LMFDB - Embedded newform 189.2.w.a.25.17

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			25.17
Character	$\chi$	$=$	189.25
Dual form			189.2.w.a.121.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45469 - 0.529465i) q^{2} +(1.56527 - 0.741574i) q^{3} +(0.303710 - 0.254843i) q^{4} +(0.0676746 + 0.0246315i) q^{5} +(1.88435 - 1.90752i) q^{6} +(-1.36843 - 2.26438i) q^{7} +(-1.24118 + 2.14978i) q^{8} +(1.90014 - 2.32153i) q^{9} +O(q^{10})$	\(q+(1.45469 - 0.529465i) q^{2} +(1.56527 - 0.741574i) q^{3} +(0.303710 - 0.254843i) q^{4} +(0.0676746 + 0.0246315i) q^{5} +(1.88435 - 1.90752i) q^{6} +(-1.36843 - 2.26438i) q^{7} +(-1.24118 + 2.14978i) q^{8} +(1.90014 - 2.32153i) q^{9} +0.111487 q^{10} +(-1.79971 + 0.655041i) q^{11} +(0.286404 - 0.624122i) q^{12} +(0.966188 + 5.47952i) q^{13} +(-3.18955 - 2.56944i) q^{14} +(0.124195 - 0.0116307i) q^{15} +(-0.804989 + 4.56532i) q^{16} +4.93976 q^{17} +(1.53495 - 4.38316i) q^{18} -5.41589 q^{19} +(0.0268307 - 0.00976556i) q^{20} +(-3.82116 - 2.52957i) q^{21} +(-2.27121 + 1.90577i) q^{22} +(-0.174590 - 0.990152i) q^{23} +(-0.348555 + 4.28541i) q^{24} +(-3.82625 - 3.21060i) q^{25} +(4.30672 + 7.45946i) q^{26} +(1.25264 - 5.04290i) q^{27} +(-0.992667 - 0.338981i) q^{28} +(0.0487538 - 0.276497i) q^{29} +(0.174508 - 0.0826761i) q^{30} +(-3.39416 + 2.84804i) q^{31} +(0.384052 + 2.17807i) q^{32} +(-2.33127 + 2.35993i) q^{33} +(7.18583 - 2.61543i) q^{34} +(-0.0368325 - 0.186947i) q^{35} +(-0.0145337 - 1.18931i) q^{36} +(3.95813 - 6.85568i) q^{37} +(-7.87846 + 2.86752i) q^{38} +(5.57581 + 7.86043i) q^{39} +(-0.136949 + 0.114914i) q^{40} +(0.363141 + 2.05947i) q^{41} +(-6.89793 - 1.65659i) q^{42} +(-4.72363 - 3.96360i) q^{43} +(-0.379658 + 0.657587i) q^{44} +(0.185774 - 0.110305i) q^{45} +(-0.778226 - 1.34793i) q^{46} +(9.88425 + 8.29387i) q^{47} +(2.12550 + 7.74291i) q^{48} +(-3.25482 + 6.19727i) q^{49} +(-7.26592 - 2.64458i) q^{50} +(7.73205 - 3.66319i) q^{51} +(1.68986 + 1.41796i) q^{52} +(5.67550 - 9.83026i) q^{53} +(-0.847828 - 7.99911i) q^{54} -0.137929 q^{55} +(6.56638 - 0.131321i) q^{56} +(-8.47733 + 4.01628i) q^{57} +(-0.0754735 - 0.428031i) q^{58} +(-0.724927 - 4.11127i) q^{59} +(0.0347553 - 0.0351827i) q^{60} +(4.52663 + 3.79830i) q^{61} +(-3.42953 + 5.94011i) q^{62} +(-7.85701 - 1.12580i) q^{63} +(-2.92386 - 5.06427i) q^{64} +(-0.0695827 + 0.394623i) q^{65} +(-2.14178 + 4.66731i) q^{66} +(-9.06882 - 3.30078i) q^{67} +(1.50025 - 1.25886i) q^{68} +(-1.00755 - 1.42038i) q^{69} +(-0.152562 - 0.252450i) q^{70} +(4.37580 + 7.57911i) q^{71} +(2.63237 + 6.96631i) q^{72} +(-2.67582 - 4.63466i) q^{73} +(2.12802 - 12.0686i) q^{74} +(-8.37001 - 2.18802i) q^{75} +(-1.64486 + 1.38020i) q^{76} +(3.94603 + 3.17885i) q^{77} +(12.2729 + 8.48232i) q^{78} +(0.626732 - 0.228112i) q^{79} +(-0.166928 + 0.289128i) q^{80} +(-1.77896 - 8.82243i) q^{81} +(1.61868 + 2.80363i) q^{82} +(0.402782 - 2.28429i) q^{83} +(-1.80517 + 0.205538i) q^{84} +(0.334296 + 0.121674i) q^{85} +(-8.97002 - 3.26482i) q^{86} +(-0.128730 - 0.468946i) q^{87} +(0.825564 - 4.68201i) q^{88} +3.95600 q^{89} +(0.211841 - 0.258821i) q^{90} +(11.0856 - 9.68613i) q^{91} +(-0.305358 - 0.256226i) q^{92} +(-3.20075 + 6.97497i) q^{93} +(18.7699 + 6.83167i) q^{94} +(-0.366518 - 0.133402i) q^{95} +(2.21634 + 3.12446i) q^{96} +(8.01916 + 6.72888i) q^{97} +(-1.45353 + 10.7384i) q^{98} +(-1.89900 + 5.42274i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.45469	−	0.529465i	1.02862	−	0.374388i	0.228067	−	0.973645i	$-0.426760\pi$
$2$	1.45469	−	0.529465i	1.02862	−	0.374388i	0.800557	+	0.599257i	$0.204537\pi$
$3$	1.56527	−	0.741574i	0.903709	−	0.428148i
$3$	1.56527	−	0.741574i	0.903709	−	0.428148i
$4$	0.303710	−	0.254843i	0.151855	−	0.127422i
$5$	0.0676746	+	0.0246315i	0.0302650	+	0.0110156i	0.357108	−	0.934063i	$-0.383763\pi$
$5$	0.0676746	+	0.0246315i	0.0302650	+	0.0110156i	−0.326843	+	0.945079i	$0.605985\pi$
$6$	1.88435	−	1.90752i	0.769283	−	0.778741i
$7$	−1.36843	−	2.26438i	−0.517216	−	0.855855i
$7$	−1.36843	−	2.26438i	−0.517216	−	0.855855i
$8$	−1.24118	+	2.14978i	−0.438822	+	0.760063i
$9$	1.90014	−	2.32153i	0.633379	−	0.773842i
$10$	0.111487			0.0352554
$11$	−1.79971	+	0.655041i	−0.542633	+	0.197502i	−0.598770	−	0.800921i	$-0.704344\pi$
$11$	−1.79971	+	0.655041i	−0.542633	+	0.197502i	0.0561372	+	0.998423i	$0.482122\pi$
$12$	0.286404	−	0.624122i	0.0826776	−	0.180168i
$13$	0.966188	+	5.47952i	0.267972	+	1.51975i	0.760436	+	0.649413i	$0.224985\pi$
$13$	0.966188	+	5.47952i	0.267972	+	1.51975i	−0.492463	+	0.870333i	$0.663903\pi$
$14$	−3.18955	−	2.56944i	−0.852443	−	0.686713i
$15$	0.124195	−	0.0116307i	0.0320670	−	0.00300304i
$16$	−0.804989	+	4.56532i	−0.201247	+	1.14133i
$17$	4.93976			1.19807			0.599033	−	0.800724i	$-0.295552\pi$
$17$	4.93976			1.19807			0.599033	+	0.800724i	$0.295552\pi$
$18$	1.53495	−	4.38316i	0.361791	−	1.03312i
$19$	−5.41589			−1.24249			−0.621245	−	0.783616i	$-0.713373\pi$
$19$	−5.41589			−1.24249			−0.621245	+	0.783616i	$0.713373\pi$
$20$	0.0268307	−	0.00976556i	0.00599952	−	0.00218365i
$21$	−3.82116	−	2.52957i	−0.833845	−	0.551998i
$22$	−2.27121	+	1.90577i	−0.484223	+	0.406311i
$23$	−0.174590	−	0.990152i	−0.0364046	−	0.206461i	0.961180	−	0.275922i	$-0.0889831\pi$
$23$	−0.174590	−	0.990152i	−0.0364046	−	0.206461i	−0.997585	+	0.0694611i	$0.977872\pi$
$24$	−0.348555	+	4.28541i	−0.0711485	+	0.874756i
$25$	−3.82625	−	3.21060i	−0.765250	−	0.642121i
$26$	4.30672	+	7.45946i	0.844618	+	1.46292i
$27$	1.25264	−	5.04290i	0.241072	−	0.970507i
$28$	−0.992667	−	0.338981i	−0.187596	−	0.0640614i
$29$	0.0487538	−	0.276497i	0.00905336	−	0.0513441i	−0.979946	−	0.199261i	$-0.936146\pi$
$29$	0.0487538	−	0.276497i	0.00905336	−	0.0513441i	0.989000	+	0.147917i	$0.0472569\pi$
$30$	0.174508	−	0.0826761i	0.0318606	−	0.0150945i
$31$	−3.39416	+	2.84804i	−0.609609	+	0.511523i	−0.894518	−	0.447032i	$-0.852481\pi$
$31$	−3.39416	+	2.84804i	−0.609609	+	0.511523i	0.284909	+	0.958555i	$0.408037\pi$
$32$	0.384052	+	2.17807i	0.0678915	+	0.385032i
$33$	−2.33127	+	2.35993i	−0.405822	+	0.410812i
$34$	7.18583	−	2.61543i	1.23236	−	0.448542i
$35$	−0.0368325	−	0.186947i	−0.00622583	−	0.0315999i
$36$	−0.0145337	−	1.18931i	−0.00242229	−	0.198218i
$37$	3.95813	−	6.85568i	0.650712	−	1.12707i	−0.332238	−	0.943196i	$-0.607804\pi$
$37$	3.95813	−	6.85568i	0.650712	−	1.12707i	0.982950	−	0.183871i	$-0.0588629\pi$
$38$	−7.87846	+	2.86752i	−1.27805	+	0.465174i
$39$	5.57581	+	7.86043i	0.892845	+	1.25868i
$40$	−0.136949	+	0.114914i	−0.0216535	+	0.0181694i
$41$	0.363141	+	2.05947i	0.0567131	+	0.321636i	0.999945	−	0.0104994i	$-0.00334212\pi$
$41$	0.363141	+	2.05947i	0.0567131	+	0.321636i	−0.943232	+	0.332135i	$0.892231\pi$
$42$	−6.89793	−	1.65659i	−1.06437	−	0.255617i
$43$	−4.72363	−	3.96360i	−0.720347	−	0.604443i	0.207134	−	0.978313i	$-0.433586\pi$
$43$	−4.72363	−	3.96360i	−0.720347	−	0.604443i	−0.927481	+	0.373870i	$0.878031\pi$
$44$	−0.379658	+	0.657587i	−0.0572356	+	0.0991349i
$45$	0.185774	−	0.110305i	0.0276935	−	0.0164433i
$46$	−0.778226	−	1.34793i	−0.114743	−	0.198741i
$47$	9.88425	+	8.29387i	1.44177	+	1.20979i	0.938324	+	0.345756i	$0.112377\pi$
$47$	9.88425	+	8.29387i	1.44177	+	1.20979i	0.503441	+	0.864029i	$0.332067\pi$
$48$	2.12550	+	7.74291i	0.306789	+	1.11759i
$49$	−3.25482	+	6.19727i	−0.464975	+	0.885324i
$50$	−7.26592	−	2.64458i	−1.02756	−	0.374000i
$51$	7.73205	−	3.66319i	1.08270	−	0.512950i
$52$	1.68986	+	1.41796i	0.234342	+	0.196636i
$53$	5.67550	−	9.83026i	0.779590	−	1.35029i	−0.152588	−	0.988290i	$-0.548761\pi$
$53$	5.67550	−	9.83026i	0.779590	−	1.35029i	0.932178	−	0.362000i	$-0.117906\pi$
$54$	−0.847828	−	7.99911i	−0.115375	−	1.08854i
$55$	−0.137929			−0.0185984
$56$	6.56638	−	0.131321i	0.877470	−	0.0175485i
$57$	−8.47733	+	4.01628i	−1.12285	+	0.531970i
$58$	−0.0754735	−	0.428031i	−0.00991015	−	0.0562033i
$59$	−0.724927	−	4.11127i	−0.0943775	−	0.535241i	−0.994936	−	0.100507i	$-0.967953\pi$
$59$	−0.724927	−	4.11127i	−0.0943775	−	0.535241i	0.900559	−	0.434734i	$-0.143158\pi$
$60$	0.0347553	−	0.0351827i	0.00448689	−	0.00454206i
$61$	4.52663	+	3.79830i	0.579576	+	0.486322i	0.884808	−	0.465956i	$-0.154290\pi$
$61$	4.52663	+	3.79830i	0.579576	+	0.486322i	−0.305232	+	0.952278i	$0.598734\pi$
$62$	−3.42953	+	5.94011i	−0.435550	+	0.754395i
$63$	−7.85701	−	1.12580i	−0.989890	−	0.141837i
$64$	−2.92386	−	5.06427i	−0.365482	−	0.633034i
$65$	−0.0695827	+	0.394623i	−0.00863068	+	0.0489470i
$66$	−2.14178	+	4.66731i	−0.263635	+	0.574506i
$67$	−9.06882	−	3.30078i	−1.10793	−	0.403254i	−0.277698	−	0.960669i	$-0.589571\pi$
$67$	−9.06882	−	3.30078i	−1.10793	−	0.403254i	−0.830235	+	0.557414i	$0.811794\pi$
$68$	1.50025	−	1.25886i	0.181933	−	0.152660i
$69$	−1.00755	−	1.42038i	−0.121295	−	0.170994i
$70$	−0.152562	−	0.252450i	−0.0182347	−	0.0301735i
$71$	4.37580	+	7.57911i	0.519312	+	0.899475i	0.999748	+	0.0224451i	$0.00714510\pi$
$71$	4.37580	+	7.57911i	0.519312	+	0.899475i	−0.480436	+	0.877030i	$0.659522\pi$
$72$	2.63237	+	6.96631i	0.310227	+	0.820987i
$73$	−2.67582	−	4.63466i	−0.313181	−	0.542446i	0.665868	−	0.746070i	$-0.268061\pi$
$73$	−2.67582	−	4.63466i	−0.313181	−	0.542446i	−0.979049	+	0.203624i	$0.934728\pi$
$74$	2.12802	−	12.0686i	0.247377	−	1.40295i
$75$	−8.37001	−	2.18802i	−0.966486	−	0.252650i
$76$	−1.64486	+	1.38020i	−0.188679	+	0.158320i
$77$	3.94603	+	3.17885i	0.449692	+	0.362264i
