LMFDB - Embedded newform 504.2.cc.b.293.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.10
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36240 - 0.379297i) q^{2} +(0.713494 + 1.57827i) q^{3} +(1.71227 + 1.03351i) q^{4} +(0.431334 + 0.249031i) q^{5} +(-0.373433 - 2.42086i) q^{6} +(-0.996137 + 2.45106i) q^{7} +(-1.94079 - 2.05751i) q^{8} +(-1.98185 + 2.25217i) q^{9} +O(q^{10})$	\(q+(-1.36240 - 0.379297i) q^{2} +(0.713494 + 1.57827i) q^{3} +(1.71227 + 1.03351i) q^{4} +(0.431334 + 0.249031i) q^{5} +(-0.373433 - 2.42086i) q^{6} +(-0.996137 + 2.45106i) q^{7} +(-1.94079 - 2.05751i) q^{8} +(-1.98185 + 2.25217i) q^{9} +(-0.493193 - 0.502883i) q^{10} +(-0.867283 - 1.50218i) q^{11} +(-0.409457 + 3.43982i) q^{12} +(-2.06976 + 3.58493i) q^{13} +(2.28682 - 2.96150i) q^{14} +(-0.0852827 + 0.858443i) q^{15} +(1.86372 + 3.53928i) q^{16} -0.682941 q^{17} +(3.55431 - 2.31665i) q^{18} -4.00106 q^{19} +(0.481184 + 0.872195i) q^{20} +(-4.57917 + 0.176650i) q^{21} +(0.611815 + 2.37553i) q^{22} +(6.01622 + 3.47346i) q^{23} +(1.86256 - 4.53110i) q^{24} +(-2.37597 - 4.11530i) q^{25} +(4.17960 - 4.09906i) q^{26} +(-4.96856 - 1.52098i) q^{27} +(-4.23885 + 3.16736i) q^{28} +(-4.12748 - 7.14900i) q^{29} +(0.441794 - 1.13719i) q^{30} +(7.47158 + 4.31372i) q^{31} +(-1.19670 - 5.52883i) q^{32} +(1.75204 - 2.44060i) q^{33} +(0.930439 + 0.259037i) q^{34} +(-1.04006 + 0.809159i) q^{35} +(-5.72110 + 1.80806i) q^{36} +1.80500i q^{37} +(5.45104 + 1.51759i) q^{38} +(-7.13475 - 0.708807i) q^{39} +(-0.324745 - 1.37079i) q^{40} +(-2.02753 + 3.51178i) q^{41} +(6.30566 + 1.49620i) q^{42} +(-3.80495 + 2.19679i) q^{43} +(0.0674922 - 3.46848i) q^{44} +(-1.41570 + 0.477895i) q^{45} +(-6.87902 - 7.01418i) q^{46} +(3.51844 + 6.09412i) q^{47} +(-4.25618 + 5.46671i) q^{48} +(-5.01542 - 4.88319i) q^{49} +(1.67610 + 6.50788i) q^{50} +(-0.487275 - 1.07786i) q^{51} +(-7.24905 + 3.99925i) q^{52} -6.29893 q^{53} +(6.19227 + 3.95674i) q^{54} -0.863921i q^{55} +(6.97637 - 2.70743i) q^{56} +(-2.85473 - 6.31473i) q^{57} +(2.91168 + 11.3053i) q^{58} +(-0.661178 - 0.381731i) q^{59} +(-1.03323 + 1.38174i) q^{60} +(5.99548 + 10.3845i) q^{61} +(-8.54310 - 8.71095i) q^{62} +(-3.54601 - 7.10111i) q^{63} +(-0.466686 + 7.98638i) q^{64} +(-1.78552 + 1.03087i) q^{65} +(-3.31269 + 2.66053i) q^{66} +(7.60820 + 4.39260i) q^{67} +(-1.16938 - 0.705825i) q^{68} +(-1.18952 + 11.9735i) q^{69} +(1.72389 - 0.707907i) q^{70} +0.880474i q^{71} +(8.48021 - 0.293305i) q^{72} +8.68914i q^{73} +(0.684629 - 2.45913i) q^{74} +(4.79980 - 6.68615i) q^{75} +(-6.85088 - 4.13512i) q^{76} +(4.54587 - 0.629390i) q^{77} +(9.45153 + 3.67186i) q^{78} +(3.67513 + 6.36551i) q^{79} +(-0.0775039 + 1.99074i) q^{80} +(-1.14453 - 8.92693i) q^{81} +(4.09431 - 4.01542i) q^{82} +(3.97905 - 2.29731i) q^{83} +(-8.02333 - 4.43014i) q^{84} +(-0.294576 - 0.170073i) q^{85} +(6.01710 - 1.54970i) q^{86} +(8.33810 - 11.6150i) q^{87} +(-1.40753 + 4.69985i) q^{88} -14.5608 q^{89} +(2.11001 - 0.114114i) q^{90} +(-6.72513 - 8.64420i) q^{91} +(6.71152 + 12.1653i) q^{92} +(-1.47727 + 14.8700i) q^{93} +(-2.48205 - 9.63717i) q^{94} +(-1.72579 - 0.996387i) q^{95} +(7.87213 - 5.83349i) q^{96} +(11.1727 - 6.45057i) q^{97} +(4.98083 + 8.55519i) q^{98} +(5.10199 + 1.02383i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.36240	−	0.379297i	−0.963362	−	0.268203i
$2$	−1.36240	−	0.379297i	−0.963362	−	0.268203i
$3$	0.713494	+	1.57827i	0.411936	+	0.911213i
$3$	0.713494	+	1.57827i	0.411936	+	0.911213i
$4$	1.71227	+	1.03351i	0.856134	+	0.516754i
$5$	0.431334	+	0.249031i	0.192899	+	0.111370i	0.593339	−	0.804953i	$-0.297809\pi$
$5$	0.431334	+	0.249031i	0.192899	+	0.111370i	−0.400440	+	0.916323i	$0.631143\pi$
$6$	−0.373433	−	2.42086i	−0.152454	−	0.988311i
$7$	−0.996137	+	2.45106i	−0.376504	+	0.926415i
$7$	−0.996137	+	2.45106i	−0.376504	+	0.926415i
$8$	−1.94079	−	2.05751i	−0.686172	−	0.727439i
$9$	−1.98185	+	2.25217i	−0.660617	+	0.750723i
$10$	−0.493193	−	0.502883i	−0.155961	−	0.159026i
$11$	−0.867283	−	1.50218i	−0.261496	−	0.452924i	0.705144	−	0.709064i	$-0.250882\pi$
$11$	−0.867283	−	1.50218i	−0.261496	−	0.452924i	−0.966640	+	0.256140i	$0.917549\pi$
$12$	−0.409457	+	3.43982i	−0.118200	+	0.992990i
$13$	−2.06976	+	3.58493i	−0.574049	+	0.994282i	0.422095	+	0.906551i	$0.361295\pi$
$13$	−2.06976	+	3.58493i	−0.574049	+	0.994282i	−0.996144	+	0.0877304i	$0.972039\pi$
$14$	2.28682	−	2.96150i	0.611178	−	0.791493i
$15$	−0.0852827	+	0.858443i	−0.0220199	+	0.221649i
$16$	1.86372	+	3.53928i	0.465931	+	0.884821i
$17$	−0.682941			−0.165638			−0.0828188	−	0.996565i	$-0.526392\pi$
$17$	−0.682941			−0.165638			−0.0828188	+	0.996565i	$0.526392\pi$
$18$	3.55431	−	2.31665i	0.837760	−	0.546039i
$19$	−4.00106			−0.917905			−0.458953	−	0.888461i	$-0.651775\pi$
$19$	−4.00106			−0.917905			−0.458953	+	0.888461i	$0.651775\pi$
$20$	0.481184	+	0.872195i	0.107596	+	0.195029i
$21$	−4.57917	+	0.176650i	−0.999257	+	0.0385482i
$22$	0.611815	+	2.37553i	0.130439	+	0.506464i
$23$	6.01622	+	3.47346i	1.25447	+	0.724267i	0.971993	−	0.235008i	$-0.0755116\pi$
$23$	6.01622	+	3.47346i	1.25447	+	0.724267i	0.282474	+	0.959275i	$0.408845\pi$
$24$	1.86256	−	4.53110i	0.380193	−	0.924907i
$25$	−2.37597	−	4.11530i	−0.475193	−	0.823059i
$26$	4.17960	−	4.09906i	0.819687	−	0.803892i
$27$	−4.96856	−	1.52098i	−0.956200	−	0.292713i
$28$	−4.23885	+	3.16736i	−0.801067	+	0.598575i
$29$	−4.12748	−	7.14900i	−0.766453	−	1.32754i	−0.939475	−	0.342618i	$-0.888686\pi$
$29$	−4.12748	−	7.14900i	−0.766453	−	1.32754i	0.173022	−	0.984918i	$-0.444647\pi$
$30$	0.441794	−	1.13719i	0.0806601	−	0.207622i
$31$	7.47158	+	4.31372i	1.34193	+	0.774766i	0.987091	−	0.160159i	$-0.0512008\pi$
$31$	7.47158	+	4.31372i	1.34193	+	0.774766i	0.354843	+	0.934926i	$0.384534\pi$
$32$	−1.19670	−	5.52883i	−0.211548	−	0.977368i
$33$	1.75204	−	2.44060i	0.304990	−	0.424854i
$34$	0.930439	+	0.259037i	0.159569	+	0.0444245i
$35$	−1.04006	+	0.809159i	−0.175802	+	0.136773i
$36$	−5.72110	+	1.80806i	−0.953516	+	0.301343i
$37$			1.80500i			0.296740i	0.988932	+	0.148370i	$0.0474026\pi$
$37$			1.80500i			0.296740i	−0.988932	+	0.148370i	$0.952597\pi$
$38$	5.45104	+	1.51759i	0.884275	+	0.246185i
$39$	−7.13475	−	0.708807i	−1.14247	−	0.113500i
$40$	−0.324745	−	1.37079i	−0.0513467	−	0.216741i
$41$	−2.02753	+	3.51178i	−0.316647	+	0.548448i	−0.979786	−	0.200048i	$-0.935890\pi$
$41$	−2.02753	+	3.51178i	−0.316647	+	0.548448i	0.663139	+	0.748496i	$0.269224\pi$
$42$	6.30566	+	1.49620i	0.972985	+	0.230868i
$43$	−3.80495	+	2.19679i	−0.580250	+	0.335007i	−0.761233	−	0.648479i	$-0.775405\pi$
$43$	−3.80495	+	2.19679i	−0.580250	+	0.335007i	0.180983	+	0.983486i	$0.442072\pi$
$44$	0.0674922	−	3.46848i	0.0101748	−	0.522893i
$45$	−1.41570	+	0.477895i	−0.211040	+	0.0712404i
$46$	−6.87902	−	7.01418i	−1.01426	−	1.03418i
$47$	3.51844	+	6.09412i	0.513218	+	0.888919i	0.999882	+	0.0153304i	$0.00488002\pi$
$47$	3.51844	+	6.09412i	0.513218	+	0.888919i	−0.486665	+	0.873589i	$0.661787\pi$
$48$	−4.25618	+	5.46671i	−0.614327	+	0.789052i
$49$	−5.01542	−	4.88319i	−0.716489	−	0.697598i
$50$	1.67610	+	6.50788i	0.237036	+	0.920353i
$51$	−0.487275	−	1.07786i	−0.0682321	−	0.150931i
$52$	−7.24905	+	3.99925i	−1.00526	+	0.554596i
$53$	−6.29893			−0.865224			−0.432612	−	0.901580i	$-0.642408\pi$
$53$	−6.29893			−0.865224			−0.432612	+	0.901580i	$0.642408\pi$
$54$	6.19227	+	3.95674i	0.842661	+	0.538445i
$55$		−	0.863921i		−	0.116491i
$56$	6.97637	−	2.70743i	0.932257	−	0.361796i
$57$	−2.85473	−	6.31473i	−0.378118	−	0.836407i
$58$	2.91168	+	11.3053i	0.382323	+	1.48446i
$59$	−0.661178	−	0.381731i	−0.0860780	−	0.0496972i	0.456343	−	0.889804i	$-0.349159\pi$
$59$	−0.661178	−	0.381731i	−0.0860780	−	0.0496972i	−0.542421	+	0.840107i	$0.682492\pi$
$60$	−1.03323	+	1.38174i	−0.133390	+	0.178382i
$61$	5.99548	+	10.3845i	0.767643	+	1.32960i	0.938838	+	0.344359i	$0.111904\pi$
$61$	5.99548	+	10.3845i	0.767643	+	1.32960i	−0.171196	+	0.985237i	$0.554763\pi$
$62$	−8.54310	−	8.71095i	−1.08497	−	1.10629i
$63$	−3.54601	−	7.10111i	−0.446756	−	0.894656i
$64$	−0.466686	+	7.98638i	−0.0583357	+	0.998297i
$65$	−1.78552	+	1.03087i	−0.221466	+	0.127864i
$66$	−3.31269	+	2.66053i	−0.407764	+	0.327489i
$67$	7.60820	+	4.39260i	0.929490	+	0.536641i	0.886650	−	0.462441i	$-0.153026\pi$
$67$	7.60820	+	4.39260i	0.929490	+	0.536641i	0.0428398	+	0.999082i	$0.486359\pi$
$68$	−1.16938	−	0.705825i	−0.141808	−	0.0855939i
$69$	−1.18952	+	11.9735i	−0.143201	+	1.44144i
$70$	1.72389	−	0.707907i	0.206044	−	0.0846111i
$71$			0.880474i			0.104493i	0.998634	+	0.0522465i	$0.0166382\pi$
$71$			0.880474i			0.104493i	−0.998634	+	0.0522465i	$0.983362\pi$
$72$	8.48021	−	0.293305i	0.999402	−	0.0345663i
$73$			8.68914i			1.01699i	0.861066	+	0.508493i	$0.169797\pi$
$73$			8.68914i			1.01699i	−0.861066	+	0.508493i	$0.830203\pi$
$74$	0.684629	−	2.45913i	0.0795865	−	0.285868i
$75$	4.79980	−	6.68615i	0.554233	−	0.772050i
$76$	−6.85088	−	4.13512i	−0.785850	−	0.474331i
$77$	4.54587	−	0.629390i	0.518050	−	0.0717257i
$78$	9.45153	+	3.67186i	1.07018	+	0.415757i
$79$	3.67513	+	6.36551i	0.413484	+	0.716176i	0.995268	−	0.0971676i	$-0.0309783\pi$
