LMFDB - Embedded newform 5077.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$0$
Dimension:	$216$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65978 q^{2} +0.381674 q^{3} +5.07442 q^{4} +4.30968 q^{5} -1.01517 q^{6} +0.973203 q^{7} -8.17726 q^{8} -2.85433 q^{9} +O(q^{10})$	\(q-2.65978 q^{2} +0.381674 q^{3} +5.07442 q^{4} +4.30968 q^{5} -1.01517 q^{6} +0.973203 q^{7} -8.17726 q^{8} -2.85433 q^{9} -11.4628 q^{10} -3.68509 q^{11} +1.93677 q^{12} -5.03583 q^{13} -2.58850 q^{14} +1.64489 q^{15} +11.6009 q^{16} -1.29329 q^{17} +7.59187 q^{18} -2.92984 q^{19} +21.8691 q^{20} +0.371446 q^{21} +9.80151 q^{22} +1.79674 q^{23} -3.12105 q^{24} +13.5733 q^{25} +13.3942 q^{26} -2.23444 q^{27} +4.93844 q^{28} +1.44401 q^{29} -4.37504 q^{30} +0.755240 q^{31} -14.5012 q^{32} -1.40650 q^{33} +3.43987 q^{34} +4.19419 q^{35} -14.4840 q^{36} +0.566761 q^{37} +7.79272 q^{38} -1.92204 q^{39} -35.2414 q^{40} -3.17553 q^{41} -0.987963 q^{42} +5.25035 q^{43} -18.6997 q^{44} -12.3012 q^{45} -4.77894 q^{46} +2.65339 q^{47} +4.42774 q^{48} -6.05288 q^{49} -36.1020 q^{50} -0.493615 q^{51} -25.5539 q^{52} +5.19541 q^{53} +5.94312 q^{54} -15.8815 q^{55} -7.95813 q^{56} -1.11824 q^{57} -3.84075 q^{58} +9.86596 q^{59} +8.34685 q^{60} +10.2285 q^{61} -2.00877 q^{62} -2.77784 q^{63} +15.3682 q^{64} -21.7028 q^{65} +3.74098 q^{66} +6.37354 q^{67} -6.56270 q^{68} +0.685769 q^{69} -11.1556 q^{70} +5.36311 q^{71} +23.3406 q^{72} -16.7987 q^{73} -1.50746 q^{74} +5.18057 q^{75} -14.8672 q^{76} -3.58634 q^{77} +5.11221 q^{78} +9.71960 q^{79} +49.9960 q^{80} +7.71015 q^{81} +8.44621 q^{82} -1.63442 q^{83} +1.88487 q^{84} -5.57367 q^{85} -13.9648 q^{86} +0.551141 q^{87} +30.1339 q^{88} +9.92552 q^{89} +32.7185 q^{90} -4.90088 q^{91} +9.11742 q^{92} +0.288255 q^{93} -7.05742 q^{94} -12.6267 q^{95} -5.53473 q^{96} +17.5691 q^{97} +16.0993 q^{98} +10.5184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) $ 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * 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 $

$2$	−2.65978	−1.88075	−0.940373	−	0.340144i	$-0.889524\pi$
$2$	−2.65978	−1.88075	−0.940373	+	0.340144i	$0.889524\pi$
$3$	0.381674	0.220359	0.110180	−	0.993912i	$-0.464857\pi$
$3$	0.381674	0.220359	0.110180	+	0.993912i	$0.464857\pi$
$4$	5.07442	2.53721
$5$	4.30968	1.92735	0.963673	−	0.267085i	$-0.0860606\pi$
$5$	4.30968	1.92735	0.963673	+	0.267085i	$0.0860606\pi$
$6$	−1.01517	−0.414440
$7$	0.973203	0.367836	0.183918	−	0.982942i	$-0.441122\pi$
$7$	0.973203	0.367836	0.183918	+	0.982942i	$0.441122\pi$
$8$	−8.17726	−2.89110
$9$	−2.85433	−0.951442
$10$	−11.4628	−3.62485
$11$	−3.68509	−1.11110	−0.555548	−	0.831485i	$-0.687491\pi$
$11$	−3.68509	−1.11110	−0.555548	+	0.831485i	$0.687491\pi$
$12$	1.93677	0.559098
$13$	−5.03583	−1.39669	−0.698344	−	0.715762i	$-0.746079\pi$
$13$	−5.03583	−1.39669	−0.698344	+	0.715762i	$0.746079\pi$
$14$	−2.58850	−0.691806
$15$	1.64489	0.424709
$16$	11.6009	2.90022
$17$	−1.29329	−0.313669	−0.156835	−	0.987625i	$-0.550129\pi$
$17$	−1.29329	−0.313669	−0.156835	+	0.987625i	$0.550129\pi$
$18$	7.59187	1.78942
$19$	−2.92984	−0.672151	−0.336076	−	0.941835i	$-0.609100\pi$
$19$	−2.92984	−0.672151	−0.336076	+	0.941835i	$0.609100\pi$
$20$	21.8691	4.89008
$21$	0.371446	0.0810561
$22$	9.80151	2.08969
$23$	1.79674	0.374647	0.187323	−	0.982298i	$-0.440019\pi$
$23$	1.79674	0.374647	0.187323	+	0.982298i	$0.440019\pi$
$24$	−3.12105	−0.637081
$25$	13.5733	2.71466
$26$	13.3942	2.62682
$27$	−2.23444	−0.430018
$28$	4.93844	0.933277
$29$	1.44401	0.268146	0.134073	−	0.990971i	$-0.457194\pi$
$29$	1.44401	0.268146	0.134073	+	0.990971i	$0.457194\pi$
$30$	−4.37504	−0.798769
$31$	0.755240	0.135645	0.0678225	−	0.997697i	$-0.478395\pi$
$31$	0.755240	0.135645	0.0678225	+	0.997697i	$0.478395\pi$
$32$	−14.5012	−2.56347
$33$	−1.40650	−0.244840
$34$	3.43987	0.589933
$35$	4.19419	0.708947
$36$	−14.4840	−2.41401
$37$	0.566761	0.0931749	0.0465875	−	0.998914i	$-0.485165\pi$
$37$	0.566761	0.0931749	0.0465875	+	0.998914i	$0.485165\pi$
$38$	7.79272	1.26415
$39$	−1.92204	−0.307773
$40$	−35.2414	−5.57215
$41$	−3.17553	−0.495935	−0.247967	−	0.968768i	$-0.579763\pi$
$41$	−3.17553	−0.495935	−0.247967	+	0.968768i	$0.579763\pi$
$42$	−0.987963	−0.152446
$43$	5.25035	0.800671	0.400336	−	0.916369i	$-0.368894\pi$
$43$	5.25035	0.800671	0.400336	+	0.916369i	$0.368894\pi$
$44$	−18.6997	−2.81908
$45$	−12.3012	−1.83376
$46$	−4.77894	−0.704616
$47$	2.65339	0.387036	0.193518	−	0.981097i	$-0.438010\pi$
$47$	2.65339	0.387036	0.193518	+	0.981097i	$0.438010\pi$
$48$	4.42774	0.639090
$49$	−6.05288	−0.864697
$50$	−36.1020	−5.10559
$51$	−0.493615	−0.0691200
$52$	−25.5539	−3.54369
$53$	5.19541	0.713645	0.356822	−	0.934172i	$-0.383860\pi$
$53$	5.19541	0.713645	0.356822	+	0.934172i	$0.383860\pi$
$54$	5.94312	0.808756
$55$	−15.8815	−2.14147
$56$	−7.95813	−1.06345
$57$	−1.11824	−0.148115
$58$	−3.84075	−0.504315
$59$	9.86596	1.28444	0.642219	−	0.766521i	$-0.278014\pi$
$59$	9.86596	1.28444	0.642219	+	0.766521i	$0.278014\pi$
$60$	8.34685	1.07757
$61$	10.2285	1.30962	0.654810	−	0.755793i	$-0.272748\pi$
$61$	10.2285	1.30962	0.654810	+	0.755793i	$0.272748\pi$
$62$	−2.00877	−0.255114
$63$	−2.77784	−0.349975
$64$	15.3682	1.92103
$65$	−21.7028	−2.69190
$66$	3.74098	0.460483
$67$	6.37354	0.778651	0.389326	−	0.921100i	$-0.372708\pi$
$67$	6.37354	0.778651	0.389326	+	0.921100i	$0.372708\pi$
$68$	−6.56270	−0.795844
$69$	0.685769	0.0825569
$70$	−11.1556	−1.33335
$71$	5.36311	0.636484	0.318242	−	0.948009i	$-0.396907\pi$
$71$	5.36311	0.636484	0.318242	+	0.948009i	$0.396907\pi$
$72$	23.3406	2.75071
$73$	−16.7987	−1.96614	−0.983071	−	0.183225i	$-0.941346\pi$
$73$	−16.7987	−1.96614	−0.983071	+	0.183225i	$0.941346\pi$
$74$	−1.50746	−0.175238
$75$	5.18057	0.598201
$76$	−14.8672	−1.70539
$77$	−3.58634	−0.408701
$78$	5.11221	0.578843
