LMFDB - Embedded newform 240.2.bl.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [240,2,Mod(109,240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(240, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 0, 2]))

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

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

chi := DirichletCharacter("240.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 240 = 2^{4} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	240.bl (of order $4$, 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:	$1.91640964851$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.1
Character	$\chi$	$=$	240.109
Dual form			240.2.bl.a.229.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40976 - 0.112110i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97486 + 0.316097i) q^{4} +(2.18678 + 0.466917i) q^{5} +(1.07613 - 0.917579i) q^{6} +1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.40976 - 0.112110i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97486 + 0.316097i) q^{4} +(2.18678 + 0.466917i) q^{5} +(1.07613 - 0.917579i) q^{6} +1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} -1.00000i q^{9} +(-3.03049 - 0.903402i) q^{10} +(-1.89490 + 1.89490i) q^{11} +(-1.61995 + 1.17292i) q^{12} +(2.65915 - 2.65915i) q^{13} +(-1.40991 - 0.112121i) q^{14} +(-1.87644 + 1.21612i) q^{15} +(3.80016 + 1.24850i) q^{16} +1.73836i q^{17} +(-0.112110 + 1.40976i) q^{18} +(5.33902 + 5.33902i) q^{19} +(4.17099 + 1.61333i) q^{20} +(-0.707179 + 0.707179i) q^{21} +(2.88380 - 2.45892i) q^{22} +0.160230 q^{23} +(2.41525 - 1.47193i) q^{24} +(4.56398 + 2.04209i) q^{25} +(-4.04689 + 3.45065i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.97506 + 0.316129i) q^{28} +(2.70291 + 2.70291i) q^{29} +(2.78168 - 1.50408i) q^{30} -4.64288 q^{31} +(-5.21736 - 2.18612i) q^{32} -2.67980i q^{33} +(0.194888 - 2.45068i) q^{34} +(2.18700 + 0.466965i) q^{35} +(0.316097 - 1.97486i) q^{36} +(5.35773 + 5.35773i) q^{37} +(-6.92819 - 8.12530i) q^{38} +3.76061i q^{39} +(-5.69924 - 2.74202i) q^{40} -9.89786i q^{41} +(1.07624 - 0.917672i) q^{42} +(-7.23165 - 7.23165i) q^{43} +(-4.34114 + 3.14320i) q^{44} +(0.466917 - 2.18678i) q^{45} +(-0.225886 - 0.0179634i) q^{46} +4.79583i q^{47} +(-3.56994 + 1.80430i) q^{48} -5.99980 q^{49} +(-6.20519 - 3.39053i) q^{50} +(-1.22921 - 1.22921i) q^{51} +(6.09201 - 4.41091i) q^{52} +(3.44618 + 3.44618i) q^{53} +(-0.917579 - 1.07613i) q^{54} +(-5.02849 + 3.25896i) q^{55} +(-2.74893 - 0.667092i) q^{56} -7.55051 q^{57} +(-3.50744 - 4.11349i) q^{58} +(0.101729 - 0.101729i) q^{59} +(-4.09013 + 1.80854i) q^{60} +(-6.01811 - 6.01811i) q^{61} +(6.54535 + 0.520513i) q^{62} -1.00010i q^{63} +(7.11016 + 3.66683i) q^{64} +(7.05657 - 4.57336i) q^{65} +(-0.300432 + 3.77788i) q^{66} +(9.04430 - 9.04430i) q^{67} +(-0.549491 + 3.43302i) q^{68} +(-0.113300 + 0.113300i) q^{69} +(-3.03080 - 0.903494i) q^{70} -4.60679i q^{71} +(-0.667024 + 2.74865i) q^{72} -12.1920 q^{73} +(-6.95248 - 8.15379i) q^{74} +(-4.67119 + 1.78325i) q^{75} +(8.85617 + 12.2315i) q^{76} +(-1.89509 + 1.89509i) q^{77} +(0.421602 - 5.30156i) q^{78} -5.73529 q^{79} +(7.72716 + 4.50455i) q^{80} -1.00000 q^{81} +(-1.10965 + 13.9536i) q^{82} +(2.04924 - 2.04924i) q^{83} +(-1.62012 + 1.17304i) q^{84} +(-0.811670 + 3.80140i) q^{85} +(9.38417 + 11.0057i) q^{86} -3.82249 q^{87} +(6.47237 - 3.94448i) q^{88} -15.0386i q^{89} +(-0.903402 + 3.03049i) q^{90} +(2.65942 - 2.65942i) q^{91} +(0.316432 + 0.0506483i) q^{92} +(3.28301 - 3.28301i) q^{93} +(0.537662 - 6.76099i) q^{94} +(9.18235 + 14.1681i) q^{95} +(5.23505 - 2.14341i) q^{96} +3.84735i q^{97} +(8.45829 + 0.672638i) q^{98} +(1.89490 + 1.89490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) $ 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/240\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$161$	$181$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.40976	−	0.112110i	−0.996853	−	0.0792738i
$2$	−1.40976	−	0.112110i	−0.996853	−	0.0792738i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.97486	+	0.316097i	0.987431	+	0.158049i
$5$	2.18678	+	0.466917i	0.977956	+	0.208812i
$5$	2.18678	+	0.466917i	0.977956	+	0.208812i
$6$	1.07613	−	0.917579i	0.439327	−	0.374600i
$7$	1.00010			0.378003			0.189001	−	0.981977i	$-0.439475\pi$
$7$	1.00010			0.378003			0.189001	+	0.981977i	$0.439475\pi$
$8$	−2.74865	−	0.667024i	−0.971795	−	0.235829i
$9$		−	1.00000i		−	0.333333i
$10$	−3.03049	−	0.903402i	−0.958325	−	0.285681i
$11$	−1.89490	+	1.89490i	−0.571334	+	0.571334i	−0.932501	−	0.361167i	$-0.882378\pi$
$11$	−1.89490	+	1.89490i	−0.571334	+	0.571334i	0.361167	+	0.932501i	$0.382378\pi$
$12$	−1.61995	+	1.17292i	−0.467640	+	0.338594i
$13$	2.65915	−	2.65915i	0.737515	−	0.737515i	−0.234581	−	0.972097i	$-0.575372\pi$
$13$	2.65915	−	2.65915i	0.737515	−	0.737515i	0.972097	+	0.234581i	$0.0753718\pi$
$14$	−1.40991	−	0.112121i	−0.376813	−	0.0299657i
$15$	−1.87644	+	1.21612i	−0.484496	+	0.314002i
$16$	3.80016	+	1.24850i	0.950041	+	0.312124i
$17$			1.73836i			0.421614i	0.977528	+	0.210807i	$0.0676092\pi$
$17$			1.73836i			0.421614i	−0.977528	+	0.210807i	$0.932391\pi$
$18$	−0.112110	+	1.40976i	−0.0264246	+	0.332284i
$19$	5.33902	+	5.33902i	1.22485	+	1.22485i	0.965886	+	0.258968i	$0.0833826\pi$
$19$	5.33902	+	5.33902i	1.22485	+	1.22485i	0.258968	+	0.965886i	$0.416617\pi$
$20$	4.17099	+	1.61333i	0.932662	+	0.360752i
$21$	−0.707179	+	0.707179i	−0.154319	+	0.154319i
$22$	2.88380	−	2.45892i	0.614828	−	0.524244i
$23$	0.160230			0.0334103			0.0167051	−	0.999860i	$-0.494682\pi$
$23$	0.160230			0.0334103			0.0167051	+	0.999860i	$0.494682\pi$
$24$	2.41525	−	1.47193i	0.493010	−	0.300457i
$25$	4.56398	+	2.04209i	0.912795	+	0.408417i
$26$	−4.04689	+	3.45065i	−0.793660	+	0.676729i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	1.97506	+	0.316129i	0.373252	+	0.0597428i
$29$	2.70291	+	2.70291i	0.501918	+	0.501918i	0.912034	−	0.410116i	$-0.134512\pi$
$29$	2.70291	+	2.70291i	0.501918	+	0.501918i	−0.410116	+	0.912034i	$0.634512\pi$
$30$	2.78168	−	1.50408i	0.507863	−	0.274606i
$31$	−4.64288			−0.833885			−0.416943	−	0.908933i	$-0.636898\pi$
$31$	−4.64288			−0.833885			−0.416943	+	0.908933i	$0.636898\pi$
$32$	−5.21736	−	2.18612i	−0.922308	−	0.386456i
$33$		−	2.67980i		−	0.466493i
$34$	0.194888	−	2.45068i	0.0334230	−	0.420287i
$35$	2.18700	+	0.466965i	0.369670	+	0.0789314i
$36$	0.316097	−	1.97486i	0.0526829	−	0.329144i
$37$	5.35773	+	5.35773i	0.880806	+	0.880806i	0.993616	−	0.112811i	$-0.0359854\pi$
$37$	5.35773	+	5.35773i	0.880806	+	0.880806i	−0.112811	+	0.993616i	$0.535985\pi$
$38$	−6.92819	−	8.12530i	−1.12390	−	1.31810i
$39$			3.76061i			0.602179i
$40$	−5.69924	−	2.74202i	−0.901128	−	0.433552i
$41$		−	9.89786i		−	1.54579i	−0.634536	−	0.772893i	$-0.718809\pi$
$41$		−	9.89786i		−	1.54579i	0.634536	−	0.772893i	$-0.281191\pi$
$42$	1.07624	−	0.917672i	0.166067	−	0.141600i
$43$	−7.23165	−	7.23165i	−1.10282	−	1.10282i	−0.994069	−	0.108747i	$-0.965316\pi$
$43$	−7.23165	−	7.23165i	−1.10282	−	1.10282i	−0.108747	−	0.994069i	$-0.534684\pi$
$44$	−4.34114	+	3.14320i	−0.654452	+	0.473855i
$45$	0.466917	−	2.18678i	0.0696039	−	0.325985i
$46$	−0.225886	−	0.0179634i	−0.0333051	−	0.00264856i
$47$			4.79583i			0.699544i	0.936835	+	0.349772i	$0.113741\pi$
$47$			4.79583i			0.699544i	−0.936835	+	0.349772i	$0.886259\pi$
$48$	−3.56994	+	1.80430i	−0.515277	+	0.260428i
$49$	−5.99980			−0.857114
$50$	−6.20519	−	3.39053i	−0.877546	−	0.479493i
$51$	−1.22921	−	1.22921i	−0.172123	−	0.172123i
$52$	6.09201	−	4.41091i	0.844809	−	0.611683i
$53$	3.44618	+	3.44618i	0.473369	+	0.473369i	0.903003	−	0.429634i	$-0.141357\pi$
$53$	3.44618	+	3.44618i	0.473369	+	0.473369i	−0.429634	+	0.903003i	$0.641357\pi$
$54$	−0.917579	−	1.07613i	−0.124867	−	0.146442i
$55$	−5.02849	+	3.25896i	−0.678041	+	0.439438i
$56$	−2.74893	−	0.667092i	−0.367341	−	0.0891439i
$57$	−7.55051			−1.00009
$58$	−3.50744	−	4.11349i	−0.460549	−	0.540127i
$59$	0.101729	−	0.101729i	0.0132440	−	0.0132440i	−0.700454	−	0.713698i	$-0.747019\pi$
$59$	0.101729	−	0.101729i	0.0132440	−	0.0132440i	0.713698	+	0.700454i	$0.247019\pi$
$60$	−4.09013	+	1.80854i	−0.528034	+	0.233481i
$61$	−6.01811	−	6.01811i	−0.770540	−	0.770540i	0.207661	−	0.978201i	$-0.433415\pi$
$61$	−6.01811	−	6.01811i	−0.770540	−	0.770540i	−0.978201	+	0.207661i	$0.933415\pi$
$62$	6.54535	+	0.520513i	0.831261	+	0.0661053i
$63$		−	1.00010i		−	0.126001i
$64$	7.11016	+	3.66683i	0.888770	+	0.458354i
$65$	7.05657	−	4.57336i	0.875259	−	0.567256i
$66$	−0.300432	+	3.77788i	−0.0369806	+	0.465024i
$67$	9.04430	−	9.04430i	1.10494	−	1.10494i	0.111131	−	0.993806i	$-0.464553\pi$
$67$	9.04430	−	9.04430i	1.10494	−	1.10494i	0.993806	−	0.111131i	$-0.0354473\pi$
$68$	−0.549491	+	3.43302i	−0.0666356	+	0.416315i
$69$	−0.113300	+	0.113300i	−0.0136397	+	0.0136397i
$70$	−3.03080	−	0.903494i	−0.362250	−	0.107988i
$71$		−	4.60679i		−	0.546726i	−0.961911	−	0.273363i	$-0.911864\pi$
$71$		−	4.60679i		−	0.546726i	0.961911	−	0.273363i	$-0.0881360\pi$
$72$	−0.667024	+	2.74865i	−0.0786096	+	0.323932i
