LMFDB - Embedded newform 456.2.bk.a.61.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [456,2,Mod(61,456)] 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("456.61"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(456, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 456 = 2^{3} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	456.bk (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:	$3.64117833217$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			61.8
Character	$\chi$	$=$	456.61
Dual form			456.2.bk.a.157.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20129 - 0.746258i) q^{2} +(0.984808 - 0.173648i) q^{3} +(0.886199 + 1.79294i) q^{4} +(-1.13283 - 1.35006i) q^{5} +(-1.31263 - 0.526318i) q^{6} +(1.93035 - 3.34346i) q^{7} +(0.273416 - 2.81518i) q^{8} +(0.939693 - 0.342020i) q^{9} +(0.353370 + 2.46719i) q^{10} +(-1.21469 + 0.701299i) q^{11} +(1.18408 + 1.61182i) q^{12} +(3.21190 + 0.566345i) q^{13} +(-4.81400 + 2.57593i) q^{14} +(-1.35006 - 1.13283i) q^{15} +(-2.42930 + 3.17781i) q^{16} +(-2.28751 - 0.832585i) q^{17} +(-1.38408 - 0.290387i) q^{18} +(-4.33543 + 0.451693i) q^{19} +(1.41666 - 3.22752i) q^{20} +(1.32044 - 3.62787i) q^{21} +(1.98254 + 0.0640044i) q^{22} +(0.514611 + 0.431810i) q^{23} +(-0.219589 - 2.81989i) q^{24} +(0.328897 - 1.86527i) q^{25} +(-3.43579 - 3.07725i) q^{26} +(0.866025 - 0.500000i) q^{27} +(7.70532 + 0.498037i) q^{28} +(-1.74380 - 4.79106i) q^{29} +(0.776426 + 2.36835i) q^{30} +(4.57031 - 7.91602i) q^{31} +(5.28977 - 2.00459i) q^{32} +(-1.07445 + 0.901573i) q^{33} +(2.12664 + 2.70725i) q^{34} +(-6.70063 + 1.18150i) q^{35} +(1.44598 + 1.38172i) q^{36} +2.64726i q^{37} +(5.54519 + 2.69273i) q^{38} +3.26145 q^{39} +(-4.11039 + 2.82000i) q^{40} +(-0.352348 - 1.99826i) q^{41} +(-4.29356 + 3.37274i) q^{42} +(-0.671130 - 0.799821i) q^{43} +(-2.33384 - 1.55637i) q^{44} +(-1.52626 - 0.881186i) q^{45} +(-0.295956 - 0.902761i) q^{46} +(7.57838 - 2.75831i) q^{47} +(-1.84057 + 3.55138i) q^{48} +(-3.95250 - 6.84594i) q^{49} +(-1.78707 + 1.99529i) q^{50} +(-2.39733 - 0.422715i) q^{51} +(1.83096 + 6.26066i) q^{52} +(-4.48652 + 5.34682i) q^{53} +(-1.41348 - 0.0456327i) q^{54} +(2.32283 + 0.845440i) q^{55} +(-8.88467 - 6.34844i) q^{56} +(-4.19113 + 1.19767i) q^{57} +(-1.48055 + 7.05678i) q^{58} +(1.49805 - 4.11585i) q^{59} +(0.834686 - 3.42449i) q^{60} +(-5.03333 + 5.99848i) q^{61} +(-11.3977 + 6.09881i) q^{62} +(0.670404 - 3.80205i) q^{63} +(-7.85049 - 1.53943i) q^{64} +(-2.87395 - 4.97782i) q^{65} +(1.96354 - 0.281232i) q^{66} +(-1.47156 - 4.04307i) q^{67} +(-0.534409 - 4.83921i) q^{68} +(0.581776 + 0.335888i) q^{69} +(8.93110 + 3.58107i) q^{70} +(7.23784 - 6.07327i) q^{71} +(-0.705921 - 2.73892i) q^{72} +(2.81397 + 15.9588i) q^{73} +(1.97553 - 3.18012i) q^{74} -1.89404i q^{75} +(-4.65192 - 7.37290i) q^{76} +5.41501i q^{77} +(-3.91795 - 2.43388i) q^{78} +(1.39093 + 7.88833i) q^{79} +(7.04221 - 0.320231i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.06795 + 2.66344i) q^{82} +(2.76991 + 1.59921i) q^{83} +(7.67474 - 0.847545i) q^{84} +(1.46733 + 4.03144i) q^{85} +(0.209349 + 1.46165i) q^{86} +(-2.54927 - 4.41546i) q^{87} +(1.64217 + 3.61131i) q^{88} +(-2.19823 + 12.4668i) q^{89} +(1.17589 + 2.19754i) q^{90} +(8.09365 - 9.64564i) q^{91} +(-0.318164 + 1.30534i) q^{92} +(3.12628 - 8.58938i) q^{93} +(-11.1623 - 2.34190i) q^{94} +(5.52112 + 5.34138i) q^{95} +(4.86131 - 2.89269i) q^{96} +(0.928978 + 0.338120i) q^{97} +(-0.360727 + 11.1736i) q^{98} +(-0.901573 + 1.07445i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/456\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$343$
$\chi(n)$	$e\left(\frac{1}{9}\right)$	$-1$	$1$	$1$

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 $

$2$	−1.20129	−	0.746258i	−0.849441	−	0.527684i
$2$	−1.20129	−	0.746258i	−0.849441	−	0.527684i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$3$	0.984808	−	0.173648i	0.568579	−	0.100256i
$4$	0.886199	+	1.79294i	0.443099	+	0.896472i
$5$	−1.13283	−	1.35006i	−0.506618	−	0.603763i	0.450745	−	0.892653i	$-0.351158\pi$
$5$	−1.13283	−	1.35006i	−0.506618	−	0.603763i	−0.957362	+	0.288890i	$0.906714\pi$
$6$	−1.31263	−	0.526318i	−0.535878	−	0.214869i
$7$	1.93035	−	3.34346i	0.729604	−	1.26371i	−0.227447	−	0.973790i	$-0.573038\pi$
$7$	1.93035	−	3.34346i	0.729604	−	1.26371i	0.957051	−	0.289920i	$-0.0936289\pi$
$8$	0.273416	−	2.81518i	0.0966672	−	0.995317i
$9$	0.939693	−	0.342020i	0.313231	−	0.114007i
$10$	0.353370	+	2.46719i	0.111746	+	0.780195i
$11$	−1.21469	+	0.701299i	−0.366241	+	0.211450i	−0.671815	−	0.740719i	$-0.734485\pi$
$11$	−1.21469	+	0.701299i	−0.366241	+	0.211450i	0.305574	+	0.952168i	$0.401152\pi$
$12$	1.18408	+	1.61182i	0.341814	+	0.465292i
$13$	3.21190	+	0.566345i	0.890821	+	0.157076i	0.600283	−	0.799788i	$-0.295055\pi$
$13$	3.21190	+	0.566345i	0.890821	+	0.157076i	0.290538	+	0.956863i	$0.406166\pi$
$14$	−4.81400	+	2.57593i	−1.28660	+	0.688448i
$15$	−1.35006	−	1.13283i	−0.348583	−	0.292496i
$16$	−2.42930	+	3.17781i	−0.607326	+	0.794453i
$17$	−2.28751	−	0.832585i	−0.554803	−	0.201932i	0.0493764	−	0.998780i	$-0.484277\pi$
$17$	−2.28751	−	0.832585i	−0.554803	−	0.201932i	−0.604179	+	0.796849i	$0.706499\pi$
$18$	−1.38408	−	0.290387i	−0.326231	−	0.0684449i
$19$	−4.33543	+	0.451693i	−0.994616	+	0.103626i
$19$	−4.33543	+	0.451693i	−0.994616	+	0.103626i
$20$	1.41666	−	3.22752i	0.316775	−	0.721696i
$21$	1.32044	−	3.62787i	0.288143	−	0.791667i
$22$	1.98254	+	0.0640044i	0.422679	+	0.0136458i
$23$	0.514611	+	0.431810i	0.107304	+	0.0900386i	0.694861	−	0.719144i	$-0.255466\pi$
$23$	0.514611	+	0.431810i	0.107304	+	0.0900386i	−0.587557	+	0.809183i	$0.699910\pi$
$24$	−0.219589	−	2.81989i	−0.0448233	−	0.575608i
$25$	0.328897	−	1.86527i	0.0657794	−	0.373054i
$26$	−3.43579	−	3.07725i	−0.673814	−	0.603499i
$27$	0.866025	−	0.500000i	0.166667	−	0.0962250i
$28$	7.70532	+	0.498037i	1.45617	+	0.0941201i
$29$	−1.74380	−	4.79106i	−0.323816	−	0.889677i	−0.989640	−	0.143569i	$-0.954142\pi$
$29$	−1.74380	−	4.79106i	−0.323816	−	0.889677i	0.665824	−	0.746109i	$-0.268080\pi$
$30$	0.776426	+	2.36835i	0.141755	+	0.432399i
$31$	4.57031	−	7.91602i	0.820853	−	1.42176i	−0.0841953	−	0.996449i	$-0.526832\pi$
$31$	4.57031	−	7.91602i	0.820853	−	1.42176i	0.905048	−	0.425309i	$-0.139835\pi$
$32$	5.28977	−	2.00459i	0.935107	−	0.354365i
$33$	−1.07445	+	0.901573i	−0.187038	+	0.156944i
$34$	2.12664	+	2.70725i	0.364716	+	0.464289i
$35$	−6.70063	+	1.18150i	−1.13261	+	0.199710i
$36$	1.44598	+	1.38172i	0.240996	+	0.230287i
$37$			2.64726i			0.435206i	0.976037	+	0.217603i	$0.0698238\pi$
$37$			2.64726i			0.435206i	−0.976037	+	0.217603i	$0.930176\pi$
$38$	5.54519	+	2.69273i	0.899549	+	0.436819i
$39$	3.26145			0.522250
$40$	−4.11039	+	2.82000i	−0.649909	+	0.445881i
$41$	−0.352348	−	1.99826i	−0.0550275	−	0.312076i	0.944854	−	0.327493i	$-0.106204\pi$
$41$	−0.352348	−	1.99826i	−0.0550275	−	0.312076i	−0.999881	+	0.0154165i	$0.995093\pi$
$42$	−4.29356	+	3.37274i	−0.662510	+	0.520425i
$43$	−0.671130	−	0.799821i	−0.102346	−	0.121972i	0.712440	−	0.701733i	$-0.247590\pi$
$43$	−0.671130	−	0.799821i	−0.102346	−	0.121972i	−0.814786	+	0.579762i	$0.803146\pi$
$44$	−2.33384	−	1.55637i	−0.351840	−	0.234632i
$45$	−1.52626	−	0.881186i	−0.227521	−	0.131360i
$46$	−0.295956	−	0.902761i	−0.0436363	−	0.133105i
$47$	7.57838	−	2.75831i	1.10542	−	0.402340i	0.276109	−	0.961126i	$-0.410955\pi$
$47$	7.57838	−	2.75831i	1.10542	−	0.402340i	0.829312	+	0.558786i	$0.188733\pi$
$48$	−1.84057	+	3.55138i	−0.265664	+	0.512597i
$49$	−3.95250	−	6.84594i	−0.564644	−	0.977991i
$50$	−1.78707	+	1.99529i	−0.252730	+	0.282176i
$51$	−2.39733	−	0.422715i	−0.335694	−	0.0591919i
$52$	1.83096	+	6.26066i	0.253908	+	0.868197i
$53$	−4.48652	+	5.34682i	−0.616270	+	0.734443i	−0.980424	−	0.196896i	$-0.936914\pi$
$53$	−4.48652	+	5.34682i	−0.616270	+	0.734443i	0.364154	+	0.931339i	$0.381358\pi$
$54$	−1.41348	−	0.0456327i	−0.192350	−	0.00620983i
$55$	2.32283	+	0.845440i	0.313210	+	0.113999i
$56$	−8.88467	−	6.34844i	−1.18726	−	0.848346i
$57$	−4.19113	+	1.19767i	−0.555129	+	0.158635i
$58$	−1.48055	+	7.05678i	−0.194406	+	0.926601i
$59$	1.49805	−	4.11585i	0.195029	−	0.535838i	−0.803175	−	0.595743i	$-0.796858\pi$
$59$	1.49805	−	4.11585i	0.195029	−	0.535838i	0.998204	+	0.0599050i	$0.0190798\pi$
$60$	0.834686	−	3.42449i	0.107758	−	0.442100i
$61$	−5.03333	+	5.99848i	−0.644451	+	0.768027i	−0.985066	−	0.172176i	$-0.944920\pi$
$61$	−5.03333	+	5.99848i	−0.644451	+	0.768027i	0.340615	+	0.940203i	$0.389365\pi$
$62$	−11.3977	+	6.09881i	−1.44750	+	0.774549i
$63$	0.670404	−	3.80205i	0.0844629	−	0.479013i
$64$	−7.85049	−	1.53943i	−0.981311	−	0.192429i
$65$	−2.87395	−	4.97782i	−0.356469	−	0.617423i
$66$	1.96354	−	0.281232i	0.241694	−	0.0346173i
$67$	−1.47156	−	4.04307i	−0.179779	−	0.493939i	0.816768	−	0.576966i	$-0.195764\pi$
$67$	−1.47156	−	4.04307i	−0.179779	−	0.493939i	−0.996547	+	0.0830267i	$0.973541\pi$
$68$	−0.534409	−	4.83921i	−0.0648066	−	0.586841i
$69$	0.581776	+	0.335888i	0.0700376	+	0.0404362i
$70$	8.93110	+	3.58107i	1.06747	+	0.428019i
$71$	7.23784	−	6.07327i	0.858974	−	0.720765i	−0.102773	−	0.994705i	$-0.532771\pi$
$71$	7.23784	−	6.07327i	0.858974	−	0.720765i	0.961747	+	0.273940i	$0.0883270\pi$
$72$	−0.705921	−	2.73892i	−0.0831936	−	0.322785i
$73$	2.81397	+	15.9588i	0.329350	+	1.86784i	0.477155	+	0.878819i	$0.341668\pi$
