LMFDB - Embedded newform 4022.2.a.e.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4022,2,Mod(1,4022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4022, 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("4022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4022 = 2 \cdot 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4022.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:	$32.1158316930$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	4022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.80060 q^{3} +1.00000 q^{4} -1.50418 q^{5} +1.80060 q^{6} +4.15262 q^{7} -1.00000 q^{8} +0.242152 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.80060 q^{3} +1.00000 q^{4} -1.50418 q^{5} +1.80060 q^{6} +4.15262 q^{7} -1.00000 q^{8} +0.242152 q^{9} +1.50418 q^{10} -3.55614 q^{11} -1.80060 q^{12} -0.0848003 q^{13} -4.15262 q^{14} +2.70843 q^{15} +1.00000 q^{16} -6.67768 q^{17} -0.242152 q^{18} -7.45613 q^{19} -1.50418 q^{20} -7.47720 q^{21} +3.55614 q^{22} -1.44600 q^{23} +1.80060 q^{24} -2.73743 q^{25} +0.0848003 q^{26} +4.96578 q^{27} +4.15262 q^{28} +6.15981 q^{29} -2.70843 q^{30} +4.75996 q^{31} -1.00000 q^{32} +6.40318 q^{33} +6.67768 q^{34} -6.24631 q^{35} +0.242152 q^{36} -0.906385 q^{37} +7.45613 q^{38} +0.152691 q^{39} +1.50418 q^{40} -11.3291 q^{41} +7.47720 q^{42} -0.304413 q^{43} -3.55614 q^{44} -0.364241 q^{45} +1.44600 q^{46} -6.44259 q^{47} -1.80060 q^{48} +10.2442 q^{49} +2.73743 q^{50} +12.0238 q^{51} -0.0848003 q^{52} +7.20566 q^{53} -4.96578 q^{54} +5.34909 q^{55} -4.15262 q^{56} +13.4255 q^{57} -6.15981 q^{58} +11.2404 q^{59} +2.70843 q^{60} +5.00052 q^{61} -4.75996 q^{62} +1.00556 q^{63} +1.00000 q^{64} +0.127555 q^{65} -6.40318 q^{66} -2.29465 q^{67} -6.67768 q^{68} +2.60366 q^{69} +6.24631 q^{70} -5.84090 q^{71} -0.242152 q^{72} -8.74434 q^{73} +0.906385 q^{74} +4.92901 q^{75} -7.45613 q^{76} -14.7673 q^{77} -0.152691 q^{78} +5.64029 q^{79} -1.50418 q^{80} -9.66782 q^{81} +11.3291 q^{82} +2.64508 q^{83} -7.47720 q^{84} +10.0445 q^{85} +0.304413 q^{86} -11.0913 q^{87} +3.55614 q^{88} +4.52718 q^{89} +0.364241 q^{90} -0.352143 q^{91} -1.44600 q^{92} -8.57077 q^{93} +6.44259 q^{94} +11.2154 q^{95} +1.80060 q^{96} +5.91349 q^{97} -10.2442 q^{98} -0.861125 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) $ 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.80060	−1.03958	−0.519788	−	0.854295i	$-0.673989\pi$
$3$	−1.80060	−1.03958	−0.519788	+	0.854295i	$0.673989\pi$
$4$	1.00000	0.500000
$5$	−1.50418	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$5$	−1.50418	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$6$	1.80060	0.735091
$7$	4.15262	1.56954	0.784771	−	0.619786i	$-0.212780\pi$
$7$	4.15262	1.56954	0.784771	+	0.619786i	$0.212780\pi$
$8$	−1.00000	−0.353553
$9$	0.242152	0.0807172
$10$	1.50418	0.475665
$11$	−3.55614	−1.07222	−0.536109	−	0.844149i	$-0.680106\pi$
$11$	−3.55614	−1.07222	−0.536109	+	0.844149i	$0.680106\pi$
$12$	−1.80060	−0.519788
$13$	−0.0848003	−0.0235194	−0.0117597	−	0.999931i	$-0.503743\pi$
$13$	−0.0848003	−0.0235194	−0.0117597	+	0.999931i	$0.503743\pi$
$14$	−4.15262	−1.10983
$15$	2.70843	0.699314
$16$	1.00000	0.250000
$17$	−6.67768	−1.61958	−0.809788	−	0.586723i	$-0.800418\pi$
$17$	−6.67768	−1.61958	−0.809788	+	0.586723i	$0.800418\pi$
$18$	−0.242152	−0.0570757
$19$	−7.45613	−1.71055	−0.855277	−	0.518171i	$-0.826613\pi$
$19$	−7.45613	−1.71055	−0.855277	+	0.518171i	$0.826613\pi$
$20$	−1.50418	−0.336346
$21$	−7.47720	−1.63166
$22$	3.55614	0.758172
$23$	−1.44600	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$23$	−1.44600	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$24$	1.80060	0.367545
$25$	−2.73743	−0.547486
$26$	0.0848003	0.0166307
$27$	4.96578	0.955664
$28$	4.15262	0.784771
$29$	6.15981	1.14385	0.571924	−	0.820307i	$-0.306197\pi$
$29$	6.15981	1.14385	0.571924	+	0.820307i	$0.306197\pi$
$30$	−2.70843	−0.494490
$31$	4.75996	0.854914	0.427457	−	0.904036i	$-0.359410\pi$
$31$	4.75996	0.854914	0.427457	+	0.904036i	$0.359410\pi$
$32$	−1.00000	−0.176777
$33$	6.40318	1.11465
$34$	6.67768	1.14521
$35$	−6.24631	−1.05582
$36$	0.242152	0.0403586
$37$	−0.906385	−0.149009	−0.0745044	−	0.997221i	$-0.523737\pi$
$37$	−0.906385	−0.149009	−0.0745044	+	0.997221i	$0.523737\pi$
$38$	7.45613	1.20954
$39$	0.152691	0.0244502
$40$	1.50418	0.237832
$41$	−11.3291	−1.76931	−0.884654	−	0.466248i	$-0.845605\pi$
$41$	−11.3291	−1.76931	−0.884654	+	0.466248i	$0.845605\pi$
$42$	7.47720	1.15376
$43$	−0.304413	−0.0464225	−0.0232113	−	0.999731i	$-0.507389\pi$
$43$	−0.304413	−0.0464225	−0.0232113	+	0.999731i	$0.507389\pi$
$44$	−3.55614	−0.536109
$45$	−0.364241	−0.0542978
$46$	1.44600	0.213201
$47$	−6.44259	−0.939748	−0.469874	−	0.882733i	$-0.655701\pi$
$47$	−6.44259	−0.939748	−0.469874	+	0.882733i	$0.655701\pi$
$48$	−1.80060	−0.259894
$49$	10.2442	1.46346
$50$	2.73743	0.387131
$51$	12.0238	1.68367
$52$	−0.0848003	−0.0117597
$53$	7.20566	0.989773	0.494887	−	0.868957i	$-0.335210\pi$
$53$	7.20566	0.989773	0.494887	+	0.868957i	$0.335210\pi$
$54$	−4.96578	−0.675756
$55$	5.34909	0.721272
$56$	−4.15262	−0.554917
$57$	13.4255	1.77825
$58$	−6.15981	−0.808822
$59$	11.2404	1.46338	0.731691	−	0.681637i	$-0.238732\pi$
$59$	11.2404	1.46338	0.731691	+	0.681637i	$0.238732\pi$
$60$	2.70843	0.349657
$61$	5.00052	0.640250	0.320125	−	0.947375i	$-0.396275\pi$
$61$	5.00052	0.640250	0.320125	+	0.947375i	$0.396275\pi$
$62$	−4.75996	−0.604515
$63$	1.00556	0.126689
$64$	1.00000	0.125000
$65$	0.127555	0.0158213
$66$	−6.40318	−0.788177
$67$	−2.29465	−0.280336	−0.140168	−	0.990128i	$-0.544764\pi$
$67$	−2.29465	−0.280336	−0.140168	+	0.990128i	$0.544764\pi$
$68$	−6.67768	−0.809788
$69$	2.60366	0.313444
$70$	6.24631	0.746576
$71$	−5.84090	−0.693187	−0.346594	−	0.938015i	$-0.612662\pi$
$71$	−5.84090	−0.693187	−0.346594	+	0.938015i	$0.612662\pi$
$72$	−0.242152	−0.0285378
$73$	−8.74434	−1.02345	−0.511724	−	0.859150i	$-0.670993\pi$
