LMFDB - Embedded newform 189.2.be.a.104.13

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			104.13
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.13

$q$-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} +(2.17886 + 1.50085i) 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} +(0.992282 - 0.706223i) 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} +(0.297075 - 4.57294i) 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} +(-7.75112 + 7.87111i) 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} +(-1.93137 - 0.848492i) 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} +(2.49489 + 6.54030i) 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} +(4.59906 + 0.366797i) 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} +(-7.06420 + 3.61899i) 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} +(2.18448 + 4.59221i) 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} +(-3.32769 - 1.52072i) 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} +(5.66288 - 5.92236i) 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} +(2.79003 - 10.7419i) 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} +(3.22198 - 0.0494945i) 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	$0.438937\pi$
$5$	−0.725040	+	4.11191i	−0.324248	+	1.83890i	−0.514909	+	0.857245i	$0.672174\pi$
$6$	−0.783093	+	0.149993i	−0.319696	+	0.0612342i
$7$	2.17886	+	1.50085i	0.823533	+	0.567268i
$7$	2.17886	+	1.50085i	0.823533	+	0.567268i
$8$	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	$-0.913496\pi$
$13$	−1.43469	−	3.94178i	−0.397912	−	1.09325i	0.565388	−	0.824825i	$-0.308726\pi$
$14$	0.992282	−	0.706223i	0.265199	−	0.188746i
$15$	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	−0.684907	−	0.728630i	$-0.740157\pi$
$17$	1.18976	−	2.06072i	0.288559	−	0.499799i	0.973466	+	0.228832i	$0.0734906\pi$
$18$	0.918441	+	1.03134i	0.216479	+	0.243089i
$19$	4.72301	−	2.72683i	1.08353	−	0.625578i	0.151686	−	0.988429i	$-0.451530\pi$
$19$	4.72301	−	2.72683i	1.08353	−	0.625578i	0.931847	+	0.362851i	$0.118196\pi$
$20$	−5.71920	+	4.79898i	−1.27885	+	1.07308i
$21$	0.297075	−	4.57294i	0.0648272	−	0.997897i
$22$	−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	−0.861896	−	0.507085i	$-0.830723\pi$
$31$	−1.18509	+	1.41234i	−0.212849	+	0.253663i	0.649048	+	0.760748i	$0.275168\pi$
$32$	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
$35$	−7.75112	+	7.87111i	−1.31018	+	1.33046i
$36$	−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	−0.769589	−	0.638539i	$-0.779539\pi$
$41$	−6.07454	+	2.21095i	−0.948684	+	0.345293i	−0.179095	+	0.983832i	$0.557317\pi$
$42$	−1.93137	−	0.848492i	−0.298017	−	0.130925i
$43$	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	−0.469497	−	0.882934i	$-0.655565\pi$
$47$	2.18349	−	1.83217i	0.318495	−	0.267249i	0.787993	+	0.615685i	$0.211120\pi$
$48$	3.63405	−	3.14159i	0.524530	−	0.453450i
$49$	2.49489	+	6.54030i	0.356413	+	0.934328i
$50$	−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
$56$	4.59906	+	0.366797i	0.614575	+	0.0490153i
$57$	−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	$-0.802105\pi$
$59$	1.15353	−	6.54201i	0.150177	−	0.851698i	0.963063	−	0.269275i	$-0.0867840\pi$
$60$	12.2152	+	4.24350i	1.57697	+	0.547833i
$61$	−1.37654	−	1.64050i	−0.176248	−	0.210045i	0.670687	−	0.741741i	$-0.265999\pi$
$61$	−1.37654	−	1.64050i	−0.176248	−	0.210045i	−0.846935	+	0.531696i	$0.821555\pi$
$62$	0.424356	+	0.735006i	0.0538933	+	0.0933459i
$63$	−7.06420	+	3.61899i	−0.890005	+	0.455950i
$64$	−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
$70$	2.18448	+	4.59221i	0.261095	+	0.548874i
$71$	−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	−0.877462	−	0.479646i	$-0.840765\pi$
$73$	−7.69650	+	4.44358i	−0.900807	+	0.520081i	−0.0233450	+	0.999727i	$0.507432\pi$
$74$	−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
