LMFDB - Embedded newform 4017.2.a.l.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.609784 q^{2} +1.00000 q^{3} -1.62816 q^{4} +2.30670 q^{5} +0.609784 q^{6} -1.80421 q^{7} -2.21240 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.609784 q^{2} +1.00000 q^{3} -1.62816 q^{4} +2.30670 q^{5} +0.609784 q^{6} -1.80421 q^{7} -2.21240 q^{8} +1.00000 q^{9} +1.40659 q^{10} -0.459865 q^{11} -1.62816 q^{12} -1.00000 q^{13} -1.10018 q^{14} +2.30670 q^{15} +1.90724 q^{16} -4.35127 q^{17} +0.609784 q^{18} -5.50358 q^{19} -3.75569 q^{20} -1.80421 q^{21} -0.280418 q^{22} -0.178634 q^{23} -2.21240 q^{24} +0.320880 q^{25} -0.609784 q^{26} +1.00000 q^{27} +2.93755 q^{28} +7.87507 q^{29} +1.40659 q^{30} +10.2252 q^{31} +5.58780 q^{32} -0.459865 q^{33} -2.65334 q^{34} -4.16178 q^{35} -1.62816 q^{36} +5.46024 q^{37} -3.35600 q^{38} -1.00000 q^{39} -5.10334 q^{40} +12.0765 q^{41} -1.10018 q^{42} +11.3645 q^{43} +0.748735 q^{44} +2.30670 q^{45} -0.108928 q^{46} +5.12704 q^{47} +1.90724 q^{48} -3.74482 q^{49} +0.195668 q^{50} -4.35127 q^{51} +1.62816 q^{52} -4.74711 q^{53} +0.609784 q^{54} -1.06077 q^{55} +3.99163 q^{56} -5.50358 q^{57} +4.80209 q^{58} +10.2884 q^{59} -3.75569 q^{60} +12.7957 q^{61} +6.23518 q^{62} -1.80421 q^{63} -0.407142 q^{64} -2.30670 q^{65} -0.280418 q^{66} +2.74229 q^{67} +7.08459 q^{68} -0.178634 q^{69} -2.53779 q^{70} +0.596535 q^{71} -2.21240 q^{72} +3.26727 q^{73} +3.32957 q^{74} +0.320880 q^{75} +8.96074 q^{76} +0.829694 q^{77} -0.609784 q^{78} -12.4564 q^{79} +4.39945 q^{80} +1.00000 q^{81} +7.36406 q^{82} +12.3221 q^{83} +2.93755 q^{84} -10.0371 q^{85} +6.92991 q^{86} +7.87507 q^{87} +1.01740 q^{88} -9.17999 q^{89} +1.40659 q^{90} +1.80421 q^{91} +0.290845 q^{92} +10.2252 q^{93} +3.12639 q^{94} -12.6951 q^{95} +5.58780 q^{96} -8.58453 q^{97} -2.28353 q^{98} -0.459865 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * 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 $

$2$	0.609784	0.431182	0.215591	−	0.976484i	$-0.430832\pi$
$2$	0.609784	0.431182	0.215591	+	0.976484i	$0.430832\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.62816	−0.814082
$5$	2.30670	1.03159	0.515795	−	0.856712i	$-0.327497\pi$
$5$	2.30670	1.03159	0.515795	+	0.856712i	$0.327497\pi$
$6$	0.609784	0.248943
$7$	−1.80421	−0.681928	−0.340964	−	0.940076i	$-0.610753\pi$
$7$	−1.80421	−0.681928	−0.340964	+	0.940076i	$0.610753\pi$
$8$	−2.21240	−0.782200
$9$	1.00000	0.333333
$10$	1.40659	0.444803
$11$	−0.459865	−0.138654	−0.0693272	−	0.997594i	$-0.522085\pi$
$11$	−0.459865	−0.138654	−0.0693272	+	0.997594i	$0.522085\pi$
$12$	−1.62816	−0.470010
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−1.10018	−0.294035
$15$	2.30670	0.595588
$16$	1.90724	0.476811
$17$	−4.35127	−1.05534	−0.527670	−	0.849450i	$-0.676934\pi$
$17$	−4.35127	−1.05534	−0.527670	+	0.849450i	$0.676934\pi$
$18$	0.609784	0.143727
$19$	−5.50358	−1.26261	−0.631304	−	0.775535i	$-0.717480\pi$
$19$	−5.50358	−1.26261	−0.631304	+	0.775535i	$0.717480\pi$
$20$	−3.75569	−0.839798
$21$	−1.80421	−0.393711
$22$	−0.280418	−0.0597853
$23$	−0.178634	−0.0372477	−0.0186239	−	0.999827i	$-0.505928\pi$
$23$	−0.178634	−0.0372477	−0.0186239	+	0.999827i	$0.505928\pi$
$24$	−2.21240	−0.451603
$25$	0.320880	0.0641760
$26$	−0.609784	−0.119588
$27$	1.00000	0.192450
$28$	2.93755	0.555145
$29$	7.87507	1.46236	0.731182	−	0.682182i	$-0.238969\pi$
$29$	7.87507	1.46236	0.731182	+	0.682182i	$0.238969\pi$
$30$	1.40659	0.256807
$31$	10.2252	1.83651	0.918253	−	0.395994i	$-0.129600\pi$
$31$	10.2252	1.83651	0.918253	+	0.395994i	$0.129600\pi$
$32$	5.58780	0.987792
$33$	−0.459865	−0.0800522
$34$	−2.65334	−0.455043
$35$	−4.16178	−0.703469
$36$	−1.62816	−0.271361
$37$	5.46024	0.897658	0.448829	−	0.893618i	$-0.351841\pi$
$37$	5.46024	0.897658	0.448829	+	0.893618i	$0.351841\pi$
$38$	−3.35600	−0.544414
$39$	−1.00000	−0.160128
$40$	−5.10334	−0.806909
$41$	12.0765	1.88604	0.943018	−	0.332743i	$-0.107974\pi$
$41$	12.0765	1.88604	0.943018	+	0.332743i	$0.107974\pi$
$42$	−1.10018	−0.169761
$43$	11.3645	1.73308	0.866538	−	0.499112i	$-0.166340\pi$
$43$	11.3645	1.73308	0.866538	+	0.499112i	$0.166340\pi$
$44$	0.748735	0.112876
$45$	2.30670	0.343863
$46$	−0.108928	−0.0160605
$47$	5.12704	0.747856	0.373928	−	0.927458i	$-0.378011\pi$
$47$	5.12704	0.747856	0.373928	+	0.927458i	$0.378011\pi$
$48$	1.90724	0.275287
$49$	−3.74482	−0.534974
$50$	0.195668	0.0276716
$51$	−4.35127	−0.609300
$52$	1.62816	0.225786
$53$	−4.74711	−0.652065	−0.326033	−	0.945359i	$-0.605712\pi$
$53$	−4.74711	−0.652065	−0.326033	+	0.945359i	$0.605712\pi$
$54$	0.609784	0.0829811
$55$	−1.06077	−0.143034
$56$	3.99163	0.533404
$57$	−5.50358	−0.728967
$58$	4.80209	0.630545
$59$	10.2884	1.33943	0.669715	−	0.742618i	$-0.266416\pi$
$59$	10.2884	1.33943	0.669715	+	0.742618i	$0.266416\pi$
$60$	−3.75569	−0.484858
$61$	12.7957	1.63832	0.819158	−	0.573568i	$-0.194441\pi$
$61$	12.7957	1.63832	0.819158	+	0.573568i	$0.194441\pi$
$62$	6.23518	0.791869
$63$	−1.80421	−0.227309
$64$	−0.407142	−0.0508927
$65$	−2.30670	−0.286111
$66$	−0.280418	−0.0345171
$67$	2.74229	0.335024	0.167512	−	0.985870i	$-0.446427\pi$
$67$	2.74229	0.335024	0.167512	+	0.985870i	$0.446427\pi$
$68$	7.08459	0.859132
$69$	−0.178634	−0.0215050
$70$	−2.53779	−0.303324
$71$	0.596535	0.0707956	0.0353978	−	0.999373i	$-0.488730\pi$
$71$	0.596535	0.0707956	0.0353978	+	0.999373i	$0.488730\pi$
$72$	−2.21240	−0.260733
$73$	3.26727	0.382405	0.191202	−	0.981551i	$-0.438761\pi$
$73$	3.26727	0.382405	0.191202	+	0.981551i	$0.438761\pi$
$74$	3.32957	0.387054
$75$	0.320880	0.0370521
