LMFDB - Embedded newform 189.2.u.a.4.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (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			4.11
Character	$\chi$	$=$	189.4
Dual form			189.2.u.a.142.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0305699 - 0.173370i) q^{2} +(-0.226706 + 1.71715i) q^{3} +(1.85026 - 0.673440i) q^{4} +(2.52551 - 0.919210i) q^{5} +(0.304634 - 0.0131890i) q^{6} +(-1.78991 - 1.94839i) q^{7} +(-0.349362 - 0.605113i) q^{8} +(-2.89721 - 0.778577i) q^{9} +O(q^{10})$	\(q+(-0.0305699 - 0.173370i) q^{2} +(-0.226706 + 1.71715i) q^{3} +(1.85026 - 0.673440i) q^{4} +(2.52551 - 0.919210i) q^{5} +(0.304634 - 0.0131890i) q^{6} +(-1.78991 - 1.94839i) q^{7} +(-0.349362 - 0.605113i) q^{8} +(-2.89721 - 0.778577i) q^{9} +(-0.236568 - 0.409748i) q^{10} +(5.66019 + 2.06014i) q^{11} +(0.736933 + 3.32985i) q^{12} +(-5.70404 + 2.07610i) q^{13} +(-0.283077 + 0.369879i) q^{14} +(1.00587 + 4.54507i) q^{15} +(2.92247 - 2.45224i) q^{16} +(-0.621796 - 1.07698i) q^{17} +(-0.0464149 + 0.526091i) q^{18} +(-1.47151 + 2.54874i) q^{19} +(4.05382 - 3.40156i) q^{20} +(3.75147 - 2.63182i) q^{21} +(0.184136 - 1.04429i) q^{22} +(-0.622595 + 3.53091i) q^{23} +(1.11827 - 0.462724i) q^{24} +(1.70302 - 1.42901i) q^{25} +(0.534306 + 0.925446i) q^{26} +(1.99375 - 4.79843i) q^{27} +(-4.62392 - 2.39965i) q^{28} +(-1.80256 - 0.656078i) q^{29} +(0.757231 - 0.313331i) q^{30} +(0.351738 - 0.128022i) q^{31} +(-1.58499 - 1.32997i) q^{32} +(-4.82077 + 9.25234i) q^{33} +(-0.167709 + 0.140724i) q^{34} +(-6.31140 - 3.27539i) q^{35} +(-5.88492 + 0.510526i) q^{36} -4.85189 q^{37} +(0.486860 + 0.177203i) q^{38} +(-2.27184 - 10.2654i) q^{39} +(-1.43854 - 1.20708i) q^{40} +(-8.12199 + 2.95616i) q^{41} +(-0.570962 - 0.569939i) q^{42} +(-1.51365 - 8.58435i) q^{43} +11.8602 q^{44} +(-8.03260 + 0.696841i) q^{45} +0.631189 q^{46} +(1.43798 + 0.523383i) q^{47} +(3.54832 + 5.57425i) q^{48} +(-0.592478 + 6.97488i) q^{49} +(-0.299809 - 0.251569i) q^{50} +(1.99031 - 0.823559i) q^{51} +(-9.15584 + 7.68266i) q^{52} +(4.07550 - 7.05897i) q^{53} +(-0.892855 - 0.198969i) q^{54} +16.1885 q^{55} +(-0.553673 + 1.76379i) q^{56} +(-4.04297 - 3.10463i) q^{57} +(-0.0586405 + 0.332567i) q^{58} +(3.18453 + 2.67214i) q^{59} +(4.92196 + 7.73217i) q^{60} +(-3.48243 - 1.26750i) q^{61} +(-0.0329478 - 0.0570673i) q^{62} +(3.66876 + 7.03848i) q^{63} +(3.63289 - 6.29234i) q^{64} +(-12.4972 + 10.4864i) q^{65} +(1.75145 + 0.552936i) q^{66} +(0.699154 - 3.96510i) q^{67} +(-1.87577 - 1.57396i) q^{68} +(-5.92196 - 1.86957i) q^{69} +(-0.374916 + 1.19434i) q^{70} +(-0.161544 + 0.279802i) q^{71} +(0.541048 + 2.02514i) q^{72} +4.85752 q^{73} +(0.148322 + 0.841174i) q^{74} +(2.06773 + 3.24831i) q^{75} +(-1.00627 + 5.70681i) q^{76} +(-6.11724 - 14.7157i) q^{77} +(-1.71026 + 0.707680i) q^{78} +(-0.357349 - 2.02663i) q^{79} +(5.12659 - 8.87951i) q^{80} +(7.78764 + 4.51140i) q^{81} +(0.760800 + 1.31774i) q^{82} +(9.46250 + 3.44407i) q^{83} +(5.16882 - 7.39595i) q^{84} +(-2.56032 - 2.14837i) q^{85} +(-1.44200 + 0.524845i) q^{86} +(1.53524 - 2.94653i) q^{87} +(-0.730838 - 4.14479i) q^{88} +(2.13585 - 3.69941i) q^{89} +(0.366367 + 1.37131i) q^{90} +(14.2547 + 7.39769i) q^{91} +(1.22590 + 6.95240i) q^{92} +(0.140092 + 0.633010i) q^{93} +(0.0467801 - 0.265303i) q^{94} +(-1.37350 + 7.78949i) q^{95} +(2.64308 - 2.42016i) q^{96} +(-0.938221 - 5.32092i) q^{97} +(1.22735 - 0.110503i) q^{98} +(-14.7948 - 10.3755i) 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} - 15 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 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.0305699	−	0.173370i	−0.0216162	−	0.122591i	0.972090	−	0.234607i	$-0.0753804\pi$
$2$	−0.0305699	−	0.173370i	−0.0216162	−	0.122591i	−0.993706	+	0.112016i	$0.964269\pi$
$3$	−0.226706	+	1.71715i	−0.130889	+	0.991397i
$3$	−0.226706	+	1.71715i	−0.130889	+	0.991397i
$4$	1.85026	−	0.673440i	0.925131	−	0.336720i
$5$	2.52551	−	0.919210i	1.12944	−	0.411083i	0.291352	−	0.956616i	$-0.405895\pi$
$5$	2.52551	−	0.919210i	1.12944	−	0.411083i	0.838089	+	0.545533i	$0.183673\pi$
$6$	0.304634	−	0.0131890i	0.124366	−	0.00538437i
$7$	−1.78991	−	1.94839i	−0.676521	−	0.736424i
$7$	−1.78991	−	1.94839i	−0.676521	−	0.736424i
$8$	−0.349362	−	0.605113i	−0.123518	−	0.213940i
$9$	−2.89721	−	0.778577i	−0.965736	−	0.259526i
$10$	−0.236568	−	0.409748i	−0.0748095	−	0.129574i
$11$	5.66019	+	2.06014i	1.70661	+	0.621155i	0.996551	−	0.0829858i	$-0.0264456\pi$
$11$	5.66019	+	2.06014i	1.70661	+	0.621155i	0.710060	+	0.704141i	$0.248668\pi$
$12$	0.736933	+	3.32985i	0.212734	+	0.961245i
$13$	−5.70404	+	2.07610i	−1.58202	+	0.575807i	−0.975641	−	0.219373i	$-0.929599\pi$
$13$	−5.70404	+	2.07610i	−1.58202	+	0.575807i	−0.606374	+	0.795179i	$0.707377\pi$
$14$	−0.283077	+	0.369879i	−0.0756555	+	0.0988543i
$15$	1.00587	+	4.54507i	0.259715	+	1.17353i
$16$	2.92247	−	2.45224i	0.730617	−	0.613060i
$17$	−0.621796	−	1.07698i	−0.150808	−	0.261207i	0.780717	−	0.624885i	$-0.214854\pi$
$17$	−0.621796	−	1.07698i	−0.150808	−	0.261207i	−0.931525	+	0.363678i	$0.881521\pi$
$18$	−0.0464149	+	0.526091i	−0.0109401	+	0.124001i
$19$	−1.47151	+	2.54874i	−0.337589	+	0.584721i	−0.983979	−	0.178286i	$-0.942945\pi$
$19$	−1.47151	+	2.54874i	−0.337589	+	0.584721i	0.646390	+	0.763007i	$0.276278\pi$
$20$	4.05382	−	3.40156i	0.906462	−	0.760612i
$21$	3.75147	−	2.63182i	0.818637	−	0.574311i
$22$	0.184136	−	1.04429i	0.0392579	−	0.222643i
$23$	−0.622595	+	3.53091i	−0.129820	+	0.736247i	0.848507	+	0.529183i	$0.177502\pi$
$23$	−0.622595	+	3.53091i	−0.129820	+	0.736247i	−0.978328	+	0.207063i	$0.933609\pi$
$24$	1.11827	−	0.462724i	0.228266	−	0.0944532i
$25$	1.70302	−	1.42901i	0.340605	−	0.285801i
$26$	0.534306	+	0.925446i	0.104786	+	0.181495i
$27$	1.99375	−	4.79843i	0.383697	−	0.923459i
$28$	−4.62392	−	2.39965i	−0.873839	−	0.453490i
$29$	−1.80256	−	0.656078i	−0.334727	−	0.121831i	0.169188	−	0.985584i	$-0.445885\pi$
$29$	−1.80256	−	0.656078i	−0.334727	−	0.121831i	−0.503915	+	0.863753i	$0.668108\pi$
$30$	0.757231	−	0.313331i	0.138251	−	0.0572061i
$31$	0.351738	−	0.128022i	0.0631740	−	0.0229935i	−0.310240	−	0.950658i	$-0.600409\pi$
$31$	0.351738	−	0.128022i	0.0631740	−	0.0229935i	0.373414	+	0.927665i	$0.378187\pi$
$32$	−1.58499	−	1.32997i	−0.280190	−	0.235107i
$33$	−4.82077	+	9.25234i	−0.839188	+	1.61063i
$34$	−0.167709	+	0.140724i	−0.0287618	+	0.0241340i
$35$	−6.31140	−	3.27539i	−1.06682	−	0.553641i
$36$	−5.88492	+	0.510526i	−0.980820	+	0.0850877i
$37$	−4.85189			−0.797645			−0.398823	−	0.917028i	$-0.630581\pi$
$37$	−4.85189			−0.797645			−0.398823	+	0.917028i	$0.630581\pi$
$38$	0.486860	+	0.177203i	0.0789791	+	0.0287461i
$39$	−2.27184	−	10.2654i	−0.363785	−	1.64377i
$40$	−1.43854	−	1.20708i	−0.227453	−	0.190856i
$41$	−8.12199	+	2.95616i	−1.26844	+	0.461675i	−0.886593	−	0.462550i	$-0.846935\pi$
$41$	−8.12199	+	2.95616i	−1.26844	+	0.461675i	−0.381848	+	0.924225i	$0.624712\pi$
$42$	−0.570962	−	0.569939i	−0.0881014	−	0.0879435i
$43$	−1.51365	−	8.58435i	−0.230830	−	1.30910i	−0.851221	−	0.524808i	$-0.824137\pi$
$43$	−1.51365	−	8.58435i	−0.230830	−	1.30910i	0.620391	−	0.784293i	$-0.286974\pi$
$44$	11.8602			1.78799
$45$	−8.03260	+	0.696841i	−1.19743	+	0.103879i
$46$	0.631189			0.0930637
$47$	1.43798	+	0.523383i	0.209751	+	0.0763432i	0.444759	−	0.895650i	$-0.353289\pi$
$47$	1.43798	+	0.523383i	0.209751	+	0.0763432i	−0.235008	+	0.971993i	$0.575512\pi$
$48$	3.54832	+	5.57425i	0.512157	+	0.804574i
$49$	−0.592478	+	6.97488i	−0.0846397	+	0.996412i
$50$	−0.299809	−	0.251569i	−0.0423993	−	0.0355773i
$51$	1.99031	−	0.823559i	0.278698	−	0.115321i
$52$	−9.15584	+	7.68266i	−1.26969	+	1.06539i
$53$	4.07550	−	7.05897i	0.559813	−	0.969624i	−0.437699	−	0.899122i	$-0.644206\pi$
$53$	4.07550	−	7.05897i	0.559813	−	0.969624i	0.997512	−	0.0705026i	$-0.0224603\pi$
$54$	−0.892855	−	0.198969i	−0.121502	−	0.0270763i
$55$	16.1885			2.18286
$56$	−0.553673	+	1.76379i	−0.0739877	+	0.235696i
$57$	−4.04297	−	3.10463i	−0.535504	−	0.411218i
$58$	−0.0586405	+	0.332567i	−0.00769988	+	0.0436682i
$59$	3.18453	+	2.67214i	0.414591	+	0.347883i	0.826101	−	0.563522i	$-0.190554\pi$
$59$	3.18453	+	2.67214i	0.414591	+	0.347883i	−0.411510	+	0.911405i	$0.634999\pi$
$60$	4.92196	+	7.73217i	0.635422	+	0.998219i
$61$	−3.48243	−	1.26750i	−0.445880	−	0.162287i	0.109315	−	0.994007i	$-0.465134\pi$
$61$	−3.48243	−	1.26750i	−0.445880	−	0.162287i	−0.555195	+	0.831720i	$0.687356\pi$
$62$	−0.0329478	−	0.0570673i	−0.00418438	−	0.00724756i
$63$	3.66876	+	7.03848i	0.462220	+	0.886765i
$64$	3.63289	−	6.29234i	0.454111	−	0.786543i
$65$	−12.4972	+	10.4864i	−1.55009	+	1.30068i
$66$	1.75145	+	0.552936i	0.215589	+	0.0680617i
$67$	0.699154	−	3.96510i	0.0854153	−	0.484414i	−0.911851	−	0.410522i	$-0.865347\pi$
$67$	0.699154	−	3.96510i	0.0854153	−	0.484414i	0.997266	−	0.0738927i	$-0.0235422\pi$
$68$	−1.87577	−	1.57396i	−0.227470	−	0.190870i
$69$	−5.92196	−	1.86957i	−0.712921	−	0.225070i
$70$	−0.374916	+	1.19434i	−0.0448111	+	0.142751i
$71$	−0.161544	+	0.279802i	−0.0191717	+	0.0332064i	−0.875452	−	0.483305i	$-0.839436\pi$
$71$	−0.161544	+	0.279802i	−0.0191717	+	0.0332064i	0.856280	+	0.516511i	$0.172770\pi$
$72$	0.541048	+	2.02514i	0.0637631	+	0.238665i
$73$	4.85752			0.568529			0.284265	−	0.958746i	$-0.408251\pi$
$73$	4.85752			0.568529			0.284265	+	0.958746i	$0.408251\pi$
