LMFDB - Embedded newform 6022.2.a.c.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0859120972$
Analytic rank:	$0$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.37453 q^{3} +1.00000 q^{4} +3.86248 q^{5} +2.37453 q^{6} -2.00027 q^{7} -1.00000 q^{8} +2.63837 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.37453 q^{3} +1.00000 q^{4} +3.86248 q^{5} +2.37453 q^{6} -2.00027 q^{7} -1.00000 q^{8} +2.63837 q^{9} -3.86248 q^{10} +0.752089 q^{11} -2.37453 q^{12} +5.18482 q^{13} +2.00027 q^{14} -9.17156 q^{15} +1.00000 q^{16} -1.46434 q^{17} -2.63837 q^{18} -2.59131 q^{19} +3.86248 q^{20} +4.74969 q^{21} -0.752089 q^{22} -1.59637 q^{23} +2.37453 q^{24} +9.91877 q^{25} -5.18482 q^{26} +0.858691 q^{27} -2.00027 q^{28} +9.36896 q^{29} +9.17156 q^{30} -2.62697 q^{31} -1.00000 q^{32} -1.78586 q^{33} +1.46434 q^{34} -7.72600 q^{35} +2.63837 q^{36} -1.57217 q^{37} +2.59131 q^{38} -12.3115 q^{39} -3.86248 q^{40} -7.98472 q^{41} -4.74969 q^{42} +0.142859 q^{43} +0.752089 q^{44} +10.1907 q^{45} +1.59637 q^{46} +7.09324 q^{47} -2.37453 q^{48} -2.99893 q^{49} -9.91877 q^{50} +3.47711 q^{51} +5.18482 q^{52} +3.05328 q^{53} -0.858691 q^{54} +2.90493 q^{55} +2.00027 q^{56} +6.15314 q^{57} -9.36896 q^{58} -5.18400 q^{59} -9.17156 q^{60} +8.93672 q^{61} +2.62697 q^{62} -5.27745 q^{63} +1.00000 q^{64} +20.0263 q^{65} +1.78586 q^{66} +1.19150 q^{67} -1.46434 q^{68} +3.79062 q^{69} +7.72600 q^{70} +7.64407 q^{71} -2.63837 q^{72} +11.9376 q^{73} +1.57217 q^{74} -23.5524 q^{75} -2.59131 q^{76} -1.50438 q^{77} +12.3115 q^{78} +2.70419 q^{79} +3.86248 q^{80} -9.95411 q^{81} +7.98472 q^{82} -10.6198 q^{83} +4.74969 q^{84} -5.65598 q^{85} -0.142859 q^{86} -22.2468 q^{87} -0.752089 q^{88} +1.08656 q^{89} -10.1907 q^{90} -10.3710 q^{91} -1.59637 q^{92} +6.23782 q^{93} -7.09324 q^{94} -10.0089 q^{95} +2.37453 q^{96} +1.69040 q^{97} +2.99893 q^{98} +1.98429 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) $ 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.37453	−1.37093	−0.685467	−	0.728104i	$-0.740402\pi$
$3$	−2.37453	−1.37093	−0.685467	+	0.728104i	$0.740402\pi$
$4$	1.00000	0.500000
$5$	3.86248	1.72735	0.863677	−	0.504045i	$-0.168156\pi$
$5$	3.86248	1.72735	0.863677	+	0.504045i	$0.168156\pi$
$6$	2.37453	0.969396
$7$	−2.00027	−0.756030	−0.378015	−	0.925799i	$-0.623393\pi$
$7$	−2.00027	−0.756030	−0.378015	+	0.925799i	$0.623393\pi$
$8$	−1.00000	−0.353553
$9$	2.63837	0.879458
$10$	−3.86248	−1.22142
$11$	0.752089	0.226763	0.113382	−	0.993552i	$-0.463832\pi$
$11$	0.752089	0.226763	0.113382	+	0.993552i	$0.463832\pi$
$12$	−2.37453	−0.685467
$13$	5.18482	1.43801	0.719005	−	0.695005i	$-0.244598\pi$
$13$	5.18482	1.43801	0.719005	+	0.695005i	$0.244598\pi$
$14$	2.00027	0.534594
$15$	−9.17156	−2.36809
$16$	1.00000	0.250000
$17$	−1.46434	−0.355154	−0.177577	−	0.984107i	$-0.556826\pi$
$17$	−1.46434	−0.355154	−0.177577	+	0.984107i	$0.556826\pi$
$18$	−2.63837	−0.621871
$19$	−2.59131	−0.594488	−0.297244	−	0.954802i	$-0.596068\pi$
$19$	−2.59131	−0.594488	−0.297244	+	0.954802i	$0.596068\pi$
$20$	3.86248	0.863677
$21$	4.74969	1.03647
$22$	−0.752089	−0.160346
$23$	−1.59637	−0.332866	−0.166433	−	0.986053i	$-0.553225\pi$
$23$	−1.59637	−0.332866	−0.166433	+	0.986053i	$0.553225\pi$
$24$	2.37453	0.484698
$25$	9.91877	1.98375
$26$	−5.18482	−1.01683
$27$	0.858691	0.165255
$28$	−2.00027	−0.378015
$29$	9.36896	1.73977	0.869886	−	0.493253i	$-0.164192\pi$
$29$	9.36896	1.73977	0.869886	+	0.493253i	$0.164192\pi$
$30$	9.17156	1.67449
$31$	−2.62697	−0.471818	−0.235909	−	0.971775i	$-0.575807\pi$
$31$	−2.62697	−0.471818	−0.235909	+	0.971775i	$0.575807\pi$
$32$	−1.00000	−0.176777
$33$	−1.78586	−0.310877
$34$	1.46434	0.251132
$35$	−7.72600	−1.30593
$36$	2.63837	0.439729
$37$	−1.57217	−0.258464	−0.129232	−	0.991614i	$-0.541251\pi$
$37$	−1.57217	−0.258464	−0.129232	+	0.991614i	$0.541251\pi$
$38$	2.59131	0.420367
$39$	−12.3115	−1.97141
$40$	−3.86248	−0.610712
$41$	−7.98472	−1.24700	−0.623502	−	0.781822i	$-0.714291\pi$
$41$	−7.98472	−1.24700	−0.623502	+	0.781822i	$0.714291\pi$
$42$	−4.74969	−0.732893
$43$	0.142859	0.0217858	0.0108929	−	0.999941i	$-0.496533\pi$
$43$	0.142859	0.0217858	0.0108929	+	0.999941i	$0.496533\pi$
$44$	0.752089	0.113382
$45$	10.1907	1.51914
$46$	1.59637	0.235372
$47$	7.09324	1.03465	0.517327	−	0.855788i	$-0.326927\pi$
$47$	7.09324	1.03465	0.517327	+	0.855788i	$0.326927\pi$
$48$	−2.37453	−0.342733
$49$	−2.99893	−0.428419
$50$	−9.91877	−1.40273
$51$	3.47711	0.486893
$52$	5.18482	0.719005
$53$	3.05328	0.419401	0.209700	−	0.977766i	$-0.432751\pi$
$53$	3.05328	0.419401	0.209700	+	0.977766i	$0.432751\pi$
$54$	−0.858691	−0.116853
$55$	2.90493	0.391701
$56$	2.00027	0.267297
$57$	6.15314	0.815004
$58$	−9.36896	−1.23020
$59$	−5.18400	−0.674900	−0.337450	−	0.941344i	$-0.609564\pi$
$59$	−5.18400	−0.674900	−0.337450	+	0.941344i	$0.609564\pi$
$60$	−9.17156	−1.18404
$61$	8.93672	1.14423	0.572115	−	0.820174i	$-0.306123\pi$
$61$	8.93672	1.14423	0.572115	+	0.820174i	$0.306123\pi$
$62$	2.62697	0.333626
$63$	−5.27745	−0.664897
$64$	1.00000	0.125000
$65$	20.0263	2.48395
$66$	1.78586	0.219824
$67$	1.19150	0.145565	0.0727826	−	0.997348i	$-0.476812\pi$
$67$	1.19150	0.145565	0.0727826	+	0.997348i	$0.476812\pi$
$68$	−1.46434	−0.177577
$69$	3.79062	0.456337
$70$	7.72600	0.923433
$71$	7.64407	0.907184	0.453592	−	0.891209i	$-0.350142\pi$
$71$	7.64407	0.907184	0.453592	+	0.891209i	$0.350142\pi$
$72$	−2.63837	−0.310935
$73$	11.9376	1.39719	0.698595	−	0.715517i	$-0.253809\pi$
$73$	11.9376	1.39719	0.698595	+	0.715517i	$0.253809\pi$
$74$	1.57217	0.182762
$75$	−23.5524	−2.71959
$76$	−2.59131	−0.297244
$77$	−1.50438	−0.171440
$78$	12.3115	1.39400
$79$	2.70419	0.304245	0.152122	−	0.988362i	$-0.451389\pi$
$79$	2.70419	0.304245	0.152122	+	0.988362i	$0.451389\pi$
$80$	3.86248	0.431839
$81$	−9.95411	−1.10601
