LMFDB - Embedded newform 6034.2.a.k.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} - 32 x^{18} + 106 x^{17} + 382 x^{16} - 1495 x^{15} - 1963 x^{14} + 10784 x^{13} + \cdots - 44 $ x^20 - 3x^19 - 32x^18 + 106x^17 + 382x^16 - 1495x^15 - 1963x^14 + 10784x^13 + 2170x^12 - 42069x^11 + 19553x^10 + 84697x^9 - 82713x^8 - 68589x^7 + 118845x^6 - 10051x^5 - 53572x^4 + 25598x^3 - 557x^2 - 1040*x - 44
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$0.814827$ of defining polynomial
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.814827 q^{3} +1.00000 q^{4} +0.275205 q^{5} -0.814827 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.33606 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.814827 q^{3} +1.00000 q^{4} +0.275205 q^{5} -0.814827 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.33606 q^{9} -0.275205 q^{10} -0.495907 q^{11} +0.814827 q^{12} +0.918014 q^{13} -1.00000 q^{14} +0.224245 q^{15} +1.00000 q^{16} -3.76776 q^{17} +2.33606 q^{18} +4.78553 q^{19} +0.275205 q^{20} +0.814827 q^{21} +0.495907 q^{22} -2.19624 q^{23} -0.814827 q^{24} -4.92426 q^{25} -0.918014 q^{26} -4.34797 q^{27} +1.00000 q^{28} -0.158548 q^{29} -0.224245 q^{30} +9.95933 q^{31} -1.00000 q^{32} -0.404078 q^{33} +3.76776 q^{34} +0.275205 q^{35} -2.33606 q^{36} +1.30811 q^{37} -4.78553 q^{38} +0.748023 q^{39} -0.275205 q^{40} -9.73898 q^{41} -0.814827 q^{42} +1.46831 q^{43} -0.495907 q^{44} -0.642895 q^{45} +2.19624 q^{46} -5.94545 q^{47} +0.814827 q^{48} +1.00000 q^{49} +4.92426 q^{50} -3.07008 q^{51} +0.918014 q^{52} +1.04651 q^{53} +4.34797 q^{54} -0.136476 q^{55} -1.00000 q^{56} +3.89938 q^{57} +0.158548 q^{58} +4.67138 q^{59} +0.224245 q^{60} +3.90709 q^{61} -9.95933 q^{62} -2.33606 q^{63} +1.00000 q^{64} +0.252642 q^{65} +0.404078 q^{66} -1.29250 q^{67} -3.76776 q^{68} -1.78956 q^{69} -0.275205 q^{70} -6.58725 q^{71} +2.33606 q^{72} -4.35370 q^{73} -1.30811 q^{74} -4.01242 q^{75} +4.78553 q^{76} -0.495907 q^{77} -0.748023 q^{78} -5.47581 q^{79} +0.275205 q^{80} +3.46533 q^{81} +9.73898 q^{82} -2.20462 q^{83} +0.814827 q^{84} -1.03691 q^{85} -1.46831 q^{86} -0.129189 q^{87} +0.495907 q^{88} -7.84816 q^{89} +0.642895 q^{90} +0.918014 q^{91} -2.19624 q^{92} +8.11514 q^{93} +5.94545 q^{94} +1.31700 q^{95} -0.814827 q^{96} -5.03352 q^{97} -1.00000 q^{98} +1.15847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) $ 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * 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
$3$	0.814827	0.470441	0.235220	−	0.971942i	$-0.424419\pi$
$3$	0.814827	0.470441	0.235220	+	0.971942i	$0.424419\pi$
$4$	1.00000	0.500000
$5$	0.275205	0.123075	0.0615377	−	0.998105i	$-0.480400\pi$
$5$	0.275205	0.123075	0.0615377	+	0.998105i	$0.480400\pi$
$6$	−0.814827	−0.332652
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.33606	−0.778685
$10$	−0.275205	−0.0870275
$11$	−0.495907	−0.149521	−0.0747607	−	0.997201i	$-0.523819\pi$
$11$	−0.495907	−0.149521	−0.0747607	+	0.997201i	$0.523819\pi$
$12$	0.814827	0.235220
$13$	0.918014	0.254611	0.127306	−	0.991864i	$-0.459367\pi$
$13$	0.918014	0.254611	0.127306	+	0.991864i	$0.459367\pi$
$14$	−1.00000	−0.267261
$15$	0.224245	0.0578997
$16$	1.00000	0.250000
$17$	−3.76776	−0.913817	−0.456909	−	0.889514i	$-0.651043\pi$
$17$	−3.76776	−0.913817	−0.456909	+	0.889514i	$0.651043\pi$
$18$	2.33606	0.550614
$19$	4.78553	1.09788	0.548938	−	0.835863i	$-0.315032\pi$
$19$	4.78553	1.09788	0.548938	+	0.835863i	$0.315032\pi$
$20$	0.275205	0.0615377
$21$	0.814827	0.177810
$22$	0.495907	0.105728
$23$	−2.19624	−0.457949	−0.228974	−	0.973432i	$-0.573537\pi$
$23$	−2.19624	−0.457949	−0.228974	+	0.973432i	$0.573537\pi$
$24$	−0.814827	−0.166326
$25$	−4.92426	−0.984852
$26$	−0.918014	−0.180037
$27$	−4.34797	−0.836766
$28$	1.00000	0.188982
$29$	−0.158548	−0.0294415	−0.0147208	−	0.999892i	$-0.504686\pi$
$29$	−0.158548	−0.0294415	−0.0147208	+	0.999892i	$0.504686\pi$
$30$	−0.224245	−0.0409413
$31$	9.95933	1.78875	0.894375	−	0.447319i	$-0.147621\pi$
$31$	9.95933	1.78875	0.894375	+	0.447319i	$0.147621\pi$
$32$	−1.00000	−0.176777
$33$	−0.404078	−0.0703410
$34$	3.76776	0.646166
$35$	0.275205	0.0465182
$36$	−2.33606	−0.389343
$37$	1.30811	0.215051	0.107526	−	0.994202i	$-0.465707\pi$
$37$	1.30811	0.215051	0.107526	+	0.994202i	$0.465707\pi$
$38$	−4.78553	−0.776315
$39$	0.748023	0.119779
$40$	−0.275205	−0.0435138
$41$	−9.73898	−1.52097	−0.760487	−	0.649354i	$-0.775040\pi$
$41$	−9.73898	−1.52097	−0.760487	+	0.649354i	$0.775040\pi$
$42$	−0.814827	−0.125731
$43$	1.46831	0.223916	0.111958	−	0.993713i	$-0.464288\pi$
$43$	1.46831	0.223916	0.111958	+	0.993713i	$0.464288\pi$
$44$	−0.495907	−0.0747607
$45$	−0.642895	−0.0958371
$46$	2.19624	0.323819
$47$	−5.94545	−0.867233	−0.433617	−	0.901097i	$-0.642763\pi$
$47$	−5.94545	−0.867233	−0.433617	+	0.901097i	$0.642763\pi$
$48$	0.814827	0.117610
$49$	1.00000	0.142857
$50$	4.92426	0.696396
$51$	−3.07008	−0.429897
$52$	0.918014	0.127306
$53$	1.04651	0.143750	0.0718749	−	0.997414i	$-0.477102\pi$
$53$	1.04651	0.143750	0.0718749	+	0.997414i	$0.477102\pi$
$54$	4.34797	0.591683
$55$	−0.136476	−0.0184024
$56$	−1.00000	−0.133631
$57$	3.89938	0.516486
$58$	0.158548	0.0208183
$59$	4.67138	0.608162	0.304081	−	0.952646i	$-0.401651\pi$
$59$	4.67138	0.608162	0.304081	+	0.952646i	$0.401651\pi$
$60$	0.224245	0.0289499
$61$	3.90709	0.500251	0.250126	−	0.968213i	$-0.419528\pi$
$61$	3.90709	0.500251	0.250126	+	0.968213i	$0.419528\pi$
$62$	−9.95933	−1.26484
$63$	−2.33606	−0.294315
$64$	1.00000	0.125000
$65$	0.252642	0.0313364
$66$	0.404078	0.0497386
$67$	−1.29250	−0.157904	−0.0789519	−	0.996878i	$-0.525157\pi$
$67$	−1.29250	−0.157904	−0.0789519	+	0.996878i	$0.525157\pi$
$68$	−3.76776	−0.456909
$69$	−1.78956	−0.215438
$70$	−0.275205	−0.0328933
$71$	−6.58725	−0.781763	−0.390882	−	0.920441i	$-0.627830\pi$
$71$	−6.58725	−0.781763	−0.390882	+	0.920441i	$0.627830\pi$
$72$	2.33606	0.275307
$73$	−4.35370	−0.509562	−0.254781	−	0.966999i	$-0.582003\pi$