$76$	8.96074	1.02787
$77$	0.829694	0.0945524
$78$	−0.609784	−0.0690444
$79$	−12.4564	−1.40145	−0.700725	−	0.713432i	$-0.747140\pi$
$79$	−12.4564	−1.40145	−0.700725	+	0.713432i	$0.747140\pi$
$80$	4.39945	0.491873
$81$	1.00000	0.111111
$82$	7.36406	0.813225
$83$	12.3221	1.35252	0.676261	−	0.736663i	$-0.263599\pi$
$83$	12.3221	1.35252	0.676261	+	0.736663i	$0.263599\pi$
$84$	2.93755	0.320513
$85$	−10.0371	−1.08868
$86$	6.92991	0.747271
$87$	7.87507	0.844296
$88$	1.01740	0.108456
$89$	−9.17999	−0.973077	−0.486539	−	0.873659i	$-0.661741\pi$
$89$	−9.17999	−0.973077	−0.486539	+	0.873659i	$0.661741\pi$
$90$	1.40659	0.148268
$91$	1.80421	0.189133
$92$	0.290845	0.0303227
$93$	10.2252	1.06031
$94$	3.12639	0.322462
$95$	−12.6951	−1.30249
$96$	5.58780	0.570302
$97$	−8.58453	−0.871627	−0.435814	−	0.900037i	$-0.643539\pi$
$97$	−8.58453	−0.871627	−0.435814	+	0.900037i	$0.643539\pi$
$98$	−2.28353	−0.230671
$99$	−0.459865	−0.0462182
$100$	−0.522446	−0.0522446
$101$	11.3455	1.12892	0.564461	−	0.825460i	$-0.309084\pi$
$101$	11.3455	1.12892	0.564461	+	0.825460i	$0.309084\pi$
$102$	−2.65334	−0.262719
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	2.21240	0.216943
$105$	−4.16178	−0.406148
$106$	−2.89471	−0.281159
$107$	−9.46219	−0.914744	−0.457372	−	0.889275i	$-0.651209\pi$
$107$	−9.46219	−0.914744	−0.457372	+	0.889275i	$0.651209\pi$
$108$	−1.62816	−0.156670
$109$	−14.7660	−1.41433	−0.707163	−	0.707050i	$-0.750025\pi$
$109$	−14.7660	−1.41433	−0.707163	+	0.707050i	$0.750025\pi$
$110$	−0.646841	−0.0616739
$111$	5.46024	0.518263
$112$	−3.44107	−0.325151
$113$	−7.03711	−0.661995	−0.330998	−	0.943632i	$-0.607385\pi$
$113$	−7.03711	−0.661995	−0.330998	+	0.943632i	$0.607385\pi$
$114$	−3.35600	−0.314318
$115$	−0.412055	−0.0384243
$116$	−12.8219	−1.19048
$117$	−1.00000	−0.0924500
$118$	6.27367	0.577538
$119$	7.85062	0.719665
$120$	−5.10334	−0.465869
$121$	−10.7885	−0.980775
$122$	7.80258	0.706413
$123$	12.0765	1.08890
$124$	−16.6484	−1.49507
$125$	−10.7933	−0.965386
$126$	−1.10018	−0.0980117
$127$	−4.77727	−0.423915	−0.211957	−	0.977279i	$-0.567984\pi$
$127$	−4.77727	−0.423915	−0.211957	+	0.977279i	$0.567984\pi$
$128$	−11.4239	−1.00974
$129$	11.3645	1.00059
$130$	−1.40659	−0.123366
$131$	7.33460	0.640827	0.320413	−	0.947278i	$-0.396178\pi$
$131$	7.33460	0.640827	0.320413	+	0.947278i	$0.396178\pi$
$132$	0.748735	0.0651690
$133$	9.92963	0.861008
$134$	1.67220	0.144456
$135$	2.30670	0.198529
$136$	9.62674	0.825486
$137$	15.0219	1.28340	0.641702	−	0.766954i	$-0.278229\pi$
$137$	15.0219	1.28340	0.641702	+	0.766954i	$0.278229\pi$
$138$	−0.108928	−0.00927256
$139$	12.2187	1.03637	0.518187	−	0.855268i	$-0.326607\pi$
$139$	12.2187	1.03637	0.518187	+	0.855268i	$0.326607\pi$
$140$	6.77606	0.572682
$141$	5.12704	0.431775
$142$	0.363757	0.0305258
$143$	0.459865	0.0384558
$144$	1.90724	0.158937
$145$	18.1655	1.50856
$146$	1.99233	0.164886
$147$	−3.74482	−0.308867
$148$	−8.89017	−0.730767
$149$	6.74285	0.552396	0.276198	−	0.961101i	$-0.410925\pi$
$149$	6.74285	0.552396	0.276198	+	0.961101i	$0.410925\pi$
$150$	0.195668	0.0159762
$151$	−22.8936	−1.86305	−0.931526	−	0.363674i	$-0.881522\pi$
$151$	−22.8936	−1.86305	−0.931526	+	0.363674i	$0.881522\pi$
$152$	12.1761	0.987612
$153$	−4.35127	−0.351780
$154$	0.505934	0.0407693
$155$	23.5866	1.89452
$156$	1.62816	0.130357
$157$	−4.01399	−0.320351	−0.160176	−	0.987089i	$-0.551206\pi$
$157$	−4.01399	−0.320351	−0.160176	+	0.987089i	$0.551206\pi$
$158$	−7.59568	−0.604280
$159$	−4.74711	−0.376470
$160$	12.8894	1.01900
$161$	0.322293	0.0254003
$162$	0.609784	0.0479091
$163$	16.5796	1.29862	0.649308	−	0.760526i	$-0.275059\pi$
$163$	16.5796	1.29862	0.649308	+	0.760526i	$0.275059\pi$
$164$	−19.6626	−1.53539
$165$	−1.06077	−0.0825810
$166$	7.51379	0.583183
$167$	−13.0332	−1.00854	−0.504269	−	0.863547i	$-0.668238\pi$
$167$	−13.0332	−1.00854	−0.504269	+	0.863547i	$0.668238\pi$
$168$	3.99163	0.307961
$169$	1.00000	0.0769231
$170$	−6.12046	−0.469418
$171$	−5.50358	−0.420870
$172$	−18.5033	−1.41086
$173$	11.4509	0.870595	0.435298	−	0.900287i	$-0.356643\pi$
$173$	11.4509	0.870595	0.435298	+	0.900287i	$0.356643\pi$
$174$	4.80209	0.364046
$175$	−0.578936	−0.0437634
$176$	−0.877075	−0.0661120
$177$	10.2884	0.773320
$178$	−5.59781	−0.419574
$179$	−0.347830	−0.0259980	−0.0129990	−	0.999916i	$-0.504138\pi$
$179$	−0.347830	−0.0259980	−0.0129990	+	0.999916i	$0.504138\pi$
$180$	−3.75569	−0.279933
$181$	−13.7851	−1.02464	−0.512318	−	0.858796i	$-0.671213\pi$
$181$	−13.7851	−1.02464	−0.512318	+	0.858796i	$0.671213\pi$
$182$	1.10018	0.0815507
$183$	12.7957	0.945882
$184$	0.395208	0.0291352
$185$	12.5952	0.926014
$186$	6.23518	0.457186
$187$	2.00100	0.146327
$188$	−8.34766	−0.608816
$189$	−1.80421	−0.131237
$190$	−7.74129	−0.561612
$191$	20.2266	1.46354	0.731772	−	0.681549i	$-0.238693\pi$
$191$	20.2266	1.46354	0.731772	+	0.681549i	$0.238693\pi$
$192$	−0.407142	−0.0293829
$193$	2.45419	0.176656	0.0883281	−	0.996091i	$-0.471848\pi$
$193$	2.45419	0.176656	0.0883281	+	0.996091i	$0.471848\pi$
$194$	−5.23471	−0.375830
$195$	−2.30670	−0.165186
$196$	6.09718	0.435513
$197$	15.2272	1.08489	0.542445	−	0.840091i	$-0.317499\pi$
$197$	15.2272	1.08489	0.542445	+	0.840091i	$0.317499\pi$
$198$	−0.280418	−0.0199284
$199$	4.05823	0.287680	0.143840	−	0.989601i	$-0.454055\pi$
$199$	4.05823	0.287680	0.143840	+	0.989601i	$0.454055\pi$
$200$	−0.709914	−0.0501985
$201$	2.74229	0.193426
$202$	6.91832	0.486771
$203$	−14.2083	−0.997227
$204$	7.08459	0.496020
$205$	27.8569	1.94561
$206$	−0.609784	−0.0424856
$207$	−0.178634	−0.0124159
