LMFDB - Embedded newform 20.3.b.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [20,3,Mod(11,20)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(20, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("20.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 20 = 2^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	20.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$0.544960528721$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.4
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	20.11
Dual form			20.3.b.a.11.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.618034 + 1.90211i) q^{2} -2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} -2.23607 q^{5} +(4.47214 - 1.45309i) q^{6} -5.25731i q^{7} +(-6.47214 - 4.70228i) q^{8} +3.47214 q^{9} +O(q^{10})$	\(q+(0.618034 + 1.90211i) q^{2} -2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} -2.23607 q^{5} +(4.47214 - 1.45309i) q^{6} -5.25731i q^{7} +(-6.47214 - 4.70228i) q^{8} +3.47214 q^{9} +(-1.38197 - 4.25325i) q^{10} +19.9192i q^{11} +(5.52786 + 7.60845i) q^{12} -8.47214 q^{13} +(10.0000 - 3.24920i) q^{14} +5.25731i q^{15} +(4.94427 - 15.2169i) q^{16} +11.8885 q^{17} +(2.14590 + 6.60440i) q^{18} -15.2169i q^{19} +(7.23607 - 5.25731i) q^{20} -12.3607 q^{21} +(-37.8885 + 12.3107i) q^{22} -0.555029i q^{23} +(-11.0557 + 15.2169i) q^{24} +5.00000 q^{25} +(-5.23607 - 16.1150i) q^{26} -29.3238i q^{27} +(12.3607 + 17.0130i) q^{28} -10.9443 q^{29} +(-10.0000 + 3.24920i) q^{30} -8.29451i q^{31} +32.0000 q^{32} +46.8328 q^{33} +(7.34752 + 22.6134i) q^{34} +11.7557i q^{35} +(-11.2361 + 8.16348i) q^{36} -18.3607 q^{37} +(28.9443 - 9.40456i) q^{38} +19.9192i q^{39} +(14.4721 + 10.5146i) q^{40} -14.5836 q^{41} +(-7.63932 - 23.5114i) q^{42} +22.2703i q^{43} +(-46.8328 - 64.4598i) q^{44} -7.76393 q^{45} +(1.05573 - 0.343027i) q^{46} +53.3902i q^{47} +(-35.7771 - 11.6247i) q^{48} +21.3607 q^{49} +(3.09017 + 9.51057i) q^{50} -27.9516i q^{51} +(27.4164 - 19.9192i) q^{52} -66.3607 q^{53} +(55.7771 - 18.1231i) q^{54} -44.5407i q^{55} +(-24.7214 + 34.0260i) q^{56} -35.7771 q^{57} +(-6.76393 - 20.8172i) q^{58} +17.4370i q^{59} +(-12.3607 - 17.0130i) q^{60} +90.1378 q^{61} +(15.7771 - 5.12629i) q^{62} -18.2541i q^{63} +(19.7771 + 60.8676i) q^{64} +18.9443 q^{65} +(28.9443 + 89.0813i) q^{66} +50.2220i q^{67} +(-38.4721 + 27.9516i) q^{68} -1.30495 q^{69} +(-22.3607 + 7.26543i) q^{70} -80.7868i q^{71} +(-22.4721 - 16.3270i) q^{72} -5.55418 q^{73} +(-11.3475 - 34.9241i) q^{74} -11.7557i q^{75} +(35.7771 + 49.2429i) q^{76} +104.721 q^{77} +(-37.8885 + 12.3107i) q^{78} -13.8448i q^{79} +(-11.0557 + 34.0260i) q^{80} -37.6950 q^{81} +(-9.01316 - 27.7396i) q^{82} -76.2155i q^{83} +(40.0000 - 29.0617i) q^{84} -26.5836 q^{85} +(-42.3607 + 13.7638i) q^{86} +25.7315i q^{87} +(93.6656 - 128.920i) q^{88} -111.443 q^{89} +(-4.79837 - 14.7679i) q^{90} +44.5407i q^{91} +(1.30495 + 1.79611i) q^{92} -19.5016 q^{93} +(-101.554 + 32.9970i) q^{94} +34.0260i q^{95} -75.2365i q^{96} -92.8328 q^{97} +(13.2016 + 40.6304i) q^{98} +69.1621i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^4 - 8 * q^8 - 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{9} - 10 q^{10} + 40 q^{12} - 16 q^{13} + 40 q^{14} - 16 q^{16} - 24 q^{17} + 22 q^{18} + 20 q^{20} + 40 q^{21} - 80 q^{22} - 80 q^{24} + 20 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} - 40 q^{30} + 128 q^{32} + 80 q^{33} + 92 q^{34} - 36 q^{36} + 16 q^{37} + 80 q^{38} + 40 q^{40} - 112 q^{41} - 120 q^{42} - 80 q^{44} - 40 q^{45} + 40 q^{46} - 4 q^{49} - 10 q^{50} + 56 q^{52} - 176 q^{53} + 80 q^{54} + 80 q^{56} - 36 q^{58} + 40 q^{60} + 128 q^{61} - 80 q^{62} - 64 q^{64} + 40 q^{65} + 80 q^{66} - 136 q^{68} + 120 q^{69} - 72 q^{72} + 264 q^{73} - 108 q^{74} + 240 q^{77} - 80 q^{78} - 80 q^{80} - 276 q^{81} + 116 q^{82} + 160 q^{84} - 160 q^{85} - 80 q^{86} + 160 q^{88} - 88 q^{89} + 30 q^{90} - 120 q^{92} - 400 q^{93} - 120 q^{94} - 264 q^{97} + 102 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^4 - 8 * q^8 - 4 * q^9 - 10 * q^10 + 40 * q^12 - 16 * q^13 + 40 * q^14 - 16 * q^16 - 24 * q^17 + 22 * q^18 + 20 * q^20 + 40 * q^21 - 80 * q^22 - 80 * q^24 + 20 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 - 40 * q^30 + 128 * q^32 + 80 * q^33 + 92 * q^34 - 36 * q^36 + 16 * q^37 + 80 * q^38 + 40 * q^40 - 112 * q^41 - 120 * q^42 - 80 * q^44 - 40 * q^45 + 40 * q^46 - 4 * q^49 - 10 * q^50 + 56 * q^52 - 176 * q^53 + 80 * q^54 + 80 * q^56 - 36 * q^58 + 40 * q^60 + 128 * q^61 - 80 * q^62 - 64 * q^64 + 40 * q^65 + 80 * q^66 - 136 * q^68 + 120 * q^69 - 72 * q^72 + 264 * q^73 - 108 * q^74 + 240 * q^77 - 80 * q^78 - 80 * q^80 - 276 * q^81 + 116 * q^82 + 160 * q^84 - 160 * q^85 - 80 * q^86 + 160 * q^88 - 88 * q^89 + 30 * q^90 - 120 * q^92 - 400 * q^93 - 120 * q^94 - 264 * q^97 + 102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/20\mathbb{Z}\right)^\times$.

$n$	$11$	$17$
$\chi(n)$	$-1$	$1$

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 $

$2$	0.618034	+	1.90211i	0.309017	+	0.951057i
$2$	0.618034	+	1.90211i	0.309017	+	0.951057i
$3$		−	2.35114i		−	0.783714i	−0.920026	−	0.391857i	$-0.871833\pi$
$3$		−	2.35114i		−	0.783714i	0.920026	−	0.391857i	$-0.128167\pi$
$4$	−3.23607	+	2.35114i	−0.809017	+	0.587785i
$5$	−2.23607			−0.447214
$5$	−2.23607			−0.447214
$6$	4.47214	−	1.45309i	0.745356	−	0.242181i
$7$		−	5.25731i		−	0.751044i	−0.926813	−	0.375522i	$-0.877463\pi$
$7$		−	5.25731i		−	0.751044i	0.926813	−	0.375522i	$-0.122537\pi$
$8$	−6.47214	−	4.70228i	−0.809017	−	0.587785i
$9$	3.47214			0.385793
$10$	−1.38197	−	4.25325i	−0.138197	−	0.425325i
$11$			19.9192i			1.81084i	0.424522	+	0.905418i	$0.360442\pi$
$11$			19.9192i			1.81084i	−0.424522	+	0.905418i	$0.639558\pi$
$12$	5.52786	+	7.60845i	0.460655	+	0.634038i
$13$	−8.47214			−0.651703			−0.325851	−	0.945421i	$-0.605651\pi$
$13$	−8.47214			−0.651703			−0.325851	+	0.945421i	$0.605651\pi$
$14$	10.0000	−	3.24920i	0.714286	−	0.232085i
$15$			5.25731i			0.350487i
$16$	4.94427	−	15.2169i	0.309017	−	0.951057i
$17$	11.8885			0.699326			0.349663	−	0.936876i	$-0.386296\pi$
$17$	11.8885			0.699326			0.349663	+	0.936876i	$0.386296\pi$
$18$	2.14590	+	6.60440i	0.119217	+	0.366911i
$19$		−	15.2169i		−	0.800890i	−0.916321	−	0.400445i	$-0.868856\pi$
$19$		−	15.2169i		−	0.800890i	0.916321	−	0.400445i	$-0.131144\pi$
$20$	7.23607	−	5.25731i	0.361803	−	0.262866i
$21$	−12.3607			−0.588604
$22$	−37.8885	+	12.3107i	−1.72221	+	0.559579i
$23$		−	0.555029i		−	0.0241317i	−0.999927	−	0.0120659i	$-0.996159\pi$
$23$		−	0.555029i		−	0.0241317i	0.999927	−	0.0120659i	$-0.00384077\pi$
$24$	−11.0557	+	15.2169i	−0.460655	+	0.634038i
$25$	5.00000			0.200000
$26$	−5.23607	−	16.1150i	−0.201387	−	0.619806i
$27$		−	29.3238i		−	1.08606i
$28$	12.3607	+	17.0130i	0.441453	+	0.607608i
$29$	−10.9443			−0.377389			−0.188694	−	0.982036i	$-0.560426\pi$
$29$	−10.9443			−0.377389			−0.188694	+	0.982036i	$0.560426\pi$
$30$	−10.0000	+	3.24920i	−0.333333	+	0.108307i
$31$		−	8.29451i		−	0.267565i	−0.991011	−	0.133782i	$-0.957288\pi$
$31$		−	8.29451i		−	0.267565i	0.991011	−	0.133782i	$-0.0427123\pi$
$32$	32.0000			1.00000
$33$	46.8328			1.41918
$34$	7.34752	+	22.6134i	0.216104	+	0.665099i
$35$			11.7557i			0.335877i
$36$	−11.2361	+	8.16348i	−0.312113	+	0.226763i
$37$	−18.3607			−0.496235			−0.248117	−	0.968730i	$-0.579812\pi$
$37$	−18.3607			−0.496235			−0.248117	+	0.968730i	$0.579812\pi$
$38$	28.9443	−	9.40456i	0.761691	−	0.247489i
$39$			19.9192i			0.510748i
$40$	14.4721	+	10.5146i	0.361803	+	0.262866i
$41$	−14.5836			−0.355697			−0.177849	−	0.984058i	$-0.556914\pi$
$41$	−14.5836			−0.355697			−0.177849	+	0.984058i	$0.556914\pi$
$42$	−7.63932	−	23.5114i	−0.181889	−	0.559795i
$43$			22.2703i			0.517915i	0.965889	+	0.258957i	$0.0833789\pi$
$43$			22.2703i			0.517915i	−0.965889	+	0.258957i	$0.916621\pi$
$44$	−46.8328	−	64.4598i	−1.06438	−	1.46500i
$45$	−7.76393			−0.172532
$46$	1.05573	−	0.343027i	0.0229506	−	0.00745711i
$47$			53.3902i			1.13596i	0.823042	+	0.567981i	$0.192275\pi$
$47$			53.3902i			1.13596i	−0.823042	+	0.567981i	$0.807725\pi$
$48$	−35.7771	−	11.6247i	−0.745356	−	0.242181i
$49$	21.3607			0.435932
$50$	3.09017	+	9.51057i	0.0618034	+	0.190211i
$51$		−	27.9516i		−	0.548071i
$52$	27.4164	−	19.9192i	0.527239	−	0.383061i