$73$	−4.35370	−0.509562	−0.254781	+	0.966999i	$0.582003\pi$
$74$	−1.30811	−0.152064
$75$	−4.01242	−0.463315
$76$	4.78553	0.548938
$77$	−0.495907	−0.0565138
$78$	−0.748023	−0.0846969
$79$	−5.47581	−0.616077	−0.308038	−	0.951374i	$-0.599673\pi$
$79$	−5.47581	−0.616077	−0.308038	+	0.951374i	$0.599673\pi$
$80$	0.275205	0.0307689
$81$	3.46533	0.385036
$82$	9.73898	1.07549
$83$	−2.20462	−0.241989	−0.120994	−	0.992653i	$-0.538608\pi$
$83$	−2.20462	−0.241989	−0.120994	+	0.992653i	$0.538608\pi$
$84$	0.814827	0.0889050
$85$	−1.03691	−0.112469
$86$	−1.46831	−0.158332
$87$	−0.129189	−0.0138505
$88$	0.495907	0.0528638
$89$	−7.84816	−0.831903	−0.415952	−	0.909387i	$-0.636551\pi$
$89$	−7.84816	−0.831903	−0.415952	+	0.909387i	$0.636551\pi$
$90$	0.642895	0.0677671
$91$	0.918014	0.0962340
$92$	−2.19624	−0.228974
$93$	8.11514	0.841501
$94$	5.94545	0.613227
$95$	1.31700	0.135122
$96$	−0.814827	−0.0831630
$97$	−5.03352	−0.511076	−0.255538	−	0.966799i	$-0.582253\pi$
$97$	−5.03352	−0.511076	−0.255538	+	0.966799i	$0.582253\pi$
$98$	−1.00000	−0.101015
$99$	1.15847	0.116430
$100$	−4.92426	−0.492426
$101$	−5.40818	−0.538134	−0.269067	−	0.963121i	$-0.586715\pi$
$101$	−5.40818	−0.538134	−0.269067	+	0.963121i	$0.586715\pi$
$102$	3.07008	0.303983
$103$	0.203809	0.0200819	0.0100410	−	0.999950i	$-0.496804\pi$
$103$	0.203809	0.0200819	0.0100410	+	0.999950i	$0.496804\pi$
$104$	−0.918014	−0.0900186
$105$	0.224245	0.0218840
$106$	−1.04651	−0.101646
$107$	12.5232	1.21066	0.605332	−	0.795973i	$-0.293040\pi$
$107$	12.5232	1.21066	0.605332	+	0.795973i	$0.293040\pi$
$108$	−4.34797	−0.418383
$109$	−13.7309	−1.31518	−0.657592	−	0.753375i	$-0.728425\pi$
$109$	−13.7309	−1.31518	−0.657592	+	0.753375i	$0.728425\pi$
$110$	0.136476	0.0130125
$111$	1.06588	0.101169
$112$	1.00000	0.0944911
$113$	9.33850	0.878492	0.439246	−	0.898367i	$-0.355246\pi$
$113$	9.33850	0.878492	0.439246	+	0.898367i	$0.355246\pi$
$114$	−3.89938	−0.365210
$115$	−0.604418	−0.0563623
$116$	−0.158548	−0.0147208
$117$	−2.14453	−0.198262
$118$	−4.67138	−0.430035
$119$	−3.76776	−0.345390
$120$	−0.224245	−0.0204707
$121$	−10.7541	−0.977643
$122$	−3.90709	−0.353731
$123$	−7.93559	−0.715528
$124$	9.95933	0.894375
$125$	−2.73121	−0.244287
$126$	2.33606	0.208112
$127$	14.6871	1.30327	0.651637	−	0.758531i	$-0.274083\pi$
$127$	14.6871	1.30327	0.651637	+	0.758531i	$0.274083\pi$
$128$	−1.00000	−0.0883883
$129$	1.19642	0.105339
$130$	−0.252642	−0.0221582
$131$	−12.3759	−1.08129	−0.540643	−	0.841252i	$-0.681819\pi$
$131$	−12.3759	−1.08129	−0.540643	+	0.841252i	$0.681819\pi$
$132$	−0.404078	−0.0351705
$133$	4.78553	0.414958
$134$	1.29250	0.111655
$135$	−1.19658	−0.102985
$136$	3.76776	0.323083
$137$	−18.2540	−1.55955	−0.779774	−	0.626061i	$-0.784666\pi$
$137$	−18.2540	−1.55955	−0.779774	+	0.626061i	$0.784666\pi$
$138$	1.78956	0.152337
$139$	−13.3725	−1.13424	−0.567121	−	0.823635i	$-0.691943\pi$
$139$	−13.3725	−1.13424	−0.567121	+	0.823635i	$0.691943\pi$
$140$	0.275205	0.0232591
$141$	−4.84452	−0.407982
$142$	6.58725	0.552790
$143$	−0.455249	−0.0380698
$144$	−2.33606	−0.194671
$145$	−0.0436331	−0.00362353
$146$	4.35370	0.360315
$147$	0.814827	0.0672058
$148$	1.30811	0.107526
$149$	−21.3385	−1.74812	−0.874061	−	0.485817i	$-0.838522\pi$
$149$	−21.3385	−1.74812	−0.874061	+	0.485817i	$0.838522\pi$
$150$	4.01242	0.327613
$151$	22.7817	1.85395	0.926973	−	0.375128i	$-0.122401\pi$
$151$	22.7817	1.85395	0.926973	+	0.375128i	$0.122401\pi$
$152$	−4.78553	−0.388158
$153$	8.80171	0.711576
$154$	0.495907	0.0399613
$155$	2.74086	0.220151
$156$	0.748023	0.0598897
$157$	0.388293	0.0309892	0.0154946	−	0.999880i	$-0.495068\pi$
$157$	0.388293	0.0309892	0.0154946	+	0.999880i	$0.495068\pi$
$158$	5.47581	0.435632
$159$	0.852728	0.0676258
$160$	−0.275205	−0.0217569
$161$	−2.19624	−0.173088
$162$	−3.46533	−0.272262
$163$	11.7802	0.922695	0.461348	−	0.887220i	$-0.347366\pi$
$163$	11.7802	0.922695	0.461348	+	0.887220i	$0.347366\pi$
$164$	−9.73898	−0.760487
$165$	−0.111204	−0.00865726
$166$	2.20462	0.171112
$167$	9.46381	0.732332	0.366166	−	0.930550i	$-0.380670\pi$
$167$	9.46381	0.732332	0.366166	+	0.930550i	$0.380670\pi$
$168$	−0.814827	−0.0628653
$169$	−12.1573	−0.935173
$170$	1.03691	0.0795272
$171$	−11.1793	−0.854900
$172$	1.46831	0.111958
$173$	−23.6687	−1.79950	−0.899748	−	0.436410i	$-0.856250\pi$
$173$	−23.6687	−1.79950	−0.899748	+	0.436410i	$0.856250\pi$
$174$	0.129189	0.00979378
$175$	−4.92426	−0.372239
$176$	−0.495907	−0.0373804
$177$	3.80637	0.286104
$178$	7.84816	0.588245
$179$	−23.0901	−1.72583	−0.862917	−	0.505346i	$-0.831365\pi$
$179$	−23.0901	−1.72583	−0.862917	+	0.505346i	$0.831365\pi$
$180$	−0.642895	−0.0479185
$181$	−20.3713	−1.51419	−0.757094	−	0.653306i	$-0.773382\pi$
$181$	−20.3713	−1.51419	−0.757094	+	0.653306i	$0.773382\pi$
$182$	−0.918014	−0.0680477
$183$	3.18360	0.235339
$184$	2.19624	0.161909
$185$	0.359998	0.0264675
$186$	−8.11514	−0.595031
$187$	1.86846	0.136635
$188$	−5.94545	−0.433617
$189$	−4.34797	−0.316268
$190$	−1.31700	−0.0955454
$191$	24.6585	1.78423	0.892113	−	0.451813i	$-0.149223\pi$
$191$	24.6585	1.78423	0.892113	+	0.451813i	$0.149223\pi$
$192$	0.814827	0.0588051
$193$	−2.64000	−0.190031	−0.0950156	−	0.995476i	$-0.530290\pi$
$193$	−2.64000	−0.190031	−0.0950156	+	0.995476i	$0.530290\pi$
$194$	5.03352	0.361386
$195$	0.205860	0.0147419
$196$	1.00000	0.0714286
$197$	8.11129	0.577906	0.288953	−	0.957343i	$-0.406693\pi$
$197$	8.11129	0.577906	0.288953	+	0.957343i	$0.406693\pi$
$198$	−1.15847	−0.0823286
$199$	−6.38861	−0.452877	−0.226438	−	0.974026i	$-0.572708\pi$
$199$	−6.38861	−0.452877	−0.226438	+	0.974026i	$0.572708\pi$
$200$	4.92426	0.348198
$201$	−1.05316	−0.0742844
$202$	5.40818	0.380518
$203$	−0.158548	−0.0111279
$204$	−3.07008	−0.214948
$205$	−2.68022	−0.187195
$206$	−0.203809	−0.0142001
$207$	5.13055	0.356598
$208$	0.918014	0.0636528
$209$	−2.37318	−0.164156
$210$	−0.224245	−0.0154744
$211$	−20.0231	−1.37844	−0.689222	−	0.724550i	$-0.742048\pi$
