LMFDB - Embedded newform 6026.2.a.l.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.66763 q^{3} +1.00000 q^{4} +1.81504 q^{5} +1.66763 q^{6} +3.25466 q^{7} -1.00000 q^{8} -0.218995 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.66763 q^{3} +1.00000 q^{4} +1.81504 q^{5} +1.66763 q^{6} +3.25466 q^{7} -1.00000 q^{8} -0.218995 q^{9} -1.81504 q^{10} -4.39695 q^{11} -1.66763 q^{12} -0.979648 q^{13} -3.25466 q^{14} -3.02682 q^{15} +1.00000 q^{16} +7.76351 q^{17} +0.218995 q^{18} +0.157018 q^{19} +1.81504 q^{20} -5.42758 q^{21} +4.39695 q^{22} -1.00000 q^{23} +1.66763 q^{24} -1.70564 q^{25} +0.979648 q^{26} +5.36811 q^{27} +3.25466 q^{28} -4.73191 q^{29} +3.02682 q^{30} -0.703607 q^{31} -1.00000 q^{32} +7.33251 q^{33} -7.76351 q^{34} +5.90732 q^{35} -0.218995 q^{36} +2.06292 q^{37} -0.157018 q^{38} +1.63370 q^{39} -1.81504 q^{40} -9.75687 q^{41} +5.42758 q^{42} -2.90522 q^{43} -4.39695 q^{44} -0.397484 q^{45} +1.00000 q^{46} +0.804280 q^{47} -1.66763 q^{48} +3.59278 q^{49} +1.70564 q^{50} -12.9467 q^{51} -0.979648 q^{52} +10.4166 q^{53} -5.36811 q^{54} -7.98063 q^{55} -3.25466 q^{56} -0.261848 q^{57} +4.73191 q^{58} -1.01160 q^{59} -3.02682 q^{60} +10.1382 q^{61} +0.703607 q^{62} -0.712753 q^{63} +1.00000 q^{64} -1.77810 q^{65} -7.33251 q^{66} +3.65418 q^{67} +7.76351 q^{68} +1.66763 q^{69} -5.90732 q^{70} +11.1555 q^{71} +0.218995 q^{72} -6.46306 q^{73} -2.06292 q^{74} +2.84438 q^{75} +0.157018 q^{76} -14.3106 q^{77} -1.63370 q^{78} +10.3440 q^{79} +1.81504 q^{80} -8.29506 q^{81} +9.75687 q^{82} +15.9904 q^{83} -5.42758 q^{84} +14.0911 q^{85} +2.90522 q^{86} +7.89110 q^{87} +4.39695 q^{88} -16.8415 q^{89} +0.397484 q^{90} -3.18842 q^{91} -1.00000 q^{92} +1.17336 q^{93} -0.804280 q^{94} +0.284993 q^{95} +1.66763 q^{96} +7.40376 q^{97} -3.59278 q^{98} +0.962910 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.66763	−0.962809	−0.481405	−	0.876498i	$-0.659873\pi$
$3$	−1.66763	−0.962809	−0.481405	+	0.876498i	$0.659873\pi$
$4$	1.00000	0.500000
$5$	1.81504	0.811710	0.405855	−	0.913938i	$-0.366974\pi$
$5$	1.81504	0.811710	0.405855	+	0.913938i	$0.366974\pi$
$6$	1.66763	0.680809
$7$	3.25466	1.23014	0.615072	−	0.788471i	$-0.289127\pi$
$7$	3.25466	1.23014	0.615072	+	0.788471i	$0.289127\pi$
$8$	−1.00000	−0.353553
$9$	−0.218995	−0.0729983
$10$	−1.81504	−0.573965
$11$	−4.39695	−1.32573	−0.662865	−	0.748739i	$-0.730660\pi$
$11$	−4.39695	−1.32573	−0.662865	+	0.748739i	$0.730660\pi$
$12$	−1.66763	−0.481405
$13$	−0.979648	−0.271706	−0.135853	−	0.990729i	$-0.543377\pi$
$13$	−0.979648	−0.271706	−0.135853	+	0.990729i	$0.543377\pi$
$14$	−3.25466	−0.869843
$15$	−3.02682	−0.781522
$16$	1.00000	0.250000
$17$	7.76351	1.88293	0.941464	−	0.337113i	$-0.109450\pi$
$17$	7.76351	1.88293	0.941464	+	0.337113i	$0.109450\pi$
$18$	0.218995	0.0516176
$19$	0.157018	0.0360224	0.0180112	−	0.999838i	$-0.494267\pi$
$19$	0.157018	0.0360224	0.0180112	+	0.999838i	$0.494267\pi$
$20$	1.81504	0.405855
$21$	−5.42758	−1.18439
$22$	4.39695	0.937433
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.66763	0.340404
$25$	−1.70564	−0.341127
$26$	0.979648	0.192125
$27$	5.36811	1.03309
$28$	3.25466	0.615072
$29$	−4.73191	−0.878694	−0.439347	−	0.898317i	$-0.644790\pi$
$29$	−4.73191	−0.878694	−0.439347	+	0.898317i	$0.644790\pi$
$30$	3.02682	0.552619
$31$	−0.703607	−0.126372	−0.0631858	−	0.998002i	$-0.520126\pi$
$31$	−0.703607	−0.126372	−0.0631858	+	0.998002i	$0.520126\pi$
$32$	−1.00000	−0.176777
$33$	7.33251	1.27643
$34$	−7.76351	−1.33143
$35$	5.90732	0.998520
$36$	−0.218995	−0.0364991
$37$	2.06292	0.339143	0.169571	−	0.985518i	$-0.445762\pi$
$37$	2.06292	0.339143	0.169571	+	0.985518i	$0.445762\pi$
$38$	−0.157018	−0.0254717
$39$	1.63370	0.261601
$40$	−1.81504	−0.286983
$41$	−9.75687	−1.52377	−0.761884	−	0.647714i	$-0.775725\pi$
$41$	−9.75687	−1.52377	−0.761884	+	0.647714i	$0.775725\pi$
$42$	5.42758	0.837493
$43$	−2.90522	−0.443042	−0.221521	−	0.975156i	$-0.571102\pi$
$43$	−2.90522	−0.443042	−0.221521	+	0.975156i	$0.571102\pi$
$44$	−4.39695	−0.662865
$45$	−0.397484	−0.0592534
$46$	1.00000	0.147442
$47$	0.804280	0.117316	0.0586582	−	0.998278i	$-0.481318\pi$
$47$	0.804280	0.117316	0.0586582	+	0.998278i	$0.481318\pi$
$48$	−1.66763	−0.240702
$49$	3.59278	0.513255
$50$	1.70564	0.241213
$51$	−12.9467	−1.81290
$52$	−0.979648	−0.135853
$53$	10.4166	1.43083	0.715413	−	0.698702i	$-0.246239\pi$
$53$	10.4166	1.43083	0.715413	+	0.698702i	$0.246239\pi$
$54$	−5.36811	−0.730507
$55$	−7.98063	−1.07611
$56$	−3.25466	−0.434922
$57$	−0.261848	−0.0346827
$58$	4.73191	0.621331
$59$	−1.01160	−0.131699	−0.0658496	−	0.997830i	$-0.520976\pi$
$59$	−1.01160	−0.131699	−0.0658496	+	0.997830i	$0.520976\pi$
$60$	−3.02682	−0.390761
$61$	10.1382	1.29806	0.649032	−	0.760761i	$-0.275174\pi$
$61$	10.1382	1.29806	0.649032	+	0.760761i	$0.275174\pi$
$62$	0.703607	0.0893582
$63$	−0.712753	−0.0897984
$64$	1.00000	0.125000
$65$	−1.77810	−0.220546
$66$	−7.33251	−0.902569
$67$	3.65418	0.446429	0.223215	−	0.974769i	$-0.428345\pi$
$67$	3.65418	0.446429	0.223215	+	0.974769i	$0.428345\pi$
$68$	7.76351	0.941464
$69$	1.66763	0.200760
$70$	−5.90732	−0.706060
$71$	11.1555	1.32391	0.661955	−	0.749544i	$-0.269727\pi$
$71$	11.1555	1.32391	0.661955	+	0.749544i	$0.269727\pi$
$72$	0.218995	0.0258088
$73$	−6.46306	−0.756444	−0.378222	−	0.925715i	$-0.623464\pi$
$73$	−6.46306	−0.756444	−0.378222	+	0.925715i	$0.623464\pi$
$74$	−2.06292	−0.239810
$75$	2.84438	0.328440
$76$	0.157018	0.0180112
$77$	−14.3106	−1.63084
$78$	−1.63370	−0.184980
