LMFDB - Embedded newform 570.2.v.c.353.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(83,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 4]))

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

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

chi := DirichletCharacter("570.83");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.v (of order $12$, degree $4$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			353.18
Character	$\chi$	$=$	570.353
Dual form			570.2.v.c.197.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(1.69291 - 0.366145i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.17042 + 0.537853i) q^{5} +(-1.54046 + 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.73188 - 1.23970i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(1.69291 - 0.366145i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.17042 + 0.537853i) q^{5} +(-1.54046 + 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.73188 - 1.23970i) q^{9} +(1.95726 - 1.08127i) q^{10} -5.54910i q^{11} +(1.28303 - 1.16354i) q^{12} +(-0.0848738 + 0.316753i) q^{13} +(0.759868 - 1.31613i) q^{14} +(-3.47739 + 1.70522i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.12997 - 1.64252i) q^{17} +(-2.31793 + 1.90452i) q^{18} +(1.73771 - 3.99755i) q^{19} +(-1.61071 + 1.55100i) q^{20} +(-1.42576 + 2.21269i) q^{21} +(1.43621 + 5.36001i) q^{22} +(7.51752 + 2.01431i) q^{23} +(-0.938163 + 1.45597i) q^{24} +(4.42143 - 2.33473i) q^{25} -0.327927i q^{26} +(4.17091 - 3.09896i) q^{27} +(-0.393337 + 1.46795i) q^{28} +(2.43524 + 4.21797i) q^{29} +(2.91755 - 2.54713i) q^{30} -4.22261 q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.03177 - 9.39411i) q^{33} +(-5.49598 + 3.17311i) q^{34} +(1.75438 - 2.91035i) q^{35} +(1.74602 - 2.43955i) q^{36} +(3.78717 - 3.78717i) q^{37} +(-0.643857 + 4.31108i) q^{38} +(-0.0277060 + 0.567310i) q^{39} +(1.15440 - 1.91504i) q^{40} +(-1.04419 - 0.602864i) q^{41} +(0.804493 - 2.50631i) q^{42} +(-8.79326 + 2.35615i) q^{43} +(-2.77455 - 4.80566i) q^{44} +(-5.26254 + 4.16001i) q^{45} -7.78271 q^{46} +(0.639288 - 2.38585i) q^{47} +(0.529363 - 1.64917i) q^{48} +4.69040i q^{49} +(-3.66650 + 3.39953i) q^{50} +(9.77608 - 5.02509i) q^{51} +(0.0848738 + 0.316753i) q^{52} +(-5.61960 - 1.50577i) q^{53} +(-3.22672 + 4.07287i) q^{54} +(2.98460 + 12.0439i) q^{55} -1.51974i q^{56} +(1.47810 - 7.40373i) q^{57} +(-3.44396 - 3.44396i) q^{58} +(-2.29536 + 3.97569i) q^{59} +(-2.15889 + 3.21546i) q^{60} +(-4.12362 - 7.14232i) q^{61} +(4.07873 - 1.09289i) q^{62} +(-1.60352 + 4.26792i) q^{63} -1.00000i q^{64} +(0.0138450 - 0.733136i) q^{65} +(4.39392 + 8.54815i) q^{66} +(-0.809136 - 0.216807i) q^{67} +(4.48745 - 4.48745i) q^{68} +(13.4640 + 0.657548i) q^{69} +(-0.941347 + 3.26525i) q^{70} +(-7.44126 - 4.29621i) q^{71} +(-1.05513 + 2.80833i) q^{72} +(9.89978 - 2.65264i) q^{73} +(-2.67793 + 4.63831i) q^{74} +(6.63022 - 5.57137i) q^{75} +(-0.493872 - 4.33083i) q^{76} +(5.96314 + 5.96314i) q^{77} +(-0.120069 - 0.555150i) q^{78} +(4.24944 + 2.45342i) q^{79} +(-0.619415 + 2.14856i) q^{80} +(5.92629 - 6.77341i) q^{81} +(1.16464 + 0.312065i) q^{82} +(2.14772 - 2.14772i) q^{83} +(-0.128400 + 2.62913i) q^{84} +(-12.4212 + 6.86198i) q^{85} +(7.88383 - 4.55173i) q^{86} +(5.66703 + 6.24898i) q^{87} +(3.92380 + 3.92380i) q^{88} +(-1.34160 - 2.32371i) q^{89} +(4.00653 - 5.38031i) q^{90} +(-0.249181 - 0.431594i) q^{91} +(7.51752 - 2.01431i) q^{92} +(-7.14850 + 1.54609i) q^{93} +2.47002i q^{94} +(-1.62147 + 9.61098i) q^{95} +(-0.0844883 + 1.72999i) q^{96} +(2.39577 + 8.94113i) q^{97} +(-1.21397 - 4.53058i) q^{98} +(-6.87921 - 15.1594i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) $ 144 * q - 4 * q^3 + 8 * q^6	$ 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) $ 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	1.69291	−	0.366145i	0.977401	−	0.211394i
$3$	1.69291	−	0.366145i	0.977401	−	0.211394i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.17042	+	0.537853i	−0.970640	+	0.240535i
$5$	−2.17042	+	0.537853i	−0.970640	+	0.240535i
$6$	−1.54046	+	0.791825i	−0.628890	+	0.323261i
$7$	−1.07462	+	1.07462i	−0.406166	+	0.406166i	−0.880399	−	0.474233i	$-0.842725\pi$
$7$	−1.07462	+	1.07462i	−0.406166	+	0.406166i	0.474233	+	0.880399i	$0.342725\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.73188	−	1.23970i	0.910625	−	0.413233i
$10$	1.95726	−	1.08127i	0.618939	−	0.341928i
$11$		−	5.54910i		−	1.67312i	−0.547879	−	0.836558i	$-0.684565\pi$
$11$		−	5.54910i		−	1.67312i	0.547879	−	0.836558i	$-0.315435\pi$
$12$	1.28303	−	1.16354i	0.370379	−	0.335886i
$13$	−0.0848738	+	0.316753i	−0.0235397	+	0.0878515i	−0.976696	−	0.214626i	$-0.931147\pi$
$13$	−0.0848738	+	0.316753i	−0.0235397	+	0.0878515i	0.953157	+	0.302477i	$0.0978136\pi$
$14$	0.759868	−	1.31613i	0.203083	−	0.351750i
$15$	−3.47739	+	1.70522i	−0.897857	+	0.440286i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.12997	−	1.64252i	1.48674	−	0.398370i	0.578103	−	0.815964i	$-0.303793\pi$
$17$	6.12997	−	1.64252i	1.48674	−	0.398370i	0.908634	+	0.417594i	$0.137127\pi$
$18$	−2.31793	+	1.90452i	−0.546342	+	0.448899i
$19$	1.73771	−	3.99755i	0.398658	−	0.917100i
$19$	1.73771	−	3.99755i	0.398658	−	0.917100i
$20$	−1.61071	+	1.55100i	−0.360166	+	0.346815i
$21$	−1.42576	+	2.21269i	−0.311126	+	0.482849i
$22$	1.43621	+	5.36001i	0.306201	+	1.14276i
$23$	7.51752	+	2.01431i	1.56751	+	0.420014i	0.935032	−	0.354563i	$-0.115370\pi$
$23$	7.51752	+	2.01431i	1.56751	+	0.420014i	0.632480	+	0.774577i	$0.282037\pi$
$24$	−0.938163	+	1.45597i	−0.191502	+	0.297199i
$25$	4.42143	−	2.33473i	0.884286	−	0.466946i
$26$		−	0.327927i		−	0.0643118i
$27$	4.17091	−	3.09896i	0.802691	−	0.596395i
$28$	−0.393337	+	1.46795i	−0.0743336	+	0.277417i
$29$	2.43524	+	4.21797i	0.452214	+	0.783257i	0.998523	−	0.0543264i	$-0.0173011\pi$
$29$	2.43524	+	4.21797i	0.452214	+	0.783257i	−0.546310	+	0.837583i	$0.683968\pi$
$30$	2.91755	−	2.54713i	0.532670	−	0.465041i
$31$	−4.22261			−0.758404			−0.379202	−	0.925314i	$-0.623801\pi$
$31$	−4.22261			−0.758404			−0.379202	+	0.925314i	$0.623801\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−2.03177	−	9.39411i	−0.353686	−	1.63530i
$34$	−5.49598	+	3.17311i	−0.942553	+	0.544183i
$35$	1.75438	−	2.91035i	0.296544	−	0.491939i
$36$	1.74602	−	2.43955i	0.291004	−	0.406591i
$37$	3.78717	−	3.78717i	0.622606	−	0.622606i	−0.323591	−	0.946197i	$-0.604890\pi$
$37$	3.78717	−	3.78717i	0.622606	−	0.622606i	0.946197	+	0.323591i	$0.104890\pi$
$38$	−0.643857	+	4.31108i	−0.104447	+	0.699350i
$39$	−0.0277060	+	0.567310i	−0.00443651	+	0.0908423i
$40$	1.15440	−	1.91504i	0.182526	−	0.302794i
$41$	−1.04419	−	0.602864i	−0.163075	−	0.0941515i	0.416241	−	0.909254i	$-0.363347\pi$
$41$	−1.04419	−	0.602864i	−0.163075	−	0.0941515i	−0.579317	+	0.815103i	$0.696680\pi$
$42$	0.804493	−	2.50631i	0.124136	−	0.386732i
$43$	−8.79326	+	2.35615i	−1.34096	+	0.359309i	−0.856790	−	0.515665i	$-0.827545\pi$
$43$	−8.79326	+	2.35615i	−1.34096	+	0.359309i	−0.484170	+	0.874974i	$0.660878\pi$
$44$	−2.77455	−	4.80566i	−0.418279	−	0.724480i
$45$	−5.26254	+	4.16001i	−0.784493	+	0.620138i
$46$	−7.78271			−1.14750
$47$	0.639288	−	2.38585i	0.0932497	−	0.348013i	−0.903499	−	0.428591i	$-0.859010\pi$
$47$	0.639288	−	2.38585i	0.0932497	−	0.348013i	0.996748	+	0.0805785i	$0.0256768\pi$
$48$	0.529363	−	1.64917i	0.0764070	−	0.238038i
$49$			4.69040i			0.670058i
$50$	−3.66650	+	3.39953i	−0.518521	+	0.480766i
$51$	9.77608	−	5.02509i	1.36892	−	0.703654i
$52$	0.0848738	+	0.316753i	0.0117699	+	0.0439258i
$53$	−5.61960	−	1.50577i	−0.771911	−	0.206833i	−0.148696	−	0.988883i	$-0.547507\pi$
$53$	−5.61960	−	1.50577i	−0.771911	−	0.206833i	−0.623216	+	0.782050i	$0.714174\pi$
$54$	−3.22672	+	4.07287i	−0.439101	+	0.554248i
$55$	2.98460	+	12.0439i	0.402443	+	1.62399i
$56$		−	1.51974i		−	0.203083i
$57$	1.47810	−	7.40373i	0.195779	−	0.980648i
$58$	−3.44396	−	3.44396i	−0.452214	−	0.452214i
$59$	−2.29536	+	3.97569i	−0.298831	+	0.517590i	−0.975869	−	0.218358i	$-0.929930\pi$
$59$	−2.29536	+	3.97569i	−0.298831	+	0.517590i	0.677038	+	0.735948i	$0.263263\pi$
$60$	−2.15889	+	3.21546i	−0.278712	+	0.415114i
$61$	−4.12362	−	7.14232i	−0.527975	−	0.914480i	−0.999468	−	0.0326100i	$-0.989618\pi$
$61$	−4.12362	−	7.14232i	−0.527975	−	0.914480i	0.471493	−	0.881870i	$-0.343715\pi$
$62$	4.07873	−	1.09289i	0.518000	−	0.138798i
$63$	−1.60352	+	4.26792i	−0.202024	+	0.537707i
$64$		−	1.00000i		−	0.125000i
$65$	0.0138450	−	0.733136i	0.00171727	−	0.0909344i
$66$	4.39392	+	8.54815i	0.540854	+	1.05220i
$67$	−0.809136	−	0.216807i	−0.0988517	−	0.0264872i	0.209054	−	0.977904i	$-0.432962\pi$
$67$	−0.809136	−	0.216807i	−0.0988517	−	0.0264872i	−0.307906	+	0.951417i	$0.599628\pi$
$68$	4.48745	−	4.48745i	0.544183	−	0.544183i
$69$	13.4640	+	0.657548i	1.62088	+	0.0791595i
$70$	−0.941347	+	3.26525i	−0.112513	+	0.390272i
$71$	−7.44126	−	4.29621i	−0.883115	−	0.509866i	−0.0114305	−	0.999935i	$-0.503639\pi$
$71$	−7.44126	−	4.29621i	−0.883115	−	0.509866i	−0.871684	+	0.490068i	$0.836972\pi$
$72$	−1.05513	+	2.80833i	−0.124348	+	0.330965i
$73$	9.89978	−	2.65264i	1.15868	−	0.310468i	0.372243	−	0.928135i	$-0.378589\pi$
$73$	9.89978	−	2.65264i	1.15868	−	0.310468i	0.786439	+	0.617668i	$0.211922\pi$
$74$	−2.67793	+	4.63831i	−0.311303	+	0.539193i
$75$	6.63022	−	5.57137i	0.765592	−	0.643326i
$76$	−0.493872	−	4.33083i	−0.0566510	−	0.496780i
