LMFDB - Embedded newform 6035.2.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.904707 q^{2} -2.66665 q^{3} -1.18150 q^{4} +1.00000 q^{5} +2.41254 q^{6} +3.83492 q^{7} +2.87833 q^{8} +4.11101 q^{9} +O(q^{10})$	\(q-0.904707 q^{2} -2.66665 q^{3} -1.18150 q^{4} +1.00000 q^{5} +2.41254 q^{6} +3.83492 q^{7} +2.87833 q^{8} +4.11101 q^{9} -0.904707 q^{10} -3.18737 q^{11} +3.15066 q^{12} -2.30569 q^{13} -3.46948 q^{14} -2.66665 q^{15} -0.241038 q^{16} +1.00000 q^{17} -3.71926 q^{18} +5.08137 q^{19} -1.18150 q^{20} -10.2264 q^{21} +2.88363 q^{22} +5.55999 q^{23} -7.67549 q^{24} +1.00000 q^{25} +2.08598 q^{26} -2.96267 q^{27} -4.53098 q^{28} +0.491748 q^{29} +2.41254 q^{30} -2.89326 q^{31} -5.53859 q^{32} +8.49958 q^{33} -0.904707 q^{34} +3.83492 q^{35} -4.85718 q^{36} -3.93319 q^{37} -4.59715 q^{38} +6.14847 q^{39} +2.87833 q^{40} +5.93087 q^{41} +9.25188 q^{42} -10.1763 q^{43} +3.76589 q^{44} +4.11101 q^{45} -5.03016 q^{46} -10.1402 q^{47} +0.642762 q^{48} +7.70661 q^{49} -0.904707 q^{50} -2.66665 q^{51} +2.72419 q^{52} -8.24150 q^{53} +2.68035 q^{54} -3.18737 q^{55} +11.0382 q^{56} -13.5502 q^{57} -0.444888 q^{58} -8.13138 q^{59} +3.15066 q^{60} -3.93974 q^{61} +2.61755 q^{62} +15.7654 q^{63} +5.49288 q^{64} -2.30569 q^{65} -7.68963 q^{66} -16.2666 q^{67} -1.18150 q^{68} -14.8265 q^{69} -3.46948 q^{70} -1.00000 q^{71} +11.8328 q^{72} +7.45040 q^{73} +3.55838 q^{74} -2.66665 q^{75} -6.00366 q^{76} -12.2233 q^{77} -5.56257 q^{78} +12.1237 q^{79} -0.241038 q^{80} -4.43263 q^{81} -5.36570 q^{82} +7.67913 q^{83} +12.0825 q^{84} +1.00000 q^{85} +9.20655 q^{86} -1.31132 q^{87} -9.17429 q^{88} -9.19418 q^{89} -3.71926 q^{90} -8.84215 q^{91} -6.56915 q^{92} +7.71530 q^{93} +9.17388 q^{94} +5.08137 q^{95} +14.7695 q^{96} +6.38610 q^{97} -6.97223 q^{98} -13.1033 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) $ 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−0.904707	−0.639725	−0.319862	−	0.947464i	$-0.603637\pi$
$2$	−0.904707	−0.639725	−0.319862	+	0.947464i	$0.603637\pi$
$3$	−2.66665	−1.53959	−0.769795	−	0.638291i	$-0.779641\pi$
$3$	−2.66665	−1.53959	−0.769795	+	0.638291i	$0.779641\pi$
$4$	−1.18150	−0.590752
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.41254	0.984914
$7$	3.83492	1.44946	0.724732	−	0.689031i	$-0.241964\pi$
$7$	3.83492	1.44946	0.724732	+	0.689031i	$0.241964\pi$
$8$	2.87833	1.01764
$9$	4.11101	1.37034
$10$	−0.904707	−0.286094
$11$	−3.18737	−0.961027	−0.480513	−	0.876987i	$-0.659550\pi$
$11$	−3.18737	−0.961027	−0.480513	+	0.876987i	$0.659550\pi$
$12$	3.15066	0.909516
$13$	−2.30569	−0.639484	−0.319742	−	0.947505i	$-0.603596\pi$
$13$	−2.30569	−0.639484	−0.319742	+	0.947505i	$0.603596\pi$
$14$	−3.46948	−0.927258
$15$	−2.66665	−0.688525
$16$	−0.241038	−0.0602594
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−3.71926	−0.876638
$19$	5.08137	1.16575	0.582873	−	0.812563i	$-0.301929\pi$
$19$	5.08137	1.16575	0.582873	+	0.812563i	$0.301929\pi$
$20$	−1.18150	−0.264192
$21$	−10.2264	−2.23158
$22$	2.88363	0.614793
$23$	5.55999	1.15934	0.579669	−	0.814852i	$-0.303182\pi$
$23$	5.55999	1.15934	0.579669	+	0.814852i	$0.303182\pi$
$24$	−7.67549	−1.56675
$25$	1.00000	0.200000
$26$	2.08598	0.409094
$27$	−2.96267	−0.570166
$28$	−4.53098	−0.856274
$29$	0.491748	0.0913153	0.0456576	−	0.998957i	$-0.485462\pi$
$29$	0.491748	0.0913153	0.0456576	+	0.998957i	$0.485462\pi$
$30$	2.41254	0.440467
$31$	−2.89326	−0.519644	−0.259822	−	0.965656i	$-0.583664\pi$
$31$	−2.89326	−0.519644	−0.259822	+	0.965656i	$0.583664\pi$
$32$	−5.53859	−0.979094
$33$	8.49958	1.47959
$34$	−0.904707	−0.155156
$35$	3.83492	0.648220
$36$	−4.85718	−0.809529
$37$	−3.93319	−0.646612	−0.323306	−	0.946295i	$-0.604794\pi$
$37$	−3.93319	−0.646612	−0.323306	+	0.946295i	$0.604794\pi$
$38$	−4.59715	−0.745756
$39$	6.14847	0.984544
$40$	2.87833	0.455104
$41$	5.93087	0.926246	0.463123	−	0.886294i	$-0.346729\pi$
$41$	5.93087	0.926246	0.463123	+	0.886294i	$0.346729\pi$
$42$	9.25188	1.42760
$43$	−10.1763	−1.55187	−0.775934	−	0.630814i	$-0.782721\pi$
$43$	−10.1763	−1.55187	−0.775934	+	0.630814i	$0.782721\pi$
$44$	3.76589	0.567729
$45$	4.11101	0.612833
$46$	−5.03016	−0.741657
$47$	−10.1402	−1.47909	−0.739547	−	0.673105i	$-0.764960\pi$
$47$	−10.1402	−1.47909	−0.739547	+	0.673105i	$0.764960\pi$
$48$	0.642762	0.0927748
$49$	7.70661	1.10094
$50$	−0.904707	−0.127945
$51$	−2.66665	−0.373405
$52$	2.72419	0.377777
$53$	−8.24150	−1.13206	−0.566028	−	0.824386i	$-0.691521\pi$
$53$	−8.24150	−1.13206	−0.566028	+	0.824386i	$0.691521\pi$
$54$	2.68035	0.364749
$55$	−3.18737	−0.429784
$56$	11.0382	1.47504
$57$	−13.5502	−1.79477
$58$	−0.444888	−0.0584166
$59$	−8.13138	−1.05862	−0.529308	−	0.848430i	$-0.677548\pi$
$59$	−8.13138	−1.05862	−0.529308	+	0.848430i	$0.677548\pi$
$60$	3.15066	0.406748
$61$	−3.93974	−0.504431	−0.252216	−	0.967671i	$-0.581159\pi$
$61$	−3.93974	−0.504431	−0.252216	+	0.967671i	$0.581159\pi$
$62$	2.61755	0.332429
$63$	15.7654	1.98625
$64$	5.49288	0.686610
$65$	−2.30569	−0.285986
$66$	−7.68963	−0.946528
$67$	−16.2666	−1.98728	−0.993638	−	0.112619i	$-0.964076\pi$
$67$	−16.2666	−1.98728	−0.993638	+	0.112619i	$0.964076\pi$
$68$	−1.18150	−0.143278
$69$	−14.8265	−1.78490
$70$	−3.46948	−0.414682
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	11.8328	1.39451
$73$	7.45040	0.872003	0.436001	−	0.899946i	$-0.356394\pi$
$73$	7.45040	0.872003	0.436001	+	0.899946i	$0.356394\pi$
$74$	3.55838	0.413653
$75$	−2.66665	−0.307918
$76$	−6.00366	−0.688667
$77$	−12.2233	−1.39297
$78$	−5.56257	−0.629837
$79$	12.1237	1.36403	0.682013	−	0.731340i	$-0.261105\pi$
$79$	12.1237	1.36403	0.682013	+	0.731340i	$0.261105\pi$
$80$	−0.241038	−0.0269488
$81$	−4.43263	−0.492515
$82$	−5.36570	−0.592543
$83$	7.67913	0.842894	0.421447	−	0.906853i	$-0.361522\pi$
$83$	7.67913	0.842894	0.421447	+	0.906853i	$0.361522\pi$