$82$	7.98472	0.881764
$83$	−10.6198	−1.16567	−0.582836	−	0.812590i	$-0.698057\pi$
$83$	−10.6198	−1.16567	−0.582836	+	0.812590i	$0.698057\pi$
$84$	4.74969	0.518233
$85$	−5.65598	−0.613477
$86$	−0.142859	−0.0154049
$87$	−22.2468	−2.38511
$88$	−0.752089	−0.0801730
$89$	1.08656	0.115176	0.0575878	−	0.998340i	$-0.481659\pi$
$89$	1.08656	0.115176	0.0575878	+	0.998340i	$0.481659\pi$
$90$	−10.1907	−1.07419
$91$	−10.3710	−1.08718
$92$	−1.59637	−0.166433
$93$	6.23782	0.646832
$94$	−7.09324	−0.731611
$95$	−10.0089	−1.02689
$96$	2.37453	0.242349
$97$	1.69040	0.171634	0.0858171	−	0.996311i	$-0.472650\pi$
$97$	1.69040	0.171634	0.0858171	+	0.996311i	$0.472650\pi$
$98$	2.99893	0.302938
$99$	1.98429	0.199429
$100$	9.91877	0.991877
$101$	1.23268	0.122656	0.0613279	−	0.998118i	$-0.480466\pi$
$101$	1.23268	0.122656	0.0613279	+	0.998118i	$0.480466\pi$
$102$	−3.47711	−0.344285
$103$	5.32416	0.524605	0.262302	−	0.964986i	$-0.415518\pi$
$103$	5.32416	0.524605	0.262302	+	0.964986i	$0.415518\pi$
$104$	−5.18482	−0.508413
$105$	18.3456	1.79035
$106$	−3.05328	−0.296561
$107$	11.7003	1.13111	0.565557	−	0.824709i	$-0.308661\pi$
$107$	11.7003	1.13111	0.565557	+	0.824709i	$0.308661\pi$
$108$	0.858691	0.0826276
$109$	−5.38580	−0.515866	−0.257933	−	0.966163i	$-0.583041\pi$
$109$	−5.38580	−0.515866	−0.257933	+	0.966163i	$0.583041\pi$
$110$	−2.90493	−0.276974
$111$	3.73317	0.354337
$112$	−2.00027	−0.189008
$113$	2.26299	0.212884	0.106442	−	0.994319i	$-0.466054\pi$
$113$	2.26299	0.212884	0.106442	+	0.994319i	$0.466054\pi$
$114$	−6.15314	−0.576295
$115$	−6.16595	−0.574977
$116$	9.36896	0.869886
$117$	13.6795	1.26467
$118$	5.18400	0.477226
$119$	2.92907	0.268507
$120$	9.17156	0.837245
$121$	−10.4344	−0.948578
$122$	−8.93672	−0.809092
$123$	18.9599	1.70956
$124$	−2.62697	−0.235909
$125$	18.9986	1.69929
$126$	5.27745	0.470153
$127$	5.73104	0.508547	0.254274	−	0.967132i	$-0.418164\pi$
$127$	5.73104	0.508547	0.254274	+	0.967132i	$0.418164\pi$
$128$	−1.00000	−0.0883883
$129$	−0.339222	−0.0298669
$130$	−20.0263	−1.75642
$131$	15.2828	1.33526	0.667632	−	0.744492i	$-0.267308\pi$
$131$	15.2828	1.33526	0.667632	+	0.744492i	$0.267308\pi$
$132$	−1.78586	−0.155439
$133$	5.18332	0.449451
$134$	−1.19150	−0.102930
$135$	3.31668	0.285454
$136$	1.46434	0.125566
$137$	4.17442	0.356645	0.178323	−	0.983972i	$-0.442933\pi$
$137$	4.17442	0.356645	0.178323	+	0.983972i	$0.442933\pi$
$138$	−3.79062	−0.322679
$139$	−8.26684	−0.701185	−0.350592	−	0.936528i	$-0.614020\pi$
$139$	−8.26684	−0.701185	−0.350592	+	0.936528i	$0.614020\pi$
$140$	−7.72600	−0.652966
$141$	−16.8431	−1.41844
$142$	−7.64407	−0.641476
$143$	3.89944	0.326088
$144$	2.63837	0.219864
$145$	36.1874	3.00520
$146$	−11.9376	−0.987962
$147$	7.12104	0.587333
$148$	−1.57217	−0.129232
$149$	−4.51289	−0.369710	−0.184855	−	0.982766i	$-0.559182\pi$
$149$	−4.51289	−0.369710	−0.184855	+	0.982766i	$0.559182\pi$
$150$	23.5524	1.92304
$151$	−10.0097	−0.814578	−0.407289	−	0.913299i	$-0.633526\pi$
$151$	−10.0097	−0.814578	−0.407289	+	0.913299i	$0.633526\pi$
$152$	2.59131	0.210183
$153$	−3.86347	−0.312343
$154$	1.50438	0.121226
$155$	−10.1466	−0.814998
$156$	−12.3115	−0.985707
$157$	19.1340	1.52706	0.763530	−	0.645772i	$-0.223464\pi$
$157$	19.1340	1.52706	0.763530	+	0.645772i	$0.223464\pi$
$158$	−2.70419	−0.215133
$159$	−7.25010	−0.574970
$160$	−3.86248	−0.305356
$161$	3.19316	0.251657
$162$	9.95411	0.782068
$163$	1.36951	0.107268	0.0536342	−	0.998561i	$-0.482920\pi$
$163$	1.36951	0.107268	0.0536342	+	0.998561i	$0.482920\pi$
$164$	−7.98472	−0.623502
$165$	−6.89783	−0.536996
$166$	10.6198	0.824254
$167$	6.87026	0.531637	0.265818	−	0.964023i	$-0.414358\pi$
$167$	6.87026	0.531637	0.265818	+	0.964023i	$0.414358\pi$
$168$	−4.74969	−0.366446
$169$	13.8823	1.06787
$170$	5.65598	0.433794
$171$	−6.83686	−0.522827
$172$	0.142859	0.0108929
$173$	−4.77790	−0.363257	−0.181628	−	0.983367i	$-0.558137\pi$
$173$	−4.77790	−0.363257	−0.181628	+	0.983367i	$0.558137\pi$
$174$	22.2468	1.68653
$175$	−19.8402	−1.49978
$176$	0.752089	0.0566908
$177$	12.3095	0.925242
$178$	−1.08656	−0.0814414
$179$	−2.88063	−0.215308	−0.107654	−	0.994188i	$-0.534334\pi$
$179$	−2.88063	−0.215308	−0.107654	+	0.994188i	$0.534334\pi$
$180$	10.1907	0.759568
$181$	−6.98882	−0.519475	−0.259737	−	0.965679i	$-0.583636\pi$
$181$	−6.98882	−0.519475	−0.259737	+	0.965679i	$0.583636\pi$
$182$	10.3710	0.768751
$183$	−21.2205	−1.56866
$184$	1.59637	0.117686
$185$	−6.07249	−0.446459
$186$	−6.23782	−0.457379
$187$	−1.10131	−0.0805360
$188$	7.09324	0.517327
$189$	−1.71761	−0.124938
$190$	10.0089	0.726122
$191$	−7.34220	−0.531263	−0.265631	−	0.964075i	$-0.585580\pi$
$191$	−7.34220	−0.531263	−0.265631	+	0.964075i	$0.585580\pi$
$192$	−2.37453	−0.171367
$193$	−8.45789	−0.608812	−0.304406	−	0.952542i	$-0.598458\pi$
$193$	−8.45789	−0.608812	−0.304406	+	0.952542i	$0.598458\pi$
$194$	−1.69040	−0.121364
$195$	−47.5529	−3.40533
$196$	−2.99893	−0.214209
$197$	−26.7674	−1.90710	−0.953550	−	0.301233i	$-0.902602\pi$
$197$	−26.7674	−1.90710	−0.953550	+	0.301233i	$0.902602\pi$
$198$	−1.98429	−0.141018
$199$	3.85394	0.273199	0.136599	−	0.990626i	$-0.456383\pi$
$199$	3.85394	0.273199	0.136599	+	0.990626i	$0.456383\pi$
$200$	−9.91877	−0.701363
$201$	−2.82925	−0.199560
$202$	−1.23268	−0.0867308
$203$	−18.7404	−1.31532
$204$	3.47711	0.243446
$205$	−30.8408	−2.15402
$206$	−5.32416	−0.370952
$207$	−4.21182	−0.292742
$208$	5.18482	0.359502
$209$	−1.94890	−0.134808
$210$	−18.3456	−1.26597
$211$	10.5880	0.728905	0.364452	−	0.931222i	$-0.381256\pi$
$211$	10.5880	0.728905	0.364452	+	0.931222i	$0.381256\pi$
$212$	3.05328	0.209700
$213$	−18.1510	−1.24369
$214$	−11.7003	−0.799818
$215$	0.551790	0.0376318
$216$	−0.858691	−0.0584265
$217$	5.25465	0.356709
$218$	5.38580	0.364772
$219$	−28.3461	−1.91545
$220$	2.90493	0.195850
$221$	−7.59233	−0.510715
