LMFDB - Embedded newform 6022.2.a.c.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.27129 q^{3} +1.00000 q^{4} +2.47111 q^{5} +1.27129 q^{6} -1.62843 q^{7} -1.00000 q^{8} -1.38382 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.27129 q^{3} +1.00000 q^{4} +2.47111 q^{5} +1.27129 q^{6} -1.62843 q^{7} -1.00000 q^{8} -1.38382 q^{9} -2.47111 q^{10} +4.15744 q^{11} -1.27129 q^{12} -4.62677 q^{13} +1.62843 q^{14} -3.14150 q^{15} +1.00000 q^{16} +6.16369 q^{17} +1.38382 q^{18} +6.97230 q^{19} +2.47111 q^{20} +2.07021 q^{21} -4.15744 q^{22} +6.05269 q^{23} +1.27129 q^{24} +1.10637 q^{25} +4.62677 q^{26} +5.57311 q^{27} -1.62843 q^{28} +5.40377 q^{29} +3.14150 q^{30} +2.70475 q^{31} -1.00000 q^{32} -5.28532 q^{33} -6.16369 q^{34} -4.02403 q^{35} -1.38382 q^{36} +5.27941 q^{37} -6.97230 q^{38} +5.88197 q^{39} -2.47111 q^{40} -8.27673 q^{41} -2.07021 q^{42} +4.18733 q^{43} +4.15744 q^{44} -3.41956 q^{45} -6.05269 q^{46} -5.63615 q^{47} -1.27129 q^{48} -4.34822 q^{49} -1.10637 q^{50} -7.83584 q^{51} -4.62677 q^{52} +2.81949 q^{53} -5.57311 q^{54} +10.2735 q^{55} +1.62843 q^{56} -8.86382 q^{57} -5.40377 q^{58} -13.1870 q^{59} -3.14150 q^{60} +3.72080 q^{61} -2.70475 q^{62} +2.25345 q^{63} +1.00000 q^{64} -11.4332 q^{65} +5.28532 q^{66} -7.27636 q^{67} +6.16369 q^{68} -7.69473 q^{69} +4.02403 q^{70} -13.1565 q^{71} +1.38382 q^{72} +3.43110 q^{73} -5.27941 q^{74} -1.40652 q^{75} +6.97230 q^{76} -6.77011 q^{77} -5.88197 q^{78} +4.80458 q^{79} +2.47111 q^{80} -2.93359 q^{81} +8.27673 q^{82} +6.82574 q^{83} +2.07021 q^{84} +15.2311 q^{85} -4.18733 q^{86} -6.86977 q^{87} -4.15744 q^{88} +1.20472 q^{89} +3.41956 q^{90} +7.53436 q^{91} +6.05269 q^{92} -3.43852 q^{93} +5.63615 q^{94} +17.2293 q^{95} +1.27129 q^{96} +13.1745 q^{97} +4.34822 q^{98} -5.75315 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.27129	−0.733980	−0.366990	−	0.930225i	$-0.619612\pi$
$3$	−1.27129	−0.733980	−0.366990	+	0.930225i	$0.619612\pi$
$4$	1.00000	0.500000
$5$	2.47111	1.10511	0.552556	−	0.833475i	$-0.313652\pi$
$5$	2.47111	1.10511	0.552556	+	0.833475i	$0.313652\pi$
$6$	1.27129	0.519002
$7$	−1.62843	−0.615489	−0.307744	−	0.951469i	$-0.599574\pi$
$7$	−1.62843	−0.615489	−0.307744	+	0.951469i	$0.599574\pi$
$8$	−1.00000	−0.353553
$9$	−1.38382	−0.461273
$10$	−2.47111	−0.781433
$11$	4.15744	1.25352	0.626758	−	0.779214i	$-0.284381\pi$
$11$	4.15744	1.25352	0.626758	+	0.779214i	$0.284381\pi$
$12$	−1.27129	−0.366990
$13$	−4.62677	−1.28323	−0.641617	−	0.767025i	$-0.721736\pi$
$13$	−4.62677	−1.28323	−0.641617	+	0.767025i	$0.721736\pi$
$14$	1.62843	0.435216
$15$	−3.14150	−0.811131
$16$	1.00000	0.250000
$17$	6.16369	1.49491	0.747457	−	0.664310i	$-0.231275\pi$
$17$	6.16369	1.49491	0.747457	+	0.664310i	$0.231275\pi$
$18$	1.38382	0.326169
$19$	6.97230	1.59955	0.799777	−	0.600297i	$-0.204951\pi$
$19$	6.97230	1.59955	0.799777	+	0.600297i	$0.204951\pi$
$20$	2.47111	0.552556
$21$	2.07021	0.451757
$22$	−4.15744	−0.886370
$23$	6.05269	1.26207	0.631036	−	0.775753i	$-0.282630\pi$
$23$	6.05269	1.26207	0.631036	+	0.775753i	$0.282630\pi$
$24$	1.27129	0.259501
$25$	1.10637	0.221274
$26$	4.62677	0.907383
$27$	5.57311	1.07255
$28$	−1.62843	−0.307744
$29$	5.40377	1.00346	0.501728	−	0.865026i	$-0.332698\pi$
$29$	5.40377	1.00346	0.501728	+	0.865026i	$0.332698\pi$
$30$	3.14150	0.573556
$31$	2.70475	0.485787	0.242894	−	0.970053i	$-0.421903\pi$
$31$	2.70475	0.485787	0.242894	+	0.970053i	$0.421903\pi$
$32$	−1.00000	−0.176777
$33$	−5.28532	−0.920056
$34$	−6.16369	−1.05706
$35$	−4.02403	−0.680184
$36$	−1.38382	−0.230636
$37$	5.27941	0.867929	0.433965	−	0.900930i	$-0.357114\pi$
$37$	5.27941	0.867929	0.433965	+	0.900930i	$0.357114\pi$
$38$	−6.97230	−1.13106
$39$	5.88197	0.941868
$40$	−2.47111	−0.390716
$41$	−8.27673	−1.29261	−0.646304	−	0.763080i	$-0.723686\pi$
$41$	−8.27673	−1.29261	−0.646304	+	0.763080i	$0.723686\pi$
$42$	−2.07021	−0.319440
$43$	4.18733	0.638562	0.319281	−	0.947660i	$-0.396559\pi$
$43$	4.18733	0.638562	0.319281	+	0.947660i	$0.396559\pi$
$44$	4.15744	0.626758
$45$	−3.41956	−0.509759
$46$	−6.05269	−0.892420
$47$	−5.63615	−0.822117	−0.411058	−	0.911609i	$-0.634841\pi$
$47$	−5.63615	−0.822117	−0.411058	+	0.911609i	$0.634841\pi$
$48$	−1.27129	−0.183495
$49$	−4.34822	−0.621174
$50$	−1.10637	−0.156465
$51$	−7.83584	−1.09724
$52$	−4.62677	−0.641617
$53$	2.81949	0.387286	0.193643	−	0.981072i	$-0.437970\pi$
$53$	2.81949	0.387286	0.193643	+	0.981072i	$0.437970\pi$
$54$	−5.57311	−0.758404
$55$	10.2735	1.38528
$56$	1.62843	0.217608
$57$	−8.86382	−1.17404
$58$	−5.40377	−0.709550
$59$	−13.1870	−1.71681	−0.858403	−	0.512976i	$-0.828543\pi$
$59$	−13.1870	−1.71681	−0.858403	+	0.512976i	$0.828543\pi$
$60$	−3.14150	−0.405566
$61$	3.72080	0.476399	0.238199	−	0.971216i	$-0.423443\pi$
$61$	3.72080	0.476399	0.238199	+	0.971216i	$0.423443\pi$
$62$	−2.70475	−0.343503
$63$	2.25345	0.283908
$64$	1.00000	0.125000
$65$	−11.4332	−1.41812
$66$	5.28532	0.650578
$67$	−7.27636	−0.888949	−0.444475	−	0.895791i	$-0.646610\pi$
$67$	−7.27636	−0.888949	−0.444475	+	0.895791i	$0.646610\pi$
$68$	6.16369	0.747457
$69$	−7.69473	−0.926336
$70$	4.02403	0.480963
$71$	−13.1565	−1.56139	−0.780694	−	0.624913i	$-0.785134\pi$
$71$	−13.1565	−1.56139	−0.780694	+	0.624913i	$0.785134\pi$
$72$	1.38382	0.163085
$73$	3.43110	0.401580	0.200790	−	0.979634i	$-0.435649\pi$
$73$	3.43110	0.401580	0.200790	+	0.979634i	$0.435649\pi$
$74$	−5.27941	−0.613719
$75$	−1.40652	−0.162411
$76$	6.97230	0.799777
$77$	−6.77011	−0.771525
$78$	−5.88197	−0.666002