$77$	5.96314	+	5.96314i	0.679563	+	0.679563i
$78$	−0.120069	−	0.555150i	−0.0135951	−	0.0628584i
$79$	4.24944	+	2.45342i	0.478100	+	0.276031i	0.719624	−	0.694364i	$-0.244314\pi$
$79$	4.24944	+	2.45342i	0.478100	+	0.276031i	−0.241524	+	0.970395i	$0.577647\pi$
$80$	−0.619415	+	2.14856i	−0.0692527	+	0.240217i
$81$	5.92629	−	6.77341i	0.658477	−	0.752601i
$82$	1.16464	+	0.312065i	0.128613	+	0.0344618i
$83$	2.14772	−	2.14772i	0.235743	−	0.235743i	−0.579342	−	0.815085i	$-0.696690\pi$
$83$	2.14772	−	2.14772i	0.235743	−	0.235743i	0.815085	+	0.579342i	$0.196690\pi$
$84$	−0.128400	+	2.62913i	−0.0140096	+	0.286861i
$85$	−12.4212	+	6.86198i	−1.34726	+	0.744286i
$86$	7.88383	−	4.55173i	0.850135	−	0.490826i
$87$	5.66703	+	6.24898i	0.607570	+	0.669961i
$88$	3.92380	+	3.92380i	0.418279	+	0.418279i
$89$	−1.34160	−	2.32371i	−0.142209	−	0.246313i	0.786119	−	0.618075i	$-0.212087\pi$
$89$	−1.34160	−	2.32371i	−0.142209	−	0.246313i	−0.928328	+	0.371762i	$0.878754\pi$
$90$	4.00653	−	5.38031i	0.422326	−	0.567134i
$91$	−0.249181	−	0.431594i	−0.0261213	−	0.0452434i
$92$	7.51752	−	2.01431i	0.783756	−	0.210007i
$93$	−7.14850	+	1.54609i	−0.741265	+	0.160322i
$94$			2.47002i			0.254763i
$95$	−1.62147	+	9.61098i	−0.166359	+	0.986065i
$96$	−0.0844883	+	1.72999i	−0.00862305	+	0.176566i
$97$	2.39577	+	8.94113i	0.243253	+	0.907834i	0.974253	+	0.225457i	$0.0723874\pi$
$97$	2.39577	+	8.94113i	0.243253	+	0.907834i	−0.731000	+	0.682378i	$0.760946\pi$
$98$	−1.21397	−	4.53058i	−0.122629	−	0.457658i
$99$	−6.87921	−	15.1594i	−0.691386	−	1.52358i
$100$	2.66171	−	4.23265i	0.266171	−	0.423265i
$101$	−4.87192	+	2.81280i	−0.484774	+	0.279884i	−0.722404	−	0.691471i	$-0.756963\pi$
$101$	−4.87192	+	2.81280i	−0.484774	+	0.279884i	0.237630	+	0.971356i	$0.423629\pi$
$102$	−8.14238	+	7.38410i	−0.806216	+	0.731135i
$103$	12.1547	+	12.1547i	1.19764	+	1.19764i	0.974871	+	0.222770i	$0.0715098\pi$
$103$	12.1547	+	12.1547i	1.19764	+	1.19764i	0.222770	+	0.974871i	$0.428490\pi$
$104$	−0.163964	−	0.283993i	−0.0160779	−	0.0278478i
$105$	1.90440	−	5.56931i	0.185850	−	0.543509i
$106$	5.81784			0.565078
$107$	−3.09394	−	3.09394i	−0.299102	−	0.299102i	0.541560	−	0.840662i	$-0.317834\pi$
$107$	−3.09394	−	3.09394i	−0.299102	−	0.299102i	−0.840662	+	0.541560i	$0.817834\pi$
$108$	2.06263	−	4.76923i	0.198477	−	0.458919i
$109$	−6.31208	−	3.64428i	−0.604588	−	0.349059i	0.166256	−	0.986083i	$-0.446832\pi$
$109$	−6.31208	−	3.64428i	−0.604588	−	0.349059i	−0.770844	+	0.637024i	$0.780165\pi$
$110$	−6.00008	−	10.8610i	−0.572085	−	1.03556i
$111$	5.02468	−	7.79798i	0.476921	−	0.740151i
$112$	0.393337	+	1.46795i	0.0371668	+	0.138708i
$113$	11.1820	−	11.1820i	1.05192	−	1.05192i	0.0533396	−	0.998576i	$-0.483013\pi$
$113$	11.1820	−	11.1820i	1.05192	−	1.05192i	0.998576	−	0.0533396i	$-0.0169866\pi$
$114$	0.488489	+	7.53401i	0.0457512	+	0.705625i
$115$	−17.3996	−	0.328585i	−1.62252	−	0.0306407i
$116$	4.21797	+	2.43524i	0.391628	+	0.226107i
$117$	0.160814	+	0.970548i	0.0148672	+	0.0897272i
$118$	1.18817	−	4.43430i	0.109380	−	0.408211i
$119$	−4.82228	+	8.35244i	−0.442058	+	0.765667i
$120$	1.25311	−	3.66466i	0.114393	−	0.334536i
$121$	−19.7925			−1.79931
$122$	5.83168	+	5.83168i	0.527975	+	0.527975i
$123$	−1.98845	−	0.638268i	−0.179293	−	0.0575507i
$124$	−3.65689	+	2.11131i	−0.328399	+	0.189601i
$125$	−8.34061	+	7.44542i	−0.746007	+	0.665938i
$126$	0.444261	−	4.53751i	0.0395779	−	0.404234i
$127$	−19.5888	−	5.24881i	−1.73823	−	0.465757i	−0.756176	−	0.654369i	$-0.772934\pi$
$127$	−19.5888	−	5.24881i	−1.73823	−	0.465757i	−0.982052	+	0.188612i	$0.939601\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−14.0235	+	7.20835i	−1.23470	+	0.634660i
$130$	0.176376	+	0.711739i	0.0154692	+	0.0624236i
$131$	−8.41111	−	4.85616i	−0.734882	−	0.424284i	0.0853235	−	0.996353i	$-0.472808\pi$
$131$	−8.41111	−	4.85616i	−0.734882	−	0.424284i	−0.820205	+	0.572069i	$0.806141\pi$
$132$	−6.45662	−	7.11965i	−0.561977	−	0.619686i
$133$	2.42845	+	6.16319i	0.210574	+	0.534417i
$134$	0.837680			0.0723645
$135$	−7.38583	+	8.96937i	−0.635671	+	0.771960i
$136$	−3.17311	+	5.49598i	−0.272092	+	0.471277i
$137$	−5.27271	+	19.6780i	−0.450478	+	1.68121i	0.250574	+	0.968098i	$0.419381\pi$
$137$	−5.27271	+	19.6780i	−0.450478	+	1.68121i	−0.701052	+	0.713110i	$0.747286\pi$
$138$	−13.1754	+	2.84960i	−1.12157	+	0.242574i
$139$	−9.46841	+	5.46659i	−0.803100	+	0.463670i	−0.844554	−	0.535471i	$-0.820134\pi$
$139$	−9.46841	+	5.46659i	−0.803100	+	0.463670i	0.0414541	+	0.999140i	$0.486801\pi$
$140$	0.0641631	−	3.39763i	0.00542277	−	0.287152i
$141$	0.208687	−	4.27310i	0.0175747	−	0.359860i
$142$	8.29964	+	2.22388i	0.696491	+	0.186624i
$143$	1.75769	+	0.470973i	0.146986	+	0.0393847i
$144$	0.292328	−	2.98572i	0.0243606	−	0.248810i
$145$	−7.55414	−	7.84495i	−0.627338	−	0.651488i
$146$	−8.87590	+	5.12450i	−0.734575	+	0.424107i
$147$	1.71737	+	7.94042i	0.141646	+	0.654915i
$148$	1.38620	−	5.17337i	0.113945	−	0.425248i
$149$	−1.46783	+	2.54235i	−0.120249	+	0.208278i	−0.919866	−	0.392233i	$-0.871703\pi$
$149$	−1.46783	+	2.54235i	−0.120249	+	0.208278i	0.799617	+	0.600511i	$0.205036\pi$
$150$	−4.96233	+	7.09755i	−0.405173	+	0.579513i
$151$	14.3038			1.16403			0.582015	−	0.813178i	$-0.302265\pi$
$151$	14.3038			1.16403			0.582015	+	0.813178i	$0.302265\pi$
$152$	1.59795	+	4.05544i	0.129610	+	0.328939i
$153$	14.7101	−	12.0865i	1.18924	−	0.977134i
$154$	−7.30333	−	4.21658i	−0.588519	−	0.339782i
$155$	9.16484	−	2.27114i	0.736138	−	0.182423i
$156$	0.259661	+	0.505158i	0.0207895	+	0.0404450i
$157$	1.49549	+	5.58125i	0.119353	+	0.445432i	0.999576	−	0.0291291i	$-0.00927340\pi$
$157$	1.49549	+	5.58125i	0.119353	+	0.445432i	−0.880222	+	0.474561i	$0.842607\pi$
$158$	−4.73964	−	1.26998i	−0.377066	−	0.101034i
$159$	−10.0648	−	0.491539i	−0.798190	−	0.0389816i
$160$	0.0422199	−	2.23567i	0.00333778	−	0.176745i
$161$	−10.2431	+	5.91383i	−0.807266	+	0.466075i
$162$	−3.97127	+	8.07645i	−0.312013	+	0.634546i
$163$	8.02418	+	8.02418i	0.628502	+	0.628502i	0.947691	−	0.319189i	$-0.103410\pi$
$163$	8.02418	+	8.02418i	0.628502	+	0.628502i	−0.319189	+	0.947691i	$0.603410\pi$
$164$	−1.20573			−0.0941515
$165$	9.46244	+	19.2964i	0.736650	+	1.50222i
$166$	−1.51867	+	2.63041i	−0.117872	+	0.204160i
$167$	2.12593	−	7.93409i	0.164510	−	0.613958i	−0.833593	−	0.552380i	$-0.813720\pi$
$167$	2.12593	−	7.93409i	0.164510	−	0.613958i	0.998102	−	0.0615785i	$-0.0196135\pi$
$168$	−0.556443	−	2.57277i	−0.0429305	−	0.198494i
$169$	11.1652	+	6.44623i	0.858862	+	0.495864i
$170$	10.2219	−	9.84300i	0.783985	−	0.754923i
$171$	−0.208545	−	13.0750i	−0.0159479	−	0.999873i
$172$	−6.43712	+	6.43712i	−0.490826	+	0.490826i
$173$	4.99724	+	18.6499i	0.379933	+	1.41793i	0.846001	+	0.533181i	$0.179003\pi$
$173$	4.99724	+	18.6499i	0.379933	+	1.41793i	−0.466068	+	0.884749i	$0.654330\pi$
$174$	−7.09129	−	4.56932i	−0.537589	−	0.346399i
$175$	−2.24240	+	7.26027i	−0.169509	+	0.548825i
$176$	−4.80566	−	2.77455i	−0.362240	−	0.209139i
$177$	−2.43016	+	7.57091i	−0.182662	+	0.569064i
$178$	1.89730	+	1.89730i	0.142209	+	0.142209i
$179$	−5.87259			−0.438938			−0.219469	−	0.975619i	$-0.570432\pi$
$179$	−5.87259			−0.438938			−0.219469	+	0.975619i	$0.570432\pi$
$180$	−2.47749	+	6.23394i	−0.184661	+	0.464651i
$181$	2.02582	+	3.50883i	0.150578	+	0.260809i	0.931440	−	0.363894i	$-0.118553\pi$
$181$	2.02582	+	3.50883i	0.150578	+	0.260809i	−0.780862	+	0.624704i	$0.785220\pi$
$182$	0.352395	+	0.352395i	0.0261213	+	0.0261213i
$183$	−9.59603	−	10.5814i	−0.709359	−	0.782203i
$184$	−6.74003	+	3.89136i	−0.496881	+	0.286875i
$185$	−6.18280	+	10.2567i	−0.454568	+	0.754086i
$186$	6.50476	−	3.34357i	0.476952	−	0.245163i
$187$	−9.11451	−	34.0158i	−0.666519	−	2.48748i
$188$	−0.639288	−	2.38585i	−0.0466248	−	0.174006i
$189$	−1.15193	+	7.81231i	−0.0837907	+	0.568262i
$190$	−0.921288	−	9.70316i	−0.0668373	−	0.703941i
$191$		−	22.4627i		−	1.62535i	−0.582720	−	0.812673i	$-0.698012\pi$
$191$		−	22.4627i		−	1.62535i	0.582720	−	0.812673i	$-0.301988\pi$
$192$	−0.366145	−	1.69291i	−0.0264242	−	0.122175i
$193$	−19.1377	+	5.12794i	−1.37757	+	0.369118i	−0.870236	−	0.492635i	$-0.836034\pi$
$193$	−19.1377	+	5.12794i	−1.37757	+	0.369118i	−0.507329	+	0.861752i	$0.669367\pi$
$194$	−4.62827	−	8.01640i	−0.332290	−	0.575544i
$195$	−0.244996	−	1.24620i	−0.0175445	−	0.0892424i
$196$	2.34520	+	4.06201i	0.167514	+	0.290143i
$197$	9.54319	+	9.54319i	0.679924	+	0.679924i	0.959983	−	0.280059i	$-0.0903539\pi$
$197$	9.54319	+	9.54319i	0.679924	+	0.679924i	−0.280059	+	0.959983i	$0.590354\pi$
$198$	10.5684	+	12.8624i	0.751060	+	0.914093i
$199$	23.6010	−	13.6261i	1.67303	−	0.965926i	0.707107	−	0.707107i	$-0.250000\pi$
$199$	23.6010	−	13.6261i	1.67303	−	0.965926i	0.965926	−	0.258819i	$-0.0833335\pi$
$200$	−1.47552	+	4.77733i	−0.104335	+	0.337808i
$201$	−1.44918	−	0.0707741i	−0.102217	−	0.00499202i
$202$	3.97790	−	3.97790i	0.279884	−	0.279884i
$203$	−7.14964	−	1.91574i	−0.501807	−	0.134459i
$204$	5.95379	−	9.23990i	0.416848	−	0.646922i
$205$	2.59058	+	0.746846i	0.180934	+	0.0521620i
$206$	−14.8864	−	8.59469i	−1.03719	−	0.598820i
$207$	23.0341	−	3.81661i	1.60098	−	0.265272i
$208$	0.231879	+	0.231879i	0.0160779	+	0.0160779i
$209$	−22.1828	−	9.64271i	−1.53441	−	0.667000i
$210$	−0.398061	+	5.87243i	−0.0274688	+	0.405237i
$211$	−5.64036	+	9.76939i	−0.388299	+	0.672553i	−0.992221	−	0.124490i	$-0.960270\pi$
$211$	−5.64036	+	9.76939i	−0.388299	+	0.672553i	0.603922	+	0.797043i	$0.293604\pi$
