LMFDB - Embedded newform 6013.2.a.f.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$0$
Dimension:	$110$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.32328 q^{2} -2.34605 q^{3} +3.39764 q^{4} -4.09939 q^{5} +5.45055 q^{6} -1.00000 q^{7} -3.24712 q^{8} +2.50397 q^{9} +O(q^{10})$	\(q-2.32328 q^{2} -2.34605 q^{3} +3.39764 q^{4} -4.09939 q^{5} +5.45055 q^{6} -1.00000 q^{7} -3.24712 q^{8} +2.50397 q^{9} +9.52403 q^{10} +1.34342 q^{11} -7.97105 q^{12} -0.281689 q^{13} +2.32328 q^{14} +9.61738 q^{15} +0.748685 q^{16} +5.75442 q^{17} -5.81742 q^{18} -2.91553 q^{19} -13.9282 q^{20} +2.34605 q^{21} -3.12114 q^{22} -4.76347 q^{23} +7.61791 q^{24} +11.8050 q^{25} +0.654443 q^{26} +1.16372 q^{27} -3.39764 q^{28} +9.31719 q^{29} -22.3439 q^{30} -3.25796 q^{31} +4.75483 q^{32} -3.15173 q^{33} -13.3691 q^{34} +4.09939 q^{35} +8.50758 q^{36} +1.46001 q^{37} +6.77359 q^{38} +0.660858 q^{39} +13.3112 q^{40} +0.311563 q^{41} -5.45055 q^{42} +11.0346 q^{43} +4.56446 q^{44} -10.2647 q^{45} +11.0669 q^{46} +8.18897 q^{47} -1.75646 q^{48} +1.00000 q^{49} -27.4263 q^{50} -13.5002 q^{51} -0.957079 q^{52} -0.121057 q^{53} -2.70365 q^{54} -5.50719 q^{55} +3.24712 q^{56} +6.83998 q^{57} -21.6465 q^{58} +7.86383 q^{59} +32.6764 q^{60} +2.12743 q^{61} +7.56915 q^{62} -2.50397 q^{63} -12.5442 q^{64} +1.15475 q^{65} +7.32237 q^{66} +0.103858 q^{67} +19.5514 q^{68} +11.1753 q^{69} -9.52403 q^{70} +14.2229 q^{71} -8.13067 q^{72} +6.18160 q^{73} -3.39202 q^{74} -27.6951 q^{75} -9.90592 q^{76} -1.34342 q^{77} -1.53536 q^{78} +0.590676 q^{79} -3.06915 q^{80} -10.2420 q^{81} -0.723849 q^{82} +16.5277 q^{83} +7.97105 q^{84} -23.5896 q^{85} -25.6365 q^{86} -21.8586 q^{87} -4.36224 q^{88} -9.27903 q^{89} +23.8479 q^{90} +0.281689 q^{91} -16.1846 q^{92} +7.64334 q^{93} -19.0253 q^{94} +11.9519 q^{95} -11.1551 q^{96} +7.46876 q^{97} -2.32328 q^{98} +3.36388 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) $ 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * 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 $

$2$	−2.32328	−1.64281	−0.821404	−	0.570346i	$-0.806809\pi$
$2$	−2.32328	−1.64281	−0.821404	+	0.570346i	$0.806809\pi$
$3$	−2.34605	−1.35449	−0.677247	−	0.735755i	$-0.736827\pi$
$3$	−2.34605	−1.35449	−0.677247	+	0.735755i	$0.736827\pi$
$4$	3.39764	1.69882
$5$	−4.09939	−1.83330	−0.916651	−	0.399689i	$-0.869118\pi$
$5$	−4.09939	−1.83330	−0.916651	+	0.399689i	$0.869118\pi$
$6$	5.45055	2.22518
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.24712	−1.14803
$9$	2.50397	0.834656
$10$	9.52403	3.01176
$11$	1.34342	0.405056	0.202528	−	0.979276i	$-0.435084\pi$
$11$	1.34342	0.405056	0.202528	+	0.979276i	$0.435084\pi$
$12$	−7.97105	−2.30104
$13$	−0.281689	−0.0781265	−0.0390632	−	0.999237i	$-0.512437\pi$
$13$	−0.281689	−0.0781265	−0.0390632	+	0.999237i	$0.512437\pi$
$14$	2.32328	0.620923
$15$	9.61738	2.48320
$16$	0.748685	0.187171
$17$	5.75442	1.39565	0.697826	−	0.716268i	$-0.254151\pi$
$17$	5.75442	1.39565	0.697826	+	0.716268i	$0.254151\pi$
$18$	−5.81742	−1.37118
$19$	−2.91553	−0.668868	−0.334434	−	0.942419i	$-0.608545\pi$
$19$	−2.91553	−0.668868	−0.334434	+	0.942419i	$0.608545\pi$
$20$	−13.9282	−3.11445
$21$	2.34605	0.511951
$22$	−3.12114	−0.665430
$23$	−4.76347	−0.993251	−0.496626	−	0.867965i	$-0.665428\pi$
$23$	−4.76347	−0.993251	−0.496626	+	0.867965i	$0.665428\pi$
$24$	7.61791	1.55500
$25$	11.8050	2.36099
$26$	0.654443	0.128347
$27$	1.16372	0.223958
$28$	−3.39764	−0.642094
$29$	9.31719	1.73016	0.865079	−	0.501635i	$-0.167268\pi$
$29$	9.31719	1.73016	0.865079	+	0.501635i	$0.167268\pi$
$30$	−22.3439	−4.07942
$31$	−3.25796	−0.585146	−0.292573	−	0.956243i	$-0.594512\pi$
$31$	−3.25796	−0.585146	−0.292573	+	0.956243i	$0.594512\pi$
$32$	4.75483	0.840542
$33$	−3.15173	−0.548646
$34$	−13.3691	−2.29279
$35$	4.09939	0.692923
$36$	8.50758	1.41793
$37$	1.46001	0.240024	0.120012	−	0.992772i	$-0.461707\pi$
$37$	1.46001	0.240024	0.120012	+	0.992772i	$0.461707\pi$
$38$	6.77359	1.09882
$39$	0.660858	0.105822
$40$	13.3112	2.10468
$41$	0.311563	0.0486580	0.0243290	−	0.999704i	$-0.492255\pi$
$41$	0.311563	0.0486580	0.0243290	+	0.999704i	$0.492255\pi$
$42$	−5.45055	−0.841037
$43$	11.0346	1.68276	0.841382	−	0.540441i	$-0.181742\pi$
$43$	11.0346	1.68276	0.841382	+	0.540441i	$0.181742\pi$
$44$	4.56446	0.688118
$45$	−10.2647	−1.53018
$46$	11.0669	1.63172
$47$	8.18897	1.19448	0.597242	−	0.802061i	$-0.296263\pi$
$47$	8.18897	1.19448	0.597242	+	0.802061i	$0.296263\pi$
$48$	−1.75646	−0.253522
$49$	1.00000	0.142857
$50$	−27.4263	−3.87866
$51$	−13.5002	−1.89040
$52$	−0.957079	−0.132723
$53$	−0.121057	−0.0166284	−0.00831421	−	0.999965i	$-0.502647\pi$
$53$	−0.121057	−0.0166284	−0.00831421	+	0.999965i	$0.502647\pi$
$54$	−2.70365	−0.367920
$55$	−5.50719	−0.742590
$56$	3.24712	0.433914
$57$	6.83998	0.905978
$58$	−21.6465	−2.84232
$59$	7.86383	1.02378	0.511892	−	0.859050i	$-0.328945\pi$
$59$	7.86383	1.02378	0.511892	+	0.859050i	$0.328945\pi$
$60$	32.6764	4.21851
$61$	2.12743	0.272389	0.136194	−	0.990682i	$-0.456513\pi$
$61$	2.12743	0.272389	0.136194	+	0.990682i	$0.456513\pi$
$62$	7.56915	0.961284
$63$	−2.50397	−0.315470
$64$	−12.5442	−1.56802
$65$	1.15475	0.143229
$66$	7.32237	0.901321
$67$	0.103858	0.0126883	0.00634415	−	0.999980i	$-0.497981\pi$
$67$	0.103858	0.0126883	0.00634415	+	0.999980i	$0.497981\pi$
$68$	19.5514	2.37096
$69$	11.1753	1.34535
$70$	−9.52403	−1.13834
$71$	14.2229	1.68795	0.843975	−	0.536382i	$-0.180209\pi$
$71$	14.2229	1.68795	0.843975	+	0.536382i	$0.180209\pi$
$72$	−8.13067	−0.958209
$73$	6.18160	0.723501	0.361751	−	0.932275i	$-0.382179\pi$
$73$	6.18160	0.723501	0.361751	+	0.932275i	$0.382179\pi$
$74$	−3.39202	−0.394314
$75$	−27.6951	−3.19795
$76$	−9.90592	−1.13629
$77$	−1.34342	−0.153097
$78$	−1.53536	−0.173845
$79$	0.590676	0.0664563	0.0332281	−	0.999448i	$-0.489421\pi$
