LMFDB - Embedded newform 5077.2.a.b.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:	$1$
Dimension:	$205$
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)

$f(q)$	$=$	$q-2.75099 q^{2} +0.881000 q^{3} +5.56794 q^{4} -0.176984 q^{5} -2.42362 q^{6} +4.01245 q^{7} -9.81537 q^{8} -2.22384 q^{9} +O(q^{10})$	\(q-2.75099 q^{2} +0.881000 q^{3} +5.56794 q^{4} -0.176984 q^{5} -2.42362 q^{6} +4.01245 q^{7} -9.81537 q^{8} -2.22384 q^{9} +0.486880 q^{10} -4.27847 q^{11} +4.90535 q^{12} -0.319284 q^{13} -11.0382 q^{14} -0.155922 q^{15} +15.8661 q^{16} -3.33235 q^{17} +6.11776 q^{18} +3.36468 q^{19} -0.985434 q^{20} +3.53497 q^{21} +11.7700 q^{22} +6.67835 q^{23} -8.64733 q^{24} -4.96868 q^{25} +0.878348 q^{26} -4.60220 q^{27} +22.3411 q^{28} -10.6511 q^{29} +0.428941 q^{30} -3.76944 q^{31} -24.0167 q^{32} -3.76933 q^{33} +9.16727 q^{34} -0.710138 q^{35} -12.3822 q^{36} +2.92659 q^{37} -9.25619 q^{38} -0.281289 q^{39} +1.73716 q^{40} +10.3393 q^{41} -9.72466 q^{42} +1.06696 q^{43} -23.8223 q^{44} +0.393583 q^{45} -18.3721 q^{46} +8.79369 q^{47} +13.9780 q^{48} +9.09977 q^{49} +13.6688 q^{50} -2.93580 q^{51} -1.77776 q^{52} +9.12457 q^{53} +12.6606 q^{54} +0.757219 q^{55} -39.3837 q^{56} +2.96428 q^{57} +29.3011 q^{58} -4.95677 q^{59} -0.868167 q^{60} +8.81938 q^{61} +10.3697 q^{62} -8.92305 q^{63} +34.3375 q^{64} +0.0565081 q^{65} +10.3694 q^{66} -6.79897 q^{67} -18.5544 q^{68} +5.88363 q^{69} +1.95358 q^{70} +12.1395 q^{71} +21.8278 q^{72} +10.1045 q^{73} -8.05101 q^{74} -4.37740 q^{75} +18.7343 q^{76} -17.1672 q^{77} +0.773824 q^{78} -11.5928 q^{79} -2.80804 q^{80} +2.61698 q^{81} -28.4432 q^{82} +9.32325 q^{83} +19.6825 q^{84} +0.589772 q^{85} -2.93519 q^{86} -9.38362 q^{87} +41.9947 q^{88} -15.4099 q^{89} -1.08274 q^{90} -1.28111 q^{91} +37.1847 q^{92} -3.32088 q^{93} -24.1913 q^{94} -0.595493 q^{95} -21.1587 q^{96} -7.54046 q^{97} -25.0334 q^{98} +9.51463 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.75099	−1.94524	−0.972622	−	0.232395i	$-0.925344\pi$
$2$	−2.75099	−1.94524	−0.972622	+	0.232395i	$0.925344\pi$
$3$	0.881000	0.508645	0.254323	−	0.967119i	$-0.418147\pi$
$3$	0.881000	0.508645	0.254323	+	0.967119i	$0.418147\pi$
$4$	5.56794	2.78397
$5$	−0.176984	−0.0791494	−0.0395747	−	0.999217i	$-0.512600\pi$
$5$	−0.176984	−0.0791494	−0.0395747	+	0.999217i	$0.512600\pi$
$6$	−2.42362	−0.989439
$7$	4.01245	1.51656	0.758282	−	0.651927i	$-0.226039\pi$
$7$	4.01245	1.51656	0.758282	+	0.651927i	$0.226039\pi$
$8$	−9.81537	−3.47026
$9$	−2.22384	−0.741280
$10$	0.486880	0.153965
$11$	−4.27847	−1.29001	−0.645003	−	0.764180i	$-0.723144\pi$
$11$	−4.27847	−1.29001	−0.645003	+	0.764180i	$0.723144\pi$
$12$	4.90535	1.41605
$13$	−0.319284	−0.0885536	−0.0442768	−	0.999019i	$-0.514098\pi$
$13$	−0.319284	−0.0885536	−0.0442768	+	0.999019i	$0.514098\pi$
$14$	−11.0382	−2.95009
$15$	−0.155922	−0.0402590
$16$	15.8661	3.96652
$17$	−3.33235	−0.808215	−0.404107	−	0.914712i	$-0.632418\pi$
$17$	−3.33235	−0.808215	−0.404107	+	0.914712i	$0.632418\pi$
$18$	6.11776	1.44197
$19$	3.36468	0.771910	0.385955	−	0.922518i	$-0.373872\pi$
$19$	3.36468	0.771910	0.385955	+	0.922518i	$0.373872\pi$
$20$	−0.985434	−0.220350
$21$	3.53497	0.771393
$22$	11.7700	2.50938
$23$	6.67835	1.39253	0.696266	−	0.717783i	$-0.254843\pi$
$23$	6.67835	1.39253	0.696266	+	0.717783i	$0.254843\pi$
$24$	−8.64733	−1.76513
$25$	−4.96868	−0.993735
$26$	0.878348	0.172258
$27$	−4.60220	−0.885694
$28$	22.3411	4.22207
$29$	−10.6511	−1.97786	−0.988930	−	0.148384i	$-0.952593\pi$
$29$	−10.6511	−1.97786	−0.988930	+	0.148384i	$0.952593\pi$
$30$	0.428941	0.0783135
$31$	−3.76944	−0.677012	−0.338506	−	0.940964i	$-0.609921\pi$
$31$	−3.76944	−0.677012	−0.338506	+	0.940964i	$0.609921\pi$
$32$	−24.0167	−4.24559
$33$	−3.76933	−0.656156
$34$	9.16727	1.57217
$35$	−0.710138	−0.120035
$36$	−12.3822	−2.06370
$37$	2.92659	0.481128	0.240564	−	0.970633i	$-0.422668\pi$
$37$	2.92659	0.481128	0.240564	+	0.970633i	$0.422668\pi$
$38$	−9.25619	−1.50155
$39$	−0.281289	−0.0450424
$40$	1.73716	0.274669
$41$	10.3393	1.61472	0.807362	−	0.590056i	$-0.200895\pi$
$41$	10.3393	1.61472	0.807362	+	0.590056i	$0.200895\pi$
$42$	−9.72466	−1.50055
$43$	1.06696	0.162710	0.0813548	−	0.996685i	$-0.474075\pi$
$43$	1.06696	0.162710	0.0813548	+	0.996685i	$0.474075\pi$
$44$	−23.8223	−3.59134
$45$	0.393583	0.0586719
$46$	−18.3721	−2.70881
$47$	8.79369	1.28269	0.641346	−	0.767252i	$-0.278376\pi$
$47$	8.79369	1.28269	0.641346	+	0.767252i	$0.278376\pi$
$48$	13.9780	2.01755
$49$	9.09977	1.29997
$50$	13.6688	1.93306
$51$	−2.93580	−0.411095
$52$	−1.77776	−0.246530
$53$	9.12457	1.25336	0.626678	−	0.779278i	$-0.284414\pi$
$53$	9.12457	1.25336	0.626678	+	0.779278i	$0.284414\pi$
$54$	12.6606	1.72289
$55$	0.757219	0.102103
$56$	−39.3837	−5.26287
$57$	2.96428	0.392628
$58$	29.3011	3.84742
$59$	−4.95677	−0.645317	−0.322658	−	0.946516i	$-0.604576\pi$
$59$	−4.95677	−0.645317	−0.322658	+	0.946516i	$0.604576\pi$
$60$	−0.868167	−0.112080
$61$	8.81938	1.12921	0.564603	−	0.825362i	$-0.309029\pi$
$61$	8.81938	1.12921	0.564603	+	0.825362i	$0.309029\pi$
$62$	10.3697	1.31695
$63$	−8.92305	−1.12420
$64$	34.3375	4.29219
$65$	0.0565081	0.00700897
$66$	10.3694	1.27638
$67$	−6.79897	−0.830627	−0.415313	−	0.909678i	$-0.636328\pi$
$67$	−6.79897	−0.830627	−0.415313	+	0.909678i	$0.636328\pi$
$68$	−18.5544	−2.25005
$69$	5.88363	0.708305
$70$	1.95358	0.233498
$71$	12.1395	1.44069	0.720346	−	0.693615i	$-0.243983\pi$
$71$	12.1395	1.44069	0.720346	+	0.693615i	$0.243983\pi$
$72$	21.8278	2.57243