$53$	−66.3607			−1.25209			−0.626044	−	0.779788i	$-0.715327\pi$
$53$	−66.3607			−1.25209			−0.626044	+	0.779788i	$0.715327\pi$
$54$	55.7771	−	18.1231i	1.03291	−	0.335612i
$55$		−	44.5407i		−	0.809830i
$56$	−24.7214	+	34.0260i	−0.441453	+	0.607608i
$57$	−35.7771			−0.627668
$58$	−6.76393	−	20.8172i	−0.116620	−	0.358918i
$59$			17.4370i			0.295543i	0.989022	+	0.147771i	$0.0472100\pi$
$59$			17.4370i			0.295543i	−0.989022	+	0.147771i	$0.952790\pi$
$60$	−12.3607	−	17.0130i	−0.206011	−	0.283550i
$61$	90.1378			1.47767			0.738834	−	0.673887i	$-0.235377\pi$
$61$	90.1378			1.47767			0.738834	+	0.673887i	$0.235377\pi$
$62$	15.7771	−	5.12629i	0.254469	−	0.0826820i
$63$		−	18.2541i		−	0.289748i
$64$	19.7771	+	60.8676i	0.309017	+	0.951057i
$65$	18.9443			0.291450
$66$	28.9443	+	89.0813i	0.438550	+	1.34972i
$67$			50.2220i			0.749582i	0.927109	+	0.374791i	$0.122285\pi$
$67$			50.2220i			0.749582i	−0.927109	+	0.374791i	$0.877715\pi$
$68$	−38.4721	+	27.9516i	−0.565767	+	0.411054i
$69$	−1.30495			−0.0189123
$70$	−22.3607	+	7.26543i	−0.319438	+	0.103792i
$71$		−	80.7868i		−	1.13784i	−0.822392	−	0.568921i	$-0.807361\pi$
$71$		−	80.7868i		−	1.13784i	0.822392	−	0.568921i	$-0.192639\pi$
$72$	−22.4721	−	16.3270i	−0.312113	−	0.226763i
$73$	−5.55418			−0.0760846			−0.0380423	−	0.999276i	$-0.512112\pi$
$73$	−5.55418			−0.0760846			−0.0380423	+	0.999276i	$0.512112\pi$
$74$	−11.3475	−	34.9241i	−0.153345	−	0.471947i
$75$		−	11.7557i		−	0.156743i
$76$	35.7771	+	49.2429i	0.470751	+	0.647933i
$77$	104.721			1.36002
$78$	−37.8885	+	12.3107i	−0.485751	+	0.157830i
$79$		−	13.8448i		−	0.175251i	−0.996154	−	0.0876253i	$-0.972072\pi$
$79$		−	13.8448i		−	0.175251i	0.996154	−	0.0876253i	$-0.0279278\pi$
$80$	−11.0557	+	34.0260i	−0.138197	+	0.425325i
$81$	−37.6950			−0.465371
$82$	−9.01316	−	27.7396i	−0.109917	−	0.338288i
$83$		−	76.2155i		−	0.918260i	−0.888369	−	0.459130i	$-0.848161\pi$
$83$		−	76.2155i		−	0.918260i	0.888369	−	0.459130i	$-0.151839\pi$
$84$	40.0000	−	29.0617i	0.476190	−	0.345973i
$85$	−26.5836			−0.312748
$86$	−42.3607	+	13.7638i	−0.492566	+	0.160044i
$87$			25.7315i			0.295765i
$88$	93.6656	−	128.920i	1.06438	−	1.46500i
$89$	−111.443			−1.25217			−0.626083	−	0.779757i	$-0.715343\pi$
$89$	−111.443			−1.25217			−0.626083	+	0.779757i	$0.715343\pi$
$90$	−4.79837	−	14.7679i	−0.0533153	−	0.164088i
$91$			44.5407i			0.489458i
$92$	1.30495	+	1.79611i	0.0141843	+	0.0195230i
$93$	−19.5016			−0.209694
$94$	−101.554	+	32.9970i	−1.08036	+	0.351031i
$95$			34.0260i			0.358169i
$96$		−	75.2365i		−	0.783714i
$97$	−92.8328			−0.957039			−0.478520	−	0.878077i	$-0.658826\pi$
$97$	−92.8328			−0.957039			−0.478520	+	0.878077i	$0.658826\pi$
$98$	13.2016	+	40.6304i	0.134710	+	0.414596i
$99$			69.1621i			0.698607i
$100$	−16.1803	+	11.7557i	−0.161803	+	0.117557i
$101$	64.1115			0.634767			0.317383	−	0.948297i	$-0.397196\pi$
$101$	64.1115			0.634767			0.317383	+	0.948297i	$0.397196\pi$
$102$	53.1672	−	17.2751i	0.521247	−	0.169363i
$103$			137.769i			1.33757i	0.743458	+	0.668783i	$0.233184\pi$
$103$			137.769i			1.33757i	−0.743458	+	0.668783i	$0.766816\pi$
$104$	54.8328	+	39.8384i	0.527239	+	0.383061i
$105$	27.6393			0.263232
$106$	−41.0132	−	126.226i	−0.386917	−	1.19081i
$107$		−	51.3320i		−	0.479739i	−0.970805	−	0.239869i	$-0.922895\pi$
$107$		−	51.3320i		−	0.479739i	0.970805	−	0.239869i	$-0.0771046\pi$
$108$	68.9443	+	94.8936i	0.638373	+	0.878645i
$109$	133.469			1.22449			0.612243	−	0.790669i	$-0.290267\pi$
$109$	133.469			1.22449			0.612243	+	0.790669i	$0.290267\pi$
$110$	84.7214	−	27.5276i	0.770194	−	0.250251i
$111$			43.1685i			0.388906i
$112$	−80.0000	−	25.9936i	−0.714286	−	0.232085i
$113$	170.721			1.51081			0.755404	−	0.655259i	$-0.227441\pi$
$113$	170.721			1.51081			0.755404	+	0.655259i	$0.227441\pi$
$114$	−22.1115	−	68.0521i	−0.193960	−	0.596948i
$115$			1.24108i			0.0107920i
$116$	35.4164	−	25.7315i	0.305314	−	0.221824i
$117$	−29.4164			−0.251422
$118$	−33.1672	+	10.7767i	−0.281078	+	0.0913277i
$119$		−	62.5018i		−	0.525225i
$120$	24.7214	−	34.0260i	0.206011	−	0.283550i
$121$	−275.774			−2.27912
$122$	55.7082	+	171.452i	0.456625	+	1.40535i
$123$			34.2881i			0.278765i
$124$	19.5016	+	26.8416i	0.157271	+	0.216464i
$125$	−11.1803			−0.0894427
$126$	34.7214	−	11.2817i	0.275566	−	0.0895369i
$127$		−	198.637i		−	1.56407i	−0.623235	−	0.782035i	$-0.714182\pi$
$127$		−	198.637i		−	1.56407i	0.623235	−	0.782035i	$-0.285818\pi$
$128$	−103.554	+	75.2365i	−0.809017	+	0.587785i
$129$	52.3607			0.405897
$130$	11.7082	+	36.0341i	0.0900631	+	0.277186i
$131$			7.77041i			0.0593161i	0.999560	+	0.0296580i	$0.00944183\pi$
$131$			7.77041i			0.0593161i	−0.999560	+	0.0296580i	$0.990558\pi$
$132$	−151.554	+	110.111i	−1.14814	+	0.834171i
$133$	−80.0000			−0.601504
$134$	−95.5279	+	31.0389i	−0.712895	+	0.231633i
$135$			65.5699i			0.485703i
$136$	−76.9443	−	55.9033i	−0.565767	−	0.411054i
$137$	0.832816			0.00607895			0.00303947	−	0.999995i	$-0.499033\pi$
$137$	0.832816			0.00607895			0.00303947	+	0.999995i	$0.499033\pi$
$138$	−0.806504	−	2.48217i	−0.00584424	−	0.0179867i
$139$		−	237.658i		−	1.70977i	−0.518817	−	0.854885i	$-0.673627\pi$
$139$		−	237.658i		−	1.70977i	0.518817	−	0.854885i	$-0.326373\pi$
$140$	−27.6393	−	38.0423i	−0.197424	−	0.271730i
$141$	125.528			0.890269
$142$	153.666	−	49.9290i	1.08215	−	0.351613i
$143$		−	168.758i		−	1.18013i
$144$	17.1672	−	52.8352i	0.119217	−	0.366911i
$145$	24.4721			0.168773
$146$	−3.43267	−	10.5647i	−0.0235114	−	0.0723607i
$147$		−	50.2220i		−	0.341646i
$148$	59.4164	−	43.1685i	0.401462	−	0.291679i
$149$	−36.9706			−0.248125			−0.124062	−	0.992274i	$-0.539592\pi$
$149$	−36.9706			−0.248125			−0.124062	+	0.992274i	$0.539592\pi$
$150$	22.3607	−	7.26543i	0.149071	−	0.0484362i
$151$			282.723i			1.87234i	0.351552	+	0.936168i	$0.385654\pi$
$151$			282.723i			1.87234i	−0.351552	+	0.936168i	$0.614346\pi$
$152$	−71.5542	+	98.4859i	−0.470751	+	0.647933i
$153$	41.2786			0.269795
$154$	64.7214	+	199.192i	0.420269	+	1.29345i
$155$			18.5471i			0.119659i
$156$	−46.8328	−	64.4598i	−0.300210	−	0.413204i
$157$	204.748			1.30413			0.652063	−	0.758165i	$-0.273904\pi$
$157$	204.748			1.30413			0.652063	+	0.758165i	$0.273904\pi$
$158$	26.3344	−	8.55656i	0.166673	−	0.0541554i
$159$			156.023i			0.981279i
$160$	−71.5542			−0.447214
$161$	−2.91796			−0.0181240
$162$	−23.2968	−	71.7002i	−0.143808	−	0.442594i
$163$			107.235i			0.657885i	0.944350	+	0.328943i	$0.106692\pi$
$163$			107.235i			0.657885i	−0.944350	+	0.328943i	$0.893308\pi$
$164$	47.1935	−	34.2881i	0.287765	−	0.209074i
$165$	−104.721			−0.634675
$166$	144.971	−	47.1038i	0.873317	−	0.283758i
$167$			33.2090i			0.198856i	0.995045	+	0.0994280i	$0.0317013\pi$
$167$			33.2090i			0.198856i	−0.995045	+	0.0994280i	$0.968299\pi$
$168$	80.0000	+	58.1234i	0.476190	+	0.345973i
$169$	−97.2229			−0.575284
$170$	−16.4296	−	50.5650i	−0.0966445	−	0.297441i
$171$		−	52.8352i		−	0.308978i
$172$	−52.3607	−	72.0683i	−0.304423	−	0.419002i
$173$	−226.361			−1.30844			−0.654222	−	0.756303i	$-0.727004\pi$
$173$	−226.361			−1.30844			−0.654222	+	0.756303i	$0.727004\pi$
$174$	−48.9443	+	15.9030i	−0.281289	+	0.0913963i
$175$		−	26.2866i		−	0.150209i
$176$	303.108	+	98.4859i	1.72221	+	0.559579i
$177$	40.9969			0.231621
$178$	−68.8754	−	211.977i	−0.386940	−	1.19088i
$179$			224.337i			1.25328i	0.779308	+	0.626641i	$0.215571\pi$
$179$			224.337i			1.25328i	−0.779308	+	0.626641i	$0.784429\pi$
$180$	25.1246	−	18.2541i	0.139581	−	0.101412i
$181$	86.2229			0.476370			0.238185	−	0.971220i	$-0.423448\pi$
$181$	86.2229			0.476370			0.238185	+	0.971220i	$0.423448\pi$
$182$	−84.7214	+	27.5276i	−0.465502	+	0.151251i
$183$		−	211.927i		−	1.15807i
$184$	−2.60990	+	3.59222i	−0.0141843	+	0.0195230i
$185$	41.0557			0.221923
$186$	−12.0526	−	37.0942i	−0.0647990	−	0.199431i
$187$			236.810i			1.26636i
$188$	−125.528	−	172.774i	−0.667701	−	0.919012i
$189$	−154.164			−0.815683
$190$	−64.7214	+	21.0292i	−0.340639	+	0.110680i
$191$		−	31.0198i		−	0.162407i	−0.996698	−	0.0812036i	$-0.974124\pi$
$191$		−	31.0198i		−	0.162407i	0.996698	−	0.0812036i	$-0.0258764\pi$
$192$	143.108	−	46.4987i	0.745356	−	0.242181i
$193$	110.223			0.571103			0.285552	−	0.958363i	$-0.407823\pi$
$193$	110.223			0.571103			0.285552	+	0.958363i	$0.407823\pi$
$194$	−57.3738	−	176.579i	−0.295741	−	0.910198i