$77$	−3.32769	−	1.52072i	−0.379226	−	0.173303i
$78$	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	0.865608	−	0.500722i	$-0.166932\pi$
$83$	10.9949	+	4.00181i	1.20685	+	0.439256i	0.341237	+	0.939977i	$0.389154\pi$
$84$	5.66288	−	5.92236i	0.617871	−	0.646182i
$85$	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	0.998338	−	0.0576296i	$-0.0183542\pi$
$89$	4.23831	+	7.34097i	0.449260	+	0.778142i	−0.549078	+	0.835771i	$0.685021\pi$
$90$	−4.90668	+	3.02878i	−0.517210	+	0.319261i
$91$	2.79003	−	10.7419i	0.292475	−	1.12605i
$92$	−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	−0.459128	−	0.888370i	$-0.651838\pi$
$97$	−5.77859	+	1.01892i	−0.586727	+	0.103456i	−0.127599	+	0.991826i	$0.540727\pi$
$98$	3.22198	−	0.0494945i	0.325469	−	0.00499970i
$99$	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	−0.443837	−	0.896108i	$-0.646383\pi$
$101$	3.63389	−	3.04919i	0.361585	−	0.303406i	0.805422	+	0.592702i	$0.201939\pi$
$102$	−0.622598	+	1.79219i	−0.0616464	+	0.177453i
$103$	−13.7651	−	2.42716i	−1.35631	−	0.239155i	−0.552241	−	0.833685i	$-0.686227\pi$
$103$	−13.7651	−	2.42716i	−1.35631	−	0.239155i	−0.804073	+	0.594530i	$0.797338\pi$
$104$	−5.60347	−	4.70187i	−0.549466	−	0.461056i
$105$	18.5881	+	4.53711i	1.81401	+	0.442776i
$106$	−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
$112$	−3.04994	+	6.67396i	−0.288192	+	0.630630i
$113$	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
$119$	5.68516	−	2.70438i	0.521158	−	0.247910i
$120$	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
$126$	0.453269	+	3.62559i	0.0403804	+	0.322993i
$127$	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	0.669770	−	0.742568i	$-0.266393\pi$
$131$	0.627073	+	0.526177i	0.0547876	+	0.0459723i	−0.614983	+	0.788541i	$0.710837\pi$
$132$	0.0630135	+	4.28234i	0.00548462	+	0.372730i
$133$	14.3834	+	1.14714i	1.24720	+	0.0994699i
$134$		−	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	−0.965492	−	0.260431i	$-0.916135\pi$
$139$	−6.38256	+	7.60644i	−0.541362	+	0.645170i	0.424131	+	0.905601i	$0.360580\pi$
$140$	−19.6639	+	1.87265i	−1.66190	+	0.158268i
$141$	−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
$147$	7.51058	−	9.51794i	0.619462	−	0.785026i
$148$	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
$154$	−1.18176	+	1.20005i	−0.0952286	+	0.0967027i
$155$	−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	−0.228079	−	0.973643i	$-0.573244\pi$
$157$	−9.71583	−	1.71316i	−0.775408	−	0.136725i	−0.547329	+	0.836917i	$0.684355\pi$
$158$	−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	$-0.827946\pi$
$167$	1.60617	−	9.10902i	0.124289	−	0.704877i	0.981728	−	0.190291i	$-0.0609432\pi$
$168$	−3.53851	−	7.16495i	−0.273002	−	0.552788i
$169$	−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	$-0.999969\pi$
$173$	−0.793657	−	4.50105i	−0.0603406	−	0.342209i	0.939659	−	0.342112i	$-0.111142\pi$
$174$	−0.183812	+	1.14031i	−0.0139347	+	0.0864470i
$175$	−19.0747	−	26.8010i	−1.44191	−	2.02596i
$176$	−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	−0.484032	−	0.875050i	$-0.660828\pi$
$181$	0.427397	−	0.246758i	0.0317681	−	0.0183413i	0.515800	+	0.856709i	$0.327495\pi$
$182$	−4.20739	−	2.89815i	−0.311873	−	0.214825i
$183$	−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
$189$	11.6548	+	7.29147i	0.847762	+	0.530376i
$190$	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
$196$	−4.09978	+	11.8261i	−0.292841	+	0.844725i
$197$	−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	0.721768	−	0.692135i	$-0.243330\pi$
$199$	6.81702	+	3.93581i	0.483246	+	0.279002i	−0.238522	+	0.971137i	$0.576663\pi$
$200$	−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
$203$	3.12260	−	2.22240i	0.219164	−	0.155982i
$204$	−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
$210$	4.88924	−	7.32642i	0.337390	−	0.505571i