$79$	10.3440	1.16379	0.581897	−	0.813262i	$-0.302311\pi$
$79$	10.3440	1.16379	0.581897	+	0.813262i	$0.302311\pi$
$80$	1.81504	0.202927
$81$	−8.29506	−0.921673
$82$	9.75687	1.07747
$83$	15.9904	1.75518	0.877589	−	0.479414i	$-0.159151\pi$
$83$	15.9904	1.75518	0.877589	+	0.479414i	$0.159151\pi$
$84$	−5.42758	−0.592197
$85$	14.0911	1.52839
$86$	2.90522	0.313278
$87$	7.89110	0.846015
$88$	4.39695	0.468717
$89$	−16.8415	−1.78519	−0.892597	−	0.450856i	$-0.851119\pi$
$89$	−16.8415	−1.78519	−0.892597	+	0.450856i	$0.851119\pi$
$90$	0.397484	0.0418985
$91$	−3.18842	−0.334237
$92$	−1.00000	−0.104257
$93$	1.17336	0.121672
$94$	−0.804280	−0.0829552
$95$	0.284993	0.0292397
$96$	1.66763	0.170202
$97$	7.40376	0.751738	0.375869	−	0.926673i	$-0.377344\pi$
$97$	7.40376	0.751738	0.375869	+	0.926673i	$0.377344\pi$
$98$	−3.59278	−0.362926
$99$	0.962910	0.0967761
$100$	−1.70564	−0.170564
$101$	0.195992	0.0195020	0.00975098	−	0.999952i	$-0.496896\pi$
$101$	0.195992	0.0195020	0.00975098	+	0.999952i	$0.496896\pi$
$102$	12.9467	1.28191
$103$	12.7062	1.25197	0.625987	−	0.779833i	$-0.284696\pi$
$103$	12.7062	1.25197	0.625987	+	0.779833i	$0.284696\pi$
$104$	0.979648	0.0960624
$105$	−9.85126	−0.961384
$106$	−10.4166	−1.01175
$107$	5.69727	0.550776	0.275388	−	0.961333i	$-0.411194\pi$
$107$	5.69727	0.550776	0.275388	+	0.961333i	$0.411194\pi$
$108$	5.36811	0.516546
$109$	−3.79450	−0.363447	−0.181724	−	0.983350i	$-0.558168\pi$
$109$	−3.79450	−0.363447	−0.181724	+	0.983350i	$0.558168\pi$
$110$	7.98063	0.760924
$111$	−3.44020	−0.326530
$112$	3.25466	0.307536
$113$	−9.92285	−0.933463	−0.466732	−	0.884399i	$-0.654569\pi$
$113$	−9.92285	−0.933463	−0.466732	+	0.884399i	$0.654569\pi$
$114$	0.261848	0.0245243
$115$	−1.81504	−0.169253
$116$	−4.73191	−0.439347
$117$	0.214538	0.0198340
$118$	1.01160	0.0931253
$119$	25.2676	2.31627
$120$	3.02682	0.276310
$121$	8.33318	0.757562
$122$	−10.1382	−0.917869
$123$	16.2709	1.46710
$124$	−0.703607	−0.0631858
$125$	−12.1710	−1.08861
$126$	0.712753	0.0634971
$127$	2.58572	0.229446	0.114723	−	0.993398i	$-0.463402\pi$
$127$	2.58572	0.229446	0.114723	+	0.993398i	$0.463402\pi$
$128$	−1.00000	−0.0883883
$129$	4.84484	0.426565
$130$	1.77810	0.155950
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	7.33251	0.638213
$133$	0.511039	0.0443127
$134$	−3.65418	−0.315673
$135$	9.74332	0.838571
$136$	−7.76351	−0.665716
$137$	12.0340	1.02813	0.514067	−	0.857750i	$-0.328138\pi$
$137$	12.0340	1.02813	0.514067	+	0.857750i	$0.328138\pi$
$138$	−1.66763	−0.141958
$139$	11.0566	0.937811	0.468905	−	0.883248i	$-0.344649\pi$
$139$	11.0566	0.937811	0.468905	+	0.883248i	$0.344649\pi$
$140$	5.90732	0.499260
$141$	−1.34125	−0.112953
$142$	−11.1555	−0.936146
$143$	4.30747	0.360208
$144$	−0.218995	−0.0182496
$145$	−8.58860	−0.713245
$146$	6.46306	0.534887
$147$	−5.99145	−0.494167
$148$	2.06292	0.169571
$149$	−15.8726	−1.30033	−0.650167	−	0.759791i	$-0.725301\pi$
$149$	−15.8726	−1.30033	−0.650167	+	0.759791i	$0.725301\pi$
$150$	−2.84438	−0.232242
$151$	−3.42324	−0.278579	−0.139290	−	0.990252i	$-0.544482\pi$
$151$	−3.42324	−0.278579	−0.139290	+	0.990252i	$0.544482\pi$
$152$	−0.157018	−0.0127358
$153$	−1.70017	−0.137451
$154$	14.3106	1.15318
$155$	−1.27707	−0.102577
$156$	1.63370	0.130800
$157$	16.2104	1.29373	0.646864	−	0.762606i	$-0.276080\pi$
$157$	16.2104	1.29373	0.646864	+	0.762606i	$0.276080\pi$
$158$	−10.3440	−0.822927
$159$	−17.3710	−1.37761
$160$	−1.81504	−0.143491
$161$	−3.25466	−0.256503
$162$	8.29506	0.651721
$163$	−6.08710	−0.476778	−0.238389	−	0.971170i	$-0.576619\pi$
$163$	−6.08710	−0.476778	−0.238389	+	0.971170i	$0.576619\pi$
$164$	−9.75687	−0.761884
$165$	13.3088	1.03609
$166$	−15.9904	−1.24110
$167$	12.7117	0.983662	0.491831	−	0.870691i	$-0.336328\pi$
$167$	12.7117	0.983662	0.491831	+	0.870691i	$0.336328\pi$
$168$	5.42758	0.418747
$169$	−12.0403	−0.926176
$170$	−14.0911	−1.08074
$171$	−0.0343861	−0.00262957
$172$	−2.90522	−0.221521
$173$	6.40873	0.487247	0.243623	−	0.969870i	$-0.421664\pi$
$173$	6.40873	0.487247	0.243623	+	0.969870i	$0.421664\pi$
$174$	−7.89110	−0.598223
$175$	−5.55126	−0.419636
$176$	−4.39695	−0.331433
$177$	1.68698	0.126801
$178$	16.8415	1.26232
$179$	5.70155	0.426154	0.213077	−	0.977035i	$-0.431651\pi$
$179$	5.70155	0.426154	0.213077	+	0.977035i	$0.431651\pi$
$180$	−0.397484	−0.0296267
$181$	−10.4754	−0.778632	−0.389316	−	0.921104i	$-0.627289\pi$
$181$	−10.4754	−0.778632	−0.389316	+	0.921104i	$0.627289\pi$
$182$	3.18842	0.236341
$183$	−16.9068	−1.24979
$184$	1.00000	0.0737210
$185$	3.74429	0.275285
$186$	−1.17336	−0.0860349
$187$	−34.1358	−2.49626
$188$	0.804280	0.0586582
$189$	17.4713	1.27085
$190$	−0.284993	−0.0206756
$191$	−4.41605	−0.319534	−0.159767	−	0.987155i	$-0.551074\pi$
$191$	−4.41605	−0.319534	−0.159767	+	0.987155i	$0.551074\pi$
$192$	−1.66763	−0.120351
$193$	11.7094	0.842863	0.421431	−	0.906860i	$-0.361528\pi$
$193$	11.7094	0.842863	0.421431	+	0.906860i	$0.361528\pi$
$194$	−7.40376	−0.531559
$195$	2.96522	0.212344
$196$	3.59278	0.256627
$197$	18.0754	1.28782	0.643909	−	0.765102i	$-0.277311\pi$
$197$	18.0754	1.28782	0.643909	+	0.765102i	$0.277311\pi$
$198$	−0.962910	−0.0684310
$199$	−13.9651	−0.989959	−0.494979	−	0.868905i	$-0.664824\pi$
$199$	−13.9651	−0.989959	−0.494979	+	0.868905i	$0.664824\pi$
$200$	1.70564	0.120607
$201$	−6.09384	−0.429826
$202$	−0.195992	−0.0137900
$203$	−15.4007	−1.08092
$204$	−12.9467	−0.906451
$205$	−17.7091	−1.23686
$206$	−12.7062	−0.885280
$207$	0.218995	0.0152212
$208$	−0.979648	−0.0679264
$209$	−0.690400	−0.0477559