$222$	−3.73317	−0.250554
$223$	13.2103	0.884624	0.442312	−	0.896861i	$-0.354158\pi$
$223$	13.2103	0.884624	0.442312	+	0.896861i	$0.354158\pi$
$224$	2.00027	0.133648
$225$	26.1694	1.74463
$226$	−2.26299	−0.150532
$227$	−21.9453	−1.45656	−0.728282	−	0.685278i	$-0.759681\pi$
$227$	−21.9453	−1.45656	−0.728282	+	0.685278i	$0.759681\pi$
$228$	6.15314	0.407502
$229$	−22.1707	−1.46508	−0.732539	−	0.680725i	$-0.761665\pi$
$229$	−22.1707	−1.46508	−0.732539	+	0.680725i	$0.761665\pi$
$230$	6.16595	0.406570
$231$	3.57219	0.235033
$232$	−9.36896	−0.615102
$233$	5.20247	0.340825	0.170413	−	0.985373i	$-0.445490\pi$
$233$	5.20247	0.340825	0.170413	+	0.985373i	$0.445490\pi$
$234$	−13.6795	−0.894256
$235$	27.3975	1.78722
$236$	−5.18400	−0.337450
$237$	−6.42116	−0.417099
$238$	−2.92907	−0.189863
$239$	0.970693	0.0627889	0.0313945	−	0.999507i	$-0.490005\pi$
$239$	0.970693	0.0627889	0.0313945	+	0.999507i	$0.490005\pi$
$240$	−9.17156	−0.592022
$241$	20.3036	1.30787	0.653934	−	0.756552i	$-0.273118\pi$
$241$	20.3036	1.30787	0.653934	+	0.756552i	$0.273118\pi$
$242$	10.4344	0.670746
$243$	21.0602	1.35101
$244$	8.93672	0.572115
$245$	−11.5833	−0.740031
$246$	−18.9599	−1.20884
$247$	−13.4355	−0.854880
$248$	2.62697	0.166813
$249$	25.2169	1.59806
$250$	−18.9986	−1.20158
$251$	−21.0658	−1.32966	−0.664829	−	0.746995i	$-0.731496\pi$
$251$	−21.0658	−1.32966	−0.664829	+	0.746995i	$0.731496\pi$
$252$	−5.27745	−0.332448
$253$	−1.20061	−0.0754818
$254$	−5.73104	−0.359597
$255$	13.4303	0.841036
$256$	1.00000	0.0625000
$257$	2.84614	0.177538	0.0887688	−	0.996052i	$-0.471707\pi$
$257$	2.84614	0.177538	0.0887688	+	0.996052i	$0.471707\pi$
$258$	0.339222	0.0211191
$259$	3.14477	0.195406
$260$	20.0263	1.24198
$261$	24.7188	1.53006
$262$	−15.2828	−0.944174
$263$	−1.28818	−0.0794326	−0.0397163	−	0.999211i	$-0.512645\pi$
$263$	−1.28818	−0.0794326	−0.0397163	+	0.999211i	$0.512645\pi$
$264$	1.78586	0.109912
$265$	11.7932	0.724453
$266$	−5.18332	−0.317810
$267$	−2.58008	−0.157898
$268$	1.19150	0.0727826
$269$	−4.92512	−0.300290	−0.150145	−	0.988664i	$-0.547974\pi$
$269$	−4.92512	−0.300290	−0.150145	+	0.988664i	$0.547974\pi$
$270$	−3.31668	−0.201847
$271$	6.42660	0.390388	0.195194	−	0.980765i	$-0.437466\pi$
$271$	6.42660	0.390388	0.195194	+	0.980765i	$0.437466\pi$
$272$	−1.46434	−0.0887886
$273$	24.6263	1.49045
$274$	−4.17442	−0.252186
$275$	7.45980	0.449843
$276$	3.79062	0.228168
$277$	24.0078	1.44249	0.721244	−	0.692681i	$-0.243571\pi$
$277$	24.0078	1.44249	0.721244	+	0.692681i	$0.243571\pi$
$278$	8.26684	0.495812
$279$	−6.93094	−0.414945
$280$	7.72600	0.461717
$281$	20.7156	1.23579	0.617893	−	0.786262i	$-0.287986\pi$
$281$	20.7156	1.23579	0.617893	+	0.786262i	$0.287986\pi$
$282$	16.8431	1.00299
$283$	−14.6873	−0.873071	−0.436536	−	0.899687i	$-0.643795\pi$
$283$	−14.6873	−0.873071	−0.436536	+	0.899687i	$0.643795\pi$
$284$	7.64407	0.453592
$285$	23.7664	1.40780
$286$	−3.89944	−0.230579
$287$	15.9716	0.942772
$288$	−2.63837	−0.155468
$289$	−14.8557	−0.873865
$290$	−36.1874	−2.12500
$291$	−4.01390	−0.235299
$292$	11.9376	0.698595
$293$	11.7519	0.686551	0.343275	−	0.939235i	$-0.388464\pi$
$293$	11.7519	0.686551	0.343275	+	0.939235i	$0.388464\pi$
$294$	−7.12104	−0.415307
$295$	−20.0231	−1.16579
$296$	1.57217	0.0913808
$297$	0.645812	0.0374738
$298$	4.51289	0.261425
$299$	−8.27688	−0.478664
$300$	−23.5524	−1.35980
$301$	−0.285756	−0.0164707
$302$	10.0097	0.575994
$303$	−2.92702	−0.168153
$304$	−2.59131	−0.148622
$305$	34.5179	1.97649
$306$	3.86347	0.220860
$307$	−7.31644	−0.417571	−0.208786	−	0.977961i	$-0.566951\pi$
$307$	−7.31644	−0.417571	−0.208786	+	0.977961i	$0.566951\pi$
$308$	−1.50438	−0.0857200
$309$	−12.6423	−0.719198
$310$	10.1466	0.576290
$311$	−11.2932	−0.640380	−0.320190	−	0.947353i	$-0.603747\pi$
$311$	−11.2932	−0.640380	−0.320190	+	0.947353i	$0.603747\pi$
$312$	12.3115	0.697000
$313$	21.7633	1.23013	0.615067	−	0.788475i	$-0.289129\pi$
$313$	21.7633	1.23013	0.615067	+	0.788475i	$0.289129\pi$
$314$	−19.1340	−1.07980
$315$	−20.3841	−1.14851
$316$	2.70419	0.152122
$317$	−20.9082	−1.17432	−0.587161	−	0.809470i	$-0.699754\pi$
$317$	−20.9082	−1.17432	−0.587161	+	0.809470i	$0.699754\pi$
$318$	7.25010	0.406565
$319$	7.04629	0.394516
$320$	3.86248	0.215919
$321$	−27.7827	−1.55068
$322$	−3.19316	−0.177948
$323$	3.79456	0.211135
$324$	−9.95411	−0.553006
$325$	51.4270	2.85266
$326$	−1.36951	−0.0758502
$327$	12.7887	0.707218
$328$	7.98472	0.440882
$329$	−14.1884	−0.782230
$330$	6.89783	0.379713
$331$	−1.42067	−0.0780871	−0.0390435	−	0.999238i	$-0.512431\pi$
$331$	−1.42067	−0.0780871	−0.0390435	+	0.999238i	$0.512431\pi$
$332$	−10.6198	−0.582836
$333$	−4.14798	−0.227308
$334$	−6.87026	−0.375924
$335$	4.60215	0.251443
$336$	4.74969	0.259117
$337$	14.5941	0.794993	0.397496	−	0.917604i	$-0.369879\pi$
$337$	14.5941	0.794993	0.397496	+	0.917604i	$0.369879\pi$
$338$	−13.8823	−0.755099
$339$	−5.37353	−0.291850
$340$	−5.65598	−0.306739
$341$	−1.97572	−0.106991
$342$	6.83686	0.369695
$343$	20.0005	1.07993
$344$	−0.142859	−0.00770244
$345$	14.6412	0.788256
$346$	4.77790	0.256861
$347$	1.94189	0.104246	0.0521229	−	0.998641i	$-0.483401\pi$
$347$	1.94189	0.104246	0.0521229	+	0.998641i	$0.483401\pi$
$348$	−22.2468	−1.19256
$349$	−15.4882	−0.829062	−0.414531	−	0.910035i	$-0.636054\pi$
$349$	−15.4882	−0.829062	−0.414531	+	0.910035i	$0.636054\pi$
$350$	19.8402	1.06050
$351$	4.45215	0.237638
$352$	−0.752089	−0.0400865
$353$	2.34311	0.124711	0.0623557	−	0.998054i	$-0.480139\pi$
$353$	2.34311	0.124711	0.0623557	+	0.998054i	$0.480139\pi$
$354$	−12.3095	−0.654245
$355$	29.5251	1.56703
$356$	1.08656	0.0575878
$357$	−6.95515	−0.368106
$358$	2.88063	0.152246
$359$	19.9733	1.05415	0.527074	−	0.849819i	$-0.323289\pi$
$359$	19.9733	1.05415	0.527074	+	0.849819i	$0.323289\pi$
$360$	−10.1907	−0.537096
$361$	−12.2851	−0.646584