$73$	2.81397	+	15.9588i	0.329350	+	1.86784i	−0.147806	+	0.989016i	$0.547221\pi$
$74$	1.97553	−	3.18012i	0.229651	−	0.369682i
$75$		−	1.89404i		−	0.218705i
$76$	−4.65192	−	7.37290i	−0.533611	−	0.845730i
$77$			5.41501i			0.617098i
$78$	−3.91795	−	2.43388i	−0.443621	−	0.275583i
$79$	1.39093	+	7.88833i	0.156491	+	0.887507i	0.957410	+	0.288733i	$0.0932340\pi$
$79$	1.39093	+	7.88833i	0.156491	+	0.887507i	−0.800918	+	0.598774i	$0.795655\pi$
$80$	7.04221	−	0.320231i	0.787343	−	0.0358029i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	−1.06795	+	2.66344i	−0.117935	+	0.294127i
$83$	2.76991	+	1.59921i	0.304037	+	0.175536i	0.644255	−	0.764811i	$-0.277168\pi$
$83$	2.76991	+	1.59921i	0.304037	+	0.175536i	−0.340218	+	0.940347i	$0.610501\pi$
$84$	7.67474	−	0.847545i	0.837383	−	0.0924747i
$85$	1.46733	+	4.03144i	0.159154	+	0.437272i
$86$	0.209349	+	1.46165i	0.0225747	+	0.157614i
$87$	−2.54927	−	4.41546i	−0.273310	−	0.473387i
$88$	1.64217	+	3.61131i	0.175056	+	0.384966i
$89$	−2.19823	+	12.4668i	−0.233012	+	1.32148i	0.613749	+	0.789501i	$0.289661\pi$
$89$	−2.19823	+	12.4668i	−0.233012	+	1.32148i	−0.846761	+	0.531974i	$0.821450\pi$
$90$	1.17589	+	2.19754i	0.123950	+	0.231641i
$91$	8.09365	−	9.64564i	0.848445	−	1.01114i
$92$	−0.318164	+	1.30534i	−0.0331708	+	0.136091i
$93$	3.12628	−	8.58938i	0.324180	−	0.890677i
$94$	−11.1623	−	2.34190i	−1.15130	−	0.241549i
$95$	5.52112	+	5.34138i	0.566455	+	0.548014i
$96$	4.86131	−	2.89269i	0.496155	−	0.295234i
$97$	0.928978	+	0.338120i	0.0943234	+	0.0343309i	0.388751	−	0.921343i	$-0.372907\pi$
$97$	0.928978	+	0.338120i	0.0943234	+	0.0343309i	−0.294427	+	0.955674i	$0.595129\pi$
$98$	−0.360727	+	11.1736i	−0.0364389	+	1.12870i
$99$	−0.901573	+	1.07445i	−0.0906115	+	0.107987i
$100$	3.63579	−	1.06330i	0.363579	−	0.106330i
$101$	19.3568	+	3.41312i	1.92607	+	0.339618i	0.999347	−	0.0361225i	$-0.0115007\pi$
$101$	19.3568	+	3.41312i	1.92607	+	0.339618i	0.926725	+	0.375741i	$0.122612\pi$
$102$	2.56444	+	2.29683i	0.253918	+	0.227420i
$103$	−2.23397	−	3.86935i	−0.220120	−	0.381259i	0.734724	−	0.678366i	$-0.237312\pi$
$103$	−2.23397	−	3.86935i	−0.220120	−	0.381259i	−0.954844	+	0.297107i	$0.903978\pi$
$104$	2.47255	−	8.88724i	0.242453	−	0.871465i
$105$	−6.39366	+	2.32710i	−0.623958	+	0.227102i
$106$	9.37972	−	3.07499i	0.911039	−	0.298670i
$107$	10.4435	+	6.02955i	1.00961	+	0.582898i	0.911077	−	0.412236i	$-0.135252\pi$
$107$	10.4435	+	6.02955i	1.00961	+	0.582898i	0.0985322	+	0.995134i	$0.468585\pi$
$108$	1.66394	+	1.10964i	0.160113	+	0.106775i
$109$	−3.55198	−	4.23308i	−0.340218	−	0.405456i	0.568624	−	0.822598i	$-0.307476\pi$
$109$	−3.55198	−	4.23308i	−0.340218	−	0.405456i	−0.908841	+	0.417142i	$0.863032\pi$
$110$	−2.15947	−	2.74905i	−0.205898	−	0.262111i
$111$	0.459691	+	2.60704i	0.0436319	+	0.247449i
$112$	5.93550	+	14.2566i	0.560852	+	1.34712i
$113$	−5.96126			−0.560788			−0.280394	−	0.959885i	$-0.590465\pi$
$113$	−5.96126			−0.560788			−0.280394	+	0.959885i	$0.590465\pi$
$114$	5.92854	+	1.68891i	0.555259	+	0.158181i
$115$		−	1.18392i		−	0.110401i
$116$	7.04475	−	7.37237i	0.654089	−	0.684508i
$117$	3.21190	−	0.566345i	0.296940	−	0.0523586i
$118$	−4.87108	+	3.82641i	−0.448419	+	0.352249i
$119$	−7.19941	+	6.04103i	−0.659969	+	0.553780i
$120$	−3.55825	+	3.49092i	−0.324823	+	0.318676i
$121$	−4.51636	+	7.82256i	−0.410578	+	0.711142i
$122$	10.5229	−	3.44977i	0.952699	−	0.312327i
$123$	−0.693990	−	1.90672i	−0.0625749	−	0.171923i
$124$	18.2432	+	1.17916i	1.63829	+	0.105891i
$125$	−10.5221	+	6.07494i	−0.941125	+	0.543359i
$126$	−3.64266	+	4.06707i	−0.324514	+	0.362324i
$127$	0.246787	−	1.39960i	0.0218988	−	0.124194i	−0.971899	−	0.235400i	$-0.924360\pi$
$127$	0.246787	−	1.39960i	0.0218988	−	0.124194i	0.993797	+	0.111206i	$0.0354712\pi$
$128$	8.28190	+	7.70779i	0.732024	+	0.681279i
$129$	−0.799821	−	0.671130i	−0.0704203	−	0.0590897i
$130$	−0.262292	+	8.12451i	−0.0230045	+	0.712567i
$131$	−5.95156	+	16.3518i	−0.519990	+	1.42866i	0.350541	+	0.936547i	$0.385998\pi$
$131$	−5.95156	+	16.3518i	−0.519990	+	1.42866i	−0.870531	+	0.492113i	$0.836225\pi$
$132$	−2.56865	−	1.12746i	−0.223572	−	0.0981329i
$133$	−6.85868	+	15.3673i	−0.594723	+	1.33251i
$134$	−1.24940	+	5.95506i	−0.107932	+	0.514439i
$135$	−1.65609	−	0.602767i	−0.142533	−	0.0518779i
$136$	−2.96932	+	6.21211i	−0.254617	+	0.532684i
$137$	10.1005	+	8.47531i	0.862942	+	0.724095i	0.962600	−	0.270927i	$-0.0873302\pi$
$137$	10.1005	+	8.47531i	0.862942	+	0.724095i	−0.0996574	+	0.995022i	$0.531775\pi$
$138$	−0.448223	−	0.837654i	−0.0381552	−	0.0713059i
$139$	21.0698	+	3.71518i	1.78712	+	0.315118i	0.966560	−	0.256442i	$-0.0825502\pi$
$139$	21.0698	+	3.71518i	1.78712	+	0.315118i	0.820561	+	0.571559i	$0.193661\pi$
$140$	−8.05645	−	10.9668i	−0.680895	−	0.926864i
$141$	6.98428	−	4.03237i	0.588182	−	0.339587i
$142$	−13.2270	+	1.89447i	−1.10998	+	0.158980i
$143$	−4.29863	+	1.56457i	−0.359469	+	0.130836i
$144$	−1.19592	+	3.81704i	−0.0996602	+	0.318086i
$145$	−4.49276	+	7.78169i	−0.373104	+	0.646234i
$146$	8.52898	−	21.2711i	0.705863	−	1.76041i
$147$	−5.08124	−	6.05559i	−0.419094	−	0.499457i
$148$	−4.74638	+	2.34600i	−0.390150	+	0.192840i
$149$	8.66943	−	1.52866i	0.710228	−	0.125232i	0.193148	−	0.981170i	$-0.438130\pi$
$149$	8.66943	−	1.52866i	0.710228	−	0.125232i	0.517080	+	0.855937i	$0.327019\pi$
$150$	−1.41344	+	2.27530i	−0.115407	+	0.185777i
$151$	2.90595			0.236483			0.118241	−	0.992985i	$-0.462274\pi$
$151$	2.90595			0.236483			0.118241	+	0.992985i	$0.462274\pi$
$152$	0.0862212	+	12.3285i	0.00699346	+	0.999976i
$153$	−2.43432			−0.196803
$154$	4.04099	−	6.50500i	0.325633	−	0.524188i
$155$	−15.8645	+	2.79733i	−1.27426	+	0.224687i
$156$	2.89029	+	5.84760i	0.231409	+	0.468183i
$157$	−3.35859	−	4.00262i	−0.268045	−	0.319444i	0.615186	−	0.788382i	$-0.289081\pi$
$157$	−3.35859	−	4.00262i	−0.268045	−	0.319444i	−0.883231	+	0.468939i	$0.844637\pi$
$158$	4.21582	−	10.5142i	0.335393	−	0.836462i
$159$	−3.48989	+	6.04467i	−0.276766	+	0.479373i
$160$	−8.69872	−	4.87062i	−0.687694	−	0.385056i
$161$	2.43712	−	0.887039i	0.192072	−	0.0699085i
$162$	−1.39993	+	0.200508i	−0.109989	+	0.0157534i
$163$	19.7570	−	11.4067i	1.54749	−	0.893441i	0.549153	−	0.835722i	$-0.314951\pi$
$163$	19.7570	−	11.4067i	1.54749	−	0.893441i	0.998333	−	0.0577189i	$-0.0183827\pi$
$164$	3.27053	−	2.40260i	0.255385	−	0.187611i
$165$	2.43435	+	0.429241i	0.189514	+	0.0334164i
$166$	−2.13405	−	3.98818i	−0.165634	−	0.309543i
$167$	−14.2725	−	11.9761i	−1.10444	−	0.926738i	−0.106727	−	0.994288i	$-0.534037\pi$
$167$	−14.2725	−	11.9761i	−1.10444	−	0.926738i	−0.997716	+	0.0675507i	$0.978482\pi$
$168$	−9.85209	−	4.70919i	−0.760105	−	0.363322i
$169$	−2.22043	−	0.808172i	−0.170803	−	0.0621671i
$170$	1.24581	−	5.93794i	0.0955494	−	0.455419i
$171$	−3.91949	+	1.90726i	−0.299731	+	0.145852i
$172$	0.839281	−	1.91210i	0.0639946	−	0.145796i
$173$	1.05276	−	2.89242i	0.0800395	−	0.219907i	−0.893218	−	0.449624i	$-0.851558\pi$
$173$	1.05276	−	2.89242i	0.0800395	−	0.219907i	0.973257	+	0.229717i	$0.0737802\pi$
$174$	−0.232660	+	7.20667i	−0.0176379	+	0.546336i
$175$	−5.60157	−	4.70028i	−0.423439	−	0.355307i
$176$	0.722243	−	5.56371i	0.0544411	−	0.419380i
$177$	0.760579	−	4.31346i	0.0571686	−	0.324219i
$178$	11.9441	−	13.3358i	0.895251	−	0.999559i
$179$	−6.78593	+	3.91786i	−0.507204	+	0.292834i	−0.731684	−	0.681644i	$-0.761265\pi$
$179$	−6.78593	+	3.91786i	−0.507204	+	0.292834i	0.224480	+	0.974479i	$0.427932\pi$
$180$	0.227349	−	3.51741i	0.0169456	−	0.262172i
$181$	−8.68260	−	23.8552i	−0.645372	−	1.77315i	−0.634151	−	0.773209i	$-0.718650\pi$
$181$	−8.68260	−	23.8552i	−0.645372	−	1.77315i	−0.0112214	−	0.999937i	$-0.503572\pi$
$182$	−16.9210	+	5.54727i	−1.25427	+	0.411191i
$183$	−3.91523	+	6.78138i	−0.289422	+	0.501294i
$184$	1.35633	−	1.33066i	0.0999897	−	0.0980975i
$185$	3.57394	−	2.99889i	0.262762	−	0.220483i
$186$	−10.1655	+	7.98533i	−0.745368	+	0.585513i
$187$	3.36250	−	0.592899i	0.245890	−	0.0433571i
$188$	11.6614	+	11.1432i	0.850499	+	0.812703i
$189$		−	3.86070i		−	0.280825i
$190$	−2.64643	−	10.5367i	−0.191992	−	0.764415i
$191$	26.0679			1.88621			0.943105	−	0.332496i	$-0.107891\pi$
$191$	26.0679			1.88621			0.943105	+	0.332496i	$0.107891\pi$
$192$	−7.99854	−	0.152822i	−0.577245	−	0.0110290i
$193$	2.82631	+	16.0288i	0.203442	+	1.15378i	0.899872	+	0.436154i	$0.143660\pi$
$193$	2.82631	+	16.0288i	0.203442	+	1.15378i	−0.696430	+	0.717625i	$0.745229\pi$
$194$	−0.863648	−	1.09944i	−0.0620063	−	0.0789350i
$195$	−3.69467	−	4.40314i	−0.264581	−	0.315315i
$196$	8.77169	−	13.1535i	0.626549	−	0.939535i
$197$	−1.59880	−	0.923066i	−0.113910	−	0.0657658i	0.441963	−	0.897033i	$-0.354282\pi$
$197$	−1.59880	−	0.923066i	−0.113910	−	0.0657658i	−0.555872	+	0.831268i	$0.687616\pi$
$198$	1.88487	−	0.617924i	0.133952	−	0.0439140i
$199$	−11.2541	+	4.09616i	−0.797782	+	0.290369i	−0.708567	−	0.705643i	$-0.750658\pi$
$199$	−11.2541	+	4.09616i	−0.797782	+	0.290369i	−0.0892151	+	0.996012i	$0.528436\pi$
$200$	−5.16114	−	1.43590i	−0.364948	−	0.101533i
$201$	−2.15127	−	3.72611i	−0.151739	−	0.262820i
$202$	−20.7061	−	18.5453i	−1.45687	−	1.30484i
$203$	−19.3849	−	3.41808i	−1.36055	−	0.239902i
$204$	−1.36661	−	4.67290i	−0.0956819	−	0.327168i
$205$	−2.29862	+	2.73938i	−0.160542	+	0.191327i
$206$	−0.203884	+	6.31534i	−0.0142053	+	0.440010i
$207$	0.631264	+	0.229761i	0.0438759	+	0.0159695i
$208$	−9.60242	+	8.83100i	−0.665808	+	0.612320i
