LMFDB - Embedded newform 6002.2.a.d.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.38888 q^{3} +1.00000 q^{4} -1.13195 q^{5} -2.38888 q^{6} -2.56197 q^{7} +1.00000 q^{8} +2.70673 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.38888 q^{3} +1.00000 q^{4} -1.13195 q^{5} -2.38888 q^{6} -2.56197 q^{7} +1.00000 q^{8} +2.70673 q^{9} -1.13195 q^{10} -1.58155 q^{11} -2.38888 q^{12} -6.01991 q^{13} -2.56197 q^{14} +2.70409 q^{15} +1.00000 q^{16} -6.63159 q^{17} +2.70673 q^{18} -7.01784 q^{19} -1.13195 q^{20} +6.12024 q^{21} -1.58155 q^{22} -0.574089 q^{23} -2.38888 q^{24} -3.71869 q^{25} -6.01991 q^{26} +0.700576 q^{27} -2.56197 q^{28} -3.40210 q^{29} +2.70409 q^{30} +1.11667 q^{31} +1.00000 q^{32} +3.77813 q^{33} -6.63159 q^{34} +2.90002 q^{35} +2.70673 q^{36} +11.5469 q^{37} -7.01784 q^{38} +14.3808 q^{39} -1.13195 q^{40} -8.84267 q^{41} +6.12024 q^{42} -3.69133 q^{43} -1.58155 q^{44} -3.06388 q^{45} -0.574089 q^{46} -10.0802 q^{47} -2.38888 q^{48} -0.436295 q^{49} -3.71869 q^{50} +15.8420 q^{51} -6.01991 q^{52} +8.48429 q^{53} +0.700576 q^{54} +1.79023 q^{55} -2.56197 q^{56} +16.7647 q^{57} -3.40210 q^{58} -6.62221 q^{59} +2.70409 q^{60} -2.09776 q^{61} +1.11667 q^{62} -6.93458 q^{63} +1.00000 q^{64} +6.81422 q^{65} +3.77813 q^{66} -5.35814 q^{67} -6.63159 q^{68} +1.37143 q^{69} +2.90002 q^{70} +3.65724 q^{71} +2.70673 q^{72} -3.30168 q^{73} +11.5469 q^{74} +8.88350 q^{75} -7.01784 q^{76} +4.05188 q^{77} +14.3808 q^{78} +0.626085 q^{79} -1.13195 q^{80} -9.79379 q^{81} -8.84267 q^{82} -1.17758 q^{83} +6.12024 q^{84} +7.50661 q^{85} -3.69133 q^{86} +8.12721 q^{87} -1.58155 q^{88} -1.01248 q^{89} -3.06388 q^{90} +15.4228 q^{91} -0.574089 q^{92} -2.66759 q^{93} -10.0802 q^{94} +7.94383 q^{95} -2.38888 q^{96} +10.7844 q^{97} -0.436295 q^{98} -4.28083 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) $ 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * 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
$3$	−2.38888	−1.37922	−0.689609	−	0.724181i	$-0.742218\pi$
$3$	−2.38888	−1.37922	−0.689609	+	0.724181i	$0.742218\pi$
$4$	1.00000	0.500000
$5$	−1.13195	−0.506223	−0.253111	−	0.967437i	$-0.581454\pi$
$5$	−1.13195	−0.506223	−0.253111	+	0.967437i	$0.581454\pi$
$6$	−2.38888	−0.975255
$7$	−2.56197	−0.968335	−0.484167	−	0.874975i	$-0.660877\pi$
$7$	−2.56197	−0.968335	−0.484167	+	0.874975i	$0.660877\pi$
$8$	1.00000	0.353553
$9$	2.70673	0.902245
$10$	−1.13195	−0.357953
$11$	−1.58155	−0.476855	−0.238427	−	0.971160i	$-0.576632\pi$
$11$	−1.58155	−0.476855	−0.238427	+	0.971160i	$0.576632\pi$
$12$	−2.38888	−0.689609
$13$	−6.01991	−1.66962	−0.834811	−	0.550537i	$-0.814423\pi$
$13$	−6.01991	−1.66962	−0.834811	+	0.550537i	$0.814423\pi$
$14$	−2.56197	−0.684716
$15$	2.70409	0.698192
$16$	1.00000	0.250000
$17$	−6.63159	−1.60840	−0.804198	−	0.594362i	$-0.797405\pi$
$17$	−6.63159	−1.60840	−0.804198	+	0.594362i	$0.797405\pi$
$18$	2.70673	0.637983
$19$	−7.01784	−1.61000	−0.805001	−	0.593274i	$-0.797835\pi$
$19$	−7.01784	−1.61000	−0.805001	+	0.593274i	$0.797835\pi$
$20$	−1.13195	−0.253111
$21$	6.12024	1.33555
$22$	−1.58155	−0.337187
$23$	−0.574089	−0.119706	−0.0598529	−	0.998207i	$-0.519063\pi$
$23$	−0.574089	−0.119706	−0.0598529	+	0.998207i	$0.519063\pi$
$24$	−2.38888	−0.487628
$25$	−3.71869	−0.743739
$26$	−6.01991	−1.18060
$27$	0.700576	0.134826
$28$	−2.56197	−0.484167
$29$	−3.40210	−0.631755	−0.315877	−	0.948800i	$-0.602299\pi$
$29$	−3.40210	−0.631755	−0.315877	+	0.948800i	$0.602299\pi$
$30$	2.70409	0.493696
$31$	1.11667	0.200560	0.100280	−	0.994959i	$-0.468026\pi$
$31$	1.11667	0.200560	0.100280	+	0.994959i	$0.468026\pi$
$32$	1.00000	0.176777
$33$	3.77813	0.657687
$34$	−6.63159	−1.13731
$35$	2.90002	0.490193
$36$	2.70673	0.451122
$37$	11.5469	1.89829	0.949147	−	0.314834i	$-0.101949\pi$
$37$	11.5469	1.89829	0.949147	+	0.314834i	$0.101949\pi$
$38$	−7.01784	−1.13844
$39$	14.3808	2.30277
$40$	−1.13195	−0.178977
$41$	−8.84267	−1.38099	−0.690496	−	0.723336i	$-0.742608\pi$
$41$	−8.84267	−1.38099	−0.690496	+	0.723336i	$0.742608\pi$
$42$	6.12024	0.944373
$43$	−3.69133	−0.562923	−0.281462	−	0.959572i	$-0.590819\pi$
$43$	−3.69133	−0.562923	−0.281462	+	0.959572i	$0.590819\pi$
$44$	−1.58155	−0.238427
$45$	−3.06388	−0.456737
$46$	−0.574089	−0.0846448
$47$	−10.0802	−1.47034	−0.735172	−	0.677880i	$-0.762899\pi$
$47$	−10.0802	−1.47034	−0.735172	+	0.677880i	$0.762899\pi$
$48$	−2.38888	−0.344805
$49$	−0.436295	−0.0623279
$50$	−3.71869	−0.525903
$51$	15.8420	2.21833
$52$	−6.01991	−0.834811
$53$	8.48429	1.16541	0.582703	−	0.812685i	$-0.301995\pi$
$53$	8.48429	1.16541	0.582703	+	0.812685i	$0.301995\pi$
$54$	0.700576	0.0953364
$55$	1.79023	0.241395
$56$	−2.56197	−0.342358
$57$	16.7647	2.22054
$58$	−3.40210	−0.446718
$59$	−6.62221	−0.862138	−0.431069	−	0.902319i	$-0.641864\pi$
$59$	−6.62221	−0.862138	−0.431069	+	0.902319i	$0.641864\pi$
$60$	2.70409	0.349096
$61$	−2.09776	−0.268591	−0.134295	−	0.990941i	$-0.542877\pi$
$61$	−2.09776	−0.268591	−0.134295	+	0.990941i	$0.542877\pi$
$62$	1.11667	0.141817
$63$	−6.93458	−0.873675
$64$	1.00000	0.125000
$65$	6.81422	0.845200
$66$	3.77813	0.465055
$67$	−5.35814	−0.654601	−0.327300	−	0.944920i	$-0.606139\pi$
$67$	−5.35814	−0.654601	−0.327300	+	0.944920i	$0.606139\pi$
$68$	−6.63159	−0.804198
$69$	1.37143	0.165101
$70$	2.90002	0.346619
$71$	3.65724	0.434035	0.217017	−	0.976168i	$-0.430367\pi$
$71$	3.65724	0.434035	0.217017	+	0.976168i	$0.430367\pi$
$72$	2.70673	0.318992
$73$	−3.30168	−0.386432	−0.193216	−	0.981156i	$-0.561892\pi$
$73$	−3.30168	−0.386432	−0.193216	+	0.981156i	$0.561892\pi$
