LMFDB - Embedded newform 6035.2.a.h.1.16

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:	$0$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-1.47530 q^{2} -1.44851 q^{3} +0.176504 q^{4} +1.00000 q^{5} +2.13699 q^{6} +2.79346 q^{7} +2.69020 q^{8} -0.901812 q^{9} +O(q^{10})$	\(q-1.47530 q^{2} -1.44851 q^{3} +0.176504 q^{4} +1.00000 q^{5} +2.13699 q^{6} +2.79346 q^{7} +2.69020 q^{8} -0.901812 q^{9} -1.47530 q^{10} -3.17492 q^{11} -0.255669 q^{12} +6.75365 q^{13} -4.12118 q^{14} -1.44851 q^{15} -4.32185 q^{16} -1.00000 q^{17} +1.33044 q^{18} -2.18956 q^{19} +0.176504 q^{20} -4.04636 q^{21} +4.68395 q^{22} -0.605952 q^{23} -3.89679 q^{24} +1.00000 q^{25} -9.96364 q^{26} +5.65182 q^{27} +0.493057 q^{28} -0.712115 q^{29} +2.13699 q^{30} -10.7605 q^{31} +0.995625 q^{32} +4.59890 q^{33} +1.47530 q^{34} +2.79346 q^{35} -0.159174 q^{36} +6.12416 q^{37} +3.23026 q^{38} -9.78274 q^{39} +2.69020 q^{40} +6.54065 q^{41} +5.96959 q^{42} -2.43119 q^{43} -0.560386 q^{44} -0.901812 q^{45} +0.893960 q^{46} +7.05413 q^{47} +6.26026 q^{48} +0.803412 q^{49} -1.47530 q^{50} +1.44851 q^{51} +1.19205 q^{52} +4.45439 q^{53} -8.33812 q^{54} -3.17492 q^{55} +7.51496 q^{56} +3.17161 q^{57} +1.05058 q^{58} -1.12540 q^{59} -0.255669 q^{60} -1.79074 q^{61} +15.8750 q^{62} -2.51917 q^{63} +7.17487 q^{64} +6.75365 q^{65} -6.78475 q^{66} +4.57235 q^{67} -0.176504 q^{68} +0.877730 q^{69} -4.12118 q^{70} -1.00000 q^{71} -2.42605 q^{72} +15.4184 q^{73} -9.03496 q^{74} -1.44851 q^{75} -0.386467 q^{76} -8.86900 q^{77} +14.4325 q^{78} +3.36461 q^{79} -4.32185 q^{80} -5.48130 q^{81} -9.64941 q^{82} -16.1083 q^{83} -0.714200 q^{84} -1.00000 q^{85} +3.58672 q^{86} +1.03151 q^{87} -8.54116 q^{88} -3.97957 q^{89} +1.33044 q^{90} +18.8660 q^{91} -0.106953 q^{92} +15.5867 q^{93} -10.4069 q^{94} -2.18956 q^{95} -1.44217 q^{96} +4.83862 q^{97} -1.18527 q^{98} +2.86318 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * 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 $

$2$	−1.47530	−1.04319	−0.521597	−	0.853192i	$-0.674663\pi$
$2$	−1.47530	−1.04319	−0.521597	+	0.853192i	$0.674663\pi$
$3$	−1.44851	−0.836299	−0.418149	−	0.908378i	$-0.637321\pi$
$3$	−1.44851	−0.836299	−0.418149	+	0.908378i	$0.637321\pi$
$4$	0.176504	0.0882521
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.13699	0.872421
$7$	2.79346	1.05583	0.527914	−	0.849298i	$-0.322974\pi$
$7$	2.79346	1.05583	0.527914	+	0.849298i	$0.322974\pi$
$8$	2.69020	0.951129
$9$	−0.901812	−0.300604
$10$	−1.47530	−0.466530
$11$	−3.17492	−0.957273	−0.478637	−	0.878013i	$-0.658869\pi$
$11$	−3.17492	−0.957273	−0.478637	+	0.878013i	$0.658869\pi$
$12$	−0.255669	−0.0738052
$13$	6.75365	1.87312	0.936562	−	0.350501i	$-0.113989\pi$
$13$	6.75365	1.87312	0.936562	+	0.350501i	$0.113989\pi$
$14$	−4.12118	−1.10143
$15$	−1.44851	−0.374004
$16$	−4.32185	−1.08046
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.33044	0.313588
$19$	−2.18956	−0.502320	−0.251160	−	0.967946i	$-0.580812\pi$
$19$	−2.18956	−0.502320	−0.251160	+	0.967946i	$0.580812\pi$
$20$	0.176504	0.0394676
$21$	−4.04636	−0.882988
$22$	4.68395	0.998621
$23$	−0.605952	−0.126350	−0.0631749	−	0.998002i	$-0.520123\pi$
$23$	−0.605952	−0.126350	−0.0631749	+	0.998002i	$0.520123\pi$
$24$	−3.89679	−0.795428
$25$	1.00000	0.200000
$26$	−9.96364	−1.95403
$27$	5.65182	1.08769
$28$	0.493057	0.0931791
$29$	−0.712115	−0.132237	−0.0661183	−	0.997812i	$-0.521061\pi$
$29$	−0.712115	−0.132237	−0.0661183	+	0.997812i	$0.521061\pi$
$30$	2.13699	0.390159
$31$	−10.7605	−1.93265	−0.966323	−	0.257333i	$-0.917156\pi$
$31$	−10.7605	−1.93265	−0.966323	+	0.257333i	$0.917156\pi$
$32$	0.995625	0.176003
$33$	4.59890	0.800567
$34$	1.47530	0.253012
$35$	2.79346	0.472181
$36$	−0.159174	−0.0265290
$37$	6.12416	1.00681	0.503403	−	0.864052i	$-0.332081\pi$
$37$	6.12416	1.00681	0.503403	+	0.864052i	$0.332081\pi$
$38$	3.23026	0.524017
$39$	−9.78274	−1.56649
$40$	2.69020	0.425358
$41$	6.54065	1.02148	0.510739	−	0.859736i	$-0.329372\pi$
$41$	6.54065	1.02148	0.510739	+	0.859736i	$0.329372\pi$
$42$	5.96959	0.921127
$43$	−2.43119	−0.370752	−0.185376	−	0.982668i	$-0.559350\pi$
$43$	−2.43119	−0.370752	−0.185376	+	0.982668i	$0.559350\pi$
$44$	−0.560386	−0.0844814
$45$	−0.901812	−0.134434
$46$	0.893960	0.131807
$47$	7.05413	1.02895	0.514475	−	0.857505i	$-0.327987\pi$
$47$	7.05413	1.02895	0.514475	+	0.857505i	$0.327987\pi$
$48$	6.26026	0.903591
$49$	0.803412	0.114773
$50$	−1.47530	−0.208639
$51$	1.44851	0.202832
$52$	1.19205	0.165307
$53$	4.45439	0.611858	0.305929	−	0.952054i	$-0.401033\pi$
$53$	4.45439	0.611858	0.305929	+	0.952054i	$0.401033\pi$
$54$	−8.33812	−1.13467
$55$	−3.17492	−0.428106
$56$	7.51496	1.00423
$57$	3.17161	0.420090
$58$	1.05058	0.137948
$59$	−1.12540	−0.146514	−0.0732572	−	0.997313i	$-0.523339\pi$
$59$	−1.12540	−0.146514	−0.0732572	+	0.997313i	$0.523339\pi$
$60$	−0.255669	−0.0330067
$61$	−1.79074	−0.229281	−0.114640	−	0.993407i	$-0.536572\pi$
$61$	−1.79074	−0.229281	−0.114640	+	0.993407i	$0.536572\pi$
$62$	15.8750	2.01612
$63$	−2.51917	−0.317386
$64$	7.17487	0.896858
$65$	6.75365	0.837687
$66$	−6.78475	−0.835146
$67$	4.57235	0.558602	0.279301	−	0.960204i	$-0.409897\pi$
$67$	4.57235	0.558602	0.279301	+	0.960204i	$0.409897\pi$
$68$	−0.176504	−0.0214043
$69$	0.877730	0.105666
$70$	−4.12118	−0.492576
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−2.42605	−0.285913
$73$	15.4184	1.80458	0.902291	−	0.431127i	$-0.141884\pi$
$73$	15.4184	1.80458	0.902291	+	0.431127i	$0.141884\pi$
$74$	−9.03496	−1.05029
$75$	−1.44851	−0.167260
$76$	−0.386467	−0.0443308
