LMFDB - Embedded newform 5077.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-2.47319 q^{2} -1.27283 q^{3} +4.11668 q^{4} +3.46270 q^{5} +3.14796 q^{6} +5.16648 q^{7} -5.23495 q^{8} -1.37990 q^{9} +O(q^{10})$	\(q-2.47319 q^{2} -1.27283 q^{3} +4.11668 q^{4} +3.46270 q^{5} +3.14796 q^{6} +5.16648 q^{7} -5.23495 q^{8} -1.37990 q^{9} -8.56393 q^{10} -1.57292 q^{11} -5.23984 q^{12} +4.04925 q^{13} -12.7777 q^{14} -4.40744 q^{15} +4.71368 q^{16} -4.77488 q^{17} +3.41275 q^{18} +0.429844 q^{19} +14.2548 q^{20} -6.57606 q^{21} +3.89012 q^{22} -8.44025 q^{23} +6.66321 q^{24} +6.99032 q^{25} -10.0146 q^{26} +5.57488 q^{27} +21.2687 q^{28} -6.30542 q^{29} +10.9004 q^{30} -5.72021 q^{31} -1.18794 q^{32} +2.00206 q^{33} +11.8092 q^{34} +17.8900 q^{35} -5.68060 q^{36} +5.65501 q^{37} -1.06309 q^{38} -5.15401 q^{39} -18.1271 q^{40} -3.85862 q^{41} +16.2638 q^{42} +0.872807 q^{43} -6.47519 q^{44} -4.77818 q^{45} +20.8744 q^{46} -7.16561 q^{47} -5.99973 q^{48} +19.6925 q^{49} -17.2884 q^{50} +6.07762 q^{51} +16.6695 q^{52} -0.455669 q^{53} -13.7877 q^{54} -5.44654 q^{55} -27.0463 q^{56} -0.547119 q^{57} +15.5945 q^{58} -9.50689 q^{59} -18.1440 q^{60} -10.6214 q^{61} +14.1472 q^{62} -7.12921 q^{63} -6.48936 q^{64} +14.0213 q^{65} -4.95147 q^{66} +1.44322 q^{67} -19.6566 q^{68} +10.7430 q^{69} -44.2454 q^{70} -10.5180 q^{71} +7.22370 q^{72} -9.84196 q^{73} -13.9859 q^{74} -8.89751 q^{75} +1.76953 q^{76} -8.12643 q^{77} +12.7469 q^{78} -9.61551 q^{79} +16.3221 q^{80} -2.95618 q^{81} +9.54310 q^{82} -2.17170 q^{83} -27.0715 q^{84} -16.5340 q^{85} -2.15862 q^{86} +8.02574 q^{87} +8.23414 q^{88} +2.77922 q^{89} +11.8174 q^{90} +20.9203 q^{91} -34.7458 q^{92} +7.28087 q^{93} +17.7219 q^{94} +1.48842 q^{95} +1.51205 q^{96} -6.04848 q^{97} -48.7033 q^{98} +2.17047 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.47319	−1.74881	−0.874405	−	0.485196i	$-0.838748\pi$
$2$	−2.47319	−1.74881	−0.874405	+	0.485196i	$0.838748\pi$
$3$	−1.27283	−0.734870	−0.367435	−	0.930049i	$-0.619764\pi$
$3$	−1.27283	−0.734870	−0.367435	+	0.930049i	$0.619764\pi$
$4$	4.11668	2.05834
$5$	3.46270	1.54857	0.774284	−	0.632838i	$-0.218110\pi$
$5$	3.46270	1.54857	0.774284	+	0.632838i	$0.218110\pi$
$6$	3.14796	1.28515
$7$	5.16648	1.95274	0.976372	−	0.216096i	$-0.0693323\pi$
$7$	5.16648	1.95274	0.976372	+	0.216096i	$0.0693323\pi$
$8$	−5.23495	−1.85083
$9$	−1.37990	−0.459966
$10$	−8.56393	−2.70815
$11$	−1.57292	−0.474252	−0.237126	−	0.971479i	$-0.576205\pi$
$11$	−1.57292	−0.474252	−0.237126	+	0.971479i	$0.576205\pi$
$12$	−5.23984	−1.51261
$13$	4.04925	1.12306	0.561530	−	0.827457i	$-0.310213\pi$
$13$	4.04925	1.12306	0.561530	+	0.827457i	$0.310213\pi$
$14$	−12.7777	−3.41498
$15$	−4.40744	−1.13800
$16$	4.71368	1.17842
$17$	−4.77488	−1.15808	−0.579039	−	0.815300i	$-0.696572\pi$
$17$	−4.77488	−1.15808	−0.579039	+	0.815300i	$0.696572\pi$
$18$	3.41275	0.804394
$19$	0.429844	0.0986129	0.0493065	−	0.998784i	$-0.484299\pi$
$19$	0.429844	0.0986129	0.0493065	+	0.998784i	$0.484299\pi$
$20$	14.2548	3.18748
$21$	−6.57606	−1.43501
$22$	3.89012	0.829377
$23$	−8.44025	−1.75991	−0.879957	−	0.475053i	$-0.842429\pi$
$23$	−8.44025	−1.75991	−0.879957	+	0.475053i	$0.842429\pi$
$24$	6.66321	1.36012
$25$	6.99032	1.39806
$26$	−10.0146	−1.96402
$27$	5.57488	1.07289
$28$	21.2687	4.01941
$29$	−6.30542	−1.17089	−0.585443	−	0.810713i	$-0.699080\pi$
$29$	−6.30542	−1.17089	−0.585443	+	0.810713i	$0.699080\pi$
$30$	10.9004	1.99014
$31$	−5.72021	−1.02738	−0.513690	−	0.857976i	$-0.671722\pi$
$31$	−5.72021	−1.02738	−0.513690	+	0.857976i	$0.671722\pi$
$32$	−1.18794	−0.210000
$33$	2.00206	0.348514
$34$	11.8092	2.02526
$35$	17.8900	3.02396
$36$	−5.68060	−0.946767
$37$	5.65501	0.929678	0.464839	−	0.885395i	$-0.346112\pi$
$37$	5.65501	0.929678	0.464839	+	0.885395i	$0.346112\pi$
$38$	−1.06309	−0.172455
$39$	−5.15401	−0.825302
$40$	−18.1271	−2.86614
$41$	−3.85862	−0.602615	−0.301307	−	0.953527i	$-0.597423\pi$
$41$	−3.85862	−0.602615	−0.301307	+	0.953527i	$0.597423\pi$
$42$	16.2638	2.50957
$43$	0.872807	0.133102	0.0665509	−	0.997783i	$-0.478801\pi$
$43$	0.872807	0.133102	0.0665509	+	0.997783i	$0.478801\pi$
$44$	−6.47519	−0.976172
$45$	−4.77818	−0.712289
$46$	20.8744	3.07776
$47$	−7.16561	−1.04521	−0.522606	−	0.852574i	$-0.675040\pi$
$47$	−7.16561	−1.04521	−0.522606	+	0.852574i	$0.675040\pi$
$48$	−5.99973	−0.865986
$49$	19.6925	2.81321
$50$	−17.2884	−2.44495
$51$	6.07762	0.851037
$52$	16.6695	2.31164
$53$	−0.455669	−0.0625910	−0.0312955	−	0.999510i	$-0.509963\pi$
$53$	−0.455669	−0.0625910	−0.0312955	+	0.999510i	$0.509963\pi$
$54$	−13.7877	−1.87627
$55$	−5.44654	−0.734412
$56$	−27.0463	−3.61421
$57$	−0.547119	−0.0724676
$58$	15.5945	2.04766
$59$	−9.50689	−1.23769	−0.618846	−	0.785512i	$-0.712399\pi$
$59$	−9.50689	−1.23769	−0.618846	+	0.785512i	$0.712399\pi$
$60$	−18.1440	−2.34238
$61$	−10.6214	−1.35993	−0.679964	−	0.733245i	$-0.738005\pi$
$61$	−10.6214	−1.35993	−0.679964	+	0.733245i	$0.738005\pi$
$62$	14.1472	1.79669
$63$	−7.12921	−0.898197
$64$	−6.48936	−0.811170
$65$	14.0213	1.73913
$66$	−4.95147	−0.609484
$67$	1.44322	0.176318	0.0881589	−	0.996106i	$-0.471902\pi$
$67$	1.44322	0.176318	0.0881589	+	0.996106i	$0.471902\pi$
$68$	−19.6566	−2.38372
$69$	10.7430	1.29331
$70$	−44.2454	−5.28833
$71$	−10.5180	−1.24826	−0.624130	−	0.781320i	$-0.714547\pi$
$71$	−10.5180	−1.24826	−0.624130	+	0.781320i	$0.714547\pi$
$72$	7.22370	0.851322
$73$	−9.84196	−1.15191	−0.575957	−	0.817480i	$-0.695371\pi$