$74$	11.5469	1.34230
$75$	8.88350	1.02578
$76$	−7.01784	−0.805001
$77$	4.05188	0.461755
$78$	14.3808	1.62831
$79$	0.626085	0.0704400	0.0352200	−	0.999380i	$-0.488787\pi$
$79$	0.626085	0.0704400	0.0352200	+	0.999380i	$0.488787\pi$
$80$	−1.13195	−0.126556
$81$	−9.79379	−1.08820
$82$	−8.84267	−0.976509
$83$	−1.17758	−0.129256	−0.0646282	−	0.997909i	$-0.520586\pi$
$83$	−1.17758	−0.129256	−0.0646282	+	0.997909i	$0.520586\pi$
$84$	6.12024	0.667773
$85$	7.50661	0.814206
$86$	−3.69133	−0.398047
$87$	8.12721	0.871328
$88$	−1.58155	−0.168594
$89$	−1.01248	−0.107322	−0.0536612	−	0.998559i	$-0.517089\pi$
$89$	−1.01248	−0.107322	−0.0536612	+	0.998559i	$0.517089\pi$
$90$	−3.06388	−0.322962
$91$	15.4228	1.61675
$92$	−0.574089	−0.0598529
$93$	−2.66759	−0.276616
$94$	−10.0802	−1.03969
$95$	7.94383	0.815019
$96$	−2.38888	−0.243814
$97$	10.7844	1.09499	0.547495	−	0.836809i	$-0.315581\pi$
$97$	10.7844	1.09499	0.547495	+	0.836809i	$0.315581\pi$
$98$	−0.436295	−0.0440725
$99$	−4.28083	−0.430240
$100$	−3.71869	−0.371869
$101$	1.59681	0.158889	0.0794444	−	0.996839i	$-0.474685\pi$
$101$	1.59681	0.158889	0.0794444	+	0.996839i	$0.474685\pi$
$102$	15.8420	1.56860
$103$	9.65520	0.951355	0.475678	−	0.879620i	$-0.342203\pi$
$103$	9.65520	0.951355	0.475678	+	0.879620i	$0.342203\pi$
$104$	−6.01991	−0.590301
$105$	−6.92779	−0.676083
$106$	8.48429	0.824067
$107$	−13.0239	−1.25907	−0.629535	−	0.776972i	$-0.716755\pi$
$107$	−13.0239	−1.25907	−0.629535	+	0.776972i	$0.716755\pi$
$108$	0.700576	0.0674130
$109$	−2.49158	−0.238650	−0.119325	−	0.992855i	$-0.538073\pi$
$109$	−2.49158	−0.238650	−0.119325	+	0.992855i	$0.538073\pi$
$110$	1.79023	0.170692
$111$	−27.5841	−2.61816
$112$	−2.56197	−0.242084
$113$	12.0342	1.13208	0.566041	−	0.824377i	$-0.308474\pi$
$113$	12.0342	1.13208	0.566041	+	0.824377i	$0.308474\pi$
$114$	16.7647	1.57016
$115$	0.649839	0.0605978
$116$	−3.40210	−0.315877
$117$	−16.2943	−1.50641
$118$	−6.62221	−0.609624
$119$	16.9899	1.55747
$120$	2.70409	0.246848
$121$	−8.49870	−0.772609
$122$	−2.09776	−0.189922
$123$	21.1240	1.90469
$124$	1.11667	0.100280
$125$	9.86911	0.882720
$126$	−6.93458	−0.617781
$127$	−5.72412	−0.507934	−0.253967	−	0.967213i	$-0.581735\pi$
$127$	−5.72412	−0.507934	−0.253967	+	0.967213i	$0.581735\pi$
$128$	1.00000	0.0883883
$129$	8.81815	0.776394
$130$	6.81422	0.597647
$131$	9.03300	0.789217	0.394608	−	0.918849i	$-0.370880\pi$
$131$	9.03300	0.789217	0.394608	+	0.918849i	$0.370880\pi$
$132$	3.77813	0.328844
$133$	17.9795	1.55902
$134$	−5.35814	−0.462873
$135$	−0.793016	−0.0682520
$136$	−6.63159	−0.568654
$137$	−12.1837	−1.04093	−0.520464	−	0.853884i	$-0.674241\pi$
$137$	−12.1837	−1.04093	−0.520464	+	0.853884i	$0.674241\pi$
$138$	1.37143	0.116744
$139$	−21.8183	−1.85060	−0.925301	−	0.379233i	$-0.876188\pi$
$139$	−21.8183	−1.85060	−0.925301	+	0.379233i	$0.876188\pi$
$140$	2.90002	0.245096
$141$	24.0803	2.02793
$142$	3.65724	0.306909
$143$	9.52078	0.796167
$144$	2.70673	0.225561
$145$	3.85101	0.319809
$146$	−3.30168	−0.273249
$147$	1.04226	0.0859638
$148$	11.5469	0.949147
$149$	−11.1580	−0.914096	−0.457048	−	0.889442i	$-0.651093\pi$
$149$	−11.1580	−0.914096	−0.457048	+	0.889442i	$0.651093\pi$
$150$	8.88350	0.725335
$151$	3.98224	0.324070	0.162035	−	0.986785i	$-0.448194\pi$
$151$	3.98224	0.324070	0.162035	+	0.986785i	$0.448194\pi$
$152$	−7.01784	−0.569222
$153$	−17.9499	−1.45117
$154$	4.05188	0.326510
$155$	−1.26401	−0.101528
$156$	14.3808	1.15139
$157$	−4.94307	−0.394500	−0.197250	−	0.980353i	$-0.563201\pi$
$157$	−4.94307	−0.394500	−0.197250	+	0.980353i	$0.563201\pi$
$158$	0.626085	0.0498086
$159$	−20.2679	−1.60735
$160$	−1.13195	−0.0894884
$161$	1.47080	0.115915
$162$	−9.79379	−0.769473
$163$	−2.10461	−0.164846	−0.0824228	−	0.996597i	$-0.526266\pi$
$163$	−2.10461	−0.164846	−0.0824228	+	0.996597i	$0.526266\pi$
$164$	−8.84267	−0.690496
$165$	−4.27664	−0.332936
$166$	−1.17758	−0.0913981
$167$	−21.2336	−1.64311	−0.821553	−	0.570133i	$-0.806892\pi$
$167$	−21.2336	−1.64311	−0.821553	+	0.570133i	$0.806892\pi$
$168$	6.12024	0.472187
$169$	23.2393	1.78764
$170$	7.50661	0.575731
$171$	−18.9954	−1.45262
$172$	−3.69133	−0.281462
$173$	1.88954	0.143659	0.0718296	−	0.997417i	$-0.477116\pi$
$173$	1.88954	0.143659	0.0718296	+	0.997417i	$0.477116\pi$
$174$	8.12721	0.616122
$175$	9.52719	0.720188
$176$	−1.58155	−0.119214
$177$	15.8196	1.18908
$178$	−1.01248	−0.0758884
$179$	−10.6516	−0.796137	−0.398069	−	0.917356i	$-0.630319\pi$
$179$	−10.6516	−0.796137	−0.398069	+	0.917356i	$0.630319\pi$
$180$	−3.06388	−0.228368
$181$	−21.7337	−1.61545	−0.807725	−	0.589560i	$-0.799301\pi$
$181$	−21.7337	−1.61545	−0.807725	+	0.589560i	$0.799301\pi$
$182$	15.4228	1.14322
$183$	5.01129	0.370446
$184$	−0.574089	−0.0423224
$185$	−13.0705	−0.960959
$186$	−2.66759	−0.195597
$187$	10.4882	0.766971
$188$	−10.0802	−0.735172
$189$	−1.79486	−0.130557
$190$	7.94383	0.576306
$191$	4.55688	0.329724	0.164862	−	0.986317i	$-0.447282\pi$
$191$	4.55688	0.329724	0.164862	+	0.986317i	$0.447282\pi$
$192$	−2.38888	−0.172402
$193$	3.97856	0.286383	0.143192	−	0.989695i	$-0.454263\pi$
$193$	3.97856	0.286383	0.143192	+	0.989695i	$0.454263\pi$
$194$	10.7844	0.774275
$195$	−16.2783	−1.16572
$196$	−0.436295	−0.0311639
$197$	10.1674	0.724399	0.362200	−	0.932101i	$-0.382026\pi$
$197$	10.1674	0.724399	0.362200	+	0.932101i	$0.382026\pi$
$198$	−4.28083	−0.304225
$199$	19.5544	1.38618	0.693088	−	0.720853i	$-0.256250\pi$
$199$	19.5544	1.38618	0.693088	+	0.720853i	$0.256250\pi$
$200$	−3.71869	−0.262951
$201$	12.7999	0.902838