$209$	4.94941	−	3.58910i	0.342358	−	0.248263i
$210$	9.41727	+	1.97579i	0.649853	+	0.136343i
$211$	7.05812	−	19.3920i	0.485901	−	1.33500i	−0.418461	−	0.908235i	$-0.637430\pi$
$211$	7.05812	−	19.3920i	0.485901	−	1.33500i	0.904362	−	0.426767i	$-0.140348\pi$
$212$	−13.5625	−	3.30573i	−0.931477	−	0.227038i
$213$	6.07327	−	7.23784i	0.416134	−	0.495929i
$214$	−8.04606	−	15.0368i	−0.550018	−	1.02789i
$215$	−0.319527	+	1.81213i	−0.0217915	+	0.123586i
$216$	−1.17081	−	2.57473i	−0.0796632	−	0.175188i
$217$	−17.6446	−	30.5614i	−1.19779	−	2.07464i
$218$	1.10799	+	7.73585i	0.0750424	+	0.523938i
$219$	5.54243	+	15.2277i	0.374523	+	1.02899i
$220$	0.542660	+	4.91393i	0.0365861	+	0.331297i
$221$	−6.87573	−	3.96970i	−0.462511	−	0.267031i
$222$	1.39330	−	3.47486i	0.0935121	−	0.233217i
$223$	14.7866	−	12.4075i	0.990187	−	0.830865i	0.00459186	−	0.999989i	$-0.498538\pi$
$223$	14.7866	−	12.4075i	0.990187	−	0.830865i	0.985595	+	0.169124i	$0.0540939\pi$
$224$	3.50882	−	21.5557i	0.234443	−	1.44025i
$225$	−0.328897	−	1.86527i	−0.0219265	−	0.124351i
$226$	7.16121	+	4.44864i	0.476356	+	0.295919i
$227$			26.9510i			1.78880i	0.447268	+	0.894400i	$0.352397\pi$
$227$			26.9510i			1.78880i	−0.447268	+	0.894400i	$0.647603\pi$
$228$	−5.86153	−	6.45309i	−0.388190	−	0.427367i
$229$			18.6758i			1.23413i	0.786912	+	0.617065i	$0.211679\pi$
$229$			18.6758i			1.23413i	−0.786912	+	0.617065i	$0.788321\pi$
$230$	−0.883510	+	1.42223i	−0.0582569	+	0.0937793i
$231$	0.940307	+	5.33274i	0.0618676	+	0.350869i
$232$	−13.9645	+	3.59917i	−0.916813	+	0.236297i
$233$	−13.4543	+	11.2895i	−0.881421	+	0.739600i	−0.966471	−	0.256776i	$-0.917340\pi$
$233$	−13.4543	+	11.2895i	−0.881421	+	0.739600i	0.0850496	+	0.996377i	$0.472895\pi$
$234$	−4.28107	−	1.71656i	−0.279862	−	0.112215i
$235$	−12.3089	−	7.10655i	−0.802944	−	0.463580i
$236$	8.70706	−	0.961547i	0.566782	−	0.0625914i
$237$	2.73959	+	7.52696i	0.177955	+	0.488928i
$238$	13.1568	−	1.88441i	0.852826	−	0.122148i
$239$	9.69350	+	16.7896i	0.627020	+	1.08603i	0.988146	+	0.153514i	$0.0490590\pi$
$239$	9.69350	+	16.7896i	0.627020	+	1.08603i	−0.361126	+	0.932517i	$0.617608\pi$
$240$	6.87962	−	1.53823i	0.444078	−	0.0992925i
$241$	0.921602	−	5.22666i	0.0593656	−	0.336679i	−0.940631	−	0.339432i	$-0.889765\pi$
$241$	0.921602	−	5.22666i	0.0593656	−	0.336679i	0.999996	+	0.00275297i	$0.000876299\pi$
$242$	11.2631	−	6.02681i	0.724020	−	0.387418i
$243$	0.642788	−	0.766044i	0.0412348	−	0.0491418i
$244$	−15.2155	−	3.70863i	−0.974071	−	0.237420i
$245$	−4.76488	+	13.0914i	−0.304417	+	0.836379i
$246$	−0.589222	+	2.80842i	−0.0375674	+	0.179058i
$247$	−14.1808	−	1.00456i	−0.902303	−	0.0639183i
$248$	−21.0354	−	15.0306i	−1.33575	−	0.954446i
$249$	3.00553	+	1.09392i	0.190468	+	0.0693246i
$250$	17.1736	+	0.554432i	1.08615	+	0.0350653i
$251$	11.2252	−	13.3777i	0.708531	−	0.844394i	−0.284932	−	0.958548i	$-0.591971\pi$
$251$	11.2252	−	13.3777i	0.708531	−	0.844394i	0.993463	+	0.114153i	$0.0364155\pi$
$252$	7.41097	−	2.16737i	0.466847	−	0.136532i
$253$	−0.927918	−	0.163617i	−0.0583377	−	0.0102865i
$254$	−1.34092	+	1.49716i	−0.0841369	+	0.0939399i
$255$	2.14509	+	3.71540i	0.134331	+	0.232667i
$256$	−4.19698	−	15.4397i	−0.262311	−	0.964983i
$257$	−10.6490	+	3.87591i	−0.664264	+	0.241772i	−0.652076	−	0.758153i	$-0.726102\pi$
$257$	−10.6490	+	3.87591i	−0.664264	+	0.241772i	−0.0121879	+	0.999926i	$0.503880\pi$
$258$	0.459982	+	1.40309i	0.0286372	+	0.0873529i
$259$	8.85101	+	5.11013i	0.549975	+	0.317528i
$260$	6.37807	−	9.56417i	0.395551	−	0.593144i
$261$	−3.27728	−	3.90571i	−0.202858	−	0.241757i
$262$	19.3522	−	15.2018i	1.19558	−	0.939172i
$263$	−0.963319	−	5.46325i	−0.0594008	−	0.336879i	0.940596	−	0.339529i	$-0.110268\pi$
$263$	−0.963319	−	5.46325i	−0.0594008	−	0.336879i	−0.999996	+	0.00265004i	$0.999156\pi$
$264$	2.24432	+	3.27128i	0.138128	+	0.201334i
$265$	12.3010			0.755643
$266$	19.7072	−	13.3422i	1.20833	−	0.818065i
$267$			12.6591i			0.774724i
$268$	5.94491	−	6.22138i	0.363143	−	0.380031i
$269$	−11.6576	+	2.05554i	−0.710774	+	0.125329i	−0.517334	−	0.855783i	$-0.673076\pi$
$269$	−11.6576	+	2.05554i	−0.710774	+	0.125329i	−0.193440	+	0.981112i	$0.561964\pi$
$270$	1.53962	+	1.95997i	0.0936986	+	0.119280i
$271$	−21.0053	+	17.6255i	−1.27598	+	1.07067i	−0.282193	+	0.959358i	$0.591062\pi$
$271$	−21.0053	+	17.6255i	−1.27598	+	1.07067i	−0.993785	+	0.111316i	$0.964494\pi$
$272$	8.20285	−	5.24667i	0.497371	−	0.318126i
$273$	6.29574	−	10.9045i	0.381036	−	0.659973i
$274$	−5.80885	−	17.7189i	−0.350925	−	1.07044i
$275$	0.908604	+	2.49637i	0.0547909	+	0.150537i
$276$	−0.0866603	+	1.34076i	−0.00521634	+	0.0807040i
$277$	−10.7024	+	6.17903i	−0.643044	+	0.371262i	−0.785786	−	0.618498i	$-0.787741\pi$
$277$	−10.7024	+	6.17903i	−0.643044	+	0.371262i	0.142742	+	0.989760i	$0.454408\pi$
$278$	−22.5385	−	20.1865i	−1.35177	−	1.21071i
$279$	1.58725	−	9.00176i	0.0950264	−	0.538921i
$280$	1.49408	+	19.1865i	0.0892883	+	1.14661i
$281$	4.36372	+	3.66159i	0.260318	+	0.218432i	0.763600	−	0.645690i	$-0.223430\pi$
$281$	4.36372	+	3.66159i	0.260318	+	0.218432i	−0.503282	+	0.864122i	$0.667874\pi$
$282$	−11.3993	−	0.368016i	−0.678821	−	0.0219151i
$283$	−2.98596	+	8.20386i	−0.177497	+	0.487669i	−0.996254	−	0.0864706i	$-0.972441\pi$
$283$	−2.98596	+	8.20386i	−0.177497	+	0.487669i	0.818757	+	0.574140i	$0.194663\pi$
$284$	17.3032	+	7.59493i	1.02676	+	0.450676i
$285$	6.36477	+	4.30150i	0.377016	+	0.254799i
$286$	6.33148	+	1.32838i	0.374388	+	0.0785486i
$287$	−7.36128	−	2.67929i	−0.434522	−	0.158153i
$288$	4.28514	−	3.69290i	0.252504	−	0.217607i
$289$	−8.48325	−	7.11830i	−0.499015	−	0.418723i
$290$	11.2043	−	5.99532i	0.657937	−	0.352057i
$291$	0.973579	+	0.171668i	0.0570722	+	0.0100634i
$292$	−26.1195	+	19.1880i	−1.52853	+	1.12289i
$293$	27.1676	−	15.6852i	1.58715	−	0.916341i	0.593374	−	0.804927i	$-0.297795\pi$
$293$	27.1676	−	15.6852i	1.58715	−	0.916341i	0.993774	−	0.111414i	$-0.0355379\pi$
$294$	1.58502	+	11.0664i	0.0924402	+	0.645408i
$295$	−7.25366	+	2.64012i	−0.422325	+	0.153714i
$296$	7.45250	+	0.723803i	0.433168	+	0.0420702i
$297$	−0.701299	+	1.21469i	−0.0406935	+	0.0704832i
$298$	−11.5553	−	4.63327i	−0.669379	−	0.268398i
$299$	1.40833	+	1.67838i	0.0814456	+	0.0970631i
$300$	3.39591	−	1.67850i	0.196063	−	0.0969082i
$301$	−3.96969	+	0.699963i	−0.228809	+	0.0403452i
$302$	−3.49089	−	2.16858i	−0.200878	−	0.124788i
$303$	19.6554			1.12917
$304$	9.09668	−	14.8745i	0.521730	−	0.853110i
$305$	13.8002			0.790197
$306$	2.92432	+	1.81663i	0.167172	+	0.103850i
$307$	−16.6392	+	2.93393i	−0.949646	+	0.167448i	−0.626955	−	0.779056i	$-0.715699\pi$
$307$	−16.6392	+	2.93393i	−0.949646	+	0.167448i	−0.322692	+	0.946504i	$0.604588\pi$
$308$	−9.70882	+	4.79878i	−0.553211	+	0.273436i
$309$	−2.87194	−	3.42264i	−0.163379	−	0.194707i
$310$	21.1454	+	8.47857i	1.20098	+	0.481550i
$311$	−7.27595	+	12.6023i	−0.412581	+	0.714611i	−0.995171	−	0.0981548i	$-0.968706\pi$
$311$	−7.27595	+	12.6023i	−0.412581	+	0.714611i	0.582590	+	0.812766i	$0.302039\pi$
$312$	0.891734	−	9.18157i	0.0504845	−	0.519804i
$313$	14.5605	−	5.29959i	0.823009	−	0.299551i	0.104022	−	0.994575i	$-0.466829\pi$
$313$	14.5605	−	5.29959i	0.823009	−	0.299551i	0.718986	+	0.695024i	$0.244606\pi$
$314$	1.04766	+	7.31468i	0.0591231	+	0.412791i
$315$	−5.89243	+	3.40200i	−0.332001	+	0.191681i
$316$	−12.9107	+	9.48448i	−0.726284	+	0.533544i
$317$	12.7965	+	2.25636i	0.718721	+	0.126730i	0.521035	−	0.853535i	$-0.325546\pi$
$317$	12.7965	+	2.25636i	0.718721	+	0.126730i	0.197686	+	0.980265i	$0.436657\pi$
$318$	8.70325	−	4.65705i	0.488054	−	0.261154i
$319$	5.47814	+	4.59670i	0.306717	+	0.257366i
$320$	6.81496	+	12.3425i	0.380968	+	0.689967i
$321$	11.3318	+	4.12445i	0.632482	+	0.230205i
$322$	−3.58965	−	0.753128i	−0.200043	−	0.0419702i
$323$	10.2934	+	2.57636i	0.572741	+	0.143353i
$324$	1.83135	+	0.803838i	0.101742	+	0.0446577i
$325$	2.11277	−	5.80479i	0.117195	−	0.321992i
$326$	−32.2462	−	1.04104i	−1.78595	−	0.0576577i
$327$	−4.23308	−	3.55198i	−0.234090	−	0.196425i
$328$	−5.72181	+	0.445565i	−0.315934	+	0.0246022i
$329$	5.40664	−	30.6626i	0.298078	−	1.69048i
$330$	−2.60403	−	2.33229i	−0.143347	−	0.128389i
$331$	3.02318	−	1.74543i	0.166169	−	0.0959376i	−0.414609	−	0.910000i	$-0.636082\pi$
$331$	3.02318	−	1.74543i	0.166169	−	0.0959376i	0.580778	+	0.814062i	$0.302748\pi$
$332$	−0.412601	+	6.38351i	−0.0226444	+	0.350341i
$333$	0.905415	+	2.48761i	0.0496164	+	0.136320i
$334$	8.20823	+	25.0378i	0.449134	+	1.37001i
$335$	−3.79134	+	6.56680i	−0.207143	+	0.358782i
$336$	8.32095	+	13.0093i	0.453945	+	0.709716i
$337$	−13.3065	+	11.1655i	−0.724849	+	0.608221i	−0.928722	−	0.370777i	$-0.879092\pi$
$337$	−13.3065	+	11.1655i	−0.724849	+	0.608221i	0.203873	+	0.978997i	$0.434647\pi$
$338$	2.06428	+	2.62787i	0.112282	+	0.142937i
$339$	−5.87070	+	1.03516i	−0.318852	+	0.0562223i
$340$	−5.92782	+	6.20350i	−0.321481	+	0.336432i
$341$			12.8206i			0.694276i
$342$	6.13175	+	0.633774i	0.331567	+	0.0342706i
$343$	−3.49397			−0.188657
$344$	−2.43514	+	1.67067i	−0.131294	+	0.0900763i
$345$	−0.205586	−	1.16593i	−0.0110684	−	0.0627718i
$346$	−3.42316	+	2.68901i	−0.184030	+	0.144562i
$347$	−19.1214	−	22.7880i	−1.02649	−	1.22332i	−0.974433	−	0.224678i	$-0.927867\pi$
$347$	−19.1214	−	22.7880i	−1.02649	−	1.22332i	−0.0520561	−	0.998644i	$-0.516577\pi$
$348$	5.65752	−	8.48368i	0.303275	−	0.454773i
$349$	1.98182	+	1.14420i	0.106084	+	0.0612477i	0.552103	−	0.833776i	$-0.313825\pi$
