LMFDB - Embedded newform 5077.2.a.c.1.17

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			1.17
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)

$f(q)$	$=$	$q-2.43559 q^{2} +3.36410 q^{3} +3.93211 q^{4} +0.698081 q^{5} -8.19357 q^{6} +2.30447 q^{7} -4.70583 q^{8} +8.31717 q^{9} +O(q^{10})$	\(q-2.43559 q^{2} +3.36410 q^{3} +3.93211 q^{4} +0.698081 q^{5} -8.19357 q^{6} +2.30447 q^{7} -4.70583 q^{8} +8.31717 q^{9} -1.70024 q^{10} -5.80455 q^{11} +13.2280 q^{12} -5.40632 q^{13} -5.61274 q^{14} +2.34841 q^{15} +3.59726 q^{16} +0.263357 q^{17} -20.2572 q^{18} +1.83023 q^{19} +2.74493 q^{20} +7.75246 q^{21} +14.1375 q^{22} +8.68402 q^{23} -15.8309 q^{24} -4.51268 q^{25} +13.1676 q^{26} +17.8875 q^{27} +9.06141 q^{28} +4.98208 q^{29} -5.71978 q^{30} +8.70493 q^{31} +0.650197 q^{32} -19.5271 q^{33} -0.641430 q^{34} +1.60870 q^{35} +32.7040 q^{36} +4.86589 q^{37} -4.45770 q^{38} -18.1874 q^{39} -3.28505 q^{40} -2.49494 q^{41} -18.8818 q^{42} -8.28345 q^{43} -22.8241 q^{44} +5.80606 q^{45} -21.1507 q^{46} +12.0630 q^{47} +12.1015 q^{48} -1.68943 q^{49} +10.9911 q^{50} +0.885958 q^{51} -21.2583 q^{52} -3.11653 q^{53} -43.5666 q^{54} -4.05205 q^{55} -10.8444 q^{56} +6.15709 q^{57} -12.1343 q^{58} +8.14615 q^{59} +9.23422 q^{60} -9.99852 q^{61} -21.2017 q^{62} +19.1666 q^{63} -8.77814 q^{64} -3.77405 q^{65} +47.5600 q^{66} +9.95834 q^{67} +1.03555 q^{68} +29.2139 q^{69} -3.91815 q^{70} +3.63439 q^{71} -39.1392 q^{72} +6.71168 q^{73} -11.8513 q^{74} -15.1811 q^{75} +7.19668 q^{76} -13.3764 q^{77} +44.2971 q^{78} -4.60439 q^{79} +2.51118 q^{80} +35.2238 q^{81} +6.07665 q^{82} -3.46577 q^{83} +30.4835 q^{84} +0.183844 q^{85} +20.1751 q^{86} +16.7602 q^{87} +27.3152 q^{88} +6.50532 q^{89} -14.1412 q^{90} -12.4587 q^{91} +34.1465 q^{92} +29.2843 q^{93} -29.3805 q^{94} +1.27765 q^{95} +2.18733 q^{96} -16.3692 q^{97} +4.11477 q^{98} -48.2774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.43559	−1.72222	−0.861112	−	0.508416i	$-0.830231\pi$
$2$	−2.43559	−1.72222	−0.861112	+	0.508416i	$0.830231\pi$
$3$	3.36410	1.94226	0.971132	−	0.238543i	$-0.0766698\pi$
$3$	3.36410	1.94226	0.971132	+	0.238543i	$0.0766698\pi$
$4$	3.93211	1.96605
$5$	0.698081	0.312191	0.156096	−	0.987742i	$-0.450109\pi$
$5$	0.698081	0.312191	0.156096	+	0.987742i	$0.450109\pi$
$6$	−8.19357	−3.34501
$7$	2.30447	0.871007	0.435503	−	0.900187i	$-0.356570\pi$
$7$	2.30447	0.871007	0.435503	+	0.900187i	$0.356570\pi$
$8$	−4.70583	−1.66376
$9$	8.31717	2.77239
$10$	−1.70024	−0.537663
$11$	−5.80455	−1.75014	−0.875069	−	0.483999i	$-0.839184\pi$
$11$	−5.80455	−1.75014	−0.875069	+	0.483999i	$0.839184\pi$
$12$	13.2280	3.81860
$13$	−5.40632	−1.49944	−0.749722	−	0.661753i	$-0.769813\pi$
$13$	−5.40632	−1.49944	−0.749722	+	0.661753i	$0.769813\pi$
$14$	−5.61274	−1.50007
$15$	2.34841	0.606358
$16$	3.59726	0.899315
$17$	0.263357	0.0638734	0.0319367	−	0.999490i	$-0.489833\pi$
$17$	0.263357	0.0638734	0.0319367	+	0.999490i	$0.489833\pi$
$18$	−20.2572	−4.77467
$19$	1.83023	0.419884	0.209942	−	0.977714i	$-0.432672\pi$
$19$	1.83023	0.419884	0.209942	+	0.977714i	$0.432672\pi$
$20$	2.74493	0.613785
$21$	7.75246	1.69172
$22$	14.1375	3.01413
$23$	8.68402	1.81074	0.905372	−	0.424620i	$-0.139592\pi$
$23$	8.68402	1.81074	0.905372	+	0.424620i	$0.139592\pi$
$24$	−15.8309	−3.23146
$25$	−4.51268	−0.902537
$26$	13.1676	2.58238
$27$	17.8875	3.44245
$28$	9.06141	1.71245
$29$	4.98208	0.925150	0.462575	−	0.886580i	$-0.346926\pi$
$29$	4.98208	0.925150	0.462575	+	0.886580i	$0.346926\pi$
$30$	−5.71978	−1.04428
$31$	8.70493	1.56345	0.781726	−	0.623622i	$-0.214340\pi$
$31$	8.70493	1.56345	0.781726	+	0.623622i	$0.214340\pi$
$32$	0.650197	0.114940
$33$	−19.5271	−3.39923
$34$	−0.641430	−0.110004
$35$	1.60870	0.271921
$36$	32.7040	5.45067
$37$	4.86589	0.799947	0.399973	−	0.916527i	$-0.369019\pi$
$37$	4.86589	0.799947	0.399973	+	0.916527i	$0.369019\pi$
$38$	−4.45770	−0.723135
$39$	−18.1874	−2.91232
$40$	−3.28505	−0.519412
$41$	−2.49494	−0.389644	−0.194822	−	0.980839i	$-0.562413\pi$
$41$	−2.49494	−0.389644	−0.194822	+	0.980839i	$0.562413\pi$
$42$	−18.8818	−2.91353
$43$	−8.28345	−1.26321	−0.631607	−	0.775289i	$-0.717604\pi$
$43$	−8.28345	−1.26321	−0.631607	+	0.775289i	$0.717604\pi$
$44$	−22.8241	−3.44087
$45$	5.80606	0.865516
$46$	−21.1507	−3.11851
$47$	12.0630	1.75957	0.879785	−	0.475373i	$-0.157687\pi$
$47$	12.0630	1.75957	0.879785	+	0.475373i	$0.157687\pi$
$48$	12.1015	1.74671
$49$	−1.68943	−0.241347
$50$	10.9911	1.55437
$51$	0.885958	0.124059
$52$	−21.2583	−2.94799
$53$	−3.11653	−0.428088	−0.214044	−	0.976824i	$-0.568664\pi$
$53$	−3.11653	−0.428088	−0.214044	+	0.976824i	$0.568664\pi$
$54$	−43.5666	−5.92866
$55$	−4.05205	−0.546378
$56$	−10.8444	−1.44915
$57$	6.15709	0.815526
$58$	−12.1343	−1.59331
$59$	8.14615	1.06054	0.530269	−	0.847829i	$-0.322091\pi$
$59$	8.14615	1.06054	0.530269	+	0.847829i	$0.322091\pi$
$60$	9.23422	1.19213
$61$	−9.99852	−1.28018	−0.640090	−	0.768300i	$-0.721103\pi$
$61$	−9.99852	−1.28018	−0.640090	+	0.768300i	$0.721103\pi$
$62$	−21.2017	−2.69261
$63$	19.1666	2.41477
$64$	−8.77814	−1.09727
$65$	−3.77405	−0.468114
$66$	47.5600	5.85423
$67$	9.95834	1.21661	0.608303	−	0.793705i	$-0.291851\pi$
$67$	9.95834	1.21661	0.608303	+	0.793705i	$0.291851\pi$
$68$	1.03555	0.125579
$69$	29.2139	3.51694
$70$	−3.91815	−0.468308
$71$	3.63439	0.431322	0.215661	−	0.976468i	$-0.430809\pi$
$71$	3.63439	0.431322	0.215661	+	0.976468i	$0.430809\pi$
$72$	−39.1392	−4.61259
$73$	6.71168	0.785542	0.392771	−	0.919636i	$-0.371516\pi$