$79$	3.67513	+	6.36551i	0.413484	+	0.716176i	−0.581784	+	0.813344i	$0.697645\pi$
$80$	−0.0775039	+	1.99074i	−0.00866520	+	0.222571i
$81$	−1.14453	−	8.92693i	−0.127170	−	0.991881i
$82$	4.09431	−	4.01542i	0.452141	−	0.443429i
$83$	3.97905	−	2.29731i	0.436758	−	0.252162i	−0.265464	−	0.964121i	$-0.585525\pi$
$83$	3.97905	−	2.29731i	0.436758	−	0.252162i	0.702221	+	0.711959i	$0.252192\pi$
$84$	−8.02333	−	4.43014i	−0.875418	−	0.483367i
$85$	−0.294576	−	0.170073i	−0.0319512	−	0.0184471i
$86$	6.01710	−	1.54970i	0.648841	−	0.167109i
$87$	8.33810	−	11.6150i	0.893938	−	1.24526i
$88$	−1.40753	+	4.69985i	−0.150044	+	0.501006i
$89$	−14.5608			−1.54344			−0.771721	−	0.635962i	$-0.780604\pi$
$89$	−14.5608			−1.54344			−0.771721	+	0.635962i	$0.780604\pi$
$90$	2.11001	−	0.114114i	0.222415	−	0.0120287i
$91$	−6.72513	−	8.64420i	−0.704985	−	0.906159i
$92$	6.71152	+	12.1653i	0.699724	+	1.26832i
$93$	−1.47727	+	14.8700i	−0.153185	+	1.54194i
$94$	−2.48205	−	9.63717i	−0.256004	−	0.993998i
$95$	−1.72579	−	0.996387i	−0.177063	−	0.102227i
$96$	7.87213	−	5.83349i	0.803445	−	0.595378i
$97$	11.1727	−	6.45057i	1.13442	−	0.654956i	0.189375	−	0.981905i	$-0.439354\pi$
$97$	11.1727	−	6.45057i	1.13442	−	0.654956i	0.945042	+	0.326949i	$0.106020\pi$
$98$	4.98083	+	8.55519i	0.503140	+	0.864205i
$99$	5.10199	+	1.02383i	0.512769	+	0.102898i
$100$	0.184898	−	9.50207i	0.0184898	−	0.950207i
$101$	−2.23797	+	1.29209i	−0.222686	+	0.128568i	−0.607194	−	0.794554i	$-0.707705\pi$
$101$	−2.23797	+	1.29209i	−0.222686	+	0.128568i	0.384507	+	0.923122i	$0.374371\pi$
$102$	0.255033	+	1.65330i	0.0252520	+	0.163701i
$103$	−5.59021	−	3.22751i	−0.550820	−	0.318016i	0.198633	−	0.980074i	$-0.436350\pi$
$103$	−5.59021	−	3.22751i	−0.550820	−	0.318016i	−0.749453	+	0.662058i	$0.769683\pi$
$104$	11.3930	−	2.69904i	1.11718	−	0.264663i
$105$	−2.01914	−	1.06416i	−0.197048	−	0.103851i
$106$	8.58166	+	2.38916i	0.833524	+	0.232056i
$107$	7.87200			0.761015			0.380508	−	0.924778i	$-0.375749\pi$
$107$	7.87200			0.761015			0.380508	+	0.924778i	$0.375749\pi$
$108$	−6.93557	−	7.73937i	−0.667375	−	0.744722i
$109$		−	9.47593i		−	0.907629i	−0.891096	−	0.453815i	$-0.850063\pi$
$109$		−	9.47593i		−	0.907629i	0.891096	−	0.453815i	$-0.149937\pi$
$110$	−0.327683	+	1.17701i	−0.0312433	+	0.112223i
$111$	−2.84877	+	1.28785i	−0.270393	+	0.122238i
$112$	−10.5315	+	1.04249i	−0.995136	+	0.0985061i
$113$	16.4082	+	9.47329i	1.54356	+	0.891172i	0.998610	+	0.0527008i	$0.0167830\pi$
$113$	16.4082	+	9.47329i	1.54356	+	0.891172i	0.544945	+	0.838472i	$0.316550\pi$
$114$	1.49413	+	9.68599i	0.139938	+	0.907176i
$115$	1.73000	+	2.99645i	0.161323	+	0.279420i
$116$	0.321201	−	16.5068i	0.0298228	−	1.53262i
$117$	−3.97191	−	11.7663i	−0.367204	−	1.08779i
$118$	0.756000	+	0.770853i	0.0695954	+	0.0709628i
$119$	0.680303	−	1.67393i	0.0623633	−	0.153449i
$120$	1.93177	−	1.49059i	0.176346	−	0.136071i
$121$	3.99564	−	6.92065i	0.363240	−	0.629150i
$122$	−4.22944	−	16.4219i	−0.382916	−	1.48677i
$123$	−6.98916	−	0.694344i	−0.630191	−	0.0626068i
$124$	8.33508	+	15.1082i	0.748512	+	1.35675i
$125$		−	4.85707i		−	0.434429i
$126$	2.13766	+	11.0195i	0.190438	+	0.981699i
$127$	13.6404			1.21039			0.605196	−	0.796076i	$-0.293095\pi$
$127$	13.6404			1.21039			0.605196	+	0.796076i	$0.293095\pi$
$128$	3.66502	−	10.7036i	0.323945	−	0.946076i
$129$	−6.18193	−	4.43783i	−0.544289	−	0.390729i
$130$	2.82360	−	0.727216i	0.247646	−	0.0637810i
$131$	0.341929	+	0.197413i	0.0298745	+	0.0172480i	0.514863	−	0.857273i	$-0.327843\pi$
$131$	0.341929	+	0.197413i	0.0298745	+	0.0172480i	−0.484988	+	0.874521i	$0.661176\pi$
$132$	5.52234	−	2.36822i	0.480658	−	0.206127i
$133$	3.98560	−	9.80684i	0.345595	−	0.850361i
$134$	−8.69932	−	8.87024i	−0.751507	−	0.766272i
$135$	−1.76434	−	1.89338i	−0.151850	−	0.162956i
$136$	1.32544	+	1.40516i	0.113656	+	0.120491i
$137$	0.708481	−	0.409042i	0.0605296	−	0.0349468i	−0.469430	−	0.882970i	$-0.655540\pi$
$137$	0.708481	−	0.409042i	0.0605296	−	0.0349468i	0.529959	+	0.848023i	$0.322207\pi$
$138$	6.16210	−	15.8615i	0.524553	−	1.35022i
$139$	8.83461	−	15.3020i	0.749342	−	1.29790i	−0.198797	−	0.980041i	$-0.563703\pi$
$139$	8.83461	−	15.3020i	0.749342	−	1.29790i	0.948139	−	0.317857i	$-0.102963\pi$
$140$	−2.61713	+	0.310588i	−0.221188	+	0.0262494i
$141$	−7.10776	+	9.90117i	−0.598582	+	0.833829i
$142$	0.333961	−	1.19956i	0.0280254	−	0.100665i
$143$	7.18028			0.600445
$144$	−11.6647	−	2.81692i	−0.972057	−	0.234743i
$145$		−	4.11148i		−	0.341440i
$146$	3.29576	−	11.8381i	0.272759	−	0.979727i
$147$	4.12850	−	11.3998i	0.340513	−	0.940240i
$148$	−1.86548	+	3.09064i	−0.153341	+	0.254049i
$149$	−10.5766	+	18.3193i	−0.866471	+	1.50077i	−0.000892544		1.00000i	$0.500284\pi$
$149$	−10.5766	+	18.3193i	−0.866471	+	1.50077i	−0.865579	+	0.500773i	$0.833049\pi$
$150$	−9.07528	+	7.28867i	−0.740993	+	0.595117i
$151$	−0.734951	−	1.27297i	−0.0598094	−	0.103593i	0.834570	−	0.550901i	$-0.185716\pi$
$151$	−0.734951	−	1.27297i	−0.0598094	−	0.103593i	−0.894380	+	0.447308i	$0.852383\pi$
$152$	7.76520	+	8.23221i	0.629841	+	0.667720i
$153$	1.35349	−	1.53810i	0.109423	−	0.124348i
$154$	−6.43202	−	0.866751i	−0.518307	−	0.0698448i
$155$	2.14850	+	3.72131i	0.172571	+	0.298903i
$156$	−11.4840	−	8.58748i	−0.919459	−	0.687549i
$157$	2.07492	−	3.59387i	0.165597	−	0.286822i	−0.771270	−	0.636508i	$-0.780378\pi$
$157$	2.07492	−	3.59387i	0.165597	−	0.286822i	0.936867	+	0.349686i	$0.113712\pi$
$158$	−2.59258	−	10.0663i	−0.206255	−	0.800835i
$159$	−4.49425	−	9.94138i	−0.356417	−	0.788403i
$160$	0.860672	−	2.68279i	0.0680421	−	0.212093i
$161$	−14.5067	+	11.2861i	−1.14328	+	0.889468i
$162$	−1.82665	+	12.5962i	−0.143515	+	0.989648i
$163$			15.6123i			1.22285i	0.791303	+	0.611424i	$0.209403\pi$
$163$			15.6123i			1.22285i	−0.791303	+	0.611424i	$0.790597\pi$
$164$	−7.10113	+	3.91765i	−0.554505	+	0.305917i
$165$	1.36350	−	0.616403i	0.106148	−	0.0479869i
$166$	−6.29242	+	1.62061i	−0.488387	+	0.125784i
$167$	−0.782182	+	1.35478i	−0.0605271	+	0.104836i	−0.894701	−	0.446665i	$-0.852611\pi$
$167$	−0.782182	+	1.35478i	−0.0605271	+	0.104836i	0.834174	+	0.551501i	$0.185945\pi$
$168$	9.25066	+	9.07884i	0.713704	+	0.700448i
$169$	−2.06783	−	3.58159i	−0.159064	−	0.275507i
$170$	0.336822	+	0.343440i	0.0258331	+	0.0263406i
$171$	7.92950	−	9.01106i	0.606384	−	0.689093i
$172$	−8.78550	−	0.170955i	−0.669888	−	0.0130352i
$173$	−1.98290	+	1.14483i	−0.150757	+	0.0870396i	−0.573481	−	0.819219i	$-0.694407\pi$
$173$	−1.98290	+	1.14483i	−0.150757	+	0.0870396i	0.422724	+	0.906259i	$0.361074\pi$
$174$	−15.7654	+	12.6617i	−1.19517	+	0.959881i
$175$	12.4536	−	1.72425i	0.941407	−	0.130341i
$176$	3.70026	−	5.86921i	0.278918	−	0.442408i
$177$	0.130727	−	1.31588i	0.00982604	−	0.0989075i
$178$	19.8376	+	5.52286i	1.48689	+	0.413956i
$179$	24.7326			1.84860			0.924299	−	0.381669i	$-0.124651\pi$
$179$	24.7326			1.84860			0.924299	+	0.381669i	$0.124651\pi$
$180$	−2.91797	−	0.644853i	−0.217492	−	0.0480645i
$181$	14.1251			1.04991			0.524955	−	0.851130i	$-0.324082\pi$
$181$	14.1251			1.04991			0.524955	+	0.851130i	$0.324082\pi$
$182$	5.88360	+	14.3277i	0.436122	+	1.06204i
$183$	−12.1117	+	16.8717i	−0.895325	+	1.24719i
$184$	−4.52952	−	19.1197i	−0.333920	−	1.40952i
$185$	−0.449500	+	0.778557i	−0.0330479	+	0.0572406i
$186$	7.65275	−	19.6985i	0.561127	−	1.44436i
$187$	0.592303	+	1.02590i	0.0433135	+	0.0750212i
$188$	−0.273806	+	14.0711i	−0.0199694	+	1.02624i
$189$	8.67739	−	10.6632i	0.631187	−	0.775631i
$190$	1.97329	+	2.01207i	0.143158	+	0.145971i
$191$	2.77844	−	1.60413i	0.201041	−	0.116071i	−0.396100	−	0.918207i	$-0.629637\pi$
$191$	2.77844	−	1.60413i	0.201041	−	0.116071i	0.597141	+	0.802136i	$0.296303\pi$
$192$	−12.9376	+	4.96168i	−0.933692	+	0.358078i
$193$	7.20125	−	12.4729i	0.518357	−	0.897821i	−0.481415	−	0.876493i	$-0.659877\pi$
$193$	7.20125	−	12.4729i	0.518357	−	0.897821i	0.999773	−	0.0213285i	$-0.00678957\pi$
$194$	−17.6684	+	4.55048i	−1.26852	+	0.326706i
$195$	−2.90095	−	2.08251i	−0.207741	−	0.149131i
$196$	−3.54093	−	13.5448i	−0.252924	−	0.967486i
$197$	0.305141			0.0217404			0.0108702	−	0.999941i	$-0.496540\pi$
$197$	0.305141			0.0217404			0.0108702	+	0.999941i	$0.496540\pi$
$198$	−6.56261	−	3.33003i	−0.466385	−	0.236655i
$199$			22.8476i			1.61962i	0.586691	+	0.809811i	$0.300430\pi$
$199$			22.8476i			1.61962i	−0.586691	+	0.809811i	$0.699570\pi$
$200$	−3.85601	+	12.8755i	−0.272661	+	0.910435i
$201$	−1.50428	+	15.1419i	−0.106104	+	1.06803i
$202$	3.53910	−	0.911493i	0.249010	−	0.0641324i
$203$	21.6342	−	2.99532i	1.51842	−	0.210231i
$204$	0.279635	−	2.34919i	0.0195784	−	0.164476i
$205$	−1.74908	+	1.00983i	−0.122161	+	0.0705299i
$206$	6.39192	+	6.51751i	0.445346	+	0.454096i
$207$	−19.7461	+	6.66564i	−1.37245	+	0.463294i
$208$	−16.5456	−	0.644155i	−1.14723	−	0.0446641i
$209$	3.47005	+	6.01030i	0.240028	+	0.415741i
$210$	2.34725	+	2.21567i	0.161976	+	0.152895i
$211$	0.199688	+	0.115290i	0.0137471	+	0.00793689i	0.506858	−	0.862030i	$-0.330807\pi$
$211$	0.199688	+	0.115290i	0.0137471	+	0.00793689i	−0.493111	+	0.869967i	$0.664140\pi$
