LMFDB - Embedded newform 189.2.w.a.184.19

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			184.19
Character	$\chi$	$=$	189.184
Dual form			189.2.w.a.151.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.351787 + 1.99508i) q^{2} +(-0.234582 + 1.71609i) q^{3} +(-1.97722 + 0.719650i) q^{4} +(0.155052 - 0.879341i) q^{5} +(-3.50627 + 0.135689i) q^{6} +(-1.72949 + 2.00222i) q^{7} +(-0.105462 - 0.182666i) q^{8} +(-2.88994 - 0.805127i) q^{9} +O(q^{10})$	\(q+(0.351787 + 1.99508i) q^{2} +(-0.234582 + 1.71609i) q^{3} +(-1.97722 + 0.719650i) q^{4} +(0.155052 - 0.879341i) q^{5} +(-3.50627 + 0.135689i) q^{6} +(-1.72949 + 2.00222i) q^{7} +(-0.105462 - 0.182666i) q^{8} +(-2.88994 - 0.805127i) q^{9} +1.80890 q^{10} +(-0.545772 - 3.09523i) q^{11} +(-0.771166 - 3.56191i) q^{12} +(3.46133 + 2.90440i) q^{13} +(-4.60300 - 2.74612i) q^{14} +(1.47266 + 0.472360i) q^{15} +(-2.89636 + 2.43033i) q^{16} +5.74615 q^{17} +(0.589651 - 6.04891i) q^{18} +1.22738 q^{19} +(0.326246 + 1.85024i) q^{20} +(-3.03028 - 3.43764i) q^{21} +(5.98324 - 2.17772i) q^{22} +(-4.25634 - 3.57150i) q^{23} +(0.338212 - 0.138133i) q^{24} +(3.94926 + 1.43741i) q^{25} +(-4.57688 + 7.92738i) q^{26} +(2.05960 - 4.77054i) q^{27} +(1.97869 - 5.20345i) q^{28} +(-0.0345809 + 0.0290169i) q^{29} +(-0.424336 + 3.10425i) q^{30} +(0.226384 - 0.0823972i) q^{31} +(-6.19078 - 5.19468i) q^{32} +(5.43972 - 0.210512i) q^{33} +(2.02142 + 11.4640i) q^{34} +(1.49247 + 1.83126i) q^{35} +(6.29347 - 0.487833i) q^{36} +(5.13755 + 8.89849i) q^{37} +(0.431777 + 2.44873i) q^{38} +(-5.79619 + 5.25865i) q^{39} +(-0.176978 + 0.0644148i) q^{40} +(3.74834 + 3.14523i) q^{41} +(5.79238 - 7.25499i) q^{42} +(-6.92531 - 2.52060i) q^{43} +(3.30659 + 5.72718i) q^{44} +(-1.15607 + 2.41641i) q^{45} +(5.62811 - 9.74817i) q^{46} +(5.21418 + 1.89781i) q^{47} +(-3.49124 - 5.54053i) q^{48} +(-1.01774 - 6.92562i) q^{49} +(-1.47846 + 8.38478i) q^{50} +(-1.34794 + 9.86092i) q^{51} +(-8.93398 - 3.25170i) q^{52} +(-3.82297 - 6.62158i) q^{53} +(10.2422 + 2.43086i) q^{54} -2.80638 q^{55} +(0.548134 + 0.104761i) q^{56} +(-0.287921 + 2.10630i) q^{57} +(-0.0700562 - 0.0587841i) q^{58} +(-2.88652 - 2.42208i) q^{59} +(-3.25171 + 0.125838i) q^{60} +(-0.765603 - 0.278657i) q^{61} +(0.244029 + 0.422670i) q^{62} +(6.61016 - 4.39383i) q^{63} +(4.40506 - 7.62979i) q^{64} +(3.09065 - 2.59336i) q^{65} +(2.33361 + 10.7786i) q^{66} +(0.114256 - 0.647980i) q^{67} +(-11.3614 + 4.13522i) q^{68} +(7.12748 - 6.46647i) q^{69} +(-3.12848 + 3.62182i) q^{70} +(3.75882 - 6.51047i) q^{71} +(0.157711 + 0.612806i) q^{72} +(4.87293 - 8.44017i) q^{73} +(-15.9459 + 13.3802i) q^{74} +(-3.39316 + 6.44011i) q^{75} +(-2.42681 + 0.883285i) q^{76} +(7.14122 + 4.26040i) q^{77} +(-12.5305 - 9.71396i) q^{78} +(-2.29784 - 13.0317i) q^{79} +(1.68801 + 2.92371i) q^{80} +(7.70354 + 4.65354i) q^{81} +(-4.95638 + 8.58471i) q^{82} +(4.92372 - 4.13150i) q^{83} +(8.46544 + 4.61625i) q^{84} +(0.890949 - 5.05282i) q^{85} +(2.59259 - 14.7033i) q^{86} +(-0.0416835 - 0.0661509i) q^{87} +(-0.507835 + 0.426124i) q^{88} -12.6111 q^{89} +(-5.22763 - 1.45640i) q^{90} +(-11.8016 + 1.90720i) q^{91} +(10.9860 + 3.99856i) q^{92} +(0.0882956 + 0.407825i) q^{93} +(-1.95200 + 11.0704i) q^{94} +(0.190307 - 1.07929i) q^{95} +(10.3668 - 9.40537i) q^{96} +(-11.8862 - 4.32622i) q^{97} +(13.4592 - 4.46682i) q^{98} +(-0.914800 + 9.38444i) 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 $

$2$	0.351787	+	1.99508i	0.248751	+	1.41074i	0.811617	+	0.584190i	$0.198588\pi$
$2$	0.351787	+	1.99508i	0.248751	+	1.41074i	−0.562866	+	0.826548i	$0.690301\pi$
$3$	−0.234582	+	1.71609i	−0.135436	+	0.990786i
$3$	−0.234582	+	1.71609i	−0.135436	+	0.990786i
$4$	−1.97722	+	0.719650i	−0.988611	+	0.359825i
$5$	0.155052	−	0.879341i	0.0693412	−	0.393253i	−0.930308	−	0.366778i	$-0.880461\pi$
$5$	0.155052	−	0.879341i	0.0693412	−	0.393253i	0.999649	−	0.0264748i	$-0.00842817\pi$
$6$	−3.50627	+	0.135689i	−1.43143	+	0.0553949i
$7$	−1.72949	+	2.00222i	−0.653685	+	0.756767i
$7$	−1.72949	+	2.00222i	−0.653685	+	0.756767i
$8$	−0.105462	−	0.182666i	−0.0372866	−	0.0645823i
$9$	−2.88994	−	0.805127i	−0.963314	−	0.268376i
$10$	1.80890			0.572026
$11$	−0.545772	−	3.09523i	−0.164556	−	0.933245i	−0.949521	−	0.313704i	$-0.898430\pi$
$11$	−0.545772	−	3.09523i	−0.164556	−	0.933245i	0.784964	−	0.619541i	$-0.212681\pi$
$12$	−0.771166	−	3.56191i	−0.222616	−	1.02824i
$13$	3.46133	+	2.90440i	0.960001	+	0.805536i	0.980953	−	0.194244i	$-0.0622253\pi$
$13$	3.46133	+	2.90440i	0.960001	+	0.805536i	−0.0209522	+	0.999780i	$0.506670\pi$
$14$	−4.60300	−	2.74612i	−1.23020	−	0.733932i
$15$	1.47266	+	0.472360i	0.380239	+	0.121963i
$16$	−2.89636	+	2.43033i	−0.724090	+	0.607583i
$17$	5.74615			1.39365			0.696823	−	0.717243i	$-0.254596\pi$
$17$	5.74615			1.39365			0.696823	+	0.717243i	$0.254596\pi$
$18$	0.589651	−	6.04891i	0.138982	−	1.42574i
$19$	1.22738			0.281581			0.140790	−	0.990039i	$-0.455036\pi$
$19$	1.22738			0.281581			0.140790	+	0.990039i	$0.455036\pi$
$20$	0.326246	+	1.85024i	0.0729509	+	0.413725i
$21$	−3.03028	−	3.43764i	−0.661262	−	0.750155i
$22$	5.98324	−	2.17772i	1.27563	−	0.464292i
$23$	−4.25634	−	3.57150i	−0.887509	−	0.744709i	0.0801999	−	0.996779i	$-0.474444\pi$
$23$	−4.25634	−	3.57150i	−0.887509	−	0.744709i	−0.967709	+	0.252070i	$0.918889\pi$
$24$	0.338212	−	0.138133i	0.0690372	−	0.0281963i
$25$	3.94926	+	1.43741i	0.789853	+	0.287483i
$26$	−4.57688	+	7.92738i	−0.897599	+	1.55469i
$27$	2.05960	−	4.77054i	0.396370	−	0.918091i
$28$	1.97869	−	5.20345i	0.373937	−	0.983360i
$29$	−0.0345809	+	0.0290169i	−0.00642152	+	0.00538829i	−0.645993	−	0.763344i	$-0.723556\pi$
$29$	−0.0345809	+	0.0290169i	−0.00642152	+	0.00538829i	0.639571	+	0.768732i	$0.279112\pi$
$30$	−0.424336	+	3.10425i	−0.0774727	+	0.566755i
$31$	0.226384	−	0.0823972i	0.0406599	−	0.0147990i	−0.321610	−	0.946872i	$-0.604224\pi$
$31$	0.226384	−	0.0823972i	0.0406599	−	0.0147990i	0.362270	+	0.932073i	$0.382002\pi$
$32$	−6.19078	−	5.19468i	−1.09439	−	0.918298i
$33$	5.43972	−	0.210512i	0.946933	−	0.0366454i
$34$	2.02142	+	11.4640i	0.346671	+	1.96607i
$35$	1.49247	+	1.83126i	0.252274	+	0.309539i
$36$	6.29347	−	0.487833i	1.04891	−	0.0813055i
$37$	5.13755	+	8.89849i	0.844607	+	1.46290i	0.885962	+	0.463758i	$0.153499\pi$
$37$	5.13755	+	8.89849i	0.844607	+	1.46290i	−0.0413547	+	0.999145i	$0.513167\pi$
$38$	0.431777	+	2.44873i	0.0700435	+	0.397236i
$39$	−5.79619	+	5.25865i	−0.928133	+	0.842057i
$40$	−0.176978	+	0.0644148i	−0.0279827	+	0.0101849i
$41$	3.74834	+	3.14523i	0.585392	+	0.491203i	0.886713	−	0.462320i	$-0.152983\pi$
$41$	3.74834	+	3.14523i	0.585392	+	0.491203i	−0.301321	+	0.953523i	$0.597427\pi$
$42$	5.79238	−	7.25499i	0.893783	−	1.11947i
$43$	−6.92531	−	2.52060i	−1.05610	−	0.384389i	−0.245138	−	0.969488i	$-0.578833\pi$
$43$	−6.92531	−	2.52060i	−1.05610	−	0.384389i	−0.810961	+	0.585100i	$0.801055\pi$
$44$	3.30659	+	5.72718i	0.498487	+	0.863405i
$45$	−1.15607	+	2.41641i	−0.172337	+	0.360217i
$46$	5.62811	−	9.74817i	0.829820	−	1.43729i
$47$	5.21418	+	1.89781i	0.760567	+	0.276824i	0.693045	−	0.720894i	$-0.256269\pi$
$47$	5.21418	+	1.89781i	0.760567	+	0.276824i	0.0675215	+	0.997718i	$0.478491\pi$
$48$	−3.49124	−	5.54053i	−0.503918	−	0.799706i
$49$	−1.01774	−	6.92562i	−0.145391	−	0.989374i
$50$	−1.47846	+	8.38478i	−0.209086	+	1.18579i
$51$	−1.34794	+	9.86092i	−0.188749	+	1.38080i
$52$	−8.93398	−	3.25170i	−1.23892	−	0.450930i
$53$	−3.82297	−	6.62158i	−0.525126	−	0.909545i	−0.999572	−	0.0292600i	$-0.990685\pi$
$53$	−3.82297	−	6.62158i	−0.525126	−	0.909545i	0.474446	−	0.880285i	$-0.342648\pi$
$54$	10.2422	+	2.43086i	1.39378	+	0.330798i
$55$	−2.80638			−0.378412
$56$	0.548134	+	0.104761i	0.0732475	+	0.0139992i
$57$	−0.287921	+	2.10630i	−0.0381361	+	0.278986i
$58$	−0.0700562	−	0.0587841i	−0.00919883	−	0.00771874i
$59$	−2.88652	−	2.42208i	−0.375793	−	0.315328i	0.435255	−	0.900307i	$-0.356658\pi$
$59$	−2.88652	−	2.42208i	−0.375793	−	0.315328i	−0.811048	+	0.584979i	$0.801103\pi$
$60$	−3.25171	+	0.125838i	−0.419793	+	0.0162456i
$61$	−0.765603	−	0.278657i	−0.0980254	−	0.0356783i	0.292542	−	0.956253i	$-0.405499\pi$
$61$	−0.765603	−	0.278657i	−0.0980254	−	0.0356783i	−0.390567	+	0.920574i	$0.627721\pi$
$62$	0.244029	+	0.422670i	0.0309917	+	0.0536791i
$63$	6.61016	−	4.39383i	0.832802	−	0.553571i
$64$	4.40506	−	7.62979i	0.550633	−	0.953724i
$65$	3.09065	−	2.59336i	0.383347	−	0.321667i
$66$	2.33361	+	10.7786i	0.287248	+	1.32676i
$67$	0.114256	−	0.647980i	0.0139586	−	0.0791633i	−0.977033	−	0.213090i	$-0.931647\pi$
$67$	0.114256	−	0.647980i	0.0139586	−	0.0791633i	0.990991	+	0.133926i	$0.0427585\pi$
$68$	−11.3614	+	4.13522i	−1.37777	+	0.501469i
$69$	7.12748	−	6.46647i	0.858047	−	0.778472i
$70$	−3.12848	+	3.62182i	−0.373925	+	0.432890i
$71$	3.75882	−	6.51047i	0.446090	−	0.772650i	−0.552038	−	0.833819i	$-0.686150\pi$
$71$	3.75882	−	6.51047i	0.446090	−	0.772650i	0.998127	+	0.0611691i	$0.0194829\pi$
$72$	0.157711	+	0.612806i	0.0185864	+	0.0722199i
$73$	4.87293	−	8.44017i	0.570334	−	0.987847i	−0.426198	−	0.904630i	$-0.640147\pi$
$73$	4.87293	−	8.44017i	0.570334	−	0.987847i	0.996531	−	0.0832170i	$-0.0265195\pi$
$74$	−15.9459	+	13.3802i	−1.85367	+	1.55542i
$75$	−3.39316	+	6.44011i	−0.391808	+	0.743640i
$76$	−2.42681	+	0.883285i	−0.278374	+	0.101320i