$211$	−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	0.874688	−	0.484687i	$-0.161066\pi$
$223$	3.66575	+	4.36867i	0.245476	+	0.292547i	−0.629211	+	0.777234i	$0.716622\pi$
$224$	8.98142	+	8.84451i	0.600096	+	0.590949i
$225$	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	$0.0217391\pi$
$227$	1.25816	+	7.13538i	0.0835071	+	0.473592i	−0.914162	+	0.405350i	$0.867150\pi$
$228$	−6.00973	−	15.7850i	−0.398004	−	1.04539i
$229$	9.81687	+	26.9716i	0.648717	+	1.78233i	0.622424	+	0.782680i	$0.286148\pi$
$229$	9.81687	+	26.9716i	0.648717	+	1.78233i	0.0262929	+	0.999654i	$0.491630\pi$
$230$	−2.85958	+	1.04080i	−0.188555	+	0.0686285i
$231$	0.693532	+	6.29900i	0.0456311	+	0.414444i
$232$	−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
$238$	−0.274752	−	2.88505i	−0.0178095	−	0.187010i
$239$	−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	−0.836654	−	0.547732i	$-0.815492\pi$
$241$	2.42697	−	6.66806i	0.156335	−	0.429527i	0.992989	+	0.118204i	$0.0377138\pi$
$242$			4.18341i			0.268920i
$243$	−6.78087	+	14.0364i	−0.434993	+	0.900434i
$244$		−	3.82924i		−	0.245142i
$245$	−28.7020	+	5.51679i	−1.83370	+	0.352454i
$246$	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	0.998506	−	0.0546399i	$-0.0174011\pi$
$251$	7.15997	+	12.4014i	0.451934	+	0.782772i	−0.546573	+	0.837412i	$0.684068\pi$
$252$	−13.8358	−	3.16218i	−0.871571	−	0.199199i
$253$	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	−0.600898	−	0.799326i	$-0.705190\pi$
$257$	−8.77573	+	3.19411i	−0.547415	+	0.199243i	0.0534825	+	0.998569i	$0.482968\pi$
$258$	−1.33929	−	3.51774i	−0.0833803	−	0.219005i
$259$	16.1072	−	7.66208i	1.00086	−	0.476099i
$260$	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
$266$	2.76081	−	6.04128i	0.169276	−	0.370415i
$267$	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	$-0.770204\pi$
$269$	−24.6194			−1.50107			−0.750536	+	0.660830i	$0.770204\pi$
$270$	8.86122	+	4.60714i	0.539277	+	0.280382i
$271$		−	17.4873i		−	1.06228i	−0.847285	−	0.531139i	$-0.821764\pi$
$271$		−	17.4873i		−	1.06228i	0.847285	−	0.531139i	$-0.178236\pi$
$272$	6.20146	+	2.25715i	0.376019	+	0.136860i
$273$	−18.4517	+	5.38974i	−1.11675	+	0.326202i
$274$	−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
$280$	−4.84273	+	18.6450i	−0.289409	+	1.11425i
$281$	−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	0.994901	−	0.100860i	$-0.0321595\pi$
$283$	2.82503	+	7.76172i	0.167931	+	0.461386i	−0.826970	+	0.562246i	$0.809937\pi$
$284$	−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
$287$	−16.5539	−	4.29962i	−0.977147	−	0.253799i
$288$	−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	−0.0105009	−	0.999945i	$-0.503343\pi$
$293$	−17.0672	−	14.3211i	−0.997078	−	0.836648i	−0.986577	+	0.163297i	$0.947787\pi$
$294$	−2.93473	−	4.74745i	−0.171157	−	0.276877i
$295$	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
$301$	−5.19148	+	11.3602i	−0.299232	+	0.654788i
$302$	−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	−0.0722533	−	0.997386i	$-0.523019\pi$
$307$	−17.0333	−	9.83418i	−0.972142	−	0.561266i	−0.899889	+	0.436120i	$0.856352\pi$
$308$	−2.81026	−	5.90774i	−0.160130	−	0.336625i
$309$	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	0.143101	−	0.989708i	$-0.454292\pi$
$311$	15.6758	−	5.70554i	0.888896	−	0.323532i	0.745794	+	0.666177i	$0.232070\pi$
$312$	−2.01624	+	12.5082i	−0.114147	+	0.708136i
$313$	−10.7102	+	1.88851i	−0.605379	+	0.106745i	−0.467932	−	0.883764i	$-0.655001\pi$
$313$	−10.7102	+	1.88851i	−0.605379	+	0.106745i	−0.137447	+	0.990509i	$0.543890\pi$
$314$	−2.27078	+	3.93310i	−0.128147	+	0.221958i
$315$	−9.75914	−	31.6712i	−0.549865	−	1.78447i
$316$	−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
$322$	−0.153304	+	1.92219i	−0.00854330	+	0.107120i
$323$		−	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
$329$	7.50735	−	0.714947i	0.413894	−	0.0394163i