$79$	4.80458	0.540557	0.270279	−	0.962782i	$-0.412884\pi$
$79$	4.80458	0.540557	0.270279	+	0.962782i	$0.412884\pi$
$80$	2.47111	0.276278
$81$	−2.93359	−0.325954
$82$	8.27673	0.914012
$83$	6.82574	0.749222	0.374611	−	0.927182i	$-0.377776\pi$
$83$	6.82574	0.749222	0.374611	+	0.927182i	$0.377776\pi$
$84$	2.07021	0.225878
$85$	15.2311	1.65205
$86$	−4.18733	−0.451532
$87$	−6.86977	−0.736517
$88$	−4.15744	−0.443185
$89$	1.20472	0.127700	0.0638499	−	0.997960i	$-0.479662\pi$
$89$	1.20472	0.127700	0.0638499	+	0.997960i	$0.479662\pi$
$90$	3.41956	0.360454
$91$	7.53436	0.789816
$92$	6.05269	0.631036
$93$	−3.43852	−0.356558
$94$	5.63615	0.581324
$95$	17.2293	1.76769
$96$	1.27129	0.129751
$97$	13.1745	1.33766	0.668832	−	0.743413i	$-0.266794\pi$
$97$	13.1745	1.33766	0.668832	+	0.743413i	$0.266794\pi$
$98$	4.34822	0.439236
$99$	−5.75315	−0.578213
$100$	1.10637	0.110637
$101$	−1.99778	−0.198786	−0.0993931	−	0.995048i	$-0.531690\pi$
$101$	−1.99778	−0.198786	−0.0993931	+	0.995048i	$0.531690\pi$
$102$	7.83584	0.775864
$103$	8.77836	0.864958	0.432479	−	0.901644i	$-0.357639\pi$
$103$	8.77836	0.864958	0.432479	+	0.901644i	$0.357639\pi$
$104$	4.62677	0.453692
$105$	5.11571	0.499242
$106$	−2.81949	−0.273853
$107$	−5.51490	−0.533145	−0.266573	−	0.963815i	$-0.585891\pi$
$107$	−5.51490	−0.533145	−0.266573	+	0.963815i	$0.585891\pi$
$108$	5.57311	0.536273
$109$	−9.68077	−0.927250	−0.463625	−	0.886032i	$-0.653451\pi$
$109$	−9.68077	−0.927250	−0.463625	+	0.886032i	$0.653451\pi$
$110$	−10.2735	−0.979539
$111$	−6.71166	−0.637043
$112$	−1.62843	−0.153872
$113$	4.34445	0.408692	0.204346	−	0.978899i	$-0.434493\pi$
$113$	4.34445	0.408692	0.204346	+	0.978899i	$0.434493\pi$
$114$	8.86382	0.830173
$115$	14.9568	1.39473
$116$	5.40377	0.501728
$117$	6.40260	0.591921
$118$	13.1870	1.21397
$119$	−10.0371	−0.920103
$120$	3.14150	0.286778
$121$	6.28434	0.571303
$122$	−3.72080	−0.336865
$123$	10.5221	0.948749
$124$	2.70475	0.242894
$125$	−9.62157	−0.860580
$126$	−2.25345	−0.200753
$127$	−5.42487	−0.481379	−0.240689	−	0.970602i	$-0.577374\pi$
$127$	−5.42487	−0.481379	−0.240689	+	0.970602i	$0.577374\pi$
$128$	−1.00000	−0.0883883
$129$	−5.32332	−0.468692
$130$	11.4332	1.00276
$131$	−12.4818	−1.09054	−0.545268	−	0.838262i	$-0.683572\pi$
$131$	−12.4818	−1.09054	−0.545268	+	0.838262i	$0.683572\pi$
$132$	−5.28532	−0.460028
$133$	−11.3539	−0.984508
$134$	7.27636	0.628582
$135$	13.7718	1.18528
$136$	−6.16369	−0.528532
$137$	14.3047	1.22213	0.611064	−	0.791581i	$-0.290742\pi$
$137$	14.3047	1.22213	0.611064	+	0.791581i	$0.290742\pi$
$138$	7.69473	0.655019
$139$	3.17135	0.268990	0.134495	−	0.990914i	$-0.457059\pi$
$139$	3.17135	0.268990	0.134495	+	0.990914i	$0.457059\pi$
$140$	−4.02403	−0.340092
$141$	7.16519	0.603418
$142$	13.1565	1.10407
$143$	−19.2355	−1.60855
$144$	−1.38382	−0.115318
$145$	13.3533	1.10893
$146$	−3.43110	−0.283960
$147$	5.52785	0.455929
$148$	5.27941	0.433965
$149$	2.31324	0.189508	0.0947541	−	0.995501i	$-0.469794\pi$
$149$	2.31324	0.189508	0.0947541	+	0.995501i	$0.469794\pi$
$150$	1.40652	0.114842
$151$	7.43824	0.605315	0.302658	−	0.953099i	$-0.402126\pi$
$151$	7.43824	0.605315	0.302658	+	0.953099i	$0.402126\pi$
$152$	−6.97230	−0.565528
$153$	−8.52943	−0.689563
$154$	6.77011	0.545551
$155$	6.68373	0.536850
$156$	5.88197	0.470934
$157$	13.2687	1.05896	0.529480	−	0.848322i	$-0.322387\pi$
$157$	13.2687	1.05896	0.529480	+	0.848322i	$0.322387\pi$
$158$	−4.80458	−0.382232
$159$	−3.58439	−0.284260
$160$	−2.47111	−0.195358
$161$	−9.85638	−0.776791
$162$	2.93359	0.230485
$163$	−4.56588	−0.357627	−0.178814	−	0.983883i	$-0.557226\pi$
$163$	−4.56588	−0.357627	−0.178814	+	0.983883i	$0.557226\pi$
$164$	−8.27673	−0.646304
$165$	−13.0606	−1.01677
$166$	−6.82574	−0.529780
$167$	10.9371	0.846339	0.423170	−	0.906051i	$-0.360917\pi$
$167$	10.9371	0.846339	0.423170	+	0.906051i	$0.360917\pi$
$168$	−2.07021	−0.159720
$169$	8.40696	0.646689
$170$	−15.2311	−1.16817
$171$	−9.64839	−0.737831
$172$	4.18733	0.319281
$173$	−0.157263	−0.0119565	−0.00597825	−	0.999982i	$-0.501903\pi$
$173$	−0.157263	−0.0119565	−0.00597825	+	0.999982i	$0.501903\pi$
$174$	6.86977	0.520796
$175$	−1.80165	−0.136192
$176$	4.15744	0.313379
$177$	16.7646	1.26010
$178$	−1.20472	−0.0902974
$179$	7.36794	0.550705	0.275353	−	0.961343i	$-0.411205\pi$
$179$	7.36794	0.550705	0.275353	+	0.961343i	$0.411205\pi$
$180$	−3.41956	−0.254879
$181$	11.5828	0.860945	0.430472	−	0.902604i	$-0.358347\pi$
$181$	11.5828	0.860945	0.430472	+	0.902604i	$0.358347\pi$
$182$	−7.53436	−0.558484
$183$	−4.73021	−0.349667
$184$	−6.05269	−0.446210
$185$	13.0460	0.959160
$186$	3.43852	0.252125
$187$	25.6252	1.87390
$188$	−5.63615	−0.411058
$189$	−9.07542	−0.660140
$190$	−17.2293	−1.24994
$191$	9.06568	0.655970	0.327985	−	0.944683i	$-0.393631\pi$
$191$	9.06568	0.655970	0.327985	+	0.944683i	$0.393631\pi$
$192$	−1.27129	−0.0917475
$193$	6.96570	0.501402	0.250701	−	0.968065i	$-0.419339\pi$
$193$	6.96570	0.501402	0.250701	+	0.968065i	$0.419339\pi$
$194$	−13.1745	−0.945872
$195$	14.5350	1.04087
$196$	−4.34822	−0.310587
$197$	−5.04014	−0.359095	−0.179547	−	0.983749i	$-0.557463\pi$
$197$	−5.04014	−0.359095	−0.179547	+	0.983749i	$0.557463\pi$
$198$	5.75315	0.408858
$199$	−17.1113	−1.21299	−0.606493	−	0.795089i	$-0.707424\pi$
$199$	−17.1113	−1.21299	−0.606493	+	0.795089i	$0.707424\pi$
$200$	−1.10637	−0.0782323
$201$	9.25038	0.652471
$202$	1.99778	0.140563
$203$	−8.79967	−0.617616
$204$	−7.83584	−0.548619
$205$	−20.4527	−1.42848
$206$	−8.77836	−0.611617
$207$	−8.37582	−0.582160