$79$	9.71960	1.09354	0.546770	−	0.837283i	$-0.315857\pi$
$79$	9.71960	1.09354	0.546770	+	0.837283i	$0.315857\pi$
$80$	49.9960	5.58972
$81$	7.71015	0.856683
$82$	8.44621	0.932728
$83$	−1.63442	−0.179400	−0.0897002	−	0.995969i	$-0.528591\pi$
$83$	−1.63442	−0.179400	−0.0897002	+	0.995969i	$0.528591\pi$
$84$	1.88487	0.205656
$85$	−5.57367	−0.604549
$86$	−13.9648	−1.50586
$87$	0.551141	0.0590885
$88$	30.1339	3.21229
$89$	9.92552	1.05210	0.526051	−	0.850453i	$-0.323672\pi$
$89$	9.92552	1.05210	0.526051	+	0.850453i	$0.323672\pi$
$90$	32.7185	3.44883
$91$	−4.90088	−0.513752
$92$	9.11742	0.950557
$93$	0.288255	0.0298907
$94$	−7.05742	−0.727917
$95$	−12.6267	−1.29547
$96$	−5.53473	−0.564886
$97$	17.5691	1.78388	0.891938	−	0.452158i	$-0.149346\pi$
$97$	17.5691	1.78388	0.891938	+	0.452158i	$0.149346\pi$
$98$	16.0993	1.62628
$99$	10.5184	1.05714
$100$	68.8766	6.88766
$101$	9.74201	0.969367	0.484683	−	0.874690i	$-0.338935\pi$
$101$	9.74201	0.969367	0.484683	+	0.874690i	$0.338935\pi$
$102$	1.31291	0.129997
$103$	−10.2660	−1.01154	−0.505772	−	0.862667i	$-0.668792\pi$
$103$	−10.2660	−1.01154	−0.505772	+	0.862667i	$0.668792\pi$
$104$	41.1793	4.03796
$105$	1.60081	0.156223
$106$	−13.8186	−1.34218
$107$	−3.44250	−0.332799	−0.166399	−	0.986058i	$-0.553214\pi$
$107$	−3.44250	−0.332799	−0.166399	+	0.986058i	$0.553214\pi$
$108$	−11.3385	−1.09105
$109$	−3.55270	−0.340287	−0.170143	−	0.985419i	$-0.554423\pi$
$109$	−3.55270	−0.340287	−0.170143	+	0.985419i	$0.554423\pi$
$110$	42.2413	4.02755
$111$	0.216318	0.0205320
$112$	11.2900	1.06680
$113$	15.7759	1.48407	0.742036	−	0.670360i	$-0.233860\pi$
$113$	15.7759	1.48407	0.742036	+	0.670360i	$0.233860\pi$
$114$	2.97428	0.278566
$115$	7.74338	0.722074
$116$	7.32751	0.680342
$117$	14.3739	1.32887
$118$	−26.2413	−2.41570
$119$	−1.25863	−0.115379
$120$	−13.4507	−1.22787
$121$	2.57986	0.234533
$122$	−27.2054	−2.46307
$123$	−1.21202	−0.109284
$124$	3.83240	0.344160
$125$	36.9482	3.30475
$126$	7.38843	0.658213
$127$	16.2957	1.44601	0.723005	−	0.690843i	$-0.242760\pi$
$127$	16.2957	1.44601	0.723005	+	0.690843i	$0.242760\pi$
$128$	−11.8737	−1.04949
$129$	2.00392	0.176435
$130$	57.7246	5.06278
$131$	−10.7018	−0.935019	−0.467509	−	0.883988i	$-0.654849\pi$
$131$	−10.7018	−0.935019	−0.467509	+	0.883988i	$0.654849\pi$
$132$	−7.13717	−0.621211
$133$	−2.85133	−0.247241
$134$	−16.9522	−1.46445
$135$	−9.62972	−0.828794
$136$	10.5756	0.906849
$137$	2.12116	0.181223	0.0906113	−	0.995886i	$-0.471118\pi$
$137$	2.12116	0.181223	0.0906113	+	0.995886i	$0.471118\pi$
$138$	−1.82399	−0.155269
$139$	−16.2412	−1.37756	−0.688780	−	0.724971i	$-0.741853\pi$
$139$	−16.2412	−1.37756	−0.688780	+	0.724971i	$0.741853\pi$
$140$	21.2831	1.79875
$141$	1.01273	0.0852870
$142$	−14.2647	−1.19707
$143$	18.5575	1.55185
$144$	−33.1126	−2.75939
$145$	6.22322	0.516810
$146$	44.6809	3.69781
$147$	−2.31022	−0.190544
$148$	2.87598	0.236404
$149$	4.90088	0.401496	0.200748	−	0.979643i	$-0.435663\pi$
$149$	4.90088	0.401496	0.200748	+	0.979643i	$0.435663\pi$
$150$	−13.7792	−1.12506
$151$	13.2338	1.07695	0.538474	−	0.842642i	$-0.319001\pi$
$151$	13.2338	1.07695	0.538474	+	0.842642i	$0.319001\pi$
$152$	23.9581	1.94326
$153$	3.69148	0.298438
$154$	9.53886	0.768663
$155$	3.25484	0.261435
$156$	−9.75325	−0.780885
$157$	13.8167	1.10270	0.551348	−	0.834276i	$-0.314114\pi$
$157$	13.8167	1.10270	0.551348	+	0.834276i	$0.314114\pi$
$158$	−25.8520	−2.05667
$159$	1.98295	0.157258
$160$	−62.4955	−4.94070
$161$	1.74859	0.137809
$162$	−20.5073	−1.61120
$163$	4.71147	0.369031	0.184515	−	0.982830i	$-0.440928\pi$
$163$	4.71147	0.369031	0.184515	+	0.982830i	$0.440928\pi$
$164$	−16.1140	−1.25829
$165$	−6.06156	−0.471892
$166$	4.34718	0.337407
$167$	−6.84022	−0.529312	−0.264656	−	0.964343i	$-0.585258\pi$
$167$	−6.84022	−0.529312	−0.264656	+	0.964343i	$0.585258\pi$
$168$	−3.03741	−0.234341
$169$	12.3596	0.950736
$170$	14.8247	1.13700
$171$	8.36271	0.639513
$172$	26.6425	2.03147
$173$	−0.751253	−0.0571167	−0.0285584	−	0.999592i	$-0.509092\pi$
$173$	−0.751253	−0.0571167	−0.0285584	+	0.999592i	$0.509092\pi$
$174$	−1.46591	−0.111131
$175$	13.2096	0.998550
$176$	−42.7502	−3.22242
$177$	3.76558	0.283038
$178$	−26.3997	−1.97874
$179$	2.53323	0.189343	0.0946713	−	0.995509i	$-0.469820\pi$
$179$	2.53323	0.189343	0.0946713	+	0.995509i	$0.469820\pi$
$180$	−62.4215	−4.65262
$181$	−18.8652	−1.40224	−0.701119	−	0.713044i	$-0.747316\pi$
$181$	−18.8652	−1.40224	−0.701119	+	0.713044i	$0.747316\pi$
$182$	13.0353	0.966237
$183$	3.90394	0.288587
$184$	−14.6924	−1.08314
$185$	2.44256	0.179580
$186$	−0.766694	−0.0562167
$187$	4.76589	0.348517
$188$	13.4644	0.981991
$189$	−2.17456	−0.158176
$190$	33.5841	2.43645
$191$	15.5155	1.12266	0.561331	−	0.827592i	$-0.310290\pi$
$191$	15.5155	1.12266	0.561331	+	0.827592i	$0.310290\pi$
$192$	5.86565	0.423317
$193$	12.8400	0.924241	0.462121	−	0.886817i	$-0.347089\pi$
$193$	12.8400	0.924241	0.462121	+	0.886817i	$0.347089\pi$
$194$	−46.7300	−3.35502
$195$	−8.28338	−0.593185
$196$	−30.7148	−2.19392
$197$	−6.85528	−0.488419	−0.244209	−	0.969723i	$-0.578528\pi$
$197$	−6.85528	−0.488419	−0.244209	+	0.969723i	$0.578528\pi$
$198$	−27.9767	−1.98822
$199$	−16.5138	−1.17063	−0.585315	−	0.810806i	$-0.699029\pi$
$199$	−16.5138	−1.17063	−0.585315	+	0.810806i	$0.699029\pi$
$200$	−110.993	−7.84835
$201$	2.43261	0.171583
$202$	−25.9116	−1.82313
$203$	1.40532	0.0986338
$204$	−2.50481	−0.175372
$205$	−13.6855	−0.955838
$206$	27.3054	1.90246
$207$	−5.12849	−0.356455
$208$	−58.4200	−4.05070
$209$	10.7967	0.746824
$210$	−4.25780	−0.293816
$211$	9.70985	0.668454	0.334227	−	0.942493i	$-0.391525\pi$
$211$	9.70985	0.668454	0.334227	+	0.942493i	$0.391525\pi$
$212$	26.3637	1.81066
$213$	2.04696	0.140255
$214$	9.15628	0.625910
$215$	22.6273	1.54317
$216$	18.2716	1.24323
$217$	0.735001	0.0498951
$218$	9.44938	0.639993