$78$	12.2729	+	8.48232i	1.38963	+	0.960433i
$79$	0.626732	−	0.228112i	0.0705128	−	0.0256646i	−0.306523	−	0.951863i	$-0.599166\pi$
$79$	0.626732	−	0.228112i	0.0705128	−	0.0256646i	0.377036	+	0.926199i	$0.376943\pi$
$80$	−0.166928	+	0.289128i	−0.0186631	+	0.0323255i
$81$	−1.77896	−	8.82243i	−0.197662	−	0.980270i
$82$	1.61868	+	2.80363i	0.178753	+	0.309609i
$83$	0.402782	−	2.28429i	0.0442110	−	0.250733i	−0.954690	−	0.297602i	$-0.903813\pi$
$83$	0.402782	−	2.28429i	0.0442110	−	0.250733i	0.998901	+	0.0468688i	$0.0149243\pi$
$84$	−1.80517	+	0.205538i	−0.196960	+	0.0224261i
$85$	0.334296	+	0.121674i	0.0362595	+	0.0131974i
$86$	−8.97002	−	3.26482i	−0.967262	−	0.352055i
$87$	−0.128730	−	0.468946i	−0.0138013	−	0.0502763i
$88$	0.825564	−	4.68201i	0.0880055	−	0.499104i
$89$	3.95600			0.419335			0.209668	−	0.977773i	$-0.432762\pi$
$89$	3.95600			0.419335			0.209668	+	0.977773i	$0.432762\pi$
$90$	0.211841	−	0.258821i	0.0223300	−	0.0272821i
$91$	11.0856	−	9.68613i	1.16208	−	1.01538i
$92$	−0.305358	−	0.256226i	−0.0318358	−	0.0267134i
$93$	−3.20075	+	6.97497i	−0.331902	+	0.723270i
$94$	18.7699	+	6.83167i	1.93596	+	0.704633i
$95$	−0.366518	−	0.133402i	−0.0376040	−	0.0136867i
$96$	2.21634	+	3.12446i	0.226205	+	0.318889i
$97$	8.01916	+	6.72888i	0.814222	+	0.683214i	0.951612	−	0.307303i	$-0.0994266\pi$
$97$	8.01916	+	6.72888i	0.814222	+	0.683214i	−0.137389	+	0.990517i	$0.543871\pi$
$98$	−1.45353	+	10.7384i	−0.146829	+	1.08475i
$99$	−1.89900	+	5.42274i	−0.190857	+	0.545006i
$100$	−1.98027			−0.198027
$101$	2.51924	−	14.2873i	0.250673	−	1.42164i	−0.556265	−	0.831005i	$-0.687766\pi$
$101$	2.51924	−	14.2873i	0.250673	−	1.42164i	0.806939	−	0.590635i	$-0.201123\pi$
$102$	9.30823	−	9.42267i	0.921652	−	0.932983i
$103$	−0.631588	−	0.229879i	−0.0622322	−	0.0226507i	0.310716	−	0.950503i	$-0.399431\pi$
$103$	−0.631588	−	0.229879i	−0.0622322	−	0.0226507i	−0.372949	+	0.927852i	$0.621653\pi$
$104$	−12.9790	−	4.72397i	−1.27270	−	0.463223i
$105$	−0.196288	−	0.265309i	−0.0191558	−	0.0258915i
$106$	3.05134	−	17.3050i	0.296372	−	1.68081i
$107$	−0.836079	−	1.44813i	−0.0808268	−	0.139996i	0.822779	−	0.568362i	$-0.192423\pi$
$107$	−0.836079	−	1.44813i	−0.0808268	−	0.139996i	−0.903605	+	0.428366i	$0.859089\pi$
$108$	−0.904709	−	1.85081i	−0.0870557	−	0.178094i
$109$	−5.00325	+	8.66588i	−0.479224	+	0.830040i	−0.999716	−	0.0238260i	$-0.992415\pi$
$109$	−5.00325	+	8.66588i	−0.479224	+	0.830040i	0.520492	+	0.853867i	$0.325749\pi$
$110$	−0.200645	+	0.0730288i	−0.0191307	+	0.00696302i
$111$	1.11155	−	13.6662i	0.105503	−	1.29714i
$112$	11.4392	−	4.42450i	1.08090	−	0.418076i
$113$	1.52854	−	1.28259i	0.143793	−	0.120656i	−0.568054	−	0.822991i	$-0.692304\pi$
$113$	1.52854	−	1.28259i	0.143793	−	0.120656i	0.711847	+	0.702335i	$0.247859\pi$
$114$	−10.2054	+	10.3309i	−0.955826	+	0.967578i
$115$	0.0125736	−	0.0713086i	0.00117250	−	0.00664956i
$116$	−0.0556563	−	0.0963995i	−0.00516756	−	0.00895047i
$117$	14.5567	+	8.16882i	1.34577	+	0.755207i
$118$	−3.23132	−	5.59681i	−0.297467	−	0.515228i
$119$	−6.75969	−	11.1855i	−0.619660	−	1.02537i
$120$	−0.129145	+	0.281428i	−0.0117892	+	0.0256908i
$121$	−5.61661	+	4.71289i	−0.510601	+	0.428445i
$122$	8.59593	+	3.12866i	0.778239	+	0.283256i
$123$	2.09566	+	2.95434i	0.188960	+	0.266383i
$124$	−0.305038	+	1.72996i	−0.0273932	+	0.155355i
$125$	−0.359902	−	0.623369i	−0.0321906	−	0.0557558i
$126$	−12.0256	+	2.52232i	−1.07133	+	0.224706i
$127$	0.922714	−	1.59819i	0.0818776	−	0.141816i	−0.822179	−	0.569229i	$-0.807242\pi$
$127$	0.922714	−	1.59819i	0.0818776	−	0.141816i	0.904056	+	0.427413i	$0.140575\pi$
$128$	−10.3231	−	8.66214i	−0.912445	−	0.765633i
$129$	−10.3331	−	2.70118i	−0.909775	−	0.237825i
$130$	0.107718	+	0.610898i	0.00944747	+	0.0535793i
$131$	−0.852533	−	4.83496i	−0.0744862	−	0.422432i	−0.999134	−	0.0416088i	$-0.986752\pi$
$131$	−0.852533	−	4.83496i	−0.0744862	−	0.422432i	0.924648	−	0.380823i	$-0.124359\pi$
$132$	−0.106618	+	1.31084i	−0.00927990	+	0.114094i
$133$	7.41124	+	12.2636i	0.642636	+	1.06339i
$134$	−14.9400			−1.29062
$135$	0.208987	−	0.310422i	0.0179867	−	0.0267169i
$136$	−6.13111	+	10.6194i	−0.525739	+	0.910606i
$137$	11.7854	+	9.88916i	1.00690	+	0.844888i	0.987925	−	0.154932i	$-0.0495160\pi$
$137$	11.7854	+	9.88916i	1.00690	+	0.844888i	0.0189727	+	0.999820i	$0.493960\pi$
$138$	−2.21772	−	1.53276i	−0.188785	−	0.130477i
$139$	2.47282	+	0.900032i	0.209742	+	0.0763397i	0.444754	−	0.895653i	$-0.353291\pi$
$139$	2.47282	+	0.900032i	0.209742	+	0.0763397i	−0.235013	+	0.971992i	$0.575513\pi$
$140$	−0.0588287	−	0.0473913i	−0.00497193	−	0.00400530i
$141$	21.6220	+	5.65224i	1.82090	+	0.476005i
$142$	10.3783	+	8.70845i	0.870929	+	0.730797i
$143$	−5.32817	−	9.22866i	−0.445564	−	0.771740i
$144$	9.06891	+	10.5435i	0.755743	+	0.878628i
$145$	0.0101099	−	0.0175109i	0.000839585	−	0.00145420i
$146$	−6.34639	−	5.32526i	−0.525231	−	0.440721i
$147$	−0.498945	+	12.1141i	−0.0411523	+	0.999153i
$148$	−0.544999	−	3.09084i	−0.0447986	−	0.254066i
$149$	−5.29428	+	4.44242i	−0.433724	+	0.363938i	−0.833355	−	0.552739i	$-0.813583\pi$
$149$	−5.29428	+	4.44242i	−0.433724	+	0.363938i	0.399631	+	0.916676i	$0.369138\pi$
$150$	−13.3343	+	1.24874i	−1.08874	+	0.101959i
$151$	16.2661	−	5.92039i	1.32372	−	0.481795i	0.419072	−	0.907953i	$-0.362356\pi$
$151$	16.2661	−	5.92039i	1.32372	−	0.481795i	0.904648	+	0.426159i	$0.140133\pi$
$152$	6.72208	−	11.6430i	0.545233	−	0.944371i
$153$	9.38621	−	11.4678i	0.758830	−	0.927114i
$154$	7.42336	+	2.53497i	0.598191	+	0.204274i
$155$	−0.299850	+	0.109137i	−0.0240845	+	0.00876606i
$156$	3.69661	+	0.966336i	0.295966	+	0.0773688i
$157$	−0.854333	−	4.84516i	−0.0681832	−	0.386686i	−0.999734	−	0.0230743i	$-0.992655\pi$
$157$	−0.854333	−	4.84516i	−0.0681832	−	0.386686i	0.931551	−	0.363612i	$-0.118457\pi$
$158$	0.790925	−	0.663665i	0.0629226	−	0.0527984i
$159$	1.59383	−	19.5958i	0.126399	−	1.55405i
$160$	−0.0276586	+	0.156860i	−0.00218660	+	0.0124008i
$161$	−2.00316	+	1.75029i	−0.157872	+	0.137942i
$162$	−7.25901	−	11.8920i	−0.570322	−	0.934327i
$163$	3.81020	+	6.59947i	0.298438	+	0.516910i	0.975779	−	0.218759i	$-0.0702010\pi$
$163$	3.81020	+	6.59947i	0.298438	+	0.516910i	−0.677341	+	0.735670i	$0.736868\pi$
$164$	0.635132	+	0.532939i	0.0495955	+	0.0416156i
$165$	−0.215897	+	0.102285i	−0.0168075	+	0.00796286i
$166$	−0.623527	−	3.53620i	−0.0483951	−	0.274462i
$167$	−17.5002	+	14.6844i	−1.35421	+	1.13631i	−0.376481	+	0.926424i	$0.622866\pi$
$167$	−17.5002	+	14.6844i	−1.35421	+	1.13631i	−0.977725	+	0.209890i	$0.932689\pi$
$168$	10.1808	−	5.07501i	0.785464	−	0.391545i
$169$	−16.8757	+	6.14224i	−1.29813	+	0.472480i
$170$	0.550720			0.0422383
$171$	−10.2909	+	12.5731i	−0.786967	+	0.961491i
$172$	−2.44471			−0.186408
$173$	−4.05368	+	22.9896i	−0.308196	+	1.74787i	0.299871	+	0.953980i	$0.403057\pi$
$173$	−4.05368	+	22.9896i	−0.308196	+	1.74787i	−0.608066	+	0.793886i	$0.708055\pi$
$174$	−0.435553	−	0.614015i	−0.0330192	−	0.0465484i
$175$	−2.03409	+	13.0576i	−0.153763	+	0.987058i
$176$	−1.54172	−	8.74355i	−0.116212	−	0.659070i
$177$	−4.18351	−	5.89765i	−0.314452	−	0.443295i
$178$	5.75476	−	2.09456i	0.431338	−	0.156994i
$179$	−25.8238			−1.93016			−0.965081	−	0.261950i	$-0.915634\pi$
$179$	−25.8238			−1.93016			−0.965081	+	0.261950i	$0.915634\pi$
$180$	0.0283109	−	0.0808440i	0.00211017	−	0.00602575i
$181$	−4.09437	+	7.09166i	−0.304332	+	0.527119i	−0.977112	−	0.212723i	$-0.931767\pi$
$181$	−4.09437	+	7.09166i	−0.304332	+	0.527119i	0.672780	+	0.739843i	$0.265100\pi$
$182$	10.9976	−	19.9598i	0.815198	−	1.47952i
$183$	9.90212	+	2.58853i	0.731986	+	0.191349i
$184$	2.34531	+	0.853623i	0.172898	+	0.0629299i
$185$	0.436731	−	0.366461i	0.0321091	−	0.0269427i
$186$	−0.963101	+	11.8411i	−0.0706180	+	0.868233i
$187$	−8.89013	+	3.23574i	−0.650111	+	0.236621i
$188$	5.11559			0.373092
$189$	−13.1332	+	4.06438i	−0.955299	+	0.295640i
$190$	−0.603803			−0.0438045
$191$	6.48947	−	2.36197i	0.469562	−	0.170906i	−0.0963922	−	0.995343i	$-0.530730\pi$
$191$	6.48947	−	2.36197i	0.469562	−	0.170906i	0.565954	+	0.824437i	$0.308508\pi$
$192$	−8.33215	−	5.75869i	−0.601321	−	0.415598i
$193$	−16.5734	+	13.9068i	−1.19298	+	1.00103i	−0.193179	+	0.981164i	$0.561880\pi$
$193$	−16.5734	+	13.9068i	−1.19298	+	1.00103i	−0.999803	+	0.0198667i	$0.993676\pi$
$194$	15.2281	+	5.54258i	1.09332	+	0.397934i
$195$	0.183727	+	0.669293i	0.0131569	+	0.0479290i
$196$	0.590808	+	2.71164i	0.0422006	+	0.193689i
$197$	−6.10665	+	10.5770i	−0.435081	+	0.753582i	−0.997302	−	0.0734046i	$-0.976614\pi$
$197$	−6.10665	+	10.5770i	−0.435081	+	0.753582i	0.562221	+	0.826987i	$0.309947\pi$
$198$	0.108686	+	8.89388i	0.00772399	+	0.632061i
$199$	−6.20365			−0.439765			−0.219883	−	0.975526i	$-0.570567\pi$
$199$	−6.20365			−0.439765			−0.219883	+	0.975526i	$0.570567\pi$
$200$	11.6512	−	4.24067i	0.823861	−	0.299861i
$201$	−16.6429	+	1.55859i	−1.17390	+	0.109934i
$202$	−3.89991	−	22.1175i	−0.274397	−	1.55618i
$203$	−0.692809	+	0.267968i	−0.0486257	+	0.0188077i
$204$	1.41476	−	3.08301i	0.0990532	−	0.215854i
$205$	−0.0261526	+	0.148319i	−0.00182658	+	0.0103590i
$206$	−1.04048			−0.0724937
$207$	−2.63041	−	1.47611i	−0.182826	−	0.102597i
$208$	−25.7935			−1.78846
$209$	9.74704	−	3.54763i	0.674217	−	0.245395i
$210$	−0.426011	−	0.282016i	−0.0293975	−	0.0194609i
$211$	18.8961	−	15.8557i	1.30086	−	1.09155i	0.310866	−	0.950454i	$-0.399381\pi$
