LMFDB - Embedded newform 270.2.p.a.259.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [270,2,Mod(49,270)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(270, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("270.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.p (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			259.13
Character	$\chi$	$=$	270.259
Dual form			270.2.p.a.49.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.642788 - 0.766044i) q^{2} +(-0.726309 - 1.57241i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.96492 - 1.06728i) q^{5} +(-1.67140 - 0.454341i) q^{6} +(4.83804 + 0.853077i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.94495 + 2.28411i) q^{9} +(0.445446 - 2.19125i) q^{10} +(-1.60584 + 0.584478i) q^{11} +(-1.42240 + 0.988321i) q^{12} +(-1.95350 - 2.32809i) q^{13} +(3.76333 - 3.15781i) q^{14} +(-3.10534 - 2.31449i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.04109 + 1.75578i) q^{17} +(0.499540 + 2.95812i) q^{18} +(-0.936774 + 1.62254i) q^{19} +(-1.39227 - 1.74974i) q^{20} +(-2.17252 - 8.22699i) q^{21} +(-0.584478 + 1.60584i) q^{22} +(-2.79477 + 0.492792i) q^{23} +(-0.157204 + 1.72490i) q^{24} +(2.72184 - 4.19423i) q^{25} -3.03911 q^{26} +(5.00420 + 1.39929i) q^{27} -4.91268i q^{28} +(2.46183 + 2.06572i) q^{29} +(-3.76908 + 0.891101i) q^{30} +(0.994686 + 5.64114i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(2.08538 + 2.10053i) q^{33} +(-0.609774 + 3.45820i) q^{34} +(10.4168 - 3.48730i) q^{35} +(2.58715 + 1.51877i) q^{36} +(1.92700 - 1.11256i) q^{37} +(0.640791 + 1.76056i) q^{38} +(-2.24187 + 4.76262i) q^{39} +(-2.23531 - 0.0581716i) q^{40} +(-0.451861 + 0.379157i) q^{41} +(-7.69871 - 3.62395i) q^{42} +(3.99619 + 10.9794i) q^{43} +(0.854450 + 1.47995i) q^{44} +(-1.38390 + 6.56390i) q^{45} +(-1.41894 + 2.45768i) q^{46} +(-13.0603 - 2.30288i) q^{47} +(1.22030 + 1.22917i) q^{48} +(16.1011 + 5.86031i) q^{49} +(-1.46341 - 4.78105i) q^{50} +(4.96957 + 3.50661i) q^{51} +(-1.95350 + 2.32809i) q^{52} -13.5050i q^{53} +(4.28856 - 2.93399i) q^{54} +(-2.53155 + 2.86233i) q^{55} +(-3.76333 - 3.15781i) q^{56} +(3.23169 + 0.294528i) q^{57} +(3.16487 - 0.558051i) q^{58} +(4.14855 + 1.50995i) q^{59} +(-1.74009 + 3.46007i) q^{60} +(1.58468 - 8.98717i) q^{61} +(4.96074 + 2.86408i) q^{62} +(-11.3583 + 9.39143i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-6.32319 - 2.48959i) q^{65} +(2.94955 - 0.247296i) q^{66} +(4.47017 + 5.32734i) q^{67} +(2.25718 + 2.69000i) q^{68} +(2.80473 + 4.03660i) q^{69} +(4.02439 - 10.2214i) q^{70} +(2.54561 + 4.40913i) q^{71} +(2.82643 - 1.00562i) q^{72} +(-11.3098 - 6.52971i) q^{73} +(0.386387 - 2.19131i) q^{74} +(-8.57195 - 1.23354i) q^{75} +(1.76056 + 0.640791i) q^{76} +(-8.26773 + 1.45782i) q^{77} +(2.20733 + 4.77872i) q^{78} +(4.76174 + 3.99557i) q^{79} +(-1.48139 + 1.67496i) q^{80} +(-1.43433 - 8.88497i) q^{81} +0.589863i q^{82} +(2.47161 - 2.94555i) q^{83} +(-7.72475 + 3.56812i) q^{84} +(-4.10161 + 6.69565i) q^{85} +(10.9794 + 3.99619i) q^{86} +(1.46011 - 5.37136i) q^{87} +(1.68294 + 0.296747i) q^{88} +(-0.280096 + 0.485141i) q^{89} +(4.13869 + 5.27932i) q^{90} +(-7.46507 - 12.9299i) q^{91} +(0.970612 + 2.66673i) q^{92} +(8.14775 - 5.66127i) q^{93} +(-10.1591 + 8.52448i) q^{94} +(-0.108987 + 4.18796i) q^{95} +(1.72600 - 0.144711i) q^{96} +(2.45704 + 6.75067i) q^{97} +(14.8388 - 8.56719i) q^{98} +(1.78827 - 4.80470i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41}+ \cdots - 36 q^{99}+O(q^{100}) $ 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$2$	0.642788	−	0.766044i	0.454519	−	0.541675i
$3$	−0.726309	−	1.57241i	−0.419335	−	0.907832i
$3$	−0.726309	−	1.57241i	−0.419335	−	0.907832i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	1.96492	−	1.06728i	0.878740	−	0.477301i
$5$	1.96492	−	1.06728i	0.878740	−	0.477301i
$6$	−1.67140	−	0.454341i	−0.682346	−	0.185484i
$7$	4.83804	+	0.853077i	1.82861	+	0.322433i	0.978825	−	0.204700i	$-0.0656218\pi$
$7$	4.83804	+	0.853077i	1.82861	+	0.322433i	0.849783	+	0.527133i	$0.176733\pi$
$8$	−0.866025	−	0.500000i	−0.306186	−	0.176777i
$9$	−1.94495	+	2.28411i	−0.648317	+	0.761370i
$10$	0.445446	−	2.19125i	0.140862	−	0.692934i
$11$	−1.60584	+	0.584478i	−0.484179	+	0.176227i	−0.572565	−	0.819860i	$-0.694051\pi$
$11$	−1.60584	+	0.584478i	−0.484179	+	0.176227i	0.0883856	+	0.996086i	$0.471829\pi$
$12$	−1.42240	+	0.988321i	−0.410612	+	0.285304i
$13$	−1.95350	−	2.32809i	−0.541803	−	0.645696i	0.423788	−	0.905762i	$-0.360700\pi$
$13$	−1.95350	−	2.32809i	−0.541803	−	0.645696i	−0.965591	+	0.260066i	$0.916256\pi$
$14$	3.76333	−	3.15781i	1.00579	−	0.843960i
$15$	−3.10534	−	2.31449i	−0.801795	−	0.597599i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−3.04109	+	1.75578i	−0.737573	+	0.425838i	−0.821186	−	0.570660i	$-0.806687\pi$
$17$	−3.04109	+	1.75578i	−0.737573	+	0.425838i	0.0836130	+	0.996498i	$0.473354\pi$
$18$	0.499540	+	2.95812i	0.117743	+	0.697235i
$19$	−0.936774	+	1.62254i	−0.214911	+	0.372236i	−0.953245	−	0.302199i	$-0.902279\pi$
$19$	−0.936774	+	1.62254i	−0.214911	+	0.372236i	0.738334	+	0.674435i	$0.235613\pi$
$20$	−1.39227	−	1.74974i	−0.311321	−	0.391254i
$21$	−2.17252	−	8.22699i	−0.474084	−	1.79528i
$22$	−0.584478	+	1.60584i	−0.124611	+	0.342366i
$23$	−2.79477	+	0.492792i	−0.582749	+	0.102754i	−0.457248	−	0.889339i	$-0.651165\pi$
$23$	−2.79477	+	0.492792i	−0.582749	+	0.102754i	−0.125501	+	0.992094i	$0.540054\pi$
$24$	−0.157204	+	1.72490i	−0.0320890	+	0.352094i
$25$	2.72184	−	4.19423i	0.544367	−	0.838847i
$26$	−3.03911			−0.596018
$27$	5.00420	+	1.39929i	0.963058	+	0.269294i
$28$		−	4.91268i		−	0.928409i
$29$	2.46183	+	2.06572i	0.457150	+	0.383595i	0.842081	−	0.539351i	$-0.181330\pi$
$29$	2.46183	+	2.06572i	0.457150	+	0.383595i	−0.384931	+	0.922945i	$0.625775\pi$
$30$	−3.76908	+	0.891101i	−0.688136	+	0.162692i
$31$	0.994686	+	5.64114i	0.178651	+	1.01318i	0.933845	+	0.357678i	$0.116431\pi$
$31$	0.994686	+	5.64114i	0.178651	+	1.01318i	−0.755194	+	0.655501i	$0.772457\pi$
$32$	−0.342020	+	0.939693i	−0.0604612	+	0.166116i
$33$	2.08538	+	2.10053i	0.363017	+	0.365655i
$34$	−0.609774	+	3.45820i	−0.104575	+	0.593077i
$35$	10.4168	−	3.48730i	1.76077	−	0.589462i
$36$	2.58715	+	1.51877i	0.431191	+	0.253129i
$37$	1.92700	−	1.11256i	0.316797	−	0.182903i	−0.333167	−	0.942868i	$-0.608117\pi$
$37$	1.92700	−	1.11256i	0.316797	−	0.182903i	0.649964	+	0.759965i	$0.274784\pi$
$38$	0.640791	+	1.76056i	0.103950	+	0.285601i
$39$	−2.24187	+	4.76262i	−0.358987	+	0.762629i
$40$	−2.23531	−	0.0581716i	−0.353434	−	0.00919774i
$41$	−0.451861	+	0.379157i	−0.0705689	+	0.0592143i	−0.677390	−	0.735624i	$-0.736889\pi$
$41$	−0.451861	+	0.379157i	−0.0705689	+	0.0592143i	0.606821	+	0.794839i	$0.292444\pi$
$42$	−7.69871	−	3.62395i	−1.18794	−	0.559188i
$43$	3.99619	+	10.9794i	0.609413	+	1.67435i	0.731511	+	0.681830i	$0.238815\pi$
$43$	3.99619	+	10.9794i	0.609413	+	1.67435i	−0.122098	+	0.992518i	$0.538962\pi$
$44$	0.854450	+	1.47995i	0.128813	+	0.223111i
$45$	−1.38390	+	6.56390i	−0.206299	+	0.978489i
$46$	−1.41894	+	2.45768i	−0.209211	+	0.362364i
$47$	−13.0603	−	2.30288i	−1.90504	−	0.335909i	−0.908416	−	0.418068i	$-0.862707\pi$
$47$	−13.0603	−	2.30288i	−1.90504	−	0.335909i	−0.996619	+	0.0821587i	$0.973819\pi$
$48$	1.22030	+	1.22917i	0.176136	+	0.177415i
$49$	16.1011	+	5.86031i	2.30015	+	0.837187i
$50$	−1.46341	−	4.78105i	−0.206957	−	0.676143i
$51$	4.96957	+	3.50661i	0.695879	+	0.491024i
$52$	−1.95350	+	2.32809i	−0.270902	+	0.322848i
$53$		−	13.5050i		−	1.85506i	−0.373754	−	0.927528i	$-0.621930\pi$
$53$		−	13.5050i		−	1.85506i	0.373754	−	0.927528i	$-0.378070\pi$
$54$	4.28856	−	2.93399i	0.583598	−	0.399265i
$55$	−2.53155	+	2.86233i	−0.341354	+	0.385957i
$56$	−3.76333	−	3.15781i	−0.502896	−	0.421980i
$57$	3.23169	+	0.294528i	0.428048	+	0.0390113i
$58$	3.16487	−	0.558051i	0.415567	−	0.0732757i
$59$	4.14855	+	1.50995i	0.540095	+	0.196579i	0.597640	−	0.801764i	$-0.296105\pi$
$59$	4.14855	+	1.50995i	0.540095	+	0.196579i	−0.0575451	+	0.998343i	$0.518327\pi$
$60$	−1.74009	+	3.46007i	−0.224645	+	0.446693i
$61$	1.58468	−	8.98717i	0.202897	−	1.15069i	−0.697817	−	0.716276i	$-0.745845\pi$
$61$	1.58468	−	8.98717i	0.202897	−	1.15069i	0.900714	−	0.434412i	$-0.143044\pi$
$62$	4.96074	+	2.86408i	0.630014	+	0.363739i
$63$	−11.3583	+	9.39143i	−1.43101	+	1.18321i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−6.32319	−	2.48959i	−0.784295	−	0.308796i
$66$	2.94955	−	0.247296i	0.363065	−	0.0304401i
$67$	4.47017	+	5.32734i	0.546119	+	0.650839i	0.966548	−	0.256487i	$-0.0825649\pi$
$67$	4.47017	+	5.32734i	0.546119	+	0.650839i	−0.420429	+	0.907325i	$0.638120\pi$
$68$	2.25718	+	2.69000i	0.273723	+	0.326211i
$69$	2.80473	+	4.03660i	0.337650	+	0.485949i
$70$	4.02439	−	10.2214i	0.481007	−	1.22169i
$71$	2.54561	+	4.40913i	0.302109	+	0.523268i	0.976613	−	0.215003i	$-0.0689761\pi$
$71$	2.54561	+	4.40913i	0.302109	+	0.523268i	−0.674505	+	0.738271i	$0.735643\pi$
$72$	2.82643	−	1.00562i	0.333098	−	0.118514i
$73$	−11.3098	−	6.52971i	−1.32371	−	0.764245i	−0.339392	−	0.940645i	$-0.610221\pi$
$73$	−11.3098	−	6.52971i	−1.32371	−	0.764245i	−0.984319	+	0.176400i	$0.943555\pi$
$74$	0.386387	−	2.19131i	0.0449165	−	0.254734i
$75$	−8.57195	−	1.23354i	−0.989804	−	0.142437i
$76$	1.76056	+	0.640791i	0.201950	+	0.0735038i
$77$	−8.26773	+	1.45782i	−0.942195	+	0.166134i