$77$	7.14122	+	4.26040i	0.813817	+	0.485518i
$78$	−12.5305	−	9.71396i	−1.41880	−	1.09989i
$79$	−2.29784	−	13.0317i	−0.258527	−	1.46618i	−0.786854	−	0.617139i	$-0.788292\pi$
$79$	−2.29784	−	13.0317i	−0.258527	−	1.46618i	0.528327	−	0.849041i	$-0.322820\pi$
$80$	1.68801	+	2.92371i	0.188725	+	0.326881i
$81$	7.70354	+	4.65354i	0.855949	+	0.517060i
$82$	−4.95638	+	8.58471i	−0.547341	+	0.948022i
$83$	4.92372	−	4.13150i	0.540449	−	0.453490i	−0.331242	−	0.943546i	$-0.607468\pi$
$83$	4.92372	−	4.13150i	0.540449	−	0.453490i	0.871691	+	0.490055i	$0.163023\pi$
$84$	8.46544	+	4.61625i	0.923655	+	0.503674i
$85$	0.890949	−	5.05282i	0.0966370	−	0.548055i
$86$	2.59259	−	14.7033i	0.279566	−	1.58550i
$87$	−0.0416835	−	0.0661509i	−0.00446894	−	0.00709212i
$88$	−0.507835	+	0.426124i	−0.0541354	+	0.0454250i
$89$	−12.6111			−1.33678			−0.668388	−	0.743812i	$-0.733016\pi$
$89$	−12.6111			−1.33678			−0.668388	+	0.743812i	$0.733016\pi$
$90$	−5.22763	−	1.45640i	−0.551041	−	0.153518i
$91$	−11.8016	+	1.90720i	−1.23714	+	0.199929i
$92$	10.9860	+	3.99856i	1.14537	+	0.416879i
$93$	0.0882956	+	0.407825i	0.00915582	+	0.0422895i
$94$	−1.95200	+	11.0704i	−0.201334	+	1.14182i
$95$	0.190307	−	1.07929i	0.0195251	−	0.110732i
$96$	10.3668	−	9.40537i	1.05806	−	0.959931i
$97$	−11.8862	−	4.32622i	−1.20686	−	0.439261i	−0.341246	−	0.939974i	$-0.610849\pi$
$97$	−11.8862	−	4.32622i	−1.20686	−	0.439261i	−0.865613	+	0.500713i	$0.833071\pi$
$98$	13.4592	−	4.46682i	1.35958	−	0.451217i
$99$	−0.914800	+	9.38444i	−0.0919408	+	0.943172i
$100$	−8.84301			−0.884301
$101$	7.78093	−	6.52898i	0.774232	−	0.649658i	−0.167557	−	0.985862i	$-0.553588\pi$
$101$	7.78093	−	6.52898i	0.774232	−	0.649658i	0.941789	+	0.336205i	$0.109143\pi$
$102$	−20.1475	+	0.779690i	−1.99490	+	0.0772009i
$103$	−2.60057	+	14.7486i	−0.256242	+	1.45322i	0.536622	+	0.843823i	$0.319700\pi$
$103$	−2.60057	+	14.7486i	−0.256242	+	1.45322i	−0.792864	+	0.609399i	$0.791411\pi$
$104$	0.165496	−	0.938575i	0.0162282	−	0.0920348i
$105$	−3.49271	+	2.13164i	−0.340854	+	0.208027i
$106$	11.8657	−	9.95654i	1.15250	−	0.967065i
$107$	7.28317	−	12.6148i	0.704090	−	1.21952i	−0.262929	−	0.964815i	$-0.584688\pi$
$107$	7.28317	−	12.6148i	0.704090	−	1.21952i	0.967019	−	0.254705i	$-0.0819783\pi$
$108$	−0.639166	+	10.9146i	−0.0615038	+	1.05026i
$109$	−1.69401	−	2.93411i	−0.162257	−	0.281037i	0.773421	−	0.633893i	$-0.218544\pi$
$109$	−1.69401	−	2.93411i	−0.162257	−	0.281037i	−0.935678	+	0.352856i	$0.885211\pi$
$110$	−0.987249	−	5.59897i	−0.0941305	−	0.533841i
$111$	−16.4758	+	6.72908i	−1.56381	+	0.638696i
$112$	0.143166	−	10.0024i	0.0135279	−	0.945135i
$113$	−12.6640	+	4.60933i	−1.19133	+	0.433609i	−0.860191	−	0.509973i	$-0.829656\pi$
$113$	−12.6640	+	4.60933i	−1.19133	+	0.433609i	−0.331140	+	0.943582i	$0.607433\pi$
$114$	−4.30353	+	0.166542i	−0.403063	+	0.0155981i
$115$	−3.80052	+	3.18901i	−0.354400	+	0.297377i
$116$	0.0474922	−	0.0822590i	0.00440954	−	0.00763755i
$117$	−7.66464	−	11.1804i	−0.708596	−	1.03363i
$118$	3.81681	−	6.61092i	0.351366	−	0.608584i
$119$	−9.93789	+	11.5050i	−0.911005	+	1.05466i
$120$	−0.0690259	−	0.318821i	−0.00630117	−	0.0291043i
$121$	1.05407	−	0.383649i	0.0958243	−	0.0348772i
$122$	0.286614	−	1.62547i	0.0259488	−	0.147163i
$123$	−6.27680	+	5.69468i	−0.565960	+	0.513472i
$124$	−0.388315	+	0.325835i	−0.0348717	+	0.0292609i
$125$	4.10858	−	7.11627i	0.367483	−	0.636499i
$126$	11.0914	+	11.6421i	0.988104	+	1.03716i
$127$	5.56469	+	9.63833i	0.493786	+	0.855263i	0.999974	−	0.00716008i	$-0.00227914\pi$
$127$	5.56469	+	9.63833i	0.493786	+	0.855263i	−0.506188	+	0.862423i	$0.668946\pi$
$128$	1.58349	+	0.576343i	0.139962	+	0.0509420i
$129$	5.95014	−	11.2932i	0.523880	−	0.994308i
$130$	6.26122	+	5.25379i	0.549145	+	0.460788i
$131$	6.02780	+	5.05793i	0.526651	+	0.441913i	0.866943	−	0.498407i	$-0.166081\pi$
$131$	6.02780	+	5.05793i	0.526651	+	0.441913i	−0.340292	+	0.940320i	$0.610526\pi$
$132$	−10.6040	+	4.33092i	−0.922963	+	0.376958i
$133$	−2.12274	+	2.45748i	−0.184065	+	0.213091i
$134$	1.33297			0.115151
$135$	−3.87559	−	2.55077i	−0.333557	−	0.219535i
$136$	−0.606003	−	1.04963i	−0.0519643	−	0.0900048i
$137$	−1.64156	−	0.597477i	−0.140248	−	0.0510459i	0.270943	−	0.962595i	$-0.412665\pi$
$137$	−1.64156	−	0.597477i	−0.140248	−	0.0510459i	−0.411190	+	0.911550i	$0.634887\pi$
$138$	15.4085	+	11.9451i	1.31166	+	1.01683i
$139$	−2.01511	+	11.4282i	−0.170919	+	0.969330i	0.771830	+	0.635828i	$0.219341\pi$
$139$	−2.01511	+	11.4282i	−0.170919	+	0.969330i	−0.942749	+	0.333502i	$0.891770\pi$
$140$	−4.26881	−	2.54674i	−0.360780	−	0.215239i
$141$	−4.47996	+	8.50283i	−0.377281	+	0.716067i
$142$	14.3112	+	5.20886i	1.20097	+	0.437118i
$143$	7.10068	−	12.2987i	0.593789	−	1.02847i
$144$	10.3270	−	4.69159i	0.860586	−	0.390966i
$145$	0.0201539	+	0.0349075i	0.00167369	+	0.00289891i
$146$	18.5531	+	6.75277i	1.53546	+	0.558863i
$147$	12.1237	−	0.121912i	0.999949	−	0.0100551i
$148$	−16.5619	−	13.8971i	−1.36138	−	1.14233i
$149$	−8.57674	+	3.12168i	−0.702634	+	0.255738i	−0.668535	−	0.743681i	$-0.733078\pi$
$149$	−8.57674	+	3.12168i	−0.702634	+	0.255738i	−0.0340988	+	0.999418i	$0.510856\pi$
$150$	−14.0422	−	4.50409i	−1.14654	−	0.367758i
$151$	1.62003	+	9.18763i	0.131836	+	0.747678i	0.977011	+	0.213189i	$0.0683850\pi$
$151$	1.62003	+	9.18763i	0.131836	+	0.747678i	−0.845175	+	0.534490i	$0.820504\pi$
$152$	−0.129443	−	0.224201i	−0.0104992	−	0.0181851i
$153$	−16.6060	−	4.62638i	−1.34252	−	0.374020i
$154$	−5.98768	+	15.7461i	−0.482501	+	1.26886i
$155$	−0.0373540	−	0.211845i	−0.00300034	−	0.0170158i
$156$	7.67597	−	14.5687i	0.614569	−	1.16643i
$157$	10.0221	+	8.40952i	0.799849	+	0.671153i	0.948162	−	0.317787i	$-0.102940\pi$
$157$	10.0221	+	8.40952i	0.799849	+	0.671153i	−0.148313	+	0.988940i	$0.547384\pi$
$158$	25.1910	−	9.16877i	2.00409	−	0.729428i
$159$	12.2600	−	5.00727i	0.972285	−	0.397103i
$160$	−5.52778	+	4.63836i	−0.437010	+	0.366695i
$161$	14.5122	−	2.34526i	1.14372	−	0.184832i
$162$	−6.57420	+	17.0063i	−0.516518	+	1.33614i
$163$	2.67921	−	4.64053i	0.209852	−	0.363474i	−0.741816	−	0.670604i	$-0.766035\pi$
$163$	2.67921	−	4.64053i	0.209852	−	0.363474i	0.951668	+	0.307129i	$0.0993684\pi$
$164$	−9.67477	−	3.52133i	−0.755472	−	0.274969i
$165$	0.658325	−	4.81601i	0.0512505	−	0.374926i
$166$	9.97478	+	8.36984i	0.774193	+	0.649625i
$167$	6.66051	−	2.42423i	0.515406	−	0.187592i	−0.0712043	−	0.997462i	$-0.522684\pi$
$167$	6.66051	−	2.42423i	0.515406	−	0.187592i	0.586610	+	0.809869i	$0.300462\pi$
$168$	−0.308361	+	0.916073i	−0.0237906	+	0.0706766i
$169$	1.28784	+	7.30371i	0.0990647	+	0.561824i
$170$	10.3942			0.797201
$171$	−3.54706	−	0.988198i	−0.271251	−	0.0755694i
$172$	15.5068			1.18238
$173$	−13.8890	+	11.6542i	−1.05596	+	0.886054i	−0.993707	−	0.112007i	$-0.964272\pi$
$173$	−13.8890	+	11.6542i	−1.05596	+	0.886054i	−0.0622501	+	0.998061i	$0.519828\pi$
$174$	0.117313	−	0.106433i	0.00889347	−	0.00806868i
$175$	−9.70822	+	5.42129i	−0.733872	+	0.409811i
$176$	9.10318	+	7.63847i	0.686178	+	0.575772i
$177$	4.83364	−	4.38536i	0.363319	−	0.329624i
$178$	−4.43643	−	25.1603i	−0.332525	−	1.88584i
$179$	−15.9280			−1.19052			−0.595259	−	0.803534i	$-0.702951\pi$
$179$	−15.9280			−1.19052			−0.595259	+	0.803534i	$0.702951\pi$
$180$	0.546841	−	5.60974i	0.0407591	−	0.418126i
$181$	−11.7915	−	20.4235i	−0.876456	−	1.51807i	−0.855203	−	0.518293i	$-0.826568\pi$
$181$	−11.7915	−	20.4235i	−0.876456	−	1.51807i	−0.0212529	−	0.999774i	$-0.506766\pi$
$182$	−7.95668	−	22.8742i	−0.589788	−	1.69555i
$183$	0.657797	−	1.24848i	0.0486257	−	0.0922901i
$184$	−0.203508	+	1.15415i	−0.0150028	+	0.0850851i
$185$	8.62139	−	3.13793i	0.633857	−	0.230705i
$186$	−0.782585	+	0.319625i	−0.0573819	+	0.0234360i
$187$	−3.13608	−	17.7856i	−0.229333	−	1.30061i
$188$	−11.6754			−0.851513
$189$	5.98960	+	12.3744i	0.435679	+	0.900102i
$190$	2.22022			0.161071
$191$	3.73858	+	21.2025i	0.270514	+	1.53416i	0.752860	+	0.658181i	$0.228674\pi$
$191$	3.73858	+	21.2025i	0.270514	+	1.53416i	−0.482345	+	0.875981i	$0.660215\pi$
$192$	12.0601	+	9.34930i	0.870361	+	0.674727i
$193$	−8.25517	+	3.00464i	−0.594220	+	0.216278i	−0.621584	−	0.783347i	$-0.713511\pi$
$193$	−8.25517	+	3.00464i	−0.594220	+	0.216278i	0.0273645	+	0.999626i	$0.491289\pi$
$194$	4.44976	−	25.2359i	0.319474	−	1.81183i
$195$	3.72543	+	5.91219i	0.266784	+	0.423380i
$196$	6.99632	+	12.9611i	0.499737	+	0.925791i
$197$	1.67466	+	2.90060i	0.119315	+	0.206659i	0.919496	−	0.393099i	$-0.128597\pi$
$197$	1.67466	+	2.90060i	0.119315	+	0.206659i	−0.800182	+	0.599758i	$0.795264\pi$
$198$	−19.0446	+	1.47622i	−1.35344	+	0.104911i
$199$	−11.4381			−0.810825			−0.405413	−	0.914134i	$-0.632872\pi$
$199$	−11.4381			−0.810825			−0.405413	+	0.914134i	$0.632872\pi$
$200$	−0.153932	−	0.872991i	−0.0108846	−	0.0617298i
$201$	1.08519	+	0.348078i	0.0765434	+	0.0245516i
$202$	15.7631	+	13.2268i	1.10909	+	0.930635i
$203$	0.00170932	−	0.119423i	0.000119971	−	0.00838184i
$204$	−4.43123	−	20.4673i	−0.310248	−	1.43300i
$205$	3.34692	−	2.80840i	0.233759	−	0.196147i
$206$	−30.3395			−2.11386
$207$	9.42508	+	13.7483i	0.655089	+	0.955574i
$208$	−17.0839			−1.18456
$209$	−0.669870	−	3.79902i	−0.0463359	−	0.262784i
$210$	−5.48149	−	6.21837i	−0.378259	−	0.429108i
$211$	16.9946	−	6.18552i	1.16995	−	0.425829i	0.317311	−	0.948322i	$-0.397220\pi$
