LMFDB - Embedded newform 504.2.cc.b.293.9

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			293.9
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36240 - 0.379297i) q^{2} +(-0.713494 - 1.57827i) q^{3} +(1.71227 + 1.03351i) q^{4} +(-0.431334 - 0.249031i) q^{5} +(0.373433 + 2.42086i) q^{6} +(2.62075 + 0.362852i) q^{7} +(-1.94079 - 2.05751i) q^{8} +(-1.98185 + 2.25217i) q^{9} +O(q^{10})$	\(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} +(2.62075 + 0.362852i) 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} +(-3.43288 - 1.48839i) 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} +(-1.29721 - 4.39514i) 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} +(4.11242 + 3.32987i) 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} +(0.100264 + 6.47997i) 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} +(6.73668 + 1.90189i) 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} +(-4.33975 - 6.09644i) 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} +(-6.01114 + 5.18326i) 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} +(1.11006 + 1.49689i) 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} +(-1.72787 - 4.25153i) 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} +(2.32123 - 8.86633i) 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} +(-8.45667 - 5.14633i) 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	0.400440	−	0.916323i	$-0.368857\pi$
$5$	−0.431334	−	0.249031i	−0.192899	−	0.111370i	−0.593339	+	0.804953i	$0.702191\pi$
$6$	0.373433	+	2.42086i	0.152454	+	0.988311i
$7$	2.62075	+	0.362852i	0.990551	+	0.137145i
$7$	2.62075	+	0.362852i	0.990551	+	0.137145i
$8$	−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	$-0.638705\pi$
$13$	2.06976	−	3.58493i	0.574049	−	0.994282i	0.996144	−	0.0877304i	$-0.0279614\pi$
$14$	−3.43288	−	1.48839i	−0.917477	−	0.397789i
$15$	−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	$-0.473608\pi$
$17$	0.682941			0.165638			0.0828188	+	0.996565i	$0.473608\pi$
$18$	3.55431	−	2.31665i	0.837760	−	0.546039i
$19$	4.00106			0.917905			0.458953	−	0.888461i	$-0.348225\pi$
$19$	4.00106			0.917905			0.458953	+	0.888461i	$0.348225\pi$
$20$	−0.481184	−	0.872195i	−0.107596	−	0.195029i
$21$	−1.29721	−	4.39514i	−0.283075	−	0.959098i
$22$	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
$28$	4.11242	+	3.32987i	0.777174	+	0.629286i
$29$	−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	−0.354843	−	0.934926i	$-0.615466\pi$
$31$	−7.47158	−	4.31372i	−1.34193	−	0.774766i	−0.987091	+	0.160159i	$0.948799\pi$
$32$	−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	−0.663139	−	0.748496i	$-0.730776\pi$
$41$	2.02753	−	3.51178i	0.316647	−	0.548448i	0.979786	+	0.200048i	$0.0641097\pi$
$42$	0.100264	+	6.47997i	0.0154711	+	0.999880i
$43$	−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	$-0.995120\pi$
$47$	−3.51844	−	6.09412i	−0.513218	−	0.888919i	0.486665	−	0.873589i	$-0.338213\pi$
$48$	4.25618	−	5.46671i	0.614327	−	0.789052i
$49$	6.73668	+	1.90189i	0.962382	+	0.271698i
$50$	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
$56$	−4.33975	−	6.09644i	−0.579924	−	0.814671i
$57$	−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	0.542421	−	0.840107i	$-0.317508\pi$
$59$	0.661178	+	0.381731i	0.0860780	+	0.0496972i	−0.456343	+	0.889804i	$0.650841\pi$
$60$	−1.03323	+	1.38174i	−0.133390	+	0.178382i
$61$	−5.99548	−	10.3845i	−0.767643	−	1.32960i	−0.938838	−	0.344359i	$-0.888096\pi$
$61$	−5.99548	−	10.3845i	−0.767643	−	1.32960i	0.171196	−	0.985237i	$-0.445237\pi$
$62$	8.54310	+	8.71095i	1.08497	+	1.10629i
$63$	−6.01114	+	5.18326i	−0.757333	+	0.653029i
$64$	−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