$212$	−5.61960	+	1.50577i	−0.385956	+	0.103416i
$213$	−14.1704	−	4.54851i	−0.970940	−	0.311659i
$214$	3.78928	+	2.18774i	0.259030	+	0.149551i
$215$	17.8178	−	9.84331i	1.21516	−	0.671308i
$216$	−0.757982	+	5.14057i	−0.0515741	+	0.349772i
$217$	4.53769	−	4.53769i	0.308038	−	0.308038i
$218$	7.04021	+	1.88642i	0.476823	+	0.127764i
$219$	15.7882	−	8.11543i	1.06687	−	0.548390i
$220$	8.60666	+	8.93799i	0.580261	+	0.602599i
$221$			2.08109i			0.139990i
$222$	−2.83520	+	8.83275i	−0.190286	+	0.592815i
$223$	−15.1888	+	4.06984i	−1.01712	+	0.272537i	−0.728602	−	0.684938i	$-0.759829\pi$
$223$	−15.1888	+	4.06984i	−1.01712	+	0.272537i	−0.288519	+	0.957474i	$0.593163\pi$
$224$	−0.759868	−	1.31613i	−0.0507708	−	0.0879376i
$225$	9.18444	−	11.8594i	0.612296	−	0.790629i
$226$	−7.90688	+	13.6951i	−0.525958	+	0.910986i
$227$	6.77684	+	6.77684i	0.449795	+	0.449795i	0.895286	−	0.445491i	$-0.146971\pi$
$227$	6.77684	+	6.77684i	0.449795	+	0.449795i	−0.445491	+	0.895286i	$0.646971\pi$
$228$	−2.42179	−	7.15087i	−0.160387	−	0.473578i
$229$		−	6.62816i		−	0.438001i	−0.975725	−	0.219001i	$-0.929720\pi$
$229$		−	6.62816i		−	0.438001i	0.975725	−	0.219001i	$-0.0702797\pi$
$230$	16.8917	−	4.18595i	1.11381	−	0.276013i
$231$	12.2784	+	7.91168i	0.807861	+	0.520550i
$232$	−4.70453	−	1.26058i	−0.308868	−	0.0827608i
$233$	4.96598	+	18.5333i	0.325332	+	1.21416i	0.913978	+	0.405764i	$0.132995\pi$
$233$	4.96598	+	18.5333i	0.325332	+	1.21416i	−0.588646	+	0.808391i	$0.700339\pi$
$234$	−0.406531	−	0.895856i	−0.0265757	−	0.0585639i
$235$	−0.104284	+	5.52214i	−0.00680273	+	0.360225i
$236$			4.59073i			0.298831i
$237$	8.09223	+	2.59750i	0.525647	+	0.168726i
$238$	2.49620	−	9.31594i	0.161804	−	0.603862i
$239$	−1.12257			−0.0726132			−0.0363066	−	0.999341i	$-0.511559\pi$
$239$	−1.12257			−0.0726132			−0.0363066	+	0.999341i	$0.511559\pi$
$240$	−0.261928	+	3.86412i	−0.0169074	+	0.249428i
$241$	9.42945	+	16.3323i	0.607404	+	1.05205i	0.991667	+	0.128831i	$0.0411224\pi$
$241$	9.42945	+	16.3323i	0.607404	+	1.05205i	−0.384262	+	0.923224i	$0.625544\pi$
$242$	19.1180	−	5.12267i	1.22895	−	0.329297i
$243$	7.55263	−	13.6366i	0.484501	−	0.874791i
$244$	−7.14232	−	4.12362i	−0.457240	−	0.263988i
$245$	−2.52275	−	10.1801i	−0.161172	−	0.650385i
$246$	2.08589	+	0.101870i	0.132992	+	0.00649498i
$247$	1.11875	+	0.889712i	0.0711843	+	0.0566110i
$248$	2.98584	−	2.98584i	0.189601	−	0.189601i
$249$	2.84952	−	4.42228i	0.180581	−	0.280250i
$250$	6.12940	−	9.35043i	0.387657	−	0.591373i
$251$	8.57297	−	4.94961i	0.541121	−	0.312417i	−0.204412	−	0.978885i	$-0.565528\pi$
$251$	8.57297	−	4.94961i	0.541121	−	0.312417i	0.745533	+	0.666468i	$0.232195\pi$
$252$	0.745271	+	4.49788i	0.0469477	+	0.283340i
$253$	11.1776	−	41.7155i	0.702731	−	2.62263i
$254$	20.2798			1.27247
$255$	−18.5154	+	16.1646i	−1.15948	+	1.01227i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.43424	+	12.8168i	−0.214222	+	0.799488i	0.772217	+	0.635359i	$0.219148\pi$
$257$	−3.43424	+	12.8168i	−0.214222	+	0.799488i	−0.986439	+	0.164129i	$0.947519\pi$
$258$	11.6800	−	10.5923i	0.727165	−	0.659446i
$259$			8.13950i			0.505764i
$260$	−0.354578	−	0.641837i	−0.0219900	−	0.0398051i
$261$	11.8818	+	8.50400i	0.735465	+	0.526384i
$262$	9.38137	+	2.51373i	0.579583	+	0.155299i
$263$	−2.18300	−	8.14708i	−0.134610	−	0.502370i	−0.999999	−	0.00127044i	$-0.999596\pi$
$263$	−2.18300	−	8.14708i	−0.134610	−	0.502370i	0.865389	−	0.501100i	$-0.167071\pi$
$264$	8.07932	+	5.20596i	0.497248	+	0.320405i
$265$	13.0068	+	0.245628i	0.798999	+	0.0150888i
$266$	−3.94086	−	5.32466i	−0.241630	−	0.326476i
$267$	−3.12202	−	3.44262i	−0.191064	−	0.210685i
$268$	−0.809136	+	0.216807i	−0.0494259	+	0.0132436i
$269$	−10.0671	+	17.4367i	−0.613800	+	1.06313i	0.376794	+	0.926297i	$0.377026\pi$
$269$	−10.0671	+	17.4367i	−0.613800	+	1.06313i	−0.990594	+	0.136835i	$0.956307\pi$
$270$	4.81272	−	10.5753i	0.292893	−	0.643594i
$271$	3.11454	−	5.39453i	0.189195	−	0.327695i	−0.755787	−	0.654817i	$-0.772746\pi$
$271$	3.11454	−	5.39453i	0.189195	−	0.327695i	0.944982	+	0.327122i	$0.106079\pi$
$272$	1.64252	−	6.12997i	0.0995925	−	0.371684i
$273$	−0.579867	−	0.639413i	−0.0350951	−	0.0386991i
$274$		−	20.3722i		−	1.23073i
$275$	−12.9556	−	24.5349i	−0.781254	−	1.47951i
$276$	11.9889	−	6.16255i	0.721650	−	0.370942i
$277$	9.19367	−	9.19367i	0.552394	−	0.552394i	−0.374737	−	0.927131i	$-0.622267\pi$
$277$	9.19367	−	9.19367i	0.552394	−	0.552394i	0.927131	+	0.374737i	$0.122267\pi$
$278$	7.73092	−	7.73092i	0.463670	−	0.463670i
$279$	−11.5357	+	5.23477i	−0.690622	+	0.313397i
$280$	0.817394	+	3.29846i	0.0488486	+	0.197121i
$281$	−10.1136	+	5.83910i	−0.603328	+	0.348332i	−0.770350	−	0.637622i	$-0.779918\pi$
$281$	−10.1136	+	5.83910i	−0.603328	+	0.348332i	0.167022	+	0.985953i	$0.446585\pi$
$282$	0.904384	+	4.18151i	0.0538553	+	0.249005i
$283$	11.0131	−	2.95096i	0.654662	−	0.175416i	0.0838264	−	0.996480i	$-0.473286\pi$
$283$	11.0131	−	2.95096i	0.654662	−	0.175416i	0.570836	+	0.821064i	$0.306619\pi$
$284$	−8.59242			−0.509866
$285$	0.774015	+	16.8642i	0.0458487	+	0.998948i
$286$	−1.81970			−0.107601
$287$	1.76995	−	0.474256i	0.104477	−	0.0279945i
$288$	0.490395	+	2.95965i	0.0288968	+	0.174399i
$289$	20.1562	−	11.6372i	1.18566	−	0.684542i
$290$	9.32717	+	5.62248i	0.547710	+	0.330164i
$291$	7.32956	+	14.2593i	0.429667	+	0.835896i
$292$	7.24714	−	7.24714i	0.424107	−	0.424107i
$293$	−19.9884	+	19.9884i	−1.16774	+	1.16774i	−0.184996	+	0.982739i	$0.559227\pi$
$293$	−19.9884	+	19.9884i	−1.16774	+	1.16774i	−0.982739	+	0.184996i	$0.940773\pi$
$294$	−3.71398	−	7.22537i	−0.216604	−	0.421392i
$295$	2.84357	−	9.86347i	0.165559	−	0.574273i
$296$			5.35586i			0.311303i
$297$	−17.1964	−	23.1448i	−0.997837	−	1.34300i
$298$	0.759803	−	2.83563i	0.0440142	−	0.164263i
$299$	−1.27608	+	2.21024i	−0.0737977	+	0.127821i
$300$	2.95626	−	8.14006i	0.170680	−	0.469966i
$301$	6.91742	−	11.9813i	0.398714	−	0.690592i
$302$	−13.8164	+	3.70210i	−0.795047	+	0.213032i
$303$	−7.21782	+	6.54564i	−0.414653	+	0.376037i
$304$	−2.59312	−	3.50367i	−0.148726	−	0.200949i
$305$	12.7915	+	13.2839i	0.732438	+	0.760635i
$306$	−11.0806	+	15.4819i	−0.633438	+	0.885041i
$307$	3.60093	+	13.4389i	0.205516	+	0.766996i	0.989292	+	0.145952i	$0.0466245\pi$
$307$	3.60093	+	13.4389i	0.205516	+	0.766996i	−0.783776	+	0.621044i	$0.786709\pi$
$308$	8.14581	+	2.18266i	0.464150	+	0.124369i
$309$	25.0272	+	16.1264i	1.42375	+	0.917402i
$310$	−8.26474	+	4.56579i	−0.469406	+	0.259320i
$311$			15.6542i			0.887668i	0.896109	+	0.443834i	$0.146382\pi$
$311$			15.6542i			0.887668i	−0.896109	+	0.443834i	$0.853618\pi$
$312$	−0.381558	−	0.420740i	−0.0216015	−	0.0238197i
$313$	−7.30687	+	27.2696i	−0.413009	+	1.54137i	0.375782	+	0.926708i	$0.377374\pi$
$313$	−7.30687	+	27.2696i	−0.413009	+	1.54137i	−0.788791	+	0.614662i	$0.789293\pi$
$314$	−2.88907	−	5.00401i	−0.163039	−	0.282393i
$315$	1.18479	−	10.1256i	0.0667555	−	0.570514i
$316$	4.90684			0.276031
$317$	3.08341	−	11.5074i	0.173182	−	0.646322i	−0.823673	−	0.567065i	$-0.808079\pi$
$317$	3.08341	−	11.5074i	0.173182	−	0.646322i	0.996854	−	0.0792567i	$-0.0252547\pi$
$318$	9.84906	−	2.13017i	0.552308	−	0.119454i
$319$	23.4059	−	13.5134i	1.31048	−	0.756605i
$320$	0.537853	+	2.17042i	0.0300669	+	0.121330i
$321$	−6.37058	−	4.10492i	−0.355571	−	0.229114i
$322$	8.36342	−	8.36342i	0.466075	−	0.466075i
$323$	4.08606	−	27.3591i	0.227354	−	1.52230i
$324$	1.74562	−	8.82909i	0.0969788	−	0.490505i
$325$	0.364270	+	1.59866i	0.0202060	+	0.0886776i
$326$	−9.82757	−	5.67395i	−0.544299	−	0.314251i
$327$	−12.0201	−	3.85830i	−0.664714	−	0.213364i
$328$	1.16464	−	0.312065i	0.0643066	−	0.0172309i
$329$	1.87689	+	3.25086i	0.103476	+	0.179226i
$330$	−14.1343	−	16.1898i	−0.778066	−	0.891218i
$331$	32.3937			1.78052			0.890261	−	0.455452i	$-0.150522\pi$
$331$	32.3937			1.78052			0.890261	+	0.455452i	$0.150522\pi$
$332$	0.786121	−	2.93384i	0.0431440	−	0.161016i
$333$	5.65113	−	15.0410i	0.309680	−	0.824243i
$334$			8.21397i			0.449449i
$335$	1.87277	+	0.0353668i	0.102321	+	0.00193229i
$336$	1.20337	+	2.34109i	0.0656490	+	0.127717i
$337$	0.217200	+	0.810601i	0.0118316	+	0.0441562i	0.971589	−	0.236673i	$-0.0760571\pi$
$337$	0.217200	+	0.810601i	0.0118316	+	0.0441562i	−0.959758	+	0.280830i	$0.909390\pi$
$338$	−12.4532	−	3.33682i	−0.677363	−	0.181499i
$339$	14.8359	−	23.0244i	0.805775	−	1.25051i
$340$	−7.32606	+	12.1532i	−0.397311	+	0.659102i
$341$			23.4317i			1.26890i
$342$	3.58551	+	12.5755i	0.193882	+	0.680007i
$343$	−12.5627	−	12.5627i	−0.678321	−	0.678321i
$344$	4.55173	−	7.88383i	0.245413	−	0.425067i
$345$	−29.5762	+	5.81450i	−1.59233	+	0.313042i
$346$	−9.65392	−	16.7211i	−0.518998	−	0.898931i
$347$	−5.08036	+	1.36128i	−0.272728	+	0.0730773i	−0.392591	−	0.919713i	$-0.628421\pi$
$347$	−5.08036	+	1.36128i	−0.272728	+	0.0730773i	0.119863	+	0.992790i	$0.461755\pi$
$348$	8.03228	+	2.57826i	0.430576	+	0.138209i
$349$			6.06639i			0.324726i	0.986731	+	0.162363i	$0.0519116\pi$
$349$			6.06639i			0.324726i	−0.986731	+	0.162363i	$0.948088\pi$
$350$	0.286895	−	7.59326i	0.0153352	−	0.405877i
$351$	0.627604	+	1.58417i	0.0334990	+	0.0845566i
$352$	5.36001	+	1.43621i	0.285690	+	0.0765503i
$353$	11.4496	−	11.4496i	0.609401	−	0.609401i	−0.333388	−	0.942790i	$-0.608192\pi$
$353$	11.4496	−	11.4496i	0.609401	−	0.609401i	0.942790	+	0.333388i	$0.108192\pi$
$354$	0.387863	−	7.94191i	0.0206147	−	0.422108i
