LMFDB - Embedded newform 5077.2.a.c.1.9

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			1.9
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)

$f(q)$	$=$	$q-2.60140 q^{2} +3.18807 q^{3} +4.76730 q^{4} -0.824320 q^{5} -8.29345 q^{6} -1.42597 q^{7} -7.19885 q^{8} +7.16377 q^{9} +O(q^{10})$	\(q-2.60140 q^{2} +3.18807 q^{3} +4.76730 q^{4} -0.824320 q^{5} -8.29345 q^{6} -1.42597 q^{7} -7.19885 q^{8} +7.16377 q^{9} +2.14439 q^{10} +1.79832 q^{11} +15.1985 q^{12} +2.40664 q^{13} +3.70951 q^{14} -2.62799 q^{15} +9.19252 q^{16} +4.37109 q^{17} -18.6358 q^{18} +4.55860 q^{19} -3.92978 q^{20} -4.54607 q^{21} -4.67815 q^{22} -7.24022 q^{23} -22.9504 q^{24} -4.32050 q^{25} -6.26064 q^{26} +13.2744 q^{27} -6.79800 q^{28} +0.631518 q^{29} +6.83645 q^{30} -1.35338 q^{31} -9.51575 q^{32} +5.73316 q^{33} -11.3710 q^{34} +1.17545 q^{35} +34.1518 q^{36} -6.27091 q^{37} -11.8588 q^{38} +7.67253 q^{39} +5.93416 q^{40} +8.27333 q^{41} +11.8262 q^{42} -12.0497 q^{43} +8.57312 q^{44} -5.90524 q^{45} +18.8347 q^{46} +9.30783 q^{47} +29.3064 q^{48} -4.96662 q^{49} +11.2394 q^{50} +13.9353 q^{51} +11.4732 q^{52} +13.0340 q^{53} -34.5320 q^{54} -1.48239 q^{55} +10.2653 q^{56} +14.5331 q^{57} -1.64283 q^{58} +11.9736 q^{59} -12.5284 q^{60} +12.8650 q^{61} +3.52069 q^{62} -10.2153 q^{63} +6.36925 q^{64} -1.98384 q^{65} -14.9143 q^{66} +9.80128 q^{67} +20.8383 q^{68} -23.0823 q^{69} -3.05783 q^{70} -4.27134 q^{71} -51.5709 q^{72} +2.29431 q^{73} +16.3132 q^{74} -13.7740 q^{75} +21.7322 q^{76} -2.56434 q^{77} -19.9594 q^{78} -11.6342 q^{79} -7.57758 q^{80} +20.8283 q^{81} -21.5223 q^{82} +12.8850 q^{83} -21.6725 q^{84} -3.60317 q^{85} +31.3461 q^{86} +2.01332 q^{87} -12.9458 q^{88} -6.50306 q^{89} +15.3619 q^{90} -3.43179 q^{91} -34.5163 q^{92} -4.31467 q^{93} -24.2134 q^{94} -3.75775 q^{95} -30.3368 q^{96} +16.0867 q^{97} +12.9202 q^{98} +12.8827 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60140	−1.83947	−0.919735	−	0.392540i	$-0.871596\pi$
$2$	−2.60140	−1.83947	−0.919735	+	0.392540i	$0.871596\pi$
$3$	3.18807	1.84063	0.920316	−	0.391177i	$-0.127932\pi$
$3$	3.18807	1.84063	0.920316	+	0.391177i	$0.127932\pi$
$4$	4.76730	2.38365
$5$	−0.824320	−0.368647	−0.184324	−	0.982866i	$-0.559009\pi$
$5$	−0.824320	−0.368647	−0.184324	+	0.982866i	$0.559009\pi$
$6$	−8.29345	−3.38578
$7$	−1.42597	−0.538964	−0.269482	−	0.963005i	$-0.586853\pi$
$7$	−1.42597	−0.538964	−0.269482	+	0.963005i	$0.586853\pi$
$8$	−7.19885	−2.54518
$9$	7.16377	2.38792
$10$	2.14439	0.678115
$11$	1.79832	0.542214	0.271107	−	0.962549i	$-0.412610\pi$
$11$	1.79832	0.542214	0.271107	+	0.962549i	$0.412610\pi$
$12$	15.1985	4.38742
$13$	2.40664	0.667482	0.333741	−	0.942665i	$-0.391689\pi$
$13$	2.40664	0.667482	0.333741	+	0.942665i	$0.391689\pi$
$14$	3.70951	0.991409
$15$	−2.62799	−0.678543
$16$	9.19252	2.29813
$17$	4.37109	1.06014	0.530072	−	0.847953i	$-0.322165\pi$
$17$	4.37109	1.06014	0.530072	+	0.847953i	$0.322165\pi$
$18$	−18.6358	−4.39251
$19$	4.55860	1.04582	0.522908	−	0.852389i	$-0.324847\pi$
$19$	4.55860	1.04582	0.522908	+	0.852389i	$0.324847\pi$
$20$	−3.92978	−0.878725
$21$	−4.54607	−0.992035
$22$	−4.67815	−0.997385
$23$	−7.24022	−1.50969	−0.754845	−	0.655904i	$-0.772288\pi$
$23$	−7.24022	−1.50969	−0.754845	+	0.655904i	$0.772288\pi$
$24$	−22.9504	−4.68474
$25$	−4.32050	−0.864099
$26$	−6.26064	−1.22781
$27$	13.2744	2.55465
$28$	−6.79800	−1.28470
$29$	0.631518	0.117270	0.0586350	−	0.998279i	$-0.481325\pi$
$29$	0.631518	0.117270	0.0586350	+	0.998279i	$0.481325\pi$
$30$	6.83645	1.24816
$31$	−1.35338	−0.243074	−0.121537	−	0.992587i	$-0.538782\pi$
$31$	−1.35338	−0.243074	−0.121537	+	0.992587i	$0.538782\pi$
$32$	−9.51575	−1.68216
$33$	5.73316	0.998015
$34$	−11.3710	−1.95010
$35$	1.17545	0.198688
$36$	34.1518	5.69197
$37$	−6.27091	−1.03093	−0.515466	−	0.856910i	$-0.672381\pi$
$37$	−6.27091	−1.03093	−0.515466	+	0.856910i	$0.672381\pi$
$38$	−11.8588	−1.92375
$39$	7.67253	1.22859
$40$	5.93416	0.938273
$41$	8.27333	1.29208	0.646038	−	0.763305i	$-0.276425\pi$
$41$	8.27333	1.29208	0.646038	+	0.763305i	$0.276425\pi$
$42$	11.8262	1.82482
$43$	−12.0497	−1.83756	−0.918781	−	0.394769i	$-0.870825\pi$
$43$	−12.0497	−1.83756	−0.918781	+	0.394769i	$0.870825\pi$
$44$	8.57312	1.29245
$45$	−5.90524	−0.880301
$46$	18.8347	2.77703
$47$	9.30783	1.35769	0.678844	−	0.734283i	$-0.262481\pi$
$47$	9.30783	1.35769	0.678844	+	0.734283i	$0.262481\pi$
$48$	29.3064	4.23001
$49$	−4.96662	−0.709517
$50$	11.2394	1.58948
$51$	13.9353	1.95133
$52$	11.4732	1.59104
$53$	13.0340	1.79036	0.895180	−	0.445705i	$-0.147047\pi$
$53$	13.0340	1.79036	0.895180	+	0.445705i	$0.147047\pi$
$54$	−34.5320	−4.69921
$55$	−1.48239	−0.199885
$56$	10.2653	1.37176
$57$	14.5331	1.92496
$58$	−1.64283	−0.215715
$59$	11.9736	1.55883	0.779415	−	0.626507i	$-0.215516\pi$
$59$	11.9736	1.55883	0.779415	+	0.626507i	$0.215516\pi$
$60$	−12.5284	−1.61741
$61$	12.8650	1.64719	0.823597	−	0.567175i	$-0.191964\pi$
$61$	12.8650	1.64719	0.823597	+	0.567175i	$0.191964\pi$
$62$	3.52069	0.447128
$63$	−10.2153	−1.28701
$64$	6.36925	0.796157
$65$	−1.98384	−0.246065
$66$	−14.9143	−1.83582
$67$	9.80128	1.19742	0.598709	−	0.800967i	$-0.295681\pi$
$67$	9.80128	1.19742	0.598709	+	0.800967i	$0.295681\pi$
$68$	20.8383	2.52701
$69$	−23.0823	−2.77878
$70$	−3.05783	−0.365480
$71$	−4.27134	−0.506914	−0.253457	−	0.967347i	$-0.581568\pi$
$71$	−4.27134	−0.506914	−0.253457	+	0.967347i	$0.581568\pi$
$72$	−51.5709	−6.07769
$73$	2.29431	0.268528	0.134264	−	0.990946i	$-0.457133\pi$