$73$	−12.1920			−1.42697			−0.713485	−	0.700671i	$-0.752884\pi$
$73$	−12.1920			−1.42697			−0.713485	+	0.700671i	$0.752884\pi$
$74$	−6.95248	−	8.15379i	−0.808209	−	0.947858i
$75$	−4.67119	+	1.78325i	−0.539383	+	0.205912i
$76$	8.85617	+	12.2315i	1.01587	+	1.40305i
$77$	−1.89509	+	1.89509i	−0.215966	+	0.215966i
$78$	0.421602	−	5.30156i	0.0477370	−	0.600284i
$79$	−5.73529			−0.645271			−0.322635	−	0.946523i	$-0.604569\pi$
$79$	−5.73529			−0.645271			−0.322635	+	0.946523i	$0.604569\pi$
$80$	7.72716	+	4.50455i	0.863923	+	0.503624i
$81$	−1.00000			−0.111111
$82$	−1.10965	+	13.9536i	−0.122540	+	1.54092i
$83$	2.04924	−	2.04924i	0.224934	−	0.224934i	−0.585639	−	0.810572i	$-0.699156\pi$
$83$	2.04924	−	2.04924i	0.224934	−	0.224934i	0.810572	+	0.585639i	$0.199156\pi$
$84$	−1.62012	+	1.17304i	−0.176769	+	0.127990i
$85$	−0.811670	+	3.80140i	−0.0880380	+	0.412320i
$86$	9.38417	+	11.0057i	1.01192	+	1.18677i
$87$	−3.82249			−0.409814
$88$	6.47237	−	3.94448i	0.689957	−	0.420483i
$89$		−	15.0386i		−	1.59409i	−0.603922	−	0.797044i	$-0.706396\pi$
$89$		−	15.0386i		−	1.59409i	0.603922	−	0.797044i	$-0.293604\pi$
$90$	−0.903402	+	3.03049i	−0.0952269	+	0.319442i
$91$	2.65942	−	2.65942i	0.278783	−	0.278783i
$92$	0.316432	+	0.0506483i	0.0329903	+	0.00528045i
$93$	3.28301	−	3.28301i	0.340432	−	0.340432i
$94$	0.537662	−	6.76099i	0.0554556	−	0.697343i
$95$	9.18235	+	14.1681i	0.942089	+	1.45362i
$96$	5.23505	−	2.14341i	0.534300	−	0.218761i
$97$			3.84735i			0.390639i	0.980740	+	0.195320i	$0.0625744\pi$
$97$			3.84735i			0.390639i	−0.980740	+	0.195320i	$0.937426\pi$
$98$	8.45829	+	0.672638i	0.854416	+	0.0679467i
$99$	1.89490	+	1.89490i	0.190445	+	0.190445i
$100$	8.36773	+	5.47550i	0.836773	+	0.547550i
$101$	5.60917	−	5.60917i	0.558133	−	0.558133i	−0.370642	−	0.928776i	$-0.620862\pi$
$101$	5.60917	−	5.60917i	0.558133	−	0.558133i	0.928776	+	0.370642i	$0.120862\pi$
$102$	1.59508	+	1.87070i	0.157937	+	0.185226i
$103$	−14.9978			−1.47778			−0.738888	−	0.673828i	$-0.764649\pi$
$103$	−14.9978			−1.47778			−0.738888	+	0.673828i	$0.764649\pi$
$104$	−9.08279	+	5.53536i	−0.890641	+	0.542786i
$105$	−1.87663	+	1.21625i	−0.183141	+	0.118694i
$106$	−4.47195	−	5.24465i	−0.434354	−	0.509406i
$107$	−1.22436	−	1.22436i	−0.118363	−	0.118363i	0.645444	−	0.763807i	$-0.276672\pi$
$107$	−1.22436	−	1.22436i	−0.118363	−	0.118363i	−0.763807	+	0.645444i	$0.776672\pi$
$108$	1.17292	+	1.61995i	0.112865	+	0.155880i
$109$	5.31222	+	5.31222i	0.508819	+	0.508819i	0.914164	−	0.405345i	$-0.132849\pi$
$109$	5.31222	+	5.31222i	0.508819	+	0.508819i	−0.405345	+	0.914164i	$0.632849\pi$
$110$	7.45434	−	4.03062i	0.710743	−	0.384305i
$111$	−7.57698			−0.719175
$112$	3.80055	+	1.24862i	0.359118	+	0.117984i
$113$		−	10.5478i		−	0.992249i	−0.868251	−	0.496125i	$-0.834756\pi$
$113$		−	10.5478i		−	0.992249i	0.868251	−	0.496125i	$-0.165244\pi$
$114$	10.6444	+	0.846488i	0.996942	+	0.0792809i
$115$	0.350387	+	0.0748141i	0.0326738	+	0.00697645i
$116$	4.48349	+	6.19226i	0.416282	+	0.574937i
$117$	−2.65915	−	2.65915i	−0.245838	−	0.245838i
$118$	−0.154819	+	0.132009i	−0.0142523	+	0.0121524i
$119$			1.73854i			0.159371i
$120$	5.96887	−	2.09106i	0.544881	−	0.190887i
$121$			3.81870i			0.347154i
$122$	7.80942	+	9.15880i	0.707031	+	0.829199i
$123$	6.99885	+	6.99885i	0.631065	+	0.631065i
$124$	−9.16904	−	1.46760i	−0.823404	−	0.131794i
$125$	9.02691	+	6.59658i	0.807391	+	0.590016i
$126$	−0.112121	+	1.40991i	−0.00998858	+	0.125604i
$127$		−	5.78563i		−	0.513391i	−0.966492	−	0.256696i	$-0.917366\pi$
$127$		−	5.78563i		−	0.513391i	0.966492	−	0.256696i	$-0.0826338\pi$
$128$	−9.61255	−	5.96649i	−0.849637	−	0.527368i
$129$	10.2271			0.900446
$130$	−10.4608	+	5.65624i	−0.917473	+	0.496085i
$131$	−1.01902	−	1.01902i	−0.0890321	−	0.0890321i	0.661188	−	0.750220i	$-0.270053\pi$
$131$	−1.01902	−	1.01902i	−0.0890321	−	0.0890321i	−0.750220	+	0.661188i	$0.770053\pi$
$132$	0.847076	−	5.29223i	0.0737285	−	0.460629i
$133$	5.33956	+	5.33956i	0.462998	+	0.462998i
$134$	−13.7643	+	11.7364i	−1.18905	+	1.01387i
$135$	1.21612	+	1.87644i	0.104667	+	0.161499i
$136$	1.15953	−	4.77814i	0.0994287	−	0.409722i
$137$	−11.1576			−0.953260			−0.476630	−	0.879104i	$-0.658142\pi$
$137$	−11.1576			−0.953260			−0.476630	+	0.879104i	$0.658142\pi$
$138$	0.172428	−	0.147024i	0.0146780	−	0.0125155i
$139$	15.9657	−	15.9657i	1.35419	−	1.35419i	0.473277	−	0.880914i	$-0.343071\pi$
$139$	15.9657	−	15.9657i	1.35419	−	1.35419i	0.880914	−	0.473277i	$-0.156929\pi$
$140$	4.17141	+	1.61350i	0.352549	+	0.136365i
$141$	−3.39117	−	3.39117i	−0.285588	−	0.285588i
$142$	−0.516468	+	6.49449i	−0.0433411	+	0.545005i
$143$			10.0777i			0.842736i
$144$	1.24850	−	3.80016i	0.104041	−	0.316680i
$145$	4.64862	+	7.17270i	0.386047	+	0.595660i
$146$	17.1879	+	1.36685i	1.42248	+	0.113121i
$147$	4.24250	−	4.24250i	0.349915	−	0.349915i
$148$	8.88722	+	12.2743i	0.730525	+	1.00895i
$149$	−14.5202	+	14.5202i	−1.18954	+	1.18954i	−0.212342	+	0.977195i	$0.568109\pi$
$149$	−14.5202	+	14.5202i	−1.18954	+	1.18954i	−0.977195	+	0.212342i	$0.931891\pi$
$150$	6.78519	−	1.99027i	0.554009	−	0.162505i
$151$		−	14.7230i		−	1.19814i	−0.800695	−	0.599072i	$-0.795536\pi$
$151$		−	14.7230i		−	1.19814i	0.800695	−	0.599072i	$-0.204464\pi$
$152$	−11.1138	−	18.2363i	−0.901451	−	1.47916i
$153$	1.73836			0.140538
$154$	2.88409	−	2.45917i	0.232407	−	0.198166i
$155$	−10.1529	−	2.16784i	−0.815503	−	0.174125i
$156$	−1.18872	+	7.42668i	−0.0951736	+	0.594610i
$157$	−9.44726	+	9.44726i	−0.753974	+	0.753974i	−0.975218	−	0.221245i	$-0.928988\pi$
$157$	−9.44726	+	9.44726i	−0.753974	+	0.753974i	0.221245	+	0.975218i	$0.428988\pi$
$158$	8.08540	+	0.642984i	0.643240	+	0.0511531i
$159$	−4.87364			−0.386505
$160$	−10.3885	−	7.21664i	−0.821280	−	0.570525i
$161$	0.160246			0.0126292
$162$	1.40976	+	0.112110i	0.110761	+	0.00880820i
$163$	−7.66138	+	7.66138i	−0.600086	+	0.600086i	−0.940335	−	0.340250i	$-0.889488\pi$
$163$	−7.66138	+	7.66138i	−0.600086	+	0.600086i	0.340250	+	0.940335i	$0.389488\pi$
$164$	3.12869	−	19.5469i	0.244310	−	1.52636i
$165$	1.25124	−	5.86011i	0.0974091	−	0.456209i
$166$	−3.11869	+	2.65921i	−0.242057	+	0.206394i
$167$	14.4195			1.11581			0.557906	−	0.829904i	$-0.311605\pi$
$167$	14.4195			1.11581			0.557906	+	0.829904i	$0.311605\pi$
$168$	2.41549	−	1.47208i	0.186359	−	0.113574i
$169$		−	1.14216i		−	0.0878581i
$170$	1.57044	−	5.26808i	0.120447	−	0.404043i
$171$	5.33902	−	5.33902i	0.408285	−	0.408285i
$172$	−11.9956	−	16.5674i	−0.914657	−	1.26325i
$173$	0.942572	−	0.942572i	0.0716624	−	0.0716624i	−0.670367	−	0.742030i	$-0.733863\pi$
$173$	0.942572	−	0.942572i	0.0716624	−	0.0716624i	0.742030	+	0.670367i	$0.233863\pi$
$174$	5.38881	+	0.428540i	0.408525	+	0.0324875i
$175$	4.56444	+	2.04229i	0.345039	+	0.154383i
$176$	−9.56672	+	4.83516i	−0.721119	+	0.364464i
$177$			0.143867i			0.0108137i
$178$	−1.68598	+	21.2008i	−0.126369	+	1.58907i
$179$	−3.23789	−	3.23789i	−0.242011	−	0.242011i	0.575671	−	0.817682i	$-0.304741\pi$
$179$	−3.23789	−	3.23789i	−0.242011	−	0.242011i	−0.817682	+	0.575671i	$0.804741\pi$
$180$	1.61333	−	4.17099i	0.120251	−	0.310887i
$181$	−13.0914	+	13.0914i	−0.973076	+	0.973076i	−0.999647	−	0.0265713i	$-0.991541\pi$
$181$	−13.0914	+	13.0914i	−0.973076	+	0.973076i	0.0265713	+	0.999647i	$0.491541\pi$
$182$	−4.04730	+	3.45100i	−0.300006	+	0.255805i
$183$	8.51089			0.629143
$184$	−0.440416	−	0.106877i	−0.0324679	−	0.00787910i
$185$	9.21454	+	14.2178i	0.677467	+	1.04531i
$186$	−4.99632	+	4.26021i	−0.366348	+	0.312373i
$187$	−3.29402	−	3.29402i	−0.240883	−	0.240883i
$188$	−1.51595	+	9.47111i	−0.110562	+	0.690752i
$189$	0.707179	+	0.707179i	0.0514397	+	0.0514397i
$190$	−11.3566	−	21.0031i	−0.823891	−	1.52373i
$191$	9.80663			0.709583			0.354791	−	0.934946i	$-0.384552\pi$
$191$	9.80663			0.709583			0.354791	+	0.934946i	$0.384552\pi$
$192$	−7.62048	+	2.43480i	−0.549961	+	0.175716i
$193$			6.82164i			0.491033i	0.969392	+	0.245516i	$0.0789575\pi$
$193$			6.82164i			0.491033i	−0.969392	+	0.245516i	$0.921043\pi$
$194$	0.431327	−	5.42385i	0.0309675	−	0.389410i
$195$	−1.75589	+	8.22360i	−0.125742	+	0.588904i
$196$	−11.8488	−	1.89652i	−0.846341	−	0.135466i
$197$	−15.5142	−	15.5142i	−1.10534	−	1.10534i	−0.993755	−	0.111587i	$-0.964407\pi$
$197$	−15.5142	−	15.5142i	−1.10534	−	1.10534i	−0.111587	−	0.993755i	$-0.535593\pi$
$198$	−2.45892	−	2.88380i	−0.174748	−	0.204943i
$199$			7.92050i			0.561469i	0.959785	+	0.280735i	$0.0905781\pi$
$199$			7.92050i			0.561469i	−0.959785	+	0.280735i	$0.909422\pi$
$200$	−11.1827	−	8.65726i	−0.790733	−	0.612161i
$201$			12.7906i			0.902177i
$202$	−8.53645	+	7.27876i	−0.600622	+	0.512132i
$203$	2.70319	+	2.70319i	0.189726	+	0.189726i
$204$	−2.03896	−	2.81606i	−0.142756	−	0.197164i
$205$	4.62148	−	21.6444i	0.322778	−	1.51171i
$206$	21.1433	+	1.68140i	1.47313	+	0.117149i
$207$		−	0.160230i		−	0.0111368i
$208$	13.4252	−	6.78527i	0.930867	−	0.470474i
$209$	−20.2338			−1.39960
$210$	2.78196	−	1.50423i	0.191974	−	0.103802i
$211$	−10.2008	−	10.2008i	−0.702253	−	0.702253i	0.262641	−	0.964894i	$-0.415406\pi$