$74$	0.148322	+	0.841174i	0.0172420	+	0.0977845i
$75$	2.06773	+	3.24831i	0.238761	+	0.375082i
$76$	−1.00627	+	5.70681i	−0.115427	+	0.654616i
$77$	−6.11724	−	14.7157i	−0.697124	−	1.67701i
$78$	−1.71026	+	0.707680i	−0.193649	+	0.0801290i
$79$	−0.357349	−	2.02663i	−0.0402049	−	0.228013i	0.958084	−	0.286487i	$-0.0924876\pi$
$79$	−0.357349	−	2.02663i	−0.0402049	−	0.228013i	−0.998289	+	0.0584741i	$0.981376\pi$
$80$	5.12659	−	8.87951i	0.573170	−	0.992760i
$81$	7.78764	+	4.51140i	0.865293	+	0.501266i
$82$	0.760800	+	1.31774i	0.0840163	+	0.145520i
$83$	9.46250	+	3.44407i	1.03864	+	0.378035i	0.804366	−	0.594134i	$-0.202505\pi$
$83$	9.46250	+	3.44407i	1.03864	+	0.378035i	0.234278	+	0.972170i	$0.424727\pi$
$84$	5.16882	−	7.39595i	0.563965	−	0.806965i
$85$	−2.56032	−	2.14837i	−0.277706	−	0.233023i
$86$	−1.44200	+	0.524845i	−0.155495	+	0.0565955i
$87$	1.53524	−	2.94653i	0.164595	−	0.315901i
$88$	−0.730838	−	4.14479i	−0.0779076	−	0.441836i
$89$	2.13585	−	3.69941i	0.226400	−	0.392136i	−0.730339	−	0.683085i	$-0.760638\pi$
$89$	2.13585	−	3.69941i	0.226400	−	0.392136i	0.956739	+	0.290949i	$0.0939710\pi$
$90$	0.366367	+	1.37131i	0.0386185	+	0.144549i
$91$	14.2547	+	7.39769i	1.49430	+	0.775489i
$92$	1.22590	+	6.95240i	0.127808	+	0.724838i
$93$	0.140092	+	0.633010i	0.0145269	+	0.0656401i
$94$	0.0467801	−	0.265303i	0.00482500	−	0.0273640i
$95$	−1.37350	+	7.78949i	−0.140918	+	0.799185i
$96$	2.64308	−	2.42016i	0.269758	−	0.247006i
$97$	−0.938221	−	5.32092i	−0.0952619	−	0.540257i	−0.994667	−	0.103141i	$-0.967111\pi$
$97$	−0.938221	−	5.32092i	−0.0952619	−	0.540257i	0.899405	−	0.437117i	$-0.144000\pi$
$98$	1.22735	−	0.110503i	0.123981	−	0.0111625i
$99$	−14.7948	−	10.3755i	−1.48693	−	1.04278i
$100$	2.18869	−	3.79092i	0.218869	−	0.379092i
$101$	−0.288498	−	1.63615i	−0.0287066	−	0.162803i	0.967084	−	0.254456i	$-0.0818963\pi$
$101$	−0.288498	−	1.63615i	−0.0287066	−	0.162803i	−0.995791	+	0.0916523i	$0.970785\pi$
$102$	−0.203624	−	0.319884i	−0.0201618	−	0.0316732i
$103$	−7.75612	+	2.82300i	−0.764233	+	0.278158i	−0.694582	−	0.719413i	$-0.744411\pi$
$103$	−7.75612	+	2.82300i	−0.764233	+	0.278158i	−0.0696509	+	0.997571i	$0.522189\pi$
$104$	3.24905	+	2.72628i	0.318595	+	0.267333i
$105$	7.05516	−	10.0951i	0.688513	−	0.985179i
$106$	−1.34840	−	0.490779i	−0.130969	−	0.0476687i
$107$	1.95477	+	3.38577i	0.188975	+	0.327315i	0.944909	−	0.327334i	$-0.106150\pi$
$107$	1.95477	+	3.38577i	0.188975	+	0.327315i	−0.755934	+	0.654648i	$0.772817\pi$
$108$	0.457497	−	10.2210i	0.0440227	−	0.983519i
$109$	−1.77525	+	3.07483i	−0.170038	+	0.294515i	−0.938433	−	0.345461i	$-0.887722\pi$
$109$	−1.77525	+	3.07483i	−0.170038	+	0.294515i	0.768395	+	0.639976i	$0.221056\pi$
$110$	−0.494882	−	2.80662i	−0.0471852	−	0.267600i
$111$	1.09995	−	8.33142i	0.104403	−	0.790783i
$112$	−10.0089	−	1.30484i	−0.945749	−	0.123296i
$113$	−2.90076	+	16.4510i	−0.272881	+	1.54758i	0.472733	+	0.881206i	$0.343267\pi$
$113$	−2.90076	+	16.4510i	−0.272881	+	1.54758i	−0.745614	+	0.666378i	$0.767844\pi$
$114$	−0.414658	+	0.795839i	−0.0388362	+	0.0745371i
$115$	1.67328	+	9.48965i	0.156034	+	0.884914i
$116$	−3.77704			−0.350689
$117$	18.1422	−	1.57386i	1.67725	−	0.145504i
$118$	0.365919	−	0.633791i	0.0336856	−	0.0583452i
$119$	−0.985430	+	3.13920i	−0.0903342	+	0.287770i
$120$	2.39886	−	2.19654i	0.218985	−	0.200516i
$121$	19.3671	+	16.2509i	1.76064	+	1.47735i
$122$	−0.113290	+	0.642498i	−0.0102568	+	0.0581691i
$123$	−3.23487	−	14.6169i	−0.291678	−	1.31796i
$124$	0.564592	−	0.473749i	0.0507019	−	0.0425439i
$125$	−3.73153	+	6.46320i	−0.333758	+	0.578087i
$126$	1.10811	−	0.851220i	0.0987184	−	0.0758327i
$127$	7.88389	+	13.6553i	0.699582	+	1.21171i	0.968611	+	0.248580i	$0.0799640\pi$
$127$	7.88389	+	13.6553i	0.699582	+	1.21171i	−0.269029	+	0.963132i	$0.586703\pi$
$128$	−5.09053	−	1.85280i	−0.449943	−	0.163766i
$129$	15.0838	−	0.653044i	1.32805	−	0.0574973i
$130$	2.20007	+	1.84608i	0.192959	+	0.161912i
$131$	−0.705933	+	4.00355i	−0.0616777	+	0.349791i	0.938314	+	0.345784i	$0.112387\pi$
$131$	−0.705933	+	4.00355i	−0.0616777	+	0.349791i	−0.999992	+	0.00400787i	$0.998724\pi$
$132$	−2.68878	+	20.3658i	−0.234028	+	1.77261i
$133$	7.59982	−	1.69491i	0.658988	−	0.146967i
$134$	−0.708805			−0.0612314
$135$	0.624459	−	13.9512i	0.0537449	−	1.20072i
$136$	−0.434464	+	0.752514i	−0.0372550	+	0.0645275i
$137$	9.88246	−	8.29237i	0.844316	−	0.708465i	−0.114215	−	0.993456i	$-0.536435\pi$
$137$	9.88246	−	8.29237i	0.844316	−	0.708465i	0.958530	+	0.284991i	$0.0919907\pi$
$138$	−0.143094	+	1.08385i	−0.0121810	+	0.0922631i
$139$	10.8278	+	9.08563i	0.918405	+	0.770633i	0.973699	−	0.227837i	$-0.0731653\pi$
$139$	10.8278	+	9.08563i	0.918405	+	0.770633i	−0.0552943	+	0.998470i	$0.517610\pi$
$140$	−13.8835	−	1.80997i	−1.17337	−	0.152970i
$141$	−1.22473	+	2.35058i	−0.103141	+	0.197954i
$142$	0.0534478	+	0.0194534i	0.00448524	+	0.00163249i
$143$	−36.5630			−3.05755
$144$	−10.3763	+	4.82929i	−0.864688	+	0.402441i
$145$	−5.15546			−0.428137
$146$	−0.148494	−	0.842150i	−0.0122894	−	0.0696968i
$147$	−11.8426	−	2.59862i	−0.976761	−	0.214331i
$148$	−8.97726	+	3.26746i	−0.737927	+	0.268583i
$149$	−13.9545	−	11.7092i	−1.14320	−	0.959258i	−0.143660	−	0.989627i	$-0.545887\pi$
$149$	−13.9545	−	11.7092i	−1.14320	−	0.959258i	−0.999539	+	0.0303696i	$0.990332\pi$
$150$	0.499951	−	0.457784i	0.0408208	−	0.0373779i
$151$	2.23442	+	0.813263i	0.181835	+	0.0661824i	0.431333	−	0.902193i	$-0.358043\pi$
$151$	2.23442	+	0.813263i	0.181835	+	0.0661824i	−0.249498	+	0.968375i	$0.580266\pi$
$152$	2.05637			0.166793
$153$	0.962960	+	3.60436i	0.0778507	+	0.291395i
$154$	−2.36427	+	1.51041i	−0.190518	+	0.121712i
$155$	0.770638	−	0.646642i	0.0618991	−	0.0519395i
$156$	−11.1166	−	17.4637i	−0.890040	−	1.39821i
$157$	2.85700	+	2.39731i	0.228013	+	0.191326i	0.749636	−	0.661850i	$-0.230229\pi$
$157$	2.85700	+	2.39731i	0.228013	+	0.191326i	−0.521623	+	0.853176i	$0.674673\pi$
$158$	−0.340433	+	0.123907i	−0.0270834	+	0.00985755i
$159$	11.1974	+	8.59855i	0.888009	+	0.681910i
$160$	−5.22543	−	1.90190i	−0.413107	−	0.150359i
$161$	7.99400	−	5.10694i	0.630015	−	0.402483i
$162$	0.544076	−	1.48806i	0.0427467	−	0.116913i
$163$	3.36378	+	5.82624i	0.263472	+	0.456346i	0.967162	−	0.254160i	$-0.0817991\pi$
$163$	3.36378	+	5.82624i	0.263472	+	0.456346i	−0.703690	+	0.710507i	$0.748466\pi$
$164$	−13.0370	+	10.9394i	−1.01802	+	0.854220i
$165$	−3.67004	+	27.7982i	−0.285712	+	2.16408i
$166$	0.307832	−	1.74580i	0.0238924	−	0.135501i
$167$	2.44213	−	13.8500i	0.188977	−	1.07174i	−0.731760	−	0.681562i	$-0.761301\pi$
$167$	2.44213	−	13.8500i	0.188977	−	1.07174i	0.920738	−	0.390182i	$-0.127588\pi$
$168$	−2.90317	−	1.35060i	−0.223984	−	0.104201i
$169$	18.2673	−	15.3281i	1.40518	−	1.17908i
$170$	−0.294195	+	0.509560i	−0.0225637	+	0.0390815i
$171$	6.24767	−	6.23854i	0.477772	−	0.477073i
$172$	−8.58170	−	14.8639i	−0.654349	−	1.13337i
$173$	14.2419	−	11.9504i	1.08279	−	0.908572i	0.0866445	−	0.996239i	$-0.472386\pi$
$173$	14.2419	−	11.9504i	1.08279	−	0.908572i	0.996150	+	0.0876670i	$0.0279411\pi$
$174$	−0.557773	−	0.176090i	−0.0422847	−	0.0133493i
$175$	−5.83252	−	0.760374i	−0.440897	−	0.0574789i
$176$	21.5937	−	7.85945i	1.62768	−	0.592429i
$177$	−5.31042	+	4.86253i	−0.399155	+	0.365490i
$178$	−0.706660	−	0.257203i	−0.0529664	−	0.0192782i
$179$	5.80869	+	10.0610i	0.434162	+	0.751991i	0.997227	−	0.0744219i	$-0.0237112\pi$
$179$	5.80869	+	10.0610i	0.434162	+	0.751991i	−0.563065	+	0.826413i	$0.690378\pi$
$180$	−14.3931	+	6.69882i	−1.07280	+	0.499300i
$181$	−12.4918	−	21.6365i	−0.928509	−	1.60823i	−0.785818	−	0.618458i	$-0.787758\pi$
$181$	−12.4918	−	21.6365i	−0.928509	−	1.60823i	−0.142691	−	0.989767i	$-0.545576\pi$
$182$	0.846775	−	2.69750i	0.0627671	−	0.199952i
$183$	2.96598	−	5.69251i	0.219251	−	0.420802i
$184$	2.35411	−	0.856827i	0.173547	−	0.0631661i
$185$	−12.2535	+	4.45990i	−0.900894	+	0.327899i
$186$	0.105463	−	0.0436389i	0.00773290	−	0.00319976i
$187$	−1.30075	−	7.37691i	−0.0951201	−	0.539453i
$188$	3.01311			0.219754
$189$	−12.9179	+	4.70414i	−0.939636	+	0.342176i
$190$	1.39246			0.101019
$191$	−0.596759	−	3.38439i	−0.0431800	−	0.244886i	0.955576	−	0.294744i	$-0.0952343\pi$
$191$	−0.596759	−	3.38439i	−0.0431800	−	0.244886i	−0.998756	+	0.0498579i	$0.984123\pi$
$192$	9.98130	+	7.66472i	0.720338	+	0.553154i
$193$	−17.8018	+	6.47934i	−1.28140	+	0.466393i	−0.890897	−	0.454206i	$-0.849923\pi$
$193$	−17.8018	+	6.47934i	−1.28140	+	0.466393i	−0.390508	+	0.920599i	$0.627701\pi$
$194$	−0.893809	+	0.325320i	−0.0641717	+	0.0233566i
$195$	−15.1736	−	23.8369i	−1.08660	−	1.70700i
$196$	3.60093	+	13.3044i	0.257209	+	0.950311i
$197$	4.00638	+	6.93925i	0.285442	+	0.494401i	0.972716	−	0.231998i	$-0.0745261\pi$
$197$	4.00638	+	6.93925i	0.285442	+	0.494401i	−0.687274	+	0.726398i	$0.741193\pi$
$198$	−1.34654	+	2.88216i	−0.0956943	+	0.204826i
$199$	−0.784854	−	1.35941i	−0.0556369	−	0.0963659i	0.836866	−	0.547408i	$-0.184386\pi$
$199$	−0.784854	−	1.35941i	−0.0556369	−	0.0963659i	−0.892502	+	0.451043i	$0.851052\pi$
$200$	−1.45968	−	0.531280i	−0.103215	−	0.0375672i
$201$	6.65017	+	2.09947i	0.469067	+	0.148085i
$202$	−0.274841	+	0.100034i	−0.0193378	+	0.00703837i
$203$	1.94811	+	4.68642i	0.136731	+	0.328922i
$204$	3.12797	−	2.86415i	0.219002	−	0.200531i
$205$	−17.7948	+	14.9316i	−1.24284	+	1.04287i
$206$	0.726528	+	1.25838i	0.0506196	+	0.0876757i