$211$	16.9946	−	6.18552i	1.16995	−	0.425829i	0.852644	+	0.522493i	$0.174998\pi$
$212$	12.3241	+	10.3411i	0.846422	+	0.710233i
$213$	10.2908	+	7.97771i	0.705114	+	0.546624i
$214$	27.7297	+	10.0928i	1.89557	+	0.689930i
$215$	−3.29025	+	5.69888i	−0.224393	+	0.388660i
$216$	−1.08863	+	0.126894i	−0.0740717	+	0.00863401i
$217$	−0.226552	+	0.595776i	−0.0153794	+	0.0404439i
$218$	5.25786	−	4.41187i	0.356107	−	0.298810i
$219$	13.3410	+	10.3423i	0.901502	+	0.698869i
$220$	5.54884	−	2.01961i	0.374103	−	0.136162i
$221$	19.8893	+	16.6891i	1.33790	+	1.12263i
$222$	−19.2211	−	30.5034i	−1.29003	−	2.04725i
$223$	−2.13914	−	12.1316i	−0.143247	−	0.812395i	−0.968758	−	0.248008i	$-0.920224\pi$
$223$	−2.13914	−	12.1316i	−0.143247	−	0.812395i	0.825511	−	0.564386i	$-0.190887\pi$
$224$	21.1078	−	3.41114i	1.41032	−	0.227916i
$225$	−10.2558	−	7.33370i	−0.683723	−	0.488914i
$226$	−13.6510	−	23.6443i	−0.908053	−	1.57279i
$227$	−4.13532	−	23.4526i	−0.274471	−	1.55660i	−0.740638	−	0.671904i	$-0.765477\pi$
$227$	−4.13532	−	23.4526i	−0.274471	−	1.55660i	0.466168	−	0.884696i	$-0.345634\pi$
$228$	−0.946515	−	4.37182i	−0.0626845	−	0.289531i
$229$	21.2430	−	7.73183i	1.40378	−	0.510933i	0.474481	−	0.880266i	$-0.342636\pi$
$229$	21.2430	−	7.73183i	1.40378	−	0.510933i	0.929297	+	0.369333i	$0.120414\pi$
$230$	−7.69932	−	6.46050i	−0.507678	−	0.425993i
$231$	−8.98644	+	11.2556i	−0.591264	+	0.740562i
$232$	0.00894740	+	0.00325659i	0.000587425	+	0.000213805i
$233$	−0.152366	−	0.263905i	−0.00998180	−	0.0172890i	0.860991	−	0.508620i	$-0.169844\pi$
$233$	−0.152366	−	0.263905i	−0.00998180	−	0.0172890i	−0.870973	+	0.491331i	$0.836511\pi$
$234$	19.6095	−	19.2247i	1.28191	−	1.25676i
$235$	2.47729	−	4.29079i	0.161600	−	0.279900i
$236$	7.45035	+	2.71171i	0.484977	+	0.176517i
$237$	22.9026	−	0.886309i	1.48768	−	0.0575720i
$238$	−26.4495	−	15.7796i	−1.71447	−	1.02284i
$239$	−4.19570	+	23.7950i	−0.271397	+	1.53917i	0.478780	+	0.877935i	$0.341079\pi$
$239$	−4.19570	+	23.7950i	−0.271397	+	1.53917i	−0.750178	+	0.661236i	$0.770032\pi$
$240$	−5.41334	+	2.21093i	−0.349429	+	0.142715i
$241$	−13.4282	−	4.88748i	−0.864989	−	0.314830i	−0.128853	−	0.991664i	$-0.541129\pi$
$241$	−13.4282	−	4.88748i	−0.864989	−	0.314830i	−0.736136	+	0.676834i	$0.763352\pi$
$242$	1.13622	+	1.96799i	0.0730390	+	0.126507i
$243$	−9.79301	+	12.1284i	−0.628222	+	0.778034i
$244$	1.71430			0.109747
$245$	−6.24778	−	0.178888i	−0.399156	−	0.0114287i
$246$	−13.5695	−	10.5194i	−0.865158	−	0.670694i
$247$	4.24838	+	3.56481i	0.270318	+	0.226823i
$248$	−0.0389263	−	0.0326630i	−0.00247182	−	0.00207410i
$249$	5.93501	+	9.41874i	0.376116	+	0.596888i
$250$	15.6429	+	5.69355i	0.989345	+	0.360092i
$251$	1.67494	+	2.90107i	0.105721	+	0.183114i	0.914033	−	0.405641i	$-0.132952\pi$
$251$	1.67494	+	2.90107i	0.105721	+	0.183114i	−0.808312	+	0.588755i	$0.799618\pi$
$252$	−9.90774	+	13.4446i	−0.624129	+	0.846929i
$253$	−8.73159	+	15.1236i	−0.548951	+	0.950810i
$254$	−17.2717	+	14.4927i	−1.08372	+	0.909351i
$255$	8.46211	+	2.71425i	0.529918	+	0.169973i
$256$	2.46692	−	13.9906i	0.154183	−	0.874413i
$257$	−16.9888	+	6.18343i	−1.05973	+	0.385711i	−0.812328	−	0.583201i	$-0.801800\pi$
$257$	−16.9888	+	6.18343i	−1.05973	+	0.385711i	−0.247405	+	0.968912i	$0.579578\pi$
$258$	24.6240	+	7.89823i	1.53302	+	0.491723i
$259$	−26.7020	−	5.10336i	−1.65918	−	0.317107i
$260$	−4.24458	+	7.35183i	−0.263238	+	0.455941i
$261$	0.123299	−	0.0560150i	0.00763203	−	0.00346724i
$262$	−7.97049	+	13.8053i	−0.492418	+	0.852893i
$263$	−18.5162	+	15.5369i	−1.14176	+	0.958049i	−0.999495	−	0.0317800i	$-0.989882\pi$
$263$	−18.5162	+	15.5369i	−1.14176	+	0.958049i	−0.142263	+	0.989829i	$0.545438\pi$
$264$	−0.612140	−	0.971453i	−0.0376746	−	0.0597888i
$265$	−6.41539	+	2.33501i	−0.394094	+	0.143439i
$266$	−5.64964	−	3.37054i	−0.346402	−	0.206661i
$267$	2.95834	−	21.6419i	0.181047	−	1.32446i
$268$	0.240409	+	1.36342i	0.0146853	+	0.0832844i
$269$	7.45250	+	12.9081i	0.454387	+	0.787022i	0.998653	−	0.0518912i	$-0.0165249\pi$
$269$	7.45250	+	12.9081i	0.454387	+	0.787022i	−0.544266	+	0.838913i	$0.683192\pi$
$270$	3.72562	−	8.62945i	0.226734	−	0.525172i
$271$	−2.69114	+	4.66119i	−0.163475	+	0.283147i	−0.936113	−	0.351700i	$-0.885604\pi$
$271$	−2.69114	+	4.66119i	−0.163475	+	0.283147i	0.772638	+	0.634847i	$0.218937\pi$
$272$	−16.6429	+	13.9651i	−1.00912	+	0.846756i
$273$	−0.504507	−	20.7000i	−0.0305341	−	1.25282i
$274$	0.614540	−	3.48523i	0.0371257	−	0.210550i
$275$	2.29372	−	13.0084i	0.138317	−	0.784434i
$276$	−9.43901	+	17.9149i	−0.568162	+	1.07835i
$277$	−0.775246	+	0.650509i	−0.0465800	+	0.0390853i	−0.665780	−	0.746148i	$-0.731901\pi$
$277$	−0.775246	+	0.650509i	−0.0465800	+	0.0390853i	0.619200	+	0.785233i	$0.287457\pi$
$278$	−23.5092			−1.40999
$279$	−0.720578	+	0.0558550i	−0.0431399	+	0.00334395i
$280$	0.177109	−	0.465753i	0.0105843	−	0.0278341i
$281$	−12.2222	−	4.44851i	−0.729114	−	0.265376i	−0.0493245	−	0.998783i	$-0.515707\pi$
$281$	−12.2222	−	4.44851i	−0.729114	−	0.265376i	−0.679790	+	0.733407i	$0.737929\pi$
$282$	−18.5398	−	5.94672i	−1.10403	−	0.354122i
$283$	−3.28461	+	18.6280i	−0.195250	+	1.10732i	0.716812	+	0.697266i	$0.245600\pi$
$283$	−3.28461	+	18.6280i	−0.195250	+	1.10732i	−0.912062	+	0.410052i	$0.865511\pi$
$284$	−2.74676	+	15.5777i	−0.162990	+	0.924365i
$285$	1.80751	+	0.579766i	0.107068	+	0.0343423i
$286$	27.0350	+	9.83992i	1.59861	+	0.581847i
$287$	−12.7801	+	2.06535i	−0.754388	+	0.121914i
$288$	13.7086	+	19.9967i	0.807788	+	1.17832i
$289$	16.0182			0.942247
$290$	−0.0625536	+	0.0524887i	−0.00367328	+	0.00308224i
$291$	10.2125	−	19.3829i	0.598666	−	1.13625i
$292$	−3.56091	+	20.1949i	−0.208386	+	1.18182i
$293$	−0.436945	+	2.47804i	−0.0255266	+	0.144769i	−0.994907	−	0.100794i	$-0.967862\pi$
$293$	−0.436945	+	2.47804i	−0.0255266	+	0.144769i	0.969381	+	0.245563i	$0.0789727\pi$
$294$	4.50820	+	24.1450i	0.262924	+	1.40817i
$295$	−2.57739	+	2.16269i	−0.150062	+	0.125917i
$296$	1.08364	−	1.87691i	0.0629851	−	0.109093i
$297$	−15.8900	−	3.77130i	−0.922029	−	0.218833i
$298$	−9.24520	−	16.0132i	−0.535560	−	0.927617i
$299$	−4.35956	−	24.7243i	−0.252120	−	1.42984i
$300$	2.07441	−	15.1754i	0.119766	−	0.876153i
$301$	17.0240	−	9.50660i	0.981249	−	0.547951i
$302$	−17.7602	+	6.46418i	−1.02198	+	0.371972i
$303$	9.37906	+	14.8844i	0.538813	+	0.855085i
$304$	−3.55494	+	2.98295i	−0.203890	+	0.171084i
$305$	−0.363742	+	0.630020i	−0.0208278	+	0.0360748i
$306$	3.38822	−	34.7579i	0.193692	−	1.98698i
$307$	3.33310	−	5.77311i	0.190230	−	0.329489i	−0.755096	−	0.655614i	$-0.772410\pi$
$307$	3.33310	−	5.77311i	0.190230	−	0.329489i	0.945326	+	0.326125i	$0.105743\pi$
$308$	−17.1858	−	3.28459i	−0.979250	−	0.187157i
$309$	−24.6999	−	7.92257i	−1.40513	−	0.450699i
$310$	0.409508	−	0.149049i	0.0232585	−	0.00846540i
$311$	−2.53672	+	14.3865i	−0.143844	+	0.815782i	0.824444	+	0.565944i	$0.191488\pi$
$311$	−2.53672	+	14.3865i	−0.143844	+	0.815782i	−0.968288	+	0.249837i	$0.919623\pi$
$312$	1.57186	+	0.504179i	0.0889889	+	0.0285435i
$313$	16.7927	−	14.0907i	0.949177	−	0.796454i	−0.0299819	−	0.999550i	$-0.509545\pi$
$313$	16.7927	−	14.0907i	0.949177	−	0.796454i	0.979159	+	0.203097i	$0.0651005\pi$
$314$	−13.2521	+	22.9533i	−0.747858	+	1.29533i
$315$	−2.83876	−	6.49386i	−0.159946	−	0.365887i
$316$	13.9216	+	24.1129i	0.783151	+	1.35646i
$317$	8.74471	+	3.18282i	0.491152	+	0.178765i	0.575710	−	0.817654i	$-0.304726\pi$
$317$	8.74471	+	3.18282i	0.491152	+	0.178765i	−0.0845581	+	0.996419i	$0.526948\pi$
$318$	14.3029	+	22.6983i	0.802065	+	1.27286i
$319$	0.108687	+	0.0911992i	0.00608530	+	0.00510618i
$320$	−6.02617	−	5.05656i	−0.336873	−	0.282670i
$321$	19.9397	+	15.4578i	1.11292	+	0.862769i
$322$	9.78420	+	28.1280i	0.545252	+	1.56751i
$323$	7.05271			0.392423
$324$	−18.5805	−	3.65723i	−1.03225	−	0.203180i
$325$	9.49489	+	16.4456i	0.526681	+	0.912239i
$326$	10.2008	+	3.71277i	0.564968	+	0.205631i
$327$	5.43258	−	2.21879i	0.300422	−	0.122699i
$328$	0.179219	−	1.01640i	0.00989570	−	0.0561213i
$329$	−12.8177	+	7.15768i	−0.706662	+	0.394616i
$330$	9.83993	−	0.380796i	0.541670	−	0.0209621i
$331$	−12.7757	−	4.64997i	−0.702215	−	0.255585i	−0.0338587	−	0.999427i	$-0.510780\pi$
$331$	−12.7757	−	4.64997i	−0.702215	−	0.255585i	−0.668356	+	0.743841i	$0.733002\pi$
$332$	−6.76207	+	11.7122i	−0.371117	+	0.642793i
$333$	−7.68280	−	29.8525i	−0.421015	−	1.63591i
$334$	7.17963	+	12.4355i	0.392852	+	0.680439i
$335$	−0.552080	−	0.200941i	−0.0301633	−	0.0109786i
$336$	17.1314	+	2.59206i	0.934595	+	0.141408i
$337$	−18.7794	−	15.7578i	−1.02298	−	0.858382i	−0.0329809	−	0.999456i	$-0.510500\pi$
$337$	−18.7794	−	15.7578i	−1.02298	−	0.858382i	−0.989999	+	0.141074i	$0.954944\pi$
$338$	−14.1185	+	5.13870i	−0.767944	+	0.279509i
$339$	−4.93928	−	22.8139i	−0.268265	−	1.23908i
$340$	1.87466	+	10.6317i	0.101668	+	0.576586i
$341$	−0.378592	−	0.655741i	−0.0205019	−	0.0355104i
$342$	0.723727	−	7.42432i	0.0391347	−	0.401461i
$343$	15.6268	+	9.94005i	0.843766	+	0.536712i
$344$	0.269930	+	1.53085i	0.0145537	+	0.0825379i
$345$	−4.58111	−	7.27012i	−0.246638	−	0.391410i
$346$	−28.1371	−	23.6098i	−1.51266	−	1.26927i
$347$	11.7888	−	4.29078i	0.632858	−	0.230341i	−0.00561693	−	0.999984i	$-0.501788\pi$
$347$	11.7888	−	4.29078i	0.632858	−	0.230341i	0.638475	+	0.769643i	$0.279566\pi$