$211$	−10.2008	−	10.2008i	−0.702253	−	0.702253i	−0.964894	+	0.262641i	$0.915406\pi$
$212$	5.71641	+	7.89506i	0.392604	+	0.542235i
$213$	3.25750	+	3.25750i	0.223200	+	0.223200i
$214$	1.58879	+	1.86332i	0.108608	+	0.127374i
$215$	−12.4374	−	19.1906i	−0.848225	−	1.30879i
$216$	−1.47193	−	2.41525i	−0.100152	−	0.164337i
$217$	−4.64335			−0.315211
$218$	−6.89342	−	8.08453i	−0.466881	−	0.547553i
$219$	8.62107	−	8.62107i	0.582558	−	0.582558i
$220$	−10.9607	+	4.84651i	−0.738972	+	0.326752i
$221$	4.62256	+	4.62256i	0.310947	+	0.310947i
$222$	10.6817	+	0.849456i	0.716911	+	0.0570117i
$223$		−	13.8689i		−	0.928732i	−0.885643	−	0.464366i	$-0.846282\pi$
$223$		−	13.8689i		−	0.928732i	0.885643	−	0.464366i	$-0.153718\pi$
$224$	−5.21789	−	2.18634i	−0.348635	−	0.146081i
$225$	2.04209	−	4.56398i	0.136139	−	0.304265i
$226$	−1.18251	+	14.8698i	−0.0786594	+	0.989126i
$227$	17.9180	−	17.9180i	1.18926	−	1.18926i	0.211987	−	0.977273i	$-0.432007\pi$
$227$	17.9180	−	17.9180i	1.18926	−	1.18926i	0.977273	−	0.211987i	$-0.0679934\pi$
$228$	−14.9112	−	2.38670i	−0.987519	−	0.158063i
$229$	−2.04384	+	2.04384i	−0.135061	+	0.135061i	−0.771405	−	0.636344i	$-0.780446\pi$
$229$	−2.04384	+	2.04384i	−0.135061	+	0.135061i	0.636344	+	0.771405i	$0.280446\pi$
$230$	−0.485575	−	0.144752i	−0.0320179	−	0.00954467i
$231$		−	2.68007i		−	0.176336i
$232$	−5.62645	−	9.23226i	−0.369394	−	0.606128i
$233$	11.1084			0.727733			0.363867	−	0.931451i	$-0.381456\pi$
$233$	11.1084			0.727733			0.363867	+	0.931451i	$0.381456\pi$
$234$	3.45065	+	4.04689i	0.225576	+	0.264553i
$235$	−2.23926	+	10.4874i	−0.146073	+	0.684123i
$236$	0.233058	−	0.168745i	0.0151708	−	0.0109844i
$237$	4.05546	−	4.05546i	0.263431	−	0.263431i
$238$	0.194908	−	2.45092i	0.0126340	−	0.158870i
$239$	−19.1106			−1.23616			−0.618080	−	0.786115i	$-0.712089\pi$
$239$	−19.1106			−1.23616			−0.618080	+	0.786115i	$0.712089\pi$
$240$	−8.64913	+	2.27873i	−0.558299	+	0.147092i
$241$	−5.95102			−0.383339			−0.191669	−	0.981460i	$-0.561390\pi$
$241$	−5.95102			−0.383339			−0.191669	+	0.981460i	$0.561390\pi$
$242$	0.428114	−	5.38346i	0.0275202	−	0.346062i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−9.98263	−	13.7873i	−0.639073	−	0.882638i
$245$	−13.1202	−	2.80141i	−0.838220	−	0.178975i
$246$	−9.08207	−	10.6514i	−0.579052	−	0.679106i
$247$	28.3945			1.80670
$248$	12.7616	+	3.09691i	0.810365	+	0.196654i
$249$			2.89807i			0.183658i
$250$	−11.9863	−	10.3116i	−0.758077	−	0.652165i
$251$	−20.8714	+	20.8714i	−1.31739	+	1.31739i	−0.401552	+	0.915836i	$0.631529\pi$
$251$	−20.8714	+	20.8714i	−1.31739	+	1.31739i	−0.915836	+	0.401552i	$0.868471\pi$
$252$	0.316129	−	1.97506i	0.0199143	−	0.124417i
$253$	−0.303620	+	0.303620i	−0.0190884	+	0.0190884i
$254$	−0.648627	+	8.15636i	−0.0406985	+	0.511776i
$255$	−2.11406	−	3.26194i	−0.132388	−	0.204270i
$256$	12.8825	+	9.48899i	0.805157	+	0.593062i
$257$			9.30565i			0.580470i	0.956955	+	0.290235i	$0.0937335\pi$
$257$			9.30565i			0.580470i	−0.956955	+	0.290235i	$0.906266\pi$
$258$	−14.4178	−	1.14656i	−0.897612	−	0.0713818i
$259$	5.35828	+	5.35828i	0.332947	+	0.332947i
$260$	15.3814	−	6.80120i	0.953913	−	0.421792i
$261$	2.70291	−	2.70291i	0.167306	−	0.167306i
$262$	1.32233	+	1.55082i	0.0816940	+	0.0958098i
$263$	20.0922			1.23894			0.619469	−	0.785021i	$-0.287348\pi$
$263$	20.0922			1.23894			0.619469	+	0.785021i	$0.287348\pi$
$264$	−1.78749	+	7.36582i	−0.110012	+	0.453335i
$265$	5.92695	+	9.14511i	0.364089	+	0.561780i
$266$	−6.92889	−	8.12613i	−0.424838	−	0.498245i
$267$	10.6339	+	10.6339i	0.650783	+	0.650783i
$268$	20.7201	−	15.0024i	1.26568	−	0.916415i
$269$	21.1446	+	21.1446i	1.28921	+	1.28921i	0.935268	+	0.353941i	$0.115159\pi$
$269$	21.1446	+	21.1446i	1.28921	+	1.28921i	0.353941	+	0.935268i	$0.384841\pi$
$270$	−1.50408	−	2.78168i	−0.0915353	−	0.169288i
$271$	21.4729			1.30438			0.652192	−	0.758053i	$-0.273849\pi$
$271$	21.4729			1.30438			0.652192	+	0.758053i	$0.273849\pi$
$272$	−2.17034	+	6.60605i	−0.131596	+	0.400551i
$273$			3.76099i			0.227625i
$274$	15.7296	+	1.25088i	0.950260	+	0.0755685i
$275$	−12.5178	+	4.77873i	−0.754854	+	0.288169i
$276$	−0.259565	+	0.187938i	−0.0156240	+	0.0113125i
$277$	4.23508	+	4.23508i	0.254461	+	0.254461i	0.822797	−	0.568336i	$-0.192412\pi$
$277$	4.23508	+	4.23508i	0.254461	+	0.254461i	−0.568336	+	0.822797i	$0.692412\pi$
$278$	−24.2977	+	20.7179i	−1.45728	+	1.24258i
$279$			4.64288i			0.277962i
$280$	−5.69982	−	2.74230i	−0.340629	−	0.163884i
$281$		−	13.5822i		−	0.810248i	−0.914262	−	0.405124i	$-0.867228\pi$
$281$		−	13.5822i		−	0.810248i	0.914262	−	0.405124i	$-0.132772\pi$
$282$	4.40056	+	5.16093i	0.262049	+	0.307329i
$283$	15.9090	+	15.9090i	0.945692	+	0.945692i	0.998599	−	0.0529078i	$-0.0168489\pi$
$283$	15.9090	+	15.9090i	0.945692	+	0.945692i	−0.0529078	+	0.998599i	$0.516849\pi$
$284$	1.45620	−	9.09779i	0.0864093	−	0.539854i
$285$	−16.5113	−	3.52546i	−0.978043	−	0.208830i
$286$	1.12981	−	14.2071i	0.0668069	−	0.840084i
$287$		−	9.89887i		−	0.584312i
$288$	−2.18612	+	5.21736i	−0.128819	+	0.307436i
$289$	13.9781			0.822241
$290$	−5.74933	−	10.6330i	−0.337612	−	0.624389i
$291$	−2.72049	−	2.72049i	−0.159478	−	0.159478i
$292$	−24.0776	−	3.85387i	−1.40903	−	0.225531i
$293$	6.55813	+	6.55813i	0.383130	+	0.383130i	0.872229	−	0.489098i	$-0.162674\pi$
$293$	6.55813	+	6.55813i	0.383130	+	0.383130i	−0.489098	+	0.872229i	$0.662674\pi$
$294$	−6.45654	+	5.50529i	−0.376553	+	0.321075i
$295$	0.269958	−	0.174960i	0.0157176	−	0.0101866i
$296$	−11.1528	−	18.3003i	−0.648243	−	1.06368i
$297$	−2.67980			−0.155498
$298$	22.0978	−	18.8421i	1.28009	−	1.09149i
$299$	0.426076	−	0.426076i	0.0246406	−	0.0246406i
$300$	−9.78864	+	2.04511i	−0.565147	+	0.118075i
$301$	−7.23238	−	7.23238i	−0.416868	−	0.416868i
$302$	−1.65060	+	20.7560i	−0.0949814	+	1.19437i
$303$			7.93257i			0.455714i
$304$	13.6234	+	26.9549i	0.781355	+	1.54597i
$305$	−10.3503	−	15.9702i	−0.592656	−	0.914452i
$306$	−2.45068	−	0.194888i	−0.140096	−	0.0111410i
$307$	−6.02585	+	6.02585i	−0.343913	+	0.343913i	−0.857836	−	0.513923i	$-0.828192\pi$
$307$	−6.02585	+	6.02585i	−0.343913	+	0.343913i	0.513923	+	0.857836i	$0.328192\pi$
$308$	−4.34158	+	3.14352i	−0.247385	+	0.179118i
$309$	10.6050	−	10.6050i	0.603300	−	0.603300i
$310$	14.0702	+	4.19438i	0.799133	+	0.238225i
$311$			21.1776i			1.20087i	0.799673	+	0.600436i	$0.205006\pi$
$311$			21.1776i			1.20087i	−0.799673	+	0.600436i	$0.794994\pi$
$312$	2.50842	−	10.3366i	0.142011	−	0.585194i
$313$	4.30438			0.243298			0.121649	−	0.992573i	$-0.461182\pi$
$313$	4.30438			0.243298			0.121649	+	0.992573i	$0.461182\pi$
$314$	14.3775	−	12.2593i	0.811371	−	0.691830i
$315$	0.466965	−	2.18700i	0.0263105	−	0.123223i
$316$	−11.3264	−	1.81291i	−0.637161	−	0.101984i
$317$	−23.4323	+	23.4323i	−1.31609	+	1.31609i	−0.399242	+	0.916845i	$0.630727\pi$
$317$	−23.4323	+	23.4323i	−1.31609	+	1.31609i	−0.916845	+	0.399242i	$0.869273\pi$
$318$	6.87067	+	0.546384i	0.385288	+	0.0306397i
$319$	−10.2435			−0.573526
$320$	13.8362	+	11.3384i	0.773468	+	0.633836i
$321$	1.73151			0.0966432
$322$	−0.225909	−	0.0179652i	−0.0125894	−	0.00100116i
$323$	−9.28113	+	9.28113i	−0.516416	+	0.516416i
$324$	−1.97486	−	0.316097i	−0.109715	−	0.0175610i
$325$	17.5665	−	6.70608i	0.974415	−	0.371987i
$326$	11.6596	−	9.94181i	0.645768	−	0.550626i
$327$	−7.51262			−0.415449
$328$	−6.60212	+	27.2058i	−0.364541	+	1.50219i
$329$			4.79632i			0.264430i
$330$	−2.42093	+	8.12109i	−0.133268	+	0.447051i
$331$	5.03806	−	5.03806i	0.276917	−	0.276917i	−0.554960	−	0.831877i	$-0.687267\pi$
$331$	5.03806	−	5.03806i	0.276917	−	0.276917i	0.831877	+	0.554960i	$0.187267\pi$
$332$	4.69473	−	3.39921i	0.257657	−	0.186556i
$333$	5.35773	−	5.35773i	0.293602	−	0.293602i
$334$	−20.3280	−	1.61657i	−1.11230	−	0.0884547i
$335$	24.0008	−	15.5549i	1.31130	−	0.849856i
$336$	−3.57031	+	1.80448i	−0.194776	+	0.0984427i
$337$		−	11.5659i		−	0.630037i	−0.949086	−	0.315018i	$-0.897989\pi$
$337$		−	11.5659i		−	0.630037i	0.949086	−	0.315018i	$-0.102011\pi$
$338$	−0.128047	+	1.61017i	−0.00696485	+	0.0875816i
$339$	7.45839	+	7.45839i	0.405084	+	0.405084i
$340$	−2.80455	+	7.25068i	−0.152098	+	0.393223i
$341$	8.79779	−	8.79779i	0.476427	−	0.476427i
$342$	−8.12530	+	6.92819i	−0.439366	+	0.374634i
$343$	−13.0011			−0.701994
$344$	15.0536	+	24.7010i	0.811635	+	1.33179i
$345$	−0.300663	+	0.194860i	−0.0161871	+	0.0104909i
$346$	−1.43448	+	1.22313i	−0.0771179	+	0.0657560i
$347$	−1.64106	−	1.64106i	−0.0880968	−	0.0880968i	0.661685	−	0.749782i	$-0.269842\pi$
$347$	−1.64106	−	1.64106i	−0.0880968	−	0.0880968i	−0.749782	+	0.661685i	$0.769842\pi$
$348$	−7.54890	−	1.20828i	−0.404663	−	0.0647706i
$349$	13.8252	+	13.8252i	0.740045	+	0.740045i	0.972586	−	0.232542i	$-0.0747042\pi$
$349$	13.8252	+	13.8252i	0.740045	+	0.740045i	−0.232542	+	0.972586i	$0.574704\pi$
$350$	−6.20582	−	3.39087i	−0.331715	−	0.181250i
$351$	3.76061			0.200726
$352$	14.0289	−	5.74390i	0.747742	−	0.306151i
$353$			3.70491i			0.197193i	0.995128	+	0.0985964i	$0.0314353\pi$
$353$			3.70491i			0.197193i	−0.995128	+	0.0985964i	$0.968565\pi$