$210$	9.85126	0.679801
$211$	3.83449	0.263977	0.131988	−	0.991251i	$-0.457864\pi$
$211$	3.83449	0.263977	0.131988	+	0.991251i	$0.457864\pi$
$212$	10.4166	0.715413
$213$	−18.6032	−1.27467
$214$	−5.69727	−0.389457
$215$	−5.27308	−0.359621
$216$	−5.36811	−0.365253
$217$	−2.29000	−0.155455
$218$	3.79450	0.256996
$219$	10.7780	0.728312
$220$	−7.98063	−0.538054
$221$	−7.60551	−0.511602
$222$	3.44020	0.230891
$223$	20.8755	1.39792	0.698962	−	0.715159i	$-0.253646\pi$
$223$	20.8755	1.39792	0.698962	+	0.715159i	$0.253646\pi$
$224$	−3.25466	−0.217461
$225$	0.373526	0.0249017
$226$	9.92285	0.660058
$227$	12.1065	0.803535	0.401767	−	0.915742i	$-0.368396\pi$
$227$	12.1065	0.803535	0.401767	+	0.915742i	$0.368396\pi$
$228$	−0.261848	−0.0173413
$229$	17.1228	1.13151	0.565753	−	0.824575i	$-0.308586\pi$
$229$	17.1228	1.13151	0.565753	+	0.824575i	$0.308586\pi$
$230$	1.81504	0.119680
$231$	23.8648	1.57019
$232$	4.73191	0.310665
$233$	−15.7787	−1.03369	−0.516847	−	0.856078i	$-0.672894\pi$
$233$	−15.7787	−1.03369	−0.516847	+	0.856078i	$0.672894\pi$
$234$	−0.214538	−0.0140248
$235$	1.45980	0.0952268
$236$	−1.01160	−0.0658496
$237$	−17.2501	−1.12051
$238$	−25.2676	−1.63785
$239$	−26.1251	−1.68989	−0.844947	−	0.534850i	$-0.820368\pi$
$239$	−26.1251	−1.68989	−0.844947	+	0.534850i	$0.820368\pi$
$240$	−3.02682	−0.195380
$241$	11.3759	0.732784	0.366392	−	0.930461i	$-0.380593\pi$
$241$	11.3759	0.732784	0.366392	+	0.930461i	$0.380593\pi$
$242$	−8.33318	−0.535677
$243$	−2.27120	−0.145697
$244$	10.1382	0.649032
$245$	6.52104	0.416614
$246$	−16.2709	−1.03739
$247$	−0.153822	−0.00978747
$248$	0.703607	0.0446791
$249$	−26.6662	−1.68990
$250$	12.1710	0.769761
$251$	2.44885	0.154570	0.0772851	−	0.997009i	$-0.475375\pi$
$251$	2.44885	0.154570	0.0772851	+	0.997009i	$0.475375\pi$
$252$	−0.712753	−0.0448992
$253$	4.39695	0.276434
$254$	−2.58572	−0.162243
$255$	−23.4988	−1.47155
$256$	1.00000	0.0625000
$257$	−3.65200	−0.227806	−0.113903	−	0.993492i	$-0.536335\pi$
$257$	−3.65200	−0.227806	−0.113903	+	0.993492i	$0.536335\pi$
$258$	−4.84484	−0.301627
$259$	6.71411	0.417194
$260$	−1.77810	−0.110273
$261$	1.03626	0.0641432
$262$	−1.00000	−0.0617802
$263$	−21.2624	−1.31110	−0.655549	−	0.755153i	$-0.727563\pi$
$263$	−21.2624	−1.31110	−0.655549	+	0.755153i	$0.727563\pi$
$264$	−7.33251	−0.451285
$265$	18.9065	1.16141
$266$	−0.511039	−0.0313338
$267$	28.0854	1.71880
$268$	3.65418	0.223215
$269$	9.57027	0.583510	0.291755	−	0.956493i	$-0.405761\pi$
$269$	9.57027	0.583510	0.291755	+	0.956493i	$0.405761\pi$
$270$	−9.74332	−0.592960
$271$	−7.16616	−0.435313	−0.217657	−	0.976025i	$-0.569841\pi$
$271$	−7.16616	−0.435313	−0.217657	+	0.976025i	$0.569841\pi$
$272$	7.76351	0.470732
$273$	5.31712	0.321807
$274$	−12.0340	−0.727000
$275$	7.49960	0.452243
$276$	1.66763	0.100380
$277$	11.4433	0.687563	0.343781	−	0.939050i	$-0.388292\pi$
$277$	11.4433	0.687563	0.343781	+	0.939050i	$0.388292\pi$
$278$	−11.0566	−0.663132
$279$	0.154086	0.00922490
$280$	−5.90732	−0.353030
$281$	−20.9651	−1.25067	−0.625337	−	0.780355i	$-0.715039\pi$
$281$	−20.9651	−1.25067	−0.625337	+	0.780355i	$0.715039\pi$
$282$	1.34125	0.0798700
$283$	4.70143	0.279471	0.139736	−	0.990189i	$-0.455375\pi$
$283$	4.70143	0.279471	0.139736	+	0.990189i	$0.455375\pi$
$284$	11.1555	0.661955
$285$	−0.475265	−0.0281523
$286$	−4.30747	−0.254706
$287$	−31.7553	−1.87445
$288$	0.218995	0.0129044
$289$	43.2721	2.54542
$290$	8.58860	0.504340
$291$	−12.3468	−0.723780
$292$	−6.46306	−0.378222
$293$	−6.41999	−0.375060	−0.187530	−	0.982259i	$-0.560048\pi$
$293$	−6.41999	−0.375060	−0.187530	+	0.982259i	$0.560048\pi$
$294$	5.99145	0.349429
$295$	−1.83609	−0.106901
$296$	−2.06292	−0.119905
$297$	−23.6033	−1.36960
$298$	15.8726	0.919475
$299$	0.979648	0.0566545
$300$	2.84438	0.164220
$301$	−9.45549	−0.545005
$302$	3.42324	0.196985
$303$	−0.326843	−0.0187767
$304$	0.157018	0.00900559
$305$	18.4012	1.05365
$306$	1.70017	0.0971922
$307$	11.0802	0.632380	0.316190	−	0.948696i	$-0.397596\pi$
$307$	11.0802	0.632380	0.316190	+	0.948696i	$0.397596\pi$
$308$	−14.3106	−0.815420
$309$	−21.1892	−1.20541
$310$	1.27707	0.0725329
$311$	−5.75885	−0.326554	−0.163277	−	0.986580i	$-0.552206\pi$
$311$	−5.75885	−0.326554	−0.163277	+	0.986580i	$0.552206\pi$
$312$	−1.63370	−0.0924898
$313$	5.85743	0.331082	0.165541	−	0.986203i	$-0.447063\pi$
$313$	5.85743	0.331082	0.165541	+	0.986203i	$0.447063\pi$
$314$	−16.2104	−0.914803
$315$	−1.29367	−0.0728903
$316$	10.3440	0.581897
$317$	−23.5665	−1.32363	−0.661813	−	0.749669i	$-0.730213\pi$
$317$	−23.5665	−1.32363	−0.661813	+	0.749669i	$0.730213\pi$
$318$	17.3710	0.974119
$319$	20.8060	1.16491
$320$	1.81504	0.101464
$321$	−9.50096	−0.530292
$322$	3.25466	0.181375
$323$	1.21901	0.0678275
$324$	−8.29506	−0.460836
$325$	1.67092	0.0926862
$326$	6.08710	0.337133
$327$	6.32784	0.349931
$328$	9.75687	0.538733
$329$	2.61766	0.144316
$330$	−13.3088	−0.732624
$331$	−24.0411	−1.32142	−0.660708	−	0.750643i	$-0.729744\pi$
$331$	−24.0411	−1.32142	−0.660708	+	0.750643i	$0.729744\pi$
$332$	15.9904	0.877589
$333$	−0.451770	−0.0247568
$334$	−12.7117	−0.695554
$335$	6.63248	0.362371
$336$	−5.42758	−0.296099
$337$	23.0216	1.25407	0.627034	−	0.778992i	$-0.284269\pi$
$337$	23.0216	1.25407	0.627034	+	0.778992i	$0.284269\pi$
$338$	12.0403	0.654905
$339$	16.5477	0.898747
$340$	14.0911	0.764196
$341$	3.09373	0.167535
$342$	0.0343861	0.00185939
$343$	−11.0893	−0.598767
$344$	2.90522	0.156639
$345$	3.02682	0.162959
$346$	−6.40873	−0.344535
$347$	−17.7692	−0.953902	−0.476951	−	0.878930i	$-0.658258\pi$
