LMFDB - Embedded newform 189.2.be.a.104.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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 $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.14
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.157445 - 0.432576i) q^{2} +(0.888001 + 1.48710i) q^{3} +(1.36976 + 1.14936i) q^{4} +(0.725040 - 4.11191i) q^{5} +(0.783093 - 0.149993i) q^{6} +(-1.09969 - 2.40638i) q^{7} +(1.51017 - 0.871900i) q^{8} +(-1.42291 + 2.64109i) q^{9} +(-1.66456 - 0.961033i) q^{10} +(-1.36185 + 0.240131i) q^{11} +(-0.492866 + 3.05759i) q^{12} +(1.43469 + 3.94178i) q^{13} +(-1.21408 + 0.0968290i) q^{14} +(6.75864 - 2.57317i) q^{15} +(0.481603 + 2.73131i) q^{16} +(-1.18976 + 2.06072i) q^{17} +(0.918441 + 1.03134i) q^{18} +(-4.72301 + 2.72683i) q^{19} +(5.71920 - 4.79898i) q^{20} +(2.60199 - 3.77222i) q^{21} +(-0.110541 + 0.626912i) q^{22} +(-1.01769 + 1.21284i) q^{23} +(2.63764 + 1.47153i) q^{24} +(-11.6836 - 4.25249i) q^{25} +1.93100 q^{26} +(-5.19109 + 0.229289i) q^{27} +(1.25949 - 4.56010i) q^{28} +(0.495461 - 1.36127i) q^{29} +(-0.0489817 - 3.32875i) q^{30} +(1.18509 - 1.41234i) q^{31} +(4.69194 + 0.827315i) q^{32} +(-1.56642 - 1.81197i) q^{33} +(0.704097 + 0.839111i) q^{34} +(-10.6921 + 2.77712i) q^{35} +(-4.98460 + 1.98221i) q^{36} +(3.37083 - 5.83846i) q^{37} +(0.435948 + 2.47239i) q^{38} +(-4.58780 + 5.63383i) q^{39} +(-2.49023 - 6.84186i) q^{40} +(6.07454 - 2.21095i) q^{41} +(-1.22210 - 1.71947i) q^{42} +(0.819766 + 4.64912i) q^{43} +(-2.14140 - 1.23634i) q^{44} +(9.82823 + 7.76576i) q^{45} +(0.364414 + 0.631183i) q^{46} +(-2.18349 + 1.83217i) q^{47} +(-3.63405 + 3.14159i) q^{48} +(-4.58135 + 5.29257i) q^{49} +(-3.67905 + 4.38452i) q^{50} +(-4.12100 + 0.0606394i) q^{51} +(-2.56536 + 7.04826i) q^{52} -11.6368i q^{53} +(-0.718125 + 2.28164i) q^{54} +5.77391i q^{55} +(-3.75885 - 2.67523i) q^{56} +(-8.24910 - 4.60214i) q^{57} +(-0.510844 - 0.428649i) q^{58} +(-1.15353 + 6.54201i) q^{59} +(12.2152 + 4.24350i) q^{60} +(1.37654 + 1.64050i) q^{61} +(-0.424356 - 0.735006i) q^{62} +(7.92022 + 0.519671i) q^{63} +(-1.67684 + 2.90438i) q^{64} +(17.2484 - 3.04137i) q^{65} +(-1.03044 + 0.392313i) q^{66} +(9.25483 - 3.36848i) q^{67} +(-3.99819 + 1.45522i) q^{68} +(-2.70732 - 0.436403i) q^{69} +(-0.482108 + 5.06240i) q^{70} +(-9.79394 - 5.65453i) q^{71} +(0.153924 + 5.22913i) q^{72} +(7.69650 - 4.44358i) q^{73} +(-1.99486 - 2.37738i) q^{74} +(-4.05122 - 21.1509i) q^{75} +(-9.60349 - 1.69335i) q^{76} +(2.07547 + 3.01307i) q^{77} +(1.71473 + 2.87159i) q^{78} +(-2.14212 - 0.779666i) q^{79} +11.5801 q^{80} +(-4.95067 - 7.51604i) q^{81} -2.97580i q^{82} +(-10.9949 - 4.00181i) q^{83} +(7.89974 - 2.17639i) q^{84} +(7.61088 + 6.38628i) q^{85} +(2.14017 + 0.377369i) q^{86} +(2.46430 - 0.472010i) q^{87} +(-1.84726 + 1.55004i) q^{88} +(-4.23831 - 7.34097i) q^{89} +(4.90668 - 3.02878i) q^{90} +(7.90771 - 7.78717i) q^{91} +(-2.78798 + 0.491595i) q^{92} +(3.15264 + 0.508187i) q^{93} +(0.448772 + 1.23299i) q^{94} +(7.78811 + 21.3976i) q^{95} +(2.93615 + 7.71202i) q^{96} +(5.77859 - 1.01892i) q^{97} +(1.56813 + 2.81507i) q^{98} +(1.30358 - 3.93845i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

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 $

$2$	0.157445	−	0.432576i	0.111330	−	0.305877i	−0.871498	−	0.490399i	$-0.836851\pi$
$2$	0.157445	−	0.432576i	0.111330	−	0.305877i	0.982829	+	0.184521i	$0.0590735\pi$
$3$	0.888001	+	1.48710i	0.512688	+	0.858575i
$3$	0.888001	+	1.48710i	0.512688	+	0.858575i
$4$	1.36976	+	1.14936i	0.684878	+	0.574681i
$5$	0.725040	−	4.11191i	0.324248	−	1.83890i	−0.190661	−	0.981656i	$-0.561063\pi$
$5$	0.725040	−	4.11191i	0.324248	−	1.83890i	0.514909	−	0.857245i	$-0.327826\pi$
$6$	0.783093	−	0.149993i	0.319696	−	0.0612342i
$7$	−1.09969	−	2.40638i	−0.415645	−	0.909527i
$7$	−1.09969	−	2.40638i	−0.415645	−	0.909527i
$8$	1.51017	−	0.871900i	0.533927	−	0.308263i
$9$	−1.42291	+	2.64109i	−0.474302	+	0.880362i
$10$	−1.66456	−	0.961033i	−0.526379	−	0.303905i
$11$	−1.36185	+	0.240131i	−0.410614	+	0.0724023i	−0.375140	−	0.926968i	$-0.622405\pi$
$11$	−1.36185	+	0.240131i	−0.410614	+	0.0724023i	−0.0354742	+	0.999371i	$0.511294\pi$
$12$	−0.492866	+	3.05759i	−0.142278	+	0.882651i
$13$	1.43469	+	3.94178i	0.397912	+	1.09325i	0.963300	+	0.268428i	$0.0865042\pi$
$13$	1.43469	+	3.94178i	0.397912	+	1.09325i	−0.565388	+	0.824825i	$0.691274\pi$
$14$	−1.21408	+	0.0968290i	−0.324477	+	0.0258786i
$15$	6.75864	−	2.57317i	1.74507	−	0.664391i
$16$	0.481603	+	2.73131i	0.120401	+	0.682827i
$17$	−1.18976	+	2.06072i	−0.288559	+	0.499799i	−0.973466	−	0.228832i	$-0.926509\pi$
$17$	−1.18976	+	2.06072i	−0.288559	+	0.499799i	0.684907	+	0.728630i	$0.259843\pi$
$18$	0.918441	+	1.03134i	0.216479	+	0.243089i
$19$	−4.72301	+	2.72683i	−1.08353	+	0.625578i	−0.931847	−	0.362851i	$-0.881804\pi$
$19$	−4.72301	+	2.72683i	−1.08353	+	0.625578i	−0.151686	+	0.988429i	$0.548470\pi$
$20$	5.71920	−	4.79898i	1.27885	−	1.07308i
$21$	2.60199	−	3.77222i	0.567801	−	0.823166i
$22$	−0.110541	+	0.626912i	−0.0235675	+	0.133658i
$23$	−1.01769	+	1.21284i	−0.212203	+	0.252894i	−0.861638	−	0.507523i	$-0.830561\pi$
$23$	−1.01769	+	1.21284i	−0.212203	+	0.252894i	0.649435	+	0.760417i	$0.275006\pi$
$24$	2.63764	+	1.47153i	0.538405	+	0.300374i
$25$	−11.6836	−	4.25249i	−2.33673	−	0.850499i
$26$	1.93100			0.378701
$27$	−5.19109	+	0.229289i	−0.999026	+	0.0441267i
$28$	1.25949	−	4.56010i	0.238021	−	0.861778i
$29$	0.495461	−	1.36127i	0.0920048	−	0.252781i	−0.885152	−	0.465303i	$-0.845945\pi$
$29$	0.495461	−	1.36127i	0.0920048	−	0.252781i	0.977156	+	0.212522i	$0.0681677\pi$
$30$	−0.0489817	−	3.32875i	−0.00894280	−	0.607745i
$31$	1.18509	−	1.41234i	0.212849	−	0.253663i	−0.649048	−	0.760748i	$-0.724832\pi$
$31$	1.18509	−	1.41234i	0.212849	−	0.253663i	0.861896	+	0.507085i	$0.169277\pi$
$32$	4.69194	+	0.827315i	0.829425	+	0.146250i
$33$	−1.56642	−	1.81197i	−0.272680	−	0.315423i
$34$	0.704097	+	0.839111i	0.120752	+	0.143906i
$35$	−10.6921	+	2.77712i	−1.80730	+	0.469418i
$36$	−4.98460	+	1.98221i	−0.830766	+	0.330368i
$37$	3.37083	−	5.83846i	0.554162	−	0.959836i	−0.443806	−	0.896123i	$-0.646372\pi$
$37$	3.37083	−	5.83846i	0.554162	−	0.959836i	0.997968	−	0.0637138i	$-0.0202945\pi$
$38$	0.435948	+	2.47239i	0.0707202	+	0.401074i
$39$	−4.58780	+	5.63383i	−0.734636	+	0.902135i
$40$	−2.49023	−	6.84186i	−0.393741	−	1.08179i
$41$	6.07454	−	2.21095i	0.948684	−	0.345293i	0.179095	−	0.983832i	$-0.442683\pi$
$41$	6.07454	−	2.21095i	0.948684	−	0.345293i	0.769589	+	0.638539i	$0.220461\pi$
$42$	−1.22210	−	1.71947i	−0.188574	−	0.265321i
$43$	0.819766	+	4.64912i	0.125013	+	0.708985i	0.981300	+	0.192484i	$0.0616544\pi$
$43$	0.819766	+	4.64912i	0.125013	+	0.708985i	−0.856287	+	0.516500i	$0.827234\pi$
$44$	−2.14140	−	1.23634i	−0.322829	−	0.186385i
$45$	9.82823	+	7.76576i	1.46511	+	1.15765i
$46$	0.364414	+	0.631183i	0.0537299	+	0.0930629i
$47$	−2.18349	+	1.83217i	−0.318495	+	0.267249i	−0.787993	−	0.615685i	$-0.788880\pi$
$47$	−2.18349	+	1.83217i	−0.318495	+	0.267249i	0.469497	+	0.882934i	$0.344435\pi$
$48$	−3.63405	+	3.14159i	−0.524530	+	0.453450i
$49$	−4.58135	+	5.29257i	−0.654478	+	0.756081i
$50$	−3.67905	+	4.38452i	−0.520297	+	0.620065i
$51$	−4.12100	+	0.0606394i	−0.577055	+	0.00849121i
$52$	−2.56536	+	7.04826i	−0.355751	+	0.977417i
$53$		−	11.6368i		−	1.59844i	−0.601040	−	0.799219i	$-0.705247\pi$
$53$		−	11.6368i		−	1.59844i	0.601040	−	0.799219i	$-0.294753\pi$
$54$	−0.718125	+	2.28164i	−0.0977244	+	0.310492i
$55$			5.77391i			0.778554i
$56$	−3.75885	−	2.67523i	−0.502298	−	0.357493i
$57$	−8.24910	−	4.60214i	−1.09262	−	0.609568i
$58$	−0.510844	−	0.428649i	−0.0670771	−	0.0562843i
$59$	−1.15353	+	6.54201i	−0.150177	+	0.851698i	0.812886	+	0.582423i	$0.197895\pi$
$59$	−1.15353	+	6.54201i	−0.150177	+	0.851698i	−0.963063	+	0.269275i	$0.913216\pi$
$60$	12.2152	+	4.24350i	1.57697	+	0.547833i
$61$	1.37654	+	1.64050i	0.176248	+	0.210045i	0.846935	−	0.531696i	$-0.178445\pi$
$61$	1.37654	+	1.64050i	0.176248	+	0.210045i	−0.670687	+	0.741741i	$0.734001\pi$
$62$	−0.424356	−	0.735006i	−0.0538933	−	0.0933459i
$63$	7.92022	+	0.519671i	0.997854	+	0.0654724i
$64$	−1.67684	+	2.90438i	−0.209606	+	0.363048i
$65$	17.2484	−	3.04137i	2.13941	−	0.377235i
$66$	−1.03044	+	0.392313i	−0.126838	+	0.0482904i
$67$	9.25483	−	3.36848i	1.13066	−	0.411525i	0.292126	−	0.956380i	$-0.405637\pi$
$67$	9.25483	−	3.36848i	1.13066	−	0.411525i	0.838531	+	0.544854i	$0.183415\pi$
$68$	−3.99819	+	1.45522i	−0.484852	+	0.176472i
$69$	−2.70732	−	0.436403i	−0.325922	−	0.0525368i
$70$	−0.482108	+	5.06240i	−0.0576229	+	0.605073i
$71$	−9.79394	−	5.65453i	−1.16233	−	0.671069i	−0.210466	−	0.977601i	$-0.567498\pi$
$71$	−9.79394	−	5.65453i	−1.16233	−	0.671069i	−0.951860	+	0.306532i	$0.900831\pi$
$72$	0.153924	+	5.22913i	0.0181401	+	0.616259i
$73$	7.69650	−	4.44358i	0.900807	−	0.520081i	0.0233450	−	0.999727i	$-0.492568\pi$
$73$	7.69650	−	4.44358i	0.900807	−	0.520081i	0.877462	+	0.479646i	$0.159235\pi$
$74$	−1.99486	−	2.37738i	−0.231897	−	0.276364i
$75$	−4.05122	−	21.1509i	−0.467794	−	2.44230i
$76$	−9.60349	−	1.69335i	−1.10160	−	0.194241i
$77$	2.07547	+	3.01307i	0.236522	+	0.343371i
$78$	1.71473	+	2.87159i	0.194155	+	0.325143i
