LMFDB - Embedded newform 270.2.r.a.113.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [270,2,Mod(23,270)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("270.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(270, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([22, 27])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 270 = 2 \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	270.r (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.15596085457$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.14
Character	$\chi$	$=$	270.113
Dual form			270.2.r.a.227.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.319012 - 1.70242i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.02590 - 0.946439i) q^{5} +(0.466174 - 1.66814i) q^{6} +(-2.76499 - 1.93607i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-2.79646 - 1.08618i) q^{9} +(2.10067 - 0.766269i) q^{10} +(0.0536510 - 0.147405i) q^{11} +(0.609788 - 1.62116i) q^{12} +(0.614250 + 7.02091i) q^{13} +(-2.58573 - 2.16968i) q^{14} +(-0.964951 - 3.75085i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-2.66312 + 0.713580i) q^{17} +(-2.69115 - 1.32578i) q^{18} +(4.34868 - 2.51071i) q^{19} +(2.15947 - 0.580268i) q^{20} +(-4.17806 + 4.08954i) q^{21} +(0.0662941 - 0.142168i) q^{22} +(4.32004 + 6.16966i) q^{23} +(0.748761 - 1.56184i) q^{24} +(3.20851 - 3.83477i) q^{25} +7.04772i q^{26} +(-2.74125 + 4.41425i) q^{27} +(-2.38679 - 2.38679i) q^{28} +(-0.210083 + 0.176281i) q^{29} +(-0.634371 - 3.82068i) q^{30} +(1.75712 - 9.96511i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-0.233830 - 0.138361i) q^{33} +(-2.71517 + 0.478758i) q^{34} +(-7.43394 - 1.30537i) q^{35} +(-2.56536 - 1.55528i) q^{36} +(0.581708 + 2.17096i) q^{37} +(4.55096 - 2.12215i) q^{38} +(12.1485 + 1.19404i) q^{39} +(2.20182 - 0.389850i) q^{40} +(-4.27452 + 5.09418i) q^{41} +(-4.51859 + 3.70984i) q^{42} +(1.49392 + 3.20373i) q^{43} +(0.0784326 - 0.135849i) q^{44} +(-6.69335 + 0.446185i) q^{45} +(3.76588 + 6.52270i) q^{46} +(-1.25741 + 1.79577i) q^{47} +(0.882035 - 1.49064i) q^{48} +(1.50267 + 4.12855i) q^{49} +(3.53052 - 3.54054i) q^{50} +(0.365246 + 4.76138i) q^{51} +(-0.614250 + 7.02091i) q^{52} +(-4.14082 + 4.14082i) q^{53} +(-3.11554 + 4.15853i) q^{54} +(-0.0308185 - 0.349405i) q^{55} +(-2.16968 - 2.58573i) q^{56} +(-2.88700 - 8.20422i) q^{57} +(-0.224648 + 0.157300i) q^{58} +(-8.92905 + 3.24991i) q^{59} +(-0.298963 - 3.86143i) q^{60} +(1.06847 + 6.05962i) q^{61} +(2.61895 - 9.77405i) q^{62} +(5.62926 + 8.41742i) q^{63} +(0.866025 + 0.500000i) q^{64} +(7.88927 + 13.6423i) q^{65} +(-0.220881 - 0.158214i) q^{66} +(-5.61930 + 0.491625i) q^{67} +(-2.74657 + 0.240294i) q^{68} +(11.8815 - 5.38633i) q^{69} +(-7.29189 - 1.94832i) q^{70} +(-6.34096 - 3.66095i) q^{71} +(-2.42005 - 1.77295i) q^{72} +(3.43691 - 12.8267i) q^{73} +(0.390282 + 2.21340i) q^{74} +(-5.50484 - 6.68556i) q^{75} +(4.71859 - 1.71743i) q^{76} +(-0.433730 + 0.303701i) q^{77} +(11.9982 + 2.24831i) q^{78} +(-4.50205 - 5.36533i) q^{79} +(2.22742 - 0.196465i) q^{80} +(6.64041 + 6.07495i) q^{81} +(-4.70224 + 4.70224i) q^{82} +(0.118923 - 1.35929i) q^{83} +(-4.82473 + 3.30190i) q^{84} +(-4.71983 + 3.96611i) q^{85} +(1.20902 + 3.32174i) q^{86} +(0.233085 + 0.413885i) q^{87} +(0.0899741 - 0.128496i) q^{88} +(-2.96196 - 5.13026i) q^{89} +(-6.70677 - 0.138877i) q^{90} +(11.8945 - 20.6019i) q^{91} +(3.18306 + 6.82610i) q^{92} +(-16.4043 - 6.17034i) q^{93} +(-1.40914 + 1.67935i) q^{94} +(6.43374 - 9.20220i) q^{95} +(1.00860 - 1.40810i) q^{96} +(-2.50284 + 1.16709i) q^{97} +(1.13712 + 4.24380i) q^{98} +(-0.310142 + 0.353938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) $ 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Character values

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

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$2$	0.996195	+	0.0871557i	0.704416	+	0.0616284i
$3$	0.319012	−	1.70242i	0.184182	−	0.982892i
$3$	0.319012	−	1.70242i	0.184182	−	0.982892i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	2.02590	−	0.946439i	0.906008	−	0.423260i
$5$	2.02590	−	0.946439i	0.906008	−	0.423260i
$6$	0.466174	−	1.66814i	0.190315	−	0.681014i
$7$	−2.76499	−	1.93607i	−1.04507	−	0.731764i	−0.0808093	−	0.996730i	$-0.525750\pi$
$7$	−2.76499	−	1.93607i	−1.04507	−	0.731764i	−0.964258	+	0.264966i	$0.914639\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	−2.79646	−	1.08618i	−0.932154	−	0.362062i
$10$	2.10067	−	0.766269i	0.664291	−	0.242316i
$11$	0.0536510	−	0.147405i	0.0161764	−	0.0444443i	−0.931342	−	0.364147i	$-0.881361\pi$
$11$	0.0536510	−	0.147405i	0.0161764	−	0.0444443i	0.947518	+	0.319702i	$0.103583\pi$
$12$	0.609788	−	1.62116i	0.176031	−	0.467989i
$13$	0.614250	+	7.02091i	0.170362	+	1.94725i	0.296035	+	0.955177i	$0.404335\pi$
$13$	0.614250	+	7.02091i	0.170362	+	1.94725i	−0.125673	+	0.992072i	$0.540109\pi$
$14$	−2.58573	−	2.16968i	−0.691065	−	0.579872i
$15$	−0.964951	−	3.75085i	−0.249149	−	0.968465i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	−2.66312	+	0.713580i	−0.645900	+	0.173068i	−0.566875	−	0.823804i	$-0.691848\pi$
$17$	−2.66312	+	0.713580i	−0.645900	+	0.173068i	−0.0790258	+	0.996873i	$0.525181\pi$
$18$	−2.69115	−	1.32578i	−0.634311	−	0.312489i
$19$	4.34868	−	2.51071i	0.997656	−	0.575997i	0.0901018	−	0.995933i	$-0.471281\pi$
$19$	4.34868	−	2.51071i	0.997656	−	0.575997i	0.907554	+	0.419936i	$0.137947\pi$
$20$	2.15947	−	0.580268i	0.482871	−	0.129752i
$21$	−4.17806	+	4.08954i	−0.911727	+	0.892411i
$22$	0.0662941	−	0.142168i	0.0141339	−	0.0303103i
$23$	4.32004	+	6.16966i	0.900792	+	1.28646i	0.957607	+	0.288079i	$0.0930165\pi$
$23$	4.32004	+	6.16966i	0.900792	+	1.28646i	−0.0568151	+	0.998385i	$0.518095\pi$
$24$	0.748761	−	1.56184i	0.152840	−	0.318810i
$25$	3.20851	−	3.83477i	0.641701	−	0.766955i
$26$			7.04772i			1.38217i
$27$	−2.74125	+	4.41425i	−0.527553	+	0.849522i
$28$	−2.38679	−	2.38679i	−0.451060	−	0.451060i
$29$	−0.210083	+	0.176281i	−0.0390115	+	0.0327345i	−0.662085	−	0.749429i	$-0.730328\pi$
$29$	−0.210083	+	0.176281i	−0.0390115	+	0.0327345i	0.623073	+	0.782163i	$0.285884\pi$
$30$	−0.634371	−	3.82068i	−0.115820	−	0.697557i
$31$	1.75712	−	9.96511i	0.315588	−	1.78979i	−0.253317	−	0.967383i	$-0.581521\pi$
$31$	1.75712	−	9.96511i	0.315588	−	1.78979i	0.568904	−	0.822404i	$-0.307367\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$	−0.233830	−	0.138361i	−0.0407045	−	0.0240855i
$34$	−2.71517	+	0.478758i	−0.465649	+	0.0821064i
$35$	−7.43394	−	1.30537i	−1.25657	−	0.220648i
$36$	−2.56536	−	1.55528i	−0.427561	−	0.259214i
$37$	0.581708	+	2.17096i	0.0956322	+	0.356904i	0.997115	−	0.0759117i	$-0.0241867\pi$
$37$	0.581708	+	2.17096i	0.0956322	+	0.356904i	−0.901482	+	0.432816i	$0.857520\pi$
$38$	4.55096	−	2.12215i	0.738262	−	0.344257i
$39$	12.1485	+	1.19404i	1.94531	+	0.191200i
$40$	2.20182	−	0.389850i	0.348139	−	0.0616407i
$41$	−4.27452	+	5.09418i	−0.667568	+	0.795577i	−0.988451	−	0.151542i	$-0.951576\pi$
$41$	−4.27452	+	5.09418i	−0.667568	+	0.795577i	0.320883	+	0.947119i	$0.396020\pi$
$42$	−4.51859	+	3.70984i	−0.697233	+	0.572440i
$43$	1.49392	+	3.20373i	0.227821	+	0.488564i	0.986676	−	0.162695i	$-0.0520187\pi$
$43$	1.49392	+	3.20373i	0.227821	+	0.488564i	−0.758855	+	0.651260i	$0.774241\pi$
$44$	0.0784326	−	0.135849i	0.0118242	−	0.0204800i
$45$	−6.69335	+	0.446185i	−0.997786	+	0.0665133i
$46$	3.76588	+	6.52270i	0.555249	+	0.961720i
$47$	−1.25741	+	1.79577i	−0.183413	+	0.261940i	−0.900321	−	0.435228i	$-0.856668\pi$
$47$	−1.25741	+	1.79577i	−0.183413	+	0.261940i	0.716908	+	0.697168i	$0.245557\pi$
$48$	0.882035	−	1.49064i	0.127311	−	0.215156i
$49$	1.50267	+	4.12855i	0.214667	+	0.589792i
$50$	3.53052	−	3.54054i	0.499291	−	0.500708i
$51$	0.365246	+	4.76138i	0.0511446	+	0.666726i
$52$	−0.614250	+	7.02091i	−0.0851811	+	0.973624i
$53$	−4.14082	+	4.14082i	−0.568786	+	0.568786i	−0.931788	−	0.363002i	$-0.881752\pi$
$53$	−4.14082	+	4.14082i	−0.568786	+	0.568786i	0.363002	+	0.931788i	$0.381752\pi$
$54$	−3.11554	+	4.15853i	−0.423972	+	0.565905i
$55$	−0.0308185	−	0.349405i	−0.00415556	−	0.0471137i
$56$	−2.16968	−	2.58573i	−0.289936	−	0.345532i
$57$	−2.88700	−	8.20422i	−0.382393	−	1.08668i
$58$	−0.224648	+	0.157300i	−0.0294977	+	0.0206545i
$59$	−8.92905	+	3.24991i	−1.16246	+	0.423102i	−0.849977	−	0.526820i	$-0.823384\pi$
$59$	−8.92905	+	3.24991i	−1.16246	+	0.423102i	−0.312486	+	0.949922i	$0.601162\pi$
$60$	−0.298963	−	3.86143i	−0.0385960	−	0.498508i
$61$	1.06847	+	6.05962i	0.136804	+	0.775855i	0.973586	+	0.228319i	$0.0733229\pi$
$61$	1.06847	+	6.05962i	0.136804	+	0.775855i	−0.836782	+	0.547536i	$0.815566\pi$
$62$	2.61895	−	9.77405i	0.332607	−	1.24131i
$63$	5.62926	+	8.41742i	0.709220	+	1.06050i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	7.88927	+	13.6423i	0.978543	+	1.69212i
$66$	−0.220881	−	0.158214i	−0.0271886	−	0.0194748i
$67$	−5.61930	+	0.491625i	−0.686506	+	0.0600615i	−0.425072	−	0.905160i	$-0.639751\pi$
$67$	−5.61930	+	0.491625i	−0.686506	+	0.0600615i	−0.261435	+	0.965221i	$0.584196\pi$
$68$	−2.74657	+	0.240294i	−0.333070	+	0.0291399i
$69$	11.8815	−	5.38633i	1.43036	−	0.648438i
$70$	−7.29189	−	1.94832i	−0.871547	−	0.232868i
$71$	−6.34096	−	3.66095i	−0.752533	−	0.434475i	0.0740754	−	0.997253i	$-0.476399\pi$
$71$	−6.34096	−	3.66095i	−0.752533	−	0.434475i	−0.826608	+	0.562778i	$0.809733\pi$
$72$	−2.42005	−	1.77295i	−0.285206	−	0.208944i
$73$	3.43691	−	12.8267i	0.402260	−	1.50125i	−0.406795	−	0.913520i	$-0.633354\pi$
$73$	3.43691	−	12.8267i	0.402260	−	1.50125i	0.809054	−	0.587734i	$-0.199980\pi$