$73$	−9.84196	−1.15191	−0.575957	+	0.817480i	$0.695371\pi$
$74$	−13.9859	−1.62583
$75$	−8.89751	−1.02740
$76$	1.76953	0.202979
$77$	−8.12643	−0.926093
$78$	12.7469	1.44330
$79$	−9.61551	−1.08183	−0.540915	−	0.841077i	$-0.681922\pi$
$79$	−9.61551	−1.08183	−0.540915	+	0.841077i	$0.681922\pi$
$80$	16.3221	1.82487
$81$	−2.95618	−0.328465
$82$	9.54310	1.05386
$83$	−2.17170	−0.238376	−0.119188	−	0.992872i	$-0.538029\pi$
$83$	−2.17170	−0.238376	−0.119188	+	0.992872i	$0.538029\pi$
$84$	−27.0715	−2.95374
$85$	−16.5340	−1.79336
$86$	−2.15862	−0.232770
$87$	8.02574	0.860449
$88$	8.23414	0.877762
$89$	2.77922	0.294597	0.147299	−	0.989092i	$-0.452942\pi$
$89$	2.77922	0.294597	0.147299	+	0.989092i	$0.452942\pi$
$90$	11.8174	1.24566
$91$	20.9203	2.19305
$92$	−34.7458	−3.62250
$93$	7.28087	0.754991
$94$	17.7219	1.82788
$95$	1.48842	0.152709
$96$	1.51205	0.154323
$97$	−6.04848	−0.614130	−0.307065	−	0.951689i	$-0.599347\pi$
$97$	−6.04848	−0.614130	−0.307065	+	0.951689i	$0.599347\pi$
$98$	−48.7033	−4.91977
$99$	2.17047	0.218140
$100$	28.7769	2.87769
$101$	−4.89022	−0.486595	−0.243297	−	0.969952i	$-0.578229\pi$
$101$	−4.89022	−0.486595	−0.243297	+	0.969952i	$0.578229\pi$
$102$	−15.0311	−1.48830
$103$	−13.5701	−1.33710	−0.668549	−	0.743668i	$-0.733084\pi$
$103$	−13.5701	−1.33710	−0.668549	+	0.743668i	$0.733084\pi$
$104$	−21.1976	−2.07860
$105$	−22.7709	−2.22222
$106$	1.12696	0.109460
$107$	13.2619	1.28208	0.641040	−	0.767508i	$-0.278503\pi$
$107$	13.2619	1.28208	0.641040	+	0.767508i	$0.278503\pi$
$108$	22.9500	2.20836
$109$	1.37259	0.131471	0.0657353	−	0.997837i	$-0.479061\pi$
$109$	1.37259	0.131471	0.0657353	+	0.997837i	$0.479061\pi$
$110$	13.4703	1.28435
$111$	−7.19788	−0.683192
$112$	24.3531	2.30115
$113$	−11.4966	−1.08151	−0.540757	−	0.841179i	$-0.681862\pi$
$113$	−11.4966	−1.08151	−0.540757	+	0.841179i	$0.681862\pi$
$114$	1.35313	0.126732
$115$	−29.2261	−2.72535
$116$	−25.9574	−2.41008
$117$	−5.58755	−0.516569
$118$	23.5124	2.16449
$119$	−24.6693	−2.26143
$120$	23.0727	2.10624
$121$	−8.52593	−0.775085
$122$	26.2687	2.37826
$123$	4.91137	0.442843
$124$	−23.5483	−2.11470
$125$	6.89190	0.616430
$126$	17.6319	1.57078
$127$	−0.0221191	−0.00196275	−0.000981375	−	1.00000i	$-0.500312\pi$
$127$	−0.0221191	−0.00196275	−0.000981375		1.00000i	$0.500312\pi$
$128$	18.4253	1.62858
$129$	−1.11094	−0.0978125
$130$	−34.6775	−3.04142
$131$	15.1720	1.32558	0.662791	−	0.748805i	$-0.269372\pi$
$131$	15.1720	1.32558	0.662791	+	0.748805i	$0.269372\pi$
$132$	8.24183	0.717359
$133$	2.22078	0.192566
$134$	−3.56937	−0.308347
$135$	19.3041	1.66144
$136$	24.9963	2.14341
$137$	4.23769	0.362051	0.181025	−	0.983478i	$-0.442058\pi$
$137$	4.23769	0.362051	0.181025	+	0.983478i	$0.442058\pi$
$138$	−26.5696	−2.26175
$139$	−20.5760	−1.74523	−0.872616	−	0.488407i	$-0.837578\pi$
$139$	−20.5760	−1.74523	−0.872616	+	0.488407i	$0.837578\pi$
$140$	73.6473	6.22433
$141$	9.12062	0.768095
$142$	26.0131	2.18297
$143$	−6.36913	−0.532613
$144$	−6.50441	−0.542034
$145$	−21.8338	−1.81320
$146$	24.3411	2.01448
$147$	−25.0652	−2.06734
$148$	23.2799	1.91359
$149$	0.984912	0.0806871	0.0403436	−	0.999186i	$-0.487155\pi$
$149$	0.984912	0.0806871	0.0403436	+	0.999186i	$0.487155\pi$
$150$	22.0052	1.79672
$151$	−15.6283	−1.27181	−0.635905	−	0.771767i	$-0.719373\pi$
$151$	−15.6283	−1.27181	−0.635905	+	0.771767i	$0.719373\pi$
$152$	−2.25021	−0.182516
$153$	6.58885	0.532677
$154$	20.0982	1.61956
$155$	−19.8074	−1.59097
$156$	−21.2174	−1.69875
$157$	12.7854	1.02038	0.510192	−	0.860060i	$-0.329574\pi$
$157$	12.7854	1.02038	0.510192	+	0.860060i	$0.329574\pi$
$158$	23.7810	1.89192
$159$	0.579990	0.0459962
$160$	−4.11348	−0.325199
$161$	−43.6064	−3.43666
$162$	7.31121	0.574423
$163$	−21.8358	−1.71031	−0.855156	−	0.518370i	$-0.826539\pi$
$163$	−21.8358	−1.71031	−0.855156	+	0.518370i	$0.826539\pi$
$164$	−15.8847	−1.24039
$165$	6.93254	0.539697
$166$	5.37104	0.416874
$167$	−11.5276	−0.892033	−0.446016	−	0.895025i	$-0.647158\pi$
$167$	−11.5276	−0.892033	−0.446016	+	0.895025i	$0.647158\pi$
$168$	34.4253	2.65597
$169$	3.39641	0.261262
$170$	40.8917	3.13625
$171$	−0.593141	−0.0453586
$172$	3.59306	0.273969
$173$	−6.80197	−0.517144	−0.258572	−	0.965992i	$-0.583252\pi$
$173$	−6.80197	−0.517144	−0.258572	+	0.965992i	$0.583252\pi$
$174$	−19.8492	−1.50476
$175$	36.1153	2.73006
$176$	−7.41423	−0.558868
$177$	12.1007	0.909542
$178$	−6.87356	−0.515195
$179$	23.7195	1.77288	0.886441	−	0.462842i	$-0.153170\pi$
$179$	23.7195	1.77288	0.886441	+	0.462842i	$0.153170\pi$
$180$	−19.6702	−1.46613
$181$	11.7254	0.871545	0.435772	−	0.900057i	$-0.356475\pi$
$181$	11.7254	0.871545	0.435772	+	0.900057i	$0.356475\pi$
$182$	−51.7400	−3.83523
$183$	13.5192	0.999371
$184$	44.1843	3.25731
$185$	19.5816	1.43967
$186$	−18.0070	−1.32034
$187$	7.51048	0.549221
$188$	−29.4985	−2.15140
$189$	28.8025	2.09507
$190$	−3.68115	−0.267059
$191$	11.6213	0.840888	0.420444	−	0.907319i	$-0.361874\pi$
$191$	11.6213	0.840888	0.420444	+	0.907319i	$0.361874\pi$
$192$	8.25987	0.596105
$193$	−24.5936	−1.77028	−0.885142	−	0.465321i	$-0.845939\pi$
$193$	−24.5936	−1.77028	−0.885142	+	0.465321i	$0.845939\pi$
$194$	14.9591	1.07400
$195$	−17.8468	−1.27804
$196$	81.0676	5.79054
$197$	14.6832	1.04614	0.523068	−	0.852291i	$-0.324787\pi$
$197$	14.6832	1.04614	0.523068	+	0.852291i	$0.324787\pi$
$198$	−5.36798	−0.381486
$199$	3.42614	0.242873	0.121436	−	0.992599i	$-0.461250\pi$
$199$	3.42614	0.242873	0.121436	+	0.992599i	$0.461250\pi$
$200$	−36.5940	−2.58759
$201$	−1.83698	−0.129571