$211$	−20.0231	−1.37844	−0.689222	+	0.724550i	$0.742048\pi$
$212$	1.04651	0.0718749
$213$	−5.36747	−0.367773
$214$	−12.5232	−0.856068
$215$	0.404087	0.0275585
$216$	4.34797	0.295842
$217$	9.95933	0.676084
$218$	13.7309	0.929975
$219$	−3.54751	−0.239719
$220$	−0.136476	−0.00920122
$221$	−3.45886	−0.232668
$222$	−1.06588	−0.0715372
$223$	−1.37940	−0.0923712	−0.0461856	−	0.998933i	$-0.514707\pi$
$223$	−1.37940	−0.0923712	−0.0461856	+	0.998933i	$0.514707\pi$
$224$	−1.00000	−0.0668153
$225$	11.5034	0.766890
$226$	−9.33850	−0.621188
$227$	−7.63572	−0.506801	−0.253400	−	0.967361i	$-0.581549\pi$
$227$	−7.63572	−0.506801	−0.253400	+	0.967361i	$0.581549\pi$
$228$	3.89938	0.258243
$229$	−3.72108	−0.245896	−0.122948	−	0.992413i	$-0.539235\pi$
$229$	−3.72108	−0.245896	−0.122948	+	0.992413i	$0.539235\pi$
$230$	0.604418	0.0398541
$231$	−0.404078	−0.0265864
$232$	0.158548	0.0104092
$233$	−4.55355	−0.298313	−0.149156	−	0.988814i	$-0.547656\pi$
$233$	−4.55355	−0.298313	−0.149156	+	0.988814i	$0.547656\pi$
$234$	2.14453	0.140192
$235$	−1.63622	−0.106735
$236$	4.67138	0.304081
$237$	−4.46184	−0.289828
$238$	3.76776	0.244228
$239$	6.51967	0.421722	0.210861	−	0.977516i	$-0.432373\pi$
$239$	6.51967	0.421722	0.210861	+	0.977516i	$0.432373\pi$
$240$	0.224245	0.0144749
$241$	16.3811	1.05520	0.527600	−	0.849493i	$-0.323092\pi$
$241$	16.3811	1.05520	0.527600	+	0.849493i	$0.323092\pi$
$242$	10.7541	0.691298
$243$	15.8675	1.01790
$244$	3.90709	0.250126
$245$	0.275205	0.0175822
$246$	7.93559	0.505955
$247$	4.39318	0.279531
$248$	−9.95933	−0.632418
$249$	−1.79639	−0.113841
$250$	2.73121	0.172737
$251$	−25.5773	−1.61443	−0.807213	−	0.590260i	$-0.799025\pi$
$251$	−25.5773	−1.61443	−0.807213	+	0.590260i	$0.799025\pi$
$252$	−2.33606	−0.147158
$253$	1.08913	0.0684732
$254$	−14.6871	−0.921553
$255$	−0.844901	−0.0529098
$256$	1.00000	0.0625000
$257$	7.94824	0.495798	0.247899	−	0.968786i	$-0.420260\pi$
$257$	7.94824	0.495798	0.247899	+	0.968786i	$0.420260\pi$
$258$	−1.19642	−0.0744860
$259$	1.30811	0.0812818
$260$	0.252642	0.0156682
$261$	0.370376	0.0229257
$262$	12.3759	0.764584
$263$	−6.63152	−0.408917	−0.204458	−	0.978875i	$-0.565543\pi$
$263$	−6.63152	−0.408917	−0.204458	+	0.978875i	$0.565543\pi$
$264$	0.404078	0.0248693
$265$	0.288006	0.0176921
$266$	−4.78553	−0.293420
$267$	−6.39490	−0.391361
$268$	−1.29250	−0.0789519
$269$	25.8954	1.57887	0.789434	−	0.613835i	$-0.210374\pi$
$269$	25.8954	1.57887	0.789434	+	0.613835i	$0.210374\pi$
$270$	1.19658	0.0728217
$271$	12.0554	0.732314	0.366157	−	0.930553i	$-0.380673\pi$
$271$	12.0554	0.732314	0.366157	+	0.930553i	$0.380673\pi$
$272$	−3.76776	−0.228454
$273$	0.748023	0.0452724
$274$	18.2540	1.10277
$275$	2.44197	0.147257
$276$	−1.78956	−0.107719
$277$	−19.2337	−1.15564	−0.577819	−	0.816165i	$-0.696096\pi$
$277$	−19.2337	−1.15564	−0.577819	+	0.816165i	$0.696096\pi$
$278$	13.3725	0.802030
$279$	−23.2656	−1.39287
$280$	−0.275205	−0.0164467
$281$	11.2487	0.671040	0.335520	−	0.942033i	$-0.391088\pi$
$281$	11.2487	0.671040	0.335520	+	0.942033i	$0.391088\pi$
$282$	4.84452	0.288487
$283$	−10.7782	−0.640700	−0.320350	−	0.947299i	$-0.603800\pi$
$283$	−10.7782	−0.640700	−0.320350	+	0.947299i	$0.603800\pi$
$284$	−6.58725	−0.390882
$285$	1.07313	0.0635667
$286$	0.455249	0.0269194
$287$	−9.73898	−0.574874
$288$	2.33606	0.137653
$289$	−2.80395	−0.164938
$290$	0.0436331	0.00256222
$291$	−4.10145	−0.240431
$292$	−4.35370	−0.254781
$293$	−0.509640	−0.0297735	−0.0148867	−	0.999889i	$-0.504739\pi$
$293$	−0.509640	−0.0297735	−0.0148867	+	0.999889i	$0.504739\pi$
$294$	−0.814827	−0.0475217
$295$	1.28559	0.0748498
$296$	−1.30811	−0.0760321
$297$	2.15618	0.125115
$298$	21.3385	1.23611
$299$	−2.01618	−0.116599
$300$	−4.01242	−0.231657
$301$	1.46831	0.0846322
$302$	−22.7817	−1.31094
$303$	−4.40674	−0.253160
$304$	4.78553	0.274469
$305$	1.07525	0.0615687
$306$	−8.80171	−0.503160
$307$	−1.59062	−0.0907815	−0.0453907	−	0.998969i	$-0.514453\pi$
$307$	−1.59062	−0.0907815	−0.0453907	+	0.998969i	$0.514453\pi$
$308$	−0.495907	−0.0282569
$309$	0.166069	0.00944736
$310$	−2.74086	−0.155670
$311$	4.62263	0.262125	0.131063	−	0.991374i	$-0.458161\pi$
$311$	4.62263	0.262125	0.131063	+	0.991374i	$0.458161\pi$
$312$	−0.748023	−0.0423484
$313$	−31.4557	−1.77798	−0.888990	−	0.457927i	$-0.848592\pi$
$313$	−31.4557	−1.77798	−0.888990	+	0.457927i	$0.848592\pi$
$314$	−0.388293	−0.0219127
$315$	−0.642895	−0.0362230
$316$	−5.47581	−0.308038
$317$	28.5895	1.60575	0.802874	−	0.596149i	$-0.203303\pi$
$317$	28.5895	1.60575	0.802874	+	0.596149i	$0.203303\pi$
$318$	−0.852728	−0.0478186
$319$	0.0786248	0.00440214
$320$	0.275205	0.0153844
$321$	10.2042	0.569546
$322$	2.19624	0.122392
$323$	−18.0307	−1.00326
$324$	3.46533	0.192518
$325$	−4.52054	−0.250754
$326$	−11.7802	−0.652444
$327$	−11.1883	−0.618716
$328$	9.73898	0.537745
$329$	−5.94545	−0.327783
$330$	0.111204	0.00612160
$331$	−5.55557	−0.305362	−0.152681	−	0.988276i	$-0.548791\pi$
$331$	−5.55557	−0.305362	−0.152681	+	0.988276i	$0.548791\pi$
$332$	−2.20462	−0.120994
$333$	−3.05581	−0.167457
$334$	−9.46381	−0.517837
$335$	−0.355702	−0.0194341
$336$	0.814827	0.0444525
$337$	−5.52070	−0.300732	−0.150366	−	0.988630i	$-0.548045\pi$
$337$	−5.52070	−0.300732	−0.150366	+	0.988630i	$0.548045\pi$
$338$	12.1573	0.661267
$339$	7.60927	0.413279
$340$	−1.03691	−0.0562343
$341$	−4.93890	−0.267456
$342$	11.1793	0.604505
$343$	1.00000	0.0539949
$344$	−1.46831	−0.0791661
$345$	−0.492496	−0.0265151
$346$	23.6687	1.27244
$347$	29.9041	1.60534	0.802668	−	0.596426i	$-0.203413\pi$
$347$	29.9041	1.60534	0.802668	+	0.596426i	$0.203413\pi$
$348$	−0.129189	−0.00692525
$349$	18.3117	0.980205	0.490102	−	0.871665i	$-0.336959\pi$
$349$	18.3117	0.980205	0.490102	+	0.871665i	$0.336959\pi$
$350$	4.92426	0.263213
$351$	−3.99149	−0.213050
$352$	0.495907	0.0264319
$353$	−13.9885	−0.744530	−0.372265	−	0.928126i	$-0.621419\pi$
$353$	−13.9885	−0.744530	−0.372265	+	0.928126i	$0.621419\pi$
$354$	−3.80637	−0.202306
