LMFDB - Embedded newform 805.2.a.j.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [805,2,Mod(1,805)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(805, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("805.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 805 = 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	805.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:	$6.42795736271$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2777.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} + x + 2 $ x^4 - x^3 - 4*x^2 + x + 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.36234$ of defining polynomial
Character	$\chi$	$=$	805.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.36234 q^{2} +2.51572 q^{3} -0.144030 q^{4} +1.00000 q^{5} -3.42727 q^{6} -1.00000 q^{7} +2.92090 q^{8} +3.32886 q^{9} +O(q^{10})$	\(q-1.36234 q^{2} +2.51572 q^{3} -0.144030 q^{4} +1.00000 q^{5} -3.42727 q^{6} -1.00000 q^{7} +2.92090 q^{8} +3.32886 q^{9} -1.36234 q^{10} -0.362340 q^{11} -0.362340 q^{12} +1.06493 q^{13} +1.36234 q^{14} +2.51572 q^{15} -3.69119 q^{16} +1.33090 q^{17} -4.53503 q^{18} +6.02209 q^{19} -0.144030 q^{20} -2.51572 q^{21} +0.493630 q^{22} -1.00000 q^{23} +7.34817 q^{24} +1.00000 q^{25} -1.45079 q^{26} +0.827308 q^{27} +0.144030 q^{28} +4.12986 q^{29} -3.42727 q^{30} +2.39582 q^{31} -0.813134 q^{32} -0.911546 q^{33} -1.81313 q^{34} -1.00000 q^{35} -0.479456 q^{36} +4.95716 q^{37} -8.20414 q^{38} +2.67906 q^{39} +2.92090 q^{40} -1.25179 q^{41} +3.42727 q^{42} +5.32607 q^{43} +0.0521879 q^{44} +3.32886 q^{45} +1.36234 q^{46} +4.61692 q^{47} -9.28602 q^{48} +1.00000 q^{49} -1.36234 q^{50} +3.34817 q^{51} -0.153382 q^{52} -1.14403 q^{53} -1.12707 q^{54} -0.362340 q^{55} -2.92090 q^{56} +15.1499 q^{57} -5.62627 q^{58} +0.321545 q^{59} -0.362340 q^{60} -9.71051 q^{61} -3.26393 q^{62} -3.32886 q^{63} +8.49015 q^{64} +1.06493 q^{65} +1.24184 q^{66} -9.69429 q^{67} -0.191689 q^{68} -2.51572 q^{69} +1.36234 q^{70} -0.0407948 q^{71} +9.72325 q^{72} -9.48533 q^{73} -6.75334 q^{74} +2.51572 q^{75} -0.867363 q^{76} +0.362340 q^{77} -3.64979 q^{78} -6.10119 q^{79} -3.69119 q^{80} -7.90529 q^{81} +1.70537 q^{82} +15.9823 q^{83} +0.362340 q^{84} +1.33090 q^{85} -7.25592 q^{86} +10.3896 q^{87} -1.05836 q^{88} +12.6849 q^{89} -4.53503 q^{90} -1.06493 q^{91} +0.144030 q^{92} +6.02723 q^{93} -6.28981 q^{94} +6.02209 q^{95} -2.04562 q^{96} +6.43180 q^{97} -1.36234 q^{98} -1.20618 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 6 * q^9	\( 4 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 5 q^{13} - 3 q^{14} + 6 q^{15} + q^{16} + 5 q^{17} + 2 q^{18} + 8 q^{19} + 3 q^{20} - 6 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 4 q^{25} - 11 q^{26} + 15 q^{27} - 3 q^{28} - 2 q^{29} + 4 q^{30} + 10 q^{33} - 4 q^{34} - 4 q^{35} + q^{36} + 13 q^{37} - 13 q^{38} - 13 q^{39} + 6 q^{40} + q^{41} - 4 q^{42} + 14 q^{43} + 15 q^{44} + 6 q^{45} - 3 q^{46} + 4 q^{47} - 23 q^{48} + 4 q^{49} + 3 q^{50} - 10 q^{51} - 5 q^{52} - q^{53} + 14 q^{54} + 7 q^{55} - 6 q^{56} + 19 q^{57} - 16 q^{58} - 7 q^{59} + 7 q^{60} - 7 q^{61} - 15 q^{62} - 6 q^{63} - 5 q^{65} + 23 q^{66} + 15 q^{67} - 11 q^{68} - 6 q^{69} - 3 q^{70} - 17 q^{72} + 3 q^{73} - 2 q^{74} + 6 q^{75} - 22 q^{76} - 7 q^{77} - 31 q^{78} - 14 q^{79} + q^{80} + 28 q^{81} + 6 q^{82} + 3 q^{83} - 7 q^{84} + 5 q^{85} + 16 q^{86} - 14 q^{87} + 13 q^{88} - 11 q^{89} + 2 q^{90} + 5 q^{91} - 3 q^{92} - 23 q^{93} - 19 q^{94} + 8 q^{95} - 15 q^{96} + 9 q^{97} + 3 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 5 * q^13 - 3 * q^14 + 6 * q^15 + q^16 + 5 * q^17 + 2 * q^18 + 8 * q^19 + 3 * q^20 - 6 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 4 * q^25 - 11 * q^26 + 15 * q^27 - 3 * q^28 - 2 * q^29 + 4 * q^30 + 10 * q^33 - 4 * q^34 - 4 * q^35 + q^36 + 13 * q^37 - 13 * q^38 - 13 * q^39 + 6 * q^40 + q^41 - 4 * q^42 + 14 * q^43 + 15 * q^44 + 6 * q^45 - 3 * q^46 + 4 * q^47 - 23 * q^48 + 4 * q^49 + 3 * q^50 - 10 * q^51 - 5 * q^52 - q^53 + 14 * q^54 + 7 * q^55 - 6 * q^56 + 19 * q^57 - 16 * q^58 - 7 * q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 6 * q^63 - 5 * q^65 + 23 * q^66 + 15 * q^67 - 11 * q^68 - 6 * q^69 - 3 * q^70 - 17 * q^72 + 3 * q^73 - 2 * q^74 + 6 * q^75 - 22 * q^76 - 7 * q^77 - 31 * q^78 - 14 * q^79 + q^80 + 28 * q^81 + 6 * q^82 + 3 * q^83 - 7 * q^84 + 5 * q^85 + 16 * q^86 - 14 * q^87 + 13 * q^88 - 11 * q^89 + 2 * q^90 + 5 * q^91 - 3 * q^92 - 23 * q^93 - 19 * q^94 + 8 * q^95 - 15 * q^96 + 9 * q^97 + 3 * q^98 + 8 * 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 $

$2$	−1.36234	−0.963320	−0.481660	−	0.876358i	$-0.659966\pi$
$2$	−1.36234	−0.963320	−0.481660	+	0.876358i	$0.659966\pi$
$3$	2.51572	1.45245	0.726226	−	0.687456i	$-0.241272\pi$
$3$	2.51572	1.45245	0.726226	+	0.687456i	$0.241272\pi$
$4$	−0.144030	−0.0720151
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.42727	−1.39918
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.92090	1.03269
$9$	3.32886	1.10962
$10$	−1.36234	−0.430810
$11$	−0.362340	−0.109250	−0.0546248	−	0.998507i	$-0.517396\pi$
$11$	−0.362340	−0.109250	−0.0546248	+	0.998507i	$0.517396\pi$
$12$	−0.362340	−0.104599
$13$	1.06493	0.295358	0.147679	−	0.989035i	$-0.452820\pi$
$13$	1.06493	0.295358	0.147679	+	0.989035i	$0.452820\pi$
$14$	1.36234	0.364101
$15$	2.51572	0.649557
$16$	−3.69119	−0.922799
$17$	1.33090	0.322790	0.161395	−	0.986890i	$-0.448401\pi$
$17$	1.33090	0.322790	0.161395	+	0.986890i	$0.448401\pi$
$18$	−4.53503	−1.06892
$19$	6.02209	1.38156	0.690781	−	0.723064i	$-0.257267\pi$
$19$	6.02209	1.38156	0.690781	+	0.723064i	$0.257267\pi$
$20$	−0.144030	−0.0322061
$21$	−2.51572	−0.548975
$22$	0.493630	0.105242
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	7.34817	1.49994
$25$	1.00000	0.200000
$26$	−1.45079	−0.284524
$27$	0.827308	0.159215
$28$	0.144030	0.0272191
$29$	4.12986	0.766895	0.383447	−	0.923563i	$-0.374737\pi$
$29$	4.12986	0.766895	0.383447	+	0.923563i	$0.374737\pi$
$30$	−3.42727	−0.625731
$31$	2.39582	0.430303	0.215151	−	0.976581i	$-0.430976\pi$
$31$	2.39582	0.430303	0.215151	+	0.976581i	$0.430976\pi$
$32$	−0.813134	−0.143743
$33$	−0.911546	−0.158680
$34$	−1.81313	−0.310950
$35$	−1.00000	−0.169031