$84$	12.0825	1.31831
$85$	1.00000	0.108465
$86$	9.20655	0.992768
$87$	−1.31132	−0.140588
$88$	−9.17429	−0.977983
$89$	−9.19418	−0.974581	−0.487291	−	0.873240i	$-0.662015\pi$
$89$	−9.19418	−0.974581	−0.487291	+	0.873240i	$0.662015\pi$
$90$	−3.71926	−0.392044
$91$	−8.84215	−0.926909
$92$	−6.56915	−0.684881
$93$	7.71530	0.800039
$94$	9.17388	0.946213
$95$	5.08137	0.521337
$96$	14.7695	1.50740
$97$	6.38610	0.648410	0.324205	−	0.945987i	$-0.394903\pi$
$97$	6.38610	0.648410	0.324205	+	0.945987i	$0.394903\pi$
$98$	−6.97223	−0.704302
$99$	−13.1033	−1.31693
$100$	−1.18150	−0.118150
$101$	−4.56785	−0.454518	−0.227259	−	0.973834i	$-0.572976\pi$
$101$	−4.56785	−0.454518	−0.227259	+	0.973834i	$0.572976\pi$
$102$	2.41254	0.238877
$103$	17.5397	1.72823	0.864117	−	0.503291i	$-0.167878\pi$
$103$	17.5397	1.72823	0.864117	+	0.503291i	$0.167878\pi$
$104$	−6.63655	−0.650767
$105$	−10.2264	−0.997993
$106$	7.45614	0.724205
$107$	14.2644	1.37899	0.689497	−	0.724288i	$-0.257831\pi$
$107$	14.2644	1.37899	0.689497	+	0.724288i	$0.257831\pi$
$108$	3.50041	0.336827
$109$	−9.30164	−0.890936	−0.445468	−	0.895298i	$-0.646963\pi$
$109$	−9.30164	−0.890936	−0.445468	+	0.895298i	$0.646963\pi$
$110$	2.88363	0.274944
$111$	10.4884	0.995517
$112$	−0.924360	−0.0873438
$113$	3.48955	0.328269	0.164135	−	0.986438i	$-0.447517\pi$
$113$	3.48955	0.328269	0.164135	+	0.986438i	$0.447517\pi$
$114$	12.2590	1.14816
$115$	5.55999	0.518471
$116$	−0.581002	−0.0539447
$117$	−9.47873	−0.876309
$118$	7.35652	0.677223
$119$	3.83492	0.351547
$120$	−7.67549	−0.700673
$121$	−0.840699	−0.0764272
$122$	3.56431	0.322697
$123$	−15.8155	−1.42604
$124$	3.41840	0.306981
$125$	1.00000	0.0894427
$126$	−14.2631	−1.27065
$127$	0.527009	0.0467645	0.0233822	−	0.999727i	$-0.492557\pi$
$127$	0.527009	0.0467645	0.0233822	+	0.999727i	$0.492557\pi$
$128$	6.10774	0.539853
$129$	27.1365	2.38924
$130$	2.08598	0.182952
$131$	−3.08755	−0.269760	−0.134880	−	0.990862i	$-0.543065\pi$
$131$	−3.08755	−0.269760	−0.134880	+	0.990862i	$0.543065\pi$
$132$	−10.0423	−0.874070
$133$	19.4866	1.68971
$134$	14.7165	1.27131
$135$	−2.96267	−0.254986
$136$	2.87833	0.246815
$137$	4.99892	0.427087	0.213543	−	0.976934i	$-0.431499\pi$
$137$	4.99892	0.427087	0.213543	+	0.976934i	$0.431499\pi$
$138$	13.4137	1.14185
$139$	−7.89743	−0.669851	−0.334926	−	0.942245i	$-0.608711\pi$
$139$	−7.89743	−0.669851	−0.334926	+	0.942245i	$0.608711\pi$
$140$	−4.53098	−0.382937
$141$	27.0402	2.27720
$142$	0.904707	0.0759214
$143$	7.34909	0.614562
$144$	−0.990908	−0.0825757
$145$	0.491748	0.0408374
$146$	−6.74043	−0.557842
$147$	−20.5508	−1.69500
$148$	4.64708	0.381987
$149$	5.95566	0.487907	0.243953	−	0.969787i	$-0.421556\pi$
$149$	5.95566	0.487907	0.243953	+	0.969787i	$0.421556\pi$
$150$	2.41254	0.196983
$151$	7.68286	0.625222	0.312611	−	0.949881i	$-0.398796\pi$
$151$	7.68286	0.625222	0.312611	+	0.949881i	$0.398796\pi$
$152$	14.6259	1.18631
$153$	4.11101	0.332355
$154$	11.0585	0.891120
$155$	−2.89326	−0.232392
$156$	−7.26445	−0.581621
$157$	−4.50553	−0.359581	−0.179790	−	0.983705i	$-0.557542\pi$
$157$	−4.50553	−0.359581	−0.179790	+	0.983705i	$0.557542\pi$
$158$	−10.9684	−0.872601
$159$	21.9772	1.74290
$160$	−5.53859	−0.437864
$161$	21.3221	1.68042
$162$	4.01024	0.315074
$163$	−8.00384	−0.626909	−0.313454	−	0.949603i	$-0.601486\pi$
$163$	−8.00384	−0.626909	−0.313454	+	0.949603i	$0.601486\pi$
$164$	−7.00735	−0.547182
$165$	8.49958	0.661691
$166$	−6.94737	−0.539220
$167$	−10.5637	−0.817445	−0.408722	−	0.912659i	$-0.634026\pi$
$167$	−10.5637	−0.817445	−0.408722	+	0.912659i	$0.634026\pi$
$168$	−29.4349	−2.27095
$169$	−7.68378	−0.591060
$170$	−0.904707	−0.0693879
$171$	20.8895	1.59746
$172$	12.0233	0.916769
$173$	18.9121	1.43786	0.718931	−	0.695082i	$-0.244632\pi$
$173$	18.9121	1.43786	0.718931	+	0.695082i	$0.244632\pi$
$174$	1.18636	0.0899377
$175$	3.83492	0.289893
$176$	0.768275	0.0579109
$177$	21.6835	1.62983
$178$	8.31805	0.623464
$179$	−10.7012	−0.799842	−0.399921	−	0.916550i	$-0.630962\pi$
$179$	−10.7012	−0.799842	−0.399921	+	0.916550i	$0.630962\pi$
$180$	−4.85718	−0.362033
$181$	−13.2218	−0.982772	−0.491386	−	0.870942i	$-0.663509\pi$
$181$	−13.2218	−0.982772	−0.491386	+	0.870942i	$0.663509\pi$
$182$	7.99956	0.592967
$183$	10.5059	0.776617
$184$	16.0035	1.17979
$185$	−3.93319	−0.289174
$186$	−6.98009	−0.511805
$187$	−3.18737	−0.233083
$188$	11.9806	0.873778
$189$	−11.3616	−0.826435
$190$	−4.59715	−0.333512
$191$	4.33035	0.313333	0.156667	−	0.987652i	$-0.449925\pi$
$191$	4.33035	0.313333	0.156667	+	0.987652i	$0.449925\pi$
$192$	−14.6476	−1.05710
$193$	−16.1506	−1.16255	−0.581274	−	0.813708i	$-0.697446\pi$
$193$	−16.1506	−1.16255	−0.581274	+	0.813708i	$0.697446\pi$
$194$	−5.77755	−0.414804
$195$	6.14847	0.440301
$196$	−9.10540	−0.650386
$197$	−5.42365	−0.386419	−0.193209	−	0.981158i	$-0.561890\pi$
$197$	−5.42365	−0.386419	−0.193209	+	0.981158i	$0.561890\pi$
$198$	11.8546	0.842473
$199$	−3.00593	−0.213084	−0.106542	−	0.994308i	$-0.533978\pi$
$199$	−3.00593	−0.213084	−0.106542	+	0.994308i	$0.533978\pi$
$200$	2.87833	0.203529
$201$	43.3772	3.05959
$202$	4.13257	0.290766
$203$	1.88581	0.132358
$204$	3.15066	0.220590
$205$	5.93087	0.414230
$206$	−15.8683	−1.10559
$207$	22.8571	1.58868
$208$	0.555759	0.0385350
$209$	−16.1962	−1.12031
$210$	9.25188	0.638440
$211$	−8.12923	−0.559639	−0.279820	−	0.960053i	$-0.590275\pi$
$211$	−8.12923	−0.559639	−0.279820	+	0.960053i	$0.590275\pi$
$212$	9.73737	0.668765
$213$	2.66665	0.182716
$214$	−12.9051	−0.882177
$215$	−10.1763	−0.694016
$216$	−8.52754	−0.580226
$217$	−11.0954	−0.753206
$218$	8.41526	0.569953
$219$	−19.8676	−1.34253
$220$	3.76589	0.253896
$221$	−2.30569	−0.155098
$222$	−9.48895	−0.636857
$223$	14.6012	0.977768	0.488884	−	0.872349i	$-0.337404\pi$
$223$	14.6012	0.977768	0.488884	+	0.872349i	$0.337404\pi$