$70$	1.11006	+	1.49689i	0.132678	+	0.178912i
$71$			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	$-0.830203\pi$
$73$		−	8.68914i		−	1.01699i	0.861066	−	0.508493i	$-0.169797\pi$
$74$	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
$77$	−1.72787	−	4.25153i	−0.196909	−	0.484507i
$78$	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	−0.702221	−	0.711959i	$-0.747808\pi$
$83$	−3.97905	+	2.29731i	−0.436758	+	0.252162i	0.265464	+	0.964121i	$0.414475\pi$
$84$	2.32123	−	8.86633i	0.253267	−	0.967396i
$85$	−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	$-0.219396\pi$
$89$	14.5608			1.54344			0.771721	+	0.635962i	$0.219396\pi$
$90$	−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	−0.945042	−	0.326949i	$-0.893980\pi$
$97$	−11.1727	+	6.45057i	−1.13442	+	0.654956i	−0.189375	+	0.981905i	$0.560646\pi$
$98$	−8.45667	−	5.14633i	−0.854253	−	0.519858i
$99$	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	−0.384507	−	0.923122i	$-0.625629\pi$
$101$	2.23797	−	1.29209i	0.222686	−	0.128568i	0.607194	+	0.794554i	$0.292295\pi$
$102$	0.255033	+	1.65330i	0.0252520	+	0.163701i
$103$	5.59021	+	3.22751i	0.550820	+	0.318016i	0.749453	−	0.662058i	$-0.230317\pi$
$103$	5.59021	+	3.22751i	0.550820	+	0.318016i	−0.198633	+	0.980074i	$0.563650\pi$
$104$	−11.3930	+	2.69904i	−1.11718	+	0.264663i
$105$	−0.534992	+	2.21882i	−0.0522099	+	0.216535i
$106$	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
$112$	3.60012	+	9.95184i	0.340179	+	0.940361i
$113$	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
$119$	1.78982	+	0.247806i	0.164072	+	0.0227164i
$120$	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
$126$	10.1556	−	4.78166i	0.904731	−	0.425984i
$127$	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	0.484988	−	0.874521i	$-0.338824\pi$
$131$	−0.341929	−	0.197413i	−0.0298745	−	0.0172480i	−0.514863	+	0.857273i	$0.672157\pi$
$132$	−5.52234	+	2.36822i	−0.480658	+	0.206127i
$133$	10.4858	+	1.45179i	0.909232	+	0.125886i
$134$	−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	$0.436297\pi$
$139$	−8.83461	+	15.3020i	−0.749342	+	1.29790i	−0.948139	+	0.317857i	$0.897037\pi$
$140$	−0.944587	−	2.46041i	−0.0798322	−	0.207942i
$141$	−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
$147$	−1.80489	−	11.9893i	−0.148865	−	0.988858i
$148$	−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
$154$	0.741452	+	6.44766i	0.0597479	+	0.519567i
$155$	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	−0.936867	−	0.349686i	$-0.886288\pi$
$157$	−2.07492	+	3.59387i	−0.165597	+	0.286822i	0.771270	+	0.636508i	$0.219622\pi$
$158$	−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	−0.834174	−	0.551501i	$-0.814055\pi$
$167$	0.782182	−	1.35478i	0.0605271	−	0.104836i	0.894701	+	0.446665i	$0.147389\pi$
$168$	−6.52542	+	11.1991i	−0.503447	+	0.864026i
$169$	−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	−0.422724	−	0.906259i	$-0.638926\pi$
$173$	1.98290	−	1.14483i	0.150757	−	0.0870396i	0.573481	+	0.819219i	$0.305593\pi$
$174$	15.7654	−	12.6617i	1.19517	−	0.959881i
$175$	−4.73358	−	11.6473i	−0.357825	−	0.880452i
$176$	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	$-0.675918\pi$
$181$	−14.1251			−1.04991			−0.524955	+	0.851130i	$0.675918\pi$
$182$	−12.4410	+	9.22604i	−0.922191	+	0.683880i
$183$	−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
$189$	12.4695	+	5.78896i	0.907021	+	0.421085i
$190$	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
$196$	9.56938	+	10.2190i	0.683527	+	0.729925i
$197$	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	$-0.699570\pi$
$199$		−	22.8476i		−	1.61962i	0.586691	−	0.809811i	$-0.300430\pi$
$200$	−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