$202$	12.0944	0.850962
$203$	−32.5768	−2.28644
$204$	25.0196	1.75172
$205$	−13.3613	−0.933190
$206$	33.5614	2.33833
$207$	11.6467	0.809501
$208$	19.0869	1.32344
$209$	−0.676108	−0.0467674
$210$	56.3169	3.88624
$211$	21.3165	1.46749	0.733745	−	0.679425i	$-0.237771\pi$
$211$	21.3165	1.46749	0.733745	+	0.679425i	$0.237771\pi$
$212$	−1.87584	−0.128833
$213$	13.3877	0.917309
$214$	−32.7993	−2.24211
$215$	3.02227	0.206117
$216$	−29.1842	−1.98573
$217$	−29.5533	−2.00621
$218$	−3.39469	−0.229917
$219$	12.5272	0.846507
$220$	−22.4217	−1.51167
$221$	−19.3347	−1.30059
$222$	17.8017	1.19477
$223$	21.0722	1.41110	0.705548	−	0.708662i	$-0.250701\pi$
$223$	21.0722	1.41110	0.705548	+	0.708662i	$0.250701\pi$
$224$	−6.13746	−0.410076
$225$	−9.64594	−0.643063
$226$	28.4334	1.89136
$227$	−14.3869	−0.954893	−0.477446	−	0.878661i	$-0.658438\pi$
$227$	−14.3869	−0.954893	−0.477446	+	0.878661i	$0.658438\pi$
$228$	−2.25231	−0.149163
$229$	25.0884	1.65789	0.828944	−	0.559331i	$-0.188942\pi$
$229$	25.0884	1.65789	0.828944	+	0.559331i	$0.188942\pi$
$230$	72.2818	4.76612
$231$	10.3436	0.680558
$232$	33.0086	2.16712
$233$	21.0936	1.38189	0.690943	−	0.722909i	$-0.257195\pi$
$233$	21.0936	1.38189	0.690943	+	0.722909i	$0.257195\pi$
$234$	13.8191	0.903382
$235$	−24.8124	−1.61858
$236$	−39.1368	−2.54759
$237$	12.2389	0.795004
$238$	61.0119	3.95481
$239$	15.4428	0.998909	0.499455	−	0.866340i	$-0.333534\pi$
$239$	15.4428	0.998909	0.499455	+	0.866340i	$0.333534\pi$
$240$	−20.7753	−1.34104
$241$	−7.53697	−0.485499	−0.242749	−	0.970089i	$-0.578049\pi$
$241$	−7.53697	−0.485499	−0.242749	+	0.970089i	$0.578049\pi$
$242$	21.0863	1.35548
$243$	−12.9619	−0.831506
$244$	−43.7248	−2.79919
$245$	68.1892	4.35645
$246$	−12.1468	−0.774449
$247$	1.74054	0.110748
$248$	29.9450	1.90151
$249$	2.76422	0.175175
$250$	−17.0450	−1.07802
$251$	−1.54052	−0.0972367	−0.0486184	−	0.998817i	$-0.515482\pi$
$251$	−1.54052	−0.0972367	−0.0486184	+	0.998817i	$0.515482\pi$
$252$	−29.3487	−1.84879
$253$	13.2758	0.834643
$254$	0.0547047	0.00343248
$255$	21.0450	1.31789
$256$	−32.5906	−2.03691
$257$	−20.8358	−1.29970	−0.649851	−	0.760062i	$-0.725169\pi$
$257$	−20.8358	−1.29970	−0.649851	+	0.760062i	$0.725169\pi$
$258$	2.74756	0.171056
$259$	29.2165	1.81542
$260$	57.7214	3.57973
$261$	8.70084	0.538568
$262$	−37.5232	−2.31819
$263$	21.8017	1.34435	0.672176	−	0.740391i	$-0.265360\pi$
$263$	21.8017	1.34435	0.672176	+	0.740391i	$0.265360\pi$
$264$	−10.4807	−0.645041
$265$	−1.57785	−0.0969264
$266$	−5.49241	−0.336761
$267$	−3.53749	−0.216491
$268$	5.94129	0.362922
$269$	−15.1076	−0.921126	−0.460563	−	0.887627i	$-0.652352\pi$
$269$	−15.1076	−0.921126	−0.460563	+	0.887627i	$0.652352\pi$
$270$	−47.7429	−2.90554
$271$	−2.93947	−0.178560	−0.0892800	−	0.996007i	$-0.528457\pi$
$271$	−2.93947	−0.178560	−0.0892800	+	0.996007i	$0.528457\pi$
$272$	−22.5073	−1.36470
$273$	−26.6281	−1.61160
$274$	−10.4806	−0.633158
$275$	−10.9952	−0.663035
$276$	44.2256	2.66207
$277$	−14.7403	−0.885662	−0.442831	−	0.896605i	$-0.646026\pi$
$277$	−14.7403	−0.885662	−0.442831	+	0.896605i	$0.646026\pi$
$278$	50.8883	3.05208
$279$	7.89332	0.472560
$280$	−93.6532	−5.59685
$281$	21.7365	1.29669	0.648347	−	0.761345i	$-0.275461\pi$
$281$	21.7365	1.29669	0.648347	+	0.761345i	$0.275461\pi$
$282$	−22.5570	−1.34325
$283$	11.7328	0.697442	0.348721	−	0.937227i	$-0.386616\pi$
$283$	11.7328	0.697442	0.348721	+	0.937227i	$0.386616\pi$
$284$	−43.2994	−2.56934
$285$	−1.89451	−0.112221
$286$	15.7521	0.931440
$287$	−19.9355	−1.17675
$288$	1.63924	0.0965929
$289$	5.79946	0.341145
$290$	53.9992	3.17094
$291$	7.69870	0.451306
$292$	−40.5162	−2.37103
$293$	−5.39510	−0.315185	−0.157592	−	0.987504i	$-0.550373\pi$
$293$	−5.39510	−0.315185	−0.157592	+	0.987504i	$0.550373\pi$
$294$	61.9911	3.61539
$295$	−32.9196	−1.91665
$296$	−29.6037	−1.72068
$297$	−8.76881	−0.508818
$298$	−2.43588	−0.141107
$299$	−34.1767	−1.97649
$300$	−36.6282	−2.11473
$301$	4.50934	0.259914
$302$	38.6517	2.22416
$303$	6.22443	0.357584
$304$	2.02615	0.116207
$305$	−36.7787	−2.10594
$306$	−16.2955	−0.931551
$307$	−8.88748	−0.507235	−0.253618	−	0.967305i	$-0.581620\pi$
$307$	−8.88748	−0.507235	−0.253618	+	0.967305i	$0.581620\pi$
$308$	−33.4539	−1.90621
$309$	17.2724	0.982593
$310$	48.9875	2.78230
$311$	−7.27263	−0.412393	−0.206196	−	0.978511i	$-0.566109\pi$
$311$	−7.27263	−0.412393	−0.206196	+	0.978511i	$0.566109\pi$
$312$	26.9810	1.52750
$313$	15.8968	0.898539	0.449270	−	0.893396i	$-0.351684\pi$
$313$	15.8968	0.898539	0.449270	+	0.893396i	$0.351684\pi$
$314$	−31.6207	−1.78446
$315$	−24.6864	−1.39092
$316$	−39.5840	−2.22677
$317$	8.19553	0.460307	0.230153	−	0.973154i	$-0.426077\pi$
$317$	8.19553	0.460307	0.230153	+	0.973154i	$0.426077\pi$
$318$	−1.43443	−0.0804387
$319$	9.91789	0.555295
$320$	−22.4707	−1.25615
$321$	−16.8802	−0.942162
$322$	107.847	6.01007
$323$	−2.05245	−0.114201
$324$	−12.1697	−0.676092
$325$	28.3056	1.57011
$326$	54.0042	2.99101
$327$	−1.74708	−0.0966138
$328$	20.1997	1.11534
$329$	−37.0210	−2.04103
$330$	−17.1455	−0.943828
$331$	−7.55254	−0.415125	−0.207562	−	0.978222i	$-0.566553\pi$
$331$	−7.55254	−0.415125	−0.207562	+	0.978222i	$0.566553\pi$
$332$	−8.94021	−0.490658
$333$	−7.80334	−0.427621
$334$	28.5100	1.56000
$335$	4.99746	0.273040
$336$	−30.9974	−1.69105
$337$	−0.100367	−0.00546736	−0.00273368	−	0.999996i	$-0.500870\pi$
$337$	−0.100367	−0.00546736	−0.00273368	+	0.999996i	$0.500870\pi$
$338$	−8.39997	−0.456898
$339$	14.6333	0.794771
$340$	−68.0651	−3.69135