$208$	−4.62677	−0.320808
$209$	28.9869	2.00507
$210$	−5.11571	−0.353017
$211$	9.11748	0.627673	0.313836	−	0.949477i	$-0.398386\pi$
$211$	9.11748	0.627673	0.313836	+	0.949477i	$0.398386\pi$
$212$	2.81949	0.193643
$213$	16.7257	1.14603
$214$	5.51490	0.376991
$215$	10.3473	0.705683
$216$	−5.57311	−0.379202
$217$	−4.40449	−0.298997
$218$	9.68077	0.655664
$219$	−4.36193	−0.294752
$220$	10.2735	0.692639
$221$	−28.5179	−1.91832
$222$	6.71166	0.450457
$223$	14.5736	0.975923	0.487961	−	0.872865i	$-0.337741\pi$
$223$	14.5736	0.975923	0.487961	+	0.872865i	$0.337741\pi$
$224$	1.62843	0.108804
$225$	−1.53102	−0.102068
$226$	−4.34445	−0.288989
$227$	−7.01856	−0.465838	−0.232919	−	0.972496i	$-0.574828\pi$
$227$	−7.01856	−0.465838	−0.232919	+	0.972496i	$0.574828\pi$
$228$	−8.86382	−0.587021
$229$	−12.6372	−0.835093	−0.417546	−	0.908656i	$-0.637110\pi$
$229$	−12.6372	−0.835093	−0.417546	+	0.908656i	$0.637110\pi$
$230$	−14.9568	−0.986225
$231$	8.60678	0.566284
$232$	−5.40377	−0.354775
$233$	28.2602	1.85139	0.925694	−	0.378273i	$-0.123482\pi$
$233$	28.2602	1.85139	0.925694	+	0.378273i	$0.123482\pi$
$234$	−6.40260	−0.418551
$235$	−13.9275	−0.908532
$236$	−13.1870	−0.858403
$237$	−6.10802	−0.396758
$238$	10.0371	0.650611
$239$	−10.8219	−0.700013	−0.350006	−	0.936747i	$-0.613821\pi$
$239$	−10.8219	−0.700013	−0.350006	+	0.936747i	$0.613821\pi$
$240$	−3.14150	−0.202783
$241$	−13.4265	−0.864877	−0.432439	−	0.901663i	$-0.642347\pi$
$241$	−13.4265	−0.864877	−0.432439	+	0.901663i	$0.642347\pi$
$242$	−6.28434	−0.403972
$243$	−12.9899	−0.833301
$244$	3.72080	0.238199
$245$	−10.7449	−0.686467
$246$	−10.5221	−0.670867
$247$	−32.2592	−2.05260
$248$	−2.70475	−0.171752
$249$	−8.67750	−0.549914
$250$	9.62157	0.608522
$251$	0.374193	0.0236189	0.0118094	−	0.999930i	$-0.496241\pi$
$251$	0.374193	0.0236189	0.0118094	+	0.999930i	$0.496241\pi$
$252$	2.25345	0.141954
$253$	25.1637	1.58203
$254$	5.42487	0.340386
$255$	−19.3632	−1.21257
$256$	1.00000	0.0625000
$257$	9.37204	0.584612	0.292306	−	0.956325i	$-0.405577\pi$
$257$	9.37204	0.584612	0.292306	+	0.956325i	$0.405577\pi$
$258$	5.32332	0.331415
$259$	−8.59714	−0.534201
$260$	−11.4332	−0.709059
$261$	−7.47784	−0.462867
$262$	12.4818	0.771125
$263$	−9.12041	−0.562389	−0.281194	−	0.959651i	$-0.590731\pi$
$263$	−9.12041	−0.562389	−0.281194	+	0.959651i	$0.590731\pi$
$264$	5.28532	0.325289
$265$	6.96725	0.427995
$266$	11.3539	0.696152
$267$	−1.53155	−0.0937292
$268$	−7.27636	−0.444475
$269$	7.71067	0.470128	0.235064	−	0.971980i	$-0.424470\pi$
$269$	7.71067	0.470128	0.235064	+	0.971980i	$0.424470\pi$
$270$	−13.7718	−0.838122
$271$	3.88695	0.236116	0.118058	−	0.993007i	$-0.462333\pi$
$271$	3.88695	0.236116	0.118058	+	0.993007i	$0.462333\pi$
$272$	6.16369	0.373729
$273$	−9.57837	−0.579709
$274$	−14.3047	−0.864176
$275$	4.59968	0.277371
$276$	−7.69473	−0.463168
$277$	−6.79622	−0.408345	−0.204173	−	0.978935i	$-0.565450\pi$
$277$	−6.79622	−0.408345	−0.204173	+	0.978935i	$0.565450\pi$
$278$	−3.17135	−0.190205
$279$	−3.74288	−0.224080
$280$	4.02403	0.240482
$281$	6.47197	0.386086	0.193043	−	0.981190i	$-0.438164\pi$
$281$	6.47197	0.386086	0.193043	+	0.981190i	$0.438164\pi$
$282$	−7.16519	−0.426681
$283$	18.5525	1.10283	0.551415	−	0.834231i	$-0.314088\pi$
$283$	18.5525	1.10283	0.551415	+	0.834231i	$0.314088\pi$
$284$	−13.1565	−0.780694
$285$	−21.9035	−1.29745
$286$	19.2355	1.13742
$287$	13.4781	0.795586
$288$	1.38382	0.0815423
$289$	20.9911	1.23477
$290$	−13.3533	−0.784133
$291$	−16.7486	−0.981819
$292$	3.43110	0.200790
$293$	9.25096	0.540447	0.270223	−	0.962798i	$-0.412902\pi$
$293$	9.25096	0.540447	0.270223	+	0.962798i	$0.412902\pi$
$294$	−5.52785	−0.322391
$295$	−32.5866	−1.89726
$296$	−5.27941	−0.306859
$297$	23.1699	1.34445
$298$	−2.31324	−0.134002
$299$	−28.0044	−1.61953
$300$	−1.40652	−0.0812056
$301$	−6.81878	−0.393028
$302$	−7.43824	−0.428022
$303$	2.53976	0.145905
$304$	6.97230	0.399889
$305$	9.19448	0.526475
$306$	8.52943	0.487595
$307$	−19.5915	−1.11815	−0.559074	−	0.829118i	$-0.688843\pi$
$307$	−19.5915	−1.11815	−0.559074	+	0.829118i	$0.688843\pi$
$308$	−6.77011	−0.385763
$309$	−11.1599	−0.634862
$310$	−6.68373	−0.379610
$311$	12.8155	0.726702	0.363351	−	0.931652i	$-0.381633\pi$
$311$	12.8155	0.726702	0.363351	+	0.931652i	$0.381633\pi$
$312$	−5.88197	−0.333001
$313$	8.30797	0.469594	0.234797	−	0.972044i	$-0.424557\pi$
$313$	8.30797	0.469594	0.234797	+	0.972044i	$0.424557\pi$
$314$	−13.2687	−0.748798
$315$	5.56852	0.313751
$316$	4.80458	0.270279
$317$	26.5391	1.49059	0.745293	−	0.666738i	$-0.232310\pi$
$317$	26.5391	1.49059	0.745293	+	0.666738i	$0.232310\pi$
$318$	3.58439	0.201003
$319$	22.4659	1.25785
$320$	2.47111	0.138139
$321$	7.01104	0.391318
$322$	9.85638	0.549274
$323$	42.9751	2.39120
$324$	−2.93359	−0.162977
$325$	−5.11893	−0.283947
$326$	4.56588	0.252881
$327$	12.3071	0.680583
$328$	8.27673	0.457006
$329$	9.17807	0.506004
$330$	13.0606	0.718962
$331$	8.85599	0.486769	0.243385	−	0.969930i	$-0.421742\pi$
$331$	8.85599	0.486769	0.243385	+	0.969930i	$0.421742\pi$
$332$	6.82574	0.374611
$333$	−7.30574	−0.400352
$334$	−10.9371	−0.598452
$335$	−17.9807	−0.982389
$336$	2.07021	0.112939
$337$	−14.0126	−0.763314	−0.381657	−	0.924304i	$-0.624646\pi$
$337$	−14.0126	−0.763314	−0.381657	+	0.924304i	$0.624646\pi$
$338$	−8.40696	−0.457278
$339$	−5.52306	−0.299972
$340$	15.2311	0.826024
$341$	11.2448	0.608942
$342$	9.64839	0.521725
$343$	18.4798	0.997814
$344$	−4.18733	−0.225766
$345$	−19.0145	−1.02371
$346$	0.157263	0.00845452