$362$	6.98882	0.367324
$363$	24.7767	1.30044
$364$	−10.3710	−0.543589
$365$	46.1087	2.41344
$366$	21.2205	1.10921
$367$	13.6255	0.711246	0.355623	−	0.934630i	$-0.384269\pi$
$367$	13.6255	0.711246	0.355623	+	0.934630i	$0.384269\pi$
$368$	−1.59637	−0.0832165
$369$	−21.0667	−1.09669
$370$	6.07249	0.315694
$371$	−6.10738	−0.317079
$372$	6.23782	0.323416
$373$	16.1357	0.835473	0.417737	−	0.908568i	$-0.362823\pi$
$373$	16.1357	0.835473	0.417737	+	0.908568i	$0.362823\pi$
$374$	1.10131	0.0569475
$375$	−45.1128	−2.32961
$376$	−7.09324	−0.365806
$377$	48.5763	2.50181
$378$	1.71761	0.0883444
$379$	21.1493	1.08637	0.543184	−	0.839614i	$-0.317218\pi$
$379$	21.1493	1.08637	0.543184	+	0.839614i	$0.317218\pi$
$380$	−10.0089	−0.513446
$381$	−13.6085	−0.697184
$382$	7.34220	0.375659
$383$	1.65529	0.0845813	0.0422906	−	0.999105i	$-0.486534\pi$
$383$	1.65529	0.0845813	0.0422906	+	0.999105i	$0.486534\pi$
$384$	2.37453	0.121175
$385$	−5.81064	−0.296138
$386$	8.45789	0.430495
$387$	0.376915	0.0191597
$388$	1.69040	0.0858171
$389$	12.1619	0.616635	0.308317	−	0.951284i	$-0.400234\pi$
$389$	12.1619	0.616635	0.308317	+	0.951284i	$0.400234\pi$
$390$	47.5529	2.40793
$391$	2.33762	0.118219
$392$	2.99893	0.151469
$393$	−36.2894	−1.83056
$394$	26.7674	1.34852
$395$	10.4449	0.525538
$396$	1.98429	0.0997144
$397$	36.8506	1.84948	0.924738	−	0.380603i	$-0.124284\pi$
$397$	36.8506	1.84948	0.924738	+	0.380603i	$0.124284\pi$
$398$	−3.85394	−0.193181
$399$	−12.3079	−0.616167
$400$	9.91877	0.495938
$401$	−11.4795	−0.573259	−0.286630	−	0.958041i	$-0.592535\pi$
$401$	−11.4795	−0.573259	−0.286630	+	0.958041i	$0.592535\pi$
$402$	2.82925	0.141110
$403$	−13.6204	−0.678479
$404$	1.23268	0.0613279
$405$	−38.4475	−1.91047
$406$	18.7404	0.930071
$407$	−1.18241	−0.0586101
$408$	−3.47711	−0.172143
$409$	−6.96144	−0.344221	−0.172110	−	0.985078i	$-0.555059\pi$
$409$	−6.96144	−0.344221	−0.172110	+	0.985078i	$0.555059\pi$
$410$	30.8408	1.52312
$411$	−9.91228	−0.488937
$412$	5.32416	0.262302
$413$	10.3694	0.510244
$414$	4.21182	0.207000
$415$	−41.0187	−2.01353
$416$	−5.18482	−0.254207
$417$	19.6298	0.961277
$418$	1.94890	0.0953238
$419$	32.7771	1.60126	0.800632	−	0.599157i	$-0.204497\pi$
$419$	32.7771	1.60126	0.800632	+	0.599157i	$0.204497\pi$
$420$	18.3456	0.895173
$421$	4.21818	0.205582	0.102791	−	0.994703i	$-0.467223\pi$
$421$	4.21818	0.205582	0.102791	+	0.994703i	$0.467223\pi$
$422$	−10.5880	−0.515414
$423$	18.7146	0.909935
$424$	−3.05328	−0.148280
$425$	−14.5244	−0.704538
$426$	18.1510	0.879421
$427$	−17.8758	−0.865072
$428$	11.7003	0.565557
$429$	−9.25933	−0.447045
$430$	−0.551790	−0.0266097
$431$	−17.2452	−0.830672	−0.415336	−	0.909668i	$-0.636336\pi$
$431$	−17.2452	−0.830672	−0.415336	+	0.909668i	$0.636336\pi$
$432$	0.858691	0.0413138
$433$	−21.0546	−1.01182	−0.505911	−	0.862586i	$-0.668843\pi$
$433$	−21.0546	−1.01182	−0.505911	+	0.862586i	$0.668843\pi$
$434$	−5.25465	−0.252231
$435$	−85.9280	−4.11993
$436$	−5.38580	−0.257933
$437$	4.13669	0.197885
$438$	28.3461	1.35443
$439$	23.6295	1.12777	0.563887	−	0.825852i	$-0.309306\pi$
$439$	23.6295	1.12777	0.563887	+	0.825852i	$0.309306\pi$
$440$	−2.90493	−0.138487
$441$	−7.91230	−0.376776
$442$	7.59233	0.361130
$443$	31.6444	1.50347	0.751735	−	0.659465i	$-0.229217\pi$
$443$	31.6444	1.50347	0.751735	+	0.659465i	$0.229217\pi$
$444$	3.73317	0.177168
$445$	4.19683	0.198949
$446$	−13.2103	−0.625524
$447$	10.7160	0.506848
$448$	−2.00027	−0.0945038
$449$	31.7462	1.49819	0.749097	−	0.662460i	$-0.230487\pi$
$449$	31.7462	1.49819	0.749097	+	0.662460i	$0.230487\pi$
$450$	−26.1694	−1.23364
$451$	−6.00522	−0.282775
$452$	2.26299	0.106442
$453$	23.7683	1.11673
$454$	21.9453	1.02995
$455$	−40.0579	−1.87794
$456$	−6.15314	−0.288147
$457$	−0.692764	−0.0324062	−0.0162031	−	0.999869i	$-0.505158\pi$
$457$	−0.692764	−0.0324062	−0.0162031	+	0.999869i	$0.505158\pi$
$458$	22.1707	1.03597
$459$	−1.25741	−0.0586910
$460$	−6.16595	−0.287489
$461$	9.45352	0.440294	0.220147	−	0.975467i	$-0.429346\pi$
$461$	9.45352	0.440294	0.220147	+	0.975467i	$0.429346\pi$
$462$	−3.57219	−0.166193
$463$	11.6738	0.542529	0.271264	−	0.962505i	$-0.412558\pi$
$463$	11.6738	0.542529	0.271264	+	0.962505i	$0.412558\pi$
$464$	9.36896	0.434943
$465$	24.0935	1.11731
$466$	−5.20247	−0.241000
$467$	30.6429	1.41798	0.708992	−	0.705216i	$-0.249150\pi$
$467$	30.6429	1.41798	0.708992	+	0.705216i	$0.249150\pi$
$468$	13.6795	0.632334
$469$	−2.38332	−0.110052
$470$	−27.3975	−1.26375
$471$	−45.4342	−2.09350
$472$	5.18400	0.238613
$473$	0.107443	0.00494022
$474$	6.42116	0.294934
$475$	−25.7026	−1.17932
$476$	2.92907	0.134254
$477$	8.05570	0.368845
$478$	−0.970693	−0.0443985
$479$	27.6756	1.26453	0.632265	−	0.774752i	$-0.282125\pi$
$479$	27.6756	1.26453	0.632265	+	0.774752i	$0.282125\pi$
$480$	9.17156	0.418623
$481$	−8.15143	−0.371673
$482$	−20.3036	−0.924802
$483$	−7.58225	−0.345004
$484$	−10.4344	−0.474289
$485$	6.52914	0.296473
$486$	−21.0602	−0.955310
$487$	10.9659	0.496913	0.248457	−	0.968643i	$-0.420077\pi$
$487$	10.9659	0.496913	0.248457	+	0.968643i	$0.420077\pi$
$488$	−8.93672	−0.404546
$489$	−3.25194	−0.147058
$490$	11.5833	0.523281
$491$	27.1844	1.22682	0.613408	−	0.789766i	$-0.289798\pi$
$491$	27.1844	1.22682	0.613408	+	0.789766i	$0.289798\pi$
$492$	18.9599	0.854779
$493$	−13.7193	−0.617887
$494$	13.4355	0.604491
$495$	7.66429	0.344484
$496$	−2.62697	−0.117955
$497$	−15.2902	−0.685858
$498$	−25.2169	−1.13000
$499$	2.86310	0.128170	0.0640850	−	0.997944i	$-0.479587\pi$
$499$	2.86310	0.128170	0.0640850	+	0.997944i	$0.479587\pi$
$500$	18.9986	0.849645
$501$	−16.3136	−0.728838
$502$	21.0658	0.940211
$503$	7.75867	0.345942	0.172971	−	0.984927i	$-0.444663\pi$
$503$	7.75867	0.345942	0.172971	+	0.984927i	$0.444663\pi$
$504$	5.27745	0.235076
$505$	4.76119	0.211870
$506$	1.20061	0.0533737
$507$	−32.9639	−1.46398
