LMFDB - Embedded newform 280.2.bj.f.131.2

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			131.2
Character	$\chi$	$=$	280.131
Dual form			280.2.bj.f.171.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.33674 - 0.461647i) q^{2} +(1.90624 - 1.10057i) q^{3} +(1.57376 + 1.23421i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.05623 + 0.591168i) q^{6} +(-0.584379 - 2.58041i) q^{7} +(-1.53395 - 2.37634i) q^{8} +(0.922503 - 1.59782i) q^{9} +O(q^{10})$	\(q+(-1.33674 - 0.461647i) q^{2} +(1.90624 - 1.10057i) q^{3} +(1.57376 + 1.23421i) 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} +(1.06817 - 0.926830i) q^{10} +(-2.90486 - 5.03137i) q^{11} +(4.35830 + 0.620657i) q^{12} +4.83332 q^{13} +(-0.410072 + 3.71912i) q^{14} +2.20114i q^{15} +(0.953472 + 3.88470i) q^{16} +(3.78236 - 2.18375i) q^{17} +(-1.97078 + 1.71001i) 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} +(-5.53941 - 2.84166i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-6.46090 - 2.23128i) q^{26} +2.54230i q^{27} +(2.26508 - 4.78220i) q^{28} +4.38898i q^{29} +(1.01615 - 2.94236i) q^{30} +(-2.03983 - 3.53308i) q^{31} +(0.518810 - 5.63301i) 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} +(-1.75282 - 2.02012i) q^{38} +(9.21347 - 5.31940i) q^{39} +(2.82495 - 0.140272i) q^{40} +3.44314i q^{41} +(3.31145 + 7.54085i) q^{42} -2.10796 q^{43} +(1.63817 - 11.5034i) q^{44} +(0.922503 + 1.59782i) q^{45} +(-0.168901 - 0.194657i) 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} +(7.60650 + 5.96531i) q^{52} +(-8.54212 + 4.93180i) q^{53} +(1.17364 - 3.39840i) q^{54} +5.80972 q^{55} +(-5.23551 + 5.34691i) q^{56} +4.16279 q^{57} +(2.02616 - 5.86693i) q^{58} +(-6.35546 + 3.66932i) q^{59} +(-2.71666 + 3.46407i) 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} +(11.8523 + 13.6597i) q^{66} +(6.04954 + 10.4781i) q^{67} +(8.64774 + 1.23151i) q^{68} +0.401124 q^{69} +(-3.01582 - 2.21469i) q^{70} -8.80669i q^{71} +(-5.21205 + 0.258804i) q^{72} +(7.34998 - 4.24351i) q^{73} +(-3.95049 - 4.55293i) 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} +(-3.84098 - 1.11662i) q^{80} +(5.56549 + 9.63970i) q^{81} +(1.58952 - 4.60260i) q^{82} +16.9697i q^{83} +(-0.945352 - 11.6089i) q^{84} +4.36749i q^{85} +(2.81781 + 0.973134i) q^{86} +(4.83037 + 8.36645i) q^{87} +(-7.50032 + 14.6208i) 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} +(-2.02272 + 1.75507i) q^{94} +(-1.63783 + 0.945600i) q^{95} +(-5.21054 - 11.3089i) q^{96} -13.2388i q^{97} +(9.83648 - 1.11522i) 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} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 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 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * 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 $

$2$	−1.33674	−	0.461647i	−0.945220	−	0.326433i
$2$	−1.33674	−	0.461647i	−0.945220	−	0.326433i
$3$	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	$0.114163\pi$
$4$	1.57376	+	1.23421i	0.786882	+	0.617103i
$5$	−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
$10$	1.06817	−	0.926830i	0.337785	−	0.293089i
$11$	−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	$-0.506364\pi$
$12$	4.35830	+	0.620657i	1.25813	+	0.179168i
$13$	4.83332			1.34052			0.670260	−	0.742126i	$-0.266182\pi$
$13$	4.83332			1.34052			0.670260	+	0.742126i	$0.266182\pi$
$14$	−0.410072	+	3.71912i	−0.109596	+	0.993976i
$15$			2.20114i			0.568331i
$16$	0.953472	+	3.88470i	0.238368	+	0.971175i
$17$	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	$0.155662\pi$
$18$	−1.97078	+	1.71001i	−0.464517	+	0.403053i
$19$	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	0.516364	−	0.856369i	$-0.327285\pi$
$23$	0.157820	+	0.0911173i	0.0329077	+	0.0189993i	−0.483456	+	0.875369i	$0.660619\pi$
$24$	−5.53941	−	2.84166i	−1.13073	−	0.580050i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−6.46090	−	2.23128i	−1.26709	−	0.437591i
$27$			2.54230i			0.489266i
$28$	2.26508	−	4.78220i	0.428060	−	0.903750i
$29$			4.38898i			0.815013i	0.913202	+	0.407506i	$0.133602\pi$
$29$			4.38898i			0.815013i	−0.913202	+	0.407506i	$0.866398\pi$
$30$	1.01615	−	2.94236i	0.185522	−	0.537198i
$31$	−2.03983	−	3.53308i	−0.366364	−	0.634560i	0.622630	−	0.782516i	$-0.286064\pi$
$31$	−2.03983	−	3.53308i	−0.366364	−	0.634560i	−0.988994	+	0.147956i	$0.952731\pi$
$32$	0.518810	−	5.63301i	0.0917136	−	0.995785i
$33$	−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	0.771731	−	0.635949i	$-0.219391\pi$
$37$	3.69132	+	2.13119i	0.606849	+	0.350365i	−0.164882	+	0.986313i	$0.552724\pi$
$38$	−1.75282	−	2.02012i	−0.284345	−	0.327707i
$39$	9.21347	−	5.31940i	1.47534	−	0.851785i
$40$	2.82495	−	0.140272i	0.446663	−	0.0221790i
$41$			3.44314i			0.537729i	0.963178	+	0.268864i	$0.0866483\pi$
$41$			3.44314i			0.537729i	−0.963178	+	0.268864i	$0.913352\pi$
$42$	3.31145	+	7.54085i	0.510968	+	1.16358i
$43$	−2.10796			−0.321461			−0.160731	−	0.986998i	$-0.551385\pi$
$43$	−2.10796			−0.321461			−0.160731	+	0.986998i	$0.551385\pi$
$44$	1.63817	−	11.5034i	0.246964	−	1.73420i
$45$	0.922503	+	1.59782i	0.137519	+	0.238189i
$46$	−0.168901	−	0.194657i	−0.0249030	−	0.0287007i
$47$	0.946816	−	1.63993i	0.138107	−	0.239209i	−0.788673	−	0.614813i	$-0.789231\pi$
$47$	0.946816	−	1.63993i	0.138107	−	0.239209i	0.926780	+	0.375604i	$0.122565\pi$
$48$	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
$52$	7.60650	+	5.96531i	1.05483	+	0.827239i
$53$	−8.54212	+	4.93180i	−1.17335	+	0.677434i	−0.954467	−	0.298317i	$-0.903575\pi$
$53$	−8.54212	+	4.93180i	−1.17335	+	0.677434i	−0.218884	+	0.975751i	$0.570242\pi$
$54$	1.17364	−	3.39840i	0.159713	−	0.462464i
$55$	5.80972			0.783383
$56$	−5.23551	+	5.34691i	−0.699625	+	0.714510i
$57$	4.16279			0.551375
$58$	2.02616	−	5.86693i	0.266047	−	0.770366i
$59$	−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	$0.491865\pi$
$60$	−2.71666	+	3.46407i	−0.350719	+	0.447210i
$61$	−4.89522	+	8.47877i	−0.626769	+	1.08560i	0.361427	+	0.932400i	$0.382290\pi$
$61$	−4.89522	+	8.47877i	−0.626769	+	1.08560i	−0.988196	+	0.153195i	$0.951044\pi$
$62$	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
$66$	11.8523	+	13.6597i	1.45892	+	1.68140i
$67$	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	$0.568599\pi$
$68$	8.64774	+	1.23151i	1.04869	+	0.149342i
$69$	0.401124			0.0482896
$70$	−3.01582	−	2.21469i	−0.360459	−	0.264706i
$71$		−	8.80669i		−	1.04516i	−0.852590	−	0.522581i	$-0.824969\pi$
$71$		−	8.80669i		−	1.04516i	0.852590	−	0.522581i	$-0.175031\pi$
$72$	−5.21205	+	0.258804i	−0.614246	+	0.0305003i
$73$	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	$0.167891\pi$
$74$	−3.95049	−	4.55293i	−0.459236	−	0.529268i
$75$	−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	0.957722	−	0.287696i	$-0.0928894\pi$