$347$	−17.7692	−0.953902	−0.476951	+	0.878930i	$0.658258\pi$
$348$	7.89110	0.423007
$349$	28.2237	1.51078	0.755389	−	0.655277i	$-0.227448\pi$
$349$	28.2237	1.51078	0.755389	+	0.655277i	$0.227448\pi$
$350$	5.55126	0.296727
$351$	−5.25886	−0.280697
$352$	4.39695	0.234358
$353$	0.429232	0.0228457	0.0114229	−	0.999935i	$-0.496364\pi$
$353$	0.429232	0.0228457	0.0114229	+	0.999935i	$0.496364\pi$
$354$	−1.68698	−0.0896619
$355$	20.2476	1.07463
$356$	−16.8415	−0.892597
$357$	−42.1371	−2.23013
$358$	−5.70155	−0.301336
$359$	21.4739	1.13335	0.566674	−	0.823942i	$-0.308230\pi$
$359$	21.4739	1.13335	0.566674	+	0.823942i	$0.308230\pi$
$360$	0.397484	0.0209492
$361$	−18.9753	−0.998702
$362$	10.4754	0.550576
$363$	−13.8967	−0.729387
$364$	−3.18842	−0.167119
$365$	−11.7307	−0.614013
$366$	16.9068	0.883733
$367$	10.3271	0.539068	0.269534	−	0.962991i	$-0.413130\pi$
$367$	10.3271	0.539068	0.269534	+	0.962991i	$0.413130\pi$
$368$	−1.00000	−0.0521286
$369$	2.13670	0.111232
$370$	−3.74429	−0.194656
$371$	33.9023	1.76012
$372$	1.17336	0.0608358
$373$	14.2230	0.736439	0.368220	−	0.929739i	$-0.379967\pi$
$373$	14.2230	0.736439	0.368220	+	0.929739i	$0.379967\pi$
$374$	34.1358	1.76512
$375$	20.2968	1.04812
$376$	−0.804280	−0.0414776
$377$	4.63561	0.238746
$378$	−17.4713	−0.898629
$379$	19.0501	0.978539	0.489269	−	0.872133i	$-0.337263\pi$
$379$	19.0501	0.978539	0.489269	+	0.872133i	$0.337263\pi$
$380$	0.284993	0.0146198
$381$	−4.31204	−0.220913
$382$	4.41605	0.225945
$383$	−1.33370	−0.0681487	−0.0340743	−	0.999419i	$-0.510848\pi$
$383$	−1.33370	−0.0681487	−0.0340743	+	0.999419i	$0.510848\pi$
$384$	1.66763	0.0851011
$385$	−25.9742	−1.32377
$386$	−11.7094	−0.595994
$387$	0.636228	0.0323413
$388$	7.40376	0.375869
$389$	18.2779	0.926725	0.463363	−	0.886169i	$-0.346643\pi$
$389$	18.2779	0.926725	0.463363	+	0.886169i	$0.346643\pi$
$390$	−2.96522	−0.150150
$391$	−7.76351	−0.392618
$392$	−3.59278	−0.181463
$393$	−1.66763	−0.0841210
$394$	−18.0754	−0.910625
$395$	18.7748	0.944664
$396$	0.962910	0.0483880
$397$	34.1518	1.71403	0.857015	−	0.515291i	$-0.172316\pi$
$397$	34.1518	1.71403	0.857015	+	0.515291i	$0.172316\pi$
$398$	13.9651	0.700006
$399$	−0.852226	−0.0426647
$400$	−1.70564	−0.0852818
$401$	−31.2834	−1.56222	−0.781110	−	0.624394i	$-0.785346\pi$
$401$	−31.2834	−1.56222	−0.781110	+	0.624394i	$0.785346\pi$
$402$	6.09384	0.303933
$403$	0.689287	0.0343358
$404$	0.195992	0.00975098
$405$	−15.0558	−0.748131
$406$	15.4007	0.764326
$407$	−9.07057	−0.449612
$408$	12.9467	0.640957
$409$	−9.33266	−0.461470	−0.230735	−	0.973017i	$-0.574113\pi$
$409$	−9.33266	−0.461470	−0.230735	+	0.973017i	$0.574113\pi$
$410$	17.7091	0.874590
$411$	−20.0683	−0.989896
$412$	12.7062	0.625987
$413$	−3.29241	−0.162009
$414$	−0.218995	−0.0107630
$415$	29.0232	1.42469
$416$	0.979648	0.0480312
$417$	−18.4384	−0.902933
$418$	0.690400	0.0337685
$419$	27.4922	1.34308	0.671541	−	0.740968i	$-0.265633\pi$
$419$	27.4922	1.34308	0.671541	+	0.740968i	$0.265633\pi$
$420$	−9.85126	−0.480692
$421$	−17.6167	−0.858584	−0.429292	−	0.903166i	$-0.641237\pi$
$421$	−17.6167	−0.858584	−0.429292	+	0.903166i	$0.641237\pi$
$422$	−3.83449	−0.186660
$423$	−0.176133	−0.00856389
$424$	−10.4166	−0.505873
$425$	−13.2417	−0.642318
$426$	18.6032	0.901330
$427$	32.9963	1.59681
$428$	5.69727	0.275388
$429$	−7.18328	−0.346812
$430$	5.27308	0.254291
$431$	6.41627	0.309061	0.154530	−	0.987988i	$-0.450614\pi$
$431$	6.41627	0.309061	0.154530	+	0.987988i	$0.450614\pi$
$432$	5.36811	0.258273
$433$	17.4669	0.839403	0.419702	−	0.907662i	$-0.362135\pi$
$433$	17.4669	0.839403	0.419702	+	0.907662i	$0.362135\pi$
$434$	2.29000	0.109923
$435$	14.3227	0.686719
$436$	−3.79450	−0.181724
$437$	−0.157018	−0.00751118
$438$	−10.7780	−0.514994
$439$	6.23618	0.297637	0.148818	−	0.988865i	$-0.452453\pi$
$439$	6.23618	0.297637	0.148818	+	0.988865i	$0.452453\pi$
$440$	7.98063	0.380462
$441$	−0.786801	−0.0374667
$442$	7.60551	0.361757
$443$	−8.20613	−0.389885	−0.194943	−	0.980815i	$-0.562452\pi$
$443$	−8.20613	−0.389885	−0.194943	+	0.980815i	$0.562452\pi$
$444$	−3.44020	−0.163265
$445$	−30.5679	−1.44906
$446$	−20.8755	−0.988482
$447$	26.4697	1.25197
$448$	3.25466	0.153768
$449$	13.8150	0.651969	0.325984	−	0.945375i	$-0.394304\pi$
$449$	13.8150	0.651969	0.325984	+	0.945375i	$0.394304\pi$
$450$	−0.373526	−0.0176082
$451$	42.9005	2.02010
$452$	−9.92285	−0.466732
$453$	5.70871	0.268219
$454$	−12.1065	−0.568185
$455$	−5.78710	−0.271303
$456$	0.261848	0.0122622
$457$	2.82103	0.131962	0.0659811	−	0.997821i	$-0.478982\pi$
$457$	2.82103	0.131962	0.0659811	+	0.997821i	$0.478982\pi$
$458$	−17.1228	−0.800096
$459$	41.6754	1.94524
$460$	−1.81504	−0.0846266
$461$	26.4695	1.23281	0.616403	−	0.787431i	$-0.288589\pi$
$461$	26.4695	1.23281	0.616403	+	0.787431i	$0.288589\pi$
$462$	−23.8648	−1.11029
$463$	23.1728	1.07693	0.538466	−	0.842647i	$-0.319004\pi$
$463$	23.1728	1.07693	0.538466	+	0.842647i	$0.319004\pi$
$464$	−4.73191	−0.219674
$465$	2.12969	0.0987621
$466$	15.7787	0.730932
$467$	26.7843	1.23943	0.619714	−	0.784828i	$-0.287249\pi$
$467$	26.7843	1.23943	0.619714	+	0.784828i	$0.287249\pi$
$468$	0.214538	0.00991702
$469$	11.8931	0.549172
$470$	−1.45980	−0.0673355
$471$	−27.0330	−1.24561
$472$	1.01160	0.0465627
$473$	12.7741	0.587354
$474$	17.2501	0.792322
$475$	−0.267815	−0.0122882
$476$	25.2676	1.15814
$477$	−2.28117	−0.104448
$478$	26.1251	1.19494
$479$	42.7267	1.95223	0.976117	−	0.217247i	$-0.0697077\pi$
$479$	42.7267	1.95223	0.976117	+	0.217247i	$0.0697077\pi$
