LMFDB - Embedded newform 475.2.bc.a.6.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(6,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 70]))

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

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

chi := DirichletCharacter("475.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.bc (of order $45$, degree $24$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$1152$
Relative dimension:	$48$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			6.19
Character	$\chi$	$=$	475.6
Dual form			475.2.bc.a.396.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.730424 - 0.456420i) q^{2} +(-0.0193247 + 0.00554125i) q^{3} +(-0.551542 - 1.13083i) q^{4} +(2.18285 - 0.484947i) q^{5} +(0.0166443 + 0.00477268i) q^{6} +(-1.43830 + 2.49120i) q^{7} +(-0.293334 + 2.79088i) q^{8} +(-2.54380 + 1.58954i) q^{9} +O(q^{10})$	\(q+(-0.730424 - 0.456420i) q^{2} +(-0.0193247 + 0.00554125i) q^{3} +(-0.551542 - 1.13083i) q^{4} +(2.18285 - 0.484947i) q^{5} +(0.0166443 + 0.00477268i) q^{6} +(-1.43830 + 2.49120i) q^{7} +(-0.293334 + 2.79088i) q^{8} +(-2.54380 + 1.58954i) q^{9} +(-1.81574 - 0.642078i) q^{10} +(-3.60347 + 4.00206i) q^{11} +(0.0169246 + 0.0187966i) q^{12} +(-0.125533 - 3.59480i) q^{13} +(2.18760 - 1.16317i) q^{14} +(-0.0394956 + 0.0214671i) q^{15} +(-0.0611315 + 0.0782447i) q^{16} +(-5.24372 + 0.366677i) q^{17} +2.58355 q^{18} +(0.594850 + 4.31812i) q^{19} +(-1.75232 - 2.20096i) q^{20} +(0.0139902 - 0.0561115i) q^{21} +(4.45868 - 1.27851i) q^{22} +(2.99557 - 0.421000i) q^{23} +(-0.00979642 - 0.0555583i) q^{24} +(4.52965 - 2.11713i) q^{25} +(-1.54904 + 2.68302i) q^{26} +(0.0807055 - 0.0896325i) q^{27} +(3.61040 + 0.252464i) q^{28} +(-0.511373 - 0.0357587i) q^{29} +(0.0386465 + 0.00234643i) q^{30} +(-5.07994 + 2.26173i) q^{31} +(5.35440 - 1.94884i) q^{32} +(0.0474594 - 0.0973061i) q^{33} +(3.99750 + 2.12551i) q^{34} +(-1.93148 + 6.13541i) q^{35} +(3.20051 + 1.99990i) q^{36} +(-1.40573 + 4.32640i) q^{37} +(1.53638 - 3.42556i) q^{38} +(0.0223456 + 0.0687726i) q^{39} +(0.713127 + 6.23433i) q^{40} +(0.686032 - 0.878080i) q^{41} +(-0.0358292 + 0.0345998i) q^{42} +(-0.503268 - 2.85417i) q^{43} +(6.51311 + 1.86760i) q^{44} +(-4.78189 + 4.70334i) q^{45} +(-2.38019 - 1.05973i) q^{46} +(-9.90282 - 0.692472i) q^{47} +(0.000747770 - 0.00185080i) q^{48} +(-0.637385 - 1.10398i) q^{49} +(-4.27487 - 0.521020i) q^{50} +(0.0993013 - 0.0361427i) q^{51} +(-3.99586 + 2.12464i) q^{52} +(0.270621 + 0.554856i) q^{53} +(-0.0998593 + 0.0286342i) q^{54} +(-5.92504 + 10.4834i) q^{55} +(-6.53075 - 4.74487i) q^{56} +(-0.0354231 - 0.0801499i) q^{57} +(0.357198 + 0.259520i) q^{58} +(3.60708 + 8.92784i) q^{59} +(0.0460591 + 0.0328227i) q^{60} +(-0.622108 + 0.0874316i) q^{61} +(4.74281 + 0.666558i) q^{62} +(-0.301134 - 8.62335i) q^{63} +(-4.60622 - 0.979083i) q^{64} +(-2.01730 - 7.78602i) q^{65} +(-0.0790779 + 0.0494134i) q^{66} +(-1.23554 - 4.95548i) q^{67} +(3.30678 + 5.72751i) q^{68} +(-0.0555555 + 0.0247349i) q^{69} +(4.21112 - 3.59988i) q^{70} +(9.96193 + 9.62012i) q^{71} +(-3.69005 - 7.56572i) q^{72} +(0.267579 - 7.66246i) q^{73} +(3.00143 - 2.51850i) q^{74} +(-0.0758024 + 0.0660128i) q^{75} +(4.55497 - 3.05430i) q^{76} +(-4.78708 - 14.7331i) q^{77} +(0.0150674 - 0.0604321i) q^{78} +(6.42532 - 1.84243i) q^{79} +(-0.0954962 + 0.200442i) q^{80} +(3.94375 - 8.08588i) q^{81} +(-0.901867 + 0.328253i) q^{82} +(14.9484 - 6.65544i) q^{83} +(-0.0711687 + 0.0151274i) q^{84} +(-11.2684 + 3.34333i) q^{85} +(-0.935102 + 2.31446i) q^{86} +(0.0100803 - 0.00214262i) q^{87} +(-10.1123 - 11.2308i) q^{88} +(4.87579 + 6.24073i) q^{89} +(5.63950 - 1.25289i) q^{90} +(9.13591 + 4.85765i) q^{91} +(-2.12826 - 3.15528i) q^{92} +(0.0856352 - 0.0718565i) q^{93} +(6.91720 + 5.02564i) q^{94} +(3.39253 + 9.13733i) q^{95} +(-0.0926729 + 0.0673308i) q^{96} +(2.07869 - 8.33719i) q^{97} +(-0.0383183 + 1.09729i) q^{98} +(2.80507 - 15.9083i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 9 q^{12} - 18 q^{13} - 18 q^{14} + 27 q^{15} - 30 q^{16} - 36 q^{17} - 144 q^{18} - 18 q^{19} - 54 q^{20} + 9 q^{21} + 6 q^{22} - 24 q^{23} - 120 q^{24} - 90 q^{25} - 24 q^{26} - 9 q^{27} + 54 q^{28} + 9 q^{30} - 45 q^{31} - 138 q^{32} + 54 q^{33} - 18 q^{34} + 45 q^{35} - 72 q^{36} - 36 q^{37} + 93 q^{38} - 36 q^{39} + 57 q^{40} - 18 q^{41} + 36 q^{42} - 252 q^{43} - 42 q^{44} - 90 q^{45} - 69 q^{46} - 18 q^{47} + 6 q^{48} - 486 q^{49} + 21 q^{50} + 12 q^{51} - 36 q^{53} - 120 q^{54} - 3 q^{55} + 234 q^{56} + 90 q^{57} + 180 q^{58} + 18 q^{59} + 69 q^{60} - 90 q^{61} - 144 q^{62} - 27 q^{63} + 93 q^{64} - 72 q^{65} + 42 q^{66} + 54 q^{67} - 48 q^{68} - 57 q^{69} + 12 q^{70} - 60 q^{71} - 318 q^{72} - 36 q^{73} - 66 q^{74} - 132 q^{75} - 48 q^{76} + 222 q^{77} - 39 q^{78} + 6 q^{79} + 129 q^{80} - 84 q^{81} + 120 q^{82} + 45 q^{83} - 63 q^{84} - 18 q^{85} + 72 q^{86} - 33 q^{87} - 45 q^{88} + 18 q^{89} + 57 q^{90} + 45 q^{91} + 324 q^{92} - 78 q^{93} - 24 q^{94} + 81 q^{95} - 132 q^{96} - 96 q^{97} - 153 q^{98} - 6 q^{99}+O(q^{100}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9 - 33 * q^10 - 9 * q^12 - 18 * q^13 - 18 * q^14 + 27 * q^15 - 30 * q^16 - 36 * q^17 - 144 * q^18 - 18 * q^19 - 54 * q^20 + 9 * q^21 + 6 * q^22 - 24 * q^23 - 120 * q^24 - 90 * q^25 - 24 * q^26 - 9 * q^27 + 54 * q^28 + 9 * q^30 - 45 * q^31 - 138 * q^32 + 54 * q^33 - 18 * q^34 + 45 * q^35 - 72 * q^36 - 36 * q^37 + 93 * q^38 - 36 * q^39 + 57 * q^40 - 18 * q^41 + 36 * q^42 - 252 * q^43 - 42 * q^44 - 90 * q^45 - 69 * q^46 - 18 * q^47 + 6 * q^48 - 486 * q^49 + 21 * q^50 + 12 * q^51 - 36 * q^53 - 120 * q^54 - 3 * q^55 + 234 * q^56 + 90 * q^57 + 180 * q^58 + 18 * q^59 + 69 * q^60 - 90 * q^61 - 144 * q^62 - 27 * q^63 + 93 * q^64 - 72 * q^65 + 42 * q^66 + 54 * q^67 - 48 * q^68 - 57 * q^69 + 12 * q^70 - 60 * q^71 - 318 * q^72 - 36 * q^73 - 66 * q^74 - 132 * q^75 - 48 * q^76 + 222 * q^77 - 39 * q^78 + 6 * q^79 + 129 * q^80 - 84 * q^81 + 120 * q^82 + 45 * q^83 - 63 * q^84 - 18 * q^85 + 72 * q^86 - 33 * q^87 - 45 * q^88 + 18 * q^89 + 57 * q^90 + 45 * q^91 + 324 * q^92 - 78 * q^93 - 24 * q^94 + 81 * q^95 - 132 * q^96 - 96 * q^97 - 153 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{2}{5}\right)$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.730424	−	0.456420i	−0.516488	−	0.322737i	0.246508	−	0.969141i	$-0.420717\pi$
$2$	−0.730424	−	0.456420i	−0.516488	−	0.322737i	−0.762996	+	0.646403i	$0.776272\pi$
$3$	−0.0193247	+	0.00554125i	−0.0111571	+	0.00319924i	−0.281211	−	0.959646i	$-0.590736\pi$
$3$	−0.0193247	+	0.00554125i	−0.0111571	+	0.00319924i	0.270054	+	0.962845i	$0.412958\pi$
$4$	−0.551542	−	1.13083i	−0.275771	−	0.565414i
$5$	2.18285	−	0.484947i	0.976199	−	0.216875i
$5$	2.18285	−	0.484947i	0.976199	−	0.216875i
$6$	0.0166443	+	0.00477268i	0.00679502	+	0.00194844i
$7$	−1.43830	+	2.49120i	−0.543624	+	0.941585i	0.455068	+	0.890457i	$0.349615\pi$
$7$	−1.43830	+	2.49120i	−0.543624	+	0.941585i	−0.998692	+	0.0511283i	$0.983718\pi$
$8$	−0.293334	+	2.79088i	−0.103709	+	0.986726i
$9$	−2.54380	+	1.58954i	−0.847934	+	0.529848i
$10$	−1.81574	−	0.642078i	−0.574189	−	0.203043i
$11$	−3.60347	+	4.00206i	−1.08649	+	1.20667i	−0.109362	+	0.994002i	$0.534881\pi$
$11$	−3.60347	+	4.00206i	−1.08649	+	1.20667i	−0.977125	+	0.212664i	$0.931786\pi$
$12$	0.0169246	+	0.0187966i	0.00488570	+	0.00542612i
$13$	−0.125533	−	3.59480i	−0.0348166	−	0.997017i	−0.883590	−	0.468261i	$-0.844881\pi$
$13$	−0.125533	−	3.59480i	−0.0348166	−	0.997017i	0.848774	−	0.528756i	$-0.177341\pi$
$14$	2.18760	−	1.16317i	0.584660	−	0.310869i
$15$	−0.0394956	+	0.0214671i	−0.0101977	+	0.00554279i
$16$	−0.0611315	+	0.0782447i	−0.0152829	+	0.0195612i
$17$	−5.24372	+	0.366677i	−1.27179	+	0.0889322i	−0.689642	−	0.724151i	$-0.742232\pi$
$17$	−5.24372	+	0.366677i	−1.27179	+	0.0889322i	−0.582148	+	0.813083i	$0.697788\pi$
$18$	2.58355			0.608949
$19$	0.594850	+	4.31812i	0.136468	+	0.990644i
$19$	0.594850	+	4.31812i	0.136468	+	0.990644i
$20$	−1.75232	−	2.20096i	−0.391831	−	0.492149i
$21$	0.0139902	−	0.0561115i	0.00305291	−	0.0122445i
$22$	4.45868	−	1.27851i	0.950594	−	0.272578i
$23$	2.99557	−	0.421000i	0.624620	−	0.0877846i	0.180240	−	0.983623i	$-0.442313\pi$
$23$	2.99557	−	0.421000i	0.624620	−	0.0877846i	0.444381	+	0.895838i	$0.353424\pi$