$79$	10.5541	+	6.09342i	1.18743	+	0.685563i	0.229708	+	0.973259i	$0.426223\pi$
$80$	−3.84098	−	1.11662i	−0.429435	−	0.124842i
$81$	5.56549	+	9.63970i	0.618387	+	1.07108i
$82$	1.58952	−	4.60260i	0.175533	−	0.508272i
$83$			16.9697i			1.86267i	0.364163	+	0.931335i	$0.381355\pi$
$83$			16.9697i			1.86267i	−0.364163	+	0.931335i	$0.618645\pi$
$84$	−0.945352	−	11.6089i	−0.103146	−	1.26663i
$85$			4.36749i			0.473721i
$86$	2.81781	+	0.973134i	0.303852	+	0.104936i
$87$	4.83037	+	8.36645i	0.517870	+	0.896977i
$88$	−7.50032	+	14.6208i	−0.799536	+	1.55858i
$89$	−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
$94$	−2.02272	+	1.75507i	−0.208627	+	0.181022i
$95$	−1.63783	+	0.945600i	−0.168038	+	0.0970165i
$96$	−5.21054	−	11.3089i	−0.531799	−	1.15421i
$97$		−	13.2388i		−	1.34420i	−0.740461	−	0.672100i	$-0.765393\pi$
$97$		−	13.2388i		−	1.34420i	0.740461	−	0.672100i	$-0.234607\pi$
$98$	9.83648	−	1.11522i	0.993634	−	0.112654i
$99$	−10.7190			−1.07730
$100$	0.281971	−	1.98002i	0.0281971	−	0.198002i
$101$	−1.23442	−	2.13807i	−0.122829	−	0.212746i	0.798053	−	0.602587i	$-0.205863\pi$
$101$	−1.23442	−	2.13807i	−0.122829	−	0.212746i	−0.920882	+	0.389841i	$0.872530\pi$
$102$	−10.2688	+	8.91004i	−1.01676	+	0.882226i
$103$	0.920346	−	1.59409i	0.0906844	−	0.157070i	−0.817115	−	0.576475i	$-0.804428\pi$
$103$	0.920346	−	1.59409i	0.0906844	−	0.157070i	0.907799	+	0.419405i	$0.137761\pi$
$104$	−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	$-0.174754\pi$
$108$	−3.13772	+	4.00098i	−0.301927	+	0.384995i
$109$	3.40525	−	1.96602i	0.326164	−	0.188311i	−0.327973	−	0.944687i	$-0.606365\pi$
$109$	3.40525	−	1.96602i	0.326164	−	0.188311i	0.654137	+	0.756376i	$0.273032\pi$
$110$	−7.76611	−	2.68204i	−0.740469	−	0.255722i
$111$	9.38206			0.890506
$112$	9.46692	−	4.73048i	0.894540	−	0.446989i
$113$	7.16641			0.674159			0.337079	−	0.941476i	$-0.390561\pi$
$113$	7.16641			0.674159			0.337079	+	0.941476i	$0.390561\pi$
$114$	−5.56458	−	1.92174i	−0.521171	−	0.179987i
$115$	−0.157820	+	0.0911173i	−0.0147168	+	0.00849673i
$116$	−5.41690	+	6.90722i	−0.502947	+	0.641319i
$117$	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
$122$	10.4578	−	9.07408i	0.946809	−	0.821528i
$123$	3.78942	+	6.56346i	0.341680	+	0.591808i
$124$	1.15034	−	8.07781i	0.103304	−	0.725409i
$125$	1.00000			0.0894427
$126$	5.56420	+	4.08612i	0.495698	+	0.364021i
$127$		−	2.88206i		−	0.255742i	−0.991791	−	0.127871i	$-0.959186\pi$
$127$		−	2.88206i		−	0.255742i	0.991791	−	0.127871i	$-0.0408143\pi$
$128$	7.76878	−	8.22472i	0.686670	−	0.726969i
$129$	−4.01829	+	2.31996i	−0.353790	+	0.204261i
$130$	5.16280	−	4.47966i	0.452808	−	0.392893i
$131$	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
$136$	−10.9913	−	5.63841i	−0.942495	−	0.483489i
$137$	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	$0.689849\pi$
$138$	−0.536199	−	0.185177i	−0.0456443	−	0.0157633i
$139$			9.93769i			0.842904i	0.906851	+	0.421452i	$0.138479\pi$
$139$			9.93769i			0.842904i	−0.906851	+	0.421452i	$0.861521\pi$
$140$	3.00897	+	4.35271i	0.254304	+	0.367872i
$141$		−	4.16814i		−	0.351021i
$142$	−4.06558	+	11.7723i	−0.341176	+	0.987908i
$143$	−14.0401	−	24.3182i	−1.17409	−	2.03359i
$144$	7.08664	+	2.06017i	0.590554	+	0.171681i
$145$	−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	0.941077	−	0.338192i	$-0.109815\pi$
$149$	13.6559	+	7.88422i	1.11873	+	0.645900i	0.177655	+	0.984093i	$0.443149\pi$
$150$	2.04008	+	2.35119i	0.166572	+	0.191974i
$151$	−5.24155	+	3.02621i	−0.426552	+	0.246270i	−0.697877	−	0.716218i	$-0.745872\pi$
$151$	−5.24155	+	3.02621i	−0.426552	+	0.246270i	0.271325	+	0.962488i	$0.412538\pi$
$152$	−0.265283	−	5.34254i	−0.0215173	−	0.433337i
$153$		−	8.05806i		−	0.651455i
$154$	19.9035	−	8.74030i	1.60387	−	0.704314i
$155$	4.07965			0.327686
$156$	21.0651	+	2.99983i	1.68655	+	0.240179i
$157$	−10.2074	−	17.6798i	−0.814641	−	1.41100i	−0.909585	−	0.415518i	$-0.863600\pi$
$157$	−10.2074	−	17.6798i	−0.814641	−	1.41100i	0.0949439	−	0.995483i	$-0.469733\pi$
$158$	−11.2951	−	13.0176i	−0.898592	−	1.03562i
$159$	−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	$0.118800\pi$
$164$	−4.24955	+	5.41870i	−0.331834	+	0.423129i
$165$	11.0747	−	6.39400i	0.862167	−	0.497772i
$166$	7.83402	−	22.6842i	0.608038	−	1.76063i
$167$	−21.6531			−1.67556			−0.837782	−	0.546005i	$-0.816148\pi$
$167$	−21.6531			−1.67556			−0.837782	+	0.546005i	$0.816148\pi$
$168$	−4.09551	+	15.9545i	−0.315976	+	1.23092i
$169$	10.3609			0.796996
$170$	2.01624	−	5.83822i	0.154638	−	0.447771i
$171$	3.02180	−	1.74464i	0.231083	−	0.133416i
$172$	−3.31744	−	2.60166i	−0.252952	−	0.198375i
$173$	5.20160	−	9.00944i	0.395470	−	0.684975i	−0.597691	−	0.801727i	$-0.703915\pi$
$173$	5.20160	−	9.00944i	0.395470	−	0.684975i	0.993161	+	0.116752i	$0.0372483\pi$
$174$	−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
$178$	5.47618	+	6.31128i	0.410457	+	0.473051i
$179$	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	$0.741536\pi$
$180$	−0.520239	+	3.65316i	−0.0387763	+	0.272290i
$181$	−11.2225			−0.834160			−0.417080	−	0.908870i	$-0.636946\pi$
$181$	−11.2225			−0.834160			−0.417080	+	0.908870i	$0.636946\pi$
$182$	−1.98201	+	17.9757i	−0.146916	+	1.33245i
$183$			21.5501i			1.59303i
$184$	−0.0255625	−	0.514803i	−0.00188449	−	0.0379518i
$185$	−3.69132	+	2.13119i	−0.271391	+	0.156688i
$186$	8.32282	+	9.59203i	0.610259	+	0.703322i
$187$	−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	0.721983	−	0.691911i	$-0.243231\pi$
$191$	6.68571	+	3.86000i	0.483761	+	0.279300i	−0.238222	+	0.971211i	$0.576564\pi$
$192$	1.74446	+	17.5225i	0.125895	+	1.26458i
$193$	−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	$-0.485445\pi$
$194$	−6.11166	+	17.6969i	−0.438791	+	1.27056i
$195$			10.6388i			0.761860i
$196$	−13.6637	−	3.05021i	−0.975977	−	0.217872i
$197$			20.4272i			1.45538i	0.685907	+	0.727689i	$0.259406\pi$
$197$			20.4272i			1.45538i	−0.685907	+	0.727689i	$0.740594\pi$
$198$	14.3285	+	4.94838i	1.01828	+	0.351666i
$199$	1.10091	+	1.90683i	0.0780413	+	0.135172i	0.902405	−	0.430889i	$-0.141800\pi$
$199$	1.10091	+	1.90683i	0.0780413	+	0.135172i	−0.824363	+	0.566061i	$0.808467\pi$
$200$	−1.29099	+	2.51661i	−0.0912870	+	0.177951i
$201$	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
$206$	−1.96617	+	1.70601i	−0.136990	+	0.118863i
$207$	0.291179	−	0.168112i	0.0202383	−	0.0116846i
$208$	4.60843	+	18.7760i	0.319537	+	1.30188i
$209$		−	10.9874i		−	0.760011i
$210$	−8.18629	−	0.902624i	−0.564908	−	0.0622870i
$211$	−28.9363			−1.99206			−0.996028	−	0.0890425i	$-0.971619\pi$
$211$	−28.9363			−1.99206			−0.996028	+	0.0890425i	$0.971619\pi$
$212$	−19.5301	−	2.78125i	−1.34134	−	0.191017i
$213$	−9.69236	−	16.7877i	−0.664110	−	1.15027i
$214$	−19.4123	+	16.8437i	−1.32700	+	1.15141i
$215$	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
