LMFDB - Embedded newform 270.2.r.a.173.1

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			173.1
Character	$\chi$	$=$	270.173
Dual form			270.2.r.a.167.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0871557 - 0.996195i) q^{2} +(-1.70242 + 0.319012i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-2.16029 - 0.577206i) q^{5} +(0.466174 + 1.66814i) q^{6} +(1.93607 + 2.76499i) q^{7} +(0.258819 + 0.965926i) q^{8} +(2.79646 - 1.08618i) q^{9} +(-0.386728 + 2.20237i) q^{10} +(0.0536510 + 0.147405i) q^{11} +(1.62116 - 0.609788i) q^{12} +(7.02091 + 0.614250i) q^{13} +(2.58573 - 2.16968i) q^{14} +(3.86185 + 0.293489i) q^{15} +(0.939693 - 0.342020i) q^{16} +(-0.713580 + 2.66312i) q^{17} +(-1.32578 - 2.69115i) q^{18} +(-4.34868 - 2.51071i) q^{19} +(2.22770 + 0.193307i) q^{20} +(-4.17806 - 4.08954i) q^{21} +(0.142168 - 0.0662941i) q^{22} +(6.16966 + 4.32004i) q^{23} +(-0.748761 - 1.56184i) q^{24} +(4.33367 + 2.49386i) q^{25} -7.04772i q^{26} +(-4.41425 + 2.74125i) q^{27} +(-2.38679 - 2.38679i) q^{28} +(0.210083 + 0.176281i) q^{29} +(-0.0442096 - 3.87273i) q^{30} +(1.75712 + 9.96511i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-0.138361 - 0.233830i) q^{33} +(2.71517 + 0.478758i) q^{34} +(-2.58649 - 7.09067i) q^{35} +(-2.56536 + 1.55528i) q^{36} +(-2.17096 - 0.581708i) q^{37} +(-2.12215 + 4.55096i) q^{38} +(-12.1485 + 1.19404i) q^{39} +(-0.00158481 - 2.23607i) q^{40} +(-4.27452 - 5.09418i) q^{41} +(-3.70984 + 4.51859i) q^{42} +(3.20373 + 1.49392i) q^{43} +(-0.0784326 - 0.135849i) q^{44} +(-6.66811 + 0.732334i) q^{45} +(3.76588 - 6.52270i) q^{46} +(-1.79577 + 1.25741i) q^{47} +(-1.49064 + 0.882035i) q^{48} +(-1.50267 + 4.12855i) q^{49} +(2.10667 - 4.53453i) q^{50} +(0.365246 - 4.76138i) q^{51} +(-7.02091 + 0.614250i) 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} +(8.20422 + 2.88700i) q^{57} +(0.157300 - 0.224648i) q^{58} +(8.92905 + 3.24991i) q^{59} +(-3.85414 + 0.381572i) q^{60} +(1.06847 - 6.05962i) q^{61} +(9.77405 - 2.61895i) q^{62} +(8.41742 + 5.62926i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-14.8126 - 5.37946i) q^{65} +(-0.220881 + 0.158214i) q^{66} +(-0.491625 + 5.61930i) q^{67} +(0.240294 - 2.74657i) q^{68} +(-11.8815 - 5.38633i) q^{69} +(-6.83826 + 3.19464i) q^{70} +(-6.34096 + 3.66095i) q^{71} +(1.77295 + 2.42005i) q^{72} +(-12.8267 + 3.43691i) q^{73} +(-0.390282 + 2.21340i) q^{74} +(-8.17329 - 2.86310i) q^{75} +(4.71859 + 1.71743i) q^{76} +(-0.303701 + 0.433730i) q^{77} +(2.24831 + 11.9982i) 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} +(-1.35929 + 0.118923i) q^{83} +(4.82473 + 3.30190i) q^{84} +(3.07870 - 5.34121i) q^{85} +(1.20902 - 3.32174i) q^{86} +(-0.413885 - 0.233085i) q^{87} +(-0.128496 + 0.0899741i) q^{88} +(2.96196 - 5.13026i) q^{89} +(1.31071 + 6.57891i) q^{90} +(11.8945 + 20.6019i) q^{91} +(-6.82610 - 3.18306i) q^{92} +(-6.17034 - 16.4043i) q^{93} +(1.40914 + 1.67935i) q^{94} +(7.94519 + 7.93394i) q^{95} +(1.00860 + 1.40810i) q^{96} +(-1.16709 + 2.50284i) q^{97} +(4.24380 + 1.13712i) 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 $\left(\mathbb{Z}/270\mathbb{Z}\right)^\times$.

$n$	$191$	$217$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$2$	−0.0871557	−	0.996195i	−0.0616284	−	0.704416i
$3$	−1.70242	+	0.319012i	−0.982892	+	0.184182i
$3$	−1.70242	+	0.319012i	−0.982892	+	0.184182i
$4$	−0.984808	+	0.173648i	−0.492404	+	0.0868241i
$5$	−2.16029	−	0.577206i	−0.966109	−	0.258134i
$5$	−2.16029	−	0.577206i	−0.966109	−	0.258134i
$6$	0.466174	+	1.66814i	0.190315	+	0.681014i
$7$	1.93607	+	2.76499i	0.731764	+	1.04507i	0.996730	+	0.0808093i	$0.0257505\pi$
$7$	1.93607	+	2.76499i	0.731764	+	1.04507i	−0.264966	+	0.964258i	$0.585361\pi$
$8$	0.258819	+	0.965926i	0.0915064	+	0.341506i
$9$	2.79646	−	1.08618i	0.932154	−	0.362062i
$10$	−0.386728	+	2.20237i	−0.122294	+	0.696451i
$11$	0.0536510	+	0.147405i	0.0161764	+	0.0444443i	0.947518	−	0.319702i	$-0.103583\pi$
$11$	0.0536510	+	0.147405i	0.0161764	+	0.0444443i	−0.931342	+	0.364147i	$0.881361\pi$
$12$	1.62116	−	0.609788i	0.467989	−	0.176031i
$13$	7.02091	+	0.614250i	1.94725	+	0.170362i	0.992072	−	0.125673i	$-0.0401089\pi$
$13$	7.02091	+	0.614250i	1.94725	+	0.170362i	0.955177	+	0.296035i	$0.0956645\pi$
$14$	2.58573	−	2.16968i	0.691065	−	0.579872i
$15$	3.86185	+	0.293489i	0.997125	+	0.0757786i
$16$	0.939693	−	0.342020i	0.234923	−	0.0855050i
$17$	−0.713580	+	2.66312i	−0.173068	+	0.645900i	0.823804	+	0.566875i	$0.191848\pi$
$17$	−0.713580	+	2.66312i	−0.173068	+	0.645900i	−0.996873	+	0.0790258i	$0.974819\pi$
$18$	−1.32578	−	2.69115i	−0.312489	−	0.634311i
$19$	−4.34868	−	2.51071i	−0.997656	−	0.575997i	−0.0901018	−	0.995933i	$-0.528719\pi$
$19$	−4.34868	−	2.51071i	−0.997656	−	0.575997i	−0.907554	+	0.419936i	$0.862053\pi$
$20$	2.22770	+	0.193307i	0.498128	+	0.0432248i
$21$	−4.17806	−	4.08954i	−0.911727	−	0.892411i
$22$	0.142168	−	0.0662941i	0.0303103	−	0.0141339i
$23$	6.16966	+	4.32004i	1.28646	+	0.900792i	0.998385	−	0.0568151i	$-0.0180946\pi$
$23$	6.16966	+	4.32004i	1.28646	+	0.900792i	0.288079	+	0.957607i	$0.406983\pi$
$24$	−0.748761	−	1.56184i	−0.152840	−	0.318810i
$25$	4.33367	+	2.49386i	0.866733	+	0.498772i
$26$		−	7.04772i		−	1.38217i
$27$	−4.41425	+	2.74125i	−0.849522	+	0.527553i
$28$	−2.38679	−	2.38679i	−0.451060	−	0.451060i
$29$	0.210083	+	0.176281i	0.0390115	+	0.0327345i	0.662085	−	0.749429i	$-0.269672\pi$
$29$	0.210083	+	0.176281i	0.0390115	+	0.0327345i	−0.623073	+	0.782163i	$0.714116\pi$
$30$	−0.0442096	−	3.87273i	−0.00807154	−	0.707061i
$31$	1.75712	+	9.96511i	0.315588	+	1.78979i	0.568904	+	0.822404i	$0.307367\pi$
$31$	1.75712	+	9.96511i	0.315588	+	1.78979i	−0.253317	+	0.967383i	$0.581521\pi$
$32$	−0.422618	−	0.906308i	−0.0747091	−	0.160214i
$33$	−0.138361	−	0.233830i	−0.0240855	−	0.0407045i
$34$	2.71517	+	0.478758i	0.465649	+	0.0821064i
$35$	−2.58649	−	7.09067i	−0.437196	−	1.19854i
$36$	−2.56536	+	1.55528i	−0.427561	+	0.259214i
$37$	−2.17096	−	0.581708i	−0.356904	−	0.0956322i	0.0759117	−	0.997115i	$-0.475813\pi$
$37$	−2.17096	−	0.581708i	−0.356904	−	0.0956322i	−0.432816	+	0.901482i	$0.642480\pi$
$38$	−2.12215	+	4.55096i	−0.344257	+	0.738262i
$39$	−12.1485	+	1.19404i	−1.94531	+	0.191200i
$40$	−0.00158481	−	2.23607i	−0.000250580	−	0.353553i
$41$	−4.27452	−	5.09418i	−0.667568	−	0.795577i	0.320883	−	0.947119i	$-0.396020\pi$
$41$	−4.27452	−	5.09418i	−0.667568	−	0.795577i	−0.988451	+	0.151542i	$0.951576\pi$
$42$	−3.70984	+	4.51859i	−0.572440	+	0.697233i
$43$	3.20373	+	1.49392i	0.488564	+	0.227821i	0.651260	−	0.758855i	$-0.274241\pi$
$43$	3.20373	+	1.49392i	0.488564	+	0.227821i	−0.162695	+	0.986676i	$0.552019\pi$
$44$	−0.0784326	−	0.135849i	−0.0118242	−	0.0204800i
$45$	−6.66811	+	0.732334i	−0.994023	+	0.109170i
$46$	3.76588	−	6.52270i	0.555249	−	0.961720i
$47$	−1.79577	+	1.25741i	−0.261940	+	0.183413i	−0.697168	−	0.716908i	$-0.745557\pi$