$355$	18.4614	+	5.32228i	0.979828	+	0.282477i
$356$	−2.32371	−	1.34160i	−0.123157	−	0.0711045i
$357$	−5.10548	+	15.9056i	−0.270211	+	0.841812i
$358$	5.67248	−	1.51994i	0.299800	−	0.0803312i
$359$	1.60117	−	2.77331i	0.0845064	−	0.146369i	−0.820674	−	0.571396i	$-0.806402\pi$
$359$	1.60117	−	2.77331i	0.0845064	−	0.146369i	0.905181	+	0.425027i	$0.139735\pi$
$360$	0.779605	−	6.66275i	0.0410888	−	0.351158i
$361$	−12.9607	−	13.8931i	−0.682144	−	0.731218i
$362$	−2.86495	−	2.86495i	−0.150578	−	0.150578i
$363$	−33.5068	+	7.24690i	−1.75865	+	0.380364i
$364$	−0.431594	−	0.249181i	−0.0226217	−	0.0130606i
$365$	−20.0599	+	11.0820i	−1.04999	+	0.580056i
$366$	12.0077	+	7.73726i	0.627654	+	0.404433i
$367$	−11.4149	−	3.05860i	−0.595851	−	0.159658i	−0.0517249	−	0.998661i	$-0.516472\pi$
$367$	−11.4149	−	3.05860i	−0.595851	−	0.159658i	−0.544126	+	0.839004i	$0.683139\pi$
$368$	5.50321	−	5.50321i	0.286875	−	0.286875i
$369$	−3.59997	−	0.352467i	−0.187407	−	0.0183487i
$370$	3.31750	−	11.5074i	0.172469	−	0.598242i
$371$	7.65703	−	4.42079i	0.397533	−	0.229516i
$372$	−5.41774	+	4.91320i	−0.280897	+	0.254738i
$373$	3.81587	+	3.81587i	0.197578	+	0.197578i	0.798961	−	0.601383i	$-0.205383\pi$
$373$	3.81587	+	3.81587i	0.197578	+	0.197578i	−0.601383	+	0.798961i	$0.705383\pi$
$374$	17.6079	+	30.4977i	0.910481	+	1.57700i
$375$	−11.3938	+	15.6583i	−0.588373	+	0.808590i
$376$	1.23501	+	2.13910i	0.0636907	+	0.110316i
$377$	−1.54274	+	0.413377i	−0.0794553	+	0.0212900i
$378$	−0.909293	−	7.84425i	−0.0467690	−	0.403465i
$379$		−	16.9464i		−	0.870479i	−0.900315	−	0.435240i	$-0.856664\pi$
$379$		−	16.9464i		−	0.870479i	0.900315	−	0.435240i	$-0.143336\pi$
$380$	3.40126	+	9.13408i	0.174481	+	0.468569i
$381$	−35.0839	−	1.71341i	−1.79740	−	0.0877806i
$382$	5.81378	+	21.6973i	0.297459	+	1.11013i
$383$	9.54345	+	35.6166i	0.487647	+	1.81992i	0.567832	+	0.823144i	$0.307782\pi$
$383$	9.54345	+	35.6166i	0.487647	+	1.81992i	−0.0801848	+	0.996780i	$0.525551\pi$
$384$	0.791825	+	1.54046i	0.0404077	+	0.0786112i
$385$	−16.1498	−	9.73522i	−0.823070	−	0.496153i
$386$	17.1584	−	9.90643i	0.873341	−	0.504224i
$387$	−21.1012	+	17.3377i	−1.07263	+	0.881325i
$388$	6.54536	+	6.54536i	0.332290	+	0.332290i
$389$	11.4391	+	19.8130i	0.579983	+	1.00456i	0.995481	+	0.0949662i	$0.0302743\pi$
$389$	11.4391	+	19.8130i	0.579983	+	1.00456i	−0.415497	+	0.909594i	$0.636392\pi$
$390$	0.559188	+	1.14033i	0.0283156	+	0.0577428i
$391$	49.3908			2.49780
$392$	−3.31662	−	3.31662i	−0.167514	−	0.167514i
$393$	−16.0173	−	5.14134i	−0.807965	−	0.259346i
$394$	−11.6880	−	6.74805i	−0.588832	−	0.339962i
$395$	−10.5426	−	3.03937i	−0.530458	−	0.152927i
$396$	−13.5373	−	9.68886i	−0.680274	−	0.486883i
$397$	−5.73223	−	21.3930i	−0.287692	−	1.07368i	−0.946849	−	0.321677i	$-0.895753\pi$
$397$	−5.73223	−	21.3930i	−0.287692	−	1.07368i	0.659157	−	0.752005i	$-0.270913\pi$
$398$	−19.2702	+	19.2702i	−0.965926	+	0.965926i
$399$	6.36777	+	9.54455i	0.318787	+	0.477825i
$400$	0.188779	−	4.99643i	0.00943897	−	0.249822i
$401$	−24.2430	−	13.9967i	−1.21064	−	0.698962i	−0.247740	−	0.968827i	$-0.579688\pi$
$401$	−24.2430	−	13.9967i	−1.21064	−	0.698962i	−0.962898	+	0.269865i	$0.913021\pi$
$402$	1.41811	−	0.306712i	0.0707291	−	0.0152974i
$403$	0.358389	−	1.33753i	0.0178526	−	0.0666269i
$404$	−2.81280	+	4.87192i	−0.139942	+	0.242387i
$405$	−9.21944	+	17.8886i	−0.458118	+	0.888891i
$406$	7.40186			0.367348
$407$	−21.0154	−	21.0154i	−1.04169	−	1.04169i
$408$	−3.35945	+	10.4660i	−0.166318	+	0.518145i
$409$	−28.0050	+	16.1687i	−1.38476	+	0.799489i	−0.992718	−	0.120460i	$-0.961563\pi$
$409$	−28.0050	+	16.1687i	−1.38476	+	0.799489i	−0.392038	+	0.919949i	$0.628230\pi$
$410$	−2.69561	−	0.0509057i	−0.133127	−	0.00251405i
$411$	−1.72121	+	35.2437i	−0.0849011	+	1.73844i
$412$	16.6037	+	4.44894i	0.818004	+	0.219183i
$413$	−1.80570	−	6.73897i	−0.0888527	−	0.331603i
$414$	−21.2614	+	9.64822i	−1.04494	+	0.474184i
$415$	−3.50630	+	5.81662i	−0.172117	+	0.285526i
$416$	−0.283993	−	0.163964i	−0.0139239	−	0.00803897i
$417$	−14.0276	+	12.7212i	−0.686934	+	0.622962i
$418$	23.9226	+	3.57283i	1.17009	+	0.174753i
$419$	11.9046			0.581579			0.290789	−	0.956787i	$-0.406082\pi$
$419$	11.9046			0.581579			0.290789	+	0.956787i	$0.406082\pi$
$420$	−1.13540	−	5.77536i	−0.0554019	−	0.281809i
$421$	0.988395	−	1.71195i	0.0481714	−	0.0834354i	−0.840934	−	0.541137i	$-0.817994\pi$
$421$	0.988395	−	1.71195i	0.0481714	−	0.0834354i	0.889106	+	0.457702i	$0.151327\pi$
$422$	2.91967	−	10.8963i	0.142127	−	0.530426i
$423$	−1.21129	−	7.31038i	−0.0588947	−	0.355443i
$424$	5.03839	−	2.90892i	0.244686	−	0.141270i
$425$	23.2684	−	21.5741i	1.12868	−	1.04650i
$426$	14.8648	+	0.725959i	0.720202	+	0.0351728i
$427$	12.1065	+	3.24394i	0.585877	+	0.156985i
$428$	−4.22640	−	1.13246i	−0.204291	−	0.0547395i
$429$	3.14806	+	0.153743i	0.151990	+	0.00742279i
$430$	−14.6630	+	14.1195i	−0.707114	+	0.680902i
$431$	21.9831	−	12.6919i	1.05889	−	0.611350i	0.133764	−	0.991013i	$-0.457294\pi$
$431$	21.9831	−	12.6919i	1.05889	−	0.611350i	0.925125	+	0.379664i	$0.123960\pi$
$432$	−0.598323	−	5.16159i	−0.0287868	−	0.248337i
$433$	−1.96581	+	7.33652i	−0.0944710	+	0.352570i	−0.996939	−	0.0781870i	$-0.975087\pi$
$433$	−1.96581	+	7.33652i	−0.0944710	+	0.352570i	0.902468	+	0.430757i	$0.141754\pi$
$434$	−3.20863	+	5.55751i	−0.154019	+	0.266769i
$435$	−15.6609	−	10.5149i	−0.750881	−	0.504150i
$436$	−7.28857			−0.349059
$437$	21.1156	−	26.5513i	1.01010	−	1.27012i
$438$	−13.1498	+	11.9252i	−0.628321	+	0.569807i
$439$	−20.3162	−	11.7296i	−0.969642	−	0.559823i	−0.0705146	−	0.997511i	$-0.522464\pi$
$439$	−20.3162	−	11.7296i	−0.969642	−	0.559823i	−0.899127	+	0.437688i	$0.855797\pi$
$440$	−10.6267	−	6.40587i	−0.506609	−	0.305388i
$441$	5.81469	+	12.8136i	0.276890	+	0.610172i
$442$	−0.538627	−	2.01018i	−0.0256199	−	0.0956147i
$443$	−3.38967	−	0.908258i	−0.161048	−	0.0431526i	0.177394	−	0.984140i	$-0.443233\pi$
$443$	−3.38967	−	0.908258i	−0.161048	−	0.0431526i	−0.338442	+	0.940987i	$0.609900\pi$
$444$	0.452508	−	9.26558i	0.0214751	−	0.439725i
$445$	4.16164	+	4.32185i	0.197281	+	0.204875i
$446$	13.6179	−	7.86232i	0.644828	−	0.372292i
$447$	−1.55403	+	4.84141i	−0.0735030	+	0.228991i
$448$	1.07462	+	1.07462i	0.0507708	+	0.0507708i
$449$	11.3256			0.534489			0.267245	−	0.963629i	$-0.413887\pi$
$449$	11.3256			0.534489			0.267245	+	0.963629i	$0.413887\pi$
$450$	−5.80204	+	13.8324i	−0.273511	+	0.652067i
$451$	−3.34535	+	5.79431i	−0.157526	+	0.272843i
$452$	4.09290	−	15.2749i	0.192514	−	0.718472i
$453$	24.2151	−	5.23727i	1.13772	−	0.246068i
$454$	−8.29990	−	4.79195i	−0.389534	−	0.224897i
$455$	0.772961	+	0.802718i	0.0362370	+	0.0376320i
$456$	4.19005	+	6.28040i	0.196217	+	0.294107i
$457$	0.535268	−	0.535268i	0.0250388	−	0.0250388i	−0.694477	−	0.719515i	$-0.744364\pi$
$457$	0.535268	−	0.535268i	0.0250388	−	0.0250388i	0.719515	+	0.694477i	$0.244364\pi$
$458$	1.71550	+	6.40232i	0.0801598	+	0.299161i
$459$	20.4774	−	25.8473i	0.955805	−	1.20645i
$460$	−15.2328	+	8.41522i	−0.710231	+	0.392362i
$461$	−9.95183	−	5.74569i	−0.463503	−	0.267603i	0.250013	−	0.968242i	$-0.419565\pi$
$461$	−9.95183	−	5.74569i	−0.463503	−	0.267603i	−0.713516	+	0.700639i	$0.752898\pi$
$462$	−13.9077	−	4.46421i	−0.647047	−	0.207694i
$463$	−13.2370	−	13.2370i	−0.615175	−	0.615175i	0.329115	−	0.944290i	$-0.393250\pi$
$463$	−13.2370	−	13.2370i	−0.615175	−	0.615175i	−0.944290	+	0.329115i	$0.893250\pi$
$464$	4.87049			0.226107
$465$	14.6837	−	7.20050i	0.680939	−	0.333915i
$466$	−9.59353	−	16.6165i	−0.444412	−	0.769744i
$467$	−8.10528	−	8.10528i	−0.375068	−	0.375068i	0.494251	−	0.869319i	$-0.335442\pi$
$467$	−8.10528	−	8.10528i	−0.375068	−	0.375068i	−0.869319	+	0.494251i	$0.835442\pi$
$468$	0.624543	+	0.760113i	0.0288695	+	0.0351362i
$469$	1.10250	−	0.636526i	0.0509085	−	0.0293920i
$470$	−1.32851	−	5.36097i	−0.0612794	−	0.247283i
$471$	4.57527	+	8.90098i	0.210817	+	0.410135i
$472$	−1.18817	−	4.43430i	−0.0546899	−	0.204105i
$473$	13.0745	+	48.7947i	0.601166	+	2.24358i
$474$	−8.48877	−	0.414570i	−0.389902	−	0.0190418i
$475$	−1.65003	−	21.7319i	−0.0757085	−	0.997130i
$476$			9.64457i			0.442058i
$477$	−17.2187	+	2.85304i	−0.788392	+	0.130632i
$478$	1.08432	−	0.290543i	0.0495958	−	0.0132891i
$479$	−4.37640	−	7.58015i	−0.199963	−	0.346346i	0.748553	−	0.663075i	$-0.230749\pi$
$479$	−4.37640	−	7.58015i	−0.199963	−	0.346346i	−0.948516	+	0.316729i	$0.897416\pi$
$480$	−0.747104	−	3.80024i	−0.0341005	−	0.173456i
$481$	0.878166	+	1.52103i	0.0400409	+	0.0693529i
$482$	−13.3353	−	13.3353i	−0.607404	−	0.607404i
$483$	−15.1752	+	13.7620i	−0.690497	+	0.626194i
$484$	−17.1408	+	9.89623i	−0.779126	+	0.449829i
$485$	−10.0088	−	18.1174i	−0.454478	−	0.822670i
$486$	−3.76585	+	15.1267i	−0.170823	+	0.686163i
$487$	−11.2313	+	11.2313i	−0.508938	+	0.508938i	−0.914200	−	0.405263i	$-0.867180\pi$
$487$	−11.2313	+	11.2313i	−0.508938	+	0.508938i	0.405263	+	0.914200i	$0.367180\pi$
$488$	7.96622	+	2.13454i	0.360614	+	0.0966262i
$489$	16.5222	+	10.6462i	0.747160	+	0.481437i
$490$	5.07160	+	9.18032i	0.229111	+	0.414725i
$491$	−23.4053	−	13.5131i	−1.05627	−	0.609837i	−0.131870	−	0.991267i	$-0.542098\pi$
$491$	−23.4053	−	13.5131i	−1.05627	−	0.609837i	−0.924398	+	0.381430i	$0.875432\pi$
$492$	−2.04119	+	0.441471i	−0.0920237	+	0.0199030i
$493$	21.8561	+	21.8561i	0.984348	+	0.984348i
$494$	−1.31090	−	0.569842i	−0.0589803	−	0.0256384i
