LMFDB - Embedded newform 6038.2.a.c.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, 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("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.2136727404$
Analytic rank:	$1$
Dimension:	$57$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.99307 q^{3} +1.00000 q^{4} +2.62099 q^{5} +2.99307 q^{6} -1.28357 q^{7} -1.00000 q^{8} +5.95844 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.99307 q^{3} +1.00000 q^{4} +2.62099 q^{5} +2.99307 q^{6} -1.28357 q^{7} -1.00000 q^{8} +5.95844 q^{9} -2.62099 q^{10} +1.37532 q^{11} -2.99307 q^{12} +0.0797974 q^{13} +1.28357 q^{14} -7.84479 q^{15} +1.00000 q^{16} -4.18998 q^{17} -5.95844 q^{18} +3.49645 q^{19} +2.62099 q^{20} +3.84182 q^{21} -1.37532 q^{22} +3.54333 q^{23} +2.99307 q^{24} +1.86957 q^{25} -0.0797974 q^{26} -8.85480 q^{27} -1.28357 q^{28} -6.75313 q^{29} +7.84479 q^{30} +8.46149 q^{31} -1.00000 q^{32} -4.11642 q^{33} +4.18998 q^{34} -3.36423 q^{35} +5.95844 q^{36} -10.5916 q^{37} -3.49645 q^{38} -0.238839 q^{39} -2.62099 q^{40} +5.80263 q^{41} -3.84182 q^{42} -0.321559 q^{43} +1.37532 q^{44} +15.6170 q^{45} -3.54333 q^{46} +1.89118 q^{47} -2.99307 q^{48} -5.35244 q^{49} -1.86957 q^{50} +12.5409 q^{51} +0.0797974 q^{52} +4.53448 q^{53} +8.85480 q^{54} +3.60469 q^{55} +1.28357 q^{56} -10.4651 q^{57} +6.75313 q^{58} -10.2697 q^{59} -7.84479 q^{60} -2.36810 q^{61} -8.46149 q^{62} -7.64809 q^{63} +1.00000 q^{64} +0.209148 q^{65} +4.11642 q^{66} -8.80780 q^{67} -4.18998 q^{68} -10.6054 q^{69} +3.36423 q^{70} +7.16209 q^{71} -5.95844 q^{72} -5.44627 q^{73} +10.5916 q^{74} -5.59576 q^{75} +3.49645 q^{76} -1.76532 q^{77} +0.238839 q^{78} -7.57132 q^{79} +2.62099 q^{80} +8.62768 q^{81} -5.80263 q^{82} -1.76525 q^{83} +3.84182 q^{84} -10.9819 q^{85} +0.321559 q^{86} +20.2125 q^{87} -1.37532 q^{88} -4.43859 q^{89} -15.6170 q^{90} -0.102426 q^{91} +3.54333 q^{92} -25.3258 q^{93} -1.89118 q^{94} +9.16415 q^{95} +2.99307 q^{96} -4.86007 q^{97} +5.35244 q^{98} +8.19475 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) $ 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.99307	−1.72805	−0.864023	−	0.503452i	$-0.832063\pi$
$3$	−2.99307	−1.72805	−0.864023	+	0.503452i	$0.832063\pi$
$4$	1.00000	0.500000
$5$	2.62099	1.17214	0.586071	−	0.810260i	$-0.300674\pi$
$5$	2.62099	1.17214	0.586071	+	0.810260i	$0.300674\pi$
$6$	2.99307	1.22191
$7$	−1.28357	−0.485145	−0.242573	−	0.970133i	$-0.577991\pi$
$7$	−1.28357	−0.485145	−0.242573	+	0.970133i	$0.577991\pi$
$8$	−1.00000	−0.353553
$9$	5.95844	1.98615
$10$	−2.62099	−0.828829
$11$	1.37532	0.414674	0.207337	−	0.978270i	$-0.433520\pi$
$11$	1.37532	0.414674	0.207337	+	0.978270i	$0.433520\pi$
$12$	−2.99307	−0.864023
$13$	0.0797974	0.0221318	0.0110659	−	0.999939i	$-0.496478\pi$
$13$	0.0797974	0.0221318	0.0110659	+	0.999939i	$0.496478\pi$
$14$	1.28357	0.343049
$15$	−7.84479	−2.02551
$16$	1.00000	0.250000
$17$	−4.18998	−1.01622	−0.508110	−	0.861292i	$-0.669656\pi$
$17$	−4.18998	−1.01622	−0.508110	+	0.861292i	$0.669656\pi$
$18$	−5.95844	−1.40442
$19$	3.49645	0.802141	0.401070	−	0.916047i	$-0.368638\pi$
$19$	3.49645	0.802141	0.401070	+	0.916047i	$0.368638\pi$
$20$	2.62099	0.586071
$21$	3.84182	0.838354
$22$	−1.37532	−0.293219
$23$	3.54333	0.738835	0.369418	−	0.929263i	$-0.379557\pi$
$23$	3.54333	0.738835	0.369418	+	0.929263i	$0.379557\pi$
$24$	2.99307	0.610957
$25$	1.86957	0.373915
$26$	−0.0797974	−0.0156495
$27$	−8.85480	−1.70411
$28$	−1.28357	−0.242573
$29$	−6.75313	−1.25402	−0.627012	−	0.779010i	$-0.715722\pi$
$29$	−6.75313	−1.25402	−0.627012	+	0.779010i	$0.715722\pi$
$30$	7.84479	1.43226
$31$	8.46149	1.51973	0.759865	−	0.650081i	$-0.225265\pi$
$31$	8.46149	1.51973	0.759865	+	0.650081i	$0.225265\pi$
$32$	−1.00000	−0.176777
$33$	−4.11642	−0.716577
$34$	4.18998	0.718576
$35$	−3.36423	−0.568659
$36$	5.95844	0.993073
$37$	−10.5916	−1.74126	−0.870628	−	0.491942i	$-0.836287\pi$
$37$	−10.5916	−1.74126	−0.870628	+	0.491942i	$0.836287\pi$
$38$	−3.49645	−0.567199
$39$	−0.238839	−0.0382448
$40$	−2.62099	−0.414414
$41$	5.80263	0.906218	0.453109	−	0.891455i	$-0.350315\pi$
$41$	5.80263	0.906218	0.453109	+	0.891455i	$0.350315\pi$
$42$	−3.84182	−0.592805
$43$	−0.321559	−0.0490372	−0.0245186	−	0.999699i	$-0.507805\pi$
$43$	−0.321559	−0.0490372	−0.0245186	+	0.999699i	$0.507805\pi$
$44$	1.37532	0.207337
$45$	15.6170	2.32804
$46$	−3.54333	−0.522436
$47$	1.89118	0.275857	0.137929	−	0.990442i	$-0.455956\pi$
$47$	1.89118	0.275857	0.137929	+	0.990442i	$0.455956\pi$
$48$	−2.99307	−0.432012
$49$	−5.35244	−0.764634
$50$	−1.86957	−0.264398
$51$	12.5409	1.75608
$52$	0.0797974	0.0110659
$53$	4.53448	0.622859	0.311430	−	0.950269i	$-0.399192\pi$
$53$	4.53448	0.622859	0.311430	+	0.950269i	$0.399192\pi$
$54$	8.85480	1.20499
$55$	3.60469	0.486057
$56$	1.28357	0.171525
$57$	−10.4651	−1.38614
$58$	6.75313	0.886729
$59$	−10.2697	−1.33700	−0.668499	−	0.743713i	$-0.733063\pi$
$59$	−10.2697	−1.33700	−0.668499	+	0.743713i	$0.733063\pi$
$60$	−7.84479	−1.01276
$61$	−2.36810	−0.303204	−0.151602	−	0.988442i	$-0.548443\pi$
$61$	−2.36810	−0.303204	−0.151602	+	0.988442i	$0.548443\pi$
$62$	−8.46149	−1.07461
$63$	−7.64809	−0.963569
$64$	1.00000	0.125000
$65$	0.209148	0.0259416
$66$	4.11642	0.506696
$67$	−8.80780	−1.07604	−0.538022	−	0.842931i	$-0.680828\pi$
$67$	−8.80780	−1.07604	−0.538022	+	0.842931i	$0.680828\pi$
$68$	−4.18998	−0.508110
$69$	−10.6054	−1.27674
$70$	3.36423	0.402102
$71$	7.16209	0.849984	0.424992	−	0.905197i	$-0.360277\pi$
$71$	7.16209	0.849984	0.424992	+	0.905197i	$0.360277\pi$
$72$	−5.95844	−0.702209
$73$	−5.44627	−0.637437	−0.318719	−	0.947849i	$-0.603253\pi$
$73$	−5.44627	−0.637437	−0.318719	+	0.947849i	$0.603253\pi$
$74$	10.5916	1.23125
$75$	−5.59576	−0.646143
$76$	3.49645	0.401070
$77$	−1.76532	−0.201177
$78$	0.238839	0.0270432
$79$	−7.57132	−0.851840	−0.425920	−	0.904761i	$-0.640049\pi$