$212$	−10.7854	−	6.50999i	−0.740748	−	0.447108i
$213$	−1.38962	+	0.628214i	−0.0952154	+	0.0430445i
$214$	−10.7248	−	2.98583i	−0.733133	−	0.204107i
$215$	−2.18828			−0.149239
$216$	6.51350	+	13.1748i	0.443187	+	0.896429i
$217$	−18.0159	+	14.0163i	−1.22300	+	0.951485i
$218$	−3.59419	+	12.9100i	−0.243429	+	0.874376i
$219$	−13.7138	+	6.19965i	−0.926691	+	0.418934i
$220$	0.892870	−	1.47927i	0.0601973	−	0.0997320i
$221$	1.41353	−	2.44830i	0.0950840	−	0.164690i
$222$	4.36964	−	0.674046i	0.293271	−	0.0452390i
$223$	3.21702	−	1.85735i	0.215428	−	0.124377i	−0.388404	−	0.921489i	$-0.626973\pi$
$223$	3.21702	−	1.85735i	0.215428	−	0.124377i	0.603831	+	0.797112i	$0.293640\pi$
$224$	14.7436	+	2.57429i	0.985097	+	0.172002i
$225$	13.9772	+	2.80483i	0.931810	+	0.186988i
$226$	−18.7614	−	19.1300i	−1.24799	−	1.27251i
$227$	−19.1964	+	11.0830i	−1.27411	+	0.735606i	−0.975758	−	0.218851i	$-0.929769\pi$
$227$	−19.1964	+	11.0830i	−1.27411	+	0.735606i	−0.298349	+	0.954457i	$0.596436\pi$
$228$	1.63826	−	13.7629i	0.108497	−	0.911471i
$229$	−7.23036	+	12.5234i	−0.477796	+	0.827566i	−0.999676	−	0.0254523i	$-0.991897\pi$
$229$	−7.23036	+	12.5234i	−0.477796	+	0.827566i	0.521880	+	0.853019i	$0.325231\pi$
$230$	−1.22041	−	4.73854i	−0.0804714	−	0.312450i
$231$	4.23680	+	6.72553i	0.278761	+	0.442507i
$232$	−6.69857	+	22.3670i	−0.439783	+	1.46847i
$233$			17.1930i			1.12635i	0.826337	+	0.563177i	$0.190421\pi$
$233$			17.1930i			1.12635i	−0.826337	+	0.563177i	$0.809579\pi$
$234$	0.948432	+	17.5369i	0.0620009	+	1.14642i
$235$			3.50481i			0.228628i
$236$	−0.737592	−	1.33696i	−0.0480131	−	0.0870286i
$237$	−7.42429	+	10.3421i	−0.482260	+	0.671791i
$238$	−1.56176	+	2.02253i	−0.101234	+	0.131101i
$239$	−1.78173	−	1.02868i	−0.115250	−	0.0665399i	0.441267	−	0.897376i	$-0.354529\pi$
$239$	−1.78173	−	1.02868i	−0.115250	−	0.0665399i	−0.556517	+	0.830836i	$0.687863\pi$
$240$	−3.19722	+	1.29806i	−0.206379	+	0.0837894i
$241$	5.83909	−	3.37120i	0.376129	−	0.217158i	−0.300004	−	0.953938i	$-0.596988\pi$
$241$	5.83909	−	3.37120i	0.376129	−	0.217158i	0.676133	+	0.736780i	$0.263655\pi$
$242$	−8.06864	+	7.91316i	−0.518672	+	0.508677i
$243$	13.2725	−	8.17569i	0.851429	−	0.524471i
$244$	−0.466569	+	23.9774i	−0.0298690	+	1.53499i
$245$	−0.947258	−	3.35528i	−0.0605181	−	0.214361i
$246$	9.25867	+	3.59694i	0.590311	+	0.229332i
$247$	8.28124	−	14.3435i	0.526923	−	0.912657i
$248$	−5.62523	−	23.7448i	−0.357203	−	1.50780i
$249$	6.46479	+	4.64089i	0.409690	+	0.294104i
$250$	−1.84227	+	6.61727i	−0.116515	+	0.418513i
$251$		−	11.7323i		−	0.740537i	−0.928925	−	0.370268i	$-0.879266\pi$
$251$		−	11.7323i		−	0.740537i	0.928925	−	0.370268i	$-0.120734\pi$
$252$	1.26733	−	15.8238i	0.0798343	−	0.996808i
$253$		−	12.0499i		−	0.757571i
$254$	−18.5837	−	5.17377i	−1.16605	−	0.324631i
$255$	0.0582430	−	0.586266i	0.00364732	−	0.0367134i
$256$	−9.05307	+	13.1925i	−0.565817	+	0.824531i
$257$	0.979848	−	1.69715i	0.0611212	−	0.105865i	−0.833846	−	0.551998i	$-0.813866\pi$
$257$	0.979848	−	1.69715i	0.0611212	−	0.105865i	0.894967	+	0.446133i	$0.147199\pi$
$258$	6.73901	+	8.39089i	0.419553	+	0.522394i
$259$	−4.42416	−	1.79802i	−0.274904	−	0.111724i
$260$	−4.12270	−	0.0802225i	−0.255679	−	0.00497519i
$261$	24.2808	+	4.87248i	1.50294	+	0.301599i
$262$	−0.390966	−	0.398648i	−0.0241540	−	0.0246285i
$263$	−2.55058	+	1.47258i	−0.157276	+	0.0908031i	−0.576572	−	0.817046i	$-0.695610\pi$
$263$	−2.55058	+	1.47258i	−0.157276	+	0.0908031i	0.419297	+	0.907849i	$0.362277\pi$
$264$	−8.42189	+	1.13186i	−0.518331	+	0.0696609i
$265$	−2.71694	−	1.56863i	−0.166900	−	0.0963600i
$266$	−9.14969	+	11.8491i	−0.561003	+	0.726516i
$267$	−10.3890	−	22.9808i	−0.635799	−	1.40640i
$268$	8.48750	+	15.3844i	0.518456	+	0.939754i
$269$		−	27.1051i		−	1.65263i	−0.563211	−	0.826313i	$-0.690434\pi$
$269$		−	27.1051i		−	1.65263i	0.563211	−	0.826313i	$-0.309566\pi$
$270$	1.68559	+	3.24875i	0.102581	+	0.197712i
$271$		−	4.16264i		−	0.252862i	−0.991975	−	0.126431i	$-0.959648\pi$
$271$		−	4.16264i		−	0.252862i	0.991975	−	0.126431i	$-0.0403522\pi$
$272$	−1.27281	−	2.41712i	−0.0771756	−	0.146560i
$273$	8.84452	−	16.7816i	0.535294	−	1.01567i
$274$	−1.12038	+	0.288554i	−0.0676848	+	0.0174322i
$275$	−4.12127	+	7.13825i	−0.248522	+	0.430453i
$276$	−14.4115	+	19.2724i	−0.867468	+	1.16006i
$277$	4.93257	−	2.84782i	0.296369	−	0.171109i	−0.344441	−	0.938808i	$-0.611932\pi$
$277$	4.93257	−	2.84782i	0.296369	−	0.171109i	0.640811	+	0.767699i	$0.278598\pi$
$278$	−17.8403	+	17.4965i	−1.06999	+	1.04937i
$279$	−24.5228	+	8.27811i	−1.46814	+	0.495597i
$280$	3.68338	+	0.569525i	0.220124	+	0.0340356i
$281$	−14.6273	+	8.44505i	−0.872589	+	0.503790i	−0.868208	−	0.496201i	$-0.834728\pi$
$281$	−14.6273	+	8.44505i	−0.872589	+	0.503790i	−0.00438136	+	0.999990i	$0.501395\pi$
$282$	13.4391	−	10.7934i	0.800287	−	0.642738i
$283$	7.99825	−	13.8534i	0.475447	−	0.823498i	−0.524158	−	0.851621i	$-0.675620\pi$
$283$	7.99825	−	13.8534i	0.475447	−	0.823498i	0.999604	+	0.0281233i	$0.00895312\pi$
$284$	−0.909977	+	1.50761i	−0.0539972	+	0.0894601i
$285$	0.341221	−	3.43468i	0.0202122	−	0.203453i
$286$	−9.78242	−	2.72346i	−0.578446	−	0.161041i
$287$	−6.58790	−	8.46782i	−0.388872	−	0.499839i
$288$	14.8235	+	8.26215i	0.873485	+	0.486852i
$289$	−16.5336			−0.972564
$290$	−1.55947	+	5.60148i	−0.0915752	+	0.328930i
$291$	18.1524	+	13.0311i	1.06411	+	0.763895i
$292$	−8.98029	+	14.8781i	−0.525532	+	0.870677i
$293$	12.1367	+	7.00713i	0.709034	+	0.409361i	0.810703	−	0.585457i	$-0.199085\pi$
$293$	12.1367	+	7.00713i	0.709034	+	0.409361i	−0.101669	+	0.994818i	$0.532418\pi$
$294$	−9.94858	+	13.9652i	−0.580213	+	0.814465i
$295$	−0.190126	−	0.329308i	−0.0110696	−	0.0191730i
$296$	3.71380	−	3.50311i	0.215860	−	0.203614i
$297$	2.02437	+	8.78279i	0.117466	+	0.509629i
$298$	21.3580	−	20.9465i	1.23724	−	1.21340i
$299$	−24.9043	+	14.3785i	−1.44025	+	0.831530i
$300$	15.1287	−	6.48786i	0.873457	−	0.374576i
$301$	−1.59422	−	11.5145i	−0.0918892	−	0.663684i
$302$	0.518463	+	2.01306i	0.0298342	+	0.115839i
$303$	−3.63605	−	2.61021i	−0.208885	−	0.149953i
$304$	−7.45686	−	14.1609i	−0.427680	−	0.812182i
$305$			5.97224i			0.341969i
$306$	−2.42739	+	1.58213i	−0.138765	+	0.0904445i
$307$	−31.4731			−1.79627			−0.898133	−	0.439724i	$-0.855076\pi$
$307$	−31.4731			−1.79627			−0.898133	+	0.439724i	$0.855076\pi$
$308$	8.43422	+	3.62051i	0.480585	+	0.206297i
$309$	1.10529	−	11.1256i	0.0628776	−	0.632916i
$310$	−1.51563	−	5.88483i	−0.0860822	−	0.334236i
$311$	7.97396	−	13.8113i	0.452162	−	0.783167i	−0.546358	−	0.837551i	$-0.683986\pi$
$311$	7.97396	−	13.8113i	0.452162	−	0.783167i	0.998520	+	0.0543845i	$0.0173197\pi$
$312$	12.3887	+	16.0554i	0.701369	+	0.908961i
$313$	26.6531	−	15.3882i	1.50652	−	0.869791i	0.506550	−	0.862210i	$-0.330920\pi$
$313$	26.6531	−	15.3882i	1.50652	−	0.869791i	0.999971	−	0.00758028i	$-0.00241290\pi$
$314$	−4.19001	+	4.10928i	−0.236456	+	0.231900i
$315$	0.238880	−	3.94602i	0.0134594	−	0.222333i
$316$	−0.285999	+	14.6977i	−0.0160887	+	0.826812i
$317$	7.94255	+	13.7569i	0.446098	+	0.772664i	0.998128	−	0.0611599i	$-0.0194800\pi$
$317$	7.94255	+	13.7569i	0.446098	+	0.772664i	−0.552030	+	0.833824i	$0.686147\pi$
$318$	2.35223	+	15.2488i	0.131906	+	0.855110i
$319$	−7.15938	+	12.4004i	−0.400848	+	0.694290i
$320$	−2.19015	+	3.32858i	−0.122433	+	0.186073i
$321$	5.61663	+	12.4241i	0.313490	+	0.693447i
$322$	24.0446	−	9.87383i	1.33996	−	0.550247i
$323$	2.73249			0.152040
$324$	7.26631	−	16.4682i	0.403684	−	0.914899i
$325$	19.6708			1.09114
$326$	5.92169	−	21.2702i	0.327972	−	1.17805i
$327$	14.9555	−	6.76102i	0.827043	−	0.373885i
$328$	11.1605	−	2.64397i	0.616237	−	0.145989i
$329$	−18.4419	+	2.55335i	−1.01674	+	0.140771i
$330$	−2.09143	+	0.322617i	−0.115129	+	0.0177595i
$331$	−19.7167	+	11.3834i	−1.08373	+	0.625690i	−0.931899	−	0.362717i	$-0.881849\pi$
$331$	−19.7167	+	11.3834i	−1.08373	+	0.625690i	−0.151827	+	0.988407i	$0.548516\pi$
$332$	9.18749	+	0.178777i	0.504229	+	0.00981165i
$333$	−4.06516	−	3.57723i	−0.222769	−	0.196031i
$334$	1.57951	−	1.54907i	0.0864269	−	0.0847615i
$335$	2.18779	+	3.78936i	0.119532	+	0.207035i
$336$	−9.15952	−	15.8778i	−0.499693	−	0.866203i
$337$	3.96559	−	6.86860i	0.216019	−	0.374157i	−0.737568	−	0.675273i	$-0.764026\pi$
$337$	3.96559	−	6.86860i	0.216019	−	0.374157i	0.953587	+	0.301116i	$0.0973592\pi$
$338$	1.45873	+	5.66389i	0.0793445	+	0.308075i
$339$	−3.24421	+	32.6557i	−0.176201	+	1.77361i
$340$	−0.328621	−	0.595658i	−0.0178220	−	0.0323041i
$341$		−	14.9649i		−	0.810392i
$342$	−14.2210	+	9.26903i	−0.768984	+	0.501212i
$343$	16.9651	−	7.42879i	0.916027	−	0.401117i
$344$	11.9045	+	3.56522i	0.641849	+	0.192224i
$345$	−3.49485	+	4.86835i	−0.188156	+	0.262103i
$346$	3.13573	−	0.807605i	0.168578	−	0.0434171i
$347$	−15.0302	+	26.0330i	−0.806862	+	1.39753i	0.108165	+	0.994133i	$0.465503\pi$
$347$	−15.0302	+	26.0330i	−0.806862	+	1.39753i	−0.915027	+	0.403393i	$0.867831\pi$
$348$	26.2813	−	11.2706i	1.40882	−	0.604165i
$349$	−9.58970	−	16.6098i	−0.513325	−	0.889104i	−0.999881	−	0.0154550i	$-0.995080\pi$
$349$	−9.58970	−	16.6098i	−0.513325	−	0.889104i	0.486556	−	0.873649i	$-0.338253\pi$