$73$	2.29431	0.268528	0.134264	+	0.990946i	$0.457133\pi$
$74$	16.3132	1.89637
$75$	−13.7740	−1.59049
$76$	21.7322	2.49286
$77$	−2.56434	−0.292234
$78$	−19.9594	−2.25995
$79$	−11.6342	−1.30894	−0.654472	−	0.756086i	$-0.727109\pi$
$79$	−11.6342	−1.30894	−0.654472	+	0.756086i	$0.727109\pi$
$80$	−7.57758	−0.847199
$81$	20.8283	2.31425
$82$	−21.5223	−2.37674
$83$	12.8850	1.41431	0.707156	−	0.707057i	$-0.249978\pi$
$83$	12.8850	1.41431	0.707156	+	0.707057i	$0.249978\pi$
$84$	−21.6725	−2.36466
$85$	−3.60317	−0.390819
$86$	31.3461	3.38014
$87$	2.01332	0.215851
$88$	−12.9458	−1.38003
$89$	−6.50306	−0.689323	−0.344661	−	0.938727i	$-0.612006\pi$
$89$	−6.50306	−0.689323	−0.344661	+	0.938727i	$0.612006\pi$
$90$	15.3619	1.61929
$91$	−3.43179	−0.359749
$92$	−34.5163	−3.59857
$93$	−4.31467	−0.447410
$94$	−24.2134	−2.49742
$95$	−3.75775	−0.385537
$96$	−30.3368	−3.09624
$97$	16.0867	1.63336	0.816681	−	0.577090i	$-0.195812\pi$
$97$	16.0867	1.63336	0.816681	+	0.577090i	$0.195812\pi$
$98$	12.9202	1.30514
$99$	12.8827	1.29476
$100$	−20.5971	−2.05971
$101$	−12.2866	−1.22256	−0.611279	−	0.791415i	$-0.709345\pi$
$101$	−12.2866	−1.22256	−0.611279	+	0.791415i	$0.709345\pi$
$102$	−36.2514	−3.58942
$103$	16.9779	1.67288	0.836441	−	0.548057i	$-0.184632\pi$
$103$	16.9779	1.67288	0.836441	+	0.548057i	$0.184632\pi$
$104$	−17.3251	−1.69886
$105$	3.74742	0.365711
$106$	−33.9067	−3.29331
$107$	1.93951	0.187499	0.0937496	−	0.995596i	$-0.470115\pi$
$107$	1.93951	0.187499	0.0937496	+	0.995596i	$0.470115\pi$
$108$	63.2829	6.08940
$109$	−4.72629	−0.452697	−0.226348	−	0.974046i	$-0.572679\pi$
$109$	−4.72629	−0.452697	−0.226348	+	0.974046i	$0.572679\pi$
$110$	3.85629	0.367683
$111$	−19.9921	−1.89756
$112$	−13.1082	−1.23861
$113$	3.71323	0.349312	0.174656	−	0.984630i	$-0.444119\pi$
$113$	3.71323	0.349312	0.174656	+	0.984630i	$0.444119\pi$
$114$	−37.8065	−3.54091
$115$	5.96825	0.556543
$116$	3.01063	0.279530
$117$	17.2406	1.59390
$118$	−31.1482	−2.86742
$119$	−6.23302	−0.571380
$120$	18.9185	1.72701
$121$	−7.76605	−0.706005
$122$	−33.4671	−3.02997
$123$	26.3759	2.37824
$124$	−6.45197	−0.579404
$125$	7.68307	0.687195
$126$	26.5741	2.36741
$127$	−12.1852	−1.08126	−0.540632	−	0.841259i	$-0.681815\pi$
$127$	−12.1852	−1.08126	−0.540632	+	0.841259i	$0.681815\pi$
$128$	2.46251	0.217657
$129$	−38.4152	−3.38227
$130$	5.16077	0.452630
$131$	−6.74280	−0.589121	−0.294561	−	0.955633i	$-0.595173\pi$
$131$	−6.74280	−0.589121	−0.294561	+	0.955633i	$0.595173\pi$
$132$	27.3317	2.37892
$133$	−6.50041	−0.563657
$134$	−25.4971	−2.20261
$135$	−10.9423	−0.941766
$136$	−31.4668	−2.69826
$137$	5.09238	0.435071	0.217536	−	0.976052i	$-0.430198\pi$
$137$	5.09238	0.435071	0.217536	+	0.976052i	$0.430198\pi$
$138$	60.0463	5.11148
$139$	−15.2190	−1.29086	−0.645430	−	0.763819i	$-0.723322\pi$
$139$	−15.2190	−1.29086	−0.645430	+	0.763819i	$0.723322\pi$
$140$	5.60373	0.473602
$141$	29.6740	2.49900
$142$	11.1115	0.932453
$143$	4.32791	0.361918
$144$	65.8531	5.48776
$145$	−0.520573	−0.0432312
$146$	−5.96841	−0.493949
$147$	−15.8339	−1.30596
$148$	−29.8953	−2.45738
$149$	3.49502	0.286323	0.143161	−	0.989699i	$-0.454273\pi$
$149$	3.49502	0.286323	0.143161	+	0.989699i	$0.454273\pi$
$150$	35.8318	2.92565
$151$	−15.1087	−1.22953	−0.614766	−	0.788710i	$-0.710750\pi$
$151$	−15.1087	−1.22953	−0.614766	+	0.788710i	$0.710750\pi$
$152$	−32.8167	−2.66179
$153$	31.3134	2.53154
$154$	6.67088	0.537555
$155$	1.11562	0.0896087
$156$	36.5772	2.92852
$157$	14.2490	1.13720	0.568599	−	0.822615i	$-0.307486\pi$
$157$	14.2490	1.13720	0.568599	+	0.822615i	$0.307486\pi$
$158$	30.2651	2.40776
$159$	41.5533	3.29539
$160$	7.84402	0.620125
$161$	10.3243	0.813669
$162$	−54.1827	−4.25700
$163$	15.6366	1.22475	0.612377	−	0.790566i	$-0.290213\pi$
$163$	15.6366	1.22475	0.612377	+	0.790566i	$0.290213\pi$
$164$	39.4414	3.07986
$165$	−4.72596	−0.367915
$166$	−33.5191	−2.60158
$167$	14.0828	1.08976	0.544880	−	0.838514i	$-0.316575\pi$
$167$	14.0828	1.08976	0.544880	+	0.838514i	$0.316575\pi$
$168$	32.7265	2.52491
$169$	−7.20808	−0.554467
$170$	9.37330	0.718900
$171$	32.6568	2.49733
$172$	−57.4445	−4.38010
$173$	−20.3110	−1.54422	−0.772110	−	0.635489i	$-0.780799\pi$
$173$	−20.3110	−1.54422	−0.772110	+	0.635489i	$0.780799\pi$
$174$	−5.23746	−0.397051
$175$	6.16088	0.465719
$176$	16.5311	1.24608
$177$	38.1727	2.86923
$178$	16.9171	1.26799
$179$	0.0792077	0.00592026	0.00296013	−	0.999996i	$-0.499058\pi$
$179$	0.0792077	0.00592026	0.00296013	+	0.999996i	$0.499058\pi$
$180$	−28.1520	−2.09833
$181$	−24.1900	−1.79803	−0.899013	−	0.437922i	$-0.855715\pi$
$181$	−24.1900	−1.79803	−0.899013	+	0.437922i	$0.855715\pi$
$182$	8.92747	0.661748
$183$	41.0145	3.03188
$184$	52.1212	3.84243
$185$	5.16924	0.380050
$186$	11.2242	0.822998
$187$	7.86060	0.574824
$188$	44.3732	3.23625
$189$	−18.9288	−1.37687
$190$	9.77542	0.709183
$191$	11.6848	0.845483	0.422742	−	0.906250i	$-0.361068\pi$
$191$	11.6848	0.845483	0.422742	+	0.906250i	$0.361068\pi$
$192$	20.3056	1.46543
$193$	7.24176	0.521273	0.260637	−	0.965437i	$-0.416068\pi$
$193$	7.24176	0.521273	0.260637	+	0.965437i	$0.416068\pi$
$194$	−41.8481	−3.00452
$195$	−6.32462	−0.452916
$196$	−23.6774	−1.69124
$197$	3.57292	0.254560	0.127280	−	0.991867i	$-0.459375\pi$
$197$	3.57292	0.254560	0.127280	+	0.991867i	$0.459375\pi$
$198$	−33.5132	−2.38168
$199$	20.6847	1.46630	0.733149	−	0.680068i	$-0.238050\pi$
$199$	20.6847	1.46630	0.733149	+	0.680068i	$0.238050\pi$
$200$	31.1026	2.19929
$201$	31.2471	2.20400