$349$	1.98182	+	1.14420i	0.106084	+	0.0612477i	−0.446019	+	0.895023i	$0.647159\pi$
$350$	3.22150	+	9.82661i	0.172196	+	0.525255i
$351$	3.06476	−	1.11548i	0.163585	−	0.0595400i
$352$	−5.01958	+	6.14465i	−0.267545	+	0.327511i
$353$	13.1165	+	22.7185i	0.698122	+	1.20918i	0.969117	+	0.246602i	$0.0793142\pi$
$353$	13.1165	+	22.7185i	0.698122	+	1.20918i	−0.270994	+	0.962581i	$0.587352\pi$
$354$	−4.13263	+	4.61413i	−0.219647	+	0.245238i
$355$	−16.3985	−	2.89150i	−0.870342	−	0.153465i
$356$	−24.3003	+	7.10674i	−1.28791	+	0.376656i
$357$	−6.04103	+	7.19941i	−0.319725	+	0.381033i
$358$	11.0756	+	0.357565i	0.585364	+	0.0188979i
$359$	−21.9718	−	7.99708i	−1.15963	−	0.422070i	−0.310663	−	0.950520i	$-0.600551\pi$
$359$	−21.9718	−	7.99708i	−1.15963	−	0.422070i	−0.848964	+	0.528450i	$0.822773\pi$
$360$	−2.89800	+	4.05577i	−0.152738	+	0.213758i
$361$	18.5919	−	3.91657i	0.978523	−	0.206135i
$362$	−7.37183	+	35.1365i	−0.387455	+	1.84674i
$363$	−3.08937	+	8.48798i	−0.162150	+	0.445503i
$364$	24.4667	+	5.96352i	1.28240	+	0.312573i
$365$	18.3575	−	21.8776i	0.960876	−	1.14513i
$366$	9.76399	−	5.22464i	0.510372	−	0.273096i
$367$	−3.07403	+	17.4337i	−0.160463	+	0.910030i	0.793157	+	0.609017i	$0.208436\pi$
$367$	−3.07403	+	17.4337i	−0.160463	+	0.910030i	−0.953620	+	0.301013i	$0.902675\pi$
$368$	−2.62236	+	0.586340i	−0.136700	+	0.0305651i
$369$	−1.01454	−	1.75724i	−0.0528151	−	0.0914784i
$370$	−6.53129	+	0.935462i	−0.339546	+	0.0486323i
$371$	9.21636	+	25.3218i	0.478490	+	1.31464i
$372$	18.1708	−	2.00665i	0.942112	−	0.104040i
$373$	−6.65317	−	3.84121i	−0.344488	−	0.198890i	0.317767	−	0.948169i	$-0.397067\pi$
$373$	−6.65317	−	3.84121i	−0.344488	−	0.198890i	−0.662255	+	0.749279i	$0.730400\pi$
$374$	−4.48179	−	1.79704i	−0.231748	−	0.0929230i
$375$	−9.30734	+	7.80979i	−0.480629	+	0.403296i
$376$	−5.69308	−	22.0887i	−0.293598	−	1.13914i
$377$	−2.88753	−	16.3760i	−0.148715	−	0.843407i
$378$	−2.88108	+	4.63782i	−0.148187	+	0.238544i
$379$		−	34.1087i		−	1.75204i	−0.482271	−	0.876022i	$-0.660188\pi$
$379$		−	34.1087i		−	1.75204i	0.482271	−	0.876022i	$-0.339812\pi$
$380$	−4.68399	+	14.6326i	−0.240284	+	0.750637i
$381$		−	1.42119i		−	0.0728096i
$382$	−31.3152	−	19.4534i	−1.60222	−	0.995322i
$383$	−0.676385	−	3.83597i	−0.0345617	−	0.196009i	0.962638	−	0.270791i	$-0.0872851\pi$
$383$	−0.676385	−	3.83597i	−0.0345617	−	0.196009i	−0.997200	+	0.0747817i	$0.976174\pi$
$384$	9.49453	+	6.15256i	0.484516	+	0.313971i
$385$	7.31057	−	6.13429i	0.372581	−	0.312633i
$386$	8.56640	−	21.3644i	0.436018	−	1.08742i
$387$	−0.904211	−	0.522046i	−0.0459636	−	0.0265371i
$388$	0.217028	+	1.96525i	0.0110179	+	0.0997703i
$389$	−4.25975	−	11.7036i	−0.215978	−	0.593395i	0.783635	−	0.621222i	$-0.213363\pi$
$389$	−4.25975	−	11.7036i	−0.215978	−	0.593395i	−0.999613	+	0.0278271i	$0.991141\pi$
$390$	1.15250	+	8.04663i	0.0583591	+	0.407457i
$391$	−0.817659	−	1.41623i	−0.0413508	−	0.0716217i
$392$	−20.3532	+	9.25523i	−1.02799	+	0.467459i
$393$	−3.02168	+	17.1368i	−0.152424	+	0.864438i
$394$	1.23178	+	2.30199i	0.0620560	+	0.115972i
$395$	9.07400	−	10.8140i	0.456563	−	0.544110i
$396$	−2.72541	−	0.664291i	−0.136957	−	0.0333819i
$397$	−7.65863	+	21.0419i	−0.384376	+	1.05606i	0.585118	+	0.810948i	$0.301048\pi$
$397$	−7.65863	+	21.0419i	−0.384376	+	1.05606i	−0.969494	+	0.245116i	$0.921174\pi$
$398$	16.5762	+	3.47778i	0.830892	+	0.174326i
$399$	−4.08598	+	16.3248i	−0.204555	+	0.817264i
$400$	5.12848	+	5.57647i	0.256424	+	0.278824i
$401$	7.17884	+	2.61288i	0.358494	+	0.130481i	0.514987	−	0.857198i	$-0.327797\pi$
$401$	7.17884	+	2.61288i	0.358494	+	0.130481i	−0.156493	+	0.987679i	$0.550019\pi$
$402$	−0.196337	+	6.08155i	−0.00979239	+	0.303320i
$403$	19.1626	−	22.8371i	0.954557	−	1.13760i
$404$	11.0344	+	37.7304i	0.548983	+	1.87716i
$405$	−1.73560	−	0.306033i	−0.0862426	−	0.0152069i
$406$	20.7361	+	18.5722i	1.02912	+	0.921724i
$407$	−1.85652	−	3.21558i	−0.0920242	−	0.159391i
$408$	−1.84549	+	6.63335i	−0.0913653	+	0.328400i
$409$	31.0896	−	11.3157i	1.53728	−	0.559524i	0.571889	−	0.820331i	$-0.306211\pi$
$409$	31.0896	−	11.3157i	1.53728	−	0.559524i	0.965391	+	0.260807i	$0.0839885\pi$
$410$	4.80559	−	1.57544i	0.237331	−	0.0778053i
$411$	11.4188	+	6.59262i	0.563246	+	0.325190i
$412$	4.95779	−	7.43441i	0.244253	−	0.366267i
$413$	−10.8694	−	12.9537i	−0.534851	−	0.637410i
$414$	−0.586870	−	0.747095i	−0.0288431	−	0.0367177i
$415$	−0.978820	−	5.55117i	−0.0480484	−	0.272496i
$416$	18.1255	−	3.44272i	0.888676	−	0.168793i
$417$	21.3949			1.04771
$418$	−8.62408	+	0.618014i	−0.421817	+	0.0302280i
$419$		−	7.11964i		−	0.347817i	−0.984762	−	0.173909i	$-0.944360\pi$
$419$		−	7.11964i		−	0.347817i	0.984762	−	0.173909i	$-0.0556397\pi$
$420$	−9.83842	−	9.40121i	−0.480066	−	0.458732i
$421$	26.8856	−	4.74065i	1.31032	−	0.231045i	0.525515	−	0.850784i	$-0.323873\pi$
$421$	26.8856	−	4.74065i	1.31032	−	0.231045i	0.784808	+	0.619739i	$0.212762\pi$
$422$	−22.9503	+	18.0283i	−1.11720	+	0.877603i
$423$	6.17796	−	5.18392i	0.300383	−	0.252051i
$424$	13.8256	+	14.0923i	0.671430	+	0.684381i
$425$	−2.30535	+	3.99298i	−0.111826	+	0.193688i
$426$	−12.6971	+	4.16253i	−0.615175	+	0.201675i
$427$	10.3396	+	28.4079i	0.500370	+	1.37476i
$428$	−1.55564	+	24.0680i	−0.0751948	+	1.16337i
$429$	−3.96164	+	2.28725i	−0.191270	+	0.110430i
$430$	1.73616	−	1.93844i	0.0837249	−	0.0934799i
$431$	0.552229	−	3.13185i	0.0266000	−	0.150856i	−0.968615	−	0.248566i	$-0.920041\pi$
$431$	0.552229	−	3.13185i	0.0266000	−	0.150856i	0.995215	+	0.0977102i	$0.0311518\pi$
$432$	−0.514932	+	3.96672i	−0.0247747	+	0.190849i
$433$	16.1971	+	13.5910i	0.778383	+	0.653141i	0.942841	−	0.333243i	$-0.108143\pi$
$433$	16.1971	+	13.5910i	0.778383	+	0.653141i	−0.164458	+	0.986384i	$0.552587\pi$
$434$	−1.61034	+	49.8805i	−0.0772990	+	2.39434i
$435$	−3.07323	+	8.44363i	−0.147350	+	0.404841i
$436$	4.44192	−	10.1199i	0.212730	−	0.484653i
$437$	−2.42611	−	1.63964i	−0.116056	−	0.0784344i
$438$	4.70572	−	22.4290i	0.224848	−	1.07170i
$439$	−29.5812	−	10.7667i	−1.41184	−	0.513866i	−0.480168	−	0.877177i	$-0.659424\pi$
$439$	−29.5812	−	10.7667i	−1.41184	−	0.513866i	−0.931668	+	0.363310i	$0.881646\pi$
$440$	3.01516	−	6.30802i	0.143742	−	0.300723i
$441$	−6.05559	−	5.08124i	−0.288361	−	0.241964i
$442$	5.29733	+	9.89983i	0.251968	+	0.470887i
$443$	1.41412	+	0.249347i	0.0671869	+	0.0118469i	0.207141	−	0.978311i	$-0.433584\pi$
$443$	1.41412	+	0.249347i	0.0671869	+	0.0118469i	−0.139954	+	0.990158i	$0.544695\pi$
$444$	−4.26690	+	3.13456i	−0.202498	+	0.148759i
$445$	19.3211	−	11.1550i	0.915906	−	0.528799i
$446$	−27.0222	+	3.87033i	−1.27954	+	0.183265i
$447$	8.27228	−	3.01086i	0.391265	−	0.142409i
$448$	−20.3012	+	23.2762i	−0.959143	+	1.09970i
$449$	10.0863	−	17.4699i	0.476001	−	0.824458i	−0.523621	−	0.851951i	$-0.675419\pi$
$449$	10.0863	−	17.4699i	0.476001	−	0.824458i	0.999622	+	0.0274936i	$0.00875258\pi$
$450$	−0.996869	+	2.48617i	−0.0469929	+	0.117199i
$451$	1.82937	+	2.18016i	0.0861417	+	0.102660i
$452$	−5.28286	−	10.6882i	−0.248485	−	0.502731i
$453$	2.86180	−	0.504612i	0.134459	−	0.0237088i
$454$	20.1124	−	32.3760i	0.943921	−	1.51948i
$455$	−22.1909			−1.04033
$456$	2.22574	+	12.1263i	0.104230	+	0.567864i
$457$	−4.46464			−0.208847			−0.104423	−	0.994533i	$-0.533300\pi$
$457$	−4.46464			−0.208847			−0.104423	+	0.994533i	$0.533300\pi$
$458$	13.9369	−	22.4350i	0.651231	−	1.04832i
$459$	−2.39733	+	0.422715i	−0.111898	+	0.0197306i
$460$	2.12271	−	1.04919i	0.0989716	−	0.0489187i
$461$	−18.3946	−	21.9218i	−0.856723	−	1.02100i	−0.999512	−	0.0312490i	$-0.990052\pi$
$461$	−18.3946	−	21.9218i	−0.856723	−	1.02100i	0.142789	−	0.989753i	$-0.454393\pi$
$462$	2.85002	−	7.10789i	0.132595	−	0.330689i
$463$	−2.44887	+	4.24156i	−0.113808	+	0.197122i	−0.917303	−	0.398190i	$-0.869638\pi$
$463$	−2.44887	+	4.24156i	−0.113808	+	0.197122i	0.803494	+	0.595312i	$0.202972\pi$
$464$	19.4613	+	6.09746i	0.903469	+	0.283067i
$465$	−15.1377	+	5.50967i	−0.701994	+	0.255505i
$466$	24.5874	−	3.52160i	1.13899	−	0.163135i
$467$	26.8895	−	15.5247i	1.24430	−	0.718397i	0.274333	−	0.961635i	$-0.411543\pi$
$467$	26.8895	−	15.5247i	1.24430	−	0.718397i	0.969967	+	0.243238i	$0.0782096\pi$
$468$	3.86181	+	5.25687i	0.178512	+	0.242999i
$469$	−16.3585	−	2.88444i	−0.755364	−	0.133191i
$470$	9.48325	+	17.7226i	0.437430	+	0.817484i
$471$	−4.00262	−	3.35859i	−0.184431	−	0.154756i
$472$	−11.1773	−	5.34262i	−0.514476	−	0.245914i
$473$	1.37613	+	0.500869i	0.0632743	+	0.0230300i
$474$	2.32601	−	11.0865i	0.106837	−	0.509220i
$475$	−0.583382	+	8.23530i	−0.0267674	+	0.377862i
$476$	−17.2113	−	7.55460i	−0.788881	−	0.346265i
$477$	−2.38723	+	6.55885i	−0.109304	+	0.300309i
$478$	0.884681	−	27.4031i	0.0404644	−	1.25339i
$479$	−6.81492	−	5.71839i	−0.311381	−	0.261280i	0.473681	−	0.880696i	$-0.342925\pi$
$479$	−6.81492	−	5.71839i	−0.311381	−	0.261280i	−0.785063	+	0.619416i	$0.787369\pi$
$480$	−9.41234	−	3.28610i	−0.429613	−	0.149989i
$481$	−1.49926	+	8.50273i	−0.0683604	+	0.387691i
$482$	−5.00755	+	5.59099i	−0.228088	+	0.254663i
$483$	2.24606	−	1.29676i	0.102199	−	0.0590048i
$484$	−18.0278	−	1.16524i	−0.819446	−	0.0529652i
$485$	−0.595894	−	1.63721i	−0.0270582	−	0.0743417i
$486$	−1.34384	+	0.440557i	−0.0609579	+	0.0199841i
$487$	−0.503217	+	0.871598i	−0.0228029	+	0.0394959i	−0.877202	−	0.480122i	$-0.840592\pi$
$487$	−0.503217	+	0.871598i	−0.0228029	+	0.0394959i	0.854399	+	0.519618i	$0.173926\pi$