$73$	−8.74434	−1.02345	−0.511724	+	0.859150i	$0.670993\pi$
$74$	0.906385	0.105365
$75$	4.92901	0.569153
$76$	−7.45613	−0.855277
$77$	−14.7673	−1.68289
$78$	−0.152691	−0.0172889
$79$	5.64029	0.634582	0.317291	−	0.948328i	$-0.397227\pi$
$79$	5.64029	0.634582	0.317291	+	0.948328i	$0.397227\pi$
$80$	−1.50418	−0.168173
$81$	−9.66782	−1.07420
$82$	11.3291	1.25109
$83$	2.64508	0.290335	0.145167	−	0.989407i	$-0.453628\pi$
$83$	2.64508	0.290335	0.145167	+	0.989407i	$0.453628\pi$
$84$	−7.47720	−0.815829
$85$	10.0445	1.08948
$86$	0.304413	0.0328257
$87$	−11.0913	−1.18912
$88$	3.55614	0.379086
$89$	4.52718	0.479880	0.239940	−	0.970788i	$-0.422872\pi$
$89$	4.52718	0.479880	0.239940	+	0.970788i	$0.422872\pi$
$90$	0.364241	0.0383943
$91$	−0.352143	−0.0369146
$92$	−1.44600	−0.150756
$93$	−8.57077	−0.888748
$94$	6.44259	0.664502
$95$	11.2154	1.15068
$96$	1.80060	0.183773
$97$	5.91349	0.600424	0.300212	−	0.953872i	$-0.402943\pi$
$97$	5.91349	0.600424	0.300212	+	0.953872i	$0.402943\pi$
$98$	−10.2442	−1.03482
$99$	−0.861125	−0.0865463
$100$	−2.73743	−0.273743
$101$	−4.55261	−0.453002	−0.226501	−	0.974011i	$-0.572729\pi$
$101$	−4.55261	−0.453002	−0.226501	+	0.974011i	$0.572729\pi$
$102$	−12.0238	−1.19054
$103$	1.30920	0.128999	0.0644994	−	0.997918i	$-0.479455\pi$
$103$	1.30920	0.128999	0.0644994	+	0.997918i	$0.479455\pi$
$104$	0.0848003	0.00831535
$105$	11.2471	1.09760
$106$	−7.20566	−0.699876
$107$	−9.32719	−0.901693	−0.450847	−	0.892601i	$-0.648878\pi$
$107$	−9.32719	−0.901693	−0.450847	+	0.892601i	$0.648878\pi$
$108$	4.96578	0.477832
$109$	−5.69058	−0.545059	−0.272529	−	0.962147i	$-0.587860\pi$
$109$	−5.69058	−0.545059	−0.272529	+	0.962147i	$0.587860\pi$
$110$	−5.34909	−0.510016
$111$	1.63204	0.154906
$112$	4.15262	0.392386
$113$	−16.9557	−1.59506	−0.797529	−	0.603280i	$-0.793860\pi$
$113$	−16.9557	−1.59506	−0.797529	+	0.603280i	$0.793860\pi$
$114$	−13.4255	−1.25741
$115$	2.17505	0.202824
$116$	6.15981	0.571924
$117$	−0.0205345	−0.00189842
$118$	−11.2404	−1.03477
$119$	−27.7299	−2.54199
$120$	−2.70843	−0.247245
$121$	1.64614	0.149650
$122$	−5.00052	−0.452725
$123$	20.3991	1.83933
$124$	4.75996	0.427457
$125$	11.6385	1.04098
$126$	−1.00556	−0.0895827
$127$	4.45950	0.395717	0.197858	−	0.980231i	$-0.436601\pi$
$127$	4.45950	0.395717	0.197858	+	0.980231i	$0.436601\pi$
$128$	−1.00000	−0.0883883
$129$	0.548125	0.0482597
$130$	−0.127555	−0.0111873
$131$	−2.92386	−0.255459	−0.127730	−	0.991809i	$-0.540769\pi$
$131$	−2.92386	−0.255459	−0.127730	+	0.991809i	$0.540769\pi$
$132$	6.40318	0.557325
$133$	−30.9625	−2.68479
$134$	2.29465	0.198228
$135$	−7.46944	−0.642867
$136$	6.67768	0.572606
$137$	0.245364	0.0209628	0.0104814	−	0.999945i	$-0.496664\pi$
$137$	0.245364	0.0209628	0.0104814	+	0.999945i	$0.496664\pi$
$138$	−2.60366	−0.221638
$139$	2.43064	0.206165	0.103082	−	0.994673i	$-0.467130\pi$
$139$	2.43064	0.206165	0.103082	+	0.994673i	$0.467130\pi$
$140$	−6.24631	−0.527909
$141$	11.6005	0.976939
$142$	5.84090	0.490157
$143$	0.301562	0.0252179
$144$	0.242152	0.0201793
$145$	−9.26549	−0.769457
$146$	8.74434	0.723686
$147$	−18.4458	−1.52138
$148$	−0.906385	−0.0745044
$149$	6.22464	0.509942	0.254971	−	0.966949i	$-0.417934\pi$
$149$	6.22464	0.509942	0.254971	+	0.966949i	$0.417934\pi$
$150$	−4.92901	−0.402452
$151$	−6.83404	−0.556147	−0.278073	−	0.960560i	$-0.589696\pi$
$151$	−6.83404	−0.556147	−0.278073	+	0.960560i	$0.589696\pi$
$152$	7.45613	0.604772
$153$	−1.61701	−0.130728
$154$	14.7673	1.18998
$155$	−7.15986	−0.575094
$156$	0.152691	0.0122251
$157$	8.40804	0.671035	0.335517	−	0.942034i	$-0.391089\pi$
$157$	8.40804	0.671035	0.335517	+	0.942034i	$0.391089\pi$
$158$	−5.64029	−0.448717
$159$	−12.9745	−1.02894
$160$	1.50418	0.118916
$161$	−6.00468	−0.473235
$162$	9.66782	0.759575
$163$	9.22924	0.722890	0.361445	−	0.932393i	$-0.382284\pi$
$163$	9.22924	0.722890	0.361445	+	0.932393i	$0.382284\pi$
$164$	−11.3291	−0.884654
$165$	−9.63157	−0.749816
$166$	−2.64508	−0.205298
$167$	19.9144	1.54103	0.770513	−	0.637425i	$-0.220000\pi$
$167$	19.9144	1.54103	0.770513	+	0.637425i	$0.220000\pi$
$168$	7.47720	0.576878
$169$	−12.9928	−0.999447
$170$	−10.0445	−0.770375
$171$	−1.80551	−0.138071
$172$	−0.304413	−0.0232113
$173$	−14.9097	−1.13356	−0.566781	−	0.823868i	$-0.691811\pi$
$173$	−14.9097	−1.13356	−0.566781	+	0.823868i	$0.691811\pi$
$174$	11.0913	0.840832
$175$	−11.3675	−0.859302
$176$	−3.55614	−0.268054
$177$	−20.2395	−1.52130
$178$	−4.52718	−0.339327
$179$	17.5867	1.31449	0.657245	−	0.753677i	$-0.271722\pi$
$179$	17.5867	1.31449	0.657245	+	0.753677i	$0.271722\pi$
$180$	−0.364241	−0.0271489
$181$	22.7988	1.69462	0.847310	−	0.531098i	$-0.178220\pi$
$181$	22.7988	1.69462	0.847310	+	0.531098i	$0.178220\pi$
$182$	0.352143	0.0261026
$183$	−9.00392	−0.665589
$184$	1.44600	0.106600
$185$	1.36337	0.100237
$186$	8.57077	0.628439
$187$	23.7468	1.73654
$188$	−6.44259	−0.469874
$189$	20.6210	1.49996
$190$	−11.2154	−0.813651
$191$	−9.75754	−0.706031	−0.353015	−	0.935618i	$-0.614844\pi$
$191$	−9.75754	−0.706031	−0.353015	+	0.935618i	$0.614844\pi$
$192$	−1.80060	−0.129947
$193$	20.4747	1.47380	0.736901	−	0.676001i	$-0.236288\pi$
$193$	20.4747	1.47380	0.736901	+	0.676001i	$0.236288\pi$
$194$	−5.91349	−0.424564
$195$	−0.229676	−0.0164474
$196$	10.2442	0.731732
$197$	3.42346	0.243911	0.121956	−	0.992536i	$-0.461083\pi$
$197$	3.42346	0.243911	0.121956	+	0.992536i	$0.461083\pi$
$198$	0.861125	0.0611975
$199$	21.4600	1.52126	0.760628	−	0.649188i	$-0.224891\pi$
$199$	21.4600	1.52126	0.760628	+	0.649188i	$0.224891\pi$
$200$	2.73743	0.193565
$201$	4.13174	0.291431
$202$	4.55261	0.320321
$203$	25.5793	1.79532
$204$	12.0238	0.841836
$205$	17.0411	1.19020
$206$	−1.30920	−0.0912160
$207$	−0.350151	−0.0243371
$208$	−0.0848003	−0.00587984
$209$	26.5151	1.83409
$210$	−11.2471	−0.776122
$211$	0.0287088	0.00197639	0.000988196	−	1.00000i	$-0.499685\pi$
$211$	0.0287088	0.00197639	0.000988196		1.00000i	$0.499685\pi$
$212$	7.20566	0.494887