$74$	0.390282	+	2.21340i	0.0453694	+	0.257303i
$75$	−5.50484	−	6.68556i	−0.635644	−	0.771982i
$76$	4.71859	−	1.71743i	0.541260	−	0.197002i
$77$	−0.433730	+	0.303701i	−0.0494281	+	0.0346100i
$78$	11.9982	+	2.24831i	1.35853	+	0.254571i
$79$	−4.50205	−	5.36533i	−0.506520	−	0.603647i	0.450819	−	0.892615i	$-0.351132\pi$
$79$	−4.50205	−	5.36533i	−0.506520	−	0.603647i	−0.957339	+	0.288969i	$0.906688\pi$
$80$	2.22742	−	0.196465i	0.249033	−	0.0219654i
$81$	6.64041	+	6.07495i	0.737823	+	0.674994i
$82$	−4.70224	+	4.70224i	−0.519276	+	0.519276i
$83$	0.118923	−	1.35929i	0.0130535	−	0.149202i	−0.986871	−	0.161512i	$-0.948363\pi$
$83$	0.118923	−	1.35929i	0.0130535	−	0.149202i	0.999924	+	0.0123101i	$0.00391853\pi$
$84$	−4.82473	+	3.30190i	−0.526421	+	0.360267i
$85$	−4.71983	+	3.96611i	−0.511938	+	0.430186i
$86$	1.20902	+	3.32174i	0.130372	+	0.358193i
$87$	0.233085	+	0.413885i	0.0249893	+	0.0443732i
$88$	0.0899741	−	0.128496i	0.00959128	−	0.0136978i
$89$	−2.96196	−	5.13026i	−0.313967	−	0.543806i	0.665251	−	0.746620i	$-0.268325\pi$
$89$	−2.96196	−	5.13026i	−0.313967	−	0.543806i	−0.979217	+	0.202814i	$0.934991\pi$
$90$	−6.70677	−	0.138877i	−0.706955	−	0.0146389i
$91$	11.8945	−	20.6019i	1.24689	−	2.15967i
$92$	3.18306	+	6.82610i	0.331857	+	0.711670i
$93$	−16.4043	−	6.17034i	−1.70104	−	0.639835i
$94$	−1.40914	+	1.67935i	−0.145342	+	0.173212i
$95$	6.43374	−	9.20220i	0.660087	−	0.944126i
$96$	1.00860	−	1.40810i	0.102939	−	0.143713i
$97$	−2.50284	+	1.16709i	−0.254125	+	0.118500i	−0.545507	−	0.838106i	$-0.683663\pi$
$97$	−2.50284	+	1.16709i	−0.254125	+	0.118500i	0.291382	+	0.956607i	$0.405885\pi$
$98$	1.13712	+	4.24380i	0.114867	+	0.428689i
$99$	−0.310142	+	0.353938i	−0.0311705	+	0.0355721i
$100$	3.82566	−	3.21936i	0.382566	−	0.321936i
$101$	2.36001	−	0.416133i	0.234829	−	0.0414068i	−0.0549949	−	0.998487i	$-0.517514\pi$
$101$	2.36001	−	0.416133i	0.234829	−	0.0414068i	0.289824	+	0.957080i	$0.406403\pi$
$102$	−0.0511259	+	4.77509i	−0.00506222	+	0.472805i
$103$	−9.34600	−	4.35811i	−0.920889	−	0.429417i	−0.0964301	−	0.995340i	$-0.530742\pi$
$103$	−9.34600	−	4.35811i	−0.920889	−	0.429417i	−0.824459	+	0.565922i	$0.808520\pi$
$104$	−1.22382	+	6.94065i	−0.120006	+	0.680587i
$105$	−4.59381	+	12.2393i	−0.448310	+	1.19443i
$106$	−4.48596	+	3.76417i	−0.435715	+	0.365608i
$107$	−6.46061	−	6.46061i	−0.624571	−	0.624571i	0.322126	−	0.946697i	$-0.395603\pi$
$107$	−6.46061	−	6.46061i	−0.624571	−	0.624571i	−0.946697	+	0.322126i	$0.895603\pi$
$108$	−3.46613	+	3.87117i	−0.333528	+	0.372504i
$109$		−	6.23309i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$109$		−	6.23309i		−	0.597022i	0.954406	−	0.298511i	$-0.0964899\pi$
$110$	−0.000248601	−	0.350761i	−2.37032e−5	−	0.0334438i
$111$	3.88146	−	0.297747i	0.368412	−	0.0282609i
$112$	−1.93607	−	2.76499i	−0.182941	−	0.261267i
$113$	−2.95310	+	6.33293i	−0.277804	+	0.595752i	−0.994860	−	0.101263i	$-0.967711\pi$
$113$	−2.95310	+	6.33293i	−0.277804	+	0.595752i	0.717056	+	0.697016i	$0.245489\pi$
$114$	−2.16097	−	8.42462i	−0.202393	−	0.789038i
$115$	14.5912	+	8.41043i	1.36063	+	0.784277i
$116$	−0.237502	+	0.137122i	−0.0220515	+	0.0127315i
$117$	5.90827	−	20.3009i	0.546220	−	1.87682i
$118$	−9.17832	+	2.45932i	−0.844933	+	0.226399i
$119$	8.74502	+	3.18293i	0.801655	+	0.291778i
$120$	0.0387200	−	3.87279i	0.00353464	−	0.353536i
$121$	8.40764	+	7.05485i	0.764331	+	0.641350i
$122$	0.536278	+	6.12968i	0.0485523	+	0.554955i
$123$	7.30880	+	8.90213i	0.659012	+	0.802678i
$124$	3.46085	−	9.50860i	0.310793	−	0.853898i
$125$	2.87072	−	10.8055i	0.256765	−	0.966474i
$126$	4.87421	+	8.87601i	0.434229	+	0.790738i
$127$	8.32416	+	2.23045i	0.738650	+	0.197921i	0.608478	−	0.793571i	$-0.291780\pi$
$127$	8.32416	+	2.23045i	0.738650	+	0.197921i	0.130172	+	0.991491i	$0.458447\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$	5.93067	−	1.52126i	0.522167	−	0.133939i
$130$	6.67024	+	14.2780i	0.585019	+	1.25226i
$131$	5.40876	+	0.953710i	0.472565	+	0.0833260i	0.404859	−	0.914379i	$-0.367321\pi$
$131$	5.40876	+	0.953710i	0.472565	+	0.0833260i	0.0677067	+	0.997705i	$0.478432\pi$
$132$	−0.206251	−	0.176863i	−0.0179519	−	0.0153939i
$133$	−16.8849	−	1.47724i	−1.46411	−	0.128093i
$134$	−5.64076			−0.487287
$135$	−1.37567	+	11.5372i	−0.118398	+	0.992966i
$136$	−2.75706			−0.236416
$137$	−15.3849	−	1.34600i	−1.31442	−	0.114997i	−0.591710	−	0.806151i	$-0.701547\pi$
$137$	−15.3849	−	1.34600i	−1.31442	−	0.114997i	−0.722707	+	0.691154i	$0.757102\pi$
$138$	12.3057	−	4.33029i	1.04753	−	0.368619i
$139$	12.2294	+	2.15638i	1.03729	+	0.182902i	0.666259	−	0.745720i	$-0.267894\pi$
$139$	12.2294	+	2.15638i	1.03729	+	0.182902i	0.371028	+	0.928622i	$0.379005\pi$
$140$	−7.09433	−	2.57643i	−0.599580	−	0.217748i
$141$	2.65603	+	2.71352i	0.223678	+	0.228520i
$142$	−5.99775	−	4.19967i	−0.503320	−	0.352429i
$143$	1.06787	+	0.286135i	0.0892999	+	0.0239278i
$144$	−2.25632	−	1.97713i	−0.188027	−	0.164761i
$145$	−0.258768	+	0.555957i	−0.0214895	+	0.0461698i
$146$	4.54175	−	12.4784i	0.375878	−	1.03272i
$147$	7.50788	−	1.24111i	0.619240	−	0.102365i
$148$	0.195887	+	2.23899i	0.0161018	+	0.184044i
$149$	5.77544	+	4.84617i	0.473143	+	0.397014i	0.847939	−	0.530093i	$-0.177843\pi$
$149$	5.77544	+	4.84617i	0.473143	+	0.397014i	−0.374797	+	0.927107i	$0.622288\pi$
$150$	−4.90121	−	7.13990i	−0.400182	−	0.582970i
$151$	7.50644	+	2.73212i	0.610865	+	0.222337i	0.628882	−	0.777501i	$-0.283513\pi$
$151$	7.50644	+	2.73212i	0.610865	+	0.222337i	−0.0180166	+	0.999838i	$0.505735\pi$
$152$	4.85032	−	1.29964i	0.393413	−	0.105415i
$153$	8.22238	+	0.897137i	0.664740	+	0.0725292i
$154$	−0.458549	+	0.264743i	−0.0369509	+	0.0213336i
$155$	−5.87164	−	21.8513i	−0.471621	−	1.75514i
$156$	11.7566	+	3.28546i	0.941279	+	0.263048i
$157$	4.08417	−	8.75854i	0.325952	−	0.699007i	−0.673230	−	0.739433i	$-0.735094\pi$
$157$	4.08417	−	8.75854i	0.325952	−	0.699007i	0.999183	+	0.0404258i	$0.0128714\pi$
$158$	−4.01729	−	5.73729i	−0.319599	−	0.456434i
$159$	5.72844	+	8.37039i	0.454295	+	0.663815i
$160$	2.23607	−	0.00158481i	0.176777	−	0.000125290i
$161$		−	25.4229i		−	2.00361i
$162$	6.08567	+	6.63058i	0.478135	+	0.520948i
$163$	−10.1046	−	10.1046i	−0.791450	−	0.791450i	0.190280	−	0.981730i	$-0.439060\pi$
$163$	−10.1046	−	10.1046i	−0.791450	−	0.791450i	−0.981730	+	0.190280i	$0.939060\pi$
$164$	−5.09418	+	4.27452i	−0.397788	+	0.333784i
$165$	−0.604665	−	0.0589983i	−0.0470731	−	0.00459301i
$166$	0.236940	−	1.34376i	0.0183901	−	0.104296i
$167$	6.46401	+	3.01422i	0.500200	+	0.233247i	0.656308	−	0.754493i	$-0.272117\pi$
$167$	6.46401	+	3.01422i	0.500200	+	0.233247i	−0.156108	+	0.987740i	$0.549895\pi$
$168$	−5.09415	+	2.86883i	−0.393022	+	0.221335i
$169$	−36.1133	+	6.36775i	−2.77795	+	0.489827i
$170$	−5.04754	+	3.53966i	−0.387129	+	0.271480i
$171$	−14.8880	+	2.29764i	−1.13852	+	0.175705i
$172$	0.914906	+	3.41448i	0.0697609	+	0.260351i
$173$	19.2728	−	8.98704i	1.46528	−	0.683272i	0.483862	−	0.875144i	$-0.339234\pi$
$173$	19.2728	−	8.98704i	1.46528	−	0.683272i	0.981420	+	0.191872i	$0.0614558\pi$
$174$	0.196125	+	0.432625i	0.0148682	+	0.0327972i
$175$	−16.2959	+	4.39123i	−1.23185	+	0.331946i
$176$	0.100831	−	0.120166i	0.00760042	−	0.00905783i
$177$	2.68423	+	16.2377i	0.201759	+	1.22050i
$178$	−2.50355	−	5.36889i	−0.187649	−	0.402415i
$179$	5.20501	−	9.01535i	0.389041	−	0.673839i	−0.603280	−	0.797530i	$-0.706140\pi$
$179$	5.20501	−	9.01535i	0.389041	−	0.673839i	0.992321	+	0.123691i	$0.0394731\pi$
$180$	−6.66914	−	0.722882i	−0.497088	−	0.0538804i
$181$	−0.473902	−	0.820822i	−0.0352248	−	0.0610112i	0.847876	−	0.530195i	$-0.177881\pi$
$181$	−0.473902	−	0.820822i	−0.0352248	−	0.0610112i	−0.883100	+	0.469184i	$0.844548\pi$
$182$	13.6449	−	19.4869i	1.01142	−	1.44446i
$183$	10.6569	+	0.114101i	0.787778	+	0.00843457i
$184$	2.57602	+	7.07755i	0.189906	+	0.521764i
$185$	3.23316	+	3.84759i	0.237707	+	0.282881i
$186$	−15.8041	−	7.57659i	−1.15881	−	0.555542i
$187$	−0.0376937	+	0.430841i	−0.00275644	+	0.0315062i
$188$	−1.55014	+	1.55014i	−0.113056	+	0.113056i
$189$	16.1258	−	6.89810i	1.17298	−	0.501763i
$190$	7.21128	−	8.60645i	0.523161	−	0.624377i
$191$	−1.20750	−	1.43904i	−0.0873714	−	0.104125i	0.720588	−	0.693364i	$-0.243872\pi$
$191$	−1.20750	−	1.43904i	−0.0873714	−	0.104125i	−0.807959	+	0.589239i	$0.799428\pi$
$192$	1.12748	−	1.31483i	0.0813690	−	0.0948898i
$193$	−6.75391	+	4.72914i	−0.486157	+	0.340411i	−0.790820	−	0.612049i	$-0.790345\pi$
$193$	−6.75391	+	4.72914i	−0.486157	+	0.340411i	0.304662	+	0.952460i	$0.401456\pi$
$194$	−2.59504	+	0.944516i	−0.186313	+	0.0678123i
$195$	25.7416	−	9.07879i	1.84340	−	0.650146i
$196$	0.762924	+	4.32676i	0.0544946	+	0.309054i
$197$	−2.78731	+	10.4024i	−0.198588	+	0.741139i	0.792721	+	0.609584i	$0.208664\pi$
$197$	−2.78731	+	10.4024i	−0.198588	+	0.741139i	−0.991309	+	0.131555i	$0.958003\pi$
$198$	−0.339810	+	0.325560i	−0.0241492	+	0.0231366i
$199$	0.415328	+	0.239790i	0.0294419	+	0.0169983i	0.514649	−	0.857401i	$-0.327922\pi$
$199$	0.415328	+	0.239790i	0.0294419	+	0.0169983i	−0.485207	+	0.874399i	$0.661256\pi$
$200$	4.09169	−	2.87369i	0.289326	−	0.203200i
$201$	−0.955672	+	9.72323i	−0.0674079	+	0.685824i
$202$	2.38729	−	0.208861i	0.167969	−	0.0146954i
$203$	0.922169	−	0.0806793i	0.0647236	−	0.00566258i
$204$	−0.467108	+	4.75247i	−0.0327041	+	0.332739i
$205$	−3.83841	+	14.3658i	−0.268086	+	1.00335i
$206$	−8.93060	−	5.15608i	−0.622224	−	0.359241i
$207$	−5.37945	−	21.9456i	−0.373897	−	1.52532i
$208$	−1.82409	+	6.80758i	−0.126478	+	0.472021i
