LMFDB - Embedded newform 5077.2.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.66174 q^{2} -1.61696 q^{3} +5.08487 q^{4} +2.63611 q^{5} +4.30394 q^{6} +0.680658 q^{7} -8.21113 q^{8} -0.385425 q^{9} +O(q^{10})$	\(q-2.66174 q^{2} -1.61696 q^{3} +5.08487 q^{4} +2.63611 q^{5} +4.30394 q^{6} +0.680658 q^{7} -8.21113 q^{8} -0.385425 q^{9} -7.01664 q^{10} -2.00479 q^{11} -8.22206 q^{12} +4.17557 q^{13} -1.81174 q^{14} -4.26249 q^{15} +11.6862 q^{16} +0.911396 q^{17} +1.02590 q^{18} +5.60915 q^{19} +13.4043 q^{20} -1.10060 q^{21} +5.33622 q^{22} +4.77034 q^{23} +13.2771 q^{24} +1.94906 q^{25} -11.1143 q^{26} +5.47411 q^{27} +3.46106 q^{28} +9.83723 q^{29} +11.3457 q^{30} -3.67394 q^{31} -14.6833 q^{32} +3.24167 q^{33} -2.42590 q^{34} +1.79429 q^{35} -1.95984 q^{36} -5.92639 q^{37} -14.9301 q^{38} -6.75175 q^{39} -21.6454 q^{40} +2.80330 q^{41} +2.92951 q^{42} +2.17855 q^{43} -10.1941 q^{44} -1.01602 q^{45} -12.6974 q^{46} +9.07110 q^{47} -18.8961 q^{48} -6.53670 q^{49} -5.18790 q^{50} -1.47369 q^{51} +21.2322 q^{52} +3.95561 q^{53} -14.5707 q^{54} -5.28483 q^{55} -5.58897 q^{56} -9.06980 q^{57} -26.1842 q^{58} +9.57314 q^{59} -21.6742 q^{60} -10.3558 q^{61} +9.77907 q^{62} -0.262343 q^{63} +15.7109 q^{64} +11.0072 q^{65} -8.62849 q^{66} -13.7957 q^{67} +4.63433 q^{68} -7.71348 q^{69} -4.77593 q^{70} -0.634066 q^{71} +3.16478 q^{72} +14.2099 q^{73} +15.7745 q^{74} -3.15157 q^{75} +28.5218 q^{76} -1.36457 q^{77} +17.9714 q^{78} +8.42465 q^{79} +30.8060 q^{80} -7.69517 q^{81} -7.46167 q^{82} +3.21676 q^{83} -5.59641 q^{84} +2.40254 q^{85} -5.79873 q^{86} -15.9065 q^{87} +16.4616 q^{88} +3.50180 q^{89} +2.70439 q^{90} +2.84213 q^{91} +24.2566 q^{92} +5.94062 q^{93} -24.1449 q^{94} +14.7863 q^{95} +23.7424 q^{96} -14.4961 q^{97} +17.3990 q^{98} +0.772696 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.66174	−1.88214	−0.941068	−	0.338217i	$-0.890176\pi$
$2$	−2.66174	−1.88214	−0.941068	+	0.338217i	$0.890176\pi$
$3$	−1.61696	−0.933555	−0.466777	−	0.884375i	$-0.654585\pi$
$3$	−1.61696	−0.933555	−0.466777	+	0.884375i	$0.654585\pi$
$4$	5.08487	2.54244
$5$	2.63611	1.17890	0.589452	−	0.807804i	$-0.299344\pi$
$5$	2.63611	1.17890	0.589452	+	0.807804i	$0.299344\pi$
$6$	4.30394	1.75708
$7$	0.680658	0.257265	0.128632	−	0.991692i	$-0.458941\pi$
$7$	0.680658	0.257265	0.128632	+	0.991692i	$0.458941\pi$
$8$	−8.21113	−2.90307
$9$	−0.385425	−0.128475
$10$	−7.01664	−2.21886
$11$	−2.00479	−0.604466	−0.302233	−	0.953234i	$-0.597732\pi$
$11$	−2.00479	−0.604466	−0.302233	+	0.953234i	$0.597732\pi$
$12$	−8.22206	−2.37350
$13$	4.17557	1.15809	0.579047	−	0.815294i	$-0.303425\pi$
$13$	4.17557	1.15809	0.579047	+	0.815294i	$0.303425\pi$
$14$	−1.81174	−0.484207
$15$	−4.26249	−1.10057
$16$	11.6862	2.92154
$17$	0.911396	0.221046	0.110523	−	0.993874i	$-0.464747\pi$
$17$	0.911396	0.221046	0.110523	+	0.993874i	$0.464747\pi$
$18$	1.02590	0.241808
$19$	5.60915	1.28683	0.643414	−	0.765518i	$-0.277517\pi$
$19$	5.60915	1.28683	0.643414	+	0.765518i	$0.277517\pi$
$20$	13.4043	2.99729
$21$	−1.10060	−0.240171
$22$	5.33622	1.13769
$23$	4.77034	0.994685	0.497343	−	0.867554i	$-0.334309\pi$
$23$	4.77034	0.994685	0.497343	+	0.867554i	$0.334309\pi$
$24$	13.2771	2.71018
$25$	1.94906	0.389813
$26$	−11.1143	−2.17969
$27$	5.47411	1.05349
$28$	3.46106	0.654079
$29$	9.83723	1.82673	0.913364	−	0.407144i	$-0.133475\pi$
$29$	9.83723	1.82673	0.913364	+	0.407144i	$0.133475\pi$
$30$	11.3457	2.07142
$31$	−3.67394	−0.659858	−0.329929	−	0.944006i	$-0.607025\pi$
$31$	−3.67394	−0.659858	−0.329929	+	0.944006i	$0.607025\pi$
$32$	−14.6833	−2.59567
$33$	3.24167	0.564302
$34$	−2.42590	−0.416039
$35$	1.79429	0.303290
$36$	−1.95984	−0.326640
$37$	−5.92639	−0.974293	−0.487146	−	0.873320i	$-0.661962\pi$
$37$	−5.92639	−0.974293	−0.487146	+	0.873320i	$0.661962\pi$
$38$	−14.9301	−2.42199
$39$	−6.75175	−1.08114
$40$	−21.6454	−3.42244
$41$	2.80330	0.437802	0.218901	−	0.975747i	$-0.429753\pi$
$41$	2.80330	0.437802	0.218901	+	0.975747i	$0.429753\pi$
$42$	2.92951	0.452034
$43$	2.17855	0.332226	0.166113	−	0.986107i	$-0.446878\pi$
$43$	2.17855	0.332226	0.166113	+	0.986107i	$0.446878\pi$
$44$	−10.1941	−1.53682
$45$	−1.01602	−0.151460
$46$	−12.6974	−1.87213
$47$	9.07110	1.32316	0.661578	−	0.749876i	$-0.269887\pi$
$47$	9.07110	1.32316	0.661578	+	0.749876i	$0.269887\pi$
$48$	−18.8961	−2.72742
$49$	−6.53670	−0.933815
$50$	−5.18790	−0.733680
$51$	−1.47369	−0.206359
$52$	21.2322	2.94438
$53$	3.95561	0.543345	0.271672	−	0.962390i	$-0.412423\pi$
$53$	3.95561	0.543345	0.271672	+	0.962390i	$0.412423\pi$
$54$	−14.5707	−1.98282
$55$	−5.28483	−0.712607
$56$	−5.58897	−0.746858
$57$	−9.06980	−1.20132
$58$	−26.1842	−3.43815
$59$	9.57314	1.24632	0.623158	−	0.782096i	$-0.285849\pi$
$59$	9.57314	1.24632	0.623158	+	0.782096i	$0.285849\pi$
$60$	−21.6742	−2.79813
$61$	−10.3558	−1.32592	−0.662960	−	0.748655i	$-0.730700\pi$
$61$	−10.3558	−1.32592	−0.662960	+	0.748655i	$0.730700\pi$
$62$	9.77907	1.24194
$63$	−0.262343	−0.0330521
$64$	15.7109	1.96386
$65$	11.0072	1.36528
$66$	−8.62849	−1.06209
$67$	−13.7957	−1.68541	−0.842707	−	0.538372i	$-0.819039\pi$
$67$	−13.7957	−1.68541	−0.842707	+	0.538372i	$0.819039\pi$
$68$	4.63433	0.561995
$69$	−7.71348	−0.928593
$70$	−4.77593	−0.570833
$71$	−0.634066	−0.0752497	−0.0376249	−	0.999292i	$-0.511979\pi$
$71$	−0.634066	−0.0752497	−0.0376249	+	0.999292i	$0.511979\pi$
$72$	3.16478	0.372973
$73$	14.2099	1.66314	0.831571	−	0.555418i	$-0.187442\pi$
$73$	14.2099	1.66314	0.831571	+	0.555418i	$0.187442\pi$
