LMFDB - Embedded newform 570.2.u.b.481.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(61,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 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("570.61");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, 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:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			481.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	570.481
Dual form			570.2.u.b.301.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.705737 - 1.22237i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.705737 - 1.22237i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(2.76604 + 4.79093i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-4.69846 + 1.71010i) q^{13} +(0.245100 + 1.39003i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(5.94356 - 4.98724i) q^{17} -1.00000 q^{18} +(-2.23396 - 3.74292i) q^{19} -1.00000 q^{20} +(-1.08125 + 0.907278i) q^{21} +(-5.19846 - 1.89209i) q^{22} +(1.44697 - 8.20616i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-1.08125 - 0.907278i) q^{28} +(1.34730 + 1.13052i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(2.71688 - 4.70578i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.960637 - 5.44804i) q^{33} +(-1.34730 + 7.64090i) q^{34} +(-1.32635 - 0.482753i) q^{35} +(0.766044 - 0.642788i) q^{36} +3.50980 q^{37} +(4.11721 + 1.43128i) q^{38} +5.00000 q^{39} +(0.766044 - 0.642788i) q^{40} +(4.89306 + 1.78093i) q^{41} +(0.245100 - 1.39003i) q^{42} +(-0.837496 - 4.74968i) q^{43} +(5.19846 - 1.89209i) q^{44} +(0.500000 - 0.866025i) q^{45} +(4.16637 + 7.21637i) q^{46} +(2.04916 + 1.71945i) q^{47} +(0.766044 + 0.642788i) q^{48} +(2.50387 + 4.33683i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-7.29086 + 2.65366i) q^{51} +(0.868241 + 4.92404i) q^{52} +(1.52822 - 8.66696i) q^{53} +(0.939693 + 0.342020i) q^{54} +(4.23783 - 3.55596i) q^{55} +1.41147 q^{56} +(0.819078 + 4.28125i) q^{57} -1.75877 q^{58} +(-5.24170 + 4.39831i) q^{59} +(0.939693 + 0.342020i) q^{60} +(1.67499 - 9.49935i) q^{61} +(0.943563 + 5.35121i) q^{62} +(1.32635 - 0.482753i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50000 + 4.33013i) q^{65} +(4.23783 + 3.55596i) q^{66} +(-5.29086 - 4.43956i) q^{67} +(-3.87939 - 6.71929i) q^{68} +(-4.16637 + 7.21637i) q^{69} +(1.32635 - 0.482753i) q^{70} +(-0.361844 - 2.05212i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-0.800660 - 0.291416i) q^{73} +(-2.68866 + 2.25606i) q^{74} +1.00000 q^{75} +(-4.07398 + 1.55007i) q^{76} +7.80840 q^{77} +(-3.83022 + 3.21394i) q^{78} +(-9.06418 - 3.29909i) q^{79} +(-0.173648 + 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-4.89306 + 1.78093i) q^{82} +(-1.18479 + 2.05212i) q^{83} +(0.705737 + 1.22237i) q^{84} +(-5.94356 - 4.98724i) q^{85} +(3.69459 + 3.10013i) q^{86} +(-0.879385 - 1.52314i) q^{87} +(-2.76604 + 4.79093i) q^{88} +(13.3623 - 4.86348i) q^{89} +(0.173648 + 0.984808i) q^{90} +(-1.22550 + 6.95015i) q^{91} +(-7.83022 - 2.84997i) q^{92} +(-4.16250 + 3.49276i) q^{93} -2.67499 q^{94} +(-3.29813 + 2.84997i) q^{95} -1.00000 q^{96} +(11.1061 - 9.31910i) q^{97} +(-4.70574 - 1.71275i) q^{98} +(-0.960637 + 5.44804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q - 6 * q^7 + 3 * q^8	$ 6 q - 6 q^{7} + 3 q^{8} + 12 q^{11} - 3 q^{12} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 9 q^{21} - 3 q^{22} + 21 q^{23} + 15 q^{26} - 3 q^{27} - 9 q^{28} + 6 q^{29} - 3 q^{30} + 3 q^{33} - 6 q^{34} - 9 q^{35} + 24 q^{37} - 6 q^{38} + 30 q^{39} - 3 q^{41} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 24 q^{47} - 9 q^{49} + 3 q^{50} - 12 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} - 24 q^{62} + 9 q^{63} - 3 q^{64} + 15 q^{65} + 6 q^{66} - 12 q^{68} - 6 q^{69} + 9 q^{70} - 36 q^{71} + 24 q^{73} + 15 q^{74} + 6 q^{75} - 9 q^{76} - 30 q^{77} - 36 q^{79} + 3 q^{82} - 6 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} - 12 q^{88} + 48 q^{89} - 24 q^{92} - 30 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 42 q^{97} - 18 q^{98} + 3 q^{99}+O(q^{100}) $ 6 * q - 6 * q^7 + 3 * q^8 + 12 * q^11 - 3 * q^12 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 9 * q^21 - 3 * q^22 + 21 * q^23 + 15 * q^26 - 3 * q^27 - 9 * q^28 + 6 * q^29 - 3 * q^30 + 3 * q^33 - 6 * q^34 - 9 * q^35 + 24 * q^37 - 6 * q^38 + 30 * q^39 - 3 * q^41 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 24 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 - 24 * q^62 + 9 * q^63 - 3 * q^64 + 15 * q^65 + 6 * q^66 - 12 * q^68 - 6 * q^69 + 9 * q^70 - 36 * q^71 + 24 * q^73 + 15 * q^74 + 6 * q^75 - 9 * q^76 - 30 * q^77 - 36 * q^79 + 3 * q^82 - 6 * q^84 - 6 * q^85 + 18 * q^86 + 6 * q^87 - 12 * q^88 + 48 * q^89 - 24 * q^92 - 30 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 42 * q^97 - 18 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$3$	−0.939693	−	0.342020i	−0.542532	−	0.197465i
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	0.705737	−	1.22237i	0.266744	−	0.462013i	−0.701275	−	0.712890i	$-0.747386\pi$
$7$	0.705737	−	1.22237i	0.266744	−	0.462013i	0.968019	+	0.250877i	$0.0807190\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	0.766044	+	0.642788i	0.255348	+	0.214263i
$10$	0.766044	+	0.642788i	0.242245	+	0.203267i
$11$	2.76604	+	4.79093i	0.833994	+	1.44452i	0.894847	+	0.446373i	$0.147284\pi$
$11$	2.76604	+	4.79093i	0.833994	+	1.44452i	−0.0608533	+	0.998147i	$0.519382\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−4.69846	+	1.71010i	−1.30312	+	0.474297i	−0.898011	−	0.439972i	$-0.854988\pi$
$13$	−4.69846	+	1.71010i	−1.30312	+	0.474297i	−0.405108	+	0.914269i	$0.632766\pi$
$14$	0.245100	+	1.39003i	0.0655057	+	0.371501i
$15$	−0.173648	+	0.984808i	−0.0448358	+	0.254276i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	5.94356	−	4.98724i	1.44153	−	1.20958i	0.503041	−	0.864262i	$-0.332214\pi$
$17$	5.94356	−	4.98724i	1.44153	−	1.20958i	0.938485	−	0.345321i	$-0.112230\pi$
$18$	−1.00000			−0.235702
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$19$	−2.23396	−	3.74292i	−0.512505	−	0.858685i
$20$	−1.00000			−0.223607
$21$	−1.08125	+	0.907278i	−0.235949	+	0.197984i
$22$	−5.19846	−	1.89209i	−1.10832	−	0.403394i
$23$	1.44697	−	8.20616i	0.301713	−	1.71110i	−0.336872	−	0.941551i	$-0.609369\pi$
$23$	1.44697	−	8.20616i	0.301713	−	1.71110i	0.638585	−	0.769551i	$-0.279520\pi$
$24$	−0.173648	−	0.984808i	−0.0354458	−	0.201023i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	2.50000	−	4.33013i	0.490290	−	0.849208i
$27$	−0.500000	−	0.866025i	−0.0962250	−	0.166667i
$28$	−1.08125	−	0.907278i	−0.204337	−	0.171459i
$29$	1.34730	+	1.13052i	0.250187	+	0.209932i	0.759253	−	0.650796i	$-0.225565\pi$
$29$	1.34730	+	1.13052i	0.250187	+	0.209932i	−0.509066	+	0.860727i	$0.670009\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	2.71688	−	4.70578i	0.487966	−	0.845182i	−0.511938	−	0.859022i	$-0.671072\pi$
$31$	2.71688	−	4.70578i	0.487966	−	0.845182i	0.999904	+	0.0138400i	$0.00440555\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−0.960637	−	5.44804i	−0.167225	−	0.948383i
$34$	−1.34730	+	7.64090i	−0.231059	+	1.31040i
$35$	−1.32635	−	0.482753i	−0.224194	−	0.0816001i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	3.50980			0.577008			0.288504	−	0.957479i	$-0.406842\pi$
$37$	3.50980			0.577008			0.288504	+	0.957479i	$0.406842\pi$
$38$	4.11721	+	1.43128i	0.667900	+	0.232185i
$39$	5.00000			0.800641
$40$	0.766044	−	0.642788i	0.121122	−	0.101634i
$41$	4.89306	+	1.78093i	0.764167	+	0.278134i	0.694554	−	0.719440i	$-0.255602\pi$
$41$	4.89306	+	1.78093i	0.764167	+	0.278134i	0.0696124	+	0.997574i	$0.477824\pi$
$42$	0.245100	−	1.39003i	0.0378197	−	0.214486i
$43$	−0.837496	−	4.74968i	−0.127717	−	0.724319i	−0.979657	−	0.200679i	$-0.935685\pi$
$43$	−0.837496	−	4.74968i	−0.127717	−	0.724319i	0.851940	−	0.523639i	$-0.175426\pi$
$44$	5.19846	−	1.89209i	0.783698	−	0.285243i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	4.16637	+	7.21637i	0.614298	+	1.06400i
$47$	2.04916	+	1.71945i	0.298901	+	0.250808i	0.779887	−	0.625921i	$-0.215277\pi$
$47$	2.04916	+	1.71945i	0.298901	+	0.250808i	−0.480986	+	0.876728i	$0.659721\pi$
$48$	0.766044	+	0.642788i	0.110569	+	0.0927784i
$49$	2.50387	+	4.33683i	0.357696	+	0.619547i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−7.29086	+	2.65366i	−1.02092	+	0.371586i
$52$	0.868241	+	4.92404i	0.120403	+	0.682841i
$53$	1.52822	−	8.66696i	0.209917	−	1.19050i	−0.679595	−	0.733587i	$-0.737845\pi$
$53$	1.52822	−	8.66696i	0.209917	−	1.19050i	0.889512	−	0.456911i	$-0.151044\pi$
$54$	0.939693	+	0.342020i	0.127876	+	0.0465430i
$55$	4.23783	−	3.55596i	0.571428	−	0.479485i
$56$	1.41147			0.188616
$57$	0.819078	+	4.28125i	0.108490	+	0.567066i
$58$	−1.75877			−0.230938
$59$	−5.24170	+	4.39831i	−0.682411	+	0.572611i	−0.916710	−	0.399554i	$-0.869165\pi$
$59$	−5.24170	+	4.39831i	−0.682411	+	0.572611i	0.234299	+	0.972165i	$0.424721\pi$
$60$	0.939693	+	0.342020i	0.121314	+	0.0441546i
$61$	1.67499	−	9.49935i	0.214461	−	1.21627i	−0.667379	−	0.744718i	$-0.732584\pi$
$61$	1.67499	−	9.49935i	0.214461	−	1.21627i	0.881840	−	0.471549i	$-0.156305\pi$
$62$	0.943563	+	5.35121i	0.119833	+	0.679605i
$63$	1.32635	−	0.482753i	0.167105	−	0.0608211i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$	4.23783	+	3.55596i	0.521640	+	0.437708i