$78$	2.20733	+	4.77872i	0.249931	+	0.541084i
$79$	4.76174	+	3.99557i	0.535738	+	0.449537i	0.870077	−	0.492915i	$-0.164069\pi$
$79$	4.76174	+	3.99557i	0.535738	+	0.449537i	−0.334340	+	0.942453i	$0.608513\pi$
$80$	−1.48139	+	1.67496i	−0.165625	+	0.187266i
$81$	−1.43433	−	8.88497i	−0.159370	−	0.987219i
$82$			0.589863i			0.0651395i
$83$	2.47161	−	2.94555i	0.271294	−	0.323316i	−0.613146	−	0.789970i	$-0.710096\pi$
$83$	2.47161	−	2.94555i	0.271294	−	0.323316i	0.884440	+	0.466654i	$0.154541\pi$
$84$	−7.72475	+	3.56812i	−0.842839	+	0.389314i
$85$	−4.10161	+	6.69565i	−0.444882	+	0.726245i
$86$	10.9794	+	3.99619i	1.18394	+	0.430920i
$87$	1.46011	−	5.37136i	0.156540	−	0.575870i
$88$	1.68294	+	0.296747i	0.179402	+	0.0316334i
$89$	−0.280096	+	0.485141i	−0.0296902	+	0.0514249i	−0.880489	−	0.474067i	$-0.842785\pi$
$89$	−0.280096	+	0.485141i	−0.0296902	+	0.0514249i	0.850799	+	0.525492i	$0.176119\pi$
$90$	4.13869	+	5.27932i	0.436256	+	0.556489i
$91$	−7.46507	−	12.9299i	−0.782552	−	1.35542i
$92$	0.970612	+	2.66673i	0.101193	+	0.278026i
$93$	8.14775	−	5.66127i	0.844882	−	0.587046i
$94$	−10.1591	+	8.52448i	−1.04783	+	0.879233i
$95$	−0.108987	+	4.18796i	−0.0111819	+	0.429676i
$96$	1.72600	−	0.144711i	0.176159	−	0.0147695i
$97$	2.45704	+	6.75067i	0.249475	+	0.685427i	0.999706	+	0.0242509i	$0.00772006\pi$
$97$	2.45704	+	6.75067i	0.249475	+	0.685427i	−0.750231	+	0.661176i	$0.770058\pi$
$98$	14.8388	−	8.56719i	1.49895	−	0.865417i
$99$	1.78827	−	4.80470i	0.179728	−	0.482890i
$100$	−4.60316	−	1.95217i	−0.460316	−	0.195217i
$101$	0.729637	−	4.13798i	0.0726016	−	0.411744i	−0.926748	−	0.375683i	$-0.877408\pi$
$101$	0.729637	−	4.13798i	0.0726016	−	0.411744i	0.999350	−	0.0360605i	$-0.0114809\pi$
$102$	5.88060	−	1.55291i	0.582266	−	0.153761i
$103$	1.69327	−	4.65221i	0.166842	−	0.458396i	−0.827891	−	0.560888i	$-0.810460\pi$
$103$	1.69327	−	4.65221i	0.166842	−	0.458396i	0.994734	+	0.102493i	$0.0326819\pi$
$104$	0.527735	+	2.99293i	0.0517487	+	0.293481i
$105$	−13.0493	−	13.8467i	−1.27348	−	1.35130i
$106$	−10.3454	−	8.68085i	−1.00484	−	0.843159i
$107$			3.08680i			0.298412i	0.988806	+	0.149206i	$0.0476718\pi$
$107$			3.08680i			0.298412i	−0.988806	+	0.149206i	$0.952328\pi$
$108$	0.509064	−	5.17116i	0.0489847	−	0.497595i
$109$	−4.45599			−0.426806			−0.213403	−	0.976964i	$-0.568455\pi$
$109$	−4.45599			−0.426806			−0.213403	+	0.976964i	$0.568455\pi$
$110$	0.565423	+	3.77915i	0.0539110	+	0.360328i
$111$	−3.14899	−	2.22198i	−0.298889	−	0.210901i
$112$	−4.83804	+	0.853077i	−0.457152	+	0.0806082i
$113$	−6.38810	+	17.5512i	−0.600942	+	1.65107i	0.148429	+	0.988923i	$0.452578\pi$
$113$	−6.38810	+	17.5512i	−0.600942	+	1.65107i	−0.749371	+	0.662151i	$0.769644\pi$
$114$	2.30291	−	2.28630i	0.215687	−	0.214131i
$115$	−4.96555	+	3.95109i	−0.463040	+	0.368441i
$116$	1.60684	−	2.78314i	0.149192	−	0.258408i
$117$	9.11708	+	0.0660108i	0.842874	+	0.00610270i
$118$	3.82332	−	2.20740i	0.351966	−	0.203207i
$119$	−16.2107	+	5.90023i	−1.48604	+	0.540873i
$120$	1.53206	+	3.55708i	0.139857	+	0.324715i
$121$	−6.18938	+	5.19351i	−0.562671	+	0.472137i
$122$	−5.86596	−	6.99077i	−0.531079	−	0.632915i
$123$	0.924381	+	0.435127i	0.0833486	+	0.0392341i
$124$	5.38272	−	1.95915i	0.483382	−	0.175937i
$125$	0.871786	−	11.1463i	0.0779750	−	0.996955i
$126$	−0.106706	+	14.7376i	−0.00950609	+	1.31293i
$127$	0.847884	+	0.489526i	0.0752375	+	0.0434384i	0.537147	−	0.843489i	$-0.319502\pi$
$127$	0.847884	+	0.489526i	0.0752375	+	0.0434384i	−0.461909	+	0.886927i	$0.652835\pi$
$128$	0.984808	+	0.173648i	0.0870455	+	0.0153485i
$129$	14.3617	−	14.2581i	1.26448	−	1.25536i
$130$	−5.97161	+	3.24357i	−0.523744	+	0.284480i
$131$	1.04705	+	5.93813i	0.0914814	+	0.518817i	0.995769	+	0.0918929i	$0.0292917\pi$
$131$	1.04705	+	5.93813i	0.0914814	+	0.518817i	−0.904287	+	0.426924i	$0.859597\pi$
$132$	1.70650	−	2.41845i	0.148531	−	0.210499i
$133$	−5.91631	+	7.05078i	−0.513009	+	0.611380i
$134$	6.95435			0.600765
$135$	11.3263	−	2.59137i	0.974812	−	0.223029i
$136$	3.51155			0.301113
$137$	7.40984	−	8.83070i	0.633065	−	0.754457i	−0.350193	−	0.936678i	$-0.613884\pi$
$137$	7.40984	−	8.83070i	0.633065	−	0.754457i	0.983258	+	0.182220i	$0.0583284\pi$
$138$	4.89506	+	0.446125i	0.416695	+	0.0379766i
$139$	−2.65204	−	15.0405i	−0.224943	−	1.27572i	−0.862793	−	0.505557i	$-0.831287\pi$
$139$	−2.65204	−	15.0405i	−0.224943	−	1.27572i	0.637850	−	0.770161i	$-0.279824\pi$
$140$	−5.24319	−	9.65303i	−0.443130	−	0.815830i
$141$	5.86472	+	22.2087i	0.493898	+	1.87031i
$142$	5.01388	+	0.884083i	0.420756	+	0.0741906i
$143$	4.49773	+	2.59676i	0.376119	+	0.217152i
$144$	1.04644	−	2.81158i	0.0872037	−	0.234298i
$145$	7.04200	+	1.43152i	0.584806	+	0.118882i
$146$	−12.2718	+	4.46659i	−1.01562	+	0.369657i
$147$	−2.47953	−	29.5739i	−0.204508	−	2.43921i
$148$	−1.43027	−	1.70453i	−0.117568	−	0.140112i
$149$	−2.56351	+	2.15104i	−0.210011	+	0.176220i	−0.741726	−	0.670703i	$-0.765992\pi$
$149$	−2.56351	+	2.15104i	−0.210011	+	0.176220i	0.531715	+	0.846924i	$0.321548\pi$
$150$	−6.45489	+	5.77359i	−0.527040	+	0.471412i
$151$	−9.83987	+	3.58142i	−0.800758	+	0.291452i	−0.709800	−	0.704403i	$-0.751215\pi$
$151$	−9.83987	+	3.58142i	−0.800758	+	0.291452i	−0.0909572	+	0.995855i	$0.528993\pi$
$152$	1.62254	−	0.936774i	0.131605	−	0.0759824i
$153$	1.90439	−	10.3611i	0.153961	−	0.837645i
$154$	−4.19764	+	7.27052i	−0.338255	+	0.585875i
$155$	7.97515	+	10.0228i	0.640579	+	0.805051i
$156$	5.07956	+	1.38079i	0.406690	+	0.110552i
$157$	−3.56492	+	9.79453i	−0.284511	+	0.781689i	0.712299	+	0.701877i	$0.247654\pi$
$157$	−3.56492	+	9.79453i	−0.284511	+	0.781689i	−0.996810	+	0.0798120i	$0.974568\pi$
$158$	6.12157	−	1.07940i	0.487006	−	0.0858724i
$159$	−21.2354	+	9.80881i	−1.68408	+	0.777889i
$160$	0.330870	+	2.21145i	0.0261576	+	0.174831i
$161$	−13.9416			−1.09875
$162$	−7.72825	−	4.61239i	−0.607189	−	0.362383i
$163$		−	15.3937i		−	1.20573i	−0.797843	−	0.602865i	$-0.794026\pi$
$163$		−	15.3937i		−	1.20573i	0.797843	−	0.602865i	$-0.205974\pi$
$164$	0.451861	+	0.379157i	0.0352844	+	0.0296072i
$165$	6.33945	+	1.90170i	0.493525	+	0.148047i
$166$	−0.667701	−	3.78672i	−0.0518237	−	0.293907i
$167$	−0.297584	+	0.817606i	−0.0230278	+	0.0632683i	−0.950674	−	0.310192i	$-0.899607\pi$
$167$	−0.297584	+	0.817606i	−0.0230278	+	0.0632683i	0.927646	+	0.373460i	$0.121829\pi$
$168$	−2.23203	+	8.21104i	−0.172205	+	0.633496i
$169$	0.653583	−	3.70666i	0.0502756	−	0.285127i
$170$	2.49270	+	7.44590i	0.191182	+	0.571074i
$171$	−1.88408	−	5.29546i	−0.144079	−	0.404954i
$172$	10.1187	−	5.84203i	0.771544	−	0.445451i
$173$	0.0394998	+	0.108525i	0.00300311	+	0.00825098i	0.941185	−	0.337891i	$-0.109714\pi$
$173$	0.0394998	+	0.108525i	0.00300311	+	0.00825098i	−0.938182	+	0.346142i	$0.887491\pi$
$174$	−3.17616	−	4.57115i	−0.240784	−	0.346538i
$175$	16.7464	−	17.9699i	1.26591	−	1.35840i
$176$	1.30909	−	1.09846i	0.0986766	−	0.0827995i
$177$	−0.638869	−	7.61991i	−0.0480203	−	0.572748i
$178$	0.191597	+	0.526409i	0.0143608	+	0.0394560i
$179$	−10.8594	−	18.8090i	−0.811670	−	1.40585i	−0.911695	−	0.410869i	$-0.865225\pi$
$179$	−10.8594	−	18.8090i	−0.811670	−	1.40585i	0.100025	−	0.994985i	$-0.468108\pi$
$180$	6.70449	+	0.223062i	0.499723	+	0.0166261i
$181$	5.19877	−	9.00453i	0.386421	−	0.669302i	−0.605544	−	0.795812i	$-0.707044\pi$
$181$	5.19877	−	9.00453i	0.386421	−	0.669302i	0.991965	+	0.126510i	$0.0403777\pi$
$182$	−14.7033	−	2.59259i	−1.08988	−	0.192176i
$183$	−15.2825	+	4.03569i	−1.12971	+	0.298327i
$184$	2.66673	+	0.970612i	0.196594	+	0.0715544i
$185$	2.59901	−	4.24273i	0.191083	−	0.311932i
$186$	0.900488	−	9.88053i	0.0660270	−	0.724475i
$187$	3.85730	−	4.59695i	0.282073	−	0.336162i
$188$			13.2617i			0.967212i
$189$	23.0168	+	11.0388i	1.67423	+	0.802954i
$190$	3.13811	+	2.77546i	0.227663	+	0.201353i
$191$	14.9579	+	12.5511i	1.08231	+	0.908169i	0.996111	−	0.0881084i	$-0.0280822\pi$
$191$	14.9579	+	12.5511i	1.08231	+	0.908169i	0.0862030	+	0.996278i	$0.472527\pi$
$192$	0.998593	−	1.41521i	0.0720673	−	0.102134i
$193$	−22.3812	+	3.94641i	−1.61104	+	0.284069i	−0.905417	−	0.424522i	$-0.860442\pi$
$193$	−22.3812	+	3.94641i	−1.61104	+	0.284069i	−0.705619	+	0.708592i	$0.749331\pi$
$194$	6.75067	+	2.45704i	0.484670	+	0.176405i
$195$	0.677933	+	11.7509i	0.0485478	+	0.841497i
$196$	2.97536	−	16.8741i	0.212525	−	1.20529i
$197$	−12.4965	−	7.21489i	−0.890342	−	0.514039i	−0.0162878	−	0.999867i	$-0.505185\pi$
$197$	−12.4965	−	7.21489i	−0.890342	−	0.514039i	−0.874054	+	0.485828i	$0.838518\pi$
$198$	−2.53114	−	4.45829i	−0.179880	−	0.316837i
$199$	−12.0598	−	20.8881i	−0.854893	−	1.48072i	−0.876744	−	0.480957i	$-0.840289\pi$
$199$	−12.0598	−	20.8881i	−0.854893	−	1.48072i	0.0218506	−	0.999761i	$-0.493044\pi$
$200$	−4.45430	+	2.27139i	−0.314966	+	0.160612i
$201$	5.13005	−	10.8982i	0.361846	−	0.768703i
$202$	−2.70087	−	3.21877i	−0.190033	−	0.226472i
$203$	10.1482	+	12.0942i	0.712265	+	0.848844i
$204$	2.59038	−	5.50299i	0.181363	−	0.385286i
$205$	−0.483207	+	1.22727i	−0.0337486	+	0.0857166i
$206$	−2.47539	−	4.28750i	−0.172468	−	0.298724i
$207$	4.31009	−	7.34201i	0.299572	−	0.510305i
$208$	2.63194	+	1.51955i	0.182492	+	0.105362i
$209$	0.555971	−	3.15307i	0.0384573	−	0.218102i
$210$	−18.9951	+	1.09587i	−1.31079	+	0.0756222i
$211$	−11.3421	−	4.12820i	−0.780825	−	0.284197i	−0.0793082	−	0.996850i	$-0.525271\pi$
$211$	−11.3421	−	4.12820i	−0.780825	−	0.284197i	−0.701517	+	0.712653i	$0.747493\pi$