$74$	15.7745	1.83375
$75$	−3.15157	−0.363911
$76$	28.5218	3.27168
$77$	−1.36457	−0.155508
$78$	17.9714	2.03486
$79$	8.42465	0.947847	0.473923	−	0.880566i	$-0.342837\pi$
$79$	8.42465	0.947847	0.473923	+	0.880566i	$0.342837\pi$
$80$	30.8060	3.44422
$81$	−7.69517	−0.855019
$82$	−7.46167	−0.824004
$83$	3.21676	0.353086	0.176543	−	0.984293i	$-0.443509\pi$
$83$	3.21676	0.353086	0.176543	+	0.984293i	$0.443509\pi$
$84$	−5.59641	−0.610618
$85$	2.40254	0.260592
$86$	−5.79873	−0.625294
$87$	−15.9065	−1.70535
$88$	16.4616	1.75481
$89$	3.50180	0.371190	0.185595	−	0.982626i	$-0.440579\pi$
$89$	3.50180	0.371190	0.185595	+	0.982626i	$0.440579\pi$
$90$	2.70439	0.285068
$91$	2.84213	0.297937
$92$	24.2566	2.52892
$93$	5.94062	0.616014
$94$	−24.1449	−2.49036
$95$	14.7863	1.51705
$96$	23.7424	2.42320
$97$	−14.4961	−1.47185	−0.735926	−	0.677062i	$-0.763253\pi$
$97$	−14.4961	−1.47185	−0.735926	+	0.677062i	$0.763253\pi$
$98$	17.3990	1.75757
$99$	0.772696	0.0776588
$100$	9.91074	0.991074
$101$	6.38621	0.635452	0.317726	−	0.948183i	$-0.397081\pi$
$101$	6.38621	0.635452	0.317726	+	0.948183i	$0.397081\pi$
$102$	3.92260	0.388395
$103$	9.20612	0.907106	0.453553	−	0.891229i	$-0.350156\pi$
$103$	9.20612	0.907106	0.453553	+	0.891229i	$0.350156\pi$
$104$	−34.2862	−3.36203
$105$	−2.90130	−0.283138
$106$	−10.5288	−1.02265
$107$	7.06637	0.683132	0.341566	−	0.939858i	$-0.389043\pi$
$107$	7.06637	0.683132	0.341566	+	0.939858i	$0.389043\pi$
$108$	27.8352	2.67844
$109$	−1.67781	−0.160705	−0.0803524	−	0.996767i	$-0.525605\pi$
$109$	−1.67781	−0.160705	−0.0803524	+	0.996767i	$0.525605\pi$
$110$	14.0669	1.34122
$111$	9.58276	0.909556
$112$	7.95429	0.751610
$113$	−13.2686	−1.24821	−0.624103	−	0.781342i	$-0.714535\pi$
$113$	−13.2686	−1.24821	−0.624103	+	0.781342i	$0.714535\pi$
$114$	24.1415	2.26106
$115$	12.5751	1.17264
$116$	50.0211	4.64434
$117$	−1.60937	−0.148786
$118$	−25.4812	−2.34574
$119$	0.620349	0.0568673
$120$	34.9999	3.19504
$121$	−6.98083	−0.634621
$122$	27.5644	2.49556
$123$	−4.53284	−0.408713
$124$	−18.6815	−1.67765
$125$	−8.04260	−0.719352
$126$	0.698289	0.0622086
$127$	17.9809	1.59555	0.797775	−	0.602955i	$-0.206010\pi$
$127$	17.9809	1.59555	0.797775	+	0.602955i	$0.206010\pi$
$128$	−12.4517	−1.10058
$129$	−3.52264	−0.310151
$130$	−29.2985	−2.56964
$131$	8.70288	0.760374	0.380187	−	0.924910i	$-0.375860\pi$
$131$	8.70288	0.760374	0.380187	+	0.924910i	$0.375860\pi$
$132$	16.4835	1.43470
$133$	3.81792	0.331055
$134$	36.7206	3.17218
$135$	14.4304	1.24197
$136$	−7.48359	−0.641713
$137$	18.5888	1.58815	0.794074	−	0.607821i	$-0.207956\pi$
$137$	18.5888	1.58815	0.794074	+	0.607821i	$0.207956\pi$
$138$	20.5313	1.74774
$139$	−15.9442	−1.35237	−0.676186	−	0.736731i	$-0.736368\pi$
$139$	−15.9442	−1.35237	−0.676186	+	0.736731i	$0.736368\pi$
$140$	9.12372	0.771095
$141$	−14.6676	−1.23524
$142$	1.68772	0.141630
$143$	−8.37112	−0.700028
$144$	−4.50415	−0.375346
$145$	25.9320	2.15354
$146$	−37.8231	−3.13026
$147$	10.5696	0.871768
$148$	−30.1349	−2.47708
$149$	−2.48712	−0.203753	−0.101876	−	0.994797i	$-0.532485\pi$
$149$	−2.48712	−0.203753	−0.101876	+	0.994797i	$0.532485\pi$
$150$	8.38866	0.684931
$151$	−15.8071	−1.28636	−0.643181	−	0.765714i	$-0.722386\pi$
$151$	−15.8071	−1.28636	−0.643181	+	0.765714i	$0.722386\pi$
$152$	−46.0575	−3.73576
$153$	−0.351275	−0.0283989
$154$	3.63214	0.292686
$155$	−9.68489	−0.777909
$156$	−34.3318	−2.74874
$157$	9.85523	0.786533	0.393267	−	0.919424i	$-0.371345\pi$
$157$	9.85523	0.786533	0.393267	+	0.919424i	$0.371345\pi$
$158$	−22.4242	−1.78398
$159$	−6.39608	−0.507242
$160$	−38.7068	−3.06004
$161$	3.24697	0.255897
$162$	20.4826	1.60926
$163$	−1.02022	−0.0799099	−0.0399550	−	0.999201i	$-0.512721\pi$
$163$	−1.02022	−0.0799099	−0.0399550	+	0.999201i	$0.512721\pi$
$164$	14.2544	1.11308
$165$	8.54539	0.665257
$166$	−8.56219	−0.664555
$167$	−15.7990	−1.22257	−0.611283	−	0.791412i	$-0.709346\pi$
$167$	−15.7990	−1.22257	−0.611283	+	0.791412i	$0.709346\pi$
$168$	9.03717	0.697233
$169$	4.43537	0.341182
$170$	−6.39493	−0.490469
$171$	−2.16191	−0.165325
$172$	11.0776	0.844662
$173$	−4.48033	−0.340633	−0.170317	−	0.985389i	$-0.554479\pi$
$173$	−4.48033	−0.340633	−0.170317	+	0.985389i	$0.554479\pi$
$174$	42.3389	3.20970
$175$	1.32665	0.100285
$176$	−23.4283	−1.76597
$177$	−15.4794	−1.16350
$178$	−9.32089	−0.698630
$179$	18.4353	1.37792	0.688959	−	0.724801i	$-0.258068\pi$
$179$	18.4353	1.37792	0.688959	+	0.724801i	$0.258068\pi$
$180$	−5.16635	−0.385077
$181$	−23.4153	−1.74045	−0.870223	−	0.492657i	$-0.836026\pi$
$181$	−23.4153	−1.74045	−0.870223	+	0.492657i	$0.836026\pi$
$182$	−7.56503	−0.560757
$183$	16.7449	1.23782
$184$	−39.1699	−2.88765
$185$	−15.6226	−1.14860
$186$	−15.8124	−1.15942
$187$	−1.82715	−0.133615
$188$	46.1254	3.36404
$189$	3.72600	0.271027
$190$	−39.3574	−2.85529
$191$	−8.06028	−0.583221	−0.291611	−	0.956537i	$-0.594191\pi$
$191$	−8.06028	−0.583221	−0.291611	+	0.956537i	$0.594191\pi$
$192$	−25.4039	−1.83337
$193$	25.7615	1.85436	0.927178	−	0.374621i	$-0.122227\pi$
$193$	25.7615	1.85436	0.927178	+	0.374621i	$0.122227\pi$
$194$	38.5848	2.77023
$195$	−17.7983	−1.27456
$196$	−33.2383	−2.37416
$197$	−21.0855	−1.50228	−0.751141	−	0.660142i	$-0.770496\pi$
$197$	−21.0855	−1.50228	−0.751141	+	0.660142i	$0.770496\pi$
$198$	−2.05672	−0.146164
$199$	19.1203	1.35540	0.677701	−	0.735337i	$-0.262976\pi$
$199$	19.1203	1.35540	0.677701	+	0.735337i	$0.262976\pi$
$200$	−16.0040	−1.13165
$201$	22.3072	1.57343
$202$	−16.9984	−1.19601