$202$	31.9623	2.24886
$203$	−0.900524	−0.0632044
$204$	66.4338	4.65129
$205$	−6.81987	−0.476320
$206$	−44.1663	−3.07722
$207$	−51.8672	−3.60502
$208$	22.1231	1.53396
$209$	8.19782	0.567055
$210$	−9.74855	−0.672714
$211$	20.9021	1.43896	0.719482	−	0.694511i	$-0.244379\pi$
$211$	20.9021	1.43896	0.719482	+	0.694511i	$0.244379\pi$
$212$	62.1370	4.26759
$213$	−13.6173	−0.933042
$214$	−5.04544	−0.344899
$215$	9.93280	0.677412
$216$	−95.5603	−6.50205
$217$	1.92988	0.131008
$218$	12.2950	0.832722
$219$	7.31440	0.494261
$220$	−7.06699	−0.476457
$221$	10.5196	0.707627
$222$	52.0074	3.49051
$223$	−12.4520	−0.833846	−0.416923	−	0.908942i	$-0.636892\pi$
$223$	−12.4520	−0.833846	−0.416923	+	0.908942i	$0.636892\pi$
$224$	13.5691	0.906626
$225$	−30.9510	−2.06340
$226$	−9.65961	−0.642548
$227$	−20.0231	−1.32898	−0.664492	−	0.747296i	$-0.731352\pi$
$227$	−20.0231	−1.32898	−0.664492	+	0.747296i	$0.731352\pi$
$228$	69.2837	4.58843
$229$	−2.59238	−0.171309	−0.0856546	−	0.996325i	$-0.527298\pi$
$229$	−2.59238	−0.171309	−0.0856546	+	0.996325i	$0.527298\pi$
$230$	−15.5258	−1.02374
$231$	−8.17529	−0.537895
$232$	−4.54621	−0.298473
$233$	9.58978	0.628247	0.314124	−	0.949382i	$-0.398289\pi$
$233$	9.58978	0.628247	0.314124	+	0.949382i	$0.398289\pi$
$234$	−44.8498	−2.93192
$235$	−7.67263	−0.500507
$236$	57.0817	3.71570
$237$	−37.0905	−2.40928
$238$	16.2146	1.05104
$239$	−22.0491	−1.42624	−0.713120	−	0.701042i	$-0.752719\pi$
$239$	−22.0491	−1.42624	−0.713120	+	0.701042i	$0.752719\pi$
$240$	−24.1578	−1.55938
$241$	−19.6537	−1.26601	−0.633003	−	0.774149i	$-0.718178\pi$
$241$	−19.6537	−1.26601	−0.633003	+	0.774149i	$0.718178\pi$
$242$	20.2026	1.29867
$243$	26.5788	1.70503
$244$	61.3313	3.92633
$245$	4.09409	0.261562
$246$	−68.6144	−4.37469
$247$	10.9709	0.698063
$248$	9.74279	0.618668
$249$	41.0782	2.60323
$250$	−19.9868	−1.26407
$251$	−0.714104	−0.0450739	−0.0225369	−	0.999746i	$-0.507174\pi$
$251$	−0.714104	−0.0450739	−0.0225369	+	0.999746i	$0.507174\pi$
$252$	−48.6993	−3.06777
$253$	−13.0202	−0.818574
$254$	31.6987	1.98895
$255$	−11.4872	−0.719354
$256$	−19.1445	−1.19653
$257$	8.40799	0.524476	0.262238	−	0.965003i	$-0.415539\pi$
$257$	8.40799	0.524476	0.262238	+	0.965003i	$0.415539\pi$
$258$	99.9335	6.22159
$259$	8.94210	0.555635
$260$	−9.45757	−0.586533
$261$	4.52405	0.280032
$262$	17.5407	1.08367
$263$	−13.8084	−0.851463	−0.425732	−	0.904849i	$-0.639983\pi$
$263$	−13.8084	−0.851463	−0.425732	+	0.904849i	$0.639983\pi$
$264$	−41.2722	−2.54013
$265$	−10.7442	−0.660011
$266$	16.9102	1.03683
$267$	−20.7322	−1.26879
$268$	46.7256	2.85422
$269$	9.63031	0.587170	0.293585	−	0.955933i	$-0.405152\pi$
$269$	9.63031	0.587170	0.293585	+	0.955933i	$0.405152\pi$
$270$	28.4654	1.73235
$271$	−25.0498	−1.52167	−0.760834	−	0.648947i	$-0.775210\pi$
$271$	−25.0498	−1.52167	−0.760834	+	0.648947i	$0.775210\pi$
$272$	40.1813	2.43635
$273$	−10.9408	−0.662166
$274$	−13.2473	−0.800300
$275$	−7.76963	−0.468526
$276$	−110.040	−6.62364
$277$	14.2425	0.855748	0.427874	−	0.903838i	$-0.359263\pi$
$277$	14.2425	0.855748	0.427874	+	0.903838i	$0.359263\pi$
$278$	39.5908	2.37450
$279$	−9.69531	−0.580443
$280$	−8.46191	−0.505696
$281$	21.9930	1.31199	0.655996	−	0.754765i	$-0.272249\pi$
$281$	21.9930	1.31199	0.655996	+	0.754765i	$0.272249\pi$
$282$	−77.1940	−4.59684
$283$	20.7316	1.23237	0.616184	−	0.787602i	$-0.288678\pi$
$283$	20.7316	1.23237	0.616184	+	0.787602i	$0.288678\pi$
$284$	−20.3627	−1.20831
$285$	−11.9800	−0.709631
$286$	−11.2586	−0.665737
$287$	−11.7975	−0.696383
$288$	−68.1686	−4.01688
$289$	2.10638	0.123905
$290$	1.35422	0.0795226
$291$	51.2856	3.00642
$292$	10.9376	0.640077
$293$	3.16247	0.184753	0.0923767	−	0.995724i	$-0.470554\pi$
$293$	3.16247	0.184753	0.0923767	+	0.995724i	$0.470554\pi$
$294$	41.1904	2.40227
$295$	−9.87008	−0.574659
$296$	45.1434	2.62390
$297$	23.8716	1.38517
$298$	−9.09195	−0.526682
$299$	−17.4246	−1.00769
$300$	−65.6649	−3.79116
$301$	17.1825	0.990380
$302$	39.3039	2.26169
$303$	−39.1704	−2.25028
$304$	41.9051	2.40342
$305$	−10.6049	−0.607234
$306$	−81.4589	−4.65669
$307$	3.20797	0.183088	0.0915442	−	0.995801i	$-0.470820\pi$
$307$	3.20797	0.183088	0.0915442	+	0.995801i	$0.470820\pi$
$308$	−12.2250	−0.696583
$309$	54.1267	3.07916
$310$	−2.90217	−0.164832
$311$	14.7951	0.838952	0.419476	−	0.907766i	$-0.362214\pi$
$311$	14.7951	0.838952	0.419476	+	0.907766i	$0.362214\pi$
$312$	−55.2334	−3.12698
$313$	18.2214	1.02993	0.514966	−	0.857210i	$-0.327804\pi$
$313$	18.2214	1.02993	0.514966	+	0.857210i	$0.327804\pi$
$314$	−37.0675	−2.09184
$315$	8.42067	0.474451
$316$	−55.4635	−3.12006
$317$	2.65399	0.149063	0.0745315	−	0.997219i	$-0.476254\pi$
$317$	2.65399	0.149063	0.0745315	+	0.997219i	$0.476254\pi$
$318$	−108.097	−6.06177
$319$	1.13567	0.0635854
$320$	−5.25030	−0.293501
$321$	6.18328	0.345117
$322$	−26.8577	−1.49672
$323$	19.9260	1.10871
$324$	99.2946	5.51637
$325$	−10.3979	−0.576771
$326$	−40.6771	−2.25290
$327$	−15.0677	−0.833248
$328$	−59.5585	−3.28857
$329$	−13.2727	−0.731745
$330$	12.2941	0.676769
$331$	21.5491	1.18444	0.592222	−	0.805775i	$-0.298251\pi$
$331$	21.5491	1.18444	0.592222	+	0.805775i	$0.298251\pi$
$332$	61.4266	3.37122
$333$	−44.9233	−2.46178
$334$	−36.6350	−2.00458
$335$	−8.07940	−0.441425
$336$	−41.7899	−2.27983
$337$	−22.7359	−1.23850	−0.619252	−	0.785192i	$-0.712564\pi$
$337$	−22.7359	−1.23850	−0.619252	+	0.785192i	$0.712564\pi$
$338$	18.7511	1.01993
$339$	11.8380	0.642954
$340$	−17.1774	−0.931575
$341$	−2.43381	−0.131798