$67$	−5.29086	−	4.43956i	−0.646381	−	0.542378i	0.259589	−	0.965719i	$-0.416413\pi$
$67$	−5.29086	−	4.43956i	−0.646381	−	0.542378i	−0.905971	+	0.423341i	$0.860857\pi$
$68$	−3.87939	−	6.71929i	−0.470445	−	0.814834i
$69$	−4.16637	+	7.21637i	−0.501573	+	0.868749i
$70$	1.32635	−	0.482753i	0.158529	−	0.0577000i
$71$	−0.361844	−	2.05212i	−0.0429430	−	0.243542i	0.955779	−	0.294087i	$-0.0950154\pi$
$71$	−0.361844	−	2.05212i	−0.0429430	−	0.243542i	−0.998722	+	0.0505446i	$0.983904\pi$
$72$	−0.173648	+	0.984808i	−0.0204646	+	0.116061i
$73$	−0.800660	−	0.291416i	−0.0937101	−	0.0341077i	0.294740	−	0.955578i	$-0.404767\pi$
$73$	−0.800660	−	0.291416i	−0.0937101	−	0.0341077i	−0.388450	+	0.921470i	$0.626989\pi$
$74$	−2.68866	+	2.25606i	−0.312551	+	0.262261i
$75$	1.00000			0.115470
$76$	−4.07398	+	1.55007i	−0.467317	+	0.177805i
$77$	7.80840			0.889850
$78$	−3.83022	+	3.21394i	−0.433687	+	0.363907i
$79$	−9.06418	−	3.29909i	−1.01980	−	0.371177i	−0.222611	−	0.974907i	$-0.571458\pi$
$79$	−9.06418	−	3.29909i	−1.01980	−	0.371177i	−0.797188	+	0.603731i	$0.793680\pi$
$80$	−0.173648	+	0.984808i	−0.0194145	+	0.110105i
$81$	0.173648	+	0.984808i	0.0192942	+	0.109423i
$82$	−4.89306	+	1.78093i	−0.540348	+	0.196670i
$83$	−1.18479	+	2.05212i	−0.130048	+	0.225250i	−0.923695	−	0.383129i	$-0.874846\pi$
$83$	−1.18479	+	2.05212i	−0.130048	+	0.225250i	0.793647	+	0.608379i	$0.208180\pi$
$84$	0.705737	+	1.22237i	0.0770022	+	0.133372i
$85$	−5.94356	−	4.98724i	−0.644670	−	0.540942i
$86$	3.69459	+	3.10013i	0.398398	+	0.334296i
$87$	−0.879385	−	1.52314i	−0.0942800	−	0.163298i
$88$	−2.76604	+	4.79093i	−0.294861	+	0.510715i
$89$	13.3623	−	4.86348i	1.41640	−	0.515528i	0.483400	−	0.875399i	$-0.339402\pi$
$89$	13.3623	−	4.86348i	1.41640	−	0.515528i	0.933002	+	0.359871i	$0.117179\pi$
$90$	0.173648	+	0.984808i	0.0183041	+	0.103808i
$91$	−1.22550	+	6.95015i	−0.128467	+	0.728574i
$92$	−7.83022	−	2.84997i	−0.816357	−	0.297130i
$93$	−4.16250	+	3.49276i	−0.431632	+	0.362182i
$94$	−2.67499			−0.275904
$95$	−3.29813	+	2.84997i	−0.338381	+	0.292401i
$96$	−1.00000			−0.102062
$97$	11.1061	−	9.31910i	1.12765	−	0.946211i	0.128685	−	0.991686i	$-0.458924\pi$
$97$	11.1061	−	9.31910i	1.12765	−	0.946211i	0.998965	+	0.0454747i	$0.0144800\pi$
$98$	−4.70574	−	1.71275i	−0.475351	−	0.173014i
$99$	−0.960637	+	5.44804i	−0.0965477	+	0.547549i
$100$	0.173648	+	0.984808i	0.0173648	+	0.0984808i
$101$	16.8084	−	6.11776i	1.67250	−	0.608740i	0.680247	−	0.732983i	$-0.261873\pi$
$101$	16.8084	−	6.11776i	1.67250	−	0.608740i	0.992252	+	0.124244i	$0.0396505\pi$
$102$	3.87939	−	6.71929i	0.384116	−	0.665309i
$103$	2.46451	+	4.26865i	0.242835	+	0.420603i	0.961521	−	0.274732i	$-0.0885893\pi$
$103$	2.46451	+	4.26865i	0.242835	+	0.420603i	−0.718686	+	0.695335i	$0.755256\pi$
$104$	−3.83022	−	3.21394i	−0.375584	−	0.315153i
$105$	1.08125	+	0.907278i	0.105519	+	0.0885413i
$106$	4.40033	+	7.62159i	0.427398	+	0.740275i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	−0.939693	+	0.342020i	−0.0904220	+	0.0329109i
$109$	1.63816	+	9.29044i	0.156907	+	0.889863i	0.957022	+	0.290016i	$0.0936607\pi$
$109$	1.63816	+	9.29044i	0.156907	+	0.889863i	−0.800115	+	0.599847i	$0.795228\pi$
$110$	−0.960637	+	5.44804i	−0.0915932	+	0.519451i
$111$	−3.29813	−	1.20042i	−0.313045	−	0.113939i
$112$	−1.08125	+	0.907278i	−0.102169	+	0.0857297i
$113$	−11.2763			−1.06079			−0.530393	−	0.847752i	$-0.677956\pi$
$113$	−11.2763			−1.06079			−0.530393	+	0.847752i	$0.677956\pi$
$114$	−3.37939	−	2.75314i	−0.316508	−	0.257855i
$115$	−8.33275			−0.777033
$116$	1.34730	−	1.13052i	0.125093	−	0.104966i
$117$	−4.69846	−	1.71010i	−0.434373	−	0.158099i
$118$	1.18820	−	6.73859i	0.109382	−	0.620338i
$119$	−1.90167	−	10.7849i	−0.174326	−	0.988653i
$120$	−0.939693	+	0.342020i	−0.0857818	+	0.0312220i
$121$	−9.80200	+	16.9776i	−0.891091	+	1.54342i
$122$	4.82295	+	8.35359i	0.436649	+	0.756299i
$123$	−3.98886	−	3.34705i	−0.359663	−	0.301793i
$124$	−4.16250	−	3.49276i	−0.373804	−	0.313659i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−0.705737	+	1.22237i	−0.0628721	+	0.108898i
$127$	−10.5890	+	3.85408i	−0.939621	+	0.341994i	−0.766016	−	0.642821i	$-0.777764\pi$
$127$	−10.5890	+	3.85408i	−0.939621	+	0.341994i	−0.173605	+	0.984815i	$0.555542\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−0.837496	+	4.74968i	−0.0737374	+	0.418186i
$130$	−4.69846	−	1.71010i	−0.412082	−	0.149986i
$131$	−7.81702	+	6.55926i	−0.682976	+	0.573085i	−0.916874	−	0.399176i	$-0.869296\pi$
$131$	−7.81702	+	6.55926i	−0.682976	+	0.573085i	0.233898	+	0.972261i	$0.424852\pi$
$132$	−5.53209			−0.481507
$133$	−6.15183	+	0.0892091i	−0.533431	+	0.00773541i
$134$	6.90673			0.596650
$135$	−0.766044	+	0.642788i	−0.0659306	+	0.0553223i
$136$	7.29086	+	2.65366i	0.625186	+	0.227549i
$137$	−3.76651	+	21.3609i	−0.321795	+	1.82499i	0.209508	+	0.977807i	$0.432814\pi$
$137$	−3.76651	+	21.3609i	−0.321795	+	1.82499i	−0.531303	+	0.847182i	$0.678297\pi$
$138$	−1.44697	−	8.20616i	−0.123174	−	0.698554i
$139$	−4.01842	+	1.46258i	−0.340838	+	0.124055i	−0.506767	−	0.862083i	$-0.669160\pi$
$139$	−4.01842	+	1.46258i	−0.340838	+	0.124055i	0.165930	+	0.986138i	$0.446938\pi$
$140$	−0.705737	+	1.22237i	−0.0596457	+	0.103309i
$141$	−1.33750	−	2.31661i	−0.112637	−	0.195094i
$142$	1.59627	+	1.33943i	0.133956	+	0.112402i
$143$	−21.1891	−	17.7798i	−1.77192	−	1.48682i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.879385	−	1.52314i	0.0730290	−	0.126490i
$146$	0.800660	−	0.291416i	0.0662631	−	0.0241178i
$147$	−0.869585	−	4.93166i	−0.0717222	−	0.406757i
$148$	0.609470	−	3.45648i	0.0500982	−	0.284121i
$149$	10.7023	+	3.89533i	0.876769	+	0.319118i	0.740905	−	0.671610i	$-0.234397\pi$
$149$	10.7023	+	3.89533i	0.876769	+	0.319118i	0.135864	+	0.990727i	$0.456619\pi$
$150$	−0.766044	+	0.642788i	−0.0625473	+	0.0524834i
$151$	12.0155			0.977806			0.488903	−	0.872338i	$-0.337397\pi$
$151$	12.0155			0.977806			0.488903	+	0.872338i	$0.337397\pi$
$152$	2.12449	−	3.80612i	0.172319	−	0.308717i
$153$	7.75877			0.627259
$154$	−5.98158	+	5.01914i	−0.482010	+	0.404454i
$155$	−5.10607	−	1.85846i	−0.410129	−	0.149275i
$156$	0.868241	−	4.92404i	0.0695149	−	0.394239i
$157$	1.23308	+	6.99313i	0.0984104	+	0.558113i	0.993649	+	0.112526i	$0.0358940\pi$
$157$	1.23308	+	6.99313i	0.0984104	+	0.558113i	−0.895238	+	0.445587i	$0.852995\pi$
$158$	9.06418	−	3.29909i	0.721107	−	0.262462i
$159$	−4.40033	+	7.62159i	−0.348969	+	0.604432i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−9.00980	−	7.56012i	−0.710072	−	0.595821i
$162$	−0.766044	−	0.642788i	−0.0601861	−	0.0505022i
$163$	−0.694593	−	1.20307i	−0.0544047	−	0.0942317i	0.837540	−	0.546375i	$-0.183993\pi$
$163$	−0.694593	−	1.20307i	−0.0544047	−	0.0942317i	−0.891945	+	0.452144i	$0.850659\pi$
$164$	2.60354	−	4.50946i	0.203302	−	0.352130i
$165$	−5.19846	+	1.89209i	−0.404700	+	0.147299i
$166$	−0.411474	−	2.33359i	−0.0319366	−	0.181121i
$167$	2.88191	−	16.3441i	0.223009	−	1.26475i	−0.643446	−	0.765492i	$-0.722496\pi$
$167$	2.88191	−	16.3441i	0.223009	−	1.26475i	0.866455	−	0.499255i	$-0.166393\pi$
$168$	−1.32635	−	0.482753i	−0.102330	−	0.0372452i
$169$	9.19253	−	7.71345i	0.707118	−	0.593342i
$170$	7.75877			0.595071
$171$	0.694593	−	4.30320i	0.0531168	−	0.329074i
$172$	−4.82295			−0.367746
$173$	−6.68345	+	5.60808i	−0.508133	+	0.426374i	−0.860472	−	0.509498i	$-0.829831\pi$
$173$	−6.68345	+	5.60808i	−0.508133	+	0.426374i	0.352339	+	0.935873i	$0.385387\pi$
$174$	1.65270	+	0.601535i	0.125291	+	0.0456022i
$175$	−0.245100	+	1.39003i	−0.0185278	+	0.105076i
$176$	−0.960637	−	5.44804i	−0.0724107	−	0.410662i
$177$	6.42989	−	2.34029i	0.483300	−	0.175907i
$178$	−7.10994	+	12.3148i	−0.532912	+	0.923031i
$179$	9.80453	+	16.9819i	0.732825	+	1.26929i	0.955671	+	0.294436i	$0.0951319\pi$
$179$	9.80453	+	16.9819i	0.732825	+	1.26929i	−0.222846	+	0.974854i	$0.571535\pi$
$180$	−0.766044	−	0.642788i	−0.0570976	−	0.0479106i
$181$	5.66044	+	4.74968i	0.420738	+	0.353041i	0.828444	−	0.560073i	$-0.189227\pi$
$181$	5.66044	+	4.74968i	0.420738	+	0.353041i	−0.407706	+	0.913113i	$0.633671\pi$
$182$	−3.52869	−	6.11186i	−0.261564	−	0.453041i
$183$	−4.82295	+	8.35359i	−0.356523	+	0.617515i
$184$	7.83022	−	2.84997i	0.577252	−	0.210102i
$185$	−0.609470	−	3.45648i	−0.0448092	−	0.254125i
$186$	0.943563	−	5.35121i	0.0691854	−	0.392370i
$187$	40.3337	+	14.6803i	2.94949	+	1.07353i
$188$	2.04916	−	1.71945i	0.149451	−	0.125404i
$189$	−1.41147			−0.102670
$190$	0.694593	−	4.30320i	0.0503911	−	0.312187i
$191$	−18.0993			−1.30962			−0.654808	−	0.755795i	$-0.727251\pi$
$191$	−18.0993			−1.30962			−0.654808	+	0.755795i	$0.727251\pi$
$192$	0.766044	−	0.642788i	0.0552845	−	0.0463892i
$193$	−10.8229	−	3.93923i	−0.779053	−	0.283552i	−0.0782752	−	0.996932i	$-0.524941\pi$
$193$	−10.8229	−	3.93923i	−0.779053	−	0.283552i	−0.700778	+	0.713380i	$0.747164\pi$
$194$	−2.51754	+	14.2777i	−0.180749	+	1.02508i
$195$	−0.868241	−	4.92404i	−0.0621760	−	0.352618i
$196$	4.70574	−	1.71275i	0.336124	−	0.122339i
$197$	−11.5103	+	19.9364i	−0.820073	+	1.42041i	0.0855550	+	0.996333i	$0.472734\pi$
$197$	−11.5103	+	19.9364i	−0.820073	+	1.42041i	−0.905628	+	0.424074i	$0.860600\pi$
$198$	−2.76604	−	4.79093i	−0.196574	−	0.340477i
$199$	−18.7442	−	15.7283i	−1.32874	−	1.11495i	−0.984370	−	0.176115i	$-0.943647\pi$
$199$	−18.7442	−	15.7283i	−1.32874	−	1.11495i	−0.344373	−	0.938833i	$-0.611908\pi$
$200$	−0.766044	−	0.642788i	−0.0541675	−	0.0454519i
