LMFDB - Embedded newform 280.2.bj.e.131.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(131,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("280.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.bj (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.11
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.e.171.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06817 + 0.926830i) q^{2} +(1.90624 - 1.10057i) q^{3} +(0.281971 + 1.98002i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.05623 + 0.591168i) q^{6} +(0.584379 + 2.58041i) q^{7} +(-1.53395 + 2.37634i) q^{8} +(0.922503 - 1.59782i) q^{9} +O(q^{10})$	\(q+(1.06817 + 0.926830i) q^{2} +(1.90624 - 1.10057i) q^{3} +(0.281971 + 1.98002i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.05623 + 0.591168i) q^{6} +(0.584379 + 2.58041i) q^{7} +(-1.53395 + 2.37634i) q^{8} +(0.922503 - 1.59782i) q^{9} +(1.33674 - 0.461647i) q^{10} +(-2.90486 - 5.03137i) q^{11} +(2.71666 + 3.46407i) q^{12} -4.83332 q^{13} +(-1.76738 + 3.29793i) q^{14} -2.20114i q^{15} +(-3.84098 + 1.11662i) q^{16} +(3.78236 - 2.18375i) q^{17} +(2.46630 - 0.851741i) q^{18} +(1.63783 + 0.945600i) q^{19} +(1.85574 + 0.745818i) q^{20} +(3.95388 + 4.27573i) q^{21} +(1.56034 - 8.06667i) q^{22} +(-0.157820 - 0.0911173i) q^{23} +(-0.308759 + 6.21810i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-5.16280 - 4.47966i) q^{26} +2.54230i q^{27} +(-4.94449 + 1.88468i) q^{28} -4.38898i q^{29} +(2.04008 - 2.35119i) q^{30} +(2.03983 + 3.53308i) q^{31} +(-5.13774 - 2.36720i) q^{32} +(-11.0747 - 6.39400i) q^{33} +(6.06416 + 1.17300i) q^{34} +(2.52689 + 0.784117i) q^{35} +(3.42385 + 1.37604i) q^{36} +(-3.69132 - 2.13119i) q^{37} +(0.873066 + 2.52805i) q^{38} +(-9.21347 + 5.31940i) q^{39} +(1.29099 + 2.51661i) q^{40} +3.44314i q^{41} +(0.260540 + 8.23178i) q^{42} -2.10796 q^{43} +(9.14314 - 7.17039i) q^{44} +(-0.922503 - 1.59782i) q^{45} +(-0.0841280 - 0.243601i) q^{46} +(-0.946816 + 1.63993i) q^{47} +(-6.09293 + 6.35581i) q^{48} +(-6.31700 + 3.01587i) q^{49} +(0.268574 - 1.38848i) q^{50} +(4.80673 - 8.32550i) q^{51} +(-1.36286 - 9.57008i) q^{52} +(8.54212 - 4.93180i) q^{53} +(-2.35628 + 2.71561i) q^{54} -5.80972 q^{55} +(-7.02833 - 2.56954i) q^{56} +4.16279 q^{57} +(4.06784 - 4.68817i) q^{58} +(-6.35546 + 3.66932i) q^{59} +(4.35830 - 0.620657i) q^{60} +(4.89522 - 8.47877i) q^{61} +(-1.09569 + 5.66450i) q^{62} +(4.66212 + 1.44670i) q^{63} +(-3.29398 - 7.29039i) q^{64} +(-2.41666 + 4.18577i) q^{65} +(-5.90354 - 17.0943i) q^{66} +(6.04954 + 10.4781i) q^{67} +(5.39039 + 6.87341i) q^{68} -0.401124 q^{69} +(1.97240 + 3.17957i) q^{70} +8.80669i q^{71} +(2.38189 + 4.64317i) q^{72} +(7.34998 - 4.24351i) q^{73} +(-1.96771 - 5.69769i) q^{74} +(-1.90624 - 1.10057i) q^{75} +(-1.41049 + 3.50957i) q^{76} +(11.2854 - 10.4360i) q^{77} +(-14.7717 - 2.85730i) q^{78} +(-10.5541 - 6.09342i) q^{79} +(-0.953472 + 3.88470i) q^{80} +(5.56549 + 9.63970i) q^{81} +(-3.19121 + 3.67786i) q^{82} +16.9697i q^{83} +(-7.35116 + 9.03441i) q^{84} -4.36749i q^{85} +(-2.25166 - 1.95372i) q^{86} +(-4.83037 - 8.36645i) q^{87} +(16.4122 + 0.814944i) q^{88} +(-5.11692 - 2.95425i) q^{89} +(0.495521 - 2.56175i) q^{90} +(-2.82449 - 12.4719i) q^{91} +(0.135914 - 0.338179i) q^{92} +(7.77680 + 4.48994i) q^{93} +(-2.53130 + 0.874188i) q^{94} +(1.63783 - 0.945600i) q^{95} +(-12.3990 + 1.14197i) q^{96} -13.2388i q^{97} +(-9.54283 - 2.63333i) q^{98} -10.7190 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 8 q^{12} - 20 q^{13} - 15 q^{14} - 3 q^{16} + 6 q^{17} - 27 q^{18} + 18 q^{19} + 2 q^{20} + 26 q^{21} - 16 q^{22} - 18 q^{23} + 6 q^{24} - 12 q^{25} - 29 q^{26} + 3 q^{28} + 10 q^{30} + 6 q^{31} - 33 q^{32} + 12 q^{33} + 20 q^{34} - 8 q^{35} - 22 q^{36} + 9 q^{38} + 18 q^{39} - 3 q^{40} - 12 q^{42} + 32 q^{43} - 25 q^{44} - 12 q^{45} + 53 q^{46} + 14 q^{48} + 8 q^{49} - 22 q^{51} - 31 q^{52} - 30 q^{53} + 10 q^{54} + 16 q^{55} + 16 q^{56} - 44 q^{57} + 30 q^{58} - 18 q^{59} + 10 q^{60} - 22 q^{61} - 8 q^{62} + 12 q^{63} + 58 q^{64} - 10 q^{65} - 8 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 3 q^{70} - 23 q^{72} + 30 q^{73} - 43 q^{74} - 12 q^{75} - 8 q^{76} + 32 q^{77} - 8 q^{78} - 6 q^{79} + 3 q^{80} - 4 q^{81} - 27 q^{82} - 16 q^{84} - 36 q^{86} - 14 q^{87} + 49 q^{88} - 60 q^{89} - 24 q^{90} + 18 q^{91} - 38 q^{92} + 18 q^{93} + 11 q^{94} + 18 q^{95} + 2 q^{96} - 19 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 8 * q^12 - 20 * q^13 - 15 * q^14 - 3 * q^16 + 6 * q^17 - 27 * q^18 + 18 * q^19 + 2 * q^20 + 26 * q^21 - 16 * q^22 - 18 * q^23 + 6 * q^24 - 12 * q^25 - 29 * q^26 + 3 * q^28 + 10 * q^30 + 6 * q^31 - 33 * q^32 + 12 * q^33 + 20 * q^34 - 8 * q^35 - 22 * q^36 + 9 * q^38 + 18 * q^39 - 3 * q^40 - 12 * q^42 + 32 * q^43 - 25 * q^44 - 12 * q^45 + 53 * q^46 + 14 * q^48 + 8 * q^49 - 22 * q^51 - 31 * q^52 - 30 * q^53 + 10 * q^54 + 16 * q^55 + 16 * q^56 - 44 * q^57 + 30 * q^58 - 18 * q^59 + 10 * q^60 - 22 * q^61 - 8 * q^62 + 12 * q^63 + 58 * q^64 - 10 * q^65 - 8 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 3 * q^70 - 23 * q^72 + 30 * q^73 - 43 * q^74 - 12 * q^75 - 8 * q^76 + 32 * q^77 - 8 * q^78 - 6 * q^79 + 3 * q^80 - 4 * q^81 - 27 * q^82 - 16 * q^84 - 36 * q^86 - 14 * q^87 + 49 * q^88 - 60 * q^89 - 24 * q^90 + 18 * q^91 - 38 * q^92 + 18 * q^93 + 11 * q^94 + 18 * q^95 + 2 * q^96 - 19 * q^98 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.06817	+	0.926830i	0.755310	+	0.655368i
$2$	1.06817	+	0.926830i	0.755310	+	0.655368i
$3$	1.90624	−	1.10057i	1.10057	−	0.635414i	0.164198	−	0.986427i	$-0.447496\pi$
$3$	1.90624	−	1.10057i	1.10057	−	0.635414i	0.936370	+	0.351014i	$0.114163\pi$
$4$	0.281971	+	1.98002i	0.140986	+	0.990012i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	3.05623	+	0.591168i	1.24770	+	0.241343i
$7$	0.584379	+	2.58041i	0.220874	+	0.975302i
$7$	0.584379	+	2.58041i	0.220874	+	0.975302i
$8$	−1.53395	+	2.37634i	−0.542334	+	0.840163i
$9$	0.922503	−	1.59782i	0.307501	−	0.532608i
$10$	1.33674	−	0.461647i	0.422715	−	0.145985i
$11$	−2.90486	−	5.03137i	−0.875849	−	1.51701i	−0.855856	−	0.517214i	$-0.826969\pi$
$11$	−2.90486	−	5.03137i	−0.875849	−	1.51701i	−0.0199929	−	0.999800i	$-0.506364\pi$
$12$	2.71666	+	3.46407i	0.784231	+	0.999992i
$13$	−4.83332			−1.34052			−0.670260	−	0.742126i	$-0.733818\pi$
$13$	−4.83332			−1.34052			−0.670260	+	0.742126i	$0.733818\pi$
$14$	−1.76738	+	3.29793i	−0.472353	+	0.881409i
$15$		−	2.20114i		−	0.568331i
$16$	−3.84098	+	1.11662i	−0.960246	+	0.279155i
$17$	3.78236	−	2.18375i	0.917357	−	0.529636i	0.0345662	−	0.999402i	$-0.488995\pi$
$17$	3.78236	−	2.18375i	0.917357	−	0.529636i	0.882791	+	0.469766i	$0.155662\pi$
$18$	2.46630	−	0.851741i	0.581313	−	0.200757i
$19$	1.63783	+	0.945600i	0.375743	+	0.216936i	0.675965	−	0.736934i	$-0.263727\pi$
$19$	1.63783	+	0.945600i	0.375743	+	0.216936i	−0.300221	+	0.953870i	$0.597061\pi$
$20$	1.85574	+	0.745818i	0.414955	+	0.166770i
$21$	3.95388	+	4.27573i	0.862808	+	0.933041i
$22$	1.56034	−	8.06667i	0.332666	−	1.71982i
$23$	−0.157820	−	0.0911173i	−0.0329077	−	0.0189993i	0.483456	−	0.875369i	$-0.339381\pi$
$23$	−0.157820	−	0.0911173i	−0.0329077	−	0.0189993i	−0.516364	+	0.856369i	$0.672715\pi$
$24$	−0.308759	+	6.21810i	−0.0630252	+	1.26926i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−5.16280	−	4.47966i	−1.01251	−	0.878534i
$27$			2.54230i			0.489266i
$28$	−4.94449	+	1.88468i	−0.934421	+	0.356172i
$29$		−	4.38898i		−	0.815013i	−0.913202	−	0.407506i	$-0.866398\pi$
$29$		−	4.38898i		−	0.815013i	0.913202	−	0.407506i	$-0.133602\pi$
$30$	2.04008	−	2.35119i	0.372466	−	0.429266i
$31$	2.03983	+	3.53308i	0.366364	+	0.634560i	0.988994	−	0.147956i	$-0.0472693\pi$
$31$	2.03983	+	3.53308i	0.366364	+	0.634560i	−0.622630	+	0.782516i	$0.713936\pi$
$32$	−5.13774	−	2.36720i	−0.908232	−	0.418466i
$33$	−11.0747	−	6.39400i	−1.92786	−	1.11305i
$34$	6.06416	+	1.17300i	1.04000	+	0.201167i
$35$	2.52689	+	0.784117i	0.427122	+	0.132540i
$36$	3.42385	+	1.37604i	0.570641	+	0.229340i
$37$	−3.69132	−	2.13119i	−0.606849	−	0.350365i	0.164882	−	0.986313i	$-0.447276\pi$
$37$	−3.69132	−	2.13119i	−0.606849	−	0.350365i	−0.771731	+	0.635949i	$0.780609\pi$
$38$	0.873066	+	2.52805i	0.141630	+	0.410104i
$39$	−9.21347	+	5.31940i	−1.47534	+	0.851785i
$40$	1.29099	+	2.51661i	0.204124	+	0.397911i
$41$			3.44314i			0.537729i	0.963178	+	0.268864i	$0.0866483\pi$
$41$			3.44314i			0.537729i	−0.963178	+	0.268864i	$0.913352\pi$
$42$	0.260540	+	8.23178i	0.0402022	+	1.27019i
$43$	−2.10796			−0.321461			−0.160731	−	0.986998i	$-0.551385\pi$
$43$	−2.10796			−0.321461			−0.160731	+	0.986998i	$0.551385\pi$
$44$	9.14314	−	7.17039i	1.37838	−	1.08098i
$45$	−0.922503	−	1.59782i	−0.137519	−	0.238189i
$46$	−0.0841280	−	0.243601i	−0.0124040	−	0.0359170i
$47$	−0.946816	+	1.63993i	−0.138107	+	0.239209i	−0.926780	−	0.375604i	$-0.877435\pi$
$47$	−0.946816	+	1.63993i	−0.138107	+	0.239209i	0.788673	+	0.614813i	$0.210769\pi$
$48$	−6.09293	+	6.35581i	−0.879438	+	0.917382i
$49$	−6.31700	+	3.01587i	−0.902429	+	0.430839i
$50$	0.268574	−	1.38848i	0.0379821	−	0.196360i
$51$	4.80673	−	8.32550i	0.673076	−	1.16580i
$52$	−1.36286	−	9.57008i	−0.188994	−	1.32713i
$53$	8.54212	−	4.93180i	1.17335	−	0.677434i	0.218884	−	0.975751i	$-0.429758\pi$
$53$	8.54212	−	4.93180i	1.17335	−	0.677434i	0.954467	+	0.298317i	$0.0964252\pi$
$54$	−2.35628	+	2.71561i	−0.320649	+	0.369547i
$55$	−5.80972			−0.783383