$219$	−6.41163	−0.433258
$220$	−80.5895	−5.43334
$221$	6.51280	0.438098
$222$	−0.575357	−0.0386154
$223$	17.7638	1.18955	0.594777	−	0.803891i	$-0.297240\pi$
$223$	17.7638	1.18955	0.594777	+	0.803891i	$0.297240\pi$
$224$	−14.1126	−0.942938
$225$	−38.7426	−2.58284
$226$	−41.9604	−2.79117
$227$	20.2750	1.34570	0.672849	−	0.739780i	$-0.265071\pi$
$227$	20.2750	1.34570	0.672849	+	0.739780i	$0.265071\pi$
$228$	−5.67443	−0.375798
$229$	8.18159	0.540655	0.270327	−	0.962768i	$-0.412868\pi$
$229$	8.18159	0.540655	0.270327	+	0.962768i	$0.412868\pi$
$230$	−20.5957	−1.35804
$231$	−1.36881	−0.0900611
$232$	−11.8081	−0.775237
$233$	15.8469	1.03817	0.519084	−	0.854723i	$-0.326273\pi$
$233$	15.8469	1.03817	0.519084	+	0.854723i	$0.326273\pi$
$234$	−38.2314	−2.49926
$235$	11.4352	0.745953
$236$	50.0640	3.25889
$237$	3.70971	0.240972
$238$	3.34769	0.216998
$239$	−7.89563	−0.510726	−0.255363	−	0.966845i	$-0.582195\pi$
$239$	−7.89563	−0.510726	−0.255363	+	0.966845i	$0.582195\pi$
$240$	19.0821	1.23175
$241$	−10.7055	−0.689600	−0.344800	−	0.938676i	$-0.612053\pi$
$241$	−10.7055	−0.689600	−0.344800	+	0.938676i	$0.612053\pi$
$242$	−6.86186	−0.441097
$243$	9.64608	0.618797
$244$	51.9035	3.32278
$245$	−26.0859	−1.66657
$246$	3.22370	0.205535
$247$	14.7542	0.938785
$248$	−6.17579	−0.392163
$249$	−0.623813	−0.0395326
$250$	−98.2739	−6.21539
$251$	24.5457	1.54931	0.774654	−	0.632385i	$-0.217924\pi$
$251$	24.5457	1.54931	0.774654	+	0.632385i	$0.217924\pi$
$252$	−14.0959	−0.887958
$253$	−6.62115	−0.416268
$254$	−43.3430	−2.71958
$255$	−2.12732	−0.133218
$256$	0.844866	0.0528042
$257$	−3.85826	−0.240672	−0.120336	−	0.992733i	$-0.538397\pi$
$257$	−3.85826	−0.240672	−0.120336	+	0.992733i	$0.538397\pi$
$258$	−5.32998	−0.331830
$259$	0.551573	0.0342731
$260$	−110.129	−6.82991
$261$	−4.12168	−0.255125
$262$	28.4644	1.75853
$263$	4.63435	0.285766	0.142883	−	0.989740i	$-0.454363\pi$
$263$	4.63435	0.285766	0.142883	+	0.989740i	$0.454363\pi$
$264$	11.5013	0.707858
$265$	22.3905	1.37544
$266$	7.58390	0.464998
$267$	3.78831	0.231841
$268$	32.3420	1.97560
$269$	−19.9946	−1.21909	−0.609547	−	0.792750i	$-0.708649\pi$
$269$	−19.9946	−1.21909	−0.609547	+	0.792750i	$0.708649\pi$
$270$	25.6129	1.55875
$271$	20.3466	1.23597	0.617983	−	0.786191i	$-0.287950\pi$
$271$	20.3466	1.23597	0.617983	+	0.786191i	$0.287950\pi$
$272$	−15.0033	−0.909709
$273$	−1.87054	−0.113210
$274$	−5.64180	−0.340834
$275$	−50.0188	−3.01625
$276$	3.47988	0.209464
$277$	0.262854	0.0157934	0.00789669	−	0.999969i	$-0.497486\pi$
$277$	0.262854	0.0157934	0.00789669	+	0.999969i	$0.497486\pi$
$278$	43.1979	2.59084
$279$	−2.15570	−0.129058
$280$	−34.2970	−2.04964
$281$	17.8023	1.06200	0.530999	−	0.847372i	$-0.321817\pi$
$281$	17.8023	1.06200	0.530999	+	0.847372i	$0.321817\pi$
$282$	−2.69363	−0.160403
$283$	−17.2900	−1.02779	−0.513893	−	0.857854i	$-0.671797\pi$
$283$	−17.2900	−1.02779	−0.513893	+	0.857854i	$0.671797\pi$
$284$	27.2147	1.61489
$285$	−4.81926	−0.285468
$286$	−49.3587	−2.91864
$287$	−3.09044	−0.182423
$288$	41.3911	2.43900
$289$	−15.3274	−0.901612
$290$	−16.5524	−0.971989
$291$	6.70568	0.393094
$292$	−85.2437	−4.98851
$293$	11.3547	0.663346	0.331673	−	0.943394i	$-0.392387\pi$
$293$	11.3547	0.663346	0.331673	+	0.943394i	$0.392387\pi$
$294$	6.14468	0.358365
$295$	42.5191	2.47556
$296$	−4.63455	−0.269378
$297$	8.23411	0.477792
$298$	−13.0353	−0.755112
$299$	−9.04809	−0.523264
$300$	26.2884	1.51776
$301$	5.10966	0.294516
$302$	−35.1989	−2.02547
$303$	3.71827	0.213609
$304$	−33.9887	−1.94938
$305$	44.0814	2.52409
$306$	−9.81850	−0.561286
$307$	−18.9996	−1.08436	−0.542182	−	0.840261i	$-0.682402\pi$
$307$	−18.9996	−1.08436	−0.542182	+	0.840261i	$0.682402\pi$
$308$	−18.1986	−1.03696
$309$	−3.91828	−0.222903
$310$	−8.65714	−0.491693
$311$	−13.1901	−0.747940	−0.373970	−	0.927441i	$-0.622004\pi$
$311$	−13.1901	−0.747940	−0.373970	+	0.927441i	$0.622004\pi$
$312$	15.7171	0.889803
$313$	−8.29781	−0.469020	−0.234510	−	0.972114i	$-0.575349\pi$
$313$	−8.29781	−0.469020	−0.234510	+	0.972114i	$0.575349\pi$
$314$	−36.7494	−2.07389
$315$	−11.9716	−0.674522
$316$	49.3213	2.77454
$317$	3.03897	0.170686	0.0853429	−	0.996352i	$-0.472801\pi$
$317$	3.03897	0.170686	0.0853429	+	0.996352i	$0.472801\pi$
$318$	−5.27421	−0.295763
$319$	−5.32131	−0.297936
$320$	66.2321	3.70249
$321$	−1.31391	−0.0733353
$322$	−4.65087	−0.259183
$323$	3.78914	0.210833
$324$	39.1245	2.17358
$325$	−68.3529	−3.79153
$326$	−12.5315	−0.694053
$327$	−1.35597	−0.0749853
$328$	25.9672	1.43380
$329$	2.58228	0.142366
$330$	16.1224	0.887509
$331$	−27.4222	−1.50726	−0.753630	−	0.657299i	$-0.771699\pi$
$331$	−27.4222	−1.50726	−0.753630	+	0.657299i	$0.771699\pi$
$332$	−8.29370	−0.455176
$333$	−1.61772	−0.0886505
$334$	18.1935	0.995501
$335$	27.4679	1.50073
$336$	4.30909	0.235080
$337$	−26.8139	−1.46064	−0.730322	−	0.683103i	$-0.760630\pi$
$337$	−26.8139	−1.46064	−0.730322	+	0.683103i	$0.760630\pi$
$338$	−32.8737	−1.78809
$339$	6.02125	0.327029
$340$	−28.2831	−1.53387
$341$	−2.78312	−0.150715
$342$	−22.2430	−1.20276
$343$	−12.7031	−0.685903
$344$	−42.9335	−2.31482
$345$	2.95544	0.159116
$346$	1.99817	0.107422
$347$	31.6801	1.70068	0.850339	−	0.526235i	$-0.176397\pi$
$347$	31.6801	1.70068	0.850339	+	0.526235i	$0.176397\pi$
$348$	2.79672	0.149920
$349$	10.4359	0.558619	0.279309	−	0.960201i	$-0.409894\pi$
$349$	10.4359	0.558619	0.279309	+	0.960201i	$0.409894\pi$
$350$	−35.1345	−1.87802
$351$	11.2523	0.600601
$352$	53.4382	2.84826
$353$	3.53381	0.188086	0.0940429	−	0.995568i	$-0.470021\pi$
$353$	3.53381	0.188086	0.0940429	+	0.995568i	$0.470021\pi$
$354$	−10.0156	−0.532323
$355$	23.1133	1.22673
$356$	50.3662	2.66940
$357$	−0.480388	−0.0254248
$358$	−6.73783	−0.356105
$359$	31.4728	1.66107	0.830536	−	0.556965i	$-0.188034\pi$
$359$	31.4728	1.66107	0.830536	+	0.556965i	$0.188034\pi$