$24$	−0.00979642	−	0.0555583i	−0.00199969	−	0.0113408i
$25$	4.52965	−	2.11713i	0.905931	−	0.423426i
$26$	−1.54904	+	2.68302i	−0.303792	+	0.526184i
$27$	0.0807055	−	0.0896325i	0.0155318	−	0.0172498i
$28$	3.61040	+	0.252464i	0.682301	+	0.0477112i
$29$	−0.511373	−	0.0357587i	−0.0949596	−	0.00664022i	0.0221976	−	0.999754i	$-0.492934\pi$
$29$	−0.511373	−	0.0357587i	−0.0949596	−	0.00664022i	−0.117157	+	0.993113i	$0.537378\pi$
$30$	0.0386465	+	0.00234643i	0.00705586	+	0.000428398i
$31$	−5.07994	+	2.26173i	−0.912384	+	0.406219i	−0.808585	−	0.588379i	$-0.799766\pi$
$31$	−5.07994	+	2.26173i	−0.912384	+	0.406219i	−0.103798	+	0.994598i	$0.533100\pi$
$32$	5.35440	−	1.94884i	0.946533	−	0.344510i
$33$	0.0474594	−	0.0973061i	0.00826162	−	0.0169388i
$34$	3.99750	+	2.12551i	0.685566	+	0.364522i
$35$	−1.93148	+	6.13541i	−0.326480	+	1.03707i
$36$	3.20051	+	1.99990i	0.533419	+	0.333317i
$37$	−1.40573	+	4.32640i	−0.231101	+	0.711256i	0.766514	+	0.642228i	$0.221990\pi$
$37$	−1.40573	+	4.32640i	−0.231101	+	0.711256i	−0.997615	+	0.0690278i	$0.978010\pi$
$38$	1.53638	−	3.42556i	0.249234	−	0.555699i
$39$	0.0223456	+	0.0687726i	0.00357815	+	0.0110124i
$40$	0.713127	+	6.23433i	0.112755	+	0.985733i
$41$	0.686032	−	0.878080i	0.107140	−	0.137133i	−0.731452	−	0.681893i	$-0.761157\pi$
$41$	0.686032	−	0.878080i	0.107140	−	0.137133i	0.838592	+	0.544760i	$0.183379\pi$
$42$	−0.0358292	+	0.0345998i	−0.00552856	+	0.00533887i
$43$	−0.503268	−	2.85417i	−0.0767476	−	0.435257i	−0.998834	−	0.0482736i	$-0.984628\pi$
$43$	−0.503268	−	2.85417i	−0.0767476	−	0.435257i	0.922087	−	0.386984i	$-0.126483\pi$
$44$	6.51311	+	1.86760i	0.981888	+	0.281552i
$45$	−4.78189	+	4.70334i	−0.712842	+	0.701133i
$46$	−2.38019	−	1.05973i	−0.350940	−	0.156249i
$47$	−9.90282	−	0.692472i	−1.44447	−	0.101007i	−0.674119	−	0.738623i	$-0.735477\pi$
$47$	−9.90282	−	0.692472i	−1.44447	−	0.101007i	−0.770355	+	0.637615i	$0.779921\pi$
$48$	0.000747770	−	0.00185080i	0.000107931	−	0.000267139i
$49$	−0.637385	−	1.10398i	−0.0910550	−	0.157712i
$50$	−4.27487	−	0.521020i	−0.604558	−	0.0736834i
$51$	0.0993013	−	0.0361427i	0.0139050	−	0.00506099i
$52$	−3.99586	+	2.12464i	−0.554126	+	0.294634i
$53$	0.270621	+	0.554856i	0.0371727	+	0.0762153i	0.916572	−	0.399869i	$-0.130944\pi$
$53$	0.270621	+	0.554856i	0.0371727	+	0.0762153i	−0.879399	+	0.476085i	$0.842056\pi$
$54$	−0.0998593	+	0.0286342i	−0.0135891	+	0.00389662i
$55$	−5.92504	+	10.4834i	−0.798933	+	1.41358i
$56$	−6.53075	−	4.74487i	−0.872708	−	0.634059i
$57$	−0.0354231	−	0.0801499i	−0.00469190	−	0.0106161i
$58$	0.357198	+	0.259520i	0.0469024	+	0.0340766i
$59$	3.60708	+	8.92784i	0.469602	+	1.16231i	0.957249	+	0.289265i	$0.0934108\pi$
$59$	3.60708	+	8.92784i	0.469602	+	1.16231i	−0.487647	+	0.873041i	$0.662145\pi$
$60$	0.0460591	+	0.0328227i	0.00594620	+	0.00423739i
$61$	−0.622108	+	0.0874316i	−0.0796528	+	0.0111945i	−0.178887	−	0.983870i	$-0.557250\pi$
$61$	−0.622108	+	0.0874316i	−0.0796528	+	0.0111945i	0.0992341	+	0.995064i	$0.468361\pi$
$62$	4.74281	+	0.666558i	0.602337	+	0.0846530i
$63$	−0.301134	−	8.62335i	−0.0379393	−	1.08644i
$64$	−4.60622	−	0.979083i	−0.575778	−	0.122385i
$65$	−2.01730	−	7.78602i	−0.250216	−	0.965737i
$66$	−0.0790779	+	0.0494134i	−0.00973382	+	0.00608237i
$67$	−1.23554	−	4.95548i	−0.150945	−	0.605409i	−0.997342	−	0.0728564i	$-0.976789\pi$
$67$	−1.23554	−	4.95548i	−0.150945	−	0.605409i	0.846397	−	0.532552i	$-0.178767\pi$
$68$	3.30678	+	5.72751i	0.401006	+	0.694563i
$69$	−0.0555555	+	0.0247349i	−0.00668810	+	0.00297773i
$70$	4.21112	−	3.59988i	0.503325	−	0.430269i
$71$	9.96193	+	9.62012i	1.18226	+	1.14170i	0.986962	+	0.160955i	$0.0514575\pi$
$71$	9.96193	+	9.62012i	1.18226	+	1.14170i	0.195302	+	0.980743i	$0.437431\pi$
$72$	−3.69005	−	7.56572i	−0.434876	−	0.891629i
$73$	0.267579	−	7.66246i	0.0313178	−	0.896823i	−0.877487	−	0.479601i	$-0.840781\pi$
$73$	0.267579	−	7.66246i	0.0313178	−	0.896823i	0.908804	−	0.417222i	$-0.136996\pi$
$74$	3.00143	−	2.51850i	0.348910	−	0.292770i
$75$	−0.0758024	+	0.0660128i	−0.00875291	+	0.00762250i
$76$	4.55497	−	3.05430i	0.522490	−	0.350352i
$77$	−4.78708	−	14.7331i	−0.545538	−	1.67899i
$78$	0.0150674	−	0.0604321i	0.00170605	−	0.00684259i
$79$	6.42532	−	1.84243i	0.722905	−	0.207290i	0.106044	−	0.994361i	$-0.466182\pi$
$79$	6.42532	−	1.84243i	0.722905	−	0.207290i	0.616861	+	0.787072i	$0.288404\pi$
$80$	−0.0954962	+	0.200442i	−0.0106768	+	0.0224101i
$81$	3.94375	−	8.08588i	0.438194	−	0.898431i
$82$	−0.901867	+	0.328253i	−0.0995946	+	0.0362495i
$83$	14.9484	−	6.65544i	1.64080	−	0.730530i	0.641468	−	0.767150i	$-0.278326\pi$
$83$	14.9484	−	6.65544i	1.64080	−	0.730530i	0.999329	+	0.0366200i	$0.0116591\pi$
$84$	−0.0711687	+	0.0151274i	−0.00776514	+	0.00165053i
$85$	−11.2684	+	3.34333i	−1.22223	+	0.362635i
$86$	−0.935102	+	2.31446i	−0.100835	+	0.249575i
$87$	0.0100803	−	0.00214262i	0.00108072	−	0.000229713i
$88$	−10.1123	−	11.2308i	−1.07797	−	1.19721i
$89$	4.87579	+	6.24073i	0.516833	+	0.661516i	0.973651	−	0.228045i	$-0.0732332\pi$
$89$	4.87579	+	6.24073i	0.516833	+	0.661516i	−0.456818	+	0.889560i	$0.651011\pi$
$90$	5.63950	−	1.25289i	0.594456	−	0.132066i
$91$	9.13591	+	4.85765i	0.957704	+	0.509220i
$92$	−2.12826	−	3.15528i	−0.221887	−	0.328961i
$93$	0.0856352	−	0.0718565i	0.00887995	−	0.00745117i
$94$	6.91720	+	5.02564i	0.713455	+	0.518355i
$95$	3.39253	+	9.13733i	0.348066	+	0.937470i
$96$	−0.0926729	+	0.0673308i	−0.00945839	+	0.00687192i
$97$	2.07869	−	8.33719i	0.211059	−	0.846513i	−0.767584	−	0.640948i	$-0.778541\pi$
$97$	2.07869	−	8.33719i	0.211059	−	0.846513i	0.978644	−	0.205565i	$-0.0659031\pi$
$98$	−0.0383183	+	1.09729i	−0.00387073	+	0.110843i
$99$	2.80507	−	15.9083i	0.281920	−	1.59885i
$100$	−4.89240	−	3.95457i	−0.489240	−	0.395457i
$101$	−13.4660	+	4.90122i	−1.33992	+	0.487689i	−0.909786	−	0.415078i	$-0.863754\pi$
$101$	−13.4660	+	4.90122i	−1.33992	+	0.487689i	−0.430129	+	0.902767i	$0.641532\pi$
$102$	−0.0890283	−	0.0189235i	−0.00881511	−	0.00187371i
$103$	−8.09253	−	3.60303i	−0.797380	−	0.355017i	−0.0327319	−	0.999464i	$-0.510421\pi$
$103$	−8.09253	−	3.60303i	−0.797380	−	0.355017i	−0.764649	+	0.644448i	$0.777087\pi$
$104$	10.0695	+	0.704127i	0.987394	+	0.0690453i
$105$	0.00332733	−	0.129267i	0.000324714	−	0.0126152i
$106$	0.0555788	−	0.528797i	0.00539829	−	0.0513613i
$107$	−5.91677	+	10.2481i	−0.571995	+	0.990725i	0.424366	+	0.905491i	$0.360497\pi$
$107$	−5.91677	+	10.2481i	−0.571995	+	0.990725i	−0.996361	+	0.0852341i	$0.972836\pi$
$108$	−0.145871	−	0.0418279i	−0.0140365	−	0.00402490i
$109$	−18.2508	−	2.56499i	−1.74811	−	0.245681i	−0.808640	−	0.588304i	$-0.799796\pi$
$109$	−18.2508	−	2.56499i	−1.74811	−	0.245681i	−0.939473	+	0.342623i	$0.888685\pi$
$110$	9.11262	−	4.95301i	0.868854	−	0.472251i
$111$	0.00319161	−	0.0913957i	0.000302934	−	0.00867489i
$112$	−0.106998	−	0.264830i	−0.0101104	−	0.0250241i
$113$	−4.91880	+	15.1385i	−0.462722	+	1.42411i	0.399103	+	0.916906i	$0.369322\pi$
$113$	−4.91880	+	15.1385i	−0.462722	+	1.42411i	−0.861825	+	0.507206i	$0.830678\pi$
$114$	−0.0107081	+	0.0747112i	−0.00100291	+	0.00699735i
$115$	6.33472	−	2.37167i	0.590715	−	0.221160i
$116$	0.241607	+	0.597997i	0.0224326	+	0.0555227i
$117$	6.03342	+	8.94491i	0.557790	+	0.826957i
$118$	1.44014	−	8.16745i	0.132576	−	0.751875i
$119$	6.62856	−	13.5906i	0.607639	−	1.24584i
$120$	−0.0483269	−	0.116525i	−0.00441162	−	0.0106372i
$121$	−1.88167	−	17.9029i	−0.171061	−	1.62753i
$122$	0.494308	+	0.220080i	0.0447526	+	0.0199251i
$123$	−0.00839165	+	0.0207701i	−0.000756650	+	0.00187277i
$124$	5.35943	+	4.49710i	0.481291	+	0.403851i
$125$	8.86085	−	6.81801i	0.792539	−	0.609822i
$126$	−3.71591	+	6.43615i	−0.331040	+	0.573378i
$127$	−4.50414	−	5.76503i	−0.399677	−	0.511564i	0.545505	−	0.838108i	$-0.316338\pi$
$127$	−4.50414	−	5.76503i	−0.399677	−	0.511564i	−0.945182	+	0.326544i	$0.894116\pi$
$128$	−5.28002	−	5.09886i	−0.466692	−	0.450679i
$129$	0.0255412	+	0.0523672i	0.00224878	+	0.00461067i
$130$	−2.08020	+	6.60783i	−0.182446	+	0.579545i
$131$	−1.82959	+	0.127938i	−0.159852	+	0.0111780i	−0.149458	−	0.988768i	$-0.547753\pi$
$131$	−1.82959	+	0.127938i	−0.159852	+	0.0111780i	−0.0103940	+	0.999946i	$0.503309\pi$
$132$	−0.136212			−0.0118558
$133$	−11.6129	−	4.72884i	−1.00696	−	0.410042i
$134$	−1.35931	+	4.18353i	−0.117427	+	0.361402i