$203$	−8.22306	−	20.2334i	−0.577146	−	1.42011i
$204$	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
$210$	1.57046	−	2.82000i	0.108372	−	0.194598i
$211$	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	−0.603831	−	0.797112i	$-0.706360\pi$
$223$	−3.21702	+	1.85735i	−0.215428	+	0.124377i	0.388404	+	0.921489i	$0.373027\pi$
$224$	−1.13010	−	14.9239i	−0.0755081	−	0.997145i
$225$	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	0.298349	−	0.954457i	$-0.403564\pi$
$227$	19.1964	−	11.0830i	1.27411	−	0.735606i	0.975758	+	0.218851i	$0.0702308\pi$
$228$	1.63826	−	13.7629i	0.108497	−	0.911471i
$229$	7.23036	−	12.5234i	0.477796	−	0.827566i	−0.521880	−	0.853019i	$-0.674769\pi$
$229$	7.23036	−	12.5234i	0.477796	−	0.827566i	0.999676	+	0.0254523i	$0.00810260\pi$
$230$	1.22041	+	4.73854i	0.0804714	+	0.312450i
$231$	−5.47723	+	5.76048i	−0.360375	+	0.379012i
$232$	−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
$238$	−2.34446	−	1.01648i	−0.151969	−	0.0658889i
$239$	−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	−0.676133	−	0.736780i	$-0.736345\pi$
$241$	−5.83909	+	3.37120i	−0.376129	+	0.217158i	0.300004	+	0.953938i	$0.403012\pi$
$242$	−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
$245$	−2.43213	−	2.49799i	−0.155383	−	0.159591i
$246$	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	$0.120734\pi$
$251$			11.7323i			0.740537i	−0.928925	+	0.370268i	$0.879266\pi$
$252$	−15.6496	+	2.66256i	−0.985834	+	0.167726i
$253$		−	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	−0.894967	−	0.446133i	$-0.852801\pi$
$257$	−0.979848	+	1.69715i	−0.0611212	+	0.105865i	0.833846	+	0.551998i	$0.186134\pi$
$258$	−6.73901	−	8.39089i	−0.419553	−	0.522394i
$259$	−0.654946	+	4.73045i	−0.0406964	+	0.293936i
$260$	−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
$266$	−13.7352	−	5.95514i	−0.842157	−	0.365133i
$267$	−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	$0.309566\pi$
$269$			27.1051i			1.65263i	−0.563211	+	0.826313i	$0.690434\pi$
$270$	1.68559	+	3.24875i	0.102581	+	0.197712i
$271$			4.16264i			0.252862i	0.991975	+	0.126431i	$0.0403522\pi$
$271$			4.16264i			0.252862i	−0.991975	+	0.126431i	$0.959648\pi$
$272$	1.27281	+	2.41712i	0.0771756	+	0.146560i
$273$	−18.4412	−	4.44646i	−1.11611	−	0.269112i
$274$	−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
$280$	0.353682	+	3.71033i	0.0211365	+	0.221735i
$281$	−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	−0.999604	−	0.0281233i	$-0.991047\pi$
$283$	−7.99825	+	13.8534i	−0.475447	+	0.823498i	0.524158	+	0.851621i	$0.324380\pi$
$284$	−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	0.101669	−	0.994818i	$-0.467582\pi$
$293$	−12.1367	−	7.00713i	−0.709034	−	0.409361i	−0.810703	+	0.585457i	$0.800915\pi$
$294$	−2.08850	+	17.0188i	−0.121804	+	0.992554i
$295$	−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
$301$	−10.7689	+	4.37661i	−0.620712	+	0.252264i
$302$	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	$-0.144924\pi$
$307$	31.4731			1.79627			0.898133	+	0.439724i	$0.144924\pi$
$308$	1.43542	−	9.06553i	0.0817908	−	0.516556i
$309$	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	−0.998520	−	0.0543845i	$-0.982680\pi$
$311$	−7.97396	+	13.8113i	−0.452162	+	0.783167i	0.546358	+	0.837551i	$0.316014\pi$
$312$	12.3887	+	16.0554i	0.701369	+	0.908961i
$313$	−26.6531	+	15.3882i	−1.50652	+	0.869791i	−0.506550	+	0.862210i	$0.669080\pi$
$313$	−26.6531	+	15.3882i	−1.50652	+	0.869791i	−0.999971	+	0.00758028i	$0.997587\pi$
$314$	4.19001	−	4.10928i	0.236456	−	0.231900i
$315$	3.88360	−	0.738755i	0.218816	−	0.0416242i
$316$	−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
$322$	−15.4831	−	20.8785i	−0.862839	−	1.16351i
