LMFDB - Embedded newform 4019.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$0$
Dimension:	$186$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43453 q^{2} +2.49356 q^{3} +3.92696 q^{4} +3.69129 q^{5} -6.07065 q^{6} +0.601351 q^{7} -4.69125 q^{8} +3.21782 q^{9} +O(q^{10})$	\(q-2.43453 q^{2} +2.49356 q^{3} +3.92696 q^{4} +3.69129 q^{5} -6.07065 q^{6} +0.601351 q^{7} -4.69125 q^{8} +3.21782 q^{9} -8.98658 q^{10} -5.31971 q^{11} +9.79209 q^{12} +3.09616 q^{13} -1.46401 q^{14} +9.20444 q^{15} +3.56709 q^{16} +0.734755 q^{17} -7.83390 q^{18} +2.83652 q^{19} +14.4956 q^{20} +1.49950 q^{21} +12.9510 q^{22} -1.79373 q^{23} -11.6979 q^{24} +8.62564 q^{25} -7.53771 q^{26} +0.543152 q^{27} +2.36148 q^{28} +7.08600 q^{29} -22.4085 q^{30} +2.28441 q^{31} +0.698289 q^{32} -13.2650 q^{33} -1.78879 q^{34} +2.21976 q^{35} +12.6363 q^{36} +9.08400 q^{37} -6.90560 q^{38} +7.72045 q^{39} -17.3168 q^{40} +1.45684 q^{41} -3.65059 q^{42} +0.573711 q^{43} -20.8903 q^{44} +11.8779 q^{45} +4.36689 q^{46} -7.18313 q^{47} +8.89475 q^{48} -6.63838 q^{49} -20.9994 q^{50} +1.83215 q^{51} +12.1585 q^{52} +1.63729 q^{53} -1.32232 q^{54} -19.6366 q^{55} -2.82109 q^{56} +7.07301 q^{57} -17.2511 q^{58} +0.375061 q^{59} +36.1455 q^{60} -3.59350 q^{61} -5.56147 q^{62} +1.93504 q^{63} -8.83420 q^{64} +11.4288 q^{65} +32.2941 q^{66} +9.13823 q^{67} +2.88535 q^{68} -4.47276 q^{69} -5.40409 q^{70} -3.82383 q^{71} -15.0956 q^{72} +6.13553 q^{73} -22.1153 q^{74} +21.5085 q^{75} +11.1389 q^{76} -3.19901 q^{77} -18.7957 q^{78} +5.08529 q^{79} +13.1672 q^{80} -8.29909 q^{81} -3.54673 q^{82} -1.18851 q^{83} +5.88849 q^{84} +2.71219 q^{85} -1.39672 q^{86} +17.6693 q^{87} +24.9561 q^{88} -15.1270 q^{89} -28.9172 q^{90} +1.86188 q^{91} -7.04389 q^{92} +5.69630 q^{93} +17.4876 q^{94} +10.4704 q^{95} +1.74122 q^{96} +5.67676 q^{97} +16.1614 q^{98} -17.1179 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) $ 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * 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 $

$2$	−2.43453	−1.72148	−0.860738	−	0.509048i	$-0.829997\pi$
$2$	−2.43453	−1.72148	−0.860738	+	0.509048i	$0.829997\pi$
$3$	2.49356	1.43966	0.719828	−	0.694153i	$-0.244221\pi$
$3$	2.49356	1.43966	0.719828	+	0.694153i	$0.244221\pi$
$4$	3.92696	1.96348
$5$	3.69129	1.65080	0.825398	−	0.564551i	$-0.190951\pi$
$5$	3.69129	1.65080	0.825398	+	0.564551i	$0.190951\pi$
$6$	−6.07065	−2.47833
$7$	0.601351	0.227289	0.113645	−	0.993521i	$-0.463747\pi$
$7$	0.601351	0.227289	0.113645	+	0.993521i	$0.463747\pi$
$8$	−4.69125	−1.65861
$9$	3.21782	1.07261
$10$	−8.98658	−2.84181
$11$	−5.31971	−1.60395	−0.801976	−	0.597356i	$-0.796218\pi$
$11$	−5.31971	−1.60395	−0.801976	+	0.597356i	$0.796218\pi$
$12$	9.79209	2.82673
$13$	3.09616	0.858721	0.429360	−	0.903133i	$-0.358739\pi$
$13$	3.09616	0.858721	0.429360	+	0.903133i	$0.358739\pi$
$14$	−1.46401	−0.391273
$15$	9.20444	2.37658
$16$	3.56709	0.891773
$17$	0.734755	0.178204	0.0891021	−	0.996022i	$-0.471600\pi$
$17$	0.734755	0.178204	0.0891021	+	0.996022i	$0.471600\pi$
$18$	−7.83390	−1.84647
$19$	2.83652	0.650742	0.325371	−	0.945587i	$-0.394511\pi$
$19$	2.83652	0.650742	0.325371	+	0.945587i	$0.394511\pi$
$20$	14.4956	3.24130
$21$	1.49950	0.327218
$22$	12.9510	2.76117
$23$	−1.79373	−0.374018	−0.187009	−	0.982358i	$-0.559879\pi$
$23$	−1.79373	−0.374018	−0.187009	+	0.982358i	$0.559879\pi$
$24$	−11.6979	−2.38782
$25$	8.62564	1.72513
$26$	−7.53771	−1.47827
$27$	0.543152	0.104530
$28$	2.36148	0.446278
$29$	7.08600	1.31584	0.657919	−	0.753089i	$-0.271437\pi$
$29$	7.08600	1.31584	0.657919	+	0.753089i	$0.271437\pi$
$30$	−22.4085	−4.09122
$31$	2.28441	0.410292	0.205146	−	0.978731i	$-0.434233\pi$
$31$	2.28441	0.410292	0.205146	+	0.978731i	$0.434233\pi$
$32$	0.698289	0.123441
$33$	−13.2650	−2.30914
$34$	−1.78879	−0.306774
$35$	2.21976	0.375208
$36$	12.6363	2.10604
$37$	9.08400	1.49340	0.746700	−	0.665161i	$-0.231637\pi$
$37$	9.08400	1.49340	0.746700	+	0.665161i	$0.231637\pi$
$38$	−6.90560	−1.12024
$39$	7.72045	1.23626
$40$	−17.3168	−2.73802
$41$	1.45684	0.227521	0.113760	−	0.993508i	$-0.463710\pi$
$41$	1.45684	0.227521	0.113760	+	0.993508i	$0.463710\pi$
$42$	−3.65059	−0.563298
$43$	0.573711	0.0874901	0.0437450	−	0.999043i	$-0.486071\pi$
$43$	0.573711	0.0874901	0.0437450	+	0.999043i	$0.486071\pi$
$44$	−20.8903	−3.14933
$45$	11.8779	1.77066
$46$	4.36689	0.643862
$47$	−7.18313	−1.04777	−0.523884	−	0.851790i	$-0.675517\pi$
$47$	−7.18313	−1.04777	−0.523884	+	0.851790i	$0.675517\pi$
$48$	8.89475	1.28385
$49$	−6.63838	−0.948340
$50$	−20.9994	−2.96976
$51$	1.83215	0.256553
$52$	12.1585	1.68608
$53$	1.63729	0.224899	0.112449	−	0.993657i	$-0.464130\pi$
$53$	1.63729	0.224899	0.112449	+	0.993657i	$0.464130\pi$
$54$	−1.32232	−0.179945
$55$	−19.6366	−2.64780
$56$	−2.82109	−0.376984
$57$	7.07301	0.936844
$58$	−17.2511	−2.26518
$59$	0.375061	0.0488288	0.0244144	−	0.999702i	$-0.492228\pi$
$59$	0.375061	0.0488288	0.0244144	+	0.999702i	$0.492228\pi$
$60$	36.1455	4.66636
$61$	−3.59350	−0.460101	−0.230051	−	0.973179i	$-0.573889\pi$
$61$	−3.59350	−0.460101	−0.230051	+	0.973179i	$0.573889\pi$
$62$	−5.56147	−0.706308
$63$	1.93504	0.243792
$64$	−8.83420	−1.10427
$65$	11.4288	1.41757
$66$	32.2941	3.97513
$67$	9.13823	1.11641	0.558206	−	0.829702i	$-0.311490\pi$
$67$	9.13823	1.11641	0.558206	+	0.829702i	$0.311490\pi$
$68$	2.88535	0.349900
$69$	−4.47276	−0.538457
$70$	−5.40409	−0.645912
$71$	−3.82383	−0.453806	−0.226903	−	0.973917i	$-0.572860\pi$
$71$	−3.82383	−0.453806	−0.226903	+	0.973917i	$0.572860\pi$
$72$	−15.0956	−1.77903
$73$	6.13553	0.718109	0.359055	−	0.933317i	$-0.383099\pi$
$73$	6.13553	0.718109	0.359055	+	0.933317i	$0.383099\pi$
$74$	−22.1153	−2.57085
$75$	21.5085	2.48359
$76$	11.1389	1.27772
$77$	−3.19901	−0.364561
$78$	−18.7957	−2.12820
$79$	5.08529	0.572140	0.286070	−	0.958209i	$-0.407651\pi$