$347$	25.4128	1.36423	0.682116	−	0.731244i	$-0.261060\pi$
$347$	25.4128	1.36423	0.682116	+	0.731244i	$0.261060\pi$
$348$	−6.86977	−0.368258
$349$	13.7334	0.735131	0.367565	−	0.929998i	$-0.380191\pi$
$349$	13.7334	0.735131	0.367565	+	0.929998i	$0.380191\pi$
$350$	1.80165	0.0963022
$351$	−25.7855	−1.37633
$352$	−4.15744	−0.221592
$353$	−0.00659109	−0.000350808 0	−0.000175404	−	1.00000i	$-0.500056\pi$
$353$	−0.00659109	−0.000350808 0	−0.000175404		1.00000i	$0.500056\pi$
$354$	−16.7646	−0.891027
$355$	−32.5111	−1.72551
$356$	1.20472	0.0638499
$357$	12.7601	0.675337
$358$	−7.36794	−0.389408
$359$	−31.4641	−1.66061	−0.830306	−	0.557308i	$-0.811834\pi$
$359$	−31.4641	−1.66061	−0.830306	+	0.557308i	$0.811834\pi$
$360$	3.41956	0.180227
$361$	29.6129	1.55858
$362$	−11.5828	−0.608780
$363$	−7.98922	−0.419325
$364$	7.53436	0.394908
$365$	8.47862	0.443791
$366$	4.73021	0.247252
$367$	3.66767	0.191451	0.0957254	−	0.995408i	$-0.469483\pi$
$367$	3.66767	0.191451	0.0957254	+	0.995408i	$0.469483\pi$
$368$	6.05269	0.315518
$369$	11.4535	0.596245
$370$	−13.0460	−0.678228
$371$	−4.59134	−0.238370
$372$	−3.43852	−0.178279
$373$	−2.21499	−0.114688	−0.0573440	−	0.998354i	$-0.518263\pi$
$373$	−2.21499	−0.114688	−0.0573440	+	0.998354i	$0.518263\pi$
$374$	−25.6252	−1.32505
$375$	12.2318	0.631648
$376$	5.63615	0.290662
$377$	−25.0020	−1.28767
$378$	9.07542	0.466789
$379$	−4.16396	−0.213888	−0.106944	−	0.994265i	$-0.534107\pi$
$379$	−4.16396	−0.213888	−0.106944	+	0.994265i	$0.534107\pi$
$380$	17.2293	0.883844
$381$	6.89658	0.353323
$382$	−9.06568	−0.463841
$383$	25.0904	1.28206	0.641030	−	0.767516i	$-0.278508\pi$
$383$	25.0904	1.28206	0.641030	+	0.767516i	$0.278508\pi$
$384$	1.27129	0.0648753
$385$	−16.7297	−0.852622
$386$	−6.96570	−0.354545
$387$	−5.79451	−0.294551
$388$	13.1745	0.668832
$389$	36.1761	1.83420	0.917100	−	0.398657i	$-0.130523\pi$
$389$	36.1761	1.83420	0.917100	+	0.398657i	$0.130523\pi$
$390$	−14.5350	−0.736007
$391$	37.3069	1.88669
$392$	4.34822	0.219618
$393$	15.8679	0.800432
$394$	5.04014	0.253918
$395$	11.8726	0.597377
$396$	−5.75315	−0.289107
$397$	5.72486	0.287323	0.143661	−	0.989627i	$-0.454112\pi$
$397$	5.72486	0.287323	0.143661	+	0.989627i	$0.454112\pi$
$398$	17.1113	0.857711
$399$	14.4341	0.722609
$400$	1.10637	0.0553186
$401$	−29.5310	−1.47471	−0.737354	−	0.675506i	$-0.763925\pi$
$401$	−29.5310	−1.47471	−0.737354	+	0.675506i	$0.763925\pi$
$402$	−9.25038	−0.461367
$403$	−12.5142	−0.623379
$404$	−1.99778	−0.0993931
$405$	−7.24922	−0.360216
$406$	8.79967	0.436720
$407$	21.9488	1.08796
$408$	7.83584	0.387932
$409$	−31.4844	−1.55680	−0.778401	−	0.627767i	$-0.783969\pi$
$409$	−31.4844	−1.55680	−0.778401	+	0.627767i	$0.783969\pi$
$410$	20.4527	1.01009
$411$	−18.1854	−0.897019
$412$	8.77836	0.432479
$413$	21.4742	1.05667
$414$	8.37582	0.411649
$415$	16.8671	0.827975
$416$	4.62677	0.226846
$417$	−4.03170	−0.197433
$418$	−28.9869	−1.41780
$419$	3.50553	0.171257	0.0856283	−	0.996327i	$-0.472710\pi$
$419$	3.50553	0.171257	0.0856283	+	0.996327i	$0.472710\pi$
$420$	5.11571	0.249621
$421$	2.37796	0.115895	0.0579474	−	0.998320i	$-0.481544\pi$
$421$	2.37796	0.115895	0.0579474	+	0.998320i	$0.481544\pi$
$422$	−9.11748	−0.443832
$423$	7.79941	0.379220
$424$	−2.81949	−0.136926
$425$	6.81934	0.330786
$426$	−16.7257	−0.810364
$427$	−6.05905	−0.293218
$428$	−5.51490	−0.266573
$429$	24.4539	1.18065
$430$	−10.3473	−0.498993
$431$	−28.2531	−1.36090	−0.680452	−	0.732793i	$-0.738217\pi$
$431$	−28.2531	−1.36090	−0.680452	+	0.732793i	$0.738217\pi$
$432$	5.57311	0.268136
$433$	29.9477	1.43919	0.719596	−	0.694393i	$-0.244327\pi$
$433$	29.9477	1.43919	0.719596	+	0.694393i	$0.244327\pi$
$434$	4.40449	0.211422
$435$	−16.9759	−0.813934
$436$	−9.68077	−0.463625
$437$	42.2011	2.01875
$438$	4.36193	0.208421
$439$	39.9808	1.90818	0.954091	−	0.299518i	$-0.0968258\pi$
$439$	39.9808	1.90818	0.954091	+	0.299518i	$0.0968258\pi$
$440$	−10.2735	−0.489769
$441$	6.01714	0.286531
$442$	28.5179	1.35646
$443$	−18.3656	−0.872578	−0.436289	−	0.899807i	$-0.643707\pi$
$443$	−18.3656	−0.872578	−0.436289	+	0.899807i	$0.643707\pi$
$444$	−6.71166	−0.318521
$445$	2.97699	0.141123
$446$	−14.5736	−0.690082
$447$	−2.94080	−0.139095
$448$	−1.62843	−0.0769361
$449$	22.5128	1.06244	0.531221	−	0.847233i	$-0.321733\pi$
$449$	22.5128	1.06244	0.531221	+	0.847233i	$0.321733\pi$
$450$	1.53102	0.0721729
$451$	−34.4100	−1.62031
$452$	4.34445	0.204346
$453$	−9.45616	−0.444289
$454$	7.01856	0.329397
$455$	18.6182	0.872836
$456$	8.86382	0.415086
$457$	−39.6024	−1.85252	−0.926261	−	0.376882i	$-0.876996\pi$
$457$	−39.6024	−1.85252	−0.926261	+	0.376882i	$0.876996\pi$
$458$	12.6372	0.590500
$459$	34.3509	1.60336
$460$	14.9568	0.697366
$461$	−2.03845	−0.0949402	−0.0474701	−	0.998873i	$-0.515116\pi$
$461$	−2.03845	−0.0949402	−0.0474701	+	0.998873i	$0.515116\pi$
$462$	−8.60678	−0.400423
$463$	−13.6605	−0.634855	−0.317428	−	0.948283i	$-0.602819\pi$
$463$	−13.6605	−0.634855	−0.317428	+	0.948283i	$0.602819\pi$
$464$	5.40377	0.250864
$465$	−8.49696	−0.394037
$466$	−28.2602	−1.30913
$467$	−9.94203	−0.460062	−0.230031	−	0.973183i	$-0.573883\pi$
$467$	−9.94203	−0.460062	−0.230031	+	0.973183i	$0.573883\pi$
$468$	6.40260	0.295960
$469$	11.8490	0.547138
$470$	13.9275	0.642429
$471$	−16.8684	−0.777256
$472$	13.1870	0.606983
$473$	17.4086	0.800448
$474$	6.10802	0.280550
$475$	7.71396	0.353941
$476$	−10.0371	−0.460051
$477$	−3.90166	−0.178645
$478$	10.8219	0.494984
$479$	−33.4531	−1.52851	−0.764255	−	0.644914i	$-0.776893\pi$
