LMFDB - Embedded newform 6014.2.a.j.1.17

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:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.00816480 q^{3} +1.00000 q^{4} +4.13053 q^{5} -0.00816480 q^{6} -5.05598 q^{7} -1.00000 q^{8} -2.99993 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.00816480 q^{3} +1.00000 q^{4} +4.13053 q^{5} -0.00816480 q^{6} -5.05598 q^{7} -1.00000 q^{8} -2.99993 q^{9} -4.13053 q^{10} +1.63632 q^{11} +0.00816480 q^{12} +7.11135 q^{13} +5.05598 q^{14} +0.0337250 q^{15} +1.00000 q^{16} -4.74535 q^{17} +2.99993 q^{18} -2.86273 q^{19} +4.13053 q^{20} -0.0412811 q^{21} -1.63632 q^{22} +3.51524 q^{23} -0.00816480 q^{24} +12.0613 q^{25} -7.11135 q^{26} -0.0489882 q^{27} -5.05598 q^{28} +6.31644 q^{29} -0.0337250 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.0133602 q^{33} +4.74535 q^{34} -20.8839 q^{35} -2.99993 q^{36} +3.47122 q^{37} +2.86273 q^{38} +0.0580627 q^{39} -4.13053 q^{40} +3.46184 q^{41} +0.0412811 q^{42} +3.09139 q^{43} +1.63632 q^{44} -12.3913 q^{45} -3.51524 q^{46} -3.16394 q^{47} +0.00816480 q^{48} +18.5629 q^{49} -12.0613 q^{50} -0.0387448 q^{51} +7.11135 q^{52} +4.85300 q^{53} +0.0489882 q^{54} +6.75889 q^{55} +5.05598 q^{56} -0.0233736 q^{57} -6.31644 q^{58} -10.4193 q^{59} +0.0337250 q^{60} -6.18501 q^{61} +1.00000 q^{62} +15.1676 q^{63} +1.00000 q^{64} +29.3736 q^{65} -0.0133602 q^{66} -3.36743 q^{67} -4.74535 q^{68} +0.0287012 q^{69} +20.8839 q^{70} -16.4171 q^{71} +2.99993 q^{72} -14.0281 q^{73} -3.47122 q^{74} +0.0984780 q^{75} -2.86273 q^{76} -8.27322 q^{77} -0.0580627 q^{78} -2.59962 q^{79} +4.13053 q^{80} +8.99940 q^{81} -3.46184 q^{82} +3.02702 q^{83} -0.0412811 q^{84} -19.6008 q^{85} -3.09139 q^{86} +0.0515725 q^{87} -1.63632 q^{88} +1.04305 q^{89} +12.3913 q^{90} -35.9548 q^{91} +3.51524 q^{92} -0.00816480 q^{93} +3.16394 q^{94} -11.8246 q^{95} -0.00816480 q^{96} +1.00000 q^{97} -18.5629 q^{98} -4.90886 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) $ 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * 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
$3$	0.00816480	0.00471395	0.00235697	−	0.999997i	$-0.499250\pi$
$3$	0.00816480	0.00471395	0.00235697	+	0.999997i	$0.499250\pi$
$4$	1.00000	0.500000
$5$	4.13053	1.84723	0.923615	−	0.383321i	$-0.125220\pi$
$5$	4.13053	1.84723	0.923615	+	0.383321i	$0.125220\pi$
$6$	−0.00816480	−0.00333326
$7$	−5.05598	−1.91098	−0.955491	−	0.295022i	$-0.904673\pi$
$7$	−5.05598	−1.91098	−0.955491	+	0.295022i	$0.904673\pi$
$8$	−1.00000	−0.353553
$9$	−2.99993	−0.999978
$10$	−4.13053	−1.30619
$11$	1.63632	0.493370	0.246685	−	0.969096i	$-0.420659\pi$
$11$	1.63632	0.493370	0.246685	+	0.969096i	$0.420659\pi$
$12$	0.00816480	0.00235697
$13$	7.11135	1.97233	0.986166	−	0.165758i	$-0.0530072\pi$
$13$	7.11135	1.97233	0.986166	+	0.165758i	$0.0530072\pi$
$14$	5.05598	1.35127
$15$	0.0337250	0.00870775
$16$	1.00000	0.250000
$17$	−4.74535	−1.15092	−0.575458	−	0.817832i	$-0.695176\pi$
$17$	−4.74535	−1.15092	−0.575458	+	0.817832i	$0.695176\pi$
$18$	2.99993	0.707091
$19$	−2.86273	−0.656755	−0.328377	−	0.944547i	$-0.606502\pi$
$19$	−2.86273	−0.656755	−0.328377	+	0.944547i	$0.606502\pi$
$20$	4.13053	0.923615
$21$	−0.0412811	−0.00900827
$22$	−1.63632	−0.348865
$23$	3.51524	0.732979	0.366489	−	0.930422i	$-0.380560\pi$
$23$	3.51524	0.732979	0.366489	+	0.930422i	$0.380560\pi$
$24$	−0.00816480	−0.00166663
$25$	12.0613	2.41226
$26$	−7.11135	−1.39465
$27$	−0.0489882	−0.00942779
$28$	−5.05598	−0.955491
$29$	6.31644	1.17293	0.586467	−	0.809973i	$-0.300518\pi$
$29$	6.31644	1.17293	0.586467	+	0.809973i	$0.300518\pi$
$30$	−0.0337250	−0.00615731
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.00000	−0.176777
$33$	0.0133602	0.00232572
$34$	4.74535	0.813820
$35$	−20.8839	−3.53002
$36$	−2.99993	−0.499989
$37$	3.47122	0.570666	0.285333	−	0.958429i	$-0.407896\pi$
$37$	3.47122	0.570666	0.285333	+	0.958429i	$0.407896\pi$
$38$	2.86273	0.464396
$39$	0.0580627	0.00929747
$40$	−4.13053	−0.653094
$41$	3.46184	0.540648	0.270324	−	0.962769i	$-0.412869\pi$
$41$	3.46184	0.540648	0.270324	+	0.962769i	$0.412869\pi$
$42$	0.0412811	0.00636981
$43$	3.09139	0.471433	0.235716	−	0.971822i	$-0.424256\pi$
$43$	3.09139	0.471433	0.235716	+	0.971822i	$0.424256\pi$
$44$	1.63632	0.246685
$45$	−12.3913	−1.84719
$46$	−3.51524	−0.518294
$47$	−3.16394	−0.461508	−0.230754	−	0.973012i	$-0.574119\pi$
$47$	−3.16394	−0.461508	−0.230754	+	0.973012i	$0.574119\pi$
$48$	0.00816480	0.00117849
$49$	18.5629	2.65185
$50$	−12.0613	−1.70572
$51$	−0.0387448	−0.00542536
$52$	7.11135	0.986166
$53$	4.85300	0.666611	0.333306	−	0.942819i	$-0.391836\pi$
$53$	4.85300	0.666611	0.333306	+	0.942819i	$0.391836\pi$
$54$	0.0489882	0.00666645
$55$	6.75889	0.911368
$56$	5.05598	0.675634
$57$	−0.0233736	−0.00309591
$58$	−6.31644	−0.829390
$59$	−10.4193	−1.35648	−0.678241	−	0.734840i	$-0.737257\pi$
$59$	−10.4193	−1.35648	−0.678241	+	0.734840i	$0.737257\pi$
$60$	0.0337250	0.00435387
$61$	−6.18501	−0.791910	−0.395955	−	0.918270i	$-0.629586\pi$
$61$	−6.18501	−0.791910	−0.395955	+	0.918270i	$0.629586\pi$
$62$	1.00000	0.127000
$63$	15.1676	1.91094
$64$	1.00000	0.125000
$65$	29.3736	3.64335
$66$	−0.0133602	−0.00164453
$67$	−3.36743	−0.411397	−0.205698	−	0.978615i	$-0.565947\pi$
$67$	−3.36743	−0.411397	−0.205698	+	0.978615i	$0.565947\pi$
$68$	−4.74535	−0.575458
$69$	0.0287012	0.00345522
$70$	20.8839	2.49610
$71$	−16.4171	−1.94836	−0.974178	−	0.225783i	$-0.927506\pi$
$71$	−16.4171	−1.94836	−0.974178	+	0.225783i	$0.927506\pi$
$72$	2.99993	0.353546
$73$	−14.0281	−1.64186	−0.820930	−	0.571029i	$-0.806544\pi$
$73$	−14.0281	−1.64186	−0.820930	+	0.571029i	$0.806544\pi$
$74$	−3.47122	−0.403522
$75$	0.0984780	0.0113713
$76$	−2.86273	−0.328377
$77$	−8.27322	−0.942821
$78$	−0.0580627	−0.00657431
$79$	−2.59962	−0.292481	−0.146240	−	0.989249i	$-0.546717\pi$
$79$	−2.59962	−0.292481	−0.146240	+	0.989249i	$0.546717\pi$