$220$	9.14314	+	7.17039i	0.616430	+	0.483428i
$221$	18.2813	−	10.5547i	1.22974	−	0.709989i
$222$	−12.5414	−	4.33120i	−0.841724	−	0.290691i
$223$	−11.0535			−0.740200			−0.370100	−	0.928992i	$-0.620677\pi$
$223$	−11.0535			−0.740200			−0.370100	+	0.928992i	$0.620677\pi$
$224$	−14.8386	+	1.95307i	−0.991449	+	0.130495i
$225$	−1.84501			−0.123000
$226$	−9.57964	−	3.30835i	−0.637229	−	0.220068i
$227$	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	$0.245381\pi$
$228$	6.55126	+	5.13774i	0.433868	+	0.340255i
$229$	5.03725	−	8.72478i	0.332871	−	0.576549i	−0.650203	−	0.759761i	$-0.725316\pi$
$229$	5.03725	−	8.72478i	0.332871	−	0.576549i	0.983074	+	0.183211i	$0.0586493\pi$
$230$	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	$0.0890438\pi$
$234$	−9.52540	+	8.26501i	−0.622695	+	0.540301i
$235$	0.946816	+	1.63993i	0.0617634	+	0.106977i
$236$	−14.5307	−	2.06929i	−0.945868	−	0.134699i
$237$	26.8249			1.74246
$238$	6.57057	+	14.9625i	0.425907	+	0.969877i
$239$			20.9534i			1.35536i	0.735355	+	0.677682i	$0.237016\pi$
$239$			20.9534i			1.35536i	−0.735355	+	0.677682i	$0.762984\pi$
$240$	−8.55076	+	2.09872i	−0.551949	+	0.135472i
$241$	−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	$0.362036\pi$
$242$	24.3039	−	21.0881i	1.56232	−	1.35559i
$243$	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
$248$	−5.26681	+	10.2669i	−0.334443	+	0.651949i
$249$	18.6764	+	32.3484i	1.18357	+	2.05000i
$250$	−1.33674	−	0.461647i	−0.0845431	−	0.0291971i
$251$		−	18.7656i		−	1.18448i	−0.805763	−	0.592238i	$-0.798244\pi$
$251$		−	18.7656i		−	1.18448i	0.805763	−	0.592238i	$-0.201756\pi$
$252$	−5.55156	−	8.03079i	−0.349716	−	0.505892i
$253$		−	1.05873i		−	0.0665620i
$254$	−1.33050	+	3.85258i	−0.0834827	+	0.241732i
$255$	4.80673	+	8.32550i	0.301009	+	0.521363i
$256$	−14.1818	+	7.40791i	−0.886361	+	0.462994i
$257$	−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
$262$	−7.41606	−	8.54699i	−0.458166	−	0.528035i
$263$	5.03985	−	2.90976i	0.310770	−	0.179423i	−0.336501	−	0.941683i	$-0.609243\pi$
$263$	5.03985	−	2.90976i	0.310770	−	0.179423i	0.647271	+	0.762260i	$0.275910\pi$
$264$	1.79380	+	36.1254i	0.110401	+	2.22337i
$265$		−	9.86359i		−	0.605916i
$266$	−4.18843	+	5.70351i	−0.256809	+	0.349705i
$267$	−13.0054			−0.795920
$268$	−3.41159	+	23.9565i	−0.208396	+	1.46337i
$269$	12.0950	+	20.9492i	0.737445	+	1.27729i	0.953642	+	0.300943i	$0.0973012\pi$
$269$	12.0950	+	20.9492i	0.737445	+	1.27729i	−0.216197	+	0.976350i	$0.569365\pi$
$270$	2.35628	+	2.71561i	0.143399	+	0.165266i
$271$	7.83742	−	13.5748i	0.476089	−	0.824611i	−0.523536	−	0.852004i	$-0.675387\pi$
$271$	7.83742	−	13.5748i	0.476089	−	0.824611i	0.999625	+	0.0273932i	$0.00872061\pi$
$272$	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
$276$	0.631274	+	0.495069i	0.0379982	+	0.0297996i
$277$	12.6984	−	7.33142i	0.762972	−	0.440502i	−0.0673898	−	0.997727i	$-0.521467\pi$
$277$	12.6984	−	7.33142i	0.762972	−	0.440502i	0.830362	+	0.557225i	$0.188134\pi$
$278$	4.58770	−	13.2841i	0.275152	−	0.796729i
$279$	−7.52699			−0.450629
$280$	−2.01280	−	7.20754i	−0.120288	−	0.430733i
$281$	15.0418			0.897320			0.448660	−	0.893703i	$-0.351901\pi$
$281$	15.0418			0.897320			0.448660	+	0.893703i	$0.351901\pi$
$282$	−1.92421	+	5.57174i	−0.114585	+	0.331792i
$283$	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	$0.286252\pi$
$284$	10.8693	−	13.8597i	0.644972	−	0.822419i
$285$	−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
$290$	4.06784	+	4.68817i	0.238872	+	0.275299i
$291$	−14.5702	−	25.2364i	−0.854123	−	1.47938i
$292$	16.8045	+	2.39310i	0.983410	+	0.140045i
$293$	2.56812			0.150031			0.0750156	−	0.997182i	$-0.476099\pi$
$293$	2.56812			0.150031			0.0750156	+	0.997182i	$0.476099\pi$
$294$	17.5233	−	12.9516i	1.02198	−	0.755353i
$295$		−	7.33865i		−	0.427273i
$296$	−0.597893	−	12.0410i	−0.0347518	−	0.699867i
$297$	12.7912	−	7.38503i	0.742223	−	0.428523i
$298$	−14.6147	−	16.8434i	−0.846605	−	0.975710i
$299$	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
$304$	−2.11175	+	7.26407i	−0.121117	+	0.416623i
$305$	−4.89522	−	8.47877i	−0.280299	−	0.485493i
$306$	−3.71997	+	10.7716i	−0.212657	+	0.615769i
$307$		−	14.4425i		−	0.824280i	−0.911121	−	0.412140i	$-0.864781\pi$
$307$		−	14.4425i		−	0.824280i	0.911121	−	0.412140i	$-0.135219\pi$
$308$	−30.6407	+	2.49518i	−1.74592	+	0.142176i
$309$		−	4.05162i		−	0.230488i
$310$	−5.45345	−	1.88336i	−0.309735	−	0.106968i
$311$	−8.26712	−	14.3191i	−0.468785	−	0.811960i	0.530578	−	0.847636i	$-0.321975\pi$
$311$	−8.26712	−	14.3191i	−0.468785	−	0.811960i	−0.999363	+	0.0356762i	$0.988641\pi$
$312$	−26.7737	−	13.7346i	−1.51576	−	0.777570i
$313$	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	0.0214339	−	0.999770i	$-0.493177\pi$
$317$	−14.8432	−	8.56971i	−0.833676	−	0.481323i	−0.855109	+	0.518447i	$0.826510\pi$
$318$	23.1912	−	20.1225i	1.30050	−	1.12842i
$319$	22.0826	−	12.7494i	1.23639	−	0.713828i
$320$	−4.66667	−	6.49786i	−0.260875	−	0.363241i
$321$		−	40.0023i		−	2.23271i
$322$	−0.403594	+	0.549586i	−0.0224914	+	0.0306272i
$323$	8.25981			0.459588
$324$	−3.13861	+	22.0396i	−0.174367	+	1.22442i
$325$	−2.41666	−	4.18577i	−0.134052	−	0.232185i
$326$	−4.08612	+	3.54545i	−0.226309	+	0.196364i
$327$	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	$0.939658\pi$
$332$	−20.9441	+	26.7064i	−1.14946	+	1.46570i
$333$	6.81051	−	3.93205i	0.373214	−	0.215475i
$334$	28.9446	+	9.99606i	1.58378	+	0.546960i
$335$	−12.0991			−0.661044
$336$	12.8400	−	19.4364i	0.700480	−	1.06034i
$337$	1.22715			0.0668470			0.0334235	−	0.999441i	$-0.489359\pi$
$337$	1.22715			0.0668470			0.0334235	+	0.999441i	$0.489359\pi$
$338$	−13.8499	−	4.78310i	−0.753337	−	0.260166i
$339$	13.6609	−	7.88712i	0.741958	−	0.428370i
$340$	−5.39039	+	6.87341i	−0.292335	+	0.372763i
$341$	−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
$346$	−11.1124	+	9.64200i	−0.597405	+	0.518357i
$347$	−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	$-0.479009\pi$
$348$	−2.72405	+	19.1285i	−0.146024	+	1.02539i
$349$	−26.6776			−1.42802			−0.714010	−	0.700136i	$-0.753123\pi$
$349$	−26.6776			−1.42802			−0.714010	+	0.700136i	$0.753123\pi$
$350$	3.42589	−	1.50443i	0.183121	−	0.0804150i
$351$			12.2877i			0.655871i
$352$	−29.8488	+	13.7528i	−1.59095	+	0.733027i
$353$	−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	$0.455129\pi$
$354$	17.2545	−	14.9714i	0.917069	−	0.795723i
$355$	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	0.751150	−	0.660131i	$-0.229499\pi$
$359$	10.5164	+	6.07165i	0.555035	+	0.320450i	−0.196115	+	0.980581i	$0.562833\pi$
$360$	2.38189	−	4.64317i	0.125537	−	0.244716i
$361$	−7.71168	−	13.3570i	−0.405878	−	0.703001i
$362$	15.0016	+	5.18081i	0.788465	+	0.272298i
$363$			50.0822i			2.62864i
$364$	10.9478	−	23.1139i	0.573823	−	1.21150i