$208$	−1.90724	−0.132244
$209$	2.53090	0.175066
$210$	−2.53779	−0.175124
$211$	19.8822	1.36874	0.684372	−	0.729133i	$-0.260076\pi$
$211$	19.8822	1.36874	0.684372	+	0.729133i	$0.260076\pi$
$212$	7.72906	0.530834
$213$	0.596535	0.0408739
$214$	−5.76989	−0.394421
$215$	26.2146	1.78782
$216$	−2.21240	−0.150534
$217$	−18.4485	−1.25237
$218$	−9.00407	−0.609832
$219$	3.26727	0.220782
$220$	1.72711	0.116442
$221$	4.35127	0.292698
$222$	3.32957	0.223466
$223$	15.4574	1.03510	0.517552	−	0.855652i	$-0.326843\pi$
$223$	15.4574	1.03510	0.517552	+	0.855652i	$0.326843\pi$
$224$	−10.0816	−0.673603
$225$	0.320880	0.0213920
$226$	−4.29111	−0.285441
$227$	27.0856	1.79773	0.898867	−	0.438221i	$-0.144391\pi$
$227$	27.0856	1.79773	0.898867	+	0.438221i	$0.144391\pi$
$228$	8.96074	0.593439
$229$	1.81920	0.120216	0.0601081	−	0.998192i	$-0.480855\pi$
$229$	1.81920	0.120216	0.0601081	+	0.998192i	$0.480855\pi$
$230$	−0.251264	−0.0165679
$231$	0.829694	0.0545898
$232$	−17.4228	−1.14386
$233$	−20.9528	−1.37267	−0.686333	−	0.727288i	$-0.740781\pi$
$233$	−20.9528	−1.37267	−0.686333	+	0.727288i	$0.740781\pi$
$234$	−0.609784	−0.0398628
$235$	11.8266	0.771480
$236$	−16.7511	−1.09041
$237$	−12.4564	−0.809127
$238$	4.78718	0.310307
$239$	5.56110	0.359718	0.179859	−	0.983692i	$-0.442436\pi$
$239$	5.56110	0.359718	0.179859	+	0.983692i	$0.442436\pi$
$240$	4.39945	0.283983
$241$	−18.4023	−1.18539	−0.592697	−	0.805425i	$-0.701937\pi$
$241$	−18.4023	−1.18539	−0.592697	+	0.805425i	$0.701937\pi$
$242$	−6.57867	−0.422893
$243$	1.00000	0.0641500
$244$	−20.8334	−1.33372
$245$	−8.63819	−0.551874
$246$	7.36406	0.469516
$247$	5.50358	0.350185
$248$	−22.6223	−1.43652
$249$	12.3221	0.780878
$250$	−6.58160	−0.416257
$251$	7.82048	0.493625	0.246812	−	0.969063i	$-0.420617\pi$
$251$	7.82048	0.493625	0.246812	+	0.969063i	$0.420617\pi$
$252$	2.93755	0.185048
$253$	0.0821474	0.00516456
$254$	−2.91310	−0.182784
$255$	−10.0371	−0.628548
$256$	−6.15180	−0.384488
$257$	17.3359	1.08139	0.540693	−	0.841220i	$-0.318162\pi$
$257$	17.3359	1.08139	0.540693	+	0.841220i	$0.318162\pi$
$258$	6.92991	0.431437
$259$	−9.85143	−0.612138
$260$	3.75569	0.232918
$261$	7.87507	0.487455
$262$	4.47252	0.276313
$263$	−7.02621	−0.433254	−0.216627	−	0.976254i	$-0.569506\pi$
$263$	−7.02621	−0.433254	−0.216627	+	0.976254i	$0.569506\pi$
$264$	1.01740	0.0626168
$265$	−10.9502	−0.672663
$266$	6.05493	0.371251
$267$	−9.17999	−0.561806
$268$	−4.46489	−0.272737
$269$	−9.40275	−0.573296	−0.286648	−	0.958036i	$-0.592541\pi$
$269$	−9.40275	−0.573296	−0.286648	+	0.958036i	$0.592541\pi$
$270$	1.40659	0.0856024
$271$	−19.4908	−1.18398	−0.591992	−	0.805944i	$-0.701658\pi$
$271$	−19.4908	−1.18398	−0.591992	+	0.805944i	$0.701658\pi$
$272$	−8.29895	−0.503198
$273$	1.80421	0.109196
$274$	9.16008	0.553381
$275$	−0.147562	−0.00889830
$276$	0.290845	0.0175068
$277$	2.46384	0.148038	0.0740190	−	0.997257i	$-0.476417\pi$
$277$	2.46384	0.148038	0.0740190	+	0.997257i	$0.476417\pi$
$278$	7.45074	0.446866
$279$	10.2252	0.612169
$280$	9.20751	0.550254
$281$	−25.5551	−1.52449	−0.762245	−	0.647288i	$-0.775903\pi$
$281$	−25.5551	−1.52449	−0.762245	+	0.647288i	$0.775903\pi$
$282$	3.12639	0.186174
$283$	6.75809	0.401727	0.200863	−	0.979619i	$-0.435625\pi$
$283$	6.75809	0.401727	0.200863	+	0.979619i	$0.435625\pi$
$284$	−0.971256	−0.0576334
$285$	−12.6951	−0.751995
$286$	0.280418	0.0165815
$287$	−21.7886	−1.28614
$288$	5.58780	0.329264
$289$	1.93359	0.113741
$290$	11.0770	0.650464
$291$	−8.58453	−0.503234
$292$	−5.31965	−0.311309
$293$	−13.4454	−0.785491	−0.392746	−	0.919647i	$-0.628475\pi$
$293$	−13.4454	−0.785491	−0.392746	+	0.919647i	$0.628475\pi$
$294$	−2.28353	−0.133178
$295$	23.7322	1.38174
$296$	−12.0802	−0.702148
$297$	−0.459865	−0.0266841
$298$	4.11168	0.238183
$299$	0.178634	0.0103307
$300$	−0.522446	−0.0301634
$301$	−20.5040	−1.18183
$302$	−13.9601	−0.803315
$303$	11.3455	0.651783
$304$	−10.4967	−0.602026
$305$	29.5158	1.69007
$306$	−2.65334	−0.151681
$307$	−2.09722	−0.119695	−0.0598474	−	0.998208i	$-0.519061\pi$
$307$	−2.09722	−0.119695	−0.0598474	+	0.998208i	$0.519061\pi$
$308$	−1.35088	−0.0769734
$309$	−1.00000	−0.0568880
$310$	14.3827	0.816883
$311$	−11.8728	−0.673246	−0.336623	−	0.941639i	$-0.609285\pi$
$311$	−11.8728	−0.673246	−0.336623	+	0.941639i	$0.609285\pi$
$312$	2.21240	0.125252
$313$	18.1520	1.02601	0.513005	−	0.858385i	$-0.328532\pi$
$313$	18.1520	1.02601	0.513005	+	0.858385i	$0.328532\pi$
$314$	−2.44767	−0.138130
$315$	−4.16178	−0.234490
$316$	20.2810	1.14089
$317$	−3.39025	−0.190415	−0.0952077	−	0.995457i	$-0.530352\pi$
$317$	−3.39025	−0.190415	−0.0952077	+	0.995457i	$0.530352\pi$
$318$	−2.89471	−0.162327
$319$	−3.62147	−0.202763
$320$	−0.939155	−0.0525004
$321$	−9.46219	−0.528128
$322$	0.196529	0.0109521
$323$	23.9476	1.33248
$324$	−1.62816	−0.0904535
$325$	−0.320880	−0.0177992
$326$	10.1100	0.559940
$327$	−14.7660	−0.816562
$328$	−26.7180	−1.47526
$329$	−9.25027	−0.509984
$330$	−0.646841	−0.0356074
$331$	−26.5725	−1.46056	−0.730279	−	0.683149i	$-0.760610\pi$
$331$	−26.5725	−1.46056	−0.730279	+	0.683149i	$0.760610\pi$
$332$	−20.0623	−1.10106
$333$	5.46024	0.299219
$334$	−7.94742	−0.434863
$335$	6.32564	0.345607
$336$	−3.44107	−0.187726
$337$	12.6203	0.687472	0.343736	−	0.939066i	$-0.388307\pi$
$337$	12.6203	0.687472	0.343736	+	0.939066i	$0.388307\pi$
$338$	0.609784	0.0331679
$339$	−7.03711	−0.382203
$340$	16.3420	0.886272
$341$	−4.70223	−0.254640
$342$	−3.35600	−0.181471
$343$	19.3859	1.04674
$344$	−25.1428	−1.35561
$345$	−0.412055	−0.0221843
$346$	6.98257	0.375385