$480$	3.02682	0.138155
$481$	−2.02094	−0.0921469
$482$	−11.3759	−0.518157
$483$	5.42758	0.246963
$484$	8.33318	0.378781
$485$	13.4381	0.610193
$486$	2.27120	0.103024
$487$	18.9522	0.858805	0.429403	−	0.903113i	$-0.358724\pi$
$487$	18.9522	0.858805	0.429403	+	0.903113i	$0.358724\pi$
$488$	−10.1382	−0.458935
$489$	10.1511	0.459046
$490$	−6.52104	−0.294591
$491$	−3.71192	−0.167517	−0.0837584	−	0.996486i	$-0.526692\pi$
$491$	−3.71192	−0.167517	−0.0837584	+	0.996486i	$0.526692\pi$
$492$	16.2709	0.733549
$493$	−36.7363	−1.65452
$494$	0.153822	0.00692079
$495$	1.74772	0.0785541
$496$	−0.703607	−0.0315929
$497$	36.3072	1.62860
$498$	26.6662	1.19494
$499$	24.6375	1.10293	0.551463	−	0.834199i	$-0.314070\pi$
$499$	24.6375	1.10293	0.551463	+	0.834199i	$0.314070\pi$
$500$	−12.1710	−0.544303
$501$	−21.1985	−0.947079
$502$	−2.44885	−0.109298
$503$	30.9946	1.38198	0.690989	−	0.722865i	$-0.257175\pi$
$503$	30.9946	1.38198	0.690989	+	0.722865i	$0.257175\pi$
$504$	0.712753	0.0317485
$505$	0.355733	0.0158299
$506$	−4.39695	−0.195468
$507$	20.0788	0.891731
$508$	2.58572	0.114723
$509$	17.7127	0.785102	0.392551	−	0.919730i	$-0.371593\pi$
$509$	17.7127	0.785102	0.392551	+	0.919730i	$0.371593\pi$
$510$	23.4988	1.04054
$511$	−21.0350	−0.930536
$512$	−1.00000	−0.0441942
$513$	0.842888	0.0372144
$514$	3.65200	0.161083
$515$	23.0622	1.01624
$516$	4.84484	0.213282
$517$	−3.53638	−0.155530
$518$	−6.71411	−0.295001
$519$	−10.6874	−0.469126
$520$	1.77810	0.0779748
$521$	5.24569	0.229818	0.114909	−	0.993376i	$-0.463342\pi$
$521$	5.24569	0.229818	0.114909	+	0.993376i	$0.463342\pi$
$522$	−1.03626	−0.0453561
$523$	2.84106	0.124231	0.0621154	−	0.998069i	$-0.480215\pi$
$523$	2.84106	0.124231	0.0621154	+	0.998069i	$0.480215\pi$
$524$	1.00000	0.0436852
$525$	9.25747	0.404029
$526$	21.2624	0.927086
$527$	−5.46246	−0.237949
$528$	7.33251	0.319106
$529$	1.00000	0.0434783
$530$	−18.9065	−0.821244
$531$	0.221535	0.00961381
$532$	0.511039	0.0221563
$533$	9.55830	0.414016
$534$	−28.0854	−1.21538
$535$	10.3408	0.447070
$536$	−3.65418	−0.157837
$537$	−9.50810	−0.410305
$538$	−9.57027	−0.412604
$539$	−15.7973	−0.680438
$540$	9.74332	0.419286
$541$	−7.79251	−0.335026	−0.167513	−	0.985870i	$-0.553574\pi$
$541$	−7.79251	−0.335026	−0.167513	+	0.985870i	$0.553574\pi$
$542$	7.16616	0.307813
$543$	17.4692	0.749674
$544$	−7.76351	−0.332858
$545$	−6.88717	−0.295014
$546$	−5.31712	−0.227552
$547$	−13.7484	−0.587837	−0.293919	−	0.955830i	$-0.594959\pi$
$547$	−13.7484	−0.587837	−0.293919	+	0.955830i	$0.594959\pi$
$548$	12.0340	0.514067
$549$	−2.22021	−0.0947564
$550$	−7.49960	−0.319784
$551$	−0.742995	−0.0316526
$552$	−1.66763	−0.0709792
$553$	33.6663	1.43164
$554$	−11.4433	−0.486180
$555$	−6.24410	−0.265047
$556$	11.0566	0.468905
$557$	17.0072	0.720619	0.360309	−	0.932833i	$-0.382671\pi$
$557$	17.0072	0.720619	0.360309	+	0.932833i	$0.382671\pi$
$558$	−0.154086	−0.00652299
$559$	2.84609	0.120377
$560$	5.90732	0.249630
$561$	56.9260	2.40342
$562$	20.9651	0.884360
$563$	26.7751	1.12843	0.564217	−	0.825626i	$-0.309178\pi$
$563$	26.7751	1.12843	0.564217	+	0.825626i	$0.309178\pi$
$564$	−1.34125	−0.0564766
$565$	−18.0104	−0.757701
$566$	−4.70143	−0.197616
$567$	−26.9976	−1.13379
$568$	−11.1555	−0.468073
$569$	−18.9969	−0.796390	−0.398195	−	0.917301i	$-0.630363\pi$
$569$	−18.9969	−0.796390	−0.398195	+	0.917301i	$0.630363\pi$
$570$	0.475265	0.0199066
$571$	42.7651	1.78967	0.894833	−	0.446402i	$-0.147295\pi$
$571$	42.7651	1.78967	0.894833	+	0.446402i	$0.147295\pi$
$572$	4.30747	0.180104
$573$	7.36435	0.307650
$574$	31.7553	1.32544
$575$	1.70564	0.0711299
$576$	−0.218995	−0.00912479
$577$	22.0943	0.919799	0.459899	−	0.887971i	$-0.347885\pi$
$577$	22.0943	0.919799	0.459899	+	0.887971i	$0.347885\pi$
$578$	−43.2721	−1.79988
$579$	−19.5270	−0.811516
$580$	−8.58860	−0.356622
$581$	52.0433	2.15912
$582$	12.3468	0.511790
$583$	−45.8011	−1.89689
$584$	6.46306	0.267443
$585$	0.389395	0.0160995
$586$	6.41999	0.265207
$587$	8.08715	0.333792	0.166896	−	0.985974i	$-0.446626\pi$
$587$	8.08715	0.333792	0.166896	+	0.985974i	$0.446626\pi$
$588$	−5.99145	−0.247083
$589$	−0.110479	−0.00455220
$590$	1.83609	0.0755907
$591$	−30.1432	−1.23992
$592$	2.06292	0.0847856
$593$	−38.9592	−1.59986	−0.799932	−	0.600091i	$-0.795131\pi$
$593$	−38.9592	−1.59986	−0.799932	+	0.600091i	$0.795131\pi$
$594$	23.6033	0.968455
$595$	45.8616	1.88014
$596$	−15.8726	−0.650167
$597$	23.2887	0.953141
$598$	−0.979648	−0.0400608
$599$	3.25386	0.132949	0.0664745	−	0.997788i	$-0.478825\pi$
$599$	3.25386	0.132949	0.0664745	+	0.997788i	$0.478825\pi$
$600$	−2.84438	−0.116121
$601$	1.45684	0.0594258	0.0297129	−	0.999558i	$-0.490541\pi$
$601$	1.45684	0.0594258	0.0297129	+	0.999558i	$0.490541\pi$
$602$	9.45549	0.385377
$603$	−0.800247	−0.0325886
$604$	−3.42324	−0.139290
$605$	15.1250	0.614920
$606$	0.326843	0.0132771
$607$	−12.3441	−0.501031	−0.250515	−	0.968113i	$-0.580600\pi$
$607$	−12.3441	−0.501031	−0.250515	+	0.968113i	$0.580600\pi$
$608$	−0.157018	−0.00636791
$609$	25.6828	1.04072
$610$	−18.4012	−0.745044
$611$	−0.787912	−0.0318755
$612$	−1.70017	−0.0687253
$613$	11.4284	0.461589	0.230794	−	0.973003i	$-0.425868\pi$
$613$	11.4284	0.461589	0.230794	+	0.973003i	$0.425868\pi$
$614$	−11.0802	−0.447160
$615$	29.5323	1.19086
$616$	14.3106	0.576589
$617$	−17.7108	−0.713012	−0.356506	−	0.934293i	$-0.616032\pi$
$617$	−17.7108	−0.713012	−0.356506	+	0.934293i	$0.616032\pi$
$618$	21.1892	0.852356
$619$	13.9431	0.560420	0.280210	−	0.959939i	$-0.409596\pi$
$619$	13.9431	0.560420	0.280210	+	0.959939i	$0.409596\pi$