$79$	−7.57132	−0.851840	−0.425920	+	0.904761i	$0.640049\pi$
$80$	2.62099	0.293035
$81$	8.62768	0.958631
$82$	−5.80263	−0.640793
$83$	−1.76525	−0.193761	−0.0968805	−	0.995296i	$-0.530886\pi$
$83$	−1.76525	−0.193761	−0.0968805	+	0.995296i	$0.530886\pi$
$84$	3.84182	0.419177
$85$	−10.9819	−1.19115
$86$	0.321559	0.0346746
$87$	20.2125	2.16701
$88$	−1.37532	−0.146610
$89$	−4.43859	−0.470490	−0.235245	−	0.971936i	$-0.575589\pi$
$89$	−4.43859	−0.470490	−0.235245	+	0.971936i	$0.575589\pi$
$90$	−15.6170	−1.64618
$91$	−0.102426	−0.0107371
$92$	3.54333	0.369418
$93$	−25.3258	−2.62616
$94$	−1.89118	−0.195061
$95$	9.16415	0.940222
$96$	2.99307	0.305478
$97$	−4.86007	−0.493466	−0.246733	−	0.969084i	$-0.579357\pi$
$97$	−4.86007	−0.493466	−0.246733	+	0.969084i	$0.579357\pi$
$98$	5.35244	0.540678
$99$	8.19475	0.823604
$100$	1.86957	0.186957
$101$	−12.6466	−1.25839	−0.629194	−	0.777248i	$-0.716615\pi$
$101$	−12.6466	−1.25839	−0.629194	+	0.777248i	$0.716615\pi$
$102$	−12.5409	−1.24173
$103$	11.9248	1.17499	0.587495	−	0.809228i	$-0.300114\pi$
$103$	11.9248	1.17499	0.587495	+	0.809228i	$0.300114\pi$
$104$	−0.0797974	−0.00782477
$105$	10.0694	0.982669
$106$	−4.53448	−0.440428
$107$	−9.78464	−0.945917	−0.472959	−	0.881085i	$-0.656814\pi$
$107$	−9.78464	−0.945917	−0.472959	+	0.881085i	$0.656814\pi$
$108$	−8.85480	−0.852054
$109$	16.5610	1.58625	0.793127	−	0.609056i	$-0.208452\pi$
$109$	16.5610	1.58625	0.793127	+	0.609056i	$0.208452\pi$
$110$	−3.60469	−0.343694
$111$	31.7015	3.00897
$112$	−1.28357	−0.121286
$113$	−3.65471	−0.343806	−0.171903	−	0.985114i	$-0.554992\pi$
$113$	−3.65471	−0.343806	−0.171903	+	0.985114i	$0.554992\pi$
$114$	10.4651	0.980147
$115$	9.28702	0.866019
$116$	−6.75313	−0.627012
$117$	0.475468	0.0439570
$118$	10.2697	0.945401
$119$	5.37815	0.493014
$120$	7.84479	0.716128
$121$	−9.10850	−0.828045
$122$	2.36810	0.214397
$123$	−17.3676	−1.56599
$124$	8.46149	0.759865
$125$	−8.20481	−0.733860
$126$	7.64809	0.681346
$127$	21.1310	1.87507	0.937537	−	0.347885i	$-0.113100\pi$
$127$	21.1310	1.87507	0.937537	+	0.347885i	$0.113100\pi$
$128$	−1.00000	−0.0883883
$129$	0.962446	0.0847386
$130$	−0.209148	−0.0183435
$131$	8.24811	0.720641	0.360321	−	0.932829i	$-0.382667\pi$
$131$	8.24811	0.720641	0.360321	+	0.932829i	$0.382667\pi$
$132$	−4.11642	−0.358288
$133$	−4.48795	−0.389155
$134$	8.80780	0.760878
$135$	−23.2083	−1.99745
$136$	4.18998	0.359288
$137$	3.09295	0.264249	0.132124	−	0.991233i	$-0.457820\pi$
$137$	3.09295	0.264249	0.132124	+	0.991233i	$0.457820\pi$
$138$	10.6054	0.902793
$139$	5.78804	0.490935	0.245468	−	0.969405i	$-0.421058\pi$
$139$	5.78804	0.490935	0.245468	+	0.969405i	$0.421058\pi$
$140$	−3.36423	−0.284329
$141$	−5.66043	−0.476694
$142$	−7.16209	−0.601029
$143$	0.109747	0.00917749
$144$	5.95844	0.496537
$145$	−17.6999	−1.46989
$146$	5.44627	0.450736
$147$	16.0202	1.32132
$148$	−10.5916	−0.870628
$149$	4.99524	0.409226	0.204613	−	0.978843i	$-0.434406\pi$
$149$	4.99524	0.409226	0.204613	+	0.978843i	$0.434406\pi$
$150$	5.59576	0.456892
$151$	5.96006	0.485023	0.242511	−	0.970149i	$-0.422029\pi$
$151$	5.96006	0.485023	0.242511	+	0.970149i	$0.422029\pi$
$152$	−3.49645	−0.283600
$153$	−24.9658	−2.01836
$154$	1.76532	0.142254
$155$	22.1775	1.78134
$156$	−0.238839	−0.0191224
$157$	15.1936	1.21258	0.606292	−	0.795242i	$-0.292656\pi$
$157$	15.1936	1.21258	0.606292	+	0.795242i	$0.292656\pi$
$158$	7.57132	0.602342
$159$	−13.5720	−1.07633
$160$	−2.62099	−0.207207
$161$	−4.54812	−0.358442
$162$	−8.62768	−0.677854
$163$	−21.4787	−1.68234	−0.841171	−	0.540769i	$-0.818133\pi$
$163$	−21.4787	−1.68234	−0.841171	+	0.540769i	$0.818133\pi$
$164$	5.80263	0.453109
$165$	−10.7891	−0.839929
$166$	1.76525	0.137010
$167$	−18.6602	−1.44397	−0.721984	−	0.691910i	$-0.756770\pi$
$167$	−18.6602	−1.44397	−0.721984	+	0.691910i	$0.756770\pi$
$168$	−3.84182	−0.296403
$169$	−12.9936	−0.999510
$170$	10.9819	0.842273
$171$	20.8334	1.59317
$172$	−0.321559	−0.0245186
$173$	2.64763	0.201295	0.100648	−	0.994922i	$-0.467909\pi$
$173$	2.64763	0.201295	0.100648	+	0.994922i	$0.467909\pi$
$174$	−20.2125	−1.53231
$175$	−2.39974	−0.181403
$176$	1.37532	0.103669
$177$	30.7378	2.31040
$178$	4.43859	0.332687
$179$	5.81606	0.434713	0.217356	−	0.976092i	$-0.430257\pi$
$179$	5.81606	0.434713	0.217356	+	0.976092i	$0.430257\pi$
$180$	15.6170	1.16402
$181$	15.9429	1.18502	0.592512	−	0.805562i	$-0.298136\pi$
$181$	15.9429	1.18502	0.592512	+	0.805562i	$0.298136\pi$
$182$	0.102426	0.00759230
$183$	7.08787	0.523950
$184$	−3.54333	−0.261218
$185$	−27.7606	−2.04100
$186$	25.3258	1.85698
$187$	−5.76256	−0.421400
$188$	1.89118	0.137929
$189$	11.3658	0.826739
$190$	−9.16415	−0.664837
$191$	14.3958	1.04164	0.520821	−	0.853666i	$-0.325626\pi$
$191$	14.3958	1.04164	0.520821	+	0.853666i	$0.325626\pi$
$192$	−2.99307	−0.216006
$193$	−17.5296	−1.26181	−0.630905	−	0.775860i	$-0.717316\pi$
$193$	−17.5296	−1.26181	−0.630905	+	0.775860i	$0.717316\pi$
$194$	4.86007	0.348933
$195$	−0.625993	−0.0448283
$196$	−5.35244	−0.382317
$197$	22.3424	1.59183	0.795917	−	0.605406i	$-0.206989\pi$
$197$	22.3424	1.59183	0.795917	+	0.605406i	$0.206989\pi$
$198$	−8.19475	−0.582376
$199$	−27.0197	−1.91537	−0.957687	−	0.287811i	$-0.907072\pi$
$199$	−27.0197	−1.91537	−0.957687	+	0.287811i	$0.907072\pi$
$200$	−1.86957	−0.132199
$201$	26.3623	1.85945
$202$	12.6466	0.889815
$203$	8.66813	0.608384
$204$	12.5409	0.878038
$205$	15.2086	1.06222
$206$	−11.9248	−0.830843
$207$	21.1127	1.46744
$208$	0.0797974	0.00553295
$209$	4.80873	0.332627
$210$	−10.0694	−0.694852
$211$	24.8314	1.70946	0.854732	−	0.519069i	$-0.173721\pi$
$211$	24.8314	1.70946	0.854732	+	0.519069i	$0.173721\pi$
$212$	4.53448	0.311430
$213$	−21.4366	−1.46881
$214$	9.78464	0.668864
$215$	−0.842801	−0.0574785
$216$	8.85480	0.602493
$217$	−10.8609	−0.737289
$218$	−16.5610	−1.12165
$219$	16.3010	1.10152