$355$	−1.81285	−0.0962159
$356$	−7.84816	−0.415952
$357$	−3.07008	−0.162486
$358$	23.0901	1.22035
$359$	14.7500	0.778473	0.389237	−	0.921138i	$-0.372739\pi$
$359$	14.7500	0.778473	0.389237	+	0.921138i	$0.372739\pi$
$360$	0.642895	0.0338835
$361$	3.90129	0.205331
$362$	20.3713	1.07069
$363$	−8.76272	−0.459923
$364$	0.918014	0.0481170
$365$	−1.19816	−0.0627146
$366$	−3.18360	−0.166409
$367$	−32.4568	−1.69423	−0.847116	−	0.531408i	$-0.821663\pi$
$367$	−32.4568	−1.69423	−0.847116	+	0.531408i	$0.821663\pi$
$368$	−2.19624	−0.114487
$369$	22.7508	1.18436
$370$	−0.359998	−0.0187154
$371$	1.04651	0.0543323
$372$	8.11514	0.420750
$373$	1.10031	0.0569717	0.0284858	−	0.999594i	$-0.490931\pi$
$373$	1.10031	0.0569717	0.0284858	+	0.999594i	$0.490931\pi$
$374$	−1.86846	−0.0966158
$375$	−2.22546	−0.114922
$376$	5.94545	0.306613
$377$	−0.145549	−0.00749614
$378$	4.34797	0.223635
$379$	−37.2258	−1.91216	−0.956081	−	0.293104i	$-0.905312\pi$
$379$	−37.2258	−1.91216	−0.956081	+	0.293104i	$0.905312\pi$
$380$	1.31700	0.0675608
$381$	11.9675	0.613113
$382$	−24.6585	−1.26164
$383$	30.0708	1.53655	0.768274	−	0.640122i	$-0.221116\pi$
$383$	30.0708	1.53655	0.768274	+	0.640122i	$0.221116\pi$
$384$	−0.814827	−0.0415815
$385$	−0.136476	−0.00695547
$386$	2.64000	0.134372
$387$	−3.43006	−0.174360
$388$	−5.03352	−0.255538
$389$	−18.1536	−0.920424	−0.460212	−	0.887809i	$-0.652227\pi$
$389$	−18.1536	−0.920424	−0.460212	+	0.887809i	$0.652227\pi$
$390$	−0.205860	−0.0104241
$391$	8.27493	0.418481
$392$	−1.00000	−0.0505076
$393$	−10.0842	−0.508681
$394$	−8.11129	−0.408641
$395$	−1.50697	−0.0758240
$396$	1.15847	0.0582151
$397$	26.5905	1.33454	0.667269	−	0.744817i	$-0.267463\pi$
$397$	26.5905	1.33454	0.667269	+	0.744817i	$0.267463\pi$
$398$	6.38861	0.320232
$399$	3.89938	0.195213
$400$	−4.92426	−0.246213
$401$	20.3136	1.01441	0.507206	−	0.861825i	$-0.330678\pi$
$401$	20.3136	1.01441	0.507206	+	0.861825i	$0.330678\pi$
$402$	1.05316	0.0525270
$403$	9.14280	0.455435
$404$	−5.40818	−0.269067
$405$	0.953676	0.0473885
$406$	0.158548	0.00786858
$407$	−0.648699	−0.0321548
$408$	3.07008	0.151992
$409$	15.9614	0.789239	0.394620	−	0.918845i	$-0.370876\pi$
$409$	15.9614	0.789239	0.394620	+	0.918845i	$0.370876\pi$
$410$	2.68022	0.132367
$411$	−14.8739	−0.733675
$412$	0.203809	0.0100410
$413$	4.67138	0.229864
$414$	−5.13055	−0.252153
$415$	−0.606724	−0.0297829
$416$	−0.918014	−0.0450093
$417$	−10.8963	−0.533593
$418$	2.37318	0.116076
$419$	−31.4919	−1.53848	−0.769240	−	0.638960i	$-0.779365\pi$
$419$	−31.4919	−1.53848	−0.769240	+	0.638960i	$0.779365\pi$
$420$	0.224245	0.0109420
$421$	−1.21137	−0.0590387	−0.0295194	−	0.999564i	$-0.509398\pi$
$421$	−1.21137	−0.0590387	−0.0295194	+	0.999564i	$0.509398\pi$
$422$	20.0231	0.974708
$423$	13.8889	0.675302
$424$	−1.04651	−0.0508232
$425$	18.5535	0.899975
$426$	5.36747	0.260055
$427$	3.90709	0.189077
$428$	12.5232	0.605332
$429$	−0.370949	−0.0179096
$430$	−0.404087	−0.0194868
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−4.34797	−0.209192
$433$	−5.33290	−0.256283	−0.128142	−	0.991756i	$-0.540901\pi$
$433$	−5.33290	−0.256283	−0.128142	+	0.991756i	$0.540901\pi$
$434$	−9.95933	−0.478063
$435$	−0.0355535	−0.00170466
$436$	−13.7309	−0.657592
$437$	−10.5102	−0.502771
$438$	3.54751	0.169507
$439$	36.5457	1.74423	0.872115	−	0.489300i	$-0.162748\pi$
$439$	36.5457	1.74423	0.872115	+	0.489300i	$0.162748\pi$
$440$	0.136476	0.00650624
$441$	−2.33606	−0.111241
$442$	3.45886	0.164521
$443$	−5.10251	−0.242428	−0.121214	−	0.992626i	$-0.538679\pi$
$443$	−5.10251	−0.242428	−0.121214	+	0.992626i	$0.538679\pi$
$444$	1.06588	0.0505845
$445$	−2.15985	−0.102387
$446$	1.37940	0.0653163
$447$	−17.3872	−0.822388
$448$	1.00000	0.0472456
$449$	−5.76809	−0.272213	−0.136107	−	0.990694i	$-0.543459\pi$
$449$	−5.76809	−0.272213	−0.136107	+	0.990694i	$0.543459\pi$
$450$	−11.5034	−0.542273
$451$	4.82963	0.227418
$452$	9.33850	0.439246
$453$	18.5631	0.872172
$454$	7.63572	0.358362
$455$	0.252642	0.0118440
$456$	−3.89938	−0.182605
$457$	−15.9742	−0.747241	−0.373621	−	0.927582i	$-0.621884\pi$
$457$	−15.9742	−0.747241	−0.373621	+	0.927582i	$0.621884\pi$
$458$	3.72108	0.173875
$459$	16.3821	0.764651
$460$	−0.604418	−0.0281811
$461$	−13.0462	−0.607622	−0.303811	−	0.952732i	$-0.598259\pi$
$461$	−13.0462	−0.607622	−0.303811	+	0.952732i	$0.598259\pi$
$462$	0.404078	0.0187994
$463$	30.6751	1.42559	0.712795	−	0.701372i	$-0.247429\pi$
$463$	30.6751	1.42559	0.712795	+	0.701372i	$0.247429\pi$
$464$	−0.158548	−0.00736039
$465$	2.23333	0.103568
$466$	4.55355	0.210939
$467$	6.63407	0.306988	0.153494	−	0.988150i	$-0.450947\pi$
$467$	6.63407	0.306988	0.153494	+	0.988150i	$0.450947\pi$
$468$	−2.14453	−0.0991310
$469$	−1.29250	−0.0596820
$470$	1.63622	0.0754732
$471$	0.316392	0.0145786
$472$	−4.67138	−0.215018
$473$	−0.728146	−0.0334802
$474$	4.46184	0.204939
$475$	−23.5652	−1.08125
$476$	−3.76776	−0.172695
$477$	−2.44472	−0.111936
$478$	−6.51967	−0.298203
$479$	−17.9641	−0.820802	−0.410401	−	0.911905i	$-0.634611\pi$
$479$	−17.9641	−0.820802	−0.410401	+	0.911905i	$0.634611\pi$
$480$	−0.224245	−0.0102353
$481$	1.20086	0.0547545
$482$	−16.3811	−0.746139
$483$	−1.78956	−0.0814278
$484$	−10.7541	−0.488822
$485$	−1.38525	−0.0629010
$486$	−15.8675	−0.719766
$487$	−25.1218	−1.13838	−0.569188	−	0.822208i	$-0.692742\pi$
$487$	−25.1218	−1.13838	−0.569188	+	0.822208i	$0.692742\pi$
$488$	−3.90709	−0.176865
$489$	9.59882	0.434073
$490$	−0.275205	−0.0124325
$491$	14.8330	0.669402	0.334701	−	0.942324i	$-0.391365\pi$
$491$	14.8330	0.669402	0.334701	+	0.942324i	$0.391365\pi$
$492$	−7.93559	−0.357764
$493$	0.597370	0.0269042
$494$	−4.39318	−0.197659
$495$	0.318816	0.0143297
$496$	9.95933	0.447187
$497$	−6.58725	−0.295479
$498$	1.79639	0.0804981
$499$	43.8768	1.96420	0.982098	−	0.188372i	$-0.0603210\pi$
$499$	43.8768	1.96420	0.982098	+	0.188372i	$0.0603210\pi$
$500$	−2.73121	−0.122143
$501$	7.71137	0.344519
$502$	25.5773	1.14157