$365$			8.48703i			0.444231i
$366$	9.94853	−	28.8070i	0.520018	−	1.50576i
$367$	5.75583	+	9.96939i	0.300452	+	0.520398i	0.976238	−	0.216700i	$-0.0695292\pi$
$367$	5.75583	+	9.96939i	0.300452	+	0.520398i	−0.675787	+	0.737097i	$0.736196\pi$
$368$	−0.203487	+	0.699960i	−0.0106075	+	0.0364880i
$369$	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	0.923304	−	0.384070i	$-0.125478\pi$
$373$	20.3241	+	11.7341i	1.05234	+	0.607570i	0.129037	+	0.991640i	$0.458811\pi$
$374$	23.5173	+	27.1037i	1.21605	+	1.40150i
$375$	1.90624	−	1.10057i	0.0984379	−	0.0568331i
$376$	−5.34941	+	0.265624i	−0.275875	+	0.0136985i
$377$			21.2133i			1.09254i
$378$	−9.45511	−	1.04252i	−0.486318	−	0.0536217i
$379$	−15.5653			−0.799536			−0.399768	−	0.916616i	$-0.630909\pi$
$379$	−15.5653			−0.799536			−0.399768	+	0.916616i	$0.630909\pi$
$380$	−3.74462	−	0.533264i	−0.192095	−	0.0273559i
$381$	−3.17191	−	5.49391i	−0.162502	−	0.281462i
$382$	−7.15512	−	8.24626i	−0.366088	−	0.421915i
$383$	−7.45943	+	12.9201i	−0.381159	+	0.660187i	−0.991228	−	0.132161i	$-0.957808\pi$
$383$	−7.45943	+	12.9201i	−0.381159	+	0.660187i	0.610069	+	0.792348i	$0.291142\pi$
$384$	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
$388$	16.3394	−	20.8348i	0.829509	−	1.05773i
$389$	−10.9524	+	6.32338i	−0.555310	+	0.320608i	−0.751261	−	0.660006i	$-0.770554\pi$
$389$	−10.9524	+	6.32338i	−0.555310	+	0.320608i	0.195951	+	0.980614i	$0.437221\pi$
$390$	4.91136	−	14.2213i	0.248697	−	0.720125i
$391$	0.795909			0.0402508
$392$	16.8567	+	10.3851i	0.851393	+	0.524529i
$393$	17.6125			0.888431
$394$	9.43015	−	27.3059i	0.475084	−	1.37565i
$395$	−10.5541	+	6.09342i	−0.531035	+	0.306593i
$396$	−16.8692	−	13.2294i	−0.847707	−	0.664804i
$397$	7.61650	−	13.1922i	0.382261	−	0.662095i	−0.609124	−	0.793075i	$-0.708479\pi$
$397$	7.61650	−	13.1922i	0.382261	−	0.662095i	0.991385	+	0.130979i	$0.0418122\pi$
$398$	−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	$0.292919\pi$
$402$	−24.6831	−	28.4472i	−1.23108	−	1.41882i
$403$	−9.85913	−	17.0765i	−0.491118	−	0.850641i
$404$	0.696139	−	4.88834i	0.0346342	−	0.243204i
$405$	−11.1310			−0.553102
$406$	−16.3231	−	1.79980i	−0.810103	−	0.0893223i
$407$		−	24.7632i		−	1.22747i
$408$	−27.1575	+	1.34850i	−1.34450	+	0.0667608i
$409$	−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	$0.401745\pi$
$410$	3.19121	+	3.67786i	0.157603	+	0.181637i
$411$	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
$416$	2.50758	−	27.2261i	0.122944	−	1.33487i
$417$	10.9371	+	18.9436i	0.535592	+	0.927673i
$418$	−5.07227	+	14.6873i	−0.248093	+	0.718378i
$419$		−	10.6898i		−	0.522230i	−0.965308	−	0.261115i	$-0.915910\pi$
$419$		−	10.6898i		−	0.522230i	0.965308	−	0.261115i	$-0.0840902\pi$
$420$	10.5263	+	4.98575i	0.513630	+	0.243280i
$421$		−	20.4941i		−	0.998823i	−0.866365	−	0.499412i	$-0.833550\pi$
$421$		−	20.4941i		−	0.998823i	0.866365	−	0.499412i	$-0.166450\pi$
$422$	38.6804	+	13.3583i	1.88293	+	0.650273i
$423$	−1.74688	−	3.02569i	−0.0849363	−	0.147114i
$424$	24.8228	+	12.7338i	1.20550	+	0.618410i
$425$	−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
$430$	−2.25166	+	1.95372i	−0.108585	+	0.0942170i
$431$	20.9544	−	12.0980i	1.00934	−	0.582740i	0.0983389	−	0.995153i	$-0.468647\pi$
$431$	20.9544	−	12.0980i	1.00934	−	0.582740i	0.910997	+	0.412412i	$0.135314\pi$
$432$	−9.87607	+	2.42401i	−0.475163	+	0.116625i
$433$			20.2949i			0.975311i	0.873036	+	0.487655i	$0.162148\pi$
$433$			20.2949i			0.975311i	−0.873036	+	0.487655i	$0.837852\pi$
$434$	13.9764	−	6.13754i	0.670890	−	0.294611i
$435$	−9.66074			−0.463197
$436$	7.78554	+	1.10872i	0.372860	+	0.0530982i
$437$	0.172321	+	0.298469i	0.00824324	+	0.0142777i
$438$	−19.9546	+	17.3142i	−0.953467	+	0.827306i
$439$	−2.52231	+	4.36878i	−0.120384	+	0.208510i	−0.919919	−	0.392109i	$-0.871746\pi$
$439$	−2.52231	+	4.36878i	−0.120384	+	0.208510i	0.799535	+	0.600619i	$0.205079\pi$
$440$	−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	$0.228254\pi$
$444$	14.7652	+	11.5794i	0.700724	+	0.549534i
$445$	5.11692	−	2.95425i	0.242565	−	0.140045i
$446$	14.7757	+	5.10283i	0.699652	+	0.241626i
$447$	34.7085			1.64166
$448$	20.7371	+	4.23946i	0.979736	+	0.200296i
$449$	−4.05786			−0.191502			−0.0957511	−	0.995405i	$-0.530525\pi$
$449$	−4.05786			−0.191502			−0.0957511	+	0.995405i	$0.530525\pi$
$450$	2.46630	+	0.851741i	0.116263	+	0.0401515i
$451$	17.3237	−	10.0019i	0.815742	−	0.470969i
$452$	11.2782	+	8.84482i	0.530484	+	0.416025i
$453$	−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	$0.207087\pi$
$458$	−10.7613	+	9.33736i	−0.502841	+	0.436306i
$459$	5.55174	+	9.61589i	0.259133	+	0.448831i
$460$	−0.360829	−	0.0513849i	−0.0168237	−	0.00239583i
$461$	18.9095			0.880702			0.440351	−	0.897826i	$-0.354854\pi$
$461$	18.9095			0.880702			0.440351	+	0.897826i	$0.354854\pi$
$462$	28.3215	−	38.5662i	1.31763	−	1.79426i
$463$			0.304782i			0.0141644i	0.999975	+	0.00708220i	$0.00225435\pi$
$463$			0.304782i			0.0141644i	−0.999975	+	0.00708220i	$0.997746\pi$
$464$	−17.0499	+	4.18477i	−0.791520	+	0.194273i
$465$	7.77680	−	4.48994i	0.360641	−	0.208216i
$466$	−7.87362	+	6.83179i	−0.364738	+	0.316477i
$467$	−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
$472$	18.4685	+	9.47415i	0.850083	+	0.436083i
$473$	6.12334	+	10.6059i	0.281552	+	0.487662i
$474$	−35.8580	−	12.3836i	−1.64701	−	0.568799i
$475$		−	1.89120i		−	0.0867742i
$476$	−1.87577	−	23.0344i	−0.0859756	−	1.05578i
$477$			18.1984i			0.833247i
$478$	9.67308	−	28.0094i	0.442436	−	1.28112i
$479$	−16.4744	−	28.5344i	−0.752732	−	1.30377i	−0.946494	−	0.322722i	$-0.895402\pi$
$479$	−16.4744	−	28.5344i	−0.752732	−	1.30377i	0.193761	−	0.981049i	$-0.437931\pi$
$480$	12.3990	+	1.14197i	0.565936	+	0.0521237i
$481$	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
$486$	−15.6392	−	18.0242i	−0.709410	−	0.817594i
$487$	−35.8923	+	20.7224i	−1.62643	+	0.939022i	−0.641289	+	0.767300i	$0.721600\pi$
$487$	−35.8923	+	20.7224i	−1.62643	+	0.939022i	−0.985145	+	0.171722i	$0.945067\pi$
$488$	27.6575	−	1.37333i	1.25199	−	0.0621677i
$489$		−	8.42012i		−	0.380771i
$490$	−3.95243	+	9.07625i	−0.178553	+	0.410023i
$491$	−25.4339			−1.14782			−0.573908	−	0.818920i	$-0.694573\pi$
$491$	−25.4339			−1.14782			−0.573908	+	0.818920i	$0.694573\pi$
$492$	−2.13701	+	15.0063i	−0.0963439	+	0.676535i
$493$	9.58441	+	16.6007i	0.431660	+	0.747658i
$494$	−8.47194	−	9.76389i	−0.381171	−	0.439298i
$495$	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	$0.120182\pi$
$500$	1.57376	+	1.23421i	0.0703809	+	0.0551954i
$501$	−41.2759	+	23.8307i	−1.84407	+	1.06468i
$502$	−8.66309	+	25.0848i	−0.386653	+	1.11959i
$503$	23.4094			1.04378			0.521888	−	0.853014i	$-0.325228\pi$
$503$	23.4094			1.04378			0.521888	+	0.853014i	$0.325228\pi$
$504$	3.71363	+	13.2980i	0.165418	+	0.592338i