$209$	−0.136780	−	0.775720i	−0.00946129	−	0.0536576i
$210$	−5.64305	+	11.7923i	−0.389408	+	0.813747i
$211$	−10.9492	+	3.98519i	−0.753775	+	0.274352i	−0.690193	−	0.723625i	$-0.742474\pi$
$211$	−10.9492	+	3.98519i	−0.753775	+	0.274352i	−0.0635814	+	0.997977i	$0.520252\pi$
$212$	−4.79696	+	3.35887i	−0.329457	+	0.230688i
$213$	−8.25532	+	9.62708i	−0.565645	+	0.659636i
$214$	−5.87295	−	6.99910i	−0.401466	−	0.478449i
$215$	6.05867	+	5.07652i	0.413198	+	0.346215i
$216$	−3.79033	+	3.55435i	−0.257899	+	0.241843i
$217$	−24.1515	+	24.1515i	−1.63951	+	1.63951i
$218$	0.543250	−	6.20937i	0.0367935	−	0.420552i
$219$	−20.7400	−	9.94293i	−1.40148	−	0.671881i
$220$	0.0303232	−	0.349448i	0.00204439	−	0.0235598i
$221$	−6.64579	−	18.2592i	−0.447044	−	1.22824i
$222$	3.89264	+	0.0416777i	0.261257	+	0.00279722i
$223$	8.17360	−	11.6731i	0.547345	−	0.781689i	−0.446224	−	0.894921i	$-0.647232\pi$
$223$	8.17360	−	11.6731i	0.547345	−	0.781689i	0.993569	+	0.113232i	$0.0361204\pi$
$224$	−1.68771	−	2.92321i	−0.112765	−	0.195315i
$225$	−13.1377	+	7.23877i	−0.875849	+	0.482585i
$226$	−3.49381	+	6.05146i	−0.232405	+	0.402537i
$227$	1.26293	+	2.70835i	0.0838233	+	0.179760i	0.943752	−	0.330655i	$-0.107270\pi$
$227$	1.26293	+	2.70835i	0.0838233	+	0.179760i	−0.859928	+	0.510415i	$0.829492\pi$
$228$	−1.41849	−	8.58091i	−0.0939420	−	0.568284i
$229$	8.45187	−	10.0725i	0.558515	−	0.665612i	−0.410716	−	0.911763i	$-0.634721\pi$
$229$	8.45187	−	10.0725i	0.558515	−	0.665612i	0.969232	+	0.246151i	$0.0791658\pi$
$230$	13.8026	+	9.65013i	0.910118	+	0.636311i
$231$	0.378661	+	0.835275i	0.0249141	+	0.0549571i
$232$	−0.248550	+	0.115901i	−0.0163181	+	0.00760925i
$233$	2.54408	+	9.49465i	0.166668	+	0.622015i	0.997822	+	0.0659714i	$0.0210146\pi$
$233$	2.54408	+	9.49465i	0.166668	+	0.622015i	−0.831153	+	0.556044i	$0.812319\pi$
$234$	7.65513	−	19.7087i	0.500432	−	1.28840i
$235$	−0.847799	+	4.82812i	−0.0553043	+	0.314952i
$236$	−9.35774	+	1.65002i	−0.609137	+	0.107407i
$237$	−10.5702	+	5.95276i	−0.686611	+	0.386674i
$238$	8.43433	+	3.93299i	0.546716	+	0.254938i
$239$	−1.34900	+	7.65056i	−0.0872595	+	0.494873i	0.909587	+	0.415514i	$0.136398\pi$
$239$	−1.34900	+	7.65056i	−0.0872595	+	0.494873i	−0.996846	+	0.0793589i	$0.974713\pi$
$240$	0.376109	−	3.85468i	0.0242777	−	0.248818i
$241$	10.5110	−	8.81980i	0.677075	−	0.568133i	−0.238075	−	0.971247i	$-0.576516\pi$
$241$	10.5110	−	8.81980i	0.677075	−	0.568133i	0.915150	+	0.403114i	$0.132072\pi$
$242$	7.76078	+	7.76078i	0.498882	+	0.498882i
$243$	12.4605	−	9.36677i	0.799340	−	0.600879i
$244$			6.15310i			0.393912i
$245$	6.95167	+	6.94182i	0.444126	+	0.443496i
$246$	6.50512	+	9.50526i	0.414751	+	0.606033i
$247$	20.2986	+	28.9895i	1.29157	+	1.84456i
$248$	4.27641	−	9.17078i	0.271552	−	0.582345i
$249$	−2.27615	−	0.636087i	−0.144245	−	0.0403104i
$250$	3.80155	−	10.5142i	0.240431	−	0.664976i
$251$	−16.4462	+	9.49521i	−1.03807	+	0.599333i	−0.919287	−	0.393587i	$-0.871234\pi$
$251$	−16.4462	+	9.49521i	−1.03807	+	0.599333i	−0.118787	+	0.992920i	$0.537901\pi$
$252$	4.08207	+	9.26705i	0.257146	+	0.583769i
$253$	1.14121	−	0.305787i	0.0717475	−	0.0192247i
$254$	8.09809	+	2.94746i	0.508119	+	0.184940i
$255$	5.24631	+	9.30037i	0.328536	+	0.582412i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−0.998091	−	11.4082i	−0.0622592	−	0.711626i	−0.961614	−	0.274406i	$-0.911519\pi$
$257$	−0.998091	−	11.4082i	−0.0622592	−	0.711626i	0.899355	−	0.437220i	$-0.144037\pi$
$258$	6.04069	−	0.998575i	0.376077	−	0.0621686i
$259$	2.59471	−	7.12891i	0.161228	−	0.442969i
$260$	5.40045	+	14.8050i	0.334922	+	0.918165i
$261$	0.778963	−	0.264773i	0.0482166	−	0.0163891i
$262$	5.30506	+	1.42149i	0.327747	+	0.0878196i
$263$	−6.53529	−	4.57606i	−0.402983	−	0.282172i	0.354462	−	0.935070i	$-0.384664\pi$
$263$	−6.53529	−	4.57606i	−0.402983	−	0.282172i	−0.757445	+	0.652899i	$0.773553\pi$
$264$	−0.190052	−	0.194166i	−0.0116969	−	0.0119501i
$265$	−4.46984	+	12.3079i	−0.274580	+	0.756069i
$266$	−16.6919	−	2.94324i	−1.02345	−	0.180462i
$267$	−9.67875	+	3.40588i	−0.592330	+	0.208436i
$268$	−5.61930	−	0.491625i	−0.343253	−	0.0300308i
$269$	23.8729			1.45556			0.727780	−	0.685811i	$-0.240552\pi$
$269$	23.8729			1.45556			0.727780	+	0.685811i	$0.240552\pi$
$270$	−2.37597	+	11.3734i	−0.144597	+	0.692165i
$271$	−13.7477			−0.835112			−0.417556	−	0.908651i	$-0.637113\pi$
$271$	−13.7477			−0.835112			−0.417556	+	0.908651i	$0.637113\pi$
$272$	−2.74657	−	0.240294i	−0.166535	−	0.0145699i
$273$	−31.2786	−	26.8218i	−1.89307	−	1.62333i
$274$	−15.2090	−	2.68176i	−0.918809	−	0.162011i
$275$	−0.393125	−	0.678689i	−0.0237063	−	0.0409265i
$276$	12.6363	−	3.24130i	0.760617	−	0.195103i
$277$	17.3388	+	12.1407i	1.04179	+	0.729467i	0.963566	−	0.267469i	$-0.0861874\pi$
$277$	17.3388	+	12.1407i	1.04179	+	0.729467i	0.0782202	+	0.996936i	$0.475076\pi$
$278$	11.9950	+	3.21404i	0.719410	+	0.192765i
$279$	−15.7377	+	25.9585i	−0.942190	+	1.55410i
$280$	−6.84278	−	3.18494i	−0.408935	−	0.190337i
$281$	−8.31974	+	22.8583i	−0.496314	+	1.36361i	0.398498	+	0.917169i	$0.369532\pi$
$281$	−8.31974	+	22.8583i	−0.496314	+	1.36361i	−0.894812	+	0.446443i	$0.852691\pi$
$282$	2.40942	+	2.93468i	0.143479	+	0.174758i
$283$	0.696445	+	7.96040i	0.0413993	+	0.473197i	0.988390	+	0.151936i	$0.0485509\pi$
$283$	0.696445	+	7.96040i	0.0413993	+	0.473197i	−0.946991	+	0.321260i	$0.895894\pi$
$284$	−5.60890	−	4.70643i	−0.332827	−	0.279275i
$285$	−13.6136	−	13.8885i	−0.806398	−	0.822685i
$286$	1.03887	+	0.378118i	0.0614297	+	0.0223586i
$287$	21.6817	−	5.80958i	1.27983	−	0.342929i
$288$	−2.07541	−	2.16625i	−0.122295	−	0.127648i
$289$	−8.13944	+	4.69931i	−0.478791	+	0.276430i
$290$	−0.306238	+	0.531289i	−0.0179829	+	0.0311984i
$291$	1.18845	+	4.63320i	0.0696679	+	0.271603i
$292$	5.61203	−	12.0350i	0.328419	−	0.704297i
$293$	7.63355	+	10.9018i	0.445957	+	0.636892i	0.977698	−	0.210014i	$-0.0673511\pi$
$293$	7.63355	+	10.9018i	0.445957	+	0.636892i	−0.531741	+	0.846907i	$0.678462\pi$
$294$	7.58748	−	0.582036i	0.442511	−	0.0339450i
$295$	−15.0135	+	15.0348i	−0.874119	+	0.875358i
$296$			2.24755i			0.130636i
$297$	0.503611	+	0.640902i	0.0292225	+	0.0371889i
$298$	5.33109	+	5.33109i	0.308822	+	0.308822i
$299$	−40.6630	+	34.1203i	−2.35160	+	1.97323i
$300$	−4.26027	−	7.53990i	−0.245967	−	0.435316i
$301$	2.07195	−	11.7506i	0.119425	−	0.677294i
$302$	7.23975	+	3.37595i	0.416601	+	0.194264i
$303$	0.0444382	−	4.15047i	0.00255291	−	0.238438i
$304$	4.94514	−	0.871961i	0.283623	−	0.0500104i
$305$	7.89968	+	11.2649i	0.452334	+	0.645027i
$306$	8.11290	+	1.61035i	0.463784	+	0.0920576i
$307$	−2.83155	−	10.5675i	−0.161605	−	0.603118i	−0.998449	−	0.0556765i	$-0.982268\pi$
$307$	−2.83155	−	10.5675i	−0.161605	−	0.603118i	0.836844	−	0.547442i	$-0.184398\pi$
$308$	−0.479878	+	0.223771i	−0.0273436	+	0.0127505i
$309$	−10.4008	+	14.5205i	−0.591682	+	0.826043i
$310$	−3.94483	−	22.2799i	−0.224051	−	1.26541i
$311$	−2.19146	+	2.61168i	−0.124266	+	0.148095i	−0.824590	−	0.565730i	$-0.808594\pi$
$311$	−2.19146	+	2.61168i	−0.124266	+	0.148095i	0.700324	+	0.713825i	$0.253039\pi$
$312$	11.4255	+	4.29762i	0.646841	+	0.243305i
$313$	−3.50123	−	7.50842i	−0.197901	−	0.424401i	0.782165	−	0.623071i	$-0.214115\pi$
$313$	−3.50123	−	7.50842i	−0.197901	−	0.424401i	−0.980066	+	0.198671i	$0.936338\pi$
$314$	4.83199	−	8.36925i	0.272685	−	0.472304i
$315$	19.3709	+	11.7251i	1.09142	+	0.660633i
$316$	−3.50197	−	6.06559i	−0.197001	−	0.341216i
$317$	17.8751	−	25.5282i	1.00396	−	1.43381i	0.105675	−	0.994401i	$-0.466300\pi$
$317$	17.8751	−	25.5282i	1.00396	−	1.43381i	0.898288	−	0.439407i	$-0.144811\pi$
$318$	4.97712	+	8.83780i	0.279103	+	0.495599i
$319$	0.0147135	+	0.0404250i	0.000823797	+	0.00226336i
$320$	2.22770	+	0.193307i	0.124532	+	0.0108062i
$321$	−13.0597	+	8.93765i	−0.728920	+	0.498851i
$322$	2.21575	−	25.3262i	0.123479	−	1.41137i
$323$	−9.78944	+	9.78944i	−0.544699	+	0.544699i
$324$	5.48462	+	7.13575i	0.304701	+	0.396431i
$325$	28.8944	+	20.1711i	1.60277	+	1.11889i
$326$	−9.18543	−	10.9468i	−0.508734	−	0.606286i
$327$	−10.6113	−	1.98843i	−0.586808	−	0.109961i
$328$	−5.44734	+	3.81427i	−0.300779	+	0.210608i
$329$	6.95347	−	2.53086i	0.383357	−	0.139531i
$330$	−0.597222	−	0.111474i	−0.0328760	−	0.00613643i
$331$	−1.55033	−	8.79236i	−0.0852138	−	0.483272i	−0.997310	−	0.0732958i	$-0.976648\pi$
$331$	−1.55033	−	8.79236i	−0.0852138	−	0.483272i	0.912096	−	0.409976i	$-0.134463\pi$
$332$	0.353155	−	1.31799i	0.0193819	−	0.0723342i
$333$	0.731343	−	6.70286i	0.0400774	−	0.367314i
$334$	6.17670	+	3.56612i	0.337974	+	0.195129i
$335$	−10.9188	+	6.31430i	−0.596558	+	0.344987i
$336$	−5.32480	+	2.41393i	−0.290491	+	0.131691i
$337$	8.64895	−	0.756685i	0.471138	−	0.0412193i	0.150885	−	0.988551i	$-0.451788\pi$
$337$	8.64895	−	0.756685i	0.471138	−	0.0412193i	0.320253	+	0.947332i	$0.396232\pi$
$338$	−36.5309	+	3.19604i	−1.98702	+	0.173842i
$339$	9.83924	+	7.04769i	0.534394	+	0.382778i
$340$	−5.33684	+	3.08627i	−0.289431	+	0.167376i
$341$	−1.37464	−	0.793647i	−0.0744407	−	0.0429784i
$342$	−15.0316	+	0.991321i	−0.812817	+	0.0536045i
$343$	−2.27710	+	8.49824i	−0.122952	+	0.458862i
$344$	0.613833	+	3.48122i	0.0330957	+	0.187695i
$345$	18.9728	−	22.1573i	1.02146	−	1.19291i
$346$	19.9827	−	7.27311i	1.07428	−	0.391005i
$347$	−14.8942	+	10.4291i	−0.799565	+	0.559862i	−0.900411	−	0.435041i	$-0.856734\pi$
$347$	−14.8942	+	10.4291i	−0.799565	+	0.559862i	0.100846	+	0.994902i	$0.467845\pi$
$348$	0.157673	+	0.448072i	0.00845217	+	0.0240192i
$349$	5.55475	+	6.61989i	0.297339	+	0.354355i	0.893943	−	0.448181i	$-0.147928\pi$