$488$	15.5106	+	15.8098i	0.702133	+	0.715676i
$489$	17.4761	−	14.6642i	0.790295	−	0.663136i
$490$	15.4936	−	12.1707i	0.699928	−	0.549818i
$491$	−5.18606	+	0.914443i	−0.234044	+	0.0412682i	−0.289440	−	0.957196i	$-0.593469\pi$
$491$	−5.18606	+	0.914443i	−0.234044	+	0.0412682i	0.0553960	+	0.998464i	$0.482358\pi$
$492$	2.80363	−	2.93402i	0.126397	−	0.132276i
$493$			12.4115i			0.558984i
$494$	16.2856	+	11.7893i	0.732724	+	0.530425i
$495$	2.47190			0.111104
$496$	14.0529	+	33.7540i	0.630995	+	1.51560i
$497$	−6.33420	−	35.9230i	−0.284128	−	1.61137i
$498$	−2.79417	−	3.55702i	−0.125210	−	0.159394i
$499$	−13.4888	−	16.0754i	−0.603843	−	0.719632i	0.374360	−	0.927283i	$-0.377862\pi$
$499$	−13.4888	−	16.0754i	−0.603843	−	0.719632i	−0.978203	+	0.207651i	$0.933418\pi$
$500$	−20.2167	−	13.4819i	−0.904118	−	0.602931i
$501$	−16.1353	−	9.31574i	−0.720874	−	0.416197i
$502$	−23.4680	+	7.69361i	−1.04743	+	0.343383i
$503$	12.1667	−	4.42833i	0.542488	−	0.197450i	−0.0562176	−	0.998419i	$-0.517904\pi$
$503$	12.1667	−	4.42833i	0.542488	−	0.197450i	0.598706	+	0.800969i	$0.295682\pi$
$504$	−10.5202	−	2.92685i	−0.468605	−	0.130372i
$505$	−17.3201	−	29.9992i	−0.770733	−	1.33495i
$506$	0.992599	+	0.889018i	0.0441264	+	0.0395217i
$507$	−2.32704	−	0.410320i	−0.103347	−	0.0182229i
$508$	2.72810	−	0.797846i	0.121040	−	0.0353987i
$509$	−4.51644	+	5.38248i	−0.200188	+	0.238574i	−0.856794	−	0.515659i	$-0.827547\pi$
$509$	−4.51644	+	5.38248i	−0.200188	+	0.238574i	0.656606	+	0.754234i	$0.271991\pi$
$510$	0.195772	−	6.06406i	0.00866894	−	0.268521i
$511$	58.7896	+	21.3977i	2.60070	+	0.946577i
$512$	−6.48023	+	21.6796i	−0.286388	+	0.958114i
$513$	−3.52875	+	2.55889i	−0.155798	+	0.112978i
$514$	15.6849	+	3.29078i	0.691833	+	0.145150i
$515$	−2.69313	+	7.39931i	−0.118673	+	0.326053i
$516$	0.494498	−	2.02879i	0.0217691	−	0.0893125i
$517$	−7.27096	+	8.66519i	−0.319776	+	0.381095i
$518$	−6.81916	−	12.7439i	−0.299617	−	0.559934i
$519$	0.534498	−	3.03129i	0.0234619	−	0.133059i
$520$	−14.7992	+	6.72966i	−0.648990	+	0.295115i
$521$	−13.8042	−	23.9096i	−0.604773	−	1.04750i	−0.992087	−	0.125550i	$-0.959931\pi$
$521$	−13.8042	−	23.9096i	−0.604773	−	1.04750i	0.387315	−	0.921948i	$-0.373403\pi$
$522$	1.02230	+	7.13758i	0.0447448	+	0.312404i
$523$	−0.148017	−	0.406674i	−0.00647235	−	0.0177826i	0.936414	−	0.350896i	$-0.114123\pi$
$523$	−0.148017	−	0.406674i	−0.00647235	−	0.0177826i	−0.942887	+	0.333114i	$0.891901\pi$
$524$	−34.5921	+	3.82011i	−1.51116	+	0.166882i
$525$	−6.33266	−	3.65617i	−0.276380	−	0.159568i
$526$	−2.91977	+	7.28184i	−0.127308	+	0.317503i
$527$	−17.0454	+	14.3028i	−0.742509	+	0.623039i
$528$	−0.254858	−	5.60460i	−0.0110913	−	0.243909i
$529$	−3.91554	−	22.2062i	−0.170241	−	0.965485i
$530$	−14.7770	−	9.17970i	−0.641874	−	0.398741i
$531$		−	4.38000i		−	0.190076i
$532$	−33.6309	+	1.32124i	−1.45808	+	0.0572830i
$533$		−	6.61778i		−	0.286648i
$534$	9.44695	−	15.2073i	0.408809	−	0.658082i
$535$	−3.69048	−	20.9297i	−0.159553	−	0.904872i
$536$	−11.7843	+	3.03726i	−0.509005	+	0.131190i
$537$	−6.00250	+	5.03670i	−0.259027	+	0.217350i
$538$	15.5381	+	6.23024i	0.669895	+	0.268605i
$539$	9.60210	+	5.54378i	0.413592	+	0.238787i
$540$	−0.386896	−	3.50345i	−0.0166494	−	0.150764i
$541$	0.357131	+	0.981210i	0.0153543	+	0.0421855i	0.947133	−	0.320841i	$-0.103966\pi$
$541$	0.357131	+	0.981210i	0.0153543	+	0.0421855i	−0.931779	+	0.363027i	$0.881743\pi$
$542$	38.3866	−	5.49802i	1.64885	−	0.236160i
$543$	−12.6931	−	21.9851i	−0.544713	−	0.943471i
$544$	−13.7694	+	0.181338i	−0.590357	+	0.00777480i
$545$	−1.69111	+	9.59074i	−0.0724390	+	0.410822i
$546$	−15.7006	+	8.40128i	−0.671925	+	0.359542i
$547$	−19.5186	+	23.2614i	−0.834557	+	0.994586i	0.165408	+	0.986225i	$0.447106\pi$
$547$	−19.5186	+	23.2614i	−0.834557	+	0.994586i	−0.999965	+	0.00836099i	$0.997339\pi$
$548$	−6.24473	+	25.6204i	−0.266762	+	1.09445i
$549$	−2.67818	+	7.35823i	−0.114302	+	0.314042i
$550$	0.771437	−	3.67692i	0.0328942	−	0.156784i
$551$	9.72423	+	19.9836i	0.414266	+	0.851332i
$552$	1.10465	−	1.54597i	0.0470172	−	0.0658007i
$553$	29.0593	+	10.5767i	1.23573	+	0.449768i
$554$	17.4678	+	0.563932i	0.742137	+	0.0239592i
$555$	2.99889	−	3.57394i	0.127296	−	0.151705i
$556$	12.0110	+	41.0694i	0.509378	+	1.74173i
$557$	−17.6925	−	3.11966i	−0.749654	−	0.132184i	−0.214248	−	0.976779i	$-0.568730\pi$
$557$	−17.6925	−	3.11966i	−0.749654	−	0.132184i	−0.535406	+	0.844595i	$0.679841\pi$
$558$	−8.62439	+	9.62923i	−0.365099	+	0.407638i
$559$	−1.70263	−	2.94904i	−0.0720135	−	0.124731i
$560$	12.5233	−	24.1636i	0.529204	−	1.02110i
$561$	3.20846	−	1.16778i	0.135461	−	0.0493038i
$562$	−2.50960	−	7.65509i	−0.105861	−	0.322911i
$563$	−34.9811	−	20.1964i	−1.47428	−	0.851175i	−0.474698	−	0.880149i	$-0.657443\pi$
$563$	−34.9811	−	20.1964i	−1.47428	−	0.851175i	−0.999580	+	0.0289734i	$0.990776\pi$
$564$	13.4193	+	8.94894i	0.565054	+	0.376818i
$565$	6.75310	+	8.04804i	0.284105	+	0.338583i
$566$	9.70921	−	7.62693i	0.408108	−	0.320584i
$567$	−0.670404	−	3.80205i	−0.0281543	−	0.159671i
$568$	−15.1184	−	22.0364i	−0.634354	−	0.924625i
$569$	−7.32215			−0.306960			−0.153480	−	0.988152i	$-0.549048\pi$
$569$	−7.32215			−0.306960			−0.153480	+	0.988152i	$0.549048\pi$
$570$	−4.43591	−	9.91711i	−0.185800	−	0.415382i
$571$			36.5520i			1.52965i	0.644236	+	0.764827i	$0.277176\pi$
$571$			36.5520i			1.52965i	−0.644236	+	0.764827i	$0.722824\pi$
$572$	−6.61463	−	6.32068i	−0.276572	−	0.264281i
$573$	25.6719	−	4.52665i	1.07246	−	0.189103i
$574$	6.84360	+	8.71201i	0.285646	+	0.363632i
$575$	0.974695	−	0.817866i	0.0406476	−	0.0341074i
$576$	−7.90356	+	1.23843i	−0.329315	+	0.0516013i
$577$	−11.7381	+	20.3309i	−0.488662	+	0.846388i	−0.999915	−	0.0130426i	$-0.995848\pi$
$577$	−11.7381	+	20.3309i	−0.488662	+	0.846388i	0.511253	+	0.859430i	$0.329182\pi$
$578$	4.87877	+	14.8818i	0.202930	+	0.619003i
$579$	5.56675	+	15.2945i	0.231346	+	0.635618i
$580$	−17.9336	−	1.15915i	−0.744653	−	0.0481310i
$581$	10.6938	−	6.17406i	0.443653	−	0.256143i
$582$	−1.04144	−	0.932764i	−0.0431692	−	0.0386643i
$583$	1.69999	−	9.64110i	0.0704062	−	0.399293i
$584$	45.6963	−	3.55843i	1.89093	−	0.147249i
$585$	−4.40314	−	3.69467i	−0.182047	−	0.152756i
$586$	−44.3414	−	1.43152i	−1.83173	−	0.0591355i
$587$	−2.02465	+	5.56267i	−0.0835661	+	0.229596i	−0.974437	−	0.224660i	$-0.927873\pi$
$587$	−2.02465	+	5.56267i	−0.0835661	+	0.229596i	0.890871	+	0.454256i	$0.150095\pi$
$588$	6.35435	−	14.4768i	0.262049	−	0.597015i
$589$	−16.2387	+	36.3837i	−0.669103	+	1.49917i
$590$	10.6840	+	2.24155i	0.439852	+	0.0922833i
$591$	−1.73480	−	0.631415i	−0.0713600	−	0.0259729i
$592$	−8.41248	−	6.43099i	−0.345751	−	0.264312i
$593$	2.64015	+	2.21535i	0.108418	+	0.0909736i	0.695385	−	0.718637i	$-0.255234\pi$
$593$	2.64015	+	2.21535i	0.108418	+	0.0909736i	−0.586967	+	0.809611i	$0.699678\pi$
$594$	1.74893	−	0.935841i	0.0717596	−	0.0383980i
$595$	16.3114	+	2.87615i	0.668704	+	0.117911i
$596$	10.4236	+	14.1891i	0.426969	+	0.581209i
$597$	−10.3718	+	5.98818i	−0.424491	+	0.245080i
$598$	−0.439307	−	3.06719i	−0.0179646	−	0.125427i
$599$	11.8677	−	4.31949i	0.484901	−	0.176489i	−0.0879897	−	0.996121i	$-0.528044\pi$
$599$	11.8677	−	4.31949i	0.484901	−	0.176489i	0.572890	+	0.819632i	$0.305822\pi$
$600$	−5.33207	−	0.517862i	−0.217681	−	0.0211416i
$601$	−1.64003	+	2.84062i	−0.0668984	+	0.115871i	−0.897535	−	0.440944i	$-0.854644\pi$
$601$	−1.64003	+	2.84062i	−0.0668984	+	0.115871i	0.830636	+	0.556816i	$0.187977\pi$
$602$	5.29110	+	2.12155i	0.215649	+	0.0864680i
$603$	−2.76562	−	3.29594i	−0.112625	−	0.134221i
$604$	2.57525	+	5.21020i	0.104785	+	0.212000i
$605$	15.6772	−	2.76431i	0.637368	−	0.112385i
$606$	−23.6118	−	14.6680i	−0.959166	−	0.595846i
$607$	16.3835			0.664985			0.332493	−	0.943106i	$-0.392110\pi$
$607$	16.3835			0.664985			0.332493	+	0.943106i	$0.392110\pi$
$608$	−22.0280	+	11.0801i	−0.893352	+	0.449358i
$609$	−19.6839			−0.797633
$610$	−16.5781	−	10.2985i	−0.671226	−	0.416974i
$611$	25.9032	−	4.56743i	1.04793	−	0.184778i
$612$	−2.15729	−	4.36460i	−0.0872032	−	0.176428i
$613$	−10.4243	−	12.4232i	−0.421035	−	0.501769i	0.513279	−	0.858222i	$-0.328431\pi$
$613$	−10.4243	−	12.4232i	−0.421035	−	0.501769i	−0.934313	+	0.356452i	$0.883986\pi$
$614$	22.1779	+	8.89259i	0.895028	+	0.358876i
$615$	−1.78801	+	3.09692i	−0.0720994	+	0.124880i
$616$	15.2442	+	1.48055i	0.614208	+	0.0596531i
$617$	−9.24502	+	3.36491i	−0.372191	+	0.135466i	−0.521341	−	0.853348i	$-0.674568\pi$
$617$	−9.24502	+	3.36491i	−0.372191	+	0.135466i	0.149151	+	0.988814i	$0.452346\pi$
$618$	0.895860	+	6.25480i	0.0360368	+	0.251605i
$619$	−0.306954	+	0.177220i	−0.0123375	+	0.00712308i	−0.506156	−	0.862442i	$-0.668934\pi$
$619$	−0.306954	+	0.177220i	−0.0123375	+	0.00712308i	0.493819	+	0.869565i	$0.335601\pi$
$620$	−19.0745	−	25.9651i	−0.766052	−	1.04278i
$621$	0.661571	+	0.116653i	0.0265479	+	0.00468112i
$622$	18.1451	−	9.70931i	0.727552	−	0.389308i
$623$	37.4389	+	31.4149i	1.49996	+	1.25861i
$624$	−7.92305	+	10.3643i	−0.317176	+	0.414903i
$625$	11.2222	+	4.08454i	0.448887	+	0.163382i
$626$	−21.4463	−	4.49954i	−0.857165	−	0.179838i
$627$	4.25098	−	4.39403i	0.169768	−	0.175481i
$628$	4.20009	−	9.56889i	0.167602	−	0.381840i
$629$	2.20407	−	6.05562i	0.0878819	−	0.241453i
$630$	9.61729	+	0.310485i	0.383162	+	0.0123700i
$631$	−6.75678	−	5.66961i	−0.268983	−	0.225704i	0.498312	−	0.866998i	$-0.333953\pi$