$201$	3.45336	+	5.98140i	0.243581	+	0.421895i
$202$	−8.94356	+	15.4907i	−0.629267	+	1.08992i
$203$	2.33275	−	0.849051i	0.163727	−	0.0595917i
$204$	1.34730	+	7.64090i	0.0943296	+	0.534970i
$205$	0.904200	−	5.12797i	0.0631521	−	0.358153i
$206$	−4.63176	−	1.68582i	−0.322710	−	0.117457i
$207$	6.38326	−	5.35619i	0.443667	−	0.372281i
$208$	5.00000			0.346688
$209$	11.7528	−	21.0558i	0.812961	−	1.45646i
$210$	−1.41147			−0.0974010
$211$	6.31386	−	5.29796i	0.434664	−	0.364727i	−0.399044	−	0.916932i	$-0.630658\pi$
$211$	6.31386	−	5.29796i	0.434664	−	0.364727i	0.833708	+	0.552205i	$0.186213\pi$
$212$	−8.26991	−	3.01000i	−0.567980	−	0.206728i
$213$	−0.361844	+	2.05212i	−0.0247932	+	0.140609i
$214$	−2.08378	−	11.8177i	−0.142444	−	0.807841i
$215$	−4.53209	+	1.64955i	−0.309086	+	0.112498i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−3.83481	−	6.64208i	−0.260324	−	0.450894i
$218$	−7.22668	−	6.06391i	−0.489453	−	0.410700i
$219$	0.652704	+	0.547683i	0.0441056	+	0.0370090i
$220$	−2.76604	−	4.79093i	−0.186487	−	0.323004i
$221$	−19.3969	+	33.5965i	−1.30478	+	2.25994i
$222$	3.29813	−	1.20042i	0.221356	−	0.0805671i
$223$	2.85457	+	16.1891i	0.191156	+	1.08410i	0.917787	+	0.397073i	$0.129974\pi$
$223$	2.85457	+	16.1891i	0.191156	+	1.08410i	−0.726631	+	0.687028i	$0.758915\pi$
$224$	0.245100	−	1.39003i	0.0163764	−	0.0928753i
$225$	−0.939693	−	0.342020i	−0.0626462	−	0.0228013i
$226$	8.63816	−	7.24827i	0.574602	−	0.482148i
$227$	19.3209			1.28237			0.641186	−	0.767385i	$-0.278443\pi$
$227$	19.3209			1.28237			0.641186	+	0.767385i	$0.278443\pi$
$228$	4.35844	−	0.0632028i	0.288645	−	0.00418571i
$229$	13.2763			0.877323			0.438662	−	0.898652i	$-0.355453\pi$
$229$	13.2763			0.877323			0.438662	+	0.898652i	$0.355453\pi$
$230$	6.38326	−	5.35619i	0.420899	−	0.353177i
$231$	−7.33750	−	2.67063i	−0.482772	−	0.175715i
$232$	−0.305407	+	1.73205i	−0.0200510	+	0.113715i
$233$	1.14796	+	6.51038i	0.0752051	+	0.426509i	0.999044	+	0.0437266i	$0.0139231\pi$
$233$	1.14796	+	6.51038i	0.0752051	+	0.426509i	−0.923838	+	0.382783i	$0.874966\pi$
$234$	4.69846	−	1.71010i	0.307148	−	0.111793i
$235$	1.33750	−	2.31661i	0.0872486	−	0.151119i
$236$	3.42127	+	5.92582i	0.222706	+	0.385738i
$237$	7.38919	+	6.20026i	0.479979	+	0.402750i
$238$	8.38919	+	7.03936i	0.543790	+	0.456294i
$239$	−2.20708	−	3.82278i	−0.142764	−	0.247275i	0.785772	−	0.618516i	$-0.212266\pi$
$239$	−2.20708	−	3.82278i	−0.142764	−	0.247275i	−0.928537	+	0.371241i	$0.878932\pi$
$240$	0.500000	−	0.866025i	0.0322749	−	0.0559017i
$241$	−11.8833	+	4.32515i	−0.765468	+	0.278607i	−0.695099	−	0.718914i	$-0.744640\pi$
$241$	−11.8833	+	4.32515i	−0.765468	+	0.278607i	−0.0703683	+	0.997521i	$0.522417\pi$
$242$	−3.40420	−	19.3062i	−0.218830	−	1.24105i
$243$	0.173648	−	0.984808i	0.0111395	−	0.0631754i
$244$	−9.06418	−	3.29909i	−0.580275	−	0.211203i
$245$	3.83615	−	3.21891i	0.245083	−	0.205649i
$246$	5.20708			0.331991
$247$	16.8969	+	13.7657i	1.07513	+	0.875889i
$248$	5.43376			0.345044
$249$	1.81521	−	1.52314i	0.115034	−	0.0965251i
$250$	−0.939693	−	0.342020i	−0.0594314	−	0.0216313i
$251$	2.51589	−	14.2683i	0.158802	−	0.900609i	−0.796426	−	0.604736i	$-0.793278\pi$
$251$	2.51589	−	14.2683i	0.158802	−	0.900609i	0.955227	−	0.295873i	$-0.0956104\pi$
$252$	−0.245100	−	1.39003i	−0.0154398	−	0.0875637i
$253$	43.3175	−	15.7663i	2.72335	−	0.991217i
$254$	5.63429	−	9.75887i	0.353527	−	0.612326i
$255$	3.87939	+	6.71929i	0.242937	+	0.420778i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	20.1138	+	16.8775i	1.25466	+	1.05279i	0.996229	+	0.0867603i	$0.0276514\pi$
$257$	20.1138	+	16.8775i	1.25466	+	1.05279i	0.258436	+	0.966028i	$0.416793\pi$
$258$	−2.41147	−	4.17680i	−0.150132	−	0.260036i
$259$	2.47700	−	4.29028i	0.153913	−	0.266585i
$260$	4.69846	−	1.71010i	0.291386	−	0.106056i
$261$	0.305407	+	1.73205i	0.0189042	+	0.107211i
$262$	1.77197	−	10.0494i	0.109473	−	0.620852i
$263$	18.6322	+	6.78158i	1.14891	+	0.418170i	0.845124	−	0.534570i	$-0.179526\pi$
$263$	18.6322	+	6.78158i	1.14891	+	0.418170i	0.303788	+	0.952740i	$0.401749\pi$
$264$	4.23783	−	3.55596i	0.260820	−	0.218854i
$265$	−8.80066			−0.540620
$266$	4.65523	−	4.02266i	0.285430	−	0.246645i
$267$	−14.2199			−0.870242
$268$	−5.29086	+	4.43956i	−0.323191	+	0.271189i
$269$	−24.6732	−	8.98032i	−1.50435	−	0.547540i	−0.547170	−	0.837021i	$-0.684295\pi$
$269$	−24.6732	−	8.98032i	−1.50435	−	0.547540i	−0.957184	+	0.289481i	$0.906517\pi$
$270$	0.173648	−	0.984808i	0.0105679	−	0.0599335i
$271$	1.75103	+	9.93058i	0.106367	+	0.603240i	0.990665	+	0.136317i	$0.0435265\pi$
$271$	1.75103	+	9.93058i	0.106367	+	0.603240i	−0.884298	+	0.466923i	$0.845362\pi$
$272$	−7.29086	+	2.65366i	−0.442073	+	0.160902i
$273$	3.52869	−	6.11186i	0.213566	−	0.369907i
$274$	−10.8452	−	18.7845i	−0.655185	−	1.13481i
$275$	−4.23783	−	3.55596i	−0.255551	−	0.214432i
$276$	6.38326	+	5.35619i	0.384227	+	0.322405i
$277$	−9.01754	−	15.6188i	−0.541812	−	0.938445i	−0.998800	−	0.0489725i	$-0.984405\pi$
$277$	−9.01754	−	15.6188i	−0.541812	−	0.938445i	0.456989	−	0.889473i	$-0.348928\pi$
$278$	2.13816	−	3.70339i	0.128238	−	0.222115i
$279$	5.10607	−	1.85846i	0.305692	−	0.111263i
$280$	−0.245100	−	1.39003i	−0.0146475	−	0.0830702i
$281$	−2.13903	+	12.1311i	−0.127604	+	0.723678i	0.852123	+	0.523341i	$0.175315\pi$
$281$	−2.13903	+	12.1311i	−0.127604	+	0.723678i	−0.979727	+	0.200337i	$0.935796\pi$
$282$	2.51367	+	0.914901i	0.149687	+	0.0544816i
$283$	0.652704	−	0.547683i	0.0387992	−	0.0325564i	−0.623182	−	0.782077i	$-0.714160\pi$
$283$	0.652704	−	0.547683i	0.0387992	−	0.0325564i	0.661981	+	0.749521i	$0.269716\pi$
$284$	−2.08378			−0.123649
$285$	4.07398	−	1.55007i	0.241322	−	0.0918180i
$286$	27.6604			1.63560
$287$	5.63017	−	4.72427i	0.332338	−	0.278865i
$288$	0.939693	+	0.342020i	0.0553719	+	0.0201537i
$289$	7.50134	−	42.5422i	0.441256	−	2.50248i
$290$	0.305407	+	1.73205i	0.0179341	+	0.101710i
$291$	−13.6236	+	4.95859i	−0.798630	+	0.290678i
$292$	−0.426022	+	0.737892i	−0.0249311	+	0.0431819i
$293$	3.13950	+	5.43777i	0.183412	+	0.317678i	0.943040	−	0.332679i	$-0.107953\pi$
$293$	3.13950	+	5.43777i	0.183412	+	0.317678i	−0.759629	+	0.650357i	$0.774619\pi$
$294$	3.83615	+	3.21891i	0.223729	+	0.187731i
$295$	5.24170	+	4.39831i	0.305183	+	0.256079i
$296$	1.75490	+	3.03958i	0.102001	+	0.176672i
$297$	2.76604	−	4.79093i	0.160502	−	0.277998i
$298$	−10.7023	+	3.89533i	−0.619970	+	0.225650i
$299$	7.23483	+	41.0308i	0.418401	+	2.37287i
$300$	0.173648	−	0.984808i	0.0100256	−	0.0568579i
$301$	−6.39693	−	2.32829i	−0.368713	−	0.134200i
$302$	−9.20439	+	7.72340i	−0.529653	+	0.444432i
$303$	−17.8871			−1.02759
$304$	0.819078	+	4.28125i	0.0469773	+	0.245547i
$305$	−9.64590			−0.552322
$306$	−5.94356	+	4.98724i	−0.339771	+	0.285102i
$307$	−22.0624	−	8.03007i	−1.25917	−	0.458300i	−0.375679	−	0.926750i	$-0.622590\pi$
$307$	−22.0624	−	8.03007i	−1.25917	−	0.458300i	−0.883490	+	0.468450i	$0.844813\pi$
$308$	1.35591	−	7.68977i	0.0772604	−	0.438165i
$309$	−0.855914	−	4.85413i	−0.0486913	−	0.276142i
$310$	5.10607	−	1.85846i	0.290005	−	0.105553i
$311$	6.10607	−	10.5760i	0.346243	−	0.599711i	−0.639336	−	0.768928i	$-0.720791\pi$
$311$	6.10607	−	10.5760i	0.346243	−	0.599711i	0.985579	+	0.169217i	$0.0541238\pi$
$312$	2.50000	+	4.33013i	0.141535	+	0.245145i
$313$	21.8949	+	18.3720i	1.23757	+	1.03845i	0.997710	+	0.0676382i	$0.0215464\pi$
$313$	21.8949	+	18.3720i	1.23757	+	1.03845i	0.239861	+	0.970807i	$0.422898\pi$
$314$	−5.43969	−	4.56444i	−0.306980	−	0.257586i
$315$	−0.705737	−	1.22237i	−0.0397638	−	0.0688729i
$316$	−4.82295	+	8.35359i	−0.271312	+	0.469926i
$317$	7.05051	−	2.56617i	0.395996	−	0.144131i	−0.136344	−	0.990662i	$-0.543535\pi$
$317$	7.05051	−	2.56617i	0.395996	−	0.144131i	0.532340	+	0.846531i	$0.321313\pi$
$318$	−1.52822	−	8.66696i	−0.0856982	−	0.486019i
$319$	−1.68954	+	9.58186i	−0.0945961	+	0.536481i
$320$	0.939693	+	0.342020i	0.0525304	+	0.0191195i
$321$	9.19253	−	7.71345i	0.513077	−	0.430523i
$322$	11.7615			0.655440
$323$	−31.9445	−	11.1050i	−1.77744	−	0.617899i
$324$	1.00000			0.0555556
$325$	3.83022	−	3.21394i	0.212463	−	0.178277i
$326$	1.30541	+	0.475129i	0.0722998	+	0.0263150i
$327$	1.63816	−	9.29044i	0.0905902	−	0.513763i
$328$	0.904200	+	5.12797i	0.0499261	+	0.283145i
$329$	3.54798	−	1.29136i	0.195607	−	0.0711950i
$330$	2.76604	−	4.79093i	0.152266	−	0.263732i
$331$	4.33615	+	7.51044i	0.238336	+	0.412811i	0.960237	−	0.279186i	$-0.0900646\pi$
$331$	4.33615	+	7.51044i	0.238336	+	0.412811i	−0.721901	+	0.691997i	$0.756731\pi$
$332$	1.81521	+	1.52314i	0.0996225	+	0.0835932i
$333$	2.68866	+	2.25606i	0.147338	+	0.123631i
$334$	8.29813	+	14.3728i	0.454054	+	0.786444i
$335$	−3.45336	+	5.98140i	−0.188677	+	0.326799i
$336$	1.32635	−	0.482753i	0.0723584	−	0.0263363i
$337$	−2.60307	−	14.7628i	−0.141798	−	0.804179i	−0.969882	−	0.243575i	$-0.921680\pi$
$337$	−2.60307	−	14.7628i	−0.141798	−	0.804179i	0.828084	−	0.560604i	$-0.189431\pi$
$338$	−2.08378	+	11.8177i	−0.113343	+	0.642798i
$339$	10.5963	+	3.85673i	0.575510	+	0.209469i
$340$	−5.94356	+	4.98724i	−0.322335	+	0.270471i
$341$	30.0601			1.62784
$342$	2.23396	+	3.74292i	0.120798	+	0.202394i
$343$	16.9486			0.915139
$344$	3.69459	−	3.10013i	0.199199	−	0.167148i
$345$	7.83022	+	2.84997i	0.421565	+	0.153437i
$346$	1.51501	−	8.59208i	0.0814477	−	0.461913i
$347$	−5.18984	−	29.4331i	−0.278605	−	1.58005i	−0.727271	−	0.686350i	$-0.759212\pi$