$77$	−8.86900	−1.01072
$78$	14.4325	1.63415
$79$	3.36461	0.378548	0.189274	−	0.981924i	$-0.439387\pi$
$79$	3.36461	0.378548	0.189274	+	0.981924i	$0.439387\pi$
$80$	−4.32185	−0.483198
$81$	−5.48130	−0.609033
$82$	−9.64941	−1.06560
$83$	−16.1083	−1.76812	−0.884058	−	0.467377i	$-0.845199\pi$
$83$	−16.1083	−1.76812	−0.884058	+	0.467377i	$0.845199\pi$
$84$	−0.714200	−0.0779256
$85$	−1.00000	−0.108465
$86$	3.58672	0.386766
$87$	1.03151	0.110589
$88$	−8.54116	−0.910490
$89$	−3.97957	−0.421834	−0.210917	−	0.977504i	$-0.567645\pi$
$89$	−3.97957	−0.421834	−0.210917	+	0.977504i	$0.567645\pi$
$90$	1.33044	0.140241
$91$	18.8660	1.97770
$92$	−0.106953	−0.0111506
$93$	15.5867	1.61627
$94$	−10.4069	−1.07339
$95$	−2.18956	−0.224644
$96$	−1.44217	−0.147191
$97$	4.83862	0.491288	0.245644	−	0.969360i	$-0.421001\pi$
$97$	4.83862	0.491288	0.245644	+	0.969360i	$0.421001\pi$
$98$	−1.18527	−0.119731
$99$	2.86318	0.287760
$100$	0.176504	0.0176504
$101$	10.1814	1.01308	0.506542	−	0.862215i	$-0.330923\pi$
$101$	10.1814	1.01308	0.506542	+	0.862215i	$0.330923\pi$
$102$	−2.13699	−0.211593
$103$	17.1391	1.68877	0.844385	−	0.535737i	$-0.179966\pi$
$103$	17.1391	1.68877	0.844385	+	0.535737i	$0.179966\pi$
$104$	18.1687	1.78158
$105$	−4.04636	−0.394884
$106$	−6.57156	−0.638286
$107$	−3.91550	−0.378526	−0.189263	−	0.981926i	$-0.560610\pi$
$107$	−3.91550	−0.378526	−0.189263	+	0.981926i	$0.560610\pi$
$108$	0.997571	0.0959913
$109$	0.934001	0.0894611	0.0447305	−	0.998999i	$-0.485757\pi$
$109$	0.934001	0.0894611	0.0447305	+	0.998999i	$0.485757\pi$
$110$	4.68395	0.446597
$111$	−8.87092	−0.841990
$112$	−12.0729	−1.14078
$113$	4.10061	0.385753	0.192876	−	0.981223i	$-0.438218\pi$
$113$	4.10061	0.385753	0.192876	+	0.981223i	$0.438218\pi$
$114$	−4.67907	−0.438235
$115$	−0.605952	−0.0565054
$116$	−0.125691	−0.0116702
$117$	−6.09052	−0.563069
$118$	1.66030	0.152843
$119$	−2.79346	−0.256076
$120$	−3.89679	−0.355726
$121$	−0.919910	−0.0836282
$122$	2.64188	0.239184
$123$	−9.47422	−0.854261
$124$	−1.89928	−0.170560
$125$	1.00000	0.0894427
$126$	3.71653	0.331095
$127$	−15.4797	−1.37360	−0.686802	−	0.726845i	$-0.740986\pi$
$127$	−15.4797	−1.37360	−0.686802	+	0.726845i	$0.740986\pi$
$128$	−12.5763	−1.11160
$129$	3.52160	0.310060
$130$	−9.96364	−0.873869
$131$	−18.8058	−1.64307	−0.821534	−	0.570160i	$-0.806881\pi$
$131$	−18.8058	−1.64307	−0.821534	+	0.570160i	$0.806881\pi$
$132$	0.811726	0.0706517
$133$	−6.11645	−0.530364
$134$	−6.74558	−0.582730
$135$	5.65182	0.486431
$136$	−2.69020	−0.230683
$137$	−9.12596	−0.779683	−0.389842	−	0.920882i	$-0.627470\pi$
$137$	−9.12596	−0.779683	−0.389842	+	0.920882i	$0.627470\pi$
$138$	−1.29491	−0.110230
$139$	−0.148114	−0.0125629	−0.00628145	−	0.999980i	$-0.501999\pi$
$139$	−0.148114	−0.0125629	−0.00628145	+	0.999980i	$0.501999\pi$
$140$	0.493057	0.0416710
$141$	−10.2180	−0.860510
$142$	1.47530	0.123804
$143$	−21.4423	−1.79309
$144$	3.89750	0.324792
$145$	−0.712115	−0.0591380
$146$	−22.7467	−1.88253
$147$	−1.16375	−0.0959847
$148$	1.08094	0.0888527
$149$	−7.88250	−0.645760	−0.322880	−	0.946440i	$-0.604651\pi$
$149$	−7.88250	−0.645760	−0.322880	+	0.946440i	$0.604651\pi$
$150$	2.13699	0.174484
$151$	5.37820	0.437672	0.218836	−	0.975762i	$-0.429774\pi$
$151$	5.37820	0.437672	0.218836	+	0.975762i	$0.429774\pi$
$152$	−5.89036	−0.477771
$153$	0.901812	0.0729072
$154$	13.0844	1.05437
$155$	−10.7605	−0.864305
$156$	−1.72670	−0.138246
$157$	−9.30288	−0.742450	−0.371225	−	0.928543i	$-0.621062\pi$
$157$	−9.30288	−0.742450	−0.371225	+	0.928543i	$0.621062\pi$
$158$	−4.96380	−0.394899
$159$	−6.45224	−0.511696
$160$	0.995625	0.0787110
$161$	−1.69270	−0.133404
$162$	8.08655	0.635339
$163$	16.3590	1.28133	0.640666	−	0.767820i	$-0.278658\pi$
$163$	16.3590	1.28133	0.640666	+	0.767820i	$0.278658\pi$
$164$	1.15445	0.0901477
$165$	4.59890	0.358024
$166$	23.7646	1.84449
$167$	18.8229	1.45656	0.728280	−	0.685280i	$-0.240320\pi$
$167$	18.8229	1.45656	0.728280	+	0.685280i	$0.240320\pi$
$168$	−10.8855	−0.839836
$169$	32.6117	2.50859
$170$	1.47530	0.113150
$171$	1.97457	0.150999
$172$	−0.429115	−0.0327197
$173$	11.6698	0.887238	0.443619	−	0.896215i	$-0.353694\pi$
$173$	11.6698	0.887238	0.443619	+	0.896215i	$0.353694\pi$
$174$	−1.52178	−0.115366
$175$	2.79346	0.211166
$176$	13.7215	1.03430
$177$	1.63015	0.122530
$178$	5.87106	0.440054
$179$	17.2350	1.28820	0.644102	−	0.764939i	$-0.277231\pi$
$179$	17.2350	1.28820	0.644102	+	0.764939i	$0.277231\pi$
$180$	−0.159174	−0.0118641
$181$	19.6867	1.46330	0.731652	−	0.681679i	$-0.238750\pi$
$181$	19.6867	1.46330	0.731652	+	0.681679i	$0.238750\pi$
$182$	−27.8330	−2.06312
$183$	2.59391	0.191747
$184$	−1.63013	−0.120175
$185$	6.12416	0.450257
$186$	−22.9951	−1.68608
$187$	3.17492	0.232173
$188$	1.24508	0.0908071
$189$	15.7881	1.14842
$190$	3.23026	0.234347
$191$	−2.67101	−0.193268	−0.0966339	−	0.995320i	$-0.530808\pi$
$191$	−2.67101	−0.193268	−0.0966339	+	0.995320i	$0.530808\pi$
$192$	−10.3929	−0.750042
$193$	−10.6457	−0.766297	−0.383149	−	0.923687i	$-0.625160\pi$
$193$	−10.6457	−0.766297	−0.383149	+	0.923687i	$0.625160\pi$
$194$	−7.13841	−0.512508
$195$	−9.78274	−0.700557
$196$	0.141806	0.0101290
$197$	−7.64261	−0.544514	−0.272257	−	0.962225i	$-0.587770\pi$
$197$	−7.64261	−0.544514	−0.272257	+	0.962225i	$0.587770\pi$
$198$	−4.22404	−0.300189
$199$	−10.9660	−0.777360	−0.388680	−	0.921373i	$-0.627069\pi$
$199$	−10.9660	−0.777360	−0.388680	+	0.921373i	$0.627069\pi$
$200$	2.69020	0.190226
$201$	−6.62311	−0.467158
$202$	−15.0206	−1.05684
$203$	−1.98927	−0.139619
$204$	0.255669	0.0179004