$350$	−17.6208	−	2.37451i	−0.941874	−	0.126923i
$351$	15.7364	−	14.6639i	0.839945	−	0.782701i
$352$	−7.26741	+	6.59271i	−0.387354	+	0.351393i
$353$	−18.2058	−	31.5333i	−0.968995	−	1.67835i	−0.698474	−	0.715635i	$-0.746137\pi$
$353$	−18.2058	−	31.5333i	−0.968995	−	1.67835i	−0.270521	−	0.962714i	$-0.587196\pi$
$354$	−0.677211	+	1.74317i	−0.0359934	+	0.0926484i
$355$	−0.219265	+	0.379779i	−0.0116374	+	0.0201566i
$356$	−24.9320	−	15.0487i	−1.32139	−	0.797579i
$357$	3.12730	−	0.120642i	0.165514	−	0.00638503i
$358$	−33.6956	−	9.38098i	−1.78087	−	0.495800i
$359$		−	24.4053i		−	1.28806i	−0.765000	−	0.644031i	$-0.777261\pi$
$359$		−	24.4053i		−	1.28806i	0.765000	−	0.644031i	$-0.222739\pi$
$360$	3.73085	+	1.98532i	0.196633	+	0.104636i
$361$	−2.99155			−0.157450
$362$	−19.2440	−	5.35760i	−1.01144	−	0.281589i
$363$	13.7735	+	1.36834i	0.722921	+	0.0718192i
$364$	−2.58138	−	21.7517i	−0.135301	−	1.14010i
$365$	−2.16386	+	3.74792i	−0.113262	+	0.196175i
$366$	22.9004	−	18.3921i	1.19702	−	0.961371i
$367$	−16.6656	+	9.62191i	−0.869939	+	0.502260i	−0.867328	−	0.497737i	$-0.834165\pi$
$367$	−16.6656	+	9.62191i	−0.869939	+	0.502260i	−0.00261134	+	0.999997i	$0.500831\pi$
$368$	−1.08102	+	27.7667i	−0.0563519	+	1.44744i
$369$	−3.89087	−	11.5262i	−0.202550	−	0.600028i
$370$	0.907703	−	0.890212i	0.0471892	−	0.0462799i
$371$	6.27459	−	15.4391i	0.325761	−	0.801556i
$372$	−17.8977	+	23.9346i	−0.927952	+	1.24095i
$373$	16.1547	+	9.32692i	0.836458	+	0.482929i	0.856059	−	0.516879i	$-0.172906\pi$
$373$	16.1547	+	9.32692i	0.836458	+	0.482929i	−0.0196005	+	0.999808i	$0.506239\pi$
$374$	−0.417834	−	1.62234i	−0.0216057	−	0.0838894i
$375$	7.66575	−	3.46549i	0.395857	−	0.178957i
$376$	5.71016	−	19.0666i	0.294479	−	0.983286i
$377$	34.1716			1.75993
$378$	−15.8666	+	11.2362i	−0.816089	+	0.577927i
$379$		−	5.64138i		−	0.289778i	−0.989448	−	0.144889i	$-0.953717\pi$
$379$		−	5.64138i		−	0.289778i	0.989448	−	0.144889i	$-0.0462825\pi$
$380$	−1.92525	−	3.48970i	−0.0987630	−	0.179018i
$381$	9.73237	+	21.5282i	0.498605	+	1.10293i
$382$	−4.39379	+	1.13162i	−0.224806	+	0.0578986i
$383$	−9.03429	+	15.6479i	−0.461631	+	0.799568i	−0.999042	−	0.0437521i	$-0.986069\pi$
$383$	−9.03429	+	15.6479i	−0.461631	+	0.799568i	0.537412	+	0.843320i	$0.319402\pi$
$384$	19.5081	−	1.85260i	0.995521	−	0.0945401i
$385$	2.11753	+	0.860584i	0.107919	+	0.0438594i
$386$	−14.5419	+	14.2617i	−0.740164	+	0.725902i
$387$	2.59331	−	12.9231i	0.131825	−	0.656919i
$388$	25.7974	+	0.501985i	1.30966	+	0.0254844i
$389$	−14.8050	−	25.6430i	−0.750643	−	1.30015i	−0.947511	−	0.319722i	$-0.896410\pi$
$389$	−14.8050	−	25.6430i	−0.750643	−	1.30015i	0.196868	−	0.980430i	$-0.436923\pi$
$390$	3.16236	+	3.93752i	0.160132	+	0.199384i
$391$	−4.10872	−	2.37217i	−0.207787	−	0.119966i
$392$	−0.313335	+	19.7965i	−0.0158258	+	0.999875i
$393$	−0.0676056	+	0.680508i	−0.00341025	+	0.0343271i
$394$	−0.415724	−	0.115739i	−0.0209439	−	0.00583084i
$395$			3.66088i			0.184199i
$396$	7.67784	+	7.02601i	0.385826	+	0.353070i
$397$	0.848670			0.0425935			0.0212968	−	0.999773i	$-0.493221\pi$
$397$	0.848670			0.0425935			0.0212968	+	0.999773i	$0.493221\pi$
$398$	8.66601	−	31.1275i	0.434388	−	1.56028i
$399$	18.3215	−	0.706787i	0.917223	−	0.0353836i
$400$	10.1371	−	16.0790i	0.506853	−	0.803950i
$401$	−7.16720	−	4.13798i	−0.357913	−	0.206641i	0.310252	−	0.950654i	$-0.399587\pi$
$401$	−7.16720	−	4.13798i	−0.357913	−	0.206641i	−0.668165	+	0.744013i	$0.732920\pi$
$402$	7.79269	−	20.0587i	0.388664	−	1.00044i
$403$	−30.9288	+	17.8567i	−1.54067	+	0.889507i
$404$	−5.16740	−	0.100551i	−0.257088	−	0.00500260i
$405$	1.72941	−	4.13551i	0.0859349	−	0.205495i
$406$	−30.6105	−	4.12495i	−1.51917	−	0.204718i
$407$	2.71143	−	1.56544i	0.134400	−	0.0775961i
$408$	−1.27202	+	3.09448i	−0.0629742	+	0.153199i
$409$	12.2324	+	7.06236i	0.604851	+	0.349211i	0.770948	−	0.636898i	$-0.219783\pi$
$409$	12.2324	+	7.06236i	0.604851	+	0.349211i	−0.166096	+	0.986110i	$0.553116\pi$
$410$	2.76598	−	0.712376i	0.136602	−	0.0351818i
$411$	1.15107	+	0.826323i	0.0567783	+	0.0407595i
$412$	−6.23628	−	11.3039i	−0.307239	−	0.556902i
$413$	1.59427	−	1.24033i	0.0784490	−	0.0610328i
$414$	29.4303	−	1.59165i	1.44642	−	0.0782255i
$415$	2.28840			0.112333
$416$	22.2974	+	7.15328i	1.09322	+	0.350718i
$417$	30.4541	+	3.02548i	1.49134	+	0.148159i
$418$	−2.44791	−	9.50461i	−0.119731	−	0.464886i
$419$	20.0184	+	11.5576i	0.977964	+	0.564628i	0.901655	−	0.432456i	$-0.142353\pi$
$419$	20.0184	+	11.5576i	0.977964	+	0.564628i	0.0763092	+	0.997084i	$0.475686\pi$
$420$	−2.35750	−	3.90893i	−0.115034	−	0.190736i
$421$	14.8560	−	8.57709i	0.724035	−	0.418022i	−0.0922010	−	0.995740i	$-0.529390\pi$
$421$	14.8560	−	8.57709i	0.724035	−	0.418022i	0.816236	+	0.577719i	$0.196057\pi$
$422$	−0.228326	−	0.232812i	−0.0111147	−	0.0113331i
$423$	−20.6980	−	4.15352i	−1.00637	−	0.201951i
$424$	12.2249	+	12.9601i	0.593693	+	0.629398i
$425$	1.62265	+	2.81050i	0.0787099	+	0.136329i
$426$	2.13150	−	0.328799i	0.103272	−	0.0159303i
$427$	−31.4253	+	4.35094i	−1.52078	+	0.210557i
$428$	13.4790	+	8.13578i	0.651531	+	0.393258i
$429$	5.12309	+	11.3324i	0.247345	+	0.547133i
$430$	2.98131	+	0.830006i	0.143771	+	0.0400264i
$431$			17.7657i			0.855743i	0.903840	+	0.427872i	$0.140736\pi$
$431$			17.7657i			0.855743i	−0.903840	+	0.427872i	$0.859264\pi$
$432$	−3.87684	−	20.4198i	−0.186525	−	0.982450i
$433$		−	37.9104i		−	1.82186i	−0.412564	−	0.910929i	$-0.635367\pi$
$433$		−	37.9104i		−	1.82186i	0.412564	−	0.910929i	$-0.364633\pi$
$434$	29.8612	−	12.2624i	1.43338	−	0.588613i
$435$	6.48901	−	2.93352i	0.311124	−	0.140651i
$436$	9.79345	−	16.2253i	0.469021	−	0.777052i
$437$	−24.0712	−	13.8975i	−1.15148	−	0.664809i
$438$	21.0352	−	3.24481i	1.00510	−	0.155043i
$439$	−15.7990	+	9.12157i	−0.754046	+	0.435349i	−0.827154	−	0.561975i	$-0.810042\pi$
$439$	−15.7990	+	9.12157i	−0.754046	+	0.435349i	0.0731080	+	0.997324i	$0.476708\pi$
$440$	−1.77753	+	1.67669i	−0.0847402	+	0.0799330i
$441$	20.9376	−	1.61782i	0.997028	−	0.0770391i
$442$	−2.85442	+	2.79942i	−0.135771	+	0.133155i
$443$	5.63674	+	9.76312i	0.267810	+	0.463860i	0.968296	−	0.249806i	$-0.0803668\pi$
$443$	5.63674	+	9.76312i	0.267810	+	0.463860i	−0.700486	+	0.713666i	$0.747033\pi$
$444$	−6.20886	−	0.739069i	−0.294659	−	0.0350747i
$445$	−6.28057	−	3.62609i	−0.297728	−	0.171893i
$446$	−5.08736	+	1.31025i	−0.240893	+	0.0620419i
$447$	−36.4590	−	3.62205i	−1.72445	−	0.171317i
$448$	−19.1102	−	9.09940i	−0.902874	−	0.429906i
$449$		−	4.80392i		−	0.226711i	−0.993554	−	0.113355i	$-0.963840\pi$
$449$		−	4.80392i		−	0.226711i	0.993554	−	0.113355i	$-0.0361599\pi$
$450$	−17.9786	−	9.12278i	−0.847520	−	0.430052i
$451$	7.03377			0.331207
$452$	18.3046	+	33.1788i	0.860974	+	1.56060i
$453$	1.48471	−	2.06821i	0.0697576	−	0.0971728i
$454$	30.3569	−	7.81840i	1.42472	−	0.366936i
$455$	−0.748106	−	5.40331i	−0.0350717	−	0.253311i
$456$	−7.45219	+	18.1292i	−0.348981	+	0.848977i
$457$	3.10434	+	5.37687i	0.145215	+	0.251519i	0.929453	−	0.368940i	$-0.120279\pi$
$457$	3.10434	+	5.37687i	0.145215	+	0.251519i	−0.784238	+	0.620460i	$0.786946\pi$
$458$	14.6007	−	14.3194i	0.682246	−	0.669100i
$459$	3.39324	+	1.03874i	0.158383	+	0.0484842i
$460$	−0.134629	+	6.91869i	−0.00627711	+	0.322586i
$461$	−20.7534	+	11.9820i	−0.966581	+	0.558056i	−0.898192	−	0.439603i	$-0.855119\pi$
$461$	−20.7534	+	11.9820i	−0.966581	+	0.558056i	−0.0683891	+	0.997659i	$0.521786\pi$
$462$	−3.22124	−	10.7699i	−0.149866	−	0.501059i
$463$	−12.7250	+	22.0404i	−0.591383	+	1.02431i	0.402664	+	0.915348i	$0.368084\pi$
$463$	−12.7250	+	22.0404i	−0.591383	+	1.02431i	−0.994046	+	0.108957i	$0.965249\pi$
$464$	17.6099	−	27.9321i	0.817518	−	1.29671i
$465$	−4.34027	+	6.04603i	−0.201275	+	0.280378i
$466$	6.52126	−	23.4238i	0.302092	−	1.08509i
$467$			9.48919i			0.439107i	0.975600	+	0.219554i	$0.0704601\pi$
$467$			9.48919i			0.439107i	−0.975600	+	0.219554i	$0.929540\pi$
$468$	5.35954	−	24.2520i	0.247745	−	1.12105i
$469$	−18.3454	+	14.2726i	−0.847110	+	0.659046i
$470$	1.32936	−	4.77495i	0.0613189	−	0.220252i
$471$	7.15253	+	0.710573i	0.329571	+	0.0327415i
$472$	0.497791	+	2.10124i	0.0229127	+	0.0967174i
$473$	6.59994	+	3.81048i	0.303466	+	0.175206i
$474$	14.0376	−	11.2741i	0.644767	−	0.517835i
$475$	9.50638	+	16.4655i	0.436183	+	0.755490i
$476$	2.89488	−	2.16312i	0.132687	−	0.0991465i
$477$	12.4835	−	14.1862i	0.571582	−	0.649544i
$478$	2.03725	+	2.07728i	0.0931817	+	0.0950125i
$479$	−15.1807	−	26.2937i	−0.693622	−	1.20139i	−0.970643	−	0.240525i	$-0.922680\pi$
$479$	−15.1807	−	26.2937i	−0.693622	−	1.20139i	0.277021	−	0.960864i	$-0.410653\pi$
$480$	4.84824	−	0.555783i	0.221291	−	0.0253679i
$481$	−6.47079	−	3.73591i	−0.295043	−	0.170343i
$482$	−9.23386	+	2.37818i	−0.420591	+	0.108323i
$483$	−28.1629	−	14.8428i	−1.28145	−	0.675371i
$484$	13.9942	−	7.72048i	0.636098	−	0.350931i
$485$	6.42557			0.291770
$486$	−21.1834	+	6.10436i	−0.960899	+	0.276899i
$487$	1.52278			0.0690037			0.0345019	−	0.999405i	$-0.489016\pi$
$487$	1.52278			0.0690037			0.0345019	+	0.999405i	$0.489016\pi$
$488$	9.73020	−	32.4898i	0.440465	−	1.47074i