$202$	1.59681	0.112351
$203$	8.71610	0.611750
$204$	15.8420	1.10917
$205$	10.0094	0.699090
$206$	9.65520	0.672710
$207$	−1.55391	−0.108004
$208$	−6.01991	−0.417405
$209$	11.0990	0.767737
$210$	−6.92779	−0.478063
$211$	−8.76873	−0.603664	−0.301832	−	0.953361i	$-0.597598\pi$
$211$	−8.76873	−0.603664	−0.301832	+	0.953361i	$0.597598\pi$
$212$	8.48429	0.582703
$213$	−8.73670	−0.598629
$214$	−13.0239	−0.890297
$215$	4.17840	0.284965
$216$	0.700576	0.0476682
$217$	−2.86088	−0.194209
$218$	−2.49158	−0.168751
$219$	7.88730	0.532974
$220$	1.79023	0.120697
$221$	39.9215	2.68541
$222$	−27.5841	−1.85132
$223$	−5.85575	−0.392130	−0.196065	−	0.980591i	$-0.562816\pi$
$223$	−5.85575	−0.392130	−0.196065	+	0.980591i	$0.562816\pi$
$224$	−2.56197	−0.171179
$225$	−10.0655	−0.671034
$226$	12.0342	0.800503
$227$	−13.1604	−0.873489	−0.436744	−	0.899586i	$-0.643869\pi$
$227$	−13.1604	−0.873489	−0.436744	+	0.899586i	$0.643869\pi$
$228$	16.7647	1.11027
$229$	10.4716	0.691981	0.345990	−	0.938238i	$-0.387543\pi$
$229$	10.4716	0.691981	0.345990	+	0.938238i	$0.387543\pi$
$230$	0.649839	0.0428491
$231$	−9.67945	−0.636861
$232$	−3.40210	−0.223359
$233$	12.3786	0.810947	0.405473	−	0.914107i	$-0.367107\pi$
$233$	12.3786	0.810947	0.405473	+	0.914107i	$0.367107\pi$
$234$	−16.2943	−1.06519
$235$	11.4102	0.744322
$236$	−6.62221	−0.431069
$237$	−1.49564	−0.0971522
$238$	16.9899	1.10129
$239$	1.87210	0.121096	0.0605481	−	0.998165i	$-0.480715\pi$
$239$	1.87210	0.121096	0.0605481	+	0.998165i	$0.480715\pi$
$240$	2.70409	0.174548
$241$	−4.93181	−0.317686	−0.158843	−	0.987304i	$-0.550776\pi$
$241$	−4.93181	−0.317686	−0.158843	+	0.987304i	$0.550776\pi$
$242$	−8.49870	−0.546317
$243$	21.2944	1.36604
$244$	−2.09776	−0.134295
$245$	0.493864	0.0315518
$246$	21.1240	1.34682
$247$	42.2467	2.68809
$248$	1.11667	0.0709087
$249$	2.81310	0.178273
$250$	9.86911	0.624177
$251$	18.0896	1.14181	0.570903	−	0.821017i	$-0.306593\pi$
$251$	18.0896	1.14181	0.570903	+	0.821017i	$0.306593\pi$
$252$	−6.93458	−0.436837
$253$	0.907950	0.0570823
$254$	−5.72412	−0.359163
$255$	−17.9324	−1.12297
$256$	1.00000	0.0625000
$257$	5.86944	0.366126	0.183063	−	0.983101i	$-0.441399\pi$
$257$	5.86944	0.366126	0.183063	+	0.983101i	$0.441399\pi$
$258$	8.81815	0.548994
$259$	−29.5828	−1.83818
$260$	6.81422	0.422600
$261$	−9.20859	−0.569998
$262$	9.03300	0.558060
$263$	22.8083	1.40642	0.703210	−	0.710982i	$-0.251749\pi$
$263$	22.8083	1.40642	0.703210	+	0.710982i	$0.251749\pi$
$264$	3.77813	0.232528
$265$	−9.60378	−0.589955
$266$	17.9795	1.10239
$267$	2.41869	0.148021
$268$	−5.35814	−0.327300
$269$	15.7828	0.962291	0.481146	−	0.876641i	$-0.340221\pi$
$269$	15.7828	0.962291	0.481146	+	0.876641i	$0.340221\pi$
$270$	−0.793016	−0.0482614
$271$	−12.1230	−0.736420	−0.368210	−	0.929743i	$-0.620029\pi$
$271$	−12.1230	−0.736420	−0.368210	+	0.929743i	$0.620029\pi$
$272$	−6.63159	−0.402099
$273$	−36.8433	−2.22986
$274$	−12.1837	−0.736047
$275$	5.88129	0.354655
$276$	1.37143	0.0825503
$277$	−31.6398	−1.90105	−0.950525	−	0.310649i	$-0.899454\pi$
$277$	−31.6398	−1.90105	−0.950525	+	0.310649i	$0.899454\pi$
$278$	−21.8183	−1.30857
$279$	3.02253	0.180954
$280$	2.90002	0.173309
$281$	−19.5987	−1.16916	−0.584579	−	0.811337i	$-0.698740\pi$
$281$	−19.5987	−1.16916	−0.584579	+	0.811337i	$0.698740\pi$
$282$	24.0803	1.43396
$283$	19.0811	1.13426	0.567128	−	0.823630i	$-0.308055\pi$
$283$	19.0811	1.13426	0.567128	+	0.823630i	$0.308055\pi$
$284$	3.65724	0.217017
$285$	−18.9768	−1.12409
$286$	9.52078	0.562975
$287$	22.6547	1.33726
$288$	2.70673	0.159496
$289$	26.9779	1.58694
$290$	3.85101	0.226139
$291$	−25.7626	−1.51023
$292$	−3.30168	−0.193216
$293$	28.8261	1.68404	0.842021	−	0.539445i	$-0.181366\pi$
$293$	28.8261	1.68404	0.842021	+	0.539445i	$0.181366\pi$
$294$	1.04226	0.0607856
$295$	7.49600	0.436434
$296$	11.5469	0.671148
$297$	−1.10800	−0.0642924
$298$	−11.1580	−0.646363
$299$	3.45596	0.199863
$300$	8.88350	0.512889
$301$	9.45710	0.545098
$302$	3.98224	0.229152
$303$	−3.81459	−0.219142
$304$	−7.01784	−0.402500
$305$	2.37456	0.135967
$306$	−17.9499	−1.02613
$307$	−5.35278	−0.305499	−0.152750	−	0.988265i	$-0.548813\pi$
$307$	−5.35278	−0.305499	−0.152750	+	0.988265i	$0.548813\pi$
$308$	4.05188	0.230878
$309$	−23.0651	−1.31213
$310$	−1.26401	−0.0717912
$311$	−26.8816	−1.52432	−0.762159	−	0.647390i	$-0.775860\pi$
$311$	−26.8816	−1.52432	−0.762159	+	0.647390i	$0.775860\pi$
$312$	14.3808	0.814154
$313$	−16.9538	−0.958288	−0.479144	−	0.877736i	$-0.659053\pi$
$313$	−16.9538	−0.958288	−0.479144	+	0.877736i	$0.659053\pi$
$314$	−4.94307	−0.278954
$315$	7.84958	0.442274
$316$	0.626085	0.0352200
$317$	31.2163	1.75328	0.876641	−	0.481146i	$-0.159779\pi$
$317$	31.2163	1.75328	0.876641	+	0.481146i	$0.159779\pi$
$318$	−20.2679	−1.13657
$319$	5.38059	0.301255
$320$	−1.13195	−0.0632778
$321$	31.1126	1.73653
$322$	1.47080	0.0819645
$323$	46.5394	2.58952
$324$	−9.79379	−0.544100
$325$	22.3862	1.24176
$326$	−2.10461	−0.116563
$327$	5.95208	0.329151
$328$	−8.84267	−0.488254
$329$	25.8251	1.42379
$330$	−4.27664	−0.235421
$331$	−10.3198	−0.567226	−0.283613	−	0.958939i	$-0.591533\pi$
$331$	−10.3198	−0.567226	−0.283613	+	0.958939i	$0.591533\pi$
$332$	−1.17758	−0.0646282
$333$	31.2543	1.71273
$334$	−21.2336	−1.16185
$335$	6.06513	0.331374
$336$	6.12024	0.333886
$337$	20.1416	1.09719	0.548593	−	0.836090i	$-0.315164\pi$
$337$	20.1416	1.09719	0.548593	+	0.836090i	$0.315164\pi$
$338$	23.2393	1.26405
$339$	−28.7482	−1.56139
$340$	7.50661	0.407103
$341$	−1.76607	−0.0956381
$342$	−18.9954	−1.02715
$343$	19.0516	1.02869