$56$	−7.02833	−	2.56954i	−0.939200	−	0.343369i
$57$	4.16279			0.551375
$58$	4.06784	−	4.68817i	0.534133	−	0.615587i
$59$	−6.35546	+	3.66932i	−0.827410	+	0.477705i	−0.852965	−	0.521968i	$-0.825198\pi$
$59$	−6.35546	+	3.66932i	−0.827410	+	0.477705i	0.0255550	+	0.999673i	$0.491865\pi$
$60$	4.35830	−	0.620657i	0.562655	−	0.0801265i
$61$	4.89522	−	8.47877i	0.626769	−	1.08560i	−0.361427	−	0.932400i	$-0.617710\pi$
$61$	4.89522	−	8.47877i	0.626769	−	1.08560i	0.988196	−	0.153195i	$-0.0489562\pi$
$62$	−1.09569	+	5.66450i	−0.139153	+	0.719393i
$63$	4.66212	+	1.44670i	0.587373	+	0.182267i
$64$	−3.29398	−	7.29039i	−0.411747	−	0.911298i
$65$	−2.41666	+	4.18577i	−0.299750	+	0.519181i
$66$	−5.90354	−	17.0943i	−0.726675	−	2.10416i
$67$	6.04954	+	10.4781i	0.739069	+	1.28011i	0.952915	+	0.303238i	$0.0980678\pi$
$67$	6.04954	+	10.4781i	0.739069	+	1.28011i	−0.213845	+	0.976868i	$0.568599\pi$
$68$	5.39039	+	6.87341i	0.653680	+	0.833523i
$69$	−0.401124			−0.0482896
$70$	1.97240	+	3.17957i	0.235747	+	0.380031i
$71$			8.80669i			1.04516i	0.852590	+	0.522581i	$0.175031\pi$
$71$			8.80669i			1.04516i	−0.852590	+	0.522581i	$0.824969\pi$
$72$	2.38189	+	4.64317i	0.280709	+	0.547202i
$73$	7.34998	−	4.24351i	0.860250	−	0.496666i	−0.00384586	−	0.999993i	$-0.501224\pi$
$73$	7.34998	−	4.24351i	0.860250	−	0.496666i	0.864096	+	0.503327i	$0.167891\pi$
$74$	−1.96771	−	5.69769i	−0.228741	−	0.662344i
$75$	−1.90624	−	1.10057i	−0.220114	−	0.127083i
$76$	−1.41049	+	3.50957i	−0.161794	+	0.402575i
$77$	11.2854	−	10.4360i	1.28610	−	1.18929i
$78$	−14.7717	−	2.85730i	−1.67257	−	0.323526i
$79$	−10.5541	−	6.09342i	−1.18743	−	0.685563i	−0.229708	−	0.973259i	$-0.573777\pi$
$79$	−10.5541	−	6.09342i	−1.18743	−	0.685563i	−0.957722	+	0.287696i	$0.907111\pi$
$80$	−0.953472	+	3.88470i	−0.106601	+	0.434323i
$81$	5.56549	+	9.63970i	0.618387	+	1.07108i
$82$	−3.19121	+	3.67786i	−0.352410	+	0.406152i
$83$			16.9697i			1.86267i	0.364163	+	0.931335i	$0.381355\pi$
$83$			16.9697i			1.86267i	−0.364163	+	0.931335i	$0.618645\pi$
$84$	−7.35116	+	9.03441i	−0.802078	+	0.985735i
$85$		−	4.36749i		−	0.473721i
$86$	−2.25166	−	1.95372i	−0.242803	−	0.210676i
$87$	−4.83037	−	8.36645i	−0.517870	−	0.896977i
$88$	16.4122	+	0.814944i	1.74954	+	0.0868734i
$89$	−5.11692	−	2.95425i	−0.542392	−	0.313150i	0.203656	−	0.979043i	$-0.434718\pi$
$89$	−5.11692	−	2.95425i	−0.542392	−	0.313150i	−0.746048	+	0.665892i	$0.768051\pi$
$90$	0.495521	−	2.56175i	0.0522325	−	0.270032i
$91$	−2.82449	−	12.4719i	−0.296087	−	1.30741i
$92$	0.135914	−	0.338179i	0.0141700	−	0.0352576i
$93$	7.77680	+	4.48994i	0.806417	+	0.465585i
$94$	−2.53130	+	0.874188i	−0.261084	+	0.0901656i
$95$	1.63783	−	0.945600i	0.168038	−	0.0970165i
$96$	−12.3990	+	1.14197i	−1.26547	+	0.116552i
$97$		−	13.2388i		−	1.34420i	−0.740461	−	0.672100i	$-0.765393\pi$
$97$		−	13.2388i		−	1.34420i	0.740461	−	0.672100i	$-0.234607\pi$
$98$	−9.54283	−	2.63333i	−0.963971	−	0.266007i
$99$	−10.7190			−1.07730
$100$	1.57376	−	1.23421i	0.157376	−	0.123421i
$101$	1.23442	+	2.13807i	0.122829	+	0.212746i	0.920882	−	0.389841i	$-0.127470\pi$
$101$	1.23442	+	2.13807i	0.122829	+	0.212746i	−0.798053	+	0.602587i	$0.794137\pi$
$102$	12.8507	−	4.43802i	1.27241	−	0.439429i
$103$	−0.920346	+	1.59409i	−0.0906844	+	0.157070i	−0.907799	−	0.419405i	$-0.862239\pi$
$103$	−0.920346	+	1.59409i	−0.0906844	+	0.157070i	0.817115	+	0.576475i	$0.195572\pi$
$104$	7.41408	−	11.4856i	0.727010	−	1.12626i
$105$	5.67983	−	1.28630i	0.554295	−	0.125530i
$106$	13.6954	+	2.64910i	1.33021	+	0.257304i
$107$	9.08674	−	15.7387i	0.878448	−	1.52152i	0.0254044	−	0.999677i	$-0.491913\pi$
$107$	9.08674	−	15.7387i	0.878448	−	1.52152i	0.853044	−	0.521839i	$-0.174754\pi$
$108$	−5.03381	+	0.716855i	−0.484379	+	0.0689794i
$109$	−3.40525	+	1.96602i	−0.326164	+	0.188311i	−0.654137	−	0.756376i	$-0.726968\pi$
$109$	−3.40525	+	1.96602i	−0.326164	+	0.188311i	0.327973	+	0.944687i	$0.393635\pi$
$110$	−6.20577	−	5.38463i	−0.591697	−	0.513404i
$111$	−9.38206			−0.890506
$112$	−5.12592	−	9.25878i	−0.484354	−	0.874872i
$113$	7.16641			0.674159			0.337079	−	0.941476i	$-0.390561\pi$
$113$	7.16641			0.674159			0.337079	+	0.941476i	$0.390561\pi$
$114$	4.44657	+	3.85820i	0.416459	+	0.361354i
$115$	−0.157820	+	0.0911173i	−0.0147168	+	0.00849673i
$116$	8.69028	−	1.23756i	0.806872	−	0.114905i
$117$	−4.45875	+	7.72278i	−0.412212	+	0.713972i
$118$	−10.1895	−	1.97097i	−0.938024	−	0.181443i
$119$	7.84529	+	8.48390i	0.719176	+	0.777717i
$120$	5.23065	+	3.37644i	0.477491	+	0.308226i
$121$	−11.3764	+	19.7046i	−1.03422	+	1.79133i
$122$	13.0873	−	4.51972i	1.18487	−	0.409196i
$123$	3.78942	+	6.56346i	0.341680	+	0.591808i
$124$	−6.42041	+	5.03513i	−0.576570	+	0.452168i
$125$	−1.00000			−0.0894427
$126$	3.63909	+	5.86632i	0.324196	+	0.522613i
$127$			2.88206i			0.255742i	0.991791	+	0.127871i	$0.0408143\pi$
$127$			2.88206i			0.255742i	−0.991791	+	0.127871i	$0.959186\pi$
$128$	3.23842	−	10.8403i	0.286239	−	0.958158i
$129$	−4.01829	+	2.31996i	−0.353790	+	0.204261i
$130$	−6.46090	+	2.23128i	−0.566659	+	0.195697i
$131$	6.92953	+	4.00076i	0.605436	+	0.349548i	0.771177	−	0.636621i	$-0.219668\pi$
$131$	6.92953	+	4.00076i	0.605436	+	0.349548i	−0.165741	+	0.986169i	$0.553002\pi$
$132$	9.53752	−	23.7312i	0.830134	−	2.06553i
$133$	−1.48292	+	4.77885i	−0.128586	+	0.414379i
$134$	−3.24950	+	16.7993i	−0.280714	+	1.45124i
$135$	2.20170	+	1.27115i	0.189492	+	0.109403i
$136$	−0.612639	+	12.3379i	−0.0525334	+	1.05797i
$137$	5.09925	+	8.83216i	0.435658	+	0.754582i	0.997349	−	0.0727651i	$-0.0231823\pi$
$137$	5.09925	+	8.83216i	0.435658	+	0.754582i	−0.561691	+	0.827347i	$0.689849\pi$
$138$	−0.428468	−	0.371773i	−0.0364736	−	0.0316475i
$139$			9.93769i			0.842904i	0.906851	+	0.421452i	$0.138479\pi$
$139$			9.93769i			0.842904i	−0.906851	+	0.421452i	$0.861521\pi$
$140$	−0.840060	+	5.22439i	−0.0709981	+	0.441542i
$141$			4.16814i			0.351021i
$142$	−8.16230	+	9.40703i	−0.684965	+	0.789421i
$143$	14.0401	+	24.3182i	1.17409	+	2.03359i
$144$	−1.75916	+	7.16730i	−0.146597	+	0.597275i
$145$	−3.80097	−	2.19449i	−0.315653	−	0.182242i
$146$	11.7840	+	2.27939i	0.975254	+	0.188644i
$147$	−8.72256	+	12.7013i	−0.719424	+	1.04758i
$148$	3.17895	−	7.90983i	0.261308	−	0.650184i
$149$	−13.6559	−	7.88422i	−1.11873	−	0.645900i	−0.177655	−	0.984093i	$-0.556851\pi$
$149$	−13.6559	−	7.88422i	−1.11873	−	0.645900i	−0.941077	+	0.338192i	$0.890185\pi$
$150$	−1.01615	−	2.94236i	−0.0829681	−	0.240242i
$151$	5.24155	−	3.02621i	0.426552	−	0.246270i	−0.271325	−	0.962488i	$-0.587462\pi$
$151$	5.24155	−	3.02621i	0.426552	−	0.246270i	0.697877	+	0.716218i	$0.254128\pi$
$152$	−4.75942	+	2.44153i	−0.386040	+	0.198034i
$153$		−	8.05806i		−	0.651455i
$154$	21.7271	−	0.687674i	1.75082	−	0.0554143i
$155$	4.07965			0.327686
$156$	−13.1305	−	16.7430i	−1.05128	−	1.34051i
$157$	10.2074	+	17.6798i	0.814641	+	1.41100i	0.909585	+	0.415518i	$0.136400\pi$
$157$	10.2074	+	17.6798i	0.814641	+	1.41100i	−0.0949439	+	0.995483i	$0.530267\pi$
$158$	−5.62601	−	16.2907i	−0.447581	−	1.29602i
$159$	10.8556	−	18.8024i	0.860902	−	1.49113i
$160$	−4.61893	+	3.26581i	−0.365158	+	0.258185i
$161$	0.142893	−	0.460486i	0.0112616	−	0.0362914i
$162$	−2.98949	+	15.4551i	−0.234876	+	1.21427i
$163$	1.91267	−	3.31285i	0.149812	−	0.259482i	−0.781346	−	0.624098i	$-0.785466\pi$
$163$	1.91267	−	3.31285i	0.149812	−	0.259482i	0.931158	+	0.364616i	$0.118800\pi$
$164$	−6.81751	+	0.970867i	−0.532358	+	0.0758120i
$165$	−11.0747	+	6.39400i	−0.862167	+	0.497772i
$166$	−15.7281	+	18.1266i	−1.22073	+	1.40689i
$167$	21.6531			1.67556			0.837782	−	0.546005i	$-0.183852\pi$
$167$	21.6531			1.67556			0.837782	+	0.546005i	$0.183852\pi$
$168$	−16.2257	+	2.83700i	−1.25184	+	0.218879i
$169$	10.3609			0.796996
$170$	4.04793	−	4.66522i	0.310462	−	0.357806i
$171$	3.02180	−	1.74464i	0.231083	−	0.133416i
$172$	−0.594385	−	4.17382i	−0.0453214	−	0.318251i
$173$	−5.20160	+	9.00944i	−0.395470	+	0.684975i	−0.993161	−	0.116752i	$-0.962752\pi$
$173$	−5.20160	+	9.00944i	−0.395470	+	0.684975i	0.597691	+	0.801727i	$0.296085\pi$
$174$	2.59462	−	13.4137i	0.196698	−	1.01689i
$175$	1.94251	−	1.79629i	0.146840	−	0.135787i
$176$	16.7756	+	16.0818i	1.26451	+	1.21221i
$177$	−8.07669	+	13.9892i	−0.607081	+	1.05150i
$178$	−2.72764	−	7.89816i	−0.204445	−	0.591992i
$179$	3.80514	+	6.59069i	0.284409	+	0.492611i	0.972466	−	0.233046i	$-0.0748692\pi$
$179$	3.80514	+	6.59069i	0.284409	+	0.492611i	−0.688056	+	0.725657i	$0.741536\pi$
$180$	2.90361	−	2.27712i	0.216422	−	0.169726i
$181$	11.2225			0.834160			0.417080	−	0.908870i	$-0.363054\pi$
$181$	11.2225			0.834160			0.417080	+	0.908870i	$0.363054\pi$
$182$	8.54233	−	15.9399i	0.633199	−	1.18155i
$183$		−	21.5501i		−	1.59303i
$184$	0.458614	−	0.235264i	0.0338095	−	0.0173439i
$185$	−3.69132	+	2.13119i	−0.271391	+	0.156688i
$186$	4.14553	+	12.0038i	0.303965	+	0.880161i
$187$	−21.9745	−	12.6870i	−1.60693	−	0.927763i
$188$	−3.51408	−	1.41230i	−0.256291	−	0.103003i
$189$	−6.56017	+	1.48567i	−0.477182	+	0.108066i
$190$	2.62589	+	0.507927i	0.190502	+	0.0368489i
$191$	−6.68571	−	3.86000i	−0.483761	−	0.279300i	0.238222	−	0.971211i	$-0.423436\pi$
$191$	−6.68571	−	3.86000i	−0.483761	−	0.279300i	−0.721983	+	0.691911i	$0.756769\pi$
$192$	−14.3027	−	10.2720i	−1.03221	−	0.741317i
$193$	−11.7011	−	20.2669i	−0.842265	−	1.45885i	−0.887975	−	0.459892i	$-0.847888\pi$
$193$	−11.7011	−	20.2669i	−0.842265	−	1.45885i	0.0457097	−	0.998955i	$-0.485445\pi$
$194$	12.2701	−	14.1413i	0.880945	−	1.01529i