$207$	4.55288	−	9.74506i	0.316447	−	0.677328i
$208$	−11.5788	+	20.0550i	−0.802843	+	1.39056i
$209$	−13.5798	+	11.3948i	−0.939335	+	0.788196i
$210$	−1.96586	−	0.914552i	−0.135657	−	0.0631101i
$211$	1.85421	−	10.5158i	0.127649	−	0.723935i	−0.852050	−	0.523461i	$-0.824641\pi$
$211$	1.85421	−	10.5158i	0.127649	−	0.723935i	0.979699	−	0.200474i	$-0.0642483\pi$
$212$	2.78695	−	15.8056i	0.191408	−	1.08553i
$213$	−0.443839	−	0.340828i	−0.0304114	−	0.0233531i
$214$	0.527235	−	0.442403i	0.0360410	−	0.0302420i
$215$	−11.7136	−	20.2885i	−0.798858	−	1.38366i
$216$	−3.60013	+	0.469948i	−0.244958	+	0.0319759i
$217$	−0.879015	−	0.456177i	−0.0596714	−	0.0309673i
$218$	0.587353	+	0.213779i	0.0397806	+	0.0144790i
$219$	−1.10123	+	8.34109i	−0.0744141	+	0.563638i
$220$	29.9531	−	10.9020i	2.01944	−	0.735014i
$221$	5.78267	+	4.85224i	0.388985	+	0.326397i
$222$	−1.47805	+	0.0639913i	−0.0992000	+	0.00429482i
$223$	0.128511	−	0.107834i	0.00860576	−	0.00722109i	−0.638475	−	0.769643i	$-0.720434\pi$
$223$	0.128511	−	0.107834i	0.00860576	−	0.00722109i	0.647080	+	0.762422i	$0.275990\pi$
$224$	0.245688	+	5.46871i	0.0164157	+	0.365393i
$225$	−6.04660	+	2.81419i	−0.403107	+	0.187613i
$226$	2.94080			0.195619
$227$	12.3424	+	4.49227i	0.819195	+	0.298162i	0.717416	−	0.696645i	$-0.245325\pi$
$227$	12.3424	+	4.49227i	0.819195	+	0.298162i	0.101778	+	0.994807i	$0.467547\pi$
$228$	−9.57133	−	3.02168i	−0.633877	−	0.200115i
$229$	−17.6285	−	14.7921i	−1.16493	−	0.977488i	−0.164964	−	0.986300i	$-0.552751\pi$
$229$	−17.6285	−	14.7921i	−1.16493	−	0.977488i	−0.999961	+	0.00881137i	$0.997195\pi$
$230$	1.59407	−	0.580195i	0.105110	−	0.0382569i
$231$	26.6559	−	7.16807i	1.75383	−	0.471624i
$232$	0.232745	+	1.31996i	0.0152804	+	0.0866597i
$233$	7.87251			0.515745			0.257873	−	0.966179i	$-0.416978\pi$
$233$	7.87251			0.515745			0.257873	+	0.966179i	$0.416978\pi$
$234$	−0.827466	−	3.09721i	−0.0540932	−	0.202471i
$235$	4.11273			0.268285
$236$	7.69174	+	2.79957i	0.500690	+	0.182236i
$237$	3.56103	−	0.154173i	0.231314	−	0.0100146i
$238$	0.574369	+	0.0748794i	0.0372308	+	0.00485371i
$239$	16.1523	+	13.5534i	1.04481	+	0.876696i	0.992538	−	0.121937i	$-0.0389105\pi$
$239$	16.1523	+	13.5534i	1.04481	+	0.876696i	0.0522680	+	0.998633i	$0.483355\pi$
$240$	14.0852	+	10.8162i	0.909198	+	0.698180i
$241$	2.17608	−	1.82595i	0.140173	−	0.117619i	−0.570005	−	0.821641i	$-0.693059\pi$
$241$	2.17608	−	1.82595i	0.140173	−	0.117619i	0.710178	+	0.704022i	$0.248614\pi$
$242$	2.22538	−	3.85446i	0.143053	−	0.247774i
$243$	−9.51225	+	12.3498i	−0.610211	+	0.792239i
$244$	−7.29700			−0.467143
$245$	4.91507	+	18.1597i	0.314012	+	1.16018i
$246$	−2.43524	+	1.00767i	−0.155265	+	0.0642465i
$247$	3.10214	−	17.5931i	0.197384	−	1.11942i
$248$	−0.200352	−	0.168115i	−0.0127223	−	0.0106753i
$249$	−8.05918	+	15.4677i	−0.510730	+	0.980228i
$250$	1.23460	+	0.449358i	0.0780830	+	0.0284199i
$251$	−3.00024	−	5.19656i	−0.189373	−	0.328004i	0.755668	−	0.654955i	$-0.227312\pi$
$251$	−3.00024	−	5.19656i	−0.189373	−	0.328004i	−0.945041	+	0.326951i	$0.893979\pi$
$252$	11.5282	+	10.5524i	0.726206	+	0.664736i
$253$	−10.7982	+	18.7030i	−0.678876	+	1.17585i
$254$	2.12642	−	1.78428i	0.133423	−	0.111955i
$255$	4.26951	−	3.90941i	0.267367	−	0.244817i
$256$	2.35777	−	13.3716i	0.147361	−	0.835724i
$257$	15.9942	+	13.4207i	0.997692	+	0.837163i	0.986663	−	0.162776i	$-0.0520448\pi$
$257$	15.9942	+	13.4207i	0.997692	+	0.837163i	0.0110292	+	0.999939i	$0.496489\pi$
$258$	−0.574328	−	2.59512i	−0.0357561	−	0.161565i
$259$	8.68442	+	9.45339i	0.539623	+	0.587405i
$260$	−16.0612	+	27.8188i	−0.996071	+	1.72525i
$261$	4.71159	+	3.30423i	0.291640	+	0.204527i
$262$	0.715677			0.0442147
$263$	−0.326824	−	1.85351i	−0.0201528	−	0.114292i	0.973072	−	0.230502i	$-0.0740367\pi$
$263$	−0.326824	−	1.85351i	−0.0201528	−	0.114292i	−0.993225	+	0.116209i	$0.962926\pi$
$264$	7.28291	−	0.315310i	0.448232	−	0.0194060i
$265$	3.80403	−	21.5737i	0.233680	−	1.32526i
$266$	−0.526173	−	1.26577i	−0.0322617	−	0.0776094i
$267$	5.86822	+	4.50626i	0.359129	+	0.275778i
$268$	−1.37664	−	7.80732i	−0.0840917	−	0.476908i
$269$	4.75096	−	8.22890i	0.289671	−	0.501725i	−0.684060	−	0.729426i	$-0.739787\pi$
$269$	4.75096	−	8.22890i	0.289671	−	0.501725i	0.973731	+	0.227701i	$0.0731208\pi$
$270$	−2.43781	+	0.318223i	−0.148360	+	0.0193664i
$271$	−15.0810	−	26.1210i	−0.916105	−	1.58674i	−0.805276	−	0.592901i	$-0.797983\pi$
$271$	−15.0810	−	26.1210i	−0.916105	−	1.58674i	−0.110829	−	0.993839i	$-0.535351\pi$
$272$	−4.45820	−	1.62265i	−0.270318	−	0.0983877i
$273$	−15.9346	+	22.8004i	−0.964405	+	1.37995i
$274$	−1.73976	−	1.45983i	−0.105103	−	0.0881916i
$275$	12.5834	−	4.57998i	0.758806	−	0.276183i
$276$	−12.2162	+	0.528895i	−0.735331	+	0.0318358i
$277$	2.12281	+	12.0391i	0.127548	+	0.723358i	0.979762	+	0.200165i	$0.0641480\pi$
$277$	2.12281	+	12.0391i	0.127548	+	0.723358i	−0.852215	+	0.523192i	$0.824741\pi$
$278$	1.24417	−	2.15497i	0.0746206	−	0.129247i
$279$	−1.11873	+	0.0970519i	−0.0669768	+	0.00581034i
$280$	0.222987	+	4.96341i	0.0133260	+	0.296620i
$281$	−5.28489	−	29.9721i	−0.315270	−	1.78799i	−0.570700	−	0.821159i	$-0.693328\pi$
$281$	−5.28489	−	29.9721i	−0.315270	−	1.78799i	0.255430	−	0.966828i	$-0.417783\pi$
$282$	0.444960	+	0.140474i	0.0264970	+	0.00836513i
$283$	−0.985249	+	5.58762i	−0.0585669	+	0.332150i	−0.999987	−	0.00508640i	$-0.998381\pi$
$283$	−0.985249	+	5.58762i	−0.0585669	+	0.332150i	0.941420	+	0.337236i	$0.109492\pi$
$284$	−0.110468	+	0.626498i	−0.00655509	+	0.0371758i
$285$	−13.0643	−	4.12443i	−0.773865	−	0.244310i
$286$	1.11773	+	6.33894i	0.0660925	+	0.374829i
$287$	20.2974	+	10.5336i	1.19812	+	0.621778i
$288$	3.55657	+	5.08723i	0.209573	+	0.299768i
$289$	7.72674	−	13.3831i	0.454514	−	0.787241i
$290$	0.157602	+	0.893804i	0.00925469	+	0.0524860i
$291$	9.34952	−	0.404782i	0.548078	−	0.0237288i
$292$	8.98768	−	3.27125i	0.525964	−	0.191435i
$293$	15.4454	+	12.9602i	0.902328	+	0.757143i	0.970644	−	0.240521i	$-0.0773182\pi$
$293$	15.4454	+	12.9602i	0.902328	+	0.757143i	−0.0683160	+	0.997664i	$0.521763\pi$
$294$	−0.0884972	+	2.13260i	−0.00516126	+	0.124376i
$295$	10.4988	+	3.82126i	0.611265	+	0.222482i
$296$	1.69507	+	2.93594i	0.0985237	+	0.170648i
$297$	21.1704	−	23.0526i	1.22843	−	1.33765i
$298$	−1.60345	+	2.77725i	−0.0928852	+	0.160882i
$299$	−3.77922	−	21.4330i	−0.218558	−	1.23950i
$300$	6.01339	+	4.61773i	0.347183	+	0.266605i
$301$	−14.0164	+	18.3144i	−0.807892	+	1.05562i
$302$	0.0726898	−	0.412244i	0.00418283	−	0.0237220i
$303$	2.87492	−	0.124468i	0.165160	−	0.00715052i
$304$	1.94967	+	11.0571i	0.111821	+	0.634169i
$305$	−9.96001			−0.570309
$306$	0.595452	−	0.277134i	0.0340397	−	0.0158427i
$307$	−1.94250	+	3.36451i	−0.110864	+	0.192023i	−0.916119	−	0.400906i	$-0.868695\pi$
$307$	−1.94250	+	3.36451i	−0.110864	+	0.192023i	0.805255	+	0.592929i	$0.202029\pi$
$308$	−21.2287	−	23.1084i	−1.20962	−	1.31672i
$309$	−3.08915	−	13.9584i	−0.175736	−	0.794066i
$310$	−0.135667	−	0.113838i	−0.00770536	−	0.00646557i
$311$	0.0578151	−	0.327886i	0.00327840	−	0.0185927i	−0.983125	−	0.182937i	$-0.941440\pi$
$311$	0.0578151	−	0.327886i	0.00327840	−	0.0185927i	0.986403	+	0.164344i	$0.0525507\pi$
$312$	−5.41800	+	4.96104i	−0.306734	+	0.280864i
$313$	−2.66081	+	2.23269i	−0.150398	+	0.126199i	−0.714882	−	0.699245i	$-0.753520\pi$
$313$	−2.66081	+	2.23269i	−0.150398	+	0.126199i	0.564484	+	0.825444i	$0.309075\pi$
$314$	0.328284	−	0.568605i	0.0185261	−	0.0320882i
$315$	15.7353	+	14.4034i	0.886584	+	0.811539i
$316$	−2.02600	−	3.50914i	−0.113971	−	0.197404i
$317$	12.8867	+	4.69039i	0.723792	+	0.263439i	0.677535	−	0.735491i	$-0.263048\pi$
$317$	12.8867	+	4.69039i	0.723792	+	0.263439i	0.0462572	+	0.998930i	$0.485271\pi$
$318$	1.14843	−	2.20415i	0.0644009	−	0.123603i
$319$	−8.85122	−	7.42705i	−0.495573	−	0.415835i
$320$	3.39090	−	19.2307i	0.189557	−	1.07503i
$321$	−6.25703	+	2.58907i	−0.349233	+	0.144508i
$322$	−1.12977	−	1.22980i	−0.0629595	−	0.0685343i
$323$	3.65993			0.203644
$324$	17.4473	+	3.10276i	0.969296	+	0.172376i
$325$	−6.74735	+	11.6867i	−0.374275	+	0.648264i
$326$	0.907268	−	0.761288i	0.0502489	−	0.0421638i
$327$	−4.87748	−	3.74546i	−0.269725	−	0.207124i
$328$	4.62633	+	3.88195i	0.255446	+	0.214345i
$329$	−1.55410	−	3.73856i	−0.0856801	−	0.206114i
$330$	4.93157	−	0.213510i	0.271474	−	0.0117533i
$331$	−16.4600	−	5.99094i	−0.904722	−	0.329292i	−0.152578	−	0.988291i	$-0.548758\pi$
$331$	−16.4600	−	5.99094i	−0.904722	−	0.329292i	−0.752143	+	0.659000i	$0.770980\pi$
$332$	19.8275			1.08817
$333$	14.0569	+	3.77757i	0.770315	+	0.207009i
$334$	−2.47583			−0.135472
$335$	−1.87904	−	10.6566i	−0.102663	−	0.582230i
$336$	4.50967	−	16.8909i	0.246023	−	0.921475i
$337$	9.84784	−	3.58432i	0.536446	−	0.195250i	−0.0595681	−	0.998224i	$-0.518972\pi$
$337$	9.84784	−	3.58432i	0.536446	−	0.195250i	0.596014	+	0.802974i	$0.296750\pi$
$338$	−3.21586	−	2.69843i	−0.174920	−	0.146775i
$339$	−27.5913	−	8.71059i	−1.49855	−	0.473095i
$340$	−6.18407	−	2.25082i	−0.335378	−	0.122068i
$341$	2.25465			0.122096
$342$	−1.27257	−	0.892451i	−0.0688127	−	0.0482582i
$343$	14.6503	−	11.3300i	0.791042	−	0.611762i
$344$	−4.66569	+	3.91498i	−0.251557	+	0.211081i
$345$	−16.6745	+	0.721914i	−0.897725	+	0.0388665i
$346$	−2.50722	−	2.10381i	−0.134789	−	0.113101i
$347$	−23.9933	+	8.73284i	−1.28803	+	0.468803i	−0.893079	−	0.449900i	$-0.851460\pi$