$224$	−21.2401	−1.41916
$225$	4.11101	0.274067
$226$	−3.15702	−0.210002
$227$	−5.58488	−0.370682	−0.185341	−	0.982674i	$-0.559339\pi$
$227$	−5.58488	−0.370682	−0.185341	+	0.982674i	$0.559339\pi$
$228$	16.0096	1.06026
$229$	−13.9992	−0.925091	−0.462546	−	0.886595i	$-0.653064\pi$
$229$	−13.9992	−0.925091	−0.462546	+	0.886595i	$0.653064\pi$
$230$	−5.03016	−0.331679
$231$	32.5952	2.14461
$232$	1.41541	0.0929264
$233$	3.67753	0.240923	0.120462	−	0.992718i	$-0.461563\pi$
$233$	3.67753	0.240923	0.120462	+	0.992718i	$0.461563\pi$
$234$	8.57547	0.560596
$235$	−10.1402	−0.661471
$236$	9.60727	0.625380
$237$	−32.3297	−2.10004
$238$	−3.46948	−0.224893
$239$	19.1034	1.23570	0.617849	−	0.786297i	$-0.288004\pi$
$239$	19.1034	1.23570	0.617849	+	0.786297i	$0.288004\pi$
$240$	0.642762	0.0414901
$241$	0.153139	0.00986454	0.00493227	−	0.999988i	$-0.498430\pi$
$241$	0.153139	0.00986454	0.00493227	+	0.999988i	$0.498430\pi$
$242$	0.760587	0.0488924
$243$	20.7083	1.32844
$244$	4.65482	0.297994
$245$	7.70661	0.492357
$246$	14.3084	0.912272
$247$	−11.7161	−0.745476
$248$	−8.32775	−0.528813
$249$	−20.4775	−1.29771
$250$	−0.904707	−0.0572187
$251$	12.4358	0.784943	0.392472	−	0.919764i	$-0.371620\pi$
$251$	12.4358	0.784943	0.392472	+	0.919764i	$0.371620\pi$
$252$	−18.6269	−1.17338
$253$	−17.7217	−1.11415
$254$	−0.476789	−0.0299164
$255$	−2.66665	−0.166992
$256$	−16.5115	−1.03197
$257$	10.3504	0.645640	0.322820	−	0.946460i	$-0.395369\pi$
$257$	10.3504	0.645640	0.322820	+	0.946460i	$0.395369\pi$
$258$	−24.5506	−1.52846
$259$	−15.0835	−0.937240
$260$	2.72419	0.168947
$261$	2.02158	0.125133
$262$	2.79333	0.172572
$263$	7.27810	0.448787	0.224393	−	0.974499i	$-0.427960\pi$
$263$	7.27810	0.448787	0.224393	+	0.974499i	$0.427960\pi$
$264$	24.4646	1.50569
$265$	−8.24150	−0.506271
$266$	−17.6297	−1.08095
$267$	24.5176	1.50046
$268$	19.2190	1.17399
$269$	13.8807	0.846319	0.423159	−	0.906055i	$-0.360921\pi$
$269$	13.8807	0.846319	0.423159	+	0.906055i	$0.360921\pi$
$270$	2.68035	0.163121
$271$	−30.0603	−1.82603	−0.913015	−	0.407925i	$-0.866252\pi$
$271$	−30.0603	−1.82603	−0.913015	+	0.407925i	$0.866252\pi$
$272$	−0.241038	−0.0146151
$273$	23.5789	1.42706
$274$	−4.52256	−0.273218
$275$	−3.18737	−0.192205
$276$	17.5176	1.05444
$277$	14.8540	0.892490	0.446245	−	0.894911i	$-0.352761\pi$
$277$	14.8540	0.892490	0.446245	+	0.894911i	$0.352761\pi$
$278$	7.14486	0.428520
$279$	−11.8942	−0.712088
$280$	11.0382	0.659657
$281$	−18.5206	−1.10484	−0.552422	−	0.833565i	$-0.686296\pi$
$281$	−18.5206	−1.10484	−0.552422	+	0.833565i	$0.686296\pi$
$282$	−24.4635	−1.45678
$283$	−4.10935	−0.244275	−0.122138	−	0.992513i	$-0.538975\pi$
$283$	−4.10935	−0.244275	−0.122138	+	0.992513i	$0.538975\pi$
$284$	1.18150	0.0701094
$285$	−13.5502	−0.802646
$286$	−6.64878	−0.393150
$287$	22.7444	1.34256
$288$	−22.7692	−1.34169
$289$	1.00000	0.0588235
$290$	−0.444888	−0.0261247
$291$	−17.0295	−0.998285
$292$	−8.80268	−0.515138
$293$	13.4600	0.786340	0.393170	−	0.919466i	$-0.371378\pi$
$293$	13.4600	0.786340	0.393170	+	0.919466i	$0.371378\pi$
$294$	18.5925	1.08434
$295$	−8.13138	−0.473427
$296$	−11.3210	−0.658020
$297$	9.44311	0.547945
$298$	−5.38813	−0.312126
$299$	−12.8196	−0.741378
$300$	3.15066	0.181903
$301$	−39.0252	−2.24938
$302$	−6.95074	−0.399970
$303$	12.1808	0.699771
$304$	−1.22480	−0.0702472
$305$	−3.93974	−0.225589
$306$	−3.71926	−0.212616
$307$	18.6687	1.06548	0.532740	−	0.846279i	$-0.321162\pi$
$307$	18.6687	1.06548	0.532740	+	0.846279i	$0.321162\pi$
$308$	14.4419	0.822902
$309$	−46.7721	−2.66077
$310$	2.61755	0.148667
$311$	−5.81172	−0.329552	−0.164776	−	0.986331i	$-0.552690\pi$
$311$	−5.81172	−0.329552	−0.164776	+	0.986331i	$0.552690\pi$
$312$	17.6973	1.00191
$313$	13.4961	0.762842	0.381421	−	0.924401i	$-0.375435\pi$
$313$	13.4961	0.762842	0.381421	+	0.924401i	$0.375435\pi$
$314$	4.07619	0.230033
$315$	15.7654	0.888279
$316$	−14.3242	−0.805801
$317$	−22.1036	−1.24146	−0.620730	−	0.784024i	$-0.713164\pi$
$317$	−22.1036	−1.24146	−0.620730	+	0.784024i	$0.713164\pi$
$318$	−19.8829	−1.11498
$319$	−1.56738	−0.0877565
$320$	5.49288	0.307061
$321$	−38.0382	−2.12309
$322$	−19.2903	−1.07500
$323$	5.08137	0.282735
$324$	5.23718	0.290954
$325$	−2.30569	−0.127897
$326$	7.24113	0.401049
$327$	24.8042	1.37168
$328$	17.0710	0.942588
$329$	−38.8867	−2.14389
$330$	−7.68963	−0.423300
$331$	23.3549	1.28370	0.641851	−	0.766830i	$-0.278167\pi$
$331$	23.3549	1.28370	0.641851	+	0.766830i	$0.278167\pi$
$332$	−9.07293	−0.497942
$333$	−16.1694	−0.886075
$334$	9.55707	0.522940
$335$	−16.2666	−0.888737
$336$	2.46494	0.134474
$337$	12.4469	0.678028	0.339014	−	0.940781i	$-0.389907\pi$
$337$	12.4469	0.678028	0.339014	+	0.940781i	$0.389907\pi$
$338$	6.95157	0.378116
$339$	−9.30540	−0.505400
$340$	−1.18150	−0.0640761
$341$	9.22187	0.499392
$342$	−18.8989	−1.02194
$343$	2.70980	0.146316
$344$	−29.2907	−1.57925
$345$	−14.8265	−0.798233
$346$	−17.1099	−0.919835
$347$	15.9488	0.856175	0.428087	−	0.903737i	$-0.359188\pi$
$347$	15.9488	0.856175	0.428087	+	0.903737i	$0.359188\pi$
$348$	1.54933	0.0830527
$349$	−14.0102	−0.749949	−0.374974	−	0.927035i	$-0.622348\pi$
$349$	−14.0102	−0.749949	−0.374974	+	0.927035i	$0.622348\pi$
$350$	−3.46948	−0.185452
$351$	6.83101	0.364612
$352$	17.6535	0.940936
$353$	−34.4811	−1.83524	−0.917622	−	0.397454i	$-0.869894\pi$
$353$	−34.4811	−1.83524	−0.917622	+	0.397454i	$0.869894\pi$
$354$	−19.6173	−1.04265
$355$	−1.00000	−0.0530745
$356$	10.8630	0.575736
$357$	−10.2264	−0.541237
$358$	9.68142	0.511679
$359$	−30.9459	−1.63326	−0.816632	−	0.577159i	$-0.804161\pi$
$359$	−30.9459	−1.63326	−0.816632	+	0.577159i	$0.804161\pi$
$360$	11.8328	0.623646
$361$	6.82030	0.358963
$362$	11.9619	0.628703
$363$	2.24185	0.117666
$364$	10.4470	0.547574
$365$	7.45040	0.389972
$366$	−9.50475	−0.496821