$205$	6.54065	0.456819
$206$	−25.2853	−1.76171
$207$	0.546455	0.0379813
$208$	−29.1883	−2.02384
$209$	6.95167	0.480857
$210$	5.96959	0.411941
$211$	−14.6538	−1.00881	−0.504403	−	0.863468i	$-0.668287\pi$
$211$	−14.6538	−1.00881	−0.504403	+	0.863468i	$0.668287\pi$
$212$	0.786220	0.0539978
$213$	1.44851	0.0992504
$214$	5.77653	0.394876
$215$	−2.43119	−0.165806
$216$	15.2045	1.03454
$217$	−30.0591	−2.04054
$218$	−1.37793	−0.0933252
$219$	−22.3337	−1.50917
$220$	−0.560386	−0.0377812
$221$	−6.75365	−0.454299
$222$	13.0872	0.878359
$223$	21.4107	1.43377	0.716884	−	0.697193i	$-0.245568\pi$
$223$	21.4107	1.43377	0.716884	+	0.697193i	$0.245568\pi$
$224$	2.78124	0.185829
$225$	−0.901812	−0.0601208
$226$	−6.04962	−0.402415
$227$	−19.7757	−1.31256	−0.656280	−	0.754518i	$-0.727871\pi$
$227$	−19.7757	−1.31256	−0.656280	+	0.754518i	$0.727871\pi$
$228$	0.559802	0.0370738
$229$	6.61558	0.437170	0.218585	−	0.975818i	$-0.429856\pi$
$229$	6.61558	0.437170	0.218585	+	0.975818i	$0.429856\pi$
$230$	0.893960	0.0589460
$231$	12.8469	0.845261
$232$	−1.91573	−0.125774
$233$	−1.74227	−0.114140	−0.0570699	−	0.998370i	$-0.518176\pi$
$233$	−1.74227	−0.114140	−0.0570699	+	0.998370i	$0.518176\pi$
$234$	8.98533	0.587389
$235$	7.05413	0.460161
$236$	−0.198638	−0.0129302
$237$	−4.87368	−0.316580
$238$	4.12118	0.267137
$239$	−7.50334	−0.485351	−0.242675	−	0.970108i	$-0.578025\pi$
$239$	−7.50334	−0.485351	−0.242675	+	0.970108i	$0.578025\pi$
$240$	6.26026	0.404098
$241$	−24.3372	−1.56769	−0.783847	−	0.620954i	$-0.786746\pi$
$241$	−24.3372	−1.56769	−0.783847	+	0.620954i	$0.786746\pi$
$242$	1.35714	0.0872404
$243$	−9.01574	−0.578360
$244$	−0.316073	−0.0202345
$245$	0.803412	0.0513281
$246$	13.9773	0.891160
$247$	−14.7875	−0.940908
$248$	−28.9479	−1.83820
$249$	23.3331	1.47867
$250$	−1.47530	−0.0933060
$251$	−18.2887	−1.15437	−0.577185	−	0.816613i	$-0.695849\pi$
$251$	−18.2887	−1.15437	−0.577185	+	0.816613i	$0.695849\pi$
$252$	−0.444645	−0.0280100
$253$	1.92385	0.120951
$254$	22.8372	1.43293
$255$	1.44851	0.0907094
$256$	4.20408	0.262755
$257$	7.27022	0.453504	0.226752	−	0.973953i	$-0.427189\pi$
$257$	7.27022	0.453504	0.226752	+	0.973953i	$0.427189\pi$
$258$	−5.19541	−0.323452
$259$	17.1076	1.06301
$260$	1.19205	0.0739276
$261$	0.642194	0.0397508
$262$	27.7441	1.71404
$263$	−10.9141	−0.672993	−0.336496	−	0.941685i	$-0.609242\pi$
$263$	−10.9141	−0.672993	−0.336496	+	0.941685i	$0.609242\pi$
$264$	12.3720	0.761442
$265$	4.45439	0.273631
$266$	9.02359	0.553272
$267$	5.76446	0.352779
$268$	0.807040	0.0492978
$269$	11.3482	0.691912	0.345956	−	0.938251i	$-0.387555\pi$
$269$	11.3482	0.691912	0.345956	+	0.938251i	$0.387555\pi$
$270$	−8.33812	−0.507442
$271$	17.3126	1.05166	0.525832	−	0.850589i	$-0.323754\pi$
$271$	17.3126	1.05166	0.525832	+	0.850589i	$0.323754\pi$
$272$	4.32185	0.262051
$273$	−27.3277	−1.65395
$274$	13.4635	0.813360
$275$	−3.17492	−0.191455
$276$	0.154923	0.00932527
$277$	27.1021	1.62840	0.814202	−	0.580581i	$-0.197175\pi$
$277$	27.1021	1.62840	0.814202	+	0.580581i	$0.197175\pi$
$278$	0.218513	0.0131055
$279$	9.70396	0.580961
$280$	7.51496	0.449105
$281$	−17.5487	−1.04686	−0.523432	−	0.852067i	$-0.675349\pi$
$281$	−17.5487	−1.04686	−0.523432	+	0.852067i	$0.675349\pi$
$282$	15.0746	0.897678
$283$	−22.3962	−1.33132	−0.665659	−	0.746256i	$-0.731849\pi$
$283$	−22.3962	−1.33132	−0.665659	+	0.746256i	$0.731849\pi$
$284$	−0.176504	−0.0104736
$285$	3.17161	0.187870
$286$	31.6337	1.87054
$287$	18.2710	1.07851
$288$	−0.897866	−0.0529073
$289$	1.00000	0.0588235
$290$	1.05058	0.0616923
$291$	−7.00880	−0.410863
$292$	2.72141	0.159258
$293$	14.6418	0.855385	0.427693	−	0.903924i	$-0.359327\pi$
$293$	14.6418	0.855385	0.427693	+	0.903924i	$0.359327\pi$
$294$	1.71688	0.100131
$295$	−1.12540	−0.0655233
$296$	16.4752	0.957602
$297$	−17.9441	−1.04122
$298$	11.6290	0.673652
$299$	−4.09239	−0.236669
$300$	−0.255669	−0.0147610
$301$	−6.79142	−0.391451
$302$	−7.93445	−0.456576
$303$	−14.7478	−0.847242
$304$	9.46297	0.542738
$305$	−1.79074	−0.102537
$306$	−1.33044	−0.0760563
$307$	9.03757	0.515801	0.257901	−	0.966171i	$-0.416969\pi$
$307$	9.03757	0.515801	0.257901	+	0.966171i	$0.416969\pi$
$308$	−1.56542	−0.0891979
$309$	−24.8263	−1.41232
$310$	15.8750	0.901638
$311$	−26.8248	−1.52109	−0.760547	−	0.649283i	$-0.775069\pi$
$311$	−26.8248	−1.52109	−0.760547	+	0.649283i	$0.775069\pi$
$312$	−26.3175	−1.48994
$313$	−21.8391	−1.23442	−0.617208	−	0.786800i	$-0.711736\pi$
$313$	−21.8391	−1.23442	−0.617208	+	0.786800i	$0.711736\pi$
$314$	13.7245	0.774519
$315$	−2.51917	−0.141939
$316$	0.593868	0.0334077
$317$	2.41643	0.135720	0.0678600	−	0.997695i	$-0.478383\pi$
$317$	2.41643	0.135720	0.0678600	+	0.997695i	$0.478383\pi$
$318$	9.51898	0.533798
$319$	2.26091	0.126586
$320$	7.17487	0.401087
$321$	5.67165	0.316561
$322$	2.49724	0.139166
$323$	2.18956	0.121830
$324$	−0.967473	−0.0537485
$325$	6.75365	0.374625
$326$	−24.1343	−1.33668
$327$	−1.35291	−0.0748162
$328$	17.5957	0.971558
$329$	19.7054	1.08639
$330$	−6.78475	−0.373488
$331$	25.8788	1.42243	0.711214	−	0.702976i	$-0.248146\pi$
$331$	25.8788	1.42243	0.711214	+	0.702976i	$0.248146\pi$
$332$	−2.84319	−0.156040
$333$	−5.52284	−0.302650
$334$	−27.7694	−1.51947
$335$	4.57235	0.249814
$336$	17.4878	0.954037
$337$	21.9869	1.19770	0.598851	−	0.800860i	$-0.295624\pi$
$337$	21.9869	1.19770	0.598851	+	0.800860i	$0.295624\pi$
$338$	−48.1120	−2.61695
$339$	−5.93978	−0.322605
$340$	−0.176504	−0.00957229
$341$	34.1637	1.85007
$342$	−2.91308	−0.157522
$343$	−17.3099	−0.934647
$344$	−6.54038	−0.352633
$345$	0.877730	0.0472554
