LMFDB - Embedded newform 6023.2.a.d.1.13

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:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.50460 q^{2} -0.513198 q^{3} +4.27304 q^{4} +1.36674 q^{5} +1.28536 q^{6} -1.89861 q^{7} -5.69306 q^{8} -2.73663 q^{9} +O(q^{10})$	\(q-2.50460 q^{2} -0.513198 q^{3} +4.27304 q^{4} +1.36674 q^{5} +1.28536 q^{6} -1.89861 q^{7} -5.69306 q^{8} -2.73663 q^{9} -3.42314 q^{10} +4.51912 q^{11} -2.19291 q^{12} -1.82678 q^{13} +4.75527 q^{14} -0.701406 q^{15} +5.71278 q^{16} -2.06176 q^{17} +6.85417 q^{18} -1.00000 q^{19} +5.84012 q^{20} +0.974364 q^{21} -11.3186 q^{22} +8.30868 q^{23} +2.92167 q^{24} -3.13203 q^{25} +4.57537 q^{26} +2.94402 q^{27} -8.11285 q^{28} +0.0175513 q^{29} +1.75675 q^{30} +6.71198 q^{31} -2.92213 q^{32} -2.31920 q^{33} +5.16389 q^{34} -2.59491 q^{35} -11.6937 q^{36} -9.34788 q^{37} +2.50460 q^{38} +0.937501 q^{39} -7.78092 q^{40} -7.82605 q^{41} -2.44040 q^{42} +9.28103 q^{43} +19.3104 q^{44} -3.74025 q^{45} -20.8099 q^{46} +11.4768 q^{47} -2.93179 q^{48} -3.39527 q^{49} +7.84449 q^{50} +1.05809 q^{51} -7.80591 q^{52} +8.40315 q^{53} -7.37361 q^{54} +6.17645 q^{55} +10.8089 q^{56} +0.513198 q^{57} -0.0439590 q^{58} -2.54164 q^{59} -2.99714 q^{60} -0.166499 q^{61} -16.8109 q^{62} +5.19580 q^{63} -4.10678 q^{64} -2.49673 q^{65} +5.80868 q^{66} -0.834826 q^{67} -8.80997 q^{68} -4.26399 q^{69} +6.49921 q^{70} -9.71132 q^{71} +15.5798 q^{72} -7.32846 q^{73} +23.4127 q^{74} +1.60735 q^{75} -4.27304 q^{76} -8.58007 q^{77} -2.34807 q^{78} -12.8687 q^{79} +7.80787 q^{80} +6.69902 q^{81} +19.6011 q^{82} -9.28046 q^{83} +4.16350 q^{84} -2.81788 q^{85} -23.2453 q^{86} -0.00900728 q^{87} -25.7276 q^{88} -12.6605 q^{89} +9.36785 q^{90} +3.46836 q^{91} +35.5033 q^{92} -3.44457 q^{93} -28.7449 q^{94} -1.36674 q^{95} +1.49963 q^{96} +14.5977 q^{97} +8.50379 q^{98} -12.3672 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.50460	−1.77102	−0.885511	−	0.464618i	$-0.846192\pi$
$2$	−2.50460	−1.77102	−0.885511	+	0.464618i	$0.846192\pi$
$3$	−0.513198	−0.296295	−0.148147	−	0.988965i	$-0.547331\pi$
$3$	−0.513198	−0.296295	−0.148147	+	0.988965i	$0.547331\pi$
$4$	4.27304	2.13652
$5$	1.36674	0.611224	0.305612	−	0.952156i	$-0.401139\pi$
$5$	1.36674	0.611224	0.305612	+	0.952156i	$0.401139\pi$
$6$	1.28536	0.524745
$7$	−1.89861	−0.717609	−0.358804	−	0.933413i	$-0.616815\pi$
$7$	−1.89861	−0.717609	−0.358804	+	0.933413i	$0.616815\pi$
$8$	−5.69306	−2.01280
$9$	−2.73663	−0.912209
$10$	−3.42314	−1.08249
$11$	4.51912	1.36257	0.681283	−	0.732020i	$-0.261422\pi$
$11$	4.51912	1.36257	0.681283	+	0.732020i	$0.261422\pi$
$12$	−2.19291	−0.633040
$13$	−1.82678	−0.506658	−0.253329	−	0.967380i	$-0.581526\pi$
$13$	−1.82678	−0.506658	−0.253329	+	0.967380i	$0.581526\pi$
$14$	4.75527	1.27090
$15$	−0.701406	−0.181102
$16$	5.71278	1.42820
$17$	−2.06176	−0.500050	−0.250025	−	0.968239i	$-0.580439\pi$
$17$	−2.06176	−0.500050	−0.250025	+	0.968239i	$0.580439\pi$
$18$	6.85417	1.61554
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	5.84012	1.30589
$21$	0.974364	0.212624
$22$	−11.3186	−2.41313
$23$	8.30868	1.73248	0.866240	−	0.499629i	$-0.166530\pi$
$23$	8.30868	1.73248	0.866240	+	0.499629i	$0.166530\pi$
$24$	2.92167	0.596382
$25$	−3.13203	−0.626406
$26$	4.57537	0.897303
$27$	2.94402	0.566578
$28$	−8.11285	−1.53318
$29$	0.0175513	0.00325919	0.00162960	−	0.999999i	$-0.499481\pi$
$29$	0.0175513	0.00325919	0.00162960	+	0.999999i	$0.499481\pi$
$30$	1.75675	0.320736
$31$	6.71198	1.20551	0.602754	−	0.797927i	$-0.294070\pi$
$31$	6.71198	1.20551	0.602754	+	0.797927i	$0.294070\pi$
$32$	−2.92213	−0.516565
$33$	−2.31920	−0.403721
$34$	5.16389	0.885599
$35$	−2.59491	−0.438619
$36$	−11.6937	−1.94895
$37$	−9.34788	−1.53678	−0.768391	−	0.639980i	$-0.778942\pi$
$37$	−9.34788	−1.53678	−0.768391	+	0.639980i	$0.778942\pi$
$38$	2.50460	0.406300
$39$	0.937501	0.150120
$40$	−7.78092	−1.23027
$41$	−7.82605	−1.22222	−0.611112	−	0.791544i	$-0.709277\pi$
$41$	−7.82605	−1.22222	−0.611112	+	0.791544i	$0.709277\pi$
$42$	−2.44040	−0.376561
$43$	9.28103	1.41534	0.707672	−	0.706541i	$-0.249746\pi$
$43$	9.28103	1.41534	0.707672	+	0.706541i	$0.249746\pi$
$44$	19.3104	2.91115
$45$	−3.74025	−0.557564
$46$	−20.8099	−3.06826
$47$	11.4768	1.67407	0.837033	−	0.547153i	$-0.184288\pi$
$47$	11.4768	1.67407	0.837033	+	0.547153i	$0.184288\pi$
$48$	−2.93179	−0.423167
$49$	−3.39527	−0.485038
$50$	7.84449	1.10938
$51$	1.05809	0.148162
$52$	−7.80591	−1.08249
$53$	8.40315	1.15426	0.577131	−	0.816652i	$-0.304172\pi$
$53$	8.40315	1.15426	0.577131	+	0.816652i	$0.304172\pi$
$54$	−7.37361	−1.00342
$55$	6.17645	0.832833
$56$	10.8089	1.44440
$57$	0.513198	0.0679747
$58$	−0.0439590	−0.00577210
$59$	−2.54164	−0.330893	−0.165447	−	0.986219i	$-0.552907\pi$
$59$	−2.54164	−0.330893	−0.165447	+	0.986219i	$0.552907\pi$
$60$	−2.99714	−0.386929
$61$	−0.166499	−0.0213181	−0.0106590	−	0.999943i	$-0.503393\pi$
$61$	−0.166499	−0.0213181	−0.0106590	+	0.999943i	$0.503393\pi$
$62$	−16.8109	−2.13498
$63$	5.19580	0.654609
$64$	−4.10678	−0.513347
$65$	−2.49673	−0.309682
$66$	5.80868	0.714999
$67$	−0.834826	−0.101990	−0.0509951	−	0.998699i	$-0.516239\pi$
$67$	−0.834826	−0.101990	−0.0509951	+	0.998699i	$0.516239\pi$
$68$	−8.80997	−1.06837
$69$	−4.26399	−0.513325
$70$	6.49921	0.776804
$71$	−9.71132	−1.15252	−0.576261	−	0.817266i	$-0.695489\pi$
$71$	−9.71132	−1.15252	−0.576261	+	0.817266i	$0.695489\pi$
$72$	15.5798	1.83610
$73$	−7.32846	−0.857732	−0.428866	−	0.903368i	$-0.641087\pi$