$47$	−1.79577	+	1.25741i	−0.261940	+	0.183413i	0.435228	+	0.900321i	$0.356668\pi$
$48$	−1.49064	+	0.882035i	−0.215156	+	0.127311i
$49$	−1.50267	+	4.12855i	−0.214667	+	0.589792i
$50$	2.10667	−	4.53453i	0.297928	−	0.641279i
$51$	0.365246	−	4.76138i	0.0511446	−	0.666726i
$52$	−7.02091	+	0.614250i	−0.973624	+	0.0851811i
$53$	4.14082	−	4.14082i	0.568786	−	0.568786i	−0.363002	−	0.931788i	$-0.618248\pi$
$53$	4.14082	−	4.14082i	0.568786	−	0.568786i	0.931788	+	0.363002i	$0.118248\pi$
$54$	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
$57$	8.20422	+	2.88700i	1.08668	+	0.382393i
$58$	0.157300	−	0.224648i	0.0206545	−	0.0294977i
$59$	8.92905	+	3.24991i	1.16246	+	0.423102i	0.849977	−	0.526820i	$-0.176616\pi$
$59$	8.92905	+	3.24991i	1.16246	+	0.423102i	0.312486	+	0.949922i	$0.398838\pi$
$60$	−3.85414	+	0.381572i	−0.497567	+	0.0492608i
$61$	1.06847	−	6.05962i	0.136804	−	0.775855i	−0.836782	−	0.547536i	$-0.815566\pi$
$61$	1.06847	−	6.05962i	0.136804	−	0.775855i	0.973586	−	0.228319i	$-0.0733229\pi$
$62$	9.77405	−	2.61895i	1.24131	−	0.332607i
$63$	8.41742	+	5.62926i	1.06050	+	0.709220i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	−14.8126	−	5.37946i	−1.83728	−	0.667240i
$66$	−0.220881	+	0.158214i	−0.0271886	+	0.0194748i
$67$	−0.491625	+	5.61930i	−0.0600615	+	0.686506i	0.905160	+	0.425072i	$0.139751\pi$
$67$	−0.491625	+	5.61930i	−0.0600615	+	0.686506i	−0.965221	+	0.261435i	$0.915804\pi$
$68$	0.240294	−	2.74657i	0.0291399	−	0.333070i
$69$	−11.8815	−	5.38633i	−1.43036	−	0.648438i
$70$	−6.83826	+	3.19464i	−0.817329	+	0.381832i
$71$	−6.34096	+	3.66095i	−0.752533	+	0.434475i	−0.826608	−	0.562778i	$-0.809733\pi$
$71$	−6.34096	+	3.66095i	−0.752533	+	0.434475i	0.0740754	+	0.997253i	$0.476399\pi$
$72$	1.77295	+	2.42005i	0.208944	+	0.285206i
$73$	−12.8267	+	3.43691i	−1.50125	+	0.402260i	−0.913520	−	0.406795i	$-0.866646\pi$
$73$	−12.8267	+	3.43691i	−1.50125	+	0.402260i	−0.587734	+	0.809054i	$0.699980\pi$
$74$	−0.390282	+	2.21340i	−0.0453694	+	0.257303i
$75$	−8.17329	−	2.86310i	−0.943770	−	0.330603i
$76$	4.71859	+	1.71743i	0.541260	+	0.197002i
$77$	−0.303701	+	0.433730i	−0.0346100	+	0.0494281i
$78$	2.24831	+	11.9982i	0.254571	+	1.35853i
$79$	4.50205	−	5.36533i	0.506520	−	0.603647i	−0.450819	−	0.892615i	$-0.648868\pi$
$79$	4.50205	−	5.36533i	0.506520	−	0.603647i	0.957339	+	0.288969i	$0.0933124\pi$
$80$	−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
$83$	−1.35929	+	0.118923i	−0.149202	+	0.0130535i	−0.161512	−	0.986871i	$-0.551637\pi$
$83$	−1.35929	+	0.118923i	−0.149202	+	0.0130535i	0.0123101	+	0.999924i	$0.496081\pi$
$84$	4.82473	+	3.30190i	0.526421	+	0.360267i
$85$	3.07870	−	5.34121i	0.333932	−	0.579335i
$86$	1.20902	−	3.32174i	0.130372	−	0.358193i
$87$	−0.413885	−	0.233085i	−0.0443732	−	0.0249893i
$88$	−0.128496	+	0.0899741i	−0.0136978	+	0.00959128i
$89$	2.96196	−	5.13026i	0.313967	−	0.543806i	−0.665251	−	0.746620i	$-0.731675\pi$
$89$	2.96196	−	5.13026i	0.313967	−	0.543806i	0.979217	+	0.202814i	$0.0650086\pi$
$90$	1.31071	+	6.57891i	0.138161	+	0.693478i
$91$	11.8945	+	20.6019i	1.24689	+	2.15967i
$92$	−6.82610	−	3.18306i	−0.711670	−	0.331857i
$93$	−6.17034	−	16.4043i	−0.639835	−	1.70104i
$94$	1.40914	+	1.67935i	0.145342	+	0.173212i
$95$	7.94519	+	7.93394i	0.815160	+	0.814005i
$96$	1.00860	+	1.40810i	0.102939	+	0.143713i
$97$	−1.16709	+	2.50284i	−0.118500	+	0.254125i	−0.956607	−	0.291382i	$-0.905885\pi$
$97$	−1.16709	+	2.50284i	−0.118500	+	0.254125i	0.838106	+	0.545507i	$0.183663\pi$
$98$	4.24380	+	1.13712i	0.428689	+	0.114867i
$99$	0.310142	+	0.353938i	0.0311705	+	0.0355721i
$100$	−4.70088	−	1.70344i	−0.470088	−	0.170344i
$101$	2.36001	+	0.416133i	0.234829	+	0.0414068i	0.289824	−	0.957080i	$-0.406403\pi$
$101$	2.36001	+	0.416133i	0.234829	+	0.0414068i	−0.0549949	+	0.998487i	$0.517514\pi$
$102$	−4.77509	+	0.0511259i	−0.472805	+	0.00506222i
$103$	−4.35811	−	9.34600i	−0.429417	−	0.920889i	−0.995340	−	0.0964301i	$-0.969258\pi$
$103$	−4.35811	−	9.34600i	−0.429417	−	0.920889i	0.565922	−	0.824459i	$-0.308520\pi$
$104$	1.22382	+	6.94065i	0.120006	+	0.680587i
$105$	6.66529	+	11.2462i	0.650466	+	1.09751i
$106$	−4.48596	−	3.76417i	−0.435715	−	0.365608i
$107$	6.46061	+	6.46061i	0.624571	+	0.624571i	0.946697	−	0.322126i	$-0.104397\pi$
$107$	6.46061	+	6.46061i	0.624571	+	0.624571i	−0.322126	+	0.946697i	$0.604397\pi$
$108$	3.87117	−	3.46613i	0.372504	−	0.333528i
$109$		−	6.23309i		−	0.597022i	−0.954406	−	0.298511i	$-0.903510\pi$
$109$		−	6.23309i		−	0.597022i	0.954406	−	0.298511i	$-0.0964899\pi$
$110$	−0.345389	+	0.0611538i	−0.0329315	+	0.00583079i
$111$	3.88146	+	0.297747i	0.368412	+	0.0282609i
$112$	2.76499	+	1.93607i	0.261267	+	0.182941i
$113$	6.33293	−	2.95310i	0.595752	−	0.277804i	−0.101263	−	0.994860i	$-0.532289\pi$
$113$	6.33293	−	2.95310i	0.595752	−	0.277804i	0.697016	+	0.717056i	$0.254511\pi$
$114$	2.16097	−	8.42462i	0.202393	−	0.789038i
$115$	−10.8347	−	12.8937i	−1.01034	−	1.20234i
$116$	−0.237502	−	0.137122i	−0.0220515	−	0.0127315i
$117$	20.3009	−	5.90827i	1.87682	−	0.546220i
$118$	2.45932	−	9.17832i	0.226399	−	0.844933i
$119$	−8.74502	+	3.18293i	−0.801655	+	0.291778i
$120$	0.716031	+	3.80622i	0.0653644	+	0.347459i
$121$	8.40764	−	7.05485i	0.764331	−	0.641350i
$122$	−6.12968	−	0.536278i	−0.554955	−	0.0485523i
$123$	8.90213	+	7.30880i	0.802678	+	0.659012i
$124$	−3.46085	−	9.50860i	−0.310793	−	0.853898i
$125$	−7.92249	−	7.88887i	−0.708609	−	0.705602i
$126$	4.87421	−	8.87601i	0.434229	−	0.790738i
$127$	−2.23045	−	8.32416i	−0.197921	−	0.738650i	−0.991491	−	0.130172i	$-0.958447\pi$
$127$	−2.23045	−	8.32416i	−0.197921	−	0.738650i	0.793571	−	0.608478i	$-0.208220\pi$
$128$	0.573576	+	0.819152i	0.0506975	+	0.0724035i
$129$	−5.93067	−	1.52126i	−0.522167	−	0.133939i
$130$	−4.06799	+	15.2251i	−0.356786	+	1.33533i
$131$	5.40876	−	0.953710i	0.472565	−	0.0833260i	0.0677067	−	0.997705i	$-0.478432\pi$
$131$	5.40876	−	0.953710i	0.472565	−	0.0833260i	0.404859	+	0.914379i	$0.367321\pi$
$132$	0.176863	+	0.206251i	0.0153939	+	0.0179519i
$133$	−1.47724	−	16.8849i	−0.128093	−	1.46411i
$134$	5.64076			0.487287
$135$	11.1183	−	3.37395i	0.956910	−	0.290383i
$136$	−2.75706			−0.236416
$137$	1.34600	+	15.3849i	0.114997	+	1.31442i	0.806151	+	0.591710i	$0.201547\pi$
$137$	1.34600	+	15.3849i	0.114997	+	1.31442i	−0.691154	+	0.722707i	$0.742898\pi$
$138$	−4.33029	+	12.3057i	−0.368619	+	1.04753i
$139$	−12.2294	+	2.15638i	−1.03729	+	0.182902i	−0.666259	−	0.745720i	$-0.732106\pi$
$139$	−12.2294	+	2.15638i	−1.03729	+	0.182902i	−0.371028	+	0.928622i	$0.620995\pi$
$140$	3.77847	+	6.53381i	0.319339	+	0.552208i
$141$	2.65603	−	2.71352i	0.223678	−	0.228520i
$142$	4.19967	+	5.99775i	0.352429	+	0.503320i
$143$	0.286135	+	1.06787i	0.0239278	+	0.0892999i
$144$	2.25632	−	1.97713i	0.188027	−	0.164761i
$145$	−0.352089	−	0.502078i	−0.0292394	−	0.0416953i
$146$	4.54175	+	12.4784i	0.375878	+	1.03272i