$79$	−2.14212	−	0.779666i	−0.241007	−	0.0877193i	0.218693	−	0.975794i	$-0.429821\pi$
$79$	−2.14212	−	0.779666i	−0.241007	−	0.0877193i	−0.459700	+	0.888074i	$0.652043\pi$
$80$	11.5801			1.29469
$81$	−4.95067	−	7.51604i	−0.550075	−	0.835116i
$82$		−	2.97580i		−	0.328622i
$83$	−10.9949	−	4.00181i	−1.20685	−	0.439256i	−0.341237	−	0.939977i	$-0.610846\pi$
$83$	−10.9949	−	4.00181i	−1.20685	−	0.439256i	−0.865608	+	0.500722i	$0.833068\pi$
$84$	7.89974	−	2.17639i	0.861932	−	0.237464i
$85$	7.61088	+	6.38628i	0.825515	+	0.692690i
$86$	2.14017	+	0.377369i	0.230780	+	0.0406927i
$87$	2.46430	−	0.472010i	0.264201	−	0.0506047i
$88$	−1.84726	+	1.55004i	−0.196919	+	0.165235i
$89$	−4.23831	−	7.34097i	−0.449260	−	0.778142i	0.549078	−	0.835771i	$-0.314979\pi$
$89$	−4.23831	−	7.34097i	−0.449260	−	0.778142i	−0.998338	+	0.0576296i	$0.981646\pi$
$90$	4.90668	−	3.02878i	0.517210	−	0.319261i
$91$	7.90771	−	7.78717i	0.828953	−	0.816317i
$92$	−2.78798	+	0.491595i	−0.290667	+	0.0512524i
$93$	3.15264	+	0.508187i	0.326914	+	0.0526965i
$94$	0.448772	+	1.23299i	0.0462873	+	0.127173i
$95$	7.78811	+	21.3976i	0.799043	+	2.19535i
$96$	2.93615	+	7.71202i	0.299670	+	0.787105i
$97$	5.77859	−	1.01892i	0.586727	−	0.103456i	0.127599	−	0.991826i	$-0.459273\pi$
$97$	5.77859	−	1.01892i	0.586727	−	0.103456i	0.459128	+	0.888370i	$0.348162\pi$
$98$	1.56813	+	2.81507i	0.158405	+	0.284365i
$99$	1.30358	−	3.93845i	0.131015	−	0.395829i
$100$	−11.1161	−	19.2536i	−1.11161	−	1.92536i
$101$	−3.63389	+	3.04919i	−0.361585	+	0.303406i	−0.805422	−	0.592702i	$-0.798061\pi$
$101$	−3.63389	+	3.04919i	−0.361585	+	0.303406i	0.443837	+	0.896108i	$0.353617\pi$
$102$	−0.622598	+	1.79219i	−0.0616464	+	0.177453i
$103$	13.7651	+	2.42716i	1.35631	+	0.239155i	0.804073	−	0.594530i	$-0.202662\pi$
$103$	13.7651	+	2.42716i	1.35631	+	0.239155i	0.552241	+	0.833685i	$0.313773\pi$
$104$	5.60347	+	4.70187i	0.549466	+	0.461056i
$105$	−13.6245	−	13.4342i	−1.32961	−	1.31104i
$106$	−5.03380	−	1.83215i	−0.488926	−	0.177954i
$107$			7.92658i			0.766292i	0.923688	+	0.383146i	$0.125159\pi$
$107$			7.92658i			0.766292i	−0.923688	+	0.383146i	$0.874841\pi$
$108$	−7.37406	−	5.65237i	−0.709570	−	0.543900i
$109$	−2.88019			−0.275872			−0.137936	−	0.990441i	$-0.544047\pi$
$109$	−2.88019			−0.275872			−0.137936	+	0.990441i	$0.544047\pi$
$110$	2.49766	+	0.909072i	0.238142	+	0.0866766i
$111$	11.6757	−	0.171804i	1.10820	−	0.0163069i
$112$	6.04295	−	4.16252i	0.571005	−	0.393322i
$113$	6.48938	+	1.14425i	0.610470	+	0.107642i	0.470332	−	0.882490i	$-0.344134\pi$
$113$	6.48938	+	1.14425i	0.610470	+	0.107642i	0.140138	+	0.990132i	$0.455245\pi$
$114$	−3.28955	+	2.84378i	−0.308095	+	0.266344i
$115$	4.24921	+	5.06401i	0.396240	+	0.472221i
$116$	2.24325	−	1.29514i	0.208280	−	0.120251i
$117$	−12.4520	−	1.81965i	−1.15119	−	0.168226i
$118$	2.64830	+	1.52900i	0.243796	+	0.140755i
$119$	6.26725	+	0.596849i	0.574518	+	0.0547131i
$120$	7.96317	−	9.77880i	0.726935	−	0.892678i
$121$	−8.53964	+	3.10817i	−0.776331	+	0.282561i
$122$	0.926371	−	0.337172i	0.0838697	−	0.0305261i
$123$	8.68210	+	7.07010i	0.782839	+	0.637489i
$124$	3.24657	−	0.572458i	0.291551	−	0.0514082i
$125$	−15.5186	+	26.8790i	−1.38803	+	2.40413i
$126$	1.47179	−	3.34428i	0.131118	−	0.297932i
$127$	4.32354	+	7.48859i	0.383652	+	0.664505i	0.991581	−	0.129486i	$-0.0413328\pi$
$127$	4.32354	+	7.48859i	0.383652	+	0.664505i	−0.607929	+	0.793991i	$0.707999\pi$
$128$	7.11724	+	8.48200i	0.629081	+	0.749710i
$129$	−6.18574	+	5.34750i	−0.544624	+	0.470821i
$130$	1.40006	−	7.94011i	0.122793	−	0.696393i
$131$	−0.627073	−	0.526177i	−0.0547876	−	0.0459723i	0.614983	−	0.788541i	$-0.289163\pi$
$131$	−0.627073	−	0.526177i	−0.0547876	−	0.0459723i	−0.669770	+	0.742568i	$0.733607\pi$
$132$	−0.0630135	−	4.28234i	−0.00548462	−	0.372730i
$133$	11.7557	+	8.36669i	1.01935	+	0.725484i
$134$		−	4.53376i		−	0.391657i
$135$	−2.82093	+	21.5115i	−0.242787	+	1.85142i
$136$			4.14940i			0.355808i
$137$	1.76175	−	4.84037i	0.150517	−	0.413541i	−0.841403	−	0.540408i	$-0.818270\pi$
$137$	1.76175	−	4.84037i	0.150517	−	0.413541i	0.991920	+	0.126867i	$0.0404921\pi$
$138$	−0.615030	+	1.10241i	−0.0523548	+	0.0938434i
$139$	6.38256	−	7.60644i	0.541362	−	0.645170i	−0.424131	−	0.905601i	$-0.639420\pi$
$139$	6.38256	−	7.60644i	0.541362	−	0.645170i	0.965492	+	0.260431i	$0.0838647\pi$
$140$	−17.8375	−	8.48516i	−1.50755	−	0.717127i
$141$	−4.66356	−	1.62010i	−0.392742	−	0.136437i
$142$	−3.98802	+	3.34634i	−0.334667	+	0.280819i
$143$	−2.90038	−	5.02361i	−0.242542	−	0.420095i
$144$	−7.89889	−	2.61444i	−0.658241	−	0.217870i
$145$	−5.23818	−	3.02426i	−0.435007	−	0.251151i
$146$	−0.710410	−	4.02894i	−0.0587940	−	0.333437i
$147$	−11.9388	−	2.11309i	−0.984695	−	0.174285i
$148$	11.3277	−	4.12295i	0.931133	−	0.338905i
$149$	−2.14963	−	5.90605i	−0.176104	−	0.483843i	0.819966	−	0.572413i	$-0.193992\pi$
$149$	−2.14963	−	5.90605i	−0.176104	−	0.483843i	−0.996070	+	0.0885701i	$0.971770\pi$
$150$	−9.78721	−	1.57764i	−0.799122	−	0.128814i
$151$	−1.64935	−	9.35394i	−0.134222	−	0.761213i	−0.975398	−	0.220451i	$-0.929247\pi$
$151$	−1.64935	−	9.35394i	−0.134222	−	0.761213i	0.841176	−	0.540762i	$-0.181864\pi$
$152$	−4.75505	+	8.23599i	−0.385685	+	0.668027i
$153$	−3.74963	−	6.07447i	−0.303140	−	0.491092i
$154$	1.63015	−	0.423406i	0.131361	−	0.0341190i
$155$	−4.94816	−	5.89698i	−0.397446	−	0.473657i
$156$	−12.7595	+	2.44393i	−1.02158	+	0.195671i
$157$	9.71583	+	1.71316i	0.775408	+	0.136725i	0.547329	−	0.836917i	$-0.315645\pi$
$157$	9.71583	+	1.71316i	0.775408	+	0.136725i	0.228079	+	0.973643i	$0.426756\pi$
$158$	−0.674529	+	0.803873i	−0.0536627	+	0.0639527i
$159$	17.3050	−	10.3335i	1.37238	−	0.819500i
$160$	6.80369	−	18.6930i	0.537879	−	1.47781i
$161$	4.03770	+	1.11520i	0.318215	+	0.0878903i
$162$	−4.03071	+	0.958179i	−0.316683	+	0.0752817i
$163$	−0.425059			−0.0332932			−0.0166466	−	0.999861i	$-0.505299\pi$
$163$	−0.425059			−0.0332932			−0.0166466	+	0.999861i	$0.505299\pi$
$164$	10.8618	+	3.95338i	0.848166	+	0.308707i
$165$	−8.58636	+	5.12724i	−0.668447	+	0.399155i
$166$	−3.46217	+	4.12606i	−0.268717	+	0.320244i
$167$	−1.60617	+	9.10902i	−0.124289	+	0.704877i	0.857439	+	0.514586i	$0.172054\pi$
$167$	−1.60617	+	9.10902i	−0.124289	+	0.704877i	−0.981728	+	0.190291i	$0.939057\pi$
$168$	0.640461	−	7.96539i	0.0494127	−	0.614543i
$169$	−3.52072	+	2.95424i	−0.270825	+	0.227249i
$170$	3.96084	−	2.28679i	0.303783	−	0.175389i
$171$	−0.481391	−	16.3539i	−0.0368129	−	1.25061i
$172$	−4.22064	+	7.31037i	−0.321821	+	0.557411i
$173$	0.793657	+	4.50105i	0.0603406	+	0.342209i	1.00000		9.72430e-5i	$3.09534e-5\pi$
$173$	0.793657	+	4.50105i	0.0603406	+	0.342209i	−0.939659	+	0.342112i	$0.888858\pi$
$174$	0.183812	−	1.14031i	0.0139347	−	0.0864470i
$175$	2.61530	+	32.7917i	0.197698	+	2.47882i
$176$	−1.31174	−	3.60399i	−0.0988765	−	0.271661i
$177$	−10.7529	+	4.09390i	−0.808240	+	0.307717i
$178$	−3.84283	+	0.677594i	−0.288032	+	0.0507878i
$179$	3.72660	+	2.15156i	0.278539	+	0.160815i	0.632762	−	0.774346i	$-0.281921\pi$
$179$	3.72660	+	2.15156i	0.278539	+	0.160815i	−0.354223	+	0.935161i	$0.615254\pi$
$180$	4.53662	+	21.9334i	0.338140	+	1.63482i
$181$	−0.427397	+	0.246758i	−0.0317681	+	0.0183413i	−0.515800	−	0.856709i	$-0.672505\pi$
$181$	−0.427397	+	0.246758i	−0.0317681	+	0.0183413i	0.484032	+	0.875050i	$0.339172\pi$
$182$	−2.12351	−	4.64673i	−0.157405	−	0.344439i
$183$	−1.21721	+	3.50382i	−0.0899788	+	0.259010i
$184$	−0.479419	+	2.71892i	−0.0353432	+	0.200441i
$185$	−21.5632	−	18.0937i	−1.58536	−	1.33027i
$186$	0.716196	−	1.28374i	0.0525140	−	0.0941287i
$187$	1.12543	−	3.09210i	0.0822997	−	0.226117i
$188$	−5.09668			−0.371714
$189$	6.26037	+	12.2396i	0.455375	+	0.890300i
$190$	10.4823			0.760466
$191$	4.69030	−	12.8865i	0.339378	−	0.932433i	−0.646193	−	0.763174i	$-0.723640\pi$
$191$	4.69030	−	12.8865i	0.339378	−	0.932433i	0.985571	−	0.169260i	$-0.0541377\pi$
$192$	−5.80813	+	0.0854651i	−0.419166	+	0.00616791i
$193$	0.558650	+	0.468763i	0.0402125	+	0.0337423i	0.662672	−	0.748909i	$-0.269422\pi$
$193$	0.558650	+	0.468763i	0.0402125	+	0.0337423i	−0.622460	+	0.782652i	$0.713867\pi$
$194$	0.469048	−	2.66010i	0.0336757	−	0.190984i
$195$	19.8394	+	22.9494i	1.42073	+	1.64344i
$196$	−12.3584	+	1.98390i	−0.882743	+	0.141707i
$197$	−17.3970	+	10.0441i	−1.23948	+	0.715615i	−0.968988	−	0.247106i	$-0.920520\pi$
$197$	−17.3970	+	10.0441i	−1.23948	+	0.715615i	−0.270494	+	0.962722i	$0.587187\pi$
$198$	−1.49844	−	1.18399i	−0.106489	−	0.0841423i
$199$	−6.81702	−	3.93581i	−0.483246	−	0.279002i	0.238522	−	0.971137i	$-0.423337\pi$
$199$	−6.81702	−	3.93581i	−0.483246	−	0.279002i	−0.721768	+	0.692135i	$0.756670\pi$
$200$	−21.3521	+	3.76495i	−1.50982	+	0.266222i
$201$	13.2276	+	10.7716i	0.932999	+	0.759770i
$202$	0.746870	+	2.05201i	0.0525496	+	0.144379i
$203$	−3.82058	+	0.304710i	−0.268152	+	0.0213864i
$204$	−5.71446	−	4.65346i	−0.400092	−	0.325807i
$205$	−4.68694	−	26.5810i	−0.327350	−	1.85650i
$206$	3.21717	−	5.57230i	0.224151	−	0.388240i
$207$	−1.75513	−	4.41356i	−0.121990	−	0.306764i
$208$	−10.0753	+	5.81696i	−0.698594	+	0.403333i
$209$	5.77725	−	4.84769i	0.399620	−	0.335321i
$210$	−7.95639	+	3.77848i	−0.549043	+	0.260740i