$73$	6.71168	0.785542	0.392771	+	0.919636i	$0.371516\pi$
$74$	−11.8513	−1.37769
$75$	−15.1811	−1.75296
$76$	7.19668	0.825515
$77$	−13.3764	−1.52438
$78$	44.2971	5.01566
$79$	−4.60439	−0.518034	−0.259017	−	0.965873i	$-0.583399\pi$
$79$	−4.60439	−0.518034	−0.259017	+	0.965873i	$0.583399\pi$
$80$	2.51118	0.280758
$81$	35.2238	3.91375
$82$	6.07665	0.671054
$83$	−3.46577	−0.380417	−0.190209	−	0.981744i	$-0.560916\pi$
$83$	−3.46577	−0.380417	−0.190209	+	0.981744i	$0.560916\pi$
$84$	30.4835	3.32602
$85$	0.183844	0.0199407
$86$	20.1751	2.17554
$87$	16.7602	1.79689
$88$	27.3152	2.91181
$89$	6.50532	0.689563	0.344781	−	0.938683i	$-0.387953\pi$
$89$	6.50532	0.689563	0.344781	+	0.938683i	$0.387953\pi$
$90$	−14.1412	−1.49061
$91$	−12.4587	−1.30603
$92$	34.1465	3.56002
$93$	29.2843	3.03664
$94$	−29.3805	−3.03037
$95$	1.27765	0.131084
$96$	2.18733	0.223243
$97$	−16.3692	−1.66204	−0.831018	−	0.556246i	$-0.812241\pi$
$97$	−16.3692	−1.66204	−0.831018	+	0.556246i	$0.812241\pi$
$98$	4.11477	0.415654
$99$	−48.2774	−4.85206
$100$	−17.7444	−1.77444
$101$	8.82414	0.878034	0.439017	−	0.898479i	$-0.355327\pi$
$101$	8.82414	0.878034	0.439017	+	0.898479i	$0.355327\pi$
$102$	−2.15783	−0.213657
$103$	−13.3868	−1.31904	−0.659521	−	0.751686i	$-0.729241\pi$
$103$	−13.3868	−1.31904	−0.659521	+	0.751686i	$0.729241\pi$
$104$	25.4412	2.49472
$105$	5.41184	0.528142
$106$	7.59060	0.737264
$107$	4.52122	0.437083	0.218541	−	0.975828i	$-0.429870\pi$
$107$	4.52122	0.437083	0.218541	+	0.975828i	$0.429870\pi$
$108$	70.3355	6.76804
$109$	19.3166	1.85019	0.925097	−	0.379732i	$-0.123984\pi$
$109$	19.3166	1.85019	0.925097	+	0.379732i	$0.123984\pi$
$110$	9.86913	0.940985
$111$	16.3693	1.55371
$112$	8.28977	0.783309
$113$	6.27471	0.590275	0.295138	−	0.955455i	$-0.404634\pi$
$113$	6.27471	0.590275	0.295138	+	0.955455i	$0.404634\pi$
$114$	−14.9962	−1.40452
$115$	6.06215	0.565298
$116$	19.5901	1.81889
$117$	−44.9653	−4.15704
$118$	−19.8407	−1.82649
$119$	0.606897	0.0556341
$120$	−11.0512	−1.00884
$121$	22.6928	2.06298
$122$	24.3523	2.20476
$123$	−8.39322	−0.756791
$124$	34.2287	3.07383
$125$	−6.64062	−0.593955
$126$	−46.6821	−4.15877
$127$	−13.6066	−1.20739	−0.603697	−	0.797214i	$-0.706306\pi$
$127$	−13.6066	−1.20739	−0.603697	+	0.797214i	$0.706306\pi$
$128$	20.0796	1.77480
$129$	−27.8664	−2.45350
$130$	9.19205	0.806196
$131$	19.1988	1.67741	0.838705	−	0.544586i	$-0.183313\pi$
$131$	19.1988	1.67741	0.838705	+	0.544586i	$0.183313\pi$
$132$	−76.7826	−6.68307
$133$	4.21771	0.365722
$134$	−24.2545	−2.09527
$135$	12.4869	1.07470
$136$	−1.23931	−0.106270
$137$	−10.0487	−0.858516	−0.429258	−	0.903182i	$-0.641225\pi$
$137$	−10.0487	−0.858516	−0.429258	+	0.903182i	$0.641225\pi$
$138$	−71.1532	−6.05696
$139$	−10.0157	−0.849517	−0.424759	−	0.905307i	$-0.639641\pi$
$139$	−10.0157	−0.849517	−0.424759	+	0.905307i	$0.639641\pi$
$140$	6.32560	0.534611
$141$	40.5811	3.41755
$142$	−8.85188	−0.742833
$143$	31.3813	2.62423
$144$	29.9190	2.49325
$145$	3.47790	0.288824
$146$	−16.3469	−1.35288
$147$	−5.68342	−0.468760
$148$	19.1332	1.57274
$149$	−1.24166	−0.101721	−0.0508604	−	0.998706i	$-0.516196\pi$
$149$	−1.24166	−0.101721	−0.0508604	+	0.998706i	$0.516196\pi$
$150$	36.9750	3.01900
$151$	−9.50459	−0.773473	−0.386736	−	0.922190i	$-0.626398\pi$
$151$	−9.50459	−0.773473	−0.386736	+	0.922190i	$0.626398\pi$
$152$	−8.61276	−0.698587
$153$	2.19038	0.177082
$154$	32.5794	2.62533
$155$	6.07675	0.488096
$156$	−71.5149	−5.72577
$157$	23.3148	1.86073	0.930364	−	0.366638i	$-0.119491\pi$
$157$	23.3148	1.86073	0.930364	+	0.366638i	$0.119491\pi$
$158$	11.2144	0.892170
$159$	−10.4843	−0.831461
$160$	0.453890	0.0358832
$161$	20.0120	1.57717
$162$	−85.7907	−6.74035
$163$	−2.88148	−0.225695	−0.112848	−	0.993612i	$-0.535997\pi$
$163$	−2.88148	−0.225695	−0.112848	+	0.993612i	$0.535997\pi$
$164$	−9.81037	−0.766061
$165$	−13.6315	−1.06121
$166$	8.44120	0.655164
$167$	−8.18008	−0.632994	−0.316497	−	0.948594i	$-0.602507\pi$
$167$	−8.18008	−0.632994	−0.316497	+	0.948594i	$0.602507\pi$
$168$	−36.4817	−2.81463
$169$	16.2283	1.24833
$170$	−0.447770	−0.0343424
$171$	15.2224	1.16408
$172$	−32.5714	−2.48355
$173$	1.01895	0.0774690	0.0387345	−	0.999250i	$-0.487667\pi$
$173$	1.01895	0.0774690	0.0387345	+	0.999250i	$0.487667\pi$
$174$	−40.8211	−3.09464
$175$	−10.3993	−0.786115
$176$	−20.8805	−1.57393
$177$	27.4045	2.05985
$178$	−15.8443	−1.18758
$179$	−14.7788	−1.10462	−0.552309	−	0.833639i	$-0.686253\pi$
$179$	−14.7788	−1.10462	−0.552309	+	0.833639i	$0.686253\pi$
$180$	22.8300	1.70165
$181$	24.4088	1.81429	0.907145	−	0.420819i	$-0.138257\pi$
$181$	24.4088	1.81429	0.907145	+	0.420819i	$0.138257\pi$
$182$	30.3443	2.24927
$183$	−33.6360	−2.48645
$184$	−40.8655	−3.01265
$185$	3.39678	0.249736
$186$	−71.3245	−5.22977
$187$	−1.52867	−0.111787
$188$	47.4330	3.45941
$189$	41.2211	2.99839
$190$	−3.11184	−0.225756
$191$	5.46866	0.395698	0.197849	−	0.980232i	$-0.436604\pi$
$191$	5.46866	0.395698	0.197849	+	0.980232i	$0.436604\pi$
$192$	−29.5305	−2.13118
$193$	5.50851	0.396511	0.198256	−	0.980150i	$-0.436472\pi$
$193$	5.50851	0.396511	0.198256	+	0.980150i	$0.436472\pi$
$194$	39.8686	2.86240
$195$	−12.6963	−0.909200
$196$	−6.64303	−0.474502
$197$	8.80728	0.627493	0.313746	−	0.949507i	$-0.398416\pi$
$197$	8.80728	0.627493	0.313746	+	0.949507i	$0.398416\pi$
$198$	117.584	8.35634
$199$	−4.57280	−0.324157	−0.162079	−	0.986778i	$-0.551820\pi$
$199$	−4.57280	−0.324157	−0.162079	+	0.986778i	$0.551820\pi$
$200$	21.2359	1.50161
$201$	33.5009	2.36297
$202$	−21.4920	−1.51217