$213$	10.5171	0.720620
$214$	9.32719	0.637594
$215$	0.457893	0.0312280
$216$	−4.96578	−0.337878
$217$	19.7663	1.34182
$218$	5.69058	0.385415
$219$	15.7450	1.06395
$220$	5.34909	0.360636
$221$	0.566269	0.0380914
$222$	−1.63204	−0.109535
$223$	10.3342	0.692029	0.346015	−	0.938229i	$-0.387535\pi$
$223$	10.3342	0.692029	0.346015	+	0.938229i	$0.387535\pi$
$224$	−4.15262	−0.277459
$225$	−0.662873	−0.0441915
$226$	16.9557	1.12788
$227$	0.512148	0.0339925	0.0169962	−	0.999856i	$-0.494590\pi$
$227$	0.512148	0.0339925	0.0169962	+	0.999856i	$0.494590\pi$
$228$	13.4255	0.889125
$229$	−21.4415	−1.41689	−0.708447	−	0.705764i	$-0.750604\pi$
$229$	−21.4415	−1.41689	−0.708447	+	0.705764i	$0.750604\pi$
$230$	−2.17505	−0.143418
$231$	26.5900	1.74949
$232$	−6.15981	−0.404411
$233$	−28.4723	−1.86528	−0.932642	−	0.360803i	$-0.882503\pi$
$233$	−28.4723	−1.86528	−0.932642	+	0.360803i	$0.882503\pi$
$234$	0.0205345	0.00134238
$235$	9.69084	0.632161
$236$	11.2404	0.731691
$237$	−10.1559	−0.659696
$238$	27.7299	1.79746
$239$	−14.7407	−0.953498	−0.476749	−	0.879039i	$-0.658185\pi$
$239$	−14.7407	−0.953498	−0.476749	+	0.879039i	$0.658185\pi$
$240$	2.70843	0.174828
$241$	26.5697	1.71151	0.855754	−	0.517384i	$-0.173094\pi$
$241$	26.5697	1.71151	0.855754	+	0.517384i	$0.173094\pi$
$242$	−1.64614	−0.105818
$243$	2.51052	0.161050
$244$	5.00052	0.320125
$245$	−15.4092	−0.984460
$246$	−20.3991	−1.30060
$247$	0.632282	0.0402311
$248$	−4.75996	−0.302258
$249$	−4.76272	−0.301825
$250$	−11.6385	−0.736085
$251$	−0.744135	−0.0469694	−0.0234847	−	0.999724i	$-0.507476\pi$
$251$	−0.744135	−0.0469694	−0.0234847	+	0.999724i	$0.507476\pi$
$252$	1.00556	0.0633445
$253$	5.14217	0.323286
$254$	−4.45950	−0.279814
$255$	−18.0860	−1.13259
$256$	1.00000	0.0625000
$257$	25.3716	1.58263	0.791317	−	0.611406i	$-0.209396\pi$
$257$	25.3716	1.58263	0.791317	+	0.611406i	$0.209396\pi$
$258$	−0.548125	−0.0341248
$259$	−3.76387	−0.233876
$260$	0.127555	0.00791064
$261$	1.49161	0.0923282
$262$	2.92386	0.180637
$263$	−10.1171	−0.623846	−0.311923	−	0.950107i	$-0.600973\pi$
$263$	−10.1171	−0.623846	−0.311923	+	0.950107i	$0.600973\pi$
$264$	−6.40318	−0.394089
$265$	−10.8386	−0.665813
$266$	30.9625	1.89843
$267$	−8.15164	−0.498872
$268$	−2.29465	−0.140168
$269$	17.8038	1.08552	0.542759	−	0.839888i	$-0.317380\pi$
$269$	17.8038	1.08552	0.542759	+	0.839888i	$0.317380\pi$
$270$	7.46944	0.454576
$271$	−10.3373	−0.627946	−0.313973	−	0.949432i	$-0.601660\pi$
$271$	−10.3373	−0.627946	−0.313973	+	0.949432i	$0.601660\pi$
$272$	−6.67768	−0.404894
$273$	0.634068	0.0383756
$274$	−0.245364	−0.0148230
$275$	9.73468	0.587024
$276$	2.60366	0.156722
$277$	14.7757	0.887787	0.443893	−	0.896080i	$-0.353597\pi$
$277$	14.7757	0.887787	0.443893	+	0.896080i	$0.353597\pi$
$278$	−2.43064	−0.145780
$279$	1.15263	0.0690063
$280$	6.24631	0.373288
$281$	−23.6329	−1.40982	−0.704910	−	0.709297i	$-0.749013\pi$
$281$	−23.6329	−1.40982	−0.704910	+	0.709297i	$0.749013\pi$
$282$	−11.6005	−0.690800
$283$	3.13384	0.186287	0.0931436	−	0.995653i	$-0.470308\pi$
$283$	3.13384	0.186287	0.0931436	+	0.995653i	$0.470308\pi$
$284$	−5.84090	−0.346594
$285$	−20.1944	−1.19621
$286$	−0.301562	−0.0178317
$287$	−47.0454	−2.77700
$288$	−0.242152	−0.0142689
$289$	27.5914	1.62303
$290$	9.26549	0.544088
$291$	−10.6478	−0.624186
$292$	−8.74434	−0.511724
$293$	20.8345	1.21716	0.608581	−	0.793491i	$-0.291739\pi$
$293$	20.8345	1.21716	0.608581	+	0.793491i	$0.291739\pi$
$294$	18.4458	1.07578
$295$	−16.9077	−0.984405
$296$	0.906385	0.0526826
$297$	−17.6590	−1.02468
$298$	−6.22464	−0.360583
$299$	0.122621	0.00709135
$300$	4.92901	0.284576
$301$	−1.26411	−0.0728621
$302$	6.83404	0.393255
$303$	8.19742	0.470930
$304$	−7.45613	−0.427638
$305$	−7.52170	−0.430691
$306$	1.61701	0.0924384
$307$	14.3822	0.820837	0.410419	−	0.911897i	$-0.365383\pi$
$307$	14.3822	0.820837	0.410419	+	0.911897i	$0.365383\pi$
$308$	−14.7673	−0.841445
$309$	−2.35733	−0.134104
$310$	7.15986	0.406653
$311$	16.9992	0.963935	0.481967	−	0.876189i	$-0.339922\pi$
$311$	16.9992	0.963935	0.481967	+	0.876189i	$0.339922\pi$
$312$	−0.152691	−0.00864443
$313$	10.4134	0.588602	0.294301	−	0.955713i	$-0.404913\pi$
$313$	10.4134	0.588602	0.294301	+	0.955713i	$0.404913\pi$
$314$	−8.40804	−0.474493
$315$	−1.51255	−0.0852227
$316$	5.64029	0.317291
$317$	−1.80348	−0.101294	−0.0506468	−	0.998717i	$-0.516128\pi$
$317$	−1.80348	−0.101294	−0.0506468	+	0.998717i	$0.516128\pi$
$318$	12.9745	0.727573
$319$	−21.9051	−1.22645
$320$	−1.50418	−0.0840865
$321$	16.7945	0.937378
$322$	6.00468	0.334628
$323$	49.7897	2.77037
$324$	−9.66782	−0.537101
$325$	0.232135	0.0128765
$326$	−9.22924	−0.511160
$327$	10.2464	0.566630
$328$	11.3291	0.625545
$329$	−26.7536	−1.47497
$330$	9.63157	0.530200
$331$	−14.6780	−0.806777	−0.403388	−	0.915029i	$-0.632168\pi$
$331$	−14.6780	−0.806777	−0.403388	+	0.915029i	$0.632168\pi$
$332$	2.64508	0.145167
$333$	−0.219483	−0.0120276
$334$	−19.9144	−1.08967
$335$	3.45158	0.188580
$336$	−7.47720	−0.407914
$337$	19.3728	1.05530	0.527652	−	0.849461i	$-0.323073\pi$
$337$	19.3728	1.05530	0.527652	+	0.849461i	$0.323073\pi$
$338$	12.9928	0.706716
$339$	30.5304	1.65818
$340$	10.0445	0.544738
$341$	−16.9271	−0.916653
$342$	1.80551	0.0976310
$343$	13.4721	0.727426
$344$	0.304413	0.0164128
$345$	−3.91639	−0.210851
$346$	14.9097	0.801549
$347$	−24.9141	−1.33746	−0.668728	−	0.743507i	$-0.733161\pi$
$347$	−24.9141	−1.33746	−0.668728	+	0.743507i	$0.733161\pi$
$348$	−11.0913	−0.594558
$349$	30.3323	1.62365	0.811825	−	0.583901i	$-0.198474\pi$
$349$	30.3323	1.62365	0.811825	+	0.583901i	$0.198474\pi$
$350$	11.3675	0.607618
$351$	−0.421099	−0.0224766
$352$	3.55614	0.189543
$353$	22.8180	1.21448	0.607240	−	0.794518i	$-0.292277\pi$
$353$	22.8180	1.21448	0.607240	+	0.794518i	$0.292277\pi$
$354$	20.2395	1.07572
$355$	8.78579	0.466301
$356$	4.52718	0.239940
$357$	49.9303	2.64259
$358$	−17.5867	−0.929485
$359$	−16.7632	−0.884727	−0.442363	−	0.896836i	$-0.645860\pi$