$211$	−3.02127	+	17.1345i	−0.207993	+	1.17959i	0.684667	+	0.728856i	$0.259948\pi$
$211$	−3.02127	+	17.1345i	−0.207993	+	1.17959i	−0.892660	+	0.450731i	$0.851163\pi$
$212$	13.3749	−	15.9396i	0.918591	−	1.09473i
$213$	−0.288199	−	19.5858i	−0.0197471	−	1.34199i
$214$	3.42885	+	1.24800i	0.234391	+	0.0853114i
$215$	19.7111			1.34429
$216$	−7.63954	+	4.87238i	−0.519805	+	0.331523i
$217$	−4.70186	−	1.29864i	−0.319183	−	0.0881576i
$218$	−0.453471	+	1.24590i	−0.0307129	+	0.0843831i
$219$	13.4425	+	7.49953i	0.908361	+	0.506771i
$220$	−6.63632	+	7.90885i	−0.447420	+	0.533215i
$221$	−9.82985	−	1.73327i	−0.661227	−	0.116592i
$222$	1.76395	−	5.07765i	0.118389	−	0.340790i
$223$	−3.66575	−	4.36867i	−0.245476	−	0.292547i	0.629211	−	0.777234i	$-0.283378\pi$
$223$	−3.66575	−	4.36867i	−0.245476	−	0.292547i	−0.874688	+	0.484687i	$0.838934\pi$
$224$	−3.16886	−	12.2004i	−0.211728	−	0.815173i
$225$	27.8559	−	24.8066i	1.85706	−	1.65377i
$226$	1.51669	−	2.62699i	0.100889	−	0.174745i
$227$	−1.25816	−	7.13538i	−0.0835071	−	0.473592i	−0.997669	−	0.0682424i	$-0.978261\pi$
$227$	−1.25816	−	7.13538i	−0.0835071	−	0.473592i	0.914162	−	0.405350i	$-0.132850\pi$
$228$	−6.00973	−	15.7850i	−0.398004	−	1.04539i
$229$	−9.81687	−	26.9716i	−0.648717	−	1.78233i	−0.622424	−	0.782680i	$-0.713852\pi$
$229$	−9.81687	−	26.9716i	−0.648717	−	1.78233i	−0.0262929	−	0.999654i	$-0.508370\pi$
$230$	2.85958	−	1.04080i	0.188555	−	0.0686285i
$231$	−2.63770	+	5.76203i	−0.173548	+	0.379113i
$232$	−0.438656	−	2.48774i	−0.0287992	−	0.163328i
$233$	19.3330	+	11.1619i	1.26655	+	0.731243i	0.974333	−	0.225109i	$-0.0722739\pi$
$233$	19.3330	+	11.1619i	1.26655	+	0.731243i	0.292216	+	0.956352i	$0.405607\pi$
$234$	−2.74764	+	5.09995i	−0.179619	+	0.333394i
$235$	5.95059	+	10.3067i	0.388174	+	0.672336i
$236$	−9.09920	+	7.63513i	−0.592307	+	0.497005i
$237$	−0.742763	−	3.87787i	−0.0482476	−	0.251895i
$238$	1.24493	−	2.61709i	0.0806967	−	0.169641i
$239$	−9.75397	+	11.6243i	−0.630932	+	0.751915i	−0.982909	−	0.184093i	$-0.941065\pi$
$239$	−9.75397	+	11.6243i	−0.630932	+	0.751915i	0.351977	+	0.936009i	$0.385510\pi$
$240$	10.2831	+	17.2207i	0.663772	+	1.11159i
$241$	−2.42697	+	6.66806i	−0.156335	+	0.429527i	−0.992989	−	0.118204i	$-0.962286\pi$
$241$	−2.42697	+	6.66806i	−0.156335	+	0.429527i	0.836654	+	0.547732i	$0.184508\pi$
$242$			4.18341i			0.268920i
$243$	6.78087	−	14.0364i	0.434993	−	0.900434i
$244$			3.82924i			0.245142i
$245$	18.4409	+	22.6754i	1.17814	+	1.44868i
$246$	4.42530	−	2.64252i	0.282147	−	0.168481i
$247$	−17.5246	−	14.7049i	−1.11507	−	0.935652i
$248$	0.558279	−	3.16616i	0.0354507	−	0.201051i
$249$	−3.81240	−	19.9041i	−0.241601	−	1.26137i
$250$	9.18389	+	10.9449i	0.580840	+	0.692219i
$251$	−7.15997	−	12.4014i	−0.451934	−	0.782772i	0.546573	−	0.837412i	$-0.315932\pi$
$251$	−7.15997	−	12.4014i	−0.451934	−	0.782772i	−0.998506	+	0.0546399i	$0.982599\pi$
$252$	10.2515	+	9.81502i	0.645783	+	0.618288i
$253$	1.09470	−	1.89608i	0.0688235	−	0.119206i
$254$	3.92010	−	0.691220i	0.245969	−	0.0433710i
$255$	−2.73855	+	16.9891i	−0.171494	+	1.06390i
$256$	−1.51319	+	0.550758i	−0.0945746	+	0.0344223i
$257$	8.77573	−	3.19411i	0.547415	−	0.199243i	−0.0534825	−	0.998569i	$-0.517032\pi$
$257$	8.77573	−	3.19411i	0.547415	−	0.199243i	0.600898	+	0.799326i	$0.294810\pi$
$258$	1.33929	+	3.51774i	0.0833803	+	0.219005i
$259$	−17.7564	−	1.69100i	−1.10333	−	0.105074i
$260$	27.1218	+	15.6588i	1.68202	+	0.971116i
$261$	2.89023	+	3.24551i	0.178901	+	0.200892i
$262$	−0.326341	+	0.188413i	−0.0201614	+	0.0116402i
$263$	15.0368	+	17.9202i	0.927211	+	1.10501i	0.994231	+	0.107255i	$0.0342063\pi$
$263$	15.0368	+	17.9202i	0.927211	+	1.10501i	−0.0670205	+	0.997752i	$0.521349\pi$
$264$	−3.94543	−	1.37062i	−0.242824	−	0.0843560i
$265$	−47.8494	−	8.43715i	−2.93937	−	0.518290i
$266$	5.47009	−	3.76793i	0.335393	−	0.231026i
$267$	7.15310	−	12.8216i	0.437763	−	0.784668i
$268$	16.5485	+	6.02314i	1.01086	+	0.367922i
$269$	24.6194			1.50107			0.750536	−	0.660830i	$-0.229796\pi$
$269$	24.6194			1.50107			0.750536	+	0.660830i	$0.229796\pi$
$270$	8.86122	+	4.60714i	0.539277	+	0.280382i
$271$			17.4873i			1.06228i	0.847285	+	0.531139i	$0.178236\pi$
$271$			17.4873i			1.06228i	−0.847285	+	0.531139i	$0.821764\pi$
$272$	−6.20146	−	2.25715i	−0.376019	−	0.136860i
$273$	18.6023	+	4.84450i	1.12586	+	0.293203i
$274$	−1.81645	−	1.52418i	−0.109736	−	0.0920792i
$275$	16.9325	+	2.98566i	1.02107	+	0.180042i
$276$	−3.20678	−	3.70945i	−0.193025	−	0.223283i
$277$	9.59499	−	8.05115i	0.576507	−	0.483747i	−0.307291	−	0.951616i	$-0.599422\pi$
$277$	9.59499	−	8.05115i	0.576507	−	0.483747i	0.883798	+	0.467869i	$0.154978\pi$
$278$	−2.28546	−	3.95854i	−0.137073	−	0.237417i
$279$	2.04383	+	5.13955i	0.122361	+	0.307697i
$280$	−13.7256	+	13.5164i	−0.820263	+	0.807760i
$281$	−18.0825	+	3.18844i	−1.07871	+	0.190206i	−0.684646	−	0.728876i	$-0.740043\pi$
$281$	−18.0825	+	3.18844i	−1.07871	+	0.190206i	−0.394067	+	0.919082i	$0.628932\pi$
$282$	−1.43507	+	1.76227i	−0.0854570	+	0.104941i
$283$	−2.82503	−	7.76172i	−0.167931	−	0.461386i	0.826970	−	0.562246i	$-0.190063\pi$
$283$	−2.82503	−	7.76172i	−0.167931	−	0.461386i	−0.994901	+	0.100860i	$0.967840\pi$
$284$	−6.91620	−	19.0021i	−0.410401	−	1.12757i
$285$	−24.9045	+	30.5828i	−1.47522	+	1.81157i
$286$	−2.62974	+	0.463694i	−0.155500	+	0.0274188i
$287$	−12.0005	−	12.1863i	−0.708369	−	0.719334i
$288$	−8.86120	+	11.2146i	−0.522151	+	0.660828i
$289$	5.66895	+	9.81891i	0.333468	+	0.577583i
$290$	−2.13295	+	1.78975i	−0.125251	+	0.105098i
$291$	6.64663	+	7.68852i	0.389633	+	0.450709i
$292$	15.6496	+	2.75945i	0.915823	+	0.161484i
$293$	17.0672	+	14.3211i	0.997078	+	0.836648i	0.986577	−	0.163297i	$-0.0522130\pi$
$293$	17.0672	+	14.3211i	0.997078	+	0.836648i	0.0105009	+	0.999945i	$0.496657\pi$
$294$	−2.79377	+	4.83174i	−0.162936	+	0.281793i
$295$	26.0638	+	9.48644i	1.51749	+	0.552322i
$296$		−	11.7561i		−	0.683311i
$297$	7.01444	−	1.55880i	0.407019	−	0.0904508i
$298$	−2.89326			−0.167602
$299$	−6.24081	−	2.27147i	−0.360915	−	0.131362i
$300$	18.7609	−	33.6279i	1.08316	−	1.94151i
$301$	10.2861	−	7.08528i	0.592879	−	0.408389i
$302$	−4.30597	−	0.759259i	−0.247781	−	0.0436904i
$303$	−7.76133	−	2.69625i	−0.445877	−	0.154895i
$304$	−9.72243	−	11.5867i	−0.557620	−	0.664546i
$305$	7.74364	−	4.47079i	0.443400	−	0.255997i
$306$	−3.21803	+	0.665605i	−0.183962	+	0.0380501i
$307$	17.0333	+	9.83418i	0.972142	+	0.561266i	0.899889	−	0.436120i	$-0.143648\pi$
$307$	17.0333	+	9.83418i	0.972142	+	0.561266i	0.0722533	+	0.997386i	$0.476981\pi$
$308$	−0.620217	+	6.51263i	−0.0353401	+	0.371091i
$309$	8.61400	+	22.6253i	0.490033	+	1.28711i
$310$	−3.32995	+	1.21200i	−0.189129	+	0.0688372i
$311$	−15.6758	+	5.70554i	−0.888896	+	0.323532i	−0.745794	−	0.666177i	$-0.767930\pi$
$311$	−15.6758	+	5.70554i	−0.888896	+	0.323532i	−0.143101	+	0.989708i	$0.545708\pi$
$312$	−2.01624	+	12.5082i	−0.114147	+	0.708136i
$313$	10.7102	−	1.88851i	0.605379	−	0.106745i	0.137447	−	0.990509i	$-0.456110\pi$
$313$	10.7102	−	1.88851i	0.605379	−	0.106745i	0.467932	+	0.883764i	$0.344999\pi$
$314$	2.27078	−	3.93310i	0.128147	−	0.221958i
$315$	7.87932	−	32.1904i	0.443949	−	1.81373i
$316$	−2.03806	−	3.53002i	−0.114650	−	0.198579i
$317$	−18.2381	−	21.7354i	−1.02436	−	1.22078i	−0.975048	−	0.221995i	$-0.928743\pi$
$317$	−18.2381	−	21.7354i	−1.02436	−	1.22078i	−0.0493075	−	0.998784i	$-0.515701\pi$
$318$	−1.74543	−	9.11269i	−0.0978790	−	0.511015i
$319$	−0.347861	+	1.97282i	−0.0194765	+	0.110457i
$320$	10.7268	+	9.00082i	0.599644	+	0.503161i
$321$	−11.7876	+	7.03882i	−0.657919	+	0.392868i
$322$	1.11812	−	1.57103i	0.0623106	−	0.0875499i
$323$		−	12.9771i		−	0.722065i
$324$	1.85744	−	15.9853i	0.103191	−	0.888070i
$325$		−	52.1553i		−	2.89306i
$326$	−0.0669233	+	0.183870i	−0.00370654	+	0.0101836i
$327$	−2.55761	−	4.28312i	−0.141436	−	0.236857i
$328$	7.24589	−	8.63532i	0.400088	−	0.476806i
$329$	6.81007	+	3.23950i	0.375452	+	0.178599i
$330$	0.866044	+	4.52151i	0.0476742	+	0.248901i
$331$	−0.689617	+	0.578657i	−0.0379048	+	0.0318059i	−0.661543	−	0.749907i	$-0.730098\pi$
$331$	−0.689617	+	0.578657i	−0.0379048	+	0.0318059i	0.623638	+	0.781713i	$0.285654\pi$
$332$	−10.4608	−	18.1186i	−0.574110	−	0.994387i
$333$	10.6235	+	17.2102i	0.582163	+	0.943116i
$334$	3.68746	+	2.12896i	0.201769	+	0.116491i
$335$	−7.14076	−	40.4973i	−0.390141	−	2.21260i
$336$	11.5562	+	5.29012i	0.630444	+	0.288600i
$337$	−20.7809	+	7.56364i	−1.13201	+	0.412018i	−0.839021	−	0.544098i	$-0.816872\pi$
$337$	−20.7809	+	7.56364i	−1.13201	+	0.412018i	−0.292988	+	0.956116i	$0.594650\pi$
$338$	0.723612	+	1.98811i	0.0393593	+	0.108139i
$339$	4.06097	+	10.6664i	0.220561	+	0.579321i
$340$	3.08489	+	17.4953i	0.167302	+	0.948816i
$341$	−1.27477	+	2.20797i	−0.0690328	+	0.119568i
$342$	−7.15010	−	2.36660i	−0.386633	−	0.127971i
$343$	17.7740	+	5.20426i	0.959707	+	0.281004i
$344$	5.29156	+	6.30624i	0.285302	+	0.340009i
$345$	−3.75736	+	10.8158i	−0.202290	+	0.582304i
$346$	2.07200	+	0.365350i	0.111392	+	0.0196413i
$347$	17.3948	−	20.7303i	0.933803	−	1.11286i	−0.0596042	−	0.998222i	$-0.518984\pi$
$347$	17.3948	−	20.7303i	0.933803	−	1.11286i	0.993407	−	0.114641i	$-0.0365717\pi$
$348$	3.91801	+	2.18584i	0.210027	+	0.117173i