$73$	10.1045	1.18265	0.591324	−	0.806434i	$-0.298606\pi$
$73$	10.1045	1.18265	0.591324	+	0.806434i	$0.298606\pi$
$74$	−8.05101	−0.935911
$75$	−4.37740	−0.505459
$76$	18.7343	2.14897
$77$	−17.1672	−1.95638
$78$	0.773824	0.0876183
$79$	−11.5928	−1.30429	−0.652146	−	0.758094i	$-0.726131\pi$
$79$	−11.5928	−1.30429	−0.652146	+	0.758094i	$0.726131\pi$
$80$	−2.80804	−0.313948
$81$	2.61698	0.290776
$82$	−28.4432	−3.14103
$83$	9.32325	1.02336	0.511680	−	0.859176i	$-0.329023\pi$
$83$	9.32325	1.02336	0.511680	+	0.859176i	$0.329023\pi$
$84$	19.6825	2.14754
$85$	0.589772	0.0639697
$86$	−2.93519	−0.316510
$87$	−9.38362	−1.00603
$88$	41.9947	4.47665
$89$	−15.4099	−1.63345	−0.816723	−	0.577030i	$-0.804212\pi$
$89$	−15.4099	−1.63345	−0.816723	+	0.577030i	$0.804212\pi$
$90$	−1.08274	−0.114131
$91$	−1.28111	−0.134297
$92$	37.1847	3.87677
$93$	−3.32088	−0.344359
$94$	−24.1913	−2.49515
$95$	−0.595493	−0.0610963
$96$	−21.1587	−2.15950
$97$	−7.54046	−0.765617	−0.382809	−	0.923828i	$-0.625043\pi$
$97$	−7.54046	−0.765617	−0.382809	+	0.923828i	$0.625043\pi$
$98$	−25.0334	−2.52875
$99$	9.51463	0.956256
$100$	−27.6653	−2.76653
$101$	−14.3820	−1.43106	−0.715531	−	0.698581i	$-0.753815\pi$
$101$	−14.3820	−1.43106	−0.715531	+	0.698581i	$0.753815\pi$
$102$	8.07636	0.799679
$103$	−4.98104	−0.490796	−0.245398	−	0.969422i	$-0.578919\pi$
$103$	−4.98104	−0.490796	−0.245398	+	0.969422i	$0.578919\pi$
$104$	3.13389	0.307304
$105$	−0.625631	−0.0610554
$106$	−25.1016	−2.43808
$107$	−10.6511	−1.02968	−0.514839	−	0.857287i	$-0.672148\pi$
$107$	−10.6511	−1.02968	−0.514839	+	0.857287i	$0.672148\pi$
$108$	−25.6248	−2.46575
$109$	−10.7012	−1.02499	−0.512493	−	0.858691i	$-0.671278\pi$
$109$	−10.7012	−1.02499	−0.512493	+	0.858691i	$0.671278\pi$
$110$	−2.08310	−0.198616
$111$	2.57832	0.244723
$112$	63.6619	6.01548
$113$	−17.9929	−1.69263	−0.846315	−	0.532682i	$-0.821184\pi$
$113$	−17.9929	−1.69263	−0.846315	+	0.532682i	$0.821184\pi$
$114$	−8.15470	−0.763758
$115$	−1.18196	−0.110218
$116$	−59.3047	−5.50630
$117$	0.710037	0.0656430
$118$	13.6360	1.25530
$119$	−13.3709	−1.22571
$120$	1.53044	0.139709
$121$	7.30530	0.664118
$122$	−24.2620	−2.19658
$123$	9.10890	0.821322
$124$	−20.9880	−1.88478
$125$	1.76429	0.157803
$126$	24.5472	2.18684
$127$	3.57741	0.317444	0.158722	−	0.987323i	$-0.449263\pi$
$127$	3.57741	0.317444	0.158722	+	0.987323i	$0.449263\pi$
$128$	−46.4287	−4.10375
$129$	0.939990	0.0827615
$130$	−0.155453	−0.0136341
$131$	−4.98573	−0.435605	−0.217802	−	0.975993i	$-0.569889\pi$
$131$	−4.98573	−0.435605	−0.217802	+	0.975993i	$0.569889\pi$
$132$	−20.9874	−1.82672
$133$	13.5006	1.17065
$134$	18.7039	1.61577
$135$	0.814514	0.0701022
$136$	32.7083	2.80471
$137$	−20.1017	−1.71740	−0.858702	−	0.512476i	$-0.828728\pi$
$137$	−20.1017	−1.71740	−0.858702	+	0.512476i	$0.828728\pi$
$138$	−16.1858	−1.37783
$139$	14.6658	1.24394	0.621970	−	0.783041i	$-0.286332\pi$
$139$	14.6658	1.24394	0.621970	+	0.783041i	$0.286332\pi$
$140$	−3.95401	−0.334174
$141$	7.74724	0.652435
$142$	−33.3956	−2.80250
$143$	1.36605	0.114235
$144$	−35.2836	−2.94030
$145$	1.88507	0.156546
$146$	−27.7975	−2.30054
$147$	8.01689	0.661222
$148$	16.2951	1.33945
$149$	−15.8680	−1.29996	−0.649978	−	0.759953i	$-0.725222\pi$
$149$	−15.8680	−1.29996	−0.649978	+	0.759953i	$0.725222\pi$
$150$	12.0422	0.983240
$151$	−5.55695	−0.452218	−0.226109	−	0.974102i	$-0.572601\pi$
$151$	−5.55695	−0.452218	−0.226109	+	0.974102i	$0.572601\pi$
$152$	−33.0255	−2.67873
$153$	7.41062	0.599113
$154$	47.2266	3.80563
$155$	0.667129	0.0535851
$156$	−1.56620	−0.125397
$157$	−14.3102	−1.14208	−0.571039	−	0.820923i	$-0.693460\pi$
$157$	−14.3102	−1.14208	−0.571039	+	0.820923i	$0.693460\pi$
$158$	31.8917	2.53716
$159$	8.03875	0.637514
$160$	4.25056	0.336036
$161$	26.7966	2.11187
$162$	−7.19929	−0.565629
$163$	10.2610	0.803701	0.401850	−	0.915705i	$-0.368367\pi$
$163$	10.2610	0.803701	0.401850	+	0.915705i	$0.368367\pi$
$164$	57.5685	4.49534
$165$	0.667109	0.0519344
$166$	−25.6482	−1.99068
$167$	−14.3295	−1.10885	−0.554426	−	0.832233i	$-0.687062\pi$
$167$	−14.3295	−1.10885	−0.554426	+	0.832233i	$0.687062\pi$
$168$	−34.6970	−2.67693
$169$	−12.8981	−0.992158
$170$	−1.62246	−0.124437
$171$	−7.48250	−0.572201
$172$	5.94076	0.452979
$173$	16.2427	1.23491	0.617457	−	0.786605i	$-0.288163\pi$
$173$	16.2427	1.23491	0.617457	+	0.786605i	$0.288163\pi$
$174$	25.8142	1.95697
$175$	−19.9366	−1.50706
$176$	−67.8826	−5.11684
$177$	−4.36691	−0.328237
$178$	42.3925	3.17745
$179$	−10.1928	−0.761845	−0.380923	−	0.924607i	$-0.624394\pi$
$179$	−10.1928	−0.761845	−0.380923	+	0.924607i	$0.624394\pi$
$180$	2.19145	0.163341
$181$	−9.24792	−0.687392	−0.343696	−	0.939081i	$-0.611679\pi$
$181$	−9.24792	−0.687392	−0.343696	+	0.939081i	$0.611679\pi$
$182$	3.52433	0.261241
$183$	7.76987	0.574366
$184$	−65.5505	−4.83245
$185$	−0.517958	−0.0380810
$186$	9.13569	0.669862
$187$	14.2574	1.04260
$188$	48.9627	3.57097
$189$	−18.4661	−1.34321
$190$	1.63819	0.118847
$191$	6.86554	0.496773	0.248386	−	0.968661i	$-0.420100\pi$
$191$	6.86554	0.496773	0.248386	+	0.968661i	$0.420100\pi$
$192$	30.2513	2.18320
$193$	−17.7852	−1.28021	−0.640104	−	0.768289i	$-0.721109\pi$
$193$	−17.7852	−1.28021	−0.640104	+	0.768289i	$0.721109\pi$
$194$	20.7437	1.48931
$195$	0.0497836	0.00356508
$196$	50.6670	3.61907
$197$	−0.779055	−0.0555053	−0.0277527	−	0.999615i	$-0.508835\pi$
$197$	−0.779055	−0.0555053	−0.0277527	+	0.999615i	$0.508835\pi$
$198$	−26.1746	−1.86015
$199$	13.7427	0.974194	0.487097	−	0.873348i	$-0.338056\pi$
$199$	13.7427	0.974194	0.487097	+	0.873348i	$0.338056\pi$