$36$	−0.479456	−0.0799093
$37$	4.95716	0.814953	0.407476	−	0.913216i	$-0.366409\pi$
$37$	4.95716	0.814953	0.407476	+	0.913216i	$0.366409\pi$
$38$	−8.20414	−1.33089
$39$	2.67906	0.428993
$40$	2.92090	0.461834
$41$	−1.25179	−0.195497	−0.0977487	−	0.995211i	$-0.531164\pi$
$41$	−1.25179	−0.195497	−0.0977487	+	0.995211i	$0.531164\pi$
$42$	3.42727	0.528839
$43$	5.32607	0.812219	0.406109	−	0.913825i	$-0.366885\pi$
$43$	5.32607	0.812219	0.406109	+	0.913825i	$0.366885\pi$
$44$	0.0521879	0.00786762
$45$	3.32886	0.496236
$46$	1.36234	0.200866
$47$	4.61692	0.673446	0.336723	−	0.941604i	$-0.390681\pi$
$47$	4.61692	0.673446	0.336723	+	0.941604i	$0.390681\pi$
$48$	−9.28602	−1.34032
$49$	1.00000	0.142857
$50$	−1.36234	−0.192664
$51$	3.34817	0.468837
$52$	−0.153382	−0.0212702
$53$	−1.14403	−0.157145	−0.0785723	−	0.996908i	$-0.525036\pi$
$53$	−1.14403	−0.157145	−0.0785723	+	0.996908i	$0.525036\pi$
$54$	−1.12707	−0.153375
$55$	−0.362340	−0.0488579
$56$	−2.92090	−0.390321
$57$	15.1499	2.00665
$58$	−5.62627	−0.738765
$59$	0.321545	0.0418616	0.0209308	−	0.999781i	$-0.493337\pi$
$59$	0.321545	0.0418616	0.0209308	+	0.999781i	$0.493337\pi$
$60$	−0.362340	−0.0467779
$61$	−9.71051	−1.24330	−0.621651	−	0.783294i	$-0.713538\pi$
$61$	−9.71051	−1.24330	−0.621651	+	0.783294i	$0.713538\pi$
$62$	−3.26393	−0.414519
$63$	−3.32886	−0.419396
$64$	8.49015	1.06127
$65$	1.06493	0.132088
$66$	1.24184	0.152859
$67$	−9.69429	−1.18435	−0.592173	−	0.805811i	$-0.701730\pi$
$67$	−9.69429	−1.18435	−0.592173	+	0.805811i	$0.701730\pi$
$68$	−0.191689	−0.0232457
$69$	−2.51572	−0.302857
$70$	1.36234	0.162831
$71$	−0.0407948	−0.00484145	−0.00242072	−	0.999997i	$-0.500771\pi$
$71$	−0.0407948	−0.00484145	−0.00242072	+	0.999997i	$0.500771\pi$
$72$	9.72325	1.14590
$73$	−9.48533	−1.11017	−0.555087	−	0.831792i	$-0.687315\pi$
$73$	−9.48533	−1.11017	−0.555087	+	0.831792i	$0.687315\pi$
$74$	−6.75334	−0.785060
$75$	2.51572	0.290491
$76$	−0.867363	−0.0994934
$77$	0.362340	0.0412925
$78$	−3.64979	−0.413258
$79$	−6.10119	−0.686438	−0.343219	−	0.939255i	$-0.611517\pi$
$79$	−6.10119	−0.686438	−0.343219	+	0.939255i	$0.611517\pi$
$80$	−3.69119	−0.412688
$81$	−7.90529	−0.878365
$82$	1.70537	0.188327
$83$	15.9823	1.75429	0.877145	−	0.480225i	$-0.159445\pi$
$83$	15.9823	1.75429	0.877145	+	0.480225i	$0.159445\pi$
$84$	0.362340	0.0395345
$85$	1.33090	0.144356
$86$	−7.25592	−0.782426
$87$	10.3896	1.11388
$88$	−1.05836	−0.112821
$89$	12.6849	1.34460	0.672300	−	0.740278i	$-0.265306\pi$
$89$	12.6849	1.34460	0.672300	+	0.740278i	$0.265306\pi$
$90$	−4.53503	−0.478034
$91$	−1.06493	−0.111635
$92$	0.144030	0.0150162
$93$	6.02723	0.624994
$94$	−6.28981	−0.648744
$95$	6.02209	0.617854
$96$	−2.04562	−0.208780
$97$	6.43180	0.653050	0.326525	−	0.945189i	$-0.394122\pi$
$97$	6.43180	0.653050	0.326525	+	0.945189i	$0.394122\pi$
$98$	−1.36234	−0.137617
$99$	−1.20618	−0.121225
$100$	−0.144030	−0.0144030
$101$	7.70568	0.766744	0.383372	−	0.923594i	$-0.374763\pi$
$101$	7.70568	0.766744	0.383372	+	0.923594i	$0.374763\pi$
$102$	−4.56134	−0.451640
$103$	1.42870	0.140774	0.0703871	−	0.997520i	$-0.477577\pi$
$103$	1.42870	0.140774	0.0703871	+	0.997520i	$0.477577\pi$
$104$	3.11055	0.305014
$105$	−2.51572	−0.245509
$106$	1.55856	0.151381
$107$	6.50433	0.628797	0.314399	−	0.949291i	$-0.398197\pi$
$107$	6.50433	0.628797	0.314399	+	0.949291i	$0.398197\pi$
$108$	−0.119157	−0.0114659
$109$	−12.3053	−1.17864	−0.589318	−	0.807901i	$-0.700604\pi$
$109$	−12.3053	−1.17864	−0.589318	+	0.807901i	$0.700604\pi$
$110$	0.493630	0.0470658
$111$	12.4708	1.18368
$112$	3.69119	0.348785
$113$	9.14403	0.860198	0.430099	−	0.902782i	$-0.358479\pi$
$113$	9.14403	0.860198	0.430099	+	0.902782i	$0.358479\pi$
$114$	−20.6393	−1.93305
$115$	−1.00000	−0.0932505
$116$	−0.594824	−0.0552280
$117$	3.54499	0.327735
$118$	−0.438054	−0.0403261
$119$	−1.33090	−0.122003
$120$	7.34817	0.670793
$121$	−10.8687	−0.988065
$122$	13.2290	1.19770
$123$	−3.14917	−0.283951
$124$	−0.345071	−0.0309883
$125$	1.00000	0.0894427
$126$	4.53503	0.404013
$127$	5.44597	0.483252	0.241626	−	0.970369i	$-0.422319\pi$
$127$	5.44597	0.483252	0.241626	+	0.970369i	$0.422319\pi$
$128$	−9.94021	−0.878599
$129$	13.3989	1.17971
$130$	−1.45079	−0.127243
$131$	−6.17404	−0.539428	−0.269714	−	0.962940i	$-0.586929\pi$
$131$	−6.17404	−0.539428	−0.269714	+	0.962940i	$0.586929\pi$
$132$	0.131290	0.0114273
$133$	−6.02209	−0.522182
$134$	13.2069	1.14090
$135$	0.827308	0.0712033
$136$	3.88741	0.333343
$137$	−2.32742	−0.198845	−0.0994225	−	0.995045i	$-0.531700\pi$
$137$	−2.32742	−0.198845	−0.0994225	+	0.995045i	$0.531700\pi$
$138$	3.42727	0.291748
$139$	3.33677	0.283021	0.141511	−	0.989937i	$-0.454804\pi$
$139$	3.33677	0.283021	0.141511	+	0.989937i	$0.454804\pi$
$140$	0.144030	0.0121728
$141$	11.6149	0.978149
$142$	0.0555763	0.00466386
$143$	−0.385866	−0.0322677
$144$	−12.2875	−1.02395
$145$	4.12986	0.342966
$146$	12.9222	1.06945
$147$	2.51572	0.207493
$148$	−0.713981	−0.0586889
$149$	−22.1571	−1.81518	−0.907589	−	0.419859i	$-0.862080\pi$
$149$	−22.1571	−1.81518	−0.907589	+	0.419859i	$0.862080\pi$
$150$	−3.42727	−0.279835
$151$	−18.6971	−1.52155	−0.760773	−	0.649018i	$-0.775180\pi$
$151$	−18.6971	−1.52155	−0.760773	+	0.649018i	$0.775180\pi$
$152$	17.5899	1.42673
$153$	4.43036	0.358174
$154$	−0.493630	−0.0397778
$155$	2.39582	0.192437
$156$	−0.385866	−0.0308940
$157$	−6.90190	−0.550832	−0.275416	−	0.961325i	$-0.588816\pi$
$157$	−6.90190	−0.550832	−0.275416	+	0.961325i	$0.588816\pi$
$158$	8.31190	0.661259
$159$	−2.87806	−0.228245
$160$	−0.813134	−0.0642838
$161$	1.00000	0.0788110
$162$	10.7697	0.846147
$163$	7.53503	0.590189	0.295095	−	0.955468i	$-0.404649\pi$
$163$	7.53503	0.590189	0.295095	+	0.955468i	$0.404649\pi$
$164$	0.180296	0.0140788
$165$	−0.911546	−0.0709638
$166$	−21.7734	−1.68994
$167$	4.32742	0.334866	0.167433	−	0.985883i	$-0.446452\pi$
$167$	4.32742	0.334866	0.167433	+	0.985883i	$0.446452\pi$
$168$	−7.34817	−0.566923
$169$	−11.8659	−0.912764
$170$	−1.81313	−0.139061
$171$	20.0467	1.53301
$172$	−0.767115	−0.0584920
$173$	−14.8715	−1.13066	−0.565329	−	0.824865i	$-0.691251\pi$
$173$	−14.8715	−1.13066	−0.565329	+	0.824865i	$0.691251\pi$
$174$	−14.1541	−1.07302
$175$	−1.00000	−0.0755929