$341$	8.99742	0.487237
$342$	1.46695	0.0793236
$343$	65.5754	3.54074
$344$	−4.56910	−0.246349
$345$	37.1999	2.00278
$346$	16.8226	0.904387
$347$	−4.91391	−0.263793	−0.131896	−	0.991264i	$-0.542107\pi$
$347$	−4.91391	−0.263793	−0.131896	+	0.991264i	$0.542107\pi$
$348$	33.0394	1.77110
$349$	13.2621	0.709904	0.354952	−	0.934885i	$-0.384497\pi$
$349$	13.2621	0.709904	0.354952	+	0.934885i	$0.384497\pi$
$350$	−89.3202	−4.77436
$351$	22.5741	1.20491
$352$	1.86853	0.0995929
$353$	−19.0018	−1.01136	−0.505681	−	0.862721i	$-0.668759\pi$
$353$	−19.0018	−1.01136	−0.505681	+	0.862721i	$0.668759\pi$
$354$	−29.9273	−1.59062
$355$	−36.4208	−1.93302
$356$	11.4412	0.606381
$357$	31.3999	1.66186
$358$	−58.6630	−3.10043
$359$	−15.4998	−0.818046	−0.409023	−	0.912524i	$-0.634130\pi$
$359$	−15.4998	−0.818046	−0.409023	+	0.912524i	$0.634130\pi$
$360$	25.0136	1.31833
$361$	−18.8152	−0.990275
$362$	−28.9993	−1.52417
$363$	10.8521	0.569587
$364$	86.1223	4.51404
$365$	−34.0798	−1.78382
$366$	−33.4357	−1.74771
$367$	−21.1702	−1.10507	−0.552537	−	0.833488i	$-0.686340\pi$
$367$	−21.1702	−1.10507	−0.552537	+	0.833488i	$0.686340\pi$
$368$	−39.7847	−2.07392
$369$	5.32450	0.277183
$370$	−48.4291	−2.51771
$371$	−2.35420	−0.122224
$372$	29.9730	1.55403
$373$	27.4537	1.42150	0.710750	−	0.703445i	$-0.248356\pi$
$373$	27.4537	1.42150	0.710750	+	0.703445i	$0.248356\pi$
$374$	−18.5749	−0.960483
$375$	−8.77223	−0.452996
$376$	37.5116	1.93452
$377$	−25.5322	−1.31498
$378$	−71.2340	−3.66388
$379$	23.3969	1.20182	0.600909	−	0.799318i	$-0.294806\pi$
$379$	23.3969	1.20182	0.600909	+	0.799318i	$0.294806\pi$
$380$	6.12735	0.314327
$381$	0.0281538	0.00144237
$382$	−28.7417	−1.47055
$383$	24.9719	1.27601	0.638003	−	0.770034i	$-0.279761\pi$
$383$	24.9719	1.27601	0.638003	+	0.770034i	$0.279761\pi$
$384$	−23.4523	−1.19680
$385$	−28.1394	−1.43412
$386$	60.8246	3.09589
$387$	−1.20439	−0.0612223
$388$	−24.8997	−1.26409
$389$	30.4596	1.54436	0.772181	−	0.635402i	$-0.219166\pi$
$389$	30.4596	1.54436	0.772181	+	0.635402i	$0.219166\pi$
$390$	44.1386	2.23505
$391$	40.3012	2.03812
$392$	−103.089	−5.20679
$393$	−19.3114	−0.974130
$394$	−36.3144	−1.82949
$395$	−33.2957	−1.67529
$396$	8.93511	0.449006
$397$	33.0219	1.65732	0.828661	−	0.559751i	$-0.189103\pi$
$397$	33.0219	1.65732	0.828661	+	0.559751i	$0.189103\pi$
$398$	−8.47350	−0.424738
$399$	−2.82668	−0.141511
$400$	32.9502	1.64751
$401$	30.7461	1.53539	0.767694	−	0.640816i	$-0.221404\pi$
$401$	30.7461	1.53539	0.767694	+	0.640816i	$0.221404\pi$
$402$	4.54321	0.226595
$403$	−23.1626	−1.15381
$404$	−20.1315	−1.00158
$405$	−10.2364	−0.508650
$406$	80.5687	3.99856
$407$	−8.89486	−0.440902
$408$	−31.8160	−1.57513
$409$	−25.5828	−1.26499	−0.632494	−	0.774565i	$-0.717969\pi$
$409$	−25.5828	−1.26499	−0.632494	+	0.774565i	$0.717969\pi$
$410$	33.0449	1.63197
$411$	−5.39387	−0.266060
$412$	−55.8636	−2.75220
$413$	−49.1171	−2.41690
$414$	−28.8045	−1.41566
$415$	−7.51997	−0.369141
$416$	−4.81026	−0.235842
$417$	26.1898	1.28252
$418$	1.67215	0.0817873
$419$	37.8362	1.84842	0.924210	−	0.381885i	$-0.124725\pi$
$419$	37.8362	1.84842	0.924210	+	0.381885i	$0.124725\pi$
$420$	−93.7406	−4.57407
$421$	−34.1724	−1.66546	−0.832730	−	0.553680i	$-0.813223\pi$
$421$	−34.1724	−1.66546	−0.832730	+	0.553680i	$0.813223\pi$
$422$	−52.7198	−2.56636
$423$	9.88782	0.480762
$424$	2.38541	0.115846
$425$	−33.3779	−1.61907
$426$	−33.1103	−1.60420
$427$	−54.8751	−2.65559
$428$	54.5951	2.63895
$429$	8.10683	0.391401
$430$	−7.47466	−0.360460
$431$	−17.7639	−0.855657	−0.427828	−	0.903860i	$-0.640721\pi$
$431$	−17.7639	−0.855657	−0.427828	+	0.903860i	$0.640721\pi$
$432$	26.2782	1.26431
$433$	−18.7717	−0.902108	−0.451054	−	0.892497i	$-0.648952\pi$
$433$	−18.7717	−0.902108	−0.451054	+	0.892497i	$0.648952\pi$
$434$	73.0911	3.50848
$435$	27.7908	1.33246
$436$	5.65052	0.270611
$437$	−3.62799	−0.173550
$438$	−30.9821	−1.48038
$439$	−26.9570	−1.28659	−0.643293	−	0.765620i	$-0.722432\pi$
$439$	−26.9570	−1.28659	−0.643293	+	0.765620i	$0.722432\pi$
$440$	28.5124	1.35927
$441$	−27.1736	−1.29398
$442$	47.8183	2.27449
$443$	8.31072	0.394854	0.197427	−	0.980318i	$-0.436741\pi$
$443$	8.31072	0.394854	0.197427	+	0.980318i	$0.436741\pi$
$444$	−29.6313	−1.40624
$445$	9.62363	0.456204
$446$	−52.1155	−2.46774
$447$	−1.25363	−0.0592945
$448$	−33.5271	−1.58401
$449$	20.8241	0.982750	0.491375	−	0.870948i	$-0.336494\pi$
$449$	20.8241	0.982750	0.491375	+	0.870948i	$0.336494\pi$
$450$	23.8563	1.12459
$451$	6.06928	0.285791
$452$	−47.3280	−2.22612
$453$	19.8922	0.934615
$454$	35.5816	1.66993
$455$	72.4410	3.39609
$456$	2.86414	0.134126
$457$	12.3942	0.579777	0.289888	−	0.957060i	$-0.406382\pi$
$457$	12.3942	0.579777	0.289888	+	0.957060i	$0.406382\pi$
$458$	−62.0485	−2.89933
$459$	−26.6193	−1.24248
$460$	−120.314	−5.60969
$461$	14.0535	0.654538	0.327269	−	0.944931i	$-0.393872\pi$
$461$	14.0535	0.654538	0.327269	+	0.944931i	$0.393872\pi$
$462$	−25.5817	−1.19017
$463$	−17.0593	−0.792812	−0.396406	−	0.918075i	$-0.629743\pi$
$463$	−17.0593	−0.792812	−0.396406	+	0.918075i	$0.629743\pi$
$464$	−29.7217	−1.37980
$465$	25.2115	1.16916
$466$	−52.1685	−2.41666
$467$	−2.84827	−0.131802	−0.0659012	−	0.997826i	$-0.520992\pi$
$467$	−2.84827	−0.131802	−0.0659012	+	0.997826i	$0.520992\pi$
$468$	−23.0022	−1.06328
$469$	7.45638	0.344304
$470$	61.3658	2.83059
$471$	−16.2736	−0.749850
$472$	49.7681	2.29076
$473$	−1.37285	−0.0631238
$474$	−30.2692	−1.39031
$475$	3.00475	0.137867
$476$	−101.556	−4.65479
$477$	0.628777	0.0287897