$79$	0.590676	0.0664563	0.0332281	+	0.999448i	$0.489421\pi$
$80$	−3.06915	−0.343141
$81$	−10.2420	−1.13801
$82$	−0.723849	−0.0799357
$83$	16.5277	1.81415	0.907074	−	0.420971i	$-0.138311\pi$
$83$	16.5277	1.81415	0.907074	+	0.420971i	$0.138311\pi$
$84$	7.97105	0.869713
$85$	−23.5896	−2.55865
$86$	−25.6365	−2.76446
$87$	−21.8586	−2.34349
$88$	−4.36224	−0.465016
$89$	−9.27903	−0.983576	−0.491788	−	0.870715i	$-0.663656\pi$
$89$	−9.27903	−0.983576	−0.491788	+	0.870715i	$0.663656\pi$
$90$	23.8479	2.51379
$91$	0.281689	0.0295290
$92$	−16.1846	−1.68736
$93$	7.64334	0.792578
$94$	−19.0253	−1.96231
$95$	11.9519	1.22624
$96$	−11.1551	−1.13851
$97$	7.46876	0.758338	0.379169	−	0.925328i	$-0.376210\pi$
$97$	7.46876	0.758338	0.379169	+	0.925328i	$0.376210\pi$
$98$	−2.32328	−0.234687
$99$	3.36388	0.338083
$100$	40.1091	4.01091
$101$	−8.12684	−0.808651	−0.404326	−	0.914615i	$-0.632494\pi$
$101$	−8.12684	−0.808651	−0.404326	+	0.914615i	$0.632494\pi$
$102$	31.3647	3.10557
$103$	−0.903454	−0.0890200	−0.0445100	−	0.999009i	$-0.514173\pi$
$103$	−0.903454	−0.0890200	−0.0445100	+	0.999009i	$0.514173\pi$
$104$	0.914677	0.0896915
$105$	−9.61738	−0.938560
$106$	0.281249	0.0273173
$107$	4.73466	0.457717	0.228858	−	0.973460i	$-0.426501\pi$
$107$	4.73466	0.457717	0.228858	+	0.973460i	$0.426501\pi$
$108$	3.95390	0.380464
$109$	−8.49500	−0.813673	−0.406837	−	0.913501i	$-0.633368\pi$
$109$	−8.49500	−0.813673	−0.406837	+	0.913501i	$0.633368\pi$
$110$	12.7948	1.21993
$111$	−3.42526	−0.325112
$112$	−0.748685	−0.0707441
$113$	−3.51199	−0.330380	−0.165190	−	0.986262i	$-0.552824\pi$
$113$	−3.51199	−0.330380	−0.165190	+	0.986262i	$0.552824\pi$
$114$	−15.8912	−1.48835
$115$	19.5273	1.82093
$116$	31.6565	2.93923
$117$	−0.705340	−0.0652087
$118$	−18.2699	−1.68188
$119$	−5.75442	−0.527507
$120$	−31.2288	−2.85078
$121$	−9.19522	−0.835930
$122$	−4.94261	−0.447483
$123$	−0.730944	−0.0659070
$124$	−11.0694	−0.994059
$125$	−27.8962	−2.49511
$126$	5.81742	0.518257
$127$	−2.96457	−0.263063	−0.131531	−	0.991312i	$-0.541989\pi$
$127$	−2.96457	−0.263063	−0.131531	+	0.991312i	$0.541989\pi$
$128$	19.6340	1.73542
$129$	−25.8878	−2.27930
$130$	−2.68282	−0.235299
$131$	−8.15784	−0.712754	−0.356377	−	0.934342i	$-0.615988\pi$
$131$	−8.15784	−0.712754	−0.356377	+	0.934342i	$0.615988\pi$
$132$	−10.7085	−0.932052
$133$	2.91553	0.252808
$134$	−0.241292	−0.0208445
$135$	−4.77053	−0.410582
$136$	−18.6853	−1.60225
$137$	12.3215	1.05270	0.526350	−	0.850268i	$-0.323560\pi$
$137$	12.3215	1.05270	0.526350	+	0.850268i	$0.323560\pi$
$138$	−25.9635	−2.21016
$139$	−12.6339	−1.07159	−0.535796	−	0.844347i	$-0.679988\pi$
$139$	−12.6339	−1.07159	−0.535796	+	0.844347i	$0.679988\pi$
$140$	13.9282	1.17715
$141$	−19.2118	−1.61792
$142$	−33.0439	−2.77298
$143$	−0.378427	−0.0316456
$144$	1.87468	0.156224
$145$	−38.1948	−3.17190
$146$	−14.3616	−1.18857
$147$	−2.34605	−0.193499
$148$	4.96059	0.407758
$149$	6.25186	0.512172	0.256086	−	0.966654i	$-0.417567\pi$
$149$	6.25186	0.512172	0.256086	+	0.966654i	$0.417567\pi$
$150$	64.3435	5.25363
$151$	−11.8721	−0.966138	−0.483069	−	0.875582i	$-0.660478\pi$
$151$	−11.8721	−0.966138	−0.483069	+	0.875582i	$0.660478\pi$
$152$	9.46706	0.767880
$153$	14.4089	1.16489
$154$	3.12114	0.251509
$155$	13.3556	1.07275
$156$	2.24536	0.179772
$157$	−1.63080	−0.130152	−0.0650759	−	0.997880i	$-0.520729\pi$
$157$	−1.63080	−0.130152	−0.0650759	+	0.997880i	$0.520729\pi$
$158$	−1.37231	−0.109175
$159$	0.284006	0.0225231
$160$	−19.4919	−1.54097
$161$	4.76347	0.375414
$162$	23.7952	1.86953
$163$	18.9649	1.48545	0.742723	−	0.669598i	$-0.233534\pi$
$163$	18.9649	1.48545	0.742723	+	0.669598i	$0.233534\pi$
$164$	1.05858	0.0826612
$165$	12.9202	1.00583
$166$	−38.3985	−2.98030
$167$	4.65242	0.360015	0.180008	−	0.983665i	$-0.442388\pi$
$167$	4.65242	0.360015	0.180008	+	0.983665i	$0.442388\pi$
$168$	−7.61791	−0.587734
$169$	−12.9207	−0.993896
$170$	54.8053	4.20337
$171$	−7.30039	−0.558274
$172$	37.4917	2.85872
$173$	−12.7340	−0.968147	−0.484074	−	0.875027i	$-0.660843\pi$
$173$	−12.7340	−0.968147	−0.484074	+	0.875027i	$0.660843\pi$
$174$	50.7838	3.84991
$175$	−11.8050	−0.892372
$176$	1.00580	0.0758149
$177$	−18.4490	−1.38671
$178$	21.5578	1.61583
$179$	19.7287	1.47459	0.737297	−	0.675569i	$-0.236102\pi$
$179$	19.7287	1.47459	0.737297	+	0.675569i	$0.236102\pi$
$180$	−34.8759	−2.59949
$181$	−2.37634	−0.176632	−0.0883158	−	0.996093i	$-0.528148\pi$
$181$	−2.37634	−0.176632	−0.0883158	+	0.996093i	$0.528148\pi$
$182$	−0.654443	−0.0485106
$183$	−4.99106	−0.368949
$184$	15.4675	1.14028
$185$	−5.98515	−0.440037
$186$	−17.7576	−1.30205
$187$	7.73059	0.565317
$188$	27.8232	2.02921
$189$	−1.16372	−0.0846480
$190$	−27.7676	−2.01447
$191$	13.7247	0.993085	0.496542	−	0.868013i	$-0.334603\pi$
$191$	13.7247	0.993085	0.496542	+	0.868013i	$0.334603\pi$
$192$	29.4293	2.12388
$193$	−5.17541	−0.372534	−0.186267	−	0.982499i	$-0.559639\pi$
$193$	−5.17541	−0.372534	−0.186267	+	0.982499i	$0.559639\pi$
$194$	−17.3520	−1.24580
$195$	−2.70911	−0.194003
$196$	3.39764	0.242689
$197$	−2.57752	−0.183640	−0.0918202	−	0.995776i	$-0.529269\pi$
$197$	−2.57752	−0.183640	−0.0918202	+	0.995776i	$0.529269\pi$
$198$	−7.81524	−0.555405
$199$	−1.58755	−0.112538	−0.0562691	−	0.998416i	$-0.517920\pi$
$199$	−1.58755	−0.112538	−0.0562691	+	0.998416i	$0.517920\pi$
$200$	−38.3321	−2.71049
$201$	−0.243657	−0.0171862
$202$	18.8810	1.32846
$203$	−9.31719	−0.653939
$204$	−45.8687	−3.21145
$205$	−1.27722	−0.0892047
$206$	2.09898	0.146243
$207$	−11.9276	−0.829023
$208$	−0.210896	−0.0146230
$209$	−3.91678	−0.270929
$210$	22.3439	1.54188
$211$	23.3912	1.61032	0.805160	−	0.593058i	$-0.202080\pi$
$211$	23.3912	1.61032	0.805160	+	0.593058i	$0.202080\pi$
$212$	−0.411308	−0.0282487
$213$	−33.3678	−2.28632
$214$	−10.9999	−0.751941
$215$	−45.2352	−3.08501
$216$	−3.77873	−0.257110
$217$	3.25796	0.221165