$135$	0.132701	−	0.234792i	0.0114211	−	0.0202077i
$136$	0.514808	−	14.7422i	0.0441444	−	1.26413i
$137$	5.45512	+	2.90054i	0.466062	+	0.247810i	0.685857	−	0.727737i	$-0.259428\pi$
$137$	5.45512	+	2.90054i	0.466062	+	0.247810i	−0.219795	+	0.975546i	$0.570539\pi$
$138$	0.0518686	+	0.00728966i	0.00441535	+	0.000620537i
$139$	1.55831	+	1.99455i	0.132174	+	0.169175i	0.849545	−	0.527517i	$-0.176877\pi$
$139$	1.55831	+	1.99455i	0.132174	+	0.169175i	−0.717371	+	0.696692i	$0.754655\pi$
$140$	8.00338	−	1.19976i	0.676409	−	0.101398i
$141$	0.195206	−	0.0414922i	0.0164393	−	0.00349428i
$142$	−2.88562	−	11.5736i	−0.242156	−	0.971234i
$143$	14.8389	+	12.4514i	1.24090	+	1.04123i
$144$	0.0311329	−	0.296210i	0.00259441	−	0.0246842i
$145$	−1.13359	+	0.169933i	−0.0941396	+	0.0141122i
$146$	−3.69274	+	5.47472i	−0.305614	+	0.453091i
$147$	0.0184347	+	0.0178022i	0.00152047	+	0.00146830i
$148$	5.66773	−	0.796548i	0.465885	−	0.0654759i
$149$	−6.46253	−	2.35217i	−0.529431	−	0.192697i	0.0634532	−	0.997985i	$-0.479789\pi$
$149$	−6.46253	−	2.35217i	−0.529431	−	0.192697i	−0.592884	+	0.805288i	$0.702011\pi$
$150$	0.0854974	−	0.0136196i	0.00698084	−	0.00111204i
$151$	−15.6294			−1.27190			−0.635952	−	0.771728i	$-0.719392\pi$
$151$	−15.6294			−1.27190			−0.635952	+	0.771728i	$0.719392\pi$
$152$	−12.2259	+	0.393508i	−0.991648	+	0.0319177i
$153$	12.7561	−	9.26788i	1.03127	−	0.749264i
$154$	−3.22788	+	12.9463i	−0.260110	+	1.04325i
$155$	−9.99191	+	7.40052i	−0.802570	+	0.594424i
$156$	0.0654455	−	0.0632000i	0.00523983	−	0.00506005i
$157$	0.355370	+	2.01540i	0.0283616	+	0.160847i	0.995699	−	0.0926449i	$-0.0295321\pi$
$157$	0.355370	+	2.01540i	0.0283616	+	0.160847i	−0.967338	+	0.253491i	$0.918421\pi$
$158$	−5.53413	−	1.58689i	−0.440272	−	0.126246i
$159$	−0.00830426	−	0.00922281i	−0.000658570	−	0.000731416i
$160$	10.7428	−	6.85063i	0.849290	−	0.541590i
$161$	−3.25972	+	8.06809i	−0.256902	+	0.635855i
$162$	−6.57116	+	4.10612i	−0.516279	+	0.322607i
$163$	−0.519988	+	0.110527i	−0.0407286	+	0.00865713i	−0.228231	−	0.973607i	$-0.573294\pi$
$163$	−0.519988	+	0.110527i	−0.0407286	+	0.00865713i	0.187502	+	0.982264i	$0.439961\pi$
$164$	−1.37133	−	0.291486i	−0.107083	−	0.0227612i
$165$	0.0564083	−	0.235420i	0.00439138	−	0.0183274i
$166$	−13.9563	−	1.96143i	−1.08322	−	0.152237i
$167$	−3.44106	+	3.32299i	−0.266277	+	0.257141i	−0.815795	−	0.578341i	$-0.803700\pi$
$167$	−3.44106	+	3.32299i	−0.266277	+	0.257141i	0.549518	+	0.835482i	$0.314811\pi$
$168$	0.152497	+	0.0555043i	0.0117654	+	0.00428225i
$169$	0.0615246	−	0.00430222i	0.00473266	−	0.000330940i
$170$	9.75670	+	2.70109i	0.748304	+	0.207164i
$171$	−8.37702	−	10.0389i	−0.640607	−	0.767694i
$172$	−2.95001	+	2.14331i	−0.224936	+	0.163426i
$173$	−2.88886	−	1.80516i	−0.219636	−	0.137244i	0.415640	−	0.909529i	$-0.363558\pi$
$173$	−2.88886	−	1.80516i	−0.219636	−	0.137244i	−0.635275	+	0.772286i	$0.719113\pi$
$174$	−0.00834080	−	0.00303580i	−0.000632314	−	0.000230144i
$175$	−1.24078	+	14.3293i	−0.0937944	+	1.08320i
$176$	−0.0928545	−	0.526604i	−0.00699917	−	0.0396943i
$177$	−0.119177	−	0.152540i	−0.00895789	−	0.0114656i
$178$	−0.713004	−	6.78378i	−0.0534419	−	0.508466i
$179$	13.0162	+	5.79517i	0.972874	+	0.433151i	0.830718	−	0.556693i	$-0.187930\pi$
$179$	13.0162	+	5.79517i	0.972874	+	0.433151i	0.142156	+	0.989844i	$0.454597\pi$
$180$	7.95608	+	2.81341i	0.593011	+	0.209699i
$181$	1.69409	+	6.79462i	0.125921	+	0.505040i	0.999821	+	0.0189347i	$0.00602745\pi$
$181$	1.69409	+	6.79462i	0.125921	+	0.505040i	−0.873900	+	0.486106i	$0.838417\pi$
$182$	−4.45596	−	7.71796i	−0.330298	−	0.572093i
$183$	0.0115375	−	0.00513685i	0.000852880	−	0.000379727i
$184$	0.296260	+	8.48379i	0.0218406	+	0.625433i
$185$	−0.970428	+	10.1256i	−0.0713473	+	0.744447i
$186$	−0.0953467	+	0.0134001i	−0.00699116	+	0.000982543i
$187$	17.4281	−	22.3070i	1.27447	−	1.63125i
$188$	4.67875	+	11.5803i	0.341233	+	0.844581i
$189$	0.107214	+	0.329971i	0.00779869	+	0.0240019i
$190$	1.69247	−	8.22254i	0.122785	−	0.596526i
$191$	0.831159	−	2.55804i	0.0601406	−	0.185094i	−0.916473	−	0.400097i	$-0.868976\pi$
$191$	0.831159	−	2.55804i	0.0601406	−	0.185094i	0.976613	+	0.215004i	$0.0689763\pi$
$192$	0.0944390	−	0.00660382i	0.00681555	−	0.000476590i
$193$	11.9838	+	4.36175i	0.862613	+	0.313965i	0.735172	−	0.677881i	$-0.237101\pi$
$193$	11.9838	+	4.36175i	0.862613	+	0.313965i	0.127441	+	0.991846i	$0.459324\pi$
$194$	−5.32358	+	5.14093i	−0.382211	+	0.369097i
$195$	0.0821280	+	0.139284i	0.00588131	+	0.00997431i
$196$	−0.896871	+	1.32967i	−0.0640622	+	0.0949762i
$197$	−1.44100	−	13.7102i	−0.102667	−	0.976808i	−0.917668	−	0.397349i	$-0.869930\pi$
$197$	−1.44100	−	13.7102i	−0.102667	−	0.976808i	0.815001	−	0.579459i	$-0.196736\pi$
$198$	−9.30976	+	10.3395i	−0.661616	+	0.734799i
$199$	8.63085	+	7.24214i	0.611825	+	0.513382i	0.895222	−	0.445621i	$-0.147017\pi$
$199$	8.63085	+	7.24214i	0.611825	+	0.513382i	−0.283397	+	0.959003i	$0.591461\pi$
$200$	4.57996	+	13.2628i	0.323852	+	0.937819i
$201$	0.0513360	+	0.0889165i	0.00362096	+	0.00627169i
$202$	12.0729	+	2.56617i	0.849446	+	0.180555i
$203$	0.824587	−	1.22250i	0.0578747	−	0.0858028i
$204$	−0.0956400	−	0.0923585i	−0.00669614	−	0.00646639i
$205$	1.07168	−	2.24941i	0.0748494	−	0.157105i
$206$	4.26649	+	6.32533i	0.297260	+	0.440706i
$207$	−6.95094	+	5.83253i	−0.483124	+	0.405389i
$208$	0.288948	+	0.209933i	0.0200349	+	0.0145562i
$209$	−19.4249	−	13.1796i	−1.34365	−	0.911651i
$210$	−0.0614306	+	0.0929014i	−0.00423911	+	0.00641081i
$211$	−16.7017	−	10.4364i	−1.14979	−	0.718470i	−0.185327	−	0.982677i	$-0.559334\pi$
$211$	−16.7017	−	10.4364i	−1.14979	−	0.718470i	−0.964466	+	0.264207i	$0.914890\pi$
$212$	0.478187	−	0.612052i	0.0328420	−	0.0420359i
$213$	−0.245818	−	0.130704i	−0.0168432	−	0.00895569i
$214$	8.99920	−	4.78496i	0.615173	−	0.327093i
$215$	−2.48268	−	5.98617i	−0.169317	−	0.408253i
$216$	0.226480	+	0.251532i	0.0154100	+	0.0171146i
$217$	1.67202	−	15.9082i	0.113504	−	1.07992i
$218$	12.1601	+	10.2036i	0.823588	+	0.691073i
$219$	0.0372888	+	0.149557i	0.00251974	+	0.0101061i
$220$	15.1228	+	0.918185i	1.01958	+	0.0619040i
$221$	1.97639	+	18.8041i	0.132946	+	1.26490i
$222$	−0.0440460	+	0.0653009i	−0.00295617	+	0.00438271i
$223$	16.9758	−	9.02621i	1.13679	−	0.604440i	0.209134	−	0.977887i	$-0.432935\pi$
$223$	16.9758	−	9.02621i	1.13679	−	0.604440i	0.927651	+	0.373447i	$0.121824\pi$
$224$	−2.84625	+	16.1419i	−0.190173	+	1.07853i
$225$	−8.15727	+	12.5856i	−0.543818	+	0.839043i
$226$	10.5023	−	8.81250i	0.698604	−	0.586199i
$227$	5.77330	+	17.7684i	0.383187	+	1.17933i	0.937787	+	0.347212i	$0.112872\pi$
$227$	5.77330	+	17.7684i	0.383187	+	1.17933i	−0.554599	+	0.832118i	$0.687128\pi$
$228$	−0.0710985	+	0.0842634i	−0.00470861	+	0.00558048i
$229$	−15.5828	+	11.3216i	−1.02974	+	0.748150i	−0.968257	−	0.249958i	$-0.919583\pi$
$229$	−15.5828	+	11.3216i	−1.02974	+	0.748150i	−0.0614836	+	0.998108i	$0.519583\pi$
$230$	−5.70951	−	1.15896i	−0.376474	−	0.0764197i
$231$	0.174148	+	0.258186i	0.0114581	+	0.0169874i
$232$	0.249801	−	1.41669i	0.0164003	−	0.0930105i
$233$	6.98216	−	14.3156i	0.457417	−	0.937843i	−0.538066	−	0.842903i	$-0.680845\pi$
$233$	6.98216	−	14.3156i	0.457417	−	0.937843i	0.995483	−	0.0949407i	$-0.0302662\pi$
$234$	−0.324321	−	9.28735i	−0.0212016	−	0.607133i
$235$	−21.9522	+	3.29078i	−1.43200	+	0.214667i
$236$	8.10640	−	9.00307i	0.527681	−	0.586050i
$237$	−0.113958	+	0.0712087i	−0.00740235	+	0.00462550i
$238$	−11.0447	+	6.90147i	−0.715919	+	0.447356i
$239$	9.13140	−	10.1414i	0.590661	−	0.655996i	−0.371514	−	0.928427i	$-0.621161\pi$
$239$	9.13140	−	10.1414i	0.590661	−	0.655996i	0.962175	+	0.272432i	$0.0878279\pi$
$240$	0.000734732	−	0.00440264i	4.74267e−5	−	0.000284189i
$241$	0.881822	+	25.2521i	0.0568032	+	1.62663i	0.609177	+	0.793034i	$0.291500\pi$
$241$	0.881822	+	25.2521i	0.0568032	+	1.62663i	−0.552374	+	0.833596i	$0.686278\pi$
$242$	−6.79680	+	13.9355i	−0.436915	+	0.895809i
$243$	−0.0942380	+	0.534450i	−0.00604537	+	0.0342850i
$244$	0.441989	+	0.655275i	0.0282954	+	0.0419497i
$245$	−1.92669	−	2.10073i	−0.123092	−	0.134211i
$246$	0.0156093	−	0.0113408i	0.000995215	−	0.000723066i
$247$	15.4481	−	2.68043i	0.982938	−	0.170552i
$248$	−4.82212	−	14.8410i	−0.306205	−	0.942402i
$249$	−0.251993	+	0.211447i	−0.0159694	+	0.0133999i