$349$	5.55475	+	6.61989i	0.297339	+	0.354355i	−0.596604	+	0.802536i	$0.703484\pi$
$350$	−16.6166	+	2.95424i	−0.888193	+	0.157911i
$351$	−32.6758	−	16.5346i	−1.74411	−	0.882551i
$352$	0.110920	−	0.110920i	0.00591208	−	0.00591208i
$353$	1.11150	−	12.7045i	0.0591590	−	0.676191i	−0.907488	−	0.420078i	$-0.862003\pi$
$353$	1.11150	−	12.7045i	0.0591590	−	0.676191i	0.966647	−	0.256113i	$-0.0824418\pi$
$354$	1.25880	+	16.4099i	0.0669047	+	0.872176i
$355$	−16.3110	−	1.41538i	−0.865697	−	0.0751205i
$356$	−2.02610	−	5.56666i	−0.107383	−	0.295032i
$357$	8.20844	−	13.8723i	0.434437	−	0.734200i
$358$	5.97095	−	8.52740i	0.315574	−	0.450687i
$359$	−13.0182	−	22.5482i	−0.687074	−	1.19005i	−0.972780	−	0.231730i	$-0.925561\pi$
$359$	−13.0182	−	22.5482i	−0.687074	−	1.19005i	0.285706	−	0.958317i	$-0.407772\pi$
$360$	−6.58076	−	1.30138i	−0.346836	−	0.0685890i
$361$	3.10735	−	5.38208i	0.163545	−	0.283267i
$362$	−0.400559	−	0.859001i	−0.0210529	−	0.0451481i
$363$	14.6924	−	12.0627i	0.771153	−	0.633130i
$364$	15.2913	−	18.2235i	0.801483	−	0.955170i
$365$	−5.17689	−	29.2384i	−0.270971	−	1.53041i
$366$	10.6064	+	1.04247i	0.554404	+	0.0544910i
$367$	22.8217	−	10.6419i	1.19128	−	0.555505i	0.277114	−	0.960837i	$-0.410622\pi$
$367$	22.8217	−	10.6419i	1.19128	−	0.555505i	0.914169	+	0.405333i	$0.132844\pi$
$368$	1.94936	+	7.27513i	0.101618	+	0.379242i
$369$	17.4868	−	9.60275i	0.910324	−	0.499899i
$370$	2.88552	+	4.11474i	0.150011	+	0.213915i
$371$	19.4662	−	3.43242i	1.01064	−	0.178202i
$372$	−15.0836	−	8.92517i	−0.782047	−	0.462749i
$373$	−13.0243	−	6.07335i	−0.674375	−	0.314466i	0.0550932	−	0.998481i	$-0.482454\pi$
$373$	−13.0243	−	6.07335i	−0.674375	−	0.314466i	−0.729468	+	0.684015i	$0.760232\pi$
$374$	−0.0751005	+	0.425916i	−0.00388335	+	0.0220236i
$375$	−17.4797	−	8.33425i	−0.902648	−	0.430379i
$376$	−1.67935	+	1.40914i	−0.0866058	+	0.0726709i
$377$	−1.36669	−	1.36669i	−0.0703883	−	0.0703883i
$378$	16.6656	−	5.46640i	0.857187	−	0.281161i
$379$		−	21.2421i		−	1.09113i	−0.838067	−	0.545567i	$-0.816314\pi$
$379$		−	21.2421i		−	1.09113i	0.838067	−	0.545567i	$-0.183686\pi$
$380$	7.93394	−	7.94519i	0.407002	−	0.407580i
$381$	6.45267	−	13.4597i	0.330580	−	0.689560i
$382$	−1.07748	−	1.53880i	−0.0551287	−	0.0787320i
$383$	−12.4126	+	26.6190i	−0.634256	+	1.36017i	0.281939	+	0.959432i	$0.409023\pi$
$383$	−12.4126	+	26.6190i	−0.634256	+	1.36017i	−0.916195	+	0.400734i	$0.868755\pi$
$384$	1.23779	−	1.21156i	0.0631656	−	0.0618273i
$385$	−0.591257	+	1.02577i	−0.0301333	+	0.0522779i
$386$	−7.14039	+	4.12250i	−0.363436	+	0.209830i
$387$	−0.697859	−	10.5818i	−0.0354742	−	0.537903i
$388$	−2.66748	+	0.714749i	−0.135421	+	0.0362859i
$389$	−8.20972	−	2.98809i	−0.416249	−	0.151502i	0.125401	−	0.992106i	$-0.459978\pi$
$389$	−8.20972	−	2.98809i	−0.416249	−	0.151502i	−0.541651	+	0.840604i	$0.682200\pi$
$390$	26.4350	−	6.80071i	1.33859	−	0.344367i
$391$	−15.9073	−	13.3478i	−0.804468	−	0.675029i
$392$	0.382919	+	4.37679i	0.0193403	+	0.221061i
$393$	3.34907	−	8.90373i	0.168938	−	0.449134i
$394$	−3.68333	+	10.1199i	−0.185563	+	0.509831i
$395$	−14.1986	−	6.60868i	−0.714411	−	0.332519i
$396$	−0.366891	+	0.294705i	−0.0184370	+	0.0148095i
$397$	−4.58547	−	1.22867i	−0.230138	−	0.0616653i	0.141907	−	0.989880i	$-0.454677\pi$
$397$	−4.58547	−	1.22867i	−0.230138	−	0.0616653i	−0.372045	+	0.928215i	$0.621343\pi$
$398$	0.392849	+	0.275076i	0.0196917	+	0.0137883i
$399$	−7.90139	+	28.2740i	−0.395564	+	1.41547i
$400$	4.32658	−	2.50614i	0.216329	−	0.125307i
$401$	16.1036	+	2.83951i	0.804178	+	0.141798i	0.560604	−	0.828084i	$-0.310569\pi$
$401$	16.1036	+	2.83951i	0.804178	+	0.141798i	0.243574	+	0.969882i	$0.421680\pi$
$402$	−1.79947	+	9.60294i	−0.0897495	+	0.478951i
$403$	71.0434	+	6.21549i	3.53893	+	0.309616i
$404$	2.39641			0.119226
$405$	19.2023	+	6.02247i	0.954172	+	0.299259i
$406$	0.925691			0.0459413
$407$	0.351220	+	0.0307278i	0.0174093	+	0.00152312i
$408$	−0.879536	+	4.69367i	−0.0435435	+	0.232371i
$409$	2.97423	+	0.524437i	0.147066	+	0.0259317i	0.246696	−	0.969093i	$-0.420655\pi$
$409$	2.97423	+	0.524437i	0.147066	+	0.0259317i	−0.0996304	+	0.995025i	$0.531766\pi$
$410$	−5.07586	+	13.9766i	−0.250679	+	0.690257i
$411$	−7.19941	+	25.7621i	−0.355121	+	1.27075i
$412$	−8.44723	−	5.91482i	−0.416165	−	0.291402i
$413$	30.9807	+	8.30126i	1.52446	+	0.408479i
$414$	−3.44629	−	22.3309i	−0.169376	−	1.09751i
$415$	−1.04556	−	2.86634i	−0.0513247	−	0.140703i
$416$	−2.41046	+	6.62269i	−0.118183	+	0.324704i
$417$	7.57240	−	20.1317i	0.370822	−	0.985854i
$418$	−0.0686514	−	0.784689i	−0.00335785	−	0.0383804i
$419$	28.7021	+	24.0840i	1.40219	+	1.17658i	0.960116	+	0.279601i	$0.0902021\pi$
$419$	28.7021	+	24.0840i	1.40219	+	1.17658i	0.442075	+	0.896978i	$0.354242\pi$
$420$	−6.64935	+	11.2556i	−0.324455	+	0.549218i
$421$	9.12077	+	3.31969i	0.444519	+	0.161792i	0.554575	−	0.832134i	$-0.312881\pi$
$421$	9.12077	+	3.31969i	0.444519	+	0.161792i	−0.110056	+	0.993925i	$0.535103\pi$
$422$	−11.2549	+	3.01573i	−0.547879	+	0.146804i
$423$	5.46685	−	3.65603i	0.265807	−	0.177762i
$424$	−5.07145	+	2.92800i	−0.246291	+	0.142196i
$425$	−5.80820	+	12.5020i	−0.281739	+	0.606435i
$426$	−9.06296	+	8.87094i	−0.439102	+	0.429799i
$427$	8.77750	−	18.8234i	0.424773	−	0.910928i
$428$	−5.24059	−	7.48433i	−0.253313	−	0.361769i
$429$	0.827786	−	1.72668i	0.0399659	−	0.0833651i
$430$	5.59317	+	5.58525i	0.269727	+	0.269344i
$431$			1.48091i			0.0713331i	0.999364	+	0.0356666i	$0.0113554\pi$
$431$			1.48091i			0.0713331i	−0.999364	+	0.0356666i	$0.988645\pi$
$432$	−4.08569	+	3.21047i	−0.196573	+	0.154464i
$433$	−2.84796	−	2.84796i	−0.136864	−	0.136864i	0.635356	−	0.772220i	$-0.280854\pi$
$433$	−2.84796	−	2.84796i	−0.136864	−	0.136864i	−0.772220	+	0.635356i	$0.780854\pi$
$434$	−26.1646	+	21.9547i	−1.25594	+	1.05386i
$435$	0.863923	+	0.617888i	0.0414219	+	0.0296255i
$436$	1.08236	−	6.13840i	0.0518359	−	0.293976i
$437$	34.2767	+	15.9835i	1.63968	+	0.764595i
$438$	−19.7945	−	11.7127i	−0.945819	−	0.559655i
$439$	4.66120	−	0.821895i	0.222467	−	0.0392269i	−0.0613035	−	0.998119i	$-0.519526\pi$
$439$	4.66120	−	0.821895i	0.222467	−	0.0392269i	0.283770	+	0.958892i	$0.408415\pi$
$440$	0.0606642	−	0.345475i	0.00289205	−	0.0164699i
$441$	0.282210	−	13.1775i	0.0134386	−	0.627500i
$442$	−5.02911	−	18.7689i	−0.239210	−	0.892746i
$443$	−23.5424	+	10.9780i	−1.11853	+	0.521580i	−0.891824	−	0.452382i	$-0.850574\pi$
$443$	−23.5424	+	10.9780i	−1.11853	+	0.521580i	−0.226709	+	0.973963i	$0.572797\pi$
$444$	3.87420	+	0.380785i	0.183861	+	0.0180713i
$445$	−10.8561	−	7.59006i	−0.514628	−	0.359803i
$446$	9.15987	−	10.9163i	0.433733	−	0.516902i
$447$	10.0926	−	8.28623i	0.477366	−	0.391925i
$448$	−1.42652	−	3.05918i	−0.0673966	−	0.144532i
$449$	−3.45907	+	5.99129i	−0.163244	+	0.282746i	−0.936030	−	0.351920i	$-0.885529\pi$
$449$	−3.45907	+	5.99129i	−0.163244	+	0.282746i	0.772787	+	0.634666i	$0.218862\pi$
$450$	−13.7186	+	6.06620i	−0.646703	+	0.285963i
$451$	0.521575	+	0.903394i	0.0245600	+	0.0425391i
$452$	−4.00793	+	5.72392i	−0.188517	+	0.269231i
$453$	7.04586	−	11.9075i	0.331043	−	0.559464i
$454$	1.02207	+	2.80812i	0.0479682	+	0.131791i
$455$	4.59860	−	52.9948i	0.215586	−	2.48444i
$456$	−0.665220	−	8.67188i	−0.0311518	−	0.406098i
$457$	1.47692	−	16.8812i	0.0690872	−	0.789671i	−0.880065	−	0.474853i	$-0.842501\pi$
$457$	1.47692	−	16.8812i	0.0690872	−	0.789671i	0.949152	−	0.314818i	$-0.101943\pi$
$458$	9.29758	−	9.29758i	0.434448	−	0.434448i
$459$	4.15034	−	13.7117i	0.193721	−	0.640009i
$460$	12.9090	+	10.8164i	0.601887	+	0.504317i
$461$	24.9242	+	29.7035i	1.16084	+	1.38343i	0.909590	+	0.415507i	$0.136396\pi$
$461$	24.9242	+	29.7035i	1.16084	+	1.38343i	0.251246	+	0.967923i	$0.419160\pi$
$462$	0.304422	+	0.865099i	0.0141630	+	0.0402480i
$463$	19.3367	−	13.5397i	0.898651	−	0.629242i	−0.0302612	−	0.999542i	$-0.509634\pi$
$463$	19.3367	−	13.5397i	0.898651	−	0.629242i	0.928912	+	0.370300i	$0.120745\pi$
$464$	−0.257705	+	0.0937970i	−0.0119637	+	0.00435442i
$465$	−39.0732	+	3.02516i	−1.81197	+	0.140288i
$466$	1.70689	+	9.68025i	0.0790701	+	0.448429i
$467$	4.42576	−	16.5171i	0.204800	−	0.764322i	−0.784711	−	0.619862i	$-0.787189\pi$
$467$	4.42576	−	16.5171i	0.204800	−	0.764322i	0.989511	−	0.144461i	$-0.0461447\pi$
$468$	9.34373	−	18.9665i	0.431914	−	0.876727i
$469$	16.4891	+	9.51999i	0.761396	+	0.439592i
$470$	−1.26537	+	4.73585i	−0.0583672	+	0.218449i
$471$	−13.6078	−	9.74705i	−0.627014	−	0.449120i
$472$	−9.46594	+	0.828162i	−0.435705	+	0.0381193i
$473$	0.552397	−	0.0483284i	0.0253992	−	0.00222214i
$474$	−11.0488	+	5.00885i	−0.507490	+	0.230064i
$475$	4.32475	−	24.7318i	0.198433	−	1.13477i
$476$	8.05945	+	4.65313i	0.369404	+	0.213276i
$477$	16.0774	−	7.08196i	0.736131	−	0.324260i
$478$	−2.01066	+	7.50387i	−0.0919653	+	0.343219i
$479$	−5.73160	−	32.5055i	−0.261884	−	1.48522i	−0.777765	−	0.628555i	$-0.783647\pi$
$479$	−5.73160	−	32.5055i	−0.261884	−	1.48522i	0.515881	−	0.856660i	$-0.327465\pi$
$480$	0.710635	−	3.80723i	0.0324359	−	0.173775i
$481$	−14.8848	+	5.41763i	−0.678689	+	0.247023i
$482$	11.2397	−	7.87014i	0.511955	−	0.358475i
$483$	−43.2805	−	8.11022i	−1.96933	−	0.369028i
$484$	7.05485	+	8.40764i	0.320675	+	0.382165i
$485$	−3.96591	+	4.73320i	−0.180083	+	0.214923i
$486$	13.2294	−	8.24512i	0.600099	−	0.374006i
$487$	−4.51491	+	4.51491i	−0.204590	+	0.204590i	−0.801963	−	0.597373i	$-0.796211\pi$
$487$	−4.51491	+	4.51491i	−0.204590	+	0.204590i	0.597373	+	0.801963i	$0.296211\pi$
$488$	−0.536278	+	6.12968i	−0.0242762	+	0.277478i