$211$	18.8961	−	15.8557i	1.30086	−	1.09155i	0.989995	−	0.141099i	$-0.0450636\pi$
$212$	−0.781466	−	4.43191i	−0.0536713	−	0.304385i
$213$	12.4698	+	8.61837i	0.854415	+	0.590521i
$214$	−1.98297	−	1.66391i	−0.135553	−	0.113743i
$215$	−0.222040	−	0.384585i	−0.0151430	−	0.0262285i
$216$	9.28639	+	8.95205i	0.631859	+	0.609110i
$217$	11.0937	+	3.78834i	0.753089	+	0.257169i
$218$	−2.68991	+	15.2552i	−0.182184	+	1.03322i
$219$	−7.62533	−	5.27017i	−0.515272	−	0.356125i
$220$	−0.0418906	+	0.0351504i	−0.00282426	+	0.00236984i
$221$	4.77273	+	27.0675i	0.321049	+	1.82076i
$222$	−5.61883	−	20.4687i	−0.377111	−	1.37377i
$223$	−0.637139	+	0.231900i	−0.0426660	+	0.0155292i	−0.363265	−	0.931686i	$-0.618338\pi$
$223$	−0.637139	+	0.231900i	−0.0426660	+	0.0155292i	0.320599	+	0.947215i	$0.396116\pi$
$224$	4.40642	−	3.85016i	0.294417	−	0.257250i
$225$	−14.7239	+	2.78215i	−0.981593	+	0.185476i
$226$	1.54446	−	2.67509i	0.102736	−	0.177944i
$227$	−19.7626	+	7.19298i	−1.31169	+	0.477415i	−0.900785	−	0.434265i	$-0.857008\pi$
$227$	−19.7626	+	7.19298i	−1.31169	+	0.477415i	−0.410901	+	0.911680i	$0.634786\pi$
$228$	−1.55113	+	3.38018i	−0.102726	+	0.223858i
$229$	2.16474	−	1.81643i	0.143050	−	0.120033i	−0.568455	−	0.822715i	$-0.692459\pi$
$229$	2.16474	−	1.81643i	0.143050	−	0.120033i	0.711505	+	0.702681i	$0.248014\pi$
$230$	−0.0194646	−	0.110389i	−0.00128346	−	0.00727886i
$231$	8.53395	+	2.04949i	0.561493	+	0.134846i
$232$	0.533896	+	0.447992i	0.0350520	+	0.0294121i
$233$	−1.96577	+	3.40480i	−0.128782	+	0.223056i	−0.923205	−	0.384308i	$-0.874440\pi$
$233$	−1.96577	+	3.40480i	−0.128782	+	0.223056i	0.794423	+	0.607365i	$0.207773\pi$
$234$	25.5007	+	4.17584i	1.66703	+	0.272983i
$235$	0.464622	+	0.804749i	0.0303086	+	0.0524960i
$236$	−1.26790	−	1.06389i	−0.0825330	−	0.0692534i
$237$	0.811842	−	0.821824i	0.0527348	−	0.0533832i
$238$	−15.7556	−	12.6924i	−1.02128	−	0.822727i
$239$	13.9755	+	5.08667i	0.904001	+	0.329029i	0.751855	−	0.659329i	$-0.229159\pi$
$239$	13.9755	+	5.08667i	0.904001	+	0.329029i	0.152146	+	0.988358i	$0.451382\pi$
$240$	−0.0468778	+	0.576353i	−0.00302595	+	0.0372034i
$241$	16.8229	+	14.1161i	1.08366	+	0.909299i	0.996220	−	0.0868711i	$-0.0276868\pi$
$241$	16.8229	+	14.1161i	1.08366	+	0.909299i	0.0874404	+	0.996170i	$0.472131\pi$
$242$	−5.67513	+	9.82961i	−0.364811	+	0.631872i
$243$	−9.32703	−	12.4903i	−0.598329	−	0.801250i
$244$	2.34276			0.149980
$245$	−0.372917	+	0.339226i	−0.0238248	+	0.0216724i
$246$	4.61277	+	3.18807i	0.294099	+	0.203264i
$247$	−5.23277	−	29.6765i	−0.332953	−	1.88827i
$248$	−1.90991	−	10.8316i	−0.121279	−	0.687809i
$249$	−1.06351	−	3.87422i	−0.0673970	−	0.245519i
$250$	−0.853600	−	0.716255i	−0.0539864	−	0.0453000i
$251$	12.5929	−	21.8115i	0.794855	−	1.37673i	−0.128076	−	0.991764i	$-0.540880\pi$
$251$	12.5929	−	21.8115i	0.794855	−	1.37673i	0.922931	−	0.384965i	$-0.125786\pi$
$252$	−2.67316	+	1.66039i	−0.168393	+	0.104595i
$253$	0.962802	+	1.66762i	0.0605309	+	0.104843i
$254$	0.496081	−	2.81342i	0.0311269	−	0.176530i
$255$	0.613494	−	0.0574528i	0.0384185	−	0.00359784i
$256$	−8.61320	−	3.13495i	−0.538325	−	0.195934i
$257$	4.70292	−	3.94622i	0.293360	−	0.246159i	−0.484214	−	0.874950i	$-0.660894\pi$
$257$	4.70292	−	3.94622i	0.293360	−	0.246159i	0.777574	+	0.628791i	$0.216450\pi$
$258$	−16.4616	+	1.54161i	−1.02485	+	0.0959763i
$259$	−20.9403	+	0.418784i	−1.30116	+	0.0260220i
$260$	0.0794341	+	0.137584i	0.00492629	+	0.00853259i
$261$	−0.549255	−	0.638565i	−0.0339980	−	0.0395262i
$262$	−3.80012	−	6.58199i	−0.234772	−	0.406637i
$263$	−1.29696	+	7.35540i	−0.0799737	+	0.453554i	0.918355	+	0.395758i	$0.129518\pi$
$263$	−1.29696	+	7.35540i	−0.0799737	+	0.453554i	−0.998328	+	0.0577954i	$0.981593\pi$
$264$	−2.17982	−	7.94082i	−0.134159	−	0.488724i
$265$	0.626222	−	0.525462i	0.0384685	−	0.0322789i
$266$	17.2742	+	13.9158i	1.05915	+	0.853234i
$267$	6.19220	−	2.93366i	0.378957	−	0.179537i
$268$	−3.59547	+	1.30865i	−0.219629	+	0.0799383i
$269$	13.9309	−	24.1291i	0.849384	−	1.47118i	−0.0323752	−	0.999476i	$-0.510307\pi$
$269$	13.9309	−	24.1291i	0.849384	−	1.47118i	0.881759	−	0.471700i	$-0.156360\pi$
$270$	0.139654	−	0.562220i	0.00849907	−	0.0342156i
$271$	−5.44738	−	9.43514i	−0.330905	−	0.573144i	0.651785	−	0.758404i	$-0.274021\pi$
$271$	−5.44738	−	9.43514i	−0.330905	−	0.573144i	−0.982690	+	0.185260i	$0.940687\pi$
$272$	−3.97645	+	22.5516i	−0.241108	+	1.36739i
$273$	10.1689	−	23.3822i	0.615450	−	1.41515i
$274$	22.3802	+	8.14571i	1.35203	+	0.492100i
$275$	8.98922	+	3.27181i	0.542070	+	0.197297i
$276$	−0.667979	−	0.174617i	−0.0402076	−	0.0105107i
$277$	0.676693	−	3.83772i	0.0406585	−	0.230586i	−0.957706	−	0.287747i	$-0.907094\pi$
$277$	0.676693	−	3.83772i	0.0406585	−	0.230586i	0.998365	+	0.0571611i	$0.0182049\pi$
$278$	4.07373			0.244326
$279$	0.162424	+	13.2913i	0.00972407	+	0.795729i
$280$	0.447612	+	0.152853i	0.0267499	+	0.00913471i
$281$	−3.59826	−	3.01930i	−0.214654	−	0.180116i	0.529120	−	0.848547i	$-0.322522\pi$
$281$	−3.59826	−	3.01930i	−0.214654	−	0.180116i	−0.743775	+	0.668430i	$0.766966\pi$
$282$	34.4461	−	3.22583i	2.05123	−	0.192095i
$283$	−2.55052	−	0.928313i	−0.151613	−	0.0551825i	0.265099	−	0.964221i	$-0.414595\pi$
$283$	−2.55052	−	0.928313i	−0.151613	−	0.0551825i	−0.416712	+	0.909039i	$0.636818\pi$
$284$	3.26046	+	1.18671i	0.193473	+	0.0704183i
$285$	−0.672627	+	0.0629906i	−0.0398430	+	0.00373124i
$286$	−12.6371	−	10.6038i	−0.747248	−	0.627016i
$287$	4.16650	−	3.64052i	0.245941	−	0.214893i
$288$	5.78619	+	3.24704i	0.340955	+	0.191334i
$289$	7.40119			0.435364
$290$	0.00543543	−	0.0308259i	0.000319180	−	0.00181016i
$291$	17.5421	+	4.58570i	1.02834	+	0.268819i
$292$	−1.99379	−	0.725679i	−0.116678	−	0.0424672i
$293$	21.4289	+	7.79950i	1.25189	+	0.455652i	0.881041	−	0.473040i	$-0.156844\pi$
$293$	21.4289	+	7.79950i	1.25189	+	0.455652i	0.370852	+	0.928692i	$0.379066\pi$
$294$	5.68817	+	17.8865i	0.331741	+	1.04316i
$295$	0.0522077	−	0.296084i	0.00303965	−	0.0172387i
$296$	9.82548	+	17.0182i	0.571094	+	0.989164i
$297$	1.04891	+	9.89630i	0.0608640	+	0.574242i
$298$	−5.34944	+	9.26550i	−0.309885	+	0.536736i
$299$	5.25687	−	1.91335i	0.304013	−	0.110652i
$300$	−3.09966	+	1.46852i	−0.178959	+	0.0847849i
$301$	−2.51115	+	16.1200i	−0.144740	+	0.929140i
$302$	20.5276	−	17.2247i	1.18123	−	0.991171i
$303$	−6.65180	−	24.2317i	−0.382136	−	1.39207i
$304$	4.35973	−	24.7253i	0.250048	−	1.41809i
$305$	0.212780	+	0.368546i	0.0121838	+	0.0211029i
$306$	7.58228	−	21.6518i	0.433450	−	1.23775i
$307$	6.16452	+	10.6773i	0.351828	+	0.609384i	0.986570	−	0.163340i	$-0.0522269\pi$
$307$	6.16452	+	10.6773i	0.351828	+	0.609384i	−0.634742	+	0.772724i	$0.718894\pi$
$308$	2.00856	−	0.0401692i	0.114448	−	0.00228885i
$309$	−1.15908	+	0.108546i	−0.0659377	+	0.00617497i
$310$	−0.378406	+	0.317520i	−0.0214920	+	0.0180339i
$311$	17.6654	+	6.42967i	1.00171	+	0.364593i	0.790244	−	0.612792i	$-0.209954\pi$
$311$	17.6654	+	6.42967i	1.00171	+	0.364593i	0.211467	+	0.977385i	$0.432176\pi$
$312$	−23.8188	+	2.23060i	−1.34847	+	0.126283i
$313$	0.608381	−	3.45030i	0.0343877	−	0.195022i	−0.962774	−	0.270306i	$-0.912875\pi$
$313$	0.608381	−	3.45030i	0.0343877	−	0.195022i	0.997162	+	0.0752837i	$0.0239862\pi$
$314$	−3.80814	−	6.59589i	−0.214906	−	0.372227i
$315$	−0.503990	−	0.269718i	−0.0283966	−	0.0151969i
$316$	0.132212	−	0.228998i	0.00743752	−	0.0128822i
$317$	0.719045	+	0.603350i	0.0403856	+	0.0338875i	0.662757	−	0.748834i	$-0.269386\pi$
$317$	0.719045	+	0.603350i	0.0403856	+	0.0338875i	−0.622371	+	0.782722i	$0.713831\pi$
$318$	−8.05676	−	29.3498i	−0.451801	−	1.64585i
$319$	0.0933739	+	0.529550i	0.00522794	+	0.0296491i
$320$	−0.0731301	−	0.414742i	−0.00408810	−	0.0231848i
$321$	−2.38258	−	1.64670i	−0.132983	−	0.0919099i
$322$	−1.98727	+	3.60674i	−0.110746	+	0.200996i
$323$	−26.7532			−1.48859
$324$	−2.78863	−	2.22611i	−0.154924	−	0.123673i
$325$	13.8957	−	24.0681i	0.770795	−	1.33506i
$326$	9.03687	+	7.58283i	0.500506	+	0.419974i
$327$	−1.40504	+	17.2747i	−0.0776990	+	0.955294i
$328$	−4.87814	−	1.77550i	−0.269350	−	0.0980355i
$329$	5.25461	−	33.7312i	0.289696	−	1.85966i
$330$	−0.259907	+	0.263103i	−0.0143074	+	0.0144833i
$331$	−13.3167	−	11.1740i	−0.731949	−	0.614178i	0.198713	−	0.980058i	$-0.436324\pi$
$331$	−13.3167	−	11.1740i	−0.731949	−	0.614178i	−0.930662	+	0.365879i	$0.880768\pi$
$332$	−0.459806	−	0.796408i	−0.0252352	−	0.0437086i
$333$	−8.39465	−	22.2156i	−0.460024	−	1.21741i
$334$	−17.6825	+	30.6271i	−0.967546	+	1.67584i
$335$	−0.532425	−	0.446758i	−0.0290895	−	0.0244090i
$336$	14.6243	−	15.4085i	0.797821	−	0.840604i
$337$	−0.984463	−	5.58317i	−0.0536271	−	0.304135i	0.946183	−	0.323633i	$-0.104904\pi$
$337$	−0.984463	−	5.58317i	−0.0536271	−	0.304135i	−0.999810	+	0.0194982i	$0.993793\pi$
$338$	−21.2968	+	17.8701i	−1.15839	+	0.972007i
$339$	1.44143	−	3.14113i	0.0782879	−	0.170603i
$340$	0.132537	−	0.0482395i	0.00718782	−	0.00261615i
$341$	4.24292	−	7.34896i	0.229767	−	0.397969i
$342$	−8.31312	+	23.7387i	−0.449522	+	1.28364i
$343$	18.4869	−	1.11035i	0.998201	−	0.0599530i
$344$	14.3837	−	5.23525i	0.775519	−	0.282266i
$345$	−0.0331995	−	0.120941i	−0.00178740	−	0.00651127i
$346$	6.27532	+	35.5891i	0.337363	+	1.91328i
$347$	−23.3378	+	19.5827i	−1.25284	+	1.05126i	−0.256432	+	0.966562i	$0.582547\pi$
$347$	−23.3378	+	19.5827i	−1.25284	+	1.05126i	−0.996407	+	0.0846947i	$0.973009\pi$