$200$	48.7694	3.44852
$201$	−5.98989	−0.422494
$202$	39.5647	2.78376
$203$	−42.7370	−2.99955
$204$	−16.3464	−1.14448
$205$	−1.82988	−0.127805
$206$	13.7028	0.954717
$207$	−14.8516	−1.03226
$208$	−5.06579	−0.351250
$209$	−14.3957	−0.995769
$210$	1.72110	0.118768
$211$	−5.07491	−0.349371	−0.174686	−	0.984624i	$-0.555891\pi$
$211$	−5.07491	−0.349371	−0.174686	+	0.984624i	$0.555891\pi$
$212$	50.8051	3.48931
$213$	10.6949	0.732801
$214$	29.3010	2.00297
$215$	−0.188834	−0.0128784
$216$	45.1723	3.07358
$217$	−15.1247	−1.02673
$218$	29.4388	1.99385
$219$	8.90210	0.601548
$220$	4.21615	0.284253
$221$	1.06397	0.0715703
$222$	−7.09293	−0.476047
$223$	−11.7894	−0.789479	−0.394739	−	0.918793i	$-0.629165\pi$
$223$	−11.7894	−0.789479	−0.394739	+	0.918793i	$0.629165\pi$
$224$	−96.3658	−6.43871
$225$	11.0495	0.736636
$226$	49.4983	3.29258
$227$	14.6355	0.971395	0.485697	−	0.874127i	$-0.338566\pi$
$227$	14.6355	0.971395	0.485697	+	0.874127i	$0.338566\pi$
$228$	16.5049	1.09307
$229$	−26.0435	−1.72100	−0.860501	−	0.509449i	$-0.829849\pi$
$229$	−26.0435	−1.72100	−0.860501	+	0.509449i	$0.829849\pi$
$230$	3.25155	0.214401
$231$	−15.1243	−0.995103
$232$	104.544	6.86368
$233$	2.29354	0.150255	0.0751275	−	0.997174i	$-0.476064\pi$
$233$	2.29354	0.150255	0.0751275	+	0.997174i	$0.476064\pi$
$234$	−1.95330	−0.127692
$235$	−1.55634	−0.101524
$236$	−27.5990	−1.79654
$237$	−10.2133	−0.663422
$238$	36.7832	2.38430
$239$	3.03492	0.196313	0.0981563	−	0.995171i	$-0.468705\pi$
$239$	3.03492	0.196313	0.0981563	+	0.995171i	$0.468705\pi$
$240$	−2.47388	−0.159688
$241$	−12.0105	−0.773662	−0.386831	−	0.922151i	$-0.626430\pi$
$241$	−12.0105	−0.773662	−0.386831	+	0.922151i	$0.626430\pi$
$242$	−20.0968	−1.29187
$243$	16.1122	1.03360
$244$	49.1058	3.14368
$245$	−1.61051	−0.102892
$246$	−25.0585	−1.59767
$247$	−1.07429	−0.0683554
$248$	36.9984	2.34940
$249$	8.21378	0.520527
$250$	−4.85355	−0.306965
$251$	−8.79536	−0.555158	−0.277579	−	0.960703i	$-0.589532\pi$
$251$	−8.79536	−0.555158	−0.277579	+	0.960703i	$0.589532\pi$
$252$	−49.6830	−3.12974
$253$	−28.5731	−1.79638
$254$	−9.84142	−0.617505
$255$	0.519589	0.0325379
$256$	59.0498	3.69061
$257$	−11.6318	−0.725570	−0.362785	−	0.931873i	$-0.618174\pi$
$257$	−11.6318	−0.725570	−0.362785	+	0.931873i	$0.618174\pi$
$258$	−2.58590	−0.160991
$259$	11.7428	0.729661
$260$	0.314634	0.0195128
$261$	23.6863	1.46615
$262$	13.7157	0.847358
$263$	−2.40798	−0.148482	−0.0742412	−	0.997240i	$-0.523653\pi$
$263$	−2.40798	−0.148482	−0.0742412	+	0.997240i	$0.523653\pi$
$264$	36.9974	2.27703
$265$	−1.61490	−0.0992025
$266$	−37.1400	−2.27720
$267$	−13.5761	−0.830845
$268$	−37.8563	−2.31244
$269$	−18.5792	−1.13279	−0.566397	−	0.824133i	$-0.691663\pi$
$269$	−18.5792	−1.13279	−0.566397	+	0.824133i	$0.691663\pi$
$270$	−2.24072	−0.136366
$271$	14.1537	0.859776	0.429888	−	0.902882i	$-0.358553\pi$
$271$	14.1537	0.859776	0.429888	+	0.902882i	$0.358553\pi$
$272$	−52.8714	−3.20580
$273$	−1.12866	−0.0683096
$274$	55.2995	3.34077
$275$	21.2583	1.28193
$276$	32.7597	1.97190
$277$	−16.3643	−0.983237	−0.491618	−	0.870811i	$-0.663595\pi$
$277$	−16.3643	−0.983237	−0.491618	+	0.870811i	$0.663595\pi$
$278$	−40.3456	−2.41977
$279$	8.38263	0.501855
$280$	6.97026	0.416553
$281$	16.9499	1.01115	0.505573	−	0.862784i	$-0.331281\pi$
$281$	16.9499	1.01115	0.505573	+	0.862784i	$0.331281\pi$
$282$	−21.3126	−1.26914
$283$	−12.0441	−0.715946	−0.357973	−	0.933732i	$-0.616532\pi$
$283$	−12.0441	−0.715946	−0.357973	+	0.933732i	$0.616532\pi$
$284$	67.5919	4.01084
$285$	−0.524629	−0.0310763
$286$	−3.75798	−0.222214
$287$	41.4859	2.44883
$288$	53.4093	3.14717
$289$	−5.89541	−0.346789
$290$	−5.18581	−0.304521
$291$	−6.64314	−0.389428
$292$	56.2615	3.29246
$293$	−2.04509	−0.119475	−0.0597377	−	0.998214i	$-0.519026\pi$
$293$	−2.04509	−0.119475	−0.0597377	+	0.998214i	$0.519026\pi$
$294$	−22.0544	−1.28624
$295$	0.877267	0.0510764
$296$	−28.7255	−1.66964
$297$	19.6904	1.14255
$298$	43.6526	2.52873
$299$	−2.13229	−0.123314
$300$	−24.3731	−1.40718
$301$	4.28112	0.246760
$302$	15.2871	0.879674
$303$	−12.6705	−0.727903
$304$	53.3843	3.06180
$305$	−1.56089	−0.0893761
$306$	−20.3865	−1.16542
$307$	−5.66892	−0.323543	−0.161771	−	0.986828i	$-0.551721\pi$
$307$	−5.66892	−0.323543	−0.161771	+	0.986828i	$0.551721\pi$
$308$	−95.5857	−5.44650
$309$	−4.38829	−0.249641
$310$	−1.83526	−0.104236
$311$	8.72043	0.494490	0.247245	−	0.968953i	$-0.420475\pi$
$311$	8.72043	0.494490	0.247245	+	0.968953i	$0.420475\pi$
$312$	2.76096	0.156309
$313$	−33.1929	−1.87617	−0.938087	−	0.346401i	$-0.887404\pi$
$313$	−33.1929	−1.87617	−0.938087	+	0.346401i	$0.887404\pi$
$314$	39.3672	2.22162
$315$	1.57923	0.0889797
$316$	−64.5480	−3.63111
$317$	12.6008	0.707730	0.353865	−	0.935296i	$-0.384867\pi$
$317$	12.6008	0.707730	0.353865	+	0.935296i	$0.384867\pi$
$318$	−22.1145	−1.24012
$319$	45.5704	2.55145
$320$	−6.07717	−0.339724
$321$	−9.38359	−0.523741
$322$	−73.7171	−4.10809
$323$	−11.2123	−0.623869
$324$	14.5712	0.809511
$325$	1.58642	0.0879988
$326$	−28.2278	−1.56339
$327$	−9.42773	−0.521354
$328$	−101.484	−5.60351
$329$	35.2843	1.94528
$330$	−1.83521	−0.101025
$331$	−8.01597	−0.440598	−0.220299	−	0.975432i	$-0.570703\pi$
$331$	−8.01597	−0.440598	−0.220299	+	0.975432i	$0.570703\pi$
$332$	51.9113	2.84900
$333$	−6.50826	−0.356650
$334$	39.4204	2.15699
$335$	1.20331	0.0657436
$336$	56.0861	3.05975
$337$	−19.8211	−1.07972	−0.539861	−	0.841754i	$-0.681523\pi$
$337$	−19.8211	−1.07972	−0.539861	+	0.841754i	$0.681523\pi$
$338$	35.4824	1.92999