$250$	−9.58406	+	0.935775i	−0.606149	+	0.0591836i
$251$	−4.20627	+	23.8550i	−0.265498	+	1.50571i	0.502116	+	0.864800i	$0.332555\pi$
$251$	−4.20627	+	23.8550i	−0.265498	+	1.50571i	−0.767614	+	0.640912i	$0.778556\pi$
$252$	−9.58544	+	5.09667i	−0.603826	+	0.321060i
$253$	−9.10959	+	13.5055i	−0.572715	+	0.849085i
$254$	0.658656	+	6.26669i	0.0413278	+	0.393207i
$255$	0.199232	−	0.127050i	0.0124764	−	0.00795617i
$256$	3.80792	+	15.2727i	0.237995	+	0.954546i
$257$	12.8234	+	10.7601i	0.799900	+	0.671195i	0.948174	−	0.317751i	$-0.102928\pi$
$257$	12.8234	+	10.7601i	0.799900	+	0.671195i	−0.148275	+	0.988946i	$0.547372\pi$
$258$	0.00524552	−	0.0499077i	0.000326572	−	0.00310712i
$259$	−8.75607	−	9.72460i	−0.544076	−	0.604257i
$260$	−7.69202	+	6.57554i	−0.477039	+	0.407798i
$261$	1.35767	−	0.721887i	0.0840378	−	0.0446837i
$262$	1.39477	+	0.741614i	0.0861693	+	0.0458171i
$263$	−12.8427	+	16.4379i	−0.791915	+	1.01361i	0.207460	+	0.978244i	$0.433480\pi$
$263$	−12.8427	+	16.4379i	−0.791915	+	1.01361i	−0.999375	+	0.0353614i	$0.988742\pi$
$264$	0.257649	+	0.160997i	0.0158572	+	0.00990866i
$265$	0.859800	+	1.07993i	0.0528171	+	0.0663395i
$266$	6.32399	+	8.75440i	0.387748	+	0.536767i
$267$	−0.128804	−	0.0935819i	−0.00788270	−	0.00572712i
$268$	−4.92235	+	4.13034i	−0.300680	+	0.252301i
$269$	0.283382	+	0.420131i	0.0172781	+	0.0256159i	0.837578	−	0.546318i	$-0.183971\pi$
$269$	0.283382	+	0.420131i	0.0172781	+	0.0256159i	−0.820300	+	0.571934i	$0.806193\pi$
$270$	−0.204092	+	0.110930i	−0.0124206	+	0.00675101i
$271$	2.89100	+	2.79180i	0.175616	+	0.169590i	0.777271	−	0.629165i	$-0.216603\pi$
$271$	2.89100	+	2.79180i	0.175616	+	0.169590i	−0.601656	+	0.798755i	$0.705492\pi$
$272$	0.291866	−	0.432709i	0.0176970	−	0.0262368i
$273$	−0.203466	−	0.0432480i	−0.0123143	−	0.00261749i
$274$	−2.66069	−	4.60844i	−0.160738	−	0.278406i
$275$	−7.84959	+	25.7570i	−0.473348	+	1.55320i
$276$	0.0586121	+	0.0491814i	0.00352804	+	0.00296037i
$277$	3.18469	−	3.53695i	0.191349	−	0.212515i	−0.639834	−	0.768513i	$-0.720997\pi$
$277$	3.18469	−	3.53695i	0.191349	−	0.212515i	0.831184	+	0.555998i	$0.187664\pi$
$278$	−0.227877	−	2.16811i	−0.0136672	−	0.130034i
$279$	9.32723	−	13.8282i	0.558407	−	0.827872i
$280$	−16.5566	−	7.19026i	−0.989448	−	0.429700i
$281$	7.47754	−	7.22097i	0.446072	−	0.430767i	−0.437388	−	0.899273i	$-0.644096\pi$
$281$	7.47754	−	7.22097i	0.446072	−	0.430767i	0.883460	+	0.468506i	$0.155207\pi$
$282$	−0.161521	−	0.0587888i	−0.00961842	−	0.00350082i
$283$	−5.61763	+	0.392823i	−0.333933	+	0.0233509i	−0.235739	−	0.971816i	$-0.575751\pi$
$283$	−5.61763	+	0.392823i	−0.333933	+	0.0233509i	−0.0981942	+	0.995167i	$0.531307\pi$
$284$	5.38429	−	16.5711i	0.319499	−	0.983316i
$285$	−0.116192	−	0.157777i	−0.00688260	−	0.00934589i
$286$	−5.15568	−	15.8676i	−0.304862	−	0.938268i
$287$	1.20076	+	2.97198i	0.0708785	+	0.175430i
$288$	−10.5228	+	13.4685i	−0.620060	+	0.793640i
$289$	10.5276	−	1.47956i	0.619272	−	0.0870330i
$290$	0.905563	+	0.393270i	0.0531765	+	0.0230936i
$291$	0.00602843	+	0.172632i	0.000353393	+	0.0101199i
$292$	−8.81251	+	3.92358i	−0.515713	+	0.229610i
$293$	10.1998	+	17.6666i	0.595881	+	1.03210i	0.993422	+	0.114511i	$0.0365302\pi$
$293$	10.1998	+	17.6666i	0.595881	+	1.03210i	−0.397541	+	0.917584i	$0.630136\pi$
$294$	−0.00533989	−	0.0214171i	−0.000311428	−	0.00124907i
$295$	12.2032	+	17.7389i	0.710500	+	1.03280i
$296$	−11.6621	−	5.19231i	−0.677847	−	0.301797i
$297$	0.0678948	+	0.645976i	0.00393966	+	0.0374833i
$298$	3.64681	+	4.66771i	0.211254	+	0.270393i
$299$	−1.88945	−	10.7156i	−0.109270	−	0.619701i
$300$	0.116457	+	0.0493107i	0.00672366	+	0.00284696i
$301$	7.83417	+	2.85140i	0.451554	+	0.164352i
$302$	11.4161	+	7.13358i	0.656923	+	0.410491i
$303$	0.233067	−	0.169333i	0.0133893	−	0.00972791i
$304$	−0.374234	−	0.217429i	−0.0214638	−	0.0124704i
$305$	−1.31557	+	0.492539i	−0.0753292	+	0.0282027i
$306$	−13.5474	+	0.947329i	−0.774455	+	0.0541552i
$307$	20.4872	+	7.45674i	1.16927	+	0.425579i	0.852400	−	0.522891i	$-0.175146\pi$
$307$	20.4872	+	7.45674i	1.16927	+	0.425579i	0.316868	+	0.948469i	$0.397369\pi$
$308$	−14.0203	+	13.5393i	−0.798883	+	0.771472i
$309$	0.176351	+	0.0247845i	0.0100322	+	0.00140994i
$310$	10.6761	−	0.845014i	0.606361	−	0.0479936i
$311$	28.7553	+	6.11212i	1.63056	+	0.346587i	0.930158	−	0.367160i	$-0.119670\pi$
$311$	28.7553	+	6.11212i	1.63056	+	0.346587i	0.700404	+	0.713746i	$0.253003\pi$
$312$	−0.198491	+	0.0421906i	−0.0112373	+	0.00238857i
$313$	−6.97490	+	4.35840i	−0.394244	+	0.246351i	−0.712527	−	0.701645i	$-0.752449\pi$
$313$	−6.97490	+	4.35840i	−0.394244	+	0.246351i	0.318283	+	0.947996i	$0.396894\pi$
$314$	0.660299	−	1.63430i	0.0372628	−	0.0922287i
$315$	−4.83920	−	18.6774i	−0.272658	−	1.05235i
$316$	−5.62731	−	6.24976i	−0.316561	−	0.351576i
$317$	23.1232	+	6.63047i	1.29873	+	0.372404i	0.852600	−	0.522564i	$-0.175025\pi$
$317$	23.1232	+	6.63047i	1.29873	+	0.372404i	0.446129	+	0.894969i	$0.352802\pi$
$318$	0.00185616	+	0.0105268i	0.000104088	+	0.000590313i
$319$	1.98583	−	1.91769i	0.111185	−	0.107370i
$320$	−10.5295	+	0.0965830i	−0.588617	+	0.00539915i
$321$	0.0575519	−	0.230828i	0.00321223	−	0.0128836i
$322$	6.06342	−	4.40533i	0.337901	−	0.245499i
$323$	−4.70259	−	22.4249i	−0.261659	−	1.24776i
$324$	−11.3189			−0.628827
$325$	−8.17927	−	16.0174i	−0.453705	−	0.888486i
$326$	0.430258	+	0.156601i	0.0238298	+	0.00867334i
$327$	0.366904	−	0.0515650i	0.0202898	−	0.00285155i
$328$	2.24938	+	2.17220i	0.124201	+	0.119940i
$329$	15.9683	−	23.6739i	0.880359	−	1.30519i
$330$	−0.148652	+	0.146210i	−0.00818304	+	0.00804862i
$331$	0.824885	−	7.84826i	0.0453398	−	0.431379i	−0.948181	−	0.317730i	$-0.897079\pi$
$331$	0.824885	−	7.84826i	0.0453398	−	0.431379i	0.993521	−	0.113649i	$-0.0362540\pi$
$332$	−15.7708	−	13.2333i	−0.865536	−	0.726271i
$333$	−3.30110	−	13.2400i	−0.180899	−	0.725546i
$334$	4.03011	−	0.856627i	0.220518	−	0.0468726i
$335$	−5.10014	−	10.2179i	−0.278651	−	0.558263i
$336$	0.00353519	+	0.00452484i	0.000192860	+	0.000246850i
$337$	−17.8979	−	2.51538i	−0.974960	−	0.137022i	−0.366338	−	0.930482i	$-0.619389\pi$
$337$	−17.8979	−	2.51538i	−0.974960	−	0.137022i	−0.608622	+	0.793460i	$0.708278\pi$
$338$	−0.0469027	−	0.0249386i	−0.00255117	−	0.00135648i
$339$	0.0111678	−	0.319803i	0.000606550	−	0.0173693i
$340$	9.99574	+	10.8987i	0.542095	+	0.591064i
$341$	9.25381	−	28.4803i	0.501122	−	1.54229i
$342$	1.53683	+	11.1561i	0.0831021	+	0.603252i
$343$	−16.4691			−0.889250
$344$	8.11329	−	0.567337i	0.437439	−	0.0305887i
$345$	−0.109274	+	0.0809340i	−0.00588312	+	0.00435734i
$346$	1.28618	+	2.63706i	0.0691455	+	0.141769i
$347$	17.7580	+	17.1487i	0.953298	+	0.920589i	0.996917	−	0.0784594i	$-0.0250001\pi$
$347$	17.7580	+	17.1487i	0.953298	+	0.920589i	−0.0436197	+	0.999048i	$0.513889\pi$
$348$	−0.00798262	−	0.0102173i	−0.000427913	−	0.000547704i
$349$	−5.30919	+	9.19578i	−0.284194	+	0.492239i	−0.972413	−	0.233264i	$-0.925059\pi$
$349$	−5.30919	+	9.19578i	−0.284194	+	0.492239i	0.688219	+	0.725503i	$0.258393\pi$
$350$	7.44649	−	9.90017i	0.398031	−	0.529186i
$351$	−0.332342	−	0.278868i	−0.0177391	−	0.0148849i
$352$	−11.4950	+	28.4512i	−0.612688	+	1.51646i
$353$	−5.77073	−	2.56930i	−0.307145	−	0.136750i	0.247376	−	0.968920i	$-0.420432\pi$
$353$	−5.77073	−	2.56930i	−0.307145	−	0.136750i	−0.554521	+	0.832170i	$0.687098\pi$
$354$	0.0174277	+	0.165813i	0.000926271	+	0.00881288i
$355$	26.4106	+	16.1683i	1.40173	+	0.858122i
$356$	4.36799	−	8.95570i	0.231503	−	0.474651i
$357$	−0.0527858	+	0.299363i	−0.00279372	+	0.0158440i
$358$	−6.86229	−	10.1738i	−0.362683	−	0.537700i
$359$	−3.95115	−	9.77943i	−0.208533	−	0.516138i	0.786278	−	0.617873i	$-0.212005\pi$
$359$	−3.95115	−	9.77943i	−0.208533	−	0.516138i	−0.994812	+	0.101734i	$0.967561\pi$
$360$	−11.7238	−	14.7253i	−0.617898	−	0.776094i
$361$	−18.2923	+	5.13727i	−0.962753	+	0.270383i
$362$	1.86380	−	5.73617i	0.0979589	−	0.301487i
$363$	0.135567	+	0.335540i	0.00711542	+	0.0176113i
$364$	0.454331	−	13.0103i	0.0238134	−	0.681927i
$365$	−3.13180	−	16.8558i	−0.163926	−	0.882271i
$366$	−0.0107719	−	0.00151389i	−0.000563054	−	7.91321e-5i
$367$	−22.9115	−	6.56978i	−1.19597	−	0.342940i	−0.382176	−	0.924090i	$-0.624825\pi$
$367$	−22.9115	−	6.56978i	−1.19597	−	0.342940i	−0.813796	+	0.581150i	$0.802603\pi$