$489$	−24.6403	+	11.1393i	−1.11427	+	0.503735i
$490$	0.0178969	+	4.93053i	0.000808497	+	0.222739i
$491$	2.86661	−	4.96511i	0.129368	−	0.224072i	−0.794064	−	0.607834i	$-0.792038\pi$
$491$	2.86661	−	4.96511i	0.129368	−	0.224072i	0.923432	+	0.383762i	$0.125372\pi$
$492$	−11.2497	−	8.41225i	−0.507176	−	0.379254i
$493$	2.81882	+	4.88235i	0.126953	+	0.219890i
$494$	−16.7228	+	16.4006i	−0.752395	+	0.737897i
$495$	1.94570	+	1.71216i	0.0874526	+	0.0769561i
$496$	−1.34252	+	34.4836i	−0.0602811	+	1.54836i
$497$	−2.15810	−	0.877073i	−0.0968040	−	0.0393421i
$498$	−7.04736	−	8.77482i	−0.315800	−	0.393209i
$499$	7.56081	+	4.36523i	0.338468	+	0.195415i	0.659594	−	0.751622i	$-0.270728\pi$
$499$	7.56081	+	4.36523i	0.338468	+	0.195415i	−0.321126	+	0.947036i	$0.604061\pi$
$500$	5.01982	−	8.31660i	0.224493	−	0.371930i
$501$	−2.69629	−	0.267865i	−0.120461	−	0.0119673i
$502$	−4.45003	+	15.9841i	−0.198614	+	0.713405i
$503$	28.8684			1.28718			0.643589	−	0.765371i	$-0.277444\pi$
$503$	28.8684			1.28718			0.643589	+	0.765371i	$0.277444\pi$
$504$	−7.72854	+	21.0777i	−0.344257	+	0.938876i
$505$	−1.28708			−0.0572745
$506$	−4.57049	+	16.4168i	−0.203183	+	0.729816i
$507$	4.17732	−	5.81904i	0.185521	−	0.258433i
$508$	23.3561	+	14.0975i	1.03626	+	0.625475i
$509$	21.3337	+	12.3170i	0.945600	+	0.545943i	0.891711	−	0.452604i	$-0.149505\pi$
$509$	21.3337	+	12.3170i	0.945600	+	0.545943i	0.0538888	+	0.998547i	$0.482838\pi$
$510$	−0.301719	+	0.776637i	−0.0133603	+	0.0343901i
$511$	−21.2976	−	8.65557i	−0.942152	−	0.382900i
$512$	17.3378	−	14.5397i	0.766229	−	0.642568i
$513$	19.8795	+	6.08553i	0.877701	+	0.268683i
$514$	−1.97867	+	1.94054i	−0.0872753	+	0.0855935i
$515$	−1.60750	−	2.78427i	−0.0708349	−	0.122690i
$516$	−5.99859	−	13.9878i	−0.264073	−	0.615780i
$517$	6.10298	−	10.5707i	0.268409	−	0.464897i
$518$	5.34549	+	4.12770i	0.234867	+	0.181361i
$519$	−3.22163	−	2.31271i	−0.141414	−	0.101517i
$520$	5.58634	+	1.67302i	0.244977	+	0.0733668i
$521$	−21.4052			−0.937778			−0.468889	−	0.883257i	$-0.655346\pi$
$521$	−21.4052			−0.937778			−0.468889	+	0.883257i	$0.655346\pi$
$522$	−31.2320	−	15.8479i	−1.36699	−	0.693644i
$523$	−8.94262			−0.391033			−0.195517	−	0.980700i	$-0.562638\pi$
$523$	−8.94262			−0.391033			−0.195517	+	0.980700i	$0.562638\pi$
$524$	0.381446	+	0.691410i	0.0166636	+	0.0302044i
$525$	11.6069	+	18.4249i	0.506568	+	0.804130i
$526$	4.03346	−	1.03881i	0.175867	−	0.0452944i
$527$	−5.10265	−	2.94601i	−0.222275	−	0.128330i
$528$	11.9033	+	1.65235i	0.518024	+	0.0719095i
$529$	12.6299	+	21.8756i	0.549126	+	0.951114i
$530$	3.10659	+	3.16763i	0.134942	+	0.137593i
$531$	2.17008	−	0.732550i	0.0941735	−	0.0317900i
$532$	16.9599	−	12.6728i	0.735303	−	0.549435i
$533$	−8.39300	−	14.5371i	−0.363541	−	0.629672i
$534$	5.43749	+	35.2496i	0.235303	+	1.52540i
$535$	3.39546	+	1.96037i	0.146799	+	0.0847543i
$536$	−5.72810	−	24.1790i	−0.247416	−	1.04438i
$537$	17.6465	+	39.0346i	0.761504	+	1.68447i
$538$	−10.2809	+	36.9280i	−0.443240	+	1.59208i
$539$	−2.98563	+	11.7692i	−0.128600	+	0.506934i
$540$	−1.06420	−	5.06543i	−0.0457960	−	0.217981i
$541$			20.0027i			0.859981i	0.902833	+	0.429991i	$0.141483\pi$
$541$			20.0027i			0.859981i	−0.902833	+	0.429991i	$0.858517\pi$
$542$	−1.57887	+	5.67117i	−0.0678184	+	0.243598i
$543$	10.0782	+	22.2932i	0.432496	+	0.956692i
$544$	0.817274	+	3.77586i	0.0350403	+	0.161889i
$545$	2.35980	−	4.08729i	0.101083	−	0.175080i
$546$	−18.4150	+	19.5086i	−0.788089	+	0.834892i
$547$	10.5096	−	6.06774i	0.449360	−	0.259438i	−0.258200	−	0.966091i	$-0.583129\pi$
$547$	10.5096	−	6.06774i	0.449360	−	0.259438i	0.707560	+	0.706654i	$0.249796\pi$
$548$	1.63586	+	0.0318317i	0.0698803	+	0.00135978i
$549$	−35.2697	−	7.07765i	−1.50528	−	0.302067i
$550$	8.32234	−	8.16197i	0.354866	−	0.348028i
$551$	16.5143	+	28.6036i	0.703531	+	1.21855i
$552$	26.9442	−	20.7906i	1.14682	−	0.884905i
$553$	−19.2632	+	2.66705i	−0.819155	+	0.113415i
$554$	−7.80030	+	2.00896i	−0.331403	+	0.0853527i
$555$	−1.54949	−	0.153935i	−0.0657720	−	0.00653417i
$556$	30.9419	−	17.0705i	1.31223	−	0.723949i
$557$	1.51405			0.0641525			0.0320763	−	0.999485i	$-0.489788\pi$
$557$	1.51405			0.0641525			0.0320763	+	0.999485i	$0.489788\pi$
$558$	36.5497	−	1.97668i	1.54727	−	0.0836797i
$559$		−	18.1873i		−	0.769242i
$560$	−4.80222	−	2.17302i	−0.202931	−	0.0918267i
$561$	−1.19654	+	1.66679i	−0.0505179	+	0.0703718i
$562$	23.1314	−	5.95747i	0.975738	−	0.251301i
$563$	−4.34221	−	2.50697i	−0.183002	−	0.105656i	0.405700	−	0.914006i	$-0.367028\pi$
$563$	−4.34221	−	2.50697i	−0.183002	−	0.105656i	−0.588702	+	0.808350i	$0.700361\pi$
$564$	−22.4033	+	9.60752i	−0.943350	+	0.404550i
$565$	4.71829	+	8.17231i	0.198500	+	0.343812i
$566$	−16.1514	+	15.8401i	−0.678892	+	0.665810i
$567$	23.0206	+	6.08713i	0.966773	+	0.255635i
$568$	1.81158	−	1.70881i	0.0760124	−	0.0717002i
$569$	−16.0815	+	9.28466i	−0.674172	+	0.389233i	−0.797655	−	0.603113i	$-0.793927\pi$
$569$	−16.0815	+	9.28466i	−0.674172	+	0.389233i	0.123484	+	0.992347i	$0.460593\pi$
$570$	−1.76764	+	4.54998i	−0.0740383	+	0.190578i
$571$	28.2362	+	16.3022i	1.18165	+	0.682225i	0.956395	−	0.292075i	$-0.0943456\pi$
$571$	28.2362	+	16.3022i	1.18165	+	0.682225i	0.225254	+	0.974300i	$0.427679\pi$
$572$	12.2946	+	7.42088i	0.514062	+	0.310282i
$573$	4.51415	+	3.24058i	0.188581	+	0.135377i
$574$	5.76355	+	14.0353i	0.240566	+	0.585823i
$575$		−	33.0113i		−	1.37667i
$576$	−17.0618	−	16.8789i	−0.710907	−	0.703286i
$577$			35.1794i			1.46454i	0.681015	+	0.732270i	$0.261539\pi$
$577$			35.1794i			1.46454i	−0.681015	+	0.732270i	$0.738461\pi$
$578$	22.5254	+	6.27114i	0.936932	+	0.260845i
$579$	24.8237	+	2.46613i	1.03164	+	0.102489i
$580$	4.24924	−	7.03995i	0.176440	−	0.292318i
$581$	1.66716	+	12.0413i	0.0691656	+	0.499559i
$582$	−19.7882	−	24.6387i	−0.820246	−	1.02131i
$583$	5.46295	+	9.46211i	0.226252	+	0.391881i
$584$	17.8780	−	16.8638i	0.739796	−	0.697828i
$585$	1.21694	−	6.06432i	0.0503143	−	0.250729i
$586$	−13.8773	−	14.1499i	−0.573265	−	0.584529i
$587$	−15.2364	+	8.79674i	−0.628873	+	0.363080i	−0.780316	−	0.625386i	$-0.784942\pi$
$587$	−15.2364	+	8.79674i	−0.628873	+	0.363080i	0.151442	+	0.988466i	$0.451608\pi$
$588$	18.8509	−	15.2527i	0.777397	−	0.629010i
$589$	−29.8942	−	17.2594i	−1.23177	−	0.711162i
$590$	0.134122	+	0.520763i	0.00552172	+	0.0214395i
$591$	0.217716	+	0.481593i	0.00895565	+	0.0198101i
$592$	−6.38840	+	3.36401i	−0.262561	+	0.138260i
$593$	26.1411			1.07349			0.536744	−	0.843745i	$-0.319654\pi$
$593$	26.1411			1.07349			0.536744	+	0.843745i	$0.319654\pi$
$594$	0.573285	−	12.7335i	0.0235222	−	0.522462i
$595$	0.710299	−	0.552608i	0.0291194	−	0.0226547i
$596$	−37.0431	+	20.4365i	−1.51735	+	0.837110i
$597$	−36.0596	+	16.3016i	−1.47582	+	0.667181i
$598$	39.3833	−	10.1431i	1.61050	−	0.414784i
$599$	−37.8024	−	21.8252i	−1.54456	−	0.891754i	−0.998542	−	0.0539817i	$-0.982809\pi$
$599$	−37.8024	−	21.8252i	−1.54456	−	0.891754i	−0.546020	−	0.837772i	$-0.683858\pi$
$600$	−23.0722	+	3.10078i	−0.941919	+	0.126589i
$601$	−19.7133	+	11.3815i	−0.804123	+	0.464261i	−0.844911	−	0.534907i	$-0.820347\pi$
$601$	−19.7133	+	11.3815i	−0.804123	+	0.464261i	0.0407879	+	0.999168i	$0.487013\pi$
$602$	−2.19544	+	16.2920i	−0.0894796	+	0.664013i
$603$	−24.9712	+	8.42948i	−1.01691	+	0.343275i
$604$	0.0571940	−	2.93925i	0.00232719	−	0.119596i
$605$	3.44691	−	1.99008i	0.140137	−	0.0809081i
$606$	3.96371	+	4.93530i	0.161015	+	0.200483i
$607$	−27.5024	−	15.8785i	−1.11629	−	0.644489i	−0.175837	−	0.984419i	$-0.556263\pi$
$607$	−27.5024	−	15.8785i	−1.11629	−	0.644489i	−0.940451	+	0.339931i	$0.889596\pi$
$608$	4.78805	+	22.1211i	0.194181	+	0.897131i
$609$	20.1633	+	32.0074i	0.817058	+	1.29700i
$610$	2.26525	−	8.13658i	0.0917173	−	0.329440i
$611$	−29.1294			−1.17845
$612$	3.90717	−	1.23480i	0.157938	−	0.0499137i
$613$		−	3.86716i		−	0.156193i	−0.996946	−	0.0780966i	$-0.975116\pi$
$613$		−	3.86716i		−	0.156193i	0.996946	−	0.0780966i	$-0.0248843\pi$
$614$	42.8790	+	11.9377i	1.73046	+	0.481765i
$615$	−2.84175	−	2.04001i	−0.114590	−	0.0822612i
$616$	−10.1175	−	8.13165i	−0.407647	−	0.327634i
$617$	−9.58909	−	5.53626i	−0.386042	−	0.222882i	0.294402	−	0.955682i	$-0.404880\pi$
$617$	−9.58909	−	5.53626i	−0.386042	−	0.222882i	−0.680444	+	0.732800i	$0.738213\pi$
$618$	−5.72577	+	14.7384i	−0.230324	+	0.592864i
$619$	3.02761	+	5.24398i	0.121690	+	0.210773i	0.920434	−	0.390897i	$-0.127835\pi$
$619$	3.02761	+	5.24398i	0.121690	+	0.210773i	−0.798744	+	0.601671i	$0.794502\pi$
$620$	−0.167197	+	8.59236i	−0.00671477	+	0.345078i
$621$	−24.6089	−	26.4087i	−0.987520	−	1.05974i
$622$	−16.1023	+	15.7920i	−0.645643	+	0.633202i
$623$	14.5045	−	35.6894i	0.581112	−	1.42987i
$624$	−10.7885	−	26.5729i	−0.431886	−	1.06377i
$625$	−10.6703	+	18.4815i	−0.426811	+	0.739258i
$626$	−42.1489	+	10.8554i	−1.68461	+	0.433869i
$627$	−7.01000	+	9.76498i	−0.279952	+	0.389976i
$628$	7.26711	−	4.00922i	0.289989	−	0.159985i
$629$		−	1.23271i		−	0.0491512i
$630$	−1.82216	+	5.28545i	−0.0725967	+	0.210577i
$631$	−21.7834			−0.867185			−0.433593	−	0.901109i	$-0.642754\pi$
$631$	−21.7834			−0.867185			−0.433593	+	0.901109i	$0.642754\pi$