$347$	−5.18984	−	29.4331i	−0.278605	−	1.58005i	0.448666	−	0.893700i	$-0.351899\pi$
$348$	−1.65270	+	0.601535i	−0.0885942	+	0.0322457i
$349$	−3.53209	+	6.11776i	−0.189068	+	0.327476i	−0.944940	−	0.327244i	$-0.893880\pi$
$349$	−3.53209	+	6.11776i	−0.189068	+	0.327476i	0.755872	+	0.654720i	$0.227213\pi$
$350$	−0.705737	−	1.22237i	−0.0377232	−	0.0653386i
$351$	3.83022	+	3.21394i	0.204442	+	0.171547i
$352$	4.23783	+	3.55596i	0.225877	+	0.189533i
$353$	−7.43376	−	12.8757i	−0.395659	−	0.685302i	0.597526	−	0.801850i	$-0.296151\pi$
$353$	−7.43376	−	12.8757i	−0.395659	−	0.685302i	−0.993185	+	0.116548i	$0.962817\pi$
$354$	−3.42127	+	5.92582i	−0.181839	+	0.314954i
$355$	−1.95811	+	0.712694i	−0.103926	+	0.0378259i
$356$	−2.46926	−	14.0038i	−0.130870	−	0.742202i
$357$	−1.90167	+	10.7849i	−0.100647	+	0.570799i
$358$	−18.4265	−	6.70669i	−0.973870	−	0.354460i
$359$	−7.26083	+	6.09256i	−0.383212	+	0.321553i	−0.813962	−	0.580918i	$-0.802694\pi$
$359$	−7.26083	+	6.09256i	−0.383212	+	0.321553i	0.430750	+	0.902471i	$0.358249\pi$
$360$	1.00000			0.0527046
$361$	−9.01889	+	16.7230i	−0.474678	+	0.880159i
$362$	−7.38919			−0.388367
$363$	15.0175	−	12.6012i	0.788216	−	0.661392i
$364$	6.63176	+	2.41376i	0.347599	+	0.126516i
$365$	−0.147956	+	0.839100i	−0.00774437	+	0.0439205i
$366$	−1.67499	−	9.49935i	−0.0875533	−	0.496539i
$367$	−2.87046	+	1.04476i	−0.149837	+	0.0545362i	−0.415850	−	0.909433i	$-0.636516\pi$
$367$	−2.87046	+	1.04476i	−0.149837	+	0.0545362i	0.266013	+	0.963969i	$0.414294\pi$
$368$	−4.16637	+	7.21637i	−0.217187	+	0.376179i
$369$	2.60354	+	4.50946i	0.135535	+	0.234753i
$370$	2.68866	+	2.25606i	0.139777	+	0.117287i
$371$	−9.51573	−	7.98465i	−0.494032	−	0.414542i
$372$	2.71688	+	4.70578i	0.140864	+	0.243983i
$373$	−5.66890	+	9.81882i	−0.293525	+	0.508399i	−0.974641	−	0.223776i	$-0.928162\pi$
$373$	−5.66890	+	9.81882i	−0.293525	+	0.508399i	0.681116	+	0.732175i	$0.261495\pi$
$374$	−40.3337	+	14.6803i	−2.08561	+	0.759098i
$375$	−0.173648	−	0.984808i	−0.00896715	−	0.0508553i
$376$	−0.464508	+	2.63435i	−0.0239551	+	0.135856i
$377$	−8.26352	−	3.00767i	−0.425593	−	0.154903i
$378$	1.08125	−	0.907278i	0.0556136	−	0.0466653i
$379$	14.4439			0.741932			0.370966	−	0.928647i	$-0.379027\pi$
$379$	14.4439			0.741932			0.370966	+	0.928647i	$0.379027\pi$
$380$	2.23396	+	3.74292i	0.114600	+	0.192008i
$381$	11.2686			0.577306
$382$	13.8648	−	11.6340i	0.709387	−	0.595246i
$383$	−12.0312	−	4.37900i	−0.614766	−	0.223757i	0.0158212	−	0.999875i	$-0.494964\pi$
$383$	−12.0312	−	4.37900i	−0.614766	−	0.223757i	−0.630587	+	0.776118i	$0.717186\pi$
$384$	−0.173648	+	0.984808i	−0.00886145	+	0.0502558i
$385$	−1.35591	−	7.68977i	−0.0691038	−	0.391907i
$386$	10.8229	−	3.93923i	0.550874	−	0.200502i
$387$	2.41147	−	4.17680i	0.122582	−	0.212318i
$388$	−7.24897	−	12.5556i	−0.368011	−	0.637413i
$389$	2.44562	+	2.05212i	0.123998	+	0.104047i	0.702678	−	0.711508i	$-0.251987\pi$
$389$	2.44562	+	2.05212i	0.123998	+	0.104047i	−0.578680	+	0.815555i	$0.696432\pi$
$390$	3.83022	+	3.21394i	0.193951	+	0.162744i
$391$	−32.3259	−	55.9902i	−1.63479	−	2.83154i
$392$	−2.50387	+	4.33683i	−0.126465	+	0.219043i
$393$	9.58899	−	3.49011i	0.483701	−	0.176053i
$394$	−3.99747	−	22.6708i	−0.201390	−	1.14214i
$395$	−1.67499	+	9.49935i	−0.0842780	+	0.477964i
$396$	5.19846	+	1.89209i	0.261233	+	0.0950809i
$397$	1.17365	−	0.984808i	0.0589037	−	0.0494261i	−0.612861	−	0.790191i	$-0.709981\pi$
$397$	1.17365	−	0.984808i	0.0589037	−	0.0494261i	0.671764	+	0.740765i	$0.265537\pi$
$398$	24.4688			1.22651
$399$	5.81134	+	2.02022i	0.290931	+	0.101137i
$400$	1.00000			0.0500000
$401$	8.39961	−	7.04811i	0.419457	−	0.351966i	−0.408500	−	0.912758i	$-0.633948\pi$
$401$	8.39961	−	7.04811i	0.419457	−	0.351966i	0.827956	+	0.560792i	$0.189503\pi$
$402$	−6.49020	−	2.36224i	−0.323702	−	0.117818i
$403$	−4.71782	+	26.7561i	−0.235011	+	1.33281i
$404$	−3.10607	−	17.6154i	−0.154533	−	0.876398i
$405$	0.939693	−	0.342020i	0.0466937	−	0.0169951i
$406$	−1.24123	+	2.14987i	−0.0616012	+	0.106696i
$407$	9.70826	+	16.8152i	0.481221	+	0.833499i
$408$	−5.94356	−	4.98724i	−0.294250	−	0.246905i
$409$	−19.7153	−	16.5431i	−0.974858	−	0.818003i	0.00844744	−	0.999964i	$-0.497311\pi$
$409$	−19.7153	−	16.5431i	−0.974858	−	0.818003i	−0.983306	+	0.181961i	$0.941756\pi$
$410$	2.60354	+	4.50946i	0.128580	+	0.222707i
$411$	10.8452	−	18.7845i	0.534956	−	0.926571i
$412$	4.63176	−	1.68582i	0.228190	−	0.0830545i
$413$	1.67711	+	9.51135i	0.0825251	+	0.468023i
$414$	−1.44697	+	8.20616i	−0.0711145	+	0.403311i
$415$	2.22668	+	0.810446i	0.109304	+	0.0397832i
$416$	−3.83022	+	3.21394i	−0.187792	+	0.157576i
$417$	4.27631			0.209412
$418$	4.53121	+	23.6843i	0.221629	+	1.15844i
$419$	−11.7811			−0.575542			−0.287771	−	0.957699i	$-0.592914\pi$
$419$	−11.7811			−0.575542			−0.287771	+	0.957699i	$0.592914\pi$
$420$	1.08125	−	0.907278i	0.0527597	−	0.0442706i
$421$	−4.10607	−	1.49449i	−0.200117	−	0.0728368i	0.240017	−	0.970769i	$-0.422847\pi$
$421$	−4.10607	−	1.49449i	−0.200117	−	0.0728368i	−0.440134	+	0.897932i	$0.645069\pi$
$422$	−1.43124	+	8.11695i	−0.0696715	+	0.395127i
$423$	0.464508	+	2.63435i	0.0225851	+	0.128087i
$424$	8.26991	−	3.01000i	0.401623	−	0.146179i
$425$	−3.87939	+	6.71929i	−0.188178	+	0.325934i
$426$	−1.04189	−	1.80460i	−0.0504797	−	0.0874334i
$427$	−10.4296	−	8.75151i	−0.504726	−	0.423515i
$428$	9.19253	+	7.71345i	0.444338	+	0.372844i
$429$	13.8302	+	23.9546i	0.667729	+	1.15654i
$430$	2.41147	−	4.17680i	0.116292	−	0.201423i
$431$	−4.02229	+	1.46399i	−0.193747	+	0.0705181i	−0.437071	−	0.899427i	$-0.643984\pi$
$431$	−4.02229	+	1.46399i	−0.193747	+	0.0705181i	0.243324	+	0.969945i	$0.421762\pi$
$432$	0.173648	+	0.984808i	0.00835465	+	0.0473816i
$433$	−5.50980	+	31.2476i	−0.264784	+	1.50167i	0.504865	+	0.863198i	$0.331542\pi$
$433$	−5.50980	+	31.2476i	−0.264784	+	1.50167i	−0.769649	+	0.638467i	$0.779569\pi$
$434$	7.20708	+	2.62316i	0.345951	+	0.125916i
$435$	−1.34730	+	1.13052i	−0.0645979	+	0.0542041i
$436$	9.43376			0.451795
$437$	−33.9474	+	12.9163i	−1.62393	+	0.617871i
$438$	−0.852044			−0.0407122
$439$	12.9513	−	10.8674i	0.618132	−	0.518674i	−0.279084	−	0.960267i	$-0.590031\pi$
$439$	12.9513	−	10.8674i	0.618132	−	0.518674i	0.897216	+	0.441592i	$0.145586\pi$
$440$	5.19846	+	1.89209i	0.247827	+	0.0902017i
$441$	−0.869585	+	4.93166i	−0.0414088	+	0.234841i
$442$	−6.73648	−	38.2045i	−0.320422	−	1.81720i
$443$	−12.3182	+	4.48346i	−0.585255	+	0.213016i	−0.617641	−	0.786460i	$-0.711912\pi$
$443$	−12.3182	+	4.48346i	−0.585255	+	0.213016i	0.0323860	+	0.999475i	$0.489689\pi$
$444$	−1.75490	+	3.03958i	−0.0832839	+	0.144252i
$445$	−7.10994	−	12.3148i	−0.337043	−	0.583776i
$446$	−12.5929	−	10.5667i	−0.596289	−	0.500346i
$447$	−8.72462	−	7.32083i	−0.412660	−	0.346263i
$448$	0.705737	+	1.22237i	0.0333429	+	0.0577517i
$449$	−4.36231	+	7.55574i	−0.205870	+	0.356578i	−0.950410	−	0.311001i	$-0.899336\pi$
$449$	−4.36231	+	7.55574i	−0.205870	+	0.356578i	0.744539	+	0.667578i	$0.232669\pi$
$450$	0.939693	−	0.342020i	0.0442975	−	0.0161230i
$451$	5.00212	+	28.3684i	0.235540	+	1.33582i
$452$	−1.95811	+	11.1050i	−0.0921018	+	0.522335i
$453$	−11.2909	−	4.10954i	−0.530491	−	0.193083i
$454$	−14.8007	+	12.4192i	−0.694629	+	0.582863i
$455$	7.05737			0.330855
$456$	−3.29813	+	2.84997i	−0.154449	+	0.133462i
$457$	9.54664			0.446573			0.223286	−	0.974753i	$-0.428321\pi$
$457$	9.54664			0.446573			0.223286	+	0.974753i	$0.428321\pi$
$458$	−10.1702	+	8.53385i	−0.475224	+	0.398761i
$459$	−7.29086	−	2.65366i	−0.340308	−	0.123862i
$460$	−1.44697	+	8.20616i	−0.0674652	+	0.382614i
$461$	1.36453	+	7.73865i	0.0635526	+	0.360425i	0.999955	+	0.00949640i	$0.00302284\pi$
$461$	1.36453	+	7.73865i	0.0635526	+	0.360425i	−0.936402	+	0.350928i	$0.885866\pi$
$462$	7.33750	−	2.67063i	0.341371	−	0.124249i
$463$	2.55896	−	4.43225i	0.118925	−	0.205984i	−0.800417	−	0.599444i	$-0.795388\pi$
$463$	2.55896	−	4.43225i	0.118925	−	0.205984i	0.919342	+	0.393459i	$0.128722\pi$
$464$	−0.879385	−	1.52314i	−0.0408244	−	0.0707100i
$465$	4.16250	+	3.49276i	0.193031	+	0.161973i
$466$	−5.06418	−	4.24935i	−0.234594	−	0.196847i
$467$	6.35504	+	11.0072i	0.294076	+	0.509355i	0.974770	−	0.223214i	$-0.0716548\pi$
$467$	6.35504	+	11.0072i	0.294076	+	0.509355i	−0.680693	+	0.732568i	$0.738321\pi$
$468$	−2.50000	+	4.33013i	−0.115563	+	0.200160i
$469$	−9.16075	+	3.33424i	−0.423004	+	0.153961i
$470$	0.464508	+	2.63435i	0.0214261	+	0.121514i
$471$	1.23308	−	6.99313i	0.0568172	−	0.322227i
$472$	−6.42989	−	2.34029i	−0.295960	−	0.107721i
$473$	20.4388	−	17.1502i	0.939778	−	0.788567i
$474$	−9.64590			−0.443051
$475$	3.37939	+	2.75314i	0.155057	+	0.126323i
$476$	−10.9513			−0.501952
$477$	6.74170	−	5.65695i	0.308681	−	0.259014i
$478$	4.14796	+	1.50973i	0.189723	+	0.0690536i
$479$	2.26352	−	12.8370i	0.103423	−	0.586540i	−0.888416	−	0.459040i	$-0.848194\pi$
$479$	2.26352	−	12.8370i	0.103423	−	0.586540i	0.991839	−	0.127500i	$-0.0406953\pi$
$480$	0.173648	+	0.984808i	0.00792592	+	0.0449501i
$481$	−16.4907	+	6.00211i	−0.751910	+	0.273673i
$482$	6.32295	−	10.9517i	0.288002	−	0.498835i
$483$	5.88073	+	10.1857i	0.267582	+	0.463466i
$484$	15.0175	+	12.6012i	0.682615	+	0.572782i
$485$	−11.1061	−	9.31910i	−0.504301	−	0.423158i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−2.59967	+	4.50276i	−0.117802	+	0.204040i	−0.918896	−	0.394499i	$-0.870918\pi$