$508$	5.73104	0.254274
$509$	−33.3243	−1.47707	−0.738536	−	0.674214i	$-0.764482\pi$
$509$	−33.3243	−1.47707	−0.738536	+	0.674214i	$0.764482\pi$
$510$	−13.4303	−0.594702
$511$	−23.8784	−1.05632
$512$	−1.00000	−0.0441942
$513$	−2.22514	−0.0982422
$514$	−2.84614	−0.125538
$515$	20.5645	0.906178
$516$	−0.339222	−0.0149334
$517$	5.33474	0.234622
$518$	−3.14477	−0.138173
$519$	11.3452	0.498001
$520$	−20.0263	−0.878210
$521$	15.3341	0.671798	0.335899	−	0.941898i	$-0.390960\pi$
$521$	15.3341	0.671798	0.335899	+	0.941898i	$0.390960\pi$
$522$	−24.7188	−1.08191
$523$	6.83842	0.299023	0.149512	−	0.988760i	$-0.452230\pi$
$523$	6.83842	0.299023	0.149512	+	0.988760i	$0.452230\pi$
$524$	15.2828	0.667632
$525$	47.1110	2.05609
$526$	1.28818	0.0561674
$527$	3.84678	0.167568
$528$	−1.78586	−0.0777194
$529$	−20.4516	−0.889200
$530$	−11.7932	−0.512266
$531$	−13.6773	−0.593546
$532$	5.18332	0.224726
$533$	−41.3993	−1.79320
$534$	2.58008	0.111651
$535$	45.1923	1.95383
$536$	−1.19150	−0.0514650
$537$	6.84012	0.295173
$538$	4.92512	0.212337
$539$	−2.25546	−0.0971497
$540$	3.31668	0.142727
$541$	27.5540	1.18464	0.592320	−	0.805703i	$-0.298212\pi$
$541$	27.5540	1.18464	0.592320	+	0.805703i	$0.298212\pi$
$542$	−6.42660	−0.276046
$543$	16.5951	0.712165
$544$	1.46434	0.0627830
$545$	−20.8026	−0.891084
$546$	−24.6263	−1.05391
$547$	−16.5748	−0.708688	−0.354344	−	0.935115i	$-0.615296\pi$
$547$	−16.5748	−0.708688	−0.354344	+	0.935115i	$0.615296\pi$
$548$	4.17442	0.178323
$549$	23.5784	1.00630
$550$	−7.45980	−0.318087
$551$	−24.2779	−1.03427
$552$	−3.79062	−0.161339
$553$	−5.40909	−0.230018
$554$	−24.0078	−1.01999
$555$	14.4193	0.612065
$556$	−8.26684	−0.350592
$557$	26.3011	1.11441	0.557207	−	0.830374i	$-0.311873\pi$
$557$	26.3011	1.11441	0.557207	+	0.830374i	$0.311873\pi$
$558$	6.93094	0.293410
$559$	0.740697	0.0313282
$560$	−7.72600	−0.326483
$561$	2.61510	0.110409
$562$	−20.7156	−0.873833
$563$	5.31207	0.223877	0.111939	−	0.993715i	$-0.464294\pi$
$563$	5.31207	0.223877	0.111939	+	0.993715i	$0.464294\pi$
$564$	−16.8431	−0.709221
$565$	8.74075	0.367726
$566$	14.6873	0.617355
$567$	19.9109	0.836178
$568$	−7.64407	−0.320738
$569$	−29.0644	−1.21844	−0.609222	−	0.793000i	$-0.708518\pi$
$569$	−29.0644	−1.21844	−0.609222	+	0.793000i	$0.708518\pi$
$570$	−23.7664	−0.995465
$571$	−18.1170	−0.758173	−0.379086	−	0.925361i	$-0.623762\pi$
$571$	−18.1170	−0.758173	−0.379086	+	0.925361i	$0.623762\pi$
$572$	3.89944	0.163044
$573$	17.4342	0.728326
$574$	−15.9716	−0.666640
$575$	−15.8340	−0.660324
$576$	2.63837	0.109932
$577$	38.7160	1.61177	0.805884	−	0.592073i	$-0.201690\pi$
$577$	38.7160	1.61177	0.805884	+	0.592073i	$0.201690\pi$
$578$	14.8557	0.617916
$579$	20.0835	0.834641
$580$	36.1874	1.50260
$581$	21.2424	0.881283
$582$	4.01390	0.166382
$583$	2.29634	0.0951047
$584$	−11.9376	−0.493981
$585$	52.8368	2.18453
$586$	−11.7519	−0.485465
$587$	38.9303	1.60682	0.803412	−	0.595423i	$-0.203016\pi$
$587$	38.9303	1.60682	0.803412	+	0.595423i	$0.203016\pi$
$588$	7.12104	0.293667
$589$	6.80732	0.280491
$590$	20.0231	0.824339
$591$	63.5600	2.61451
$592$	−1.57217	−0.0646160
$593$	−3.57191	−0.146681	−0.0733405	−	0.997307i	$-0.523366\pi$
$593$	−3.57191	−0.146681	−0.0733405	+	0.997307i	$0.523366\pi$
$594$	−0.645812	−0.0264980
$595$	11.3135	0.463807
$596$	−4.51289	−0.184855
$597$	−9.15128	−0.374537
$598$	8.27688	0.338467
$599$	35.5941	1.45434	0.727168	−	0.686459i	$-0.240836\pi$
$599$	35.5941	1.45434	0.727168	+	0.686459i	$0.240836\pi$
$600$	23.5524	0.961521
$601$	35.0001	1.42768	0.713841	−	0.700308i	$-0.246954\pi$
$601$	35.0001	1.42768	0.713841	+	0.700308i	$0.246954\pi$
$602$	0.285756	0.0116465
$603$	3.14363	0.128018
$604$	−10.0097	−0.407289
$605$	−40.3025	−1.63853
$606$	2.92702	0.118902
$607$	30.5631	1.24052	0.620258	−	0.784398i	$-0.287028\pi$
$607$	30.5631	1.24052	0.620258	+	0.784398i	$0.287028\pi$
$608$	2.59131	0.105092
$609$	44.4996	1.80322
$610$	−34.5179	−1.39759
$611$	36.7771	1.48784
$612$	−3.86347	−0.156172
$613$	−6.32635	−0.255519	−0.127759	−	0.991805i	$-0.540779\pi$
$613$	−6.32635	−0.255519	−0.127759	+	0.991805i	$0.540779\pi$
$614$	7.31644	0.295268
$615$	73.2323	2.95301
$616$	1.50438	0.0606132
$617$	−14.4439	−0.581489	−0.290744	−	0.956801i	$-0.593903\pi$
$617$	−14.4439	−0.581489	−0.290744	+	0.956801i	$0.593903\pi$
$618$	12.6423	0.508550
$619$	−22.8050	−0.916609	−0.458305	−	0.888795i	$-0.651543\pi$
$619$	−22.8050	−0.916609	−0.458305	+	0.888795i	$0.651543\pi$
$620$	−10.1466	−0.407499
$621$	−1.37079	−0.0550078
$622$	11.2932	0.452817
$623$	−2.17342	−0.0870762
$624$	−12.3115	−0.492854
$625$	23.7881	0.951523
$626$	−21.7633	−0.869836
$627$	4.62771	0.184813
$628$	19.1340	0.763530
$629$	2.30219	0.0917945
$630$	20.3841	0.812121
$631$	−8.73276	−0.347646	−0.173823	−	0.984777i	$-0.555612\pi$
$631$	−8.73276	−0.347646	−0.173823	+	0.984777i	$0.555612\pi$
$632$	−2.70419	−0.107567
$633$	−25.1414	−0.999280
$634$	20.9082	0.830371
$635$	22.1360	0.878441
$636$	−7.25010	−0.287485
$637$	−15.5489	−0.616070
$638$	−7.04629	−0.278965
$639$	20.1679	0.797830
$640$	−3.86248	−0.152678
$641$	17.7164	0.699754	0.349877	−	0.936796i	$-0.386223\pi$
$641$	17.7164	0.699754	0.349877	+	0.936796i	$0.386223\pi$
$642$	27.7827	1.09650
$643$	0.571265	0.0225285	0.0112642	−	0.999937i	$-0.496414\pi$
$643$	0.571265	0.0225285	0.0112642	+	0.999937i	$0.496414\pi$
$644$	3.19316	0.125828
$645$	−1.31024	−0.0515906
$646$	−3.79456	−0.149295
$647$	−28.1599	−1.10708	−0.553541	−	0.832822i	$-0.686724\pi$
$647$	−28.1599	−1.10708	−0.553541	+	0.832822i	$0.686724\pi$
$648$	9.95411	0.391034
$649$	−3.89883	−0.153043
$650$	−51.4270	−2.01713
$651$	−12.4773	−0.489024
$652$	1.36951	0.0536342
$653$	−3.55631	−0.139169	−0.0695846	−	0.997576i	$-0.522167\pi$
$653$	−3.55631	−0.139169	−0.0695846	+	0.997576i	$0.522167\pi$
$654$	−12.7887	−0.500079
$655$	59.0295	2.30647
$656$	−7.98472	−0.311751