$330$	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
$336$	12.6332	−	1.39094i	0.689196	−	0.0758818i
$337$	−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
$343$	−4.37999	+	17.9949i	−0.236497	+	0.971632i
$344$	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	−0.804423	−	0.594057i	$-0.797525\pi$
$349$	3.61775	−	9.93968i	0.193654	−	0.532059i	0.998076	+	0.0619986i	$0.0197474\pi$
$350$	−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	0.322582	−	0.946541i	$-0.395449\pi$
$353$	−0.727677	−	0.264853i	−0.0387303	−	0.0140967i	−0.361313	+	0.932445i	$0.617671\pi$
$354$	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
$357$	−9.07010	−	6.05288i	−0.480041	−	0.320352i
$358$	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
$364$	16.1679	−	11.5070i	0.847431	−	0.603129i
$365$	−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	0.752883	−	0.658155i	$-0.228663\pi$
$367$	32.2888	−	5.69339i	1.68546	−	0.297193i	0.932580	+	0.360962i	$0.117552\pi$
$368$	−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
$371$	17.4651	−	25.3550i	0.906743	−	1.31637i
$372$	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
$378$	4.98910	−	3.89358i	0.256612	−	0.200264i
$379$	−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	$-0.855565\pi$
$383$	1.87324	−	10.6237i	0.0957180	−	0.542844i	0.994525	−	0.104499i	$-0.0333239\pi$
$384$	6.29343	−	18.1161i	0.321160	−	0.924481i
$385$	8.66579	−	12.5806i	0.441649	−	0.641165i
$386$	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
$392$	9.47021	+	7.70170i	0.478318	+	0.388995i
$393$	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	−0.875095	−	0.483952i	$-0.839201\pi$
$397$	−17.8034	+	10.2788i	−0.893528	+	0.515878i	−0.0184329	+	0.999830i	$0.505868\pi$
$398$	2.77584	−	2.32921i	0.139140	−	0.116753i
$399$	−11.0665	−	22.4081i	−0.554020	−	1.12181i
$400$	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	−0.781236	−	0.624236i	$-0.785410\pi$
$409$	−0.623352	+	0.742883i	−0.0308228	+	0.0367332i	0.750413	+	0.660969i	$0.229855\pi$
$410$	−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
$413$	12.3320	−	12.5229i	0.606817	−	0.616210i
$414$	−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	−0.978461	−	0.206434i	$-0.933814\pi$
$419$	−32.6552	+	11.8855i	−1.59531	+	0.580646i	−0.616851	+	0.787080i	$0.711592\pi$
$420$	20.2464	+	27.5792i	0.987922	+	1.34573i
$421$	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
$427$	−0.537154	−	5.64042i	−0.0259947	−	0.272959i
$428$	−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	$-0.663839\pi$
$433$		−	36.2251i		−	1.74087i	0.492286	−	0.870433i	$-0.336161\pi$
$434$	−0.178521	+	2.23837i	−0.00856928	+	0.107445i
$435$	−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	$0.154277\pi$
$439$	24.9337	+	29.7148i	1.19002	+	1.41821i	0.305196	+	0.952290i	$0.401278\pi$
$440$	−5.03427	−	8.71962i	−0.240000	−	0.415692i
$441$	−20.8235	−	2.71701i	−0.991595	−	0.129382i
$442$	−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
$448$	−8.01266	+	3.81155i	−0.378563	+	0.180079i
$449$	−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
$455$	42.1466	+	19.2606i	1.97587	+	0.902952i
$456$	−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	0.120133	−	0.992758i	$-0.461668\pi$
$461$	−9.14600	−	3.32887i	−0.425972	−	0.155041i	−0.546105	+	0.837717i	$0.683890\pi$
$462$	2.83399	+	0.691739i	0.131849	+	0.0321826i
$463$	−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	0.978970	−	0.204003i	$-0.0653952\pi$
$467$	6.75996	+	11.7086i	0.312813	+	0.541809i	−0.666157	+	0.745812i	$0.732062\pi$
$468$	14.9648	+	16.8043i	0.691748	+	0.776781i
$469$	25.2206	+	6.55065i	1.16458	+	0.302481i
$470$	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
$476$	10.8956	+	2.82996i	0.499399	+	0.129711i
$477$	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	−0.794157	−	0.607713i	$-0.792087\pi$