$349$	−3.61775	+	9.93968i	−0.193654	+	0.532059i	−0.998076	−	0.0619986i	$-0.980253\pi$
$349$	−3.61775	+	9.93968i	−0.193654	+	0.532059i	0.804423	+	0.594057i	$0.202475\pi$
$350$	14.5967	+	4.03157i	0.780225	+	0.215496i
$351$	−8.35142	−	20.1332i	−0.445766	−	1.07463i
$352$	−6.58839			−0.351162
$353$	0.727677	+	0.264853i	0.0387303	+	0.0140967i	0.361313	−	0.932445i	$-0.382329\pi$
$353$	0.727677	+	0.264853i	0.0387303	+	0.0140967i	−0.322582	+	0.946541i	$0.604551\pi$
$354$	0.0779296	+	5.29602i	0.00414191	+	0.281481i
$355$	−30.3519	+	36.1720i	−1.61091	+	1.91981i
$356$	2.63198	−	14.9267i	0.139495	−	0.791113i
$357$	4.67776	+	9.85001i	0.247573	+	0.521318i
$358$	1.51745	−	1.27329i	0.0801995	−	0.0672953i
$359$	−2.11285	+	1.21985i	−0.111512	+	0.0643813i	−0.554719	−	0.832038i	$-0.687174\pi$
$359$	−2.11285	+	1.21985i	−0.111512	+	0.0643813i	0.443207	+	0.896419i	$0.353841\pi$
$360$	21.6133	+	3.15841i	1.13912	+	0.166463i
$361$	5.37123	−	9.30324i	0.282696	−	0.489644i
$362$	0.0394500	+	0.223732i	0.00207345	+	0.0117591i
$363$	−12.2054	−	9.93920i	−0.640616	−	0.521673i
$364$	19.7819	−	1.57770i	1.03685	−	0.0826940i
$365$	−12.6913	−	34.8691i	−0.664293	−	1.82513i
$366$	1.32403	+	1.07819i	0.0692079	+	0.0563581i
$367$	−32.2888	+	5.69339i	−1.68546	+	0.297193i	−0.932580	−	0.360962i	$-0.882448\pi$
$367$	−32.2888	+	5.69339i	−1.68546	+	0.297193i	−0.752883	+	0.658155i	$0.771337\pi$
$368$	−3.80275	−	2.19552i	−0.198232	−	0.114449i
$369$	−2.80419	+	19.1894i	−0.145981	+	0.998959i
$370$	−11.2219	+	6.47897i	−0.583399	+	0.336825i
$371$	−28.0026	+	12.7969i	−1.45382	+	0.664383i
$372$	3.73426	+	4.31962i	0.193612	+	0.223962i
$373$	4.41268	−	25.0256i	0.228480	−	1.29577i	−0.627439	−	0.778666i	$-0.715897\pi$
$373$	4.41268	−	25.0256i	0.228480	−	1.29577i	0.855919	−	0.517109i	$-0.172992\pi$
$374$	−1.16037	−	0.973669i	−0.0600015	−	0.0503472i
$375$	−53.7522	+	0.790950i	−2.77575	+	0.0408445i
$376$	−1.69999	+	4.67068i	−0.0876703	+	0.240872i
$377$	6.07665			0.312963
$378$	6.28022	−	0.781024i	0.323019	−	0.0401715i
$379$	−18.7107			−0.961102			−0.480551	−	0.876967i	$-0.659563\pi$
$379$	−18.7107			−0.961102			−0.480551	+	0.876967i	$0.659563\pi$
$380$	−13.9258	+	38.2609i	−0.714380	+	1.96274i
$381$	−7.29695	+	13.0794i	−0.373834	+	0.670078i
$382$	−4.83592	−	4.05782i	−0.247427	−	0.207616i
$383$	−1.87324	+	10.6237i	−0.0957180	+	0.542844i	0.898807	+	0.438345i	$0.144435\pi$
$383$	−1.87324	+	10.6237i	−0.0957180	+	0.542844i	−0.994525	+	0.104499i	$0.966676\pi$
$384$	−6.29343	+	18.1161i	−0.321160	+	0.924481i
$385$	13.8942	−	6.34954i	0.708116	−	0.323602i
$386$	0.290732	−	0.167854i	0.0147979	−	0.00854356i
$387$	−13.4452	−	4.45020i	−0.683457	−	0.226216i
$388$	9.08637	+	5.24602i	0.461291	+	0.266326i
$389$	4.97680	−	0.877544i	0.252334	−	0.0444932i	−0.0460504	−	0.998939i	$-0.514663\pi$
$389$	4.97680	−	0.877544i	0.252334	−	0.0444932i	0.298384	+	0.954446i	$0.403552\pi$
$390$	13.0509	−	4.96881i	0.660861	−	0.251605i
$391$	−1.28851	−	3.54016i	−0.0651629	−	0.179034i
$392$	−2.30404	+	11.9872i	−0.116372	+	0.605444i
$393$	0.225634	−	1.39976i	0.0113817	−	0.0706087i
$394$	1.60579	+	9.10690i	0.0808987	+	0.458799i
$395$	−4.75903	+	8.24289i	−0.239453	+	0.414745i
$396$	6.31230	−	3.89643i	0.317205	−	0.195803i
$397$	17.8034	−	10.2788i	0.893528	−	0.515878i	0.0184329	−	0.999830i	$-0.494132\pi$
$397$	17.8034	−	10.2788i	0.893528	−	0.515878i	0.875095	+	0.483952i	$0.160799\pi$
$398$	−2.77584	+	2.32921i	−0.139140	+	0.116753i
$399$	−2.00302	+	24.9114i	−0.100276	+	1.24713i
$400$	5.98799	−	33.9596i	0.299400	−	1.69798i
$401$	−19.5802	+	23.3347i	−0.977786	+	1.16528i	0.00845455	+	0.999964i	$0.497309\pi$
$401$	−19.5802	+	23.3347i	−0.977786	+	1.16528i	−0.986241	+	0.165316i	$0.947136\pi$
$402$	6.74214	−	4.02599i	0.336267	−	0.200798i
$403$	7.26736	+	2.64510i	0.362013	+	0.131762i
$404$	−8.48216			−0.422003
$405$	−34.4947	+	14.9073i	−1.71406	+	0.740748i
$406$	−0.469721	+	1.70067i	−0.0233118	+	0.0844027i
$407$	−3.18858	+	8.76056i	−0.158052	+	0.434245i
$408$	−6.17056	+	3.68467i	−0.305488	+	0.182419i
$409$	0.623352	−	0.742883i	0.0308228	−	0.0367332i	−0.750413	−	0.660969i	$-0.770145\pi$
$409$	0.623352	−	0.742883i	0.0308228	−	0.0367332i	0.781236	+	0.624236i	$0.214590\pi$
$410$	−12.2362	−	2.15758i	−0.604304	−	0.106555i
$411$	8.76254	−	1.67836i	0.432224	−	0.0827876i
$412$	16.0651	+	19.1457i	0.791472	+	0.943240i
$413$	17.0111	−	4.41837i	0.837062	−	0.217414i
$414$	−2.18554	+	0.0643331i	−0.107413	+	0.00316180i
$415$	−24.4268	+	42.3085i	−1.19906	+	2.07684i
$416$	3.47039	+	19.6815i	0.170150	+	0.964967i
$417$	16.9792	+	2.73695i	0.831476	+	0.134029i
$418$	−1.18739	−	3.26234i	−0.0580774	−	0.159566i
$419$	32.6552	−	11.8855i	1.59531	−	0.580646i	0.616851	−	0.787080i	$-0.288408\pi$
$419$	32.6552	−	11.8855i	1.59531	−	0.580646i	0.978461	+	0.206434i	$0.0661858\pi$
$420$	−3.22150	−	34.0610i	−0.157193	−	1.66200i
$421$	1.63994	+	9.30054i	0.0799256	+	0.453280i	0.998337	+	0.0576531i	$0.0183617\pi$
$421$	1.63994	+	9.30054i	0.0799256	+	0.453280i	−0.918411	+	0.395627i	$0.870527\pi$
$422$	6.93628	+	4.00466i	0.337653	+	0.194944i
$423$	−1.73201	−	8.37380i	−0.0842131	−	0.407148i
$424$	−10.1461	−	17.5736i	−0.492739	−	0.853450i
$425$	22.6639	−	19.0173i	1.09936	−	0.922474i
$426$	−8.51770	−	2.95900i	−0.412684	−	0.143364i
$427$	2.43390	−	5.11654i	0.117784	−	0.247607i
$428$	−9.11051	+	10.8575i	−0.440373	+	0.524816i
$429$	4.89504	−	8.77412i	0.236335	−	0.423618i
$430$	3.10341	−	8.52656i	0.149660	−	0.411187i
$431$			34.0032i			1.63788i	0.573882	+	0.818938i	$0.305437\pi$
$431$			34.0032i			1.63788i	−0.573882	+	0.818938i	$0.694563\pi$
$432$	−3.12630	−	14.0680i	−0.150414	−	0.676849i
$433$			36.2251i			1.74087i	0.492286	+	0.870433i	$0.336161\pi$
$433$			36.2251i			1.74087i	−0.492286	+	0.870433i	$0.663839\pi$
$434$	−1.30204	+	1.82945i	−0.0625001	+	0.0878162i
$435$	−0.154140	−	10.4752i	−0.00739045	−	0.502248i
$436$	−3.94516	−	3.31038i	−0.188939	−	0.158539i
$437$	1.49936	−	8.50332i	0.0717243	−	0.406769i
$438$	5.36057	−	4.63415i	0.256138	−	0.221428i
$439$	−24.9337	−	29.7148i	−1.19002	−	1.41821i	−0.884825	−	0.465923i	$-0.845723\pi$
$439$	−24.9337	−	29.7148i	−1.19002	−	1.41821i	−0.305196	−	0.952290i	$-0.598722\pi$
$440$	5.03427	+	8.71962i	0.240000	+	0.415692i
$441$	−7.45930	−	19.6306i	−0.355205	−	0.934789i
$442$	−2.29743	+	3.97926i	−0.109278	+	0.189274i
$443$	−12.4872	+	2.20183i	−0.593285	+	0.104612i	−0.462225	−	0.886762i	$-0.652949\pi$
$443$	−12.4872	+	2.20183i	−0.593285	+	0.104612i	−0.131059	+	0.991375i	$0.541838\pi$
$444$	16.1903	+	13.1842i	0.768356	+	0.625695i
$445$	−33.2584	+	12.1051i	−1.57660	+	0.573834i
$446$	−2.46693	+	0.897889i	−0.116813	+	0.0425163i
$447$	6.87399	−	8.44128i	0.325129	−	0.399259i
$448$	8.83306	+	0.841199i	0.417323	+	0.0397429i
$449$	−14.9676	−	8.64153i	−0.706363	−	0.407819i	0.103350	−	0.994645i	$-0.467044\pi$
$449$	−14.9676	−	8.64153i	−0.706363	−	0.407819i	−0.809713	+	0.586826i	$0.800377\pi$
$450$	−6.34495	−	15.9555i	−0.299104	−	0.752148i
$451$	−7.74171	+	4.46968i	−0.364543	+	0.210469i
$452$	7.57371	+	9.02599i	0.356237	+	0.424547i
$453$	12.4456	−	10.7591i	0.584744	−	0.505505i
$454$	−3.28469	−	0.579179i	−0.154158	−	0.0271822i
$455$	−26.2867	−	38.1618i	−1.23234	−	1.78905i
$456$	−16.4702	+	0.242354i	−0.771287	+	0.0113493i
$457$	−34.2674	−	12.4723i	−1.60296	−	0.583430i	−0.622931	−	0.782277i	$-0.714058\pi$
$457$	−34.2674	−	12.4723i	−1.60296	−	0.583430i	−0.980031	+	0.198847i	$0.936280\pi$
$458$	−13.2129			−0.617397
$459$	5.70364	−	10.9702i	0.266223	−	0.512045i
$460$			11.8203i			0.551126i
$461$	9.14600	+	3.32887i	0.425972	+	0.155041i	0.546105	−	0.837717i	$-0.316110\pi$
$461$	9.14600	+	3.32887i	0.425972	+	0.155041i	−0.120133	+	0.992758i	$0.538332\pi$
$462$	2.07722	+	2.04820i	0.0966411	+	0.0952911i
$463$	−16.0196	−	13.4420i	−0.744493	−	0.624704i	0.189547	−	0.981872i	$-0.439298\pi$
$463$	−16.0196	−	13.4420i	−0.744493	−	0.624704i	−0.934040	+	0.357168i	$0.883742\pi$
$464$	3.95666	+	0.697665i	0.183683	+	0.0323883i
$465$	4.37541	−	12.5949i	0.202905	−	0.584075i
$466$	7.87227	−	6.60562i	0.364676	−	0.305999i
$467$	−6.75996	−	11.7086i	−0.312813	−	0.541809i	0.666157	−	0.745812i	$-0.267938\pi$
$467$	−6.75996	−	11.7086i	−0.312813	−	0.541809i	−0.978970	+	0.204003i	$0.934605\pi$
$468$	−14.9648	−	16.8043i	−0.691748	−	0.776781i
$469$	−18.2833	−	18.5663i	−0.844246	−	0.857314i
$470$	5.39533	−	0.951342i	0.248868	−	0.0438821i
$471$	6.08003	+	15.9697i	0.280153	+	0.735843i
$472$	3.96194	+	10.8853i	0.182363	+	0.501039i
$473$	−2.23280	−	6.13457i	−0.102664	−	0.282068i
$474$	−1.79442	−	0.289250i	−0.0824204	−	0.0132857i
$475$	66.7778	−	11.7747i	3.06397	−	0.540261i
$476$	7.89861	+	8.02088i	0.362032	+	0.367636i
$477$	30.7338	+	16.5581i	1.40720	+	0.758143i
$478$	3.49269	+	6.04952i	0.159752	+	0.276699i
$479$	7.30076	−	6.12607i	0.333580	−	0.279907i	−0.460576	−	0.887620i	$-0.652357\pi$
$479$	7.30076	−	6.12607i	0.333580	−	0.279907i	0.794157	+	0.607713i	$0.207913\pi$
$480$	33.8399	−	6.48166i	1.54457	−	0.295846i
$481$	27.8500	+	4.91071i	1.26985	+	0.223909i
$482$	2.50233	+	2.09970i	0.113978	+	0.0956387i
$483$	1.92707	+	6.99474i	0.0876846	+	0.318272i
$484$	−15.2696	−	5.55769i	−0.694075	−	0.252622i
$485$		−	24.4998i		−	1.11248i
$486$	−5.00418	−	5.14319i	−0.226994	−	0.233300i