$347$	−23.9933	+	8.73284i	−1.28803	+	0.468803i	−0.394948	+	0.918704i	$0.629237\pi$
$348$	0.856278	−	6.48574i	0.0459013	−	0.347672i
$349$	3.01755	+	1.09830i	0.161526	+	0.0587906i	0.421517	−	0.906820i	$-0.361498\pi$
$349$	3.01755	+	1.09830i	0.161526	+	0.0587906i	−0.259992	+	0.965611i	$0.583720\pi$
$350$	0.0464729	+	1.03443i	0.00248408	+	0.0552926i
$351$	−1.41038	+	31.5097i	−0.0752808	+	1.68186i
$352$	−6.23144	−	10.7932i	−0.332137	−	0.575278i
$353$	13.1621	−	11.0443i	0.700546	−	0.587828i	−0.221383	−	0.975187i	$-0.571057\pi$
$353$	13.1621	−	11.0443i	0.700546	−	0.587828i	0.921929	+	0.387359i	$0.126613\pi$
$354$	1.00536	+	0.772022i	0.0534342	+	0.0410325i
$355$	−0.150783	+	0.855135i	−0.00800275	+	0.0453859i
$356$	1.46056	−	8.28324i	0.0774095	−	0.439011i
$357$	−5.16708	−	2.40381i	−0.273471	−	0.127223i
$358$	1.56670	−	1.31462i	0.0828027	−	0.0694797i
$359$	−10.6001	+	18.3599i	−0.559450	+	0.968996i	0.438092	+	0.898930i	$0.355654\pi$
$359$	−10.6001	+	18.3599i	−0.559450	+	0.968996i	−0.997542	+	0.0700661i	$0.977679\pi$
$360$	3.22795	+	4.61718i	0.170128	+	0.243347i
$361$	5.16929	+	8.95347i	0.272068	+	0.471235i
$362$	−3.36925	+	2.82714i	−0.177084	+	0.148591i
$363$	−32.2958	+	29.5720i	−1.69509	+	1.55213i
$364$	31.3569	+	4.08794i	1.64355	+	0.214266i
$365$	12.2677	−	4.46508i	0.642121	−	0.233713i
$366$	−1.07758	−	0.340194i	−0.0563261	−	0.0177822i
$367$	18.7954	+	6.84096i	0.981111	+	0.357095i	0.782272	−	0.622937i	$-0.214061\pi$
$367$	18.7954	+	6.84096i	0.981111	+	0.357095i	0.198839	+	0.980032i	$0.436283\pi$
$368$	6.83914	+	11.8457i	0.356515	+	0.617502i
$369$	25.8327	−	2.24103i	1.34480	−	0.116663i
$370$	1.14780	+	1.98805i	0.0596714	+	0.103354i
$371$	−21.0484	+	4.69421i	−1.09278	+	0.243711i
$372$	0.685502	+	1.07689i	0.0355416	+	0.0558342i
$373$	−29.4768	+	10.7287i	−1.52625	+	0.555510i	−0.962700	−	0.270571i	$-0.912788\pi$
$373$	−29.4768	+	10.7287i	−1.52625	+	0.555510i	−0.563551	+	0.826081i	$0.690565\pi$
$374$	−1.23917	+	0.451023i	−0.0640762	+	0.0233218i
$375$	−10.2523	−	7.87285i	−0.529428	−	0.406552i
$376$	−0.185671	−	1.05299i	−0.00957524	−	0.0543039i
$377$	11.6440			0.599694
$378$	1.21046	+	2.09577i	0.0622591	+	0.107795i
$379$	2.42639			0.124635			0.0623177	−	0.998056i	$-0.480151\pi$
$379$	2.42639			0.124635			0.0623177	+	0.998056i	$0.480151\pi$
$380$	2.70443	+	15.3376i	0.138734	+	0.786801i
$381$	−25.2355	+	10.4421i	−1.29286	+	0.534964i
$382$	−0.568510	+	0.206921i	−0.0290875	+	0.0105870i
$383$	19.5174	−	7.10375i	0.997293	−	0.362985i	0.208753	−	0.977968i	$-0.433060\pi$
$383$	19.5174	−	7.10375i	0.997293	−	0.362985i	0.788540	+	0.614984i	$0.210837\pi$
$384$	4.33559	−	8.32116i	0.221250	−	0.424637i
$385$	−28.9760	−	31.5417i	−1.47675	−	1.60751i
$386$	1.66753	+	2.88824i	0.0848749	+	0.147008i
$387$	−2.29821	+	26.0491i	−0.116824	+	1.32415i
$388$	−5.31928	−	9.21326i	−0.270045	−	0.467732i
$389$	−8.27808	−	3.01298i	−0.419715	−	0.152764i	0.123524	−	0.992342i	$-0.460580\pi$
$389$	−8.27808	−	3.01298i	−0.419715	−	0.152764i	−0.543240	+	0.839578i	$0.682803\pi$
$390$	−3.66877	+	3.35934i	−0.185775	+	0.170107i
$391$	4.18986	−	1.52498i	0.211890	−	0.0771218i
$392$	4.42758	−	2.07824i	0.223627	−	0.104967i
$393$	−6.71465	−	2.11982i	−0.338709	−	0.106931i
$394$	1.08059	−	0.906719i	0.0544391	−	0.0456799i
$395$	−2.76538	−	4.78978i	−0.139141	−	0.241000i
$396$	−34.3615	−	9.23409i	−1.72673	−	0.464030i
$397$	5.22369	−	9.04770i	0.262169	−	0.454091i	−0.704649	−	0.709556i	$-0.748895\pi$
$397$	5.22369	−	9.04770i	0.262169	−	0.454091i	0.966818	+	0.255466i	$0.0822287\pi$
$398$	−0.211688	+	0.177628i	−0.0106110	+	0.00890366i
$399$	1.18749	+	13.4343i	0.0594488	+	0.672555i
$400$	1.47276	−	8.35244i	0.0736381	−	0.417622i
$401$	−2.83748	+	16.0922i	−0.141697	+	0.803605i	0.828263	+	0.560340i	$0.189330\pi$
$401$	−2.83748	+	16.0922i	−0.141697	+	0.803605i	−0.969960	+	0.243265i	$0.921782\pi$
$402$	0.160690	−	1.21712i	0.00801451	−	0.0607046i
$403$	−1.74054	+	1.46049i	−0.0867025	+	0.0727520i
$404$	−1.63565	−	2.83303i	−0.0813765	−	0.140948i
$405$	23.8147	+	4.23510i	1.18336	+	0.210444i
$406$	0.752933	−	0.481009i	0.0373674	−	0.0238721i
$407$	−27.4626	−	9.99556i	−1.36127	−	0.495462i
$408$	−1.19368	−	0.916639i	−0.0590961	−	0.0453804i
$409$	−4.58686	+	1.66948i	−0.226806	+	0.0825505i	−0.452923	−	0.891550i	$-0.649619\pi$
$409$	−4.58686	+	1.66948i	−0.226806	+	0.0825505i	0.226118	+	0.974100i	$0.427397\pi$
$410$	3.13269	+	2.62864i	0.154712	+	0.129819i
$411$	11.9988	+	18.8496i	0.591859	+	0.929782i
$412$	−12.4497	+	10.4466i	−0.613354	+	0.514666i
$413$	−0.493630	−	10.9876i	−0.0242899	−	0.540664i
$414$	−1.82869	−	0.491429i	−0.0898750	−	0.0241524i
$415$	27.0634			1.32849
$416$	11.8020	+	4.29558i	0.578641	+	0.210608i
$417$	−18.0561	+	16.5332i	−0.884213	+	0.809637i
$418$	2.39066	+	2.00600i	0.116931	+	0.0981167i
$419$	−26.9191	+	9.79775i	−1.31508	+	0.478651i	−0.901880	−	0.431987i	$-0.857813\pi$
$419$	−26.9191	+	9.79775i	−1.31508	+	0.478651i	−0.413204	+	0.910638i	$0.635590\pi$
$420$	6.25547	−	23.4298i	0.305236	−	1.14326i
$421$	0.140839	+	0.798739i	0.00686408	+	0.0389281i	0.988047	−	0.154150i	$-0.0492640\pi$
$421$	0.140839	+	0.798739i	0.00686408	+	0.0389281i	−0.981183	+	0.193078i	$0.938153\pi$
$422$	−1.87981			−0.0915075
$423$	−3.75864	−	2.63593i	−0.182751	−	0.128163i
$424$	−5.69530			−0.276588
$425$	−2.59795	−	0.945575i	−0.126019	−	0.0458671i
$426$	−0.0455214	+	0.0873677i	−0.00220552	+	0.00423298i
$427$	3.76363	+	9.05386i	0.182135	+	0.438147i
$428$	5.89696	+	4.94813i	0.285040	+	0.239177i
$429$	8.28905	−	62.7841i	0.400199	−	3.03125i
$430$	−3.15934	+	2.65100i	−0.152357	+	0.127843i
$431$	6.65677	−	11.5299i	0.320645	−	0.555374i	−0.659976	−	0.751287i	$-0.729434\pi$
$431$	6.65677	−	11.5299i	0.320645	−	0.555374i	0.980621	+	0.195913i	$0.0627669\pi$
$432$	−5.94025	−	18.9124i	−0.285801	−	0.909924i
$433$	−20.0155			−0.961881			−0.480941	−	0.876753i	$-0.659705\pi$
$433$	−20.0155			−0.961881			−0.480941	+	0.876753i	$0.659705\pi$
$434$	−0.0522161	+	0.166341i	−0.00250646	+	0.00798460i
$435$	1.16877	−	8.85269i	0.0560384	−	0.424454i
$436$	−1.21397	+	6.88476i	−0.0581386	+	0.329720i
$437$	−8.08322	−	6.78263i	−0.386673	−	0.324457i
$438$	1.47976	−	0.0640656i	0.0707058	−	0.00306117i
$439$	7.64847	+	2.78382i	0.365042	+	0.132864i	0.518027	−	0.855364i	$-0.326667\pi$
$439$	7.64847	+	2.78382i	0.365042	+	0.132864i	−0.152986	+	0.988228i	$0.548889\pi$
$440$	−5.65566	−	9.79590i	−0.269623	−	0.467001i
$441$	7.14701	−	19.7464i	0.340334	−	0.940305i
$442$	0.664459	−	1.15088i	0.0316051	−	0.0547416i
$443$	−23.2674	+	19.5237i	−1.10547	+	0.927599i	−0.997781	−	0.0665854i	$-0.978790\pi$
$443$	−23.2674	+	19.5237i	−1.10547	+	0.927599i	−0.107689	+	0.994185i	$0.534345\pi$
$444$	−3.57551	−	16.1561i	−0.169686	−	0.766733i
$445$	1.99358	−	11.3062i	0.0945049	−	0.535964i
$446$	−0.0226238	−	0.0189836i	−0.00107127	−	0.000898901i
$447$	23.2701	−	21.3074i	1.10064	−	1.00781i
$448$	−18.7625	+	4.18440i	−0.886444	+	0.197695i
$449$	−13.1727	+	22.8158i	−0.621659	+	1.07675i	0.367517	+	0.930017i	$0.380208\pi$
$449$	−13.1727	+	22.8158i	−0.621659	+	1.07675i	−0.989177	+	0.146729i	$0.953125\pi$
$450$	0.672742	+	0.962273i	0.0317134	+	0.0453620i
$451$	−52.0621			−2.45151
$452$	5.71162	+	32.3922i	0.268652	+	1.52360i
$453$	−1.90305	+	3.65247i	−0.0894132	+	0.171608i
$454$	0.401521	−	2.27714i	0.0188443	−	0.106871i
$455$	42.8005	+	5.57982i	2.00652	+	0.261586i
$456$	−0.466191	+	3.53109i	−0.0218314	+	0.165358i
$457$	1.75841	+	9.97245i	0.0822551	+	0.466492i	0.997915	+	0.0645384i	$0.0205575\pi$
$457$	1.75841	+	9.97245i	0.0822551	+	0.466492i	−0.915660	+	0.401953i	$0.868331\pi$
$458$	−2.02561	+	3.50846i	−0.0946505	+	0.163939i
$459$	−6.40753	+	0.836416i	−0.299078	+	0.0390406i
$460$	9.48672	+	16.4315i	0.442321	+	0.766122i
$461$	13.6186	+	4.95676i	0.634281	+	0.230859i	0.639093	−	0.769129i	$-0.279310\pi$
$461$	13.6186	+	4.95676i	0.634281	+	0.230859i	−0.00481277	+	0.999988i	$0.501532\pi$
$462$	−2.05760	−	4.40222i	−0.0957282	−	0.204810i
$463$	−27.9630	−	23.4637i	−1.29955	−	1.09045i	−0.990222	−	0.139498i	$-0.955451\pi$
$463$	−27.9630	−	23.4637i	−1.29955	−	1.09045i	−0.309329	−	0.950955i	$-0.600104\pi$
$464$	−6.87679	+	2.50295i	−0.319247	+	0.116196i
$465$	0.935673	+	1.46990i	0.0433908	+	0.0681649i
$466$	−0.240662	−	1.36486i	−0.0111484	−	0.0632260i
$467$	−16.1910	+	28.0436i	−0.749229	+	1.29770i	0.198964	+	0.980007i	$0.436242\pi$
$467$	−16.1910	+	28.0436i	−0.749229	+	1.29770i	−0.948193	+	0.317696i	$0.897091\pi$
$468$	32.5079	−	15.1297i	1.50268	−	0.699373i
$469$	−8.97700	+	5.73493i	−0.414519	+	0.264814i
$470$	−0.125726	−	0.713027i	−0.00579930	−	0.0328895i
$471$	−4.76423	+	4.36241i	−0.219524	+	0.201009i
$472$	0.504391	−	2.86054i	0.0232165	−	0.131667i
$473$	9.11740	−	51.7074i	0.419219	−	2.37751i
$474$	−0.135589	−	0.612665i	−0.00622783	−	0.0281406i
$475$	1.13614	+	6.44336i	0.0521296	+	0.295642i
$476$	0.290761	+	6.47197i	0.0133270	+	0.296642i
$477$	−17.3035	+	17.2782i	−0.792274	+	0.791116i
$478$	1.85598	−	3.21466i	0.0848907	−	0.147035i
$479$	−6.01067	−	34.0882i	−0.274634	−	1.55753i	−0.740121	−	0.672474i	$-0.765232\pi$
$479$	−6.01067	−	34.0882i	−0.274634	−	1.55753i	0.465486	−	0.885055i	$-0.345880\pi$
$480$	4.45049	−	8.54168i	0.203136	−	0.389872i
$481$	27.6753	−	10.0730i	1.26189	−	0.459289i
$482$	−0.383088	−	0.321449i	−0.0174492	−	0.0146416i
$483$	6.95710	+	14.8847i	0.316559	+	0.677276i
$484$	46.7781	+	17.0259i	2.12628	+	0.773902i