$620$	−1.27707	−0.0512885
$621$	−5.36811	−0.215415
$622$	5.75885	0.230909
$623$	−54.8132	−2.19605
$624$	1.63370	0.0654002
$625$	−13.5626	−0.542505
$626$	−5.85743	−0.234110
$627$	1.15133	0.0459799
$628$	16.2104	0.646864
$629$	16.0155	0.638581
$630$	1.29367	0.0515412
$631$	11.5886	0.461334	0.230667	−	0.973033i	$-0.425909\pi$
$631$	11.5886	0.461334	0.230667	+	0.973033i	$0.425909\pi$
$632$	−10.3440	−0.411464
$633$	−6.39452	−0.254160
$634$	23.5665	0.935945
$635$	4.69319	0.186244
$636$	−17.3710	−0.688806
$637$	−3.51967	−0.139454
$638$	−20.8060	−0.823717
$639$	−2.44299	−0.0966431
$640$	−1.81504	−0.0717457
$641$	−29.5993	−1.16910	−0.584552	−	0.811357i	$-0.698730\pi$
$641$	−29.5993	−1.16910	−0.584552	+	0.811357i	$0.698730\pi$
$642$	9.50096	0.374973
$643$	−17.2703	−0.681074	−0.340537	−	0.940231i	$-0.610609\pi$
$643$	−17.2703	−0.681074	−0.340537	+	0.940231i	$0.610609\pi$
$644$	−3.25466	−0.128251
$645$	8.79357	0.346247
$646$	−1.21901	−0.0479613
$647$	44.9777	1.76825	0.884127	−	0.467246i	$-0.154754\pi$
$647$	44.9777	1.76825	0.884127	+	0.467246i	$0.154754\pi$
$648$	8.29506	0.325861
$649$	4.44796	0.174598
$650$	−1.67092	−0.0655390
$651$	3.81888	0.149674
$652$	−6.08710	−0.238389
$653$	8.00491	0.313256	0.156628	−	0.987658i	$-0.449938\pi$
$653$	8.00491	0.313256	0.156628	+	0.987658i	$0.449938\pi$
$654$	−6.32784	−0.247438
$655$	1.81504	0.0709194
$656$	−9.75687	−0.380942
$657$	1.41538	0.0552191
$658$	−2.61766	−0.102047
$659$	−35.7361	−1.39208	−0.696040	−	0.718003i	$-0.745056\pi$
$659$	−35.7361	−1.39208	−0.696040	+	0.718003i	$0.745056\pi$
$660$	13.3088	0.518044
$661$	4.67094	0.181678	0.0908392	−	0.995866i	$-0.471045\pi$
$661$	4.67094	0.181678	0.0908392	+	0.995866i	$0.471045\pi$
$662$	24.0411	0.934383
$663$	12.6832	0.492575
$664$	−15.9904	−0.620549
$665$	0.927555	0.0359690
$666$	0.451770	0.0175057
$667$	4.73191	0.183220
$668$	12.7117	0.491831
$669$	−34.8126	−1.34593
$670$	−6.63248	−0.256235
$671$	−44.5772	−1.72088
$672$	5.42758	0.209373
$673$	−7.16965	−0.276370	−0.138185	−	0.990406i	$-0.544127\pi$
$673$	−7.16965	−0.276370	−0.138185	+	0.990406i	$0.544127\pi$
$674$	−23.0216	−0.886760
$675$	−9.15604	−0.352416
$676$	−12.0403	−0.463088
$677$	−9.37827	−0.360436	−0.180218	−	0.983627i	$-0.557680\pi$
$677$	−9.37827	−0.360436	−0.180218	+	0.983627i	$0.557680\pi$
$678$	−16.5477	−0.635510
$679$	24.0967	0.924746
$680$	−14.0911	−0.540368
$681$	−20.1892	−0.773651
$682$	−3.09373	−0.118465
$683$	−15.0110	−0.574381	−0.287190	−	0.957873i	$-0.592721\pi$
$683$	−15.0110	−0.574381	−0.287190	+	0.957873i	$0.592721\pi$
$684$	−0.0343861	−0.00131479
$685$	21.8422	0.834546
$686$	11.0893	0.423392
$687$	−28.5546	−1.08942
$688$	−2.90522	−0.110760
$689$	−10.2046	−0.388763
$690$	−3.02682	−0.115229
$691$	22.1702	0.843393	0.421696	−	0.906737i	$-0.361435\pi$
$691$	22.1702	0.843393	0.421696	+	0.906737i	$0.361435\pi$
$692$	6.40873	0.243623
$693$	3.13394	0.119049
$694$	17.7692	0.674511
$695$	20.0682	0.761230
$696$	−7.89110	−0.299111
$697$	−75.7476	−2.86914
$698$	−28.2237	−1.06828
$699$	26.3130	0.995250
$700$	−5.55126	−0.209818
$701$	14.6300	0.552569	0.276285	−	0.961076i	$-0.410897\pi$
$701$	14.6300	0.552569	0.276285	+	0.961076i	$0.410897\pi$
$702$	5.25886	0.198483
$703$	0.323916	0.0122167
$704$	−4.39695	−0.165716
$705$	−2.43441	−0.0916853
$706$	−0.429232	−0.0161544
$707$	0.637887	0.0239902
$708$	1.68698	0.0634006
$709$	39.4916	1.48314	0.741569	−	0.670877i	$-0.234082\pi$
$709$	39.4916	1.48314	0.741569	+	0.670877i	$0.234082\pi$
$710$	−20.2476	−0.759879
$711$	−2.26529	−0.0849550
$712$	16.8415	0.631161
$713$	0.703607	0.0263503
$714$	42.1371	1.57694
$715$	7.81822	0.292385
$716$	5.70155	0.213077
$717$	43.5672	1.62705
$718$	−21.4739	−0.801398
$719$	19.5376	0.728630	0.364315	−	0.931276i	$-0.381303\pi$
$719$	19.5376	0.728630	0.364315	+	0.931276i	$0.381303\pi$
$720$	−0.397484	−0.0148134
$721$	41.3542	1.54011
$722$	18.9753	0.706189
$723$	−18.9708	−0.705531
$724$	−10.4754	−0.389316
$725$	8.07092	0.299747
$726$	13.8967	0.515755
$727$	−51.3987	−1.90627	−0.953136	−	0.302541i	$-0.902165\pi$
$727$	−51.3987	−1.90627	−0.953136	+	0.302541i	$0.902165\pi$
$728$	3.18842	0.118171
$729$	28.6727	1.06195
$730$	11.7307	0.434173
$731$	−22.5547	−0.834216
$732$	−16.9068	−0.624894
$733$	16.9372	0.625588	0.312794	−	0.949821i	$-0.398735\pi$
$733$	16.9372	0.625588	0.312794	+	0.949821i	$0.398735\pi$
$734$	−10.3271	−0.381179
$735$	−10.8747	−0.401120
$736$	1.00000	0.0368605
$737$	−16.0673	−0.591845
$738$	−2.13670	−0.0786532
$739$	12.0533	0.443387	0.221693	−	0.975116i	$-0.428842\pi$
$739$	12.0533	0.443387	0.221693	+	0.975116i	$0.428842\pi$
$740$	3.74429	0.137643
$741$	0.256519	0.00942347
$742$	−33.9023	−1.24459
$743$	4.01872	0.147433	0.0737163	−	0.997279i	$-0.476514\pi$
$743$	4.01872	0.147433	0.0737163	+	0.997279i	$0.476514\pi$
$744$	−1.17336	−0.0430174
$745$	−28.8094	−1.05549
$746$	−14.2230	−0.520741
$747$	−3.50182	−0.128125
$748$	−34.1358	−1.24813
$749$	18.5427	0.677534
$750$	−20.2968	−0.741133
$751$	14.0463	0.512557	0.256279	−	0.966603i	$-0.417504\pi$
$751$	14.0463	0.512557	0.256279	+	0.966603i	$0.417504\pi$
$752$	0.804280	0.0293291
$753$	−4.08379	−0.148822
$754$	−4.63561	−0.168819
$755$	−6.21331	−0.226125
$756$	17.4713	0.635427
$757$	−44.6733	−1.62368	−0.811839	−	0.583881i	$-0.801533\pi$
$757$	−44.6733	−1.62368	−0.811839	+	0.583881i	$0.801533\pi$
$758$	−19.0501	−0.691932
$759$	−7.33251	−0.266153
$760$	−0.284993	−0.0103378
$761$	36.3455	1.31752	0.658762	−	0.752352i	$-0.271081\pi$
$761$	36.3455	1.31752	0.658762	+	0.752352i	$0.271081\pi$