$632$	5.96445	−	19.9157i	0.237253	−	0.792205i
$633$	−0.0394820	+	0.397420i	−0.00156927	+	0.0157960i
$634$	−5.60298	−	21.7550i	−0.222523	−	0.864001i
$635$	5.88359	+	3.39689i	0.233483	+	0.134801i
$636$	2.57914	−	21.6672i	0.102270	−	0.859159i
$637$	27.8866	−	7.87291i	1.10491	−	0.311936i
$638$	14.4574	−	14.1788i	0.572373	−	0.561344i
$639$	−1.98298	−	1.74497i	−0.0784454	−	0.0690299i
$640$	4.24638	−	3.70414i	0.167853	−	0.146419i
$641$	41.2777	−	23.8317i	1.63037	−	0.941294i	0.646392	−	0.763006i	$-0.276277\pi$
$641$	41.2777	−	23.8317i	1.63037	−	0.941294i	0.983978	−	0.178289i	$-0.0570560\pi$
$642$	−2.93967	−	19.0570i	−0.116019	−	0.752119i
$643$	−10.5121	+	18.2076i	−0.414558	+	0.718036i	−0.995382	−	0.0959934i	$-0.969397\pi$
$643$	−10.5121	+	18.2076i	−0.414558	+	0.718036i	0.580824	+	0.814029i	$0.302731\pi$
$644$	−36.5035	+	4.33205i	−1.43844	+	0.170707i
$645$	−1.56132	−	3.45368i	−0.0614770	−	0.135989i
$646$	−3.72274	−	1.03642i	−0.146469	−	0.0407775i
$647$	−15.0636			−0.592212			−0.296106	−	0.955155i	$-0.595688\pi$
$647$	−15.0636			−0.592212			−0.296106	+	0.955155i	$0.595688\pi$
$648$	−16.1459	+	19.6802i	−0.634273	+	0.773109i
$649$			1.32428i			0.0519824i
$650$	−26.7994	−	7.46105i	−1.05116	−	0.292647i
$651$	−34.9756	−	18.4334i	−1.37080	−	0.722461i
$652$	−16.1354	+	26.7324i	−0.631911	+	1.04692i
$653$	11.2326	−	19.4555i	0.439567	−	0.761353i	−0.558089	−	0.829781i	$-0.688465\pi$
$653$	11.2326	−	19.4555i	0.439567	−	0.761353i	0.997656	+	0.0684284i	$0.0217985\pi$
$654$	−22.9399	+	3.53863i	−0.897020	+	0.138371i
$655$	0.0983238	+	0.170302i	0.00384183	+	0.00665424i
$656$	−16.2079	−	0.631011i	−0.632814	−	0.0246368i
$657$	−19.5694	−	17.2206i	−0.763475	−	0.671839i
$658$	26.0938	+	3.51629i	1.01724	+	0.137079i
$659$	−15.6835	−	27.1647i	−0.610944	−	1.05819i	−0.991082	−	0.133256i	$-0.957457\pi$
$659$	−15.6835	−	27.1647i	−0.610944	−	1.05819i	0.380137	−	0.924930i	$-0.375877\pi$
$660$	2.97173	+	0.353739i	0.115675	+	0.0137693i
$661$	−1.92273	+	3.33026i	−0.0747854	+	0.129532i	−0.900993	−	0.433834i	$-0.857160\pi$
$661$	−1.92273	+	3.33026i	−0.0747854	+	0.129532i	0.826208	+	0.563366i	$0.190494\pi$
$662$	31.1797	−	8.03031i	1.21183	−	0.312107i
$663$	4.87261	+	0.484073i	0.189237	+	0.0187999i
$664$	−12.4492	−	3.72835i	−0.483124	−	0.144688i
$665$	4.16133	−	3.23749i	0.161370	−	0.125544i
$666$	4.18154	+	6.41552i	0.162031	+	0.248597i
$667$		−	57.3466i		−	2.22047i
$668$	−2.73948	+	1.51135i	−0.105994	+	0.0584760i
$669$	5.22672	+	3.75211i	0.202077	+	0.145065i
$670$	−1.54335	−	5.99244i	−0.0596248	−	0.231508i
$671$	10.3996	−	18.0126i	0.401471	−	0.695367i
$672$	6.45655	+	25.1060i	0.249067	+	0.968486i
$673$	−9.03995	−	15.6577i	−0.348465	−	0.603558i	0.637512	−	0.770440i	$-0.279963\pi$
$673$	−9.03995	−	15.6577i	−0.348465	−	0.603558i	−0.985977	+	0.166882i	$0.946630\pi$
$674$	−8.00796	+	7.85365i	−0.308455	+	0.302511i
$675$	5.54586	+	24.0609i	0.213460	+	0.926105i
$676$	0.160919	−	8.26977i	0.00618920	−	0.318068i
$677$	20.0252	−	11.5616i	0.769632	−	0.444347i	−0.0631112	−	0.998006i	$-0.520102\pi$
$677$	20.0252	−	11.5616i	0.769632	−	0.444347i	0.832743	+	0.553659i	$0.186769\pi$
$678$	16.8061	−	43.2596i	0.645435	−	1.66137i
$679$	4.68120	+	33.8107i	0.179648	+	1.29754i
$680$	0.221782	+	0.936169i	0.00850494	+	0.0359004i
$681$	−31.1885	−	22.3893i	−1.19514	−	0.857960i
$682$	−5.67612	+	20.3881i	−0.217350	+	0.780702i
$683$	26.5735			1.01681			0.508403	−	0.861119i	$-0.330236\pi$
$683$	26.5735			1.01681			0.508403	+	0.861119i	$0.330236\pi$
$684$	22.8904	−	7.23414i	0.875237	−	0.276604i
$685$	0.407456			0.0155681
$686$	−25.9309	+	3.68620i	−0.990047	+	0.140740i
$687$	−24.9240	−	2.47610i	−0.950910	−	0.0944689i
$688$	−14.8664	−	9.37260i	−0.566778	−	0.357327i
$689$	13.0373	−	22.5812i	0.496681	−	0.860276i
$690$	6.60793	−	5.30706i	0.251560	−	0.202036i
$691$	−11.4541	−	19.8392i	−0.435736	−	0.754717i	0.561619	−	0.827396i	$-0.310179\pi$
$691$	−11.4541	−	19.8392i	−0.435736	−	0.754717i	−0.997355	+	0.0726787i	$0.976845\pi$
$692$	−4.57844	−	0.0890907i	−0.174046	−	0.00338672i
$693$	−7.59174	+	11.4854i	−0.288386	+	0.436295i
$694$	30.3514	−	29.7665i	1.15212	−	1.12992i
$695$	7.62134	−	4.40018i	0.289094	−	0.166908i
$696$	−40.0805	+	5.38660i	−1.51925	+	0.204179i
$697$	1.38468	−	2.39834i	0.0524486	−	0.0908436i
$698$	6.76494	+	26.2666i	0.256057	+	0.994205i
$699$	−27.1352	+	12.2671i	−1.02635	+	0.463986i
$700$	23.1060	+	9.91856i	0.873324	+	0.374886i
$701$	12.3519			0.466525			0.233263	−	0.972414i	$-0.425060\pi$
$701$	12.3519			0.466525			0.233263	+	0.972414i	$0.425060\pi$
$702$	−27.0012	+	14.0094i	−1.01909	+	0.528749i
$703$		−	7.22189i		−	0.272379i
$704$	12.4017	−	6.22541i	0.467407	−	0.234629i
$705$	−5.53152	+	2.50066i	−0.208329	+	0.0941803i
$706$	12.8431	+	49.8664i	0.483355	+	1.87675i
$707$	−0.937677	−	6.77251i	−0.0352650	−	0.254707i
$708$	1.58381	−	2.11803i	0.0595232	−	0.0796004i
$709$	−5.08599	+	2.93640i	−0.191009	+	0.110279i	−0.592455	−	0.805604i	$-0.701841\pi$
$709$	−5.08599	+	2.93640i	−0.191009	+	0.110279i	0.401446	+	0.915883i	$0.368508\pi$
$710$	0.442776	−	0.434244i	0.0166171	−	0.0162969i
$711$	−21.6198	−	4.33849i	−0.810805	−	0.162706i
$712$	28.2594	+	29.9590i	1.05907	+	1.12276i
$713$	29.9671	+	51.9045i	1.12228	+	1.94384i
$714$	−4.30640	−	1.02181i	−0.161163	−	0.0382404i
$715$	3.09710	+	1.78811i	0.115825	+	0.0668716i
$716$	42.3488	+	25.5613i	1.58265	+	0.955270i
$717$	0.352280	−	3.54600i	0.0131561	−	0.132428i
$718$	−9.25684	+	33.2498i	−0.345462	+	1.24087i
$719$	49.7442			1.85515			0.927573	−	0.373642i	$-0.121891\pi$
$719$	49.7442			1.85515			0.927573	+	0.373642i	$0.121891\pi$
$720$	−4.32988	−	4.11990i	−0.161365	−	0.153540i
$721$	13.4794	−	10.4869i	0.502001	−	0.390553i
$722$	4.07568	+	1.13468i	0.151681	+	0.0422285i
$723$	9.48681	+	6.81031i	0.352818	+	0.253278i
$724$	24.1860	+	14.5984i	0.898864	+	0.542545i
$725$	−19.6135	+	33.9716i	−0.728427	+	1.26167i
$726$	−18.2460	−	7.08847i	−0.677173	−	0.263078i
$727$	21.8757	−	12.6299i	0.811325	−	0.468419i	−0.0360908	−	0.999349i	$-0.511491\pi$
$727$	21.8757	−	12.6299i	0.811325	−	0.468419i	0.847416	+	0.530930i	$0.178157\pi$
$728$	−4.73347	+	30.6136i	−0.175434	+	1.13462i
$729$	22.3732	+	15.1142i	0.828638	+	0.559784i
$730$	4.36962	−	4.28542i	0.161727	−	0.158611i
$731$	2.59856	−	1.50028i	0.0961112	−	0.0554898i
$732$	−38.1756	+	16.3714i	−1.41101	+	0.605103i
$733$	−20.6852	+	35.8278i	−0.764025	+	1.32333i	0.176735	+	0.984258i	$0.443446\pi$
$733$	−20.6852	+	35.8278i	−0.764025	+	1.32333i	−0.940760	+	0.339072i	$0.889887\pi$
$734$	26.3548	−	6.78767i	0.972775	−	0.250538i
$735$	4.61967	−	3.88900i	0.170399	−	0.143448i
$736$	12.0046	−	37.4193i	0.442495	−	1.37929i
$737$		−	15.2385i		−	0.561318i
$738$	0.929079	+	17.1790i	0.0341999	+	0.632369i
$739$		−	0.348855i		−	0.0128328i	−0.999979	−	0.00641641i	$-0.997958\pi$
$739$		−	0.348855i		−	0.0128328i	0.999979	−	0.00641641i	$-0.00204242\pi$
$740$	−1.57431	+	0.868536i	−0.0578727	+	0.0319280i
$741$	28.5465	+	2.83598i	1.04868	+	0.104182i
$742$	−14.4045	+	18.6543i	−0.528806	+	0.684819i
$743$	4.02434	+	2.32345i	0.147639	+	0.0852393i	0.572000	−	0.820254i	$-0.306168\pi$
$743$	4.02434	+	2.32345i	0.147639	+	0.0852393i	−0.424361	+	0.905493i	$0.639501\pi$
$744$	33.4621	−	25.8199i	1.22678	−	0.946605i
$745$	−9.12413	+	5.26782i	−0.334282	+	0.192998i
$746$	−18.4715	−	18.8344i	−0.676289	−	0.689577i
$747$	−2.71197	+	13.5144i	−0.0992257	+	0.494467i
$748$	−0.0460932	+	2.36877i	−0.00168533	+	0.0866106i
$749$	−7.84159	+	19.2948i	−0.286526	+	0.705016i
$750$	−11.7583	+	1.81379i	−0.429351	+	0.0662303i
$751$	0.0719323	−	0.124590i	0.00262485	−	0.00454637i	−0.864710	−	0.502271i	$-0.832498\pi$
$751$	0.0719323	−	0.124590i	0.00262485	−	0.00454637i	0.867335	+	0.497725i	$0.165831\pi$
$752$	−15.0114	+	23.8105i	−0.547411	+	0.868281i
$753$	18.5167	−	8.37094i	0.674786	−	0.305054i
$754$	−46.5554	−	12.9612i	−1.69545	−	0.472018i
$755$		−	0.732102i		−	0.0266439i
$756$	25.8785	−	9.29003i	0.941191	−	0.337875i
$757$		−	3.29120i		−	0.119621i	−0.998210	−	0.0598104i	$-0.980950\pi$
$757$		−	3.29120i		−	0.119621i	0.998210	−	0.0598104i	$-0.0190496\pi$
$758$	−2.13976	+	7.68581i	−0.0777195	+	0.279161i
$759$	19.0180	−	8.59754i	0.690308	−	0.312071i
$760$	1.29932	+	5.48461i	0.0471314	+	0.198948i
$761$	0.257686	−	0.446325i	0.00934111	−	0.0161793i	−0.861317	−	0.508068i	$-0.830360\pi$
$761$	0.257686	−	0.446325i	0.00934111	−	0.0161793i	0.870658	+	0.491889i	$0.163693\pi$
$762$	−5.09379	−	33.0215i	−0.184529	−	1.19624i
$763$	23.2261	+	9.43932i	0.840841	+	0.341726i
$764$	6.41532	+	0.124834i	0.232098	+	0.00451633i
$765$	0.966840	−	0.326374i	0.0349562	−	0.0118001i
$766$	18.2435	−	17.8920i	0.659165	−	0.646463i
$767$	2.73696	−	1.58019i	0.0988260	−	0.0570572i
$768$	−27.2806	−	4.87539i	−0.984403	−	0.175926i
$769$	−34.9769	−	20.1939i	−1.26130	−	0.728211i	−0.287973	−	0.957639i	$-0.592981\pi$
$769$	−34.9769	−	20.1939i	−1.26130	−	0.728211i	−0.973326	+	0.229428i	$0.926315\pi$
$770$	−2.55850	−	1.97563i	−0.0922020	−	0.0711968i
$771$	3.37767	+	0.335557i	0.121644	+	0.0120848i
$772$	25.2213	−	13.9144i	0.907736	−	0.500792i