$73$	−7.32846	−0.857732	−0.428866	+	0.903368i	$0.641087\pi$
$74$	23.4127	2.72168
$75$	1.60735	0.185601
$76$	−4.27304	−0.490151
$77$	−8.58007	−0.977789
$78$	−2.34807	−0.265866
$79$	−12.8687	−1.44784	−0.723921	−	0.689883i	$-0.757662\pi$
$79$	−12.8687	−1.44784	−0.723921	+	0.689883i	$0.757662\pi$
$80$	7.80787	0.872947
$81$	6.69902	0.744335
$82$	19.6011	2.16458
$83$	−9.28046	−1.01866	−0.509332	−	0.860570i	$-0.670107\pi$
$83$	−9.28046	−1.01866	−0.509332	+	0.860570i	$0.670107\pi$
$84$	4.16350	0.454275
$85$	−2.81788	−0.305642
$86$	−23.2453	−2.50660
$87$	−0.00900728	−0.000965682 0
$88$	−25.7276	−2.74257
$89$	−12.6605	−1.34202	−0.671008	−	0.741450i	$-0.734138\pi$
$89$	−12.6605	−1.34202	−0.671008	+	0.741450i	$0.734138\pi$
$90$	9.36785	0.987458
$91$	3.46836	0.363582
$92$	35.5033	3.70148
$93$	−3.44457	−0.357186
$94$	−28.7449	−2.96481
$95$	−1.36674	−0.140224
$96$	1.49963	0.153056
$97$	14.5977	1.48217	0.741087	−	0.671409i	$-0.234311\pi$
$97$	14.5977	1.48217	0.741087	+	0.671409i	$0.234311\pi$
$98$	8.50379	0.859013
$99$	−12.3672	−1.24295
$100$	−13.3833	−1.33833
$101$	15.1087	1.50337	0.751686	−	0.659522i	$-0.229241\pi$
$101$	15.1087	1.50337	0.751686	+	0.659522i	$0.229241\pi$
$102$	−2.65009	−0.262398
$103$	12.4564	1.22736	0.613682	−	0.789554i	$-0.289688\pi$
$103$	12.4564	1.22736	0.613682	+	0.789554i	$0.289688\pi$
$104$	10.4000	1.01980
$105$	1.33170	0.129961
$106$	−21.0466	−2.04422
$107$	−14.3783	−1.39000	−0.694999	−	0.719010i	$-0.744595\pi$
$107$	−14.3783	−1.39000	−0.694999	+	0.719010i	$0.744595\pi$
$108$	12.5799	1.21050
$109$	−7.43761	−0.712394	−0.356197	−	0.934411i	$-0.615927\pi$
$109$	−7.43761	−0.712394	−0.356197	+	0.934411i	$0.615927\pi$
$110$	−15.4696	−1.47496
$111$	4.79731	0.455341
$112$	−10.8464	−1.02489
$113$	14.9837	1.40954	0.704772	−	0.709434i	$-0.251049\pi$
$113$	14.9837	1.40954	0.704772	+	0.709434i	$0.251049\pi$
$114$	−1.28536	−0.120385
$115$	11.3558	1.05893
$116$	0.0749973	0.00696333
$117$	4.99923	0.462179
$118$	6.36580	0.586019
$119$	3.91448	0.358840
$120$	3.99315	0.364523
$121$	9.42245	0.856587
$122$	0.417015	0.0377548
$123$	4.01631	0.362138
$124$	28.6806	2.57559
$125$	−11.1143	−0.994098
$126$	−13.0134	−1.15933
$127$	18.0555	1.60217	0.801083	−	0.598554i	$-0.204258\pi$
$127$	18.0555	1.60217	0.801083	+	0.598554i	$0.204258\pi$
$128$	16.1301	1.42571
$129$	−4.76300	−0.419359
$130$	6.25333	0.548453
$131$	−4.65334	−0.406564	−0.203282	−	0.979120i	$-0.565161\pi$
$131$	−4.65334	−0.406564	−0.203282	+	0.979120i	$0.565161\pi$
$132$	−9.91004	−0.862558
$133$	1.89861	0.164631
$134$	2.09091	0.180627
$135$	4.02371	0.346306
$136$	11.7377	1.00650
$137$	−14.1215	−1.20648	−0.603239	−	0.797561i	$-0.706123\pi$
$137$	−14.1215	−1.20648	−0.603239	+	0.797561i	$0.706123\pi$
$138$	10.6796	0.909109
$139$	11.0416	0.936538	0.468269	−	0.883586i	$-0.344878\pi$
$139$	11.0416	0.936538	0.468269	+	0.883586i	$0.344878\pi$
$140$	−11.0881	−0.937119
$141$	−5.88987	−0.496017
$142$	24.3230	2.04114
$143$	−8.25545	−0.690356
$144$	−15.6338	−1.30281
$145$	0.0239880	0.00199209
$146$	18.3549	1.51906
$147$	1.74244	0.143714
$148$	−39.9439	−3.28337
$149$	9.44357	0.773648	0.386824	−	0.922154i	$-0.373572\pi$
$149$	9.44357	0.773648	0.386824	+	0.922154i	$0.373572\pi$
$150$	−4.02577	−0.328703
$151$	9.40252	0.765166	0.382583	−	0.923921i	$-0.375035\pi$
$151$	9.40252	0.765166	0.382583	+	0.923921i	$0.375035\pi$
$152$	5.69306	0.461768
$153$	5.64226	0.456150
$154$	21.4897	1.73169
$155$	9.17352	0.736835
$156$	4.00598	0.320735
$157$	5.43678	0.433902	0.216951	−	0.976182i	$-0.430389\pi$
$157$	5.43678	0.433902	0.216951	+	0.976182i	$0.430389\pi$
$158$	32.2310	2.56416
$159$	−4.31248	−0.342002
$160$	−3.99379	−0.315737
$161$	−15.7750	−1.24324
$162$	−16.7784	−1.31823
$163$	22.3496	1.75056	0.875279	−	0.483618i	$-0.160678\pi$
$163$	22.3496	1.75056	0.875279	+	0.483618i	$0.160678\pi$
$164$	−33.4410	−2.61130
$165$	−3.16974	−0.246764
$166$	23.2439	1.80408
$167$	1.67028	0.129250	0.0646249	−	0.997910i	$-0.479415\pi$
$167$	1.67028	0.129250	0.0646249	+	0.997910i	$0.479415\pi$
$168$	−5.54711	−0.427969
$169$	−9.66286	−0.743297
$170$	7.05768	0.541299
$171$	2.73663	0.209275
$172$	39.6582	3.02391
$173$	−1.48262	−0.112722	−0.0563609	−	0.998410i	$-0.517950\pi$
$173$	−1.48262	−0.112722	−0.0563609	+	0.998410i	$0.517950\pi$
$174$	0.0225597	0.00171024
$175$	5.94651	0.449514
$176$	25.8168	1.94601
$177$	1.30436	0.0980420
$178$	31.7097	2.37674
$179$	8.16533	0.610306	0.305153	−	0.952303i	$-0.401292\pi$
$179$	8.16533	0.610306	0.305153	+	0.952303i	$0.401292\pi$
$180$	−15.9822	−1.19125
$181$	−3.79605	−0.282158	−0.141079	−	0.989998i	$-0.545057\pi$
$181$	−3.79605	−0.282158	−0.141079	+	0.989998i	$0.545057\pi$
$182$	−8.68686	−0.643913
$183$	0.0854471	0.00631643
$184$	−47.3018	−3.48714
$185$	−12.7761	−0.939318
$186$	8.62729	0.632584
$187$	−9.31733	−0.681351
$188$	49.0409	3.57667
$189$	−5.58956	−0.406581
$190$	3.42314	0.248340
$191$	24.2219	1.75263	0.876316	−	0.481736i	$-0.159994\pi$
$191$	24.2219	1.75263	0.876316	+	0.481736i	$0.159994\pi$
$192$	2.10759	0.152102
$193$	−9.81488	−0.706491	−0.353245	−	0.935531i	$-0.614922\pi$
$193$	−9.81488	−0.706491	−0.353245	+	0.935531i	$0.614922\pi$
$194$	−36.5615	−2.62496
$195$	1.28132	0.0917570
$196$	−14.5081	−1.03629
$197$	−17.3897	−1.23897	−0.619483	−	0.785010i	$-0.712658\pi$
$197$	−17.3897	−1.23897	−0.619483	+	0.785010i	$0.712658\pi$
$198$	30.9748	2.20128
$199$	−12.0080	−0.851221	−0.425611	−	0.904906i	$-0.639941\pi$
$199$	−12.0080	−0.851221	−0.425611	+	0.904906i	$0.639941\pi$
$200$	17.8308	1.26083
$201$	0.428431	0.0302192