$176$	1.33747	0.100815
$177$	0.808918	0.0608020
$178$	−17.2812	−1.29528
$179$	−4.56473	−0.341184	−0.170592	−	0.985342i	$-0.554568\pi$
$179$	−4.56473	−0.341184	−0.170592	+	0.985342i	$0.554568\pi$
$180$	−0.479456	−0.0357365
$181$	0.959651	0.0713303	0.0356651	−	0.999364i	$-0.488645\pi$
$181$	0.959651	0.0713303	0.0356651	+	0.999364i	$0.488645\pi$
$182$	1.45079	0.107540
$183$	−24.4289	−1.80584
$184$	−2.92090	−0.215331
$185$	4.95716	0.364458
$186$	−8.21113	−0.602069
$187$	−0.482237	−0.0352647
$188$	−0.664975	−0.0484983
$189$	−0.827308	−0.0601778
$190$	−8.20414	−0.595191
$191$	−13.8054	−0.998927	−0.499463	−	0.866335i	$-0.666469\pi$
$191$	−13.8054	−0.998927	−0.499463	+	0.866335i	$0.666469\pi$
$192$	21.3589	1.54144
$193$	−0.748519	−0.0538796	−0.0269398	−	0.999637i	$-0.508576\pi$
$193$	−0.748519	−0.0538796	−0.0269398	+	0.999637i	$0.508576\pi$
$194$	−8.76229	−0.629096
$195$	2.67906	0.191852
$196$	−0.144030	−0.0102879
$197$	−4.31921	−0.307731	−0.153865	−	0.988092i	$-0.549172\pi$
$197$	−4.31921	−0.307731	−0.153865	+	0.988092i	$0.549172\pi$
$198$	1.64322	0.116779
$199$	1.73260	0.122821	0.0614103	−	0.998113i	$-0.480440\pi$
$199$	1.73260	0.122821	0.0614103	+	0.998113i	$0.480440\pi$
$200$	2.92090	0.206539
$201$	−24.3881	−1.72021
$202$	−10.4978	−0.738620
$203$	−4.12986	−0.289859
$204$	−0.482237	−0.0337633
$205$	−1.25179	−0.0874291
$206$	−1.94638	−0.135611
$207$	−3.32886	−0.231371
$208$	−3.93086	−0.272556
$209$	−2.18204	−0.150935
$210$	3.42727	0.236504
$211$	−24.6304	−1.69563	−0.847814	−	0.530294i	$-0.822082\pi$
$211$	−24.6304	−1.69563	−0.847814	+	0.530294i	$0.822082\pi$
$212$	0.164775	0.0113168
$213$	−0.102628	−0.00703197
$214$	−8.86111	−0.605733
$215$	5.32607	0.363235
$216$	2.41648	0.164421
$217$	−2.39582	−0.162639
$218$	16.7640	1.13540
$219$	−23.8625	−1.61248
$220$	0.0521879	0.00351851
$221$	1.41731	0.0953385
$222$	−16.9895	−1.14026
$223$	−6.85628	−0.459131	−0.229565	−	0.973293i	$-0.573730\pi$
$223$	−6.85628	−0.459131	−0.229565	+	0.973293i	$0.573730\pi$
$224$	0.813134	0.0543298
$225$	3.32886	0.221924
$226$	−12.4573	−0.828646
$227$	−24.4028	−1.61967	−0.809834	−	0.586659i	$-0.800443\pi$
$227$	−24.4028	−1.61967	−0.809834	+	0.586659i	$0.800443\pi$
$228$	−2.18204	−0.144509
$229$	−15.2363	−1.00684	−0.503422	−	0.864041i	$-0.667926\pi$
$229$	−15.2363	−1.00684	−0.503422	+	0.864041i	$0.667926\pi$
$230$	1.36234	0.0898300
$231$	0.911546	0.0599753
$232$	12.0629	0.791967
$233$	13.0510	0.855003	0.427501	−	0.904015i	$-0.359394\pi$
$233$	13.0510	0.855003	0.427501	+	0.904015i	$0.359394\pi$
$234$	−4.82948	−0.315713
$235$	4.61692	0.301174
$236$	−0.0463122	−0.00301467
$237$	−15.3489	−0.997019
$238$	1.81313	0.117528
$239$	−24.4591	−1.58213	−0.791063	−	0.611735i	$-0.790472\pi$
$239$	−24.4591	−1.58213	−0.791063	+	0.611735i	$0.790472\pi$
$240$	−9.28602	−0.599410
$241$	−13.7522	−0.885857	−0.442929	−	0.896557i	$-0.646060\pi$
$241$	−13.7522	−0.885857	−0.442929	+	0.896557i	$0.646060\pi$
$242$	14.8069	0.951822
$243$	−22.3694	−1.43500
$244$	1.39861	0.0895366
$245$	1.00000	0.0638877
$246$	4.29023	0.273535
$247$	6.41309	0.408055
$248$	6.99796	0.444371
$249$	40.2071	2.54802
$250$	−1.36234	−0.0861619
$251$	23.7834	1.50119	0.750596	−	0.660762i	$-0.229767\pi$
$251$	23.7834	1.50119	0.750596	+	0.660762i	$0.229767\pi$
$252$	0.479456	0.0302029
$253$	0.362340	0.0227801
$254$	−7.41926	−0.465526
$255$	3.34817	0.209670
$256$	−3.43837	−0.214898
$257$	−12.4808	−0.778531	−0.389266	−	0.921126i	$-0.627271\pi$
$257$	−12.4808	−0.778531	−0.389266	+	0.921126i	$0.627271\pi$
$258$	−18.2539	−1.13644
$259$	−4.95716	−0.308023
$260$	−0.153382	−0.00951233
$261$	13.7477	0.850961
$262$	8.41114	0.519642
$263$	31.0204	1.91280	0.956399	−	0.292064i	$-0.0943420\pi$
$263$	31.0204	1.91280	0.956399	+	0.292064i	$0.0943420\pi$
$264$	−2.66253	−0.163868
$265$	−1.14403	−0.0702772
$266$	8.20414	0.503028
$267$	31.9118	1.95297
$268$	1.39627	0.0852908
$269$	5.56443	0.339270	0.169635	−	0.985507i	$-0.445741\pi$
$269$	5.56443	0.339270	0.169635	+	0.985507i	$0.445741\pi$
$270$	−1.12707	−0.0685916
$271$	−29.4030	−1.78611	−0.893054	−	0.449950i	$-0.851442\pi$
$271$	−29.4030	−1.78611	−0.893054	+	0.449950i	$0.851442\pi$
$272$	−4.91260	−0.297870
$273$	−2.67906	−0.162144
$274$	3.17074	0.191551
$275$	−0.362340	−0.0218499
$276$	0.362340	0.0218103
$277$	−9.21439	−0.553639	−0.276819	−	0.960922i	$-0.589280\pi$
$277$	−9.21439	−0.553639	−0.276819	+	0.960922i	$0.589280\pi$
$278$	−4.54582	−0.272640
$279$	7.97535	0.477472
$280$	−2.92090	−0.174557
$281$	21.4711	1.28086	0.640428	−	0.768018i	$-0.278757\pi$
$281$	21.4711	1.28086	0.640428	+	0.768018i	$0.278757\pi$
$282$	−15.8234	−0.942270
$283$	11.4273	0.679281	0.339640	−	0.940555i	$-0.389695\pi$
$283$	11.4273	0.679281	0.339640	+	0.940555i	$0.389695\pi$
$284$	0.00587568	0.000348657 0
$285$	15.1499	0.897403
$286$	0.525680	0.0310841
$287$	1.25179	0.0738911
$288$	−2.70680	−0.159500
$289$	−15.2287	−0.895807
$290$	−5.62627	−0.330386
$291$	16.1806	0.948524
$292$	1.36617	0.0799493
$293$	−3.21905	−0.188059	−0.0940294	−	0.995569i	$-0.529975\pi$
$293$	−3.21905	−0.188059	−0.0940294	+	0.995569i	$0.529975\pi$
$294$	−3.42727	−0.199882
$295$	0.321545	0.0187211
$296$	14.4794	0.841596
$297$	−0.299767	−0.0173942
$298$	30.1855	1.74860
$299$	−1.06493	−0.0615864
$300$	−0.362340	−0.0209197
$301$	−5.32607	−0.306990
$302$	25.4718	1.46574
$303$	19.3854	1.11366
$304$	−22.2287	−1.27490
$305$	−9.71051	−0.556022
$306$	−6.03566	−0.345036
$307$	0.183478	0.0104716	0.00523582	−	0.999986i	$-0.498333\pi$
$307$	0.183478	0.0104716	0.00523582	+	0.999986i	$0.498333\pi$
$308$	−0.0521879	−0.00297368
$309$	3.59422	0.204468
$310$	−3.26393	−0.185379
$311$	−9.56051	−0.542127	−0.271063	−	0.962561i	$-0.587375\pi$
$311$	−9.56051	−0.542127	−0.271063	+	0.962561i	$0.587375\pi$
$312$	7.82527	0.443018
$313$	33.1105	1.87151	0.935757	−	0.352644i	$-0.114717\pi$
$313$	33.1105	1.87151	0.935757	+	0.352644i	$0.114717\pi$
$314$	9.40273	0.530627
$315$	−3.32886	−0.187560
$316$	0.878756	0.0494339
$317$	6.79865	0.381850	0.190925	−	0.981605i	$-0.438851\pi$
$317$	6.79865	0.381850	0.190925	+	0.981605i	$0.438851\pi$
$318$	3.92090	0.219873
$319$	−1.49641	−0.0837829
$320$	8.49015	0.474614
$321$	16.3631	0.913298
$322$	−1.36234	−0.0759202