$503$	−43.3928	−1.93479	−0.967395	−	0.253273i	$-0.918493\pi$
$503$	−43.3928	−1.93479	−0.967395	+	0.253273i	$0.918493\pi$
$504$	2.33606	0.104056
$505$	−1.48836	−0.0662312
$506$	−1.08913	−0.0484178
$507$	−9.90606	−0.439944
$508$	14.6871	0.651637
$509$	−1.54311	−0.0683970	−0.0341985	−	0.999415i	$-0.510888\pi$
$509$	−1.54311	−0.0683970	−0.0341985	+	0.999415i	$0.510888\pi$
$510$	0.844901	0.0374129
$511$	−4.35370	−0.192596
$512$	−1.00000	−0.0441942
$513$	−20.8073	−0.918665
$514$	−7.94824	−0.350582
$515$	0.0560894	0.00247159
$516$	1.19642	0.0526695
$517$	2.94839	0.129670
$518$	−1.30811	−0.0574749
$519$	−19.2859	−0.846556
$520$	−0.252642	−0.0110791
$521$	2.62862	0.115162	0.0575810	−	0.998341i	$-0.481661\pi$
$521$	2.62862	0.115162	0.0575810	+	0.998341i	$0.481661\pi$
$522$	−0.370376	−0.0162109
$523$	8.20216	0.358655	0.179328	−	0.983789i	$-0.442608\pi$
$523$	8.20216	0.358655	0.179328	+	0.983789i	$0.442608\pi$
$524$	−12.3759	−0.540643
$525$	−4.01242	−0.175117
$526$	6.63152	0.289148
$527$	−37.5244	−1.63459
$528$	−0.404078	−0.0175853
$529$	−18.1765	−0.790283
$530$	−0.288006	−0.0125102
$531$	−10.9126	−0.473567
$532$	4.78553	0.207479
$533$	−8.94052	−0.387257
$534$	6.39490	0.276734
$535$	3.44645	0.149003
$536$	1.29250	0.0558274
$537$	−18.8144	−0.811903
$538$	−25.8954	−1.11643
$539$	−0.495907	−0.0213602
$540$	−1.19658	−0.0514927
$541$	−16.3050	−0.701007	−0.350503	−	0.936561i	$-0.613989\pi$
$541$	−16.3050	−0.701007	−0.350503	+	0.936561i	$0.613989\pi$
$542$	−12.0554	−0.517824
$543$	−16.5991	−0.712336
$544$	3.76776	0.161542
$545$	−3.77882	−0.161867
$546$	−0.748023	−0.0320124
$547$	−25.7542	−1.10117	−0.550585	−	0.834779i	$-0.685595\pi$
$547$	−25.7542	−1.10117	−0.550585	+	0.834779i	$0.685595\pi$
$548$	−18.2540	−0.779774
$549$	−9.12717	−0.389538
$550$	−2.44197	−0.104126
$551$	−0.758734	−0.0323232
$552$	1.78956	0.0761687
$553$	−5.47581	−0.232855
$554$	19.2337	0.817160
$555$	0.293336	0.0124514
$556$	−13.3725	−0.567121
$557$	−19.3645	−0.820501	−0.410251	−	0.911973i	$-0.634559\pi$
$557$	−19.3645	−0.820501	−0.410251	+	0.911973i	$0.634559\pi$
$558$	23.2656	0.984910
$559$	1.34793	0.0570114
$560$	0.275205	0.0116295
$561$	1.52247	0.0642788
$562$	−11.2487	−0.474497
$563$	−36.6548	−1.54482	−0.772408	−	0.635126i	$-0.780948\pi$
$563$	−36.6548	−1.54482	−0.772408	+	0.635126i	$0.780948\pi$
$564$	−4.84452	−0.203991
$565$	2.57000	0.108121
$566$	10.7782	0.453043
$567$	3.46533	0.145530
$568$	6.58725	0.276395
$569$	−22.6387	−0.949062	−0.474531	−	0.880239i	$-0.657382\pi$
$569$	−22.6387	−0.949062	−0.474531	+	0.880239i	$0.657382\pi$
$570$	−1.07313	−0.0449485
$571$	−18.6158	−0.779048	−0.389524	−	0.921016i	$-0.627360\pi$
$571$	−18.6158	−0.779048	−0.389524	+	0.921016i	$0.627360\pi$
$572$	−0.455249	−0.0190349
$573$	20.0924	0.839373
$574$	9.73898	0.406497
$575$	10.8149	0.451012
$576$	−2.33606	−0.0973357
$577$	−42.4478	−1.76712	−0.883562	−	0.468314i	$-0.844862\pi$
$577$	−42.4478	−1.76712	−0.883562	+	0.468314i	$0.844862\pi$
$578$	2.80395	0.116629
$579$	−2.15114	−0.0893984
$580$	−0.0436331	−0.00181177
$581$	−2.20462	−0.0914632
$582$	4.10145	0.170011
$583$	−0.518973	−0.0214937
$584$	4.35370	0.180157
$585$	−0.590186	−0.0244012
$586$	0.509640	0.0210530
$587$	−15.4004	−0.635644	−0.317822	−	0.948150i	$-0.602951\pi$
$587$	−15.4004	−0.635644	−0.317822	+	0.948150i	$0.602951\pi$
$588$	0.814827	0.0336029
$589$	47.6607	1.96382
$590$	−1.28559	−0.0529268
$591$	6.60930	0.271870
$592$	1.30811	0.0537628
$593$	−18.0701	−0.742050	−0.371025	−	0.928623i	$-0.620994\pi$
$593$	−18.0701	−0.742050	−0.371025	+	0.928623i	$0.620994\pi$
$594$	−2.15618	−0.0884693
$595$	−1.03691	−0.0425091
$596$	−21.3385	−0.874061
$597$	−5.20562	−0.213052
$598$	2.01618	0.0824478
$599$	−9.56096	−0.390650	−0.195325	−	0.980739i	$-0.562576\pi$
$599$	−9.56096	−0.390650	−0.195325	+	0.980739i	$0.562576\pi$
$600$	4.01242	0.163807
$601$	35.6813	1.45547	0.727734	−	0.685859i	$-0.240573\pi$
$601$	35.6813	1.45547	0.727734	+	0.685859i	$0.240573\pi$
$602$	−1.46831	−0.0598440
$603$	3.01935	0.122957
$604$	22.7817	0.926973
$605$	−2.95958	−0.120324
$606$	4.40674	0.179011
$607$	0.739890	0.0300312	0.0150156	−	0.999887i	$-0.495220\pi$
$607$	0.739890	0.0300312	0.0150156	+	0.999887i	$0.495220\pi$
$608$	−4.78553	−0.194079
$609$	−0.129189	−0.00523500
$610$	−1.07525	−0.0435356
$611$	−5.45801	−0.220807
$612$	8.80171	0.355788
$613$	20.8299	0.841310	0.420655	−	0.907221i	$-0.361800\pi$
$613$	20.8299	0.841310	0.420655	+	0.907221i	$0.361800\pi$
$614$	1.59062	0.0641922
$615$	−2.18392	−0.0880640
$616$	0.495907	0.0199806
$617$	−30.2521	−1.21790	−0.608952	−	0.793207i	$-0.708410\pi$
$617$	−30.2521	−1.21790	−0.608952	+	0.793207i	$0.708410\pi$
$618$	−0.166069	−0.00668029
$619$	24.3421	0.978393	0.489196	−	0.872174i	$-0.337290\pi$
$619$	24.3421	0.978393	0.489196	+	0.872174i	$0.337290\pi$
$620$	2.74086	0.110076
$621$	9.54919	0.383196
$622$	−4.62263	−0.185350
$623$	−7.84816	−0.314430
$624$	0.748023	0.0299449
$625$	23.8697	0.954787
$626$	31.4557	1.25722
$627$	−1.93373	−0.0772257
$628$	0.388293	0.0154946
$629$	−4.92864	−0.196518
$630$	0.642895	0.0256135
$631$	−26.3935	−1.05071	−0.525355	−	0.850883i	$-0.676067\pi$
$631$	−26.3935	−1.05071	−0.525355	+	0.850883i	$0.676067\pi$
$632$	5.47581	0.217816
$633$	−16.3153	−0.648477
$634$	−28.5895	−1.13543
$635$	4.04198	0.160401
$636$	0.852728	0.0338129
$637$	0.918014	0.0363730
$638$	−0.0786248	−0.00311279
$639$	15.3882	0.608747
$640$	−0.275205	−0.0108784
$641$	35.2102	1.39072	0.695359	−	0.718663i	$-0.255245\pi$
$641$	35.2102	1.39072	0.695359	+	0.718663i	$0.255245\pi$
$642$	−10.2042	−0.402730
$643$	35.9023	1.41585	0.707924	−	0.706289i	$-0.249632\pi$
$643$	35.9023	1.41585	0.707924	+	0.706289i	$0.249632\pi$
$644$	−2.19624	−0.0865442
$645$	0.329261	0.0129647
$646$	18.0307	0.709410
$647$	−22.1431	−0.870534	−0.435267	−	0.900302i	$-0.643346\pi$
$647$	−22.1431	−0.870534	−0.435267	+	0.900302i	$0.643346\pi$
$648$	−3.46533	−0.136131
$649$	−2.31657	−0.0909333
$650$	4.52054	0.177310
$651$	8.11514	0.318057