$147$	1.24111	−	7.50788i	0.102365	−	0.619240i
$148$	2.23899	+	0.195887i	0.184044	+	0.0161018i
$149$	−5.77544	+	4.84617i	−0.473143	+	0.397014i	−0.847939	−	0.530093i	$-0.822157\pi$
$149$	−5.77544	+	4.84617i	−0.473143	+	0.397014i	0.374797	+	0.927107i	$0.377712\pi$
$150$	−2.13986	+	8.39172i	−0.174719	+	0.685181i
$151$	7.50644	−	2.73212i	0.610865	−	0.222337i	−0.0180166	−	0.999838i	$-0.505735\pi$
$151$	7.50644	−	2.73212i	0.610865	−	0.222337i	0.628882	+	0.777501i	$0.283513\pi$
$152$	1.29964	−	4.85032i	0.105415	−	0.393413i
$153$	0.897137	+	8.22238i	0.0725292	+	0.664740i
$154$	0.458549	+	0.264743i	0.0369509	+	0.0213336i
$155$	1.95605	−	22.5417i	0.157113	−	1.81059i
$156$	11.7566	−	3.28546i	0.941279	−	0.263048i
$157$	8.75854	−	4.08417i	0.699007	−	0.325952i	−0.0404258	−	0.999183i	$-0.512871\pi$
$157$	8.75854	−	4.08417i	0.699007	−	0.325952i	0.739433	+	0.673230i	$0.235094\pi$
$158$	−5.73729	−	4.01729i	−0.456434	−	0.319599i
$159$	−5.72844	+	8.37039i	−0.454295	+	0.663815i
$160$	0.389850	+	2.20182i	0.0308203	+	0.174069i
$161$			25.4229i			2.00361i
$162$	−6.63058	−	6.08567i	−0.520948	−	0.478135i
$163$	−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
$165$	0.163930	+	0.585002i	0.0127620	+	0.0455423i
$166$	0.236940	+	1.34376i	0.0183901	+	0.104296i
$167$	−3.01422	−	6.46401i	−0.233247	−	0.500200i	0.754493	−	0.656308i	$-0.227883\pi$
$167$	−3.01422	−	6.46401i	−0.233247	−	0.500200i	−0.987740	+	0.156108i	$0.950105\pi$
$168$	2.86883	−	5.09415i	0.221335	−	0.393022i
$169$	36.1133	+	6.36775i	2.77795	+	0.489827i
$170$	−5.58921	−	2.60147i	−0.428673	−	0.199524i
$171$	−14.8880	−	2.29764i	−1.13852	−	0.175705i
$172$	−3.41448	−	0.914906i	−0.260351	−	0.0697609i
$173$	−8.98704	+	19.2728i	−0.683272	+	1.46528i	0.191872	+	0.981420i	$0.438544\pi$
$173$	−8.98704	+	19.2728i	−0.683272	+	1.46528i	−0.875144	+	0.483862i	$0.839234\pi$
$174$	−0.196125	+	0.432625i	−0.0148682	+	0.0327972i
$175$	1.49477	+	16.8108i	0.112994	+	1.27078i
$176$	0.100831	+	0.120166i	0.00760042	+	0.00905783i
$177$	−16.2377	−	2.68423i	−1.22050	−	0.201759i
$178$	−5.36889	−	2.50355i	−0.402415	−	0.187649i
$179$	−5.20501	−	9.01535i	−0.389041	−	0.673839i	0.603280	−	0.797530i	$-0.293860\pi$
$179$	−5.20501	−	9.01535i	−0.389041	−	0.673839i	−0.992321	+	0.123691i	$0.960527\pi$
$180$	6.43964	−	1.87911i	0.479982	−	0.140061i
$181$	−0.473902	+	0.820822i	−0.0352248	+	0.0610112i	−0.883100	−	0.469184i	$-0.844548\pi$
$181$	−0.473902	+	0.820822i	−0.0352248	+	0.0610112i	0.847876	+	0.530195i	$0.177881\pi$
$182$	19.4869	−	13.6449i	1.44446	−	1.01142i
$183$	0.114101	+	10.6569i	0.00843457	+	0.787778i
$184$	−2.57602	+	7.07755i	−0.189906	+	0.521764i
$185$	4.35413	+	2.50975i	0.320122	+	0.184520i
$186$	−15.8041	+	7.57659i	−1.15881	+	0.555542i
$187$	−0.430841	+	0.0376937i	−0.0315062	+	0.00275644i
$188$	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	−0.807959	−	0.589239i	$-0.799428\pi$
$191$	−1.20750	+	1.43904i	−0.0873714	+	0.104125i	0.720588	+	0.693364i	$0.243872\pi$
$192$	1.31483	−	1.12748i	0.0948898	−	0.0813690i
$193$	4.72914	−	6.75391i	0.340411	−	0.486157i	−0.612049	−	0.790820i	$-0.709655\pi$
$193$	4.72914	−	6.75391i	0.340411	−	0.486157i	0.952460	+	0.304662i	$0.0985435\pi$
$194$	2.59504	+	0.944516i	0.186313	+	0.0678123i
$195$	26.9334	+	4.43270i	1.92874	+	0.317432i
$196$	0.762924	−	4.32676i	0.0544946	−	0.309054i
$197$	−10.4024	+	2.78731i	−0.741139	+	0.198588i	−0.609584	−	0.792721i	$-0.708664\pi$
$197$	−10.4024	+	2.78731i	−0.741139	+	0.198588i	−0.131555	+	0.991309i	$0.541997\pi$
$198$	0.325560	−	0.339810i	0.0231366	−	0.0241492i
$199$	−0.415328	+	0.239790i	−0.0294419	+	0.0169983i	−0.514649	−	0.857401i	$-0.672078\pi$
$199$	−0.415328	+	0.239790i	−0.0294419	+	0.0169983i	0.485207	+	0.874399i	$0.338744\pi$
$200$	−1.28725	+	4.83146i	−0.0910222	+	0.341636i
$201$	−0.955672	−	9.72323i	−0.0674079	−	0.685824i
$202$	0.208861	−	2.38729i	0.0146954	−	0.167969i
$203$	−0.0806793	+	0.922169i	−0.00566258	+	0.0647236i
$204$	0.467108	+	4.75247i	0.0327041	+	0.332739i
$205$	6.29380	+	13.4722i	0.439578	+	0.940936i
$206$	−8.93060	+	5.15608i	−0.622224	+	0.359241i
$207$	21.9456	+	5.37945i	1.52532	+	0.373897i
$208$	6.80758	−	1.82409i	0.472021	−	0.126478i
$209$	0.136780	−	0.775720i	0.00946129	−	0.0536576i
$210$	10.6225	−	7.62010i	0.733019	−	0.525837i
$211$	−10.9492	−	3.98519i	−0.753775	−	0.274352i	−0.0635814	−	0.997977i	$-0.520252\pi$
$211$	−10.9492	−	3.98519i	−0.753775	−	0.274352i	−0.690193	+	0.723625i	$0.742474\pi$
$212$	−3.35887	+	4.79696i	−0.230688	+	0.329457i
$213$	9.62708	−	8.25532i	0.659636	−	0.565645i
$214$	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
$218$	−6.20937	+	0.543250i	−0.420552	+	0.0367935i
$219$	20.7400	−	9.94293i	1.40148	−	0.671881i
$220$	0.0910238	+	0.338745i	0.00613682	+	0.0228382i
$221$	−6.64579	+	18.2592i	−0.447044	+	1.22824i
$222$	−0.0416777	−	3.89264i	−0.00279722	−	0.261257i
$223$	−11.6731	+	8.17360i	−0.781689	+	0.547345i	−0.894921	−	0.446224i	$-0.852768\pi$
$223$	−11.6731	+	8.17360i	−0.781689	+	0.547345i	0.113232	+	0.993569i	$0.463880\pi$
$224$	1.68771	−	2.92321i	0.112765	−	0.195315i
$225$	14.8277	+	2.26682i	0.988515	+	0.151121i
$226$	−3.49381	−	6.05146i	−0.232405	−	0.402537i
$227$	−2.70835	−	1.26293i	−0.179760	−	0.0838233i	0.330655	−	0.943752i	$-0.392730\pi$
$227$	−2.70835	−	1.26293i	−0.179760	−	0.0838233i	−0.510415	+	0.859928i	$0.670508\pi$
$228$	−8.58091	−	1.41849i	−0.568284	−	0.0939420i
$229$	−8.45187	−	10.0725i	−0.558515	−	0.665612i	0.410716	−	0.911763i	$-0.365279\pi$
$229$	−8.45187	−	10.0725i	−0.558515	−	0.665612i	−0.969232	+	0.246151i	$0.920834\pi$
$230$	−11.9003	+	11.9172i	−0.784684	+	0.785797i
$231$	0.378661	−	0.835275i	0.0249141	−	0.0549571i
$232$	−0.115901	+	0.248550i	−0.00760925	+	0.0163181i
$233$	9.49465	+	2.54408i	0.622015	+	0.166668i	0.556044	−	0.831153i	$-0.312319\pi$
$233$	9.49465	+	2.54408i	0.622015	+	0.166668i	0.0659714	+	0.997822i	$0.478985\pi$
$234$	−7.65513	−	19.7087i	−0.500432	−	1.28840i
$235$	4.60517	−	1.67984i	0.300408	−	0.109581i
$236$	−9.35774	−	1.65002i	−0.609137	−	0.107407i
$237$	−5.95276	+	10.5702i	−0.386674	+	0.686611i
$238$	3.93299	+	8.43433i	0.254938	+	0.546716i
$239$	1.34900	+	7.65056i	0.0872595	+	0.494873i	0.996846	+	0.0793589i	$0.0252873\pi$
$239$	1.34900	+	7.65056i	0.0872595	+	0.494873i	−0.909587	+	0.415514i	$0.863602\pi$
$240$	3.72933	−	1.04504i	0.240727	−	0.0674570i
$241$	10.5110	+	8.81980i	0.677075	+	0.568133i	0.915150	−	0.403114i	$-0.132072\pi$
$241$	10.5110	+	8.81980i	0.677075	+	0.568133i	−0.238075	+	0.971247i	$0.576516\pi$
$242$	−7.76078	−	7.76078i	−0.498882	−	0.498882i
$243$	−9.36677	+	12.4605i	−0.600879	+	0.799340i
$244$			6.15310i			0.393912i
$245$	5.62921	−	8.05149i	0.359637	−	0.514391i
$246$	6.50512	−	9.50526i	0.414751	−	0.606033i
$247$	−28.9895	−	20.2986i	−1.84456	−	1.29157i
$248$	−9.17078	+	4.27641i	−0.582345	+	0.271552i
$249$	2.27615	−	0.636087i	0.144245	−	0.0403104i