$203$	6.69579	0.469952
$204$	−7.49355	−0.524653
$205$	7.38981	0.516127
$206$	−24.5043	−1.70730
$207$	−1.83861	−0.127792
$208$	48.7964	3.38342
$209$	−11.2452	−0.777844
$210$	7.72251	0.532904
$211$	−16.4658	−1.13355	−0.566775	−	0.823872i	$-0.691809\pi$
$211$	−16.4658	−1.13355	−0.566775	+	0.823872i	$0.691809\pi$
$212$	20.1138	1.38142
$213$	1.02526	0.0702498
$214$	−18.8088	−1.28575
$215$	5.74289	0.391662
$216$	−44.9487	−3.05837
$217$	−2.50069	−0.169758
$218$	4.46589	0.302468
$219$	−22.9769	−1.55264
$220$	−26.8727	−1.81176
$221$	3.80560	0.255992
$222$	−25.5068	−1.71191
$223$	9.76731	0.654068	0.327034	−	0.945013i	$-0.393951\pi$
$223$	9.76731	0.654068	0.327034	+	0.945013i	$0.393951\pi$
$224$	−9.99433	−0.667774
$225$	−0.751218	−0.0500812
$226$	35.3176	2.34929
$227$	22.1171	1.46796	0.733980	−	0.679171i	$-0.237660\pi$
$227$	22.1171	1.46796	0.733980	+	0.679171i	$0.237660\pi$
$228$	−46.1188	−3.05429
$229$	6.38480	0.421919	0.210960	−	0.977495i	$-0.432341\pi$
$229$	6.38480	0.421919	0.210960	+	0.977495i	$0.432341\pi$
$230$	−33.4718	−2.20706
$231$	2.20647	0.145175
$232$	−80.7748	−5.30313
$233$	−23.4136	−1.53388	−0.766940	−	0.641719i	$-0.778221\pi$
$233$	−23.4136	−1.53388	−0.766940	+	0.641719i	$0.778221\pi$
$234$	4.28373	0.280036
$235$	23.9124	1.55987
$236$	48.6782	3.16868
$237$	−13.6224	−0.884867
$238$	−1.65121	−0.107032
$239$	−2.80201	−0.181247	−0.0906235	−	0.995885i	$-0.528886\pi$
$239$	−2.80201	−0.181247	−0.0906235	+	0.995885i	$0.528886\pi$
$240$	−49.8123	−3.21537
$241$	−15.4865	−0.997572	−0.498786	−	0.866725i	$-0.666221\pi$
$241$	−15.4865	−0.997572	−0.498786	+	0.866725i	$0.666221\pi$
$242$	18.5812	1.19444
$243$	−3.97952	−0.255286
$244$	−52.6577	−3.37107
$245$	−17.2315	−1.10088
$246$	12.0653	0.769253
$247$	23.4214	1.49027
$248$	30.1672	1.91562
$249$	−5.20139	−0.329625
$250$	21.4073	1.35392
$251$	−9.68107	−0.611064	−0.305532	−	0.952182i	$-0.598834\pi$
$251$	−9.68107	−0.611064	−0.305532	+	0.952182i	$0.598834\pi$
$252$	−1.33398	−0.0840329
$253$	−9.56352	−0.601253
$254$	−47.8606	−3.00304
$255$	−3.88482	−0.243277
$256$	1.72134	0.107584
$257$	−30.7802	−1.92001	−0.960007	−	0.279975i	$-0.909674\pi$
$257$	−30.7802	−1.92001	−0.960007	+	0.279975i	$0.909674\pi$
$258$	9.37635	0.583746
$259$	−4.03385	−0.250651
$260$	55.9704	3.47114
$261$	−3.79152	−0.234689
$262$	−23.1648	−1.43113
$263$	−0.0904159	−0.00557529	−0.00278764	−	0.999996i	$-0.500887\pi$
$263$	−0.0904159	−0.00557529	−0.00278764	+	0.999996i	$0.500887\pi$
$264$	−26.6178	−1.63821
$265$	10.4274	0.640551
$266$	−10.1623	−0.623091
$267$	−5.66229	−0.346526
$268$	−70.1494	−4.28506
$269$	27.7840	1.69402	0.847010	−	0.531577i	$-0.178400\pi$
$269$	27.7840	1.69402	0.847010	+	0.531577i	$0.178400\pi$
$270$	−38.4099	−2.33755
$271$	2.25199	0.136799	0.0683995	−	0.997658i	$-0.478211\pi$
$271$	2.25199	0.136799	0.0683995	+	0.997658i	$0.478211\pi$
$272$	10.6507	0.645796
$273$	−4.59563	−0.278140
$274$	−49.4786	−2.98911
$275$	−3.90745	−0.235628
$276$	−39.2220	−2.36089
$277$	19.8887	1.19499	0.597497	−	0.801871i	$-0.296162\pi$
$277$	19.8887	1.19499	0.597497	+	0.801871i	$0.296162\pi$
$278$	42.4394	2.54535
$279$	1.41603	0.0847754
$280$	−14.7331	−0.880473
$281$	−17.0303	−1.01594	−0.507972	−	0.861374i	$-0.669605\pi$
$281$	−17.0303	−1.01594	−0.507972	+	0.861374i	$0.669605\pi$
$282$	39.0415	2.32489
$283$	19.0078	1.12990	0.564949	−	0.825126i	$-0.308896\pi$
$283$	19.0078	1.12990	0.564949	+	0.825126i	$0.308896\pi$
$284$	−3.22414	−0.191318
$285$	−23.9090	−1.41625
$286$	22.2818	1.31755
$287$	1.90809	0.112631
$288$	5.65933	0.333479
$289$	−16.1694	−0.951139
$290$	−69.0243	−4.05325
$291$	23.4396	1.37405
$292$	72.2555	4.22843
$293$	13.0262	0.760999	0.380499	−	0.924781i	$-0.375752\pi$
$293$	13.0262	0.760999	0.380499	+	0.924781i	$0.375752\pi$
$294$	−28.1336	−1.64079
$295$	25.2358	1.46929
$296$	48.6624	2.82844
$297$	−10.9744	−0.636801
$298$	6.62007	0.383490
$299$	19.9189	1.15194
$300$	−16.0253	−0.925222
$301$	1.48285	0.0854699
$302$	42.0744	2.42111
$303$	−10.3263	−0.593229
$304$	65.5496	3.75953
$305$	−27.2989	−1.56313
$306$	0.935004	0.0534506
$307$	17.1830	0.980686	0.490343	−	0.871530i	$-0.336872\pi$
$307$	17.1830	0.980686	0.490343	+	0.871530i	$0.336872\pi$
$308$	−6.93868	−0.395368
$309$	−14.8860	−0.846833
$310$	25.7787	1.46413
$311$	−22.9925	−1.30379	−0.651893	−	0.758311i	$-0.726025\pi$
$311$	−22.9925	−1.30379	−0.651893	+	0.758311i	$0.726025\pi$
$312$	55.4395	3.13864
$313$	13.5496	0.765871	0.382936	−	0.923775i	$-0.374913\pi$
$313$	13.5496	0.765871	0.382936	+	0.923775i	$0.374913\pi$
$314$	−26.2321	−1.48036
$315$	−0.691564	−0.0389652
$316$	42.8382	2.40984
$317$	9.09508	0.510831	0.255415	−	0.966831i	$-0.417788\pi$
$317$	9.09508	0.510831	0.255415	+	0.966831i	$0.417788\pi$
$318$	17.0247	0.954699
$319$	−19.7215	−1.10419
$320$	41.4156	2.31520
$321$	−11.4261	−0.637741
$322$	−8.64260	−0.481634
$323$	5.11216	0.284448
$324$	−39.1290	−2.17383
$325$	8.13845	0.451440
$326$	2.71557	0.150401
$327$	2.71295	0.150027
$328$	−23.0183	−1.27097
$329$	6.17432	0.340401
$330$	−22.7456	−1.25210
$331$	4.96006	0.272629	0.136315	−	0.990666i	$-0.456474\pi$
$331$	4.96006	0.272629	0.136315	+	0.990666i	$0.456474\pi$
$332$	16.3568	0.897697
$333$	2.28418	0.125172
$334$	42.0530	2.30104
$335$	−36.3670	−1.98694
$336$	−12.8618	−0.701669
$337$	−8.84982	−0.482080	−0.241040	−	0.970515i	$-0.577489\pi$
$337$	−8.84982	−0.482080	−0.241040	+	0.970515i	$0.577489\pi$
$338$	−11.8058	−0.642152
$339$	21.4549	1.16527
$340$	12.2166	0.662538
$341$	7.36546	0.398862
$342$	5.75445	0.311165
