LMFDB - Embedded newform 189.2.w.a.184.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(25,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([10, 12]))

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

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

chi := DirichletCharacter("189.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.w (of order $9$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			184.10
Character	$\chi$	$=$	189.184
Dual form			189.2.w.a.151.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0572325 - 0.324581i) q^{2} +(-0.758800 + 1.55699i) q^{3} +(1.77731 - 0.646887i) q^{4} +(-0.607976 + 3.44800i) q^{5} +(0.548799 + 0.157182i) q^{6} +(-2.50814 + 0.842165i) q^{7} +(-0.641276 - 1.11072i) q^{8} +(-1.84845 - 2.36289i) q^{9} +O(q^{10})$	\(q+(-0.0572325 - 0.324581i) q^{2} +(-0.758800 + 1.55699i) q^{3} +(1.77731 - 0.646887i) q^{4} +(-0.607976 + 3.44800i) q^{5} +(0.548799 + 0.157182i) q^{6} +(-2.50814 + 0.842165i) q^{7} +(-0.641276 - 1.11072i) q^{8} +(-1.84845 - 2.36289i) q^{9} +1.15395 q^{10} +(0.460961 + 2.61424i) q^{11} +(-0.341423 + 3.25811i) q^{12} +(0.586193 + 0.491874i) q^{13} +(0.416898 + 0.765896i) q^{14} +(-4.90718 - 3.56296i) q^{15} +(2.57393 - 2.15978i) q^{16} -1.81099 q^{17} +(-0.661159 + 0.735205i) q^{18} +4.97172 q^{19} +(1.14991 + 6.52145i) q^{20} +(0.591931 - 4.54418i) q^{21} +(0.822152 - 0.299239i) q^{22} +(6.18751 + 5.19194i) q^{23} +(2.21599 - 0.155645i) q^{24} +(-6.82062 - 2.48250i) q^{25} +(0.126104 - 0.218418i) q^{26} +(5.08160 - 1.08505i) q^{27} +(-3.91295 + 3.11927i) q^{28} +(3.32963 - 2.79389i) q^{29} +(-0.875620 + 1.79670i) q^{30} +(0.527385 - 0.191953i) q^{31} +(-2.81332 - 2.36066i) q^{32} +(-4.42013 - 1.26597i) q^{33} +(0.103648 + 0.587815i) q^{34} +(-1.37890 - 9.16008i) q^{35} +(-4.81378 - 3.00385i) q^{36} +(-4.72185 - 8.17848i) q^{37} +(-0.284544 - 1.61373i) q^{38} +(-1.21065 + 0.539463i) q^{39} +(4.21965 - 1.53583i) q^{40} +(-2.66071 - 2.23260i) q^{41} +(-1.50884 + 0.0679449i) q^{42} +(4.12091 + 1.49989i) q^{43} +(2.51039 + 4.34812i) q^{44} +(9.27106 - 4.93686i) q^{45} +(1.33108 - 2.30550i) q^{46} +(-0.170852 - 0.0621850i) q^{47} +(1.40967 + 5.64643i) q^{48} +(5.58152 - 4.22453i) q^{49} +(-0.415414 + 2.35593i) q^{50} +(1.37418 - 2.81970i) q^{51} +(1.36003 + 0.495011i) q^{52} +(0.656663 + 1.13737i) q^{53} +(-0.643021 - 1.58729i) q^{54} -9.29416 q^{55} +(2.54382 + 2.24579i) q^{56} +(-3.77254 + 7.74092i) q^{57} +(-1.09741 - 0.920835i) q^{58} +(-11.2763 - 9.46193i) q^{59} +(-11.0264 - 3.15808i) q^{60} +(9.86293 + 3.58981i) q^{61} +(-0.0924878 - 0.160194i) q^{62} +(6.62610 + 4.36976i) q^{63} +(2.75482 - 4.77148i) q^{64} +(-2.05237 + 1.72215i) q^{65} +(-0.157937 + 1.50715i) q^{66} +(-2.08665 + 11.8340i) q^{67} +(-3.21869 + 1.17151i) q^{68} +(-12.7789 + 5.69426i) q^{69} +(-2.89428 + 0.971820i) q^{70} +(2.38709 - 4.13456i) q^{71} +(-1.43915 + 3.56837i) q^{72} +(2.98388 - 5.16823i) q^{73} +(-2.38434 + 2.00070i) q^{74} +(9.04073 - 8.73593i) q^{75} +(8.83627 - 3.21614i) q^{76} +(-3.35778 - 6.16867i) q^{77} +(0.244388 + 0.362079i) q^{78} +(2.89696 + 16.4295i) q^{79} +(5.88205 + 10.1880i) q^{80} +(-2.16650 + 8.73535i) q^{81} +(-0.572381 + 0.991393i) q^{82} +(-0.412252 + 0.345921i) q^{83} +(-1.88753 - 8.45933i) q^{84} +(1.10104 - 6.24431i) q^{85} +(0.250986 - 1.42341i) q^{86} +(1.82354 + 7.30421i) q^{87} +(2.60809 - 2.18845i) q^{88} -5.76971 q^{89} +(-2.13302 - 2.72667i) q^{90} +(-1.88449 - 0.740017i) q^{91} +(14.3557 + 5.22505i) q^{92} +(-0.101311 + 0.966788i) q^{93} +(-0.0104058 + 0.0590143i) q^{94} +(-3.02268 + 17.1425i) q^{95} +(5.81027 - 2.58905i) q^{96} +(-9.14484 - 3.32845i) q^{97} +(-1.69065 - 1.56988i) q^{98} +(5.32510 - 5.92148i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.0572325	−	0.324581i	−0.0404695	−	0.229514i	0.957864	−	0.287222i	$-0.0927318\pi$
$2$	−0.0572325	−	0.324581i	−0.0404695	−	0.229514i	−0.998333	+	0.0577083i	$0.981621\pi$
$3$	−0.758800	+	1.55699i	−0.438093	+	0.898929i
$3$	−0.758800	+	1.55699i	−0.438093	+	0.898929i
$4$	1.77731	−	0.646887i	0.888654	−	0.323444i
$5$	−0.607976	+	3.44800i	−0.271895	+	1.54199i	0.476760	+	0.879034i	$0.341811\pi$
$5$	−0.607976	+	3.44800i	−0.271895	+	1.54199i	−0.748655	+	0.662960i	$0.769300\pi$
$6$	0.548799	+	0.157182i	0.224046	+	0.0641693i
$7$	−2.50814	+	0.842165i	−0.947987	+	0.318308i
$7$	−2.50814	+	0.842165i	−0.947987	+	0.318308i
$8$	−0.641276	−	1.11072i	−0.226725	−	0.392700i
$9$	−1.84845	−	2.36289i	−0.616148	−	0.787630i
$10$	1.15395			0.364912
$11$	0.460961	+	2.61424i	0.138985	+	0.788223i	0.972001	+	0.234975i	$0.0755008\pi$
$11$	0.460961	+	2.61424i	0.138985	+	0.788223i	−0.833016	+	0.553248i	$0.813388\pi$
$12$	−0.341423	+	3.25811i	−0.0985604	+	0.940536i
$13$	0.586193	+	0.491874i	0.162581	+	0.136421i	0.720449	−	0.693508i	$-0.243936\pi$
$13$	0.586193	+	0.491874i	0.162581	+	0.136421i	−0.557868	+	0.829930i	$0.688380\pi$
$14$	0.416898	+	0.765896i	0.111421	+	0.204694i
$15$	−4.90718	−	3.56296i	−1.26703	−	0.919952i
$16$	2.57393	−	2.15978i	0.643483	−	0.539946i
$17$	−1.81099			−0.439230			−0.219615	−	0.975587i	$-0.570480\pi$
$17$	−1.81099			−0.439230			−0.219615	+	0.975587i	$0.570480\pi$
$18$	−0.661159	+	0.735205i	−0.155837	+	0.173290i
$19$	4.97172			1.14059			0.570295	−	0.821440i	$-0.306829\pi$
$19$	4.97172			1.14059			0.570295	+	0.821440i	$0.306829\pi$
$20$	1.14991	+	6.52145i	0.257127	+	1.45824i
$21$	0.591931	−	4.54418i	0.129170	−	0.991622i
$22$	0.822152	−	0.299239i	0.175283	−	0.0637979i
$23$	6.18751	+	5.19194i	1.29019	+	1.08259i	0.991753	+	0.128164i	$0.0409083\pi$
$23$	6.18751	+	5.19194i	1.29019	+	1.08259i	0.298433	+	0.954431i	$0.403536\pi$
$24$	2.21599	−	0.155645i	0.452336	−	0.0317709i
$25$	−6.82062	−	2.48250i	−1.36412	−	0.496501i
$26$	0.126104	−	0.218418i	0.0247310	−	0.0428354i
$27$	5.08160	−	1.08505i	0.977954	−	0.208818i
$28$	−3.91295	+	3.11927i	−0.739478	+	0.589486i
$29$	3.32963	−	2.79389i	0.618297	−	0.518813i	−0.278971	−	0.960300i	$-0.589993\pi$
$29$	3.32963	−	2.79389i	0.618297	−	0.518813i	0.897268	+	0.441487i	$0.145549\pi$
$30$	−0.875620	+	1.79670i	−0.159866	+	0.328030i
$31$	0.527385	−	0.191953i	0.0947212	−	0.0344757i	−0.294225	−	0.955736i	$-0.595061\pi$
$31$	0.527385	−	0.191953i	0.0947212	−	0.0344757i	0.388946	+	0.921261i	$0.372839\pi$
$32$	−2.81332	−	2.36066i	−0.497330	−	0.417309i
$33$	−4.42013	−	1.26597i	−0.769445	−	0.220378i
$34$	0.103648	+	0.587815i	0.0177754	+	0.100809i
$35$	−1.37890	−	9.16008i	−0.233077	−	1.54834i
$36$	−4.81378	−	3.00385i	−0.802297	−	0.500641i
$37$	−4.72185	−	8.17848i	−0.776267	−	1.34453i	−0.934079	−	0.357065i	$-0.883777\pi$
$37$	−4.72185	−	8.17848i	−0.776267	−	1.34453i	0.157812	−	0.987469i	$-0.449556\pi$
$38$	−0.284544	−	1.61373i	−0.0461591	−	0.261781i
$39$	−1.21065	+	0.539463i	−0.193859	+	0.0863832i
$40$	4.21965	−	1.53583i	0.667186	−	0.242836i
$41$	−2.66071	−	2.23260i	−0.415533	−	0.348673i	0.410928	−	0.911668i	$-0.365205\pi$
$41$	−2.66071	−	2.23260i	−0.415533	−	0.348673i	−0.826461	+	0.562995i	$0.809649\pi$
$42$	−1.50884	+	0.0679449i	−0.232818	+	0.0104841i
$43$	4.12091	+	1.49989i	0.628433	+	0.228731i	0.636549	−	0.771236i	$-0.280361\pi$
$43$	4.12091	+	1.49989i	0.628433	+	0.228731i	−0.00811609	+	0.999967i	$0.502583\pi$
$44$	2.51039	+	4.34812i	0.378455	+	0.655504i
$45$	9.27106	−	4.93686i	1.38205	−	0.735944i
$46$	1.33108	−	2.30550i	0.196257	−	0.339927i
$47$	−0.170852	−	0.0621850i	−0.0249213	−	0.00907061i	0.329529	−	0.944145i	$-0.393110\pi$
$47$	−0.170852	−	0.0621850i	−0.0249213	−	0.00907061i	−0.354451	+	0.935075i	$0.615332\pi$
$48$	1.40967	+	5.64643i	0.203468	+	0.814992i
$49$	5.58152	−	4.22453i	0.797359	−	0.603505i
$50$	−0.415414	+	2.35593i	−0.0587484	+	0.333179i
$51$	1.37418	−	2.81970i	0.192424	−	0.394837i
$52$	1.36003	+	0.495011i	0.188602	+	0.0686457i
$53$	0.656663	+	1.13737i	0.0901995	+	0.156230i	0.907595	−	0.419847i	$-0.137916\pi$
$53$	0.656663	+	1.13737i	0.0901995	+	0.156230i	−0.817395	+	0.576077i	$0.804583\pi$
$54$	−0.643021	−	1.58729i	−0.0875040	−	0.216003i
$55$	−9.29416			−1.25322
$56$	2.54382	+	2.24579i	0.339932	+	0.300106i
$57$	−3.77254	+	7.74092i	−0.499685	+	1.02531i
$58$	−1.09741	−	0.920835i	−0.144097	−	0.120912i
$59$	−11.2763	−	9.46193i	−1.46805	−	1.23184i	−0.917925	−	0.396753i	$-0.870137\pi$
$59$	−11.2763	−	9.46193i	−1.46805	−	1.23184i	−0.550122	−	0.835084i	$-0.685419\pi$
$60$	−11.0264	−	3.15808i	−1.42350	−	0.407707i
$61$	9.86293	+	3.58981i	1.26282	+	0.459628i	0.884714	−	0.466135i	$-0.154354\pi$
$61$	9.86293	+	3.58981i	1.26282	+	0.459628i	0.378105	+	0.925763i	$0.376576\pi$
$62$	−0.0924878	−	0.160194i	−0.0117460	−	0.0203446i
$63$	6.62610	+	4.36976i	0.834810	+	0.550538i
$64$	2.75482	−	4.77148i	0.344352	−	0.596435i
$65$	−2.05237	+	1.72215i	−0.254566	+	0.213606i
$66$	−0.157937	+	1.50715i	−0.0194406	+	0.185517i
$67$	−2.08665	+	11.8340i	−0.254924	+	1.44575i	0.541342	+	0.840802i	$0.317916\pi$
$67$	−2.08665	+	11.8340i	−0.254924	+	1.44575i	−0.796267	+	0.604946i	$0.793195\pi$
$68$	−3.21869	+	1.17151i	−0.390324	+	0.142066i
$69$	−12.7789	+	5.69426i	−1.53840	+	0.685509i
$70$	−2.89428	+	0.971820i	−0.345932	+	0.116155i
$71$	2.38709	−	4.13456i	0.283296	−	0.490682i	−0.688899	−	0.724857i	$-0.741906\pi$
$71$	2.38709	−	4.13456i	0.283296	−	0.490682i	0.972194	+	0.234175i	$0.0752389\pi$
$72$	−1.43915	+	3.56837i	−0.169606	+	0.420537i
$73$	2.98388	−	5.16823i	0.349237	−	0.604896i	−0.636877	−	0.770965i	$-0.719774\pi$
$73$	2.98388	−	5.16823i	0.349237	−	0.604896i	0.986114	+	0.166069i	$0.0531076\pi$
$74$	−2.38434	+	2.00070i	−0.277174	+	0.232577i
$75$	9.04073	−	8.73593i	1.04393	−	1.00874i
$76$	8.83627	−	3.21614i	1.01359	−	0.368917i
$77$	−3.35778	−	6.16867i	−0.382654	−	0.702985i