$368$	−0.150183	+	0.260124i	−0.00782881	+	0.0135599i
$369$	−0.349381	+	3.32414i	−0.0181881	+	0.173048i
$370$	5.33034	−	6.95305i	0.277111	−	0.361472i
$371$	−1.77149	−	0.123875i	−0.0919711	−	0.00643125i
$372$	−0.128489	−	0.0572068i	−0.00666183	−	0.00296604i
$373$	6.20041	+	1.31794i	0.321045	+	0.0682403i	0.365616	−	0.930766i	$-0.380859\pi$
$373$	6.20041	+	1.31794i	0.321045	+	0.0682403i	−0.0445702	+	0.999006i	$0.514192\pi$
$374$	−22.9113	+	8.33903i	−1.18471	+	0.431201i
$375$	−0.133453	+	0.180856i	−0.00689146	+	0.00933936i
$376$	4.83744	−	27.4345i	0.249472	−	1.41483i
$377$	−0.0643510	+	1.84277i	−0.00331424	+	0.0949075i
$378$	0.0722936	−	0.289954i	0.00371838	−	0.0149136i
$379$	−14.3802	+	10.4478i	−0.738660	+	0.536668i	−0.892291	−	0.451460i	$-0.850903\pi$
$379$	−14.3802	+	10.4478i	−0.738660	+	0.536668i	0.153631	+	0.988128i	$0.450903\pi$
$380$	8.46163	−	8.87598i	0.434072	−	0.455328i
$381$	0.118986	+	0.0864486i	0.00609586	+	0.00442890i
$382$	−1.77464	+	1.48910i	−0.0907985	+	0.0761890i
$383$	9.21530	+	13.6622i	0.470880	+	0.698108i	0.987414	−	0.158159i	$-0.0505557\pi$
$383$	9.21530	+	13.6622i	0.470880	+	0.698108i	−0.516534	+	0.856267i	$0.672778\pi$
$384$	0.130289	+	0.0692757i	0.00664876	+	0.00353521i
$385$	−17.5942	−	29.8387i	−0.896685	−	1.52072i
$386$	−6.76247	−	8.65557i	−0.344201	−	0.440557i
$387$	5.81705	+	6.46049i	0.295697	+	0.328405i
$388$	−10.5744	+	2.24766i	−0.536834	+	0.114108i
$389$	9.84588	−	24.3694i	0.499206	−	1.23558i	−0.441777	−	0.897125i	$-0.645652\pi$
$389$	9.84588	−	24.3694i	0.499206	−	1.23558i	0.940983	−	0.338453i	$-0.109904\pi$
$390$	0.00358354	−	0.139221i	0.000181459	−	0.00704973i
$391$	−15.5536	+	3.30602i	−0.786578	+	0.167192i
$392$	3.26806	−	1.45503i	0.165062	−	0.0734902i
$393$	0.0346473	−	0.0126106i	0.00174773	−	0.000636120i
$394$	−5.20505	+	10.6719i	−0.262226	+	0.537644i
$395$	13.1320	−	7.13769i	0.660744	−	0.359136i
$396$	−19.5367	+	5.60205i	−0.981755	+	0.281514i
$397$	1.53156	−	6.14275i	0.0768667	−	0.308296i	−0.919540	−	0.392997i	$-0.871438\pi$
$397$	1.53156	−	6.14275i	0.0768667	−	0.308296i	0.996406	+	0.0847017i	$0.0269937\pi$
$398$	−2.99872	−	9.22912i	−0.150312	−	0.462614i
$399$	0.250618	+	0.0270333i	0.0125466	+	0.00135336i
$400$	−0.111250	+	0.483845i	−0.00556251	+	0.0241922i
$401$	29.4324	−	24.6967i	1.46978	−	1.23329i	0.553445	−	0.832886i	$-0.313313\pi$
$401$	29.4324	−	24.6967i	1.46978	−	1.23329i	0.916337	−	0.400408i	$-0.131132\pi$
$402$	0.00308621	−	0.0883776i	0.000153926	−	0.00440787i
$403$	8.76818	+	17.9774i	0.436774	+	0.895519i
$404$	12.9695	+	12.5245i	0.645256	+	0.623116i
$405$	4.68738	−	19.5628i	0.232918	−	0.972081i
$406$	−1.16027	+	0.516586i	−0.0575833	+	0.0256378i
$407$	−12.2490	−	21.2159i	−0.607160	−	1.05163i
$408$	0.0717417	+	0.287740i	0.00355174	+	0.0142453i
$409$	−29.4328	+	18.3916i	−1.45536	+	0.909407i	−0.455540	+	0.890215i	$0.650554\pi$
$409$	−29.4328	+	18.3916i	−1.45536	+	0.909407i	−0.999816	+	0.0191922i	$0.993891\pi$
$410$	−1.80945	+	1.15388i	−0.0893626	+	0.0569863i
$411$	−0.121491	−	0.0258237i	−0.00599270	−	0.00127379i
$412$	0.388964	+	11.1385i	0.0191629	+	0.548753i
$413$	−27.4291	−	3.85491i	−1.34970	−	0.189688i
$414$	7.73922	−	1.08768i	0.380362	−	0.0534564i
$415$	29.4025	−	21.7770i	1.44331	−	1.06899i
$416$	−7.67785	−	19.0033i	−0.376437	−	0.931715i
$417$	−0.0411661	−	0.0299089i	−0.00201591	−	0.00146465i
$418$	8.17299	+	18.4926i	0.399754	+	0.904502i
$419$	−19.1294	−	13.8984i	−0.934534	−	0.678979i	0.0125644	−	0.999921i	$-0.496001\pi$
$419$	−19.1294	−	13.8984i	−0.934534	−	0.678979i	−0.947099	+	0.320942i	$0.896001\pi$
$420$	−0.148014	+	0.0675338i	−0.00722237	+	0.00329531i
$421$	37.9075	−	10.8698i	1.84750	−	0.529761i	0.847498	−	0.530799i	$-0.178108\pi$
$421$	37.9075	−	10.8698i	1.84750	−	0.529761i	0.999999	+	0.00103740i	$0.000330215\pi$
$422$	7.43596	+	15.2460i	0.361977	+	0.742162i
$423$	26.2915	−	13.9794i	1.27834	−	0.679704i
$424$	−1.62792	+	0.592514i	−0.0790587	+	0.0287750i
$425$	−22.9759	+	12.7626i	−1.11450	+	0.619075i
$426$	0.119896	+	0.207666i	0.00580897	+	0.0100614i
$427$	0.676966	−	1.67555i	0.0327607	−	0.0810855i
$428$	14.8522	+	1.03857i	0.717910	+	0.0502011i
$429$	−0.355754	−	0.158392i	−0.0171759	−	0.00764722i
$430$	−0.918797	+	5.50559i	−0.0443083	+	0.265503i
$431$	22.1815	+	6.36044i	1.06845	+	0.306372i	0.763373	−	0.645958i	$-0.223542\pi$
$431$	22.1815	+	6.36044i	1.06845	+	0.306372i	0.305072	+	0.952329i	$0.401319\pi$
$432$	0.00207962	+	0.0117941i	0.000100056	+	0.000567446i
$433$	26.7579	−	25.8398i	1.28590	−	1.24178i	0.331429	−	0.943480i	$-0.392469\pi$
$433$	26.7579	−	25.8398i	1.28590	−	1.24178i	0.954472	−	0.298300i	$-0.0964195\pi$
$434$	−8.48209	+	10.8566i	−0.407153	+	0.521132i
$435$	0.0209646	−	0.00956541i	0.00100518	−	0.000458626i
$436$	7.16554	+	22.0533i	0.343167	+	1.05616i
$437$	3.59985	+	12.6848i	0.172204	+	0.606797i
$438$	0.0410242	−	0.126259i	0.00196021	−	0.00603291i
$439$	6.81631	+	4.25930i	0.325325	+	0.203285i	0.682742	−	0.730659i	$-0.260787\pi$
$439$	6.81631	+	4.25930i	0.325325	+	0.203285i	−0.357418	+	0.933945i	$0.616343\pi$
$440$	−27.5199	−	19.6112i	−1.31196	−	0.934929i
$441$	3.37621	+	1.79516i	0.160772	+	0.0854840i
$442$	7.13895	−	14.6370i	0.339565	−	0.696212i
$443$	−25.2230	+	9.18041i	−1.19838	+	0.436174i	−0.862658	−	0.505787i	$-0.831202\pi$
$443$	−25.2230	+	9.18041i	−1.19838	+	0.436174i	−0.335721	+	0.941962i	$0.608980\pi$
$444$	−0.105113	+	0.0467994i	−0.00498845	+	0.00222100i
$445$	13.6695	+	11.2581i	0.647998	+	0.533683i
$446$	−16.5193	−	1.15514i	−0.782211	−	0.0546975i
$447$	0.137920	+	0.00964431i	0.00652340	+	0.000456160i
$448$	9.06420	−	10.0668i	0.428243	−	0.475612i
$449$	−17.8970	+	30.9985i	−0.844611	+	1.46291i	0.0413477	+	0.999145i	$0.486835\pi$
$449$	−17.8970	+	30.9985i	−0.844611	+	1.46291i	−0.885959	+	0.463764i	$0.846498\pi$
$450$	11.7026	−	5.46972i	0.551666	−	0.257845i
$451$	1.04204	+	5.90968i	0.0490675	+	0.278276i
$452$	19.8320	−	2.78720i	0.932818	−	0.131099i
$453$	0.302033	−	0.0866066i	0.0141908	−	0.00406913i
$454$	3.89289	−	15.6135i	0.182702	−	0.732779i
$455$	22.2980	+	6.17308i	1.04535	+	0.289399i
$456$	0.234080	−	0.0753510i	0.0109618	−	0.00352863i
$457$	3.18149			0.148824			0.0744120	−	0.997228i	$-0.476292\pi$
$457$	3.18149			0.148824			0.0744120	+	0.997228i	$0.476292\pi$
$458$	16.5494	−	1.15725i	0.773304	−	0.0540747i
$459$	−0.390331	+	0.499601i	−0.0182191	+	0.0233194i
$460$	−6.17582	−	5.85540i	−0.287949	−	0.273009i
$461$	−18.4745	+	9.82307i	−0.860443	+	0.457506i	−0.840192	−	0.542289i	$-0.817558\pi$
$461$	−18.4745	+	9.82307i	−0.860443	+	0.457506i	−0.0202513	+	0.999795i	$0.506447\pi$
$462$	−0.00936121	−	0.268070i	−0.000435523	−	0.0124717i
$463$	17.6698	+	19.6243i	0.821184	+	0.912017i	0.997380	−	0.0723382i	$-0.0230461\pi$
$463$	17.6698	+	19.6243i	0.821184	+	0.912017i	−0.176197	+	0.984355i	$0.556379\pi$
$464$	0.0340589	−	0.0378262i	0.00158115	−	0.00175604i
$465$	0.152082	−	0.198380i	0.00705264	−	0.00919966i
$466$	−11.6338	+	7.26963i	−0.538927	+	0.336759i
$467$	−0.325128	+	3.09339i	−0.0150451	+	0.143145i	−0.999466	−	0.0326850i	$-0.989594\pi$
$467$	−0.325128	+	3.09339i	−0.0150451	+	0.143145i	0.984421	+	0.175830i	$0.0562609\pi$
$468$	6.78747	−	11.7563i	0.313751	−	0.543433i
$469$	14.1222	+	4.04947i	0.652101	+	0.186987i
$470$	17.5364	+	7.61574i	0.808892	+	0.351288i
$471$	−0.0180353	−	0.0369778i	−0.000831021	−	0.00170385i
$472$	−25.9746	+	7.44811i	−1.19558	+	0.342827i
$473$	13.2361	+	8.27082i	0.608596	+	0.380293i
$474$	0.115739			0.00531605
$475$	11.8365	+	18.3002i	0.543095	+	0.839671i
$476$	−19.0245			−0.871987
$477$	−1.57037	−	0.981278i	−0.0719025	−	0.0449296i
$478$	−11.2986	+	3.23981i	−0.516784	+	0.148185i
$479$	7.97367	+	16.3485i	0.364326	+	0.746980i	0.999681	−	0.0252403i	$-0.00803508\pi$
$479$	7.97367	+	16.3485i	0.364326	+	0.746980i	−0.635355	+	0.772220i	$0.719146\pi$
$480$	−0.169639	+	0.191914i	−0.00774293	+	0.00875965i
$481$	15.7290	+	4.51022i	0.717180	+	0.205648i
$482$	10.8814	−	18.8472i	0.495636	−	0.858467i
$483$	0.0182856	−	0.173976i	0.000832024	−	0.00791618i
$484$	−19.2072	+	12.0020i	−0.873057	+	0.545546i
$485$	0.494383	−	19.2069i	0.0224488	−	0.872139i
$486$	0.312767	−	0.347363i	0.0141874	−	0.0157567i
$487$	4.41103	+	4.89894i	0.199883	+	0.221992i	0.834750	−	0.550629i	$-0.185612\pi$
$487$	4.41103	+	4.89894i	0.199883	+	0.221992i	−0.634867	+	0.772621i	$0.718945\pi$