$80$	4.13053	0.461808
$81$	8.99940	0.999933
$82$	−3.46184	−0.382296
$83$	3.02702	0.332259	0.166129	−	0.986104i	$-0.446873\pi$
$83$	3.02702	0.332259	0.166129	+	0.986104i	$0.446873\pi$
$84$	−0.0412811	−0.00450413
$85$	−19.6008	−2.12601
$86$	−3.09139	−0.333353
$87$	0.0515725	0.00552915
$88$	−1.63632	−0.174433
$89$	1.04305	0.110563	0.0552817	−	0.998471i	$-0.482394\pi$
$89$	1.04305	0.110563	0.0552817	+	0.998471i	$0.482394\pi$
$90$	12.3913	1.30616
$91$	−35.9548	−3.76909
$92$	3.51524	0.366489
$93$	−0.00816480	−0.000846650 0
$94$	3.16394	0.326336
$95$	−11.8246	−1.21318
$96$	−0.00816480	−0.000833316 0
$97$	1.00000	0.101535
$97$	1.00000	0.101535
$98$	−18.5629	−1.87514
$99$	−4.90886	−0.493359
$100$	12.0613	1.20613
$101$	−1.09965	−0.109419	−0.0547094	−	0.998502i	$-0.517423\pi$
$101$	−1.09965	−0.109419	−0.0547094	+	0.998502i	$0.517423\pi$
$102$	0.0387448	0.00383631
$103$	18.6367	1.83633	0.918165	−	0.396199i	$-0.129671\pi$
$103$	18.6367	1.83633	0.918165	+	0.396199i	$0.129671\pi$
$104$	−7.11135	−0.697325
$105$	−0.170513	−0.0166403
$106$	−4.85300	−0.471365
$107$	−2.86324	−0.276799	−0.138400	−	0.990376i	$-0.544196\pi$
$107$	−2.86324	−0.276799	−0.138400	+	0.990376i	$0.544196\pi$
$108$	−0.0489882	−0.00471390
$109$	10.9718	1.05091	0.525454	−	0.850822i	$-0.323896\pi$
$109$	10.9718	1.05091	0.525454	+	0.850822i	$0.323896\pi$
$110$	−6.75889	−0.644434
$111$	0.0283418	0.00269009
$112$	−5.05598	−0.477745
$113$	17.1312	1.61157	0.805785	−	0.592208i	$-0.201744\pi$
$113$	17.1312	1.61157	0.805785	+	0.592208i	$0.201744\pi$
$114$	0.0233736	0.00218914
$115$	14.5198	1.35398
$116$	6.31644	0.586467
$117$	−21.3336	−1.97229
$118$	10.4193	0.959178
$119$	23.9924	2.19938
$120$	−0.0337250	−0.00307865
$121$	−8.32245	−0.756586
$122$	6.18501	0.559965
$123$	0.0282652	0.00254859
$124$	−1.00000	−0.0898027
$125$	29.1669	2.60877
$126$	−15.1676	−1.35124
$127$	7.96363	0.706658	0.353329	−	0.935499i	$-0.385050\pi$
$127$	7.96363	0.706658	0.353329	+	0.935499i	$0.385050\pi$
$128$	−1.00000	−0.0883883
$129$	0.0252406	0.00222231
$130$	−29.3736	−2.57624
$131$	9.08467	0.793731	0.396865	−	0.917877i	$-0.370098\pi$
$131$	9.08467	0.793731	0.396865	+	0.917877i	$0.370098\pi$
$132$	0.0133602	0.00116286
$133$	14.4739	1.25505
$134$	3.36743	0.290901
$135$	−0.202348	−0.0174153
$136$	4.74535	0.406910
$137$	15.5658	1.32988	0.664940	−	0.746897i	$-0.268457\pi$
$137$	15.5658	1.32988	0.664940	+	0.746897i	$0.268457\pi$
$138$	−0.0287012	−0.00244321
$139$	−8.96916	−0.760754	−0.380377	−	0.924832i	$-0.624206\pi$
$139$	−8.96916	−0.760754	−0.380377	+	0.924832i	$0.624206\pi$
$140$	−20.8839	−1.76501
$141$	−0.0258329	−0.00217553
$142$	16.4171	1.37770
$143$	11.6365	0.973090
$144$	−2.99993	−0.249994
$145$	26.0903	2.16668
$146$	14.0281	1.16097
$147$	0.151563	0.0125007
$148$	3.47122	0.285333
$149$	21.6417	1.77295	0.886477	−	0.462773i	$-0.153145\pi$
$149$	21.6417	1.77295	0.886477	+	0.462773i	$0.153145\pi$
$150$	−0.0984780	−0.00804070
$151$	16.8785	1.37355	0.686776	−	0.726870i	$-0.259026\pi$
$151$	16.8785	1.37355	0.686776	+	0.726870i	$0.259026\pi$
$152$	2.86273	0.232198
$153$	14.2357	1.15089
$154$	8.27322	0.666675
$155$	−4.13053	−0.331772
$156$	0.0580627	0.00464874
$157$	−6.66381	−0.531830	−0.265915	−	0.963996i	$-0.585674\pi$
$157$	−6.66381	−0.531830	−0.265915	+	0.963996i	$0.585674\pi$
$158$	2.59962	0.206815
$159$	0.0396238	0.00314237
$160$	−4.13053	−0.326547
$161$	−17.7730	−1.40071
$162$	−8.99940	−0.707060
$163$	5.09860	0.399353	0.199677	−	0.979862i	$-0.436011\pi$
$163$	5.09860	0.399353	0.199677	+	0.979862i	$0.436011\pi$
$164$	3.46184	0.270324
$165$	0.0551849	0.00429614
$166$	−3.02702	−0.234943
$167$	10.1304	0.783916	0.391958	−	0.919983i	$-0.371798\pi$
$167$	10.1304	0.783916	0.391958	+	0.919983i	$0.371798\pi$
$168$	0.0412811	0.00318490
$169$	37.5713	2.89010
$170$	19.6008	1.50331
$171$	8.58799	0.656740
$172$	3.09139	0.235716
$173$	−20.7354	−1.57648	−0.788242	−	0.615365i	$-0.789009\pi$
$173$	−20.7354	−1.57648	−0.788242	+	0.615365i	$0.789009\pi$
$174$	−0.0515725	−0.00390970
$175$	−60.9817	−4.60978
$176$	1.63632	0.123342
$177$	−0.0850718	−0.00639438
$178$	−1.04305	−0.0781801
$179$	−8.13021	−0.607680	−0.303840	−	0.952723i	$-0.598269\pi$
$179$	−8.13021	−0.607680	−0.303840	+	0.952723i	$0.598269\pi$
$180$	−12.3913	−0.923595
$181$	10.4489	0.776662	0.388331	−	0.921520i	$-0.373052\pi$
$181$	10.4489	0.776662	0.388331	+	0.921520i	$0.373052\pi$
$182$	35.9548	2.66515
$183$	−0.0504994	−0.00373302
$184$	−3.51524	−0.259147
$185$	14.3380	1.05415
$186$	0.00816480	0.000598672 0
$187$	−7.76492	−0.567827
$188$	−3.16394	−0.230754
$189$	0.247684	0.0180163
$190$	11.8246	0.857846
$191$	20.9017	1.51239	0.756197	−	0.654344i	$-0.227055\pi$
$191$	20.9017	1.51239	0.756197	+	0.654344i	$0.227055\pi$
$192$	0.00816480	0.000589243 0
$193$	−12.0832	−0.869768	−0.434884	−	0.900487i	$-0.643211\pi$
$193$	−12.0832	−0.869768	−0.434884	+	0.900487i	$0.643211\pi$
$194$	−1.00000	−0.0717958
$195$	0.239830	0.0171746
$196$	18.5629	1.32592
$197$	−12.9114	−0.919901	−0.459950	−	0.887945i	$-0.652133\pi$
$197$	−12.9114	−0.919901	−0.459950	+	0.887945i	$0.652133\pi$
$198$	4.90886	0.348858
$199$	13.4145	0.950931	0.475466	−	0.879734i	$-0.342280\pi$
$199$	13.4145	0.950931	0.475466	+	0.879734i	$0.342280\pi$
$200$	−12.0613	−0.852862
$201$	−0.0274944	−0.00193930
$202$	1.09965	0.0773708
$203$	−31.9358	−2.24145
$204$	−0.0387448	−0.00271268
$205$	14.2992	0.998702
$206$	−18.6367	−1.29848
$207$	−10.5455	−0.732962
$208$	7.11135	0.493083
$209$	−4.68435	−0.324023
$210$	0.170513	0.0117665
$211$	4.56635	0.314360	0.157180	−	0.987570i	$-0.449760\pi$
$211$	4.56635	0.314360	0.157180	+	0.987570i	$0.449760\pi$
$212$	4.85300	0.333306
$213$	−0.134043	−0.00918444
$214$	2.86324	0.195727
$215$	12.7691	0.870844
$216$	0.0489882	0.00333323
$217$	5.05598	0.343222
$218$	−10.9718	−0.743104
$219$	−0.114536	−0.00773964
$220$	6.75889	0.455684
$221$	−33.7458	−2.26999
$222$	−0.0283418	−0.00190218