$212$	−13.2998	+	2.34512i	−0.913437	+	0.161064i
$213$	5.08407	−	7.20514i	0.348355	−	0.493688i
$214$	2.36463	+	1.98416i	0.161642	+	0.135634i
$215$	19.5703	+	17.3087i	1.33468	+	1.18044i
$216$	−3.63412	−	3.71392i	−0.247270	−	0.252700i
$217$			28.1406i			1.91031i
$218$	−2.86425	+	3.41348i	−0.193992	+	0.231190i
$219$	−2.05299	+	22.5262i	−0.138728	+	1.52218i
$220$	3.25844	+	1.99605i	0.219684	+	0.134574i
$221$	10.0284	+	3.65003i	0.674582	+	0.245528i
$222$	−3.72627	+	0.984008i	−0.250091	+	0.0660423i
$223$	13.3431	+	2.35275i	0.893522	+	0.157552i	0.601513	−	0.798863i	$-0.294565\pi$
$223$	13.3431	+	2.35275i	0.893522	+	0.157552i	0.292010	+	0.956415i	$0.405676\pi$
$224$	−2.45634	+	4.25450i	−0.164121	+	0.284266i
$225$	4.28626	+	14.3746i	0.285751	+	0.958304i
$226$	9.33877	+	16.1752i	0.621206	+	1.07596i
$227$	4.07566	+	11.1978i	0.270511	+	0.743222i	0.998347	+	0.0574715i	$0.0183038\pi$
$227$	4.07566	+	11.1978i	0.270511	+	0.743222i	−0.727836	+	0.685751i	$0.759474\pi$
$228$	−0.271123	−	3.23374i	−0.0179555	−	0.214159i
$229$	5.29005	−	4.43888i	0.349576	−	0.293329i	−0.451044	−	0.892502i	$-0.648948\pi$
$229$	5.29005	−	4.43888i	0.349576	−	0.293329i	0.800620	+	0.599173i	$0.204504\pi$
$230$	−0.165084	+	6.34354i	−0.0108853	+	0.418281i
$231$	8.29722	+	11.9414i	0.545917	+	0.785689i
$232$	−1.09915	−	3.01988i	−0.0721625	−	0.198265i
$233$	−7.25634	+	4.18945i	−0.475379	+	0.274460i	−0.718489	−	0.695539i	$-0.755166\pi$
$233$	−7.25634	+	4.18945i	−0.475379	+	0.274460i	0.243110	+	0.969999i	$0.421832\pi$
$234$	5.91091	−	6.94166i	0.386408	−	0.453790i
$235$	−28.1202	+	9.41395i	−1.83436	+	0.614098i
$236$	0.766621	−	4.34772i	0.0499028	−	0.283013i
$237$	2.82419	−	10.3894i	0.183451	−	0.674866i
$238$	−5.90023	+	16.2107i	−0.382455	+	1.05079i
$239$	1.69855	+	9.63295i	0.109870	+	0.623104i	0.989163	+	0.146822i	$0.0469045\pi$
$239$	1.69855	+	9.63295i	0.109870	+	0.623104i	−0.879293	+	0.476281i	$0.841984\pi$
$240$	3.70967	+	1.11282i	0.239458	+	0.0718324i
$241$	1.98516	+	1.66575i	0.127875	+	0.107300i	0.704482	−	0.709721i	$-0.251179\pi$
$241$	1.98516	+	1.66575i	0.127875	+	0.107300i	−0.576607	+	0.817022i	$0.695624\pi$
$242$			8.07966i			0.519380i
$243$	−12.9291	+	8.70859i	−0.829399	+	0.558656i
$244$	−9.12581			−0.584220
$245$	37.8919	−	5.66925i	2.42082	−	0.362195i
$246$	0.927507	−	0.428423i	0.0591357	−	0.0273152i
$247$	5.60741	−	0.988738i	0.356791	−	0.0629119i
$248$	1.95915	−	5.38272i	0.124406	−	0.341803i
$249$	−6.42676	−	1.74701i	−0.407279	−	0.110712i
$250$	−7.97819	−	7.83253i	−0.504585	−	0.495373i
$251$	−8.85227	+	15.3326i	−0.558750	+	0.967784i	0.438851	+	0.898560i	$0.355386\pi$
$251$	−8.85227	+	15.3326i	−0.558750	+	0.967784i	−0.997601	+	0.0692241i	$0.977948\pi$
$252$	11.2211	+	9.55492i	0.706863	+	0.601903i
$253$	4.19992	−	2.42482i	0.264047	−	0.152447i
$254$	0.920008	−	0.334855i	0.0577264	−	0.0210107i
$255$	13.5074	+	1.58631i	0.845863	+	0.0993383i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	9.62165	+	11.4666i	0.600182	+	0.715269i	0.977529	−	0.210803i	$-0.0676079\pi$
$257$	9.62165	+	11.4666i	0.600182	+	0.715269i	−0.377347	+	0.926072i	$0.623163\pi$
$258$	−1.69081	−	20.1666i	−0.105265	−	1.25552i
$259$	10.2720	−	3.73871i	0.638272	−	0.232312i
$260$	−1.35376	+	6.65944i	−0.0839564	+	0.413001i
$261$	−9.50647	+	1.60537i	−0.588436	+	0.0993698i
$262$	5.22191	+	3.01487i	0.322610	+	0.186259i
$263$	−23.6900	−	4.17719i	−1.46079	−	0.257577i	−0.613917	−	0.789371i	$-0.710407\pi$
$263$	−23.6900	−	4.17719i	−1.46079	−	0.257577i	−0.846874	+	0.531794i	$0.821518\pi$
$264$	−0.755724	−	2.86180i	−0.0465116	−	0.176132i
$265$	−14.4136	−	26.5363i	−0.885420	−	1.63011i
$266$	1.59828	+	9.06431i	0.0979970	+	0.555768i
$267$	0.966278	+	0.0880643i	0.0591352	+	0.00538945i
$268$	4.47017	−	5.32734i	0.273059	−	0.325419i
$269$	5.14018			0.313402			0.156701	−	0.987646i	$-0.449914\pi$
$269$	5.14018			0.313402			0.156701	+	0.987646i	$0.449914\pi$
$270$	5.29530	−	10.3421i	0.322261	−	0.629403i
$271$	17.7186			1.07633			0.538165	−	0.842839i	$-0.319118\pi$
$271$	17.7186			1.07633			0.538165	+	0.842839i	$0.319118\pi$
$272$	2.25718	−	2.69000i	0.136862	−	0.163105i
$273$	−14.9091	+	21.1292i	−0.902342	+	1.27880i
$274$	−2.00176	−	11.3525i	−0.120931	−	0.685831i
$275$	−1.91940	+	8.32612i	−0.115744	+	0.502084i
$276$	3.48824	−	3.46307i	0.209967	−	0.208452i
$277$	10.5207	+	1.85508i	0.632127	+	0.111461i	0.480526	−	0.876981i	$-0.340446\pi$
$277$	10.5207	+	1.85508i	0.632127	+	0.111461i	0.151602	+	0.988442i	$0.451557\pi$
$278$	−13.2264	−	7.63626i	−0.793266	−	0.457992i
$279$	−14.8196	−	8.69978i	−0.887227	−	0.520842i
$280$	−10.7649	−	2.18833i	−0.643326	−	0.130778i
$281$	0.897496	−	0.326662i	0.0535401	−	0.0194870i	−0.315111	−	0.949055i	$-0.602042\pi$
$281$	0.897496	−	0.326662i	0.0535401	−	0.0194870i	0.368651	+	0.929568i	$0.379820\pi$
$282$	20.7826	+	9.78284i	1.23759	+	0.582560i
$283$	−11.6666	−	13.9037i	−0.693505	−	0.826487i	0.298270	−	0.954481i	$-0.403590\pi$
$283$	−11.6666	−	13.9037i	−0.693505	−	0.826487i	−0.991775	+	0.127995i	$0.959146\pi$
$284$	3.90011	−	3.27258i	0.231429	−	0.194192i
$285$	6.66436	−	2.87038i	0.394763	−	0.170027i
$286$	4.88032	−	1.77629i	0.288579	−	0.105034i
$287$	−2.50957	+	1.44890i	−0.148135	+	0.0855260i
$288$	−1.48115	−	2.60887i	−0.0872776	−	0.153729i
$289$	−2.33450	+	4.04348i	−0.137324	+	0.237852i
$290$	5.62312	−	4.47432i	0.330201	−	0.262741i
$291$	8.83026	−	8.76655i	0.517639	−	0.513904i
$292$	−4.46659	+	12.2718i	−0.261387	+	0.718155i
$293$	29.1511	−	5.14012i	1.70302	−	0.300289i	0.764274	−	0.644891i	$-0.223097\pi$
$293$	29.1511	−	5.14012i	1.70302	−	0.300289i	0.938749	+	0.344602i	$0.111986\pi$
$294$	−24.2487	−	17.1103i	−1.41421	−	0.997892i
$295$	9.76311	−	1.46072i	0.568430	−	0.0850466i
$296$	−2.22511			−0.129332
$297$	−8.85380	+	0.677804i	−0.513749	+	0.0393302i
$298$			3.34643i			0.193853i
$299$	6.60684	+	5.54379i	0.382083	+	0.320606i
$300$	0.273707	+	8.65593i	0.0158025	+	0.499750i
$301$	9.96741	+	56.5280i	0.574512	+	3.25822i
$302$	−3.58142	+	9.83987i	−0.206088	+	0.566221i
$303$	−7.03654	+	1.85816i	−0.404239	+	0.106748i
$304$	0.325338	−	1.84509i	0.0186594	−	0.105823i
$305$	−6.47803	−	19.3504i	−0.370931	−	1.10800i
$306$	−6.71294	−	8.11883i	−0.383753	−	0.464123i
$307$	−13.1006	+	7.56363i	−0.747690	+	0.431679i	−0.824859	−	0.565339i	$-0.808745\pi$
$307$	−13.1006	+	7.56363i	−0.747690	+	0.431679i	0.0771685	+	0.997018i	$0.475412\pi$
$308$	2.87135	+	7.88897i	0.163610	+	0.449516i
$309$	−8.54502	+	0.716431i	−0.486109	+	0.0407563i
$310$	12.8042	+	0.333217i	0.727232	+	0.0189254i
$311$	0.414050	−	0.347430i	0.0234786	−	0.0197009i	−0.630973	−	0.775805i	$-0.717344\pi$
$311$	0.414050	−	0.347430i	0.0234786	−	0.0197009i	0.654451	+	0.756104i	$0.272900\pi$
$312$	4.32282	−	3.00361i	0.244732	−	0.170046i
$313$	−5.42339	−	14.9006i	−0.306548	−	0.842234i	−0.993323	−	0.115364i	$-0.963196\pi$
$313$	−5.42339	−	14.9006i	−0.306548	−	0.842234i	0.686775	−	0.726870i	$-0.259026\pi$
$314$	5.21156	+	9.02669i	0.294105	+	0.509405i
$315$	−12.2949	+	30.5759i	−0.692737	+	1.72276i
$316$	3.10800	−	5.38322i	0.174839	−	0.302830i
$317$	−4.51242	−	0.795661i	−0.253443	−	0.0446888i	0.0454833	−	0.998965i	$-0.485517\pi$
$317$	−4.51242	−	0.795661i	−0.253443	−	0.0446888i	−0.298926	+	0.954276i	$0.596628\pi$
$318$	−6.13588	+	22.5723i	−0.344083	+	1.26579i
$319$	−5.16067	−	1.87833i	−0.288942	−	0.105166i
$320$	1.90675	+	1.16803i	0.106591	+	0.0652951i
$321$	4.85372	−	2.24197i	0.270908	−	0.125135i
$322$	−8.96147	+	10.6799i	−0.499403	+	0.595166i
$323$		−	6.57906i		−	0.366069i
$324$	−8.50092	+	2.95540i	−0.472273	+	0.164189i
$325$	−15.0817	+	1.85675i	−0.836580	+	0.102994i
$326$	−11.7923	−	9.89491i	−0.653115	−	0.548028i
$327$	3.23642	+	7.00664i	0.178975	+	0.387468i
$328$	0.580902	−	0.102429i	0.0320749	−	0.00565568i
$329$	−61.2216	−	22.2828i	−3.37525	−	1.22849i
$330$	5.53171	−	3.63391i	0.304510	−	0.200040i
$331$	−2.29684	+	13.0260i	−0.126246	+	0.715975i	0.854314	+	0.519757i	$0.173977\pi$
$331$	−2.29684	+	13.0260i	−0.126246	+	0.715975i	−0.980560	+	0.196219i	$0.937134\pi$
$332$	−3.32999	−	1.92257i	−0.182757	−	0.105515i
$333$	−1.20673	+	6.56536i	−0.0661282	+	0.359779i
$334$	0.435039	+	0.753510i	0.0238043	+	0.0412302i
$335$	14.4693	+	5.69690i	0.790542	+	0.311255i
$336$	4.85530	+	6.98779i	0.264878	+	0.381215i
$337$	16.8834	+	20.1208i	0.919697	+	1.09605i	0.995097	+	0.0988991i	$0.0315321\pi$
$337$	16.8834	+	20.1208i	0.919697	+	1.09605i	−0.0754002	+	0.997153i	$0.524023\pi$
$338$	−2.41935	−	2.88327i	−0.131595	−	0.156829i
$339$	32.2374	−	2.70284i	1.75089	−	0.146798i
$340$	7.30617	+	2.87661i	0.396233	+	0.156006i
$341$	−4.89443	−	8.47740i	−0.265048	−	0.459077i
$342$	−5.26762	−	1.96056i	−0.284840	−	0.106015i
$343$	43.1168	+	24.8935i	2.32809	+	1.34412i
$344$	2.02892	−	11.5066i	0.109392	−	0.620392i
$345$	9.81926	+	4.93817i	0.528651	+	0.265862i
$346$	0.108525	+	0.0394998i	0.00583433	+	0.00212352i
$347$	1.33782	−	0.235894i	0.0718181	−	0.0126635i	−0.137624	−	0.990485i	$-0.543946\pi$
$347$	1.33782	−	0.235894i	0.0718181	−	0.0126635i	0.209442	+	0.977821i	$0.432835\pi$
$348$	−5.54330	−	0.505203i	−0.297152	−	0.0270817i
$349$	−9.86690	−	8.27931i	−0.528163	−	0.443181i	0.339304	−	0.940677i	$-0.389809\pi$
$349$	−9.86690	−	8.27931i	−0.528163	−	0.443181i	−0.867466	+	0.497496i	$0.834253\pi$
$350$	−3.00142	−	24.3793i	−0.160432	−	1.30313i
$351$	−6.51802	−	14.3837i	−0.347906	−	0.767747i