$354$	0.0161289	−	0.202818i	0.000857244	−	0.0107797i
$355$	2.15099	−	10.0740i	0.114163	−	0.534674i
$356$	4.75366	−	29.6992i	0.251943	−	1.57405i
$357$	−1.22933	−	1.22933i	−0.0650631	−	0.0650631i
$358$	4.20166	+	4.92766i	0.222064	+	0.260435i
$359$		−	12.9673i		−	0.684387i	−0.939630	−	0.342194i	$-0.888830\pi$
$359$		−	12.9673i		−	0.684387i	0.939630	−	0.342194i	$-0.111170\pi$
$360$	−2.74202	+	5.69924i	−0.144517	+	0.300376i
$361$			38.0102i			2.00054i
$362$	19.9234	−	16.9881i	1.04715	−	0.892874i
$363$	−2.70023	−	2.70023i	−0.141725	−	0.141725i
$364$	6.09262	−	4.41135i	0.319340	−	0.231218i
$365$	−26.6612	−	5.69267i	−1.39551	−	0.297968i
$366$	−11.9983	−	0.954157i	−0.627163	−	0.0498746i
$367$		−	3.12457i		−	0.163101i	−0.996669	−	0.0815507i	$-0.974013\pi$
$367$		−	3.12457i		−	0.163101i	0.996669	−	0.0815507i	$-0.0259873\pi$
$368$	0.608900	+	0.200047i	0.0317411	+	0.0104282i
$369$	−9.89786			−0.515262
$370$	−11.3964	−	21.0767i	−0.592469	−	1.09573i
$371$	3.44653	+	3.44653i	0.178935	+	0.178935i
$372$	7.52124	−	5.44574i	0.389958	−	0.282349i
$373$	−21.1651	−	21.1651i	−1.09589	−	1.09589i	−0.994886	−	0.101002i	$-0.967795\pi$
$373$	−21.1651	−	21.1651i	−1.09589	−	1.09589i	−0.101002	−	0.994886i	$-0.532205\pi$
$374$	4.27450	+	5.01308i	0.221029	+	0.259220i
$375$	−11.0475	+	1.71850i	−0.570489	+	0.0887429i
$376$	3.19894	−	13.1821i	0.164973	−	0.679813i
$377$	14.3749			0.740344
$378$	−0.917672	−	1.07624i	−0.0472000	−	0.0553556i
$379$	2.37189	−	2.37189i	0.121836	−	0.121836i	−0.643560	−	0.765396i	$-0.722543\pi$
$379$	2.37189	−	2.37189i	0.121836	−	0.121836i	0.765396	+	0.643560i	$0.222543\pi$
$380$	13.6554	+	30.8826i	0.700506	+	1.58424i
$381$	4.09106	+	4.09106i	0.209591	+	0.209591i
$382$	−13.8250	−	1.09942i	−0.707350	−	0.0562513i
$383$			3.48238i			0.177942i	0.996034	+	0.0889708i	$0.0283578\pi$
$383$			3.48238i			0.177942i	−0.996034	+	0.0889708i	$0.971642\pi$
$384$	11.0160	−	2.57815i	0.562160	−	0.131566i
$385$	−5.02900	+	3.25929i	−0.256301	+	0.166109i
$386$	0.764775	−	9.61690i	0.0389260	−	0.489487i
$387$	−7.23165	+	7.23165i	−0.367605	+	0.367605i
$388$	−1.21614	+	7.59799i	−0.0617400	+	0.385730i
$389$	5.90261	−	5.90261i	0.299274	−	0.299274i	−0.541455	−	0.840730i	$-0.682126\pi$
$389$	5.90261	−	5.90261i	0.299274	−	0.299274i	0.840730	+	0.541455i	$0.182126\pi$
$390$	3.39734	−	11.3965i	0.172031	−	0.577083i
$391$			0.278537i			0.0140862i
$392$	16.4913	+	4.00201i	0.832939	+	0.202132i
$393$	1.44111			0.0726944
$394$	20.1321	+	23.6106i	1.01424	+	1.18949i
$395$	−12.5418	−	2.67791i	−0.631046	−	0.134740i
$396$	3.14320	+	4.34114i	0.157952	+	0.218151i
$397$	−9.12810	+	9.12810i	−0.458126	+	0.458126i	−0.898040	−	0.439914i	$-0.855009\pi$
$397$	−9.12810	+	9.12810i	−0.458126	+	0.458126i	0.439914	+	0.898040i	$0.355009\pi$
$398$	0.887968	−	11.1660i	0.0445098	−	0.559702i
$399$	−7.55128			−0.378037
$400$	14.7943	+	13.4584i	0.739716	+	0.672919i
$401$	−0.825205			−0.0412088			−0.0206044	−	0.999788i	$-0.506559\pi$
$401$	−0.825205			−0.0412088			−0.0206044	+	0.999788i	$0.506559\pi$
$402$	1.43395	−	18.0317i	0.0715190	−	0.899338i
$403$	−12.3461	+	12.3461i	−0.615003	+	0.615003i
$404$	12.8504	−	9.30430i	0.639331	−	0.462906i
$405$	−2.18678	−	0.466917i	−0.108662	−	0.0232013i
$406$	−3.50780	−	4.11390i	−0.174089	−	0.204170i
$407$	−20.3047			−1.00647
$408$	2.55875	+	4.19857i	0.126677	+	0.207860i
$409$		−	35.3312i		−	1.74702i	−0.486809	−	0.873508i	$-0.661839\pi$
$409$		−	35.3312i		−	1.74702i	0.486809	−	0.873508i	$-0.338161\pi$
$410$	−8.94175	+	29.9954i	−0.441602	+	1.48137i
$411$	7.88963	−	7.88963i	0.389167	−	0.389167i
$412$	−29.6186	−	4.74076i	−1.45920	−	0.233561i
$413$	0.101740	−	0.101740i	0.00500628	−	0.00500628i
$414$	−0.0179634	+	0.225886i	−0.000882853	+	0.0111017i
$415$	5.43806	−	3.52441i	0.266944	−	0.173006i
$416$	−19.6870	+	8.06052i	−0.965233	+	0.395200i
$417$			22.5789i			1.10569i
$418$	28.5249	+	2.26842i	1.39520	+	0.110952i
$419$	−11.7984	−	11.7984i	−0.576392	−	0.576392i	0.357516	−	0.933907i	$-0.383624\pi$
$419$	−11.7984	−	11.7984i	−0.576392	−	0.576392i	−0.933907	+	0.357516i	$0.883624\pi$
$420$	−4.09055	+	1.80872i	−0.199598	+	0.0882566i
$421$	24.9466	−	24.9466i	1.21582	−	1.21582i	0.246739	−	0.969082i	$-0.420641\pi$
$421$	24.9466	−	24.9466i	1.21582	−	1.21582i	0.969082	−	0.246739i	$-0.0793590\pi$
$422$	13.2371	+	15.5243i	0.644372	+	0.755713i
$423$	4.79583			0.233181
$424$	−7.17366	−	11.7710i	−0.348384	−	0.571652i
$425$	−3.54988	+	7.93383i	−0.172195	+	0.384847i
$426$	−4.22710	−	4.95749i	−0.204804	−	0.240191i
$427$	−6.01872	−	6.01872i	−0.291266	−	0.291266i
$428$	−2.03093	−	2.80496i	−0.0981685	−	0.135583i
$429$	−7.12598	−	7.12598i	−0.344045	−	0.344045i
$430$	15.3824	+	28.4485i	0.741803	+	1.37191i
$431$	10.8925			0.524672			0.262336	−	0.964977i	$-0.415507\pi$
$431$	10.8925			0.524672			0.262336	+	0.964977i	$0.415507\pi$
$432$	1.80430	+	3.56994i	0.0868095	+	0.171759i
$433$		−	3.09561i		−	0.148765i	−0.997230	−	0.0743827i	$-0.976301\pi$
$433$		−	3.09561i		−	0.148765i	0.997230	−	0.0743827i	$-0.0236986\pi$
$434$	6.54602	+	0.520566i	0.314219	+	0.0249880i
$435$	−8.35894	−	1.78479i	−0.400780	−	0.0855740i
$436$	8.81173	+	12.1701i	0.422005	+	0.582842i
$437$	0.855471	+	0.855471i	0.0409227	+	0.0409227i
$438$	−13.1202	+	11.1872i	−0.626906	+	0.534543i
$439$			26.4374i			1.26179i	0.775869	+	0.630894i	$0.217312\pi$
$439$			26.4374i			1.26179i	−0.775869	+	0.630894i	$0.782688\pi$
$440$	15.9954	−	5.60363i	0.762549	−	0.267142i
$441$			5.99980i			0.285705i
$442$	−5.99848	−	7.03495i	−0.285318	−	0.334618i
$443$	−18.8131	−	18.8131i	−0.893840	−	0.893840i	0.101042	−	0.994882i	$-0.467782\pi$
$443$	−18.8131	−	18.8131i	−0.893840	−	0.893840i	−0.994882	+	0.101042i	$0.967782\pi$
$444$	−14.9635	−	2.39506i	−0.710136	−	0.113665i
$445$	7.02178	−	32.8860i	0.332864	−	1.55895i
$446$	−1.55485	+	19.5519i	−0.0736241	+	0.925809i
$447$		−	20.5346i		−	0.971253i
$448$	7.11088	+	3.66721i	0.335957	+	0.173259i
$449$	−16.9583			−0.800310			−0.400155	−	0.916447i	$-0.631044\pi$
$449$	−16.9583			−0.800310			−0.400155	+	0.916447i	$0.631044\pi$
$450$	−3.39053	+	6.20519i	−0.159831	+	0.292515i
$451$	18.7555	+	18.7555i	0.883161	+	0.883161i
$452$	3.33412	−	20.8304i	0.156824	−	0.979778i
$453$	10.4108	+	10.4108i	0.489140	+	0.489140i
$454$	−27.2689	+	23.2513i	−1.27979	+	1.09124i
$455$	7.05728	−	4.57383i	0.330851	−	0.214424i
$456$	20.7537	+	5.03637i	0.971881	+	0.235850i
$457$	5.71266			0.267227			0.133614	−	0.991034i	$-0.457342\pi$
$457$	5.71266			0.267227			0.133614	+	0.991034i	$0.457342\pi$
$458$	3.11047	−	2.65220i	0.145343	−	0.123929i
$459$	−1.22921	+	1.22921i	−0.0573744	+	0.0573744i
$460$	0.668318	+	0.258504i	0.0311605	+	0.0120528i
$461$	−23.4428	−	23.4428i	−1.09184	−	1.09184i	−0.995332	−	0.0965077i	$-0.969233\pi$
$461$	−23.4428	−	23.4428i	−1.09184	−	1.09184i	−0.0965077	−	0.995332i	$-0.530767\pi$
$462$	−0.300463	+	3.77826i	−0.0139788	+	0.175781i
$463$		−	16.7093i		−	0.776547i	−0.921544	−	0.388273i	$-0.873072\pi$
$463$		−	16.7093i		−	0.776547i	0.921544	−	0.388273i	$-0.126928\pi$
$464$	6.89693	+	13.6461i	0.320182	+	0.633504i
$465$	8.71210	−	5.64631i	0.404014	−	0.261841i
$466$	−15.6602	−	1.24536i	−0.725443	−	0.0576902i
$467$	−14.3258	+	14.3258i	−0.662918	+	0.662918i	−0.956067	−	0.293149i	$-0.905297\pi$
$467$	−14.3258	+	14.3258i	−0.662918	+	0.662918i	0.293149	+	0.956067i	$0.405297\pi$
$468$	−4.41091	−	6.09201i	−0.203894	−	0.281603i
$469$	9.04522	−	9.04522i	0.417669	−	0.417669i
$470$	4.33257	−	14.5337i	0.199846	−	0.670391i
$471$		−	13.3604i		−	0.615617i
$472$	−0.347474	+	0.211762i	−0.0159938	+	0.00974716i
$473$	27.4065			1.26015
$474$	−6.17190	+	5.26258i	−0.283485	+	0.241719i
$475$	13.4644	+	35.2699i	0.617790	+	1.61829i
$476$	−0.549547	+	3.43337i	−0.0251884	+	0.157368i
$477$	3.44618	−	3.44618i	0.157790	−	0.157790i
$478$	26.9414	+	2.14249i	1.23227	+	0.0979951i
$479$	11.2464			0.513860			0.256930	−	0.966430i	$-0.417289\pi$
$479$	11.2464			0.513860			0.256930	+	0.966430i	$0.417289\pi$
$480$	12.4487	−	2.24282i	0.568202	−	0.102370i
$481$	28.4940			1.29922
$482$	8.38952	+	0.667169i	0.382132	+	0.0303887i
$483$	−0.113311	+	0.113311i	−0.00515584	+	0.00515584i
$484$	−1.20708	+	7.54140i	−0.0548673	+	0.342791i
$485$	−1.79639	+	8.41330i	−0.0815701	+	0.382028i
$486$	−1.07613	+	0.917579i	−0.0488141	+	0.0416222i
$487$	6.82860			0.309434			0.154717	−	0.987959i	$-0.450553\pi$
$487$	6.82860			0.309434			0.154717	+	0.987959i	$0.450553\pi$
$488$	12.5275	+	20.5559i	0.567091	+	0.930522i
$489$		−	10.8348i		−	0.489968i
$490$	18.1823	+	5.42023i	0.821393	+	0.244861i
$491$	−26.3274	+	26.3274i	−1.18814	+	1.18814i	−0.210560	+	0.977581i	$0.567529\pi$
$491$	−26.3274	+	26.3274i	−1.18814	+	1.18814i	−0.977581	+	0.210560i	$0.932471\pi$
$492$	11.6094	+	16.0341i	0.523394	+	0.722872i
$493$	−4.69863	+	4.69863i	−0.211616	+	0.211616i
$494$	−40.0295	−	3.18331i	−1.80101	−	0.143224i
$495$	3.25896	+	5.02849i	0.146479	+	0.226014i
$496$	−17.6437	−	5.79662i	−0.792225	−	0.260276i
$497$		−	4.60726i		−	0.206664i
$498$	0.324903	−	4.08559i	0.0145592	−	0.183080i
$499$	−16.9896	−	16.9896i	−0.760558	−	0.760558i	0.215865	−	0.976423i	$-0.430743\pi$
