LMFDB - Embedded newform 6023.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.95928 q^{2} +1.09252 q^{3} +1.83878 q^{4} +1.35010 q^{5} -2.14055 q^{6} +3.30535 q^{7} +0.315883 q^{8} -1.80641 q^{9} +O(q^{10})$	\(q-1.95928 q^{2} +1.09252 q^{3} +1.83878 q^{4} +1.35010 q^{5} -2.14055 q^{6} +3.30535 q^{7} +0.315883 q^{8} -1.80641 q^{9} -2.64522 q^{10} -1.41714 q^{11} +2.00889 q^{12} -1.08653 q^{13} -6.47611 q^{14} +1.47501 q^{15} -4.29645 q^{16} +0.206874 q^{17} +3.53925 q^{18} -1.00000 q^{19} +2.48253 q^{20} +3.61116 q^{21} +2.77657 q^{22} -2.29702 q^{23} +0.345108 q^{24} -3.17723 q^{25} +2.12882 q^{26} -5.25108 q^{27} +6.07781 q^{28} +3.93219 q^{29} -2.88995 q^{30} -1.07866 q^{31} +7.78619 q^{32} -1.54825 q^{33} -0.405325 q^{34} +4.46256 q^{35} -3.32157 q^{36} -2.28592 q^{37} +1.95928 q^{38} -1.18706 q^{39} +0.426474 q^{40} -10.0767 q^{41} -7.07527 q^{42} +8.76642 q^{43} -2.60580 q^{44} -2.43883 q^{45} +4.50051 q^{46} -0.177489 q^{47} -4.69395 q^{48} +3.92537 q^{49} +6.22508 q^{50} +0.226014 q^{51} -1.99789 q^{52} +7.11912 q^{53} +10.2883 q^{54} -1.91328 q^{55} +1.04411 q^{56} -1.09252 q^{57} -7.70426 q^{58} -8.86463 q^{59} +2.71221 q^{60} -1.63279 q^{61} +2.11339 q^{62} -5.97081 q^{63} -6.66241 q^{64} -1.46693 q^{65} +3.03345 q^{66} +3.90385 q^{67} +0.380396 q^{68} -2.50954 q^{69} -8.74339 q^{70} -5.36832 q^{71} -0.570613 q^{72} -10.3438 q^{73} +4.47876 q^{74} -3.47118 q^{75} -1.83878 q^{76} -4.68414 q^{77} +2.32577 q^{78} -7.59418 q^{79} -5.80064 q^{80} -0.317683 q^{81} +19.7430 q^{82} +5.04706 q^{83} +6.64011 q^{84} +0.279301 q^{85} -17.1759 q^{86} +4.29599 q^{87} -0.447650 q^{88} +15.1720 q^{89} +4.77834 q^{90} -3.59137 q^{91} -4.22371 q^{92} -1.17845 q^{93} +0.347751 q^{94} -1.35010 q^{95} +8.50655 q^{96} +0.326395 q^{97} -7.69089 q^{98} +2.55993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * 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 $

$2$	−1.95928	−1.38542	−0.692710	−	0.721216i	$-0.743583\pi$
$2$	−1.95928	−1.38542	−0.692710	+	0.721216i	$0.743583\pi$
$3$	1.09252	0.630765	0.315383	−	0.948965i	$-0.397867\pi$
$3$	1.09252	0.630765	0.315383	+	0.948965i	$0.397867\pi$
$4$	1.83878	0.919388
$5$	1.35010	0.603783	0.301891	−	0.953342i	$-0.402382\pi$
$5$	1.35010	0.603783	0.301891	+	0.953342i	$0.402382\pi$
$6$	−2.14055	−0.873875
$7$	3.30535	1.24931	0.624653	−	0.780902i	$-0.285240\pi$
$7$	3.30535	1.24931	0.624653	+	0.780902i	$0.285240\pi$
$8$	0.315883	0.111682
$9$	−1.80641	−0.602135
$10$	−2.64522	−0.836493
$11$	−1.41714	−0.427283	−0.213642	−	0.976912i	$-0.568532\pi$
$11$	−1.41714	−0.427283	−0.213642	+	0.976912i	$0.568532\pi$
$12$	2.00889	0.579918
$13$	−1.08653	−0.301350	−0.150675	−	0.988583i	$-0.548145\pi$
$13$	−1.08653	−0.301350	−0.150675	+	0.988583i	$0.548145\pi$
$14$	−6.47611	−1.73081
$15$	1.47501	0.380845
$16$	−4.29645	−1.07411
$17$	0.206874	0.0501744	0.0250872	−	0.999685i	$-0.492014\pi$
$17$	0.206874	0.0501744	0.0250872	+	0.999685i	$0.492014\pi$
$18$	3.53925	0.834210
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.48253	0.555111
$21$	3.61116	0.788019
$22$	2.77657	0.591966
$23$	−2.29702	−0.478962	−0.239481	−	0.970901i	$-0.576977\pi$
$23$	−2.29702	−0.478962	−0.239481	+	0.970901i	$0.576977\pi$
$24$	0.345108	0.0704448
$25$	−3.17723	−0.635446
$26$	2.12882	0.417496
$27$	−5.25108	−1.01057
$28$	6.07781	1.14860
$29$	3.93219	0.730189	0.365095	−	0.930970i	$-0.381037\pi$
$29$	3.93219	0.730189	0.365095	+	0.930970i	$0.381037\pi$
$30$	−2.88995	−0.527630
$31$	−1.07866	−0.193732	−0.0968662	−	0.995297i	$-0.530882\pi$
$31$	−1.07866	−0.193732	−0.0968662	+	0.995297i	$0.530882\pi$
$32$	7.78619	1.37642
$33$	−1.54825	−0.269515
$34$	−0.405325	−0.0695126
$35$	4.46256	0.754310
$36$	−3.32157	−0.553596
$37$	−2.28592	−0.375803	−0.187901	−	0.982188i	$-0.560169\pi$
$37$	−2.28592	−0.375803	−0.187901	+	0.982188i	$0.560169\pi$
$38$	1.95928	0.317837
$39$	−1.18706	−0.190081
$40$	0.426474	0.0674314
$41$	−10.0767	−1.57371	−0.786855	−	0.617138i	$-0.788292\pi$
$41$	−10.0767	−1.57371	−0.786855	+	0.617138i	$0.788292\pi$
$42$	−7.07527	−1.09174
$43$	8.76642	1.33687	0.668433	−	0.743772i	$-0.266965\pi$
$43$	8.76642	1.33687	0.668433	+	0.743772i	$0.266965\pi$
$44$	−2.60580	−0.392839
$45$	−2.43883	−0.363559
$46$	4.50051	0.663563
$47$	−0.177489	−0.0258895	−0.0129447	−	0.999916i	$-0.504121\pi$
$47$	−0.177489	−0.0258895	−0.0129447	+	0.999916i	$0.504121\pi$
$48$	−4.69395	−0.677514
$49$	3.92537	0.560767
$50$	6.22508	0.880360
$51$	0.226014	0.0316483
$52$	−1.99789	−0.277057
$53$	7.11912	0.977887	0.488943	−	0.872315i	$-0.337382\pi$
$53$	7.11912	0.977887	0.488943	+	0.872315i	$0.337382\pi$
$54$	10.2883	1.40007
$55$	−1.91328	−0.257986
$56$	1.04411	0.139524
$57$	−1.09252	−0.144707
$58$	−7.70426	−1.01162
$59$	−8.86463	−1.15408	−0.577038	−	0.816717i	$-0.695792\pi$
$59$	−8.86463	−1.15408	−0.577038	+	0.816717i	$0.695792\pi$
$60$	2.71221	0.350144
$61$	−1.63279	−0.209057	−0.104529	−	0.994522i	$-0.533333\pi$
$61$	−1.63279	−0.209057	−0.104529	+	0.994522i	$0.533333\pi$
$62$	2.11339	0.268401
$63$	−5.97081	−0.752251
$64$	−6.66241	−0.832801
$65$	−1.46693	−0.181950
$66$	3.03345	0.373392
$67$	3.90385	0.476932	0.238466	−	0.971151i	$-0.423355\pi$
$67$	3.90385	0.476932	0.238466	+	0.971151i	$0.423355\pi$
$68$	0.380396	0.0461298
$69$	−2.50954	−0.302113
$70$	−8.74339	−1.04504
$71$	−5.36832	−0.637102	−0.318551	−	0.947906i	$-0.603196\pi$
$71$	−5.36832	−0.637102	−0.318551	+	0.947906i	$0.603196\pi$
$72$	−0.570613	−0.0672474
$73$	−10.3438	−1.21065	−0.605325	−	0.795978i	$-0.706957\pi$
$73$	−10.3438	−1.21065	−0.605325	+	0.795978i	$0.706957\pi$