$652$	11.7802	0.461348
$653$	5.19388	0.203252	0.101626	−	0.994823i	$-0.467595\pi$
$653$	5.19388	0.203252	0.101626	+	0.994823i	$0.467595\pi$
$654$	11.1883	0.437498
$655$	−3.40591	−0.133080
$656$	−9.73898	−0.380243
$657$	10.1705	0.396788
$658$	5.94545	0.231778
$659$	−42.0553	−1.63824	−0.819121	−	0.573620i	$-0.805538\pi$
$659$	−42.0553	−1.63824	−0.819121	+	0.573620i	$0.805538\pi$
$660$	−0.111204	−0.00432863
$661$	−21.2054	−0.824793	−0.412397	−	0.911004i	$-0.635308\pi$
$661$	−21.2054	−0.824793	−0.412397	+	0.911004i	$0.635308\pi$
$662$	5.55557	0.215923
$663$	−2.81837	−0.109457
$664$	2.20462	0.0855560
$665$	1.31700	0.0510712
$666$	3.05581	0.118410
$667$	0.348209	0.0134827
$668$	9.46381	0.366166
$669$	−1.12397	−0.0434552
$670$	0.355702	0.0137420
$671$	−1.93755	−0.0747983
$672$	−0.814827	−0.0314327
$673$	−36.6686	−1.41347	−0.706736	−	0.707477i	$-0.749833\pi$
$673$	−36.6686	−1.41347	−0.706736	+	0.707477i	$0.749833\pi$
$674$	5.52070	0.212650
$675$	21.4105	0.824091
$676$	−12.1573	−0.467587
$677$	51.5771	1.98227	0.991135	−	0.132858i	$-0.0424155\pi$
$677$	51.5771	1.98227	0.991135	+	0.132858i	$0.0424155\pi$
$678$	−7.60927	−0.292232
$679$	−5.03352	−0.193169
$680$	1.03691	0.0397636
$681$	−6.22180	−0.238420
$682$	4.93890	0.189120
$683$	35.2323	1.34813	0.674063	−	0.738674i	$-0.264548\pi$
$683$	35.2323	1.34813	0.674063	+	0.738674i	$0.264548\pi$
$684$	−11.1793	−0.427450
$685$	−5.02361	−0.191942
$686$	−1.00000	−0.0381802
$687$	−3.03204	−0.115680
$688$	1.46831	0.0559789
$689$	0.960714	0.0366003
$690$	0.492496	0.0187490
$691$	−15.8277	−0.602113	−0.301057	−	0.953606i	$-0.597339\pi$
$691$	−15.8277	−0.602113	−0.301057	+	0.953606i	$0.597339\pi$
$692$	−23.6687	−0.899748
$693$	1.15847	0.0440065
$694$	−29.9041	−1.13514
$695$	−3.68018	−0.139597
$696$	0.129189	0.00489689
$697$	36.6942	1.38989
$698$	−18.3117	−0.693110
$699$	−3.71036	−0.140339
$700$	−4.92426	−0.186120
$701$	−43.7093	−1.65088	−0.825440	−	0.564490i	$-0.809073\pi$
$701$	−43.7093	−1.65088	−0.825440	+	0.564490i	$0.809073\pi$
$702$	3.99149	0.150649
$703$	6.25998	0.236100
$704$	−0.495907	−0.0186902
$705$	−1.33324	−0.0502126
$706$	13.9885	0.526462
$707$	−5.40818	−0.203396
$708$	3.80637	0.143052
$709$	−12.4489	−0.467527	−0.233764	−	0.972293i	$-0.575104\pi$
$709$	−12.4489	−0.467527	−0.233764	+	0.972293i	$0.575104\pi$
$710$	1.81285	0.0680349
$711$	12.7918	0.479730
$712$	7.84816	0.294122
$713$	−21.8731	−0.819155
$714$	3.07008	0.114895
$715$	−0.125287	−0.00468546
$716$	−23.0901	−0.862917
$717$	5.31240	0.198395
$718$	−14.7500	−0.550464
$719$	53.4095	1.99184	0.995918	−	0.0902599i	$-0.0287698\pi$
$719$	53.4095	1.99184	0.995918	+	0.0902599i	$0.0287698\pi$
$720$	−0.642895	−0.0239593
$721$	0.203809	0.00759026
$722$	−3.90129	−0.145191
$723$	13.3478	0.496409
$724$	−20.3713	−0.757094
$725$	0.780730	0.0289956
$726$	8.76272	0.325215
$727$	35.2915	1.30889	0.654445	−	0.756110i	$-0.272902\pi$
$727$	35.2915	1.30889	0.654445	+	0.756110i	$0.272902\pi$
$728$	−0.918014	−0.0340238
$729$	2.53332	0.0938268
$730$	1.19816	0.0443459
$731$	−5.53226	−0.204618
$732$	3.18360	0.117669
$733$	0.0597677	0.00220757	0.00110378	−	0.999999i	$-0.499649\pi$
$733$	0.0597677	0.00220757	0.00110378	+	0.999999i	$0.499649\pi$
$734$	32.4568	1.19800
$735$	0.224245	0.00827139
$736$	2.19624	0.0809546
$737$	0.640958	0.0236100
$738$	−22.7508	−0.837469
$739$	46.2822	1.70252	0.851258	−	0.524747i	$-0.175840\pi$
$739$	46.2822	1.70252	0.851258	+	0.524747i	$0.175840\pi$
$740$	0.359998	0.0132338
$741$	3.57968	0.131503
$742$	−1.04651	−0.0384187
$743$	47.0536	1.72623	0.863115	−	0.505008i	$-0.168510\pi$
$743$	47.0536	1.72623	0.863115	+	0.505008i	$0.168510\pi$
$744$	−8.11514	−0.297515
$745$	−5.87248	−0.215151
$746$	−1.10031	−0.0402851
$747$	5.15012	0.188433
$748$	1.86846	0.0683177
$749$	12.5232	0.457588
$750$	2.22546	0.0812624
$751$	−4.94748	−0.180536	−0.0902680	−	0.995918i	$-0.528772\pi$
$751$	−4.94748	−0.180536	−0.0902680	+	0.995918i	$0.528772\pi$
$752$	−5.94545	−0.216808
$753$	−20.8411	−0.759492
$754$	0.145549	0.00530057
$755$	6.26963	0.228175
$756$	−4.34797	−0.158134
$757$	22.9337	0.833538	0.416769	−	0.909012i	$-0.363162\pi$
$757$	22.9337	0.833538	0.416769	+	0.909012i	$0.363162\pi$
$758$	37.2258	1.35210
$759$	0.887455	0.0322126
$760$	−1.31700	−0.0477727
$761$	43.7553	1.58613	0.793064	−	0.609138i	$-0.208485\pi$
$761$	43.7553	1.58613	0.793064	+	0.609138i	$0.208485\pi$
$762$	−11.9675	−0.433536
$763$	−13.7309	−0.497093
$764$	24.6585	0.892113
$765$	2.42228	0.0875776
$766$	−30.0708	−1.08650
$767$	4.28839	0.154845
$768$	0.814827	0.0294026
$769$	−31.9551	−1.15233	−0.576165	−	0.817333i	$-0.695451\pi$
$769$	−31.9551	−1.15233	−0.576165	+	0.817333i	$0.695451\pi$
$770$	0.136476	0.00491826
$771$	6.47644	0.233243
$772$	−2.64000	−0.0950156
$773$	19.4282	0.698785	0.349393	−	0.936976i	$-0.386388\pi$
$773$	19.4282	0.698785	0.349393	+	0.936976i	$0.386388\pi$
$774$	3.43006	0.123291
$775$	−49.0424	−1.76165
$776$	5.03352	0.180693
$777$	1.06588	0.0382383
$778$	18.1536	0.650838
$779$	−46.6062	−1.66984
$780$	0.205860	0.00737096
$781$	3.26666	0.116890
$782$	−8.27493	−0.295911
$783$	0.689359	0.0246357
$784$	1.00000	0.0357143
$785$	0.106860	0.00381401
$786$	10.0842	0.359692
$787$	−11.9423	−0.425697	−0.212848	−	0.977085i	$-0.568274\pi$
$787$	−11.9423	−0.425697	−0.212848	+	0.977085i	$0.568274\pi$
$788$	8.11129	0.288953
$789$	−5.40354	−0.192371
$790$	1.50697	0.0536156
$791$	9.33850	0.332039
$792$	−1.15847	−0.0411643
$793$	3.58676	0.127370
$794$	−26.5905	−0.943660
$795$	0.234675	0.00832307
$796$	−6.38861	−0.226438
$797$	−16.9371	−0.599943	−0.299971	−	0.953948i	$-0.596977\pi$
$797$	−16.9371	−0.599943	−0.299971	+	0.953948i	$0.596977\pi$
$798$	−3.89938	−0.138037
$799$	22.4011	0.792493
$800$	4.92426	0.174099
$801$	18.3337	0.647791
$802$	−20.3136	−0.717297
$803$	2.15903	0.0761904
$804$	−1.05316	−0.0371422
$805$	−0.604418	−0.0213029
$806$	−9.14280	−0.322042
$807$	21.1003	0.742764
$808$	5.40818	0.190259
$809$	−33.3849	−1.17375	−0.586875	−	0.809678i	$-0.699642\pi$