$195$		−	44.5407i		−	0.228414i
$196$	−69.1246	+	50.2220i	−0.352677	+	0.256235i
$197$	−172.525			−0.875760			−0.437880	−	0.899033i	$-0.644271\pi$
$197$	−172.525			−0.875760			−0.437880	+	0.899033i	$0.644271\pi$
$198$	−131.554	+	42.7445i	−0.664415	+	0.215882i
$199$		−	272.208i		−	1.36788i	−0.729538	−	0.683940i	$-0.760265\pi$
$199$		−	272.208i		−	1.36788i	0.729538	−	0.683940i	$-0.239735\pi$
$200$	−32.3607	−	23.5114i	−0.161803	−	0.117557i
$201$	118.079			0.587457
$202$	39.6231	+	121.947i	0.196154	+	0.603699i
$203$			57.5374i			0.283436i
$204$	65.7183	+	90.4534i	0.322148	+	0.443399i
$205$	32.6099			0.159073
$206$	−262.053	+	85.1461i	−1.27210	+	0.413330i
$207$		−	1.92714i		−	0.00930984i
$208$	−41.8885	+	128.920i	−0.201387	+	0.619806i
$209$	303.108			1.45028
$210$	17.0820	+	52.5731i	0.0813430	+	0.250348i
$211$		−	205.266i		−	0.972826i	−0.873729	−	0.486413i	$-0.838305\pi$
$211$		−	205.266i		−	0.972826i	0.873729	−	0.486413i	$-0.161695\pi$
$212$	214.748	−	156.023i	1.01296	−	0.735959i
$213$	−189.941			−0.891743
$214$	97.6393	−	31.7249i	0.456259	−	0.148247i
$215$		−	49.7980i		−	0.231618i
$216$	−137.889	+	189.787i	−0.638373	+	0.878645i
$217$	−43.6068			−0.200953
$218$	82.4884	+	253.873i	0.378387	+	1.16456i
$219$			13.0586i			0.0596285i
$220$	104.721	+	144.137i	0.476006	+	0.655166i
$221$	−100.721			−0.455753
$222$	−82.1115	+	26.6796i	−0.369871	+	0.120179i
$223$			235.731i			1.05709i	0.848905	+	0.528545i	$0.177262\pi$
$223$			235.731i			1.05709i	−0.848905	+	0.528545i	$0.822738\pi$
$224$		−	168.234i		−	0.751044i
$225$	17.3607			0.0771586
$226$	105.512	+	324.731i	0.466865	+	1.43686i
$227$		−	58.5165i		−	0.257782i	−0.991659	−	0.128891i	$-0.958858\pi$
$227$		−	58.5165i		−	0.257782i	0.991659	−	0.128891i	$-0.0411417\pi$
$228$	115.777	−	84.1170i	0.507794	−	0.368934i
$229$	162.721			0.710574			0.355287	−	0.934757i	$-0.384383\pi$
$229$	162.721			0.710574			0.355287	+	0.934757i	$0.384383\pi$
$230$	−2.36068	+	0.767031i	−0.0102638	+	0.00333492i
$231$		−	246.215i		−	1.06586i
$232$	70.8328	+	51.4631i	0.305314	+	0.221824i
$233$	319.050			1.36931			0.684656	−	0.728867i	$-0.259953\pi$
$233$	319.050			1.36931			0.684656	+	0.728867i	$0.259953\pi$
$234$	−18.1803	−	55.9533i	−0.0776938	−	0.239117i
$235$		−	119.384i		−	0.508017i
$236$	−40.9969	−	56.4274i	−0.173716	−	0.239099i
$237$	−32.5511			−0.137346
$238$	118.885	−	38.6282i	0.499519	−	0.162303i
$239$			236.810i			0.990837i	0.868654	+	0.495419i	$0.164985\pi$
$239$			236.810i			0.990837i	−0.868654	+	0.495419i	$0.835015\pi$
$240$	80.0000	+	25.9936i	0.333333	+	0.108307i
$241$	−0.917961			−0.00380897			−0.00190448	−	0.999998i	$-0.500606\pi$
$241$	−0.917961			−0.00380897			−0.00190448	+	0.999998i	$0.500606\pi$
$242$	−170.438	−	524.553i	−0.704288	−	2.16758i
$243$		−	175.287i		−	0.721347i
$244$	−291.692	+	211.927i	−1.19546	+	0.868552i
$245$	−47.7639			−0.194955
$246$	−65.2198	+	21.1912i	−0.265121	+	0.0861431i
$247$			128.920i			0.521942i
$248$	−39.0031	+	53.6832i	−0.157271	+	0.216464i
$249$	−179.193			−0.719653
$250$	−6.90983	−	21.2663i	−0.0276393	−	0.0850651i
$251$		−	136.690i		−	0.544582i	−0.962215	−	0.272291i	$-0.912219\pi$
$251$		−	136.690i		−	0.544582i	0.962215	−	0.272291i	$-0.0877813\pi$
$252$	42.9180	+	59.0715i	0.170309	+	0.234411i
$253$	11.0557			0.0436985
$254$	377.830	−	122.764i	1.48752	−	0.483324i
$255$			62.5018i			0.245105i
$256$	−207.108	−	150.473i	−0.809017	−	0.587785i
$257$	−274.944			−1.06982			−0.534911	−	0.844908i	$-0.679655\pi$
$257$	−274.944			−1.06982			−0.534911	+	0.844908i	$0.679655\pi$
$258$	32.3607	+	99.5959i	0.125429	+	0.386031i
$259$			96.5278i			0.372694i
$260$	−61.3050	+	44.5407i	−0.235788	+	0.171310i
$261$	−38.0000			−0.145594
$262$	−14.7802	+	4.80238i	−0.0564130	+	0.0183297i
$263$			406.385i			1.54519i	0.634899	+	0.772596i	$0.281042\pi$
$263$			406.385i			1.54519i	−0.634899	+	0.772596i	$0.718958\pi$
$264$	−303.108	−	220.221i	−1.14814	−	0.834171i
$265$	148.387			0.559951
$266$	−49.4427	−	152.169i	−0.185875	−	0.572064i
$267$			262.018i			0.981339i
$268$	−118.079	−	162.522i	−0.440593	−	0.606424i
$269$	−348.525			−1.29563			−0.647816	−	0.761797i	$-0.724317\pi$
$269$	−348.525			−1.29563			−0.647816	+	0.761797i	$0.724317\pi$
$270$	−124.721	+	40.5244i	−0.461931	+	0.150090i
$271$		−	247.849i		−	0.914571i	−0.889320	−	0.457286i	$-0.848822\pi$
$271$		−	247.849i		−	0.914571i	0.889320	−	0.457286i	$-0.151178\pi$
$272$	58.7802	−	180.907i	0.216104	−	0.665099i
$273$	104.721			0.383595
$274$	0.514708	+	1.58411i	0.00187850	+	0.00578142i
$275$			99.5959i			0.362167i
$276$	4.22291	−	3.06813i	0.0153004	−	0.0111164i
$277$	−54.7539			−0.197667			−0.0988337	−	0.995104i	$-0.531511\pi$
$277$	−54.7539			−0.197667			−0.0988337	+	0.995104i	$0.531511\pi$
$278$	452.053	−	146.881i	1.62609	−	0.528348i
$279$		−	28.7997i		−	0.103225i
$280$	55.2786	−	76.0845i	0.197424	−	0.271730i
$281$	−50.3607			−0.179220			−0.0896098	−	0.995977i	$-0.528562\pi$
$281$	−50.3607			−0.179220			−0.0896098	+	0.995977i	$0.528562\pi$
$282$	77.5805	+	238.768i	0.275108	+	0.846696i
$283$		−	147.336i		−	0.520621i	−0.965525	−	0.260310i	$-0.916175\pi$
$283$		−	147.336i		−	0.520621i	0.965525	−	0.260310i	$-0.0838249\pi$
$284$	189.941	+	261.432i	0.668807	+	0.920534i
$285$	80.0000			0.280702
$286$	320.997	−	104.298i	1.12237	−	0.364679i
$287$			76.6705i			0.267145i
$288$	111.108			0.385793
$289$	−147.663			−0.510943
$290$	15.1246	+	46.5488i	0.0521538	+	0.160513i
$291$			218.263i			0.750045i
$292$	17.9737	−	13.0586i	0.0615537	−	0.0447214i
$293$	178.859			0.610441			0.305220	−	0.952282i	$-0.401270\pi$
$293$	178.859			0.610441			0.305220	+	0.952282i	$0.401270\pi$
$294$	95.5279	−	31.0389i	0.324925	−	0.105574i
$295$		−	38.9904i		−	0.132171i
$296$	118.833	+	86.3371i	0.401462	+	0.291679i
$297$	584.105			1.96668
$298$	−22.8491	−	70.3222i	−0.0766748	−	0.235981i
$299$			4.70228i			0.0157267i
$300$	27.6393	+	38.0423i	0.0921311	+	0.126808i
$301$	117.082			0.388977
$302$	−537.771	+	174.732i	−1.78070	+	0.578584i
$303$		−	150.735i		−	0.497475i
$304$	−231.554	−	75.2365i	−0.761691	−	0.247489i
$305$	−201.554			−0.660833
$306$	25.5116	+	78.5166i	0.0833713	+	0.256590i
$307$		−	284.550i		−	0.926873i	−0.886130	−	0.463436i	$-0.846616\pi$
$307$		−	284.550i		−	0.926873i	0.886130	−	0.463436i	$-0.153384\pi$
$308$	−338.885	+	246.215i	−1.10028	+	0.799398i
$309$	323.915			1.04827
$310$	−35.2786	+	11.4627i	−0.113802	+	0.0369765i
$311$			282.199i			0.907392i	0.891157	+	0.453696i	$0.149895\pi$
$311$			282.199i			0.907392i	−0.891157	+	0.453696i	$0.850105\pi$
$312$	93.6656	−	128.920i	0.300210	−	0.413204i
$313$	−567.548			−1.81325			−0.906626	−	0.421935i	$-0.861351\pi$
$313$	−567.548			−1.81325			−0.906626	+	0.421935i	$0.861351\pi$
$314$	126.541	+	389.453i	0.402997	+	1.24030i
$315$			40.8174i			0.129579i
$316$	32.5511	+	44.8027i	0.103010	+	0.141781i
$317$	161.141			0.508331			0.254165	−	0.967161i	$-0.418199\pi$
$317$	161.141			0.508331			0.254165	+	0.967161i	$0.418199\pi$
$318$	−296.774	+	96.4277i	−0.933252	+	0.303232i
$319$		−	218.001i		−	0.683389i
$320$	−44.2229	−	136.104i	−0.138197	−	0.425325i
$321$	−120.689			−0.375978
$322$	−1.80340	−	5.55029i	−0.00560062	−	0.0172369i
$323$		−	180.907i		−	0.560083i
$324$	121.984	−	88.6264i	0.376493	−	0.273538i
$325$	−42.3607			−0.130341
$326$	−203.974	+	66.2751i	−0.625686	+	0.203298i
$327$		−	313.805i		−	0.959647i
$328$	94.3870	+	68.5762i	0.287765	+	0.209074i
$329$	280.689			0.853158
$330$	−64.7214	−	199.192i	−0.196125	−	0.603612i
$331$			331.966i			1.00292i	0.865181	+	0.501459i	$0.167203\pi$
$331$			331.966i			1.00292i	−0.865181	+	0.501459i	$0.832797\pi$
$332$	179.193	+	246.639i	0.539739	+	0.742888i
$333$	−63.7508			−0.191444
$334$	−63.1672	+	20.5243i	−0.189123	+	0.0614499i
$335$		−	112.300i		−	0.335223i
$336$	−61.1146	+	188.091i	−0.181889	+	0.559795i
$337$	−269.108			−0.798541			−0.399271	−	0.916833i	$-0.630737\pi$
$337$	−269.108			−0.798541			−0.399271	+	0.916833i	$0.630737\pi$
$338$	−60.0871	−	184.929i	−0.177772	−	0.547127i
$339$		−	401.390i		−	1.18404i
$340$	86.0263	−	62.5018i	0.253019	−	0.183829i
$341$	165.220			0.484516
$342$	100.498	−	32.6539i	0.293855	−	0.0954793i
$343$		−	369.908i		−	1.07845i
$344$	104.721	−	144.137i	0.304423	−	0.419002i
$345$	2.91796			0.00845786
$346$	−139.899	−	430.564i	−0.404331	−	1.24440i