$631$	−6.75678	−	5.66961i	−0.268983	−	0.225704i	−0.767295	+	0.641294i	$0.778398\pi$
$632$	22.5874	−	1.75891i	0.898478	−	0.0699657i
$633$	3.58350	−	20.3230i	0.142431	−	0.807768i
$634$	−13.6884	−	12.2600i	−0.543638	−	0.486907i
$635$	−2.16910	+	1.25233i	−0.0860781	+	0.0496972i
$636$	−13.9305	−	0.900403i	−0.552380	−	0.0357033i
$637$	−8.81790	−	24.2270i	−0.349378	−	0.959907i
$638$	−3.15051	−	9.61008i	−0.124730	−	0.380467i
$639$	4.72417	−	8.18250i	0.186885	−	0.323695i
$640$	1.02395	−	19.9127i	0.0404751	−	0.787117i
$641$	9.83276	−	8.25066i	0.388371	−	0.325882i	−0.427607	−	0.903965i	$-0.640643\pi$
$641$	9.83276	−	8.25066i	0.388371	−	0.325882i	0.815978	+	0.578083i	$0.196199\pi$
$642$	−10.5349	−	13.4111i	−0.415781	−	0.529296i
$643$	−17.0380	+	3.00426i	−0.671913	+	0.118476i	−0.499188	−	0.866494i	$-0.666368\pi$
$643$	−17.0380	+	3.00426i	−0.671913	+	0.118476i	−0.172725	+	0.984970i	$0.555257\pi$
$644$	3.75019	+	3.58353i	0.147778	+	0.141211i
$645$			1.84008i			0.0724531i
$646$	−10.4428	−	10.7765i	−0.410865	−	0.423996i
$647$	2.20258			0.0865925			0.0432963	−	0.999062i	$-0.486214\pi$
$647$	2.20258			0.0865925			0.0432963	+	0.999062i	$0.486214\pi$
$648$	−1.60011	−	2.33230i	−0.0628584	−	0.0916215i
$649$	1.06679	+	6.05004i	0.0418750	+	0.237485i
$650$	−6.86992	+	5.39657i	−0.269460	+	0.211671i
$651$	−22.6835	−	27.0331i	−0.889036	−	1.05951i
$652$	37.9602	+	25.3146i	1.48664	+	0.991395i
$653$	−32.3211	−	18.6606i	−1.26482	−	0.730246i	−0.290819	−	0.956778i	$-0.593928\pi$
$653$	−32.3211	−	18.6606i	−1.26482	−	0.730246i	−0.974004	+	0.226532i	$0.927261\pi$
$654$	2.43447	+	7.42593i	0.0951954	+	0.290377i
$655$	28.8179	−	10.4889i	1.12601	−	0.409834i
$656$	7.20606	+	3.73469i	0.281350	+	0.145815i
$657$	8.10249	+	14.0339i	0.316108	+	0.547516i
$658$	−29.3771	+	32.7999i	−1.14524	+	1.27867i
$659$	−26.4355	−	4.66130i	−1.02978	−	0.181578i	−0.366867	−	0.930273i	$-0.619570\pi$
$659$	−26.4355	−	4.66130i	−1.02978	−	0.181578i	−0.662915	+	0.748695i	$0.730681\pi$
$660$	1.38771	+	4.74504i	0.0540165	+	0.184701i
$661$	−16.8217	+	20.0473i	−0.654288	+	0.779750i	−0.986554	−	0.163436i	$-0.947742\pi$
$661$	−16.8217	+	20.0473i	−0.654288	+	0.779750i	0.332266	+	0.943186i	$0.392187\pi$
$662$	−4.93425	−	0.159298i	−0.191775	−	0.00619127i
$663$	−7.46060	−	2.71544i	−0.289746	−	0.105459i
$664$	5.25940	−	7.36055i	0.204104	−	0.285645i
$665$	28.5164	−	8.14895i	1.10582	−	0.316003i
$666$	0.768729	−	3.66401i	0.0297876	−	0.141978i
$667$	1.17145	−	3.21852i	0.0453586	−	0.124622i
$668$	8.82415	−	36.2031i	0.341417	−	1.40074i
$669$	12.4075	−	14.7866i	0.479700	−	0.571685i
$670$	9.45503	−	5.05932i	0.365280	−	0.195458i
$671$	1.90718	−	10.8161i	0.0736258	−	0.417552i
$672$	−0.287592	−	21.8375i	−0.0110941	−	0.842401i
$673$	11.7321	+	20.3206i	0.452240	+	0.783303i	0.998525	−	0.0542969i	$-0.0172917\pi$
$673$	11.7321	+	20.3206i	0.452240	+	0.783303i	−0.546285	+	0.837599i	$0.683958\pi$
$674$	24.3172	−	3.48290i	0.936665	−	0.134156i
$675$	−0.647801	−	1.77982i	−0.0249339	−	0.0685052i
$676$	−0.518739	−	4.69732i	−0.0199515	−	0.180666i
$677$	31.0849	+	17.9469i	1.19469	+	0.689754i	0.959366	−	0.282163i	$-0.0910520\pi$
$677$	31.0849	+	17.9469i	1.19469	+	0.689754i	0.235323	+	0.971917i	$0.424385\pi$
$678$	7.82491	+	3.13752i	0.300514	+	0.120496i
$679$	2.92375	−	2.45331i	0.112203	−	0.0941496i
$680$	11.7504	−	3.02853i	0.450609	−	0.116139i
$681$	4.67999	+	26.5415i	0.179338	+	1.01707i
$682$	9.56749	−	15.4013i	0.366358	−	0.589746i
$683$		−	8.71517i		−	0.333477i	−0.986001	−	0.166738i	$-0.946676\pi$
$683$		−	8.71517i		−	0.333477i	0.986001	−	0.166738i	$-0.0533235\pi$
$684$	−6.89305	−	5.33721i	−0.263562	−	0.204073i
$685$		−	23.2373i		−	0.887852i
$686$	4.19728	+	2.60740i	0.160253	+	0.0995511i
$687$	3.24302	+	18.3921i	0.123729	+	0.701701i
$688$	4.17206	−	0.189716i	0.159058	−	0.00723285i
$689$	−17.4384	+	14.6326i	−0.664350	+	0.557456i
$690$	−0.623119	+	1.55405i	−0.0237218	+	0.0591615i
$691$	41.4215	+	23.9147i	1.57575	+	0.909759i	0.995443	+	0.0953615i	$0.0304007\pi$
$691$	41.4215	+	23.9147i	1.57575	+	0.909759i	0.580307	+	0.814398i	$0.302933\pi$
$692$	6.11891	−	0.675729i	0.232606	−	0.0256874i
$693$	1.85204	+	5.08845i	0.0703533	+	0.193294i
$694$	5.96464	+	41.6444i	0.226414	+	1.58080i
$695$	−18.8529	−	32.6541i	−0.715130	−	1.23864i
$696$	−13.1273	+	5.96939i	−0.497591	+	0.226269i
$697$	−0.857726	+	4.86441i	−0.0324887	+	0.184253i
$698$	−1.52687	−	2.85346i	−0.0577928	−	0.108005i
$699$	−11.2895	+	13.4543i	−0.427008	+	0.508889i
$700$	3.46323	−	14.2087i	0.130898	−	0.537038i
$701$	−16.1081	+	44.2567i	−0.608395	+	1.67155i	0.125339	+	0.992114i	$0.459998\pi$
$701$	−16.1081	+	44.2567i	−0.608395	+	1.67155i	−0.733734	+	0.679437i	$0.762224\pi$
$702$	−4.51411	−	0.947084i	−0.170374	−	0.0357454i
$703$	−1.19575	−	11.4770i	−0.0450985	−	0.432863i
$704$	10.6155	−	3.63561i	0.400086	−	0.137022i
$705$	−13.3559	−	4.86116i	−0.503014	−	0.183082i
$706$	1.19709	−	37.0798i	0.0450529	−	1.39552i
$707$	48.7770	−	58.1302i	1.83445	−	2.18621i
$708$	8.40781	−	2.45890i	0.315985	−	0.0924113i
$709$	−10.6711	−	1.88160i	−0.400762	−	0.0706651i	−0.0303654	−	0.999539i	$-0.509667\pi$
$709$	−10.6711	−	1.88160i	−0.400762	−	0.0706651i	−0.370397	+	0.928874i	$0.620778\pi$
$710$	17.5416	+	15.7110i	0.658324	+	0.589625i
$711$	4.00501	+	6.93688i	0.150200	+	0.260153i
$712$	34.4952	+	9.59703i	1.29276	+	0.359664i
$713$	5.77015	−	2.10016i	0.216094	−	0.0786517i
$714$	12.6296	−	4.14043i	0.472653	−	0.154952i
$715$	6.98188	+	4.03099i	0.261108	+	0.150751i
$716$	−13.0382	−	8.69479i	−0.487260	−	0.324940i
$717$	12.4617	+	14.8513i	0.465391	+	0.554632i
$718$	20.4266	+	26.0034i	0.762315	+	0.970440i
$719$	−1.94093	−	11.0075i	−0.0723843	−	0.410512i	−0.999372	−	0.0354214i	$-0.988723\pi$
$719$	−1.94093	−	11.0075i	−0.0723843	−	0.410512i	0.926988	−	0.375091i	$-0.122388\pi$
$720$	6.50799	−	2.70950i	0.242539	−	0.100977i
$721$	−17.2494			−0.642401
$722$	−25.2571	−	9.16944i	−0.939972	−	0.341251i
$723$		−	5.30729i		−	0.197380i
$724$	35.0766	−	36.7079i	1.30361	−	1.36424i
$725$	−9.51014	+	1.67689i	−0.353198	+	0.0622783i
$726$	10.0455	−	7.89106i	0.372822	−	0.292865i
$727$	−40.4978	+	33.9817i	−1.50198	+	1.26031i	−0.624188	+	0.781274i	$0.714570\pi$
$727$	−40.4978	+	33.9817i	−1.50198	+	1.26031i	−0.877794	+	0.479038i	$0.840986\pi$
$728$	−24.9413	−	25.4224i	−0.924385	−	0.942216i
$729$	0.500000	−	0.866025i	0.0185185	−	0.0320750i
$730$	−38.3791	+	12.5820i	−1.42047	+	0.465679i
$731$	0.869296	+	2.38837i	0.0321521	+	0.0883371i
$732$	−15.6283	−	1.01014i	−0.577639	−	0.0373359i
$733$	2.61759	−	1.51127i	0.0966830	−	0.0558199i	−0.450879	−	0.892585i	$-0.648889\pi$
$733$	2.61759	−	1.51127i	0.0966830	−	0.0558199i	0.547562	+	0.836765i	$0.315556\pi$
$734$	16.7028	−	18.6489i	0.616512	−	0.688343i
$735$	−2.41919	+	13.7199i	−0.0892333	+	0.506067i
$736$	3.58777	+	1.25259i	0.132247	+	0.0461710i
$737$	4.62288	+	3.87906i	0.170286	+	0.142887i
$738$	−0.0925929	+	2.86807i	−0.00340839	+	0.105575i
$739$	15.1799	−	41.7064i	0.558401	−	1.53419i	−0.263557	−	0.964644i	$-0.584896\pi$
$739$	15.1799	−	41.7064i	0.558401	−	1.53419i	0.821957	−	0.569549i	$-0.192882\pi$
$740$	8.54408	+	3.75027i	0.314086	+	0.137863i
$741$	−14.1398	+	1.47318i	−0.519439	+	0.0541185i
$742$	7.82502	−	37.2966i	0.287265	−	1.36920i
$743$	−14.5347	−	5.29019i	−0.533226	−	0.194078i	0.0613523	−	0.998116i	$-0.480459\pi$
$743$	−14.5347	−	5.29019i	−0.533226	−	0.194078i	−0.594578	+	0.804038i	$0.702681\pi$
$744$	−23.3259	−	11.1495i	−0.855169	−	0.408761i
$745$	−11.8848	−	9.97251i	−0.435425	−	0.365365i
$746$	5.12586	+	9.57938i	0.187671	+	0.350726i
$747$	3.14983	+	0.555399i	0.115246	+	0.0203210i
$748$	4.04288	+	5.50334i	0.147822	+	0.201222i
$749$	40.3192	−	23.2783i	1.47323	−	0.850570i
$750$	17.0089	−	2.43615i	0.621079	−	0.0889556i
$751$	18.6560	−	6.79024i	0.680769	−	0.247779i	0.0215910	−	0.999767i	$-0.493127\pi$
$751$	18.6560	−	6.79024i	0.680769	−	0.247779i	0.659177	+	0.751987i	$0.270905\pi$
$752$	−9.64481	+	30.7834i	−0.351710	+	1.12256i
$753$	8.73169	−	15.1237i	0.318200	−	0.551139i
$754$	−8.75196	+	21.8272i	−0.318727	+	0.794899i
$755$	−3.29195	−	3.92319i	−0.119806	−	0.142780i
$756$	6.92202	−	3.42135i	0.251752	−	0.124433i
$757$	6.45522	−	1.13823i	0.234619	−	0.0413697i	−0.0551023	−	0.998481i	$-0.517548\pi$
$757$	6.45522	−	1.13823i	0.234619	−	0.0413697i	0.289721	+	0.957111i	$0.406437\pi$
$758$	−25.4539	+	40.9744i	−0.924526	+	1.48826i
$759$	−0.942233			−0.0342009
$760$	16.5465	−	14.0825i	0.600206	−	0.510828i
$761$	−47.1381			−1.70875			−0.854377	−	0.519654i	$-0.826061\pi$
$761$	−47.1381			−1.70875			−0.854377	+	0.519654i	$0.826061\pi$
$762$	−1.06057	+	1.70726i	−0.0384205	+	0.0618475i
$763$	−21.0097	+	3.70458i	−0.760603	+	0.134115i
$764$	23.1014	+	46.7384i	0.835778	+	1.69093i
$765$	2.75767	+	3.28646i	0.0997038	+	0.118822i
$766$	−2.05009	+	5.11287i	−0.0740727	+	0.184736i
$767$	7.14257	−	12.3713i	0.257903	−	0.446702i
$768$	−6.81430	−	14.4764i	−0.245890	−	0.522371i
$769$	−3.83681	+	1.39648i	−0.138359	+	0.0503585i	−0.410271	−	0.911963i	$-0.634566\pi$
$769$	−3.83681	+	1.39648i	−0.138359	+	0.0503585i	0.271913	+	0.962322i	$0.412344\pi$
$770$	−13.3599	+	1.91350i	−0.481457	+	0.0689579i
$771$	−9.81414	+	5.66620i	−0.353448	+	0.204063i
$772$	−26.2341	+	19.2721i	−0.944186	+	0.693619i
$773$	18.0782	+	3.18768i	0.650229	+	0.114653i	0.489027	−	0.872268i	$-0.337352\pi$
$773$	18.0782	+	3.18768i	0.650229	+	0.114653i	0.161202	+	0.986921i	$0.448463\pi$
$774$	0.696639	+	1.30190i	0.0250402	+	0.0467960i