$348$	0.130023	+	0.100797i	0.00696997	+	0.00540331i
$349$	19.9884	−	16.7723i	1.06996	−	0.897800i	0.0749083	−	0.997190i	$-0.476134\pi$
$349$	19.9884	−	16.7723i	1.06996	−	0.897800i	0.995049	+	0.0993900i	$0.0316891\pi$
$350$	−14.2312	−	17.4616i	−0.760687	−	0.933361i
$351$	20.9845	−	10.5305i	1.12007	−	0.562078i
$352$	−12.7000	+	21.9970i	−0.676910	+	1.17244i
$353$	22.3840	+	8.14711i	1.19138	+	0.433627i	0.860208	−	0.509944i	$-0.170334\pi$
$353$	22.3840	+	8.14711i	1.19138	+	0.433627i	0.331172	+	0.943570i	$0.392556\pi$
$354$	10.4496	+	8.10080i	0.555389	+	0.430553i
$355$	−5.14211	−	4.31474i	−0.272915	−	0.229003i
$356$	24.9350	−	9.07560i	1.32155	−	0.481006i
$357$	−17.4124	−	19.7532i	−0.921564	−	1.04545i
$358$	−5.60328	−	31.7778i	−0.296143	−	1.67951i
$359$	−18.6890			−0.986366			−0.493183	−	0.869926i	$-0.664167\pi$
$359$	−18.6890			−0.986366			−0.493183	+	0.869926i	$0.664167\pi$
$360$	0.563319	−	0.0436652i	0.0296895	−	0.00230136i
$361$	−17.4935			−0.920712
$362$	36.5985	−	30.7098i	1.92357	−	1.61407i
$363$	0.411113	+	1.89887i	0.0215778	+	0.0996650i
$364$	21.9618	−	12.2640i	1.15111	−	0.642807i
$365$	−6.66623	−	5.59363i	−0.348926	−	0.292784i
$366$	2.72222	+	0.873162i	0.142293	+	0.0456409i
$367$	4.28546	+	24.3040i	0.223699	+	1.26866i	0.865157	+	0.501501i	$0.167219\pi$
$367$	4.28546	+	24.3040i	0.223699	+	1.26866i	−0.641458	+	0.767158i	$0.721670\pi$
$368$	21.0078			1.09511
$369$	−8.30018	−	12.1074i	−0.432090	−	0.630288i
$370$	9.29333	+	16.0965i	0.483137	+	0.836818i
$371$	19.8696	+	3.79753i	1.03158	+	0.197158i
$372$	−0.468072	−	0.742820i	−0.0242684	−	0.0385134i
$373$	5.21360	−	29.5678i	0.269950	−	1.53096i	−0.484610	−	0.874730i	$-0.661038\pi$
$373$	5.21360	−	29.5678i	0.269950	−	1.53096i	0.754560	−	0.656231i	$-0.227850\pi$
$374$	34.3806	−	12.5135i	1.77778	−	0.647058i
$375$	11.2484	+	8.72005i	0.580864	+	0.450301i
$376$	−0.203235	−	1.15260i	−0.0104810	−	0.0594410i
$377$	−0.203973			−0.0105051
$378$	−22.5808	+	16.3029i	−1.16143	+	0.838531i
$379$	29.6444			1.52273			0.761365	−	0.648324i	$-0.224530\pi$
$379$	29.6444			1.52273			0.761365	+	0.648324i	$0.224530\pi$
$380$	0.400429	+	2.27094i	0.0205416	+	0.116497i
$381$	−17.8456	+	7.28855i	−0.914259	+	0.373404i
$382$	−40.9857	+	14.9176i	−2.09701	+	0.763249i
$383$	0.542179	−	3.07485i	0.0277040	−	0.157117i	−0.967817	−	0.251654i	$-0.919026\pi$
$383$	0.542179	−	3.07485i	0.0277040	−	0.157117i	0.995521	+	0.0945361i	$0.0301368\pi$
$384$	−1.36051	+	2.58221i	−0.0694285	+	0.131773i
$385$	4.85360	−	5.61898i	0.247363	−	0.286370i
$386$	−8.89856	−	15.4128i	−0.452925	−	0.784489i
$387$	17.9843	+	12.8602i	0.914195	+	0.653718i
$388$	26.6150			1.35117
$389$	−1.24377	−	7.05376i	−0.0630615	−	0.357640i	−0.999968	−	0.00805830i	$-0.997435\pi$
$389$	−1.24377	−	7.05376i	−0.0630615	−	0.357640i	0.936906	−	0.349581i	$-0.113676\pi$
$390$	−10.4847	+	9.51239i	−0.530916	+	0.481679i
$391$	−24.4576	−	20.5223i	−1.23687	−	1.03786i
$392$	−1.15774	+	0.916300i	−0.0584749	+	0.0462801i
$393$	−10.0939	+	9.15776i	−0.509169	+	0.461948i
$394$	−5.19781	+	4.36148i	−0.261862	+	0.219728i
$395$	−11.8156			−0.594507
$396$	−4.94475	−	19.2135i	−0.248483	−	0.965513i
$397$	18.4934			0.928157			0.464079	−	0.885794i	$-0.346386\pi$
$397$	18.4934			0.928157			0.464079	+	0.885794i	$0.346386\pi$
$398$	−4.02378	−	22.8200i	−0.201694	−	1.14386i
$399$	−3.71931	−	4.21930i	−0.186198	−	0.211229i
$400$	−14.9319	+	5.43476i	−0.746594	+	0.271738i
$401$	−14.0554	−	11.7939i	−0.701896	−	0.588960i	0.220417	−	0.975406i	$-0.429258\pi$
$401$	−14.0554	−	11.7939i	−0.701896	−	0.588960i	−0.922312	+	0.386445i	$0.873703\pi$
$402$	−0.312690	+	2.28750i	−0.0155955	+	0.114090i
$403$	1.02291	+	0.372308i	0.0509546	+	0.0185460i
$404$	−10.6861	+	18.5088i	−0.531651	+	0.920847i
$405$	5.28650	−	6.05250i	0.262688	−	0.300751i
$406$	0.238860	−	0.0386012i	0.0118544	−	0.00191574i
$407$	24.7389	−	20.7584i	1.22626	−	1.02896i
$408$	1.94342	−	0.793733i	0.0962134	−	0.0392957i
$409$	0.100901	−	0.0367251i	0.00498925	−	0.00181594i	−0.339524	−	0.940597i	$-0.610266\pi$
$409$	0.100901	−	0.0367251i	0.00498925	−	0.00181594i	0.344514	+	0.938781i	$0.388044\pi$
$410$	6.78039	+	5.68942i	0.334860	+	0.280981i
$411$	1.41040	−	2.67690i	0.0695701	−	0.132042i
$412$	−5.47191	−	31.0328i	−0.269582	−	1.52887i
$413$	9.84174	−	1.59048i	0.484280	−	0.0782626i
$414$	−24.1134	+	23.6403i	−1.18511	+	1.16186i
$415$	−2.86956	−	4.97023i	−0.140861	−	0.243979i
$416$	−6.34090	−	35.9610i	−0.310888	−	1.76313i
$417$	−19.1392	−	6.13896i	−0.937250	−	0.300626i
$418$	7.34372	−	2.67289i	0.359193	−	0.130736i
$419$	1.12657	+	0.945301i	0.0550364	+	0.0461810i	0.669891	−	0.742460i	$-0.266341\pi$
$419$	1.12657	+	0.945301i	0.0550364	+	0.0461810i	−0.614855	+	0.788641i	$0.710785\pi$
$420$	5.37183	−	6.72825i	0.262119	−	0.328305i
$421$	29.7174	+	10.8162i	1.44834	+	0.527152i	0.942126	−	0.335258i	$-0.108823\pi$
$421$	29.7174	+	10.8162i	1.44834	+	0.527152i	0.506211	+	0.862410i	$0.331046\pi$
$422$	18.3191	+	31.7296i	0.891760	+	1.54457i
$423$	−13.5407	−	9.68263i	−0.658372	−	0.470786i
$424$	−0.806361	+	1.39666i	−0.0391603	+	0.0678277i
$425$	22.6930	+	8.25959i	1.10077	+	0.400649i
$426$	−12.2960	+	23.3375i	−0.595745	+	1.13070i
$427$	1.88203	−	1.05097i	0.0910779	−	0.0508600i
$428$	−5.32219	+	30.1836i	−0.257258	+	1.45898i
$429$	19.4401	+	15.0705i	0.938576	+	0.727610i
$430$	−12.5272	−	4.55953i	−0.604116	−	0.219880i
$431$	−13.4216	−	23.2470i	−0.646498	−	1.11977i	−0.983953	−	0.178425i	$-0.942900\pi$
$431$	−13.4216	−	23.2470i	−0.646498	−	1.11977i	0.337456	−	0.941341i	$-0.390434\pi$
$432$	5.62867	+	18.8227i	0.270809	+	0.905608i
$433$	4.77702			0.229569			0.114785	−	0.993390i	$-0.463382\pi$
$433$	4.77702			0.229569			0.114785	+	0.993390i	$0.463382\pi$
$434$	−1.26832	−	0.242405i	−0.0608814	−	0.0116358i
$435$	−0.0646323	+	0.0263972i	−0.00309888	+	0.00126565i
$436$	5.46096	+	4.58229i	0.261533	+	0.219452i
$437$	−5.22416	−	4.38359i	−0.249905	−	0.209695i
$438$	−15.9406	+	30.2547i	−0.761671	+	1.44563i
$439$	−18.9217	−	6.88695i	−0.903086	−	0.328696i	−0.151597	−	0.988442i	$-0.548442\pi$
$439$	−18.9217	−	6.88695i	−0.903086	−	0.328696i	−0.751489	+	0.659746i	$0.770664\pi$
$440$	0.295968	+	0.512631i	0.0141097	+	0.0244387i
$441$	−2.63479	+	20.8341i	−0.125466	+	0.992098i
$442$	−26.2994	+	45.5519i	−1.25094	+	2.16668i
$443$	20.6066	−	17.2910i	0.979048	−	0.821518i	−0.00489783	−	0.999988i	$-0.501559\pi$
$443$	20.6066	−	17.2910i	0.979048	−	0.821518i	0.983945	+	0.178470i	$0.0571146\pi$
$444$	27.7337	−	25.1617i	1.31618	−	1.19412i
$445$	−1.95537	+	11.0895i	−0.0926936	+	0.525692i
$446$	23.4511	−	8.53551i	1.11044	−	0.404168i
$447$	−3.34514	−	15.4508i	−0.158220	−	0.730796i
$448$	7.65798	+	22.0155i	0.361806	+	1.04014i
$449$	7.02501	−	12.1677i	0.331531	−	0.574228i	−0.651281	−	0.758836i	$-0.725768\pi$
$449$	7.02501	−	12.1677i	0.331531	−	0.574228i	0.982812	+	0.184608i	$0.0591016\pi$
$450$	11.0235	−	23.0412i	0.519652	−	1.08617i
$451$	7.68946	−	13.3185i	0.362083	−	0.627145i
$452$	21.7225	−	18.2273i	1.02174	−	0.857341i
$453$	−16.1468	+	0.624867i	−0.758645	+	0.0293588i
$454$	45.3351	−	16.5006i	2.12768	−	0.774412i
$455$	−0.152769	+	10.6733i	−0.00716194	+	0.500373i
$456$	0.415115	−	0.169542i	0.0194395	−	0.00793953i
$457$	6.37787	+	36.1707i	0.298344	+	1.69199i	0.653291	+	0.757107i	$0.273388\pi$
$457$	6.37787	+	36.1707i	0.298344	+	1.69199i	−0.354947	+	0.934886i	$0.615501\pi$
$458$	22.8987	+	39.6617i	1.06998	+	1.85327i
$459$	11.8348	−	27.4122i	0.552399	−	1.27949i
$460$	5.21949	−	9.04043i	0.243360	−	0.421512i
$461$	−32.4211	+	27.2046i	−1.51000	+	1.26704i	−0.646251	+	0.763125i	$0.723664\pi$
$461$	−32.4211	+	27.2046i	−1.51000	+	1.26704i	−0.863752	+	0.503917i	$0.831892\pi$
$462$	−25.6171	−	13.9691i	−1.19182	−	0.649903i
$463$	−3.29439	+	18.6834i	−0.153103	+	0.868293i	0.807396	+	0.590010i	$0.200876\pi$
$463$	−3.29439	+	18.6834i	−0.153103	+	0.868293i	−0.960499	+	0.278283i	$0.910235\pi$
$464$	0.0296382	−	0.168086i	0.00137592	−	0.00780322i
$465$	0.372308	−	0.0144080i	0.0172654	−	0.000668153i
$466$	0.472912	−	0.396820i	0.0219072	−	0.0183824i
$467$	14.9158			0.690219			0.345110	−	0.938562i	$-0.387842\pi$
$467$	14.9158			0.690219			0.345110	+	0.938562i	$0.387842\pi$
$468$	23.2007	+	16.5902i	1.07245	+	0.766883i
$469$	1.09979	+	1.34944i	0.0507836	+	0.0623113i
$470$	9.43196	+	3.43295i	0.435064	+	0.158350i
$471$	−16.7825	+	15.2261i	−0.773297	+	0.701581i
$472$	−0.138013	+	0.782710i	−0.00635255	+	0.0360271i
$473$	−4.02220	+	22.8111i	−0.184941	+	1.04885i
$474$	9.82511	+	45.3809i	0.451282	+	2.08441i
$475$	4.84725	+	1.76426i	0.222407	+	0.0809496i
$476$	11.3698	−	29.8998i	0.521135	−	1.37046i
$477$	5.71696	+	22.2140i	0.261762	+	1.01711i
$478$	−48.9490			−2.23888
$479$	10.1870	−	8.54789i	0.465455	−	0.390563i	−0.379678	−	0.925119i	$-0.623965\pi$
$479$	10.1870	−	8.54789i	0.465455	−	0.390563i	0.845133	+	0.534555i	$0.179521\pi$
$480$	−6.66314	−	10.5743i	−0.304129	−	0.482647i
$481$	−8.06205	+	45.7221i	−0.367598	+	2.08475i
$482$	5.02705	−	28.5098i	0.228976	−	1.29859i
$483$	0.620384	+	25.4544i	0.0282284	+	1.15822i
$484$	−1.80803	+	1.51712i	−0.0821833	+	0.0689600i
$485$	−5.64719	+	9.78122i	−0.256426	+	0.444143i
$486$	−27.6421	−	15.2713i	−1.25387	−	0.692720i
$487$	6.60006	+	11.4316i	0.299077	+	0.518017i	0.975925	−	0.218106i	$-0.0699878\pi$