$339$	−15.8517	−0.860949
$340$	3.28382	0.178090
$341$	16.1274	0.873350
$342$	20.5843	1.11307
$343$	8.42522	0.454919
$344$	−10.4726	−0.564644
$345$	−1.04130	−0.0560620
$346$	−44.6836	−2.40221
$347$	−5.43580	−0.291809	−0.145904	−	0.989299i	$-0.546609\pi$
$347$	−5.43580	−0.291809	−0.145904	+	0.989299i	$0.546609\pi$
$348$	−52.2474	−2.80076
$349$	−6.20930	−0.332376	−0.166188	−	0.986094i	$-0.553146\pi$
$349$	−6.20930	−0.332376	−0.166188	+	0.986094i	$0.553146\pi$
$350$	54.8453	2.93160
$351$	1.46941	0.0784314
$352$	102.755	5.47684
$353$	−6.77591	−0.360645	−0.180323	−	0.983608i	$-0.557714\pi$
$353$	−6.77591	−0.360645	−0.180323	+	0.983608i	$0.557714\pi$
$354$	12.0133	0.638501
$355$	−2.14849	−0.114030
$356$	−85.8014	−4.54747
$357$	−11.7798	−0.623451
$358$	28.0403	1.48197
$359$	−4.03779	−0.213107	−0.106553	−	0.994307i	$-0.533981\pi$
$359$	−4.03779	−0.213107	−0.106553	+	0.994307i	$0.533981\pi$
$360$	−3.86316	−0.203606
$361$	−7.67894	−0.404155
$362$	25.4409	1.33714
$363$	6.43596	0.337801
$364$	−7.13316	−0.373879
$365$	−1.78834	−0.0936059
$366$	−21.3748	−1.11728
$367$	26.4817	1.38233	0.691166	−	0.722696i	$-0.257097\pi$
$367$	26.4817	1.38233	0.691166	+	0.722696i	$0.257097\pi$
$368$	105.959	5.52351
$369$	−22.9929	−1.19696
$370$	1.42490	0.0740768
$371$	36.6119	1.90080
$372$	−18.4904	−0.958685
$373$	−30.9065	−1.60028	−0.800140	−	0.599814i	$-0.795241\pi$
$373$	−30.9065	−1.60028	−0.800140	+	0.599814i	$0.795241\pi$
$374$	−39.2219	−2.02812
$375$	1.55434	0.0802658
$376$	−86.3133	−4.45127
$377$	3.40073	0.175147
$378$	50.8001	2.61287
$379$	17.5962	0.903855	0.451927	−	0.892055i	$-0.350737\pi$
$379$	17.5962	0.903855	0.451927	+	0.892055i	$0.350737\pi$
$380$	−3.31567	−0.170090
$381$	3.15170	0.161466
$382$	−18.8870	−0.966344
$383$	15.9815	0.816615	0.408308	−	0.912844i	$-0.366119\pi$
$383$	15.9815	0.816615	0.408308	+	0.912844i	$0.366119\pi$
$384$	−40.9036	−2.08736
$385$	3.03830	0.154846
$386$	48.9269	2.49031
$387$	−2.37275	−0.120613
$388$	−41.9848	−2.13146
$389$	8.36687	0.424217	0.212109	−	0.977246i	$-0.431967\pi$
$389$	8.36687	0.424217	0.212109	+	0.977246i	$0.431967\pi$
$390$	−0.136954	−0.00693494
$391$	−22.2546	−1.12547
$392$	−89.3176	−4.51122
$393$	−4.39242	−0.221568
$394$	2.14317	0.107971
$395$	2.05173	0.103234
$396$	52.9769	2.66219
$397$	2.31138	0.116005	0.0580024	−	0.998316i	$-0.481527\pi$
$397$	2.31138	0.116005	0.0580024	+	0.998316i	$0.481527\pi$
$398$	−37.8060	−1.89504
$399$	11.8940	0.595446
$400$	−78.8334	−3.94167
$401$	14.2846	0.713337	0.356668	−	0.934231i	$-0.383913\pi$
$401$	14.2846	0.713337	0.356668	+	0.934231i	$0.383913\pi$
$402$	16.4781	0.821854
$403$	1.20352	0.0599518
$404$	−80.0781	−3.98403
$405$	−0.463163	−0.0230147
$406$	117.569	5.83486
$407$	−12.5213	−0.620658
$408$	28.8160	1.42660
$409$	−2.52330	−0.124769	−0.0623845	−	0.998052i	$-0.519871\pi$
$409$	−2.52330	−0.124769	−0.0623845	+	0.998052i	$0.519871\pi$
$410$	5.03399	0.248611
$411$	−17.7096	−0.873549
$412$	−27.7341	−1.36636
$413$	−19.8888	−0.978664
$414$	40.8565	2.00799
$415$	−1.65006	−0.0809984
$416$	7.66815	0.375962
$417$	12.9206	0.632725
$418$	39.6023	1.93701
$419$	33.6137	1.64214	0.821068	−	0.570830i	$-0.193379\pi$
$419$	33.6137	1.64214	0.821068	+	0.570830i	$0.193379\pi$
$420$	−3.48348	−0.169976
$421$	−35.7564	−1.74266	−0.871330	−	0.490697i	$-0.836742\pi$
$421$	−35.7564	−1.74266	−0.871330	+	0.490697i	$0.836742\pi$
$422$	13.9610	0.679612
$423$	−19.5558	−0.950833
$424$	−89.5610	−4.34947
$425$	16.5574	0.803152
$426$	−29.4215	−1.42548
$427$	35.3874	1.71251
$428$	−59.3045	−2.86659
$429$	1.20349	0.0581050
$430$	0.519481	0.0250516
$431$	19.8510	0.956188	0.478094	−	0.878309i	$-0.341328\pi$
$431$	19.8510	0.956188	0.478094	+	0.878309i	$0.341328\pi$
$432$	−73.0189	−3.51312
$433$	41.5086	1.99478	0.997389	−	0.0722157i	$-0.0230070\pi$
$433$	41.5086	1.99478	0.997389	+	0.0722157i	$0.0230070\pi$
$434$	41.6079	1.99724
$435$	1.66075	0.0796266
$436$	−59.5835	−2.85353
$437$	22.4705	1.07491
$438$	−24.4896	−1.17016
$439$	20.7305	0.989413	0.494706	−	0.869060i	$-0.335276\pi$
$439$	20.7305	0.989413	0.494706	+	0.869060i	$0.335276\pi$
$440$	−7.43238	−0.354325
$441$	−20.2364	−0.963639
$442$	−2.92697	−0.139222
$443$	13.9684	0.663659	0.331830	−	0.943339i	$-0.392334\pi$
$443$	13.9684	0.663659	0.331830	+	0.943339i	$0.392334\pi$
$444$	14.3559	0.681303
$445$	2.72730	0.129286
$446$	32.4326	1.53573
$447$	−13.9797	−0.661216
$448$	137.778	6.50938
$449$	−25.8024	−1.21769	−0.608845	−	0.793289i	$-0.708367\pi$
$449$	−25.8024	−1.21769	−0.608845	+	0.793289i	$0.708367\pi$
$450$	−30.3972	−1.43294
$451$	−44.2363	−2.08301
$452$	−100.183	−4.71223
$453$	−4.89567	−0.230019
$454$	−40.2622	−1.88960
$455$	0.226736	0.0106295
$456$	−29.0955	−1.36252
$457$	40.7349	1.90550	0.952749	−	0.303758i	$-0.0982415\pi$
$457$	40.7349	1.90550	0.952749	+	0.303758i	$0.0982415\pi$
$458$	71.6453	3.34777
$459$	15.3362	0.715831
$460$	−6.58107	−0.306844
$461$	−4.86105	−0.226402	−0.113201	−	0.993572i	$-0.536110\pi$
$461$	−4.86105	−0.226402	−0.113201	+	0.993572i	$0.536110\pi$
$462$	41.6067	1.93572
$463$	−26.7055	−1.24111	−0.620554	−	0.784164i	$-0.713092\pi$
$463$	−26.7055	−1.24111	−0.620554	+	0.784164i	$0.713092\pi$
$464$	−168.991	−7.84522
$465$	0.587740	0.0272558
$466$	−6.30951	−0.292282
$467$	−7.60881	−0.352094	−0.176047	−	0.984382i	$-0.556331\pi$
$467$	−7.60881	−0.352094	−0.176047	+	0.984382i	$0.556331\pi$
$468$	3.95345	0.182748
$469$	−27.2805	−1.25970
$470$	4.28147	0.197489
$471$	−12.6073	−0.580913
$472$	48.6525	2.23941
$473$	−4.56495	−0.209897
$474$	28.0965	1.29052