$352$		−	1.70890i		−	0.0910847i
$353$	7.21529	−	8.59885i	0.384031	−	0.457670i	−0.539051	−	0.842273i	$-0.681217\pi$
$353$	7.21529	−	8.59885i	0.384031	−	0.457670i	0.923082	+	0.384603i	$0.125662\pi$
$354$	−6.24785	−	4.40858i	−0.332069	−	0.234314i
$355$	9.70770	+	5.94673i	0.515231	+	0.315619i
$356$	0.526409	+	0.191597i	0.0278996	+	0.0101546i
$357$	21.0516	+	21.2046i	1.11417	+	1.12226i
$358$	−21.3889	−	3.77143i	−1.13044	−	0.199326i
$359$	10.6848	−	18.5066i	0.563922	−	0.976742i	−0.433227	−	0.901285i	$-0.642625\pi$
$359$	10.6848	−	18.5066i	0.563922	−	0.976742i	0.997149	−	0.0754570i	$-0.0240416\pi$
$360$	4.48044	−	4.99256i	0.236140	−	0.263131i
$361$	7.74491	+	13.4146i	0.407627	+	0.706030i
$362$	−3.55617	−	9.77049i	−0.186908	−	0.513526i
$363$	12.6617	+	5.96016i	0.664568	+	0.312827i
$364$	−11.4372	+	9.59691i	−0.599470	+	0.503015i
$365$	−29.1919	−	0.759687i	−1.52797	−	0.0397639i
$366$	−6.73187	+	14.3012i	−0.351881	+	0.747533i
$367$	−7.52447	−	20.6733i	−0.392774	−	1.07914i	−0.965729	−	0.259551i	$-0.916425\pi$
$367$	−7.52447	−	20.6733i	−0.392774	−	1.07914i	0.572955	−	0.819587i	$-0.305797\pi$
$368$	2.45768	−	1.41894i	0.128115	−	0.0739673i
$369$	0.0128121	−	1.76954i	0.000666971	−	0.0921187i
$370$	−1.57951	−	4.71813i	−0.0821150	−	0.245284i
$371$	11.5208	−	65.3378i	0.598131	−	3.39217i
$372$	−6.99010	−	7.04090i	−0.362420	−	0.365053i
$373$	2.74156	−	7.53236i	0.141952	−	0.390011i	−0.848260	−	0.529580i	$-0.822350\pi$
$373$	2.74156	−	7.53236i	0.141952	−	0.390011i	0.990212	+	0.139569i	$0.0445717\pi$
$374$	−1.04204	−	5.90972i	−0.0538828	−	0.305584i
$375$	−18.1597	+	6.72485i	−0.937765	+	0.347270i
$376$	10.1591	+	8.52448i	0.523915	+	0.439617i
$377$		−	9.76674i		−	0.503013i
$378$	23.2511	−	10.5363i	1.19591	−	0.541929i
$379$	2.91784			0.149879			0.0749397	−	0.997188i	$-0.476124\pi$
$379$	2.91784			0.149879			0.0749397	+	0.997188i	$0.476124\pi$
$380$	4.14327	−	0.619901i	0.212545	−	0.0318002i
$381$	0.153910	−	1.68877i	0.00788507	−	0.0865182i
$382$	19.2295	−	3.39068i	0.983865	−	0.173482i
$383$	10.9754	−	30.1547i	0.560818	−	1.54083i	−0.257624	−	0.966245i	$-0.582940\pi$
$383$	10.9754	−	30.1547i	0.560818	−	1.54083i	0.818442	−	0.574589i	$-0.194838\pi$
$384$	−0.442228	−	1.67464i	−0.0225674	−	0.0854588i
$385$	−14.6895	+	11.6885i	−0.748648	+	0.595700i
$386$	−11.3632	+	19.6817i	−0.578374	+	1.00177i
$387$	−32.8506	−	12.2267i	−1.66989	−	0.621519i
$388$	6.22145	−	3.59196i	0.315846	−	0.182354i
$389$	−4.14632	+	1.50914i	−0.210227	+	0.0765163i	−0.444987	−	0.895537i	$-0.646792\pi$
$389$	−4.14632	+	1.50914i	−0.210227	+	0.0765163i	0.234760	+	0.972053i	$0.424570\pi$
$390$	9.43745	+	7.03398i	0.477884	+	0.356180i
$391$	7.63391	−	6.40561i	0.386063	−	0.323946i
$392$	−11.0138	−	13.1257i	−0.556280	−	0.662948i
$393$	8.57670	−	5.95931i	0.432637	−	0.300608i
$394$	−13.5595	+	4.93527i	−0.683120	+	0.248635i
$395$	13.6208	+	2.76889i	0.685339	+	0.139318i
$396$	−5.04223	−	0.926773i	−0.253382	−	0.0465721i
$397$	−24.4475	−	14.1148i	−1.22699	−	0.708401i	−0.260588	−	0.965450i	$-0.583916\pi$
$397$	−24.4475	−	14.1148i	−1.22699	−	0.708401i	−0.966398	+	0.257049i	$0.917250\pi$
$398$	−23.7531	−	4.18831i	−1.19063	−	0.209941i
$399$	15.3838	+	4.18182i	0.770153	+	0.209353i
$400$	−1.12318	+	4.87221i	−0.0561589	+	0.243611i
$401$	−1.89585	−	10.7519i	−0.0946741	−	0.536924i	−0.994847	−	0.101390i	$-0.967671\pi$
$401$	−1.89585	−	10.7519i	−0.0946741	−	0.536924i	0.900173	−	0.435533i	$-0.143440\pi$
$402$	−5.05101	−	10.9351i	−0.251921	−	0.545393i
$403$	11.1900	−	13.3357i	0.557412	−	0.664298i
$404$	−4.20181			−0.209048
$405$	−12.3011	−	15.9274i	−0.611245	−	0.791441i
$406$	15.7878			0.783536
$407$	−2.44420	+	2.91288i	−0.121154	+	0.144386i
$408$	−2.55047	−	5.52160i	−0.126267	−	0.273360i
$409$	−5.66086	−	32.1043i	−0.279911	−	1.58746i	−0.722916	−	0.690936i	$-0.757199\pi$
$409$	−5.66086	−	32.1043i	−0.279911	−	1.58746i	0.443004	−	0.896519i	$-0.353913\pi$
$410$	0.629548	+	1.15903i	0.0310911	+	0.0572407i
$411$	−19.2673	−	5.23749i	−0.950386	−	0.258346i
$412$	−4.87556	−	0.859693i	−0.240202	−	0.0423541i
$413$	18.7828	+	10.8442i	0.924239	+	0.533610i
$414$	−2.85384	−	8.02107i	−0.140258	−	0.394214i
$415$	1.71280	−	8.42566i	0.0840780	−	0.413599i
$416$	2.85583	−	1.03944i	0.140018	−	0.0509625i
$417$	−21.7236	+	15.0941i	−1.06381	+	0.739163i
$418$	−2.05802	−	2.45265i	−0.100661	−	0.119963i
$419$	16.4911	−	13.8377i	0.805643	−	0.676015i	−0.143921	−	0.989589i	$-0.545971\pi$
$419$	16.4911	−	13.8377i	0.805643	−	0.676015i	0.949564	+	0.313575i	$0.101527\pi$
$420$	−11.3703	+	15.2555i	−0.554816	+	0.744393i
$421$	−1.68708	+	0.614047i	−0.0822232	+	0.0299268i	−0.382804	−	0.923829i	$-0.625042\pi$
$421$	−1.68708	+	0.614047i	−0.0822232	+	0.0299268i	0.300581	+	0.953756i	$0.402819\pi$
$422$	−10.4530	+	6.03502i	−0.508843	+	0.293780i
$423$	30.6616	−	25.3521i	1.49082	−	1.23266i
$424$	−6.75250	+	11.6957i	−0.327931	+	0.567992i
$425$	−0.913225	+	17.5340i	−0.0442979	+	0.850523i
$426$	−2.25149	−	8.52600i	−0.109085	−	0.413086i
$427$	15.3335	−	42.1284i	0.742040	−	2.03874i
$428$	3.03990	−	0.536017i	0.146939	−	0.0259094i
$429$	0.816441	−	8.95832i	0.0394181	−	0.432512i
$430$	25.8388	−	3.86591i	1.24606	−	0.186431i
$431$	1.18671			0.0571618			0.0285809	−	0.999591i	$-0.490901\pi$
$431$	1.18671			0.0571618			0.0285809	+	0.999591i	$0.490901\pi$
$432$	−5.18099	+	0.396632i	−0.249271	+	0.0190830i
$433$		−	21.3493i		−	1.02598i	−0.858394	−	0.512991i	$-0.828537\pi$
$433$		−	21.3493i		−	1.02598i	0.858394	−	0.512991i	$-0.171463\pi$
$434$	21.5570	+	18.0885i	1.03477	+	0.868273i
$435$	−2.86372	−	12.1126i	−0.137305	−	0.580757i
$436$	0.773774	+	4.38829i	0.0370570	+	0.210161i
$437$	1.81849	−	4.99626i	0.0869901	−	0.239003i
$438$	15.9365	+	16.0523i	0.761473	+	0.767006i
$439$	−4.37887	+	24.8338i	−0.208992	+	1.18525i	0.682040	+	0.731315i	$0.261093\pi$
$439$	−4.37887	+	24.8338i	−0.208992	+	1.18525i	−0.891033	+	0.453939i	$0.850018\pi$
$440$	3.62355	−	1.21308i	0.172746	−	0.0578311i
$441$	−44.7014	+	25.3786i	−2.12864	+	1.20850i
$442$	9.24220	−	5.33599i	0.439607	−	0.253807i
$443$	8.16012	+	22.4197i	0.387699	+	1.06519i	0.968035	+	0.250817i	$0.0806992\pi$
$443$	8.16012	+	22.4197i	0.387699	+	1.06519i	−0.580336	+	0.814377i	$0.697079\pi$
$444$	−1.64141	+	3.48700i	−0.0778978	+	0.165486i
$445$	−0.0325873	+	1.25221i	−0.00154479	+	0.0593602i
$446$	10.3791	−	8.70911i	0.491465	−	0.412388i
$447$	5.24422	+	2.46857i	0.248043	+	0.116759i
$448$	1.68023	+	4.61641i	0.0793836	+	0.218105i
$449$	8.93169	+	15.4701i	0.421512	+	0.730081i	0.996088	−	0.0883708i	$-0.0281660\pi$
$449$	8.93169	+	15.4701i	0.421512	+	0.730081i	−0.574575	+	0.818452i	$0.694833\pi$
$450$	13.7667	+	5.95633i	0.648969	+	0.280784i
$451$	0.504008	−	0.872968i	0.0237328	−	0.0411065i
$452$	18.3938	+	3.24332i	0.865171	+	0.152553i
$453$	12.7783	+	12.8711i	0.600375	+	0.604737i
$454$	11.1978	+	4.07566i	0.525538	+	0.191280i
$455$	−28.4681	−	17.4389i	−1.33460	−	0.817549i
$456$	−2.65146	−	1.87091i	−0.124166	−	0.0876135i
$457$	−14.5997	+	17.3992i	−0.682945	+	0.813902i	−0.990483	−	0.137634i	$-0.956050\pi$
$457$	−14.5997	+	17.3992i	−0.682945	+	0.813902i	0.307538	+	0.951536i	$0.400495\pi$
$458$		−	6.90566i		−	0.322681i
$459$	−17.6751	+	4.53087i	−0.825002	+	0.211483i
$460$	4.75332	+	4.20401i	0.221625	+	0.196013i
$461$	−3.07499	−	2.58023i	−0.143217	−	0.120173i	0.568365	−	0.822777i	$-0.307576\pi$
$461$	−3.07499	−	2.58023i	−0.143217	−	0.120173i	−0.711581	+	0.702604i	$0.752021\pi$
$462$	14.4810	+	1.31977i	0.673718	+	0.0614011i
$463$	−19.9050	+	3.50978i	−0.925062	+	0.163113i	−0.615835	−	0.787875i	$-0.711181\pi$
$463$	−19.9050	+	3.50978i	−0.925062	+	0.163113i	−0.309227	+	0.950988i	$0.600070\pi$
$464$	−3.01988	−	1.09915i	−0.140194	−	0.0510266i
$465$	9.96754	−	19.8199i	0.462234	−	0.919124i
$466$	−1.45498	+	8.25161i	−0.0674007	+	0.382248i
$467$	−20.3636	−	11.7570i	−0.942317	−	0.544047i	−0.0516312	−	0.998666i	$-0.516442\pi$
$467$	−20.3636	−	11.7570i	−0.942317	−	0.544047i	−0.890686	+	0.454619i	$0.849775\pi$
$468$	−1.51816	−	8.99003i	−0.0701768	−	0.415564i
$469$	17.0822	+	29.5873i	0.788785	+	1.36622i
$470$	−10.8638	+	27.5925i	−0.501110	+	1.27275i
$471$	17.9903	−	1.50834i	0.828947	−	0.0695006i
$472$	−2.83778	−	3.38193i	−0.130619	−	0.155666i
$473$	−12.8345	−	15.2955i	−0.590130	−	0.703289i
$474$	−6.14341	−	8.84165i	−0.282176	−	0.406111i
$475$	4.25557	+	8.34534i	0.195259	+	0.382911i
$476$	8.62556	+	14.9399i	0.395352	+	0.684769i
$477$	30.8469	+	26.2666i	1.41238	+	1.20266i
$478$	8.47107	+	4.89078i	0.387458	+	0.223699i
$479$	0.141266	−	0.801161i	0.00645462	−	0.0366060i	−0.981410	−	0.191921i	$-0.938528\pi$
$479$	0.141266	−	0.801161i	0.00645462	−	0.0366060i	0.987865	+	0.155315i	$0.0496393\pi$
$480$	3.23700	−	2.12646i	0.147748	−	0.0970592i
$481$	−6.35453	−	2.31286i	−0.289742	−	0.105457i
$482$	2.55207	−	0.449999i	0.116244	−	0.0204969i
$483$	10.1259	+	21.9219i	0.460744	+	0.997481i
$484$	6.18938	+	5.19351i	0.281335	+	0.236068i
$485$	12.0327	+	10.6422i	0.546378	+	0.483237i
$486$	−1.63947	+	15.5020i	−0.0743679	+	0.703185i
$487$			6.33699i			0.287156i	0.989639	+	0.143578i	$0.0458609\pi$
$487$			6.33699i			0.287156i	−0.989639	+	0.143578i	$0.954139\pi$
$488$	−5.86596	+	6.99077i	−0.265539	+	0.316457i
$489$	−24.2053	+	11.1806i	−1.09460	+	0.505605i
$490$	20.0135	−	32.6710i	0.904120	−	1.47593i
$491$	38.3055	+	13.9421i	1.72870	+	0.629196i	0.998537	−	0.0540737i	$-0.0172206\pi$