$347$		−	503.075i		−	1.44978i	−0.688863	−	0.724892i	$-0.741890\pi$
$347$		−	503.075i		−	1.44978i	0.688863	−	0.724892i	$-0.258110\pi$
$348$	−60.4984	−	83.2690i	−0.173846	−	0.239279i
$349$	−0.504658			−0.00144601			−0.000723006	−	1.00000i	$-0.500230\pi$
$349$	−0.504658			−0.00144601			−0.000723006		1.00000i	$0.500230\pi$
$350$	50.0000	−	16.2460i	0.142857	−	0.0464171i
$351$			248.435i			0.707791i
$352$			637.414i			1.81084i
$353$	−335.994			−0.951824			−0.475912	−	0.879493i	$-0.657882\pi$
$353$	−335.994			−0.951824			−0.475912	+	0.879493i	$0.657882\pi$
$354$	25.3375	+	77.9807i	0.0715748	+	0.220285i
$355$			180.645i			0.508859i
$356$	360.636	−	262.018i	1.01302	−	0.736004i
$357$	−146.950			−0.411626
$358$	−426.715	+	138.648i	−1.19194	+	0.387285i
$359$			98.4859i			0.274334i	0.990548	+	0.137167i	$0.0437997\pi$
$359$			98.4859i			0.274334i	−0.990548	+	0.137167i	$0.956200\pi$
$360$	50.2492	+	36.5082i	0.139581	+	0.101412i
$361$	129.446			0.358576
$362$	53.2887	+	164.006i	0.147206	+	0.453054i
$363$			648.384i			1.78618i
$364$	−104.721	−	144.137i	−0.287696	−	0.395980i
$365$	12.4195			0.0340261
$366$	403.108	−	130.978i	1.10139	−	0.357863i
$367$			498.473i			1.35824i	0.734029	+	0.679118i	$0.237638\pi$
$367$			498.473i			1.35824i	−0.734029	+	0.679118i	$0.762362\pi$
$368$	−8.44582	−	2.74421i	−0.0229506	−	0.00745711i
$369$	−50.6362			−0.137226
$370$	25.3738	+	78.0926i	0.0685779	+	0.211061i
$371$			348.879i			0.940374i
$372$	63.1084	−	45.8509i	0.169646	−	0.123255i
$373$	600.354			1.60953			0.804765	−	0.593594i	$-0.202291\pi$
$373$	600.354			1.60953			0.804765	+	0.593594i	$0.202291\pi$
$374$	−450.440	+	146.357i	−1.20438	+	0.391328i
$375$			26.2866i			0.0700975i
$376$	251.056	−	345.549i	0.667701	−	0.919012i
$377$	92.7214			0.245945
$378$	−95.2786	−	293.238i	−0.252060	−	0.775761i
$379$			303.490i			0.800765i	0.916348	+	0.400383i	$0.131123\pi$
$379$			303.490i			0.800765i	−0.916348	+	0.400383i	$0.868877\pi$
$380$	−80.0000	−	110.111i	−0.210526	−	0.289765i
$381$	−467.023			−1.22578
$382$	59.0031	−	19.1713i	0.154458	−	0.0501866i
$383$		−	332.583i		−	0.868362i	−0.900826	−	0.434181i	$-0.857038\pi$
$383$		−	332.583i		−	0.868362i	0.900826	−	0.434181i	$-0.142962\pi$
$384$	176.892	+	243.470i	0.460655	+	0.634038i
$385$	−234.164			−0.608218
$386$	68.1215	+	209.656i	0.176481	+	0.543151i
$387$			77.3256i			0.199808i
$388$	300.413	−	218.263i	0.774261	−	0.562534i
$389$	392.354			1.00862			0.504312	−	0.863522i	$-0.331746\pi$
$389$	392.354			1.00862			0.504312	+	0.863522i	$0.331746\pi$
$390$	84.7214	−	27.5276i	0.217234	−	0.0705837i
$391$		−	6.59849i		−	0.0168759i
$392$	−138.249	−	100.444i	−0.352677	−	0.256235i
$393$	18.2693			0.0464868
$394$	−106.626	−	328.162i	−0.270625	−	0.832897i
$395$			30.9579i			0.0783744i
$396$	−162.610	−	223.813i	−0.410631	−	0.565185i
$397$	334.190			0.841789			0.420895	−	0.907110i	$-0.361716\pi$
$397$	334.190			0.841789			0.420895	+	0.907110i	$0.361716\pi$
$398$	517.771	−	168.234i	1.30093	−	0.422698i
$399$			188.091i			0.471407i
$400$	24.7214	−	76.0845i	0.0618034	−	0.190211i
$401$	121.003			0.301753			0.150877	−	0.988553i	$-0.451790\pi$
$401$	121.003			0.301753			0.150877	+	0.988553i	$0.451790\pi$
$402$	72.9768	+	224.599i	0.181534	+	0.558705i
$403$			70.2722i			0.174373i
$404$	−207.469	+	150.735i	−0.513537	+	0.373107i
$405$	84.2887			0.208120
$406$	−109.443	+	35.5601i	−0.269563	+	0.0875864i
$407$		−	365.730i		−	0.898599i
$408$	−131.437	+	180.907i	−0.322148	+	0.443399i
$409$	−607.410			−1.48511			−0.742555	−	0.669785i	$-0.766386\pi$
$409$	−607.410			−1.48511			−0.742555	+	0.669785i	$0.766386\pi$
$410$	20.1540	+	62.0277i	0.0491562	+	0.151287i
$411$		−	1.95807i		−	0.00476415i
$412$	−323.915	−	445.831i	−0.786201	−	1.08211i
$413$	91.6718			0.221966
$414$	3.66563	−	1.19104i	0.00885418	−	0.00287690i
$415$			170.423i			0.410658i
$416$	−271.108			−0.651703
$417$	−558.768			−1.33997
$418$	187.331	+	576.546i	0.448161	+	1.37930i
$419$		−	466.760i		−	1.11398i	−0.830518	−	0.556992i	$-0.811955\pi$
$419$		−	466.760i		−	1.11398i	0.830518	−	0.556992i	$-0.188045\pi$
$420$	−89.4427	+	64.9839i	−0.212959	+	0.154724i
$421$	−73.0883			−0.173606			−0.0868031	−	0.996225i	$-0.527665\pi$
$421$	−73.0883			−0.173606			−0.0868031	+	0.996225i	$0.527665\pi$
$422$	390.440	−	126.862i	0.925212	−	0.300620i
$423$			185.378i			0.438246i
$424$	429.495	+	312.047i	1.01296	+	0.735959i
$425$	59.4427			0.139865
$426$	−117.390	−	361.290i	−0.275564	−	0.848098i
$427$		−	473.882i		−	1.10979i
$428$	120.689	+	166.114i	0.281983	+	0.388117i
$429$	−396.774			−0.924881
$430$	94.7214	−	30.7768i	0.220282	−	0.0715740i
$431$		−	463.630i		−	1.07571i	−0.843038	−	0.537853i	$-0.819235\pi$
$431$		−	463.630i		−	1.07571i	0.843038	−	0.537853i	$-0.180765\pi$
$432$	−446.217	−	144.985i	−1.03291	−	0.335612i
$433$	−99.8359			−0.230568			−0.115284	−	0.993333i	$-0.536778\pi$
$433$	−99.8359			−0.230568			−0.115284	+	0.993333i	$0.536778\pi$
$434$	−26.9505	−	82.9451i	−0.0620979	−	0.191118i
$435$		−	57.5374i		−	0.132270i
$436$	−431.915	+	313.805i	−0.990630	+	0.719735i
$437$	−8.44582			−0.0193268
$438$	−24.8390	+	8.07069i	−0.0567101	+	0.0184262i
$439$			374.086i			0.852133i	0.904692	+	0.426066i	$0.140101\pi$
$439$			374.086i			0.852133i	−0.904692	+	0.426066i	$0.859899\pi$
$440$	−209.443	+	288.273i	−0.476006	+	0.655166i
$441$	74.1672			0.168180
$442$	−62.2492	−	191.583i	−0.140835	−	0.433447i
$443$		−	290.100i		−	0.654854i	−0.944877	−	0.327427i	$-0.893818\pi$
$443$		−	290.100i		−	0.654854i	0.944877	−	0.327427i	$-0.106182\pi$
$444$	−101.495	−	139.696i	−0.228593	−	0.314631i
$445$	249.193			0.559985
$446$	−448.387	+	145.690i	−1.00535	+	0.326659i
$447$			86.9231i			0.194459i
$448$	320.000	−	103.974i	0.714286	−	0.232085i
$449$	299.921			0.667976			0.333988	−	0.942577i	$-0.391606\pi$
$449$	299.921			0.667976			0.333988	+	0.942577i	$0.391606\pi$
$450$	10.7295	+	33.0220i	0.0238433	+	0.0733822i
$451$		−	290.493i		−	0.644109i
$452$	−552.466	+	401.390i	−1.22227	+	0.888031i
$453$	664.721			1.46738
$454$	111.305	−	36.1652i	0.245165	−	0.0796590i
$455$		−	99.5959i		−	0.218892i
$456$	231.554	+	168.234i	0.507794	+	0.368934i
$457$	822.328			1.79941			0.899703	−	0.436503i	$-0.143783\pi$
$457$	822.328			1.79941			0.899703	+	0.436503i	$0.143783\pi$
$458$	100.567	+	309.514i	0.219579	+	0.675796i
$459$		−	348.617i		−	0.759513i
$460$	−2.91796	−	4.01623i	−0.00634339	−	0.00873093i
$461$	−456.885			−0.991075			−0.495537	−	0.868587i	$-0.665029\pi$
$461$	−456.885			−0.991075			−0.495537	+	0.868587i	$0.665029\pi$
$462$	468.328	−	152.169i	1.01370	−	0.329370i
$463$			400.249i			0.864469i	0.901761	+	0.432234i	$0.142275\pi$
$463$			400.249i			0.864469i	−0.901761	+	0.432234i	$0.857725\pi$
$464$	−54.1115	+	166.538i	−0.116620	+	0.358918i
$465$	43.6068			0.0937781
$466$	197.183	+	606.868i	0.423140	+	1.30229i
$467$			913.145i			1.95534i	0.210139	+	0.977672i	$0.432608\pi$
$467$			913.145i			1.95534i	−0.210139	+	0.977672i	$0.567392\pi$
$468$	95.1935	−	69.1621i	0.203405	−	0.147782i
$469$	264.033			0.562969
$470$	227.082	−	73.7834i	0.483153	−	0.156986i
$471$		−	481.391i		−	1.02206i
$472$	81.9938	−	112.855i	0.173716	−	0.239099i
$473$	−443.607			−0.937858
$474$	−20.1177	−	61.9158i	−0.0424423	−	0.130624i
$475$		−	76.0845i		−	0.160178i
$476$	146.950	+	202.260i	0.308720	+	0.424916i
$477$	−230.413			−0.483047
$478$	−450.440	+	146.357i	−0.942342	+	0.306186i
$479$		−	526.131i		−	1.09840i	−0.835692	−	0.549198i	$-0.814933\pi$
$479$		−	526.131i		−	1.09840i	0.835692	−	0.549198i	$-0.185067\pi$
$480$			168.234i			0.350487i
$481$	155.554			0.323397
$482$	−0.567331	−	1.74606i	−0.00117704	−	0.00362254i
$483$			6.86054i			0.0142040i
$484$	892.423	−	648.384i	1.84385	−	1.33964i
$485$	207.580			0.428001
$486$	333.416	−	108.334i	0.686042	−	0.222909i
$487$			443.541i			0.910762i	0.890297	+	0.455381i	$0.150497\pi$
$487$			443.541i			0.910762i	−0.890297	+	0.455381i	$0.849503\pi$
$488$	−583.384	−	423.853i	−1.19546	−	0.868552i
$489$	252.125			0.515594
$490$	−29.5197	−	90.8524i	−0.0602444	−	0.185413i
$491$		−	287.163i		−	0.584854i	−0.956288	−	0.292427i	$-0.905537\pi$
$491$		−	287.163i		−	0.584854i	0.956288	−	0.292427i	$-0.0944628\pi$
$492$	−80.6161	−	110.959i	−0.163854	−	0.225526i
$493$	−130.111			−0.263918
$494$	−245.220	+	79.6767i	−0.496396	+	0.161289i
$495$		−	154.651i		−	0.312427i
$496$	−126.217	−	41.0103i	−0.254469	−	0.0826820i