$479$	−7.30076	+	6.12607i	−0.333580	+	0.279907i	0.460576	+	0.887620i	$0.347643\pi$
$480$	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
$483$	5.24389	+	5.01414i	0.238605	+	0.228151i
$484$	−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
$490$	−2.13255	+	13.2844i	−0.0963388	+	0.600127i
$491$	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
$497$	−12.8530	−	27.0197i	−0.576538	−	1.21200i
$498$	−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	$-0.616712\pi$
$503$	14.1117	−	24.4422i	0.629211	−	1.08982i	0.987710	−	0.156295i	$-0.0499550\pi$
$504$	−7.51277	+	11.6246i	−0.334645	+	0.517800i
$505$	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	0.668140	−	0.744035i	$-0.267091\pi$
$509$	1.16032	+	0.973624i	0.0514303	+	0.0431551i	−0.616710	+	0.787190i	$0.711535\pi$
$510$	−6.91792	−	3.85948i	−0.306330	−	0.170901i
$511$	−23.4388	−	1.86935i	−1.03687	−	0.0826953i
$512$			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
$518$	−0.778430	−	8.17396i	−0.0342023	−	0.359143i
$519$	−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	0.719524	−	0.694468i	$-0.244360\pi$
$521$	−5.51610	−	9.55416i	−0.241665	−	0.418575i	−0.961189	+	0.275892i	$0.911027\pi$
$522$	1.85898	−	0.739255i	0.0813654	−	0.0323563i
$523$	−11.2904	−	6.51851i	−0.493695	−	0.285035i	0.232411	−	0.972618i	$-0.425338\pi$
$523$	−11.2904	−	6.51851i	−0.493695	−	0.285035i	−0.726106	+	0.687583i	$0.758672\pi$
$524$	0.254170	+	1.44147i	0.0111035	+	0.0629708i
$525$	−22.9173	+	52.1652i	−1.00019	+	2.27668i
$526$	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
$532$	18.3832	+	18.1030i	0.797014	+	0.784864i
$533$	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
$546$	−0.573654	+	8.83036i	−0.0245501	+	0.377904i
$547$	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
$553$	−3.49721	−	4.91378i	−0.148717	−	0.208955i
$554$	−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
$560$	−25.2314	−	17.3800i	−1.06622	−	0.734437i
$561$	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	0.290885	−	0.956758i	$-0.406050\pi$
$563$	−14.2562	−	11.9624i	−0.600826	−	0.504153i	−0.891711	+	0.452605i	$0.850495\pi$
$564$	−4.52586	−	7.57925i	−0.190573	−	0.319144i
$565$	−9.41012	+	25.8541i	−0.395887	+	1.08769i
$566$	3.80232			0.159823
$567$	0.493622	−	23.8066i	0.0207302	−	0.999785i
$568$	−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
$574$	−4.46624	+	6.48387i	−0.186417	+	0.270631i
$575$	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	0.444593	−	0.895733i	$-0.353348\pi$
$577$	−2.61437	−	1.50941i	−0.108838	−	0.0628374i	−0.553431	+	0.832895i	$0.686682\pi$
$578$	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
$581$	17.9502	+	25.2211i	0.744701	+	1.04635i
$582$	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	−0.556547	−	0.830816i	$-0.687874\pi$
$587$	3.99771	−	3.35448i	0.165003	−	0.138454i	0.721550	+	0.692362i	$0.243430\pi$
$588$	21.2272	−	4.40488i	0.875396	−	0.181654i
$589$	−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	$-0.212979\pi$
$593$	38.2020			1.56877			0.784385	+	0.620274i	$0.212979\pi$
$594$	−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	0.894514	−	0.447039i	$-0.147522\pi$
$601$	7.32851	+	8.73377i	0.298936	+	0.356258i	−0.595578	+	0.803297i	$0.703077\pi$
$602$	4.09675	+	4.03431i	0.166971	+	0.164426i
$603$	−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	$0.0243089\pi$
$607$	6.95549	+	19.1101i	0.282315	+	0.775654i	−0.714771	+	0.699359i	$0.753469\pi$
$608$	24.4160	−	8.88671i	0.990201	−	0.360404i
$609$	−6.07780	−	2.67011i	−0.246285	−	0.108198i
$610$	−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
$616$	−6.35131	+	0.604854i	−0.255902	+	0.0243703i
$617$	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	$-0.640628\pi$
$619$	11.9681	−	32.8822i	0.481040	−	1.32165i	0.908603	−	0.417661i	$-0.137150\pi$
$620$		−	13.7646i		−	0.552802i