$74$	4.47876	0.520645
$75$	−3.47118	−0.400818
$76$	−1.83878	−0.210922
$77$	−4.68414	−0.533807
$78$	2.32577	0.263342
$79$	−7.59418	−0.854413	−0.427206	−	0.904154i	$-0.640502\pi$
$79$	−7.59418	−0.854413	−0.427206	+	0.904154i	$0.640502\pi$
$80$	−5.80064	−0.648531
$81$	−0.317683	−0.0352981
$82$	19.7430	2.18025
$83$	5.04706	0.553987	0.276994	−	0.960872i	$-0.410662\pi$
$83$	5.04706	0.553987	0.276994	+	0.960872i	$0.410662\pi$
$84$	6.64011	0.724495
$85$	0.279301	0.0302944
$86$	−17.1759	−1.85212
$87$	4.29599	0.460578
$88$	−0.447650	−0.0477196
$89$	15.1720	1.60823	0.804113	−	0.594477i	$-0.202641\pi$
$89$	15.1720	1.60823	0.804113	+	0.594477i	$0.202641\pi$
$90$	4.77834	0.503682
$91$	−3.59137	−0.376478
$92$	−4.22371	−0.440352
$93$	−1.17845	−0.122200
$94$	0.347751	0.0358678
$95$	−1.35010	−0.138517
$96$	8.50655	0.868196
$97$	0.326395	0.0331404	0.0165702	−	0.999863i	$-0.494725\pi$
$97$	0.326395	0.0331404	0.0165702	+	0.999863i	$0.494725\pi$
$98$	−7.69089	−0.776897
$99$	2.55993	0.257282
$100$	−5.84222	−0.584222
$101$	−8.43482	−0.839296	−0.419648	−	0.907687i	$-0.637847\pi$
$101$	−8.43482	−0.839296	−0.419648	+	0.907687i	$0.637847\pi$
$102$	−0.442824	−0.0438462
$103$	1.22447	0.120651	0.0603254	−	0.998179i	$-0.480786\pi$
$103$	1.22447	0.120651	0.0603254	+	0.998179i	$0.480786\pi$
$104$	−0.343217	−0.0336552
$105$	4.87542	0.475792
$106$	−13.9484	−1.35478
$107$	−6.20596	−0.599952	−0.299976	−	0.953947i	$-0.596979\pi$
$107$	−6.20596	−0.599952	−0.299976	+	0.953947i	$0.596979\pi$
$108$	−9.65556	−0.929107
$109$	−11.0781	−1.06109	−0.530544	−	0.847657i	$-0.678012\pi$
$109$	−11.0781	−1.06109	−0.530544	+	0.847657i	$0.678012\pi$
$110$	3.74864	0.357419
$111$	−2.49741	−0.237043
$112$	−14.2013	−1.34190
$113$	−4.03396	−0.379483	−0.189741	−	0.981834i	$-0.560765\pi$
$113$	−4.03396	−0.379483	−0.189741	+	0.981834i	$0.560765\pi$
$114$	2.14055	0.200481
$115$	−3.10121	−0.289189
$116$	7.23042	0.671327
$117$	1.96272	0.181453
$118$	17.3683	1.59888
$119$	0.683793	0.0626832
$120$	0.465930	0.0425334
$121$	−8.99172	−0.817429
$122$	3.19909	0.289632
$123$	−11.0089	−0.992642
$124$	−1.98341	−0.178115
$125$	−11.0401	−0.987454
$126$	11.6985	1.04218
$127$	−13.2846	−1.17882	−0.589409	−	0.807835i	$-0.700639\pi$
$127$	−13.2846	−1.17882	−0.589409	+	0.807835i	$0.700639\pi$
$128$	−2.51885	−0.222637
$129$	9.57747	0.843249
$130$	2.87412	0.252077
$131$	−16.7920	−1.46713	−0.733563	−	0.679622i	$-0.762144\pi$
$131$	−16.7920	−1.46713	−0.733563	+	0.679622i	$0.762144\pi$
$132$	−2.84688	−0.247789
$133$	−3.30535	−0.286611
$134$	−7.64874	−0.660751
$135$	−7.08948	−0.610166
$136$	0.0653481	0.00560356
$137$	−7.63686	−0.652461	−0.326231	−	0.945290i	$-0.605779\pi$
$137$	−7.63686	−0.652461	−0.326231	+	0.945290i	$0.605779\pi$
$138$	4.91688	0.418553
$139$	−21.0840	−1.78832	−0.894162	−	0.447743i	$-0.852228\pi$
$139$	−21.0840	−1.78832	−0.894162	+	0.447743i	$0.852228\pi$
$140$	8.20564	0.693503
$141$	−0.193910	−0.0163302
$142$	10.5180	0.882653
$143$	1.53977	0.128762
$144$	7.76114	0.646762
$145$	5.30885	0.440876
$146$	20.2664	1.67726
$147$	4.28853	0.353712
$148$	−4.20329	−0.345509
$149$	14.9169	1.22204	0.611021	−	0.791615i	$-0.290759\pi$
$149$	14.9169	1.22204	0.611021	+	0.791615i	$0.290759\pi$
$150$	6.80101	0.555300
$151$	20.8606	1.69761	0.848806	−	0.528705i	$-0.177322\pi$
$151$	20.8606	1.69761	0.848806	+	0.528705i	$0.177322\pi$
$152$	−0.315883	−0.0256215
$153$	−0.373699	−0.0302118
$154$	9.17754	0.739547
$155$	−1.45629	−0.116972
$156$	−2.18273	−0.174758
$157$	0.966394	0.0771266	0.0385633	−	0.999256i	$-0.487722\pi$
$157$	0.966394	0.0771266	0.0385633	+	0.999256i	$0.487722\pi$
$158$	14.8791	1.18372
$159$	7.77777	0.616817
$160$	10.5121	0.831057
$161$	−7.59247	−0.598370
$162$	0.622429	0.0489027
$163$	8.34446	0.653589	0.326794	−	0.945095i	$-0.394032\pi$
$163$	8.34446	0.653589	0.326794	+	0.945095i	$0.394032\pi$
$164$	−18.5287	−1.44685
$165$	−2.09029	−0.162729
$166$	−9.88861	−0.767505
$167$	8.37398	0.647998	0.323999	−	0.946057i	$-0.394973\pi$
$167$	8.37398	0.647998	0.323999	+	0.946057i	$0.394973\pi$
$168$	1.14070	0.0880072
$169$	−11.8194	−0.909188
$170$	−0.547229	−0.0419705
$171$	1.80641	0.138139
$172$	16.1195	1.22910
$173$	−9.66201	−0.734589	−0.367295	−	0.930105i	$-0.619716\pi$
$173$	−9.66201	−0.734589	−0.367295	+	0.930105i	$0.619716\pi$
$174$	−8.41704	−0.638094
$175$	−10.5019	−0.793867
$176$	6.08867	0.458951
$177$	−9.68477	−0.727952
$178$	−29.7261	−2.22807
$179$	−3.63403	−0.271620	−0.135810	−	0.990735i	$-0.543364\pi$
$179$	−3.63403	−0.271620	−0.135810	+	0.990735i	$0.543364\pi$
$180$	−4.48446	−0.334252
$181$	0.636349	0.0472994	0.0236497	−	0.999720i	$-0.492471\pi$
$181$	0.636349	0.0472994	0.0236497	+	0.999720i	$0.492471\pi$
$182$	7.03651	0.521581
$183$	−1.78385	−0.131866
$184$	−0.725590	−0.0534912
$185$	−3.08622	−0.226903
$186$	2.30892	0.169298
$187$	−0.293170	−0.0214387
$188$	−0.326363	−0.0238025
$189$	−17.3567	−1.26251
$190$	2.64522	0.191905
$191$	−15.6053	−1.12916	−0.564581	−	0.825377i	$-0.690962\pi$
$191$	−15.6053	−1.12916	−0.564581	+	0.825377i	$0.690962\pi$
$192$	−7.27880	−0.525302
$193$	13.9641	1.00516	0.502578	−	0.864532i	$-0.332385\pi$
$193$	13.9641	1.00516	0.502578	+	0.864532i	$0.332385\pi$
$194$	−0.639500	−0.0459134
$195$	−1.60264	−0.114768
$196$	7.21787	0.515562
$197$	15.8403	1.12858	0.564288	−	0.825578i	$-0.309151\pi$
$197$	15.8403	1.12858	0.564288	+	0.825578i	$0.309151\pi$
$198$	−5.01561	−0.356444
$199$	0.692954	0.0491222	0.0245611	−	0.999698i	$-0.492181\pi$
$199$	0.692954	0.0491222	0.0245611	+	0.999698i	$0.492181\pi$
$200$	−1.00363	−0.0709676
$201$	4.26503	0.300832