$657$	31.4958	1.22877
$658$	14.1884	0.553120
$659$	−14.3390	−0.558566	−0.279283	−	0.960209i	$-0.590097\pi$
$659$	−14.3390	−0.558566	−0.279283	+	0.960209i	$0.590097\pi$
$660$	−6.89783	−0.268498
$661$	−7.71539	−0.300094	−0.150047	−	0.988679i	$-0.547942\pi$
$661$	−7.71539	−0.300094	−0.150047	+	0.988679i	$0.547942\pi$
$662$	1.42067	0.0552159
$663$	18.0282	0.700156
$664$	10.6198	0.412127
$665$	20.0205	0.776361
$666$	4.14798	0.160731
$667$	−14.9563	−0.579111
$668$	6.87026	0.265818
$669$	−31.3681	−1.21276
$670$	−4.60215	−0.177797
$671$	6.72121	0.259469
$672$	−4.74969	−0.183223
$673$	−45.0135	−1.73514	−0.867572	−	0.497312i	$-0.834320\pi$
$673$	−45.0135	−1.73514	−0.867572	+	0.497312i	$0.834320\pi$
$674$	−14.5941	−0.562145
$675$	8.51715	0.327825
$676$	13.8823	0.533936
$677$	9.50393	0.365266	0.182633	−	0.983181i	$-0.441538\pi$
$677$	9.50393	0.365266	0.182633	+	0.983181i	$0.441538\pi$
$678$	5.37353	0.206369
$679$	−3.38125	−0.129761
$680$	5.65598	0.216897
$681$	52.1098	1.99685
$682$	1.97572	0.0756542
$683$	40.1929	1.53794	0.768969	−	0.639286i	$-0.220770\pi$
$683$	40.1929	1.53794	0.768969	+	0.639286i	$0.220770\pi$
$684$	−6.83686	−0.261414
$685$	16.1236	0.616053
$686$	−20.0005	−0.763624
$687$	52.6448	2.00852
$688$	0.142859	0.00544645
$689$	15.8307	0.603102
$690$	−14.6412	−0.557381
$691$	15.5507	0.591577	0.295788	−	0.955253i	$-0.404418\pi$
$691$	15.5507	0.591577	0.295788	+	0.955253i	$0.404418\pi$
$692$	−4.77790	−0.181628
$693$	−3.96912	−0.150774
$694$	−1.94189	−0.0737130
$695$	−31.9305	−1.21119
$696$	22.2468	0.843264
$697$	11.6923	0.442878
$698$	15.4882	0.586236
$699$	−12.3534	−0.467249
$700$	−19.8402	−0.749888
$701$	4.20877	0.158963	0.0794816	−	0.996836i	$-0.474674\pi$
$701$	4.20877	0.158963	0.0794816	+	0.996836i	$0.474674\pi$
$702$	−4.45215	−0.168036
$703$	4.07400	0.153654
$704$	0.752089	0.0283454
$705$	−65.0561	−2.45015
$706$	−2.34311	−0.0881843
$707$	−2.46568	−0.0927315
$708$	12.3095	0.462621
$709$	−24.4568	−0.918495	−0.459247	−	0.888308i	$-0.651881\pi$
$709$	−24.4568	−0.918495	−0.459247	+	0.888308i	$0.651881\pi$
$710$	−29.5251	−1.10806
$711$	7.13465	0.267570
$712$	−1.08656	−0.0407207
$713$	4.19362	0.157052
$714$	6.95515	0.260290
$715$	15.0615	0.563269
$716$	−2.88063	−0.107654
$717$	−2.30494	−0.0860794
$718$	−19.9733	−0.745396
$719$	17.6061	0.656596	0.328298	−	0.944574i	$-0.393525\pi$
$719$	17.6061	0.656596	0.328298	+	0.944574i	$0.393525\pi$
$720$	10.1907	0.379784
$721$	−10.6497	−0.396617
$722$	12.2851	0.457204
$723$	−48.2113	−1.79300
$724$	−6.98882	−0.259737
$725$	92.9285	3.45128
$726$	−24.7767	−0.919548
$727$	3.46349	0.128454	0.0642269	−	0.997935i	$-0.479542\pi$
$727$	3.46349	0.128454	0.0642269	+	0.997935i	$0.479542\pi$
$728$	10.3710	0.384376
$729$	−20.1457	−0.746137
$730$	−46.1087	−1.70656
$731$	−0.209194	−0.00773731
$732$	−21.2205	−0.784331
$733$	17.3025	0.639082	0.319541	−	0.947572i	$-0.396471\pi$
$733$	17.3025	0.639082	0.319541	+	0.947572i	$0.396471\pi$
$734$	−13.6255	−0.502927
$735$	27.5049	1.01453
$736$	1.59637	0.0588429
$737$	0.896116	0.0330088
$738$	21.0667	0.775475
$739$	37.5998	1.38313	0.691566	−	0.722313i	$-0.256921\pi$
$739$	37.5998	1.38313	0.691566	+	0.722313i	$0.256921\pi$
$740$	−6.07249	−0.223229
$741$	31.9029	1.17198
$742$	6.10738	0.224209
$743$	−47.9271	−1.75828	−0.879138	−	0.476567i	$-0.841881\pi$
$743$	−47.9271	−1.75828	−0.879138	+	0.476567i	$0.841881\pi$
$744$	−6.23782	−0.228690
$745$	−17.4310	−0.638621
$746$	−16.1357	−0.590769
$747$	−28.0189	−1.02516
$748$	−1.10131	−0.0402680
$749$	−23.4038	−0.855156
$750$	45.1128	1.64729
$751$	34.9898	1.27680	0.638398	−	0.769706i	$-0.279597\pi$
$751$	34.9898	1.27680	0.638398	+	0.769706i	$0.279597\pi$
$752$	7.09324	0.258664
$753$	50.0212	1.82287
$754$	−48.5763	−1.76905
$755$	−38.6623	−1.40706
$756$	−1.71761	−0.0624689
$757$	14.4138	0.523879	0.261939	−	0.965084i	$-0.415638\pi$
$757$	14.4138	0.523879	0.261939	+	0.965084i	$0.415638\pi$
$758$	−21.1493	−0.768179
$759$	2.85088	0.103481
$760$	10.0089	0.363061
$761$	50.0972	1.81602	0.908011	−	0.418946i	$-0.137600\pi$
$761$	50.0972	1.81602	0.908011	+	0.418946i	$0.137600\pi$
$762$	13.6085	0.492984
$763$	10.7730	0.390010
$764$	−7.34220	−0.265631
$765$	−14.9226	−0.539527
$766$	−1.65529	−0.0598080
$767$	−26.8781	−0.970512
$768$	−2.37453	−0.0856833
$769$	−46.2509	−1.66785	−0.833926	−	0.551877i	$-0.813912\pi$
$769$	−46.2509	−1.66785	−0.833926	+	0.551877i	$0.813912\pi$
$770$	5.81064	0.209401
$771$	−6.75824	−0.243392
$772$	−8.45789	−0.304406
$773$	−47.8899	−1.72248	−0.861240	−	0.508199i	$-0.830312\pi$
$773$	−47.8899	−1.72248	−0.861240	+	0.508199i	$0.830312\pi$
$774$	−0.376915	−0.0135479
$775$	−26.0563	−0.935971
$776$	−1.69040	−0.0606818
$777$	−7.46733	−0.267889
$778$	−12.1619	−0.436027
$779$	20.6909	0.741329
$780$	−47.5529	−1.70267
$781$	5.74902	0.205716
$782$	−2.33762	−0.0835933
$783$	8.04504	0.287506
$784$	−2.99893	−0.107105
$785$	73.9048	2.63778
$786$	36.2894	1.29440
$787$	−37.5708	−1.33925	−0.669627	−	0.742697i	$-0.733546\pi$
$787$	−37.5708	−1.33925	−0.669627	+	0.742697i	$0.733546\pi$
$788$	−26.7674	−0.953550
$789$	3.05882	0.108897
$790$	−10.4449	−0.371612
$791$	−4.52658	−0.160947
$792$	−1.98429	−0.0705088
$793$	46.3352	1.64541
$794$	−36.8506	−1.30778
$795$	−28.0034	−0.993177
$796$	3.85394	0.136599
$797$	24.1040	0.853807	0.426904	−	0.904297i	$-0.359604\pi$
$797$	24.1040	0.853807	0.426904	+	0.904297i	$0.359604\pi$
$798$	12.3079	0.435696
$799$	−10.3869	−0.367462
$800$	−9.91877	−0.350681
$801$	2.86676	0.101292
$802$	11.4795	0.405355
$803$	8.97814	0.316832
$804$	−2.82925	−0.0997800
$805$	12.3335	0.434700
$806$	13.6204	0.479757
$807$	11.6948	0.411678
$808$	−1.23268	−0.0433654
$809$	27.7666	0.976221	0.488110	−	0.872782i	$-0.337686\pi$
$809$	27.7666	0.976221	0.488110	+	0.872782i	$0.337686\pi$
$810$	38.4475	1.35091
$811$	−47.0266	−1.65133	−0.825665	−	0.564161i	$-0.809200\pi$