$195$			10.6388i			0.761860i
$196$	−7.75271	−	11.6574i	−0.553765	−	0.832673i
$197$		−	20.4272i		−	1.45538i	−0.685907	−	0.727689i	$-0.740594\pi$
$197$		−	20.4272i		−	1.45538i	0.685907	−	0.727689i	$-0.259406\pi$
$198$	−11.4497	−	9.93468i	−0.813694	−	0.706027i
$199$	−1.10091	−	1.90683i	−0.0780413	−	0.135172i	0.824363	−	0.566061i	$-0.191533\pi$
$199$	−1.10091	−	1.90683i	−0.0780413	−	0.135172i	−0.902405	+	0.430889i	$0.858200\pi$
$200$	2.82495	+	0.140272i	0.199754	+	0.00991876i
$201$	23.0638	+	13.3159i	1.62679	+	0.939230i
$202$	−0.663064	+	3.42792i	−0.0466530	+	0.241187i
$203$	11.3253	−	2.56482i	0.794884	−	0.180015i
$204$	17.8400	+	7.16988i	1.24905	+	0.501992i
$205$	2.98185	+	1.72157i	0.208261	+	0.120240i
$206$	−2.46053	+	0.849749i	−0.171433	+	0.0592048i
$207$	−0.291179	+	0.168112i	−0.0202383	+	0.0116846i
$208$	18.5647	−	5.39697i	1.28723	−	0.374213i
$209$		−	10.9874i		−	0.760011i
$210$	7.25920	+	3.89026i	0.500932	+	0.268453i
$211$	−28.9363			−1.99206			−0.996028	−	0.0890425i	$-0.971619\pi$
$211$	−28.9363			−1.99206			−0.996028	+	0.0890425i	$0.971619\pi$
$212$	12.1737	+	15.5230i	0.836093	+	1.06612i
$213$	9.69236	+	16.7877i	0.664110	+	1.15027i
$214$	24.2933	−	8.38972i	1.66065	−	0.573510i
$215$	−1.05398	+	1.82555i	−0.0718810	+	0.124501i
$216$	−6.04136	−	3.89977i	−0.411063	−	0.265346i
$217$	−7.92476	+	7.32824i	−0.537968	+	0.497473i
$218$	−5.45955	−	1.05605i	−0.369768	−	0.0715244i
$219$	9.34056	−	16.1783i	0.631176	−	1.09323i
$220$	−1.63817	−	11.5034i	−0.110446	−	0.775558i
$221$	−18.2813	+	10.5547i	−1.22974	+	0.709989i
$222$	−10.0216	−	8.69558i	−0.672608	−	0.583609i
$223$	11.0535			0.740200			0.370100	−	0.928992i	$-0.379323\pi$
$223$	11.0535			0.740200			0.370100	+	0.928992i	$0.379323\pi$
$224$	3.10596	−	14.6408i	0.207526	−	0.978230i
$225$	−1.84501			−0.123000
$226$	7.65493	+	6.64204i	0.509199	+	0.441822i
$227$	7.11916	−	4.11025i	0.472515	−	0.272807i	−0.244777	−	0.969579i	$-0.578715\pi$
$227$	7.11916	−	4.11025i	0.472515	−	0.272807i	0.717292	+	0.696773i	$0.245381\pi$
$228$	1.17379	+	8.24243i	0.0777359	+	0.545868i
$229$	−5.03725	+	8.72478i	−0.332871	+	0.576549i	−0.983074	−	0.183211i	$-0.941351\pi$
$229$	−5.03725	+	8.72478i	−0.332871	+	0.576549i	0.650203	+	0.759761i	$0.274684\pi$
$230$	−0.253029	−	0.0489435i	−0.0166842	−	0.00322724i
$231$	10.0273	−	32.3138i	0.659747	−	2.12609i
$232$	10.4297	+	6.73248i	0.684743	+	0.442009i
$233$	3.68557	−	6.38359i	0.241450	−	0.418203i	−0.719678	−	0.694308i	$-0.755711\pi$
$233$	3.68557	−	6.38359i	0.241450	−	0.418203i	0.961127	+	0.276105i	$0.0890438\pi$
$234$	−11.9204	+	4.11673i	−0.779262	+	0.269119i
$235$	0.946816	+	1.63993i	0.0617634	+	0.106977i
$236$	−9.05740	−	11.5493i	−0.589587	−	0.751796i
$237$	−26.8249			−1.74246
$238$	0.516963	+	16.3335i	0.0335097	+	1.05874i
$239$		−	20.9534i		−	1.35536i	−0.735355	−	0.677682i	$-0.762984\pi$
$239$		−	20.9534i		−	1.35536i	0.735355	−	0.677682i	$-0.237016\pi$
$240$	2.45783	+	8.45454i	0.158652	+	0.545738i
$241$	−2.42132	+	1.39795i	−0.155971	+	0.0900498i	−0.575954	−	0.817482i	$-0.695369\pi$
$241$	−2.42132	+	1.39795i	−0.155971	+	0.0900498i	0.419983	+	0.907532i	$0.362036\pi$
$242$	−30.4148	+	10.5038i	−1.95514	+	0.675209i
$243$	14.6132	+	8.43695i	0.937439	+	0.541231i
$244$	18.1685	+	7.30188i	1.16312	+	0.467455i
$245$	−0.546681	+	6.97862i	−0.0349262	+	0.445848i
$246$	−2.03548	+	10.5230i	−0.129777	+	0.670924i
$247$	−7.91614	−	4.57039i	−0.503692	−	0.290807i
$248$	−11.5248	−	0.572263i	−0.731826	−	0.0363387i
$249$	18.6764	+	32.3484i	1.18357	+	2.05000i
$250$	−1.06817	−	0.926830i	−0.0675570	−	0.0586179i
$251$		−	18.7656i		−	1.18448i	−0.805763	−	0.592238i	$-0.798244\pi$
$251$		−	18.7656i		−	1.18448i	0.805763	−	0.592238i	$-0.201756\pi$
$252$	−1.54992	+	9.63904i	−0.0976356	+	0.607203i
$253$			1.05873i			0.0665620i
$254$	−2.67118	+	3.07853i	−0.167605	+	0.193164i
$255$	−4.80673	−	8.32550i	−0.301009	−	0.521363i
$256$	13.5063	−	8.57783i	0.844145	−	0.536114i
$257$	−6.76564	−	3.90615i	−0.422029	−	0.243659i	0.273916	−	0.961754i	$-0.411681\pi$
$257$	−6.76564	−	3.90615i	−0.422029	−	0.243659i	−0.695945	+	0.718095i	$0.745014\pi$
$258$	−6.44242	−	1.24616i	−0.401088	−	0.0775826i
$259$	3.34220	−	10.7705i	0.207674	−	0.669248i
$260$	−8.96936	−	3.60477i	−0.556256	−	0.223558i
$261$	−7.01281	−	4.04885i	−0.434082	−	0.250617i
$262$	3.69388	+	10.6960i	0.228209	+	0.660800i
$263$	−5.03985	+	2.90976i	−0.310770	+	0.179423i	−0.647271	−	0.762260i	$-0.724090\pi$
$263$	−5.03985	+	2.90976i	−0.310770	+	0.179423i	0.336501	+	0.941683i	$0.390757\pi$
$264$	32.1824	−	16.5092i	1.98069	−	1.01607i
$265$		−	9.86359i		−	0.605916i
$266$	−6.01320	+	3.73020i	−0.368693	+	0.228713i
$267$	−13.0054			−0.795920
$268$	−19.0411	+	14.9328i	−1.16312	+	0.912164i
$269$	−12.0950	−	20.9492i	−0.737445	−	1.27729i	−0.953642	−	0.300943i	$-0.902699\pi$
$269$	−12.0950	−	20.9492i	−0.737445	−	1.27729i	0.216197	−	0.976350i	$-0.430635\pi$
$270$	1.17364	+	3.39840i	0.0714257	+	0.206820i
$271$	−7.83742	+	13.5748i	−0.476089	+	0.824611i	−0.999625	−	0.0273932i	$-0.991279\pi$
$271$	−7.83742	+	13.5748i	−0.476089	+	0.824611i	0.523536	+	0.852004i	$0.324613\pi$
$272$	−12.0896	+	12.6112i	−0.733038	+	0.764666i
$273$	−19.1104	−	20.6660i	−1.15661	−	1.25076i
$274$	−2.73905	+	14.1604i	−0.165472	+	0.855460i
$275$	−2.90486	+	5.03137i	−0.175170	+	0.303403i
$276$	−0.113105	−	0.794234i	−0.00680813	−	0.0478073i
$277$	−12.6984	+	7.33142i	−0.762972	+	0.440502i	−0.830362	−	0.557225i	$-0.811866\pi$
$277$	−12.6984	+	7.33142i	−0.762972	+	0.440502i	0.0673898	+	0.997727i	$0.478533\pi$
$278$	−9.21055	+	10.6151i	−0.552412	+	0.636653i
$279$	7.52699			0.450629
$280$	−5.73945	+	4.80194i	−0.342998	+	0.286971i
$281$	15.0418			0.897320			0.448660	−	0.893703i	$-0.351901\pi$
$281$	15.0418			0.897320			0.448660	+	0.893703i	$0.351901\pi$
$282$	−3.86316	+	4.45228i	−0.230048	+	0.265130i
$283$	4.29409	−	2.47919i	0.255257	−	0.147373i	−0.366912	−	0.930256i	$-0.619585\pi$
$283$	4.29409	−	2.47919i	0.255257	−	0.147373i	0.622169	+	0.782883i	$0.286252\pi$
$284$	−17.4374	+	2.48323i	−1.03472	+	0.147353i
$285$	2.08140	−	3.60508i	0.123291	−	0.213547i
$286$	−7.54162	+	38.9888i	−0.445945	+	2.30545i
$287$	−8.88471	+	2.01210i	−0.524448	+	0.118771i
$288$	−8.52195	+	6.02544i	−0.502161	+	0.355053i
$289$	1.03750	−	1.79700i	0.0610294	−	0.105706i
$290$	−2.02616	−	5.86693i	−0.118980	−	0.344518i
$291$	−14.5702	−	25.2364i	−0.854123	−	1.47938i
$292$	10.4747	+	13.3566i	0.612988	+	0.781635i
$293$	−2.56812			−0.150031			−0.0750156	−	0.997182i	$-0.523901\pi$
$293$	−2.56812			−0.150031			−0.0750156	+	0.997182i	$0.523901\pi$
$294$	−21.0891	+	5.48278i	−1.22994	+	0.319762i
$295$			7.33865i			0.427273i
$296$	10.7267	−	5.50269i	0.623479	−	0.319838i
$297$	12.7912	−	7.38503i	0.742223	−	0.428523i
$298$	−7.27944	−	21.0784i	−0.421687	−	1.22104i
$299$	0.762793	+	0.440399i	0.0441135	+	0.0254689i
$300$	1.64165	−	4.08473i	0.0947805	−	0.235832i
$301$	−1.23185	−	5.43941i	−0.0710026	−	0.313522i
$302$	8.40365	+	1.62552i	0.483576	+	0.0935384i
$303$	4.70619	+	2.71712i	0.270363	+	0.156094i
$304$	−7.34675	−	1.80321i	−0.421365	−	0.103421i
$305$	−4.89522	−	8.47877i	−0.280299	−	0.485493i
$306$	7.46845	−	8.60737i	0.426943	−	0.492050i
$307$		−	14.4425i		−	0.824280i	−0.911121	−	0.412140i	$-0.864781\pi$
$307$		−	14.4425i		−	0.824280i	0.911121	−	0.412140i	$-0.135219\pi$
$308$	23.8456	+	19.4028i	1.35873	+	1.10558i
$309$			4.05162i			0.230488i
$310$	4.35776	+	3.78115i	0.247504	+	0.214755i
$311$	8.26712	+	14.3191i	0.468785	+	0.811960i	0.999363	−	0.0356762i	$-0.0113585\pi$
$311$	8.26712	+	14.3191i	0.468785	+	0.811960i	−0.530578	+	0.847636i	$0.678025\pi$
$312$	1.49233	−	30.0540i	0.0844866	−	1.70147i
$313$	2.19818	+	1.26912i	0.124248	+	0.0717348i	0.560836	−	0.827927i	$-0.310480\pi$
$313$	2.19818	+	1.26912i	0.124248	+	0.0717348i	−0.436588	+	0.899662i	$0.643813\pi$
$314$	−5.48290	+	28.3456i	−0.309418	+	1.59963i
$315$	3.58394	−	3.31417i	0.201932	−	0.186732i
$316$	9.08916	−	22.6156i	0.511305	−	1.27222i
$317$	14.8432	+	8.56971i	0.833676	+	0.481323i	0.855109	−	0.518447i	$-0.173490\pi$
$317$	14.8432	+	8.56971i	0.833676	+	0.481323i	−0.0214339	+	0.999770i	$0.506823\pi$
$318$	29.0222	−	10.0229i	1.62748	−	0.562054i
$319$	−22.0826	+	12.7494i	−1.23639	+	0.713828i
$320$	−7.96065	−	0.792525i	−0.445014	−	0.0443035i
$321$		−	40.0023i		−	2.23271i
$322$	0.579427	−	0.359440i	0.0322902	−	0.0200308i
$323$	8.25981			0.459588
$324$	−17.5175	+	13.7379i	−0.973196	+	0.763217i
$325$	2.41666	+	4.18577i	0.134052	+	0.232185i
$326$	5.11351	−	1.76596i	0.283211	−	0.0978074i
$327$	−4.32749	+	7.49543i	−0.239311	+	0.414498i
$328$	−8.18208	−	5.28162i	−0.451780	−	0.291629i
$329$	−4.78499	−	1.48483i	−0.263805	−	0.0818612i
$330$	−17.7558	−	3.43452i	−0.977427	−	0.189064i
$331$	−11.9027	+	20.6161i	−0.654233	+	1.13317i	0.327852	+	0.944729i	$0.393675\pi$
$331$	−11.9027	+	20.6161i	−0.654233	+	1.13317i	−0.982085	+	0.188436i	$0.939658\pi$
$332$	−33.6005	+	4.78498i	−1.84407	+	0.262610i
$333$	−6.81051	+	3.93205i	−0.373214	+	0.215475i
$334$	23.1291	+	20.0687i	1.26557	+	1.09811i
$335$	12.0991			0.661044
$336$	−19.9612	−	12.0080i	−1.08897	−	0.655092i
$337$	1.22715			0.0668470			0.0334235	−	0.999441i	$-0.489359\pi$
$337$	1.22715			0.0668470			0.0334235	+	0.999441i	$0.489359\pi$
$338$	11.0672	+	9.60284i	0.601979	+	0.522326i
$339$	13.6609	−	7.88712i	0.741958	−	0.428370i
$340$	8.64774	−	1.23151i	0.468990	−	0.0667878i
$341$	11.8508	−	20.5262i	0.641758	−	1.11156i
$342$	4.84478	+	0.937129i	0.261976	+	0.0506741i