$809$	−33.3849	−1.17375	−0.586875	+	0.809678i	$0.699642\pi$
$810$	−0.953676	−0.0335088
$811$	−29.3250	−1.02974	−0.514870	−	0.857268i	$-0.672160\pi$
$811$	−29.3250	−1.02974	−0.514870	+	0.857268i	$0.672160\pi$
$812$	−0.158548	−0.00556393
$813$	9.82307	0.344510
$814$	0.648699	0.0227369
$815$	3.24197	0.113561
$816$	−3.07008	−0.107474
$817$	7.02665	0.245832
$818$	−15.9614	−0.558076
$819$	−2.14453	−0.0749360
$820$	−2.68022	−0.0935973
$821$	17.4989	0.610716	0.305358	−	0.952238i	$-0.401224\pi$
$821$	17.4989	0.610716	0.305358	+	0.952238i	$0.401224\pi$
$822$	14.8739	0.518787
$823$	23.9409	0.834527	0.417264	−	0.908786i	$-0.362989\pi$
$823$	23.9409	0.834527	0.417264	+	0.908786i	$0.362989\pi$
$824$	−0.203809	−0.00710004
$825$	1.98979	0.0692755
$826$	−4.67138	−0.162538
$827$	7.14295	0.248385	0.124192	−	0.992258i	$-0.460366\pi$
$827$	7.14295	0.248385	0.124192	+	0.992258i	$0.460366\pi$
$828$	5.13055	0.178299
$829$	37.8597	1.31492	0.657461	−	0.753489i	$-0.271631\pi$
$829$	37.8597	1.31492	0.657461	+	0.753489i	$0.271631\pi$
$830$	0.606724	0.0210597
$831$	−15.6721	−0.543660
$832$	0.918014	0.0318264
$833$	−3.76776	−0.130545
$834$	10.8963	0.377307
$835$	2.60449	0.0901321
$836$	−2.37318	−0.0820780
$837$	−43.3028	−1.49676
$838$	31.4919	1.08787
$839$	−44.5703	−1.53874	−0.769368	−	0.638805i	$-0.779429\pi$
$839$	−44.5703	−1.53874	−0.769368	+	0.638805i	$0.779429\pi$
$840$	−0.224245	−0.00773718
$841$	−28.9749	−0.999133
$842$	1.21137	0.0417467
$843$	9.16574	0.315685
$844$	−20.0231	−0.689222
$845$	−3.34574	−0.115097
$846$	−13.8889	−0.477511
$847$	−10.7541	−0.369514
$848$	1.04651	0.0359374
$849$	−8.78240	−0.301411
$850$	−18.5535	−0.636378
$851$	−2.87292	−0.0984824
$852$	−5.36747	−0.183887
$853$	−43.7802	−1.49900	−0.749502	−	0.662002i	$-0.769707\pi$
$853$	−43.7802	−1.49900	−0.749502	+	0.662002i	$0.769707\pi$
$854$	−3.90709	−0.133698
$855$	−3.07659	−0.105217
$856$	−12.5232	−0.428034
$857$	6.05688	0.206899	0.103449	−	0.994635i	$-0.467012\pi$
$857$	6.05688	0.206899	0.103449	+	0.994635i	$0.467012\pi$
$858$	0.370949	0.0126640
$859$	−17.9053	−0.610919	−0.305460	−	0.952205i	$-0.598810\pi$
$859$	−17.9053	−0.610919	−0.305460	+	0.952205i	$0.598810\pi$
$860$	0.404087	0.0137793
$861$	−7.93559	−0.270444
$862$	−1.00000	−0.0340601
$863$	−31.0674	−1.05755	−0.528773	−	0.848763i	$-0.677348\pi$
$863$	−31.0674	−1.05755	−0.528773	+	0.848763i	$0.677348\pi$
$864$	4.34797	0.147921
$865$	−6.51374	−0.221474
$866$	5.33290	0.181219
$867$	−2.28473	−0.0775937
$868$	9.95933	0.338042
$869$	2.71549	0.0921167
$870$	0.0355535	0.00120537
$871$	−1.18653	−0.0402041
$872$	13.7309	0.464988
$873$	11.7586	0.397968
$874$	10.5102	0.355513
$875$	−2.73121	−0.0923317
$876$	−3.54751	−0.119859
$877$	37.0113	1.24978	0.624891	−	0.780712i	$-0.285144\pi$
$877$	37.0113	1.24978	0.624891	+	0.780712i	$0.285144\pi$
$878$	−36.5457	−1.23336
$879$	−0.415269	−0.0140067
$880$	−0.136476	−0.00460061
$881$	8.29840	0.279580	0.139790	−	0.990181i	$-0.455357\pi$
$881$	8.29840	0.279580	0.139790	+	0.990181i	$0.455357\pi$
$882$	2.33606	0.0786591
$883$	−21.8699	−0.735982	−0.367991	−	0.929829i	$-0.619954\pi$
$883$	−21.8699	−0.735982	−0.367991	+	0.929829i	$0.619954\pi$
$884$	−3.45886	−0.116334
$885$	1.04753	0.0352124
$886$	5.10251	0.171422
$887$	−28.0254	−0.941002	−0.470501	−	0.882399i	$-0.655927\pi$
$887$	−28.0254	−0.941002	−0.470501	+	0.882399i	$0.655927\pi$
$888$	−1.06588	−0.0357686
$889$	14.6871	0.492591
$890$	2.15985	0.0723985
$891$	−1.71848	−0.0575712
$892$	−1.37940	−0.0461856
$893$	−28.4521	−0.952114
$894$	17.3872	0.581516
$895$	−6.35451	−0.212408
$896$	−1.00000	−0.0334077
$897$	−1.64284	−0.0548528
$898$	5.76809	0.192484
$899$	−1.57903	−0.0526635
$900$	11.5034	0.383445
$901$	−3.94302	−0.131361
$902$	−4.82963	−0.160809
$903$	1.19642	0.0398144
$904$	−9.33850	−0.310594
$905$	−5.60629	−0.186359
$906$	−18.5631	−0.616719
$907$	56.5642	1.87818	0.939091	−	0.343668i	$-0.111670\pi$
$907$	56.5642	1.87818	0.939091	+	0.343668i	$0.111670\pi$
$908$	−7.63572	−0.253400
$909$	12.6338	0.419037
$910$	−0.252642	−0.00837500
$911$	31.1936	1.03349	0.516745	−	0.856139i	$-0.327144\pi$
$911$	31.1936	1.03349	0.516745	+	0.856139i	$0.327144\pi$
$912$	3.89938	0.129121
$913$	1.09329	0.0361825
$914$	15.9742	0.528379
$915$	0.876143	0.0289644
$916$	−3.72108	−0.122948
$917$	−12.3759	−0.408688
$918$	−16.3821	−0.540690
$919$	−7.11468	−0.234692	−0.117346	−	0.993091i	$-0.537439\pi$
$919$	−7.11468	−0.234692	−0.117346	+	0.993091i	$0.537439\pi$
$920$	0.604418	0.0199271
$921$	−1.29608	−0.0427073
$922$	13.0462	0.429654
$923$	−6.04719	−0.199046
$924$	−0.404078	−0.0132932
$925$	−6.44146	−0.211794
$926$	−30.6751	−1.00805
$927$	−0.476110	−0.0156375
$928$	0.158548	0.00520458
$929$	7.75684	0.254494	0.127247	−	0.991871i	$-0.459386\pi$
$929$	7.75684	0.254494	0.127247	+	0.991871i	$0.459386\pi$
$930$	−2.23333	−0.0732337
$931$	4.78553	0.156839
$932$	−4.55355	−0.149156
$933$	3.76664	0.123314
$934$	−6.63407	−0.217073
$935$	0.514210	0.0168165
$936$	2.14453	0.0700962
$937$	−9.26566	−0.302696	−0.151348	−	0.988481i	$-0.548361\pi$
$937$	−9.26566	−0.302696	−0.151348	+	0.988481i	$0.548361\pi$
$938$	1.29250	0.0422016
$939$	−25.6309	−0.836434
$940$	−1.63622	−0.0533676
$941$	−20.3133	−0.662194	−0.331097	−	0.943597i	$-0.607419\pi$
$941$	−20.3133	−0.662194	−0.331097	+	0.943597i	$0.607419\pi$
$942$	−0.316392	−0.0103086
$943$	21.3892	0.696528
$944$	4.67138	0.152040
$945$	−1.19658	−0.0389248
$946$	0.728146	0.0236741
$947$	−26.2176	−0.851957	−0.425978	−	0.904733i	$-0.640070\pi$
$947$	−26.2176	−0.851957	−0.425978	+	0.904733i	$0.640070\pi$
$948$	−4.46184	−0.144914
$949$	−3.99675	−0.129740
$950$	23.5652	0.764556
$951$	23.2955	0.755409
$952$	3.76776	0.122114
$953$	58.3578	1.89039	0.945197	−	0.326501i	$-0.105870\pi$
$953$	58.3578	1.89039	0.945197	+	0.326501i	$0.105870\pi$
$954$	2.44472	0.0791506
$955$	6.78614	0.219594
$956$	6.51967	0.210861
$957$	0.0640656	0.00207095
$958$	17.9641	0.580394
$959$	−18.2540	−0.589454
$960$	0.224245	0.00723747