$367$	−11.7659	−0.614173	−0.307087	−	0.951682i	$-0.599354\pi$
$367$	−11.7659	−0.614173	−0.307087	+	0.951682i	$0.599354\pi$
$368$	−1.34017	−0.0698610
$369$	24.3819	1.26927
$370$	3.55838	0.184991
$371$	−31.6055	−1.64088
$372$	−9.11566	−0.472625
$373$	−25.3759	−1.31391	−0.656957	−	0.753928i	$-0.728157\pi$
$373$	−25.3759	−1.31391	−0.656957	+	0.753928i	$0.728157\pi$
$374$	2.88363	0.149109
$375$	−2.66665	−0.137705
$376$	−29.1867	−1.50519
$377$	−1.13382	−0.0583947
$378$	10.2789	0.528691
$379$	−2.93942	−0.150988	−0.0754940	−	0.997146i	$-0.524053\pi$
$379$	−2.93942	−0.150988	−0.0754940	+	0.997146i	$0.524053\pi$
$380$	−6.00366	−0.307981
$381$	−1.40535	−0.0719981
$382$	−3.91770	−0.200447
$383$	36.2330	1.85142	0.925710	−	0.378233i	$-0.123468\pi$
$383$	36.2330	1.85142	0.925710	+	0.378233i	$0.123468\pi$
$384$	−16.2872	−0.831152
$385$	−12.2233	−0.622957
$386$	14.6116	0.743711
$387$	−41.8348	−2.12658
$388$	−7.54520	−0.383050
$389$	−10.2440	−0.519393	−0.259697	−	0.965690i	$-0.583623\pi$
$389$	−10.2440	−0.519393	−0.259697	+	0.965690i	$0.583623\pi$
$390$	−5.56257	−0.281672
$391$	5.55999	0.281181
$392$	22.1822	1.12037
$393$	8.23340	0.415320
$394$	4.90681	0.247202
$395$	12.1237	0.610011
$396$	15.4816	0.777979
$397$	−12.0107	−0.602801	−0.301401	−	0.953498i	$-0.597454\pi$
$397$	−12.0107	−0.602801	−0.301401	+	0.953498i	$0.597454\pi$
$398$	2.71948	0.136315
$399$	−51.9640	−2.60145
$400$	−0.241038	−0.0120519
$401$	7.99374	0.399188	0.199594	−	0.979879i	$-0.436038\pi$
$401$	7.99374	0.399188	0.199594	+	0.979879i	$0.436038\pi$
$402$	−39.2437	−1.95730
$403$	6.67097	0.332305
$404$	5.39694	0.268508
$405$	−4.43263	−0.220259
$406$	−1.70611	−0.0846728
$407$	12.5365	0.621411
$408$	−7.67549	−0.379994
$409$	−17.3257	−0.856701	−0.428350	−	0.903613i	$-0.640905\pi$
$409$	−17.3257	−0.856701	−0.428350	+	0.903613i	$0.640905\pi$
$410$	−5.36570	−0.264993
$411$	−13.3304	−0.657539
$412$	−20.7232	−1.02096
$413$	−31.1832	−1.53443
$414$	−20.6790	−1.01632
$415$	7.67913	0.376954
$416$	12.7703	0.626115
$417$	21.0597	1.03130
$418$	14.6528	0.716692
$419$	−30.0819	−1.46960	−0.734799	−	0.678285i	$-0.762724\pi$
$419$	−30.0819	−1.46960	−0.734799	+	0.678285i	$0.762724\pi$
$420$	12.0825	0.589566
$421$	−31.6244	−1.54128	−0.770639	−	0.637272i	$-0.780063\pi$
$421$	−31.6244	−1.54128	−0.770639	+	0.637272i	$0.780063\pi$
$422$	7.35457	0.358015
$423$	−41.6863	−2.02686
$424$	−23.7218	−1.15203
$425$	1.00000	0.0485071
$426$	−2.41254	−0.116888
$427$	−15.1086	−0.731155
$428$	−16.8535	−0.814644
$429$	−19.5974	−0.946173
$430$	9.20655	0.443979
$431$	−12.5362	−0.603846	−0.301923	−	0.953332i	$-0.597629\pi$
$431$	−12.5362	−0.603846	−0.301923	+	0.953332i	$0.597629\pi$
$432$	0.714115	0.0343579
$433$	25.1136	1.20688	0.603440	−	0.797408i	$-0.293796\pi$
$433$	25.1136	1.20688	0.603440	+	0.797408i	$0.293796\pi$
$434$	10.0381	0.481844
$435$	−1.31132	−0.0628729
$436$	10.9899	0.526322
$437$	28.2523	1.35149
$438$	17.9743	0.858848
$439$	17.8014	0.849613	0.424807	−	0.905284i	$-0.360342\pi$
$439$	17.8014	0.849613	0.424807	+	0.905284i	$0.360342\pi$
$440$	−9.17429	−0.437367
$441$	31.6820	1.50866
$442$	2.08598	0.0992199
$443$	1.33221	0.0632951	0.0316476	−	0.999499i	$-0.489925\pi$
$443$	1.33221	0.0632951	0.0316476	+	0.999499i	$0.489925\pi$
$444$	−12.3921	−0.588104
$445$	−9.19418	−0.435846
$446$	−13.2098	−0.625503
$447$	−15.8816	−0.751176
$448$	21.0648	0.995216
$449$	−39.1850	−1.84925	−0.924627	−	0.380874i	$-0.875623\pi$
$449$	−39.1850	−1.84925	−0.924627	+	0.380874i	$0.875623\pi$
$450$	−3.71926	−0.175328
$451$	−18.9039	−0.890148
$452$	−4.12292	−0.193926
$453$	−20.4875	−0.962586
$454$	5.05269	0.237134
$455$	−8.84215	−0.414526
$456$	−39.0020	−1.82644
$457$	−22.4831	−1.05171	−0.525857	−	0.850573i	$-0.676255\pi$
$457$	−22.4831	−1.05171	−0.525857	+	0.850573i	$0.676255\pi$
$458$	12.6652	0.591804
$459$	−2.96267	−0.138286
$460$	−6.56915	−0.306288
$461$	19.3278	0.900184	0.450092	−	0.892982i	$-0.351391\pi$
$461$	19.3278	0.900184	0.450092	+	0.892982i	$0.351391\pi$
$462$	−29.4891	−1.37196
$463$	10.5809	0.491738	0.245869	−	0.969303i	$-0.420927\pi$
$463$	10.5809	0.491738	0.245869	+	0.969303i	$0.420927\pi$
$464$	−0.118530	−0.00550261
$465$	7.71530	0.357788
$466$	−3.32709	−0.154124
$467$	−23.9989	−1.11054	−0.555269	−	0.831671i	$-0.687385\pi$
$467$	−23.9989	−1.11054	−0.555269	+	0.831671i	$0.687385\pi$
$468$	11.1992	0.517681
$469$	−62.3810	−2.88048
$470$	9.17388	0.423159
$471$	12.0147	0.553606
$472$	−23.4048	−1.07729
$473$	32.4355	1.49139
$474$	29.2489	1.34345
$475$	5.08137	0.233149
$476$	−4.53098	−0.207677
$477$	−33.8809	−1.55130
$478$	−17.2830	−0.790507
$479$	−36.2235	−1.65509	−0.827547	−	0.561396i	$-0.810264\pi$
$479$	−36.2235	−1.65509	−0.827547	+	0.561396i	$0.810264\pi$
$480$	14.7695	0.674131
$481$	9.06872	0.413498
$482$	−0.138546	−0.00631059
$483$	−56.8585	−2.58715
$484$	0.993290	0.0451495
$485$	6.38610	0.289978
$486$	−18.7349	−0.849834
$487$	−28.5060	−1.29173	−0.645864	−	0.763452i	$-0.723503\pi$
$487$	−28.5060	−1.29173	−0.645864	+	0.763452i	$0.723503\pi$
$488$	−11.3399	−0.513331
$489$	21.3434	0.965182
$490$	−6.97223	−0.314973
$491$	10.1603	0.458528	0.229264	−	0.973364i	$-0.426368\pi$
$491$	10.1603	0.458528	0.229264	+	0.973364i	$0.426368\pi$
$492$	18.6861	0.842436
$493$	0.491748	0.0221472
$494$	10.5996	0.476900
$495$	−13.1033	−0.588949
$496$	0.697384	0.0313135
$497$	−3.83492	−0.172020
$498$	18.5262	0.830178
$499$	15.6920	0.702469	0.351234	−	0.936288i	$-0.385762\pi$
$499$	15.6920	0.702469	0.351234	+	0.936288i	$0.385762\pi$
$500$	−1.18150	−0.0528385
$501$	28.1697	1.25853
$502$	−11.2508	−0.502148
$503$	−42.8045	−1.90856	−0.954280	−	0.298915i	$-0.903375\pi$
$503$	−42.8045	−1.90856	−0.954280	+	0.298915i	$0.903375\pi$
$504$	45.3780	2.02130
$505$	−4.56785	−0.203267
$506$	16.0330	0.712752
$507$	20.4899	0.909989
$508$	−0.622663	−0.0276262