$489$	−20.4257	+	13.9787i	−0.923680	+	0.632139i
$490$	6.32019	+	7.52128i	0.285517	+	0.339777i
$491$	0.523591	+	1.43855i	0.0236293	+	0.0649211i	0.950946	−	0.309355i	$-0.100113\pi$
$491$	0.523591	+	1.43855i	0.0236293	+	0.0649211i	−0.927317	+	0.374277i	$0.877891\pi$
$492$	5.65192	+	10.0360i	0.254808	+	0.452460i
$493$	0.433686	−	0.619367i	0.0195322	−	0.0278949i
$494$	17.6948	+	30.6483i	0.796127	+	1.37893i
$495$	−0.293335	+	1.01057i	−0.0131844	+	0.0454218i
$496$	5.05942	−	8.76317i	0.227175	−	0.393478i
$497$	10.4448	+	22.3990i	0.468514	+	1.00473i
$498$	−2.21205	−	0.832046i	−0.0991243	−	0.0372849i
$499$	−11.0899	+	13.2165i	−0.496454	+	0.591651i	−0.954847	−	0.297099i	$-0.903981\pi$
$499$	−11.0899	+	13.2165i	−0.496454	+	0.591651i	0.458393	+	0.888750i	$0.348425\pi$
$500$	4.70346	−	10.1429i	0.210345	−	0.453602i
$501$	7.19355	−	10.0429i	0.321384	−	0.448683i
$502$	−17.2112	+	8.02570i	−0.768172	+	0.358205i
$503$	8.52155	+	31.8029i	0.379957	+	1.41802i	0.845965	+	0.533239i	$0.179025\pi$
$503$	8.52155	+	31.8029i	0.379957	+	1.41802i	−0.466007	+	0.884781i	$0.654308\pi$
$504$	3.25886	+	9.58756i	0.145161	+	0.427064i
$505$	4.38728	−	3.07664i	0.195231	−	0.136909i
$506$	1.16352	−	0.205160i	0.0517249	−	0.00912049i
$507$	−0.680003	+	63.5114i	−0.0302000	+	2.82064i
$508$	7.81038	+	3.64204i	0.346530	+	0.161589i
$509$	5.96465	−	33.8272i	0.264378	−	1.49936i	−0.506421	−	0.862286i	$-0.669032\pi$
$509$	5.96465	−	33.8272i	0.264378	−	1.49936i	0.770800	−	0.637078i	$-0.219857\pi$
$510$	4.41576	+	9.72223i	0.195533	+	0.430508i
$511$	−34.3364	+	28.8116i	−1.51895	+	1.27455i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.837911	+	26.0786i	−0.0369947	+	1.15140i
$514$		−	11.4518i		−	0.505118i
$515$	−23.0587	+	0.0163428i	−1.01609	+	0.000720149i
$516$	6.10474	−	0.468294i	0.268746	−	0.0206155i
$517$	0.197244	+	0.281694i	0.00867480	+	0.0123889i
$518$	3.20616	−	6.87564i	0.140871	−	0.302098i
$519$	−9.15147	−	35.6773i	−0.401705	−	1.56606i
$520$	4.08957	+	15.2193i	0.179339	+	0.667411i
$521$	16.0538	−	9.26867i	0.703330	−	0.406068i	−0.105256	−	0.994445i	$-0.533566\pi$
$521$	16.0538	−	9.26867i	0.703330	−	0.406068i	0.808586	+	0.588377i	$0.200233\pi$
$522$	0.799076	−	0.195875i	0.0349746	−	0.00857320i
$523$	−31.5805	+	8.46196i	−1.38092	+	0.370016i	−0.871454	−	0.490477i	$-0.836823\pi$
$523$	−31.5805	+	8.46196i	−1.38092	+	0.370016i	−0.509463	+	0.860493i	$0.670156\pi$
$524$	5.16098	+	1.87844i	0.225458	+	0.0820601i
$525$	2.27714	+	29.1432i	0.0993823	+	1.27191i
$526$	−6.11159	−	5.12823i	−0.266478	−	0.223601i
$527$	2.43149	+	27.7921i	0.105917	+	1.21064i
$528$	−0.172406	−	0.209991i	−0.00750301	−	0.00913868i
$529$	−11.5355	+	31.6935i	−0.501543	+	1.37798i
$530$	−5.52553	+	11.8715i	−0.240014	+	0.515665i
$531$	28.4997	+	0.610351i	1.23678	+	0.0264870i
$532$	−16.3719	−	4.38684i	−0.709812	−	0.190194i
$533$	−38.3914	−	26.8819i	−1.66291	−	1.16438i
$534$	−9.93876	+	2.54936i	−0.430092	+	0.110321i
$535$	−19.2031	−	6.97395i	−0.830222	−	0.301510i
$536$	−5.55506	−	0.979508i	−0.239942	−	0.0423083i
$537$	−13.6874	−	11.7371i	−0.590657	−	0.506494i
$538$	23.7821	+	2.08066i	1.02532	+	0.0897038i
$539$	0.689188			0.0296854
$540$	−3.35818	+	11.1231i	−0.144513	+	0.478661i
$541$	45.6107			1.96096			0.980479	−	0.196626i	$-0.0629984\pi$
$541$	45.6107			1.96096			0.980479	+	0.196626i	$0.0629984\pi$
$542$	−13.6954	−	1.19819i	−0.588266	−	0.0514666i
$543$	−1.54856	+	0.544927i	−0.0664552	+	0.0233851i
$544$	−2.71517	−	0.478758i	−0.116412	−	0.0205266i
$545$	−5.89924	−	12.6276i	−0.252696	−	0.540907i
$546$	−28.8220	−	29.4458i	−1.23347	−	1.26016i
$547$	−5.72610	−	4.00946i	−0.244830	−	0.171432i	0.444720	−	0.895669i	$-0.353303\pi$
$547$	−5.72610	−	4.00946i	−0.244830	−	0.171432i	−0.689551	+	0.724237i	$0.742192\pi$
$548$	−14.9174	−	3.99710i	−0.637240	−	0.170748i
$549$	3.59392	−	18.1061i	0.153385	−	0.772748i
$550$	−0.332478	−	0.710370i	−0.0141769	−	0.0302903i
$551$	−0.470995	+	1.29405i	−0.0200650	+	0.0551283i
$552$	12.8707	−	2.12764i	0.547815	−	0.0905582i
$553$	2.06047	+	23.5513i	0.0876203	+	1.00150i
$554$	16.2147	+	13.6057i	0.688895	+	0.578052i
$555$	7.58164	−	4.27677i	0.321823	−	0.181539i
$556$	11.6692	+	4.24724i	0.494884	+	0.180123i
$557$	−44.1035	+	11.8175i	−1.86872	+	0.500723i	−0.868738	+	0.495271i	$0.835069\pi$
$557$	−44.1035	+	11.8175i	−1.86872	+	0.500723i	−0.999985	+	0.00545188i	$0.998265\pi$
$558$	−17.9402	+	24.4881i	−0.759470	+	1.03666i
$559$	−21.5754	+	12.4566i	−0.912544	+	0.526858i
$560$	−6.53916	−	3.76921i	−0.276330	−	0.159278i
$561$	0.721447	+	0.201614i	0.0304595	+	0.00851215i
$562$	−10.2803	+	22.0462i	−0.433649	+	0.929963i
$563$	−16.4145	−	23.4423i	−0.691787	−	0.987974i	−0.999336	−	0.0364420i	$-0.988398\pi$
$563$	−16.4145	−	23.4423i	−0.691787	−	0.987974i	0.307549	−	0.951532i	$-0.400491\pi$
$564$	2.14448	+	3.13351i	0.0902989	+	0.131945i
$565$	0.0110740	+	15.6248i	0.000465888	+	0.657340i
$566$			7.99081i			0.335879i
$567$	−6.59914	−	29.6534i	−0.277138	−	1.24533i
$568$	−5.17737	−	5.17737i	−0.217238	−	0.217238i
$569$	10.7604	−	9.02905i	0.451099	−	0.378517i	−0.388744	−	0.921346i	$-0.627091\pi$
$569$	10.7604	−	9.02905i	0.451099	−	0.378517i	0.839844	+	0.542828i	$0.182647\pi$
$570$	−12.3513	−	15.0222i	−0.517339	−	0.629210i
$571$	−2.43093	+	13.7865i	−0.101731	+	0.576947i	0.890744	+	0.454505i	$0.150184\pi$
$571$	−2.43093	+	13.7865i	−0.101731	+	0.576947i	−0.992476	+	0.122442i	$0.960927\pi$
$572$	1.00196	+	0.467222i	0.0418941	+	0.0195355i
$573$	−2.83505	+	1.59659i	−0.118436	+	0.0666987i
$574$	22.1055	−	3.89779i	0.922665	−	0.162691i
$575$	37.5201	+	3.22900i	1.56470	+	0.134659i
$576$	−1.87872	−	2.33889i	−0.0782798	−	0.0974540i
$577$	7.72593	+	28.8336i	0.321635	+	1.20036i	0.917652	+	0.397386i	$0.130082\pi$
$577$	7.72593	+	28.8336i	0.321635	+	1.20036i	−0.596017	+	0.802972i	$0.703251\pi$
$578$	−8.51804	+	3.97203i	−0.354304	+	0.165215i
$579$	5.89640	+	13.0066i	0.245046	+	0.540538i
$580$	−0.351377	+	0.502577i	−0.0145902	+	0.0208684i
$581$	−2.96050	+	3.52819i	−0.122822	+	0.146374i
$582$	0.780114	+	4.71915i	0.0323368	+	0.195615i
$583$	0.388219	+	0.832537i	0.0160784	+	0.0344802i
$584$	6.63960	−	11.5001i	0.274748	−	0.475878i
$585$	−7.24401	−	46.7193i	−0.299503	−	1.93161i
$586$	6.65434	+	11.5257i	0.274888	+	0.476121i
$587$	−18.9349	+	27.0418i	−0.781525	+	1.11613i	0.208880	+	0.977941i	$0.433018\pi$
$587$	−18.9349	+	27.0418i	−0.781525	+	1.11613i	−0.990405	+	0.138193i	$0.955871\pi$
$588$	7.60934	+	0.0814716i	0.313804	+	0.00335983i
$589$	−17.3784	−	47.7467i	−0.716064	−	1.96737i
$590$	−16.2667	+	13.6691i	−0.669690	+	0.562746i
$591$	16.8200	+	8.06365i	0.691883	+	0.331694i
$592$	−0.195887	+	2.23899i	−0.00805089	+	0.0920221i
$593$	−6.32665	+	6.32665i	−0.259804	+	0.259804i	−0.824974	−	0.565170i	$-0.808811\pi$
$593$	−6.32665	+	6.32665i	−0.259804	+	0.259804i	0.565170	+	0.824974i	$0.308811\pi$
$594$	0.445836	+	0.682356i	0.0182929	+	0.0279974i
$595$	20.7289	−	1.82835i	0.849804	−	0.0749551i
$596$	4.84617	+	5.77544i	0.198507	+	0.236571i
$597$	0.540718	−	0.630567i	0.0221301	−	0.0258074i
$598$	−43.4821	+	30.4465i	−1.77811	+	1.24505i
$599$	7.37153	−	2.68302i	0.301193	−	0.109625i	−0.187003	−	0.982359i	$-0.559877\pi$
$599$	7.37153	−	2.68302i	0.301193	−	0.109625i	0.488196	+	0.872734i	$0.337655\pi$
$600$	−3.58692	−	7.88251i	−0.146435	−	0.321802i
$601$	−3.87288	−	21.9642i	−0.157978	−	0.895938i	−0.956012	−	0.293326i	$-0.905238\pi$
$601$	−3.87288	−	21.9642i	−0.157978	−	0.895938i	0.798034	−	0.602612i	$-0.205873\pi$
$602$	3.08820	−	11.5253i	0.125866	−	0.469737i
$603$	16.2481	+	4.72878i	0.661676	+	0.192571i
$604$	6.91797	+	3.99409i	0.281488	+	0.162517i
$605$	23.7100	+	6.33506i	0.963948	+	0.257557i
$606$	0.406006	−	4.13080i	0.0164929	−	0.167802i
$607$	28.1948	−	2.46673i	1.14439	−	0.100121i	0.500852	−	0.865533i	$-0.333020\pi$
$607$	28.1948	−	2.46673i	1.14439	−	0.100121i	0.643541	+	0.765412i	$0.277465\pi$
$608$	5.00232	−	0.437646i	0.202871	−	0.0177489i
$609$	0.156833	−	1.59566i	0.00635519	−	0.0646592i
$610$	6.88781	+	11.9105i	0.278879	+	0.482244i
$611$	−13.3803	−	7.72513i	−0.541310	−	0.312525i
$612$	7.94168	+	2.31131i	0.321023	+	0.0934291i
$613$	6.67128	−	24.8976i	0.269451	−	1.00560i	−0.690019	−	0.723791i	$-0.742398\pi$
$613$	6.67128	−	24.8976i	0.269451	−	1.00560i	0.959470	−	0.281812i	$-0.0909355\pi$
$614$	−1.89976	−	10.7741i	−0.0766679	−	0.434806i
$615$	23.2322	+	11.1175i	0.936812	+	0.448299i
$616$	−0.497555	+	0.181095i	−0.0200471	+	0.00729653i
$617$	−27.4565	+	19.2253i	−1.10536	+	0.773981i	−0.976033	−	0.217622i	$-0.930170\pi$
$617$	−27.4565	+	19.2253i	−1.10536	+	0.773981i	−0.129326	+	0.991602i	$0.541281\pi$
$618$	−11.6268	+	13.5588i	−0.467698	+	0.545414i
$619$	−16.3858	−	19.5278i	−0.658601	−	0.784890i	0.328583	−	0.944475i	$-0.393429\pi$
$619$	−16.3858	−	19.5278i	−0.658601	−	0.784890i	−0.987184	+	0.159585i	$0.948984\pi$
$620$	−1.98800	−	22.5389i	−0.0798399	−	0.905185i
$621$	−39.0767	+	2.15716i	−1.56809	+	0.0865640i
$622$	−2.41074	+	2.41074i	−0.0966620	+	0.0966620i
$623$	−1.74274	+	19.9196i	−0.0698215	+	0.798064i
$624$	11.0074	+	5.27706i	0.440651	+	0.211251i
$625$	−4.41098	−	24.6078i	−0.176439	−	0.984312i
$626$	−2.83351	−	7.78500i	−0.113250	−	0.311151i
$627$	−1.36423	−	0.0146066i	−0.0544823	−	0.000583330i
$628$	5.54303	−	7.91626i	0.221191	−	0.315893i
$629$	−3.09831	−	5.36643i	−0.123538	−	0.213974i
$630$	18.2753	+	13.3687i	0.728103	+	0.532623i
$631$	−5.38398	+	9.32532i	−0.214333	+	0.371235i	−0.953066	−	0.302763i	$-0.902091\pi$
$631$	−5.38398	+	9.32532i	−0.214333	+	0.371235i	0.738733	+	0.673998i	$0.235424\pi$
$632$	−2.95999	−	6.34772i	−0.117742	−	0.252499i