$475$	−16.7180	−0.767074
$476$	−74.4484	−3.41234
$477$	−20.2916	−0.929088
$478$	−8.34903	−0.381876
$479$	1.20573	0.0550914	0.0275457	−	0.999621i	$-0.491231\pi$
$479$	1.20573	0.0550914	0.0275457	+	0.999621i	$0.491231\pi$
$480$	3.74474	0.170923
$481$	−0.934413	−0.0426056
$482$	33.0407	1.50496
$483$	23.6078	1.07419
$484$	40.6755	1.84888
$485$	1.33454	0.0605982
$486$	−44.3244	−2.01059
$487$	9.61278	0.435597	0.217798	−	0.975994i	$-0.430113\pi$
$487$	9.61278	0.435597	0.217798	+	0.975994i	$0.430113\pi$
$488$	−86.5655	−3.91864
$489$	9.03991	0.408799
$490$	4.43049	0.200149
$491$	−6.66728	−0.300890	−0.150445	−	0.988618i	$-0.548071\pi$
$491$	−6.66728	−0.300890	−0.150445	+	0.988618i	$0.548071\pi$
$492$	50.7178	2.28654
$493$	35.4932	1.59854
$494$	2.95536	0.132968
$495$	−1.68393	−0.0756871
$496$	−59.8063	−2.68538
$497$	48.7091	2.18490
$498$	−22.5960	−1.01255
$499$	13.6288	0.610111	0.305055	−	0.952335i	$-0.401325\pi$
$499$	13.6288	0.610111	0.305055	+	0.952335i	$0.401325\pi$
$500$	9.82347	0.439319
$501$	−12.6243	−0.564012
$502$	24.1959	1.07992
$503$	−23.4564	−1.04587	−0.522934	−	0.852373i	$-0.675163\pi$
$503$	−23.4564	−1.04587	−0.522934	+	0.852373i	$0.675163\pi$
$504$	87.5830	3.90126
$505$	2.54538	0.113268
$506$	78.6044	3.49439
$507$	−11.3632	−0.504657
$508$	19.9188	0.883754
$509$	−10.2954	−0.456334	−0.228167	−	0.973622i	$-0.573273\pi$
$509$	−10.2954	−0.456334	−0.228167	+	0.973622i	$0.573273\pi$
$510$	−1.42938	−0.0632942
$511$	40.5440	1.79356
$512$	−69.5880	−3.07538
$513$	−15.4849	−0.683676
$514$	31.9989	1.41141
$515$	0.881561	0.0388462
$516$	5.23381	0.230406
$517$	−37.6235	−1.65468
$518$	−32.3043	−1.41937
$519$	14.3099	0.628133
$520$	−0.554648	−0.0243229
$521$	32.8033	1.43714	0.718569	−	0.695456i	$-0.244797\pi$
$521$	32.8033	1.43714	0.718569	+	0.695456i	$0.244797\pi$
$522$	−65.1609	−2.85201
$523$	41.2189	1.80238	0.901188	−	0.433429i	$-0.142696\pi$
$523$	41.2189	1.80238	0.901188	+	0.433429i	$0.142696\pi$
$524$	−27.7602	−1.21271
$525$	−17.5641	−0.766561
$526$	6.62433	0.288835
$527$	12.5611	0.547171
$528$	−59.8045	−2.60266
$529$	21.6004	0.939147
$530$	4.44257	0.192973
$531$	11.0231	0.478360
$532$	75.1706	3.25906
$533$	−3.30117	−0.142990
$534$	37.3478	1.61620
$535$	1.88506	0.0814984
$536$	66.7344	2.88249
$537$	−8.97985	−0.387509
$538$	51.1112	2.20356
$539$	−38.9331	−1.67697
$540$	4.53516	0.195162
$541$	−24.1304	−1.03745	−0.518723	−	0.854942i	$-0.673592\pi$
$541$	−24.1304	−1.03745	−0.518723	+	0.854942i	$0.673592\pi$
$542$	−38.9367	−1.67247
$543$	−8.14741	−0.349639
$544$	80.0321	3.43135
$545$	1.89393	0.0811271
$546$	3.10493	0.132879
$547$	−36.2298	−1.54908	−0.774538	−	0.632527i	$-0.782018\pi$
$547$	−36.2298	−1.54908	−0.774538	+	0.632527i	$0.782018\pi$
$548$	−111.925	−4.78120
$549$	−19.6129	−0.837058
$550$	−58.4814	−2.49366
$551$	−35.8375	−1.52673
$552$	−57.7499	−2.45800
$553$	−46.5155	−1.97804
$554$	45.0181	1.91263
$555$	−0.456320	−0.0193697
$556$	81.6585	3.46309
$557$	−34.5968	−1.46591	−0.732956	−	0.680276i	$-0.761860\pi$
$557$	−34.5968	−1.46591	−0.732956	+	0.680276i	$0.761860\pi$
$558$	−23.0605	−0.976230
$559$	−0.340663	−0.0144085
$560$	−11.2671	−0.476122
$561$	12.5607	0.530315
$562$	−46.6289	−1.96692
$563$	−36.0513	−1.51938	−0.759690	−	0.650285i	$-0.774649\pi$
$563$	−36.0513	−1.51938	−0.759690	+	0.650285i	$0.774649\pi$
$564$	43.1362	1.81636
$565$	3.18445	0.133971
$566$	33.1331	1.39269
$567$	10.5005	0.440980
$568$	−119.153	−4.99957
$569$	21.6755	0.908683	0.454342	−	0.890828i	$-0.349875\pi$
$569$	21.6755	0.908683	0.454342	+	0.890828i	$0.349875\pi$
$570$	1.44325	0.0604510
$571$	20.9847	0.878182	0.439091	−	0.898443i	$-0.355301\pi$
$571$	20.9847	0.878182	0.439091	+	0.898443i	$0.355301\pi$
$572$	7.60608	0.318026
$573$	6.04854	0.252681
$574$	−114.127	−4.76357
$575$	−33.1826	−1.38381
$576$	−76.3611	−3.18171
$577$	18.0700	0.752266	0.376133	−	0.926566i	$-0.377254\pi$
$577$	18.0700	0.752266	0.376133	+	0.926566i	$0.377254\pi$
$578$	16.2182	0.674589
$579$	−15.6688	−0.651172
$580$	10.4960	0.435821
$581$	37.4091	1.55199
$582$	18.2752	0.757532
$583$	−39.0392	−1.61684
$584$	−99.1798	−4.10409
$585$	−0.125665	−0.00519560
$586$	5.62602	0.232409
$587$	16.2082	0.668985	0.334493	−	0.942398i	$-0.391435\pi$
$587$	16.2082	0.668985	0.334493	+	0.942398i	$0.391435\pi$
$588$	44.6376	1.84082
$589$	−12.6830	−0.522592
$590$	−2.41335	−0.0993561
$591$	−0.686347	−0.0282325
$592$	46.4335	1.90840
$593$	3.95549	0.162433	0.0812163	−	0.996696i	$-0.474120\pi$
$593$	3.95549	0.162433	0.0812163	+	0.996696i	$0.474120\pi$
$594$	−54.1680	−2.22254
$595$	2.36643	0.0970142
$596$	−88.3519	−3.61904
$597$	12.1073	0.495519
$598$	5.86592	0.239875
$599$	−26.3695	−1.07743	−0.538714	−	0.842489i	$-0.681090\pi$
$599$	−26.3695	−1.07743	−0.538714	+	0.842489i	$0.681090\pi$
$600$	42.9658	1.75407
$601$	37.2229	1.51835	0.759177	−	0.650884i	$-0.225602\pi$
$601$	37.2229	1.51835	0.759177	+	0.650884i	$0.225602\pi$
$602$	−11.7773	−0.480008
$603$	15.1198	0.615727
$604$	−30.9408	−1.25896
$605$	−1.29292	−0.0525646
$606$	34.8565	1.41595
$607$	4.90410	0.199051	0.0995257	−	0.995035i	$-0.468267\pi$
$607$	4.90410	0.199051	0.0995257	+	0.995035i	$0.468267\pi$
$608$	−80.8084	−3.27721
$609$	−37.6513	−1.52571
$610$	4.29398	0.173858
$611$	−2.80769	−0.113587
$612$	41.2619	1.66791
$613$	−40.9942	−1.65574	−0.827871	−	0.560919i	$-0.810448\pi$
$613$	−40.9942	−1.65574	−0.827871	+	0.560919i	$0.810448\pi$
$614$	15.5951	0.629369
$615$	−1.61213	−0.0650072
$616$	168.502	6.78913
$617$	−2.39285	−0.0963326	−0.0481663	−	0.998839i	$-0.515338\pi$