$323$	8.01478	0.445954
$324$	1.13860	0.0632556
$325$	1.06493	0.0590716
$326$	−10.2653	−0.568541
$327$	−30.9568	−1.71191
$328$	−3.65636	−0.201889
$329$	−4.61692	−0.254539
$330$	1.24184	0.0683608
$331$	17.6428	0.969738	0.484869	−	0.874587i	$-0.338867\pi$
$331$	17.6428	0.969738	0.484869	+	0.874587i	$0.338867\pi$
$332$	−2.30194	−0.126335
$333$	16.5017	0.904286
$334$	−5.89542	−0.322583
$335$	−9.69429	−0.529656
$336$	9.28602	0.506594
$337$	−9.25592	−0.504202	−0.252101	−	0.967701i	$-0.581122\pi$
$337$	−9.25592	−0.504202	−0.252101	+	0.967701i	$0.581122\pi$
$338$	16.1654	0.879283
$339$	23.0038	1.24940
$340$	−0.191689	−0.0103958
$341$	−0.868103	−0.0470104
$342$	−27.3104	−1.47678
$343$	−1.00000	−0.0539949
$344$	15.5569	0.838773
$345$	−2.51572	−0.135442
$346$	20.2600	1.08919
$347$	−14.2355	−0.764201	−0.382101	−	0.924121i	$-0.624799\pi$
$347$	−14.2355	−0.764201	−0.382101	+	0.924121i	$0.624799\pi$
$348$	−1.49641	−0.0802161
$349$	10.2100	0.546529	0.273265	−	0.961939i	$-0.411897\pi$
$349$	10.2100	0.546529	0.273265	+	0.961939i	$0.411897\pi$
$350$	1.36234	0.0728201
$351$	0.881023	0.0470255
$352$	0.294631	0.0157039
$353$	−19.1189	−1.01760	−0.508798	−	0.860886i	$-0.669910\pi$
$353$	−19.1189	−1.01760	−0.508798	+	0.860886i	$0.669910\pi$
$354$	−1.10202	−0.0585718
$355$	−0.0407948	−0.00216516
$356$	−1.82701	−0.0968315
$357$	−3.34817	−0.177204
$358$	6.21871	0.328669
$359$	−15.3220	−0.808664	−0.404332	−	0.914612i	$-0.632496\pi$
$359$	−15.3220	−0.808664	−0.404332	+	0.914612i	$0.632496\pi$
$360$	9.72325	0.512460
$361$	17.2656	0.908715
$362$	−1.30737	−0.0687139
$363$	−27.3426	−1.43512
$364$	0.153382	0.00803939
$365$	−9.48533	−0.496485
$366$	33.2805	1.73960
$367$	−9.72194	−0.507481	−0.253741	−	0.967272i	$-0.581661\pi$
$367$	−9.72194	−0.507481	−0.253741	+	0.967272i	$0.581661\pi$
$368$	3.69119	0.192417
$369$	−4.16704	−0.216928
$370$	−6.75334	−0.351090
$371$	1.14403	0.0593951
$372$	−0.868103	−0.0450090
$373$	−30.1482	−1.56101	−0.780507	−	0.625147i	$-0.785039\pi$
$373$	−30.1482	−1.56101	−0.780507	+	0.625147i	$0.785039\pi$
$374$	0.656970	0.0339711
$375$	2.51572	0.129911
$376$	13.4855	0.695464
$377$	4.39800	0.226508
$378$	1.12707	0.0579705
$379$	−12.5862	−0.646511	−0.323256	−	0.946312i	$-0.604777\pi$
$379$	−12.5862	−0.646511	−0.323256	+	0.946312i	$0.604777\pi$
$380$	−0.867363	−0.0444948
$381$	13.7005	0.701900
$382$	18.8077	0.962286
$383$	18.2816	0.934148	0.467074	−	0.884218i	$-0.345308\pi$
$383$	18.2816	0.934148	0.467074	+	0.884218i	$0.345308\pi$
$384$	−25.0068	−1.27612
$385$	0.362340	0.0184665
$386$	1.01974	0.0519032
$387$	17.7297	0.901253
$388$	−0.926373	−0.0470295
$389$	28.0843	1.42393	0.711965	−	0.702215i	$-0.247806\pi$
$389$	28.0843	1.42393	0.711965	+	0.702215i	$0.247806\pi$
$390$	−3.64979	−0.184814
$391$	−1.33090	−0.0673063
$392$	2.92090	0.147528
$393$	−15.5322	−0.783494
$394$	5.88423	0.296443
$395$	−6.10119	−0.306984
$396$	0.173726	0.00873005
$397$	−6.14268	−0.308292	−0.154146	−	0.988048i	$-0.549263\pi$
$397$	−6.14268	−0.308292	−0.154146	+	0.988048i	$0.549263\pi$
$398$	−2.36039	−0.118315
$399$	−15.1499	−0.758444
$400$	−3.69119	−0.184560
$401$	18.6924	0.933454	0.466727	−	0.884401i	$-0.345433\pi$
$401$	18.6924	0.933454	0.466727	+	0.884401i	$0.345433\pi$
$402$	33.2249	1.65711
$403$	2.55138	0.127093
$404$	−1.10985	−0.0552171
$405$	−7.90529	−0.392817
$406$	5.62627	0.279227
$407$	−1.79618	−0.0890332
$408$	9.77965	0.484165
$409$	13.8484	0.684760	0.342380	−	0.939562i	$-0.388767\pi$
$409$	13.8484	0.684760	0.342380	+	0.939562i	$0.388767\pi$
$410$	1.70537	0.0842222
$411$	−5.85514	−0.288813
$412$	−0.205776	−0.0101379
$413$	−0.321545	−0.0158222
$414$	4.53503	0.222885
$415$	15.9823	0.784543
$416$	−0.865929	−0.0424556
$417$	8.39439	0.411075
$418$	2.97269	0.145399
$419$	−28.0372	−1.36971	−0.684853	−	0.728681i	$-0.740134\pi$
$419$	−28.0372	−1.36971	−0.684853	+	0.728681i	$0.740134\pi$
$420$	0.362340	0.0176804
$421$	−0.979950	−0.0477598	−0.0238799	−	0.999715i	$-0.507602\pi$
$421$	−0.979950	−0.0477598	−0.0238799	+	0.999715i	$0.507602\pi$
$422$	33.5550	1.63343
$423$	15.3690	0.747268
$424$	−3.34160	−0.162282
$425$	1.33090	0.0645580
$426$	0.139815	0.00677404
$427$	9.71051	0.469924
$428$	−0.936820	−0.0452829
$429$	−0.970731	−0.0468673
$430$	−7.25592	−0.349912
$431$	19.2787	0.928623	0.464311	−	0.885672i	$-0.346302\pi$
$431$	19.2787	0.928623	0.464311	+	0.885672i	$0.346302\pi$
$432$	−3.05375	−0.146924
$433$	17.1395	0.823673	0.411836	−	0.911258i	$-0.364888\pi$
$433$	17.1395	0.823673	0.411836	+	0.911258i	$0.364888\pi$
$434$	3.26393	0.156674
$435$	10.3896	0.498142
$436$	1.77234	0.0848796
$437$	−6.02209	−0.288076
$438$	32.5088	1.55333
$439$	37.0875	1.77009	0.885046	−	0.465504i	$-0.154127\pi$
$439$	37.0875	1.77009	0.885046	+	0.465504i	$0.154127\pi$
$440$	−1.05836	−0.0504552
$441$	3.32886	0.158517
$442$	−1.93086	−0.0918415
$443$	25.9758	1.23415	0.617073	−	0.786906i	$-0.288318\pi$
$443$	25.9758	1.23415	0.617073	+	0.786906i	$0.288318\pi$
$444$	−1.79618	−0.0852428
$445$	12.6849	0.601324
$446$	9.34059	0.442290
$447$	−55.7411	−2.63646
$448$	−8.49015	−0.401122
$449$	27.4405	1.29500	0.647498	−	0.762068i	$-0.275816\pi$
$449$	27.4405	1.29500	0.647498	+	0.762068i	$0.275816\pi$
$450$	−4.53503	−0.213783
$451$	0.453575	0.0213580
$452$	−1.31702	−0.0619472
$453$	−47.0366	−2.20997
$454$	33.2448	1.56026
$455$	−1.06493	−0.0499246
$456$	44.2513	2.07226
$457$	−3.05248	−0.142789	−0.0713945	−	0.997448i	$-0.522745\pi$
$457$	−3.05248	−0.142789	−0.0713945	+	0.997448i	$0.522745\pi$
$458$	20.7570	0.969913
$459$	1.10106	0.0513931
$460$	0.144030	0.00671544
$461$	−21.2366	−0.989089	−0.494544	−	0.869152i	$-0.664665\pi$
$461$	−21.2366	−0.989089	−0.494544	+	0.869152i	$0.664665\pi$
$462$	−1.24184	−0.0577754
$463$	11.0623	0.514108	0.257054	−	0.966397i	$-0.417248\pi$
$463$	11.0623	0.514108	0.257054	+	0.966397i	$0.417248\pi$
$464$	−15.2441	−0.707690
$465$	6.02723	0.279506
$466$	−17.7800	−0.823641
$467$	20.4458	0.946121	0.473060	−	0.881030i	$-0.343149\pi$
$467$	20.4458	0.946121	0.473060	+	0.881030i	$0.343149\pi$
$468$	−0.510586	−0.0236018
$469$	9.69429	0.447641
$470$	−6.28981	−0.290127
$471$	−17.3633	−0.800057
$472$	0.939200	0.0432302
$473$	−1.92985	−0.0887345
$474$	20.9104	0.960448
$475$	6.02209	0.276313
$476$	0.191689	0.00878606