$499$	−16.9896	−	16.9896i	−0.760558	−	0.760558i	−0.976423	+	0.215865i	$0.930743\pi$
$500$	15.7417	+	15.8807i	0.703992	+	0.710208i
$501$	−10.1961	+	10.1961i	−0.455528	+	0.455528i
$502$	31.7635	−	27.0838i	1.41768	−	1.20881i
$503$	−12.7938			−0.570447			−0.285223	−	0.958461i	$-0.592068\pi$
$503$	−12.7938			−0.570447			−0.285223	+	0.958461i	$0.592068\pi$
$504$	−0.667092	+	2.74893i	−0.0297146	+	0.122447i
$505$	14.8850	−	9.64698i	0.662375	−	0.429285i
$506$	0.462071	−	0.393993i	0.0205416	−	0.0175151i
$507$	0.807626	+	0.807626i	0.0358679	+	0.0358679i
$508$	1.82882	−	11.4258i	0.0811408	−	0.506939i
$509$	15.4048	+	15.4048i	0.682807	+	0.682807i	0.960632	−	0.277825i	$-0.0896134\pi$
$509$	15.4048	+	15.4048i	0.682807	+	0.682807i	−0.277825	+	0.960632i	$0.589613\pi$
$510$	2.61463	+	4.83556i	0.115778	+	0.214122i
$511$	−12.1933			−0.539398
$512$	−17.0975	−	14.8215i	−0.755608	−	0.655024i
$513$			7.55051i			0.333363i
$514$	1.04326	−	13.1188i	0.0460161	−	0.578643i
$515$	−32.7968	−	7.00273i	−1.44520	−	0.308577i
$516$	20.1971	+	3.23276i	0.889128	+	0.142314i
$517$	−9.08763	−	9.08763i	−0.399674	−	0.399674i
$518$	−6.95318	−	8.15461i	−0.305505	−	0.358293i
$519$			1.33300i			0.0585121i
$520$	−22.4466	+	7.86367i	−0.984348	+	0.344845i
$521$			2.66408i			0.116715i	0.998296	+	0.0583577i	$0.0185864\pi$
$521$			2.66408i			0.116715i	−0.998296	+	0.0583577i	$0.981414\pi$
$522$	−4.11349	+	3.50744i	−0.180042	+	0.153516i
$523$	−10.1050	−	10.1050i	−0.441861	−	0.441861i	0.450776	−	0.892637i	$-0.351147\pi$
$523$	−10.1050	−	10.1050i	−0.441861	−	0.441861i	−0.892637	+	0.450776i	$0.851147\pi$
$524$	−1.69031	−	2.33453i	−0.0738417	−	0.101985i
$525$	−4.67167	+	1.78343i	−0.203888	+	0.0778351i
$526$	−28.3252	−	2.25254i	−1.23504	−	0.0982154i
$527$		−	8.07099i		−	0.351578i
$528$	3.34572	−	10.1837i	0.145604	−	0.443187i
$529$	−22.9743			−0.998884
$530$	−7.33033	−	13.5569i	−0.318409	−	0.588874i
$531$	−0.101729	−	0.101729i	−0.00441468	−	0.00441468i
$532$	8.85707	+	12.2327i	0.384003	+	0.530355i
$533$	−26.3199	−	26.3199i	−1.14004	−	1.14004i
$534$	−13.7991	−	16.1834i	−0.597145	−	0.700325i
$535$	−2.10573	−	3.24907i	−0.0910385	−	0.140470i
$536$	−30.8924	+	18.8268i	−1.33435	+	0.813196i
$537$	4.57907			0.197601
$538$	−27.4383	−	32.1794i	−1.18295	−	1.38735i
$539$	11.3690	−	11.3690i	0.489699	−	0.489699i
$540$	1.80854	+	4.09013i	0.0778271	+	0.176011i
$541$	14.4482	+	14.4482i	0.621177	+	0.621177i	0.945832	−	0.324656i	$-0.105248\pi$
$541$	14.4482	+	14.4482i	0.621177	+	0.621177i	−0.324656	+	0.945832i	$0.605248\pi$
$542$	−30.2717	−	2.40733i	−1.30028	−	0.103404i
$543$		−	18.5140i		−	0.794513i
$544$	3.80027	−	9.06965i	0.162935	−	0.388858i
$545$	9.13627	+	14.0970i	0.391355	+	0.603850i
$546$	0.421645	−	5.30210i	0.0180447	−	0.226909i
$547$	−18.9410	+	18.9410i	−0.809860	+	0.809860i	−0.984612	−	0.174753i	$-0.944087\pi$
$547$	−18.9410	+	18.9410i	−0.809860	+	0.809860i	0.174753	+	0.984612i	$0.444087\pi$
$548$	−22.0348	−	3.52689i	−0.941278	−	0.150661i
$549$	−6.01811	+	6.01811i	−0.256847	+	0.256847i
$550$	18.1829	−	5.33351i	0.775323	−	0.227421i
$551$			28.8618i			1.22955i
$552$	0.386995	−	0.235848i	0.0164716	−	0.0100383i
$553$	−5.73588			−0.243914
$554$	−5.49566	−	6.44525i	−0.233488	−	0.273833i
$555$	−16.5691	−	3.53782i	−0.703321	−	0.150172i
$556$	36.5767	−	26.4833i	1.55120	−	1.12314i
$557$	29.6116	−	29.6116i	1.25468	−	1.25468i	0.301086	−	0.953597i	$-0.402651\pi$
$557$	29.6116	−	29.6116i	1.25468	−	1.25468i	0.953597	−	0.301086i	$-0.0973492\pi$
$558$	0.520513	−	6.54535i	0.0220351	−	0.277087i
$559$	−38.4601			−1.62669
$560$	7.72795	+	4.50500i	0.326565	+	0.190371i
$561$	4.65845			0.196680
$562$	−1.52271	+	19.1477i	−0.0642314	+	0.807698i
$563$	4.19738	−	4.19738i	0.176898	−	0.176898i	−0.613104	−	0.790002i	$-0.710079\pi$
$563$	4.19738	−	4.19738i	0.176898	−	0.176898i	0.790002	+	0.613104i	$0.210079\pi$
$564$	−5.62515	−	7.76903i	−0.236862	−	0.327135i
$565$	4.92493	−	23.0656i	0.207193	−	0.970376i
$566$	−20.6444	−	24.2115i	−0.867747	−	1.01768i
$567$	−1.00010			−0.0420003
$568$	−3.07284	+	12.6625i	−0.128934	+	0.531305i
$569$		−	41.7953i		−	1.75215i	−0.482173	−	0.876076i	$-0.660152\pi$
$569$		−	41.7953i		−	1.75215i	0.482173	−	0.876076i	$-0.339848\pi$
$570$	22.8817	+	6.82115i	0.958410	+	0.285706i
$571$	−10.7600	+	10.7600i	−0.450290	+	0.450290i	−0.895451	−	0.445160i	$-0.853147\pi$
$571$	−10.7600	+	10.7600i	−0.450290	+	0.450290i	0.445160	+	0.895451i	$0.353147\pi$
$572$	−3.18552	+	19.9020i	−0.133193	+	0.832144i
$573$	−6.93433	+	6.93433i	−0.289686	+	0.289686i
$574$	−1.10976	+	13.9551i	−0.0463206	+	0.582473i
$575$	0.731286	+	0.327204i	0.0304967	+	0.0136453i
$576$	3.66683	−	7.11016i	0.152785	−	0.296257i
$577$		−	10.6682i		−	0.444124i	−0.975032	−	0.222062i	$-0.928721\pi$
$577$		−	10.6682i		−	0.444124i	0.975032	−	0.222062i	$-0.0712788\pi$
$578$	−19.7058	−	1.56709i	−0.819654	−	0.0651822i
$579$	−4.82363	−	4.82363i	−0.200463	−	0.200463i
$580$	6.91312	+	15.6345i	0.287052	+	0.649188i
$581$	2.04945	−	2.04945i	0.0850256	−	0.0850256i
$582$	3.53025	+	4.14024i	0.146334	+	0.171618i
$583$	−13.0604			−0.540904
$584$	33.5116	+	8.13238i	1.38672	+	0.336520i
$585$	−4.57336	−	7.05657i	−0.189085	−	0.291753i
$586$	−8.51018	−	9.98065i	−0.351552	−	0.412297i
$587$	17.6711	+	17.6711i	0.729365	+	0.729365i	0.970493	−	0.241128i	$-0.0775175\pi$
$587$	17.6711	+	17.6711i	0.729365	+	0.729365i	−0.241128	+	0.970493i	$0.577518\pi$
$588$	9.71939	−	7.03731i	0.400821	−	0.290214i
$589$	−24.7884	−	24.7884i	−1.02139	−	1.02139i
$590$	−0.400192	+	0.216387i	−0.0164757	+	0.00890852i
$591$	21.9404			0.902507
$592$	13.6711	+	27.0494i	0.561881	+	1.11172i
$593$			4.79734i			0.197003i	0.995137	+	0.0985016i	$0.0314050\pi$
$593$			4.79734i			0.197003i	−0.995137	+	0.0985016i	$0.968595\pi$
$594$	3.77788	+	0.300432i	0.155008	+	0.0123269i
$595$	−0.811752	+	3.80179i	−0.0332786	+	0.155858i
$596$	−33.2651	+	24.0855i	−1.36259	+	0.986582i
$597$	−5.60064	−	5.60064i	−0.229219	−	0.229219i
$598$	−0.648433	+	0.552898i	−0.0265164	+	0.0226097i
$599$			1.03944i			0.0424705i	0.999775	+	0.0212353i	$0.00675991\pi$
$599$			1.03944i			0.0424705i	−0.999775	+	0.0212353i	$0.993240\pi$
$600$	14.0289	−	1.78572i	0.572729	−	0.0729017i
$601$			6.22752i			0.254026i	0.991901	+	0.127013i	$0.0405390\pi$
$601$			6.22752i			0.254026i	−0.991901	+	0.127013i	$0.959461\pi$
$602$	9.38512	+	11.0068i	0.382509	+	0.448602i
$603$	−9.04430	−	9.04430i	−0.368312	−	0.368312i
$604$	4.65391	−	29.0760i	0.189365	−	1.18308i
$605$	−1.78301	+	8.35063i	−0.0724898	+	0.339501i
$606$	0.889321	−	11.1830i	0.0361262	−	0.454280i
$607$			25.3718i			1.02981i	0.857247	+	0.514905i	$0.172173\pi$
$607$			25.3718i			1.02981i	−0.857247	+	0.514905i	$0.827827\pi$
$608$	−16.1838	−	39.5273i	−0.656341	−	1.60304i
$609$	−3.82288			−0.154911
$610$	12.8010	+	23.6746i	0.518299	+	0.958556i
$611$	12.7528	+	12.7528i	0.515925	+	0.515925i
$612$	3.43302	+	0.549491i	0.138772	+	0.0222119i
$613$	−17.1175	−	17.1175i	−0.691369	−	0.691369i	0.271164	−	0.962533i	$-0.412591\pi$
$613$	−17.1175	−	17.1175i	−0.691369	−	0.691369i	−0.962533	+	0.271164i	$0.912591\pi$
$614$	9.17058	−	7.81946i	0.370094	−	0.315568i
$615$	12.0370	+	18.5728i	0.485380	+	0.748927i
$616$	6.47302	−	3.94488i	0.260806	−	0.158944i
$617$	8.28793			0.333659			0.166830	−	0.985986i	$-0.446647\pi$
$617$	8.28793			0.333659			0.166830	+	0.985986i	$0.446647\pi$
$618$	−16.1395	+	13.7617i	−0.649227	+	0.553575i
$619$	2.23506	−	2.23506i	0.0898348	−	0.0898348i	−0.660761	−	0.750596i	$-0.729766\pi$
$619$	2.23506	−	2.23506i	0.0898348	−	0.0898348i	0.750596	+	0.660761i	$0.229766\pi$
$620$	−19.3654	−	7.49050i	−0.777733	−	0.300826i
$621$	0.113300	+	0.113300i	0.00454656	+	0.00454656i
$622$	2.37422	−	29.8554i	0.0951977	−	1.19709i
$623$		−	15.0401i		−	0.602570i
$624$	−4.69511	+	14.2909i	−0.187955	+	0.572095i
$625$	16.6598	+	18.6401i	0.666391	+	0.745603i
$626$	−6.06815	−	0.482564i	−0.242532	−	0.0192872i
$627$	14.3075	−	14.3075i	0.571385	−	0.571385i
$628$	−21.6433	+	15.6708i	−0.863662	+	0.625333i
$629$	−9.31367	+	9.31367i	−0.371360	+	0.371360i
$630$	−0.903494	+	3.03080i	−0.0359961	+	0.120750i
$631$			17.2372i			0.686201i	0.939299	+	0.343100i	$0.111477\pi$
$631$			17.2372i			0.686201i	−0.939299	+	0.343100i	$0.888523\pi$
$632$	15.7643	+	3.82558i	0.627071	+	0.152173i
$633$	14.4261			0.573387
$634$	35.6609	−	30.4070i	1.41628	−	1.20761i
$635$	2.70141	−	12.6519i	0.107202	−	0.502074i
$636$	−9.62476	−	1.54054i	−0.381647	−	0.0610865i
$637$	−15.9544	+	15.9544i	−0.632135	+	0.632135i
$638$	14.4409	+	1.14840i	0.571721	+	0.0454656i
$639$	−4.60679			−0.182242
$640$	−18.2346	−	17.5356i	−0.720787	−	0.693157i
$641$	24.8101			0.979941			0.489971	−	0.871739i	$-0.337007\pi$
$641$	24.8101			0.979941			0.489971	+	0.871739i	$0.337007\pi$
$642$	−2.44101	−	0.194119i	−0.0963391	−	0.00766128i
$643$	20.7142	−	20.7142i	0.816887	−	0.816887i	−0.168769	−	0.985656i	$-0.553979\pi$
$643$	20.7142	−	20.7142i	0.816887	−	0.816887i	0.985656	+	0.168769i	$0.0539792\pi$
$644$	0.316464	+	0.0506534i	0.0124704	+	0.00199602i
$645$	22.3644	+	4.77521i	0.880596	+	0.188024i