$479$	−33.4531	−1.52851	−0.764255	+	0.644914i	$0.776893\pi$
$480$	3.14150	0.143389
$481$	−24.4266	−1.11376
$482$	13.4265	0.611561
$483$	12.5303	0.570149
$484$	6.28434	0.285652
$485$	32.5555	1.47827
$486$	12.9899	0.589233
$487$	−19.6239	−0.889242	−0.444621	−	0.895719i	$-0.646662\pi$
$487$	−19.6239	−0.889242	−0.444621	+	0.895719i	$0.646662\pi$
$488$	−3.72080	−0.168432
$489$	5.80456	0.262491
$490$	10.7449	0.485406
$491$	−6.96977	−0.314541	−0.157271	−	0.987556i	$-0.550269\pi$
$491$	−6.96977	−0.314541	−0.157271	+	0.987556i	$0.550269\pi$
$492$	10.5221	0.474374
$493$	33.3072	1.50008
$494$	32.2592	1.45141
$495$	−14.2166	−0.638991
$496$	2.70475	0.121447
$497$	21.4244	0.961017
$498$	8.67750	0.388848
$499$	−24.7594	−1.10838	−0.554191	−	0.832389i	$-0.686972\pi$
$499$	−24.7594	−1.10838	−0.554191	+	0.832389i	$0.686972\pi$
$500$	−9.62157	−0.430290
$501$	−13.9043	−0.621196
$502$	−0.374193	−0.0167011
$503$	38.1053	1.69903	0.849515	−	0.527565i	$-0.176895\pi$
$503$	38.1053	1.69903	0.849515	+	0.527565i	$0.176895\pi$
$504$	−2.25345	−0.100377
$505$	−4.93672	−0.219681
$506$	−25.1637	−1.11866
$507$	−10.6877	−0.474657
$508$	−5.42487	−0.240689
$509$	0.865665	0.0383699	0.0191850	−	0.999816i	$-0.493893\pi$
$509$	0.865665	0.0383699	0.0191850	+	0.999816i	$0.493893\pi$
$510$	19.3632	0.857417
$511$	−5.58731	−0.247168
$512$	−1.00000	−0.0441942
$513$	38.8574	1.71560
$514$	−9.37204	−0.413383
$515$	21.6923	0.955876
$516$	−5.32332	−0.234346
$517$	−23.4320	−1.03054
$518$	8.59714	0.377737
$519$	0.199927	0.00877583
$520$	11.4332	0.501381
$521$	26.9605	1.18116	0.590580	−	0.806979i	$-0.298899\pi$
$521$	26.9605	1.18116	0.590580	+	0.806979i	$0.298899\pi$
$522$	7.47784	0.327296
$523$	10.1452	0.443620	0.221810	−	0.975090i	$-0.428804\pi$
$523$	10.1452	0.443620	0.221810	+	0.975090i	$0.428804\pi$
$524$	−12.4818	−0.545268
$525$	2.29042	0.0999622
$526$	9.12041	0.397669
$527$	16.6712	0.726210
$528$	−5.28532	−0.230014
$529$	13.6350	0.592827
$530$	−6.96725	−0.302638
$531$	18.2485	0.791916
$532$	−11.3539	−0.492254
$533$	38.2945	1.65872
$534$	1.53155	0.0662765
$535$	−13.6279	−0.589186
$536$	7.27636	0.314291
$537$	−9.36679	−0.404207
$538$	−7.71067	−0.332431
$539$	−18.0775	−0.778651
$540$	13.7718	0.592642
$541$	−26.5059	−1.13958	−0.569789	−	0.821791i	$-0.692975\pi$
$541$	−26.5059	−1.13958	−0.569789	+	0.821791i	$0.692975\pi$
$542$	−3.88695	−0.166959
$543$	−14.7251	−0.631917
$544$	−6.16369	−0.264266
$545$	−23.9222	−1.02472
$546$	9.57837	0.409916
$547$	−12.5424	−0.536275	−0.268137	−	0.963381i	$-0.586408\pi$
$547$	−12.5424	−0.536275	−0.268137	+	0.963381i	$0.586408\pi$
$548$	14.3047	0.611064
$549$	−5.14891	−0.219750
$550$	−4.59968	−0.196131
$551$	37.6767	1.60508
$552$	7.69473	0.327509
$553$	−7.82392	−0.332707
$554$	6.79622	0.288744
$555$	−16.5852	−0.704004
$556$	3.17135	0.134495
$557$	−3.67110	−0.155550	−0.0777748	−	0.996971i	$-0.524782\pi$
$557$	−3.67110	−0.155550	−0.0777748	+	0.996971i	$0.524782\pi$
$558$	3.74288	0.158449
$559$	−19.3738	−0.819425
$560$	−4.02403	−0.170046
$561$	−32.5771	−1.37541
$562$	−6.47197	−0.273004
$563$	−43.7570	−1.84414	−0.922068	−	0.387027i	$-0.873502\pi$
$563$	−43.7570	−1.84414	−0.922068	+	0.387027i	$0.873502\pi$
$564$	7.16519	0.301709
$565$	10.7356	0.451650
$566$	−18.5525	−0.779818
$567$	4.77715	0.200621
$568$	13.1565	0.552034
$569$	0.816256	0.0342192	0.0171096	−	0.999854i	$-0.494554\pi$
$569$	0.816256	0.0342192	0.0171096	+	0.999854i	$0.494554\pi$
$570$	21.9035	0.917435
$571$	15.1924	0.635781	0.317891	−	0.948127i	$-0.397025\pi$
$571$	15.1924	0.635781	0.317891	+	0.948127i	$0.397025\pi$
$572$	−19.2355	−0.804277
$573$	−11.5251	−0.481469
$574$	−13.4781	−0.562564
$575$	6.69653	0.279264
$576$	−1.38382	−0.0576591
$577$	26.4207	1.09991	0.549953	−	0.835195i	$-0.314645\pi$
$577$	26.4207	1.09991	0.549953	+	0.835195i	$0.314645\pi$
$578$	−20.9911	−0.873113
$579$	−8.85543	−0.368019
$580$	13.3533	0.554466
$581$	−11.1152	−0.461138
$582$	16.7486	0.694251
$583$	11.7219	0.485470
$584$	−3.43110	−0.141980
$585$	15.8215	0.654140
$586$	−9.25096	−0.382154
$587$	25.1877	1.03961	0.519803	−	0.854286i	$-0.326005\pi$
$587$	25.1877	1.03961	0.519803	+	0.854286i	$0.326005\pi$
$588$	5.52785	0.227965
$589$	18.8583	0.777043
$590$	32.5866	1.34157
$591$	6.40748	0.263569
$592$	5.27941	0.216982
$593$	11.4380	0.469700	0.234850	−	0.972032i	$-0.424540\pi$
$593$	11.4380	0.469700	0.234850	+	0.972032i	$0.424540\pi$
$594$	−23.1699	−0.950672
$595$	−24.8028	−1.01682
$596$	2.31324	0.0947541
$597$	21.7534	0.890308
$598$	28.0044	1.14518
$599$	15.5141	0.633888	0.316944	−	0.948444i	$-0.397343\pi$
$599$	15.5141	0.633888	0.316944	+	0.948444i	$0.397343\pi$
$600$	1.40652	0.0574210
$601$	19.8659	0.810347	0.405173	−	0.914240i	$-0.367211\pi$
$601$	19.8659	0.810347	0.405173	+	0.914240i	$0.367211\pi$
$602$	6.81878	0.277913
$603$	10.0692	0.410048
$604$	7.43824	0.302658
$605$	15.5293	0.631355
$606$	−2.53976	−0.103171
$607$	2.47186	0.100330	0.0501649	−	0.998741i	$-0.484025\pi$
$607$	2.47186	0.100330	0.0501649	+	0.998741i	$0.484025\pi$
$608$	−6.97230	−0.282764
$609$	11.1869	0.453318
$610$	−9.19448	−0.372274
$611$	26.0771	1.05497
$612$	−8.52943	−0.344782
$613$	−9.05649	−0.365788	−0.182894	−	0.983133i	$-0.558547\pi$
$613$	−9.05649	−0.365788	−0.182894	+	0.983133i	$0.558547\pi$
$614$	19.5915	0.790650
$615$	26.0013	1.04847
$616$	6.77011	0.272775
$617$	38.3249	1.54290	0.771451	−	0.636288i	$-0.219531\pi$
$617$	38.3249	1.54290	0.771451	+	0.636288i	$0.219531\pi$
$618$	11.1599	0.448915
$619$	−36.6894	−1.47467	−0.737336	−	0.675526i	$-0.763917\pi$