$491$	38.3055	+	13.9421i	1.72870	+	0.629196i	0.730166	+	0.683270i	$0.239443\pi$
$492$	0.267999	−	0.985896i	0.0120823	−	0.0444476i
$493$	−11.1136	−	1.95963i	−0.500531	−	0.0882571i
$494$	2.84696	−	4.93107i	0.128091	−	0.221859i
$495$	−1.61414	−	11.3494i	−0.0725502	−	0.510119i
$496$	−2.86408	−	4.96074i	−0.128601	−	0.222744i
$497$	8.55446	+	23.5032i	0.383720	+	1.05426i
$498$	−5.46932	+	3.80023i	−0.245086	+	0.170292i
$499$	9.76917	−	8.19731i	0.437328	−	0.366962i	−0.397380	−	0.917654i	$-0.630081\pi$
$499$	9.76917	−	8.19731i	0.437328	−	0.366962i	0.834708	+	0.550692i	$0.185636\pi$
$500$	−11.1283	+	1.07699i	−0.497675	+	0.0481646i
$501$	1.50175	−	0.125910i	0.0670933	−	0.00562523i
$502$	6.05531	+	16.6368i	0.270262	+	0.742538i
$503$	−20.3800	+	11.7664i	−0.908698	+	0.524637i	−0.880012	−	0.474952i	$-0.842466\pi$
$503$	−20.3800	+	11.7664i	−0.908698	+	0.524637i	−0.0286857	+	0.999588i	$0.509132\pi$
$504$	14.5323	−	2.45408i	0.647319	−	0.109313i
$505$	−2.98269	−	8.90952i	−0.132728	−	0.396469i
$506$	0.842133	−	4.77597i	0.0374374	−	0.212318i
$507$	−6.30309	+	1.66447i	−0.279930	+	0.0739219i
$508$	0.334855	−	0.920008i	0.0148568	−	0.0408187i
$509$	1.41848	+	8.04458i	0.0628729	+	0.356570i	0.999972	+	0.00750603i	$0.00238927\pi$
$509$	1.41848	+	8.04458i	0.0628729	+	0.356570i	−0.937099	+	0.349064i	$0.886500\pi$
$510$	9.89754	−	9.32757i	0.438270	−	0.413032i
$511$	−49.1469	−	41.2391i	−2.17413	−	1.82431i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.95821	+	6.80869i	−0.307213	+	0.300611i
$514$	14.9686			0.660238
$515$	−1.63806	−	10.9484i	−0.0721817	−	0.482445i
$516$	−16.5354	−	11.6676i	−0.727929	−	0.513639i
$517$	22.3187	−	3.93538i	0.981574	−	0.173078i
$518$	3.73871	−	10.2720i	0.164269	−	0.451327i
$519$	0.141956	−	0.140932i	0.00623119	−	0.00618624i
$520$	4.23125	+	5.31764i	0.185553	+	0.233194i
$521$	8.56872	−	14.8415i	0.375402	−	0.650216i	−0.614985	−	0.788539i	$-0.710838\pi$
$521$	8.56872	−	14.8415i	0.375402	−	0.650216i	0.990387	+	0.138323i	$0.0441712\pi$
$522$	−4.88086	+	8.31429i	−0.213629	+	0.363907i
$523$	−22.8566	+	13.1963i	−0.999449	+	0.577032i	−0.908085	−	0.418786i	$-0.862456\pi$
$523$	−22.8566	+	13.1963i	−0.999449	+	0.577032i	−0.0913635	+	0.995818i	$0.529123\pi$
$524$	5.66610	−	2.06229i	0.247525	−	0.0900916i
$525$	−40.4192	−	13.2804i	−1.76404	−	0.579606i
$526$	−18.4276	+	15.4626i	−0.803480	+	0.674200i
$527$	−12.9295	−	15.4088i	−0.563219	−	0.671218i
$528$	−2.67804	−	1.26061i	−0.116547	−	0.0548611i
$529$	−14.0451	+	5.11198i	−0.610655	+	0.222260i
$530$	−29.5929	−	6.01575i	−1.28543	−	0.261307i
$531$	−11.5176	+	6.53897i	−0.499822	+	0.283767i
$532$	7.97102	+	4.60207i	0.345587	+	0.199525i
$533$	1.76542	+	0.311291i	0.0764689	+	0.0134835i
$534$	0.688572	−	0.683605i	0.0297974	−	0.0295825i
$535$	3.29447	+	6.06532i	0.142432	+	0.262227i
$536$	−1.20761	−	6.84870i	−0.0521609	−	0.295819i
$537$	−21.6883	+	30.7366i	−0.935917	+	1.32638i
$538$	3.30404	−	3.93761i	0.142447	−	0.169762i
$539$	−29.2810			−1.26122
$540$	−4.51879	−	10.7042i	−0.194458	−	0.460637i
$541$	33.3125			1.43222			0.716109	−	0.697989i	$-0.245921\pi$
$541$	33.3125			1.43222			0.716109	+	0.697989i	$0.245921\pi$
$542$	11.3893	−	13.5733i	0.489213	−	0.583021i
$543$	−17.9347	−	1.63453i	−0.769653	−	0.0701444i
$544$	−0.609774	−	3.45820i	−0.0261439	−	0.148269i
$545$	−8.75567	+	4.75577i	−0.375052	+	0.203715i
$546$	6.60253	+	25.0027i	0.282562	+	1.07002i
$547$	−3.29379	−	0.580783i	−0.140832	−	0.0248325i	0.102788	−	0.994703i	$-0.467224\pi$
$547$	−3.29379	−	0.580783i	−0.140832	−	0.0248325i	−0.243620	+	0.969871i	$0.578335\pi$
$548$	−9.98324	−	5.76383i	−0.426463	−	0.246219i
$549$	17.4456	+	21.0992i	0.744558	+	0.900491i
$550$	5.14442	+	6.82227i	0.219359	+	0.290903i
$551$	−5.65789	+	2.05930i	−0.241034	+	0.0877293i
$552$	−0.410672	−	4.89816i	−0.0174794	−	0.208480i
$553$	19.6290	+	23.3929i	0.834708	+	0.994767i
$554$	8.18365	−	6.86690i	0.347690	−	0.291747i
$555$	−8.55900	−	1.00517i	−0.363309	−	0.0426671i
$556$	−14.3515	+	5.22351i	−0.608638	+	0.221526i
$557$	−13.2151	+	7.62972i	−0.559940	+	0.323281i	−0.753121	−	0.657882i	$-0.771453\pi$
$557$	−13.2151	+	7.62972i	−0.559940	+	0.323281i	0.193181	+	0.981163i	$0.438119\pi$
$558$	−16.1903	+	5.76038i	−0.685389	+	0.243856i
$559$	17.7546	−	30.7518i	0.750938	−	1.30066i
$560$	−8.59590	+	6.83976i	−0.363243	+	0.289033i
$561$	−10.0299	−	2.72645i	−0.423462	−	0.115111i
$562$	0.326662	−	0.897496i	0.0137794	−	0.0378586i
$563$	−4.67804	+	0.824864i	−0.197156	+	0.0347639i	−0.271354	−	0.962480i	$-0.587471\pi$
$563$	−4.67804	+	0.824864i	−0.197156	+	0.0347639i	0.0741982	+	0.997244i	$0.476360\pi$
$564$	20.8529	−	9.63212i	0.878065	−	0.405585i
$565$	6.17984	+	41.3045i	0.259988	+	1.73769i
$566$	−18.1499			−0.762899
$567$	0.640217	−	44.2095i	0.0268866	−	1.85662i
$568$		−	5.09123i		−	0.213623i
$569$	11.9472	+	10.0249i	0.500851	+	0.420264i	0.857896	−	0.513823i	$-0.171771\pi$
$569$	11.9472	+	10.0249i	0.500851	+	0.420264i	−0.357045	+	0.934087i	$0.616216\pi$
$570$	2.08493	−	6.95024i	0.0873280	−	0.291114i
$571$	−2.21164	−	12.5428i	−0.0925541	−	0.524900i	−0.995469	−	0.0950820i	$-0.969689\pi$
$571$	−2.21164	−	12.5428i	−0.0925541	−	0.524900i	0.902915	−	0.429818i	$-0.141422\pi$
$572$	1.77629	−	4.88032i	0.0742704	−	0.204056i
$573$	8.87152	−	32.6359i	0.370613	−	1.36339i
$574$	−0.503199	+	2.85378i	−0.0210031	+	0.119115i
$575$	−5.54001	+	13.0632i	−0.231034	+	0.544773i
$576$	−2.95057	−	0.542321i	−0.122941	−	0.0225967i
$577$	1.88744	−	1.08971i	0.0785750	−	0.0453653i	−0.460198	−	0.887816i	$-0.652221\pi$
$577$	1.88744	−	1.08971i	0.0785750	−	0.0453653i	0.538773	+	0.842451i	$0.318888\pi$
$578$	1.59689	+	4.38743i	0.0664221	+	0.182493i
$579$	22.4611	+	32.3262i	0.933450	+	1.34343i
$580$	0.186945	−	7.18360i	0.00776249	−	0.298283i
$581$	14.4705	−	12.1422i	0.600338	−	0.503744i
$582$	−1.03959	−	12.3994i	−0.0430924	−	0.513972i
$583$	7.89338	+	21.6869i	0.326910	+	0.898179i
$584$	6.52971	+	11.3098i	0.270201	+	0.468002i
$585$	17.9848	−	9.60075i	0.743580	−	0.396942i
$586$	14.8004	−	25.6350i	0.611398	−	1.05897i
$587$	22.4555	+	3.95952i	0.926839	+	0.163427i	0.616640	−	0.787245i	$-0.288493\pi$
$587$	22.4555	+	3.95952i	0.926839	+	0.163427i	0.310199	+	0.950672i	$0.399604\pi$
$588$	−28.6940	+	7.57731i	−1.18332	+	0.312483i
$589$	−10.0848	−	3.67056i	−0.415536	−	0.151243i
$590$	5.15663	−	8.41791i	0.212295	−	0.346560i
$591$	−2.26841	+	24.8899i	−0.0933100	+	1.02384i
$592$	−1.43027	+	1.70453i	−0.0587839	+	0.0700560i
$593$		−	7.34260i		−	0.301525i	−0.988570	−	0.150762i	$-0.951827\pi$
$593$		−	7.34260i		−	0.301525i	0.988570	−	0.150762i	$-0.0481728\pi$
$594$	−5.17188	+	7.21808i	−0.212205	+	0.296162i
$595$	−25.5557	+	28.8949i	−1.04768	+	1.18457i
$596$	2.56351	+	2.15104i	0.105006	+	0.0881101i
$597$	−24.0856	+	34.1341i	−0.985757	+	1.39702i
$598$	8.49359	−	1.49765i	0.347329	−	0.0612434i
$599$	0.893762	+	0.325303i	0.0365181	+	0.0132915i	0.360215	−	0.932869i	$-0.382703\pi$
$599$	0.893762	+	0.325303i	0.0365181	+	0.0132915i	−0.323697	+	0.946161i	$0.604926\pi$
$600$	6.80676	+	5.35425i	0.277885	+	0.218586i
$601$	−1.03949	+	5.89522i	−0.0424015	+	0.240471i	−0.998641	−	0.0521136i	$-0.983404\pi$
$601$	−1.03949	+	5.89522i	−0.0424015	+	0.240471i	0.956240	+	0.292585i	$0.0945153\pi$
$602$	49.7099	+	28.7000i	2.02602	+	1.16973i
$603$	−20.8625	−	0.151052i	−0.849587	−	0.00615131i
$604$	5.23569	+	9.06848i	0.213037	+	0.368991i
$605$	−6.61874	+	16.8106i	−0.269090	+	0.683449i
$606$	−3.09957	+	6.58470i	−0.125911	+	0.267485i
$607$	0.988617	+	1.17819i	0.0401267	+	0.0478212i	0.785735	−	0.618564i	$-0.212285\pi$
$607$	0.988617	+	1.17819i	0.0401267	+	0.0478212i	−0.745608	+	0.666385i	$0.767841\pi$
$608$	−1.20429	−	1.43522i	−0.0488406	−	0.0582059i
$609$	11.6463	−	24.7413i	0.471930	−	1.00257i
$610$	−18.9872	−	7.47572i	−0.768771	−	0.302683i
$611$	20.1519	+	34.9041i	0.815259	+	1.41207i
$612$	−10.5344	−	0.0762725i	−0.425827	−	0.00308313i
$613$	21.5040	+	12.4153i	0.868539	+	0.501451i	0.866862	−	0.498547i	$-0.166133\pi$
$613$	21.5040	+	12.4153i	0.868539	+	0.501451i	0.00167654	+	0.999999i	$0.499466\pi$
$614$	−2.62682	+	14.8974i	−0.106010	+	0.601212i
$615$	2.28074	−	0.131581i	0.0919682	−	0.00530585i
$616$	7.88897	+	2.87135i	0.317856	+	0.115690i
$617$	25.4673	−	4.49056i	1.02527	−	0.180783i	0.364370	−	0.931254i	$-0.381284\pi$
$617$	25.4673	−	4.49056i	1.02527	−	0.180783i	0.660903	+	0.750471i	$0.270173\pi$
$618$	−4.94381	+	7.00637i	−0.198869	+	0.281838i
$619$	23.9463	+	20.0933i	0.962481	+	0.807618i	0.981355	−	0.192204i	$-0.0615636\pi$
$619$	23.9463	+	20.0933i	0.962481	+	0.807618i	−0.0188738	+	0.999822i	$0.506008\pi$
$620$	8.48566	−	9.59443i	0.340792	−	0.385321i
$621$	−14.6751	−	1.44466i	−0.588892	−	0.0579723i
$622$		−	0.540505i		−	0.0216723i
$623$	−1.76898	+	2.10819i	−0.0708727	+	0.0844628i
$624$	0.477758	−	5.24216i	0.0191256	−	0.209854i
$625$	−10.1832	−	22.8320i	−0.407328	−	0.913282i
$626$	−14.9006	−	5.42339i	−0.595550	−	0.216762i
$627$	−5.36172	+	1.41589i	−0.214127	+	0.0565450i
$628$	10.2648	+	1.80996i	0.409609	+	0.0722251i
$629$	−3.90680	+	6.76677i	−0.155774	+	0.269809i
$630$	15.5195	+	29.0722i	0.618311	+	1.15826i
$631$	4.69150	+	8.12591i	0.186765	+	0.323487i	0.944170	−	0.329459i	$-0.106866\pi$
$631$	4.69150	+	8.12591i	0.186765	+	0.323487i	−0.757405	+	0.652946i	$0.773533\pi$
$632$	−2.12600	−	5.84114i	−0.0845678	−	0.232348i
$633$	1.74667	+	20.8328i	0.0694238	+	0.828031i