$348$	−0.158604	−	0.109618i	−0.00850209	−	0.00587614i
$349$	−1.25473	+	7.11595i	−0.0671644	+	0.380908i	0.932634	+	0.360824i	$0.117504\pi$
$349$	−1.25473	+	7.11595i	−0.0671644	+	0.380908i	−0.999798	+	0.0200840i	$0.993607\pi$
$350$	3.95454	+	20.0717i	0.211379	+	1.07288i
$351$	28.8430	+	1.99150i	1.53953	+	0.106299i
$352$	−2.11791	−	3.66832i	−0.112885	−	0.195522i
$353$	6.77778	+	5.68723i	0.360745	+	0.302701i	0.805088	−	0.593156i	$-0.202118\pi$
$353$	6.77778	+	5.68723i	0.360745	+	0.302701i	−0.444343	+	0.895857i	$0.646563\pi$
$354$	−9.20833	−	6.36425i	−0.489417	−	0.338256i
$355$	0.109445	+	0.620696i	0.00580876	+	0.0329431i
$356$	1.20148	−	1.00816i	0.0636782	−	0.0534323i
$357$	−18.8756	−	12.4955i	−0.999002	−	0.661331i
$358$	−37.5657	+	13.6728i	−1.98541	+	0.722630i
$359$	19.4952			1.02892			0.514459	−	0.857515i	$-0.327993\pi$
$359$	19.4952			1.02892			0.514459	+	0.857515i	$0.327993\pi$
$360$	0.00655354	+	0.536281i	0.000345402	+	0.0282645i
$361$	10.3319			0.543783
$362$	−2.20127	+	12.4840i	−0.115696	+	0.656146i
$363$	−5.29655	+	11.5421i	−0.277997	+	0.605802i
$364$	0.898354	−	5.76686i	0.0470865	−	0.302266i
$365$	−0.0669264	−	0.379559i	−0.00350309	−	0.0198670i
$366$	15.7751	−	1.47731i	0.824576	−	0.0772205i
$367$	−8.68813	+	3.16222i	−0.453517	+	0.165067i	−0.558671	−	0.829389i	$-0.688689\pi$
$367$	−8.68813	+	3.16222i	−0.453517	+	0.165067i	0.105154	+	0.994456i	$0.466466\pi$
$368$	4.66090			0.242966
$369$	5.47114	+	3.07024i	0.284816	+	0.159830i
$370$	0.441281	−	0.764321i	0.0229411	−	0.0397352i
$371$	−30.0259	+	0.600488i	−1.55887	+	0.0311758i
$372$	0.805424	+	2.93406i	0.0417593	+	0.152124i
$373$	−6.28949	−	2.28919i	−0.325657	−	0.118530i	0.174018	−	0.984743i	$-0.444325\pi$
$373$	−6.28949	−	2.28919i	−0.325657	−	0.118530i	−0.499675	+	0.866213i	$0.666547\pi$
$374$	−11.2192	+	9.41403i	−0.580131	+	0.486788i
$375$	−1.02562	−	0.708847i	−0.0529627	−	0.0366047i
$376$	−30.0981	+	10.9548i	−1.55219	+	0.564952i
$377$	1.56218			0.0804561
$378$	−16.9528	+	12.8660i	−0.871959	+	0.661755i
$379$	29.4838			1.51448			0.757240	−	0.653137i	$-0.226547\pi$
$379$	29.4838			1.51448			0.757240	+	0.653137i	$0.226547\pi$
$380$	−0.145312	+	0.0528892i	−0.00745435	+	0.00271316i
$381$	0.259122	−	3.18586i	0.0132752	−	0.163216i
$382$	8.18961	−	6.87190i	0.419017	−	0.351597i
$383$	−22.2259	−	8.08956i	−1.13569	−	0.413357i	−0.295334	−	0.955394i	$-0.595431\pi$
$383$	−22.2259	−	8.08956i	−1.13569	−	0.413357i	−0.840355	+	0.542037i	$0.817653\pi$
$384$	−22.5821	−	5.90322i	−1.15239	−	0.301247i
$385$	0.188746	+	0.312324i	0.00961939	+	0.0159175i
$386$	−16.7461	+	29.0051i	−0.852355	+	1.47632i
$387$	−18.1771	+	3.43465i	−0.923996	+	0.174593i
$388$	4.15031			0.210700
$389$	−33.0982	+	12.0467i	−1.67814	+	0.610794i	−0.993053	−	0.117664i	$-0.962460\pi$
$389$	−33.0982	+	12.0467i	−1.67814	+	0.610794i	−0.685090	+	0.728458i	$0.740237\pi$
$390$	0.621633	+	0.876339i	0.0314776	+	0.0443751i
$391$	−0.862434	−	4.89111i	−0.0436152	−	0.247354i
$392$	−9.28296	−	14.6891i	−0.468860	−	0.741910i
$393$	−4.91992	−	6.93580i	−0.248177	−	0.349865i
$394$	−3.28314	+	18.6196i	−0.165402	+	0.938041i
$395$	0.0480326			0.00241678
$396$	0.805202	+	2.13089i	0.0404629	+	0.107081i
$397$	−11.9341			−0.598954			−0.299477	−	0.954103i	$-0.596812\pi$
$397$	−11.9341			−0.598954			−0.299477	+	0.954103i	$0.596812\pi$
$398$	−9.02441	+	3.28462i	−0.452353	+	0.164643i
$399$	20.6950	+	13.6999i	1.03604	+	0.685853i
$400$	17.7375	−	14.8835i	0.886876	−	0.744177i
$401$	−3.73998	−	21.2105i	−0.186766	−	1.05920i	−0.923666	−	0.383199i	$-0.874822\pi$
$401$	−3.73998	−	21.2105i	−0.186766	−	1.05920i	0.736900	−	0.676001i	$-0.236289\pi$
$402$	−23.3851	+	11.0791i	−1.16634	+	0.552576i
$403$	−18.8853	−	15.8466i	−0.940743	−	0.789377i
$404$	−2.87590	−	4.98121i	−0.143082	−	0.247825i
$405$	0.0969198	−	0.640873i	0.00481598	−	0.0318452i
$406$	−0.865945	+	0.756629i	−0.0429761	+	0.0375509i
$407$	−2.63273	+	14.9310i	−0.130500	+	0.740101i
$408$	−1.72178	+	21.1689i	−0.0852407	+	1.04802i
$409$	−8.10186	+	6.79827i	−0.400611	+	0.336153i	−0.820730	−	0.571317i	$-0.806433\pi$
$409$	−8.10186	+	6.79827i	−0.400611	+	0.336153i	0.420119	+	0.907469i	$0.361988\pi$
$410$	0.0404856	+	0.229605i	0.00199944	+	0.0113394i
$411$	25.7809	+	6.73942i	1.27168	+	0.332431i
$412$	−0.250403	+	0.0911393i	−0.0123365	+	0.00449011i
$413$	−8.31746	+	7.26747i	−0.409275	+	0.357609i
$414$	−4.60798	−	0.754575i	−0.226470	−	0.0370853i
$415$	0.0835236	−	0.144667i	0.00410001	−	0.00710143i
$416$	−11.5637	+	4.20884i	−0.566957	+	0.206356i
$417$	4.53807	−	0.424984i	0.222230	−	0.0208116i
$418$	12.3006	−	10.3214i	0.601642	−	0.504838i
$419$	−2.23909	−	12.6985i	−0.109387	−	0.620363i	−0.989377	−	0.145372i	$-0.953562\pi$
$419$	−2.23909	−	12.6985i	−0.109387	−	0.620363i	0.879990	−	0.474992i	$-0.157549\pi$
$420$	−0.127227	−	0.0305544i	−0.00620804	−	0.00149090i
$421$	−19.2104	−	16.1194i	−0.936258	−	0.785614i	0.0406721	−	0.999173i	$-0.487050\pi$
$421$	−19.2104	−	16.1194i	−0.936258	−	0.785614i	−0.976930	+	0.213559i	$0.931495\pi$
$422$	19.0930	−	33.0700i	0.929432	−	1.60982i
$423$	38.0359	−	7.18705i	1.84937	−	0.349446i
$424$	14.0886	+	24.4022i	0.684203	+	1.18507i
$425$	−18.9007	−	15.8596i	−0.916820	−	0.769304i
$426$	22.7028	+	5.93477i	1.09996	+	0.287541i
$427$	2.40642	−	15.4477i	0.116455	−	0.747566i
$428$	−0.622972	−	0.226743i	−0.0301125	−	0.0109601i
$429$	−15.1838	−	10.4941i	−0.733079	−	0.506661i
$430$	−0.526625	−	0.441891i	−0.0253961	−	0.0213099i
$431$	2.36771	−	4.10100i	0.114049	−	0.197538i	−0.803350	−	0.595507i	$-0.796951\pi$
$431$	2.36771	−	4.10100i	0.114049	−	0.197538i	0.917399	+	0.397969i	$0.130285\pi$
$432$	22.0141	+	9.77820i	1.05915	+	0.470454i
$433$	−22.8881			−1.09993			−0.549965	−	0.835188i	$-0.685359\pi$
$433$	−22.8881			−1.09993			−0.549965	+	0.835188i	$0.685359\pi$
$434$	18.1437	−	0.362856i	0.870926	−	0.0174176i
$435$	0.00283914	−	0.0349066i	0.000136126	−	0.00167364i
$436$	0.688902	+	3.90696i	0.0329924	+	0.187109i
$437$	0.945563	+	5.36255i	0.0452324	+	0.256526i
$438$	−13.8829	−	3.62914i	−0.663350	−	0.173407i
$439$	26.5002	+	22.2363i	1.26478	+	1.06128i	0.995155	+	0.0983158i	$0.0313455\pi$
$439$	26.5002	+	22.2363i	1.26478	+	1.06128i	0.269629	+	0.962964i	$0.413099\pi$
$440$	0.171195	−	0.296518i	0.00816139	−	0.0141359i
$441$	8.20250	+	19.3318i	0.390595	+	0.920562i
$442$	21.2742	+	36.8479i	1.01191	+	1.75268i
$443$	1.55640	−	8.82680i	0.0739470	−	0.419374i	−0.925252	−	0.379353i	$-0.876146\pi$
$443$	1.55640	−	8.82680i	0.0739470	−	0.419374i	0.999199	−	0.0400208i	$-0.0127424\pi$
$444$	−3.14516	−	4.43385i	−0.149263	−	0.210421i
$445$	0.267721	+	0.0974424i	0.0126912	+	0.00461921i
$446$	−0.804060	+	0.674686i	−0.0380733	+	0.0319473i
$447$	−4.99258	+	10.8797i	−0.236141	+	0.514592i
$448$	−7.46634	+	13.5508i	−0.352752	+	0.640215i
$449$	−13.3130	−	23.0588i	−0.628280	−	1.08821i	−0.987897	−	0.155112i	$-0.950426\pi$
$449$	−13.3130	−	23.0588i	−0.628280	−	1.08821i	0.359617	−	0.933100i	$-0.382907\pi$
$450$	−19.9457	+	11.8430i	−0.940249	+	0.558282i
$451$	−2.00259	−	3.46858i	−0.0942982	−	0.163329i
$452$	0.137372	−	0.779075i	0.00646143	−	0.0366446i
$453$	21.0705	−	21.3296i	0.989978	−	1.00215i
$454$	−24.9400	+	20.9272i	−1.17049	+	0.982160i
$455$	0.988796	−	0.382451i	0.0463555	−	0.0179296i
$456$	1.88774	−	23.2093i	0.0884014	−	1.08688i
$457$	38.0291	−	13.8415i	1.77893	−	0.647476i	0.779139	−	0.626852i	$-0.215657\pi$
$457$	38.0291	−	13.8415i	1.77893	−	0.647476i	0.999787	−	0.0206244i	$-0.00656541\pi$
$458$	2.18729	−	3.78850i	0.102206	−	0.177025i
$459$	6.18776	−	24.9107i	0.288820	−	1.16273i
$460$	−0.0143538	−	0.0248615i	−0.000669248	−	0.00115917i
$461$	−1.89406	+	10.7417i	−0.0882150	+	0.500292i	0.908401	+	0.418099i	$0.137304\pi$
$461$	−1.89406	+	10.7417i	−0.0882150	+	0.500292i	−0.996616	+	0.0821931i	$0.973808\pi$
$462$	13.4994	−	1.53706i	0.628050	−	0.0715103i
$463$	−13.4098	−	4.88077i	−0.623207	−	0.226829i	0.0110652	−	0.999939i	$-0.496478\pi$
$463$	−13.4098	−	4.88077i	−0.623207	−	0.226829i	−0.634272	+	0.773110i	$0.718700\pi$
$464$	1.22305	+	0.445154i	0.0567786	+	0.0206657i
$465$	−0.388413	+	0.393189i	−0.0180122	+	0.0182337i
$466$	−1.05686	+	5.99375i	−0.0489581	+	0.277655i
$467$	1.34754			0.0623569			0.0311784	−	0.999514i	$-0.490074\pi$
$467$	1.34754			0.0623569			0.0311784	+	0.999514i	$0.490074\pi$
$468$	6.50280	−	1.22873i	0.300592	−	0.0567982i
$469$	4.93578	+	25.0521i	0.227913	+	1.15680i
$470$	1.10197	+	0.924662i	0.0508300	+	0.0426515i
$471$	−4.93031	−	6.95043i	−0.227177	−	0.320259i
$472$	9.73809	+	3.54438i	0.448232	+	0.163143i
$473$	11.0975	+	4.03916i	0.510263	+	0.185721i
$474$	0.745855	−	1.62534i	0.0342582	−	0.0746545i
$475$	20.7225	+	17.3883i	0.950816	+	0.797829i
$476$	−4.90353	−	1.67448i	−0.224753	−	0.0767499i
$477$	−12.0370	−	31.8547i	−0.551134	−	1.45852i
$478$	23.0233			1.05306
$479$	−5.04661	+	28.6207i	−0.230585	+	1.30772i	0.621129	+	0.783709i	$0.286674\pi$
$479$	−5.04661	+	28.6207i	−0.230585	+	1.30772i	−0.851714	+	0.524007i	$0.824437\pi$
$480$	0.0730299	+	0.266039i	0.00333334	+	0.0121429i
$481$	41.3902	+	15.0648i	1.88723	+	0.686895i
$482$	31.9462	+	11.6275i	1.45511	+	0.529616i
$483$	−1.83753	+	4.22517i	−0.0836103	+	0.192252i
$484$	−0.504773	+	2.86271i	−0.0229442	+	0.130123i
$485$	0.376951	+	0.652898i	0.0171165	+	0.0296466i
$486$	−20.1811	−	13.2312i	−0.915434	−	0.600177i
$487$	17.7347	−	30.7175i	0.803638	−	1.39194i	−0.113569	−	0.993530i	$-0.536228\pi$