$344$	−3.69133	−0.199023
$345$	−1.55239	−0.0835776
$346$	1.88954	0.101582
$347$	−15.3098	−0.821871	−0.410935	−	0.911664i	$-0.634798\pi$
$347$	−15.3098	−0.821871	−0.410935	+	0.911664i	$0.634798\pi$
$348$	8.12721	0.435664
$349$	28.1826	1.50858	0.754289	−	0.656542i	$-0.227982\pi$
$349$	28.1826	1.50858	0.754289	+	0.656542i	$0.227982\pi$
$350$	9.52719	0.509250
$351$	−4.21740	−0.225108
$352$	−1.58155	−0.0842968
$353$	−6.41960	−0.341681	−0.170840	−	0.985299i	$-0.554648\pi$
$353$	−6.41960	−0.341681	−0.170840	+	0.985299i	$0.554648\pi$
$354$	15.8196	0.840805
$355$	−4.13981	−0.219718
$356$	−1.01248	−0.0536612
$357$	−40.5869	−2.14809
$358$	−10.6516	−0.562954
$359$	−20.5633	−1.08529	−0.542644	−	0.839963i	$-0.682577\pi$
$359$	−20.5633	−1.08529	−0.542644	+	0.839963i	$0.682577\pi$
$360$	−3.06388	−0.161481
$361$	30.2500	1.59211
$362$	−21.7337	−1.14230
$363$	20.3024	1.06560
$364$	15.4228	0.808376
$365$	3.73733	0.195621
$366$	5.01129	0.261945
$367$	−23.5265	−1.22808	−0.614038	−	0.789277i	$-0.710456\pi$
$367$	−23.5265	−1.22808	−0.614038	+	0.789277i	$0.710456\pi$
$368$	−0.574089	−0.0299265
$369$	−23.9347	−1.24599
$370$	−13.0705	−0.679501
$371$	−21.7365	−1.12850
$372$	−2.66759	−0.138308
$373$	−16.6212	−0.860615	−0.430308	−	0.902682i	$-0.641595\pi$
$373$	−16.6212	−0.860615	−0.430308	+	0.902682i	$0.641595\pi$
$374$	10.4882	0.542331
$375$	−23.5761	−1.21746
$376$	−10.0802	−0.519845
$377$	20.4804	1.05479
$378$	−1.79486	−0.0923175
$379$	−12.3977	−0.636825	−0.318413	−	0.947952i	$-0.603150\pi$
$379$	−12.3977	−0.636825	−0.318413	+	0.947952i	$0.603150\pi$
$380$	7.94383	0.407510
$381$	13.6742	0.700552
$382$	4.55688	0.233150
$383$	−2.41511	−0.123407	−0.0617033	−	0.998095i	$-0.519653\pi$
$383$	−2.41511	−0.123407	−0.0617033	+	0.998095i	$0.519653\pi$
$384$	−2.38888	−0.121907
$385$	−4.58652	−0.233751
$386$	3.97856	0.202504
$387$	−9.99146	−0.507895
$388$	10.7844	0.547495
$389$	32.4492	1.64524	0.822621	−	0.568590i	$-0.192511\pi$
$389$	32.4492	1.64524	0.822621	+	0.568590i	$0.192511\pi$
$390$	−16.2783	−0.824286
$391$	3.80712	0.192534
$392$	−0.436295	−0.0220362
$393$	−21.5787	−1.08850
$394$	10.1674	0.512228
$395$	−0.708695	−0.0356583
$396$	−4.28083	−0.215120
$397$	17.4932	0.877958	0.438979	−	0.898497i	$-0.355340\pi$
$397$	17.4932	0.877958	0.438979	+	0.898497i	$0.355340\pi$
$398$	19.5544	0.980175
$399$	−42.9508	−2.15023
$400$	−3.71869	−0.185935
$401$	−28.2043	−1.40845	−0.704227	−	0.709975i	$-0.748706\pi$
$401$	−28.2043	−1.40845	−0.704227	+	0.709975i	$0.748706\pi$
$402$	12.7999	0.638403
$403$	−6.72226	−0.334860
$404$	1.59681	0.0794444
$405$	11.0861	0.550871
$406$	8.71610	0.432573
$407$	−18.2619	−0.905210
$408$	15.8420	0.784298
$409$	−15.9511	−0.788733	−0.394366	−	0.918953i	$-0.629036\pi$
$409$	−15.9511	−0.788733	−0.394366	+	0.918953i	$0.629036\pi$
$410$	10.0094	0.494331
$411$	29.1055	1.43567
$412$	9.65520	0.475678
$413$	16.9659	0.834839
$414$	−1.55391	−0.0763703
$415$	1.33296	0.0654325
$416$	−6.01991	−0.295150
$417$	52.1212	2.55239
$418$	11.0990	0.542872
$419$	−22.6340	−1.10574	−0.552871	−	0.833267i	$-0.686468\pi$
$419$	−22.6340	−1.10574	−0.552871	+	0.833267i	$0.686468\pi$
$420$	−6.92779	−0.338042
$421$	10.1895	0.496605	0.248303	−	0.968682i	$-0.420127\pi$
$421$	10.1895	0.496605	0.248303	+	0.968682i	$0.420127\pi$
$422$	−8.76873	−0.426855
$423$	−27.2843	−1.32661
$424$	8.48429	0.412033
$425$	24.6608	1.19623
$426$	−8.73670	−0.423295
$427$	5.37441	0.260086
$428$	−13.0239	−0.629535
$429$	−22.7440	−1.09809
$430$	4.17840	0.201500
$431$	−7.64170	−0.368088	−0.184044	−	0.982918i	$-0.558919\pi$
$431$	−7.64170	−0.368088	−0.184044	+	0.982918i	$0.558919\pi$
$432$	0.700576	0.0337065
$433$	0.752089	0.0361431	0.0180715	−	0.999837i	$-0.494247\pi$
$433$	0.752089	0.0361431	0.0180715	+	0.999837i	$0.494247\pi$
$434$	−2.86088	−0.137327
$435$	−9.19958	−0.441086
$436$	−2.49158	−0.119325
$437$	4.02886	0.192727
$438$	7.88730	0.376870
$439$	14.6089	0.697243	0.348622	−	0.937264i	$-0.386650\pi$
$439$	14.6089	0.697243	0.348622	+	0.937264i	$0.386650\pi$
$440$	1.79023	0.0853459
$441$	−1.18093	−0.0562350
$442$	39.9215	1.89887
$443$	20.2320	0.961252	0.480626	−	0.876926i	$-0.340410\pi$
$443$	20.2320	0.961252	0.480626	+	0.876926i	$0.340410\pi$
$444$	−27.5841	−1.30908
$445$	1.14607	0.0543291
$446$	−5.85575	−0.277278
$447$	26.6550	1.26074
$448$	−2.56197	−0.121042
$449$	12.5449	0.592032	0.296016	−	0.955183i	$-0.404342\pi$
$449$	12.5449	0.592032	0.296016	+	0.955183i	$0.404342\pi$
$450$	−10.0655	−0.474493
$451$	13.9851	0.658533
$452$	12.0342	0.566041
$453$	−9.51309	−0.446964
$454$	−13.1604	−0.617650
$455$	−17.4579	−0.818437
$456$	16.7647	0.785081
$457$	1.60042	0.0748644	0.0374322	−	0.999299i	$-0.488082\pi$
$457$	1.60042	0.0748644	0.0374322	+	0.999299i	$0.488082\pi$
$458$	10.4716	0.489304
$459$	−4.64593	−0.216854
$460$	0.649839	0.0302989
$461$	−19.4523	−0.905984	−0.452992	−	0.891515i	$-0.649643\pi$
$461$	−19.4523	−0.905984	−0.452992	+	0.891515i	$0.649643\pi$
$462$	−9.67945	−0.450329
$463$	−40.7107	−1.89198	−0.945992	−	0.324189i	$-0.894909\pi$
$463$	−40.7107	−1.89198	−0.945992	+	0.324189i	$0.894909\pi$
$464$	−3.40210	−0.157939
$465$	3.01958	0.140029
$466$	12.3786	0.573426
$467$	35.2631	1.63178	0.815892	−	0.578205i	$-0.196247\pi$
$467$	35.2631	1.63178	0.815892	+	0.578205i	$0.196247\pi$
$468$	−16.2943	−0.753204
$469$	13.7274	0.633873
$470$	11.4102	0.526315
$471$	11.8084	0.544102
$472$	−6.62221	−0.304812
$473$	5.83802	0.268433
$474$	−1.49564	−0.0686970
$475$	26.0972	1.19742
$476$	16.9899	0.778733
$477$	22.9647	1.05148
$478$	1.87210	0.0856280