$478$	−38.1929	−1.74690
$479$	−38.6704	−1.76690	−0.883448	−	0.468530i	$-0.844784\pi$
$479$	−38.6704	−1.76690	−0.883448	+	0.468530i	$0.844784\pi$
$480$	5.23577	0.238979
$481$	22.8985	1.04408
$482$	18.6404	0.849046
$483$	55.5036	2.52550
$484$	−35.0985	−1.59539
$485$	−20.9441	−0.951023
$486$	32.0573	1.45415
$487$	−10.1059	−0.457940	−0.228970	−	0.973433i	$-0.573536\pi$
$487$	−10.1059	−0.457940	−0.228970	+	0.973433i	$0.573536\pi$
$488$	55.6024	2.51700
$489$	27.7933	1.25686
$490$	−168.645	−7.61861
$491$	25.8182	1.16516	0.582579	−	0.812774i	$-0.302044\pi$
$491$	25.8182	1.16516	0.582579	+	0.812774i	$0.302044\pi$
$492$	20.2185	0.911522
$493$	30.1076	1.35598
$494$	−4.30470	−0.193678
$495$	7.51568	0.337805
$496$	−26.9633	−1.21069
$497$	−54.3412	−2.43753
$498$	−6.83644	−0.306348
$499$	18.7518	0.839445	0.419722	−	0.907653i	$-0.362127\pi$
$499$	18.7518	0.839445	0.419722	+	0.907653i	$0.362127\pi$
$500$	28.3717	1.26882
$501$	14.6727	0.655528
$502$	3.81000	0.170049
$503$	−17.3983	−0.775753	−0.387877	−	0.921711i	$-0.626791\pi$
$503$	−17.3983	−0.775753	−0.387877	+	0.921711i	$0.626791\pi$
$504$	37.3211	1.66241
$505$	−16.9334	−0.753526
$506$	−32.8336	−1.45963
$507$	−4.32306	−0.191994
$508$	−0.0910571	−0.00404000
$509$	−7.37687	−0.326974	−0.163487	−	0.986545i	$-0.552274\pi$
$509$	−7.37687	−0.326974	−0.163487	+	0.986545i	$0.552274\pi$
$510$	−52.0483	−2.30474
$511$	−50.8483	−2.24939
$512$	43.7522	1.93359
$513$	2.39632	0.105800
$514$	51.5309	2.27293
$515$	−46.9891	−2.07059
$516$	−4.57337	−0.201331
$517$	11.2709	0.495694
$518$	−72.2580	−3.17483
$519$	8.65776	0.380034
$520$	−73.4011	−3.21885
$521$	9.01569	0.394985	0.197492	−	0.980304i	$-0.436720\pi$
$521$	9.01569	0.394985	0.197492	+	0.980304i	$0.436720\pi$
$522$	−21.5188	−0.941854
$523$	−30.4966	−1.33352	−0.666761	−	0.745272i	$-0.732320\pi$
$523$	−30.4966	−1.33352	−0.666761	+	0.745272i	$0.732320\pi$
$524$	62.4581	2.72850
$525$	−45.9688	−2.00624
$526$	−53.9198	−2.35102
$527$	27.3133	1.18979
$528$	9.43707	0.410696
$529$	48.2379	2.09730
$530$	3.90232	0.169506
$531$	13.1185	0.569296
$532$	9.14222	0.396366
$533$	−15.6245	−0.676772
$534$	8.74888	0.378601
$535$	45.9222	1.98539
$536$	−7.55521	−0.326335
$537$	−30.1910	−1.30284
$538$	37.3640	1.61088
$539$	−30.9746	−1.33417
$540$	79.4690	3.41980
$541$	3.93633	0.169236	0.0846180	−	0.996413i	$-0.473033\pi$
$541$	3.93633	0.169236	0.0846180	+	0.996413i	$0.473033\pi$
$542$	7.26987	0.312268
$543$	−14.9245	−0.640472
$544$	5.67227	0.243196
$545$	4.75288	0.203591
$546$	65.8564	2.81839
$547$	11.8521	0.506757	0.253379	−	0.967367i	$-0.418458\pi$
$547$	11.8521	0.506757	0.253379	+	0.967367i	$0.418458\pi$
$548$	17.4452	0.745223
$549$	14.6564	0.625521
$550$	27.1932	1.15952
$551$	−2.71034	−0.115465
$552$	−56.2392	−2.39370
$553$	−49.6783	−2.11254
$554$	36.4557	1.54885
$555$	−24.9241	−1.05797
$556$	−84.7047	−3.59228
$557$	24.3174	1.03036	0.515181	−	0.857082i	$-0.327725\pi$
$557$	24.3174	1.03036	0.515181	+	0.857082i	$0.327725\pi$
$558$	−19.5217	−0.826419
$559$	3.53421	0.149481
$560$	84.3277	3.56350
$561$	−9.55958	−0.403606
$562$	−53.7586	−2.26767
$563$	−45.7520	−1.92822	−0.964108	−	0.265512i	$-0.914459\pi$
$563$	−45.7520	−1.92822	−0.964108	+	0.265512i	$0.914459\pi$
$564$	37.5467	1.58100
$565$	−39.8095	−1.67480
$566$	−29.0174	−1.21969
$567$	−15.2730	−0.641408
$568$	55.0614	2.31032
$569$	27.8533	1.16767	0.583835	−	0.811872i	$-0.301551\pi$
$569$	27.8533	1.16767	0.583835	+	0.811872i	$0.301551\pi$
$570$	4.68549	0.196254
$571$	44.9562	1.88136	0.940678	−	0.339300i	$-0.110190\pi$
$571$	44.9562	1.88136	0.940678	+	0.339300i	$0.110190\pi$
$572$	−26.2196	−1.09630
$573$	−14.7920	−0.617943
$574$	49.3042	2.05792
$575$	−59.0001	−2.46047
$576$	8.95467	0.373111
$577$	7.48666	0.311674	0.155837	−	0.987783i	$-0.450193\pi$
$577$	7.48666	0.311674	0.155837	+	0.987783i	$0.450193\pi$
$578$	−14.3432	−0.596598
$579$	31.3035	1.30093
$580$	−89.8827	−3.73218
$581$	−11.2201	−0.465487
$582$	−19.0404	−0.789248
$583$	0.716729	0.0296839
$584$	51.5222	2.13200
$585$	−19.3480	−0.799943
$586$	13.3431	0.551199
$587$	27.4524	1.13308	0.566542	−	0.824033i	$-0.308281\pi$
$587$	27.4524	1.13308	0.566542	+	0.824033i	$0.308281\pi$
$588$	−103.185	−4.25529
$589$	−2.45880	−0.101313
$590$	81.4164	3.35186
$591$	−18.6893	−0.768774
$592$	26.6559	1.09555
$593$	1.53239	0.0629277	0.0314638	−	0.999505i	$-0.489983\pi$
$593$	1.53239	0.0629277	0.0314638	+	0.999505i	$0.489983\pi$
$594$	21.6870	0.889826
$595$	−85.4225	−3.50198
$596$	4.05457	0.166081
$597$	−4.36090	−0.178480
$598$	84.5255	3.45650
$599$	−43.8770	−1.79277	−0.896383	−	0.443281i	$-0.853815\pi$
$599$	−43.8770	−1.79277	−0.896383	+	0.443281i	$0.853815\pi$
$600$	46.5780	1.90154
$601$	−11.5578	−0.471451	−0.235725	−	0.971820i	$-0.575747\pi$
$601$	−11.5578	−0.471451	−0.235725	+	0.971820i	$0.575747\pi$
$602$	−11.1525	−0.454540
$603$	−1.99150	−0.0811003
$604$	−64.3366	−2.61782
$605$	−29.5228	−1.20027
$606$	−15.3942	−0.625347
$607$	11.5393	0.468365	0.234182	−	0.972193i	$-0.424759\pi$
$607$	11.5393	0.468365	0.234182	+	0.972193i	$0.424759\pi$
$608$	−0.510628	−0.0207087
$609$	41.4648	1.68024
$610$	90.9608	3.68290
$611$	−29.0153	−1.17384
$612$	27.1242	1.09643
$613$	−0.274556	−0.0110892	−0.00554462	−	0.999985i	$-0.501765\pi$
$613$	−0.274556	−0.0110892	−0.00554462	+	0.999985i	$0.501765\pi$
$614$	21.9804	0.887058
$615$	17.0066	0.685773
$616$	42.5415	1.71405
$617$	14.9897	0.603463	0.301732	−	0.953393i	$-0.402435\pi$
$617$	14.9897	0.603463	0.301732	+	0.953393i	$0.402435\pi$