$485$	−7.26053	−	12.5756i	−0.329683	−	0.571029i
$486$	2.43188	+	1.27161i	0.110312	+	0.0576815i
$487$	−8.17536	+	14.1601i	−0.370461	+	0.641657i	−0.989636	−	0.143596i	$-0.954134\pi$
$487$	−8.17536	+	14.1601i	−0.370461	+	0.641657i	0.619176	+	0.785252i	$0.287467\pi$
$488$	0.449648	+	2.55008i	0.0203546	+	0.115437i
$489$	−10.7671	+	4.45527i	−0.486906	+	0.201474i
$490$	2.99811	−	1.40727i	0.135441	−	0.0635740i
$491$	4.46823	−	25.3406i	0.201648	−	1.14360i	−0.700979	−	0.713181i	$-0.747254\pi$
$491$	4.46823	−	25.3406i	0.201648	−	1.14360i	0.902628	−	0.430422i	$-0.141635\pi$
$492$	−15.8289	−	24.8665i	−0.713624	−	1.12107i
$493$	0.414240	+	2.34927i	0.0186564	+	0.105806i
$494$	−3.14496			−0.141498
$495$	−46.9016	−	12.6040i	−2.10807	−	0.566509i
$496$	0.714001	−	1.23669i	0.0320596	−	0.0555289i
$497$	0.834313	−	0.186068i	0.0374240	−	0.00834630i
$498$	2.92802	+	0.924378i	0.131208	+	0.0414224i
$499$	17.5974	+	14.7659i	0.787766	+	0.661014i	0.945191	−	0.326517i	$-0.105875\pi$
$499$	17.5974	+	14.7659i	0.787766	+	0.661014i	−0.157425	+	0.987531i	$0.550319\pi$
$500$	−2.55173	+	14.4716i	−0.114117	+	0.647189i
$501$	23.2289	+	7.33337i	1.03779	+	0.327631i
$502$	−0.809213	+	0.679011i	−0.0361170	+	0.0303057i
$503$	−2.97449	+	5.15197i	−0.132626	+	0.229715i	−0.924688	−	0.380726i	$-0.875674\pi$
$503$	−2.97449	+	5.15197i	−0.132626	+	0.229715i	0.792062	+	0.610441i	$0.209008\pi$
$504$	2.97735	−	4.67899i	0.132622	−	0.208419i
$505$	−2.23257	−	3.86693i	−0.0993481	−	0.172076i
$506$	3.57265	+	1.30034i	0.158824	+	0.0578071i
$507$	22.1793	+	34.8426i	0.985017	+	1.54742i
$508$	23.7833	+	19.9566i	1.05521	+	0.885429i
$509$	0.929970	−	5.27412i	0.0412202	−	0.233771i	−0.957237	−	0.289306i	$-0.906575\pi$
$509$	0.929970	−	5.27412i	0.0412202	−	0.233771i	0.998457	+	0.0555351i	$0.0176865\pi$
$510$	−0.808295	−	0.620697i	−0.0357919	−	0.0274849i
$511$	−8.69450	−	9.46436i	−0.384622	−	0.418678i
$512$	−13.2248			−0.584458
$513$	9.29612	+	12.1425i	0.410434	+	0.536105i
$514$	1.83782	−	3.18320i	0.0810628	−	0.140405i
$515$	−16.9932	+	14.2590i	−0.748811	+	0.628327i
$516$	27.4691	−	11.3663i	1.20926	−	0.500375i
$517$	7.06101	+	5.92489i	0.310543	+	0.260576i
$518$	1.37346	−	1.79461i	0.0603462	−	0.0788507i
$519$	17.2919	+	27.1648i	0.759030	+	1.19240i
$520$	10.7115	+	3.89867i	0.469731	+	0.170968i
$521$	10.9764			0.480886			0.240443	−	0.970663i	$-0.422707\pi$
$521$	10.9764			0.480886			0.240443	+	0.970663i	$0.422707\pi$
$522$	0.428823	−	0.917860i	0.0187691	−	0.0401736i
$523$	−2.51309			−0.109890			−0.0549449	−	0.998489i	$-0.517498\pi$
$523$	−2.51309			−0.109890			−0.0549449	+	0.998489i	$0.517498\pi$
$524$	1.38999	+	7.88301i	0.0607219	+	0.344371i
$525$	2.62794	−	9.84292i	0.114693	−	0.429580i
$526$	−0.311353	+	0.113323i	−0.0135756	+	0.00494112i
$527$	−0.356587	−	0.299212i	−0.0155332	−	0.0130339i
$528$	8.60044	+	38.8614i	0.374286	+	1.69122i
$529$	9.53320	+	3.46980i	0.414487	+	0.150861i
$530$	−3.85654			−0.167517
$531$	−7.14579	−	10.2211i	−0.310101	−	0.443560i
$532$	12.9202	−	8.25405i	0.560163	−	0.357859i
$533$	40.1908	−	33.7241i	1.74086	−	1.46075i
$534$	0.601861	−	1.15513i	0.0260451	−	0.0499875i
$535$	8.04903	+	6.75394i	0.347990	+	0.291998i
$536$	−2.64359	+	0.962189i	−0.114186	+	0.0415602i
$537$	−18.5930	+	7.69352i	−0.802349	+	0.332000i
$538$	−1.57188	−	0.572119i	−0.0677688	−	0.0246658i
$539$	−17.7228	+	38.2585i	−0.763374	+	1.64791i
$540$	−8.23986	−	26.2338i	−0.354587	−	1.12892i
$541$	1.00845	+	1.74669i	0.0433568	+	0.0750962i	0.886889	−	0.461982i	$-0.152861\pi$
$541$	1.00845	+	1.74669i	0.0433568	+	0.0750962i	−0.843533	+	0.537078i	$0.819528\pi$
$542$	−4.06759	+	3.41312i	−0.174718	+	0.146606i
$543$	39.9850	−	16.5452i	1.71592	−	0.710023i
$544$	−0.446809	+	2.53398i	−0.0191568	+	0.108643i
$545$	−1.65700	+	9.39733i	−0.0709782	+	0.402537i
$546$	4.44004	+	2.06558i	0.190016	+	0.0883986i
$547$	11.8798	−	9.96834i	0.507944	−	0.426215i	−0.352461	−	0.935826i	$-0.614655\pi$
$547$	11.8798	−	9.96834i	0.507944	−	0.426215i	0.860405	+	0.509611i	$0.170211\pi$
$548$	12.7007	−	21.9983i	0.542548	−	0.939721i
$549$	9.10248	+	6.38356i	0.388485	+	0.272444i
$550$	−1.17871	−	2.04158i	−0.0502602	−	0.0870531i
$551$	4.32467	−	3.62883i	0.184237	−	0.154593i
$552$	0.937609	+	4.23661i	0.0399073	+	0.180322i
$553$	−3.30904	+	4.32372i	−0.140715	+	0.183863i
$554$	2.02233	−	0.736066i	0.0859204	−	0.0312725i
$555$	−4.88038	−	22.0522i	−0.207161	−	0.936062i
$556$	26.1530	+	9.51890i	1.10913	+	0.403691i
$557$	−12.5965	−	21.8177i	−0.533729	−	0.924445i	−0.999224	−	0.0393948i	$-0.987457\pi$
$557$	−12.5965	−	21.8177i	−0.533729	−	0.924445i	0.465495	−	0.885051i	$-0.345876\pi$
$558$	0.0510255	+	0.190988i	0.00216008	+	0.00808519i
$559$	26.4559	+	45.8230i	1.11897	+	1.93810i
$560$	−26.4769	+	5.90487i	−1.11885	+	0.249526i
$561$	12.9621	−	0.561190i	0.547262	−	0.0236934i
$562$	−5.03472	+	1.83249i	−0.212377	+	0.0772989i
$563$	−34.7761	+	12.6575i	−1.46564	+	0.533448i	−0.946912	−	0.321493i	$-0.895815\pi$
$563$	−34.7761	+	12.6575i	−1.46564	+	0.533448i	−0.518725	+	0.854941i	$0.673593\pi$
$564$	−0.683091	+	5.17396i	−0.0287633	+	0.217863i
$565$	7.79606	+	44.2136i	0.327983	+	1.86008i
$566$	0.998848			0.0419847
$567$	−5.14915	−	23.2484i	−0.216244	−	0.976339i
$568$	0.225749			0.00947222
$569$	−3.79960	−	21.5486i	−0.159288	−	0.903365i	−0.954761	−	0.297376i	$-0.903889\pi$
$569$	−3.79960	−	21.5486i	−0.159288	−	0.903365i	0.795473	−	0.605989i	$-0.207223\pi$
$570$	−0.315678	+	2.39106i	−0.0132223	+	0.100150i
$571$	27.4591	−	9.99428i	1.14913	−	0.418248i	0.303925	−	0.952696i	$-0.401703\pi$
$571$	27.4591	−	9.99428i	1.14913	−	0.418248i	0.845201	+	0.534448i	$0.179481\pi$
$572$	−67.6511	+	24.6230i	−2.82863	+	1.02954i
$573$	5.94679	−	0.257463i	0.248431	−	0.0107557i
$574$	1.20572	−	3.84097i	0.0503260	−	0.160319i
$575$	3.98540	+	6.90292i	0.166203	+	0.287872i
$576$	−15.4243	+	15.4017i	−0.642679	+	0.641740i
$577$	−14.3225	−	24.8072i	−0.596252	−	1.03274i	−0.993369	−	0.114971i	$-0.963323\pi$
$577$	−14.3225	−	24.8072i	−0.596252	−	1.03274i	0.397117	−	0.917768i	$-0.370011\pi$
$578$	−2.55644	−	0.930468i	−0.106334	−	0.0387024i
$579$	−7.09022	−	32.0373i	−0.294659	−	1.33143i
$580$	−9.53894	+	3.47189i	−0.396083	+	0.144162i
$581$	−10.2266	−	24.6012i	−0.424270	−	1.02063i
$582$	−0.355991	−	1.60856i	−0.0147563	−	0.0666768i
$583$	37.6106	−	31.5590i	1.55767	−	1.30704i
$584$	−1.69703	−	2.93935i	−0.0702237	−	0.121631i
$585$	44.3715	−	20.6513i	1.83454	−	0.853826i
$586$	1.77475	−	3.07396i	0.0733144	−	0.126984i
$587$	−11.7360	+	9.84769i	−0.484397	+	0.406458i	−0.852013	−	0.523520i	$-0.824619\pi$
$587$	−11.7360	+	9.84769i	−0.484397	+	0.406458i	0.367616	+	0.929978i	$0.380174\pi$
$588$	−23.6619	+	3.16715i	−0.975802	+	0.130611i
$589$	−0.191293	+	1.08487i	−0.00788208	+	0.0447015i
$590$	0.341545	−	1.93700i	0.0140612	−	0.0797450i
$591$	−12.8240	+	5.30638i	−0.527509	+	0.218275i
$592$	−14.1795	+	11.8980i	−0.582773	+	0.489005i
$593$	5.48163	+	9.49445i	0.225103	+	0.389890i	0.956350	−	0.292222i	$-0.0943947\pi$
$593$	5.48163	+	9.49445i	0.225103	+	0.389890i	−0.731247	+	0.682113i	$0.761061\pi$
$594$	−4.64382	−	2.96561i	−0.190538	−	0.121680i
$595$	0.396872	+	8.83389i	0.0162702	+	0.362154i
$596$	−33.7050	−	12.2676i	−1.38061	−	0.502501i
$597$	2.51224	−	1.03953i	0.102819	−	0.0425450i
$598$	−3.60033	+	1.31041i	−0.147228	+	0.0535867i
$599$	26.0096	+	21.8247i	1.06272	+	0.891732i	0.994374	−	0.105930i	$-0.0337819\pi$
$599$	26.0096	+	21.8247i	1.06272	+	0.891732i	0.0683508	+	0.997661i	$0.478226\pi$
$600$	1.24321	−	2.38605i	0.0507537	−	0.0974100i
$601$	−9.51678	+	7.98553i	−0.388198	+	0.325736i	−0.815911	−	0.578178i	$-0.803764\pi$
$601$	−9.51678	+	7.98553i	−0.388198	+	0.325736i	0.427713	+	0.903915i	$0.359319\pi$
$602$	3.60365	+	1.87016i	0.146874	+	0.0762221i
$603$	−5.11273	+	10.9434i	−0.208207	+	0.445649i
$604$	4.68195			0.190506
$605$	63.8496	+	23.2394i	2.59586	+	0.944815i
$606$	−0.109465	−	0.494622i	−0.00444672	−	0.0200926i
$607$	7.13805	+	5.98954i	0.289725	+	0.243108i	0.776052	−	0.630669i	$-0.217219\pi$
$607$	7.13805	+	5.98954i	0.289725	+	0.243108i	−0.486327	+	0.873777i	$0.661664\pi$
$608$	5.72208	−	2.08267i	0.232061	−	0.0844633i
$609$	−8.48893	+	2.28276i	−0.343989	+	0.0925023i
$610$	0.304476	+	1.72677i	0.0123279	+	0.0699149i
$611$	−9.28890			−0.375789
$612$	4.20905	+	6.02051i	0.170141	+	0.243365i
$613$	−10.4679			−0.422795			−0.211397	−	0.977400i	$-0.567801\pi$
$613$	−10.4679			−0.422795			−0.211397	+	0.977400i	$0.567801\pi$
$614$	0.642689	+	0.233920i	0.0259368	+	0.00944023i
$615$	−21.6056	−	33.9415i	−0.871224	−	1.36865i
$616$	−6.76755	+	8.84273i	−0.272672	+	0.356284i
$617$	−6.40756	−	5.37658i	−0.257959	−	0.216453i	0.504632	−	0.863335i	$-0.331628\pi$
$617$	−6.40756	−	5.37658i	−0.257959	−	0.216453i	−0.762590	+	0.646882i	$0.776073\pi$
$618$	−2.32554	+	0.962274i	−0.0935470	+	0.0387084i
$619$	12.0719	−	10.1295i	0.485210	−	0.407140i	−0.367096	−	0.930183i	$-0.619648\pi$
$619$	12.0719	−	10.1295i	0.485210	−	0.407140i	0.852306	+	0.523044i	$0.175203\pi$
$620$	0.990407	−	1.71544i	0.0397757	−	0.0688936i
$621$	15.7016	+	10.0272i	0.630082	+	0.402379i
$622$	−0.0586131			−0.00235017
$623$	−11.0309	+	2.46010i	−0.441943	+	0.0985619i
$624$	−31.8125	−	24.4291i	−1.27352	−	0.977945i
$625$	−5.41319	+	30.6998i	−0.216528	+	1.22799i
$626$	0.468423	+	0.393053i	0.0187219	+	0.0157096i
$627$	−16.4880	−	25.9018i	−0.658466	−	1.03442i
$628$	6.90064	+	2.51163i	0.275366	+	0.100225i