$811$	−47.0266	−1.65133	−0.825665	+	0.564161i	$0.809200\pi$
$812$	−18.7404	−0.657660
$813$	−15.2601	−0.535196
$814$	1.18241	0.0414436
$815$	5.28971	0.185290
$816$	3.47711	0.121723
$817$	−0.370192	−0.0129514
$818$	6.96144	0.243401
$819$	−27.3626	−0.956128
$820$	−30.8408	−1.07701
$821$	−19.9735	−0.697078	−0.348539	−	0.937294i	$-0.613322\pi$
$821$	−19.9735	−0.697078	−0.348539	+	0.937294i	$0.613322\pi$
$822$	9.91228	0.345730
$823$	−29.0234	−1.01169	−0.505846	−	0.862624i	$-0.668820\pi$
$823$	−29.0234	−1.01169	−0.505846	+	0.862624i	$0.668820\pi$
$824$	−5.32416	−0.185476
$825$	−17.7135	−0.616704
$826$	−10.3694	−0.360797
$827$	17.3446	0.603132	0.301566	−	0.953445i	$-0.402491\pi$
$827$	17.3446	0.603132	0.301566	+	0.953445i	$0.402491\pi$
$828$	−4.21182	−0.146371
$829$	−49.8341	−1.73081	−0.865404	−	0.501074i	$-0.832938\pi$
$829$	−49.8341	−1.73081	−0.865404	+	0.501074i	$0.832938\pi$
$830$	41.0187	1.42378
$831$	−57.0071	−1.97755
$832$	5.18482	0.179751
$833$	4.39145	0.152155
$834$	−19.6298	−0.679726
$835$	26.5362	0.918325
$836$	−1.94890	−0.0674041
$837$	−2.25576	−0.0779704
$838$	−32.7771	−1.13226
$839$	−31.6707	−1.09340	−0.546698	−	0.837330i	$-0.684115\pi$
$839$	−31.6707	−1.09340	−0.546698	+	0.837330i	$0.684115\pi$
$840$	−18.3456	−0.632983
$841$	58.7773	2.02680
$842$	−4.21818	−0.145368
$843$	−49.1896	−1.69418
$844$	10.5880	0.364452
$845$	53.6202	1.84459
$846$	−18.7146	−0.643421
$847$	20.8715	0.717154
$848$	3.05328	0.104850
$849$	34.8755	1.19692
$850$	14.5244	0.498184
$851$	2.50977	0.0860338
$852$	−18.1510	−0.621844
$853$	8.82671	0.302221	0.151110	−	0.988517i	$-0.451715\pi$
$853$	8.82671	0.302221	0.151110	+	0.988517i	$0.451715\pi$
$854$	17.8758	0.611698
$855$	−26.4072	−0.903108
$856$	−11.7003	−0.399909
$857$	41.1736	1.40646	0.703232	−	0.710960i	$-0.251739\pi$
$857$	41.1736	1.40646	0.703232	+	0.710960i	$0.251739\pi$
$858$	9.25933	0.316108
$859$	11.8028	0.402707	0.201354	−	0.979519i	$-0.435466\pi$
$859$	11.8028	0.402707	0.201354	+	0.979519i	$0.435466\pi$
$860$	0.551790	0.0188159
$861$	−37.9249	−1.29248
$862$	17.2452	0.587374
$863$	37.9743	1.29266	0.646330	−	0.763058i	$-0.276303\pi$
$863$	37.9743	1.29266	0.646330	+	0.763058i	$0.276303\pi$
$864$	−0.858691	−0.0292133
$865$	−18.4545	−0.627473
$866$	21.0546	0.715466
$867$	35.2753	1.19801
$868$	5.25465	0.178354
$869$	2.03379	0.0689916
$870$	85.9280	2.91323
$871$	6.17772	0.209324
$872$	5.38580	0.182386
$873$	4.45991	0.150945
$874$	−4.13669	−0.139926
$875$	−38.0024	−1.28471
$876$	−28.3461	−0.957727
$877$	25.5079	0.861340	0.430670	−	0.902510i	$-0.358277\pi$
$877$	25.5079	0.861340	0.430670	+	0.902510i	$0.358277\pi$
$878$	−23.6295	−0.797456
$879$	−27.9051	−0.941216
$880$	2.90493	0.0979252
$881$	30.9119	1.04145	0.520724	−	0.853725i	$-0.325662\pi$
$881$	30.9119	1.04145	0.520724	+	0.853725i	$0.325662\pi$
$882$	7.91230	0.266421
$883$	−20.9647	−0.705517	−0.352759	−	0.935714i	$-0.614756\pi$
$883$	−20.9647	−0.705517	−0.352759	+	0.935714i	$0.614756\pi$
$884$	−7.59233	−0.255358
$885$	47.5454	1.59822
$886$	−31.6444	−1.06311
$887$	16.5365	0.555242	0.277621	−	0.960691i	$-0.410454\pi$
$887$	16.5365	0.555242	0.277621	+	0.960691i	$0.410454\pi$
$888$	−3.73317	−0.125277
$889$	−11.4636	−0.384477
$890$	−4.19683	−0.140678
$891$	−7.48637	−0.250803
$892$	13.2103	0.442312
$893$	−18.3808	−0.615090
$894$	−10.7160	−0.358396
$895$	−11.1264	−0.371913
$896$	2.00027	0.0668242
$897$	19.6537	0.656217
$898$	−31.7462	−1.05938
$899$	−24.6120	−0.820856
$900$	26.1694	0.872314
$901$	−4.47104	−0.148952
$902$	6.00522	0.199952
$903$	0.678535	0.0225802
$904$	−2.26299	−0.0752659
$905$	−26.9942	−0.897317
$906$	−23.7683	−0.789649
$907$	−9.52271	−0.316196	−0.158098	−	0.987423i	$-0.550536\pi$
$907$	−9.52271	−0.316196	−0.158098	+	0.987423i	$0.550536\pi$
$908$	−21.9453	−0.728282
$909$	3.25226	0.107871
$910$	40.0579	1.32791
$911$	2.37142	0.0785686	0.0392843	−	0.999228i	$-0.487492\pi$
$911$	2.37142	0.0785686	0.0392843	+	0.999228i	$0.487492\pi$
$912$	6.15314	0.203751
$913$	−7.98702	−0.264332
$914$	0.692764	0.0229146
$915$	−81.9637	−2.70963
$916$	−22.1707	−0.732539
$917$	−30.5697	−1.00950
$918$	1.25741	0.0415008
$919$	−26.1097	−0.861280	−0.430640	−	0.902524i	$-0.641712\pi$
$919$	−26.1097	−0.861280	−0.430640	+	0.902524i	$0.641712\pi$
$920$	6.16595	0.203285
$921$	17.3731	0.572463
$922$	−9.45352	−0.311335
$923$	39.6331	1.30454
$924$	3.57219	0.117516
$925$	−15.5940	−0.512728
$926$	−11.6738	−0.383626
$927$	14.0471	0.461368
$928$	−9.36896	−0.307551
$929$	−7.33287	−0.240584	−0.120292	−	0.992739i	$-0.538383\pi$
$929$	−7.33287	−0.240584	−0.120292	+	0.992739i	$0.538383\pi$
$930$	−24.0935	−0.790056
$931$	7.77117	0.254690
$932$	5.20247	0.170413
$933$	26.8160	0.877918
$934$	−30.6429	−1.00267
$935$	−4.25380	−0.139114
$936$	−13.6795	−0.447128
$937$	5.46446	0.178516	0.0892581	−	0.996009i	$-0.471550\pi$
$937$	5.46446	0.178516	0.0892581	+	0.996009i	$0.471550\pi$
$938$	2.38332	0.0778182
$939$	−51.6775	−1.68643
$940$	27.3975	0.893608
$941$	3.61561	0.117866	0.0589328	−	0.998262i	$-0.481230\pi$
$941$	3.61561	0.117866	0.0589328	+	0.998262i	$0.481230\pi$
$942$	45.4342	1.48033
$943$	12.7466	0.415085
$944$	−5.18400	−0.168725
$945$	−6.63424	−0.215812
$946$	−0.107443	−0.00349326
$947$	−29.5188	−0.959234	−0.479617	−	0.877478i	$-0.659224\pi$
$947$	−29.5188	−0.959234	−0.479617	+	0.877478i	$0.659224\pi$
$948$	−6.42116	−0.208550
$949$	61.8942	2.00917
$950$	25.7026	0.833904
$951$	49.6471	1.60992
$952$	−2.92907	−0.0949316
$953$	20.4796	0.663400	0.331700	−	0.943385i	$-0.392378\pi$
$953$	20.4796	0.663400	0.331700	+	0.943385i	$0.392378\pi$
$954$	−8.05570	−0.260813
$955$	−28.3591	−0.917679
$956$	0.970693	0.0313945
$957$	−16.7316	−0.540856
$958$	−27.6756	−0.894158
$959$	−8.34997	−0.269634
$960$	−9.17156	−0.296011
$961$	−24.0990	−0.777387
$962$	8.15143	0.262813
$963$	30.8698	0.994767