$202$	−37.8413	−2.66250
$203$	−0.0333231	−0.00233882
$204$	4.52126	0.316551
$205$	−10.6962	−0.747052
$206$	−31.1983	−2.17369
$207$	−22.7378	−1.58038
$208$	−10.4360	−0.723607
$209$	−4.51912	−0.312594
$210$	−3.33538	−0.230163
$211$	1.04697	0.0720761	0.0360381	−	0.999350i	$-0.488526\pi$
$211$	1.04697	0.0720761	0.0360381	+	0.999350i	$0.488526\pi$
$212$	35.9070	2.46610
$213$	4.98383	0.341486
$214$	36.0118	2.46172
$215$	12.6847	0.865091
$216$	−16.7605	−1.14041
$217$	−12.7435	−0.865083
$218$	18.6283	1.26166
$219$	3.76095	0.254141
$220$	26.3922	1.77936
$221$	3.76638	0.253354
$222$	−12.0154	−0.806418
$223$	10.7113	0.717280	0.358640	−	0.933476i	$-0.383241\pi$
$223$	10.7113	0.717280	0.358640	+	0.933476i	$0.383241\pi$
$224$	5.54800	0.370692
$225$	8.57120	0.571413
$226$	−37.5281	−2.49633
$227$	14.8784	0.987511	0.493756	−	0.869601i	$-0.335624\pi$
$227$	14.8784	0.987511	0.493756	+	0.869601i	$0.335624\pi$
$228$	2.19291	0.145229
$229$	13.4868	0.891231	0.445615	−	0.895225i	$-0.352985\pi$
$229$	13.4868	0.891231	0.445615	+	0.895225i	$0.352985\pi$
$230$	−28.4417	−1.87539
$231$	4.40327	0.289714
$232$	−0.0999205	−0.00656010
$233$	4.66212	0.305425	0.152713	−	0.988271i	$-0.451199\pi$
$233$	4.66212	0.305425	0.152713	+	0.988271i	$0.451199\pi$
$234$	−12.5211	−0.818529
$235$	15.6858	1.02323
$236$	−10.8605	−0.706960
$237$	6.60419	0.428988
$238$	−9.80422	−0.635513
$239$	−28.7103	−1.85711	−0.928556	−	0.371193i	$-0.878949\pi$
$239$	−28.7103	−1.85711	−0.928556	+	0.371193i	$0.878949\pi$
$240$	−4.00698	−0.258650
$241$	−8.12760	−0.523545	−0.261772	−	0.965130i	$-0.584307\pi$
$241$	−8.12760	−0.523545	−0.261772	+	0.965130i	$0.584307\pi$
$242$	−23.5995	−1.51703
$243$	−12.2700	−0.787120
$244$	−0.711459	−0.0455465
$245$	−4.64044	−0.296467
$246$	−10.0593	−0.641355
$247$	1.82678	0.116235
$248$	−38.2117	−2.42645
$249$	4.76271	0.301825
$250$	27.8370	1.76057
$251$	−17.7220	−1.11860	−0.559302	−	0.828964i	$-0.688931\pi$
$251$	−17.7220	−1.11860	−0.559302	+	0.828964i	$0.688931\pi$
$252$	22.2019	1.39859
$253$	37.5479	2.36062
$254$	−45.2218	−2.83747
$255$	1.44613	0.0905602
$256$	−32.1860	−2.01162
$257$	4.70706	0.293619	0.146809	−	0.989165i	$-0.453100\pi$
$257$	4.70706	0.293619	0.146809	+	0.989165i	$0.453100\pi$
$258$	11.9294	0.742694
$259$	17.7480	1.10281
$260$	−10.6686	−0.661641
$261$	−0.0480313	−0.00297307
$262$	11.6548	0.720034
$263$	19.5037	1.20265	0.601326	−	0.799004i	$-0.294639\pi$
$263$	19.5037	1.20265	0.601326	+	0.799004i	$0.294639\pi$
$264$	13.2034	0.812611
$265$	11.4849	0.705512
$266$	−4.75527	−0.291565
$267$	6.49736	0.397632
$268$	−3.56725	−0.217904
$269$	−18.6127	−1.13483	−0.567417	−	0.823430i	$-0.692057\pi$
$269$	−18.6127	−1.13483	−0.567417	+	0.823430i	$0.692057\pi$
$270$	−10.0778	−0.613315
$271$	17.2742	1.04933	0.524667	−	0.851308i	$-0.324190\pi$
$271$	17.2742	1.04933	0.524667	+	0.851308i	$0.324190\pi$
$272$	−11.7784	−0.714169
$273$	−1.77995	−0.107728
$274$	35.3686	2.13670
$275$	−14.1540	−0.853519
$276$	−18.2202	−1.09673
$277$	−15.8347	−0.951415	−0.475708	−	0.879604i	$-0.657808\pi$
$277$	−15.8347	−0.951415	−0.475708	+	0.879604i	$0.657808\pi$
$278$	−27.6549	−1.65863
$279$	−18.3682	−1.09968
$280$	14.7730	0.882853
$281$	−7.94931	−0.474216	−0.237108	−	0.971483i	$-0.576200\pi$
$281$	−7.94931	−0.474216	−0.237108	+	0.971483i	$0.576200\pi$
$282$	14.7518	0.878457
$283$	11.4964	0.683387	0.341694	−	0.939811i	$-0.388999\pi$
$283$	11.4964	0.683387	0.341694	+	0.939811i	$0.388999\pi$
$284$	−41.4968	−2.46238
$285$	0.701406	0.0415477
$286$	20.6766	1.22264
$287$	14.8586	0.877078
$288$	7.99679	0.471216
$289$	−12.7492	−0.749950
$290$	−0.0600804	−0.00352804
$291$	−7.49151	−0.439160
$292$	−31.3148	−1.83256
$293$	−17.7281	−1.03568	−0.517842	−	0.855476i	$-0.673265\pi$
$293$	−17.7281	−1.03568	−0.517842	+	0.855476i	$0.673265\pi$
$294$	−4.36413	−0.254521
$295$	−3.47375	−0.202250
$296$	53.2181	3.09324
$297$	13.3044	0.772000
$298$	−23.6524	−1.37015
$299$	−15.1782	−0.877775
$300$	6.86827	0.396540
$301$	−17.6211	−1.01566
$302$	−23.5496	−1.35513
$303$	−7.75375	−0.445441
$304$	−5.71278	−0.327651
$305$	−0.227561	−0.0130301
$306$	−14.1316	−0.807852
$307$	−3.38877	−0.193407	−0.0967037	−	0.995313i	$-0.530830\pi$
$307$	−3.38877	−0.193407	−0.0967037	+	0.995313i	$0.530830\pi$
$308$	−36.6630	−2.08907
$309$	−6.39258	−0.363661
$310$	−22.9760	−1.30495
$311$	19.8594	1.12612	0.563060	−	0.826416i	$-0.309624\pi$
$311$	19.8594	1.12612	0.563060	+	0.826416i	$0.309624\pi$
$312$	−5.33725	−0.302162
$313$	16.2630	0.919239	0.459619	−	0.888116i	$-0.347986\pi$
$313$	16.2630	0.919239	0.459619	+	0.888116i	$0.347986\pi$
$314$	−13.6170	−0.768450
$315$	7.10129	0.400113
$316$	−54.9885	−3.09334
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	10.8011	0.605693
$319$	0.0793164	0.00444086
$320$	−5.61289	−0.313770
$321$	7.37889	0.411849
$322$	39.5100	2.20181
$323$	2.06176	0.114719
$324$	28.6252	1.59029
$325$	5.72154	0.317374
$326$	−55.9770	−3.10028
$327$	3.81696	0.211079
$328$	44.5542	2.46009
$329$	−21.7900	−1.20132
$330$	7.93894	0.437024
$331$	−4.17707	−0.229593	−0.114796	−	0.993389i	$-0.536622\pi$
$331$	−4.17707	−0.229593	−0.114796	+	0.993389i	$0.536622\pi$
$332$	−39.6558	−2.17639
$333$	25.5817	1.40187
$334$	−4.18338	−0.228904
$335$	−1.14099	−0.0623389
$336$	5.56633	0.303668
$337$	−7.31259	−0.398342	−0.199171	−	0.979965i	$-0.563825\pi$
$337$	−7.31259	−0.398342	−0.199171	+	0.979965i	$0.563825\pi$
$338$	24.2016	1.31640
$339$	−7.68958	−0.417641
$340$	−12.0409	−0.653010
$341$	30.3323	1.64258
$342$	−6.85417	−0.370631
$343$	19.7366	1.06568