$223$	4.87565	0.326498	0.163249	−	0.986585i	$-0.447803\pi$
$223$	4.87565	0.326498	0.163249	+	0.986585i	$0.447803\pi$
$224$	5.05598	0.337817
$225$	−36.1831	−2.41221
$226$	−17.1312	−1.13955
$227$	26.2778	1.74412	0.872059	−	0.489401i	$-0.162785\pi$
$227$	26.2778	1.74412	0.872059	+	0.489401i	$0.162785\pi$
$228$	−0.0233736	−0.00154795
$229$	−5.58111	−0.368810	−0.184405	−	0.982850i	$-0.559036\pi$
$229$	−5.58111	−0.368810	−0.184405	+	0.982850i	$0.559036\pi$
$230$	−14.5198	−0.957409
$231$	−0.0675491	−0.00444441
$232$	−6.31644	−0.414695
$233$	−2.91580	−0.191020	−0.0955101	−	0.995428i	$-0.530448\pi$
$233$	−2.91580	−0.191020	−0.0955101	+	0.995428i	$0.530448\pi$
$234$	21.3336	1.39462
$235$	−13.0688	−0.852512
$236$	−10.4193	−0.678241
$237$	−0.0212254	−0.00137874
$238$	−23.9924	−1.55519
$239$	13.0961	0.847119	0.423560	−	0.905868i	$-0.360780\pi$
$239$	13.0961	0.847119	0.423560	+	0.905868i	$0.360780\pi$
$240$	0.0337250	0.00217694
$241$	−9.40883	−0.606076	−0.303038	−	0.952978i	$-0.598001\pi$
$241$	−9.40883	−0.606076	−0.303038	+	0.952978i	$0.598001\pi$
$242$	8.32245	0.534987
$243$	0.220443	0.0141414
$244$	−6.18501	−0.395955
$245$	76.6748	4.89857
$246$	−0.0282652	−0.00180212
$247$	−20.3578	−1.29534
$248$	1.00000	0.0635001
$249$	0.0247150	0.00156625
$250$	−29.1669	−1.84468
$251$	29.5281	1.86380	0.931900	−	0.362715i	$-0.118150\pi$
$251$	29.5281	1.86380	0.931900	+	0.362715i	$0.118150\pi$
$252$	15.1676	0.955469
$253$	5.75207	0.361630
$254$	−7.96363	−0.499683
$255$	−0.160037	−0.0100219
$256$	1.00000	0.0625000
$257$	5.52076	0.344375	0.172188	−	0.985064i	$-0.444916\pi$
$257$	5.52076	0.344375	0.172188	+	0.985064i	$0.444916\pi$
$258$	−0.0252406	−0.00157141
$259$	−17.5504	−1.09053
$260$	29.3736	1.82168
$261$	−18.9489	−1.17291
$262$	−9.08467	−0.561252
$263$	11.5844	0.714322	0.357161	−	0.934043i	$-0.383745\pi$
$263$	11.5844	0.714322	0.357161	+	0.934043i	$0.383745\pi$
$264$	−0.0133602	−0.000822266 0
$265$	20.0455	1.23138
$266$	−14.4739	−0.887451
$267$	0.00851631	0.000521190 0
$268$	−3.36743	−0.205698
$269$	20.7634	1.26597	0.632985	−	0.774164i	$-0.281830\pi$
$269$	20.7634	1.26597	0.632985	+	0.774164i	$0.281830\pi$
$270$	0.202348	0.0123145
$271$	26.9428	1.63666	0.818330	−	0.574749i	$-0.194900\pi$
$271$	26.9428	1.63666	0.818330	+	0.574749i	$0.194900\pi$
$272$	−4.74535	−0.287729
$273$	−0.293564	−0.0177673
$274$	−15.5658	−0.940367
$275$	19.7362	1.19014
$276$	0.0287012	0.00172761
$277$	−30.6635	−1.84239	−0.921197	−	0.389097i	$-0.872787\pi$
$277$	−30.6635	−1.84239	−0.921197	+	0.389097i	$0.872787\pi$
$278$	8.96916	0.537934
$279$	2.99993	0.179601
$280$	20.8839	1.24805
$281$	−3.99823	−0.238514	−0.119257	−	0.992863i	$-0.538051\pi$
$281$	−3.99823	−0.238514	−0.119257	+	0.992863i	$0.538051\pi$
$282$	0.0258329	0.00153833
$283$	−3.25705	−0.193612	−0.0968058	−	0.995303i	$-0.530863\pi$
$283$	−3.25705	−0.193612	−0.0968058	+	0.995303i	$0.530863\pi$
$284$	−16.4171	−0.974178
$285$	−0.0965453	−0.00571885
$286$	−11.6365	−0.688078
$287$	−17.5030	−1.03317
$288$	2.99993	0.176773
$289$	5.51831	0.324606
$290$	−26.0903	−1.53207
$291$	0.00816480	0.000478629 0
$292$	−14.0281	−0.820930
$293$	11.8289	0.691051	0.345525	−	0.938409i	$-0.387701\pi$
$293$	11.8289	0.691051	0.345525	+	0.938409i	$0.387701\pi$
$294$	−0.151563	−0.00883931
$295$	−43.0374	−2.50573
$296$	−3.47122	−0.201761
$297$	−0.0801606	−0.00465139
$298$	−21.6417	−1.25367
$299$	24.9981	1.44568
$300$	0.0984780	0.00568563
$301$	−15.6300	−0.900899
$302$	−16.8785	−0.971247
$303$	−0.00897838	−0.000515794 0
$304$	−2.86273	−0.164189
$305$	−25.5474	−1.46284
$306$	−14.2357	−0.813802
$307$	−11.0294	−0.629484	−0.314742	−	0.949177i	$-0.601918\pi$
$307$	−11.0294	−0.629484	−0.314742	+	0.949177i	$0.601918\pi$
$308$	−8.27322	−0.471410
$309$	0.152165	0.00865636
$310$	4.13053	0.234598
$311$	13.9971	0.793704	0.396852	−	0.917883i	$-0.370103\pi$
$311$	13.9971	0.793704	0.396852	+	0.917883i	$0.370103\pi$
$312$	−0.0580627	−0.00328715
$313$	−30.4926	−1.72354	−0.861772	−	0.507295i	$-0.830645\pi$
$313$	−30.4926	−1.72354	−0.861772	+	0.507295i	$0.830645\pi$
$314$	6.66381	0.376061
$315$	62.6503	3.52994
$316$	−2.59962	−0.146240
$317$	33.8372	1.90049	0.950244	−	0.311507i	$-0.100834\pi$
$317$	33.8372	1.90049	0.950244	+	0.311507i	$0.100834\pi$
$318$	−0.0396238	−0.00222199
$319$	10.3357	0.578690
$320$	4.13053	0.230904
$321$	−0.0233777	−0.00130482
$322$	17.7730	0.990450
$323$	13.5846	0.755869
$324$	8.99940	0.499967
$325$	85.7721	4.75778
$326$	−5.09860	−0.282385
$327$	0.0895825	0.00495392
$328$	−3.46184	−0.191148
$329$	15.9968	0.881934
$330$	−0.0551849	−0.00303783
$331$	31.6924	1.74197	0.870987	−	0.491307i	$-0.163481\pi$
$331$	31.6924	1.74197	0.870987	+	0.491307i	$0.163481\pi$
$332$	3.02702	0.166129
$333$	−10.4134	−0.570653
$334$	−10.1304	−0.554312
$335$	−13.9093	−0.759944
$336$	−0.0412811	−0.00225207
$337$	−29.7355	−1.61980	−0.809898	−	0.586571i	$-0.800478\pi$
$337$	−29.7355	−1.61980	−0.809898	+	0.586571i	$0.800478\pi$
$338$	−37.5713	−2.04361
$339$	0.139873	0.00759686
$340$	−19.6008	−1.06300
$341$	−1.63632	−0.0886119
$342$	−8.58799	−0.464385
$343$	−58.4620	−3.15665
$344$	−3.09139	−0.166677
$345$	0.118551	0.00638259
$346$	20.7354	1.11474
$347$	−34.1399	−1.83272	−0.916362	−	0.400350i	$-0.868889\pi$
$347$	−34.1399	−1.83272	−0.916362	+	0.400350i	$0.868889\pi$
$348$	0.0515725	0.00276457
$349$	10.5456	0.564492	0.282246	−	0.959342i	$-0.408920\pi$
$349$	10.5456	0.564492	0.282246	+	0.959342i	$0.408920\pi$
$350$	60.9817	3.25961
$351$	−0.348372	−0.0185947
$352$	−1.63632	−0.0872163
$353$	−21.3309	−1.13533	−0.567663	−	0.823261i	$-0.692153\pi$
$353$	−21.3309	−1.13533	−0.567663	+	0.823261i	$0.692153\pi$
$354$	0.0850718	0.00452151
$355$	−67.8115	−3.59906
$356$	1.04305	0.0552817
$357$	0.195893	0.0103678
$358$	8.13021	0.429695
$359$	5.17414	0.273081	0.136540	−	0.990635i	$-0.456402\pi$
$359$	5.17414	0.273081	0.136540	+	0.990635i	$0.456402\pi$
$360$	12.3913	0.653080
$361$	−10.8048	−0.568674
$362$	−10.4489	−0.549183