$487$	6.60006	+	11.4316i	0.299077	+	0.518017i	−0.676848	+	0.736123i	$0.736654\pi$
$488$	0.0298412	+	0.169238i	0.00135085	+	0.00766103i
$489$	7.33508	+	5.68635i	0.331704	+	0.257146i
$490$	−1.84099	−	12.5278i	−0.0831676	−	0.565948i
$491$	15.3102	−	5.57245i	0.690939	−	0.251481i	0.0274020	−	0.999624i	$-0.491277\pi$
$491$	15.3102	−	5.57245i	0.690939	−	0.251481i	0.663537	+	0.748143i	$0.269054\pi$
$492$	8.31244	−	15.7768i	0.374754	−	0.711271i
$493$	−0.198707	+	0.166735i	−0.00894932	+	0.00750937i
$494$	−5.61757	+	9.72992i	−0.252747	+	0.437770i
$495$	8.11028	+	2.25949i	0.364530	+	0.101557i
$496$	−0.455438	+	0.788842i	−0.0204498	+	0.0354200i
$497$	6.53452	+	18.7857i	0.293113	+	0.842656i
$498$	−16.7033	+	15.1542i	−0.748493	+	0.679078i
$499$	−0.207754	+	0.0756161i	−0.00930033	+	0.00338504i	−0.346666	−	0.937989i	$-0.612686\pi$
$499$	−0.207754	+	0.0756161i	−0.00930033	+	0.00338504i	0.337366	+	0.941374i	$0.390464\pi$
$500$	−3.00235	+	17.0272i	−0.134269	+	0.761479i
$501$	2.59777	+	11.9987i	0.116060	+	0.536064i
$502$	−5.19867	+	4.36220i	−0.232028	+	0.194695i
$503$	0.112688	−	0.195182i	0.00502452	−	0.00870272i	−0.863502	−	0.504345i	$-0.831734\pi$
$503$	0.112688	−	0.195182i	0.00502452	−	0.00870272i	0.868527	+	0.495642i	$0.165067\pi$
$504$	−1.49973	−	0.744070i	−0.0668033	−	0.0331435i
$505$	−4.53475	−	7.85442i	−0.201794	−	0.349517i
$506$	−33.2445	−	12.1000i	−1.47790	−	0.537910i
$507$	−12.8359	+	0.496738i	−0.570064	+	0.0220609i
$508$	−17.9389	−	15.0525i	−0.795908	−	0.667846i
$509$	−24.8793	−	20.8762i	−1.10275	−	0.925320i	−0.105146	−	0.994457i	$-0.533531\pi$
$509$	−24.8793	−	20.8762i	−1.10275	−	0.925320i	−0.997607	+	0.0691366i	$0.977976\pi$
$510$	−2.43829	+	17.8375i	−0.107969	+	0.789856i
$511$	8.47136	+	24.3538i	0.374751	+	1.07735i
$512$	32.1505			1.42086
$513$	2.52791	−	5.85527i	0.111610	−	0.258517i
$514$	−18.3129	−	31.7189i	−0.807748	−	1.39906i
$515$	12.5658	+	4.57358i	0.553716	+	0.201536i
$516$	−3.63761	+	26.6111i	−0.160137	+	1.17149i
$517$	3.02839	−	17.1748i	0.133188	−	0.755348i
$518$	0.788200	−	55.0681i	0.0346315	−	2.41955i
$519$	−16.7416	−	26.5686i	−0.734875	−	1.16623i
$520$	−0.799667	−	0.291055i	−0.0350677	−	0.0127636i
$521$	−11.7781	+	20.4003i	−0.516009	+	0.893754i	0.483818	+	0.875169i	$0.339250\pi$
$521$	−11.7781	+	20.4003i	−0.516009	+	0.893754i	−0.999827	+	0.0185855i	$0.994084\pi$
$522$	0.155130	+	0.226287i	0.00678985	+	0.00990431i
$523$	6.29514	+	10.9035i	0.275267	+	0.476777i	0.970202	−	0.242296i	$-0.0779004\pi$
$523$	6.29514	+	10.9035i	0.275267	+	0.476777i	−0.694935	+	0.719072i	$0.744567\pi$
$524$	−15.5582	−	5.66274i	−0.679665	−	0.247378i
$525$	−7.02606	−	17.9319i	−0.306642	−	0.782614i
$526$	−37.5113	−	31.4757i	−1.63557	−	1.37241i
$527$	1.30084	−	0.473466i	0.0566654	−	0.0206245i
$528$	−15.2438	+	13.8300i	−0.663400	+	0.601876i
$529$	1.36697	+	7.75246i	0.0594334	+	0.337063i
$530$	−6.91539	−	11.9778i	−0.300386	−	0.520283i
$531$	6.39181	+	9.32369i	0.277381	+	0.404614i
$532$	2.42860	−	6.38662i	0.105293	−	0.276895i
$533$	3.83923	+	21.7734i	0.166296	+	0.943110i
$534$	44.2180	−	1.71119i	1.91350	−	0.0740506i
$535$	−9.96346	−	8.36033i	−0.430758	−	0.361449i
$536$	−0.130414	+	0.0474668i	−0.00563302	+	0.00205025i
$537$	3.73642	−	27.3340i	0.161239	−	1.17955i
$538$	−23.1311	+	19.4093i	−0.997252	+	0.836794i
$539$	−20.8809	+	6.92994i	−0.899404	+	0.298494i
$540$	9.49856	+	2.25437i	0.408753	+	0.0970127i
$541$	5.81252	−	10.0676i	0.249900	−	0.432839i	−0.713598	−	0.700555i	$-0.752936\pi$
$541$	5.81252	−	10.0676i	0.249900	−	0.432839i	0.963498	+	0.267716i	$0.0862690\pi$
$542$	−10.2462	−	3.72930i	−0.440111	−	0.160187i
$543$	37.8147	−	15.4443i	1.62278	−	0.662780i
$544$	−35.5731	−	29.8494i	−1.52518	−	1.27978i
$545$	−2.84274	+	1.03467i	−0.121770	+	0.0443205i
$546$	41.1207	−	8.28853i	1.75981	−	0.354716i
$547$	−5.74175	−	32.5631i	−0.245500	−	1.39230i	−0.819330	−	0.573323i	$-0.805654\pi$
$547$	−5.74175	−	32.5631i	−0.245500	−	1.39230i	0.573830	−	0.818974i	$-0.305457\pi$
$548$	3.67570			0.157018
$549$	1.98819	+	1.42171i	0.0848541	+	0.0606771i
$550$	26.7597			1.14104
$551$	−0.0424440	+	0.0356147i	−0.00180818	+	0.00151724i
$552$	−1.93289	−	0.619980i	−0.0822692	−	0.0263881i
$553$	30.0664	+	17.9374i	1.27855	+	0.762776i
$554$	−1.57054	−	1.31784i	−0.0667259	−	0.0559897i
$555$	3.36256	+	15.5312i	0.142733	+	0.659263i
$556$	−4.24002	−	24.0463i	−0.179817	−	1.01979i
$557$	−31.4617			−1.33307			−0.666537	−	0.745472i	$-0.732224\pi$
$557$	−31.4617			−1.33307			−0.666537	+	0.745472i	$0.732224\pi$
$558$	−0.364926	−	1.41797i	−0.0154485	−	0.0600273i
$559$	−16.6499	−	28.8385i	−0.704217	−	1.21974i
$560$	−8.77329	−	1.67677i	−0.370739	−	0.0708566i
$561$	31.2574	−	1.20963i	1.31969	−	0.0510707i
$562$	4.57555	−	25.9492i	0.193008	−	1.09460i
$563$	−11.7079	+	4.26132i	−0.493428	+	0.179593i	−0.576736	−	0.816931i	$-0.695674\pi$
$563$	−11.7079	+	4.26132i	−0.493428	+	0.179593i	0.0833076	+	0.996524i	$0.473452\pi$
$564$	2.73882	−	20.0360i	0.115325	−	0.843667i
$565$	2.08959	+	11.8507i	0.0879099	+	0.498562i
$566$	−38.3198			−1.61070
$567$	−22.6406	+	7.37591i	−0.950815	+	0.309759i
$568$	−1.58566			−0.0665327
$569$	−5.48364	−	31.0993i	−0.229886	−	1.30375i	−0.853121	−	0.521714i	$-0.825293\pi$
$569$	−5.48364	−	31.0993i	−0.229886	−	1.30375i	0.623234	−	0.782035i	$-0.285818\pi$
$570$	−0.520822	+	3.81009i	−0.0218148	+	0.159587i
$571$	−11.7658	+	4.28241i	−0.492384	+	0.179213i	−0.576266	−	0.817263i	$-0.695491\pi$
$571$	−11.7658	+	4.28241i	−0.492384	+	0.179213i	0.0838813	+	0.996476i	$0.473268\pi$
$572$	−5.18884	+	29.4274i	−0.216956	+	1.23042i
$573$	−37.2625	+	1.44202i	−1.55666	+	0.0602414i
$574$	−8.61643	−	24.7709i	−0.359643	−	1.03392i
$575$	−11.6757	−	20.2229i	−0.486911	−	0.843354i
$576$	−18.8733	+	18.5030i	−0.786388	+	0.770959i
$577$	12.4119			0.516713			0.258357	−	0.966050i	$-0.416819\pi$
$577$	12.4119			0.516713			0.258357	+	0.966050i	$0.416819\pi$
$578$	5.63500	+	31.9577i	0.234385	+	1.32926i
$579$	−3.21972	−	14.8715i	−0.133807	−	0.618037i
$580$	−0.0649699	−	0.0545162i	−0.00269773	−	0.00226366i
$581$	−0.243378	+	17.0037i	−0.0100970	+	0.705434i
$582$	42.2632	+	13.5561i	1.75187	+	0.561917i
$583$	−18.4088	+	15.4468i	−0.762416	+	0.639743i
$584$	−2.05565			−0.0850633
$585$	−11.0198	+	5.00630i	−0.455612	+	0.206985i
$586$	−5.09761			−0.210580
$587$	−0.730292	−	4.14169i	−0.0301424	−	0.170946i	0.966020	−	0.258466i	$-0.0832170\pi$
$587$	−0.730292	−	4.14169i	−0.0301424	−	0.170946i	−0.996163	+	0.0875200i	$0.972106\pi$
$588$	−23.8836	+	8.96590i	−0.984943	+	0.369747i
$589$	0.277860	−	0.101133i	0.0114490	−	0.00416710i
$590$	−5.22145	−	4.38131i	−0.214964	−	0.180376i
$591$	−5.37054	+	2.19345i	−0.220914	+	0.0902263i
$592$	−36.5065	−	13.2873i	−1.50041	−	0.546103i
$593$	11.3399	−	19.6412i	0.465673	−	0.806569i	−0.533559	−	0.845763i	$-0.679146\pi$
$593$	11.3399	−	19.6412i	0.465673	−	0.806569i	0.999232	+	0.0391942i	$0.0124791\pi$
$594$	1.93417	−	33.0285i	0.0793599	−	1.35518i
$595$	8.57596	+	10.5227i	0.351580	+	0.431387i
$596$	14.7116	−	12.3445i	0.602611	−	0.505651i
$597$	2.68317	−	19.6288i	0.109815	−	0.803354i
$598$	47.7934	−	17.3954i	1.95442	−	0.711350i
$599$	−4.77957	−	4.01053i	−0.195288	−	0.163866i	0.539901	−	0.841729i	$-0.318462\pi$
$599$	−4.77957	−	4.01053i	−0.195288	−	0.163866i	−0.735188	+	0.677863i	$0.762906\pi$
$600$	1.53424	−	0.0593737i	0.0626352	−	0.00242392i
$601$	4.34521	+	24.6429i	0.177245	+	1.00520i	0.935521	+	0.353271i	$0.114931\pi$
$601$	4.34521	+	24.6429i	0.177245	+	1.00520i	−0.758276	+	0.651933i	$0.773958\pi$
$602$	24.9553	+	30.6201i	1.01710	+	1.24798i
$603$	−0.851900	+	1.78063i	−0.0346921	+	0.0725130i
$604$	−9.81503	−	17.0001i	−0.399368	−	0.691725i
$605$	−0.173924	−	0.986370i	−0.00707100	−	0.0401016i
$606$	−26.3961	+	23.9482i	−1.07227	+	0.972827i
$607$	11.3906	−	4.14582i	0.462328	−	0.168274i	−0.100346	−	0.994953i	$-0.531995\pi$
$607$	11.3906	−	4.14582i	0.462328	−	0.168274i	0.562674	+	0.826679i	$0.309773\pi$
$608$	−7.59844	−	6.37585i	−0.308158	−	0.258575i
$609$	0.204540	+	0.0309477i	0.00828836	+	0.00125407i
$610$	−1.38490	−	0.504063i	−0.0560731	−	0.0204089i
$611$	12.5360	+	21.7130i	0.507153	+	0.878415i
$612$	36.1632	−	2.80316i	1.46181	−	0.113311i
$613$	2.16690	−	3.75318i	0.0875202	−	0.151589i	−0.818942	−	0.573876i	$-0.805439\pi$
$613$	2.16690	−	3.75318i	0.0875202	−	0.151589i	0.906462	+	0.422287i	$0.138772\pi$
$614$	12.6904	+	4.61892i	0.512142	+	0.186404i
$615$	4.03434	+	6.40241i	0.162680	+	0.258170i
$616$	0.0251021	−	1.75377i	0.00101139	−	0.0706615i
$617$	4.00429	−	22.7095i	0.161207	−	0.914249i	−0.791683	−	0.610932i	$-0.790795\pi$
$617$	4.00429	−	22.7095i	0.161207	−	0.914249i	0.952890	−	0.303317i	$-0.0980941\pi$
$618$	7.11709	−	52.0654i	0.286292	−	2.09438i
$619$	−5.53714	−	2.01536i	−0.222557	−	0.0810040i	0.228335	−	0.973583i	$-0.426672\pi$
$619$	−5.53714	−	2.01536i	−0.222557	−	0.0810040i	−0.450892	+	0.892579i	$0.648894\pi$
$620$	0.226311	+	0.391983i	0.00908888	+	0.0157424i
$621$	−25.8043	+	12.9492i	−1.03549	+	0.519634i
$622$	−29.5946			−1.18664
$623$	21.8108	−	25.2502i	0.873831	−	1.01163i
$624$	4.00757	−	29.3176i	0.160431	−	1.17364i
$625$	10.4768	+	8.79104i	0.419070	+	0.351642i
$626$	34.0196	+	28.5458i	1.35970	+	1.14092i
$627$	6.67661	−	0.258378i	0.266638	−	0.0103186i
$628$	−25.8678	−	9.41511i	−1.03224	−	0.375704i
$629$	29.5211	+	51.1320i	1.17708	+	2.03877i