$203$	11.4810	0.805812
$204$	3.48368	0.243907
$205$	−1.74167	−0.121643
$206$	32.6048	2.27169
$207$	72.2264	5.02009
$208$	−19.4480	−1.34847
$209$	−10.6237	−0.734855
$210$	−13.1810	−0.909578
$211$	−0.768490	−0.0529050	−0.0264525	−	0.999650i	$-0.508421\pi$
$211$	−0.768490	−0.0529050	−0.0264525	+	0.999650i	$0.508421\pi$
$212$	−12.2545	−0.841645
$213$	12.2264	0.837742
$214$	−11.0118	−0.752755
$215$	−5.78252	−0.394365
$216$	−84.1754	−5.72741
$217$	20.0602	1.36178
$218$	−47.0473	−3.18645
$219$	22.5788	1.52573
$220$	−15.9331	−1.07421
$221$	−1.42379	−0.0957746
$222$	−39.8690	−2.67583
$223$	−24.3337	−1.62950	−0.814752	−	0.579810i	$-0.803127\pi$
$223$	−24.3337	−1.62950	−0.814752	+	0.579810i	$0.803127\pi$
$224$	1.49836	0.100113
$225$	−37.5327	−2.50218
$226$	−15.2826	−1.01659
$227$	22.8151	1.51429	0.757147	−	0.653244i	$-0.226593\pi$
$227$	22.8151	1.51429	0.757147	+	0.653244i	$0.226593\pi$
$228$	24.2103	1.60337
$229$	27.7522	1.83392	0.916960	−	0.398980i	$-0.130636\pi$
$229$	27.7522	1.83392	0.916960	+	0.398980i	$0.130636\pi$
$230$	−14.7649	−0.973570
$231$	−44.9995	−2.96075
$232$	−23.4448	−1.53923
$233$	12.2766	0.804268	0.402134	−	0.915581i	$-0.368269\pi$
$233$	12.2766	0.804268	0.402134	+	0.915581i	$0.368269\pi$
$234$	109.517	7.15936
$235$	8.42095	0.549322
$236$	32.0316	2.08508
$237$	−15.4896	−1.00616
$238$	−1.47815	−0.0958144
$239$	−21.3553	−1.38136	−0.690680	−	0.723160i	$-0.742689\pi$
$239$	−21.3553	−1.38136	−0.690680	+	0.723160i	$0.742689\pi$
$240$	8.44786	0.545307
$241$	1.12725	0.0726126	0.0363063	−	0.999341i	$-0.488441\pi$
$241$	1.12725	0.0726126	0.0363063	+	0.999341i	$0.488441\pi$
$242$	−55.2704	−3.55292
$243$	64.8338	4.15909
$244$	−39.3153	−2.51690
$245$	−1.17936	−0.0753466
$246$	20.4425	1.30336
$247$	−9.89483	−0.629593
$248$	−40.9639	−2.60121
$249$	−11.6592	−0.738871
$250$	16.1739	1.02292
$251$	−12.3755	−0.781136	−0.390568	−	0.920574i	$-0.627721\pi$
$251$	−12.3755	−0.781136	−0.390568	+	0.920574i	$0.627721\pi$
$252$	75.3653	4.74757
$253$	−50.4068	−3.16905
$254$	33.1402	2.07940
$255$	0.618471	0.0387301
$256$	−31.3494	−1.95933
$257$	1.94872	0.121558	0.0607790	−	0.998151i	$-0.480641\pi$
$257$	1.94872	0.121558	0.0607790	+	0.998151i	$0.480641\pi$
$258$	67.8711	4.22547
$259$	11.2133	0.696759
$260$	−14.8400	−0.920337
$261$	41.4368	2.56487
$262$	−46.7605	−2.88888
$263$	22.1492	1.36578	0.682890	−	0.730521i	$-0.260723\pi$
$263$	22.1492	1.36578	0.682890	+	0.730521i	$0.260723\pi$
$264$	91.8911	5.65551
$265$	−2.17559	−0.133646
$266$	−10.2726	−0.629855
$267$	21.8845	1.33931
$268$	39.1573	2.39191
$269$	−17.7632	−1.08304	−0.541520	−	0.840688i	$-0.682151\pi$
$269$	−17.7632	−1.08304	−0.541520	+	0.840688i	$0.682151\pi$
$270$	−30.4130	−1.85088
$271$	1.35906	0.0825570	0.0412785	−	0.999148i	$-0.486857\pi$
$271$	1.35906	0.0825570	0.0412785	+	0.999148i	$0.486857\pi$
$272$	0.947363	0.0574423
$273$	−41.9123	−2.53665
$274$	24.4745	1.47856
$275$	26.1941	1.57956
$276$	114.872	6.91450
$277$	14.9807	0.900104	0.450052	−	0.893002i	$-0.351405\pi$
$277$	14.9807	0.900104	0.450052	+	0.893002i	$0.351405\pi$
$278$	24.3941	1.46306
$279$	72.4004	4.33450
$280$	−7.57029	−0.452411
$281$	−15.8865	−0.947707	−0.473853	−	0.880604i	$-0.657137\pi$
$281$	−15.8865	−0.947707	−0.473853	+	0.880604i	$0.657137\pi$
$282$	−98.8391	−5.88578
$283$	10.8258	0.643528	0.321764	−	0.946820i	$-0.395724\pi$
$283$	10.8258	0.643528	0.321764	+	0.946820i	$0.395724\pi$
$284$	14.2908	0.848003
$285$	4.29815	0.254600
$286$	−76.4320	−4.51952
$287$	−5.74950	−0.339382
$288$	5.40780	0.318657
$289$	−16.9306	−0.995920
$290$	−8.47074	−0.497419
$291$	−55.0675	−3.22811
$292$	26.3910	1.54442
$293$	5.35413	0.312792	0.156396	−	0.987694i	$-0.450012\pi$
$293$	5.35413	0.312792	0.156396	+	0.987694i	$0.450012\pi$
$294$	13.8425	0.807310
$295$	5.68668	0.331091
$296$	−22.8980	−1.33092
$297$	−103.829	−6.02476
$298$	3.02418	0.175186
$299$	−46.9486	−2.71511
$300$	−59.6938	−3.44642
$301$	−19.0889	−1.10027
$302$	23.1493	1.33209
$303$	29.6853	1.70537
$304$	6.58383	0.377608
$305$	−6.97978	−0.399661
$306$	−5.33488	−0.304975
$307$	−15.8980	−0.907345	−0.453672	−	0.891169i	$-0.649886\pi$
$307$	−15.8980	−0.907345	−0.453672	+	0.891169i	$0.649886\pi$
$308$	−52.5974	−2.99702
$309$	−45.0346	−2.56193
$310$	−14.8005	−0.840611
$311$	−5.04910	−0.286308	−0.143154	−	0.989700i	$-0.545724\pi$
$311$	−5.04910	−0.286308	−0.143154	+	0.989700i	$0.545724\pi$
$312$	85.5868	4.84540
$313$	−6.85572	−0.387508	−0.193754	−	0.981050i	$-0.562066\pi$
$313$	−6.85572	−0.387508	−0.193754	+	0.981050i	$0.562066\pi$
$314$	−56.7855	−3.20459
$315$	13.3799	0.753870
$316$	−18.1049	−1.01848
$317$	−12.1738	−0.683751	−0.341876	−	0.939745i	$-0.611062\pi$
$317$	−12.1738	−0.683751	−0.341876	+	0.939745i	$0.611062\pi$
$318$	25.5355	1.43196
$319$	−28.9188	−1.61914
$320$	−6.12785	−0.342557
$321$	15.2098	0.848930
$322$	−48.7412	−2.71624
$323$	0.482004	0.0268194
$324$	138.504	7.69465
$325$	24.3970	1.35330
$326$	7.01812	0.388698
$327$	64.9829	3.59356
$328$	11.7408	0.648274
$329$	27.7988	1.53260
$330$	33.2007	1.82764
$331$	−13.7816	−0.757503	−0.378751	−	0.925498i	$-0.623646\pi$
$331$	−13.7816	−0.757503	−0.378751	+	0.925498i	$0.623646\pi$
$332$	−13.6278	−0.747921
$333$	40.4704	2.21776
$334$	19.9233	1.09016
$335$	6.95173	0.379814
$336$	27.8876	1.52139
$337$	1.01125	0.0550861	0.0275431	−	0.999621i	$-0.491232\pi$
$337$	1.01125	0.0550861	0.0275431	+	0.999621i	$0.491232\pi$
$338$	−39.5256	−2.14991
$339$	21.1088	1.14647
$340$	0.722896	0.0392045
$341$	−50.5282	−2.73626
$342$	−37.0754	−2.00481
$343$	−20.0245	−1.08122
$344$	38.9805	2.10169