$633$	3.29153	+	19.9115i	0.130826	+	0.791410i
$634$	20.0320	−	23.8732i	0.795571	−	0.948125i
$635$	18.9749	−	3.35965i	0.752995	−	0.133324i
$636$	4.18791	+	9.23796i	0.166062	+	0.366309i
$637$	−28.0631	+	13.0860i	−1.11190	+	0.518488i
$638$	0.0111342	+	0.0415535i	0.000440808	+	0.00164512i
$639$	13.7558	+	17.1252i	0.544170	+	0.677461i
$640$	2.20237	+	0.386728i	0.0870564	+	0.0152868i
$641$	34.5159	−	6.08608i	1.36330	−	0.240386i	0.556319	−	0.830969i	$-0.312213\pi$
$641$	34.5159	−	6.08608i	1.36330	−	0.240386i	0.806977	+	0.590583i	$0.201102\pi$
$642$	−13.7890	+	7.76542i	−0.544206	+	0.306477i
$643$	12.3592	+	5.76318i	0.487398	+	0.227278i	0.650753	−	0.759290i	$-0.274454\pi$
$643$	12.3592	+	5.76318i	0.487398	+	0.227278i	−0.163354	+	0.986567i	$0.552231\pi$
$644$	4.41465	−	25.0367i	0.173961	−	0.986584i
$645$	10.5751	−	8.69493i	0.416396	−	0.342362i
$646$	−10.6054	+	8.89899i	−0.417264	+	0.350126i
$647$	19.4755	+	19.4755i	0.765662	+	0.765662i	0.977340	−	0.211677i	$-0.0678926\pi$
$647$	19.4755	+	19.4755i	0.765662	+	0.765662i	−0.211677	+	0.977340i	$0.567893\pi$
$648$	4.84183	+	7.58661i	0.190205	+	0.298030i
$649$			1.49055i			0.0585091i
$650$	27.0264	+	22.6127i	1.06006	+	0.886942i
$651$	33.4114	+	48.8206i	1.30950	+	1.91343i
$652$	−8.19640	−	11.7057i	−0.320996	−	0.458430i
$653$	18.3431	−	39.3369i	0.717821	−	1.53937i	−0.119604	−	0.992822i	$-0.538163\pi$
$653$	18.3431	−	39.3369i	0.717821	−	1.53937i	0.837426	−	0.546551i	$-0.184060\pi$
$654$	−10.3977	−	2.90570i	−0.406580	−	0.113622i
$655$	11.8602	−	3.18694i	0.463417	−	0.124524i
$656$	−5.75905	+	3.32499i	−0.224853	+	0.129819i
$657$	−23.5434	+	32.1363i	−0.918514	+	1.25376i
$658$	7.14759	−	1.91519i	0.278642	−	0.0746619i
$659$	7.20356	+	2.62188i	0.280611	+	0.102134i	0.478492	−	0.878092i	$-0.341184\pi$
$659$	7.20356	+	2.62188i	0.280611	+	0.102134i	−0.197881	+	0.980226i	$0.563406\pi$
$660$	−0.585233	−	0.163101i	−0.0227802	−	0.00634869i
$661$	0.132252	+	0.110973i	0.00514401	+	0.00431634i	0.645356	−	0.763882i	$-0.276709\pi$
$661$	0.132252	+	0.110973i	0.00514401	+	0.00431634i	−0.640212	+	0.768198i	$0.721153\pi$
$662$	−0.778126	−	8.89402i	−0.0302427	−	0.345676i
$663$	−33.2048	+	5.48903i	−1.28957	+	0.213176i
$664$	0.466682	−	1.28220i	0.0181108	−	0.0497589i
$665$	−35.6053	+	12.9878i	−1.38071	+	0.503647i
$666$	1.31275	−	6.61361i	0.0508681	−	0.256272i
$667$	−1.99516	−	0.534602i	−0.0772530	−	0.0206999i
$668$	5.84239	+	4.09089i	0.226049	+	0.158281i
$669$	−17.2650	−	17.6388i	−0.667505	−	0.681954i
$670$	−11.4276	+	5.33864i	−0.441486	+	0.206250i
$671$	0.950543	+	0.167606i	0.0366953	+	0.00647037i
$672$	−5.51492	+	1.94066i	−0.212743	+	0.0748625i
$673$	37.8215	+	3.30895i	1.45791	+	0.127551i	0.788360	−	0.615214i	$-0.210930\pi$
$673$	37.8215	+	3.30895i	1.45791	+	0.127551i	0.669552	+	0.742765i	$0.266486\pi$
$674$	8.68199			0.334418
$675$	8.13233	+	24.6752i	0.313013	+	0.949749i
$676$	−36.6704			−1.41040
$677$	−39.8783	−	3.48890i	−1.53265	−	0.134089i	−0.710636	−	0.703560i	$-0.751593\pi$
$677$	−39.8783	−	3.48890i	−1.53265	−	0.134089i	−0.822012	+	0.569470i	$0.807148\pi$
$678$	9.18755	+	7.87842i	0.352846	+	0.302569i
$679$	9.17989	+	1.61866i	0.352292	+	0.0621186i
$680$	−5.58552	+	2.60939i	−0.214195	+	0.100066i
$681$	5.01364	−	1.28603i	0.192123	−	0.0492808i
$682$	−1.30023	−	0.910434i	−0.0497886	−	0.0348623i
$683$	9.73412	+	2.60825i	0.372466	+	0.0998019i	0.440196	−	0.897902i	$-0.354909\pi$
$683$	9.73412	+	2.60825i	0.372466	+	0.0998019i	−0.0677301	+	0.997704i	$0.521576\pi$
$684$	−15.0608	−	0.322543i	−0.575865	−	0.0123327i
$685$	−32.4420	+	11.8340i	−1.23955	+	0.452153i
$686$	−3.00910	+	8.26744i	−0.114888	+	0.315652i
$687$	−14.4514	−	17.6019i	−0.551357	−	0.671554i
$688$	0.308089	+	3.52147i	0.0117458	+	0.134255i
$689$	−31.6158	−	26.5288i	−1.20447	−	1.01067i
$690$	20.8318	−	20.4194i	0.793052	−	0.777351i
$691$	−10.8420	−	3.94617i	−0.412449	−	0.150119i	0.127458	−	0.991844i	$-0.459318\pi$
$691$	−10.8420	−	3.94617i	−0.412449	−	0.150119i	−0.539907	+	0.841725i	$0.681541\pi$
$692$	20.5406	−	5.50383i	0.780835	−	0.209224i
$693$	1.54279	−	0.378178i	0.0586056	−	0.0143658i
$694$	−15.7465	+	9.09126i	−0.597730	+	0.345100i
$695$	26.8164	−	7.20582i	1.01721	−	0.273332i
$696$	0.118021	+	0.460109i	0.00447358	+	0.0174404i
$697$	7.74844	−	16.6166i	0.293493	−	0.629398i
$698$	4.95665	+	7.07883i	0.187612	+	0.267938i
$699$	16.9755	−	1.30219i	0.642071	−	0.0492533i
$700$	−16.8108	+	1.49477i	−0.635389	+	0.0564970i
$701$			9.18014i			0.346729i	0.984858	+	0.173365i	$0.0554639\pi$
$701$			9.18014i			0.346729i	−0.984858	+	0.173365i	$0.944536\pi$
$702$	−31.1104	−	19.3196i	−1.17419	−	0.729170i
$703$	7.98032	+	7.98032i	0.300984	+	0.300984i
$704$	0.120166	−	0.100831i	0.00452891	−	0.00380021i
$705$	7.94902	+	2.98354i	0.299377	+	0.112367i
$706$	2.21453	−	12.5593i	0.0833451	−	0.472674i
$707$	−7.33105	−	3.41852i	−0.275712	−	0.128567i
$708$	−0.176203	+	16.4572i	−0.00662213	+	0.618498i
$709$	−0.207408	+	0.0365716i	−0.00778937	+	0.00137348i	−0.177542	−	0.984113i	$-0.556814\pi$
$709$	−0.207408	+	0.0365716i	−0.00778937	+	0.00137348i	0.169752	+	0.985487i	$0.445703\pi$
$710$	−16.1256	−	2.83159i	−0.605181	−	0.106268i
$711$	6.76206	+	19.8940i	0.253597	+	0.746083i
$712$	−1.53322	−	5.72206i	−0.0574599	−	0.214443i
$713$	69.0722	−	32.2089i	2.58677	−	1.20623i
$714$	9.38626	−	13.1041i	0.351272	−	0.490408i
$715$	2.43421	−	0.430995i	0.0910342	−	0.0161183i
$716$	6.69144	−	7.97455i	0.250071	−	0.298023i
$717$	12.5941	+	4.73718i	0.470335	+	0.176913i
$718$	−11.0035	−	23.5970i	−0.410645	−	0.880632i
$719$	6.88689	−	11.9284i	0.256838	−	0.444856i	−0.708555	−	0.705655i	$-0.750653\pi$
$719$	6.88689	−	11.9284i	0.256838	−	0.444856i	0.965393	+	0.260799i	$0.0839861\pi$
$720$	−6.44229	−	1.86998i	−0.240090	−	0.0696902i
$721$	17.4040	+	30.1446i	0.648158	+	1.12264i
$722$	3.56460	−	5.09078i	0.132661	−	0.189459i
$723$	−11.6618	−	20.7078i	−0.433709	−	0.770131i
$724$	−0.324168	−	0.890644i	−0.0120476	−	0.0331005i
$725$	0.00194370	+	1.37122i	7.21871e−5	+	0.0509258i
$726$	15.6879	−	10.7363i	0.582232	−	0.398462i
$727$	−2.37274	+	27.1205i	−0.0880000	+	1.00585i	0.815926	+	0.578156i	$0.196228\pi$
$727$	−2.37274	+	27.1205i	−0.0880000	+	1.00585i	−0.903926	+	0.427689i	$0.859328\pi$
$728$	16.8214	−	16.8214i	0.623443	−	0.623443i
$729$	−11.9711	−	24.2011i	−0.443375	−	0.896336i
$730$	−2.60889	−	29.5783i	−0.0965595	−	1.09474i
$731$	−6.26461	−	7.46587i	−0.231705	−	0.276135i
$732$	10.4752	+	1.96291i	0.387173	+	0.0725513i
$733$	24.5528	−	17.1921i	0.906880	−	0.635004i	−0.0242446	−	0.999706i	$-0.507718\pi$
$733$	24.5528	−	17.1921i	0.906880	−	0.635004i	0.931124	+	0.364702i	$0.118829\pi$
$734$	23.6624	−	8.61240i	0.873394	−	0.317889i
$735$	14.0356	−	9.62012i	0.517709	−	0.354844i
$736$	1.30788	+	7.41734i	0.0482090	+	0.273407i
$737$	−0.229013	+	0.854688i	−0.00843581	+	0.0314829i
$738$	18.2571	−	8.04214i	0.672055	−	0.296035i
$739$	34.9872	+	20.1999i	1.28703	+	0.743065i	0.978123	−	0.208029i	$-0.0667048\pi$
$739$	34.9872	+	20.1999i	1.28703	+	0.743065i	0.308903	+	0.951093i	$0.400038\pi$
$740$	2.51592	+	4.35057i	0.0924870	+	0.159930i
$741$	55.8277	−	25.3088i	2.05088	−	0.929742i
$742$	19.6913	−	1.72277i	0.722891	−	0.0632447i
$743$	−44.8398	+	3.92298i	−1.64501	+	0.143920i	−0.871679	−	0.490077i	$-0.836969\pi$
$743$	−44.8398	+	3.92298i	−1.64501	+	0.143920i	−0.773335	+	0.633997i	$0.781413\pi$
$744$	−14.2483	−	10.2058i	−0.522368	−	0.374164i
$745$	16.2870	+	4.35173i	0.596711	+	0.159435i
$746$	−12.4454	−	7.18538i	−0.455660	−	0.263076i
$747$	−1.80901	+	3.67204i	−0.0661881	+	0.134353i
$748$	−0.111936	+	0.417750i	−0.00409278	+	0.0152745i
$749$	5.35534	+	30.3717i	0.195680	+	1.10976i
$750$	−16.6868	−	9.82599i	−0.609316	−	0.358795i
$751$	−30.1604	+	10.9775i	−1.10057	+	0.400574i	−0.827526	−	0.561428i	$-0.810252\pi$
$751$	−30.1604	+	10.9775i	−1.10057	+	0.400574i	−0.273043	+	0.962002i	$0.588030\pi$
$752$	−1.79577	+	1.25741i	−0.0654851	+	0.0458532i
$753$	10.9183	+	31.0274i	0.397885	+	1.13070i
$754$	−1.24238	−	1.48061i	−0.0452447	−	0.0539206i
$755$	17.7930	−	1.56940i	0.647555	−	0.0571162i
$756$	17.0786	−	3.99309i	0.621144	−	0.145227i
$757$	−17.3572	+	17.3572i	−0.630859	+	0.630859i	−0.948284	−	0.317424i	$-0.897182\pi$
$757$	−17.3572	+	17.3572i	−0.630859	+	0.630859i	0.317424	+	0.948284i	$0.397182\pi$
$758$	1.85137	−	21.1613i	0.0672449	−	0.768612i
$759$	−0.156517	−	2.04037i	−0.00568121	−	0.0740609i
$760$	8.59622	−	7.22347i	0.311818	−	0.262023i
$761$	−4.09191	−	11.2424i	−0.148332	−	0.407538i	0.843167	−	0.537651i	$-0.180688\pi$
$761$	−4.09191	−	11.2424i	−0.148332	−	0.407538i	−0.991499	+	0.130113i	$0.958466\pi$
$762$	7.60121	−	12.8461i	0.275363	−	0.465364i
$763$	−12.0677	+	17.2344i	−0.436879	+	0.623928i
$764$	−0.939266	−	1.62686i	−0.0339814	−	0.0588576i
$765$	17.5068	−	5.96448i	0.632959	−	0.215646i
$766$	−14.6854	+	25.4359i	−0.530605	+	0.919035i
$767$	−28.3020	−	60.6937i	−1.02192	−	2.19152i
$768$	1.33867	−	1.09907i	0.0483051	−	0.0396593i
$769$	3.23373	−	3.85381i	0.116611	−	0.138972i	−0.704581	−	0.709624i	$-0.748865\pi$
$769$	3.23373	−	3.85381i	0.116611	−	0.138972i	0.821192	+	0.570652i	$0.193309\pi$
$770$	−0.678409	+	0.970331i	−0.0244482	+	0.0349683i
$771$	−19.7400	−	1.94020i	−0.710919	−	0.0698744i
$772$	−7.47251	+	3.48449i	−0.268942	+	0.125410i
$773$	0.745136	+	2.78088i	0.0268007	+	0.100021i	0.978031	−	0.208461i	$-0.0668455\pi$
$773$	0.745136	+	2.78088i	0.0268007	+	0.100021i	−0.951230	+	0.308483i	$0.900179\pi$
$774$	0.227060	−	10.6023i	0.00816151	−	0.381093i
$775$	−32.5762	−	38.7113i	−1.17017	−	1.39055i