$220$	3.60469	0.243028
$221$	−0.334349	−0.0224908
$222$	−31.7015	−2.12766
$223$	6.38891	0.427833	0.213917	−	0.976852i	$-0.431378\pi$
$223$	6.38891	0.427833	0.213917	+	0.976852i	$0.431378\pi$
$224$	1.28357	0.0857623
$225$	11.1397	0.742650
$226$	3.65471	0.243107
$227$	−22.0566	−1.46395	−0.731973	−	0.681333i	$-0.761400\pi$
$227$	−22.0566	−1.46395	−0.731973	+	0.681333i	$0.761400\pi$
$228$	−10.4651	−0.693068
$229$	−17.7481	−1.17283	−0.586413	−	0.810012i	$-0.699460\pi$
$229$	−17.7481	−1.17283	−0.586413	+	0.810012i	$0.699460\pi$
$230$	−9.28702	−0.612368
$231$	5.28373	0.347644
$232$	6.75313	0.443364
$233$	−12.7529	−0.835473	−0.417736	−	0.908568i	$-0.637176\pi$
$233$	−12.7529	−0.835473	−0.417736	+	0.908568i	$0.637176\pi$
$234$	−0.475468	−0.0310823
$235$	4.95676	0.323344
$236$	−10.2697	−0.668499
$237$	22.6614	1.47202
$238$	−5.37815	−0.348614
$239$	−4.57042	−0.295636	−0.147818	−	0.989015i	$-0.547225\pi$
$239$	−4.57042	−0.295636	−0.147818	+	0.989015i	$0.547225\pi$
$240$	−7.84479	−0.506379
$241$	26.3501	1.69736	0.848680	−	0.528907i	$-0.177398\pi$
$241$	26.3501	1.69736	0.848680	+	0.528907i	$0.177398\pi$
$242$	9.10850	0.585516
$243$	0.741200	0.0475480
$244$	−2.36810	−0.151602
$245$	−14.0287	−0.896259
$246$	17.3676	1.10732
$247$	0.279007	0.0177528
$248$	−8.46149	−0.537305
$249$	5.28350	0.334828
$250$	8.20481	0.518917
$251$	−12.2302	−0.771965	−0.385982	−	0.922506i	$-0.626137\pi$
$251$	−12.2302	−0.771965	−0.385982	+	0.922506i	$0.626137\pi$
$252$	−7.64809	−0.481785
$253$	4.87321	0.306376
$254$	−21.1310	−1.32588
$255$	32.8695	2.05837
$256$	1.00000	0.0625000
$257$	8.96989	0.559526	0.279763	−	0.960069i	$-0.409744\pi$
$257$	8.96989	0.559526	0.279763	+	0.960069i	$0.409744\pi$
$258$	−0.962446	−0.0599193
$259$	13.5952	0.844762
$260$	0.209148	0.0129708
$261$	−40.2381	−2.49067
$262$	−8.24811	−0.509570
$263$	22.9826	1.41717	0.708585	−	0.705626i	$-0.249334\pi$
$263$	22.9826	1.41717	0.708585	+	0.705626i	$0.249334\pi$
$264$	4.11642	0.253348
$265$	11.8848	0.730079
$266$	4.48795	0.275174
$267$	13.2850	0.813029
$268$	−8.80780	−0.538022
$269$	27.1848	1.65748	0.828742	−	0.559630i	$-0.189057\pi$
$269$	27.1848	1.65748	0.828742	+	0.559630i	$0.189057\pi$
$270$	23.2083	1.41241
$271$	1.59005	0.0965887	0.0482944	−	0.998833i	$-0.484621\pi$
$271$	1.59005	0.0965887	0.0482944	+	0.998833i	$0.484621\pi$
$272$	−4.18998	−0.254055
$273$	0.306567	0.0185543
$274$	−3.09295	−0.186852
$275$	2.57126	0.155053
$276$	−10.6054	−0.638371
$277$	−6.54896	−0.393489	−0.196745	−	0.980455i	$-0.563037\pi$
$277$	−6.54896	−0.393489	−0.196745	+	0.980455i	$0.563037\pi$
$278$	−5.78804	−0.347144
$279$	50.4173	3.01840
$280$	3.36423	0.201051
$281$	15.5495	0.927603	0.463801	−	0.885939i	$-0.346485\pi$
$281$	15.5495	0.927603	0.463801	+	0.885939i	$0.346485\pi$
$282$	5.66043	0.337074
$283$	−32.1638	−1.91194	−0.955970	−	0.293465i	$-0.905192\pi$
$283$	−32.1638	−1.91194	−0.955970	+	0.293465i	$0.905192\pi$
$284$	7.16209	0.424992
$285$	−27.4289	−1.62475
$286$	−0.109747	−0.00648947
$287$	−7.44810	−0.439647
$288$	−5.95844	−0.351104
$289$	0.555950	0.0327029
$290$	17.6999	1.03937
$291$	14.5465	0.852732
$292$	−5.44627	−0.318719
$293$	−1.97924	−0.115628	−0.0578142	−	0.998327i	$-0.518413\pi$
$293$	−1.97924	−0.115628	−0.0578142	+	0.998327i	$0.518413\pi$
$294$	−16.0202	−0.934317
$295$	−26.9167	−1.56715
$296$	10.5916	0.615627
$297$	−12.1782	−0.706649
$298$	−4.99524	−0.289366
$299$	0.282748	0.0163518
$300$	−5.59576	−0.323071
$301$	0.412744	0.0237902
$302$	−5.96006	−0.342963
$303$	37.8522	2.17455
$304$	3.49645	0.200535
$305$	−6.20675	−0.355398
$306$	24.9658	1.42720
$307$	14.0061	0.799370	0.399685	−	0.916653i	$-0.369120\pi$
$307$	14.0061	0.799370	0.399685	+	0.916653i	$0.369120\pi$
$308$	−1.76532	−0.100589
$309$	−35.6918	−2.03044
$310$	−22.1775	−1.25960
$311$	16.8560	0.955815	0.477908	−	0.878410i	$-0.341395\pi$
$311$	16.8560	0.955815	0.477908	+	0.878410i	$0.341395\pi$
$312$	0.238839	0.0135216
$313$	−0.292752	−0.0165473	−0.00827365	−	0.999966i	$-0.502634\pi$
$313$	−0.292752	−0.0165473	−0.00827365	+	0.999966i	$0.502634\pi$
$314$	−15.1936	−0.857427
$315$	−20.0456	−1.12944
$316$	−7.57132	−0.425920
$317$	−4.00220	−0.224786	−0.112393	−	0.993664i	$-0.535852\pi$
$317$	−4.00220	−0.224786	−0.112393	+	0.993664i	$0.535852\pi$
$318$	13.5720	0.761080
$319$	−9.28770	−0.520011
$320$	2.62099	0.146518
$321$	29.2861	1.63459
$322$	4.54812	0.253457
$323$	−14.6501	−0.815151
$324$	8.62768	0.479315
$325$	0.149187	0.00827541
$326$	21.4787	1.18960
$327$	−49.5681	−2.74112
$328$	−5.80263	−0.320397
$329$	−2.42747	−0.133831
$330$	10.7891	0.593919
$331$	−17.4536	−0.959334	−0.479667	−	0.877451i	$-0.659243\pi$
$331$	−17.4536	−0.959334	−0.479667	+	0.877451i	$0.659243\pi$
$332$	−1.76525	−0.0968805
$333$	−63.1097	−3.45839
$334$	18.6602	1.02104
$335$	−23.0851	−1.26128
$336$	3.84182	0.209588
$337$	−14.1992	−0.773478	−0.386739	−	0.922189i	$-0.626399\pi$
$337$	−14.1992	−0.773478	−0.386739	+	0.922189i	$0.626399\pi$
$338$	12.9936	0.706760
$339$	10.9388	0.594113
$340$	−10.9819	−0.595577
$341$	11.6373	0.630193
$342$	−20.8334	−1.12654
$343$	15.8553	0.856104
$344$	0.321559	0.0173373
$345$	−27.7967	−1.49652
$346$	−2.64763	−0.142337
$347$	−36.1675	−1.94157	−0.970786	−	0.239946i	$-0.922870\pi$
$347$	−36.1675	−1.94157	−0.970786	+	0.239946i	$0.922870\pi$
$348$	20.2125	1.08351
$349$	4.62979	0.247827	0.123913	−	0.992293i	$-0.460455\pi$
$349$	4.62979	0.247827	0.123913	+	0.992293i	$0.460455\pi$
$350$	2.39974	0.128271
$351$	−0.706590	−0.0377150
$352$	−1.37532	−0.0733048
$353$	−32.6394	−1.73722	−0.868609	−	0.495498i	$-0.834986\pi$
$353$	−32.6394	−1.73722	−0.868609	+	0.495498i	$0.834986\pi$
$354$	−30.7378	−1.63370
$355$	18.7717	0.996301
$356$	−4.43859	−0.235245
$357$	−16.0972	−0.851952
$358$	−5.81606	−0.307388
$359$	9.68917	0.511375	0.255688	−	0.966759i	$-0.417698\pi$
$359$	9.68917	0.511375	0.255688	+	0.966759i	$0.417698\pi$