$629$	3.01688	+	5.22540i	0.120291	+	0.208350i
$630$	2.01610	−	3.16835i	0.0803232	−	0.126230i
$631$	−15.5729	+	26.9730i	−0.619947	+	1.07378i	0.369548	+	0.929212i	$0.379513\pi$
$631$	−15.5729	+	26.9730i	−0.619947	+	1.07378i	−0.989495	+	0.144568i	$0.953821\pi$
$632$	−1.10149	+	0.924262i	−0.0438150	+	0.0367652i
$633$	17.6368	+	5.56795i	0.700999	+	0.221306i
$634$	0.419229	−	2.37757i	0.0166497	−	0.0944252i
$635$	32.4629	+	27.2396i	1.28825	+	1.08097i
$636$	26.5087	+	8.36882i	1.05114	+	0.331845i
$637$	−11.1010	−	41.0150i	−0.439839	−	1.62507i
$638$	−1.01705	+	1.76158i	−0.0402654	+	0.0697418i
$639$	0.685874	−	0.684871i	0.0271327	−	0.0270931i
$640$	−14.5593			−0.575506
$641$	−3.08710	−	17.5078i	−0.121933	−	0.691517i	−0.983082	−	0.183165i	$-0.941366\pi$
$641$	−3.08710	−	17.5078i	−0.121933	−	0.691517i	0.861149	−	0.508352i	$-0.169745\pi$
$642$	0.640144	+	1.00564i	0.0252645	+	0.0396893i
$643$	7.38804	−	41.8996i	0.291356	−	1.65236i	−0.390300	−	0.920688i	$-0.627629\pi$
$643$	7.38804	−	41.8996i	0.291356	−	1.65236i	0.681656	−	0.731673i	$-0.261260\pi$
$644$	11.3518	−	14.8327i	0.447323	−	0.584489i
$645$	37.4939	−	15.5144i	1.47632	−	0.610880i
$646$	−0.111884	−	0.634524i	−0.00440200	−	0.0249650i
$647$	17.6945	−	30.6478i	0.695642	−	1.20489i	−0.274321	−	0.961638i	$-0.588453\pi$
$647$	17.6945	−	30.6478i	0.695642	−	1.20489i	0.969964	−	0.243250i	$-0.0782135\pi$
$648$	0.00920037	−	6.28851i	0.000361425	−	0.247036i
$649$	12.5201	+	21.6854i	0.491455	+	0.851226i
$650$	2.23240	+	0.812528i	0.0875620	+	0.0318700i
$651$	0.982602	−	1.40598i	0.0385112	−	0.0551048i
$652$	10.1475	+	8.51477i	0.397407	+	0.333464i
$653$	2.71012	−	0.986404i	0.106055	−	0.0386010i	−0.288447	−	0.957496i	$-0.593139\pi$
$653$	2.71012	−	0.986404i	0.106055	−	0.0386010i	0.394503	+	0.918895i	$0.370917\pi$
$654$	−0.500247	+	0.960109i	−0.0195612	+	0.0375432i
$655$	1.89726	+	10.7599i	0.0741320	+	0.420424i
$656$	−16.4870	+	28.5564i	−0.643710	+	1.11494i
$657$	−14.0732	−	3.78195i	−0.549049	−	0.147548i
$658$	−0.600648	+	0.383722i	−0.0234157	+	0.0149590i
$659$	4.36648	+	24.7636i	0.170094	+	0.964651i	0.943655	+	0.330930i	$0.107362\pi$
$659$	4.36648	+	24.7636i	0.170094	+	0.964651i	−0.773561	+	0.633721i	$0.781527\pi$
$660$	11.9299	+	53.9055i	0.464370	+	2.09827i
$661$	2.93132	−	16.6243i	0.114015	−	0.646612i	−0.873218	−	0.487330i	$-0.837971\pi$
$661$	2.93132	−	16.6243i	0.114015	−	0.646612i	0.987233	−	0.159282i	$-0.0509180\pi$
$662$	−0.535472	+	3.03681i	−0.0208117	+	0.118029i
$663$	−9.64299	+	8.82968i	−0.374503	+	0.342916i
$664$	−1.22179	−	6.92910i	−0.0474146	−	0.268901i
$665$	17.6354	−	11.2663i	0.683873	−	0.436890i
$666$	0.225200	−	2.55254i	0.00872631	−	0.0989088i
$667$	3.43882	−	5.95622i	0.133152	−	0.230626i
$668$	−4.80857	−	27.2707i	−0.186049	−	1.05514i
$669$	0.156033	+	0.245120i	0.00603257	+	0.00947689i
$670$	−1.79009	+	0.651540i	−0.0691573	+	0.0251712i
$671$	−17.1000	−	14.3486i	−0.660138	−	0.553921i
$672$	−9.44629	−	0.817906i	−0.364398	−	0.0315514i
$673$	−47.6825	−	17.3550i	−1.83802	−	0.668986i	−0.990371	−	0.138436i	$-0.955792\pi$
$673$	−47.6825	−	17.3550i	−1.83802	−	0.668986i	−0.847654	−	0.530550i	$-0.821985\pi$
$674$	−0.922463	−	1.59775i	−0.0355320	−	0.0615432i
$675$	−3.46159	−	11.0209i	−0.133237	−	0.424195i
$676$	23.4767	−	40.6629i	0.902951	−	1.56396i
$677$	3.50666	+	19.8872i	0.134772	+	0.764328i	0.975018	+	0.222124i	$0.0712990\pi$
$677$	3.50666	+	19.8872i	0.134772	+	0.764328i	−0.840247	+	0.542204i	$0.817590\pi$
$678$	−0.666697	+	5.04980i	−0.0256044	+	0.193936i
$679$	−8.68792	+	11.3520i	−0.333412	+	0.435648i
$680$	−0.405524	+	2.29984i	−0.0155511	+	0.0881949i
$681$	−10.5120	+	20.1753i	−0.402821	+	0.773121i
$682$	−0.0689243	−	0.390889i	−0.00263925	−	0.0149679i
$683$	−4.18921			−0.160296			−0.0801479	−	0.996783i	$-0.525539\pi$
$683$	−4.18921			−0.160296			−0.0801479	+	0.996783i	$0.525539\pi$
$684$	7.35855	−	15.7504i	0.281361	−	0.602231i
$685$	17.3358	−	30.0265i	0.662367	−	1.14725i
$686$	−2.41215	−	2.19357i	−0.0920961	−	0.0837510i
$687$	29.3967	−	26.9174i	1.12155	−	1.02696i
$688$	−25.4745	−	21.3756i	−0.971206	−	0.814938i
$689$	−8.59167	+	48.7258i	−0.327317	+	1.85630i
$690$	0.634896	+	2.86880i	0.0241701	+	0.109213i
$691$	−8.30107	+	6.96543i	−0.315788	+	0.264977i	−0.786879	−	0.617107i	$-0.788305\pi$
$691$	−8.30107	+	6.96543i	−0.315788	+	0.264977i	0.471092	+	0.882084i	$0.343860\pi$
$692$	18.3034	−	31.7025i	0.695792	−	1.20515i
$693$	6.26558	+	47.3973i	0.238010	+	1.80047i
$694$	2.24749	+	3.89276i	0.0853135	+	0.147767i
$695$	35.6974	+	12.9928i	1.35408	+	0.492844i
$696$	−2.31934	+	0.100414i	−0.0879142	+	0.00380620i
$697$	8.23396	+	6.90911i	0.311883	+	0.261701i
$698$	0.0981663	−	0.556729i	0.00371565	−	0.0210725i
$699$	−1.78475	+	13.5183i	−0.0675053	+	0.511308i
$700$	−11.3038	+	2.52096i	−0.427242	+	0.0952833i
$701$	−9.79318			−0.369883			−0.184942	−	0.982750i	$-0.559210\pi$
$701$	−9.79318			−0.369883			−0.184942	+	0.982750i	$0.559210\pi$
$702$	5.50596	−	0.718728i	0.207809	−	0.0271266i
$703$	7.13962	−	12.3662i	0.269276	−	0.466400i
$704$	33.5259	−	28.1316i	1.26356	−	1.06025i
$705$	−0.932382	+	7.06218i	−0.0351155	+	0.265977i
$706$	−2.31711	−	1.94429i	−0.0872058	−	0.0731743i
$707$	−2.67149	+	3.49067i	−0.100472	+	0.131280i
$708$	−6.55104	+	12.5732i	−0.246203	+	0.472530i
$709$	−31.8045	−	11.5759i	−1.19444	−	0.434741i	−0.333160	−	0.942870i	$-0.608115\pi$
$709$	−31.8045	−	11.5759i	−1.19444	−	0.434741i	−0.861281	+	0.508129i	$0.830337\pi$
$710$	0.152865			0.00573691
$711$	−0.542569	+	6.14978i	−0.0203479	+	0.230635i
$712$	−2.98474			−0.111858
$713$	0.233045	+	1.32166i	0.00872759	+	0.0494966i
$714$	−0.258792	+	0.969302i	−0.00968505	+	0.0362752i
$715$	−92.3401	+	33.6090i	−3.45332	+	1.25691i
$716$	17.5231	+	14.7036i	0.654868	+	0.549499i
$717$	−26.9350	+	24.6633i	−1.00591	+	0.921068i
$718$	3.50710	+	1.27648i	0.130884	+	0.0476378i
$719$	−35.7389			−1.33284			−0.666418	−	0.745579i	$-0.732173\pi$
$719$	−35.7389			−1.33284			−0.666418	+	0.745579i	$0.732173\pi$
$720$	−21.7662	+	21.7344i	−0.811178	+	0.809992i
$721$	19.3830	+	10.0591i	0.721862	+	0.374620i
$722$	1.39424	−	1.16991i	0.0518883	−	0.0435395i
$723$	2.64209	+	4.15060i	0.0982605	+	0.154363i
$724$	−37.6840	−	31.6206i	−1.40051	−	1.17517i
$725$	−4.00734	+	1.45855i	−0.148829	+	0.0541693i
$726$	6.11419	+	4.69513i	0.226919	+	0.174253i
$727$	10.8621	+	3.95349i	0.402854	+	0.146627i	0.535497	−	0.844537i	$-0.320124\pi$
$727$	10.8621	+	3.95349i	0.402854	+	0.146627i	−0.132643	+	0.991164i	$0.542347\pi$
$728$	−0.503631	−	11.2102i	−0.0186658	−	0.415478i
$729$	−19.0499	−	19.1337i	−0.705553	−	0.708657i
$730$	−1.14913	−	1.99036i	−0.0425314	−	0.0736665i
$731$	−8.30401	+	6.96789i	−0.307135	+	0.257717i
$732$	1.65427	−	12.5300i	0.0611437	−	0.463124i
$733$	4.30583	−	24.4196i	0.159039	−	0.901957i	−0.795960	−	0.605349i	$-0.793033\pi$
$733$	4.30583	−	24.4196i	0.159039	−	0.901957i	0.954999	−	0.296608i	$-0.0958554\pi$
$734$	0.611448	−	3.46769i	0.0225690	−	0.127995i
$735$	−32.2973	+	4.32299i	−1.19130	+	0.159456i
$736$	5.68281	−	4.76844i	0.209471	−	0.175767i
$737$	12.1260	−	21.0029i	0.446667	−	0.773650i
$738$	−1.17823	−	4.41012i	−0.0433713	−	0.162339i
$739$	16.9528	+	29.3632i	0.623620	+	1.08014i	0.988806	+	0.149207i	$0.0476721\pi$
$739$	16.9528	+	29.3632i	0.623620	+	1.08014i	−0.365186	+	0.930935i	$0.618995\pi$
$740$	−19.6687	+	16.5040i	−0.723035	+	0.606698i
$741$	29.5067	+	9.31531i	1.08396	+	0.342206i
$742$	1.45729	+	3.50567i	0.0534986	+	0.128697i
$743$	−11.2797	+	4.10548i	−0.413812	+	0.150615i	−0.540533	−	0.841323i	$-0.681777\pi$
$743$	−11.2797	+	4.10548i	−0.413812	+	0.150615i	0.126720	+	0.991939i	$0.459555\pi$
$744$	0.334100	−	0.305921i	0.0122487	−	0.0112156i
$745$	−46.0055	−	16.7446i	−1.68551	−	0.613476i
$746$	2.76114	+	4.78243i	0.101093	+	0.175097i
$747$	−24.7334	−	17.3455i	−0.904946	−	0.634637i
$748$	−7.37463	−	12.7732i	−0.269643	−	0.467036i
$749$	3.09795	−	9.86887i	0.113197	−	0.360601i
$750$	−1.05151	+	2.01812i	−0.0383956	+	0.0736915i
$751$	−28.8921	+	10.5159i	−1.05429	+	0.383729i	−0.810279	−	0.586044i	$-0.800684\pi$
$751$	−28.8921	+	10.5159i	−1.05429	+	0.383729i	−0.244008	+	0.969773i	$0.578462\pi$
$752$	5.48591	−	1.99671i	0.200051	−	0.0728125i
$753$	9.60345	−	3.97376i	0.349969	−	0.144812i
$754$	−0.355955	−	2.01872i	−0.0129631	−	0.0735174i
$755$	6.39061			0.232578
$756$	−20.7335	+	17.4033i	−0.754069	+	0.632952i
$757$	4.17342			0.151686			0.0758428	−	0.997120i	$-0.475835\pi$
$757$	4.17342			0.151686			0.0758428	+	0.997120i	$0.475835\pi$
$758$	−0.0741745	−	0.420665i	−0.00269414	−	0.0152792i
$759$	−29.6678	−	22.7822i	−1.07687	−	0.826941i
$760$	5.19337	−	1.89023i	0.188383	−	0.0685659i
$761$	7.31913	−	2.66395i	0.265318	−	0.0965680i	−0.205936	−	0.978566i	$-0.566024\pi$
$761$	7.31913	−	2.66395i	0.265318	−	0.0965680i	0.471254	+	0.881998i	$0.343802\pi$
$762$	2.58180	+	4.05588i	0.0935287	+	0.146929i
$763$	9.16851	−	2.04476i	0.331922	−	0.0740252i
$764$	−3.38335	−	5.86013i	−0.122405	−	0.212012i
$765$	5.74512	+	8.21768i	0.207715	+	0.297111i
$766$	−1.82823	−	3.16658i	−0.0660565	−	0.114413i
$767$	−23.7123	−	8.63058i	−0.856202	−	0.311632i
$768$	22.4265	+	7.08007i	0.809247	+	0.255480i
$769$	25.5217	−	9.28915i	0.920337	−	0.334975i	0.161965	−	0.986797i	$-0.448217\pi$
$769$	25.5217	−	9.28915i	0.920337	−	0.334975i	0.758373	+	0.651821i	$0.225995\pi$
$770$	−4.58260	+	5.98780i	−0.165146	+	0.215785i