$202$	16.5262	1.16278
$203$	12.9973	0.912230
$204$	0.415589	0.0290970
$205$	−13.6045	−0.950179
$206$	−2.39908	−0.167152
$207$	4.14935	0.288400
$208$	4.66824	0.323684
$209$	1.41714	0.0980255
$210$	−9.55231	−0.659172
$211$	−14.7828	−1.01769	−0.508844	−	0.860859i	$-0.669927\pi$
$211$	−14.7828	−1.01769	−0.508844	+	0.860859i	$0.669927\pi$
$212$	13.0905	0.899057
$213$	−5.86498	−0.401862
$214$	12.1592	0.831186
$215$	11.8355	0.807177
$216$	−1.65873	−0.112862
$217$	−3.56534	−0.242031
$218$	21.7051	1.47005
$219$	−11.3008	−0.763636
$220$	−3.51809	−0.237189
$221$	−0.224776	−0.0151201
$222$	4.89312	0.328405
$223$	−10.2385	−0.685621	−0.342811	−	0.939405i	$-0.611379\pi$
$223$	−10.2385	−0.685621	−0.342811	+	0.939405i	$0.611379\pi$
$224$	25.7361	1.71957
$225$	5.73937	0.382625
$226$	7.90365	0.525743
$227$	2.60023	0.172583	0.0862917	−	0.996270i	$-0.472498\pi$
$227$	2.60023	0.172583	0.0862917	+	0.996270i	$0.472498\pi$
$228$	−2.00889	−0.133042
$229$	−4.16679	−0.275349	−0.137675	−	0.990478i	$-0.543963\pi$
$229$	−4.16679	−0.275349	−0.137675	+	0.990478i	$0.543963\pi$
$230$	6.07613	0.400648
$231$	−5.11751	−0.336707
$232$	1.24211	0.0815487
$233$	17.2285	1.12867	0.564337	−	0.825544i	$-0.309132\pi$
$233$	17.2285	1.12867	0.564337	+	0.825544i	$0.309132\pi$
$234$	−3.84551	−0.251389
$235$	−0.239628	−0.0156316
$236$	−16.3001	−1.06104
$237$	−8.29678	−0.538934
$238$	−1.33974	−0.0868426
$239$	−13.7896	−0.891973	−0.445987	−	0.895040i	$-0.647147\pi$
$239$	−13.7896	−0.891973	−0.445987	+	0.895040i	$0.647147\pi$
$240$	−6.33730	−0.409071
$241$	−23.4523	−1.51070	−0.755348	−	0.655323i	$-0.772532\pi$
$241$	−23.4523	−1.51070	−0.755348	+	0.655323i	$0.772532\pi$
$242$	17.6173	1.13248
$243$	15.4062	0.988306
$244$	−3.00233	−0.192205
$245$	5.29963	0.338581
$246$	21.5696	1.37523
$247$	1.08653	0.0691344
$248$	−0.340729	−0.0216363
$249$	5.51400	0.349436
$250$	21.6306	1.36804
$251$	19.4600	1.22831	0.614153	−	0.789187i	$-0.289498\pi$
$251$	19.4600	1.22831	0.614153	+	0.789187i	$0.289498\pi$
$252$	−10.9790	−0.691611
$253$	3.25519	0.204652
$254$	26.0283	1.63316
$255$	0.305141	0.0191087
$256$	18.2600	1.14125
$257$	9.70056	0.605104	0.302552	−	0.953133i	$-0.402161\pi$
$257$	9.70056	0.605104	0.302552	+	0.953133i	$0.402161\pi$
$258$	−18.7649	−1.16825
$259$	−7.55578	−0.469493
$260$	−2.69735	−0.167283
$261$	−7.10313	−0.439673
$262$	32.9002	2.03258
$263$	29.8241	1.83903	0.919516	−	0.393053i	$-0.128581\pi$
$263$	29.8241	1.83903	0.919516	+	0.393053i	$0.128581\pi$
$264$	−0.489065	−0.0300999
$265$	9.61152	0.590431
$266$	6.47611	0.397076
$267$	16.5756	1.01441
$268$	7.17831	0.438485
$269$	2.46262	0.150149	0.0750744	−	0.997178i	$-0.476081\pi$
$269$	2.46262	0.150149	0.0750744	+	0.997178i	$0.476081\pi$
$270$	13.8903	0.845335
$271$	−15.7138	−0.954544	−0.477272	−	0.878756i	$-0.658374\pi$
$271$	−15.7138	−0.954544	−0.477272	+	0.878756i	$0.658374\pi$
$272$	−0.888827	−0.0538930
$273$	−3.92364	−0.237469
$274$	14.9627	0.903933
$275$	4.50257	0.271515
$276$	−4.61447	−0.277759
$277$	14.2146	0.854070	0.427035	−	0.904235i	$-0.359558\pi$
$277$	14.2146	0.854070	0.427035	+	0.904235i	$0.359558\pi$
$278$	41.3095	2.47758
$279$	1.94849	0.116653
$280$	1.40965	0.0842425
$281$	10.3988	0.620341	0.310170	−	0.950681i	$-0.399614\pi$
$281$	10.3988	0.620341	0.310170	+	0.950681i	$0.399614\pi$
$282$	0.379924	0.0226241
$283$	−13.5063	−0.802867	−0.401434	−	0.915888i	$-0.631488\pi$
$283$	−13.5063	−0.802867	−0.401434	+	0.915888i	$0.631488\pi$
$284$	−9.87113	−0.585744
$285$	−1.47501	−0.0873719
$286$	−3.01683	−0.178389
$287$	−33.3069	−1.96605
$288$	−14.0650	−0.828789
$289$	−16.9572	−0.997483
$290$	−10.4015	−0.610798
$291$	0.356593	0.0209038
$292$	−19.0199	−1.11306
$293$	1.48763	0.0869083	0.0434541	−	0.999055i	$-0.486164\pi$
$293$	1.48763	0.0869083	0.0434541	+	0.999055i	$0.486164\pi$
$294$	−8.40243	−0.490040
$295$	−11.9681	−0.696812
$296$	−0.722083	−0.0419703
$297$	7.44151	0.431800
$298$	−29.2264	−1.69304
$299$	2.49579	0.144335
$300$	−6.38272	−0.368507
$301$	28.9761	1.67016
$302$	−40.8717	−2.35190
$303$	−9.21519	−0.529399
$304$	4.29645	0.246419
$305$	−2.20443	−0.126225
$306$	0.732181	0.0418560
$307$	7.14367	0.407711	0.203855	−	0.979001i	$-0.434653\pi$
$307$	7.14367	0.407711	0.203855	+	0.979001i	$0.434653\pi$
$308$	−8.61309	−0.490776
$309$	1.33776	0.0761024
$310$	2.85329	0.162056
$311$	11.1425	0.631831	0.315916	−	0.948787i	$-0.397688\pi$
$311$	11.1425	0.631831	0.315916	+	0.948787i	$0.397688\pi$
$312$	−0.374971	−0.0212285
$313$	23.4691	1.32655	0.663276	−	0.748375i	$-0.269165\pi$
$313$	23.4691	1.32655	0.663276	+	0.748375i	$0.269165\pi$
$314$	−1.89344	−0.106853
$315$	−8.06119	−0.454196
$316$	−13.9640	−0.785537
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−15.2388	−0.854551
$319$	−5.57245	−0.311997
$320$	−8.99492	−0.502831
$321$	−6.78012	−0.378429
$322$	14.8758	0.828994
$323$	−0.206874	−0.0115108
$324$	−0.584148	−0.0324526
$325$	3.45217	0.191492
$326$	−16.3491	−0.905495
$327$	−12.1030	−0.669298
$328$	−3.18305	−0.175754
$329$	−0.586665	−0.0323439
$330$	4.09546	0.225448
$331$	−14.2958	−0.785766	−0.392883	−	0.919589i	$-0.628522\pi$
$331$	−14.2958	−0.785766	−0.392883	+	0.919589i	$0.628522\pi$
$332$	9.28042	0.509329
$333$	4.12930	0.226284
$334$	−16.4070	−0.897749
$335$	5.27059	0.287963
$336$	−15.5152	−0.846422
$337$	15.9290	0.867708	0.433854	−	0.900983i	$-0.357153\pi$
$337$	15.9290	0.867708	0.433854	+	0.900983i	$0.357153\pi$
$338$	23.1576	1.25961
$339$	−4.40717	−0.239364
$340$	0.513572	0.0278524
$341$	1.52861	0.0827786
$342$	−3.53925	−0.191381
$343$	−10.1628	−0.548737
$344$	2.76916	0.149303