$618$	−42.7180	−1.71837
$619$	−2.92828	−0.117698	−0.0588488	−	0.998267i	$-0.518743\pi$
$619$	−2.92828	−0.117698	−0.0588488	+	0.998267i	$0.518743\pi$
$620$	−81.5407	−3.27475
$621$	−47.0534	−1.88819
$622$	17.9866	0.721197
$623$	14.3588	0.575273
$624$	−24.2944	−0.972553
$625$	−11.0870	−0.443480
$626$	−39.3158	−1.57137
$627$	0.860572	0.0343679
$628$	52.6333	2.10030
$629$	−27.0020	−1.07664
$630$	61.0541	2.43245
$631$	15.7476	0.626903	0.313452	−	0.949604i	$-0.398515\pi$
$631$	15.7476	0.626903	0.313452	+	0.949604i	$0.398515\pi$
$632$	50.3367	2.00229
$633$	−27.1323	−1.07841
$634$	−20.2691	−0.804990
$635$	−0.0765918	−0.00303945
$636$	2.38763	0.0946758
$637$	79.7397	3.15940
$638$	−24.5289	−0.971107
$639$	14.5138	0.574158
$640$	63.8014	2.52197
$641$	46.2285	1.82592	0.912958	−	0.408053i	$-0.133792\pi$
$641$	46.2285	1.82592	0.912958	+	0.408053i	$0.133792\pi$
$642$	41.7480	1.64766
$643$	5.90977	0.233059	0.116529	−	0.993187i	$-0.462823\pi$
$643$	5.90977	0.233059	0.116529	+	0.993187i	$0.462823\pi$
$644$	−179.513	−7.07382
$645$	−3.84684	−0.151469
$646$	5.07611	0.199717
$647$	0.341045	0.0134079	0.00670393	−	0.999978i	$-0.497866\pi$
$647$	0.341045	0.0134079	0.00670393	+	0.999978i	$0.497866\pi$
$648$	15.4755	0.607934
$649$	14.9535	0.586978
$650$	−70.0051	−2.74582
$651$	37.6164	1.47430
$652$	−89.8910	−3.52040
$653$	−7.69933	−0.301298	−0.150649	−	0.988587i	$-0.548136\pi$
$653$	−7.69933	−0.301298	−0.150649	+	0.988587i	$0.548136\pi$
$654$	4.32086	0.168959
$655$	52.5360	2.05275
$656$	−18.1883	−0.710134
$657$	13.5809	0.529842
$658$	91.5600	3.56938
$659$	−3.20144	−0.124710	−0.0623552	−	0.998054i	$-0.519861\pi$
$659$	−3.20144	−0.124710	−0.0623552	+	0.998054i	$0.519861\pi$
$660$	28.5390	1.11088
$661$	−17.8351	−0.693705	−0.346853	−	0.937920i	$-0.612750\pi$
$661$	−17.8351	−0.693705	−0.346853	+	0.937920i	$0.612750\pi$
$662$	18.6789	0.725975
$663$	24.6098	0.955765
$664$	11.3688	0.441194
$665$	7.68990	0.298201
$666$	19.2992	0.747827
$667$	53.2193	2.06066
$668$	−47.4554	−1.83611
$669$	−26.8213	−1.03697
$670$	−12.3597	−0.477496
$671$	16.7065	0.644949
$672$	7.81196	0.301353
$673$	31.7315	1.22316	0.611580	−	0.791183i	$-0.290534\pi$
$673$	31.7315	1.22316	0.611580	+	0.791183i	$0.290534\pi$
$674$	0.248228	0.00956138
$675$	38.9702	1.49996
$676$	13.9819	0.537766
$677$	20.6278	0.792790	0.396395	−	0.918080i	$-0.370261\pi$
$677$	20.6278	0.792790	0.396395	+	0.918080i	$0.370261\pi$
$678$	−36.1909	−1.38990
$679$	−31.2493	−1.19924
$680$	86.5546	3.31922
$681$	18.3121	0.701722
$682$	−22.2523	−0.852086
$683$	10.4330	0.399208	0.199604	−	0.979877i	$-0.436034\pi$
$683$	10.4330	0.399208	0.199604	+	0.979877i	$0.436034\pi$
$684$	−2.44177	−0.0933634
$685$	14.6739	0.560660
$686$	−162.180	−6.19208
$687$	−31.9333	−1.21833
$688$	4.11413	0.156850
$689$	−1.84512	−0.0702934
$690$	−92.0025	−3.50248
$691$	15.1266	0.575443	0.287722	−	0.957714i	$-0.407102\pi$
$691$	15.1266	0.575443	0.287722	+	0.957714i	$0.407102\pi$
$692$	−28.0015	−1.06446
$693$	11.2137	0.425972
$694$	12.1530	0.461323
$695$	−71.2485	−2.70261
$696$	−42.0143	−1.59255
$697$	18.4244	0.697875
$698$	−32.7997	−1.24149
$699$	−26.8486	−1.01551
$700$	148.675	5.61940
$701$	34.3288	1.29658	0.648291	−	0.761393i	$-0.275484\pi$
$701$	34.3288	1.29658	0.648291	+	0.761393i	$0.275484\pi$
$702$	−55.8300	−2.10717
$703$	2.43077	0.0916782
$704$	10.2072	0.384699
$705$	31.5820	1.18945
$706$	46.9950	1.76868
$707$	−25.2652	−0.950195
$708$	49.8146	1.87215
$709$	50.4344	1.89410	0.947052	−	0.321079i	$-0.104046\pi$
$709$	50.4344	1.89410	0.947052	+	0.321079i	$0.104046\pi$
$710$	90.0757	3.38048
$711$	13.2684	0.497605
$712$	−14.5491	−0.545251
$713$	48.2800	1.80810
$714$	−77.6579	−2.90627
$715$	−22.0544	−0.824788
$716$	97.6457	3.64919
$717$	−19.6560	−0.734068
$718$	38.3339	1.43061
$719$	−10.6400	−0.396806	−0.198403	−	0.980120i	$-0.563576\pi$
$719$	−10.6400	−0.396806	−0.198403	+	0.980120i	$0.563576\pi$
$720$	−22.5228	−0.839377
$721$	−70.1094	−2.61101
$722$	46.5337	1.73180
$723$	9.59329	0.356778
$724$	48.2698	1.79393
$725$	−44.0769	−1.63698
$726$	−26.8393	−0.996099
$727$	21.0187	0.779542	0.389771	−	0.920912i	$-0.372554\pi$
$727$	21.0187	0.779542	0.389771	+	0.920912i	$0.372554\pi$
$728$	−109.517	−4.05897
$729$	25.3669	0.939514
$730$	84.2859	3.11956
$731$	−4.16755	−0.154142
$732$	55.6543	2.05704
$733$	−1.89593	−0.0700279	−0.0350140	−	0.999387i	$-0.511148\pi$
$733$	−1.89593	−0.0700279	−0.0350140	+	0.999387i	$0.511148\pi$
$734$	52.3579	1.93257
$735$	−86.7934	−3.20142
$736$	10.0265	0.369582
$737$	−2.27007	−0.0836191
$738$	−13.1685	−0.484740
$739$	14.8998	0.548099	0.274050	−	0.961716i	$-0.411637\pi$
$739$	14.8998	0.548099	0.274050	+	0.961716i	$0.411637\pi$
$740$	80.6113	2.96333
$741$	−2.21542	−0.0813855
$742$	5.82240	0.213747
$743$	−21.6822	−0.795443	−0.397722	−	0.917506i	$-0.630199\pi$
$743$	−21.6822	−0.795443	−0.397722	+	0.917506i	$0.630199\pi$
$744$	−38.1150	−1.39736
$745$	3.41046	0.124950
$746$	−67.8983	−2.48593
$747$	2.99673	0.109645
$748$	30.9182	1.13048
$749$	68.5175	2.50357
$750$	21.6954	0.792204
$751$	−20.4733	−0.747081	−0.373540	−	0.927614i	$-0.621856\pi$
$751$	−20.4733	−0.747081	−0.373540	+	0.927614i	$0.621856\pi$
$752$	−33.7764	−1.23170
$753$	1.96082	0.0714563
$754$	63.1460	2.29964
$755$	−54.1161	−1.96949
$756$	118.570	4.31237
$757$	8.29139	0.301356	0.150678	−	0.988583i	$-0.451854\pi$
$757$	8.29139	0.301356	0.150678	+	0.988583i	$0.451854\pi$
$758$	−57.8650	−2.10175
$759$	−16.8979	−0.613354
$760$	−7.79181	−0.282639
$761$	−1.55021	−0.0561952	−0.0280976	−	0.999605i	$-0.508945\pi$