$79$	5.08529	0.572140	0.286070	+	0.958209i	$0.407651\pi$
$80$	13.1672	1.47214
$81$	−8.29909	−0.922121
$82$	−3.54673	−0.391671
$83$	−1.18851	−0.130456	−0.0652278	−	0.997870i	$-0.520777\pi$
$83$	−1.18851	−0.130456	−0.0652278	+	0.997870i	$0.520777\pi$
$84$	5.88849	0.642486
$85$	2.71219	0.294179
$86$	−1.39672	−0.150612
$87$	17.6693	1.89435
$88$	24.9561	2.66033
$89$	−15.1270	−1.60346	−0.801731	−	0.597685i	$-0.796087\pi$
$89$	−15.1270	−1.60346	−0.801731	+	0.597685i	$0.796087\pi$
$90$	−28.9172	−3.04814
$91$	1.86188	0.195178
$92$	−7.04389	−0.734376
$93$	5.69630	0.590679
$94$	17.4876	1.80371
$95$	10.4704	1.07424
$96$	1.74122	0.177713
$97$	5.67676	0.576387	0.288194	−	0.957572i	$-0.406945\pi$
$97$	5.67676	0.576387	0.288194	+	0.957572i	$0.406945\pi$
$98$	16.1614	1.63254
$99$	−17.1179	−1.72041
$100$	33.8725	3.38725
$101$	4.69810	0.467478	0.233739	−	0.972299i	$-0.424904\pi$
$101$	4.69810	0.467478	0.233739	+	0.972299i	$0.424904\pi$
$102$	−4.46044	−0.441649
$103$	0.0154012	0.00151752	0.000758762	−	1.00000i	$-0.499758\pi$
$103$	0.0154012	0.00151752	0.000758762		1.00000i	$0.499758\pi$
$104$	−14.5249	−1.42428
$105$	5.53510	0.540171
$106$	−3.98604	−0.387158
$107$	5.38239	0.520335	0.260168	−	0.965563i	$-0.416222\pi$
$107$	5.38239	0.520335	0.260168	+	0.965563i	$0.416222\pi$
$108$	2.13294	0.205242
$109$	5.66536	0.542643	0.271322	−	0.962489i	$-0.412539\pi$
$109$	5.66536	0.542643	0.271322	+	0.962489i	$0.412539\pi$
$110$	47.8060	4.55812
$111$	22.6515	2.14998
$112$	2.14507	0.202691
$113$	17.1675	1.61498	0.807491	−	0.589880i	$-0.200825\pi$
$113$	17.1675	1.61498	0.807491	+	0.589880i	$0.200825\pi$
$114$	−17.2195	−1.61275
$115$	−6.62117	−0.617427
$116$	27.8264	2.58362
$117$	9.96290	0.921070
$118$	−0.913100	−0.0840577
$119$	0.441846	0.0405039
$120$	−43.1803	−3.94181
$121$	17.2993	1.57266
$122$	8.74851	0.792053
$123$	3.63272	0.327551
$124$	8.97078	0.805600
$125$	13.3833	1.19704
$126$	−4.71092	−0.419682
$127$	−4.41377	−0.391659	−0.195829	−	0.980638i	$-0.562740\pi$
$127$	−4.41377	−0.391659	−0.195829	+	0.980638i	$0.562740\pi$
$128$	20.1106	1.77754
$129$	1.43058	0.125956
$130$	−27.8239	−2.44032
$131$	10.1268	0.884780	0.442390	−	0.896823i	$-0.354131\pi$
$131$	10.1268	0.884780	0.442390	+	0.896823i	$0.354131\pi$
$132$	−52.0911	−4.53395
$133$	1.70574	0.147907
$134$	−22.2473	−1.92188
$135$	2.00493	0.172557
$136$	−3.44692	−0.295571
$137$	−4.27066	−0.364867	−0.182434	−	0.983218i	$-0.558397\pi$
$137$	−4.27066	−0.364867	−0.182434	+	0.983218i	$0.558397\pi$
$138$	10.8891	0.926940
$139$	−14.2167	−1.20585	−0.602924	−	0.797799i	$-0.705998\pi$
$139$	−14.2167	−1.20585	−0.602924	+	0.797799i	$0.705998\pi$
$140$	8.71692	0.736714
$141$	−17.9115	−1.50842
$142$	9.30926	0.781216
$143$	−16.4707	−1.37735
$144$	11.4783	0.956523
$145$	26.1565	2.17218
$146$	−14.9372	−1.23621
$147$	−16.5532	−1.36528
$148$	35.6725	2.93226
$149$	14.8062	1.21297	0.606487	−	0.795093i	$-0.292578\pi$
$149$	14.8062	1.21297	0.606487	+	0.795093i	$0.292578\pi$
$150$	−52.3632	−4.27544
$151$	5.28959	0.430461	0.215230	−	0.976563i	$-0.430950\pi$
$151$	5.28959	0.430461	0.215230	+	0.976563i	$0.430950\pi$
$152$	−13.3068	−1.07932
$153$	2.36431	0.191143
$154$	7.78811	0.627584
$155$	8.43242	0.677308
$156$	30.3179	2.42738
$157$	19.5849	1.56304	0.781522	−	0.623878i	$-0.214444\pi$
$157$	19.5849	1.56304	0.781522	+	0.623878i	$0.214444\pi$
$158$	−12.3803	−0.984925
$159$	4.08267	0.323777
$160$	2.57759	0.203776
$161$	−1.07866	−0.0850102
$162$	20.2044	1.58741
$163$	−10.1123	−0.792057	−0.396029	−	0.918238i	$-0.629612\pi$
$163$	−10.1123	−0.792057	−0.396029	+	0.918238i	$0.629612\pi$
$164$	5.72096	0.446732
$165$	−48.9650	−3.81192
$166$	2.89346	0.224576
$167$	−21.2967	−1.64799	−0.823995	−	0.566597i	$-0.808260\pi$
$167$	−21.2967	−1.64799	−0.823995	+	0.566597i	$0.808260\pi$
$168$	−7.03454	−0.542727
$169$	−3.41378	−0.262599
$170$	−6.60293	−0.506422
$171$	9.12741	0.697990
$172$	2.25294	0.171785
$173$	−7.48612	−0.569159	−0.284579	−	0.958652i	$-0.591854\pi$
$173$	−7.48612	−0.569159	−0.284579	+	0.958652i	$0.591854\pi$
$174$	−43.0166	−3.26108
$175$	5.18703	0.392103
$176$	−18.9759	−1.43036
$177$	0.935237	0.0702967
$178$	36.8273	2.76032
$179$	10.0049	0.747799	0.373900	−	0.927469i	$-0.378020\pi$
$179$	10.0049	0.747799	0.373900	+	0.927469i	$0.378020\pi$
$180$	46.6441	3.47665
$181$	4.19987	0.312174	0.156087	−	0.987743i	$-0.450112\pi$
$181$	4.19987	0.312174	0.156087	+	0.987743i	$0.450112\pi$
$182$	−4.53281	−0.335994
$183$	−8.96060	−0.662387
$184$	8.41482	0.620349
$185$	33.5317	2.46530
$186$	−13.8678	−1.01684
$187$	−3.90868	−0.285831
$188$	−28.2079	−2.05727
$189$	0.326625	0.0237585
$190$	−25.4906	−1.84928
$191$	5.03540	0.364349	0.182174	−	0.983266i	$-0.441686\pi$
$191$	5.03540	0.364349	0.182174	+	0.983266i	$0.441686\pi$
$192$	−22.0286	−1.58977
$193$	8.26807	0.595149	0.297575	−	0.954699i	$-0.403822\pi$
$193$	8.26807	0.595149	0.297575	+	0.954699i	$0.403822\pi$
$194$	−13.8203	−0.992237
$195$	28.4984	2.04082
$196$	−26.0686	−1.86205
$197$	−10.7100	−0.763059	−0.381530	−	0.924357i	$-0.624603\pi$
$197$	−10.7100	−0.763059	−0.381530	+	0.924357i	$0.624603\pi$
$198$	41.6741	2.96165
$199$	−26.4384	−1.87417	−0.937085	−	0.349101i	$-0.886487\pi$
$199$	−26.4384	−1.87417	−0.937085	+	0.349101i	$0.886487\pi$
$200$	−40.4650	−2.86131
$201$	22.7867	1.60725
$202$	−11.4377	−0.804753
$203$	4.26117	0.299076
$204$	7.19479	0.503736
$205$	5.37763	0.375590
$206$	−0.0374947	−0.00261238
$207$	−5.77189	−0.401174
$208$	11.0443	0.765784
$209$	−15.0894	−1.04376
$210$	−13.4754	−0.929891
$211$	14.3172	0.985639	0.492820	−	0.870131i	$-0.335966\pi$
$211$	14.3172	0.985639	0.492820	+	0.870131i	$0.335966\pi$
$212$	6.42956	0.441584
$213$	−9.53495	−0.653324
$214$	−13.1036	−0.895745
$215$	2.11773	0.144428
$216$	−2.54806	−0.173374
$217$	1.37373	0.0932550
$218$	−13.7925	−0.934148
$219$	15.2993	1.03383