$617$	−2.39285	−0.0963326	−0.0481663	+	0.998839i	$0.515338\pi$
$618$	12.0721	0.485613
$619$	26.4061	1.06135	0.530675	−	0.847575i	$-0.321939\pi$
$619$	26.4061	1.06135	0.530675	+	0.847575i	$0.321939\pi$
$620$	3.71454	0.149179
$621$	−30.7351	−1.23336
$622$	−23.9898	−0.961904
$623$	−61.8315	−2.47723
$624$	−4.46296	−0.178661
$625$	24.5311	0.981245
$626$	91.3133	3.64961
$627$	−12.6826	−0.506493
$628$	−79.6784	−3.17951
$629$	−9.75242	−0.388855
$630$	−4.34445	−0.173087
$631$	−45.8956	−1.82707	−0.913537	−	0.406756i	$-0.866660\pi$
$631$	−45.8956	−1.82707	−0.913537	+	0.406756i	$0.866660\pi$
$632$	113.788	4.52623
$633$	−4.47099	−0.177706
$634$	−34.6646	−1.37671
$635$	−0.633143	−0.0251255
$636$	44.7593	1.77482
$637$	−2.90541	−0.115117
$638$	−125.364	−4.96320
$639$	−26.9963	−1.06796
$640$	8.21711	0.324810
$641$	−25.4099	−1.00363	−0.501816	−	0.864974i	$-0.667335\pi$
$641$	−25.4099	−1.00363	−0.501816	+	0.864974i	$0.667335\pi$
$642$	25.8141	1.01880
$643$	4.59635	0.181262	0.0906311	−	0.995885i	$-0.471112\pi$
$643$	4.59635	0.181262	0.0906311	+	0.995885i	$0.471112\pi$
$644$	149.202	5.87937
$645$	−0.166363	−0.00655053
$646$	30.8449	1.21358
$647$	28.0562	1.10300	0.551501	−	0.834175i	$-0.314055\pi$
$647$	28.0562	1.10300	0.551501	+	0.834175i	$0.314055\pi$
$648$	−25.6866	−1.00907
$649$	21.2074	0.832463
$650$	−4.36423	−0.171179
$651$	−13.3249	−0.522242
$652$	57.1324	2.23748
$653$	−27.6065	−1.08032	−0.540162	−	0.841561i	$-0.681637\pi$
$653$	−27.6065	−1.08032	−0.540162	+	0.841561i	$0.681637\pi$
$654$	25.9356	1.01416
$655$	0.882392	0.0344779
$656$	164.044	6.40484
$657$	−22.4709	−0.876673
$658$	−97.0666	−3.78405
$659$	19.8143	0.771855	0.385928	−	0.922529i	$-0.373881\pi$
$659$	19.8143	0.771855	0.385928	+	0.922529i	$0.373881\pi$
$660$	3.71443	0.144584
$661$	20.5575	0.799596	0.399798	−	0.916603i	$-0.369080\pi$
$661$	20.5575	0.799596	0.399798	+	0.916603i	$0.369080\pi$
$662$	22.0519	0.857070
$663$	0.937356	0.0364039
$664$	−91.5111	−3.55132
$665$	−2.38939	−0.0926564
$666$	17.9041	0.693772
$667$	−71.1318	−2.75423
$668$	−79.7859	−3.08701
$669$	−10.3865	−0.401565
$670$	−3.31028	−0.127887
$671$	−37.7335	−1.45668
$672$	−84.8982	−3.27502
$673$	38.3551	1.47848	0.739241	−	0.673441i	$-0.235185\pi$
$673$	38.3551	1.47848	0.739241	+	0.673441i	$0.235185\pi$
$674$	54.5275	2.10032
$675$	22.8668	0.880145
$676$	−71.8156	−2.76214
$677$	18.0238	0.692711	0.346356	−	0.938103i	$-0.387419\pi$
$677$	18.0238	0.692711	0.346356	+	0.938103i	$0.387419\pi$
$678$	43.6080	1.67475
$679$	−30.2557	−1.16111
$680$	−5.78883	−0.221991
$681$	12.8939	0.494095
$682$	−44.3664	−1.69888
$683$	−36.2964	−1.38884	−0.694421	−	0.719569i	$-0.744340\pi$
$683$	−36.2964	−1.38884	−0.694421	+	0.719569i	$0.744340\pi$
$684$	−41.6621	−1.59299
$685$	3.55767	0.135932
$686$	−23.1777	−0.884928
$687$	−22.9443	−0.875380
$688$	16.9285	0.645391
$689$	−2.91333	−0.110989
$690$	2.86462	0.109054
$691$	−18.8246	−0.716122	−0.358061	−	0.933698i	$-0.616562\pi$
$691$	−18.8246	−0.716122	−0.358061	+	0.933698i	$0.616562\pi$
$692$	90.4387	3.43796
$693$	38.1770	1.45022
$694$	14.9538	0.567639
$695$	−2.59561	−0.0984572
$696$	92.1036	3.49118
$697$	−34.4541	−1.30504
$698$	17.0817	0.646552
$699$	2.02061	0.0764265
$700$	−111.006	−4.19562
$701$	40.1612	1.51687	0.758434	−	0.651750i	$-0.225965\pi$
$701$	40.1612	1.51687	0.758434	+	0.651750i	$0.225965\pi$
$702$	−4.04233	−0.152568
$703$	9.84702	0.371387
$704$	−146.912	−5.53695
$705$	−1.37113	−0.0516399
$706$	18.6404	0.701543
$707$	−57.7071	−2.17030
$708$	−24.3147	−0.913803
$709$	−9.79075	−0.367699	−0.183850	−	0.982954i	$-0.558856\pi$
$709$	−9.79075	−0.367699	−0.183850	+	0.982954i	$0.558856\pi$
$710$	5.91047	0.221816
$711$	25.7805	0.966845
$712$	151.254	5.66848
$713$	−25.1737	−0.942761
$714$	32.4060	1.21276
$715$	−0.241768	−0.00904161
$716$	−56.7529	−2.12095
$717$	2.67376	0.0998535
$718$	11.1079	0.414544
$719$	31.6076	1.17877	0.589383	−	0.807854i	$-0.299371\pi$
$719$	31.6076	1.17877	0.589383	+	0.807854i	$0.299371\pi$
$720$	6.24462	0.232723
$721$	−19.9862	−0.744324
$722$	21.1247	0.786179
$723$	−10.5812	−0.393520
$724$	−51.4919	−1.91368
$725$	52.9219	1.96547
$726$	−17.7053	−0.657104
$727$	16.0122	0.593860	0.296930	−	0.954899i	$-0.404037\pi$
$727$	16.0122	0.593860	0.296930	+	0.954899i	$0.404037\pi$
$728$	12.5746	0.466046
$729$	6.34386	0.234958
$730$	4.91970	0.182086
$731$	−3.55549	−0.131504
$732$	43.2622	1.59902
$733$	−28.1720	−1.04056	−0.520279	−	0.853996i	$-0.674172\pi$
$733$	−28.1720	−1.04056	−0.520279	+	0.853996i	$0.674172\pi$
$734$	−72.8508	−2.68897
$735$	−1.41886	−0.0523354
$736$	−160.392	−5.91212
$737$	29.0892	1.07151
$738$	63.2532	2.32838
$739$	16.0910	0.591919	0.295959	−	0.955201i	$-0.404361\pi$
$739$	16.0910	0.591919	0.295959	+	0.955201i	$0.404361\pi$
$740$	−2.88396	−0.106016
$741$	−0.946448	−0.0347686
$742$	−100.719	−3.69751
$743$	−20.0181	−0.734394	−0.367197	−	0.930143i	$-0.619683\pi$
$743$	−20.0181	−0.734394	−0.367197	+	0.930143i	$0.619683\pi$
$744$	32.5956	1.19501
$745$	2.80837	0.102891
$746$	85.0235	3.11293
$747$	−20.7334	−0.758596
$748$	79.3842	2.90257
$749$	−42.7369	−1.56157
$750$	−4.27597	−0.156136
$751$	24.8348	0.906237	0.453118	−	0.891450i	$-0.350312\pi$
$751$	24.8348	0.906237	0.453118	+	0.891450i	$0.350312\pi$
$752$	139.521	5.08782
$753$	−7.74871	−0.282379
$754$	−9.35537	−0.340703
$755$	0.983488	0.0357928
$756$	−102.818	−3.73946
$757$	−39.2158	−1.42532	−0.712661	−	0.701509i	$-0.752510\pi$
$757$	−39.2158	−1.42532	−0.712661	+	0.701509i	$0.752510\pi$
$758$	−48.4069	−1.75822
$759$	−25.1729	−0.913719
$760$	5.84498	0.212020