$345$	20.3937	1.09796
$346$	−2.48173	−0.133419
$347$	−7.09913	−0.381101	−0.190551	−	0.981677i	$-0.561027\pi$
$347$	−7.09913	−0.381101	−0.190551	+	0.981677i	$0.561027\pi$
$348$	65.9030	3.53277
$349$	31.0340	1.66121	0.830606	−	0.556861i	$-0.187995\pi$
$349$	31.0340	1.66121	0.830606	+	0.556861i	$0.187995\pi$
$350$	25.3285	1.35387
$351$	−96.7055	−5.16176
$352$	−3.77410	−0.201160
$353$	−13.8451	−0.736902	−0.368451	−	0.929647i	$-0.620112\pi$
$353$	−13.8451	−0.736902	−0.368451	+	0.929647i	$0.620112\pi$
$354$	−66.7461	−3.54752
$355$	2.53710	0.134655
$356$	25.5796	1.35572
$357$	2.04166	0.108056
$358$	35.9951	1.90240
$359$	9.92910	0.524038	0.262019	−	0.965063i	$-0.415612\pi$
$359$	9.92910	0.524038	0.262019	+	0.965063i	$0.415612\pi$
$360$	−27.3223	−1.44001
$361$	−15.6502	−0.823697
$362$	−59.4498	−3.12461
$363$	76.3408	4.00685
$364$	−48.9889	−2.56772
$365$	4.68529	0.245240
$366$	81.9236	4.28222
$367$	−2.06995	−0.108051	−0.0540254	−	0.998540i	$-0.517205\pi$
$367$	−2.06995	−0.108051	−0.0540254	+	0.998540i	$0.517205\pi$
$368$	31.2387	1.62843
$369$	−20.7508	−1.08024
$370$	−8.27318	−0.430102
$371$	−7.18194	−0.372868
$372$	115.149	5.97019
$373$	9.62535	0.498382	0.249191	−	0.968454i	$-0.419835\pi$
$373$	9.62535	0.498382	0.249191	+	0.968454i	$0.419835\pi$
$374$	3.72321	0.192523
$375$	−22.3397	−1.15362
$376$	−56.7664	−2.92750
$377$	−26.9348	−1.38721
$378$	−100.398	−5.16390
$379$	4.97991	0.255801	0.127900	−	0.991787i	$-0.459176\pi$
$379$	4.97991	0.255801	0.127900	+	0.991787i	$0.459176\pi$
$380$	5.02386	0.257719
$381$	−45.7741	−2.34508
$382$	−13.3194	−0.681481
$383$	27.1364	1.38661	0.693304	−	0.720646i	$-0.256154\pi$
$383$	27.1364	1.38661	0.693304	+	0.720646i	$0.256154\pi$
$384$	67.5497	3.44713
$385$	−9.33781	−0.475899
$386$	−13.4165	−0.682881
$387$	−68.8948	−3.50212
$388$	−64.3653	−3.26765
$389$	−9.41954	−0.477589	−0.238795	−	0.971070i	$-0.576752\pi$
$389$	−9.41954	−0.477589	−0.238795	+	0.971070i	$0.576752\pi$
$390$	30.9230	1.56585
$391$	2.28700	0.115658
$392$	7.95018	0.401545
$393$	64.5868	3.25797
$394$	−21.4509	−1.08068
$395$	−3.21423	−0.161726
$396$	−189.832	−9.53942
$397$	−8.01922	−0.402473	−0.201237	−	0.979543i	$-0.564496\pi$
$397$	−8.01922	−0.402473	−0.201237	+	0.979543i	$0.564496\pi$
$398$	11.1375	0.558271
$399$	14.1888	0.710329
$400$	−16.2333	−0.811665
$401$	11.8733	0.592924	0.296462	−	0.955045i	$-0.404193\pi$
$401$	11.8733	0.592924	0.296462	+	0.955045i	$0.404193\pi$
$402$	−81.5944	−4.06956
$403$	−47.0617	−2.34431
$404$	34.6975	1.72626
$405$	24.5890	1.22184
$406$	−27.9631	−1.38779
$407$	−28.2443	−1.40002
$408$	−4.16917	−0.206405
$409$	−0.538172	−0.0266109	−0.0133055	−	0.999911i	$-0.504235\pi$
$409$	−0.538172	−0.0266109	−0.0133055	+	0.999911i	$0.504235\pi$
$410$	4.24200	0.209497
$411$	−33.8047	−1.66746
$412$	−52.6384	−2.59331
$413$	18.7725	0.923736
$414$	−175.914	−8.64571
$415$	−2.41939	−0.118763
$416$	−3.51518	−0.172346
$417$	−33.6937	−1.64999
$418$	25.8749	1.26559
$419$	−18.5896	−0.908162	−0.454081	−	0.890960i	$-0.650032\pi$
$419$	−18.5896	−0.908162	−0.454081	+	0.890960i	$0.650032\pi$
$420$	21.2800	1.03836
$421$	8.81101	0.429422	0.214711	−	0.976678i	$-0.431119\pi$
$421$	8.81101	0.429422	0.214711	+	0.976678i	$0.431119\pi$
$422$	1.87173	0.0911143
$423$	100.330	4.87821
$424$	14.6659	0.712237
$425$	−1.18845	−0.0576481
$426$	−29.7786	−1.44278
$427$	−23.0413	−1.11504
$428$	17.7779	0.859329
$429$	105.570	5.09696
$430$	14.0839	0.679184
$431$	18.6929	0.900405	0.450202	−	0.892927i	$-0.351352\pi$
$431$	18.6929	0.900405	0.450202	+	0.892927i	$0.351352\pi$
$432$	64.3459	3.09584
$433$	−32.5207	−1.56285	−0.781423	−	0.624001i	$-0.785506\pi$
$433$	−32.5207	−1.56285	−0.781423	+	0.624001i	$0.785506\pi$
$434$	−48.8585	−2.34528
$435$	11.7000	0.560972
$436$	75.9549	3.63758
$437$	15.8938	0.760303
$438$	−54.9926	−2.62765
$439$	−39.3507	−1.87811	−0.939053	−	0.343772i	$-0.888295\pi$
$439$	−39.3507	−1.87811	−0.939053	+	0.343772i	$0.888295\pi$
$440$	19.0682	0.909042
$441$	−14.0513	−0.669109
$442$	3.46778	0.164945
$443$	−14.6061	−0.693956	−0.346978	−	0.937873i	$-0.612792\pi$
$443$	−14.6061	−0.693956	−0.346978	+	0.937873i	$0.612792\pi$
$444$	64.3660	3.05467
$445$	4.54124	0.215275
$446$	59.2669	2.80637
$447$	−4.17707	−0.197568
$448$	−20.2289	−0.955727
$449$	39.5940	1.86856	0.934278	−	0.356544i	$-0.116045\pi$
$449$	39.5940	1.86856	0.934278	+	0.356544i	$0.116045\pi$
$450$	91.4144	4.30932
$451$	14.4820	0.681930
$452$	24.6729	1.16051
$453$	−31.9744	−1.50229
$454$	−55.5684	−2.60795
$455$	−8.69718	−0.407730
$456$	−28.9742	−1.35684
$457$	27.0443	1.26508	0.632539	−	0.774529i	$-0.282013\pi$
$457$	27.0443	1.26508	0.632539	+	0.774529i	$0.282013\pi$
$458$	−67.5931	−3.15842
$459$	4.71079	0.219881
$460$	23.8370	1.11141
$461$	−8.56537	−0.398929	−0.199464	−	0.979905i	$-0.563920\pi$
$461$	−8.56537	−0.398929	−0.199464	+	0.979905i	$0.563920\pi$
$462$	109.600	5.09908
$463$	−29.2393	−1.35887	−0.679434	−	0.733737i	$-0.737775\pi$
$463$	−29.2393	−1.35887	−0.679434	+	0.733737i	$0.737775\pi$
$464$	17.9219	0.832001
$465$	20.4428	0.948011
$466$	−29.9008	−1.38513
$467$	3.21866	0.148942	0.0744710	−	0.997223i	$-0.476273\pi$
$467$	3.21866	0.148942	0.0744710	+	0.997223i	$0.476273\pi$
$468$	−176.808	−8.17297
$469$	22.9487	1.05967
$470$	−20.5100	−0.946056
$471$	78.4335	3.61402
$472$	−38.3344	−1.76448
$473$	48.0817	2.21080
$474$	37.7264	1.73283
$475$	−8.25926	−0.378961
$476$	2.38638	0.109380
$477$	−25.9207	−1.18683
$478$	52.0128	2.37901
$479$	0.0110735	0.000505962 0	0.000252981	−	1.00000i	$-0.499919\pi$