$488$	−0.0615261	−	1.76188i	−0.00278516	−	0.0797565i
$489$	0.00943613	−	0.00501728i	0.000426716	−	0.000226889i
$490$	0.448485	+	2.41380i	0.0202605	+	0.109045i
$491$	−8.96488	+	11.4745i	−0.404580	+	0.517838i	−0.946549	−	0.322560i	$-0.895457\pi$
$491$	−8.96488	+	11.4745i	−0.404580	+	0.517838i	0.541969	+	0.840398i	$0.317679\pi$
$492$	0.0281157	−	0.00196604i	0.00126756	−	8.86361e-5i
$493$	2.69461			0.121359
$494$	−12.5071	−	5.09296i	−0.562719	−	0.229143i
$495$	−1.59165	−	36.0858i	−0.0715395	−	1.62193i
$496$	0.133575	−	0.535741i	0.00599771	−	0.0240555i
$497$	−38.2938	+	10.9806i	−1.71771	+	0.492547i
$498$	0.280570	−	0.0394315i	0.0125726	−	0.00176697i
$499$	−4.20784	−	23.8638i	−0.188369	−	1.06829i	−0.921550	−	0.388259i	$-0.873077\pi$
$499$	−4.20784	−	23.8638i	−0.188369	−	1.06829i	0.733182	−	0.680033i	$-0.238034\pi$
$500$	−12.5971	−	6.25968i	−0.563361	−	0.279941i
$501$	0.0480837	−	0.0832835i	0.00214822	−	0.00372083i
$502$	13.9602	−	15.5044i	0.623076	−	0.691996i
$503$	−35.6535	−	2.49314i	−1.58971	−	0.111164i	−0.752706	−	0.658357i	$-0.771252\pi$
$503$	−35.6535	−	2.49314i	−1.58971	−	0.111164i	−0.837006	+	0.547193i	$0.815696\pi$
$504$	24.1551	+	1.68909i	1.07595	+	0.0752380i
$505$	−27.0174	+	17.2289i	−1.20226	+	0.766676i
$506$	12.8180	−	5.70696i	0.569832	−	0.253705i
$507$	−0.00116510		0.000424062i	−5.17440e−5		1.88333e-5i
$508$	−4.03504	+	8.27306i	−0.179026	+	0.367058i
$509$	−31.7815	−	16.8985i	−1.40869	−	0.749015i	−0.421242	−	0.906948i	$-0.638406\pi$
$509$	−31.7815	−	16.8985i	−1.40869	−	0.749015i	−0.987450	+	0.157934i	$0.949517\pi$
$510$	−0.203512	+	0.00186674i	−0.00901167	+	8.26606e-5i
$511$	18.7039	+	11.6875i	0.827410	+	0.517023i
$512$	−0.347047	+	1.06810i	−0.0153375	+	0.0472039i
$513$	0.435051	+	0.295178i	0.0192080	+	0.0130324i
$514$	−4.45538	−	13.7123i	−0.196519	−	0.604822i
$515$	−19.4120	−	3.94041i	−0.855396	−	0.173635i
$516$	0.0451313	−	0.0577654i	0.00198679	−	0.00254298i
$517$	38.4558	−	37.1364i	1.69129	−	1.63326i
$518$	1.95715	+	11.0995i	0.0859920	+	0.487685i
$519$	0.0658290	+	0.0188762i	0.00288957	+	0.000828571i
$520$	22.3216	−	3.34616i	0.978868	−	0.146739i
$521$	14.3473	+	6.38781i	0.628565	+	0.279855i	0.696192	−	0.717855i	$-0.254876\pi$
$521$	14.3473	+	6.38781i	0.628565	+	0.279855i	−0.0676271	+	0.997711i	$0.521543\pi$
$522$	−1.32116	−	0.0923845i	−0.0578256	−	0.00404356i
$523$	2.35143	−	5.82000i	0.102821	−	0.254491i	−0.867000	−	0.498307i	$-0.833955\pi$
$523$	2.35143	−	5.82000i	0.102821	−	0.254491i	0.969821	+	0.243817i	$0.0783995\pi$
$524$	1.15377	+	1.99839i	0.0504028	+	0.0873002i
$525$	−0.0554248	−	0.283785i	−0.00241893	−	0.0123854i
$526$	16.8832	−	6.14498i	0.736143	−	0.267934i
$527$	25.8085	−	13.7226i	1.12423	−	0.597766i
$528$	0.00471243	+	0.00966191i	0.000205082	+	0.000420481i
$529$	−13.3128	+	3.81739i	−0.578818	+	0.165973i
$530$	−0.135118	−	1.18124i	−0.00586916	−	0.0513096i
$531$	−23.3669	−	16.9770i	−1.01404	−	0.736741i
$532$	1.05748	+	15.7403i	0.0458475	+	0.682429i
$533$	−3.24264	−	2.35592i	−0.140454	−	0.102046i
$534$	0.0513692	+	0.127143i	0.00222296	+	0.00550203i
$535$	−7.94560	+	25.2394i	−0.343518	+	1.09120i
$536$	14.1926	−	1.99464i	0.613027	−	0.0861553i
$537$	−0.283645	−	0.0398638i	−0.0122402	−	0.00172025i
$538$	−0.0152330	−	0.436215i	−0.000656740	−	0.0188066i
$539$	6.71501	+	1.42732i	0.289236	+	0.0614790i
$540$	−0.338699	−	0.0205642i	−0.0145753	−	0.000884943i
$541$	34.6913	−	21.6775i	1.49149	−	0.931989i	0.493430	−	0.869785i	$-0.335743\pi$
$541$	34.6913	−	21.6775i	1.49149	−	0.931989i	0.998064	−	0.0622032i	$-0.0198127\pi$
$542$	−0.837420	−	3.35871i	−0.0359703	−	0.144269i
$543$	−0.0703884	−	0.121916i	−0.00302066	−	0.00523193i
$544$	−27.3624	+	12.1825i	−1.17315	+	0.522321i
$545$	−41.0827	+	3.25170i	−1.75979	+	0.139288i
$546$	0.128877	+	0.124455i	0.00551543	+	0.00532619i
$547$	12.4847	+	25.5973i	0.533805	+	1.09446i	0.979902	+	0.199478i	$0.0639247\pi$
$547$	12.4847	+	25.5973i	0.533805	+	1.09446i	−0.446097	+	0.894985i	$0.647186\pi$
$548$	0.271284	−	7.76857i	0.0115887	−	0.331857i
$549$	1.44354	−	1.21128i	0.0616089	−	0.0516960i
$550$	17.4895	−	15.2308i	0.745755	−	0.649443i
$551$	−0.149780	−	2.22944i	−0.00638085	−	0.0949774i
$552$	−0.0527359	−	0.162305i	−0.00224459	−	0.00690814i
$553$	−4.65164	+	18.6567i	−0.197808	+	0.793365i
$554$	−3.94051	+	1.12992i	−0.167416	+	0.0480058i
$555$	−0.0373552	−	0.201051i	−0.00158564	−	0.00853413i
$556$	1.39602	−	2.86225i	0.0592042	−	0.121387i
$557$	9.53142	−	3.46915i	0.403859	−	0.146993i	−0.132100	−	0.991236i	$-0.542172\pi$
$557$	9.53142	−	3.46915i	0.403859	−	0.146993i	0.535960	+	0.844244i	$0.319950\pi$
$558$	−13.1243	+	5.84331i	−0.555595	+	0.247367i
$559$	−10.1970	+	2.16744i	−0.431287	+	0.0916729i
$560$	−0.361989	−	0.526195i	−0.0152968	−	0.0222358i
$561$	−0.213184	+	0.527649i	−0.00900063	+	0.0222773i
$562$	−8.75757	+	1.86148i	−0.369416	+	0.0785217i
$563$	−28.0542	−	31.1573i	−1.18234	−	1.31313i	−0.939295	−	0.343111i	$-0.888519\pi$
$563$	−28.0542	−	31.1573i	−1.18234	−	1.31313i	−0.243048	−	0.970014i	$-0.578147\pi$
$564$	−0.154585	−	0.197859i	−0.00650919	−	0.00833138i
$565$	−3.39563	+	35.4304i	−0.142855	+	1.49057i
$566$	4.28254	+	2.27707i	0.180009	+	0.0957123i
$567$	14.4713	+	21.4545i	0.607736	+	0.901006i
$568$	−29.7708	+	24.9807i	−1.24916	+	1.04817i
$569$	31.1258	+	22.6142i	1.30486	+	0.948038i	0.999991	−	0.00435483i	$-0.00138619\pi$
$569$	31.1258	+	22.6142i	1.30486	+	0.948038i	0.304872	+	0.952393i	$0.401386\pi$
$570$	0.0128567	+	0.168276i	0.000538509	+	0.00704831i
$571$	26.3138	−	19.1181i	1.10120	−	0.800067i	0.119943	−	0.992781i	$-0.461729\pi$
$571$	26.3138	−	19.1181i	1.10120	−	0.800067i	0.981255	+	0.192713i	$0.0617287\pi$
$572$	5.89604	−	23.6477i	0.246526	−	0.988762i
$573$	−0.00188708	+	0.0540390i	−7.88340e−5	+	0.00225751i
$574$	0.479408	−	2.71886i	0.0200101	−	0.113483i
$575$	12.6776	−	8.24900i	0.528692	−	0.344007i
$576$	13.2736	−	4.83120i	0.553067	−	0.201300i
$577$	−15.5803	−	3.31170i	−0.648617	−	0.137868i	−0.128157	−	0.991754i	$-0.540906\pi$
$577$	−15.5803	−	3.31170i	−0.648617	−	0.137868i	−0.520460	+	0.853886i	$0.674239\pi$
$578$	−8.36493	−	3.72431i	−0.347935	−	0.154911i
$579$	−0.255752	−	0.0178839i	−0.0106287	−	0.000743231i
$580$	0.817388	+	1.18817i	0.0339402	+	0.0493361i
$581$	−4.92013	+	46.8119i	−0.204121	+	1.94208i
$582$	0.0743892	−	0.128846i	0.00308353	−	0.00534084i
$583$	−3.19574	−	0.916364i	−0.132354	−	0.0379519i
$584$	21.3065	+	2.99444i	0.881671	+	0.123911i
$585$	17.5078	+	16.5995i	0.723860	+	0.686305i
$586$	0.613192	−	17.5595i	0.0253307	−	0.725378i
$587$	3.89828	+	9.64858i	0.160899	+	0.398239i	0.986000	−	0.166746i	$-0.0533261\pi$
$587$	3.89828	+	9.64858i	0.160899	+	0.398239i	−0.825101	+	0.564986i	$0.808882\pi$
$588$	0.00996371	−	0.0306651i	0.000410896	−	0.00126461i
$589$	−12.7882	−	20.5904i	−0.526930	−	0.848412i
$590$	−0.817167	−	18.5267i	−0.0336422	−	0.762732i
$591$	0.103818	+	0.256959i	0.00427051	+	0.0105699i
$592$	−0.252583	−	0.374470i	−0.0103811	−	0.0153906i
$593$	−1.07216	+	6.08054i	−0.0440285	+	0.249698i	−0.998876	−	0.0473981i	$-0.984907\pi$
$593$	−1.07216	+	6.08054i	−0.0440285	+	0.249698i	0.954848	+	0.297096i	$0.0960182\pi$
$594$	0.245244	−	0.502825i	0.0100625	−	0.0206312i
$595$	7.87844	−	32.8806i	0.322984	−	1.34797i
$596$	0.904457	+	8.60533i	0.0370480	+	0.352488i
$597$	−0.206919	−	0.0921261i	−0.00846862	−	0.00377047i
$598$	−3.51072	+	8.68934i	−0.143564	+	0.355333i
$599$	−4.46357	−	3.74538i	−0.182377	−	0.153032i	0.547029	−	0.837114i	$-0.315759\pi$
$599$	−4.46357	−	3.74538i	−0.182377	−	0.153032i	−0.729406	+	0.684082i	$0.760203\pi$
$600$	−0.161998	−	0.230919i	−0.00661356	−	0.00942725i
$601$	6.82835	−	11.8270i	0.278534	−	0.482435i	−0.692487	−	0.721431i	$-0.743485\pi$
$601$	6.82835	−	11.8270i	0.278534	−	0.482435i	0.971021	+	0.238996i	$0.0768182\pi$
$602$	−4.42083	−	5.65840i	−0.180179	−	0.230619i
$603$	11.0199	+	10.6418i	0.448766	+	0.433368i
$604$	8.62028	+	17.6742i	0.350754	+	0.719153i
$605$	−12.7893	−	38.1667i	−0.519960	−	1.55170i
$606$	−0.247524	+	0.0173086i	−0.0100550	+	0.000703113i
$607$	−25.2435			−1.02460			−0.512301	−	0.858806i	$-0.671207\pi$
$607$	−25.2435			−1.02460			−0.512301	+	0.858806i	$0.671207\pi$
$608$	11.6004	+	21.9617i	0.470458	+	0.890663i
$609$	−0.00916067	+	0.0281937i	−0.000371209	+	0.00114246i
$610$	1.18573	+	0.240689i	0.0480087	+	0.00974520i