$363$	−0.0679511	−0.00356651
$364$	−35.9548	−1.88455
$365$	−57.9433	−3.03289
$366$	0.0504994	0.00263964
$367$	−15.4167	−0.804745	−0.402373	−	0.915476i	$-0.631814\pi$
$367$	−15.4167	−0.804745	−0.402373	+	0.915476i	$0.631814\pi$
$368$	3.51524	0.183245
$369$	−10.3853	−0.540636
$370$	−14.3380	−0.745397
$371$	−24.5367	−1.27388
$372$	−0.00816480	−0.000423325 0
$373$	16.5222	0.855488	0.427744	−	0.903900i	$-0.359308\pi$
$373$	16.5222	0.855488	0.427744	+	0.903900i	$0.359308\pi$
$374$	7.76492	0.401514
$375$	0.238142	0.0122976
$376$	3.16394	0.163168
$377$	44.9184	2.31342
$378$	−0.247684	−0.0127395
$379$	17.4199	0.894799	0.447399	−	0.894334i	$-0.352350\pi$
$379$	17.4199	0.894799	0.447399	+	0.894334i	$0.352350\pi$
$380$	−11.8246	−0.606588
$381$	0.0650215	0.00333115
$382$	−20.9017	−1.06942
$383$	31.2611	1.59737	0.798683	−	0.601753i	$-0.205531\pi$
$383$	31.2611	1.59737	0.798683	+	0.601753i	$0.205531\pi$
$384$	−0.00816480	−0.000416658 0
$385$	−34.1728	−1.74161
$386$	12.0832	0.615019
$387$	−9.27396	−0.471422
$388$	1.00000	0.0507673
$389$	2.26631	0.114906	0.0574531	−	0.998348i	$-0.481702\pi$
$389$	2.26631	0.114906	0.0574531	+	0.998348i	$0.481702\pi$
$390$	−0.239830	−0.0121443
$391$	−16.6810	−0.843596
$392$	−18.5629	−0.937570
$393$	0.0741744	0.00374161
$394$	12.9114	0.650468
$395$	−10.7378	−0.540279
$396$	−4.90886	−0.246680
$397$	13.4330	0.674183	0.337092	−	0.941472i	$-0.390557\pi$
$397$	13.4330	0.674183	0.337092	+	0.941472i	$0.390557\pi$
$398$	−13.4145	−0.672410
$399$	0.118176	0.00591622
$400$	12.0613	0.603065
$401$	0.775879	0.0387456	0.0193728	−	0.999812i	$-0.493833\pi$
$401$	0.775879	0.0387456	0.0193728	+	0.999812i	$0.493833\pi$
$402$	0.0274944	0.00137129
$403$	−7.11135	−0.354241
$404$	−1.09965	−0.0547094
$405$	37.1723	1.84711
$406$	31.9358	1.58495
$407$	5.68004	0.281549
$408$	0.0387448	0.00191815
$409$	9.19985	0.454903	0.227452	−	0.973789i	$-0.426961\pi$
$409$	9.19985	0.454903	0.227452	+	0.973789i	$0.426961\pi$
$410$	−14.2992	−0.706189
$411$	0.127092	0.00626898
$412$	18.6367	0.918165
$413$	52.6800	2.59221
$414$	10.5455	0.518283
$415$	12.5032	0.613759
$416$	−7.11135	−0.348662
$417$	−0.0732314	−0.00358615
$418$	4.68435	0.229119
$419$	12.2091	0.596455	0.298228	−	0.954495i	$-0.403605\pi$
$419$	12.2091	0.596455	0.298228	+	0.954495i	$0.403605\pi$
$420$	−0.170513	−0.00832017
$421$	11.8252	0.576323	0.288162	−	0.957582i	$-0.406956\pi$
$421$	11.8252	0.576323	0.288162	+	0.957582i	$0.406956\pi$
$422$	−4.56635	−0.222286
$423$	9.49162	0.461498
$424$	−4.85300	−0.235683
$425$	−57.2350	−2.77631
$426$	0.134043	0.00649438
$427$	31.2713	1.51332
$428$	−2.86324	−0.138400
$429$	0.0950093	0.00458709
$430$	−12.7691	−0.615780
$431$	12.8137	0.617214	0.308607	−	0.951190i	$-0.400137\pi$
$431$	12.8137	0.617214	0.308607	+	0.951190i	$0.400137\pi$
$432$	−0.0489882	−0.00235695
$433$	2.15822	0.103717	0.0518587	−	0.998654i	$-0.483485\pi$
$433$	2.15822	0.103717	0.0518587	+	0.998654i	$0.483485\pi$
$434$	−5.05598	−0.242695
$435$	0.213022	0.0102136
$436$	10.9718	0.525454
$437$	−10.0632	−0.481387
$438$	0.114536	0.00547275
$439$	18.8607	0.900172	0.450086	−	0.892985i	$-0.351393\pi$
$439$	18.8607	0.900172	0.450086	+	0.892985i	$0.351393\pi$
$440$	−6.75889	−0.322217
$441$	−55.6876	−2.65179
$442$	33.7458	1.60512
$443$	−27.1352	−1.28923	−0.644617	−	0.764506i	$-0.722983\pi$
$443$	−27.1352	−1.28923	−0.644617	+	0.764506i	$0.722983\pi$
$444$	0.0283418	0.00134504
$445$	4.30836	0.204236
$446$	−4.87565	−0.230869
$447$	0.176700	0.00835761
$448$	−5.05598	−0.238873
$449$	−19.4714	−0.918912	−0.459456	−	0.888200i	$-0.651956\pi$
$449$	−19.4714	−0.918912	−0.459456	+	0.888200i	$0.651956\pi$
$450$	36.1831	1.70569
$451$	5.66468	0.266740
$452$	17.1312	0.805785
$453$	0.137809	0.00647485
$454$	−26.2778	−1.23328
$455$	−148.513	−6.96238
$456$	0.0233736	0.00109457
$457$	32.3524	1.51338	0.756691	−	0.653772i	$-0.226815\pi$
$457$	32.3524	1.51338	0.756691	+	0.653772i	$0.226815\pi$
$458$	5.58111	0.260788
$459$	0.232466	0.0108506
$460$	14.5198	0.676990
$461$	−19.5564	−0.910832	−0.455416	−	0.890279i	$-0.650510\pi$
$461$	−19.5564	−0.910832	−0.455416	+	0.890279i	$0.650510\pi$
$462$	0.0675491	0.00314267
$463$	−20.5023	−0.952824	−0.476412	−	0.879222i	$-0.658063\pi$
$463$	−20.5023	−0.952824	−0.476412	+	0.879222i	$0.658063\pi$
$464$	6.31644	0.293234
$465$	−0.0337250	−0.00156396
$466$	2.91580	0.135072
$467$	6.80208	0.314763	0.157381	−	0.987538i	$-0.449695\pi$
$467$	6.80208	0.314763	0.157381	+	0.987538i	$0.449695\pi$
$468$	−21.3336	−0.986144
$469$	17.0256	0.786171
$470$	13.0688	0.602817
$471$	−0.0544087	−0.00250702
$472$	10.4193	0.479589
$473$	5.05851	0.232591
$474$	0.0212254	0.000974915 0
$475$	−34.5282	−1.58426
$476$	23.9924	1.09969
$477$	−14.5587	−0.666596
$478$	−13.0961	−0.599004
$479$	−13.2665	−0.606163	−0.303081	−	0.952965i	$-0.598015\pi$
$479$	−13.2665	−0.606163	−0.303081	+	0.952965i	$0.598015\pi$
$480$	−0.0337250	−0.00153933
$481$	24.6851	1.12554
$482$	9.40883	0.428560
$483$	−0.145113	−0.00660287
$484$	−8.32245	−0.378293
$485$	4.13053	0.187558
$486$	−0.220443	−0.00999950
$487$	3.44539	0.156126	0.0780628	−	0.996948i	$-0.475127\pi$
$487$	3.44539	0.156126	0.0780628	+	0.996948i	$0.475127\pi$
$488$	6.18501	0.279982
$489$	0.0416290	0.00188253
$490$	−76.6748	−3.46382
$491$	−38.0498	−1.71716	−0.858582	−	0.512676i	$-0.828654\pi$
$491$	−38.0498	−1.71716	−0.858582	+	0.512676i	$0.828654\pi$
$492$	0.0282652	0.00127429
$493$	−29.9737	−1.34995
$494$	20.3578	0.915943
$495$	−20.2762	−0.911348
$496$	−1.00000	−0.0449013
$497$	83.0047	3.72327
$498$	−0.0247150	−0.00110751
$499$	−0.992190	−0.0444165	−0.0222083	−	0.999753i	$-0.507070\pi$
$499$	−0.992190	−0.0444165	−0.0222083	+	0.999753i	$0.507070\pi$
$500$	29.1669	1.30438
$501$	0.0827129	0.00369534
$502$	−29.5281	−1.31791
$503$	−14.8666	−0.662870	−0.331435	−	0.943478i	$-0.607533\pi$
$503$	−14.8666	−0.662870	−0.331435	+	0.943478i	$0.607533\pi$
$504$	−15.1676	−0.675619
$505$	−4.54212	−0.202122