$479$	3.99818	0.182682	0.0913408	−	0.995820i	$-0.470885\pi$
$479$	3.99818	0.182682	0.0913408	+	0.995820i	$0.470885\pi$
$480$	2.70409	0.123424
$481$	−69.5111	−3.16943
$482$	−4.93181	−0.224638
$483$	−3.51356	−0.159873
$484$	−8.49870	−0.386305
$485$	−12.2074	−0.554309
$486$	21.2944	0.965935
$487$	26.6204	1.20629	0.603144	−	0.797632i	$-0.293914\pi$
$487$	26.6204	1.20629	0.603144	+	0.797632i	$0.293914\pi$
$488$	−2.09776	−0.0949612
$489$	5.02765	0.227358
$490$	0.493864	0.0223105
$491$	−24.4879	−1.10512	−0.552562	−	0.833472i	$-0.686350\pi$
$491$	−24.4879	−1.10512	−0.552562	+	0.833472i	$0.686350\pi$
$492$	21.1240	0.952345
$493$	22.5614	1.01611
$494$	42.2467	1.90077
$495$	4.84568	0.217797
$496$	1.11667	0.0501400
$497$	−9.36976	−0.420291
$498$	2.81310	0.126058
$499$	3.53929	0.158440	0.0792201	−	0.996857i	$-0.474757\pi$
$499$	3.53929	0.158440	0.0792201	+	0.996857i	$0.474757\pi$
$500$	9.86911	0.441360
$501$	50.7245	2.26620
$502$	18.0896	0.807379
$503$	−42.6874	−1.90334	−0.951668	−	0.307128i	$-0.900632\pi$
$503$	−42.6874	−1.90334	−0.951668	+	0.307128i	$0.900632\pi$
$504$	−6.93458	−0.308891
$505$	−1.80751	−0.0804331
$506$	0.907950	0.0403633
$507$	−55.5158	−2.46554
$508$	−5.72412	−0.253967
$509$	32.8585	1.45643	0.728214	−	0.685350i	$-0.240351\pi$
$509$	32.8585	1.45643	0.728214	+	0.685350i	$0.240351\pi$
$510$	−17.9324	−0.794059
$511$	8.45881	0.374196
$512$	1.00000	0.0441942
$513$	−4.91653	−0.217070
$514$	5.86944	0.258890
$515$	−10.9292	−0.481598
$516$	8.81815	0.388197
$517$	15.9423	0.701141
$518$	−29.5828	−1.29979
$519$	−4.51388	−0.198137
$520$	6.81422	0.298823
$521$	−15.9635	−0.699375	−0.349688	−	0.936866i	$-0.613712\pi$
$521$	−15.9635	−0.699375	−0.349688	+	0.936866i	$0.613712\pi$
$522$	−9.20859	−0.403049
$523$	−43.0297	−1.88156	−0.940780	−	0.339019i	$-0.889905\pi$
$523$	−43.0297	−1.88156	−0.940780	+	0.339019i	$0.889905\pi$
$524$	9.03300	0.394608
$525$	−22.7593	−0.993297
$526$	22.8083	0.994490
$527$	−7.40531	−0.322580
$528$	3.77813	0.164422
$529$	−22.6704	−0.985671
$530$	−9.60378	−0.417161
$531$	−17.9246	−0.777860
$532$	17.9795	0.779510
$533$	53.2320	2.30574
$534$	2.41869	0.104667
$535$	14.7424	0.637370
$536$	−5.35814	−0.231436
$537$	25.4453	1.09805
$538$	15.7828	0.680443
$539$	0.690022	0.0297213
$540$	−0.793016	−0.0341260
$541$	5.01320	0.215534	0.107767	−	0.994176i	$-0.465630\pi$
$541$	5.01320	0.215534	0.107767	+	0.994176i	$0.465630\pi$
$542$	−12.1230	−0.520728
$543$	51.9190	2.22806
$544$	−6.63159	−0.284327
$545$	2.82034	0.120810
$546$	−36.8433	−1.57675
$547$	−3.69923	−0.158167	−0.0790837	−	0.996868i	$-0.525199\pi$
$547$	−3.69923	−0.158167	−0.0790837	+	0.996868i	$0.525199\pi$
$548$	−12.1837	−0.520464
$549$	−5.67808	−0.242335
$550$	5.88129	0.250779
$551$	23.8754	1.01713
$552$	1.37143	0.0583719
$553$	−1.60401	−0.0682095
$554$	−31.6398	−1.34424
$555$	31.2237	1.32537
$556$	−21.8183	−0.925301
$557$	−1.22665	−0.0519747	−0.0259873	−	0.999662i	$-0.508273\pi$
$557$	−1.22665	−0.0519747	−0.0259873	+	0.999662i	$0.508273\pi$
$558$	3.02253	0.127954
$559$	22.2215	0.939869
$560$	2.90002	0.122548
$561$	−25.0550	−1.05782
$562$	−19.5987	−0.826720
$563$	−26.1204	−1.10084	−0.550421	−	0.834887i	$-0.685533\pi$
$563$	−26.1204	−1.10084	−0.550421	+	0.834887i	$0.685533\pi$
$564$	24.0803	1.01396
$565$	−13.6221	−0.573086
$566$	19.0811	0.802040
$567$	25.0914	1.05374
$568$	3.65724	0.153454
$569$	−2.22919	−0.0934526	−0.0467263	−	0.998908i	$-0.514879\pi$
$569$	−2.22919	−0.0934526	−0.0467263	+	0.998908i	$0.514879\pi$
$570$	−18.9768	−0.794852
$571$	−7.48778	−0.313354	−0.156677	−	0.987650i	$-0.550078\pi$
$571$	−7.48778	−0.313354	−0.156677	+	0.987650i	$0.550078\pi$
$572$	9.52078	0.398084
$573$	−10.8858	−0.454762
$574$	22.6547	0.945588
$575$	2.13486	0.0890299
$576$	2.70673	0.112781
$577$	−20.8508	−0.868030	−0.434015	−	0.900906i	$-0.642903\pi$
$577$	−20.8508	−0.868030	−0.434015	+	0.900906i	$0.642903\pi$
$578$	26.9779	1.12213
$579$	−9.50430	−0.394985
$580$	3.85101	0.159904
$581$	3.01693	0.125163
$582$	−25.7626	−1.06789
$583$	−13.4183	−0.555730
$584$	−3.30168	−0.136624
$585$	18.4443	0.762578
$586$	28.8261	1.19080
$587$	−15.7768	−0.651177	−0.325589	−	0.945511i	$-0.605562\pi$
$587$	−15.7768	−0.651177	−0.325589	+	0.945511i	$0.605562\pi$
$588$	1.04226	0.0429819
$589$	−7.83662	−0.322902
$590$	7.49600	0.308605
$591$	−24.2887	−0.999105
$592$	11.5469	0.474573
$593$	−8.69869	−0.357212	−0.178606	−	0.983921i	$-0.557159\pi$
$593$	−8.69869	−0.357212	−0.178606	+	0.983921i	$0.557159\pi$
$594$	−1.10800	−0.0454616
$595$	−19.2317	−0.788424
$596$	−11.1580	−0.457048
$597$	−46.7131	−1.91184
$598$	3.45596	0.141325
$599$	−22.2138	−0.907633	−0.453816	−	0.891095i	$-0.649938\pi$
$599$	−22.2138	−0.907633	−0.453816	+	0.891095i	$0.649938\pi$
$600$	8.88350	0.362667
$601$	−22.9061	−0.934361	−0.467180	−	0.884162i	$-0.654730\pi$
$601$	−22.9061	−0.934361	−0.467180	+	0.884162i	$0.654730\pi$
$602$	9.45710	0.385443
$603$	−14.5031	−0.590610
$604$	3.98224	0.162035
$605$	9.62009	0.391112
$606$	−3.81459	−0.154957
$607$	−44.4157	−1.80278	−0.901390	−	0.433009i	$-0.857452\pi$
$607$	−44.4157	−1.80278	−0.901390	+	0.433009i	$0.857452\pi$
$608$	−7.01784	−0.284611
$609$	−20.8217	−0.843738
$610$	2.37456	0.0961430
$611$	60.6817	2.45492
$612$	−17.9499	−0.725583
$613$	15.5590	0.628423	0.314212	−	0.949353i	$-0.398260\pi$
$613$	15.5590	0.628423	0.314212	+	0.949353i	$0.398260\pi$
$614$	−5.35278	−0.216020
$615$	−23.9113	−0.964198
$616$	4.05188	0.163255
$617$	−4.93839	−0.198812	−0.0994060	−	0.995047i	$-0.531694\pi$
$617$	−4.93839	−0.198812	−0.0994060	+	0.995047i	$0.531694\pi$
$618$	−23.0651	−0.927814