$505$	2.46883			0.109862
$506$	−0.488760	+	1.41525i	−0.0217280	+	0.0629157i
$507$	19.7505	−	11.4029i	0.877149	−	0.506422i
$508$	3.55706	−	4.53569i	0.157819	−	0.201239i
$509$	−8.44031	+	14.6190i	−0.374110	+	0.647978i	−0.990193	−	0.139703i	$-0.955385\pi$
$509$	−8.44031	+	14.6190i	−0.374110	+	0.647978i	0.616083	+	0.787681i	$0.288719\pi$
$510$	−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
$514$	7.24067	+	8.34485i	0.319372	+	0.368076i
$515$	0.920346	+	1.59409i	0.0405553	+	0.0702438i
$516$	−9.18715	−	1.30832i	−0.404442	−	0.0575957i
$517$	−11.0015			−0.483844
$518$	−9.43984	+	12.8545i	−0.414763	+	0.564795i
$519$		−	22.8989i		−	1.00515i
$520$	13.6539	−	0.677981i	0.598761	−	0.0297314i
$521$	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	$0.152945\pi$
$522$	−7.50519	−	8.64971i	−0.328493	−	0.378587i
$523$	−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
$528$	14.2793	−	49.1185i	0.621428	−	2.13761i
$529$	−11.4834	−	19.8898i	−0.499278	−	0.864775i
$530$	−4.55349	+	13.1851i	−0.197791	+	0.572724i
$531$			13.5399i			0.587580i
$532$	8.23186	−	5.69056i	0.356896	−	0.246717i
$533$			16.6418i			0.720837i
$534$	17.3849	+	6.00391i	0.752319	+	0.259815i
$535$	9.08674	+	15.7387i	0.392854	+	0.680443i
$536$	15.6198	−	30.4487i	0.674675	−	1.31518i
$537$	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	0.583301	−	0.812256i	$-0.301761\pi$
$541$	3.98939	+	2.30327i	0.171517	+	0.0990254i	−0.411784	+	0.911282i	$0.635094\pi$
$542$	−16.7434	+	14.5279i	−0.719190	+	0.624027i
$543$	−21.3927	+	12.3511i	−0.918050	+	0.530036i
$544$	−10.3387	−	22.4390i	−0.443270	−	0.962066i
$545$			3.93204i			0.168430i
$546$	16.0053	+	36.4473i	0.684963	+	1.55980i
$547$	4.27444			0.182762			0.0913808	−	0.995816i	$-0.470872\pi$
$547$	4.27444			0.182762			0.0913808	+	0.995816i	$0.470872\pi$
$548$	−2.87568	+	20.1933i	−0.122843	+	0.862613i
$549$	9.03171	+	15.6434i	0.385464	+	0.667644i
$550$	6.20577	−	5.38463i	0.264615	−	0.229601i
$551$	−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
$556$	−12.2651	+	15.6396i	−0.520158	+	0.663266i
$557$	16.1482	−	9.32317i	0.684221	−	0.395035i	−0.117222	−	0.993106i	$-0.537399\pi$
$557$	16.1482	−	9.32317i	0.684221	−	0.395035i	0.801443	+	0.598070i	$0.204066\pi$
$558$	10.0616	+	3.47481i	0.425944	+	0.147100i
$559$	−10.1885			−0.430926
$560$	−0.636741	+	10.5638i	−0.0269072	+	0.446403i
$561$	−55.8515			−2.35805
$562$	−20.1071	−	6.94401i	−0.848165	−	0.292915i
$563$	−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	$0.487936\pi$
$564$	5.14435	−	6.55968i	0.216616	−	0.276212i
$565$	−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	$0.174932\pi$
$570$	4.44657	−	3.85820i	0.186246	−	0.161602i
$571$	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	$0.690072\pi$
$572$	7.91781	−	55.5995i	0.331060	−	2.32473i
$573$	16.9928			0.709883
$574$	−12.8055	−	1.41194i	−0.534490	−	0.0589331i
$575$		−	0.182235i		−	0.00759971i
$576$	8.61004	+	11.9886i	0.358752	+	0.499525i
$577$	−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	$0.589578\pi$
$578$	−2.21645	+	1.92317i	−0.0921922	+	0.0799935i
$579$	−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
$584$	−21.3586	−	10.9567i	−0.883823	−	0.453391i
$585$	4.45875	+	7.72278i	0.184347	+	0.319298i
$586$	−3.43292	−	1.18556i	−0.141812	−	0.0489752i
$587$			22.4911i			0.928306i	0.885755	+	0.464153i	$0.153641\pi$
$587$			22.4911i			0.928306i	−0.885755	+	0.464153i	$0.846359\pi$
$588$	−29.4032	+	9.22339i	−1.21257	+	0.380366i
$589$		−	7.71544i		−	0.317909i
$590$	−3.38786	+	9.80989i	−0.139476	+	0.403867i
$591$	22.4815	+	38.9392i	0.924767	+	1.60174i
$592$	−4.75944	+	16.3717i	−0.195612	+	0.672873i
$593$	−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
$598$	−0.816350	−	0.940841i	−0.0333830	−	0.0384738i
$599$	5.50041	−	3.17566i	0.224741	−	0.129754i	−0.383403	−	0.923581i	$-0.625248\pi$
$599$	5.50041	−	3.17566i	0.224741	−	0.129754i	0.608143	+	0.793827i	$0.291915\pi$
$600$	0.308759	+	6.21810i	0.0126050	+	0.253853i
$601$		−	3.72971i		−	0.152138i	−0.997103	−	0.0760691i	$-0.975763\pi$
$601$		−	3.72971i		−	0.152138i	0.997103	−	0.0760691i	$-0.0242369\pi$
$602$	0.864416	−	7.83977i	0.0352310	−	0.319525i
$603$	22.3229			0.909059
$604$	−11.9839	−	1.70661i	−0.487620	−	0.0694409i
$605$	−11.3764	−	19.7046i	−0.462518	−	0.801105i
$606$	5.03662	+	5.80469i	0.204599	+	0.235799i
$607$	−9.66175	+	16.7346i	−0.392158	+	0.679238i	−0.992734	−	0.120330i	$-0.961605\pi$
$607$	−9.66175	+	16.7346i	−0.392158	+	0.679238i	0.600576	+	0.799568i	$0.294938\pi$
$608$	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
$612$	9.94530	−	12.6815i	0.402015	−	0.512619i
$613$	−26.3430	+	15.2092i	−1.06399	+	0.614292i	−0.926532	−	0.376216i	$-0.877225\pi$
$613$	−26.3430	+	15.2092i	−1.06399	+	0.614292i	−0.137453	+	0.990508i	$0.543892\pi$
$614$	−6.66735	+	19.3060i	−0.269072	+	0.779126i
$615$	−7.57883			−0.305608
$616$	42.1107	+	10.8098i	1.69669	+	0.435538i
$617$	9.32522			0.375419			0.187710	−	0.982225i	$-0.439894\pi$
$617$	9.32522			0.375419			0.187710	+	0.982225i	$0.439894\pi$
$618$	−1.87042	+	5.41597i	−0.0752391	+	0.217862i
$619$	−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	$0.402512\pi$
$620$	6.42041	+	5.03513i	0.257850	+	0.202216i
$621$	−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
$626$	−2.35251	−	2.71127i	−0.0940254	−	0.108364i
$627$	−12.0923	−	20.9445i	−0.482921	−	0.836444i
$628$	5.75640	−	40.4219i	0.229705	−	1.61301i
$629$	18.6159			0.742264
$630$	−6.32078	+	2.77568i	−0.251826	+	0.110586i
$631$		−	7.84644i		−	0.312362i	−0.987728	−	0.156181i	$-0.950082\pi$
$631$		−	7.84644i		−	0.312362i	0.987728	−	0.156181i	$-0.0499183\pi$
$632$	−1.70948	−	34.4272i	−0.0679994	−	1.36944i
$633$	−55.1595	+	31.8464i	−2.19239	+	1.26578i
$634$	15.8853	+	18.3078i	0.630887	+	0.727096i
$635$	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
$640$	3.23842	+	10.8403i	0.128010	+	0.428501i
$641$	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	$0.746781\pi$
$642$	−18.4669	+	53.4728i	−0.728832	+	2.11040i
$643$			5.68857i			0.224335i	0.993689	+	0.112168i	$0.0357794\pi$
$643$			5.68857i			0.224335i	−0.993689	+	0.112168i	$0.964221\pi$
$644$	0.793215	−	0.548338i	0.0312571	−	0.0216075i
$645$		−	4.63992i		−	0.182697i
$646$	−11.0412	−	3.81311i	−0.434412	−	0.150025i
$647$	−0.225415	−	0.390431i	−0.00886200	−	0.0153494i	0.861560	−	0.507655i	$-0.169488\pi$
$647$	−0.225415	−	0.390431i	−0.00886200	−	0.0153494i	−0.870422	+	0.492306i	$0.836154\pi$
$648$	14.3700	−	28.0123i	0.564507	−	1.10043i
$649$	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	0.425875	−	0.904782i	$-0.359966\pi$
$653$	−3.69894	−	2.13559i	−0.144751	−	0.0835720i	−0.570626	+	0.821210i	$0.693300\pi$
$654$	−9.24497	+	8.02169i	−0.361507	+	0.313673i
$655$	−6.92953	+	4.00076i	−0.270759	+	0.156323i
$656$	−13.3756	+	3.28294i	−0.522229	+	0.128177i