$250$	−7.16836	+	8.57990i	−0.453367	+	0.542640i
$251$	−16.4462	−	9.49521i	−1.03807	−	0.599333i	−0.118787	−	0.992920i	$-0.537901\pi$
$251$	−16.4462	−	9.49521i	−1.03807	−	0.599333i	−0.919287	+	0.393587i	$0.871234\pi$
$252$	−9.26705	−	4.08207i	−0.583769	−	0.257146i
$253$	−0.305787	+	1.14121i	−0.0192247	+	0.0717475i
$254$	−8.09809	+	2.94746i	−0.508119	+	0.184940i
$255$	−3.53733	+	10.0751i	−0.221516	+	0.630928i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	11.4082	+	0.998091i	0.711626	+	0.0622592i	0.437220	−	0.899355i	$-0.355963\pi$
$257$	11.4082	+	0.998091i	0.711626	+	0.0622592i	0.274406	+	0.961614i	$0.411519\pi$
$258$	−0.998575	+	6.04069i	−0.0621686	+	0.376077i
$259$	−2.59471	−	7.12891i	−0.161228	−	0.442969i
$260$	15.5217	+	2.72555i	0.962616	+	0.169032i
$261$	0.778963	+	0.264773i	0.0482166	+	0.0163891i
$262$	−1.42149	−	5.30506i	−0.0878196	−	0.327747i
$263$	−4.57606	−	6.53529i	−0.282172	−	0.402983i	0.652899	−	0.757445i	$-0.273553\pi$
$263$	−4.57606	−	6.53529i	−0.282172	−	0.402983i	−0.935070	+	0.354462i	$0.884664\pi$
$264$	0.190052	−	0.194166i	0.0116969	−	0.0119501i
$265$	−11.3355	+	6.55525i	−0.696332	+	0.402686i
$266$	−16.6919	+	2.94324i	−1.02345	+	0.180462i
$267$	−3.40588	+	9.67875i	−0.208436	+	0.592330i
$268$	−0.491625	−	5.61930i	−0.0300308	−	0.343253i
$269$	−23.8729			−1.45556			−0.727780	−	0.685811i	$-0.759448\pi$
$269$	−23.8729			−1.45556			−0.727780	+	0.685811i	$0.759448\pi$
$270$	−4.33013	−	10.7819i	−0.263523	−	0.656167i
$271$	−13.7477			−0.835112			−0.417556	−	0.908651i	$-0.637113\pi$
$271$	−13.7477			−0.835112			−0.417556	+	0.908651i	$0.637113\pi$
$272$	0.240294	+	2.74657i	0.0145699	+	0.166535i
$273$	−26.8218	−	31.2786i	−1.62333	−	1.89307i
$274$	15.2090	−	2.68176i	0.918809	−	0.162011i
$275$	−0.135102	+	0.772602i	−0.00814694	+	0.0465897i
$276$	12.6363	+	3.24130i	0.760617	+	0.195103i
$277$	−12.1407	−	17.3388i	−0.729467	−	1.04179i	−0.996936	−	0.0782202i	$-0.975076\pi$
$277$	−12.1407	−	17.3388i	−0.729467	−	1.04179i	0.267469	−	0.963566i	$-0.413813\pi$
$278$	3.21404	+	11.9950i	0.192765	+	0.719410i
$279$	15.7377	+	25.9585i	0.942190	+	1.55410i
$280$	6.17963	−	4.33355i	0.369304	−	0.258979i
$281$	−8.31974	−	22.8583i	−0.496314	−	1.36361i	−0.894812	−	0.446443i	$-0.852691\pi$
$281$	−8.31974	−	22.8583i	−0.496314	−	1.36361i	0.398498	−	0.917169i	$-0.369532\pi$
$282$	−2.93468	−	2.40942i	−0.174758	−	0.143479i
$283$	7.96040	+	0.696445i	0.473197	+	0.0413993i	0.321260	−	0.946991i	$-0.395894\pi$
$283$	7.96040	+	0.696445i	0.473197	+	0.0413993i	0.151936	+	0.988390i	$0.451449\pi$
$284$	5.60890	−	4.70643i	0.332827	−	0.279275i
$285$	−16.0571	−	10.9723i	−0.951139	−	0.649942i
$286$	1.03887	−	0.378118i	0.0614297	−	0.0223586i
$287$	5.80958	−	21.6817i	0.342929	−	1.27983i
$288$	−2.16625	−	2.07541i	−0.127648	−	0.122295i
$289$	8.13944	+	4.69931i	0.478791	+	0.276430i
$290$	−0.469481	+	0.394509i	−0.0275689	+	0.0231663i
$291$	1.18845	−	4.63320i	0.0696679	−	0.271603i
$292$	12.0350	−	5.61203i	0.704297	−	0.328419i
$293$	10.9018	+	7.63355i	0.636892	+	0.445957i	0.846907	−	0.531741i	$-0.178462\pi$
$293$	10.9018	+	7.63355i	0.636892	+	0.445957i	−0.210014	+	0.977698i	$0.567351\pi$
$294$	−7.58748	−	0.582036i	−0.442511	−	0.0339450i
$295$	−17.4134	−	12.1746i	−1.01385	−	0.708834i
$296$		−	2.24755i		−	0.130636i
$297$	−0.640902	−	0.503611i	−0.0371889	−	0.0292225i
$298$	5.33109	+	5.33109i	0.308822	+	0.308822i
$299$	40.6630	+	34.1203i	2.35160	+	1.97323i
$300$	8.54629	+	1.40033i	0.493420	+	0.0808480i
$301$	2.07195	+	11.7506i	0.119425	+	0.677294i
$302$	−3.37595	−	7.23975i	−0.194264	−	0.416601i
$303$	−4.15047	+	0.0444382i	−0.238438	+	0.00255291i
$304$	−4.94514	−	0.871961i	−0.283623	−	0.0500104i
$305$	−5.80586	+	12.4738i	−0.332442	+	0.714246i
$306$	8.11290	−	1.61035i	0.463784	−	0.0920576i
$307$	10.5675	+	2.83155i	0.603118	+	0.161605i	0.547442	−	0.836844i	$-0.315602\pi$
$307$	10.5675	+	2.83155i	0.603118	+	0.161605i	0.0556765	+	0.998449i	$0.482268\pi$
$308$	0.223771	−	0.479878i	0.0127505	−	0.0273436i
$309$	10.4008	+	14.5205i	0.591682	+	0.826043i
$310$	−22.6264	+	0.0160364i	−1.28509	+	0.000910806i
$311$	−2.19146	−	2.61168i	−0.124266	−	0.148095i	0.700324	−	0.713825i	$-0.253039\pi$
$311$	−2.19146	−	2.61168i	−0.124266	−	0.148095i	−0.824590	+	0.565730i	$0.808594\pi$
$312$	−4.29762	−	11.4255i	−0.243305	−	0.646841i
$313$	−7.50842	−	3.50123i	−0.424401	−	0.197901i	0.198671	−	0.980066i	$-0.436338\pi$
$313$	−7.50842	−	3.50123i	−0.424401	−	0.197901i	−0.623071	+	0.782165i	$0.714115\pi$
$314$	−4.83199	−	8.36925i	−0.272685	−	0.472304i
$315$	−14.9348	−	17.0194i	−0.841480	−	0.958934i
$316$	−3.50197	+	6.06559i	−0.197001	+	0.341216i
$317$	25.5282	−	17.8751i	1.43381	−	1.00396i	0.439407	−	0.898288i	$-0.355189\pi$
$317$	25.5282	−	17.8751i	1.43381	−	1.00396i	0.994401	−	0.105675i	$-0.0337004\pi$
$318$	8.83780	+	4.97712i	0.495599	+	0.279103i
$319$	−0.0147135	+	0.0404250i	−0.000823797	+	0.00226336i
$320$	2.15947	−	0.580268i	0.120718	−	0.0324379i
$321$	−13.0597	−	8.93765i	−0.728920	−	0.498851i
$322$	25.3262	−	2.21575i	1.41137	−	0.123479i
$323$	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
$327$	1.98843	+	10.6113i	0.109961	+	0.586808i
$328$	3.81427	−	5.44734i	0.210608	−	0.300779i
$329$	−6.95347	−	2.53086i	−0.383357	−	0.139531i
$330$	0.568488	−	0.214293i	0.0312942	−	0.0117964i
$331$	−1.55033	+	8.79236i	−0.0852138	+	0.483272i	0.912096	+	0.409976i	$0.134463\pi$
$331$	−1.55033	+	8.79236i	−0.0852138	+	0.483272i	−0.997310	+	0.0732958i	$0.976648\pi$
$332$	1.31799	−	0.353155i	0.0723342	−	0.0193819i
$333$	−6.70286	+	0.731343i	−0.367314	+	0.0400774i
$334$	−6.17670	+	3.56612i	−0.337974	+	0.195129i
$335$	4.30554	−	11.8555i	0.235237	−	0.647736i
$336$	−5.32480	−	2.41393i	−0.290491	−	0.131691i
$337$	0.756685	−	8.64895i	0.0412193	−	0.471138i	−0.947332	−	0.320253i	$-0.896232\pi$
$337$	0.756685	−	8.64895i	0.0412193	−	0.471138i	0.988551	−	0.150885i	$-0.0482124\pi$
$338$	3.19604	−	36.5309i	0.173842	−	1.98702i
$339$	−9.83924	+	7.04769i	−0.534394	+	0.382778i
$340$	−2.10444	+	5.79467i	−0.114129	+	0.314260i
$341$	−1.37464	+	0.793647i	−0.0744407	+	0.0429784i
$342$	−0.991321	+	15.0316i	−0.0536045	+	0.812817i
$343$	8.49824	−	2.27710i	0.458862	−	0.122952i
$344$	−0.613833	+	3.48122i	−0.0330957	+	0.187695i
$345$	22.5584	+	18.4941i	1.21450	+	0.995688i
$346$	19.9827	+	7.27311i	1.07428	+	0.391005i
$347$	−10.4291	+	14.8942i	−0.559862	+	0.799565i	−0.994902	−	0.100846i	$-0.967845\pi$
$347$	−10.4291	+	14.8942i	−0.559862	+	0.799565i	0.435041	+	0.900411i	$0.356734\pi$
$348$	0.448072	+	0.157673i	0.0240192	+	0.00845217i
$349$	−5.55475	+	6.61989i	−0.297339	+	0.354355i	−0.893943	−	0.448181i	$-0.852072\pi$
$349$	−5.55475	+	6.61989i	−0.297339	+	0.354355i	0.596604	+	0.802536i	$0.296516\pi$
$350$	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
$353$	−12.7045	+	1.11150i	−0.676191	+	0.0591590i	−0.420078	−	0.907488i	$-0.637997\pi$