$78$	0.244388	+	0.362079i	0.0276715	+	0.0409973i
$79$	2.89696	+	16.4295i	0.325933	+	1.84846i	0.503033	+	0.864267i	$0.332217\pi$
$79$	2.89696	+	16.4295i	0.325933	+	1.84846i	−0.177100	+	0.984193i	$0.556672\pi$
$80$	5.88205	+	10.1880i	0.657634	+	1.13905i
$81$	−2.16650	+	8.73535i	−0.240722	+	0.970594i
$82$	−0.572381	+	0.991393i	−0.0632089	+	0.109481i
$83$	−0.412252	+	0.345921i	−0.0452506	+	0.0379698i	−0.665132	−	0.746725i	$-0.731625\pi$
$83$	−0.412252	+	0.345921i	−0.0452506	+	0.0379698i	0.619882	+	0.784695i	$0.287180\pi$
$84$	−1.88753	−	8.45933i	−0.205946	−	0.922988i
$85$	1.10104	−	6.24431i	0.119425	−	0.677291i
$86$	0.250986	−	1.42341i	0.0270645	−	0.153491i
$87$	1.82354	+	7.30421i	0.195504	+	0.783093i
$88$	2.60809	−	2.18845i	0.278024	−	0.233289i
$89$	−5.76971			−0.611588			−0.305794	−	0.952098i	$-0.598922\pi$
$89$	−5.76971			−0.611588			−0.305794	+	0.952098i	$0.598922\pi$
$90$	−2.13302	−	2.72667i	−0.224840	−	0.287416i
$91$	−1.88449	−	0.740017i	−0.197548	−	0.0775749i
$92$	14.3557	+	5.22505i	1.49669	+	0.544749i
$93$	−0.101311	+	0.966788i	−0.0105055	+	0.100251i
$94$	−0.0104058	+	0.0590143i	−0.00107328	+	0.00608686i
$95$	−3.02268	+	17.1425i	−0.310121	+	1.75878i
$96$	5.81027	−	2.58905i	0.593008	−	0.264244i
$97$	−9.14484	−	3.32845i	−0.928518	−	0.337953i	−0.166896	−	0.985974i	$-0.553374\pi$
$97$	−9.14484	−	3.32845i	−0.928518	−	0.337953i	−0.761622	+	0.648021i	$0.775597\pi$
$98$	−1.69065	−	1.56988i	−0.170781	−	0.158581i
$99$	5.32510	−	5.92148i	0.535193	−	0.595131i
$100$	−13.7282			−1.37282
$101$	6.58667	−	5.52687i	0.655398	−	0.549945i	−0.253305	−	0.967386i	$-0.581518\pi$
$101$	6.58667	−	5.52687i	0.655398	−	0.549945i	0.908704	+	0.417442i	$0.137073\pi$
$102$	−0.993871	−	0.284655i	−0.0984079	−	0.0281851i
$103$	−2.38429	+	13.5220i	−0.234931	+	1.33236i	0.607827	+	0.794069i	$0.292041\pi$
$103$	−2.38429	+	13.5220i	−0.234931	+	1.33236i	−0.842758	+	0.538292i	$0.819070\pi$
$104$	0.170424	−	0.966525i	0.0167115	−	0.0947755i
$105$	15.3085	+	4.80374i	1.49395	+	0.468797i
$106$	0.331588	−	0.278235i	0.0322067	−	0.0270246i
$107$	8.29892	−	14.3742i	0.802287	−	1.38960i	−0.115820	−	0.993270i	$-0.536950\pi$
$107$	8.29892	−	14.3742i	0.802287	−	1.38960i	0.918107	−	0.396332i	$-0.129717\pi$
$108$	8.32966	−	5.21569i	0.801522	−	0.501880i
$109$	−1.98567	−	3.43928i	−0.190193	−	0.329423i	0.755121	−	0.655585i	$-0.227578\pi$
$109$	−1.98567	−	3.43928i	−0.190193	−	0.329423i	−0.945314	+	0.326162i	$0.894245\pi$
$110$	0.531928	+	3.01671i	0.0507173	+	0.287632i
$111$	16.3168	−	1.14605i	1.54872	−	0.108778i
$112$	−4.63688	+	7.58471i	−0.438144	+	0.716688i
$113$	−7.11720	+	2.59045i	−0.669530	+	0.243689i	−0.654346	−	0.756196i	$-0.727056\pi$
$113$	−7.11720	+	2.59045i	−0.669530	+	0.243689i	−0.0151846	+	0.999885i	$0.504834\pi$
$114$	2.72847	+	0.781464i	0.255545	+	0.0731908i
$115$	−21.6637	+	18.1780i	−2.02015	+	1.69511i
$116$	4.11044	−	7.11950i	0.381645	−	0.661029i
$117$	0.0786993	−	2.29431i	0.00727575	−	0.212109i
$118$	−2.42580	+	4.20160i	−0.223313	+	0.386789i
$119$	4.54222	−	1.52516i	0.416385	−	0.139811i
$120$	−0.810601	+	7.73535i	−0.0739974	+	0.706138i
$121$	3.71485	−	1.35210i	0.337714	−	0.122918i
$122$	0.600707	−	3.40678i	0.0543854	−	0.308435i
$123$	5.49508	−	2.44860i	0.495475	−	0.220783i
$124$	0.813155	−	0.682318i	0.0730234	−	0.0612739i
$125$	3.95347	−	6.84762i	0.353609	−	0.612469i
$126$	1.03912	−	2.40080i	0.0925717	−	0.213880i
$127$	−5.17150	−	8.95730i	−0.458896	−	0.794832i	0.540007	−	0.841661i	$-0.318422\pi$
$127$	−5.17150	−	8.95730i	−0.458896	−	0.794832i	−0.998903	+	0.0468291i	$0.985088\pi$
$128$	−8.60850	−	3.13324i	−0.760891	−	0.276942i
$129$	−5.46226	+	5.27811i	−0.480925	+	0.464712i
$130$	0.676439	+	0.567600i	0.0593277	+	0.0497818i
$131$	2.30919	+	1.93764i	0.201755	+	0.169292i	0.738067	−	0.674727i	$-0.235739\pi$
$131$	2.30919	+	1.93764i	0.201755	+	0.169292i	−0.536313	+	0.844019i	$0.680183\pi$
$132$	−8.67487	+	0.609300i	−0.755050	+	0.0530327i
$133$	−12.4698	+	4.18701i	−1.08127	+	0.363060i
$134$	3.96051			0.342136
$135$	0.651774	+	18.1811i	0.0560958	+	1.56478i
$136$	1.16135	+	2.01151i	0.0995847	+	0.172486i
$137$	−2.38526	−	0.868164i	−0.203786	−	0.0741722i	0.238110	−	0.971238i	$-0.423472\pi$
$137$	−2.38526	−	0.868164i	−0.203786	−	0.0741722i	−0.441897	+	0.897066i	$0.645694\pi$
$138$	2.57962	+	3.82190i	0.219592	+	0.325341i
$139$	0.627384	−	3.55807i	0.0532140	−	0.301792i	−0.946572	−	0.322494i	$-0.895479\pi$
$139$	0.627384	−	3.55807i	0.0532140	−	0.301792i	0.999786	+	0.0207017i	$0.00659003\pi$
$140$	−8.37627	−	15.3883i	−0.707924	−	1.30055i
$141$	0.226464	−	0.218829i	0.0190717	−	0.0184287i
$142$	−1.47862	−	0.538174i	−0.124083	−	0.0451626i
$143$	−1.01566	+	1.75918i	−0.0849342	+	0.147110i
$144$	−9.86110	−	2.08967i	−0.821759	−	0.174139i
$145$	7.60901	+	13.1792i	0.631894	+	1.09447i
$146$	−1.84829	−	0.672721i	−0.152965	−	0.0556748i
$147$	2.34231	+	11.8959i	0.193190	+	0.981161i
$148$	−13.6827	−	11.4812i	−1.12471	−	0.943747i
$149$	−5.22087	+	1.90024i	−0.427710	+	0.155674i	−0.546901	−	0.837198i	$-0.684192\pi$
$149$	−5.22087	+	1.90024i	−0.427710	+	0.155674i	0.119190	+	0.992871i	$0.461970\pi$
$150$	−3.35294	−	2.43447i	−0.273767	−	0.198774i
$151$	0.909649	+	5.15888i	0.0740262	+	0.419824i	0.999189	+	0.0402541i	$0.0128167\pi$
$151$	0.909649	+	5.15888i	0.0740262	+	0.419824i	−0.925163	+	0.379569i	$0.876072\pi$
$152$	−3.18824	−	5.52220i	−0.258601	−	0.447910i
$153$	3.34752	+	4.27918i	0.270631	+	0.345951i
$154$	−1.81006	+	1.44292i	−0.145859	+	0.116274i
$155$	0.341215	+	1.93513i	0.0274071	+	0.155433i
$156$	−1.80272	+	1.74194i	−0.144333	+	0.139467i
$157$	−0.866797	−	0.727329i	−0.0691780	−	0.0580472i	0.607543	−	0.794287i	$-0.292155\pi$
$157$	−0.866797	−	0.727329i	−0.0691780	−	0.0580472i	−0.676721	+	0.736240i	$0.736600\pi$
$158$	5.16690	−	1.88060i	0.411057	−	0.149612i
$159$	−2.26916	+	0.159380i	−0.179956	+	0.0126396i
$160$	9.84999	−	8.26512i	0.778710	−	0.653415i
$161$	−19.8916	−	7.81120i	−1.56768	−	0.615609i
$162$	2.95933	+	0.203260i	0.232507	+	0.0159696i
$163$	0.829258	−	1.43632i	0.0649525	−	0.112501i	−0.831720	−	0.555195i	$-0.812644\pi$
$163$	0.829258	−	1.43632i	0.0649525	−	0.112501i	0.896673	+	0.442694i	$0.145977\pi$
$164$	−6.17313	−	2.24684i	−0.482041	−	0.175448i
$165$	7.05241	−	14.4709i	0.549029	−	1.12656i
$166$	0.135874	+	0.114012i	0.0105458	+	0.00884902i
$167$	3.97386	−	1.44637i	0.307507	−	0.111923i	−0.183657	−	0.982990i	$-0.558794\pi$
$167$	3.97386	−	1.44637i	0.307507	−	0.111923i	0.491164	+	0.871067i	$0.336572\pi$
$168$	−5.42692	+	2.25661i	−0.418696	+	0.174101i
$169$	−2.15574	−	12.2258i	−0.165827	−	0.940449i
$170$	−2.08980			−0.160281
$171$	−9.18995	−	11.7476i	−0.702773	−	0.898363i
$172$	8.29439			0.632441
$173$	−1.43180	+	1.20142i	−0.108858	+	0.0913425i	−0.695592	−	0.718437i	$-0.744858\pi$
$173$	−1.43180	+	1.20142i	−0.108858	+	0.0913425i	0.586734	+	0.809780i	$0.300413\pi$
$174$	2.26645	−	1.00993i	0.171819	−	0.0765623i
$175$	19.1977	+	0.482373i	1.45121	+	0.0364640i
$176$	6.83268	+	5.73330i	0.515032	+	0.432163i
$177$	23.2886	−	10.3774i	1.75048	−	0.780011i
$178$	0.330215	+	1.87274i	0.0247506	+	0.140368i
$179$	−4.17986			−0.312417			−0.156209	−	0.987724i	$-0.549927\pi$
$179$	−4.17986			−0.312417			−0.156209	+	0.987724i	$0.549927\pi$
$180$	13.2839	−	14.7717i	0.990126	−	1.10101i
$181$	2.15229	+	3.72787i	0.159978	+	0.277091i	0.934861	−	0.355015i	$-0.115524\pi$
$181$	2.15229	+	3.72787i	0.159978	+	0.277091i	−0.774882	+	0.632106i	$0.782191\pi$
$182$	−0.132342	+	0.654024i	−0.00980983	+	0.0484795i
$183$	−13.0733	+	12.6325i	−0.966406	+	0.933825i
$184$	1.79890	−	10.2021i	0.132617	−	0.752107i
$185$	31.0702	−	11.3086i	2.28433	−	0.831427i
$186$	0.319600	−	0.0224479i	0.0234342	−	0.00164596i
$187$	−0.834797	−	4.73437i	−0.0610464	−	0.346212i
$188$	−0.343883			−0.0250802
$189$	−11.8316	+	7.00101i	−0.860620	+	0.509248i
$190$	5.73713			0.416215
$191$	−3.34136	−	18.9498i	−0.241772	−	1.37116i	−0.827871	−	0.560919i	$-0.810448\pi$
$191$	−3.34136	−	18.9498i	−0.241772	−	1.37116i	0.586099	−	0.810240i	$-0.300663\pi$
$192$	5.33880	+	7.90982i	0.385295	+	0.570842i
$193$	14.4769	−	5.26915i	1.04207	−	0.379282i	0.236404	−	0.971655i	$-0.424031\pi$
$193$	14.4769	−	5.26915i	1.04207	−	0.379282i	0.805664	+	0.592373i	$0.201809\pi$
$194$	−0.556972	+	3.15874i	−0.0399882	+	0.226785i
$195$	−1.12403	−	4.50229i	−0.0804932	−	0.322416i
$196$	7.18728	−	11.1189i	0.513377	−	0.794208i
$197$	−1.06006	−	1.83609i	−0.0755265	−	0.130816i	0.825789	−	0.563980i	$-0.190730\pi$
$197$	−1.06006	−	1.83609i	−0.0755265	−	0.130816i	−0.901315	+	0.433164i	$0.857397\pi$
$198$	−2.22677	−	1.38953i	−0.158250	−	0.0987495i
$199$	3.94708			0.279801			0.139901	−	0.990166i	$-0.455322\pi$
$199$	3.94708			0.279801			0.139901	+	0.990166i	$0.455322\pi$
$200$	1.61653	+	9.16779i	0.114306	+	0.648261i
$201$	−16.8420	−	12.2285i	−1.18794	−	0.862532i
$202$	−2.17089	−	1.82160i	−0.152743	−	0.128167i
$203$	−5.99825	+	9.81156i	−0.420995	+	0.688637i
$204$	0.618315	−	5.90042i	0.0432907	−	0.413112i
$205$	9.31565	−	7.81676i	0.650633	−	0.545946i
$206$	4.52545			0.315303
$207$	0.830704	−	24.2174i	0.0577380	−	1.68323i
$208$	2.57116			0.178278
$209$	2.29177	+	12.9973i	0.158525	+	0.899040i
$210$	0.683062	−	5.24378i	0.0471357	−	0.361855i
$211$	−16.8567	+	6.13535i	−1.16047	+	0.422375i	−0.849264	−	0.527969i	$-0.822954\pi$
$211$	−16.8567	+	6.13535i	−1.16047	+	0.422375i	−0.311202	+	0.950344i	$0.600732\pi$
$212$	1.90284	+	1.59668i	0.130688	+	0.109660i
$213$	4.62615	+	6.85399i	0.316979	+	0.469627i
$214$	−5.14055	−	1.87101i	−0.351401	−	0.127899i
$215$	−7.67704	+	13.2970i	−0.523570	+	0.906849i
$216$	−4.46390	−	4.94843i	−0.303730	−	0.336698i