$346$	−17.2164	−0.925561
$347$	6.91494	0.371214	0.185607	−	0.982624i	$-0.440575\pi$
$347$	6.91494	0.371214	0.185607	+	0.982624i	$0.440575\pi$
$348$	0.182066	0.00975974
$349$	−14.3878	−0.770159	−0.385080	−	0.922883i	$-0.625826\pi$
$349$	−14.3878	−0.770159	−0.385080	+	0.922883i	$0.625826\pi$
$350$	−4.12118	−0.220287
$351$	38.1704	2.03739
$352$	−3.16102	−0.168483
$353$	24.3463	1.29582	0.647912	−	0.761715i	$-0.275642\pi$
$353$	24.3463	1.29582	0.647912	+	0.761715i	$0.275642\pi$
$354$	−2.40496	−0.127822
$355$	−1.00000	−0.0530745
$356$	−0.702412	−0.0372278
$357$	4.04636	0.214156
$358$	−25.4268	−1.34385
$359$	19.6166	1.03533	0.517663	−	0.855585i	$-0.326802\pi$
$359$	19.6166	1.03533	0.517663	+	0.855585i	$0.326802\pi$
$360$	−2.42605	−0.127864
$361$	−14.2058	−0.747675
$362$	−29.0438	−1.52651
$363$	1.33250	0.0699382
$364$	3.32994	0.174536
$365$	15.4184	0.807034
$366$	−3.82679	−0.200029
$367$	28.0149	1.46237	0.731183	−	0.682181i	$-0.238969\pi$
$367$	28.0149	1.46237	0.731183	+	0.682181i	$0.238969\pi$
$368$	2.61884	0.136516
$369$	−5.89844	−0.307061
$370$	−9.03496	−0.469705
$371$	12.4432	0.646017
$372$	2.75113	0.142639
$373$	16.8286	0.871353	0.435676	−	0.900103i	$-0.356509\pi$
$373$	16.8286	0.871353	0.435676	+	0.900103i	$0.356509\pi$
$374$	−4.68395	−0.242201
$375$	−1.44851	−0.0748009
$376$	18.9770	0.978665
$377$	−4.80938	−0.247695
$378$	−23.2922	−1.19802
$379$	26.3533	1.35368	0.676840	−	0.736131i	$-0.263349\pi$
$379$	26.3533	1.35368	0.676840	+	0.736131i	$0.263349\pi$
$380$	−0.386467	−0.0198253
$381$	22.4226	1.14874
$382$	3.94054	0.201616
$383$	7.60791	0.388746	0.194373	−	0.980928i	$-0.437733\pi$
$383$	7.60791	0.388746	0.194373	+	0.980928i	$0.437733\pi$
$384$	18.2169	0.929630
$385$	−8.86900	−0.452006
$386$	15.7056	0.799396
$387$	2.19247	0.111450
$388$	0.854037	0.0433572
$389$	10.4910	0.531915	0.265957	−	0.963985i	$-0.414312\pi$
$389$	10.4910	0.531915	0.265957	+	0.963985i	$0.414312\pi$
$390$	14.4325	0.730816
$391$	0.605952	0.0306443
$392$	2.16134	0.109164
$393$	27.2404	1.37410
$394$	11.2751	0.568033
$395$	3.36461	0.169292
$396$	0.505363	0.0253955
$397$	−1.89994	−0.0953552	−0.0476776	−	0.998863i	$-0.515182\pi$
$397$	−1.89994	−0.0953552	−0.0476776	+	0.998863i	$0.515182\pi$
$398$	16.1781	0.810937
$399$	8.85975	0.443543
$400$	−4.32185	−0.216093
$401$	−25.6659	−1.28170	−0.640848	−	0.767668i	$-0.721417\pi$
$401$	−25.6659	−1.28170	−0.640848	+	0.767668i	$0.721417\pi$
$402$	9.77106	0.487336
$403$	−72.6727	−3.62009
$404$	1.79706	0.0894069
$405$	−5.48130	−0.272368
$406$	2.93476	0.145650
$407$	−19.4437	−0.963788
$408$	3.89679	0.192920
$409$	30.0836	1.48754	0.743769	−	0.668437i	$-0.233036\pi$
$409$	30.0836	1.48754	0.743769	+	0.668437i	$0.233036\pi$
$410$	−9.64941	−0.476551
$411$	13.2191	0.652048
$412$	3.02513	0.149038
$413$	−3.14376	−0.154694
$414$	−0.806184	−0.0396218
$415$	−16.1083	−0.790726
$416$	6.72410	0.329676
$417$	0.214546	0.0105063
$418$	−10.2558	−0.501627
$419$	−6.75147	−0.329831	−0.164915	−	0.986308i	$-0.552735\pi$
$419$	−6.75147	−0.329831	−0.164915	+	0.986308i	$0.552735\pi$
$420$	−0.714200	−0.0348494
$421$	8.73318	0.425629	0.212815	−	0.977093i	$-0.431737\pi$
$421$	8.73318	0.425629	0.212815	+	0.977093i	$0.431737\pi$
$422$	21.6187	1.05238
$423$	−6.36150	−0.309307
$424$	11.9832	0.581956
$425$	−1.00000	−0.0485071
$426$	−2.13699	−0.103537
$427$	−5.00236	−0.242081
$428$	−0.691103	−0.0334057
$429$	31.0594	1.49956
$430$	3.58672	0.172967
$431$	−5.83778	−0.281196	−0.140598	−	0.990067i	$-0.544902\pi$
$431$	−5.83778	−0.281196	−0.140598	+	0.990067i	$0.544902\pi$
$432$	−24.4264	−1.17521
$433$	7.28120	0.349912	0.174956	−	0.984576i	$-0.444022\pi$
$433$	7.28120	0.349912	0.174956	+	0.984576i	$0.444022\pi$
$434$	44.3461	2.12868
$435$	1.03151	0.0494570
$436$	0.164855	0.00789513
$437$	1.32677	0.0634680
$438$	32.9488	1.57436
$439$	11.8157	0.563934	0.281967	−	0.959424i	$-0.409013\pi$
$439$	11.8157	0.563934	0.281967	+	0.959424i	$0.409013\pi$
$440$	−8.54116	−0.407184
$441$	−0.724527	−0.0345013
$442$	9.96364	0.473922
$443$	35.2814	1.67627	0.838135	−	0.545463i	$-0.183646\pi$
$443$	35.2814	1.67627	0.838135	+	0.545463i	$0.183646\pi$
$444$	−1.56576	−0.0743075
$445$	−3.97957	−0.188650
$446$	−31.5872	−1.49570
$447$	11.4179	0.540048
$448$	20.0427	0.946928
$449$	23.4444	1.10641	0.553205	−	0.833045i	$-0.313404\pi$
$449$	23.4444	1.10641	0.553205	+	0.833045i	$0.313404\pi$
$450$	1.33044	0.0627176
$451$	−20.7660	−0.977834
$452$	0.723775	0.0340435
$453$	−7.79039	−0.366025
$454$	29.1751	1.36925
$455$	18.8660	0.884453
$456$	8.53226	0.399560
$457$	−1.85634	−0.0868360	−0.0434180	−	0.999057i	$-0.513825\pi$
$457$	−1.85634	−0.0868360	−0.0434180	+	0.999057i	$0.513825\pi$
$458$	−9.75995	−0.456052
$459$	−5.65182	−0.263804
$460$	−0.106953	−0.00498672
$461$	−17.4279	−0.811699	−0.405849	−	0.913940i	$-0.633024\pi$
$461$	−17.4279	−0.811699	−0.405849	+	0.913940i	$0.633024\pi$
$462$	−18.9529	−0.881770
$463$	14.3695	0.667808	0.333904	−	0.942607i	$-0.391634\pi$
$463$	14.3695	0.667808	0.333904	+	0.942607i	$0.391634\pi$
$464$	3.07766	0.142877
$465$	15.5867	0.722818
$466$	2.57037	0.119070
$467$	27.2132	1.25928	0.629638	−	0.776889i	$-0.283203\pi$
$467$	27.2132	1.25928	0.629638	+	0.776889i	$0.283203\pi$
$468$	−1.07500	−0.0496920
$469$	12.7727	0.589787
$470$	−10.4069	−0.480036
$471$	13.4753	0.620911
$472$	−3.02755	−0.139354
$473$	7.71881	0.354911
$474$	7.19013	0.330254
$475$	−2.18956	−0.100464
$476$	−0.493057	−0.0225993
$477$	−4.01703	−0.183927
$478$	11.0697	0.506315
$479$	−2.22972	−0.101879	−0.0509393	−	0.998702i	$-0.516221\pi$
$479$	−2.22972	−0.101879	−0.0509393	+	0.998702i	$0.516221\pi$