$495$	23.0843	+	29.2023i	1.03756	+	1.31255i
$496$	−2.11131	+	3.65689i	−0.0948005	+	0.164199i
$497$	12.6133	−	3.37971i	0.565782	−	0.151601i
$498$	−1.60786	+	5.00910i	−0.0720498	+	0.224463i
$499$	−13.8947	−	8.02211i	−0.622012	−	0.359119i	0.155640	−	0.987814i	$-0.450256\pi$
$499$	−13.8947	−	8.02211i	−0.622012	−	0.359119i	−0.777652	+	0.628695i	$0.783589\pi$
$500$	−3.50047	+	10.6182i	−0.156546	+	0.474861i
$501$	0.693984	−	14.2101i	0.0310049	−	0.634860i
$502$	−6.99980	+	6.99980i	−0.312417	+	0.312417i
$503$	2.99645	+	0.802896i	0.133605	+	0.0357994i	0.325002	−	0.945713i	$-0.394635\pi$
$503$	2.99645	+	0.802896i	0.133605	+	0.0357994i	−0.191397	+	0.981513i	$0.561302\pi$
$504$	−1.88401	−	4.15173i	−0.0839207	−	0.184933i
$505$	9.06122	−	8.72533i	0.403219	−	0.388272i
$506$			43.1870i			1.91990i
$507$	21.2619	+	6.82480i	0.944275	+	0.303100i
$508$	−19.5888	+	5.24881i	−0.869114	+	0.232878i
$509$	3.84072	+	6.65232i	0.170237	+	0.294859i	0.938503	−	0.345272i	$-0.112213\pi$
$509$	3.84072	+	6.65232i	0.170237	+	0.294859i	−0.768266	+	0.640131i	$0.778880\pi$
$510$	13.7008	−	20.4060i	0.606682	−	0.903592i
$511$	−7.78789	+	13.4890i	−0.344516	+	0.596719i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−5.14040	−	22.0585i	−0.226954	−	0.973905i
$514$		−	13.2689i		−	0.585266i
$515$	−32.9183	−	19.8434i	−1.45055	−	0.874404i
$516$	−8.54053	+	13.2544i	−0.375976	+	0.583491i
$517$	−13.2393	−	3.54747i	−0.582265	−	0.156017i
$518$	−2.10666	−	7.86215i	−0.0925612	−	0.345443i
$519$	15.2884	+	29.7429i	0.671088	+	1.30557i
$520$	0.508616	+	0.528196i	0.0223043	+	0.0231629i
$521$		−	26.4763i		−	1.15995i	−0.814635	−	0.579974i	$-0.803063\pi$
$521$		−	26.4763i		−	1.15995i	0.814635	−	0.579974i	$-0.196937\pi$
$522$	−13.6779	−	5.13899i	−0.598667	−	0.224928i
$523$	−0.00467848	+	0.0174603i	−0.000204576	+	0.000763486i	−0.966028	−	0.258437i	$-0.916792\pi$
$523$	−0.00467848	+	0.0174603i	−0.000204576	+	0.000763486i	0.965823	+	0.259201i	$0.0834591\pi$
$524$	−9.71231			−0.424284
$525$	−1.13787	+	13.1120i	−0.0496606	+	0.572255i
$526$	4.21724	+	7.30447i	0.183880	+	0.318490i
$527$	−25.8845	+	6.93573i	−1.12755	+	0.302125i
$528$	−9.15142	−	2.93749i	−0.398265	−	0.127838i
$529$	32.5371	+	18.7853i	1.41466	+	0.816753i
$530$	−12.6271	+	3.12914i	−0.548488	+	0.135921i
$531$	−1.34200	+	13.7066i	−0.0582377	+	0.594818i
$532$	5.18470	+	4.12325i	0.224785	+	0.178766i
$533$	0.279583	−	0.279583i	0.0121101	−	0.0121101i
$534$	3.90665	+	2.51727i	0.169057	+	0.108933i
$535$	8.37922	+	5.05105i	0.362265	+	0.218376i
$536$	0.725452	−	0.418840i	0.0313347	−	0.0180911i
$537$	−9.94175	+	2.15022i	−0.429018	+	0.0927887i
$538$	5.21109	−	19.4481i	0.224666	−	0.838466i
$539$	26.0275			1.12108
$540$	−1.91163	+	11.4606i	−0.0822635	+	0.493186i
$541$	−9.18693	−	15.9122i	−0.394977	−	0.684120i	0.598121	−	0.801406i	$-0.295914\pi$
$541$	−9.18693	−	15.9122i	−0.394977	−	0.684120i	−0.993098	+	0.117285i	$0.962581\pi$
$542$	−1.61220	+	6.01682i	−0.0692500	+	0.258445i
$543$	4.71428	+	5.19838i	0.202309	+	0.223084i
$544$			6.34621i			0.272092i
$545$	15.6599	+	4.51465i	0.670798	+	0.193386i
$546$	0.725601	+	0.467545i	0.0310528	+	0.0200091i
$547$	−43.1101	−	11.5513i	−1.84325	−	0.493899i	−0.844146	−	0.536113i	$-0.819892\pi$
$547$	−43.1101	−	11.5513i	−1.84325	−	0.493899i	−0.999109	+	0.0422142i	$0.986559\pi$
$548$	5.27271	+	19.6780i	0.225239	+	0.840604i
$549$	−20.1195	−	14.3999i	−0.858681	−	0.614572i
$550$	18.8643	+	20.3458i	0.804376	+	0.867546i
$551$	21.0933	−	2.40540i	0.898603	−	0.102473i
$552$	−9.98545	+	9.05553i	−0.425009	+	0.385429i
$553$	−7.20300	+	1.93004i	−0.306303	+	0.0820736i
$554$	−6.50091	+	11.2599i	−0.276197	+	0.478387i
$555$	−6.71148	+	19.6274i	−0.284887	+	0.833137i
$556$	−5.46659	+	9.46841i	−0.231835	+	0.401550i
$557$	1.61934	−	6.04346i	0.0686137	−	0.256070i	−0.923096	−	0.384570i	$-0.874350\pi$
$557$	1.61934	−	6.04346i	0.0686137	−	0.256070i	0.991709	+	0.128500i	$0.0410164\pi$
$558$	9.78773	−	8.04205i	0.414348	−	0.340447i
$559$		−	2.98527i		−	0.126263i
$560$	−1.64325	−	2.97451i	−0.0694398	−	0.125696i
$561$	−27.8847	−	54.2484i	−1.17729	−	2.29037i
$562$	8.25774	−	8.25774i	0.348332	−	0.348332i
$563$	15.5095	−	15.5095i	0.653649	−	0.653649i	−0.300221	−	0.953870i	$-0.597060\pi$
$563$	15.5095	−	15.5095i	0.653649	−	0.653649i	0.953870	+	0.300221i	$0.0970605\pi$
$564$	−1.95582	−	3.80496i	−0.0823550	−	0.160218i
$565$	−18.2554	+	30.2839i	−0.768010	+	1.27405i
$566$	−9.87410	+	5.70081i	−0.415039	+	0.239623i
$567$	0.910320	+	13.6473i	0.0382298	+	0.573132i
$568$	8.29964	−	2.22388i	0.348245	−	0.0933120i
$569$	18.4866			0.774998			0.387499	−	0.921870i	$-0.373339\pi$
$569$	18.4866			0.774998			0.387499	+	0.921870i	$0.373339\pi$
$570$	−5.11241	−	16.0892i	−0.214135	−	0.673904i
$571$	−26.7844			−1.12089			−0.560446	−	0.828191i	$-0.689370\pi$
$571$	−26.7844			−1.12089			−0.560446	+	0.828191i	$0.689370\pi$
$572$	1.75769	−	0.470973i	0.0734929	−	0.0196924i
$573$	−8.22461	−	38.0273i	−0.343588	−	1.58861i
$574$	−1.58689	+	0.916193i	−0.0662356	+	0.0382412i
$575$	37.9411	−	8.64524i	1.58225	−	0.360531i
$576$	−1.23970	−	2.73188i	−0.0516541	−	0.113828i
$577$	16.5592	−	16.5592i	0.689367	−	0.689367i	−0.272725	−	0.962092i	$-0.587925\pi$
$577$	16.5592	−	16.5592i	0.689367	−	0.689367i	0.962092	+	0.272725i	$0.0879249\pi$
$578$	−16.4575	+	16.4575i	−0.684542	+	0.684542i
$579$	−30.5209	+	15.6883i	−1.26840	+	0.651985i
$580$	−10.4646	−	3.01685i	−0.434517	−	0.125268i
$581$			4.61595i			0.191502i
$582$	−10.7704	−	11.8764i	−0.446447	−	0.492293i
$583$	−8.35564	+	31.1837i	−0.346055	+	1.29150i
$584$	−5.12450	+	8.87590i	−0.212053	+	0.367287i
$585$	−0.871045	−	2.02000i	−0.0360133	−	0.0835168i
$586$	14.1339	−	24.4807i	0.583868	−	1.01129i
$587$	31.2785	−	8.38105i	1.29100	−	0.345923i	0.452961	−	0.891530i	$-0.350368\pi$
$587$	31.2785	−	8.38105i	1.29100	−	0.345923i	0.838041	+	0.545608i	$0.183701\pi$
$588$	5.45749	+	6.01792i	0.225063	+	0.248175i
$589$	−7.33768	+	16.8801i	−0.302344	+	0.695532i
$590$	−0.193820	+	10.2633i	−0.00797945	+	0.422535i
$591$	19.6499	+	12.6616i	0.808290	+	0.520827i
$592$	−1.38620	−	5.17337i	−0.0569724	−	0.212624i
$593$	−26.2062	−	7.02193i	−1.07616	−	0.288356i	−0.323138	−	0.946352i	$-0.604738\pi$
$593$	−26.2062	−	7.02193i	−1.07616	−	0.288356i	−0.753022	+	0.657996i	$0.771405\pi$
$594$	22.6008	+	17.9054i	0.927321	+	0.734666i
$595$	5.97399	−	20.7220i	0.244910	−	0.849518i
$596$			2.93566i			0.120249i
$597$	34.9653	−	31.7091i	1.43103	−	1.29777i
$598$	0.660548	−	2.46520i	0.0270118	−	0.100809i
$599$	18.8225	+	32.6016i	0.769068	+	1.33206i	0.938069	+	0.346449i	$0.112612\pi$
$599$	18.8225	+	32.6016i	0.769068	+	1.33206i	−0.169001	+	0.985616i	$0.554054\pi$
$600$	−0.748727	+	8.62783i	−0.0305666	+	0.352230i
$601$	8.80796			0.359284			0.179642	−	0.983732i	$-0.442506\pi$
$601$	8.80796			0.359284			0.179642	+	0.983732i	$0.442506\pi$
$602$	−3.58072	+	13.3634i	−0.145939	+	0.544653i
$603$	−2.47924	+	0.410794i	−0.100962	+	0.0167288i
$604$	12.3875	−	7.15191i	0.504039	−	0.291007i
$605$	42.9579	−	10.6454i	1.74649	−	0.432798i
$606$	5.27774	−	8.19071i	0.214393	−	0.332725i
$607$	−19.7817	+	19.7817i	−0.802914	+	0.802914i	−0.983550	−	0.180636i	$-0.942184\pi$
$607$	−19.7817	+	19.7817i	−0.802914	+	0.802914i	0.180636	+	0.983550i	$0.442184\pi$
$608$	3.41158	+	2.71314i	0.138358	+	0.110032i
$609$	−12.8051	−	0.625370i	−0.518890	−	0.0253413i
$610$	−15.7938	−	9.52059i	−0.639471	−	0.385478i
$611$	0.701468	+	0.404993i	0.0283784	+	0.0163843i
$612$	6.69607	−	17.8222i	0.270673	−	0.720422i
$613$	−15.1814	+	4.06784i	−0.613171	+	0.164299i	−0.552021	−	0.833830i	$-0.686143\pi$
$613$	−15.1814	+	4.06784i	−0.613171	+	0.164299i	−0.0611496	+	0.998129i	$0.519477\pi$
$614$	−6.95647	−	12.0490i	−0.280740	−	0.486256i
$615$	4.65907	+	0.315813i	0.187872	+	0.0127348i
$616$	−8.43316			−0.339782
$617$	3.63321	−	13.5593i	0.146268	−	0.545878i	−0.853428	−	0.521211i	$-0.825481\pi$
$617$	3.63321	−	13.5593i	0.146268	−	0.545878i	0.999696	−	0.0246676i	$-0.00785274\pi$
$618$	−28.3483	−	9.09943i	−1.14033	−	0.366033i
$619$			37.7827i			1.51861i	0.650732	+	0.759307i	$0.274462\pi$
$619$			37.7827i			1.51861i	−0.650732	+	0.759307i	$0.725538\pi$
$620$	6.80141	−	6.54929i	0.273151	−	0.263026i
$621$	37.5972	−	14.8950i	1.50872	−	0.597715i
$622$	−4.05161	−	15.1208i	−0.162455	−	0.606289i
$623$	3.93880	+	1.05540i	0.157805	+	0.0422836i
$624$	0.477452	+	0.307649i	0.0191134	+	0.0123158i
$625$	14.0981	−	20.6457i	0.563923	−	0.825827i
$626$		−	28.2316i		−	1.12836i
$627$	−41.0840	−	8.20213i	−1.64074	−	0.327562i
$628$	4.08576	+	4.08576i	0.163039	+	0.163039i
$629$	16.9947	−	29.4357i	0.677624	−	1.17368i
$630$	1.47628	+	10.0872i	0.0588164	+	0.401885i
$631$	−23.5081	−	40.7172i	−0.935843	−	1.62093i	−0.773124	−	0.634255i	$-0.781307\pi$
$631$	−23.5081	−	40.7172i	−0.935843	−	1.62093i	−0.162719	−	0.986673i	$-0.552026\pi$
$632$	−4.73964	+	1.26998i	−0.188533	+	0.0505172i
$633$	−5.97160	+	18.6039i	−0.237350	+	0.739438i
$634$			11.9134i			0.473141i
$635$	45.3390	+	0.856213i	1.79922	+	0.0339778i
$636$	−8.96213	+	4.60671i	−0.355372	+	0.182668i
$637$	−1.48570	−	0.398092i	−0.0588656	−	0.0157730i
$638$	−19.1108	+	19.1108i	−0.756605	+	0.756605i
$639$	−25.6546	−	2.51180i	−1.01488	−	0.0993653i
$640$	−1.08127	−	1.95726i	−0.0427410	−	0.0773674i
$641$	36.9801	+	21.3505i	1.46063	+	0.843293i	0.999040	−	0.0438018i	$-0.0139470\pi$
$641$	36.9801	+	21.3505i	1.46063	+	0.843293i	0.461587	+	0.887095i	$0.347280\pi$