$487$	17.7347	−	30.7175i	0.803638	−	1.39194i	0.917207	−	0.398411i	$-0.130438\pi$
$488$	−13.7839	+	5.01692i	−0.623966	+	0.227105i
$489$	10.8580	+	7.50440i	0.491015	+	0.339361i
$490$	−0.362872	+	0.690917i	−0.0163929	+	0.0312124i
$491$	24.9334	−	20.9216i	1.12523	−	0.944179i	0.126372	−	0.991983i	$-0.459667\pi$
$491$	24.9334	−	20.9216i	1.12523	−	0.944179i	0.998857	+	0.0478042i	$0.0152223\pi$
$492$	1.38937	+	0.363196i	0.0626375	+	0.0163742i
$493$	0.240832	−	1.36583i	0.0108465	−	0.0615137i
$494$	−23.3247	−	40.3996i	−1.04943	−	1.81767i
$495$	−0.262085	+	0.320207i	−0.0117798	+	0.0143922i
$496$	−10.2699	−	17.7881i	−0.461134	−	0.798708i
$497$	11.1740	−	20.2799i	0.501223	−	0.909679i
$498$	−3.59834	−	5.07271i	−0.161245	−	0.227314i
$499$	3.14078	−	2.63543i	0.140601	−	0.117978i	−0.569775	−	0.821801i	$-0.692970\pi$
$499$	3.14078	−	2.63543i	0.140601	−	0.117978i	0.710376	+	0.703823i	$0.248525\pi$
$500$	−0.268167	−	0.0976050i	−0.0119928	−	0.00436503i
$501$	−16.5030	+	35.9628i	−0.737298	+	1.60670i
$502$	6.77034	−	38.3965i	0.302175	−	1.71372i
$503$	4.14085	+	7.17215i	0.184631	+	0.319791i	0.943452	−	0.331509i	$-0.107558\pi$
$503$	4.14085	+	7.17215i	0.184631	+	0.319791i	−0.758821	+	0.651299i	$0.774224\pi$
$504$	12.1722	−	15.4935i	0.542191	−	0.690137i
$505$	0.522407	−	0.904835i	0.0232468	−	0.0402646i
$506$	2.28353	+	1.91611i	0.101515	+	0.0851815i
$507$	−21.8600	+	22.1288i	−0.970838	+	0.982774i
$508$	−0.127050	−	0.720534i	−0.00563691	−	0.0319685i
$509$	−2.82102	−	15.9988i	−0.125040	−	0.709135i	−0.981284	−	0.192564i	$-0.938320\pi$
$509$	−2.82102	−	15.9988i	−0.125040	−	0.709135i	0.856245	−	0.516570i	$-0.172792\pi$
$510$	0.862026	−	0.408400i	0.0381711	−	0.0180842i
$511$	−6.83297	+	12.4013i	−0.302273	+	0.548600i
$512$	12.7624			0.564024
$513$	−6.78419	+	27.3118i	−0.299529	+	1.20585i
$514$	4.75193	−	8.23058i	0.209598	−	0.363035i
$515$	−0.0370802	−	0.0311140i	−0.00163395	−	0.00137105i
$516$	−3.82663	+	1.81293i	−0.168458	+	0.0798100i
$517$	−23.2216	−	8.45198i	−1.02129	−	0.371717i
$518$	−30.2399	+	11.6963i	−1.32867	+	0.513908i
$519$	10.7034	+	38.9910i	0.469826	+	1.71152i
$520$	−0.761990	−	0.639385i	−0.0334155	−	0.0280389i
$521$	0.578978	+	1.00282i	0.0253655	+	0.0439343i	0.878430	−	0.477872i	$-0.158592\pi$
$521$	0.578978	+	1.00282i	0.0253655	+	0.0439343i	−0.853064	+	0.521806i	$0.825258\pi$
$522$	−1.13710	−	0.638105i	−0.0497693	−	0.0279291i
$523$	−2.16441	+	3.74886i	−0.0946429	+	0.163926i	−0.909460	−	0.415792i	$-0.863504\pi$
$523$	−2.16441	+	3.74886i	−0.0946429	+	0.163926i	0.814817	+	0.579719i	$0.196838\pi$
$524$	−1.49108	−	1.25116i	−0.0651381	−	0.0546574i
$525$	6.49924	+	21.9470i	0.283650	+	0.957846i
$526$	2.00776	+	11.3866i	0.0875423	+	0.496477i
$527$	−16.7663	+	14.0686i	−0.730352	+	0.612839i
$528$	−8.89720	−	12.5427i	−0.387201	−	0.545852i
$529$	20.6630	−	7.52072i	0.898392	−	0.326988i
$530$	0.632747	−	1.09595i	0.0274848	−	0.0476050i
$531$	−10.9219	−	6.12903i	−0.473969	−	0.265977i
$532$	5.37617	+	1.83589i	0.233087	+	0.0795957i
$533$	−10.9341	+	3.97968i	−0.473607	+	0.172379i
$534$	7.45448	−	7.54614i	0.322587	−	0.326553i
$535$	−0.0209116	−	0.118596i	−0.000904088	−	0.00512734i
$536$	18.3520	−	15.3991i	0.792684	−	0.665141i
$537$	−40.4212	+	19.1503i	−1.74430	+	0.826395i
$538$	7.48973	−	42.4764i	0.322905	−	1.83129i
$539$	1.79828	−	13.2853i	0.0774572	−	0.572240i
$540$	−0.0156375	−	0.147537i	−0.000672932	−	0.00634899i
$541$	−18.3514	−	31.7856i	−0.788988	−	1.36657i	−0.926587	−	0.376080i	$-0.877272\pi$
$541$	−18.3514	−	31.7856i	−0.788988	−	1.36657i	0.137599	−	0.990488i	$-0.456062\pi$
$542$	−12.9198	−	10.8410i	−0.554955	−	0.465662i
$543$	−1.14981	+	14.1366i	−0.0493430	+	0.606661i
$544$	1.89712	+	10.7591i	0.0813385	+	0.461294i
$545$	−0.552047	+	0.463222i	−0.0236471	+	0.0198423i
$546$	2.41260	−	39.3980i	0.103250	−	1.68608i
$547$	−14.1820	+	5.16181i	−0.606377	+	0.220703i	−0.626917	−	0.779086i	$-0.715684\pi$
$547$	−14.1820	+	5.16181i	−0.606377	+	0.220703i	0.0205404	+	0.999789i	$0.493461\pi$
$548$	6.09954			0.260560
$549$	17.4191	−	3.29141i	0.743428	−	0.140474i
$550$	14.8089			0.631452
$551$	−0.264045	+	1.49748i	−0.0112487	+	0.0637946i
$552$	4.30406	−	0.403070i	0.183193	−	0.0171558i
$553$	−1.37417	−	1.10700i	−0.0584355	−	0.0470746i
$554$	−1.04756	−	5.94099i	−0.0445064	−	0.252408i
$555$	0.411844	−	0.897478i	0.0174818	−	0.0380958i
$556$	0.980388	−	0.356832i	0.0415777	−	0.0151330i
$557$	34.3404			1.45505			0.727525	−	0.686082i	$-0.240671\pi$
$557$	34.3404			1.45505			0.727525	+	0.686082i	$0.240671\pi$
$558$	7.27355	+	19.2488i	0.307914	+	0.814865i
$559$	17.1547	−	29.7128i	0.725567	−	1.25672i
$560$	0.883124	−	0.0176616i	0.0373188	−	0.000746339i
$561$	−11.5159	+	11.6575i	−0.486202	+	0.492180i
$562$	−6.83298	−	2.48700i	−0.288232	−	0.104908i
$563$	15.2260	−	12.7761i	0.641698	−	0.538448i	−0.262841	−	0.964839i	$-0.584660\pi$
$563$	15.2260	−	12.7761i	0.641698	−	0.538448i	0.904539	+	0.426391i	$0.140215\pi$
$564$	8.00727	−	3.79358i	0.337167	−	0.159739i
$565$	0.135035	−	0.0491489i	0.00568098	−	0.00206771i
$566$	−4.20173			−0.176612
$567$	−17.5430	+	16.1011i	−0.736735	+	0.676182i
$568$	−21.7246			−0.911543
$569$	−23.0523	+	8.39037i	−0.966405	+	0.351743i	−0.776540	−	0.630068i	$-0.783027\pi$
$569$	−23.0523	+	8.39037i	−0.966405	+	0.351743i	−0.189865	+	0.981810i	$0.560805\pi$
$570$	−0.945115	+	0.447765i	−0.0395865	+	0.0187548i
$571$	2.73890	−	2.29821i	0.114619	−	0.0961770i	−0.583677	−	0.811986i	$-0.698386\pi$
$571$	2.73890	−	2.29821i	0.114619	−	0.0961770i	0.698296	+	0.715809i	$0.253942\pi$
$572$	−3.97008	−	1.44499i	−0.165998	−	0.0604182i
$573$	8.40619	−	8.50955i	0.351174	−	0.355491i
$574$	4.13344	−	7.50186i	0.172527	−	0.313122i
$575$	−2.51096	+	4.34911i	−0.104714	+	0.181370i
$576$	−17.3126	−	2.83500i	−0.721357	−	0.118125i
$577$	−36.8297			−1.53324			−0.766620	−	0.642101i	$-0.778063\pi$
$577$	−36.8297			−1.53324			−0.766620	+	0.642101i	$0.778063\pi$
$578$	10.7665	−	3.91867i	0.447825	−	0.162995i
$579$	−15.6290	+	34.0582i	−0.649519	+	1.41541i
$580$	−0.00139205	−	0.00789470i	−5.78017e−5	−	0.000327810i
$581$	−5.72367	+	2.21383i	−0.237458	+	0.0918450i
$582$	27.9464	−	2.61714i	1.15841	−	0.108484i
$583$	−3.77504	+	21.4093i	−0.156346	+	0.886683i
$584$	13.2847			0.549724
$585$	0.783911	+	0.911377i	0.0324107	+	0.0376808i
$586$	35.3021			1.45832
$587$	20.3928	−	7.42238i	0.841702	−	0.306354i	0.115049	−	0.993360i	$-0.463297\pi$
$587$	20.3928	−	7.42238i	0.841702	−	0.306354i	0.726652	+	0.687005i	$0.241075\pi$
$588$	2.93566	+	3.80633i	0.121064	+	0.156970i
$589$	18.3824	−	15.4247i	0.757434	−	0.635562i
$590$	−0.0808202	−	0.458354i	−0.00332732	−	0.0188701i
$591$	−1.71491	+	21.0844i	−0.0705419	+	0.867298i
$592$	28.1121	+	23.5889i	1.15540	+	0.969496i
$593$	−21.4332	−	37.1235i	−0.880158	−	1.52448i	−0.851165	−	0.524898i	$-0.824103\pi$
$593$	−21.4332	−	37.1235i	−0.880158	−	1.52448i	−0.0289927	−	0.999580i	$-0.509230\pi$
$594$	6.76559	+	13.8407i	0.277596	+	0.567892i
$595$	−0.181944	−	0.923474i	−0.00745896	−	0.0378588i
$596$	−0.475804	+	2.69842i	−0.0194897	+	0.110532i
$597$	−9.71038	+	4.60046i	−0.397420	+	0.188284i
$598$	6.63409	−	5.56666i	0.271288	−	0.227638i
$599$	0.629853	+	3.57208i	0.0257351	+	0.145951i	0.994968	−	0.100195i	$-0.0319467\pi$
$599$	0.629853	+	3.57208i	0.0257351	+	0.145951i	−0.969233	+	0.246146i	$0.920836\pi$
$600$	15.0924	−	15.2780i	0.616146	−	0.623721i
$601$	−7.71351	+	2.80749i	−0.314641	+	0.114520i	−0.494513	−	0.869170i	$-0.664654\pi$
$601$	−7.71351	+	2.80749i	−0.314641	+	0.114520i	0.179873	+	0.983690i	$0.442431\pi$
$602$	4.88201	+	24.7792i	0.198976	+	1.00992i
$603$	−24.8948	+	14.7816i	−1.01380	+	0.601951i
$604$	3.43142	−	5.94340i	0.139623	−	0.241834i
$605$	−0.496188	+	0.180598i	−0.0201729	+	0.00734234i
$606$	−22.5062	−	31.7278i	−0.914250	−	1.28885i
$607$	−0.839966	+	0.704815i	−0.0340932	+	0.0286076i	−0.659675	−	0.751551i	$-0.729306\pi$
$607$	−0.839966	+	0.704815i	−0.0340932	+	0.0286076i	0.625582	+	0.780159i	$0.284862\pi$
$608$	−2.07998	−	11.7962i	−0.0843545	−	0.478398i
$609$	−0.885715	+	0.933211i	−0.0358910	+	0.0378156i
$610$	0.504662	+	0.423462i	0.0204332	+	0.0171455i
$611$	−35.8964	+	62.1744i	−1.45221	+	2.51531i
$612$	−0.0717932	−	5.87489i	−0.00290207	−	0.237478i
$613$	3.16223	+	5.47714i	0.127721	+	0.221219i	0.922793	−	0.385295i	$-0.125900\pi$
$613$	3.16223	+	5.47714i	0.127721	+	0.221219i	−0.795072	+	0.606515i	$0.792567\pi$
$614$	14.6207	+	12.2683i	0.590045	+	0.495106i
$615$	0.0690534	+	0.251553i	0.00278450	+	0.0101436i
$616$	−11.7316	+	4.53759i	−0.472678	+	0.182825i
$617$	−20.1375	−	7.32946i	−0.810706	−	0.295073i	−0.0967904	−	0.995305i	$-0.530858\pi$
$617$	−20.1375	−	7.32946i	−0.810706	−	0.295073i	−0.713915	+	0.700232i	$0.753080\pi$
$618$	−1.62863	+	0.771593i	−0.0655132	+	0.0310380i
$619$	−3.21008	−	2.69358i	−0.129024	−	0.108264i	0.575992	−	0.817455i	$-0.304616\pi$
$619$	−3.21008	−	2.69358i	−0.129024	−	0.108264i	−0.705016	+	0.709191i	$0.749060\pi$
$620$	−0.0632549	+	0.109561i	−0.00254038	+	0.00440006i
$621$	−5.21194	−	0.359865i	−0.209148	−	0.0144409i
$622$	29.1020			1.16688
$623$	−5.41349	−	8.95788i	−0.216887	−	0.358890i
$624$	−40.3738	+	19.1278i	−1.61625	+	0.765725i
$625$	4.32770	+	24.5436i	0.173108	+	0.981744i
$626$	−0.941805	−	5.34124i	−0.0376421	−	0.213479i
$627$	12.6259	−	12.7811i	0.504230	−	0.510430i
$628$	−1.49423	−	1.25381i	−0.0596261	−	0.0500323i
$629$	19.5522	−	33.8654i	0.779597	−	1.35030i