$343$	−11.4737	−	14.5380i	−0.619521	−	0.784980i
$344$	3.23352	−	5.00924i	0.174340	−	0.270080i
$345$	−0.200562	+	0.347383i	−0.0107979	+	0.0187025i
$346$	−13.9064	+	4.80260i	−0.747613	+	0.258189i
$347$	−15.4834	−	26.8181i	−0.831194	−	1.43967i	−0.897092	−	0.441844i	$-0.854325\pi$
$347$	−15.4834	−	26.8181i	−0.831194	−	1.43967i	0.0658983	−	0.997826i	$-0.479009\pi$
$348$	15.2037	−	11.9233i	0.815006	−	0.639158i
$349$	26.6776			1.42802			0.714010	−	0.700136i	$-0.246877\pi$
$349$	26.6776			1.42802			0.714010	+	0.700136i	$0.246877\pi$
$350$	3.73978	−	0.118366i	0.199900	−	0.00632693i
$351$		−	12.2877i		−	0.655871i
$352$	3.01415	+	32.7262i	0.160654	+	1.74431i
$353$	−12.1501	+	7.01487i	−0.646685	+	0.373364i	−0.787185	−	0.616717i	$-0.788462\pi$
$353$	−12.1501	+	7.01487i	−0.646685	+	0.373364i	0.140500	+	0.990081i	$0.455129\pi$
$354$	−21.5929	+	7.45715i	−1.14765	+	0.396343i
$355$	7.62681	+	4.40334i	0.404789	+	0.233705i
$356$	4.40667	−	10.9646i	0.233553	−	0.581124i
$357$	24.2921	+	7.53807i	1.28568	+	0.398957i
$358$	−2.04392	+	10.5667i	−0.108025	+	0.558467i
$359$	−10.5164	−	6.07165i	−0.555035	−	0.320450i	0.196115	−	0.980581i	$-0.437167\pi$
$359$	−10.5164	−	6.07165i	−0.555035	−	0.320450i	−0.751150	+	0.660131i	$0.770501\pi$
$360$	5.21205	+	0.258804i	0.274699	+	0.0136402i
$361$	−7.71168	−	13.3570i	−0.405878	−	0.703001i
$362$	11.9875	+	10.4013i	0.630049	+	0.546682i
$363$			50.0822i			2.62864i
$364$	23.8983	−	9.10927i	1.25261	−	0.477456i
$365$		−	8.48703i		−	0.444231i
$366$	19.9733	−	23.0192i	1.04402	−	1.20323i
$367$	−5.75583	−	9.96939i	−0.300452	−	0.520398i	0.675787	−	0.737097i	$-0.263804\pi$
$367$	−5.75583	−	9.96939i	−0.300452	−	0.520398i	−0.976238	+	0.216700i	$0.930471\pi$
$368$	0.707927	+	0.173756i	0.0369032	+	0.00905764i
$369$	5.50153	+	3.17631i	0.286398	+	0.165352i
$370$	−5.91820	−	1.14476i	−0.307673	−	0.0595133i
$371$	17.7179	+	19.1601i	0.919866	+	0.994744i
$372$	−6.69735	+	16.6643i	−0.347241	+	0.864003i
$373$	−20.3241	−	11.7341i	−1.05234	−	0.607570i	−0.129037	−	0.991640i	$-0.541189\pi$
$373$	−20.3241	−	11.7341i	−1.05234	−	0.607570i	−0.923304	+	0.384070i	$0.874522\pi$
$374$	−11.7138	−	33.9184i	−0.605705	−	1.75388i
$375$	−1.90624	+	1.10057i	−0.0984379	+	0.0568331i
$376$	−2.44467	−	4.76553i	−0.126074	−	0.245764i
$377$			21.2133i			1.09254i
$378$	−8.38433	−	4.49322i	−0.431243	−	0.231106i
$379$	−15.5653			−0.799536			−0.399768	−	0.916616i	$-0.630909\pi$
$379$	−15.5653			−0.799536			−0.399768	+	0.916616i	$0.630909\pi$
$380$	2.33413	+	2.97630i	0.119738	+	0.152681i
$381$	3.17191	+	5.49391i	0.162502	+	0.281462i
$382$	−3.56391	−	10.3196i	−0.182345	−	0.527999i
$383$	7.45943	−	12.9201i	0.381159	−	0.660187i	−0.610069	−	0.792348i	$-0.708858\pi$
$383$	7.45943	−	12.9201i	0.381159	−	0.660187i	0.991228	+	0.132161i	$0.0421917\pi$
$384$	−5.75730	−	24.2284i	−0.293801	−	1.23640i
$385$	−3.39508	−	14.9915i	−0.173029	−	0.764035i
$386$	6.28524	−	32.4935i	0.319910	−	1.65387i
$387$	−1.94460	+	3.36815i	−0.0988498	+	0.171213i
$388$	26.2132	−	3.73297i	1.33077	−	0.189513i
$389$	10.9524	−	6.32338i	0.555310	−	0.320608i	−0.195951	−	0.980614i	$-0.562779\pi$
$389$	10.9524	−	6.32338i	0.555310	−	0.320608i	0.751261	+	0.660006i	$0.229446\pi$
$390$	−9.86036	+	11.3640i	−0.499299	+	0.575440i
$391$	−0.795909			−0.0402508
$392$	2.52325	−	19.6375i	0.127444	−	0.991846i
$393$	17.6125			0.888431
$394$	18.9326	−	21.8197i	0.953808	−	1.09926i
$395$	−10.5541	+	6.09342i	−0.531035	+	0.306593i
$396$	−3.02244	−	21.2238i	−0.151883	−	1.06654i
$397$	−7.61650	+	13.1922i	−0.382261	+	0.662095i	−0.991385	−	0.130979i	$-0.958188\pi$
$397$	−7.61650	+	13.1922i	−0.382261	+	0.662095i	0.609124	+	0.793075i	$0.291521\pi$
$398$	0.591351	−	3.05717i	0.0296417	−	0.153242i
$399$	2.43265	+	10.7417i	0.121785	+	0.537758i
$400$	2.88751	+	2.76808i	0.144376	+	0.138404i
$401$	−7.73594	+	13.3990i	−0.386315	+	0.669117i	−0.991951	−	0.126625i	$-0.959585\pi$
$401$	−7.73594	+	13.3990i	−0.386315	+	0.669117i	0.605636	+	0.795742i	$0.292919\pi$
$402$	12.2945	+	35.5998i	0.613192	+	1.77556i
$403$	−9.85913	−	17.0765i	−0.491118	−	0.850641i
$404$	−3.88536	+	3.04705i	−0.193304	+	0.151596i
$405$	11.1310			0.553102
$406$	14.4745	+	7.75701i	0.718360	+	0.384974i
$407$			24.7632i			1.22747i
$408$	12.4109	+	24.1933i	0.614432	+	1.19775i
$409$	−7.47055	+	4.31313i	−0.369395	+	0.213270i	−0.673194	−	0.739466i	$-0.735078\pi$
$409$	−7.47055	+	4.31313i	−0.369395	+	0.213270i	0.303799	+	0.952736i	$0.401745\pi$
$410$	1.58952	+	4.60260i	0.0785006	+	0.227306i
$411$	19.4408	+	11.2241i	0.958944	+	0.553646i
$412$	−3.41584	−	1.37282i	−0.168286	−	0.0676340i
$413$	−13.1823	−	14.2554i	−0.648661	−	0.701462i
$414$	−0.466839	−	0.0903011i	−0.0229439	−	0.00443806i
$415$	14.6962	+	8.48487i	0.721409	+	0.416506i
$416$	24.8323	+	11.4414i	1.21750	+	0.560963i
$417$	10.9371	+	18.9436i	0.535592	+	0.927673i
$418$	10.1834	−	11.7364i	0.498087	−	0.574044i
$419$		−	10.6898i		−	0.522230i	−0.965308	−	0.261115i	$-0.915910\pi$
$419$		−	10.6898i		−	0.522230i	0.965308	−	0.261115i	$-0.0840902\pi$
$420$	4.14845	+	10.8835i	0.202424	+	0.531060i
$421$			20.4941i			0.998823i	0.866365	+	0.499412i	$0.166450\pi$
$421$			20.4941i			0.998823i	−0.866365	+	0.499412i	$0.833550\pi$
$422$	−30.9088	−	26.8190i	−1.50462	−	1.30553i
$423$	1.74688	+	3.02569i	0.0849363	+	0.147114i
$424$	−1.38359	+	27.8641i	−0.0671931	+	1.35320i
$425$	−3.78236	−	2.18375i	−0.183471	−	0.105927i
$426$	−5.20623	+	26.9152i	−0.252243	+	1.30405i
$427$	24.7393	+	7.67685i	1.19722	+	0.371509i
$428$	33.7252	+	13.5541i	1.63017	+	0.655162i
$429$	53.5277	+	30.9042i	2.58434	+	1.49207i
$430$	−2.81781	+	0.973134i	−0.135887	+	0.0469287i
$431$	−20.9544	+	12.0980i	−1.00934	+	0.582740i	−0.910997	−	0.412412i	$-0.864686\pi$
$431$	−20.9544	+	12.0980i	−1.00934	+	0.582740i	−0.0983389	+	0.995153i	$0.531353\pi$
$432$	−2.83878	−	9.76493i	−0.136581	−	0.469815i
$433$			20.2949i			0.975311i	0.873036	+	0.487655i	$0.162148\pi$
$433$			20.2949i			0.975311i	−0.873036	+	0.487655i	$0.837852\pi$
$434$	−15.2570	+	0.482892i	−0.732361	+	0.0231796i
$435$	−9.66074			−0.463197
$436$	−4.85295	−	6.18811i	−0.232414	−	0.296357i
$437$	−0.172321	−	0.298469i	−0.00824324	−	0.0142777i
$438$	24.9719	−	8.62407i	1.19320	−	0.412074i
$439$	2.52231	−	4.36878i	0.120384	−	0.208510i	−0.799535	−	0.600619i	$-0.794921\pi$
$439$	2.52231	−	4.36878i	0.120384	−	0.208510i	0.919919	+	0.392109i	$0.128254\pi$
$440$	8.91184	−	13.8059i	0.424855	−	0.658169i
$441$	−1.00863	+	12.8756i	−0.0480300	+	0.613124i
$442$	−29.3100	−	5.66946i	−1.39414	−	0.269669i
$443$	−4.04696	+	7.00955i	−0.192277	+	0.333034i	−0.946005	−	0.324153i	$-0.894921\pi$
$443$	−4.04696	+	7.00955i	−0.192277	+	0.333034i	0.753727	+	0.657187i	$0.228254\pi$
$444$	−2.64547	−	18.5767i	−0.125548	−	0.881611i
$445$	−5.11692	+	2.95425i	−0.242565	+	0.140045i
$446$	11.8070	+	10.2448i	0.559080	+	0.485103i
$447$	−34.7085			−1.64166
$448$	16.8872	−	12.7601i	0.797847	−	0.602860i
$449$	−4.05786			−0.191502			−0.0957511	−	0.995405i	$-0.530525\pi$
$449$	−4.05786			−0.191502			−0.0957511	+	0.995405i	$0.530525\pi$
$450$	−1.97078	−	1.71001i	−0.0929034	−	0.0806106i
$451$	17.3237	−	10.0019i	0.815742	−	0.470969i
$452$	2.02072	+	14.1897i	0.0950466	+	0.667425i
$453$	6.66111	−	11.5374i	0.312966	−	0.542074i
$454$	11.4140	+	2.20781i	0.535684	+	0.103618i
$455$	−12.2132	−	3.78988i	−0.572566	−	0.177673i
$456$	−6.38553	+	9.89221i	−0.299030	+	0.463245i
$457$	−2.70734	+	4.68925i	−0.126644	+	0.219354i	−0.922374	−	0.386297i	$-0.873754\pi$
$457$	−2.70734	+	4.68925i	−0.126644	+	0.219354i	0.795730	+	0.605651i	$0.207087\pi$
$458$	−13.4670	+	4.65086i	−0.629273	+	0.217320i
$459$	5.55174	+	9.61589i	0.259133	+	0.448831i
$460$	−0.224915	−	0.286794i	−0.0104867	−	0.0133719i
$461$	−18.9095			−0.880702			−0.440351	−	0.897826i	$-0.645146\pi$
$461$	−18.9095			−0.880702			−0.440351	+	0.897826i	$0.645146\pi$
$462$	40.6603	−	25.2231i	1.89169	−	1.17348i
$463$		−	0.304782i		−	0.0141644i	−0.999975	−	0.00708220i	$-0.997746\pi$
$463$		−	0.304782i		−	0.0141644i	0.999975	−	0.00708220i	$-0.00225435\pi$
$464$	4.90081	+	16.8580i	0.227515	+	0.782613i
$465$	7.77680	−	4.48994i	0.360641	−	0.208216i
$466$	9.85331	−	3.40286i	0.456446	−	0.157634i
$467$	−3.35368	−	1.93625i	−0.155190	−	0.0895989i	0.420394	−	0.907342i	$-0.361892\pi$
$467$	−3.35368	−	1.93625i	−0.155190	−	0.0895989i	−0.575584	+	0.817743i	$0.695225\pi$
$468$	−16.5485	−	6.65083i	−0.764956	−	0.307435i
$469$	−23.5026	+	21.7335i	−1.08525	+	1.00356i
$470$	−0.508580	+	2.62926i	−0.0234590	+	0.121279i
$471$	38.9156	+	22.4680i	1.79314	+	1.03527i
$472$	1.02941	−	20.7313i	0.0473825	−	0.954235i
$473$	6.12334	+	10.6059i	0.281552	+	0.487662i
$474$	−28.6535	−	24.8621i	−1.31610	−	1.14196i
$475$		−	1.89120i		−	0.0867742i
$476$	−14.5862	+	17.9261i	−0.668556	+	0.821640i
$477$		−	18.1984i		−	0.833247i
$478$	19.4203	−	22.3818i	0.888263	−	1.02372i
$479$	16.4744	+	28.5344i	0.752732	+	1.30377i	0.946494	+	0.322722i	$0.104598\pi$
$479$	16.4744	+	28.5344i	0.752732	+	1.30377i	−0.193761	+	0.981049i	$0.562069\pi$
$480$	−5.21054	+	11.3089i	−0.237828	+	0.516177i
$481$	17.8413	+	10.3007i	0.813494	+	0.469671i
$482$	−3.88204	−	0.750906i	−0.176822	−	0.0342028i
$483$	−0.234408	−	1.03506i	−0.0106659	−	0.0470970i
$484$	−42.2234	−	16.9695i	−1.91924	−	0.771341i
$485$	−11.4652	−	6.61941i	−0.520606	−	0.300572i
$486$	7.78978	+	22.5561i	0.353351	+	1.02316i
$487$	35.8923	−	20.7224i	1.62643	−	0.939022i	0.641289	−	0.767300i	$-0.278400\pi$