$359$	−16.7632	−0.884727	−0.442363	+	0.896836i	$0.645860\pi$
$360$	0.364241	0.0191972
$361$	36.5939	1.92599
$362$	−22.7988	−1.19828
$363$	−2.96404	−0.155572
$364$	−0.352143	−0.0184573
$365$	13.1531	0.688464
$366$	9.00392	0.470642
$367$	−26.2834	−1.37198	−0.685990	−	0.727611i	$-0.740631\pi$
$367$	−26.2834	−1.37198	−0.685990	+	0.727611i	$0.740631\pi$
$368$	−1.44600	−0.0753778
$369$	−2.74336	−0.142814
$370$	−1.36337	−0.0708783
$371$	29.9224	1.55349
$372$	−8.57077	−0.444374
$373$	−21.5092	−1.11370	−0.556851	−	0.830613i	$-0.687990\pi$
$373$	−21.5092	−1.11370	−0.556851	+	0.830613i	$0.687990\pi$
$374$	−23.7468	−1.22792
$375$	−20.9563	−1.08218
$376$	6.44259	0.332251
$377$	−0.522353	−0.0269026
$378$	−20.6210	−1.06063
$379$	−3.68784	−0.189431	−0.0947157	−	0.995504i	$-0.530194\pi$
$379$	−3.68784	−0.189431	−0.0947157	+	0.995504i	$0.530194\pi$
$380$	11.2154	0.575338
$381$	−8.02977	−0.411378
$382$	9.75754	0.499239
$383$	33.9351	1.73400	0.867001	−	0.498306i	$-0.166044\pi$
$383$	33.9351	1.73400	0.867001	+	0.498306i	$0.166044\pi$
$384$	1.80060	0.0918864
$385$	22.2127	1.13207
$386$	−20.4747	−1.04214
$387$	−0.0737140	−0.00374709
$388$	5.91349	0.300212
$389$	23.1164	1.17205	0.586023	−	0.810294i	$-0.300693\pi$
$389$	23.1164	1.17205	0.586023	+	0.810294i	$0.300693\pi$
$390$	0.229676	0.0116301
$391$	9.65591	0.488320
$392$	−10.2442	−0.517412
$393$	5.26470	0.265569
$394$	−3.42346	−0.172471
$395$	−8.48404	−0.426878
$396$	−0.861125	−0.0432732
$397$	−11.2524	−0.564743	−0.282372	−	0.959305i	$-0.591121\pi$
$397$	−11.2524	−0.564743	−0.282372	+	0.959305i	$0.591121\pi$
$398$	−21.4600	−1.07569
$399$	55.7510	2.79104
$400$	−2.73743	−0.136871
$401$	30.3391	1.51506	0.757532	−	0.652798i	$-0.226405\pi$
$401$	30.3391	1.51506	0.757532	+	0.652798i	$0.226405\pi$
$402$	−4.13174	−0.206073
$403$	−0.403646	−0.0201070
$404$	−4.55261	−0.226501
$405$	14.5422	0.722607
$406$	−25.5793	−1.26948
$407$	3.22324	0.159770
$408$	−12.0238	−0.595268
$409$	5.81890	0.287726	0.143863	−	0.989598i	$-0.454048\pi$
$409$	5.81890	0.287726	0.143863	+	0.989598i	$0.454048\pi$
$410$	−17.0411	−0.841598
$411$	−0.441801	−0.0217924
$412$	1.30920	0.0644994
$413$	46.6773	2.29684
$414$	0.350151	0.0172090
$415$	−3.97868	−0.195306
$416$	0.0848003	0.00415768
$417$	−4.37661	−0.214324
$418$	−26.5151	−1.29689
$419$	−30.4288	−1.48654	−0.743271	−	0.668990i	$-0.766727\pi$
$419$	−30.4288	−1.48654	−0.743271	+	0.668990i	$0.766727\pi$
$420$	11.2471	0.548801
$421$	−0.608052	−0.0296346	−0.0148173	−	0.999890i	$-0.504717\pi$
$421$	−0.608052	−0.0296346	−0.0148173	+	0.999890i	$0.504717\pi$
$422$	−0.0287088	−0.00139752
$423$	−1.56008	−0.0758538
$424$	−7.20566	−0.349938
$425$	18.2797	0.886695
$426$	−10.5171	−0.509556
$427$	20.7652	1.00490
$428$	−9.32719	−0.450847
$429$	−0.542991	−0.0262159
$430$	−0.457893	−0.0220816
$431$	−18.8938	−0.910084	−0.455042	−	0.890470i	$-0.650376\pi$
$431$	−18.8938	−0.910084	−0.455042	+	0.890470i	$0.650376\pi$
$432$	4.96578	0.238916
$433$	38.7744	1.86338	0.931690	−	0.363255i	$-0.118335\pi$
$433$	38.7744	1.86338	0.931690	+	0.363255i	$0.118335\pi$
$434$	−19.7663	−0.948813
$435$	16.6834	0.799909
$436$	−5.69058	−0.272529
$437$	10.7815	0.515751
$438$	−15.7450	−0.752327
$439$	−18.5542	−0.885546	−0.442773	−	0.896634i	$-0.646005\pi$
$439$	−18.5542	−0.885546	−0.442773	+	0.896634i	$0.646005\pi$
$440$	−5.34909	−0.255008
$441$	2.48066	0.118127
$442$	−0.566269	−0.0269347
$443$	28.3679	1.34780	0.673899	−	0.738823i	$-0.264618\pi$
$443$	28.3679	1.34780	0.673899	+	0.738823i	$0.264618\pi$
$444$	1.63204	0.0774530
$445$	−6.80972	−0.322812
$446$	−10.3342	−0.489338
$447$	−11.2081	−0.530123
$448$	4.15262	0.196193
$449$	34.0794	1.60831	0.804154	−	0.594421i	$-0.202619\pi$
$449$	34.0794	1.60831	0.804154	+	0.594421i	$0.202619\pi$
$450$	0.662873	0.0312481
$451$	40.2879	1.89708
$452$	−16.9557	−0.797529
$453$	12.3054	0.578156
$454$	−0.512148	−0.0240363
$455$	0.529688	0.0248322
$456$	−13.4255	−0.628706
$457$	−40.6394	−1.90103	−0.950515	−	0.310678i	$-0.899444\pi$
$457$	−40.6394	−1.90103	−0.950515	+	0.310678i	$0.899444\pi$
$458$	21.4415	1.00190
$459$	−33.1599	−1.54777
$460$	2.17505	0.101412
$461$	−1.75365	−0.0816754	−0.0408377	−	0.999166i	$-0.513003\pi$
$461$	−1.75365	−0.0816754	−0.0408377	+	0.999166i	$0.513003\pi$
$462$	−26.5900	−1.23708
$463$	17.8519	0.829650	0.414825	−	0.909901i	$-0.363843\pi$
$463$	17.8519	0.829650	0.414825	+	0.909901i	$0.363843\pi$
$464$	6.15981	0.285962
$465$	12.8920	0.597853
$466$	28.4723	1.31896
$467$	7.80821	0.361321	0.180660	−	0.983546i	$-0.442176\pi$
$467$	7.80821	0.361321	0.180660	+	0.983546i	$0.442176\pi$
$468$	−0.0205345	−0.000949208 0
$469$	−9.52881	−0.440000
$470$	−9.69084	−0.447005
$471$	−15.1395	−0.697591
$472$	−11.2404	−0.517383
$473$	1.08253	0.0497750
$474$	10.1559	0.466476
$475$	20.4106	0.936504
$476$	−27.7299	−1.27100
$477$	1.74486	0.0798917
$478$	14.7407	0.674225
$479$	−42.7372	−1.95271	−0.976356	−	0.216169i	$-0.930644\pi$
$479$	−42.7372	−1.95271	−0.976356	+	0.216169i	$0.930644\pi$
$480$	−2.70843	−0.123622
$481$	0.0768617	0.00350459
$482$	−26.5697	−1.21022
$483$	10.8120	0.491963
$484$	1.64614	0.0748248
$485$	−8.89498	−0.403900
$486$	−2.51052	−0.113880
$487$	23.7626	1.07679	0.538394	−	0.842694i	$-0.319031\pi$
$487$	23.7626	1.07679	0.538394	+	0.842694i	$0.319031\pi$
$488$	−5.00052	−0.226363
$489$	−16.6182	−0.751499
$490$	15.4092	0.696118
$491$	28.8593	1.30240	0.651202	−	0.758905i	$-0.274265\pi$
$491$	28.8593	1.30240	0.651202	+	0.758905i	$0.274265\pi$
$492$	20.3991	0.919665
$493$	−41.1332	−1.85255
$494$	−0.632282	−0.0284477
$495$	1.29529	0.0582190
$496$	4.75996	0.213729
$497$	−24.2550	−1.08799
$498$	4.76272	0.213423
$499$	−3.04099	−0.136133	−0.0680667	−	0.997681i	$-0.521683\pi$
$499$	−3.04099	−0.136133	−0.0680667	+	0.997681i	$0.521683\pi$
$500$	11.6385	0.520490
$501$	−35.8579	−1.60201
$502$	0.744135	0.0332123
$503$	−38.2027	−1.70338	−0.851688	−	0.524050i	$-0.824421\pi$
$503$	−38.2027	−1.70338	−0.851688	+	0.524050i	$0.824421\pi$