$630$	−0.875957	−	0.125512i	−0.0348990	−	0.00500052i
$631$	6.32422	+	10.9539i	0.251763	+	0.436066i	0.964011	−	0.265861i	$-0.0856563\pi$
$631$	6.32422	+	10.9539i	0.251763	+	0.436066i	−0.712248	+	0.701928i	$0.752323\pi$
$632$	−0.287495	+	1.63046i	−0.0114359	+	0.0648564i
$633$	17.8193	−	38.8313i	0.708254	−	1.54341i
$634$	1.36544	+	0.496981i	0.0542287	+	0.0197376i
$635$	0.101810	−	0.0854289i	0.00404021	−	0.00339014i
$636$	−4.50980	−	6.35762i	−0.178825	−	0.252096i
$637$	−37.1028	−	11.8472i	−1.47007	−	0.469401i
$638$	0.416209	+	0.720894i	0.0164779	+	0.0285405i
$639$	25.9097	+	4.24281i	1.02497	+	0.167843i
$640$	−0.485253	−	0.840482i	−0.0191813	−	0.0332230i
$641$	4.75969	−	26.9936i	0.187997	−	1.06618i	−0.734048	−	0.679098i	$-0.762371\pi$
$641$	4.75969	−	26.9936i	0.187997	−	1.06618i	0.922044	−	0.387084i	$-0.126518\pi$
$642$	−4.33780	−	1.13395i	−0.171199	−	0.0447534i
$643$	13.1335	−	11.0203i	0.517935	−	0.434599i	−0.345976	−	0.938243i	$-0.612452\pi$
$643$	13.1335	−	11.0203i	0.517935	−	0.434599i	0.863911	+	0.503644i	$0.168008\pi$
$644$	−0.162333	+	1.04207i	−0.00639681	+	0.0410635i
$645$	−0.632751	−	0.437320i	−0.0249146	−	0.0172195i
$646$	−38.9177	+	14.1649i	−1.53120	+	0.557309i
$647$	−5.59987	+	9.69925i	−0.220153	+	0.381317i	−0.954854	−	0.297074i	$-0.903989\pi$
$647$	−5.59987	+	9.69925i	−0.220153	+	0.381317i	0.734701	+	0.678391i	$0.237322\pi$
$648$	21.1743	+	7.12583i	0.831806	+	0.279929i
$649$	3.99771	+	6.92423i	0.156924	+	0.271800i
$650$	7.47079	−	42.3689i	0.293028	−	1.66185i
$651$	20.1740	−	2.29702i	0.790679	−	0.0900275i
$652$	2.83903	+	1.03332i	0.111185	+	0.0404680i
$653$	40.0565	+	14.5794i	1.56753	+	0.570534i	0.972446	−	0.233129i	$-0.0748964\pi$
$653$	40.0565	+	14.5794i	1.56753	+	0.570534i	0.595085	+	0.803663i	$0.297119\pi$
$654$	7.10245	+	25.8733i	0.277728	+	1.01173i
$655$	0.0613976	−	0.348203i	0.00239900	−	0.0136054i
$656$	−9.69448			−0.378506
$657$	−15.8439	−	2.59450i	−0.618130	−	0.101221i
$658$	−10.2157	−	51.8507i	−0.398248	−	2.02135i
$659$	13.4137	+	11.2554i	0.522524	+	0.438450i	0.865511	−	0.500891i	$-0.166994\pi$
$659$	13.4137	+	11.2554i	0.522524	+	0.438450i	−0.342987	+	0.939340i	$0.611439\pi$
$660$	−0.0395035	+	0.0860848i	−0.00153767	+	0.00335084i
$661$	−5.56844	−	2.02675i	−0.216587	−	0.0788313i	0.231448	−	0.972847i	$-0.425654\pi$
$661$	−5.56844	−	2.02675i	−0.216587	−	0.0788313i	−0.448035	+	0.894016i	$0.647876\pi$
$662$	−25.2879	−	9.20404i	−0.982842	−	0.357725i
$663$	27.5432	+	38.8286i	1.06969	+	1.50798i
$664$	4.41080	+	3.70110i	0.171172	+	0.143631i
$665$	0.199481	+	1.01249i	0.00773554	+	0.0392625i
$666$	−23.9740	−	27.8722i	−0.928975	−	1.08003i
$667$	−0.282286			−0.0109301
$668$	−1.57277	+	8.91962i	−0.0608523	+	0.345110i
$669$	−0.825324	+	0.835472i	−0.0319089	+	0.0323012i
$670$	−1.01106	−	0.367995i	−0.0390606	−	0.0142169i
$671$	−10.6347	−	3.87070i	−0.410547	−	0.149427i
$672$	4.04206	−	9.29423i	0.155926	−	0.358533i
$673$	7.09779	−	40.2535i	0.273600	−	1.55166i	−0.469776	−	0.882786i	$-0.655665\pi$
$673$	7.09779	−	40.2535i	0.273600	−	1.55166i	0.743375	−	0.668874i	$-0.233224\pi$
$674$	−4.38819	−	7.60056i	−0.169027	−	0.292763i
$675$	−20.9837	+	15.2737i	−0.807663	+	0.587884i
$676$	−3.56000	+	6.16611i	−0.136923	+	0.237158i
$677$	5.10890	−	1.85949i	0.196351	−	0.0714659i	−0.241973	−	0.970283i	$-0.577795\pi$
$677$	5.10890	−	1.85949i	0.196351	−	0.0714659i	0.438324	+	0.898817i	$0.355572\pi$
$678$	0.433726	−	5.33257i	0.0166571	−	0.204796i
$679$	4.26310	−	27.3664i	0.163603	−	1.05023i
$680$	−0.676493	+	0.567645i	−0.0259423	+	0.0217682i
$681$	−25.5996	+	25.9143i	−0.980979	+	0.993040i
$682$	2.28114	−	12.9370i	0.0873492	−	0.495382i
$683$	16.5034	+	28.5848i	0.631486	+	1.09377i	0.987248	+	0.159190i	$0.0508882\pi$
$683$	16.5034	+	28.5848i	0.631486	+	1.09377i	−0.355762	+	0.934577i	$0.615778\pi$
$684$	0.0787132	+	6.44116i	0.00300967	+	0.246284i
$685$	0.553990	+	0.959538i	0.0211669	+	0.0366621i
$686$	26.3049	−	11.4034i	1.00433	−	0.435384i
$687$	2.04138	−	4.44852i	0.0778836	−	0.169722i
$688$	21.8976	−	18.3742i	0.834837	−	0.700511i
$689$	59.3487	+	21.6012i	2.26101	+	0.822939i
$690$	−0.112329	−	0.158355i	−0.00427630	−	0.00602846i
$691$	5.69526	−	32.2994i	0.216658	−	1.22873i	−0.661348	−	0.750079i	$-0.730015\pi$
$691$	5.69526	−	32.2994i	0.216658	−	1.22873i	0.878006	−	0.478649i	$-0.158873\pi$
$692$	4.62760	+	8.01523i	0.175915	+	0.304693i
$693$	14.8778	−	3.12056i	0.565160	−	0.118540i
$694$	−23.5810	+	40.8434i	−0.895121	+	1.55040i
$695$	0.145178	+	0.121819i	0.00550691	+	0.00462085i
$696$	1.16791	+	0.305305i	0.0442695	+	0.0115725i
$697$	1.79383	+	10.1733i	0.0679460	+	0.385341i
$698$	1.94239	+	11.0159i	0.0735207	+	0.416956i
$699$	−0.552038	+	6.78720i	−0.0208800	+	0.256715i
$700$	2.70985	+	4.48409i	0.102423	+	0.169483i
$701$	3.85629			0.145650			0.0728251	−	0.997345i	$-0.476799\pi$
$701$	3.85629			0.145650			0.0728251	+	0.997345i	$0.476799\pi$
$702$	43.0122	−	12.3743i	1.62339	−	0.467039i
$703$	−21.4368	+	37.1296i	−0.808504	+	1.40037i
$704$	8.57940	+	7.19897i	0.323348	+	0.271322i
$705$	1.32404	+	0.915097i	0.0498662	+	0.0344646i
$706$	12.8708	+	4.68458i	0.484398	+	0.176307i
$707$	−35.7993	+	13.8466i	−1.34637	+	0.520755i
$708$	−2.77355	−	0.725038i	−0.104237	−	0.0272486i
$709$	26.4618	+	22.2041i	0.993793	+	0.833892i	0.986112	−	0.166079i	$-0.0531106\pi$
$709$	26.4618	+	22.2041i	0.993793	+	0.833892i	0.00768095	+	0.999971i	$0.497555\pi$
$710$	0.487846	+	0.844975i	0.0183086	+	0.0317113i
$711$	0.661309	−	1.88842i	0.0248010	−	0.0708212i
$712$	−4.91010	+	8.50454i	−0.184014	+	0.318721i
$713$	3.41258	+	2.86349i	0.127802	+	0.107239i
$714$	−34.0741	−	8.18313i	−1.27519	−	0.306246i
$715$	−0.133266	−	0.755787i	−0.00498385	−	0.0282648i
$716$	−7.84296	+	6.58103i	−0.293105	+	0.245944i
$717$	25.6476	−	2.40186i	0.957827	−	0.0896992i
$718$	28.3595	−	10.3220i	1.05837	−	0.385215i
$719$	−14.6327	+	25.3446i	−0.545708	+	0.945194i	0.452854	+	0.891585i	$0.350406\pi$
$719$	−14.6327	+	25.3446i	−0.545708	+	0.945194i	−0.998562	+	0.0536093i	$0.982927\pi$
$720$	0.354032	+	0.936911i	0.0131940	+	0.0349166i
$721$	0.343748	+	1.74473i	0.0128018	+	0.0649771i
$722$	15.0297	−	5.47036i	0.559348	−	0.203586i
$723$	36.8006	+	9.62008i	1.36863	+	0.357775i
$724$	0.563759	+	3.19723i	0.0209519	+	0.118824i
$725$	−1.07427	+	0.901416i	−0.0398972	+	0.0334777i
$726$	−1.59373	+	19.5945i	−0.0591487	+	0.727221i
$727$	−5.41948	+	30.7354i	−0.200997	+	1.13991i	0.702618	+	0.711567i	$0.252014\pi$
$727$	−5.41948	+	30.7354i	−0.200997	+	1.13991i	−0.903615	+	0.428345i	$0.859097\pi$
$728$	7.06393	+	35.8538i	0.261807	+	1.32883i
$729$	−23.8618	−	12.6339i	−0.883769	−	0.467923i
$730$	−0.298320	−	0.516706i	−0.0110413	−	0.0191242i
$731$	−23.3336	−	19.5792i	−0.863024	−	0.724163i
$732$	3.66704	−	1.73733i	0.135538	−	0.0642134i
$733$	−4.25459	−	24.1290i	−0.157147	−	0.891225i	−0.956797	−	0.290758i	$-0.906093\pi$
$733$	−4.25459	−	24.1290i	−0.157147	−	0.891225i	0.799650	−	0.600467i	$-0.205019\pi$
$734$	−10.9643	+	9.20013i	−0.404699	+	0.339583i
$735$	−0.332155	+	0.807526i	−0.0122517	+	0.0297861i
$736$	2.08957	−	0.760540i	0.0770224	−	0.0280339i
$737$	18.4834			0.680844
$738$	9.58441	+	1.56948i	0.352807	+	0.0577735i
$739$	−45.5697			−1.67631			−0.838155	−	0.545432i	$-0.816366\pi$
$739$	−45.5697			−1.67631			−0.838155	+	0.545432i	$0.816366\pi$
$740$	0.0392496	−	0.222596i	0.00144285	−	0.00818278i
$741$	−30.1980	−	42.5712i	−1.10935	−	1.56389i
$742$	−43.3606	+	16.7712i	−1.59182	+	0.615690i
$743$	−3.19026	−	18.0929i	−0.117039	−	0.663762i	−0.985720	−	0.168391i	$-0.946143\pi$
$743$	−3.19026	−	18.0929i	−0.117039	−	0.663762i	0.868681	−	0.495372i	$-0.164968\pi$
$744$	−11.0220	−	15.5381i	−0.404085	−	0.569654i
$745$	−0.467712	+	0.170233i	−0.0171356	+	0.00623686i
$746$	−10.3613			−0.379355
$747$	−4.53769	−	5.27553i	−0.166025	−	0.193021i
$748$	−1.87542	+	3.24832i	−0.0685721	+	0.118770i
$749$	−2.13501	+	3.87486i	−0.0780114	+	0.141584i
$750$	−1.86727	−	0.488125i	−0.0681830	−	0.0178238i
$751$	−47.5372	−	17.3021i	−1.73466	−	0.631363i	−0.735711	−	0.677296i	$-0.763152\pi$
$751$	−47.5372	−	17.3021i	−1.73466	−	0.631363i	−0.998945	+	0.0459328i	$0.985374\pi$
$752$	−45.8209	+	38.4483i	−1.67092	+	1.40206i
$753$	3.53641	−	43.4794i	0.128874	−	1.58448i
$754$	2.27249	−	0.827117i	0.0827591	−	0.0301218i
$755$	1.24663			0.0453696
$756$	−2.95291	+	4.58130i	−0.107396	+	0.166620i
$757$	−22.9761			−0.835081			−0.417540	−	0.908658i	$-0.637108\pi$
$757$	−22.9761			−0.835081			−0.417540	+	0.908658i	$0.637108\pi$
$758$	42.8899	−	15.6106i	1.55783	−	0.567004i
$759$	2.74371	+	1.89629i	0.0995904	+	0.0688310i
$760$	0.741699	−	0.622359i	0.0269043	−	0.0225753i
$761$	27.5653	+	10.0329i	0.999240	+	0.363694i	0.789291	−	0.614019i	$-0.210448\pi$
$761$	27.5653	+	10.0329i	0.999240	+	0.363694i	0.209948	+	0.977712i	$0.432670\pi$
$762$	−1.30986	−	4.77164i	−0.0474511	−	0.172858i
$763$	26.4694	−	0.529361i	0.958257	−	0.0191642i
$764$	1.36899	−	2.37115i	0.0495282	−	0.0857853i
$765$	0.917677	−	0.544880i	0.0331787	−	0.0197002i
$766$	−36.6150			−1.32295
$767$	21.8274	−	7.94451i	0.788141	−	0.286860i
$768$	−15.8068	+	1.48028i	−0.570378	+	0.0534151i
$769$	5.81568	+	32.9824i	0.209719	+	1.18938i	0.889839	+	0.456275i	$0.150816\pi$
$769$	5.81568	+	32.9824i	0.209719	+	1.18938i	−0.680120	+	0.733101i	$0.738072\pi$
$770$	0.439933	+	0.354402i	0.0158541	+	0.0127718i
$771$	4.43493	−	9.66447i	0.159720	−	0.348057i