$342$	−84.9534	−4.59376
$343$	17.0640	0.921369
$344$	86.7440	4.67692
$345$	19.0272	1.02439
$346$	52.8372	2.84055
$347$	−28.7558	−1.54369	−0.771847	−	0.635809i	$-0.780667\pi$
$347$	−28.7558	−1.54369	−0.771847	+	0.635809i	$0.780667\pi$
$348$	9.59810	0.514512
$349$	−7.60056	−0.406848	−0.203424	−	0.979091i	$-0.565207\pi$
$349$	−7.60056	−0.406848	−0.203424	+	0.979091i	$0.565207\pi$
$350$	−16.0269	−0.856676
$351$	31.9467	1.70519
$352$	−17.1124	−0.912091
$353$	−31.0886	−1.65468	−0.827341	−	0.561700i	$-0.810147\pi$
$353$	−31.0886	−1.65468	−0.827341	+	0.561700i	$0.810147\pi$
$354$	−99.3025	−5.27787
$355$	3.52095	0.186873
$356$	−31.0020	−1.64310
$357$	−19.8713	−1.05170
$358$	−0.206051	−0.0108901
$359$	27.5887	1.45607	0.728037	−	0.685538i	$-0.240433\pi$
$359$	27.5887	1.45607	0.728037	+	0.685538i	$0.240433\pi$
$360$	42.5109	2.24052
$361$	1.78086	0.0937295
$362$	62.9278	3.30741
$363$	−24.7587	−1.29949
$364$	−16.3604	−0.857516
$365$	−1.89124	−0.0989922
$366$	−106.695	−5.57705
$367$	27.6723	1.44448	0.722241	−	0.691642i	$-0.243112\pi$
$367$	27.6723	1.44448	0.722241	+	0.691642i	$0.243112\pi$
$368$	−66.5559	−3.46946
$369$	59.2682	3.08538
$370$	−13.4473	−0.699090
$371$	−18.5861	−0.964941
$372$	−20.5693	−1.06647
$373$	−8.14428	−0.421695	−0.210847	−	0.977519i	$-0.567622\pi$
$373$	−8.14428	−0.421695	−0.210847	+	0.977519i	$0.567622\pi$
$374$	−20.4486	−1.05737
$375$	24.4941	1.26487
$376$	−67.0057	−3.45556
$377$	1.51984	0.0782756
$378$	49.2414	2.53271
$379$	−1.56581	−0.0804301	−0.0402150	−	0.999191i	$-0.512804\pi$
$379$	−1.56581	−0.0804301	−0.0402150	+	0.999191i	$0.512804\pi$
$380$	−17.9143	−0.918984
$381$	−38.8473	−1.99021
$382$	−30.3969	−1.55524
$383$	24.8717	1.27088	0.635442	−	0.772149i	$-0.280818\pi$
$383$	24.8717	1.27088	0.635442	+	0.772149i	$0.280818\pi$
$384$	7.85064	0.400626
$385$	2.11384	0.107731
$386$	−18.8387	−0.958866
$387$	−86.3212	−4.38795
$388$	76.6903	3.89336
$389$	−27.2585	−1.38206	−0.691031	−	0.722825i	$-0.742843\pi$
$389$	−27.2585	−1.38206	−0.691031	+	0.722825i	$0.742843\pi$
$390$	16.4529	0.833125
$391$	−31.6476	−1.60049
$392$	35.7540	1.80585
$393$	−21.4965	−1.08435
$394$	−9.29461	−0.468256
$395$	9.59027	0.482539
$396$	61.4158	3.08626
$397$	18.3168	0.919292	0.459646	−	0.888102i	$-0.347976\pi$
$397$	18.3168	0.919292	0.459646	+	0.888102i	$0.347976\pi$
$398$	−53.8092	−2.69721
$399$	−20.7237	−1.03749
$400$	−39.7163	−1.98581
$401$	30.4433	1.52027	0.760133	−	0.649767i	$-0.225134\pi$
$401$	30.4433	1.52027	0.760133	+	0.649767i	$0.225134\pi$
$402$	−81.2864	−4.05420
$403$	−3.25710	−0.162248
$404$	−58.5737	−2.91415
$405$	−17.1692	−0.853143
$406$	2.34262	0.116262
$407$	−11.2771	−0.558985
$408$	−100.318	−4.96649
$409$	−21.2894	−1.05269	−0.526346	−	0.850270i	$-0.676438\pi$
$409$	−21.2894	−1.05269	−0.526346	+	0.850270i	$0.676438\pi$
$410$	17.7412	0.876177
$411$	16.2348	0.800805
$412$	80.9387	3.98756
$413$	−17.0740	−0.840155
$414$	134.928	6.63133
$415$	−10.6214	−0.521382
$416$	−22.9010	−1.12281
$417$	−48.5192	−2.37600
$418$	−21.3258	−1.04308
$419$	33.1648	1.62021	0.810104	−	0.586286i	$-0.199410\pi$
$419$	33.1648	1.62021	0.810104	+	0.586286i	$0.199410\pi$
$420$	17.8651	0.871726
$421$	−1.26217	−0.0615143	−0.0307571	−	0.999527i	$-0.509792\pi$
$421$	−1.26217	−0.0615143	−0.0307571	+	0.999527i	$0.509792\pi$
$422$	−54.3749	−2.64693
$423$	66.6792	3.24205
$424$	−93.8300	−4.55679
$425$	−18.8853	−0.916070
$426$	35.4241	1.71630
$427$	−18.3451	−0.887780
$428$	9.24620	0.446932
$429$	13.7977	0.666157
$430$	−25.8392	−1.24608
$431$	−1.06547	−0.0513221	−0.0256610	−	0.999671i	$-0.508169\pi$
$431$	−1.06547	−0.0513221	−0.0256610	+	0.999671i	$0.508169\pi$
$432$	122.025	5.87093
$433$	−0.603457	−0.0290003	−0.0145001	−	0.999895i	$-0.504616\pi$
$433$	−0.603457	−0.0290003	−0.0145001	+	0.999895i	$0.504616\pi$
$434$	−5.02038	−0.240986
$435$	−1.65962	−0.0795728
$436$	−22.5316	−1.07907
$437$	−33.0053	−1.57886
$438$	−19.0277	−0.909179
$439$	34.6997	1.65613	0.828064	−	0.560633i	$-0.189442\pi$
$439$	34.6997	1.65613	0.828064	+	0.560633i	$0.189442\pi$
$440$	10.6715	0.508744
$441$	−35.5797	−1.69427
$442$	−27.3658	−1.30166
$443$	28.8771	1.37199	0.685997	−	0.727605i	$-0.259366\pi$
$443$	28.8771	1.37199	0.685997	+	0.727605i	$0.259366\pi$
$444$	−95.3082	−4.52312
$445$	5.36060	0.254117
$446$	32.3926	1.53383
$447$	11.1423	0.527015
$448$	−9.08234	−0.429100
$449$	−11.3623	−0.536219	−0.268110	−	0.963388i	$-0.586399\pi$
$449$	−11.3623	−0.536219	−0.268110	+	0.963388i	$0.586399\pi$
$450$	80.5161	3.79557
$451$	14.8781	0.700581
$452$	17.7021	0.832636
$453$	−48.1677	−2.26312
$454$	52.0883	2.44462
$455$	2.82889	0.132621
$456$	−104.622	−4.89937
$457$	1.63769	0.0766081	0.0383041	−	0.999266i	$-0.487804\pi$
$457$	1.63769	0.0766081	0.0383041	+	0.999266i	$0.487804\pi$
$458$	6.74382	0.315118
$459$	58.0234	2.70830
$460$	28.4524	1.32660
$461$	−2.42125	−0.112769	−0.0563844	−	0.998409i	$-0.517957\pi$
$461$	−2.42125	−0.112769	−0.0563844	+	0.998409i	$0.517957\pi$
$462$	21.2672	0.989441
$463$	19.9211	0.925812	0.462906	−	0.886407i	$-0.346807\pi$
$463$	19.9211	0.925812	0.462906	+	0.886407i	$0.346807\pi$
$464$	5.80525	0.269502
$465$	3.55667	0.164937
$466$	−24.9469	−1.15564
$467$	−15.1931	−0.703054	−0.351527	−	0.936178i	$-0.614337\pi$
$467$	−15.1931	−0.703054	−0.351527	+	0.936178i	$0.614337\pi$
$468$	82.1912	3.79929
$469$	−13.9763	−0.645365
$470$	19.9596	0.920668
$471$	45.4269	2.09316
$472$	−86.1962	−3.96750
$473$	−21.6692	−0.996350
$474$	96.4872	4.43180
$475$	−19.6954	−0.903688