$360$	100.590	5.30157
$361$	−10.4160	−0.548213
$362$	50.1772	2.63726
$363$	0.984666	0.0516816
$364$	−24.8691	−1.30350
$365$	−72.3971	−3.78944
$366$	−10.3836	−0.542759
$367$	0.916875	0.0478605	0.0239302	−	0.999714i	$-0.492382\pi$
$367$	0.916875	0.0478605	0.0239302	+	0.999714i	$0.492382\pi$
$368$	20.8438	1.08656
$369$	9.06400	0.471853
$370$	−6.49666	−0.337745
$371$	5.05619	0.262504
$372$	1.46273	0.0758388
$373$	31.6486	1.63870	0.819351	−	0.573292i	$-0.194334\pi$
$373$	31.6486	1.63870	0.819351	+	0.573292i	$0.194334\pi$
$374$	−12.6762	−0.655471
$375$	14.1021	0.728232
$376$	−21.6974	−1.11896
$377$	−7.27179	−0.374516
$378$	5.78386	0.297489
$379$	25.4255	1.30602	0.653011	−	0.757348i	$-0.273506\pi$
$379$	25.4255	1.30602	0.653011	+	0.757348i	$0.273506\pi$
$380$	−64.0729	−3.28687
$381$	6.21964	0.318642
$382$	−41.2677	−2.11144
$383$	−3.72533	−0.190356	−0.0951778	−	0.995460i	$-0.530342\pi$
$383$	−3.72533	−0.190356	−0.0951778	+	0.995460i	$0.530342\pi$
$384$	−4.53187	−0.231266
$385$	−15.4559	−0.787708
$386$	−34.1515	−1.73826
$387$	−14.9862	−0.761792
$388$	89.1531	4.52606
$389$	−30.9040	−1.56690	−0.783448	−	0.621457i	$-0.786541\pi$
$389$	−30.9040	−1.56690	−0.783448	+	0.621457i	$0.786541\pi$
$390$	22.0320	1.11563
$391$	−2.32371	−0.117515
$392$	49.4960	2.49992
$393$	−4.08459	−0.206040
$394$	18.2335	0.918592
$395$	41.8883	2.10763
$396$	53.3749	2.68219
$397$	0.774018	0.0388468	0.0194234	−	0.999811i	$-0.493817\pi$
$397$	0.774018	0.0388468	0.0194234	+	0.999811i	$0.493817\pi$
$398$	43.9229	2.20166
$399$	−1.08828	−0.0544820
$400$	157.462	7.87311
$401$	−0.316313	−0.0157959	−0.00789796	−	0.999969i	$-0.502514\pi$
$401$	−0.316313	−0.0157959	−0.00789796	+	0.999969i	$0.502514\pi$
$402$	−6.47020	−0.322704
$403$	−3.80326	−0.189454
$404$	49.4350	2.45948
$405$	33.2282	1.65112
$406$	−3.73783	−0.185505
$407$	−2.08856	−0.103526
$408$	4.03642	0.199833
$409$	−14.4091	−0.712483	−0.356241	−	0.934394i	$-0.615942\pi$
$409$	−14.4091	−0.712483	−0.356241	+	0.934394i	$0.615942\pi$
$410$	36.4004	1.79769
$411$	0.809589	0.0399341
$412$	−52.0942	−2.56650
$413$	9.60158	0.472463
$414$	13.6406	0.670401
$415$	−7.04380	−0.345767
$416$	73.0256	3.58037
$417$	−6.19883	−0.303558
$418$	−28.7168	−1.40459
$419$	−17.1892	−0.839747	−0.419874	−	0.907583i	$-0.637926\pi$
$419$	−17.1892	−0.839747	−0.419874	+	0.907583i	$0.637926\pi$
$420$	8.12318	0.396371
$421$	−39.7919	−1.93934	−0.969670	−	0.244418i	$-0.921403\pi$
$421$	−39.7919	−1.93934	−0.969670	+	0.244418i	$0.921403\pi$
$422$	−25.8260	−1.25719
$423$	−7.57363	−0.368242
$424$	−42.4842	−2.06322
$425$	−17.5542	−0.851506
$426$	−5.44445	−0.263785
$427$	9.95437	0.481726
$428$	−17.4687	−0.844380
$429$	7.08290	0.341965
$430$	−60.1836	−2.90231
$431$	21.9760	1.05855	0.529273	−	0.848451i	$-0.322465\pi$
$431$	21.9760	1.05855	0.529273	+	0.848451i	$0.322465\pi$
$432$	−25.9215	−1.24715
$433$	−20.7102	−0.995268	−0.497634	−	0.867387i	$-0.665798\pi$
$433$	−20.7102	−0.995268	−0.497634	+	0.867387i	$0.665798\pi$
$434$	−1.95494	−0.0938401
$435$	2.37524	0.113884
$436$	−18.0279	−0.863378
$437$	−5.26417	−0.251819
$438$	17.0535	0.814848
$439$	20.2231	0.965195	0.482598	−	0.875842i	$-0.339693\pi$
$439$	20.2231	0.965195	0.482598	+	0.875842i	$0.339693\pi$
$440$	129.867	6.19119
$441$	17.2769	0.822709
$442$	−17.3226	−0.823952
$443$	26.9756	1.28165	0.640824	−	0.767688i	$-0.278593\pi$
$443$	26.9756	1.28165	0.640824	+	0.767688i	$0.278593\pi$
$444$	1.09769	0.0520939
$445$	42.7758	2.02777
$446$	−47.2479	−2.23725
$447$	1.87054	0.0884733
$448$	14.9564	0.706624
$449$	−35.5051	−1.67559	−0.837795	−	0.545984i	$-0.816156\pi$
$449$	−35.5051	−1.67559	−0.837795	+	0.545984i	$0.816156\pi$
$450$	103.047	4.85767
$451$	11.7021	0.551031
$452$	80.0535	3.76540
$453$	5.05098	0.237316
$454$	−53.9269	−2.53092
$455$	−21.1212	−0.990178
$456$	9.14416	0.428215
$457$	−15.6417	−0.731688	−0.365844	−	0.930676i	$-0.619220\pi$
$457$	−15.6417	−0.731688	−0.365844	+	0.930676i	$0.619220\pi$
$458$	−21.7612	−1.01683
$459$	2.88978	0.134884
$460$	39.2931	1.83205
$461$	38.4059	1.78874	0.894369	−	0.447329i	$-0.147625\pi$
$461$	38.4059	1.78874	0.894369	+	0.447329i	$0.147625\pi$
$462$	3.64073	0.169382
$463$	−18.6123	−0.864985	−0.432492	−	0.901638i	$-0.642366\pi$
$463$	−18.6123	−0.864985	−0.432492	+	0.901638i	$0.642366\pi$
$464$	16.7518	0.777682
$465$	1.24229	0.0576096
$466$	−42.1494	−1.95253
$467$	31.3497	1.45069	0.725346	−	0.688384i	$-0.241680\pi$
$467$	31.3497	1.45069	0.725346	+	0.688384i	$0.241680\pi$
$468$	72.9391	3.37161
$469$	6.20274	0.286416
$470$	−30.4152	−1.40295
$471$	5.27348	0.242989
$472$	−80.6766	−3.71344
$473$	−19.3480	−0.889622
$474$	−9.86701	−0.453207
$475$	−39.7676	−1.82466
$476$	−6.38684	−0.292740
$477$	−14.8294	−0.678991
$478$	21.0006	0.960546
$479$	−14.7356	−0.673288	−0.336644	−	0.941632i	$-0.609292\pi$
$479$	−14.7356	−0.673288	−0.336644	+	0.941632i	$0.609292\pi$
$480$	−23.8529	−1.08873
$481$	−2.85411	−0.130136
$482$	28.4742	1.29696
$483$	0.667392	0.0303674
$484$	13.0913	0.595059
$485$	75.7173	3.43815
$486$	−25.6564	−1.16380
$487$	42.2872	1.91622	0.958108	−	0.286408i	$-0.0924613\pi$
$487$	42.2872	1.91622	0.958108	+	0.286408i	$0.0924613\pi$
$488$	−83.6409	−3.78624
$489$	1.79824	0.0813194
$490$	69.3828	3.13439
$491$	2.59784	0.117239	0.0586194	−	0.998280i	$-0.481330\pi$
$491$	2.59784	0.117239	0.0586194	+	0.998280i	$0.481330\pi$
$492$	−6.15028	−0.277276
$493$	−1.86753	−0.0841092
$494$	−39.2428	−1.76562
$495$	45.3311	2.03748
$496$	8.76143	0.393400
$497$	5.21940	0.234122
$498$	1.65920	0.0743507
$499$	−36.6971	−1.64279	−0.821394	−	0.570361i	$-0.806804\pi$
$499$	−36.6971	−1.64279	−0.821394	+	0.570361i	$0.806804\pi$
$500$	187.490	8.38483
$501$	−2.61073	−0.116639
$502$	−65.2860	−2.91386
$503$	−21.8764	−0.975420	−0.487710	−	0.873006i	$-0.662168\pi$
$503$	−21.8764	−0.975420	−0.487710	+	0.873006i	$0.662168\pi$