$504$	−1.00556	−0.0447913
$505$	6.84797	0.304731
$506$	−5.14217	−0.228597
$507$	23.3948	1.03900
$508$	4.45950	0.197858
$509$	−12.0924	−0.535985	−0.267993	−	0.963421i	$-0.586360\pi$
$509$	−12.0924	−0.535985	−0.267993	+	0.963421i	$0.586360\pi$
$510$	18.0860	0.800863
$511$	−36.3119	−1.60634
$512$	−1.00000	−0.0441942
$513$	−37.0255	−1.63471
$514$	−25.3716	−1.11909
$515$	−1.96927	−0.0867765
$516$	0.548125	0.0241299
$517$	22.9108	1.00761
$518$	3.76387	0.165375
$519$	26.8463	1.17842
$520$	−0.127555	−0.00559367
$521$	26.8090	1.17452	0.587261	−	0.809397i	$-0.300206\pi$
$521$	26.8090	1.17452	0.587261	+	0.809397i	$0.300206\pi$
$522$	−1.49161	−0.0652859
$523$	0.876561	0.0383294	0.0191647	−	0.999816i	$-0.493899\pi$
$523$	0.876561	0.0383294	0.0191647	+	0.999816i	$0.493899\pi$
$524$	−2.92386	−0.127730
$525$	20.4683	0.893309
$526$	10.1171	0.441126
$527$	−31.7855	−1.38460
$528$	6.40318	0.278663
$529$	−20.9091	−0.909091
$530$	10.8386	0.470801
$531$	2.72189	0.118120
$532$	−30.9625	−1.34239
$533$	0.960711	0.0416130
$534$	8.15164	0.352756
$535$	14.0298	0.606562
$536$	2.29465	0.0991138
$537$	−31.6665	−1.36651
$538$	−17.8038	−0.767577
$539$	−36.4300	−1.56915
$540$	−7.46944	−0.321434
$541$	37.7059	1.62110	0.810552	−	0.585667i	$-0.199167\pi$
$541$	37.7059	1.62110	0.810552	+	0.585667i	$0.199167\pi$
$542$	10.3373	0.444025
$543$	−41.0514	−1.76169
$544$	6.67768	0.286303
$545$	8.55969	0.366657
$546$	−0.634068	−0.0271356
$547$	−6.33478	−0.270856	−0.135428	−	0.990787i	$-0.543241\pi$
$547$	−6.33478	−0.270856	−0.135428	+	0.990787i	$0.543241\pi$
$548$	0.245364	0.0104814
$549$	1.21088	0.0516792
$550$	−9.73468	−0.415088
$551$	−45.9283	−1.95661
$552$	−2.60366	−0.110819
$553$	23.4220	0.996004
$554$	−14.7757	−0.627760
$555$	−2.45488	−0.104204
$556$	2.43064	0.103082
$557$	16.8580	0.714295	0.357147	−	0.934048i	$-0.383749\pi$
$557$	16.8580	0.714295	0.357147	+	0.934048i	$0.383749\pi$
$558$	−1.15263	−0.0487948
$559$	0.0258143	0.00109183
$560$	−6.24631	−0.263955
$561$	−42.7584	−1.80526
$562$	23.6329	0.996893
$563$	−18.7785	−0.791419	−0.395710	−	0.918376i	$-0.629501\pi$
$563$	−18.7785	−0.791419	−0.395710	+	0.918376i	$0.629501\pi$
$564$	11.6005	0.488470
$565$	25.5045	1.07298
$566$	−3.13384	−0.131725
$567$	−40.1468	−1.68601
$568$	5.84090	0.245079
$569$	−32.8507	−1.37717	−0.688586	−	0.725154i	$-0.741768\pi$
$569$	−32.8507	−1.37717	−0.688586	+	0.725154i	$0.741768\pi$
$570$	20.1944	0.845851
$571$	34.0949	1.42683	0.713414	−	0.700743i	$-0.247148\pi$
$571$	34.0949	1.42683	0.713414	+	0.700743i	$0.247148\pi$
$572$	0.301562	0.0126089
$573$	17.5694	0.733972
$574$	47.0454	1.96364
$575$	3.95832	0.165073
$576$	0.242152	0.0100896
$577$	−8.89679	−0.370378	−0.185189	−	0.982703i	$-0.559290\pi$
$577$	−8.89679	−0.370378	−0.185189	+	0.982703i	$0.559290\pi$
$578$	−27.5914	−1.14765
$579$	−36.8667	−1.53213
$580$	−9.26549	−0.384728
$581$	10.9840	0.455693
$582$	10.6478	0.441366
$583$	−25.6243	−1.06125
$584$	8.74434	0.361843
$585$	0.0308877	0.00127705
$586$	−20.8345	−0.860664
$587$	39.1341	1.61524	0.807618	−	0.589706i	$-0.200756\pi$
$587$	39.1341	1.61524	0.807618	+	0.589706i	$0.200756\pi$
$588$	−18.4458	−0.760690
$589$	−35.4909	−1.46238
$590$	16.9077	0.696079
$591$	−6.16427	−0.253564
$592$	−0.906385	−0.0372522
$593$	31.6373	1.29919	0.649595	−	0.760281i	$-0.274939\pi$
$593$	31.6373	1.29919	0.649595	+	0.760281i	$0.274939\pi$
$594$	17.6590	0.724558
$595$	41.7108	1.70998
$596$	6.22464	0.254971
$597$	−38.6408	−1.58146
$598$	−0.122621	−0.00501434
$599$	4.52556	0.184909	0.0924547	−	0.995717i	$-0.470529\pi$
$599$	4.52556	0.184909	0.0924547	+	0.995717i	$0.470529\pi$
$600$	−4.92901	−0.201226
$601$	−28.7396	−1.17231	−0.586155	−	0.810199i	$-0.699359\pi$
$601$	−28.7396	−1.17231	−0.586155	+	0.810199i	$0.699359\pi$
$602$	1.26411	0.0515213
$603$	−0.555653	−0.0226280
$604$	−6.83404	−0.278073
$605$	−2.47611	−0.100668
$606$	−8.19742	−0.332997
$607$	−3.27246	−0.132825	−0.0664125	−	0.997792i	$-0.521155\pi$
$607$	−3.27246	−0.132825	−0.0664125	+	0.997792i	$0.521155\pi$
$608$	7.45613	0.302386
$609$	−46.0581	−1.86637
$610$	7.52170	0.304545
$611$	0.546333	0.0221023
$612$	−1.61701	−0.0653638
$613$	31.9207	1.28926	0.644632	−	0.764493i	$-0.277011\pi$
$613$	31.9207	1.28926	0.644632	+	0.764493i	$0.277011\pi$
$614$	−14.3822	−0.580419
$615$	−30.6841	−1.23730
$616$	14.7673	0.594992
$617$	13.1015	0.527447	0.263724	−	0.964598i	$-0.415049\pi$
$617$	13.1015	0.527447	0.263724	+	0.964598i	$0.415049\pi$
$618$	2.35733	0.0948259
$619$	−19.7706	−0.794646	−0.397323	−	0.917679i	$-0.630061\pi$
$619$	−19.7706	−0.794646	−0.397323	+	0.917679i	$0.630061\pi$
$620$	−7.15986	−0.287547
$621$	−7.18050	−0.288144
$622$	−16.9992	−0.681605
$623$	18.7997	0.753193
$624$	0.152691	0.00611254
$625$	−3.81934	−0.152774
$626$	−10.4134	−0.416204
$627$	−47.7430	−1.90667
$628$	8.40804	0.335517
$629$	6.05255	0.241331
$630$	1.51255	0.0602615
$631$	−38.9970	−1.55245	−0.776223	−	0.630459i	$-0.782867\pi$
$631$	−38.9970	−1.55245	−0.776223	+	0.630459i	$0.782867\pi$
$632$	−5.64029	−0.224359
$633$	−0.0516929	−0.00205461
$634$	1.80348	0.0716253
$635$	−6.70792	−0.266196
$636$	−12.9745	−0.514472
$637$	−0.868715	−0.0344197
$638$	21.9051	0.867233
$639$	−1.41438	−0.0559521
$640$	1.50418	0.0594581
$641$	12.0221	0.474843	0.237422	−	0.971407i	$-0.423698\pi$
$641$	12.0221	0.474843	0.237422	+	0.971407i	$0.423698\pi$
$642$	−16.7945	−0.662827
$643$	−15.3451	−0.605151	−0.302576	−	0.953125i	$-0.597846\pi$
$643$	−15.3451	−0.605151	−0.302576	+	0.953125i	$0.597846\pi$
$644$	−6.00468	−0.236617
$645$	−0.824481	−0.0324639
$646$	−49.7897	−1.95895
$647$	1.49102	0.0586182	0.0293091	−	0.999570i	$-0.490669\pi$
$647$	1.49102	0.0586182	0.0293091	+	0.999570i	$0.490669\pi$
$648$	9.66782	0.379788
$649$	−39.9726	−1.56906
$650$	−0.232135	−0.00910507
$651$	−35.5912	−1.39493
$652$	9.22924	0.361445
$653$	−0.692515	−0.0271002	−0.0135501	−	0.999908i	$-0.504313\pi$
$653$	−0.692515	−0.0271002	−0.0135501	+	0.999908i	$0.504313\pi$