$611$	−1.24617	+	35.6855i	−0.0504145	+	1.44368i
$612$	−17.5159	−	9.31338i	−0.708039	−	0.376471i
$613$	−3.09683	−	0.435231i	−0.125080	−	0.0175788i	0.0763554	−	0.997081i	$-0.475672\pi$
$613$	−3.09683	−	0.435231i	−0.125080	−	0.0175788i	−0.201435	+	0.979502i	$0.564561\pi$
$614$	−11.5610	−	14.7974i	−0.466563	−	0.597173i
$615$	−0.00824533	+	0.0494074i	−0.000332484	+	0.00199230i
$616$	42.5226	−	9.03846i	1.71328	−	0.364170i
$617$	6.57815	+	26.3835i	0.264826	+	1.06216i	0.944465	+	0.328613i	$0.106581\pi$
$617$	6.57815	+	26.3835i	0.264826	+	1.06216i	−0.679638	+	0.733547i	$0.737863\pi$
$618$	−0.117499	−	0.0985930i	−0.00472649	−	0.00396599i
$619$	−1.69725	+	16.1483i	−0.0682182	+	0.649053i	0.905974	+	0.423333i	$0.139140\pi$
$619$	−1.69725	+	16.1483i	−0.0682182	+	0.649053i	−0.974192	+	0.225720i	$0.927527\pi$
$620$	13.8797	+	7.21744i	0.557421	+	0.289859i
$621$	0.204024	−	0.302478i	0.00818719	−	0.0121380i
$622$	−18.2139	−	17.5889i	−0.730309	−	0.705251i
$623$	−22.5597	+	3.17056i	−0.903836	+	0.127026i
$624$	−0.00674711	−	0.00245575i	−0.000270100	−	9.83085e-5i
$625$	16.0355	−	19.1797i	0.641421	−	0.767189i
$626$	7.08389			0.283129
$627$	0.448411	+	0.147053i	0.0179078	+	0.00587272i
$628$	2.08307	−	1.51344i	0.0831237	−	0.0603929i
$629$	5.78488	−	23.2019i	0.230658	−	0.925120i
$630$	−4.99008	+	15.8512i	−0.198810	+	0.631525i
$631$	20.7790	−	20.0660i	0.827197	−	0.798815i	−0.154753	−	0.987953i	$-0.549458\pi$
$631$	20.7790	−	20.0660i	0.827197	−	0.798815i	0.981950	+	0.189138i	$0.0605694\pi$
$632$	3.25725	+	18.4728i	0.129566	+	0.734807i
$633$	0.380585	+	0.109131i	0.0151269	+	0.00433757i
$634$	−13.8635	−	15.3969i	−0.550589	−	0.611491i
$635$	−12.6276	−	10.3999i	−0.501110	−	0.412708i
$636$	−0.00584927	+	0.0144775i	−0.000231939	+	0.000574068i
$637$	−3.88858	+	2.42986i	−0.154071	+	0.0962745i
$638$	−2.32577	+	0.494357i	−0.0920780	+	0.0195718i
$639$	−40.6328	−	8.63676i	−1.60741	−	0.341665i
$640$	−13.9982	−	8.56950i	−0.553326	−	0.338739i
$641$	−31.0617	−	4.36543i	−1.22686	−	0.172424i	−0.504176	−	0.863601i	$-0.668204\pi$
$641$	−31.0617	−	4.36543i	−1.22686	−	0.172424i	−0.722686	+	0.691177i	$0.757093\pi$
$642$	−0.147392	+	0.142335i	−0.00581709	+	0.00561750i
$643$	30.1976	+	10.9910i	1.19088	+	0.433444i	0.860032	−	0.510241i	$-0.170444\pi$
$643$	30.1976	+	10.9910i	1.19088	+	0.433444i	0.330846	+	0.943685i	$0.392666\pi$
$644$	10.9215	−	0.763706i	0.430367	−	0.0300942i
$645$	0.0811478	+	0.101923i	0.00319519	+	0.00401323i
$646$	−6.80029	+	18.5260i	−0.267554	+	0.728897i
$647$	−32.1929	+	23.3895i	−1.26564	+	0.919538i	−0.999020	−	0.0442651i	$-0.985905\pi$
$647$	−32.1929	+	23.3895i	−1.26564	+	0.919538i	−0.266616	+	0.963803i	$0.585905\pi$
$648$	21.4099	+	13.3784i	0.841060	+	0.525553i
$649$	−48.7278	−	17.7355i	−1.91273	−	0.696177i
$650$	−1.33632	+	15.4327i	−0.0524149	+	0.605320i
$651$	0.0558401	+	0.316685i	0.00218855	+	0.0124119i
$652$	0.411782	+	0.527057i	0.0161266	+	0.0206411i
$653$	−2.36060	−	22.4596i	−0.0923774	−	0.878913i	−0.938350	−	0.345686i	$-0.887646\pi$
$653$	−2.36060	−	22.4596i	−0.0923774	−	0.878913i	0.845973	−	0.533226i	$-0.179021\pi$
$654$	−0.291531	−	0.129798i	−0.0113998	−	0.00507550i
$655$	−3.93168	+	1.16652i	−0.153624	+	0.0455799i
$656$	0.0267670	+	0.107357i	0.00104508	+	0.00419157i
$657$	11.4992	+	19.9171i	0.448625	+	0.777041i
$658$	−22.4688	+	10.0038i	−0.875927	+	0.389988i
$659$	0.0503530	+	1.44192i	0.00196147	+	0.0561693i	0.999977	−	0.00680107i	$-0.00216487\pi$
$659$	0.0503530	+	1.44192i	0.00196147	+	0.0561693i	−0.998015	+	0.0629704i	$0.979943\pi$
$660$	−0.297331	+	0.0660557i	−0.0115736	+	0.00257122i
$661$	11.2537	−	1.58161i	0.437719	−	0.0615174i	0.0831280	−	0.996539i	$-0.473509\pi$
$661$	11.2537	−	1.58161i	0.437719	−	0.0615174i	0.354591	+	0.935021i	$0.384620\pi$
$662$	−4.18462	+	5.35606i	−0.162640	+	0.208169i
$663$	−0.142391	−	0.352431i	−0.00553002	−	0.0136873i
$664$	14.1897	+	43.6714i	0.550667	+	1.69478i
$665$	−27.6424	−	4.69071i	−1.07192	−	0.181898i
$666$	−3.63178	+	11.1775i	−0.140729	+	0.433119i
$667$	−1.54691	+	0.108170i	−0.0598966	+	0.00418838i
$668$	5.65562	+	2.05848i	0.218823	+	0.0796449i
$669$	−0.278035	+	0.268496i	−0.0107495	+	0.0103806i
$670$	−0.938382	+	9.79121i	−0.0362528	+	0.378267i
$671$	1.89184	−	2.80477i	0.0730338	−	0.108277i
$672$	−0.0344435	−	0.327708i	−0.00132869	−	0.0126416i
$673$	12.4187	−	13.7924i	0.478705	−	0.531656i	−0.454621	−	0.890685i	$-0.650225\pi$
$673$	12.4187	−	13.7924i	0.478705	−	0.531656i	0.933327	+	0.359029i	$0.116892\pi$
$674$	11.9250	+	10.0062i	0.459333	+	0.385426i
$675$	0.175804	−	0.576868i	0.00676670	−	0.0222037i
$676$	−0.0387985	−	0.0672009i	−0.00149225	−	0.00258465i
$677$	−14.4606	−	3.07369i	−0.555766	−	0.118132i	−0.0785376	−	0.996911i	$-0.525025\pi$
$677$	−14.4606	−	3.07369i	−0.555766	−	0.118132i	−0.477228	+	0.878780i	$0.658358\pi$
$678$	−0.154122	+	0.228495i	−0.00591900	+	0.00877528i
$679$	17.7798	+	17.1698i	0.682327	+	0.658916i
$680$	−6.02542	−	32.4296i	−0.231064	−	1.24362i
$681$	−0.210026	−	0.311377i	−0.00804822	−	0.0119320i
$682$	−19.7582	+	16.5791i	−0.756580	+	0.634846i
$683$	−25.0921	−	18.2305i	−0.960121	−	0.697569i	−0.00694251	−	0.999976i	$-0.502210\pi$
$683$	−25.0921	−	18.2305i	−0.960121	−	0.697569i	−0.953179	+	0.302407i	$0.902210\pi$
$684$	−6.73199	+	15.0098i	−0.257404	+	0.573916i
$685$	13.3143	+	3.68599i	0.508713	+	0.140834i
$686$	12.0295	+	7.51684i	0.459287	+	0.286994i
$687$	0.238396	−	0.305134i	0.00909539	−	0.0116416i
$688$	0.254089	+	0.135102i	0.00968707	+	0.00515071i
$689$	1.96062	−	1.04248i	0.0746937	−	0.0397154i
$690$	0.116756	−	0.00924129i	0.00444484	−	0.000351810i
$691$	17.8140	+	19.7844i	0.677676	+	0.752635i	0.979657	−	0.200679i	$-0.0643147\pi$
$691$	17.8140	+	19.7844i	0.677676	+	0.752635i	−0.301981	+	0.953314i	$0.597648\pi$
$692$	−0.447998	+	4.26242i	−0.0170303	+	0.162033i
$693$	35.5963	+	29.8688i	1.35219	+	1.13462i
$694$	−5.14386	−	20.6309i	−0.195258	−	0.783138i
$695$	4.36880	+	3.59809i	0.165718	+	0.136483i
$696$	0.00302294	+	0.0287613i	0.000114584	+	0.00109019i
$697$	−3.27539	+	4.85596i	−0.124064	+	0.183933i
$698$	8.07509	−	4.29360i	0.305647	−	0.162515i
$699$	−0.0556017	+	0.315333i	−0.00210305	+	0.0119270i
$700$	16.8884	−	6.50011i	0.638320	−	0.245681i
$701$	−12.6120	+	10.5827i	−0.476349	+	0.399704i	−0.849104	−	0.528226i	$-0.822858\pi$
$701$	−12.6120	+	10.5827i	−0.476349	+	0.399704i	0.372755	+	0.927930i	$0.378413\pi$
$702$	0.115470	+	0.355379i	0.00435812	+	0.0134129i
$703$	−19.5181	−	3.49656i	−0.736139	−	0.131875i
$704$	20.5167	−	14.9063i	0.773254	−	0.561802i
$705$	0.405983	−	0.185236i	0.0152902	−	0.00697638i
$706$	3.04241	+	4.51055i	0.114502	+	0.169757i
$707$	7.15814	−	40.5958i	0.269210	−	1.52676i
$708$	−0.106765	+	0.218901i	−0.00401247	+	0.00822679i
$709$	1.31022	+	37.5197i	0.0492062	+	1.40908i	0.733408	+	0.679788i	$0.237928\pi$
$709$	1.31022	+	37.5197i	0.0492062	+	1.40908i	−0.684202	+	0.729292i	$0.739849\pi$
$710$	−11.9114	−	23.8640i	−0.447029	−	0.895601i
$711$	−13.4161	+	14.9001i	−0.503144	+	0.558798i
$712$	−18.8474	+	11.7771i	−0.706335	+	0.441367i
$713$	−14.2651	+	8.91384i	−0.534233	+	0.333826i
$714$	0.175191	−	0.194570i	0.00655637	−	0.00728159i
$715$	38.4294	+	19.9833i	1.43718	+	0.747334i
$716$	−0.625617	−	17.9153i	−0.0233804	−	0.669527i
$717$	−0.120265	+	0.246579i	−0.00449137	+	0.00920867i
$718$	−1.57751	+	8.94651i	−0.0588722	+	0.333881i
$719$	22.7525	+	33.7320i	0.848527	+	1.25799i	0.964325	+	0.264720i	$0.0852794\pi$
$719$	22.7525	+	33.7320i	0.848527	+	1.25799i	−0.115799	+	0.993273i	$0.536943\pi$
$720$	−0.0756876	−	0.661680i	−0.00282071	−	0.0246593i
$721$	20.6153	−	14.9779i	0.767754	−	0.557806i
$722$	15.7059	+	4.59658i	0.584513	+	0.171067i
$723$	−0.156969	−	0.483101i	−0.00583775	−	0.0179667i
$724$	6.74919	−	5.66324i	0.250832	−	0.210473i
$725$	−2.39205	+	0.920669i	−0.0888384	+	0.0341928i
$726$	0.0541256	−	0.306962i	0.00200879	−	0.0113924i
$727$	−35.5370	+	18.8953i	−1.31799	+	0.700790i	−0.971450	−	0.237244i	$-0.923756\pi$
$727$	−35.5370	+	18.8953i	−1.31799	+	0.700790i	−0.346544	+	0.938034i	$0.612645\pi$
$728$	−16.2370	+	24.0724i	−0.601783	+	0.892181i
$729$	2.81999	+	26.8304i	0.104444	+	0.993718i
$730$	−5.40575	+	13.7413i	−0.200076	+	0.508587i
$731$	3.68556	+	14.7820i	0.136315	+	0.546731i
$732$	−0.0121723	−	0.0102138i	−0.000449902	−	0.000377513i