$217$	−1.16110	+	0.925589i	−0.0788206	+	0.0628331i
$218$	−1.00268	+	0.841350i	−0.0679102	+	0.0569834i
$219$	5.78272	+	8.56753i	0.390760	+	0.578940i
$220$	−16.5186	+	6.01227i	−1.11368	+	0.405347i
$221$	−1.06159	−	0.890781i	−0.0714104	−	0.0599204i
$222$	−1.30583	−	5.23053i	−0.0876419	−	0.351050i
$223$	1.33929	+	7.59550i	0.0896855	+	0.508632i	0.996247	+	0.0865578i	$0.0275867\pi$
$223$	1.33929	+	7.59550i	0.0896855	+	0.508632i	−0.906561	+	0.422074i	$0.861302\pi$
$224$	9.04426	+	3.55157i	0.604295	+	0.237300i
$225$	6.74167	+	20.7052i	0.449444	+	1.38034i
$226$	1.24815	+	2.16185i	0.0830255	+	0.143804i
$227$	−3.08679	−	17.5061i	−0.204878	−	1.16192i	−0.897632	−	0.440746i	$-0.854714\pi$
$227$	−3.08679	−	17.5061i	−0.204878	−	1.16192i	0.692754	−	0.721174i	$-0.256397\pi$
$228$	−1.69746	+	16.1984i	−0.112417	+	1.07277i
$229$	−14.3474	+	5.22203i	−0.948103	+	0.345081i	−0.769361	−	0.638815i	$-0.779425\pi$
$229$	−14.3474	+	5.22203i	−0.948103	+	0.345081i	−0.178742	+	0.983896i	$0.557203\pi$
$230$	7.14010	+	5.99126i	0.470805	+	0.395052i
$231$	12.1524	−	0.547241i	0.799572	−	0.0360058i
$232$	−5.23845	−	1.90664i	−0.343921	−	0.125177i
$233$	4.79072	+	8.29777i	0.313850	+	0.543605i	0.979192	−	0.202934i	$-0.0650477\pi$
$233$	4.79072	+	8.29777i	0.313850	+	0.543605i	−0.665342	+	0.746539i	$0.731714\pi$
$234$	−0.749195	+	0.105765i	−0.0489764	+	0.00691406i
$235$	0.318288	−	0.551290i	0.0207628	−	0.0359622i
$236$	−26.1622	−	9.52227i	−1.70302	−	0.619847i
$237$	−27.7788	−	7.95614i	−1.80442	−	0.516807i
$238$	−0.755000	−	1.38703i	−0.0489394	−	0.0899080i
$239$	−4.10452	+	23.2779i	−0.265499	+	1.50572i	0.502110	+	0.864804i	$0.332557\pi$
$239$	−4.10452	+	23.2779i	−0.265499	+	1.50572i	−0.767609	+	0.640918i	$0.778554\pi$
$240$	−20.3260	+	1.42764i	−1.31203	+	0.0921539i
$241$	−13.9657	−	5.08309i	−0.899609	−	0.327431i	−0.149513	−	0.988760i	$-0.547771\pi$
$241$	−13.9657	−	5.08309i	−0.899609	−	0.327431i	−0.750096	+	0.661329i	$0.769993\pi$
$242$	−0.651476	−	1.12839i	−0.0418784	−	0.0725356i
$243$	−11.9569	−	10.0016i	−0.767037	−	0.641603i
$244$	19.8517			1.27087
$245$	11.1728	+	21.8135i	0.713802	+	1.39361i
$246$	−1.10927	−	1.64346i	−0.0707243	−	0.104783i
$247$	2.91439	+	2.44546i	0.185438	+	0.155601i
$248$	−0.551406	−	0.462684i	−0.0350143	−	0.0293805i
$249$	−0.225779	−	0.904358i	−0.0143081	−	0.0573114i
$250$	−2.44888	−	0.891318i	−0.154881	−	0.0563719i
$251$	9.61292	+	16.6501i	0.606762	+	1.05094i	0.991770	+	0.128030i	$0.0408653\pi$
$251$	9.61292	+	16.6501i	0.606762	+	1.05094i	−0.385008	+	0.922913i	$0.625801\pi$
$252$	14.6034	+	3.48007i	0.919925	+	0.219224i
$253$	−10.7208	+	18.5689i	−0.674009	+	1.16742i
$254$	−2.61140	+	2.19122i	−0.163854	+	0.137489i
$255$	8.88687	+	6.45249i	0.556517	+	0.404071i
$256$	1.38917	−	7.87837i	0.0868231	−	0.492398i
$257$	−19.7464	+	7.18709i	−1.23174	+	0.448318i	−0.874194	−	0.485576i	$-0.838610\pi$
$257$	−19.7464	+	7.18709i	−1.23174	+	0.448318i	−0.357549	+	0.933894i	$0.616388\pi$
$258$	2.02580	+	1.47087i	0.126120	+	0.0915724i
$259$	18.7307	+	16.5362i	1.16387	+	1.02751i
$260$	−2.53367	+	4.38844i	−0.157131	+	0.272159i
$261$	−12.7563	−	2.70319i	−0.789595	−	0.167324i
$262$	0.496761	−	0.860415i	0.0306900	−	0.0531566i
$263$	21.0642	−	17.6750i	1.29888	−	1.08989i	0.308537	−	0.951212i	$-0.400161\pi$
$263$	21.0642	−	17.6750i	1.29888	−	1.08989i	0.990338	−	0.138673i	$-0.0442838\pi$
$264$	1.42838	+	5.72137i	0.0879105	+	0.352126i
$265$	−4.32090	+	1.57268i	−0.265431	+	0.0966089i
$266$	2.07270	+	3.80782i	0.127085	+	0.233472i
$267$	4.37805	−	8.98338i	0.267932	−	0.549774i
$268$	3.94662	+	22.3824i	0.241078	+	1.36722i
$269$	2.50292	+	4.33519i	0.152606	+	0.264321i	0.932185	−	0.361983i	$-0.117900\pi$
$269$	2.50292	+	4.33519i	0.152606	+	0.264321i	−0.779579	+	0.626304i	$0.784567\pi$
$270$	5.86393	−	1.25210i	0.356868	−	0.0762004i
$271$	14.7196	−	25.4951i	0.894152	−	1.54872i	0.0593009	−	0.998240i	$-0.481113\pi$
$271$	14.7196	−	25.4951i	0.894152	−	1.54872i	0.834851	−	0.550476i	$-0.185554\pi$
$272$	−4.66137	+	3.91136i	−0.282637	+	0.237161i
$273$	2.58215	−	2.37261i	0.156279	−	0.143597i
$274$	−0.145275	+	0.823898i	−0.00877641	+	0.0497735i
$275$	3.34582	−	18.9751i	0.201761	−	1.14424i
$276$	−19.0285	+	18.3870i	−1.14538	+	1.10676i
$277$	12.1659	−	10.2084i	0.730978	−	0.613364i	−0.199420	−	0.979914i	$-0.563906\pi$
$277$	12.1659	−	10.2084i	0.730978	−	0.613364i	0.930398	+	0.366550i	$0.119461\pi$
$278$	−1.19079			−0.0714189
$279$	−1.42841	−	0.891340i	−0.0855164	−	0.0533631i
$280$	−9.29006	+	7.40572i	−0.555187	+	0.442576i
$281$	10.6507	+	3.87653i	0.635366	+	0.231254i	0.639565	−	0.768737i	$-0.279114\pi$
$281$	10.6507	+	3.87653i	0.635366	+	0.231254i	−0.00419896	+	0.999991i	$0.501337\pi$
$282$	−0.0839889	−	0.0609818i	−0.00500146	−	0.00363142i
$283$	−1.23559	+	7.00738i	−0.0734482	+	0.416546i	0.925808	+	0.377993i	$0.123386\pi$
$283$	−1.23559	+	7.00738i	−0.0734482	+	0.416546i	−0.999257	+	0.0385523i	$0.987725\pi$
$284$	1.56800	−	8.89257i	0.0930437	−	0.527677i
$285$	−24.3971	−	17.7140i	−1.44516	−	1.04929i
$286$	0.629127	+	0.228984i	0.0372011	+	0.0135401i
$287$	8.55364	+	3.35891i	0.504905	+	0.198270i
$288$	−0.377702	+	11.0111i	−0.0222563	+	0.648836i
$289$	−13.7203			−0.807077
$290$	3.84224	−	3.22402i	0.225624	−	0.189321i
$291$	12.1215	−	11.7128i	0.710574	−	0.686617i
$292$	1.96001	−	11.1158i	0.114701	−	0.650501i
$293$	4.75331	−	26.9573i	0.277691	−	1.57486i	−0.452591	−	0.891718i	$-0.649500\pi$
$293$	4.75331	−	26.9573i	0.277691	−	1.57486i	0.730282	−	0.683146i	$-0.239389\pi$
$294$	3.72715	−	1.44110i	0.217372	−	0.0840469i
$295$	39.4805	−	33.1280i	2.29864	−	1.92879i
$296$	−6.05602	+	10.4893i	−0.351999	+	0.609680i
$297$	5.17901	+	12.7844i	0.300517	+	0.741824i
$298$	0.915587	+	1.58584i	0.0530385	+	0.0918654i
$299$	1.07329	+	6.08696i	0.0620702	+	0.352018i
$300$	10.4170	−	21.3748i	0.601425	−	1.23407i
$301$	−11.5990	−	0.291442i	−0.668553	−	0.0167984i
$302$	1.62241	−	0.590511i	0.0933595	−	0.0339801i
$303$	3.60733	+	14.4492i	0.207236	+	0.830084i
$304$	12.7969	−	10.7378i	0.733950	−	0.615857i
$305$	−18.3741	+	31.8249i	−1.05210	+	1.82229i
$306$	1.19736	−	1.33145i	0.0684482	−	0.0761140i
$307$	8.05168	−	13.9459i	0.459534	−	0.795936i	−0.539402	−	0.842048i	$-0.681350\pi$
$307$	8.05168	−	13.9459i	0.459534	−	0.795936i	0.998936	+	0.0461121i	$0.0146831\pi$
$308$	−9.95823	−	8.79152i	−0.567423	−	0.500944i
$309$	−19.2444	−	13.9728i	−1.09478	−	0.794885i
$310$	0.608578	−	0.221504i	0.0345649	−	0.0125806i
$311$	−2.54404	+	14.4280i	−0.144259	+	0.818135i	0.823700	+	0.567026i	$0.191906\pi$
$311$	−2.54404	+	14.4280i	−0.144259	+	0.818135i	−0.967959	+	0.251108i	$0.919205\pi$
$312$	1.37555	+	0.998748i	0.0778753	+	0.0565430i
$313$	−4.41806	+	3.70719i	−0.249723	+	0.209543i	−0.759053	−	0.651029i	$-0.774338\pi$
$313$	−4.41806	+	3.70719i	−0.249723	+	0.209543i	0.509330	+	0.860571i	$0.329893\pi$
$314$	−0.186469	+	0.322973i	−0.0105230	+	0.0182264i
$315$	−19.0955	+	20.1901i	−1.07591	+	1.13758i
$316$	15.7768	+	27.3262i	0.887514	+	1.53722i
$317$	22.3570	+	8.13729i	1.25570	+	0.457036i	0.882322	−	0.470646i	$-0.155979\pi$
$317$	22.3570	+	8.13729i	1.25570	+	0.457036i	0.373373	+	0.927681i	$0.378201\pi$
$318$	0.181601	+	0.727404i	0.0101837	+	0.0407908i
$319$	8.83873	+	7.41658i	0.494874	+	0.415249i
$320$	14.7772	+	12.3996i	0.826072	+	0.693156i
$321$	16.0832	+	23.8285i	0.897678	+	1.32998i
$322$	−1.39692	+	6.90350i	−0.0778475	+	0.384717i
$323$	−9.00375			−0.500982
$324$	1.80025	+	16.9269i	0.100014	+	0.940382i
$325$	−2.77712	−	4.81011i	−0.154047	−	0.266817i
$326$	−0.513663	−	0.186958i	−0.0284491	−	0.0103546i
$327$	6.86166	−	0.481945i	0.379450	−	0.0266516i
$328$	−0.773550	+	4.38702i	−0.0427121	+	0.242233i
$329$	0.480890	+	0.0120831i	0.0265123	+	0.000666163i
$330$	−5.10062	−	1.46087i	−0.280780	−	0.0804185i
$331$	−25.3128	−	9.21312i	−1.39132	−	0.506399i	−0.465730	−	0.884927i	$-0.654208\pi$
$331$	−25.3128	−	9.21312i	−1.39132	−	0.506399i	−0.925590	+	0.378528i	$0.876430\pi$
$332$	−0.508928	+	0.881489i	−0.0279310	+	0.0483780i
$333$	−10.5968	+	26.2747i	−0.580700	+	1.43984i
$334$	−0.696898	−	1.20706i	−0.0381326	−	0.0660475i
$335$	−39.5349	−	14.3895i	−2.16002	−	0.786183i
$336$	−8.29087	−	12.9749i	−0.452304	−	0.707837i
$337$	7.78610	+	6.53331i	0.424136	+	0.355892i	0.829734	−	0.558159i	$-0.188492\pi$
$337$	7.78610	+	6.53331i	0.424136	+	0.355892i	−0.405598	+	0.914052i	$0.632937\pi$
$338$	−3.84490	+	1.39943i	−0.209135	+	0.0761189i
$339$	1.36722	−	13.0471i	0.0742574	−	0.708619i
$340$	−2.08248	−	11.8103i	−0.112938	−	0.640504i
$341$	0.744914	+	1.29023i	0.0403394	+	0.0698698i
$342$	−3.28710	+	3.65523i	−0.177746	+	0.197652i
$343$	−10.4415	+	15.2963i	−0.563786	+	0.825921i
$344$	−0.976681	−	5.53903i	−0.0526591	−	0.298645i
$345$	−11.8646	−	47.5236i	−0.638767	−	2.55859i
$346$	0.471905	+	0.395976i	0.0253698	+	0.0212878i
$347$	10.4190	−	3.79222i	0.559323	−	0.203577i	−0.0468610	−	0.998901i	$-0.514922\pi$
$347$	10.4190	−	3.79222i	0.559323	−	0.203577i	0.606184	+	0.795325i	$0.292700\pi$
$348$	7.96599	+	11.8022i	0.427022	+	0.632664i
$349$	4.39411	−	3.68710i	0.235212	−	0.197366i	−0.517562	−	0.855646i	$-0.673160\pi$
$349$	4.39411	−	3.68710i	0.235212	−	0.197366i	0.752773	+	0.658280i	$0.228716\pi$
$350$	−0.942165	−	6.25884i	−0.0503609	−	0.334549i
$351$	3.51251	+	1.86346i	0.187484	+	0.0994640i
$352$	4.87449	−	8.44287i	0.259811	−	0.450006i
$353$	−22.5127	−	8.19394i	−1.19823	−	0.436119i	−0.335623	−	0.941996i	$-0.608947\pi$
$353$	−22.5127	−	8.19394i	−1.19823	−	0.436119i	−0.862606	+	0.505877i	$0.831169\pi$
$354$	−4.70117	−	6.96512i	−0.249864	−	0.370192i
$355$	12.8047	+	10.7444i	0.679602	+	0.570254i
$356$	−10.2545	+	3.73235i	−0.543490	+	0.197814i