$479$	0.0110735	0.000505962 0	0.000252981		1.00000i	$0.499919\pi$
$480$	1.52693	0.0696946
$481$	−26.3066	−1.19948
$482$	−2.74552	−0.125055
$483$	67.3225	3.06328
$484$	89.2305	4.05593
$485$	−11.4270	−0.518873
$486$	−157.909	−7.16288
$487$	15.0702	0.682898	0.341449	−	0.939900i	$-0.389082\pi$
$487$	15.0702	0.682898	0.341449	+	0.939900i	$0.389082\pi$
$488$	47.0513	2.12991
$489$	−9.69360	−0.438360
$490$	2.87244	0.129764
$491$	0.103892	0.00468859	0.00234430	−	0.999997i	$-0.499254\pi$
$491$	0.103892	0.00468859	0.00234430	+	0.999997i	$0.499254\pi$
$492$	−33.0031	−1.48789
$493$	1.31207	0.0590925
$494$	24.0998	1.08430
$495$	−33.7015	−1.51477
$496$	31.3139	1.40604
$497$	8.37532	0.375685
$498$	28.3970	1.27250
$499$	−16.0334	−0.717752	−0.358876	−	0.933385i	$-0.616840\pi$
$499$	−16.0334	−0.717752	−0.358876	+	0.933385i	$0.616840\pi$
$500$	−26.1117	−1.16775
$501$	−27.5186	−1.22944
$502$	30.1417	1.34529
$503$	−6.32825	−0.282163	−0.141081	−	0.989998i	$-0.545058\pi$
$503$	−6.32825	−0.282163	−0.141081	+	0.989998i	$0.545058\pi$
$504$	−90.1949	−4.01760
$505$	6.15996	0.274115
$506$	122.770	5.45781
$507$	54.5938	2.42459
$508$	−53.5027	−2.37380
$509$	8.06870	0.357639	0.178820	−	0.983882i	$-0.442772\pi$
$509$	8.06870	0.357639	0.178820	+	0.983882i	$0.442772\pi$
$510$	−1.50634	−0.0667020
$511$	15.4668	0.684213
$512$	36.1951	1.59961
$513$	32.7383	1.44543
$514$	−4.74630	−0.209350
$515$	−9.34509	−0.411794
$516$	−109.574	−4.82371
$517$	−70.0203	−3.07949
$518$	−27.3110	−1.19997
$519$	3.42783	0.150465
$520$	17.7600	0.778829
$521$	1.92215	0.0842108	0.0421054	−	0.999113i	$-0.486593\pi$
$521$	1.92215	0.0842108	0.0421054	+	0.999113i	$0.486593\pi$
$522$	−100.923	−4.41729
$523$	−33.6375	−1.47086	−0.735432	−	0.677599i	$-0.763021\pi$
$523$	−33.6375	−1.47086	−0.735432	+	0.677599i	$0.763021\pi$
$524$	75.4919	3.29788
$525$	−34.9844	−1.52684
$526$	−53.9465	−2.35218
$527$	2.29250	0.0998630
$528$	−70.2440	−3.05698
$529$	52.4122	2.27879
$530$	5.29885	0.230167
$531$	67.7529	2.94023
$532$	16.5845	0.719029
$533$	13.4884	0.584249
$534$	−53.3018	−2.30660
$535$	3.15618	0.136454
$536$	−46.8623	−2.02414
$537$	−49.7173	−2.14546
$538$	43.2638	1.86524
$539$	9.80639	0.422391
$540$	49.0999	2.11292
$541$	15.7327	0.676402	0.338201	−	0.941074i	$-0.390182\pi$
$541$	15.7327	0.676402	0.338201	+	0.941074i	$0.390182\pi$
$542$	−3.31012	−0.142182
$543$	82.1135	3.52383
$544$	0.171234	0.00734159
$545$	13.4845	0.577614
$546$	102.081	4.36867
$547$	21.0991	0.902134	0.451067	−	0.892490i	$-0.351044\pi$
$547$	21.0991	0.902134	0.451067	+	0.892490i	$0.351044\pi$
$548$	−39.5125	−1.68789
$549$	−83.1594	−3.54915
$550$	−63.7981	−2.72036
$551$	9.11838	0.388456
$552$	−137.476	−5.85135
$553$	−10.6107	−0.451211
$554$	−36.4869	−1.55018
$555$	11.4271	0.485054
$556$	−39.3827	−1.67020
$557$	−19.6892	−0.834260	−0.417130	−	0.908847i	$-0.636964\pi$
$557$	−19.6892	−0.834260	−0.417130	+	0.908847i	$0.636964\pi$
$558$	−176.338	−7.46497
$559$	44.7830	1.89412
$560$	5.78693	0.244542
$561$	−5.14259	−0.217120
$562$	38.6929	1.63216
$563$	−25.8145	−1.08795	−0.543977	−	0.839100i	$-0.683082\pi$
$563$	−25.8145	−1.08795	−0.543977	+	0.839100i	$0.683082\pi$
$564$	159.569	6.71908
$565$	4.38026	0.184279
$566$	−26.3673	−1.10830
$567$	81.1720	3.40890
$568$	−17.1028	−0.717617
$569$	−26.4602	−1.10927	−0.554635	−	0.832094i	$-0.687142\pi$
$569$	−26.4602	−1.10927	−0.554635	+	0.832094i	$0.687142\pi$
$570$	−10.4685	−0.438478
$571$	2.76419	0.115678	0.0578389	−	0.998326i	$-0.481579\pi$
$571$	2.76419	0.115678	0.0578389	+	0.998326i	$0.481579\pi$
$572$	123.395	5.15939
$573$	18.3971	0.768551
$574$	14.0034	0.584492
$575$	−39.1882	−1.63426
$576$	−73.0092	−3.04205
$577$	−17.6003	−0.732711	−0.366355	−	0.930475i	$-0.619395\pi$
$577$	−17.6003	−0.732711	−0.366355	+	0.930475i	$0.619395\pi$
$578$	41.2361	1.71520
$579$	18.5312	0.770129
$580$	13.6755	0.567843
$581$	−7.98675	−0.331346
$582$	134.122	5.55953
$583$	18.0901	0.749214
$584$	−31.5840	−1.30696
$585$	−31.3894	−1.29779
$586$	−13.0405	−0.538697
$587$	4.62540	0.190911	0.0954553	−	0.995434i	$-0.469569\pi$
$587$	4.62540	0.190911	0.0954553	+	0.995434i	$0.469569\pi$
$588$	−22.3478	−0.921609
$589$	15.9321	0.656469
$590$	−13.8504	−0.570213
$591$	29.6286	1.21876
$592$	17.5039	0.719404
$593$	25.5520	1.04930	0.524648	−	0.851319i	$-0.324197\pi$
$593$	25.5520	1.04930	0.524648	+	0.851319i	$0.324197\pi$
$594$	252.884	10.3760
$595$	0.423663	0.0173685
$596$	−4.88234	−0.199988
$597$	−15.3834	−0.629599
$598$	114.348	4.67603
$599$	−43.6239	−1.78242	−0.891211	−	0.453588i	$-0.850144\pi$
$599$	−43.6239	−1.78242	−0.891211	+	0.453588i	$0.850144\pi$
$600$	71.4397	2.91651
$601$	−15.0550	−0.614105	−0.307053	−	0.951693i	$-0.599343\pi$
$601$	−15.0550	−0.614105	−0.307053	+	0.951693i	$0.599343\pi$
$602$	46.4929	1.89491
$603$	82.8252	3.37290
$604$	−37.3731	−1.52069
$605$	15.8414	0.644045
$606$	−72.3012	−2.93704
$607$	27.2296	1.10522	0.552608	−	0.833441i	$-0.313633\pi$
$607$	27.2296	1.10522	0.552608	+	0.833441i	$0.313633\pi$
$608$	1.19001	0.0482614
$609$	38.6234	1.56510
$610$	16.9999	0.688305
$611$	−65.2165	−2.63838
$612$	8.61282	0.348153
$613$	−22.7527	−0.918974	−0.459487	−	0.888184i	$-0.651967\pi$
$613$	−22.7527	−0.918974	−0.459487	+	0.888184i	$0.651967\pi$
$614$	38.7209	1.56265
$615$	−5.85915	−0.236264
$616$	62.9470	2.53621
$617$	−37.5318	−1.51098	−0.755488	−	0.655163i	$-0.772600\pi$
$617$	−37.5318	−1.51098	−0.755488	+	0.655163i	$0.772600\pi$
$618$	109.686	4.41222
$619$	17.0447	0.685083	0.342541	−	0.939503i	$-0.388712\pi$
$619$	17.0447	0.685083	0.342541	+	0.939503i	$0.388712\pi$