$218$	19.7363	1.33671
$219$	−14.5024	−0.979979
$220$	−18.7115	−1.26153
$221$	−1.62096	−0.109037
$222$	7.95785	0.534096
$223$	−27.6538	−1.85184	−0.925918	−	0.377725i	$-0.876706\pi$
$223$	−27.6538	−1.85184	−0.925918	+	0.377725i	$0.876706\pi$
$224$	−4.75483	−0.317695
$225$	29.5593	1.97062
$226$	8.15934	0.542751
$227$	6.81573	0.452376	0.226188	−	0.974084i	$-0.427374\pi$
$227$	6.81573	0.452376	0.226188	+	0.974084i	$0.427374\pi$
$228$	23.2398	1.53909
$229$	0.0617311	0.00407931	0.00203965	−	0.999998i	$-0.499351\pi$
$229$	0.0617311	0.00407931	0.00203965	+	0.999998i	$0.499351\pi$
$230$	−45.3674	−2.99144
$231$	3.15173	0.207369
$232$	−30.2540	−1.98627
$233$	18.5964	1.21829	0.609146	−	0.793058i	$-0.291512\pi$
$233$	18.5964	1.21829	0.609146	+	0.793058i	$0.291512\pi$
$234$	1.63870	0.107125
$235$	−33.5698	−2.18985
$236$	26.7185	1.73922
$237$	−1.38576	−0.0900147
$238$	13.3691	0.866592
$239$	6.18953	0.400367	0.200184	−	0.979758i	$-0.435846\pi$
$239$	6.18953	0.400367	0.200184	+	0.979758i	$0.435846\pi$
$240$	7.20039	0.464783
$241$	14.7835	0.952288	0.476144	−	0.879367i	$-0.342034\pi$
$241$	14.7835	0.952288	0.476144	+	0.879367i	$0.342034\pi$
$242$	21.3631	1.37327
$243$	20.5372	1.31746
$244$	7.22823	0.462740
$245$	−4.09939	−0.261900
$246$	1.69819	0.108273
$247$	0.821272	0.0522563
$248$	10.5790	0.671765
$249$	−38.7748	−2.45725
$250$	64.8108	4.09899
$251$	−14.2269	−0.897992	−0.448996	−	0.893534i	$-0.648218\pi$
$251$	−14.2269	−0.897992	−0.448996	+	0.893534i	$0.648218\pi$
$252$	−8.50758	−0.535927
$253$	−6.39933	−0.402323
$254$	6.88753	0.432162
$255$	55.3424	3.46568
$256$	−20.5270	−1.28294
$257$	−10.4398	−0.651214	−0.325607	−	0.945505i	$-0.605569\pi$
$257$	−10.4398	−0.651214	−0.325607	+	0.945505i	$0.605569\pi$
$258$	60.1447	3.74445
$259$	−1.46001	−0.0907206
$260$	3.92343	0.243321
$261$	23.3299	1.44409
$262$	18.9530	1.17092
$263$	−16.3292	−1.00690	−0.503450	−	0.864024i	$-0.667936\pi$
$263$	−16.3292	−1.00690	−0.503450	+	0.864024i	$0.667936\pi$
$264$	10.2340	0.629862
$265$	0.496258	0.0304849
$266$	−6.77359	−0.415316
$267$	21.7691	1.33225
$268$	0.352873	0.0215552
$269$	−18.1476	−1.10648	−0.553241	−	0.833021i	$-0.686609\pi$
$269$	−18.1476	−1.10648	−0.553241	+	0.833021i	$0.686609\pi$
$270$	11.0833	0.674508
$271$	−2.35155	−0.142847	−0.0714233	−	0.997446i	$-0.522754\pi$
$271$	−2.35155	−0.142847	−0.0714233	+	0.997446i	$0.522754\pi$
$272$	4.30825	0.261226
$273$	−0.660858	−0.0399969
$274$	−28.6264	−1.72938
$275$	15.8590	0.956335
$276$	37.9698	2.28552
$277$	27.1182	1.62938	0.814689	−	0.579899i	$-0.196908\pi$
$277$	27.1182	1.62938	0.814689	+	0.579899i	$0.196908\pi$
$278$	29.3521	1.76042
$279$	−8.15782	−0.488396
$280$	−13.3112	−0.795495
$281$	6.86927	0.409787	0.204893	−	0.978784i	$-0.434315\pi$
$281$	6.86927	0.409787	0.204893	+	0.978784i	$0.434315\pi$
$282$	44.6344	2.65794
$283$	−19.8878	−1.18221	−0.591103	−	0.806596i	$-0.701307\pi$
$283$	−19.8878	−1.18221	−0.591103	+	0.806596i	$0.701307\pi$
$284$	48.3244	2.86753
$285$	−28.0397	−1.66093
$286$	0.879192	0.0519877
$287$	−0.311563	−0.0183910
$288$	11.9059	0.701564
$289$	16.1133	0.947842
$290$	88.7372	5.21083
$291$	−17.5221	−1.02716
$292$	21.0029	1.22910
$293$	−11.9346	−0.697226	−0.348613	−	0.937267i	$-0.613347\pi$
$293$	−11.9346	−0.697226	−0.348613	+	0.937267i	$0.613347\pi$
$294$	5.45055	0.317882
$295$	−32.2369	−1.87690
$296$	−4.74082	−0.275555
$297$	1.56336	0.0907154
$298$	−14.5248	−0.841401
$299$	1.34182	0.0775993
$300$	−94.0980	−5.43275
$301$	−11.0346	−0.636025
$302$	27.5823	1.58718
$303$	19.0660	1.09531
$304$	−2.18281	−0.125193
$305$	−8.72114	−0.499371
$306$	−33.4759	−1.91369
$307$	30.3211	1.73052	0.865258	−	0.501328i	$-0.167155\pi$
$307$	30.3211	1.73052	0.865258	+	0.501328i	$0.167155\pi$
$308$	−4.56446	−0.260084
$309$	2.11955	0.120577
$310$	−31.0289	−1.76232
$311$	9.08023	0.514892	0.257446	−	0.966293i	$-0.417119\pi$
$311$	9.08023	0.514892	0.257446	+	0.966293i	$0.417119\pi$
$312$	−2.14588	−0.121487
$313$	−17.7195	−1.00157	−0.500783	−	0.865573i	$-0.666955\pi$
$313$	−17.7195	−1.00157	−0.500783	+	0.865573i	$0.666955\pi$
$314$	3.78881	0.213815
$315$	10.2647	0.578352
$316$	2.00691	0.112897
$317$	31.3195	1.75908	0.879539	−	0.475827i	$-0.157851\pi$
$317$	31.3195	1.75908	0.879539	+	0.475827i	$0.157851\pi$
$318$	−0.659825	−0.0370012
$319$	12.5169	0.700811
$320$	51.4234	2.87466
$321$	−11.1078	−0.619975
$322$	−11.0669	−0.616733
$323$	−16.7772	−0.933506
$324$	−34.7988	−1.93327
$325$	−3.32533	−0.184456
$326$	−44.0609	−2.44030
$327$	19.9297	1.10212
$328$	−1.01168	−0.0558608
$329$	−8.18897	−0.451473
$330$	−30.0172	−1.65239
$331$	−13.3781	−0.735325	−0.367662	−	0.929959i	$-0.619842\pi$
$331$	−13.3781	−0.735325	−0.367662	+	0.929959i	$0.619842\pi$
$332$	56.1551	3.08191
$333$	3.65582	0.200338
$334$	−10.8089	−0.591436
$335$	−0.425755	−0.0232615
$336$	1.75646	0.0958225
$337$	2.38201	0.129756	0.0648782	−	0.997893i	$-0.479334\pi$
$337$	2.38201	0.129756	0.0648782	+	0.997893i	$0.479334\pi$
$338$	30.0183	1.63278
$339$	8.23931	0.447498
$340$	−80.1489	−4.34669
$341$	−4.37680	−0.237017
$342$	16.9609	0.917138
$343$	−1.00000	−0.0539949
$344$	−35.8307	−1.93186
$345$	−45.8121	−2.46644
$346$	29.5847	1.59048
$347$	−28.0144	−1.50389	−0.751945	−	0.659226i	$-0.770884\pi$
$347$	−28.0144	−1.50389	−0.751945	+	0.659226i	$0.770884\pi$
$348$	−74.2678	−3.98117
$349$	−14.6077	−0.781935	−0.390967	−	0.920405i	$-0.627859\pi$
$349$	−14.6077	−0.781935	−0.390967	+	0.920405i	$0.627859\pi$
$350$	27.4263	1.46600
$351$	−0.327807	−0.0174970
$352$	6.38772	0.340467
$353$	15.2025	0.809148	0.404574	−	0.914505i	$-0.367420\pi$
$353$	15.2025	0.809148	0.404574	+	0.914505i	$0.367420\pi$
$354$	42.8621	2.27810
$355$	−58.3053	−3.09452
$356$	−31.5268	−1.67092
$357$	13.5002	0.714505
$358$	−45.8354	−2.42247
$359$	22.9784	1.21275	0.606377	−	0.795177i	$-0.292622\pi$
$359$	22.9784	1.21275	0.606377	+	0.795177i	$0.292622\pi$