$642$	7.21594	+	2.31622i	0.284790	+	0.0914140i
$643$	−20.0852	+	5.38182i	−0.792084	+	0.212238i	−0.632106	−	0.774882i	$-0.717809\pi$
$643$	−20.0852	+	5.38182i	−0.792084	+	0.212238i	−0.159978	+	0.987121i	$0.551142\pi$
$644$	−5.91383	+	10.2431i	−0.233038	+	0.403633i
$645$	26.5598	−	23.1877i	1.04579	−	0.913015i
$646$	3.13422	+	27.4844i	0.123314	+	1.08136i
$647$	−8.55101	−	8.55101i	−0.336175	−	0.336175i	0.518751	−	0.854926i	$-0.326397\pi$
$647$	−8.55101	−	8.55101i	−0.336175	−	0.336175i	−0.854926	+	0.518751i	$0.826397\pi$
$648$	0.598999	+	8.98004i	0.0235309	+	0.352769i
$649$	22.0615	+	12.7372i	0.865988	+	0.499979i
$650$	−0.765621	−	1.44991i	−0.0300301	−	0.0568700i
$651$	6.02044	−	9.34334i	0.235960	−	0.366194i
$652$	10.9612	+	2.93705i	0.429275	+	0.115024i
$653$	−3.37460	+	3.37460i	−0.132058	+	0.132058i	−0.770046	−	0.637988i	$-0.779767\pi$
$653$	−3.37460	+	3.37460i	−0.132058	+	0.132058i	0.637988	+	0.770046i	$0.279767\pi$
$654$	12.6091	+	0.615798i	0.493056	+	0.0240796i
$655$	20.8675	+	6.01595i	0.815361	+	0.235063i
$656$	−1.04419	+	0.602864i	−0.0407688	+	0.0235379i
$657$	23.7565	−	19.5194i	0.926830	−	0.761525i
$658$	−2.65432	−	2.65432i	−0.103476	−	0.103476i
$659$	−14.0786	−	24.3848i	−0.548424	−	0.949898i	−0.998383	−	0.0568487i	$-0.981895\pi$
$659$	−14.0786	−	24.3848i	−0.548424	−	0.949898i	0.449959	−	0.893049i	$-0.351439\pi$
$660$	17.8429	+	11.9799i	0.694533	+	0.466317i
$661$	8.42839	+	14.5984i	0.327827	+	0.567812i	0.982080	−	0.188463i	$-0.0603505\pi$
$661$	8.42839	+	14.5984i	0.327827	+	0.567812i	−0.654254	+	0.756275i	$0.727017\pi$
$662$	−31.2900	+	8.38412i	−1.21612	+	0.325858i
$663$	0.761982	+	3.52310i	0.0295929	+	0.136826i
$664$			3.03734i			0.117872i
$665$	−8.58565	−	12.0706i	−0.332937	−	0.468076i
$666$	−1.56567	+	15.9911i	−0.0606683	+	0.619644i
$667$	9.81070	+	36.6140i	0.379872	+	1.41770i
$668$	−2.12593	−	7.93409i	−0.0822548	−	0.306979i
$669$	−24.2232	+	12.4512i	−0.936522	+	0.481390i
$670$	−1.81812	+	0.450548i	−0.0702399	+	0.0174062i
$671$	−39.6334	+	22.8823i	−1.53003	+	0.883363i
$672$	−1.76828	−	1.94987i	−0.0682129	−	0.0752177i
$673$	−1.30451	−	1.30451i	−0.0502852	−	0.0502852i	0.681517	−	0.731802i	$-0.261321\pi$
$673$	−1.30451	−	1.30451i	−0.0502852	−	0.0502852i	−0.731802	+	0.681517i	$0.761321\pi$
$674$	−0.419598	−	0.726765i	−0.0161623	−	0.0279939i
$675$	11.2061	−	23.4398i	0.431324	−	0.902197i
$676$	12.8925			0.495864
$677$	−19.7011	−	19.7011i	−0.757177	−	0.757177i	0.218631	−	0.975808i	$-0.429841\pi$
$677$	−19.7011	−	19.7011i	−0.757177	−	0.757177i	−0.975808	+	0.218631i	$0.929841\pi$
$678$	−8.37123	+	26.0796i	−0.321495	+	1.00158i
$679$	−12.1828	−	7.03375i	−0.467533	−	0.269930i
$680$	3.93094	−	13.6352i	0.150745	−	0.522888i
$681$	13.9539	+	8.99126i	0.534714	+	0.344546i
$682$	−6.06457	−	22.6333i	−0.232224	−	0.866673i
$683$	−8.63638	+	8.63638i	−0.330462	+	0.330462i	−0.852762	−	0.522300i	$-0.825074\pi$
$683$	−8.63638	+	8.63638i	−0.330462	+	0.330462i	0.522300	+	0.852762i	$0.325074\pi$
$684$	−6.71812	−	11.2190i	−0.256874	−	0.428971i
$685$	0.860112	−	45.5455i	0.0328632	−	1.74020i
$686$	15.3861	+	8.88316i	0.587444	+	0.339161i
$687$	−2.42687	−	11.2209i	−0.0925908	−	0.428103i
$688$	−2.35615	+	8.79326i	−0.0898273	+	0.335240i
$689$	0.953913	−	1.65223i	0.0363412	−	0.0629448i
$690$	27.0635	−	13.2713i	1.03029	−	0.505228i
$691$	22.1493			0.842597			0.421299	−	0.906922i	$-0.361574\pi$
$691$	22.1493			0.842597			0.421299	+	0.906922i	$0.361574\pi$
$692$	13.6527	+	13.6527i	0.518998	+	0.518998i
$693$	23.6831	+	8.89807i	0.899645	+	0.338010i
$694$	4.55493	−	2.62979i	0.172903	−	0.0998254i
$695$	17.6102	−	16.9574i	0.667992	−	0.643230i
$696$	−8.42589	−	0.411499i	−0.319383	−	0.0155978i
$697$	−7.39107	−	1.98043i	−0.279957	−	0.0750142i
$698$	−1.57010	−	5.85968i	−0.0594290	−	0.221792i
$699$	15.1928	+	29.5569i	0.574645	+	1.11794i
$700$	1.68816	+	7.40878i	0.0638065	+	0.280026i
$701$	8.04403	+	4.64422i	0.303819	+	0.175410i	0.644157	−	0.764893i	$-0.277208\pi$
$701$	8.04403	+	4.64422i	0.303819	+	0.175410i	−0.340338	+	0.940303i	$0.610542\pi$
$702$	−1.01623	−	1.36775i	−0.0383552	−	0.0516225i
$703$	−8.55838	−	21.7204i	−0.322785	−	0.819199i
$704$	−5.54910			−0.209139
$705$	1.84536	+	9.38666i	0.0695003	+	0.353522i
$706$	−8.09610	+	14.0229i	−0.304701	+	0.527757i
$707$	2.21276	−	8.25812i	0.0832193	−	0.310578i
$708$	1.68087	+	7.77168i	0.0631710	+	0.292078i
$709$	−15.4954	+	8.94626i	−0.581941	+	0.335984i	−0.761904	−	0.647689i	$-0.775735\pi$
$709$	−15.4954	+	8.94626i	−0.581941	+	0.335984i	0.179963	+	0.983673i	$0.442402\pi$
$710$	−19.2098	−	0.362771i	−0.720932	−	0.0136146i
$711$	14.6505	+	1.43440i	0.549435	+	0.0537943i
$712$	2.59177	+	0.694462i	0.0971305	+	0.0260260i
$713$	−31.7436	−	8.50567i	−1.18881	−	0.318540i
$714$	0.814853	−	16.6850i	0.0304951	−	0.624420i
$715$	−4.06824	−	0.0768275i	−0.152144	−	0.00287318i
$716$	−5.08581	+	2.93629i	−0.190066	+	0.109734i
$717$	−1.90041	+	0.411024i	−0.0709722	+	0.0153500i
$718$	−0.828826	+	3.09322i	−0.0309315	+	0.115438i
$719$	−7.88538	+	13.6579i	−0.294075	+	0.509353i	−0.974769	−	0.223215i	$-0.928345\pi$
$719$	−7.88538	+	13.6579i	−0.294075	+	0.509353i	0.680694	+	0.732568i	$0.261678\pi$
$720$	0.971406	+	6.63750i	0.0362022	+	0.247365i
$721$	−26.1233			−0.972883
$722$	16.1149	+	10.0653i	0.599735	+	0.374590i
$723$	21.9432	+	24.1965i	0.816075	+	0.899878i
$724$	3.50883	+	2.02582i	0.130405	+	0.0752892i
$725$	20.6151	+	12.9638i	0.765625	+	0.481464i
$726$	30.4895	−	15.6722i	1.13157	−	0.581649i
$727$	2.13311	+	7.96089i	0.0791128	+	0.295253i	0.994134	−	0.108152i	$-0.0344933\pi$
$727$	2.13311	+	7.96089i	0.0791128	+	0.295253i	−0.915022	+	0.403405i	$0.867827\pi$
$728$	0.481381	+	0.128986i	0.0178412	+	0.00478053i
$729$	7.79292	−	25.8509i	0.288627	−	0.957442i
$730$	16.5082	−	15.8962i	0.610996	−	0.588346i
$731$	−50.0324	+	28.8862i	−1.85052	+	1.06840i
$732$	−13.6011	−	4.36579i	−0.502712	−	0.161364i
$733$	36.6964	+	36.6964i	1.35541	+	1.35541i	0.879485	+	0.475927i	$0.157887\pi$
$733$	36.6964	+	36.6964i	1.35541	+	1.35541i	0.475927	+	0.879485i	$0.342113\pi$
$734$	11.8175			0.436193
$735$	−7.99818	−	16.3103i	−0.295017	−	0.601616i
$736$	−3.89136	+	6.74003i	−0.143437	+	0.248441i
$737$	−1.20309	+	4.48998i	−0.0443162	+	0.165390i
$738$	3.56853	−	0.591283i	0.131359	−	0.0217654i
$739$	−10.8990	−	6.29255i	−0.400927	−	0.231475i	0.285957	−	0.958242i	$-0.407689\pi$
$739$	−10.8990	−	6.29255i	−0.400927	−	0.231475i	−0.686884	+	0.726767i	$0.741022\pi$
$740$	−0.226124	+	11.9739i	−0.00831248	+	0.440171i
$741$	2.21970	+	1.09658i	0.0815428	+	0.0402837i
$742$	−6.25194	+	6.25194i	−0.229516	+	0.229516i
$743$	4.64313	+	17.3284i	0.170340	+	0.635717i	0.997299	+	0.0734545i	$0.0234024\pi$
$743$	4.64313	+	17.3284i	0.170340	+	0.635717i	−0.826959	+	0.562263i	$0.809931\pi$
$744$	3.96150	−	6.14800i	0.145236	−	0.225397i
$745$	1.81839	−	6.30744i	0.0666206	−	0.231087i
$746$	−4.67347	−	2.69823i	−0.171108	−	0.0987891i
$747$	3.20478	−	8.52984i	0.117257	−	0.312091i
$748$	−24.9013	−	24.9013i	−0.910481	−	0.910481i
$749$	6.64958			0.242971
$750$	6.95289	−	18.0737i	0.253884	−	0.659957i
$751$	−0.654469	−	1.13357i	−0.0238819	−	0.0413647i	0.853837	−	0.520540i	$-0.174269\pi$
$751$	−0.654469	−	1.13357i	−0.0238819	−	0.0413647i	−0.877719	+	0.479175i	$0.840936\pi$
$752$	−1.74657	−	1.74657i	−0.0636907	−	0.0636907i
$753$	12.7010	−	11.5182i	0.462850	−	0.419746i
$754$	1.38319	−	0.798583i	0.0503726	−	0.0290827i
$755$	−31.0453	+	7.69335i	−1.12985	+	0.279990i
$756$	2.90855	+	7.34162i	0.105783	+	0.267012i
$757$	6.25895	+	23.3587i	0.227485	+	0.848987i	0.981394	+	0.192007i	$0.0614997\pi$
$757$	6.25895	+	23.3587i	0.227485	+	0.848987i	−0.753908	+	0.656980i	$0.771834\pi$
$758$	4.38606	+	16.3690i	0.159309	+	0.594548i
$759$	3.64880	−	74.7131i	0.132443	−	2.71191i
$760$	−5.64944	−	7.94254i	−0.204927	−	0.288106i
$761$		−	3.83472i		−	0.139009i	−0.997582	−	0.0695043i	$-0.977858\pi$
$761$		−	3.83472i		−	0.139009i	0.997582	−	0.0695043i	$-0.0221418\pi$
$762$	34.3319	−	7.42536i	1.24371	−	0.268992i
$763$	10.6993	−	2.86686i	0.387339	−	0.103787i
$764$	−11.2314	−	19.4533i	−0.406337	−	0.703795i
$765$	−25.4263	+	34.1446i	−0.919290	+	1.23450i
$766$	−18.4365	−	31.9330i	−0.666139	−	1.15379i
$767$	−1.06450	−	1.06450i	−0.0384367	−	0.0384367i
$768$	−1.16354	−	1.28303i	−0.0419858	−	0.0462973i
$769$	−10.7161	+	6.18694i	−0.386432	+	0.223107i	−0.680613	−	0.732643i	$-0.738287\pi$
$769$	−10.7161	+	6.18694i	−0.386432	+	0.223107i	0.294181	+	0.955750i	$0.404953\pi$
$770$	18.1192	+	5.22363i	0.652970	+	0.188246i
$771$	−1.12107	+	22.9550i	−0.0403742	+	0.826706i
$772$	−14.0098	+	14.0098i	−0.504224	+	0.504224i
$773$	−3.52291	−	0.943960i	−0.126710	−	0.0339519i	0.194907	−	0.980822i	$-0.437560\pi$
$773$	−3.52291	−	0.943960i	−0.126710	−	0.0339519i	−0.321617	+	0.946870i	$0.604226\pi$
$774$	15.8949	−	22.2083i	0.571329	−	0.798262i
$775$	−18.6700	+	9.85866i	−0.670646	+	0.354134i
$776$	−8.01640	−	4.62827i	−0.287772	−	0.166145i
$777$	2.98023	+	13.7794i	0.106915	+	0.494334i
$778$	−16.1773	−	16.1773i	−0.579983	−	0.579983i
$779$	−4.22447	+	3.12660i	−0.151357	+	0.112022i
$780$	−0.835273	−	0.956745i	−0.0299076	−	0.0342570i
$781$	−23.8401	+	41.2922i	−0.853065	+	1.47755i
$782$	−47.7078	+	12.7833i	−1.70603	+	0.457129i
$783$	23.2285	+	10.0460i	0.830118	+	0.359016i
$784$	4.06201	+	2.34520i	0.145072	+	0.0837572i
$785$	−6.24773	−	11.3093i	−0.222991	−	0.403646i
$786$	16.8022	+	0.820576i	0.599314	+	0.0292690i