$506$	−5.75207	−0.255711
$507$	0.306762	0.0136238
$508$	7.96363	0.353329
$509$	35.2271	1.56141	0.780707	−	0.624898i	$-0.214859\pi$
$509$	35.2271	1.56141	0.780707	+	0.624898i	$0.214859\pi$
$510$	0.160037	0.00708654
$511$	70.9256	3.13756
$512$	−1.00000	−0.0441942
$513$	0.140240	0.00619174
$514$	−5.52076	−0.243510
$515$	76.9795	3.39212
$516$	0.0252406	0.00111115
$517$	−5.17723	−0.227694
$518$	17.5504	0.771122
$519$	−0.169300	−0.00743146
$520$	−29.3736	−1.28812
$521$	−16.7513	−0.733887	−0.366944	−	0.930243i	$-0.619596\pi$
$521$	−16.7513	−0.733887	−0.366944	+	0.930243i	$0.619596\pi$
$522$	18.9489	0.829371
$523$	−11.8271	−0.517161	−0.258581	−	0.965990i	$-0.583255\pi$
$523$	−11.8271	−0.517161	−0.258581	+	0.965990i	$0.583255\pi$
$524$	9.08467	0.396865
$525$	−0.497903	−0.0217303
$526$	−11.5844	−0.505102
$527$	4.74535	0.206711
$528$	0.0133602	0.000581430 0
$529$	−10.6431	−0.462742
$530$	−20.0455	−0.870720
$531$	31.2573	1.35645
$532$	14.4739	0.627523
$533$	24.6183	1.06634
$534$	−0.00851631	−0.000368537 0
$535$	−11.8267	−0.511312
$536$	3.36743	0.145451
$537$	−0.0663815	−0.00286457
$538$	−20.7634	−0.895175
$539$	30.3750	1.30834
$540$	−0.202348	−0.00870765
$541$	7.59924	0.326717	0.163358	−	0.986567i	$-0.447767\pi$
$541$	7.59924	0.326717	0.163358	+	0.986567i	$0.447767\pi$
$542$	−26.9428	−1.15729
$543$	0.0853133	0.00366114
$544$	4.74535	0.203455
$545$	45.3193	1.94127
$546$	0.293564	0.0125634
$547$	−32.8792	−1.40581	−0.702907	−	0.711281i	$-0.748115\pi$
$547$	−32.8792	−1.40581	−0.702907	+	0.711281i	$0.748115\pi$
$548$	15.5658	0.664940
$549$	18.5546	0.791892
$550$	−19.7362	−0.841553
$551$	−18.0822	−0.770330
$552$	−0.0287012	−0.00122161
$553$	13.1436	0.558925
$554$	30.6635	1.30277
$555$	0.117067	0.00496921
$556$	−8.96916	−0.380377
$557$	−8.99653	−0.381195	−0.190598	−	0.981668i	$-0.561043\pi$
$557$	−8.99653	−0.381195	−0.190598	+	0.981668i	$0.561043\pi$
$558$	−2.99993	−0.126997
$559$	21.9839	0.929822
$560$	−20.8839	−0.882505
$561$	−0.0633990	−0.00267671
$562$	3.99823	0.168655
$563$	−22.5988	−0.952427	−0.476214	−	0.879330i	$-0.657991\pi$
$563$	−22.5988	−0.952427	−0.476214	+	0.879330i	$0.657991\pi$
$564$	−0.0258329	−0.00108776
$565$	70.7611	2.97694
$566$	3.25705	0.136904
$567$	−45.5008	−1.91085
$568$	16.4171	0.688848
$569$	−11.5611	−0.484668	−0.242334	−	0.970193i	$-0.577913\pi$
$569$	−11.5611	−0.484668	−0.242334	+	0.970193i	$0.577913\pi$
$570$	0.0965453	0.00404384
$571$	−37.5019	−1.56941	−0.784704	−	0.619871i	$-0.787185\pi$
$571$	−37.5019	−1.56941	−0.784704	+	0.619871i	$0.787185\pi$
$572$	11.6365	0.486545
$573$	0.170658	0.00712935
$574$	17.5030	0.730560
$575$	42.3984	1.76813
$576$	−2.99993	−0.124997
$577$	0.145996	0.00607790	0.00303895	−	0.999995i	$-0.499033\pi$
$577$	0.145996	0.00607790	0.00303895	+	0.999995i	$0.499033\pi$
$578$	−5.51831	−0.229531
$579$	−0.0986569	−0.00410004
$580$	26.0903	1.08334
$581$	−15.3046	−0.634941
$582$	−0.00816480	−0.000338442 0
$583$	7.94108	0.328886
$584$	14.0281	0.580485
$585$	−88.1190	−3.64327
$586$	−11.8289	−0.488647
$587$	−5.54898	−0.229031	−0.114515	−	0.993421i	$-0.536532\pi$
$587$	−5.54898	−0.229031	−0.114515	+	0.993421i	$0.536532\pi$
$588$	0.151563	0.00625034
$589$	2.86273	0.117957
$590$	43.0374	1.77182
$591$	−0.105419	−0.00433636
$592$	3.47122	0.142666
$593$	3.43299	0.140976	0.0704880	−	0.997513i	$-0.477544\pi$
$593$	3.43299	0.140976	0.0704880	+	0.997513i	$0.477544\pi$
$594$	0.0801606	0.00328903
$595$	99.1013	4.06276
$596$	21.6417	0.886477
$597$	0.109527	0.00448264
$598$	−24.9981	−1.02225
$599$	38.4983	1.57300	0.786499	−	0.617591i	$-0.211891\pi$
$599$	38.4983	1.57300	0.786499	+	0.617591i	$0.211891\pi$
$600$	−0.0984780	−0.00402035
$601$	24.4728	0.998268	0.499134	−	0.866525i	$-0.333652\pi$
$601$	24.4728	0.998268	0.499134	+	0.866525i	$0.333652\pi$
$602$	15.6300	0.637032
$603$	10.1021	0.411387
$604$	16.8785	0.686776
$605$	−34.3761	−1.39759
$606$	0.00897838	0.000364722 0
$607$	36.8649	1.49630	0.748151	−	0.663529i	$-0.230942\pi$
$607$	36.8649	1.49630	0.748151	+	0.663529i	$0.230942\pi$
$608$	2.86273	0.116099
$609$	−0.260749	−0.0105661
$610$	25.5474	1.03438
$611$	−22.4999	−0.910248
$612$	14.2357	0.575445
$613$	33.3567	1.34727	0.673633	−	0.739066i	$-0.264733\pi$
$613$	33.3567	1.34727	0.673633	+	0.739066i	$0.264733\pi$
$614$	11.0294	0.445112
$615$	0.116750	0.00470783
$616$	8.27322	0.333337
$617$	−29.0490	−1.16947	−0.584735	−	0.811224i	$-0.698802\pi$
$617$	−29.0490	−1.16947	−0.584735	+	0.811224i	$0.698802\pi$
$618$	−0.152165	−0.00612097
$619$	10.7497	0.432067	0.216034	−	0.976386i	$-0.430688\pi$
$619$	10.7497	0.432067	0.216034	+	0.976386i	$0.430688\pi$
$620$	−4.13053	−0.165886
$621$	−0.172206	−0.00691037
$622$	−13.9971	−0.561233
$623$	−5.27365	−0.211284
$624$	0.0580627	0.00232437
$625$	60.1684	2.40674
$626$	30.4926	1.21873
$627$	−0.0382467	−0.00152743
$628$	−6.66381	−0.265915
$629$	−16.4722	−0.656788
$630$	−62.6503	−2.49605
$631$	−18.3729	−0.731413	−0.365706	−	0.930730i	$-0.619173\pi$
$631$	−18.3729	−0.731413	−0.365706	+	0.930730i	$0.619173\pi$
$632$	2.59962	0.103407
$633$	0.0372833	0.00148188
$634$	−33.8372	−1.34385
$635$	32.8940	1.30536
$636$	0.0396238	0.00157119
$637$	132.008	5.23033
$638$	−10.3357	−0.409196
$639$	49.2503	1.94831
$640$	−4.13053	−0.163274
$641$	−28.1525	−1.11196	−0.555979	−	0.831196i	$-0.687657\pi$
$641$	−28.1525	−1.11196	−0.555979	+	0.831196i	$0.687657\pi$
$642$	0.0233777	0.000922646 0
$643$	−25.3753	−1.00071	−0.500353	−	0.865822i	$-0.666796\pi$
$643$	−25.3753	−1.00071	−0.500353	+	0.865822i	$0.666796\pi$
$644$	−17.7730	−0.700354
$645$	0.104257	0.00410512
$646$	−13.5846	−0.534480
$647$	5.57507	0.219179	0.109589	−	0.993977i	$-0.465046\pi$
$647$	5.57507	0.219179	0.109589	+	0.993977i	$0.465046\pi$
$648$	−8.99940	−0.353530
$649$	−17.0494	−0.669247
$650$	−85.7721	−3.36426
$651$	0.0412811	0.00161793
$652$	5.09860	0.199677
$653$	−27.0056	−1.05681	−0.528406	−	0.848992i	$-0.677210\pi$
