5} +0.242040 q^{6} +3.95726 q^{7} +1.00000 q^{8} -2.94142 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +0.242040 q^{3} +1.00000 q^{4} -4.38700 q^{5} +0.242040 q^{6} +3.95726 q^{7} +1.00000 q^{8} -2.94142 q^{9} -4.38700 q^{10} -1.54975 q^{11} +0.242040 q^{12} +6.50581 q^{13} +3.95726 q^{14} -1.06183 q^{15} +1.00000 q^{16} -7.22807 q^{17} -2.94142 q^{18} -0.462811 q^{19} -4.38700 q^{20} +0.957815 q^{21} -1.54975 q^{22} +4.63265 q^{23} +0.242040 q^{24} +14.2458 q^{25} +6.50581 q^{26} -1.43806 q^{27} +3.95726 q^{28} -6.10344 q^{29} -1.06183 q^{30} +1.00000 q^{31} +1.00000 q^{32} -0.375101 q^{33} -7.22807 q^{34} -17.3605 q^{35} -2.94142 q^{36} -5.34859 q^{37} -0.462811 q^{38} +1.57467 q^{39} -4.38700 q^{40} +3.21458 q^{41} +0.957815 q^{42} +0.697805 q^{43} -1.54975 q^{44} +12.9040 q^{45} +4.63265 q^{46} +8.48120 q^{47} +0.242040 q^{48} +8.65991 q^{49} +14.2458 q^{50} -1.74948 q^{51} +6.50581 q^{52} -4.59473 q^{53} -1.43806 q^{54} +6.79876 q^{55} +3.95726 q^{56} -0.112019 q^{57} -6.10344 q^{58} +3.45887 q^{59} -1.06183 q^{60} +10.0104 q^{61} +1.00000 q^{62} -11.6400 q^{63} +1.00000 q^{64} -28.5410 q^{65} -0.375101 q^{66} +15.8002 q^{67} -7.22807 q^{68} +1.12129 q^{69} -17.3605 q^{70} -6.77749 q^{71} -2.94142 q^{72} -4.83570 q^{73} -5.34859 q^{74} +3.44806 q^{75} -0.462811 q^{76} -6.13276 q^{77} +1.57467 q^{78} -3.54838 q^{79} -4.38700 q^{80} +8.47618 q^{81} +3.21458 q^{82} -2.81607 q^{83} +0.957815 q^{84} +31.7096 q^{85} +0.697805 q^{86} -1.47728 q^{87} -1.54975 q^{88} -9.32741 q^{89} +12.9040 q^{90} +25.7452 q^{91} +4.63265 q^{92} +0.242040 q^{93} +8.48120 q^{94} +2.03036 q^{95} +0.242040 q^{96} +1.00000 q^{97} +8.65991 q^{98} +4.55846 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9}+O(q^{10}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9	\( 37 q + 37 q^{2} + 9 q^{3} + 37 q^{4} + 9 q^{5} + 9 q^{6} + 19 q^{7} + 37 q^{8} + 52 q^{9} + 9 q^{10} + 5 q^{11} + 9 q^{12} + 16 q^{13} + 19 q^{14} + 22 q^{15} + 37 q^{16} + 3 q^{17} + 52 q^{18} + 36 q^{19} + 9 q^{20} + 6 q^{21} + 5 q^{22} + 11 q^{23} + 9 q^{24} + 58 q^{25} + 16 q^{26} + 24 q^{27} + 19 q^{28} + 5 q^{29} + 22 q^{30} + 37 q^{31} + 37 q^{32} + q^{33} + 3 q^{34} + 28 q^{35} + 52 q^{36} + 21 q^{37} + 36 q^{38} + 38 q^{39} + 9 q^{40} + 21 q^{41} + 6 q^{42} + 14 q^{43} + 5 q^{44} + 55 q^{45} + 11 q^{46} + 59 q^{47} + 9 q^{48} + 82 q^{49} + 58 q^{50} + 46 q^{51} + 16 q^{52} + 8 q^{53} + 24 q^{54} + 25 q^{55} + 19 q^{56} + 5 q^{58} + 41 q^{59} + 22 q^{60} + 16 q^{61} + 37 q^{62} + 23 q^{63} + 37 q^{64} - 46 q^{65} + q^{66} + 45 q^{67} + 3 q^{68} + 68 q^{69} + 28 q^{70} + 55 q^{71} + 52 q^{72} + 29 q^{73} + 21 q^{74} - 12 q^{75} + 36 q^{76} + 30 q^{77} + 38 q^{78} + 25 q^{79} + 9 q^{80} + 73 q^{81} + 21 q^{82} + 70 q^{83} + 6 q^{84} - 21 q^{85} + 14 q^{86} + 37 q^{87} + 5 q^{88} + 55 q^{90} + 18 q^{91} + 11 q^{92} + 9 q^{93} + 59 q^{94} - 9 q^{95} + 9 q^{96} + 37 q^{97} + 82 q^{98} + 33 q^{99}+O(q^{100}) \) 37 * q + 37 * q^2 + 9 * q^3 + 37 * q^4 + 9 * q^5 + 9 * q^6 + 19 * q^7 + 37 * q^8 + 52 * q^9 + 9 * q^10 + 5 * q^11 + 9 * q^12 + 16 * q^13 + 19 * q^14 + 22 * q^15 + 37 * q^16 + 3 * q^17 + 52 * q^18 + 36 * q^19 + 9 * q^20 + 6 * q^21 + 5 * q^22 + 11 * q^23 + 9 * q^24 + 58 * q^25 + 16 * q^26 + 24 * q^27 + 19 * q^28 + 5 * q^29 + 22 * q^30 + 37 * q^31 + 37 * q^32 + q^33 + 3 * q^34 + 28 * q^35 + 52 * q^36 + 21 * q^37 + 36 * q^38 + 38 * q^39 + 9 * q^40 + 21 * q^41 + 6 * q^42 + 14 * q^43 + 5 * q^44 + 55 * q^45 + 11 * q^46 + 59 * q^47 + 9 * q^48 + 82 * q^49 + 58 * q^50 + 46 * q^51 + 16 * q^52 + 8 * q^53 + 24 * q^54 + 25 * q^55 + 19 * q^56 + 5 * q^58 + 41 * q^59 + 22 * q^60 + 16 * q^61 + 37 * q^62 + 23 * q^63 + 37 * q^64 - 46 * q^65 + q^66 + 45 * q^67 + 3 * q^68 + 68 * q^69 + 28 * q^70 + 55 * q^71 + 52 * q^72 + 29 * q^73 + 21 * q^74 - 12 * q^75 + 36 * q^76 + 30 * q^77 + 38 * q^78 + 25 * q^79 + 9 * q^80 + 73 * q^81 + 21 * q^82 + 70 * q^83 + 6 * q^84 - 21 * q^85 + 14 * q^86 + 37 * q^87 + 5 * q^88 + 55 * q^90 + 18 * q^91 + 11 * q^92 + 9 * q^93 + 59 * q^94 - 9 * q^95 + 9 * q^96 + 37 * q^97 + 82 * q^98 + 33 * q^99

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