$509$	38.6500	1.71313	0.856565	−	0.516039i	$-0.172594\pi$
$509$	38.6500	1.71313	0.856565	+	0.516039i	$0.172594\pi$
$510$	2.41254	0.106829
$511$	28.5717	1.26394
$512$	2.72258	0.120322
$513$	−15.0544	−0.664668
$514$	−9.36408	−0.413032
$515$	17.5397	0.772890
$516$	−32.0620	−1.41145
$517$	32.3204	1.42145
$518$	13.6461	0.599576
$519$	−50.4319	−2.21372
$520$	−6.63655	−0.291032
$521$	0.446738	0.0195720	0.00978598	−	0.999952i	$-0.496885\pi$
$521$	0.446738	0.0195720	0.00978598	+	0.999952i	$0.496885\pi$
$522$	−1.82894	−0.0800504
$523$	−8.24716	−0.360623	−0.180311	−	0.983610i	$-0.557711\pi$
$523$	−8.24716	−0.360623	−0.180311	+	0.983610i	$0.557711\pi$
$524$	3.64795	0.159361
$525$	−10.2264	−0.446316
$526$	−6.58455	−0.287100
$527$	−2.89326	−0.126032
$528$	−2.04872	−0.0891590
$529$	7.91344	0.344062
$530$	7.45614	0.323874
$531$	−33.4282	−1.45066
$532$	−23.0236	−0.998198
$533$	−13.6748	−0.592320
$534$	−22.1813	−0.959878
$535$	14.2644	0.616705
$536$	−46.8205	−2.02234
$537$	28.5362	1.23143
$538$	−12.5579	−0.541411
$539$	−24.5638	−1.05804
$540$	3.50041	0.150634
$541$	−10.0544	−0.432273	−0.216136	−	0.976363i	$-0.569346\pi$
$541$	−10.0544	−0.432273	−0.216136	+	0.976363i	$0.569346\pi$
$542$	27.1957	1.16816
$543$	35.2580	1.51307
$544$	−5.53859	−0.237465
$545$	−9.30164	−0.398438
$546$	−21.3320	−0.912926
$547$	1.15291	0.0492951	0.0246475	−	0.999696i	$-0.492154\pi$
$547$	1.15291	0.0492951	0.0246475	+	0.999696i	$0.492154\pi$
$548$	−5.90625	−0.252303
$549$	−16.1963	−0.691241
$550$	2.88363	0.122959
$551$	2.49875	0.106450
$552$	−42.6756	−1.81640
$553$	46.4935	1.97710
$554$	−13.4385	−0.570948
$555$	10.4884	0.445209
$556$	9.33085	0.395716
$557$	4.80775	0.203711	0.101856	−	0.994799i	$-0.467522\pi$
$557$	4.80775	0.203711	0.101856	+	0.994799i	$0.467522\pi$
$558$	10.7608	0.455540
$559$	23.4634	0.992395
$560$	−0.924360	−0.0390613
$561$	8.49958	0.358853
$562$	16.7557	0.706796
$563$	2.42232	0.102089	0.0510443	−	0.998696i	$-0.483745\pi$
$563$	2.42232	0.102089	0.0510443	+	0.998696i	$0.483745\pi$
$564$	−31.9482	−1.34526
$565$	3.48955	0.146807
$566$	3.71775	0.156269
$567$	−16.9988	−0.713882
$568$	−2.87833	−0.120772
$569$	−31.7865	−1.33256	−0.666279	−	0.745702i	$-0.732114\pi$
$569$	−31.7865	−1.33256	−0.666279	+	0.745702i	$0.732114\pi$
$570$	12.2590	0.513472
$571$	5.26252	0.220230	0.110115	−	0.993919i	$-0.464878\pi$
$571$	5.26252	0.220230	0.110115	+	0.993919i	$0.464878\pi$
$572$	−8.68298	−0.363054
$573$	−11.5475	−0.482404
$574$	−20.5770	−0.858869
$575$	5.55999	0.231867
$576$	22.5813	0.940887
$577$	1.70818	0.0711125	0.0355562	−	0.999368i	$-0.488680\pi$
$577$	1.70818	0.0711125	0.0355562	+	0.999368i	$0.488680\pi$
$578$	−0.904707	−0.0376309
$579$	43.0681	1.78985
$580$	−0.581002	−0.0241248
$581$	29.4489	1.22174
$582$	15.4067	0.638628
$583$	26.2687	1.08794
$584$	21.4447	0.887388
$585$	−9.47873	−0.391897
$586$	−12.1773	−0.503041
$587$	35.0377	1.44616	0.723081	−	0.690763i	$-0.242725\pi$
$587$	35.0377	1.44616	0.723081	+	0.690763i	$0.242725\pi$
$588$	24.2809	1.00133
$589$	−14.7017	−0.605773
$590$	7.35652	0.302863
$591$	14.4630	0.594927
$592$	0.948046	0.0389644
$593$	−30.8995	−1.26889	−0.634445	−	0.772968i	$-0.718771\pi$
$593$	−30.8995	−1.26889	−0.634445	+	0.772968i	$0.718771\pi$
$594$	−8.54325	−0.350534
$595$	3.83492	0.157216
$596$	−7.03664	−0.288232
$597$	8.01574	0.328063
$598$	11.5980	0.474278
$599$	−24.9347	−1.01881	−0.509403	−	0.860528i	$-0.670134\pi$
$599$	−24.9347	−1.01881	−0.509403	+	0.860528i	$0.670134\pi$
$600$	−7.67549	−0.313351
$601$	20.1074	0.820198	0.410099	−	0.912041i	$-0.365494\pi$
$601$	20.1074	0.820198	0.410099	+	0.912041i	$0.365494\pi$
$602$	35.3064	1.43898
$603$	−66.8720	−2.72324
$604$	−9.07734	−0.369352
$605$	−0.840699	−0.0341793
$606$	−11.0201	−0.447661
$607$	−9.83946	−0.399371	−0.199686	−	0.979860i	$-0.563992\pi$
$607$	−9.83946	−0.399371	−0.199686	+	0.979860i	$0.563992\pi$
$608$	−28.1436	−1.14137
$609$	−5.02880	−0.203777
$610$	3.56431	0.144315
$611$	23.3801	0.945858
$612$	−4.85718	−0.196340
$613$	7.77220	0.313916	0.156958	−	0.987605i	$-0.449831\pi$
$613$	7.77220	0.313916	0.156958	+	0.987605i	$0.449831\pi$
$614$	−16.8897	−0.681614
$615$	−15.8155	−0.637744
$616$	−35.1827	−1.41755
$617$	−31.0346	−1.24941	−0.624703	−	0.780862i	$-0.714780\pi$
$617$	−31.0346	−1.24941	−0.624703	+	0.780862i	$0.714780\pi$
$618$	42.3150	1.70216
$619$	−21.4247	−0.861133	−0.430566	−	0.902559i	$-0.641686\pi$
$619$	−21.4247	−0.861133	−0.430566	+	0.902559i	$0.641686\pi$
$620$	3.41840	0.137286
$621$	−16.4724	−0.661014
$622$	5.25790	0.210823
$623$	−35.2590	−1.41262
$624$	−1.48201	−0.0593280
$625$	1.00000	0.0400000
$626$	−12.2100	−0.488009
$627$	43.1895	1.72482
$628$	5.32331	0.212423
$629$	−3.93319	−0.156826
$630$	−14.2631	−0.568254
$631$	28.8332	1.14783	0.573916	−	0.818914i	$-0.305424\pi$
$631$	28.8332	1.14783	0.573916	+	0.818914i	$0.305424\pi$
$632$	34.8961	1.38809
$633$	21.6778	0.861615
$634$	19.9973	0.794193
$635$	0.527009	0.0209137
$636$	−25.9661	−1.02962
$637$	−17.7691	−0.704037
$638$	1.41802	0.0561400
$639$	−4.11101	−0.162629
$640$	6.10774	0.241429
$641$	24.2942	0.959563	0.479781	−	0.877388i	$-0.340716\pi$
$641$	24.2942	0.959563	0.479781	+	0.877388i	$0.340716\pi$
$642$	34.4134	1.35819
$643$	−3.67055	−0.144752	−0.0723762	−	0.997377i	$-0.523058\pi$
$643$	−3.67055	−0.144752	−0.0723762	+	0.997377i	$0.523058\pi$
$644$	−25.1922	−0.992710
$645$	27.1365	1.06850
$646$	−4.59715	−0.180872
$647$	21.5830	0.848515	0.424257	−	0.905542i	$-0.360535\pi$
$647$	21.5830	0.848515	0.424257	+	0.905542i	$0.360535\pi$
$648$	−12.7586	−0.501204
$649$	25.9177	1.01736
$650$	2.08598	0.0818188
$651$	29.5876	1.15963
$652$	9.45657	0.370348
$653$	15.5986	0.610421	0.305210	−	0.952285i	$-0.401273\pi$
$653$	15.5986	0.610421	0.305210	+	0.952285i	$0.401273\pi$
$654$	−22.4405	−0.877494
$655$	−3.08755	−0.120640
$656$	−1.42956	−0.0558150