$497$	−424.721			−0.854570
$498$	−110.748	−	340.846i	−0.222385	−	0.684430i
$499$			810.936i			1.62512i	0.582876	+	0.812561i	$0.301927\pi$
$499$			810.936i			1.62512i	−0.582876	+	0.812561i	$0.698073\pi$
$500$	36.1803	−	26.2866i	0.0723607	−	0.0525731i
$501$	78.0789			0.155846
$502$	260.000	−	84.4791i	0.517928	−	0.168285i
$503$			642.471i			1.27728i	0.769506	+	0.638639i	$0.220502\pi$
$503$			642.471i			1.27728i	−0.769506	+	0.638639i	$0.779498\pi$
$504$	−85.8359	+	118.143i	−0.170309	+	0.234411i
$505$	−143.358			−0.283876
$506$	6.83282	+	21.0292i	0.0135036	+	0.0415598i
$507$			228.585i			0.450858i
$508$	467.023	+	642.802i	0.919337	+	1.26536i
$509$	−915.050			−1.79774			−0.898870	−	0.438216i	$-0.855611\pi$
$509$	−915.050			−1.79774			−0.898870	+	0.438216i	$0.855611\pi$
$510$	−118.885	+	38.6282i	−0.233109	+	0.0757416i
$511$			29.2000i			0.0571429i
$512$	158.217	−	486.941i	0.309017	−	0.951057i
$513$	−446.217			−0.869818
$514$	−169.925	−	522.975i	−0.330593	−	1.01746i
$515$		−	308.061i		−	0.598177i
$516$	−169.443	+	123.107i	−0.328377	+	0.238580i
$517$	−1063.49			−2.05704
$518$	−183.607	+	59.6575i	−0.354453	+	0.115169i
$519$			532.206i			1.02544i
$520$	−122.610	−	89.0813i	−0.235788	−	0.171310i
$521$	1006.98			1.93279			0.966396	−	0.257058i	$-0.0827533\pi$
$521$	1006.98			1.93279			0.966396	+	0.257058i	$0.0827533\pi$
$522$	−23.4853	−	72.2803i	−0.0449910	−	0.138468i
$523$		−	774.173i		−	1.48025i	−0.672467	−	0.740127i	$-0.734765\pi$
$523$		−	774.173i		−	1.48025i	0.672467	−	0.740127i	$-0.265235\pi$
$524$	−18.2693	−	25.1456i	−0.0348651	−	0.0479877i
$525$	−61.8034			−0.117721
$526$	−772.991	+	251.160i	−1.46956	+	0.477490i
$527$		−	98.6096i		−	0.187115i
$528$	231.554	−	712.650i	0.438550	−	1.34972i
$529$	528.692			0.999418
$530$	91.7082	+	282.249i	0.173034	+	0.532545i
$531$			60.5437i			0.114018i
$532$	258.885	−	188.091i	0.486627	−	0.353555i
$533$	123.554			0.231809
$534$	−498.387	+	161.936i	−0.933309	+	0.303250i
$535$			114.782i			0.214546i
$536$	236.158	−	325.043i	0.440593	−	0.606424i
$537$	527.449			0.982214
$538$	−215.400	−	662.933i	−0.400372	−	1.23222i
$539$			425.487i			0.789401i
$540$	−154.164	−	212.189i	−0.285489	−	0.392942i
$541$	−259.115			−0.478955			−0.239477	−	0.970902i	$-0.576976\pi$
$541$	−259.115			−0.478955			−0.239477	+	0.970902i	$0.576976\pi$
$542$	471.437	−	153.179i	0.869809	−	0.282618i
$543$		−	202.722i		−	0.373337i
$544$	380.433			0.699326
$545$	−298.446			−0.547607
$546$	64.7214	+	199.192i	0.118537	+	0.364820i
$547$		−	149.818i		−	0.273890i	−0.990579	−	0.136945i	$-0.956272\pi$
$547$		−	149.818i		−	0.273890i	0.990579	−	0.136945i	$-0.0437284\pi$
$548$	−2.69505	+	1.95807i	−0.00491797	+	0.00357312i
$549$	312.971			0.570074
$550$	−189.443	+	61.5537i	−0.344441	+	0.111916i
$551$			166.538i			0.302247i
$552$	8.44582	+	6.13625i	0.0153004	+	0.0111164i
$553$	−72.7864			−0.131621
$554$	−33.8398	−	104.148i	−0.0610826	−	0.187993i
$555$		−	96.5278i		−	0.173924i
$556$	558.768	+	769.078i	1.00498	+	1.38323i
$557$	511.698			0.918668			0.459334	−	0.888264i	$-0.348088\pi$
$557$	511.698			0.918668			0.459334	+	0.888264i	$0.348088\pi$
$558$	54.7802	−	17.7992i	0.0981724	−	0.0318981i
$559$		−	188.677i		−	0.337526i
$560$	178.885	+	58.1234i	0.319438	+	0.103792i
$561$	556.774			0.992467
$562$	−31.1246	−	95.7917i	−0.0553819	−	0.170448i
$563$			490.726i			0.871627i	0.900037	+	0.435814i	$0.143539\pi$
$563$			490.726i			0.871627i	−0.900037	+	0.435814i	$0.856461\pi$
$564$	−406.217	+	295.134i	−0.720242	+	0.523287i
$565$	−381.745			−0.675654
$566$	280.249	−	91.0585i	0.495140	−	0.160881i
$567$			198.175i			0.349514i
$568$	−379.882	+	522.863i	−0.668807	+	0.920534i
$569$	−232.748			−0.409047			−0.204523	−	0.978862i	$-0.565564\pi$
$569$	−232.748			−0.409047			−0.204523	+	0.978862i	$0.565564\pi$
$570$	49.4427	+	152.169i	0.0867416	+	0.266963i
$571$		−	210.755i		−	0.369098i	−0.982823	−	0.184549i	$-0.940918\pi$
$571$		−	210.755i		−	0.369098i	0.982823	−	0.184549i	$-0.0590824\pi$
$572$	396.774	+	546.113i	0.693661	+	0.954742i
$573$	−72.9318			−0.127281
$574$	−145.836	+	47.3850i	−0.254070	+	0.0825522i
$575$		−	2.77515i		−	0.00482634i
$576$	68.6687	+	211.341i	0.119217	+	0.366911i
$577$	341.712			0.592222			0.296111	−	0.955154i	$-0.404310\pi$
$577$	341.712			0.592222			0.296111	+	0.955154i	$0.404310\pi$
$578$	−91.2605	−	280.871i	−0.157890	−	0.485936i
$579$		−	259.150i		−	0.447581i
$580$	−79.1935	+	57.5374i	−0.136541	+	0.0992025i
$581$	−400.689			−0.689654
$582$	−415.161	+	134.894i	−0.713335	+	0.231777i
$583$		−	1321.85i		−	2.26733i
$584$	35.9474	+	26.1173i	0.0615537	+	0.0447214i
$585$	65.7771			0.112439
$586$	110.541	+	340.210i	0.188637	+	0.580564i
$587$			618.412i			1.05351i	0.850016	+	0.526756i	$0.176592\pi$
$587$			618.412i			1.05351i	−0.850016	+	0.526756i	$0.823408\pi$
$588$	118.079	+	162.522i	0.200815	+	0.276397i
$589$	−126.217			−0.214290
$590$	74.1641	−	24.0974i	0.125702	−	0.0408430i
$591$			405.630i			0.686345i
$592$	−90.7802	+	279.393i	−0.153345	+	0.471947i
$593$	120.663			0.203478			0.101739	−	0.994811i	$-0.467559\pi$
$593$	120.663			0.203478			0.101739	+	0.994811i	$0.467559\pi$
$594$	360.997	+	1111.03i	0.607739	+	1.87043i
$595$			139.758i			0.234888i
$596$	119.639	−	86.9231i	0.200737	−	0.145844i
$597$	−640.000			−1.07203
$598$	−8.94427	+	2.90617i	−0.0149570	+	0.00485982i
$599$		−	849.927i		−	1.41891i	−0.704751	−	0.709455i	$-0.748941\pi$
$599$		−	849.927i		−	1.41891i	0.704751	−	0.709455i	$-0.251059\pi$
$600$	−55.2786	+	76.0845i	−0.0921311	+	0.126808i
$601$	−11.3576			−0.0188978			−0.00944890	−	0.999955i	$-0.503008\pi$
$601$	−11.3576			−0.0188978			−0.00944890	+	0.999955i	$0.503008\pi$
$602$	72.3607	+	222.703i	0.120200	+	0.369939i
$603$			174.378i			0.289183i
$604$	−664.721	−	914.910i	−1.10053	−	1.51475i
$605$	616.649			1.01926
$606$	286.715	−	93.1594i	0.473127	−	0.153728i
$607$		−	1115.12i		−	1.83710i	−0.395305	−	0.918550i	$-0.629361\pi$
$607$		−	1115.12i		−	1.83710i	0.395305	−	0.918550i	$-0.370639\pi$
$608$		−	486.941i		−	0.800890i
$609$	135.279			0.222132
$610$	−124.567	−	383.379i	−0.204209	−	0.628490i
$611$		−	452.329i		−	0.740309i
$612$	−133.580	+	97.0519i	−0.218269	+	0.158582i
$613$	499.475			0.814805			0.407402	−	0.913249i	$-0.366435\pi$
$613$	499.475			0.814805			0.407402	+	0.913249i	$0.366435\pi$
$614$	541.246	−	175.862i	0.881508	−	0.286419i
$615$		−	76.6705i		−	0.124667i
$616$	−677.771	−	492.429i	−1.10028	−	0.799398i
$617$	545.935			0.884822			0.442411	−	0.896813i	$-0.354123\pi$
$617$	545.935			0.884822			0.442411	+	0.896813i	$0.354123\pi$
$618$	200.190	+	616.123i	0.323933	+	0.996962i
$619$			455.011i			0.735075i	0.930009	+	0.367537i	$0.119799\pi$
$619$			455.011i			0.735075i	−0.930009	+	0.367537i	$0.880201\pi$
$620$	−43.6068	−	60.0196i	−0.0703335	−	0.0968058i
$621$	−16.2755			−0.0262086
$622$	−536.774	+	174.408i	−0.862981	+	0.280399i
$623$			585.889i			0.940432i
$624$	303.108	+	98.4859i	0.485751	+	0.157830i
$625$	25.0000			0.0400000
$626$	−350.764	−	1079.54i	−0.560326	−	1.72451i
$627$		−	712.650i		−	1.13660i
$628$	−662.577	+	481.391i	−1.05506	+	0.766546i
$629$	−218.282			−0.347030
$630$	−77.6393	+	25.2265i	−0.123237	+	0.0400421i
$631$			267.706i			0.424257i	0.977242	+	0.212128i	$0.0680395\pi$
$631$			267.706i			0.424257i	−0.977242	+	0.212128i	$0.931960\pi$
$632$	−65.1021	+	89.6054i	−0.103010	+	0.141781i
$633$	−482.610			−0.762417
$634$	99.5905	+	306.508i	0.157083	+	0.483451i
$635$			444.165i			0.699473i
$636$	−366.833	−	504.902i	−0.576781	−	0.793871i
$637$	−180.971			−0.284098
$638$	414.663	−	134.732i	0.649941	−	0.211179i
$639$		−	280.503i		−	0.438971i
$640$	231.554	−	168.234i	0.361803	−	0.262866i
$641$	−418.571			−0.652997			−0.326499	−	0.945198i	$-0.605869\pi$
$641$	−418.571			−0.652997			−0.326499	+	0.945198i	$0.605869\pi$
$642$	−74.5898	−	229.564i	−0.116183	−	0.357576i
$643$			439.339i			0.683265i	0.939834	+	0.341633i	$0.110980\pi$
$643$			439.339i			0.683265i	−0.939834	+	0.341633i	$0.889020\pi$
$644$	9.44272	−	6.86054i	0.0146626	−	0.0106530i
$645$	−117.082			−0.181523
$646$	344.105	−	111.807i	0.532671	−	0.173075i
$647$			419.644i			0.648600i	0.945954	+	0.324300i	$0.105129\pi$
$647$			419.644i			0.648600i	−0.945954	+	0.324300i	$0.894871\pi$
$648$	243.967	+	177.253i	0.376493	+	0.273538i
$649$	−347.331			−0.535179
$650$	−26.1803	−	80.5748i	−0.0402774	−	0.123961i