$787$	8.45948	−	8.45948i	0.301548	−	0.301548i	−0.540071	−	0.841619i	$-0.681603\pi$
$787$	8.45948	−	8.45948i	0.301548	−	0.301548i	0.841619	+	0.540071i	$0.181603\pi$
$788$	13.0362	+	3.49305i	0.464397	+	0.124435i
$789$	−6.67863	−	12.9930i	−0.237766	−	0.462562i
$790$	10.9701	+	0.207166i	0.390297	+	0.00737064i
$791$			24.0327i			0.854506i
$792$	15.5837	+	5.85501i	0.553742	+	0.208049i
$793$	2.61234	−	0.699974i	0.0927668	−	0.0248568i
$794$	11.0738	+	19.1804i	0.392995	+	0.680687i
$795$	22.1092	−	4.34653i	0.784132	−	0.154155i
$796$	13.6261	−	23.6010i	0.482963	−	0.836516i
$797$	−25.9354	−	25.9354i	−0.918680	−	0.918680i	0.0782539	−	0.996933i	$-0.475066\pi$
$797$	−25.9354	−	25.9354i	−0.918680	−	0.918680i	−0.996933	+	0.0782539i	$0.975066\pi$
$798$	−8.62111	−	7.57123i	−0.305184	−	0.268019i
$799$		−	15.6753i		−	0.554551i
$800$	1.11083	+	4.87505i	0.0392736	+	0.172359i
$801$	−6.54578	−	4.68492i	−0.231284	−	0.165534i
$802$	27.0396	+	7.24523i	0.954800	+	0.255838i
$803$	−14.7197	−	54.9348i	−0.519449	−	1.93861i
$804$	−1.29041	+	0.663296i	−0.0455093	+	0.0233926i
$805$	19.0510	−	18.3447i	0.671458	−	0.646567i
$806$			1.38471i			0.0487743i
$807$	−10.6583	+	33.2047i	−0.375189	+	1.16886i
$808$	1.45601	−	5.43392i	0.0512224	−	0.191165i
$809$	−15.0218			−0.528139			−0.264069	−	0.964504i	$-0.585065\pi$
$809$	−15.0218			−0.528139			−0.264069	+	0.964504i	$0.585065\pi$
$810$	4.27539	−	19.6652i	0.150222	−	0.690966i
$811$	22.8510	+	39.5790i	0.802406	+	1.38981i	0.918029	+	0.396514i	$0.129780\pi$
$811$	22.8510	+	39.5790i	0.802406	+	1.38981i	−0.115623	+	0.993293i	$0.536886\pi$
$812$	−7.14964	+	1.91574i	−0.250903	+	0.0672293i
$813$	3.29744	−	10.2728i	0.115646	−	0.360284i
$814$	25.7384	+	14.8601i	0.902132	+	0.520846i
$815$	−21.7317	−	13.1000i	−0.761227	−	0.458873i
$816$	0.536181	−	10.9789i	0.0187701	−	0.384338i
$817$	−5.86133	+	39.2458i	−0.205062	+	1.37304i
$818$	22.8660	−	22.8660i	0.799489	−	0.799489i
$819$	−1.21578	−	0.870153i	−0.0424828	−	0.0304056i
$820$	2.61693	−	0.648503i	0.0913872	−	0.0226467i
$821$	−27.0755	+	15.6321i	−0.944942	+	0.545563i	−0.891506	−	0.453009i	$-0.850351\pi$
$821$	−27.0755	+	15.6321i	−0.944942	+	0.545563i	−0.0534361	+	0.998571i	$0.517017\pi$
$822$	−7.45917	−	34.4883i	−0.260169	−	1.20292i
$823$	7.92423	−	29.5736i	0.276221	−	1.03087i	−0.678797	−	0.734326i	$-0.737498\pi$
$823$	7.92423	−	29.5736i	0.276221	−	1.03087i	0.955019	−	0.296546i	$-0.0958349\pi$
$824$	−17.1894			−0.598820
$825$	−30.9160	−	36.7918i	−1.07636	−	1.28092i
$826$	3.48835	+	6.04199i	0.121375	+	0.210228i
$827$	−9.16046	+	34.1873i	−0.318540	+	1.18881i	0.602108	+	0.798415i	$0.294328\pi$
$827$	−9.16046	+	34.1873i	−0.318540	+	1.18881i	−0.920648	+	0.390394i	$0.872339\pi$
$828$	18.0398	−	14.8223i	0.626926	−	0.515111i
$829$			2.88415i			0.100171i	0.998745	+	0.0500854i	$0.0159493\pi$
$829$			2.88415i			0.100171i	−0.998745	+	0.0500854i	$0.984051\pi$
$830$	1.88137	−	6.52592i	0.0653034	−	0.226518i
$831$	12.1978	−	18.9303i	0.423138	−	0.656683i
$832$	0.316753	+	0.0848738i	0.0109814	+	0.00294247i
$833$	7.70409	+	28.7520i	0.266931	+	0.996199i
$834$	10.2571	−	15.9184i	0.355174	−	0.551208i
$835$	−0.346793	+	18.3637i	−0.0120013	+	0.635503i
$836$	−24.0322	+	2.74054i	−0.831171	+	0.0947837i
$837$	−17.6121	+	13.0857i	−0.608764	+	0.452308i
$838$	−11.4990	+	3.08114i	−0.397226	+	0.106436i
$839$	−4.21356	+	7.29810i	−0.145468	+	0.251958i	−0.929548	−	0.368702i	$-0.879802\pi$
$839$	−4.21356	+	7.29810i	−0.145468	+	0.251958i	0.784079	+	0.620661i	$0.213135\pi$
$840$	2.59149	+	5.28471i	0.0894148	+	0.182340i
$841$	2.63917	−	4.57117i	0.0910057	−	0.157627i
$842$	−0.511631	+	1.90943i	−0.0176320	+	0.0658034i
$843$	−14.9835	+	13.5881i	−0.516058	+	0.468000i
$844$			11.2807i			0.388299i
$845$	−27.7003	−	7.98579i	−0.952918	−	0.274719i
$846$	3.06208	+	6.74778i	0.105276	+	0.231994i
$847$	21.2693	−	21.2693i	0.730821	−	0.730821i
$848$	−4.11383	+	4.11383i	−0.141270	+	0.141270i
$849$	17.5637	−	9.02810i	0.602786	−	0.309844i
$850$	−16.8918	+	26.8613i	−0.579382	+	0.921335i
$851$	36.0987	−	20.8416i	1.23745	−	0.714440i
$852$	−14.5462	+	3.14607i	−0.498344	+	0.107783i
$853$	−15.8659	+	4.25126i	−0.543239	+	0.145560i	−0.519995	−	0.854169i	$-0.674066\pi$
$853$	−15.8659	+	4.25126i	−0.543239	+	0.145560i	−0.0232441	+	0.999730i	$0.507399\pi$
$854$	−12.5336			−0.428892
$855$	7.48507	+	28.2661i	0.255984	+	0.966681i
$856$	4.37549			0.149551
$857$	−17.4111	+	4.66530i	−0.594753	+	0.159364i	−0.543624	−	0.839329i	$-0.682948\pi$
$857$	−17.4111	+	4.66530i	−0.594753	+	0.159364i	−0.0511283	+	0.998692i	$0.516282\pi$
$858$	−3.08058	+	0.666273i	−0.105169	+	0.0227462i
$859$	37.3902	−	21.5872i	1.27574	−	0.736546i	0.299675	−	0.954041i	$-0.403122\pi$
$859$	37.3902	−	21.5872i	1.27574	−	0.736546i	0.976061	+	0.217495i	$0.0697886\pi$
$860$	10.5090	−	17.4335i	0.358354	−	0.594476i
$861$	2.82272	−	1.45093i	0.0961979	−	0.0494476i
$862$	−17.9491	+	17.9491i	−0.611350	+	0.611350i
$863$	−7.38719	+	7.38719i	−0.251463	+	0.251463i	−0.821570	−	0.570107i	$-0.806902\pi$
$863$	−7.38719	+	7.38719i	−0.251463	+	0.251463i	0.570107	+	0.821570i	$0.306902\pi$
$864$	1.91385	+	4.83086i	0.0651106	+	0.164349i
$865$	−20.8770	−	37.7904i	−0.709840	−	1.28491i
$866$		−	7.59532i		−	0.258100i
$867$	29.8618	−	27.0808i	1.01416	−	0.919714i
$868$	1.66091	−	6.19859i	0.0563749	−	0.210394i
$869$	13.6143	−	23.5806i	0.461832	−	0.799916i
$870$	17.8487	+	6.10326i	0.605127	+	0.206920i
$871$	0.137349	−	0.237895i	0.00465389	−	0.00806077i
$872$	7.04021	−	1.88642i	0.238412	−	0.0638822i
$873$	17.6293	+	21.4560i	0.596660	+	0.726177i
$874$	−13.5241	+	31.1117i	−0.457459	+	1.05237i
$875$	0.961989	−	16.9639i	0.0325212	−	0.573485i
$876$	9.61525	−	14.9223i	0.324869	−	0.504176i
$877$	−5.12473	−	19.1257i	−0.173050	−	0.645830i	−0.996876	−	0.0789874i	$-0.974831\pi$
$877$	−5.12473	−	19.1257i	−0.173050	−	0.645830i	0.823826	−	0.566843i	$-0.191835\pi$
$878$	22.6598	+	6.07168i	0.764732	+	0.204909i
$879$	−26.5199	+	41.1572i	−0.894494	+	1.38820i
$880$	11.9226	+	3.43719i	0.401910	+	0.115868i
$881$			48.8801i			1.64681i	0.567451	+	0.823407i	$0.307929\pi$
$881$			48.8801i			1.64681i	−0.567451	+	0.823407i	$0.692071\pi$
$882$	−8.93296	−	10.8720i	−0.300788	−	0.366081i
$883$	13.8030	−	51.5136i	0.464509	−	1.73357i	−0.194003	−	0.981001i	$-0.562147\pi$
$883$	13.8030	−	51.5136i	0.464509	−	1.73357i	0.658512	−	0.752570i	$-0.271186\pi$
$884$	1.04055	+	1.80228i	0.0349974	+	0.0606173i
$885$	1.20244	−	17.7391i	0.0404195	−	0.596293i
$886$	3.50924			0.117895
$887$	−6.07378	+	22.6677i	−0.203938	+	0.761106i	0.785833	+	0.618439i	$0.212234\pi$
$887$	−6.07378	+	22.6677i	−0.203938	+	0.761106i	−0.989771	+	0.142667i	$0.954432\pi$
$888$	1.96102	+	9.06698i	0.0658076	+	0.304268i
$889$	26.6909	−	15.4100i	0.895184	−	0.516835i
$890$	−5.13841	−	3.09747i	−0.172240	−	0.103828i
$891$	−37.5863	−	32.8856i	−1.25919	−	1.10171i
$892$	−11.1190	+	11.1190i	−0.372292	+	0.372292i
$893$	−8.42666	−	6.70150i	−0.281987	−	0.224257i
$894$	0.248028	−	5.07865i	0.00829531	−	0.169856i
$895$	12.7460	−	3.15859i	0.426051	−	0.105580i
$896$	−1.31613	−	0.759868i	−0.0439688	−	0.0253854i
$897$	−1.35102	+	4.20896i	−0.0451093	+	0.140533i
$898$	−10.9397	+	2.93129i	−0.365063	+	0.0978184i
$899$	−10.2831	−	17.8109i	−0.342961	−	0.594025i
$900$	2.02424	−	14.8628i	0.0674746	−	0.495426i
$901$	−36.9212			−1.23002
$902$	1.73168	−	6.46271i	0.0576586	−	0.215185i
$903$	7.32366	−	22.8161i	0.243716	−	0.759271i
$904$			15.8138i			0.525958i
$905$	−6.28412	−	6.52604i	−0.208891	−	0.216933i
$906$	−22.0345	+	11.3261i	−0.732046	+	0.376286i
$907$	2.50288	+	9.34088i	0.0831068	+	0.310159i	0.994949	−	0.100382i	$-0.0320065\pi$
$907$	2.50288	+	9.34088i	0.0831068	+	0.310159i	−0.911842	+	0.410541i	$0.865340\pi$
$908$	9.25734	+	2.48050i	0.307216	+	0.0823181i
$909$	−9.82245	+	13.7239i	−0.325790	+	0.455194i
$910$	−0.954382	−	0.575309i	−0.0316375	−	0.0190713i
$911$		−	4.05796i		−	0.134446i	−0.997738	−	0.0672232i	$-0.978586\pi$
$911$		−	4.05796i		−	0.134446i	0.997738	−	0.0672232i	$-0.0214140\pi$
$912$	−5.67277	−	4.98194i	−0.187844	−	0.164968i
$913$	−11.9179	−	11.9179i	−0.394426	−	0.394426i
$914$	−0.378492	+	0.655567i	−0.0125194	+	0.0216842i
$915$	26.5186	+	17.8049i	0.876679	+	0.588612i
$916$	−3.31408	−	5.74016i	−0.109500	−	0.189660i
$917$	14.2572	−	3.82021i	0.470814	−	0.126154i
$918$	−13.0899	+	30.2666i	−0.432031	+	0.998945i
$919$		−	5.35052i		−	0.176497i	−0.996098	−	0.0882487i	$-0.971873\pi$
$919$		−	5.35052i		−	0.176497i	0.996098	−	0.0882487i	$-0.0281270\pi$
$920$	12.5357	−	12.0710i	0.413290	−	0.397969i
$921$	11.0166	+	21.4323i	0.363010	+	0.706218i
$922$	11.0998	+	2.97419i	0.365553	+	0.0979497i
$923$	1.99241	−	1.99241i	0.0655808	−	0.0655808i
$924$	14.5893	+	0.712503i	0.479952	+	0.0234396i
$925$	7.90268	−	25.5867i	0.259839	−	0.841286i
$926$	16.2119	+	9.35997i	0.532757	+	0.307588i
$927$	48.2734	+	18.1370i	1.58551	+	0.595698i
$928$	−4.70453	+	1.26058i	−0.154434	+	0.0413804i
$929$	16.4259	−	28.4504i	0.538915	−	0.933428i	−0.460048	−	0.887894i	$-0.652168\pi$
$929$	16.4259	−	28.4504i	0.538915	−	0.933428i	0.998963	−	0.0455340i	$-0.0144989\pi$
$930$	−12.3197	+	10.7556i	−0.403979	+	0.352689i
$931$	18.7501	+	8.15056i	0.614510	+	0.267124i
$932$	13.5673	+	13.5673i	0.444412	+	0.444412i
$933$	5.73170	+	26.5011i	0.187648	+	0.867608i
$934$	9.92690	+	5.73130i	0.324818	+	0.187534i
$935$	38.0778	+	68.9262i	1.24528	+	2.25413i
$936$	−0.799994	−	0.572569i	−0.0261486	−	0.0187150i