$360$	−15.6170	−0.823088
$361$	−6.77484	−0.356570
$362$	−15.9429	−0.837938
$363$	27.2623	1.43090
$364$	−0.102426	−0.00536857
$365$	−14.2746	−0.747167
$366$	−7.08787	−0.370489
$367$	19.6556	1.02601	0.513007	−	0.858384i	$-0.328531\pi$
$367$	19.6556	1.02601	0.513007	+	0.858384i	$0.328531\pi$
$368$	3.54333	0.184709
$369$	34.5746	1.79988
$370$	27.7606	1.44320
$371$	−5.82034	−0.302177
$372$	−25.3258	−1.31308
$373$	−33.8367	−1.75200	−0.875999	−	0.482313i	$-0.839797\pi$
$373$	−33.8367	−1.75200	−0.875999	+	0.482313i	$0.839797\pi$
$374$	5.76256	0.297975
$375$	24.5575	1.26814
$376$	−1.89118	−0.0975303
$377$	−0.538882	−0.0277538
$378$	−11.3658	−0.584593
$379$	−21.4887	−1.10380	−0.551899	−	0.833911i	$-0.686097\pi$
$379$	−21.4887	−1.10380	−0.551899	+	0.833911i	$0.686097\pi$
$380$	9.16415	0.470111
$381$	−63.2465	−3.24022
$382$	−14.3958	−0.736553
$383$	−22.5898	−1.15428	−0.577142	−	0.816644i	$-0.695832\pi$
$383$	−22.5898	−1.15428	−0.577142	+	0.816644i	$0.695832\pi$
$384$	2.99307	0.152739
$385$	−4.62689	−0.235808
$386$	17.5296	0.892235
$387$	−1.91599	−0.0973951
$388$	−4.86007	−0.246733
$389$	−15.9843	−0.810434	−0.405217	−	0.914221i	$-0.632804\pi$
$389$	−15.9843	−0.810434	−0.405217	+	0.914221i	$0.632804\pi$
$390$	0.625993	0.0316984
$391$	−14.8465	−0.750819
$392$	5.35244	0.270339
$393$	−24.6871	−1.24530
$394$	−22.3424	−1.12560
$395$	−19.8443	−0.998476
$396$	8.19475	0.411802
$397$	−14.5736	−0.731430	−0.365715	−	0.930727i	$-0.619176\pi$
$397$	−14.5736	−0.731430	−0.365715	+	0.930727i	$0.619176\pi$
$398$	27.0197	1.35437
$399$	13.4327	0.672477
$400$	1.86957	0.0934787
$401$	−29.4184	−1.46908	−0.734541	−	0.678564i	$-0.762603\pi$
$401$	−29.4184	−1.46908	−0.734541	+	0.678564i	$0.762603\pi$
$402$	−26.3623	−1.31483
$403$	0.675205	0.0336343
$404$	−12.6466	−0.629194
$405$	22.6130	1.12365
$406$	−8.66813	−0.430192
$407$	−14.5669	−0.722054
$408$	−12.5409	−0.620867
$409$	−5.18557	−0.256410	−0.128205	−	0.991748i	$-0.540922\pi$
$409$	−5.18557	−0.256410	−0.128205	+	0.991748i	$0.540922\pi$
$410$	−15.2086	−0.751100
$411$	−9.25740	−0.456634
$412$	11.9248	0.587495
$413$	13.1819	0.648638
$414$	−21.1127	−1.03763
$415$	−4.62669	−0.227115
$416$	−0.0797974	−0.00391239
$417$	−17.3240	−0.848359
$418$	−4.80873	−0.235203
$419$	6.86867	0.335556	0.167778	−	0.985825i	$-0.446341\pi$
$419$	6.86867	0.335556	0.167778	+	0.985825i	$0.446341\pi$
$420$	10.0694	0.491334
$421$	−26.0331	−1.26877	−0.634387	−	0.773015i	$-0.718748\pi$
$421$	−26.0331	−1.26877	−0.634387	+	0.773015i	$0.718748\pi$
$422$	−24.8314	−1.20877
$423$	11.2685	0.547893
$424$	−4.53448	−0.220214
$425$	−7.83348	−0.379980
$426$	21.4366	1.03861
$427$	3.03963	0.147098
$428$	−9.78464	−0.472959
$429$	−0.328479	−0.0158591
$430$	0.842801	0.0406435
$431$	2.86352	0.137931	0.0689654	−	0.997619i	$-0.478030\pi$
$431$	2.86352	0.137931	0.0689654	+	0.997619i	$0.478030\pi$
$432$	−8.85480	−0.426027
$433$	19.5357	0.938828	0.469414	−	0.882978i	$-0.344465\pi$
$433$	19.5357	0.938828	0.469414	+	0.882978i	$0.344465\pi$
$434$	10.8609	0.521342
$435$	52.9768	2.54004
$436$	16.5610	0.793127
$437$	12.3891	0.592650
$438$	−16.3010	−0.778893
$439$	11.7617	0.561355	0.280677	−	0.959802i	$-0.409441\pi$
$439$	11.7617	0.561355	0.280677	+	0.959802i	$0.409441\pi$
$440$	−3.60469	−0.171847
$441$	−31.8922	−1.51868
$442$	0.334349	0.0159034
$443$	−1.58141	−0.0751349	−0.0375674	−	0.999294i	$-0.511961\pi$
$443$	−1.58141	−0.0751349	−0.0375674	+	0.999294i	$0.511961\pi$
$444$	31.7015	1.50449
$445$	−11.6335	−0.551481
$446$	−6.38891	−0.302524
$447$	−14.9511	−0.707162
$448$	−1.28357	−0.0606431
$449$	−29.3209	−1.38374	−0.691871	−	0.722022i	$-0.743213\pi$
$449$	−29.3209	−1.38374	−0.691871	+	0.722022i	$0.743213\pi$
$450$	−11.1397	−0.525133
$451$	7.98046	0.375785
$452$	−3.65471	−0.171903
$453$	−17.8388	−0.838142
$454$	22.0566	1.03517
$455$	−0.268457	−0.0125854
$456$	10.4651	0.490073
$457$	−31.1984	−1.45940	−0.729700	−	0.683768i	$-0.760340\pi$
$457$	−31.1984	−1.45940	−0.729700	+	0.683768i	$0.760340\pi$
$458$	17.7481	0.829313
$459$	37.1015	1.73175
$460$	9.28702	0.433010
$461$	7.37616	0.343542	0.171771	−	0.985137i	$-0.445051\pi$
$461$	7.37616	0.343542	0.171771	+	0.985137i	$0.445051\pi$
$462$	−5.28373	−0.245821
$463$	23.5690	1.09534	0.547671	−	0.836694i	$-0.315514\pi$
$463$	23.5690	1.09534	0.547671	+	0.836694i	$0.315514\pi$
$464$	−6.75313	−0.313506
$465$	−66.3786	−3.07823
$466$	12.7529	0.590768
$467$	−5.07242	−0.234724	−0.117362	−	0.993089i	$-0.537444\pi$
$467$	−5.07242	−0.234724	−0.117362	+	0.993089i	$0.537444\pi$
$468$	0.475468	0.0219785
$469$	11.3055	0.522038
$470$	−4.95676	−0.228638
$471$	−45.4756	−2.09540
$472$	10.2697	0.472700
$473$	−0.442246	−0.0203345
$474$	−22.6614	−1.04087
$475$	6.53687	0.299932
$476$	5.37815	0.246507
$477$	27.0184	1.23709
$478$	4.57042	0.209046
$479$	−39.2617	−1.79391	−0.896955	−	0.442121i	$-0.854226\pi$
$479$	−39.2617	−1.79391	−0.896955	+	0.442121i	$0.854226\pi$
$480$	7.84479	0.358064
$481$	−0.845185	−0.0385371
$482$	−26.3501	−1.20021
$483$	13.6128	0.619405
$484$	−9.10850	−0.414023
$485$	−12.7382	−0.578411
$486$	−0.741200	−0.0336215
$487$	23.2516	1.05363	0.526816	−	0.849980i	$-0.323386\pi$
$487$	23.2516	1.05363	0.526816	+	0.849980i	$0.323386\pi$
$488$	2.36810	0.107199
$489$	64.2872	2.90717
$490$	14.0287	0.633751
$491$	16.7519	0.756004	0.378002	−	0.925805i	$-0.376611\pi$
$491$	16.7519	0.756004	0.378002	+	0.925805i	$0.376611\pi$
$492$	−17.3676	−0.782994
$493$	28.2955	1.27436
$494$	−0.279007	−0.0125531
$495$	21.4783	0.965380
$496$	8.46149	0.379932
$497$	−9.19307	−0.412365
$498$	−5.28350	−0.236759
$499$	−9.91429	−0.443825	−0.221912	−	0.975067i	$-0.571230\pi$
$499$	−9.91429	−0.443825	−0.221912	+	0.975067i	$0.571230\pi$
$500$	−8.20481	−0.366930
$501$	55.8511	2.49524
$502$	12.2302	0.545861
$503$	0.102424	0.00456684	0.00228342	−	0.999997i	$-0.499273\pi$
$503$	0.102424	0.00456684	0.00228342	+	0.999997i	$0.499273\pi$