$345$	−3.38812	−0.182410
$346$	18.9306	1.01771
$347$	−12.0200	−0.645266	−0.322633	−	0.946524i	$-0.604568\pi$
$347$	−12.0200	−0.645266	−0.322633	+	0.946524i	$0.604568\pi$
$348$	7.89936	0.423450
$349$	−20.8762	−1.11748	−0.558739	−	0.829344i	$-0.688714\pi$
$349$	−20.8762	−1.11748	−0.558739	+	0.829344i	$0.688714\pi$
$350$	20.5761	1.09984
$351$	5.70547	0.304536
$352$	−11.0341	−0.588120
$353$	−20.8151	−1.10788	−0.553939	−	0.832557i	$-0.686876\pi$
$353$	−20.8151	−1.10788	−0.553939	+	0.832557i	$0.686876\pi$
$354$	18.9752	1.00852
$355$	−7.24776	−0.384671
$356$	27.8978	1.47858
$357$	0.747056	0.0395384
$358$	7.12008	0.376308
$359$	−14.0575	−0.741928	−0.370964	−	0.928647i	$-0.620973\pi$
$359$	−14.0575	−0.741928	−0.370964	+	0.928647i	$0.620973\pi$
$360$	−0.770384	−0.0406028
$361$	1.00000	0.0526316
$362$	−1.24679	−0.0655296
$363$	−9.82361	−0.515606
$364$	−6.60373	−0.346130
$365$	−13.9652	−0.730970
$366$	3.49506	0.182690
$367$	6.86269	0.358229	0.179115	−	0.983828i	$-0.442677\pi$
$367$	6.86269	0.358229	0.179115	+	0.983828i	$0.442677\pi$
$368$	9.86905	0.514460
$369$	18.2025	0.947586
$370$	6.04677	0.314356
$371$	23.5312	1.22168
$372$	−2.16691	−0.112349
$373$	−5.93413	−0.307257	−0.153629	−	0.988129i	$-0.549096\pi$
$373$	−5.93413	−0.307257	−0.153629	+	0.988129i	$0.549096\pi$
$374$	0.574401	0.0297016
$375$	−12.0615	−0.622852
$376$	−0.0560658	−0.00289138
$377$	−4.27245	−0.220042
$378$	34.0066	1.74911
$379$	−9.97409	−0.512335	−0.256167	−	0.966632i	$-0.582460\pi$
$379$	−9.97409	−0.512335	−0.256167	+	0.966632i	$0.582460\pi$
$380$	−2.48253	−0.127351
$381$	−14.5137	−0.743558
$382$	30.5752	1.56436
$383$	−9.02950	−0.461386	−0.230693	−	0.973027i	$-0.574099\pi$
$383$	−9.02950	−0.461386	−0.230693	+	0.973027i	$0.574099\pi$
$384$	−2.75189	−0.140432
$385$	−6.32406	−0.322304
$386$	−27.3595	−1.39256
$387$	−15.8357	−0.804975
$388$	0.600168	0.0304689
$389$	−12.2856	−0.622906	−0.311453	−	0.950262i	$-0.600816\pi$
$389$	−12.2856	−0.622906	−0.311453	+	0.950262i	$0.600816\pi$
$390$	3.14003	0.159001
$391$	−0.475195	−0.0240316
$392$	1.23996	0.0626273
$393$	−18.3456	−0.925412
$394$	−31.0356	−1.56355
$395$	−10.2529	−0.515880
$396$	4.70713	0.236542
$397$	−26.5271	−1.33136	−0.665679	−	0.746238i	$-0.731858\pi$
$397$	−26.5271	−1.33136	−0.665679	+	0.746238i	$0.731858\pi$
$398$	−1.35769	−0.0680549
$399$	−3.61116	−0.180784
$400$	13.6508	0.682542
$401$	16.6067	0.829299	0.414650	−	0.909981i	$-0.363904\pi$
$401$	16.6067	0.829299	0.414650	+	0.909981i	$0.363904\pi$
$402$	−8.35638	−0.416779
$403$	1.17200	0.0583813
$404$	−15.5098	−0.771639
$405$	−0.428903	−0.0213124
$406$	−25.4653	−1.26382
$407$	3.23946	0.160574
$408$	0.0713940	0.00353453
$409$	8.32216	0.411504	0.205752	−	0.978604i	$-0.434036\pi$
$409$	8.32216	0.411504	0.205752	+	0.978604i	$0.434036\pi$
$410$	26.6550	1.31640
$411$	−8.34341	−0.411550
$412$	2.25153	0.110925
$413$	−29.3007	−1.44180
$414$	−8.12974	−0.399555
$415$	6.81404	0.334488
$416$	−8.45995	−0.414783
$417$	−23.0347	−1.12801
$418$	−2.77657	−0.135806
$419$	3.26974	0.159737	0.0798687	−	0.996805i	$-0.474550\pi$
$419$	3.26974	0.159737	0.0798687	+	0.996805i	$0.474550\pi$
$420$	8.96481	0.437438
$421$	−36.7913	−1.79310	−0.896548	−	0.442946i	$-0.853933\pi$
$421$	−36.7913	−1.79310	−0.896548	+	0.442946i	$0.853933\pi$
$422$	28.9636	1.40993
$423$	0.320618	0.0155890
$424$	2.24881	0.109212
$425$	−0.657288	−0.0318832
$426$	11.4911	0.556747
$427$	−5.39695	−0.261177
$428$	−11.4114	−0.551589
$429$	1.68222	0.0812184
$430$	−23.1891	−1.11828
$431$	38.2369	1.84181	0.920904	−	0.389790i	$-0.127452\pi$
$431$	38.2369	1.84181	0.920904	+	0.389790i	$0.127452\pi$
$432$	22.5610	1.08547
$433$	27.5835	1.32558	0.662788	−	0.748807i	$-0.269373\pi$
$433$	27.5835	1.32558	0.662788	+	0.748807i	$0.269373\pi$
$434$	6.98550	0.335315
$435$	5.80001	0.278089
$436$	−20.3701	−0.975552
$437$	2.29702	0.109881
$438$	22.1414	1.05796
$439$	−20.1410	−0.961277	−0.480639	−	0.876919i	$-0.659595\pi$
$439$	−20.1410	−0.961277	−0.480639	+	0.876919i	$0.659595\pi$
$440$	−0.604372	−0.0288123
$441$	−7.09080	−0.337657
$442$	0.440399	0.0209476
$443$	25.1639	1.19557	0.597787	−	0.801655i	$-0.296047\pi$
$443$	25.1639	1.19557	0.597787	+	0.801655i	$0.296047\pi$
$444$	−4.59217	−0.217935
$445$	20.4837	0.971019
$446$	20.0601	0.949873
$447$	16.2970	0.770821
$448$	−22.0216	−1.04042
$449$	−17.7979	−0.839935	−0.419967	−	0.907539i	$-0.637958\pi$
$449$	−17.7979	−0.839935	−0.419967	+	0.907539i	$0.637958\pi$
$450$	−11.2450	−0.530096
$451$	14.2800	0.672420
$452$	−7.41754	−0.348892
$453$	22.7906	1.07079
$454$	−5.09458	−0.239100
$455$	−4.84871	−0.227311
$456$	−0.345108	−0.0161612
$457$	5.26763	0.246409	0.123205	−	0.992381i	$-0.460683\pi$
$457$	5.26763	0.246409	0.123205	+	0.992381i	$0.460683\pi$
$458$	8.16390	0.381474
$459$	−1.08631	−0.0507048
$460$	−5.70242	−0.265877
$461$	−25.6696	−1.19555	−0.597776	−	0.801663i	$-0.703949\pi$
$461$	−25.6696	−1.19555	−0.597776	+	0.801663i	$0.703949\pi$
$462$	10.0266	0.466481
$463$	20.6569	0.960007	0.480004	−	0.877266i	$-0.340635\pi$
$463$	20.6569	0.960007	0.480004	+	0.877266i	$0.340635\pi$
$464$	−16.8945	−0.784306
$465$	−1.59103	−0.0737821
$466$	−33.7554	−1.56369
$467$	34.5045	1.59668	0.798340	−	0.602208i	$-0.205712\pi$
$467$	34.5045	1.59668	0.798340	+	0.602208i	$0.205712\pi$
$468$	3.60900	0.166826
$469$	12.9036	0.595834
$470$	0.469498	0.0216563
$471$	1.05580	0.0486488
$472$	−2.80019	−0.128889
$473$	−12.4232	−0.571221
$474$	16.2557	0.746650
$475$	3.17723	0.145781
$476$	1.25734	0.0576302
$477$	−12.8600	−0.588820
$478$	27.0176	1.23576
$479$	32.6560	1.49209	0.746045	−	0.665896i	$-0.231951\pi$