$476$	−29.7146	−1.36197
$477$	93.3727	4.27524
$478$	57.3587	2.62353
$479$	11.0230	0.503656	0.251828	−	0.967772i	$-0.418968\pi$
$479$	11.0230	0.503656	0.251828	+	0.967772i	$0.418968\pi$
$480$	25.0073	1.14142
$481$	−15.0918	−0.688128
$482$	51.1272	2.32878
$483$	32.9146	1.49766
$484$	−37.0231	−1.68287
$485$	−13.2606	−0.602134
$486$	−69.1422	−3.13635
$487$	22.0897	1.00098	0.500491	−	0.865742i	$-0.333153\pi$
$487$	22.0897	1.00098	0.500491	+	0.865742i	$0.333153\pi$
$488$	−92.6133	−4.19241
$489$	49.8506	2.25432
$490$	−10.6504	−0.481134
$491$	11.7629	0.530853	0.265426	−	0.964131i	$-0.414487\pi$
$491$	11.7629	0.530853	0.265426	+	0.964131i	$0.414487\pi$
$492$	125.742	5.66888
$493$	2.76042	0.124323
$494$	−28.5398	−1.28407
$495$	−10.6195	−0.477311
$496$	−12.4410	−0.558617
$497$	6.09078	0.273209
$498$	−106.861	−4.78856
$499$	−6.27557	−0.280933	−0.140467	−	0.990085i	$-0.544860\pi$
$499$	−6.27557	−0.280933	−0.140467	+	0.990085i	$0.544860\pi$
$500$	36.6275	1.63803
$501$	44.8969	2.00584
$502$	1.85767	0.0829120
$503$	5.91347	0.263669	0.131834	−	0.991272i	$-0.457913\pi$
$503$	5.91347	0.263669	0.131834	+	0.991272i	$0.457913\pi$
$504$	73.5384	3.27566
$505$	10.1281	0.450693
$506$	33.8708	1.50574
$507$	−22.9798	−1.02057
$508$	−58.0906	−2.57736
$509$	−20.6735	−0.916337	−0.458169	−	0.888865i	$-0.651494\pi$
$509$	−20.6735	−0.916337	−0.458169	+	0.888865i	$0.651494\pi$
$510$	29.8827	1.32323
$511$	−3.27160	−0.144727
$512$	44.8775	1.98332
$513$	60.5126	2.67170
$514$	−21.8726	−0.964757
$515$	−13.9952	−0.616703
$516$	−183.137	−8.06215
$517$	16.7385	0.736156
$518$	−23.2620	−1.02207
$519$	−64.7530	−2.84234
$520$	14.2814	0.626281
$521$	−19.8494	−0.869618	−0.434809	−	0.900523i	$-0.643184\pi$
$521$	−19.8494	−0.869618	−0.434809	+	0.900523i	$0.643184\pi$
$522$	−11.7689	−0.515110
$523$	42.9355	1.87744	0.938720	−	0.344681i	$-0.112013\pi$
$523$	42.9355	1.87744	0.938720	+	0.344681i	$0.112013\pi$
$524$	−32.1449	−1.40426
$525$	19.6413	0.857217
$526$	35.9212	1.56624
$527$	−5.91574	−0.257694
$528$	52.7022	2.29357
$529$	29.4207	1.27916
$530$	27.9500	1.21407
$531$	85.7762	3.72237
$532$	−30.9894	−1.34356
$533$	19.9109	0.862438
$534$	53.9328	2.33390
$535$	−1.59877	−0.0691210
$536$	−70.5580	−3.04764
$537$	0.252519	0.0108970
$538$	−25.0523	−1.08008
$539$	−8.93157	−0.384710
$540$	−52.1653	−2.24484
$541$	−3.01733	−0.129725	−0.0648626	−	0.997894i	$-0.520661\pi$
$541$	−3.01733	−0.129725	−0.0648626	+	0.997894i	$0.520661\pi$
$542$	65.1646	2.79906
$543$	−77.1192	−3.30950
$544$	−41.5942	−1.78333
$545$	3.89598	0.166885
$546$	28.4614	1.21803
$547$	−4.87379	−0.208388	−0.104194	−	0.994557i	$-0.533226\pi$
$547$	−4.87379	−0.208388	−0.104194	+	0.994557i	$0.533226\pi$
$548$	24.2769	1.03706
$549$	92.1619	3.93337
$550$	20.2119	0.861840
$551$	2.87884	0.122643
$552$	166.166	7.07250
$553$	16.5899	0.705475
$554$	−37.0504	−1.57412
$555$	16.4799	0.699531
$556$	−72.5536	−3.07696
$557$	−21.0920	−0.893698	−0.446849	−	0.894609i	$-0.647454\pi$
$557$	−21.0920	−0.893698	−0.446849	+	0.894609i	$0.647454\pi$
$558$	25.2214	1.06771
$559$	−28.9993	−1.22654
$560$	10.8054	0.456610
$561$	25.0601	1.05804
$562$	−57.2126	−2.41337
$563$	15.0170	0.632892	0.316446	−	0.948611i	$-0.397510\pi$
$563$	15.0170	0.632892	0.316446	+	0.948611i	$0.397510\pi$
$564$	141.465	5.95674
$565$	−3.06089	−0.128773
$566$	−53.9314	−2.26690
$567$	−29.7004	−1.24730
$568$	30.7487	1.29019
$569$	4.00846	0.168043	0.0840217	−	0.996464i	$-0.473223\pi$
$569$	4.00846	0.168043	0.0840217	+	0.996464i	$0.473223\pi$
$570$	31.1647	1.30534
$571$	−31.6235	−1.32340	−0.661702	−	0.749767i	$-0.730166\pi$
$571$	−31.6235	−1.32340	−0.661702	+	0.749767i	$0.730166\pi$
$572$	20.6324	0.862685
$573$	37.2520	1.55622
$574$	30.6900	1.28098
$575$	31.2813	1.30452
$576$	45.6279	1.90116
$577$	−6.73542	−0.280399	−0.140200	−	0.990123i	$-0.544774\pi$
$577$	−6.73542	−0.280399	−0.140200	+	0.990123i	$0.544774\pi$
$578$	−5.47956	−0.227919
$579$	23.0872	0.959472
$580$	−2.48173	−0.103048
$581$	−18.3736	−0.762264
$582$	−133.415	−5.53021
$583$	23.4393	0.970758
$584$	−16.5164	−0.683452
$585$	−14.2118	−0.587585
$586$	−8.22685	−0.339848
$587$	33.9177	1.39993	0.699967	−	0.714175i	$-0.253198\pi$
$587$	33.9177	1.39993	0.699967	+	0.714175i	$0.253198\pi$
$588$	−75.4850	−3.11295
$589$	−6.16953	−0.254211
$590$	25.6761	1.05707
$591$	11.3907	0.468551
$592$	−57.6455	−2.36921
$593$	18.6364	0.765304	0.382652	−	0.923893i	$-0.375011\pi$
$593$	18.6364	0.765304	0.382652	+	0.923893i	$0.375011\pi$
$594$	−62.0995	−2.54797
$595$	5.13800	0.210638
$596$	16.6618	0.682493
$597$	65.9442	2.69891
$598$	45.3284	1.85362
$599$	5.11087	0.208824	0.104412	−	0.994534i	$-0.466704\pi$
$599$	5.11087	0.208824	0.104412	+	0.994534i	$0.466704\pi$
$600$	99.1572	4.04808
$601$	37.8996	1.54596	0.772978	−	0.634433i	$-0.218766\pi$
$601$	37.8996	1.54596	0.772978	+	0.634433i	$0.218766\pi$
$602$	−44.6985	−1.82177
$603$	70.2141	2.85934
$604$	−72.0279	−2.93077
$605$	6.40171	0.260267
$606$	101.898	4.13932
$607$	−23.1216	−0.938478	−0.469239	−	0.883071i	$-0.655472\pi$
$607$	−23.1216	−0.938478	−0.469239	+	0.883071i	$0.655472\pi$
$608$	−43.3785	−1.75923
$609$	−2.87093	−0.116336
$610$	27.5876	1.11699
$611$	22.4006	0.906232
$612$	149.280	6.03431
$613$	−8.32519	−0.336251	−0.168126	−	0.985766i	$-0.553771\pi$
$613$	−8.32519	−0.336251	−0.168126	+	0.985766i	$0.553771\pi$
$614$	−8.34522	−0.336786
$615$	−21.7422	−0.876730
$616$	18.4603	0.743787
$617$	40.7735	1.64148	0.820739	−	0.571303i	$-0.193562\pi$
$617$	40.7735	1.64148	0.820739	+	0.571303i	$0.193562\pi$