$357$	−1.07198	+	8.22949i	−0.0567354	+	0.435551i
$358$	0.239224	+	1.35670i	0.0126434	+	0.0717041i
$359$	12.9951			0.685856			0.342928	−	0.939362i	$-0.388581\pi$
$359$	12.9951			0.685856			0.342928	+	0.939362i	$0.388581\pi$
$360$	−11.4288	−	7.13169i	−0.602350	−	0.375873i
$361$	5.71798			0.300946
$362$	1.08682	−	0.911948i	0.0571219	−	0.0479309i
$363$	−0.713628	+	6.80997i	−0.0374558	+	0.357431i
$364$	−3.82803	−	0.0961852i	−0.200643	−	0.00504147i
$365$	16.0059	+	13.4306i	0.837790	+	0.702989i
$366$	4.84851	+	3.52036i	0.253436	+	0.184012i
$367$	−3.80019	−	21.5519i	−0.198368	−	1.12500i	−0.907540	−	0.419966i	$-0.862042\pi$
$367$	−3.80019	−	21.5519i	−0.198368	−	1.12500i	0.709172	−	0.705036i	$-0.249069\pi$
$368$	27.1397			1.41475
$369$	−0.357213	+	10.4138i	−0.0185958	+	0.542120i
$370$	−5.44880	−	9.43759i	−0.283269	−	0.490637i
$371$	−2.60486	−	2.29967i	−0.135237	−	0.119393i
$372$	0.445341	+	1.78382i	0.0230899	+	0.0924866i
$373$	1.59992	−	9.07360i	0.0828407	−	0.469813i	−0.914961	−	0.403542i	$-0.867779\pi$
$373$	1.59992	−	9.07360i	0.0828407	−	0.469813i	0.997802	−	0.0662708i	$-0.0211101\pi$
$374$	−1.48891	+	0.541920i	−0.0769898	+	0.0280220i
$375$	7.66178	+	11.3515i	0.395653	+	0.586189i
$376$	0.0404929	+	0.229647i	0.00208826	+	0.0118431i
$377$	3.32605			0.171300
$378$	2.94955	+	3.43962i	0.151708	+	0.176915i
$379$	7.04401			0.361826			0.180913	−	0.983499i	$-0.442095\pi$
$379$	7.04401			0.361826			0.180913	+	0.983499i	$0.442095\pi$
$380$	5.71702	+	32.4228i	0.293277	+	1.66326i
$381$	17.8706	−	1.25518i	0.915537	−	0.0643049i
$382$	−5.95952	+	2.16909i	−0.304915	+	0.110980i
$383$	3.57500	−	20.2748i	0.182674	−	1.03599i	−0.746234	−	0.665684i	$-0.768140\pi$
$383$	3.57500	−	20.2748i	0.182674	−	1.03599i	0.928908	−	0.370311i	$-0.120749\pi$
$384$	11.4106	−	11.0259i	0.582292	−	0.562661i
$385$	23.3110	−	7.82722i	1.18804	−	0.398912i
$386$	−2.53882	−	4.39736i	−0.129222	−	0.223820i
$387$	−4.07321	−	12.5097i	−0.207053	−	0.635905i
$388$	−18.4063			−0.934440
$389$	−1.63662	−	9.28175i	−0.0829801	−	0.470604i	−0.997774	−	0.0666831i	$-0.978758\pi$
$389$	−1.63662	−	9.28175i	−0.0829801	−	0.470604i	0.914794	−	0.403920i	$-0.132353\pi$
$390$	−1.39703	+	0.622516i	−0.0707414	+	0.0315223i
$391$	−11.2055	−	9.40257i	−0.566689	−	0.475508i
$392$	−8.27158	−	3.49042i	−0.417778	−	0.176293i
$393$	−4.76910	+	2.12510i	−0.240569	+	0.107197i
$394$	−0.535290	+	0.449161i	−0.0269675	+	0.0226284i
$395$	−58.4101			−2.93893
$396$	5.63381	−	13.9690i	0.283110	−	0.701970i
$397$	24.2309			1.21611			0.608056	−	0.793894i	$-0.291950\pi$
$397$	24.2309			1.21611			0.608056	+	0.793894i	$0.291950\pi$
$398$	−0.225901	−	1.28115i	−0.0113234	−	0.0642182i
$399$	2.94292	−	22.5924i	0.147330	−	1.13104i
$400$	−22.9175	+	8.34128i	−1.14587	+	0.417064i
$401$	−19.8850	−	16.6855i	−0.993009	−	0.833233i	−0.00700802	−	0.999975i	$-0.502231\pi$
$401$	−19.8850	−	16.6855i	−0.993009	−	0.833233i	−0.986000	+	0.166742i	$0.946675\pi$
$402$	−3.00523	+	6.16648i	−0.149887	+	0.307556i
$403$	0.403566	+	0.146886i	0.0201031	+	0.00731691i
$404$	8.13128	−	14.0838i	0.404546	−	0.700695i
$405$	−28.8023	−	12.7810i	−1.43120	−	0.635092i
$406$	3.52795	+	1.38538i	0.175089	+	0.0687554i
$407$	19.2039	−	16.1140i	0.951903	−	0.798742i
$408$	−4.01314	+	0.281872i	−0.198680	+	0.0139548i
$409$	16.5791	−	6.03428i	0.819782	−	0.298376i	0.102123	−	0.994772i	$-0.467436\pi$
$409$	16.5791	−	6.03428i	0.819782	−	0.298376i	0.717658	+	0.696396i	$0.245214\pi$
$410$	−3.07033	−	2.57631i	−0.151633	−	0.127235i
$411$	3.16166	−	3.05507i	0.155953	−	0.150695i
$412$	4.50958	+	25.5751i	0.222171	+	1.26000i
$413$	36.2510	+	14.2353i	1.78379	+	0.700475i
$414$	−7.90807	+	1.11639i	−0.388661	+	0.0548677i
$415$	−0.942097	−	1.63176i	−0.0462457	−	0.0800999i
$416$	−0.488003	−	2.76760i	−0.0239263	−	0.135693i
$417$	5.06383	+	3.67670i	0.247977	+	0.180049i
$418$	4.08751	−	1.48773i	0.199927	−	0.0727673i
$419$	6.74776	+	5.66205i	0.329650	+	0.276609i	0.792557	−	0.609798i	$-0.208749\pi$
$419$	6.74776	+	5.66205i	0.329650	+	0.276609i	−0.462907	+	0.886407i	$0.653194\pi$
$420$	30.3154	−	1.36514i	1.47924	−	0.0666121i
$421$	−6.10836	−	2.22326i	−0.297703	−	0.108355i	0.188850	−	0.982006i	$-0.439524\pi$
$421$	−6.10836	−	2.22326i	−0.297703	−	0.108355i	−0.486554	+	0.873651i	$0.661746\pi$
$422$	2.95618	+	5.12025i	0.143904	+	0.249250i
$423$	0.168874	+	0.518650i	0.00821093	+	0.0252176i
$424$	0.842204	−	1.45874i	0.0409010	−	0.0708427i
$425$	12.3521	+	4.49580i	0.599165	+	0.218078i
$426$	1.95991	−	1.89383i	0.0949580	−	0.0917566i
$427$	−27.7608	−	0.697533i	−1.34344	−	0.0337560i
$428$	5.45128	−	30.9158i	0.263498	−	1.49437i
$429$	−1.96835	−	2.91625i	−0.0950327	−	0.140798i
$430$	4.75534	+	1.73080i	0.229323	+	0.0834667i
$431$	−1.39051	−	2.40844i	−0.0669786	−	0.116010i	0.830591	−	0.556882i	$-0.188003\pi$
$431$	−1.39051	−	2.40844i	−0.0669786	−	0.116010i	−0.897570	+	0.440872i	$0.854669\pi$
$432$	10.7362	−	13.7680i	0.516546	−	0.662414i
$433$	−18.3922			−0.883872			−0.441936	−	0.897047i	$-0.645708\pi$
$433$	−18.3922			−0.883872			−0.441936	+	0.897047i	$0.645708\pi$
$434$	0.366882	+	0.323898i	0.0176109	+	0.0155476i
$435$	−26.2936	+	1.84679i	−1.26068	+	0.0885470i
$436$	−5.75397	−	4.82815i	−0.275565	−	0.231227i
$437$	30.7626	+	25.8129i	1.47157	+	1.23480i
$438$	2.44990	−	2.36731i	0.117061	−	0.113114i
$439$	−13.8666	−	5.04705i	−0.661819	−	0.240882i	−0.0107974	−	0.999942i	$-0.503437\pi$
$439$	−13.8666	−	5.04705i	−0.661819	−	0.240882i	−0.651021	+	0.759059i	$0.725659\pi$
$440$	5.96012	+	10.3232i	0.284138	+	0.492141i
$441$	−20.2992	−	5.37969i	−0.966630	−	0.256176i
$442$	−0.228373	+	0.395554i	−0.0108626	+	0.0188146i
$443$	−24.8367	+	20.8405i	−1.18003	+	0.990160i	−0.180048	+	0.983658i	$0.557625\pi$
$443$	−24.8367	+	20.8405i	−1.18003	+	0.990160i	−0.999979	+	0.00650261i	$0.997930\pi$
$444$	28.2586	−	12.5920i	1.34109	−	0.597589i
$445$	3.50784	−	19.8940i	0.166288	−	0.943064i
$446$	2.38871	−	0.869418i	0.113109	−	0.0411681i
$447$	1.00294	−	9.57076i	0.0474373	−	0.452681i
$448$	−2.89108	+	14.2875i	−0.136591	+	0.675023i
$449$	−5.38939	+	9.33469i	−0.254341	+	0.440531i	−0.964716	−	0.263292i	$-0.915192\pi$
$449$	−5.38939	+	9.33469i	−0.254341	+	0.440531i	0.710375	+	0.703823i	$0.248525\pi$
$450$	6.33467	−	3.37323i	0.298619	−	0.159015i
$451$	4.61006	−	7.98487i	0.217079	−	0.375993i
$452$	−10.9737	+	9.20805i	−0.516161	+	0.433110i
$453$	−8.72257	−	2.49824i	−0.409822	−	0.117378i
$454$	−5.50549	+	2.00383i	−0.258385	+	0.0940445i
$455$	3.69731	−	6.04782i	0.173332	−	0.283526i
$456$	11.0173	−	0.773823i	0.515930	−	0.0362376i
$457$	−0.544905	−	3.09031i	−0.0254896	−	0.144558i	0.969407	−	0.245459i	$-0.0789387\pi$
$457$	−0.544905	−	3.09031i	−0.0254896	−	0.144558i	−0.994897	+	0.100901i	$0.967828\pi$
$458$	2.51611	+	4.35803i	0.117570	+	0.203637i
$459$	−9.20275	+	1.96502i	−0.429547	+	0.0917194i
$460$	−26.7439	+	46.3218i	−1.24694	+	2.15977i
$461$	29.6120	−	24.8474i	1.37917	−	1.15726i	0.409648	−	0.912244i	$-0.365651\pi$
$461$	29.6120	−	24.8474i	1.37917	−	1.15726i	0.969519	−	0.245015i	$-0.0787930\pi$
$462$	−0.873139	−	3.91314i	−0.0406221	−	0.182056i
$463$	−0.105767	+	0.599835i	−0.00491541	+	0.0278767i	−0.987167	−	0.159692i	$-0.948950\pi$
$463$	−0.105767	+	0.599835i	−0.00491541	+	0.0278767i	0.982251	+	0.187569i	$0.0600609\pi$
$464$	2.53603	−	14.3826i	0.117732	−	0.667694i
$465$	−3.27189	−	0.937106i	−0.151730	−	0.0434573i
$466$	2.41912	−	2.02988i	0.112063	−	0.0940324i
$467$	−27.9930			−1.29536			−0.647681	−	0.761912i	$-0.724261\pi$
$467$	−27.9930			−1.29536			−0.647681	+	0.761912i	$0.724261\pi$
$468$	−1.34429	−	4.12861i	−0.0621397	−	0.190845i
$469$	−4.73255	−	31.4385i	−0.218529	−	1.45169i
$470$	−0.197155	−	0.0717586i	−0.00909409	−	0.00330998i
$471$	1.79017	−	0.797699i	0.0824868	−	0.0367560i
$472$	−3.27836	+	18.5925i	−0.150899	+	0.855790i
$473$	−2.02149	+	11.4644i	−0.0929482	+	0.527136i
$474$	−0.992569	+	9.47182i	−0.0455902	+	0.435055i
$475$	−33.9102	−	12.3423i	−1.55591	−	0.566304i
$476$	7.08632	−	5.64898i	0.324801	−	0.258920i
$477$	1.47368	−	3.65399i	0.0674753	−	0.167305i
$478$	7.79049			0.356329
$479$	−29.1975	+	24.4996i	−1.33407	+	1.11941i	−0.350957	+	0.936392i	$0.614144\pi$
$479$	−29.1975	+	24.4996i	−1.33407	+	1.11941i	−0.983109	+	0.183022i	$0.941412\pi$
$480$	5.39455	+	21.6079i	0.246226	+	0.986262i
$481$	1.25487	−	7.11672i	0.0572172	−	0.324495i
$482$	−0.850587	+	4.82392i	−0.0387432	+	0.219724i
$483$	27.2557	−	25.0439i	1.24018	−	1.13954i
$484$	5.72778	−	4.80618i	0.260354	−	0.218463i
$485$	17.0364	−	29.5078i	0.773581	−	1.33988i
$486$	−2.56201	+	4.45341i	−0.116215	+	0.202011i
$487$	11.6367	+	20.1554i	0.527311	+	0.913330i	0.999493	+	0.0318291i	$0.0101332\pi$
$487$	11.6367	+	20.1554i	0.527311	+	0.913330i	−0.472182	+	0.881501i	$0.656533\pi$
$488$	−2.33757	−	13.2570i	−0.105817	−	0.600118i
$489$	1.60709	+	2.38103i	0.0726753	+	0.107674i
$490$	6.44081	−	4.87492i	0.290966	−	0.220226i
$491$	−5.97898	+	2.17617i	−0.269827	+	0.0982092i	−0.473391	−	0.880853i	$-0.656970\pi$
$491$	−5.97898	+	2.17617i	−0.269827	+	0.0982092i	0.203563	+	0.979062i	$0.434748\pi$
$492$	8.18248	−	7.90662i	0.368895	−	0.356458i
$493$	−6.02994	+	5.05972i	−0.271575	+	0.227878i
$494$	0.626953	−	1.08592i	0.0282080	−	0.0488576i
$495$	17.1797	+	21.9611i	0.772172	+	0.987077i
$496$	0.942877	−	1.63311i	0.0423364	−	0.0733289i
$497$	−2.50517	+	12.3804i	−0.112372	+	0.555336i
$498$	−0.280616	+	0.125042i	−0.0125747	+	0.00560328i
$499$	14.6914	−	5.34723i	0.657678	−	0.239375i	0.00844430	−	0.999964i	$-0.497312\pi$
$499$	14.6914	−	5.34723i	0.657678	−	0.239375i	0.649233	+	0.760589i	$0.275090\pi$
$500$	2.59690	−	14.7278i	0.116137	−	0.658646i
$501$	−0.763384	+	7.28477i	−0.0341055	+	0.325460i