$620$	23.8944	0.959623
$621$	155.335	6.23339
$622$	12.2975	0.493086
$623$	14.9913	0.600614
$624$	−65.4249	−2.61909
$625$	17.9277	0.717109
$626$	16.6977	0.667376
$627$	−35.7391	−1.42728
$628$	91.6765	3.65829
$629$	1.28146	0.0510953
$630$	−32.5879	−1.29833
$631$	25.9830	1.03437	0.517184	−	0.855874i	$-0.326980\pi$
$631$	25.9830	1.03437	0.517184	+	0.855874i	$0.326980\pi$
$632$	21.6675	0.861885
$633$	−2.58528	−0.102756
$634$	29.6505	1.17757
$635$	−9.49853	−0.376938
$636$	−41.2255	−1.63470
$637$	9.13362	0.361887
$638$	70.4343	2.78852
$639$	30.2278	1.19579
$640$	14.0172	0.554077
$641$	−41.2948	−1.63105	−0.815524	−	0.578724i	$-0.803551\pi$
$641$	−41.2948	−1.63105	−0.815524	+	0.578724i	$0.803551\pi$
$642$	−37.0450	−1.46205
$643$	−7.98273	−0.314808	−0.157404	−	0.987534i	$-0.550312\pi$
$643$	−7.98273	−0.314808	−0.157404	+	0.987534i	$0.550312\pi$
$644$	78.6895	3.10080
$645$	−19.4530	−0.765960
$646$	−1.17397	−0.0461891
$647$	25.0426	0.984527	0.492263	−	0.870446i	$-0.336170\pi$
$647$	25.0426	0.984527	0.492263	+	0.870446i	$0.336170\pi$
$648$	−165.757	−6.51155
$649$	−47.2848	−1.85609
$650$	−59.4212	−2.33069
$651$	67.4846	2.64493
$652$	−11.3303	−0.443729
$653$	11.1259	0.435390	0.217695	−	0.976017i	$-0.430146\pi$
$653$	11.1259	0.435390	0.217695	+	0.976017i	$0.430146\pi$
$654$	−158.272	−6.18892
$655$	13.4023	0.523673
$656$	−8.97494	−0.350413
$657$	55.8221	2.17783
$658$	−67.7065	−2.63947
$659$	−21.4361	−0.835032	−0.417516	−	0.908670i	$-0.637099\pi$
$659$	−21.4361	−0.835032	−0.417516	+	0.908670i	$0.637099\pi$
$660$	−53.6005	−2.08640
$661$	15.4402	0.600555	0.300277	−	0.953852i	$-0.402921\pi$
$661$	15.4402	0.600555	0.300277	+	0.953852i	$0.402921\pi$
$662$	33.5662	1.30459
$663$	−4.78978	−0.186020
$664$	16.3093	0.632924
$665$	2.94430	0.114175
$666$	−98.5694	−3.81948
$667$	43.2645	1.67521
$668$	−32.1650	−1.24450
$669$	−81.8609	−3.16493
$670$	−16.9316	−0.654124
$671$	58.0369	2.24049
$672$	5.04062	0.194446
$673$	−27.6330	−1.06517	−0.532587	−	0.846375i	$-0.678780\pi$
$673$	−27.6330	−1.06517	−0.532587	+	0.846375i	$0.678780\pi$
$674$	−2.46299	−0.0948707
$675$	−80.7205	−3.10693
$676$	63.8116	2.45429
$677$	−27.5464	−1.05869	−0.529347	−	0.848405i	$-0.677563\pi$
$677$	−27.5464	−1.05869	−0.529347	+	0.848405i	$0.677563\pi$
$678$	−51.4123	−1.97448
$679$	−37.7222	−1.44764
$680$	−0.865140	−0.0331766
$681$	76.7524	2.94116
$682$	123.066	4.71244
$683$	23.7929	0.910409	0.455204	−	0.890387i	$-0.349566\pi$
$683$	23.7929	0.910409	0.455204	+	0.890387i	$0.349566\pi$
$684$	59.8559	2.28865
$685$	−7.01479	−0.268021
$686$	48.7715	1.86211
$687$	93.3613	3.56196
$688$	−29.7977	−1.13603
$689$	16.8490	0.641895
$690$	−49.6707	−1.89093
$691$	45.9747	1.74896	0.874479	−	0.485063i	$-0.161203\pi$
$691$	45.9747	1.74896	0.874479	+	0.485063i	$0.161203\pi$
$692$	4.00660	0.152308
$693$	−111.254	−4.22618
$694$	17.2906	0.656342
$695$	−6.99174	−0.265212
$696$	−78.8708	−2.98959
$697$	−0.657059	−0.0248879
$698$	−75.5861	−2.86098
$699$	41.2998	1.56210
$700$	−40.8913	−1.54555
$701$	4.66394	0.176154	0.0880772	−	0.996114i	$-0.471928\pi$
$701$	4.66394	0.176154	0.0880772	+	0.996114i	$0.471928\pi$
$702$	235.535	8.88970
$703$	8.90571	0.335885
$704$	50.9531	1.92037
$705$	28.3289	1.06693
$706$	33.7211	1.26911
$707$	20.3349	0.764774
$708$	107.757	4.04977
$709$	−19.1799	−0.720315	−0.360157	−	0.932892i	$-0.617277\pi$
$709$	−19.1799	−0.720315	−0.360157	+	0.932892i	$0.617277\pi$
$710$	−6.17933	−0.231906
$711$	−38.2954	−1.43619
$712$	−30.6129	−1.14727
$713$	75.5938	2.83101
$714$	−4.97265	−0.186097
$715$	21.9067	0.819263
$716$	−58.1118	−2.17174
$717$	−71.8414	−2.68297
$718$	−24.1832	−0.902511
$719$	5.19867	0.193878	0.0969389	−	0.995290i	$-0.469095\pi$
$719$	5.19867	0.193878	0.0969389	+	0.995290i	$0.469095\pi$
$720$	20.8859	0.778371
$721$	−30.8495	−1.14890
$722$	38.1176	1.41859
$723$	3.79218	0.141033
$724$	95.9779	3.56699
$725$	−22.4826	−0.834982
$726$	−185.935	−6.90070
$727$	−24.7358	−0.917398	−0.458699	−	0.888592i	$-0.651684\pi$
$727$	−24.7358	−0.917398	−0.458699	+	0.888592i	$0.651684\pi$
$728$	58.6285	2.17292
$729$	112.436	4.16430
$730$	−11.4115	−0.422357
$731$	−2.18150	−0.0806858
$732$	−132.260	−4.88849
$733$	−5.67125	−0.209473	−0.104736	−	0.994500i	$-0.533400\pi$
$733$	−5.67125	−0.209473	−0.104736	+	0.994500i	$0.533400\pi$
$734$	5.04157	0.186088
$735$	−3.96749	−0.146343
$736$	5.64632	0.208126
$737$	−57.8037	−2.12923
$738$	50.5405	1.86042
$739$	29.6650	1.09125	0.545623	−	0.838031i	$-0.316293\pi$
$739$	29.6650	1.09125	0.545623	+	0.838031i	$0.316293\pi$
$740$	13.3565	0.490995
$741$	−33.2872	−1.22284
$742$	17.4923	0.642162
$743$	−44.9300	−1.64832	−0.824160	−	0.566357i	$-0.808352\pi$
$743$	−44.9300	−1.64832	−0.824160	+	0.566357i	$0.808352\pi$
$744$	−137.807	−5.05224
$745$	−0.866779	−0.0317563
$746$	−23.4434	−0.858324
$747$	−28.8254	−1.05466
$748$	−6.01089	−0.219780
$749$	10.4190	0.380702
$750$	54.4104	1.98679
$751$	41.3512	1.50893	0.754463	−	0.656343i	$-0.227898\pi$
$751$	41.3512	1.50893	0.754463	+	0.656343i	$0.227898\pi$
$752$	43.3938	1.58241
$753$	−41.6325	−1.51717
$754$	65.6021	2.38909
$755$	−6.63497	−0.241471
$756$	162.086	5.89500
$757$	−52.3079	−1.90116	−0.950581	−	0.310475i	$-0.899512\pi$
$757$	−52.3079	−1.90116	−0.950581	+	0.310475i	$0.899512\pi$
$758$	−12.1290	−0.440546
$759$	−169.574	−6.15513
$760$	−6.01241	−0.218093
$761$	7.44041	0.269715	0.134857	−	0.990865i	$-0.456942\pi$
$761$	7.44041	0.269715	0.134857	+	0.990865i	$0.456942\pi$
$762$	111.487	4.03875
$763$	44.5144	1.61153
$764$	21.5034	0.777964
$765$	1.52906	0.0552834