$619$	26.0297	1.04622	0.523111	−	0.852264i	$-0.324771\pi$
$619$	26.0297	1.04622	0.523111	+	0.852264i	$0.324771\pi$
$620$	−1.26401	−0.0507641
$621$	−0.402193	−0.0161395
$622$	−26.8816	−1.07785
$623$	2.59394	0.103924
$624$	14.3808	0.575694
$625$	7.42214	0.296886
$626$	−16.9538	−0.677612
$627$	−26.5143	−1.05888
$628$	−4.94307	−0.197250
$629$	−76.5741	−3.05321
$630$	7.84958	0.312735
$631$	−34.0685	−1.35625	−0.678124	−	0.734948i	$-0.737207\pi$
$631$	−34.0685	−1.35625	−0.678124	+	0.734948i	$0.737207\pi$
$632$	0.626085	0.0249043
$633$	20.9474	0.832585
$634$	31.2163	1.23976
$635$	6.47941	0.257128
$636$	−20.2679	−0.803675
$637$	2.62646	0.104064
$638$	5.38059	0.213020
$639$	9.89918	0.391606
$640$	−1.13195	−0.0447442
$641$	−42.8172	−1.69118	−0.845589	−	0.533835i	$-0.820750\pi$
$641$	−42.8172	−1.69118	−0.845589	+	0.533835i	$0.820750\pi$
$642$	31.1126	1.22791
$643$	−2.98251	−0.117619	−0.0588094	−	0.998269i	$-0.518730\pi$
$643$	−2.98251	−0.117619	−0.0588094	+	0.998269i	$0.518730\pi$
$644$	1.47080	0.0579577
$645$	−9.98168	−0.393028
$646$	46.5394	1.83107
$647$	10.1968	0.400879	0.200440	−	0.979706i	$-0.435763\pi$
$647$	10.1968	0.400879	0.200440	+	0.979706i	$0.435763\pi$
$648$	−9.79379	−0.384737
$649$	10.4733	0.411115
$650$	22.3862	0.878059
$651$	6.83430	0.267857
$652$	−2.10461	−0.0824228
$653$	−45.7947	−1.79209	−0.896043	−	0.443967i	$-0.853571\pi$
$653$	−45.7947	−1.79209	−0.896043	+	0.443967i	$0.853571\pi$
$654$	5.95208	0.232745
$655$	−10.2249	−0.399519
$656$	−8.84267	−0.345248
$657$	−8.93676	−0.348656
$658$	25.8251	1.00677
$659$	−41.5509	−1.61859	−0.809297	−	0.587399i	$-0.800152\pi$
$659$	−41.5509	−1.61859	−0.809297	+	0.587399i	$0.800152\pi$
$660$	−4.27664	−0.166468
$661$	10.7391	0.417702	0.208851	−	0.977947i	$-0.433028\pi$
$661$	10.7391	0.417702	0.208851	+	0.977947i	$0.433028\pi$
$662$	−10.3198	−0.401089
$663$	−95.3676	−3.70377
$664$	−1.17758	−0.0456990
$665$	−20.3519	−0.789212
$666$	31.2543	1.21108
$667$	1.95311	0.0756248
$668$	−21.2336	−0.821553
$669$	13.9887	0.540833
$670$	6.06513	0.234317
$671$	3.31771	0.128079
$672$	6.12024	0.236093
$673$	−9.67671	−0.373010	−0.186505	−	0.982454i	$-0.559716\pi$
$673$	−9.67671	−0.373010	−0.186505	+	0.982454i	$0.559716\pi$
$674$	20.1416	0.775827
$675$	−2.60523	−0.100275
$676$	23.2393	0.893819
$677$	48.5153	1.86460	0.932298	−	0.361691i	$-0.117800\pi$
$677$	48.5153	1.86460	0.932298	+	0.361691i	$0.117800\pi$
$678$	−28.7482	−1.10407
$679$	−27.6294	−1.06032
$680$	7.50661	0.287865
$681$	31.4387	1.20473
$682$	−1.76607	−0.0676263
$683$	−17.4750	−0.668663	−0.334331	−	0.942456i	$-0.608510\pi$
$683$	−17.4750	−0.668663	−0.334331	+	0.942456i	$0.608510\pi$
$684$	−18.9954	−0.726308
$685$	13.7914	0.526941
$686$	19.0516	0.727393
$687$	−25.0153	−0.954393
$688$	−3.69133	−0.140731
$689$	−51.0746	−1.94579
$690$	−1.55239	−0.0590983
$691$	−23.6780	−0.900755	−0.450378	−	0.892838i	$-0.648711\pi$
$691$	−23.6780	−0.900755	−0.450378	+	0.892838i	$0.648711\pi$
$692$	1.88954	0.0718296
$693$	10.9674	0.416616
$694$	−15.3098	−0.581151
$695$	24.6972	0.936817
$696$	8.12721	0.308061
$697$	58.6409	2.22118
$698$	28.1826	1.06673
$699$	−29.5709	−1.11847
$700$	9.52719	0.360094
$701$	−30.4934	−1.15172	−0.575860	−	0.817549i	$-0.695333\pi$
$701$	−30.4934	−1.15172	−0.575860	+	0.817549i	$0.695333\pi$
$702$	−4.21740	−0.159176
$703$	−81.0340	−3.05626
$704$	−1.58155	−0.0596069
$705$	−27.2576	−1.02658
$706$	−6.41960	−0.241605
$707$	−4.09099	−0.153858
$708$	15.8196	0.594539
$709$	9.38935	0.352624	0.176312	−	0.984334i	$-0.443583\pi$
$709$	9.38935	0.352624	0.176312	+	0.984334i	$0.443583\pi$
$710$	−4.13981	−0.155364
$711$	1.69464	0.0635541
$712$	−1.01248	−0.0379442
$713$	−0.641069	−0.0240082
$714$	−40.5869	−1.51893
$715$	−10.7770	−0.403038
$716$	−10.6516	−0.398069
$717$	−4.47222	−0.167018
$718$	−20.5633	−0.767415
$719$	−49.9669	−1.86345	−0.931726	−	0.363163i	$-0.881697\pi$
$719$	−49.9669	−1.86345	−0.931726	+	0.363163i	$0.881697\pi$
$720$	−3.06388	−0.114184
$721$	−24.7364	−0.921231
$722$	30.2500	1.12579
$723$	11.7815	0.438158
$724$	−21.7337	−0.807725
$725$	12.6514	0.469861
$726$	20.3024	0.753491
$727$	38.9638	1.44509	0.722545	−	0.691324i	$-0.242972\pi$
$727$	38.9638	1.44509	0.722545	+	0.691324i	$0.242972\pi$
$728$	15.4228	0.571608
$729$	−21.4884	−0.795867
$730$	3.73733	0.138325
$731$	24.4794	0.905404
$732$	5.01129	0.185223
$733$	37.0017	1.36669	0.683345	−	0.730096i	$-0.260525\pi$
$733$	37.0017	1.36669	0.683345	+	0.730096i	$0.260525\pi$
$734$	−23.5265	−0.868380
$735$	−1.17978	−0.0435168
$736$	−0.574089	−0.0211612
$737$	8.47415	0.312150
$738$	−23.9347	−0.881050
$739$	22.9175	0.843033	0.421517	−	0.906821i	$-0.361498\pi$
$739$	22.9175	0.843033	0.421517	+	0.906821i	$0.361498\pi$
$740$	−13.0705	−0.480480
$741$	−100.922	−3.70747
$742$	−21.7365	−0.797973
$743$	−26.2616	−0.963446	−0.481723	−	0.876324i	$-0.659989\pi$
$743$	−26.2616	−0.963446	−0.481723	+	0.876324i	$0.659989\pi$
$744$	−2.66759	−0.0977987
$745$	12.6302	0.462736
$746$	−16.6212	−0.608547
$747$	−3.18740	−0.116621
$748$	10.4882	0.383486
$749$	33.3669	1.21920
$750$	−23.5761	−0.860877
$751$	−19.7156	−0.719434	−0.359717	−	0.933062i	$-0.617127\pi$
$751$	−19.7156	−0.719434	−0.359717	+	0.933062i	$0.617127\pi$
$752$	−10.0802	−0.367586
$753$	−43.2139	−1.57480
$754$	20.4804	0.745851
$755$	−4.50769	−0.164052
$756$	−1.79486	−0.0652783
$757$	3.30190	0.120009	0.0600047	−	0.998198i	$-0.480888\pi$
$757$	3.30190	0.120009	0.0600047	+	0.998198i	$0.480888\pi$
$758$	−12.3977	−0.450303
$759$	−2.16898	−0.0787290
$760$	7.94383	0.288153