$761$	−1.55021	−0.0561952	−0.0280976	+	0.999605i	$0.508945\pi$
$762$	−0.0696299	−0.00252242
$763$	7.09147	0.256728
$764$	47.8412	1.73083
$765$	22.8152	0.824887
$766$	−61.7604	−2.23149
$767$	−38.4958	−1.39000
$768$	41.4824	1.49687
$769$	5.49962	0.198321	0.0991607	−	0.995071i	$-0.468384\pi$
$769$	5.49962	0.198321	0.0991607	+	0.995071i	$0.468384\pi$
$770$	69.5942	2.50800
$771$	26.5205	0.955112
$772$	−101.244	−3.64384
$773$	0.712111	0.0256129	0.0128064	−	0.999918i	$-0.495923\pi$
$773$	0.712111	0.0256129	0.0128064	+	0.999918i	$0.495923\pi$
$774$	2.97868	0.107066
$775$	−39.9861	−1.43634
$776$	31.6635	1.13665
$777$	−37.1877	−1.33410
$778$	−75.3324	−2.70080
$779$	−1.65860	−0.0594256
$780$	−73.4696	−2.63063
$781$	16.5440	0.591990
$782$	−99.6726	−3.56428
$783$	−35.1519	−1.25623
$784$	92.8241	3.31515
$785$	44.2720	1.58014
$786$	47.7607	1.70357
$787$	−14.1041	−0.502757	−0.251378	−	0.967889i	$-0.580884\pi$
$787$	−14.1041	−0.502757	−0.251378	+	0.967889i	$0.580884\pi$
$788$	60.4461	2.15330
$789$	−27.7499	−0.987924
$790$	82.3466	2.92976
$791$	−59.3971	−2.11192
$792$	−11.3623	−0.403741
$793$	−43.0086	−1.52728
$794$	−81.6695	−2.89834
$795$	2.00834	0.0712283
$796$	14.1043	0.499914
$797$	−8.51124	−0.301484	−0.150742	−	0.988573i	$-0.548166\pi$
$797$	−8.51124	−0.301484	−0.150742	+	0.988573i	$0.548166\pi$
$798$	6.99091	0.247476
$799$	34.2149	1.21044
$800$	−8.30408	−0.293594
$801$	−3.83505	−0.135505
$802$	−76.0411	−2.68510
$803$	15.4806	0.546298
$804$	−7.56226	−0.266700
$805$	−150.996	−5.32191
$806$	57.2855	2.01779
$807$	19.2294	0.676908
$808$	25.6001	0.900607
$809$	1.21782	0.0428163	0.0214082	−	0.999771i	$-0.493185\pi$
$809$	1.21782	0.0428163	0.0214082	+	0.999771i	$0.493185\pi$
$810$	25.3165	0.889533
$811$	−48.1415	−1.69048	−0.845238	−	0.534389i	$-0.820542\pi$
$811$	−48.1415	−1.69048	−0.845238	+	0.534389i	$0.820542\pi$
$812$	−134.108	−4.70627
$813$	3.74145	0.131218
$814$	21.9987	0.771054
$815$	−75.6110	−2.64854
$816$	28.6480	1.00288
$817$	0.375170	0.0131256
$818$	63.2712	2.21223
$819$	−28.8680	−1.00873
$820$	−55.0040	−1.92082
$821$	25.6438	0.894976	0.447488	−	0.894290i	$-0.352319\pi$
$821$	25.6438	0.894976	0.447488	+	0.894290i	$0.352319\pi$
$822$	13.3401	0.465289
$823$	−6.14530	−0.214212	−0.107106	−	0.994248i	$-0.534158\pi$
$823$	−6.14530	−0.214212	−0.107106	+	0.994248i	$0.534158\pi$
$824$	71.0386	2.47475
$825$	13.9950	0.487244
$826$	121.476	4.22669
$827$	6.31854	0.219717	0.109859	−	0.993947i	$-0.464960\pi$
$827$	6.31854	0.219717	0.109859	+	0.993947i	$0.464960\pi$
$828$	47.9457	1.66623
$829$	47.4396	1.64765	0.823823	−	0.566848i	$-0.191837\pi$
$829$	47.4396	1.64765	0.823823	+	0.566848i	$0.191837\pi$
$830$	18.5983	0.645558
$831$	18.7620	0.650846
$832$	−26.2770	−0.910993
$833$	−94.0292	−3.25792
$834$	−64.7723	−2.24288
$835$	−39.9167	−1.38137
$836$	−2.78332	−0.0962631
$837$	−31.8895	−1.10226
$838$	−93.5762	−3.23254
$839$	28.6664	0.989673	0.494837	−	0.868986i	$-0.335228\pi$
$839$	28.6664	0.989673	0.494837	+	0.868986i	$0.335228\pi$
$840$	119.205	4.11295
$841$	10.7583	0.370976
$842$	84.5148	2.91257
$843$	−27.6670	−0.952901
$844$	87.7532	3.02059
$845$	11.7608	0.404583
$846$	−24.4545	−0.840762
$847$	−44.0490	−1.51354
$848$	−2.14788	−0.0737585
$849$	−14.9339	−0.512529
$850$	82.5501	2.83144
$851$	−47.7297	−1.63615
$852$	55.1128	1.88813
$853$	−25.1771	−0.862047	−0.431023	−	0.902341i	$-0.641847\pi$
$853$	−25.1771	−0.862047	−0.431023	+	0.902341i	$0.641847\pi$
$854$	135.717	4.64413
$855$	−2.05387	−0.0702409
$856$	−69.4256	−2.37292
$857$	17.9120	0.611863	0.305932	−	0.952053i	$-0.401032\pi$
$857$	17.9120	0.611863	0.305932	+	0.952053i	$0.401032\pi$
$858$	−20.0497	−0.684487
$859$	−52.1517	−1.77939	−0.889696	−	0.456553i	$-0.849084\pi$
$859$	−52.1517	−1.77939	−0.889696	+	0.456553i	$0.849084\pi$
$860$	12.4417	0.424259
$861$	25.3745	0.864760
$862$	43.9335	1.49638
$863$	−16.0440	−0.546145	−0.273073	−	0.961993i	$-0.588040\pi$
$863$	−16.0440	−0.546145	−0.273073	+	0.961993i	$0.588040\pi$
$864$	−6.62261	−0.225306
$865$	−23.5532	−0.800833
$866$	46.4259	1.57762
$867$	−7.38174	−0.250697
$868$	−121.662	−4.12946
$869$	15.1244	0.513060
$870$	−68.7319	−2.33023
$871$	5.84397	0.198015
$872$	−7.18546	−0.243330
$873$	8.34629	0.282479
$874$	8.97271	0.303507
$875$	35.6068	1.20373
$876$	51.5703	1.74240
$877$	−45.8397	−1.54790	−0.773949	−	0.633248i	$-0.781721\pi$
$877$	−45.8397	−1.54790	−0.773949	+	0.633248i	$0.781721\pi$
$878$	66.6698	2.25000
$879$	6.86705	0.231620
$880$	−25.6733	−0.865446
$881$	8.26352	0.278405	0.139202	−	0.990264i	$-0.455546\pi$
$881$	8.26352	0.278405	0.139202	+	0.990264i	$0.455546\pi$
$882$	67.2056	2.26293
$883$	0.615703	0.0207201	0.0103600	−	0.999946i	$-0.496702\pi$
$883$	0.615703	0.0207201	0.0103600	+	0.999946i	$0.496702\pi$
$884$	−79.5946	−2.67706
$885$	41.9011	1.40849
$886$	−20.5540	−0.690525
$887$	24.7628	0.831454	0.415727	−	0.909489i	$-0.363527\pi$
$887$	24.7628	0.831454	0.415727	+	0.909489i	$0.363527\pi$
$888$	37.6805	1.26448
$889$	−0.114278	−0.00383275
$890$	−23.8011	−0.797815
$891$	4.64983	0.155775
$892$	86.7473	2.90452
$893$	−3.08009	−0.103071
$894$	3.10046	0.103695
$895$	82.1338	2.74543
$896$	95.1940	3.18021
$897$	43.5012	1.45246
$898$	−51.5020	−1.71864
$899$	36.0683	1.20295
$900$	−39.7092	−1.32364
$901$	2.17576	0.0724852
$902$	−15.0105	−0.499795
$903$	−5.73963	−0.191003
$904$	60.1844	2.00170
$905$	40.6017	1.34965
$906$	−49.1971	−1.63447
$907$	−12.2849	−0.407913	−0.203957	−	0.978980i	$-0.565380\pi$