$630$	11.9572	−	7.94802i	0.476384	−	0.316657i
$631$	13.0197	−	22.5509i	0.518308	−	0.897735i	−0.481466	−	0.876465i	$-0.659895\pi$
$631$	13.0197	−	22.5509i	0.518308	−	0.897735i	0.999774	−	0.0212707i	$-0.00677118\pi$
$632$	−2.13812	+	1.79409i	−0.0850497	+	0.0713652i
$633$	6.62830	+	30.6152i	0.263451	+	1.21685i
$634$	−3.27371	+	18.5661i	−0.130016	+	0.737355i
$635$	9.33819	−	3.39882i	0.370575	−	0.134878i
$636$	−20.6374	+	18.7234i	−0.818324	+	0.742433i
$637$	16.5921	−	26.9278i	0.657401	−	1.06692i
$638$	−0.143715	+	0.248922i	−0.00568975	+	0.00985493i
$639$	−16.1045	+	15.7885i	−0.637085	+	0.624585i
$640$	0.752324	−	1.30306i	0.0297382	−	0.0515081i
$641$	−16.4390	+	13.7940i	−0.649301	+	0.544829i	−0.906859	−	0.421434i	$-0.861527\pi$
$641$	−16.4390	+	13.7940i	−0.649301	+	0.544829i	0.257557	+	0.966263i	$0.417082\pi$
$642$	−23.8251	+	45.2192i	−0.940300	+	1.78466i
$643$	−36.9983	+	13.4663i	−1.45907	+	0.531058i	−0.945109	−	0.326756i	$-0.894044\pi$
$643$	−36.9983	+	13.4663i	−1.45907	+	0.531058i	−0.513961	+	0.857814i	$0.671822\pi$
$644$	−27.0061	+	15.0808i	−1.06419	+	0.594267i
$645$	−9.00797	−	6.98322i	−0.354688	−	0.274964i
$646$	2.48105	+	14.0708i	0.0976158	+	0.553607i
$647$	−0.110173	−	0.190824i	−0.00433133	−	0.00750208i	0.863852	−	0.503746i	$-0.168045\pi$
$647$	−0.110173	−	0.190824i	−0.00433133	−	0.00750208i	−0.868183	+	0.496244i	$0.834712\pi$
$648$	0.0376110	−	1.89795i	0.00147750	−	0.0745586i
$649$	−5.92150	+	10.2563i	−0.232439	+	0.402597i
$650$	−29.4702	+	24.7285i	−1.15592	+	0.969930i
$651$	−0.969261	−	0.528543i	−0.0379883	−	0.0207152i
$652$	−1.95784	+	11.1035i	−0.0766749	+	0.434845i
$653$	4.32225	−	24.5127i	0.169143	−	0.959256i	−0.775547	−	0.631290i	$-0.782526\pi$
$653$	4.32225	−	24.5127i	0.169143	−	0.959256i	0.944690	−	0.327966i	$-0.106363\pi$
$654$	6.33778	+	10.0579i	0.247827	+	0.393296i
$655$	5.38226	−	4.51625i	0.210302	−	0.176465i
$656$	−18.5005			−0.722323
$657$	−20.8779	+	20.4683i	−0.814525	+	0.798544i
$658$	−18.7893	−	23.0544i	−0.732483	−	0.898754i
$659$	−0.718602	−	0.261550i	−0.0279928	−	0.0101885i	0.327986	−	0.944683i	$-0.393630\pi$
$659$	−0.718602	−	0.261550i	−0.0279928	−	0.0101885i	−0.355979	+	0.934494i	$0.615852\pi$
$660$	2.16419	+	9.99608i	0.0842408	+	0.389097i
$661$	−3.69556	+	20.9586i	−0.143741	+	0.815193i	0.824629	+	0.565674i	$0.191384\pi$
$661$	−3.69556	+	20.9586i	−0.143741	+	0.815193i	−0.968370	+	0.249520i	$0.919727\pi$
$662$	4.78276	−	27.1244i	0.185887	−	1.05422i
$663$	−33.3057	+	30.2170i	−1.29349	+	1.17353i
$664$	−1.27395	−	0.463681i	−0.0494390	−	0.0179943i
$665$	1.83183	+	2.24765i	0.0710353	+	0.0871601i
$666$	56.8556	−	25.8296i	2.20311	−	1.00088i
$667$	0.250822			0.00971187
$668$	−11.4247	+	9.58648i	−0.442036	+	0.370912i
$669$	21.3208	−	0.825094i	0.824310	−	0.0319000i
$670$	0.206679	−	1.17213i	0.00798470	−	0.0452835i
$671$	−0.444661	+	2.52180i	−0.0171659	+	0.0973529i
$672$	0.902337	+	37.0230i	0.0348084	+	1.42819i
$673$	−18.7235	+	15.7109i	−0.721737	+	0.605609i	−0.927865	−	0.372916i	$-0.878358\pi$
$673$	−18.7235	+	15.7109i	−0.721737	+	0.605609i	0.206128	+	0.978525i	$0.433914\pi$
$674$	24.8318	−	43.0099i	0.956485	−	1.65668i
$675$	14.9911	−	15.8796i	0.577009	−	0.611207i
$676$	−7.80247	−	13.5143i	−0.300095	−	0.519779i
$677$	4.91971	+	27.9011i	0.189080	+	1.07233i	0.920600	+	0.390506i	$0.127700\pi$
$677$	4.91971	+	27.9011i	0.189080	+	1.07233i	−0.731520	+	0.681820i	$0.761189\pi$
$678$	43.7780	−	17.8799i	1.68129	−	0.686674i
$679$	29.2190	−	16.3166i	1.12132	−	0.626173i
$680$	−1.01694	+	0.370137i	−0.0389980	+	0.0141941i
$681$	41.2168	−	1.59505i	1.57943	−	0.0611224i
$682$	1.17507	−	0.986005i	0.0449959	−	0.0377561i
$683$	1.72661	−	2.99057i	0.0660668	−	0.114431i	−0.831100	−	0.556123i	$-0.812288\pi$
$683$	1.72661	−	2.99057i	0.0660668	−	0.114431i	0.897167	+	0.441692i	$0.145622\pi$
$684$	7.72449	−	0.598757i	0.295353	−	0.0228940i
$685$	−0.779912	+	1.35085i	−0.0297989	+	0.0516132i
$686$	−14.3339	+	34.6735i	−0.547272	+	1.32384i
$687$	8.28530	+	38.2687i	0.316104	+	1.46004i
$688$	26.1841	−	9.53022i	0.998259	−	0.363336i
$689$	5.99917	−	34.0230i	0.228550	−	1.29617i
$690$	12.8929	−	11.6972i	0.490825	−	0.445306i
$691$	37.7308	−	31.6599i	1.43535	−	1.20440i	0.492884	−	0.870095i	$-0.335943\pi$
$691$	37.7308	−	31.6599i	1.43535	−	1.20440i	0.942465	−	0.334306i	$-0.108502\pi$
$692$	19.0746	−	33.0382i	0.725107	−	1.25592i
$693$	−17.2075	−	18.0619i	−0.653660	−	0.686115i
$694$	12.7076	+	22.0103i	0.482375	+	0.835499i
$695$	9.73687	+	3.54393i	0.369340	+	0.134429i
$696$	−0.00768749	+	0.0145906i	−0.000291394	+	0.000553056i
$697$	21.5385	+	18.0730i	0.815829	+	0.684562i
$698$	40.4938	+	33.9784i	1.53271	+	1.28610i
$699$	0.488627	−	0.199566i	0.0184816	−	0.00754828i
$700$	15.2939	−	17.7056i	0.578054	−	0.669209i
$701$	−26.2546			−0.991624			−0.495812	−	0.868430i	$-0.665130\pi$
$701$	−26.2546			−0.991624			−0.495812	+	0.868430i	$0.665130\pi$
$702$	28.3914	+	38.1614i	1.07156	+	1.44031i
$703$	6.30573	+	10.9218i	0.237825	+	0.411925i
$704$	−26.0201	−	9.47053i	−0.980668	−	0.356934i
$705$	6.78226	+	5.25779i	0.255435	+	0.198020i
$706$	−8.37976	+	47.5240i	−0.315377	+	1.78859i
$707$	−0.384608	+	26.8709i	−0.0144647	+	1.01058i
$708$	−6.40125	+	12.1494i	−0.240574	+	0.456601i
$709$	7.39480	+	2.69149i	0.277718	+	0.101081i	0.477124	−	0.878836i	$-0.341679\pi$
$709$	7.39480	+	2.69149i	0.277718	+	0.101081i	−0.199407	+	0.979917i	$0.563901\pi$
$710$	6.79934	−	11.7768i	0.255175	−	0.441976i
$711$	−3.85154	+	39.5109i	−0.144444	+	1.48177i
$712$	1.33000	+	2.30363i	0.0498439	+	0.0863321i
$713$	−1.25785	−	0.457821i	−0.0471069	−	0.0171455i
$714$	33.2838	−	41.6882i	1.24562	−	1.56014i
$715$	−9.71382	−	8.15086i	−0.363276	−	0.304825i
$716$	31.4933	−	11.4626i	1.17696	−	0.428378i
$717$	−39.8502	−	12.7821i	−1.48823	−	0.477355i
$718$	−6.57454	−	37.2861i	−0.245360	−	1.39150i
$719$	5.36852	+	9.29854i	0.200212	+	0.346777i	0.948597	−	0.316488i	$-0.102504\pi$
$719$	5.36852	+	9.29854i	0.200212	+	0.346777i	−0.748385	+	0.663265i	$0.769170\pi$
$720$	−2.52428	−	9.80842i	−0.0940745	−	0.365538i
$721$	−25.0322	−	30.7144i	−0.932248	−	1.14387i
$722$	−6.15400	−	34.9011i	−0.229028	−	1.29888i
$723$	11.5374	−	21.8976i	0.429080	−	0.814380i
$724$	38.0122	+	31.8960i	1.41271	+	1.18541i
$725$	−0.178279	+	0.0648881i	−0.00662110	+	0.00240988i
$726$	−3.64379	+	1.48820i	−0.135234	+	0.0552324i
$727$	−3.16208	+	2.65330i	−0.117275	+	0.0984056i	−0.699539	−	0.714594i	$-0.746611\pi$
$727$	−3.16208	+	2.65330i	−0.117275	+	0.0984056i	0.582264	+	0.813000i	$0.302167\pi$
$728$	1.59301	+	1.95461i	0.0590407	+	0.0724428i
$729$	−18.5161	−	19.6508i	−0.685782	−	0.727807i
$730$	8.81467	−	15.2675i	0.326246	−	0.565074i
$731$	−39.7938	−	14.4838i	−1.47183	−	0.535701i
$732$	−0.402144	+	2.94190i	−0.0148637	+	0.108736i
$733$	−15.0457	−	12.6249i	−0.555726	−	0.466310i	0.321148	−	0.947029i	$-0.395931\pi$
$733$	−15.0457	−	12.6249i	−0.555726	−	0.466310i	−0.876875	+	0.480719i	$0.840376\pi$
$734$	−46.9810	+	17.0997i	−1.73410	+	0.631161i
$735$	1.77260	−	10.6798i	0.0653834	−	0.393931i
$736$	7.79730	+	44.2207i	0.287412	+	1.63000i
$737$	−2.06800			−0.0761758
$738$	21.2354	−	20.8188i	0.781687	−	0.766351i
$739$	−25.9618			−0.955019			−0.477509	−	0.878627i	$-0.658460\pi$
$739$	−25.9618			−0.955019			−0.477509	+	0.878627i	$0.658460\pi$
$740$	−14.7882	+	12.4088i	−0.543625	+	0.456155i
$741$	−7.11413	+	6.45436i	−0.261344	+	0.237107i
$742$	−0.586519	+	40.9775i	−0.0215318	+	1.50433i
$743$	−11.7874	−	9.89080i	−0.432438	−	0.362858i	0.400433	−	0.916326i	$-0.368860\pi$
$743$	−11.7874	−	9.89080i	−0.432438	−	0.362858i	−0.832871	+	0.553468i	$0.813304\pi$
$744$	0.0651841	−	0.0591389i	0.00238977	−	0.00216814i
$745$	1.41518	+	8.02590i	0.0518483	+	0.294046i
$746$	60.8243			2.22694
$747$	−17.5557	+	7.97556i	−0.642328	+	0.291811i
$748$	19.0002	+	32.9092i	0.694715	+	1.20328i
$749$	12.6614	+	36.3996i	0.462639	+	1.33001i
$750$	−13.4402	+	25.5091i	−0.490767	+	0.931460i
$751$	−2.84804	+	16.1520i	−0.103927	+	0.589396i	0.887717	+	0.460389i	$0.152290\pi$
$751$	−2.84804	+	16.1520i	−0.103927	+	0.589396i	−0.991644	+	0.129007i	$0.958821\pi$
$752$	−19.7144	+	7.17547i	−0.718912	+	0.261662i
$753$	−5.37142	+	2.19381i	−0.195745	+	0.0799467i
$754$	−0.0717550	−	0.406943i	−0.00261316	−	0.0148200i
$755$	8.33024			0.303169
$756$	−20.7480	−	20.1564i	−0.754597	−	0.733083i
$757$	−15.8693			−0.576779			−0.288389	−	0.957513i	$-0.593120\pi$
$757$	−15.8693			−0.576779			−0.288389	+	0.957513i	$0.593120\pi$
$758$	10.4285	+	59.1430i	0.378781	+	2.14817i
$759$	−23.9052	−	18.5319i	−0.867702	−	0.672666i
$760$	−0.217220	+	0.0790615i	−0.00787939	+	0.00286786i
$761$	−4.30253	+	24.4009i	−0.155967	+	0.884531i	0.801930	+	0.597418i	$0.203807\pi$
$761$	−4.30253	+	24.4009i	−0.155967	+	0.884531i	−0.957897	+	0.287113i	$0.907304\pi$
$762$	−20.8191	−	33.0395i	−0.754197	−	1.19690i
$763$	8.80448	+	1.68274i	0.318744	+	0.0609191i
$764$	−22.6504	−	39.2317i	−0.819463	−	1.41935i
$765$	−6.64295	+	13.8850i	−0.240177	+	0.502015i
$766$	6.32531			0.228543
$767$	−2.95652	−	16.7673i	−0.106754	−	0.605431i
$768$	23.4305	+	7.51540i	0.845474	+	0.271189i
$769$	−18.0600	−	15.1541i	−0.651261	−	0.546473i	0.256193	−	0.966626i	$-0.417532\pi$
$769$	−18.0600	−	15.1541i	−0.651261	−	0.546473i	−0.907453	+	0.420153i	$0.861976\pi$
$770$	12.9178	+	7.70666i	0.465524	+	0.277729i
$771$	−6.62606	−	30.6049i	−0.238632	−	1.10221i