$360$	33.3308	1.75669
$361$	−10.4997	−0.552616
$362$	5.52090	0.290172
$363$	21.5725	1.13226
$364$	0.957079	0.0501645
$365$	−25.3408	−1.32640
$366$	11.5956	0.606113
$367$	−26.0219	−1.35833	−0.679165	−	0.733986i	$-0.737658\pi$
$367$	−26.0219	−1.35833	−0.679165	+	0.733986i	$0.737658\pi$
$368$	−3.56634	−0.185908
$369$	0.780144	0.0406127
$370$	13.9052	0.722896
$371$	0.121057	0.00628495
$372$	25.9693	1.34645
$373$	17.1631	0.888671	0.444335	−	0.895861i	$-0.353440\pi$
$373$	17.1631	0.888671	0.444335	+	0.895861i	$0.353440\pi$
$374$	−17.9604	−0.928708
$375$	65.4460	3.37962
$376$	−26.5905	−1.37130
$377$	−2.62455	−0.135171
$378$	2.70365	0.139061
$379$	3.26809	0.167870	0.0839352	−	0.996471i	$-0.473251\pi$
$379$	3.26809	0.167870	0.0839352	+	0.996471i	$0.473251\pi$
$380$	40.6082	2.08316
$381$	6.95503	0.356317
$382$	−31.8864	−1.63145
$383$	−8.08066	−0.412902	−0.206451	−	0.978457i	$-0.566191\pi$
$383$	−8.08066	−0.412902	−0.206451	+	0.978457i	$0.566191\pi$
$384$	−46.0624	−2.35061
$385$	5.50719	0.280673
$386$	12.0239	0.612003
$387$	27.6303	1.40453
$388$	25.3762	1.28828
$389$	4.79146	0.242937	0.121468	−	0.992595i	$-0.461240\pi$
$389$	4.79146	0.242937	0.121468	+	0.992595i	$0.461240\pi$
$390$	6.29403	0.318711
$391$	−27.4110	−1.38623
$392$	−3.24712	−0.164004
$393$	19.1387	0.965421
$394$	5.98830	0.301686
$395$	−2.42141	−0.121834
$396$	11.4293	0.574342
$397$	27.8057	1.39553	0.697763	−	0.716328i	$-0.254179\pi$
$397$	27.8057	1.39553	0.697763	+	0.716328i	$0.254179\pi$
$398$	3.68832	0.184879
$399$	−6.83998	−0.342427
$400$	8.83820	0.441910
$401$	3.71225	0.185381	0.0926904	−	0.995695i	$-0.470453\pi$
$401$	3.71225	0.185381	0.0926904	+	0.995695i	$0.470453\pi$
$402$	0.566084	0.0282337
$403$	0.917731	0.0457154
$404$	−27.6121	−1.37375
$405$	41.9861	2.08631
$406$	21.6465	1.07430
$407$	1.96141	0.0972233
$408$	43.8366	2.17024
$409$	−15.7080	−0.776710	−0.388355	−	0.921510i	$-0.626956\pi$
$409$	−15.7080	−0.776710	−0.388355	+	0.921510i	$0.626956\pi$
$410$	2.96734	0.146546
$411$	−28.9070	−1.42588
$412$	−3.06961	−0.151229
$413$	−7.86383	−0.386954
$414$	27.7111	1.36193
$415$	−67.7533	−3.32588
$416$	−1.33938	−0.0656686
$417$	29.6398	1.45147
$418$	9.09978	0.445085
$419$	−25.8771	−1.26418	−0.632089	−	0.774896i	$-0.717802\pi$
$419$	−25.8771	−1.26418	−0.632089	+	0.774896i	$0.717802\pi$
$420$	−32.6764	−1.59445
$421$	−32.0555	−1.56229	−0.781146	−	0.624349i	$-0.785364\pi$
$421$	−32.0555	−1.56229	−0.781146	+	0.624349i	$0.785364\pi$
$422$	−54.3445	−2.64545
$423$	20.5049	0.996983
$424$	0.393085	0.0190899
$425$	67.9307	3.29512
$426$	77.5227	3.75599
$427$	−2.12743	−0.102953
$428$	16.0867	0.777578
$429$	0.887809	0.0428638
$430$	105.094	5.06809
$431$	5.89245	0.283829	0.141915	−	0.989879i	$-0.454674\pi$
$431$	5.89245	0.283829	0.141915	+	0.989879i	$0.454674\pi$
$432$	0.871258	0.0419184
$433$	−6.98113	−0.335492	−0.167746	−	0.985830i	$-0.553649\pi$
$433$	−6.98113	−0.335492	−0.167746	+	0.985830i	$0.553649\pi$
$434$	−7.56915	−0.363331
$435$	89.6070	4.29632
$436$	−28.8630	−1.38229
$437$	13.8880	0.664354
$438$	33.6931	1.60992
$439$	1.67101	0.0797530	0.0398765	−	0.999205i	$-0.487304\pi$
$439$	1.67101	0.0797530	0.0398765	+	0.999205i	$0.487304\pi$
$440$	17.8825	0.852515
$441$	2.50397	0.119237
$442$	3.76594	0.179127
$443$	−19.9174	−0.946302	−0.473151	−	0.880981i	$-0.656883\pi$
$443$	−19.9174	−0.946302	−0.473151	+	0.880981i	$0.656883\pi$
$444$	−11.6378	−0.552306
$445$	38.0383	1.80319
$446$	64.2476	3.04221
$447$	−14.6672	−0.693734
$448$	12.5442	0.592656
$449$	30.5775	1.44304	0.721520	−	0.692394i	$-0.243444\pi$
$449$	30.5775	1.44304	0.721520	+	0.692394i	$0.243444\pi$
$450$	−68.6745	−3.23735
$451$	0.418560	0.0197092
$452$	−11.9325	−0.561256
$453$	27.8526	1.30863
$454$	−15.8349	−0.743167
$455$	−1.15475	−0.0541356
$456$	−22.2102	−1.04009
$457$	18.4825	0.864574	0.432287	−	0.901736i	$-0.357707\pi$
$457$	18.4825	0.864574	0.432287	+	0.901736i	$0.357707\pi$
$458$	−0.143419	−0.00670152
$459$	6.69652	0.312567
$460$	66.3467	3.09343
$461$	5.11799	0.238368	0.119184	−	0.992872i	$-0.461972\pi$
$461$	5.11799	0.238368	0.119184	+	0.992872i	$0.461972\pi$
$462$	−7.32237	−0.340667
$463$	−8.01754	−0.372606	−0.186303	−	0.982492i	$-0.559651\pi$
$463$	−8.01754	−0.372606	−0.186303	+	0.982492i	$0.559651\pi$
$464$	6.97564	0.323836
$465$	−31.3330	−1.45303
$466$	−43.2047	−2.00142
$467$	28.0497	1.29798	0.648992	−	0.760795i	$-0.275191\pi$
$467$	28.0497	1.29798	0.648992	+	0.760795i	$0.275191\pi$
$468$	−2.39649	−0.110778
$469$	−0.103858	−0.00479573
$470$	77.9920	3.59750
$471$	3.82594	0.176290
$472$	−25.5348	−1.17533
$473$	14.8241	0.681614
$474$	3.21951	0.147877
$475$	−34.4177	−1.57919
$476$	−19.5514	−0.896139
$477$	−0.303122	−0.0138790
$478$	−14.3800	−0.657727
$479$	−23.9063	−1.09231	−0.546153	−	0.837686i	$-0.683908\pi$
$479$	−23.9063	−1.09231	−0.546153	+	0.837686i	$0.683908\pi$
$480$	45.7290	2.08723
$481$	−0.411269	−0.0187523
$482$	−34.3462	−1.56443
$483$	−11.1753	−0.508496
$484$	−31.2421	−1.42009
$485$	−30.6173	−1.39026
$486$	−47.7138	−2.16434
$487$	3.97539	0.180142	0.0900710	−	0.995935i	$-0.471291\pi$
$487$	3.97539	0.180142	0.0900710	+	0.995935i	$0.471291\pi$
$488$	−6.90800	−0.312710
$489$	−44.4927	−2.01203
$490$	9.52403	0.430252
$491$	30.5849	1.38028	0.690139	−	0.723677i	$-0.257549\pi$
$491$	30.5849	1.38028	0.690139	+	0.723677i	$0.257549\pi$
$492$	−2.48348	−0.111964
$493$	53.6150	2.41470
$494$	−1.90805	−0.0858471
$495$	−13.7898	−0.619807
$496$	−2.43918	−0.109523
$497$	−14.2229	−0.637986
$498$	90.0848	4.03680
$499$	37.4753	1.67763	0.838813	−	0.544419i	$-0.183250\pi$
$499$	37.4753	1.67763	0.838813	+	0.544419i	$0.183250\pi$
$500$	−94.7813	−4.23875
$501$	−10.9148	−0.487639
$502$	33.0530	1.47523
$503$	30.0312	1.33903	0.669513	−	0.742801i	$-0.266503\pi$
$503$	30.0312	1.33903	0.669513	+	0.742801i	$0.266503\pi$
$504$	8.13067	0.362169