$504$	7.64809	0.340673
$505$	−33.1467	−1.47501
$506$	−4.87321	−0.216641
$507$	38.8908	1.72720
$508$	21.1310	0.937537
$509$	−9.72845	−0.431206	−0.215603	−	0.976481i	$-0.569172\pi$
$509$	−9.72845	−0.431206	−0.215603	+	0.976481i	$0.569172\pi$
$510$	−32.8695	−1.45549
$511$	6.99068	0.309250
$512$	−1.00000	−0.0441942
$513$	−30.9604	−1.36693
$514$	−8.96989	−0.395645
$515$	31.2549	1.37725
$516$	0.962446	0.0423693
$517$	2.60098	0.114391
$518$	−13.5952	−0.597337
$519$	−7.92452	−0.347848
$520$	−0.209148	−0.00917174
$521$	−31.9285	−1.39881	−0.699406	−	0.714725i	$-0.746552\pi$
$521$	−31.9285	−1.39881	−0.699406	+	0.714725i	$0.746552\pi$
$522$	40.2381	1.76117
$523$	38.2295	1.67166	0.835830	−	0.548988i	$-0.184987\pi$
$523$	38.2295	1.67166	0.835830	+	0.548988i	$0.184987\pi$
$524$	8.24811	0.360321
$525$	7.18257	0.313473
$526$	−22.9826	−1.00209
$527$	−35.4535	−1.54438
$528$	−4.11642	−0.179144
$529$	−10.4448	−0.454122
$530$	−11.8848	−0.516244
$531$	−61.1913	−2.65548
$532$	−4.48795	−0.194577
$533$	0.463034	0.0200562
$534$	−13.2850	−0.574898
$535$	−25.6454	−1.10875
$536$	8.80780	0.380439
$537$	−17.4078	−0.751204
$538$	−27.1848	−1.17202
$539$	−7.36131	−0.317074
$540$	−23.2083	−0.998727
$541$	−23.3300	−1.00304	−0.501518	−	0.865147i	$-0.667225\pi$
$541$	−23.3300	−1.00304	−0.501518	+	0.865147i	$0.667225\pi$
$542$	−1.59005	−0.0682985
$543$	−47.7180	−2.04778
$544$	4.18998	0.179644
$545$	43.4061	1.85931
$546$	−0.306567	−0.0131199
$547$	−8.74383	−0.373859	−0.186930	−	0.982373i	$-0.559854\pi$
$547$	−8.74383	−0.373859	−0.186930	+	0.982373i	$0.559854\pi$
$548$	3.09295	0.132124
$549$	−14.1102	−0.602207
$550$	−2.57126	−0.109639
$551$	−23.6120	−1.00590
$552$	10.6054	0.451397
$553$	9.71834	0.413266
$554$	6.54896	0.278239
$555$	83.0892	3.52694
$556$	5.78804	0.245468
$557$	−11.9343	−0.505674	−0.252837	−	0.967509i	$-0.581364\pi$
$557$	−11.9343	−0.505674	−0.252837	+	0.967509i	$0.581364\pi$
$558$	−50.4173	−2.13433
$559$	−0.0256595	−0.00108528
$560$	−3.36423	−0.142165
$561$	17.2477	0.728199
$562$	−15.5495	−0.655914
$563$	−36.8727	−1.55400	−0.776999	−	0.629502i	$-0.783259\pi$
$563$	−36.8727	−1.55400	−0.776999	+	0.629502i	$0.783259\pi$
$564$	−5.66043	−0.238347
$565$	−9.57894	−0.402989
$566$	32.1638	1.35195
$567$	−11.0743	−0.465075
$568$	−7.16209	−0.300515
$569$	6.54540	0.274397	0.137199	−	0.990544i	$-0.456190\pi$
$569$	6.54540	0.274397	0.137199	+	0.990544i	$0.456190\pi$
$570$	27.4289	1.14887
$571$	−9.67780	−0.405004	−0.202502	−	0.979282i	$-0.564907\pi$
$571$	−9.67780	−0.405004	−0.202502	+	0.979282i	$0.564907\pi$
$572$	0.109747	0.00458875
$573$	−43.0875	−1.80001
$574$	7.44810	0.310878
$575$	6.62452	0.276262
$576$	5.95844	0.248268
$577$	−19.5759	−0.814957	−0.407479	−	0.913215i	$-0.633592\pi$
$577$	−19.5759	−0.814957	−0.407479	+	0.913215i	$0.633592\pi$
$578$	−0.555950	−0.0231245
$579$	52.4673	2.18047
$580$	−17.6999	−0.734947
$581$	2.26582	0.0940022
$582$	−14.5465	−0.602972
$583$	6.23636	0.258284
$584$	5.44627	0.225368
$585$	1.24619	0.0515238
$586$	1.97924	0.0817616
$587$	34.1540	1.40969	0.704844	−	0.709363i	$-0.251017\pi$
$587$	34.1540	1.40969	0.704844	+	0.709363i	$0.251017\pi$
$588$	16.0202	0.660662
$589$	29.5852	1.21904
$590$	26.9167	1.10814
$591$	−66.8724	−2.75076
$592$	−10.5916	−0.435314
$593$	−13.9498	−0.572850	−0.286425	−	0.958103i	$-0.592467\pi$
$593$	−13.9498	−0.572850	−0.286425	+	0.958103i	$0.592467\pi$
$594$	12.1782	0.499677
$595$	14.0961	0.577882
$596$	4.99524	0.204613
$597$	80.8717	3.30986
$598$	−0.282748	−0.0115624
$599$	−18.0422	−0.737185	−0.368593	−	0.929591i	$-0.620160\pi$
$599$	−18.0422	−0.737185	−0.368593	+	0.929591i	$0.620160\pi$
$600$	5.59576	0.228446
$601$	15.2337	0.621395	0.310698	−	0.950509i	$-0.399437\pi$
$601$	15.2337	0.621395	0.310698	+	0.950509i	$0.399437\pi$
$602$	−0.412744	−0.0168222
$603$	−52.4807	−2.13718
$604$	5.96006	0.242511
$605$	−23.8733	−0.970586
$606$	−37.8522	−1.53764
$607$	8.16480	0.331399	0.165700	−	0.986176i	$-0.447012\pi$
$607$	8.16480	0.331399	0.165700	+	0.986176i	$0.447012\pi$
$608$	−3.49645	−0.141800
$609$	−25.9443	−1.05132
$610$	6.20675	0.251304
$611$	0.150911	0.00610522
$612$	−24.9658	−1.00918
$613$	−11.2988	−0.456352	−0.228176	−	0.973620i	$-0.573276\pi$
$613$	−11.2988	−0.456352	−0.228176	+	0.973620i	$0.573276\pi$
$614$	−14.0061	−0.565240
$615$	−45.5204	−1.83556
$616$	1.76532	0.0711269
$617$	−11.6629	−0.469530	−0.234765	−	0.972052i	$-0.575432\pi$
$617$	−11.6629	−0.469530	−0.234765	+	0.972052i	$0.575432\pi$
$618$	35.6918	1.43574
$619$	−7.37342	−0.296363	−0.148181	−	0.988960i	$-0.547342\pi$
$619$	−7.37342	−0.296363	−0.148181	+	0.988960i	$0.547342\pi$
$620$	22.1775	0.890668
$621$	−31.3755	−1.25905
$622$	−16.8560	−0.675864
$623$	5.69726	0.228256
$624$	−0.238839	−0.00956120
$625$	−30.8526	−1.23410
$626$	0.292752	0.0117007
$627$	−14.3929	−0.574795
$628$	15.1936	0.606292
$629$	44.3788	1.76950
$630$	20.0456	0.798634
$631$	9.16511	0.364857	0.182429	−	0.983219i	$-0.441604\pi$
$631$	9.16511	0.364857	0.182429	+	0.983219i	$0.441604\pi$
$632$	7.57132	0.301171
$633$	−74.3220	−2.95403
$634$	4.00220	0.158948
$635$	55.3841	2.19785
$636$	−13.5720	−0.538165
$637$	−0.427111	−0.0169227
$638$	9.28770	0.367704
$639$	42.6749	1.68819
$640$	−2.62099	−0.103604
$641$	29.4047	1.16141	0.580707	−	0.814113i	$-0.302776\pi$
$641$	29.4047	1.16141	0.580707	+	0.814113i	$0.302776\pi$
$642$	−29.2861	−1.15583
$643$	−41.5761	−1.63960	−0.819800	−	0.572649i	$-0.805916\pi$
$643$	−41.5761	−1.63960	−0.819800	+	0.572649i	$0.805916\pi$
$644$	−4.54812	−0.179221
$645$	2.52256	0.0993256
$646$	14.6501	0.576399
$647$	−18.8617	−0.741530	−0.370765	−	0.928727i	$-0.620904\pi$
$647$	−18.8617	−0.741530	−0.370765	+	0.928727i	$0.620904\pi$
$648$	−8.62768	−0.338927
$649$	−14.1241	−0.554419
$650$	−0.149187	−0.00585160
$651$	32.5075	1.27407
$652$	−21.4787	−0.841171
$653$	12.3193	0.482093	0.241047	−	0.970514i	$-0.422509\pi$