$651$			102.526i			0.157490i
$652$	−252.125	−	347.021i	−0.386695	−	0.532240i
$653$	−370.085			−0.566746			−0.283373	−	0.959010i	$-0.591453\pi$
$653$	−370.085			−0.566746			−0.283373	+	0.959010i	$0.591453\pi$
$654$	596.892	−	193.942i	0.912678	−	0.296547i
$655$		−	17.3752i		−	0.0265270i
$656$	−72.1052	+	221.917i	−0.109917	+	0.338288i
$657$	−19.2849			−0.0293529
$658$	173.475	+	533.902i	0.263640	+	0.811401i
$659$		−	322.823i		−	0.489868i	−0.969540	−	0.244934i	$-0.921234\pi$
$659$		−	322.823i		−	0.489868i	0.969540	−	0.244934i	$-0.0787664\pi$
$660$	338.885	−	246.215i	0.513463	−	0.373053i
$661$	−812.735			−1.22955			−0.614777	−	0.788701i	$-0.710754\pi$
$661$	−812.735			−1.22955			−0.614777	+	0.788701i	$0.710754\pi$
$662$	−631.437	+	205.166i	−0.953832	+	0.309919i
$663$			236.810i			0.357180i
$664$	−358.387	+	493.277i	−0.539739	+	0.742888i
$665$	178.885			0.269001
$666$	−39.4001	−	121.261i	−0.0591594	−	0.182074i
$667$			6.07439i			0.00910703i
$668$	−78.0789	−	107.466i	−0.116885	−	0.160878i
$669$	554.237			0.828456
$670$	213.607	−	69.4051i	0.318816	−	0.103590i
$671$			1795.47i			2.67581i
$672$	−395.542			−0.588604
$673$	467.378			0.694469			0.347235	−	0.937778i	$-0.387121\pi$
$673$	467.378			0.694469			0.347235	+	0.937778i	$0.387121\pi$
$674$	−166.318	−	511.875i	−0.246763	−	0.759458i
$675$		−	146.619i		−	0.217213i
$676$	314.620	−	228.585i	0.465414	−	0.338143i
$677$	548.237			0.809803			0.404902	−	0.914360i	$-0.367306\pi$
$677$	548.237			0.809803			0.404902	+	0.914360i	$0.367306\pi$
$678$	763.489	−	248.073i	1.12609	−	0.365889i
$679$			488.051i			0.718779i
$680$	172.053	+	125.004i	0.253019	+	0.183829i
$681$	−137.580			−0.202027
$682$	102.111	+	314.267i	0.149724	+	0.460802i
$683$			23.9663i			0.0350898i	0.999846	+	0.0175449i	$0.00558500\pi$
$683$			23.9663i			0.0350898i	−0.999846	+	0.0175449i	$0.994415\pi$
$684$	124.223	+	170.978i	0.181612	+	0.249968i
$685$	−1.86223			−0.00271859
$686$	703.607	−	228.616i	1.02567	−	0.333259i
$687$		−	382.581i		−	0.556886i
$688$	338.885	+	110.111i	0.492566	+	0.160044i
$689$	562.217			0.815989
$690$	1.80340	+	5.55029i	0.00261362	+	0.00804390i
$691$		−	186.981i		−	0.270595i	−0.990805	−	0.135298i	$-0.956801\pi$
$691$		−	186.981i		−	0.270595i	0.990805	−	0.135298i	$-0.0431990\pi$
$692$	732.519	−	532.206i	1.05855	−	0.769084i
$693$	363.607			0.524685
$694$	956.906	−	310.917i	1.37883	−	0.448008i
$695$			531.420i			0.764633i
$696$	120.997	−	166.538i	0.173846	−	0.239279i
$697$	−173.378			−0.248748
$698$	−0.311896	−	0.959917i	−0.000446842	−	0.00137524i
$699$		−	750.130i		−	1.07315i
$700$	61.8034	+	85.0651i	0.0882906	+	0.121522i
$701$	−706.636			−1.00804			−0.504020	−	0.863692i	$-0.668146\pi$
$701$	−706.636			−1.00804			−0.504020	+	0.863692i	$0.668146\pi$
$702$	−472.551	+	153.541i	−0.673150	+	0.218720i
$703$			279.393i			0.397429i
$704$	−1212.43	+	393.943i	−1.72221	+	0.559579i
$705$	−280.689			−0.398140
$706$	−207.656	−	639.098i	−0.294130	−	0.905238i
$707$		−	337.054i		−	0.476738i
$708$	−132.669	+	96.3895i	−0.187385	+	0.136143i
$709$	−188.597			−0.266005			−0.133002	−	0.991116i	$-0.542462\pi$
$709$	−188.597			−0.266005			−0.133002	+	0.991116i	$0.542462\pi$
$710$	−343.607	+	111.645i	−0.483953	+	0.157246i
$711$		−	48.0710i		−	0.0676104i
$712$	721.272	+	524.035i	1.01302	+	0.736004i
$713$	−4.60369			−0.00645679
$714$	−90.8204	−	279.516i	−0.127199	−	0.391480i
$715$			377.354i			0.527769i
$716$	−527.449	−	725.971i	−0.736661	−	1.01393i
$717$	556.774			0.776533
$718$	−187.331	+	60.8676i	−0.260907	+	0.0847738i
$719$			156.085i			0.217086i	0.994092	+	0.108543i	$0.0346186\pi$
$719$			156.085i			0.217086i	−0.994092	+	0.108543i	$0.965381\pi$
$720$	−38.3870	+	118.143i	−0.0533153	+	0.164088i
$721$	724.296			1.00457
$722$	80.0019	+	246.221i	0.110806	+	0.341026i
$723$			2.15825i			0.00298514i
$724$	−279.023	+	202.722i	−0.385391	+	0.280003i
$725$	−54.7214			−0.0754777
$726$	−1233.30	+	400.723i	−1.69876	+	0.551960i
$727$		−	715.164i		−	0.983719i	−0.870675	−	0.491859i	$-0.836317\pi$
$727$		−	715.164i		−	0.983719i	0.870675	−	0.491859i	$-0.163683\pi$
$728$	209.443	−	288.273i	0.287696	−	0.395980i
$729$	−751.381			−1.03070
$730$	7.67568	+	23.6233i	0.0105146	+	0.0323607i
$731$			264.762i			0.362191i
$732$	498.269	+	685.809i	0.680696	+	0.936897i
$733$	1233.29			1.68252			0.841259	−	0.540632i	$-0.181815\pi$
$733$	1233.29			1.68252			0.841259	+	0.540632i	$0.181815\pi$
$734$	−948.152	+	308.073i	−1.29176	+	0.419718i
$735$			112.300i			0.152789i
$736$		−	17.7609i		−	0.0241317i
$737$	−1000.38			−1.35737
$738$	−31.2949	−	96.3158i	−0.0424050	−	0.130509i
$739$			8.55656i			0.0115786i	0.999983	+	0.00578928i	$0.00184280\pi$
$739$			8.55656i			0.0115786i	−0.999983	+	0.00578928i	$0.998157\pi$
$740$	−132.859	+	96.5278i	−0.179539	+	0.130443i
$741$	303.108			0.409053
$742$	−663.607	+	215.619i	−0.894349	+	0.290592i
$743$		−	1010.56i		−	1.36011i	−0.733163	−	0.680053i	$-0.761957\pi$
$743$		−	1010.56i		−	1.36011i	0.733163	−	0.680053i	$-0.238043\pi$
$744$	126.217	+	91.7018i	0.169646	+	0.123255i
$745$	82.6687			0.110965
$746$	371.039	+	1141.94i	0.497372	+	1.53075i
$747$		−	264.631i		−	0.354258i
$748$	−556.774	−	766.334i	−0.744350	−	1.02451i
$749$	−269.868			−0.360305
$750$	−50.0000	+	16.2460i	−0.0666667	+	0.0216613i
$751$		−	1104.31i		−	1.47046i	−0.677820	−	0.735228i	$-0.737075\pi$
$751$		−	1104.31i		−	1.47046i	0.677820	−	0.735228i	$-0.262925\pi$
$752$	812.433	+	263.976i	1.08036	+	0.351031i
$753$	−321.378			−0.426796
$754$	57.3050	+	176.367i	0.0760013	+	0.233908i
$755$		−	632.188i		−	0.837335i
$756$	498.885	−	362.461i	0.659901	−	0.479446i
$757$	−875.633			−1.15671			−0.578357	−	0.815783i	$-0.696306\pi$
$757$	−875.633			−1.15671			−0.578357	+	0.815783i	$0.696306\pi$
$758$	−577.272	+	187.567i	−0.761573	+	0.247450i
$759$		−	25.9936i		−	0.0342471i
$760$	160.000	−	220.221i	0.210526	−	0.289765i
$761$	−647.207			−0.850470			−0.425235	−	0.905083i	$-0.639808\pi$
$761$	−647.207			−0.850470			−0.425235	+	0.905083i	$0.639808\pi$
$762$	−288.636	−	888.331i	−0.378788	−	1.16579i
$763$		−	701.688i		−	0.919644i
$764$	72.9318	+	100.382i	0.0954605	+	0.131390i
$765$	−92.3018			−0.120656
$766$	632.610	−	205.547i	0.825861	−	0.268339i
$767$		−	147.729i		−	0.192606i
$768$	−353.783	+	486.941i	−0.460655	+	0.634038i
$769$	631.430			0.821106			0.410553	−	0.911837i	$-0.365336\pi$
$769$	631.430			0.821106			0.410553	+	0.911837i	$0.365336\pi$
$770$	−144.721	−	445.407i	−0.187950	−	0.578450i
$771$			646.433i			0.838434i
$772$	−356.689	+	259.150i	−0.462032	+	0.335686i
$773$	−421.522			−0.545306			−0.272653	−	0.962112i	$-0.587901\pi$
$773$	−421.522			−0.545306			−0.272653	+	0.962112i	$0.587901\pi$
$774$	−147.082	+	47.7899i	−0.190028	+	0.0617440i
$775$		−	41.4725i		−	0.0535129i
$776$	600.827	+	436.526i	0.774261	+	0.562534i
$777$	226.950			0.292086
$778$	242.488	+	746.303i	0.311682	+	0.959258i
$779$			221.917i			0.284874i
$780$	104.721	+	144.137i	0.134258	+	0.184790i
$781$	1609.21			2.06044
$782$	12.5511	−	4.07809i	0.0160500	−	0.00521495i
$783$			320.927i			0.409869i
$784$	105.613	−	325.043i	0.134710	−	0.414596i
$785$	−457.830			−0.583223
$786$	11.2911	+	34.7503i	0.0143652	+	0.0442116i
$787$			838.633i			1.06561i	0.846239	+	0.532804i	$0.178862\pi$
$787$			838.633i			1.06561i	−0.846239	+	0.532804i	$0.821138\pi$
$788$	558.302	−	405.630i	0.708505	−	0.514759i
$789$	955.469			1.21099
$790$	−58.8854	+	19.1330i	−0.0745385	+	0.0242190i
$791$		−	897.535i		−	1.13468i
$792$	325.220	−	447.627i	0.410631	−	0.565185i
$793$	−763.659			−0.963001
$794$	206.541	+	635.668i	0.260127	+	0.800589i
$795$		−	348.879i		−	0.438841i
$796$	640.000	+	880.884i	0.804020	+	1.10664i
$797$	1213.57			1.52268			0.761339	−	0.648354i	$-0.224542\pi$
$797$	1213.57			1.52268			0.761339	+	0.648354i	$0.224542\pi$
$798$	−357.771	+	116.247i	−0.448334	+	0.145673i
$799$			634.732i			0.794408i
$800$	160.000			0.200000
$801$	−386.944			−0.483076
$802$	74.7840	+	230.162i	0.0932469	+	0.286985i
$803$		−	110.635i		−	0.137777i
$804$	−382.111	+	277.620i	−0.475263	+	0.345299i
$805$	6.52476			0.00810529
$806$	−133.666	+	43.4306i	−0.165838	+	0.0538841i
$807$			819.431i			1.01540i
$808$	−414.938	−	301.470i	−0.513537	−	0.373107i
$809$	−229.214			−0.283330			−0.141665	−	0.989915i	$-0.545246\pi$
$809$	−229.214			−0.283330			−0.141665	+	0.989915i	$0.545246\pi$