$323$	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
$329$	−7.00970	−	17.2479i	−0.386458	−	0.950905i
$330$	−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
$336$	13.1380	−	12.7825i	0.716736	−	0.697344i
$337$	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	$0.00491967\pi$
$349$	9.58970	+	16.6098i	0.513325	+	0.889104i	−0.486556	+	0.873649i	$0.661747\pi$
$350$	2.03125	+	17.6637i	0.108575	+	0.944165i
$351$	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	$0.253863\pi$
$353$	18.2058	+	31.5333i	0.968995	+	1.67835i	0.270521	+	0.962714i	$0.412804\pi$
$354$	−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
$357$	−0.885921	−	3.00162i	−0.0468879	−	0.158863i
$358$	−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
$364$	20.4491	−	7.85072i	1.07182	−	0.411489i
$365$	−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	0.00261134	−	0.999997i	$-0.499169\pi$
$367$	16.6656	−	9.62191i	0.869939	−	0.502260i	0.867328	+	0.497737i	$0.165835\pi$
$368$	−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
$371$	−16.5079	−	2.28558i	−0.857048	−	0.118661i
$372$	−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
$378$	−14.7927	−	12.6165i	−0.760854	−	0.648924i
$379$		−	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	−0.537412	−	0.843320i	$-0.680598\pi$
$383$	9.03429	−	15.6479i	0.461631	−	0.799568i	0.999042	+	0.0437521i	$0.0139312\pi$
$384$	−19.5081	+	1.85260i	−0.995521	+	0.0945401i
$385$	−0.313475	+	2.26412i	−0.0159762	+	0.115390i
$386$	−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
$392$	−9.16131	−	17.5519i	−0.462716	−	0.886507i
$393$	−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	$-0.506779\pi$
$397$	−0.848670			−0.0425935			−0.0212968	+	0.999773i	$0.506779\pi$
$398$	−8.66601	+	31.1275i	−0.434388	+	1.56028i
$399$	−5.19023	−	17.5852i	−0.259836	−	0.880361i
$400$	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
$406$	3.52864	+	30.6850i	0.175123	+	1.52287i
$407$	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	0.166096	−	0.986110i	$-0.446884\pi$
$409$	−12.2324	−	7.06236i	−0.604851	−	0.349211i	−0.770948	+	0.636898i	$0.780217\pi$
$410$	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	−0.0763092	−	0.997084i	$-0.524314\pi$
$419$	−20.0184	−	11.5576i	−0.977964	−	0.564628i	−0.901655	+	0.432456i	$0.857647\pi$
$420$	−3.20922	+	3.24630i	−0.156594	+	0.158403i
$421$	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
$427$	−11.9446	−	29.3906i	−0.578042	−	1.42231i
$428$	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	$0.364633\pi$
$433$			37.9104i			1.82186i	−0.412564	+	0.910929i	$0.635367\pi$
$434$	19.2286	+	25.9291i	0.923000	+	1.24464i
$435$	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	−0.0731080	−	0.997324i	$-0.523292\pi$
$439$	15.7990	−	9.12157i	0.754046	−	0.435349i	0.827154	+	0.561975i	$0.189958\pi$
$440$	1.77753	−	1.67669i	0.0847402	−	0.0799330i
$441$	−17.6345	+	11.4029i	−0.839737	+	0.542994i
$442$	−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
$448$	−4.12094	+	20.7610i	−0.194696	+	0.980864i
$449$		−	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
$455$	−5.05345	+	2.05378i	−0.236910	+	0.0962825i
$456$	−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	0.0683891	−	0.997659i	$-0.478214\pi$
$461$	20.7534	−	11.9820i	0.966581	−	0.558056i	0.898192	+	0.439603i	$0.144881\pi$
$462$	9.64711	−	5.77058i	0.448824	−	0.268472i
$463$	−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	$-0.929540\pi$
$467$		−	9.48919i		−	0.439107i	0.975600	−	0.219554i	$-0.0704601\pi$
$468$	−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
$476$	2.80854	+	2.27410i	0.128729	+	0.104233i
$477$	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	$0.0773195\pi$