$766$	−66.0933	−2.38805
$767$	−44.0408	−1.59022
$768$	−105.462	−3.80554
$769$	−10.4939	−0.378420	−0.189210	−	0.981937i	$-0.560593\pi$
$769$	−10.4939	−0.378420	−0.189210	+	0.981937i	$0.560593\pi$
$770$	22.7431	0.819604
$771$	6.55570	0.236098
$772$	21.6601	0.779563
$773$	−39.6059	−1.42453	−0.712263	−	0.701913i	$-0.752330\pi$
$773$	−39.6059	−1.42453	−0.712263	+	0.701913i	$0.752330\pi$
$774$	167.800	6.03144
$775$	−39.2826	−1.41107
$776$	77.0304	2.76523
$777$	37.7226	1.35329
$778$	22.9421	0.822516
$779$	−4.56632	−0.163605
$780$	−49.9232	−1.78754
$781$	−21.0960	−0.754873
$782$	−5.57019	−0.199190
$783$	89.1169	3.18478
$784$	−6.07733	−0.217047
$785$	16.2757	0.580903
$786$	−157.307	−5.61096
$787$	−25.3454	−0.903466	−0.451733	−	0.892153i	$-0.649194\pi$
$787$	−25.3454	−0.903466	−0.451733	+	0.892153i	$0.649194\pi$
$788$	34.6312	1.23368
$789$	74.5123	2.65271
$790$	7.82856	0.278528
$791$	14.4599	0.514134
$792$	227.185	8.07267
$793$	54.0552	1.91956
$794$	19.5315	0.693149
$795$	−7.31891	−0.259575
$796$	−17.9808	−0.637311
$797$	11.5777	0.410105	0.205052	−	0.978751i	$-0.434264\pi$
$797$	11.5777	0.410105	0.205052	+	0.978751i	$0.434264\pi$
$798$	−34.5581	−1.22334
$799$	3.17687	0.112390
$800$	−2.93413	−0.103737
$801$	54.1058	1.91174
$802$	−28.9185	−1.02115
$803$	−38.9583	−1.37481
$804$	131.729	4.64572
$805$	13.9700	0.492379
$806$	114.623	4.03742
$807$	−59.7571	−2.10355
$808$	−41.5249	−1.46084
$809$	−2.92118	−0.102703	−0.0513516	−	0.998681i	$-0.516353\pi$
$809$	−2.92118	−0.102703	−0.0513516	+	0.998681i	$0.516353\pi$
$810$	−59.8889	−2.10428
$811$	14.6169	0.513270	0.256635	−	0.966508i	$-0.417386\pi$
$811$	14.6169	0.513270	0.256635	+	0.966508i	$0.417386\pi$
$812$	45.1447	1.58427
$813$	4.57201	0.160348
$814$	68.7915	2.41114
$815$	−2.01151	−0.0704601
$816$	3.18702	0.111568
$817$	−15.1606	−0.530404
$818$	1.31077	0.0458299
$819$	−103.621	−3.62081
$820$	−6.84843	−0.239158
$821$	−11.6140	−0.405330	−0.202665	−	0.979248i	$-0.564960\pi$
$821$	−11.6140	−0.405330	−0.202665	+	0.979248i	$0.564960\pi$
$822$	82.3345	2.87175
$823$	−27.8542	−0.970935	−0.485468	−	0.874255i	$-0.661351\pi$
$823$	−27.8542	−0.970935	−0.485468	+	0.874255i	$0.661351\pi$
$824$	62.9961	2.19457
$825$	88.1195	3.06793
$826$	−45.7223	−1.59088
$827$	33.9391	1.18018	0.590089	−	0.807339i	$-0.299093\pi$
$827$	33.9391	1.18018	0.590089	+	0.807339i	$0.299093\pi$
$828$	284.002	9.86976
$829$	2.11439	0.0734357	0.0367178	−	0.999326i	$-0.488310\pi$
$829$	2.11439	0.0734357	0.0367178	+	0.999326i	$0.488310\pi$
$830$	5.89264	0.204536
$831$	50.3966	1.74824
$832$	47.4574	1.64529
$833$	−0.444923	−0.0154157
$834$	82.0641	2.84165
$835$	−5.71036	−0.197615
$836$	−41.7735	−1.44477
$837$	155.709	5.38210
$838$	45.2767	1.56406
$839$	−51.5577	−1.77997	−0.889985	−	0.455990i	$-0.849285\pi$
$839$	−51.5577	−1.77997	−0.889985	+	0.455990i	$0.849285\pi$
$840$	−25.4672	−0.878702
$841$	−4.17884	−0.144098
$842$	−21.4600	−0.739561
$843$	−53.4436	−1.84070
$844$	−3.02179	−0.104014
$845$	11.3287	0.389719
$846$	−244.363	−8.40137
$847$	52.2948	1.79687
$848$	−11.2110	−0.384986
$849$	36.4191	1.24990
$850$	2.89457	0.0992829
$851$	42.2555	1.44850
$852$	48.0757	1.64705
$853$	−55.9086	−1.91427	−0.957136	−	0.289637i	$-0.906465\pi$
$853$	−55.9086	−1.91427	−0.957136	+	0.289637i	$0.906465\pi$
$854$	56.1191	1.92036
$855$	10.6264	0.363416
$856$	−21.2761	−0.727202
$857$	13.6102	0.464916	0.232458	−	0.972606i	$-0.425323\pi$
$857$	13.6102	0.464916	0.232458	+	0.972606i	$0.425323\pi$
$858$	−257.125	−8.77810
$859$	34.3481	1.17194	0.585971	−	0.810332i	$-0.300713\pi$
$859$	34.3481	1.17194	0.585971	+	0.810332i	$0.300713\pi$
$860$	−22.7375	−0.775342
$861$	−19.3419	−0.659170
$862$	−45.5282	−1.55070
$863$	−3.33437	−0.113503	−0.0567517	−	0.998388i	$-0.518074\pi$
$863$	−3.33437	−0.113503	−0.0567517	+	0.998388i	$0.518074\pi$
$864$	11.6304	0.395674
$865$	0.711306	0.0241851
$866$	79.2072	2.69157
$867$	−56.9564	−1.93434
$868$	78.8790	2.67733
$869$	26.7264	0.906631
$870$	−28.4964	−0.966119
$871$	−53.8380	−1.82423
$872$	−90.9005	−3.07828
$873$	−136.145	−4.60781
$874$	−38.7108	−1.30941
$875$	−15.3031	−0.517339
$876$	88.7821	2.99967
$877$	2.11186	0.0713126	0.0356563	−	0.999364i	$-0.488648\pi$
$877$	2.11186	0.0713126	0.0356563	+	0.999364i	$0.488648\pi$
$878$	95.8422	3.23452
$879$	18.0118	0.607524
$880$	−14.5763	−0.491366
$881$	−30.0894	−1.01374	−0.506869	−	0.862023i	$-0.669197\pi$
$881$	−30.0894	−1.01374	−0.506869	+	0.862023i	$0.669197\pi$
$882$	34.2232	1.15236
$883$	−29.6099	−0.996451	−0.498226	−	0.867047i	$-0.666015\pi$
$883$	−29.6099	−0.996451	−0.498226	+	0.867047i	$0.666015\pi$
$884$	−5.59850	−0.188298
$885$	19.1305	0.643066
$886$	35.5745	1.19515
$887$	0.0254004	0.000852862 0	0.000426431	−	1.00000i	$-0.499864\pi$
$887$	0.0254004	0.000852862 0	0.000426431		1.00000i	$0.499864\pi$
$888$	−77.0312	−2.58500
$889$	−31.3560	−1.05165
$890$	−11.0606	−0.370753
$891$	−204.458	−6.84960
$892$	−95.6827	−3.20369
$893$	22.0781	0.738815
$894$	10.1736	0.340257
$895$	−10.3168	−0.344852
$896$	46.2727	1.54586
$897$	−157.940	−5.27346
$898$	−96.4349	−3.21807
$899$	43.3687	1.44643
$900$	−147.583	−4.91943
$901$	−0.820760	−0.0273435
$902$	−35.2722	−1.17444
$903$	−64.2171	−2.13701
$904$	−29.5277	−0.982077
$905$	17.0393	0.566405
$906$	77.8766	2.58728
$907$	7.77114	0.258036	0.129018	−	0.991642i	$-0.458817\pi$
$907$	7.77114	0.258036	0.129018	+	0.991642i	$0.458817\pi$
$908$	89.7116	2.97719
$909$	73.3918	2.43425
$910$	21.1828	0.702202
$911$	−18.2150	−0.603490	−0.301745	−	0.953389i	$-0.597569\pi$