$775$	−13.2623	−	11.1284i	−0.476397	−	0.399744i
$776$	1.20587	−	2.52279i	0.0432881	−	0.0905630i
$777$	9.60390	+	3.49554i	0.344538	+	0.125402i
$778$	−3.61668	+	17.2383i	−0.129664	+	0.618022i
$779$	2.43018	+	8.50418i	0.0870703	+	0.304694i
$780$	4.62037	−	10.5264i	0.165436	−	0.376906i
$781$	−4.53252	+	12.4530i	−0.162186	+	0.445604i
$782$	−0.0746240	+	2.31148i	−0.00266855	+	0.0826585i
$783$	−3.90571	−	3.27728i	−0.139579	−	0.117120i
$784$	31.3569	+	4.07054i	1.11989	+	0.145377i
$785$	−1.59903	+	9.06858i	−0.0570720	+	0.323671i
$786$	16.4184	−	18.3314i	0.585625	−	0.653858i
$787$	−33.2689	+	19.2078i	−1.18591	+	0.684684i	−0.957374	−	0.288852i	$-0.906726\pi$
$787$	−33.2689	+	19.2078i	−1.18591	+	0.684684i	−0.228533	+	0.973536i	$0.573393\pi$
$788$	0.238154	−	3.68458i	0.00848389	−	0.131258i
$789$	−1.89737	−	5.21298i	−0.0675481	−	0.185587i
$790$	−18.9705	+	6.21918i	−0.674941	+	0.221269i
$791$	−11.5073	+	19.9313i	−0.409153	+	0.708674i
$792$	2.77827	+	2.83186i	0.0987216	+	0.100626i
$793$	−19.5638	+	16.4159i	−0.694730	+	0.582947i
$794$	24.9029	−	19.5621i	0.883772	−	0.694235i
$795$	12.1141	−	2.13604i	0.429643	−	0.0757576i
$796$	−17.3176	−	16.5480i	−0.613805	−	0.586527i
$797$			12.1149i			0.429133i	0.976709	+	0.214567i	$0.0688339\pi$
$797$			12.1149i			0.429133i	−0.976709	+	0.214567i	$0.931166\pi$
$798$	17.0910	−	16.5617i	0.605014	−	0.586277i
$799$	−19.6322			−0.694536
$800$	−1.99931	−	10.5261i	−0.0706863	−	0.372155i
$801$	2.19823	+	12.4668i	0.0776706	+	0.440492i
$802$	−6.67399	−	8.49610i	−0.235667	−	0.300008i
$803$	−14.6100	−	17.4115i	−0.515575	−	0.614438i
$804$	4.77426	−	7.15919i	0.168375	−	0.252485i
$805$	−3.95840	−	2.28538i	−0.139515	−	0.0805491i
$806$	−40.0622	+	13.1338i	−1.41113	+	0.462617i
$807$	−11.1235	+	4.04863i	−0.391566	+	0.142519i
$808$	14.9010	−	53.5596i	0.524216	−	1.88422i
$809$	18.3495	+	31.7822i	0.645133	+	1.11740i	0.984271	+	0.176667i	$0.0565315\pi$
$809$	18.3495	+	31.7822i	0.645133	+	1.11740i	−0.339138	+	0.940737i	$0.610135\pi$
$810$	1.85658	+	1.66284i	0.0652335	+	0.0584262i
$811$	−10.4637	−	1.84503i	−0.367429	−	0.0647876i	−0.0131146	−	0.999914i	$-0.504175\pi$
$811$	−10.4637	−	1.84503i	−0.367429	−	0.0647876i	−0.354314	+	0.935126i	$0.615286\pi$
$812$	−11.0504	−	37.7851i	−0.387794	−	1.32600i
$813$	−17.6255	+	21.0053i	−0.618153	+	0.736687i
$814$	−0.169436	+	5.24829i	−0.00593873	+	0.183952i
$815$	−37.7810	−	13.7512i	−1.32341	−	0.481682i
$816$	7.16716	−	6.59137i	0.250901	−	0.230744i
$817$	3.27091	+	3.16443i	0.114435	+	0.110709i
$818$	−45.7920	−	9.60741i	−1.60108	−	0.335915i
$819$	4.30654	−	11.8321i	0.150483	−	0.413448i
$820$	−6.94860	−	1.69365i	−0.242656	−	0.0591449i
$821$	16.1517	−	19.2488i	0.563698	−	0.671789i	−0.406627	−	0.913594i	$-0.633295\pi$
$821$	16.1517	−	19.2488i	0.563698	−	0.671789i	0.970325	+	0.241805i	$0.0777395\pi$
$822$	−8.79745	−	16.4410i	−0.306846	−	0.573445i
$823$	0.915930	−	5.19450i	0.0319273	−	0.181069i	−0.964674	−	0.263447i	$-0.915141\pi$
$823$	0.915930	−	5.19450i	0.0319273	−	0.181069i	0.996601	+	0.0823785i	$0.0262516\pi$
$824$	−11.5037	+	5.23109i	−0.400752	+	0.182234i
$825$	1.32829	+	2.30067i	0.0462451	+	0.0800989i
$826$	3.39057	+	23.6726i	0.117973	+	0.823674i
$827$	0.0398691	+	0.109540i	0.00138639	+	0.00380906i	0.940384	−	0.340115i	$-0.110466\pi$
$827$	0.0398691	+	0.109540i	0.00138639	+	0.00380906i	−0.938997	+	0.343924i	$0.888244\pi$
$828$	0.147476	+	1.33544i	0.00512515	+	0.0464096i
$829$	33.3262	+	19.2409i	1.15747	+	0.668264i	0.950696	−	0.310125i	$-0.100371\pi$
$829$	33.3262	+	19.2409i	1.15747	+	0.668264i	0.206771	+	0.978389i	$0.433704\pi$
$830$	−2.96675	+	7.39902i	−0.102977	+	0.256824i
$831$	−9.46682	+	7.94361i	−0.328400	+	0.275561i
$832$	−24.3431	−	9.39059i	−0.843947	−	0.325560i
$833$	3.34156	+	18.9509i	0.115778	+	0.656611i
$834$	−25.7015	−	15.9661i	−0.889969	−	0.552860i
$835$			32.8356i			1.13632i
$836$	10.8212	+	5.69337i	0.374260	+	0.196909i
$837$		−	9.14063i		−	0.315946i
$838$	−5.31309	+	8.55276i	−0.183537	+	0.295450i
$839$	−5.71975	−	32.4383i	−0.197468	−	1.11989i	−0.908861	−	0.417100i	$-0.863046\pi$
$839$	−5.71975	−	32.4383i	−0.197468	−	1.11989i	0.711393	−	0.702795i	$-0.248065\pi$
$840$	4.80308	+	18.6356i	0.165722	+	0.642989i
$841$	2.30189	−	1.93151i	0.0793755	−	0.0666039i
$842$	−35.8351	−	14.3687i	−1.23496	−	0.495177i
$843$	4.93325	+	2.84821i	0.169910	+	0.0980977i
$844$	41.0237	−	4.53037i	1.41209	−	0.155942i
$845$	1.42430	+	3.91323i	0.0489974	+	0.134619i
$846$	−11.2901	+	1.61705i	−0.388160	+	0.0555953i
$847$	17.4363	+	30.2006i	0.599119	+	1.03770i
$848$	−6.09209	−	27.2464i	−0.209203	−	0.935644i
$849$	−1.51601	+	8.59774i	−0.0520294	+	0.295074i
$850$	5.74919	−	3.07635i	0.197196	−	0.105518i
$851$	−1.14311	+	1.36231i	−0.0391853	+	0.0466993i
$852$	18.3592	+	4.47487i	0.628975	+	0.153307i
$853$	6.36413	−	17.4853i	0.217904	−	0.598685i	−0.781787	−	0.623545i	$-0.785692\pi$
$853$	6.36413	−	17.4853i	0.217904	−	0.598685i	0.999691	+	0.0248599i	$0.00791398\pi$
$854$	8.77872	−	41.8422i	0.300402	−	1.43181i
$855$	7.01502	+	3.13092i	0.239909	+	0.107075i
$856$	19.8297	−	27.7517i	0.677765	−	0.948534i
$857$	−49.8035	−	18.1270i	−1.70126	−	0.619206i	−0.705288	−	0.708921i	$-0.749182\pi$
$857$	−49.8035	−	18.1270i	−1.70126	−	0.619206i	−0.995968	+	0.0897146i	$0.971405\pi$
$858$	6.46596	+	0.208747i	0.220744	+	0.00712651i
$859$	−24.1638	+	28.7973i	−0.824459	+	0.982551i	−0.999998	−	0.00192096i	$-0.999389\pi$
$859$	−24.1638	+	28.7973i	−0.824459	+	0.982551i	0.175540	+	0.984472i	$0.443833\pi$
$860$	−3.53220	+	1.03301i	−0.120447	+	0.0352253i
$861$	−7.71470	−	1.36031i	−0.262916	−	0.0463592i
$862$	−3.00055	+	3.35016i	−0.102199	+	0.114107i
$863$	19.6013	+	33.9505i	0.667236	+	1.15569i	0.978674	+	0.205421i	$0.0658562\pi$
$863$	19.6013	+	33.9505i	0.667236	+	1.15569i	−0.311437	+	0.950267i	$0.600810\pi$
$864$	3.57878	−	4.38091i	0.121752	−	0.149042i
$865$	−5.09753	+	1.85535i	−0.173321	+	0.0630837i
$866$	−9.31505	−	28.4139i	−0.316538	−	0.965545i
$867$	−9.59045	−	5.53705i	−0.325709	−	0.188048i
$868$	39.1582	−	58.7193i	1.32912	−	1.99306i
$869$	−7.22162	−	8.60639i	−0.244977	−	0.291952i
$870$	9.99297	−	7.84984i	0.338793	−	0.266134i
$871$	−2.43672	−	13.8193i	−0.0825652	−	0.468251i
$872$	−12.8881	+	8.84207i	−0.436445	+	0.299430i
$873$	0.988598			0.0334590
$874$	1.69087	+	3.78018i	0.0571945	+	0.127866i
$875$			46.9070i			1.58575i
$876$	−22.3907	+	23.4320i	−0.756513	+	0.791695i
$877$	−6.02474	+	1.06232i	−0.203441	+	0.0358721i	−0.274440	−	0.961604i	$-0.588492\pi$
$877$	−6.02474	+	1.06232i	−0.203441	+	0.0358721i	0.0709990	+	0.997476i	$0.477381\pi$
$878$	27.5010	+	35.0092i	0.928112	+	1.18150i
$879$	24.0312	−	20.1645i	0.810551	−	0.680133i
$880$	−8.32950	+	5.32768i	−0.280787	+	0.179596i
$881$	11.3547	−	19.6668i	0.382548	−	0.662593i	−0.608878	−	0.793264i	$-0.708380\pi$
$881$	11.3547	−	19.6668i	0.382548	−	0.662593i	0.991426	+	0.130671i	$0.0417133\pi$
$882$	3.48261	+	10.6231i	0.117265	+	0.357698i
$883$	12.7263	+	34.9653i	0.428275	+	1.17667i	0.946859	+	0.321649i	$0.104237\pi$
$883$	12.7263	+	34.9653i	0.428275	+	1.17667i	−0.518585	+	0.855026i	$0.673541\pi$
$884$	1.02420	−	15.8457i	0.0344474	−	0.532950i
$885$	−6.68501	+	3.85959i	−0.224714	+	0.129739i
$886$	−1.51269	−	1.35484i	−0.0508199	−	0.0455166i
$887$	−1.38199	+	7.83763i	−0.0464025	+	0.263162i	−0.999179	−	0.0405104i	$-0.987102\pi$
$887$	−1.38199	+	7.83763i	−0.0464025	+	0.263162i	0.952777	+	0.303672i	$0.0982127\pi$
$888$	7.46497	−	0.581307i	0.250508	−	0.0195074i
$889$	−4.20312	−	3.52683i	−0.140968	−	0.118286i
$890$	−31.5347	−	1.01807i	−1.05705	−	0.0341257i
$891$	−0.479717	+	1.31801i	−0.0160711	+	0.0441550i
$892$	35.3498	+	15.5161i	1.18360	+	0.519519i
$893$	−31.6097	+	15.3816i	−1.05778	+	0.514724i
$894$	−12.1843	−	2.55633i	−0.407504	−	0.0854964i
$895$	12.9766	+	4.72311i	0.433761	+	0.157876i
$896$	41.7577	−	12.8115i	1.39503	−	0.428003i
$897$	1.67838	+	1.40833i	0.0560394	+	0.0470227i
$898$	−25.1536	+	13.4595i	−0.839388	+	0.449150i
$899$	−45.8958	−	8.09267i	−1.53071	−	0.269906i
$900$	3.05285	−	2.24269i	0.101762	−	0.0747564i
$901$	14.7146	−	8.49550i	0.490216	−	0.283026i
$902$	−0.570646	−	3.98419i	−0.0190004	−	0.132659i
$903$	−3.78783	+	1.37866i	−0.126051	+	0.0458789i
$904$	−1.62991	+	16.7820i	−0.0542099	+	0.558162i
$905$	−22.3700	+	38.7460i	−0.743604	+	1.28796i
$906$	−3.81442	−	1.52945i	−0.126726	−	0.0508127i
$907$	−17.8323	−	21.2517i	−0.592112	−	0.705652i	0.383898	−	0.923375i	$-0.374581\pi$
$907$	−17.8323	−	21.2517i	−0.592112	−	0.705652i	−0.976010	+	0.217724i	$0.930137\pi$
$908$	−48.3216	+	23.8839i	−1.60361	+	0.792617i
$909$	19.3568	−	3.41312i	0.642024	−	0.113206i
$910$	26.6577	+	16.5601i	0.883695	+	0.548963i
$911$	28.0567			0.929560			0.464780	−	0.885426i	$-0.346133\pi$
$911$	28.0567			0.929560			0.464780	+	0.885426i	$0.346133\pi$
$912$	6.37555	−	16.2281i	0.211116	−	0.537367i
$913$	−4.48609			−0.148468
$914$	5.36333	+	3.33177i	0.177403	+	0.110205i
$915$	13.5905	−	2.39638i	0.449289	−	0.0792219i
$916$	−33.4847	+	16.5505i	−1.10636	+	0.546843i
$917$	43.1830	+	51.4635i	1.42603	+	1.69947i
$918$	3.19535	+	1.28123i	0.105462	+	0.0422867i
$919$	22.0192	−	38.1384i	0.726347	−	1.25807i	−0.232070	−	0.972699i	$-0.574550\pi$
$919$	22.0192	−	38.1384i	0.726347	−	1.25807i	0.958417	−	0.285371i	$-0.0921168\pi$
$920$	−3.33295	−	0.323703i	−0.109884	−	0.0106722i
$921$	−15.8769	+	5.77872i	−0.523161	+	0.190415i
$922$	5.73793	+	40.0616i	0.188969	+	1.31936i