$776$	−2.71962	+	0.479543i	−0.0976288	+	0.0172146i
$777$	−11.3087	−	6.69150i	−0.405696	−	0.240056i
$778$	−7.91805	−	3.69225i	−0.283876	−	0.132373i
$779$	−5.79852	+	32.8850i	−0.207753	+	1.17823i
$780$	26.9271	−	4.47087i	0.964144	−	0.160083i
$781$	−0.879842	+	0.738275i	−0.0314832	+	0.0264175i
$782$	−14.6835	−	14.6835i	−0.525079	−	0.525079i
$783$	−0.202256	−	1.41059i	−0.00722806	−	0.0504103i
$784$			4.39351i			0.156911i
$785$	−0.0153155	−	21.6093i	−0.000546635	−	0.771269i
$786$	4.11234	−	8.57796i	0.146682	−	0.305966i
$787$	−27.4814	−	39.2475i	−0.979605	−	1.39902i	−0.916060	−	0.401042i	$-0.868648\pi$
$787$	−27.4814	−	39.2475i	−0.979605	−	1.39902i	−0.0635454	−	0.997979i	$-0.520241\pi$
$788$	−4.55132	+	9.76033i	−0.162134	+	0.347697i
$789$	−9.87520	+	9.66598i	−0.351567	+	0.344118i
$790$	−13.5686	−	7.82103i	−0.482750	−	0.278260i
$791$	20.4262	−	11.7931i	0.726274	−	0.419314i
$792$	−0.391180	+	0.261607i	−0.0139000	+	0.00929579i
$793$	−41.8877	+	11.2238i	−1.48748	+	0.398568i
$794$	−4.46093	−	1.62365i	−0.158312	−	0.0576210i
$795$	19.5273	+	11.5359i	0.692562	+	0.409137i
$796$	0.367380	+	0.308268i	0.0130214	+	0.0109263i
$797$	−2.92961	−	33.4856i	−0.103772	−	1.18612i	−0.852313	−	0.523032i	$-0.824801\pi$
$797$	−2.92961	−	33.4856i	−0.103772	−	1.18612i	0.748541	−	0.663088i	$-0.230755\pi$
$798$	−10.3356	+	27.4778i	−0.365875	+	0.972702i
$799$	2.06721	−	5.67962i	0.0731327	−	0.200930i
$800$	4.52854	−	2.11951i	0.160108	−	0.0749361i
$801$	2.71059	+	17.5638i	0.0957740	+	0.620587i
$802$	15.7949	+	4.23223i	0.557737	+	0.149445i
$803$	−1.70633	−	1.19478i	−0.0602150	−	0.0421630i
$804$	−2.62957	+	9.40956i	−0.0927379	+	0.331850i
$805$	−24.0613	−	51.5042i	−0.848048	−	1.81528i
$806$	70.2314	+	12.3837i	2.47379	+	0.436197i
$807$	7.61576	−	40.6418i	0.268087	−	1.43066i
$808$	2.38729	+	0.208861i	0.0839847	+	0.00734771i
$809$	−39.5234			−1.38957			−0.694784	−	0.719218i	$-0.744500\pi$
$809$	−39.5234			−1.38957			−0.694784	+	0.719218i	$0.744500\pi$
$810$	18.6044	+	7.67315i	0.653691	+	0.269607i
$811$	−21.1540			−0.742818			−0.371409	−	0.928469i	$-0.621125\pi$
$811$	−21.1540			−0.742818			−0.371409	+	0.928469i	$0.621125\pi$
$812$	0.922169	+	0.0806793i	0.0323618	+	0.00283129i
$813$	−4.38568	+	23.4043i	−0.153812	+	0.820825i
$814$	0.347205	+	0.0612217i	0.0121695	+	0.00214582i
$815$	−30.0341	−	10.9074i	−1.05205	−	0.382070i
$816$	−1.28527	+	4.59915i	−0.0449934	+	0.161003i
$817$	14.5402	+	10.1812i	0.508699	+	0.356195i
$818$	2.91720	+	0.781662i	0.101998	+	0.0273302i
$819$	−55.6402	+	44.6929i	−1.94422	+	1.56170i
$820$	−6.27469	+	13.4811i	−0.219122	+	0.470779i
$821$	−14.3479	+	39.4206i	−0.500745	+	1.37579i	0.389803	+	0.920898i	$0.372543\pi$
$821$	−14.3479	+	39.4206i	−0.500745	+	1.37579i	−0.890548	+	0.454889i	$0.849679\pi$
$822$	−9.41733	+	25.0366i	−0.328467	+	0.873251i
$823$	4.02896	+	46.0512i	0.140441	+	1.60524i	0.660307	+	0.750996i	$0.270426\pi$
$823$	4.02896	+	46.0512i	0.140441	+	1.60524i	−0.519866	+	0.854248i	$0.674018\pi$
$824$	−7.89958	−	6.62853i	−0.275195	−	0.230916i
$825$	−1.28083	+	0.452754i	−0.0445926	+	0.0157629i
$826$	30.1393	+	10.9698i	1.04868	+	0.381689i
$827$	47.9396	−	12.8454i	1.66702	−	0.446677i	0.702717	−	0.711469i	$-0.251970\pi$
$827$	47.9396	−	12.8454i	1.66702	−	0.446677i	0.964306	+	0.264792i	$0.0853032\pi$
$828$	−1.48691	−	22.5463i	−0.0516737	−	0.783539i
$829$	−39.6831	+	22.9111i	−1.37825	+	0.795734i	−0.991949	−	0.126639i	$-0.959581\pi$
$829$	−39.6831	+	22.9111i	−1.37825	+	0.795734i	−0.386302	+	0.922372i	$0.626248\pi$
$830$	−0.791767	−	2.94656i	−0.0274826	−	0.102277i
$831$	26.1999	−	25.6448i	0.908865	−	0.889609i
$832$	−2.97850	+	6.38741i	−0.103261	+	0.221444i
$833$	−6.94782	−	9.92252i	−0.240728	−	0.343795i
$834$	9.29818	−	19.3951i	0.321970	−	0.671598i
$835$	15.9482	−	0.0113032i	0.551909	−	0.000391164i
$836$		−	0.787686i		−	0.0272427i
$837$	39.1718	+	35.0732i	1.35397	+	1.21231i
$838$	26.4939	+	26.4939i	0.915216	+	0.915216i
$839$	38.0359	−	31.9159i	1.31314	−	1.10186i	0.325433	−	0.945565i	$-0.394490\pi$
$839$	38.0359	−	31.9159i	1.31314	−	1.10186i	0.987711	−	0.156293i	$-0.0499545\pi$
$840$	−7.60503	+	10.6333i	−0.262399	+	0.366882i
$841$	−5.02274	+	28.4854i	−0.173198	+	0.982254i
$842$	8.79673	+	4.10198i	0.303155	+	0.141364i
$843$	36.2603	+	21.4558i	1.24887	+	0.738976i
$844$	−11.4749	+	2.02333i	−0.394982	+	0.0696460i
$845$	−67.1351	+	47.0795i	−2.30952	+	1.61958i
$846$	5.76469	−	3.16565i	0.198194	−	0.108837i
$847$	−9.58838	−	35.7843i	−0.329460	−	1.22956i
$848$	−5.30734	+	2.47486i	−0.182255	+	0.0849869i
$849$	13.7741	+	1.35382i	0.472726	+	0.0464631i
$850$	−6.87572	+	11.9482i	−0.235835	+	0.409819i
$851$	−10.8811	+	12.9676i	−0.373000	+	0.444524i
$852$	−9.80163	+	8.04730i	−0.335798	+	0.275696i
$853$	−6.54631	−	14.0386i	−0.224141	−	0.480673i	0.761790	−	0.647824i	$-0.224321\pi$
$853$	−6.54631	−	14.0386i	−0.224141	−	0.480673i	−0.985931	+	0.167152i	$0.946543\pi$
$854$	10.3847	−	17.9868i	0.355356	−	0.615494i
$855$	−27.9870	+	18.7454i	−0.957135	+	0.641079i
$856$	−4.56834	−	7.91260i	−0.156143	−	0.270447i
$857$	−12.8243	+	18.3150i	−0.438071	+	0.625630i	−0.976107	−	0.217292i	$-0.930278\pi$
$857$	−12.8243	+	18.3150i	−0.438071	+	0.625630i	0.538036	+	0.842922i	$0.319166\pi$
$858$	0.975127	−	1.64797i	0.0332903	−	0.0562607i
$859$	3.57578	+	9.82439i	0.122004	+	0.335204i	0.985627	−	0.168934i	$-0.0540325\pi$
$859$	3.57578	+	9.82439i	0.122004	+	0.335204i	−0.863623	+	0.504138i	$0.831810\pi$
$860$	5.08510	+	6.05147i	0.173400	+	0.206353i
$861$	−2.97363	−	38.7646i	−0.101341	−	1.32109i
$862$	−0.129070	+	1.47528i	−0.00439615	+	0.0502482i
$863$	12.2209	−	12.2209i	0.416005	−	0.416005i	−0.467819	−	0.883824i	$-0.654960\pi$
$863$	12.2209	−	12.2209i	0.416005	−	0.416005i	0.883824	+	0.467819i	$0.154960\pi$
$864$	−4.34995	+	2.84216i	−0.147988	+	0.0966924i
$865$	30.5389	−	36.4473i	1.03836	−	1.23925i
$866$	−2.58890	−	3.08534i	−0.0879746	−	0.104844i
$867$	5.40361	+	15.3559i	0.183516	+	0.521513i
$868$	−27.9785	+	19.5907i	−0.949651	+	0.664953i
$869$	−1.03242	+	0.375769i	−0.0350223	+	0.0127471i
$870$	0.806783	+	0.690833i	0.0273525	+	0.0234214i
$871$	−6.90330	−	39.1506i	−0.233909	−	1.32657i
$872$	1.61324	−	6.02070i	0.0546313	−	0.203887i
$873$	8.26678	−	0.545186i	0.279788	−	0.0184518i
$874$	32.7532	+	18.9101i	1.10790	+	0.639644i
$875$	−28.8577	+	24.3192i	−0.975567	+	0.822139i
$876$	−18.6984	−	13.3933i	−0.631759	−	0.452519i
$877$	−33.2624	+	2.91008i	−1.12319	+	0.0982665i	−0.633582	−	0.773676i	$-0.718416\pi$
$877$	−33.2624	+	2.91008i	−1.12319	+	0.0982665i	−0.489609	+	0.871942i	$0.662860\pi$
$878$	4.71509	−	0.412517i	0.159127	−	0.0139218i
$879$	20.9947	−	9.51768i	0.708134	−	0.321024i
$880$	0.0905435	−	0.338873i	0.00305222	−	0.0114234i
$881$	26.7397	+	15.4382i	0.900882	+	0.520125i	0.877486	−	0.479602i	$-0.159219\pi$
$881$	26.7397	+	15.4382i	0.900882	+	0.520125i	0.0233961	+	0.999726i	$0.492552\pi$
$882$	1.42963	−	13.1028i	0.0481382	−	0.441193i
$883$	4.35431	−	16.2505i	0.146534	−	0.546874i	−0.853148	−	0.521669i	$-0.825310\pi$
$883$	4.35431	−	16.2505i	0.146534	−	0.546874i	0.999682	−	0.0252047i	$-0.00802374\pi$
$884$	−3.37416	−	19.1358i	−0.113485	−	0.643607i
$885$	20.8060	+	30.3555i	0.699386	+	1.02039i
$886$	−24.4096	+	8.88437i	−0.820057	+	0.298476i
$887$	−17.0340	+	11.9273i	−0.571946	+	0.400481i	−0.823461	−	0.567372i	$-0.807960\pi$
$887$	−17.0340	+	11.9273i	−0.571946	+	0.400481i	0.251515	+	0.967853i	$0.419071\pi$
$888$	3.82627	+	0.716995i	0.128401	+	0.0240608i
$889$	−18.6979	−	22.2833i	−0.627108	−	0.747358i
$890$	−10.1533	−	8.50734i	−0.340338	−	0.285167i
$891$	1.25174	−	0.652902i	0.0419350	−	0.0218730i
$892$	10.0764	−	10.0764i	0.337384	−	0.337384i
$893$	−0.959422	+	10.9662i	−0.0321058	+	0.366971i
$894$	10.7764	−	7.37507i	0.360418	−	0.246659i
$895$	2.01234	−	23.1904i	0.0672649	−	0.775169i
$896$	−1.15446	−	3.17186i	−0.0385679	−	0.105965i
$897$	45.1151	+	80.1103i	1.50635	+	2.67481i
$898$	−3.96808	+	5.66701i	−0.132417	+	0.189111i
$899$	1.38752	+	2.40325i	0.0462763	+	0.0801529i
$900$	−14.1951	+	4.84745i	−0.473172	+	0.161582i
$901$	8.07268	−	13.9823i	0.268940	−	0.465818i
$902$	0.440854	+	0.945414i	0.0146788	+	0.0314788i
$903$	−19.3435	−	7.27591i	−0.643711	−	0.242127i
$904$	−4.49156	+	5.35283i	−0.149387	+	0.178032i
$905$	−1.73693	−	1.21438i	−0.0577376	−	0.0403674i
$906$	8.05685	−	11.2481i	0.267671	−	0.373694i
$907$	20.7260	−	9.66469i	0.688195	−	0.320911i	−0.0468760	−	0.998901i	$-0.514927\pi$
$907$	20.7260	−	9.66469i	0.688195	−	0.320911i	0.735071	+	0.677990i	$0.237149\pi$
$908$	0.773438	+	2.88651i	0.0256675	+	0.0957922i
$909$	−7.05166	−	1.39970i	−0.233889	−	0.0464252i
$910$	9.19991	−	52.3924i	0.304974	−	1.73679i
$911$	−9.67975	+	1.70680i	−0.320705	+	0.0565489i	−0.331683	−	0.943391i	$-0.607616\pi$
$911$	−9.67975	+	1.70680i	−0.320705	+	0.0565489i	0.0109786	+	0.999940i	$0.496505\pi$
$912$	0.0931154	−	8.69686i	0.00308336	−	0.287982i
$913$	−0.193986	−	0.0904573i	−0.00642001	−	0.00299370i
$914$	2.94259	−	16.6883i	0.0973323	−	0.551999i
$915$	21.6977	−	9.85492i	0.717303	−	0.325794i
$916$	10.0725	−	8.45187i	0.332806	−	0.279258i
$917$	−13.1087	−	13.1087i	−0.432888	−	0.432888i
$918$	5.32961	−	13.2978i	0.175903	−	0.438894i
$919$			4.32140i			0.142550i	0.997457	+	0.0712749i	$0.0227067\pi$
$919$			4.32140i			0.142550i	−0.997457	+	0.0712749i	$0.977293\pi$
$920$	11.9172	+	11.9003i	0.392899	+	0.392342i
$921$	−18.8936	+	1.44933i	−0.622565	+	0.0477570i
$922$	22.2405	+	31.7628i	0.732453	+	1.04605i
$923$	21.8083	−	46.7680i	0.717828	−	1.53939i
$924$	0.227865	+	0.888339i	0.00749620	+	0.0292242i
$925$	10.1916	+	4.73483i	0.335097	+	0.155680i