$657$		−	15.6586i		−	0.610901i
$658$	5.71084	+	4.19381i	0.222632	+	0.163492i
$659$	15.5436			0.605493			0.302746	−	0.953071i	$-0.402097\pi$
$659$	15.5436			0.605493			0.302746	+	0.953071i	$0.402097\pi$
$660$	25.3205	+	3.60585i	0.985601	+	0.140357i
$661$	−14.4897	−	25.0969i	−0.563583	−	0.976155i	−0.997180	−	0.0750479i	$-0.976089\pi$
$661$	−14.4897	−	25.0969i	−0.563583	−	0.976155i	0.433597	−	0.901107i	$-0.357244\pi$
$662$	25.4283	−	22.0636i	0.988297	−	0.857527i
$663$	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
$668$	−34.0768	−	26.7243i	−1.31847	−	1.03400i
$669$	−21.0707	+	12.1652i	−0.814641	+	0.470333i
$670$	16.1734	+	5.58550i	0.624832	+	0.215787i
$671$	56.8797			2.19582
$672$	−26.1366	+	20.0540i	−1.00824	+	0.773599i
$673$	32.3539			1.24715			0.623576	−	0.781763i	$-0.285679\pi$
$673$	32.3539			1.24715			0.623576	+	0.781763i	$0.285679\pi$
$674$	−1.64038	−	0.566508i	−0.0631851	−	0.0218211i
$675$	2.20170	−	1.27115i	0.0847433	−	0.0489266i
$676$	16.3057	+	12.7875i	0.627142	+	0.491829i
$677$	−22.4527	+	38.8892i	−0.862927	+	1.49463i	0.00616405	+	0.999981i	$0.498038\pi$
$677$	−22.4527	+	38.8892i	−0.862927	+	1.49463i	−0.869091	+	0.494652i	$0.835295\pi$
$678$	−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
$682$	25.3174	−	21.9674i	0.969453	−	0.841176i
$683$	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	$0.764312\pi$
$684$	6.90885	+	0.983875i	0.264167	+	0.0376194i
$685$	−10.1985			−0.389665
$686$	−8.62595	−	24.7304i	−0.329340	−	0.944211i
$687$		−	22.1754i		−	0.846043i
$688$	−2.00989	−	8.18881i	−0.0766261	−	0.312195i
$689$	−41.2868	+	23.8369i	−1.57290	+	0.908115i
$690$	0.428468	−	0.371773i	0.0163115	−	0.0141532i
$691$	−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
$696$	12.4720	−	24.3123i	0.472748	−	0.921557i
$697$	7.51896	+	13.0232i	0.284801	+	0.493289i
$698$	35.6611	+	12.3156i	1.34979	+	0.466153i
$699$		−	16.2249i		−	0.613681i
$700$	−5.27404	+	0.429483i	−0.199340	+	0.0162329i
$701$			6.00307i			0.226733i	0.993553	+	0.113366i	$0.0361634\pi$
$701$			6.00307i			0.226733i	−0.993553	+	0.113366i	$0.963837\pi$
$702$	5.67259	−	16.4255i	0.214098	−	0.619942i
$703$	4.03050	+	6.98103i	0.152013	+	0.263294i
$704$	46.2492	−	4.60435i	1.74308	−	0.173533i
$705$	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	0.295397	−	0.955375i	$-0.404548\pi$
$709$	−10.2323	−	5.90764i	−0.384283	−	0.221866i	−0.679680	+	0.733508i	$0.737881\pi$
$710$	−8.16230	−	9.40703i	−0.306326	−	0.353040i
$711$	19.4724	−	11.2424i	0.730272	−	0.421623i
$712$	0.828801	+	16.6912i	0.0310606	+	0.625530i
$713$		−	0.743454i		−	0.0278426i
$714$	28.9924	+	21.2908i	1.08501	+	0.796790i
$715$	28.0802			1.05014
$716$	−2.14588	+	15.0685i	−0.0801952	+	0.563137i
$717$	23.0607	+	39.9423i	0.861217	+	1.49167i
$718$	−11.2548	−	12.9711i	−0.420025	−	0.484077i
$719$	3.06796	−	5.31386i	0.114415	−	0.198173i	−0.803130	−	0.595803i	$-0.796834\pi$
$719$	3.06796	−	5.31386i	0.114415	−	0.198173i	0.917546	+	0.397630i	$0.130167\pi$
$720$	−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
$724$	−17.6615	−	13.8508i	−0.656386	−	0.514762i
$725$	3.80097	−	2.19449i	0.141164	−	0.0815013i
$726$	23.1203	−	66.9471i	0.858074	−	2.48464i
$727$	−14.8986			−0.552558			−0.276279	−	0.961077i	$-0.589101\pi$
$727$	−14.8986			−0.552558			−0.276279	+	0.961077i	$0.589101\pi$
$728$	−25.3049	+	25.8433i	−0.937862	+	0.957816i
$729$	3.74887			0.138847
$730$	3.91801	−	11.3450i	0.145012	−	0.419896i
$731$	−7.97308	+	4.60326i	−0.294895	+	0.170258i
$732$	−26.5973	+	33.9148i	−0.983063	+	1.25353i
$733$	23.7602	−	41.1539i	0.877604	−	1.52006i	0.0236421	−	0.999720i	$-0.492474\pi$
$733$	23.7602	−	41.1539i	0.877604	−	1.52006i	0.853962	−	0.520335i	$-0.174193\pi$
$734$	−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
$738$	−5.88781	−	6.78568i	−0.216733	−	0.249784i
$739$	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	$0.810449\pi$
$740$	−8.43959	−	1.20187i	−0.310246	−	0.0441814i
$741$	20.1201			0.739130
$742$	−14.8390	−	33.7915i	−0.544759	−	1.24053i
$743$		−	48.0392i		−	1.76239i	−0.472755	−	0.881194i	$-0.656741\pi$
$743$		−	48.0392i		−	1.76239i	0.472755	−	0.881194i	$-0.343259\pi$
$744$	1.25963	+	25.3677i	0.0461803	+	0.930024i
$745$	−13.6559	+	7.88422i	−0.500312	+	0.288855i
$746$	−21.7511	−	25.0680i	−0.796363	−	0.917806i
$747$	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	0.497446	−	0.867495i	$-0.334271\pi$
$751$	−0.139857	−	0.0807464i	−0.00510345	−	0.00294648i	−0.502550	+	0.864548i	$0.667605\pi$
$752$	7.27341	+	2.11446i	0.265234	+	0.0771066i
$753$	−20.6529	−	35.7718i	−0.752633	−	1.30360i
$754$	9.79305	−	28.3568i	0.356642	−	1.03269i
$755$		−	6.05243i		−	0.220270i
$756$	12.1578	+	5.75851i	0.442174	+	0.209435i
$757$		−	17.0175i		−	0.618513i	−0.950979	−	0.309257i	$-0.899920\pi$
$757$		−	17.0175i		−	0.618513i	0.950979	−	0.309257i	$-0.100080\pi$
$758$	20.8068	+	7.18567i	0.755738	+	0.260995i
$759$	−1.16521	−	2.01820i	−0.0422944	−	0.0732560i
$760$	4.75942	+	2.44153i	0.172642	+	0.0885635i
$761$	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
$766$	15.9359	−	13.8272i	0.575786	−	0.499599i
$767$	−30.7179	+	17.7350i	−1.10916	+	0.640374i
$768$	−18.8810	+	29.7293i	−0.681309	+	1.07276i
$769$		−	16.2516i		−	0.586049i	−0.956105	−	0.293025i	$-0.905338\pi$
$769$		−	16.2516i		−	0.586049i	0.956105	−	0.293025i	$-0.0946618\pi$
$770$	−2.38240	+	21.6070i	−0.0858559	+	0.778664i
$771$	−17.1959			−0.619296
$772$	6.59876	−	46.3370i	0.237494	−	1.66771i
$773$	−2.07903	−	3.60098i	−0.0747774	−	0.129518i	0.826212	−	0.563359i	$-0.190491\pi$
$773$	−2.07903	−	3.60098i	−0.0747774	−	0.129518i	−0.900989	+	0.433841i	$0.857158\pi$
$774$	4.15433	−	3.60464i	0.149324	−	0.129566i
$775$	−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
$780$	−13.1305	+	16.7430i	−0.470146	+	0.599494i
$781$	−44.3097	+	25.5822i	−1.58552	+	0.915403i
$782$	−1.06393	−	0.367428i	−0.0380459	−	0.0131392i
$783$	−11.1581			−0.398758
$784$	−17.7388	−	21.6641i	−0.633530	−	0.773718i
$785$	20.4149			0.728637
$786$	−23.5433	−	8.13073i	−0.839763	−	0.290014i
$787$	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	$0.331063\pi$
$788$	−25.2114	+	32.1476i	−0.898118	+	1.14521i
$789$	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
$794$	−16.2714	+	14.1184i	−0.577451	+	0.501043i
$795$	−10.8556	−	18.8024i	−0.385007	−	0.666852i
$796$	−0.620849	+	4.35965i	−0.0220054	+	0.154524i
$797$	4.32443			0.153179			0.0765895	−	0.997063i	$-0.475597\pi$
$797$	4.32443			0.153179			0.0765895	+	0.997063i	$0.475597\pi$
$798$	−1.70704	+	15.4819i	−0.0604287	+	0.548054i
$799$		−	8.27042i		−	0.292586i
$800$	−5.13774	+	2.36720i	−0.181646	+	0.0836933i
$801$	−9.44075	+	5.45062i	−0.333572	+	0.192588i
$802$	16.5266	−	14.3398i	0.583574	−	0.506356i
$803$	−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
$808$	−3.18725	+	6.21309i	−0.112127	+	0.218576i