$653$	−27.0056	−1.05681	−0.528406	+	0.848992i	$0.677210\pi$
$654$	−0.0895825	−0.00350295
$655$	37.5245	1.46620
$656$	3.46184	0.135162
$657$	42.0832	1.64182
$658$	−15.9968	−0.623621
$659$	20.8908	0.813791	0.406895	−	0.913475i	$-0.366611\pi$
$659$	20.8908	0.813791	0.406895	+	0.913475i	$0.366611\pi$
$660$	0.0551849	0.00214807
$661$	−13.8922	−0.540344	−0.270172	−	0.962812i	$-0.587081\pi$
$661$	−13.8922	−0.540344	−0.270172	+	0.962812i	$0.587081\pi$
$662$	−31.6924	−1.23176
$663$	−0.275528	−0.0107006
$664$	−3.02702	−0.117471
$665$	59.7849	2.31836
$666$	10.4134	0.403513
$667$	22.2038	0.859736
$668$	10.1304	0.391958
$669$	0.0398087	0.00153909
$670$	13.9093	0.537362
$671$	−10.1207	−0.390704
$672$	0.0412811	0.00159245
$673$	−3.38537	−0.130496	−0.0652482	−	0.997869i	$-0.520784\pi$
$673$	−3.38537	−0.130496	−0.0652482	+	0.997869i	$0.520784\pi$
$674$	29.7355	1.14537
$675$	−0.590862	−0.0227423
$676$	37.5713	1.44505
$677$	9.48425	0.364509	0.182255	−	0.983251i	$-0.441660\pi$
$677$	9.48425	0.364509	0.182255	+	0.983251i	$0.441660\pi$
$678$	−0.139873	−0.00537179
$679$	−5.05598	−0.194031
$680$	19.6008	0.751657
$681$	0.214553	0.00822168
$682$	1.63632	0.0626581
$683$	−28.7298	−1.09932	−0.549658	−	0.835390i	$-0.685242\pi$
$683$	−28.7298	−1.09932	−0.549658	+	0.835390i	$0.685242\pi$
$684$	8.58799	0.328370
$685$	64.2952	2.45659
$686$	58.4620	2.23209
$687$	−0.0455686	−0.00173855
$688$	3.09139	0.117858
$689$	34.5114	1.31478
$690$	−0.118551	−0.00451317
$691$	11.5237	0.438381	0.219191	−	0.975682i	$-0.429658\pi$
$691$	11.5237	0.438381	0.219191	+	0.975682i	$0.429658\pi$
$692$	−20.7354	−0.788242
$693$	24.8191	0.942800
$694$	34.1399	1.29593
$695$	−37.0474	−1.40529
$696$	−0.0515725	−0.00195485
$697$	−16.4276	−0.622240
$698$	−10.5456	−0.399156
$699$	−0.0238069	−0.000900459 0
$700$	−60.9817	−2.30489
$701$	50.3882	1.90313	0.951567	−	0.307440i	$-0.0994724\pi$
$701$	50.3882	1.90313	0.951567	+	0.307440i	$0.0994724\pi$
$702$	0.348372	0.0131485
$703$	−9.93716	−0.374787
$704$	1.63632	0.0616712
$705$	−0.106704	−0.00401870
$706$	21.3309	0.802797
$707$	5.55978	0.209097
$708$	−0.0850718	−0.00319719
$709$	13.2239	0.496633	0.248317	−	0.968679i	$-0.420123\pi$
$709$	13.2239	0.496633	0.248317	+	0.968679i	$0.420123\pi$
$710$	67.8115	2.54492
$711$	7.79870	0.292474
$712$	−1.04305	−0.0390900
$713$	−3.51524	−0.131647
$714$	−0.195893	−0.00733111
$715$	48.0648	1.79752
$716$	−8.13021	−0.303840
$717$	0.106927	0.00399328
$718$	−5.17414	−0.193097
$719$	−17.9946	−0.671085	−0.335543	−	0.942025i	$-0.608920\pi$
$719$	−17.9946	−0.671085	−0.335543	+	0.942025i	$0.608920\pi$
$720$	−12.3913	−0.461797
$721$	−94.2268	−3.50919
$722$	10.8048	0.402113
$723$	−0.0768212	−0.00285701
$724$	10.4489	0.388331
$725$	76.1845	2.82942
$726$	0.0679511	0.00252190
$727$	26.2896	0.975026	0.487513	−	0.873116i	$-0.337904\pi$
$727$	26.2896	0.975026	0.487513	+	0.873116i	$0.337904\pi$
$728$	35.9548	1.33257
$729$	−26.9964	−0.999867
$730$	57.9433	2.14458
$731$	−14.6697	−0.542579
$732$	−0.0504994	−0.00186651
$733$	49.5131	1.82881	0.914404	−	0.404802i	$-0.132660\pi$
$733$	49.5131	1.82881	0.914404	+	0.404802i	$0.132660\pi$
$734$	15.4167	0.569041
$735$	0.626034	0.0230916
$736$	−3.51524	−0.129574
$737$	−5.51020	−0.202971
$738$	10.3853	0.382287
$739$	−1.68774	−0.0620844	−0.0310422	−	0.999518i	$-0.509883\pi$
$739$	−1.68774	−0.0620844	−0.0310422	+	0.999518i	$0.509883\pi$
$740$	14.3380	0.527075
$741$	−0.166218	−0.00610616
$742$	24.5367	0.900770
$743$	24.4496	0.896970	0.448485	−	0.893790i	$-0.351964\pi$
$743$	24.4496	0.896970	0.448485	+	0.893790i	$0.351964\pi$
$744$	0.00816480	0.000299336 0
$745$	89.3916	3.27505
$746$	−16.5222	−0.604922
$747$	−9.08087	−0.332252
$748$	−7.76492	−0.283914
$749$	14.4765	0.528958
$750$	−0.238142	−0.00869571
$751$	−38.9673	−1.42194	−0.710968	−	0.703224i	$-0.751743\pi$
$751$	−38.9673	−1.42194	−0.710968	+	0.703224i	$0.751743\pi$
$752$	−3.16394	−0.115377
$753$	0.241091	0.00878586
$754$	−44.9184	−1.63583
$755$	69.7171	2.53727
$756$	0.247684	0.00900816
$757$	20.6307	0.749836	0.374918	−	0.927058i	$-0.377671\pi$
$757$	20.6307	0.749836	0.374918	+	0.927058i	$0.377671\pi$
$758$	−17.4199	−0.632718
$759$	0.0469645	0.00170470
$760$	11.8246	0.428923
$761$	17.3502	0.628945	0.314472	−	0.949267i	$-0.398172\pi$
$761$	17.3502	0.628945	0.314472	+	0.949267i	$0.398172\pi$
$762$	−0.0650215	−0.00235548
$763$	−55.4732	−2.00826
$764$	20.9017	0.756197
$765$	58.8011	2.12596
$766$	−31.2611	−1.12951
$767$	−74.0955	−2.67543
$768$	0.00816480	0.000294622 0
$769$	35.1884	1.26893	0.634464	−	0.772953i	$-0.281221\pi$
$769$	35.1884	1.26893	0.634464	+	0.772953i	$0.281221\pi$
$770$	34.1728	1.23150
$771$	0.0450759	0.00162337
$772$	−12.0832	−0.434884
$773$	−19.0973	−0.686883	−0.343441	−	0.939174i	$-0.611593\pi$
$773$	−19.0973	−0.686883	−0.343441	+	0.939174i	$0.611593\pi$
$774$	9.27396	0.333346
$775$	−12.0613	−0.433255
$776$	−1.00000	−0.0358979
$777$	−0.143296	−0.00514071
$778$	−2.26631	−0.0812510
$779$	−9.91029	−0.355073
$780$	0.239830	0.00858729
$781$	−26.8637	−0.961260
$782$	16.6810	0.596513
$783$	−0.309431	−0.0110582
$784$	18.5629	0.662962
$785$	−27.5251	−0.982413
$786$	−0.0741744	−0.00264571
$787$	36.5401	1.30252	0.651258	−	0.758857i	$-0.274242\pi$
$787$	36.5401	1.30252	0.651258	+	0.758857i	$0.274242\pi$
$788$	−12.9114	−0.459950
$789$	0.0945840	0.00336728
$790$	10.7378	0.382035
$791$	−86.6151	−3.07968
$792$	4.90886	0.174429
$793$	−43.9838	−1.56191
$794$	−13.4330	−0.476720
$795$	0.163667	0.00580468
$796$	13.4145	0.475466
$797$	−25.9036	−0.917552	−0.458776	−	0.888552i	$-0.651712\pi$
$797$	−25.9036	−0.917552	−0.458776	+	0.888552i	$0.651712\pi$
$798$	−0.118176	−0.00418340
$799$	15.0140	0.531157
$800$	−12.0613	−0.426431
$801$	−3.12909	−0.110561
$802$	−0.775879	−0.0273973
$803$	−22.9544	−0.810044
$804$	−0.0274944	−0.000969651 0
$805$	−73.4119	−2.58743
$806$	7.11135	0.250487
$807$	0.169529	0.00596771
$808$	1.09965	0.0386854
$809$	−28.5693	−1.00444	−0.502222	−	0.864739i	$-0.667484\pi$