$761$	16.2211	0.588013	0.294007	−	0.955803i	$-0.405011\pi$
$761$	16.2211	0.588013	0.294007	+	0.955803i	$0.405011\pi$
$762$	13.6742	0.495365
$763$	6.38337	0.231093
$764$	4.55688	0.164862
$765$	20.3184	0.734613
$766$	−2.41511	−0.0872616
$767$	39.8651	1.43945
$768$	−2.38888	−0.0862012
$769$	−10.4564	−0.377066	−0.188533	−	0.982067i	$-0.560373\pi$
$769$	−10.4564	−0.377066	−0.188533	+	0.982067i	$0.560373\pi$
$770$	−4.58652	−0.165287
$771$	−14.0214	−0.504968
$772$	3.97856	0.143192
$773$	−8.83440	−0.317751	−0.158876	−	0.987299i	$-0.550787\pi$
$773$	−8.83440	−0.317751	−0.158876	+	0.987299i	$0.550787\pi$
$774$	−9.99146	−0.359136
$775$	−4.15256	−0.149164
$776$	10.7844	0.387138
$777$	70.6696	2.53526
$778$	32.4492	1.16336
$779$	62.0564	2.22340
$780$	−16.2783	−0.582858
$781$	−5.78411	−0.206972
$782$	3.80712	0.136142
$783$	−2.38343	−0.0851770
$784$	−0.436295	−0.0155820
$785$	5.59530	0.199705
$786$	−21.5787	−0.769687
$787$	4.75856	0.169624	0.0848122	−	0.996397i	$-0.472971\pi$
$787$	4.75856	0.169624	0.0848122	+	0.996397i	$0.472971\pi$
$788$	10.1674	0.362200
$789$	−54.4863	−1.93976
$790$	−0.708695	−0.0252143
$791$	−30.8313	−1.09623
$792$	−4.28083	−0.152113
$793$	12.6283	0.448445
$794$	17.4932	0.620810
$795$	22.9422	0.813677
$796$	19.5544	0.693088
$797$	26.4894	0.938304	0.469152	−	0.883117i	$-0.344560\pi$
$797$	26.4894	0.938304	0.469152	+	0.883117i	$0.344560\pi$
$798$	−42.9508	−1.52044
$799$	66.8475	2.36490
$800$	−3.71869	−0.131476
$801$	−2.74051	−0.0968311
$802$	−28.2043	−0.995927
$803$	5.22176	0.184272
$804$	12.7999	0.451419
$805$	−1.66487	−0.0586790
$806$	−6.72226	−0.236782
$807$	−37.7031	−1.32721
$808$	1.59681	0.0561757
$809$	34.5495	1.21470	0.607348	−	0.794436i	$-0.292234\pi$
$809$	34.5495	1.21470	0.607348	+	0.794436i	$0.292234\pi$
$810$	11.0861	0.389525
$811$	23.3426	0.819668	0.409834	−	0.912160i	$-0.365587\pi$
$811$	23.3426	0.819668	0.409834	+	0.912160i	$0.365587\pi$
$812$	8.71610	0.305875
$813$	28.9604	1.01568
$814$	−18.2619	−0.640080
$815$	2.38231	0.0834486
$816$	15.8420	0.554583
$817$	25.9052	0.906307
$818$	−15.9511	−0.557718
$819$	41.7455	1.45871
$820$	10.0094	0.349545
$821$	−20.0749	−0.700617	−0.350309	−	0.936634i	$-0.613923\pi$
$821$	−20.0749	−0.700617	−0.350309	+	0.936634i	$0.613923\pi$
$822$	29.1055	1.01517
$823$	45.9238	1.60080	0.800401	−	0.599465i	$-0.204620\pi$
$823$	45.9238	1.60080	0.800401	+	0.599465i	$0.204620\pi$
$824$	9.65520	0.336355
$825$	−14.0497	−0.489147
$826$	16.9659	0.590320
$827$	−40.1192	−1.39508	−0.697540	−	0.716545i	$-0.745722\pi$
$827$	−40.1192	−1.39508	−0.697540	+	0.716545i	$0.745722\pi$
$828$	−1.55391	−0.0540020
$829$	10.6836	0.371058	0.185529	−	0.982639i	$-0.440600\pi$
$829$	10.6836	0.371058	0.185529	+	0.982639i	$0.440600\pi$
$830$	1.33296	0.0462678
$831$	75.5835	2.62196
$832$	−6.01991	−0.208703
$833$	2.89333	0.100248
$834$	52.1212	1.80481
$835$	24.0353	0.831777
$836$	11.0990	0.383869
$837$	0.782314	0.0270407
$838$	−22.6340	−0.781878
$839$	−31.6134	−1.09142	−0.545708	−	0.837976i	$-0.683739\pi$
$839$	−31.6134	−1.09142	−0.545708	+	0.837976i	$0.683739\pi$
$840$	−6.92779	−0.239032
$841$	−17.4257	−0.600886
$842$	10.1895	0.351153
$843$	46.8188	1.61253
$844$	−8.76873	−0.301832
$845$	−26.3057	−0.904943
$846$	−27.2843	−0.938055
$847$	21.7734	0.748145
$848$	8.48429	0.291352
$849$	−45.5825	−1.56439
$850$	24.6608	0.845860
$851$	−6.62893	−0.227237
$852$	−8.73670	−0.299315
$853$	−37.0326	−1.26797	−0.633986	−	0.773345i	$-0.718582\pi$
$853$	−37.0326	−1.26797	−0.633986	+	0.773345i	$0.718582\pi$
$854$	5.37441	0.183908
$855$	21.5018	0.735347
$856$	−13.0239	−0.445149
$857$	21.4412	0.732417	0.366209	−	0.930533i	$-0.380656\pi$
$857$	21.4412	0.732417	0.366209	+	0.930533i	$0.380656\pi$
$858$	−22.7440	−0.776466
$859$	30.6793	1.04676	0.523382	−	0.852098i	$-0.324670\pi$
$859$	30.6793	1.04676	0.523382	+	0.852098i	$0.324670\pi$
$860$	4.17840	0.142482
$861$	−54.1192	−1.84438
$862$	−7.64170	−0.260277
$863$	−53.1939	−1.81074	−0.905371	−	0.424622i	$-0.860407\pi$
$863$	−53.1939	−1.81074	−0.905371	+	0.424622i	$0.860407\pi$
$864$	0.700576	0.0238341
$865$	−2.13886	−0.0727235
$866$	0.752089	0.0255570
$867$	−64.4470	−2.18873
$868$	−2.86088	−0.0971047
$869$	−0.990183	−0.0335897
$870$	−9.19958	−0.311895
$871$	32.2555	1.09294
$872$	−2.49158	−0.0843756
$873$	29.1905	0.987949
$874$	4.02886	0.136278
$875$	−25.2844	−0.854768
$876$	7.88730	0.266487
$877$	48.2335	1.62873	0.814364	−	0.580354i	$-0.197086\pi$
$877$	48.2335	1.62873	0.814364	+	0.580354i	$0.197086\pi$
$878$	14.6089	0.493025
$879$	−68.8621	−2.32266
$880$	1.79023	0.0603487
$881$	1.96926	0.0663462	0.0331731	−	0.999450i	$-0.489439\pi$
$881$	1.96926	0.0663462	0.0331731	+	0.999450i	$0.489439\pi$
$882$	−1.18093	−0.0397641
$883$	21.7551	0.732118	0.366059	−	0.930592i	$-0.380707\pi$
$883$	21.7551	0.732118	0.366059	+	0.930592i	$0.380707\pi$
$884$	39.9215	1.34271
$885$	−17.9070	−0.601938
$886$	20.2320	0.679708
$887$	−4.38959	−0.147388	−0.0736940	−	0.997281i	$-0.523479\pi$
$887$	−4.38959	−0.147388	−0.0736940	+	0.997281i	$0.523479\pi$
$888$	−27.5841	−0.925660
$889$	14.6650	0.491850
$890$	1.14607	0.0384164
$891$	15.4894	0.518913
$892$	−5.85575	−0.196065
$893$	70.7410	2.36726
$894$	26.6550	0.891476
$895$	12.0571	0.403023
$896$	−2.56197	−0.0855895
$897$	−8.25587	−0.275655
$898$	12.5449	0.418630
$899$	−3.79903	−0.126705
$900$	−10.0655	−0.335517
$901$	−56.2643	−1.87444
$902$	13.9851	0.465653
$903$	−22.5918	−0.751810
$904$	12.0342	0.400252
$905$	24.6014	0.817777
$906$	−9.51309	−0.316051
$907$	−48.6112	−1.61411	−0.807054	−	0.590478i	$-0.798939\pi$
$907$	−48.6112	−1.61411	−0.807054	+	0.590478i	$0.798939\pi$