$809$	−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	$-0.388701\pi$
$810$	14.8792	+	5.13857i	0.522804	+	0.180551i
$811$		−	17.6473i		−	0.619680i	−0.950789	−	0.309840i	$-0.899725\pi$
$811$		−	17.6473i		−	0.619680i	0.950789	−	0.309840i	$-0.100275\pi$
$812$	20.9890	+	9.94138i	0.736568	+	0.348874i
$813$		−	34.5025i		−	1.21005i
$814$	−11.4318	+	33.1020i	−0.400686	+	1.16023i
$815$	1.91267	+	3.31285i	0.0669981	+	0.116044i
$816$	36.9251	+	10.7346i	1.29264	+	0.375785i
$817$	−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	0.979763	−	0.200163i	$-0.0641471\pi$
$821$	37.1429	+	21.4445i	1.29630	+	0.748418i	0.316535	+	0.948581i	$0.397480\pi$
$822$	−20.8058	−	23.9786i	−0.725684	−	0.836349i
$823$	31.2832	−	18.0614i	1.09046	−	0.629580i	0.156764	−	0.987636i	$-0.449894\pi$
$823$	31.2832	−	18.0614i	1.09046	−	0.629580i	0.933700	+	0.358056i	$0.116560\pi$
$824$	−5.19986	+	0.258199i	−0.181146	+	0.00899477i
$825$			12.7880i			0.445221i
$826$	−11.0405	−	25.1414i	−0.384147	−	0.874781i
$827$	−7.53954			−0.262176			−0.131088	−	0.991371i	$-0.541847\pi$
$827$	−7.53954			−0.262176			−0.131088	+	0.991371i	$0.541847\pi$
$828$	0.665732	+	0.0948055i	0.0231358	+	0.00329472i
$829$	28.0133	+	48.5204i	0.972941	+	1.68518i	0.686570	+	0.727063i	$0.259115\pi$
$829$	28.0133	+	48.5204i	0.972941	+	1.68518i	0.286370	+	0.958119i	$0.407551\pi$
$830$	15.7281	+	18.1266i	0.545929	+	0.629182i
$831$	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
$836$	13.5607	−	17.2915i	0.469005	−	0.598039i
$837$	8.98215	−	5.18585i	0.310469	−	0.179249i
$838$	−4.93490	+	14.2895i	−0.170473	+	0.493623i
$839$	−33.7497			−1.16517			−0.582584	−	0.812770i	$-0.697958\pi$
$839$	−33.7497			−1.16517			−0.582584	+	0.812770i	$0.697958\pi$
$840$	−11.7693	−	11.5241i	−0.406079	−	0.397619i
$841$	9.73688			0.335755
$842$	−9.46105	+	27.3954i	−0.326049	+	0.944108i
$843$	28.6733	−	16.5546i	0.987562	−	0.570169i
$844$	−45.5389	−	35.7133i	−1.56751	−	1.22930i
$845$	−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
$850$	4.04793	+	4.66522i	0.138843	+	0.160016i
$851$	0.388376	+	0.672687i	0.0133133	+	0.0230594i
$852$	5.46593	−	38.3822i	0.187260	−	1.31495i
$853$	−53.4433			−1.82987			−0.914933	−	0.403607i	$-0.867756\pi$
$853$	−53.4433			−1.82987			−0.914933	+	0.403607i	$0.867756\pi$
$854$	−29.5262	−	21.6828i	−1.01036	−	0.741970i
$855$			3.48928i			0.119331i
$856$	−51.3391	+	2.54924i	−1.75473	+	0.0871312i
$857$	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	$0.124414\pi$
$858$	57.2860	+	66.0219i	1.95571	+	2.25395i
$859$	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	−0.0363065	−	0.999341i	$-0.511559\pi$
$863$	−27.0242	−	15.6024i	−0.919914	−	0.531113i	−0.883608	+	0.468228i	$0.844893\pi$
$864$	14.3208	+	1.31897i	0.487204	+	0.0448723i
$865$	5.20160	+	9.00944i	0.176860	+	0.306330i
$866$	9.36907	−	27.1291i	0.318374	−	0.921883i
$867$		−	4.56736i		−	0.155116i
$868$	−21.5163	+	1.75214i	−0.730310	+	0.0594716i
$869$		−	70.8021i		−	2.40180i
$870$	12.9139	+	4.45985i	0.437823	+	0.151203i
$871$	29.2394	+	50.6441i	0.990738	+	1.71601i
$872$	−9.89543	−	5.07625i	−0.335102	−	0.171903i
$873$	−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	0.576485	−	0.817107i	$-0.304424\pi$
$877$	4.65217	+	2.68593i	0.157092	+	0.0906974i	−0.419393	+	0.907805i	$0.637757\pi$
$878$	5.38852	−	4.67552i	0.181854	−	0.157791i
$879$	4.89545	−	2.82639i	0.165120	−	0.0953318i
$880$	5.53941	+	22.5690i	0.186733	+	0.760802i
$881$			12.9255i			0.435471i	0.976008	+	0.217736i	$0.0698670\pi$
$881$			12.9255i			0.435471i	−0.976008	+	0.217736i	$0.930133\pi$
$882$	7.29226	−	16.7457i	0.245543	−	0.563858i
$883$	42.5290			1.43122			0.715608	−	0.698502i	$-0.246150\pi$
$883$	42.5290			1.43122			0.715608	+	0.698502i	$0.246150\pi$
$884$	41.7973	+	5.95226i	1.40579	+	0.200196i
$885$	−8.07669	−	13.9892i	−0.271495	−	0.470243i
$886$	8.64569	−	7.50170i	0.290458	−	0.252025i
$887$	−19.2391	+	33.3231i	−0.645987	+	1.11888i	0.338086	+	0.941115i	$0.390220\pi$
$887$	−19.2391	+	33.3231i	−0.645987	+	1.11888i	−0.984073	+	0.177766i	$0.943113\pi$
$888$	−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
$892$	−17.3957	−	13.6423i	−0.582450	−	0.456779i
$893$	3.10144	−	1.79062i	0.103786	−	0.0599207i
$894$	−46.3964	−	16.0231i	−1.55173	−	0.535891i
$895$	−7.61028			−0.254383
$896$	−25.7630	−	15.2403i	−0.860683	−	0.509142i
$897$	1.93876			0.0647332
$898$	5.42431	+	1.87330i	0.181012	+	0.0625127i
$899$	15.5066	−	8.95275i	0.517175	−	0.298591i
$900$	−2.90361	−	2.27712i	−0.0967869	−	0.0759039i
$901$	−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
$906$	14.2304	−	12.3474i	0.472773	−	0.410216i
$907$	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	$0.379105\pi$
$908$	16.2768	+	2.31794i	0.540164	+	0.0769236i
$909$	−4.55501			−0.151080
$910$	−14.5764	−	10.7043i	−0.483203	−	0.354844i
$911$			40.9457i			1.35659i	0.734790	+	0.678295i	$0.237281\pi$
$911$			40.9457i			1.35659i	−0.734790	+	0.678295i	$0.762719\pi$
$912$	3.96911	+	16.1712i	0.131430	+	0.535482i
$913$	85.3810	−	49.2947i	2.82570	−	1.63142i
$914$	5.78380	−	5.01849i	0.191311	−	0.165997i
$915$	−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	0.827058	−	0.562116i	$-0.190013\pi$
$919$	22.8509	+	13.1930i	0.753781	+	0.435196i	−0.0732776	+	0.997312i	$0.523346\pi$
$920$	0.458614	+	0.235264i	0.0151200	+	0.00775642i
$921$	−15.8950	−	27.5310i	−0.523759	−	0.907177i
$922$	−25.2771	−	8.72949i	−0.832457	−	0.287490i
$923$		−	42.5655i		−	1.40106i
$924$	−55.6625	+	38.4787i	−1.83116	+	1.26585i
$925$		−	4.26237i		−	0.140146i
$926$	0.140701	−	0.407415i	0.00462373	−	0.0133885i
$927$	−1.69805	−	2.94110i	−0.0557711	−	0.0965984i
$928$	24.7232	+	2.27705i	0.811578	+	0.0747477i
$929$	−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
$934$	3.58915	+	4.13648i	0.117441	+	0.135350i
$935$	21.9745	−	12.6870i	0.718642	−	0.414908i
$936$	−25.1915	+	1.25088i	−0.823409	+	0.0408863i
$937$		−	14.4033i		−	0.470535i	−0.971931	−	0.235268i	$-0.924403\pi$
$937$		−	14.4033i		−	0.470535i	0.971931	−	0.235268i	$-0.0755967\pi$
$938$	−41.4501	+	18.2022i	−1.35339	+	0.594322i
$939$	5.58701			0.182325
$940$	−0.533949	+	3.74943i	−0.0174155	+	0.122293i
$941$	−5.58349	−	9.67088i	−0.182016	−	0.315262i	0.760551	−	0.649279i	$-0.224929\pi$
$941$	−5.58349	−	9.67088i	−0.182016	−	0.315262i	−0.942567	+	0.334017i	$0.891596\pi$
$942$	41.6480	+	47.9991i	1.35696	+	1.56390i
$943$	−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	$0.275636\pi$
$948$	42.2161	+	33.1075i	1.37111	+	1.07528i
$949$	35.5248	−	20.5102i	1.15318	−	0.665791i
$950$	−0.873066	+	2.52805i	−0.0283260	+	0.0820207i
$951$	−37.7262			−1.22336
$952$	−8.12631	+	31.6570i	−0.263375	+	1.02601i
$953$	29.6708			0.961132			0.480566	−	0.876959i	$-0.340431\pi$
$953$	29.6708			0.961132			0.480566	+	0.876959i	$0.340431\pi$