$654$	−10.2464	−0.400668
$655$	4.39803	0.171845
$656$	−11.3291	−0.442327
$657$	−2.11745	−0.0826098
$658$	26.7536	1.04296
$659$	37.0230	1.44221	0.721106	−	0.692825i	$-0.243634\pi$
$659$	37.0230	1.44221	0.721106	+	0.692825i	$0.243634\pi$
$660$	−9.63157	−0.374908
$661$	4.59123	0.178578	0.0892890	−	0.996006i	$-0.471541\pi$
$661$	4.59123	0.178578	0.0892890	+	0.996006i	$0.471541\pi$
$662$	14.6780	0.570477
$663$	−1.01962	−0.0395989
$664$	−2.64508	−0.102649
$665$	46.5733	1.80603
$666$	0.219483	0.00850478
$667$	−8.90707	−0.344883
$668$	19.9144	0.770513
$669$	−18.6077	−0.719416
$670$	−3.45158	−0.133346
$671$	−17.7825	−0.686487
$672$	7.47720	0.288439
$673$	−17.3518	−0.668864	−0.334432	−	0.942420i	$-0.608544\pi$
$673$	−17.3518	−0.668864	−0.334432	+	0.942420i	$0.608544\pi$
$674$	−19.3728	−0.746212
$675$	−13.5935	−0.523212
$676$	−12.9928	−0.499723
$677$	3.64824	0.140213	0.0701066	−	0.997540i	$-0.477666\pi$
$677$	3.64824	0.140213	0.0701066	+	0.997540i	$0.477666\pi$
$678$	−30.5304	−1.17251
$679$	24.5565	0.942391
$680$	−10.0445	−0.385188
$681$	−0.922173	−0.0353377
$682$	16.9271	0.648172
$683$	47.2876	1.80941	0.904705	−	0.426039i	$-0.140091\pi$
$683$	47.2876	1.80941	0.904705	+	0.426039i	$0.140091\pi$
$684$	−1.80551	−0.0690355
$685$	−0.369072	−0.0141015
$686$	−13.4721	−0.514368
$687$	38.6075	1.47297
$688$	−0.304413	−0.0116056
$689$	−0.611042	−0.0232788
$690$	3.91639	0.149094
$691$	31.5328	1.19956	0.599781	−	0.800164i	$-0.295254\pi$
$691$	31.5328	1.19956	0.599781	+	0.800164i	$0.295254\pi$
$692$	−14.9097	−0.566781
$693$	−3.57593	−0.135838
$694$	24.9141	0.945724
$695$	−3.65614	−0.138685
$696$	11.0913	0.420416
$697$	75.6521	2.86553
$698$	−30.3323	−1.14809
$699$	51.2672	1.93910
$700$	−11.3675	−0.429651
$701$	−34.7674	−1.31315	−0.656574	−	0.754261i	$-0.727995\pi$
$701$	−34.7674	−1.31315	−0.656574	+	0.754261i	$0.727995\pi$
$702$	0.421099	0.0158934
$703$	6.75813	0.254888
$704$	−3.55614	−0.134027
$705$	−17.4493	−0.657179
$706$	−22.8180	−0.858768
$707$	−18.9053	−0.711006
$708$	−20.2395	−0.760648
$709$	−18.2264	−0.684506	−0.342253	−	0.939608i	$-0.611190\pi$
$709$	−18.2264	−0.684506	−0.342253	+	0.939608i	$0.611190\pi$
$710$	−8.78579	−0.329725
$711$	1.36581	0.0512217
$712$	−4.52718	−0.169663
$713$	−6.88289	−0.257766
$714$	−49.9303	−1.86860
$715$	−0.453605	−0.0169638
$716$	17.5867	0.657245
$717$	26.5421	0.991234
$718$	16.7632	0.625596
$719$	−1.28906	−0.0480738	−0.0240369	−	0.999711i	$-0.507652\pi$
$719$	−1.28906	−0.0480738	−0.0240369	+	0.999711i	$0.507652\pi$
$720$	−0.364241	−0.0135744
$721$	5.43659	0.202469
$722$	−36.5939	−1.36188
$723$	−47.8414	−1.77924
$724$	22.7988	0.847310
$725$	−16.8620	−0.626240
$726$	2.96404	0.110006
$727$	4.01202	0.148798	0.0743989	−	0.997229i	$-0.476296\pi$
$727$	4.01202	0.148798	0.0743989	+	0.997229i	$0.476296\pi$
$728$	0.352143	0.0130513
$729$	24.4830	0.906778
$730$	−13.1531	−0.486818
$731$	2.03277	0.0751848
$732$	−9.00392	−0.332794
$733$	2.98855	0.110385	0.0551923	−	0.998476i	$-0.482423\pi$
$733$	2.98855	0.110385	0.0551923	+	0.998476i	$0.482423\pi$
$734$	26.2834	0.970137
$735$	27.7458	1.02342
$736$	1.44600	0.0533002
$737$	8.16011	0.300581
$738$	2.74336	0.100984
$739$	−45.8547	−1.68679	−0.843396	−	0.537292i	$-0.819447\pi$
$739$	−45.8547	−1.68679	−0.843396	+	0.537292i	$0.819447\pi$
$740$	1.36337	0.0501185
$741$	−1.13849	−0.0418233
$742$	−29.9224	−1.09848
$743$	50.1424	1.83955	0.919773	−	0.392451i	$-0.128373\pi$
$743$	50.1424	1.83955	0.919773	+	0.392451i	$0.128373\pi$
$744$	8.57077	0.314220
$745$	−9.36300	−0.343034
$746$	21.5092	0.787506
$747$	0.640509	0.0234350
$748$	23.7468	0.868268
$749$	−38.7323	−1.41525
$750$	20.9563	0.765216
$751$	−14.0033	−0.510986	−0.255493	−	0.966811i	$-0.582238\pi$
$751$	−14.0033	−0.510986	−0.255493	+	0.966811i	$0.582238\pi$
$752$	−6.44259	−0.234937
$753$	1.33989	0.0488282
$754$	0.522353	0.0190230
$755$	10.2797	0.374115
$756$	20.6210	0.749978
$757$	23.3782	0.849695	0.424847	−	0.905265i	$-0.360328\pi$
$757$	23.3782	0.849695	0.424847	+	0.905265i	$0.360328\pi$
$758$	3.68784	0.133948
$759$	−9.25898	−0.336080
$760$	−11.2154	−0.406825
$761$	23.7402	0.860583	0.430291	−	0.902690i	$-0.358411\pi$
$761$	23.7402	0.860583	0.430291	+	0.902690i	$0.358411\pi$
$762$	8.02977	0.290888
$763$	−23.6308	−0.855493
$764$	−9.75754	−0.353015
$765$	2.43228	0.0879394
$766$	−33.9351	−1.22613
$767$	−0.953193	−0.0344178
$768$	−1.80060	−0.0649735
$769$	−10.1023	−0.364297	−0.182148	−	0.983271i	$-0.558305\pi$
$769$	−10.1023	−0.364297	−0.182148	+	0.983271i	$0.558305\pi$
$770$	−22.2127	−0.800492
$771$	−45.6840	−1.64527
$772$	20.4747	0.736901
$773$	42.8627	1.54166	0.770832	−	0.637038i	$-0.219841\pi$
$773$	42.8627	1.54166	0.770832	+	0.637038i	$0.219841\pi$
$774$	0.0737140	0.00264960
$775$	−13.0300	−0.468053
$776$	−5.91349	−0.212282
$777$	6.77722	0.243131
$778$	−23.1164	−0.828762
$779$	84.4712	3.02650
$780$	−0.229676	−0.00822371
$781$	20.7711	0.743247
$782$	−9.65591	−0.345295
$783$	30.5882	1.09313
$784$	10.2442	0.365866
$785$	−12.6472	−0.451400
$786$	−5.26470	−0.187786
$787$	−3.41447	−0.121713	−0.0608563	−	0.998147i	$-0.519383\pi$
$787$	−3.41447	−0.121713	−0.0608563	+	0.998147i	$0.519383\pi$
$788$	3.42346	0.121956
$789$	18.2168	0.648535
$790$	8.48404	0.301849
$791$	−70.4106	−2.50351
$792$	0.861125	0.0305988
$793$	−0.424045	−0.0150583
$794$	11.2524	0.399334
$795$	19.5160	0.692162
$796$	21.4600	0.760628
$797$	22.1910	0.786047	0.393023	−	0.919528i	$-0.371429\pi$
$797$	22.1910	0.786047	0.393023	+	0.919528i	$0.371429\pi$
$798$	−55.7510	−1.97356
$799$	43.0216	1.52199
$800$	2.73743	0.0967827
$801$	1.09626	0.0387346
$802$	−30.3391	−1.07131
$803$	31.0961	1.09736
$804$	4.13174	0.145715
$805$	9.03214	0.318341
$806$	0.403646	0.0142178
$807$	−32.0575	−1.12848
$808$	4.55261	0.160160
$809$	−13.1542	−0.462478	−0.231239	−	0.972897i	$-0.574278\pi$
$809$	−13.1542	−0.462478	−0.231239	+	0.972897i	$0.574278\pi$
$810$	−14.5422	−0.510960
$811$	−27.0920	−0.951329	−0.475665	−	0.879627i	$-0.657792\pi$