$809$	−28.5693	−1.00444	−0.502222	+	0.864739i	$0.667484\pi$
$810$	−37.1723	−1.30610
$811$	5.68048	0.199469	0.0997343	−	0.995014i	$-0.468201\pi$
$811$	5.68048	0.199469	0.0997343	+	0.995014i	$0.468201\pi$
$812$	−31.9358	−1.12073
$813$	0.219983	0.00771513
$814$	−5.68004	−0.199085
$815$	21.0599	0.737697
$816$	−0.0387448	−0.00135634
$817$	−8.84980	−0.309615
$818$	−9.19985	−0.321665
$819$	107.862	3.76901
$820$	14.2992	0.499351
$821$	−8.73556	−0.304873	−0.152437	−	0.988313i	$-0.548712\pi$
$821$	−8.73556	−0.304873	−0.152437	+	0.988313i	$0.548712\pi$
$822$	−0.127092	−0.00443284
$823$	35.5055	1.23764	0.618821	−	0.785532i	$-0.287610\pi$
$823$	35.5055	1.23764	0.618821	+	0.785532i	$0.287610\pi$
$824$	−18.6367	−0.649240
$825$	0.161142	0.00561024
$826$	−52.6800	−1.83297
$827$	−34.1496	−1.18750	−0.593750	−	0.804650i	$-0.702353\pi$
$827$	−34.1496	−1.18750	−0.593750	+	0.804650i	$0.702353\pi$
$828$	−10.5455	−0.366481
$829$	50.9026	1.76792	0.883960	−	0.467562i	$-0.154868\pi$
$829$	50.9026	1.76792	0.883960	+	0.467562i	$0.154868\pi$
$830$	−12.5032	−0.433993
$831$	−0.250362	−0.00868495
$832$	7.11135	0.246542
$833$	−88.0876	−3.05205
$834$	0.0732314	0.00253579
$835$	41.8441	1.44807
$836$	−4.68435	−0.162011
$837$	0.0489882	0.00169328
$838$	−12.2091	−0.421757
$839$	−2.84337	−0.0981639	−0.0490819	−	0.998795i	$-0.515630\pi$
$839$	−2.84337	−0.0981639	−0.0490819	+	0.998795i	$0.515630\pi$
$840$	0.170513	0.00588325
$841$	10.8975	0.375774
$842$	−11.8252	−0.407522
$843$	−0.0326447	−0.00112434
$844$	4.56635	0.157180
$845$	155.189	5.33867
$846$	−9.49162	−0.326328
$847$	42.0781	1.44582
$848$	4.85300	0.166653
$849$	−0.0265932	−0.000912675 0
$850$	57.2350	1.96315
$851$	12.2022	0.418286
$852$	−0.134043	−0.00459222
$853$	8.90157	0.304784	0.152392	−	0.988320i	$-0.451302\pi$
$853$	8.90157	0.304784	0.152392	+	0.988320i	$0.451302\pi$
$854$	−31.2713	−1.07008
$855$	35.4730	1.21315
$856$	2.86324	0.0978634
$857$	15.9212	0.543860	0.271930	−	0.962317i	$-0.412338\pi$
$857$	15.9212	0.543860	0.271930	+	0.962317i	$0.412338\pi$
$858$	−0.0950093	−0.00324357
$859$	−28.9559	−0.987962	−0.493981	−	0.869473i	$-0.664459\pi$
$859$	−28.9559	−0.987962	−0.493981	+	0.869473i	$0.664459\pi$
$860$	12.7691	0.435422
$861$	−0.142908	−0.00487030
$862$	−12.8137	−0.436436
$863$	−29.8682	−1.01673	−0.508363	−	0.861143i	$-0.669749\pi$
$863$	−29.8682	−1.01673	−0.508363	+	0.861143i	$0.669749\pi$
$864$	0.0489882	0.00166661
$865$	−85.6483	−2.91213
$866$	−2.15822	−0.0733393
$867$	0.0450559	0.00153018
$868$	5.05598	0.171611
$869$	−4.25382	−0.144301
$870$	−0.213022	−0.00722211
$871$	−23.9469	−0.811411
$872$	−10.9718	−0.371552
$873$	−2.99993	−0.101532
$874$	10.0632	0.340392
$875$	−147.467	−4.98531
$876$	−0.114536	−0.00386982
$877$	35.0939	1.18504	0.592518	−	0.805557i	$-0.298134\pi$
$877$	35.0939	1.18504	0.592518	+	0.805557i	$0.298134\pi$
$878$	−18.8607	−0.636518
$879$	0.0965804	0.00325758
$880$	6.75889	0.227842
$881$	−10.3885	−0.349997	−0.174998	−	0.984569i	$-0.555992\pi$
$881$	−10.3885	−0.349997	−0.174998	+	0.984569i	$0.555992\pi$
$882$	55.6876	1.87510
$883$	−35.2526	−1.18635	−0.593173	−	0.805075i	$-0.702125\pi$
$883$	−35.2526	−1.18635	−0.593173	+	0.805075i	$0.702125\pi$
$884$	−33.7458	−1.13499
$885$	−0.351392	−0.0118119
$886$	27.1352	0.911626
$887$	−40.3978	−1.35643	−0.678213	−	0.734866i	$-0.737245\pi$
$887$	−40.3978	−1.35643	−0.678213	+	0.734866i	$0.737245\pi$
$888$	−0.0283418	−0.000951090 0
$889$	−40.2640	−1.35041
$890$	−4.30836	−0.144417
$891$	14.7259	0.493337
$892$	4.87565	0.163249
$893$	9.05750	0.303098
$894$	−0.176700	−0.00590972
$895$	−33.5821	−1.12253
$896$	5.05598	0.168908
$897$	0.204104	0.00681485
$898$	19.4714	0.649769
$899$	−6.31644	−0.210665
$900$	−36.1831	−1.20610
$901$	−23.0292	−0.767213
$902$	−5.66468	−0.188613
$903$	−0.127616	−0.00424679
$904$	−17.1312	−0.569776
$905$	43.1596	1.43467
$906$	−0.137809	−0.00457841
$907$	2.92330	0.0970667	0.0485333	−	0.998822i	$-0.484545\pi$
$907$	2.92330	0.0970667	0.0485333	+	0.998822i	$0.484545\pi$
$908$	26.2778	0.872059
$909$	3.29886	0.109416
$910$	148.513	4.92314
$911$	−11.4492	−0.379327	−0.189664	−	0.981849i	$-0.560740\pi$
$911$	−11.4492	−0.379327	−0.189664	+	0.981849i	$0.560740\pi$
$912$	−0.0233736	−0.000773977 0
$913$	4.95319	0.163927
$914$	−32.3524	−1.07012
$915$	−0.208589	−0.00689575
$916$	−5.58111	−0.184405
$917$	−45.9319	−1.51680
$918$	−0.232466	−0.00767253
$919$	−20.3237	−0.670418	−0.335209	−	0.942144i	$-0.608807\pi$
$919$	−20.3237	−0.670418	−0.335209	+	0.942144i	$0.608807\pi$
$920$	−14.5198	−0.478704
$921$	−0.0900532	−0.00296735
$922$	19.5564	0.644056
$923$	−116.748	−3.84280
$924$	−0.0675491	−0.00222220
$925$	41.8675	1.37659
$926$	20.5023	0.673749
$927$	−55.9089	−1.83629
$928$	−6.31644	−0.207347
$929$	44.8132	1.47027	0.735137	−	0.677918i	$-0.237118\pi$
$929$	44.8132	1.47027	0.735137	+	0.677918i	$0.237118\pi$
$930$	0.0337250	0.00110588
$931$	−53.1406	−1.74161
$932$	−2.91580	−0.0955101
$933$	0.114284	0.00374148
$934$	−6.80208	−0.222571
$935$	−32.0732	−1.04891
$936$	21.3336	0.697309
$937$	12.2264	0.399418	0.199709	−	0.979855i	$-0.436000\pi$
$937$	12.2264	0.399418	0.199709	+	0.979855i	$0.436000\pi$
$938$	−17.0256	−0.555907
$939$	−0.248966	−0.00812470
$940$	−13.0688	−0.426256
$941$	−16.6818	−0.543810	−0.271905	−	0.962324i	$-0.587654\pi$
$941$	−16.6818	−0.543810	−0.271905	+	0.962324i	$0.587654\pi$
$942$	0.0544087	0.00177273
$943$	12.1692	0.396284
$944$	−10.4193	−0.339120
$945$	1.02307	0.0332803
$946$	−5.05851	−0.164466
$947$	−26.2996	−0.854621	−0.427310	−	0.904105i	$-0.640539\pi$
$947$	−26.2996	−0.854621	−0.427310	+	0.904105i	$0.640539\pi$
$948$	−0.0212254	−0.000689369 0
$949$	−99.7584	−3.23829
$950$	34.5282	1.12024
$951$	0.276274	0.00895880
$952$	−23.9924	−0.777597
$953$	11.1210	0.360246	0.180123	−	0.983644i	$-0.442350\pi$
$953$	11.1210	0.360246	0.180123	+	0.983644i	$0.442350\pi$
$954$	14.5587	0.471355
$955$	86.3351	2.79374