$653$	12.3193	0.482093	0.241047	+	0.970514i	$0.422509\pi$
$654$	49.5681	1.93827
$655$	21.6182	0.844693
$656$	5.80263	0.226555
$657$	−32.4513	−1.26604
$658$	2.42747	0.0946327
$659$	−12.2286	−0.476358	−0.238179	−	0.971221i	$-0.576551\pi$
$659$	−12.2286	−0.476358	−0.238179	+	0.971221i	$0.576551\pi$
$660$	−10.7891	−0.419964
$661$	−8.04334	−0.312850	−0.156425	−	0.987690i	$-0.549997\pi$
$661$	−8.04334	−0.312850	−0.156425	+	0.987690i	$0.549997\pi$
$662$	17.4536	0.678352
$663$	1.00073	0.0388651
$664$	1.76525	0.0685048
$665$	−11.7629	−0.456144
$666$	63.1097	2.44545
$667$	−23.9286	−0.926517
$668$	−18.6602	−0.721984
$669$	−19.1224	−0.739316
$670$	23.0851	0.891857
$671$	−3.25689	−0.125731
$672$	−3.84182	−0.148201
$673$	16.3382	0.629790	0.314895	−	0.949127i	$-0.398031\pi$
$673$	16.3382	0.629790	0.314895	+	0.949127i	$0.398031\pi$
$674$	14.1992	0.546932
$675$	−16.5547	−0.637191
$676$	−12.9936	−0.499755
$677$	29.1365	1.11981	0.559904	−	0.828558i	$-0.310838\pi$
$677$	29.1365	1.11981	0.559904	+	0.828558i	$0.310838\pi$
$678$	−10.9388	−0.420101
$679$	6.23826	0.239402
$680$	10.9819	0.421136
$681$	66.0168	2.52977
$682$	−11.6373	−0.445613
$683$	40.6891	1.55692	0.778462	−	0.627692i	$-0.216000\pi$
$683$	40.6891	1.55692	0.778462	+	0.627692i	$0.216000\pi$
$684$	20.8334	0.796584
$685$	8.10658	0.309737
$686$	−15.8553	−0.605357
$687$	53.1212	2.02670
$688$	−0.321559	−0.0122593
$689$	0.361840	0.0137850
$690$	27.7967	1.05820
$691$	−34.9218	−1.32849	−0.664244	−	0.747516i	$-0.731246\pi$
$691$	−34.9218	−1.32849	−0.664244	+	0.747516i	$0.731246\pi$
$692$	2.64763	0.100648
$693$	−10.5186	−0.399567
$694$	36.1675	1.37290
$695$	15.1704	0.575445
$696$	−20.2125	−0.766155
$697$	−24.3129	−0.920917
$698$	−4.62979	−0.175240
$699$	38.1704	1.44374
$700$	−2.39974	−0.0907015
$701$	−4.24357	−0.160277	−0.0801387	−	0.996784i	$-0.525536\pi$
$701$	−4.24357	−0.160277	−0.0801387	+	0.996784i	$0.525536\pi$
$702$	0.706590	0.0266685
$703$	−37.0332	−1.39673
$704$	1.37532	0.0518343
$705$	−14.8359	−0.558753
$706$	32.6394	1.22840
$707$	16.2329	0.610501
$708$	30.7378	1.15520
$709$	−13.1737	−0.494748	−0.247374	−	0.968920i	$-0.579568\pi$
$709$	−13.1737	−0.494748	−0.247374	+	0.968920i	$0.579568\pi$
$710$	−18.7717	−0.704491
$711$	−45.1132	−1.69188
$712$	4.43859	0.166343
$713$	29.9819	1.12283
$714$	16.0972	0.602421
$715$	0.287645	0.0107573
$716$	5.81606	0.217356
$717$	13.6796	0.510873
$718$	−9.68917	−0.361597
$719$	−20.4845	−0.763944	−0.381972	−	0.924174i	$-0.624755\pi$
$719$	−20.4845	−0.763944	−0.381972	+	0.924174i	$0.624755\pi$
$720$	15.6170	0.582011
$721$	−15.3064	−0.570041
$722$	6.77484	0.252133
$723$	−78.8676	−2.93312
$724$	15.9429	0.592512
$725$	−12.6255	−0.468898
$726$	−27.2623	−1.01180
$727$	−33.9525	−1.25923	−0.629614	−	0.776908i	$-0.716787\pi$
$727$	−33.9525	−1.25923	−0.629614	+	0.776908i	$0.716787\pi$
$728$	0.102426	0.00379615
$729$	−28.1015	−1.04080
$730$	14.2746	0.528327
$731$	1.34732	0.0498326
$732$	7.08787	0.261975
$733$	−24.2173	−0.894487	−0.447244	−	0.894412i	$-0.647594\pi$
$733$	−24.2173	−0.894487	−0.447244	+	0.894412i	$0.647594\pi$
$734$	−19.6556	−0.725502
$735$	41.9887	1.54878
$736$	−3.54333	−0.130609
$737$	−12.1135	−0.446208
$738$	−34.5746	−1.27271
$739$	29.0001	1.06679	0.533393	−	0.845868i	$-0.320917\pi$
$739$	29.0001	1.06679	0.533393	+	0.845868i	$0.320917\pi$
$740$	−27.7606	−1.02050
$741$	−0.835087	−0.0306777
$742$	5.82034	0.213671
$743$	30.6015	1.12266	0.561330	−	0.827592i	$-0.310290\pi$
$743$	30.6015	1.12266	0.561330	+	0.827592i	$0.310290\pi$
$744$	25.3258	0.928489
$745$	13.0925	0.479671
$746$	33.8367	1.23885
$747$	−10.5181	−0.384838
$748$	−5.76256	−0.210700
$749$	12.5593	0.458907
$750$	−24.5575	−0.896714
$751$	−47.9024	−1.74798	−0.873991	−	0.485941i	$-0.838477\pi$
$751$	−47.9024	−1.74798	−0.873991	+	0.485941i	$0.838477\pi$
$752$	1.89118	0.0689643
$753$	36.6058	1.33399
$754$	0.538882	0.0196249
$755$	15.6212	0.568515
$756$	11.3658	0.413370
$757$	−43.7127	−1.58877	−0.794383	−	0.607418i	$-0.792205\pi$
$757$	−43.7127	−1.58877	−0.794383	+	0.607418i	$0.792205\pi$
$758$	21.4887	0.780503
$759$	−14.5858	−0.529432
$760$	−9.16415	−0.332419
$761$	−39.6940	−1.43891	−0.719454	−	0.694540i	$-0.755608\pi$
$761$	−39.6940	−1.43891	−0.719454	+	0.694540i	$0.755608\pi$
$762$	63.2465	2.29118
$763$	−21.2572	−0.769563
$764$	14.3958	0.520821
$765$	−65.4349	−2.36580
$766$	22.5898	0.816201
$767$	−0.819494	−0.0295902
$768$	−2.99307	−0.108003
$769$	8.30283	0.299408	0.149704	−	0.988731i	$-0.452168\pi$
$769$	8.30283	0.299408	0.149704	+	0.988731i	$0.452168\pi$
$770$	4.62689	0.166741
$771$	−26.8475	−0.966887
$772$	−17.5296	−0.630905
$773$	39.2589	1.41204	0.706022	−	0.708190i	$-0.250488\pi$
$773$	39.2589	1.41204	0.706022	+	0.708190i	$0.250488\pi$
$774$	1.91599	0.0688687
$775$	15.8194	0.568249
$776$	4.86007	0.174466
$777$	−40.6912	−1.45979
$778$	15.9843	0.573063
$779$	20.2886	0.726914
$780$	−0.625993	−0.0224142
$781$	9.85016	0.352466
$782$	14.8465	0.530909
$783$	59.7976	2.13699
$784$	−5.35244	−0.191159
$785$	39.8224	1.42132
$786$	24.6871	0.880561
$787$	−50.3496	−1.79477	−0.897384	−	0.441250i	$-0.854535\pi$
$787$	−50.3496	−1.79477	−0.897384	+	0.441250i	$0.854535\pi$
$788$	22.3424	0.795917
$789$	−68.7885	−2.44894
$790$	19.8443	0.706029
$791$	4.69108	0.166796
$792$	−8.19475	−0.291188
$793$	−0.188968	−0.00671044
$794$	14.5736	0.517199
$795$	−35.5721	−1.26161
$796$	−27.0197	−0.957687
$797$	16.6973	0.591449	0.295724	−	0.955273i	$-0.404439\pi$
$797$	16.6973	0.591449	0.295724	+	0.955273i	$0.404439\pi$
$798$	−13.4327	−0.475513
$799$	−7.92402	−0.280332
$800$	−1.86957	−0.0660994
$801$	−26.4471	−0.934462
$802$	29.4184	1.03880
$803$	−7.49036	−0.264329
$804$	26.3623	0.929727
$805$	−11.9206	−0.420145
$806$	−0.675205	−0.0237831
$807$	−81.3658	−2.86421
$808$	12.6466	0.444907
$809$	7.41572	0.260723	0.130361	−	0.991467i	$-0.458386\pi$
$809$	7.41572	0.260723	0.130361	+	0.991467i	$0.458386\pi$