$954$	8.40123	−	24.3266i	0.272000	−	0.787602i
$955$	−6.68571	+	3.86000i	−0.216344	+	0.124907i
$956$	−25.8608	+	32.9758i	−0.836399	+	1.06651i
$957$	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
$962$	−19.0940	−	22.0058i	−0.615615	−	0.709494i
$963$	−16.7651	−	29.0380i	−0.540248	−	0.935736i
$964$	−5.53594	−	0.788362i	−0.178301	−	0.0253914i
$965$	23.4022			0.753345
$966$	−0.164489	+	1.49183i	−0.00529236	+	0.0479987i
$967$		−	50.5419i		−	1.62532i	−0.582740	−	0.812658i	$-0.698020\pi$
$967$		−	50.5419i		−	1.62532i	0.582740	−	0.812658i	$-0.301980\pi$
$968$	64.2757	−	3.19160i	2.06590	−	0.102582i
$969$	15.7452	−	9.09048i	0.505808	−	0.292028i
$970$	−12.2701	−	14.1413i	−0.393971	−	0.454050i
$971$	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
$976$	−37.6049	−	10.9322i	−1.20370	−	0.349931i
$977$	−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	$0.973397\pi$
$978$	−3.88712	+	11.2555i	−0.124296	+	0.359912i
$979$			34.3268i			1.09709i
$980$	9.47340	−	10.3080i	0.302617	−	0.329277i
$981$		−	7.25465i		−	0.231623i
$982$	33.9986	+	11.7415i	1.08494	+	0.374686i
$983$	9.60664	+	16.6392i	0.306404	+	0.530708i	0.977573	−	0.210597i	$-0.0675408\pi$
$983$	9.60664	+	16.6392i	0.306404	+	0.530708i	−0.671169	+	0.741305i	$0.734207\pi$
$984$	9.78423	−	19.0730i	0.311910	−	0.608025i
$985$	−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
$990$	−11.4497	+	9.93468i	−0.363895	+	0.315745i
$991$	−52.2605	+	30.1726i	−1.66011	+	0.958465i	−0.687450	+	0.726232i	$0.741270\pi$
$991$	−52.2605	+	30.1726i	−1.66011	+	0.958465i	−0.972660	+	0.232233i	$0.925397\pi$
$992$	−20.9602	+	9.65737i	−0.665487	+	0.306622i
$993$			52.3991i			1.66283i
$994$	32.7531	+	3.61137i	1.03887	+	0.114546i
$995$	−2.20182			−0.0698023
$996$	−10.5324	+	73.9593i	−0.333732	+	2.34349i
$997$	−8.59147	−	14.8809i	−0.272095	−	0.471282i	0.697303	−	0.716776i	$-0.254383\pi$
$997$	−8.59147	−	14.8809i	−0.272095	−	0.471282i	−0.969398	+	0.245495i	$0.921050\pi$
$998$	−6.94436	+	6.02549i	−0.219820	+	0.190734i
$999$	−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.f.131.2	yes	24
4.3	odd	2		1120.2.bz.e.271.4		24
7.3	odd	6		280.2.bj.e.171.11	yes	24
8.3	odd	2		280.2.bj.e.131.11	✓	24
8.5	even	2		1120.2.bz.f.271.4		24
28.3	even	6		1120.2.bz.f.591.4		24
56.3	even	6	inner	280.2.bj.f.171.2	yes	24
56.45	odd	6		1120.2.bz.e.591.4		24

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

\(f(q)\)	\(=\)	\(q+(-1.33674 - 0.461647i) q^{2} +(1.90624 - 1.10057i) q^{3} +(1.57376 + 1.23421i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-3.05623 + 0.591168i) q^{6} +(-0.584379 - 2.58041i) q^{7} +(-1.53395 - 2.37634i) q^{8} +(0.922503 - 1.59782i) q^{9} +O(q^{10})\)	\(q+(-1.33674 - 0.461647i) q^{2} +(1.90624 - 1.10057i) q^{3} +(1.57376 + 1.23421i) 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} +(1.06817 - 0.926830i) q^{10} +(-2.90486 - 5.03137i) q^{11} +(4.35830 + 0.620657i) q^{12} +4.83332 q^{13} +(-0.410072 + 3.71912i) q^{14} +2.20114i q^{15} +(0.953472 + 3.88470i) q^{16} +(3.78236 - 2.18375i) q^{17} +(-1.97078 + 1.71001i) 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} +(-5.53941 - 2.84166i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-6.46090 - 2.23128i) q^{26} +2.54230i q^{27} +(2.26508 - 4.78220i) q^{28} +4.38898i q^{29} +(1.01615 - 2.94236i) q^{30} +(-2.03983 - 3.53308i) q^{31} +(0.518810 - 5.63301i) 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} +(-1.75282 - 2.02012i) q^{38} +(9.21347 - 5.31940i) q^{39} +(2.82495 - 0.140272i) q^{40} +3.44314i q^{41} +(3.31145 + 7.54085i) q^{42} -2.10796 q^{43} +(1.63817 - 11.5034i) q^{44} +(0.922503 + 1.59782i) q^{45} +(-0.168901 - 0.194657i) 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} +(7.60650 + 5.96531i) q^{52} +(-8.54212 + 4.93180i) q^{53} +(1.17364 - 3.39840i) q^{54} +5.80972 q^{55} +(-5.23551 + 5.34691i) q^{56} +4.16279 q^{57} +(2.02616 - 5.86693i) q^{58} +(-6.35546 + 3.66932i) q^{59} +(-2.71666 + 3.46407i) 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} +(11.8523 + 13.6597i) q^{66} +(6.04954 + 10.4781i) q^{67} +(8.64774 + 1.23151i) q^{68} +0.401124 q^{69} +(-3.01582 - 2.21469i) q^{70} -8.80669i q^{71} +(-5.21205 + 0.258804i) q^{72} +(7.34998 - 4.24351i) q^{73} +(-3.95049 - 4.55293i) 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} +(-3.84098 - 1.11662i) q^{80} +(5.56549 + 9.63970i) q^{81} +(1.58952 - 4.60260i) q^{82} +16.9697i q^{83} +(-0.945352 - 11.6089i) q^{84} +4.36749i q^{85} +(2.81781 + 0.973134i) q^{86} +(4.83037 + 8.36645i) q^{87} +(-7.50032 + 14.6208i) 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} +(-2.02272 + 1.75507i) q^{94} +(-1.63783 + 0.945600i) q^{95} +(-5.21054 - 11.3089i) q^{96} -13.2388i q^{97} +(9.83648 - 1.11522i) 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	\( 24 q + 3 q^{2} + 12 q^{3} + q^{4} - 12 q^{5} - 2 q^{6} + 10 q^{7} - 6 q^{8} + 12 q^{9} - 3 q^{10} + 8 q^{11} + 10 q^{12} + 20 q^{13} + 5 q^{14} - 3 q^{16} + 6 q^{17} + 3 q^{18} + 18 q^{19} - 2 q^{20} - 26 q^{21} - 16 q^{22} + 18 q^{23} - 18 q^{24} - 12 q^{25} - 37 q^{26} - 41 q^{28} - 8 q^{30} - 6 q^{31} + 3 q^{32} + 12 q^{33} - 20 q^{34} - 8 q^{35} - 22 q^{36} + 15 q^{38} - 18 q^{39} + 3 q^{40} - 12 q^{42} + 32 q^{43} + 35 q^{44} + 12 q^{45} - 49 q^{46} - 14 q^{48} + 8 q^{49} - 22 q^{51} - 41 q^{52} + 30 q^{53} + 104 q^{54} - 16 q^{55} + 44 q^{56} - 44 q^{57} - 54 q^{58} - 18 q^{59} - 8 q^{60} + 22 q^{61} + 8 q^{62} - 12 q^{63} + 58 q^{64} - 10 q^{65} + 8 q^{66} - 8 q^{67} + 18 q^{68} - 12 q^{69} - q^{70} - 17 q^{72} + 30 q^{73} + 53 q^{74} - 12 q^{75} + 8 q^{76} - 32 q^{77} - 8 q^{78} + 6 q^{79} - 3 q^{80} - 4 q^{81} - 57 q^{82} + 42 q^{86} + 14 q^{87} - 17 q^{88} - 60 q^{89} + 24 q^{90} + 18 q^{91} - 38 q^{92} - 18 q^{93} + 19 q^{94} - 18 q^{95} - 74 q^{96} + 3 q^{98} - 56 q^{99}+O(q^{100}) \) 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 + 10 * q^12 + 20 * q^13 + 5 * q^14 - 3 * q^16 + 6 * q^17 + 3 * q^18 + 18 * q^19 - 2 * q^20 - 26 * q^21 - 16 * q^22 + 18 * q^23 - 18 * q^24 - 12 * q^25 - 37 * q^26 - 41 * q^28 - 8 * q^30 - 6 * q^31 + 3 * q^32 + 12 * q^33 - 20 * q^34 - 8 * q^35 - 22 * q^36 + 15 * q^38 - 18 * q^39 + 3 * q^40 - 12 * q^42 + 32 * q^43 + 35 * q^44 + 12 * q^45 - 49 * q^46 - 14 * q^48 + 8 * q^49 - 22 * q^51 - 41 * q^52 + 30 * q^53 + 104 * q^54 - 16 * q^55 + 44 * q^56 - 44 * q^57 - 54 * q^58 - 18 * q^59 - 8 * q^60 + 22 * q^61 + 8 * q^62 - 12 * q^63 + 58 * q^64 - 10 * q^65 + 8 * q^66 - 8 * q^67 + 18 * q^68 - 12 * q^69 - q^70 - 17 * q^72 + 30 * q^73 + 53 * q^74 - 12 * q^75 + 8 * q^76 - 32 * q^77 - 8 * q^78 + 6 * q^79 - 3 * q^80 - 4 * q^81 - 57 * q^82 + 42 * q^86 + 14 * q^87 - 17 * q^88 - 60 * q^89 + 24 * q^90 + 18 * q^91 - 38 * q^92 - 18 * q^93 + 19 * q^94 - 18 * q^95 - 74 * q^96 + 3 * q^98 - 56 * q^99

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