$343$	−9.21387	−0.497502
$344$	−17.8884	−0.964475
$345$	−20.3336	−1.09472
$346$	11.9255	0.641118
$347$	25.7960	1.38480	0.692402	−	0.721512i	$-0.256553\pi$
$347$	25.7960	1.38480	0.692402	+	0.721512i	$0.256553\pi$
$348$	−80.8823	−4.33575
$349$	−27.0834	−1.44974	−0.724872	−	0.688884i	$-0.758101\pi$
$349$	−27.0834	−1.44974	−0.724872	+	0.688884i	$0.758101\pi$
$350$	−3.53119	−0.188750
$351$	22.8575	1.22004
$352$	29.4369	1.56899
$353$	21.9967	1.17077	0.585384	−	0.810756i	$-0.300944\pi$
$353$	21.9967	1.17077	0.585384	+	0.810756i	$0.300944\pi$
$354$	41.2022	2.18987
$355$	−1.67146	−0.0887121
$356$	17.8062	0.943727
$357$	−1.00308	−0.0530887
$358$	−49.0700	−2.59343
$359$	−15.1633	−0.800286	−0.400143	−	0.916453i	$-0.631040\pi$
$359$	−15.1633	−0.800286	−0.400143	+	0.916453i	$0.631040\pi$
$360$	8.34270	0.439699
$361$	12.4626	0.655927
$362$	62.3255	3.27576
$363$	11.2878	0.592454
$364$	14.4519	0.757485
$365$	37.4588	1.96068
$366$	−44.5706	−2.32974
$367$	−35.5893	−1.85775	−0.928874	−	0.370397i	$-0.879222\pi$
$367$	−35.5893	−1.85775	−0.928874	+	0.370397i	$0.879222\pi$
$368$	55.7471	2.90602
$369$	−1.08046	−0.0562467
$370$	41.5833	2.16182
$371$	2.69242	0.139783
$372$	30.2073	1.56618
$373$	−8.18005	−0.423547	−0.211774	−	0.977319i	$-0.567924\pi$
$373$	−8.18005	−0.423547	−0.211774	+	0.977319i	$0.567924\pi$
$374$	4.86341	0.251481
$375$	13.0046	0.671554
$376$	−74.4840	−3.84122
$377$	41.0760	2.11552
$378$	−9.91765	−0.510109
$379$	21.6650	1.11286	0.556428	−	0.830896i	$-0.312172\pi$
$379$	21.6650	1.11286	0.556428	+	0.830896i	$0.312172\pi$
$380$	75.1866	3.85699
$381$	−29.0745	−1.48953
$382$	21.4544	1.09770
$383$	8.48955	0.433796	0.216898	−	0.976194i	$-0.430406\pi$
$383$	8.48955	0.433796	0.216898	+	0.976194i	$0.430406\pi$
$384$	20.1339	1.02745
$385$	−3.59716	−0.183328
$386$	−68.5706	−3.49015
$387$	−0.839668	−0.0426827
$388$	−73.7106	−3.74209
$389$	−22.5242	−1.14202	−0.571010	−	0.820943i	$-0.693448\pi$
$389$	−22.5242	−1.14202	−0.571010	+	0.820943i	$0.693448\pi$
$390$	47.3746	2.39890
$391$	4.34767	0.219871
$392$	53.6738	2.71093
$393$	−14.0722	−0.709851
$394$	56.1242	2.82750
$395$	22.2083	1.11742
$396$	3.92906	0.197443
$397$	−16.5501	−0.830628	−0.415314	−	0.909678i	$-0.636328\pi$
$397$	−16.5501	−0.830628	−0.415314	+	0.909678i	$0.636328\pi$
$398$	−50.8933	−2.55105
$399$	−6.17343	−0.309058
$400$	22.7771	1.13885
$401$	17.8378	0.890779	0.445390	−	0.895337i	$-0.353065\pi$
$401$	17.8378	0.890779	0.445390	+	0.895337i	$0.353065\pi$
$402$	−59.3759	−2.96140
$403$	−15.3408	−0.764178
$404$	32.4731	1.61560
$405$	−20.2853	−1.00798
$406$	−17.8225	−0.884514
$407$	11.8811	0.588927
$408$	12.1007	0.599074
$409$	16.8763	0.834479	0.417240	−	0.908797i	$-0.362998\pi$
$409$	16.8763	0.834479	0.417240	+	0.908797i	$0.362998\pi$
$410$	−19.6698	−0.971421
$411$	−30.0574	−1.48262
$412$	46.8119	2.30626
$413$	6.51603	0.320633
$414$	4.89391	0.240523
$415$	8.47973	0.416254
$416$	−61.3112	−3.00603
$417$	25.7813	1.26251
$418$	29.9317	1.46401
$419$	−31.6886	−1.54809	−0.774044	−	0.633132i	$-0.781769\pi$
$419$	−31.6886	−1.54809	−0.774044	+	0.633132i	$0.781769\pi$
$420$	−14.7527	−0.719860
$421$	−16.0953	−0.784438	−0.392219	−	0.919872i	$-0.628292\pi$
$421$	−16.0953	−0.784438	−0.392219	+	0.919872i	$0.628292\pi$
$422$	43.8277	2.13350
$423$	−3.49623	−0.169993
$424$	−32.4800	−1.57737
$425$	1.77637	0.0861665
$426$	−2.72898	−0.132220
$427$	−7.04873	−0.341112
$428$	35.9316	1.73682
$429$	13.5358	0.653515
$430$	−15.2861	−0.737161
$431$	−7.36666	−0.354839	−0.177420	−	0.984135i	$-0.556775\pi$
$431$	−7.36666	−0.354839	−0.177420	+	0.984135i	$0.556775\pi$
$432$	63.9715	3.07783
$433$	32.9697	1.58442	0.792211	−	0.610247i	$-0.208930\pi$
$433$	32.9697	1.58442	0.792211	+	0.610247i	$0.208930\pi$
$434$	6.65620	0.319508
$435$	−41.9311	−2.01044
$436$	−8.53143	−0.408581
$437$	26.7576	1.27999
$438$	61.1586	2.92227
$439$	11.2381	0.536363	0.268181	−	0.963368i	$-0.413577\pi$
$439$	11.2381	0.536363	0.268181	+	0.963368i	$0.413577\pi$
$440$	43.3945	2.06875
$441$	2.51941	0.119972
$442$	−10.1295	−0.481812
$443$	−10.2615	−0.487539	−0.243769	−	0.969833i	$-0.578384\pi$
$443$	−10.2615	−0.487539	−0.243769	+	0.969833i	$0.578384\pi$
$444$	48.7271	2.31249
$445$	9.23112	0.437597
$446$	−25.9981	−1.23104
$447$	4.02158	0.190214
$448$	10.6937	0.505232
$449$	30.7370	1.45057	0.725285	−	0.688449i	$-0.241708\pi$
$449$	30.7370	1.45057	0.725285	+	0.688449i	$0.241708\pi$
$450$	1.99955	0.0942597
$451$	−5.62002	−0.264637
$452$	−67.4692	−3.17348
$453$	25.5595	1.20089
$454$	−58.8699	−2.76290
$455$	7.49217	0.351238
$456$	74.4734	3.48754
$457$	15.2764	0.714599	0.357300	−	0.933990i	$-0.383697\pi$
$457$	15.2764	0.714599	0.357300	+	0.933990i	$0.383697\pi$
$458$	−16.9947	−0.794109
$459$	4.98908	0.232870
$460$	63.9430	2.98136
$461$	−32.3365	−1.50606	−0.753031	−	0.657985i	$-0.771409\pi$
$461$	−32.3365	−1.50606	−0.753031	+	0.657985i	$0.771409\pi$
$462$	−5.87305	−0.273239
$463$	32.5799	1.51411	0.757057	−	0.653349i	$-0.226636\pi$
$463$	32.5799	1.51411	0.757057	+	0.653349i	$0.226636\pi$
$464$	114.960	5.33687
$465$	15.6601	0.726221
$466$	62.3211	2.88697
$467$	−14.9305	−0.690900	−0.345450	−	0.938437i	$-0.612274\pi$
$467$	−14.9305	−0.690900	−0.345450	+	0.938437i	$0.612274\pi$
$468$	−8.18344	−0.378280
$469$	−9.39016	−0.433597
$470$	−63.6486	−2.93589
$471$	−15.9356	−0.734272
$472$	−78.6063	−3.61815
$473$	−4.36752	−0.200819
$474$	36.2592	1.66544
$475$	10.9326	0.501622
$476$	3.15439	0.144581
$477$	−1.52459	−0.0698063
$478$	7.45823	0.341132