$811$	−27.0920	−0.951329	−0.475665	+	0.879627i	$0.657792\pi$
$812$	25.5793	0.897659
$813$	18.6133	0.652797
$814$	−3.22324	−0.112974
$815$	−13.8825	−0.486282
$816$	12.0238	0.420918
$817$	2.26974	0.0794082
$818$	−5.81890	−0.203453
$819$	−0.0852720	−0.00297965
$820$	17.0411	0.595099
$821$	35.0374	1.22281	0.611407	−	0.791316i	$-0.290604\pi$
$821$	35.0374	1.22281	0.611407	+	0.791316i	$0.290604\pi$
$822$	0.441801	0.0154096
$823$	−33.2630	−1.15948	−0.579738	−	0.814803i	$-0.696845\pi$
$823$	−33.2630	−1.15948	−0.579738	+	0.814803i	$0.696845\pi$
$824$	−1.30920	−0.0456080
$825$	−17.5282	−0.610255
$826$	−46.6773	−1.62411
$827$	−26.8221	−0.932694	−0.466347	−	0.884602i	$-0.654430\pi$
$827$	−26.8221	−0.932694	−0.466347	+	0.884602i	$0.654430\pi$
$828$	−0.350151	−0.0121686
$829$	−13.0709	−0.453971	−0.226985	−	0.973898i	$-0.572887\pi$
$829$	−13.0709	−0.453971	−0.226985	+	0.973898i	$0.572887\pi$
$830$	3.97868	0.138102
$831$	−26.6051	−0.922921
$832$	−0.0848003	−0.00293992
$833$	−68.4078	−2.37019
$834$	4.37661	0.151550
$835$	−29.9550	−1.03664
$836$	26.5151	0.917043
$837$	23.6369	0.817010
$838$	30.4288	1.05114
$839$	26.6214	0.919074	0.459537	−	0.888159i	$-0.348015\pi$
$839$	26.6214	0.919074	0.459537	+	0.888159i	$0.348015\pi$
$840$	−11.2471	−0.388061
$841$	8.94323	0.308387
$842$	0.608052	0.0209548
$843$	42.5533	1.46561
$844$	0.0287088	0.000988196 0
$845$	19.5436	0.672320
$846$	1.56008	0.0536368
$847$	6.83581	0.234881
$848$	7.20566	0.247443
$849$	−5.64278	−0.193660
$850$	−18.2797	−0.626988
$851$	1.31063	0.0449279
$852$	10.5171	0.360310
$853$	14.0884	0.482376	0.241188	−	0.970478i	$-0.422463\pi$
$853$	14.0884	0.482376	0.241188	+	0.970478i	$0.422463\pi$
$854$	−20.7652	−0.710572
$855$	2.71583	0.0928793
$856$	9.32719	0.318797
$857$	4.58258	0.156538	0.0782690	−	0.996932i	$-0.475061\pi$
$857$	4.58258	0.156538	0.0782690	+	0.996932i	$0.475061\pi$
$858$	0.542991	0.0185374
$859$	−26.4376	−0.902040	−0.451020	−	0.892514i	$-0.648940\pi$
$859$	−26.4376	−0.902040	−0.451020	+	0.892514i	$0.648940\pi$
$860$	0.457893	0.0156140
$861$	84.7099	2.88691
$862$	18.8938	0.643527
$863$	−16.7545	−0.570330	−0.285165	−	0.958478i	$-0.592048\pi$
$863$	−16.7545	−0.570330	−0.285165	+	0.958478i	$0.592048\pi$
$864$	−4.96578	−0.168939
$865$	22.4269	0.762538
$866$	−38.7744	−1.31761
$867$	−49.6811	−1.68726
$868$	19.7663	0.670912
$869$	−20.0577	−0.680410
$870$	−16.6834	−0.565621
$871$	0.194587	0.00659333
$872$	5.69058	0.192707
$873$	1.43196	0.0484645
$874$	−10.7815	−0.364691
$875$	48.3303	1.63386
$876$	15.7450	0.531975
$877$	4.50027	0.151963	0.0759817	−	0.997109i	$-0.475791\pi$
$877$	4.50027	0.151963	0.0759817	+	0.997109i	$0.475791\pi$
$878$	18.5542	0.626175
$879$	−37.5145	−1.26533
$880$	5.34909	0.180318
$881$	−5.43861	−0.183232	−0.0916158	−	0.995794i	$-0.529203\pi$
$881$	−5.43861	−0.183232	−0.0916158	+	0.995794i	$0.529203\pi$
$882$	−2.48066	−0.0835282
$883$	33.7651	1.13629	0.568143	−	0.822930i	$-0.307662\pi$
$883$	33.7651	1.13629	0.568143	+	0.822930i	$0.307662\pi$
$884$	0.566269	0.0190457
$885$	30.4440	1.02336
$886$	−28.3679	−0.953038
$887$	−36.6476	−1.23050	−0.615252	−	0.788330i	$-0.710946\pi$
$887$	−36.6476	−1.23050	−0.615252	+	0.788330i	$0.710946\pi$
$888$	−1.63204	−0.0547675
$889$	18.5186	0.621095
$890$	6.80972	0.228262
$891$	34.3801	1.15178
$892$	10.3342	0.346015
$893$	48.0368	1.60749
$894$	11.2081	0.374854
$895$	−26.4536	−0.884247
$896$	−4.15262	−0.138729
$897$	−0.220791	−0.00737200
$898$	−34.0794	−1.13725
$899$	29.3204	0.977891
$900$	−0.662873	−0.0220958
$901$	−48.1171	−1.60301
$902$	−40.2879	−1.34144
$903$	2.27615	0.0757457
$904$	16.9557	0.563938
$905$	−34.2936	−1.13996
$906$	−12.3054	−0.408818
$907$	−3.62377	−0.120325	−0.0601626	−	0.998189i	$-0.519162\pi$
$907$	−3.62377	−0.120325	−0.0601626	+	0.998189i	$0.519162\pi$
$908$	0.512148	0.0169962
$909$	−1.10242	−0.0365650
$910$	−0.529688	−0.0175590
$911$	−36.4576	−1.20790	−0.603948	−	0.797024i	$-0.706406\pi$
$911$	−36.4576	−1.20790	−0.603948	+	0.797024i	$0.706406\pi$
$912$	13.4255	0.444562
$913$	−9.40627	−0.311302
$914$	40.6394	1.34423
$915$	13.5436	0.447736
$916$	−21.4415	−0.708447
$917$	−12.1417	−0.400954
$918$	33.1599	1.09444
$919$	−49.8445	−1.64422	−0.822109	−	0.569330i	$-0.807203\pi$
$919$	−49.8445	−1.64422	−0.822109	+	0.569330i	$0.807203\pi$
$920$	−2.17505	−0.0717092
$921$	−25.8966	−0.853322
$922$	1.75365	0.0577532
$923$	0.495310	0.0163033
$924$	26.5900	0.874746
$925$	2.48117	0.0815802
$926$	−17.8519	−0.586651
$927$	0.317024	0.0104124
$928$	−6.15981	−0.202206
$929$	−36.5077	−1.19778	−0.598889	−	0.800832i	$-0.704391\pi$
$929$	−36.5077	−1.19778	−0.598889	+	0.800832i	$0.704391\pi$
$930$	−12.8920	−0.422746
$931$	−76.3824	−2.50333
$932$	−28.4723	−0.932642
$933$	−30.6087	−1.00208
$934$	−7.80821	−0.255493
$935$	−35.7195	−1.16815
$936$	0.0205345	0.000671192 0
$937$	−10.9193	−0.356719	−0.178360	−	0.983965i	$-0.557079\pi$
$937$	−10.9193	−0.356719	−0.178360	+	0.983965i	$0.557079\pi$
$938$	9.52881	0.311127
$939$	−18.7504	−0.611896
$940$	9.69084	0.316080
$941$	4.48724	0.146280	0.0731398	−	0.997322i	$-0.476698\pi$
$941$	4.48724	0.146280	0.0731398	+	0.997322i	$0.476698\pi$
$942$	15.1395	0.493272
$943$	16.3818	0.533466
$944$	11.2404	0.365845
$945$	−31.0177	−1.00901
$946$	−1.08253	−0.0351962
$947$	39.4077	1.28058	0.640289	−	0.768134i	$-0.278815\pi$
$947$	39.4077	1.28058	0.640289	+	0.768134i	$0.278815\pi$
$948$	−10.1559	−0.329848
$949$	0.741522	0.0240708
$950$	−20.4106	−0.662208
$951$	3.24734	0.105302
$952$	27.7299	0.898730
$953$	25.4983	0.825970	0.412985	−	0.910738i	$-0.364486\pi$
$953$	25.4983	0.825970	0.412985	+	0.910738i	$0.364486\pi$
$954$	−1.74486	−0.0564920
$955$	14.6771	0.474941
$956$	−14.7407	−0.476749
$957$	39.4424	1.27499
$958$	42.7372	1.38078
$959$	1.01890	0.0329020
$960$	2.70843	0.0874142
$961$	−8.34278	−0.269122
$962$	−0.0768617	−0.00247812
$963$	−2.25859	−0.0727822
$964$	26.5697	0.855754
$965$	−30.7977	−0.991415
$966$	−10.8120	−0.347871