$502$	4.85413	−	4.07310i	0.216651	−	0.181791i
$503$	−1.94708	+	3.37244i	−0.0868161	+	0.150370i	−0.906164	−	0.422927i	$-0.861003\pi$
$503$	−1.94708	+	3.37244i	−0.0868161	+	0.150370i	0.819348	+	0.573297i	$0.194336\pi$
$504$	0.604432	−	10.1620i	0.0269235	−	0.452651i
$505$	15.0521	+	26.0711i	0.669811	+	1.16015i
$506$	6.64071	+	2.41702i	0.295215	+	0.107450i
$507$	20.6713	+	5.92049i	0.918045	+	0.262938i
$508$	−14.9857	−	12.5745i	−0.664883	−	0.557903i
$509$	11.8046	+	9.90526i	0.523231	+	0.439043i	0.865756	−	0.500466i	$-0.166838\pi$
$509$	11.8046	+	9.90526i	0.523231	+	0.439043i	−0.342525	+	0.939509i	$0.611282\pi$
$510$	1.58574	−	3.25381i	0.0702178	−	0.144081i
$511$	−3.13148	+	15.4756i	−0.138529	+	0.684598i
$512$	−20.9586			−0.926249
$513$	25.2643	−	5.39458i	1.11545	−	0.238176i
$514$	3.46293	+	5.99797i	0.152743	+	0.264559i
$515$	−45.1743	−	16.4421i	−1.99062	−	0.724525i
$516$	−6.29378	+	12.9143i	−0.277068	+	0.568520i
$517$	0.0838104	−	0.475312i	0.00368598	−	0.0209042i
$518$	4.29534	−	7.02604i	0.188726	−	0.308707i
$519$	−0.784156	−	3.14094i	−0.0344206	−	0.137872i
$520$	3.22897	+	1.17525i	0.141600	+	0.0515380i
$521$	13.1274	−	22.7374i	0.575124	−	0.996144i	−0.420904	−	0.907105i	$-0.638287\pi$
$521$	13.1274	−	22.7374i	0.575124	−	0.996144i	0.996028	−	0.0890386i	$-0.0283794\pi$
$522$	−0.147333	+	4.29517i	−0.00644857	+	0.187994i
$523$	−6.32607	−	10.9571i	−0.276620	−	0.479119i	0.693923	−	0.720049i	$-0.255881\pi$
$523$	−6.32607	−	10.9571i	−0.276620	−	0.479119i	−0.970542	+	0.240930i	$0.922548\pi$
$524$	5.35757	+	1.95000i	0.234046	+	0.0851859i
$525$	−15.3183	+	29.5247i	−0.668545	+	1.28856i
$526$	−6.94253	−	5.82547i	−0.302709	−	0.254003i
$527$	−0.955092	+	0.347625i	−0.0416044	+	0.0151428i
$528$	−14.1113	+	6.28799i	−0.614117	+	0.273650i
$529$	7.33517	+	41.5998i	0.318920	+	1.80869i
$530$	0.757758	+	1.31248i	0.0329149	+	0.0570103i
$531$	−1.51390	+	44.1345i	−0.0656975	+	1.91527i
$532$	−19.4541	+	15.5081i	−0.843441	+	0.672362i
$533$	−0.461530	−	2.61747i	−0.0199911	−	0.113375i
$534$	−3.16641	−	0.906894i	−0.137024	−	0.0392451i
$535$	44.5166	+	37.3538i	1.92462	+	1.61495i
$536$	14.4824	−	5.27115i	0.625543	−	0.227679i
$537$	3.17168	−	6.50800i	0.136868	−	0.280841i
$538$	1.26387	−	1.06052i	0.0544895	−	0.0457221i
$539$	13.6168	+	12.6441i	0.586517	+	0.544619i
$540$	12.9195	+	31.8917i	0.555967	+	1.37240i
$541$	−18.8187	+	32.5949i	−0.809079	+	1.40137i	0.104423	+	0.994533i	$0.466700\pi$
$541$	−18.8187	+	32.5949i	−0.809079	+	1.40137i	−0.913502	+	0.406833i	$0.866633\pi$
$542$	−9.11767	−	3.31856i	−0.391638	−	0.142544i
$543$	−7.43742	+	0.522385i	−0.319170	+	0.0224177i
$544$	5.09491	+	4.27514i	0.218442	+	0.183295i
$545$	13.0659	−	4.75559i	0.559681	−	0.203707i
$546$	−0.917889	−	0.702329i	−0.0392820	−	0.0300569i
$547$	−3.30801	−	18.7606i	−0.141440	−	0.802147i	−0.970157	−	0.242478i	$-0.922040\pi$
$547$	−3.30801	−	18.7606i	−0.141440	−	0.802147i	0.828717	−	0.559668i	$-0.189071\pi$
$548$	−4.80094			−0.205086
$549$	−9.74875	−	29.9406i	−0.416066	−	1.27783i
$550$	−6.35045			−0.270784
$551$	16.5540	−	13.8904i	0.705223	−	0.591753i
$552$	14.5195	+	10.5422i	0.617993	+	0.448706i
$553$	−21.1023	−	38.7677i	−0.897361	−	1.64857i
$554$	−4.00975	−	3.36458i	−0.170358	−	0.142947i
$555$	−5.96863	+	56.9570i	−0.253354	+	2.41769i
$556$	−1.18662	−	6.72964i	−0.0503238	−	0.285400i
$557$	−14.6739			−0.621753			−0.310876	−	0.950450i	$-0.600623\pi$
$557$	−14.6739			−0.621753			−0.310876	+	0.950450i	$0.600623\pi$
$558$	−0.207561	+	0.514648i	−0.00878677	+	0.0217868i
$559$	1.67789	+	2.90619i	0.0709673	+	0.122919i
$560$	−23.3330	−	20.5993i	−0.985999	−	0.870479i
$561$	8.00482	+	2.29267i	0.337964	+	0.0967965i
$562$	0.648685	−	3.67888i	0.0273631	−	0.155184i
$563$	22.6293	−	8.23639i	0.953711	−	0.347122i	0.182145	−	0.983272i	$-0.441696\pi$
$563$	22.6293	−	8.23639i	0.953711	−	0.347122i	0.771566	+	0.636149i	$0.219474\pi$
$564$	0.260938	−	0.535423i	0.0109875	−	0.0225454i
$565$	−4.60479	−	26.1151i	−0.193725	−	1.09867i
$566$	2.34518			0.0985754
$567$	−1.92272	−	23.7340i	−0.0807467	−	0.996735i
$568$	−6.12314			−0.256921
$569$	4.35649	+	24.7069i	0.182633	+	1.03577i	0.928958	+	0.370184i	$0.120705\pi$
$569$	4.35649	+	24.7069i	0.182633	+	1.03577i	−0.746325	+	0.665582i	$0.768184\pi$
$570$	−4.35334	+	8.93267i	−0.182341	+	0.374148i
$571$	−29.9613	+	10.9050i	−1.25384	+	0.456361i	−0.881698	−	0.471814i	$-0.843599\pi$
$571$	−29.9613	+	10.9050i	−1.25384	+	0.456361i	−0.372144	+	0.928175i	$0.621377\pi$
$572$	−0.667156	+	3.78363i	−0.0278952	+	0.158202i
$573$	32.0401	+	9.17663i	1.33849	+	0.383359i
$574$	0.600694	−	2.96859i	0.0250725	−	0.123907i
$575$	−29.3137	−	50.7728i	−1.22247	−	2.11737i
$576$	−16.3666	+	2.31049i	−0.681942	+	0.0962706i
$577$	23.3140			0.970574			0.485287	−	0.874355i	$-0.338715\pi$
$577$	23.3140			0.970574			0.485287	+	0.874355i	$0.338715\pi$
$578$	0.785247	+	4.45336i	0.0326620	+	0.185235i
$579$	−2.78103	+	26.5386i	−0.115576	+	1.10291i
$580$	22.0490	+	18.5013i	0.915535	+	0.768225i
$581$	0.742664	−	1.21480i	0.0308109	−	0.0503985i
$582$	−4.49551	−	3.26405i	−0.186345	−	0.135299i
$583$	−2.67067	+	2.24096i	−0.110608	+	0.0928110i
$584$	−7.65396			−0.316723
$585$	7.86294	+	1.66624i	0.325093	+	0.0688906i
$586$	−9.02190			−0.372691
$587$	−5.26847	−	29.8790i	−0.217453	−	1.23324i	−0.876599	−	0.481222i	$-0.840193\pi$
$587$	−5.26847	−	29.8790i	−0.217453	−	1.23324i	0.659146	−	0.752015i	$-0.270918\pi$
$588$	11.8583	+	19.6276i	0.489030	+	0.809427i
$589$	2.62201	−	0.954334i	0.108038	−	0.0393227i
$590$	−13.0123	−	10.9186i	−0.535708	−	0.449513i
$591$	3.66315	−	0.257290i	0.150682	−	0.0105835i
$592$	−29.8175	−	10.8527i	−1.22549	−	0.446042i
$593$	0.321518	−	0.556885i	0.0132031	−	0.0228685i	−0.859348	−	0.511391i	$-0.829131\pi$
$593$	0.321518	−	0.556885i	0.0132031	−	0.0228685i	0.872551	+	0.488522i	$0.162464\pi$
$594$	3.85316	−	2.41269i	0.158097	−	0.0989939i
$595$	2.49718	+	16.5889i	0.102374	+	0.680077i
$596$	−8.04985	+	6.75463i	−0.329735	+	0.276680i
$597$	−2.99504	+	6.14557i	−0.122579	+	0.251521i
$598$	1.91429	−	0.696743i	0.0782810	−	0.0284919i
$599$	−7.11487	−	5.97008i	−0.290706	−	0.243931i	0.485758	−	0.874094i	$-0.338544\pi$
$599$	−7.11487	−	5.97008i	−0.290706	−	0.243931i	−0.776463	+	0.630163i	$0.782988\pi$
$600$	−15.5008	−	4.43960i	−0.632817	−	0.181246i
$601$	1.97340	+	11.1917i	0.0804968	+	0.456520i	0.998238	+	0.0593406i	$0.0188998\pi$
$601$	1.97340	+	11.1917i	0.0804968	+	0.456520i	−0.917741	+	0.397179i	$0.869989\pi$
$602$	0.569241	+	3.78149i	0.0232005	+	0.154122i
$603$	31.8194	−	16.9439i	1.29579	−	0.690009i
$604$	4.95394	+	8.58047i	0.201573	+	0.349134i
$605$	2.40349	+	13.6309i	0.0977157	+	0.554174i
$606$	4.48348	−	1.99784i	0.182129	−	0.0811565i
$607$	−36.1061	+	13.1415i	−1.46550	+	0.533398i	−0.946874	−	0.321604i	$-0.895778\pi$
$607$	−36.1061	+	13.1415i	−1.46550	+	0.533398i	−0.518625	+	0.855002i	$0.673556\pi$
$608$	−13.9870	−	11.7365i	−0.567250	−	0.475979i
$609$	−10.7250	−	16.7842i	−0.434601	−	0.680132i
$610$	11.3814	+	4.14248i	0.460818	+	0.167724i
$611$	−0.0695649	−	0.120490i	−0.00281429	−	0.00487450i
$612$	8.71772	+	5.43995i	0.352393	+	0.219897i
$613$	−0.839408	+	1.45390i	−0.0339034	+	0.0587223i	−0.882479	−	0.470351i	$-0.844127\pi$
$613$	−0.839408	+	1.45390i	−0.0339034	+	0.0587223i	0.848576	+	0.529074i	$0.177461\pi$
$614$	−4.98741	−	1.81527i	−0.201275	−	0.0732582i
$615$	5.10191	+	20.4357i	0.205729	+	0.824049i
$616$	−4.69842	+	7.68538i	−0.189305	+	0.309653i
$617$	−7.33634	+	41.6064i	−0.295350	+	1.67501i	0.370427	+	0.928861i	$0.379211\pi$
$617$	−7.33634	+	41.6064i	−0.295350	+	1.67501i	−0.665777	+	0.746151i	$0.731900\pi$
$618$	−3.43391	+	7.04608i	−0.138132	+	0.283435i
$619$	6.28044	+	2.28589i	0.252432	+	0.0918778i	0.465137	−	0.885239i	$-0.346005\pi$
$619$	6.28044	+	2.28589i	0.252432	+	0.0918778i	−0.212705	+	0.977116i	$0.568227\pi$
$620$	1.85825	+	3.21859i	0.0746293	+	0.129262i
$621$	37.0760	+	19.6696i	1.48781	+	0.789313i
$622$	4.82865			0.193611
$623$	14.4712	−	4.85904i	0.579777	−	0.194674i
$624$	−1.95100	+	4.00328i	−0.0781024	+	0.160259i
$625$	−6.59414	−	5.53314i	−0.263766	−	0.221326i
$626$	1.45614	+	1.22185i	0.0581991	+	0.0488349i
$627$	−21.9756	−	6.29406i	−0.877622	−	0.251361i
$628$	−2.01107	−	0.731968i	−0.0802503	−	0.0292087i
$629$	8.55124	+	14.8112i	0.340960	+	0.590560i
$630$	7.64621	+	5.04250i	0.304632	+	0.200898i
$631$	−7.14106	+	12.3687i	−0.284281	+	0.492389i	−0.972435	−	0.233176i	$-0.925088\pi$
$631$	−7.14106	+	12.3687i	−0.284281	+	0.492389i	0.688154	+	0.725565i	$0.258422\pi$
$632$	16.3908	−	13.7535i	0.651992	−	0.547087i
$633$	3.23820	−	30.9013i	0.128707	−	1.22822i
$634$	1.36167	−	7.72239i	0.0540787	−	0.306695i
$635$	34.0289	−	12.3855i	1.35040	−	0.491504i
$636$	−3.92989	+	1.75115i	−0.155830	+	0.0694378i
$637$	5.34978	+	0.269013i	0.211966	+	0.0106587i
$638$	1.90142	−	3.29336i	0.0752780	−	0.130385i
$639$	−14.1819	+	2.00208i	−0.561028	+	0.0792010i
$640$	16.0372	−	27.7772i	0.633925	−	1.09799i
$641$	22.9718	−	19.2756i	0.907331	−	0.761341i	−0.0642780	−	0.997932i	$-0.520474\pi$
$641$	22.9718	−	19.2756i	0.907331	−	0.761341i	0.971609	+	0.236591i	$0.0760300\pi$
$642$	6.81380	−	6.58408i	0.268919	−	0.259853i
$643$	4.25499	−	1.54869i	0.167801	−	0.0610744i	−0.256754	−	0.966477i	$-0.582653\pi$
$643$	4.25499	−	1.54869i	0.167801	−	0.0610744i	0.424554	+	0.905402i	$0.360431\pi$
$644$	−40.4065	−	1.01528i	−1.59224	−	0.0400074i
$645$	−14.8780	−	22.0429i	−0.585821	−	0.867937i
$646$	0.515307	+	2.92245i	0.0202745	+	0.114982i
$647$	18.5452	+	32.1213i	0.729088	+	1.26282i	0.957269	+	0.289198i	$0.0933887\pi$
$647$	18.5452	+	32.1213i	0.729088	+	1.26282i	−0.228182	+	0.973619i	$0.573278\pi$