$480$	−1.44217	−0.0658260
$481$	41.3604	1.88587
$482$	35.9046	1.63541
$483$	2.45190	0.111565
$484$	−0.162368	−0.00738037
$485$	4.83862	0.219710
$486$	13.3009	0.603341
$487$	27.5625	1.24898	0.624488	−	0.781034i	$-0.285308\pi$
$487$	27.5625	1.24898	0.624488	+	0.781034i	$0.285308\pi$
$488$	−4.81745	−0.218076
$489$	−23.6961	−1.07158
$490$	−1.18527	−0.0535452
$491$	20.4636	0.923511	0.461755	−	0.887007i	$-0.347220\pi$
$491$	20.4636	0.923511	0.461755	+	0.887007i	$0.347220\pi$
$492$	−1.67224	−0.0753904
$493$	0.712115	0.0320721
$494$	21.8160	0.981549
$495$	2.86318	0.128690
$496$	46.5054	2.08815
$497$	−2.79346	−0.125304
$498$	−34.4233	−1.54254
$499$	33.1161	1.48248	0.741240	−	0.671240i	$-0.234238\pi$
$499$	33.1161	1.48248	0.741240	+	0.671240i	$0.234238\pi$
$500$	0.176504	0.00789351
$501$	−27.2652	−1.21812
$502$	26.9812	1.20423
$503$	24.4433	1.08987	0.544936	−	0.838477i	$-0.316554\pi$
$503$	24.4433	1.08987	0.544936	+	0.838477i	$0.316554\pi$
$504$	−6.77708	−0.301875
$505$	10.1814	0.453065
$506$	−2.83825	−0.126176
$507$	−47.2385	−2.09794
$508$	−2.73224	−0.121223
$509$	7.69835	0.341223	0.170612	−	0.985338i	$-0.445426\pi$
$509$	7.69835	0.341223	0.170612	+	0.985338i	$0.445426\pi$
$510$	−2.13699	−0.0946274
$511$	43.0705	1.90533
$512$	18.9504	0.837495
$513$	−12.3750	−0.546370
$514$	−10.7257	−0.473092
$515$	17.1391	0.755241
$516$	0.621578	0.0273634
$517$	−22.3963	−0.984987
$518$	−25.2388	−1.10893
$519$	−16.9038	−0.741996
$520$	18.1687	0.796748
$521$	−20.2328	−0.886416	−0.443208	−	0.896419i	$-0.646160\pi$
$521$	−20.2328	−0.886416	−0.443208	+	0.896419i	$0.646160\pi$
$522$	−0.947428	−0.0414678
$523$	5.98773	0.261825	0.130912	−	0.991394i	$-0.458209\pi$
$523$	5.98773	0.261825	0.130912	+	0.991394i	$0.458209\pi$
$524$	−3.31930	−0.145004
$525$	−4.04636	−0.176598
$526$	16.1016	0.702061
$527$	10.7605	0.468735
$528$	−19.8758	−0.864983
$529$	−22.6328	−0.984036
$530$	−6.57156	−0.285450
$531$	1.01490	0.0440428
$532$	−1.07958	−0.0468057
$533$	44.1733	1.91336
$534$	−8.50430	−0.368017
$535$	−3.91550	−0.169282
$536$	12.3005	0.531302
$537$	−24.9651	−1.07732
$538$	−16.7420	−0.721798
$539$	−2.55077	−0.109869
$540$	0.997571	0.0429286
$541$	11.2940	0.485568	0.242784	−	0.970080i	$-0.421939\pi$
$541$	11.2940	0.485568	0.242784	+	0.970080i	$0.421939\pi$
$542$	−25.5412	−1.09709
$543$	−28.5165	−1.22376
$544$	−0.995625	−0.0426871
$545$	0.934001	0.0400082
$546$	40.3165	1.72539
$547$	−15.1855	−0.649283	−0.324642	−	0.945837i	$-0.605244\pi$
$547$	−15.1855	−0.649283	−0.324642	+	0.945837i	$0.605244\pi$
$548$	−1.61077	−0.0688087
$549$	1.61491	0.0689227
$550$	4.68395	0.199724
$551$	1.55922	0.0664250
$552$	2.36127	0.100502
$553$	9.39890	0.399682
$554$	−39.9836	−1.69874
$555$	−8.87092	−0.376550
$556$	−0.0261428	−0.00110870
$557$	−37.1205	−1.57284	−0.786422	−	0.617689i	$-0.788069\pi$
$557$	−37.1205	−1.57284	−0.786422	+	0.617689i	$0.788069\pi$
$558$	−14.3162	−0.606055
$559$	−16.4194	−0.694465
$560$	−12.0729	−0.510174
$561$	−4.59890	−0.194166
$562$	25.8895	1.09208
$563$	−9.72234	−0.409748	−0.204874	−	0.978788i	$-0.565678\pi$
$563$	−9.72234	−0.409748	−0.204874	+	0.978788i	$0.565678\pi$
$564$	−1.80352	−0.0759419
$565$	4.10061	0.172514
$566$	33.0411	1.38882
$567$	−15.3118	−0.643034
$568$	−2.69020	−0.112878
$569$	43.9781	1.84366	0.921830	−	0.387595i	$-0.126694\pi$
$569$	43.9781	1.84366	0.921830	+	0.387595i	$0.126694\pi$
$570$	−4.67907	−0.195985
$571$	1.43332	0.0599826	0.0299913	−	0.999550i	$-0.490452\pi$
$571$	1.43332	0.0599826	0.0299913	+	0.999550i	$0.490452\pi$
$572$	−3.78465	−0.158244
$573$	3.86900	0.161630
$574$	−26.9552	−1.12509
$575$	−0.605952	−0.0252700
$576$	−6.47038	−0.269599
$577$	15.1156	0.629269	0.314634	−	0.949213i	$-0.398118\pi$
$577$	15.1156	0.629269	0.314634	+	0.949213i	$0.398118\pi$
$578$	−1.47530	−0.0613643
$579$	15.4205	0.640853
$580$	−0.125691	−0.00521905
$581$	−44.9979	−1.86683
$582$	10.3401	0.428610
$583$	−14.1423	−0.585715
$584$	41.4785	1.71639
$585$	−6.09052	−0.251812
$586$	−21.6011	−0.892332
$587$	−0.608077	−0.0250980	−0.0125490	−	0.999921i	$-0.503995\pi$
$587$	−0.608077	−0.0250980	−0.0125490	+	0.999921i	$0.503995\pi$
$588$	−0.205407	−0.00847086
$589$	23.5608	0.970807
$590$	1.66030	0.0683534
$591$	11.0704	0.455376
$592$	−26.4677	−1.08782
$593$	−3.11667	−0.127986	−0.0639932	−	0.997950i	$-0.520384\pi$
$593$	−3.11667	−0.127986	−0.0639932	+	0.997950i	$0.520384\pi$
$594$	26.4728	1.08619
$595$	−2.79346	−0.114521
$596$	−1.39130	−0.0569897
$597$	15.8844	0.650106
$598$	6.03749	0.246891
$599$	−30.3665	−1.24074	−0.620370	−	0.784309i	$-0.713018\pi$
$599$	−30.3665	−1.24074	−0.620370	+	0.784309i	$0.713018\pi$
$600$	−3.89679	−0.159086
$601$	17.7059	0.722239	0.361120	−	0.932520i	$-0.382395\pi$
$601$	17.7059	0.722239	0.361120	+	0.932520i	$0.382395\pi$
$602$	10.0194	0.408359
$603$	−4.12340	−0.167918
$604$	0.949276	0.0386255
$605$	−0.919910	−0.0373997
$606$	21.7575	0.883837
$607$	43.9015	1.78191	0.890953	−	0.454095i	$-0.150037\pi$
$607$	43.9015	1.78191	0.890953	+	0.454095i	$0.150037\pi$
$608$	−2.17998	−0.0884099
$609$	2.88147	0.116763
$610$	2.64188	0.106966
$611$	47.6411	1.92735
$612$	0.159174	0.00643422
$613$	−9.47564	−0.382718	−0.191359	−	0.981520i	$-0.561289\pi$
$613$	−9.47564	−0.382718	−0.191359	+	0.981520i	$0.561289\pi$
$614$	−13.3331	−0.538080
$615$	−9.47422	−0.382037
$616$	−23.8594	−0.961321
$617$	18.3648	0.739340	0.369670	−	0.929163i	$-0.379471\pi$
$617$	18.3648	0.739340	0.369670	+	0.929163i	$0.379471\pi$
$618$	36.6261	1.47332
$619$	12.3641	0.496955	0.248477	−	0.968638i	$-0.420070\pi$