$487$	35.8923	−	20.7224i	1.62643	−	0.939022i	0.985145	−	0.171722i	$-0.0549332\pi$
$488$	12.6394	+	24.6387i	0.572159	+	1.11534i
$489$		−	8.42012i		−	0.380771i
$490$	−7.05195	+	6.94767i	−0.318574	+	0.313864i
$491$	−25.4339			−1.14782			−0.573908	−	0.818920i	$-0.694573\pi$
$491$	−25.4339			−1.14782			−0.573908	+	0.818920i	$0.694573\pi$
$492$	−11.9273	+	9.35384i	−0.537724	+	0.421704i
$493$	−9.58441	−	16.6007i	−0.431660	−	0.747658i
$494$	−4.21980	−	12.2189i	−0.189858	−	0.549753i
$495$	−5.35949	+	9.28291i	−0.240891	+	0.417236i
$496$	−11.7800	−	11.2928i	−0.528940	−	0.507062i
$497$	−22.7248	+	5.14644i	−1.01935	+	0.230849i
$498$	−10.0320	+	51.8634i	−0.449543	+	2.32405i
$499$	3.25059	−	5.63019i	0.145516	−	0.252042i	−0.784049	−	0.620699i	$-0.786849\pi$
$499$	3.25059	−	5.63019i	0.145516	−	0.252042i	0.929565	+	0.368657i	$0.120182\pi$
$500$	−0.281971	−	1.98002i	−0.0126101	−	0.0885493i
$501$	41.2759	−	23.8307i	1.84407	−	1.06468i
$502$	17.3926	−	20.0449i	0.776268	−	0.894647i
$503$	−23.4094			−1.04378			−0.521888	−	0.853014i	$-0.674772\pi$
$503$	−23.4094			−1.04378			−0.521888	+	0.853014i	$0.674772\pi$
$504$	−10.5893	+	8.85962i	−0.471686	+	0.394639i
$505$	2.46883			0.109862
$506$	−0.981266	+	1.13091i	−0.0436226	+	0.0502749i
$507$	19.7505	−	11.4029i	0.877149	−	0.506422i
$508$	−5.70656	+	0.812659i	−0.253187	+	0.0360559i
$509$	8.44031	−	14.6190i	0.374110	−	0.647978i	−0.616083	−	0.787681i	$-0.711281\pi$
$509$	8.44031	−	14.6190i	0.374110	−	0.647978i	0.990193	+	0.139703i	$0.0446148\pi$
$510$	2.58192	−	13.3481i	0.114330	−	0.591062i
$511$	15.2452	+	16.4861i	0.674406	+	0.729303i
$512$	22.3772	+	3.35550i	0.988943	+	0.148294i
$513$	−2.40400	+	4.16385i	−0.106139	+	0.183838i
$514$	−3.60652	−	10.4430i	−0.159077	−	0.460622i
$515$	0.920346	+	1.59409i	0.0405553	+	0.0702438i
$516$	−5.72661	−	7.30214i	−0.252100	−	0.321459i
$517$	11.0015			0.483844
$518$	13.5525	−	8.40710i	0.595462	−	0.369387i
$519$			22.8989i			1.00515i
$520$	−6.23978	−	12.1636i	−0.273633	−	0.533408i
$521$	21.2245	−	12.2540i	0.929864	−	0.536857i	0.0430955	−	0.999071i	$-0.486278\pi$
$521$	21.2245	−	12.2540i	0.929864	−	0.536857i	0.886769	+	0.462214i	$0.152945\pi$
$522$	−3.73827	−	10.8245i	−0.163620	−	0.473777i
$523$	−25.2087	−	14.5543i	−1.10230	−	0.636414i	−0.165476	−	0.986214i	$-0.552916\pi$
$523$	−25.2087	−	14.5543i	−1.10230	−	0.636414i	−0.936824	+	0.349800i	$0.886249\pi$
$524$	−5.96768	+	14.8487i	−0.260699	+	0.648669i
$525$	1.72595	−	5.56203i	0.0753266	−	0.242747i
$526$	−8.08027	−	1.56297i	−0.352316	−	0.0681488i
$527$	15.4307	+	8.90893i	0.672173	+	0.388079i
$528$	49.6775	+	12.1930i	2.16194	+	0.530632i
$529$	−11.4834	−	19.8898i	−0.499278	−	0.864775i
$530$	9.14188	−	10.5360i	0.397098	−	0.457654i
$531$			13.5399i			0.587580i
$532$	−9.88038	−	1.58872i	−0.428369	−	0.0688799i
$533$		−	16.6418i		−	0.720837i
$534$	−13.8920	−	12.0538i	−0.601166	−	0.521620i
$535$	−9.08674	−	15.7387i	−0.392854	−	0.680443i
$536$	−34.1793	−	1.69717i	−1.47632	−	0.0733065i
$537$	14.5070	+	8.37563i	0.626024	+	0.361435i
$538$	6.49680	−	33.5872i	0.280097	−	1.44805i
$539$	33.5240	+	23.0225i	1.44398	+	0.991649i
$540$	−1.89609	+	4.71784i	−0.0815948	+	0.203023i
$541$	−3.98939	−	2.30327i	−0.171517	−	0.0990254i	0.411784	−	0.911282i	$-0.364906\pi$
$541$	−3.98939	−	2.30327i	−0.171517	−	0.0990254i	−0.583301	+	0.812256i	$0.698239\pi$
$542$	−20.9532	+	7.23623i	−0.900018	+	0.310823i
$543$	21.3927	−	12.3511i	0.918050	−	0.530036i
$544$	−24.6021	+	2.26590i	−1.05481	+	0.0971497i
$545$			3.93204i			0.168430i
$546$	−1.25927	−	39.7868i	−0.0538919	−	1.70272i
$547$	4.27444			0.182762			0.0913808	−	0.995816i	$-0.470872\pi$
$547$	4.27444			0.182762			0.0913808	+	0.995816i	$0.470872\pi$
$548$	−16.0500	+	12.5870i	−0.685624	+	0.537692i
$549$	−9.03171	−	15.6434i	−0.385464	−	0.667644i
$550$	−7.76611	+	2.68204i	−0.331148	+	0.114363i
$551$	4.15022	−	7.18839i	0.176805	−	0.306236i
$552$	0.615305	−	0.953206i	0.0261891	−	0.0405711i
$553$	9.55590	−	30.7948i	0.406358	−	1.30953i
$554$	−20.3590	−	3.93806i	−0.864971	−	0.167312i
$555$	−4.69103	+	8.12511i	−0.199123	+	0.344892i
$556$	−19.6768	+	2.80214i	−0.834484	+	0.118837i
$557$	−16.1482	+	9.32317i	−0.684221	+	0.395035i	−0.801443	−	0.598070i	$-0.795934\pi$
$557$	−16.1482	+	9.32317i	−0.684221	+	0.395035i	0.117222	+	0.993106i	$0.462601\pi$
$558$	8.04010	+	6.97624i	0.340364	+	0.295328i
$559$	10.1885			0.430926
$560$	−10.5813	−	0.190211i	−0.447141	−	0.00803789i
$561$	−55.8515			−2.35805
$562$	16.0672	+	13.9412i	0.677755	+	0.588075i
$563$	−19.1853	+	11.0766i	−0.808565	+	0.466825i	−0.846457	−	0.532457i	$-0.821269\pi$
$563$	−19.1853	+	11.0766i	−0.808565	+	0.466825i	0.0378926	+	0.999282i	$0.487936\pi$
$564$	−8.25302	+	1.17530i	−0.347515	+	0.0494889i
$565$	3.58320	−	6.20629i	0.150746	−	0.261101i
$566$	6.88461	+	1.33169i	0.289382	+	0.0559753i
$567$	−21.6220	+	19.9945i	−0.908039	+	0.839688i
$568$	−20.9277	−	13.5090i	−0.878106	−	0.566827i
$569$	−0.619323	+	1.07270i	−0.0259634	+	0.0449699i	−0.878715	−	0.477346i	$-0.841599\pi$
$569$	−0.619323	+	1.07270i	−0.0259634	+	0.0449699i	0.852752	+	0.522316i	$0.174932\pi$
$570$	5.56458	−	1.92174i	0.233075	−	0.0804928i
$571$	10.3953	+	18.0051i	0.435028	+	0.753490i	0.997298	−	0.0734633i	$-0.0234052\pi$
$571$	10.3953	+	18.0051i	0.435028	+	0.753490i	−0.562270	+	0.826954i	$0.690072\pi$
$572$	−44.1917	+	34.6568i	−1.84775	+	1.44907i
$573$	−16.9928			−0.709883
$574$	−11.3553	−	6.08536i	−0.473959	−	0.253998i
$575$			0.182235i			0.00759971i
$576$	−14.6874	−	1.46221i	−0.611977	−	0.0609255i
$577$	−29.9908	+	17.3152i	−1.24853	+	0.720842i	−0.970817	−	0.239821i	$-0.922911\pi$
$577$	−29.9908	+	17.3152i	−1.24853	+	0.720842i	−0.277717	+	0.960663i	$0.589578\pi$
$578$	2.77374	−	0.957917i	0.115372	−	0.0398441i
$579$	−44.6103	−	25.7558i	−1.85394	−	1.07037i
$580$	3.27338	−	8.14478i	0.135920	−	0.338194i
$581$	−43.7888	+	9.91675i	−1.81667	+	0.411416i
$582$	7.82637	−	40.4609i	0.324414	−	1.67716i
$583$	−49.6274	−	28.6524i	−2.05536	−	1.18666i
$584$	−1.19050	+	23.9754i	−0.0492631	+	0.992109i
$585$	4.45875	+	7.72278i	0.184347	+	0.319298i
$586$	−2.74319	−	2.38021i	−0.113320	−	0.0983256i
$587$			22.4911i			0.928306i	0.885755	+	0.464153i	$0.153641\pi$
$587$			22.4911i			0.928306i	−0.885755	+	0.464153i	$0.846359\pi$
$588$	−27.6083	−	13.6895i	−1.13855	−	0.564545i
$589$			7.71544i			0.317909i
$590$	−6.80168	+	7.83892i	−0.280021	+	0.322723i
$591$	−22.4815	−	38.9392i	−0.924767	−	1.60174i
$592$	16.5580	+	4.06405i	0.680531	+	0.167032i
$593$	−3.70525	−	2.13923i	−0.152156	−	0.0878474i	0.421989	−	0.906601i	$-0.361332\pi$
$593$	−3.70525	−	2.13923i	−0.152156	−	0.0878474i	−0.574145	+	0.818754i	$0.694665\pi$
$594$	20.5079	+	3.96685i	0.841448	+	0.162762i
$595$	11.2699	−	2.55227i	0.462021	−	0.104633i
$596$	11.7604	−	29.2621i	0.481724	−	1.19862i
$597$	−4.19719	−	2.42325i	−0.171780	−	0.0991771i
$598$	0.406617	+	1.17740i	0.0166278	+	0.0481475i
$599$	−5.50041	+	3.17566i	−0.224741	+	0.129754i	−0.608143	−	0.793827i	$-0.708085\pi$
$599$	−5.50041	+	3.17566i	−0.224741	+	0.129754i	0.383403	+	0.923581i	$0.374752\pi$
$600$	5.53941	−	2.84166i	0.226145	−	0.116010i
$601$		−	3.72971i		−	0.152138i	−0.997103	−	0.0760691i	$-0.975763\pi$
$601$		−	3.72971i		−	0.152138i	0.997103	−	0.0760691i	$-0.0242369\pi$
$602$	3.72558	−	6.95192i	0.151843	−	0.283339i
$603$	22.3229			0.909059
$604$	7.46994	+	9.52510i	0.303948	+	0.387571i
$605$	11.3764	+	19.7046i	0.462518	+	0.801105i
$606$	2.50870	+	7.26418i	0.101909	+	0.295087i
$607$	9.66175	−	16.7346i	0.392158	−	0.679238i	−0.600576	−	0.799568i	$-0.705062\pi$
$607$	9.66175	−	16.7346i	0.392158	−	0.679238i	0.992734	+	0.120330i	$0.0383952\pi$
$608$	−6.17630	−	8.73532i	−0.250482	−	0.354264i
$609$	18.7661	−	17.3535i	0.760440	−	0.703199i
$610$	2.62946	−	13.5938i	0.106464	−	0.550397i
$611$	4.57626	−	7.92631i	0.185136	−	0.320664i
$612$	15.9551	−	2.27214i	0.644948	−	0.0918458i
$613$	26.3430	−	15.2092i	1.06399	−	0.614292i	0.137453	−	0.990508i	$-0.456108\pi$
$613$	26.3430	−	15.2092i	1.06399	−	0.614292i	0.926532	+	0.376216i	$0.122775\pi$
$614$	13.3858	−	15.4271i	0.540207	−	0.622587i
$615$	7.57883			0.305608
$616$	7.48803	+	42.8263i	0.301701	+	1.72552i
$617$	9.32522			0.375419			0.187710	−	0.982225i	$-0.439894\pi$
$617$	9.32522			0.375419			0.187710	+	0.982225i	$0.439894\pi$
$618$	−3.75516	+	4.32781i	−0.151055	+	0.174090i
$619$	−9.29185	+	5.36465i	−0.373471	+	0.215624i	−0.674974	−	0.737842i	$-0.735845\pi$
$619$	−9.29185	+	5.36465i	−0.373471	+	0.215624i	0.301503	+	0.953465i	$0.402512\pi$
$620$	1.15034	+	8.07781i	0.0461989	+	0.324413i
$621$	0.231647	−	0.401225i	0.00929569	−	0.0161006i
$622$	−4.44066	+	22.9574i	−0.178054	+	0.920508i
$623$	4.63296	−	14.9301i	0.185616	−	0.598163i
$624$	29.4490	−	30.7197i	1.17891	−	1.22977i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.17177	+	3.39297i	0.0468333	+	0.135610i
$627$	−12.0923	−	20.9445i	−0.482921	−	0.836444i
$628$	−32.1282	+	25.1961i	−1.28205	+	1.00543i
$629$	−18.6159			−0.742264
$630$	6.89993	−	0.218386i	0.274900	−	0.00870071i
$631$			7.84644i			0.312362i	0.987728	+	0.156181i	$0.0499183\pi$
$631$			7.84644i			0.312362i	−0.987728	+	0.156181i	$0.950082\pi$
$632$	30.6695	−	15.7331i	1.21997	−	0.625830i
$633$	−55.1595	+	31.8464i	−2.19239	+	1.26578i
$634$	7.91235	+	22.9110i	0.314240	+	0.909912i
$635$	2.49594	+	1.44103i	0.0990484	+	0.0571856i
$636$	40.2901	+	16.1925i	1.59761	+	0.642076i
$637$	30.5321	−	14.5767i	1.20972	−	0.577548i
$638$	−35.4044	−	6.84830i	−1.40167	−	0.271127i
$639$	14.0715	+	8.12420i	0.556661	+	0.321388i