$487$	−2.59967	+	4.50276i	−0.117802	+	0.204040i	0.801094	+	0.598538i	$0.204252\pi$
$488$	9.06418	−	3.29909i	0.410316	−	0.149343i
$489$	0.241230	+	1.36808i	0.0109088	+	0.0618667i
$490$	−0.869585	+	4.93166i	−0.0392838	+	0.222790i
$491$	−6.07145	−	2.20983i	−0.274001	−	0.0997281i	0.201365	−	0.979516i	$-0.435462\pi$
$491$	−6.07145	−	2.20983i	−0.274001	−	0.0997281i	−0.475366	+	0.879788i	$0.657684\pi$
$492$	−3.98886	+	3.34705i	−0.179832	+	0.150897i
$493$	13.6459			0.614580
$494$	−21.7922	+	0.316014i	−0.980478	+	0.0142181i
$495$	5.53209			0.248649
$496$	−4.16250	+	3.49276i	−0.186902	+	0.156829i
$497$	−2.76382	−	1.00595i	−0.123974	−	0.0451230i
$498$	−0.411474	+	2.33359i	−0.0184386	+	0.104570i
$499$	−4.96105	−	28.1355i	−0.222087	−	1.25952i	−0.868176	−	0.496256i	$-0.834708\pi$
$499$	−4.96105	−	28.1355i	−0.222087	−	1.25952i	0.646089	−	0.763262i	$-0.276403\pi$
$500$	0.939693	−	0.342020i	0.0420243	−	0.0152956i
$501$	−8.29813	+	14.3728i	−0.370733	+	0.642129i
$502$	7.24422	+	12.5474i	0.323325	+	0.560016i
$503$	9.40807	+	7.89431i	0.419485	+	0.351990i	0.827967	−	0.560777i	$-0.189497\pi$
$503$	9.40807	+	7.89431i	0.419485	+	0.351990i	−0.408482	+	0.912766i	$0.633942\pi$
$504$	1.08125	+	0.907278i	0.0481628	+	0.0404134i
$505$	−8.94356	−	15.4907i	−0.397983	−	0.689327i
$506$	−23.0488	+	39.9216i	−1.02464	+	1.77473i
$507$	−11.2763	+	4.10424i	−0.500799	+	0.182276i
$508$	1.95677	+	11.0974i	0.0868175	+	0.492366i
$509$	5.26588	−	29.8643i	0.233406	−	1.32371i	−0.612538	−	0.790441i	$-0.709851\pi$
$509$	5.26588	−	29.8643i	0.233406	−	1.32371i	0.845944	−	0.533271i	$-0.179037\pi$
$510$	−7.29086	−	2.65366i	−0.322845	−	0.117506i
$511$	−0.921274	+	0.773041i	−0.0407548	+	0.0341973i
$512$	−1.00000			−0.0441942
$513$	−2.12449	+	3.80612i	−0.0937983	+	0.168044i
$514$	−26.2567			−1.15813
$515$	3.77584	−	3.16831i	0.166384	−	0.139612i
$516$	4.53209	+	1.64955i	0.199514	+	0.0726172i
$517$	−2.56970	+	14.5735i	−0.113015	+	0.640941i
$518$	0.860252	+	4.87873i	0.0377973	+	0.214359i
$519$	8.19846	−	2.98400i	0.359873	−	0.130983i
$520$	−2.50000	+	4.33013i	−0.109632	+	0.189889i
$521$	−16.1480	−	27.9691i	−0.707455	−	1.22535i	−0.965798	−	0.259295i	$-0.916510\pi$
$521$	−16.1480	−	27.9691i	−0.707455	−	1.22535i	0.258344	−	0.966053i	$-0.416823\pi$
$522$	−1.34730	−	1.13052i	−0.0589696	−	0.0494813i
$523$	20.6236	+	17.3053i	0.901807	+	0.756706i	0.970543	−	0.240929i	$-0.0774520\pi$
$523$	20.6236	+	17.3053i	0.901807	+	0.756706i	−0.0687354	+	0.997635i	$0.521896\pi$
$524$	5.10220	+	8.83726i	0.222890	+	0.386058i
$525$	0.705737	−	1.22237i	0.0308009	−	0.0533487i
$526$	−18.6322	+	6.78158i	−0.812404	+	0.295691i
$527$	−7.32089	−	41.5188i	−0.318903	−	1.80859i
$528$	−0.960637	+	5.44804i	−0.0418064	+	0.237096i
$529$	−43.6343	−	15.8816i	−1.89715	−	0.690504i
$530$	6.74170	−	5.65695i	0.292841	−	0.245722i
$531$	−6.84255			−0.296941
$532$	−0.980400	+	6.07386i	−0.0425057	+	0.263335i
$533$	−26.0354			−1.12772
$534$	10.8931	−	9.14036i	0.471389	−	0.395542i
$535$	11.2763	+	4.10424i	0.487517	+	0.177442i
$536$	1.19934	−	6.80180i	0.0518036	−	0.293793i
$537$	−3.40508	−	19.3112i	−0.146940	−	0.833338i
$538$	24.6732	−	8.98032i	1.06374	−	0.387169i
$539$	−13.8516	+	23.9917i	−0.596632	+	1.03340i
$540$	0.500000	+	0.866025i	0.0215166	+	0.0372678i
$541$	11.9855	+	10.0570i	0.515295	+	0.432384i	0.862988	−	0.505225i	$-0.168590\pi$
$541$	11.9855	+	10.0570i	0.515295	+	0.432384i	−0.347693	+	0.937608i	$0.613035\pi$
$542$	−7.72462	−	6.48173i	−0.331801	−	0.278414i
$543$	−3.69459	−	6.39922i	−0.158550	−	0.274617i
$544$	3.87939	−	6.71929i	0.166327	−	0.288087i
$545$	8.86484	−	3.22654i	0.379728	−	0.138210i
$546$	1.22550	+	6.95015i	0.0524465	+	0.297439i
$547$	−6.21987	+	35.2747i	−0.265943	+	1.50824i	0.500395	+	0.865797i	$0.333188\pi$
$547$	−6.21987	+	35.2747i	−0.265943	+	1.50824i	−0.766337	+	0.642438i	$0.777923\pi$
$548$	20.3824	+	7.41858i	0.870692	+	0.316906i
$549$	7.38919	−	6.20026i	0.315363	−	0.264621i
$550$	5.53209			0.235889
$551$	1.22163	−	7.56834i	0.0520432	−	0.322422i
$552$	−8.33275			−0.354665
$553$	−10.4296	+	8.75151i	−0.443514	+	0.372152i
$554$	16.9474	+	6.16836i	0.720027	+	0.262069i
$555$	−0.609470	+	3.45648i	−0.0258706	+	0.146719i
$556$	0.742574	+	4.21134i	0.0314921	+	0.178601i
$557$	−31.5590	+	11.4865i	−1.33720	+	0.486700i	−0.908929	−	0.416951i	$-0.863099\pi$
$557$	−31.5590	+	11.4865i	−1.33720	+	0.486700i	−0.428269	+	0.903651i	$0.640877\pi$
$558$	−2.71688	+	4.70578i	−0.115015	+	0.199211i
$559$	12.0574	+	20.8840i	0.509972	+	0.883298i
$560$	1.08125	+	0.907278i	0.0456912	+	0.0383395i
$561$	−32.8803	−	27.5899i	−1.38821	−	1.16484i
$562$	−6.15910	−	10.6679i	−0.259806	−	0.449997i
$563$	9.37464	−	16.2373i	0.395094	−	0.684323i	−0.598019	−	0.801482i	$-0.704045\pi$
$563$	9.37464	−	16.2373i	0.395094	−	0.684323i	0.993113	+	0.117159i	$0.0373787\pi$
$564$	−2.51367	+	0.914901i	−0.105845	+	0.0385243i
$565$	1.95811	+	11.1050i	0.0823783	+	0.467191i
$566$	−0.147956	+	0.839100i	−0.00621905	+	0.0352700i
$567$	1.32635	+	0.482753i	0.0557015	+	0.0202737i
$568$	1.59627	−	1.33943i	0.0669779	−	0.0562011i
$569$	16.2736			0.682226			0.341113	−	0.940022i	$-0.389196\pi$
$569$	16.2736			0.682226			0.341113	+	0.940022i	$0.389196\pi$
$570$	−2.12449	+	3.80612i	−0.0889849	+	0.159421i
$571$	−15.5681			−0.651505			−0.325752	−	0.945455i	$-0.605618\pi$
$571$	−15.5681			−0.651505			−0.325752	+	0.945455i	$0.605618\pi$
$572$	−21.1891	+	17.7798i	−0.885962	+	0.743410i
$573$	17.0077	+	6.19031i	0.710509	+	0.258604i
$574$	−1.27626	+	7.23800i	−0.0532699	+	0.302108i
$575$	1.44697	+	8.20616i	0.0603427	+	0.342220i
$576$	−0.939693	+	0.342020i	−0.0391539	+	0.0142508i
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	−0.886090	−	0.463513i	$-0.846589\pi$
$577$	−1.00000	+	1.73205i	−0.0416305	+	0.0721062i	0.844459	+	0.535620i	$0.179922\pi$
$578$	21.5993	+	37.4110i	0.898411	+	1.55609i
$579$	8.82295	+	7.40333i	0.366669	+	0.307672i
$580$	−1.34730	−	1.13052i	−0.0559434	−	0.0469421i
$581$	1.67230	+	2.89652i	0.0693789	+	0.120168i
$582$	7.24897	−	12.5556i	0.300479	−	0.520446i
$583$	45.7499	−	16.6516i	1.89477	−	0.689639i
$584$	−0.147956	−	0.839100i	−0.00612246	−	0.0347222i
$585$	−0.868241	+	4.92404i	−0.0358973	+	0.203584i
$586$	−5.90033	−	2.14754i	−0.243740	−	0.0887142i
$587$	−25.1976	+	21.1433i	−1.04002	+	0.872677i	−0.992009	−	0.126170i	$-0.959731\pi$
$587$	−25.1976	+	21.1433i	−1.04002	+	0.872677i	−0.0480071	+	0.998847i	$0.515287\pi$
$588$	−5.00774			−0.206516
$589$	−23.6827	+	0.343429i	−0.975830	+	0.0141507i
$590$	−6.84255			−0.281703
$591$	17.6348	−	14.7973i	0.725397	−	0.608680i
$592$	−3.29813	−	1.20042i	−0.135552	−	0.0493371i
$593$	−3.71688	+	21.0795i	−0.152634	+	0.865631i	0.808283	+	0.588794i	$0.200397\pi$
$593$	−3.71688	+	21.0795i	−0.152634	+	0.865631i	−0.960917	+	0.276836i	$0.910714\pi$
$594$	0.960637	+	5.44804i	0.0394154	+	0.223536i
$595$	−10.2909	+	3.74557i	−0.421884	+	0.153553i
$596$	5.69459	−	9.86332i	0.233260	−	0.404017i
$597$	12.2344	+	21.1906i	0.500722	+	0.867275i
$598$	−31.9163	−	26.7809i	−1.30515	−	1.09515i
$599$	24.2422	+	20.3416i	0.990508	+	0.831135i	0.985641	−	0.168853i	$-0.0540064\pi$
$599$	24.2422	+	20.3416i	0.990508	+	0.831135i	0.00486674	+	0.999988i	$0.498451\pi$
$600$	0.500000	+	0.866025i	0.0204124	+	0.0353553i
$601$	−7.12108	+	12.3341i	−0.290475	+	0.503117i	−0.973922	−	0.226883i	$-0.927147\pi$
$601$	−7.12108	+	12.3341i	−0.290475	+	0.503117i	0.683447	+	0.730000i	$0.260480\pi$
$602$	6.39693	−	2.32829i	0.260719	−	0.0948940i
$603$	−1.19934	−	6.80180i	−0.0488409	−	0.276991i
$604$	2.08647	−	11.8329i	0.0848971	−	0.481475i
$605$	18.4217	+	6.70497i	0.748950	+	0.272596i
$606$	13.7023	−	11.4976i	0.556619	−	0.467059i
$607$	−6.15064			−0.249647			−0.124823	−	0.992179i	$-0.539836\pi$
$607$	−6.15064			−0.249647			−0.124823	+	0.992179i	$0.539836\pi$
$608$	−3.37939	−	2.75314i	−0.137052	−	0.111654i
$609$	−2.48246			−0.100594
$610$	7.38919	−	6.20026i	0.299179	−	0.251041i
$611$	−12.5684	−	4.57451i	−0.508461	−	0.185065i
$612$	1.34730	−	7.64090i	0.0544612	−	0.308865i
$613$	1.12819	+	6.39830i	0.0455673	+	0.258425i	0.999078	−	0.0429345i	$-0.0136707\pi$
$613$	1.12819	+	6.39830i	0.0455673	+	0.258425i	−0.953511	+	0.301360i	$0.902560\pi$
$614$	22.0624	−	8.03007i	0.890367	−	0.324067i
$615$	−2.60354	+	4.50946i	−0.104985	+	0.181839i
$616$	3.90420	+	6.76227i	0.157305	+	0.272460i
$617$	21.5371	+	18.0718i	0.867053	+	0.727544i	0.963475	−	0.267797i	$-0.0862956\pi$
$617$	21.5371	+	18.0718i	0.867053	+	0.727544i	−0.0964227	+	0.995340i	$0.530740\pi$
$618$	3.77584	+	3.16831i	0.151887	+	0.127448i
$619$	16.1841	+	28.0316i	0.650493	+	1.12669i	0.983003	+	0.183587i	$0.0587710\pi$
$619$	16.1841	+	28.0316i	0.650493	+	1.12669i	−0.332510	+	0.943100i	$0.607896\pi$
$620$	−2.71688	+	4.70578i	−0.109113	+	0.188989i
$621$	−7.83022	+	2.84997i	−0.314216	+	0.114365i
$622$	2.12061	+	12.0266i	0.0850289	+	0.482223i
$623$	3.48529	−	19.7661i	0.139635	−	0.791911i
$624$	−4.69846	−	1.71010i	−0.188089	−	0.0684588i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−28.5817			−1.14236
$627$	−18.2456	+	15.7663i	−0.728658	+	0.629644i
$628$	7.10101			0.283361
$629$	20.8607	−	17.5042i	0.831771	−	0.697939i
$630$	1.32635	+	0.482753i	0.0528431	+	0.0192333i
$631$	0.290859	−	1.64955i	0.0115789	−	0.0656674i	−0.978471	−	0.206385i	$-0.933830\pi$
$631$	0.290859	−	1.64955i	0.0115789	−	0.0656674i	0.990050	+	0.140718i	$0.0449411\pi$
$632$	−1.67499	−	9.49935i	−0.0666276	−	0.377864i
$633$	−7.74510	+	2.81899i	−0.307840	+	0.112045i