$908$	−13.1604	−0.436744
$909$	4.32215	0.143357
$910$	−17.4579	−0.578722
$911$	−0.188837	−0.00625646	−0.00312823	−	0.999995i	$-0.500996\pi$
$911$	−0.188837	−0.00625646	−0.00312823	+	0.999995i	$0.500996\pi$
$912$	16.7647	0.555136
$913$	1.86240	0.0616365
$914$	1.60042	0.0529372
$915$	−5.67253	−0.187528
$916$	10.4716	0.345990
$917$	−23.1423	−0.764226
$918$	−4.64593	−0.153339
$919$	24.1034	0.795099	0.397549	−	0.917581i	$-0.369861\pi$
$919$	24.1034	0.795099	0.397549	+	0.917581i	$0.369861\pi$
$920$	0.649839	0.0214246
$921$	12.7871	0.421350
$922$	−19.4523	−0.640627
$923$	−22.0163	−0.724674
$924$	−9.67945	−0.318431
$925$	−42.9393	−1.41183
$926$	−40.7107	−1.33784
$927$	26.1341	0.858355
$928$	−3.40210	−0.111680
$929$	−3.93298	−0.129037	−0.0645184	−	0.997917i	$-0.520551\pi$
$929$	−3.93298	−0.129037	−0.0645184	+	0.997917i	$0.520551\pi$
$930$	3.01958	0.0990158
$931$	3.06185	0.100348
$932$	12.3786	0.405473
$933$	64.2169	2.10237
$934$	35.2631	1.15384
$935$	−11.8721	−0.388258
$936$	−16.2943	−0.532595
$937$	44.4548	1.45228	0.726138	−	0.687549i	$-0.241313\pi$
$937$	44.4548	1.45228	0.726138	+	0.687549i	$0.241313\pi$
$938$	13.7274	0.448216
$939$	40.5007	1.32169
$940$	11.4102	0.372161
$941$	32.1671	1.04862	0.524308	−	0.851528i	$-0.324324\pi$
$941$	32.1671	1.04862	0.524308	+	0.851528i	$0.324324\pi$
$942$	11.8084	0.384738
$943$	5.07648	0.165313
$944$	−6.62221	−0.215535
$945$	2.03169	0.0660907
$946$	5.83802	0.189811
$947$	−3.11123	−0.101101	−0.0505507	−	0.998721i	$-0.516098\pi$
$947$	−3.11123	−0.101101	−0.0505507	+	0.998721i	$0.516098\pi$
$948$	−1.49564	−0.0485761
$949$	19.8758	0.645196
$950$	26.0972	0.846704
$951$	−74.5719	−2.41816
$952$	16.9899	0.550647
$953$	10.3093	0.333950	0.166975	−	0.985961i	$-0.446600\pi$
$953$	10.3093	0.333950	0.166975	+	0.985961i	$0.446600\pi$
$954$	22.9647	0.743510
$955$	−5.15815	−0.166914
$956$	1.87210	0.0605481
$957$	−12.8536	−0.415497
$958$	3.99818	0.129175
$959$	31.2144	1.00797
$960$	2.70409	0.0872740
$961$	−29.7530	−0.959776
$962$	−69.5111	−2.24113
$963$	−35.2523	−1.13599
$964$	−4.93181	−0.158843
$965$	−4.50353	−0.144974
$966$	−3.51356	−0.113047
$967$	−13.0802	−0.420632	−0.210316	−	0.977633i	$-0.567449\pi$
$967$	−13.0802	−0.420632	−0.210316	+	0.977633i	$0.567449\pi$
$968$	−8.49870	−0.273159
$969$	−111.177	−3.57152
$970$	−12.2074	−0.391956
$971$	−34.4316	−1.10496	−0.552481	−	0.833525i	$-0.686319\pi$
$971$	−34.4316	−1.10496	−0.552481	+	0.833525i	$0.686319\pi$
$972$	21.2944	0.683019
$973$	55.8978	1.79200
$974$	26.6204	0.852974
$975$	−53.4779	−1.71266
$976$	−2.09776	−0.0671477
$977$	−57.4748	−1.83878	−0.919391	−	0.393344i	$-0.871318\pi$
$977$	−57.4748	−1.83878	−0.919391	+	0.393344i	$0.871318\pi$
$978$	5.02765	0.160767
$979$	1.60128	0.0511772
$980$	0.493864	0.0157759
$981$	−6.74405	−0.215321
$982$	−24.4879	−0.781441
$983$	9.42552	0.300628	0.150314	−	0.988638i	$-0.451972\pi$
$983$	9.42552	0.300628	0.150314	+	0.988638i	$0.451972\pi$
$984$	21.1240	0.673410
$985$	−11.5090	−0.366707
$986$	22.5614	0.718500
$987$	−61.6931	−1.96371
$988$	42.2467	1.34405
$989$	2.11915	0.0673852
$990$	4.84568	0.154006
$991$	−54.5282	−1.73215	−0.866073	−	0.499917i	$-0.833364\pi$
$991$	−54.5282	−1.73215	−0.866073	+	0.499917i	$0.833364\pi$
$992$	1.11667	0.0354544
$993$	24.6526	0.782328
$994$	−9.36976	−0.297191
$995$	−22.1346	−0.701714
$996$	2.81310	0.0891364
$997$	6.06316	0.192022	0.0960111	−	0.995380i	$-0.469392\pi$
$997$	6.06316	0.192022	0.0960111	+	0.995380i	$0.469392\pi$
$998$	3.53929	0.112034
$999$	8.08946	0.255939

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.d.1.14	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.d.1.14	✓	79	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.38888 q^{3} +1.00000 q^{4} -1.13195 q^{5} -2.38888 q^{6} -2.56197 q^{7} +1.00000 q^{8} +2.70673 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.38888 q^{3} +1.00000 q^{4} -1.13195 q^{5} -2.38888 q^{6} -2.56197 q^{7} +1.00000 q^{8} +2.70673 q^{9} -1.13195 q^{10} -1.58155 q^{11} -2.38888 q^{12} -6.01991 q^{13} -2.56197 q^{14} +2.70409 q^{15} +1.00000 q^{16} -6.63159 q^{17} +2.70673 q^{18} -7.01784 q^{19} -1.13195 q^{20} +6.12024 q^{21} -1.58155 q^{22} -0.574089 q^{23} -2.38888 q^{24} -3.71869 q^{25} -6.01991 q^{26} +0.700576 q^{27} -2.56197 q^{28} -3.40210 q^{29} +2.70409 q^{30} +1.11667 q^{31} +1.00000 q^{32} +3.77813 q^{33} -6.63159 q^{34} +2.90002 q^{35} +2.70673 q^{36} +11.5469 q^{37} -7.01784 q^{38} +14.3808 q^{39} -1.13195 q^{40} -8.84267 q^{41} +6.12024 q^{42} -3.69133 q^{43} -1.58155 q^{44} -3.06388 q^{45} -0.574089 q^{46} -10.0802 q^{47} -2.38888 q^{48} -0.436295 q^{49} -3.71869 q^{50} +15.8420 q^{51} -6.01991 q^{52} +8.48429 q^{53} +0.700576 q^{54} +1.79023 q^{55} -2.56197 q^{56} +16.7647 q^{57} -3.40210 q^{58} -6.62221 q^{59} +2.70409 q^{60} -2.09776 q^{61} +1.11667 q^{62} -6.93458 q^{63} +1.00000 q^{64} +6.81422 q^{65} +3.77813 q^{66} -5.35814 q^{67} -6.63159 q^{68} +1.37143 q^{69} +2.90002 q^{70} +3.65724 q^{71} +2.70673 q^{72} -3.30168 q^{73} +11.5469 q^{74} +8.88350 q^{75} -7.01784 q^{76} +4.05188 q^{77} +14.3808 q^{78} +0.626085 q^{79} -1.13195 q^{80} -9.79379 q^{81} -8.84267 q^{82} -1.17758 q^{83} +6.12024 q^{84} +7.50661 q^{85} -3.69133 q^{86} +8.12721 q^{87} -1.58155 q^{88} -1.01248 q^{89} -3.06388 q^{90} +15.4228 q^{91} -0.574089 q^{92} -2.66759 q^{93} -10.0802 q^{94} +7.94383 q^{95} -2.38888 q^{96} +10.7844 q^{97} -0.436295 q^{98} -4.28083 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * q^99

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