$344$	−52.8375	−2.84880
$345$	−5.82776	−0.313756
$346$	3.71338	0.199633
$347$	26.6048	1.42822	0.714110	−	0.700034i	$-0.246832\pi$
$347$	26.6048	1.42822	0.714110	+	0.700034i	$0.246832\pi$
$348$	−0.0384885	−0.00206320
$349$	31.3207	1.67656	0.838280	−	0.545240i	$-0.183561\pi$
$349$	31.3207	1.67656	0.838280	+	0.545240i	$0.183561\pi$
$350$	−14.8937	−0.796099
$351$	−5.37809	−0.287061
$352$	−13.2055	−0.703854
$353$	−5.04528	−0.268533	−0.134267	−	0.990945i	$-0.542868\pi$
$353$	−5.04528	−0.268533	−0.134267	+	0.990945i	$0.542868\pi$
$354$	−3.26691	−0.173634
$355$	−13.2728	−0.704448
$356$	−54.0990	−2.86724
$357$	−2.00890	−0.106322
$358$	−20.4509	−1.08086
$359$	22.7678	1.20164	0.600819	−	0.799385i	$-0.294841\pi$
$359$	22.7678	1.20164	0.600819	+	0.799385i	$0.294841\pi$
$360$	21.2935	1.12227
$361$	1.00000	0.0526316
$362$	9.50759	0.499708
$363$	−4.83558	−0.253802
$364$	14.8204	0.776801
$365$	−10.0161	−0.524266
$366$	−0.214011	−0.0111865
$367$	20.8232	1.08696	0.543482	−	0.839421i	$-0.317106\pi$
$367$	20.8232	1.08696	0.543482	+	0.839421i	$0.317106\pi$
$368$	47.4657	2.47432
$369$	21.4170	1.11492
$370$	31.9991	1.66355
$371$	−15.9543	−0.828308
$372$	−14.7188	−0.763134
$373$	−17.6106	−0.911842	−0.455921	−	0.890020i	$-0.650690\pi$
$373$	−17.6106	−0.911842	−0.455921	+	0.890020i	$0.650690\pi$
$374$	23.3362	1.20669
$375$	5.70386	0.294546
$376$	−65.3382	−3.36956
$377$	−0.0320624	−0.00165130
$378$	13.9996	0.720064
$379$	25.7846	1.32447	0.662233	−	0.749298i	$-0.269609\pi$
$379$	25.7846	1.32447	0.662233	+	0.749298i	$0.269609\pi$
$380$	−5.84012	−0.299592
$381$	−9.26603	−0.474713
$382$	−60.6662	−3.10395
$383$	24.3265	1.24303	0.621514	−	0.783403i	$-0.286518\pi$
$383$	24.3265	1.24303	0.621514	+	0.783403i	$0.286518\pi$
$384$	−8.27794	−0.422432
$385$	−11.7267	−0.597648
$386$	24.5824	1.25121
$387$	−25.3987	−1.29109
$388$	62.3766	3.16669
$389$	−4.28644	−0.217331	−0.108666	−	0.994078i	$-0.534658\pi$
$389$	−4.28644	−0.217331	−0.108666	+	0.994078i	$0.534658\pi$
$390$	−3.20919	−0.162504
$391$	−17.1305	−0.866326
$392$	19.3295	0.976285
$393$	2.38808	0.120463
$394$	43.5543	2.19424
$395$	−17.5881	−0.884955
$396$	−52.8453	−2.65558
$397$	2.34457	0.117670	0.0588352	−	0.998268i	$-0.481261\pi$
$397$	2.34457	0.117670	0.0588352	+	0.998268i	$0.481261\pi$
$398$	30.0752	1.50753
$399$	−0.974364	−0.0487792
$400$	−17.8926	−0.894630
$401$	12.6422	0.631322	0.315661	−	0.948872i	$-0.397774\pi$
$401$	12.6422	0.631322	0.315661	+	0.948872i	$0.397774\pi$
$402$	−1.07305	−0.0535189
$403$	−12.2613	−0.610781
$404$	64.5600	3.21198
$405$	9.15580	0.454955
$406$	0.0834612	0.00414211
$407$	−42.2442	−2.09397
$408$	−6.02377	−0.298221
$409$	−15.6375	−0.773223	−0.386611	−	0.922243i	$-0.626355\pi$
$409$	−15.6375	−0.773223	−0.386611	+	0.922243i	$0.626355\pi$
$410$	26.7896	1.32305
$411$	7.24710	0.357473
$412$	53.2266	2.62228
$413$	4.82559	0.237452
$414$	56.9491	2.79889
$415$	−12.6840	−0.622631
$416$	5.33810	0.261722
$417$	−5.66653	−0.277491
$418$	11.3186	0.553611
$419$	−31.5440	−1.54103	−0.770513	−	0.637425i	$-0.780000\pi$
$419$	−31.5440	−1.54103	−0.770513	+	0.637425i	$0.780000\pi$
$420$	5.69041	0.277663
$421$	−14.8476	−0.723627	−0.361814	−	0.932250i	$-0.617842\pi$
$421$	−14.8476	−0.723627	−0.361814	+	0.932250i	$0.617842\pi$
$422$	−2.62224	−0.127648
$423$	−31.4078	−1.52710
$424$	−47.8397	−2.32330
$425$	6.45748	0.313234
$426$	−12.4825	−0.604780
$427$	0.316118	0.0152980
$428$	−61.4389	−2.96976
$429$	4.23668	0.204549
$430$	−31.7702	−1.53210
$431$	11.4475	0.551408	0.275704	−	0.961243i	$-0.411089\pi$
$431$	11.4475	0.551408	0.275704	+	0.961243i	$0.411089\pi$
$432$	16.8186	0.809184
$433$	20.5020	0.985261	0.492630	−	0.870239i	$-0.336035\pi$
$433$	20.5020	0.985261	0.492630	+	0.870239i	$0.336035\pi$
$434$	31.9173	1.53208
$435$	−0.0123106	−0.000590247 0
$436$	−31.7812	−1.52204
$437$	−8.30868	−0.397458
$438$	−9.41969	−0.450090
$439$	−4.45724	−0.212732	−0.106366	−	0.994327i	$-0.533922\pi$
$439$	−4.45724	−0.212732	−0.106366	+	0.994327i	$0.533922\pi$
$440$	−35.1629	−1.67633
$441$	9.29158	0.442456
$442$	−9.43330	−0.448696
$443$	−8.49336	−0.403532	−0.201766	−	0.979434i	$-0.564668\pi$
$443$	−8.49336	−0.403532	−0.201766	+	0.979434i	$0.564668\pi$
$444$	20.4991	0.972844
$445$	−17.3036	−0.820272
$446$	−26.8275	−1.27032
$447$	−4.84642	−0.229228
$448$	7.79719	0.368382
$449$	−15.1559	−0.715252	−0.357626	−	0.933865i	$-0.616414\pi$
$449$	−15.1559	−0.715252	−0.357626	+	0.933865i	$0.616414\pi$
$450$	−21.4675	−1.01199
$451$	−35.3669	−1.66536
$452$	64.0258	3.01152
$453$	−4.82535	−0.226715
$454$	−37.2644	−1.74890
$455$	4.74033	0.222230
$456$	−2.92167	−0.136820
$457$	−8.06879	−0.377442	−0.188721	−	0.982031i	$-0.560434\pi$
$457$	−8.06879	−0.377442	−0.188721	+	0.982031i	$0.560434\pi$
$458$	−33.7790	−1.57839
$459$	−6.06986	−0.283317
$460$	48.5237	2.26243
$461$	36.7918	1.71356	0.856782	−	0.515678i	$-0.172460\pi$
$461$	36.7918	1.71356	0.856782	+	0.515678i	$0.172460\pi$
$462$	−11.0284	−0.513090
$463$	−15.6788	−0.728657	−0.364329	−	0.931270i	$-0.618702\pi$
$463$	−15.6788	−0.728657	−0.364329	+	0.931270i	$0.618702\pi$
$464$	0.100267	0.00465476
$465$	−4.70783	−0.218320
$466$	−11.6768	−0.540915
$467$	−1.73928	−0.0804842	−0.0402421	−	0.999190i	$-0.512813\pi$
$467$	−1.73928	−0.0804842	−0.0402421	+	0.999190i	$0.512813\pi$
$468$	21.3619	0.987454
$469$	1.58501	0.0731891
$470$	−39.2867	−1.81216
$471$	−2.79014	−0.128563
$472$	14.4697	0.666022
$473$	41.9421	1.92850
$474$	−16.5409	−0.759747
$475$	3.13203	0.143707
$476$	16.7267	0.766668
$477$	−22.9963	−1.05293
$478$	71.9078	3.28899