$771$	−26.6714	+	24.4219i	−0.960548	+	0.879534i
$772$	−28.5746	+	23.9770i	−1.02842	+	0.862950i
$773$	−14.5035	−	25.1208i	−0.521654	−	0.903531i	−0.999683	−	0.0251869i	$-0.991982\pi$
$773$	−14.5035	−	25.1208i	−0.521654	−	0.903531i	0.478029	−	0.878344i	$-0.341351\pi$
$774$	4.58641	−	0.397878i	0.164855	−	0.0143014i
$775$	0.416073	−	0.720660i	0.0149458	−	0.0258869i
$776$	−2.89198	+	2.42666i	−0.103816	+	0.0871119i
$777$	−18.2017	+	12.7693i	−0.652982	+	0.458096i
$778$	−0.269301	+	1.52728i	−0.00965491	+	0.0547557i
$779$	4.41714	−	25.0509i	0.158261	−	0.897540i
$780$	−44.1278	−	33.8861i	−1.58003	−	1.21332i
$781$	−1.49080	+	1.25093i	−0.0533450	+	0.0447618i
$782$	−0.392471	−	0.679779i	−0.0140347	−	0.0243089i
$783$	−6.74200	+	7.34141i	−0.240939	+	0.262361i
$784$	15.3726	+	21.8368i	0.549021	+	0.779884i
$785$	9.41900	+	3.42824i	0.336179	+	0.122359i
$786$	−0.162248	+	1.22892i	−0.00578721	+	0.0438343i
$787$	22.4175	−	8.15931i	0.799099	−	0.290848i	0.0899856	−	0.995943i	$-0.471318\pi$
$787$	22.4175	−	8.15931i	0.799099	−	0.290848i	0.709113	+	0.705095i	$0.249096\pi$
$788$	12.0860	+	10.1414i	0.430546	+	0.361271i
$789$	3.25684	−	0.141003i	0.115947	−	0.00501986i
$790$	−0.745869	+	0.625859i	−0.0265368	+	0.0222670i
$791$	37.2452	−	23.7940i	1.32429	−	0.846016i
$792$	−1.10964	+	12.5773i	−0.0394295	+	0.446916i
$793$	22.4954			0.798834
$794$	−1.72829	−	0.629046i	−0.0613348	−	0.0223240i
$795$	36.1829	+	11.4230i	1.28328	+	0.405132i
$796$	−2.36767	−	1.98671i	−0.0839197	−	0.0704170i
$797$	−18.8510	+	6.86120i	−0.667736	+	0.243036i	−0.653573	−	0.756864i	$-0.726731\pi$
$797$	−18.8510	+	6.86120i	−0.667736	+	0.243036i	−0.0141634	+	0.999900i	$0.504509\pi$
$798$	2.29281	−	0.616560i	0.0811644	−	0.0218260i
$799$	−0.330458	−	1.87412i	−0.0116908	−	0.0663015i
$800$	−4.59981			−0.162628
$801$	−9.06828	+	9.05502i	−0.320412	+	0.319944i
$802$	2.87665			0.101578
$803$	27.4945	+	10.0072i	0.970258	+	0.353145i
$804$	13.7184	−	0.593932i	0.483812	−	0.0209464i
$805$	15.4946	−	20.2458i	0.546111	−	0.713570i
$806$	0.306413	+	0.257111i	0.0107929	+	0.00905636i
$807$	13.0532	+	10.0237i	0.459494	+	0.352849i
$808$	−0.889267	+	0.746183i	−0.0312843	+	0.0262506i
$809$	−26.9796	+	46.7300i	−0.948552	+	1.64294i	−0.200074	+	0.979781i	$0.564118\pi$
$809$	−26.9796	+	46.7300i	−0.948552	+	1.64294i	−0.748478	+	0.663160i	$0.769215\pi$
$810$	0.00622998	−	4.25823i	0.000218899	−	0.149619i
$811$	−25.5051			−0.895604			−0.447802	−	0.894133i	$-0.647793\pi$
$811$	−25.5051			−0.895604			−0.447802	+	0.894133i	$0.647793\pi$
$812$	6.76054	+	7.35916i	0.237249	+	0.258256i
$813$	48.2727	−	19.9745i	1.69300	−	0.700537i
$814$	−0.893407	+	5.06677i	−0.0313139	+	0.177590i
$815$	13.8508	+	11.6222i	0.485172	+	0.407108i
$816$	3.79704	−	7.28753i	0.132923	−	0.255115i
$817$	24.1066	+	8.77409i	0.843384	+	0.306967i
$818$	0.429658	+	0.744190i	0.0150227	+	0.0260200i
$819$	−35.5393	−	32.5311i	−1.24184	−	1.13673i
$820$	−22.8695	+	39.6112i	−0.798638	+	1.38328i
$821$	−16.9342	+	14.2095i	−0.591008	+	0.495914i	−0.888541	−	0.458797i	$-0.848280\pi$
$821$	−16.9342	+	14.2095i	−0.591008	+	0.495914i	0.297533	+	0.954711i	$0.403836\pi$
$822$	2.90116	−	2.65647i	0.101190	−	0.0926551i
$823$	−1.32797	+	7.53132i	−0.0462903	+	0.262525i	−0.999166	−	0.0408362i	$-0.986998\pi$
$823$	−1.32797	+	7.53132i	−0.0462903	+	0.262525i	0.952876	+	0.303361i	$0.0981089\pi$
$824$	4.41792	+	3.70708i	0.153906	+	0.129142i
$825$	5.01178	+	22.6459i	0.174488	+	0.788428i
$826$	−1.88983	+	0.421471i	−0.0657558	+	0.0146648i
$827$	18.5067	−	32.0546i	0.643541	−	1.11465i	−0.341095	−	0.940029i	$-0.610798\pi$
$827$	18.5067	−	32.0546i	0.643541	−	1.11465i	0.984636	−	0.174617i	$-0.0558688\pi$
$828$	1.86130	−	21.0970i	0.0646847	−	0.733172i
$829$	35.6050			1.23661			0.618306	−	0.785937i	$-0.287819\pi$
$829$	35.6050			1.23661			0.618306	+	0.785937i	$0.287819\pi$
$830$	−0.827326	−	4.69200i	−0.0287169	−	0.162862i
$831$	−21.1542	+	0.915858i	−0.733829	+	0.0317708i
$832$	−7.65858	+	43.4340i	−0.265514	+	1.50580i
$833$	7.88022	−	3.69887i	0.273034	−	0.128158i
$834$	3.41835	+	2.62498i	0.118368	+	0.0908956i
$835$	−6.56343	−	37.2231i	−0.227137	−	1.28816i
$836$	−17.4525	+	30.2286i	−0.603607	+	1.04548i
$837$	0.0869710	−	1.94304i	0.00300616	−	0.0671611i
$838$	2.52155	+	4.36746i	0.0871057	+	0.150871i
$839$	27.0935	+	9.86122i	0.935371	+	0.340447i	0.764336	−	0.644818i	$-0.223067\pi$
$839$	27.0935	+	9.86122i	0.935371	+	0.340447i	0.171034	+	0.985265i	$0.445289\pi$
$840$	−8.57347	−	0.742333i	−0.295813	−	0.0256129i
$841$	−19.3965	−	16.2756i	−0.668845	−	0.561228i
$842$	0.134172	−	0.0488347i	0.00462388	−	0.00168296i
$843$	52.6647	−	2.28009i	1.81387	−	0.0785306i
$844$	−3.65096	−	20.7056i	−0.125671	−	0.712717i
$845$	32.0445	−	55.5026i	1.10236	−	1.90935i
$846$	−0.342091	+	0.732217i	−0.0117613	+	0.0251741i
$847$	−3.00206	−	66.8222i	−0.103152	−	2.29604i
$848$	−5.39979	−	30.6237i	−0.185429	−	1.05162i
$849$	−9.37142	−	2.95857i	−0.321626	−	0.101538i
$850$	−0.0845159	+	0.479313i	−0.00289887	+	0.0164403i
$851$	3.02076	−	17.1316i	0.103550	−	0.587264i
$852$	−1.05075	−	0.331722i	−0.0359980	−	0.0113646i
$853$	5.69579	+	32.3025i	0.195020	+	1.10601i	0.912390	+	0.409322i	$0.134235\pi$
$853$	5.69579	+	32.3025i	0.195020	+	1.10601i	−0.717370	+	0.696693i	$0.754654\pi$
$854$	1.45462	−	0.929278i	0.0497760	−	0.0317992i
$855$	10.0440	−	21.4984i	0.343498	−	0.735230i
$856$	1.36585	−	2.36572i	0.0466837	−	0.0808585i
$857$	5.03409	+	28.5497i	0.171961	+	0.975240i	0.941593	+	0.336752i	$0.109328\pi$
$857$	5.03409	+	28.5497i	0.171961	+	0.975240i	−0.769632	+	0.638487i	$0.779560\pi$
$858$	−11.1383	+	0.482227i	−0.380256	+	0.0164630i
$859$	−25.2646	+	9.19558i	−0.862019	+	0.313749i	−0.734931	−	0.678142i	$-0.762785\pi$
$859$	−25.2646	+	9.19558i	−0.862019	+	0.313749i	−0.127088	+	0.991891i	$0.540563\pi$
$860$	−35.3362	−	29.6506i	−1.20496	−	1.01108i
$861$	−22.6893	+	32.4656i	−0.773249	+	1.10642i
$862$	−2.20243	−	0.801620i	−0.0750152	−	0.0273033i
$863$	20.0602	+	34.7453i	0.682858	+	1.18275i	0.974105	+	0.226097i	$0.0725967\pi$
$863$	20.0602	+	34.7453i	0.682858	+	1.18275i	−0.291247	+	0.956648i	$0.594070\pi$
$864$	−9.54184	+	4.95387i	−0.324620	+	0.168534i
$865$	24.9832	−	43.2722i	0.849454	−	1.47130i
$866$	0.611870	+	3.47009i	0.0207922	+	0.117918i
$867$	21.2291	+	16.3020i	0.720978	+	0.553645i
$868$	−1.93362	−	0.252082i	−0.0656312	−	0.00855622i
$869$	2.15247	−	12.2073i	0.0730176	−	0.414103i
$870$	−1.57052	+	0.0679951i	−0.0532458	+	0.00230525i
$871$	4.24394	+	24.0686i	0.143801	+	0.815534i
$872$	2.48082			0.0840112
$873$	−1.42452	+	16.1463i	−0.0482127	+	0.546469i
$874$	−0.928804	+	1.60874i	−0.0314173	+	0.0544163i
$875$	19.2720	−	4.29803i	0.651511	−	0.145300i
$876$	3.57966	+	16.1748i	0.120946	+	0.546496i
$877$	3.42798	+	2.87642i	0.115755	+	0.0971298i	0.698828	−	0.715290i	$-0.253705\pi$
$877$	3.42798	+	2.87642i	0.115755	+	0.0971298i	−0.583073	+	0.812420i	$0.698150\pi$
$878$	0.248819	−	1.41112i	0.00839722	−	0.0476230i
$879$	−25.7562	+	23.5839i	−0.868734	+	0.795464i
$880$	47.3105	−	39.6982i	1.59484	−	1.33823i
$881$	28.6467	−	49.6176i	0.965132	−	1.67166i	0.255874	−	0.966710i	$-0.417637\pi$
$881$	28.6467	−	49.6176i	0.965132	−	1.67166i	0.709259	−	0.704948i	$-0.249030\pi$
$882$	−3.64193	−	0.635436i	−0.122630	−	0.0213962i
$883$	24.0480	+	41.6524i	0.809280	+	1.40171i	0.913364	+	0.407145i	$0.133476\pi$
$883$	24.0480	+	41.6524i	0.809280	+	1.40171i	−0.104084	+	0.994569i	$0.533191\pi$
$884$	13.9672	+	5.08363i	0.469766	+	0.170981i
$885$	−8.94182	+	17.1617i	−0.300576	+	0.576886i
$886$	4.09612	+	3.43705i	0.137612	+	0.115470i
$887$	−6.80693	+	38.6040i	−0.228554	+	1.29620i	0.627219	+	0.778843i	$0.284193\pi$
$887$	−6.80693	+	38.6040i	−0.228554	+	1.29620i	−0.855773	+	0.517352i	$0.826918\pi$
$888$	−5.42573	+	2.24509i	−0.182076	+	0.0753401i
$889$	12.4945	−	39.8026i	0.419052	−	1.33494i
$890$	−2.02110			−0.0677474
$891$	34.7854	+	41.5790i	1.16535	+	1.39295i
$892$	0.165160	−	0.286066i	0.00552997	−	0.00957819i
$893$	−3.44998	+	2.89487i	−0.115449	+	0.0968733i
$894$	−4.40545	−	3.38298i	−0.147340	−	0.113144i
$895$	23.9180	+	20.0696i	0.799492	+	0.670853i
$896$	5.50158	+	13.2347i	0.183795	+	0.442140i
$897$	37.6605	−	1.63049i	1.25745	−	0.0544406i
$898$	4.35828	+	1.58628i	0.145438	+	0.0529350i
$899$	−0.718021			−0.0239474
$900$	−9.29261	+	9.27902i	−0.309754	+	0.309301i
$901$	−10.1365			−0.337696
$902$	1.59153	+	9.02603i	0.0529922	+	0.300534i
$903$	−28.2709	−	28.2202i	−0.940797	−	0.939111i
$904$	10.9682	−	3.99208i	0.364795	−	0.132775i
$905$	−51.4366	−	43.1605i	−1.70981	−	1.43470i
$906$	0.691406	+	0.218278i	0.0229704	+	0.00725179i
$907$	−24.0838	−	8.76579i	−0.799689	−	0.291063i	−0.0903317	−	0.995912i	$-0.528793\pi$
$907$	−24.0838	−	8.76579i	−0.799689	−	0.291063i	−0.709358	+	0.704849i	$0.751015\pi$
$908$	25.8620			0.858260
$909$	−0.438032	+	4.96489i	−0.0145286	+	0.164675i
$910$	−0.341031	−	7.59092i	−0.0113051	−	0.251637i
$911$	−8.76645	+	7.35592i	−0.290445	+	0.243713i	−0.776354	−	0.630297i	$-0.782933\pi$
$911$	−8.76645	+	7.35592i	−0.290445	+	0.243713i	0.485909	+	0.874010i	$0.338489\pi$
$912$	−19.4287	+	0.841157i	−0.643349	+	0.0278535i
$913$	46.4642	+	38.9881i	1.53774	+	1.29032i
$914$	1.67517	−	0.609714i	0.0554098	−	0.0201675i
$915$	2.25799	−	17.1028i	0.0746470	−	0.565402i
$916$	−42.5790	−	15.4975i	−1.40685	−	0.512051i
$917$	9.06404	−	5.79053i	0.299321	−	0.191220i
$918$	0.340887	+	1.08531i	0.0112510	+	0.0358205i