$810$	−22.6130	−0.794541
$811$	20.4149	0.716863	0.358431	−	0.933556i	$-0.383312\pi$
$811$	20.4149	0.716863	0.358431	+	0.933556i	$0.383312\pi$
$812$	8.66813	0.304192
$813$	−4.75913	−0.166910
$814$	14.5669	0.510569
$815$	−56.2954	−1.97194
$816$	12.5409	0.439019
$817$	−1.12431	−0.0393347
$818$	5.18557	0.181309
$819$	−0.610298	−0.0213255
$820$	15.2086	0.531108
$821$	−0.0942290	−0.00328862	−0.00164431	−	0.999999i	$-0.500523\pi$
$821$	−0.0942290	−0.00328862	−0.00164431	+	0.999999i	$0.500523\pi$
$822$	9.25740	0.322889
$823$	−27.7765	−0.968228	−0.484114	−	0.875005i	$-0.660858\pi$
$823$	−27.7765	−0.968228	−0.484114	+	0.875005i	$0.660858\pi$
$824$	−11.9248	−0.415422
$825$	−7.69595	−0.267939
$826$	−13.1819	−0.458657
$827$	18.5431	0.644806	0.322403	−	0.946603i	$-0.395509\pi$
$827$	18.5431	0.644806	0.322403	+	0.946603i	$0.395509\pi$
$828$	21.1127	0.733718
$829$	40.2990	1.39964	0.699821	−	0.714318i	$-0.253263\pi$
$829$	40.2990	1.39964	0.699821	+	0.714318i	$0.253263\pi$
$830$	4.62669	0.160595
$831$	19.6015	0.679968
$832$	0.0797974	0.00276648
$833$	22.4266	0.777037
$834$	17.3240	0.599881
$835$	−48.9081	−1.69253
$836$	4.80873	0.166314
$837$	−74.9248	−2.58978
$838$	−6.86867	−0.237274
$839$	38.9972	1.34633	0.673166	−	0.739491i	$-0.264934\pi$
$839$	38.9972	1.34633	0.673166	+	0.739491i	$0.264934\pi$
$840$	−10.0694	−0.347426
$841$	16.6047	0.572576
$842$	26.0331	0.897159
$843$	−46.5405	−1.60294
$844$	24.8314	0.854732
$845$	−34.0561	−1.17157
$846$	−11.2685	−0.387419
$847$	11.6914	0.401722
$848$	4.53448	0.155715
$849$	96.2684	3.30392
$850$	7.83348	0.268686
$851$	−37.5297	−1.28650
$852$	−21.4366	−0.734406
$853$	−29.4379	−1.00793	−0.503967	−	0.863723i	$-0.668127\pi$
$853$	−29.4379	−1.00793	−0.503967	+	0.863723i	$0.668127\pi$
$854$	−3.03963	−0.104014
$855$	54.6040	1.86742
$856$	9.78464	0.334432
$857$	−30.7666	−1.05097	−0.525484	−	0.850803i	$-0.676116\pi$
$857$	−30.7666	−1.05097	−0.525484	+	0.850803i	$0.676116\pi$
$858$	0.328479	0.0112141
$859$	−24.6436	−0.840828	−0.420414	−	0.907332i	$-0.638115\pi$
$859$	−24.6436	−0.840828	−0.420414	+	0.907332i	$0.638115\pi$
$860$	−0.842801	−0.0287393
$861$	22.2926	0.759731
$862$	−2.86352	−0.0975317
$863$	9.05831	0.308348	0.154174	−	0.988044i	$-0.450728\pi$
$863$	9.05831	0.308348	0.154174	+	0.988044i	$0.450728\pi$
$864$	8.85480	0.301246
$865$	6.93940	0.235947
$866$	−19.5357	−0.663851
$867$	−1.66399	−0.0565122
$868$	−10.8609	−0.368645
$869$	−10.4130	−0.353236
$870$	−52.9768	−1.79608
$871$	−0.702839	−0.0238148
$872$	−16.5610	−0.560825
$873$	−28.9584	−0.980095
$874$	−12.3891	−0.419067
$875$	10.5315	0.356029
$876$	16.3010	0.550761
$877$	−8.94934	−0.302198	−0.151099	−	0.988519i	$-0.548281\pi$
$877$	−8.94934	−0.302198	−0.151099	+	0.988519i	$0.548281\pi$
$878$	−11.7617	−0.396938
$879$	5.92399	0.199811
$880$	3.60469	0.121514
$881$	−9.93640	−0.334766	−0.167383	−	0.985892i	$-0.553532\pi$
$881$	−9.93640	−0.334766	−0.167383	+	0.985892i	$0.553532\pi$
$882$	31.8922	1.07387
$883$	55.0339	1.85204	0.926019	−	0.377477i	$-0.123208\pi$
$883$	55.0339	1.85204	0.926019	+	0.377477i	$0.123208\pi$
$884$	−0.334349	−0.0112454
$885$	80.5635	2.70811
$886$	1.58141	0.0531284
$887$	22.2771	0.747991	0.373995	−	0.927431i	$-0.377988\pi$
$887$	22.2771	0.747991	0.373995	+	0.927431i	$0.377988\pi$
$888$	−31.7015	−1.06383
$889$	−27.1232	−0.909683
$890$	11.6335	0.389956
$891$	11.8658	0.397520
$892$	6.38891	0.213917
$893$	6.61242	0.221276
$894$	14.9511	0.500039
$895$	15.2438	0.509545
$896$	1.28357	0.0428812
$897$	−0.846284	−0.0282566
$898$	29.3209	0.978453
$899$	−57.1415	−1.90578
$900$	11.1397	0.371325
$901$	−18.9994	−0.632962
$902$	−7.98046	−0.265720
$903$	−1.23537	−0.0411105
$904$	3.65471	0.121554
$905$	41.7860	1.38901
$906$	17.8388	0.592656
$907$	−18.6027	−0.617691	−0.308845	−	0.951112i	$-0.599943\pi$
$907$	−18.6027	−0.617691	−0.308845	+	0.951112i	$0.599943\pi$
$908$	−22.0566	−0.731973
$909$	−75.3543	−2.49934
$910$	0.268457	0.00889925
$911$	−30.9569	−1.02565	−0.512825	−	0.858493i	$-0.671401\pi$
$911$	−30.9569	−1.02565	−0.512825	+	0.858493i	$0.671401\pi$
$912$	−10.4651	−0.346534
$913$	−2.42778	−0.0803477
$914$	31.1984	1.03195
$915$	18.5772	0.614144
$916$	−17.7481	−0.586413
$917$	−10.5871	−0.349615
$918$	−37.1015	−1.22453
$919$	−14.7228	−0.485661	−0.242831	−	0.970069i	$-0.578076\pi$
$919$	−14.7228	−0.485661	−0.242831	+	0.970069i	$0.578076\pi$
$920$	−9.28702	−0.306184
$921$	−41.9212	−1.38135
$922$	−7.37616	−0.242921
$923$	0.571516	0.0188117
$924$	5.28373	0.173822
$925$	−19.8019	−0.651081
$926$	−23.5690	−0.774524
$927$	71.0535	2.33370
$928$	6.75313	0.221682
$929$	−8.15938	−0.267701	−0.133850	−	0.991002i	$-0.542734\pi$
$929$	−8.15938	−0.267701	−0.133850	+	0.991002i	$0.542734\pi$
$930$	66.3786	2.17664
$931$	−18.7145	−0.613344
$932$	−12.7529	−0.417736
$933$	−50.4511	−1.65169
$934$	5.07242	0.165975
$935$	−15.1036	−0.493941
$936$	−0.475468	−0.0155411
$937$	24.1021	0.787383	0.393691	−	0.919243i	$-0.371198\pi$
$937$	24.1021	0.787383	0.393691	+	0.919243i	$0.371198\pi$
$938$	−11.3055	−0.369136
$939$	0.876225	0.0285945
$940$	4.95676	0.161672
$941$	−11.9701	−0.390215	−0.195107	−	0.980782i	$-0.562506\pi$
$941$	−11.9701	−0.390215	−0.195107	+	0.980782i	$0.562506\pi$
$942$	45.4756	1.48167
$943$	20.5606	0.669546
$944$	−10.2697	−0.334250
$945$	29.7896	0.969055
$946$	0.442246	0.0143786
$947$	55.7942	1.81307	0.906534	−	0.422133i	$-0.138719\pi$
$947$	55.7942	1.81307	0.906534	+	0.422133i	$0.138719\pi$
$948$	22.6614	0.736010
$949$	−0.434598	−0.0141076
$950$	−6.53687	−0.212084
$951$	11.9788	0.388441
$952$	−5.37815	−0.174307
$953$	15.4423	0.500225	0.250112	−	0.968217i	$-0.419532\pi$
$953$	15.4423	0.500225	0.250112	+	0.968217i	$0.419532\pi$
$954$	−27.0184	−0.874754
$955$	37.7312	1.22095
$956$	−4.57042	−0.147818
$957$	27.7987	0.898604
$958$	39.2617	1.26849
$959$	−3.97003	−0.128199
$960$	−7.84479	−0.253189
$961$	40.5969	1.30958
$962$	0.845185	0.0272499