$505$	33.3151	1.48250
$506$	14.8675	0.660939
$507$	30.3125	1.34623
$508$	−10.0725	−0.446896
$509$	43.4705	1.92679	0.963397	−	0.268077i	$-0.0863882\pi$
$509$	43.4705	1.92679	0.963397	+	0.268077i	$0.0863882\pi$
$510$	−128.576	−5.69344
$511$	−6.18160	−0.273458
$512$	8.42200	0.372203
$513$	−3.39285	−0.149798
$514$	24.2545	1.06982
$515$	3.70361	0.163200
$516$	−87.9575	−3.87211
$517$	11.0012	0.483833
$518$	3.39202	0.149037
$519$	29.8746	1.31135
$520$	−3.74962	−0.164431
$521$	−3.65935	−0.160319	−0.0801595	−	0.996782i	$-0.525543\pi$
$521$	−3.65935	−0.160319	−0.0801595	+	0.996782i	$0.525543\pi$
$522$	−54.2020	−2.37236
$523$	−11.0892	−0.484896	−0.242448	−	0.970164i	$-0.577950\pi$
$523$	−11.0892	−0.484896	−0.242448	+	0.970164i	$0.577950\pi$
$524$	−27.7174	−1.21084
$525$	27.6951	1.20871
$526$	37.9373	1.65415
$527$	−18.7476	−0.816660
$528$	−2.35966	−0.102691
$529$	−0.309384	−0.0134515
$530$	−1.15295	−0.0500809
$531$	19.6908	0.854507
$532$	9.90592	0.429476
$533$	−0.0877639	−0.00380148
$534$	−50.5758	−2.18863
$535$	−19.4092	−0.839132
$536$	−0.337240	−0.0145665
$537$	−46.2846	−1.99733
$538$	42.1621	1.81774
$539$	1.34342	0.0578652
$540$	−16.2086	−0.697505
$541$	−11.7164	−0.503728	−0.251864	−	0.967763i	$-0.581043\pi$
$541$	−11.7164	−0.503728	−0.251864	+	0.967763i	$0.581043\pi$
$542$	5.46332	0.234670
$543$	5.57501	0.239247
$544$	27.3612	1.17310
$545$	34.8243	1.49171
$546$	1.53536	0.0657073
$547$	42.9610	1.83688	0.918440	−	0.395560i	$-0.129449\pi$
$547$	42.9610	1.83688	0.918440	+	0.395560i	$0.129449\pi$
$548$	41.8642	1.78835
$549$	5.32701	0.227351
$550$	−36.8450	−1.57108
$551$	−27.1645	−1.15725
$552$	−36.2877	−1.54451
$553$	−0.590676	−0.0251181
$554$	−63.0033	−2.67675
$555$	14.0415	0.596027
$556$	−42.9254	−1.82044
$557$	−10.0617	−0.426327	−0.213164	−	0.977017i	$-0.568377\pi$
$557$	−10.0617	−0.426327	−0.213164	+	0.977017i	$0.568377\pi$
$558$	18.9529	0.802341
$559$	−3.10833	−0.131468
$560$	3.06915	0.129695
$561$	−18.1364	−0.765719
$562$	−15.9593	−0.673201
$563$	−4.92750	−0.207669	−0.103835	−	0.994595i	$-0.533111\pi$
$563$	−4.92750	−0.207669	−0.103835	+	0.994595i	$0.533111\pi$
$564$	−65.2747	−2.74856
$565$	14.3970	0.605686
$566$	46.2049	1.94214
$567$	10.2420	0.430126
$568$	−46.1835	−1.93782
$569$	24.0555	1.00846	0.504230	−	0.863569i	$-0.331776\pi$
$569$	24.0555	1.00846	0.504230	+	0.863569i	$0.331776\pi$
$570$	65.1442	2.72859
$571$	39.3248	1.64569	0.822845	−	0.568266i	$-0.192386\pi$
$571$	39.3248	1.64569	0.822845	+	0.568266i	$0.192386\pi$
$572$	−1.28576	−0.0537602
$573$	−32.1989	−1.34513
$574$	0.723849	0.0302129
$575$	−56.2326	−2.34506
$576$	−31.4102	−1.30876
$577$	−25.1660	−1.04767	−0.523836	−	0.851819i	$-0.675500\pi$
$577$	−25.1660	−1.04767	−0.523836	+	0.851819i	$0.675500\pi$
$578$	−37.4358	−1.55712
$579$	12.1418	0.504596
$580$	−129.772	−5.38849
$581$	−16.5277	−0.685684
$582$	40.7088	1.68743
$583$	−0.162630	−0.00673545
$584$	−20.0724	−0.830600
$585$	2.89146	0.119547
$586$	27.7274	1.14541
$587$	−2.62221	−0.108230	−0.0541151	−	0.998535i	$-0.517234\pi$
$587$	−2.62221	−0.108230	−0.0541151	+	0.998535i	$0.517234\pi$
$588$	−7.97105	−0.328721
$589$	9.49866	0.391386
$590$	74.8954	3.08339
$591$	6.04699	0.248740
$592$	1.09309	0.0449256
$593$	11.9520	0.490811	0.245406	−	0.969420i	$-0.421079\pi$
$593$	11.9520	0.490811	0.245406	+	0.969420i	$0.421079\pi$
$594$	−3.63213	−0.149028
$595$	23.5896	0.967078
$596$	21.2416	0.870088
$597$	3.72447	0.152432
$598$	−3.11742	−0.127481
$599$	−5.83575	−0.238442	−0.119221	−	0.992868i	$-0.538040\pi$
$599$	−5.83575	−0.238442	−0.119221	+	0.992868i	$0.538040\pi$
$600$	89.9292	3.67134
$601$	1.66667	0.0679850	0.0339925	−	0.999422i	$-0.489178\pi$
$601$	1.66667	0.0679850	0.0339925	+	0.999422i	$0.489178\pi$
$602$	25.6365	1.04487
$603$	0.260058	0.0105904
$604$	−40.3372	−1.64130
$605$	37.6948	1.53251
$606$	−44.2957	−1.79939
$607$	41.6766	1.69160	0.845801	−	0.533498i	$-0.179123\pi$
$607$	41.6766	1.69160	0.845801	+	0.533498i	$0.179123\pi$
$608$	−13.8628	−0.562212
$609$	21.8586	0.885756
$610$	20.2617	0.820371
$611$	−2.30674	−0.0933209
$612$	48.9562	1.97894
$613$	30.2658	1.22242	0.611211	−	0.791468i	$-0.290683\pi$
$613$	30.2658	1.22242	0.611211	+	0.791468i	$0.290683\pi$
$614$	−70.4444	−2.84291
$615$	2.99642	0.120827
$616$	4.36224	0.175760
$617$	−27.1129	−1.09152	−0.545762	−	0.837940i	$-0.683760\pi$
$617$	−27.1129	−1.09152	−0.545762	+	0.837940i	$0.683760\pi$
$618$	−4.92432	−0.198085
$619$	23.0700	0.927263	0.463631	−	0.886028i	$-0.346546\pi$
$619$	23.0700	0.927263	0.463631	+	0.886028i	$0.346546\pi$
$620$	45.3776	1.82241
$621$	−5.54333	−0.222446
$622$	−21.0959	−0.845870
$623$	9.27903	0.371757
$624$	0.494774	0.0198068
$625$	55.3325	2.21330
$626$	41.1675	1.64538
$627$	9.18897	0.366972
$628$	−5.54087	−0.221105
$629$	8.40151	0.334990
$630$	−23.8479	−0.950122
$631$	−19.6609	−0.782688	−0.391344	−	0.920244i	$-0.627990\pi$
$631$	−19.6609	−0.782688	−0.391344	+	0.920244i	$0.627990\pi$
$632$	−1.91799	−0.0762937
$633$	−54.8771	−2.18117
$634$	−72.7640	−2.88983
$635$	12.1529	0.482273
$636$	0.964949	0.0382627
$637$	−0.281689	−0.0111609
$638$	−29.0803	−1.15130
$639$	35.6138	1.40886
$640$	−80.4874	−3.18154
$641$	−46.3899	−1.83229	−0.916145	−	0.400848i	$-0.868716\pi$
$641$	−46.3899	−1.83229	−0.916145	+	0.400848i	$0.868716\pi$
$642$	25.8065	1.01850
$643$	−33.6704	−1.32783	−0.663915	−	0.747808i	$-0.731106\pi$
$643$	−33.6704	−1.32783	−0.663915	+	0.747808i	$0.731106\pi$
$644$	16.1846	0.637761
$645$	106.124	4.17864
$646$	38.9781	1.53357
$647$	49.0302	1.92758	0.963788	−	0.266670i	$-0.0859235\pi$
$647$	49.0302	1.92758	0.963788	+	0.266670i	$0.0859235\pi$
$648$	33.2571	1.30646
$649$	10.5644	0.414690
$650$	7.72568	0.303026
$651$	−7.64334	−0.299566
$652$	64.4360	2.52351
$653$	−26.2888	−1.02876	−0.514380	−	0.857563i	$-0.671978\pi$
$653$	−26.2888	−1.02876	−0.514380	+	0.857563i	$0.671978\pi$