$479$	−7.95011	−0.363250	−0.181625	−	0.983368i	$-0.558136\pi$
$479$	−7.95011	−0.363250	−0.181625	+	0.983368i	$0.558136\pi$
$480$	2.04960	0.0935512
$481$	17.0766	0.778624
$482$	20.3564	0.927209
$483$	8.09568	0.368366
$484$	40.2625	1.83011
$485$	19.9512	0.905939
$486$	30.7315	1.39401
$487$	15.5369	0.704043	0.352021	−	0.935992i	$-0.385494\pi$
$487$	15.5369	0.704043	0.352021	+	0.935992i	$0.385494\pi$
$488$	0.947891	0.0429090
$489$	−11.4698	−0.518681
$490$	11.6225	0.525049
$491$	−19.2374	−0.868171	−0.434085	−	0.900872i	$-0.642928\pi$
$491$	−19.2374	−0.868171	−0.434085	+	0.900872i	$0.642928\pi$
$492$	17.1618	0.773716
$493$	−0.0361865	−0.00162976
$494$	−4.57537	−0.205855
$495$	−16.9027	−0.759718
$496$	38.3441	1.72170
$497$	18.4380	0.827059
$498$	−11.9287	−0.534538
$499$	22.7029	1.01632	0.508161	−	0.861262i	$-0.330326\pi$
$499$	22.7029	1.01632	0.508161	+	0.861262i	$0.330326\pi$
$500$	−47.4920	−2.12391
$501$	−0.857182	−0.0382960
$502$	44.3866	1.98107
$503$	17.1372	0.764110	0.382055	−	0.924140i	$-0.375216\pi$
$503$	17.1372	0.764110	0.382055	+	0.924140i	$0.375216\pi$
$504$	−29.5800	−1.31760
$505$	20.6496	0.918896
$506$	−94.0427	−4.18071
$507$	4.95896	0.220235
$508$	77.1518	3.42306
$509$	36.1687	1.60315	0.801575	−	0.597894i	$-0.203996\pi$
$509$	36.1687	1.60315	0.801575	+	0.597894i	$0.203996\pi$
$510$	−3.62198	−0.160384
$511$	13.9139	0.615516
$512$	48.3529	2.13692
$513$	−2.94402	−0.129982
$514$	−11.7893	−0.520005
$515$	17.0246	0.750193
$516$	−20.3525	−0.895969
$517$	51.8651	2.28102
$518$	−44.4518	−1.95310
$519$	0.760879	0.0333989
$520$	14.2141	0.623327
$521$	−41.8201	−1.83217	−0.916086	−	0.400981i	$-0.868669\pi$
$521$	−41.8201	−1.83217	−0.916086	+	0.400981i	$0.868669\pi$
$522$	0.120299	0.00526536
$523$	−5.66808	−0.247848	−0.123924	−	0.992292i	$-0.539548\pi$
$523$	−5.66808	−0.247848	−0.123924	+	0.992292i	$0.539548\pi$
$524$	−19.8839	−0.868632
$525$	−3.05174	−0.133189
$526$	−48.8491	−2.12992
$527$	−13.8385	−0.602814
$528$	−13.2491	−0.576593
$529$	46.0341	2.00148
$530$	−28.7651	−1.24948
$531$	6.95552	0.301844
$532$	8.11285	0.351737
$533$	14.2965	0.619250
$534$	−16.2733	−0.704216
$535$	−19.6513	−0.849600
$536$	4.75272	0.205286
$537$	−4.19043	−0.180830
$538$	46.6174	2.00982
$539$	−15.3436	−0.660896
$540$	17.1935	0.739889
$541$	0.847386	0.0364320	0.0182160	−	0.999834i	$-0.494201\pi$
$541$	0.847386	0.0364320	0.0182160	+	0.999834i	$0.494201\pi$
$542$	−43.2651	−1.85839
$543$	1.94812	0.0836019
$544$	6.02473	0.258308
$545$	−10.1653	−0.435432
$546$	4.45807	0.190788
$547$	1.47582	0.0631014	0.0315507	−	0.999502i	$-0.489955\pi$
$547$	1.47582	0.0631014	0.0315507	+	0.999502i	$0.489955\pi$
$548$	−60.3415	−2.57766
$549$	0.455647	0.0194465
$550$	35.4502	1.51160
$551$	−0.0175513	−0.000747710 0
$552$	24.2752	1.03322
$553$	24.4327	1.03898
$554$	39.6597	1.68498
$555$	6.55667	0.278315
$556$	47.1813	2.00093
$557$	41.8595	1.77364	0.886822	−	0.462111i	$-0.152908\pi$
$557$	41.8595	1.77364	0.886822	+	0.462111i	$0.152908\pi$
$558$	46.0051	1.94755
$559$	−16.9544	−0.717096
$560$	−14.8241	−0.626434
$561$	4.78163	0.201881
$562$	19.9099	0.839847
$563$	−19.4620	−0.820227	−0.410114	−	0.912034i	$-0.634511\pi$
$563$	−19.4620	−0.820227	−0.410114	+	0.912034i	$0.634511\pi$
$564$	−25.1677	−1.05975
$565$	20.4787	0.861547
$566$	−28.7938	−1.21029
$567$	−12.7188	−0.534141
$568$	55.2871	2.31980
$569$	13.1818	0.552609	0.276305	−	0.961070i	$-0.410890\pi$
$569$	13.1818	0.552609	0.276305	+	0.961070i	$0.410890\pi$
$570$	−1.75675	−0.0735820
$571$	21.4061	0.895819	0.447910	−	0.894079i	$-0.352169\pi$
$571$	21.4061	0.895819	0.447910	+	0.894079i	$0.352169\pi$
$572$	−35.2759	−1.47496
$573$	−12.4306	−0.519296
$574$	−37.2150	−1.55332
$575$	−26.0230	−1.08523
$576$	11.2387	0.468280
$577$	11.7399	0.488740	0.244370	−	0.969682i	$-0.421419\pi$
$577$	11.7399	0.488740	0.244370	+	0.969682i	$0.421419\pi$
$578$	31.9316	1.32818
$579$	5.03697	0.209330
$580$	0.102502	0.00425615
$581$	17.6200	0.731001
$582$	18.7633	0.777763
$583$	37.9749	1.57276
$584$	41.7214	1.72644
$585$	6.83263	0.282494
$586$	44.4018	1.83422
$587$	−10.4721	−0.432231	−0.216116	−	0.976368i	$-0.569339\pi$
$587$	−10.4721	−0.432231	−0.216116	+	0.976368i	$0.569339\pi$
$588$	7.44552	0.307048
$589$	−6.71198	−0.276563
$590$	8.70038	0.358189
$591$	8.92436	0.367099
$592$	−53.4024	−2.19483
$593$	−22.2950	−0.915544	−0.457772	−	0.889070i	$-0.651352\pi$
$593$	−22.2950	−0.915544	−0.457772	+	0.889070i	$0.651352\pi$
$594$	−33.3222	−1.36723
$595$	5.35007	0.219331
$596$	40.3528	1.65291
$597$	6.16245	0.252212
$598$	38.0153	1.55456
$599$	15.0550	0.615133	0.307566	−	0.951527i	$-0.400485\pi$
$599$	15.0550	0.615133	0.307566	+	0.951527i	$0.400485\pi$
$600$	−9.15074	−0.373577
$601$	30.1074	1.22811	0.614053	−	0.789265i	$-0.289538\pi$
$601$	30.1074	1.22811	0.614053	+	0.789265i	$0.289538\pi$
$602$	44.1338	1.79876
$603$	2.28461	0.0930365
$604$	40.1773	1.63479
$605$	12.8780	0.523566
$606$	19.4201	0.788886
$607$	−47.1296	−1.91293	−0.956465	−	0.291847i	$-0.905730\pi$
$607$	−47.1296	−1.91293	−0.956465	+	0.291847i	$0.905730\pi$
$608$	2.92213	0.118508
$609$	0.0171013	0.000692981 0
$610$	0.569950	0.0230766
$611$	−20.9656	−0.848179
$612$	24.1096	0.974573
$613$	1.96983	0.0795608	0.0397804	−	0.999208i	$-0.487334\pi$
$613$	1.96983	0.0795608	0.0397804	+	0.999208i	$0.487334\pi$
$614$	8.48753	0.342529
$615$	5.48924	0.221348
$616$	48.8468	1.96809
$617$	43.4929	1.75096	0.875479	−	0.483255i	$-0.160546\pi$
$617$	43.4929	1.75096	0.875479	+	0.483255i	$0.160546\pi$
$618$	16.0109	0.644052