$347$	6.42429	0.344874	0.172437	−	0.985021i	$-0.444836\pi$
$347$	6.42429	0.344874	0.172437	+	0.985021i	$0.444836\pi$
$348$	−12.8219	−0.687326
$349$	3.61744	0.193637	0.0968184	−	0.995302i	$-0.469133\pi$
$349$	3.61744	0.193637	0.0968184	+	0.995302i	$0.469133\pi$
$350$	−0.353026	−0.0188700
$351$	−1.00000	−0.0533761
$352$	−2.56963	−0.136962
$353$	5.74063	0.305543	0.152771	−	0.988262i	$-0.451180\pi$
$353$	5.74063	0.305543	0.152771	+	0.988262i	$0.451180\pi$
$354$	6.27367	0.333442
$355$	1.37603	0.0730320
$356$	14.9465	0.792165
$357$	7.85062	0.415499
$358$	−0.212101	−0.0112099
$359$	−9.64317	−0.508947	−0.254474	−	0.967080i	$-0.581902\pi$
$359$	−9.64317	−0.508947	−0.254474	+	0.967080i	$0.581902\pi$
$360$	−5.10334	−0.268970
$361$	11.2894	0.594181
$362$	−8.40592	−0.441805
$363$	−10.7885	−0.566251
$364$	−2.93755	−0.153970
$365$	7.53662	0.394485
$366$	7.80258	0.407847
$367$	16.5607	0.864461	0.432231	−	0.901763i	$-0.357727\pi$
$367$	16.5607	0.864461	0.432231	+	0.901763i	$0.357727\pi$
$368$	−0.340698	−0.0177601
$369$	12.0765	0.628678
$370$	7.68032	0.399281
$371$	8.56478	0.444661
$372$	−16.6484	−0.863177
$373$	−17.8173	−0.922543	−0.461272	−	0.887259i	$-0.652607\pi$
$373$	−17.8173	−0.922543	−0.461272	+	0.887259i	$0.652607\pi$
$374$	1.22018	0.0630938
$375$	−10.7933	−0.557366
$376$	−11.3430	−0.584973
$377$	−7.87507	−0.405587
$378$	−1.10018	−0.0565871
$379$	−11.2779	−0.579305	−0.289652	−	0.957132i	$-0.593540\pi$
$379$	−11.2779	−0.579305	−0.289652	+	0.957132i	$0.593540\pi$
$380$	20.6698	1.06034
$381$	−4.77727	−0.244747
$382$	12.3338	0.631054
$383$	−37.1832	−1.89997	−0.949987	−	0.312290i	$-0.898904\pi$
$383$	−37.1832	−1.89997	−0.949987	+	0.312290i	$0.898904\pi$
$384$	−11.4239	−0.582972
$385$	1.91386	0.0975392
$386$	1.49652	0.0761710
$387$	11.3645	0.577692
$388$	13.9770	0.709576
$389$	5.93321	0.300826	0.150413	−	0.988623i	$-0.451940\pi$
$389$	5.93321	0.300826	0.150413	+	0.988623i	$0.451940\pi$
$390$	−1.40659	−0.0712255
$391$	0.777284	0.0393090
$392$	8.28502	0.418457
$393$	7.33460	0.369981
$394$	9.28527	0.467785
$395$	−28.7331	−1.44572
$396$	0.748735	0.0376254
$397$	24.1837	1.21375	0.606873	−	0.794799i	$-0.292424\pi$
$397$	24.1837	1.21375	0.606873	+	0.794799i	$0.292424\pi$
$398$	2.47464	0.124043
$399$	9.92963	0.497103
$400$	0.611997	0.0305999
$401$	34.5069	1.72319	0.861597	−	0.507593i	$-0.169465\pi$
$401$	34.5069	1.72319	0.861597	+	0.507593i	$0.169465\pi$
$402$	1.67220	0.0834019
$403$	−10.2252	−0.509355
$404$	−18.4724	−0.919035
$405$	2.30670	0.114621
$406$	−8.66399	−0.429987
$407$	−2.51097	−0.124464
$408$	9.62674	0.476595
$409$	−5.19714	−0.256982	−0.128491	−	0.991711i	$-0.541013\pi$
$409$	−5.19714	−0.256982	−0.128491	+	0.991711i	$0.541013\pi$
$410$	16.9867	0.838914
$411$	15.0219	0.740973
$412$	1.62816	0.0802139
$413$	−18.5624	−0.913395
$414$	−0.108928	−0.00535352
$415$	28.4233	1.39525
$416$	−5.58780	−0.273964
$417$	12.2187	0.598350
$418$	1.54330	0.0754855
$419$	−7.06429	−0.345113	−0.172557	−	0.985000i	$-0.555203\pi$
$419$	−7.06429	−0.345113	−0.172557	+	0.985000i	$0.555203\pi$
$420$	6.77606	0.330638
$421$	0.772782	0.0376631	0.0188315	−	0.999823i	$-0.494005\pi$
$421$	0.772782	0.0376631	0.0188315	+	0.999823i	$0.494005\pi$
$422$	12.1238	0.590178
$423$	5.12704	0.249285
$424$	10.5025	0.510045
$425$	−1.39624	−0.0677275
$426$	0.363757	0.0176241
$427$	−23.0861	−1.11721
$428$	15.4060	0.744677
$429$	0.459865	0.0222025
$430$	15.9852	0.770877
$431$	−8.26552	−0.398136	−0.199068	−	0.979986i	$-0.563791\pi$
$431$	−8.26552	−0.398136	−0.199068	+	0.979986i	$0.563791\pi$
$432$	1.90724	0.0917624
$433$	10.7704	0.517595	0.258797	−	0.965932i	$-0.416674\pi$
$433$	10.7704	0.517595	0.258797	+	0.965932i	$0.416674\pi$
$434$	−11.2496	−0.539998
$435$	18.1655	0.870967
$436$	24.0415	1.15138
$437$	0.983126	0.0470293
$438$	1.99233	0.0951971
$439$	12.7098	0.606607	0.303303	−	0.952894i	$-0.401910\pi$
$439$	12.7098	0.606607	0.303303	+	0.952894i	$0.401910\pi$
$440$	2.34685	0.111882
$441$	−3.74482	−0.178325
$442$	2.65334	0.126206
$443$	−17.4231	−0.827796	−0.413898	−	0.910323i	$-0.635833\pi$
$443$	−17.4231	−0.827796	−0.413898	+	0.910323i	$0.635833\pi$
$444$	−8.89017	−0.421909
$445$	−21.1755	−1.00382
$446$	9.42567	0.446318
$447$	6.74285	0.318926
$448$	0.734570	0.0347052
$449$	−23.6482	−1.11603	−0.558014	−	0.829831i	$-0.688437\pi$
$449$	−23.6482	−1.11603	−0.558014	+	0.829831i	$0.688437\pi$
$450$	0.195668	0.00922386
$451$	−5.55357	−0.261507
$452$	11.4576	0.538918
$453$	−22.8936	−1.07563
$454$	16.5164	0.775151
$455$	4.16178	0.195107
$456$	12.1761	0.570198
$457$	12.0085	0.561732	0.280866	−	0.959747i	$-0.409378\pi$
$457$	12.0085	0.561732	0.280866	+	0.959747i	$0.409378\pi$
$458$	1.10932	0.0518351
$459$	−4.35127	−0.203100
$460$	0.670893	0.0312805
$461$	−17.2409	−0.802989	−0.401495	−	0.915861i	$-0.631509\pi$
$461$	−17.2409	−0.802989	−0.401495	+	0.915861i	$0.631509\pi$
$462$	0.505934	0.0235382
$463$	16.1869	0.752268	0.376134	−	0.926565i	$-0.377253\pi$
$463$	16.1869	0.752268	0.376134	+	0.926565i	$0.377253\pi$
$464$	15.0197	0.697272
$465$	23.5866	1.09380
$466$	−12.7767	−0.591869
$467$	9.26041	0.428521	0.214260	−	0.976777i	$-0.431266\pi$
$467$	9.26041	0.428521	0.214260	+	0.976777i	$0.431266\pi$
$468$	1.62816	0.0752619
$469$	−4.94767	−0.228462
$470$	7.21164	0.332648
$471$	−4.01399	−0.184955
$472$	−22.7619	−1.04770
$473$	−5.22615	−0.240299
$474$	−7.59568	−0.348881
$475$	−1.76599	−0.0810292
$476$	−12.7821	−0.585867
$477$	−4.74711	−0.217355
$478$	3.39107	0.155104
$479$	−0.912459	−0.0416913	−0.0208457	−	0.999783i	$-0.506636\pi$
$479$	−0.912459	−0.0416913	−0.0208457	+	0.999783i	$0.506636\pi$