$618$	−140.805	−5.66402
$619$	1.31896	0.0530135	0.0265067	−	0.999649i	$-0.491562\pi$
$619$	1.31896	0.0530135	0.0265067	+	0.999649i	$0.491562\pi$
$620$	5.31849	0.213596
$621$	−96.1093	−3.85673
$622$	−38.4880	−1.54323
$623$	9.27314	0.371521
$624$	70.5299	2.82346
$625$	15.2692	0.610767
$626$	−47.4011	−1.89453
$627$	26.1352	1.04374
$628$	67.9294	2.71068
$629$	−27.4107	−1.09294
$630$	−21.9056	−0.872738
$631$	21.0886	0.839525	0.419763	−	0.907634i	$-0.362113\pi$
$631$	21.0886	0.839525	0.419763	+	0.907634i	$0.362113\pi$
$632$	83.7526	3.33150
$633$	66.6374	2.64860
$634$	−6.90410	−0.274197
$635$	10.0445	0.398605
$636$	198.097	7.85506
$637$	−11.9529	−0.473590
$638$	−2.95434	−0.116963
$639$	−30.5989	−1.21047
$640$	−2.02990	−0.0802387
$641$	−50.4418	−1.99233	−0.996166	−	0.0874886i	$-0.972116\pi$
$641$	−50.4418	−1.99233	−0.996166	+	0.0874886i	$0.972116\pi$
$642$	−16.0852	−0.634832
$643$	−28.0031	−1.10433	−0.552167	−	0.833733i	$-0.686199\pi$
$643$	−28.0031	−1.10433	−0.552167	+	0.833733i	$0.686199\pi$
$644$	49.2190	1.93950
$645$	31.6664	1.24686
$646$	−51.8357	−2.03945
$647$	−14.8178	−0.582549	−0.291274	−	0.956640i	$-0.594079\pi$
$647$	−14.8178	−0.582549	−0.291274	+	0.956640i	$0.594079\pi$
$648$	−149.940	−5.89019
$649$	21.5324	0.845219
$650$	27.0491	1.06095
$651$	6.15257	0.241138
$652$	74.5444	2.91938
$653$	−20.3400	−0.795966	−0.397983	−	0.917393i	$-0.630290\pi$
$653$	−20.3400	−0.795966	−0.397983	+	0.917393i	$0.630290\pi$
$654$	39.1972	1.53273
$655$	5.55823	0.217178
$656$	76.0528	2.96936
$657$	16.4359	0.641225
$658$	34.5275	1.34602
$659$	10.7671	0.419426	0.209713	−	0.977763i	$-0.432747\pi$
$659$	10.7671	0.419426	0.209713	+	0.977763i	$0.432747\pi$
$660$	−22.5300	−0.876981
$661$	−38.0378	−1.47950	−0.739750	−	0.672882i	$-0.765056\pi$
$661$	−38.0378	−1.47950	−0.739750	+	0.672882i	$0.765056\pi$
$662$	−56.0578	−2.17875
$663$	33.5373	1.30248
$664$	−92.7572	−3.59968
$665$	5.35842	0.207791
$666$	116.864	4.52838
$667$	−4.57233	−0.177041
$668$	67.1369	2.59760
$669$	−39.6977	−1.53480
$670$	21.0178	0.811987
$671$	23.1354	0.893131
$672$	43.2593	1.66876
$673$	3.67183	0.141538	0.0707692	−	0.997493i	$-0.477455\pi$
$673$	3.67183	0.141538	0.0707692	+	0.997493i	$0.477455\pi$
$674$	59.1453	2.27819
$675$	−57.3519	−2.20747
$676$	−34.3630	−1.32166
$677$	−27.3889	−1.05264	−0.526320	−	0.850287i	$-0.676429\pi$
$677$	−27.3889	−1.05264	−0.526320	+	0.850287i	$0.676429\pi$
$678$	−30.7955	−1.18269
$679$	−22.9392	−0.880324
$680$	25.9387	0.994704
$681$	−63.8351	−2.44617
$682$	6.33132	0.242439
$683$	−30.3469	−1.16119	−0.580596	−	0.814191i	$-0.697181\pi$
$683$	−30.3469	−1.16119	−0.580596	+	0.814191i	$0.697181\pi$
$684$	155.685	5.95275
$685$	−4.19775	−0.160388
$686$	−44.3903	−1.69483
$687$	−8.26467	−0.315317
$688$	−110.767	−4.22296
$689$	31.3682	1.19503
$690$	−49.4974	−1.88433
$691$	2.50557	0.0953164	0.0476582	−	0.998864i	$-0.484824\pi$
$691$	2.50557	0.0953164	0.0476582	+	0.998864i	$0.484824\pi$
$692$	−96.8288	−3.68088
$693$	−18.3703	−0.697832
$694$	74.8055	2.83958
$695$	12.5453	0.475872
$696$	−14.4936	−0.549379
$697$	36.1634	1.36979
$698$	19.7721	0.748385
$699$	30.5729	1.15637
$700$	29.3707	1.11011
$701$	24.3239	0.918700	0.459350	−	0.888255i	$-0.348082\pi$
$701$	24.3239	0.918700	0.459350	+	0.888255i	$0.348082\pi$
$702$	−83.1061	−3.13664
$703$	−28.5866	−1.07816
$704$	11.4539	0.431687
$705$	−24.4609	−0.921250
$706$	80.8741	3.04374
$707$	17.5202	0.658916
$708$	181.980	6.83924
$709$	25.5022	0.957756	0.478878	−	0.877881i	$-0.341044\pi$
$709$	25.5022	0.957756	0.478878	+	0.877881i	$0.341044\pi$
$710$	−9.15940	−0.343746
$711$	−83.3444	−3.12566
$712$	46.8146	1.75445
$713$	9.79877	0.366967
$714$	51.6932	1.93457
$715$	−3.56758	−0.133420
$716$	0.377606	0.0141118
$717$	−70.2941	−2.62518
$718$	−71.7692	−2.67840
$719$	5.85169	0.218231	0.109116	−	0.994029i	$-0.465198\pi$
$719$	5.85169	0.218231	0.109116	+	0.994029i	$0.465198\pi$
$720$	−54.2840	−2.02305
$721$	−24.2099	−0.901624
$722$	−4.63273	−0.172413
$723$	−62.6573	−2.33025
$724$	−115.321	−4.28586
$725$	−2.72847	−0.101333
$726$	64.4073	2.39038
$727$	−30.9860	−1.14921	−0.574603	−	0.818432i	$-0.694844\pi$
$727$	−30.9860	−1.14921	−0.574603	+	0.818432i	$0.694844\pi$
$728$	24.7049	0.915626
$729$	22.2502	0.824082
$730$	4.91988	0.182093
$731$	−52.6702	−1.94808
$732$	195.528	7.22693
$733$	37.1073	1.37059	0.685295	−	0.728266i	$-0.259673\pi$
$733$	37.1073	1.37059	0.685295	+	0.728266i	$0.259673\pi$
$734$	−71.9867	−2.65708
$735$	13.0522	0.481438
$736$	68.8961	2.53954
$737$	17.6258	0.649256
$738$	−154.180	−5.67546
$739$	34.8479	1.28190	0.640950	−	0.767583i	$-0.278541\pi$
$739$	34.8479	1.28190	0.640950	+	0.767583i	$0.278541\pi$
$740$	24.6433	0.905905
$741$	34.9760	1.28488
$742$	48.3499	1.77498
$743$	−37.7360	−1.38440	−0.692200	−	0.721706i	$-0.743358\pi$
$743$	−37.7360	−1.38440	−0.692200	+	0.721706i	$0.743358\pi$
$744$	31.0607	1.13874
$745$	−2.88101	−0.105552
$746$	21.1865	0.775695
$747$	92.3051	3.37727
$748$	37.4738	1.37018
$749$	−2.76567	−0.101055
$750$	−63.7191	−2.32669
$751$	−32.7059	−1.19346	−0.596728	−	0.802443i	$-0.703533\pi$
$751$	−32.7059	−1.19346	−0.596728	+	0.802443i	$0.703533\pi$
$752$	85.5625	3.12014
$753$	−2.27661	−0.0829643
$754$	−3.95371	−0.143986
$755$	12.4544	0.453263
$756$	−90.2392	−3.28197
$757$	3.73832	0.135871	0.0679357	−	0.997690i	$-0.478359\pi$
$757$	3.73832	0.135871	0.0679357	+	0.997690i	$0.478359\pi$
$758$	4.07329	0.147949
$759$	−41.5093	−1.50669
$760$	27.0515	0.981260
$761$	−24.9894	−0.905867	−0.452933	−	0.891544i	$-0.649622\pi$