$634$	−3.51004	+	2.94527i	−0.139401	+	0.116972i
$635$	2.18848	+	0.0569530i	0.0868474	+	0.00226011i
$636$	13.3473	+	19.2095i	0.529254	+	0.761707i
$637$	−17.8101	−	48.9328i	−0.705661	−	1.93879i
$638$	−4.75610	+	2.74594i	−0.188296	+	0.108713i
$639$	−15.0220	−	2.76108i	−0.594263	−	0.109227i
$640$	2.12040	−	0.709858i	0.0838162	−	0.0280596i
$641$	4.96759	−	28.1726i	0.196208	−	1.11275i	−0.714480	−	0.699656i	$-0.753337\pi$
$641$	4.96759	−	28.1726i	0.196208	−	1.11275i	0.910688	−	0.413095i	$-0.135552\pi$
$642$	1.40246	−	5.15927i	0.0553507	−	0.203620i
$643$	5.72276	−	15.7232i	0.225684	−	0.620061i	−0.774234	−	0.632900i	$-0.781865\pi$
$643$	5.72276	−	15.7232i	0.225684	−	0.620061i	0.999918	+	0.0128386i	$0.00408677\pi$
$644$	2.42093	+	13.7298i	0.0953980	+	0.541029i
$645$	13.0023	−	43.3440i	0.511965	−	1.70667i
$646$	−5.03985	−	4.22894i	−0.198290	−	0.166385i
$647$		−	2.79100i		−	0.109725i	−0.998494	−	0.0548627i	$-0.982528\pi$
$647$		−	2.79100i		−	0.109725i	0.998494	−	0.0548627i	$-0.0174721\pi$
$648$	−3.20032	+	8.41178i	−0.125720	+	0.330446i
$649$	−7.54444			−0.296145
$650$	−8.27195	+	12.7467i	−0.324453	+	0.499968i
$651$	44.2486	−	20.4388i	1.73424	−	0.801059i
$652$	−15.1599	+	2.67310i	−0.593707	+	0.104686i
$653$	−6.16910	+	16.9495i	−0.241416	+	0.663284i	0.758517	+	0.651654i	$0.225924\pi$
$653$	−6.16910	+	16.9495i	−0.241416	+	0.663284i	−0.999932	+	0.0116306i	$0.996298\pi$
$654$	7.44773	+	2.02454i	0.291229	+	0.0791657i
$655$	8.39501	+	10.5505i	0.328020	+	0.412241i
$656$	0.294932	−	0.510836i	0.0115151	−	0.0199448i
$657$	36.9116	−	13.1329i	1.44006	−	0.512361i
$658$	−56.4221	+	32.5753i	−2.19956	+	1.26992i
$659$	−2.65675	+	0.966978i	−0.103492	+	0.0376681i	−0.393247	−	0.919433i	$-0.628648\pi$
$659$	−2.65675	+	0.966978i	−0.103492	+	0.0376681i	0.289755	+	0.957101i	$0.406426\pi$
$660$	0.771977	−	6.57336i	0.0300492	−	0.255868i
$661$	−4.54165	+	3.81090i	−0.176650	+	0.148227i	−0.726826	−	0.686822i	$-0.759005\pi$
$661$	−4.54165	+	3.81090i	−0.176650	+	0.148227i	0.550176	+	0.835049i	$0.314561\pi$
$662$	8.50214	+	10.1325i	0.330445	+	0.393809i
$663$	−1.54435	−	18.4198i	−0.0599776	−	0.715365i
$664$	−3.61325	+	1.31511i	−0.140221	+	0.0510363i
$665$	−4.09994	+	20.1686i	−0.158989	+	0.782104i
$666$	4.25369	+	5.14454i	0.164827	+	0.199347i
$667$	−7.89820	−	4.56003i	−0.305820	−	0.176565i
$668$	0.856860	+	0.151088i	0.0331529	+	0.00584575i
$669$	−5.99174	−	22.6897i	−0.231654	−	0.877235i
$670$	13.6648	−	7.42223i	0.527916	−	0.286746i
$671$	2.70806	+	15.3582i	0.104543	+	0.592895i
$672$	8.47389	+	0.772290i	0.326887	+	0.0297917i
$673$	−18.4460	+	21.9831i	−0.711040	+	0.847385i	−0.993728	−	0.111827i	$-0.964330\pi$
$673$	−18.4460	+	21.9831i	−0.711040	+	0.847385i	0.282687	+	0.959212i	$0.408774\pi$
$674$	26.2659			1.01172
$675$	19.4896	−	17.1801i	0.750154	−	0.661263i
$676$	−3.76384			−0.144763
$677$	−18.7170	+	22.3061i	−0.719354	+	0.857292i	−0.994568	−	0.104091i	$-0.966807\pi$
$677$	−18.7170	+	22.3061i	−0.719354	+	0.857292i	0.275214	+	0.961383i	$0.411251\pi$
$678$	18.6513	−	26.4326i	0.716298	−	1.01514i
$679$	6.12843	+	34.7561i	0.235188	+	1.33382i
$680$	6.89992	−	3.74780i	0.264600	−	0.143722i
$681$	14.6473	−	14.5416i	0.561286	−	0.557237i
$682$	−9.64015	−	1.69982i	−0.369140	−	0.0650894i
$683$	8.06101	+	4.65403i	0.308446	+	0.178081i	0.646231	−	0.763142i	$-0.276344\pi$
$683$	8.06101	+	4.65403i	0.308446	+	0.178081i	−0.337785	+	0.941223i	$0.609678\pi$
$684$	−4.88784	+	2.77501i	−0.186891	+	0.106105i
$685$	5.13494	−	25.2600i	0.196196	−	0.965134i
$686$	46.7845	−	17.0281i	1.78624	−	0.650138i
$687$	−10.8219	−	5.09413i	−0.412883	−	0.194353i
$688$	−7.51037	−	8.95052i	−0.286330	−	0.341235i
$689$	−31.4409	+	26.3820i	−1.19780	+	1.00508i
$690$	10.0946	−	4.34779i	0.384293	−	0.165518i
$691$	−21.9757	+	7.99850i	−0.835995	+	0.304277i	−0.724317	−	0.689467i	$-0.757845\pi$
$691$	−21.9757	+	7.99850i	−0.835995	+	0.304277i	−0.111678	+	0.993744i	$0.535622\pi$
$692$	0.100017	−	0.0577448i	0.00380207	−	0.00219513i
$693$	12.7505	−	21.7198i	0.484351	−	0.825067i
$694$	0.679231	−	1.17646i	0.0257833	−	0.0446579i
$695$	−21.2634	−	26.7229i	−0.806568	−	1.01366i
$696$	−3.95017	+	3.92168i	−0.149731	+	0.148651i
$697$	0.708438	−	1.94642i	0.0268340	−	0.0737258i
$698$	−12.6846	+	2.23664i	−0.480121	+	0.0846582i
$699$	11.8579	+	8.36711i	0.448506	+	0.316473i
$700$	−20.6049	−	13.3715i	−0.778793	−	0.505395i
$701$	−19.0529			−0.719617			−0.359808	−	0.933026i	$-0.617158\pi$
$701$	−19.0529			−0.719617			−0.359808	+	0.933026i	$0.617158\pi$
$702$	−15.2083	−	4.25260i	−0.574000	−	0.160504i
$703$			4.16886i			0.157231i
$704$	−1.30909	−	1.09846i	−0.0493383	−	0.0413997i
$705$	35.2266	+	37.3791i	1.32671	+	1.40778i
$706$	−1.94920	−	11.0545i	−0.0733591	−	0.416040i
$707$	7.06003	−	19.3973i	0.265520	−	0.729509i
$708$	−7.39321	+	1.95235i	−0.277854	+	0.0733737i
$709$	5.37627	−	30.4903i	0.201910	−	1.14509i	−0.700319	−	0.713830i	$-0.746959\pi$
$709$	5.37627	−	30.4903i	0.201910	−	1.14509i	0.902229	−	0.431258i	$-0.141930\pi$
$710$	10.7954	−	3.61405i	0.405146	−	0.135633i
$711$	−18.3877	+	3.10515i	−0.689592	+	0.116452i
$712$	0.485141	−	0.280096i	0.0181814	−	0.0104971i
$713$	−5.55983	−	15.2755i	−0.208217	−	0.572072i
$714$	29.7753	−	2.49642i	1.11431	−	0.0934263i
$715$	11.6091	+	0.302116i	0.434157	+	0.0112985i
$716$	−16.6376	+	13.9606i	−0.621775	+	0.521731i
$717$	13.9133	−	9.66731i	0.519601	−	0.361032i
$718$	−7.30883	−	20.0809i	−0.272763	−	0.749411i
$719$	15.3964	+	26.6674i	0.574189	+	0.994525i	0.996129	+	0.0879013i	$0.0280160\pi$
$719$	15.3964	+	26.6674i	0.574189	+	0.994525i	−0.421940	+	0.906624i	$0.638651\pi$
$720$	−0.944550	−	6.64137i	−0.0352013	−	0.247509i
$721$	12.1608	−	21.0631i	0.452891	−	0.784431i
$722$	15.2545	+	2.68978i	0.567713	+	0.100103i
$723$	1.17740	−	4.33134i	0.0437880	−	0.161084i
$724$	−9.77049	−	3.55617i	−0.363117	−	0.132164i
$725$	15.3648	−	4.70293i	0.570635	−	0.174663i
$726$	12.7045	−	5.86833i	0.471510	−	0.217794i
$727$	26.9452	−	32.1121i	0.999343	−	1.19097i	0.0177785	−	0.999842i	$-0.494341\pi$
$727$	26.9452	−	32.1121i	0.999343	−	1.19097i	0.981565	−	0.191129i	$-0.0612149\pi$
$728$			14.9301i			0.553348i
$729$	23.0840	+	14.0047i	0.854962	+	0.518691i
$730$	−19.3461	+	21.8740i	−0.716032	+	0.809591i
$731$	−31.4302	−	26.3731i	−1.16249	−	0.975443i
$732$	6.62815	+	14.3495i	0.244984	+	0.530373i
$733$	46.9779	−	8.28348i	1.73517	−	0.305957i	0.785419	−	0.618964i	$-0.212447\pi$
$733$	46.9779	−	8.28348i	1.73517	−	0.305957i	0.949751	+	0.313007i	$0.101336\pi$
$734$	−20.6733	−	7.52447i	−0.763066	−	0.277733i
$735$	−36.4356	−	55.4640i	−1.34395	−	2.04582i
$736$	0.492792	−	2.79477i	0.0181646	−	0.103016i
$737$	−10.2921	−	5.94215i	−0.379114	−	0.218882i
$738$	−1.34731	−	1.14725i	−0.0495953	−	0.0422310i
$739$	−5.47160	−	9.47708i	−0.201276	−	0.348620i	0.747664	−	0.664077i	$-0.231175\pi$
$739$	−5.47160	−	9.47708i	−0.201276	−	0.348620i	−0.948940	+	0.315457i	$0.897842\pi$
$740$	−4.62959	−	1.82278i	−0.170187	−	0.0670067i
$741$	−5.62741	−	8.09902i	−0.206728	−	0.297525i
$742$	−42.6462	−	50.8238i	−1.56559	−	1.86580i
$743$	12.6830	+	15.1150i	0.465293	+	0.554515i	0.946756	−	0.321952i	$-0.104339\pi$
$743$	12.6830	+	15.1150i	0.465293	+	0.554515i	−0.481463	+	0.876466i	$0.659894\pi$
$744$	−9.88679	+	0.828928i	−0.362467	+	0.0303900i
$745$	−2.74134	+	6.96261i	−0.100435	+	0.255090i
$746$	−4.00789	−	6.94186i	−0.146739	−	0.254160i
$747$	1.92080	+	11.3744i	0.0702785	+	0.416166i
$748$	−5.19692	−	3.00044i	−0.190018	−	0.109707i
$749$	−2.63328	+	14.9341i	−0.0962179	+	0.545679i
$750$	−6.52133	+	18.2338i	−0.238125	+	0.665805i
$751$	30.6111	+	11.1415i	1.11702	+	0.406561i	0.833563	−	0.552425i	$-0.186297\pi$
$751$	30.6111	+	11.1415i	1.11702	+	0.406561i	0.283454	+	0.958986i	$0.408520\pi$
$752$	13.0603	−	2.30288i	0.476259	−	0.0839773i
$753$	30.5386	+	2.78322i	1.11289	+	0.101426i
$754$	−7.48176	−	6.27794i	−0.272470	−	0.228629i
$755$	−15.5122	+	17.5391i	−0.564547	+	0.638313i
$756$	6.87427	−	24.5840i	0.250015	−	0.894111i
$757$		−	7.47944i		−	0.271845i	−0.990719	−	0.135923i	$-0.956600\pi$
$757$		−	7.47944i		−	0.271845i	0.990719	−	0.135923i	$-0.0433998\pi$
$758$	1.87555	−	2.23519i	0.0681231	−	0.0811859i
$759$	−6.86326	−	4.84283i	−0.249121	−	0.175784i
$760$	2.18837	−	3.57239i	0.0793805	−	0.129584i
$761$	11.8203	+	4.30226i	0.428487	+	0.155957i	0.547256	−	0.836965i	$-0.315672\pi$
$761$	11.8203	+	4.30226i	0.428487	+	0.155957i	−0.118769	+	0.992922i	$0.537895\pi$
$762$	−1.19474	−	1.20342i	−0.0432809	−	0.0435954i
$763$	−21.5582	−	3.80130i	−0.780461	−	0.137616i
$764$	9.76306	−	16.9101i	0.353215	−	0.611787i
$765$	−7.31618	−	22.3913i	−0.264517	−	0.809557i
$766$	−16.0450	−	27.7907i	−0.579729	−	1.00412i
$767$	−4.58889	−	12.6079i	−0.165695	−	0.455244i
$768$	−1.56711	−	0.737674i	−0.0565482	−	0.0266185i
$769$	5.24656	−	4.40239i	0.189196	−	0.158754i	−0.543270	−	0.839558i	$-0.682814\pi$
$769$	5.24656	−	4.40239i	0.189196	−	0.158754i	0.732466	+	0.680804i	$0.238369\pi$
$770$	−0.488366	+	18.7660i	−0.0175995	+	0.676281i
$771$	11.0420	−	23.4575i	0.397667	−	0.844801i
$772$	7.77292	+	21.3559i	0.279754	+	0.768616i
$773$	20.2379	−	11.6843i	0.727906	−	0.420256i	−0.0897499	−	0.995964i	$-0.528607\pi$
$773$	20.2379	−	11.6843i	0.727906	−	0.420256i	0.817655	+	0.575708i	$0.195273\pi$
$774$	−30.4822	+	17.3059i	−1.09566	+	0.622046i
$775$	26.3677	+	11.1823i	0.947154	+	0.401681i
$776$	1.24747	−	7.07477i	0.0447817	−	0.253970i
$777$	−13.3394	−	13.4364i	−0.478550	−	0.482027i