$619$	12.3641	0.496955	0.248477	+	0.968638i	$0.420070\pi$
$620$	−1.89928	−0.0762768
$621$	−3.42474	−0.137430
$622$	39.5746	1.58680
$623$	−11.1168	−0.445384
$624$	42.2796	1.69254
$625$	1.00000	0.0400000
$626$	32.2191	1.28773
$627$	−10.0696	−0.402141
$628$	−1.64200	−0.0655228
$629$	−6.12416	−0.244186
$630$	3.71653	0.148070
$631$	−27.5468	−1.09662	−0.548310	−	0.836275i	$-0.684729\pi$
$631$	−27.5468	−1.09662	−0.548310	+	0.836275i	$0.684729\pi$
$632$	9.05148	0.360048
$633$	21.2262	0.843664
$634$	−3.56495	−0.141582
$635$	−15.4797	−0.614294
$636$	−1.13885	−0.0451583
$637$	5.42596	0.214984
$638$	−3.33551	−0.132054
$639$	0.901812	0.0356751
$640$	−12.5763	−0.497123
$641$	20.6550	0.815823	0.407912	−	0.913021i	$-0.366257\pi$
$641$	20.6550	0.815823	0.407912	+	0.913021i	$0.366257\pi$
$642$	−8.36738	−0.330234
$643$	−0.674865	−0.0266141	−0.0133070	−	0.999911i	$-0.504236\pi$
$643$	−0.674865	−0.0266141	−0.0133070	+	0.999911i	$0.504236\pi$
$644$	−0.298769	−0.0117732
$645$	3.52160	0.138663
$646$	−3.23026	−0.127093
$647$	22.2792	0.875887	0.437944	−	0.899002i	$-0.355707\pi$
$647$	22.2792	0.875887	0.437944	+	0.899002i	$0.355707\pi$
$648$	−14.7458	−0.579269
$649$	3.57305	0.140254
$650$	−9.96364	−0.390806
$651$	43.5409	1.70650
$652$	2.88743	0.113080
$653$	−7.25865	−0.284053	−0.142027	−	0.989863i	$-0.545362\pi$
$653$	−7.25865	−0.284053	−0.142027	+	0.989863i	$0.545362\pi$
$654$	1.99595	0.0780477
$655$	−18.8058	−0.734802
$656$	−28.2678	−1.10367
$657$	−13.9045	−0.542465
$658$	−29.0714	−1.13332
$659$	28.7071	1.11827	0.559136	−	0.829076i	$-0.311133\pi$
$659$	28.7071	1.11827	0.559136	+	0.829076i	$0.311133\pi$
$660$	0.811726	0.0315964
$661$	1.12725	0.0438448	0.0219224	−	0.999760i	$-0.493021\pi$
$661$	1.12725	0.0438448	0.0219224	+	0.999760i	$0.493021\pi$
$662$	−38.1789	−1.48387
$663$	9.78274	0.379930
$664$	−43.3346	−1.68171
$665$	−6.11645	−0.237186
$666$	8.14784	0.315722
$667$	0.431508	0.0167081
$668$	3.32232	0.128544
$669$	−31.0137	−1.19906
$670$	−6.74558	−0.260605
$671$	5.68545	0.219484
$672$	−4.02866	−0.155409
$673$	22.6826	0.874351	0.437175	−	0.899376i	$-0.355979\pi$
$673$	22.6826	0.874351	0.437175	+	0.899376i	$0.355979\pi$
$674$	−32.4372	−1.24944
$675$	5.65182	0.217539
$676$	5.75611	0.221389
$677$	44.1411	1.69648	0.848240	−	0.529612i	$-0.177663\pi$
$677$	44.1411	1.69648	0.848240	+	0.529612i	$0.177663\pi$
$678$	8.76295	0.336539
$679$	13.5165	0.518715
$680$	−2.69020	−0.103164
$681$	28.6454	1.09769
$682$	−50.4017	−1.92998
$683$	9.11629	0.348825	0.174412	−	0.984673i	$-0.444197\pi$
$683$	9.11629	0.348825	0.174412	+	0.984673i	$0.444197\pi$
$684$	0.348521	0.0133260
$685$	−9.12596	−0.348685
$686$	25.5373	0.975018
$687$	−9.58274	−0.365604
$688$	10.5072	0.400585
$689$	30.0834	1.14609
$690$	−1.29491	−0.0492965
$691$	−14.4333	−0.549070	−0.274535	−	0.961577i	$-0.588524\pi$
$691$	−14.4333	−0.549070	−0.274535	+	0.961577i	$0.588524\pi$
$692$	2.05977	0.0783007
$693$	7.99817	0.303825
$694$	−10.2016	−0.387247
$695$	−0.148114	−0.00561830
$696$	2.77496	0.105185
$697$	−6.54065	−0.247745
$698$	21.2262	0.803425
$699$	2.52370	0.0954550
$700$	0.493057	0.0186358
$701$	−13.3552	−0.504417	−0.252209	−	0.967673i	$-0.581157\pi$
$701$	−13.3552	−0.504417	−0.252209	+	0.967673i	$0.581157\pi$
$702$	−56.3127	−2.12539
$703$	−13.4092	−0.505738
$704$	−22.7796	−0.858538
$705$	−10.2180	−0.384832
$706$	−35.9181	−1.35179
$707$	28.4412	1.06964
$708$	0.287729	0.0108135
$709$	−19.5853	−0.735541	−0.367770	−	0.929917i	$-0.619879\pi$
$709$	−19.5853	−0.735541	−0.367770	+	0.929917i	$0.619879\pi$
$710$	1.47530	0.0553669
$711$	−3.03425	−0.113793
$712$	−10.7058	−0.401219
$713$	6.52036	0.244189
$714$	−5.96959	−0.223406
$715$	−21.4423	−0.801895
$716$	3.04205	0.113687
$717$	10.8687	0.405898
$718$	−28.9404	−1.08004
$719$	5.06756	0.188988	0.0944940	−	0.995525i	$-0.469877\pi$
$719$	5.06756	0.188988	0.0944940	+	0.995525i	$0.469877\pi$
$720$	3.89750	0.145251
$721$	47.8775	1.78305
$722$	20.9578	0.779969
$723$	35.2527	1.31106
$724$	3.47479	0.129140
$725$	−0.712115	−0.0264473
$726$	−1.96584	−0.0729590
$727$	22.8484	0.847401	0.423701	−	0.905802i	$-0.360731\pi$
$727$	22.8484	0.847401	0.423701	+	0.905802i	$0.360731\pi$
$728$	50.7534	1.88105
$729$	29.5033	1.09272
$730$	−22.7467	−0.841892
$731$	2.43119	0.0899207
$732$	0.457836	0.0169221
$733$	−28.6986	−1.06001	−0.530003	−	0.847996i	$-0.677809\pi$
$733$	−28.6986	−1.06001	−0.530003	+	0.847996i	$0.677809\pi$
$734$	−41.3303	−1.52553
$735$	−1.16375	−0.0429257
$736$	−0.603301	−0.0222380
$737$	−14.5168	−0.534734
$738$	8.70196	0.320324
$739$	−26.9185	−0.990214	−0.495107	−	0.868832i	$-0.664871\pi$
$739$	−26.9185	−0.990214	−0.495107	+	0.868832i	$0.664871\pi$
$740$	1.08094	0.0397362
$741$	21.4199	0.786880
$742$	−18.3574	−0.673921
$743$	14.1168	0.517895	0.258947	−	0.965891i	$-0.416624\pi$
$743$	14.1168	0.517895	0.258947	+	0.965891i	$0.416624\pi$
$744$	41.9314	1.53728
$745$	−7.88250	−0.288793
$746$	−24.8272	−0.908989
$747$	14.5267	0.531503
$748$	0.560386	0.0204898
$749$	−10.9378	−0.399658
$750$	2.13699	0.0780317
$751$	−5.82408	−0.212524	−0.106262	−	0.994338i	$-0.533888\pi$
$751$	−5.82408	−0.212524	−0.106262	+	0.994338i	$0.533888\pi$
$752$	−30.4869	−1.11174
$753$	26.4914	0.965398
$754$	7.09526	0.258394
$755$	5.37820	0.195733
$756$	2.78667	0.101350
$757$	27.3994	0.995848	0.497924	−	0.867221i	$-0.334096\pi$
$757$	27.3994	0.995848	0.497924	+	0.867221i	$0.334096\pi$
$758$	−38.8790	−1.41215
$759$	−2.78672	−0.101151
$760$	−5.89036	−0.213666
$761$	−46.9250	−1.70103	−0.850514	−	0.525952i	$-0.823709\pi$
$761$	−46.9250	−1.70103	−0.850514	+	0.525952i	$0.823709\pi$