$353$	−12.7045	+	1.11150i	−0.676191	+	0.0591590i	−0.256113	+	0.966647i	$0.582442\pi$
$354$	−1.25880	+	16.4099i	−0.0669047	+	0.872176i
$355$	15.8114	−	4.24866i	0.839182	−	0.225496i
$356$	−2.02610	+	5.56666i	−0.107383	+	0.295032i
$357$	13.8723	−	8.20844i	0.734200	−	0.434437i
$358$	−8.52740	+	5.97095i	−0.450687	+	0.315574i
$359$	13.0182	−	22.5482i	0.687074	−	1.19005i	−0.285706	−	0.958317i	$-0.592228\pi$
$359$	13.0182	−	22.5482i	0.687074	−	1.19005i	0.972780	−	0.231730i	$-0.0744387\pi$
$360$	−2.43321	−	6.25136i	−0.128242	−	0.329475i
$361$	3.10735	+	5.38208i	0.163545	+	0.283267i
$362$	0.859001	+	0.400559i	0.0451481	+	0.0210529i
$363$	−12.0627	+	14.6924i	−0.633130	+	0.771153i
$364$	−15.2913	−	18.2235i	−0.801483	−	0.955170i
$365$	29.6932	−	0.0210449i	1.55421	−	0.00110154i
$366$	10.6064	−	1.04247i	0.554404	−	0.0544910i
$367$	10.6419	−	22.8217i	0.555505	−	1.19128i	−0.405333	−	0.914169i	$-0.632844\pi$
$367$	10.6419	−	22.8217i	0.555505	−	1.19128i	0.960837	−	0.277114i	$-0.0893780\pi$
$368$	7.27513	+	1.94936i	0.379242	+	0.101618i
$369$	−17.4868	−	9.60275i	−0.910324	−	0.499899i
$370$	2.12071	−	4.55630i	0.110250	−	0.236871i
$371$	19.4662	+	3.43242i	1.01064	+	0.178202i
$372$	8.92517	+	15.0836i	0.462749	+	0.782047i
$373$	−6.07335	−	13.0243i	−0.314466	−	0.674375i	0.684015	−	0.729468i	$-0.260232\pi$
$373$	−6.07335	−	13.0243i	−0.314466	−	0.674375i	−0.998481	+	0.0550932i	$0.982454\pi$
$374$	0.0751005	+	0.425916i	0.00388335	+	0.0220236i
$375$	16.0040	+	10.9028i	0.826445	+	0.563018i
$376$	−1.67935	−	1.40914i	−0.0866058	−	0.0726709i
$377$	1.36669	+	1.36669i	0.0703883	+	0.0703883i
$378$	−5.46640	+	16.6656i	−0.281161	+	0.857187i
$379$		−	21.2421i		−	1.09113i	−0.838067	−	0.545567i	$-0.816314\pi$
$379$		−	21.2421i		−	1.09113i	0.838067	−	0.545567i	$-0.183686\pi$
$380$	−9.20220	−	6.43374i	−0.472063	−	0.330044i
$381$	6.45267	+	13.4597i	0.330580	+	0.689560i
$382$	1.53880	+	1.07748i	0.0787320	+	0.0551287i
$383$	26.6190	−	12.4126i	1.36017	−	0.634256i	0.400734	−	0.916195i	$-0.368755\pi$
$383$	26.6190	−	12.4126i	1.36017	−	0.634256i	0.959432	+	0.281939i	$0.0909774\pi$
$384$	−1.23779	−	1.21156i	−0.0631656	−	0.0618273i
$385$	0.906433	−	0.761683i	0.0461961	−	0.0388190i
$386$	−7.14039	−	4.12250i	−0.363436	−	0.209830i
$387$	10.5818	+	0.697859i	0.537903	+	0.0354742i
$388$	0.714749	−	2.66748i	0.0362859	−	0.135421i
$389$	8.20972	−	2.98809i	0.416249	−	0.151502i	−0.125401	−	0.992106i	$-0.540022\pi$
$389$	8.20972	−	2.98809i	0.416249	−	0.151502i	0.541651	+	0.840604i	$0.317800\pi$
$390$	2.06843	−	27.2172i	0.104739	−	1.37820i
$391$	−15.9073	+	13.3478i	−0.804468	+	0.675029i
$392$	−4.37679	−	0.382919i	−0.221061	−	0.0193403i
$393$	−8.90373	+	3.34907i	−0.449134	+	0.168938i
$394$	3.68333	+	10.1199i	0.185563	+	0.509831i
$395$	−12.8226	+	8.99203i	−0.645175	+	0.452438i
$396$	−0.366891	−	0.294705i	−0.0184370	−	0.0148095i
$397$	1.22867	+	4.58547i	0.0616653	+	0.230138i	0.989880	−	0.141907i	$-0.0453234\pi$
$397$	1.22867	+	4.58547i	0.0616653	+	0.230138i	−0.928215	+	0.372045i	$0.878657\pi$
$398$	0.275076	+	0.392849i	0.0137883	+	0.0196917i
$399$	7.90139	+	28.2740i	0.395564	+	1.41547i
$400$	4.92526	+	0.861260i	0.246263	+	0.0430630i
$401$	16.1036	−	2.83951i	0.804178	−	0.141798i	0.243574	−	0.969882i	$-0.421680\pi$
$401$	16.1036	−	2.83951i	0.804178	−	0.141798i	0.560604	+	0.828084i	$0.310569\pi$
$402$	−9.60294	+	1.79947i	−0.478951	+	0.0897495i
$403$	6.21549	+	71.0434i	0.309616	+	3.53893i
$404$	−2.39641			−0.119226
$405$	−17.8517	+	9.29074i	−0.887057	+	0.461661i
$406$	0.925691			0.0459413
$407$	−0.0307278	−	0.351220i	−0.00152312	−	0.0174093i
$408$	4.69367	−	0.879536i	0.232371	−	0.0435435i
$409$	−2.97423	+	0.524437i	−0.147066	+	0.0259317i	−0.246696	−	0.969093i	$-0.579345\pi$
$409$	−2.97423	+	0.524437i	−0.147066	+	0.0259317i	0.0996304	+	0.995025i	$0.468234\pi$
$410$	12.8723	−	7.44402i	0.635720	−	0.367634i
$411$	−7.19941	−	25.7621i	−0.355121	−	1.27075i
$412$	5.91482	+	8.44723i	0.291402	+	0.416165i
$413$	8.30126	+	30.9807i	0.408479	+	1.52446i
$414$	3.44629	−	22.3309i	0.169376	−	1.09751i
$415$	3.00510	+	0.527685i	0.147515	+	0.0259030i
$416$	−2.41046	−	6.62269i	−0.118183	−	0.324704i
$417$	20.1317	−	7.57240i	0.985854	−	0.370822i
$418$	−0.784689	−	0.0686514i	−0.0383804	−	0.00335785i
$419$	−28.7021	+	24.0840i	−1.40219	+	1.17658i	−0.442075	+	0.896978i	$0.645758\pi$
$419$	−28.7021	+	24.0840i	−1.40219	+	1.17658i	−0.960116	+	0.279601i	$0.909798\pi$
$420$	−8.51691	−	9.91790i	−0.415583	−	0.483944i
$421$	9.12077	−	3.31969i	0.444519	−	0.161792i	−0.110056	−	0.993925i	$-0.535103\pi$
$421$	9.12077	−	3.31969i	0.444519	−	0.161792i	0.554575	+	0.832134i	$0.312881\pi$
$422$	−3.01573	+	11.2549i	−0.146804	+	0.547879i
$423$	−3.65603	+	5.46685i	−0.177762	+	0.265807i
$424$	5.07145	+	2.92800i	0.246291	+	0.142196i
$425$	−9.73385	+	9.76149i	−0.472161	+	0.473502i
$426$	−9.06296	−	8.87094i	−0.439102	−	0.429799i
$427$	18.8234	−	8.77750i	0.910928	−	0.424773i
$428$	−7.48433	−	5.24059i	−0.361769	−	0.253313i
$429$	−0.827786	−	1.72668i	−0.0399659	−	0.0833651i
$430$	−4.52915	+	6.47806i	−0.218415	+	0.312400i
$431$		−	1.48091i		−	0.0713331i	−0.999364	−	0.0356666i	$-0.988645\pi$
$431$		−	1.48091i		−	0.0713331i	0.999364	−	0.0356666i	$-0.0113554\pi$
$432$	−3.21047	+	4.08569i	−0.154464	+	0.196573i
$433$	−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
$435$	0.759573	+	0.742427i	0.0364187	+	0.0355966i
$436$	1.08236	+	6.13840i	0.0518359	+	0.293976i
$437$	−15.9835	−	34.2767i	−0.764595	−	1.63968i
$438$	−11.7127	−	19.7945i	−0.559655	−	0.945819i
$439$	−4.66120	−	0.821895i	−0.222467	−	0.0392269i	0.0613035	−	0.998119i	$-0.480474\pi$
$439$	−4.66120	−	0.821895i	−0.222467	−	0.0392269i	−0.283770	+	0.958892i	$0.591585\pi$
$440$	0.329523	−	0.120201i	0.0157094	−	0.00573035i
$441$	0.282210	+	13.1775i	0.0134386	+	0.627500i
$442$	18.7689	+	5.02911i	0.892746	+	0.239210i
$443$	10.9780	−	23.5424i	0.521580	−	1.11853i	−0.452382	−	0.891824i	$-0.649426\pi$
$443$	10.9780	−	23.5424i	0.521580	−	1.11853i	0.973963	−	0.226709i	$-0.0727965\pi$
$444$	−3.87420	+	0.380785i	−0.183861	+	0.0180713i
$445$	−9.35989	+	9.37316i	−0.443701	+	0.444331i
$446$	9.15987	+	10.9163i	0.433733	+	0.516902i
$447$	8.28623	−	10.0926i	0.391925	−	0.477366i
$448$	−3.05918	−	1.42652i	−0.144532	−	0.0673966i
$449$	3.45907	+	5.99129i	0.163244	+	0.282746i	0.936030	−	0.351920i	$-0.114471\pi$
$449$	3.45907	+	5.99129i	0.163244	+	0.282746i	−0.772787	+	0.634666i	$0.781138\pi$
$450$	0.965875	−	14.9689i	0.0455318	−	0.705639i
$451$	0.521575	−	0.903394i	0.0245600	−	0.0425391i
$452$	−5.72392	+	4.00793i	−0.269231	+	0.188517i
$453$	−11.9075	+	7.04586i	−0.559464	+	0.331043i
$454$	−1.02207	+	2.80812i	−0.0479682	+	0.131791i
$455$	−13.8040	−	51.3717i	−0.647143	−	2.40834i
$456$	−0.665220	+	8.67188i	−0.0311518	+	0.406098i
$457$	16.8812	−	1.47692i	0.789671	−	0.0690872i	0.314818	−	0.949152i	$-0.398057\pi$
$457$	16.8812	−	1.47692i	0.789671	−	0.0690872i	0.474853	+	0.880065i	$0.342501\pi$