$761$	−24.9894	−0.905867	−0.452933	+	0.891544i	$0.649622\pi$
$762$	101.058	3.66093
$763$	6.73953	0.243987
$764$	55.7050	2.01533
$765$	−25.8123	−0.933246
$766$	−64.7013	−2.33775
$767$	28.8162	1.04049
$768$	−61.0339	−2.20237
$769$	−17.1057	−0.616847	−0.308424	−	0.951249i	$-0.599801\pi$
$769$	−17.1057	−0.616847	−0.308424	+	0.951249i	$0.599801\pi$
$770$	−5.49894	−0.198168
$771$	26.8052	0.965367
$772$	34.5236	1.24253
$773$	−46.5027	−1.67259	−0.836293	−	0.548282i	$-0.815282\pi$
$773$	−46.5027	−1.67259	−0.836293	+	0.548282i	$0.815282\pi$
$774$	224.556	8.07151
$775$	5.84728	0.210040
$776$	−115.806	−4.15720
$777$	28.5080	1.02272
$778$	70.9104	2.54226
$779$	37.7148	1.35127
$780$	−30.1514	−1.07959
$781$	−7.68122	−0.274856
$782$	82.3282	2.94405
$783$	8.38301	0.299584
$784$	−45.6558	−1.63056
$785$	−11.7458	−0.419225
$786$	55.9210	1.99464
$787$	−31.1264	−1.10954	−0.554769	−	0.832005i	$-0.687193\pi$
$787$	−31.1264	−1.10954	−0.554769	+	0.832005i	$0.687193\pi$
$788$	17.0332	0.606782
$789$	−44.0221	−1.56723
$790$	−24.9481	−0.887615
$791$	−5.29494	−0.188267
$792$	−92.7410	−3.29541
$793$	30.9615	1.09947
$794$	−47.6493	−1.69101
$795$	−34.2532	−1.21484
$796$	98.6100	3.49514
$797$	26.8002	0.949312	0.474656	−	0.880171i	$-0.342573\pi$
$797$	26.8002	0.949312	0.474656	+	0.880171i	$0.342573\pi$
$798$	53.9108	1.90842
$799$	40.6853	1.43934
$800$	41.1128	1.45356
$801$	−46.5864	−1.64605
$802$	−79.1953	−2.79648
$803$	4.12589	0.145600
$804$	148.964	5.25357
$805$	−8.51053	−0.299957
$806$	8.47304	0.298450
$807$	30.7021	1.08076
$808$	88.4492	3.11163
$809$	15.1798	0.533694	0.266847	−	0.963739i	$-0.414018\pi$
$809$	15.1798	0.533694	0.266847	+	0.963739i	$0.414018\pi$
$810$	44.6639	1.56933
$811$	−37.7197	−1.32452	−0.662259	−	0.749275i	$-0.730402\pi$
$811$	−37.7197	−1.32452	−0.662259	+	0.749275i	$0.730402\pi$
$812$	−4.29306	−0.150657
$813$	−79.8604	−2.80083
$814$	29.3363	1.02824
$815$	−12.8896	−0.451502
$816$	128.101	4.48442
$817$	−54.9298	−1.92175
$818$	55.3823	1.93640
$819$	−24.5845	−0.859053
$820$	−32.5123	−1.13538
$821$	20.2932	0.708238	0.354119	−	0.935200i	$-0.384781\pi$
$821$	20.2932	0.708238	0.354119	+	0.935200i	$0.384781\pi$
$822$	−42.2334	−1.47306
$823$	−24.6537	−0.859373	−0.429686	−	0.902978i	$-0.641376\pi$
$823$	−24.6537	−0.859373	−0.429686	+	0.902978i	$0.641376\pi$
$824$	−122.221	−4.25778
$825$	−24.7701	−0.862384
$826$	44.4162	1.54544
$827$	15.6082	0.542749	0.271375	−	0.962474i	$-0.412522\pi$
$827$	15.6082	0.542749	0.271375	+	0.962474i	$0.412522\pi$
$828$	−247.266	−8.59310
$829$	−10.0770	−0.349987	−0.174994	−	0.984570i	$-0.555991\pi$
$829$	−10.0770	−0.349987	−0.174994	+	0.984570i	$0.555991\pi$
$830$	27.6304	0.959067
$831$	45.4060	1.57512
$832$	15.3285	0.531420
$833$	−21.7095	−0.752190
$834$	126.218	4.37058
$835$	−11.6087	−0.401737
$836$	39.0814	1.35166
$837$	−17.9653	−0.620971
$838$	−86.2751	−2.98032
$839$	37.5963	1.29797	0.648983	−	0.760803i	$-0.275194\pi$
$839$	37.5963	1.29797	0.648983	+	0.760803i	$0.275194\pi$
$840$	−26.9771	−0.930799
$841$	−28.6012	−0.986248
$842$	3.28341	0.113154
$843$	70.1151	2.41489
$844$	99.6467	3.42998
$845$	5.94176	0.204403
$846$	−173.459	−5.96366
$847$	11.0741	0.380511
$848$	119.816	4.11448
$849$	66.0939	2.26834
$850$	49.1282	1.68508
$851$	45.4027	1.55639
$852$	−64.9177	−2.22404
$853$	−42.3545	−1.45019	−0.725095	−	0.688649i	$-0.758204\pi$
$853$	−42.3545	−1.45019	−0.725095	+	0.688649i	$0.758204\pi$
$854$	47.7229	1.63304
$855$	−26.9196	−0.920632
$856$	−13.9622	−0.477219
$857$	31.8298	1.08729	0.543643	−	0.839317i	$-0.317045\pi$
$857$	31.8298	1.08729	0.543643	+	0.839317i	$0.317045\pi$
$858$	−35.8933	−1.22538
$859$	−27.2677	−0.930361	−0.465181	−	0.885216i	$-0.654011\pi$
$859$	−27.2677	−0.930361	−0.465181	+	0.885216i	$0.654011\pi$
$860$	47.3526	1.61471
$861$	−37.6112	−1.28178
$862$	2.77173	0.0944054
$863$	−9.87885	−0.336280	−0.168140	−	0.985763i	$-0.553776\pi$
$863$	−9.87885	−0.336280	−0.168140	+	0.985763i	$0.553776\pi$
$864$	−126.316	−4.29734
$865$	16.7428	0.569272
$866$	1.56983	0.0533451
$867$	6.71529	0.228063
$868$	9.20029	0.312278
$869$	−20.9219	−0.709727
$870$	4.31735	0.146372
$871$	23.5882	0.799255
$872$	34.0239	1.15219
$873$	115.242	3.90034
$874$	85.8600	2.90426
$875$	−10.9558	−0.370374
$876$	34.8699	1.17815
$877$	9.42358	0.318212	0.159106	−	0.987262i	$-0.449139\pi$
$877$	9.42358	0.318212	0.159106	+	0.987262i	$0.449139\pi$
$878$	−90.2680	−3.04640
$879$	10.0822	0.340063
$880$	−13.6269	−0.459363
$881$	13.1083	0.441628	0.220814	−	0.975316i	$-0.429129\pi$
$881$	13.1083	0.441628	0.220814	+	0.975316i	$0.429129\pi$
$882$	92.5572	3.11656
$883$	36.1622	1.21696	0.608478	−	0.793571i	$-0.291780\pi$
$883$	36.1622	1.21696	0.608478	+	0.793571i	$0.291780\pi$
$884$	50.1502	1.68673
$885$	−31.4665	−1.05773
$886$	−75.1210	−2.52374
$887$	−45.8068	−1.53804	−0.769021	−	0.639224i	$-0.779256\pi$
$887$	−45.8068	−1.53804	−0.769021	+	0.639224i	$0.779256\pi$
$888$	143.920	4.82964
$889$	17.3757	0.582763
$890$	−13.9451	−0.467440
$891$	37.4559	1.25482
$892$	−59.3623	−1.98760
$893$	42.4307	1.41989
$894$	−28.9857	−0.969428
$895$	−0.0652925	−0.00218249
$896$	−3.51145	−0.117309
$897$	−55.5508	−1.85479
$898$	29.5579	0.986359
$899$	−0.854685	−0.0285053
$900$	−147.553	−4.91843
$901$	56.9728	1.89804
$902$	−38.7039	−1.28870
$903$	54.7788	1.82292
$904$	−26.7310	−0.889060
$905$	19.9403	0.662837
$906$	125.304	4.16293
$907$	−39.2536	−1.30340	−0.651698	−	0.758479i	$-0.725943\pi$
$907$	−39.2536	−1.30340	−0.651698	+	0.758479i	$0.725943\pi$