$772$	14.1600	−	11.8817i	0.509630	−	0.427630i
$773$	6.30291			0.226700			0.113350	−	0.993555i	$-0.463842\pi$
$773$	6.30291			0.226700			0.113350	+	0.993555i	$0.463842\pi$
$774$	−19.3304	+	40.4043i	−0.694818	+	1.45230i
$775$	1.01249			0.0363697
$776$	0.463292	+	2.62746i	0.0166312	+	0.0943203i
$777$	15.0216	−	44.6260i	0.538898	−	1.60095i
$778$	13.6353	−	4.96284i	0.488849	−	0.177927i
$779$	4.60064	+	3.86040i	0.164835	+	0.138313i
$780$	−11.6207	−	9.00870i	−0.416088	−	0.322563i
$781$	−22.2028	−	8.08116i	−0.794479	−	0.289167i
$782$	32.3399	−	56.0144i	1.15647	−	2.00307i
$783$	0.0672032	+	0.224733i	0.00240165	+	0.00803130i
$784$	19.7793	+	17.5856i	0.706404	+	0.628058i
$785$	8.94878	−	7.50892i	0.319396	−	0.268005i
$786$	−21.8214	−	16.9166i	−0.778344	−	0.603393i
$787$	6.97760	−	2.53964i	0.248725	−	0.0905284i	−0.214649	−	0.976691i	$-0.568861\pi$
$787$	6.97760	−	2.53964i	0.248725	−	0.0905284i	0.463374	+	0.886163i	$0.346639\pi$
$788$	−5.39859	−	4.52996i	−0.192317	−	0.161373i
$789$	−22.3193	−	35.4202i	−0.794587	−	1.26099i
$790$	−4.15657	−	23.5731i	−0.147884	−	0.838693i
$791$	12.6734	−	33.3279i	0.450615	−	1.18500i
$792$	1.81070	−	0.822603i	0.0643404	−	0.0292299i
$793$	−1.84068	−	3.18814i	−0.0653643	−	0.113214i
$794$	6.50574	+	36.8959i	0.230880	+	1.30939i
$795$	−2.50216	−	11.5571i	−0.0887425	−	0.409890i
$796$	22.6157	−	8.23143i	0.801591	−	0.291755i
$797$	2.15575	+	1.80889i	0.0763606	+	0.0640741i	0.680169	−	0.733055i	$-0.261906\pi$
$797$	2.15575	+	1.80889i	0.0763606	+	0.0640741i	−0.603808	+	0.797129i	$0.706351\pi$
$798$	7.10945	−	8.90463i	0.251672	−	0.315221i
$799$	29.9615	+	10.9051i	1.05996	+	0.385794i
$800$	−16.9821	−	29.4139i	−0.600408	−	1.03994i
$801$	36.4454	+	10.1536i	1.28774	+	0.358758i
$802$	18.5853	−	32.1908i	0.656271	−	1.13670i
$803$	−28.7837	−	10.4764i	−1.01576	−	0.369705i
$804$	−2.39616	+	0.0927290i	−0.0845060	+	0.00327030i
$805$	0.187858	−	13.1248i	0.00662112	−	0.462589i
$806$	−0.382940	+	2.17176i	−0.0134885	+	0.0764969i
$807$	−23.8997	+	9.76118i	−0.841311	+	0.343610i
$808$	−2.01322	−	0.732753i	−0.0708249	−	0.0257781i
$809$	−13.4130	−	23.2321i	−0.471577	−	0.816796i	0.527894	−	0.849310i	$-0.322982\pi$
$809$	−13.4130	−	23.2321i	−0.471577	−	0.816796i	−0.999471	+	0.0325145i	$0.989649\pi$
$810$	13.9350	+	8.41781i	0.489625	+	0.295772i
$811$	10.4409			0.366628			0.183314	−	0.983054i	$-0.441317\pi$
$811$	10.4409			0.366628			0.183314	+	0.983054i	$0.441317\pi$
$812$	0.0825629	+	0.237356i	0.00289739	+	0.00832955i
$813$	−7.36774	−	5.71167i	−0.258398	−	0.200317i
$814$	50.1176	+	42.0537i	1.75662	+	1.47398i
$815$	−3.66519	−	3.07546i	−0.128386	−	0.107729i
$816$	−20.0612	−	31.8367i	−0.702282	−	1.11451i
$817$	−8.49999	−	3.09374i	−0.297377	−	0.108236i
$818$	0.108766	+	0.188387i	0.00380290	+	0.00658681i
$819$	35.6414	+	3.99005i	1.24541	+	0.139424i
$820$	−4.59653	+	7.96143i	−0.160518	+	0.278025i
$821$	−25.1065	+	21.0669i	−0.876223	+	0.735239i	−0.965399	−	0.260777i	$-0.916021\pi$
$821$	−25.1065	+	21.0669i	−0.876223	+	0.735239i	0.0891758	+	0.996016i	$0.471577\pi$
$822$	5.83681	+	1.87218i	0.203582	+	0.0652997i
$823$	−0.718184	+	4.07302i	−0.0250343	+	0.141977i	−0.994763	−	0.102208i	$-0.967409\pi$
$823$	−0.718184	+	4.07302i	−0.0250343	+	0.141977i	0.969729	+	0.244185i	$0.0785203\pi$
$824$	2.96834	−	1.08039i	0.103407	−	0.0376370i
$825$	21.7855	+	6.98776i	0.758473	+	0.243283i
$826$	6.63535	+	19.0756i	0.230873	+	0.663725i
$827$	−1.68730	+	2.92249i	−0.0586731	+	0.101625i	−0.893870	−	0.448326i	$-0.852020\pi$
$827$	−1.68730	+	2.92249i	−0.0586731	+	0.101625i	0.835197	+	0.549951i	$0.185354\pi$
$828$	−28.5295	−	20.4007i	−0.991467	−	0.708974i
$829$	−2.13210	+	3.69291i	−0.0740510	+	0.128260i	−0.900673	−	0.434497i	$-0.856926\pi$
$829$	−2.13210	+	3.69291i	−0.0740510	+	0.128260i	0.826622	+	0.562757i	$0.190259\pi$
$830$	8.90655	−	7.47348i	0.309151	−	0.259408i
$831$	−0.934475	−	1.48299i	−0.0324166	−	0.0514444i
$832$	37.4074	−	13.6152i	1.29687	−	0.472021i
$833$	−5.84808	−	39.7956i	−0.202624	−	1.37884i
$834$	5.51482	−	40.3439i	0.190963	−	1.39700i
$835$	−1.09900	−	6.23274i	−0.0380325	−	0.215693i
$836$	4.05845	+	7.02944i	0.140364	+	0.243118i
$837$	0.0731821	−	1.24968i	0.00252954	−	0.0431953i
$838$	−1.48964	+	2.58014i	−0.0514589	+	0.0891294i
$839$	32.5305	−	27.2963i	1.12308	−	0.942374i	0.124322	−	0.992242i	$-0.460324\pi$
$839$	32.5305	−	27.2963i	1.12308	−	0.942374i	0.998756	+	0.0498679i	$0.0158800\pi$
$840$	0.757729	+	0.413193i	0.0261441	+	0.0142565i
$841$	−5.03544	+	28.5574i	−0.173636	+	0.984739i
$842$	−11.1251	+	63.0937i	−0.383397	+	2.17435i
$843$	10.5012	−	19.9309i	0.361679	−	0.686455i
$844$	−29.1506	+	24.4603i	−1.00341	+	0.841958i
$845$	6.62213			0.227808
$846$	14.5542	−	30.4211i	0.500384	−	1.04590i
$847$	−1.05485	+	2.77399i	−0.0362450	+	0.0953154i
$848$	27.1654	+	9.88738i	0.932862	+	0.339534i
$849$	−31.1968	−	10.0065i	−1.07067	−	0.343421i
$850$	−8.49546	+	48.1802i	−0.291392	+	1.65257i
$851$	9.91377	−	56.2238i	0.339839	−	1.92733i
$852$	−26.0884	−	8.36793i	−0.893773	−	0.286681i
$853$	12.8564	+	4.67934i	0.440194	+	0.160218i	0.552603	−	0.833444i	$-0.313635\pi$
$853$	12.8564	+	4.67934i	0.440194	+	0.160218i	−0.112409	+	0.993662i	$0.535857\pi$
$854$	2.75885	+	3.38510i	0.0944058	+	0.115836i
$855$	−1.41894	+	2.96586i	−0.0485267	+	0.101430i
$856$	−3.07240			−0.105013
$857$	−15.9711	+	13.4014i	−0.545563	+	0.457782i	−0.873435	−	0.486940i	$-0.838113\pi$
$857$	−15.9711	+	13.4014i	−0.545563	+	0.457782i	0.327872	+	0.944722i	$0.393668\pi$
$858$	−23.2281	+	44.0862i	−0.792995	+	1.50508i
$859$	−7.24341	+	41.0794i	−0.247142	+	1.40161i	0.568323	+	0.822805i	$0.307592\pi$
$859$	−7.24341	+	41.0794i	−0.247142	+	1.40161i	−0.815465	+	0.578806i	$0.803519\pi$
$860$	2.40436	−	13.6358i	0.0819879	−	0.464976i
$861$	−0.546340	−	22.4164i	−0.0186192	−	0.763949i
$862$	41.6581	−	34.9553i	1.41888	−	1.19058i
$863$	−19.8828	+	34.4380i	−0.676818	+	1.17228i	0.299116	+	0.954217i	$0.403308\pi$
$863$	−19.8828	+	34.4380i	−0.676818	+	1.17228i	−0.975934	+	0.218066i	$0.930025\pi$
$864$	−37.5319	+	18.8344i	−1.27686	+	0.640759i
$865$	8.09452	+	14.0201i	0.275222	+	0.476699i
$866$	1.68050	+	9.53057i	0.0571056	+	0.323862i
$867$	−3.75757	+	27.4887i	−0.127614	+	0.933566i
$868$	0.0191943	−	1.34102i	0.000651496	−	0.0455172i
$869$	−39.0819	+	14.2247i	−1.32576	+	0.482539i
$870$	−0.0754015	−	0.119661i	−0.00255635	−	0.00405688i
$871$	2.27747	−	1.91103i	0.0771693	−	0.0647527i
$872$	−0.357309	+	0.618877i	−0.0121000	+	0.0209578i
$873$	30.8673	+	22.0724i	1.04470	+	0.747038i
$874$	6.90784	−	11.9647i	0.233661	−	0.404713i
$875$	7.14257	+	20.5338i	0.241463	+	0.694169i
$876$	−33.8210	−	10.8482i	−1.14270	−	0.366526i
$877$	−10.8684	+	3.95578i	−0.367001	+	0.133577i	−0.518936	−	0.854813i	$-0.673672\pi$
$877$	−10.8684	+	3.95578i	−0.367001	+	0.133577i	0.151935	+	0.988390i	$0.451449\pi$
$878$	7.08362	−	40.1732i	0.239061	−	1.35578i
$879$	−4.15004	−	1.33114i	−0.139977	−	0.0448982i
$880$	8.12828	−	6.82044i	0.274004	−	0.229917i
$881$	27.8765	−	48.2835i	0.939183	−	1.62671i	0.172183	−	0.985065i	$-0.444918\pi$
$881$	27.8765	−	48.2835i	0.939183	−	1.62671i	0.767000	−	0.641648i	$-0.221749\pi$
$882$	−42.4926	+	2.07252i	−1.43080	+	0.0697853i
$883$	2.15109	+	3.72580i	0.0723900	+	0.125383i	0.899948	−	0.435997i	$-0.143604\pi$
$883$	2.15109	+	3.72580i	0.0723900	+	0.125383i	−0.827558	+	0.561380i	$0.810271\pi$
$884$	−51.3360	−	18.6848i	−1.72662	−	0.628436i
$885$	−3.10677	−	4.93037i	−0.104433	−	0.165733i
$886$	41.7461	+	35.0291i	1.40249	+	1.17683i
$887$	25.8665	+	21.7046i	0.868513	+	0.728769i	0.963785	−	0.266682i	$-0.0859274\pi$
$887$	25.8665	+	21.7046i	0.868513	+	0.728769i	−0.0952713	+	0.995451i	$0.530372\pi$
$888$	2.96676	+	2.29991i	0.0995578	+	0.0771799i
$889$	−28.9221	−	5.52766i	−0.970015	−	0.185392i
$890$	−22.8123			−0.764671
$891$	10.1994	−	26.3840i	0.341692	−	0.883896i
$892$	12.9601	+	22.4475i	0.433936	+	0.751599i
$893$	6.39979	+	2.32933i	0.214161	+	0.0779482i
$894$	29.6488	−	12.1092i	0.991604	−	0.404993i
$895$	−2.46967	+	14.0062i	−0.0825519	+	0.468175i
$896$	−3.89259	+	2.17371i	−0.130042	+	0.0726185i
$897$	43.4518	−	1.68154i	1.45081	−	0.0561451i
$898$	26.7469	+	9.73506i	0.892554	+	0.324863i
$899$	−0.00543768	+	0.00941834i	−0.000181357	+	0.000314119i
$900$	25.5558	+	7.11974i	0.851860	+	0.237325i
$901$	−21.9674	−	38.0486i	−0.731839	−	1.26758i
$902$	29.2767	+	10.6558i	0.974806	+	0.354800i
$903$	12.3207	+	31.4449i	0.410006	+	1.04642i
$904$	2.17755	+	1.82718i	0.0724242	+	0.0607711i
$905$	−19.7875	+	7.20206i	−0.657759	+	0.239405i
$906$	−6.92691	−	31.9945i	−0.230131	−	1.06295i
$907$	−6.05264	−	34.3262i	−0.200975	−	1.13978i	−0.903650	−	0.428272i	$-0.859122\pi$
$907$	−6.05264	−	34.3262i	−0.200975	−	1.13978i	0.702675	−	0.711511i	$-0.251989\pi$
$908$	25.0541	+	43.3949i	0.831449	+	1.44011i
$909$	−27.7431	+	12.6037i	−0.920181	+	0.418040i
$910$	−21.3479	+	3.44995i	−0.707677	+	0.114365i
$911$	4.81005	+	27.2792i	0.159364	+	0.903799i	0.954687	+	0.297612i	$0.0961903\pi$
$911$	4.81005	+	27.2792i	0.159364	+	0.903799i	−0.795323	+	0.606186i	$0.792699\pi$
$912$	−4.28509	−	6.80034i	−0.141893	−	0.225182i
$913$	−15.4751	−	12.9852i	−0.512152	−	0.429747i
$914$	−69.9199	+	25.4488i	−2.31274	+	0.841770i
$915$	−0.995845	−	0.772006i	−0.0329216	−	0.0255217i
$916$	−36.4380	+	30.5751i	−1.20394	+	1.01023i