$621$	−5.00484	+	6.52929i	−0.200837	+	0.262011i
$622$		−	7.67930i		−	0.307912i
$623$	−1.78300	+	22.3561i	−0.0714345	+	0.895677i
$624$	−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
$630$	−15.2367	−	0.764901i	−0.607046	−	0.0304744i
$631$	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
$637$	22.2010	−	19.2176i	0.879637	−	0.761430i
$638$	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	0.445719	−	0.895173i	$-0.352948\pi$
$643$	14.1593	+	2.49667i	0.558390	+	0.0984592i	0.112671	+	0.993632i	$0.464059\pi$
$644$	−6.81243	−	3.11322i	−0.268447	−	0.122678i
$645$	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	$-0.648761\pi$
$647$	−22.9189			−0.901035			−0.450518	+	0.892768i	$0.648761\pi$
$648$	−14.0296	−	7.03405i	−0.551135	−	0.276323i
$649$			9.18625i			0.360592i
$650$	22.5611	+	8.21158i	0.884921	+	0.322085i
$651$	6.10646	+	5.83891i	0.239331	+	0.228845i
$652$	−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
$658$	0.872724	−	3.36006i	0.0340223	−	0.130989i
$659$	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	$-0.939689\pi$
$661$	−9.01985	−	24.7818i	−0.350832	−	0.963902i	0.631272	−	0.775561i	$-0.282533\pi$
$662$	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
$665$	−15.1455	+	58.3113i	−0.587316	+	2.26122i
$666$	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
$672$	5.17712	−	21.2102i	0.199712	−	0.818200i
$673$	−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	0.973885	−	0.227043i	$-0.0729057\pi$
$677$	40.9538	+	14.9060i	1.57398	+	0.572883i	0.600099	+	0.799926i	$0.295128\pi$
$678$	−5.25342	+	0.0773026i	−0.201756	+	0.00296879i
$679$	−14.1200	−	6.45272i	−0.541877	−	0.247633i
$680$	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
$686$	7.09454	+	4.72787i	0.270871	+	0.180511i
$687$	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	−0.215233	−	0.976563i	$-0.569051\pi$
$691$	−2.19447	+	0.386945i	−0.0834817	+	0.0147201i	0.131751	+	0.991283i	$0.457940\pi$
$692$	4.08622	−	7.07754i	0.155335	−	0.269048i
$693$	8.75136	−	6.62487i	0.332437	−	0.251658i
$694$	−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
$700$	4.67638	−	58.6345i	0.176751	−	2.21618i
$701$			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
$707$	12.4941	−	1.18985i	0.469890	−	0.0447490i
$708$	−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
$714$	−4.04637	+	2.97051i	−0.151432	+	0.111169i
$715$	−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	−0.880484	−	0.474076i	$-0.842782\pi$
$719$	−0.795849	+	1.37845i	−0.0296802	+	0.0514075i	0.850804	+	0.525483i	$0.176116\pi$
$720$	16.4774	−	30.5839i	0.614075	−	1.13980i
$721$	−26.3494	−	25.9478i	−0.981304	−	0.966346i
$722$	−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	−0.969998	−	0.243114i	$-0.921831\pi$
$727$	−1.90536	+	5.23493i	−0.0706659	+	0.194153i	0.899332	+	0.437267i	$0.144053\pi$
$728$	−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	−0.919009	−	0.394236i	$-0.871009\pi$
$733$	−10.0493	+	11.9762i	−0.371178	+	0.442352i	0.547831	+	0.836589i	$0.315454\pi$
$734$	2.62088	−	14.8638i	0.0967385	−	0.548631i
$735$	33.6914	+	37.7837i	1.24273	+	1.39367i
$736$	−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
$742$	−8.21817	−	11.5470i	−0.301699	−	0.423903i
$743$	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
$749$	−11.8966	+	17.2709i	−0.434693	+	0.631067i
$750$	−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
$756$	7.58371	+	23.3831i	0.275817	+	0.850436i
$757$	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	$-0.668391\pi$
$761$	7.30569	−	41.4326i	0.264831	−	1.50193i	0.769515	−	0.638628i	$-0.220498\pi$
$762$	−4.50897	−	5.21576i	−0.163343	−	0.188947i
$763$	−6.27554	−	4.32274i	−0.227190	−	0.156494i
$764$	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	$0.104940\pi$
$769$	11.9091	+	32.7199i	0.429452	+	1.17991i	−0.516694	+	0.856170i	$0.672838\pi$