$762$	4.31204	0.156209
$763$	−12.3498	−0.447093
$764$	−4.41605	−0.159767
$765$	−3.08587	−0.111570
$766$	1.33370	0.0481884
$767$	0.991012	0.0357834
$768$	−1.66763	−0.0601756
$769$	−30.7304	−1.10817	−0.554083	−	0.832461i	$-0.686931\pi$
$769$	−30.7304	−1.10817	−0.554083	+	0.832461i	$0.686931\pi$
$770$	25.9742	0.936046
$771$	6.09021	0.219334
$772$	11.7094	0.421431
$773$	−16.9779	−0.610654	−0.305327	−	0.952248i	$-0.598766\pi$
$773$	−16.9779	−0.610654	−0.305327	+	0.952248i	$0.598766\pi$
$774$	−0.636228	−0.0228687
$775$	1.20010	0.0431088
$776$	−7.40376	−0.265779
$777$	−11.1967	−0.401678
$778$	−18.2779	−0.655294
$779$	−1.53200	−0.0548897
$780$	2.96522	0.106172
$781$	−49.0500	−1.75515
$782$	7.76351	0.277623
$783$	−25.4014	−0.907773
$784$	3.59278	0.128314
$785$	29.4224	1.05013
$786$	1.66763	0.0594826
$787$	−32.7956	−1.16904	−0.584518	−	0.811381i	$-0.698716\pi$
$787$	−32.7956	−1.16904	−0.584518	+	0.811381i	$0.698716\pi$
$788$	18.0754	0.643909
$789$	35.4580	1.26234
$790$	−18.7748	−0.667978
$791$	−32.2955	−1.14829
$792$	−0.962910	−0.0342155
$793$	−9.93187	−0.352691
$794$	−34.1518	−1.21200
$795$	−31.5291	−1.11822
$796$	−13.9651	−0.494979
$797$	4.32273	0.153119	0.0765594	−	0.997065i	$-0.475607\pi$
$797$	4.32273	0.153119	0.0765594	+	0.997065i	$0.475607\pi$
$798$	0.852226	0.0301685
$799$	6.24404	0.220898
$800$	1.70564	0.0603033
$801$	3.68820	0.130316
$802$	31.2834	1.10466
$803$	28.4178	1.00284
$804$	−6.09384	−0.214913
$805$	−5.90732	−0.208206
$806$	−0.689287	−0.0242791
$807$	−15.9597	−0.561809
$808$	−0.195992	−0.00689498
$809$	−28.1468	−0.989587	−0.494794	−	0.869010i	$-0.664756\pi$
$809$	−28.1468	−0.989587	−0.494794	+	0.869010i	$0.664756\pi$
$810$	15.0558	0.529008
$811$	−5.72826	−0.201147	−0.100573	−	0.994930i	$-0.532068\pi$
$811$	−5.72826	−0.201147	−0.100573	+	0.994930i	$0.532068\pi$
$812$	−15.4007	−0.540460
$813$	11.9505	0.419124
$814$	9.07057	0.317923
$815$	−11.0483	−0.387006
$816$	−12.9467	−0.453225
$817$	−0.456171	−0.0159594
$818$	9.33266	0.326309
$819$	0.698247	0.0243987
$820$	−17.7091	−0.618428
$821$	−34.9857	−1.22101	−0.610505	−	0.792012i	$-0.709034\pi$
$821$	−34.9857	−1.22101	−0.610505	+	0.792012i	$0.709034\pi$
$822$	20.0683	0.699962
$823$	−38.5382	−1.34336	−0.671678	−	0.740843i	$-0.734426\pi$
$823$	−38.5382	−1.34336	−0.671678	+	0.740843i	$0.734426\pi$
$824$	−12.7062	−0.442640
$825$	−12.5066	−0.435424
$826$	3.29241	0.114558
$827$	−13.4101	−0.466316	−0.233158	−	0.972439i	$-0.574906\pi$
$827$	−13.4101	−0.466316	−0.233158	+	0.972439i	$0.574906\pi$
$828$	0.218995	0.00761060
$829$	−12.1840	−0.423169	−0.211584	−	0.977360i	$-0.567862\pi$
$829$	−12.1840	−0.423169	−0.211584	+	0.977360i	$0.567862\pi$
$830$	−29.0232	−1.00741
$831$	−19.0833	−0.661992
$832$	−0.979648	−0.0339632
$833$	27.8926	0.966422
$834$	18.4384	0.638470
$835$	23.0723	0.798448
$836$	−0.690400	−0.0238780
$837$	−3.77704	−0.130554
$838$	−27.4922	−0.949702
$839$	−4.77082	−0.164707	−0.0823535	−	0.996603i	$-0.526244\pi$
$839$	−4.77082	−0.164707	−0.0823535	+	0.996603i	$0.526244\pi$
$840$	9.85126	0.339901
$841$	−6.60900	−0.227896
$842$	17.6167	0.607111
$843$	34.9622	1.20416
$844$	3.83449	0.131988
$845$	−21.8536	−0.751786
$846$	0.176133	0.00605558
$847$	27.1216	0.931910
$848$	10.4166	0.357706
$849$	−7.84027	−0.269077
$850$	13.2417	0.454188
$851$	−2.06292	−0.0707161
$852$	−18.6032	−0.637336
$853$	37.0458	1.26843	0.634213	−	0.773159i	$-0.281324\pi$
$853$	37.0458	1.26843	0.634213	+	0.773159i	$0.281324\pi$
$854$	−32.9963	−1.12911
$855$	−0.0624121	−0.00213445
$856$	−5.69727	−0.194729
$857$	−50.5912	−1.72816	−0.864082	−	0.503351i	$-0.832100\pi$
$857$	−50.5912	−1.72816	−0.864082	+	0.503351i	$0.832100\pi$
$858$	7.18328	0.245233
$859$	53.0704	1.81074	0.905369	−	0.424627i	$-0.139595\pi$
$859$	53.0704	1.81074	0.905369	+	0.424627i	$0.139595\pi$
$860$	−5.27308	−0.179811
$861$	52.9562	1.80474
$862$	−6.41627	−0.218539
$863$	9.60382	0.326918	0.163459	−	0.986550i	$-0.447735\pi$
$863$	9.60382	0.326918	0.163459	+	0.986550i	$0.447735\pi$
$864$	−5.36811	−0.182627
$865$	11.6321	0.395503
$866$	−17.4669	−0.593548
$867$	−72.1621	−2.45075
$868$	−2.29000	−0.0777276
$869$	−45.4822	−1.54288
$870$	−14.3227	−0.485583
$871$	−3.57981	−0.121297
$872$	3.79450	0.128498
$873$	−1.62138	−0.0548756
$874$	0.157018	0.00531121
$875$	−39.6124	−1.33914
$876$	10.7780	0.364156
$877$	−28.5359	−0.963589	−0.481794	−	0.876284i	$-0.660015\pi$
$877$	−28.5359	−0.963589	−0.481794	+	0.876284i	$0.660015\pi$
$878$	−6.23618	−0.210461
$879$	10.7062	0.361111
$880$	−7.98063	−0.269027
$881$	−41.5124	−1.39859	−0.699294	−	0.714834i	$-0.746502\pi$
$881$	−41.5124	−1.39859	−0.699294	+	0.714834i	$0.746502\pi$
$882$	0.786801	0.0264930
$883$	20.8370	0.701220	0.350610	−	0.936522i	$-0.385974\pi$
$883$	20.8370	0.701220	0.350610	+	0.936522i	$0.385974\pi$
$884$	−7.60551	−0.255801
$885$	3.06193	0.102926
$886$	8.20613	0.275690
$887$	29.0471	0.975307	0.487654	−	0.873037i	$-0.337853\pi$
$887$	29.0471	0.975307	0.487654	+	0.873037i	$0.337853\pi$
$888$	3.44020	0.115446
$889$	8.41564	0.282252
$890$	30.5679	1.02464
$891$	36.4730	1.22189
$892$	20.8755	0.698962
$893$	0.126286	0.00422601
$894$	−26.4697	−0.885279
$895$	10.3485	0.345913
$896$	−3.25466	−0.108730
$897$	−1.63370	−0.0545475
$898$	−13.8150	−0.461012
$899$	3.32941	0.111042
$900$	0.373526	0.0124509
$901$	80.8691	2.69414
$902$	−42.9005	−1.42843
$903$	15.7683	0.524736
$904$	9.92285	0.330029
$905$	−19.0133	−0.632023
$906$	−5.70871	−0.189659
$907$	17.2121	0.571518	0.285759	−	0.958302i	$-0.407754\pi$