$479$	15.1807	+	26.2937i	0.693622	+	1.20139i	−0.277021	+	0.960864i	$0.589347\pi$
$480$	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
$483$	7.46203	−	30.9479i	0.339534	−	1.40818i
$484$	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
$490$	2.36606	+	4.32576i	0.106887	+	0.195418i
$491$	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
$497$	−0.319482	+	2.30750i	−0.0143307	+	0.103506i
$498$	−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	$-0.722556\pi$
$503$	−28.8684			−1.28718			−0.643589	+	0.765371i	$0.722556\pi$
$504$	22.3310	+	2.30838i	0.994700	+	0.102823i
$505$	−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	−0.0538888	−	0.998547i	$-0.517162\pi$
$509$	−21.3337	−	12.3170i	−0.945600	−	0.545943i	−0.891711	+	0.452604i	$0.850495\pi$
$510$	0.301719	−	0.776637i	0.0133603	−	0.0343901i
$511$	3.15287	−	22.7721i	0.139475	−	1.00738i
$512$	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
$518$	2.68654	−	6.19634i	0.118040	−	0.272252i
$519$	−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	$-0.344654\pi$
$521$	21.4052			0.937778			0.468889	+	0.883257i	$0.344654\pi$
$522$	−31.2320	−	15.8479i	−1.36699	−	0.693644i
$523$	8.94262			0.391033			0.195517	−	0.980700i	$-0.437362\pi$
$523$	8.94262			0.391033			0.195517	+	0.980700i	$0.437362\pi$
$524$	−0.381446	−	0.691410i	−0.0166636	−	0.0302044i
$525$	−15.0052	+	15.7811i	−0.654879	+	0.688745i
$526$	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
$532$	16.4540	+	13.3230i	0.713372	+	0.577625i
$533$	−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
$546$	23.4378	+	13.0525i	1.00304	+	0.558598i
$547$	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
$553$	7.32187	+	18.0160i	0.311357	+	0.766116i
$554$	−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
$560$	0.925462	−	5.18911i	0.0391079	−	0.219280i
$561$	−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	0.588702	−	0.808350i	$-0.299639\pi$
$563$	4.34221	+	2.50697i	0.183002	+	0.105656i	−0.405700	+	0.914006i	$0.632972\pi$
$564$	−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
$567$	0.239624	−	23.8106i	0.0100633	−	0.999949i
$568$	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
$574$	−12.1872	+	9.03778i	−0.508683	+	0.377230i
$575$		−	33.0113i		−	1.37667i
$576$	−17.0618	−	16.8789i	−0.710907	−	0.703286i
$577$		−	35.1794i		−	1.46454i	−0.681015	−	0.732270i	$-0.738461\pi$
$577$		−	35.1794i		−	1.46454i	0.681015	−	0.732270i	$-0.261539\pi$
$578$	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
$581$	−11.2617	+	4.57686i	−0.467214	+	0.189880i
$582$	−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	−0.151442	−	0.988466i	$-0.548392\pi$
$587$	15.2364	−	8.79674i	0.628873	−	0.363080i	0.780316	+	0.625386i	$0.215058\pi$
$588$	9.30053	−	22.3942i	0.383547	−	0.923521i
$589$	−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	$-0.680346\pi$
$593$	−26.1411			−1.07349			−0.536744	+	0.843745i	$0.680346\pi$
$594$	−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	−0.0407879	−	0.999168i	$-0.512987\pi$
$601$	19.7133	−	11.3815i	0.804123	−	0.464261i	0.844911	+	0.534907i	$0.179653\pi$
$602$	16.3316	−	1.87807i	0.665628	−	0.0765442i
$603$	−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	0.940451	−	0.339931i	$-0.110404\pi$
$607$	27.5024	+	15.8785i	1.11629	+	0.644489i	0.175837	+	0.984419i	$0.443737\pi$
$608$	−4.78805	−	22.1211i	−0.194181	−	0.897131i
$609$	−26.0666	+	27.4146i	−1.05627	+	1.11090i
$610$	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
$616$	−5.39414	+	11.8064i	−0.217336	+	0.475694i
$617$	−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	0.798744	−	0.601671i	$-0.205498\pi$