$640$	−7.76878	−	8.22472i	−0.307088	−	0.325111i
$641$	6.79977	+	11.7775i	0.268575	+	0.465185i	0.968494	−	0.249037i	$-0.0801141\pi$
$641$	6.79977	+	11.7775i	0.268575	+	0.465185i	−0.699919	+	0.714222i	$0.746781\pi$
$642$	37.0754	−	42.7292i	1.46325	−	1.68639i
$643$			5.68857i			0.224335i	0.993689	+	0.112168i	$0.0357794\pi$
$643$			5.68857i			0.224335i	−0.993689	+	0.112168i	$0.964221\pi$
$644$	0.952066	+	0.153088i	0.0375166	+	0.00603252i
$645$			4.63992i			0.182697i
$646$	8.82287	+	7.65544i	0.347131	+	0.301199i
$647$	0.225415	+	0.390431i	0.00886200	+	0.0153494i	0.870422	−	0.492306i	$-0.163846\pi$
$647$	0.225415	+	0.390431i	0.00886200	+	0.0153494i	−0.861560	+	0.507655i	$0.830512\pi$
$648$	−31.4444	−	1.56137i	−1.23525	−	0.0613364i
$649$	36.9234	+	21.3178i	1.44937	+	0.836795i
$650$	−1.29810	+	6.71095i	−0.0509158	+	0.263225i
$651$	−7.04127	+	22.6911i	−0.275969	+	0.889336i
$652$	7.09884	+	2.85301i	0.278012	+	0.111733i
$653$	3.69894	+	2.13559i	0.144751	+	0.0835720i	0.570626	−	0.821210i	$-0.306700\pi$
$653$	3.69894	+	2.13559i	0.144751	+	0.0835720i	−0.425875	+	0.904782i	$0.640034\pi$
$654$	−11.5695	+	3.99554i	−0.452402	+	0.156238i
$655$	6.92953	−	4.00076i	0.270759	−	0.156323i
$656$	−3.84468	−	13.2251i	−0.150109	−	0.516352i
$657$		−	15.6586i		−	0.610901i
$658$	−3.73500	−	6.02092i	−0.145605	−	0.234720i
$659$	15.5436			0.605493			0.302746	−	0.953071i	$-0.402097\pi$
$659$	15.5436			0.605493			0.302746	+	0.953071i	$0.402097\pi$
$660$	−15.7830	−	20.1253i	−0.614353	−	0.783377i
$661$	14.4897	+	25.0969i	0.563583	+	0.976155i	0.997180	+	0.0750479i	$0.0239110\pi$
$661$	14.4897	+	25.0969i	0.563583	+	0.976155i	−0.433597	+	0.901107i	$0.642756\pi$
$662$	−31.8218	+	10.9897i	−1.23679	+	0.427127i
$663$	−23.2324	+	40.2398i	−0.902273	+	1.56278i
$664$	−40.3259	−	26.0308i	−1.56495	−	1.01019i
$665$	3.39715	+	3.67367i	0.131736	+	0.142459i
$666$	−10.9191	−	2.11209i	−0.423107	−	0.0818420i
$667$	−0.399912	+	0.692668i	−0.0154846	+	0.0268202i
$668$	6.10554	+	42.8736i	0.236230	+	1.65883i
$669$	21.0707	−	12.1652i	0.814641	−	0.470333i
$670$	12.9239	+	11.2138i	0.499293	+	0.433227i
$671$	−56.8797			−2.19582
$672$	−10.1925	−	31.3272i	−0.393184	−	1.20847i
$673$	32.3539			1.24715			0.623576	−	0.781763i	$-0.285679\pi$
$673$	32.3539			1.24715			0.623576	+	0.781763i	$0.285679\pi$
$674$	1.31080	+	1.13736i	0.0504902	+	0.0438094i
$675$	2.20170	−	1.27115i	0.0847433	−	0.0489266i
$676$	2.92149	+	20.5149i	0.112365	+	0.789035i
$677$	22.4527	−	38.8892i	0.862927	−	1.49463i	−0.00616405	−	0.999981i	$-0.501962\pi$
$677$	22.4527	−	38.8892i	0.862927	−	1.49463i	0.869091	−	0.494652i	$-0.164705\pi$
$678$	21.9022	+	4.23655i	0.841148	+	0.162704i
$679$	34.1616	−	7.73649i	1.31100	−	0.296899i
$680$	10.3786	+	6.69953i	0.398003	+	0.256915i
$681$	9.04722	−	15.6703i	0.346690	−	0.600485i
$682$	31.6830	−	10.9418i	1.21321	−	0.418983i
$683$	5.62256	+	9.73856i	0.215141	+	0.372636i	0.953316	−	0.301974i	$-0.0976454\pi$
$683$	5.62256	+	9.73856i	0.215141	+	0.372636i	−0.738175	+	0.674609i	$0.764312\pi$
$684$	4.30649	+	5.49130i	0.164663	+	0.209965i
$685$	10.1985			0.389665
$686$	1.21844	−	26.1632i	0.0465202	−	0.998917i
$687$			22.1754i			0.846043i
$688$	8.09666	−	2.35379i	0.308682	−	0.0897375i
$689$	−41.2868	+	23.8369i	−1.57290	+	0.908115i
$690$	−0.536199	+	0.185177i	−0.0204128	+	0.00704958i
$691$	−8.53812	−	4.92949i	−0.324805	−	0.187527i	0.328727	−	0.944425i	$-0.393380\pi$
$691$	−8.53812	−	4.92949i	−0.324805	−	0.187527i	−0.653533	+	0.756898i	$0.726714\pi$
$692$	−19.3056	−	7.75889i	−0.733889	−	0.294949i
$693$	−6.26394	−	27.6593i	−0.237948	−	1.05069i
$694$	8.31689	−	42.9968i	0.315705	−	1.63213i
$695$	8.60629	+	4.96884i	0.326455	+	0.188479i
$696$	27.2911	+	1.35514i	1.03447	+	0.0513663i
$697$	7.51896	+	13.0232i	0.284801	+	0.493289i
$698$	28.4962	+	24.7256i	1.07860	+	0.935879i
$699$		−	16.2249i		−	0.613681i
$700$	4.10443	+	3.33971i	0.155133	+	0.126229i
$701$		−	6.00307i		−	0.226733i	−0.993553	−	0.113366i	$-0.963837\pi$
$701$		−	6.00307i		−	0.226733i	0.993553	−	0.113366i	$-0.0361634\pi$
$702$	11.3886	−	13.1254i	0.429837	−	0.495386i
$703$	−4.03050	−	6.98103i	−0.152013	−	0.263294i
$704$	−27.1121	+	37.7508i	−1.02182	+	1.42279i
$705$	3.60972	+	2.08407i	0.135950	+	0.0784907i
$706$	−19.4800	−	3.76802i	−0.733138	−	0.141811i
$707$	−4.79573	+	4.43474i	−0.180362	+	0.166785i
$708$	−29.9764	−	12.0475i	−1.12658	−	0.452772i
$709$	10.2323	+	5.90764i	0.384283	+	0.221866i	0.679680	−	0.733508i	$-0.262119\pi$
$709$	10.2323	+	5.90764i	0.384283	+	0.221866i	−0.295397	+	0.955375i	$0.595452\pi$
$710$	4.06558	+	11.7723i	0.152578	+	0.441806i
$711$	−19.4724	+	11.2424i	−0.730272	+	0.421623i
$712$	14.8694	−	7.62785i	0.557255	−	0.285866i
$713$		−	0.743454i		−	0.0278426i
$714$	18.9616	+	30.5666i	0.709619	+	1.14393i
$715$	28.0802			1.05014
$716$	−11.9768	+	9.39265i	−0.447593	+	0.351020i
$717$	−23.0607	−	39.9423i	−0.861217	−	1.49167i
$718$	−5.60592	−	16.2325i	−0.209211	−	0.605791i
$719$	−3.06796	+	5.31386i	−0.114415	+	0.198173i	−0.917546	−	0.397630i	$-0.869833\pi$
$719$	−3.06796	+	5.31386i	−0.114415	+	0.198173i	0.803130	+	0.595803i	$0.203166\pi$
$720$	5.32748	+	5.10713i	0.198543	+	0.190331i
$721$	−4.65122	−	1.44332i	−0.173221	−	0.0537520i
$722$	4.14231	−	21.4150i	0.154161	−	0.796983i
$723$	−3.07708	+	5.32966i	−0.114438	+	0.198212i
$724$	3.16441	+	22.2208i	0.117604	+	0.825828i
$725$	−3.80097	+	2.19449i	−0.141164	+	0.0815013i
$726$	−46.4177	+	53.4963i	−1.72272	+	1.98543i
$727$	14.8986			0.552558			0.276279	−	0.961077i	$-0.410899\pi$
$727$	14.8986			0.552558			0.276279	+	0.961077i	$0.410899\pi$
$728$	33.9702	+	12.4194i	1.25902	+	0.460294i
$729$	3.74887			0.138847
$730$	7.86603	−	9.06558i	0.291135	−	0.335532i
$731$	−7.97308	+	4.60326i	−0.294895	+	0.170258i
$732$	42.6697	−	6.07651i	1.57712	−	0.224594i
$733$	−23.7602	+	41.1539i	−0.877604	+	1.52006i	−0.0236421	+	0.999720i	$0.507526\pi$
$733$	−23.7602	+	41.1539i	−0.877604	+	1.52006i	−0.853962	+	0.520335i	$0.825807\pi$
$734$	3.09173	−	15.9837i	0.114118	−	0.589968i
$735$	6.63835	+	13.9046i	0.244859	+	0.512879i
$736$	0.595144	+	0.841728i	0.0219373	+	0.0310265i
$737$	35.1462	−	60.8750i	1.29463	−	2.24236i
$738$	2.93267	+	8.49183i	0.107953	+	0.312589i
$739$	1.95274	+	3.38225i	0.0718328	+	0.124418i	0.899705	−	0.436499i	$-0.143782\pi$
$739$	1.95274	+	3.38225i	0.0718328	+	0.124418i	−0.827872	+	0.560917i	$0.810449\pi$
$740$	−5.26064	−	6.70797i	−0.193385	−	0.246590i
$741$	−20.1201			−0.739130
$742$	1.16751	+	36.8877i	0.0428608	+	1.35419i
$743$			48.0392i			1.76239i	0.472755	+	0.881194i	$0.343259\pi$
$743$			48.0392i			1.76239i	−0.472755	+	0.881194i	$0.656741\pi$
$744$	−22.5989	+	11.5930i	−0.828515	+	0.425019i
$745$	−13.6559	+	7.88422i	−0.500312	+	0.288855i
$746$	−10.8340	−	31.3710i	−0.396662	−	1.14857i
$747$	27.1146	+	15.6546i	0.992073	+	0.572773i
$748$	18.9243	−	47.0873i	0.691942	−	1.72168i
$749$	45.9223	+	14.2501i	1.67797	+	0.520688i
$750$	−3.05623	−	0.591168i	−0.111598	−	0.0215864i
$751$	0.139857	+	0.0807464i	0.00510345	+	0.00294648i	0.502550	−	0.864548i	$-0.332395\pi$
$751$	0.139857	+	0.0807464i	0.00510345	+	0.00294648i	−0.497446	+	0.867495i	$0.665729\pi$
$752$	1.80552	−	7.35619i	0.0658407	−	0.268253i
$753$	−20.6529	−	35.7718i	−0.752633	−	1.30360i
$754$	−19.6611	+	22.6594i	−0.716017	+	0.825207i
$755$		−	6.05243i		−	0.220270i
$756$	−4.79143	−	12.5704i	−0.174263	−	0.457180i
$757$			17.0175i			0.618513i	0.950979	+	0.309257i	$0.100080\pi$
$757$			17.0175i			0.618513i	−0.950979	+	0.309257i	$0.899920\pi$
$758$	−16.6264	−	14.4264i	−0.603897	−	0.523990i
$759$	1.16521	+	2.01820i	0.0422944	+	0.0732560i
$760$	−0.265283	+	5.34254i	−0.00962284	+	0.193794i
$761$	23.5345	+	13.5876i	0.853125	+	0.492552i	0.861704	−	0.507411i	$-0.169398\pi$
$761$	23.5345	+	13.5876i	0.853125	+	0.492552i	−0.00857924	+	0.999963i	$0.502731\pi$
$762$	−1.70379	+	8.80825i	−0.0617216	+	0.319089i
$763$	−7.06309	−	7.63803i	−0.255701	−	0.276515i
$764$	5.75771	−	14.3263i	0.208307	−	0.518306i
$765$	−6.97848	−	4.02903i	−0.252308	−	0.145670i
$766$	19.9427	−	6.88724i	0.720558	−	0.248846i
$767$	30.7179	−	17.7350i	1.10916	−	0.640374i
$768$	16.3058	−	31.2161i	0.588386	−	1.12641i
$769$		−	16.2516i		−	0.586049i	−0.956105	−	0.293025i	$-0.905338\pi$
$769$		−	16.2516i		−	0.586049i	0.956105	−	0.293025i	$-0.0946618\pi$
$770$	10.2680	−	19.1601i	0.370034	−	0.690481i
$771$	−17.1959			−0.619296
$772$	36.8296	−	28.8832i	1.32553	−	1.03953i
$773$	2.07903	+	3.60098i	0.0747774	+	0.129518i	0.900989	−	0.433841i	$-0.142842\pi$
$773$	2.07903	+	3.60098i	0.0747774	+	0.129518i	−0.826212	+	0.563359i	$0.809509\pi$
$774$	−5.19887	+	1.79544i	−0.186870	+	0.0645357i
$775$	2.03983	−	3.53308i	0.0732727	−	0.126912i
$776$	31.4599	+	20.3077i	1.12935	+	0.729005i
$777$	−5.48268	−	24.2095i	−0.196690	−	0.868513i
$778$	17.5597	+	3.39659i	0.629547	+	0.121774i
$779$	−3.25584	+	5.63928i	−0.116652	+	0.202048i
$780$	−21.0651	+	2.99983i	−0.754250	+	0.107411i
$781$	44.3097	−	25.5822i	1.58552	−	0.915403i
$782$	−0.850165	−	0.737672i	−0.0304018	−	0.0263791i
$783$	11.1581			0.398758
$784$	20.8959	−	18.6376i	0.746283	−	0.665628i
$785$	20.4149			0.728637
$786$	18.8131	+	16.3238i	0.671041	+	0.582249i
$787$	0.346588	−	0.200103i	0.0123545	−	0.00713289i	−0.493810	−	0.869570i	$-0.664396\pi$
$787$	0.346588	−	0.200103i	0.0123545	−	0.00713289i	0.506165	+	0.862437i	$0.331063\pi$
$788$	40.4463	−	5.75988i	1.44084	−	0.205187i
$789$	−6.40478	+	11.0934i	−0.228016	+	0.394936i