$907$	17.2121	0.571518	0.285759	+	0.958302i	$0.407754\pi$
$908$	12.1065	0.401767
$909$	−0.0429213	−0.00142361
$910$	5.78710	0.191841
$911$	−32.1285	−1.06446	−0.532232	−	0.846598i	$-0.678647\pi$
$911$	−32.1285	−1.06446	−0.532232	+	0.846598i	$0.678647\pi$
$912$	−0.261848	−0.00867066
$913$	−70.3091	−2.32689
$914$	−2.82103	−0.0933114
$915$	−30.6865	−1.01446
$916$	17.1228	0.565753
$917$	3.25466	0.107478
$918$	−41.6754	−1.37549
$919$	−13.4404	−0.443359	−0.221680	−	0.975120i	$-0.571154\pi$
$919$	−13.4404	−0.443359	−0.221680	+	0.975120i	$0.571154\pi$
$920$	1.81504	0.0598400
$921$	−18.4777	−0.608861
$922$	−26.4695	−0.871725
$923$	−10.9284	−0.359714
$924$	23.8648	0.785094
$925$	−3.51860	−0.115691
$926$	−23.1728	−0.761507
$927$	−2.78258	−0.0913920
$928$	4.73191	0.155333
$929$	57.5646	1.88863	0.944317	−	0.329036i	$-0.106724\pi$
$929$	57.5646	1.88863	0.944317	+	0.329036i	$0.106724\pi$
$930$	−2.12969	−0.0698353
$931$	0.564131	0.0184887
$932$	−15.7787	−0.516847
$933$	9.60366	0.314410
$934$	−26.7843	−0.876408
$935$	−61.9578	−2.02624
$936$	−0.214538	−0.00701239
$937$	−22.8005	−0.744859	−0.372430	−	0.928060i	$-0.621475\pi$
$937$	−22.8005	−0.744859	−0.372430	+	0.928060i	$0.621475\pi$
$938$	−11.8931	−0.388323
$939$	−9.76806	−0.318769
$940$	1.45980	0.0476134
$941$	14.9731	0.488110	0.244055	−	0.969761i	$-0.421522\pi$
$941$	14.9731	0.488110	0.244055	+	0.969761i	$0.421522\pi$
$942$	27.0330	0.880781
$943$	9.75687	0.317727
$944$	−1.01160	−0.0329248
$945$	31.7112	1.03156
$946$	−12.7741	−0.415322
$947$	14.8837	0.483655	0.241828	−	0.970319i	$-0.422253\pi$
$947$	14.8837	0.483655	0.241828	+	0.970319i	$0.422253\pi$
$948$	−17.2501	−0.560256
$949$	6.33153	0.205530
$950$	0.267815	0.00868907
$951$	39.3003	1.27440
$952$	−25.2676	−0.818926
$953$	52.2306	1.69192	0.845958	−	0.533249i	$-0.179029\pi$
$953$	52.2306	1.69192	0.845958	+	0.533249i	$0.179029\pi$
$954$	2.28117	0.0738557
$955$	−8.01529	−0.259369
$956$	−26.1251	−0.844947
$957$	−34.6968	−1.12159
$958$	−42.7267	−1.38044
$959$	39.1665	1.26475
$960$	−3.02682	−0.0976902
$961$	−30.5049	−0.984030
$962$	2.02094	0.0651577
$963$	−1.24767	−0.0402057
$964$	11.3759	0.366392
$965$	21.2531	0.684160
$966$	−5.42758	−0.174629
$967$	−40.5882	−1.30523	−0.652614	−	0.757691i	$-0.726328\pi$
$967$	−40.5882	−1.30523	−0.652614	+	0.757691i	$0.726328\pi$
$968$	−8.33318	−0.267838
$969$	−2.03286	−0.0653050
$970$	−13.4381	−0.431472
$971$	−21.0380	−0.675141	−0.337571	−	0.941300i	$-0.609605\pi$
$971$	−21.0380	−0.675141	−0.337571	+	0.941300i	$0.609605\pi$
$972$	−2.27120	−0.0728487
$973$	35.9855	1.15364
$974$	−18.9522	−0.607267
$975$	−2.78649	−0.0892391
$976$	10.1382	0.324516
$977$	−6.36560	−0.203654	−0.101827	−	0.994802i	$-0.532469\pi$
$977$	−6.36560	−0.203654	−0.101827	+	0.994802i	$0.532469\pi$
$978$	−10.1511	−0.324595
$979$	74.0512	2.36669
$980$	6.52104	0.208307
$981$	0.830976	0.0265310
$982$	3.71192	0.118452
$983$	−10.8410	−0.345773	−0.172886	−	0.984942i	$-0.555309\pi$
$983$	−10.8410	−0.345773	−0.172886	+	0.984942i	$0.555309\pi$
$984$	−16.2709	−0.518697
$985$	32.8075	1.04533
$986$	36.7363	1.16992
$987$	−4.36529	−0.138949
$988$	−0.153822	−0.00489374
$989$	2.90522	0.0923806
$990$	−1.74772	−0.0555461
$991$	4.53732	0.144133	0.0720664	−	0.997400i	$-0.477041\pi$
$991$	4.53732	0.144133	0.0720664	+	0.997400i	$0.477041\pi$
$992$	0.703607	0.0223395
$993$	40.0917	1.27227
$994$	−36.3072	−1.15159
$995$	−25.3472	−0.803559
$996$	−26.6662	−0.844951
$997$	37.7142	1.19442	0.597211	−	0.802084i	$-0.296276\pi$
$997$	37.7142	1.19442	0.597211	+	0.802084i	$0.296276\pi$
$998$	−24.6375	−0.779887
$999$	11.0740	0.350366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.10	✓	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.66763 q^{3} +1.00000 q^{4} +1.81504 q^{5} +1.66763 q^{6} +3.25466 q^{7} -1.00000 q^{8} -0.218995 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.66763 q^{3} +1.00000 q^{4} +1.81504 q^{5} +1.66763 q^{6} +3.25466 q^{7} -1.00000 q^{8} -0.218995 q^{9} -1.81504 q^{10} -4.39695 q^{11} -1.66763 q^{12} -0.979648 q^{13} -3.25466 q^{14} -3.02682 q^{15} +1.00000 q^{16} +7.76351 q^{17} +0.218995 q^{18} +0.157018 q^{19} +1.81504 q^{20} -5.42758 q^{21} +4.39695 q^{22} -1.00000 q^{23} +1.66763 q^{24} -1.70564 q^{25} +0.979648 q^{26} +5.36811 q^{27} +3.25466 q^{28} -4.73191 q^{29} +3.02682 q^{30} -0.703607 q^{31} -1.00000 q^{32} +7.33251 q^{33} -7.76351 q^{34} +5.90732 q^{35} -0.218995 q^{36} +2.06292 q^{37} -0.157018 q^{38} +1.63370 q^{39} -1.81504 q^{40} -9.75687 q^{41} +5.42758 q^{42} -2.90522 q^{43} -4.39695 q^{44} -0.397484 q^{45} +1.00000 q^{46} +0.804280 q^{47} -1.66763 q^{48} +3.59278 q^{49} +1.70564 q^{50} -12.9467 q^{51} -0.979648 q^{52} +10.4166 q^{53} -5.36811 q^{54} -7.98063 q^{55} -3.25466 q^{56} -0.261848 q^{57} +4.73191 q^{58} -1.01160 q^{59} -3.02682 q^{60} +10.1382 q^{61} +0.703607 q^{62} -0.712753 q^{63} +1.00000 q^{64} -1.77810 q^{65} -7.33251 q^{66} +3.65418 q^{67} +7.76351 q^{68} +1.66763 q^{69} -5.90732 q^{70} +11.1555 q^{71} +0.218995 q^{72} -6.46306 q^{73} -2.06292 q^{74} +2.84438 q^{75} +0.157018 q^{76} -14.3106 q^{77} -1.63370 q^{78} +10.3440 q^{79} +1.81504 q^{80} -8.29506 q^{81} +9.75687 q^{82} +15.9904 q^{83} -5.42758 q^{84} +14.0911 q^{85} +2.90522 q^{86} +7.89110 q^{87} +4.39695 q^{88} -16.8415 q^{89} +0.397484 q^{90} -3.18842 q^{91} -1.00000 q^{92} +1.17336 q^{93} -0.804280 q^{94} +0.284993 q^{95} +1.66763 q^{96} +7.40376 q^{97} -3.59278 q^{98} +0.962910 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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