$772$	−1.48948	+	8.44725i	−0.0536075	+	0.304023i
$773$	−47.8452			−1.72087			−0.860436	−	0.509558i	$-0.829809\pi$
$773$	−47.8452			−1.72087			−0.860436	+	0.509558i	$0.829809\pi$
$774$	−24.6236	+	14.6205i	−0.885078	+	0.525524i
$775$	22.1308			0.794963
$776$	−24.4188	+	8.88772i	−0.876585	+	0.319051i
$777$	−32.4666	+	16.1843i	−1.16473	+	0.580607i
$778$	−41.7694	+	35.0486i	−1.49750	+	1.25655i
$779$	−1.96673	−	11.1539i	−0.0704654	−	0.399629i
$780$	0.226364	+	0.156450i	0.00810514	+	0.00560180i
$781$	−12.8398	−	10.7739i	−0.459444	−	0.385520i
$782$	−3.84425	−	6.65843i	−0.137470	−	0.238105i
$783$	−1.33328	−	0.592213i	−0.0476474	−	0.0211640i
$784$	−25.6724	−	19.8480i	−0.916872	−	0.708859i
$785$	0.0615272	−	0.348938i	0.00219600	−	0.0124541i
$786$	−10.8292	−	7.48453i	−0.386266	−	0.266964i
$787$	2.28279	−	1.91549i	0.0813728	−	0.0682798i	−0.601194	−	0.799103i	$-0.705308\pi$
$787$	2.28279	−	1.91549i	0.0813728	−	0.0682798i	0.682567	+	0.730823i	$0.260864\pi$
$788$	0.840831	+	4.76859i	0.0299534	+	0.169874i
$789$	3.42449	+	12.4750i	0.121915	+	0.444121i
$790$	0.0698727	−	0.0254316i	0.00248596	−	0.000904815i
$791$	−4.99597	−	1.70605i	−0.177636	−	0.0606602i
$792$	−9.30072	−	10.8130i	−0.330487	−	0.384224i
$793$	−16.4393	+	28.4737i	−0.583776	+	1.01113i
$794$	−17.3604	+	6.31868i	−0.616098	+	0.224241i
$795$	0.590537	−	1.28688i	0.0209442	−	0.0456409i
$796$	−1.88411	+	1.58096i	−0.0667806	+	0.0560356i
$797$	3.52012	+	19.9636i	0.124689	+	0.707146i	0.981492	+	0.191502i	$0.0613360\pi$
$797$	3.52012	+	19.9636i	0.124689	+	0.707146i	−0.856803	+	0.515643i	$0.827553\pi$
$798$	37.3585	+	8.97189i	1.32248	+	0.317601i
$799$	48.8258	+	40.9697i	1.72733	+	1.44940i
$800$	5.52343	−	9.56687i	0.195283	−	0.338240i
$801$	7.51694	−	9.18395i	0.265598	−	0.324499i
$802$	−16.6707	−	28.8745i	−0.588664	−	1.01960i
$803$	7.85160	+	6.58828i	0.277077	+	0.232495i
$804$	−4.65743	+	4.71469i	−0.164255	+	0.166274i
$805$	−0.178676	+	0.0691090i	−0.00629749	+	0.00243577i
$806$	−35.8625	−	13.0529i	−1.26320	−	0.459769i
$807$	3.91217	−	48.0993i	0.137715	−	1.69318i
$808$	27.5878	+	23.1489i	0.970534	+	0.814375i
$809$	−1.83232	+	3.17367i	−0.0644208	+	0.111580i	−0.896437	−	0.443171i	$-0.853853\pi$
$809$	−1.83232	+	3.17367i	−0.0644208	+	0.111580i	0.832016	+	0.554751i	$0.187187\pi$
$810$	−0.198331	−	0.983590i	−0.00696866	−	0.0345598i
$811$	−27.2153			−0.955658			−0.477829	−	0.878453i	$-0.658576\pi$
$811$	−27.2153			−0.955658			−0.477829	+	0.878453i	$0.658576\pi$
$812$	−0.142124	+	0.257942i	−0.00498756	+	0.00905200i
$813$	−15.5235	−	10.7289i	−0.544432	−	0.376279i
$814$	4.07561	+	23.1139i	0.142850	+	0.810143i
$815$	0.0952990	+	0.540468i	0.00333818	+	0.0189318i
$816$	10.4994	+	38.2481i	0.367554	+	1.33895i
$817$	25.5827	+	21.4664i	0.895024	+	0.751015i
$818$	−8.18627	+	14.1790i	−0.286226	+	0.495759i
$819$	−1.42252	−	44.1404i	−0.0497069	−	1.54239i
$820$	0.0298552	+	0.0517108i	0.00104259	+	0.00180582i
$821$	5.41453	−	30.7073i	0.188969	−	1.07169i	−0.731781	−	0.681540i	$-0.761311\pi$
$821$	5.41453	−	30.7073i	0.188969	−	1.07169i	0.920750	−	0.390154i	$-0.127578\pi$
$822$	41.0716	−	3.84630i	1.43254	−	0.134155i
$823$	26.5953	+	9.67990i	0.927054	+	0.337420i	0.761041	−	0.648703i	$-0.224688\pi$
$823$	26.5953	+	9.67990i	0.927054	+	0.337420i	0.166013	+	0.986124i	$0.446911\pi$
$824$	1.27810	−	1.07246i	0.0445248	−	0.0373608i
$825$	16.4968	−	1.54491i	0.574346	−	0.0537867i
$826$	−8.25148	+	14.9757i	−0.287106	+	0.521073i
$827$	0.505252	+	0.875122i	0.0175693	+	0.0304310i	0.874676	−	0.484707i	$-0.161074\pi$
$827$	0.505252	+	0.875122i	0.0175693	+	0.0304310i	−0.857107	+	0.515138i	$0.827741\pi$
$828$	−1.17506	+	0.222033i	−0.0408361	+	0.00771616i
$829$	−12.0029	−	20.7897i	−0.416879	−	0.722055i	0.578745	−	0.815509i	$-0.303543\pi$
$829$	−12.0029	−	20.7897i	−0.416879	−	0.722055i	−0.995624	+	0.0934535i	$0.970209\pi$
$830$	0.0449051	−	0.254669i	0.00155868	−	0.00883970i
$831$	−1.78674	−	6.50888i	−0.0619814	−	0.225790i
$832$	24.9248	−	20.9144i	0.864112	−	0.725076i
$833$	−16.0780	+	30.6130i	−0.557071	+	1.06068i
$834$	6.37648	−	3.02097i	0.220799	−	0.104608i
$835$	−1.54602	+	0.562705i	−0.0535022	+	0.0194732i
$836$	2.05619	−	3.56142i	0.0711147	−	0.123174i
$837$	10.1107	+	20.6840i	0.349477	+	0.714944i
$838$	−9.98061	−	17.2869i	−0.344774	−	0.597167i
$839$	4.16417	−	23.6162i	0.143763	−	0.815321i	−0.824589	−	0.565733i	$-0.808593\pi$
$839$	4.16417	−	23.6162i	0.143763	−	0.815321i	0.968352	−	0.249589i	$-0.0802954\pi$
$840$	0.813985	−	0.0926811i	0.0280852	−	0.00319780i
$841$	27.1770	+	9.89162i	0.937138	+	0.341090i
$842$	−36.4799	−	13.2776i	−1.25718	−	0.457577i
$843$	−7.87129	−	2.05764i	−0.271101	−	0.0708690i
$844$	1.69822	−	9.63109i	0.0584552	−	0.331516i
$845$	−1.29335			−0.0444925
$846$	51.5252	−	30.5936i	1.77147	−	1.05183i
$847$	18.3577	+	6.26889i	0.630778	+	0.215401i
$848$	40.3095	+	33.8237i	1.38424	+	1.16151i
$849$	−4.68066	+	0.438338i	−0.160640	+	0.0150437i
$850$	−35.8919	−	13.0636i	−1.23108	−	0.448077i
$851$	−7.47921	−	2.72221i	−0.256384	−	0.0933162i
$852$	5.98353	−	0.560350i	0.204992	−	0.0191973i
$853$	29.2727	+	24.5627i	1.00228	+	0.841010i	0.987298	−	0.158878i	$-0.0507876\pi$
$853$	29.2727	+	24.5627i	1.00228	+	0.841010i	0.0149784	+	0.999888i	$0.495232\pi$
$854$	−4.67841	−	23.7458i	−0.160092	−	0.812564i
$855$	−1.00613	+	0.597400i	−0.0344089	+	0.0204306i
$856$	4.15089			0.141874
$857$	−2.08790	+	11.8411i	−0.0713213	+	0.404483i	0.928157	+	0.372189i	$0.121393\pi$
$857$	−2.08790	+	11.8411i	−0.0713213	+	0.404483i	−0.999478	+	0.0322944i	$0.989719\pi$
$858$	−27.6440	−	7.22645i	−0.943750	−	0.246707i
$859$	−32.1869	−	11.7151i	−1.09820	−	0.399714i	−0.271550	−	0.962424i	$-0.587536\pi$
$859$	−32.1869	−	11.7151i	−1.09820	−	0.399714i	−0.826654	+	0.562711i	$0.809759\pi$
$860$	−0.165445	−	0.0602170i	−0.00564163	−	0.00205338i
$861$	3.82197	−	8.78817i	0.130253	−	0.299500i
$862$	1.27296	−	7.21931i	0.0433572	−	0.245891i
$863$	15.6504	+	27.1073i	0.532746	+	0.922743i	0.999269	+	0.0382338i	$0.0121732\pi$
$863$	15.6504	+	27.1073i	0.532746	+	0.922743i	−0.466523	+	0.884509i	$0.654493\pi$
$864$	11.4649	+	0.791606i	0.390043	+	0.0269310i
$865$	−0.840601	+	1.45596i	−0.0285813	+	0.0495042i
$866$	−33.2951	+	12.1184i	−1.13141	+	0.411801i
$867$	11.5848	−	5.48852i	0.393442	−	0.186400i
$868$	4.33470	−	1.67660i	0.147129	−	0.0569074i
$869$	−0.978513	+	0.821070i	−0.0331938	+	0.0278529i
$870$	−0.0143517	−	0.0522816i	−0.000486570	−	0.00177251i
$871$	9.32452	−	52.8820i	0.315949	−	1.79184i
$872$	−12.4198	−	21.5118i	−0.420589	−	0.728481i
$873$	30.8588	−	5.83090i	1.04441	−	0.197346i
$874$	4.21479	+	7.30023i	0.142567	+	0.246934i
$875$	−0.919044	+	1.66799i	−0.0310694	+	0.0563883i
$876$	−3.65896	+	0.342657i	−0.123625	+	0.0115773i
$877$	−37.3544	+	31.3440i	−1.26137	+	1.05841i	−0.265832	+	0.964019i	$0.585647\pi$
$877$	−37.3544	+	31.3440i	−1.26137	+	1.05841i	−0.995535	+	0.0943933i	$0.969909\pi$
$878$	50.3230	+	18.3161i	1.69832	+	0.618137i
$879$	39.3260	−	3.68283i	1.32643	−	0.124219i
$880$	0.111032	−	0.629692i	0.00374288	−	0.0212269i
$881$	12.3918	+	21.4632i	0.417490	+	0.723113i	0.995686	−	0.0927841i	$-0.0295766\pi$
$881$	12.3918	+	21.4632i	0.417490	+	0.723113i	−0.578197	+	0.815898i	$0.696243\pi$
$882$	22.1676	+	23.7789i	0.746423	+	0.800678i
$883$	−12.3547	+	21.3989i	−0.415768	+	0.720131i	−0.995509	−	0.0946699i	$-0.969820\pi$
$883$	−12.3547	+	21.3989i	−0.415768	+	0.720131i	0.579741	+	0.814801i	$0.303154\pi$
$884$	8.34750	+	7.00438i	0.280757	+	0.235583i
$885$	−0.137849	−	0.502168i	−0.00463376	−	0.0168802i
$886$	−2.40939	−	13.6644i	−0.0809452	−	0.459063i
$887$	−4.54357	−	25.7679i	−0.152558	−	0.865201i	−0.960984	−	0.276603i	$-0.910791\pi$
$887$	−4.54357	−	25.7679i	−0.152558	−	0.865201i	0.808426	−	0.588598i	$-0.200320\pi$
$888$	27.9998	+	19.3518i	0.939611	+	0.649404i
$889$	−4.88157	+	0.0976264i	−0.163723	+	0.00327429i
$890$	0.441044			0.0147838
$891$	8.98067	+	14.7125i	0.300864	+	0.492888i
$892$	−0.134408	+	0.232801i	−0.00450030	+	0.00779476i
$893$	−53.5320	−	44.9187i	−1.79138	−	1.50315i
$894$	−1.50226	+	18.4700i	−0.0502432	+	0.617729i
$895$	−1.74762	−	0.636081i	−0.0584164	−	0.0212618i
$896$	−5.48793	+	35.2290i	−0.183339	+	1.17692i
$897$	6.80954	−	6.89326i	0.227364	−	0.230159i
$898$	−31.5752	−	26.4947i	−1.05368	−	0.884140i
$899$	0.621995	+	1.07733i	0.0207447	+	0.0359309i
$900$	−3.76279	+	4.59725i	−0.125426	+	0.153242i
$901$	28.0356	−	48.5591i	0.934001	−	1.61774i
$902$	−4.74965	−	3.98543i	−0.158146	−	0.132700i
$903$	8.02353	+	27.0943i	0.267006	+	0.901642i
$904$	0.860114	+	4.87795i	0.0286070	+	0.162238i
$905$	−0.451764	+	0.379075i	−0.0150171	+	0.0126009i
$906$	19.3578	−	42.1840i	0.643121	−	1.40147i
$907$	−29.4394	+	10.7150i	−0.977518	+	0.355787i	−0.780875	−	0.624688i	$-0.785226\pi$
$907$	−29.4394	+	10.7150i	−0.977518	+	0.355787i	−0.196643	+	0.980475i	$0.563004\pi$
$908$	−4.16901	+	7.22094i	−0.138353	+	0.239635i
$909$	−28.3814	−	32.9963i	−0.941353	−	1.09442i
$910$	1.23590	−	1.07988i	0.0409697	−	0.0357977i
$911$	40.7331	−	14.8256i	1.34955	−	0.491195i	0.436741	−	0.899587i	$-0.356133\pi$
$911$	40.7331	−	14.8256i	1.34955	−	0.491195i	0.912806	+	0.408392i	$0.133910\pi$
$912$	−11.5115	−	41.9348i	−0.381182	−	1.38860i
$913$	0.771412	+	4.37490i	0.0255300	+	0.144788i
$914$	47.9921	−	40.2701i	1.58744	−	1.33202i
$915$	0.606363	+	0.419082i	0.0200457	+	0.0138544i
$916$	0.194548	−	1.10334i	0.00642806	−	0.0364553i