$480$	12.8894	0.588318
$481$	−5.46024	−0.248966
$482$	−11.2214	−0.511121
$483$	0.322293	0.0146648
$484$	17.5655	0.798431
$485$	−19.8020	−0.899161
$486$	0.609784	0.0276604
$487$	2.80211	0.126976	0.0634878	−	0.997983i	$-0.479778\pi$
$487$	2.80211	0.126976	0.0634878	+	0.997983i	$0.479778\pi$
$488$	−28.3090	−1.28149
$489$	16.5796	0.749756
$490$	−5.26743	−0.237958
$491$	33.7562	1.52340	0.761699	−	0.647932i	$-0.224366\pi$
$491$	33.7562	1.52340	0.761699	+	0.647932i	$0.224366\pi$
$492$	−19.6626	−0.886456
$493$	−34.2666	−1.54329
$494$	3.35600	0.150993
$495$	−1.06077	−0.0476781
$496$	19.5020	0.875667
$497$	−1.07627	−0.0482775
$498$	7.51379	0.336701
$499$	18.4910	0.827770	0.413885	−	0.910329i	$-0.364172\pi$
$499$	18.4910	0.827770	0.413885	+	0.910329i	$0.364172\pi$
$500$	17.5733	0.785903
$501$	−13.0332	−0.582279
$502$	4.76880	0.212842
$503$	−5.80580	−0.258868	−0.129434	−	0.991588i	$-0.541316\pi$
$503$	−5.80580	−0.258868	−0.129434	+	0.991588i	$0.541316\pi$
$504$	3.99163	0.177801
$505$	26.1708	1.16458
$506$	0.0500921	0.00222687
$507$	1.00000	0.0444116
$508$	7.77819	0.345101
$509$	−25.6611	−1.13741	−0.568703	−	0.822543i	$-0.692555\pi$
$509$	−25.6611	−1.13741	−0.568703	+	0.822543i	$0.692555\pi$
$510$	−6.12046	−0.271019
$511$	−5.89484	−0.260773
$512$	19.0965	0.843952
$513$	−5.50358	−0.242989
$514$	10.5712	0.466274
$515$	−2.30670	−0.101645
$516$	−18.5033	−0.814563
$517$	−2.35775	−0.103694
$518$	−6.00724	−0.263943
$519$	11.4509	0.502638
$520$	5.10334	0.223796
$521$	27.9752	1.22562	0.612808	−	0.790232i	$-0.290040\pi$
$521$	27.9752	1.22562	0.612808	+	0.790232i	$0.290040\pi$
$522$	4.80209	0.210182
$523$	6.01085	0.262836	0.131418	−	0.991327i	$-0.458047\pi$
$523$	6.01085	0.262836	0.131418	+	0.991327i	$0.458047\pi$
$524$	−11.9419	−0.521685
$525$	−0.578936	−0.0252668
$526$	−4.28447	−0.186812
$527$	−44.4928	−1.93814
$528$	−0.877075	−0.0381698
$529$	−22.9681	−0.998613
$530$	−6.67723	−0.290040
$531$	10.2884	0.446477
$532$	−16.1671	−0.700931
$533$	−12.0765	−0.523092
$534$	−5.59781	−0.242241
$535$	−21.8265	−0.943640
$536$	−6.06702	−0.262055
$537$	−0.347830	−0.0150100
$538$	−5.73364	−0.247195
$539$	1.72211	0.0741766
$540$	−3.75569	−0.161619
$541$	13.2920	0.571467	0.285734	−	0.958309i	$-0.407763\pi$
$541$	13.2920	0.571467	0.285734	+	0.958309i	$0.407763\pi$
$542$	−11.8852	−0.510513
$543$	−13.7851	−0.591574
$544$	−24.3140	−1.04246
$545$	−34.0608	−1.45900
$546$	1.10018	0.0470833
$547$	35.4763	1.51686	0.758428	−	0.651757i	$-0.225968\pi$
$547$	35.4763	1.51686	0.758428	+	0.651757i	$0.225968\pi$
$548$	−24.4580	−1.04480
$549$	12.7957	0.546105
$550$	−0.0899806	−0.00383679
$551$	−43.3411	−1.84639
$552$	0.395208	0.0168212
$553$	22.4739	0.955688
$554$	1.50241	0.0638314
$555$	12.5952	0.534635
$556$	−19.8940	−0.843693
$557$	4.22253	0.178914	0.0894572	−	0.995991i	$-0.471487\pi$
$557$	4.22253	0.178914	0.0894572	+	0.995991i	$0.471487\pi$
$558$	6.23518	0.263956
$559$	−11.3645	−0.480669
$560$	−7.93754	−0.335422
$561$	2.00100	0.0844822
$562$	−15.5831	−0.657333
$563$	−34.7785	−1.46574	−0.732870	−	0.680368i	$-0.761820\pi$
$563$	−34.7785	−1.46574	−0.732870	+	0.680368i	$0.761820\pi$
$564$	−8.34766	−0.351500
$565$	−16.2325	−0.682907
$566$	4.12097	0.173217
$567$	−1.80421	−0.0757698
$568$	−1.31977	−0.0553763
$569$	−35.7850	−1.50019	−0.750093	−	0.661332i	$-0.769992\pi$
$569$	−35.7850	−1.50019	−0.750093	+	0.661332i	$0.769992\pi$
$570$	−7.74129	−0.324247
$571$	18.2367	0.763182	0.381591	−	0.924331i	$-0.375376\pi$
$571$	18.2367	0.763182	0.381591	+	0.924331i	$0.375376\pi$
$572$	−0.748735	−0.0313062
$573$	20.2266	0.844978
$574$	−13.2863	−0.554561
$575$	−0.0573200	−0.00239041
$576$	−0.407142	−0.0169642
$577$	18.1293	0.754733	0.377367	−	0.926064i	$-0.376830\pi$
$577$	18.1293	0.754733	0.377367	+	0.926064i	$0.376830\pi$
$578$	1.17907	0.0490430
$579$	2.45419	0.101993
$580$	−29.5763	−1.22809
$581$	−22.2316	−0.922322
$582$	−5.23471	−0.216986
$583$	2.18303	0.0904117
$584$	−7.22849	−0.299117
$585$	−2.30670	−0.0953704
$586$	−8.19881	−0.338690
$587$	32.5082	1.34176	0.670878	−	0.741568i	$-0.265918\pi$
$587$	32.5082	1.34176	0.670878	+	0.741568i	$0.265918\pi$
$588$	6.09718	0.251443
$589$	−56.2754	−2.31879
$590$	14.4715	0.595782
$591$	15.2272	0.626362
$592$	10.4140	0.428014
$593$	−30.0034	−1.23209	−0.616045	−	0.787711i	$-0.711266\pi$
$593$	−30.0034	−1.23209	−0.616045	+	0.787711i	$0.711266\pi$
$594$	−0.280418	−0.0115057
$595$	18.1091	0.742399
$596$	−10.9785	−0.449695
$597$	4.05823	0.166092
$598$	0.108928	0.00445439
$599$	8.82247	0.360476	0.180238	−	0.983623i	$-0.442313\pi$
$599$	8.82247	0.360476	0.180238	+	0.983623i	$0.442313\pi$
$600$	−0.709914	−0.0289821
$601$	3.76052	0.153395	0.0766973	−	0.997054i	$-0.475562\pi$
$601$	3.76052	0.153395	0.0766973	+	0.997054i	$0.475562\pi$
$602$	−12.5030	−0.509585
$603$	2.74229	0.111675
$604$	37.2745	1.51668
$605$	−24.8859	−1.01176
$606$	6.91832	0.281037
$607$	−15.9912	−0.649062	−0.324531	−	0.945875i	$-0.605206\pi$
$607$	−15.9912	−0.649062	−0.324531	+	0.945875i	$0.605206\pi$
$608$	−30.7529	−1.24720
$609$	−14.2083	−0.575749
$610$	17.9982	0.728728
$611$	−5.12704	−0.207418
$612$	7.08459	0.286377
$613$	23.9799	0.968538	0.484269	−	0.874919i	$-0.339086\pi$
$613$	23.9799	0.968538	0.484269	+	0.874919i	$0.339086\pi$
$614$	−1.27885	−0.0516102
$615$	27.8569	1.12330
$616$	−1.83561	−0.0739589
$617$	5.81852	0.234245	0.117122	−	0.993117i	$-0.462633\pi$
$617$	5.81852	0.234245	0.117122	+	0.993117i	$0.462633\pi$
$618$	−0.609784	−0.0245291
$619$	2.45153	0.0985353	0.0492676	−	0.998786i	$-0.484311\pi$