$762$	−33.0800	−1.19836
$763$	2.60909	0.0944555
$764$	−0.471445	−0.0170563
$765$	0.901812	0.0326051
$766$	−11.2239	−0.405537
$767$	−7.60055	−0.274440
$768$	−6.08966	−0.219742
$769$	31.9368	1.15167	0.575835	−	0.817566i	$-0.304677\pi$
$769$	31.9368	1.15167	0.575835	+	0.817566i	$0.304677\pi$
$770$	13.0844	0.471530
$771$	−10.5310	−0.379265
$772$	−1.87902	−0.0676274
$773$	−0.304096	−0.0109376	−0.00546878	−	0.999985i	$-0.501741\pi$
$773$	−0.304096	−0.0109376	−0.00546878	+	0.999985i	$0.501741\pi$
$774$	−3.23455	−0.116264
$775$	−10.7605	−0.386529
$776$	13.0169	0.467278
$777$	−24.7805	−0.888997
$778$	−15.4773	−0.554890
$779$	−14.3212	−0.513109
$780$	−1.72670	−0.0618256
$781$	3.17492	0.113607
$782$	−0.893960	−0.0319680
$783$	−4.02475	−0.143833
$784$	−3.47223	−0.124008
$785$	−9.30288	−0.332034
$786$	−40.1877	−1.43345
$787$	−25.9970	−0.926694	−0.463347	−	0.886177i	$-0.653352\pi$
$787$	−25.9970	−0.926694	−0.463347	+	0.886177i	$0.653352\pi$
$788$	−1.34895	−0.0480545
$789$	15.8092	0.562823
$790$	−4.96380	−0.176604
$791$	11.4549	0.407289
$792$	7.70252	0.273697
$793$	−12.0940	−0.429471
$794$	2.80297	0.0994739
$795$	−6.45224	−0.228838
$796$	−1.93555	−0.0686037
$797$	11.5646	0.409638	0.204819	−	0.978800i	$-0.434339\pi$
$797$	11.5646	0.409638	0.204819	+	0.978800i	$0.434339\pi$
$798$	−13.0708	−0.462701
$799$	−7.05413	−0.249557
$800$	0.995625	0.0352006
$801$	3.58883	0.126805
$802$	37.8649	1.33706
$803$	−48.9520	−1.72748
$804$	−1.16901	−0.0412277
$805$	−1.69270	−0.0596599
$806$	107.214	3.77645
$807$	−16.4380	−0.578645
$808$	27.3899	0.963574
$809$	0.518073	0.0182145	0.00910723	−	0.999959i	$-0.497101\pi$
$809$	0.518073	0.0182145	0.00910723	+	0.999959i	$0.497101\pi$
$810$	8.08655	0.284132
$811$	−18.4950	−0.649446	−0.324723	−	0.945809i	$-0.605271\pi$
$811$	−18.4950	−0.649446	−0.324723	+	0.945809i	$0.605271\pi$
$812$	−0.351114	−0.0123217
$813$	−25.0775	−0.879505
$814$	28.6852	1.00542
$815$	16.3590	0.573029
$816$	−6.26026	−0.219153
$817$	5.32323	0.186236
$818$	−44.3823	−1.55179
$819$	−17.0136	−0.594504
$820$	1.15445	0.0403153
$821$	29.6144	1.03355	0.516775	−	0.856121i	$-0.327132\pi$
$821$	29.6144	1.03355	0.516775	+	0.856121i	$0.327132\pi$
$822$	−19.5021	−0.680212
$823$	−40.0102	−1.39467	−0.697335	−	0.716746i	$-0.745631\pi$
$823$	−40.0102	−1.39467	−0.697335	+	0.716746i	$0.745631\pi$
$824$	46.1077	1.60624
$825$	4.59890	0.160113
$826$	4.63798	0.161376
$827$	−35.2959	−1.22736	−0.613679	−	0.789555i	$-0.710311\pi$
$827$	−35.2959	−1.22736	−0.613679	+	0.789555i	$0.710311\pi$
$828$	0.0964517	0.00335193
$829$	12.5832	0.437033	0.218517	−	0.975833i	$-0.429878\pi$
$829$	12.5832	0.437033	0.218517	+	0.975833i	$0.429878\pi$
$830$	23.7646	0.824880
$831$	−39.2577	−1.36183
$832$	48.4565	1.67993
$833$	−0.803412	−0.0278366
$834$	−0.316519	−0.0109601
$835$	18.8229	0.651393
$836$	1.22700	0.0424367
$837$	−60.8165	−2.10213
$838$	9.96042	0.344077
$839$	32.6235	1.12629	0.563145	−	0.826358i	$-0.309591\pi$
$839$	32.6235	1.12629	0.563145	+	0.826358i	$0.309591\pi$
$840$	−10.8855	−0.375586
$841$	−28.4929	−0.982514
$842$	−12.8841	−0.444014
$843$	25.4194	0.875492
$844$	−2.58645	−0.0890293
$845$	32.6117	1.12188
$846$	9.38511	0.322667
$847$	−2.56973	−0.0882970
$848$	−19.2512	−0.661090
$849$	32.4412	1.11338
$850$	1.47530	0.0506023
$851$	−3.71095	−0.127210
$852$	0.255669	0.00875906
$853$	−13.4163	−0.459365	−0.229683	−	0.973266i	$-0.573769\pi$
$853$	−13.4163	−0.459365	−0.229683	+	0.973266i	$0.573769\pi$
$854$	7.37997	0.252537
$855$	1.97457	0.0675290
$856$	−10.5335	−0.360027
$857$	6.78494	0.231769	0.115884	−	0.993263i	$-0.463030\pi$
$857$	6.78494	0.231769	0.115884	+	0.993263i	$0.463030\pi$
$858$	−45.8218	−1.56433
$859$	−4.78464	−0.163250	−0.0816249	−	0.996663i	$-0.526011\pi$
$859$	−4.78464	−0.163250	−0.0816249	+	0.996663i	$0.526011\pi$
$860$	−0.429115	−0.0146327
$861$	−26.4658	−0.901953
$862$	8.61246	0.293342
$863$	3.36831	0.114659	0.0573293	−	0.998355i	$-0.481741\pi$
$863$	3.36831	0.114659	0.0573293	+	0.998355i	$0.481741\pi$
$864$	5.62709	0.191438
$865$	11.6698	0.396785
$866$	−10.7419	−0.365026
$867$	−1.44851	−0.0491941
$868$	−5.30555	−0.180082
$869$	−10.6824	−0.362374
$870$	−1.52178	−0.0515932
$871$	30.8800	1.04633
$872$	2.51265	0.0850890
$873$	−4.36353	−0.147683
$874$	−1.95738	−0.0662094
$875$	2.79346	0.0944361
$876$	−3.94199	−0.133188
$877$	−6.49468	−0.219310	−0.109655	−	0.993970i	$-0.534975\pi$
$877$	−6.49468	−0.219310	−0.109655	+	0.993970i	$0.534975\pi$
$878$	−17.4317	−0.588292
$879$	−21.2089	−0.715358
$880$	13.7215	0.462553
$881$	−40.3900	−1.36077	−0.680387	−	0.732853i	$-0.738188\pi$
$881$	−40.3900	−1.36077	−0.680387	+	0.732853i	$0.738188\pi$
$882$	1.06889	0.0359915
$883$	1.50562	0.0506683	0.0253341	−	0.999679i	$-0.491935\pi$
$883$	1.50562	0.0506683	0.0253341	+	0.999679i	$0.491935\pi$
$884$	−1.19205	−0.0400929
$885$	1.63015	0.0547970
$886$	−52.0506	−1.74867
$887$	−27.3455	−0.918172	−0.459086	−	0.888392i	$-0.651823\pi$
$887$	−27.3455	−0.918172	−0.459086	+	0.888392i	$0.651823\pi$
$888$	−23.8645	−0.800842
$889$	−43.2420	−1.45029
$890$	5.87106	0.196798
$891$	17.4027	0.583011
$892$	3.77908	0.126533
$893$	−15.4455	−0.516862
$894$	−16.8448	−0.563375
$895$	17.2350	0.576103
$896$	−35.1314	−1.17366
$897$	5.92787	0.197926
$898$	−34.5875	−1.15420
$899$	7.66273	0.255566
$900$	−0.159174	−0.00530579
$901$	−4.45439	−0.148397
$902$	30.6361	1.02007
$903$	9.83745	0.327370
$904$	11.0315	0.366901
$905$	19.6867	0.654409
$906$	11.4932	0.381834
$907$	2.49508	0.0828478	0.0414239	−	0.999142i	$-0.486811\pi$
$907$	2.49508	0.0828478	0.0414239	+	0.999142i	$0.486811\pi$