$619$	8.13256	0.326875	0.163438	−	0.986554i	$-0.447742\pi$
$619$	8.13256	0.326875	0.163438	+	0.986554i	$0.447742\pi$
$620$	39.1988	1.57426
$621$	24.4610	0.981584
$622$	−49.7398	−1.99438
$623$	24.0375	0.963042
$624$	5.35574	0.214401
$625$	0.469749	0.0187899
$626$	−40.7324	−1.62799
$627$	2.31920	0.0926200
$628$	23.2316	0.927040
$629$	19.2731	0.768468
$630$	−17.7859	−0.708608
$631$	−7.82544	−0.311526	−0.155763	−	0.987794i	$-0.549784\pi$
$631$	−7.82544	−0.311526	−0.155763	+	0.987794i	$0.549784\pi$
$632$	73.2623	2.91422
$633$	−0.537301	−0.0213558
$634$	−2.50460	−0.0994705
$635$	24.6771	0.979281
$636$	−18.4274	−0.730694
$637$	6.20241	0.245749
$638$	−0.198656	−0.00786487
$639$	26.5763	1.05134
$640$	22.0456	0.871430
$641$	41.2215	1.62815	0.814075	−	0.580760i	$-0.197245\pi$
$641$	41.2215	1.62815	0.814075	+	0.580760i	$0.197245\pi$
$642$	−18.4812	−0.729394
$643$	8.32234	0.328201	0.164101	−	0.986444i	$-0.447528\pi$
$643$	8.32234	0.328201	0.164101	+	0.986444i	$0.447528\pi$
$644$	−67.4071	−2.65621
$645$	−6.50977	−0.256322
$646$	−5.16389	−0.203170
$647$	13.8714	0.545341	0.272670	−	0.962107i	$-0.412093\pi$
$647$	13.8714	0.545341	0.272670	+	0.962107i	$0.412093\pi$
$648$	−38.1379	−1.49820
$649$	−11.4860	−0.450864
$650$	−14.3302	−0.562076
$651$	6.53992	0.256320
$652$	95.5009	3.74010
$653$	41.3044	1.61637	0.808183	−	0.588931i	$-0.200451\pi$
$653$	41.3044	1.61637	0.808183	+	0.588931i	$0.200451\pi$
$654$	−9.55998	−0.373825
$655$	−6.35989	−0.248501
$656$	−44.7085	−1.74557
$657$	20.0553	0.782431
$658$	54.5754	2.12757
$659$	22.4660	0.875151	0.437576	−	0.899182i	$-0.355837\pi$
$659$	22.4660	0.875151	0.437576	+	0.899182i	$0.355837\pi$
$660$	−13.5444	−0.527216
$661$	39.2383	1.52619	0.763097	−	0.646283i	$-0.223678\pi$
$661$	39.2383	1.52619	0.763097	+	0.646283i	$0.223678\pi$
$662$	10.4619	0.406614
$663$	−1.93290	−0.0750676
$664$	52.8342	2.05037
$665$	2.59491	0.100626
$666$	−64.0720	−2.48274
$667$	0.145828	0.00564648
$668$	7.13715	0.276145
$669$	−5.49700	−0.212526
$670$	2.85772	0.110404
$671$	−0.752431	−0.0290473
$672$	−2.84722	−0.109834
$673$	11.3567	0.437768	0.218884	−	0.975751i	$-0.429758\pi$
$673$	11.3567	0.437768	0.218884	+	0.975751i	$0.429758\pi$
$674$	18.3151	0.705473
$675$	−9.22077	−0.354908
$676$	−41.2898	−1.58807
$677$	44.8574	1.72401	0.862004	−	0.506901i	$-0.169209\pi$
$677$	44.8574	1.72401	0.862004	+	0.506901i	$0.169209\pi$
$678$	19.2593	0.739651
$679$	−27.7154	−1.06362
$680$	16.0424	0.615197
$681$	−7.63554	−0.292594
$682$	−75.9703	−2.90905
$683$	−35.6323	−1.36343	−0.681715	−	0.731618i	$-0.738766\pi$
$683$	−35.6323	−1.36343	−0.681715	+	0.731618i	$0.738766\pi$
$684$	11.6937	0.447120
$685$	−19.3003	−0.737427
$686$	−49.4323	−1.88734
$687$	−6.92138	−0.264067
$688$	53.0205	2.02139
$689$	−15.3507	−0.584817
$690$	14.5962	0.555669
$691$	13.5408	0.515116	0.257558	−	0.966263i	$-0.417082\pi$
$691$	13.5408	0.515116	0.257558	+	0.966263i	$0.417082\pi$
$692$	−6.33531	−0.240832
$693$	23.4804	0.891948
$694$	−66.6344	−2.52941
$695$	15.0910	0.572434
$696$	0.0512790	0.00194373
$697$	16.1354	0.611172
$698$	−78.4460	−2.96923
$699$	−2.39259	−0.0904960
$700$	25.4097	0.960396
$701$	−11.4926	−0.434068	−0.217034	−	0.976164i	$-0.569638\pi$
$701$	−11.4926	−0.434068	−0.217034	+	0.976164i	$0.569638\pi$
$702$	13.4700	0.508392
$703$	9.34788	0.352562
$704$	−18.5590	−0.699470
$705$	−8.04991	−0.303177
$706$	12.6364	0.475578
$707$	−28.6856	−1.07883
$708$	5.57360	0.209469
$709$	27.7234	1.04118	0.520588	−	0.853808i	$-0.325713\pi$
$709$	27.7234	1.04118	0.520588	+	0.853808i	$0.325713\pi$
$710$	33.2432	1.24759
$711$	35.2168	1.32073
$712$	72.0773	2.70121
$713$	55.7677	2.08852
$714$	5.03150	0.188299
$715$	−11.2830	−0.421962
$716$	34.8908	1.30393
$717$	14.7340	0.550253
$718$	−57.0243	−2.12813
$719$	36.9822	1.37920	0.689601	−	0.724189i	$-0.257786\pi$
$719$	36.9822	1.37920	0.689601	+	0.724189i	$0.257786\pi$
$720$	−21.3672	−0.796310
$721$	−23.6498	−0.880766
$722$	−2.50460	−0.0932117
$723$	4.17107	0.155124
$724$	−16.2207	−0.602836
$725$	−0.0549711	−0.00204158
$726$	12.1112	0.449489
$727$	32.0007	1.18684	0.593420	−	0.804893i	$-0.297777\pi$
$727$	32.0007	1.18684	0.593420	+	0.804893i	$0.297777\pi$
$728$	−19.7456	−0.731819
$729$	−13.8001	−0.511116
$730$	25.0863	0.928486
$731$	−19.1352	−0.707742
$732$	0.365119	0.0134952
$733$	16.8738	0.623248	0.311624	−	0.950205i	$-0.399127\pi$
$733$	16.8738	0.623248	0.311624	+	0.950205i	$0.399127\pi$
$734$	−52.1539	−1.92504
$735$	2.38146	0.0878415
$736$	−24.2791	−0.894938
$737$	−3.77268	−0.138969
$738$	−53.6411	−1.97455
$739$	16.7535	0.616288	0.308144	−	0.951340i	$-0.400292\pi$
$739$	16.7535	0.616288	0.308144	+	0.951340i	$0.400292\pi$
$740$	−54.5928	−2.00687
$741$	−0.937501	−0.0344400
$742$	39.9593	1.46695
$743$	−16.0313	−0.588132	−0.294066	−	0.955785i	$-0.595009\pi$
$743$	−16.0313	−0.588132	−0.294066	+	0.955785i	$0.595009\pi$
$744$	19.6102	0.718944
$745$	12.9069	0.472872
$746$	44.1075	1.61489
$747$	25.3972	0.929234
$748$	−39.8133	−1.45572
$749$	27.2988	0.997475
$750$	−14.2859	−0.521647
$751$	51.7869	1.88973	0.944865	−	0.327461i	$-0.106193\pi$
$751$	51.7869	1.88973	0.944865	+	0.327461i	$0.106193\pi$
$752$	65.5645	2.39089
$753$	9.09490	0.331437
$754$	0.0803036	0.00292448
$755$	12.8508	0.467687
$756$	−23.8844	−0.868668
$757$	2.12369	0.0771868	0.0385934	−	0.999255i	$-0.487712\pi$
$757$	2.12369	0.0771868	0.0385934	+	0.999255i	$0.487712\pi$
$758$	−64.5802	−2.34566
$759$	−19.2695	−0.699439
$760$	7.78092	0.282244
$761$	−17.1672	−0.622311	−0.311156	−	0.950359i	$-0.600716\pi$