$619$	2.45153	0.0985353	0.0492676	+	0.998786i	$0.484311\pi$
$620$	−38.4028	−1.54229
$621$	−0.178634	−0.00716832
$622$	−7.23986	−0.290292
$623$	16.5627	0.663569
$624$	−1.90724	−0.0763509
$625$	−26.5014	−1.06006
$626$	11.0688	0.442398
$627$	2.53090	0.101075
$628$	6.53544	0.260792
$629$	−23.7590	−0.947334
$630$	−2.53779	−0.101108
$631$	−19.0022	−0.756464	−0.378232	−	0.925711i	$-0.623468\pi$
$631$	−19.0022	−0.756464	−0.378232	+	0.925711i	$0.623468\pi$
$632$	27.5584	1.09621
$633$	19.8822	0.790245
$634$	−2.06732	−0.0821038
$635$	−11.0198	−0.437306
$636$	7.72906	0.306477
$637$	3.74482	0.148375
$638$	−2.20831	−0.0874279
$639$	0.596535	0.0235985
$640$	−26.3515	−1.04163
$641$	−37.5281	−1.48227	−0.741135	−	0.671356i	$-0.765712\pi$
$641$	−37.5281	−1.48227	−0.741135	+	0.671356i	$0.765712\pi$
$642$	−5.76989	−0.227719
$643$	47.7585	1.88341	0.941705	−	0.336439i	$-0.109223\pi$
$643$	47.7585	1.88341	0.941705	+	0.336439i	$0.109223\pi$
$644$	−0.524746	−0.0206779
$645$	26.2146	1.03220
$646$	14.6029	0.574542
$647$	12.0175	0.472457	0.236229	−	0.971697i	$-0.424089\pi$
$647$	12.0175	0.472457	0.236229	+	0.971697i	$0.424089\pi$
$648$	−2.21240	−0.0869111
$649$	−4.73125	−0.185718
$650$	−0.195668	−0.00767471
$651$	−18.4485	−0.723053
$652$	−26.9943	−1.05718
$653$	−10.4526	−0.409042	−0.204521	−	0.978862i	$-0.565564\pi$
$653$	−10.4526	−0.409042	−0.204521	+	0.978862i	$0.565564\pi$
$654$	−9.00407	−0.352087
$655$	16.9187	0.661070
$656$	23.0329	0.899283
$657$	3.26727	0.127468
$658$	−5.64066	−0.219896
$659$	25.9909	1.01246	0.506230	−	0.862398i	$-0.331039\pi$
$659$	25.9909	1.01246	0.506230	+	0.862398i	$0.331039\pi$
$660$	1.72711	0.0672277
$661$	49.5537	1.92742	0.963708	−	0.266960i	$-0.0860191\pi$
$661$	49.5537	1.92742	0.963708	+	0.266960i	$0.0860191\pi$
$662$	−16.2035	−0.629766
$663$	4.35127	0.168990
$664$	−27.2613	−1.05794
$665$	22.9047	0.888207
$666$	3.32957	0.129018
$667$	−1.40675	−0.0544697
$668$	21.2201	0.821032
$669$	15.4574	0.597618
$670$	3.85727	0.149019
$671$	−5.88427	−0.227160
$672$	−10.0816	−0.388905
$673$	−2.80052	−0.107952	−0.0539761	−	0.998542i	$-0.517189\pi$
$673$	−2.80052	−0.107952	−0.0539761	+	0.998542i	$0.517189\pi$
$674$	7.69566	0.296426
$675$	0.320880	0.0123507
$676$	−1.62816	−0.0626217
$677$	2.09907	0.0806737	0.0403368	−	0.999186i	$-0.487157\pi$
$677$	2.09907	0.0806737	0.0403368	+	0.999186i	$0.487157\pi$
$678$	−4.29111	−0.164799
$679$	15.4883	0.594387
$680$	22.2060	0.851562
$681$	27.0856	1.03792
$682$	−2.86734	−0.109796
$683$	35.1408	1.34463	0.672314	−	0.740266i	$-0.265301\pi$
$683$	35.1408	1.34463	0.672314	+	0.740266i	$0.265301\pi$
$684$	8.96074	0.342622
$685$	34.6510	1.32395
$686$	11.8212	0.451336
$687$	1.81920	0.0694068
$688$	21.6749	0.826350
$689$	4.74711	0.180850
$690$	−0.251264	−0.00956547
$691$	13.9215	0.529601	0.264800	−	0.964303i	$-0.414694\pi$
$691$	13.9215	0.529601	0.264800	+	0.964303i	$0.414694\pi$
$692$	−18.6439	−0.708736
$693$	0.829694	0.0315175
$694$	3.91743	0.148704
$695$	28.1848	1.06911
$696$	−17.4228	−0.660408
$697$	−52.5483	−1.99041
$698$	2.20585	0.0834928
$699$	−20.9528	−0.792509
$700$	0.942602	0.0356270
$701$	−5.74812	−0.217104	−0.108552	−	0.994091i	$-0.534621\pi$
$701$	−5.74812	−0.217104	−0.108552	+	0.994091i	$0.534621\pi$
$702$	−0.609784	−0.0230148
$703$	−30.0509	−1.13339
$704$	0.187230	0.00705650
$705$	11.8266	0.445414
$706$	3.50054	0.131745
$707$	−20.4697	−0.769844
$708$	−16.7511	−0.629546
$709$	14.4938	0.544325	0.272163	−	0.962251i	$-0.412261\pi$
$709$	14.4938	0.544325	0.272163	+	0.962251i	$0.412261\pi$
$710$	0.839080	0.0314901
$711$	−12.4564	−0.467150
$712$	20.3098	0.761141
$713$	−1.82657	−0.0684057
$714$	4.78718	0.179156
$715$	1.06077	0.0396706
$716$	0.566324	0.0211645
$717$	5.56110	0.207683
$718$	−5.88025	−0.219449
$719$	−13.4017	−0.499800	−0.249900	−	0.968272i	$-0.580398\pi$
$719$	−13.4017	−0.499800	−0.249900	+	0.968272i	$0.580398\pi$
$720$	4.39945	0.163958
$721$	1.80421	0.0671924
$722$	6.88411	0.256200
$723$	−18.4023	−0.684388
$724$	22.4444	0.834138
$725$	2.52695	0.0938487
$726$	−6.57867	−0.244157
$727$	42.9336	1.59232	0.796159	−	0.605087i	$-0.206862\pi$
$727$	42.9336	1.59232	0.796159	+	0.605087i	$0.206862\pi$
$728$	−3.99163	−0.147940
$729$	1.00000	0.0370370
$730$	4.59571	0.170095
$731$	−49.4502	−1.82898
$732$	−20.8334	−0.770025
$733$	−33.1903	−1.22591	−0.612955	−	0.790118i	$-0.710019\pi$
$733$	−33.1903	−1.22591	−0.612955	+	0.790118i	$0.710019\pi$
$734$	10.0984	0.372740
$735$	−8.63819	−0.318624
$736$	−0.998169	−0.0367930
$737$	−1.26108	−0.0464525
$738$	7.36406	0.271075
$739$	−24.8965	−0.915834	−0.457917	−	0.888995i	$-0.651404\pi$
$739$	−24.8965	−0.915834	−0.457917	+	0.888995i	$0.651404\pi$
$740$	−20.5070	−0.753852
$741$	5.50358	0.202179
$742$	5.22267	0.191730
$743$	41.6298	1.52725	0.763625	−	0.645661i	$-0.223418\pi$
$743$	41.6298	1.52725	0.763625	+	0.645661i	$0.223418\pi$
$744$	−22.6223	−0.829372
$745$	15.5538	0.569846
$746$	−10.8647	−0.397784
$747$	12.3221	0.450840
$748$	−3.25795	−0.119123
$749$	17.0718	0.623790
$750$	−6.58160	−0.240326
$751$	21.3819	0.780238	0.390119	−	0.920764i	$-0.372434\pi$
$751$	21.3819	0.780238	0.390119	+	0.920764i	$0.372434\pi$
$752$	9.77852	0.356586
$753$	7.82048	0.284994
$754$	−4.80209	−0.174882
$755$	−52.8087	−1.92190
$756$	2.93755	0.106838
$757$	−21.2047	−0.770696	−0.385348	−	0.922771i	$-0.625919\pi$
$757$	−21.2047	−0.770696	−0.385348	+	0.922771i	$0.625919\pi$
$758$	−6.87705	−0.249786
$759$	0.0821474	0.00298176
$760$	28.0867	1.01881
$761$	13.7164	0.497219	0.248610	−	0.968604i	$-0.420026\pi$
$761$	13.7164	0.497219	0.248610	+	0.968604i	$0.420026\pi$