$479$	32.6560	1.49209	0.746045	+	0.665896i	$0.231951\pi$
$480$	11.4847	0.524202
$481$	2.48373	0.113248
$482$	45.9497	2.09295
$483$	−8.29490	−0.377431
$484$	−16.5338	−0.751535
$485$	0.440666	0.0200096
$486$	−30.1850	−1.36922
$487$	26.9587	1.22161	0.610807	−	0.791780i	$-0.290845\pi$
$487$	26.9587	1.22161	0.610807	+	0.791780i	$0.290845\pi$
$488$	−0.515771	−0.0233478
$489$	9.11647	0.412261
$490$	−10.3835	−0.469077
$491$	−28.1663	−1.27113	−0.635564	−	0.772048i	$-0.719232\pi$
$491$	−28.1663	−1.27113	−0.635564	+	0.772048i	$0.719232\pi$
$492$	−20.2430	−0.912623
$493$	0.813469	0.0366368
$494$	−2.12882	−0.0957802
$495$	3.45615	0.155343
$496$	4.63440	0.208091
$497$	−17.7442	−0.795935
$498$	−10.8035	−0.484115
$499$	−22.8390	−1.02241	−0.511207	−	0.859458i	$-0.670801\pi$
$499$	−22.8390	−1.02241	−0.511207	+	0.859458i	$0.670801\pi$
$500$	−20.3002	−0.907854
$501$	9.14872	0.408735
$502$	−38.1277	−1.70172
$503$	6.32814	0.282158	0.141079	−	0.989998i	$-0.454943\pi$
$503$	6.32814	0.282158	0.141079	+	0.989998i	$0.454943\pi$
$504$	−1.88608	−0.0840126
$505$	−11.3879	−0.506753
$506$	−6.37784	−0.283529
$507$	−12.9130	−0.573484
$508$	−24.4274	−1.08379
$509$	8.44673	0.374395	0.187197	−	0.982322i	$-0.440060\pi$
$509$	8.44673	0.374395	0.187197	+	0.982322i	$0.440060\pi$
$510$	−0.597857	−0.0264736
$511$	−34.1899	−1.51247
$512$	−30.7387	−1.35847
$513$	5.25108	0.231841
$514$	−19.0061	−0.838323
$515$	1.65316	0.0728469
$516$	17.6108	0.775273
$517$	0.251527	0.0110621
$518$	14.8039	0.650445
$519$	−10.5559	−0.463353
$520$	−0.463377	−0.0203204
$521$	32.4555	1.42190	0.710951	−	0.703241i	$-0.248265\pi$
$521$	32.4555	1.42190	0.710951	+	0.703241i	$0.248265\pi$
$522$	13.9170	0.609131
$523$	4.73071	0.206860	0.103430	−	0.994637i	$-0.467018\pi$
$523$	4.73071	0.206860	0.103430	+	0.994637i	$0.467018\pi$
$524$	−30.8767	−1.34886
$525$	−11.4735	−0.500744
$526$	−58.4337	−2.54783
$527$	−0.223147	−0.00972041
$528$	6.65198	0.289490
$529$	−17.7237	−0.770595
$530$	−18.8317	−0.817995
$531$	16.0131	0.694910
$532$	−6.07781	−0.263506
$533$	10.9486	0.474237
$534$	−32.4763	−1.40539
$535$	−8.37866	−0.362241
$536$	1.23316	0.0532645
$537$	−3.97024	−0.171329
$538$	−4.82496	−0.208019
$539$	−5.56278	−0.239606
$540$	−13.0360	−0.560979
$541$	−0.870463	−0.0374241	−0.0187121	−	0.999825i	$-0.505957\pi$
$541$	−0.870463	−0.0374241	−0.0187121	+	0.999825i	$0.505957\pi$
$542$	30.7877	1.32244
$543$	0.695222	0.0298348
$544$	1.61076	0.0690609
$545$	−14.9565	−0.640667
$546$	7.68751	0.328995
$547$	−2.52665	−0.108032	−0.0540159	−	0.998540i	$-0.517202\pi$
$547$	−2.52665	−0.108032	−0.0540159	+	0.998540i	$0.517202\pi$
$548$	−14.0425	−0.599865
$549$	2.94948	0.125881
$550$	−8.82180	−0.376163
$551$	−3.93219	−0.167517
$552$	−0.792720	−0.0337404
$553$	−25.1015	−1.06742
$554$	−27.8503	−1.18325
$555$	−3.37175	−0.143123
$556$	−38.7688	−1.64416
$557$	−28.2554	−1.19722	−0.598609	−	0.801041i	$-0.704280\pi$
$557$	−28.2554	−1.19722	−0.598609	+	0.801041i	$0.704280\pi$
$558$	−3.81764	−0.161614
$559$	−9.52500	−0.402865
$560$	−19.1732	−0.810214
$561$	−0.320293	−0.0135228
$562$	−20.3742	−0.859433
$563$	−28.9467	−1.21996	−0.609979	−	0.792417i	$-0.708822\pi$
$563$	−28.9467	−1.21996	−0.609979	+	0.792417i	$0.708822\pi$
$564$	−0.356557	−0.0150138
$565$	−5.44624	−0.229125
$566$	26.4627	1.11231
$567$	−1.05005	−0.0440981
$568$	−1.69576	−0.0711525
$569$	24.2234	1.01550	0.507749	−	0.861505i	$-0.330478\pi$
$569$	24.2234	1.01550	0.507749	+	0.861505i	$0.330478\pi$
$570$	2.88995	0.121047
$571$	−9.16192	−0.383414	−0.191707	−	0.981452i	$-0.561402\pi$
$571$	−9.16192	−0.383414	−0.191707	+	0.981452i	$0.561402\pi$
$572$	2.83128	0.118382
$573$	−17.0491	−0.712237
$574$	65.2576	2.72380
$575$	7.29817	0.304355
$576$	12.0350	0.501459
$577$	35.5549	1.48017	0.740086	−	0.672513i	$-0.234785\pi$
$577$	35.5549	1.48017	0.740086	+	0.672513i	$0.234785\pi$
$578$	33.2239	1.38193
$579$	15.2560	0.634017
$580$	9.76178	0.405336
$581$	16.6823	0.692100
$582$	−0.698665	−0.0289606
$583$	−10.0888	−0.417834
$584$	−3.26743	−0.135207
$585$	2.64986	0.109558
$586$	−2.91468	−0.120404
$587$	14.0418	0.579568	0.289784	−	0.957092i	$-0.406416\pi$
$587$	14.0418	0.579568	0.289784	+	0.957092i	$0.406416\pi$
$588$	7.88565	0.325199
$589$	1.07866	0.0444453
$590$	23.4489	0.965377
$591$	17.3058	0.711867
$592$	9.82135	0.403655
$593$	4.86700	0.199864	0.0999318	−	0.994994i	$-0.468138\pi$
$593$	4.86700	0.199864	0.0999318	+	0.994994i	$0.468138\pi$
$594$	−14.5800	−0.598224
$595$	0.923189	0.0378471
$596$	27.4289	1.12353
$597$	0.757064	0.0309846
$598$	−4.88995	−0.199965
$599$	−24.7783	−1.01241	−0.506207	−	0.862412i	$-0.668953\pi$
$599$	−24.7783	−1.01241	−0.506207	+	0.862412i	$0.668953\pi$
$600$	−1.09649	−0.0447639
$601$	9.44860	0.385417	0.192708	−	0.981256i	$-0.438273\pi$
$601$	9.44860	0.385417	0.192708	+	0.981256i	$0.438273\pi$
$602$	−56.7723	−2.31387
$603$	−7.05194	−0.287177
$604$	38.3580	1.56076
$605$	−12.1397	−0.493550
$606$	18.0551	0.733440
$607$	−21.7500	−0.882804	−0.441402	−	0.897309i	$-0.645519\pi$
$607$	−21.7500	−0.882804	−0.441402	+	0.897309i	$0.645519\pi$
$608$	−7.78619	−0.315772
$609$	14.1998	0.575403
$610$	4.31909	0.174875
$611$	0.192848	0.00780179
$612$	−0.687149	−0.0277763
$613$	−40.6741	−1.64281	−0.821406	−	0.570344i	$-0.806810\pi$
$613$	−40.6741	−1.64281	−0.821406	+	0.570344i	$0.806810\pi$
$614$	−13.9964	−0.564850
$615$	−14.8631	−0.599340
$616$	−1.47964	−0.0596164
$617$	−15.8428	−0.637808	−0.318904	−	0.947787i	$-0.603315\pi$
$617$	−15.8428	−0.637808	−0.318904	+	0.947787i	$0.603315\pi$
$618$	−2.62104	−0.105434