$634$	−3.75150	+	6.49778i	−0.148991	+	0.258060i
$635$	5.63429	+	9.75887i	0.223590	+	0.387269i
$636$	6.74170	+	5.65695i	0.267326	+	0.224313i
$637$	−19.1808	−	16.0946i	−0.759969	−	0.637690i
$638$	−4.86484	−	8.42615i	−0.192601	−	0.333594i
$639$	1.04189	−	1.80460i	0.0412165	−	0.0713891i
$640$	−0.939693	+	0.342020i	−0.0371446	+	0.0135195i
$641$	3.39764	+	19.2690i	0.134199	+	0.761079i	0.975414	+	0.220379i	$0.0707294\pi$
$641$	3.39764	+	19.2690i	0.134199	+	0.761079i	−0.841216	+	0.540700i	$0.818159\pi$
$642$	−2.08378	+	11.8177i	−0.0822402	+	0.466407i
$643$	−19.4979	−	7.09667i	−0.768924	−	0.279865i	−0.0723775	−	0.997377i	$-0.523059\pi$
$643$	−19.4979	−	7.09667i	−0.768924	−	0.279865i	−0.696546	+	0.717512i	$0.745281\pi$
$644$	−9.00980	+	7.56012i	−0.355036	+	0.297910i
$645$	4.82295			0.189903
$646$	31.6091	−	12.0266i	1.24364	−	0.473180i
$647$	8.33275			0.327594			0.163797	−	0.986494i	$-0.447626\pi$
$647$	8.33275			0.327594			0.163797	+	0.986494i	$0.447626\pi$
$648$	−0.766044	+	0.642788i	−0.0300931	+	0.0252511i
$649$	−35.5707	−	12.9467i	−1.39627	−	0.508202i
$650$	−0.868241	+	4.92404i	−0.0340552	+	0.193137i
$651$	1.33181	+	7.55310i	0.0521979	+	0.296029i
$652$	−1.30541	+	0.475129i	−0.0511237	+	0.0186075i
$653$	−3.35844	+	5.81699i	−0.131426	+	0.227636i	−0.924226	−	0.381845i	$-0.875289\pi$
$653$	−3.35844	+	5.81699i	−0.131426	+	0.227636i	0.792801	+	0.609481i	$0.208622\pi$
$654$	4.71688	+	8.16988i	0.184445	+	0.319468i
$655$	7.81702	+	6.55926i	0.305436	+	0.256291i
$656$	−3.98886	−	3.34705i	−0.155739	−	0.130680i
$657$	−0.426022	−	0.737892i	−0.0166207	−	0.0287879i
$658$	−1.88784	+	3.26984i	−0.0735957	+	0.127472i
$659$	−38.8717	+	14.1481i	−1.51423	+	0.551133i	−0.959698	−	0.281032i	$-0.909323\pi$
$659$	−38.8717	+	14.1481i	−1.51423	+	0.551133i	−0.554528	+	0.832165i	$0.687101\pi$
$660$	0.960637	+	5.44804i	0.0373928	+	0.212065i
$661$	2.56799	−	14.5638i	0.0998833	−	0.566466i	−0.893258	−	0.449545i	$-0.851586\pi$
$661$	2.56799	−	14.5638i	0.0998833	−	0.566466i	0.993141	−	0.116922i	$-0.0373026\pi$
$662$	−8.14930	−	2.96610i	−0.316732	−	0.115281i
$663$	29.7178	−	24.9362i	1.15414	−	0.968442i
$664$	−2.36959			−0.0919577
$665$	1.15611	+	6.04288i	0.0448319	+	0.234333i
$666$	−3.50980			−0.136002
$667$	11.2267	−	9.42030i	0.434699	−	0.364756i
$668$	−15.5954	−	5.67626i	−0.603404	−	0.219621i
$669$	2.85457	−	16.1891i	0.110364	−	0.625906i
$670$	−1.19934	−	6.80180i	−0.0463346	−	0.262776i
$671$	50.1438	−	18.2509i	1.93578	−	0.704567i
$672$	−0.705737	+	1.22237i	−0.0272244	+	0.0471540i
$673$	9.55943	+	16.5574i	0.368489	+	0.638242i	0.989330	−	0.145695i	$-0.0465419\pi$
$673$	9.55943	+	16.5574i	0.368489	+	0.638242i	−0.620841	+	0.783937i	$0.713209\pi$
$674$	11.4834	+	9.63571i	0.442324	+	0.371154i
$675$	0.766044	+	0.642788i	0.0294851	+	0.0247409i
$676$	−6.00000	−	10.3923i	−0.230769	−	0.399704i
$677$	18.7113	−	32.4088i	0.719132	−	1.24557i	−0.242212	−	0.970223i	$-0.577873\pi$
$677$	18.7113	−	32.4088i	0.719132	−	1.24557i	0.961344	−	0.275350i	$-0.0887937\pi$
$678$	−10.5963	+	3.85673i	−0.406947	+	0.148117i
$679$	−3.55344	−	20.1526i	−0.136369	−	0.773385i
$680$	1.34730	−	7.64090i	0.0516665	−	0.293015i
$681$	−18.1557	−	6.60813i	−0.695728	−	0.253224i
$682$	−23.0273	+	19.3222i	−0.881762	+	0.739887i
$683$	38.0702			1.45671			0.728357	−	0.685198i	$-0.240284\pi$
$683$	38.0702			1.45671			0.728357	+	0.685198i	$0.240284\pi$
$684$	−4.11721	−	1.43128i	−0.157426	−	0.0547265i
$685$	21.6905			0.828750
$686$	−12.9834	+	10.8944i	−0.495708	+	0.415949i
$687$	−12.4757	−	4.54077i	−0.475976	−	0.173241i
$688$	−0.837496	+	4.74968i	−0.0319292	+	0.181080i
$689$	7.64109	+	43.3348i	0.291102	+	1.65092i
$690$	−7.83022	+	2.84997i	−0.298091	+	0.108496i
$691$	−7.10488	+	12.3060i	−0.270283	+	0.468143i	−0.968934	−	0.247319i	$-0.920450\pi$
$691$	−7.10488	+	12.3060i	−0.270283	+	0.468143i	0.698652	+	0.715462i	$0.253784\pi$
$692$	4.36231	+	7.55574i	0.165830	+	0.287226i
$693$	5.98158	+	5.01914i	0.227221	+	0.190661i
$694$	22.8949	+	19.2111i	0.869077	+	0.729242i
$695$	2.13816	+	3.70339i	0.0811049	+	0.140478i
$696$	0.879385	−	1.52314i	0.0333330	−	0.0577345i
$697$	37.9641	−	13.8178i	1.43799	−	0.523387i
$698$	−1.22668	−	6.95686i	−0.0464306	−	0.263321i
$699$	1.14796	−	6.51038i	0.0434197	−	0.246245i
$700$	1.32635	+	0.482753i	0.0501314	+	0.0182463i
$701$	19.9973	−	16.7797i	0.755288	−	0.633762i	−0.181608	−	0.983371i	$-0.558130\pi$
$701$	19.9973	−	16.7797i	0.755288	−	0.633762i	0.936896	+	0.349609i	$0.113686\pi$
$702$	−5.00000			−0.188713
$703$	−7.84074	−	13.1369i	−0.295719	−	0.495467i
$704$	−5.53209			−0.208498
$705$	−2.04916	+	1.71945i	−0.0771759	+	0.0647583i
$706$	13.9709	+	5.08499i	0.525802	+	0.191376i
$707$	4.38413	−	24.8637i	0.164882	−	0.935094i
$708$	−1.18820	−	6.73859i	−0.0446551	−	0.253252i
$709$	33.2148	−	12.0892i	1.24741	−	0.454020i	0.367884	−	0.929872i	$-0.380083\pi$
$709$	33.2148	−	12.0892i	1.24741	−	0.454020i	0.879525	+	0.475852i	$0.157860\pi$
$710$	1.04189	−	1.80460i	0.0391014	−	0.0677256i
$711$	−4.82295	−	8.35359i	−0.180875	−	0.313284i
$712$	10.8931	+	9.14036i	0.408235	+	0.342549i
$713$	−34.6851	−	29.1043i	−1.29897	−	1.08996i
$714$	−5.47565	−	9.48411i	−0.204921	−	0.354934i
$715$	−13.8302	+	23.9546i	−0.517221	+	0.895853i
$716$	18.4265	−	6.70669i	0.688630	−	0.250641i
$717$	0.766511	+	4.34710i	0.0286259	+	0.162345i
$718$	1.64590	−	9.33434i	0.0614243	−	0.348355i
$719$	28.2713	+	10.2899i	1.05434	+	0.383748i	0.810299	−	0.586017i	$-0.199305\pi$
$719$	28.2713	+	10.2899i	1.05434	+	0.383748i	0.244041	+	0.969765i	$0.421527\pi$
$720$	−0.766044	+	0.642788i	−0.0285488	+	0.0239553i
$721$	6.95718			0.259099
$722$	−3.84049	−	18.6078i	−0.142928	−	0.692511i
$723$	12.6459			0.470306
$724$	5.66044	−	4.74968i	0.210369	−	0.176520i
$725$	−1.65270	−	0.601535i	−0.0613799	−	0.0223404i
$726$	−3.40420	+	19.3062i	−0.126342	+	0.716519i
$727$	−5.79797	−	32.8819i	−0.215035	−	1.21952i	−0.880846	−	0.473403i	$-0.843025\pi$
$727$	−5.79797	−	32.8819i	−0.215035	−	1.21952i	0.665811	−	0.746120i	$-0.268086\pi$
$728$	−6.63176	+	2.41376i	−0.245789	+	0.0894600i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	−0.426022	−	0.737892i	−0.0157678	−	0.0273106i
$731$	−28.6655	−	24.0532i	−1.06023	−	0.889640i
$732$	7.38919	+	6.20026i	0.273112	+	0.229168i
$733$	−6.67159	−	11.5555i	−0.246421	−	0.426813i	0.716109	−	0.697988i	$-0.245921\pi$
$733$	−6.67159	−	11.5555i	−0.246421	−	0.426813i	−0.962530	+	0.271175i	$0.912588\pi$
$734$	1.52734	−	2.64543i	0.0563752	−	0.0976447i
$735$	−4.70574	+	1.71275i	−0.173574	+	0.0631757i
$736$	−1.44697	−	8.20616i	−0.0533359	−	0.302483i
$737$	6.63486	−	37.6281i	0.244398	−	1.38605i
$738$	−4.89306	−	1.78093i	−0.180116	−	0.0655568i
$739$	8.07785	−	6.77812i	0.297148	−	0.249337i	−0.482008	−	0.876167i	$-0.660092\pi$
$739$	8.07785	−	6.77812i	0.297148	−	0.249337i	0.779156	+	0.626830i	$0.215648\pi$
$740$	−3.50980			−0.129023
$741$	−11.1698	−	18.7146i	−0.410332	−	0.687498i
$742$	12.4219			0.456022
$743$	−22.4481	+	18.8362i	−0.823543	+	0.691034i	−0.953799	−	0.300446i	$-0.902864\pi$
$743$	−22.4481	+	18.8362i	−0.823543	+	0.691034i	0.130256	+	0.991480i	$0.458420\pi$
$744$	−5.10607	−	1.85846i	−0.187197	−	0.0681343i
$745$	1.97771	−	11.2162i	0.0724577	−	0.410928i
$746$	−1.96879	−	11.1656i	−0.0720825	−	0.408800i
$747$	−2.22668	+	0.810446i	−0.0814700	+	0.0296527i
$748$	21.4611	−	37.1717i	0.784696	−	1.35913i
$749$	8.46884	+	14.6685i	0.309445	+	0.535974i
$750$	0.766044	+	0.642788i	0.0279720	+	0.0234713i
$751$	−3.52166	−	2.95502i	−0.128507	−	0.107830i	0.576269	−	0.817260i	$-0.304508\pi$
$751$	−3.52166	−	2.95502i	−0.128507	−	0.107830i	−0.704776	+	0.709430i	$0.748953\pi$
$752$	−1.33750	−	2.31661i	−0.0487735	−	0.0844781i
$753$	−7.24422	+	12.5474i	−0.263994	+	0.457251i
$754$	8.26352	−	3.00767i	0.300940	−	0.109533i
$755$	−2.08647	−	11.8329i	−0.0759343	−	0.430645i
$756$	−0.245100	+	1.39003i	−0.00891420	+	0.0505549i
$757$	−7.65183	−	2.78504i	−0.278110	−	0.101224i	0.199199	−	0.979959i	$-0.436166\pi$
$757$	−7.65183	−	2.78504i	−0.278110	−	0.101224i	−0.477310	+	0.878735i	$0.658388\pi$
$758$	−11.0646	+	9.28434i	−0.401886	+	0.337222i
$759$	−46.0975			−1.67323
$760$	−4.11721	−	1.43128i	−0.149347	−	0.0519181i
$761$	19.2772			0.698800			0.349400	−	0.936974i	$-0.386386\pi$
$761$	19.2772			0.698800			0.349400	+	0.936974i	$0.386386\pi$
$762$	−8.63223	+	7.24330i	−0.312713	+	0.262397i
$763$	12.5125	+	4.55417i	0.452982	+	0.164872i
$764$	−3.14290	+	17.8243i	−0.113706	+	0.644860i
$765$	−1.34730	−	7.64090i	−0.0487116	−	0.276257i
$766$	12.0312	−	4.37900i	0.434705	−	0.158220i
$767$	17.1064	−	29.6291i	0.617675	−	1.06984i
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	−22.7815	−	19.1160i	−0.821523	−	0.689340i	0.131805	−	0.991276i	$-0.457923\pi$
$769$	−22.7815	−	19.1160i	−0.821523	−	0.689340i	−0.953328	+	0.301936i	$0.902367\pi$
$770$	5.98158	+	5.01914i	0.215561	+	0.180877i
$771$	−13.1284	−	22.7390i	−0.472806	−	0.818924i
$772$	−5.75877	+	9.97448i	−0.207263	+	0.358990i
$773$	−5.39141	+	1.96231i	−0.193915	+	0.0705794i	−0.437152	−	0.899387i	$-0.644013\pi$
$773$	−5.39141	+	1.96231i	−0.193915	+	0.0705794i	0.243237	+	0.969967i	$0.421791\pi$
$774$	0.837496	+	4.74968i	0.0301032	+	0.170724i
$775$	−0.943563	+	5.35121i	−0.0338938	+	0.192221i
$776$	13.6236	+	4.95859i	0.489059	+	0.178003i
$777$	−3.79498	+	3.18436i	−0.136144	+	0.114238i
$778$	−3.19253			−0.114458
$779$	−4.26500	−	22.2928i	−0.152810	−	0.798723i