$477$	−3.80831	−0.174371
$478$	33.3216	1.52409
$479$	4.03656	0.184435	0.0922176	−	0.995739i	$-0.470604\pi$
$479$	4.03656	0.184435	0.0922176	+	0.995739i	$0.470604\pi$
$480$	−2.04562	−0.0933692
$481$	5.27902	0.240703
$482$	18.7352	0.853364
$483$	2.51572	0.114469
$484$	1.56542	0.0711556
$485$	6.43180	0.292053
$486$	30.4748	1.38236
$487$	−5.39892	−0.244648	−0.122324	−	0.992490i	$-0.539035\pi$
$487$	−5.39892	−0.244648	−0.122324	+	0.992490i	$0.539035\pi$
$488$	−28.3634	−1.28395
$489$	18.9560	0.857222
$490$	−1.36234	−0.0615442
$491$	40.4037	1.82339	0.911696	−	0.410866i	$-0.134774\pi$
$491$	40.4037	1.82339	0.911696	+	0.410866i	$0.134774\pi$
$492$	0.453575	0.0204487
$493$	5.49641	0.247546
$494$	−8.73681	−0.393088
$495$	−1.20618	−0.0542136
$496$	−8.84346	−0.397083
$497$	0.0407948	0.00182989
$498$	−54.7758	−2.45456
$499$	12.4697	0.558221	0.279111	−	0.960259i	$-0.409960\pi$
$499$	12.4697	0.558221	0.279111	+	0.960259i	$0.409960\pi$
$500$	−0.144030	−0.00644123
$501$	10.8866	0.486377
$502$	−32.4010	−1.44613
$503$	−18.3201	−0.816853	−0.408427	−	0.912791i	$-0.633922\pi$
$503$	−18.3201	−0.816853	−0.408427	+	0.912791i	$0.633922\pi$
$504$	−9.72325	−0.433108
$505$	7.70568	0.342898
$506$	−0.493630	−0.0219445
$507$	−29.8514	−1.32575
$508$	−0.784384	−0.0348014
$509$	−6.97723	−0.309260	−0.154630	−	0.987972i	$-0.549419\pi$
$509$	−6.97723	−0.309260	−0.154630	+	0.987972i	$0.549419\pi$
$510$	−4.56134	−0.201979
$511$	9.48533	0.419606
$512$	24.5646	1.08561
$513$	4.98212	0.219966
$514$	17.0031	0.749974
$515$	1.42870	0.0629561
$516$	−1.92985	−0.0849569
$517$	−1.67289	−0.0735737
$518$	6.75334	0.296725
$519$	−37.4125	−1.64223
$520$	3.11055	0.136406
$521$	16.1976	0.709628	0.354814	−	0.934937i	$-0.384544\pi$
$521$	16.1976	0.709628	0.354814	+	0.934937i	$0.384544\pi$
$522$	−18.7290	−0.819747
$523$	8.61956	0.376907	0.188454	−	0.982082i	$-0.439652\pi$
$523$	8.61956	0.376907	0.188454	+	0.982082i	$0.439652\pi$
$524$	0.889248	0.0388470
$525$	−2.51572	−0.109795
$526$	−42.2603	−1.84264
$527$	3.18859	0.138897
$528$	3.36469	0.146430
$529$	1.00000	0.0434783
$530$	1.55856	0.0676994
$531$	1.07038	0.0464504
$532$	0.867363	0.0376050
$533$	−1.33307	−0.0577417
$534$	−43.4747	−1.88133
$535$	6.50433	0.281207
$536$	−28.3160	−1.22307
$537$	−11.4836	−0.495553
$538$	−7.58065	−0.326825
$539$	−0.362340	−0.0156071
$540$	−0.119157	−0.00512771
$541$	−34.7028	−1.49199	−0.745995	−	0.665952i	$-0.768026\pi$
$541$	−34.7028	−1.49199	−0.745995	+	0.665952i	$0.768026\pi$
$542$	40.0569	1.72059
$543$	2.41421	0.103604
$544$	−1.08220	−0.0463988
$545$	−12.3053	−0.527102
$546$	3.64979	0.156197
$547$	−13.5053	−0.577446	−0.288723	−	0.957413i	$-0.593231\pi$
$547$	−13.5053	−0.577446	−0.288723	+	0.957413i	$0.593231\pi$
$548$	0.335219	0.0143198
$549$	−32.3249	−1.37959
$550$	0.493630	0.0210485
$551$	24.8704	1.05951
$552$	−7.34817	−0.312759
$553$	6.10119	0.259449
$554$	12.5531	0.533331
$555$	12.4708	0.529358
$556$	−0.480596	−0.0203818
$557$	−23.1940	−0.982763	−0.491382	−	0.870944i	$-0.663508\pi$
$557$	−23.1940	−0.982763	−0.491382	+	0.870944i	$0.663508\pi$
$558$	−10.8651	−0.459958
$559$	5.67188	0.239895
$560$	3.69119	0.155981
$561$	−1.21317	−0.0512202
$562$	−29.2509	−1.23387
$563$	−3.44792	−0.145313	−0.0726564	−	0.997357i	$-0.523148\pi$
$563$	−3.44792	−0.145313	−0.0726564	+	0.997357i	$0.523148\pi$
$564$	−1.67289	−0.0704415
$565$	9.14403	0.384692
$566$	−15.5678	−0.654364
$567$	7.90529	0.331991
$568$	−0.119157	−0.00499973
$569$	10.1165	0.424106	0.212053	−	0.977258i	$-0.431985\pi$
$569$	10.1165	0.424106	0.212053	+	0.977258i	$0.431985\pi$
$570$	−20.6393	−0.864486
$571$	31.0036	1.29746	0.648730	−	0.761018i	$-0.275300\pi$
$571$	31.0036	1.29746	0.648730	+	0.761018i	$0.275300\pi$
$572$	0.0555763	0.00232376
$573$	−34.7306	−1.45089
$574$	−1.70537	−0.0711807
$575$	−1.00000	−0.0417029
$576$	28.2625	1.17760
$577$	−28.6449	−1.19250	−0.596251	−	0.802798i	$-0.703344\pi$
$577$	−28.6449	−1.19250	−0.596251	+	0.802798i	$0.703344\pi$
$578$	20.7467	0.862948
$579$	−1.88306	−0.0782575
$580$	−0.594824	−0.0246987
$581$	−15.9823	−0.663060
$582$	−22.0435	−0.913732
$583$	0.414528	0.0171680
$584$	−27.7057	−1.14647
$585$	3.54499	0.146567
$586$	4.38544	0.181161
$587$	18.9813	0.783443	0.391721	−	0.920084i	$-0.371880\pi$
$587$	18.9813	0.783443	0.391721	+	0.920084i	$0.371880\pi$
$588$	−0.362340	−0.0149426
$589$	14.4279	0.594490
$590$	−0.438054	−0.0180344
$591$	−10.8659	−0.446965
$592$	−18.2979	−0.752037
$593$	−32.0593	−1.31652	−0.658258	−	0.752792i	$-0.728707\pi$
$593$	−32.0593	−1.31652	−0.658258	+	0.752792i	$0.728707\pi$
$594$	0.408384	0.0167562
$595$	−1.33090	−0.0545614
$596$	3.19129	0.130720
$597$	4.35873	0.178391
$598$	1.45079	0.0593274
$599$	−27.3549	−1.11769	−0.558846	−	0.829271i	$-0.688756\pi$
$599$	−27.3549	−1.11769	−0.558846	+	0.829271i	$0.688756\pi$
$600$	7.34817	0.299988
$601$	−30.8825	−1.25972	−0.629862	−	0.776707i	$-0.716888\pi$
$601$	−30.8825	−1.25972	−0.629862	+	0.776707i	$0.716888\pi$
$602$	7.25592	0.295729
$603$	−32.2709	−1.31417
$604$	2.69294	0.109574
$605$	−10.8687	−0.441876
$606$	−26.4094	−1.07281
$607$	35.9184	1.45788	0.728941	−	0.684576i	$-0.240013\pi$
$607$	35.9184	1.45788	0.728941	+	0.684576i	$0.240013\pi$
$608$	−4.89676	−0.198590
$609$	−10.3896	−0.421007
$610$	13.2290	0.535627
$611$	4.91668	0.198908
$612$	−0.638106	−0.0257939
$613$	30.2918	1.22347	0.611736	−	0.791062i	$-0.290471\pi$
$613$	30.2918	1.22347	0.611736	+	0.791062i	$0.290471\pi$
$614$	−0.249959	−0.0100875
$615$	−3.14917	−0.126987
$616$	1.05836	0.0426424
$617$	6.00662	0.241817	0.120909	−	0.992664i	$-0.461419\pi$
$617$	6.00662	0.241817	0.120909	+	0.992664i	$0.461419\pi$
$618$	−4.89654	−0.196968
$619$	−9.20533	−0.369993	−0.184997	−	0.982739i	$-0.559227\pi$
$619$	−9.20533	−0.369993	−0.184997	+	0.982739i	$0.559227\pi$
$620$	−0.345071	−0.0138584
$621$	−0.827308	−0.0331987
$622$	13.0247	0.522242
$623$	−12.6849	−0.508211
$624$	−9.88894	−0.395874
$625$	1.00000	0.0400000
$626$	−45.1077	−1.80287
$627$	−5.48941	−0.219226
$628$	0.994082	0.0396682
$629$	6.59747	0.263058
$630$	4.53503	0.180680
$631$	10.6849	0.425361	0.212680	−	0.977122i	$-0.431781\pi$
$631$	10.6849	0.425361	0.212680	+	0.977122i	$0.431781\pi$
$632$	−17.8210	−0.708880
$633$	−61.9633	−2.46282