$220$	−77.1121	−5.19890
$221$	2.27492	0.153028
$222$	−55.1458	−3.70114
$223$	3.16593	0.212006	0.106003	−	0.994366i	$-0.466195\pi$
$223$	3.16593	0.212006	0.106003	+	0.994366i	$0.466195\pi$
$224$	0.419917	0.0280569
$225$	27.7558	1.85038
$226$	−41.7949	−2.78015
$227$	−8.05663	−0.534738	−0.267369	−	0.963594i	$-0.586154\pi$
$227$	−8.05663	−0.534738	−0.267369	+	0.963594i	$0.586154\pi$
$228$	27.7754	1.83947
$229$	−19.4781	−1.28715	−0.643576	−	0.765382i	$-0.722550\pi$
$229$	−19.4781	−1.28715	−0.643576	+	0.765382i	$0.722550\pi$
$230$	16.1195	1.06289
$231$	−7.97692	−0.524843
$232$	−33.2422	−2.18246
$233$	4.21749	0.276297	0.138149	−	0.990412i	$-0.455885\pi$
$233$	4.21749	0.276297	0.138149	+	0.990412i	$0.455885\pi$
$234$	−24.2550	−1.58560
$235$	−26.5150	−1.72965
$236$	1.47285	0.0958744
$237$	12.6805	0.823684
$238$	−1.07569	−0.0697265
$239$	22.3511	1.44577	0.722887	−	0.690966i	$-0.242815\pi$
$239$	22.3511	1.44577	0.722887	+	0.690966i	$0.242815\pi$
$240$	32.8331	2.11937
$241$	−14.0275	−0.903588	−0.451794	−	0.892122i	$-0.649216\pi$
$241$	−14.0275	−0.903588	−0.451794	+	0.892122i	$0.649216\pi$
$242$	−42.1158	−2.70730
$243$	−22.3237	−1.43207
$244$	−14.1115	−0.903399
$245$	−24.5042	−1.56552
$246$	−8.84398	−0.563872
$247$	8.78231	0.558805
$248$	−10.7167	−0.680513
$249$	−2.96361	−0.187811
$250$	−32.5821	−2.06067
$251$	−23.6110	−1.49032	−0.745158	−	0.666888i	$-0.767626\pi$
$251$	−23.6110	−1.49032	−0.745158	+	0.666888i	$0.767626\pi$
$252$	7.59883	0.478681
$253$	9.54210	0.599907
$254$	10.7455	0.674231
$255$	6.76301	0.423516
$256$	−31.2915	−1.95572
$257$	7.43931	0.464052	0.232026	−	0.972710i	$-0.425465\pi$
$257$	7.43931	0.464052	0.232026	+	0.972710i	$0.425465\pi$
$258$	−3.48280	−0.216829
$259$	5.46267	0.339434
$260$	44.8806	2.78338
$261$	22.8015	1.41138
$262$	−24.6540	−1.52313
$263$	−10.4682	−0.645498	−0.322749	−	0.946485i	$-0.604607\pi$
$263$	−10.4682	−0.645498	−0.322749	+	0.946485i	$0.604607\pi$
$264$	62.2294	3.82996
$265$	6.04371	0.371262
$266$	−4.15269	−0.254618
$267$	−37.7201	−2.30843
$268$	35.8854	2.19205
$269$	−14.3566	−0.875338	−0.437669	−	0.899136i	$-0.644196\pi$
$269$	−14.3566	−0.875338	−0.437669	+	0.899136i	$0.644196\pi$
$270$	−4.88108	−0.297053
$271$	22.1562	1.34589	0.672946	−	0.739692i	$-0.265029\pi$
$271$	22.1562	1.34589	0.672946	+	0.739692i	$0.265029\pi$
$272$	2.62094	0.158918
$273$	4.64270	0.280989
$274$	10.3971	0.628110
$275$	−45.8859	−2.76702
$276$	−17.5643	−1.05725
$277$	−17.3505	−1.04249	−0.521245	−	0.853407i	$-0.674532\pi$
$277$	−17.3505	−1.04249	−0.521245	+	0.853407i	$0.674532\pi$
$278$	34.6111	2.07584
$279$	7.35082	0.440082
$280$	−10.4135	−0.622323
$281$	25.3707	1.51349	0.756746	−	0.653709i	$-0.226788\pi$
$281$	25.3707	1.51349	0.756746	+	0.653709i	$0.226788\pi$
$282$	43.6063	2.59672
$283$	20.4560	1.21598	0.607992	−	0.793943i	$-0.291975\pi$
$283$	20.4560	1.21598	0.607992	+	0.793943i	$0.291975\pi$
$284$	−15.0160	−0.891038
$285$	26.1086	1.54654
$286$	40.0984	2.37107
$287$	0.876074	0.0517130
$288$	2.24697	0.132404
$289$	−16.4601	−0.968243
$290$	−63.6789	−3.73935
$291$	14.1553	0.829799
$292$	24.0940	1.40999
$293$	−28.3662	−1.65717	−0.828585	−	0.559863i	$-0.810854\pi$
$293$	−28.3662	−1.65717	−0.828585	+	0.559863i	$0.810854\pi$
$294$	40.2993	2.35030
$295$	1.38446	0.0806064
$296$	−42.6153	−2.47696
$297$	−2.88941	−0.167661
$298$	−36.0463	−2.08811
$299$	−5.55367	−0.321177
$300$	84.4630	4.87648
$301$	0.345001	0.0198856
$302$	−12.8777	−0.741028
$303$	11.7150	0.673008
$304$	10.1181	0.580314
$305$	−13.2647	−0.759533
$306$	−5.75600	−0.329048
$307$	32.1940	1.83741	0.918705	−	0.394944i	$-0.129236\pi$
$307$	32.1940	1.83741	0.918705	+	0.394944i	$0.129236\pi$
$308$	−12.5624	−0.715809
$309$	0.0384037	0.00218471
$310$	−20.5290	−1.16597
$311$	2.09951	0.119053	0.0595263	−	0.998227i	$-0.481041\pi$
$311$	2.09951	0.119053	0.0595263	+	0.998227i	$0.481041\pi$
$312$	−36.2186	−2.05047
$313$	14.2327	0.804478	0.402239	−	0.915535i	$-0.368232\pi$
$313$	14.2327	0.804478	0.402239	+	0.915535i	$0.368232\pi$
$314$	−47.6801	−2.69074
$315$	7.14280	0.402451
$316$	19.9697	1.12338
$317$	−8.68030	−0.487534	−0.243767	−	0.969834i	$-0.578383\pi$
$317$	−8.68030	−0.487534	−0.243767	+	0.969834i	$0.578383\pi$
$318$	−9.93940	−0.557374
$319$	−37.6955	−2.11054
$320$	−32.6096	−1.82293
$321$	13.4213	0.749104
$322$	2.62603	0.146343
$323$	2.08414	0.115965
$324$	−32.5902	−1.81057
$325$	26.7064	1.48140
$326$	24.6188	1.36351
$327$	14.1269	0.781220
$328$	−6.83441	−0.377367
$329$	−4.31958	−0.238146
$330$	119.207	6.56212
$331$	−19.6921	−1.08238	−0.541189	−	0.840901i	$-0.682026\pi$
$331$	−19.6921	−1.08238	−0.541189	+	0.840901i	$0.682026\pi$
$332$	−4.66722	−0.256147
$333$	29.2307	1.60183
$334$	51.8476	2.83697
$335$	33.7319	1.84297
$336$	5.34886	0.291804
$337$	15.5386	0.846440	0.423220	−	0.906027i	$-0.360900\pi$
$337$	15.5386	0.846440	0.423220	+	0.906027i	$0.360900\pi$
$338$	8.31097	0.452057
$339$	42.8081	2.32502
$340$	10.6507	0.577614
$341$	−12.1524	−0.658089
$342$	−22.2210	−1.20157
$343$	−8.20145	−0.442837
$344$	−2.69142	−0.145112
$345$	−16.5102	−0.888882
$346$	18.2252	0.979794
$347$	−25.0547	−1.34501	−0.672504	−	0.740093i	$-0.734781\pi$
$347$	−25.0547	−1.34501	−0.672504	+	0.740093i	$0.734781\pi$
$348$	69.3868	3.71952
$349$	−13.2362	−0.708516	−0.354258	−	0.935148i	$-0.615267\pi$
$349$	−13.2362	−0.708516	−0.354258	+	0.935148i	$0.615267\pi$
$350$	−12.6280	−0.674996
$351$	1.68169	0.0897618
$352$	−3.71470	−0.197994
$353$	−7.63692	−0.406472	−0.203236	−	0.979130i	$-0.565146\pi$
$353$	−7.63692	−0.406472	−0.203236	+	0.979130i	$0.565146\pi$
$354$	−2.27687	−0.121014
$355$	−14.1149	−0.749140
$356$	−59.4032	−3.14837
$357$	1.10177	0.0583117
$358$	−24.3572	−1.28732
$359$	−24.6093	−1.29883	−0.649414	−	0.760435i	$-0.724986\pi$
$359$	−24.6093	−1.29883	−0.649414	+	0.760435i	$0.724986\pi$
$360$	−55.7223	−2.93682
$361$	−10.9542	−0.576535