$773$			24.5583i			0.883300i	0.897187	+	0.441650i	$0.145607\pi$
$773$			24.5583i			0.883300i	−0.897187	+	0.441650i	$0.854393\pi$
$774$	−8.43482	+	16.6228i	−0.303183	+	0.597495i
$775$		−	40.9970i		−	1.47266i
$776$	−34.9560	−	10.4688i	−1.25485	−	0.375807i
$777$	−0.318853	−	8.26538i	−0.0114388	−	0.296519i
$778$	10.4440	+	40.5515i	0.374436	+	1.45384i
$779$	8.11226	−	14.0508i	0.290652	−	0.503424i
$780$	−2.81491	−	6.56396i	−0.100790	−	0.235027i
$781$	1.32263	−	0.763621i	0.0473274	−	0.0273245i
$782$	4.69796	+	4.79027i	0.167999	+	0.171300i
$783$	9.63414	+	41.7981i	0.344296	+	1.49374i
$784$	7.93564	−	26.8519i	0.283416	−	0.958997i
$785$	1.78997	−	1.03344i	0.0638867	−	0.0368850i
$786$	0.350220	−	0.901481i	0.0124919	−	0.0321548i
$787$	7.28792	−	12.6231i	0.259786	−	0.449963i	−0.706398	−	0.707815i	$-0.749681\pi$
$787$	7.28792	−	12.6231i	0.259786	−	0.449963i	0.966185	+	0.257851i	$0.0830145\pi$
$788$	0.522483	+	0.315365i	0.0186127	+	0.0112344i
$789$	−4.14395	−	2.97482i	−0.147528	−	0.105906i
$790$	1.38856	−	4.98759i	0.0494028	−	0.177450i
$791$	−39.5645	+	30.7809i	−1.40675	+	1.09444i
$792$	−7.79534	−	12.4844i	−0.276995	−	0.443614i
$793$	−49.6369			−1.76266
$794$	−1.15623	−	0.321898i	−0.0410330	−	0.0114237i
$795$	0.537189	−	5.40727i	0.0190521	−	0.191776i
$796$	−23.6131	+	39.1212i	−0.836946	+	1.38661i
$797$	−35.7856	−	20.6609i	−1.26759	−	0.731845i	−0.293061	−	0.956094i	$-0.594674\pi$
$797$	−35.7856	−	20.6609i	−1.26759	−	0.731845i	−0.974532	+	0.224249i	$0.928007\pi$
$798$	−25.2293	−	5.98637i	−0.893108	−	0.211915i
$799$	−2.40289	−	4.16193i	−0.0850081	−	0.147238i
$800$	−19.9094	+	18.0611i	−0.703905	+	0.638555i
$801$	28.8573	−	32.7934i	1.01962	−	1.15870i
$802$	8.19507	+	8.35609i	0.289378	+	0.295064i
$803$	13.0526	−	7.53594i	0.460618	−	0.265938i
$804$	−18.2250	+	24.3723i	−0.642745	+	0.859543i
$805$	−9.06780	+	1.25547i	−0.319598	+	0.0442494i
$806$	48.9104	−	12.5968i	1.72279	−	0.443705i
$807$	42.7790	−	19.3393i	1.50589	−	0.680776i
$808$	7.00192	+	2.09697i	0.246327	+	0.0737710i
$809$		−	13.2197i		−	0.464780i	−0.972623	−	0.232390i	$-0.925345\pi$
$809$		−	13.2197i		−	0.464780i	0.972623	−	0.232390i	$-0.0746546\pi$
$810$	−3.92473	+	4.97827i	−0.137901	+	0.174918i
$811$	34.1402			1.19883			0.599413	−	0.800440i	$-0.295401\pi$
$811$	34.1402			1.19883			0.599413	+	0.800440i	$0.295401\pi$
$812$	40.1392	+	17.2303i	1.40861	+	0.604665i
$813$	6.56975	−	2.97002i	0.230411	−	0.104163i
$814$	−4.28782	+	1.10432i	−0.150288	+	0.0387065i
$815$	−3.88794	+	6.73411i	−0.136189	+	0.235886i
$816$	2.90672	−	3.73344i	0.101756	−	0.130697i
$817$	15.2238	−	8.78948i	0.532614	−	0.307505i
$818$	−13.9866	−	14.2615i	−0.489032	−	0.498640i
$819$	32.7964	+	1.98539i	1.14600	+	0.0693753i
$820$	−4.03857	−	0.0785855i	−0.141033	−	0.00274433i
$821$	10.7370	+	18.5970i	0.374724	+	0.649040i	0.990286	−	0.139048i	$-0.0444043\pi$
$821$	10.7370	+	18.5970i	0.374724	+	0.649040i	−0.615562	+	0.788088i	$0.711071\pi$
$822$	−1.25480	−	1.56238i	−0.0437662	−	0.0544943i
$823$	−17.6090	+	30.4997i	−0.613811	+	1.06315i	0.376781	+	0.926302i	$0.377031\pi$
$823$	−17.6090	+	30.4997i	−0.613811	+	1.06315i	−0.990592	+	0.136849i	$0.956302\pi$
$824$	4.20878	+	17.7658i	0.146620	+	0.618901i
$825$	−14.2066	−	1.41136i	−0.494609	−	0.0491374i
$826$	−2.64249	+	1.08513i	−0.0919440	+	0.0377564i
$827$	29.7325			1.03390			0.516950	−	0.856016i	$-0.327067\pi$
$827$	29.7325			1.03390			0.516950	+	0.856016i	$0.327067\pi$
$828$	−40.6996	−	8.99435i	−1.41441	−	0.312575i
$829$	17.8875			0.621257			0.310628	−	0.950531i	$-0.399461\pi$
$829$	17.8875			0.621257			0.310628	+	0.950531i	$0.399461\pi$
$830$	−3.11772	−	0.867983i	−0.108218	−	0.0301281i
$831$	8.01398	+	5.75301i	0.278002	+	0.199570i
$832$	−27.6647	−	18.2029i	−0.959101	−	0.631073i
$833$	3.42524	+	3.33493i	0.118677	+	0.115549i
$834$	−40.3431	−	15.6730i	−1.39697	−	0.542713i
$835$	−0.674764	+	0.389575i	−0.0233512	+	0.0134818i
$836$	−0.270040	+	13.8776i	−0.00933953	+	0.479966i
$837$	−30.5619	−	32.7971i	−1.05637	−	1.13363i
$838$	−22.8893	−	23.3391i	−0.790699	−	0.806234i
$839$	13.9545	+	24.1698i	0.481761	+	0.834435i	0.999781	−	0.0209337i	$-0.00666388\pi$
$839$	13.9545	+	24.1698i	0.481761	+	0.834435i	−0.518020	+	0.855369i	$0.673331\pi$
$840$	1.72921	+	6.21971i	0.0596635	+	0.214601i
$841$	−19.5721	+	33.8999i	−0.674901	+	1.16896i
$842$	−23.4930	+	6.05061i	−0.809623	+	0.208518i
$843$	−23.7650	−	17.0602i	−0.818510	−	0.587585i
$844$	0.222767	+	0.403787i	0.00766794	+	0.0138989i
$845$		−	2.05982i		−	0.0708599i
$846$	26.6236	+	13.5094i	0.915338	+	0.464464i
$847$	12.9827	+	16.6875i	0.446092	+	0.573389i
$848$	−11.7395	−	22.2937i	−0.403134	−	0.765569i
$849$	27.5710	+	2.73907i	0.946235	+	0.0940045i
$850$	−1.14468	−	4.44450i	−0.0392621	−	0.152445i
$851$	−6.26959	+	10.8592i	−0.214919	+	0.372250i
$852$	−3.02867	−	0.360517i	−0.103761	−	0.0123511i
$853$	−14.7886	−	25.6147i	−0.506353	−	0.877029i	−0.999973	−	0.00735150i	$-0.997660\pi$
$853$	−14.7886	−	25.6147i	−0.506353	−	0.877029i	0.493620	−	0.869678i	$-0.335673\pi$
$854$	44.4642	+	5.99180i	1.52153	+	0.205035i
$855$	5.66430	−	1.91209i	0.193715	−	0.0653920i
$856$	−15.2779	−	16.1967i	−0.522187	−	0.553592i
$857$	−2.33838	−	4.05019i	−0.0798775	−	0.138352i	0.823319	−	0.567578i	$-0.192120\pi$
$857$	−2.33838	−	4.05019i	−0.0798775	−	0.138352i	−0.903197	+	0.429226i	$0.858786\pi$
$858$	−2.68136	−	17.3824i	−0.0915400	−	0.593427i
$859$	22.7435	−	39.3929i	0.775999	−	1.34407i	−0.158232	−	0.987402i	$-0.550579\pi$
$859$	22.7435	−	39.3929i	0.775999	−	1.34407i	0.934231	−	0.356668i	$-0.116087\pi$
$860$	−3.74691	−	2.26160i	−0.127769	−	0.0771199i
$861$	8.66404	−	16.4392i	0.295270	−	0.560247i
$862$	6.73847	−	24.2040i	0.229513	−	0.824391i
$863$		−	6.04047i		−	0.205620i	−0.994701	−	0.102810i	$-0.967217\pi$
$863$		−	6.04047i		−	0.205620i	0.994701	−	0.102810i	$-0.0327834\pi$
$864$	−2.46337	+	29.2905i	−0.0838055	+	0.996482i
$865$	−1.14039			−0.0387744
$866$	−14.3793	+	51.6491i	−0.488628	+	1.75511i
$867$	−11.7966	−	26.0944i	−0.400634	−	0.886213i
$868$	−45.3340	+	5.38000i	−1.53873	+	0.182609i
$869$	6.37476	−	11.0414i	0.216249	−	0.374554i
$870$	−9.95330	+	1.53536i	−0.337448	+	0.0520537i
$871$	−31.4944	+	18.1833i	−1.06715	+	0.616117i
$872$	−19.4968	+	18.3908i	−0.660245	+	0.622790i
$873$	−7.61489	+	37.9469i	−0.257725	+	1.28431i
$874$	27.5233	+	28.0641i	0.930991	+	0.949283i
$875$	11.9050	+	4.83830i	0.402462	+	0.163565i
$876$	−29.8891	−	3.55783i	−1.00986	−	0.120208i
$877$	21.4203	+	12.3670i	0.723312	+	0.417604i	0.815971	−	0.578094i	$-0.196203\pi$
$877$	21.4203	+	12.3670i	0.723312	+	0.417604i	−0.0926584	+	0.995698i	$0.529536\pi$
$878$	24.9844	−	6.43471i	0.843181	−	0.217161i
$879$	−2.39965	+	24.1545i	−0.0809382	+	0.814712i
$880$	3.05766	−	1.61011i	0.103074	−	0.0542768i
$881$	10.1789			0.342935			0.171467	−	0.985190i	$-0.445149\pi$
$881$	10.1789			0.342935			0.171467	+	0.985190i	$0.445149\pi$
$882$	−29.1390	−	5.73744i	−0.981161	−	0.193190i
$883$			49.1052i			1.65252i	0.563289	+	0.826260i	$0.309536\pi$
$883$			49.1052i			1.65252i	−0.563289	+	0.826260i	$0.690464\pi$
$884$	4.95067	−	2.73125i	0.166509	−	0.0918620i
$885$	0.384081	−	0.535028i	0.0129108	−	0.0179848i
$886$	−3.97638	−	15.4393i	−0.133589	−	0.518693i
$887$	−7.79927	+	13.5087i	−0.261874	+	0.453579i	−0.966740	−	0.255761i	$-0.917674\pi$
$887$	−7.79927	+	13.5087i	−0.261874	+	0.453579i	0.704866	+	0.709341i	$0.251007\pi$
$888$	8.17862	+	3.36191i	0.274457	+	0.112818i
$889$	−13.5877	+	33.4336i	−0.455718	+	1.12133i
$890$	7.18128	+	7.32238i	0.240717	+	0.245447i
$891$	−12.4172	+	9.46146i	−0.415992	+	0.316971i
$892$	7.42798	+	0.144539i	0.248707	+	0.00483953i
$893$	−14.0775	−	24.3829i	−0.471085	−	0.815944i
$894$	48.2980	+	18.7635i	1.61533	+	0.627545i
$895$	10.6680	+	6.15917i	0.356592	+	0.205878i
$896$	22.5844	+	19.6455i	0.754492	+	0.656309i
$897$	−40.4622	−	29.0466i	−1.35099	−	0.969838i
$898$	−1.82211	+	6.54486i	−0.0608046	+	0.218405i
$899$		−	71.2191i		−	2.37529i
$900$	21.0338	+	19.2481i	0.701128	+	0.641604i
$901$	4.30180			0.143314
$902$	−9.58280	−	2.66788i	−0.319072	−	0.0888308i
$903$	17.0355	−	10.7316i	0.566905	−	0.357126i
$904$	−12.3535	−	52.1457i	−0.410871	−	1.73434i
$905$	6.09264	+	3.51759i	0.202526	+	0.116929i
$906$	−2.80723	+	2.25458i	−0.0932639	+	0.0749034i
$907$	16.1947	−	9.35001i	0.537736	−	0.310462i	−0.206425	−	0.978462i	$-0.566183\pi$
$907$	16.1947	−	9.35001i	0.537736	−	0.310462i	0.744161	+	0.668000i	$0.232850\pi$
$908$	−44.3237	−	0.862483i	−1.47093	−	0.0286225i
$909$	1.52531	−	7.60103i	0.0505915	−	0.252110i
$910$	−1.03024	+	7.64522i	−0.0341520	+	0.253437i
$911$	−47.5094	+	27.4296i	−1.57406	+	0.908782i	−0.578392	+	0.815759i	$0.696320\pi$
$911$	−47.5094	+	27.4296i	−1.57406	+	0.908782i	−0.995664	+	0.0930226i	$0.970347\pi$
$912$	17.0292	−	21.8726i	0.563894	−	0.724275i
$913$	−6.90193	−	3.98483i	−0.228421	−	0.131879i
$914$	−2.18992	−	8.50291i	−0.0724361	−	0.281251i
$915$	−9.42579	+	4.26116i	−0.311607	+	0.140870i
$916$	−25.3233	+	13.9707i	−0.836705	+	0.461605i
$917$	−0.824479	+	0.641439i	−0.0272267	+	0.0211822i
$918$	−4.22895	−	2.70222i	−0.139576	−	0.0891866i
$919$	17.0403			0.562107			0.281054	−	0.959692i	$-0.409316\pi$