$911$	−18.2150	−0.603490	−0.301745	+	0.953389i	$0.597569\pi$
$912$	22.1486	0.733415
$913$	20.1172	0.665783
$914$	−65.8688	−2.17875
$915$	−23.4807	−0.776247
$916$	109.125	3.60559
$917$	44.2431	1.46104
$918$	−11.4736	−0.378684
$919$	−40.2448	−1.32755	−0.663777	−	0.747930i	$-0.731048\pi$
$919$	−40.2448	−1.32755	−0.663777	+	0.747930i	$0.731048\pi$
$920$	−28.5274	−0.940522
$921$	−53.4823	−1.76230
$922$	20.8617	0.687045
$923$	−19.6487	−0.646744
$924$	−176.943	−5.82100
$925$	−21.9582	−0.721981
$926$	71.2151	2.34027
$927$	−111.340	−3.65690
$928$	3.23934	0.106336
$929$	17.9221	0.588005	0.294003	−	0.955805i	$-0.405013\pi$
$929$	17.9221	0.588005	0.294003	+	0.955805i	$0.405013\pi$
$930$	−49.7903	−1.63269
$931$	−3.09206	−0.101338
$932$	48.2730	1.58123
$933$	−16.9857	−0.556086
$934$	−7.83935	−0.256512
$935$	−1.06713	−0.0348990
$936$	211.599	6.91633
$937$	1.94084	0.0634046	0.0317023	−	0.999497i	$-0.489907\pi$
$937$	1.94084	0.0634046	0.0317023	+	0.999497i	$0.489907\pi$
$938$	−55.8936	−1.82499
$939$	−23.0633	−0.752643
$940$	33.1121	1.08000
$941$	−43.9923	−1.43411	−0.717054	−	0.697017i	$-0.754510\pi$
$941$	−43.9923	−1.43411	−0.717054	+	0.697017i	$0.754510\pi$
$942$	−191.032	−6.22416
$943$	−21.6661	−0.705545
$944$	29.3038	0.953759
$945$	28.7757	0.936073
$946$	−117.107	−3.80749
$947$	33.3161	1.08263	0.541313	−	0.840821i	$-0.317927\pi$
$947$	33.3161	1.08263	0.541313	+	0.840821i	$0.317927\pi$
$948$	−60.9068	−1.97816
$949$	−36.2855	−1.17788
$950$	20.1162	0.652655
$951$	−40.9540	−1.32803
$952$	−2.85595	−0.0925620
$953$	9.51135	0.308103	0.154051	−	0.988063i	$-0.450768\pi$
$953$	9.51135	0.308103	0.154051	+	0.988063i	$0.450768\pi$
$954$	63.1323	2.04398
$955$	3.81757	0.123534
$956$	−83.9714	−2.71583
$957$	−97.2856	−3.14480
$958$	−0.0269706	−0.000871380 0
$959$	−23.1568	−0.747773
$960$	−20.6147	−0.665337
$961$	44.7758	1.44438
$962$	64.0721	2.06577
$963$	37.6037	1.21176
$964$	4.43247	0.142760
$965$	3.84539	0.123787
$966$	−163.970	−5.27565
$967$	−17.8383	−0.573642	−0.286821	−	0.957984i	$-0.592598\pi$
$967$	−17.8383	−0.573642	−0.286821	+	0.957984i	$0.592598\pi$
$968$	−106.788	−3.43231
$969$	1.62151	0.0520904
$970$	27.8315	0.893615
$971$	−3.32060	−0.106563	−0.0532815	−	0.998580i	$-0.516968\pi$
$971$	−3.32060	−0.106563	−0.0532815	+	0.998580i	$0.516968\pi$
$972$	254.934	8.17700
$973$	−23.0808	−0.739935
$974$	−36.7050	−1.17610
$975$	82.0740	2.62847
$976$	−35.9673	−1.15128
$977$	−5.05406	−0.161694	−0.0808468	−	0.996727i	$-0.525762\pi$
$977$	−5.05406	−0.161694	−0.0808468	+	0.996727i	$0.525762\pi$
$978$	23.6097	0.754954
$979$	−37.7605	−1.20683
$980$	−4.63737	−0.148135
$981$	160.659	5.12945
$982$	−0.253039	−0.00807480
$983$	13.2633	0.423033	0.211517	−	0.977374i	$-0.432160\pi$
$983$	13.2633	0.423033	0.211517	+	0.977374i	$0.432160\pi$
$984$	39.4971	1.25912
$985$	6.14819	0.195898
$986$	−3.19566	−0.101770
$987$	93.5179	2.97671
$988$	−38.9076	−1.23781
$989$	−71.9337	−2.28736
$990$	82.0832	2.60878
$991$	−24.0399	−0.763654	−0.381827	−	0.924234i	$-0.624705\pi$
$991$	−24.0399	−0.763654	−0.381827	+	0.924234i	$0.624705\pi$
$992$	5.65992	0.179703
$993$	−46.3625	−1.47127
$994$	−20.3989	−0.647013
$995$	−3.19219	−0.101199
$996$	−45.8452	−1.45266
$997$	34.6612	1.09773	0.548865	−	0.835911i	$-0.315060\pi$
$997$	34.6612	1.09773	0.548865	+	0.835911i	$0.315060\pi$
$998$	39.0508	1.23613
$999$	87.0384	2.75377

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.c.1.17	✓	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.c.1.17	✓	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)

\(f(q)\)	\(=\)	\(q-2.43559 q^{2} +3.36410 q^{3} +3.93211 q^{4} +0.698081 q^{5} -8.19357 q^{6} +2.30447 q^{7} -4.70583 q^{8} +8.31717 q^{9} +O(q^{10})\)	\(q-2.43559 q^{2} +3.36410 q^{3} +3.93211 q^{4} +0.698081 q^{5} -8.19357 q^{6} +2.30447 q^{7} -4.70583 q^{8} +8.31717 q^{9} -1.70024 q^{10} -5.80455 q^{11} +13.2280 q^{12} -5.40632 q^{13} -5.61274 q^{14} +2.34841 q^{15} +3.59726 q^{16} +0.263357 q^{17} -20.2572 q^{18} +1.83023 q^{19} +2.74493 q^{20} +7.75246 q^{21} +14.1375 q^{22} +8.68402 q^{23} -15.8309 q^{24} -4.51268 q^{25} +13.1676 q^{26} +17.8875 q^{27} +9.06141 q^{28} +4.98208 q^{29} -5.71978 q^{30} +8.70493 q^{31} +0.650197 q^{32} -19.5271 q^{33} -0.641430 q^{34} +1.60870 q^{35} +32.7040 q^{36} +4.86589 q^{37} -4.45770 q^{38} -18.1874 q^{39} -3.28505 q^{40} -2.49494 q^{41} -18.8818 q^{42} -8.28345 q^{43} -22.8241 q^{44} +5.80606 q^{45} -21.1507 q^{46} +12.0630 q^{47} +12.1015 q^{48} -1.68943 q^{49} +10.9911 q^{50} +0.885958 q^{51} -21.2583 q^{52} -3.11653 q^{53} -43.5666 q^{54} -4.05205 q^{55} -10.8444 q^{56} +6.15709 q^{57} -12.1343 q^{58} +8.14615 q^{59} +9.23422 q^{60} -9.99852 q^{61} -21.2017 q^{62} +19.1666 q^{63} -8.77814 q^{64} -3.77405 q^{65} +47.5600 q^{66} +9.95834 q^{67} +1.03555 q^{68} +29.2139 q^{69} -3.91815 q^{70} +3.63439 q^{71} -39.1392 q^{72} +6.71168 q^{73} -11.8513 q^{74} -15.1811 q^{75} +7.19668 q^{76} -13.3764 q^{77} +44.2971 q^{78} -4.60439 q^{79} +2.51118 q^{80} +35.2238 q^{81} +6.07665 q^{82} -3.46577 q^{83} +30.4835 q^{84} +0.183844 q^{85} +20.1751 q^{86} +16.7602 q^{87} +27.3152 q^{88} +6.50532 q^{89} -14.1412 q^{90} -12.4587 q^{91} +34.1465 q^{92} +29.2843 q^{93} -29.3805 q^{94} +1.27765 q^{95} +2.18733 q^{96} -16.3692 q^{97} +4.11477 q^{98} -48.2774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 25 q^{2} + 62 q^{3} + 223 q^{4} + 46 q^{5} + 26 q^{6} + 30 q^{7} + 75 q^{8} + 234 q^{9}+O(q^{10}) \) 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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