$761$	−17.1672	−0.622311	−0.311156	+	0.950359i	$0.600716\pi$
$762$	23.2077	0.840728
$763$	14.1211	0.511220
$764$	103.501	3.74453
$765$	7.71149	0.278810
$766$	−60.9283	−2.20143
$767$	4.64302	0.167650
$768$	16.5178	0.596034
$769$	21.1385	0.762272	0.381136	−	0.924519i	$-0.375533\pi$
$769$	21.1385	0.762272	0.381136	+	0.924519i	$0.375533\pi$
$770$	29.3707	1.05845
$771$	−2.41565	−0.0869977
$772$	−41.9394	−1.50943
$773$	−6.37504	−0.229294	−0.114647	−	0.993406i	$-0.536574\pi$
$773$	−6.37504	−0.229294	−0.114647	+	0.993406i	$0.536574\pi$
$774$	63.6137	2.28655
$775$	−21.0221	−0.755137
$776$	−83.1057	−2.98332
$777$	−9.10824	−0.326756
$778$	10.7358	0.384898
$779$	7.82605	0.280397
$780$	5.47512	0.196041
$781$	−43.8866	−1.57039
$782$	42.9051	1.53428
$783$	0.0516714	0.00184659
$784$	−19.3964	−0.692729
$785$	7.43065	0.265211
$786$	−5.98120	−0.213342
$787$	−8.02493	−0.286058	−0.143029	−	0.989719i	$-0.545684\pi$
$787$	−8.02493	−0.286058	−0.143029	+	0.989719i	$0.545684\pi$
$788$	−74.3069	−2.64708
$789$	−10.0093	−0.356339
$790$	44.0513	1.56728
$791$	−28.4482	−1.01150
$792$	70.4070	2.50180
$793$	0.304158	0.0108010
$794$	−5.87221	−0.208397
$795$	−5.89403	−0.209040
$796$	−51.3105	−1.81865
$797$	−30.6374	−1.08523	−0.542616	−	0.839981i	$-0.682566\pi$
$797$	−30.6374	−1.08523	−0.542616	+	0.839981i	$0.682566\pi$
$798$	2.44040	0.0863891
$799$	−23.6624	−0.837116
$800$	9.15221	0.323579
$801$	34.6472	1.22420
$802$	−31.6637	−1.11809
$803$	−33.1182	−1.16872
$804$	1.83070	0.0645639
$805$	−21.5602	−0.759899
$806$	30.7098	1.08171
$807$	9.55198	0.336246
$808$	−86.0147	−3.02599
$809$	−17.0376	−0.599010	−0.299505	−	0.954095i	$-0.596822\pi$
$809$	−17.0376	−0.599010	−0.299505	+	0.954095i	$0.596822\pi$
$810$	−22.9316	−0.805736
$811$	31.2615	1.09774	0.548871	−	0.835907i	$-0.315058\pi$
$811$	31.2615	1.09774	0.548871	+	0.835907i	$0.315058\pi$
$812$	−0.142391	−0.00499694
$813$	−8.86509	−0.310912
$814$	105.805	3.70846
$815$	30.5461	1.06998
$816$	6.04463	0.211604
$817$	−9.28103	−0.324702
$818$	39.1657	1.36939
$819$	−9.49160	−0.331663
$820$	−45.7051	−1.59609
$821$	48.0183	1.67585	0.837925	−	0.545785i	$-0.183768\pi$
$821$	48.0183	1.67585	0.837925	+	0.545785i	$0.183768\pi$
$822$	−18.1511	−0.633092
$823$	37.8028	1.31772	0.658862	−	0.752264i	$-0.271038\pi$
$823$	37.8028	1.31772	0.658862	+	0.752264i	$0.271038\pi$
$824$	−70.9149	−2.47044
$825$	7.26381	0.252893
$826$	−12.0862	−0.420532
$827$	5.58864	0.194336	0.0971680	−	0.995268i	$-0.469022\pi$
$827$	5.58864	0.194336	0.0971680	+	0.995268i	$0.469022\pi$
$828$	−97.1593	−3.37652
$829$	−35.7302	−1.24096	−0.620481	−	0.784222i	$-0.713062\pi$
$829$	−35.7302	−1.24096	−0.620481	+	0.784222i	$0.713062\pi$
$830$	31.7683	1.10269
$831$	8.12633	0.281899
$832$	7.50219	0.260092
$833$	7.00021	0.242543
$834$	14.1924	0.491443
$835$	2.28283	0.0790005
$836$	−19.3104	−0.667863
$837$	19.7602	0.683014
$838$	79.0052	2.72919
$839$	5.47141	0.188894	0.0944470	−	0.995530i	$-0.469892\pi$
$839$	5.47141	0.188894	0.0944470	+	0.995530i	$0.469892\pi$
$840$	−7.58145	−0.261585
$841$	−28.9997	−0.999989
$842$	37.1873	1.28156
$843$	4.07957	0.140508
$844$	4.47373	0.153992
$845$	−13.2066	−0.454321
$846$	78.6640	2.70452
$847$	−17.8896	−0.614694
$848$	48.0054	1.64851
$849$	−5.89990	−0.202484
$850$	−16.1734	−0.554744
$851$	−77.6686	−2.66244
$852$	21.2961	0.729592
$853$	43.8837	1.50255	0.751275	−	0.659990i	$-0.229439\pi$
$853$	43.8837	1.50255	0.751275	+	0.659990i	$0.229439\pi$
$854$	−0.791751	−0.0270931
$855$	3.74025	0.127914
$856$	81.8563	2.79779
$857$	−25.8772	−0.883947	−0.441974	−	0.897028i	$-0.645722\pi$
$857$	−25.8772	−0.883947	−0.441974	+	0.897028i	$0.645722\pi$
$858$	−10.6112	−0.362260
$859$	23.6977	0.808554	0.404277	−	0.914637i	$-0.367523\pi$
$859$	23.6977	0.808554	0.404277	+	0.914637i	$0.367523\pi$
$860$	54.2023	1.84828
$861$	−7.62542	−0.259874
$862$	−28.6715	−0.976556
$863$	−40.4249	−1.37608	−0.688039	−	0.725674i	$-0.741528\pi$
$863$	−40.4249	−1.37608	−0.688039	+	0.725674i	$0.741528\pi$
$864$	−8.60283	−0.292674
$865$	−2.02636	−0.0688982
$866$	−51.3493	−1.74492
$867$	6.54284	0.222206
$868$	−54.4533	−1.84827
$869$	−58.1552	−1.97278
$870$	0.0308331	0.00104534
$871$	1.52505	0.0516742
$872$	42.3428	1.43391
$873$	−39.9485	−1.35205
$874$	20.8099	0.703907
$875$	21.1019	0.713373
$876$	16.0707	0.542978
$877$	15.6891	0.529783	0.264891	−	0.964278i	$-0.414664\pi$
$877$	15.6891	0.529783	0.264891	+	0.964278i	$0.414664\pi$
$878$	11.1636	0.376753
$879$	9.09800	0.306868
$880$	35.2847	1.18945
$881$	50.1600	1.68993	0.844966	−	0.534820i	$-0.179621\pi$
$881$	50.1600	1.68993	0.844966	+	0.534820i	$0.179621\pi$
$882$	−23.2717	−0.783600
$883$	−39.2097	−1.31951	−0.659756	−	0.751480i	$-0.729340\pi$
$883$	−39.2097	−1.31951	−0.659756	+	0.751480i	$0.729340\pi$
$884$	16.0939	0.541297
$885$	1.78272	0.0599256
$886$	21.2725	0.714663
$887$	−17.8662	−0.599889	−0.299945	−	0.953957i	$-0.596968\pi$
$887$	−17.8662	−0.599889	−0.299945	+	0.953957i	$0.596968\pi$
$888$	−27.3114	−0.916510
$889$	−34.2804	−1.14973
$890$	43.3388	1.45272
$891$	30.2737	1.01421
$892$	45.7697	1.53248
$893$	−11.4768	−0.384057
$894$	12.1384	0.405968
$895$	11.1599	0.373033
$896$	−30.6249	−1.02311
$897$	7.78939	0.260080
$898$	37.9596	1.26673
$899$	0.117804	0.00392898
$900$	36.6251	1.22084
$901$	−17.3253	−0.577188
$902$	88.5800	2.94939
$903$	9.04310	0.300936
$904$	−85.3029	−2.83713
$905$	−5.18820	−0.172462
$906$	12.0856	0.401517
$907$	21.9433	0.728616	0.364308	−	0.931278i	$-0.381306\pi$
$907$	21.9433	0.728616	0.364308	+	0.931278i	$0.381306\pi$
$908$	63.5758	2.10984