$458$	−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	0.251246	−	0.967923i	$-0.419160\pi$
$461$	24.9242	−	29.7035i	1.16084	−	1.38343i	0.909590	−	0.415507i	$-0.136396\pi$
$462$	−0.865099	−	0.304422i	−0.0402480	−	0.0141630i
$463$	−13.5397	+	19.3367i	−0.629242	+	0.898651i	−0.999542	−	0.0302612i	$-0.990366\pi$
$463$	−13.5397	+	19.3367i	−0.629242	+	0.898651i	0.370300	+	0.928912i	$0.379255\pi$
$464$	0.257705	+	0.0937970i	0.0119637	+	0.00435442i
$465$	3.86107	+	38.9994i	0.179053	+	1.80856i
$466$	1.70689	−	9.68025i	0.0790701	−	0.448429i
$467$	16.5171	−	4.42576i	0.764322	−	0.204800i	0.144461	−	0.989511i	$-0.453855\pi$
$467$	16.5171	−	4.42576i	0.764322	−	0.204800i	0.619862	+	0.784711i	$0.287189\pi$
$468$	−18.9665	+	9.34373i	−0.876727	+	0.431914i
$469$	−16.4891	+	9.51999i	−0.761396	+	0.439592i
$470$	−2.07482	−	4.44124i	−0.0957042	−	0.204859i
$471$	−13.6078	+	9.74705i	−0.627014	+	0.449120i
$472$	−0.828162	+	9.46594i	−0.0381193	+	0.435705i
$473$	−0.0483284	+	0.552397i	−0.00222214	+	0.0253992i
$474$	11.0488	+	5.00885i	0.507490	+	0.230064i
$475$	−12.5844	−	21.7256i	−0.577410	−	0.996838i
$476$	8.05945	−	4.65313i	0.369404	−	0.213276i
$477$	7.08196	−	16.0774i	0.324260	−	0.736131i
$478$	7.50387	−	2.01066i	0.343219	−	0.0919653i
$479$	5.73160	−	32.5055i	0.261884	−	1.48522i	−0.515881	−	0.856660i	$-0.672535\pi$
$479$	5.73160	−	32.5055i	0.261884	−	1.48522i	0.777765	−	0.628555i	$-0.216353\pi$
$480$	−1.36610	−	3.62406i	−0.0623534	−	0.165415i
$481$	−14.8848	−	5.41763i	−0.678689	−	0.247023i
$482$	7.87014	−	11.2397i	0.358475	−	0.511955i
$483$	−8.11022	−	43.2805i	−0.369028	−	1.96933i
$484$	−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	$0.296211\pi$
$488$	6.12968	−	0.536278i	0.277478	−	0.0242762i
$489$	20.4257	+	13.9787i	0.923680	+	0.632139i
$490$	−8.51147	−	4.90606i	−0.384509	−	0.221633i
$491$	0.523591	−	1.43855i	0.0236293	−	0.0649211i	−0.927317	−	0.374277i	$-0.877891\pi$
$491$	0.523591	−	1.43855i	0.0236293	−	0.0649211i	0.950946	+	0.309355i	$0.100113\pi$
$492$	−10.0360	−	5.65192i	−0.452460	−	0.254808i
$493$	−0.619367	+	0.433686i	−0.0278949	+	0.0195322i
$494$	−17.6948	+	30.6483i	−0.796127	+	1.37893i
$495$	−0.465701	−	0.943622i	−0.0209317	−	0.0424127i
$496$	5.05942	+	8.76317i	0.227175	+	0.393478i
$497$	−22.3990	−	10.4448i	−1.00473	−	0.468514i
$498$	−0.832046	−	2.21205i	−0.0372849	−	0.0991243i
$499$	11.0899	+	13.2165i	0.496454	+	0.591651i	0.954847	−	0.297099i	$-0.0960191\pi$
$499$	11.0899	+	13.2165i	0.496454	+	0.591651i	−0.458393	+	0.888750i	$0.651575\pi$
$500$	9.17201	+	6.39329i	0.410185	+	0.285917i
$501$	7.19355	+	10.0429i	0.321384	+	0.448683i
$502$	−8.02570	+	17.2112i	−0.358205	+	0.768172i
$503$	31.8029	+	8.52155i	1.41802	+	0.379957i	0.884781	−	0.466007i	$-0.154308\pi$
$503$	31.8029	+	8.52155i	1.41802	+	0.379957i	0.533239	+	0.845965i	$0.320975\pi$
$504$	−3.25886	+	9.58756i	−0.145161	+	0.427064i
$505$	−4.85809	−	2.26117i	−0.216182	−	0.100621i
$506$	1.16352	+	0.205160i	0.0517249	+	0.00912049i
$507$	−63.5114	+	0.680003i	−2.82064	+	0.0302000i
$508$	3.64204	+	7.81038i	0.161589	+	0.346530i
$509$	−5.96465	−	33.8272i	−0.264378	−	1.49936i	−0.770800	−	0.637078i	$-0.780143\pi$
$509$	−5.96465	−	33.8272i	−0.264378	−	1.49936i	0.506421	−	0.862286i	$-0.330968\pi$
$510$	10.3451	+	2.64577i	0.458088	+	0.117157i
$511$	−34.3364	−	28.8116i	−1.51895	−	1.27455i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	26.0786	−	0.837911i	1.15140	−	0.0369947i
$514$		−	11.4518i		−	0.505118i
$515$	4.02020	+	22.7056i	0.177151	+	1.00053i
$516$	6.10474	+	0.468294i	0.268746	+	0.0206155i
$517$	−0.281694	−	0.197244i	−0.0123889	−	0.00867480i
$518$	−6.87564	+	3.20616i	−0.302098	+	0.140871i
$519$	9.15147	−	35.6773i	0.401705	−	1.56606i
$520$	1.36238	−	15.7002i	0.0597442	−	0.688499i
$521$	16.0538	+	9.26867i	0.703330	+	0.406068i	0.808586	−	0.588377i	$-0.200233\pi$
$521$	16.0538	+	9.26867i	0.703330	+	0.406068i	−0.105256	+	0.994445i	$0.533566\pi$
$522$	0.195875	−	0.799076i	0.00857320	−	0.0349746i
$523$	8.46196	−	31.5805i	0.370016	−	1.38092i	−0.490477	−	0.871454i	$-0.663177\pi$
$523$	8.46196	−	31.5805i	0.370016	−	1.38092i	0.860493	−	0.509463i	$-0.170156\pi$
$524$	−5.16098	+	1.87844i	−0.225458	+	0.0820601i
$525$	−7.90758	−	28.1422i	−0.345115	−	1.22823i
$526$	−6.11159	+	5.12823i	−0.266478	+	0.223601i
$527$	−27.7921	−	2.43149i	−1.21064	−	0.105917i
$528$	−0.209991	−	0.172406i	−0.00913868	−	0.00750301i
$529$	11.5355	+	31.6935i	0.501543	+	1.37798i
$530$	7.51826	+	10.7210i	0.326572	+	0.465691i
$531$	28.4997	−	0.610351i	1.23678	−	0.0264870i
$532$	4.38684	+	16.3719i	0.190194	+	0.709812i
$533$	−26.8819	−	38.3914i	−1.16438	−	1.66291i
$534$	9.93876	+	2.54936i	0.430092	+	0.110321i
$535$	−10.2277	−	17.6859i	−0.442180	−	0.764627i
$536$	−5.55506	+	0.979508i	−0.239942	+	0.0423083i
$537$	11.7371	+	13.6874i	0.506494	+	0.590657i
$538$	2.08066	+	23.7821i	0.0897038	+	1.02532i
$539$	−0.689188			−0.0296854
$540$	−10.3635	+	5.25336i	−0.445974	+	0.226069i
$541$	45.6107			1.96096			0.980479	−	0.196626i	$-0.0629984\pi$
$541$	45.6107			1.96096			0.980479	+	0.196626i	$0.0629984\pi$
$542$	1.19819	+	13.6954i	0.0514666	+	0.588266i
$543$	0.544927	−	1.54856i	0.0233851	−	0.0664552i
$544$	2.71517	−	0.478758i	0.116412	−	0.0205266i
$545$	−3.59778	+	13.4653i	−0.154112	+	0.576788i
$546$	−28.8220	+	29.4458i	−1.23347	+	1.26016i
$547$	4.00946	+	5.72610i	0.171432	+	0.244830i	0.895669	−	0.444720i	$-0.146697\pi$
$547$	4.00946	+	5.72610i	0.171432	+	0.244830i	−0.724237	+	0.689551i	$0.757808\pi$
$548$	−3.99710	−	14.9174i	−0.170748	−	0.637240i
$549$	−3.59392	−	18.1061i	−0.153385	−	0.772748i
$550$	0.781437	+	0.0672509i	0.0333206	+	0.00286759i
$551$	−0.470995	−	1.29405i	−0.0200650	−	0.0551283i
$552$	2.12764	−	12.8707i	0.0905582	−	0.547815i
$553$	23.5513	+	2.06047i	1.00150	+	0.0876203i
$554$	−16.2147	+	13.6057i	−0.688895	+	0.578052i
$555$	−8.21320	−	2.88362i	−0.348631	−	0.122403i
$556$	11.6692	−	4.24724i	0.494884	−	0.180123i
$557$	−11.8175	+	44.1035i	−0.500723	+	1.86872i	−0.00545188	+	0.999985i	$0.501735\pi$
$557$	−11.8175	+	44.1035i	−0.500723	+	1.86872i	−0.495271	+	0.868738i	$0.664931\pi$
$558$	24.4881	−	17.9402i	1.03666	−	0.759470i
$559$	21.5754	+	12.4566i	0.912544	+	0.526858i
$560$	−4.85565	−	5.77842i	−0.205189	−	0.244183i
$561$	0.721447	−	0.201614i	0.0304595	−	0.00851215i
$562$	−22.0462	+	10.2803i	−0.929963	+	0.433649i
$563$	−23.4423	−	16.4145i	−0.987974	−	0.691787i	−0.0364420	−	0.999336i	$-0.511602\pi$
$563$	−23.4423	−	16.4145i	−0.987974	−	0.691787i	−0.951532	+	0.307549i	$0.900491\pi$
$564$	−2.14448	+	3.13351i	−0.0902989	+	0.131945i
$565$	−15.3855	+	2.72412i	−0.647272	+	0.114605i
$566$		−	7.99081i		−	0.335879i
$567$	29.6534	+	6.59914i	1.24533	+	0.277138i
$568$	−5.17737	−	5.17737i	−0.217238	−	0.217238i
$569$	−10.7604	−	9.02905i	−0.451099	−	0.378517i	0.388744	−	0.921346i	$-0.372909\pi$
$569$	−10.7604	−	9.02905i	−0.451099	−	0.378517i	−0.839844	+	0.542828i	$0.817353\pi$