$487$	16.1416			0.731447			0.365724	−	0.930724i	$-0.380822\pi$
$487$	16.1416			0.731447			0.365724	+	0.930724i	$0.380822\pi$
$488$	3.50918	+	1.27724i	0.158853	+	0.0578178i
$489$	−0.377453	−	0.632104i	−0.0170690	−	0.0285847i
$490$	12.7122	−	4.40696i	0.574281	−	0.199086i
$491$	18.8388	+	3.32178i	0.850181	+	0.149910i	0.581729	−	0.813383i	$-0.302377\pi$
$491$	18.8388	+	3.32178i	0.850181	+	0.149910i	0.268453	+	0.963293i	$0.413488\pi$
$492$	3.76626	+	19.6632i	0.169796	+	0.886485i
$493$	2.21572	+	2.64059i	0.0997908	+	0.118926i
$494$	−9.12015	+	5.26552i	−0.410335	+	0.236907i
$495$	−15.2494	−	8.21574i	−0.685410	−	0.369270i
$496$	4.42827	+	2.55666i	0.198835	+	0.114797i
$497$	−2.83663	+	29.7862i	−0.127240	+	1.33609i
$498$	−9.21025	−	1.48464i	−0.412721	−	0.0665282i
$499$	37.5122	−	13.6533i	1.67928	−	0.611207i	0.686066	−	0.727539i	$-0.259336\pi$
$499$	37.5122	−	13.6533i	1.67928	−	0.611207i	0.993210	+	0.116332i	$0.0371138\pi$
$500$	−52.1504	+	18.9812i	−2.33224	+	0.848865i
$501$	−14.9723	+	5.70030i	−0.668911	+	0.254671i
$502$	−6.49186	+	1.14469i	−0.289746	+	0.0510900i
$503$	−14.1117	+	24.4422i	−0.629211	+	1.08982i	0.358500	+	0.933530i	$0.383288\pi$
$503$	−14.1117	+	24.4422i	−0.629211	+	1.08982i	−0.987710	+	0.156295i	$0.950045\pi$
$504$	12.4140	−	6.12085i	0.552965	−	0.272644i
$505$	9.90328	+	17.1530i	0.440690	+	0.763298i
$506$	−0.647845	−	0.772071i	−0.0288002	−	0.0343227i
$507$	−7.51964	−	2.61228i	−0.333959	−	0.116016i
$508$	−2.68491	+	15.2269i	−0.119123	+	0.675583i
$509$	−1.16032	−	0.973624i	−0.0514303	−	0.0431551i	0.616710	−	0.787190i	$-0.288465\pi$
$509$	−1.16032	−	0.973624i	−0.0514303	−	0.0431551i	−0.668140	+	0.744035i	$0.732909\pi$
$510$	6.91792	+	3.85948i	0.306330	+	0.170901i
$511$	−19.1567	−	13.6341i	−0.847444	−	0.603139i
$512$			22.8862i			1.01144i
$513$	23.8924	−	15.2382i	1.05487	−	0.672782i
$514$		−	4.29906i		−	0.189624i
$515$	19.9605	−	54.8410i	0.879564	−	2.41658i
$516$	−14.6192	+	0.215117i	−0.643573	+	0.00947000i
$517$	2.53364	−	3.01947i	0.111429	−	0.132796i
$518$	−3.52714	+	7.41477i	−0.154974	+	0.325786i
$519$	−5.98873	+	5.17719i	−0.262876	+	0.227253i
$520$	23.3964	−	19.6319i	1.02600	−	0.860916i
$521$	5.51610	+	9.55416i	0.241665	+	0.418575i	0.961189	−	0.275892i	$-0.0889733\pi$
$521$	5.51610	+	9.55416i	0.241665	+	0.418575i	−0.719524	+	0.694468i	$0.755640\pi$
$522$	1.85898	−	0.739255i	0.0813654	−	0.0323563i
$523$	11.2904	+	6.51851i	0.493695	+	0.285035i	0.726106	−	0.687583i	$-0.241328\pi$
$523$	11.2904	+	6.51851i	0.493695	+	0.285035i	−0.232411	+	0.972618i	$0.574662\pi$
$524$	−0.254170	−	1.44147i	−0.0111035	−	0.0629708i
$525$	−46.4420	+	33.0083i	−2.02690	+	1.44060i
$526$	10.1193	−	3.68313i	0.441223	−	0.160592i
$527$	1.50046	+	4.12248i	0.0653611	+	0.179578i
$528$	4.19465	−	5.15104i	0.182549	−	0.224170i
$529$	3.55863	+	20.1820i	0.154723	+	0.877478i
$530$	−11.1833	+	19.3701i	−0.485774	+	0.841385i
$531$	−15.6366	−	12.3553i	−0.678573	−	0.536173i
$532$	6.48604	+	24.9718i	0.281206	+	1.08267i
$533$	17.4302	+	20.7725i	0.754985	+	0.899756i
$534$	−4.42008	−	5.11295i	−0.191276	−	0.221259i
$535$	32.5934	+	5.74709i	1.40913	+	0.248468i
$536$	11.0394	−	13.1563i	0.476831	−	0.568265i
$537$	0.109660	+	7.45240i	0.00473218	+	0.321595i
$538$	3.87619	−	10.6498i	0.167115	−	0.459144i
$539$	4.96820	−	8.30782i	0.213996	−	0.357843i
$540$	−28.5885	+	26.2233i	−1.23025	+	1.12847i
$541$	34.4095			1.47938			0.739689	−	0.672949i	$-0.234972\pi$
$541$	34.4095			1.47938			0.739689	+	0.672949i	$0.234972\pi$
$542$	7.56458	+	2.75328i	0.324927	+	0.118264i
$543$	−0.746481	−	0.416459i	−0.0320346	−	0.0178719i
$544$	−7.28714	+	8.68448i	−0.312434	+	0.372344i
$545$	−2.08825	+	11.8431i	−0.0894510	+	0.507302i
$546$	5.02445	−	7.28417i	0.215027	−	0.311734i
$547$	26.9501	−	22.6138i	1.15230	−	0.966896i	0.152531	−	0.988299i	$-0.451258\pi$
$547$	26.9501	−	22.6138i	1.15230	−	0.966896i	0.999771	+	0.0214028i	$0.00681326\pi$
$548$	7.97651	−	4.60524i	0.340740	−	0.196726i
$549$	−6.29140	+	1.30129i	−0.268511	+	0.0555377i
$550$	3.95746	−	6.85453i	0.168747	−	0.292278i
$551$	1.37188	+	7.78032i	0.0584441	+	0.331453i
$552$	−4.46902	+	1.70146i	−0.190214	+	0.0724191i
$553$	0.479497	+	6.01214i	0.0203903	+	0.255662i
$554$	−1.97205	−	5.41817i	−0.0837845	−	0.230196i
$555$	7.75887	−	48.1338i	0.329346	−	2.04316i
$556$	17.4851	−	3.08310i	0.741534	−	0.130752i
$557$	19.3350	+	11.1631i	0.819251	+	0.472995i	0.850158	−	0.526527i	$-0.176506\pi$
$557$	19.3350	+	11.1631i	0.819251	+	0.472995i	−0.0309069	+	0.999522i	$0.509840\pi$
$558$	2.54503	−	0.0749152i	0.107740	−	0.00317141i
$559$	−17.1497	+	9.90139i	−0.725356	+	0.418784i
$560$	−12.7345	−	27.8661i	−0.538132	−	1.17756i
$561$	5.59763	−	1.07216i	0.236332	−	0.0452667i
$562$	−1.46776	+	8.32406i	−0.0619136	+	0.351129i
$563$	14.2562	+	11.9624i	0.600826	+	0.504153i	0.891711	−	0.452605i	$-0.149505\pi$
$563$	14.2562	+	11.9624i	0.600826	+	0.504153i	−0.290885	+	0.956758i	$0.593950\pi$
$564$	−4.52586	−	7.57925i	−0.190573	−	0.319144i
$565$	9.41012	−	25.8541i	0.395887	−	1.08769i
$566$	−3.80232			−0.159823
$567$	−12.6422	+	20.1785i	−0.530924	+	0.847419i
$568$	−19.7207			−0.827464
$569$	−10.4577	+	28.7324i	−0.438411	+	1.20452i	0.502115	+	0.864801i	$0.332555\pi$
$569$	−10.4577	+	28.7324i	−0.438411	+	1.20452i	−0.940526	+	0.339723i	$0.889667\pi$
$570$	9.30830	+	15.5882i	0.389882	+	0.652917i
$571$	−26.3530	−	22.1128i	−1.10284	−	0.925390i	−0.105224	−	0.994449i	$-0.533556\pi$
$571$	−26.3530	−	22.1128i	−1.10284	−	0.925390i	−0.997613	+	0.0690584i	$0.978001\pi$
$572$	1.80113	−	10.2147i	0.0753090	−	0.427098i
$573$	23.3284	−	4.46830i	0.974559	−	0.186666i
$574$	−7.16092	+	3.27247i	−0.298891	+	0.136590i
$575$	17.0479	−	9.84261i	0.710947	−	0.410465i
$576$	−5.28472	−	8.56136i	−0.220197	−	0.356723i
$577$	2.61437	+	1.50941i	0.108838	+	0.0628374i	0.553431	−	0.832895i	$-0.313318\pi$
$577$	2.61437	+	1.50941i	0.108838	+	0.0628374i	−0.444593	+	0.895733i	$0.646652\pi$
$578$	5.13997	−	0.906315i	0.213794	−	0.0376977i
$579$	−0.201014	+	1.24703i	−0.00835384	+	0.0518247i
$580$	−3.69905	−	10.1631i	−0.153595	−	0.421998i
$581$	2.46112	+	30.8587i	0.102105	+	1.28023i
$582$	4.37234	−	1.66466i	0.181239	−	0.0690022i
$583$	2.79436	+	15.8476i	0.115731	+	0.656341i
$584$	7.74871	−	13.4212i	0.320644	−	0.555371i
$585$	−16.5104	+	49.8822i	−0.682622	+	2.06238i
$586$	8.88211	−	5.12809i	0.366916	−	0.211839i
$587$	−3.99771	+	3.35448i	−0.165003	+	0.138454i	−0.721550	−	0.692362i	$-0.756570\pi$
$587$	−3.99771	+	3.35448i	−0.165003	+	0.138454i	0.556547	+	0.830816i	$0.312126\pi$
$588$	−13.9245	−	16.6164i	−0.574238	−	0.685249i
$589$	−1.74599	+	9.90202i	−0.0719424	+	0.408006i
$590$	8.20721	−	9.78097i	0.337886	−	0.402676i
$591$	−30.3851	−	16.9517i	−1.24988	−	0.697301i
$592$	17.5700	+	6.39497i	0.722124	+	0.262832i
$593$	−38.2020			−1.56877			−0.784385	−	0.620274i	$-0.787021\pi$
$593$	−38.2020			−1.56877			−0.784385	+	0.620274i	$0.787021\pi$
$594$	0.430087	−	3.27970i	0.0176467	−	0.134568i
$595$	6.99820	−	25.3376i	0.286898	−	1.03874i
$596$	3.84373	−	10.5605i	0.157445	−	0.432577i
$597$	−0.200600	−	13.6326i	−0.00820999	−	0.557944i
$598$	−1.96516	+	2.34199i	−0.0803616	+	0.0957712i
$599$	−13.2464	−	2.33569i	−0.541231	−	0.0954337i	−0.103652	−	0.994614i	$-0.533053\pi$
$599$	−13.2464	−	2.33569i	−0.541231	−	0.0954337i	−0.437579	+	0.899180i	$0.644164\pi$
$600$	−24.5595	−	28.4093i	−1.00264	−	1.15980i
$601$	−7.32851	−	8.73377i	−0.298936	−	0.356258i	0.595578	−	0.803297i	$-0.296923\pi$
$601$	−7.32851	−	8.73377i	−0.298936	−	0.356258i	−0.894514	+	0.447039i	$0.852478\pi$
$602$	−1.44543	−	5.56505i	−0.0589115	−	0.226814i
$603$	−4.27231	+	29.2358i	−0.173982	+	1.19057i
$604$	8.49185	−	14.7083i	0.345528	−	0.598473i
$605$	6.58894	+	37.3678i	0.267879	+	1.51922i
$606$	−2.38831	+	2.93286i	−0.0970186	+	0.119139i
$607$	−6.95549	−	19.1101i	−0.282315	−	0.775654i	−0.997085	−	0.0762945i	$-0.975691\pi$
$607$	−6.95549	−	19.1101i	−0.282315	−	0.775654i	0.714771	−	0.699359i	$-0.246531\pi$
$608$	−24.4160	+	8.88671i	−0.990201	+	0.360404i
$609$	−3.84582	−	5.41099i	−0.155840	−	0.219264i
$610$	−0.714762	−	4.05361i	−0.0289399	−	0.164126i
$611$	−10.3547	−	5.97826i	−0.418904	−	0.241855i
$612$	1.84569	−	12.6302i	0.0746075	−	0.510546i
$613$	−15.2811	−	26.4677i	−0.617199	−	1.06902i	−0.989994	−	0.141106i	$-0.954934\pi$
$613$	−15.2811	−	26.4677i	−0.617199	−	1.06902i	0.372796	−	0.927913i	$-0.378399\pi$
$614$	6.93583	−	5.81985i	0.279907	−	0.234870i
$615$	35.3665	−	30.5739i	1.42611	−	1.23286i
$616$	5.76141	+	2.74065i	0.232134	+	0.110424i
$617$	10.8908	−	12.9791i	0.438446	−	0.522519i	−0.500894	−	0.865509i	$-0.666995\pi$
$617$	10.8908	−	12.9791i	0.438446	−	0.522519i	0.939339	+	0.342990i	$0.111440\pi$
$618$	11.1434	−	0.163972i	0.448253	−	0.00659592i
$619$	−11.9681	+	32.8822i	−0.481040	+	1.32165i	0.427563	+	0.903985i	$0.359372\pi$
$619$	−11.9681	+	32.8822i	−0.481040	+	1.32165i	−0.908603	+	0.417661i	$0.862850\pi$
$620$		−	13.7646i		−	0.552802i
$621$	5.00484	−	6.52929i	0.200837	−	0.262011i
$622$			7.67930i			0.307912i
$623$	−13.0043	+	18.2718i	−0.521008	+	0.732045i
$624$	−17.5972	−	9.81742i	−0.704453	−	0.393011i
$625$	51.6495	+	43.3391i	2.06598	+	1.73356i
$626$	0.869350	−	4.93033i	0.0347462	−	0.197056i
$627$	12.3392	+	4.28657i	0.492779	+	0.171189i