$619$	−3.02761	−	5.24398i	−0.121690	−	0.210773i	−0.920434	+	0.390897i	$0.872165\pi$
$620$	−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
$623$	38.1602	+	5.28341i	1.52886	+	0.211675i
$624$	−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
$630$	−5.57123	−	0.466558i	−0.221963	−	0.0185881i
$631$	−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
$637$	20.7615	−	20.2141i	0.822599	−	0.800911i
$638$	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	−0.580824	−	0.814029i	$-0.697269\pi$
$643$	10.5121	−	18.2076i	0.414558	−	0.718036i	0.995382	+	0.0959934i	$0.0306028\pi$
$644$	13.1750	+	34.3175i	0.519169	+	1.35230i
$645$	−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	$-0.404312\pi$
$647$	15.0636			0.592212			0.296106	+	0.955155i	$0.404312\pi$
$648$	−16.1459	+	19.6802i	−0.634273	+	0.773109i
$649$		−	1.32428i		−	0.0519824i
$650$	26.7994	+	7.46105i	1.05116	+	0.292647i
$651$	−9.26714	+	38.4344i	−0.363208	+	1.50636i
$652$	−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
$658$	3.00797	+	26.1572i	0.117263	+	1.01972i
$659$	−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	−0.826208	−	0.563366i	$-0.809506\pi$
$661$	1.92273	−	3.33026i	0.0747854	−	0.129532i	0.900993	+	0.433834i	$0.142840\pi$
$662$	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
$672$	−22.7476	+	12.4317i	−0.877507	+	0.479564i
$673$	−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	−0.832743	−	0.553659i	$-0.813231\pi$
$677$	−20.0252	+	11.5616i	−0.769632	+	0.444347i	0.0631112	+	0.998006i	$0.479898\pi$
$678$	−16.8061	+	43.2596i	−0.645435	+	1.66137i
$679$	−31.6215	+	12.8513i	−1.21352	+	0.493188i
$680$	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
$686$	−20.2955	−	16.5558i	−0.774885	−	0.632102i
$687$	−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	0.997355	−	0.0726787i	$-0.0231548\pi$
$691$	11.4541	+	19.8392i	0.435736	+	0.754717i	−0.561619	+	0.827396i	$0.689821\pi$
$692$	4.57844	+	0.0890907i	0.174046	+	0.00338672i
$693$	12.9995	+	4.53446i	0.493812	+	0.172250i
$694$	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
$700$	3.93241	−	24.8355i	0.148631	−	0.938693i
$701$	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
$707$	6.33401	−	2.57420i	0.238215	−	0.0968129i
$708$	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
$714$	0.0684745	+	4.42543i	0.00256259	+	0.165618i
$715$	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	$-0.878109\pi$
$719$	−49.7442			−1.85515			−0.927573	+	0.373642i	$0.878109\pi$
$720$	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	−0.847416	−	0.530930i	$-0.821843\pi$
$727$	−21.8757	+	12.6299i	−0.811325	+	0.468419i	0.0360908	+	0.999349i	$0.488509\pi$
$728$	−30.8376	+	2.93955i	−1.14292	+	0.108947i
$729$	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	$-0.556554\pi$
$733$	20.6852	−	35.8278i	0.764025	−	1.32333i	0.940760	−	0.339072i	$-0.110113\pi$
$734$	−26.3548	+	6.78767i	−0.972775	+	0.250538i
$735$	−2.20718	+	5.62085i	−0.0814132	+	0.207328i
$736$	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
$742$	21.6235	+	9.37527i	0.793823	+	0.344177i
$743$	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
$749$	20.6306	+	2.85637i	0.753824	+	0.104369i
$750$	−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
$756$	15.3682	+	22.7996i	0.558934	+	0.829212i
$757$		−	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	−0.870658	−	0.491889i	$-0.836307\pi$
$761$	−0.257686	+	0.446325i	−0.00934111	+	0.0161793i	0.861317	+	0.508068i	$0.169640\pi$
$762$	5.09379	+	33.0215i	0.184529	+	1.19624i
$763$	3.43836	−	24.8341i	0.124477	−	0.899053i
$764$	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	0.973326	−	0.229428i	$-0.0736854\pi$
$769$	34.9769	+	20.1939i	1.26130	+	0.728211i	0.287973	+	0.957639i	$0.407019\pi$