$504$	22.7151	1.01181
$505$	41.9849	1.86830
$506$	17.6108	0.782895
$507$	4.71732	0.209504
$508$	82.6912	3.66883
$509$	41.0281	1.81854	0.909268	−	0.416210i	$-0.136642\pi$
$509$	41.0281	1.81854	0.909268	+	0.416210i	$0.136642\pi$
$510$	5.65820	0.250549
$511$	−16.3486	−0.723218
$512$	21.5002	0.950183
$513$	6.54655	0.289037
$514$	10.2621	0.452643
$515$	−44.2433	−1.94959
$516$	10.1687	0.447653
$517$	−9.77796	−0.430034
$518$	−1.46706	−0.0644590
$519$	−0.286734	−0.0125862
$520$	177.469	7.78255
$521$	−31.8562	−1.39565	−0.697823	−	0.716270i	$-0.745848\pi$
$521$	−31.8562	−1.39565	−0.697823	+	0.716270i	$0.745848\pi$
$522$	10.9627	0.479826
$523$	40.8190	1.78489	0.892446	−	0.451155i	$-0.148988\pi$
$523$	40.8190	1.78489	0.892446	+	0.451155i	$0.148988\pi$
$524$	−54.3053	−2.37234
$525$	5.04175	0.220040
$526$	−12.3263	−0.537454
$527$	−0.976745	−0.0425477
$528$	−16.3166	−0.710090
$529$	−19.7717	−0.859640
$530$	−59.5538	−2.58685
$531$	−28.1607	−1.22207
$532$	−14.4688	−0.627303
$533$	15.9914	0.692666
$534$	−10.0761	−0.436034
$535$	−14.8360	−0.641418
$536$	−52.1181	−2.25116
$537$	0.966868	0.0417234
$538$	53.1813	2.29281
$539$	22.3054	0.960761
$540$	−48.8652	−2.10282
$541$	−18.3008	−0.786813	−0.393406	−	0.919365i	$-0.628703\pi$
$541$	−18.3008	−0.786813	−0.393406	+	0.919365i	$0.628703\pi$
$542$	−54.1174	−2.32454
$543$	−7.20034	−0.308996
$544$	18.7543	0.804083
$545$	−15.3110	−0.655850
$546$	4.97521	0.212919
$547$	−29.1204	−1.24510	−0.622549	−	0.782581i	$-0.713903\pi$
$547$	−29.1204	−1.24510	−0.622549	+	0.782581i	$0.713903\pi$
$548$	10.7636	0.459799
$549$	−29.1954	−1.24603
$550$	133.039	5.67280
$551$	−4.23072	−0.180235
$552$	−5.60772	−0.238680
$553$	9.45914	0.402243
$554$	−0.699134	−0.0297033
$555$	0.932259	0.0395722
$556$	−82.4145	−3.49516
$557$	−14.9732	−0.634434	−0.317217	−	0.948353i	$-0.602748\pi$
$557$	−14.9732	−0.634434	−0.317217	+	0.948353i	$0.602748\pi$
$558$	5.73368	0.242726
$559$	−26.4399	−1.11829
$560$	48.6562	2.05610
$561$	1.81902	0.0767989
$562$	−47.3502	−1.99735
$563$	7.38518	0.311248	0.155624	−	0.987816i	$-0.450261\pi$
$563$	7.38518	0.311248	0.155624	+	0.987816i	$0.450261\pi$
$564$	5.13900	0.216391
$565$	67.9891	2.86032
$566$	45.9876	1.93300
$567$	7.50354	0.315119
$568$	−43.8556	−1.84014
$569$	−11.3481	−0.475738	−0.237869	−	0.971297i	$-0.576449\pi$
$569$	−11.3481	−0.475738	−0.237869	+	0.971297i	$0.576449\pi$
$570$	12.8182	0.536894
$571$	−11.5038	−0.481421	−0.240710	−	0.970597i	$-0.577380\pi$
$571$	−11.5038	−0.481421	−0.240710	+	0.970597i	$0.577380\pi$
$572$	94.1683	3.93737
$573$	5.92185	0.247389
$574$	8.21987	0.343091
$575$	24.3877	1.01704
$576$	−43.8659	−1.82775
$577$	−0.987143	−0.0410953	−0.0205476	−	0.999789i	$-0.506541\pi$
$577$	−0.987143	−0.0410953	−0.0205476	+	0.999789i	$0.506541\pi$
$578$	40.7675	1.69570
$579$	4.90068	0.203665
$580$	31.5792	1.31126
$581$	−1.59062	−0.0659899
$582$	−17.8356	−0.739310
$583$	−19.1455	−0.792927
$584$	137.368	5.68431
$585$	61.9468	2.56119
$586$	−30.2009	−1.24759
$587$	11.4599	0.473003	0.236501	−	0.971631i	$-0.423999\pi$
$587$	11.4599	0.473003	0.236501	+	0.971631i	$0.423999\pi$
$588$	−11.7230	−0.483450
$589$	−2.21273	−0.0911740
$590$	−113.091	−4.65590
$591$	−2.61648	−0.107628
$592$	6.57492	0.270228
$593$	22.8000	0.936284	0.468142	−	0.883653i	$-0.344924\pi$
$593$	22.8000	0.936284	0.468142	+	0.883653i	$0.344924\pi$
$594$	−21.9009	−0.898605
$595$	−5.42431	−0.222375
$596$	24.8691	1.01868
$597$	−6.30287	−0.257959
$598$	24.0659	0.984128
$599$	16.2486	0.663898	0.331949	−	0.943297i	$-0.392294\pi$
$599$	16.2486	0.663898	0.331949	+	0.943297i	$0.392294\pi$
$600$	−42.3629	−1.72946
$601$	9.55812	0.389884	0.194942	−	0.980815i	$-0.437548\pi$
$601$	9.55812	0.389884	0.194942	+	0.980815i	$0.437548\pi$
$602$	−13.5905	−0.553909
$603$	−18.1921	−0.740842
$604$	67.1536	2.73244
$605$	11.1184	0.452026
$606$	−9.88977	−0.401744
$607$	15.2516	0.619042	0.309521	−	0.950893i	$-0.399831\pi$
$607$	15.2516	0.619042	0.309521	+	0.950893i	$0.399831\pi$
$608$	42.4862	1.72304
$609$	0.536372	0.0217349
$610$	−117.247	−4.74718
$611$	−13.3620	−0.540569
$612$	18.7321	0.757200
$613$	−21.9613	−0.887009	−0.443505	−	0.896272i	$-0.646265\pi$
$613$	−21.9613	−0.887009	−0.443505	+	0.896272i	$0.646265\pi$
$614$	50.5347	2.03941
$615$	−5.22340	−0.210628
$616$	29.3264	1.18159
$617$	20.8786	0.840541	0.420270	−	0.907399i	$-0.361935\pi$
$617$	20.8786	0.840541	0.420270	+	0.907399i	$0.361935\pi$
$618$	10.4217	0.419224
$619$	10.3499	0.415998	0.207999	−	0.978129i	$-0.433305\pi$
$619$	10.3499	0.415998	0.207999	+	0.978129i	$0.433305\pi$
$620$	16.5164	0.663315
$621$	−4.01472	−0.161105
$622$	35.0826	1.40669
$623$	9.65954	0.387001
$624$	−22.2974	−0.892609
$625$	91.3681	3.65472
$626$	22.0703	0.882108
$627$	4.12082	0.164570
$628$	70.1118	2.79777
$629$	−0.732987	−0.0292261
$630$	31.8417	1.26860
$631$	−42.4745	−1.69088	−0.845441	−	0.534069i	$-0.820662\pi$
$631$	−42.4745	−1.69088	−0.845441	+	0.534069i	$0.820662\pi$
$632$	−79.4797	−3.16153
$633$	3.70599	0.147300
$634$	−8.08299	−0.321017
$635$	70.2292	2.78696
$636$	10.0623	0.398997
$637$	30.4813	1.20771
$638$	14.1535	0.560342
$639$	−15.3081	−0.605578
$640$	−51.1717	−2.02274
$641$	−30.8240	−1.21748	−0.608738	−	0.793371i	$-0.708324\pi$
$641$	−30.8240	−1.21748	−0.608738	+	0.793371i	$0.708324\pi$
$642$	3.49471	0.137925
$643$	−24.8861	−0.981413	−0.490707	−	0.871325i	$-0.663261\pi$
$643$	−24.8861	−0.981413	−0.490707	+	0.871325i	$0.663261\pi$
$644$	8.87310	0.349649
$645$	8.63625	0.340052
$646$	−10.0783	−0.396524
$647$	−9.85005	−0.387245	−0.193623	−	0.981076i	$-0.562024\pi$
$647$	−9.85005	−0.387245	−0.193623	+	0.981076i	$0.562024\pi$
$648$	−63.0479	−2.47676
$649$	−36.3569	−1.42713
$650$	181.803	7.13092
$651$	0.280531	0.0109949
$652$	23.9080	0.936308
$653$	−29.1305	−1.13996	−0.569982	−	0.821657i	$-0.693050\pi$
$653$	−29.1305	−1.13996	−0.569982	+	0.821657i	$0.693050\pi$