$619$	−20.8158	−0.836658	−0.418329	−	0.908296i	$-0.637384\pi$
$619$	−20.8158	−0.836658	−0.418329	+	0.908296i	$0.637384\pi$
$620$	−2.67780	−0.107543
$621$	12.0618	0.484025
$622$	−21.8312	−0.875351
$623$	50.1487	2.00917
$624$	5.10013	0.204169
$625$	0.980961	0.0392384
$626$	−45.9825	−1.83783
$627$	1.54825	0.0618311
$628$	1.77698	0.0709093
$629$	−0.472898	−0.0188557
$630$	15.7941	0.629253
$631$	4.70719	0.187390	0.0936950	−	0.995601i	$-0.470132\pi$
$631$	4.70719	0.187390	0.0936950	+	0.995601i	$0.470132\pi$
$632$	−2.39887	−0.0954221
$633$	−16.1504	−0.641922
$634$	1.95928	0.0778129
$635$	−17.9355	−0.711750
$636$	14.3016	0.567094
$637$	−4.26504	−0.168987
$638$	10.9180	0.432247
$639$	9.69735	0.383621
$640$	−3.40070	−0.134425
$641$	36.0110	1.42235	0.711175	−	0.703015i	$-0.248163\pi$
$641$	36.0110	1.42235	0.711175	+	0.703015i	$0.248163\pi$
$642$	13.2841	0.524283
$643$	7.47568	0.294812	0.147406	−	0.989076i	$-0.452908\pi$
$643$	7.47568	0.294812	0.147406	+	0.989076i	$0.452908\pi$
$644$	−13.9608	−0.550134
$645$	12.9305	0.509139
$646$	0.405325	0.0159473
$647$	5.01812	0.197283	0.0986413	−	0.995123i	$-0.468550\pi$
$647$	5.01812	0.197283	0.0986413	+	0.995123i	$0.468550\pi$
$648$	−0.100351	−0.00394215
$649$	12.5624	0.493117
$650$	−6.76376	−0.265296
$651$	−3.89520	−0.152665
$652$	15.3436	0.600901
$653$	2.78281	0.108900	0.0544498	−	0.998517i	$-0.482660\pi$
$653$	2.78281	0.108900	0.0544498	+	0.998517i	$0.482660\pi$
$654$	23.7132	0.927258
$655$	−22.6709	−0.885825
$656$	43.2939	1.69034
$657$	18.6851	0.728975
$658$	1.14944	0.0448098
$659$	−19.2027	−0.748030	−0.374015	−	0.927423i	$-0.622019\pi$
$659$	−19.2027	−0.748030	−0.374015	+	0.927423i	$0.622019\pi$
$660$	−3.84357	−0.149611
$661$	−0.771891	−0.0300231	−0.0150115	−	0.999887i	$-0.504779\pi$
$661$	−0.771891	−0.0300231	−0.0150115	+	0.999887i	$0.504779\pi$
$662$	28.0094	1.08862
$663$	−0.245571	−0.00953721
$664$	1.59428	0.0618701
$665$	−4.46256	−0.173051
$666$	−8.09045	−0.313499
$667$	−9.03232	−0.349733
$668$	15.3979	0.595761
$669$	−11.1857	−0.432466
$670$	−10.3266	−0.398950
$671$	2.31389	0.0893267
$672$	28.1172	1.08464
$673$	−28.2625	−1.08944	−0.544720	−	0.838618i	$-0.683364\pi$
$673$	−28.2625	−1.08944	−0.544720	+	0.838618i	$0.683364\pi$
$674$	−31.2094	−1.20214
$675$	16.6839	0.642164
$676$	−21.7333	−0.835897
$677$	27.6614	1.06311	0.531556	−	0.847023i	$-0.321607\pi$
$677$	27.6614	1.06311	0.531556	+	0.847023i	$0.321607\pi$
$678$	8.63487	0.331620
$679$	1.07885	0.0414026
$680$	0.0882265	0.00338333
$681$	2.84080	0.108860
$682$	−2.99496	−0.114683
$683$	−14.6514	−0.560621	−0.280311	−	0.959909i	$-0.590437\pi$
$683$	−14.6514	−0.560621	−0.280311	+	0.959909i	$0.590437\pi$
$684$	3.32157	0.127004
$685$	−10.3105	−0.393945
$686$	19.9117	0.760231
$687$	−4.55229	−0.173681
$688$	−37.6645	−1.43595
$689$	−7.73516	−0.294686
$690$	6.63828	0.252715
$691$	−19.3766	−0.737121	−0.368560	−	0.929604i	$-0.620149\pi$
$691$	−19.3766	−0.737121	−0.368560	+	0.929604i	$0.620149\pi$
$692$	−17.7663	−0.675373
$693$	8.46146	0.321424
$694$	23.5505	0.893964
$695$	−28.4655	−1.07976
$696$	1.35703	0.0514381
$697$	−2.08460	−0.0789600
$698$	40.9023	1.54817
$699$	18.8224	0.711929
$700$	−19.3106	−0.729872
$701$	−51.8637	−1.95887	−0.979433	−	0.201772i	$-0.935330\pi$
$701$	−51.8637	−1.95887	−0.979433	+	0.201772i	$0.935330\pi$
$702$	−11.1786	−0.421910
$703$	2.28592	0.0862151
$704$	9.44155	0.355842
$705$	−0.261798	−0.00985988
$706$	40.7827	1.53488
$707$	−27.8801	−1.04854
$708$	−17.8081	−0.669270
$709$	24.6515	0.925805	0.462903	−	0.886409i	$-0.346808\pi$
$709$	24.6515	0.925805	0.462903	+	0.886409i	$0.346808\pi$
$710$	14.2004	0.532931
$711$	13.7182	0.514472
$712$	4.79257	0.179609
$713$	2.47770	0.0927905
$714$	−1.46369	−0.0547773
$715$	2.07884	0.0777441
$716$	−6.68217	−0.249724
$717$	−15.0653	−0.562626
$718$	27.5426	1.02788
$719$	−16.3896	−0.611229	−0.305615	−	0.952155i	$-0.598862\pi$
$719$	−16.3896	−0.611229	−0.305615	+	0.952155i	$0.598862\pi$
$720$	10.4783	0.390504
$721$	4.04732	0.150730
$722$	−1.95928	−0.0729168
$723$	−25.6221	−0.952895
$724$	1.17010	0.0434865
$725$	−12.4935	−0.463996
$726$	19.2472	0.714331
$727$	−17.7282	−0.657502	−0.328751	−	0.944417i	$-0.606628\pi$
$727$	−17.7282	−0.657502	−0.328751	+	0.944417i	$0.606628\pi$
$728$	−1.13445	−0.0420457
$729$	17.7846	0.658687
$730$	27.3616	1.01270
$731$	1.81355	0.0670765
$732$	−3.28010	−0.121236
$733$	4.28168	0.158148	0.0790738	−	0.996869i	$-0.474804\pi$
$733$	4.28168	0.158148	0.0790738	+	0.996869i	$0.474804\pi$
$734$	−13.4459	−0.496298
$735$	5.78994	0.213565
$736$	−17.8850	−0.659251
$737$	−5.53230	−0.203785
$738$	−35.6639	−1.31280
$739$	−22.8692	−0.841258	−0.420629	−	0.907233i	$-0.638191\pi$
$739$	−22.8692	−0.841258	−0.420629	+	0.907233i	$0.638191\pi$
$740$	−5.67487	−0.208612
$741$	1.18706	0.0436076
$742$	−46.1042	−1.69254
$743$	−26.0113	−0.954264	−0.477132	−	0.878832i	$-0.658324\pi$
$743$	−26.0113	−0.954264	−0.477132	+	0.878832i	$0.658324\pi$
$744$	−0.372253	−0.0136475
$745$	20.1393	0.737848
$746$	11.6266	0.425680
$747$	−9.11704	−0.333575
$748$	−0.539073	−0.0197105
$749$	−20.5129	−0.749524
$750$	23.6318	0.862911
$751$	−27.6445	−1.00876	−0.504380	−	0.863482i	$-0.668279\pi$
$751$	−27.6445	−1.00876	−0.504380	+	0.863482i	$0.668279\pi$
$752$	0.762575	0.0278082
$753$	21.2604	0.774773
$754$	8.37093	0.304851
$755$	28.1639	1.02499
$756$	−31.9151	−1.16074
$757$	−17.3556	−0.630802	−0.315401	−	0.948959i	$-0.602139\pi$
$757$	−17.3556	−0.630802	−0.315401	+	0.948959i	$0.602139\pi$
$758$	19.5420	0.709799
$759$	3.55636	0.129088
$760$	−0.426474	−0.0154698
$761$	12.3745	0.448577	0.224288	−	0.974523i	$-0.427994\pi$