$778$	−1.50914	+	4.14632i	−0.0541052	+	0.148653i
$779$	−0.191905	−	1.08835i	−0.00687571	−	0.0389941i
$780$	11.4546	−	2.70815i	0.410141	−	0.0969673i
$781$	−6.66489	−	5.59251i	−0.238489	−	0.200116i
$782$		−	9.96536i		−	0.356360i
$783$	9.42893	+	13.7821i	0.336963	+	0.492532i
$784$	−17.1344			−0.611942
$785$	3.44870	+	23.0502i	0.123089	+	0.822698i
$786$	0.947896	−	10.4007i	0.0338103	−	0.370981i
$787$	−33.7847	+	5.95715i	−1.20429	+	0.212350i	−0.739554	−	0.673097i	$-0.764963\pi$
$787$	−33.7847	+	5.95715i	−1.20429	+	0.212350i	−0.464741	+	0.885447i	$0.653852\pi$
$788$	−4.93527	+	13.5595i	−0.175812	+	0.483039i
$789$	10.6380	+	40.2844i	0.378723	+	1.43416i
$790$	10.8764	−	8.65435i	0.386965	−	0.307908i
$791$	−45.8784	+	79.4637i	−1.63125	+	2.82540i
$792$	−3.95104	+	3.26686i	−0.140394	+	0.116083i
$793$	−24.0186	+	13.8671i	−0.852926	+	0.492437i
$794$	−26.5271	+	9.65509i	−0.941413	+	0.342646i
$795$	−31.2572	+	41.9376i	−1.10858	+	1.48737i
$796$	−18.4766	+	15.5037i	−0.654886	+	0.549515i
$797$	12.4239	+	14.8062i	0.440076	+	0.524463i	0.939801	−	0.341722i	$-0.111010\pi$
$797$	12.4239	+	14.8062i	0.440076	+	0.524463i	−0.499725	+	0.866184i	$0.666566\pi$
$798$	13.0920	−	9.09664i	0.463451	−	0.322018i
$799$	43.7608	−	15.9276i	1.54815	−	0.563479i
$800$	3.01037	+	3.99220i	0.106433	+	0.141146i
$801$	−0.563343	−	1.58335i	−0.0199047	−	0.0559448i
$802$	−9.45505	−	5.45888i	−0.333869	−	0.192760i
$803$	21.9782	+	3.87535i	0.775593	+	0.136758i
$804$	−11.6235	−	3.15965i	−0.409929	−	0.111432i
$805$	−27.3941	+	14.8795i	−0.965516	+	0.524435i
$806$	−3.02296	−	17.1440i	−0.106479	−	0.603873i
$807$	−3.73336	−	8.08247i	−0.131420	−	0.284517i
$808$	−2.70087	+	3.21877i	−0.0950163	+	0.113236i
$809$	49.6252			1.74473			0.872365	−	0.488855i	$-0.162585\pi$
$809$	49.6252			1.74473			0.872365	+	0.488855i	$0.162585\pi$
$810$	−20.1081	−	0.814794i	−0.706527	−	0.0286289i
$811$	−12.5774			−0.441651			−0.220826	−	0.975313i	$-0.570875\pi$
$811$	−12.5774			−0.441651			−0.220826	+	0.975313i	$0.570875\pi$
$812$	10.1482	−	12.0942i	0.356132	−	0.424422i
$813$	−12.8692	−	27.8610i	−0.451342	−	0.977127i
$814$	0.660296	+	3.74472i	0.0231434	+	0.131253i
$815$	−16.4294	−	30.2475i	−0.575497	−	1.05952i
$816$	−5.86920	−	1.59544i	−0.205463	−	0.0558517i
$817$	−21.5581	−	3.80128i	−0.754223	−	0.132990i
$818$	−28.2321	−	16.2998i	−0.987111	−	0.569909i
$819$	44.0525	+	8.09694i	1.53932	+	0.282930i
$820$	1.29254	+	0.262752i	0.0451374	+	0.00917569i
$821$	−47.7802	+	17.3906i	−1.66754	+	0.606935i	−0.991521	−	0.129947i	$-0.958519\pi$
$821$	−47.7802	+	17.3906i	−1.66754	+	0.606935i	−0.676021	+	0.736883i	$0.736297\pi$
$822$	−16.3969	+	11.3930i	−0.571909	+	0.397377i
$823$	4.12743	+	4.91888i	0.143873	+	0.171461i	0.833169	−	0.553019i	$-0.186524\pi$
$823$	4.12743	+	4.91888i	0.143873	+	0.171461i	−0.689296	+	0.724480i	$0.742080\pi$
$824$	−3.79252	+	3.18230i	−0.132119	+	0.110861i
$825$	14.4862	−	3.02925i	0.504343	−	0.105465i
$826$	20.3805	−	7.41789i	0.709128	−	0.258101i
$827$	49.3913	−	28.5161i	1.71750	−	0.991601i	0.794084	−	0.607808i	$-0.207951\pi$
$827$	49.3913	−	28.5161i	1.71750	−	0.991601i	0.923419	−	0.383793i	$-0.125382\pi$
$828$	−7.97891	−	2.96968i	−0.277286	−	0.103204i
$829$	−0.902922	+	1.56391i	−0.0313598	+	0.0543167i	−0.881279	−	0.472596i	$-0.843317\pi$
$829$	−0.902922	+	1.56391i	−0.0313598	+	0.0543167i	0.849920	+	0.526912i	$0.176650\pi$
$830$	−5.35346	−	6.72799i	−0.185821	−	0.233532i
$831$	−4.72432	−	17.8902i	−0.163885	−	0.620605i
$832$	1.03944	−	2.85583i	0.0360359	−	0.0990079i
$833$	−59.2542	+	10.4481i	−2.05304	+	0.362006i
$834$	−2.40089	+	26.3436i	−0.0831361	+	0.912204i
$835$	0.287883	+	1.92414i	0.00996259	+	0.0665875i
$836$	−3.20171			−0.110733
$837$	−2.91600	+	29.6212i	−0.100792	+	1.02386i
$838$		−	21.5276i		−	0.743659i
$839$	−6.50987	−	5.46243i	−0.224746	−	0.188584i	0.523461	−	0.852050i	$-0.324640\pi$
$839$	−6.50987	−	5.46243i	−0.224746	−	0.188584i	−0.748207	+	0.663466i	$0.769085\pi$
$840$	4.37769	+	18.5163i	0.151045	+	0.638871i
$841$	−3.24239	−	18.3885i	−0.111807	−	0.634087i
$842$	−0.614047	+	1.68708i	−0.0211614	+	0.0581406i
$843$	−1.16551	−	1.17397i	−0.0401421	−	0.0404338i
$844$	−2.09594	+	11.8867i	−0.0721453	+	0.409156i
$845$	−2.67179	−	7.98084i	−0.0919124	−	0.274549i
$846$	0.288051	−	39.7842i	0.00990340	−	1.36781i
$847$	−34.3749	+	19.8464i	−1.18114	+	0.681930i
$848$	4.61899	+	12.6906i	0.158617	+	0.435796i
$849$	−13.3887	+	28.4430i	−0.459500	+	0.976160i
$850$	12.8448	+	11.9702i	0.440573	+	0.410575i
$851$	−4.83726	+	4.05895i	−0.165819	+	0.139139i
$852$	−7.97852	−	3.75567i	−0.273340	−	0.128667i
$853$	9.62472	+	26.4437i	0.329544	+	0.905415i	0.988227	+	0.152995i	$0.0488917\pi$
$853$	9.62472	+	26.4437i	0.329544	+	0.905415i	−0.658683	+	0.752421i	$0.728886\pi$
$854$	−22.4161	−	38.8258i	−0.767062	−	1.32859i
$855$	−9.35380	−	8.39433i	−0.319893	−	0.287080i
$856$	1.54340	−	2.67325i	0.0527523	−	0.0913697i
$857$	16.1568	+	2.84888i	0.551906	+	0.0973159i	0.442645	−	0.896697i	$-0.354040\pi$
$857$	16.1568	+	2.84888i	0.551906	+	0.0973159i	0.109261	+	0.994013i	$0.465151\pi$
$858$	−6.33768	−	6.38373i	−0.216365	−	0.217937i
$859$	−30.7935	−	11.2079i	−1.05066	−	0.382409i	−0.241749	−	0.970339i	$-0.577721\pi$
$859$	−30.7935	−	11.2079i	−1.05066	−	0.382409i	−0.808912	+	0.587929i	$0.799943\pi$
$860$	13.6474	−	22.2786i	0.465372	−	0.759694i
$861$	4.10100	+	2.89373i	0.139762	+	0.0986180i
$862$	0.762802	−	0.909072i	0.0259811	−	0.0309631i
$863$			6.61925i			0.225322i	0.993633	+	0.112661i	$0.0359374\pi$
$863$			6.61925i			0.225322i	−0.993633	+	0.112661i	$0.964063\pi$
$864$	−3.02644	+	4.22382i	−0.102962	+	0.143697i
$865$	0.193440	+	0.171085i	0.00657716	+	0.00581708i
$866$	−16.3545	−	13.7231i	−0.555749	−	0.466329i
$867$	8.05358	+	0.733984i	0.273514	+	0.0249274i
$868$	27.7131	−	4.88657i	0.940644	−	0.165861i
$869$	−9.98192	−	3.63312i	−0.338613	−	0.123245i
$870$	−11.1196	−	5.59212i	−0.376989	−	0.189591i
$871$	3.67006	−	20.8139i	0.124355	−	0.705253i
$872$	3.85900	+	2.22799i	0.130682	+	0.0754494i
$873$	−20.1981	−	7.51756i	−0.683603	−	0.254431i
$874$	−2.65845	−	4.60457i	−0.0899235	−	0.155752i
$875$	13.7264	−	53.1826i	0.464037	−	1.79790i
$876$	22.5405	−	1.88984i	0.761573	−	0.0638518i
$877$	6.85687	+	8.17170i	0.231540	+	0.275939i	0.869287	−	0.494307i	$-0.164578\pi$
$877$	6.85687	+	8.17170i	0.231540	+	0.275939i	−0.637747	+	0.770246i	$0.720134\pi$
$878$	16.2091	+	19.3173i	0.547032	+	0.651927i
$879$	−29.2551	−	42.1041i	−0.986748	−	1.42014i
$880$	1.39990	−	3.55555i	0.0471908	−	0.119858i
$881$	−22.3367	−	38.6883i	−0.752542	−	1.30344i	−0.946587	−	0.322449i	$-0.895494\pi$
$881$	−22.3367	−	38.6883i	−0.752542	−	1.30344i	0.194045	−	0.980993i	$-0.437839\pi$
$882$	−9.29235	+	50.5563i	−0.312890	+	1.70232i
$883$	4.99769	+	2.88542i	0.168186	+	0.0971021i	0.581730	−	0.813382i	$-0.302376\pi$
$883$	4.99769	+	2.88542i	0.168186	+	0.0971021i	−0.413544	+	0.910484i	$0.635709\pi$
$884$	1.85317	−	10.5098i	0.0623288	−	0.353484i
$885$	−9.38789	−	14.2907i	−0.315570	−	0.480376i
$886$	22.4197	+	8.16012i	0.753206	+	0.274145i
$887$	52.7486	−	9.30100i	1.77112	−	0.312297i	0.809593	−	0.586991i	$-0.199688\pi$
$887$	52.7486	−	9.30100i	1.77112	−	0.312297i	0.961532	+	0.274694i	$0.0885766\pi$
$888$	1.61612	+	3.49879i	0.0542334	+	0.117412i
$889$	3.68449	+	3.09166i	0.123574	+	0.103691i
$890$	0.938298	+	0.829865i	0.0314518	+	0.0278171i
$891$	7.49638	+	13.4295i	0.251138	+	0.449905i
$892$		−	13.5490i		−	0.453653i
$893$	15.9710	−	19.0335i	0.534450	−	0.636933i
$894$	5.26196	−	2.43054i	0.175986	−	0.0812894i
$895$	−41.4123	−	25.3683i	−1.38426	−	0.847969i
$896$	4.61641	+	1.68023i	0.154223	+	0.0561327i
$897$	3.91852	−	14.4152i	0.130836	−	0.481308i
$898$	17.5920	+	3.10194i	0.587052	+	0.103513i
$899$	−9.20428	+	15.9423i	−0.306980	+	0.531705i
$900$	13.4119	−	6.71726i	0.447063	−	0.223909i
$901$	23.7118	+	41.0700i	0.789953	+	1.36824i
$902$	−0.344762	−	0.947226i	−0.0114793	−	0.0315392i
$903$	81.6458	−	56.7297i	2.71700	−	1.88784i
$904$	14.3078	−	12.0057i	0.475871	−	0.399304i
$905$	0.604841	−	23.2417i	0.0201056	−	0.772581i
$906$	18.0735	−	1.51532i	0.600453	−	0.0503432i
$907$	−3.84178	−	10.5552i	−0.127564	−	0.350480i	0.859426	−	0.511260i	$-0.170821\pi$
$907$	−3.84178	−	10.5552i	−0.127564	−	0.350480i	−0.986990	+	0.160780i	$0.948599\pi$
$908$	10.3199	−	5.95821i	0.342479	−	0.197730i
$909$	8.03249	+	9.71473i	0.266421	+	0.322217i
$910$	−31.6579	+	10.5983i	−1.04945	+	0.351330i
$911$	−9.89618	+	56.1240i	−0.327875	+	1.85947i	0.160774	+	0.986991i	$0.448601\pi$
$911$	−9.89618	+	56.1240i	−0.327875	+	1.85947i	−0.488649	+	0.872480i	$0.662510\pi$
$912$	−3.13753	+	0.828536i	−0.103894	+	0.0274356i
$913$	−2.24740	+	6.17468i	−0.0743780	+	0.204352i
$914$	3.94409	+	22.3680i	0.130459	+	0.739869i
$915$	−25.7217	+	24.2405i	−0.850333	+	0.801365i
$916$	−5.29005	−	4.43888i	−0.174788	−	0.146665i
$917$			29.6221i			0.978209i
$918$	−7.89047	+	16.4523i	−0.260424	+	0.543006i
$919$	2.68556			0.0885886			0.0442943	−	0.999019i	$-0.485896\pi$
$919$	2.68556			0.0885886			0.0442943	+	0.999019i	$0.485896\pi$
$920$	6.27584	−	0.938969i	0.206908	−	0.0309569i
$921$	21.4082	+	15.1060i	0.705424	+	0.497759i
$922$	−3.95314	+	0.697045i	−0.130190	+	0.0229559i
$923$	5.29200	−	14.5397i	0.174188	−	0.478579i
$924$	10.3192	−	10.2448i	0.339477	−	0.337028i
$925$	0.578670	−	11.1105i	0.0190265	−	0.365311i
$926$	−10.1060	+	17.5041i	−0.332104	+	0.575222i