$770$	1.28585	−	2.96574i	0.0463389	−	0.106878i
$771$	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	$-0.854393\pi$
$773$		−	24.5583i		−	0.883300i	0.897187	−	0.441650i	$-0.145607\pi$
$774$	−8.43482	+	16.6228i	−0.303183	+	0.597495i
$775$			40.9970i			1.47266i
$776$	34.9560	+	10.4688i	1.25485	+	0.375807i
$777$	7.93321	−	2.34147i	0.284602	−	0.0839997i
$778$	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
$784$	5.82398	+	27.3876i	0.207999	+	0.978129i
$785$	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	−0.966185	−	0.257851i	$-0.916986\pi$
$787$	−7.28792	+	12.6231i	−0.259786	+	0.449963i	0.706398	+	0.707815i	$0.250319\pi$
$788$	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	0.974532	−	0.224249i	$-0.0719928\pi$
$797$	35.7856	+	20.6609i	1.26759	+	0.731845i	0.293061	+	0.956094i	$0.405326\pi$
$798$	0.401162	+	25.9267i	0.0142010	+	0.917796i
$799$	−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
$805$	−3.44663	−	8.48068i	−0.121478	−	0.298905i
$806$	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	$-0.704599\pi$
$811$	−34.1402			−1.19883			−0.599413	+	0.800440i	$0.704599\pi$
$812$	6.83130	−	43.1436i	0.239732	−	1.51404i
$813$	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
$819$	6.13999	+	32.2777i	0.214549	+	1.12787i
$820$	−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
$826$	−1.70158	−	2.29453i	−0.0592056	−	0.0798369i
$827$	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	$-0.600539\pi$
$829$	−17.8875			−0.621257			−0.310628	+	0.950531i	$0.600539\pi$
$830$	−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
$833$	4.60075	+	1.29888i	0.159407	+	0.0450034i
$834$	−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	0.518020	−	0.855369i	$-0.326669\pi$
$839$	−13.9545	−	24.1698i	−0.481761	−	0.834435i	−0.999781	+	0.0209337i	$0.993336\pi$
$840$	5.60355	−	3.20551i	0.193341	−	0.110601i
$841$	−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	$0.00234008\pi$
$853$	14.7886	+	25.6147i	0.506353	+	0.877029i	−0.493620	+	0.869678i	$0.664327\pi$
$854$	5.12562	+	44.5723i	0.175395	+	1.52523i
$855$	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	0.903197	−	0.429226i	$-0.141214\pi$
$857$	2.33838	+	4.05019i	0.0798775	+	0.138352i	−0.823319	+	0.567578i	$0.807880\pi$
$858$	−2.68136	−	17.3824i	−0.0915400	−	0.593427i
$859$	−22.7435	+	39.3929i	−0.775999	+	1.34407i	0.158232	+	0.987402i	$0.449421\pi$
$859$	−22.7435	+	39.3929i	−0.775999	+	1.34407i	−0.934231	+	0.356668i	$0.883913\pi$
$860$	3.74691	+	2.26160i	0.127769	+	0.0771199i
$861$	−18.0649	−	4.35573i	−0.615650	−	0.148443i
$862$	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
$868$	−16.3621	−	42.6192i	−0.555367	−	1.44659i
$869$	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
$875$	−1.76239	+	12.7292i	−0.0595798	+	0.430324i
$876$	−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	$-0.554851\pi$
$881$	−10.1789			−0.342935			−0.171467	+	0.985190i	$0.554851\pi$
$882$	28.3503	−	8.84658i	0.954603	−	0.297880i
$883$			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	−0.704866	−	0.709341i	$-0.748993\pi$
$887$	7.79927	−	13.5087i	0.261874	−	0.453579i	0.966740	+	0.255761i	$0.0823262\pi$
$888$	−8.17862	−	3.36191i	−0.274457	−	0.112818i
$889$	35.7482	+	4.94946i	1.19896	+	0.165999i
$890$	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
$896$	13.4889	−	26.7217i	0.450634	−	0.892709i
$897$	−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
$903$	14.5910	+	13.8736i	0.485559	+	0.461684i
$904$	−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
$910$	7.66382	−	0.881305i	0.254053	−	0.0292150i
$911$	−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
$924$	−15.3320	+	4.20272i	−0.504385	+	0.138259i