$362$	−10.2247	−0.537400
$363$	43.1368	2.26409
$364$	7.31153	0.383228
$365$	22.6480	1.18545
$366$	21.8149	1.14028
$367$	−0.284992	−0.0148765	−0.00743824	−	0.999972i	$-0.502368\pi$
$367$	−0.284992	−0.0148765	−0.00743824	+	0.999972i	$0.502368\pi$
$368$	−6.39839	−0.333539
$369$	4.68786	0.244040
$370$	−81.6341	−4.24395
$371$	0.984585	0.0511171
$372$	22.3692	1.15979
$373$	23.9465	1.23990	0.619952	−	0.784639i	$-0.287152\pi$
$373$	23.9465	1.23990	0.619952	+	0.784639i	$0.287152\pi$
$374$	9.51582	0.492051
$375$	33.3720	1.72332
$376$	33.6979	1.73784
$377$	21.9394	1.12994
$378$	−0.795180	−0.0408997
$379$	3.26051	0.167481	0.0837405	−	0.996488i	$-0.473313\pi$
$379$	3.26051	0.167481	0.0837405	+	0.996488i	$0.473313\pi$
$380$	41.1169	2.10925
$381$	−11.0060	−0.563854
$382$	−12.2589	−0.627218
$383$	13.9046	0.710494	0.355247	−	0.934773i	$-0.384397\pi$
$383$	13.9046	0.710494	0.355247	+	0.934773i	$0.384397\pi$
$384$	50.1469	2.55905
$385$	−11.8085	−0.601816
$386$	−20.1289	−1.02453
$387$	1.84610	0.0938425
$388$	22.2924	1.13173
$389$	−7.94227	−0.402689	−0.201344	−	0.979521i	$-0.564531\pi$
$389$	−7.94227	−0.402689	−0.201344	+	0.979521i	$0.564531\pi$
$390$	−69.3805	−3.51322
$391$	−1.31795	−0.0666515
$392$	31.1423	1.57292
$393$	25.2517	1.27378
$394$	26.0740	1.31359
$395$	18.7713	0.944486
$396$	−67.2212	−3.37799
$397$	11.3180	0.568032	0.284016	−	0.958820i	$-0.408333\pi$
$397$	11.3180	0.568032	0.284016	+	0.958820i	$0.408333\pi$
$398$	64.3653	3.22634
$399$	4.25336	0.212935
$400$	30.7684	1.53842
$401$	16.2927	0.813620	0.406810	−	0.913513i	$-0.366641\pi$
$401$	16.2927	0.813620	0.406810	+	0.913513i	$0.366641\pi$
$402$	−55.4750	−2.76684
$403$	7.07290	0.352326
$404$	18.4493	0.917885
$405$	−30.6343	−1.52223
$406$	−10.3740	−0.514852
$407$	−48.3242	−2.39534
$408$	−8.59509	−0.425520
$409$	25.7301	1.27227	0.636136	−	0.771577i	$-0.280532\pi$
$409$	25.7301	1.27227	0.636136	+	0.771577i	$0.280532\pi$
$410$	−13.0920	−0.646569
$411$	−10.6491	−0.525283
$412$	0.0604798	0.00297963
$413$	0.225544	0.0110983
$414$	14.0519	0.690612
$415$	−4.38712	−0.215355
$416$	2.16202	0.106002
$417$	−35.4502	−1.73600
$418$	36.7358	1.79681
$419$	−12.2672	−0.599294	−0.299647	−	0.954050i	$-0.596869\pi$
$419$	−12.2672	−0.599294	−0.299647	+	0.954050i	$0.596869\pi$
$420$	21.7361	1.06061
$421$	−24.3308	−1.18581	−0.592904	−	0.805273i	$-0.702019\pi$
$421$	−24.3308	−1.18581	−0.592904	+	0.805273i	$0.702019\pi$
$422$	−34.8558	−1.69675
$423$	−23.1140	−1.12384
$424$	−7.68093	−0.373019
$425$	6.33773	0.307425
$426$	23.2132	1.12468
$427$	−2.16096	−0.104576
$428$	21.1364	1.02167
$429$	−41.0706	−1.98291
$430$	−5.15570	−0.248630
$431$	−16.4251	−0.791167	−0.395584	−	0.918430i	$-0.629458\pi$
$431$	−16.4251	−0.791167	−0.395584	+	0.918430i	$0.629458\pi$
$432$	1.93747	0.0932168
$433$	−7.36783	−0.354075	−0.177038	−	0.984204i	$-0.556651\pi$
$433$	−7.36783	−0.354075	−0.177038	+	0.984204i	$0.556651\pi$
$434$	−3.34440	−0.160536
$435$	65.2227	3.12719
$436$	22.2477	1.06547
$437$	−5.08793	−0.243389
$438$	−37.2466	−1.77971
$439$	−33.1716	−1.58319	−0.791596	−	0.611045i	$-0.790749\pi$
$439$	−33.1716	−1.58319	−0.791596	+	0.611045i	$0.790749\pi$
$440$	92.1202	4.39166
$441$	−21.3611	−1.01720
$442$	−5.53837	−0.263433
$443$	−4.95690	−0.235510	−0.117755	−	0.993043i	$-0.537570\pi$
$443$	−4.95690	−0.235510	−0.117755	+	0.993043i	$0.537570\pi$
$444$	88.9514	4.22144
$445$	−55.8383	−2.64699
$446$	−7.70756	−0.364963
$447$	36.9202	1.74627
$448$	−5.31245	−0.250990
$449$	9.78207	0.461644	0.230822	−	0.972996i	$-0.425858\pi$
$449$	9.78207	0.461644	0.230822	+	0.972996i	$0.425858\pi$
$450$	−67.5724	−3.18539
$451$	−7.74998	−0.364932
$452$	67.4161	3.17099
$453$	13.1899	0.619715
$454$	19.6142	0.920538
$455$	6.87274	0.322199
$456$	−33.1813	−1.55386
$457$	27.9404	1.30700	0.653499	−	0.756928i	$-0.273300\pi$
$457$	27.9404	1.30700	0.653499	+	0.756928i	$0.273300\pi$
$458$	47.4202	2.21580
$459$	0.399084	0.0186276
$460$	−26.0010	−1.21231
$461$	9.97962	0.464797	0.232399	−	0.972621i	$-0.425343\pi$
$461$	9.97962	0.464797	0.232399	+	0.972621i	$0.425343\pi$
$462$	19.4201	0.903504
$463$	−0.624714	−0.0290329	−0.0145165	−	0.999895i	$-0.504621\pi$
$463$	−0.624714	−0.0290329	−0.0145165	+	0.999895i	$0.504621\pi$
$464$	25.2764	1.17343
$465$	21.0267	0.975091
$466$	−10.2676	−0.475639
$467$	−32.4701	−1.50254	−0.751268	−	0.659998i	$-0.770557\pi$
$467$	−32.4701	−1.50254	−0.751268	+	0.659998i	$0.770557\pi$
$468$	39.1239	1.80850
$469$	5.49528	0.253749
$470$	64.5518	2.97755
$471$	48.8360	2.25024
$472$	−1.75951	−0.0809879
$473$	−3.05197	−0.140330
$474$	−30.8710	−1.41795
$475$	24.4668	1.12261
$476$	1.73511	0.0795286
$477$	5.26850	0.241228
$478$	−54.4146	−2.48886
$479$	4.41468	0.201712	0.100856	−	0.994901i	$-0.467842\pi$
$479$	4.41468	0.201712	0.100856	+	0.994901i	$0.467842\pi$
$480$	6.42737	0.293368
$481$	28.1255	1.28241
$482$	34.1503	1.55551
$483$	−2.68970	−0.122385
$484$	67.9337	3.08789
$485$	20.9546	0.951498
$486$	54.3478	2.46527
$487$	36.9204	1.67303	0.836513	−	0.547948i	$-0.184591\pi$
$487$	36.9204	1.67303	0.836513	+	0.547948i	$0.184591\pi$
$488$	16.8580	0.763127
$489$	−25.2156	−1.14029
$490$	59.6563	2.69500
$491$	13.5450	0.611276	0.305638	−	0.952148i	$-0.401130\pi$
$491$	13.5450	0.611276	0.305638	+	0.952148i	$0.401130\pi$
$492$	14.2655	0.643140
$493$	5.20647	0.234488
$494$	−21.3809	−0.961970
$495$	−63.1871	−2.84005
$496$	8.14870	0.365887
$497$	−2.29947	−0.103145
$498$	7.21501	0.323312
$499$	−1.60533	−0.0718645	−0.0359322	−	0.999354i	$-0.511440\pi$
$499$	−1.60533	−0.0718645	−0.0359322	+	0.999354i	$0.511440\pi$
$500$	52.5556	2.35036
$501$	−53.1046	−2.37254
$502$	57.4819	2.56554
$503$	−34.7901	−1.55121	−0.775607	−	0.631217i	$-0.782556\pi$
$503$	−34.7901	−1.55121	−0.775607	+	0.631217i	$0.782556\pi$
$504$	−9.07776	−0.404356
$505$	17.3421	0.771712
$506$	−23.2306	−1.03273
$507$	−8.51246	−0.378051