$646$	14.1247	−	12.0437i	0.555729	−	0.473852i
$647$	−14.3607			−0.564577			−0.282289	−	0.959330i	$-0.591094\pi$
$647$	−14.3607			−0.564577			−0.282289	+	0.959330i	$0.591094\pi$
$648$	2.74865	+	0.667024i	0.107977	+	0.0262032i
$649$			0.385534i			0.0151335i
$650$	−25.5164	+	7.48461i	−1.00084	+	0.293570i
$651$	3.28334	−	3.28334i	0.128684	−	0.128684i
$652$	−17.5519	+	12.7084i	−0.687386	+	0.497701i
$653$	−8.23394	+	8.23394i	−0.322219	+	0.322219i	−0.849618	−	0.527399i	$-0.823167\pi$
$653$	−8.23394	+	8.23394i	−0.322219	+	0.322219i	0.527399	+	0.849618i	$0.323167\pi$
$654$	10.5910	+	0.842241i	0.414141	+	0.0329342i
$655$	−1.75257	−	2.70416i	−0.0684785	−	0.105660i
$656$	12.3575	−	37.6135i	0.482478	−	1.46856i
$657$			12.1920i			0.475656i
$658$	0.537716	−	6.76168i	0.0209624	−	0.263598i
$659$	32.8934	+	32.8934i	1.28134	+	1.28134i	0.939904	+	0.341440i	$0.110915\pi$
$659$	32.8934	+	32.8934i	1.28134	+	1.28134i	0.341440	+	0.939904i	$0.389085\pi$
$660$	4.32340	−	11.1774i	0.168288	−	0.435080i
$661$	−15.8937	+	15.8937i	−0.618193	+	0.618193i	−0.945068	−	0.326875i	$-0.894004\pi$
$661$	−15.8937	+	15.8937i	−0.618193	+	0.618193i	0.326875	+	0.945068i	$0.394004\pi$
$662$	−7.66728	+	6.53765i	−0.297997	+	0.254093i
$663$	−6.53729			−0.253887
$664$	−6.99955	+	4.26576i	−0.271635	+	0.165544i
$665$	9.18328	+	14.1695i	0.356113	+	0.549471i
$666$	−8.15379	+	6.95248i	−0.315953	+	0.269403i
$667$	0.433087	+	0.433087i	0.0167692	+	0.0167692i
$668$	28.4765	+	4.55796i	1.10179	+	0.176353i
$669$	9.80681	+	9.80681i	0.379153	+	0.379153i
$670$	−35.5793	+	19.2380i	−1.37455	+	0.743229i
$671$	22.8075			0.880472
$672$	5.23559	−	2.14363i	0.201967	−	0.0826922i
$673$			1.87365i			0.0722238i	0.999348	+	0.0361119i	$0.0114973\pi$
$673$			1.87365i			0.0722238i	−0.999348	+	0.0361119i	$0.988503\pi$
$674$	−1.29666	+	16.3052i	−0.0499454	+	0.628054i
$675$	1.78325	+	4.67119i	0.0686372	+	0.179794i
$676$	0.361032	−	2.25560i	0.0138859	−	0.0867538i
$677$	27.7045	+	27.7045i	1.06477	+	1.06477i	0.997752	+	0.0670200i	$0.0213491\pi$
$677$	27.7045	+	27.7045i	1.06477	+	1.06477i	0.0670200	+	0.997752i	$0.478651\pi$
$678$	−9.67840	−	11.3507i	−0.371697	−	0.435922i
$679$			3.84774i			0.147663i
$680$	4.76663	−	9.90732i	0.182792	−	0.379929i
$681$			25.3399i			0.971026i
$682$	−13.3891	+	11.4165i	−0.512696	+	0.437160i
$683$	15.9666	+	15.9666i	0.610945	+	0.610945i	0.943192	−	0.332247i	$-0.107807\pi$
$683$	15.9666	+	15.9666i	0.610945	+	0.610945i	−0.332247	+	0.943192i	$0.607807\pi$
$684$	12.2315	−	8.85617i	0.467682	−	0.338624i
$685$	−24.3992	−	5.20968i	−0.932246	−	0.199052i
$686$	18.3285	+	1.45756i	0.699785	+	0.0556498i
$687$		−	2.89043i		−	0.110277i
$688$	−18.4528	−	36.5102i	−0.703505	−	1.39194i
$689$	18.3278			0.698235
$690$	0.445709	−	0.240998i	0.0169678	−	0.00917465i
$691$	−8.47128	−	8.47128i	−0.322263	−	0.322263i	0.527372	−	0.849635i	$-0.323177\pi$
$691$	−8.47128	−	8.47128i	−0.322263	−	0.322263i	−0.849635	+	0.527372i	$0.823177\pi$
$692$	2.15940	−	1.56351i	0.0820879	−	0.0594356i
$693$	1.89509	+	1.89509i	0.0719887	+	0.0719887i
$694$	2.12953	+	2.49749i	0.0808358	+	0.0948034i
$695$	42.3680	−	27.4587i	1.60711	−	1.04157i
$696$	10.5067	+	2.54970i	0.398255	+	0.0966460i
$697$	17.2061			0.651726
$698$	−17.9403	−	21.0402i	−0.679050	−	0.796382i
$699$	−7.85480	+	7.85480i	−0.297096	+	0.297096i
$700$	8.36858	+	5.47606i	0.316303	+	0.206975i
$701$	12.7252	+	12.7252i	0.480624	+	0.480624i	0.905331	−	0.424707i	$-0.139623\pi$
$701$	12.7252	+	12.7252i	0.480624	+	0.480624i	−0.424707	+	0.905331i	$0.639623\pi$
$702$	−5.30156	−	0.421602i	−0.200095	−	0.0159123i
$703$			57.2100i			2.15772i
$704$	−20.4213	+	6.52476i	−0.769658	+	0.245911i
$705$	−5.83233	−	8.99912i	−0.219658	−	0.338926i
$706$	0.415358	−	5.22305i	0.0156322	−	0.196572i
$707$	5.60974	−	5.60974i	0.210976	−	0.210976i
$708$	−0.0454760	+	0.284118i	−0.00170909	+	0.0106778i
$709$	−5.12731	+	5.12731i	−0.192560	+	0.192560i	−0.796801	−	0.604241i	$-0.793476\pi$
$709$	−5.12731	+	5.12731i	−0.192560	+	0.192560i	0.604241	+	0.796801i	$0.293476\pi$
$710$	−4.16179	+	13.9608i	−0.156189	+	0.523941i
$711$			5.73529i			0.215090i
$712$	−10.0311	+	41.3358i	−0.375932	+	1.54913i
$713$	−0.743928			−0.0278603
$714$	1.59524	+	1.87089i	0.0597005	+	0.0700161i
$715$	−4.70543	+	22.0376i	−0.175973	+	0.824158i
$716$	−5.37090	−	7.41787i	−0.200720	−	0.277219i
$717$	13.5132	−	13.5132i	0.504660	−	0.504660i
$718$	−1.45376	+	18.2808i	−0.0542540	+	0.682233i
$719$	7.22269			0.269361			0.134681	−	0.990889i	$-0.456999\pi$
$719$	7.22269			0.269361			0.134681	+	0.990889i	$0.456999\pi$
$720$	4.50455	−	7.72716i	0.167875	−	0.287974i
$721$	−14.9993			−0.558604
$722$	4.26133	−	53.5853i	0.158590	−	1.99424i
$723$	4.20801	−	4.20801i	0.156497	−	0.156497i
$724$	−29.9919	+	21.7155i	−1.11464	+	0.807052i
$725$	6.81645	+	17.8556i	0.253156	+	0.663140i
$726$	3.50395	+	4.10940i	0.130044	+	0.152514i
$727$	50.4488			1.87104			0.935522	−	0.353268i	$-0.114930\pi$
$727$	50.4488			1.87104			0.935522	+	0.353268i	$0.114930\pi$
$728$	−9.08371	+	5.53592i	−0.336665	+	0.205175i
$729$			1.00000i			0.0370370i
$730$	36.9478	+	11.0143i	1.36750	+	0.407658i
$731$	12.5712	−	12.5712i	0.464963	−	0.464963i
$732$	16.8078	+	2.69027i	0.621236	+	0.0994353i
$733$	9.19912	−	9.19912i	0.339777	−	0.339777i	−0.516506	−	0.856283i	$-0.672768\pi$
$733$	9.19912	−	9.19912i	0.339777	−	0.339777i	0.856283	+	0.516506i	$0.172768\pi$
$734$	−0.350296	+	4.40491i	−0.0129297	+	0.162588i
$735$	11.2583	−	7.29650i	0.415268	−	0.269135i
$736$	−0.835978	−	0.350282i	−0.0308146	−	0.0129116i
$737$			34.2761i			1.26258i
$738$	13.9536	+	1.10965i	0.513641	+	0.0408468i
$739$	5.53064	+	5.53064i	0.203448	+	0.203448i	0.801476	−	0.598028i	$-0.204049\pi$
$739$	5.53064	+	5.53064i	0.203448	+	0.203448i	−0.598028	+	0.801476i	$0.704049\pi$
$740$	13.7033	+	30.9908i	0.503742	+	1.13925i
$741$	−20.0779	+	20.0779i	−0.737581	+	0.737581i
$742$	−4.47240	−	5.24518i	−0.164187	−	0.192557i
$743$	7.49683			0.275032			0.137516	−	0.990500i	$-0.456088\pi$
$743$	7.49683			0.275032			0.137516	+	0.990500i	$0.456088\pi$
$744$	−11.2137	+	6.83400i	−0.411114	+	0.250546i
$745$	−38.5320	+	24.9726i	−1.41170	+	0.914926i
$746$	27.4650	+	32.2106i	1.00556	+	1.17931i
$747$	−2.04924	−	2.04924i	−0.0749779	−	0.0749779i
$748$	−5.46401	−	7.54647i	−0.199784	−	0.275926i
$749$	−1.22448	−	1.22448i	−0.0447417	−	0.0447417i
$750$	15.7670	−	1.18414i	0.575729	−	0.0432388i
$751$	8.92232			0.325580			0.162790	−	0.986661i	$-0.447951\pi$
$751$	8.92232			0.325580			0.162790	+	0.986661i	$0.447951\pi$
$752$	−5.98759	+	18.2250i	−0.218345	+	0.664596i
$753$		−	29.5166i		−	1.07564i
$754$	−20.2652	−	1.61157i	−0.738015	−	0.0586899i
$755$	6.87444	−	32.1960i	0.250186	−	1.17173i
$756$	1.17304	+	1.62012i	0.0426632	+	0.0589231i
$757$	7.26524	+	7.26524i	0.264060	+	0.264060i	0.826701	−	0.562641i	$-0.190215\pi$
$757$	7.26524	+	7.26524i	0.264060	+	0.264060i	−0.562641	+	0.826701i	$0.690215\pi$
$758$	−3.60971	+	3.07788i	−0.131111	+	0.111794i
$759$		−	0.429384i		−	0.0155856i
$760$	−15.7886	−	45.0680i	−0.572713	−	1.63479i
$761$		−	21.6817i		−	0.785963i	−0.919546	−	0.392981i	$-0.871444\pi$
$761$		−	21.6817i		−	0.785963i	0.919546	−	0.392981i	$-0.128556\pi$
$762$	−5.30877	−	6.22607i	−0.192316	−	0.225547i
$763$	5.31276	+	5.31276i	0.192335	+	0.192335i
$764$	19.3667	+	3.09985i	0.700664	+	0.112149i
$765$	3.80140	+	0.811670i	0.137440	+	0.0293460i
$766$	0.390410	−	4.90934i	0.0141061	−	0.177382i
$767$		−	0.541027i		−	0.0195354i
$768$	−15.8190	+	2.39958i	−0.570820	+	0.0865872i
$769$	0.339883			0.0122565			0.00612824	−	0.999981i	$-0.498049\pi$
$769$	0.339883			0.0122565			0.00612824	+	0.999981i	$0.498049\pi$
$770$	7.45509	−	4.03103i	0.268663	−	0.145268i
$771$	−6.58009	−	6.58009i	−0.236976	−	0.236976i
$772$	−2.15630	+	13.4718i	−0.0776071	+	0.484861i
$773$	30.8536	+	30.8536i	1.10973	+	1.10973i	0.993186	+	0.116541i	$0.0371806\pi$
$773$	30.8536	+	30.8536i	1.10973	+	1.10973i	0.116541	+	0.993186i	$0.462819\pi$
$774$	11.0057	−	9.38417i	0.395590	−	0.337307i
$775$	−21.1900	−	9.48115i	−0.761167	−	0.340573i
$776$	2.56628	−	10.5750i	0.0921240	−	0.379621i
$777$	−7.57775			−0.271850
$778$	−8.98303	+	7.65954i	−0.322057	+	0.274608i
$779$	52.8449	−	52.8449i	1.89336	−	1.89336i
$780$	−6.06710	+	15.6855i	−0.217237	+	0.561629i
$781$	8.72942	+	8.72942i	0.312363	+	0.312363i
$782$	0.0312269	−	0.392672i	0.00111667	−	0.0140419i
$783$			3.82249i			0.136605i
$784$	−22.8002	−	7.49073i	−0.814293	−	0.267526i
$785$	−25.0701	+	16.2480i	−0.894791	+	0.579914i
$786$	−2.03162	−	0.161563i	−0.0724656	−	0.00576276i
$787$	−9.03797	+	9.03797i	−0.322169	+	0.322169i	−0.849599	−	0.527430i	$-0.823156\pi$
$787$	−9.03797	+	9.03797i	−0.322169	+	0.322169i	0.527430	+	0.849599i	$0.323156\pi$
$788$	−25.7344	−	35.5424i	−0.916751	−	1.26615i
$789$	−14.2073	+	14.2073i	−0.505795	+	0.505795i
$790$	17.3807	+	5.18128i	0.618379	+	0.184342i
$791$		−	10.5488i		−	0.375073i
$792$	−3.94448	−	6.47237i	−0.140161	−	0.229986i
$793$	−32.0061			−1.13657
$794$	13.8918	−	11.8451i	0.493002	−	0.420367i
$795$	−10.6576	−	2.27558i	−0.377984	−	0.0807067i