$479$	34.3785	1.57079	0.785396	−	0.618993i	$-0.212459\pi$
$479$	34.3785	1.57079	0.785396	+	0.618993i	$0.212459\pi$
$480$	62.5876	2.85672
$481$	−24.7460	−1.12832
$482$	41.2210	1.87757
$483$	−5.25024	−0.238894
$484$	−35.4966	−1.61348
$485$	−38.2132	−1.73517
$486$	10.5925	0.480484
$487$	12.9336	0.586078	0.293039	−	0.956100i	$-0.405333\pi$
$487$	12.9336	0.586078	0.293039	+	0.956100i	$0.405333\pi$
$488$	85.0326	3.84924
$489$	1.64966	0.0746003
$490$	45.8657	2.07200
$491$	6.86706	0.309906	0.154953	−	0.987922i	$-0.450477\pi$
$491$	6.86706	0.309906	0.154953	+	0.987922i	$0.450477\pi$
$492$	−23.0489	−1.03913
$493$	8.96561	0.403791
$494$	−62.3417	−2.80489
$495$	2.03691	0.0915522
$496$	−42.9343	−1.92781
$497$	−0.431582	−0.0193591
$498$	13.8448	0.620399
$499$	−19.7705	−0.885050	−0.442525	−	0.896756i	$-0.645917\pi$
$499$	−19.7705	−0.885050	−0.442525	+	0.896756i	$0.645917\pi$
$500$	−40.8956	−1.82891
$501$	25.5465	1.14133
$502$	25.7685	1.15010
$503$	29.5126	1.31590	0.657951	−	0.753061i	$-0.271423\pi$
$503$	29.5126	1.31590	0.657951	+	0.753061i	$0.271423\pi$
$504$	2.15413	0.0959527
$505$	16.8347	0.749136
$506$	25.4556	1.13164
$507$	−7.17184	−0.318512
$508$	91.4308	4.05658
$509$	14.5122	0.643244	0.321622	−	0.946868i	$-0.395772\pi$
$509$	14.5122	0.643244	0.321622	+	0.946868i	$0.395772\pi$
$510$	10.3404	0.457880
$511$	9.67208	0.427868
$512$	20.3216	0.898094
$513$	30.7051	1.35567
$514$	81.9289	3.61373
$515$	24.2683	1.06939
$516$	−17.9122	−0.788539
$517$	−18.1856	−0.799803
$518$	10.7371	0.471759
$519$	7.24453	0.318000
$520$	−90.3820	−3.96351
$521$	−23.9637	−1.04987	−0.524935	−	0.851142i	$-0.675910\pi$
$521$	−23.9637	−1.04987	−0.524935	+	0.851142i	$0.675910\pi$
$522$	10.0920	0.441717
$523$	−6.51305	−0.284796	−0.142398	−	0.989809i	$-0.545481\pi$
$523$	−6.51305	−0.284796	−0.142398	+	0.989809i	$0.545481\pi$
$524$	44.2530	1.93320
$525$	−2.14514	−0.0936215
$526$	0.240664	0.0104934
$527$	−3.34841	−0.145859
$528$	37.8827	1.64863
$529$	−0.243822	−0.0106009
$530$	−27.7551	−1.20560
$531$	−3.68973	−0.160121
$532$	19.4136	0.841687
$533$	11.7054	0.507017
$534$	15.0715	0.652210
$535$	18.6277	0.805346
$536$	113.278	4.89288
$537$	−29.8092	−1.28636
$538$	−73.9538	−3.18838
$539$	13.1047	0.564459
$540$	73.3765	3.15762
$541$	−2.72116	−0.116992	−0.0584959	−	0.998288i	$-0.518630\pi$
$541$	−2.72116	−0.116992	−0.0584959	+	0.998288i	$0.518630\pi$
$542$	−5.99423	−0.257474
$543$	37.8617	1.62480
$544$	−13.3823	−0.573762
$545$	−4.42288	−0.189455
$546$	12.2324	0.523498
$547$	23.3099	0.996661	0.498330	−	0.866987i	$-0.333947\pi$
$547$	23.3099	0.996661	0.498330	+	0.866987i	$0.333947\pi$
$548$	94.5217	4.03777
$549$	3.99138	0.170348
$550$	10.4006	0.443485
$551$	55.1785	2.35069
$552$	63.3364	2.69578
$553$	5.73430	0.243847
$554$	−52.9385	−2.24914
$555$	25.2612	1.07228
$556$	−81.0744	−3.43832
$557$	−34.8636	−1.47722	−0.738610	−	0.674133i	$-0.764517\pi$
$557$	−34.8636	−1.47722	−0.738610	+	0.674133i	$0.764517\pi$
$558$	−3.76910	−0.159559
$559$	9.09668	0.384749
$560$	20.9684	0.886075
$561$	2.95444	0.124737
$562$	45.3303	1.91214
$563$	−18.9316	−0.797870	−0.398935	−	0.916979i	$-0.630620\pi$
$563$	−18.9316	−0.797870	−0.398935	+	0.916979i	$0.630620\pi$
$564$	−74.5831	−3.14052
$565$	−34.9775	−1.47151
$566$	−50.5940	−2.12662
$567$	−5.23778	−0.219966
$568$	5.20640	0.218456
$569$	18.3113	0.767651	0.383826	−	0.923406i	$-0.374606\pi$
$569$	18.3113	0.767651	0.383826	+	0.923406i	$0.374606\pi$
$570$	63.6395	2.66557
$571$	−5.74605	−0.240465	−0.120232	−	0.992746i	$-0.538364\pi$
$571$	−5.74605	−0.240465	−0.120232	+	0.992746i	$0.538364\pi$
$572$	−42.5661	−1.77978
$573$	13.0332	0.544469
$574$	−5.07885	−0.211987
$575$	9.29770	0.387741
$576$	−6.05537	−0.252307
$577$	27.5417	1.14658	0.573288	−	0.819354i	$-0.305667\pi$
$577$	27.5417	1.14658	0.573288	+	0.819354i	$0.305667\pi$
$578$	43.0387	1.79017
$579$	−41.6555	−1.73114
$580$	131.861	5.47523
$581$	2.18952	0.0908364
$582$	−62.3902	−2.58616
$583$	−7.93015	−0.328433
$584$	−116.679	−4.82823
$585$	−4.24247	−0.175405
$586$	−34.6724	−1.43230
$587$	−19.0635	−0.786833	−0.393416	−	0.919360i	$-0.628707\pi$
$587$	−19.0635	−0.786833	−0.393416	+	0.919360i	$0.628707\pi$
$588$	53.7452	2.21641
$589$	−20.6077	−0.849124
$590$	−67.1712	−2.76540
$591$	34.0945	1.40246
$592$	−69.2569	−2.84644
$593$	−38.7243	−1.59021	−0.795107	−	0.606469i	$-0.792586\pi$
$593$	−38.7243	−1.59021	−0.795107	+	0.606469i	$0.792586\pi$
$594$	29.2111	1.19855
$595$	1.63531	0.0670410
$596$	−12.6467	−0.518028
$597$	−30.9168	−1.26534
$598$	−53.0190	−2.16811
$599$	17.2168	0.703458	0.351729	−	0.936102i	$-0.385594\pi$
$599$	17.2168	0.703458	0.351729	+	0.936102i	$0.385594\pi$
$600$	25.8779	1.05646
$601$	42.6850	1.74116	0.870580	−	0.492027i	$-0.163744\pi$
$601$	42.6850	1.74116	0.870580	+	0.492027i	$0.163744\pi$
$602$	−3.94696	−0.160866
$603$	5.31722	0.216534
$604$	−80.3770	−3.27050
$605$	−18.4022	−0.748157
$606$	27.4859	1.11654
$607$	−1.61173	−0.0654182	−0.0327091	−	0.999465i	$-0.510413\pi$
$607$	−1.61173	−0.0654182	−0.0327091	+	0.999465i	$0.510413\pi$
$608$	−82.3611	−3.34018
$609$	−10.8269	−0.438726
$610$	72.6627	2.94202
$611$	37.8770	1.53234
$612$	−1.78619	−0.0722024
$613$	38.0835	1.53818	0.769089	−	0.639142i	$-0.220710\pi$
$613$	38.0835	1.53818	0.769089	+	0.639142i	$0.220710\pi$
$614$	−45.7367	−1.84578
$615$	−11.9491	−0.481833
$616$	11.2047	0.451450
$617$	30.5323	1.22918	0.614591	−	0.788846i	$-0.289321\pi$
$617$	30.5323	1.22918	0.614591	+	0.788846i	$0.289321\pi$
$618$	39.6226	1.59386
$619$	−39.8407	−1.60133	−0.800666	−	0.599112i	$-0.795521\pi$