$619$	−36.6894	−1.47467	−0.737336	+	0.675526i	$0.763917\pi$
$620$	6.68373	0.268425
$621$	33.7323	1.35363
$622$	−12.8155	−0.513856
$623$	−1.96180	−0.0785978
$624$	5.88197	0.235467
$625$	−29.3078	−1.17231
$626$	−8.30797	−0.332053
$627$	−36.8508	−1.47168
$628$	13.2687	0.529480
$629$	32.5406	1.29748
$630$	−5.56852	−0.221855
$631$	44.3198	1.76434	0.882171	−	0.470930i	$-0.156081\pi$
$631$	44.3198	1.76434	0.882171	+	0.470930i	$0.156081\pi$
$632$	−4.80458	−0.191116
$633$	−11.5910	−0.460700
$634$	−26.5391	−1.05400
$635$	−13.4054	−0.531978
$636$	−3.58439	−0.142130
$637$	20.1182	0.797111
$638$	−22.4659	−0.889433
$639$	18.2062	0.720226
$640$	−2.47111	−0.0976791
$641$	15.0077	0.592770	0.296385	−	0.955069i	$-0.404219\pi$
$641$	15.0077	0.592770	0.296385	+	0.955069i	$0.404219\pi$
$642$	−7.01104	−0.276704
$643$	−12.9883	−0.512208	−0.256104	−	0.966649i	$-0.582439\pi$
$643$	−12.9883	−0.512208	−0.256104	+	0.966649i	$0.582439\pi$
$644$	−9.85638	−0.388396
$645$	−13.1545	−0.517958
$646$	−42.9751	−1.69083
$647$	−11.5143	−0.452675	−0.226337	−	0.974049i	$-0.572675\pi$
$647$	−11.5143	−0.452675	−0.226337	+	0.974049i	$0.572675\pi$
$648$	2.93359	0.115242
$649$	−54.8244	−2.15204
$650$	5.11893	0.200781
$651$	5.59940	0.219458
$652$	−4.56588	−0.178814
$653$	24.6412	0.964284	0.482142	−	0.876093i	$-0.339859\pi$
$653$	24.6412	0.964284	0.482142	+	0.876093i	$0.339859\pi$
$654$	−12.3071	−0.481245
$655$	−30.8437	−1.20516
$656$	−8.27673	−0.323152
$657$	−4.74802	−0.185238
$658$	−9.17807	−0.357799
$659$	28.8636	1.12437	0.562183	−	0.827013i	$-0.309962\pi$
$659$	28.8636	1.12437	0.562183	+	0.827013i	$0.309962\pi$
$660$	−13.0606	−0.508383
$661$	−45.7665	−1.78011	−0.890055	−	0.455853i	$-0.849334\pi$
$661$	−45.7665	−1.78011	−0.890055	+	0.455853i	$0.849334\pi$
$662$	−8.85599	−0.344198
$663$	36.2546	1.40801
$664$	−6.82574	−0.264890
$665$	−28.0567	−1.08799
$666$	7.30574	0.283092
$667$	32.7074	1.26643
$668$	10.9371	0.423170
$669$	−18.5273	−0.716308
$670$	17.9807	0.694654
$671$	15.4690	0.597174
$672$	−2.07021	−0.0798600
$673$	44.9062	1.73101	0.865504	−	0.500903i	$-0.166999\pi$
$673$	44.9062	1.73101	0.865504	+	0.500903i	$0.166999\pi$
$674$	14.0126	0.539745
$675$	6.16594	0.237327
$676$	8.40696	0.323345
$677$	29.8347	1.14664	0.573321	−	0.819331i	$-0.305655\pi$
$677$	29.8347	1.14664	0.573321	+	0.819331i	$0.305655\pi$
$678$	5.52306	0.212112
$679$	−21.4537	−0.823317
$680$	−15.2311	−0.584087
$681$	8.92263	0.341916
$682$	−11.2448	−0.430587
$683$	−28.7846	−1.10141	−0.550706	−	0.834700i	$-0.685641\pi$
$683$	−28.7846	−1.10141	−0.550706	+	0.834700i	$0.685641\pi$
$684$	−9.64839	−0.368916
$685$	35.3483	1.35059
$686$	−18.4798	−0.705561
$687$	16.0656	0.612941
$688$	4.18733	0.159641
$689$	−13.0451	−0.496979
$690$	19.0145	0.723870
$691$	44.9909	1.71153	0.855767	−	0.517361i	$-0.173086\pi$
$691$	44.9909	1.71153	0.855767	+	0.517361i	$0.173086\pi$
$692$	−0.157263	−0.00597825
$693$	9.36860	0.355884
$694$	−25.4128	−0.964658
$695$	7.83674	0.297264
$696$	6.86977	0.260398
$697$	−51.0152	−1.93234
$698$	−13.7334	−0.519816
$699$	−35.9270	−1.35888
$700$	−1.80165	−0.0680960
$701$	−5.03757	−0.190266	−0.0951332	−	0.995465i	$-0.530328\pi$
$701$	−5.03757	−0.190266	−0.0951332	+	0.995465i	$0.530328\pi$
$702$	25.7855	0.973210
$703$	36.8096	1.38830
$704$	4.15744	0.156690
$705$	17.7059	0.666845
$706$	0.00659109	0.000248059 0
$707$	3.25324	0.122351
$708$	16.7646	0.630051
$709$	40.4451	1.51895	0.759475	−	0.650537i	$-0.225456\pi$
$709$	40.4451	1.51895	0.759475	+	0.650537i	$0.225456\pi$
$710$	32.5111	1.22012
$711$	−6.64866	−0.249344
$712$	−1.20472	−0.0451487
$713$	16.3710	0.613099
$714$	−12.7601	−0.477536
$715$	−47.5330	−1.77763
$716$	7.36794	0.275353
$717$	13.7578	0.513796
$718$	31.4641	1.17423
$719$	−25.2373	−0.941191	−0.470595	−	0.882349i	$-0.655961\pi$
$719$	−25.2373	−0.941191	−0.470595	+	0.882349i	$0.655961\pi$
$720$	−3.41956	−0.127440
$721$	−14.2949	−0.532372
$722$	−29.6129	−1.10208
$723$	17.0690	0.634803
$724$	11.5828	0.430472
$725$	5.97859	0.222039
$726$	7.98922	0.296508
$727$	−18.7586	−0.695718	−0.347859	−	0.937547i	$-0.613091\pi$
$727$	−18.7586	−0.695718	−0.347859	+	0.937547i	$0.613091\pi$
$728$	−7.53436	−0.279242
$729$	25.3147	0.937581
$730$	−8.47862	−0.313808
$731$	25.8094	0.954596
$732$	−4.73021	−0.174834
$733$	−3.20317	−0.118312	−0.0591560	−	0.998249i	$-0.518841\pi$
$733$	−3.20317	−0.118312	−0.0591560	+	0.998249i	$0.518841\pi$
$734$	−3.66767	−0.135376
$735$	13.6599	0.503853
$736$	−6.05269	−0.223105
$737$	−30.2511	−1.11431
$738$	−11.4535	−0.421609
$739$	6.65623	0.244853	0.122427	−	0.992478i	$-0.460932\pi$
$739$	6.65623	0.244853	0.122427	+	0.992478i	$0.460932\pi$
$740$	13.0460	0.479580
$741$	41.0108	1.50657
$742$	4.59134	0.168553
$743$	−10.9869	−0.403071	−0.201536	−	0.979481i	$-0.564593\pi$
$743$	−10.9869	−0.403071	−0.201536	+	0.979481i	$0.564593\pi$
$744$	3.43852	0.126062
$745$	5.71627	0.209428
$746$	2.21499	0.0810967
$747$	−9.44558	−0.345596
$748$	25.6252	0.936950
$749$	8.98062	0.328145
$750$	−12.2318	−0.446643
$751$	12.6466	0.461480	0.230740	−	0.973015i	$-0.425885\pi$
$751$	12.6466	0.461480	0.230740	+	0.973015i	$0.425885\pi$
$752$	−5.63615	−0.205529
$753$	−0.475709	−0.0173358
$754$	25.0020	0.910519
$755$	18.3807	0.668941
$756$	−9.07542	−0.330070
$757$	25.6636	0.932759	0.466380	−	0.884585i	$-0.345558\pi$
$757$	25.6636	0.932759	0.466380	+	0.884585i	$0.345558\pi$
$758$	4.16396	0.151242
$759$	−31.9904	−1.16118
$760$	−17.2293	−0.624972
$761$	38.3929	1.39174	0.695871	−	0.718167i	$-0.255019\pi$
$761$	38.3929	1.39174	0.695871	+	0.718167i	$0.255019\pi$