$570$	−9.53106	+	16.9523i	−0.399212	+	0.710052i
$571$	−2.43093	−	13.7865i	−0.101731	−	0.576947i	−0.992476	−	0.122442i	$-0.960927\pi$
$571$	−2.43093	−	13.7865i	−0.101731	−	0.576947i	0.890744	−	0.454505i	$-0.150184\pi$
$572$	−0.467222	−	1.00196i	−0.0195355	−	0.0418941i
$573$	1.59659	−	2.83505i	0.0666987	−	0.118436i
$574$	−22.1055	−	3.89779i	−0.922665	−	0.162691i
$575$	15.9637	+	34.1079i	0.665731	+	1.42240i
$576$	−1.87872	+	2.33889i	−0.0782798	+	0.0974540i
$577$	−28.8336	−	7.72593i	−1.20036	−	0.321635i	−0.397386	−	0.917652i	$-0.630082\pi$
$577$	−28.8336	−	7.72593i	−1.20036	−	0.321635i	−0.802972	+	0.596017i	$0.796749\pi$
$578$	3.97203	−	8.51804i	0.165215	−	0.354304i
$579$	−5.89640	+	13.0066i	−0.245046	+	0.540538i
$580$	0.433925	+	0.433311i	0.0180178	+	0.0179922i
$581$	−2.96050	−	3.52819i	−0.122822	−	0.146374i
$582$	−4.71915	−	0.780114i	−0.195615	−	0.0323368i
$583$	0.832537	+	0.388219i	0.0344802	+	0.0160784i
$584$	−6.63960	−	11.5001i	−0.274748	−	0.475878i
$585$	−47.2660	+	1.04577i	−1.95421	+	0.0432371i
$586$	6.65434	−	11.5257i	0.274888	−	0.476121i
$587$	−27.0418	+	18.9349i	−1.11613	+	0.781525i	−0.977941	−	0.208880i	$-0.933018\pi$
$587$	−27.0418	+	18.9349i	−1.11613	+	0.781525i	−0.138193	+	0.990405i	$0.544129\pi$
$588$	0.0814716	+	7.60934i	0.00335983	+	0.313804i
$589$	17.3784	−	47.7467i	0.716064	−	1.96737i
$590$	−10.6106	+	18.4083i	−0.436832	+	0.757856i
$591$	16.8200	−	8.06365i	0.691883	−	0.331694i
$592$	−2.23899	+	0.195887i	−0.0920221	+	0.00805089i
$593$	6.32665	−	6.32665i	0.259804	−	0.259804i	−0.565170	−	0.824974i	$-0.691189\pi$
$593$	6.32665	−	6.32665i	0.259804	−	0.259804i	0.824974	+	0.565170i	$0.191189\pi$
$594$	−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
$597$	0.630567	−	0.540718i	0.0258074	−	0.0221301i
$598$	30.4465	−	43.4821i	1.24505	−	1.77811i
$599$	−7.37153	−	2.68302i	−0.301193	−	0.109625i	0.187003	−	0.982359i	$-0.440123\pi$
$599$	−7.37153	−	2.68302i	−0.301193	−	0.109625i	−0.488196	+	0.872734i	$0.662345\pi$
$600$	0.650142	−	8.63582i	0.0265419	−	0.352556i
$601$	−3.87288	+	21.9642i	−0.157978	+	0.895938i	0.798034	+	0.602612i	$0.205873\pi$
$601$	−3.87288	+	21.9642i	−0.157978	+	0.895938i	−0.956012	+	0.293326i	$0.905238\pi$
$602$	11.5253	−	3.08820i	0.469737	−	0.125866i
$603$	4.72878	+	16.2481i	0.192571	+	0.661676i
$604$	−6.91797	+	3.99409i	−0.281488	+	0.162517i
$605$	−22.2350	+	10.3875i	−0.903981	+	0.422314i
$606$	0.406006	+	4.13080i	0.0164929	+	0.167802i
$607$	2.46673	−	28.1948i	0.100121	−	1.14439i	−0.765412	−	0.643541i	$-0.777465\pi$
$607$	2.46673	−	28.1948i	0.100121	−	1.14439i	0.865533	−	0.500852i	$-0.166980\pi$
$608$	−0.437646	+	5.00232i	−0.0177489	+	0.202871i
$609$	−0.156833	−	1.59566i	−0.00635519	−	0.0646592i
$610$	12.9323	+	4.69660i	0.523614	+	0.190160i
$611$	−13.3803	+	7.72513i	−0.541310	+	0.312525i
$612$	−2.31131	−	7.94168i	−0.0934291	−	0.321023i
$613$	−24.8976	+	6.67128i	−1.00560	+	0.269451i	−0.723791	−	0.690019i	$-0.757602\pi$
$613$	−24.8976	+	6.67128i	−1.00560	+	0.269451i	−0.281812	+	0.959470i	$0.590936\pi$
$614$	1.89976	−	10.7741i	0.0766679	−	0.434806i
$615$	−15.0125	−	20.9275i	−0.605361	−	0.843876i
$616$	−0.497555	−	0.181095i	−0.0200471	−	0.00729653i
$617$	−19.2253	+	27.4565i	−0.773981	+	1.10536i	0.217622	+	0.976033i	$0.430170\pi$
$617$	−19.2253	+	27.4565i	−0.773981	+	1.10536i	−0.991602	+	0.129326i	$0.958719\pi$
$618$	13.5588	−	11.6268i	0.545414	−	0.467698i
$619$	16.3858	−	19.5278i	0.658601	−	0.784890i	−0.328583	−	0.944475i	$-0.606571\pi$
$619$	16.3858	−	19.5278i	0.658601	−	0.784890i	0.987184	+	0.159585i	$0.0510156\pi$
$620$	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
$623$	19.9196	−	1.74274i	0.798064	−	0.0698215i
$624$	−11.0074	+	5.27706i	−0.440651	+	0.211251i
$625$	12.5613	+	21.6151i	0.502453	+	0.864604i
$626$	−2.83351	+	7.78500i	−0.113250	+	0.311151i
$627$	0.0146066	+	1.36423i	0.000583330	+	0.0544823i
$628$	−7.91626	+	5.54303i	−0.315893	+	0.221191i
$629$	3.09831	−	5.36643i	0.123538	−	0.213974i
$630$	−15.6530	+	16.3613i	−0.623630	+	0.651850i
$631$	−5.38398	−	9.32532i	−0.214333	−	0.371235i	0.738733	−	0.673998i	$-0.235424\pi$
$631$	−5.38398	−	9.32532i	−0.214333	−	0.371235i	−0.953066	+	0.302763i	$0.902091\pi$
$632$	6.34772	+	2.95999i	0.252499	+	0.117742i
$633$	19.9115	+	3.29153i	0.791410	+	0.130826i
$634$	−20.0320	−	23.8732i	−0.795571	−	0.948125i
$635$	0.0136576	+	19.2700i	0.000541983	+	0.764706i
$636$	4.18791	−	9.23796i	0.166062	−	0.366309i
$637$	−13.0860	+	28.0631i	−0.518488	+	1.11190i
$638$	0.0415535	+	0.0111342i	0.00164512	+	0.000440808i
$639$	−13.7558	+	17.1252i	−0.544170	+	0.677461i
$640$	−0.766269	−	2.10067i	−0.0302895	−	0.0830364i
$641$	34.5159	+	6.08608i	1.36330	+	0.240386i	0.806977	−	0.590583i	$-0.201102\pi$
$641$	34.5159	+	6.08608i	1.36330	+	0.240386i	0.556319	+	0.830969i	$0.312213\pi$
$642$	−7.76542	+	13.7890i	−0.306477	+	0.544206i
$643$	5.76318	+	12.3592i	0.227278	+	0.487398i	0.986567	−	0.163354i	$-0.0522313\pi$
$643$	5.76318	+	12.3592i	0.227278	+	0.487398i	−0.759290	+	0.650753i	$0.774454\pi$
$644$	−4.41465	−	25.0367i	−0.173961	−	0.986584i
$645$	11.9339	+	6.70957i	0.469896	+	0.264189i
$646$	−10.6054	−	8.89899i	−0.417264	−	0.350126i
$647$	−19.4755	−	19.4755i	−0.765662	−	0.765662i	0.211677	−	0.977340i	$-0.432107\pi$
$647$	−19.4755	−	19.4755i	−0.765662	−	0.765662i	−0.977340	+	0.211677i	$0.932107\pi$
$648$	7.58661	+	4.84183i	0.298030	+	0.190205i
$649$			1.49055i			0.0585091i
$650$	17.5760	−	30.5425i	0.689389	−	1.19797i
$651$	33.4114	−	48.8206i	1.30950	−	1.91343i
$652$	11.7057	+	8.19640i	0.458430	+	0.320996i
$653$	−39.3369	+	18.3431i	−1.53937	+	0.717821i	−0.992822	−	0.119604i	$-0.961837\pi$
$653$	−39.3369	+	18.3431i	−1.53937	+	0.717821i	−0.546551	+	0.837426i	$0.684060\pi$
$654$	10.3977	−	2.90570i	0.406580	−	0.113622i
$655$	−12.2349	−	1.06168i	−0.478059	−	0.0414833i
$656$	−5.75905	−	3.32499i	−0.224853	−	0.129819i
$657$	−32.1363	+	23.5434i	−1.25376	+	0.918514i
$658$	−1.91519	+	7.14759i	−0.0746619	+	0.278642i
$659$	−7.20356	+	2.62188i	−0.280611	+	0.102134i	−0.478492	−	0.878092i	$-0.658816\pi$
$659$	−7.20356	+	2.62188i	−0.280611	+	0.102134i	0.197881	+	0.980226i	$0.436594\pi$
$660$	−0.263024	−	0.547648i	−0.0102382	−	0.0213172i
$661$	0.132252	−	0.110973i	0.00514401	−	0.00431634i	−0.640212	−	0.768198i	$-0.721153\pi$
$661$	0.132252	−	0.110973i	0.00514401	−	0.00431634i	0.645356	+	0.763882i	$0.276709\pi$
$662$	8.89402	+	0.778126i	0.345676	+	0.0302427i
$663$	5.48903	−	33.2048i	0.213176	−	1.28957i
$664$	−0.466682	−	1.28220i	−0.0181108	−	0.0497589i
$665$	−6.55483	+	37.3290i	−0.254185	+	1.44756i
$666$	1.31275	+	6.61361i	0.0508681	+	0.256272i
$667$	0.534602	+	1.99516i	0.0206999	+	0.0772530i
$668$	4.09089	+	5.84239i	0.158281	+	0.226049i
$669$	17.2650	−	17.6388i	0.667505	−	0.681954i
$670$	−12.1857	−	3.25588i	−0.470773	−	0.125786i
$671$	0.950543	−	0.167606i	0.0366953	−	0.00647037i