$937$	25.6500	+	6.87291i	0.837950	+	0.224528i	0.652179	−	0.758065i	$-0.273855\pi$
$937$	25.6500	+	6.87291i	0.837950	+	0.224528i	0.185771	+	0.982593i	$0.440522\pi$
$938$	−0.900183	+	0.900183i	−0.0293920	+	0.0293920i
$939$	−2.38524	+	48.8403i	−0.0778393	+	1.59384i
$940$	2.67076	+	4.83446i	0.0871105	+	0.157683i
$941$	16.0727	−	9.27957i	0.523954	−	0.302505i	−0.214597	−	0.976703i	$-0.568844\pi$
$941$	16.0727	−	9.27957i	0.523954	−	0.302505i	0.738551	+	0.674198i	$0.235510\pi$
$942$	−6.72312	−	7.41351i	−0.219051	−	0.241545i
$943$	−6.63537	−	6.63537i	−0.216077	−	0.216077i
$944$	2.29536	+	3.97569i	0.0747077	+	0.129398i
$945$	−1.70169	−	17.5755i	−0.0553561	−	0.571732i
$946$	−25.2580	−	43.7481i	−0.821208	−	1.42237i
$947$	41.5402	−	11.1307i	1.34988	−	0.361698i	0.489787	−	0.871842i	$-0.337074\pi$
$947$	41.5402	−	11.1307i	1.34988	−	0.361698i	0.860089	+	0.510144i	$0.170408\pi$
$948$	8.30682	−	1.79661i	0.269793	−	0.0583512i
$949$			3.36093i			0.109100i
$950$	7.21845	+	20.5644i	0.234197	+	0.667197i
$951$	1.00654	−	20.6100i	0.0326393	−	0.668325i
$952$	−2.49620	−	9.31594i	−0.0809022	−	0.301931i
$953$	−0.134563	−	0.502197i	−0.00435894	−	0.0162678i	0.963712	−	0.266944i	$-0.0860138\pi$
$953$	−0.134563	−	0.502197i	−0.00435894	−	0.0162678i	−0.968071	+	0.250676i	$0.919347\pi$
$954$	15.8936	−	7.21236i	0.514575	−	0.233509i
$955$	12.0816	+	48.7535i	0.390953	+	1.57763i
$956$	−0.972177	+	0.561287i	−0.0314425	+	0.0181533i
$957$	34.6762	−	31.4469i	1.12092	−	1.01653i
$958$	6.18917	+	6.18917i	0.199963	+	0.199963i
$959$	−15.4802	−	26.8125i	−0.499881	−	0.865819i
$960$	1.70522	+	3.47739i	0.0550358	+	0.112232i
$961$	−13.1695			−0.424823
$962$	−1.24191	−	1.24191i	−0.0400409	−	0.0400409i
$963$	−12.2878	−	4.61670i	−0.395969	−	0.148771i
$964$	16.3323	+	9.42945i	0.526027	+	0.303702i
$965$	38.7788	−	21.4231i	1.24834	−	0.689633i
$966$	11.0963	−	17.2207i	0.357017	−	0.554068i
$967$	4.33353	+	16.1729i	0.139357	+	0.520087i	0.999942	+	0.0107801i	$0.00343147\pi$
$967$	4.33353	+	16.1729i	0.139357	+	0.520087i	−0.860585	+	0.509307i	$0.829902\pi$
$968$	13.9954	−	13.9954i	0.449829	−	0.449829i
$969$	−3.10006	−	47.8125i	−0.0995882	−	1.53596i
$970$	14.3569	+	14.9096i	0.460973	+	0.478719i
$971$	−18.2443	−	10.5334i	−0.585487	−	0.338031i	0.177824	−	0.984062i	$-0.443094\pi$
$971$	−18.2443	−	10.5334i	−0.585487	−	0.338031i	−0.763311	+	0.646031i	$0.776428\pi$
$972$	−0.277553	−	15.5860i	−0.00890251	−	0.499921i
$973$	4.30042	−	16.0494i	0.137865	−	0.514519i
$974$	7.94171	−	13.7554i	0.254469	−	0.440753i
$975$	1.20202	+	2.57301i	0.0384953	+	0.0824022i
$976$	−8.24724			−0.263988
$977$	39.3563	+	39.3563i	1.25912	+	1.25912i	0.951514	+	0.307605i	$0.0995275\pi$
$977$	39.3563	+	39.3563i	1.25912	+	1.25912i	0.307605	+	0.951514i	$0.400473\pi$
$978$	−18.7147	−	6.00717i	−0.598429	−	0.192088i
$979$	−12.8945	+	7.44465i	−0.412110	+	0.237932i
$980$	−7.27483	−	7.55488i	−0.232386	−	0.241332i
$981$	−21.7616	−	2.13065i	−0.694796	−	0.0680264i
$982$	26.1053	+	6.99488i	0.833052	+	0.223216i
$983$	4.81352	+	17.9643i	0.153528	+	0.572973i	0.999227	+	0.0393131i	$0.0125170\pi$
$983$	4.81352	+	17.9643i	0.153528	+	0.572973i	−0.845699	+	0.533660i	$0.820816\pi$
$984$	1.85737	−	0.954725i	0.0592109	−	0.0304355i
$985$	−25.8455	−	15.5799i	−0.823507	−	0.496416i
$986$	−26.7681	−	15.4546i	−0.852471	−	0.492174i
$987$	4.36768	+	4.81620i	0.139025	+	0.153301i
$988$	1.41372	+	0.211138i	0.0449765	+	0.00671720i
$989$	−70.8496			−2.25289
$990$	−29.8558	−	22.2326i	−0.948881	−	0.706599i
$991$	5.33927	−	9.24789i	0.169608	−	0.293769i	−0.768674	−	0.639640i	$-0.779083\pi$
$991$	5.33927	−	9.24789i	0.169608	−	0.293769i	0.938282	+	0.345871i	$0.112417\pi$
$992$	1.09289	−	4.07873i	0.0346994	−	0.129500i
$993$	54.8396	−	11.8608i	1.74028	−	0.376391i
$994$	−11.3087	+	6.52911i	−0.358692	+	0.207091i
$995$	−43.8953	+	42.2681i	−1.39157	+	1.33999i
$996$	0.256619	−	5.25456i	0.00813130	−	0.166497i
$997$	−27.6729	−	7.41494i	−0.876411	−	0.234834i	−0.207553	−	0.978224i	$-0.566550\pi$
$997$	−27.6729	−	7.41494i	−0.876411	−	0.234834i	−0.668858	+	0.743390i	$0.733217\pi$
$998$	15.4975	+	4.15255i	0.490566	+	0.131447i
$999$	4.05965	−	27.5322i	0.128442	−	0.871080i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.v.c.353.18	yes	144
3.2	odd	2	inner	570.2.v.c.353.34	yes	144
5.2	odd	4	inner	570.2.v.c.467.10	yes	144
15.2	even	4	inner	570.2.v.c.467.24	yes	144
19.7	even	3	inner	570.2.v.c.83.24	yes	144
57.26	odd	6	inner	570.2.v.c.83.10	✓	144
95.7	odd	12	inner	570.2.v.c.197.34	yes	144
285.197	even	12	inner	570.2.v.c.197.18	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.v.c.83.10	✓	144	57.26	odd	6	inner
570.2.v.c.83.24	yes	144	19.7	even	3	inner
570.2.v.c.197.18	yes	144	285.197	even	12	inner
570.2.v.c.197.34	yes	144	95.7	odd	12	inner
570.2.v.c.353.18	yes	144	1.1	even	1	trivial
570.2.v.c.353.34	yes	144	3.2	odd	2	inner
570.2.v.c.467.10	yes	144	5.2	odd	4	inner
570.2.v.c.467.24	yes	144	15.2	even	4	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.v (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.69291 - 0.366145i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.17042 + 0.537853i) q^{5} +(-1.54046 + 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.73188 - 1.23970i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(1.69291 - 0.366145i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.17042 + 0.537853i) q^{5} +(-1.54046 + 0.791825i) q^{6} +(-1.07462 + 1.07462i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.73188 - 1.23970i) q^{9} +(1.95726 - 1.08127i) q^{10} -5.54910i q^{11} +(1.28303 - 1.16354i) q^{12} +(-0.0848738 + 0.316753i) q^{13} +(0.759868 - 1.31613i) q^{14} +(-3.47739 + 1.70522i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.12997 - 1.64252i) q^{17} +(-2.31793 + 1.90452i) q^{18} +(1.73771 - 3.99755i) q^{19} +(-1.61071 + 1.55100i) q^{20} +(-1.42576 + 2.21269i) q^{21} +(1.43621 + 5.36001i) q^{22} +(7.51752 + 2.01431i) q^{23} +(-0.938163 + 1.45597i) q^{24} +(4.42143 - 2.33473i) q^{25} -0.327927i q^{26} +(4.17091 - 3.09896i) q^{27} +(-0.393337 + 1.46795i) q^{28} +(2.43524 + 4.21797i) q^{29} +(2.91755 - 2.54713i) q^{30} -4.22261 q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.03177 - 9.39411i) q^{33} +(-5.49598 + 3.17311i) q^{34} +(1.75438 - 2.91035i) q^{35} +(1.74602 - 2.43955i) q^{36} +(3.78717 - 3.78717i) q^{37} +(-0.643857 + 4.31108i) q^{38} +(-0.0277060 + 0.567310i) q^{39} +(1.15440 - 1.91504i) q^{40} +(-1.04419 - 0.602864i) q^{41} +(0.804493 - 2.50631i) q^{42} +(-8.79326 + 2.35615i) q^{43} +(-2.77455 - 4.80566i) q^{44} +(-5.26254 + 4.16001i) q^{45} -7.78271 q^{46} +(0.639288 - 2.38585i) q^{47} +(0.529363 - 1.64917i) q^{48} +4.69040i q^{49} +(-3.66650 + 3.39953i) q^{50} +(9.77608 - 5.02509i) q^{51} +(0.0848738 + 0.316753i) q^{52} +(-5.61960 - 1.50577i) q^{53} +(-3.22672 + 4.07287i) q^{54} +(2.98460 + 12.0439i) q^{55} -1.51974i q^{56} +(1.47810 - 7.40373i) q^{57} +(-3.44396 - 3.44396i) q^{58} +(-2.29536 + 3.97569i) q^{59} +(-2.15889 + 3.21546i) q^{60} +(-4.12362 - 7.14232i) q^{61} +(4.07873 - 1.09289i) q^{62} +(-1.60352 + 4.26792i) q^{63} -1.00000i q^{64} +(0.0138450 - 0.733136i) q^{65} +(4.39392 + 8.54815i) q^{66} +(-0.809136 - 0.216807i) q^{67} +(4.48745 - 4.48745i) q^{68} +(13.4640 + 0.657548i) q^{69} +(-0.941347 + 3.26525i) q^{70} +(-7.44126 - 4.29621i) q^{71} +(-1.05513 + 2.80833i) q^{72} +(9.89978 - 2.65264i) q^{73} +(-2.67793 + 4.63831i) q^{74} +(6.63022 - 5.57137i) q^{75} +(-0.493872 - 4.33083i) q^{76} +(5.96314 + 5.96314i) q^{77} +(-0.120069 - 0.555150i) q^{78} +(4.24944 + 2.45342i) q^{79} +(-0.619415 + 2.14856i) q^{80} +(5.92629 - 6.77341i) q^{81} +(1.16464 + 0.312065i) q^{82} +(2.14772 - 2.14772i) q^{83} +(-0.128400 + 2.62913i) q^{84} +(-12.4212 + 6.86198i) q^{85} +(7.88383 - 4.55173i) q^{86} +(5.66703 + 6.24898i) q^{87} +(3.92380 + 3.92380i) q^{88} +(-1.34160 - 2.32371i) q^{89} +(4.00653 - 5.38031i) q^{90} +(-0.249181 - 0.431594i) q^{91} +(7.51752 - 2.01431i) q^{92} +(-7.14850 + 1.54609i) q^{93} +2.47002i q^{94} +(-1.62147 + 9.61098i) q^{95} +(-0.0844883 + 1.72999i) q^{96} +(2.39577 + 8.94113i) q^{97} +(-1.21397 - 4.53058i) q^{98} +(-6.87921 - 15.1594i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 4 q^{3} + 8 q^{6}+O(q^{10}) \) 144 * q - 4 * q^3 + 8 * q^6	\( 144 q - 4 q^{3} + 8 q^{6} - 16 q^{10} - 8 q^{12} - 32 q^{13} + 4 q^{15} + 72 q^{16} + 32 q^{18} - 24 q^{21} + 8 q^{22} + 40 q^{25} - 16 q^{27} - 8 q^{30} - 16 q^{33} - 16 q^{37} + 8 q^{40} - 44 q^{42} - 16 q^{43} - 56 q^{45} - 48 q^{46} + 4 q^{48} + 32 q^{51} + 32 q^{52} + 8 q^{55} - 64 q^{57} + 32 q^{58} - 24 q^{60} + 76 q^{63} + 16 q^{66} - 56 q^{67} - 8 q^{70} + 16 q^{72} + 88 q^{73} + 32 q^{75} + 48 q^{76} - 56 q^{81} - 152 q^{87} - 16 q^{88} - 4 q^{90} + 80 q^{91} - 52 q^{93} + 16 q^{96} + 32 q^{97}+O(q^{100}) \) 144 * q - 4 * q^3 + 8 * q^6 - 16 * q^10 - 8 * q^12 - 32 * q^13 + 4 * q^15 + 72 * q^16 + 32 * q^18 - 24 * q^21 + 8 * q^22 + 40 * q^25 - 16 * q^27 - 8 * q^30 - 16 * q^33 - 16 * q^37 + 8 * q^40 - 44 * q^42 - 16 * q^43 - 56 * q^45 - 48 * q^46 + 4 * q^48 + 32 * q^51 + 32 * q^52 + 8 * q^55 - 64 * q^57 + 32 * q^58 - 24 * q^60 + 76 * q^63 + 16 * q^66 - 56 * q^67 - 8 * q^70 + 16 * q^72 + 88 * q^73 + 32 * q^75 + 48 * q^76 - 56 * q^81 - 152 * q^87 - 16 * q^88 - 4 * q^90 + 80 * q^91 - 52 * q^93 + 16 * q^96 + 32 * q^97

Introduction

L-functions

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