$810$	52.0933	+	160.327i	0.0643127	+	0.197934i
$811$			454.225i			0.560080i	0.959988	+	0.280040i	$0.0903478\pi$
$811$			454.225i			0.560080i	−0.959988	+	0.280040i	$0.909652\pi$
$812$	−135.279	−	186.195i	−0.166599	−	0.229304i
$813$	−582.728			−0.716762
$814$	695.659	−	226.033i	0.854618	−	0.277682i
$815$		−	239.785i		−	0.294215i
$816$	−425.337	−	138.201i	−0.521247	−	0.169363i
$817$	338.885			0.414792
$818$	−375.400	−	1155.36i	−0.458924	−	1.41242i
$819$			154.651i			0.188829i
$820$	−105.528	+	76.6705i	−0.128693	+	0.0935006i
$821$	1130.90			1.37747			0.688733	−	0.725015i	$-0.258167\pi$
$821$	1130.90			1.37747			0.688733	+	0.725015i	$0.258167\pi$
$822$	3.72447	−	1.21015i	0.00453098	−	0.00147220i
$823$			780.148i			0.947931i	0.880543	+	0.473966i	$0.157178\pi$
$823$			780.148i			0.947931i	−0.880543	+	0.473966i	$0.842822\pi$
$824$	647.830	−	891.661i	0.786201	−	1.08211i
$825$	234.164			0.283835
$826$	56.6563	+	174.370i	0.0685912	+	0.211102i
$827$			209.175i			0.252932i	0.991971	+	0.126466i	$0.0403635\pi$
$827$			209.175i			0.252932i	−0.991971	+	0.126466i	$0.959636\pi$
$828$	4.53097	+	6.23634i	0.00547219	+	0.00753182i
$829$	−508.525			−0.613419			−0.306710	−	0.951803i	$-0.599228\pi$
$829$	−508.525			−0.613419			−0.306710	+	0.951803i	$0.599228\pi$
$830$	−324.164	+	105.327i	−0.390559	+	0.126900i
$831$			128.734i			0.154915i
$832$	−167.554	−	515.679i	−0.201387	−	0.619806i
$833$	253.947			0.304859
$834$	−345.337	−	1062.84i	−0.414074	−	1.27439i
$835$		−	74.2575i		−	0.0889311i
$836$	−980.879	+	712.650i	−1.17330	+	0.852453i
$837$	−243.226			−0.290593
$838$	887.830	−	288.473i	1.05946	−	0.344240i
$839$		−	274.028i		−	0.326613i	−0.986575	−	0.163306i	$-0.947784\pi$
$839$		−	274.028i		−	0.326613i	0.986575	−	0.163306i	$-0.0522159\pi$
$840$	−178.885	−	129.968i	−0.212959	−	0.154724i
$841$	−721.223			−0.857578
$842$	−45.1710	−	139.022i	−0.0536473	−	0.165109i
$843$			118.405i			0.140457i
$844$	482.610	+	664.256i	0.571813	+	0.787033i
$845$	217.397			0.257275
$846$	−352.610	+	114.570i	−0.416797	+	0.135425i
$847$			1449.83i			1.71172i
$848$	−328.105	+	1009.80i	−0.386917	+	1.19081i
$849$	−346.407			−0.408018
$850$	36.7376	+	113.067i	0.0432207	+	0.133020i
$851$			10.1907i			0.0119750i
$852$	614.663	−	446.578i	0.721435	−	0.524153i
$853$	−1583.28			−1.85613			−0.928066	−	0.372416i	$-0.878529\pi$
$853$	−1583.28			−1.85613			−0.928066	+	0.372416i	$0.878529\pi$
$854$	901.378	−	292.875i	1.05548	−	0.342945i
$855$			118.143i			0.138179i
$856$	−241.378	+	332.228i	−0.281983	+	0.388117i
$857$	−1007.38			−1.17547			−0.587735	−	0.809054i	$-0.699980\pi$
$857$	−1007.38			−1.17547			−0.587735	+	0.809054i	$0.699980\pi$
$858$	−245.220	−	754.709i	−0.285804	−	0.879614i
$859$		−	76.6086i		−	0.0891835i	−0.999005	−	0.0445917i	$-0.985801\pi$
$859$		−	76.6086i		−	0.0891835i	0.999005	−	0.0445917i	$-0.0141987\pi$
$860$	117.082	+	161.150i	0.136142	+	0.187383i
$861$	180.263			0.209365
$862$	881.876	−	286.539i	1.02306	−	0.332412i
$863$		−	255.450i		−	0.296002i	−0.988987	−	0.148001i	$-0.952716\pi$
$863$		−	255.450i		−	0.296002i	0.988987	−	0.148001i	$-0.0472839\pi$
$864$		−	938.360i		−	1.08606i
$865$	506.158			0.585154
$866$	−61.7020	−	189.899i	−0.0712494	−	0.219283i
$867$			347.175i			0.400433i
$868$	141.115	−	102.526i	0.162574	−	0.118117i
$869$	275.777			0.317350
$870$	109.443	−	35.5601i	0.125796	−	0.0408737i
$871$		−	425.487i		−	0.488504i
$872$	−863.830	−	627.609i	−0.990630	−	0.719735i
$873$	−322.328			−0.369219
$874$	−5.21981	−	16.0649i	−0.00597232	−	0.0183809i
$875$			58.7785i			0.0671755i
$876$	−30.7027	−	42.2587i	−0.0350488	−	0.0482405i
$877$	601.522			0.685886			0.342943	−	0.939356i	$-0.388576\pi$
$877$	601.522			0.685886			0.342943	+	0.939356i	$0.388576\pi$
$878$	−711.554	+	231.198i	−0.810426	+	0.263323i
$879$		−	420.523i		−	0.478411i
$880$	−677.771	−	220.221i	−0.770194	−	0.250251i
$881$	237.850			0.269977			0.134989	−	0.990847i	$-0.456900\pi$
$881$	237.850			0.269977			0.134989	+	0.990847i	$0.456900\pi$
$882$	45.8378	+	141.074i	0.0519703	+	0.159948i
$883$		−	1.30294i		−	0.00147559i	−1.00000		0.000737794i	$-0.999765\pi$
$883$		−	1.30294i		−	0.00147559i	1.00000		0.000737794i	$-0.000234847\pi$
$884$	325.941	−	236.810i	0.368712	−	0.267885i
$885$	−91.6718			−0.103584
$886$	551.803	−	179.292i	0.622803	−	0.202361i
$887$		−	536.353i		−	0.604682i	−0.953200	−	0.302341i	$-0.902232\pi$
$887$		−	536.353i		−	0.604682i	0.953200	−	0.302341i	$-0.0977682\pi$
$888$	202.991	−	279.393i	0.228593	−	0.314631i
$889$	−1044.30			−1.17469
$890$	154.010	+	473.994i	0.173045	+	0.532578i
$891$		−	750.855i		−	0.842710i
$892$	−554.237	−	762.842i	−0.621342	−	0.855203i
$893$	812.433			0.909780
$894$	−165.337	+	53.7214i	−0.184941	+	0.0600911i
$895$		−	501.634i		−	0.560485i
$896$	395.542	+	544.417i	0.441453	+	0.607608i
$897$	11.0557			0.0123252
$898$	185.361	+	570.484i	0.206416	+	0.635283i
$899$			90.7773i			0.100976i
$900$	−56.1803	+	40.8174i	−0.0624226	+	0.0453527i
$901$	−788.932			−0.875618
$902$	552.551	−	179.535i	0.612584	−	0.199041i
$903$		−	275.276i		−	0.304846i
$904$	−1104.93	−	802.780i	−1.22227	−	0.888031i
$905$	−192.800			−0.213039
$906$	410.820	+	1264.38i	0.453444	+	1.39556i
$907$			332.159i			0.366217i	0.983093	+	0.183108i	$0.0586159\pi$
$907$			332.159i			0.366217i	−0.983093	+	0.183108i	$0.941384\pi$
$908$	137.580	+	189.363i	0.151520	+	0.208550i
$909$	222.604			0.244889
$910$	189.443	−	61.5537i	0.208179	−	0.0676414i
$911$		−	1450.06i		−	1.59172i	−0.605478	−	0.795862i	$-0.707018\pi$
$911$		−	1450.06i		−	1.59172i	0.605478	−	0.795862i	$-0.292982\pi$
$912$	−176.892	+	544.417i	−0.193960	+	0.596948i
$913$	1518.15			1.66282
$914$	508.227	+	1564.16i	0.556047	+	1.71134i
$915$			473.882i			0.517904i
$916$	−526.577	+	382.581i	−0.574866	+	0.417665i
$917$	40.8514			0.0445490
$918$	663.108	−	215.457i	0.722340	−	0.234703i
$919$			814.405i			0.886186i	0.896476	+	0.443093i	$0.146119\pi$
$919$			814.405i			0.886186i	−0.896476	+	0.443093i	$0.853881\pi$
$920$	5.83592	−	8.03246i	0.00634339	−	0.00873093i
$921$	−669.017			−0.726403
$922$	−282.371	−	869.048i	−0.306259	−	0.942568i
$923$			684.437i			0.741535i
$924$	578.885	+	796.767i	0.626499	+	0.862302i
$925$	−91.8034			−0.0992469
$926$	−761.319	+	247.367i	−0.822159	+	0.267136i
$927$			478.353i			0.516023i
$928$	−350.217			−0.377389
$929$	400.039			0.430612			0.215306	−	0.976547i	$-0.430925\pi$
$929$	400.039			0.430612			0.215306	+	0.976547i	$0.430925\pi$
$930$	26.9505	+	82.9451i	0.0289790	+	0.0891882i
$931$		−	325.043i		−	0.349134i
$932$	−1032.47	+	750.130i	−1.10780	+	0.804861i
$933$	663.489			0.711135
$934$	−1736.91	+	564.355i	−1.85964	+	0.604234i
$935$		−	529.524i		−	0.566335i
$936$	190.387	+	138.324i	0.203405	+	0.147782i
$937$	249.279			0.266039			0.133020	−	0.991113i	$-0.457533\pi$
$937$	249.279			0.266039			0.133020	+	0.991113i	$0.457533\pi$
$938$	163.181	+	502.220i	0.173967	+	0.535415i
$939$			1334.39i			1.42107i
$940$	280.689	+	386.335i	0.298605	+	0.410995i
$941$	724.229			0.769638			0.384819	−	0.922992i	$-0.374264\pi$
$941$	724.229			0.769638			0.384819	+	0.922992i	$0.374264\pi$
$942$	915.659	−	297.516i	0.972038	−	0.315834i
$943$			8.09432i			0.00858358i
$944$	265.337	+	86.2134i	0.281078	+	0.0913277i
$945$	344.721			0.364785
$946$	−274.164	−	843.790i	−0.289814	−	0.891956i
$947$		−	1141.54i		−	1.20542i	−0.797959	−	0.602712i	$-0.794087\pi$
$947$		−	1141.54i		−	1.20542i	0.797959	−	0.602712i	$-0.205913\pi$
$948$	105.337	−	76.5322i	0.111115	−	0.0807301i
$949$	47.0557			0.0495845
$950$	144.721	−	47.0228i	0.152338	−	0.0494977i
$951$		−	378.865i		−	0.398386i
$952$	−293.901	+	404.520i	−0.308720	+	0.424916i
$953$	1295.33			1.35921			0.679604	−	0.733579i	$-0.262152\pi$
$953$	1295.33			1.35921			0.679604	+	0.733579i	$0.262152\pi$
$954$	−142.403	−	438.272i	−0.149270	−	0.459405i
$955$			69.3623i			0.0726307i
$956$	−556.774	−	766.334i	−0.582400	−	0.801604i
$957$	−512.551			−0.535581
$958$	1000.76	−	325.167i	1.04464	−	0.339423i
$959$		−	4.37837i		−	0.00456556i
$960$	−320.000	+	103.974i	−0.333333	+	0.108307i
$961$	892.201			0.928409
$962$	96.1378	+	295.882i	0.0999353	+	0.307569i
$963$		−	178.232i		−	0.185080i
$964$	2.97058	−	2.15825i	0.00308152	−	0.00223885i
$965$	−246.466			−0.255405
$966$	−13.0495	+	4.24005i	−0.0135088	+	0.00438928i
$967$		−	398.477i		−	0.412075i	−0.978544	−	0.206037i	$-0.933943\pi$