$925$	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	$0.148832\pi$
$929$	25.5012	+	44.1694i	0.836667	+	1.44915i	−0.0559987	+	0.998431i	$0.517834\pi$
$930$	−8.20643	+	6.59087i	−0.269099	+	0.216123i
$931$	26.9538	+	7.60956i	0.883376	+	0.249393i
$932$	−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	$0.0290599\pi$
$937$			5.58136i			0.182335i	−0.995836	+	0.0911675i	$0.970940\pi$
$938$	−19.5802	−	26.4033i	−0.639315	−	0.862097i
$939$	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	−0.380481	−	0.924789i	$-0.624241\pi$
$941$	−42.0752	−	24.2921i	−1.37161	−	0.791900i	−0.991131	+	0.132889i	$0.957575\pi$
$942$	−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
$945$	−3.93688	−	5.60226i	−0.128067	−	0.182242i
$946$	−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
$952$	−2.96379	−	4.16351i	−0.0960571	−	0.134940i
$953$		−	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
$959$	2.00517	−	0.814923i	0.0647504	−	0.0263152i
$960$	−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
$966$	−21.9047	+	39.3331i	−0.704773	+	1.26552i
$967$	−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	$-0.912566\pi$
$971$		−	16.9042i		−	0.542483i	0.962511	−	0.271241i	$-0.0874341\pi$
$972$	−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
$980$	−1.58277	−	6.79086i	−0.0505596	−	0.216926i
$981$	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	0.599854	−	0.800109i	$-0.295225\pi$
$983$	−12.3213	−	21.3411i	−0.392988	−	0.680675i	−0.992842	+	0.119434i	$0.961892\pi$
$984$	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
$987$	−22.2203	+	23.3694i	−0.707281	+	0.743857i
$988$	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
$994$	1.31049	−	3.02257i	0.0415662	−	0.0958700i
$995$	−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	0.866221	−	0.499661i	$-0.166542\pi$
$997$	0.0123580	+	0.0214046i	0.000391381	+	0.000677892i	−0.865830	+	0.500339i	$0.833209\pi$
$998$	−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.293.9	✓	168
7.6	odd	2	inner	504.2.cc.b.293.10	yes	168
8.5	even	2	inner	504.2.cc.b.293.40	yes	168
9.2	odd	6	inner	504.2.cc.b.461.39	yes	168
56.13	odd	2	inner	504.2.cc.b.293.39	yes	168
63.20	even	6	inner	504.2.cc.b.461.40	yes	168
72.29	odd	6	inner	504.2.cc.b.461.10	yes	168
504.461	even	6	inner	504.2.cc.b.461.9	yes	168

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

\(f(q)\)	\(=\)	\(q+(-1.36240 - 0.379297i) q^{2} +(-0.713494 - 1.57827i) q^{3} +(1.71227 + 1.03351i) q^{4} +(-0.431334 - 0.249031i) q^{5} +(0.373433 + 2.42086i) q^{6} +(2.62075 + 0.362852i) q^{7} +(-1.94079 - 2.05751i) q^{8} +(-1.98185 + 2.25217i) q^{9} +O(q^{10})\)	\(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} +(2.62075 + 0.362852i) 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} +(-3.43288 - 1.48839i) 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} +(-1.29721 - 4.39514i) 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} +(4.11242 + 3.32987i) 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} +(0.100264 + 6.47997i) 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} +(6.73668 + 1.90189i) 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} +(-4.33975 - 6.09644i) 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} +(-6.01114 + 5.18326i) 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} +(1.11006 + 1.49689i) 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} +(-1.72787 - 4.25153i) 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} +(2.32123 - 8.86633i) 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} +(-8.45667 - 5.14633i) 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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