$657$	30.6286	1.19494
$658$	35.1811	1.37150
$659$	41.7044	1.62457	0.812287	−	0.583258i	$-0.198222\pi$
$659$	41.7044	1.62457	0.812287	+	0.583258i	$0.198222\pi$
$660$	−10.0423	−0.390896
$661$	−23.7335	−0.923125	−0.461562	−	0.887108i	$-0.652711\pi$
$661$	−23.7335	−0.923125	−0.461562	+	0.887108i	$0.652711\pi$
$662$	−21.1294	−0.821216
$663$	6.14847	0.238787
$664$	22.1031	0.857766
$665$	19.4866	0.755660
$666$	14.6285	0.566844
$667$	2.73411	0.105865
$668$	12.4811	0.482907
$669$	−38.9362	−1.50536
$670$	14.7165	0.568547
$671$	12.5574	0.484772
$672$	56.6398	2.18493
$673$	−43.5032	−1.67692	−0.838462	−	0.544960i	$-0.816545\pi$
$673$	−43.5032	−1.67692	−0.838462	+	0.544960i	$0.816545\pi$
$674$	−11.2608	−0.433751
$675$	−2.96267	−0.114033
$676$	9.07842	0.349170
$677$	−9.09999	−0.349741	−0.174871	−	0.984591i	$-0.555951\pi$
$677$	−9.09999	−0.349741	−0.174871	+	0.984591i	$0.555951\pi$
$678$	8.41867	0.323317
$679$	24.4902	0.939847
$680$	2.87833	0.110379
$681$	14.8929	0.570698
$682$	−8.34310	−0.319474
$683$	35.9933	1.37725	0.688623	−	0.725119i	$-0.258215\pi$
$683$	35.9933	1.37725	0.688623	+	0.725119i	$0.258215\pi$
$684$	−24.6811	−0.943705
$685$	4.99892	0.190999
$686$	−2.45158	−0.0936017
$687$	37.3309	1.42426
$688$	2.45287	0.0935146
$689$	19.0024	0.723933
$690$	13.4137	0.510649
$691$	21.3413	0.811863	0.405931	−	0.913904i	$-0.366947\pi$
$691$	21.3413	0.811863	0.405931	+	0.913904i	$0.366947\pi$
$692$	−22.3447	−0.849420
$693$	−50.2501	−1.90884
$694$	−14.4290	−0.547716
$695$	−7.89743	−0.299567
$696$	−3.77441	−0.143069
$697$	5.93087	0.224648
$698$	12.6751	0.479761
$699$	−9.80668	−0.370923
$700$	−4.53098	−0.171255
$701$	1.42822	0.0539432	0.0269716	−	0.999636i	$-0.491414\pi$
$701$	1.42822	0.0539432	0.0269716	+	0.999636i	$0.491414\pi$
$702$	−6.18006	−0.233251
$703$	−19.9860	−0.753785
$704$	−17.5078	−0.659851
$705$	27.0402	1.01839
$706$	31.1953	1.17405
$707$	−17.5173	−0.658807
$708$	−25.6192	−0.962828
$709$	28.9592	1.08759	0.543793	−	0.839219i	$-0.316988\pi$
$709$	28.9592	1.08759	0.543793	+	0.839219i	$0.316988\pi$
$710$	0.904707	0.0339531
$711$	49.8407	1.86917
$712$	−26.4639	−0.991777
$713$	−16.0865	−0.602443
$714$	9.25188	0.346243
$715$	7.34909	0.274840
$716$	12.6435	0.472509
$717$	−50.9421	−1.90247
$718$	27.9970	1.04484
$719$	−48.7250	−1.81714	−0.908568	−	0.417738i	$-0.862823\pi$
$719$	−48.7250	−1.81714	−0.908568	+	0.417738i	$0.862823\pi$
$720$	−0.990908	−0.0369290
$721$	67.2632	2.50501
$722$	−6.17038	−0.229638
$723$	−0.408367	−0.0151873
$724$	15.6217	0.580575
$725$	0.491748	0.0182631
$726$	−2.02822	−0.0752742
$727$	−50.7792	−1.88330	−0.941648	−	0.336599i	$-0.890723\pi$
$727$	−50.7792	−1.88330	−0.941648	+	0.336599i	$0.890723\pi$
$728$	−25.4506	−0.943263
$729$	−41.9238	−1.55273
$730$	−6.74043	−0.249474
$731$	−10.1763	−0.376383
$732$	−12.4128	−0.458788
$733$	18.5399	0.684788	0.342394	−	0.939557i	$-0.388762\pi$
$733$	18.5399	0.684788	0.342394	+	0.939557i	$0.388762\pi$
$734$	10.6447	0.392902
$735$	−20.5508	−0.758028
$736$	−30.7945	−1.13510
$737$	51.8475	1.90983
$738$	−22.0584	−0.811983
$739$	−21.9117	−0.806035	−0.403017	−	0.915192i	$-0.632039\pi$
$739$	−21.9117	−0.806035	−0.403017	+	0.915192i	$0.632039\pi$
$740$	4.64708	0.170830
$741$	31.2427	1.14773
$742$	28.5937	1.04971
$743$	12.4786	0.457795	0.228897	−	0.973451i	$-0.426488\pi$
$743$	12.4786	0.457795	0.228897	+	0.973451i	$0.426488\pi$
$744$	22.2072	0.814155
$745$	5.95566	0.218198
$746$	22.9578	0.840543
$747$	31.5690	1.15505
$748$	3.76589	0.137694
$749$	54.7030	1.99880
$750$	2.41254	0.0880933
$751$	1.68838	0.0616098	0.0308049	−	0.999525i	$-0.490193\pi$
$751$	1.68838	0.0616098	0.0308049	+	0.999525i	$0.490193\pi$
$752$	2.44416	0.0891294
$753$	−33.1620	−1.20849
$754$	1.02578	0.0373565
$755$	7.68286	0.279608
$756$	13.4238	0.488218
$757$	−39.3561	−1.43042	−0.715210	−	0.698909i	$-0.753669\pi$
$757$	−39.3561	−1.43042	−0.715210	+	0.698909i	$0.753669\pi$
$758$	2.65932	0.0965908
$759$	47.2575	1.71534
$760$	14.6259	0.530536
$761$	−20.1892	−0.731857	−0.365928	−	0.930643i	$-0.619249\pi$
$761$	−20.1892	−0.731857	−0.365928	+	0.930643i	$0.619249\pi$
$762$	1.27143	0.0460590
$763$	−35.6710	−1.29138
$764$	−5.11633	−0.185102
$765$	4.11101	0.148634
$766$	−32.7803	−1.18440
$767$	18.7485	0.676968
$768$	44.0303	1.58881
$769$	−2.13685	−0.0770570	−0.0385285	−	0.999258i	$-0.512267\pi$
$769$	−2.13685	−0.0770570	−0.0385285	+	0.999258i	$0.512267\pi$
$770$	11.0585	0.398521
$771$	−27.6009	−0.994021
$772$	19.0821	0.686778
$773$	−18.7617	−0.674812	−0.337406	−	0.941359i	$-0.609550\pi$
$773$	−18.7617	−0.674812	−0.337406	+	0.941359i	$0.609550\pi$
$774$	37.8482	1.36043
$775$	−2.89326	−0.103929
$776$	18.3813	0.659850
$777$	40.2222	1.44297
$778$	9.26786	0.332269
$779$	30.1369	1.07977
$780$	−7.26445	−0.260109
$781$	3.18737	0.114053
$782$	−5.03016	−0.179878
$783$	−1.45689	−0.0520649
$784$	−1.85758	−0.0663423
$785$	−4.50553	−0.160809
$786$	−7.44882	−0.265690
$787$	−19.3807	−0.690848	−0.345424	−	0.938447i	$-0.612265\pi$
$787$	−19.3807	−0.690848	−0.345424	+	0.938447i	$0.612265\pi$
$788$	6.40806	0.228278
$789$	−19.4081	−0.690948
$790$	−10.9684	−0.390239
$791$	13.3822	0.475815
$792$	−37.7156	−1.34017
$793$	9.08382	0.322576
$794$	10.8662	0.385627
$795$	21.9772	0.779450
$796$	3.55152	0.125880
$797$	−15.1629	−0.537096	−0.268548	−	0.963266i	$-0.586544\pi$
$797$	−15.1629	−0.537096	−0.268548	+	0.963266i	$0.586544\pi$
$798$	47.0122	1.66421
$799$	−10.1402	−0.358733
$800$	−5.53859	−0.195819
$801$	−37.7974	−1.33550
$802$	−7.23199	−0.255371
$803$	−23.7471	−0.838018
$804$	−51.2503	−1.80746
$805$	21.3221	0.751505
$806$	−6.03527	−0.212583
$807$	−37.0148	−1.30298
$808$	−13.1478	−0.462537
$809$	31.4026	1.10406	0.552028	−	0.833825i	$-0.313854\pi$
$809$	31.4026	1.10406	0.552028	+	0.833825i	$0.313854\pi$
$810$	4.01024	0.140905
$811$	16.8995	0.593421	0.296710	−	0.954968i	$-0.404110\pi$