$762$	−6.89658	−0.249837
$763$	15.7645	0.570712
$764$	9.06568	0.327985
$765$	−21.0771	−0.762045
$766$	−25.0904	−0.906553
$767$	61.0133	2.20306
$768$	−1.27129	−0.0458738
$769$	21.0770	0.760057	0.380029	−	0.924975i	$-0.375914\pi$
$769$	21.0770	0.760057	0.380029	+	0.924975i	$0.375914\pi$
$770$	16.7297	0.602895
$771$	−11.9146	−0.429094
$772$	6.96570	0.250701
$773$	−25.6138	−0.921265	−0.460633	−	0.887591i	$-0.652377\pi$
$773$	−25.6138	−0.921265	−0.460633	+	0.887591i	$0.652377\pi$
$774$	5.79451	0.208279
$775$	2.99246	0.107492
$776$	−13.1745	−0.472936
$777$	10.9295	0.392093
$778$	−36.1761	−1.29698
$779$	−57.7078	−2.06760
$780$	14.5350	0.520435
$781$	−54.6974	−1.95723
$782$	−37.3069	−1.33409
$783$	30.1158	1.07625
$784$	−4.34822	−0.155293
$785$	32.7885	1.17027
$786$	−15.8679	−0.565991
$787$	−41.1050	−1.46523	−0.732617	−	0.680641i	$-0.761702\pi$
$787$	−41.1050	−1.46523	−0.732617	+	0.680641i	$0.761702\pi$
$788$	−5.04014	−0.179547
$789$	11.5947	0.412782
$790$	−11.8726	−0.422409
$791$	−7.07463	−0.251545
$792$	5.75315	0.204429
$793$	−17.2152	−0.611331
$794$	−5.72486	−0.203168
$795$	−8.85741	−0.314140
$796$	−17.1113	−0.606493
$797$	−45.0922	−1.59725	−0.798624	−	0.601830i	$-0.794438\pi$
$797$	−45.0922	−1.59725	−0.798624	+	0.601830i	$0.794438\pi$
$798$	−14.4341	−0.510962
$799$	−34.7395	−1.22899
$800$	−1.10637	−0.0391162
$801$	−1.66711	−0.0589045
$802$	29.5310	1.04278
$803$	14.2646	0.503387
$804$	9.25038	0.326236
$805$	−24.3562	−0.858442
$806$	12.5142	0.440795
$807$	−9.80251	−0.345065
$808$	1.99778	0.0702816
$809$	−32.8906	−1.15637	−0.578186	−	0.815905i	$-0.696239\pi$
$809$	−32.8906	−1.15637	−0.578186	+	0.815905i	$0.696239\pi$
$810$	7.24922	0.254712
$811$	−6.57165	−0.230762	−0.115381	−	0.993321i	$-0.536809\pi$
$811$	−6.57165	−0.230762	−0.115381	+	0.993321i	$0.536809\pi$
$812$	−8.79967	−0.308808
$813$	−4.94145	−0.173304
$814$	−21.9488	−0.769306
$815$	−11.2828	−0.395218
$816$	−7.83584	−0.274309
$817$	29.1953	1.02142
$818$	31.4844	1.10083
$819$	−10.4262	−0.364321
$820$	−20.4527	−0.714239
$821$	51.0305	1.78098	0.890488	−	0.455008i	$-0.150363\pi$
$821$	51.0305	1.78098	0.890488	+	0.455008i	$0.150363\pi$
$822$	18.1854	0.634288
$823$	19.5267	0.680659	0.340329	−	0.940306i	$-0.389461\pi$
$823$	19.5267	0.680659	0.340329	+	0.940306i	$0.389461\pi$
$824$	−8.77836	−0.305809
$825$	−5.84753	−0.203585
$826$	−21.4742	−0.747182
$827$	−35.5064	−1.23468	−0.617340	−	0.786697i	$-0.711790\pi$
$827$	−35.5064	−1.23468	−0.617340	+	0.786697i	$0.711790\pi$
$828$	−8.37582	−0.291080
$829$	−7.14508	−0.248159	−0.124079	−	0.992272i	$-0.539598\pi$
$829$	−7.14508	−0.248159	−0.124079	+	0.992272i	$0.539598\pi$
$830$	−16.8671	−0.585467
$831$	8.63997	0.299717
$832$	−4.62677	−0.160404
$833$	−26.8010	−0.928601
$834$	4.03170	0.139607
$835$	27.0268	0.935300
$836$	28.9869	1.00253
$837$	15.0739	0.521029
$838$	−3.50553	−0.121097
$839$	−54.8915	−1.89506	−0.947532	−	0.319661i	$-0.896431\pi$
$839$	−54.8915	−1.89506	−0.947532	+	0.319661i	$0.896431\pi$
$840$	−5.11571	−0.176509
$841$	0.200773	0.00692321
$842$	−2.37796	−0.0819500
$843$	−8.22776	−0.283379
$844$	9.11748	0.313836
$845$	20.7745	0.714665
$846$	−7.79941	−0.268149
$847$	−10.2336	−0.351631
$848$	2.81949	0.0968216
$849$	−23.5856	−0.809455
$850$	−6.81934	−0.233901
$851$	31.9546	1.09539
$852$	16.7257	0.573014
$853$	32.0519	1.09744	0.548718	−	0.836007i	$-0.315116\pi$
$853$	32.0519	1.09744	0.548718	+	0.836007i	$0.315116\pi$
$854$	6.05905	0.207337
$855$	−23.8422	−0.815387
$856$	5.51490	0.188495
$857$	4.32461	0.147726	0.0738630	−	0.997268i	$-0.476467\pi$
$857$	4.32461	0.147726	0.0738630	+	0.997268i	$0.476467\pi$
$858$	−24.4539	−0.834844
$859$	12.8983	0.440084	0.220042	−	0.975490i	$-0.429381\pi$
$859$	12.8983	0.440084	0.220042	+	0.975490i	$0.429381\pi$
$860$	10.3473	0.352842
$861$	−17.1346	−0.583944
$862$	28.2531	0.962305
$863$	−7.89701	−0.268817	−0.134409	−	0.990926i	$-0.542914\pi$
$863$	−7.89701	−0.268817	−0.134409	+	0.990926i	$0.542914\pi$
$864$	−5.57311	−0.189601
$865$	−0.388614	−0.0132133
$866$	−29.9477	−1.01766
$867$	−26.6857	−0.906295
$868$	−4.40449	−0.149498
$869$	19.9748	0.677597
$870$	16.9759	0.575538
$871$	33.6660	1.14073
$872$	9.68077	0.327832
$873$	−18.2311	−0.617028
$874$	−42.2011	−1.42747
$875$	15.6681	0.529677
$876$	−4.36193	−0.147376
$877$	−41.3605	−1.39664	−0.698322	−	0.715784i	$-0.746070\pi$
$877$	−41.3605	−1.39664	−0.698322	+	0.715784i	$0.746070\pi$
$878$	−39.9808	−1.34929
$879$	−11.7607	−0.396677
$880$	10.2735	0.346319
$881$	14.0390	0.472984	0.236492	−	0.971633i	$-0.424002\pi$
$881$	14.0390	0.472984	0.236492	+	0.971633i	$0.424002\pi$
$882$	−6.01714	−0.202608
$883$	−53.4825	−1.79983	−0.899915	−	0.436066i	$-0.856372\pi$
$883$	−53.4825	−1.79983	−0.899915	+	0.436066i	$0.856372\pi$
$884$	−28.5179	−0.959162
$885$	41.4270	1.39255
$886$	18.3656	0.617006
$887$	−4.79787	−0.161097	−0.0805483	−	0.996751i	$-0.525667\pi$
$887$	−4.79787	−0.161097	−0.0805483	+	0.996751i	$0.525667\pi$
$888$	6.71166	0.225229
$889$	8.83401	0.296283
$890$	−2.97699	−0.0997889
$891$	−12.1962	−0.408589
$892$	14.5736	0.487961
$893$	−39.2969	−1.31502
$894$	2.94080	0.0983552
$895$	18.2070	0.608592
$896$	1.62843	0.0544020
$897$	35.6017	1.18871
$898$	−22.5128	−0.751260
$899$	14.6159	0.487466
$900$	−1.53102	−0.0510340
$901$	17.3784	0.578960
$902$	34.4100	1.14573
$903$	8.66865	0.288475
$904$	−4.34445	−0.144494
$905$	28.6224	0.951441
$906$	9.45616	0.314160
$907$	−22.6997	−0.753733	−0.376866	−	0.926268i	$-0.622998\pi$
$907$	−22.6997	−0.753733	−0.376866	+	0.926268i	$0.622998\pi$