$762$	−2.91310	−0.105531
$763$	26.6410	0.964469
$764$	−32.9322	−1.19145
$765$	−10.0371	−0.362892
$766$	−22.6737	−0.819235
$767$	−10.2884	−0.371491
$768$	−6.15180	−0.221984
$769$	−31.7159	−1.14370	−0.571852	−	0.820357i	$-0.693775\pi$
$769$	−31.7159	−1.14370	−0.571852	+	0.820357i	$0.693775\pi$
$770$	1.16704	0.0420572
$771$	17.3359	0.624339
$772$	−3.99582	−0.143813
$773$	16.1498	0.580869	0.290434	−	0.956895i	$-0.406200\pi$
$773$	16.1498	0.580869	0.290434	+	0.956895i	$0.406200\pi$
$774$	6.92991	0.249090
$775$	3.28108	0.117860
$776$	18.9924	0.681787
$777$	−9.85143	−0.353418
$778$	3.61798	0.129711
$779$	−66.4641	−2.38132
$780$	3.75569	0.134475
$781$	−0.274325	−0.00981613
$782$	0.473975	0.0169493
$783$	7.87507	0.281432
$784$	−7.14229	−0.255082
$785$	−9.25909	−0.330471
$786$	4.47252	0.159529
$787$	6.02087	0.214621	0.107310	−	0.994226i	$-0.465776\pi$
$787$	6.02087	0.214621	0.107310	+	0.994226i	$0.465776\pi$
$788$	−24.7923	−0.883189
$789$	−7.02621	−0.250140
$790$	−17.5210	−0.623369
$791$	12.6964	0.451433
$792$	1.01740	0.0361518
$793$	−12.7957	−0.454387
$794$	14.7468	0.523346
$795$	−10.9502	−0.388362
$796$	−6.60747	−0.234195
$797$	−27.2739	−0.966092	−0.483046	−	0.875595i	$-0.660470\pi$
$797$	−27.2739	−0.966092	−0.483046	+	0.875595i	$0.660470\pi$
$798$	6.05493	0.214342
$799$	−22.3092	−0.789241
$800$	1.79301	0.0633926
$801$	−9.17999	−0.324359
$802$	21.0418	0.743010
$803$	−1.50250	−0.0530221
$804$	−4.46489	−0.157465
$805$	0.743435	0.0262026
$806$	−6.23518	−0.219625
$807$	−9.40275	−0.330992
$808$	−25.1008	−0.883043
$809$	10.8671	0.382067	0.191033	−	0.981584i	$-0.438816\pi$
$809$	10.8671	0.382067	0.191033	+	0.981584i	$0.438816\pi$
$810$	1.40659	0.0494225
$811$	−12.1025	−0.424978	−0.212489	−	0.977163i	$-0.568157\pi$
$811$	−12.1025	−0.424978	−0.212489	+	0.977163i	$0.568157\pi$
$812$	23.1334	0.811825
$813$	−19.4908	−0.683573
$814$	−1.53115	−0.0536668
$815$	38.2442	1.33964
$816$	−8.29895	−0.290521
$817$	−62.5457	−2.18820
$818$	−3.16913	−0.110806
$819$	1.80421	0.0630443
$820$	−45.3557	−1.58389
$821$	−10.0205	−0.349717	−0.174859	−	0.984594i	$-0.555947\pi$
$821$	−10.0205	−0.349717	−0.174859	+	0.984594i	$0.555947\pi$
$822$	9.16008	0.319495
$823$	39.9560	1.39278	0.696390	−	0.717664i	$-0.254788\pi$
$823$	39.9560	1.39278	0.696390	+	0.717664i	$0.254788\pi$
$824$	2.21240	0.0770724
$825$	−0.147562	−0.00513743
$826$	−11.3190	−0.393840
$827$	−8.11143	−0.282062	−0.141031	−	0.990005i	$-0.545042\pi$
$827$	−8.11143	−0.282062	−0.141031	+	0.990005i	$0.545042\pi$
$828$	0.290845	0.0101076
$829$	14.3198	0.497349	0.248674	−	0.968587i	$-0.420005\pi$
$829$	14.3198	0.497349	0.248674	+	0.968587i	$0.420005\pi$
$830$	17.3321	0.601605
$831$	2.46384	0.0854698
$832$	0.407142	0.0141151
$833$	16.2947	0.564579
$834$	7.45074	0.257998
$835$	−30.0637	−1.04040
$836$	−4.12073	−0.142518
$837$	10.2252	0.353436
$838$	−4.30769	−0.148807
$839$	−49.7926	−1.71903	−0.859515	−	0.511111i	$-0.829234\pi$
$839$	−49.7926	−1.71903	−0.859515	+	0.511111i	$0.829234\pi$
$840$	9.20751	0.317689
$841$	33.0168	1.13851
$842$	0.471230	0.0162396
$843$	−25.5551	−0.880165
$844$	−32.3714	−1.11427
$845$	2.30670	0.0793530
$846$	3.12639	0.107487
$847$	19.4648	0.668818
$848$	−9.05389	−0.310912
$849$	6.75809	0.231937
$850$	−0.851403	−0.0292029
$851$	−0.975383	−0.0334357
$852$	−0.971256	−0.0332747
$853$	38.4911	1.31791	0.658954	−	0.752183i	$-0.270999\pi$
$853$	38.4911	1.31791	0.658954	+	0.752183i	$0.270999\pi$
$854$	−14.0775	−0.481723
$855$	−12.6951	−0.434164
$856$	20.9341	0.715513
$857$	−52.3549	−1.78841	−0.894205	−	0.447657i	$-0.852259\pi$
$857$	−52.3549	−1.78841	−0.894205	+	0.447657i	$0.852259\pi$
$858$	0.280418	0.00957332
$859$	−55.2491	−1.88508	−0.942538	−	0.334099i	$-0.891568\pi$
$859$	−55.2491	−1.88508	−0.942538	+	0.334099i	$0.891568\pi$
$860$	−42.6817	−1.45543
$861$	−21.7886	−0.742553
$862$	−5.04018	−0.171669
$863$	−25.1949	−0.857644	−0.428822	−	0.903389i	$-0.641071\pi$
$863$	−25.1949	−0.857644	−0.428822	+	0.903389i	$0.641071\pi$
$864$	5.58780	0.190101
$865$	26.4138	0.898097
$866$	6.56764	0.223178
$867$	1.93359	0.0656682
$868$	30.0372	1.01953
$869$	5.72824	0.194317
$870$	11.0770	0.375545
$871$	−2.74229	−0.0929188
$872$	32.6682	1.10629
$873$	−8.58453	−0.290542
$874$	0.599494	0.0202782
$875$	19.4735	0.658324
$876$	−5.31965	−0.179734
$877$	−50.9076	−1.71903	−0.859514	−	0.511111i	$-0.829234\pi$
$877$	−50.9076	−1.71903	−0.859514	+	0.511111i	$0.829234\pi$
$878$	7.75025	0.261558
$879$	−13.4454	−0.453504
$880$	−2.02315	−0.0682004
$881$	−20.3738	−0.686412	−0.343206	−	0.939260i	$-0.611513\pi$
$881$	−20.3738	−0.686412	−0.343206	+	0.939260i	$0.611513\pi$
$882$	−2.28353	−0.0768905
$883$	24.9741	0.840447	0.420223	−	0.907421i	$-0.361952\pi$
$883$	24.9741	0.840447	0.420223	+	0.907421i	$0.361952\pi$
$884$	−7.08459	−0.238280
$885$	23.7322	0.797749
$886$	−10.6243	−0.356931
$887$	53.0825	1.78234	0.891169	−	0.453672i	$-0.149886\pi$
$887$	53.0825	1.78234	0.891169	+	0.453672i	$0.149886\pi$
$888$	−12.0802	−0.405385
$889$	8.61922	0.289079
$890$	−12.9125	−0.432828
$891$	−0.459865	−0.0154061
$892$	−25.1672	−0.842659
$893$	−28.2171	−0.944249
$894$	4.11168	0.137515
$895$	−0.802340	−0.0268193
$896$	20.6111	0.688568
$897$	0.178634	0.00596441
$898$	−14.4203	−0.481212
$899$	80.5245	2.68564
$900$	−0.522446	−0.0174149
$901$	20.6560	0.688150
$902$	−3.38647	−0.112757
$903$	−20.5040	−0.682331
$904$	15.5689	0.517813
$905$	−31.7981	−1.05700
$906$	−13.9601	−0.463794
$907$	−31.4475	−1.04420	−0.522098	−	0.852885i	$-0.674851\pi$
$907$	−31.4475	−1.04420	−0.522098	+	0.852885i	$0.674851\pi$
$908$	−44.0998	−1.46350