$964$	20.3036	0.653934
$965$	−32.6684	−1.05163
$966$	7.58225	0.243955
$967$	−24.7626	−0.796312	−0.398156	−	0.917318i	$-0.630350\pi$
$967$	−24.7626	−0.796312	−0.398156	+	0.917318i	$0.630350\pi$
$968$	10.4344	0.335373
$969$	−9.01028	−0.289452
$970$	−6.52914	−0.209638
$971$	−39.6917	−1.27377	−0.636884	−	0.770960i	$-0.719777\pi$
$971$	−39.6917	−1.27377	−0.636884	+	0.770960i	$0.719777\pi$
$972$	21.0602	0.675507
$973$	16.5359	0.530117
$974$	−10.9659	−0.351371
$975$	−122.115	−3.91080
$976$	8.93672	0.286057
$977$	43.5929	1.39466	0.697330	−	0.716750i	$-0.254371\pi$
$977$	43.5929	1.39466	0.697330	+	0.716750i	$0.254371\pi$
$978$	3.25194	0.103986
$979$	0.817193	0.0261176
$980$	−11.5833	−0.370015
$981$	−14.2098	−0.453683
$982$	−27.1844	−0.867490
$983$	−12.4492	−0.397068	−0.198534	−	0.980094i	$-0.563618\pi$
$983$	−12.4492	−0.397068	−0.198534	+	0.980094i	$0.563618\pi$
$984$	−18.9599	−0.604420
$985$	−103.389	−3.29424
$986$	13.7193	0.436912
$987$	33.6906	1.07239
$988$	−13.4355	−0.427440
$989$	−0.228056	−0.00725174
$990$	−7.66429	−0.243587
$991$	5.89894	0.187386	0.0936929	−	0.995601i	$-0.470133\pi$
$991$	5.89894	0.187386	0.0936929	+	0.995601i	$0.470133\pi$
$992$	2.62697	0.0834065
$993$	3.37342	0.107052
$994$	15.2902	0.484975
$995$	14.8858	0.471911
$996$	25.2169	0.799029
$997$	18.7624	0.594211	0.297106	−	0.954845i	$-0.403979\pi$
$997$	18.7624	0.594211	0.297106	+	0.954845i	$0.403979\pi$
$998$	−2.86310	−0.0906299
$999$	−1.35001	−0.0427125

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.c.1.11	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.c.1.11	✓	61	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.37453 q^{3} +1.00000 q^{4} +3.86248 q^{5} +2.37453 q^{6} -2.00027 q^{7} -1.00000 q^{8} +2.63837 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.37453 q^{3} +1.00000 q^{4} +3.86248 q^{5} +2.37453 q^{6} -2.00027 q^{7} -1.00000 q^{8} +2.63837 q^{9} -3.86248 q^{10} +0.752089 q^{11} -2.37453 q^{12} +5.18482 q^{13} +2.00027 q^{14} -9.17156 q^{15} +1.00000 q^{16} -1.46434 q^{17} -2.63837 q^{18} -2.59131 q^{19} +3.86248 q^{20} +4.74969 q^{21} -0.752089 q^{22} -1.59637 q^{23} +2.37453 q^{24} +9.91877 q^{25} -5.18482 q^{26} +0.858691 q^{27} -2.00027 q^{28} +9.36896 q^{29} +9.17156 q^{30} -2.62697 q^{31} -1.00000 q^{32} -1.78586 q^{33} +1.46434 q^{34} -7.72600 q^{35} +2.63837 q^{36} -1.57217 q^{37} +2.59131 q^{38} -12.3115 q^{39} -3.86248 q^{40} -7.98472 q^{41} -4.74969 q^{42} +0.142859 q^{43} +0.752089 q^{44} +10.1907 q^{45} +1.59637 q^{46} +7.09324 q^{47} -2.37453 q^{48} -2.99893 q^{49} -9.91877 q^{50} +3.47711 q^{51} +5.18482 q^{52} +3.05328 q^{53} -0.858691 q^{54} +2.90493 q^{55} +2.00027 q^{56} +6.15314 q^{57} -9.36896 q^{58} -5.18400 q^{59} -9.17156 q^{60} +8.93672 q^{61} +2.62697 q^{62} -5.27745 q^{63} +1.00000 q^{64} +20.0263 q^{65} +1.78586 q^{66} +1.19150 q^{67} -1.46434 q^{68} +3.79062 q^{69} +7.72600 q^{70} +7.64407 q^{71} -2.63837 q^{72} +11.9376 q^{73} +1.57217 q^{74} -23.5524 q^{75} -2.59131 q^{76} -1.50438 q^{77} +12.3115 q^{78} +2.70419 q^{79} +3.86248 q^{80} -9.95411 q^{81} +7.98472 q^{82} -10.6198 q^{83} +4.74969 q^{84} -5.65598 q^{85} -0.142859 q^{86} -22.2468 q^{87} -0.752089 q^{88} +1.08656 q^{89} -10.1907 q^{90} -10.3710 q^{91} -1.59637 q^{92} +6.23782 q^{93} -7.09324 q^{94} -10.0089 q^{95} +2.37453 q^{96} +1.69040 q^{97} +2.99893 q^{98} +1.98429 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9}+O(q^{10}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9	\( 61 q - 61 q^{2} + 8 q^{3} + 61 q^{4} + 16 q^{5} - 8 q^{6} + 2 q^{7} - 61 q^{8} + 67 q^{9} - 16 q^{10} + 14 q^{11} + 8 q^{12} + 27 q^{13} - 2 q^{14} + 61 q^{16} + 60 q^{17} - 67 q^{18} - 29 q^{19} + 16 q^{20} + 30 q^{21} - 14 q^{22} + 39 q^{23} - 8 q^{24} + 61 q^{25} - 27 q^{26} + 32 q^{27} + 2 q^{28} + 36 q^{29} - 40 q^{31} - 61 q^{32} + 28 q^{33} - 60 q^{34} + 55 q^{35} + 67 q^{36} + 20 q^{37} + 29 q^{38} + 17 q^{39} - 16 q^{40} + 44 q^{41} - 30 q^{42} + 22 q^{43} + 14 q^{44} + 52 q^{45} - 39 q^{46} + 64 q^{47} + 8 q^{48} + 49 q^{49} - 61 q^{50} + 15 q^{51} + 27 q^{52} + 65 q^{53} - 32 q^{54} + 5 q^{55} - 2 q^{56} + 9 q^{57} - 36 q^{58} + 2 q^{59} + 45 q^{61} + 40 q^{62} + 28 q^{63} + 61 q^{64} + 41 q^{65} - 28 q^{66} - 20 q^{67} + 60 q^{68} + 21 q^{69} - 55 q^{70} - q^{71} - 67 q^{72} + 25 q^{73} - 20 q^{74} + 27 q^{75} - 29 q^{76} + 131 q^{77} - 17 q^{78} - 17 q^{79} + 16 q^{80} + 85 q^{81} - 44 q^{82} + 104 q^{83} + 30 q^{84} + 44 q^{85} - 22 q^{86} + 86 q^{87} - 14 q^{88} + 32 q^{89} - 52 q^{90} - 68 q^{91} + 39 q^{92} + 52 q^{93} - 64 q^{94} + 58 q^{95} - 8 q^{96} + 5 q^{97} - 49 q^{98} + 15 q^{99}+O(q^{100}) \) 61 * q - 61 * q^2 + 8 * q^3 + 61 * q^4 + 16 * q^5 - 8 * q^6 + 2 * q^7 - 61 * q^8 + 67 * q^9 - 16 * q^10 + 14 * q^11 + 8 * q^12 + 27 * q^13 - 2 * q^14 + 61 * q^16 + 60 * q^17 - 67 * q^18 - 29 * q^19 + 16 * q^20 + 30 * q^21 - 14 * q^22 + 39 * q^23 - 8 * q^24 + 61 * q^25 - 27 * q^26 + 32 * q^27 + 2 * q^28 + 36 * q^29 - 40 * q^31 - 61 * q^32 + 28 * q^33 - 60 * q^34 + 55 * q^35 + 67 * q^36 + 20 * q^37 + 29 * q^38 + 17 * q^39 - 16 * q^40 + 44 * q^41 - 30 * q^42 + 22 * q^43 + 14 * q^44 + 52 * q^45 - 39 * q^46 + 64 * q^47 + 8 * q^48 + 49 * q^49 - 61 * q^50 + 15 * q^51 + 27 * q^52 + 65 * q^53 - 32 * q^54 + 5 * q^55 - 2 * q^56 + 9 * q^57 - 36 * q^58 + 2 * q^59 + 45 * q^61 + 40 * q^62 + 28 * q^63 + 61 * q^64 + 41 * q^65 - 28 * q^66 - 20 * q^67 + 60 * q^68 + 21 * q^69 - 55 * q^70 - q^71 - 67 * q^72 + 25 * q^73 - 20 * q^74 + 27 * q^75 - 29 * q^76 + 131 * q^77 - 17 * q^78 - 17 * q^79 + 16 * q^80 + 85 * q^81 - 44 * q^82 + 104 * q^83 + 30 * q^84 + 44 * q^85 - 22 * q^86 + 86 * q^87 - 14 * q^88 + 32 * q^89 - 52 * q^90 - 68 * q^91 + 39 * q^92 + 52 * q^93 - 64 * q^94 + 58 * q^95 - 8 * q^96 + 5 * q^97 - 49 * q^98 + 15 * q^99

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