$907$	−12.2849	−0.407913	−0.203957	+	0.978980i	$0.565380\pi$
$908$	−59.2263	−1.96549
$909$	6.74801	0.223817
$910$	−179.160	−5.93911
$911$	−4.16950	−0.138142	−0.0690709	−	0.997612i	$-0.522003\pi$
$911$	−4.16950	−0.138142	−0.0690709	+	0.997612i	$0.522003\pi$
$912$	−2.57894	−0.0853974
$913$	3.41591	0.113050
$914$	−30.6533	−1.01392
$915$	46.8131	1.54759
$916$	103.281	3.41250
$917$	78.3856	2.58852
$918$	65.8348	2.17287
$919$	22.3994	0.738888	0.369444	−	0.929253i	$-0.379548\pi$
$919$	22.3994	0.738888	0.369444	+	0.929253i	$0.379548\pi$
$920$	152.997	5.04417
$921$	11.3123	0.372752
$922$	−34.7571	−1.14466
$923$	−42.5901	−1.40187
$924$	42.5812	1.40082
$925$	39.5304	1.29975
$926$	42.1909	1.38648
$927$	18.7253	0.615020
$928$	7.49045	0.245886
$929$	58.2813	1.91215	0.956074	−	0.293125i	$-0.0946953\pi$
$929$	58.2813	1.91215	0.956074	+	0.293125i	$0.0946953\pi$
$930$	−62.3529	−2.04463
$931$	8.46469	0.277419
$932$	86.8355	2.84439
$933$	9.25683	0.303055
$934$	7.04433	0.230497
$935$	26.0066	0.850506
$936$	29.2506	0.956085
$937$	6.20367	0.202665	0.101333	−	0.994853i	$-0.467689\pi$
$937$	6.20367	0.202665	0.101333	+	0.994853i	$0.467689\pi$
$938$	−18.4411	−0.602122
$939$	−20.2339	−0.660309
$940$	−102.145	−3.33159
$941$	39.4632	1.28646	0.643231	−	0.765672i	$-0.277593\pi$
$941$	39.4632	1.28646	0.643231	+	0.765672i	$0.277593\pi$
$942$	40.2478	1.31135
$943$	32.5677	1.06055
$944$	−44.8125	−1.45852
$945$	99.7344	3.24436
$946$	3.39533	0.110392
$947$	−50.4622	−1.63980	−0.819900	−	0.572507i	$-0.805971\pi$
$947$	−50.4622	−1.63980	−0.819900	+	0.572507i	$0.805971\pi$
$948$	50.3837	1.63639
$949$	−39.8525	−1.29367
$950$	−7.43131	−0.241104
$951$	−10.4315	−0.338266
$952$	129.143	4.18553
$953$	−10.8389	−0.351107	−0.175554	−	0.984470i	$-0.556172\pi$
$953$	−10.8389	−0.351107	−0.175554	+	0.984470i	$0.556172\pi$
$954$	−1.55509	−0.0503478
$955$	40.2411	1.30217
$956$	63.5729	2.05609
$957$	−12.6238	−0.408070
$958$	95.6393	3.08997
$959$	21.8939	0.706992
$960$	28.6015	0.923109
$961$	1.72084	0.0555109
$962$	−56.6325	−1.82590
$963$	−18.3001	−0.589713
$964$	−31.0273	−0.999321
$965$	−85.1603	−2.74141
$966$	−137.271	−4.41662
$967$	−44.9909	−1.44681	−0.723405	−	0.690424i	$-0.757424\pi$
$967$	−44.9909	−1.44681	−0.723405	+	0.690424i	$0.757424\pi$
$968$	44.6329	1.43455
$969$	2.61243	0.0839232
$970$	51.7988	1.66316
$971$	−56.8906	−1.82571	−0.912853	−	0.408288i	$-0.866126\pi$
$971$	−56.8906	−1.82571	−0.912853	+	0.408288i	$0.866126\pi$
$972$	−53.3600	−1.71152
$973$	−106.305	−3.40799
$974$	24.9937	0.800851
$975$	−36.0282	−1.15383
$976$	−50.0658	−1.60257
$977$	−44.2662	−1.41620	−0.708100	−	0.706112i	$-0.750447\pi$
$977$	−44.2662	−1.41620	−0.708100	+	0.706112i	$0.750447\pi$
$978$	−68.7382	−2.19801
$979$	−4.37149	−0.139713
$980$	280.713	8.96705
$981$	−1.89404	−0.0604720
$982$	−63.8533	−2.03764
$983$	−8.62043	−0.274949	−0.137475	−	0.990505i	$-0.543899\pi$
$983$	−8.62043	−0.274949	−0.137475	+	0.990505i	$0.543899\pi$
$984$	−25.7108	−0.819630
$985$	50.8437	1.62001
$986$	−74.4619	−2.37135
$987$	47.1215	1.49989
$988$	7.16526	0.227957
$989$	−7.36671	−0.234248
$990$	−18.5877	−0.590757
$991$	15.3951	0.489040	0.244520	−	0.969644i	$-0.421370\pi$
$991$	15.3951	0.489040	0.244520	+	0.969644i	$0.421370\pi$
$992$	6.79527	0.215750
$993$	9.61311	0.305063
$994$	134.396	4.26279
$995$	11.8637	0.376105
$996$	11.3794	0.360570
$997$	54.5814	1.72861	0.864305	−	0.502968i	$-0.167759\pi$
$997$	54.5814	1.72861	0.864305	+	0.502968i	$0.167759\pi$
$998$	−46.3767	−1.46803
$999$	31.5260	0.997438

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.18	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.18	✓	205	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.47319 q^{2} -1.27283 q^{3} +4.11668 q^{4} +3.46270 q^{5} +3.14796 q^{6} +5.16648 q^{7} -5.23495 q^{8} -1.37990 q^{9} +O(q^{10})\)	\(q-2.47319 q^{2} -1.27283 q^{3} +4.11668 q^{4} +3.46270 q^{5} +3.14796 q^{6} +5.16648 q^{7} -5.23495 q^{8} -1.37990 q^{9} -8.56393 q^{10} -1.57292 q^{11} -5.23984 q^{12} +4.04925 q^{13} -12.7777 q^{14} -4.40744 q^{15} +4.71368 q^{16} -4.77488 q^{17} +3.41275 q^{18} +0.429844 q^{19} +14.2548 q^{20} -6.57606 q^{21} +3.89012 q^{22} -8.44025 q^{23} +6.66321 q^{24} +6.99032 q^{25} -10.0146 q^{26} +5.57488 q^{27} +21.2687 q^{28} -6.30542 q^{29} +10.9004 q^{30} -5.72021 q^{31} -1.18794 q^{32} +2.00206 q^{33} +11.8092 q^{34} +17.8900 q^{35} -5.68060 q^{36} +5.65501 q^{37} -1.06309 q^{38} -5.15401 q^{39} -18.1271 q^{40} -3.85862 q^{41} +16.2638 q^{42} +0.872807 q^{43} -6.47519 q^{44} -4.77818 q^{45} +20.8744 q^{46} -7.16561 q^{47} -5.99973 q^{48} +19.6925 q^{49} -17.2884 q^{50} +6.07762 q^{51} +16.6695 q^{52} -0.455669 q^{53} -13.7877 q^{54} -5.44654 q^{55} -27.0463 q^{56} -0.547119 q^{57} +15.5945 q^{58} -9.50689 q^{59} -18.1440 q^{60} -10.6214 q^{61} +14.1472 q^{62} -7.12921 q^{63} -6.48936 q^{64} +14.0213 q^{65} -4.95147 q^{66} +1.44322 q^{67} -19.6566 q^{68} +10.7430 q^{69} -44.2454 q^{70} -10.5180 q^{71} +7.22370 q^{72} -9.84196 q^{73} -13.9859 q^{74} -8.89751 q^{75} +1.76953 q^{76} -8.12643 q^{77} +12.7469 q^{78} -9.61551 q^{79} +16.3221 q^{80} -2.95618 q^{81} +9.54310 q^{82} -2.17170 q^{83} -27.0715 q^{84} -16.5340 q^{85} -2.15862 q^{86} +8.02574 q^{87} +8.23414 q^{88} +2.77922 q^{89} +11.8174 q^{90} +20.9203 q^{91} -34.7458 q^{92} +7.28087 q^{93} +17.7219 q^{94} +1.48842 q^{95} +1.51205 q^{96} -6.04848 q^{97} -48.7033 q^{98} +2.17047 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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