$908$	−95.4563	−3.16783
$909$	−88.0181	−2.91938
$910$	−7.35909	−0.243951
$911$	−22.2348	−0.736670	−0.368335	−	0.929693i	$-0.620072\pi$
$911$	−22.2348	−0.736670	−0.368335	+	0.929693i	$0.620072\pi$
$912$	133.596	4.42381
$913$	23.1713	0.766859
$914$	−4.26030	−0.140918
$915$	−33.8091	−1.11769
$916$	−12.3586	−0.408341
$917$	9.61500	0.317515
$918$	−150.942	−4.98184
$919$	−44.3861	−1.46416	−0.732080	−	0.681218i	$-0.761450\pi$
$919$	−44.3861	−1.46416	−0.732080	+	0.681218i	$0.761450\pi$
$920$	−42.9646	−1.41650
$921$	10.2272	0.336998
$922$	6.29864	0.207435
$923$	−10.2796	−0.338356
$924$	−38.9740	−1.28215
$925$	27.0934	0.890827
$926$	−51.8228	−1.70300
$927$	121.626	3.99471
$928$	−6.00937	−0.197267
$929$	36.2956	1.19082	0.595411	−	0.803422i	$-0.296989\pi$
$929$	36.2956	1.19082	0.595411	+	0.803422i	$0.296989\pi$
$930$	−9.25233	−0.303396
$931$	−22.6409	−0.742024
$932$	45.7173	1.49752
$933$	47.1677	1.54420
$934$	39.5234	1.29325
$935$	−6.47965	−0.211907
$936$	−124.113	−4.05675
$937$	−39.7978	−1.30014	−0.650069	−	0.759875i	$-0.725260\pi$
$937$	−39.7978	−1.30014	−0.650069	+	0.759875i	$0.725260\pi$
$938$	36.3580	1.18713
$939$	58.0909	1.89573
$940$	−36.5777	−1.19303
$941$	−19.7247	−0.643006	−0.321503	−	0.946909i	$-0.604188\pi$
$941$	−19.7247	−0.643006	−0.321503	+	0.946909i	$0.604188\pi$
$942$	−118.174	−3.85031
$943$	−59.9007	−1.95063
$944$	110.068	3.58240
$945$	15.6034	0.507578
$946$	56.3703	1.83276
$947$	−39.6986	−1.29003	−0.645016	−	0.764169i	$-0.723149\pi$
$947$	−39.6986	−1.29003	−0.645016	+	0.764169i	$0.723149\pi$
$948$	−176.821	−5.74289
$949$	5.52157	0.179238
$950$	51.2357	1.66231
$951$	8.46111	0.274370
$952$	44.8706	1.45426
$953$	−52.7575	−1.70898	−0.854491	−	0.519467i	$-0.826131\pi$
$953$	−52.7575	−1.70898	−0.854491	+	0.519467i	$0.826131\pi$
$954$	−242.900	−7.86418
$955$	−9.63202	−0.311685
$956$	−105.115	−3.39966
$957$	3.62060	0.117037
$958$	−28.6754	−0.926460
$959$	−7.26156	−0.234488
$960$	−16.7383	−0.540227
$961$	−29.1684	−0.940915
$962$	39.2599	1.26579
$963$	13.8942	0.447734
$964$	−93.6951	−3.01772
$965$	−5.96953	−0.192166
$966$	−85.6240	−2.75491
$967$	−9.53586	−0.306653	−0.153326	−	0.988176i	$-0.548999\pi$
$967$	−9.53586	−0.306653	−0.153326	+	0.988176i	$0.548999\pi$
$968$	55.9067	1.79691
$969$	63.5255	2.04073
$970$	34.4962	1.10761
$971$	−38.3400	−1.23039	−0.615194	−	0.788375i	$-0.710922\pi$
$971$	−38.3400	−1.23039	−0.615194	+	0.788375i	$0.710922\pi$
$972$	126.709	4.06420
$973$	21.7018	0.695728
$974$	−57.4643	−1.84127
$975$	−33.1492	−1.06162
$976$	118.262	3.78547
$977$	12.5427	0.401277	0.200639	−	0.979665i	$-0.435698\pi$
$977$	12.5427	0.401277	0.200639	+	0.979665i	$0.435698\pi$
$978$	−129.681	−4.14676
$979$	−11.6946	−0.373760
$980$	19.5177	0.623471
$981$	−33.8581	−1.08100
$982$	−30.6001	−0.976487
$983$	9.55640	0.304802	0.152401	−	0.988319i	$-0.451300\pi$
$983$	9.55640	0.304802	0.152401	+	0.988319i	$0.451300\pi$
$984$	−189.876	−6.05304
$985$	−2.94523	−0.0938429
$986$	−7.18096	−0.228688
$987$	−42.3141	−1.34687
$988$	52.3016	1.66394
$989$	87.2424	2.77415
$990$	27.6256	0.877999
$991$	0.216805	0.00688705	0.00344353	−	0.999994i	$-0.498904\pi$
$991$	0.216805	0.00688705	0.00344353	+	0.999994i	$0.498904\pi$
$992$	12.8784	0.408891
$993$	68.6999	2.18012
$994$	−15.8446	−0.502559
$995$	−17.0508	−0.540547
$996$	195.832	6.20518
$997$	−17.5624	−0.556208	−0.278104	−	0.960551i	$-0.589706\pi$
$997$	−17.5624	−0.556208	−0.278104	+	0.960551i	$0.589706\pi$
$998$	16.3253	0.516768
$999$	−83.2424	−2.63367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.9	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-2.60140 q^{2} +3.18807 q^{3} +4.76730 q^{4} -0.824320 q^{5} -8.29345 q^{6} -1.42597 q^{7} -7.19885 q^{8} +7.16377 q^{9} +O(q^{10})\)	\(q-2.60140 q^{2} +3.18807 q^{3} +4.76730 q^{4} -0.824320 q^{5} -8.29345 q^{6} -1.42597 q^{7} -7.19885 q^{8} +7.16377 q^{9} +2.14439 q^{10} +1.79832 q^{11} +15.1985 q^{12} +2.40664 q^{13} +3.70951 q^{14} -2.62799 q^{15} +9.19252 q^{16} +4.37109 q^{17} -18.6358 q^{18} +4.55860 q^{19} -3.92978 q^{20} -4.54607 q^{21} -4.67815 q^{22} -7.24022 q^{23} -22.9504 q^{24} -4.32050 q^{25} -6.26064 q^{26} +13.2744 q^{27} -6.79800 q^{28} +0.631518 q^{29} +6.83645 q^{30} -1.35338 q^{31} -9.51575 q^{32} +5.73316 q^{33} -11.3710 q^{34} +1.17545 q^{35} +34.1518 q^{36} -6.27091 q^{37} -11.8588 q^{38} +7.67253 q^{39} +5.93416 q^{40} +8.27333 q^{41} +11.8262 q^{42} -12.0497 q^{43} +8.57312 q^{44} -5.90524 q^{45} +18.8347 q^{46} +9.30783 q^{47} +29.3064 q^{48} -4.96662 q^{49} +11.2394 q^{50} +13.9353 q^{51} +11.4732 q^{52} +13.0340 q^{53} -34.5320 q^{54} -1.48239 q^{55} +10.2653 q^{56} +14.5331 q^{57} -1.64283 q^{58} +11.9736 q^{59} -12.5284 q^{60} +12.8650 q^{61} +3.52069 q^{62} -10.2153 q^{63} +6.36925 q^{64} -1.98384 q^{65} -14.9143 q^{66} +9.80128 q^{67} +20.8383 q^{68} -23.0823 q^{69} -3.05783 q^{70} -4.27134 q^{71} -51.5709 q^{72} +2.29431 q^{73} +16.3132 q^{74} -13.7740 q^{75} +21.7322 q^{76} -2.56434 q^{77} -19.9594 q^{78} -11.6342 q^{79} -7.57758 q^{80} +20.8283 q^{81} -21.5223 q^{82} +12.8850 q^{83} -21.6725 q^{84} -3.60317 q^{85} +31.3461 q^{86} +2.01332 q^{87} -12.9458 q^{88} -6.50306 q^{89} +15.3619 q^{90} -3.43179 q^{91} -34.5163 q^{92} -4.31467 q^{93} -24.2134 q^{94} -3.75775 q^{95} -30.3368 q^{96} +16.0867 q^{97} +12.9202 q^{98} +12.8827 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 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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