$908$	−7.01856	−0.232919
$909$	2.76456	0.0916947
$910$	−18.6182	−0.617188
$911$	−14.6978	−0.486959	−0.243480	−	0.969906i	$-0.578289\pi$
$911$	−14.6978	−0.486959	−0.243480	+	0.969906i	$0.578289\pi$
$912$	−8.86382	−0.293510
$913$	28.3776	0.939162
$914$	39.6024	1.30993
$915$	−11.6889	−0.386422
$916$	−12.6372	−0.417546
$917$	20.3257	0.671212
$918$	−34.3509	−1.13375
$919$	24.0565	0.793551	0.396776	−	0.917916i	$-0.370129\pi$
$919$	24.0565	0.793551	0.396776	+	0.917916i	$0.370129\pi$
$920$	−14.9568	−0.493112
$921$	24.9066	0.820699
$922$	2.03845	0.0671329
$923$	60.8720	2.00363
$924$	8.60678	0.283142
$925$	5.84099	0.192051
$926$	13.6605	0.448910
$927$	−12.1477	−0.398982
$928$	−5.40377	−0.177388
$929$	−18.3443	−0.601858	−0.300929	−	0.953647i	$-0.597297\pi$
$929$	−18.3443	−0.601858	−0.300929	+	0.953647i	$0.597297\pi$
$930$	8.49696	0.278626
$931$	−30.3171	−0.993601
$932$	28.2602	0.925694
$933$	−16.2923	−0.533385
$934$	9.94203	0.325313
$935$	63.3226	2.07087
$936$	−6.40260	−0.209276
$937$	52.0628	1.70082	0.850409	−	0.526122i	$-0.176355\pi$
$937$	52.0628	1.70082	0.850409	+	0.526122i	$0.176355\pi$
$938$	−11.8490	−0.386885
$939$	−10.5619	−0.344673
$940$	−13.9275	−0.454266
$941$	15.6023	0.508621	0.254310	−	0.967123i	$-0.418151\pi$
$941$	15.6023	0.508621	0.254310	+	0.967123i	$0.418151\pi$
$942$	16.8684	0.549603
$943$	−50.0965	−1.63136
$944$	−13.1870	−0.429202
$945$	−22.4263	−0.729529
$946$	−17.4086	−0.566002
$947$	−12.3821	−0.402364	−0.201182	−	0.979554i	$-0.564478\pi$
$947$	−12.3821	−0.402364	−0.201182	+	0.979554i	$0.564478\pi$
$948$	−6.10802	−0.198379
$949$	−15.8749	−0.515321
$950$	−7.71396	−0.250274
$951$	−33.7389	−1.09406
$952$	10.0371	0.325305
$953$	−18.1193	−0.586943	−0.293472	−	0.955968i	$-0.594811\pi$
$953$	−18.1193	−0.586943	−0.293472	+	0.955968i	$0.594811\pi$
$954$	3.90166	0.126321
$955$	22.4023	0.724920
$956$	−10.8219	−0.350006
$957$	−28.5607	−0.923236
$958$	33.4531	1.08082
$959$	−23.2941	−0.752206
$960$	−3.14150	−0.101391
$961$	−23.6843	−0.764011
$962$	24.4266	0.787545
$963$	7.63162	0.245925
$964$	−13.4265	−0.432439
$965$	17.2130	0.554106
$966$	−12.5303	−0.403157
$967$	53.6050	1.72382	0.861911	−	0.507060i	$-0.169268\pi$
$967$	53.6050	1.72382	0.861911	+	0.507060i	$0.169268\pi$
$968$	−6.28434	−0.201986
$969$	−54.6338	−1.75509
$970$	−32.5555	−1.04529
$971$	3.40768	0.109358	0.0546788	−	0.998504i	$-0.482587\pi$
$971$	3.40768	0.109358	0.0546788	+	0.998504i	$0.482587\pi$
$972$	−12.9899	−0.416651
$973$	−5.16431	−0.165560
$974$	19.6239	0.628789
$975$	6.50765	0.208411
$976$	3.72080	0.119100
$977$	−15.9817	−0.511301	−0.255651	−	0.966769i	$-0.582290\pi$
$977$	−15.9817	−0.511301	−0.255651	+	0.966769i	$0.582290\pi$
$978$	−5.80456	−0.185609
$979$	5.00855	0.160074
$980$	−10.7449	−0.343234
$981$	13.3964	0.427715
$982$	6.96977	0.222414
$983$	−30.9238	−0.986316	−0.493158	−	0.869940i	$-0.664158\pi$
$983$	−30.9238	−0.986316	−0.493158	+	0.869940i	$0.664158\pi$
$984$	−10.5221	−0.335433
$985$	−12.4547	−0.396840
$986$	−33.3072	−1.06072
$987$	−11.6680	−0.371397
$988$	−32.2592	−1.02630
$989$	25.3446	0.805912
$990$	14.2166	0.451835
$991$	24.3367	0.773079	0.386540	−	0.922273i	$-0.373670\pi$
$991$	24.3367	0.773079	0.386540	+	0.922273i	$0.373670\pi$
$992$	−2.70475	−0.0858759
$993$	−11.2585	−0.357279
$994$	−21.4244	−0.679541
$995$	−42.2838	−1.34049
$996$	−8.67750	−0.274957
$997$	4.92444	0.155958	0.0779792	−	0.996955i	$-0.475153\pi$
$997$	4.92444	0.155958	0.0779792	+	0.996955i	$0.475153\pi$
$998$	24.7594	0.783745
$999$	29.4227	0.930894

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.19	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.19	✓	61	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.27129 q^{3} +1.00000 q^{4} +2.47111 q^{5} +1.27129 q^{6} -1.62843 q^{7} -1.00000 q^{8} -1.38382 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.27129 q^{3} +1.00000 q^{4} +2.47111 q^{5} +1.27129 q^{6} -1.62843 q^{7} -1.00000 q^{8} -1.38382 q^{9} -2.47111 q^{10} +4.15744 q^{11} -1.27129 q^{12} -4.62677 q^{13} +1.62843 q^{14} -3.14150 q^{15} +1.00000 q^{16} +6.16369 q^{17} +1.38382 q^{18} +6.97230 q^{19} +2.47111 q^{20} +2.07021 q^{21} -4.15744 q^{22} +6.05269 q^{23} +1.27129 q^{24} +1.10637 q^{25} +4.62677 q^{26} +5.57311 q^{27} -1.62843 q^{28} +5.40377 q^{29} +3.14150 q^{30} +2.70475 q^{31} -1.00000 q^{32} -5.28532 q^{33} -6.16369 q^{34} -4.02403 q^{35} -1.38382 q^{36} +5.27941 q^{37} -6.97230 q^{38} +5.88197 q^{39} -2.47111 q^{40} -8.27673 q^{41} -2.07021 q^{42} +4.18733 q^{43} +4.15744 q^{44} -3.41956 q^{45} -6.05269 q^{46} -5.63615 q^{47} -1.27129 q^{48} -4.34822 q^{49} -1.10637 q^{50} -7.83584 q^{51} -4.62677 q^{52} +2.81949 q^{53} -5.57311 q^{54} +10.2735 q^{55} +1.62843 q^{56} -8.86382 q^{57} -5.40377 q^{58} -13.1870 q^{59} -3.14150 q^{60} +3.72080 q^{61} -2.70475 q^{62} +2.25345 q^{63} +1.00000 q^{64} -11.4332 q^{65} +5.28532 q^{66} -7.27636 q^{67} +6.16369 q^{68} -7.69473 q^{69} +4.02403 q^{70} -13.1565 q^{71} +1.38382 q^{72} +3.43110 q^{73} -5.27941 q^{74} -1.40652 q^{75} +6.97230 q^{76} -6.77011 q^{77} -5.88197 q^{78} +4.80458 q^{79} +2.47111 q^{80} -2.93359 q^{81} +8.27673 q^{82} +6.82574 q^{83} +2.07021 q^{84} +15.2311 q^{85} -4.18733 q^{86} -6.86977 q^{87} -4.15744 q^{88} +1.20472 q^{89} +3.41956 q^{90} +7.53436 q^{91} +6.05269 q^{92} -3.43852 q^{93} +5.63615 q^{94} +17.2293 q^{95} +1.27129 q^{96} +13.1745 q^{97} +4.34822 q^{98} -5.75315 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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