$961$	68.1883	2.19962
$962$	−1.20086	−0.0387173
$963$	−29.2549	−0.942726
$964$	16.3811	0.527600
$965$	−0.726541	−0.0233882
$966$	1.78956	0.0575782
$967$	31.0031	0.996992	0.498496	−	0.866892i	$-0.333886\pi$
$967$	31.0031	0.996992	0.498496	+	0.866892i	$0.333886\pi$
$968$	10.7541	0.345649
$969$	−14.6919	−0.471973
$970$	1.38525	0.0444777
$971$	58.1722	1.86683	0.933417	−	0.358793i	$-0.116811\pi$
$971$	58.1722	1.86683	0.933417	+	0.358793i	$0.116811\pi$
$972$	15.8675	0.508952
$973$	−13.3725	−0.428703
$974$	25.1218	0.804953
$975$	−3.68346	−0.117965
$976$	3.90709	0.125063
$977$	−42.5072	−1.35992	−0.679962	−	0.733247i	$-0.738004\pi$
$977$	−42.5072	−1.35992	−0.679962	+	0.733247i	$0.738004\pi$
$978$	−9.59882	−0.306936
$979$	3.89196	0.124387
$980$	0.275205	0.00879111
$981$	32.0762	1.02411
$982$	−14.8330	−0.473339
$983$	−21.3525	−0.681039	−0.340520	−	0.940237i	$-0.610603\pi$
$983$	−21.3525	−0.681039	−0.340520	+	0.940237i	$0.610603\pi$
$984$	7.93559	0.252977
$985$	2.23227	0.0711260
$986$	−0.597370	−0.0190241
$987$	−4.84452	−0.154203
$988$	4.39318	0.139766
$989$	−3.22477	−0.102542
$990$	−0.318816	−0.0101326
$991$	−50.6895	−1.61020	−0.805102	−	0.593136i	$-0.797890\pi$
$991$	−50.6895	−1.61020	−0.805102	+	0.593136i	$0.797890\pi$
$992$	−9.95933	−0.316209
$993$	−4.52683	−0.143655
$994$	6.58725	0.208935
$995$	−1.75818	−0.0557380
$996$	−1.79639	−0.0569207
$997$	−32.4961	−1.02916	−0.514580	−	0.857442i	$-0.672052\pi$
$997$	−32.4961	−1.02916	−0.514580	+	0.857442i	$0.672052\pi$
$998$	−43.8768	−1.38890
$999$	−5.68760	−0.179948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.k.1.12	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.k.1.12	✓	20	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.814827 q^{3} +1.00000 q^{4} +0.275205 q^{5} -0.814827 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.33606 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.814827 q^{3} +1.00000 q^{4} +0.275205 q^{5} -0.814827 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.33606 q^{9} -0.275205 q^{10} -0.495907 q^{11} +0.814827 q^{12} +0.918014 q^{13} -1.00000 q^{14} +0.224245 q^{15} +1.00000 q^{16} -3.76776 q^{17} +2.33606 q^{18} +4.78553 q^{19} +0.275205 q^{20} +0.814827 q^{21} +0.495907 q^{22} -2.19624 q^{23} -0.814827 q^{24} -4.92426 q^{25} -0.918014 q^{26} -4.34797 q^{27} +1.00000 q^{28} -0.158548 q^{29} -0.224245 q^{30} +9.95933 q^{31} -1.00000 q^{32} -0.404078 q^{33} +3.76776 q^{34} +0.275205 q^{35} -2.33606 q^{36} +1.30811 q^{37} -4.78553 q^{38} +0.748023 q^{39} -0.275205 q^{40} -9.73898 q^{41} -0.814827 q^{42} +1.46831 q^{43} -0.495907 q^{44} -0.642895 q^{45} +2.19624 q^{46} -5.94545 q^{47} +0.814827 q^{48} +1.00000 q^{49} +4.92426 q^{50} -3.07008 q^{51} +0.918014 q^{52} +1.04651 q^{53} +4.34797 q^{54} -0.136476 q^{55} -1.00000 q^{56} +3.89938 q^{57} +0.158548 q^{58} +4.67138 q^{59} +0.224245 q^{60} +3.90709 q^{61} -9.95933 q^{62} -2.33606 q^{63} +1.00000 q^{64} +0.252642 q^{65} +0.404078 q^{66} -1.29250 q^{67} -3.76776 q^{68} -1.78956 q^{69} -0.275205 q^{70} -6.58725 q^{71} +2.33606 q^{72} -4.35370 q^{73} -1.30811 q^{74} -4.01242 q^{75} +4.78553 q^{76} -0.495907 q^{77} -0.748023 q^{78} -5.47581 q^{79} +0.275205 q^{80} +3.46533 q^{81} +9.73898 q^{82} -2.20462 q^{83} +0.814827 q^{84} -1.03691 q^{85} -1.46831 q^{86} -0.129189 q^{87} +0.495907 q^{88} -7.84816 q^{89} +0.642895 q^{90} +0.918014 q^{91} -2.19624 q^{92} +8.11514 q^{93} +5.94545 q^{94} +1.31700 q^{95} -0.814827 q^{96} -5.03352 q^{97} -1.00000 q^{98} +1.15847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9}+O(q^{10}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9	\( 20 q - 20 q^{2} + 3 q^{3} + 20 q^{4} - 3 q^{5} - 3 q^{6} + 20 q^{7} - 20 q^{8} + 13 q^{9} + 3 q^{10} - 8 q^{11} + 3 q^{12} - 4 q^{13} - 20 q^{14} - 25 q^{15} + 20 q^{16} + 9 q^{17} - 13 q^{18} - 14 q^{19} - 3 q^{20} + 3 q^{21} + 8 q^{22} - 23 q^{23} - 3 q^{24} + 31 q^{25} + 4 q^{26} - 21 q^{27} + 20 q^{28} - 48 q^{29} + 25 q^{30} - q^{31} - 20 q^{32} - 29 q^{33} - 9 q^{34} - 3 q^{35} + 13 q^{36} - q^{37} + 14 q^{38} - q^{39} + 3 q^{40} - 27 q^{41} - 3 q^{42} - 3 q^{43} - 8 q^{44} - 12 q^{45} + 23 q^{46} - 26 q^{47} + 3 q^{48} + 20 q^{49} - 31 q^{50} - 17 q^{51} - 4 q^{52} - 43 q^{53} + 21 q^{54} - 16 q^{55} - 20 q^{56} - 25 q^{57} + 48 q^{58} - 19 q^{59} - 25 q^{60} + 9 q^{61} + q^{62} + 13 q^{63} + 20 q^{64} - 87 q^{65} + 29 q^{66} + 32 q^{67} + 9 q^{68} - 23 q^{69} + 3 q^{70} - 63 q^{71} - 13 q^{72} + 2 q^{73} + q^{74} - 8 q^{75} - 14 q^{76} - 8 q^{77} + q^{78} - 51 q^{79} - 3 q^{80} + 4 q^{81} + 27 q^{82} - 24 q^{83} + 3 q^{84} + 31 q^{85} + 3 q^{86} - 33 q^{87} + 8 q^{88} - 35 q^{89} + 12 q^{90} - 4 q^{91} - 23 q^{92} + 17 q^{93} + 26 q^{94} - 30 q^{95} - 3 q^{96} + 5 q^{97} - 20 q^{98} - 31 q^{99}+O(q^{100}) \) 20 * q - 20 * q^2 + 3 * q^3 + 20 * q^4 - 3 * q^5 - 3 * q^6 + 20 * q^7 - 20 * q^8 + 13 * q^9 + 3 * q^10 - 8 * q^11 + 3 * q^12 - 4 * q^13 - 20 * q^14 - 25 * q^15 + 20 * q^16 + 9 * q^17 - 13 * q^18 - 14 * q^19 - 3 * q^20 + 3 * q^21 + 8 * q^22 - 23 * q^23 - 3 * q^24 + 31 * q^25 + 4 * q^26 - 21 * q^27 + 20 * q^28 - 48 * q^29 + 25 * q^30 - q^31 - 20 * q^32 - 29 * q^33 - 9 * q^34 - 3 * q^35 + 13 * q^36 - q^37 + 14 * q^38 - q^39 + 3 * q^40 - 27 * q^41 - 3 * q^42 - 3 * q^43 - 8 * q^44 - 12 * q^45 + 23 * q^46 - 26 * q^47 + 3 * q^48 + 20 * q^49 - 31 * q^50 - 17 * q^51 - 4 * q^52 - 43 * q^53 + 21 * q^54 - 16 * q^55 - 20 * q^56 - 25 * q^57 + 48 * q^58 - 19 * q^59 - 25 * q^60 + 9 * q^61 + q^62 + 13 * q^63 + 20 * q^64 - 87 * q^65 + 29 * q^66 + 32 * q^67 + 9 * q^68 - 23 * q^69 + 3 * q^70 - 63 * q^71 - 13 * q^72 + 2 * q^73 + q^74 - 8 * q^75 - 14 * q^76 - 8 * q^77 + q^78 - 51 * q^79 - 3 * q^80 + 4 * q^81 + 27 * q^82 - 24 * q^83 + 3 * q^84 + 31 * q^85 + 3 * q^86 - 33 * q^87 + 8 * q^88 - 35 * q^89 + 12 * q^90 - 4 * q^91 - 23 * q^92 + 17 * q^93 + 26 * q^94 - 30 * q^95 - 3 * q^96 + 5 * q^97 - 20 * q^98 - 31 * q^99

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