$770$	−4.07767	−	5.72935i	−0.146949	−	0.206472i
$771$	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	$0.510353\pi$
$773$	−24.5173	+	42.4653i	−0.881827	+	1.52737i	−0.849307	+	0.527899i	$0.822980\pi$
$774$	−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
$777$	−25.6975	−	17.1491i	−0.921893	−	0.615220i
$778$	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	−0.505642	−	0.862743i	$-0.668744\pi$
$787$	12.1134	−	14.4362i	0.431798	−	0.514596i	0.937440	+	0.348147i	$0.113189\pi$
$788$	−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
$791$	12.4221	+	12.2328i	0.441680	+	0.434947i
$792$	−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	−0.655588	−	0.755118i	$-0.727579\pi$
$797$	−18.9831	+	6.90930i	−0.672418	+	0.244740i	−0.0168292	+	0.999858i	$0.505357\pi$
$798$	−11.4356	+	1.25908i	−0.404815	+	0.0445709i
$799$	−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
$805$	−1.65812	−	17.4112i	−0.0584411	−	0.613664i
$806$	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	$0.0881908\pi$
$811$			15.5791i			0.547057i	−0.961864	+	0.273529i	$0.911809\pi$
$812$	6.83155	+	0.544848i	0.239740	+	0.0191204i
$813$	−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
$819$	24.4002	+	22.6534i	0.852613	+	0.791573i
$820$	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
$826$	−3.47549	−	7.30618i	−0.120928	−	0.254214i
$827$	−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	−0.288255	−	0.957554i	$-0.593075\pi$
$829$	11.4272	−	6.59749i	0.396883	−	0.229140i	0.685138	+	0.728413i	$0.259742\pi$
$830$	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
$833$	16.4461	+	2.64010i	0.569822	+	0.0914739i
$834$	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	0.326401	−	0.945231i	$-0.394164\pi$
$839$	−0.902087	−	0.328333i	−0.0311435	−	0.0113353i	−0.357545	+	0.933896i	$0.616386\pi$
$840$	32.0272	−	9.35513i	1.10504	−	0.322783i
$841$	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
$847$	−23.2716	−	6.04444i	−0.799622	−	0.207689i
$848$	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	−0.486331	−	0.873775i	$-0.661665\pi$
$853$	−18.8229	+	3.31898i	−0.644483	+	0.113640i	−0.158153	+	0.987415i	$0.550554\pi$
$854$	−2.52448	−	0.655694i	−0.0863859	−	0.0224374i
$855$	−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	−0.900082	−	0.435722i	$-0.856493\pi$
$857$	−18.3633	+	15.4086i	−0.627277	+	0.526348i	0.272804	+	0.962070i	$0.412049\pi$
$858$	−3.02477	−	3.49892i	−0.103264	−	0.119451i
$859$	36.0276	+	6.35264i	1.22925	+	0.216749i	0.750301	−	0.661096i	$-0.229908\pi$
$859$	36.0276	+	6.35264i	1.22925	+	0.216749i	0.478944	+	0.877845i	$0.341020\pi$
$860$	−26.9994	−	22.6552i	−0.920673	−	0.772536i
$861$	8.30595	+	28.4353i	0.283066	+	0.969073i
$862$	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
$868$	−7.93301	−	3.62531i	−0.269264	−	0.123051i
$869$	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
$875$	74.1544	−	35.2746i	2.50687	−	1.19250i
$876$	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	−0.899135	−	0.437671i	$-0.855804\pi$
$881$	−2.09355	+	3.62614i	−0.0705336	+	0.122168i	0.828602	+	0.559839i	$0.189137\pi$
$882$	−4.45386	+	8.57996i	−0.149969	+	0.288902i
$883$	−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	0.880960	−	0.473190i	$-0.156898\pi$
$887$	16.9146	+	14.1930i	0.567937	+	0.476555i	−0.313024	+	0.949745i	$0.601342\pi$
$888$	−17.4825	+	10.4395i	−0.586674	+	0.350325i
$889$	−1.81886	+	22.8056i	−0.0610025	+	0.764876i
$890$			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
$896$	2.77728	+	29.1630i	0.0927825	+	0.974269i
$897$	−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
$903$	21.5037	−	2.36760i	0.715598	−	0.0787887i
$904$	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
$910$	14.9674	−	15.1991i	0.496166	−	0.503846i
$911$	−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
$924$	−6.28986	+	9.42521i	−0.206921	+	0.310067i