$761$	−14.9245	−0.541014	−0.270507	−	0.962718i	$-0.587191\pi$
$761$	−14.9245	−0.541014	−0.270507	+	0.962718i	$0.587191\pi$
$762$	−8.67028	−0.314091
$763$	−42.9379	−1.55446
$764$	38.2269	1.38300
$765$	−1.31156	−0.0474195
$766$	−43.9649	−1.58852
$767$	1.58262	0.0571451
$768$	52.0228	1.87721
$769$	11.3485	0.409238	0.204619	−	0.978842i	$-0.434404\pi$
$769$	11.3485	0.409238	0.204619	+	0.978842i	$0.434404\pi$
$770$	−8.35834	−0.301214
$771$	−10.2476	−0.369058
$772$	−99.0270	−3.56406
$773$	−7.85085	−0.282375	−0.141188	−	0.989983i	$-0.545092\pi$
$773$	−7.85085	−0.282375	−0.141188	+	0.989983i	$0.545092\pi$
$774$	6.52740	0.234622
$775$	18.7291	0.672770
$776$	74.0124	2.65689
$777$	10.3454	0.371139
$778$	−23.0172	−0.825205
$779$	34.7883	1.24642
$780$	0.277192	0.00992507
$781$	−51.9384	−1.85850
$782$	61.2223	2.18930
$783$	49.0185	1.75178
$784$	144.378	5.15635
$785$	2.53267	0.0903949
$786$	12.0835	0.431004
$787$	−47.7825	−1.70326	−0.851630	−	0.524143i	$-0.824386\pi$
$787$	−47.7825	−1.70326	−0.851630	+	0.524143i	$0.824386\pi$
$788$	−4.33773	−0.154525
$789$	−2.12143	−0.0755249
$790$	−5.64430	−0.200815
$791$	−72.1957	−2.56698
$792$	−93.3896	−3.31845
$793$	−2.81589	−0.0999953
$794$	−6.35858	−0.225658
$795$	−1.42273	−0.0504589
$796$	76.5185	2.71213
$797$	−49.1940	−1.74254	−0.871271	−	0.490802i	$-0.836704\pi$
$797$	−49.1940	−1.74254	−0.871271	+	0.490802i	$0.836704\pi$
$798$	−32.7203	−1.15829
$799$	−29.3037	−1.03669
$800$	119.331	4.21899
$801$	34.2692	1.21084
$802$	−39.2966	−1.38761
$803$	−43.2320	−1.52562
$804$	−33.3514	−1.17621
$805$	−4.74255	−0.167153
$806$	−3.31088	−0.116621
$807$	−16.3683	−0.576190
$808$	141.165	4.96615
$809$	11.1563	0.392236	0.196118	−	0.980580i	$-0.437166\pi$
$809$	11.1563	0.392236	0.196118	+	0.980580i	$0.437166\pi$
$810$	1.27416	0.0447693
$811$	11.8262	0.415274	0.207637	−	0.978206i	$-0.433423\pi$
$811$	11.8262	0.415274	0.207637	+	0.978206i	$0.433423\pi$
$812$	−237.957	−8.35066
$813$	12.4694	0.437321
$814$	34.4460	1.20733
$815$	−1.81602	−0.0636125
$816$	−46.5797	−1.63062
$817$	3.58997	0.125597
$818$	6.94156	0.242706
$819$	2.84899	0.0995518
$820$	−10.1887	−0.355804
$821$	38.8210	1.35486	0.677431	−	0.735586i	$-0.263093\pi$
$821$	38.8210	1.35486	0.677431	+	0.735586i	$0.263093\pi$
$822$	48.7189	1.69927
$823$	5.63237	0.196332	0.0981661	−	0.995170i	$-0.468702\pi$
$823$	5.63237	0.196332	0.0981661	+	0.995170i	$0.468702\pi$
$824$	48.8907	1.70319
$825$	18.7286	0.652046
$826$	54.7139	1.90374
$827$	−19.7142	−0.685529	−0.342765	−	0.939421i	$-0.611363\pi$
$827$	−19.7142	−0.685529	−0.342765	+	0.939421i	$0.611363\pi$
$828$	−82.6927	−2.87377
$829$	−33.5848	−1.16645	−0.583223	−	0.812312i	$-0.698209\pi$
$829$	−33.5848	−1.16645	−0.583223	+	0.812312i	$0.698209\pi$
$830$	4.53930	0.157562
$831$	−14.4170	−0.500119
$832$	−10.9634	−0.380088
$833$	−30.3237	−1.05065
$834$	−35.5444	−1.23080
$835$	2.53609	0.0877650
$836$	−80.1542	−2.77219
$837$	17.3477	0.599625
$838$	−92.4709	−3.19435
$839$	−47.9081	−1.65397	−0.826986	−	0.562222i	$-0.809947\pi$
$839$	−47.9081	−1.65397	−0.826986	+	0.562222i	$0.809947\pi$
$840$	6.14080	0.211878
$841$	84.4459	2.91193
$842$	98.3655	3.38990
$843$	14.9328	0.514314
$844$	−28.2568	−0.972639
$845$	2.28274	0.0785288
$846$	53.7977	1.84960
$847$	29.3122	1.00718
$848$	144.771	4.97147
$849$	−10.6108	−0.364163
$850$	−45.5492	−1.56232
$851$	19.5448	0.669986
$852$	59.5485	2.04010
$853$	12.5352	0.429198	0.214599	−	0.976702i	$-0.431155\pi$
$853$	12.5352	0.429198	0.214599	+	0.976702i	$0.431155\pi$
$854$	−97.3502	−3.33126
$855$	1.32428	0.0452894
$856$	104.544	3.57324
$857$	18.4907	0.631630	0.315815	−	0.948821i	$-0.397722\pi$
$857$	18.4907	0.631630	0.315815	+	0.948821i	$0.397722\pi$
$858$	−3.31078	−0.113028
$859$	22.3414	0.762279	0.381140	−	0.924518i	$-0.375532\pi$
$859$	22.3414	0.762279	0.381140	+	0.924518i	$0.375532\pi$
$860$	−1.05142	−0.0358530
$861$	36.5490	1.24559
$862$	−54.6098	−1.86002
$863$	−50.3365	−1.71347	−0.856737	−	0.515754i	$-0.827512\pi$
$863$	−50.3365	−1.71347	−0.856737	+	0.515754i	$0.827512\pi$
$864$	110.530	3.76029
$865$	−2.87470	−0.0977427
$866$	−114.190	−3.88033
$867$	−5.19386	−0.176393
$868$	−84.2134	−2.85839
$869$	49.5994	1.68255
$870$	−4.56869	−0.154893
$871$	2.17081	0.0735549
$872$	105.036	3.55696
$873$	16.7688	0.567537
$874$	−61.8161	−2.09096
$875$	7.07914	0.239318
$876$	49.5664	1.67469
$877$	−19.6316	−0.662913	−0.331457	−	0.943470i	$-0.607540\pi$
$877$	−19.6316	−0.662913	−0.331457	+	0.943470i	$0.607540\pi$
$878$	−57.0294	−1.92465
$879$	−1.80172	−0.0607707
$880$	12.0141	0.404995
$881$	−37.0868	−1.24949	−0.624743	−	0.780831i	$-0.714796\pi$
$881$	−37.0868	−1.24949	−0.624743	+	0.780831i	$0.714796\pi$
$882$	55.6702	1.87451
$883$	−34.9260	−1.17535	−0.587676	−	0.809096i	$-0.699957\pi$
$883$	−34.9260	−1.17535	−0.587676	+	0.809096i	$0.699957\pi$
$884$	5.92412	0.199250
$885$	0.772872	0.0259798
$886$	−38.4269	−1.29098
$887$	−19.2861	−0.647563	−0.323781	−	0.946132i	$-0.604954\pi$
$887$	−19.2861	−0.647563	−0.323781	+	0.946132i	$0.604954\pi$
$888$	−25.3072	−0.849253
$889$	14.3542	0.481424
$890$	−7.50277	−0.251493
$891$	−11.1967	−0.375103
$892$	−65.6428	−2.19788
$893$	29.5879	0.990122
$894$	38.4579	1.28623
$895$	1.80396	0.0602996
$896$	−186.293	−6.22361
$897$	−1.87855	−0.0627230
$898$	70.9821	2.36870
$899$	40.1487	1.33903
$900$	61.5232	2.05077
$901$	−30.4063	−1.01298
$902$	121.694	4.05195
$903$	3.77167	0.125513
$904$	176.607	5.87386
$905$	1.63673	0.0544067
$906$	13.4679	0.447442
$907$	42.1452	1.39941	0.699704	−	0.714433i	$-0.253315\pi$
$907$	42.1452	1.39941	0.699704	+	0.714433i	$0.253315\pi$