$733$	4.29164	−	40.8323i	0.158515	−	1.50817i	−0.569146	−	0.822237i	$-0.692726\pi$
$733$	4.29164	−	40.8323i	0.158515	−	1.50817i	0.727661	−	0.685937i	$-0.240607\pi$
$734$	13.7366	+	15.2560i	0.507026	+	0.563109i
$735$	0.0488733	+	0.0299196i	0.00180272	+	0.00110360i
$736$	15.2190	−	8.09210i	0.560981	−	0.298279i
$737$	24.2844	+	12.9122i	0.894526	+	0.475628i
$738$	1.77240	−	2.26857i	0.0652429	−	0.0835071i
$739$	−25.0060	−	15.6255i	−0.919862	−	0.574794i	−0.0147147	−	0.999892i	$-0.504684\pi$
$739$	−25.0060	−	15.6255i	−0.919862	−	0.574794i	−0.905147	+	0.425098i	$0.860240\pi$
$740$	11.9855	−	4.48729i	0.440597	−	0.164956i
$741$	−0.283676	+	0.137400i	−0.0104211	+	0.00504752i
$742$	1.23740	+	0.899024i	0.0454264	+	0.0330042i
$743$	−2.57376	+	2.15964i	−0.0944221	+	0.0792296i	−0.688777	−	0.724973i	$-0.741852\pi$
$743$	−2.57376	+	2.15964i	−0.0944221	+	0.0792296i	0.594355	+	0.804203i	$0.297408\pi$
$744$	0.175423	+	0.260076i	0.00643133	+	0.00953484i
$745$	−15.2474	−	2.00044i	−0.558621	−	0.0732906i
$746$	−3.92740	−	3.79265i	−0.143792	−	0.138859i
$747$	−27.4466	+	40.6912i	−1.00422	+	1.48881i
$748$	−34.8377	−	7.40499i	−1.27379	−	0.270753i
$749$	−17.0201	−	29.4797i	−0.621901	−	1.07716i
$750$	0.180023	−	0.0711912i	0.00657352	−	0.00259954i
$751$	16.1911	+	13.5860i	0.590823	+	0.495760i	0.888481	−	0.458913i	$-0.151761\pi$
$751$	16.1911	+	13.5860i	0.590823	+	0.495760i	−0.297658	+	0.954673i	$0.596205\pi$
$752$	0.659556	−	0.732511i	0.0240515	−	0.0267119i
$753$	−0.0509017	−	0.484297i	−0.00185496	−	0.0176488i
$754$	0.888081	−	1.31663i	0.0323420	−	0.0479490i
$755$	−34.1167	+	7.57944i	−1.24163	+	0.275844i
$756$	0.314008	−	0.303234i	0.0114204	−	0.0110285i
$757$	47.7055	+	17.3634i	1.73389	+	0.631083i	0.998895	−	0.0469953i	$-0.0149646\pi$
$757$	47.7055	+	17.3634i	1.73389	+	0.631083i	0.734990	+	0.678078i	$0.237187\pi$
$758$	15.2722	−	1.06794i	0.554712	−	0.0387892i
$759$	0.101202	−	0.311468i	0.00367340	−	0.0113056i
$760$	−26.4964	+	6.78786i	−0.961124	+	0.246221i
$761$	−11.4184	−	35.1421i	−0.413916	−	1.27390i	−0.913217	−	0.407473i	$-0.866410\pi$
$761$	−11.4184	−	35.1421i	−0.413916	−	1.27390i	0.499302	−	0.866428i	$-0.333590\pi$
$762$	−0.0474536	−	0.117452i	−0.00171906	−	0.00425483i
$763$	32.6400	−	41.7773i	1.18165	−	1.51244i
$764$	−3.35113	+	0.470970i	−0.121240	+	0.0170391i
$765$	23.3503	−	26.4164i	0.844232	−	0.955088i
$766$	−0.495361	−	14.1853i	−0.0178981	−	0.512535i
$767$

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.bc (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.730424 - 0.456420i) q^{2} +(-0.0193247 + 0.00554125i) q^{3} +(-0.551542 - 1.13083i) q^{4} +(2.18285 - 0.484947i) q^{5} +(0.0166443 + 0.00477268i) q^{6} +(-1.43830 + 2.49120i) q^{7} +(-0.293334 + 2.79088i) q^{8} +(-2.54380 + 1.58954i) q^{9} +O(q^{10})\)	\(q+(-0.730424 - 0.456420i) q^{2} +(-0.0193247 + 0.00554125i) q^{3} +(-0.551542 - 1.13083i) q^{4} +(2.18285 - 0.484947i) q^{5} +(0.0166443 + 0.00477268i) q^{6} +(-1.43830 + 2.49120i) q^{7} +(-0.293334 + 2.79088i) q^{8} +(-2.54380 + 1.58954i) q^{9} +(-1.81574 - 0.642078i) q^{10} +(-3.60347 + 4.00206i) q^{11} +(0.0169246 + 0.0187966i) q^{12} +(-0.125533 - 3.59480i) q^{13} +(2.18760 - 1.16317i) q^{14} +(-0.0394956 + 0.0214671i) q^{15} +(-0.0611315 + 0.0782447i) q^{16} +(-5.24372 + 0.366677i) q^{17} +2.58355 q^{18} +(0.594850 + 4.31812i) q^{19} +(-1.75232 - 2.20096i) q^{20} +(0.0139902 - 0.0561115i) q^{21} +(4.45868 - 1.27851i) q^{22} +(2.99557 - 0.421000i) q^{23} +(-0.00979642 - 0.0555583i) q^{24} +(4.52965 - 2.11713i) q^{25} +(-1.54904 + 2.68302i) q^{26} +(0.0807055 - 0.0896325i) q^{27} +(3.61040 + 0.252464i) q^{28} +(-0.511373 - 0.0357587i) q^{29} +(0.0386465 + 0.00234643i) q^{30} +(-5.07994 + 2.26173i) q^{31} +(5.35440 - 1.94884i) q^{32} +(0.0474594 - 0.0973061i) q^{33} +(3.99750 + 2.12551i) q^{34} +(-1.93148 + 6.13541i) q^{35} +(3.20051 + 1.99990i) q^{36} +(-1.40573 + 4.32640i) q^{37} +(1.53638 - 3.42556i) q^{38} +(0.0223456 + 0.0687726i) q^{39} +(0.713127 + 6.23433i) q^{40} +(0.686032 - 0.878080i) q^{41} +(-0.0358292 + 0.0345998i) q^{42} +(-0.503268 - 2.85417i) q^{43} +(6.51311 + 1.86760i) q^{44} +(-4.78189 + 4.70334i) q^{45} +(-2.38019 - 1.05973i) q^{46} +(-9.90282 - 0.692472i) q^{47} +(0.000747770 - 0.00185080i) q^{48} +(-0.637385 - 1.10398i) q^{49} +(-4.27487 - 0.521020i) q^{50} +(0.0993013 - 0.0361427i) q^{51} +(-3.99586 + 2.12464i) q^{52} +(0.270621 + 0.554856i) q^{53} +(-0.0998593 + 0.0286342i) q^{54} +(-5.92504 + 10.4834i) q^{55} +(-6.53075 - 4.74487i) q^{56} +(-0.0354231 - 0.0801499i) q^{57} +(0.357198 + 0.259520i) q^{58} +(3.60708 + 8.92784i) q^{59} +(0.0460591 + 0.0328227i) q^{60} +(-0.622108 + 0.0874316i) q^{61} +(4.74281 + 0.666558i) q^{62} +(-0.301134 - 8.62335i) q^{63} +(-4.60622 - 0.979083i) q^{64} +(-2.01730 - 7.78602i) q^{65} +(-0.0790779 + 0.0494134i) q^{66} +(-1.23554 - 4.95548i) q^{67} +(3.30678 + 5.72751i) q^{68} +(-0.0555555 + 0.0247349i) q^{69} +(4.21112 - 3.59988i) q^{70} +(9.96193 + 9.62012i) q^{71} +(-3.69005 - 7.56572i) q^{72} +(0.267579 - 7.66246i) q^{73} +(3.00143 - 2.51850i) q^{74} +(-0.0758024 + 0.0660128i) q^{75} +(4.55497 - 3.05430i) q^{76} +(-4.78708 - 14.7331i) q^{77} +(0.0150674 - 0.0604321i) q^{78} +(6.42532 - 1.84243i) q^{79} +(-0.0954962 + 0.200442i) q^{80} +(3.94375 - 8.08588i) q^{81} +(-0.901867 + 0.328253i) q^{82} +(14.9484 - 6.65544i) q^{83} +(-0.0711687 + 0.0151274i) q^{84} +(-11.2684 + 3.34333i) q^{85} +(-0.935102 + 2.31446i) q^{86} +(0.0100803 - 0.00214262i) q^{87} +(-10.1123 - 11.2308i) q^{88} +(4.87579 + 6.24073i) q^{89} +(5.63950 - 1.25289i) q^{90} +(9.13591 + 4.85765i) q^{91} +(-2.12826 - 3.15528i) q^{92} +(0.0856352 - 0.0718565i) q^{93} +(6.91720 + 5.02564i) q^{94} +(3.39253 + 9.13733i) q^{95} +(-0.0926729 + 0.0673308i) q^{96} +(2.07869 - 8.33719i) q^{97} +(-0.0383183 + 1.09729i) q^{98} +(2.80507 - 15.9083i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9	\( 1152 q - 18 q^{2} - 18 q^{3} - 18 q^{4} - 24 q^{5} - 18 q^{6} - 30 q^{7} - 9 q^{8} - 18 q^{9} - 33 q^{10} - 9 q^{12} - 18 q^{13} - 18 q^{14} + 27 q^{15} - 30 q^{16} - 36 q^{17} - 144 q^{18} - 18 q^{19} - 54 q^{20} + 9 q^{21} + 6 q^{22} - 24 q^{23} - 120 q^{24} - 90 q^{25} - 24 q^{26} - 9 q^{27} + 54 q^{28} + 9 q^{30} - 45 q^{31} - 138 q^{32} + 54 q^{33} - 18 q^{34} + 45 q^{35} - 72 q^{36} - 36 q^{37} + 93 q^{38} - 36 q^{39} + 57 q^{40} - 18 q^{41} + 36 q^{42} - 252 q^{43} - 42 q^{44} - 90 q^{45} - 69 q^{46} - 18 q^{47} + 6 q^{48} - 486 q^{49} + 21 q^{50} + 12 q^{51} - 36 q^{53} - 120 q^{54} - 3 q^{55} + 234 q^{56} + 90 q^{57} + 180 q^{58} + 18 q^{59} + 69 q^{60} - 90 q^{61} - 144 q^{62} - 27 q^{63} + 93 q^{64} - 72 q^{65} + 42 q^{66} + 54 q^{67} - 48 q^{68} - 57 q^{69} + 12 q^{70} - 60 q^{71} - 318 q^{72} - 36 q^{73} - 66 q^{74} - 132 q^{75} - 48 q^{76} + 222 q^{77} - 39 q^{78} + 6 q^{79} + 129 q^{80} - 84 q^{81} + 120 q^{82} + 45 q^{83} - 63 q^{84} - 18 q^{85} + 72 q^{86} - 33 q^{87} - 45 q^{88} + 18 q^{89} + 57 q^{90} + 45 q^{91} + 324 q^{92} - 78 q^{93} - 24 q^{94} + 81 q^{95} - 132 q^{96} - 96 q^{97} - 153 q^{98} - 6 q^{99}+O(q^{100}) \) 1152 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 24 * q^5 - 18 * q^6 - 30 * q^7 - 9 * q^8 - 18 * q^9 - 33 * q^10 - 9 * q^12 - 18 * q^13 - 18 * q^14 + 27 * q^15 - 30 * q^16 - 36 * q^17 - 144 * q^18 - 18 * q^19 - 54 * q^20 + 9 * q^21 + 6 * q^22 - 24 * q^23 - 120 * q^24 - 90 * q^25 - 24 * q^26 - 9 * q^27 + 54 * q^28 + 9 * q^30 - 45 * q^31 - 138 * q^32 + 54 * q^33 - 18 * q^34 + 45 * q^35 - 72 * q^36 - 36 * q^37 + 93 * q^38 - 36 * q^39 + 57 * q^40 - 18 * q^41 + 36 * q^42 - 252 * q^43 - 42 * q^44 - 90 * q^45 - 69 * q^46 - 18 * q^47 + 6 * q^48 - 486 * q^49 + 21 * q^50 + 12 * q^51 - 36 * q^53 - 120 * q^54 - 3 * q^55 + 234 * q^56 + 90 * q^57 + 180 * q^58 + 18 * q^59 + 69 * q^60 - 90 * q^61 - 144 * q^62 - 27 * q^63 + 93 * q^64 - 72 * q^65 + 42 * q^66 + 54 * q^67 - 48 * q^68 - 57 * q^69 + 12 * q^70 - 60 * q^71 - 318 * q^72 - 36 * q^73 - 66 * q^74 - 132 * q^75 - 48 * q^76 + 222 * q^77 - 39 * q^78 + 6 * q^79 + 129 * q^80 - 84 * q^81 + 120 * q^82 + 45 * q^83 - 63 * q^84 - 18 * q^85 + 72 * q^86 - 33 * q^87 - 45 * q^88 + 18 * q^89 + 57 * q^90 + 45 * q^91 + 324 * q^92 - 78 * q^93 - 24 * q^94 + 81 * q^95 - 132 * q^96 - 96 * q^97 - 153 * q^98 - 6 * q^99

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