$628$	11.3393	+	13.5136i	0.452486	+	0.539252i
$629$	8.02096	+	13.8927i	0.319817	+	0.553939i
$630$	−12.6842	−	8.47662i	−0.505353	−	0.337717i
$631$	8.12831	−	14.0786i	0.323583	−	0.560462i	−0.657642	−	0.753331i	$-0.728446\pi$
$631$	8.12831	−	14.0786i	0.323583	−	0.560462i	0.981225	+	0.192869i	$0.0617792\pi$
$632$	−3.91476	+	0.690278i	−0.155721	+	0.0274578i
$633$	−28.1635	+	10.7225i	−1.11940	+	0.426182i
$634$	−12.2737	+	4.46726i	−0.487450	+	0.177417i
$635$	33.9271	−	12.3485i	1.34636	−	0.490034i
$636$	35.5806	+	5.73538i	1.41086	+	0.227423i
$637$	−27.4350	−	10.4655i	−1.08701	−	0.414657i
$638$	0.798625	+	0.461087i	0.0316179	+	0.0182546i
$639$	28.8700	−	17.8208i	1.14208	−	0.704978i
$640$	40.0375	−	23.1157i	1.58262	−	0.913727i
$641$	17.7198	+	21.1176i	0.699889	+	0.834095i	0.992514	−	0.122132i	$-0.0389731\pi$
$641$	17.7198	+	21.1176i	0.699889	+	0.834095i	−0.292625	+	0.956227i	$0.594529\pi$
$642$	1.18893	+	6.20725i	0.0469233	+	0.244981i
$643$	−14.1593	−	2.49667i	−0.558390	−	0.0984592i	−0.112671	−	0.993632i	$-0.535941\pi$
$643$	−14.1593	−	2.49667i	−0.558390	−	0.0984592i	−0.445719	+	0.895173i	$0.647052\pi$
$644$	4.24889	+	6.16833i	0.167430	+	0.243066i
$645$	17.5035	+	29.3123i	0.689200	+	1.15417i
$646$	−5.61357	−	2.04317i	−0.220863	−	0.0803876i
$647$	22.9189			0.901035			0.450518	−	0.892768i	$-0.351239\pi$
$647$	22.9189			0.901035			0.450518	+	0.892768i	$0.351239\pi$
$648$	−14.0296	−	7.03405i	−0.551135	−	0.276323i
$649$		−	9.18625i		−	0.360592i
$650$	−22.5611	−	8.21158i	−0.884921	−	0.322085i
$651$	−2.24405	−	8.14531i	−0.0879512	−	0.319240i
$652$	−0.582228	−	0.488547i	−0.0228018	−	0.0191330i
$653$	−26.7113	−	4.70992i	−1.04529	−	0.184313i	−0.375470	−	0.926834i	$-0.622519\pi$
$653$	−26.7113	−	4.70992i	−1.04529	−	0.184313i	−0.669823	+	0.742521i	$0.733630\pi$
$654$	−2.25546	+	0.432007i	−0.0881953	+	0.0168928i
$655$	−2.61824	+	2.19697i	−0.102303	+	0.0858426i
$656$	8.96431	+	15.5266i	0.349998	+	0.606214i
$657$	0.784462	+	26.6499i	0.0306048	+	1.03971i
$658$	2.47354	−	2.43583i	0.0964285	−	0.0949586i
$659$	2.75685	−	0.486108i	0.107392	−	0.0189361i	−0.119694	−	0.992811i	$-0.538191\pi$
$659$	2.75685	−	0.486108i	0.107392	−	0.0189361i	0.227086	+	0.973875i	$0.427080\pi$
$660$	−17.6543	−	2.84576i	−0.687192	−	0.110771i
$661$	9.01985	+	24.7818i	0.350832	+	0.963902i	0.982104	+	0.188341i	$0.0603109\pi$
$661$	9.01985	+	24.7818i	0.350832	+	0.963902i	−0.631272	+	0.775561i	$0.717467\pi$
$662$	0.141737	+	0.389418i	0.00550875	+	0.0151352i
$663$	−6.15139	−	16.1571i	−0.238900	−	0.627489i
$664$	−20.0934	+	3.54300i	−0.779774	+	0.137495i
$665$	42.9264	−	42.2720i	1.66461	−	1.63924i
$666$	9.11735	−	1.88580i	0.353290	−	0.0730732i
$667$	1.14677	+	1.98626i	0.0444031	+	0.0769084i
$668$	−12.6696	+	10.6311i	−0.490202	+	0.411328i
$669$	3.24144	−	9.33069i	0.125321	−	0.360746i
$670$	−18.6424	−	3.28716i	−0.720219	−	0.126994i
$671$	−2.26859	−	1.90357i	−0.0875778	−	0.0734865i
$672$	15.3292	−	15.5464i	0.591336	−	0.599714i
$673$	−27.5049	−	10.0110i	−1.06024	−	0.385895i	−0.247720	−	0.968832i	$-0.579681\pi$
$673$	−27.5049	−	10.0110i	−1.06024	−	0.385895i	−0.812518	+	0.582937i	$0.801904\pi$
$674$			10.1802i			0.392126i
$675$	61.6258	+	19.3962i	2.37198	+	0.746558i
$676$	−8.21802			−0.316078
$677$	−40.9538	−	14.9060i	−1.57398	−	0.572883i	−0.600099	−	0.799926i	$-0.704872\pi$
$677$	−40.9538	−	14.9060i	−1.57398	−	0.572883i	−0.973885	+	0.227043i	$0.927094\pi$
$678$	5.25342	−	0.0773026i	0.201756	−	0.00296879i
$679$	−8.80660	−	12.7850i	−0.337966	−	0.490643i
$680$	17.0620	+	3.00848i	0.654296	+	0.115370i
$681$	9.49375	−	8.20724i	0.363801	−	0.314502i
$682$	0.754408	+	0.899069i	0.0288878	+	0.0344271i
$683$	−41.6692	+	24.0577i	−1.59443	+	0.920542i	−0.601892	+	0.798578i	$0.705586\pi$
$683$	−41.6692	+	24.0577i	−1.59443	+	0.920542i	−0.992534	+	0.121965i	$0.961081\pi$
$684$	18.1372	−	22.9542i	0.693492	−	0.877674i
$685$	−18.6258	−	10.7536i	−0.711656	−	0.410875i
$686$	5.04966	−	6.86923i	0.192797	−	0.262268i
$687$	31.3920	−	38.5495i	1.19768	−	1.47075i
$688$	−12.3034	+	4.47807i	−0.469062	+	0.170725i
$689$	45.8697	−	16.6952i	1.74750	−	0.636037i
$690$	4.08708	+	3.32824i	0.155593	+	0.126704i
$691$	2.19447	−	0.386945i	0.0834817	−	0.0147201i	−0.131751	−	0.991283i	$-0.542060\pi$
$691$	2.19447	−	0.386945i	0.0834817	−	0.0147201i	0.215233	+	0.976563i	$0.430949\pi$
$692$	−4.08622	+	7.07754i	−0.155335	+	0.269048i
$693$	−10.9110	+	1.19418i	−0.414473	+	0.0453631i
$694$	−6.22872	−	10.7885i	−0.236439	−	0.409524i
$695$	−26.6494	−	31.7595i	−1.01087	−	1.20471i
$696$	3.30999	−	2.86144i	0.125465	−	0.108463i
$697$	−2.67108	+	15.1484i	−0.101174	+	0.573788i
$698$	3.73007	+	3.12990i	0.141185	+	0.118468i
$699$	0.568899	+	38.6619i	0.0215178	+	1.46233i
$700$	−34.1072	+	47.9226i	−1.28913	+	1.81130i
$701$			21.8097i			0.823740i	0.911243	+	0.411870i	$0.135124\pi$
$701$			21.8097i			0.823740i	−0.911243	+	0.411870i	$0.864876\pi$
$702$	−10.0240	+	0.442758i	−0.378332	+	0.0167108i
$703$			36.7668i			1.38669i
$704$	1.58618	−	4.35800i	0.0597815	−	0.164248i
$705$	−10.0430	+	18.0015i	−0.378239	+	0.677975i
$706$	0.229138	−	0.273076i	0.00862371	−	0.0102773i
$707$	11.3337	+	5.39134i	0.426247	+	0.202762i
$708$	−19.4343	−	6.75137i	−0.730385	−	0.253732i
$709$	−30.0452	+	25.2109i	−1.12837	+	0.946817i	−0.998997	−	0.0447792i	$-0.985742\pi$
$709$	−30.0452	+	25.2109i	−1.12837	+	0.946817i	−0.129375	+	0.991596i	$0.541297\pi$
$710$	10.8684	+	18.8246i	0.407883	+	0.706474i
$711$	5.10720	−	4.54812i	0.191535	−	0.170568i
$712$	−12.8012	−	7.39077i	−0.479745	−	0.276981i
$713$	0.506877	+	2.87464i	0.0189827	+	0.107656i
$714$	4.99736	−	0.472653i	0.187022	−	0.0176886i
$715$	−22.7595	+	8.28378i	−0.851157	+	0.309796i
$716$	2.63162	+	7.23032i	0.0983483	+	0.270210i
$717$	−25.9480	−	4.18267i	−0.969047	−	0.156205i
$718$	0.195022	+	1.10603i	0.00727816	+	0.0412765i
$719$	0.795849	−	1.37845i	0.0296802	−	0.0514075i	−0.850804	−	0.525483i	$-0.823884\pi$
$719$	0.795849	−	1.37845i	0.0296802	−	0.0514075i	0.880484	+	0.474076i	$0.157218\pi$
$720$	−16.4774	+	30.5839i	−0.614075	+	1.13980i
$721$	−9.29672	−	35.7932i	−0.346228	−	1.33301i
$722$	−3.17869	−	3.78821i	−0.118298	−	0.140983i
$723$	−12.0712	+	2.31210i	−0.448933	+	0.0859879i
$724$	−0.869043	−	0.153236i	−0.0322977	−	0.00569496i
$725$	−11.5776	+	13.7976i	−0.429980	+	0.512430i
$726$	−6.22113	+	3.71487i	−0.230888	+	0.137872i
$727$	1.90536	−	5.23493i	0.0706659	−	0.194153i	−0.899332	−	0.437267i	$-0.855947\pi$
$727$	1.90536	−	5.23493i	0.0706659	−	0.194153i	0.969998	+	0.243114i	$0.0781688\pi$
$728$	5.15239	−	18.6547i	0.190960	−	0.691390i
$729$	26.8949	−	2.38052i	0.996106	−	0.0881674i
$730$	−17.0817			−0.632222
$731$	−10.5559	−	3.84202i	−0.390423	−	0.142102i
$732$	−5.69444	+	3.40037i	−0.210473	+	0.125681i
$733$	10.0493	−	11.9762i	0.371178	−	0.442352i	−0.547831	−	0.836589i	$-0.684546\pi$
$733$	10.0493	−	11.9762i	0.371178	−	0.442352i	0.919009	+	0.394236i	$0.128991\pi$
$734$	−2.62088	+	14.8638i	−0.0967385	+	0.548631i
$735$	−17.3449	+	47.5591i	−0.639778	+	1.75425i
$736$	−5.77834	+	4.84860i	−0.212993	+	0.178722i
$737$	−11.7948	+	6.80975i	−0.434468	+	0.250840i
$738$	7.85935	+	4.23429i	0.289307	+	0.155866i
$739$	−2.30238	+	3.98783i	−0.0846943	+	0.146695i	−0.905261	−	0.424856i	$-0.860325\pi$
$739$	−2.30238	+	3.98783i	−0.0846943	+	0.146695i	0.820567	+	0.571551i	$0.193658\pi$
$740$	−8.74015	−	49.5678i	−0.321294	−	1.82215i
$741$	6.30572	−	39.1188i	0.231646	−	1.43707i
$742$	1.12678	+	14.1280i	0.0413654	+	0.518657i
$743$	6.72183	+	18.4681i	0.246600	+	0.677528i	0.999805	+	0.0197424i	$0.00628462\pi$
$743$	6.72183	+	18.4681i	0.246600	+	0.677528i	−0.753205	+	0.657786i	$0.771493\pi$
$744$	5.20413	−	1.98134i	0.190793	−	0.0726393i
$745$	−25.8437	+	4.55694i	−0.946840	+	0.166953i
$746$	−10.1307	−	5.84896i	−0.370911	−	0.214146i
$747$	26.2138	−	23.3442i	0.959114	−	0.854121i
$748$	5.09550	−	2.94189i	0.186310	−	0.107566i
$749$	19.0744	−	8.71682i	0.696963	−	0.318506i
$750$	−8.12086	+	23.3764i	−0.296532	+	0.853587i
$751$	−2.66294	+	15.1023i	−0.0971722	+	0.551091i	0.896888	+	0.442258i	$0.145822\pi$
$751$	−2.66294	+	15.1023i	−0.0971722	+	0.551091i	−0.994060	+	0.108833i	$0.965289\pi$
$752$	−6.05580	−	5.08142i	−0.220832	−	0.185300i
$753$	12.0841	−	21.6601i	0.440368	−	0.789336i
$754$	0.956737	−	2.62861i	0.0348423	−	0.0957284i
$755$	−39.6584			−1.44332
$756$	−5.49255	+	23.9607i	−0.199762	+	0.871442i
$757$	13.1222			0.476934			0.238467	−	0.971151i	$-0.423355\pi$
$757$	13.1222			0.476934			0.238467	+	0.971151i	$0.423355\pi$
$758$	−2.94589	+	8.09378i	−0.107000	+	0.293979i
$759$	3.79176	−	0.0557947i	0.137632	−	0.00202522i
$760$	30.4180	+	25.5237i	1.10338	+	0.925843i
$761$	−7.30569	+	41.4326i	−0.264831	+	1.50193i	0.504684	+	0.863304i	$0.331609\pi$
$761$	−7.30569	+	41.4326i	−0.264831	+	1.50193i	−0.769515	+	0.638628i	$0.779502\pi$
$762$	4.50897	+	5.21576i	0.163343	+	0.188947i
$763$	3.16733	+	6.93084i	0.114665	+	0.250913i
$764$	21.2358	−	12.2605i	0.768284	−	0.443569i
$765$	−27.6963	+	11.0139i	−1.00136	+	0.398208i
$766$	4.30061	+	2.48296i	0.155387	+	0.0897129i
$767$	−27.4421	+	4.83879i	−0.990879	+	0.174719i
$768$	−2.16275	−	1.76119i	−0.0780414	−	0.0635515i
$769$	−11.9091	−	32.7199i	−0.429452	−	1.17991i	−0.946146	−	0.323740i	$-0.895060\pi$