$780$	−5.00000			−0.179029
$781$	8.83069	−	7.40983i	0.315987	−	0.265144i
$782$	60.7529	+	22.1122i	2.17252	+	0.790732i
$783$	0.305407	−	1.73205i	0.0109144	−	0.0618984i
$784$	−0.869585	−	4.93166i	−0.0310566	−	0.176131i
$785$	6.67277	−	2.42869i	0.238161	−	0.0866837i
$786$	−5.10220	+	8.83726i	−0.181989	+	0.315215i
$787$	−0.687786	−	1.19128i	−0.0245169	−	0.0424645i	0.853507	−	0.521082i	$-0.174471\pi$
$787$	−0.687786	−	1.19128i	−0.0245169	−	0.0424645i	−0.878024	+	0.478617i	$0.841138\pi$
$788$	17.6348	+	14.7973i	0.628212	+	0.527132i
$789$	−15.1891	−	12.7452i	−0.540747	−	0.453741i
$790$	−4.82295	−	8.35359i	−0.171593	−	0.297207i
$791$	−7.95811	+	13.7839i	−0.282958	+	0.490097i
$792$	−5.19846	+	1.89209i	−0.184719	+	0.0672323i
$793$	8.37496	+	47.4968i	0.297404	+	1.68666i
$794$	−0.266044	+	1.50881i	−0.00944156	+	0.0535458i
$795$	8.26991	+	3.01000i	0.293304	+	0.106754i
$796$	−18.7442	+	15.7283i	−0.664371	+	0.557474i
$797$	33.5131			1.18709			0.593547	−	0.804799i	$-0.297727\pi$
$797$	33.5131			1.18709			0.593547	+	0.804799i	$0.297727\pi$
$798$	−5.75031	+	2.18788i	−0.203559	+	0.0774500i
$799$	20.7547			0.734247
$800$	−0.766044	+	0.642788i	−0.0270838	+	0.0227260i
$801$	13.3623	+	4.86348i	0.472134	+	0.171843i
$802$	−1.90404	+	10.7983i	−0.0672339	+	0.381303i
$803$	−0.818505	−	4.64197i	−0.0288844	−	0.163812i
$804$	6.49020	−	2.36224i	0.228892	−	0.0833098i
$805$	−5.88073	+	10.1857i	−0.207268	+	0.359000i
$806$	−13.5844	−	23.5289i	−0.478490	−	0.828770i
$807$	20.1138	+	16.8775i	0.708040	+	0.594116i
$808$	13.7023	+	11.4976i	0.482046	+	0.404485i
$809$	11.1236	+	19.2667i	0.391085	+	0.677379i	0.992593	−	0.121487i	$-0.0387664\pi$
$809$	11.1236	+	19.2667i	0.391085	+	0.677379i	−0.601508	+	0.798867i	$0.705433\pi$
$810$	−0.500000	+	0.866025i	−0.0175682	+	0.0304290i
$811$	−15.5513	+	5.66020i	−0.546079	+	0.198757i	−0.600304	−	0.799772i	$-0.704954\pi$
$811$	−15.5513	+	5.66020i	−0.546079	+	0.198757i	0.0542244	+	0.998529i	$0.482731\pi$
$812$	−0.431074	−	2.44474i	−0.0151277	−	0.0857937i
$813$	1.75103	−	9.93058i	0.0614113	−	0.348281i
$814$	−18.2456	−	6.64084i	−0.639507	−	0.232761i
$815$	−1.06418	+	0.892951i	−0.0372765	+	0.0312787i
$816$	7.75877			0.271611
$817$	−15.9067	+	13.7452i	−0.556506	+	0.480885i
$818$	25.7365			0.899855
$819$	−5.40626	+	4.53639i	−0.188910	+	0.158514i
$820$	−4.89306	−	1.78093i	−0.170873	−	0.0621927i
$821$	−9.29860	+	52.7350i	−0.324523	+	1.84046i	0.188480	+	0.982077i	$0.439644\pi$
$821$	−9.29860	+	52.7350i	−0.324523	+	1.84046i	−0.513003	+	0.858387i	$0.671467\pi$
$822$	3.76651	+	21.3609i	0.131372	+	0.745049i
$823$	−0.391407	+	0.142460i	−0.0136436	+	0.00496586i	−0.348833	−	0.937185i	$-0.613422\pi$
$823$	−0.391407	+	0.142460i	−0.0136436	+	0.00496586i	0.335189	+	0.942151i	$0.391200\pi$
$824$	−2.46451	+	4.26865i	−0.0858552	+	0.148706i
$825$	2.76604	+	4.79093i	0.0963013	+	0.166799i
$826$	−7.39852	−	6.20809i	−0.257427	−	0.216007i
$827$	−33.2618	−	27.9099i	−1.15662	−	0.970523i	−0.156771	−	0.987635i	$-0.550109\pi$
$827$	−33.2618	−	27.9099i	−1.15662	−	0.970523i	−0.999854	+	0.0171115i	$0.994553\pi$
$828$	−4.16637	−	7.21637i	−0.144792	−	0.250786i
$829$	4.47565	−	7.75206i	0.155446	−	0.269240i	−0.777775	−	0.628542i	$-0.783652\pi$
$829$	4.47565	−	7.75206i	0.155446	−	0.269240i	0.933221	+	0.359302i	$0.116985\pi$
$830$	−2.22668	+	0.810446i	−0.0772892	+	0.0281310i
$831$	3.13176	+	17.7611i	0.108640	+	0.616125i
$832$	0.868241	−	4.92404i	0.0301008	−	0.170710i
$833$	36.5107	+	13.2888i	1.26502	+	0.460430i
$834$	−3.27584	+	2.74876i	−0.113433	+	0.0951818i
$835$	−16.5963			−0.574337
$836$	−18.6951	−	15.2306i	−0.646582	−	0.526761i
$837$	−5.43376			−0.187818
$838$	9.02481	−	7.57272i	0.311757	−	0.261595i
$839$	2.40198	+	0.874249i	0.0829255	+	0.0301824i	0.383150	−	0.923686i	$-0.374839\pi$
$839$	2.40198	+	0.874249i	0.0829255	+	0.0301824i	−0.300224	+	0.953869i	$0.597062\pi$
$840$	−0.245100	+	1.39003i	−0.00845675	+	0.0479606i
$841$	−4.49866	−	25.5131i	−0.155126	−	0.879764i
$842$	4.10607	−	1.49449i	0.141504	−	0.0515034i
$843$	6.15910	−	10.6679i	0.212131	−	0.367421i
$844$	−4.12108	−	7.13792i	−0.141853	−	0.245697i
$845$	−9.19253	−	7.71345i	−0.316233	−	0.265351i
$846$	−2.04916	−	1.71945i	−0.0704517	−	0.0591160i
$847$	13.8353	+	23.9634i	0.475386	+	0.823392i
$848$	−4.40033	+	7.62159i	−0.151108	+	0.261727i
$849$	−0.800660	+	0.291416i	−0.0274786	+	0.0100014i
$850$	−1.34730	−	7.64090i	−0.0462119	−	0.262081i
$851$	5.07856	−	28.8020i	0.174091	−	0.987319i
$852$	1.95811	+	0.712694i	0.0670838	+	0.0244165i
$853$	−10.1107	+	8.48384i	−0.346182	+	0.290481i	−0.799255	−	0.600992i	$-0.794772\pi$
$853$	−10.1107	+	8.48384i	−0.346182	+	0.290481i	0.453073	+	0.891474i	$0.350328\pi$
$854$	13.6149			0.465893
$855$	−4.35844	+	0.0632028i	−0.149056	+	0.00216149i
$856$	−12.0000			−0.410152
$857$	20.6013	−	17.2866i	0.703728	−	0.590498i	−0.219104	−	0.975702i	$-0.570313\pi$
$857$	20.6013	−	17.2866i	0.703728	−	0.590498i	0.922831	+	0.385204i	$0.125869\pi$
$858$	−25.9923	−	9.46043i	−0.887363	−	0.322974i
$859$	−9.36396	+	53.1057i	−0.319494	+	1.81194i	0.226340	+	0.974048i	$0.427324\pi$
$859$	−9.36396	+	53.1057i	−0.319494	+	1.81194i	−0.545834	+	0.837893i	$0.683787\pi$
$860$	0.837496	+	4.74968i	0.0285584	+	0.161963i
$861$	−6.90642	+	2.51373i	−0.235370	+	0.0856678i
$862$	2.14022	−	3.70696i	0.0728960	−	0.126260i
$863$	−17.3478	−	30.0472i	−0.590525	−	1.02282i	−0.994162	−	0.107900i	$-0.965587\pi$
$863$	−17.3478	−	30.0472i	−0.590525	−	1.02282i	0.403637	−	0.914919i	$-0.367746\pi$
$864$	−0.766044	−	0.642788i	−0.0260614	−	0.0218681i
$865$	6.68345	+	5.60808i	0.227244	+	0.190680i
$866$	−15.8648	−	27.4787i	−0.539109	−	0.933764i
$867$	−21.5993	+	37.4110i	−0.733549	+	1.27054i
$868$	−7.20708	+	2.62316i	−0.244624	+	0.0890360i
$869$	−9.26621	−	52.5513i	−0.314335	−	1.78268i
$870$	0.305407	−	1.73205i	0.0103543	−	0.0587220i
$871$	32.4510	+	11.8112i	1.09956	+	0.400207i
$872$	−7.22668	+	6.06391i	−0.244726	+	0.205350i
$873$	14.4979			0.490681
$874$	17.7028	−	31.7155i	0.598806	−	1.07279i
$875$	1.41147			0.0477165
$876$	0.652704	−	0.547683i	0.0220528	−	0.0185045i
$877$	−2.21079	−	0.804662i	−0.0746531	−	0.0271715i	0.304424	−	0.952537i	$-0.401536\pi$
$877$	−2.21079	−	0.804662i	−0.0746531	−	0.0271715i	−0.379077	+	0.925365i	$0.623758\pi$
$878$	−2.93582	+	16.6499i	−0.0990792	+	0.561906i
$879$	−1.09034	−	6.18361i	−0.0367761	−	0.208568i
$880$	−5.19846	+	1.89209i	−0.175240	+	0.0637822i
$881$	8.81449	−	15.2671i	0.296968	−	0.514363i	−0.678473	−	0.734625i	$-0.737358\pi$
$881$	8.81449	−	15.2671i	0.296968	−	0.514363i	0.975441	+	0.220262i	$0.0706913\pi$
$882$	−2.50387	−	4.33683i	−0.0843097	−	0.146029i
$883$	6.90167	+	5.79119i	0.232260	+	0.194889i	0.751488	−	0.659746i	$-0.229336\pi$
$883$	6.90167	+	5.79119i	0.232260	+	0.194889i	−0.519229	+	0.854635i	$0.673781\pi$
$884$	29.7178	+	24.9362i	0.999518	+	0.838695i
$885$	−3.42127	−	5.92582i	−0.115005	−	0.199194i
$886$	6.55438	−	11.3525i	0.220199	−	0.381395i
$887$	−28.9088	+	10.5220i	−0.970664	+	0.353293i	−0.778204	−	0.628012i	$-0.783869\pi$
$887$	−28.9088	+	10.5220i	−0.970664	+	0.353293i	−0.192460	+	0.981305i	$0.561647\pi$
$888$	−0.609470	−	3.45648i	−0.0204525	−	0.115992i
$889$	−2.76193	+	15.6637i	−0.0926320	+	0.525342i
$890$	13.3623	+	4.86348i	0.447906	+	0.163024i
$891$	−4.23783	+	3.55596i	−0.141973	+	0.119129i
$892$	16.4388			0.550412
$893$	1.85803	−	11.5110i	0.0621766	−	0.385202i
$894$	11.3892			0.380911
$895$	15.0214	−	12.6045i	0.502110	−	0.421321i
$896$	−1.32635	−	0.482753i	−0.0443103	−	0.0161276i
$897$	7.23483	−	41.0308i	0.241564	−	1.36998i
$898$	−1.51501	−	8.59208i	−0.0505567	−	0.286721i
$899$	8.98040	−	3.26860i	0.299513	−	0.109014i
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−34.1411	−	59.1342i	−1.13741	−	1.97005i
$902$	−22.0667	−	18.5162i	−0.734741	−	0.616521i
$903$	5.21482	+	4.37576i	0.173538	+	0.145616i
$904$	−5.63816	−	9.76557i	−0.187522	−	0.324798i
$905$	3.69459	−	6.39922i	0.122812	−	0.212717i
$906$	11.2909	−	4.10954i	0.375114	−	0.136530i
$907$	4.91117	+	27.8526i	0.163073	+	0.924831i	0.951029	+	0.309101i	$0.100028\pi$
$907$	4.91117	+	27.8526i	0.163073	+	0.924831i	−0.787957	+	0.615731i	$0.788861\pi$
$908$	3.35504	−	19.0274i	0.111341	−	0.631445i
$909$	16.8084	+	6.11776i	0.557499	+	0.202913i
$910$	−5.40626	+	4.53639i	−0.179216	+	0.150380i
$911$	39.8289			1.31959			0.659796	−	0.751445i	$-0.270643\pi$
$911$	39.8289			1.31959			0.659796	+	0.751445i	$0.270643\pi$
$912$	0.694593	−	4.30320i	0.0230003	−	0.142493i
$913$	−13.1088			−0.433836
$914$	−7.31315	+	6.13646i	−0.241897	+	0.202976i
$915$	9.06418	+	3.29909i	0.299652	+	0.109065i
$916$	2.30541	−	13.0746i	0.0761728	−	0.431997i
$917$	2.50110	+	14.1844i	0.0825935	+	0.468411i
$918$	7.29086	−	2.65366i	0.240634	−	0.0875837i
$919$	−21.8999	+	37.9318i	−0.722412	+	1.25125i	0.237619	+	0.971358i	$0.423633\pi$
$919$	−21.8999	+	37.9318i	−0.722412	+	1.25125i	−0.960031	+	0.279895i	$0.909700\pi$
$920$	−4.16637	−	7.21637i	−0.137361	−	0.237917i
$921$	17.9855	+	15.0916i	0.592641	+	0.497285i
$922$	−6.01960	−	5.05104i	−0.198245	−	0.166347i
$923$	5.20945	+	9.02302i	0.171471	+	0.296996i
$924$	−3.90420	+	6.76227i	−0.128439	+	0.222462i
$925$	−3.29813	+	1.20042i	−0.108442	+	0.0394696i
$926$	0.888719	+	5.04017i	0.0292051	+	0.165630i
$927$	−0.855914	+	4.85413i	−0.0281119	+	0.159431i
$928$	1.65270	+	0.601535i	0.0542527	+	0.0197464i
$929$	14.7758	−	12.3984i	0.484780	−	0.406778i	−0.367371	−	0.930074i	$-0.619742\pi$