$654$	3.60658	0.141028
$655$	−46.1212	−1.80210
$656$	−36.8389	−1.43832
$657$	47.9490	1.87067
$658$	−6.86830	−0.267754
$659$	−14.4102	−0.561343	−0.280671	−	0.959804i	$-0.590557\pi$
$659$	−14.4102	−0.561343	−0.280671	+	0.959804i	$0.590557\pi$
$660$	−30.7589	−1.19729
$661$	−1.99796	−0.0777117	−0.0388559	−	0.999245i	$-0.512371\pi$
$661$	−1.99796	−0.0777117	−0.0388559	+	0.999245i	$0.512371\pi$
$662$	72.9369	2.83477
$663$	2.48576	0.0965390
$664$	13.3650	0.518664
$665$	−12.2883	−0.476520
$666$	4.30278	0.166729
$667$	2.59452	0.100460
$668$	−34.7101	−1.34297
$669$	6.77999	0.262129
$670$	−73.0584	−2.82249
$671$	−37.6928	−1.45511
$672$	−5.38641	−0.207785
$673$	8.23879	0.317582	0.158791	−	0.987312i	$-0.449240\pi$
$673$	8.23879	0.317582	0.158791	+	0.987312i	$0.449240\pi$
$674$	71.3189	2.74710
$675$	−30.3288	−1.16735
$676$	62.7176	2.41222
$677$	45.0078	1.72979	0.864894	−	0.501954i	$-0.167385\pi$
$677$	45.0078	1.72979	0.864894	+	0.501954i	$0.167385\pi$
$678$	−16.0152	−0.615059
$679$	17.0983	0.656174
$680$	45.5774	1.74781
$681$	7.73842	0.296537
$682$	7.40249	0.283456
$683$	10.5565	0.403934	0.201967	−	0.979392i	$-0.435267\pi$
$683$	10.5565	0.403934	0.201967	+	0.979392i	$0.435267\pi$
$684$	42.4359	1.62258
$685$	9.14149	0.349279
$686$	33.7874	1.29001
$687$	3.12270	0.119138
$688$	60.9086	2.32212
$689$	−26.1632	−0.996738
$690$	−7.86082	−0.299256
$691$	21.6051	0.821895	0.410948	−	0.911659i	$-0.365198\pi$
$691$	21.6051	0.821895	0.410948	+	0.911659i	$0.365198\pi$
$692$	−3.81217	−0.144917
$693$	10.2366	0.388855
$694$	−84.2621	−3.19855
$695$	−69.9943	−2.65503
$696$	−4.50682	−0.170831
$697$	4.10689	0.155560
$698$	−27.7571	−1.05062
$699$	6.04836	0.228770
$700$	67.0309	2.53353
$701$	−18.7447	−0.707979	−0.353990	−	0.935249i	$-0.615175\pi$
$701$	−18.7447	−0.707979	−0.353990	+	0.935249i	$0.615175\pi$
$702$	−29.9285	−1.12958
$703$	−1.66052	−0.0626276
$704$	−56.6333	−2.13445
$705$	4.36453	0.164378
$706$	−9.39915	−0.353742
$707$	9.48095	0.356568
$708$	19.1081	0.718127
$709$	−26.6013	−0.999032	−0.499516	−	0.866305i	$-0.666489\pi$
$709$	−26.6013	−0.999032	−0.499516	+	0.866305i	$0.666489\pi$
$710$	−61.4762	−2.30716
$711$	−27.7429	−1.04044
$712$	−81.1636	−3.04173
$713$	1.35697	0.0508190
$714$	1.27772	0.0478176
$715$	79.9767	2.99096
$716$	12.8547	0.480402
$717$	−3.01355	−0.112543
$718$	−83.7107	−3.12406
$719$	−32.0325	−1.19461	−0.597306	−	0.802013i	$-0.703762\pi$
$719$	−32.0325	−1.19461	−0.597306	+	0.802013i	$0.703762\pi$
$720$	−142.705	−5.31829
$721$	−9.99094	−0.372082
$722$	27.7044	1.03105
$723$	−4.08600	−0.151960
$724$	−95.7298	−3.55777
$725$	19.6000	0.727926
$726$	−2.61899	−0.0971999
$727$	−30.2168	−1.12068	−0.560339	−	0.828263i	$-0.689329\pi$
$727$	−30.2168	−1.12068	−0.560339	+	0.828263i	$0.689329\pi$
$728$	40.0758	1.48531
$729$	−19.4488	−0.720326
$730$	192.560	7.12697
$731$	−6.79024	−0.251146
$732$	19.8102	0.732206
$733$	−10.4059	−0.384352	−0.192176	−	0.981360i	$-0.561554\pi$
$733$	−10.4059	−0.384352	−0.192176	+	0.981360i	$0.561554\pi$
$734$	−2.43868	−0.0900134
$735$	−9.95631	−0.367244
$736$	−26.0549	−0.960397
$737$	−23.4870	−0.865156
$738$	−24.1082	−0.887436
$739$	−1.81729	−0.0668500	−0.0334250	−	0.999441i	$-0.510641\pi$
$739$	−1.81729	−0.0668500	−0.0334250	+	0.999441i	$0.510641\pi$
$740$	12.3945	0.455633
$741$	5.63128	0.206870
$742$	−13.4483	−0.493704
$743$	22.2227	0.815271	0.407635	−	0.913145i	$-0.366353\pi$
$743$	22.2227	0.815271	0.407635	+	0.913145i	$0.366353\pi$
$744$	−2.35714	−0.0864168
$745$	21.1212	0.773821
$746$	−84.1782	−3.08198
$747$	4.66515	0.170689
$748$	24.1841	0.884259
$749$	−3.35025	−0.122415
$750$	−37.5086	−1.36962
$751$	−0.417084	−0.0152196	−0.00760980	−	0.999971i	$-0.502422\pi$
$751$	−0.417084	−0.0152196	−0.00760980	+	0.999971i	$0.502422\pi$
$752$	30.7816	1.12249
$753$	9.36843	0.341405
$754$	19.3413	0.704370
$755$	57.0332	2.07565
$756$	−11.0346	−0.401326
$757$	31.1517	1.13223	0.566114	−	0.824327i	$-0.308446\pi$
$757$	31.1517	1.13223	0.566114	+	0.824327i	$0.308446\pi$
$758$	−67.6263	−2.45630
$759$	−2.52712	−0.0917286
$760$	103.251	3.74533
$761$	−23.8080	−0.863040	−0.431520	−	0.902103i	$-0.642023\pi$
$761$	−23.8080	−0.863040	−0.431520	+	0.902103i	$0.642023\pi$
$762$	−16.5429	−0.599285
$763$	−3.45749	−0.125170
$764$	78.7320	2.84843
$765$	15.9091	0.575193
$766$	9.90856	0.358011
$767$	−49.6833	−1.79396
$768$	0.322463	0.0116359
$769$	23.5490	0.849198	0.424599	−	0.905382i	$-0.360415\pi$
$769$	23.5490	0.849198	0.424599	+	0.905382i	$0.360415\pi$
$770$	41.1094	1.48148
$771$	−1.47260	−0.0530343
$772$	65.1553	2.34499
$773$	−33.0463	−1.18859	−0.594296	−	0.804246i	$-0.702569\pi$
$773$	−33.0463	−1.18859	−0.594296	+	0.804246i	$0.702569\pi$
$774$	39.8600	1.43274
$775$	10.2511	0.368230
$776$	−143.667	−5.15736
$777$	0.210521	0.00755240
$778$	82.1978	2.94693
$779$	9.30380	0.333343
$780$	−42.0333	−1.50503
$781$	−19.7635	−0.707195
$782$	6.18056	0.221016
$783$	−3.22656	−0.115308
$784$	−70.2186	−2.50781
$785$	59.5456	2.12527
$786$	10.8641	0.387509
$787$	−1.54959	−0.0552368	−0.0276184	−	0.999619i	$-0.508792\pi$
$787$	−1.54959	−0.0552368	−0.0276184	+	0.999619i	$0.508792\pi$
$788$	−34.7866	−1.23922
$789$	1.76881	0.0629713
$790$	−111.414	−3.96392
$791$	15.3532	0.545895
$792$	−86.0120	−3.05630
$793$	−51.5088	−1.82913
$794$	−2.05871	−0.0730610
$795$	8.54588	0.303091
$796$	−83.7977	−2.97013
$797$	21.5306	0.762653	0.381326	−	0.924440i	$-0.375467\pi$
$797$	21.5306	0.762653	0.381326	+	0.924440i	$0.375467\pi$
$798$	2.89457	0.102467
$799$	−3.43160	−0.121401
$800$	−196.829	−6.95896
$801$	−28.3307	−1.00101
$802$	0.841322	0.0297081
$803$	61.9048	2.18457
$804$	12.3441	0.435342
$805$	7.53588	0.265605
$806$	10.1158	0.356314
$807$	−7.63142	−0.268639
$808$	−79.6630	−2.80253
$809$	6.72929	0.236589	0.118295	−	0.992979i	$-0.462257\pi$
$809$	6.72929	0.236589	0.118295	+	0.992979i	$0.462257\pi$