$956$	13.0961	0.423560
$957$	0.0843892	0.00272792
$958$	13.2665	0.428622
$959$	−78.7006	−2.54137
$960$	0.0337250	0.00108847
$961$	1.00000	0.0322581
$962$	−24.6851	−0.795879
$963$	8.58951	0.276793
$964$	−9.40883	−0.303038
$965$	−49.9100	−1.60666
$966$	0.145113	0.00466893
$967$	30.7916	0.990191	0.495096	−	0.868839i	$-0.335133\pi$
$967$	30.7916	0.990191	0.495096	+	0.868839i	$0.335133\pi$
$968$	8.32245	0.267494
$969$	0.110916	0.00356313
$970$	−4.13053	−0.132623
$971$	14.7668	0.473888	0.236944	−	0.971523i	$-0.423854\pi$
$971$	14.7668	0.473888	0.236944	+	0.971523i	$0.423854\pi$
$972$	0.220443	0.00707071
$973$	45.3479	1.45379
$974$	−3.44539	−0.110397
$975$	0.700312	0.0224279
$976$	−6.18501	−0.197977
$977$	−21.1065	−0.675256	−0.337628	−	0.941280i	$-0.609625\pi$
$977$	−21.1065	−0.675256	−0.337628	+	0.941280i	$0.609625\pi$
$978$	−0.0416290	−0.00133115
$979$	1.70677	0.0545486
$980$	76.6748	2.44929
$981$	−32.9146	−1.05088
$982$	38.0498	1.21422
$983$	−40.6203	−1.29559	−0.647793	−	0.761816i	$-0.724308\pi$
$983$	−40.6203	−1.29559	−0.647793	+	0.761816i	$0.724308\pi$
$984$	−0.0282652	−0.000901062 0
$985$	−53.3311	−1.69927
$986$	29.9737	0.954557
$987$	0.130611	0.00415739
$988$	−20.3578	−0.647669
$989$	10.8670	0.345550
$990$	20.2762	0.644420
$991$	24.1316	0.766565	0.383283	−	0.923631i	$-0.374794\pi$
$991$	24.1316	0.766565	0.383283	+	0.923631i	$0.374794\pi$
$992$	1.00000	0.0317500
$993$	0.258762	0.00821157
$994$	−83.0047	−2.63275
$995$	55.4092	1.75659
$996$	0.0247150	0.000783126 0
$997$	−20.5513	−0.650866	−0.325433	−	0.945565i	$-0.605510\pi$
$997$	−20.5513	−0.650866	−0.325433	+	0.945565i	$0.605510\pi$
$998$	0.992190	0.0314072
$999$	−0.170049	−0.00538012

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6014.2.a.j.1.17	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6014.2.a.j.1.17	✓	32	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.00816480 q^{3} +1.00000 q^{4} +4.13053 q^{5} -0.00816480 q^{6} -5.05598 q^{7} -1.00000 q^{8} -2.99993 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.00816480 q^{3} +1.00000 q^{4} +4.13053 q^{5} -0.00816480 q^{6} -5.05598 q^{7} -1.00000 q^{8} -2.99993 q^{9} -4.13053 q^{10} +1.63632 q^{11} +0.00816480 q^{12} +7.11135 q^{13} +5.05598 q^{14} +0.0337250 q^{15} +1.00000 q^{16} -4.74535 q^{17} +2.99993 q^{18} -2.86273 q^{19} +4.13053 q^{20} -0.0412811 q^{21} -1.63632 q^{22} +3.51524 q^{23} -0.00816480 q^{24} +12.0613 q^{25} -7.11135 q^{26} -0.0489882 q^{27} -5.05598 q^{28} +6.31644 q^{29} -0.0337250 q^{30} -1.00000 q^{31} -1.00000 q^{32} +0.0133602 q^{33} +4.74535 q^{34} -20.8839 q^{35} -2.99993 q^{36} +3.47122 q^{37} +2.86273 q^{38} +0.0580627 q^{39} -4.13053 q^{40} +3.46184 q^{41} +0.0412811 q^{42} +3.09139 q^{43} +1.63632 q^{44} -12.3913 q^{45} -3.51524 q^{46} -3.16394 q^{47} +0.00816480 q^{48} +18.5629 q^{49} -12.0613 q^{50} -0.0387448 q^{51} +7.11135 q^{52} +4.85300 q^{53} +0.0489882 q^{54} +6.75889 q^{55} +5.05598 q^{56} -0.0233736 q^{57} -6.31644 q^{58} -10.4193 q^{59} +0.0337250 q^{60} -6.18501 q^{61} +1.00000 q^{62} +15.1676 q^{63} +1.00000 q^{64} +29.3736 q^{65} -0.0133602 q^{66} -3.36743 q^{67} -4.74535 q^{68} +0.0287012 q^{69} +20.8839 q^{70} -16.4171 q^{71} +2.99993 q^{72} -14.0281 q^{73} -3.47122 q^{74} +0.0984780 q^{75} -2.86273 q^{76} -8.27322 q^{77} -0.0580627 q^{78} -2.59962 q^{79} +4.13053 q^{80} +8.99940 q^{81} -3.46184 q^{82} +3.02702 q^{83} -0.0412811 q^{84} -19.6008 q^{85} -3.09139 q^{86} +0.0515725 q^{87} -1.63632 q^{88} +1.04305 q^{89} +12.3913 q^{90} -35.9548 q^{91} +3.51524 q^{92} -0.00816480 q^{93} +3.16394 q^{94} -11.8246 q^{95} -0.00816480 q^{96} +1.00000 q^{97} -18.5629 q^{98} -4.90886 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9}+O(q^{10}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9	\( 32 q - 32 q^{2} - 2 q^{3} + 32 q^{4} + 2 q^{6} + 5 q^{7} - 32 q^{8} + 30 q^{9} - 4 q^{11} - 2 q^{12} + 10 q^{13} - 5 q^{14} - q^{15} + 32 q^{16} + 14 q^{17} - 30 q^{18} + 33 q^{19} + 4 q^{22} - 2 q^{23} + 2 q^{24} + 46 q^{25} - 10 q^{26} - 5 q^{27} + 5 q^{28} - q^{29} + q^{30} - 32 q^{31} - 32 q^{32} + 32 q^{33} - 14 q^{34} + 8 q^{35} + 30 q^{36} + 31 q^{37} - 33 q^{38} + 4 q^{39} + 31 q^{41} + 15 q^{43} - 4 q^{44} + q^{45} + 2 q^{46} - 14 q^{47} - 2 q^{48} + 75 q^{49} - 46 q^{50} + 27 q^{51} + 10 q^{52} - 31 q^{53} + 5 q^{54} + 14 q^{55} - 5 q^{56} + 51 q^{57} + q^{58} - 8 q^{59} - q^{60} + 24 q^{61} + 32 q^{62} + 23 q^{63} + 32 q^{64} + 20 q^{65} - 32 q^{66} + 17 q^{67} + 14 q^{68} - 31 q^{69} - 8 q^{70} - 31 q^{71} - 30 q^{72} + 19 q^{73} - 31 q^{74} - 40 q^{75} + 33 q^{76} + 8 q^{77} - 4 q^{78} + 39 q^{79} + 116 q^{81} - 31 q^{82} - 6 q^{83} + 56 q^{85} - 15 q^{86} - 17 q^{87} + 4 q^{88} + 8 q^{89} - q^{90} + 34 q^{91} - 2 q^{92} + 2 q^{93} + 14 q^{94} - 22 q^{95} + 2 q^{96} + 32 q^{97} - 75 q^{98} - 27 q^{99}+O(q^{100}) \) 32 * q - 32 * q^2 - 2 * q^3 + 32 * q^4 + 2 * q^6 + 5 * q^7 - 32 * q^8 + 30 * q^9 - 4 * q^11 - 2 * q^12 + 10 * q^13 - 5 * q^14 - q^15 + 32 * q^16 + 14 * q^17 - 30 * q^18 + 33 * q^19 + 4 * q^22 - 2 * q^23 + 2 * q^24 + 46 * q^25 - 10 * q^26 - 5 * q^27 + 5 * q^28 - q^29 + q^30 - 32 * q^31 - 32 * q^32 + 32 * q^33 - 14 * q^34 + 8 * q^35 + 30 * q^36 + 31 * q^37 - 33 * q^38 + 4 * q^39 + 31 * q^41 + 15 * q^43 - 4 * q^44 + q^45 + 2 * q^46 - 14 * q^47 - 2 * q^48 + 75 * q^49 - 46 * q^50 + 27 * q^51 + 10 * q^52 - 31 * q^53 + 5 * q^54 + 14 * q^55 - 5 * q^56 + 51 * q^57 + q^58 - 8 * q^59 - q^60 + 24 * q^61 + 32 * q^62 + 23 * q^63 + 32 * q^64 + 20 * q^65 - 32 * q^66 + 17 * q^67 + 14 * q^68 - 31 * q^69 - 8 * q^70 - 31 * q^71 - 30 * q^72 + 19 * q^73 - 31 * q^74 - 40 * q^75 + 33 * q^76 + 8 * q^77 - 4 * q^78 + 39 * q^79 + 116 * q^81 - 31 * q^82 - 6 * q^83 + 56 * q^85 - 15 * q^86 - 17 * q^87 + 4 * q^88 + 8 * q^89 - q^90 + 34 * q^91 - 2 * q^92 + 2 * q^93 + 14 * q^94 - 22 * q^95 + 2 * q^96 + 32 * q^97 - 75 * q^98 - 27 * q^99

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