$790$	−16.9211	−	3.27307i	−0.602027	−	0.116451i
$791$	4.18790	+	18.4922i	0.148904	+	0.657509i
$792$	16.4424	−	25.4719i	0.584256	−	0.905106i
$793$	−23.6601	+	40.9806i	−0.840196	+	1.45526i
$794$	−20.3626	+	7.03226i	−0.722642	+	0.249566i
$795$	−10.8556	−	18.8024i	−0.385007	−	0.666852i
$796$	3.46514	−	2.71750i	0.122819	−	0.0963191i
$797$	−4.32443			−0.153179			−0.0765895	−	0.997063i	$-0.524403\pi$
$797$	−4.32443			−0.153179			−0.0765895	+	0.997063i	$0.524403\pi$
$798$	−7.35725	+	13.7286i	−0.260444	+	0.485987i
$799$			8.27042i			0.292586i
$800$	0.518810	+	5.63301i	0.0183427	+	0.199157i
$801$	−9.44075	+	5.45062i	−0.333572	+	0.192588i
$802$	−20.6819	+	7.14254i	−0.730305	+	0.252212i
$803$	−42.7014	−	24.6536i	−1.50690	−	0.870008i
$804$	−19.8624	+	49.4215i	−0.700494	+	1.74296i
$805$	−0.327346	−	0.353992i	−0.0115374	−	0.0124766i
$806$	5.29581	−	27.3783i	0.186537	−	0.964361i
$807$	−46.1120	−	26.6228i	−1.62322	−	0.937165i
$808$	−6.97432	−	0.346309i	−0.245356	−	0.0121831i
$809$	−18.2699	−	31.6444i	−0.642335	−	1.11256i	−0.984910	−	0.173066i	$-0.944633\pi$
$809$	−18.2699	−	31.6444i	−0.642335	−	1.11256i	0.342576	−	0.939490i	$-0.388701\pi$
$810$	11.8898	+	10.3165i	0.417764	+	0.362486i
$811$		−	17.6473i		−	0.619680i	−0.950789	−	0.309840i	$-0.899725\pi$
$811$		−	17.6473i		−	0.619680i	0.950789	−	0.309840i	$-0.100275\pi$
$812$	8.27183	+	21.7012i	0.290284	+	0.761564i
$813$			34.5025i			1.21005i
$814$	−22.9513	+	26.4513i	−0.804442	+	0.927117i
$815$	−1.91267	−	3.31285i	−0.0669981	−	0.116044i
$816$	−9.16616	+	37.3454i	−0.320880	+	1.30735i
$817$	−3.45248	−	1.99329i	−0.120787	−	0.0697364i
$818$	−11.9773	−	2.31679i	−0.418778	−	0.0810045i
$819$	−22.5335	−	6.99236i	−0.787385	−	0.244333i
$820$	−2.56796	+	6.38957i	−0.0896770	+	0.223133i
$821$	−37.1429	−	21.4445i	−1.29630	−	0.748418i	−0.316535	−	0.948581i	$-0.602520\pi$
$821$	−37.1429	−	21.4445i	−1.29630	−	0.748418i	−0.979763	+	0.200163i	$0.935853\pi$
$822$	10.3632	+	30.0076i	0.361457	+	1.04664i
$823$	−31.2832	+	18.0614i	−1.09046	+	0.629580i	−0.933700	−	0.358056i	$-0.883440\pi$
$823$	−31.2832	+	18.0614i	−1.09046	+	0.629580i	−0.156764	+	0.987636i	$0.550106\pi$
$824$	−2.37632	−	4.63231i	−0.0827831	−	0.161374i
$825$			12.7880i			0.445221i
$826$	−0.868647	−	27.4450i	−0.0302241	−	0.954933i
$827$	−7.53954			−0.262176			−0.131088	−	0.991371i	$-0.541847\pi$
$827$	−7.53954			−0.262176			−0.131088	+	0.991371i	$0.541847\pi$
$828$	−0.414970	−	0.529138i	−0.0144212	−	0.0183888i
$829$	−28.0133	−	48.5204i	−0.972941	−	1.68518i	−0.686570	−	0.727063i	$-0.740885\pi$
$829$	−28.0133	−	48.5204i	−0.972941	−	1.68518i	−0.286370	−	0.958119i	$-0.592449\pi$
$830$	7.83402	+	22.6842i	0.271923	+	0.787379i
$831$	−16.1375	+	27.9509i	−0.559802	+	0.969606i
$832$	15.9208	+	35.2367i	0.551956	+	1.22161i
$833$	−17.3073	+	25.2018i	−0.599662	+	0.873192i
$834$	−5.87485	+	30.3718i	−0.203429	+	1.05169i
$835$	10.8265	−	18.7521i	0.374667	−	0.648943i
$836$	21.7552	−	3.09812i	0.752420	−	0.107151i
$837$	−8.98215	+	5.18585i	−0.310469	+	0.179249i
$838$	9.90762	−	11.4185i	0.342253	−	0.394446i
$839$	33.7497			1.16517			0.582584	−	0.812770i	$-0.302042\pi$
$839$	33.7497			1.16517			0.582584	+	0.812770i	$0.302042\pi$
$840$	−5.65591	+	15.4703i	−0.195148	+	0.533777i
$841$	9.73688			0.335755
$842$	−18.9946	+	21.8912i	−0.654597	+	0.754421i
$843$	28.6733	−	16.5546i	0.987562	−	0.570169i
$844$	−8.15919	−	57.2945i	−0.280851	−	1.97216i
$845$	5.18047	−	8.97285i	0.178214	−	0.308675i
$846$	−0.938334	+	4.85101i	−0.0322606	+	0.166781i
$847$	−57.4940	−	17.8409i	−1.97552	−	0.613021i
$848$	−27.3032	+	28.4812i	−0.937596	+	0.978050i
$849$	5.45705	−	9.45188i	0.187285	−	0.324388i
$850$	−2.01624	−	5.83822i	−0.0691564	−	0.200249i
$851$	0.388376	+	0.672687i	0.0133133	+	0.0230594i
$852$	−30.5070	+	23.9247i	−1.04515	+	0.819648i
$853$	53.4433			1.82987			0.914933	−	0.403607i	$-0.132244\pi$
$853$	53.4433			1.82987			0.914933	+	0.403607i	$0.132244\pi$
$854$	19.3107	+	31.1293i	0.660797	+	1.06522i
$855$		−	3.48928i		−	0.119331i
$856$	23.4618	+	45.7356i	0.801909	+	1.56321i
$857$	30.9412	−	17.8639i	1.05693	−	0.610220i	0.132350	−	0.991203i	$-0.457748\pi$
$857$	30.9412	−	17.8639i	1.05693	−	0.610220i	0.924582	+	0.380983i	$0.124414\pi$
$858$	28.5337	+	82.6220i	0.974123	+	2.82067i
$859$	4.24262	+	2.44948i	0.144756	+	0.0835751i	0.570629	−	0.821208i	$-0.306700\pi$
$859$	4.24262	+	2.44948i	0.144756	+	0.0835751i	−0.425873	+	0.904783i	$0.640033\pi$
$860$	−3.91182	−	1.57216i	−0.133392	−	0.0536101i
$861$	−14.7220	+	13.6138i	−0.501723	+	0.463957i
$862$	−33.5956	−	6.49842i	−1.14427	−	0.221337i
$863$	27.0242	+	15.6024i	0.919914	+	0.531113i	0.883608	−	0.468228i	$-0.155107\pi$
$863$	27.0242	+	15.6024i	0.919914	+	0.531113i	0.0363065	+	0.999341i	$0.488441\pi$
$864$	6.01814	−	13.0617i	0.204741	−	0.444367i
$865$	5.20160	+	9.00944i	0.176860	+	0.306330i
$866$	−18.8099	+	21.6784i	−0.639187	+	0.736662i
$867$		−	4.56736i		−	0.155116i
$868$	−16.7446	−	13.6249i	−0.568350	−	0.462458i
$869$			70.8021i			2.40180i
$870$	−10.3193	−	8.95387i	−0.349857	−	0.303565i
$871$	−29.2394	−	50.6441i	−0.990738	−	1.71601i
$872$	0.551558	−	11.1078i	0.0186781	−	0.376158i
$873$	−21.1533	−	12.2129i	−0.715931	−	0.413343i
$874$	0.0925619	−	0.478528i	0.00313095	−	0.0161864i
$875$	−0.584379	−	2.58041i	−0.0197556	−	0.0872337i
$876$	34.6672	+	13.9327i	1.17130	+	0.470742i
$877$	−4.65217	−	2.68593i	−0.157092	−	0.0906974i	0.419393	−	0.907805i	$-0.362243\pi$
$877$	−4.65217	−	2.68593i	−0.157092	−	0.0906974i	−0.576485	+	0.817107i	$0.695576\pi$
$878$	6.74337	−	2.32884i	0.227578	−	0.0785944i
$879$	−4.89545	+	2.82639i	−0.165120	+	0.0953318i
$880$	22.3151	−	6.48724i	0.752240	−	0.218685i
$881$			12.9255i			0.435471i	0.976008	+	0.217736i	$0.0698670\pi$
$881$			12.9255i			0.435471i	−0.976008	+	0.217736i	$0.930133\pi$
$882$	−13.0109	+	12.8185i	−0.438099	+	0.431621i
$883$	42.5290			1.43122			0.715608	−	0.698502i	$-0.246150\pi$
$883$	42.5290			1.43122			0.715608	+	0.698502i	$0.246150\pi$
$884$	−26.0534	−	33.2214i	−0.876272	−	1.11736i
$885$	8.07669	+	13.9892i	0.271495	+	0.470243i
$886$	−10.8195	+	3.73653i	−0.363488	+	0.125531i
$887$	19.2391	−	33.3231i	0.645987	−	1.11888i	−0.338086	−	0.941115i	$-0.609780\pi$
$887$	19.2391	−	33.3231i	0.645987	−	1.11888i	0.984073	−	0.177766i	$-0.0568871\pi$
$888$	14.3916	−	22.2950i	0.482952	−	0.748170i
$889$	−7.43690	+	1.68422i	−0.249426	+	0.0564868i
$890$	−8.20382	−	1.58687i	−0.274993	−	0.0531920i
$891$	32.3339	−	56.0040i	1.08323	−	1.87620i
$892$	3.11678	+	21.8863i	0.104357	+	0.732806i
$893$	−3.10144	+	1.79062i	−0.103786	+	0.0599207i
$894$	−37.0746	−	32.1689i	−1.23996	−	1.07589i
$895$	7.61028			0.254383
$896$	29.8649	+	2.02160i	0.997717	+	0.0675369i
$897$	1.93876			0.0647332
$898$	−4.33448	−	3.76095i	−0.144643	−	0.125504i
$899$	15.5066	−	8.95275i	0.517175	−	0.298591i
$900$	−0.520239	−	3.65316i	−0.0173413	−	0.121772i
$901$	21.5396	−	37.3077i	0.717588	−	1.24290i
$902$	27.7747	+	5.37248i	0.924796	+	0.178884i
$903$	−8.33464	−	9.01308i	−0.277359	−	0.299937i
$904$	−10.9929	+	17.0298i	−0.365619	+	0.566403i
$905$	5.61124	−	9.71894i	0.186524	−	0.323069i
$906$	17.8084	−	6.15016i	0.591644	−	0.204325i
$907$	29.8056	+	51.6248i	0.989679	+	1.71417i	0.618941	+	0.785438i	$0.287562\pi$
$907$	29.8056	+	51.6248i	0.989679	+	1.71417i	0.370738	+	0.928737i	$0.379105\pi$
$908$	10.1458	+	12.9371i	0.336700	+	0.429334i
$909$	4.55501			0.151080
$910$	−9.53324	−	15.3678i	−0.316024	−	0.509439i
$911$		−	40.9457i		−	1.35659i	−0.734790	−	0.678295i	$-0.762719\pi$
$911$		−	40.9457i		−	1.35659i	0.734790	−	0.678295i	$-0.237281\pi$
$912$	−15.9892	+	4.64825i	−0.529456	+	0.153919i
$913$	85.3810	−	49.2947i	2.82570	−	1.63142i
$914$	−7.23804	+	2.49967i	−0.239413	+	0.0826817i
$915$	−18.6629	−	10.7751i	−0.616978	−	0.356212i
$916$	−18.6956	−	7.51374i	−0.617721	−	0.248261i
$917$	−6.27413	+	20.2190i	−0.207190	+	0.667689i
$918$	−2.98210	+	15.4169i	−0.0984241	+	0.508834i
$919$	−22.8509	−	13.1930i	−0.753781	−	0.435196i	0.0732776	−	0.997312i	$-0.476654\pi$
$919$	−22.8509	−	13.1930i	−0.753781	−	0.435196i	−0.827058	+	0.562116i	$0.809987\pi$
$920$	0.0255625	−	0.514803i	0.000842771	−	0.0169726i
$921$	−15.8950	−	27.5310i	−0.523759	−	0.907177i
$922$	−20.1985	−	17.5259i	−0.665202	−	0.577184i
$923$		−	42.5655i		−	1.40106i
$924$	66.8096	+	10.7427i	2.19787	+	0.353409i
$925$			4.26237i			0.140146i
$926$	0.282481	−	0.325558i	0.00928289	−	0.0106985i
$927$	1.69805	+	2.94110i	0.0557711	+	0.0965984i
$928$	−10.3896	+	22.5494i	−0.341055	+	0.740221i
$929$	−38.7083	−	22.3482i	−1.26998	−	0.733222i	−0.294994	−	0.955499i	$-0.595318\pi$
$929$	−38.7083	−	22.3482i	−1.26998	−	0.733222i	−0.974984	+	0.222277i	$0.928651\pi$
$930$	12.4684	+	2.41176i	0.408853	+	0.0790848i
$931$	−13.1980	−	1.03388i	−0.432546	−	0.0338842i
$932$	13.6789	+	5.49752i	0.448067	+	0.180077i
$933$	31.5182	+	18.1971i	1.03186	+	0.595745i
$934$	−1.78773	−	5.17654i	−0.0584962	−	0.169381i
$935$	−21.9745	+	12.6870i	−0.718642	+	0.414908i
$936$	−11.5124	−	22.4419i	−0.376296	−	0.733536i
$937$		−	14.4033i		−	0.470535i	−0.971931	−	0.235268i	$-0.924403\pi$
$937$		−	14.4033i		−	0.470535i	0.971931	−	0.235268i	$-0.0755967\pi$
$938$	−45.2480	+	1.43212i	−1.47740	+	0.0467604i
$939$	5.58701			0.182325
$940$	−2.98013	+	2.33713i	−0.0972011	+	0.0762288i
$941$	5.58349	+	9.67088i	0.182016	+	0.315262i	0.942567	−	0.334017i	$-0.108404\pi$
$941$	5.58349	+	9.67088i	0.182016	+	0.315262i	−0.760551	+	0.649279i	$0.775071\pi$
$942$	20.7445	+	60.0678i	0.675892	+	1.95711i