$919$	17.0403			0.562107			0.281054	+	0.959692i	$0.409316\pi$
$920$	2.80765	−	9.37496i	0.0925656	−	0.309083i
$921$	−22.4559	−	49.6730i	−0.739947	−	1.63678i
$922$	32.8191	−	8.45255i	1.08084	−	0.278370i
$923$	−3.15644	−	1.82237i	−0.103896	−	0.0599841i
$924$	0.303649	+	15.8947i	0.00998931	+	0.522896i
$925$	7.42809	−	4.28861i	0.244234	−	0.141009i
$926$	25.6965	−	25.2013i	0.844438	−	0.828166i
$927$	18.3479	−	6.19365i	0.602623	−	0.203426i
$928$	−34.5862	+	31.3753i	−1.13535	+	1.02994i
$929$	−25.5012	−	44.1694i	−0.836667	−	1.44915i	−0.892666	−	0.450719i	$-0.851168\pi$
$929$	−25.5012	−	44.1694i	−0.836667	−	1.44915i	0.0559987	−	0.998431i	$-0.482166\pi$
$930$	8.20643	−	6.59087i	0.269099	−	0.216123i
$931$	20.0670	+	19.5379i	0.657669	+	0.640329i
$932$	−17.7691	+	29.4391i	−0.582048	+	0.964309i
$933$	27.4873	+	2.73075i	0.899893	+	0.0894006i
$934$	3.59922	−	12.9281i	0.117770	−	0.423019i
$935$			0.590007i			0.0192953i
$936$	−16.5005	+	31.0081i	−0.539337	+	1.01353i
$937$		−	5.58136i		−	0.182335i	−0.995836	−	0.0911675i	$-0.970940\pi$
$937$		−	5.58136i		−	0.182335i	0.995836	−	0.0911675i	$-0.0290599\pi$
$938$	30.4072	−	12.4866i	0.992832	−	0.407702i
$939$	43.3035	+	31.0863i	1.41316	+	1.01446i
$940$	−3.62224	+	6.00117i	−0.118145	+	0.195736i
$941$	42.0752	+	24.2921i	1.37161	+	0.791900i	0.991131	−	0.132889i	$-0.0424252\pi$
$941$	42.0752	+	24.2921i	1.37161	+	0.791900i	0.380481	+	0.924789i	$0.375759\pi$
$942$	−9.47508	−	3.68102i	−0.308715	−	0.119934i
$943$	−24.3961	+	14.0851i	−0.794446	+	0.458674i
$944$	0.118803	−	3.05154i	0.00386671	−	0.0993191i
$945$	6.39831	−	2.43845i	0.208137	−	0.0793227i
$946$	−7.54646	−	7.69473i	−0.245357	−	0.250177i
$947$	−17.3249	−	30.0077i	−0.562984	−	0.975118i	−0.997234	−	0.0743251i	$-0.976320\pi$
$947$	−17.3249	−	30.0077i	−0.562984	−	0.975118i	0.434250	−	0.900793i	$-0.357014\pi$
$948$	−23.4010	+	10.0354i	−0.760029	+	0.325934i
$949$	−31.1500	−	17.9845i	−1.01117	−	0.583800i
$950$	−6.70617	−	26.0384i	−0.217577	−	0.844797i
$951$	−16.0451	+	22.3509i	−0.520298	+	0.724779i
$952$	−4.76445	+	1.84902i	−0.154417	+	0.0599270i
$953$		−	58.5846i		−	1.89774i	−0.315666	−	0.948870i	$-0.602228\pi$
$953$		−	58.5846i		−	1.89774i	0.315666	−	0.948870i	$-0.397772\pi$
$954$	−22.3884	+	14.5924i	−0.724850	+	0.472446i
$955$	1.59792			0.0517073
$956$	−1.98765	−	3.60281i	−0.0642851	−	0.116523i
$957$	−24.6793	−	2.45179i	−0.797770	−	0.0792551i
$958$	10.7090	+	41.5805i	0.345993	+	1.34340i
$959$	0.296843	+	2.14399i	0.00958556	+	0.0692331i
$960$	−6.81605	−	1.08172i	−0.219987	−	0.0349124i
$961$	21.7163	+	37.6137i	0.700526	+	1.21335i
$962$	7.39879	+	7.54416i	0.238546	+	0.243233i
$963$	−15.6011	+	17.7291i	−0.502740	+	0.571312i
$964$	13.4822	+	0.262347i	0.434234	+	0.00844964i
$965$	6.21229	−	3.58667i	0.199981	−	0.115459i
$966$	32.7392	+	30.9039i	1.05337	+	0.994318i
$967$	−1.60816	+	2.78542i	−0.0517150	+	0.0895731i	−0.890724	−	0.454544i	$-0.849802\pi$
$967$	−1.60816	+	2.78542i	−0.0517150	+	0.0895731i	0.839009	+	0.544117i	$0.183135\pi$
$968$	−21.9940	+	5.21045i	−0.706914	+	0.167470i
$969$	1.94961	+	4.31259i	0.0626306	+	0.138540i
$970$	−8.75419	−	2.43720i	−0.281080	−	0.0782537i
$971$			16.9042i			0.542483i	0.962511	+	0.271241i	$0.0874341\pi$
$971$			16.9042i			0.542483i	−0.962511	+	0.271241i	$0.912566\pi$
$972$	31.1756	−	0.281775i	0.999959	−	0.00903795i
$973$	28.7057	+	36.8971i	0.920261	+	1.18287i
$974$	−2.07464	−	0.577586i	−0.0664756	−	0.0185070i
$975$	14.0350	+	31.0457i	0.449479	+	0.994258i
$976$	−25.5797	+	40.5735i	−0.818786	+	1.29873i
$977$	−19.8443	−	11.4571i	−0.634875	−	0.366545i	0.147762	−	0.989023i	$-0.452793\pi$
$977$	−19.8443	−	11.4571i	−0.634875	−	0.366545i	−0.782638	+	0.622477i	$0.786126\pi$
$978$	37.7951	−	5.83014i	1.20855	−	0.186427i
$979$	12.6283	+	21.8729i	0.403603	+	0.699061i
$980$	1.84575	−	6.72414i	0.0589603	−	0.214795i
$981$	21.3414	+	18.7799i	0.681378	+	0.599595i
$982$	−5.78871	+	5.67717i	−0.184725	+	0.181166i
$983$	12.3213	+	21.3411i	0.392988	+	0.680675i	0.992842	−	0.119434i	$-0.0381081\pi$
$983$	12.3213	+	21.3411i	0.392988	+	0.680675i	−0.599854	+	0.800109i	$0.704775\pi$
$984$	12.1359	+	15.7278i	0.386877	+	0.501385i
$985$	0.131618	+	0.0759895i	0.00419369	+	0.00242123i
$986$	−1.98851	−	7.72088i	−0.0633270	−	0.245883i
$987$	−17.1881	−	27.2845i	−0.547103	−	0.868475i
$988$	29.0038	−	16.0012i	0.922735	−	0.509067i
$989$	−30.5219			−0.970540
$990$	−2.00140	−	3.07065i	−0.0636087	−	0.0975916i
$991$	2.51864			0.0800073			0.0400037	−	0.999200i	$-0.487263\pi$
$991$	2.51864			0.0800073			0.0400037	+	0.999200i	$0.487263\pi$
$992$	14.9086	−	46.4713i	0.473348	−	1.47546i
$993$	−32.0338	−	22.9962i	−1.01656	−	0.729761i
$994$	2.60752	+	2.01348i	0.0827056	+	0.0638638i
$995$	−5.68975	+	9.85494i	−0.180377	+	0.312423i
$996$	6.27306	+	14.6279i	0.198770	+	0.463502i
$997$	−0.0123580	−	0.0214046i	−0.000391381	−	0.000677892i	0.865830	−	0.500339i	$-0.166791\pi$
$997$	−0.0123580	−	0.0214046i	−0.000391381	−	0.000677892i	−0.866221	+	0.499661i	$0.833458\pi$
$998$	−8.64513	−	8.81499i	−0.273657	−	0.279034i
$999$	2.74536	−	8.96824i	0.0868595	−	0.283742i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.10	yes	168
7.6	odd	2	inner	504.2.cc.b.293.9	✓	168
8.5	even	2	inner	504.2.cc.b.293.39	yes	168
9.2	odd	6	inner	504.2.cc.b.461.40	yes	168
56.13	odd	2	inner	504.2.cc.b.293.40	yes	168
63.20	even	6	inner	504.2.cc.b.461.39	yes	168
72.29	odd	6	inner	504.2.cc.b.461.9	yes	168
504.461	even	6	inner	504.2.cc.b.461.10	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.9	✓	168	7.6	odd	2	inner
504.2.cc.b.293.10	yes	168	1.1	even	1	trivial
504.2.cc.b.293.39	yes	168	8.5	even	2	inner
504.2.cc.b.293.40	yes	168	56.13	odd	2	inner
504.2.cc.b.461.9	yes	168	72.29	odd	6	inner
504.2.cc.b.461.10	yes	168	504.461	even	6	inner
504.2.cc.b.461.39	yes	168	63.20	even	6	inner
504.2.cc.b.461.40	yes	168	9.2	odd	6	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.36240 - 0.379297i) q^{2} +(0.713494 + 1.57827i) q^{3} +(1.71227 + 1.03351i) q^{4} +(0.431334 + 0.249031i) q^{5} +(-0.373433 - 2.42086i) q^{6} +(-0.996137 + 2.45106i) q^{7} +(-1.94079 - 2.05751i) q^{8} +(-1.98185 + 2.25217i) q^{9} +O(q^{10})\)	\(q+(-1.36240 - 0.379297i) q^{2} +(0.713494 + 1.57827i) q^{3} +(1.71227 + 1.03351i) q^{4} +(0.431334 + 0.249031i) q^{5} +(-0.373433 - 2.42086i) q^{6} +(-0.996137 + 2.45106i) q^{7} +(-1.94079 - 2.05751i) q^{8} +(-1.98185 + 2.25217i) q^{9} +(-0.493193 - 0.502883i) q^{10} +(-0.867283 - 1.50218i) q^{11} +(-0.409457 + 3.43982i) q^{12} +(-2.06976 + 3.58493i) q^{13} +(2.28682 - 2.96150i) q^{14} +(-0.0852827 + 0.858443i) q^{15} +(1.86372 + 3.53928i) q^{16} -0.682941 q^{17} +(3.55431 - 2.31665i) q^{18} -4.00106 q^{19} +(0.481184 + 0.872195i) q^{20} +(-4.57917 + 0.176650i) q^{21} +(0.611815 + 2.37553i) q^{22} +(6.01622 + 3.47346i) q^{23} +(1.86256 - 4.53110i) q^{24} +(-2.37597 - 4.11530i) q^{25} +(4.17960 - 4.09906i) q^{26} +(-4.96856 - 1.52098i) q^{27} +(-4.23885 + 3.16736i) q^{28} +(-4.12748 - 7.14900i) q^{29} +(0.441794 - 1.13719i) q^{30} +(7.47158 + 4.31372i) q^{31} +(-1.19670 - 5.52883i) q^{32} +(1.75204 - 2.44060i) q^{33} +(0.930439 + 0.259037i) q^{34} +(-1.04006 + 0.809159i) q^{35} +(-5.72110 + 1.80806i) q^{36} +1.80500i q^{37} +(5.45104 + 1.51759i) q^{38} +(-7.13475 - 0.708807i) q^{39} +(-0.324745 - 1.37079i) q^{40} +(-2.02753 + 3.51178i) q^{41} +(6.30566 + 1.49620i) q^{42} +(-3.80495 + 2.19679i) q^{43} +(0.0674922 - 3.46848i) q^{44} +(-1.41570 + 0.477895i) q^{45} +(-6.87902 - 7.01418i) q^{46} +(3.51844 + 6.09412i) q^{47} +(-4.25618 + 5.46671i) q^{48} +(-5.01542 - 4.88319i) q^{49} +(1.67610 + 6.50788i) q^{50} +(-0.487275 - 1.07786i) q^{51} +(-7.24905 + 3.99925i) q^{52} -6.29893 q^{53} +(6.19227 + 3.95674i) q^{54} -0.863921i q^{55} +(6.97637 - 2.70743i) q^{56} +(-2.85473 - 6.31473i) q^{57} +(2.91168 + 11.3053i) q^{58} +(-0.661178 - 0.381731i) q^{59} +(-1.03323 + 1.38174i) q^{60} +(5.99548 + 10.3845i) q^{61} +(-8.54310 - 8.71095i) q^{62} +(-3.54601 - 7.10111i) q^{63} +(-0.466686 + 7.98638i) q^{64} +(-1.78552 + 1.03087i) q^{65} +(-3.31269 + 2.66053i) q^{66} +(7.60820 + 4.39260i) q^{67} +(-1.16938 - 0.705825i) q^{68} +(-1.18952 + 11.9735i) q^{69} +(1.72389 - 0.707907i) q^{70} +0.880474i q^{71} +(8.48021 - 0.293305i) q^{72} +8.68914i q^{73} +(0.684629 - 2.45913i) q^{74} +(4.79980 - 6.68615i) q^{75} +(-6.85088 - 4.13512i) q^{76} +(4.54587 - 0.629390i) q^{77} +(9.45153 + 3.67186i) q^{78} +(3.67513 + 6.36551i) q^{79} +(-0.0775039 + 1.99074i) q^{80} +(-1.14453 - 8.92693i) q^{81} +(4.09431 - 4.01542i) q^{82} +(3.97905 - 2.29731i) q^{83} +(-8.02333 - 4.43014i) q^{84} +(-0.294576 - 0.170073i) q^{85} +(6.01710 - 1.54970i) q^{86} +(8.33810 - 11.6150i) q^{87} +(-1.40753 + 4.69985i) q^{88} -14.5608 q^{89} +(2.11001 - 0.114114i) q^{90} +(-6.72513 - 8.64420i) q^{91} +(6.71152 + 12.1653i) q^{92} +(-1.47727 + 14.8700i) q^{93} +(-2.48205 - 9.63717i) q^{94} +(-1.72579 - 0.996387i) q^{95} +(7.87213 - 5.83349i) q^{96} +(11.1727 - 6.45057i) q^{97} +(4.98083 + 8.55519i) q^{98} +(5.10199 + 1.02383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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