$811$	16.8995	0.593421	0.296710	+	0.954968i	$0.404110\pi$
$812$	−2.22810	−0.0781909
$813$	80.1601	2.81134
$814$	−11.3419	−0.397532
$815$	−8.00384	−0.280362
$816$	0.642762	0.0225012
$817$	−51.7094	−1.80908
$818$	15.6747	0.548053
$819$	−36.3502	−1.27018
$820$	−7.00735	−0.244707
$821$	−28.9767	−1.01129	−0.505646	−	0.862741i	$-0.668746\pi$
$821$	−28.9767	−1.01129	−0.505646	+	0.862741i	$0.668746\pi$
$822$	12.0601	0.420644
$823$	8.82609	0.307658	0.153829	−	0.988097i	$-0.450840\pi$
$823$	8.82609	0.307658	0.153829	+	0.988097i	$0.450840\pi$
$824$	50.4849	1.75873
$825$	8.49958	0.295917
$826$	28.2117	0.981610
$827$	37.4407	1.30194	0.650970	−	0.759103i	$-0.274362\pi$
$827$	37.4407	1.30194	0.650970	+	0.759103i	$0.274362\pi$
$828$	−27.0058	−0.938517
$829$	−18.1573	−0.630631	−0.315315	−	0.948987i	$-0.602110\pi$
$829$	−18.1573	−0.630631	−0.315315	+	0.948987i	$0.602110\pi$
$830$	−6.94737	−0.241147
$831$	−39.6104	−1.37407
$832$	−12.6649	−0.439076
$833$	7.70661	0.267018
$834$	−19.0528	−0.659746
$835$	−10.5637	−0.365572
$836$	19.1359	0.661828
$837$	8.57177	0.296284
$838$	27.2153	0.940138
$839$	33.1009	1.14277	0.571385	−	0.820682i	$-0.306406\pi$
$839$	33.1009	1.14277	0.571385	+	0.820682i	$0.306406\pi$
$840$	−29.4349	−1.01560
$841$	−28.7582	−0.991662
$842$	28.6108	0.985993
$843$	49.3878	1.70101
$844$	9.60472	0.330608
$845$	−7.68378	−0.264330
$846$	37.7139	1.29663
$847$	−3.22401	−0.110778
$848$	1.98651	0.0682171
$849$	10.9582	0.376084
$850$	−0.904707	−0.0310312
$851$	−21.8685	−0.749641
$852$	−3.15066	−0.107940
$853$	14.8209	0.507458	0.253729	−	0.967275i	$-0.418343\pi$
$853$	14.8209	0.507458	0.253729	+	0.967275i	$0.418343\pi$
$854$	13.6688	0.467738
$855$	20.8895	0.714408
$856$	41.0578	1.40333
$857$	51.7711	1.76847	0.884233	−	0.467046i	$-0.154682\pi$
$857$	51.7711	1.76847	0.884233	+	0.467046i	$0.154682\pi$
$858$	17.7299	0.605290
$859$	52.8611	1.80360	0.901799	−	0.432155i	$-0.142247\pi$
$859$	52.8611	1.80360	0.901799	+	0.432155i	$0.142247\pi$
$860$	12.0233	0.409992
$861$	−60.6513	−2.06699
$862$	11.3416	0.386295
$863$	35.4963	1.20831	0.604154	−	0.796867i	$-0.293511\pi$
$863$	35.4963	1.20831	0.604154	+	0.796867i	$0.293511\pi$
$864$	16.4090	0.558246
$865$	18.9121	0.643031
$866$	−22.7204	−0.772071
$867$	−2.66665	−0.0905641
$868$	13.1093	0.444958
$869$	−38.6427	−1.31086
$870$	1.18636	0.0402213
$871$	37.5057	1.27083
$872$	−26.7732	−0.906655
$873$	26.2533	0.888540
$874$	−25.5601	−0.864583
$875$	3.83492	0.129644
$876$	23.4736	0.793101
$877$	31.2208	1.05425	0.527126	−	0.849787i	$-0.323270\pi$
$877$	31.2208	1.05425	0.527126	+	0.849787i	$0.323270\pi$
$878$	−16.1050	−0.543519
$879$	−35.8930	−1.21064
$880$	0.768275	0.0258985
$881$	−22.5259	−0.758918	−0.379459	−	0.925209i	$-0.623890\pi$
$881$	−22.5259	−0.758918	−0.379459	+	0.925209i	$0.623890\pi$
$882$	−28.6629	−0.965130
$883$	−8.85240	−0.297907	−0.148953	−	0.988844i	$-0.547590\pi$
$883$	−8.85240	−0.297907	−0.148953	+	0.988844i	$0.547590\pi$
$884$	2.72419	0.0916244
$885$	21.6835	0.728884
$886$	−1.20526	−0.0404914
$887$	12.9092	0.433449	0.216724	−	0.976233i	$-0.430463\pi$
$887$	12.9092	0.433449	0.216724	+	0.976233i	$0.430463\pi$
$888$	30.1891	1.01308
$889$	2.02104	0.0677834
$890$	8.31805	0.278822
$891$	14.1284	0.473320
$892$	−17.2514	−0.577619
$893$	−51.5259	−1.72425
$894$	14.3682	0.480546
$895$	−10.7012	−0.357700
$896$	23.4227	0.782497
$897$	34.1854	1.14142
$898$	35.4509	1.18301
$899$	−1.42275	−0.0474515
$900$	−4.85718	−0.161906
$901$	−8.24150	−0.274564
$902$	17.1025	0.569449
$903$	104.066	3.46312
$904$	10.0441	0.334061
$905$	−13.2218	−0.439509
$906$	18.5352	0.615790
$907$	46.0153	1.52791	0.763956	−	0.645269i	$-0.223255\pi$
$907$	46.0153	1.52791	0.763956	+	0.645269i	$0.223255\pi$
$908$	6.59857	0.218981
$909$	−18.7785	−0.622843
$910$	7.99956	0.265183
$911$	10.4554	0.346402	0.173201	−	0.984887i	$-0.444589\pi$
$911$	10.4554	0.346402	0.173201	+	0.984887i	$0.444589\pi$
$912$	3.26611	0.108152
$913$	−24.4762	−0.810044
$914$	20.3406	0.672808
$915$	10.5059	0.347314
$916$	16.5401	0.546500
$917$	−11.8405	−0.391008
$918$	2.68035	0.0884647
$919$	−52.2507	−1.72359	−0.861795	−	0.507256i	$-0.830660\pi$
$919$	−52.2507	−1.72359	−0.861795	+	0.507256i	$0.830660\pi$
$920$	16.0035	0.527619
$921$	−49.7829	−1.64040
$922$	−17.4860	−0.575870
$923$	2.30569	0.0758928
$924$	−38.5114	−1.26693
$925$	−3.93319	−0.129322
$926$	−9.57266	−0.314577
$927$	72.1057	2.36826
$928$	−2.72359	−0.0894063
$929$	−37.9752	−1.24593	−0.622963	−	0.782251i	$-0.714071\pi$
$929$	−37.9752	−1.24593	−0.622963	+	0.782251i	$0.714071\pi$
$930$	−6.98009	−0.228886
$931$	39.1601	1.28342
$932$	−4.34502	−0.142326
$933$	15.4978	0.507375
$934$	21.7120	0.710438
$935$	−3.18737	−0.104238
$936$	−27.2829	−0.891770
$937$	−41.7975	−1.36546	−0.682732	−	0.730669i	$-0.739208\pi$
$937$	−41.7975	−1.36546	−0.682732	+	0.730669i	$0.739208\pi$
$938$	56.4365	1.84272
$939$	−35.9892	−1.17446
$940$	11.9806	0.390766
$941$	−12.8317	−0.418302	−0.209151	−	0.977883i	$-0.567070\pi$
$941$	−12.8317	−0.418302	−0.209151	+	0.977883i	$0.567070\pi$
$942$	−10.8698	−0.354156
$943$	32.9755	1.07383
$944$	1.95997	0.0637916
$945$	−11.3616	−0.369593
$946$	−29.3447	−0.954077
$947$	−16.8285	−0.546852	−0.273426	−	0.961893i	$-0.588157\pi$
$947$	−16.8285	−0.546852	−0.273426	+	0.961893i	$0.588157\pi$
$948$	38.1977	1.24060
$949$	−17.1783	−0.557632
$950$	−4.59715	−0.149151
$951$	58.9424	1.91134
$952$	11.0382	0.357749
$953$	30.2845	0.981011	0.490505	−	0.871438i	$-0.336812\pi$
$953$	30.2845	0.981011	0.490505	+	0.871438i	$0.336812\pi$
$954$	30.6523	0.992404
$955$	4.33035	0.140127
$956$	−22.5708	−0.729992
$957$	4.17965	0.135109
$958$	32.7717	1.05880
$959$	19.1705	0.619047
$960$	−14.6476	−0.472749
$961$	−22.6291	−0.729970
$962$	−8.20454	−0.264525
$963$	58.6412	1.88969
$964$	−0.180934	−0.00582750
$965$	−16.1506	−0.519907