$810$	−88.3797	−3.10535
$811$	−41.7926	−1.46754	−0.733768	−	0.679400i	$-0.762240\pi$
$811$	−41.7926	−1.46754	−0.733768	+	0.679400i	$0.762240\pi$
$812$	7.13115	0.250254
$813$	7.76575	0.272357
$814$	5.55511	0.194707
$815$	20.3049	0.711250
$816$	−5.72637	−0.200463
$817$	−15.3827	−0.538172
$818$	38.3249	1.34000
$819$	13.9887	0.488805
$820$	−69.4460	−2.42516
$821$	−39.0111	−1.36150	−0.680749	−	0.732517i	$-0.738345\pi$
$821$	−39.0111	−1.36150	−0.680749	+	0.732517i	$0.738345\pi$
$822$	−2.15333	−0.0751059
$823$	41.1351	1.43388	0.716940	−	0.697135i	$-0.245542\pi$
$823$	41.1351	1.43388	0.716940	+	0.697135i	$0.245542\pi$
$824$	83.9481	2.92447
$825$	−19.0909	−0.664658
$826$	−25.5381	−0.888583
$827$	−29.1296	−1.01294	−0.506468	−	0.862259i	$-0.669049\pi$
$827$	−29.1296	−1.01294	−0.506468	+	0.862259i	$0.669049\pi$
$828$	−26.0241	−0.904399
$829$	39.1164	1.35857	0.679285	−	0.733874i	$-0.262290\pi$
$829$	39.1164	1.35857	0.679285	+	0.733874i	$0.262290\pi$
$830$	18.7349	0.650299
$831$	0.100325	0.00348022
$832$	−77.3918	−2.68308
$833$	7.82814	0.271229
$834$	16.4875	0.570916
$835$	−29.4791	−1.02017
$836$	54.7870	1.89485
$837$	−1.68754	−0.0583299
$838$	45.7194	1.57935
$839$	45.1837	1.55991	0.779957	−	0.625833i	$-0.215241\pi$
$839$	45.1837	1.55991	0.779957	+	0.625833i	$0.215241\pi$
$840$	−13.0903	−0.451657
$841$	−26.9148	−0.928098
$842$	105.838	3.64741
$843$	6.79468	0.234021
$844$	49.2718	1.69601
$845$	53.2658	1.83240
$846$	20.1442	0.692571
$847$	2.51073	0.0862697
$848$	60.2713	2.06972
$849$	−6.59915	−0.226482
$850$	46.6904	1.60147
$851$	1.01832	0.0349077
$852$	10.3871	0.355857
$853$	−4.79182	−0.164069	−0.0820344	−	0.996630i	$-0.526142\pi$
$853$	−4.79182	−0.164069	−0.0820344	+	0.996630i	$0.526142\pi$
$854$	−26.4764	−0.906004
$855$	36.0406	1.23256
$856$	28.1502	0.962154
$857$	−34.8743	−1.19128	−0.595642	−	0.803250i	$-0.703102\pi$
$857$	−34.8743	−1.19128	−0.595642	+	0.803250i	$0.703102\pi$
$858$	−18.8389	−0.643150
$859$	13.0873	0.446532	0.223266	−	0.974758i	$-0.428328\pi$
$859$	13.0873	0.446532	0.223266	+	0.974758i	$0.428328\pi$
$860$	114.820	3.91534
$861$	−1.17954	−0.0401985
$862$	−58.4513	−1.99086
$863$	41.1000	1.39906	0.699531	−	0.714603i	$-0.253392\pi$
$863$	41.1000	1.39906	0.699531	+	0.714603i	$0.253392\pi$
$864$	32.4021	1.10234
$865$	−3.23766	−0.110084
$866$	55.0845	1.87185
$867$	−5.85006	−0.198679
$868$	3.72970	0.126594
$869$	−35.8176	−1.21503
$870$	−6.31761	−0.214187
$871$	−32.0960	−1.08753
$872$	29.0513	0.983802
$873$	−50.1480	−1.69725
$874$	14.0015	0.473608
$875$	35.9581	1.21560
$876$	−32.5353	−1.09927
$877$	20.0958	0.678586	0.339293	−	0.940681i	$-0.389812\pi$
$877$	20.0958	0.678586	0.339293	+	0.940681i	$0.389812\pi$
$878$	−53.7889	−1.81529
$879$	4.33377	0.146175
$880$	−184.240	−6.21071
$881$	39.1032	1.31742	0.658710	−	0.752397i	$-0.271102\pi$
$881$	39.1032	1.31742	0.658710	+	0.752397i	$0.271102\pi$
$882$	−45.9527	−1.54731
$883$	29.4412	0.990776	0.495388	−	0.868672i	$-0.335026\pi$
$883$	29.4412	0.990776	0.495388	+	0.868672i	$0.335026\pi$
$884$	33.0486	1.11155
$885$	16.2284	0.545512
$886$	−71.7490	−2.41046
$887$	9.60624	0.322546	0.161273	−	0.986910i	$-0.448440\pi$
$887$	9.60624	0.322546	0.161273	+	0.986910i	$0.448440\pi$
$888$	−1.76889	−0.0593600
$889$	15.8590	0.531895
$890$	−113.774	−3.81371
$891$	−28.4126	−0.951857
$892$	90.1411	3.01815
$893$	−7.77399	−0.260147
$894$	−4.97521	−0.166396
$895$	10.9174	0.364929
$896$	−11.5555	−0.386042
$897$	−3.45342	−0.115306
$898$	94.4357	3.15136
$899$	1.09057	0.0363727
$900$	−196.596	−6.55321
$901$	−6.71918	−0.223848
$902$	−31.1250	−1.03635
$903$	1.95022	0.0648993
$904$	−129.004	−4.29060
$905$	−81.3029	−2.70260
$906$	−13.4345	−0.446331
$907$	45.6832	1.51689	0.758443	−	0.651740i	$-0.225960\pi$
$907$	45.6832	1.51689	0.758443	+	0.651740i	$0.225960\pi$
$908$	102.884	3.41431
$909$	−27.8069	−0.922296
$910$	56.1777	1.86227
$911$	34.0288	1.12742	0.563712	−	0.825971i	$-0.309373\pi$
$911$	34.0288	1.12742	0.563712	+	0.825971i	$0.309373\pi$
$912$	−12.9726	−0.429565
$913$	6.02296	0.199331
$914$	41.6034	1.37612
$915$	16.8247	0.556207
$916$	41.5168	1.37175
$917$	−10.4150	−0.343934
$918$	−7.68618	−0.253682
$919$	−19.8316	−0.654185	−0.327092	−	0.944992i	$-0.606069\pi$
$919$	−19.8316	−0.654185	−0.327092	+	0.944992i	$0.606069\pi$
$920$	−63.3196	−2.08759
$921$	−7.25165	−0.238950
$922$	−102.151	−3.36416
$923$	−27.0077	−0.888970
$924$	−6.94591	−0.228504
$925$	7.69282	0.252938
$926$	49.5045	1.62682
$927$	29.3026	0.962425
$928$	−20.9399	−0.687386
$929$	10.1442	0.332821	0.166410	−	0.986057i	$-0.446782\pi$
$929$	10.1442	0.332821	0.166410	+	0.986057i	$0.446782\pi$
$930$	−3.30420	−0.108349
$931$	17.7340	0.581207
$932$	80.4140	2.63405
$933$	−5.03430	−0.164816
$934$	−83.3833	−2.72839
$935$	20.5395	0.671712
$936$	−117.539	−3.84189
$937$	−34.8160	−1.13739	−0.568695	−	0.822549i	$-0.692551\pi$
$937$	−34.8160	−1.13739	−0.568695	+	0.822549i	$0.692551\pi$
$938$	−16.4979	−0.538676
$939$	−3.16706	−0.103353
$940$	58.0271	1.89264
$941$	45.2417	1.47484	0.737418	−	0.675436i	$-0.236045\pi$
$941$	45.2417	1.47484	0.737418	+	0.675436i	$0.236045\pi$
$942$	−14.0263	−0.457001
$943$	−5.70561	−0.185800
$944$	114.454	3.72515
$945$	−9.37167	−0.304860
$946$	51.4614	1.67315
$947$	2.74647	0.0892484	0.0446242	−	0.999004i	$-0.485791\pi$
$947$	2.74647	0.0892484	0.0446242	+	0.999004i	$0.485791\pi$
$948$	18.8246	0.611396
$949$	84.5955	2.74609
$950$	105.773	3.43173
$951$	1.15990	0.0376122
$952$	10.2922	0.333572
$953$	0.142756	0.00462430	0.00231215	−	0.999997i	$-0.499264\pi$
$953$	0.142756	0.00462430	0.00231215	+	0.999997i	$0.499264\pi$
$954$	39.4429	1.27701
$955$	66.8667	2.16376
$956$	−40.0657	−1.29582
$957$	−2.03100	−0.0656530
$958$	39.1935	1.26628
$959$	2.06431	0.0666602
$960$	25.2790	0.815878
$961$	−30.4296	−0.981600
$962$	7.59130	0.244753
$963$	9.82601	0.316639