$917$	−9.78155	+	8.54674i	−0.323015	+	0.282238i
$918$	−4.18806	−	39.5136i	−0.138227	−	1.30414i
$919$	15.0526	+	26.0718i	0.496538	+	0.860030i	0.999992	−	0.00399256i	$-0.00127088\pi$
$919$	15.0526	+	26.0718i	0.496538	+	0.860030i	−0.503454	+	0.864022i	$0.667938\pi$
$920$	0.137692	+	0.115537i	0.00453956	+	0.00380915i
$921$	17.5671	+	12.1414i	0.578856	+	0.400071i
$922$	2.93210	+	16.6288i	0.0965635	+	0.547639i
$923$	−37.3021	+	31.3002i	−1.22781	+	1.03026i
$924$	3.11415	−	1.55237i	0.102448	−	0.0510692i
$925$	−37.1557	+	13.5236i	−1.22167	+	0.444652i
$926$	−22.0914			−0.725967
$927$	−1.73377	+	1.02945i	−0.0569446	+	0.0338114i
$928$	0.620952			0.0203838
$929$	1.19780	−	6.79304i	0.0392984	−	0.222872i	−0.958833	−	0.283969i	$-0.908349\pi$
$929$	1.19780	−	6.79304i	0.0392984	−	0.222872i	0.998132	+	0.0610967i	$0.0194598\pi$
$930$	−0.356843	+	0.777621i	−0.0117013	+	0.0254992i
$931$	17.6278	−	33.5637i	0.577727	−	1.10001i
$932$	0.270668	+	1.53504i	0.00886604	+	0.0502818i
$933$	32.4191	−	3.03601i	1.06135	−	0.0993944i
$934$	1.96026	−	0.713477i	0.0641417	−	0.0233457i
$935$	−0.681338			−0.0222821
$936$	−35.6287	+	21.1549i	−1.16456	+	0.691469i
$937$	−15.7464	+	27.2736i	−0.514413	+	0.890989i	0.485448	+	0.874266i	$0.338657\pi$
$937$	−15.7464	+	27.2736i	−0.514413	+	0.890989i	−0.999860	+	0.0167230i	$0.994677\pi$
$938$	20.4443	+	33.8298i	0.667529	+	1.10458i
$939$	−1.60637	−	5.85181i	−0.0524219	−	0.190966i
$940$	0.346195	+	0.126005i	0.0112916	+	0.00410982i
$941$	−36.8138	+	30.8905i	−1.20010	+	1.00700i	−0.200469	+	0.979700i	$0.564247\pi$
$941$	−36.8138	+	30.8905i	−1.20010	+	1.00700i	−0.999627	+	0.0273000i	$0.991309\pi$
$942$	−10.8521	−	7.50033i	−0.353580	−	0.244374i
$943$	1.97579	−	0.719129i	0.0643406	−	0.0234181i
$944$	19.3528			0.629880
$945$	−0.988896	−	0.0484358i	−0.0321688	−	0.00157562i
$946$	18.2820			0.594400
$947$	45.1615	−	16.4374i	1.46755	−	0.534145i	0.520116	−	0.854095i	$-0.325889\pi$
$947$	45.1615	−	16.4374i	1.46755	−	0.534145i	0.947434	+	0.319951i	$0.103666\pi$
$948$	0.0371286	−	0.456489i	0.00120588	−	0.0148261i
$949$	22.8104	−	19.1402i	0.740457	−	0.621317i
$950$	39.3514	+	14.3228i	1.27673	+	0.464691i
$951$	1.57293	+	0.411181i	0.0510057	+	0.0133335i
$952$	32.4363	−	0.648694i	1.05127	−	0.0210243i
$953$	15.7747	−	27.3226i	0.510994	−	0.885067i	−0.488925	−	0.872326i	$-0.662611\pi$
$953$	15.7747	−	27.3226i	0.510994	−	0.885067i	0.999919	−	0.0127415i	$-0.00405585\pi$
$954$	−34.3760	−	39.9656i	−1.11296	−	1.29393i
$955$	0.497351			0.0160939
$956$	5.54081	−	2.01669i	0.179203	−	0.0652244i
$957$	0.538856	+	0.759644i	0.0174187	+	0.0245558i
$958$	7.81242	+	44.3064i	0.252408	+	1.43148i
$959$	6.26530	−	40.2193i	0.202317	−	1.29875i
$960$	−0.422030	−	0.594951i	−0.0136210	−	0.0192020i
$961$	−1.97409	+	11.1956i	−0.0636804	+	0.361150i
$962$	68.1862			2.19841
$963$	−4.95054	−	0.810669i	−0.159529	−	0.0261235i
$964$	8.70669			0.280424
$965$	−1.46415	+	0.532905i	−0.0471325	+	0.0171548i
$966$	−0.435958	+	7.11923i	−0.0140267	+	0.229057i
$967$	−5.89186	+	4.94386i	−0.189470	+	0.158984i	−0.732588	−	0.680672i	$-0.761688\pi$
$967$	−5.89186	+	4.94386i	−0.189470	+	0.158984i	0.543119	+	0.839656i	$0.317243\pi$
$968$	−3.16049	−	17.9240i	−0.101582	−	0.576100i
$969$	−41.8759	+	19.8395i	−1.34525	+	0.637335i
$970$	0.894035	+	0.750184i	0.0287057	+	0.0240870i
$971$	16.3198	+	28.2667i	0.523727	+	0.907121i	0.999619	+	0.0276176i	$0.00879207\pi$
$971$	16.3198	+	28.2667i	0.523727	+	0.907121i	−0.475892	+	0.879504i	$0.657875\pi$
$972$	−6.01577	−	1.41649i	−0.192956	−	0.0454339i
$973$	−1.34585	−	6.83102i	−0.0431461	−	0.218993i
$974$	9.53478	−	54.0744i	0.305514	−	1.73266i
$975$	3.90228	−	47.9777i	0.124973	−	1.53652i
$976$	−20.9843	+	17.6079i	−0.671692	+	0.563616i
$977$	−6.85959	−	38.9027i	−0.219458	−	1.24461i	−0.873001	−	0.487718i	$-0.837829\pi$
$977$	−6.85959	−	38.9027i	−0.219458	−	1.24461i	0.653543	−	0.756889i	$-0.273282\pi$
$978$	19.7684	+	5.16767i	0.632122	+	0.165244i
$979$	−7.11965	+	2.59134i	−0.227545	+	0.0828196i
$980$	−0.0268093	+	0.198062i	−0.000856391	+	0.00632686i
$981$	10.6112	+	28.0815i	0.338790	+	0.896574i
$982$	25.1932	−	43.6359i	0.803947	−	1.39248i
$983$	46.8652	−	17.0575i	1.49477	−	0.544051i	0.540067	−	0.841622i	$-0.318399\pi$
$983$	46.8652	−	17.0575i	1.49477	−	0.544051i	0.954700	+	0.297572i	$0.0961767\pi$
$984$	−8.95227	+	0.838368i	−0.285388	+	0.0267262i
$985$	−0.673794	+	0.565380i	−0.0214689	+	0.0180145i
$986$	−0.372820	−	2.11437i	−0.0118730	−	0.0673353i
$987$	−16.7893	−	56.6951i	−0.534410	−	1.80463i
$988$	−9.15210	−	7.67952i	−0.291167	−	0.244318i
$989$	−3.09986	+	5.36912i	−0.0985699	+	0.170728i
$990$	−0.211715	+	0.604567i	−0.00672874	+	0.0192144i
$991$	−10.6088	−	18.3749i	−0.336998	−	0.583698i	0.646868	−	0.762602i	$-0.276078\pi$
$991$	−10.6088	−	18.3749i	−0.336998	−	0.583698i	−0.983867	+	0.178904i	$0.942745\pi$
$992$	−7.50676	−	6.29892i	−0.238340	−	0.199991i
$993$	−29.1305	−	7.61504i	−0.924428	−	0.241656i
$994$	5.51726	−	35.4173i	0.174997	−	1.12337i
$995$	−0.419830	−	0.152805i	−0.0133095	−	0.00484426i
$996$	−1.31032	−	0.905613i	−0.0415190	−	0.0286954i
$997$	26.6234	+	22.3397i	0.843172	+	0.707506i	0.958275	−	0.285848i	$-0.0922753\pi$
$997$	26.6234	+	22.3397i	0.843172	+	0.707506i	−0.115103	+	0.993354i	$0.536720\pi$
$998$	3.17351	−	5.49668i	0.100456	−	0.173994i
$999$	−29.6144	−	28.5482i	−0.936958	−	0.903225i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.w.a.25.17	yes	132
3.2	odd	2		567.2.w.a.235.6		132
7.2	even	3		189.2.u.a.79.6	yes	132
21.2	odd	6		567.2.u.a.478.17		132
27.13	even	9		189.2.u.a.67.6	✓	132
27.14	odd	18		567.2.u.a.172.17		132
189.121	even	9	inner	189.2.w.a.121.17	yes	132
189.149	odd	18		567.2.w.a.415.6		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.67.6	✓	132	27.13	even	9
189.2.u.a.79.6	yes	132	7.2	even	3
189.2.w.a.25.17	yes	132	1.1	even	1	trivial
189.2.w.a.121.17	yes	132	189.121	even	9	inner
567.2.u.a.172.17		132	27.14	odd	18
567.2.u.a.478.17		132	21.2	odd	6
567.2.w.a.235.6		132	3.2	odd	2
567.2.w.a.415.6		132	189.149	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)

\(f(q)\)	\(=\)	\(q+(1.45469 - 0.529465i) q^{2} +(1.56527 - 0.741574i) q^{3} +(0.303710 - 0.254843i) q^{4} +(0.0676746 + 0.0246315i) q^{5} +(1.88435 - 1.90752i) q^{6} +(-1.36843 - 2.26438i) q^{7} +(-1.24118 + 2.14978i) q^{8} +(1.90014 - 2.32153i) q^{9} +O(q^{10})\)	\(q+(1.45469 - 0.529465i) q^{2} +(1.56527 - 0.741574i) q^{3} +(0.303710 - 0.254843i) q^{4} +(0.0676746 + 0.0246315i) q^{5} +(1.88435 - 1.90752i) q^{6} +(-1.36843 - 2.26438i) q^{7} +(-1.24118 + 2.14978i) q^{8} +(1.90014 - 2.32153i) q^{9} +0.111487 q^{10} +(-1.79971 + 0.655041i) q^{11} +(0.286404 - 0.624122i) q^{12} +(0.966188 + 5.47952i) q^{13} +(-3.18955 - 2.56944i) q^{14} +(0.124195 - 0.0116307i) q^{15} +(-0.804989 + 4.56532i) q^{16} +4.93976 q^{17} +(1.53495 - 4.38316i) q^{18} -5.41589 q^{19} +(0.0268307 - 0.00976556i) q^{20} +(-3.82116 - 2.52957i) q^{21} +(-2.27121 + 1.90577i) q^{22} +(-0.174590 - 0.990152i) q^{23} +(-0.348555 + 4.28541i) q^{24} +(-3.82625 - 3.21060i) q^{25} +(4.30672 + 7.45946i) q^{26} +(1.25264 - 5.04290i) q^{27} +(-0.992667 - 0.338981i) q^{28} +(0.0487538 - 0.276497i) q^{29} +(0.174508 - 0.0826761i) q^{30} +(-3.39416 + 2.84804i) q^{31} +(0.384052 + 2.17807i) q^{32} +(-2.33127 + 2.35993i) q^{33} +(7.18583 - 2.61543i) q^{34} +(-0.0368325 - 0.186947i) q^{35} +(-0.0145337 - 1.18931i) q^{36} +(3.95813 - 6.85568i) q^{37} +(-7.87846 + 2.86752i) q^{38} +(5.57581 + 7.86043i) q^{39} +(-0.136949 + 0.114914i) q^{40} +(0.363141 + 2.05947i) q^{41} +(-6.89793 - 1.65659i) q^{42} +(-4.72363 - 3.96360i) q^{43} +(-0.379658 + 0.657587i) q^{44} +(0.185774 - 0.110305i) q^{45} +(-0.778226 - 1.34793i) q^{46} +(9.88425 + 8.29387i) q^{47} +(2.12550 + 7.74291i) q^{48} +(-3.25482 + 6.19727i) q^{49} +(-7.26592 - 2.64458i) q^{50} +(7.73205 - 3.66319i) q^{51} +(1.68986 + 1.41796i) q^{52} +(5.67550 - 9.83026i) q^{53} +(-0.847828 - 7.99911i) q^{54} -0.137929 q^{55} +(6.56638 - 0.131321i) q^{56} +(-8.47733 + 4.01628i) q^{57} +(-0.0754735 - 0.428031i) q^{58} +(-0.724927 - 4.11127i) q^{59} +(0.0347553 - 0.0351827i) q^{60} +(4.52663 + 3.79830i) q^{61} +(-3.42953 + 5.94011i) q^{62} +(-7.85701 - 1.12580i) q^{63} +(-2.92386 - 5.06427i) q^{64} +(-0.0695827 + 0.394623i) q^{65} +(-2.14178 + 4.66731i) q^{66} +(-9.06882 - 3.30078i) q^{67} +(1.50025 - 1.25886i) q^{68} +(-1.00755 - 1.42038i) q^{69} +(-0.152562 - 0.252450i) q^{70} +(4.37580 + 7.57911i) q^{71} +(2.63237 + 6.96631i) q^{72} +(-2.67582 - 4.63466i) q^{73} +(2.12802 - 12.0686i) q^{74} +(-8.37001 - 2.18802i) q^{75} +(-1.64486 + 1.38020i) q^{76} +(3.94603 + 3.17885i) q^{77} +(12.2729 + 8.48232i) q^{78} +(0.626732 - 0.228112i) q^{79} +(-0.166928 + 0.289128i) q^{80} +(-1.77896 - 8.82243i) q^{81} +(1.61868 + 2.80363i) q^{82} +(0.402782 - 2.28429i) q^{83} +(-1.80517 + 0.205538i) q^{84} +(0.334296 + 0.121674i) q^{85} +(-8.97002 - 3.26482i) q^{86} +(-0.128730 - 0.468946i) q^{87} +(0.825564 - 4.68201i) q^{88} +3.95600 q^{89} +(0.211841 - 0.258821i) q^{90} +(11.0856 - 9.68613i) q^{91} +(-0.305358 - 0.256226i) q^{92} +(-3.20075 + 6.97497i) q^{93} +(18.7699 + 6.83167i) q^{94} +(-0.366518 - 0.133402i) q^{95} +(2.21634 + 3.12446i) q^{96} +(8.01916 + 6.72888i) q^{97} +(-1.45353 + 10.7384i) q^{98} +(-1.89900 + 5.42274i) 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

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