$966$	51.4403	1.65507
$967$	−40.5067	−1.30261	−0.651304	−	0.758817i	$-0.725778\pi$
$967$	−40.5067	−1.30261	−0.651304	+	0.758817i	$0.725778\pi$
$968$	−2.41981	−0.0777756
$969$	−13.5502	−0.435296
$970$	−5.77755	−0.185506
$971$	−33.2284	−1.06635	−0.533175	−	0.846005i	$-0.679001\pi$
$971$	−33.2284	−1.06635	−0.533175	+	0.846005i	$0.679001\pi$
$972$	−24.4669	−0.784777
$973$	−30.2860	−0.970925
$974$	25.7895	0.826350
$975$	6.14847	0.196909
$976$	0.949624	0.0303967
$977$	−34.6478	−1.10848	−0.554240	−	0.832357i	$-0.686991\pi$
$977$	−34.6478	−1.10848	−0.554240	+	0.832357i	$0.686991\pi$
$978$	−19.3095	−0.617451
$979$	29.3052	0.936599
$980$	−9.10540	−0.290861
$981$	−38.2391	−1.22088
$982$	−9.19210	−0.293332
$983$	−5.38816	−0.171856	−0.0859278	−	0.996301i	$-0.527385\pi$
$983$	−5.38816	−0.171856	−0.0859278	+	0.996301i	$0.527385\pi$
$984$	−45.5223	−1.45120
$985$	−5.42365	−0.172812
$986$	−0.444888	−0.0141681
$987$	103.697	3.30072
$988$	13.8426	0.440392
$989$	−56.5800	−1.79914
$990$	11.8546	0.376765
$991$	4.75769	0.151133	0.0755664	−	0.997141i	$-0.475924\pi$
$991$	4.75769	0.151133	0.0755664	+	0.997141i	$0.475924\pi$
$992$	16.0246	0.508781
$993$	−62.2793	−1.97637
$994$	3.46948	0.110045
$995$	−3.00593	−0.0952943
$996$	24.1943	0.766626
$997$	−35.0579	−1.11029	−0.555147	−	0.831752i	$-0.687338\pi$
$997$	−35.0579	−1.11029	−0.555147	+	0.831752i	$0.687338\pi$
$998$	−14.1966	−0.449386
$999$	11.6527	0.368676

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.a.1.14	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.a.1.14	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-0.904707 q^{2} -2.66665 q^{3} -1.18150 q^{4} +1.00000 q^{5} +2.41254 q^{6} +3.83492 q^{7} +2.87833 q^{8} +4.11101 q^{9} +O(q^{10})\)	\(q-0.904707 q^{2} -2.66665 q^{3} -1.18150 q^{4} +1.00000 q^{5} +2.41254 q^{6} +3.83492 q^{7} +2.87833 q^{8} +4.11101 q^{9} -0.904707 q^{10} -3.18737 q^{11} +3.15066 q^{12} -2.30569 q^{13} -3.46948 q^{14} -2.66665 q^{15} -0.241038 q^{16} +1.00000 q^{17} -3.71926 q^{18} +5.08137 q^{19} -1.18150 q^{20} -10.2264 q^{21} +2.88363 q^{22} +5.55999 q^{23} -7.67549 q^{24} +1.00000 q^{25} +2.08598 q^{26} -2.96267 q^{27} -4.53098 q^{28} +0.491748 q^{29} +2.41254 q^{30} -2.89326 q^{31} -5.53859 q^{32} +8.49958 q^{33} -0.904707 q^{34} +3.83492 q^{35} -4.85718 q^{36} -3.93319 q^{37} -4.59715 q^{38} +6.14847 q^{39} +2.87833 q^{40} +5.93087 q^{41} +9.25188 q^{42} -10.1763 q^{43} +3.76589 q^{44} +4.11101 q^{45} -5.03016 q^{46} -10.1402 q^{47} +0.642762 q^{48} +7.70661 q^{49} -0.904707 q^{50} -2.66665 q^{51} +2.72419 q^{52} -8.24150 q^{53} +2.68035 q^{54} -3.18737 q^{55} +11.0382 q^{56} -13.5502 q^{57} -0.444888 q^{58} -8.13138 q^{59} +3.15066 q^{60} -3.93974 q^{61} +2.61755 q^{62} +15.7654 q^{63} +5.49288 q^{64} -2.30569 q^{65} -7.68963 q^{66} -16.2666 q^{67} -1.18150 q^{68} -14.8265 q^{69} -3.46948 q^{70} -1.00000 q^{71} +11.8328 q^{72} +7.45040 q^{73} +3.55838 q^{74} -2.66665 q^{75} -6.00366 q^{76} -12.2233 q^{77} -5.56257 q^{78} +12.1237 q^{79} -0.241038 q^{80} -4.43263 q^{81} -5.36570 q^{82} +7.67913 q^{83} +12.0825 q^{84} +1.00000 q^{85} +9.20655 q^{86} -1.31132 q^{87} -9.17429 q^{88} -9.19418 q^{89} -3.71926 q^{90} -8.84215 q^{91} -6.56915 q^{92} +7.71530 q^{93} +9.17388 q^{94} +5.08137 q^{95} +14.7695 q^{96} +6.38610 q^{97} -6.97223 q^{98} -13.1033 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9}+O(q^{10}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9	\( 36 q - 3 q^{2} - 8 q^{3} + 23 q^{4} + 36 q^{5} - 10 q^{6} - 7 q^{7} - 9 q^{8} + 10 q^{9} - 3 q^{10} - 20 q^{11} - 8 q^{12} - 29 q^{13} - 12 q^{14} - 8 q^{15} + q^{16} + 36 q^{17} - 8 q^{18} - 19 q^{19} + 23 q^{20} - 19 q^{21} - 10 q^{22} - 10 q^{23} - 23 q^{24} + 36 q^{25} - 32 q^{26} - 23 q^{27} - 20 q^{28} - 52 q^{29} - 10 q^{30} - 15 q^{31} - 16 q^{32} - 19 q^{33} - 3 q^{34} - 7 q^{35} + 9 q^{36} - 52 q^{37} + 7 q^{38} - 10 q^{39} - 9 q^{40} - 51 q^{41} - 2 q^{42} - 13 q^{43} - 27 q^{44} + 10 q^{45} + 12 q^{46} - 24 q^{47} + 12 q^{48} - 15 q^{49} - 3 q^{50} - 8 q^{51} - 49 q^{52} - 13 q^{53} - 48 q^{54} - 20 q^{55} - 12 q^{56} - 20 q^{57} - 20 q^{58} - 14 q^{59} - 8 q^{60} - 75 q^{61} - 7 q^{62} + 16 q^{63} - 41 q^{64} - 29 q^{65} - q^{66} - 5 q^{67} + 23 q^{68} - 37 q^{69} - 12 q^{70} - 36 q^{71} - 23 q^{72} - 21 q^{73} + q^{74} - 8 q^{75} - 40 q^{76} - 31 q^{77} + 84 q^{78} - 49 q^{79} + q^{80} - 56 q^{81} - 51 q^{82} + 6 q^{83} + 10 q^{84} + 36 q^{85} - 41 q^{86} - 4 q^{87} - 21 q^{88} - 78 q^{89} - 8 q^{90} - 25 q^{91} - 24 q^{92} - 36 q^{93} + 6 q^{94} - 19 q^{95} - 71 q^{96} - 48 q^{97} + 51 q^{98} - 17 q^{99}+O(q^{100}) \) 36 * q - 3 * q^2 - 8 * q^3 + 23 * q^4 + 36 * q^5 - 10 * q^6 - 7 * q^7 - 9 * q^8 + 10 * q^9 - 3 * q^10 - 20 * q^11 - 8 * q^12 - 29 * q^13 - 12 * q^14 - 8 * q^15 + q^16 + 36 * q^17 - 8 * q^18 - 19 * q^19 + 23 * q^20 - 19 * q^21 - 10 * q^22 - 10 * q^23 - 23 * q^24 + 36 * q^25 - 32 * q^26 - 23 * q^27 - 20 * q^28 - 52 * q^29 - 10 * q^30 - 15 * q^31 - 16 * q^32 - 19 * q^33 - 3 * q^34 - 7 * q^35 + 9 * q^36 - 52 * q^37 + 7 * q^38 - 10 * q^39 - 9 * q^40 - 51 * q^41 - 2 * q^42 - 13 * q^43 - 27 * q^44 + 10 * q^45 + 12 * q^46 - 24 * q^47 + 12 * q^48 - 15 * q^49 - 3 * q^50 - 8 * q^51 - 49 * q^52 - 13 * q^53 - 48 * q^54 - 20 * q^55 - 12 * q^56 - 20 * q^57 - 20 * q^58 - 14 * q^59 - 8 * q^60 - 75 * q^61 - 7 * q^62 + 16 * q^63 - 41 * q^64 - 29 * q^65 - q^66 - 5 * q^67 + 23 * q^68 - 37 * q^69 - 12 * q^70 - 36 * q^71 - 23 * q^72 - 21 * q^73 + q^74 - 8 * q^75 - 40 * q^76 - 31 * q^77 + 84 * q^78 - 49 * q^79 + q^80 - 56 * q^81 - 51 * q^82 + 6 * q^83 + 10 * q^84 + 36 * q^85 - 41 * q^86 - 4 * q^87 - 21 * q^88 - 78 * q^89 - 8 * q^90 - 25 * q^91 - 24 * q^92 - 36 * q^93 + 6 * q^94 - 19 * q^95 - 71 * q^96 - 48 * q^97 + 51 * q^98 - 17 * q^99

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