$964$	−54.3240	−1.74966
$965$	55.3361	1.78133
$966$	−1.77512	−0.0571134
$967$	6.53144	0.210037	0.105018	−	0.994470i	$-0.466510\pi$
$967$	6.53144	0.210037	0.105018	+	0.994470i	$0.466510\pi$
$968$	−21.0962	−0.678058
$969$	1.44621	0.0464591
$970$	−201.391	−6.46628
$971$	−18.7874	−0.602917	−0.301459	−	0.953479i	$-0.597474\pi$
$971$	−18.7874	−0.602917	−0.301459	+	0.953479i	$0.597474\pi$
$972$	48.9482	1.57002
$973$	−15.8060	−0.506716
$974$	−112.475	−3.60392
$975$	−26.0885	−0.835500
$976$	118.659	3.79818
$977$	−39.2935	−1.25711	−0.628555	−	0.777765i	$-0.716353\pi$
$977$	−39.2935	−1.25711	−0.628555	+	0.777765i	$0.716353\pi$
$978$	−4.78293	−0.152941
$979$	−36.5764	−1.16899
$980$	−132.371	−4.22843
$981$	10.1406	0.323763
$982$	−6.90968	−0.220497
$983$	−21.2400	−0.677451	−0.338725	−	0.940885i	$-0.609996\pi$
$983$	−21.2400	−0.677451	−0.338725	+	0.940885i	$0.609996\pi$
$984$	9.91098	0.315951
$985$	−29.5440	−0.941352
$986$	4.96721	0.158188
$987$	0.985589	0.0313716
$988$	74.8688	2.38189
$989$	9.43353	0.299969
$990$	−120.571	−3.83198
$991$	−32.2931	−1.02582	−0.512912	−	0.858441i	$-0.671433\pi$
$991$	−32.2931	−1.02582	−0.512912	+	0.858441i	$0.671433\pi$
$992$	−10.9519	−0.347723
$993$	−10.4663	−0.332139
$994$	−13.8824	−0.440324
$995$	−71.1690	−2.25621
$996$	−3.16549	−0.100302
$997$	−2.03159	−0.0643412	−0.0321706	−	0.999482i	$-0.510242\pi$
$997$	−2.03159	−0.0643412	−0.0321706	+	0.999482i	$0.510242\pi$
$998$	97.6062	3.08967
$999$	−1.26639	−0.0400669

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.6	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.6	✓	216	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65978 q^{2} +0.381674 q^{3} +5.07442 q^{4} +4.30968 q^{5} -1.01517 q^{6} +0.973203 q^{7} -8.17726 q^{8} -2.85433 q^{9} +O(q^{10})\)	\(q-2.65978 q^{2} +0.381674 q^{3} +5.07442 q^{4} +4.30968 q^{5} -1.01517 q^{6} +0.973203 q^{7} -8.17726 q^{8} -2.85433 q^{9} -11.4628 q^{10} -3.68509 q^{11} +1.93677 q^{12} -5.03583 q^{13} -2.58850 q^{14} +1.64489 q^{15} +11.6009 q^{16} -1.29329 q^{17} +7.59187 q^{18} -2.92984 q^{19} +21.8691 q^{20} +0.371446 q^{21} +9.80151 q^{22} +1.79674 q^{23} -3.12105 q^{24} +13.5733 q^{25} +13.3942 q^{26} -2.23444 q^{27} +4.93844 q^{28} +1.44401 q^{29} -4.37504 q^{30} +0.755240 q^{31} -14.5012 q^{32} -1.40650 q^{33} +3.43987 q^{34} +4.19419 q^{35} -14.4840 q^{36} +0.566761 q^{37} +7.79272 q^{38} -1.92204 q^{39} -35.2414 q^{40} -3.17553 q^{41} -0.987963 q^{42} +5.25035 q^{43} -18.6997 q^{44} -12.3012 q^{45} -4.77894 q^{46} +2.65339 q^{47} +4.42774 q^{48} -6.05288 q^{49} -36.1020 q^{50} -0.493615 q^{51} -25.5539 q^{52} +5.19541 q^{53} +5.94312 q^{54} -15.8815 q^{55} -7.95813 q^{56} -1.11824 q^{57} -3.84075 q^{58} +9.86596 q^{59} +8.34685 q^{60} +10.2285 q^{61} -2.00877 q^{62} -2.77784 q^{63} +15.3682 q^{64} -21.7028 q^{65} +3.74098 q^{66} +6.37354 q^{67} -6.56270 q^{68} +0.685769 q^{69} -11.1556 q^{70} +5.36311 q^{71} +23.3406 q^{72} -16.7987 q^{73} -1.50746 q^{74} +5.18057 q^{75} -14.8672 q^{76} -3.58634 q^{77} +5.11221 q^{78} +9.71960 q^{79} +49.9960 q^{80} +7.71015 q^{81} +8.44621 q^{82} -1.63442 q^{83} +1.88487 q^{84} -5.57367 q^{85} -13.9648 q^{86} +0.551141 q^{87} +30.1339 q^{88} +9.92552 q^{89} +32.7185 q^{90} -4.90088 q^{91} +9.11742 q^{92} +0.288255 q^{93} -7.05742 q^{94} -12.6267 q^{95} -5.53473 q^{96} +17.5691 q^{97} +16.0993 q^{98} +10.5184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9} + 24 q^{10} + 89 q^{11} + 114 q^{12} + 34 q^{13} + 53 q^{14} + 61 q^{15} + 229 q^{16} + 76 q^{17} + 57 q^{18} + 54 q^{19} + 118 q^{20} + 25 q^{21} + 26 q^{22} + 109 q^{23} + 65 q^{24} + 232 q^{25} + 58 q^{26} + 236 q^{27} + 57 q^{28} + 54 q^{29} + 6 q^{30} + 77 q^{31} + 155 q^{32} + 80 q^{33} + 28 q^{34} + 137 q^{35} + 257 q^{36} + 42 q^{37} + 104 q^{38} + 46 q^{39} + 47 q^{40} + 109 q^{41} + 27 q^{42} + 68 q^{43} + 145 q^{44} + 109 q^{45} - 7 q^{46} + 264 q^{47} + 198 q^{48} + 222 q^{49} + 86 q^{50} + 57 q^{51} + 68 q^{52} + 95 q^{53} + 79 q^{54} + 50 q^{55} + 108 q^{56} + 55 q^{57} + 38 q^{58} + 292 q^{59} + 91 q^{60} + 16 q^{61} + 91 q^{62} + 113 q^{63} + 231 q^{64} + 68 q^{65} - 15 q^{66} + 152 q^{67} + 199 q^{68} + 83 q^{69} + 24 q^{70} + 131 q^{71} + 162 q^{72} + 71 q^{73} + 10 q^{74} + 232 q^{75} + 60 q^{76} + 131 q^{77} + 102 q^{78} + 10 q^{79} + 236 q^{80} + 268 q^{81} + 54 q^{82} + 299 q^{83} - 9 q^{85} + 35 q^{86} + 103 q^{87} + 45 q^{88} + 134 q^{89} + 8 q^{90} + 79 q^{91} + 206 q^{92} + 95 q^{93} + 18 q^{94} + 119 q^{95} + 77 q^{96} + 129 q^{97} + 150 q^{98} + 221 q^{99}+O(q^{100}) \) 216 * q + 25 * q^2 + 62 * q^3 + 223 * q^4 + 46 * q^5 + 26 * q^6 + 30 * q^7 + 75 * q^8 + 234 * q^9 + 24 * q^10 + 89 * q^11 + 114 * q^12 + 34 * q^13 + 53 * q^14 + 61 * q^15 + 229 * q^16 + 76 * q^17 + 57 * q^18 + 54 * q^19 + 118 * q^20 + 25 * q^21 + 26 * q^22 + 109 * q^23 + 65 * q^24 + 232 * q^25 + 58 * q^26 + 236 * q^27 + 57 * q^28 + 54 * q^29 + 6 * q^30 + 77 * q^31 + 155 * q^32 + 80 * q^33 + 28 * q^34 + 137 * q^35 + 257 * q^36 + 42 * q^37 + 104 * q^38 + 46 * q^39 + 47 * q^40 + 109 * q^41 + 27 * q^42 + 68 * q^43 + 145 * q^44 + 109 * q^45 - 7 * q^46 + 264 * q^47 + 198 * q^48 + 222 * q^49 + 86 * q^50 + 57 * q^51 + 68 * q^52 + 95 * q^53 + 79 * q^54 + 50 * q^55 + 108 * q^56 + 55 * q^57 + 38 * q^58 + 292 * q^59 + 91 * q^60 + 16 * q^61 + 91 * q^62 + 113 * q^63 + 231 * q^64 + 68 * q^65 - 15 * q^66 + 152 * q^67 + 199 * q^68 + 83 * q^69 + 24 * q^70 + 131 * q^71 + 162 * q^72 + 71 * q^73 + 10 * q^74 + 232 * q^75 + 60 * q^76 + 131 * q^77 + 102 * q^78 + 10 * q^79 + 236 * q^80 + 268 * q^81 + 54 * q^82 + 299 * q^83 - 9 * q^85 + 35 * q^86 + 103 * q^87 + 45 * q^88 + 134 * q^89 + 8 * q^90 + 79 * q^91 + 206 * q^92 + 95 * q^93 + 18 * q^94 + 119 * q^95 + 77 * q^96 + 129 * q^97 + 150 * q^98 + 221 * q^99

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