$923$	26.6868	−	15.4076i	0.878407	−	0.507149i
$924$	−8.72802	+	6.41179i	−0.287131	+	0.210932i
$925$	4.93784	+	0.870674i	0.162355	+	0.0286276i
$926$	6.10710	−	3.26786i	0.200692	−	0.107389i
$927$	−3.42264	−	2.87194i	−0.112414	−	0.0943269i
$928$	−18.8284	−	21.8480i	−0.618073	−	0.717195i
$929$	−46.1889	−	16.8114i	−1.51541	−	0.551564i	−0.555413	−	0.831575i	$-0.687440\pi$
$929$	−46.1889	−	16.8114i	−1.51541	−	0.551564i	−0.959997	+	0.280011i	$0.909662\pi$
$930$	22.2964	+	4.67790i	0.731128	+	0.153395i
$931$	20.2281	+	27.8948i	0.662949	+	0.914215i
$932$	−32.1647	−	14.1181i	−1.05359	−	0.462453i
$933$	−4.97704	+	13.6743i	−0.162941	+	0.447677i
$934$	−43.8876	−	1.41687i	−1.43605	−	0.0463613i
$935$	−4.60959	−	3.86790i	−0.150750	−	0.126494i
$936$	−0.716177	−	9.19693i	−0.0234090	−	0.300611i
$937$	−8.27289	+	46.9179i	−0.270263	+	1.53274i	0.483353	+	0.875426i	$0.339419\pi$
$937$	−8.27289	+	46.9179i	−0.270263	+	1.53274i	−0.753616	+	0.657314i	$0.771692\pi$
$938$	17.4988	+	15.6727i	0.571354	+	0.511731i
$939$	13.4190	−	7.74749i	0.437914	−	0.252830i
$940$	1.83351	−	28.3670i	0.0598026	−	0.925229i
$941$	−13.8300	−	37.9976i	−0.450846	−	1.23869i	−0.932130	−	0.362123i	$-0.882052\pi$
$941$	−13.8300	−	37.9976i	−0.450846	−	1.23869i	0.481285	−	0.876564i	$-0.340170\pi$
$942$	2.30193	+	7.02163i	0.0750009	+	0.228777i
$943$	0.681548	−	1.18048i	0.0221942	−	0.0384416i
$944$	9.44019	+	14.7592i	0.307252	+	0.480370i
$945$	−5.21216	+	4.37352i	−0.169552	+	0.142271i
$946$	−1.27935	−	1.62863i	−0.0415952	−	0.0529514i
$947$	42.8139	−	7.54924i	1.39126	−	0.245317i	0.572715	−	0.819755i	$-0.305890\pi$
$947$	42.8139	−	7.54924i	1.39126	−	0.245317i	0.818549	+	0.574437i	$0.194779\pi$
$948$	−11.0676	+	11.5823i	−0.359459	+	0.376176i
$949$			52.8518i			1.71564i
$950$	6.84647	−	9.45764i	0.222129	−	0.306846i
$951$	12.9939			0.421355
$952$	15.0381	+	21.9194i	0.487389	+	0.710411i
$953$	9.22533	+	52.3194i	0.298838	+	1.69479i	0.651182	+	0.758922i	$0.274274\pi$
$953$	9.22533	+	52.3194i	0.298838	+	1.69479i	−0.352344	+	0.935871i	$0.614615\pi$
$954$	7.76234	−	6.09760i	0.251315	−	0.197417i
$955$	−29.5306	−	35.1932i	−0.955587	−	1.13882i
$956$	−21.5125	+	32.2589i	−0.695764	+	1.04333i
$957$	6.19312	+	3.57560i	0.200195	+	0.115583i
$958$	3.91930	+	11.9551i	0.126627	+	0.386253i
$959$	47.8344	−	17.4103i	1.54465	−	0.562208i
$960$	8.85468	+	10.9716i	0.285784	+	0.354107i
$961$	−26.2755	−	45.5106i	−0.847598	−	1.46808i
$962$	8.14627	−	9.09541i	0.262646	−	0.293248i
$963$	11.8759	+	2.09404i	0.382695	+	0.0674795i
$964$	10.1878	−	2.97948i	0.328128	−	0.0959627i
$965$	18.4381	−	21.9736i	0.593542	−	0.707356i
$966$	−3.66589	−	0.118350i	−0.117948	−	0.00380784i
$967$	56.1726	+	20.4452i	1.80639	+	0.657472i	0.997590	+	0.0693900i	$0.0221053\pi$
$967$	56.1726	+	20.4452i	1.80639	+	0.657472i	0.808801	+	0.588082i	$0.200117\pi$
$968$	20.7871	+	14.8532i	0.668122	+	0.477399i
$969$	10.5844	+	0.749791i	0.340020	+	0.0240868i
$970$	−0.505935	+	2.41145i	−0.0162446	+	0.0774270i
$971$	10.7820	−	29.6232i	0.346010	−	0.950655i	−0.637603	−	0.770365i	$-0.720074\pi$
$971$	10.7820	−	29.6232i	0.346010	−	0.950655i	0.983613	−	0.180290i	$-0.0577037\pi$
$972$	1.94311	+	0.473615i	0.0623254	+	0.0151912i
$973$	53.0937	−	63.2747i	1.70211	−	2.02849i
$974$	1.25495	−	0.671513i	0.0402111	−	0.0215166i
$975$	1.07268	−	6.08348i	0.0343533	−	0.194827i
$976$	−6.83458	−	30.5671i	−0.218770	−	0.978429i
$977$	10.8342	+	18.7654i	0.346616	+	0.600357i	0.985646	−	0.168825i	$-0.0539972\pi$
$977$	10.8342	+	18.7654i	0.346616	+	0.600357i	−0.639030	+	0.769182i	$0.720664\pi$
$978$	−31.9371	+	4.57427i	−1.02124	+	0.146269i
$979$	−6.07278	−	16.6848i	−0.194087	−	0.533249i
$980$	−27.6948	+	3.05842i	−0.884677	+	0.0976976i
$981$	−4.78557	−	2.76295i	−0.152791	−	0.0882141i
$982$	6.91238	+	2.77163i	0.220583	+	0.0884462i
$983$	−26.5087	+	22.2434i	−0.845495	+	0.709455i	−0.958793	−	0.284106i	$-0.908303\pi$
$983$	−26.5087	+	22.2434i	−0.845495	+	0.709455i	0.113298	+	0.993561i	$0.463859\pi$
$984$	−5.55751	+	1.43238i	−0.177167	+	0.0456625i
$985$	0.564977	+	3.20414i	0.0180017	+	0.102093i
$986$	9.26215	−	14.9098i	0.294967	−	0.474824i
$987$		−	31.1356i		−	0.991056i
$988$	−10.7659	−	26.3156i	−0.342509	−	0.837212i
$989$		−	0.701397i		−	0.0223031i
$990$	−2.96947	−	1.84467i	−0.0943760	−	0.0586276i
$991$	4.27387	+	24.2383i	0.135764	+	0.769957i	0.974325	+	0.225148i	$0.0722866\pi$
$991$	4.27387	+	24.2383i	0.135764	+	0.769957i	−0.838560	+	0.544809i	$0.816602\pi$
$992$	8.30752	−	51.0355i	0.263764	−	1.62038i
$993$	2.67416	−	2.24388i	0.0848618	−	0.0712075i
$994$	−19.1986	+	47.8809i	−0.608943	+	1.51869i
$995$	18.2790	+	10.5534i	0.579485	+	0.334566i
$996$	0.702153	+	6.35818i	0.0222486	+	0.201467i
$997$	−3.07287	−	8.44264i	−0.0973188	−	0.267381i	0.881475	−	0.472232i	$-0.156551\pi$
$997$	−3.07287	−	8.44264i	−0.0973188	−	0.267381i	−0.978793	+	0.204851i	$0.934329\pi$
$998$	4.20764	+	29.3773i	0.133191	+	0.929923i
$999$	1.32363	+	2.29259i	0.0418777	+	0.0725344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	456.2.bk.a.61.8	yes	240
8.5	even	2	inner	456.2.bk.a.61.3	✓	240
19.5	even	9	inner	456.2.bk.a.157.3	yes	240
152.5	even	18	inner	456.2.bk.a.157.8	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.bk.a.61.3	✓	240	8.5	even	2	inner
456.2.bk.a.61.8	yes	240	1.1	even	1	trivial
456.2.bk.a.157.3	yes	240	19.5	even	9	inner
456.2.bk.a.157.8	yes	240	152.5	even	18	inner

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:	\( N \)	\(=\)	\( 456 = 2^{3} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	456.bk (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20129 - 0.746258i) q^{2} +(0.984808 - 0.173648i) q^{3} +(0.886199 + 1.79294i) q^{4} +(-1.13283 - 1.35006i) q^{5} +(-1.31263 - 0.526318i) q^{6} +(1.93035 - 3.34346i) q^{7} +(0.273416 - 2.81518i) q^{8} +(0.939693 - 0.342020i) q^{9} +(0.353370 + 2.46719i) q^{10} +(-1.21469 + 0.701299i) q^{11} +(1.18408 + 1.61182i) q^{12} +(3.21190 + 0.566345i) q^{13} +(-4.81400 + 2.57593i) q^{14} +(-1.35006 - 1.13283i) q^{15} +(-2.42930 + 3.17781i) q^{16} +(-2.28751 - 0.832585i) q^{17} +(-1.38408 - 0.290387i) q^{18} +(-4.33543 + 0.451693i) q^{19} +(1.41666 - 3.22752i) q^{20} +(1.32044 - 3.62787i) q^{21} +(1.98254 + 0.0640044i) q^{22} +(0.514611 + 0.431810i) q^{23} +(-0.219589 - 2.81989i) q^{24} +(0.328897 - 1.86527i) q^{25} +(-3.43579 - 3.07725i) q^{26} +(0.866025 - 0.500000i) q^{27} +(7.70532 + 0.498037i) q^{28} +(-1.74380 - 4.79106i) q^{29} +(0.776426 + 2.36835i) q^{30} +(4.57031 - 7.91602i) q^{31} +(5.28977 - 2.00459i) q^{32} +(-1.07445 + 0.901573i) q^{33} +(2.12664 + 2.70725i) q^{34} +(-6.70063 + 1.18150i) q^{35} +(1.44598 + 1.38172i) q^{36} +2.64726i q^{37} +(5.54519 + 2.69273i) q^{38} +3.26145 q^{39} +(-4.11039 + 2.82000i) q^{40} +(-0.352348 - 1.99826i) q^{41} +(-4.29356 + 3.37274i) q^{42} +(-0.671130 - 0.799821i) q^{43} +(-2.33384 - 1.55637i) q^{44} +(-1.52626 - 0.881186i) q^{45} +(-0.295956 - 0.902761i) q^{46} +(7.57838 - 2.75831i) q^{47} +(-1.84057 + 3.55138i) q^{48} +(-3.95250 - 6.84594i) q^{49} +(-1.78707 + 1.99529i) q^{50} +(-2.39733 - 0.422715i) q^{51} +(1.83096 + 6.26066i) q^{52} +(-4.48652 + 5.34682i) q^{53} +(-1.41348 - 0.0456327i) q^{54} +(2.32283 + 0.845440i) q^{55} +(-8.88467 - 6.34844i) q^{56} +(-4.19113 + 1.19767i) q^{57} +(-1.48055 + 7.05678i) q^{58} +(1.49805 - 4.11585i) q^{59} +(0.834686 - 3.42449i) q^{60} +(-5.03333 + 5.99848i) q^{61} +(-11.3977 + 6.09881i) q^{62} +(0.670404 - 3.80205i) q^{63} +(-7.85049 - 1.53943i) q^{64} +(-2.87395 - 4.97782i) q^{65} +(1.96354 - 0.281232i) q^{66} +(-1.47156 - 4.04307i) q^{67} +(-0.534409 - 4.83921i) q^{68} +(0.581776 + 0.335888i) q^{69} +(8.93110 + 3.58107i) q^{70} +(7.23784 - 6.07327i) q^{71} +(-0.705921 - 2.73892i) q^{72} +(2.81397 + 15.9588i) q^{73} +(1.97553 - 3.18012i) q^{74} -1.89404i q^{75} +(-4.65192 - 7.37290i) q^{76} +5.41501i q^{77} +(-3.91795 - 2.43388i) q^{78} +(1.39093 + 7.88833i) q^{79} +(7.04221 - 0.320231i) q^{80} +(0.766044 - 0.642788i) q^{81} +(-1.06795 + 2.66344i) q^{82} +(2.76991 + 1.59921i) q^{83} +(7.67474 - 0.847545i) q^{84} +(1.46733 + 4.03144i) q^{85} +(0.209349 + 1.46165i) q^{86} +(-2.54927 - 4.41546i) q^{87} +(1.64217 + 3.61131i) q^{88} +(-2.19823 + 12.4668i) q^{89} +(1.17589 + 2.19754i) q^{90} +(8.09365 - 9.64564i) q^{91} +(-0.318164 + 1.30534i) q^{92} +(3.12628 - 8.58938i) q^{93} +(-11.1623 - 2.34190i) q^{94} +(5.52112 + 5.34138i) q^{95} +(4.86131 - 2.89269i) q^{96} +(0.928978 + 0.338120i) q^{97} +(-0.360727 + 11.1736i) q^{98} +(-0.901573 + 1.07445i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 6 q^{4} + 6 q^{6} - 24 q^{10} + 18 q^{14} - 6 q^{16} + 60 q^{20} - 36 q^{28} - 72 q^{31} - 90 q^{32} + 66 q^{34} - 6 q^{36} + 72 q^{38} - 114 q^{40} - 60 q^{44} + 30 q^{46} + 72 q^{47} + 24 q^{48}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q + 6 * q^4 + 6 * q^6 - 24 * q^10 + 18 * q^14 - 6 * q^16 + 60 * q^20 - 36 * q^28 - 72 * q^31 - 90 * q^32 + 66 * q^34 - 6 * q^36 + 72 * q^38 - 114 * q^40 - 60 * q^44 + 30 * q^46 + 72 * q^47 + 24 * q^48 - 120 * q^49 + 18 * q^50 + 6 * q^52 - 6 * q^54 + 72 * q^58 - 12 * q^60 + 12 * q^62 + 30 * q^64 - 48 * q^66 - 78 * q^68 - 108 * q^70 - 36 * q^72 - 24 * q^73 - 96 * q^74 - 48 * q^76 - 96 * q^78 - 114 * q^80 - 66 * q^82 - 36 * q^84 - 24 * q^86 - 24 * q^88 + 6 * q^90 - 108 * q^94 + 120 * q^95 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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