$963$	−58.3012	−1.87873
$964$	26.3501	0.848680
$965$	−45.9449	−1.47902
$966$	−13.6128	−0.437986
$967$	−1.66787	−0.0536351	−0.0268175	−	0.999640i	$-0.508537\pi$
$967$	−1.66787	−0.0536351	−0.0268175	+	0.999640i	$0.508537\pi$
$968$	9.10850	0.292758
$969$	43.8486	1.40862
$970$	12.7382	0.408999
$971$	−19.6473	−0.630512	−0.315256	−	0.949007i	$-0.602090\pi$
$971$	−19.6473	−0.630512	−0.315256	+	0.949007i	$0.602090\pi$
$972$	0.741200	0.0237740
$973$	−7.42938	−0.238175
$974$	−23.2516	−0.745030
$975$	−0.446527	−0.0143003
$976$	−2.36810	−0.0758009
$977$	22.2008	0.710266	0.355133	−	0.934816i	$-0.384436\pi$
$977$	22.2008	0.710266	0.355133	+	0.934816i	$0.384436\pi$
$978$	−64.2872	−2.05568
$979$	−6.10448	−0.195100
$980$	−14.0287	−0.448130
$981$	98.6776	3.15053
$982$	−16.7519	−0.534575
$983$	−1.82881	−0.0583301	−0.0291650	−	0.999575i	$-0.509285\pi$
$983$	−1.82881	−0.0583301	−0.0291650	+	0.999575i	$0.509285\pi$
$984$	17.3676	0.553660
$985$	58.5593	1.86585
$986$	−28.2955	−0.901111
$987$	7.26558	0.231266
$988$	0.279007	0.00887641
$989$	−1.13939	−0.0362304
$990$	−21.4783	−0.682627
$991$	−23.6651	−0.751746	−0.375873	−	0.926671i	$-0.622657\pi$
$991$	−23.6651	−0.751746	−0.375873	+	0.926671i	$0.622657\pi$
$992$	−8.46149	−0.268653
$993$	52.2396	1.65777
$994$	9.19307	0.291586
$995$	−70.8182	−2.24509
$996$	5.28350	0.167414
$997$	−25.0208	−0.792417	−0.396209	−	0.918161i	$-0.629674\pi$
$997$	−25.0208	−0.792417	−0.396209	+	0.918161i	$0.629674\pi$
$998$	9.91429	0.313831
$999$	93.7869	2.96729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.c.1.4	✓	57

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.c.1.4	✓	57	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.99307 q^{3} +1.00000 q^{4} +2.62099 q^{5} +2.99307 q^{6} -1.28357 q^{7} -1.00000 q^{8} +5.95844 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.99307 q^{3} +1.00000 q^{4} +2.62099 q^{5} +2.99307 q^{6} -1.28357 q^{7} -1.00000 q^{8} +5.95844 q^{9} -2.62099 q^{10} +1.37532 q^{11} -2.99307 q^{12} +0.0797974 q^{13} +1.28357 q^{14} -7.84479 q^{15} +1.00000 q^{16} -4.18998 q^{17} -5.95844 q^{18} +3.49645 q^{19} +2.62099 q^{20} +3.84182 q^{21} -1.37532 q^{22} +3.54333 q^{23} +2.99307 q^{24} +1.86957 q^{25} -0.0797974 q^{26} -8.85480 q^{27} -1.28357 q^{28} -6.75313 q^{29} +7.84479 q^{30} +8.46149 q^{31} -1.00000 q^{32} -4.11642 q^{33} +4.18998 q^{34} -3.36423 q^{35} +5.95844 q^{36} -10.5916 q^{37} -3.49645 q^{38} -0.238839 q^{39} -2.62099 q^{40} +5.80263 q^{41} -3.84182 q^{42} -0.321559 q^{43} +1.37532 q^{44} +15.6170 q^{45} -3.54333 q^{46} +1.89118 q^{47} -2.99307 q^{48} -5.35244 q^{49} -1.86957 q^{50} +12.5409 q^{51} +0.0797974 q^{52} +4.53448 q^{53} +8.85480 q^{54} +3.60469 q^{55} +1.28357 q^{56} -10.4651 q^{57} +6.75313 q^{58} -10.2697 q^{59} -7.84479 q^{60} -2.36810 q^{61} -8.46149 q^{62} -7.64809 q^{63} +1.00000 q^{64} +0.209148 q^{65} +4.11642 q^{66} -8.80780 q^{67} -4.18998 q^{68} -10.6054 q^{69} +3.36423 q^{70} +7.16209 q^{71} -5.95844 q^{72} -5.44627 q^{73} +10.5916 q^{74} -5.59576 q^{75} +3.49645 q^{76} -1.76532 q^{77} +0.238839 q^{78} -7.57132 q^{79} +2.62099 q^{80} +8.62768 q^{81} -5.80263 q^{82} -1.76525 q^{83} +3.84182 q^{84} -10.9819 q^{85} +0.321559 q^{86} +20.2125 q^{87} -1.37532 q^{88} -4.43859 q^{89} -15.6170 q^{90} -0.102426 q^{91} +3.54333 q^{92} -25.3258 q^{93} -1.89118 q^{94} +9.16415 q^{95} +2.99307 q^{96} -4.86007 q^{97} +5.35244 q^{98} +8.19475 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9}+O(q^{10}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9	\( 57 q - 57 q^{2} - 5 q^{3} + 57 q^{4} - 15 q^{5} + 5 q^{6} - 28 q^{7} - 57 q^{8} + 50 q^{9} + 15 q^{10} + 13 q^{11} - 5 q^{12} - 43 q^{13} + 28 q^{14} - 10 q^{15} + 57 q^{16} - 50 q^{18} - 6 q^{19} - 15 q^{20} - 23 q^{21} - 13 q^{22} - q^{23} + 5 q^{24} + 20 q^{25} + 43 q^{26} - 20 q^{27} - 28 q^{28} - 4 q^{29} + 10 q^{30} - 34 q^{31} - 57 q^{32} - 43 q^{33} + 26 q^{35} + 50 q^{36} - 64 q^{37} + 6 q^{38} + 8 q^{39} + 15 q^{40} + 27 q^{41} + 23 q^{42} - 29 q^{43} + 13 q^{44} - 76 q^{45} + q^{46} - 25 q^{47} - 5 q^{48} + 7 q^{49} - 20 q^{50} + 27 q^{51} - 43 q^{52} - 34 q^{53} + 20 q^{54} - 36 q^{55} + 28 q^{56} - 33 q^{57} + 4 q^{58} + 19 q^{59} - 10 q^{60} - 58 q^{61} + 34 q^{62} - 65 q^{63} + 57 q^{64} + 17 q^{65} + 43 q^{66} - 84 q^{67} - 33 q^{69} - 26 q^{70} + 22 q^{71} - 50 q^{72} - 82 q^{73} + 64 q^{74} + 8 q^{75} - 6 q^{76} - 41 q^{77} - 8 q^{78} + 8 q^{79} - 15 q^{80} + 25 q^{81} - 27 q^{82} - 23 q^{83} - 23 q^{84} - 58 q^{85} + 29 q^{86} - 17 q^{87} - 13 q^{88} + 18 q^{89} + 76 q^{90} - 4 q^{91} - q^{92} - 60 q^{93} + 25 q^{94} + 36 q^{95} + 5 q^{96} - 156 q^{97} - 7 q^{98} + 25 q^{99}+O(q^{100}) \) 57 * q - 57 * q^2 - 5 * q^3 + 57 * q^4 - 15 * q^5 + 5 * q^6 - 28 * q^7 - 57 * q^8 + 50 * q^9 + 15 * q^10 + 13 * q^11 - 5 * q^12 - 43 * q^13 + 28 * q^14 - 10 * q^15 + 57 * q^16 - 50 * q^18 - 6 * q^19 - 15 * q^20 - 23 * q^21 - 13 * q^22 - q^23 + 5 * q^24 + 20 * q^25 + 43 * q^26 - 20 * q^27 - 28 * q^28 - 4 * q^29 + 10 * q^30 - 34 * q^31 - 57 * q^32 - 43 * q^33 + 26 * q^35 + 50 * q^36 - 64 * q^37 + 6 * q^38 + 8 * q^39 + 15 * q^40 + 27 * q^41 + 23 * q^42 - 29 * q^43 + 13 * q^44 - 76 * q^45 + q^46 - 25 * q^47 - 5 * q^48 + 7 * q^49 - 20 * q^50 + 27 * q^51 - 43 * q^52 - 34 * q^53 + 20 * q^54 - 36 * q^55 + 28 * q^56 - 33 * q^57 + 4 * q^58 + 19 * q^59 - 10 * q^60 - 58 * q^61 + 34 * q^62 - 65 * q^63 + 57 * q^64 + 17 * q^65 + 43 * q^66 - 84 * q^67 - 33 * q^69 - 26 * q^70 + 22 * q^71 - 50 * q^72 - 82 * q^73 + 64 * q^74 + 8 * q^75 - 6 * q^76 - 41 * q^77 - 8 * q^78 + 8 * q^79 - 15 * q^80 + 25 * q^81 - 27 * q^82 - 23 * q^83 - 23 * q^84 - 58 * q^85 + 29 * q^86 - 17 * q^87 - 13 * q^88 + 18 * q^89 + 76 * q^90 - 4 * q^91 - q^92 - 60 * q^93 + 25 * q^94 + 36 * q^95 + 5 * q^96 - 156 * q^97 - 7 * q^98 + 25 * q^99

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