$769$	−11.9091	−	32.7199i	−0.429452	−	1.17991i	0.516694	−	0.856170i	$-0.327162\pi$
$770$	−0.559082	−	7.01001i	−0.0201479	−	0.252623i
$771$	12.5428	+	10.2140i	0.451718	+	0.367848i
$772$	0.226436	+	1.28418i	0.00814961	+	0.0462187i
$773$	24.5173	−	42.4653i	0.881827	−	1.52737i	0.0325201	−	0.999471i	$-0.489647\pi$
$773$	24.5173	−	42.4653i	0.881827	−	1.52737i	0.849307	−	0.527899i	$-0.177020\pi$
$774$	−4.04192	+	5.11540i	−0.145284	+	0.183869i
$775$	−19.8521	+	11.4616i	−0.713109	+	0.411714i
$776$	7.83829	−	6.57711i	0.281378	−	0.236104i
$777$	−13.2531	−	27.9071i	−0.475451	−	1.00116i
$778$	0.403966	−	2.29101i	0.0144829	−	0.0821366i
$779$	−22.6612	+	27.0066i	−0.811923	+	0.967613i
$780$	0.798093	+	54.2377i	0.0285763	+	1.94202i
$781$	14.6957	+	5.34881i	0.525854	+	0.191395i
$782$	−1.73426			−0.0620169
$783$	−2.25986	+	7.18007i	−0.0807608	+	0.256595i
$784$	−16.6620	−	9.96415i	−0.595072	−	0.355862i
$785$	14.0887	−	38.7085i	0.502848	−	1.38156i
$786$	−0.569979	−	0.317989i	−0.0203305	−	0.0113423i
$787$	−12.1134	+	14.4362i	−0.431798	+	0.514596i	−0.937440	−	0.348147i	$-0.886811\pi$
$787$	−12.1134	+	14.4362i	−0.431798	+	0.514596i	0.505642	+	0.862743i	$0.331256\pi$
$788$	−35.3739	−	6.23738i	−1.26014	−	0.222197i
$789$	−13.2963	+	38.2744i	−0.473362	+	1.36260i
$790$	2.81639	+	3.35644i	0.100203	+	0.119417i
$791$	−4.38282	−	16.8743i	−0.155835	−	0.599979i
$792$	−1.46530	−	7.08435i	−0.0520672	−	0.251731i
$793$	−4.49158	+	7.77965i	−0.159501	+	0.276264i
$794$	−1.64331	−	9.31967i	−0.0583189	−	0.330743i
$795$	−29.9435	−	78.6489i	−1.06199	−	2.78939i
$796$	−4.81399	−	13.2263i	−0.170627	−	0.468795i
$797$	18.9831	−	6.90930i	0.672418	−	0.244740i	0.0168292	−	0.999858i	$-0.494643\pi$
$797$	18.9831	−	6.90930i	0.672418	−	0.244740i	0.655588	+	0.755118i	$0.272421\pi$
$798$	10.4607	+	4.78863i	0.370305	+	0.169516i
$799$	−1.17776	−	6.67941i	−0.0416662	−	0.236301i
$800$	−51.3007	−	29.6185i	−1.81375	−	1.04717i
$801$	25.4189	−	0.748226i	0.898132	−	0.0264373i
$802$	7.01124	+	12.1438i	0.247576	+	0.428813i
$803$	−9.41445	+	7.89966i	−0.332229	+	0.278773i
$804$	5.73806	+	29.9577i	0.202366	+	1.05653i
$805$	7.51311	−	15.7941i	0.264802	−	0.556668i
$806$	2.28841	−	2.72723i	0.0806060	−	0.0960624i
$807$	21.8621	+	36.6114i	0.769581	+	1.28878i
$808$	−2.82921	+	7.77320i	−0.0995313	+	0.273460i
$809$		−	21.6939i		−	0.762716i	−0.924428	−	0.381358i	$-0.875457\pi$
$809$		−	21.6939i		−	0.762716i	0.924428	−	0.381358i	$-0.124543\pi$
$810$	1.01752	+	17.2686i	0.0357518	+	0.606758i
$811$		−	15.5791i		−	0.547057i	−0.961864	−	0.273529i	$-0.911809\pi$
$811$		−	15.5791i		−	0.547057i	0.961864	−	0.273529i	$-0.0881908\pi$
$812$	−5.58349	−	3.97385i	−0.195942	−	0.139455i
$813$	−26.0053	+	15.5287i	−0.912045	+	0.544617i
$814$	3.28758	+	2.75861i	0.115230	+	0.0966891i
$815$	−0.308185	+	1.74780i	−0.0107953	+	0.0612229i
$816$	−2.15031	−	11.2265i	−0.0752759	−	0.393006i
$817$	−16.5491	−	19.7225i	−0.578981	−	0.690003i
$818$	−0.223209	−	0.386610i	−0.00780434	−	0.0135175i
$819$	9.31464	+	31.9654i	0.325480	+	1.11696i
$820$	24.1312	−	41.7965i	0.842698	−	1.45960i
$821$	39.3325	−	6.93539i	1.37271	−	0.242047i	0.561830	−	0.827253i	$-0.310098\pi$
$821$	39.3325	−	6.93539i	1.37271	−	0.242047i	0.810885	+	0.585206i	$0.198986\pi$
$822$	0.653595	−	4.05471i	0.0227968	−	0.141424i
$823$	47.2385	−	17.1934i	1.64663	−	0.599324i	0.658449	−	0.752625i	$-0.271213\pi$
$823$	47.2385	−	17.1934i	1.64663	−	0.599324i	0.988180	+	0.153301i	$0.0489904\pi$
$824$	22.9039	−	8.33635i	0.797896	−	0.290410i
$825$	10.5961	+	27.8316i	0.368911	+	0.968971i
$826$	0.767030	−	8.05425i	0.0266884	−	0.280243i
$827$	−29.4328	−	16.9930i	−1.02348	−	0.590905i	−0.108368	−	0.994111i	$-0.534563\pi$
$827$	−29.4328	−	16.9930i	−1.02348	−	0.590905i	−0.915109	+	0.403206i	$0.867896\pi$
$828$	2.66869	−	8.06278i	0.0927432	−	0.280201i
$829$	−11.4272	+	6.59749i	−0.396883	+	0.229140i	−0.685138	−	0.728413i	$-0.740258\pi$
$829$	−11.4272	+	6.59749i	−0.396883	+	0.229140i	0.288255	+	0.957554i	$0.406925\pi$
$830$	14.4557	+	17.2277i	0.501766	+	0.597982i
$831$	20.4932	+	7.11923i	0.710901	+	0.246963i
$832$	−13.8542	−	2.44287i	−0.480307	−	0.0846912i
$833$	−5.45582	−	15.7378i	−0.189033	−	0.545281i
$834$	3.85723	−	6.91388i	0.133565	−	0.239408i
$835$	36.2909	+	13.2088i	1.25590	+	0.457110i
$836$	13.4852			0.466394
$837$	−5.82808	+	7.60329i	−0.201448	+	0.262808i
$838$		−	15.9972i		−	0.552613i
$839$	0.902087	+	0.328333i	0.0311435	+	0.0113353i	0.357545	−	0.933896i	$-0.383614\pi$
$839$	0.902087	+	0.328333i	0.0311435	+	0.0113353i	−0.326401	+	0.945231i	$0.605836\pi$
$840$	−32.2886	−	8.40874i	−1.11406	−	0.290129i
$841$	20.6077	+	17.2919i	0.710611	+	0.596274i
$842$	4.28139	+	0.754924i	0.147546	+	0.0260164i
$843$	−20.7988	−	24.0591i	−0.716349	−	0.828639i
$844$	−23.8321	+	19.9975i	−0.820336	+	0.688343i
$845$	9.59488	+	16.6188i	0.330074	+	0.571705i
$846$	−3.89500	−	0.569187i	−0.133913	−	0.0195690i
$847$	16.8704	+	17.1316i	0.579675	+	0.588649i
$848$	31.7837	−	5.60432i	1.09146	−	0.192453i
$849$	9.03378	−	11.0935i	0.310039	−	0.380728i
$850$	−4.65810	−	12.7980i	−0.159772	−	0.438969i
$851$	3.65063	+	10.0300i	0.125142	+	0.343825i
$852$	22.1163	−	27.1589i	0.757694	−	0.930450i
$853$	18.8229	−	3.31898i	0.644483	−	0.113640i	0.158153	−	0.987415i	$-0.449446\pi$
$853$	18.8229	−	3.31898i	0.644483	−	0.113640i	0.486331	+	0.873775i	$0.338335\pi$
$854$	−1.83009	−	1.85842i	−0.0626243	−	0.0635937i
$855$	−67.5948	−	9.87781i	−2.31169	−	0.337814i
$856$	6.91119	+	11.9705i	0.236220	+	0.409144i
$857$	18.3633	−	15.4086i	0.627277	−	0.526348i	−0.272804	−	0.962070i	$-0.587951\pi$
$857$	18.3633	−	15.4086i	0.627277	−	0.526348i	0.900082	+	0.435722i	$0.143507\pi$
$858$	−3.02477	−	3.49892i	−0.103264	−	0.119451i
$859$	−36.0276	−	6.35264i	−1.22925	−	0.216749i	−0.478944	−	0.877845i	$-0.658980\pi$
$859$	−36.0276	−	6.35264i	−1.22925	−	0.216749i	−0.750301	+	0.661096i	$0.770092\pi$
$860$	26.9994	+	22.6552i	0.920673	+	0.772536i
$861$	7.46570	−	28.6674i	0.254430	−	0.976982i
$862$	14.7090	+	5.35362i	0.500989	+	0.182345i
$863$			2.63865i			0.0898208i	0.998991	+	0.0449104i	$0.0143002\pi$
$863$			2.63865i			0.0898208i	−0.998991	+	0.0449104i	$0.985700\pi$
$864$	−24.5460	−	3.21886i	−0.835071	−	0.109508i
$865$	19.0833			0.648853
$866$	15.6701	+	5.70345i	0.532492	+	0.193811i
$867$	−9.56762	+	17.1495i	−0.324933	+	0.582427i
$868$	−4.94779	−	7.18296i	−0.167939	−	0.243806i
$869$	3.10447	+	0.547401i	0.105312	+	0.0185693i
$870$	−4.55559	−	1.58259i	−0.154449	−	0.0536548i
$871$	26.5556	+	31.6478i	0.899803	+	1.07234i
$872$	−4.34959	+	2.51124i	−0.147296	+	0.0850413i
$873$	−5.53134	+	16.7116i	−0.187208	+	0.565602i
$874$	−3.44226	−	1.98739i	−0.116436	−	0.0672245i
$875$	81.7469	+	7.78500i	2.76355	+	0.263181i
$876$	9.79330	+	25.7228i	0.330885	+	0.869094i
$877$	−6.60150	+	2.40275i	−0.222917	+	0.0811351i	−0.451064	−	0.892492i	$-0.648955\pi$
$877$	−6.60150	+	2.40275i	−0.222917	+	0.0811351i	0.228147	+	0.973627i	$0.426733\pi$
$878$	−16.7796	+	6.10728i	−0.566284	+	0.206111i
$879$	−6.14113	+	38.0977i	−0.207135	+	1.28501i
$880$	−15.7703	+	2.78074i	−0.531618	+	0.0937386i
$881$	2.09355	−	3.62614i	0.0705336	−	0.122168i	−0.828602	−	0.559839i	$-0.810863\pi$
$881$	2.09355	−	3.62614i	0.0705336	−	0.122168i	0.899135	+	0.437671i	$0.144196\pi$
$882$	−9.66613	+	0.135983i	−0.325476	+	0.00457878i
$883$	−18.5670	−	32.1591i	−0.624831	−	1.08224i	−0.988574	−	0.150739i	$-0.951835\pi$
$883$	−18.5670	−	32.1591i	−0.624831	−	1.08224i	0.363743	−	0.931500i	$-0.381499\pi$
$884$	−11.4723	−	13.6722i	−0.385857	−	0.459846i
$885$	9.03743	+	47.1833i	0.303790	+	1.58605i
$886$	−1.01358	+	5.74833i	−0.0340520	+	0.193119i
$887$	−16.9146	−	14.1930i	−0.567937	−	0.476555i	0.313024	−	0.949745i	$-0.398658\pi$
$887$	−16.9146	−	14.1930i	−0.567937	−	0.476555i	−0.880960	+	0.473190i	$0.843102\pi$
$888$	17.4825	−	10.4395i	0.586674	−	0.350325i
$889$	13.2658	−	18.6393i	0.444922	−	0.625141i
$890$			16.2926i			0.546130i
$891$	8.54692	+	9.04692i	0.286333	+	0.303083i
$892$		−	10.1973i		−	0.341430i
$893$	5.31665	−	14.6074i	0.177915	−	0.488817i
$894$	−2.56922	−	4.30256i	−0.0859276	−	0.143899i
$895$	11.5489	−	13.7635i	0.386038	−	0.460063i
$896$	12.5841	−	26.4544i	0.420407	−	0.883780i
$897$	−2.16396	−	11.2977i	−0.0722524	−	0.377221i
$898$	−6.09468	+	5.11404i	−0.203382	+	0.170658i
$899$	−1.33540	−	2.31298i	−0.0445381	−	0.0771423i
$900$	66.6675	−	1.96241i	2.22225	−	0.0654138i
$901$	23.9802	+	13.8450i	0.798897	+	0.461243i
$902$	0.714583	+	4.05260i	0.0237930	+	0.134937i
$903$	19.6705	+	9.00463i	0.654595	+	0.299655i
$904$	10.7978	−	3.93007i	0.359129	−	0.130712i
$905$	0.704764	+	1.93632i	0.0234272	+	0.0643656i
$906$	−2.69462	−	7.07761i	−0.0895226	−	0.235138i
$907$	−7.80605	−	44.2703i	−0.259196	−	1.46997i	−0.785069	−	0.619408i	$-0.787373\pi$
$907$	−7.80605	−	44.2703i	−0.259196	−	1.46997i	0.525873	−	0.850563i	$-0.323739\pi$
$908$	6.47776	−	11.2198i	0.214972	−	0.372343i
$909$	−2.88250	−	13.9361i	−0.0956064	−	0.462232i
$910$	−20.6466	+	5.36262i	−0.684427	+	0.177769i
$911$	−17.2752	−	20.5878i	−0.572353	−	0.682103i	0.399759	−	0.916620i	$-0.369094\pi$
$911$	−17.2752	−	20.5878i	−0.572353	−	0.682103i	−0.972112	+	0.234517i	$0.924649\pi$
$912$	8.59707	−	24.7472i	0.284677	−	0.819463i
$913$	15.9344	+	2.80966i	0.527350	+	0.0929861i