$634$	−9.26207	−0.367844
$635$	5.44597	0.216117
$636$	0.414528	0.0164371
$637$	1.06493	0.0421940
$638$	2.03862	0.0807098
$639$	−0.135800	−0.00537216
$640$	−9.94021	−0.392921
$641$	−32.0087	−1.26427	−0.632133	−	0.774860i	$-0.717821\pi$
$641$	−32.0087	−1.26427	−0.632133	+	0.774860i	$0.717821\pi$
$642$	−22.2921	−0.879798
$643$	15.9336	0.628358	0.314179	−	0.949364i	$-0.398271\pi$
$643$	15.9336	0.628358	0.314179	+	0.949364i	$0.398271\pi$
$644$	−0.144030	−0.00567558
$645$	13.3989	0.527582
$646$	−10.9189	−0.429597
$647$	33.3993	1.31306	0.656531	−	0.754299i	$-0.272023\pi$
$647$	33.3993	1.31306	0.656531	+	0.754299i	$0.272023\pi$
$648$	−23.0905	−0.907082
$649$	−0.116509	−0.00457336
$650$	−1.45079	−0.0569048
$651$	−6.02723	−0.236226
$652$	−1.08527	−0.0425025
$653$	9.26032	0.362384	0.181192	−	0.983448i	$-0.442004\pi$
$653$	9.26032	0.362384	0.181192	+	0.983448i	$0.442004\pi$
$654$	42.1737	1.64912
$655$	−6.17404	−0.241240
$656$	4.62062	0.180405
$657$	−31.5753	−1.23187
$658$	6.28981	0.245202
$659$	−18.3799	−0.715980	−0.357990	−	0.933725i	$-0.616538\pi$
$659$	−18.3799	−0.715980	−0.357990	+	0.933725i	$0.616538\pi$
$660$	0.131290	0.00511046
$661$	−37.8968	−1.47402	−0.737008	−	0.675884i	$-0.763762\pi$
$661$	−37.8968	−1.47402	−0.737008	+	0.675884i	$0.763762\pi$
$662$	−24.0355	−0.934168
$663$	3.56555	0.138475
$664$	46.6828	1.81164
$665$	−6.02209	−0.233527
$666$	−22.4809	−0.871117
$667$	−4.12986	−0.159909
$668$	−0.623279	−0.0241154
$669$	−17.2485	−0.666866
$670$	13.2069	0.510228
$671$	3.51850	0.135830
$672$	2.04562	0.0789114
$673$	−19.5137	−0.752197	−0.376099	−	0.926580i	$-0.622735\pi$
$673$	−19.5137	−0.752197	−0.376099	+	0.926580i	$0.622735\pi$
$674$	12.6097	0.485708
$675$	0.827308	0.0318431
$676$	1.70905	0.0657328
$677$	−46.9388	−1.80401	−0.902003	−	0.431730i	$-0.857903\pi$
$677$	−46.9388	−1.80401	−0.902003	+	0.431730i	$0.857903\pi$
$678$	−31.3390	−1.20357
$679$	−6.43180	−0.246830
$680$	3.88741	0.149075
$681$	−61.3905	−2.35249
$682$	1.18265	0.0452860
$683$	51.0747	1.95432	0.977159	−	0.212511i	$-0.0681641\pi$
$683$	51.0747	1.95432	0.977159	+	0.212511i	$0.0681641\pi$
$684$	−2.88733	−0.110400
$685$	−2.32742	−0.0889262
$686$	1.36234	0.0520144
$687$	−38.3303	−1.46239
$688$	−19.6596	−0.749514
$689$	−1.21831	−0.0464139
$690$	3.42727	0.130474
$691$	−34.6866	−1.31954	−0.659770	−	0.751468i	$-0.729346\pi$
$691$	−34.6866	−1.31954	−0.659770	+	0.751468i	$0.729346\pi$
$692$	2.14194	0.0814245
$693$	1.20618	0.0458189
$694$	19.3936	0.736170
$695$	3.33677	0.126571
$696$	30.3469	1.15029
$697$	−1.66601	−0.0631046
$698$	−13.9095	−0.526483
$699$	32.8328	1.24185
$700$	0.144030	0.00544383
$701$	10.2957	0.388864	0.194432	−	0.980916i	$-0.437714\pi$
$701$	10.2957	0.388864	0.194432	+	0.980916i	$0.437714\pi$
$702$	−1.20025	−0.0453006
$703$	29.8525	1.12591
$704$	−3.07632	−0.115943
$705$	11.6149	0.437441
$706$	26.0465	0.980271
$707$	−7.70568	−0.289802
$708$	−0.116509	−0.00437866
$709$	28.3988	1.06654	0.533270	−	0.845945i	$-0.320963\pi$
$709$	28.3988	1.06654	0.533270	+	0.845945i	$0.320963\pi$
$710$	0.0555763	0.00208574
$711$	−20.3100	−0.761684
$712$	37.0514	1.38856
$713$	−2.39582	−0.0897243
$714$	4.56134	0.170704
$715$	−0.385866	−0.0144306
$716$	0.657459	0.0245704
$717$	−61.5322	−2.29796
$718$	20.8738	0.779002
$719$	21.4397	0.799566	0.399783	−	0.916610i	$-0.369085\pi$
$719$	21.4397	0.799566	0.399783	+	0.916610i	$0.369085\pi$
$720$	−12.2875	−0.457926
$721$	−1.42870	−0.0532076
$722$	−23.5216	−0.875383
$723$	−34.5967	−1.28667
$724$	−0.138219	−0.00513686
$725$	4.12986	0.153379
$726$	37.2500	1.38248
$727$	36.0470	1.33691	0.668455	−	0.743752i	$-0.266956\pi$
$727$	36.0470	1.33691	0.668455	+	0.743752i	$0.266956\pi$
$728$	−3.11055	−0.115284
$729$	−32.5594	−1.20590
$730$	12.9222	0.478274
$731$	7.08845	0.262176
$732$	3.51850	0.130048
$733$	−18.3814	−0.678931	−0.339465	−	0.940619i	$-0.610246\pi$
$733$	−18.3814	−0.678931	−0.339465	+	0.940619i	$0.610246\pi$
$734$	13.2446	0.488867
$735$	2.51572	0.0927938
$736$	0.813134	0.0299725
$737$	3.51263	0.129389
$738$	5.67693	0.208971
$739$	26.3563	0.969532	0.484766	−	0.874644i	$-0.338905\pi$
$739$	26.3563	0.969532	0.484766	+	0.874644i	$0.338905\pi$
$740$	−0.713981	−0.0262465
$741$	16.1336	0.592681
$742$	−1.55856	−0.0572165
$743$	22.9594	0.842300	0.421150	−	0.906991i	$-0.361627\pi$
$743$	22.9594	0.842300	0.421150	+	0.906991i	$0.361627\pi$
$744$	17.6049	0.645428
$745$	−22.1571	−0.811773
$746$	41.0721	1.50376
$747$	53.2029	1.94659
$748$	0.0694567	0.00253959
$749$	−6.50433	−0.237663
$750$	−3.42727	−0.125146
$751$	42.4462	1.54889	0.774443	−	0.632644i	$-0.218030\pi$
$751$	42.4462	1.54889	0.774443	+	0.632644i	$0.218030\pi$
$752$	−17.0419	−0.621455
$753$	59.8323	2.18041
$754$	−5.99157	−0.218200
$755$	−18.6971	−0.680456
$756$	0.119157	0.00433371
$757$	27.9077	1.01432	0.507161	−	0.861851i	$-0.330695\pi$
$757$	27.9077	1.01432	0.507161	+	0.861851i	$0.330695\pi$
$758$	17.1467	0.622797
$759$	0.911546	0.0330870
$760$	17.5899	0.638053
$761$	−11.3993	−0.413224	−0.206612	−	0.978423i	$-0.566244\pi$
$761$	−11.3993	−0.413224	−0.206612	+	0.978423i	$0.566244\pi$
$762$	−18.6648	−0.676154
$763$	12.3053	0.445483
$764$	1.98840	0.0719378
$765$	4.43036	0.160180
$766$	−24.9058	−0.899883
$767$	0.342422	0.0123642
$768$	−8.64997	−0.312129
$769$	48.9532	1.76530	0.882648	−	0.470034i	$-0.155758\pi$
$769$	48.9532	1.76530	0.882648	+	0.470034i	$0.155758\pi$
$770$	−0.493630	−0.0177892
$771$	−31.3982	−1.13078
$772$	0.107809	0.00388014
$773$	−43.8053	−1.57557	−0.787783	−	0.615953i	$-0.788771\pi$
$773$	−43.8053	−1.57557	−0.787783	+	0.615953i	$0.788771\pi$
$774$	−24.1539	−0.868195
$775$	2.39582	0.0860606
$776$	18.7866	0.674400
$777$	−12.4708	−0.447389
$778$	−38.2603	−1.37170
$779$	−7.53842	−0.270092
$780$	−0.385866	−0.0138162
$781$	0.0147816	0.000528926 0
$782$	1.81313	0.0648375
$783$	3.41666	0.122102
$784$	−3.69119	−0.131828
$785$	−6.90190	−0.246339
$786$	21.1601	0.754755
$787$	−21.1522	−0.753996	−0.376998	−	0.926214i	$-0.623044\pi$
$787$	−21.1522	−0.753996	−0.376998	+	0.926214i	$0.623044\pi$
$788$	0.622097	0.0221613
$789$	78.0386	2.77825
$790$	8.31190	0.295724
$791$	−9.14403	−0.325124
$792$	−3.52312	−0.125189
$793$	−10.3410	−0.367219
$794$	8.36842	0.296984
$795$	−2.87806	−0.102074