$654$	−46.3024	−1.81057
$655$	33.4421	1.30669
$656$	0.233263	0.00910737
$657$	15.4785	0.603875
$658$	19.0253	0.741683
$659$	25.8873	1.00843	0.504213	−	0.863579i	$-0.331783\pi$
$659$	25.8873	1.00843	0.504213	+	0.863579i	$0.331783\pi$
$660$	43.8981	1.70873
$661$	−10.8027	−0.420175	−0.210087	−	0.977683i	$-0.567375\pi$
$661$	−10.8027	−0.420175	−0.210087	+	0.977683i	$0.567375\pi$
$662$	31.0810	1.20800
$663$	3.80285	0.147690
$664$	−53.6673	−2.08269
$665$	−11.9519	−0.463474
$666$	−8.49350	−0.329116
$667$	−44.3821	−1.71848
$668$	15.8073	0.611601
$669$	64.8773	2.50830
$670$	0.989150	0.0382142
$671$	2.85803	0.110333
$672$	11.1551	0.430316
$673$	−14.3176	−0.551904	−0.275952	−	0.961171i	$-0.588993\pi$
$673$	−14.3176	−0.551904	−0.275952	+	0.961171i	$0.588993\pi$
$674$	−5.53408	−0.213165
$675$	13.7377	0.528763
$676$	−43.8997	−1.68845
$677$	−12.9362	−0.497177	−0.248589	−	0.968609i	$-0.579967\pi$
$677$	−12.9362	−0.497177	−0.248589	+	0.968609i	$0.579967\pi$
$678$	−19.1422	−0.735154
$679$	−7.46876	−0.286625
$680$	76.5981	2.93740
$681$	−15.9901	−0.612741
$682$	10.1685	0.389374
$683$	29.2506	1.11924	0.559622	−	0.828748i	$-0.310946\pi$
$683$	29.2506	1.11924	0.559622	+	0.828748i	$0.310946\pi$
$684$	−24.8041	−0.948408
$685$	−50.5107	−1.92992
$686$	2.32328	0.0887033
$687$	−0.144824	−0.00552540
$688$	8.26146	0.314965
$689$	0.0341004	0.00129912
$690$	106.434	4.05189
$691$	44.2729	1.68422	0.842110	−	0.539306i	$-0.181313\pi$
$691$	44.2729	1.68422	0.842110	+	0.539306i	$0.181313\pi$
$692$	−43.2655	−1.64471
$693$	−3.36388	−0.127783
$694$	65.0853	2.47060
$695$	51.7912	1.96455
$696$	70.9775	2.69040
$697$	1.79286	0.0679095
$698$	33.9379	1.28457
$699$	−43.6282	−1.65017
$700$	−40.1091	−1.51598
$701$	−10.1727	−0.384217	−0.192109	−	0.981374i	$-0.561533\pi$
$701$	−10.1727	−0.384217	−0.192109	+	0.981374i	$0.561533\pi$
$702$	0.761588	0.0287443
$703$	−4.25670	−0.160544
$704$	−16.8521	−0.635137
$705$	78.7565	2.96614
$706$	−35.3197	−1.32928
$707$	8.12684	0.305641
$708$	−62.6830	−2.35577
$709$	6.48600	0.243587	0.121793	−	0.992555i	$-0.461135\pi$
$709$	6.48600	0.243587	0.121793	+	0.992555i	$0.461135\pi$
$710$	135.460	5.08371
$711$	1.47903	0.0554681
$712$	30.1301	1.12917
$713$	15.5192	0.581197
$714$	−31.3647	−1.17379
$715$	1.55132	0.0580160
$716$	67.0311	2.50507
$717$	−14.5210	−0.542295
$718$	−53.3853	−1.99232
$719$	0.394331	0.0147061	0.00735304	−	0.999973i	$-0.497659\pi$
$719$	0.394331	0.0147061	0.00735304	+	0.999973i	$0.497659\pi$
$720$	−7.68505	−0.286405
$721$	0.903454	0.0336464
$722$	24.3938	0.907842
$723$	−34.6829	−1.28987
$724$	−8.07394	−0.300066
$725$	109.989	4.08489
$726$	−50.1190	−1.86009
$727$	18.3032	0.678829	0.339414	−	0.940637i	$-0.389771\pi$
$727$	18.3032	0.678829	0.339414	+	0.940637i	$0.389771\pi$
$728$	−0.914677	−0.0339002
$729$	−17.4553	−0.646493
$730$	58.8737	2.17902
$731$	63.4978	2.34855
$732$	−16.9578	−0.626779
$733$	31.8030	1.17467	0.587335	−	0.809344i	$-0.300177\pi$
$733$	31.8030	1.17467	0.587335	+	0.809344i	$0.300177\pi$
$734$	60.4561	2.23148
$735$	9.61738	0.354742
$736$	−22.6495	−0.834870
$737$	0.139525	0.00513948
$738$	−1.81249	−0.0667188
$739$	16.0780	0.591437	0.295719	−	0.955275i	$-0.404441\pi$
$739$	16.0780	0.591437	0.295719	+	0.955275i	$0.404441\pi$
$740$	−20.3354	−0.747544
$741$	−1.92675	−0.0707809
$742$	−0.281249	−0.0103250
$743$	−7.44665	−0.273191	−0.136595	−	0.990627i	$-0.543616\pi$
$743$	−7.44665	−0.273191	−0.136595	+	0.990627i	$0.543616\pi$
$744$	−24.8188	−0.909902
$745$	−25.6288	−0.938966
$746$	−39.8747	−1.45992
$747$	41.3848	1.51419
$748$	26.2658	0.960372
$749$	−4.73466	−0.173001
$750$	−152.050	−5.55206
$751$	−23.2253	−0.847504	−0.423752	−	0.905778i	$-0.639287\pi$
$751$	−23.2253	−0.847504	−0.423752	+	0.905778i	$0.639287\pi$
$752$	6.13096	0.223573
$753$	33.3770	1.21633
$754$	6.09757	0.222060
$755$	48.6683	1.77122
$756$	−3.95390	−0.143802
$757$	−41.4020	−1.50478	−0.752391	−	0.658717i	$-0.771100\pi$
$757$	−41.4020	−1.50478	−0.752391	+	0.658717i	$0.771100\pi$
$758$	−7.59269	−0.275779
$759$	15.0132	0.544944
$760$	−38.8091	−1.40775
$761$	6.37492	0.231091	0.115545	−	0.993302i	$-0.463138\pi$
$761$	6.37492	0.231091	0.115545	+	0.993302i	$0.463138\pi$
$762$	−16.1585	−0.585361
$763$	8.49500	0.307540
$764$	46.6316	1.68707
$765$	−59.0675	−2.13559
$766$	18.7736	0.678320
$767$	−2.21515	−0.0799846
$768$	48.1574	1.73773
$769$	−36.5213	−1.31699	−0.658495	−	0.752585i	$-0.728807\pi$
$769$	−36.5213	−1.31699	−0.658495	+	0.752585i	$0.728807\pi$
$770$	−12.7948	−0.461091
$771$	24.4922	0.882067
$772$	−17.5842	−0.632869
$773$	34.2251	1.23099	0.615496	−	0.788140i	$-0.288956\pi$
$773$	34.2251	1.23099	0.615496	+	0.788140i	$0.288956\pi$
$774$	−64.1931	−2.30737
$775$	−38.4601	−1.38153
$776$	−24.2519	−0.870594
$777$	3.42526	0.122881
$778$	−11.1319	−0.399098
$779$	−0.908371	−0.0325458
$780$	−9.20459	−0.329577
$781$	19.1074	0.683715
$782$	63.6834	2.27731
$783$	10.8426	0.387482
$784$	0.748685	0.0267387
$785$	6.68527	0.238608
$786$	−44.4647	−1.58600
$787$	48.2313	1.71926	0.859631	−	0.510916i	$-0.170694\pi$
$787$	48.2313	1.71926	0.859631	+	0.510916i	$0.170694\pi$
$788$	−8.75747	−0.311972
$789$	38.3091	1.36384
$790$	5.62562	0.200151
$791$	3.51199	0.124872
$792$	−10.9229	−0.388129
$793$	−0.599273	−0.0212808
$794$	−64.6004	−2.29258
$795$	−1.16425	−0.0412917
$796$	−5.39391	−0.191182
$797$	−38.2109	−1.35350	−0.676749	−	0.736214i	$-0.736612\pi$
$797$	−38.2109	−1.35350	−0.676749	+	0.736214i	$0.736612\pi$
$798$	15.8912	0.562543
$799$	47.1228	1.66708
$800$	56.1306	1.98452
$801$	−23.2344	−0.820947
$802$	−8.62460	−0.304545
$803$	8.30448	0.293059
$804$	−0.827859	−0.0291963
$805$	−19.5273	−0.688247
$806$	−2.13215	−0.0751017
$807$	42.5753	1.49872
$808$	26.3888	0.928355
$809$	−30.2213	−1.06252	−0.531261	−	0.847208i	$-0.678282\pi$
$809$	−30.2213	−1.06252	−0.531261	+	0.847208i	$0.678282\pi$
$810$	−97.5456	−3.42740