$908$	81.4898	2.70433
$909$	31.9832	1.06082
$910$	−0.623748	−0.0206770
$911$	24.9196	0.825624	0.412812	−	0.910816i	$-0.364547\pi$
$911$	24.9196	0.825624	0.412812	+	0.910816i	$0.364547\pi$
$912$	47.0315	1.55737
$913$	−39.8893	−1.32014
$914$	−112.061	−3.70666
$915$	−1.37514	−0.0454607
$916$	−145.009	−4.79122
$917$	−20.0050	−0.660623
$918$	−42.1896	−1.39247
$919$	25.0714	0.827030	0.413515	−	0.910497i	$-0.364301\pi$
$919$	25.0714	0.827030	0.413515	+	0.910497i	$0.364301\pi$
$920$	11.6014	0.382485
$921$	−4.99432	−0.164568
$922$	13.3727	0.440406
$923$	−3.87595	−0.127578
$924$	−84.2109	−2.77034
$925$	−14.5413	−0.478114
$926$	73.4664	2.41426
$927$	11.0770	0.363817
$928$	255.804	8.39718
$929$	8.97454	0.294445	0.147223	−	0.989103i	$-0.452967\pi$
$929$	8.97454	0.294445	0.147223	+	0.989103i	$0.452967\pi$
$930$	−1.61687	−0.0530192
$931$	30.6178	1.00346
$932$	12.7703	0.418305
$933$	7.68270	0.251520
$934$	20.9318	0.684908
$935$	−2.52332	−0.0825214
$936$	−6.96928	−0.227798
$937$	34.1829	1.11671	0.558353	−	0.829603i	$-0.311433\pi$
$937$	34.1829	1.11671	0.558353	+	0.829603i	$0.311433\pi$
$938$	75.0485	2.45042
$939$	−29.2429	−0.954307
$940$	−8.66560	−0.282641
$941$	13.3209	0.434247	0.217124	−	0.976144i	$-0.430333\pi$
$941$	13.3209	0.434247	0.217124	+	0.976144i	$0.430333\pi$
$942$	34.6825	1.13002
$943$	69.0493	2.24856
$944$	−78.6445	−2.55966
$945$	3.26820	0.106314
$946$	12.5581	0.408300
$947$	−7.32312	−0.237970	−0.118985	−	0.992896i	$-0.537964\pi$
$947$	−7.32312	−0.237970	−0.118985	+	0.992896i	$0.537964\pi$
$948$	−56.8668	−1.84695
$949$	−3.22622	−0.104728
$950$	45.9910	1.49215
$951$	11.1013	0.359984
$952$	131.240	4.25353
$953$	−7.52720	−0.243830	−0.121915	−	0.992541i	$-0.538904\pi$
$953$	−7.52720	−0.243830	−0.121915	+	0.992541i	$0.538904\pi$
$954$	55.8219	1.80730
$955$	−1.21509	−0.0393193
$956$	16.8983	0.546529
$957$	40.1475	1.29778
$958$	−3.31696	−0.107166
$959$	−80.6571	−2.60455
$960$	−5.35398	−0.172799
$961$	−16.7913	−0.541655
$962$	2.57056	0.0828782
$963$	23.6863	0.763279
$964$	−66.8736	−2.15385
$965$	3.14769	0.101328
$966$	−64.9447	−2.08956
$967$	−27.8261	−0.894828	−0.447414	−	0.894327i	$-0.647655\pi$
$967$	−27.8261	−0.894828	−0.447414	+	0.894327i	$0.647655\pi$
$968$	−71.7042	−2.30466
$969$	−9.87803	−0.317328
$970$	−3.67130	−0.117878
$971$	30.1111	0.966310	0.483155	−	0.875535i	$-0.339491\pi$
$971$	30.1111	0.966310	0.483155	+	0.875535i	$0.339491\pi$
$972$	89.7116	2.87750
$973$	58.8460	1.88652
$974$	−26.4446	−0.847341
$975$	1.39764	0.0447602
$976$	139.929	4.47902
$977$	9.20483	0.294489	0.147244	−	0.989100i	$-0.452960\pi$
$977$	9.20483	0.294489	0.147244	+	0.989100i	$0.452960\pi$
$978$	−24.8687	−0.795213
$979$	65.9308	2.10716
$980$	−8.96722	−0.286447
$981$	23.7977	0.759802
$982$	18.3416	0.585305
$983$	27.6885	0.883125	0.441562	−	0.897231i	$-0.354424\pi$
$983$	27.6885	0.883125	0.441562	+	0.897231i	$0.354424\pi$
$984$	−89.4072	−2.85020
$985$	0.137880	0.00439322
$986$	−97.6415	−3.10954
$987$	31.0854	0.989460
$988$	−5.98158	−0.190299
$989$	7.12553	0.226579
$990$	4.63248	0.147230
$991$	−8.05795	−0.255969	−0.127985	−	0.991776i	$-0.540851\pi$
$991$	−8.05795	−0.255969	−0.127985	+	0.991776i	$0.540851\pi$
$992$	90.5295	2.87431
$993$	−7.06207	−0.224108
$994$	−133.998	−4.25016
$995$	−2.43223	−0.0771069
$996$	45.7339	1.44913
$997$	8.43907	0.267268	0.133634	−	0.991031i	$-0.457335\pi$
$997$	8.43907	0.267268	0.133634	+	0.991031i	$0.457335\pi$
$998$	−37.4928	−1.18681
$999$	−13.4687	−0.426132

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.6	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.6	✓	205	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)

\(f(q)\)	\(=\)	\(q-2.75099 q^{2} +0.881000 q^{3} +5.56794 q^{4} -0.176984 q^{5} -2.42362 q^{6} +4.01245 q^{7} -9.81537 q^{8} -2.22384 q^{9} +O(q^{10})\)	\(q-2.75099 q^{2} +0.881000 q^{3} +5.56794 q^{4} -0.176984 q^{5} -2.42362 q^{6} +4.01245 q^{7} -9.81537 q^{8} -2.22384 q^{9} +0.486880 q^{10} -4.27847 q^{11} +4.90535 q^{12} -0.319284 q^{13} -11.0382 q^{14} -0.155922 q^{15} +15.8661 q^{16} -3.33235 q^{17} +6.11776 q^{18} +3.36468 q^{19} -0.985434 q^{20} +3.53497 q^{21} +11.7700 q^{22} +6.67835 q^{23} -8.64733 q^{24} -4.96868 q^{25} +0.878348 q^{26} -4.60220 q^{27} +22.3411 q^{28} -10.6511 q^{29} +0.428941 q^{30} -3.76944 q^{31} -24.0167 q^{32} -3.76933 q^{33} +9.16727 q^{34} -0.710138 q^{35} -12.3822 q^{36} +2.92659 q^{37} -9.25619 q^{38} -0.281289 q^{39} +1.73716 q^{40} +10.3393 q^{41} -9.72466 q^{42} +1.06696 q^{43} -23.8223 q^{44} +0.393583 q^{45} -18.3721 q^{46} +8.79369 q^{47} +13.9780 q^{48} +9.09977 q^{49} +13.6688 q^{50} -2.93580 q^{51} -1.77776 q^{52} +9.12457 q^{53} +12.6606 q^{54} +0.757219 q^{55} -39.3837 q^{56} +2.96428 q^{57} +29.3011 q^{58} -4.95677 q^{59} -0.868167 q^{60} +8.81938 q^{61} +10.3697 q^{62} -8.92305 q^{63} +34.3375 q^{64} +0.0565081 q^{65} +10.3694 q^{66} -6.79897 q^{67} -18.5544 q^{68} +5.88363 q^{69} +1.95358 q^{70} +12.1395 q^{71} +21.8278 q^{72} +10.1045 q^{73} -8.05101 q^{74} -4.37740 q^{75} +18.7343 q^{76} -17.1672 q^{77} +0.773824 q^{78} -11.5928 q^{79} -2.80804 q^{80} +2.61698 q^{81} -28.4432 q^{82} +9.32325 q^{83} +19.6825 q^{84} +0.589772 q^{85} -2.93519 q^{86} -9.38362 q^{87} +41.9947 q^{88} -15.4099 q^{89} -1.08274 q^{90} -1.28111 q^{91} +37.1847 q^{92} -3.32088 q^{93} -24.1913 q^{94} -0.595493 q^{95} -21.1587 q^{96} -7.54046 q^{97} -25.0334 q^{98} +9.51463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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