$927$	7.33284	+	12.9159i	0.240842	+	0.424215i
$928$	−2.78314	+	1.60684i	−0.0913609	+	0.0527473i
$929$	28.1650	−	10.2512i	0.924063	−	0.336331i	0.164209	−	0.986426i	$-0.447493\pi$
$929$	28.1650	−	10.2512i	0.924063	−	0.336331i	0.759854	+	0.650094i	$0.225271\pi$
$930$	−8.77588	−	20.3755i	−0.287772	−	0.668140i
$931$	−24.5916	+	20.6348i	−0.805959	+	0.676280i
$932$	5.38585	+	6.41861i	0.176420	+	0.210249i
$933$	−0.847031	−	0.398716i	−0.0277305	−	0.0130534i
$934$	−22.0958	+	8.04223i	−0.722998	+	0.263150i
$935$	2.67307	−	13.1494i	0.0874187	−	0.430033i
$936$	−7.86262	−	4.61571i	−0.256998	−	0.150869i
$937$	5.92175	+	3.41892i	0.193455	+	0.111691i	0.593599	−	0.804761i	$-0.297707\pi$
$937$	5.92175	+	3.41892i	0.193455	+	0.111691i	−0.400144	+	0.916452i	$0.631040\pi$
$938$	33.6455	+	5.93260i	1.09856	+	0.193706i
$939$	−19.4909	+	19.3503i	−0.636061	+	0.631472i
$940$	14.1540	+	26.0583i	0.461651	+	0.849927i
$941$	3.82436	+	21.6890i	0.124670	+	0.707041i	0.981503	+	0.191447i	$0.0613179\pi$
$941$	3.82436	+	21.6890i	0.124670	+	0.707041i	−0.856833	+	0.515595i	$0.827571\pi$
$942$	10.4085	−	14.7509i	0.339126	−	0.480610i
$943$	1.07600	−	1.28233i	0.0350394	−	0.0417583i
$944$	−4.41479			−0.143689
$945$	57.0077	−	2.87494i	1.85446	−	0.0935218i
$946$	−19.9669			−0.649180
$947$	−22.7604	+	27.1248i	−0.739615	+	0.881439i	−0.996378	−	0.0850354i	$-0.972900\pi$
$947$	−22.7604	+	27.1248i	−0.739615	+	0.881439i	0.256763	+	0.966474i	$0.417344\pi$
$948$	−10.7220	−	0.977179i	−0.348235	−	0.0317373i
$949$	6.89192	+	39.0860i	0.223721	+	1.26879i
$950$	9.12833	+	2.10433i	0.296162	+	0.0682734i
$951$	2.02630	+	7.67327i	0.0657074	+	0.248823i
$952$	16.9890	+	2.99562i	0.550618	+	0.0970888i
$953$	−29.0786	−	16.7885i	−0.941948	−	0.543834i	−0.0513778	−	0.998679i	$-0.516361\pi$
$953$	−29.0786	−	16.7885i	−0.941948	−	0.543834i	−0.890571	+	0.454845i	$0.849695\pi$
$954$	39.9494	−	6.74630i	1.29341	−	0.218419i
$955$	42.7866	+	8.69782i	1.38454	+	0.281455i
$956$	9.19165	−	3.34549i	0.297279	−	0.108201i
$957$	0.794734	+	9.47894i	0.0256901	+	0.306411i
$958$	−0.522921	−	0.623193i	−0.0168948	−	0.0201344i
$959$	43.3824	−	36.4021i	1.40089	−	1.17549i
$960$	0.451739	−	3.84655i	0.0145798	−	0.124147i
$961$	−1.70264	+	0.619708i	−0.0549237	+	0.0199906i
$962$	−5.85637	+	3.38118i	−0.188817	+	0.109013i
$963$	−7.05059	−	6.00367i	−0.227202	−	0.193466i
$964$	1.29572	−	2.24426i	0.0417324	−	0.0722826i
$965$	−39.7655	+	31.6414i	−1.28010	+	1.01857i
$966$	23.3019	+	6.33424i	0.749728	+	0.203801i
$967$	−16.0170	+	44.0063i	−0.515072	+	1.41515i	0.360818	+	0.932636i	$0.382498\pi$
$967$	−16.0170	+	44.0063i	−0.515072	+	1.41515i	−0.875890	+	0.482512i	$0.839725\pi$
$968$	7.95691	−	1.40302i	0.255745	−	0.0450947i
$969$	−10.3450	+	4.77843i	−0.332329	+	0.153505i
$970$	15.8869	−	2.37694i	0.510097	−	0.0763190i
$971$	−16.6770			−0.535189			−0.267595	−	0.963532i	$-0.586229\pi$
$971$	−16.6770			−0.535189			−0.267595	+	0.963532i	$0.586229\pi$
$972$	10.8214	+	11.2204i	0.347096	+	0.359895i
$973$		−	75.0289i		−	2.40532i
$974$	4.85442	+	4.07334i	0.155545	+	0.130518i
$975$	13.8735	+	22.3660i	0.444308	+	0.716285i
$976$	1.58468	+	8.98717i	0.0507244	+	0.287672i
$977$	10.0246	−	27.5423i	0.320714	−	0.881155i	−0.669651	−	0.742676i	$-0.733556\pi$
$977$	10.0246	−	27.5423i	0.320714	−	0.881155i	0.990365	−	0.138479i	$-0.0442215\pi$
$978$	−6.99401	+	25.7291i	−0.223644	+	0.822725i
$979$	0.166236	−	0.942769i	0.00531292	−	0.0301310i
$980$	−12.1630	−	36.3318i	−0.388532	−	1.16058i
$981$	8.66668	−	10.1780i	0.276706	−	0.324958i
$982$	35.3025	−	20.3819i	1.12655	−	0.650413i
$983$	12.6632	+	34.7919i	0.403894	+	1.10969i	0.960346	+	0.278809i	$0.0899398\pi$
$983$	12.6632	+	34.7919i	0.403894	+	1.10969i	−0.556453	+	0.830879i	$0.687838\pi$
$984$	−0.582974	−	0.839021i	−0.0185845	−	0.0267470i
$985$	−32.2550	−	0.839403i	−1.02773	−	0.0267456i
$986$	−8.64484	+	7.25388i	−0.275308	+	0.231011i
$987$	9.42800	+	112.450i	0.300097	+	3.57931i
$988$	−1.94743	−	5.35053i	−0.0619561	−	0.170223i
$989$	−16.5790	−	28.7156i	−0.527181	−	0.913104i
$990$	−9.73172	−	6.05877i	−0.309294	−	0.192560i
$991$	−7.96238	+	13.7912i	−0.252933	+	0.438093i	−0.964332	−	0.264695i	$-0.914729\pi$
$991$	−7.96238	+	13.7912i	−0.252933	+	0.438093i	0.711399	+	0.702788i	$0.248062\pi$
$992$	−5.64114	−	0.994686i	−0.179107	−	0.0315813i
$993$	22.1505	−	5.84934i	0.702925	−	0.185623i
$994$	23.5032	+	8.55446i	0.745476	+	0.271331i
$995$	−45.9899	−	28.1724i	−1.45798	−	0.893125i
$996$	−0.604469	+	6.63249i	−0.0191533	+	0.210158i
$997$	−14.5728	+	17.3672i	−0.461526	+	0.550026i	−0.945740	−	0.324924i	$-0.894661\pi$
$997$	−14.5728	+	17.3672i	−0.461526	+	0.550026i	0.484214	+	0.874950i	$0.339106\pi$
$998$		−	12.7527i		−	0.403681i
$999$	11.1999	−	2.87101i	0.354349	−	0.0908347i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.p.a.259.13	yes	108
3.2	odd	2		810.2.p.a.289.2		108
5.4	even	2	inner	270.2.p.a.259.6	yes	108
15.14	odd	2		810.2.p.a.289.13		108
27.5	odd	18		810.2.p.a.199.13		108
27.22	even	9	inner	270.2.p.a.49.6	✓	108
135.49	even	18	inner	270.2.p.a.49.13	yes	108
135.59	odd	18		810.2.p.a.199.2		108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.p.a.49.6	✓	108	27.22	even	9	inner
270.2.p.a.49.13	yes	108	135.49	even	18	inner
270.2.p.a.259.6	yes	108	5.4	even	2	inner
270.2.p.a.259.13	yes	108	1.1	even	1	trivial
810.2.p.a.199.2		108	135.59	odd	18
810.2.p.a.199.13		108	27.5	odd	18
810.2.p.a.289.2		108	3.2	odd	2
810.2.p.a.289.13		108	15.14	odd	2

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:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.642788 - 0.766044i) q^{2} +(-0.726309 - 1.57241i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.96492 - 1.06728i) q^{5} +(-1.67140 - 0.454341i) q^{6} +(4.83804 + 0.853077i) q^{7} +(-0.866025 - 0.500000i) q^{8} +(-1.94495 + 2.28411i) q^{9} +(0.445446 - 2.19125i) q^{10} +(-1.60584 + 0.584478i) q^{11} +(-1.42240 + 0.988321i) q^{12} +(-1.95350 - 2.32809i) q^{13} +(3.76333 - 3.15781i) q^{14} +(-3.10534 - 2.31449i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-3.04109 + 1.75578i) q^{17} +(0.499540 + 2.95812i) q^{18} +(-0.936774 + 1.62254i) q^{19} +(-1.39227 - 1.74974i) q^{20} +(-2.17252 - 8.22699i) q^{21} +(-0.584478 + 1.60584i) q^{22} +(-2.79477 + 0.492792i) q^{23} +(-0.157204 + 1.72490i) q^{24} +(2.72184 - 4.19423i) q^{25} -3.03911 q^{26} +(5.00420 + 1.39929i) q^{27} -4.91268i q^{28} +(2.46183 + 2.06572i) q^{29} +(-3.76908 + 0.891101i) q^{30} +(0.994686 + 5.64114i) q^{31} +(-0.342020 + 0.939693i) q^{32} +(2.08538 + 2.10053i) q^{33} +(-0.609774 + 3.45820i) q^{34} +(10.4168 - 3.48730i) q^{35} +(2.58715 + 1.51877i) q^{36} +(1.92700 - 1.11256i) q^{37} +(0.640791 + 1.76056i) q^{38} +(-2.24187 + 4.76262i) q^{39} +(-2.23531 - 0.0581716i) q^{40} +(-0.451861 + 0.379157i) q^{41} +(-7.69871 - 3.62395i) q^{42} +(3.99619 + 10.9794i) q^{43} +(0.854450 + 1.47995i) q^{44} +(-1.38390 + 6.56390i) q^{45} +(-1.41894 + 2.45768i) q^{46} +(-13.0603 - 2.30288i) q^{47} +(1.22030 + 1.22917i) q^{48} +(16.1011 + 5.86031i) q^{49} +(-1.46341 - 4.78105i) q^{50} +(4.96957 + 3.50661i) q^{51} +(-1.95350 + 2.32809i) q^{52} -13.5050i q^{53} +(4.28856 - 2.93399i) q^{54} +(-2.53155 + 2.86233i) q^{55} +(-3.76333 - 3.15781i) q^{56} +(3.23169 + 0.294528i) q^{57} +(3.16487 - 0.558051i) q^{58} +(4.14855 + 1.50995i) q^{59} +(-1.74009 + 3.46007i) q^{60} +(1.58468 - 8.98717i) q^{61} +(4.96074 + 2.86408i) q^{62} +(-11.3583 + 9.39143i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-6.32319 - 2.48959i) q^{65} +(2.94955 - 0.247296i) q^{66} +(4.47017 + 5.32734i) q^{67} +(2.25718 + 2.69000i) q^{68} +(2.80473 + 4.03660i) q^{69} +(4.02439 - 10.2214i) q^{70} +(2.54561 + 4.40913i) q^{71} +(2.82643 - 1.00562i) q^{72} +(-11.3098 - 6.52971i) q^{73} +(0.386387 - 2.19131i) q^{74} +(-8.57195 - 1.23354i) q^{75} +(1.76056 + 0.640791i) q^{76} +(-8.26773 + 1.45782i) q^{77} +(2.20733 + 4.77872i) q^{78} +(4.76174 + 3.99557i) q^{79} +(-1.48139 + 1.67496i) q^{80} +(-1.43433 - 8.88497i) q^{81} +0.589863i q^{82} +(2.47161 - 2.94555i) q^{83} +(-7.72475 + 3.56812i) q^{84} +(-4.10161 + 6.69565i) q^{85} +(10.9794 + 3.99619i) q^{86} +(1.46011 - 5.37136i) q^{87} +(1.68294 + 0.296747i) q^{88} +(-0.280096 + 0.485141i) q^{89} +(4.13869 + 5.27932i) q^{90} +(-7.46507 - 12.9299i) q^{91} +(0.970612 + 2.66673i) q^{92} +(8.14775 - 5.66127i) q^{93} +(-10.1591 + 8.52448i) q^{94} +(-0.108987 + 4.18796i) q^{95} +(1.72600 - 0.144711i) q^{96} +(2.45704 + 6.75067i) q^{97} +(14.8388 - 8.56719i) q^{98} +(1.78827 - 4.80470i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q + 6 q^{5} - 6 q^{6} + 12 q^{9} - 12 q^{11} + 6 q^{14} + 18 q^{15} + 12 q^{20} - 72 q^{21} - 18 q^{25} - 72 q^{26} + 6 q^{29} + 36 q^{30} + 36 q^{31} + 18 q^{35} - 30 q^{36} - 48 q^{39} - 12 q^{41}+ \cdots - 36 q^{99}+O(q^{100}) \) 108 * q + 6 * q^5 - 6 * q^6 + 12 * q^9 - 12 * q^11 + 6 * q^14 + 18 * q^15 + 12 * q^20 - 72 * q^21 - 18 * q^25 - 72 * q^26 + 6 * q^29 + 36 * q^30 + 36 * q^31 + 18 * q^35 - 30 * q^36 - 48 * q^39 - 12 * q^41 - 12 * q^44 - 66 * q^45 + 18 * q^49 - 12 * q^50 + 48 * q^51 - 36 * q^54 - 6 * q^56 - 84 * q^59 + 18 * q^60 - 18 * q^61 + 54 * q^64 - 6 * q^65 - 60 * q^69 - 48 * q^74 + 12 * q^75 - 72 * q^79 - 12 * q^81 - 36 * q^86 - 132 * q^89 + 30 * q^90 - 36 * q^94 - 18 * q^95 - 36 * q^99

Introduction

L-functions

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