$917$	−20.5521	+	3.32134i	−0.678689	+	0.109680i
$918$	58.8530	+	13.9681i	1.94244	+	0.461015i
$919$	3.35232	−	5.80639i	0.110583	−	0.191535i	−0.805423	−	0.592701i	$-0.798062\pi$
$919$	3.35232	−	5.80639i	0.110583	−	0.191535i	0.916005	+	0.401166i	$0.131395\pi$
$920$	0.983337	+	0.357905i	0.0324197	+	0.0117998i
$921$	9.12530	+	7.07418i	0.300689	+	0.233102i
$922$	−65.6807	−	55.1127i	−2.16308	−	1.81504i
$923$	31.9195	−	11.6178i	1.05064	−	0.382403i
$924$	9.66812	−	28.7219i	0.318058	−	0.944880i
$925$	7.49870	+	42.5273i	0.246556	+	1.39829i
$926$	−38.4340			−1.26302
$927$	19.3900	−	40.5288i	0.636851	−	1.33114i
$928$	0.364816			0.0119757
$929$	−21.2390	+	17.8217i	−0.696830	+	0.584710i	−0.920870	−	0.389870i	$-0.872520\pi$
$929$	−21.2390	+	17.8217i	−0.696830	+	0.584710i	0.224040	+	0.974580i	$0.428075\pi$
$930$	0.159718	+	0.737717i	0.00523737	+	0.0241907i
$931$	−1.24915	−	8.50038i	−0.0409394	−	0.278589i
$932$	0.491180	+	0.412149i	0.0160891	+	0.0135004i
$933$	−24.0934	−	7.72805i	−0.788783	−	0.253005i
$934$	5.24717	+	29.7582i	0.171693	+	0.973718i
$935$	−16.1259			−0.527373
$936$	−1.23395	+	2.57918i	−0.0403328	+	0.0843032i
$937$	5.30815	+	9.19398i	0.173410	+	0.300354i	0.939610	−	0.342248i	$-0.111188\pi$
$937$	5.30815	+	9.19398i	0.173410	+	0.300354i	−0.766200	+	0.642602i	$0.777855\pi$
$938$	−2.30535	+	2.66889i	−0.0752725	+	0.0871424i
$939$	20.2417	+	32.1232i	0.660563	+	1.04830i
$940$	−1.81028	+	10.2666i	−0.0590449	+	0.334860i
$941$	23.9722	−	8.72516i	0.781471	−	0.284432i	0.0796851	−	0.996820i	$-0.474609\pi$
$941$	23.9722	−	8.72516i	0.781471	−	0.284432i	0.701786	+	0.712388i	$0.252386\pi$
$942$	−36.2812	−	28.1262i	−1.18211	−	0.916400i
$943$	−4.72104	−	26.7744i	−0.153738	−	0.871893i
$944$	14.2469			0.463696
$945$	11.8100	−	3.34824i	0.384178	−	0.108918i
$946$	−46.9249			−1.52566
$947$	−6.50665	−	36.9010i	−0.211438	−	1.19912i	−0.886982	−	0.461803i	$-0.847203\pi$
$947$	−6.50665	−	36.9010i	−0.211438	−	1.19912i	0.675545	−	0.737319i	$-0.263908\pi$
$948$	−44.6457	+	18.2343i	−1.45003	+	0.592223i
$949$	41.3805	−	15.0613i	1.34327	−	0.488909i
$950$	−1.81464	+	10.2913i	−0.0588746	+	0.333895i
$951$	−7.51335	+	14.2601i	−0.243637	+	0.462416i
$952$	3.14966	+	0.601970i	0.102081	+	0.0195100i
$953$	−12.1658	−	21.0717i	−0.394088	−	0.682581i	0.598896	−	0.800827i	$-0.295606\pi$
$953$	−12.1658	−	21.0717i	−0.394088	−	0.682581i	−0.992984	+	0.118246i	$0.962273\pi$
$954$	−42.3076	+	19.2204i	−1.36976	+	0.622284i
$955$	19.2239			0.622072
$956$	−8.82824	−	50.0675i	−0.285526	−	1.61930i
$957$	−0.182002	+	0.165123i	−0.00588330	+	0.00533768i
$958$	20.6374	+	17.3168i	0.666765	+	0.559482i
$959$	4.03533	−	2.25342i	0.130308	−	0.0727667i
$960$	10.0912	−	9.15529i	0.325690	−	0.295486i
$961$	−23.7029	+	19.8891i	−0.764610	+	0.641584i
$962$	−94.0556			−3.03248
$963$	−31.2045	+	30.5922i	−1.00555	+	0.985821i
$964$	30.0679			0.968422
$965$	1.36212	+	7.72498i	0.0438483	+	0.248676i
$966$	−50.5655	+	10.1923i	−1.62692	+	0.327931i
$967$	25.7639	−	9.37729i	0.828511	−	0.301553i	0.107263	−	0.994231i	$-0.465791\pi$
$967$	25.7639	−	9.37729i	0.828511	−	0.301553i	0.721247	+	0.692678i	$0.243569\pi$
$968$	−0.181244	−	0.152082i	−0.00582542	−	0.00488810i
$969$	−1.65444	+	12.1031i	−0.0531481	+	0.388808i
$970$	−21.5010	−	7.82572i	−0.690355	−	0.251269i
$971$	−19.2320	+	33.3107i	−0.617183	+	1.06899i	0.372814	+	0.927906i	$0.378393\pi$
$971$	−19.2320	+	33.3107i	−0.617183	+	1.06899i	−0.989997	+	0.141086i	$0.954941\pi$
$972$	10.6348	−	31.0280i	0.341111	−	0.995223i
$973$	−19.3967	−	23.7997i	−0.621829	−	0.762983i
$974$	−20.4853	+	17.1892i	−0.656391	+	0.550777i
$975$	−30.4495	+	12.4363i	−0.975165	+	0.398279i
$976$	2.89469	−	1.05358i	0.0926567	−	0.0337243i
$977$	2.29374	+	1.92468i	0.0733834	+	0.0615759i	0.678742	−	0.734377i	$-0.262526\pi$
$977$	2.29374	+	1.92468i	0.0733834	+	0.0615759i	−0.605358	+	0.795953i	$0.706970\pi$
$978$	−8.76437	+	16.6345i	−0.280254	+	0.531912i
$979$	6.88280	+	39.0343i	0.219975	+	1.24754i
$980$	12.4820	−	4.14252i	0.398723	−	0.132328i
$981$	2.53326	+	9.84329i	0.0808807	+	0.314272i
$982$	16.5034	+	28.5848i	0.526646	+	0.912178i
$983$	1.90484	+	10.8029i	0.0607551	+	0.344559i	0.999999	+	0.00130907i	$0.000416690\pi$
$983$	1.90484	+	10.8029i	0.0607551	+	0.344559i	−0.939244	+	0.343250i	$0.888472\pi$
$984$	1.70219	+	0.545984i	0.0542640	+	0.0174053i
$985$	2.81027	−	1.02286i	0.0895428	−	0.0325909i
$986$	−0.402553	−	0.337782i	−0.0128199	−	0.0107572i
$987$	−9.27645	−	23.6754i	−0.295273	−	0.753596i
$988$	−10.9654	−	3.99108i	−0.348856	−	0.126973i
$989$	20.4741	+	35.4623i	0.651040	+	1.12763i
$990$	−1.65479	+	16.9756i	−0.0525925	+	0.539519i
$991$	−22.3557	+	38.7211i	−0.710151	+	1.23002i	0.254650	+	0.967033i	$0.418040\pi$
$991$	−22.3557	+	38.7211i	−0.710151	+	1.23002i	−0.964800	+	0.262984i	$0.915293\pi$
$992$	−1.82952	−	0.665892i	−0.0580874	−	0.0211421i
$993$	10.9767	−	20.8334i	0.348335	−	0.661130i
$994$	−35.1804	+	19.6455i	−1.11585	+	0.623118i
$995$	−1.77349	+	10.0580i	−0.0562235	+	0.318860i
$996$	−18.5130	−	14.3518i	−0.586608	−	0.454754i
$997$	1.61995	+	0.589615i	0.0513044	+	0.0186733i	0.367545	−	0.930006i	$-0.380198\pi$
$997$	1.61995	+	0.589615i	0.0513044	+	0.0186733i	−0.316240	+	0.948679i	$0.602421\pi$
$998$	−0.223946	−	0.387885i	−0.00708888	−	0.0122783i
$999$	53.0319	−	6.18154i	1.67785	−	0.195575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.184.19	yes	132
3.2	odd	2		567.2.w.a.37.4		132
7.4	even	3		189.2.u.a.130.4	yes	132
21.11	odd	6		567.2.u.a.361.19		132
27.11	odd	18		567.2.u.a.289.19		132
27.16	even	9		189.2.u.a.16.4	✓	132
189.11	odd	18		567.2.w.a.46.4		132
189.151	even	9	inner	189.2.w.a.151.19	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.4	✓	132	27.16	even	9
189.2.u.a.130.4	yes	132	7.4	even	3
189.2.w.a.151.19	yes	132	189.151	even	9	inner
189.2.w.a.184.19	yes	132	1.1	even	1	trivial
567.2.u.a.289.19		132	27.11	odd	18
567.2.u.a.361.19		132	21.11	odd	6
567.2.w.a.37.4		132	3.2	odd	2
567.2.w.a.46.4		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)

\(f(q)\)	\(=\)	\(q+(0.351787 + 1.99508i) q^{2} +(-0.234582 + 1.71609i) q^{3} +(-1.97722 + 0.719650i) q^{4} +(0.155052 - 0.879341i) q^{5} +(-3.50627 + 0.135689i) q^{6} +(-1.72949 + 2.00222i) q^{7} +(-0.105462 - 0.182666i) q^{8} +(-2.88994 - 0.805127i) q^{9} +O(q^{10})\)	\(q+(0.351787 + 1.99508i) q^{2} +(-0.234582 + 1.71609i) q^{3} +(-1.97722 + 0.719650i) q^{4} +(0.155052 - 0.879341i) q^{5} +(-3.50627 + 0.135689i) q^{6} +(-1.72949 + 2.00222i) q^{7} +(-0.105462 - 0.182666i) q^{8} +(-2.88994 - 0.805127i) q^{9} +1.80890 q^{10} +(-0.545772 - 3.09523i) q^{11} +(-0.771166 - 3.56191i) q^{12} +(3.46133 + 2.90440i) q^{13} +(-4.60300 - 2.74612i) q^{14} +(1.47266 + 0.472360i) q^{15} +(-2.89636 + 2.43033i) q^{16} +5.74615 q^{17} +(0.589651 - 6.04891i) q^{18} +1.22738 q^{19} +(0.326246 + 1.85024i) q^{20} +(-3.03028 - 3.43764i) q^{21} +(5.98324 - 2.17772i) q^{22} +(-4.25634 - 3.57150i) q^{23} +(0.338212 - 0.138133i) q^{24} +(3.94926 + 1.43741i) q^{25} +(-4.57688 + 7.92738i) q^{26} +(2.05960 - 4.77054i) q^{27} +(1.97869 - 5.20345i) q^{28} +(-0.0345809 + 0.0290169i) q^{29} +(-0.424336 + 3.10425i) q^{30} +(0.226384 - 0.0823972i) q^{31} +(-6.19078 - 5.19468i) q^{32} +(5.43972 - 0.210512i) q^{33} +(2.02142 + 11.4640i) q^{34} +(1.49247 + 1.83126i) q^{35} +(6.29347 - 0.487833i) q^{36} +(5.13755 + 8.89849i) q^{37} +(0.431777 + 2.44873i) q^{38} +(-5.79619 + 5.25865i) q^{39} +(-0.176978 + 0.0644148i) q^{40} +(3.74834 + 3.14523i) q^{41} +(5.79238 - 7.25499i) q^{42} +(-6.92531 - 2.52060i) q^{43} +(3.30659 + 5.72718i) q^{44} +(-1.15607 + 2.41641i) q^{45} +(5.62811 - 9.74817i) q^{46} +(5.21418 + 1.89781i) q^{47} +(-3.49124 - 5.54053i) q^{48} +(-1.01774 - 6.92562i) q^{49} +(-1.47846 + 8.38478i) q^{50} +(-1.34794 + 9.86092i) q^{51} +(-8.93398 - 3.25170i) q^{52} +(-3.82297 - 6.62158i) q^{53} +(10.2422 + 2.43086i) q^{54} -2.80638 q^{55} +(0.548134 + 0.104761i) q^{56} +(-0.287921 + 2.10630i) q^{57} +(-0.0700562 - 0.0587841i) q^{58} +(-2.88652 - 2.42208i) q^{59} +(-3.25171 + 0.125838i) q^{60} +(-0.765603 - 0.278657i) q^{61} +(0.244029 + 0.422670i) q^{62} +(6.61016 - 4.39383i) q^{63} +(4.40506 - 7.62979i) q^{64} +(3.09065 - 2.59336i) q^{65} +(2.33361 + 10.7786i) q^{66} +(0.114256 - 0.647980i) q^{67} +(-11.3614 + 4.13522i) q^{68} +(7.12748 - 6.46647i) q^{69} +(-3.12848 + 3.62182i) q^{70} +(3.75882 - 6.51047i) q^{71} +(0.157711 + 0.612806i) q^{72} +(4.87293 - 8.44017i) q^{73} +(-15.9459 + 13.3802i) q^{74} +(-3.39316 + 6.44011i) q^{75} +(-2.42681 + 0.883285i) q^{76} +(7.14122 + 4.26040i) q^{77} +(-12.5305 - 9.71396i) q^{78} +(-2.29784 - 13.0317i) q^{79} +(1.68801 + 2.92371i) q^{80} +(7.70354 + 4.65354i) q^{81} +(-4.95638 + 8.58471i) q^{82} +(4.92372 - 4.13150i) q^{83} +(8.46544 + 4.61625i) q^{84} +(0.890949 - 5.05282i) q^{85} +(2.59259 - 14.7033i) q^{86} +(-0.0416835 - 0.0661509i) q^{87} +(-0.507835 + 0.426124i) q^{88} -12.6111 q^{89} +(-5.22763 - 1.45640i) q^{90} +(-11.8016 + 1.90720i) q^{91} +(10.9860 + 3.99856i) q^{92} +(0.0882956 + 0.407825i) q^{93} +(-1.95200 + 11.0704i) q^{94} +(0.190307 - 1.07929i) q^{95} +(10.3668 - 9.40537i) q^{96} +(-11.8862 - 4.32622i) q^{97} +(13.4592 - 4.46682i) q^{98} +(-0.914800 + 9.38444i) 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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