$943$	0.313730	−	0.543396i	0.0102165	−	0.0176954i
$944$	20.3140	−	21.1904i	0.661164	−	0.689690i
$945$	−1.99346	+	6.42410i	−0.0648472	+	0.208976i
$946$	−3.28914	+	17.0042i	−0.106939	+	0.552856i
$947$	−10.3303	+	17.8927i	−0.335691	+	0.581434i	−0.983617	−	0.180269i	$-0.942303\pi$
$947$	−10.3303	+	17.8927i	−0.335691	+	0.581434i	0.647926	+	0.761703i	$0.275636\pi$
$948$	−7.56385	−	53.1139i	−0.245662	−	1.72506i
$949$	−35.5248	+	20.5102i	−1.15318	+	0.665791i
$950$	1.75282	−	2.02012i	0.0568691	−	0.0655414i
$951$	37.7262			1.22336
$952$	−32.1949	+	5.62917i	−1.04344	+	0.182442i
$953$	29.6708			0.961132			0.480566	−	0.876959i	$-0.340431\pi$
$953$	29.6708			0.961132			0.480566	+	0.876959i	$0.340431\pi$
$954$	16.8668	−	19.4390i	0.546084	−	0.629360i
$955$	−6.68571	+	3.86000i	−0.216344	+	0.124907i
$956$	41.4883	−	5.90826i	1.34183	−	0.191087i
$957$	−28.0631	+	48.6067i	−0.907152	+	1.57123i
$958$	−8.84916	+	45.7485i	−0.285904	+	1.47807i
$959$	−19.8107	+	18.3195i	−0.639720	+	0.591566i
$960$	−16.0471	+	7.25050i	−0.517919	+	0.234009i
$961$	7.17822	−	12.4330i	0.231555	−	0.401066i
$962$	9.51056	+	27.5388i	0.306633	+	0.887885i
$963$	−16.7651	−	29.0380i	−0.540248	−	0.935736i
$964$	−3.45071	−	4.40009i	−0.111140	−	0.141717i
$965$	−23.4022			−0.753345
$966$	0.708939	−	1.32288i	0.0228098	−	0.0425629i
$967$			50.5419i			1.62532i	0.582740	+	0.812658i	$0.301980\pi$
$967$			50.5419i			1.62532i	−0.582740	+	0.812658i	$0.698020\pi$
$968$	−29.3738	−	57.2602i	−0.944111	−	1.84041i
$969$	15.7452	−	9.09048i	0.505808	−	0.292028i
$970$	−6.11166	−	17.6969i	−0.196234	−	0.568214i
$971$	30.5599	+	17.6438i	0.980715	+	0.566216i	0.902486	−	0.430719i	$-0.141740\pi$
$971$	30.5599	+	17.6438i	0.980715	+	0.566216i	0.0782293	+	0.996935i	$0.475073\pi$
$972$	−12.5849	+	31.3135i	−0.403659	+	1.00438i
$973$	−25.6433	+	5.80737i	−0.822086	+	0.186176i
$974$	57.5452	+	11.1310i	1.84387	+	0.356660i
$975$	9.21347	+	5.31940i	0.295067	+	0.170357i
$976$	−9.33491	+	38.0329i	−0.298803	+	1.21740i
$977$	−13.3142	−	23.0609i	−0.425960	−	0.737784i	0.570550	−	0.821263i	$-0.306730\pi$
$977$	−13.3142	−	23.0609i	−0.425960	−	0.737784i	−0.996510	+	0.0834788i	$0.973397\pi$
$978$	7.80402	−	8.99411i	0.249545	−	0.287600i
$979$			34.3268i			1.09709i
$980$	−13.9720	+	0.885327i	−0.446318	+	0.0282807i
$981$			7.25465i			0.231623i
$982$	−27.1677	−	23.5729i	−0.866957	−	0.752242i
$983$	−9.60664	−	16.6392i	−0.306404	−	0.530708i	0.671169	−	0.741305i	$-0.265793\pi$
$983$	−9.60664	−	16.6392i	−0.306404	−	0.530708i	−0.977573	+	0.210597i	$0.932459\pi$
$984$	−21.4098	−	1.06310i	−0.682520	−	0.0338904i
$985$	−17.6905	−	10.2136i	−0.563666	−	0.325432i
$986$	5.14825	−	26.6155i	0.163954	−	0.847609i
$987$	−10.7555	+	2.43577i	−0.342351	+	0.0775315i
$988$	6.81735	−	16.9629i	0.216889	−	0.539660i
$989$	0.332678	+	0.192072i	0.0105786	+	0.00610753i
$990$	−14.3285	+	4.94838i	−0.455390	+	0.157270i
$991$	52.2605	−	30.1726i	1.66011	−	0.958465i	0.687450	−	0.726232i	$-0.258730\pi$
$991$	52.2605	−	30.1726i	1.66011	−	0.958465i	0.972660	−	0.232233i	$-0.0746033\pi$
$992$	−2.11657	−	22.9807i	−0.0672011	−	0.729639i
$993$			52.3991i			1.66283i
$994$	−29.0438	−	15.5648i	−0.921215	−	0.493685i
$995$	−2.20182			−0.0698023
$996$	−58.7844	+	46.1010i	−1.86266	+	1.46076i
$997$	8.59147	+	14.8809i	0.272095	+	0.471282i	0.969398	−	0.245495i	$-0.0789503\pi$
$997$	8.59147	+	14.8809i	0.272095	+	0.471282i	−0.697303	+	0.716776i	$0.745617\pi$
$998$	8.69041	−	3.00125i	0.275090	−	0.0950028i
$999$	5.41811	−	9.38444i	0.171421	−	0.296911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.bj.e.131.11	✓	24
4.3	odd	2		1120.2.bz.f.271.4		24
7.3	odd	6		280.2.bj.f.171.2	yes	24
8.3	odd	2		280.2.bj.f.131.2	yes	24
8.5	even	2		1120.2.bz.e.271.4		24
28.3	even	6		1120.2.bz.e.591.4		24
56.3	even	6	inner	280.2.bj.e.171.11	yes	24
56.45	odd	6		1120.2.bz.f.591.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.bj.e.131.11	✓	24	1.1	even	1	trivial
280.2.bj.e.171.11	yes	24	56.3	even	6	inner
280.2.bj.f.131.2	yes	24	8.3	odd	2
280.2.bj.f.171.2	yes	24	7.3	odd	6
1120.2.bz.e.271.4		24	8.5	even	2
1120.2.bz.e.591.4		24	28.3	even	6
1120.2.bz.f.271.4		24	4.3	odd	2
1120.2.bz.f.591.4		24	56.45	odd	6

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06817 + 0.926830i) q^{2} +(1.90624 - 1.10057i) q^{3} +(0.281971 + 1.98002i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.05623 + 0.591168i) q^{6} +(0.584379 + 2.58041i) q^{7} +(-1.53395 + 2.37634i) q^{8} +(0.922503 - 1.59782i) q^{9} +O(q^{10})\)	\(q+(1.06817 + 0.926830i) q^{2} +(1.90624 - 1.10057i) q^{3} +(0.281971 + 1.98002i) q^{4} +(0.500000 - 0.866025i) q^{5} +(3.05623 + 0.591168i) q^{6} +(0.584379 + 2.58041i) q^{7} +(-1.53395 + 2.37634i) q^{8} +(0.922503 - 1.59782i) q^{9} +(1.33674 - 0.461647i) q^{10} +(-2.90486 - 5.03137i) q^{11} +(2.71666 + 3.46407i) q^{12} -4.83332 q^{13} +(-1.76738 + 3.29793i) q^{14} -2.20114i q^{15} +(-3.84098 + 1.11662i) q^{16} +(3.78236 - 2.18375i) q^{17} +(2.46630 - 0.851741i) q^{18} +(1.63783 + 0.945600i) q^{19} +(1.85574 + 0.745818i) q^{20} +(3.95388 + 4.27573i) q^{21} +(1.56034 - 8.06667i) q^{22} +(-0.157820 - 0.0911173i) q^{23} +(-0.308759 + 6.21810i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-5.16280 - 4.47966i) q^{26} +2.54230i q^{27} +(-4.94449 + 1.88468i) q^{28} -4.38898i q^{29} +(2.04008 - 2.35119i) q^{30} +(2.03983 + 3.53308i) q^{31} +(-5.13774 - 2.36720i) q^{32} +(-11.0747 - 6.39400i) q^{33} +(6.06416 + 1.17300i) q^{34} +(2.52689 + 0.784117i) q^{35} +(3.42385 + 1.37604i) q^{36} +(-3.69132 - 2.13119i) q^{37} +(0.873066 + 2.52805i) q^{38} +(-9.21347 + 5.31940i) q^{39} +(1.29099 + 2.51661i) q^{40} +3.44314i q^{41} +(0.260540 + 8.23178i) q^{42} -2.10796 q^{43} +(9.14314 - 7.17039i) q^{44} +(-0.922503 - 1.59782i) q^{45} +(-0.0841280 - 0.243601i) q^{46} +(-0.946816 + 1.63993i) q^{47} +(-6.09293 + 6.35581i) q^{48} +(-6.31700 + 3.01587i) q^{49} +(0.268574 - 1.38848i) q^{50} +(4.80673 - 8.32550i) q^{51} +(-1.36286 - 9.57008i) q^{52} +(8.54212 - 4.93180i) q^{53} +(-2.35628 + 2.71561i) q^{54} -5.80972 q^{55} +(-7.02833 - 2.56954i) q^{56} +4.16279 q^{57} +(4.06784 - 4.68817i) q^{58} +(-6.35546 + 3.66932i) q^{59} +(4.35830 - 0.620657i) q^{60} +(4.89522 - 8.47877i) q^{61} +(-1.09569 + 5.66450i) q^{62} +(4.66212 + 1.44670i) q^{63} +(-3.29398 - 7.29039i) q^{64} +(-2.41666 + 4.18577i) q^{65} +(-5.90354 - 17.0943i) q^{66} +(6.04954 + 10.4781i) q^{67} +(5.39039 + 6.87341i) q^{68} -0.401124 q^{69} +(1.97240 + 3.17957i) q^{70} +8.80669i q^{71} +(2.38189 + 4.64317i) q^{72} +(7.34998 - 4.24351i) q^{73} +(-1.96771 - 5.69769i) q^{74} +(-1.90624 - 1.10057i) q^{75} +(-1.41049 + 3.50957i) q^{76} +(11.2854 - 10.4360i) q^{77} +(-14.7717 - 2.85730i) q^{78} +(-10.5541 - 6.09342i) q^{79} +(-0.953472 + 3.88470i) q^{80} +(5.56549 + 9.63970i) q^{81} +(-3.19121 + 3.67786i) q^{82} +16.9697i q^{83} +(-7.35116 + 9.03441i) q^{84} -4.36749i q^{85} +(-2.25166 - 1.95372i) q^{86} +(-4.83037 - 8.36645i) q^{87} +(16.4122 + 0.814944i) q^{88} +(-5.11692 - 2.95425i) q^{89} +(0.495521 - 2.56175i) q^{90} +(-2.82449 - 12.4719i) q^{91} +(0.135914 - 0.338179i) q^{92} +(7.77680 + 4.48994i) q^{93} +(-2.53130 + 0.874188i) q^{94} +(1.63783 - 0.945600i) q^{95} +(-12.3990 + 1.14197i) q^{96} -13.2388i q^{97} +(-9.54283 - 2.63333i) q^{98} -10.7190 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9	\( 24 q - 3 q^{2} + 12 q^{3} + q^{4} + 12 q^{5} + 2 q^{6} - 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 8 q^{12} - 20 q^{13} - 15 q^{14} - 3 q^{16} + 6 q^{17} - 27 q^{18} + 18 q^{19} + 2 q^{20} + 26 q^{21} - 16 q^{22} - 18 q^{23} + 6 q^{24} - 12 q^{25} - 29 q^{26} + 3 q^{28} + 10 q^{30} + 6 q^{31} - 33 q^{32} + 12 q^{33} + 20 q^{34} - 8 q^{35} - 22 q^{36} + 9 q^{38} + 18 q^{39} - 3 q^{40} - 12 q^{42} + 32 q^{43} - 25 q^{44} - 12 q^{45} + 53 q^{46} + 14 q^{48} + 8 q^{49} - 22 q^{51} - 31 q^{52} - 30 q^{53} + 10 q^{54} + 16 q^{55} + 16 q^{56} - 44 q^{57} + 30 q^{58} - 18 q^{59} + 10 q^{60} - 22 q^{61} - 8 q^{62} + 12 q^{63} + 58 q^{64} - 10 q^{65} - 8 q^{66} - 8 q^{67} - 6 q^{68} + 12 q^{69} + 3 q^{70} - 23 q^{72} + 30 q^{73} - 43 q^{74} - 12 q^{75} - 8 q^{76} + 32 q^{77} - 8 q^{78} - 6 q^{79} + 3 q^{80} - 4 q^{81} - 27 q^{82} - 16 q^{84} - 36 q^{86} - 14 q^{87} + 49 q^{88} - 60 q^{89} - 24 q^{90} + 18 q^{91} - 38 q^{92} + 18 q^{93} + 11 q^{94} + 18 q^{95} + 2 q^{96} - 19 q^{98} - 56 q^{99}+O(q^{100}) \) 24 * q - 3 * q^2 + 12 * q^3 + q^4 + 12 * q^5 + 2 * q^6 - 10 * q^7 - 6 * q^8 + 12 * q^9 - 3 * q^10 + 8 * q^11 + 8 * q^12 - 20 * q^13 - 15 * q^14 - 3 * q^16 + 6 * q^17 - 27 * q^18 + 18 * q^19 + 2 * q^20 + 26 * q^21 - 16 * q^22 - 18 * q^23 + 6 * q^24 - 12 * q^25 - 29 * q^26 + 3 * q^28 + 10 * q^30 + 6 * q^31 - 33 * q^32 + 12 * q^33 + 20 * q^34 - 8 * q^35 - 22 * q^36 + 9 * q^38 + 18 * q^39 - 3 * q^40 - 12 * q^42 + 32 * q^43 - 25 * q^44 - 12 * q^45 + 53 * q^46 + 14 * q^48 + 8 * q^49 - 22 * q^51 - 31 * q^52 - 30 * q^53 + 10 * q^54 + 16 * q^55 + 16 * q^56 - 44 * q^57 + 30 * q^58 - 18 * q^59 + 10 * q^60 - 22 * q^61 - 8 * q^62 + 12 * q^63 + 58 * q^64 - 10 * q^65 - 8 * q^66 - 8 * q^67 - 6 * q^68 + 12 * q^69 + 3 * q^70 - 23 * q^72 + 30 * q^73 - 43 * q^74 - 12 * q^75 - 8 * q^76 + 32 * q^77 - 8 * q^78 - 6 * q^79 + 3 * q^80 - 4 * q^81 - 27 * q^82 - 16 * q^84 - 36 * q^86 - 14 * q^87 + 49 * q^88 - 60 * q^89 - 24 * q^90 + 18 * q^91 - 38 * q^92 + 18 * q^93 + 11 * q^94 + 18 * q^95 + 2 * q^96 - 19 * q^98 - 56 * q^99

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