$967$	2.07654	0.0667770	0.0333885	−	0.999442i	$-0.489370\pi$
$967$	2.07654	0.0667770	0.0333885	+	0.999442i	$0.489370\pi$
$968$	−1.64614	−0.0529091
$969$	−89.6512	−2.88001
$970$	8.89498	0.285601
$971$	−23.6094	−0.757662	−0.378831	−	0.925466i	$-0.623674\pi$
$971$	−23.6094	−0.757662	−0.378831	+	0.925466i	$0.623674\pi$
$972$	2.51052	0.0805251
$973$	10.0935	0.323584
$974$	−23.7626	−0.761403
$975$	−0.417981	−0.0133861
$976$	5.00052	0.160063
$977$	−1.14616	−0.0366690	−0.0183345	−	0.999832i	$-0.505836\pi$
$977$	−1.14616	−0.0366690	−0.0183345	+	0.999832i	$0.505836\pi$
$978$	16.6182	0.531390
$979$	−16.0993	−0.514536
$980$	−15.4092	−0.492230
$981$	−1.37798	−0.0439956
$982$	−28.8593	−0.920938
$983$	36.5628	1.16617	0.583086	−	0.812410i	$-0.301845\pi$
$983$	36.5628	1.16617	0.583086	+	0.812410i	$0.301845\pi$
$984$	−20.3991	−0.650301
$985$	−5.14951	−0.164077
$986$	41.1332	1.30995
$987$	48.1725	1.53335
$988$	0.632282	0.0201156
$989$	0.440180	0.0139969
$990$	−1.29529	−0.0411671
$991$	−32.5689	−1.03458	−0.517292	−	0.855809i	$-0.673060\pi$
$991$	−32.5689	−1.03458	−0.517292	+	0.855809i	$0.673060\pi$
$992$	−4.75996	−0.151129
$993$	26.4292	0.838706
$994$	24.2550	0.769323
$995$	−32.2797	−1.02334
$996$	−4.76272	−0.150913
$997$	−36.8733	−1.16779	−0.583895	−	0.811830i	$-0.698472\pi$
$997$	−36.8733	−1.16779	−0.583895	+	0.811830i	$0.698472\pi$
$998$	3.04099	0.0962608
$999$	−4.50091	−0.142402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4022.2.a.e.1.11	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4022.2.a.e.1.11	✓	46	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:	\( N \)	\(=\)	\( 4022 = 2 \cdot 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.80060 q^{3} +1.00000 q^{4} -1.50418 q^{5} +1.80060 q^{6} +4.15262 q^{7} -1.00000 q^{8} +0.242152 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.80060 q^{3} +1.00000 q^{4} -1.50418 q^{5} +1.80060 q^{6} +4.15262 q^{7} -1.00000 q^{8} +0.242152 q^{9} +1.50418 q^{10} -3.55614 q^{11} -1.80060 q^{12} -0.0848003 q^{13} -4.15262 q^{14} +2.70843 q^{15} +1.00000 q^{16} -6.67768 q^{17} -0.242152 q^{18} -7.45613 q^{19} -1.50418 q^{20} -7.47720 q^{21} +3.55614 q^{22} -1.44600 q^{23} +1.80060 q^{24} -2.73743 q^{25} +0.0848003 q^{26} +4.96578 q^{27} +4.15262 q^{28} +6.15981 q^{29} -2.70843 q^{30} +4.75996 q^{31} -1.00000 q^{32} +6.40318 q^{33} +6.67768 q^{34} -6.24631 q^{35} +0.242152 q^{36} -0.906385 q^{37} +7.45613 q^{38} +0.152691 q^{39} +1.50418 q^{40} -11.3291 q^{41} +7.47720 q^{42} -0.304413 q^{43} -3.55614 q^{44} -0.364241 q^{45} +1.44600 q^{46} -6.44259 q^{47} -1.80060 q^{48} +10.2442 q^{49} +2.73743 q^{50} +12.0238 q^{51} -0.0848003 q^{52} +7.20566 q^{53} -4.96578 q^{54} +5.34909 q^{55} -4.15262 q^{56} +13.4255 q^{57} -6.15981 q^{58} +11.2404 q^{59} +2.70843 q^{60} +5.00052 q^{61} -4.75996 q^{62} +1.00556 q^{63} +1.00000 q^{64} +0.127555 q^{65} -6.40318 q^{66} -2.29465 q^{67} -6.67768 q^{68} +2.60366 q^{69} +6.24631 q^{70} -5.84090 q^{71} -0.242152 q^{72} -8.74434 q^{73} +0.906385 q^{74} +4.92901 q^{75} -7.45613 q^{76} -14.7673 q^{77} -0.152691 q^{78} +5.64029 q^{79} -1.50418 q^{80} -9.66782 q^{81} +11.3291 q^{82} +2.64508 q^{83} -7.47720 q^{84} +10.0445 q^{85} +0.304413 q^{86} -11.0913 q^{87} +3.55614 q^{88} +4.52718 q^{89} +0.364241 q^{90} -0.352143 q^{91} -1.44600 q^{92} -8.57077 q^{93} +6.44259 q^{94} +11.2154 q^{95} +1.80060 q^{96} +5.91349 q^{97} -10.2442 q^{98} -0.861125 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9}+O(q^{10}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9	\( 46 q - 46 q^{2} + 8 q^{3} + 46 q^{4} + 14 q^{5} - 8 q^{6} + 28 q^{7} - 46 q^{8} + 58 q^{9} - 14 q^{10} - 6 q^{11} + 8 q^{12} + 37 q^{13} - 28 q^{14} + 9 q^{15} + 46 q^{16} + 6 q^{17} - 58 q^{18} + 18 q^{19} + 14 q^{20} + 19 q^{21} + 6 q^{22} - 4 q^{23} - 8 q^{24} + 86 q^{25} - 37 q^{26} + 32 q^{27} + 28 q^{28} + 15 q^{29} - 9 q^{30} + 18 q^{31} - 46 q^{32} + 37 q^{33} - 6 q^{34} - 2 q^{35} + 58 q^{36} + 74 q^{37} - 18 q^{38} - 3 q^{39} - 14 q^{40} - 18 q^{41} - 19 q^{42} + 25 q^{43} - 6 q^{44} + 94 q^{45} + 4 q^{46} + 18 q^{47} + 8 q^{48} + 92 q^{49} - 86 q^{50} - 10 q^{51} + 37 q^{52} + 17 q^{53} - 32 q^{54} + 37 q^{55} - 28 q^{56} + 43 q^{57} - 15 q^{58} - 24 q^{59} + 9 q^{60} + 46 q^{61} - 18 q^{62} + 80 q^{63} + 46 q^{64} + 24 q^{65} - 37 q^{66} + 61 q^{67} + 6 q^{68} + 59 q^{69} + 2 q^{70} - 8 q^{71} - 58 q^{72} + 101 q^{73} - 74 q^{74} + 34 q^{75} + 18 q^{76} + 40 q^{77} + 3 q^{78} + 9 q^{79} + 14 q^{80} + 58 q^{81} + 18 q^{82} + 18 q^{83} + 19 q^{84} + 60 q^{85} - 25 q^{86} + 20 q^{87} + 6 q^{88} - 25 q^{89} - 94 q^{90} + 51 q^{91} - 4 q^{92} + 63 q^{93} - 18 q^{94} - 31 q^{95} - 8 q^{96} + 76 q^{97} - 92 q^{98} + 21 q^{99}+O(q^{100}) \) 46 * q - 46 * q^2 + 8 * q^3 + 46 * q^4 + 14 * q^5 - 8 * q^6 + 28 * q^7 - 46 * q^8 + 58 * q^9 - 14 * q^10 - 6 * q^11 + 8 * q^12 + 37 * q^13 - 28 * q^14 + 9 * q^15 + 46 * q^16 + 6 * q^17 - 58 * q^18 + 18 * q^19 + 14 * q^20 + 19 * q^21 + 6 * q^22 - 4 * q^23 - 8 * q^24 + 86 * q^25 - 37 * q^26 + 32 * q^27 + 28 * q^28 + 15 * q^29 - 9 * q^30 + 18 * q^31 - 46 * q^32 + 37 * q^33 - 6 * q^34 - 2 * q^35 + 58 * q^36 + 74 * q^37 - 18 * q^38 - 3 * q^39 - 14 * q^40 - 18 * q^41 - 19 * q^42 + 25 * q^43 - 6 * q^44 + 94 * q^45 + 4 * q^46 + 18 * q^47 + 8 * q^48 + 92 * q^49 - 86 * q^50 - 10 * q^51 + 37 * q^52 + 17 * q^53 - 32 * q^54 + 37 * q^55 - 28 * q^56 + 43 * q^57 - 15 * q^58 - 24 * q^59 + 9 * q^60 + 46 * q^61 - 18 * q^62 + 80 * q^63 + 46 * q^64 + 24 * q^65 - 37 * q^66 + 61 * q^67 + 6 * q^68 + 59 * q^69 + 2 * q^70 - 8 * q^71 - 58 * q^72 + 101 * q^73 - 74 * q^74 + 34 * q^75 + 18 * q^76 + 40 * q^77 + 3 * q^78 + 9 * q^79 + 14 * q^80 + 58 * q^81 + 18 * q^82 + 18 * q^83 + 19 * q^84 + 60 * q^85 - 25 * q^86 + 20 * q^87 + 6 * q^88 - 25 * q^89 - 94 * q^90 + 51 * q^91 - 4 * q^92 + 63 * q^93 - 18 * q^94 - 31 * q^95 - 8 * q^96 + 76 * q^97 - 92 * q^98 + 21 * q^99

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