$648$	11.0919	−	3.19539i	0.435730	−	0.125527i
$649$	19.5378	−	33.8405i	0.766926	−	1.32836i
$650$	−1.40233	+	1.17670i	−0.0550040	+	0.0461538i
$651$	−0.560092	−	2.51016i	−0.0219517	−	0.0983809i
$652$	0.544712	−	3.08921i	0.0213326	−	0.120983i
$653$	−1.27114	+	7.20899i	−0.0497435	+	0.282110i	−0.999525	−	0.0308029i	$-0.990194\pi$
$653$	−1.27114	+	7.20899i	−0.0497435	+	0.282110i	0.949782	+	0.312913i	$0.101305\pi$
$654$	−0.549140	−	2.19958i	−0.0214731	−	0.0860105i
$655$	−8.08491	+	6.78405i	−0.315904	+	0.265075i
$656$	−11.6704			−0.455653
$657$	−17.7275	+	2.50261i	−0.691616	+	0.0976362i
$658$	−0.0236006	−	0.156780i	−0.000920046	−	0.00611190i
$659$	25.4987	+	9.28075i	0.993287	+	0.361527i	0.786992	−	0.616963i	$-0.211637\pi$
$659$	25.4987	+	9.28075i	0.993287	+	0.361527i	0.206295	+	0.978490i	$0.433859\pi$
$660$	3.17324	−	30.2814i	0.123518	−	1.17870i
$661$	−5.13170	+	29.1033i	−0.199600	+	1.13199i	0.706114	+	0.708098i	$0.250446\pi$
$661$	−5.13170	+	29.1033i	−0.199600	+	1.13199i	−0.905714	+	0.423889i	$0.860665\pi$
$662$	−1.54169	+	8.74337i	−0.0599196	+	0.339821i
$663$	2.19247	−	0.976964i	0.0851486	−	0.0379421i
$664$	0.648590	+	0.236067i	0.0251702	+	0.00916119i
$665$	−6.85550	−	45.5414i	−0.265845	−	1.76602i
$666$	9.13476	+	1.93575i	0.353965	+	0.0750089i
$667$	35.1078			1.35938
$668$	6.12714	−	5.14128i	0.237066	−	0.198922i
$669$	−12.8424	−	3.67820i	−0.496515	−	0.142207i
$670$	−2.40789	+	13.6558i	−0.0930250	+	0.527571i
$671$	−4.83820	+	27.4388i	−0.186777	+	1.05926i
$672$	−12.3926	+	11.3869i	−0.478053	+	0.439260i
$673$	−16.8216	+	14.1150i	−0.648424	+	0.544093i	−0.906592	−	0.422007i	$-0.861326\pi$
$673$	−16.8216	+	14.1150i	−0.648424	+	0.544093i	0.258168	+	0.966100i	$0.416881\pi$
$674$	1.67497	−	2.90114i	0.0645176	−	0.111748i
$675$	−37.3533	−	5.21436i	−1.43773	−	0.200701i
$676$	−11.7402	−	20.3345i	−0.451544	−	0.782098i
$677$	1.86397	+	10.5711i	0.0716384	+	0.406281i	0.999448	+	0.0332270i	$0.0105784\pi$
$677$	1.86397	+	10.5711i	0.0716384	+	0.406281i	−0.927809	+	0.373054i	$0.878310\pi$
$678$	−4.31308	+	0.302940i	−0.165643	+	0.0116343i
$679$	25.7396	+	0.646748i	0.987797	+	0.0248199i
$680$	−7.64177	+	2.78138i	−0.293048	+	0.106661i
$681$	29.5991	+	8.47750i	1.13424	+	0.324859i
$682$	0.376151	−	0.315628i	0.0144036	−	0.0120860i
$683$	−2.29631	+	3.97733i	−0.0878659	+	0.152188i	−0.906609	−	0.421972i	$-0.861338\pi$
$683$	−2.29631	+	3.97733i	−0.0878659	+	0.152188i	0.818743	+	0.574160i	$0.194671\pi$
$684$	−23.9328	−	14.9343i	−0.915092	−	0.571027i
$685$	4.44361	−	7.69656i	0.169782	−	0.294070i
$686$	5.56248	+	2.51366i	0.212376	+	0.0959721i
$687$	2.75615	−	26.3013i	0.105154	−	1.00346i
$688$	13.8464	−	5.03967i	0.527888	−	0.192136i
$689$	−0.174513	+	0.989715i	−0.00664843	+	0.0377051i
$690$	−14.7463	+	6.57092i	−0.561380	+	0.250150i
$691$	−12.5061	+	10.4939i	−0.475754	+	0.399205i	−0.848888	−	0.528572i	$-0.822728\pi$
$691$	−12.5061	+	10.4939i	−0.475754	+	0.399205i	0.373134	+	0.927777i	$0.378283\pi$
$692$	−1.76756	+	3.06151i	−0.0671927	+	0.116381i
$693$	−8.36923	+	19.3365i	−0.317921	+	0.734533i
$694$	−1.82719	−	3.16479i	−0.0693592	−	0.120134i
$695$	11.8868	+	4.32645i	0.450893	+	0.164111i
$696$	6.94356	−	6.70946i	0.263195	−	0.254322i
$697$	4.81852	+	4.04322i	0.182515	+	0.153148i
$698$	−1.44825	−	1.21523i	−0.0548171	−	0.0459970i
$699$	−16.5547	+	1.16276i	−0.626158	+	0.0439797i
$700$	34.4323	−	11.5614i	1.30142	−	0.436982i
$701$	15.1798			0.573334			0.286667	−	0.958030i	$-0.407453\pi$
$701$	15.1798			0.573334			0.286667	+	0.958030i	$0.407453\pi$
$702$	0.403814	−	1.24674i	0.0152410	−	0.0470554i
$703$	−23.4757	−	40.6611i	−0.885403	−	1.53356i
$704$	13.7437	+	5.00228i	0.517984	+	0.188531i
$705$	0.616838	+	0.913890i	0.0232315	+	0.0344191i
$706$	−1.37115	+	7.77616i	−0.0516038	+	0.292659i
$707$	−11.8657	+	19.4092i	−0.446257	+	0.729959i
$708$	34.6780	−	33.5089i	1.30328	−	1.25934i
$709$	15.1280	+	5.50612i	0.568142	+	0.206787i	0.610089	−	0.792333i	$-0.291134\pi$
$709$	15.1280	+	5.50612i	0.568142	+	0.206787i	−0.0419467	+	0.999120i	$0.513356\pi$
$710$	2.75459	−	4.77109i	0.103378	−	0.179056i
$711$	33.4662	−	37.2142i	1.25508	−	1.39564i
$712$	3.69997	+	6.40854i	0.138662	+	0.240170i
$713$	4.25981	+	1.55044i	0.159531	+	0.0580646i
$714$	2.73249	−	0.123048i	0.102261	−	0.00460495i
$715$	−5.44817	−	4.57156i	−0.203750	−	0.170967i
$716$	−7.42889	+	2.70390i	−0.277631	+	0.101049i
$717$	−33.1290	−	24.0540i	−1.23722	−	0.898312i
$718$	−0.743743	−	4.21798i	−0.0277562	−	0.157413i
$719$	24.3069	+	42.1007i	0.906493	+	1.57009i	0.818901	+	0.573935i	$0.194584\pi$
$719$	24.3069	+	42.1007i	0.906493	+	1.57009i	0.0875916	+	0.996156i	$0.472083\pi$
$720$	13.2005	−	32.7306i	0.491954	−	1.21980i
$721$	−5.40761	−	35.9230i	−0.201390	−	1.33784i
$722$	−0.327254	−	1.85595i	−0.0121791	−	0.0690714i
$723$	18.5115	−	17.8874i	0.688450	−	0.665240i
$724$	6.23679	+	5.23329i	0.231788	+	0.194494i
$725$	−29.6460	+	10.7903i	−1.10102	+	0.400740i
$726$	2.25123	−	0.158121i	0.0835510	−	0.00586841i
$727$	−24.9856	+	20.9654i	−0.926666	+	0.777565i	−0.975216	−	0.221256i	$-0.928984\pi$
$727$	−24.9856	+	20.9654i	−0.926666	+	0.777565i	0.0485502	+	0.998821i	$0.484540\pi$
$728$	0.386525	+	2.56770i	0.0143256	+	0.0951654i
$729$	24.6453	−	11.0276i	0.912790	−	0.408430i
$730$	3.44326	−	5.96390i	0.127441	−	0.220734i
$731$	−7.46294	−	2.71629i	−0.276027	−	0.100466i
$732$	−15.0634	+	30.9089i	−0.556761	+	1.14242i
$733$	−18.9010	−	15.8598i	−0.698125	−	0.585797i	0.223114	−	0.974792i	$-0.428378\pi$
$733$	−18.9010	−	15.8598i	−0.698125	−	0.585797i	−0.921240	+	0.388996i	$0.872822\pi$
$734$	−6.77787	+	2.46694i	−0.250176	+	0.0910565i
$735$	−42.4413	+	0.843832i	−1.56547	+	0.0311252i
$736$	−5.15108	−	29.2132i	−0.189871	−	1.07681i
$737$	−31.8987			−1.17500
$738$	3.40057	−	0.480062i	0.125177	−	0.0176713i
$739$	−16.8462			−0.619699			−0.309849	−	0.950786i	$-0.600279\pi$
$739$	−16.8462			−0.619699			−0.309849	+	0.950786i	$0.600279\pi$
$740$	47.9059	−	40.1978i	1.76106	−	1.47770i
$741$	−6.01900	+	2.68206i	−0.221113	+	0.0985279i
$742$	−0.597348	+	0.977104i	−0.0219293	+	0.0358706i
$743$	−9.71999	−	8.15604i	−0.356592	−	0.299216i	0.446839	−	0.894615i	$-0.352550\pi$
$743$	−9.71999	−	8.15604i	−0.356592	−	0.299216i	−0.803431	+	0.595398i	$0.796994\pi$
$744$	1.13880	−	0.507449i	0.0417505	−	0.0186040i
$745$	−3.37787	−	19.1569i	−0.123756	−	0.701854i
$746$	−3.03669			−0.111181
$747$	1.57940	+	0.334691i	0.0577872	+	0.0122457i
$748$	−4.54630	−	7.87442i	−0.166229	−	0.287917i
$749$	−8.70944	+	43.0414i	−0.318236	+	1.57270i
$750$	3.24598	−	3.13655i	0.118526	−	0.114531i
$751$	−1.60966	+	9.12883i	−0.0587373	+	0.333116i	−0.999989	−	0.00458870i	$-0.998539\pi$
$751$	−1.60966	+	9.12883i	−0.0587373	+	0.333116i	0.941252	+	0.337705i	$0.109650\pi$
$752$	−0.574067	+	0.208943i	−0.0209341	+	0.00761938i
$753$	−33.2183	+	2.33317i	−1.21054	+	0.0850253i
$754$	−0.190358	−	1.07957i	−0.00693243	−	0.0393157i
$755$	−18.3409			−0.667493
$756$	−16.4995	+	20.0966i	−0.600080	+	0.730907i
$757$	−9.59655			−0.348792			−0.174396	−	0.984676i	$-0.555797\pi$
$757$	−9.59655			−0.348792			−0.174396	+	0.984676i	$0.555797\pi$
$758$	−0.403146	−	2.28635i	−0.0146429	−	0.0830441i
$759$	−20.7767	−	30.7823i	−0.754148	−	1.11733i
$760$	20.9789	−	7.63571i	0.760986	−	0.276976i
$761$	−5.23368	+	29.6816i	−0.189721	+	1.07596i	0.730018	+	0.683428i	$0.239512\pi$
$761$	−5.23368	+	29.6816i	−0.189721	+	1.07596i	−0.919739	+	0.392531i	$0.871600\pi$
$762$	−1.43019	−	5.72862i	−0.0518102	−	0.207526i
$763$	7.87677	+	6.95393i	0.285158	+	0.251749i
$764$	−18.1970	−	31.5181i	−0.658344	−	1.14029i
$765$	−16.7898	+	8.94063i	−0.607038	+	0.323249i
$766$	−6.78543			−0.245168
$767$	−1.95600	−	11.0930i	−0.0706270	−	0.400546i
$768$	11.2125	+	8.14103i	0.404595	+	0.293764i
$769$	27.5661	+	23.1307i	0.994060	+	0.834115i	0.986150	−	0.165853i	$-0.0530378\pi$
$769$	27.5661	+	23.1307i	0.994060	+	0.834115i	0.00790953	+	0.999969i	$0.497482\pi$
$770$	−3.87472	−	7.11836i	−0.139635	−	0.256528i
$771$	3.79330	−	36.1985i	0.136612	−	1.30366i
$772$	22.3213	−	18.7298i	0.803361	−	0.674100i
$773$	15.6362			0.562394			0.281197	−	0.959650i	$-0.409269\pi$
$773$	15.6362			0.562394			0.281197	+	0.959650i	$0.409269\pi$
$774$	−3.82731	+	2.03805i	−0.137570	+	0.0732562i
$775$	−4.07362			−0.146329
$776$	2.16738	+	12.2918i	0.0778045	+	0.441251i
$777$	−39.9596	+	16.6159i	−1.43354	+	0.596091i
$778$	−2.91902	+	1.06244i	−0.104652	+	0.0380902i
$779$	−13.2283	−	11.0998i	−0.473952	−	0.397693i
$780$	−4.91022	−	7.27484i	−0.175814	−	0.260481i
$781$	11.9091	+	4.33456i	0.426141	+	0.155103i
$782$	−2.41058	+	4.17525i	−0.0862021	+	0.149306i
$783$	13.8883	−	17.8103i	0.496328	−	0.636487i
$784$	5.24236	−	22.9285i	0.187227	−	0.818876i
$785$	3.03483	−	2.54652i	0.108318	−	0.0908892i
$786$	0.962717	+	1.42634i	0.0343390	+	0.0508757i
$787$	−17.4211	+	6.34078i	−0.620997	+	0.226024i	−0.633308	−	0.773900i	$-0.718303\pi$
$787$	−17.4211	+	6.34078i	−0.620997	+	0.226024i	0.0123112	+	0.999924i	$0.496081\pi$
$788$	−3.07180	−	2.57755i	−0.109428	−	0.0918213i
$789$	11.5363	+	46.2086i	0.410702	+	1.64507i
$790$	3.34296	+	18.9589i	0.118937	+	0.674526i
$791$	15.6693	−	12.4911i	0.557138	−	0.444131i
$792$	−9.99198	−	2.11741i	−0.355050	−	0.0752388i
$793$	4.01584	+	6.95564i	0.142607	+	0.247002i
$794$	−1.38679	−	7.86489i	−0.0492154	−	0.279115i
$795$	0.830051	−	7.92095i	0.0294389	−	0.280927i
$796$	7.01518	−	2.55332i	0.248646	−	0.0904999i
$797$	−10.6516	−	8.93779i	−0.377301	−	0.316593i	0.434341	−	0.900749i	$-0.356981\pi$
$797$	−10.6516	−	8.93779i	−0.377301	−	0.316593i	−0.811642	+	0.584156i	$0.801426\pi$
$798$	−7.50151	+	0.337803i	−0.265550	+	0.0119581i
$799$	0.309411	+	0.112617i	0.0109462	+	0.00398409i