$796$	−2.50365	+	15.6419i	−0.0887395	+	0.554412i
$797$	26.5763	−	26.5763i	0.941380	−	0.941380i	−0.0569944	−	0.998374i	$-0.518152\pi$
$797$	26.5763	−	26.5763i	0.941380	−	0.941380i	0.998374	+	0.0569944i	$0.0181517\pi$
$798$	10.6455	+	0.846574i	0.376847	+	0.0299684i
$799$	−8.33689			−0.294938
$800$	−19.3477	−	20.6317i	−0.684043	−	0.729441i
$801$	−15.0386			−0.531362
$802$	1.16334	+	0.0925138i	0.0410791	+	0.00326678i
$803$	23.1027	−	23.1027i	0.815277	−	0.815277i
$804$	−4.04306	+	25.2596i	−0.142588	+	0.890838i
$805$	0.350423	+	0.0748217i	0.0123508	+	0.00263712i
$806$	18.7892	−	16.0210i	0.661821	−	0.564314i
$807$	−29.9030			−1.05263
$808$	−19.1591	+	11.6762i	−0.674015	+	0.410767i
$809$			40.1166i			1.41043i	0.708996	+	0.705213i	$0.249148\pi$
$809$			40.1166i			1.41043i	−0.708996	+	0.705213i	$0.750852\pi$
$810$	3.03049	+	0.903402i	0.106481	+	0.0317423i
$811$	−4.55343	+	4.55343i	−0.159893	+	0.159893i	−0.782519	−	0.622627i	$-0.786066\pi$
$811$	−4.55343	+	4.55343i	−0.159893	+	0.159893i	0.622627	+	0.782519i	$0.286066\pi$
$812$	4.48395	+	6.19289i	0.157356	+	0.217328i
$813$	−15.1836	+	15.1836i	−0.532513	+	0.532513i
$814$	28.6249	+	2.27637i	1.00330	+	0.0797866i
$815$	−20.3309	+	13.1765i	−0.712162	+	0.461552i
$816$	−3.13652	−	6.20585i	−0.109800	−	0.217248i
$817$		−	77.2198i		−	2.70158i
$818$	−3.96099	+	49.8087i	−0.138493	+	1.74152i
$819$	−2.65942	−	2.65942i	−0.0929276	−	0.0929276i
$820$	15.9685	−	41.2839i	0.557645	−	1.44170i
$821$	15.8058	−	15.8058i	0.551627	−	0.551627i	−0.375283	−	0.926910i	$-0.622455\pi$
$821$	15.8058	−	15.8058i	0.551627	−	0.551627i	0.926910	+	0.375283i	$0.122455\pi$
$822$	−12.0070	+	10.2380i	−0.418793	+	0.357091i
$823$	−3.03903			−0.105934			−0.0529669	−	0.998596i	$-0.516868\pi$
$823$	−3.03903			−0.105934			−0.0529669	+	0.998596i	$0.516868\pi$
$824$	41.2237	+	10.0039i	1.43610	+	0.348502i
$825$	5.47237	−	12.2305i	0.190524	−	0.425812i
$826$	−0.154835	+	0.132023i	−0.00538739	+	0.00459366i
$827$	1.52610	+	1.52610i	0.0530678	+	0.0530678i	0.733143	−	0.680075i	$-0.238053\pi$
$827$	1.52610	+	1.52610i	0.0530678	+	0.0530678i	−0.680075	+	0.733143i	$0.738053\pi$
$828$	0.0506483	−	0.316432i	0.00176015	−	0.0109968i
$829$	28.7055	+	28.7055i	0.996984	+	0.996984i	0.999995	−	0.00301145i	$-0.000958576\pi$
$829$	28.7055	+	28.7055i	0.996984	+	0.996984i	−0.00301145	+	0.999995i	$0.500959\pi$
$830$	−8.06150	+	4.35892i	−0.279819	+	0.151300i
$831$	−5.98931			−0.207767
$832$	28.6576	−	9.15631i	0.993525	−	0.317438i
$833$		−	10.4298i		−	0.361371i
$834$	2.53132	−	31.8309i	0.0876524	−	1.10221i
$835$	31.5321	+	6.73270i	1.09121	+	0.232995i
$836$	−39.9590	−	6.39586i	−1.38201	−	0.221205i
$837$	−3.28301	−	3.28301i	−0.113477	−	0.113477i
$838$	15.3103	+	17.9557i	0.528885	+	0.620270i
$839$			11.9438i			0.412346i	0.978516	+	0.206173i	$0.0661010\pi$
$839$			11.9438i			0.412346i	−0.978516	+	0.206173i	$0.933899\pi$
$840$	5.96948	−	2.09128i	0.205967	−	0.0721559i
$841$		−	14.3885i		−	0.496157i
$842$	−37.9655	+	32.3720i	−1.30838	+	1.11561i
$843$	9.60409	+	9.60409i	0.330782	+	0.330782i
$844$	−16.9207	−	23.3696i	−0.582436	−	0.804416i
$845$	0.533292	−	2.49764i	0.0183458	−	0.0859213i
$846$	−6.76099	−	0.537662i	−0.232448	−	0.0184852i
$847$			3.81908i			0.131225i
$848$	8.79351	+	17.3986i	0.301970	+	0.597471i
$849$	−22.4987			−0.772154
$850$	5.89395	−	10.7868i	0.202161	−	0.369986i
$851$	0.858469	+	0.858469i	0.0294280	+	0.0294280i
$852$	5.40342	+	7.46279i	0.185118	+	0.255671i
$853$	−3.53433	−	3.53433i	−0.121013	−	0.121013i	0.644007	−	0.765020i	$-0.277271\pi$
$853$	−3.53433	−	3.53433i	−0.121013	−	0.121013i	−0.765020	+	0.644007i	$0.777271\pi$
$854$	7.81021	+	9.15973i	0.267260	+	0.313440i
$855$	14.1681	−	9.18235i	0.484539	−	0.314030i
$856$	2.54866	+	4.18201i	0.0871114	+	0.142938i
$857$	−56.1606			−1.91841			−0.959205	−	0.282710i	$-0.908767\pi$
$857$	−56.1606			−1.91841			−0.959205	+	0.282710i	$0.908767\pi$
$858$	9.24704	+	10.8448i	0.315689	+	0.370237i
$859$	−4.66448	+	4.66448i	−0.159150	+	0.159150i	−0.782190	−	0.623040i	$-0.785897\pi$
$859$	−4.66448	+	4.66448i	−0.159150	+	0.159150i	0.623040	+	0.782190i	$0.285897\pi$
$860$	−18.4961	−	41.8302i	−0.630712	−	1.42640i
$861$	6.99956	+	6.99956i	0.238544	+	0.238544i
$862$	−15.3558	−	1.22116i	−0.523021	−	0.0415928i
$863$			12.5882i			0.428507i	0.976778	+	0.214253i	$0.0687319\pi$
$863$			12.5882i			0.428507i	−0.976778	+	0.214253i	$0.931268\pi$
$864$	−2.14341	−	5.23505i	−0.0729203	−	0.178100i
$865$	2.50130	−	1.62109i	0.0850467	−	0.0551188i
$866$	−0.347049	+	4.36407i	−0.0117932	+	0.148297i
$867$	−9.88401	+	9.88401i	−0.335679	+	0.335679i
$868$	−9.16997	−	1.46775i	−0.311249	−	0.0498187i
$869$	10.8678	−	10.8678i	0.368665	−	0.368665i
$870$	11.5840	+	3.45325i	0.392735	+	0.117076i
$871$		−	48.1003i		−	1.62982i
$872$	−11.0581	−	18.1448i	−0.374473	−	0.614461i
$873$	3.84735			0.130213
$874$	−1.11010	−	1.30192i	−0.0375498	−	0.0440380i
$875$	9.02783	+	6.59725i	0.305196	+	0.223028i
$876$	19.7505	−	14.3003i	0.667308	−	0.483163i
$877$	23.7329	−	23.7329i	0.801403	−	0.801403i	−0.181912	−	0.983315i	$-0.558228\pi$
$877$	23.7329	−	23.7329i	0.801403	−	0.801403i	0.983315	+	0.181912i	$0.0582285\pi$
$878$	2.96390	−	37.2704i	0.100027	−	1.25782i
$879$	−9.27460			−0.312825
$880$	−23.1779	+	6.10654i	−0.781326	+	0.205852i
$881$	−3.75776			−0.126602			−0.0633011	−	0.997994i	$-0.520163\pi$
$881$	−3.75776			−0.126602			−0.0633011	+	0.997994i	$0.520163\pi$
$882$	0.672638	−	8.45829i	0.0226489	−	0.284805i
$883$	17.1877	−	17.1877i	0.578413	−	0.578413i	−0.356053	−	0.934466i	$-0.615878\pi$
$883$	17.1877	−	17.1877i	0.578413	−	0.578413i	0.934466	+	0.356053i	$0.115878\pi$
$884$	7.66774	+	10.5901i	0.257894	+	0.356184i
$885$	−0.0671740	+	0.314605i	−0.00225803	+	0.0105753i
$886$	24.4129	+	28.6312i	0.820169	+	0.961885i
$887$	−49.8359			−1.67333			−0.836663	−	0.547718i	$-0.815497\pi$
$887$	−49.8359			−1.67333			−0.836663	+	0.547718i	$0.815497\pi$
$888$	20.8265	+	5.05403i	0.698890	+	0.169602i
$889$		−	5.78621i		−	0.194063i
$890$	−13.5859	+	45.5743i	−0.455400	+	1.52765i
$891$	1.89490	−	1.89490i	0.0634816	−	0.0634816i
$892$	4.38393	−	27.3892i	0.146785	−	0.917059i
$893$	−25.6050	+	25.6050i	−0.856840	+	0.856840i
$894$	−2.30214	+	28.9489i	−0.0769949	+	0.968196i
$895$	−5.56871	−	8.59236i	−0.186142	−	0.287211i
$896$	−9.61352	−	5.96709i	−0.321165	−	0.199347i
$897$			0.602562i			0.0201190i
$898$	23.9071	+	1.90119i	0.797792	+	0.0634437i
$899$	−12.5493	−	12.5493i	−0.418542	−	0.418542i
$900$	5.47550	−	8.36773i	0.182517	−	0.278924i
$901$	−5.99070	+	5.99070i	−0.199579	+	0.199579i
$902$	−24.3381	−	28.5435i	−0.810370	−	0.950393i
$903$	10.2281			0.340371
$904$	−7.03561	+	28.9921i	−0.234001	+	0.964262i
$905$	−34.7405	+	22.5153i	−1.15481	+	0.748435i
$906$	−13.5096	−	15.8439i	−0.448825	−	0.526377i
$907$	−25.1326	−	25.1326i	−0.834515	−	0.834515i	0.153616	−	0.988131i	$-0.450908\pi$
$907$	−25.1326	−	25.1326i	−0.834515	−	0.834515i	−0.988131	+	0.153616i	$0.950908\pi$
$908$	41.0494	−	29.7218i	1.36227	−	0.986351i
$909$	−5.60917	−	5.60917i	−0.186044	−	0.186044i
$910$	−10.4619	+	5.65682i	−0.346808	+	0.187522i
$911$	−49.4774			−1.63926			−0.819629	−	0.572894i	$-0.805821\pi$
$911$	−49.4774			−1.63926			−0.819629	+	0.572894i	$0.805821\pi$
$912$	−28.6932	−	9.42679i	−0.950126	−	0.312152i
$913$			7.76623i			0.257025i
$914$	−8.05350	−	0.640447i	−0.266386	−	0.0211841i
$915$	18.6114	+	3.97388i	0.615274	+	0.131372i
$916$	−4.68236	+	3.39026i	−0.154710	+	0.112017i
$917$	−1.01912	−	1.01912i	−0.0336544	−	0.0336544i
$918$	1.87070	−	1.59508i	0.0617422	−	0.0526456i
$919$		−	4.92570i		−	0.162484i	−0.996694	−	0.0812420i	$-0.974111\pi$
$919$		−	4.92570i		−	0.162484i	0.996694	−	0.0812420i	$-0.0258886\pi$
$920$	−0.913189	−	0.439355i	−0.0301069	−	0.0144851i
$921$		−	8.52184i		−	0.280804i
$922$	30.4206	+	35.6770i	1.00185	+	1.17496i
$923$	−12.2502	−	12.2502i	−0.403219	−	0.403219i
$924$	0.847162	−	5.29277i	0.0278696	−	0.174119i
$925$	13.5116	+	35.3935i	0.444259	+	1.16373i
$926$	−1.87328	+	23.5561i	−0.0615598	+	0.774103i
$927$			14.9978i			0.492592i
$928$	−8.19317	−	20.0110i	−0.268954	−	0.656892i
$929$	15.7829			0.517822			0.258911	−	0.965901i	$-0.416636\pi$
$929$	15.7829			0.517822			0.258911	+	0.965901i	$0.416636\pi$
$930$	−12.9150	+	6.98325i	−0.423500	+	0.228990i
$931$	−32.0330	−	32.0330i	−1.04984	−	1.04984i
$932$	21.9375	+	3.51133i	0.718587	+	0.115017i
$933$	−14.9748	−	14.9748i	−0.490254	−	0.490254i
$934$	21.8020	−	18.5899i	0.713384	−	0.608279i
$935$	−5.66525	−	8.74132i	−0.185274	−	0.285872i
$936$	5.53536	+	9.08279i	0.180929	+	0.296880i
$937$	23.6323			0.772033			0.386017	−	0.922492i	$-0.373851\pi$
$937$	23.6323			0.772033			0.386017	+	0.922492i	$0.373851\pi$
$938$	−13.7657	+	11.7375i	−0.449465	+	0.383245i
$939$	−3.04366	+	3.04366i	−0.0993259	+	0.0993259i
$940$	−7.73727	+	20.0034i	−0.252362	+	0.652438i
$941$	−22.0372	−	22.0372i	−0.718391	−	0.718391i	0.249884	−	0.968276i	$-0.419607\pi$
$941$	−22.0372	−	22.0372i	−0.718391	−	0.718391i	−0.968276	+	0.249884i	$0.919607\pi$
$942$	−1.49784	+	18.8351i	−0.0488023	+	0.613679i
$943$		−	1.58594i		−	0.0516452i