$967$		−	398.477i		−	0.412075i	0.978544	−	0.206037i	$-0.0660569\pi$
$968$	1784.85	+	1296.77i	1.84385	+	1.33964i
$969$	−425.337			−0.438945
$970$	128.292	+	394.842i	0.132260	+	0.407053i
$971$		−	928.093i		−	0.955811i	−0.878411	−	0.477906i	$-0.841396\pi$
$971$		−	928.093i		−	0.955811i	0.878411	−	0.477906i	$-0.158604\pi$
$972$	412.125	+	567.242i	0.423997	+	0.583582i
$973$	−1249.44			−1.28411
$974$	−843.666	+	274.124i	−0.866186	+	0.281441i
$975$			99.5959i			0.102150i
$976$	445.666	−	1371.62i	0.456625	−	1.40535i
$977$	−1378.05			−1.41049			−0.705247	−	0.708962i	$-0.749164\pi$
$977$	−1378.05			−1.41049			−0.705247	+	0.708962i	$0.749164\pi$
$978$	155.822	+	479.571i	0.159327	+	0.490359i
$979$		−	2219.85i		−	2.26747i
$980$	154.567	−	112.300i	0.157722	−	0.114592i
$981$	463.423			0.472398
$982$	546.217	−	177.477i	0.556229	−	0.180730i
$983$			311.291i			0.316675i	0.987385	+	0.158337i	$0.0506134\pi$
$983$			311.291i			0.316675i	−0.987385	+	0.158337i	$0.949387\pi$
$984$	161.232	−	221.917i	0.163854	−	0.225526i
$985$	385.777			0.391652
$986$	−80.4133	−	247.487i	−0.0815551	−	0.251001i
$987$		−	659.939i		−	0.668631i
$988$	−303.108	−	417.193i	−0.306790	−	0.422260i
$989$	12.3607			0.0124982
$990$	294.164	−	95.5797i	0.297135	−	0.0965452i
$991$			961.147i			0.969876i	0.874549	+	0.484938i	$0.161158\pi$
$991$			961.147i			0.969876i	−0.874549	+	0.484938i	$0.838842\pi$
$992$		−	265.424i		−	0.267565i
$993$	780.498			0.786000
$994$	−262.492	−	807.868i	−0.264077	−	0.812745i
$995$			608.676i			0.611735i
$996$	579.882	−	421.309i	0.582211	−	0.423001i
$997$	−1089.68			−1.09296			−0.546479	−	0.837473i	$-0.684032\pi$
$997$	−1089.68			−1.09296			−0.546479	+	0.837473i	$0.684032\pi$
$998$	−1542.49	+	501.186i	−1.54558	+	0.502190i
$999$			538.404i			0.538943i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	20.3.b.a.11.4	yes	4
3.2	odd	2		180.3.c.a.91.1		4
4.3	odd	2	inner	20.3.b.a.11.3	✓	4
5.2	odd	4		100.3.d.b.99.2		8
5.3	odd	4		100.3.d.b.99.7		8
5.4	even	2		100.3.b.f.51.1		4
8.3	odd	2		320.3.b.c.191.2		4
8.5	even	2		320.3.b.c.191.3		4
12.11	even	2		180.3.c.a.91.2		4
15.2	even	4		900.3.f.e.199.7		8
15.8	even	4		900.3.f.e.199.2		8
15.14	odd	2		900.3.c.k.451.4		4
16.3	odd	4		1280.3.g.e.1151.4		8
16.5	even	4		1280.3.g.e.1151.3		8
16.11	odd	4		1280.3.g.e.1151.5		8
16.13	even	4		1280.3.g.e.1151.6		8
20.3	even	4		100.3.d.b.99.1		8
20.7	even	4		100.3.d.b.99.8		8
20.19	odd	2		100.3.b.f.51.2		4
24.5	odd	2		2880.3.e.e.2431.1		4
24.11	even	2		2880.3.e.e.2431.2		4
40.3	even	4		1600.3.h.n.1599.6		8
40.13	odd	4		1600.3.h.n.1599.3		8
40.19	odd	2		1600.3.b.s.1151.3		4
40.27	even	4		1600.3.h.n.1599.4		8
40.29	even	2		1600.3.b.s.1151.2		4
40.37	odd	4		1600.3.h.n.1599.5		8
60.23	odd	4		900.3.f.e.199.8		8
60.47	odd	4		900.3.f.e.199.1		8
60.59	even	2		900.3.c.k.451.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.3.b.a.11.3	✓	4	4.3	odd	2	inner
20.3.b.a.11.4	yes	4	1.1	even	1	trivial
100.3.b.f.51.1		4	5.4	even	2
100.3.b.f.51.2		4	20.19	odd	2
100.3.d.b.99.1		8	20.3	even	4
100.3.d.b.99.2		8	5.2	odd	4
100.3.d.b.99.7		8	5.3	odd	4
100.3.d.b.99.8		8	20.7	even	4
180.3.c.a.91.1		4	3.2	odd	2
180.3.c.a.91.2		4	12.11	even	2
320.3.b.c.191.2		4	8.3	odd	2
320.3.b.c.191.3		4	8.5	even	2
900.3.c.k.451.3		4	60.59	even	2
900.3.c.k.451.4		4	15.14	odd	2
900.3.f.e.199.1		8	60.47	odd	4
900.3.f.e.199.2		8	15.8	even	4
900.3.f.e.199.7		8	15.2	even	4
900.3.f.e.199.8		8	60.23	odd	4
1280.3.g.e.1151.3		8	16.5	even	4
1280.3.g.e.1151.4		8	16.3	odd	4
1280.3.g.e.1151.5		8	16.11	odd	4
1280.3.g.e.1151.6		8	16.13	even	4
1600.3.b.s.1151.2		4	40.29	even	2
1600.3.b.s.1151.3		4	40.19	odd	2
1600.3.h.n.1599.3		8	40.13	odd	4
1600.3.h.n.1599.4		8	40.27	even	4
1600.3.h.n.1599.5		8	40.37	odd	4
1600.3.h.n.1599.6		8	40.3	even	4
2880.3.e.e.2431.1		4	24.5	odd	2
2880.3.e.e.2431.2		4	24.11	even	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:	\( N \)	\(=\)	\( 20 = 2^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	20.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.618034 + 1.90211i) q^{2} -2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} -2.23607 q^{5} +(4.47214 - 1.45309i) q^{6} -5.25731i q^{7} +(-6.47214 - 4.70228i) q^{8} +3.47214 q^{9} +O(q^{10})\)	\(q+(0.618034 + 1.90211i) q^{2} -2.35114i q^{3} +(-3.23607 + 2.35114i) q^{4} -2.23607 q^{5} +(4.47214 - 1.45309i) q^{6} -5.25731i q^{7} +(-6.47214 - 4.70228i) q^{8} +3.47214 q^{9} +(-1.38197 - 4.25325i) q^{10} +19.9192i q^{11} +(5.52786 + 7.60845i) q^{12} -8.47214 q^{13} +(10.0000 - 3.24920i) q^{14} +5.25731i q^{15} +(4.94427 - 15.2169i) q^{16} +11.8885 q^{17} +(2.14590 + 6.60440i) q^{18} -15.2169i q^{19} +(7.23607 - 5.25731i) q^{20} -12.3607 q^{21} +(-37.8885 + 12.3107i) q^{22} -0.555029i q^{23} +(-11.0557 + 15.2169i) q^{24} +5.00000 q^{25} +(-5.23607 - 16.1150i) q^{26} -29.3238i q^{27} +(12.3607 + 17.0130i) q^{28} -10.9443 q^{29} +(-10.0000 + 3.24920i) q^{30} -8.29451i q^{31} +32.0000 q^{32} +46.8328 q^{33} +(7.34752 + 22.6134i) q^{34} +11.7557i q^{35} +(-11.2361 + 8.16348i) q^{36} -18.3607 q^{37} +(28.9443 - 9.40456i) q^{38} +19.9192i q^{39} +(14.4721 + 10.5146i) q^{40} -14.5836 q^{41} +(-7.63932 - 23.5114i) q^{42} +22.2703i q^{43} +(-46.8328 - 64.4598i) q^{44} -7.76393 q^{45} +(1.05573 - 0.343027i) q^{46} +53.3902i q^{47} +(-35.7771 - 11.6247i) q^{48} +21.3607 q^{49} +(3.09017 + 9.51057i) q^{50} -27.9516i q^{51} +(27.4164 - 19.9192i) q^{52} -66.3607 q^{53} +(55.7771 - 18.1231i) q^{54} -44.5407i q^{55} +(-24.7214 + 34.0260i) q^{56} -35.7771 q^{57} +(-6.76393 - 20.8172i) q^{58} +17.4370i q^{59} +(-12.3607 - 17.0130i) q^{60} +90.1378 q^{61} +(15.7771 - 5.12629i) q^{62} -18.2541i q^{63} +(19.7771 + 60.8676i) q^{64} +18.9443 q^{65} +(28.9443 + 89.0813i) q^{66} +50.2220i q^{67} +(-38.4721 + 27.9516i) q^{68} -1.30495 q^{69} +(-22.3607 + 7.26543i) q^{70} -80.7868i q^{71} +(-22.4721 - 16.3270i) q^{72} -5.55418 q^{73} +(-11.3475 - 34.9241i) q^{74} -11.7557i q^{75} +(35.7771 + 49.2429i) q^{76} +104.721 q^{77} +(-37.8885 + 12.3107i) q^{78} -13.8448i q^{79} +(-11.0557 + 34.0260i) q^{80} -37.6950 q^{81} +(-9.01316 - 27.7396i) q^{82} -76.2155i q^{83} +(40.0000 - 29.0617i) q^{84} -26.5836 q^{85} +(-42.3607 + 13.7638i) q^{86} +25.7315i q^{87} +(93.6656 - 128.920i) q^{88} -111.443 q^{89} +(-4.79837 - 14.7679i) q^{90} +44.5407i q^{91} +(1.30495 + 1.79611i) q^{92} -19.5016 q^{93} +(-101.554 + 32.9970i) q^{94} +34.0260i q^{95} -75.2365i q^{96} -92.8328 q^{97} +(13.2016 + 40.6304i) q^{98} +69.1621i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^4 - 8 * q^8 - 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{4} - 8 q^{8} - 4 q^{9} - 10 q^{10} + 40 q^{12} - 16 q^{13} + 40 q^{14} - 16 q^{16} - 24 q^{17} + 22 q^{18} + 20 q^{20} + 40 q^{21} - 80 q^{22} - 80 q^{24} + 20 q^{25} - 12 q^{26} - 40 q^{28} - 8 q^{29} - 40 q^{30} + 128 q^{32} + 80 q^{33} + 92 q^{34} - 36 q^{36} + 16 q^{37} + 80 q^{38} + 40 q^{40} - 112 q^{41} - 120 q^{42} - 80 q^{44} - 40 q^{45} + 40 q^{46} - 4 q^{49} - 10 q^{50} + 56 q^{52} - 176 q^{53} + 80 q^{54} + 80 q^{56} - 36 q^{58} + 40 q^{60} + 128 q^{61} - 80 q^{62} - 64 q^{64} + 40 q^{65} + 80 q^{66} - 136 q^{68} + 120 q^{69} - 72 q^{72} + 264 q^{73} - 108 q^{74} + 240 q^{77} - 80 q^{78} - 80 q^{80} - 276 q^{81} + 116 q^{82} + 160 q^{84} - 160 q^{85} - 80 q^{86} + 160 q^{88} - 88 q^{89} + 30 q^{90} - 120 q^{92} - 400 q^{93} - 120 q^{94} - 264 q^{97} + 102 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^4 - 8 * q^8 - 4 * q^9 - 10 * q^10 + 40 * q^12 - 16 * q^13 + 40 * q^14 - 16 * q^16 - 24 * q^17 + 22 * q^18 + 20 * q^20 + 40 * q^21 - 80 * q^22 - 80 * q^24 + 20 * q^25 - 12 * q^26 - 40 * q^28 - 8 * q^29 - 40 * q^30 + 128 * q^32 + 80 * q^33 + 92 * q^34 - 36 * q^36 + 16 * q^37 + 80 * q^38 + 40 * q^40 - 112 * q^41 - 120 * q^42 - 80 * q^44 - 40 * q^45 + 40 * q^46 - 4 * q^49 - 10 * q^50 + 56 * q^52 - 176 * q^53 + 80 * q^54 + 80 * q^56 - 36 * q^58 + 40 * q^60 + 128 * q^61 - 80 * q^62 - 64 * q^64 + 40 * q^65 + 80 * q^66 - 136 * q^68 + 120 * q^69 - 72 * q^72 + 264 * q^73 - 108 * q^74 + 240 * q^77 - 80 * q^78 - 80 * q^80 - 276 * q^81 + 116 * q^82 + 160 * q^84 - 160 * q^85 - 80 * q^86 + 160 * q^88 - 88 * q^89 + 30 * q^90 - 120 * q^92 - 400 * q^93 - 120 * q^94 - 264 * q^97 + 102 * q^98

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