$909$	11.3455	0.376307
$910$	2.53779	0.0841268
$911$	−2.96090	−0.0980991	−0.0490495	−	0.998796i	$-0.515619\pi$
$911$	−2.96090	−0.0980991	−0.0490495	+	0.998796i	$0.515619\pi$
$912$	−10.4967	−0.347580
$913$	−5.66648	−0.187533
$914$	7.32256	0.242209
$915$	29.5158	0.975762
$916$	−2.96196	−0.0978658
$917$	−13.2332	−0.436998
$918$	−2.65334	−0.0875732
$919$	2.89613	0.0955344	0.0477672	−	0.998858i	$-0.484789\pi$
$919$	2.89613	0.0955344	0.0477672	+	0.998858i	$0.484789\pi$
$920$	0.911629	0.0300555
$921$	−2.09722	−0.0691058
$922$	−10.5132	−0.346235
$923$	−0.596535	−0.0196352
$924$	−1.35088	−0.0444406
$925$	1.75208	0.0576082
$926$	9.87050	0.324365
$927$	−1.00000	−0.0328443
$928$	44.0043	1.44451
$929$	41.8245	1.37222	0.686108	−	0.727499i	$-0.259318\pi$
$929$	41.8245	1.37222	0.686108	+	0.727499i	$0.259318\pi$
$930$	14.3827	0.471628
$931$	20.6099	0.675463
$932$	34.1146	1.11746
$933$	−11.8728	−0.388699
$934$	5.64685	0.184770
$935$	4.61571	0.150950
$936$	2.21240	0.0723144
$937$	53.9376	1.76206	0.881032	−	0.473057i	$-0.156850\pi$
$937$	53.9376	1.76206	0.881032	+	0.473057i	$0.156850\pi$
$938$	−3.01701	−0.0985088
$939$	18.1520	0.592368
$940$	−19.2556	−0.628048
$941$	−50.6550	−1.65131	−0.825653	−	0.564178i	$-0.809193\pi$
$941$	−50.6550	−1.65131	−0.825653	+	0.564178i	$0.809193\pi$
$942$	−2.44767	−0.0797493
$943$	−2.15727	−0.0702505
$944$	19.6224	0.638655
$945$	−4.16178	−0.135383
$946$	−3.18682	−0.103612
$947$	−10.4391	−0.339227	−0.169613	−	0.985511i	$-0.554252\pi$
$947$	−10.4391	−0.339227	−0.169613	+	0.985511i	$0.554252\pi$
$948$	20.2810	0.658696
$949$	−3.26727	−0.106060
$950$	−1.07687	−0.0349384
$951$	−3.39025	−0.109936
$952$	−17.3687	−0.562922
$953$	−13.9452	−0.451730	−0.225865	−	0.974159i	$-0.572521\pi$
$953$	−13.9452	−0.451730	−0.225865	+	0.974159i	$0.572521\pi$
$954$	−2.89471	−0.0937196
$955$	46.6567	1.50978
$956$	−9.05439	−0.292840
$957$	−3.62147	−0.117065
$958$	−0.556403	−0.0179766
$959$	−27.1026	−0.875189
$960$	−0.939155	−0.0303111
$961$	73.5554	2.37276
$962$	−3.32957	−0.107350
$963$	−9.46219	−0.304915
$964$	29.9619	0.965008
$965$	5.66108	0.182237
$966$	0.196529	0.00632322
$967$	6.90766	0.222135	0.111068	−	0.993813i	$-0.464573\pi$
$967$	6.90766	0.222135	0.111068	+	0.993813i	$0.464573\pi$
$968$	23.8685	0.767162
$969$	23.9476	0.769308
$970$	−12.0749	−0.387702
$971$	−5.84531	−0.187585	−0.0937924	−	0.995592i	$-0.529899\pi$
$971$	−5.84531	−0.187585	−0.0937924	+	0.995592i	$0.529899\pi$
$972$	−1.62816	−0.0522234
$973$	−22.0450	−0.706732
$974$	1.70868	0.0547497
$975$	−0.320880	−0.0102764
$976$	24.4044	0.781167
$977$	−17.5859	−0.562624	−0.281312	−	0.959616i	$-0.590770\pi$
$977$	−17.5859	−0.562624	−0.281312	+	0.959616i	$0.590770\pi$
$978$	10.1100	0.323281
$979$	4.22156	0.134922
$980$	14.0644	0.449270
$981$	−14.7660	−0.471442
$982$	20.5840	0.656862
$983$	36.8636	1.17576	0.587882	−	0.808946i	$-0.299962\pi$
$983$	36.8636	1.17576	0.587882	+	0.808946i	$0.299962\pi$
$984$	−26.7180	−0.851740
$985$	35.1245	1.11916
$986$	−20.8952	−0.665439
$987$	−9.25027	−0.294439
$988$	−8.96074	−0.285079
$989$	−2.03009	−0.0645531
$990$	−0.646841	−0.0205580
$991$	−0.805461	−0.0255863	−0.0127932	−	0.999918i	$-0.504072\pi$
$991$	−0.805461	−0.0255863	−0.0127932	+	0.999918i	$0.504072\pi$
$992$	57.1365	1.81409
$993$	−26.5725	−0.843253
$994$	−0.656295	−0.0208164
$995$	9.36114	0.296768
$996$	−20.0623	−0.635699
$997$	24.6444	0.780497	0.390248	−	0.920710i	$-0.372389\pi$
$997$	24.6444	0.780497	0.390248	+	0.920710i	$0.372389\pi$
$998$	11.2755	0.356920
$999$	5.46024	0.172754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.18	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.18	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+0.609784 q^{2} +1.00000 q^{3} -1.62816 q^{4} +2.30670 q^{5} +0.609784 q^{6} -1.80421 q^{7} -2.21240 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.609784 q^{2} +1.00000 q^{3} -1.62816 q^{4} +2.30670 q^{5} +0.609784 q^{6} -1.80421 q^{7} -2.21240 q^{8} +1.00000 q^{9} +1.40659 q^{10} -0.459865 q^{11} -1.62816 q^{12} -1.00000 q^{13} -1.10018 q^{14} +2.30670 q^{15} +1.90724 q^{16} -4.35127 q^{17} +0.609784 q^{18} -5.50358 q^{19} -3.75569 q^{20} -1.80421 q^{21} -0.280418 q^{22} -0.178634 q^{23} -2.21240 q^{24} +0.320880 q^{25} -0.609784 q^{26} +1.00000 q^{27} +2.93755 q^{28} +7.87507 q^{29} +1.40659 q^{30} +10.2252 q^{31} +5.58780 q^{32} -0.459865 q^{33} -2.65334 q^{34} -4.16178 q^{35} -1.62816 q^{36} +5.46024 q^{37} -3.35600 q^{38} -1.00000 q^{39} -5.10334 q^{40} +12.0765 q^{41} -1.10018 q^{42} +11.3645 q^{43} +0.748735 q^{44} +2.30670 q^{45} -0.108928 q^{46} +5.12704 q^{47} +1.90724 q^{48} -3.74482 q^{49} +0.195668 q^{50} -4.35127 q^{51} +1.62816 q^{52} -4.74711 q^{53} +0.609784 q^{54} -1.06077 q^{55} +3.99163 q^{56} -5.50358 q^{57} +4.80209 q^{58} +10.2884 q^{59} -3.75569 q^{60} +12.7957 q^{61} +6.23518 q^{62} -1.80421 q^{63} -0.407142 q^{64} -2.30670 q^{65} -0.280418 q^{66} +2.74229 q^{67} +7.08459 q^{68} -0.178634 q^{69} -2.53779 q^{70} +0.596535 q^{71} -2.21240 q^{72} +3.26727 q^{73} +3.32957 q^{74} +0.320880 q^{75} +8.96074 q^{76} +0.829694 q^{77} -0.609784 q^{78} -12.4564 q^{79} +4.39945 q^{80} +1.00000 q^{81} +7.36406 q^{82} +12.3221 q^{83} +2.93755 q^{84} -10.0371 q^{85} +6.92991 q^{86} +7.87507 q^{87} +1.01740 q^{88} -9.17999 q^{89} +1.40659 q^{90} +1.80421 q^{91} +0.290845 q^{92} +10.2252 q^{93} +3.12639 q^{94} -12.6951 q^{95} +5.58780 q^{96} -8.58453 q^{97} -2.28353 q^{98} -0.459865 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

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