$925$	−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	$0.0863466\pi$
$929$	4.56421	+	25.8849i	0.149747	+	0.849256i	−0.813686	+	0.581305i	$0.802542\pi$
$930$	4.75937	+	3.87570i	0.156066	+	0.127089i
$931$	29.6177	+	24.0868i	0.970681	+	0.789412i
$932$	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	$-0.321918\pi$
$937$	46.8366	−	27.0411i	1.53009	−	0.883396i	0.999357	−	0.0358542i	$-0.0114152\pi$
$938$	6.80450	−	9.87845i	0.222175	−	0.322543i
$939$	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	0.420341	−	0.907366i	$-0.361910\pi$
$941$	−12.2779	−	10.3024i	−0.400249	−	0.335849i	−0.820590	+	0.571518i	$0.806355\pi$
$942$	7.86536	−	0.115737i	0.256267	−	0.00377090i
$943$	3.50048	−	9.61750i	0.113991	−	0.313189i
$944$	18.4238			0.599643
$945$	−38.4320	+	42.6369i	−1.25019	+	1.38698i
$946$	−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
$952$	6.22763	−	9.04098i	0.201839	−	0.293020i
$953$	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
$959$	11.1033	−	7.90239i	0.358544	−	0.255181i
$960$	−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
$966$	2.99462	−	1.47893i	0.0963503	−	0.0475839i
$967$	−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	$-0.387635\pi$
$971$	21.5459			0.691440			0.345720	+	0.938338i	$0.387635\pi$
$972$	−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
$980$	−45.6555	−	25.4323i	−1.45841	−	0.812406i
$981$	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	0.997901	−	0.0647570i	$-0.0206272\pi$
$983$	1.19243	+	6.76260i	0.0380326	+	0.215694i	−0.959868	+	0.280451i	$0.909516\pi$
$984$	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
$987$	−7.72973	−	10.5293i	−0.246040	−	0.335150i
$988$	−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
$994$	−13.7117	+	1.30581i	−0.434909	+	0.0414177i
$995$	−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	$0.244365\pi$
$997$	−8.78012	+	24.1232i	−0.278069	+	0.763989i	−0.997581	+	0.0695089i	$0.977857\pi$
$998$		−	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.104.13	yes	132
3.2	odd	2		567.2.be.a.503.10		132
7.6	odd	2	inner	189.2.be.a.104.14	yes	132
21.20	even	2		567.2.be.a.503.9		132
27.7	even	9		567.2.be.a.62.9		132
27.20	odd	18	inner	189.2.be.a.20.14	yes	132
189.20	even	18	inner	189.2.be.a.20.13	✓	132
189.34	odd	18		567.2.be.a.62.10		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.13	✓	132	189.20	even	18	inner
189.2.be.a.20.14	yes	132	27.20	odd	18	inner
189.2.be.a.104.13	yes	132	1.1	even	1	trivial
189.2.be.a.104.14	yes	132	7.6	odd	2	inner
567.2.be.a.62.9		132	27.7	even	9
567.2.be.a.62.10		132	189.34	odd	18
567.2.be.a.503.9		132	21.20	even	2
567.2.be.a.503.10		132	3.2	odd	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} +(2.17886 + 1.50085i) 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} +(0.992282 - 0.706223i) 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} +(0.297075 - 4.57294i) 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} +(-7.75112 + 7.87111i) 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} +(-1.93137 - 0.848492i) 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} +(2.49489 + 6.54030i) 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} +(4.59906 + 0.366797i) 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} +(-7.06420 + 3.61899i) 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} +(2.18448 + 4.59221i) 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} +(-3.32769 - 1.52072i) 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} +(5.66288 - 5.92236i) 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} +(2.79003 - 10.7419i) 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} +(3.22198 - 0.0494945i) 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

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Database

Properties

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