$929$	14.7758	−	12.3984i	0.484780	−	0.406778i	0.852151	+	0.523296i	$0.175298\pi$
$930$	−5.43376			−0.178180
$931$	10.6389	−	19.0601i	0.348675	−	0.624669i
$932$	6.61081			0.216544
$933$	−9.35504	+	7.84981i	−0.306270	+	0.256991i
$934$	−11.9436	−	4.34710i	−0.390805	−	0.142242i
$935$	7.45336	−	42.2701i	0.243751	−	1.38238i
$936$	−0.868241	−	4.92404i	−0.0283793	−	0.160947i
$937$	−53.4074	+	19.4387i	−1.74474	+	0.635034i	−0.999496	−	0.0317548i	$-0.989890\pi$
$937$	−53.4074	+	19.4387i	−1.74474	+	0.635034i	−0.745247	+	0.666789i	$0.767668\pi$
$938$	4.87433	−	8.44259i	0.159153	−	0.275660i
$939$	−14.2909	−	24.7525i	−0.466365	−	0.807767i
$940$	−2.04916	−	1.71945i	−0.0668363	−	0.0560823i
$941$	−40.4201	−	33.9165i	−1.31766	−	1.10565i	−0.986796	−	0.161969i	$-0.948216\pi$
$941$	−40.4201	−	33.9165i	−1.31766	−	1.10565i	−0.330863	−	0.943679i	$-0.607340\pi$
$942$	3.55051	+	6.14966i	0.115682	+	0.200367i
$943$	21.6946	−	37.5762i	0.706475	−	1.22365i
$944$	6.42989	−	2.34029i	0.209275	−	0.0761699i
$945$	0.245100	+	1.39003i	0.00797310	+	0.0452177i
$946$	−4.63310	+	26.2756i	−0.150635	+	0.854295i
$947$	37.7648	+	13.7452i	1.22719	+	0.446661i	0.872634	−	0.488374i	$-0.162410\pi$
$947$	37.7648	+	13.7452i	1.22719	+	0.446661i	0.354556	+	0.935035i	$0.384632\pi$
$948$	7.38919	−	6.20026i	0.239990	−	0.201375i
$949$	4.26022			0.138293
$950$	−4.35844	+	0.0632028i	−0.141406	+	0.00205057i
$951$	−7.50299			−0.243301
$952$	8.38919	−	7.03936i	0.271895	−	0.228147i
$953$	−12.1557	−	4.42431i	−0.393762	−	0.143318i	0.137548	−	0.990495i	$-0.456078\pi$
$953$	−12.1557	−	4.42431i	−0.393762	−	0.143318i	−0.531310	+	0.847178i	$0.678300\pi$
$954$	−1.52822	+	8.66696i	−0.0494779	+	0.280603i
$955$	3.14290	+	17.8243i	0.101702	+	0.576781i
$956$	−4.14796	+	1.50973i	−0.134154	+	0.0488282i
$957$	4.86484	−	8.42615i	0.157258	−	0.272379i
$958$	6.51754	+	11.2887i	0.210572	+	0.364722i
$959$	23.4529	+	19.6793i	0.757333	+	0.635477i
$960$	−0.766044	−	0.642788i	−0.0247240	−	0.0207459i
$961$	0.737111	+	1.27671i	0.0237778	+	0.0411843i
$962$	8.77450	−	15.1979i	0.282901	−	0.489999i
$963$	−11.2763	+	4.10424i	−0.363374	+	0.132257i
$964$	2.19594	+	12.4538i	0.0707264	+	0.401109i
$965$	−2.00000	+	11.3426i	−0.0643823	+	0.365130i
$966$	−11.0522	−	4.02266i	−0.355597	−	0.129427i
$967$	−31.4047	+	26.3516i	−1.00991	+	0.847412i	−0.988326	−	0.152355i	$-0.951314\pi$
$967$	−31.4047	+	26.3516i	−1.00991	+	0.847412i	−0.0215802	+	0.999767i	$0.506870\pi$
$968$	−19.6040			−0.630097
$969$	26.2199	+	21.3609i	0.842304	+	0.686212i
$970$	14.4979			0.465501
$971$	14.0792	−	11.8138i	0.451823	−	0.379124i	−0.388289	−	0.921538i	$-0.626934\pi$
$971$	14.0792	−	11.8138i	0.451823	−	0.379124i	0.840112	+	0.542413i	$0.182489\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	−1.04812	+	5.94420i	−0.0336013	+	0.190562i
$974$	−0.902856	−	5.12035i	−0.0289294	−	0.164067i
$975$	−4.69846	+	1.71010i	−0.150471	+	0.0547671i
$976$	−4.82295	+	8.35359i	−0.154379	+	0.267392i
$977$	8.53209	+	14.7780i	0.272966	+	0.472790i	0.969620	−	0.244617i	$-0.0786621\pi$
$977$	8.53209	+	14.7780i	0.272966	+	0.472790i	−0.696654	+	0.717407i	$0.745329\pi$
$978$	−1.06418	−	0.892951i	−0.0340287	−	0.0285534i
$979$	60.2614	+	50.5653i	1.92596	+	1.61607i
$980$	−2.50387	−	4.33683i	−0.0799832	−	0.138535i
$981$	−4.71688	+	8.16988i	−0.150598	+	0.260844i
$982$	6.07145	−	2.20983i	0.193748	−	0.0705184i
$983$	−2.07057	−	11.7428i	−0.0660411	−	0.374537i	−0.999859	−	0.0167890i	$-0.994656\pi$
$983$	−2.07057	−	11.7428i	−0.0660411	−	0.374537i	0.933818	−	0.357748i	$-0.116455\pi$
$984$	0.904200	−	5.12797i	0.0288248	−	0.163474i
$985$	21.6322	+	7.87349i	0.689260	+	0.250870i
$986$	−10.4534	+	8.77141i	−0.332903	+	0.279339i
$987$	−3.77568			−0.120181
$988$	16.4907	−	14.2498i	0.524638	−	0.453348i
$989$	−40.1884			−1.27792
$990$	−4.23783	+	3.55596i	−0.134687	+	0.113016i
$991$	−14.3405	−	5.21951i	−0.455541	−	0.165803i	0.104051	−	0.994572i	$-0.466820\pi$
$991$	−14.3405	−	5.21951i	−0.455541	−	0.165803i	−0.559591	+	0.828769i	$0.689042\pi$
$992$	0.943563	−	5.35121i	0.0299582	−	0.169901i
$993$	−1.50593	−	8.54055i	−0.0477892	−	0.271026i
$994$	2.76382	−	1.00595i	0.0876631	−	0.0319068i
$995$	−12.2344	+	21.1906i	−0.387857	+	0.671788i
$996$	−1.18479	−	2.05212i	−0.0375416	−	0.0650239i
$997$	−11.1866	−	9.38667i	−0.354283	−	0.297279i	0.448224	−	0.893921i	$-0.352057\pi$
$997$	−11.1866	−	9.38667i	−0.354283	−	0.297279i	−0.802507	+	0.596642i	$0.796501\pi$
$998$	21.8855	+	18.3641i	0.692774	+	0.581307i
$999$	−1.75490	−	3.03958i	−0.0555226	−	0.0961679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.u.b.481.1	yes	6
19.16	even	9	inner	570.2.u.b.301.1	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.u.b.301.1	✓	6	19.16	even	9	inner
570.2.u.b.481.1	yes	6	1.1	even	1	trivial

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.705737 - 1.22237i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(-0.939693 - 0.342020i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.705737 - 1.22237i) q^{7} +(0.500000 + 0.866025i) q^{8} +(0.766044 + 0.642788i) q^{9} +(0.766044 + 0.642788i) q^{10} +(2.76604 + 4.79093i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-4.69846 + 1.71010i) q^{13} +(0.245100 + 1.39003i) q^{14} +(-0.173648 + 0.984808i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(5.94356 - 4.98724i) q^{17} -1.00000 q^{18} +(-2.23396 - 3.74292i) q^{19} -1.00000 q^{20} +(-1.08125 + 0.907278i) q^{21} +(-5.19846 - 1.89209i) q^{22} +(1.44697 - 8.20616i) q^{23} +(-0.173648 - 0.984808i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-0.500000 - 0.866025i) q^{27} +(-1.08125 - 0.907278i) q^{28} +(1.34730 + 1.13052i) q^{29} +(-0.500000 - 0.866025i) q^{30} +(2.71688 - 4.70578i) q^{31} +(0.939693 - 0.342020i) q^{32} +(-0.960637 - 5.44804i) q^{33} +(-1.34730 + 7.64090i) q^{34} +(-1.32635 - 0.482753i) q^{35} +(0.766044 - 0.642788i) q^{36} +3.50980 q^{37} +(4.11721 + 1.43128i) q^{38} +5.00000 q^{39} +(0.766044 - 0.642788i) q^{40} +(4.89306 + 1.78093i) q^{41} +(0.245100 - 1.39003i) q^{42} +(-0.837496 - 4.74968i) q^{43} +(5.19846 - 1.89209i) q^{44} +(0.500000 - 0.866025i) q^{45} +(4.16637 + 7.21637i) q^{46} +(2.04916 + 1.71945i) q^{47} +(0.766044 + 0.642788i) q^{48} +(2.50387 + 4.33683i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-7.29086 + 2.65366i) q^{51} +(0.868241 + 4.92404i) q^{52} +(1.52822 - 8.66696i) q^{53} +(0.939693 + 0.342020i) q^{54} +(4.23783 - 3.55596i) q^{55} +1.41147 q^{56} +(0.819078 + 4.28125i) q^{57} -1.75877 q^{58} +(-5.24170 + 4.39831i) q^{59} +(0.939693 + 0.342020i) q^{60} +(1.67499 - 9.49935i) q^{61} +(0.943563 + 5.35121i) q^{62} +(1.32635 - 0.482753i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(2.50000 + 4.33013i) q^{65} +(4.23783 + 3.55596i) q^{66} +(-5.29086 - 4.43956i) q^{67} +(-3.87939 - 6.71929i) q^{68} +(-4.16637 + 7.21637i) q^{69} +(1.32635 - 0.482753i) q^{70} +(-0.361844 - 2.05212i) q^{71} +(-0.173648 + 0.984808i) q^{72} +(-0.800660 - 0.291416i) q^{73} +(-2.68866 + 2.25606i) q^{74} +1.00000 q^{75} +(-4.07398 + 1.55007i) q^{76} +7.80840 q^{77} +(-3.83022 + 3.21394i) q^{78} +(-9.06418 - 3.29909i) q^{79} +(-0.173648 + 0.984808i) q^{80} +(0.173648 + 0.984808i) q^{81} +(-4.89306 + 1.78093i) q^{82} +(-1.18479 + 2.05212i) q^{83} +(0.705737 + 1.22237i) q^{84} +(-5.94356 - 4.98724i) q^{85} +(3.69459 + 3.10013i) q^{86} +(-0.879385 - 1.52314i) q^{87} +(-2.76604 + 4.79093i) q^{88} +(13.3623 - 4.86348i) q^{89} +(0.173648 + 0.984808i) q^{90} +(-1.22550 + 6.95015i) q^{91} +(-7.83022 - 2.84997i) q^{92} +(-4.16250 + 3.49276i) q^{93} -2.67499 q^{94} +(-3.29813 + 2.84997i) q^{95} -1.00000 q^{96} +(11.1061 - 9.31910i) q^{97} +(-4.70574 - 1.71275i) q^{98} +(-0.960637 + 5.44804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q - 6 * q^7 + 3 * q^8	\( 6 q - 6 q^{7} + 3 q^{8} + 12 q^{11} - 3 q^{12} + 6 q^{17} - 6 q^{18} - 18 q^{19} - 6 q^{20} - 9 q^{21} - 3 q^{22} + 21 q^{23} + 15 q^{26} - 3 q^{27} - 9 q^{28} + 6 q^{29} - 3 q^{30} + 3 q^{33} - 6 q^{34} - 9 q^{35} + 24 q^{37} - 6 q^{38} + 30 q^{39} - 3 q^{41} + 3 q^{44} + 3 q^{45} + 6 q^{46} + 24 q^{47} - 9 q^{49} + 3 q^{50} - 12 q^{51} + 24 q^{53} + 6 q^{55} - 12 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} - 24 q^{62} + 9 q^{63} - 3 q^{64} + 15 q^{65} + 6 q^{66} - 12 q^{68} - 6 q^{69} + 9 q^{70} - 36 q^{71} + 24 q^{73} + 15 q^{74} + 6 q^{75} - 9 q^{76} - 30 q^{77} - 36 q^{79} + 3 q^{82} - 6 q^{84} - 6 q^{85} + 18 q^{86} + 6 q^{87} - 12 q^{88} + 48 q^{89} - 24 q^{92} - 30 q^{93} - 6 q^{94} - 6 q^{95} - 6 q^{96} + 42 q^{97} - 18 q^{98} + 3 q^{99}+O(q^{100}) \) 6 * q - 6 * q^7 + 3 * q^8 + 12 * q^11 - 3 * q^12 + 6 * q^17 - 6 * q^18 - 18 * q^19 - 6 * q^20 - 9 * q^21 - 3 * q^22 + 21 * q^23 + 15 * q^26 - 3 * q^27 - 9 * q^28 + 6 * q^29 - 3 * q^30 + 3 * q^33 - 6 * q^34 - 9 * q^35 + 24 * q^37 - 6 * q^38 + 30 * q^39 - 3 * q^41 + 3 * q^44 + 3 * q^45 + 6 * q^46 + 24 * q^47 - 9 * q^49 + 3 * q^50 - 12 * q^51 + 24 * q^53 + 6 * q^55 - 12 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 - 24 * q^62 + 9 * q^63 - 3 * q^64 + 15 * q^65 + 6 * q^66 - 12 * q^68 - 6 * q^69 + 9 * q^70 - 36 * q^71 + 24 * q^73 + 15 * q^74 + 6 * q^75 - 9 * q^76 - 30 * q^77 - 36 * q^79 + 3 * q^82 - 6 * q^84 - 6 * q^85 + 18 * q^86 + 6 * q^87 - 12 * q^88 + 48 * q^89 - 24 * q^92 - 30 * q^93 - 6 * q^94 - 6 * q^95 - 6 * q^96 + 42 * q^97 - 18 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more