$508$	−17.3327	−0.769014
$509$	−5.63955	−0.249969	−0.124984	−	0.992159i	$-0.539888\pi$
$509$	−5.63955	−0.249969	−0.124984	+	0.992159i	$0.539888\pi$
$510$	−16.4648	−0.729073
$511$	3.68961	0.163219
$512$	35.9591	1.58918
$513$	1.54066	0.0680218
$514$	−18.1113	−0.798854
$515$	0.0568503	0.00250512
$516$	5.61783	0.247311
$517$	38.2122	1.68057
$518$	−13.2991	−0.584327
$519$	−18.6671	−0.819393
$520$	−53.6155	−2.35120
$521$	18.7120	0.819787	0.409893	−	0.912133i	$-0.365566\pi$
$521$	18.7120	0.819787	0.409893	+	0.912133i	$0.365566\pi$
$522$	−55.5110	−2.42965
$523$	−36.5166	−1.59676	−0.798380	−	0.602153i	$-0.794310\pi$
$523$	−36.5166	−1.59676	−0.798380	+	0.602153i	$0.794310\pi$
$524$	39.7674	1.73725
$525$	12.9342	0.564493
$526$	25.4853	1.11121
$527$	1.67848	0.0731158
$528$	−47.3175	−2.05923
$529$	−19.7825	−0.860111
$530$	−14.7136	−0.639119
$531$	1.20688	0.0523742
$532$	6.69838	0.290412
$533$	4.51062	0.195377
$534$	91.8309	3.97391
$535$	19.8680	0.858968
$536$	−42.8697	−1.85169
$537$	24.9477	1.07657
$538$	34.9517	1.50687
$539$	35.3142	1.52109
$540$	7.87329	0.338813
$541$	−15.4034	−0.662246	−0.331123	−	0.943588i	$-0.607427\pi$
$541$	−15.4034	−0.662246	−0.331123	+	0.943588i	$0.607427\pi$
$542$	−53.9400	−2.31692
$543$	10.4726	0.449423
$544$	0.513072	0.0219978
$545$	20.9125	0.895794
$546$	−11.3028	−0.483716
$547$	15.4116	0.658952	0.329476	−	0.944164i	$-0.393128\pi$
$547$	15.4116	0.658952	0.329476	+	0.944164i	$0.393128\pi$
$548$	−16.7707	−0.716409
$549$	−11.5633	−0.493508
$550$	111.711	4.76336
$551$	20.0996	0.856270
$552$	20.9828	0.893088
$553$	3.05804	0.130041
$554$	42.2404	1.79462
$555$	83.6131	3.54918
$556$	−55.8285	−2.36766
$557$	−29.1179	−1.23376	−0.616882	−	0.787056i	$-0.711604\pi$
$557$	−29.1179	−1.23376	−0.616882	+	0.787056i	$0.711604\pi$
$558$	−17.8958	−0.757591
$559$	1.77630	0.0751295
$560$	7.91810	0.334601
$561$	−9.74652	−0.411498
$562$	−61.7659	−2.60544
$563$	12.8153	0.540098	0.270049	−	0.962847i	$-0.412960\pi$
$563$	12.8153	0.540098	0.270049	+	0.962847i	$0.412960\pi$
$564$	−70.3379	−2.96176
$565$	63.3702	2.66601
$566$	−49.8009	−2.09329
$567$	−4.99066	−0.209588
$568$	17.9386	0.752685
$569$	−16.0969	−0.674819	−0.337409	−	0.941358i	$-0.609551\pi$
$569$	−16.0969	−0.674819	−0.337409	+	0.941358i	$0.609551\pi$
$570$	−63.5622	−2.66233
$571$	−23.5591	−0.985918	−0.492959	−	0.870053i	$-0.664085\pi$
$571$	−23.5591	−0.985918	−0.492959	+	0.870053i	$0.664085\pi$
$572$	−64.6797	−2.70439
$573$	12.5561	0.524537
$574$	−2.13283	−0.0890227
$575$	−15.4720	−0.645228
$576$	−28.4269	−1.18445
$577$	8.56909	0.356736	0.178368	−	0.983964i	$-0.442918\pi$
$577$	8.56909	0.356736	0.178368	+	0.983964i	$0.442918\pi$
$578$	40.0728	1.66681
$579$	20.6169	0.856809
$580$	102.716	4.26503
$581$	−0.714710	−0.0296511
$582$	−34.4616	−1.42848
$583$	−8.70990	−0.360727
$584$	−28.7833	−1.19106
$585$	36.7760	1.52050
$586$	69.0585	2.85278
$587$	−7.07398	−0.291974	−0.145987	−	0.989286i	$-0.546636\pi$
$587$	−7.07398	−0.291974	−0.145987	+	0.989286i	$0.546636\pi$
$588$	−65.0036	−2.68070
$589$	6.47977	0.266994
$590$	−3.37052	−0.138762
$591$	−26.7061	−1.09854
$592$	32.4035	1.33177
$593$	1.55758	0.0639621	0.0319810	−	0.999488i	$-0.489818\pi$
$593$	1.55758	0.0639621	0.0319810	+	0.999488i	$0.489818\pi$
$594$	7.03437	0.288624
$595$	1.63098	0.0668637
$596$	58.1435	2.38165
$597$	−65.9257	−2.69816
$598$	13.5206	0.552898
$599$	−6.57098	−0.268483	−0.134241	−	0.990949i	$-0.542860\pi$
$599$	−6.57098	−0.268483	−0.134241	+	0.990949i	$0.542860\pi$
$600$	−100.902	−4.11930
$601$	45.8307	1.86947	0.934736	−	0.355342i	$-0.115636\pi$
$601$	45.8307	1.86947	0.934736	+	0.355342i	$0.115636\pi$
$602$	−0.839918	−0.0342325
$603$	29.4052	1.19747
$604$	20.7720	0.845201
$605$	63.8568	2.59615
$606$	−28.5205	−1.15857
$607$	41.8400	1.69823	0.849116	−	0.528206i	$-0.177135\pi$
$607$	41.8400	1.69823	0.849116	+	0.528206i	$0.177135\pi$
$608$	1.98071	0.0803284
$609$	10.6255	0.430566
$610$	32.2933	1.30752
$611$	−22.2401	−0.899740
$612$	9.28455	0.375306
$613$	12.7214	0.513813	0.256906	−	0.966436i	$-0.417297\pi$
$613$	12.7214	0.513813	0.256906	+	0.966436i	$0.417297\pi$
$614$	−78.3775	−3.16306
$615$	13.4094	0.540720
$616$	15.0074	0.604664
$617$	−46.8984	−1.88806	−0.944029	−	0.329862i	$-0.892998\pi$
$617$	−46.8984	−1.88806	−0.944029	+	0.329862i	$0.892998\pi$
$618$	−0.0934952	−0.00376093
$619$	11.5737	0.465187	0.232593	−	0.972574i	$-0.425279\pi$
$619$	11.5737	0.465187	0.232593	+	0.972574i	$0.425279\pi$
$620$	33.1138	1.32988
$621$	−0.974266	−0.0390960
$622$	−5.11134	−0.204946
$623$	−9.09666	−0.364450
$624$	27.5396	1.10247
$625$	6.27341	0.250936
$626$	−34.6499	−1.38489
$627$	−37.6264	−1.50265
$628$	76.9090	3.06900
$629$	6.67451	0.266130
$630$	−17.3894	−0.692810
$631$	10.0405	0.399705	0.199852	−	0.979826i	$-0.435954\pi$
$631$	10.0405	0.399705	0.199852	+	0.979826i	$0.435954\pi$
$632$	−23.8564	−0.948955
$633$	35.7008	1.41898
$634$	21.1325	0.839279
$635$	−16.2925	−0.646549
$636$	16.0325	0.635729
$637$	−20.5535	−0.814359
$638$	91.7709	3.63325
$639$	−12.3044	−0.486755
$640$	74.2340	2.93436
$641$	−16.0539	−0.634093	−0.317046	−	0.948410i	$-0.602691\pi$
$641$	−16.0539	−0.634093	−0.317046	+	0.948410i	$0.602691\pi$
$642$	−32.6746	−1.28956
$643$	20.4249	0.805481	0.402741	−	0.915314i	$-0.368058\pi$
$643$	20.4249	0.805481	0.402741	+	0.915314i	$0.368058\pi$
$644$	−4.23585	−0.166916
$645$	5.28069	0.207927
$646$	−5.07392	−0.199631
$647$	−22.2969	−0.876581	−0.438290	−	0.898833i	$-0.644416\pi$
$647$	−22.2969	−0.876581	−0.438290	+	0.898833i	$0.644416\pi$
$648$	38.9331	1.52944
$649$	−1.99522	−0.0783191
$650$	−65.0176	−2.55020
$651$	3.42548	0.134255
$652$	−39.7106	−1.55519
$653$	−1.68848	−0.0660753	−0.0330377	−	0.999454i	$-0.510518\pi$
$653$	−1.68848	−0.0660753	−0.0330377	+	0.999454i	$0.510518\pi$
$654$	−34.3924	−1.34485
$655$	37.3809	1.46059
$656$	5.19669	0.202897