$926$	20.4431	−	11.8029i	0.671803	−	0.387866i
$927$	21.4020	+	22.3388i	0.702935	+	0.733702i
$928$	−0.264900	+	0.0709796i	−0.00869575	+	0.00233002i
$929$	−29.4359	−	10.7138i	−0.965761	−	0.351508i	−0.189473	−	0.981886i	$-0.560678\pi$
$929$	−29.4359	−	10.7138i	−0.965761	−	0.351508i	−0.776289	+	0.630378i	$0.782900\pi$
$930$	−39.1881	−	0.391802i	−1.28503	−	0.0128477i
$931$	16.9002	+	14.1810i	0.553882	+	0.464762i
$932$	0.856705	+	9.79218i	0.0280623	+	0.320753i
$933$	3.74707	+	4.56394i	0.122674	+	0.149417i
$934$	5.84848	−	16.0686i	0.191368	−	0.525779i
$935$	0.331401	+	0.908513i	0.0108380	+	0.0297116i
$936$	10.9612	−	18.0800i	0.358278	−	0.590963i
$937$	25.3282	+	6.78666i	0.827435	+	0.221711i	0.647595	−	0.761985i	$-0.275775\pi$
$937$	25.3282	+	6.78666i	0.827435	+	0.221711i	0.179841	+	0.983696i	$0.442442\pi$
$938$	15.5966	+	10.9209i	0.509248	+	0.356579i
$939$	−13.8994	+	3.56529i	−0.453590	+	0.116349i
$940$	−1.67331	+	4.60755i	−0.0545774	+	0.150282i
$941$	22.1394	+	3.90377i	0.721722	+	0.127259i	0.522432	−	0.852681i	$-0.325025\pi$
$941$	22.1394	+	3.90377i	0.721722	+	0.127259i	0.199291	+	0.979940i	$0.436136\pi$
$942$	−12.7065	−	10.8960i	−0.414000	−	0.355010i
$943$	−49.8955	−	4.36529i	−1.62482	−	0.142153i
$944$	−9.50209			−0.309267
$945$	26.1405	−	29.2369i	0.850351	−	0.951077i
$946$	0.554507			0.0180286
$947$	−36.2086	−	3.16785i	−1.17662	−	0.102941i	−0.517977	−	0.855394i	$-0.673315\pi$
$947$	−36.2086	−	3.16785i	−1.17662	−	0.102941i	−0.658646	+	0.752453i	$0.728870\pi$
$948$	−11.4433	+	4.02682i	−0.371663	+	0.130785i
$949$	92.1663	+	16.2514i	2.99184	+	0.527543i
$950$	6.46382	−	24.2608i	0.209714	−	0.787124i
$951$	−37.7574	−	38.5747i	−1.22437	−	1.25087i
$952$	7.62324	+	5.33785i	0.247071	+	0.173001i
$953$	−7.20699	−	1.93111i	−0.233457	−	0.0625547i	0.140194	−	0.990124i	$-0.455227\pi$
$953$	−7.20699	−	1.93111i	−0.233457	−	0.0625547i	−0.373651	+	0.927569i	$0.621894\pi$
$954$	16.6334	−	5.65377i	0.538526	−	0.183048i
$955$	−3.80822	−	1.77252i	−0.123231	−	0.0573574i
$956$	−2.65701	+	7.30007i	−0.0859338	+	0.236101i
$957$	0.0735140	−	0.0121525i	0.00237637	−	0.000392833i
$958$	−2.87675	−	32.8814i	−0.0929435	−	1.06235i
$959$	39.9330	+	33.5078i	1.28950	+	1.08202i
$960$	1.03975	−	3.73081i	0.0335579	−	0.120411i
$961$	−67.0855	−	24.4171i	−2.16405	−	0.787650i
$962$	−15.3003	+	4.09972i	−0.493303	+	0.132180i
$963$	11.0494	+	25.0843i	0.356063	+	0.808329i
$964$	11.8829	−	6.86058i	0.382722	−	0.220965i
$965$	−9.20688	+	15.9729i	−0.296380	+	0.514186i
$966$	−42.4089	−	11.8515i	−1.36449	−	0.381316i
$967$	−22.8262	+	48.9510i	−0.734042	+	1.57416i	0.0823126	+	0.996607i	$0.473769\pi$
$967$	−22.8262	+	48.9510i	−0.734042	+	1.57416i	−0.816354	+	0.577551i	$0.804008\pi$
$968$	6.29523	+	8.99052i	0.202336	+	0.288966i
$969$	13.5428	+	19.7887i	0.435057	+	0.635704i
$970$	−4.36334	+	4.36953i	−0.140099	+	0.140297i
$971$		−	31.5940i		−	1.01390i	−0.861975	−	0.506951i	$-0.830773\pi$
$971$		−	31.5940i		−	1.01390i	0.861975	−	0.506951i	$-0.169227\pi$
$972$	13.8977	−	7.06073i	0.445769	−	0.226473i
$973$	−29.6393	−	29.6393i	−0.950194	−	0.950194i
$974$	−4.89123	+	4.10423i	−0.156725	+	0.131508i
$975$	43.5573	−	42.7556i	1.39495	−	1.36927i
$976$	−1.06847	+	6.05962i	−0.0342010	+	0.193964i
$977$	−10.5588	−	4.92366i	−0.337807	−	0.157522i	0.246311	−	0.969191i	$-0.420782\pi$
$977$	−10.5588	−	4.92366i	−0.337807	−	0.157522i	−0.584118	+	0.811669i	$0.698559\pi$
$978$	−21.5663	+	12.1453i	−0.689613	+	0.388364i
$979$	−0.915138	+	0.161363i	−0.0292479	+	0.00515720i
$980$	5.64062	+	8.04350i	0.180183	+	0.256940i
$981$	−6.77029	+	17.4306i	−0.216159	+	0.556516i
$982$	0.396220	+	1.47871i	0.0126439	+	0.0471877i
$983$	24.5995	−	11.4709i	0.784601	−	0.365865i	0.0113256	−	0.999936i	$-0.496395\pi$
$983$	24.5995	−	11.4709i	0.784601	−	0.365865i	0.773275	+	0.634070i	$0.218617\pi$
$984$	4.75572	+	10.4905i	0.151607	+	0.334423i
$985$	4.19842	+	23.7122i	0.133773	+	0.755532i
$986$	0.486017	−	0.579212i	0.0154779	−	0.0184459i
$987$	−2.09034	−	12.6451i	−0.0665361	−	0.402498i
$988$	14.9563	+	32.0739i	0.475823	+	1.02041i
$989$	−13.3121	+	23.0573i	−0.423301	+	0.733178i
$990$	−0.380296	+	0.981160i	−0.0120866	+	0.0311833i
$991$	21.5210	+	37.2754i	0.683636	+	1.18409i	0.973863	+	0.227135i	$0.0729358\pi$
$991$	21.5210	+	37.2754i	0.683636	+	1.18409i	−0.290227	+	0.956958i	$0.593731\pi$
$992$	5.80393	−	8.28887i	0.184275	−	0.263172i
$993$	−15.4629	−	0.165557i	−0.490699	−	0.00525381i
$994$	8.45288	+	23.2241i	0.268109	+	0.736623i
$995$	1.06836	+	0.0927063i	0.0338693	+	0.00293899i
$996$	−2.13111	−	1.02167i	−0.0675269	−	0.0323729i
$997$	5.39187	−	61.6293i	0.170762	−	1.95182i	−0.114626	−	0.993409i	$-0.536567\pi$
$997$	5.39187	−	61.6293i	0.170762	−	1.95182i	0.285388	−	0.958412i	$-0.407878\pi$
$998$	−12.1996	+	12.1996i	−0.386173	+	0.386173i
$999$	−11.1778	−	3.38335i	−0.353649	−	0.107044i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	270.2.r.a.113.14	✓	216
3.2	odd	2		810.2.s.a.773.2		216
5.2	odd	4	inner	270.2.r.a.167.1	yes	216
15.2	even	4		810.2.s.a.287.18		216
27.11	odd	18	inner	270.2.r.a.173.1	yes	216
27.16	even	9		810.2.s.a.683.18		216
135.92	even	36	inner	270.2.r.a.227.14	yes	216
135.97	odd	36		810.2.s.a.197.2		216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.14	✓	216	1.1	even	1	trivial
270.2.r.a.167.1	yes	216	5.2	odd	4	inner
270.2.r.a.173.1	yes	216	27.11	odd	18	inner
270.2.r.a.227.14	yes	216	135.92	even	36	inner
810.2.s.a.197.2		216	135.97	odd	36
810.2.s.a.287.18		216	15.2	even	4
810.2.s.a.683.18		216	27.16	even	9
810.2.s.a.773.2		216	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 270 = 2 \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	270.r (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.319012 - 1.70242i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.02590 - 0.946439i) q^{5} +(0.466174 - 1.66814i) q^{6} +(-2.76499 - 1.93607i) q^{7} +(0.965926 + 0.258819i) q^{8} +(-2.79646 - 1.08618i) q^{9} +(2.10067 - 0.766269i) q^{10} +(0.0536510 - 0.147405i) q^{11} +(0.609788 - 1.62116i) q^{12} +(0.614250 + 7.02091i) q^{13} +(-2.58573 - 2.16968i) q^{14} +(-0.964951 - 3.75085i) q^{15} +(0.939693 + 0.342020i) q^{16} +(-2.66312 + 0.713580i) q^{17} +(-2.69115 - 1.32578i) q^{18} +(4.34868 - 2.51071i) q^{19} +(2.15947 - 0.580268i) q^{20} +(-4.17806 + 4.08954i) q^{21} +(0.0662941 - 0.142168i) q^{22} +(4.32004 + 6.16966i) q^{23} +(0.748761 - 1.56184i) q^{24} +(3.20851 - 3.83477i) q^{25} +7.04772i q^{26} +(-2.74125 + 4.41425i) q^{27} +(-2.38679 - 2.38679i) q^{28} +(-0.210083 + 0.176281i) q^{29} +(-0.634371 - 3.82068i) q^{30} +(1.75712 - 9.96511i) q^{31} +(0.906308 + 0.422618i) q^{32} +(-0.233830 - 0.138361i) q^{33} +(-2.71517 + 0.478758i) q^{34} +(-7.43394 - 1.30537i) q^{35} +(-2.56536 - 1.55528i) q^{36} +(0.581708 + 2.17096i) q^{37} +(4.55096 - 2.12215i) q^{38} +(12.1485 + 1.19404i) q^{39} +(2.20182 - 0.389850i) q^{40} +(-4.27452 + 5.09418i) q^{41} +(-4.51859 + 3.70984i) q^{42} +(1.49392 + 3.20373i) q^{43} +(0.0784326 - 0.135849i) q^{44} +(-6.69335 + 0.446185i) q^{45} +(3.76588 + 6.52270i) q^{46} +(-1.25741 + 1.79577i) q^{47} +(0.882035 - 1.49064i) q^{48} +(1.50267 + 4.12855i) q^{49} +(3.53052 - 3.54054i) q^{50} +(0.365246 + 4.76138i) q^{51} +(-0.614250 + 7.02091i) q^{52} +(-4.14082 + 4.14082i) q^{53} +(-3.11554 + 4.15853i) q^{54} +(-0.0308185 - 0.349405i) q^{55} +(-2.16968 - 2.58573i) q^{56} +(-2.88700 - 8.20422i) q^{57} +(-0.224648 + 0.157300i) q^{58} +(-8.92905 + 3.24991i) q^{59} +(-0.298963 - 3.86143i) q^{60} +(1.06847 + 6.05962i) q^{61} +(2.61895 - 9.77405i) q^{62} +(5.62926 + 8.41742i) q^{63} +(0.866025 + 0.500000i) q^{64} +(7.88927 + 13.6423i) q^{65} +(-0.220881 - 0.158214i) q^{66} +(-5.61930 + 0.491625i) q^{67} +(-2.74657 + 0.240294i) q^{68} +(11.8815 - 5.38633i) q^{69} +(-7.29189 - 1.94832i) q^{70} +(-6.34096 - 3.66095i) q^{71} +(-2.42005 - 1.77295i) q^{72} +(3.43691 - 12.8267i) q^{73} +(0.390282 + 2.21340i) q^{74} +(-5.50484 - 6.68556i) q^{75} +(4.71859 - 1.71743i) q^{76} +(-0.433730 + 0.303701i) q^{77} +(11.9982 + 2.24831i) q^{78} +(-4.50205 - 5.36533i) q^{79} +(2.22742 - 0.196465i) q^{80} +(6.64041 + 6.07495i) q^{81} +(-4.70224 + 4.70224i) q^{82} +(0.118923 - 1.35929i) q^{83} +(-4.82473 + 3.30190i) q^{84} +(-4.71983 + 3.96611i) q^{85} +(1.20902 + 3.32174i) q^{86} +(0.233085 + 0.413885i) q^{87} +(0.0899741 - 0.128496i) q^{88} +(-2.96196 - 5.13026i) q^{89} +(-6.70677 - 0.138877i) q^{90} +(11.8945 - 20.6019i) q^{91} +(3.18306 + 6.82610i) q^{92} +(-16.4043 - 6.17034i) q^{93} +(-1.40914 + 1.67935i) q^{94} +(6.43374 - 9.20220i) q^{95} +(1.00860 - 1.40810i) q^{96} +(-2.50284 + 1.16709i) q^{97} +(1.13712 + 4.24380i) q^{98} +(-0.310142 + 0.353938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q + 12 q^{6} + 24 q^{11} - 24 q^{20} + 24 q^{23} + 36 q^{25} + 12 q^{27} - 72 q^{30} - 12 q^{33} - 108 q^{35} - 12 q^{36} - 36 q^{38} - 72 q^{41} - 48 q^{42} - 60 q^{45} - 48 q^{47} - 12 q^{48} - 48 q^{50}+ \cdots - 72 q^{97}+O(q^{100}) \) 216 * q + 12 * q^6 + 24 * q^11 - 24 * q^20 + 24 * q^23 + 36 * q^25 + 12 * q^27 - 72 * q^30 - 12 * q^33 - 108 * q^35 - 12 * q^36 - 36 * q^38 - 72 * q^41 - 48 * q^42 - 60 * q^45 - 48 * q^47 - 12 * q^48 - 48 * q^50 - 192 * q^51 - 12 * q^56 - 36 * q^57 + 36 * q^61 + 84 * q^63 + 24 * q^65 - 72 * q^67 + 36 * q^68 - 48 * q^72 - 36 * q^75 - 240 * q^77 + 24 * q^78 - 24 * q^81 - 60 * q^83 + 72 * q^86 - 252 * q^87 - 48 * q^92 - 96 * q^93 - 60 * q^95 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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