$619$	−39.8407	−1.60133	−0.800666	+	0.599112i	$0.795521\pi$
$620$	−49.2464	−1.97778
$621$	26.1134	1.04789
$622$	61.2001	2.45390
$623$	2.38353	0.0954941
$624$	−78.9021	−3.15861
$625$	−30.9465	−1.23786
$626$	−36.0657	−1.44147
$627$	18.1830	0.726160
$628$	50.1126	1.99971
$629$	−5.40129	−0.215363
$630$	1.84077	0.0733379
$631$	36.8049	1.46518	0.732589	−	0.680671i	$-0.238312\pi$
$631$	36.8049	1.46518	0.732589	+	0.680671i	$0.238312\pi$
$632$	−69.1759	−2.75167
$633$	26.6246	1.05823
$634$	−24.2088	−0.961453
$635$	47.3997	1.88100
$636$	−32.5233	−1.28963
$637$	−27.2945	−1.08145
$638$	52.4937	2.07824
$639$	0.244385	0.00966772
$640$	−32.8239	−1.29748
$641$	21.6913	0.856753	0.428377	−	0.903600i	$-0.359086\pi$
$641$	21.6913	0.856753	0.428377	+	0.903600i	$0.359086\pi$
$642$	30.4132	1.20031
$643$	19.9996	0.788706	0.394353	−	0.918959i	$-0.370969\pi$
$643$	19.9996	0.788706	0.394353	+	0.918959i	$0.370969\pi$
$644$	16.5104	0.650603
$645$	−9.28605	−0.365638
$646$	−13.6072	−0.535370
$647$	−10.4150	−0.409457	−0.204729	−	0.978819i	$-0.565631\pi$
$647$	−10.4150	−0.409457	−0.204729	+	0.978819i	$0.565631\pi$
$648$	63.1861	2.48218
$649$	−19.1921	−0.753355
$650$	−21.6624	−0.849671
$651$	4.04353	0.158479
$652$	−5.18770	−0.203166
$653$	−16.7596	−0.655855	−0.327928	−	0.944703i	$-0.606350\pi$
$653$	−16.7596	−0.655855	−0.327928	+	0.944703i	$0.606350\pi$
$654$	−7.22118	−0.282371
$655$	22.9417	0.896407
$656$	32.7599	1.27906
$657$	−5.47686	−0.213673
$658$	−16.4344	−0.640681
$659$	−8.46774	−0.329856	−0.164928	−	0.986306i	$-0.552739\pi$
$659$	−8.46774	−0.329856	−0.164928	+	0.986306i	$0.552739\pi$
$660$	43.4522	1.69137
$661$	−23.8168	−0.926368	−0.463184	−	0.886262i	$-0.653293\pi$
$661$	−23.8168	−0.926368	−0.463184	+	0.886262i	$0.653293\pi$
$662$	−13.2024	−0.513126
$663$	−6.15351	−0.238983
$664$	−26.4133	−1.02503
$665$	10.0644	0.390282
$666$	−6.07990	−0.235591
$667$	46.9270	1.81702
$668$	−80.3361	−3.10830
$669$	−15.7934	−0.610608
$670$	96.7995	3.73969
$671$	20.7611	0.801473
$672$	16.1605	0.623404
$673$	−6.38265	−0.246033	−0.123017	−	0.992405i	$-0.539257\pi$
$673$	−6.38265	−0.246033	−0.123017	+	0.992405i	$0.539257\pi$
$674$	23.5559	0.907341
$675$	10.6694	0.410665
$676$	22.5533	0.867434
$677$	−1.83434	−0.0704995	−0.0352498	−	0.999379i	$-0.511223\pi$
$677$	−1.83434	−0.0704995	−0.0352498	+	0.999379i	$0.511223\pi$
$678$	−57.1074	−2.19320
$679$	−9.86686	−0.378655
$680$	−19.7276	−0.756517
$681$	−35.7625	−1.37042
$682$	−19.6049	−0.750712
$683$	35.3606	1.35304	0.676519	−	0.736425i	$-0.263488\pi$
$683$	35.3606	1.35304	0.676519	+	0.736425i	$0.263488\pi$
$684$	−10.9930	−0.420329
$685$	49.0021	1.87227
$686$	24.5249	0.936367
$687$	−10.3240	−0.393885
$688$	25.4589	0.970612
$689$	16.5169	0.629244
$690$	54.1227	2.06042
$691$	−14.5132	−0.552107	−0.276053	−	0.961142i	$-0.589027\pi$
$691$	−14.5132	−0.552107	−0.276053	+	0.961142i	$0.589027\pi$
$692$	−22.7819	−0.866038
$693$	0.525941	0.0199789
$694$	−68.6624	−2.60639
$695$	−42.0307	−1.59432
$696$	130.610	4.95076
$697$	2.55492	0.0967745
$698$	72.0892	2.72862
$699$	37.8590	1.43196
$700$	6.74582	0.254968
$701$	11.2428	0.424635	0.212317	−	0.977201i	$-0.431899\pi$
$701$	11.2428	0.424635	0.212317	+	0.977201i	$0.431899\pi$
$702$	−60.8409	−2.29629
$703$	−33.2420	−1.25375
$704$	−31.4970	−1.18709
$705$	−38.6655	−1.45623
$706$	−58.5496	−2.20354
$707$	4.34682	0.163479
$708$	−78.7109	−2.95814
$709$	−17.2272	−0.646979	−0.323490	−	0.946232i	$-0.604856\pi$
$709$	−17.2272	−0.646979	−0.323490	+	0.946232i	$0.604856\pi$
$710$	4.44901	0.166968
$711$	−3.24707	−0.121775
$712$	−28.7538	−1.07759
$713$	−17.5259	−0.656351
$714$	2.66995	0.0999202
$715$	−22.0672	−0.825266
$716$	93.7410	3.50327
$717$	4.53075	0.169204
$718$	40.3607	1.50625
$719$	17.9695	0.670148	0.335074	−	0.942192i	$-0.391239\pi$
$719$	17.9695	0.670148	0.335074	+	0.942192i	$0.391239\pi$
$720$	−11.8734	−0.442496
$721$	6.26622	0.233366
$722$	−33.1722	−1.23454
$723$	25.0411	0.931288
$724$	−119.064	−4.42498
$725$	19.1734	0.712082
$726$	−30.0451	−1.11508
$727$	−5.77920	−0.214339	−0.107169	−	0.994241i	$-0.534179\pi$
$727$	−5.77920	−0.214339	−0.107169	+	0.994241i	$0.534179\pi$
$728$	−23.3371	−0.864932
$729$	29.5203	1.09334
$730$	−99.7057	−3.69027
$731$	1.98552	0.0734371
$732$	85.1457	3.14708
$733$	1.63100	0.0602423	0.0301211	−	0.999546i	$-0.490411\pi$
$733$	1.63100	0.0602423	0.0301211	+	0.999546i	$0.490411\pi$
$734$	94.7296	3.49653
$735$	27.8627	1.02773
$736$	−70.0445	−2.58188
$737$	27.6574	1.01878
$738$	2.87592	0.105864
$739$	−15.3862	−0.565989	−0.282994	−	0.959122i	$-0.591328\pi$
$739$	−15.3862	−0.565989	−0.282994	+	0.959122i	$0.591328\pi$
$740$	−79.4389	−2.92023
$741$	−37.8716	−1.39125
$742$	−7.16652	−0.263091
$743$	−7.43856	−0.272894	−0.136447	−	0.990647i	$-0.543568\pi$
$743$	−7.43856	−0.272894	−0.136447	+	0.990647i	$0.543568\pi$
$744$	−48.7793	−1.78833
$745$	−6.55631	−0.240205
$746$	21.7732	0.797173
$747$	−1.23982	−0.0453627
$748$	−9.29084	−0.339707
$749$	4.80978	0.175746
$750$	−34.6149	−1.26396
$751$	40.8810	1.49177	0.745884	−	0.666076i	$-0.232027\pi$
$751$	40.8810	1.49177	0.745884	+	0.666076i	$0.232027\pi$
$752$	106.007	3.86566
$753$	15.6539	0.570461
$754$	−109.334	−3.98170
$755$	−41.6692	−1.51650
$756$	18.9462	0.689068
$757$	−38.1164	−1.38537	−0.692683	−	0.721243i	$-0.743571\pi$
$757$	−38.1164	−1.38537	−0.692683	+	0.721243i	$0.743571\pi$
$758$	−57.6666	−2.09455
$759$	15.4639	0.561303
$760$	−121.413	−4.40410
$761$	36.3184	1.31654	0.658270	−	0.752782i	$-0.271288\pi$