$761$	12.3745	0.448577	0.224288	+	0.974523i	$0.427994\pi$
$762$	28.4363	1.03014
$763$	−36.6170	−1.32562
$764$	−28.6947	−1.03814
$765$	−0.504531	−0.0182414
$766$	17.6913	0.639213
$767$	9.63171	0.347781
$768$	19.9493	0.719859
$769$	−14.9409	−0.538784	−0.269392	−	0.963031i	$-0.586823\pi$
$769$	−14.9409	−0.538784	−0.269392	+	0.963031i	$0.586823\pi$
$770$	12.3906	0.446526
$771$	10.5980	0.381679
$772$	25.6768	0.924128
$773$	−16.1533	−0.580992	−0.290496	−	0.956876i	$-0.593820\pi$
$773$	−16.1533	−0.580992	−0.290496	+	0.956876i	$0.593820\pi$
$774$	31.0266	1.11523
$775$	3.42714	0.123107
$776$	0.103103	0.00370117
$777$	−8.25482	−0.296140
$778$	24.0710	0.862987
$779$	10.0767	0.361034
$780$	−2.94690	−0.105516
$781$	7.60764	0.272223
$782$	0.931040	0.0332939
$783$	−20.6482	−0.737908
$784$	−16.8652	−0.602327
$785$	1.30473	0.0465677
$786$	35.9441	1.28208
$787$	8.65422	0.308490	0.154245	−	0.988033i	$-0.450706\pi$
$787$	8.65422	0.308490	0.154245	+	0.988033i	$0.450706\pi$
$788$	29.1268	1.03760
$789$	32.5833	1.16000
$790$	20.0883	0.714710
$791$	−13.3337	−0.474090
$792$	0.808637	0.0287337
$793$	1.77408	0.0629994
$794$	51.9740	1.84449
$795$	10.5008	0.372424
$796$	1.27419	0.0451624
$797$	25.9918	0.920677	0.460339	−	0.887743i	$-0.347728\pi$
$797$	25.9918	0.920677	0.460339	+	0.887743i	$0.347728\pi$
$798$	7.07527	0.250462
$799$	−0.0367180	−0.00129899
$800$	−24.7385	−0.874639
$801$	−27.4067	−0.968369
$802$	−32.5372	−1.14893
$803$	14.6586	0.517290
$804$	7.84243	0.276581
$805$	−10.2506	−0.361286
$806$	−2.29627	−0.0808826
$807$	2.69046	0.0947086
$808$	−2.66442	−0.0937339
$809$	−11.2645	−0.396037	−0.198019	−	0.980198i	$-0.563451\pi$
$809$	−11.2645	−0.396037	−0.198019	+	0.980198i	$0.563451\pi$
$810$	0.840342	0.0295266
$811$	−32.6225	−1.14553	−0.572766	−	0.819719i	$-0.694130\pi$
$811$	−32.6225	−1.14553	−0.572766	+	0.819719i	$0.694130\pi$
$812$	23.8991	0.838693
$813$	−17.1676	−0.602093
$814$	−6.34701	−0.222463
$815$	11.2659	0.394626
$816$	−0.971059	−0.0339939
$817$	−8.76642	−0.306698
$818$	−16.3054	−0.570106
$819$	6.48748	0.226691
$820$	−25.0156	−0.873583
$821$	−35.7329	−1.24709	−0.623544	−	0.781788i	$-0.714308\pi$
$821$	−35.7329	−1.24709	−0.623544	+	0.781788i	$0.714308\pi$
$822$	16.3471	0.570169
$823$	−44.1765	−1.53990	−0.769948	−	0.638107i	$-0.779718\pi$
$823$	−44.1765	−1.53990	−0.769948	+	0.638107i	$0.779718\pi$
$824$	0.386790	0.0134745
$825$	4.91914	0.171263
$826$	57.4084	1.99749
$827$	−3.54828	−0.123386	−0.0616928	−	0.998095i	$-0.519650\pi$
$827$	−3.54828	−0.123386	−0.0616928	+	0.998095i	$0.519650\pi$
$828$	7.62973	0.265151
$829$	45.0046	1.56308	0.781538	−	0.623858i	$-0.214436\pi$
$829$	45.0046	1.56308	0.781538	+	0.623858i	$0.214436\pi$
$830$	−13.3506	−0.463406
$831$	15.5297	0.538718
$832$	7.23893	0.250965
$833$	0.812058	0.0281361
$834$	45.1314	1.56277
$835$	11.3057	0.391250
$836$	2.60580	0.0901234
$837$	5.66412	0.195780
$838$	−6.40634	−0.221303
$839$	9.67733	0.334099	0.167049	−	0.985949i	$-0.446576\pi$
$839$	9.67733	0.334099	0.167049	+	0.985949i	$0.446576\pi$
$840$	1.54006	0.0531372
$841$	−13.5379	−0.466824
$842$	72.0844	2.48419
$843$	11.3609	0.391290
$844$	−27.1822	−0.935650
$845$	−15.9574	−0.548952
$846$	−0.628179	−0.0215972
$847$	−29.7208	−1.02122
$848$	−30.5870	−1.05036
$849$	−14.7559	−0.506421
$850$	1.28781	0.0441715
$851$	5.25081	0.179995
$852$	−10.7844	−0.369467
$853$	3.44644	0.118004	0.0590019	−	0.998258i	$-0.481208\pi$
$853$	3.44644	0.118004	0.0590019	+	0.998258i	$0.481208\pi$
$854$	10.5741	0.361839
$855$	2.43883	0.0834061
$856$	−1.96036	−0.0670036
$857$	53.9772	1.84383	0.921913	−	0.387398i	$-0.126626\pi$
$857$	53.9772	1.84383	0.921913	+	0.387398i	$0.126626\pi$
$858$	−3.29594	−0.112522
$859$	−21.2518	−0.725103	−0.362551	−	0.931964i	$-0.618094\pi$
$859$	−21.2518	−0.725103	−0.362551	+	0.931964i	$0.618094\pi$
$860$	21.7629	0.742109
$861$	−36.3884	−1.24011
$862$	−74.9168	−2.55168
$863$	−26.4634	−0.900823	−0.450412	−	0.892821i	$-0.648723\pi$
$863$	−26.4634	−0.900823	−0.450412	+	0.892821i	$0.648723\pi$
$864$	−40.8859	−1.39097
$865$	−13.0447	−0.443532
$866$	−54.0437	−1.83648
$867$	−18.5260	−0.629177
$868$	−6.55587	−0.222521
$869$	10.7620	0.365076
$870$	−11.3638	−0.385270
$871$	−4.24167	−0.143723
$872$	−3.49938	−0.118504
$873$	−0.589602	−0.0199550
$874$	−4.50051	−0.152232
$875$	−36.4914	−1.23363
$876$	−20.7796	−0.702078
$877$	−52.9999	−1.78968	−0.894840	−	0.446387i	$-0.852710\pi$
$877$	−52.9999	−1.78968	−0.894840	+	0.446387i	$0.852710\pi$
$878$	39.4618	1.33177
$879$	1.62526	0.0548187
$880$	8.22031	0.277106
$881$	−42.6380	−1.43651	−0.718255	−	0.695780i	$-0.755059\pi$
$881$	−42.6380	−1.43651	−0.718255	+	0.695780i	$0.755059\pi$
$882$	13.8929	0.467797
$883$	−7.80742	−0.262740	−0.131370	−	0.991333i	$-0.541938\pi$
$883$	−7.80742	−0.262740	−0.131370	+	0.991333i	$0.541938\pi$
$884$	−0.413312	−0.0139012
$885$	−13.0754	−0.439525
$886$	−49.3031	−1.65637
$887$	16.7371	0.561978	0.280989	−	0.959711i	$-0.409338\pi$
$887$	16.7371	0.561978	0.280989	+	0.959711i	$0.409338\pi$
$888$	−0.788889	−0.0264734
$889$	−43.9103	−1.47271
$890$	−40.1332	−1.34527
$891$	0.450200	0.0150823
$892$	−18.8263	−0.630352
$893$	0.177489	0.00593945
$894$	−31.9304	−1.06791
$895$	−4.90630	−0.164000
$896$	−8.32570	−0.278142
$897$	2.72669	0.0910416
$898$	34.8711	1.16366
$899$	−4.24148	−0.141461
$900$	10.5534	0.351780
$901$	1.47276	0.0490649
$902$	−27.9785	−0.931584
$903$	31.6569	1.05348
$904$	−1.27426	−0.0423812
$905$	0.859134	0.0285586
$906$	−44.6531	−1.48350
$907$	21.6370	0.718443	0.359222	−	0.933252i	$-0.383042\pi$