$811$	3.25522	0.114306	0.0571531	−	0.998365i	$-0.481798\pi$
$811$	3.25522	0.114306	0.0571531	+	0.998365i	$0.481798\pi$
$812$	−31.6565	−1.11092
$813$	5.51687	0.193485
$814$	−4.55690	−0.159719
$815$	−77.7445	−2.72327
$816$	−10.1074	−0.353829
$817$	−32.1717	−1.12555
$818$	36.4941	1.27599
$819$	0.705340	0.0246466
$820$	−4.33953	−0.151543
$821$	13.4860	0.470664	0.235332	−	0.971915i	$-0.424382\pi$
$821$	13.4860	0.470664	0.235332	+	0.971915i	$0.424382\pi$
$822$	67.1591	2.34244
$823$	−2.89739	−0.100997	−0.0504983	−	0.998724i	$-0.516081\pi$
$823$	−2.89739	−0.100997	−0.0504983	+	0.998724i	$0.516081\pi$
$824$	2.93362	0.102197
$825$	−37.2061	−1.29535
$826$	18.2699	0.635691
$827$	−36.0024	−1.25193	−0.625963	−	0.779852i	$-0.715294\pi$
$827$	−36.0024	−1.25193	−0.625963	+	0.779852i	$0.715294\pi$
$828$	−40.5256	−1.40836
$829$	−5.38808	−0.187136	−0.0935679	−	0.995613i	$-0.529827\pi$
$829$	−5.38808	−0.187136	−0.0935679	+	0.995613i	$0.529827\pi$
$830$	157.410	5.46379
$831$	−63.6208	−2.20698
$832$	3.53356	0.122504
$833$	5.75442	0.199379
$834$	−68.8615	−2.38448
$835$	−19.0721	−0.660016
$836$	−13.3078	−0.460260
$837$	−3.79134	−0.131048
$838$	60.1198	2.07680
$839$	33.2268	1.14712	0.573558	−	0.819165i	$-0.305563\pi$
$839$	33.2268	1.14712	0.573558	+	0.819165i	$0.305563\pi$
$840$	31.2288	1.07749
$841$	57.8100	1.99345
$842$	74.4741	2.56655
$843$	−16.1157	−0.555054
$844$	79.4750	2.73564
$845$	52.9667	1.82211
$846$	−47.6387	−1.63785
$847$	9.19522	0.315952
$848$	−0.0906334	−0.00311236
$849$	46.6578	1.60129
$850$	−157.822	−5.41326
$851$	−6.95471	−0.238404
$852$	−113.372	−3.88405
$853$	12.9789	0.444389	0.222194	−	0.975002i	$-0.428678\pi$
$853$	12.9789	0.444389	0.222194	+	0.975002i	$0.428678\pi$
$854$	4.94261	0.169133
$855$	29.9271	1.02349
$856$	−15.3740	−0.525472
$857$	13.7223	0.468745	0.234372	−	0.972147i	$-0.424697\pi$
$857$	13.7223	0.468745	0.234372	+	0.972147i	$0.424697\pi$
$858$	−2.06263	−0.0704171
$859$	1.00000	0.0341196
$859$	1.00000	0.0341196
$860$	−153.693	−5.24089
$861$	0.730944	0.0249105
$862$	−13.6898	−0.466278
$863$	−23.7043	−0.806903	−0.403452	−	0.915001i	$-0.632190\pi$
$863$	−23.7043	−0.806903	−0.403452	+	0.915001i	$0.632190\pi$
$864$	5.53328	0.188246
$865$	52.2015	1.77491
$866$	16.2191	0.551149
$867$	−37.8027	−1.28385
$868$	11.0694	0.375719
$869$	0.793526	0.0269185
$870$	−208.182	−7.05804
$871$	−0.0292557	−0.000991293 0
$872$	27.5843	0.934121
$873$	18.7015	0.632951
$874$	−32.2658	−1.09141
$875$	27.8962	0.943064
$876$	−49.2738	−1.66481
$877$	−13.2065	−0.445951	−0.222976	−	0.974824i	$-0.571577\pi$
$877$	−13.2065	−0.445951	−0.222976	+	0.974824i	$0.571577\pi$
$878$	−3.88223	−0.131019
$879$	27.9992	0.944388
$880$	−4.12315	−0.138991
$881$	−48.9751	−1.65001	−0.825007	−	0.565123i	$-0.808829\pi$
$881$	−48.9751	−1.65001	−0.825007	+	0.565123i	$0.808829\pi$
$882$	−5.81742	−0.195883
$883$	0.810642	0.0272803	0.0136401	−	0.999907i	$-0.495658\pi$
$883$	0.810642	0.0272803	0.0136401	+	0.999907i	$0.495658\pi$
$884$	−5.50743	−0.185235
$885$	75.6294	2.54226
$886$	46.2736	1.55459
$887$	−45.5633	−1.52987	−0.764933	−	0.644110i	$-0.777228\pi$
$887$	−45.5633	−1.52987	−0.764933	+	0.644110i	$0.777228\pi$
$888$	11.1222	0.373237
$889$	2.96457	0.0994284
$890$	−88.3738	−2.96230
$891$	−13.7594	−0.460956
$892$	−93.9577	−3.14594
$893$	−23.8752	−0.798952
$894$	34.0760	1.13967
$895$	−80.8756	−2.70337
$896$	−19.6340	−0.655926
$897$	−3.14797	−0.105108
$898$	−71.0401	−2.37064
$899$	−30.3550	−1.01240
$900$	100.432	3.34773
$901$	−0.696611	−0.0232075
$902$	−0.972433	−0.0323785
$903$	25.8878	0.861493
$904$	11.4038	0.379286
$905$	9.74152	0.323819
$906$	−64.7094	−2.14983
$907$	−33.5517	−1.11406	−0.557032	−	0.830491i	$-0.688060\pi$
$907$	−33.5517	−1.11406	−0.557032	+	0.830491i	$0.688060\pi$
$908$	23.1574	0.768505
$909$	−20.3494	−0.674945
$910$	2.68282	0.0889345
$911$	29.3228	0.971507	0.485753	−	0.874096i	$-0.338545\pi$
$911$	29.3228	0.971507	0.485753	+	0.874096i	$0.338545\pi$
$912$	5.12099	0.169573
$913$	22.2036	0.734832
$914$	−42.9400	−1.42033
$915$	20.4603	0.676396
$916$	0.209740	0.00693001
$917$	8.15784	0.269396
$918$	−15.5579	−0.513487
$919$	−37.4274	−1.23462	−0.617308	−	0.786722i	$-0.711777\pi$
$919$	−37.4274	−1.23462	−0.617308	+	0.786722i	$0.711777\pi$
$920$	−63.4074	−2.09048
$921$	−71.1349	−2.34397
$922$	−11.8905	−0.391594
$923$	−4.00644	−0.131874
$924$	10.7085	0.352283
$925$	17.2354	0.566696
$926$	18.6270	0.612121
$927$	−2.26222	−0.0743010
$928$	44.3016	1.45427
$929$	14.9050	0.489016	0.244508	−	0.969647i	$-0.421374\pi$
$929$	14.9050	0.489016	0.244508	+	0.969647i	$0.421374\pi$
$930$	72.7954	2.38706
$931$	−2.91553	−0.0955525
$932$	63.1840	2.06966
$933$	−21.3027	−0.697419
$934$	−65.1673	−2.13234
$935$	−31.6907	−1.03640
$936$	2.29032	0.0748615
$937$	2.93051	0.0957357	0.0478678	−	0.998854i	$-0.484757\pi$
$937$	2.93051	0.0957357	0.0478678	+	0.998854i	$0.484757\pi$
$938$	0.241292	0.00787847
$939$	41.5709	1.35662
$940$	−114.058	−3.72016
$941$	−12.7533	−0.415745	−0.207873	−	0.978156i	$-0.566654\pi$
$941$	−12.7533	−0.415745	−0.207873	+	0.978156i	$0.566654\pi$
$942$	−8.88874	−0.289611
$943$	−1.48412	−0.0483296
$944$	5.88753	0.191623
$945$	4.77053	0.155185
$946$	−34.4406	−1.11976
$947$	−41.7173	−1.35563	−0.677816	−	0.735232i	$-0.737073\pi$
$947$	−41.7173	−1.35563	−0.677816	+	0.735232i	$0.737073\pi$
$948$	−4.70831	−0.152919
$949$	−1.74129	−0.0565246
$950$	79.9621	2.59431
$951$	−73.4772	−2.38266
$952$	18.6853	0.605593
$953$	30.1128	0.975451	0.487725	−	0.872997i	$-0.337827\pi$
$953$	30.1128	0.975451	0.487725	+	0.872997i	$0.337827\pi$
$954$	0.704239	0.0228006
$955$	−56.2629	−1.82062
$956$	21.0298	0.680152
$957$	−29.3653	−0.949245
$958$	55.5410	1.79445
$959$	−12.3215	−0.397883
$960$	−120.642	−3.89371
$961$	−20.3857	−0.657604
$962$	0.955494	0.0308064
$963$	11.8554	0.382036
$964$	50.2290	1.61777
$965$	21.2160	0.682968