$800$	13.3283	+	23.0852i	0.471226	+	0.816187i
$801$	10.6650	+	13.6332i	0.376829	+	0.481705i
$802$	−4.27773	+	7.40925i	−0.151052	+	0.261630i
$803$	14.8864	+	5.41822i	0.525331	+	0.191205i
$804$	−37.8439	−	10.8389i	−1.33465	−	0.382259i
$805$	39.0266	−	63.8373i	1.37551	−	2.24997i
$806$	0.0245794	−	0.139397i	0.000865773	−	0.00491004i
$807$	−8.64907	+	0.607488i	−0.304462	+	0.0213846i
$808$	−10.3627	−	3.77171i	−0.364558	−	0.132688i
$809$	3.24319	+	5.61738i	0.114025	+	0.197496i	0.917389	−	0.397991i	$-0.130292\pi$
$809$	3.24319	+	5.61738i	0.114025	+	0.197496i	−0.803365	+	0.595487i	$0.796959\pi$
$810$	−2.50004	+	10.0802i	−0.0878425	+	0.354182i
$811$	8.32039			0.292168			0.146084	−	0.989272i	$-0.453333\pi$
$811$	8.32039			0.292168			0.146084	+	0.989272i	$0.453333\pi$
$812$	−4.31377	+	21.3184i	−0.151384	+	0.748128i
$813$	28.5264	+	42.2640i	1.00046	+	1.48226i
$814$	−6.32940	−	5.31100i	−0.221845	−	0.186150i
$815$	4.44826	+	3.73253i	0.155816	+	0.130745i
$816$	−2.55290	−	10.2257i	−0.0893693	−	0.357969i
$817$	20.4880	+	7.45703i	0.716785	+	0.260888i
$818$	−2.90748	−	5.03590i	−0.101658	−	0.176076i
$819$	1.73480	+	5.82073i	0.0606188	+	0.203393i
$820$	11.5002	−	19.9190i	0.401605	−	0.695600i
$821$	−32.2542	+	27.0645i	−1.12568	+	0.944558i	−0.998877	−	0.0473701i	$-0.984916\pi$
$821$	−32.2542	+	27.0645i	−1.12568	+	0.944558i	−0.126803	+	0.991928i	$0.540472\pi$
$822$	−1.17257	−	0.851367i	−0.0408980	−	0.0296948i
$823$	−5.27658	+	29.9250i	−0.183930	+	1.04312i	0.743392	+	0.668856i	$0.233216\pi$
$823$	−5.27658	+	29.9250i	−0.183930	+	1.04312i	−0.927322	+	0.374264i	$0.877895\pi$
$824$	16.5482	−	6.02304i	0.576483	−	0.209823i
$825$	27.0052	+	19.6077i	0.940202	+	0.682653i
$826$	2.54579	−	12.5811i	0.0885794	−	0.437753i
$827$	−9.28753	+	16.0865i	−0.322959	+	0.559382i	−0.981097	−	0.193516i	$-0.938011\pi$
$827$	−9.28753	+	16.0865i	−0.322959	+	0.559382i	0.658138	+	0.752897i	$0.271344\pi$
$828$	−14.1895	−	43.5792i	−0.493120	−	1.51448i
$829$	1.45516	−	2.52041i	0.0505398	−	0.0875374i	−0.839649	−	0.543130i	$-0.817239\pi$
$829$	1.45516	−	2.52041i	0.0505398	−	0.0875374i	0.890189	+	0.455592i	$0.150573\pi$
$830$	−0.475720	+	0.399177i	−0.0165125	+	0.0138556i
$831$	6.66292	+	26.6884i	0.231134	+	0.925809i
$832$	3.96182	−	1.44198i	0.137351	−	0.0499918i
$833$	−10.1081	+	7.65060i	−0.350225	+	0.265078i
$834$	0.903573	−	1.85405i	0.0312882	−	0.0642006i
$835$	2.57107	+	14.5812i	0.0889754	+	0.504605i
$836$	12.4809	+	21.6176i	0.431662	+	0.747661i
$837$	2.47168	−	1.54767i	0.0854339	−	0.0534952i
$838$	1.45160	−	2.51425i	0.0501448	−	0.0868534i
$839$	−0.0810751	+	0.0680301i	−0.00279902	+	0.00234866i	−0.644186	−	0.764869i	$-0.722804\pi$
$839$	−0.0810751	+	0.0680301i	−0.00279902	+	0.00234866i	0.641387	+	0.767217i	$0.278359\pi$
$840$	−4.48134	−	20.0840i	−0.154621	−	0.692964i
$841$	−1.75519	+	9.95418i	−0.0605238	+	0.343248i
$842$	−0.372033	+	2.10991i	−0.0128211	+	0.0727121i
$843$	−14.1175	+	13.6415i	−0.486231	+	0.469839i
$844$	−25.9907	+	21.8088i	−0.894638	+	0.750691i
$845$	43.4654			1.49525
$846$	0.158679	−	0.0844970i	0.00545550	−	0.00290507i
$847$	−8.17868	+	6.51976i	−0.281023	+	0.224022i
$848$	4.14668	+	1.50927i	0.142398	+	0.0518285i
$849$	−9.97287	−	7.24100i	−0.342268	−	0.248511i
$850$	0.752312	−	4.26657i	0.0258041	−	0.146342i
$851$	13.2457	−	75.1200i	0.454056	−	2.57508i
$852$	12.6559	+	9.18904i	0.433582	+	0.314811i
$853$	45.1064	+	16.4174i	1.54441	+	0.562120i	0.967098	−	0.254402i	$-0.0818788\pi$
$853$	45.1064	+	16.4174i	1.54441	+	0.562120i	0.577314	+	0.816522i	$0.304101\pi$
$854$	1.36241	+	9.05056i	0.0466208	+	0.309704i
$855$	46.0931	−	24.5447i	1.57635	−	0.839411i
$856$	−21.2876			−0.727595
$857$	24.1627	−	20.2749i	0.825382	−	0.692578i	−0.128844	−	0.991665i	$-0.541127\pi$
$857$	24.1627	−	20.2749i	0.825382	−	0.692578i	0.954226	+	0.299087i	$0.0966821\pi$
$858$	−0.833907	+	0.805793i	−0.0284691	+	0.0275093i
$859$	4.88607	−	27.7103i	0.166711	−	0.945463i	−0.780572	−	0.625065i	$-0.785072\pi$
$859$	4.88607	−	27.7103i	0.166711	−	0.945463i	0.947283	−	0.320398i	$-0.103817\pi$
$860$	−5.04279	+	28.5991i	−0.171958	+	0.975220i
$861$	−11.7203	+	10.7692i	−0.399427	+	0.367013i
$862$	−0.702152	+	0.589176i	−0.0239154	+	0.0200674i
$863$	16.4615	−	28.5121i	0.560356	−	0.970564i	−0.437110	−	0.899408i	$-0.643998\pi$
$863$	16.4615	−	28.5121i	0.560356	−	0.970564i	0.997465	−	0.0711562i	$-0.0226689\pi$
$864$	−16.8576	−	8.94331i	−0.573508	−	0.304258i
$865$	−3.27201	−	5.66729i	−0.111252	−	0.192694i
$866$	1.05263	+	5.96976i	0.0357698	+	0.202861i
$867$	10.4110	−	21.3624i	0.353575	−	0.725505i
$868$	−1.46488	+	2.39616i	−0.0497213	+	0.0813309i
$869$	−41.6152	+	15.1467i	−1.41170	+	0.513816i
$870$	2.10428	+	8.42872i	0.0713419	+	0.285760i
$871$	−7.04399	+	5.91061i	−0.238677	+	0.200273i
$872$	−2.54672	+	4.41105i	−0.0862429	+	0.149377i
$873$	9.03898	+	27.7607i	0.305923	+	0.939558i
$874$	6.61776	−	11.4623i	0.223849	−	0.387718i
$875$	−4.14903	+	20.5042i	−0.140263	+	0.693170i
$876$	15.8199	+	11.4864i	0.534505	+	0.388088i
$877$	18.4882	−	6.72914i	0.624301	−	0.227227i	−0.0104481	−	0.999945i	$-0.503326\pi$
$877$	18.4882	−	6.72914i	0.624301	−	0.227227i	0.634749	+	0.772719i	$0.281104\pi$
$878$	−0.844555	+	4.78971i	−0.0285024	+	0.161645i
$879$	38.3655	+	27.8561i	1.29404	+	0.939562i
$880$	−23.9225	+	20.0734i	−0.806428	+	0.676673i
$881$	26.7023	−	46.2497i	0.899623	−	1.55819i	0.0716468	−	0.997430i	$-0.477175\pi$
$881$	26.7023	−	46.2497i	0.899623	−	1.55819i	0.827976	−	0.560763i	$-0.189492\pi$
$882$	−0.584373	+	6.89665i	−0.0196769	+	0.232222i
$883$	−10.0833	−	17.4649i	−0.339332	−	0.587740i	0.644976	−	0.764203i	$-0.276868\pi$
$883$	−10.0833	−	17.4649i	−0.339332	−	0.587740i	−0.984307	+	0.176464i	$0.943534\pi$
$884$	−2.46301	−	0.896462i	−0.0828400	−	0.0301513i
$885$	21.6223	+	86.6083i	0.726826	+	2.91131i
$886$	8.18590	+	6.86878i	0.275011	+	0.230761i
$887$	−10.2003	−	8.55905i	−0.342492	−	0.287385i	0.455275	−	0.890351i	$-0.349541\pi$
$887$	−10.2003	−	8.55905i	−0.342492	−	0.287385i	−0.797767	+	0.602966i	$0.793985\pi$
$888$	−11.7365	−	17.3885i	−0.393851	−	0.583519i
$889$	20.5144	+	18.1109i	0.688029	+	0.607420i
$890$	−6.65797			−0.223176
$891$	−23.8350	−	1.63710i	−0.798501	−	0.0548448i
$892$	7.29376	+	12.6332i	0.244213	+	0.422990i
$893$	−0.849427	−	0.309166i	−0.0284250	−	0.0103459i
$894$	−3.16389	+	0.222223i	−0.105816	+	0.00743226i
$895$	2.54125	−	14.4122i	0.0849447	−	0.481745i
$896$	24.2300	+	0.608817i	0.809468	+	0.0203391i
$897$	−10.2918	−	2.94767i	−0.343632	−	0.0984199i
$898$	3.33832	+	1.21505i	0.111401	+	0.0405467i
$899$	1.21970	−	2.11259i	0.0406794	−	0.0704588i
$900$	25.3759	+	32.4383i	0.845864	+	1.08128i
$901$	−1.18921	−	2.05978i	−0.0396184	−	0.0686211i
$902$	−2.85558	−	1.03935i	−0.0950806	−	0.0346065i
$903$	9.25507	−	17.8384i	0.307989	−	0.593623i
$904$	7.44136	+	6.24405i	0.247496	+	0.207674i
$905$	−14.1623	+	5.15464i	−0.470769	+	0.171346i
$906$	−0.311668	+	2.97417i	−0.0103545	+	0.0988100i
$907$	−1.54561	−	8.76559i	−0.0513212	−	0.291057i	0.948335	−	0.317270i	$-0.102766\pi$
$907$	−1.54561	−	8.76559i	−0.0513212	−	0.291057i	−0.999656	+	0.0262134i	$0.991655\pi$
$908$	−16.8106	−	29.1169i	−0.557881	−	0.966278i
$909$	−25.2345	−	5.34746i	−0.836976	−	0.177364i
$910$	−2.17462	−	0.853946i	−0.0720878	−	0.0283080i
$911$	1.31823	+	7.47606i	0.0436749	+	0.247693i	0.998827	−	0.0484232i	$-0.0154196\pi$
$911$	1.31823	+	7.47606i	0.0436749	+	0.247693i	−0.955152	+	0.296116i	$0.904309\pi$
$912$	7.00847	+	28.0725i	0.232074	+	0.929572i
$913$	−1.09435	−	0.918271i	−0.0362178	−	0.0303903i
$914$	−0.971870	+	0.353732i	−0.0321466	+	0.0117004i
$915$	−35.6088	−	52.7570i	−1.17719	−	1.74409i
$916$	−22.1217	+	18.5623i	−0.730921	+	0.613315i
$917$	−7.42357	−	2.91515i	−0.245148	−	0.0962667i
$918$	1.16451	+	2.87458i	0.0384344	+	0.0948752i
$919$	−1.48229	+	2.56740i	−0.0488962	+	0.0846906i	−0.889438	−	0.457057i	$-0.848904\pi$
$919$	−1.48229	+	2.56740i	−0.0488962	+	0.0846906i	0.840541	+	0.541747i	$0.182237\pi$
$920$	34.0831	+	12.4052i	1.12369	+	0.408988i
$921$	15.6041	+	23.1186i	0.514172	+	0.761783i
$922$	−9.75977	−	8.18942i	−0.321421	−	0.269704i
$923$	3.43298	−	1.24950i	0.112998	−	0.0411279i
$924$	21.2446	−	8.83388i	0.698897	−	0.290613i
$925$	11.9028	+	67.5044i	0.391363	+	2.21953i
$926$	0.200749			0.00659701
$927$	36.3582	−	19.3608i	1.19416	−	0.635894i
$928$	−15.9627			−0.524003
$929$	−22.5176	+	18.8945i	−0.738780	+	0.619910i	−0.932510	−	0.361145i	$-0.882386\pi$
$929$	−22.5176	+	18.8945i	−0.738780	+	0.619910i	0.193730	+	0.981055i	$0.437941\pi$
$930$	−0.116909	+	1.11563i	−0.00383359	+	0.0365829i
$931$	27.7497	−	21.0032i	0.909461	−	0.688352i
$932$	13.8823	+	11.6486i	0.454730	+	0.381564i
$933$	−20.5338	−	14.9090i	−0.672246	−	0.488098i
$934$	1.60211	+	9.08601i	0.0524226	+	0.297303i
$935$	16.8317			0.550454
$936$	−2.59881	+	1.38387i	−0.0849448	+	0.0452333i
$937$	−29.8116	−	51.6352i	−0.973902	−	1.68685i	−0.683511	−	0.729940i	$-0.739548\pi$
$937$	−29.8116	−	51.6352i	−0.973902	−	1.68685i	−0.290391	−	0.956908i	$-0.593785\pi$
$938$	−9.93350	+	3.33540i	−0.324340	+	0.108905i
$939$	−2.41964	−	9.69189i	−0.0789620	−	0.316283i
$940$	0.209072	−	1.18571i	0.00681919	−	0.0386736i
$941$	−47.2025	+	17.1803i	−1.53876	+	0.560062i	−0.965747	−	0.259487i	$-0.916447\pi$
$941$	−47.2025	+	17.1803i	−1.53876	+	0.560062i	−0.573010	+	0.819548i	$0.694224\pi$
$942$	−0.361374	−	0.535402i	−0.0117742	−	0.0174444i
$943$	−4.87164	−	27.6285i	−0.158643	−	0.899706i
$944$	−49.4601			−1.60979
$945$	−16.9462	−	45.0517i	−0.551260	−	1.46553i
$946$	3.83684			0.124746
$947$	−1.30470	−	7.39932i	−0.0423971	−	0.240446i	0.956243	−	0.292572i	$-0.0945112\pi$