$761$	36.3184	1.31654	0.658270	+	0.752782i	$0.271288\pi$
$762$	77.3889	2.80351
$763$	−1.14201	−0.0413436
$764$	−40.9855	−1.48280
$765$	−0.925999	−0.0334796
$766$	−22.5970	−0.816463
$767$	39.9733	1.44335
$768$	−2.78334	−0.100435
$769$	−42.6925	−1.53953	−0.769765	−	0.638328i	$-0.779626\pi$
$769$	−42.6925	−1.53953	−0.769765	+	0.638328i	$0.779626\pi$
$770$	9.57472	0.345049
$771$	49.7705	1.79244
$772$	130.994	4.71458
$773$	29.8969	1.07532	0.537659	−	0.843162i	$-0.319309\pi$
$773$	29.8969	1.07532	0.537659	+	0.843162i	$0.319309\pi$
$774$	2.23498	0.0803347
$775$	−7.16073	−0.257221
$776$	119.029	4.27290
$777$	6.52259	0.233996
$778$	59.9535	2.14944
$779$	15.7242	0.563377
$780$	−90.5022	−3.24050
$781$	1.27117	0.0454859
$782$	−11.5724	−0.413827
$783$	53.8501	1.92445
$784$	−76.3891	−2.72818
$785$	25.9795	0.927246
$786$	37.4567	1.33604
$787$	3.86180	0.137658	0.0688291	−	0.997628i	$-0.478074\pi$
$787$	3.86180	0.137658	0.0688291	+	0.997628i	$0.478074\pi$
$788$	−107.217	−3.81945
$789$	0.146199	0.00520484
$790$	−59.1127	−2.10314
$791$	−9.03139	−0.321119
$792$	−6.34471	−0.225449
$793$	−43.2412	−1.53554
$794$	44.0522	1.56335
$795$	−16.8608	−0.597989
$796$	97.2243	3.44602
$797$	2.06707	0.0732194	0.0366097	−	0.999330i	$-0.488344\pi$
$797$	2.06707	0.0732194	0.0366097	+	0.999330i	$0.488344\pi$
$798$	16.4321	0.581690
$799$	8.26736	0.292478
$800$	−28.6187	−1.01183
$801$	−1.34968	−0.0476887
$802$	−47.4797	−1.67657
$803$	−28.4878	−1.00531
$804$	113.429	4.00034
$805$	8.55937	0.301678
$806$	40.8332	1.43829
$807$	−44.9257	−1.58146
$808$	−52.4380	−1.84476
$809$	−33.3770	−1.17347	−0.586737	−	0.809778i	$-0.699588\pi$
$809$	−33.3770	−1.17347	−0.586737	+	0.809778i	$0.699588\pi$
$810$	53.9942	1.89716
$811$	−7.62688	−0.267816	−0.133908	−	0.990994i	$-0.542753\pi$
$811$	−7.62688	−0.267816	−0.133908	+	0.990994i	$0.542753\pi$
$812$	34.0472	1.19482
$813$	−3.64140	−0.127709
$814$	−31.6245	−1.10844
$815$	−2.68941	−0.0942061
$816$	−17.2219	−0.602886
$817$	12.2198	0.427517
$818$	−44.9204	−1.57060
$819$	−1.09543	−0.0382775
$820$	37.5762	1.31222
$821$	10.9776	0.383121	0.191561	−	0.981481i	$-0.438645\pi$
$821$	10.9776	0.383121	0.191561	+	0.981481i	$0.438645\pi$
$822$	80.0051	2.79050
$823$	55.1854	1.92364	0.961821	−	0.273681i	$-0.0882411\pi$
$823$	55.1854	1.92364	0.961821	+	0.273681i	$0.0882411\pi$
$824$	−75.5927	−2.63340
$825$	6.31822	0.219972
$826$	−17.3440	−0.603475
$827$	−28.7320	−0.999110	−0.499555	−	0.866282i	$-0.666503\pi$
$827$	−28.7320	−0.999110	−0.499555	+	0.866282i	$0.666503\pi$
$828$	−9.34911	−0.324904
$829$	−17.9299	−0.622731	−0.311365	−	0.950290i	$-0.600786\pi$
$829$	−17.9299	−0.622731	−0.311365	+	0.950290i	$0.600786\pi$
$830$	−22.5709	−0.783446
$831$	−32.1593	−1.11559
$832$	65.6019	2.27434
$833$	−5.95752	−0.206416
$834$	−68.6231	−2.37622
$835$	−41.6480	−1.44129
$836$	−57.1802	−1.97762
$837$	−20.1115	−0.695157
$838$	84.3468	2.91371
$839$	7.56294	0.261102	0.130551	−	0.991442i	$-0.458325\pi$
$839$	7.56294	0.261102	0.130551	+	0.991442i	$0.458325\pi$
$840$	23.8230	0.821970
$841$	67.7711	2.33694
$842$	42.8416	1.47642
$843$	27.5374	0.948440
$844$	−83.7264	−2.88198
$845$	11.6921	0.402221
$846$	9.30607	0.319949
$847$	−4.75156	−0.163266
$848$	46.2260	1.58741
$849$	−30.7350	−1.05482
$850$	−4.72823	−0.162177
$851$	−28.2709	−0.969115
$852$	5.21332	0.178606
$853$	−16.9372	−0.579919	−0.289960	−	0.957039i	$-0.593642\pi$
$853$	−16.9372	−0.579919	−0.289960	+	0.957039i	$0.593642\pi$
$854$	18.7619	0.642019
$855$	−5.69903	−0.194903
$856$	−58.0229	−1.98318
$857$	−9.79698	−0.334658	−0.167329	−	0.985901i	$-0.553514\pi$
$857$	−9.79698	−0.334658	−0.167329	+	0.985901i	$0.553514\pi$
$858$	−36.0288	−1.23000
$859$	11.3842	0.388424	0.194212	−	0.980960i	$-0.437785\pi$
$859$	11.3842	0.388424	0.194212	+	0.980960i	$0.437785\pi$
$860$	29.2019	0.995775
$861$	−3.08532	−0.105147
$862$	19.6081	0.667856
$863$	10.6202	0.361514	0.180757	−	0.983528i	$-0.442145\pi$
$863$	10.6202	0.361514	0.180757	+	0.983528i	$0.442145\pi$
$864$	−80.3782	−2.73452
$865$	−11.8106	−0.401573
$866$	−87.7568	−2.98210
$867$	26.1453	0.887940
$868$	−12.7157	−0.431599
$869$	−16.8896	−0.572941
$870$	111.610	3.78393
$871$	−57.6049	−1.95187
$872$	13.7767	0.466538
$873$	5.58715	0.189096
$874$	−71.2218	−2.40911
$875$	−5.47426	−0.185064
$876$	−116.835	−3.94748
$877$	−30.6423	−1.03472	−0.517359	−	0.855769i	$-0.673085\pi$
$877$	−30.6423	−1.03472	−0.517359	+	0.855769i	$0.673085\pi$
$878$	−29.9128	−1.00951
$879$	−21.0629	−0.710434
$880$	−61.7595	−2.08191
$881$	−24.0134	−0.809034	−0.404517	−	0.914531i	$-0.632560\pi$
$881$	−24.0134	−0.809034	−0.404517	+	0.914531i	$0.632560\pi$
$882$	−6.70603	−0.225804
$883$	5.01111	0.168637	0.0843187	−	0.996439i	$-0.473129\pi$
$883$	5.01111	0.168637	0.0843187	+	0.996439i	$0.473129\pi$
$884$	19.3510	0.650843
$885$	−40.8054	−1.37166
$886$	27.3135	0.917614
$887$	23.7496	0.797433	0.398717	−	0.917074i	$-0.369456\pi$
$887$	23.7496	0.797433	0.398717	+	0.917074i	$0.369456\pi$
$888$	−78.6854	−2.64051
$889$	12.2389	0.410479
$890$	−24.5709	−0.823617
$891$	15.4272	0.516830
$892$	49.6655	1.66292
$893$	50.8812	1.70267
$894$	−10.7044	−0.358009
$895$	48.5974	1.62443
$896$	−8.47532	−0.283141
$897$	−32.2081	−1.07540
$898$	−81.8141	−2.73017
$899$	−36.1414	−1.20538
$900$	−3.81985	−0.127328
$901$	3.60513	0.120104
$902$	14.9591	0.498082
$903$	−2.39771	−0.0797908
$904$	108.950	3.62364
$905$	−61.7253	−2.05182
$906$	−68.0328	−2.26024
$907$	22.1124	0.734230	0.367115	−	0.930176i	$-0.380346\pi$