$657$	19.7430	0.770249
$658$	10.5162	0.409963
$659$	−33.4864	−1.30445	−0.652223	−	0.758027i	$-0.726163\pi$
$659$	−33.4864	−1.30445	−0.652223	+	0.758027i	$0.726163\pi$
$660$	−192.283	−7.48462
$661$	30.4639	1.18491	0.592454	−	0.805605i	$-0.298159\pi$
$661$	30.4639	1.18491	0.592454	+	0.805605i	$0.298159\pi$
$662$	47.9412	1.86329
$663$	5.67264	0.220307
$664$	5.57558	0.216374
$665$	6.29639	0.244164
$666$	−71.1631	−2.75752
$667$	−12.7103	−0.492146
$668$	−83.6314	−3.23579
$669$	7.89441	0.305216
$670$	−82.1214	−3.17263
$671$	19.1164	0.737980
$672$	1.04709	0.0403923
$673$	27.0782	1.04379	0.521895	−	0.853010i	$-0.325225\pi$
$673$	27.0782	1.04379	0.521895	+	0.853010i	$0.325225\pi$
$674$	−37.8292	−1.45713
$675$	4.68503	0.180327
$676$	−13.4058	−0.515607
$677$	39.1940	1.50635	0.753173	−	0.657822i	$-0.228522\pi$
$677$	39.1940	1.50635	0.753173	+	0.657822i	$0.228522\pi$
$678$	−104.218	−4.00246
$679$	3.41372	0.131007
$680$	−12.7236	−0.487927
$681$	−20.0897	−0.769838
$682$	29.5854	1.13288
$683$	−36.9955	−1.41559	−0.707797	−	0.706416i	$-0.750311\pi$
$683$	−36.9955	−1.41559	−0.707797	+	0.706416i	$0.750311\pi$
$684$	35.8430	1.37049
$685$	−15.7643	−0.602321
$686$	19.9667	0.762333
$687$	−48.5698	−1.85306
$688$	2.04648	0.0780213
$689$	5.06931	0.193125
$690$	40.1948	1.53019
$691$	−26.1845	−0.996106	−0.498053	−	0.867147i	$-0.665952\pi$
$691$	−26.1845	−0.996106	−0.498053	+	0.867147i	$0.665952\pi$
$692$	−29.3977	−1.11753
$693$	−10.2939	−0.391031
$694$	60.9966	2.31540
$695$	−52.4781	−1.99061
$696$	−82.8913	−3.14199
$697$	1.07042	0.0405451
$698$	32.2239	1.21969
$699$	10.5166	0.397773
$700$	20.3693	0.769886
$701$	0.832365	0.0314380	0.0157190	−	0.999876i	$-0.494996\pi$
$701$	0.832365	0.0314380	0.0157190	+	0.999876i	$0.494996\pi$
$702$	−4.09413	−0.154523
$703$	25.7669	0.971817
$704$	46.9954	1.77120
$705$	−66.1167	−2.49010
$706$	18.5924	0.699733
$707$	2.82521	0.106253
$708$	3.67264	0.138026
$709$	42.3148	1.58916	0.794582	−	0.607157i	$-0.207690\pi$
$709$	42.3148	1.58916	0.794582	+	0.607157i	$0.207690\pi$
$710$	34.3632	1.28963
$711$	16.3636	0.613681
$712$	70.9647	2.65951
$713$	−4.09760	−0.153456
$714$	−2.68229	−0.100382
$715$	−60.7981	−2.27372
$716$	39.2887	1.46829
$717$	55.7338	2.08142
$718$	59.9121	2.23590
$719$	−23.7287	−0.884930	−0.442465	−	0.896786i	$-0.645896\pi$
$719$	−23.7287	−0.884930	−0.442465	+	0.896786i	$0.645896\pi$
$720$	42.3696	1.57902
$721$	0.00926152	0.000344917 0
$722$	26.6683	0.992492
$723$	−34.9783	−1.30086
$724$	16.4927	0.612947
$725$	61.1213	2.26999
$726$	−105.018	−3.89758
$727$	−39.8410	−1.47762	−0.738811	−	0.673913i	$-0.764612\pi$
$727$	−39.8410	−1.47762	−0.738811	+	0.673913i	$0.764612\pi$
$728$	−8.73455	−0.323724
$729$	−30.7681	−1.13956
$730$	−55.1374	−2.04073
$731$	0.421537	0.0155911
$732$	−35.1879	−1.30058
$733$	−37.7531	−1.39444	−0.697222	−	0.716855i	$-0.745581\pi$
$733$	−37.7531	−1.39444	−0.697222	+	0.716855i	$0.745581\pi$
$734$	0.693824	0.0256095
$735$	−61.1026	−2.25380
$736$	−1.25254	−0.0461692
$737$	−48.6127	−1.79067
$738$	−11.4128	−0.420110
$739$	−1.66619	−0.0612918	−0.0306459	−	0.999530i	$-0.509756\pi$
$739$	−1.66619	−0.0612918	−0.0306459	+	0.999530i	$0.509756\pi$
$740$	131.678	4.84056
$741$	21.8992	0.804487
$742$	−2.39701	−0.0879969
$743$	−10.7136	−0.393043	−0.196521	−	0.980500i	$-0.562965\pi$
$743$	−10.7136	−0.393043	−0.196521	+	0.980500i	$0.562965\pi$
$744$	−26.7228	−0.979705
$745$	54.6542	2.00237
$746$	−58.2987	−2.13447
$747$	−3.82440	−0.139928
$748$	−15.3492	−0.561224
$749$	3.23671	0.118267
$750$	−81.2452	−2.96665
$751$	−20.1714	−0.736064	−0.368032	−	0.929813i	$-0.619968\pi$
$751$	−20.1714	−0.736064	−0.368032	+	0.929813i	$0.619968\pi$
$752$	−25.6229	−0.934371
$753$	−58.8754	−2.14554
$754$	−53.4123	−1.94516
$755$	19.5254	0.710603
$756$	1.28264	0.0466493
$757$	−34.6586	−1.25969	−0.629844	−	0.776722i	$-0.716881\pi$
$757$	−34.6586	−1.25969	−0.629844	+	0.776722i	$0.716881\pi$
$758$	−7.93782	−0.288315
$759$	23.7938	0.863659
$760$	−49.1193	−1.78174
$761$	−45.1246	−1.63577	−0.817883	−	0.575385i	$-0.804852\pi$
$761$	−45.1246	−1.63577	−0.817883	+	0.575385i	$0.804852\pi$
$762$	26.7944	0.970661
$763$	3.40687	0.123337
$764$	19.7738	0.715392
$765$	8.72736	0.315538
$766$	−33.8513	−1.22310
$767$	1.16125	0.0419303
$768$	−78.0271	−2.81556
$769$	−4.51050	−0.162653	−0.0813263	−	0.996688i	$-0.525916\pi$
$769$	−4.51050	−0.162653	−0.0813263	+	0.996688i	$0.525916\pi$
$770$	28.7482	1.03601
$771$	18.5503	0.668074
$772$	32.4684	1.16856
$773$	41.5940	1.49603	0.748016	−	0.663681i	$-0.231007\pi$
$773$	41.5940	1.49603	0.748016	+	0.663681i	$0.231007\pi$
$774$	−4.49439	−0.161548
$775$	19.7045	0.707806
$776$	−26.6311	−0.956001
$777$	13.6215	0.488668
$778$	19.3357	0.693219
$779$	4.13236	0.148057
$780$	111.912	4.00710
$781$	20.3417	0.727883
$782$	3.20859	0.114739
$783$	3.84878	0.137544
$784$	−23.6797	−0.845704
$785$	72.2935	2.58027
$786$	−61.4761	−2.19278
$787$	24.7458	0.882094	0.441047	−	0.897484i	$-0.354607\pi$
$787$	24.7458	0.882094	0.441047	+	0.897484i	$0.354607\pi$
$788$	−42.0579	−1.49825
$789$	−26.1031	−0.929295
$790$	−45.6993	−1.62591
$791$	10.3237	0.367068
$792$	80.3043	2.85349
$793$	−11.1261	−0.395098
$794$	−27.5540	−0.977853
$795$	15.0703	0.534489
$796$	−103.823	−3.67990
$797$	−51.9929	−1.84168	−0.920842	−	0.389937i	$-0.872497\pi$
$797$	−51.9929	−1.84168	−0.920842	+	0.389937i	$0.872497\pi$
$798$	−10.3550	−0.366562
$799$	−5.27784	−0.186717
$800$	6.02319	0.212952
$801$	−48.6761	−1.71989
$802$	−39.6652	−1.40063
$803$	−32.6392	−1.15181
$804$	89.4824	3.15580
$805$	−3.98164	−0.140335
$806$	−17.2192	−0.606521
$807$	−35.7990	−1.26019
$808$	−22.0400	−0.775363
$809$	20.2651	0.712484	0.356242	−	0.934394i	$-0.384058\pi$
$809$	20.2651	0.712484	0.356242	+	0.934394i	$0.384058\pi$
$810$	74.5804	2.62049
$811$	10.0684	0.353550	0.176775	−	0.984251i	$-0.443433\pi$