$947$	−1.30470	−	7.39932i	−0.0423971	−	0.240446i	−0.998640	+	0.0521265i	$0.983400\pi$
$948$	−54.5181	+	3.82921i	−1.77067	+	0.124367i
$949$	4.29125	−	1.56189i	0.139300	−	0.0507010i
$950$	−2.06532	+	11.7130i	−0.0670078	+	0.380020i
$951$	−29.6342	+	28.6351i	−0.960955	+	0.928557i
$952$	−4.60684	−	4.06710i	−0.149309	−	0.131816i
$953$	−18.5333	−	32.1007i	−0.600354	−	1.03984i	−0.992767	−	0.120054i	$-0.961693\pi$
$953$	−18.5333	−	32.1007i	−0.600354	−	1.03984i	0.392413	−	0.919789i	$-0.371640\pi$
$954$	−1.27036	−	0.269203i	−0.0411295	−	0.00871577i
$955$	67.3704			2.18005
$956$	7.76318	+	44.0272i	0.251079	+	1.42394i
$957$	−18.2544	+	8.13413i	−0.590080	+	0.262939i
$958$	9.62315	+	8.07478i	0.310910	+	0.260884i
$959$	6.71370	+	0.168692i	0.216797	+	0.00544735i
$960$	−30.5190	+	13.5992i	−0.984995	+	0.438913i
$961$	−23.5061	+	19.7239i	−0.758261	+	0.636256i
$962$	−2.38178			−0.0767915
$963$	−49.3047	+	6.96040i	−1.58882	+	0.224296i
$964$	−28.1095			−0.905346
$965$	9.36645	+	53.1198i	0.301517	+	1.70999i
$966$	−9.68871	−	7.41338i	−0.311729	−	0.238521i
$967$	13.7353	−	4.99925i	0.441698	−	0.160765i	−0.111591	−	0.993754i	$-0.535595\pi$
$967$	13.7353	−	4.99925i	0.441698	−	0.160765i	0.553289	+	0.832989i	$0.313372\pi$
$968$	−3.88405	−	3.25911i	−0.124838	−	0.104752i
$969$	6.83204	−	14.0188i	0.219477	−	0.450348i
$970$	−10.5527	−	3.84088i	−0.338828	−	0.123323i
$971$	−0.0882826	+	0.152910i	−0.00283312	+	0.00490711i	−0.867438	−	0.497544i	$-0.834235\pi$
$971$	−0.0882826	+	0.152910i	−0.00283312	+	0.00490711i	0.864605	+	0.502452i	$0.167568\pi$
$972$	−27.7210	−	10.0411i	−0.889153	−	0.322070i
$973$	1.42292	+	9.45250i	0.0456167	+	0.303033i
$974$	5.87608	−	4.93062i	0.188282	−	0.157987i
$975$	9.59659	−	0.674039i	0.307337	−	0.0215865i
$976$	33.1397	−	12.0619i	1.06078	−	0.386091i
$977$	23.7854	+	19.9583i	0.760963	+	0.638523i	0.938377	−	0.345613i	$-0.112329\pi$
$977$	23.7854	+	19.9583i	0.760963	+	0.638523i	−0.177415	+	0.984136i	$0.556773\pi$
$978$	0.680859	−	0.657905i	0.0217715	−	0.0210375i
$979$	−2.65961	−	15.0834i	−0.0850015	−	0.482067i
$980$	33.9683	+	31.5418i	1.08508	+	1.00756i
$981$	−4.45624	+	11.0492i	−0.142277	+	0.352775i
$982$	1.04854	+	1.81612i	0.0334601	+	0.0579547i
$983$	5.40348	+	30.6446i	0.172344	+	0.977412i	0.941165	+	0.337948i	$0.109733\pi$
$983$	5.40348	+	30.6446i	0.172344	+	0.977412i	−0.768821	+	0.639465i	$0.779156\pi$
$984$	−6.24358	−	4.53328i	−0.199038	−	0.144516i
$985$	6.97532	−	2.53881i	0.222252	−	0.0808932i
$986$	1.98740	+	1.66763i	0.0632917	+	0.0531080i
$987$	−0.383713	+	0.739573i	−0.0122137	+	0.0235409i
$988$	6.76170	+	2.46106i	0.215118	+	0.0782966i
$989$	17.7109	+	30.6761i	0.563173	+	0.975443i
$990$	6.14492	−	6.83311i	0.195298	−	0.217171i
$991$	−14.1482	+	24.5054i	−0.449431	+	0.778438i	−0.998349	−	0.0574383i	$-0.981707\pi$
$991$	−14.1482	+	24.5054i	−0.449431	+	0.778438i	0.548918	+	0.835876i	$0.315040\pi$
$992$	−1.93684	−	0.704952i	−0.0614947	−	0.0223822i
$993$	33.5521	−	32.4210i	1.06475	−	1.02885i
$994$	4.16182	+	0.104572i	0.132005	+	0.00331683i
$995$	−2.39973	+	13.6095i	−0.0760765	+	0.431452i
$996$	−0.986296	−	1.46127i	−0.0312520	−	0.0463021i
$997$	−40.2981	−	14.6673i	−1.27625	−	0.464518i	−0.387061	−	0.922054i	$-0.626510\pi$
$997$	−40.2981	−	14.6673i	−1.27625	−	0.464518i	−0.889191	+	0.457536i	$0.848732\pi$
$998$	−2.57644	−	4.46252i	−0.0815558	−	0.141259i
$999$	−32.8686	−	36.4363i	−1.03992	−	1.15279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.184.10	yes	132
3.2	odd	2		567.2.w.a.37.13		132
7.4	even	3		189.2.u.a.130.13	yes	132
21.11	odd	6		567.2.u.a.361.10		132
27.11	odd	18		567.2.u.a.289.10		132
27.16	even	9		189.2.u.a.16.13	✓	132
189.11	odd	18		567.2.w.a.46.13		132
189.151	even	9	inner	189.2.w.a.151.10	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.13	✓	132	27.16	even	9
189.2.u.a.130.13	yes	132	7.4	even	3
189.2.w.a.151.10	yes	132	189.151	even	9	inner
189.2.w.a.184.10	yes	132	1.1	even	1	trivial
567.2.u.a.289.10		132	27.11	odd	18
567.2.u.a.361.10		132	21.11	odd	6
567.2.w.a.37.13		132	3.2	odd	2
567.2.w.a.46.13		132	189.11	odd	18

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.w (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0572325 - 0.324581i) q^{2} +(-0.758800 + 1.55699i) q^{3} +(1.77731 - 0.646887i) q^{4} +(-0.607976 + 3.44800i) q^{5} +(0.548799 + 0.157182i) q^{6} +(-2.50814 + 0.842165i) q^{7} +(-0.641276 - 1.11072i) q^{8} +(-1.84845 - 2.36289i) q^{9} +O(q^{10})\)	\(q+(-0.0572325 - 0.324581i) q^{2} +(-0.758800 + 1.55699i) q^{3} +(1.77731 - 0.646887i) q^{4} +(-0.607976 + 3.44800i) q^{5} +(0.548799 + 0.157182i) q^{6} +(-2.50814 + 0.842165i) q^{7} +(-0.641276 - 1.11072i) q^{8} +(-1.84845 - 2.36289i) q^{9} +1.15395 q^{10} +(0.460961 + 2.61424i) q^{11} +(-0.341423 + 3.25811i) q^{12} +(0.586193 + 0.491874i) q^{13} +(0.416898 + 0.765896i) q^{14} +(-4.90718 - 3.56296i) q^{15} +(2.57393 - 2.15978i) q^{16} -1.81099 q^{17} +(-0.661159 + 0.735205i) q^{18} +4.97172 q^{19} +(1.14991 + 6.52145i) q^{20} +(0.591931 - 4.54418i) q^{21} +(0.822152 - 0.299239i) q^{22} +(6.18751 + 5.19194i) q^{23} +(2.21599 - 0.155645i) q^{24} +(-6.82062 - 2.48250i) q^{25} +(0.126104 - 0.218418i) q^{26} +(5.08160 - 1.08505i) q^{27} +(-3.91295 + 3.11927i) q^{28} +(3.32963 - 2.79389i) q^{29} +(-0.875620 + 1.79670i) q^{30} +(0.527385 - 0.191953i) q^{31} +(-2.81332 - 2.36066i) q^{32} +(-4.42013 - 1.26597i) q^{33} +(0.103648 + 0.587815i) q^{34} +(-1.37890 - 9.16008i) q^{35} +(-4.81378 - 3.00385i) q^{36} +(-4.72185 - 8.17848i) q^{37} +(-0.284544 - 1.61373i) q^{38} +(-1.21065 + 0.539463i) q^{39} +(4.21965 - 1.53583i) q^{40} +(-2.66071 - 2.23260i) q^{41} +(-1.50884 + 0.0679449i) q^{42} +(4.12091 + 1.49989i) q^{43} +(2.51039 + 4.34812i) q^{44} +(9.27106 - 4.93686i) q^{45} +(1.33108 - 2.30550i) q^{46} +(-0.170852 - 0.0621850i) q^{47} +(1.40967 + 5.64643i) q^{48} +(5.58152 - 4.22453i) q^{49} +(-0.415414 + 2.35593i) q^{50} +(1.37418 - 2.81970i) q^{51} +(1.36003 + 0.495011i) q^{52} +(0.656663 + 1.13737i) q^{53} +(-0.643021 - 1.58729i) q^{54} -9.29416 q^{55} +(2.54382 + 2.24579i) q^{56} +(-3.77254 + 7.74092i) q^{57} +(-1.09741 - 0.920835i) q^{58} +(-11.2763 - 9.46193i) q^{59} +(-11.0264 - 3.15808i) q^{60} +(9.86293 + 3.58981i) q^{61} +(-0.0924878 - 0.160194i) q^{62} +(6.62610 + 4.36976i) q^{63} +(2.75482 - 4.77148i) q^{64} +(-2.05237 + 1.72215i) q^{65} +(-0.157937 + 1.50715i) q^{66} +(-2.08665 + 11.8340i) q^{67} +(-3.21869 + 1.17151i) q^{68} +(-12.7789 + 5.69426i) q^{69} +(-2.89428 + 0.971820i) q^{70} +(2.38709 - 4.13456i) q^{71} +(-1.43915 + 3.56837i) q^{72} +(2.98388 - 5.16823i) q^{73} +(-2.38434 + 2.00070i) q^{74} +(9.04073 - 8.73593i) q^{75} +(8.83627 - 3.21614i) q^{76} +(-3.35778 - 6.16867i) q^{77} +(0.244388 + 0.362079i) q^{78} +(2.89696 + 16.4295i) q^{79} +(5.88205 + 10.1880i) q^{80} +(-2.16650 + 8.73535i) q^{81} +(-0.572381 + 0.991393i) q^{82} +(-0.412252 + 0.345921i) q^{83} +(-1.88753 - 8.45933i) q^{84} +(1.10104 - 6.24431i) q^{85} +(0.250986 - 1.42341i) q^{86} +(1.82354 + 7.30421i) q^{87} +(2.60809 - 2.18845i) q^{88} -5.76971 q^{89} +(-2.13302 - 2.72667i) q^{90} +(-1.88449 - 0.740017i) q^{91} +(14.3557 + 5.22505i) q^{92} +(-0.101311 + 0.966788i) q^{93} +(-0.0104058 + 0.0590143i) q^{94} +(-3.02268 + 17.1425i) q^{95} +(5.81027 - 2.58905i) q^{96} +(-9.14484 - 3.32845i) q^{97} +(-1.69065 - 1.56988i) q^{98} +(5.32510 - 5.92148i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} + 3 q^{9} - 6 q^{10} + 3 q^{11} - 3 q^{12} - 12 q^{13} + 15 q^{14} - 9 q^{16} - 54 q^{17} - 3 q^{18} - 6 q^{19} - 18 q^{20} - 21 q^{21} - 12 q^{22} + 45 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 57 q^{30} - 3 q^{31} + 51 q^{32} + 15 q^{33} - 18 q^{34} - 12 q^{35} - 60 q^{36} + 3 q^{37} - 57 q^{38} - 66 q^{39} - 66 q^{40} + 33 q^{42} - 12 q^{43} + 3 q^{44} + 33 q^{45} + 3 q^{46} - 21 q^{47} + 90 q^{48} + 12 q^{49} - 39 q^{50} - 48 q^{51} + 9 q^{52} + 9 q^{53} - 63 q^{54} - 24 q^{55} + 57 q^{56} - 18 q^{57} - 3 q^{58} - 18 q^{59} + 81 q^{60} + 33 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} + 81 q^{65} + 69 q^{66} - 3 q^{67} + 6 q^{68} - 6 q^{69} - 42 q^{70} - 18 q^{71} - 105 q^{72} + 21 q^{73} - 93 q^{74} + 18 q^{75} - 24 q^{76} + 87 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} + 39 q^{81} - 6 q^{82} - 42 q^{83} - 36 q^{84} - 63 q^{85} + 159 q^{86} + 30 q^{87} + 57 q^{88} - 150 q^{89} - 39 q^{90} + 6 q^{91} - 66 q^{92} - 27 q^{93} + 33 q^{94} - 147 q^{95} + 81 q^{96} - 12 q^{97} + 99 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 + 3 * q^9 - 6 * q^10 + 3 * q^11 - 3 * q^12 - 12 * q^13 + 15 * q^14 - 9 * q^16 - 54 * q^17 - 3 * q^18 - 6 * q^19 - 18 * q^20 - 21 * q^21 - 12 * q^22 + 45 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 57 * q^30 - 3 * q^31 + 51 * q^32 + 15 * q^33 - 18 * q^34 - 12 * q^35 - 60 * q^36 + 3 * q^37 - 57 * q^38 - 66 * q^39 - 66 * q^40 + 33 * q^42 - 12 * q^43 + 3 * q^44 + 33 * q^45 + 3 * q^46 - 21 * q^47 + 90 * q^48 + 12 * q^49 - 39 * q^50 - 48 * q^51 + 9 * q^52 + 9 * q^53 - 63 * q^54 - 24 * q^55 + 57 * q^56 - 18 * q^57 - 3 * q^58 - 18 * q^59 + 81 * q^60 + 33 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 + 81 * q^65 + 69 * q^66 - 3 * q^67 + 6 * q^68 - 6 * q^69 - 42 * q^70 - 18 * q^71 - 105 * q^72 + 21 * q^73 - 93 * q^74 + 18 * q^75 - 24 * q^76 + 87 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 + 39 * q^81 - 6 * q^82 - 42 * q^83 - 36 * q^84 - 63 * q^85 + 159 * q^86 + 30 * q^87 + 57 * q^88 - 150 * q^89 - 39 * q^90 + 6 * q^91 - 66 * q^92 - 27 * q^93 + 33 * q^94 - 147 * q^95 + 81 * q^96 - 12 * q^97 + 99 * q^98 + 24 * q^99

Introduction

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