$907$	22.1124	0.734230	0.367115	+	0.930176i	$0.380346\pi$
$908$	112.462	3.73220
$909$	−2.46141	−0.0816397
$910$	−19.9422	−0.661078
$911$	20.6068	0.682732	0.341366	−	0.939930i	$-0.389110\pi$
$911$	20.6068	0.682732	0.341366	+	0.939930i	$0.389110\pi$
$912$	−105.991	−3.50972
$913$	−6.44892	−0.213428
$914$	−40.6618	−1.34497
$915$	44.1414	1.45927
$916$	32.4659	1.07270
$917$	5.92368	0.195617
$918$	−13.2797	−0.438294
$919$	7.45967	0.246072	0.123036	−	0.992402i	$-0.460737\pi$
$919$	7.45967	0.246072	0.123036	+	0.992402i	$0.460737\pi$
$920$	−103.256	−3.40425
$921$	−27.7843	−0.915524
$922$	86.0715	2.83461
$923$	−2.64758	−0.0871463
$924$	11.2196	0.369098
$925$	−11.5509	−0.379792
$926$	−86.7192	−2.84977
$927$	−3.54827	−0.116541
$928$	−144.443	−4.74158
$929$	35.5088	1.16501	0.582503	−	0.812828i	$-0.302073\pi$
$929$	35.5088	1.16501	0.582503	+	0.812828i	$0.302073\pi$
$930$	−41.6832	−1.36685
$931$	−36.6654	−1.20166
$932$	−119.055	−3.89979
$933$	37.1781	1.21716
$934$	39.7411	1.30037
$935$	−4.81657	−0.157519
$936$	13.2148	0.431938
$937$	−11.8146	−0.385965	−0.192983	−	0.981202i	$-0.561816\pi$
$937$	−11.8146	−0.385965	−0.192983	+	0.981202i	$0.561816\pi$
$938$	24.9942	0.816089
$939$	−21.9093	−0.714983
$940$	121.591	3.96588
$941$	17.3855	0.566753	0.283376	−	0.959009i	$-0.408545\pi$
$941$	17.3855	0.566753	0.283376	+	0.959009i	$0.408545\pi$
$942$	42.4164	1.38200
$943$	13.3727	0.435476
$944$	111.873	3.64117
$945$	9.82213	0.319514
$946$	11.6252	0.377969
$947$	−21.5703	−0.700939	−0.350470	−	0.936574i	$-0.613978\pi$
$947$	−21.5703	−0.700939	−0.350470	+	0.936574i	$0.613978\pi$
$948$	−69.2679	−2.24972
$949$	59.3344	1.92608
$950$	−29.0997	−0.944120
$951$	−14.7064	−0.476888
$952$	−5.09377	−0.165090
$953$	1.39750	0.0452693	0.0226347	−	0.999744i	$-0.492795\pi$
$953$	1.39750	0.0452693	0.0226347	+	0.999744i	$0.492795\pi$
$954$	4.05807	0.131385
$955$	−21.2478	−0.687561
$956$	−14.2479	−0.460809
$957$	31.8890	1.03083
$958$	−91.5066	−2.95645
$959$	12.6526	0.408574
$960$	−66.9675	−2.16137
$961$	−17.5022	−0.564587
$962$	65.8676	2.12366
$963$	−2.72356	−0.0877654
$964$	−78.7467	−2.53626
$965$	67.9102	2.18611
$966$	13.9748	0.449631
$967$	16.1482	0.519291	0.259645	−	0.965704i	$-0.416394\pi$
$967$	16.1482	0.519291	0.259645	+	0.965704i	$0.416394\pi$
$968$	57.3206	1.84235
$969$	−8.26618	−0.265548
$970$	101.714	3.26583
$971$	45.7792	1.46913	0.734563	−	0.678541i	$-0.237387\pi$
$971$	45.7792	1.46913	0.734563	+	0.678541i	$0.237387\pi$
$972$	−20.2354	−0.649049
$973$	−10.8526	−0.347917
$974$	−34.4260	−1.10308
$975$	−13.1596	−0.421444
$976$	−121.019	−3.87373
$977$	23.2206	0.742893	0.371447	−	0.928454i	$-0.378862\pi$
$977$	23.2206	0.742893	0.371447	+	0.928454i	$0.378862\pi$
$978$	−4.39098	−0.140408
$979$	−7.02036	−0.224372
$980$	−87.6198	−2.79891
$981$	0.646669	0.0206466
$982$	−18.2783	−0.583285
$983$	12.6677	0.404037	0.202019	−	0.979382i	$-0.435250\pi$
$983$	12.6677	0.404037	0.202019	+	0.979382i	$0.435250\pi$
$984$	37.2198	1.18652
$985$	−55.5837	−1.77104
$986$	−23.8641	−0.759989
$987$	−9.98365	−0.317783
$988$	119.095	3.78891
$989$	10.3924	0.330460
$990$	−5.42173	−0.172314
$991$	23.0838	0.733281	0.366641	−	0.930363i	$-0.380508\pi$
$991$	23.0838	0.733281	0.366641	+	0.930363i	$0.380508\pi$
$992$	53.9456	1.71277
$993$	−8.02024	−0.254515
$994$	1.14876	0.0364364
$995$	50.4032	1.59789
$996$	−26.4484	−0.838050
$997$	4.47299	0.141661	0.0708305	−	0.997488i	$-0.477435\pi$
$997$	4.47299	0.141661	0.0708305	+	0.997488i	$0.477435\pi$
$998$	52.6241	1.66579
$999$	−32.4417	−1.02641

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.5	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.66174 q^{2} -1.61696 q^{3} +5.08487 q^{4} +2.63611 q^{5} +4.30394 q^{6} +0.680658 q^{7} -8.21113 q^{8} -0.385425 q^{9} +O(q^{10})\)	\(q-2.66174 q^{2} -1.61696 q^{3} +5.08487 q^{4} +2.63611 q^{5} +4.30394 q^{6} +0.680658 q^{7} -8.21113 q^{8} -0.385425 q^{9} -7.01664 q^{10} -2.00479 q^{11} -8.22206 q^{12} +4.17557 q^{13} -1.81174 q^{14} -4.26249 q^{15} +11.6862 q^{16} +0.911396 q^{17} +1.02590 q^{18} +5.60915 q^{19} +13.4043 q^{20} -1.10060 q^{21} +5.33622 q^{22} +4.77034 q^{23} +13.2771 q^{24} +1.94906 q^{25} -11.1143 q^{26} +5.47411 q^{27} +3.46106 q^{28} +9.83723 q^{29} +11.3457 q^{30} -3.67394 q^{31} -14.6833 q^{32} +3.24167 q^{33} -2.42590 q^{34} +1.79429 q^{35} -1.95984 q^{36} -5.92639 q^{37} -14.9301 q^{38} -6.75175 q^{39} -21.6454 q^{40} +2.80330 q^{41} +2.92951 q^{42} +2.17855 q^{43} -10.1941 q^{44} -1.01602 q^{45} -12.6974 q^{46} +9.07110 q^{47} -18.8961 q^{48} -6.53670 q^{49} -5.18790 q^{50} -1.47369 q^{51} +21.2322 q^{52} +3.95561 q^{53} -14.5707 q^{54} -5.28483 q^{55} -5.58897 q^{56} -9.06980 q^{57} -26.1842 q^{58} +9.57314 q^{59} -21.6742 q^{60} -10.3558 q^{61} +9.77907 q^{62} -0.262343 q^{63} +15.7109 q^{64} +11.0072 q^{65} -8.62849 q^{66} -13.7957 q^{67} +4.63433 q^{68} -7.71348 q^{69} -4.77593 q^{70} -0.634066 q^{71} +3.16478 q^{72} +14.2099 q^{73} +15.7745 q^{74} -3.15157 q^{75} +28.5218 q^{76} -1.36457 q^{77} +17.9714 q^{78} +8.42465 q^{79} +30.8060 q^{80} -7.69517 q^{81} -7.46167 q^{82} +3.21676 q^{83} -5.59641 q^{84} +2.40254 q^{85} -5.79873 q^{86} -15.9065 q^{87} +16.4616 q^{88} +3.50180 q^{89} +2.70439 q^{90} +2.84213 q^{91} +24.2566 q^{92} +5.94062 q^{93} -24.1449 q^{94} +14.7863 q^{95} +23.7424 q^{96} -14.4961 q^{97} +17.3990 q^{98} +0.772696 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 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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