$944$	0.513597	−	0.259579i	0.0167162	−	0.00844859i
$945$	1.21625	+	1.87663i	0.0395645	+	0.0610469i
$946$	−38.6367	−	3.07255i	−1.25619	−	0.0998972i
$947$	8.89469	−	8.89469i	0.289039	−	0.289039i	−0.547661	−	0.836700i	$-0.684482\pi$
$947$	8.89469	−	8.89469i	0.289039	−	0.289039i	0.836700	+	0.547661i	$0.184482\pi$
$948$	9.29091	−	6.72706i	0.301755	−	0.218485i
$949$	−32.4204	+	32.4204i	−1.05241	+	1.05241i
$950$	−15.0275	−	51.2317i	−0.487557	−	1.66217i
$951$		−	33.1382i		−	1.07458i
$952$	1.15965	−	4.77863i	0.0375843	−	0.154876i
$953$	−24.1239			−0.781450			−0.390725	−	0.920507i	$-0.627776\pi$
$953$	−24.1239			−0.781450			−0.390725	+	0.920507i	$0.627776\pi$
$954$	−5.24465	+	4.47195i	−0.169802	+	0.144785i
$955$	21.4449	+	4.57888i	0.693941	+	0.148169i
$956$	−37.7407	−	6.04080i	−1.22062	−	0.195373i
$957$	7.24325	−	7.24325i	0.234141	−	0.234141i
$958$	−15.8547	−	1.26083i	−0.512243	−	0.0407356i
$959$	−11.1588			−0.360335
$960$	−17.8011	+	1.76622i	−0.574529	+	0.0570046i
$961$	−9.44370			−0.304636
$962$	−40.1698	−	3.19447i	−1.29513	−	0.102994i
$963$	−1.22436	+	1.22436i	−0.0394544	+	0.0394544i
$964$	−11.7524	−	1.88110i	−0.378521	−	0.0605862i
$965$	−3.18514	+	14.9174i	−0.102533	+	0.480208i
$966$	0.172445	−	0.147039i	0.00554834	−	0.00473089i
$967$	−17.5889			−0.565620			−0.282810	−	0.959176i	$-0.591267\pi$
$967$	−17.5889			−0.565620			−0.282810	+	0.959176i	$0.591267\pi$
$968$	2.54716	−	10.4963i	0.0818689	−	0.337363i
$969$		−	13.1255i		−	0.421652i
$970$	3.47571	−	11.6594i	0.111598	−	0.374359i
$971$	4.45325	−	4.45325i	0.142911	−	0.142911i	−0.632031	−	0.774943i	$-0.717779\pi$
$971$	4.45325	−	4.45325i	0.142911	−	0.142911i	0.774943	+	0.632031i	$0.217779\pi$
$972$	1.61995	−	1.17292i	0.0519600	−	0.0376216i
$973$	15.9673	−	15.9673i	0.511888	−	0.511888i
$974$	−9.62671	−	0.765556i	−0.308460	−	0.0245300i
$975$	−7.67948	+	17.1633i	−0.245940	+	0.549666i
$976$	−15.3562	−	30.3834i	−0.491540	−	0.972549i
$977$		−	33.1408i		−	1.06027i	−0.847914	−	0.530134i	$-0.822142\pi$
$977$		−	33.1408i		−	1.06027i	0.847914	−	0.530134i	$-0.177858\pi$
$978$	−1.21469	+	15.2745i	−0.0388416	+	0.488426i
$979$	28.4967	+	28.4967i	0.910757	+	0.910757i
$980$	−25.0251	−	9.67966i	−0.799397	−	0.309205i
$981$	5.31222	−	5.31222i	0.169606	−	0.169606i
$982$	40.0670	−	34.1639i	1.27859	−	1.09021i
$983$	27.3732			0.873070			0.436535	−	0.899687i	$-0.356206\pi$
$983$	27.3732			0.873070			0.436535	+	0.899687i	$0.356206\pi$
$984$	−14.5690	−	23.9058i	−0.464442	−	0.762089i
$985$	−26.6822	−	41.1699i	−0.850167	−	1.31178i
$986$	7.15072	−	6.09719i	0.227725	−	0.194174i
$987$	−3.39151	−	3.39151i	−0.107953	−	0.107953i
$988$	56.0752	+	8.97542i	1.78399	+	0.285546i
$989$	−1.15873	−	1.15873i	−0.0368454	−	0.0368454i
$990$	−4.03062	−	7.45434i	−0.128102	−	0.236914i
$991$	−11.5423			−0.366653			−0.183327	−	0.983052i	$-0.558687\pi$
$991$	−11.5423			−0.366653			−0.183327	+	0.983052i	$0.558687\pi$
$992$	24.2236	+	10.1499i	0.769099	+	0.322260i
$993$			7.12489i			0.226102i
$994$	−0.516521	+	6.49515i	−0.0163830	+	0.206014i
$995$	−3.69822	+	17.3204i	−0.117241	+	0.549092i
$996$	−0.916072	+	5.72329i	−0.0290268	+	0.181349i
$997$	28.5401	+	28.5401i	0.903874	+	0.903874i	0.995769	−	0.0918946i	$-0.0292923\pi$
$997$	28.5401	+	28.5401i	0.903874	+	0.903874i	−0.0918946	+	0.995769i	$0.529292\pi$
$998$	22.0466	+	25.8560i	0.697872	+	0.818456i
$999$			7.57698i			0.239725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	240.2.bl.a.109.1	✓	48
3.2	odd	2		720.2.bm.h.109.24		48
4.3	odd	2		960.2.bl.a.529.23		48
5.4	even	2	inner	240.2.bl.a.109.24	yes	48
8.3	odd	2		1920.2.bl.b.289.6		48
8.5	even	2		1920.2.bl.a.289.19		48
15.14	odd	2		720.2.bm.h.109.1		48
16.3	odd	4		1920.2.bl.b.1249.19		48
16.5	even	4	inner	240.2.bl.a.229.24	yes	48
16.11	odd	4		960.2.bl.a.49.5		48
16.13	even	4		1920.2.bl.a.1249.6		48
20.19	odd	2		960.2.bl.a.529.5		48
40.19	odd	2		1920.2.bl.b.289.19		48
40.29	even	2		1920.2.bl.a.289.6		48
48.5	odd	4		720.2.bm.h.469.1		48
80.19	odd	4		1920.2.bl.b.1249.6		48
80.29	even	4		1920.2.bl.a.1249.19		48
80.59	odd	4		960.2.bl.a.49.23		48
80.69	even	4	inner	240.2.bl.a.229.1	yes	48
240.149	odd	4		720.2.bm.h.469.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.1	✓	48	1.1	even	1	trivial
240.2.bl.a.109.24	yes	48	5.4	even	2	inner
240.2.bl.a.229.1	yes	48	80.69	even	4	inner
240.2.bl.a.229.24	yes	48	16.5	even	4	inner
720.2.bm.h.109.1		48	15.14	odd	2
720.2.bm.h.109.24		48	3.2	odd	2
720.2.bm.h.469.1		48	48.5	odd	4
720.2.bm.h.469.24		48	240.149	odd	4
960.2.bl.a.49.5		48	16.11	odd	4
960.2.bl.a.49.23		48	80.59	odd	4
960.2.bl.a.529.5		48	20.19	odd	2
960.2.bl.a.529.23		48	4.3	odd	2
1920.2.bl.a.289.6		48	40.29	even	2
1920.2.bl.a.289.19		48	8.5	even	2
1920.2.bl.a.1249.6		48	16.13	even	4
1920.2.bl.a.1249.19		48	80.29	even	4
1920.2.bl.b.289.6		48	8.3	odd	2
1920.2.bl.b.289.19		48	40.19	odd	2
1920.2.bl.b.1249.6		48	80.19	odd	4
1920.2.bl.b.1249.19		48	16.3	odd	4

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:	\( N \)	\(=\)	\( 240 = 2^{4} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	240.bl (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40976 - 0.112110i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97486 + 0.316097i) q^{4} +(2.18678 + 0.466917i) q^{5} +(1.07613 - 0.917579i) q^{6} +1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.40976 - 0.112110i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.97486 + 0.316097i) q^{4} +(2.18678 + 0.466917i) q^{5} +(1.07613 - 0.917579i) q^{6} +1.00010 q^{7} +(-2.74865 - 0.667024i) q^{8} -1.00000i q^{9} +(-3.03049 - 0.903402i) q^{10} +(-1.89490 + 1.89490i) q^{11} +(-1.61995 + 1.17292i) q^{12} +(2.65915 - 2.65915i) q^{13} +(-1.40991 - 0.112121i) q^{14} +(-1.87644 + 1.21612i) q^{15} +(3.80016 + 1.24850i) q^{16} +1.73836i q^{17} +(-0.112110 + 1.40976i) q^{18} +(5.33902 + 5.33902i) q^{19} +(4.17099 + 1.61333i) q^{20} +(-0.707179 + 0.707179i) q^{21} +(2.88380 - 2.45892i) q^{22} +0.160230 q^{23} +(2.41525 - 1.47193i) q^{24} +(4.56398 + 2.04209i) q^{25} +(-4.04689 + 3.45065i) q^{26} +(0.707107 + 0.707107i) q^{27} +(1.97506 + 0.316129i) q^{28} +(2.70291 + 2.70291i) q^{29} +(2.78168 - 1.50408i) q^{30} -4.64288 q^{31} +(-5.21736 - 2.18612i) q^{32} -2.67980i q^{33} +(0.194888 - 2.45068i) q^{34} +(2.18700 + 0.466965i) q^{35} +(0.316097 - 1.97486i) q^{36} +(5.35773 + 5.35773i) q^{37} +(-6.92819 - 8.12530i) q^{38} +3.76061i q^{39} +(-5.69924 - 2.74202i) q^{40} -9.89786i q^{41} +(1.07624 - 0.917672i) q^{42} +(-7.23165 - 7.23165i) q^{43} +(-4.34114 + 3.14320i) q^{44} +(0.466917 - 2.18678i) q^{45} +(-0.225886 - 0.0179634i) q^{46} +4.79583i q^{47} +(-3.56994 + 1.80430i) q^{48} -5.99980 q^{49} +(-6.20519 - 3.39053i) q^{50} +(-1.22921 - 1.22921i) q^{51} +(6.09201 - 4.41091i) q^{52} +(3.44618 + 3.44618i) q^{53} +(-0.917579 - 1.07613i) q^{54} +(-5.02849 + 3.25896i) q^{55} +(-2.74893 - 0.667092i) q^{56} -7.55051 q^{57} +(-3.50744 - 4.11349i) q^{58} +(0.101729 - 0.101729i) q^{59} +(-4.09013 + 1.80854i) q^{60} +(-6.01811 - 6.01811i) q^{61} +(6.54535 + 0.520513i) q^{62} -1.00010i q^{63} +(7.11016 + 3.66683i) q^{64} +(7.05657 - 4.57336i) q^{65} +(-0.300432 + 3.77788i) q^{66} +(9.04430 - 9.04430i) q^{67} +(-0.549491 + 3.43302i) q^{68} +(-0.113300 + 0.113300i) q^{69} +(-3.03080 - 0.903494i) q^{70} -4.60679i q^{71} +(-0.667024 + 2.74865i) q^{72} -12.1920 q^{73} +(-6.95248 - 8.15379i) q^{74} +(-4.67119 + 1.78325i) q^{75} +(8.85617 + 12.2315i) q^{76} +(-1.89509 + 1.89509i) q^{77} +(0.421602 - 5.30156i) q^{78} -5.73529 q^{79} +(7.72716 + 4.50455i) q^{80} -1.00000 q^{81} +(-1.10965 + 13.9536i) q^{82} +(2.04924 - 2.04924i) q^{83} +(-1.62012 + 1.17304i) q^{84} +(-0.811670 + 3.80140i) q^{85} +(9.38417 + 11.0057i) q^{86} -3.82249 q^{87} +(6.47237 - 3.94448i) q^{88} -15.0386i q^{89} +(-0.903402 + 3.03049i) q^{90} +(2.65942 - 2.65942i) q^{91} +(0.316432 + 0.0506483i) q^{92} +(3.28301 - 3.28301i) q^{93} +(0.537662 - 6.76099i) q^{94} +(9.18235 + 14.1681i) q^{95} +(5.23505 - 2.14341i) q^{96} +3.84735i q^{97} +(8.45829 + 0.672638i) q^{98} +(1.89490 + 1.89490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} - 16 q^{14} - 4 q^{16} + 8 q^{19} - 4 q^{24} - 40 q^{26} - 8 q^{30} - 48 q^{31} - 28 q^{34} + 24 q^{35} - 4 q^{36} - 16 q^{40} - 40 q^{44} - 4 q^{46} + 48 q^{49} - 32 q^{50} + 8 q^{51} - 4 q^{54} + 48 q^{56} - 32 q^{59} - 24 q^{60} + 16 q^{61} + 48 q^{64} + 16 q^{65} + 24 q^{66} - 16 q^{69} + 40 q^{74} - 16 q^{75} + 60 q^{76} - 96 q^{79} + 72 q^{80} - 48 q^{81} + 16 q^{86} + 8 q^{90} - 32 q^{91} + 44 q^{94} - 48 q^{95} - 40 q^{96}+O(q^{100}) \) 48 * q + 12 * q^10 - 16 * q^14 - 4 * q^16 + 8 * q^19 - 4 * q^24 - 40 * q^26 - 8 * q^30 - 48 * q^31 - 28 * q^34 + 24 * q^35 - 4 * q^36 - 16 * q^40 - 40 * q^44 - 4 * q^46 + 48 * q^49 - 32 * q^50 + 8 * q^51 - 4 * q^54 + 48 * q^56 - 32 * q^59 - 24 * q^60 + 16 * q^61 + 48 * q^64 + 16 * q^65 + 24 * q^66 - 16 * q^69 + 40 * q^74 - 16 * q^75 + 60 * q^76 - 96 * q^79 + 72 * q^80 - 48 * q^81 + 16 * q^86 + 8 * q^90 - 32 * q^91 + 44 * q^94 - 48 * q^95 - 40 * q^96

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