$966$	25.9635	0.835362
$967$	−24.3354	−0.782573	−0.391286	−	0.920269i	$-0.627970\pi$
$967$	−24.3354	−0.782573	−0.391286	+	0.920269i	$0.627970\pi$
$968$	29.8580	0.959671
$969$	39.3601	1.26443
$970$	71.1327	2.28393
$971$	−8.79638	−0.282289	−0.141145	−	0.989989i	$-0.545078\pi$
$971$	−8.79638	−0.282289	−0.141145	+	0.989989i	$0.545078\pi$
$972$	69.7782	2.23814
$973$	12.6339	0.405024
$974$	−9.23595	−0.295939
$975$	7.80140	0.249845
$976$	1.59277	0.0509834
$977$	−34.9268	−1.11741	−0.558704	−	0.829367i	$-0.688701\pi$
$977$	−34.9268	−1.11741	−0.558704	+	0.829367i	$0.688701\pi$
$978$	103.369	3.30538
$979$	−12.4656	−0.398403
$980$	−13.9282	−0.444921
$981$	−21.2712	−0.679137
$982$	−71.0574	−2.26753
$983$	44.2226	1.41048	0.705241	−	0.708968i	$-0.250839\pi$
$983$	44.2226	1.41048	0.705241	+	0.708968i	$0.250839\pi$
$984$	2.37346	0.0756631
$985$	10.5662	0.336668
$986$	−124.563	−3.96689
$987$	19.2118	0.611517
$988$	2.79039	0.0887741
$989$	−52.5631	−1.67141
$990$	32.0377	1.01822
$991$	−56.4998	−1.79477	−0.897387	−	0.441244i	$-0.854537\pi$
$991$	−56.4998	−1.79477	−0.897387	+	0.441244i	$0.854537\pi$
$992$	−15.4910	−0.491840
$993$	31.3857	0.995993
$994$	33.0439	1.04809
$995$	6.50797	0.206316
$996$	−131.743	−4.17443
$997$	52.7913	1.67192	0.835958	−	0.548793i	$-0.184913\pi$
$997$	52.7913	1.67192	0.835958	+	0.548793i	$0.184913\pi$
$998$	−87.0658	−2.75602
$999$	1.69904	0.0537553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.f.1.9	✓	110

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.f.1.9	✓	110	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32328 q^{2} -2.34605 q^{3} +3.39764 q^{4} -4.09939 q^{5} +5.45055 q^{6} -1.00000 q^{7} -3.24712 q^{8} +2.50397 q^{9} +O(q^{10})\)	\(q-2.32328 q^{2} -2.34605 q^{3} +3.39764 q^{4} -4.09939 q^{5} +5.45055 q^{6} -1.00000 q^{7} -3.24712 q^{8} +2.50397 q^{9} +9.52403 q^{10} +1.34342 q^{11} -7.97105 q^{12} -0.281689 q^{13} +2.32328 q^{14} +9.61738 q^{15} +0.748685 q^{16} +5.75442 q^{17} -5.81742 q^{18} -2.91553 q^{19} -13.9282 q^{20} +2.34605 q^{21} -3.12114 q^{22} -4.76347 q^{23} +7.61791 q^{24} +11.8050 q^{25} +0.654443 q^{26} +1.16372 q^{27} -3.39764 q^{28} +9.31719 q^{29} -22.3439 q^{30} -3.25796 q^{31} +4.75483 q^{32} -3.15173 q^{33} -13.3691 q^{34} +4.09939 q^{35} +8.50758 q^{36} +1.46001 q^{37} +6.77359 q^{38} +0.660858 q^{39} +13.3112 q^{40} +0.311563 q^{41} -5.45055 q^{42} +11.0346 q^{43} +4.56446 q^{44} -10.2647 q^{45} +11.0669 q^{46} +8.18897 q^{47} -1.75646 q^{48} +1.00000 q^{49} -27.4263 q^{50} -13.5002 q^{51} -0.957079 q^{52} -0.121057 q^{53} -2.70365 q^{54} -5.50719 q^{55} +3.24712 q^{56} +6.83998 q^{57} -21.6465 q^{58} +7.86383 q^{59} +32.6764 q^{60} +2.12743 q^{61} +7.56915 q^{62} -2.50397 q^{63} -12.5442 q^{64} +1.15475 q^{65} +7.32237 q^{66} +0.103858 q^{67} +19.5514 q^{68} +11.1753 q^{69} -9.52403 q^{70} +14.2229 q^{71} -8.13067 q^{72} +6.18160 q^{73} -3.39202 q^{74} -27.6951 q^{75} -9.90592 q^{76} -1.34342 q^{77} -1.53536 q^{78} +0.590676 q^{79} -3.06915 q^{80} -10.2420 q^{81} -0.723849 q^{82} +16.5277 q^{83} +7.97105 q^{84} -23.5896 q^{85} -25.6365 q^{86} -21.8586 q^{87} -4.36224 q^{88} -9.27903 q^{89} +23.8479 q^{90} +0.281689 q^{91} -16.1846 q^{92} +7.64334 q^{93} -19.0253 q^{94} +11.9519 q^{95} -11.1551 q^{96} +7.46876 q^{97} -2.32328 q^{98} +3.36388 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9}+O(q^{10}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9	\( 110 q + 16 q^{2} + 29 q^{3} + 118 q^{4} + 12 q^{6} - 110 q^{7} + 57 q^{8} + 127 q^{9} + 3 q^{10} + 52 q^{11} + 62 q^{12} - 9 q^{13} - 16 q^{14} + 39 q^{15} + 146 q^{16} + 11 q^{17} + 60 q^{18} + 14 q^{19} + 18 q^{20} - 29 q^{21} + 32 q^{22} + 73 q^{23} + 24 q^{24} + 132 q^{25} - 7 q^{26} + 116 q^{27} - 118 q^{28} + 35 q^{29} + 18 q^{30} + 36 q^{31} + 140 q^{32} + 42 q^{33} - 7 q^{34} + 180 q^{36} + 49 q^{37} + 45 q^{39} + 6 q^{40} - 14 q^{41} - 12 q^{42} + 58 q^{43} + 92 q^{44} + 17 q^{45} + 27 q^{46} + 87 q^{47} + 98 q^{48} + 110 q^{49} + 91 q^{50} + 42 q^{51} + 16 q^{52} + 95 q^{53} + 41 q^{54} + 8 q^{55} - 57 q^{56} + 61 q^{57} + 46 q^{58} + 114 q^{59} + 81 q^{60} - 47 q^{61} + 31 q^{62} - 127 q^{63} + 199 q^{64} + 62 q^{65} + 21 q^{66} + 95 q^{67} + 60 q^{68} - 39 q^{69} - 3 q^{70} + 131 q^{71} + 186 q^{72} + 31 q^{73} + 23 q^{74} + 121 q^{75} + 14 q^{76} - 52 q^{77} + 110 q^{78} + 9 q^{79} + 61 q^{80} + 194 q^{81} + 45 q^{82} + 73 q^{83} - 62 q^{84} + 59 q^{85} + 72 q^{86} + 64 q^{87} + 100 q^{88} - 17 q^{89} + 11 q^{90} + 9 q^{91} + 192 q^{92} + 85 q^{93} - 11 q^{94} + 108 q^{95} + 68 q^{96} + 32 q^{97} + 16 q^{98} + 160 q^{99}+O(q^{100}) \) 110 * q + 16 * q^2 + 29 * q^3 + 118 * q^4 + 12 * q^6 - 110 * q^7 + 57 * q^8 + 127 * q^9 + 3 * q^10 + 52 * q^11 + 62 * q^12 - 9 * q^13 - 16 * q^14 + 39 * q^15 + 146 * q^16 + 11 * q^17 + 60 * q^18 + 14 * q^19 + 18 * q^20 - 29 * q^21 + 32 * q^22 + 73 * q^23 + 24 * q^24 + 132 * q^25 - 7 * q^26 + 116 * q^27 - 118 * q^28 + 35 * q^29 + 18 * q^30 + 36 * q^31 + 140 * q^32 + 42 * q^33 - 7 * q^34 + 180 * q^36 + 49 * q^37 + 45 * q^39 + 6 * q^40 - 14 * q^41 - 12 * q^42 + 58 * q^43 + 92 * q^44 + 17 * q^45 + 27 * q^46 + 87 * q^47 + 98 * q^48 + 110 * q^49 + 91 * q^50 + 42 * q^51 + 16 * q^52 + 95 * q^53 + 41 * q^54 + 8 * q^55 - 57 * q^56 + 61 * q^57 + 46 * q^58 + 114 * q^59 + 81 * q^60 - 47 * q^61 + 31 * q^62 - 127 * q^63 + 199 * q^64 + 62 * q^65 + 21 * q^66 + 95 * q^67 + 60 * q^68 - 39 * q^69 - 3 * q^70 + 131 * q^71 + 186 * q^72 + 31 * q^73 + 23 * q^74 + 121 * q^75 + 14 * q^76 - 52 * q^77 + 110 * q^78 + 9 * q^79 + 61 * q^80 + 194 * q^81 + 45 * q^82 + 73 * q^83 - 62 * q^84 + 59 * q^85 + 72 * q^86 + 64 * q^87 + 100 * q^88 - 17 * q^89 + 11 * q^90 + 9 * q^91 + 192 * q^92 + 85 * q^93 - 11 * q^94 + 108 * q^95 + 68 * q^96 + 32 * q^97 + 16 * q^98 + 160 * q^99

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