$796$	−0.249546	−0.00884493
$797$	−5.36333	−0.189979	−0.0949894	−	0.995478i	$-0.530282\pi$
$797$	−5.36333	−0.189979	−0.0949894	+	0.995478i	$0.530282\pi$
$798$	20.6393	0.730624
$799$	6.14464	0.217382
$800$	−0.813134	−0.0287486
$801$	42.2263	1.49199
$802$	−25.4654	−0.899215
$803$	3.43691	0.121286
$804$	3.51263	0.123881
$805$	1.00000	0.0352454
$806$	−3.47585	−0.122431
$807$	13.9986	0.492773
$808$	22.5075	0.791811
$809$	53.7732	1.89056	0.945282	−	0.326255i	$-0.105787\pi$
$809$	53.7732	1.89056	0.945282	+	0.326255i	$0.105787\pi$
$810$	10.7697	0.378408
$811$	−54.9942	−1.93111	−0.965554	−	0.260204i	$-0.916210\pi$
$811$	−54.9942	−1.93111	−0.965554	+	0.260204i	$0.916210\pi$
$812$	0.594824	0.0208742
$813$	−73.9699	−2.59424
$814$	2.44700	0.0857675
$815$	7.53503	0.263941
$816$	−12.3587	−0.432642
$817$	32.0741	1.12213
$818$	−18.8662	−0.659643
$819$	−3.54499	−0.123872
$820$	0.180296	0.00629622
$821$	−29.7883	−1.03962	−0.519810	−	0.854282i	$-0.673997\pi$
$821$	−29.7883	−1.03962	−0.519810	+	0.854282i	$0.673997\pi$
$822$	7.97669	0.278219
$823$	24.6064	0.857726	0.428863	−	0.903370i	$-0.358914\pi$
$823$	24.6064	0.857726	0.428863	+	0.903370i	$0.358914\pi$
$824$	4.17309	0.145377
$825$	−0.911546	−0.0317360
$826$	0.438054	0.0152418
$827$	6.34025	0.220472	0.110236	−	0.993905i	$-0.464839\pi$
$827$	6.34025	0.220472	0.110236	+	0.993905i	$0.464839\pi$
$828$	0.479456	0.0166622
$829$	−42.4940	−1.47588	−0.737939	−	0.674868i	$-0.764201\pi$
$829$	−42.4940	−1.47588	−0.737939	+	0.674868i	$0.764201\pi$
$830$	−21.7734	−0.755765
$831$	−23.1808	−0.804134
$832$	9.04140	0.313454
$833$	1.33090	0.0461128
$834$	−11.4360	−0.395997
$835$	4.32742	0.149757
$836$	0.314280	0.0108696
$837$	1.98208	0.0685109
$838$	38.1962	1.31946
$839$	35.0125	1.20877	0.604383	−	0.796694i	$-0.293420\pi$
$839$	35.0125	1.20877	0.604383	+	0.796694i	$0.293420\pi$
$840$	−7.34817	−0.253536
$841$	−11.9443	−0.411872
$842$	1.33502	0.0460080
$843$	54.0152	1.86038
$844$	3.54752	0.122111
$845$	−11.8659	−0.408200
$846$	−20.9379	−0.719858
$847$	10.8687	0.373453
$848$	4.22284	0.145013
$849$	28.7478	0.986623
$850$	−1.81313	−0.0621900
$851$	−4.95716	−0.169929
$852$	0.0147816	0.000506408 0
$853$	16.1072	0.551501	0.275751	−	0.961229i	$-0.411074\pi$
$853$	16.1072	0.551501	0.275751	+	0.961229i	$0.411074\pi$
$854$	−13.2290	−0.452687
$855$	20.0467	0.685582
$856$	18.9985	0.649355
$857$	17.3243	0.591785	0.295893	−	0.955221i	$-0.404383\pi$
$857$	17.3243	0.591785	0.295893	+	0.955221i	$0.404383\pi$
$858$	1.32247	0.0451482
$859$	25.7948	0.880107	0.440053	−	0.897972i	$-0.354960\pi$
$859$	25.7948	0.880107	0.440053	+	0.897972i	$0.354960\pi$
$860$	−0.767115	−0.0261584
$861$	3.14917	0.107323
$862$	−26.2642	−0.894561
$863$	4.66571	0.158823	0.0794114	−	0.996842i	$-0.474696\pi$
$863$	4.66571	0.158823	0.0794114	+	0.996842i	$0.474696\pi$
$864$	−0.672712	−0.0228861
$865$	−14.8715	−0.505646
$866$	−23.3499	−0.793460
$867$	−38.3112	−1.30112
$868$	0.345071	0.0117125
$869$	2.21071	0.0749931
$870$	−14.1541	−0.479870
$871$	−10.3237	−0.349806
$872$	−35.9426	−1.21717
$873$	21.4105	0.724636
$874$	8.20414	0.277509
$875$	−1.00000	−0.0338062
$876$	3.43691	0.116123
$877$	1.95544	0.0660304	0.0330152	−	0.999455i	$-0.489489\pi$
$877$	1.95544	0.0660304	0.0330152	+	0.999455i	$0.489489\pi$
$878$	−50.5258	−1.70516
$879$	−8.09823	−0.273147
$880$	1.33747	0.0450860
$881$	2.24154	0.0755195	0.0377597	−	0.999287i	$-0.487978\pi$
$881$	2.24154	0.0755195	0.0377597	+	0.999287i	$0.487978\pi$
$882$	−4.53503	−0.152702
$883$	−50.0221	−1.68338	−0.841688	−	0.539964i	$-0.818438\pi$
$883$	−50.0221	−1.68338	−0.841688	+	0.539964i	$0.818438\pi$
$884$	−0.204135	−0.00686581
$885$	0.808918	0.0271915
$886$	−35.3878	−1.18888
$887$	24.7297	0.830341	0.415170	−	0.909744i	$-0.363722\pi$
$887$	24.7297	0.830341	0.415170	+	0.909744i	$0.363722\pi$
$888$	36.4261	1.22238
$889$	−5.44597	−0.182652
$890$	−17.2812	−0.579267
$891$	2.86440	0.0959610
$892$	0.987512	0.0330643
$893$	27.8035	0.930408
$894$	75.9383	2.53976
$895$	−4.56473	−0.152582
$896$	9.94021	0.332079
$897$	−2.67906	−0.0894513
$898$	−37.3832	−1.24749
$899$	9.89441	0.329997
$900$	−0.479456	−0.0159819
$901$	−1.52259	−0.0507247
$902$	−0.617923	−0.0205746
$903$	−13.3989	−0.445888
$904$	26.7088	0.888321
$905$	0.959651	0.0318999
$906$	64.0799	2.12891
$907$	27.0249	0.897346	0.448673	−	0.893696i	$-0.351897\pi$
$907$	27.0249	0.897346	0.448673	+	0.893696i	$0.351897\pi$
$908$	3.51473	0.116641
$909$	25.6511	0.850793
$910$	1.45079	0.0480933
$911$	6.58215	0.218076	0.109038	−	0.994038i	$-0.465223\pi$
$911$	6.58215	0.218076	0.109038	+	0.994038i	$0.465223\pi$
$912$	−55.9213	−1.85174
$913$	−5.79104	−0.191656
$914$	4.15852	0.137552
$915$	−24.4289	−0.807595
$916$	2.19449	0.0725080
$917$	6.17404	0.203885
$918$	−1.50002	−0.0495080
$919$	−29.1085	−0.960202	−0.480101	−	0.877213i	$-0.659400\pi$
$919$	−29.1085	−0.960202	−0.480101	+	0.877213i	$0.659400\pi$
$920$	−2.92090	−0.0962991
$921$	0.461580	0.0152096
$922$	28.9315	0.952808
$923$	−0.0434435	−0.00142996
$924$	−0.131290	−0.00431913
$925$	4.95716	0.162991
$926$	−15.0706	−0.495250
$927$	4.75594	0.156206
$928$	−3.35812	−0.110236
$929$	−32.7443	−1.07430	−0.537152	−	0.843485i	$-0.680500\pi$
$929$	−32.7443	−1.07430	−0.537152	+	0.843485i	$0.680500\pi$
$930$	−8.21113	−0.269254
$931$	6.02209	0.197366
$932$	−1.87974	−0.0615731
$933$	−24.0516	−0.787414
$934$	−27.8542	−0.911417
$935$	−0.482237	−0.0157708
$936$	10.3546	0.338449
$937$	14.3647	0.469275	0.234637	−	0.972083i	$-0.424610\pi$
$937$	14.3647	0.469275	0.234637	+	0.972083i	$0.424610\pi$
$938$	−13.2069	−0.431221
$939$	83.2967	2.71829
$940$	−0.664975	−0.0216891
$941$	−36.0898	−1.17649	−0.588247	−	0.808681i	$-0.700182\pi$
$941$	−36.0898	−1.17649	−0.588247	+	0.808681i	$0.700182\pi$
$942$	23.6547	0.770710
$943$	1.25179	0.0407640
$944$	−1.18689	−0.0386298
$945$	−0.827308	−0.0269123
$946$	2.62911	0.0854797
$947$	59.6092	1.93704	0.968520	−	0.248936i	$-0.0800807\pi$
$947$	59.6092	1.93704	0.968520	+	0.248936i	$0.0800807\pi$
$948$	2.21071	0.0718004
$949$	−10.1012	−0.327899
$950$	−8.20414	−0.266177
$951$	17.1035	0.554619
$952$	−3.88741	−0.125992
$953$	44.8608	1.45318	0.726591	−	0.687070i	$-0.241103\pi$
$953$	44.8608	1.45318	0.726591	+	0.687070i	$0.241103\pi$