$907$	21.6370	0.718443	0.359222	+	0.933252i	$0.383042\pi$
$908$	4.78124	0.158671
$909$	15.2367	0.505370
$910$	9.49998	0.314921
$911$	38.4160	1.27278	0.636389	−	0.771368i	$-0.280427\pi$
$911$	38.4160	1.27278	0.636389	+	0.771368i	$0.280427\pi$
$912$	4.69395	0.155432
$913$	−7.15238	−0.236709
$914$	−10.3208	−0.341380
$915$	−2.40838	−0.0796185
$916$	−7.66179	−0.253153
$917$	−55.5036	−1.83289
$918$	2.12839	0.0702475
$919$	19.4972	0.643152	0.321576	−	0.946884i	$-0.395787\pi$
$919$	19.4972	0.643152	0.321576	+	0.946884i	$0.395787\pi$
$920$	−0.979619	−0.0322971
$921$	7.80458	0.257170
$922$	50.2939	1.65634
$923$	5.83285	0.191991
$924$	−9.40995	−0.309565
$925$	7.26290	0.238803
$926$	−40.4726	−1.33001
$927$	−2.21189	−0.0726481
$928$	30.6168	1.00504
$929$	58.8023	1.92924	0.964620	−	0.263645i	$-0.0849247\pi$
$929$	58.8023	1.92924	0.964620	+	0.263645i	$0.0849247\pi$
$930$	3.11727	0.102219
$931$	−3.92537	−0.128649
$932$	31.6793	1.03769
$933$	12.1733	0.398537
$934$	−67.6040	−2.21207
$935$	−0.395808	−0.0129443
$936$	0.619989	0.0202650
$937$	10.8334	0.353911	0.176955	−	0.984219i	$-0.443375\pi$
$937$	10.8334	0.353911	0.176955	+	0.984219i	$0.443375\pi$
$938$	−25.2818	−0.825480
$939$	25.6404	0.836743
$940$	−0.440622	−0.0143715
$941$	28.4602	0.927775	0.463888	−	0.885894i	$-0.346454\pi$
$941$	28.4602	0.927775	0.463888	+	0.885894i	$0.346454\pi$
$942$	−2.06861	−0.0673990
$943$	23.1463	0.753747
$944$	38.0865	1.23961
$945$	−23.4333	−0.762284
$946$	24.3406	0.791380
$947$	−10.1038	−0.328330	−0.164165	−	0.986433i	$-0.552493\pi$
$947$	−10.1038	−0.328330	−0.164165	+	0.986433i	$0.552493\pi$
$948$	−15.2559	−0.495489
$949$	11.2389	0.364829
$950$	−6.22508	−0.201968
$951$	−1.09252	−0.0354273
$952$	0.215999	0.00700056
$953$	33.0190	1.06959	0.534795	−	0.844982i	$-0.320389\pi$
$953$	33.0190	1.06959	0.534795	+	0.844982i	$0.320389\pi$
$954$	25.1964	0.815763
$955$	−21.0688	−0.681769
$956$	−25.3559	−0.820069
$957$	−6.08800	−0.196797
$958$	−63.9822	−2.06717
$959$	−25.2425	−0.815124
$960$	−9.82710	−0.317168
$961$	−29.8365	−0.962468
$962$	−4.86631	−0.156896
$963$	11.2105	0.361252
$964$	−43.1236	−1.38892
$965$	18.8529	0.606896
$966$	16.2520	0.522901
$967$	9.35160	0.300727	0.150364	−	0.988631i	$-0.451956\pi$
$967$	9.35160	0.300727	0.150364	+	0.988631i	$0.451956\pi$
$968$	−2.84033	−0.0912917
$969$	−0.226014	−0.00726061
$970$	−0.863388	−0.0277217
$971$	−32.0250	−1.02773	−0.513866	−	0.857871i	$-0.671787\pi$
$971$	−32.0250	−1.02773	−0.513866	+	0.857871i	$0.671787\pi$
$972$	28.3285	0.908637
$973$	−69.6902	−2.23417
$974$	−52.8195	−1.69245
$975$	3.77155	0.120786
$976$	7.01521	0.224551
$977$	−3.79725	−0.121485	−0.0607423	−	0.998153i	$-0.519347\pi$
$977$	−3.79725	−0.121485	−0.0607423	+	0.998153i	$0.519347\pi$
$978$	−17.8617	−0.571155
$979$	−21.5008	−0.687167
$980$	9.74484	0.311287
$981$	20.0115	0.638919
$982$	55.1857	1.76105
$983$	12.8516	0.409904	0.204952	−	0.978772i	$-0.434296\pi$
$983$	12.8516	0.409904	0.204952	+	0.978772i	$0.434296\pi$
$984$	−3.47753	−0.110860
$985$	21.3860	0.681415
$986$	−1.59381	−0.0507574
$987$	−0.640942	−0.0204014
$988$	1.99789	0.0635613
$989$	−20.1367	−0.640308
$990$	−6.77157	−0.215215
$991$	−3.54322	−0.112554	−0.0562770	−	0.998415i	$-0.517923\pi$
$991$	−3.54322	−0.112554	−0.0562770	+	0.998415i	$0.517923\pi$
$992$	−8.39863	−0.266657
$993$	−15.6184	−0.495634
$994$	34.7658	1.10270
$995$	0.935557	0.0296591
$996$	10.1390	0.321267
$997$	−13.6204	−0.431363	−0.215681	−	0.976464i	$-0.569197\pi$
$997$	−13.6204	−0.431363	−0.215681	+	0.976464i	$0.569197\pi$
$998$	44.7480	1.41647
$999$	12.0036	0.379776

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.18	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.18	✓	99	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-1.95928 q^{2} +1.09252 q^{3} +1.83878 q^{4} +1.35010 q^{5} -2.14055 q^{6} +3.30535 q^{7} +0.315883 q^{8} -1.80641 q^{9} +O(q^{10})\)	\(q-1.95928 q^{2} +1.09252 q^{3} +1.83878 q^{4} +1.35010 q^{5} -2.14055 q^{6} +3.30535 q^{7} +0.315883 q^{8} -1.80641 q^{9} -2.64522 q^{10} -1.41714 q^{11} +2.00889 q^{12} -1.08653 q^{13} -6.47611 q^{14} +1.47501 q^{15} -4.29645 q^{16} +0.206874 q^{17} +3.53925 q^{18} -1.00000 q^{19} +2.48253 q^{20} +3.61116 q^{21} +2.77657 q^{22} -2.29702 q^{23} +0.345108 q^{24} -3.17723 q^{25} +2.12882 q^{26} -5.25108 q^{27} +6.07781 q^{28} +3.93219 q^{29} -2.88995 q^{30} -1.07866 q^{31} +7.78619 q^{32} -1.54825 q^{33} -0.405325 q^{34} +4.46256 q^{35} -3.32157 q^{36} -2.28592 q^{37} +1.95928 q^{38} -1.18706 q^{39} +0.426474 q^{40} -10.0767 q^{41} -7.07527 q^{42} +8.76642 q^{43} -2.60580 q^{44} -2.43883 q^{45} +4.50051 q^{46} -0.177489 q^{47} -4.69395 q^{48} +3.92537 q^{49} +6.22508 q^{50} +0.226014 q^{51} -1.99789 q^{52} +7.11912 q^{53} +10.2883 q^{54} -1.91328 q^{55} +1.04411 q^{56} -1.09252 q^{57} -7.70426 q^{58} -8.86463 q^{59} +2.71221 q^{60} -1.63279 q^{61} +2.11339 q^{62} -5.97081 q^{63} -6.66241 q^{64} -1.46693 q^{65} +3.03345 q^{66} +3.90385 q^{67} +0.380396 q^{68} -2.50954 q^{69} -8.74339 q^{70} -5.36832 q^{71} -0.570613 q^{72} -10.3438 q^{73} +4.47876 q^{74} -3.47118 q^{75} -1.83878 q^{76} -4.68414 q^{77} +2.32577 q^{78} -7.59418 q^{79} -5.80064 q^{80} -0.317683 q^{81} +19.7430 q^{82} +5.04706 q^{83} +6.64011 q^{84} +0.279301 q^{85} -17.1759 q^{86} +4.29599 q^{87} -0.447650 q^{88} +15.1720 q^{89} +4.77834 q^{90} -3.59137 q^{91} -4.22371 q^{92} -1.17845 q^{93} +0.347751 q^{94} -1.35010 q^{95} +8.50655 q^{96} +0.326395 q^{97} -7.69089 q^{98} +2.55993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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