$919$	9.50561	+	16.4642i	0.313561	+	0.543104i	0.979131	−	0.203232i	$-0.0651446\pi$
$919$	9.50561	+	16.4642i	0.313561	+	0.543104i	−0.665569	+	0.746336i	$0.731811\pi$
$920$	5.15773	−	4.32785i	0.170045	−	0.142685i
$921$	−5.33700	−	4.09832i	−0.175860	−	0.135044i
$922$	0.443037	−	2.51259i	0.0145906	−	0.0827477i
$923$	0.340555	−	1.93138i	0.0112095	−	0.0635722i
$924$	44.4932	−	31.2140i	1.46372	−	1.02686i
$925$	−8.26287	+	6.93337i	−0.271682	+	0.227968i
$926$	−3.21310	+	5.56524i	−0.105589	+	0.182885i
$927$	24.6690	−	2.14008i	0.810237	−	0.0702893i
$928$	1.98448	+	3.43723i	0.0651439	+	0.112832i
$929$	−32.8330	+	27.5502i	−1.07722	+	0.903891i	−0.995687	−	0.0927796i	$-0.970425\pi$
$929$	−32.8330	+	27.5502i	−1.07722	+	0.903891i	−0.0815291	+	0.996671i	$0.525980\pi$
$930$	0.226234	−	0.207153i	0.00741849	−	0.00679280i
$931$	−16.9053	−	11.7737i	−0.554049	−	0.385868i
$932$	14.5662	−	5.30167i	0.477132	−	0.173662i
$933$	0.549922	+	0.173611i	0.0180036	+	0.00568377i
$934$	5.35689	+	1.94975i	0.175283	+	0.0637977i
$935$	−10.0660	−	17.4348i	−0.329193	−	0.570178i
$936$	−7.29056	−	10.4282i	−0.238299	−	0.340857i
$937$	−14.2060	−	24.6055i	−0.464090	−	0.803828i	0.535070	−	0.844808i	$-0.320285\pi$
$937$	−14.2060	−	24.6055i	−0.464090	−	0.803828i	−0.999160	+	0.0409802i	$0.986952\pi$
$938$	1.26869	+	1.38103i	0.0414243	+	0.0450923i
$939$	−3.23064	−	5.07518i	−0.105428	−	0.165622i
$940$	7.60964	−	2.76968i	0.248199	−	0.0903370i
$941$	7.16820	−	2.60901i	0.233677	−	0.0850513i	−0.222528	−	0.974926i	$-0.571431\pi$
$941$	7.16820	−	2.60901i	0.233677	−	0.0850513i	0.456204	+	0.889875i	$0.349209\pi$
$942$	0.901956	+	0.692619i	0.0293873	+	0.0225668i
$943$	−5.38124	−	30.5185i	−0.175237	−	0.993820i
$944$	15.8594			0.516180
$945$	−28.3001	+	23.7546i	−0.920601	+	0.772736i
$946$	−9.24325			−0.300524
$947$	−9.36413	−	53.1066i	−0.304293	−	1.72573i	−0.626812	−	0.779170i	$-0.715641\pi$
$947$	−9.36413	−	53.1066i	−0.304293	−	1.72573i	0.322519	−	0.946563i	$-0.395470\pi$
$948$	6.48502	−	2.68340i	0.210624	−	0.0871529i
$949$	−27.7075	+	10.0847i	−0.899422	+	0.327363i
$950$	1.08236	−	0.393946i	0.0351163	−	0.0127813i
$951$	−10.9756	+	21.0651i	−0.355909	+	0.683084i
$952$	2.24384	−	0.500421i	0.0727233	−	0.0162187i
$953$	−16.1132	−	27.9088i	−0.521957	−	0.904056i	−0.999674	−	0.0255420i	$-0.991869\pi$
$953$	−16.1132	−	27.9088i	−0.521957	−	0.904056i	0.477717	−	0.878514i	$-0.341464\pi$
$954$	3.52450	+	2.47173i	0.114110	+	0.0800251i
$955$	−4.61808	−	7.99876i	−0.149438	−	0.258834i
$956$	39.0134	+	14.1997i	1.26178	+	0.459252i
$957$	14.7600	−	13.5151i	0.477123	−	0.436881i
$958$	−5.72614	+	2.08415i	−0.185003	+	0.0673357i
$959$	−33.8455	−	4.41237i	−1.09293	−	0.142483i
$960$	32.2533	+	10.1824i	1.04097	+	0.328636i
$961$	−23.6400	+	19.8364i	−0.762582	+	0.639882i
$962$	−2.59239	−	4.49016i	−0.0835821	−	0.144768i
$963$	−3.02731	−	11.3312i	−0.0975536	−	0.365143i
$964$	2.79665	−	4.84394i	0.0900740	−	0.156013i
$965$	−39.0028	+	32.7273i	−1.25555	+	1.05353i
$966$	2.36788	−	1.66118i	0.0761854	−	0.0534475i
$967$	−9.39938	+	53.3065i	−0.302264	+	1.71422i	0.333850	+	0.942626i	$0.391652\pi$
$967$	−9.39938	+	53.3065i	−0.302264	+	1.71422i	−0.636113	+	0.771596i	$0.719459\pi$
$968$	3.06751	−	17.3967i	0.0985934	−	0.559151i
$969$	−0.829728	+	6.28465i	−0.0266547	+	0.201892i
$970$	−1.95828	+	1.64320i	−0.0628767	+	0.0527598i
$971$	18.6096	+	32.2328i	0.597212	+	1.03440i	0.993231	+	0.116159i	$0.0370582\pi$
$971$	18.6096	+	32.2328i	0.597212	+	1.03440i	−0.396019	+	0.918242i	$0.629608\pi$
$972$	−9.28332	+	29.2563i	−0.297763	+	0.938395i
$973$	−1.67841	−	37.3593i	−0.0538073	−	1.19768i
$974$	2.70487	+	0.984492i	0.0866696	+	0.0315451i
$975$	−18.5382	−	14.2357i	−0.593699	−	0.455906i
$976$	−13.2855	+	4.83553i	−0.425259	+	0.154782i
$977$	−21.1925	−	17.7826i	−0.678009	−	0.568917i	0.237415	−	0.971408i	$-0.423700\pi$
$977$	−21.1925	−	17.7826i	−0.678009	−	0.568917i	−0.915424	+	0.402492i	$0.868144\pi$
$978$	1.10156	+	1.73050i	0.0352241	+	0.0553354i
$979$	19.7106	−	16.5392i	0.629954	−	0.528594i
$980$	21.3237	+	30.2903i	0.681160	+	0.967587i
$981$	7.53726	−	7.52624i	0.240646	−	0.240294i
$982$	−4.52990			−0.144555
$983$	41.9794	+	15.2793i	1.33894	+	0.487333i	0.909477	−	0.415754i	$-0.136482\pi$
$983$	41.9794	+	15.2793i	1.33894	+	0.487333i	0.429458	+	0.903087i	$0.358705\pi$
$984$	−7.71471	+	7.06404i	−0.245936	+	0.225193i
$985$	16.4968	+	13.8424i	0.525630	+	0.441056i
$986$	0.394631	−	0.143634i	0.0125676	−	0.00457424i
$987$	6.77199	−	1.82106i	0.215555	−	0.0579650i
$988$	−6.10814	−	34.6410i	−0.194326	−	1.10208i
$989$	31.2530			0.993787
$990$	−0.751389	+	8.51666i	−0.0238807	+	0.270677i
$991$	−38.5402			−1.22427			−0.612134	−	0.790754i	$-0.709689\pi$
$991$	−38.5402			−1.22427			−0.612134	+	0.790754i	$0.709689\pi$
$992$	−0.727767	−	0.264886i	−0.0231066	−	0.00841013i
$993$	14.0189	−	26.9061i	0.444877	−	0.853838i
$994$	−0.0577636	−	0.138957i	−0.00183215	−	0.00440745i
$995$	−3.23174	−	2.71175i	−0.102453	−	0.0859682i
$996$	−4.49501	+	34.0467i	−0.142430	+	1.07881i
$997$	−17.8642	+	14.9898i	−0.565765	+	0.474733i	−0.880238	−	0.474533i	$-0.842617\pi$
$997$	−17.8642	+	14.9898i	−0.565765	+	0.474733i	0.314472	+	0.949267i	$0.398172\pi$
$998$	2.02203	−	3.50226i	0.0640062	−	0.110862i
$999$	−9.67344	+	23.2815i	−0.306054	+	0.736593i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.4.11	✓	132
3.2	odd	2		567.2.u.a.550.12		132
7.2	even	3		189.2.w.a.58.11	yes	132
21.2	odd	6		567.2.w.a.226.12		132
27.7	even	9		189.2.w.a.88.11	yes	132
27.20	odd	18		567.2.w.a.424.12		132
189.128	odd	18		567.2.u.a.100.12		132
189.142	even	9	inner	189.2.u.a.142.11	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.4.11	✓	132	1.1	even	1	trivial
189.2.u.a.142.11	yes	132	189.142	even	9	inner
189.2.w.a.58.11	yes	132	7.2	even	3
189.2.w.a.88.11	yes	132	27.7	even	9
567.2.u.a.100.12		132	189.128	odd	18
567.2.u.a.550.12		132	3.2	odd	2
567.2.w.a.226.12		132	21.2	odd	6
567.2.w.a.424.12		132	27.20	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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0305699 - 0.173370i) q^{2} +(-0.226706 + 1.71715i) q^{3} +(1.85026 - 0.673440i) q^{4} +(2.52551 - 0.919210i) q^{5} +(0.304634 - 0.0131890i) q^{6} +(-1.78991 - 1.94839i) q^{7} +(-0.349362 - 0.605113i) q^{8} +(-2.89721 - 0.778577i) q^{9} +O(q^{10})\)	\(q+(-0.0305699 - 0.173370i) q^{2} +(-0.226706 + 1.71715i) q^{3} +(1.85026 - 0.673440i) q^{4} +(2.52551 - 0.919210i) q^{5} +(0.304634 - 0.0131890i) q^{6} +(-1.78991 - 1.94839i) q^{7} +(-0.349362 - 0.605113i) q^{8} +(-2.89721 - 0.778577i) q^{9} +(-0.236568 - 0.409748i) q^{10} +(5.66019 + 2.06014i) q^{11} +(0.736933 + 3.32985i) q^{12} +(-5.70404 + 2.07610i) q^{13} +(-0.283077 + 0.369879i) q^{14} +(1.00587 + 4.54507i) q^{15} +(2.92247 - 2.45224i) q^{16} +(-0.621796 - 1.07698i) q^{17} +(-0.0464149 + 0.526091i) q^{18} +(-1.47151 + 2.54874i) q^{19} +(4.05382 - 3.40156i) q^{20} +(3.75147 - 2.63182i) q^{21} +(0.184136 - 1.04429i) q^{22} +(-0.622595 + 3.53091i) q^{23} +(1.11827 - 0.462724i) q^{24} +(1.70302 - 1.42901i) q^{25} +(0.534306 + 0.925446i) q^{26} +(1.99375 - 4.79843i) q^{27} +(-4.62392 - 2.39965i) q^{28} +(-1.80256 - 0.656078i) q^{29} +(0.757231 - 0.313331i) q^{30} +(0.351738 - 0.128022i) q^{31} +(-1.58499 - 1.32997i) q^{32} +(-4.82077 + 9.25234i) q^{33} +(-0.167709 + 0.140724i) q^{34} +(-6.31140 - 3.27539i) q^{35} +(-5.88492 + 0.510526i) q^{36} -4.85189 q^{37} +(0.486860 + 0.177203i) q^{38} +(-2.27184 - 10.2654i) q^{39} +(-1.43854 - 1.20708i) q^{40} +(-8.12199 + 2.95616i) q^{41} +(-0.570962 - 0.569939i) q^{42} +(-1.51365 - 8.58435i) q^{43} +11.8602 q^{44} +(-8.03260 + 0.696841i) q^{45} +0.631189 q^{46} +(1.43798 + 0.523383i) q^{47} +(3.54832 + 5.57425i) q^{48} +(-0.592478 + 6.97488i) q^{49} +(-0.299809 - 0.251569i) q^{50} +(1.99031 - 0.823559i) q^{51} +(-9.15584 + 7.68266i) q^{52} +(4.07550 - 7.05897i) q^{53} +(-0.892855 - 0.198969i) q^{54} +16.1885 q^{55} +(-0.553673 + 1.76379i) q^{56} +(-4.04297 - 3.10463i) q^{57} +(-0.0586405 + 0.332567i) q^{58} +(3.18453 + 2.67214i) q^{59} +(4.92196 + 7.73217i) q^{60} +(-3.48243 - 1.26750i) q^{61} +(-0.0329478 - 0.0570673i) q^{62} +(3.66876 + 7.03848i) q^{63} +(3.63289 - 6.29234i) q^{64} +(-12.4972 + 10.4864i) q^{65} +(1.75145 + 0.552936i) q^{66} +(0.699154 - 3.96510i) q^{67} +(-1.87577 - 1.57396i) q^{68} +(-5.92196 - 1.86957i) q^{69} +(-0.374916 + 1.19434i) q^{70} +(-0.161544 + 0.279802i) q^{71} +(0.541048 + 2.02514i) q^{72} +4.85752 q^{73} +(0.148322 + 0.841174i) q^{74} +(2.06773 + 3.24831i) q^{75} +(-1.00627 + 5.70681i) q^{76} +(-6.11724 - 14.7157i) q^{77} +(-1.71026 + 0.707680i) q^{78} +(-0.357349 - 2.02663i) q^{79} +(5.12659 - 8.87951i) q^{80} +(7.78764 + 4.51140i) q^{81} +(0.760800 + 1.31774i) q^{82} +(9.46250 + 3.44407i) q^{83} +(5.16882 - 7.39595i) q^{84} +(-2.56032 - 2.14837i) q^{85} +(-1.44200 + 0.524845i) q^{86} +(1.53524 - 2.94653i) q^{87} +(-0.730838 - 4.14479i) q^{88} +(2.13585 - 3.69941i) q^{89} +(0.366367 + 1.37131i) q^{90} +(14.2547 + 7.39769i) q^{91} +(1.22590 + 6.95240i) q^{92} +(0.140092 + 0.633010i) q^{93} +(0.0467801 - 0.265303i) q^{94} +(-1.37350 + 7.78949i) q^{95} +(2.64308 - 2.42016i) q^{96} +(-0.938221 - 5.32092i) q^{97} +(1.22735 - 0.110503i) q^{98} +(-14.7948 - 10.3755i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

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