$811$	10.0684	0.353550	0.176775	+	0.984251i	$0.443433\pi$
$812$	16.7335	0.587229
$813$	55.2477	1.93762
$814$	117.647	4.12353
$815$	−37.3275	−1.30753
$816$	6.53546	0.228787
$817$	1.62734	0.0569334
$818$	−62.6408	−2.19019
$819$	5.99120	0.209349
$820$	21.1177	0.737464
$821$	44.1178	1.53972	0.769861	−	0.638212i	$-0.220326\pi$
$821$	44.1178	1.53972	0.769861	+	0.638212i	$0.220326\pi$
$822$	25.9257	0.904262
$823$	−32.2660	−1.12472	−0.562361	−	0.826892i	$-0.690107\pi$
$823$	−32.2660	−1.12472	−0.562361	+	0.826892i	$0.690107\pi$
$824$	−0.0722508	−0.00251698
$825$	−114.419	−3.98356
$826$	−0.549094	−0.0191054
$827$	6.98761	0.242983	0.121491	−	0.992592i	$-0.461232\pi$
$827$	6.98761	0.242983	0.121491	+	0.992592i	$0.461232\pi$
$828$	−22.6660	−0.787697
$829$	6.75511	0.234615	0.117307	−	0.993096i	$-0.462574\pi$
$829$	6.75511	0.234615	0.117307	+	0.993096i	$0.462574\pi$
$830$	10.6806	0.370729
$831$	−43.2644	−1.50083
$832$	−27.3521	−0.948263
$833$	−4.87758	−0.168998
$834$	86.3048	2.98849
$835$	−78.6124	−2.72049
$836$	−59.2556	−2.04940
$837$	1.24078	0.0428877
$838$	29.8650	1.03167
$839$	−24.1545	−0.833905	−0.416952	−	0.908928i	$-0.636902\pi$
$839$	−24.1545	−0.833905	−0.416952	+	0.908928i	$0.636902\pi$
$840$	−25.9665	−0.895931
$841$	21.2114	0.731428
$842$	59.2341	2.04134
$843$	63.2634	2.17891
$844$	56.2232	1.93528
$845$	−12.6013	−0.433497
$846$	56.2719	1.93467
$847$	10.4030	0.357450
$848$	5.84036	0.200559
$849$	51.0083	1.75060
$850$	−15.4294	−0.529225
$851$	−16.2942	−0.558558
$852$	−37.4433	−1.28279
$853$	−33.5108	−1.14739	−0.573694	−	0.819070i	$-0.694490\pi$
$853$	−33.5108	−1.14739	−0.573694	+	0.819070i	$0.694490\pi$
$854$	5.26093	0.180025
$855$	33.6919	1.15224
$856$	−25.2501	−0.863032
$857$	−32.8649	−1.12264	−0.561322	−	0.827598i	$-0.689707\pi$
$857$	−32.8649	−1.12264	−0.561322	+	0.827598i	$0.689707\pi$
$858$	99.9877	3.41352
$859$	26.6143	0.908069	0.454035	−	0.890984i	$-0.349984\pi$
$859$	26.6143	0.908069	0.454035	+	0.890984i	$0.349984\pi$
$860$	8.31625	0.283582
$861$	2.18454	0.0744489
$862$	39.9874	1.36198
$863$	33.0835	1.12618	0.563088	−	0.826397i	$-0.309613\pi$
$863$	33.0835	1.12618	0.563088	+	0.826397i	$0.309613\pi$
$864$	0.379278	0.0129033
$865$	−27.6334	−0.939565
$866$	17.9372	0.609532
$867$	−41.0443	−1.39394
$868$	5.39459	0.183104
$869$	−27.0523	−0.917685
$870$	−158.787	−5.38338
$871$	28.2934	0.958686
$872$	−26.5776	−0.900032
$873$	18.2668	0.618237
$874$	12.3867	0.418988
$875$	8.04805	0.272074
$876$	60.0797	2.02990
$877$	−36.8752	−1.24519	−0.622594	−	0.782545i	$-0.713921\pi$
$877$	−36.8752	−1.24519	−0.622594	+	0.782545i	$0.713921\pi$
$878$	80.7573	2.72543
$879$	−70.7327	−2.38575
$880$	−70.0456	−2.36124
$881$	35.5834	1.19884	0.599418	−	0.800436i	$-0.295399\pi$
$881$	35.5834	1.19884	0.599418	+	0.800436i	$0.295399\pi$
$882$	52.0044	1.75108
$883$	−22.4567	−0.755728	−0.377864	−	0.925861i	$-0.623341\pi$
$883$	−22.4567	−0.755728	−0.377864	+	0.925861i	$0.623341\pi$
$884$	8.93352	0.300467
$885$	3.45223	0.116045
$886$	12.0678	0.405424
$887$	18.5758	0.623713	0.311856	−	0.950129i	$-0.399049\pi$
$887$	18.5758	0.623713	0.311856	+	0.950129i	$0.399049\pi$
$888$	−106.264	−3.56597
$889$	−2.65423	−0.0890199
$890$	135.940	4.55673
$891$	44.1487	1.47904
$892$	12.4325	0.416270
$893$	−20.3751	−0.681826
$894$	−89.8835	−3.00615
$895$	36.9309	1.23446
$896$	12.0935	0.404016
$897$	−13.8484	−0.462384
$898$	−23.8148	−0.794710
$899$	16.1873	0.539878
$900$	108.996	3.63319
$901$	1.20301	0.0400779
$902$	18.8676	0.628222
$903$	0.860281	0.0286283
$904$	−80.5370	−2.67862
$905$	15.5029	0.515335
$906$	−32.1113	−1.06683
$907$	37.8416	1.25651	0.628255	−	0.778008i	$-0.283770\pi$
$907$	37.8416	1.25651	0.628255	+	0.778008i	$0.283770\pi$
$908$	−31.6381	−1.04995
$909$	15.1177	0.501421
$910$	−16.7319	−0.554658
$911$	−17.0920	−0.566282	−0.283141	−	0.959078i	$-0.591376\pi$
$911$	−17.0920	−0.566282	−0.283141	+	0.959078i	$0.591376\pi$
$912$	25.2301	0.835452
$913$	6.32251	0.209244
$914$	−68.0219	−2.24997
$915$	−33.0762	−1.09347
$916$	−76.4899	−2.52730
$917$	6.08975	0.201101
$918$	−0.971583	−0.0320670
$919$	30.6834	1.01215	0.506076	−	0.862489i	$-0.331096\pi$
$919$	30.6834	1.01215	0.506076	+	0.862489i	$0.331096\pi$
$920$	31.0615	1.02407
$921$	80.2776	2.64524
$922$	−24.2957	−0.800138
$923$	−11.8392	−0.389692
$924$	−31.3250	−1.03052
$925$	78.3553	2.57630
$926$	1.52089	0.0499795
$927$	0.0495583	0.00162771
$928$	4.94808	0.162429
$929$	57.6983	1.89302	0.946510	−	0.322674i	$-0.104582\pi$
$929$	57.6983	1.89302	0.946510	+	0.322674i	$0.104582\pi$
$930$	−51.1903	−1.67860
$931$	−18.8299	−0.617124
$932$	16.5619	0.542504
$933$	5.23526	0.171395
$934$	79.0495	2.58658
$935$	−14.4281	−0.471849
$936$	−46.7385	−1.52769
$937$	−7.60650	−0.248494	−0.124247	−	0.992251i	$-0.539651\pi$
$937$	−7.60650	−0.248494	−0.124247	+	0.992251i	$0.539651\pi$
$938$	−13.3785	−0.436822
$939$	35.4899	1.15817
$940$	−104.123	−3.39613
$941$	−23.5063	−0.766284	−0.383142	−	0.923689i	$-0.625158\pi$
$941$	−23.5063	−0.766284	−0.383142	+	0.923689i	$0.625158\pi$
$942$	−118.893	−3.87374
$943$	−2.61318	−0.0850967
$944$	1.33788	0.0435442
$945$	1.20567	0.0392204
$946$	7.43014	0.241575
$947$	−32.2998	−1.04960	−0.524802	−	0.851224i	$-0.675861\pi$
$947$	−32.2998	−1.04960	−0.524802	+	0.851224i	$0.675861\pi$
$948$	49.7956	1.61729
$949$	18.9966	0.616655
$950$	−59.5652	−1.93255
$951$	−21.6448	−0.701881
$952$	−2.07281	−0.0671801
$953$	−34.2499	−1.10946	−0.554731	−	0.832030i	$-0.687179\pi$
$953$	−34.2499	−1.10946	−0.554731	+	0.832030i	$0.687179\pi$
$954$	−12.8264	−0.415269
$955$	18.5871	0.601466
$956$	87.7719	2.83875
$957$	−93.9958	−3.03845
$958$	−10.7477	−0.347242
$959$	−2.56817	−0.0829304
$960$	−81.3139	−2.62439
$961$	−25.7815	−0.831660
$962$	−68.4726	−2.20764
$963$	17.3196	0.558116
$964$	−55.0853	−1.77418
$965$	30.5199	0.982470
$966$	6.54816	0.210684
$967$	−9.48334	−0.304964	−0.152482	−	0.988306i	$-0.548727\pi$