$908$	−3.49050	−0.115836
$909$	−9.18169	−0.304537
$910$	−27.8330	−0.922656
$911$	18.5568	0.614814	0.307407	−	0.951578i	$-0.400539\pi$
$911$	18.5568	0.614814	0.307407	+	0.951578i	$0.400539\pi$
$912$	−13.7072	−0.453892
$913$	51.1425	1.69257
$914$	2.73866	0.0905867
$915$	2.59391	0.0857520
$916$	1.16768	0.0385812
$917$	−52.5331	−1.73480
$918$	8.33812	0.275199
$919$	49.7170	1.64001	0.820006	−	0.572355i	$-0.193970\pi$
$919$	49.7170	1.64001	0.820006	+	0.572355i	$0.193970\pi$
$920$	−1.63013	−0.0537439
$921$	−13.0910	−0.431364
$922$	25.7114	0.846759
$923$	−6.75365	−0.222299
$924$	2.26752	0.0745961
$925$	6.12416	0.201361
$926$	−21.1993	−0.696653
$927$	−15.4563	−0.507651
$928$	−0.709000	−0.0232741
$929$	−11.5107	−0.377653	−0.188826	−	0.982010i	$-0.560468\pi$
$929$	−11.5107	−0.377653	−0.188826	+	0.982010i	$0.560468\pi$
$930$	−22.9951	−0.754039
$931$	−1.75912	−0.0576529
$932$	−0.307518	−0.0100731
$933$	38.8560	1.27209
$934$	−40.1476	−1.31367
$935$	3.17492	0.103831
$936$	−16.3847	−0.535551
$937$	15.6928	0.512662	0.256331	−	0.966589i	$-0.417486\pi$
$937$	15.6928	0.512662	0.256331	+	0.966589i	$0.417486\pi$
$938$	−18.8435	−0.615262
$939$	31.6341	1.03234
$940$	1.24508	0.0406102
$941$	−45.8087	−1.49332	−0.746660	−	0.665206i	$-0.768344\pi$
$941$	−45.8087	−1.49332	−0.746660	+	0.665206i	$0.768344\pi$
$942$	−19.8801	−0.647730
$943$	−3.96333	−0.129064
$944$	4.86381	0.158304
$945$	15.7881	0.513588
$946$	−11.3875	−0.370241
$947$	21.4976	0.698578	0.349289	−	0.937015i	$-0.386423\pi$
$947$	21.4976	0.698578	0.349289	+	0.937015i	$0.386423\pi$
$948$	−0.860226	−0.0279388
$949$	104.130	3.38021
$950$	3.23026	0.104803
$951$	−3.50022	−0.113503
$952$	−7.51496	−0.243561
$953$	11.3089	0.366330	0.183165	−	0.983082i	$-0.441366\pi$
$953$	11.3089	0.366330	0.183165	+	0.983082i	$0.441366\pi$
$954$	5.92631	0.191871
$955$	−2.67101	−0.0864320
$956$	−1.32437	−0.0428332
$957$	−3.27495	−0.105864
$958$	3.28950	0.106279
$959$	−25.4930	−0.823211
$960$	−10.3929	−0.335429
$961$	84.7887	2.73512
$962$	−61.0189	−1.96733
$963$	3.53105	0.113786
$964$	−4.29561	−0.138352
$965$	−10.6457	−0.342698
$966$	−3.61729	−0.116384
$967$	3.89133	0.125137	0.0625683	−	0.998041i	$-0.480071\pi$
$967$	3.89133	0.125137	0.0625683	+	0.998041i	$0.480071\pi$
$968$	−2.47474	−0.0795412
$969$	−3.17161	−0.101887
$970$	−7.13841	−0.229200
$971$	−49.0945	−1.57552	−0.787759	−	0.615983i	$-0.788759\pi$
$971$	−49.0945	−1.57552	−0.787759	+	0.615983i	$0.788759\pi$
$972$	−1.59132	−0.0510415
$973$	−0.413751	−0.0132643
$974$	−40.6629	−1.30292
$975$	−9.78274	−0.313298
$976$	7.73932	0.247730
$977$	−36.8153	−1.17783	−0.588914	−	0.808196i	$-0.700444\pi$
$977$	−36.8153	−1.17783	−0.588914	+	0.808196i	$0.700444\pi$
$978$	34.9589	1.11786
$979$	12.6348	0.403810
$980$	0.141806	0.00452982
$981$	−0.842293	−0.0268924
$982$	−30.1900	−0.963400
$983$	6.47597	0.206551	0.103276	−	0.994653i	$-0.467068\pi$
$983$	6.47597	0.206551	0.103276	+	0.994653i	$0.467068\pi$
$984$	−25.4875	−0.812513
$985$	−7.64261	−0.243514
$986$	−1.05058	−0.0334574
$987$	−28.5435	−0.908551
$988$	−2.61006	−0.0830371
$989$	1.47318	0.0468445
$990$	−4.22404	−0.134249
$991$	−22.8503	−0.725864	−0.362932	−	0.931816i	$-0.618224\pi$
$991$	−22.8503	−0.725864	−0.362932	+	0.931816i	$0.618224\pi$
$992$	−10.7134	−0.340152
$993$	−37.4858	−1.18957
$994$	4.12118	0.130716
$995$	−10.9660	−0.347646
$996$	4.11839	0.130496
$997$	−21.9278	−0.694459	−0.347230	−	0.937780i	$-0.612878\pi$
$997$	−21.9278	−0.694459	−0.347230	+	0.937780i	$0.612878\pi$
$998$	−48.8561	−1.54651
$999$	34.6127	1.09510

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.16	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.16	✓	59	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)

\(f(q)\)	\(=\)	\(q-1.47530 q^{2} -1.44851 q^{3} +0.176504 q^{4} +1.00000 q^{5} +2.13699 q^{6} +2.79346 q^{7} +2.69020 q^{8} -0.901812 q^{9} +O(q^{10})\)	\(q-1.47530 q^{2} -1.44851 q^{3} +0.176504 q^{4} +1.00000 q^{5} +2.13699 q^{6} +2.79346 q^{7} +2.69020 q^{8} -0.901812 q^{9} -1.47530 q^{10} -3.17492 q^{11} -0.255669 q^{12} +6.75365 q^{13} -4.12118 q^{14} -1.44851 q^{15} -4.32185 q^{16} -1.00000 q^{17} +1.33044 q^{18} -2.18956 q^{19} +0.176504 q^{20} -4.04636 q^{21} +4.68395 q^{22} -0.605952 q^{23} -3.89679 q^{24} +1.00000 q^{25} -9.96364 q^{26} +5.65182 q^{27} +0.493057 q^{28} -0.712115 q^{29} +2.13699 q^{30} -10.7605 q^{31} +0.995625 q^{32} +4.59890 q^{33} +1.47530 q^{34} +2.79346 q^{35} -0.159174 q^{36} +6.12416 q^{37} +3.23026 q^{38} -9.78274 q^{39} +2.69020 q^{40} +6.54065 q^{41} +5.96959 q^{42} -2.43119 q^{43} -0.560386 q^{44} -0.901812 q^{45} +0.893960 q^{46} +7.05413 q^{47} +6.26026 q^{48} +0.803412 q^{49} -1.47530 q^{50} +1.44851 q^{51} +1.19205 q^{52} +4.45439 q^{53} -8.33812 q^{54} -3.17492 q^{55} +7.51496 q^{56} +3.17161 q^{57} +1.05058 q^{58} -1.12540 q^{59} -0.255669 q^{60} -1.79074 q^{61} +15.8750 q^{62} -2.51917 q^{63} +7.17487 q^{64} +6.75365 q^{65} -6.78475 q^{66} +4.57235 q^{67} -0.176504 q^{68} +0.877730 q^{69} -4.12118 q^{70} -1.00000 q^{71} -2.42605 q^{72} +15.4184 q^{73} -9.03496 q^{74} -1.44851 q^{75} -0.386467 q^{76} -8.86900 q^{77} +14.4325 q^{78} +3.36461 q^{79} -4.32185 q^{80} -5.48130 q^{81} -9.64941 q^{82} -16.1083 q^{83} -0.714200 q^{84} -1.00000 q^{85} +3.58672 q^{86} +1.03151 q^{87} -8.54116 q^{88} -3.97957 q^{89} +1.33044 q^{90} +18.8660 q^{91} -0.106953 q^{92} +15.5867 q^{93} -10.4069 q^{94} -2.18956 q^{95} -1.44217 q^{96} +4.83862 q^{97} -1.18527 q^{98} +2.86318 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

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