$909$	−41.3469	−1.37139
$910$	−11.8726	−0.393575
$911$	−13.8686	−0.459488	−0.229744	−	0.973251i	$-0.573789\pi$
$911$	−13.8686	−0.459488	−0.229744	+	0.973251i	$0.573789\pi$
$912$	2.93179	0.0970812
$913$	−41.9395	−1.38800
$914$	20.2091	0.668458
$915$	0.116784	0.00386075
$916$	57.6295	1.90413
$917$	8.83489	0.291754
$918$	15.2026	0.501761
$919$	−56.9959	−1.88012	−0.940060	−	0.341008i	$-0.889232\pi$
$919$	−56.9959	−1.88012	−0.940060	+	0.341008i	$0.889232\pi$
$920$	−64.6492	−2.13142
$921$	1.73911	0.0573056
$922$	−92.1489	−3.03476
$923$	17.7405	0.583935
$924$	18.8153	0.618979
$925$	29.2778	0.962649
$926$	39.2693	1.29047
$927$	−34.0885	−1.11961
$928$	−0.0512872	−0.00168359
$929$	−52.4640	−1.72129	−0.860645	−	0.509206i	$-0.829939\pi$
$929$	−52.4640	−1.72129	−0.860645	+	0.509206i	$0.829939\pi$
$930$	11.7912	0.386650
$931$	3.39527	0.111275
$932$	19.9214	0.652547
$933$	−10.1918	−0.333664
$934$	4.35620	0.142539
$935$	−12.7343	−0.416458
$936$	−28.4609	−0.930274
$937$	12.6933	0.414673	0.207336	−	0.978270i	$-0.433521\pi$
$937$	12.6933	0.414673	0.207336	+	0.978270i	$0.433521\pi$
$938$	−3.96983	−0.129620
$939$	−8.34613	−0.272366
$940$	67.0260	2.18615
$941$	7.75830	0.252913	0.126457	−	0.991972i	$-0.459640\pi$
$941$	7.75830	0.252913	0.126457	+	0.991972i	$0.459640\pi$
$942$	6.98820	0.227688
$943$	−65.0241	−2.11748
$944$	−14.5198	−0.472580
$945$	−7.63947	−0.248512
$946$	−105.048	−3.41541
$947$	18.6976	0.607590	0.303795	−	0.952737i	$-0.401746\pi$
$947$	18.6976	0.607590	0.303795	+	0.952737i	$0.401746\pi$
$948$	28.2199	0.916541
$949$	13.3875	0.434577
$950$	−7.84449	−0.254509
$951$	−0.513198	−0.0166416
$952$	−22.2854	−0.722273
$953$	−26.1870	−0.848280	−0.424140	−	0.905597i	$-0.639424\pi$
$953$	−26.1870	−0.848280	−0.424140	+	0.905597i	$0.639424\pi$
$954$	57.5966	1.86476
$955$	33.1049	1.07125
$956$	−122.680	−3.96776
$957$	−0.0407050	−0.00131581
$958$	19.9119	0.643324
$959$	26.8112	0.865778
$960$	2.88052	0.0929684
$961$	14.0507	0.453250
$962$	−42.7700	−1.37896
$963$	39.3479	1.26797
$964$	−34.7296	−1.11856
$965$	−13.4144	−0.431824
$966$	−20.2765	−0.652385
$967$	−3.48081	−0.111935	−0.0559676	−	0.998433i	$-0.517824\pi$
$967$	−3.48081	−0.111935	−0.0559676	+	0.998433i	$0.517824\pi$
$968$	−53.6426	−1.72414
$969$	−1.05809	−0.0339907
$970$	−49.9700	−1.60444
$971$	54.8425	1.75998	0.879990	−	0.474992i	$-0.157549\pi$
$971$	54.8425	1.75998	0.879990	+	0.474992i	$0.157549\pi$
$972$	−52.4302	−1.68170
$973$	−20.9638	−0.672067
$974$	−38.9137	−1.24688
$975$	−2.93628	−0.0940362
$976$	−0.951175	−0.0304464
$977$	−46.5870	−1.49045	−0.745225	−	0.666813i	$-0.767658\pi$
$977$	−46.5870	−1.49045	−0.745225	+	0.666813i	$0.767658\pi$
$978$	28.7273	0.918596
$979$	−57.2146	−1.82859
$980$	−19.8288	−0.633407
$981$	20.3540	0.649852
$982$	48.1820	1.53755
$983$	−47.3357	−1.50977	−0.754887	−	0.655855i	$-0.772308\pi$
$983$	−47.3357	−1.50977	−0.754887	+	0.655855i	$0.772308\pi$
$984$	−22.8651	−0.728913
$985$	−23.7672	−0.757285
$986$	0.0906328	0.00288634
$987$	11.1826	0.355946
$988$	7.80591	0.248339
$989$	77.1131	2.45205
$990$	42.3344	1.34548
$991$	17.8098	0.565747	0.282874	−	0.959157i	$-0.408712\pi$
$991$	17.8098	0.565747	0.282874	+	0.959157i	$0.408712\pi$
$992$	−19.6133	−0.622723
$993$	2.14366	0.0680271
$994$	−46.1800	−1.46474
$995$	−16.4117	−0.520287
$996$	20.3513	0.644854
$997$	−22.7177	−0.719478	−0.359739	−	0.933053i	$-0.617134\pi$
$997$	−22.7177	−0.719478	−0.359739	+	0.933053i	$0.617134\pi$
$998$	−56.8618	−1.79993
$999$	−27.5204	−0.870707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.13	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.13	✓	140	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)

\(f(q)\)	\(=\)	\(q-2.50460 q^{2} -0.513198 q^{3} +4.27304 q^{4} +1.36674 q^{5} +1.28536 q^{6} -1.89861 q^{7} -5.69306 q^{8} -2.73663 q^{9} +O(q^{10})\)	\(q-2.50460 q^{2} -0.513198 q^{3} +4.27304 q^{4} +1.36674 q^{5} +1.28536 q^{6} -1.89861 q^{7} -5.69306 q^{8} -2.73663 q^{9} -3.42314 q^{10} +4.51912 q^{11} -2.19291 q^{12} -1.82678 q^{13} +4.75527 q^{14} -0.701406 q^{15} +5.71278 q^{16} -2.06176 q^{17} +6.85417 q^{18} -1.00000 q^{19} +5.84012 q^{20} +0.974364 q^{21} -11.3186 q^{22} +8.30868 q^{23} +2.92167 q^{24} -3.13203 q^{25} +4.57537 q^{26} +2.94402 q^{27} -8.11285 q^{28} +0.0175513 q^{29} +1.75675 q^{30} +6.71198 q^{31} -2.92213 q^{32} -2.31920 q^{33} +5.16389 q^{34} -2.59491 q^{35} -11.6937 q^{36} -9.34788 q^{37} +2.50460 q^{38} +0.937501 q^{39} -7.78092 q^{40} -7.82605 q^{41} -2.44040 q^{42} +9.28103 q^{43} +19.3104 q^{44} -3.74025 q^{45} -20.8099 q^{46} +11.4768 q^{47} -2.93179 q^{48} -3.39527 q^{49} +7.84449 q^{50} +1.05809 q^{51} -7.80591 q^{52} +8.40315 q^{53} -7.37361 q^{54} +6.17645 q^{55} +10.8089 q^{56} +0.513198 q^{57} -0.0439590 q^{58} -2.54164 q^{59} -2.99714 q^{60} -0.166499 q^{61} -16.8109 q^{62} +5.19580 q^{63} -4.10678 q^{64} -2.49673 q^{65} +5.80868 q^{66} -0.834826 q^{67} -8.80997 q^{68} -4.26399 q^{69} +6.49921 q^{70} -9.71132 q^{71} +15.5798 q^{72} -7.32846 q^{73} +23.4127 q^{74} +1.60735 q^{75} -4.27304 q^{76} -8.58007 q^{77} -2.34807 q^{78} -12.8687 q^{79} +7.80787 q^{80} +6.69902 q^{81} +19.6011 q^{82} -9.28046 q^{83} +4.16350 q^{84} -2.81788 q^{85} -23.2453 q^{86} -0.00900728 q^{87} -25.7276 q^{88} -12.6605 q^{89} +9.36785 q^{90} +3.46836 q^{91} +35.5033 q^{92} -3.44457 q^{93} -28.7449 q^{94} -1.36674 q^{95} +1.49963 q^{96} +14.5977 q^{97} +8.50379 q^{98} -12.3672 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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