$967$	−9.48334	−0.304964	−0.152482	+	0.988306i	$0.548727\pi$
$968$	−81.1554	−2.60843
$969$	5.19693	0.166949
$970$	−51.0146	−1.63798
$971$	0.642932	0.0206327	0.0103163	−	0.999947i	$-0.496716\pi$
$971$	0.642932	0.0206327	0.0103163	+	0.999947i	$0.496716\pi$
$972$	−87.6642	−2.81183
$973$	−8.54925	−0.274076
$974$	−89.8841	−2.88007
$975$	66.5938	2.13271
$976$	−12.8184	−0.410306
$977$	−23.2839	−0.744919	−0.372460	−	0.928048i	$-0.621485\pi$
$977$	−23.2839	−0.744919	−0.372460	+	0.928048i	$0.621485\pi$
$978$	61.3883	1.96298
$979$	80.4714	2.57188
$980$	−96.2270	−3.07386
$981$	18.2301	0.582043
$982$	−32.9757	−1.05230
$983$	−20.0409	−0.639204	−0.319602	−	0.947552i	$-0.603549\pi$
$983$	−20.0409	−0.639204	−0.319602	+	0.947552i	$0.603549\pi$
$984$	−17.0420	−0.543279
$985$	−39.5339	−1.25965
$986$	−12.6753	−0.403665
$987$	−10.7711	−0.342849
$988$	34.4878	1.09720
$989$	−1.02908	−0.0327228
$990$	153.831	4.88908
$991$	19.1982	0.609852	0.304926	−	0.952376i	$-0.401368\pi$
$991$	19.1982	0.609852	0.304926	+	0.952376i	$0.401368\pi$
$992$	1.59518	0.0506470
$993$	−49.1035	−1.55825
$994$	5.59813	0.177562
$995$	−97.5919	−3.09387
$996$	−11.6380	−0.368763
$997$	−47.9412	−1.51831	−0.759157	−	0.650908i	$-0.774388\pi$
$997$	−47.9412	−1.51831	−0.759157	+	0.650908i	$0.774388\pi$
$998$	3.90823	0.123713
$999$	4.93399	0.156105

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.b.1.17	✓	186

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.b.1.17	✓	186	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43453 q^{2} +2.49356 q^{3} +3.92696 q^{4} +3.69129 q^{5} -6.07065 q^{6} +0.601351 q^{7} -4.69125 q^{8} +3.21782 q^{9} +O(q^{10})\)	\(q-2.43453 q^{2} +2.49356 q^{3} +3.92696 q^{4} +3.69129 q^{5} -6.07065 q^{6} +0.601351 q^{7} -4.69125 q^{8} +3.21782 q^{9} -8.98658 q^{10} -5.31971 q^{11} +9.79209 q^{12} +3.09616 q^{13} -1.46401 q^{14} +9.20444 q^{15} +3.56709 q^{16} +0.734755 q^{17} -7.83390 q^{18} +2.83652 q^{19} +14.4956 q^{20} +1.49950 q^{21} +12.9510 q^{22} -1.79373 q^{23} -11.6979 q^{24} +8.62564 q^{25} -7.53771 q^{26} +0.543152 q^{27} +2.36148 q^{28} +7.08600 q^{29} -22.4085 q^{30} +2.28441 q^{31} +0.698289 q^{32} -13.2650 q^{33} -1.78879 q^{34} +2.21976 q^{35} +12.6363 q^{36} +9.08400 q^{37} -6.90560 q^{38} +7.72045 q^{39} -17.3168 q^{40} +1.45684 q^{41} -3.65059 q^{42} +0.573711 q^{43} -20.8903 q^{44} +11.8779 q^{45} +4.36689 q^{46} -7.18313 q^{47} +8.89475 q^{48} -6.63838 q^{49} -20.9994 q^{50} +1.83215 q^{51} +12.1585 q^{52} +1.63729 q^{53} -1.32232 q^{54} -19.6366 q^{55} -2.82109 q^{56} +7.07301 q^{57} -17.2511 q^{58} +0.375061 q^{59} +36.1455 q^{60} -3.59350 q^{61} -5.56147 q^{62} +1.93504 q^{63} -8.83420 q^{64} +11.4288 q^{65} +32.2941 q^{66} +9.13823 q^{67} +2.88535 q^{68} -4.47276 q^{69} -5.40409 q^{70} -3.82383 q^{71} -15.0956 q^{72} +6.13553 q^{73} -22.1153 q^{74} +21.5085 q^{75} +11.1389 q^{76} -3.19901 q^{77} -18.7957 q^{78} +5.08529 q^{79} +13.1672 q^{80} -8.29909 q^{81} -3.54673 q^{82} -1.18851 q^{83} +5.88849 q^{84} +2.71219 q^{85} -1.39672 q^{86} +17.6693 q^{87} +24.9561 q^{88} -15.1270 q^{89} -28.9172 q^{90} +1.86188 q^{91} -7.04389 q^{92} +5.69630 q^{93} +17.4876 q^{94} +10.4704 q^{95} +1.74122 q^{96} +5.67676 q^{97} +16.1614 q^{98} -17.1179 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9}+O(q^{10}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9	\( 186 q + 6 q^{2} + 10 q^{3} + 212 q^{4} + 38 q^{5} + 47 q^{6} + 32 q^{7} + 15 q^{8} + 216 q^{9} + 50 q^{10} + 25 q^{11} + 17 q^{12} + 113 q^{13} + 12 q^{14} + 12 q^{15} + 252 q^{16} + 35 q^{17} + 13 q^{18} + 97 q^{19} + 55 q^{20} + 115 q^{21} + 14 q^{22} + 27 q^{23} + 122 q^{24} + 244 q^{25} + 39 q^{26} + 34 q^{27} + 66 q^{28} + 91 q^{29} + 4 q^{30} + 135 q^{31} + 21 q^{32} + 32 q^{33} + 58 q^{34} + 17 q^{35} + 273 q^{36} + 133 q^{37} - 3 q^{38} + 55 q^{39} + 142 q^{40} + 97 q^{41} - 8 q^{42} + 67 q^{43} + 44 q^{44} + 154 q^{45} + 101 q^{46} + 20 q^{47} - 7 q^{48} + 312 q^{49} + 21 q^{50} + 23 q^{51} + 193 q^{52} + 22 q^{53} + 141 q^{54} + 88 q^{55} + 28 q^{56} + 65 q^{57} + 62 q^{58} + 41 q^{59} + q^{60} + 377 q^{61} + 29 q^{62} + 39 q^{63} + 311 q^{64} + 21 q^{65} + 35 q^{66} + 42 q^{67} + 24 q^{68} + 137 q^{69} + 35 q^{70} + 17 q^{71} - 8 q^{72} + 213 q^{73} - 9 q^{74} + 2 q^{75} + 242 q^{76} + 60 q^{77} + 103 q^{79} + 80 q^{80} + 270 q^{81} + 84 q^{82} + 42 q^{83} + 137 q^{84} + 294 q^{85} - 9 q^{86} + 22 q^{87} - 13 q^{88} + 78 q^{89} + 69 q^{90} + 118 q^{91} + 49 q^{92} + 51 q^{93} + 93 q^{94} + 10 q^{95} + 260 q^{96} + 142 q^{97} - 31 q^{98} + 78 q^{99}+O(q^{100}) \) 186 * q + 6 * q^2 + 10 * q^3 + 212 * q^4 + 38 * q^5 + 47 * q^6 + 32 * q^7 + 15 * q^8 + 216 * q^9 + 50 * q^10 + 25 * q^11 + 17 * q^12 + 113 * q^13 + 12 * q^14 + 12 * q^15 + 252 * q^16 + 35 * q^17 + 13 * q^18 + 97 * q^19 + 55 * q^20 + 115 * q^21 + 14 * q^22 + 27 * q^23 + 122 * q^24 + 244 * q^25 + 39 * q^26 + 34 * q^27 + 66 * q^28 + 91 * q^29 + 4 * q^30 + 135 * q^31 + 21 * q^32 + 32 * q^33 + 58 * q^34 + 17 * q^35 + 273 * q^36 + 133 * q^37 - 3 * q^38 + 55 * q^39 + 142 * q^40 + 97 * q^41 - 8 * q^42 + 67 * q^43 + 44 * q^44 + 154 * q^45 + 101 * q^46 + 20 * q^47 - 7 * q^48 + 312 * q^49 + 21 * q^50 + 23 * q^51 + 193 * q^52 + 22 * q^53 + 141 * q^54 + 88 * q^55 + 28 * q^56 + 65 * q^57 + 62 * q^58 + 41 * q^59 + q^60 + 377 * q^61 + 29 * q^62 + 39 * q^63 + 311 * q^64 + 21 * q^65 + 35 * q^66 + 42 * q^67 + 24 * q^68 + 137 * q^69 + 35 * q^70 + 17 * q^71 - 8 * q^72 + 213 * q^73 - 9 * q^74 + 2 * q^75 + 242 * q^76 + 60 * q^77 + 103 * q^79 + 80 * q^80 + 270 * q^81 + 84 * q^82 + 42 * q^83 + 137 * q^84 + 294 * q^85 - 9 * q^86 + 22 * q^87 - 13 * q^88 + 78 * q^89 + 69 * q^90 + 118 * q^91 + 49 * q^92 + 51 * q^93 + 93 * q^94 + 10 * q^95 + 260 * q^96 + 142 * q^97 - 31 * q^98 + 78 * q^99

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