$914$	−10.7904	+	12.8595i	−0.356916	+	0.425356i
$915$	13.5249	+	7.54547i	0.447118	+	0.249445i
$916$	17.5534	−	48.2277i	0.579982	−	1.59349i
$917$	−0.576594	+	2.08761i	−0.0190408	+	0.0689390i
$918$	−3.84743	−	4.19446i	−0.126984	−	0.138438i
$919$	18.6916			0.616578			0.308289	−	0.951293i	$-0.400244\pi$
$919$	18.6916			0.616578			0.308289	+	0.951293i	$0.400244\pi$
$920$	10.8323	+	3.94265i	0.357132	+	0.129985i
$921$	0.501227	+	34.0629i	0.0165160	+	1.12241i
$922$	2.87998	−	3.43223i	0.0948471	−	0.113034i
$923$	8.23765	−	46.7181i	0.271146	−	1.53774i
$924$	−10.2357	+	4.86090i	−0.336728	+	0.159912i
$925$	−64.2116	+	53.8799i	−2.11126	+	1.77156i
$926$	−8.33689	+	4.81331i	−0.273967	+	0.158175i
$927$	−25.9968	+	32.9012i	−0.853846	+	1.08062i
$928$	3.45087	−	5.97708i	0.113280	−	0.196207i
$929$	−4.56421	−	25.8849i	−0.149747	−	0.849256i	−0.963432	−	0.267951i	$-0.913653\pi$
$929$	−4.56421	−	25.8849i	−0.149747	−	0.849256i	0.813686	−	0.581305i	$-0.197458\pi$
$930$	−4.75937	−	3.87570i	−0.156066	−	0.127089i
$931$	7.20581	−	37.4894i	0.236161	−	1.22867i
$932$	13.6524	+	37.5098i	0.447201	+	1.22867i
$933$	−22.4049	−	18.2450i	−0.733502	−	0.597313i
$934$	−6.12917	+	1.08074i	−0.200553	+	0.0353628i
$935$	−11.8984	−	6.86956i	−0.389120	−	0.224659i
$936$	−20.3913	+	8.10893i	−0.666509	+	0.265049i
$937$	−46.8366	+	27.0411i	−1.53009	+	0.883396i	−0.530729	+	0.847541i	$0.678082\pi$
$937$	−46.8366	+	27.0411i	−1.53009	+	0.883396i	−0.999357	+	0.0358542i	$0.988585\pi$
$938$	−10.9100	+	4.98575i	−0.356223	+	0.162791i
$939$	12.3191	+	14.2502i	0.402019	+	0.465037i
$940$	−3.69530	+	20.9571i	−0.120527	+	0.683544i
$941$	12.2779	+	10.3024i	0.400249	+	0.335849i	0.820590	−	0.571518i	$-0.193645\pi$
$941$	12.2779	+	10.3024i	0.400249	+	0.335849i	−0.420341	+	0.907366i	$0.638090\pi$
$942$	7.86536	−	0.115737i	0.256267	−	0.00377090i
$943$	−3.50048	+	9.61750i	−0.113991	+	0.313189i
$944$	−18.4238			−0.599643
$945$	54.8671	−	16.8679i	1.78483	−	0.548711i
$946$	−3.00521			−0.0977077
$947$	8.01520	−	22.0216i	0.260459	−	0.715605i	−0.738678	−	0.674059i	$-0.764549\pi$
$947$	8.01520	−	22.0216i	0.260459	−	0.715605i	0.999137	−	0.0415463i	$-0.0132284\pi$
$948$	3.43968	−	6.16545i	0.111716	−	0.200244i
$949$	28.5577	+	23.9628i	0.927022	+	0.777864i
$950$	5.42035	−	30.7403i	0.175859	−	0.997348i
$951$	16.1271	−	46.4229i	0.522956	−	1.50536i
$952$	9.98504	−	4.56307i	0.323617	−	0.147890i
$953$	1.12625	−	0.650242i	0.0364829	−	0.0210634i	−0.481648	−	0.876365i	$-0.659961\pi$
$953$	1.12625	−	0.650242i	0.0364829	−	0.0210634i	0.518131	+	0.855302i	$0.326628\pi$
$954$	12.0015	−	10.6877i	0.388563	−	0.346027i
$955$	−49.5874	−	28.6293i	−1.60461	−	0.926422i
$956$	−26.7211	+	4.71165i	−0.864223	+	0.152386i
$957$	−3.24267	+	1.23456i	−0.104821	+	0.0399078i
$958$	−1.50052	−	4.12265i	−0.0484797	−	0.133197i
$959$	−13.5852	+	1.08348i	−0.438688	+	0.0349875i
$960$	−3.85970	+	23.9445i	−0.124571	+	0.772804i
$961$	4.79284	+	27.1815i	0.154608	+	0.876824i
$962$	6.50909	−	11.2741i	0.209862	−	0.363491i
$963$	−20.9348	−	11.2788i	−0.674614	−	0.363454i
$964$	−10.9884	+	6.34414i	−0.353912	+	0.204331i
$965$	2.33255	−	1.95725i	0.0750876	−	0.0630060i
$966$	3.32916	+	0.267683i	0.107114	+	0.00861257i
$967$	−4.85865	+	27.5548i	−0.156244	+	0.886102i	0.801396	+	0.598134i	$0.204091\pi$
$967$	−4.85865	+	27.5548i	−0.156244	+	0.886102i	−0.957640	+	0.287968i	$0.907020\pi$
$968$	−10.1863	+	12.1396i	−0.327401	+	0.390181i
$969$	19.2982	−	11.5237i	0.619947	−	0.370194i
$970$	−10.5980	−	3.85736i	−0.340282	−	0.123852i
$971$	−21.5459			−0.691440			−0.345720	−	0.938338i	$-0.612365\pi$
$971$	−21.5459			−0.691440			−0.345720	+	0.938338i	$0.612365\pi$
$972$	25.4210	−	11.4327i	0.815379	−	0.366705i
$973$	−25.3229	−	6.99412i	−0.811814	−	0.224221i
$974$	2.54141	−	6.98248i	0.0814322	−	0.223733i
$975$	77.5600	−	46.3140i	2.48391	−	1.48324i
$976$	−3.81777	+	4.54984i	−0.122204	+	0.145637i
$977$	43.2803	+	7.63149i	1.38466	+	0.244153i	0.815825	−	0.578298i	$-0.196283\pi$
$977$	43.2803	+	7.63149i	1.38466	+	0.244153i	0.568835	+	0.822451i	$0.307394\pi$
$978$	−0.332861	+	0.0637557i	−0.0106437	+	0.00203868i
$979$	7.53475	+	8.97957i	0.240812	+	0.286988i
$980$	−0.802715	+	52.2550i	−0.0256418	+	1.66922i
$981$	4.09825	−	7.60683i	0.130847	−	0.242868i
$982$	4.40299	−	7.62619i	0.140505	−	0.243362i
$983$	−1.19243	−	6.76260i	−0.0380326	−	0.215694i	0.959868	−	0.280451i	$-0.0904839\pi$
$983$	−1.19243	−	6.76260i	−0.0380326	−	0.215694i	−0.997901	+	0.0647570i	$0.979373\pi$
$984$	19.2759	+	3.10716i	0.614494	+	0.0990527i
$985$	28.6871	+	78.8171i	0.914046	+	2.51132i
$986$	1.49111	−	0.542718i	0.0474865	−	0.0172837i
$987$	1.22992	+	13.0039i	0.0391487	+	0.413919i
$988$	−7.10321	−	40.2843i	−0.225983	−	1.28161i
$989$	−6.47290	−	3.73713i	−0.205826	−	0.118834i
$990$	−5.95487	+	5.30300i	−0.189258	+	0.168540i
$991$	2.09397	+	3.62686i	0.0665171	+	0.115211i	0.897366	−	0.441287i	$-0.145478\pi$
$991$	2.09397	+	3.62686i	0.0665171	+	0.115211i	−0.830849	+	0.556498i	$0.812145\pi$
$992$	6.72882	−	5.64615i	0.213640	−	0.179265i
$993$	−1.47290	−	0.511678i	−0.0467411	−	0.0162376i
$994$	12.4382	+	5.91674i	0.394515	+	0.187667i
$995$	−21.1263	+	25.1773i	−0.669749	+	0.798175i
$996$	17.6549	−	31.6455i	0.559417	−	1.00273i
$997$	8.78012	−	24.1232i	0.278069	−	0.763989i	−0.719512	−	0.694480i	$-0.755635\pi$
$997$	8.78012	−	24.1232i	0.278069	−	0.763989i	0.997581	−	0.0695089i	$-0.0221432\pi$
$998$		−	18.3765i		−	0.581698i
$999$	−16.1596	+	31.0809i	−0.511268	+	0.983355i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.14	yes	132
3.2	odd	2		567.2.be.a.503.9		132
7.6	odd	2	inner	189.2.be.a.104.13	yes	132
21.20	even	2		567.2.be.a.503.10		132
27.7	even	9		567.2.be.a.62.10		132
27.20	odd	18	inner	189.2.be.a.20.13	✓	132
189.20	even	18	inner	189.2.be.a.20.14	yes	132
189.34	odd	18		567.2.be.a.62.9		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.13	✓	132	27.20	odd	18	inner
189.2.be.a.20.14	yes	132	189.20	even	18	inner
189.2.be.a.104.13	yes	132	7.6	odd	2	inner
189.2.be.a.104.14	yes	132	1.1	even	1	trivial
567.2.be.a.62.9		132	189.34	odd	18
567.2.be.a.62.10		132	27.7	even	9
567.2.be.a.503.9		132	3.2	odd	2
567.2.be.a.503.10		132	21.20	even	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.157445 - 0.432576i) q^{2} +(0.888001 + 1.48710i) q^{3} +(1.36976 + 1.14936i) q^{4} +(0.725040 - 4.11191i) q^{5} +(0.783093 - 0.149993i) q^{6} +(-1.09969 - 2.40638i) q^{7} +(1.51017 - 0.871900i) q^{8} +(-1.42291 + 2.64109i) q^{9} +(-1.66456 - 0.961033i) q^{10} +(-1.36185 + 0.240131i) q^{11} +(-0.492866 + 3.05759i) q^{12} +(1.43469 + 3.94178i) q^{13} +(-1.21408 + 0.0968290i) q^{14} +(6.75864 - 2.57317i) q^{15} +(0.481603 + 2.73131i) q^{16} +(-1.18976 + 2.06072i) q^{17} +(0.918441 + 1.03134i) q^{18} +(-4.72301 + 2.72683i) q^{19} +(5.71920 - 4.79898i) q^{20} +(2.60199 - 3.77222i) q^{21} +(-0.110541 + 0.626912i) q^{22} +(-1.01769 + 1.21284i) q^{23} +(2.63764 + 1.47153i) q^{24} +(-11.6836 - 4.25249i) q^{25} +1.93100 q^{26} +(-5.19109 + 0.229289i) q^{27} +(1.25949 - 4.56010i) q^{28} +(0.495461 - 1.36127i) q^{29} +(-0.0489817 - 3.32875i) q^{30} +(1.18509 - 1.41234i) q^{31} +(4.69194 + 0.827315i) q^{32} +(-1.56642 - 1.81197i) q^{33} +(0.704097 + 0.839111i) q^{34} +(-10.6921 + 2.77712i) q^{35} +(-4.98460 + 1.98221i) q^{36} +(3.37083 - 5.83846i) q^{37} +(0.435948 + 2.47239i) q^{38} +(-4.58780 + 5.63383i) q^{39} +(-2.49023 - 6.84186i) q^{40} +(6.07454 - 2.21095i) q^{41} +(-1.22210 - 1.71947i) q^{42} +(0.819766 + 4.64912i) q^{43} +(-2.14140 - 1.23634i) q^{44} +(9.82823 + 7.76576i) q^{45} +(0.364414 + 0.631183i) q^{46} +(-2.18349 + 1.83217i) q^{47} +(-3.63405 + 3.14159i) q^{48} +(-4.58135 + 5.29257i) q^{49} +(-3.67905 + 4.38452i) q^{50} +(-4.12100 + 0.0606394i) q^{51} +(-2.56536 + 7.04826i) q^{52} -11.6368i q^{53} +(-0.718125 + 2.28164i) q^{54} +5.77391i q^{55} +(-3.75885 - 2.67523i) q^{56} +(-8.24910 - 4.60214i) q^{57} +(-0.510844 - 0.428649i) q^{58} +(-1.15353 + 6.54201i) q^{59} +(12.2152 + 4.24350i) q^{60} +(1.37654 + 1.64050i) q^{61} +(-0.424356 - 0.735006i) q^{62} +(7.92022 + 0.519671i) q^{63} +(-1.67684 + 2.90438i) q^{64} +(17.2484 - 3.04137i) q^{65} +(-1.03044 + 0.392313i) q^{66} +(9.25483 - 3.36848i) q^{67} +(-3.99819 + 1.45522i) q^{68} +(-2.70732 - 0.436403i) q^{69} +(-0.482108 + 5.06240i) q^{70} +(-9.79394 - 5.65453i) q^{71} +(0.153924 + 5.22913i) q^{72} +(7.69650 - 4.44358i) q^{73} +(-1.99486 - 2.37738i) q^{74} +(-4.05122 - 21.1509i) q^{75} +(-9.60349 - 1.69335i) q^{76} +(2.07547 + 3.01307i) q^{77} +(1.71473 + 2.87159i) q^{78} +(-2.14212 - 0.779666i) q^{79} +11.5801 q^{80} +(-4.95067 - 7.51604i) q^{81} -2.97580i q^{82} +(-10.9949 - 4.00181i) q^{83} +(7.89974 - 2.17639i) q^{84} +(7.61088 + 6.38628i) q^{85} +(2.14017 + 0.377369i) q^{86} +(2.46430 - 0.472010i) q^{87} +(-1.84726 + 1.55004i) q^{88} +(-4.23831 - 7.34097i) q^{89} +(4.90668 - 3.02878i) q^{90} +(7.90771 - 7.78717i) q^{91} +(-2.78798 + 0.491595i) q^{92} +(3.15264 + 0.508187i) q^{93} +(0.448772 + 1.23299i) q^{94} +(7.78811 + 21.3976i) q^{95} +(2.93615 + 7.71202i) q^{96} +(5.77859 - 1.01892i) q^{97} +(1.56813 + 2.81507i) q^{98} +(1.30358 - 3.93845i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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