$954$	5.18821	0.167975
$955$	−13.8054	−0.446734
$956$	3.52284	0.113937
$957$	−3.76455	−0.121691
$958$	−5.49917	−0.177670
$959$	2.32742	0.0751563
$960$	21.3589	0.689354
$961$	−25.2600	−0.814840
$962$	−7.19182	−0.231874
$963$	21.6520	0.697725
$964$	1.98073	0.0637951
$965$	−0.748519	−0.0240957
$966$	−3.42727	−0.110271
$967$	−19.9939	−0.642961	−0.321480	−	0.946916i	$-0.604180\pi$
$967$	−19.9939	−0.642961	−0.321480	+	0.946916i	$0.604180\pi$
$968$	−31.7464	−1.02037
$969$	20.1630	0.647728
$970$	−8.76229	−0.281340
$971$	20.5934	0.660873	0.330437	−	0.943828i	$-0.392804\pi$
$971$	20.5934	0.660873	0.330437	+	0.943828i	$0.392804\pi$
$972$	3.22187	0.103342
$973$	−3.33677	−0.106972
$974$	7.35516	0.235675
$975$	2.67906	0.0857987
$976$	35.8434	1.14732
$977$	−42.8918	−1.37223	−0.686115	−	0.727493i	$-0.740685\pi$
$977$	−42.8918	−1.37223	−0.686115	+	0.727493i	$0.740685\pi$
$978$	−25.8246	−0.825779
$979$	−4.59626	−0.146897
$980$	−0.144030	−0.00460088
$981$	−40.9627	−1.30784
$982$	−55.0435	−1.75651
$983$	27.9954	0.892914	0.446457	−	0.894805i	$-0.352686\pi$
$983$	27.9954	0.892914	0.446457	+	0.894805i	$0.352686\pi$
$984$	−9.19839	−0.293234
$985$	−4.31921	−0.137621
$986$	−7.48798	−0.238466
$987$	−11.6149	−0.369706
$988$	−0.923679	−0.0293861
$989$	−5.32607	−0.169359
$990$	1.64322	0.0522250
$991$	7.26603	0.230813	0.115407	−	0.993318i	$-0.463183\pi$
$991$	7.26603	0.230813	0.115407	+	0.993318i	$0.463183\pi$
$992$	−1.94813	−0.0618530
$993$	44.3845	1.40850
$994$	−0.0555763	−0.00176277
$995$	1.73260	0.0549270
$996$	−5.79104	−0.183496
$997$	−50.7417	−1.60701	−0.803503	−	0.595300i	$-0.797033\pi$
$997$	−50.7417	−1.60701	−0.803503	+	0.595300i	$0.797033\pi$
$998$	−16.9880	−0.537746
$999$	4.10110	0.129753

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	805.2.a.j.1.1	✓	4
3.2	odd	2		7245.2.a.bc.1.4		4
5.4	even	2		4025.2.a.l.1.4		4
7.6	odd	2		5635.2.a.w.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
805.2.a.j.1.1	✓	4	1.1	even	1	trivial
4025.2.a.l.1.4		4	5.4	even	2
5635.2.a.w.1.1		4	7.6	odd	2
7245.2.a.bc.1.4		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 805 = 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	805.a (trivial)

\(f(q)\)	\(=\)	\(q-1.36234 q^{2} +2.51572 q^{3} -0.144030 q^{4} +1.00000 q^{5} -3.42727 q^{6} -1.00000 q^{7} +2.92090 q^{8} +3.32886 q^{9} +O(q^{10})\)	\(q-1.36234 q^{2} +2.51572 q^{3} -0.144030 q^{4} +1.00000 q^{5} -3.42727 q^{6} -1.00000 q^{7} +2.92090 q^{8} +3.32886 q^{9} -1.36234 q^{10} -0.362340 q^{11} -0.362340 q^{12} +1.06493 q^{13} +1.36234 q^{14} +2.51572 q^{15} -3.69119 q^{16} +1.33090 q^{17} -4.53503 q^{18} +6.02209 q^{19} -0.144030 q^{20} -2.51572 q^{21} +0.493630 q^{22} -1.00000 q^{23} +7.34817 q^{24} +1.00000 q^{25} -1.45079 q^{26} +0.827308 q^{27} +0.144030 q^{28} +4.12986 q^{29} -3.42727 q^{30} +2.39582 q^{31} -0.813134 q^{32} -0.911546 q^{33} -1.81313 q^{34} -1.00000 q^{35} -0.479456 q^{36} +4.95716 q^{37} -8.20414 q^{38} +2.67906 q^{39} +2.92090 q^{40} -1.25179 q^{41} +3.42727 q^{42} +5.32607 q^{43} +0.0521879 q^{44} +3.32886 q^{45} +1.36234 q^{46} +4.61692 q^{47} -9.28602 q^{48} +1.00000 q^{49} -1.36234 q^{50} +3.34817 q^{51} -0.153382 q^{52} -1.14403 q^{53} -1.12707 q^{54} -0.362340 q^{55} -2.92090 q^{56} +15.1499 q^{57} -5.62627 q^{58} +0.321545 q^{59} -0.362340 q^{60} -9.71051 q^{61} -3.26393 q^{62} -3.32886 q^{63} +8.49015 q^{64} +1.06493 q^{65} +1.24184 q^{66} -9.69429 q^{67} -0.191689 q^{68} -2.51572 q^{69} +1.36234 q^{70} -0.0407948 q^{71} +9.72325 q^{72} -9.48533 q^{73} -6.75334 q^{74} +2.51572 q^{75} -0.867363 q^{76} +0.362340 q^{77} -3.64979 q^{78} -6.10119 q^{79} -3.69119 q^{80} -7.90529 q^{81} +1.70537 q^{82} +15.9823 q^{83} +0.362340 q^{84} +1.33090 q^{85} -7.25592 q^{86} +10.3896 q^{87} -1.05836 q^{88} +12.6849 q^{89} -4.53503 q^{90} -1.06493 q^{91} +0.144030 q^{92} +6.02723 q^{93} -6.28981 q^{94} +6.02209 q^{95} -2.04562 q^{96} +6.43180 q^{97} -1.36234 q^{98} -1.20618 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 6 * q^9	\( 4 q + 3 q^{2} + 6 q^{3} + 3 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 7 q^{11} + 7 q^{12} - 5 q^{13} - 3 q^{14} + 6 q^{15} + q^{16} + 5 q^{17} + 2 q^{18} + 8 q^{19} + 3 q^{20} - 6 q^{21} + 14 q^{22} - 4 q^{23} + 6 q^{24} + 4 q^{25} - 11 q^{26} + 15 q^{27} - 3 q^{28} - 2 q^{29} + 4 q^{30} + 10 q^{33} - 4 q^{34} - 4 q^{35} + q^{36} + 13 q^{37} - 13 q^{38} - 13 q^{39} + 6 q^{40} + q^{41} - 4 q^{42} + 14 q^{43} + 15 q^{44} + 6 q^{45} - 3 q^{46} + 4 q^{47} - 23 q^{48} + 4 q^{49} + 3 q^{50} - 10 q^{51} - 5 q^{52} - q^{53} + 14 q^{54} + 7 q^{55} - 6 q^{56} + 19 q^{57} - 16 q^{58} - 7 q^{59} + 7 q^{60} - 7 q^{61} - 15 q^{62} - 6 q^{63} - 5 q^{65} + 23 q^{66} + 15 q^{67} - 11 q^{68} - 6 q^{69} - 3 q^{70} - 17 q^{72} + 3 q^{73} - 2 q^{74} + 6 q^{75} - 22 q^{76} - 7 q^{77} - 31 q^{78} - 14 q^{79} + q^{80} + 28 q^{81} + 6 q^{82} + 3 q^{83} - 7 q^{84} + 5 q^{85} + 16 q^{86} - 14 q^{87} + 13 q^{88} - 11 q^{89} + 2 q^{90} + 5 q^{91} - 3 q^{92} - 23 q^{93} - 19 q^{94} + 8 q^{95} - 15 q^{96} + 9 q^{97} + 3 q^{98} + 8 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 6 * q^3 + 3 * q^4 + 4 * q^5 + 4 * q^6 - 4 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 7 * q^11 + 7 * q^12 - 5 * q^13 - 3 * q^14 + 6 * q^15 + q^16 + 5 * q^17 + 2 * q^18 + 8 * q^19 + 3 * q^20 - 6 * q^21 + 14 * q^22 - 4 * q^23 + 6 * q^24 + 4 * q^25 - 11 * q^26 + 15 * q^27 - 3 * q^28 - 2 * q^29 + 4 * q^30 + 10 * q^33 - 4 * q^34 - 4 * q^35 + q^36 + 13 * q^37 - 13 * q^38 - 13 * q^39 + 6 * q^40 + q^41 - 4 * q^42 + 14 * q^43 + 15 * q^44 + 6 * q^45 - 3 * q^46 + 4 * q^47 - 23 * q^48 + 4 * q^49 + 3 * q^50 - 10 * q^51 - 5 * q^52 - q^53 + 14 * q^54 + 7 * q^55 - 6 * q^56 + 19 * q^57 - 16 * q^58 - 7 * q^59 + 7 * q^60 - 7 * q^61 - 15 * q^62 - 6 * q^63 - 5 * q^65 + 23 * q^66 + 15 * q^67 - 11 * q^68 - 6 * q^69 - 3 * q^70 - 17 * q^72 + 3 * q^73 - 2 * q^74 + 6 * q^75 - 22 * q^76 - 7 * q^77 - 31 * q^78 - 14 * q^79 + q^80 + 28 * q^81 + 6 * q^82 + 3 * q^83 - 7 * q^84 + 5 * q^85 + 16 * q^86 - 14 * q^87 + 13 * q^88 - 11 * q^89 + 2 * q^90 + 5 * q^91 - 3 * q^92 - 23 * q^93 - 19 * q^94 + 8 * q^95 - 15 * q^96 + 9 * q^97 + 3 * q^98 + 8 * q^99

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