$672$	−1.94066	+	5.51492i	−0.0748625	+	0.212743i
$673$	3.30895	+	37.8215i	0.127551	+	1.45791i	0.742765	+	0.669552i	$0.233514\pi$
$673$	3.30895	+	37.8215i	0.127551	+	1.45791i	−0.615214	+	0.788360i	$0.710930\pi$
$674$	−8.68199			−0.334418
$675$	−25.9662	+	0.871144i	−0.999438	+	0.0335303i
$676$	−36.6704			−1.41040
$677$	3.48890	+	39.8783i	0.134089	+	1.53265i	0.703560	+	0.710636i	$0.251593\pi$
$677$	3.48890	+	39.8783i	0.134089	+	1.53265i	−0.569470	+	0.822012i	$0.692852\pi$
$678$	7.87842	+	9.18755i	0.302569	+	0.352846i
$679$	−9.17989	+	1.61866i	−0.352292	+	0.0621186i
$680$	5.95604	+	1.59139i	0.228404	+	0.0610271i
$681$	5.01364	+	1.28603i	0.192123	+	0.0492808i
$682$	0.910434	+	1.30023i	0.0348623	+	0.0497886i
$683$	2.60825	+	9.73412i	0.0998019	+	0.372466i	0.997704	−	0.0677301i	$-0.0215757\pi$
$683$	2.60825	+	9.73412i	0.0998019	+	0.372466i	−0.897902	+	0.440196i	$0.854909\pi$
$684$	15.0608	−	0.322543i	0.575865	−	0.0123327i
$685$	5.97249	−	34.0126i	0.228197	−	1.29955i
$686$	−3.00910	−	8.26744i	−0.114888	−	0.315652i
$687$	17.6019	+	14.4514i	0.671554	+	0.551357i
$688$	3.52147	+	0.308089i	0.134255	+	0.0117458i
$689$	31.6158	−	26.5288i	1.20447	−	1.01067i
$690$	16.4576	−	24.0844i	0.626531	−	0.916879i
$691$	−10.8420	+	3.94617i	−0.412449	+	0.150119i	−0.539907	−	0.841725i	$-0.681541\pi$
$691$	−10.8420	+	3.94617i	−0.412449	+	0.150119i	0.127458	+	0.991844i	$0.459318\pi$
$692$	5.50383	−	20.5406i	0.209224	−	0.780835i
$693$	−0.378178	+	1.54279i	−0.0143658	+	0.0586056i
$694$	15.7465	+	9.09126i	0.597730	+	0.345100i
$695$	27.6637	+	2.40051i	1.04935	+	0.0910565i
$696$	0.118021	−	0.460109i	0.00447358	−	0.0174404i
$697$	16.6166	−	7.74844i	0.629398	−	0.293493i
$698$	7.07883	+	4.95665i	0.267938	+	0.187612i
$699$	−16.9755	−	1.30219i	−0.642071	−	0.0492533i
$700$	−4.39123	−	16.2959i	−0.165973	−	0.615925i
$701$		−	9.18014i		−	0.346729i	−0.984858	−	0.173365i	$-0.944536\pi$
$701$		−	9.18014i		−	0.346729i	0.984858	−	0.173365i	$-0.0554639\pi$
$702$	19.3196	+	31.1104i	0.729170	+	1.17419i
$703$	7.98032	+	7.98032i	0.300984	+	0.300984i
$704$	−0.120166	−	0.100831i	−0.00452891	−	0.00380021i
$705$	−7.30404	+	4.32890i	−0.275086	+	0.163036i
$706$	2.21453	+	12.5593i	0.0833451	+	0.472674i
$707$	3.41852	+	7.33105i	0.128567	+	0.275712i
$708$	16.4572	−	0.176203i	0.618498	−	0.00662213i
$709$	0.207408	+	0.0365716i	0.00778937	+	0.00137348i	0.177542	−	0.984113i	$-0.443186\pi$
$709$	0.207408	+	0.0365716i	0.00778937	+	0.00137348i	−0.169752	+	0.985487i	$0.554297\pi$
$710$	−5.61055	−	15.3809i	−0.210560	−	0.577236i
$711$	6.76206	−	19.8940i	0.253597	−	0.746083i
$712$	5.72206	+	1.53322i	0.214443	+	0.0574599i
$713$	−32.2089	+	69.0722i	−1.20623	+	2.58677i
$714$	−9.38626	−	13.1041i	−0.351272	−	0.490408i
$715$	−0.00175207	−	2.47207i	−6.55237e−5	−	0.0924501i
$716$	6.69144	+	7.97455i	0.250071	+	0.298023i
$717$	−4.73718	−	12.5941i	−0.176913	−	0.470335i
$718$	−23.5970	−	11.0035i	−0.880632	−	0.410645i
$719$	−6.88689	−	11.9284i	−0.256838	−	0.444856i	0.708555	−	0.705655i	$-0.249347\pi$
$719$	−6.88689	−	11.9284i	−0.256838	−	0.444856i	−0.965393	+	0.260799i	$0.916014\pi$
$720$	−6.01550	+	2.96880i	−0.224184	+	0.110641i
$721$	17.4040	−	30.1446i	0.648158	−	1.12264i
$722$	5.09078	−	3.56460i	0.189459	−	0.132661i
$723$	−20.7078	−	11.6618i	−0.770131	−	0.433709i
$724$	0.324168	−	0.890644i	0.0120476	−	0.0331005i
$725$	0.470811	+	1.28786i	0.0174855	+	0.0478299i
$726$	15.6879	+	10.7363i	0.582232	+	0.398462i
$727$	−27.1205	+	2.37274i	−1.00585	+	0.0880000i	−0.578156	−	0.815926i	$-0.696228\pi$
$727$	−27.1205	+	2.37274i	−1.00585	+	0.0880000i	−0.427689	+	0.903926i	$0.640672\pi$
$728$	−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
$732$	−1.96291	−	10.4752i	−0.0725513	−	0.387173i
$733$	−17.1921	+	24.5528i	−0.635004	+	0.906880i	−0.999706	−	0.0242446i	$-0.992282\pi$
$733$	−17.1921	+	24.5528i	−0.635004	+	0.906880i	0.364702	+	0.931124i	$0.381171\pi$
$734$	−23.6624	−	8.61240i	−0.873394	−	0.317889i
$735$	−7.01476	+	15.5028i	−0.258743	+	0.571829i
$736$	1.30788	−	7.41734i	0.0482090	−	0.273407i
$737$	−0.854688	+	0.229013i	−0.0314829	+	0.00843581i
$738$	−8.04214	+	18.2571i	−0.296035	+	0.672055i
$739$	−34.9872	+	20.1999i	−1.28703	+	0.743065i	−0.978123	−	0.208029i	$-0.933295\pi$
$739$	−34.9872	+	20.1999i	−1.28703	+	0.743065i	−0.308903	+	0.951093i	$0.599962\pi$
$740$	−4.72380	−	1.71553i	−0.173650	−	0.0630642i
$741$	55.8277	+	25.3088i	2.05088	+	0.929742i
$742$	1.72277	−	19.6913i	0.0632447	−	0.722891i
$743$	3.92298	−	44.8398i	0.143920	−	1.64501i	−0.490077	−	0.871679i	$-0.663031\pi$
$743$	3.92298	−	44.8398i	0.143920	−	1.64501i	0.633997	−	0.773335i	$-0.281413\pi$
$744$	14.2483	−	10.2058i	0.522368	−	0.374164i
$745$	15.2738	−	7.13549i	0.559590	−	0.261424i
$746$	−12.4454	+	7.18538i	−0.455660	+	0.263076i
$747$	−3.67204	+	1.80901i	−0.134353	+	0.0661881i
$748$	0.417750	−	0.111936i	0.0152745	−	0.00409278i
$749$	−5.35534	+	30.3717i	−0.195680	+	1.10976i
$750$	9.46646	−	16.8934i	0.345666	−	0.616859i
$751$	−30.1604	−	10.9775i	−1.10057	−	0.400574i	−0.273043	−	0.962002i	$-0.588030\pi$
$751$	−30.1604	−	10.9775i	−1.10057	−	0.400574i	−0.827526	+	0.561428i	$0.810252\pi$
$752$	−1.25741	+	1.79577i	−0.0458532	+	0.0654851i
$753$	31.0274	+	10.9183i	1.13070	+	0.397885i
$754$	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	$0.397182\pi$
$758$	−21.1613	+	1.85137i	−0.768612	+	0.0672449i
$759$	0.156517	−	2.04037i	0.00568121	−	0.0740609i
$760$	−5.60723	+	9.72792i	−0.203396	+	0.352869i
$761$	−4.09191	+	11.2424i	−0.148332	+	0.407538i	−0.991499	−	0.130113i	$-0.958466\pi$
$761$	−4.09191	+	11.2424i	−0.148332	+	0.407538i	0.843167	+	0.537651i	$0.180688\pi$
$762$	12.8461	−	7.60121i	0.465364	−	0.275363i
$763$	17.2344	−	12.0677i	0.623928	−	0.436879i
$764$	0.939266	−	1.62686i	0.0339814	−	0.0588576i
$765$	2.80794	−	18.2805i	0.101521	−	0.660934i
$766$	−14.6854	−	25.4359i	−0.530605	−	0.919035i
$767$	60.6937	+	28.3020i	2.19152	+	1.02192i
$768$	−1.09907	+	1.33867i	−0.0396593	+	0.0483051i
$769$	−3.23373	−	3.85381i	−0.116611	−	0.138972i	0.704581	−	0.709624i	$-0.251135\pi$
$769$	−3.23373	−	3.85381i	−0.116611	−	0.138972i	−0.821192	+	0.570652i	$0.806691\pi$
$770$	−0.837785	−	0.836599i	−0.0301917	−	0.0301489i
$771$	−19.7400	+	1.94020i	−0.710919	+	0.0698744i
$772$	−3.48449	+	7.47251i	−0.125410	+	0.268942i
$773$	2.78088	+	0.745136i	0.100021	+	0.0268007i	0.308483	−	0.951230i	$-0.400179\pi$
$773$	2.78088	+	0.745136i	0.100021	+	0.0268007i	−0.208461	+	0.978031i	$0.566845\pi$
$774$	−0.227060	−	10.6023i	−0.00816151	−	0.381093i
$775$	−17.2368	+	47.5675i	−0.619165	+	1.70867i
$776$	−2.71962	−	0.479543i	−0.0976288	−	0.0172146i
$777$	6.69150	+	11.3087i	0.240056	+	0.405696i
$778$	−3.69225	−	7.91805i	−0.132373	−	0.283876i
$779$	5.79852	+	32.8850i	0.207753	+	1.17823i
$780$	−27.2939	+	0.311577i	−0.977280	+	0.0111563i
$781$	−0.879842	−	0.738275i	−0.0314832	−	0.0264175i
$782$	14.6835	+	14.6835i	0.525079	+	0.525079i
$783$	−1.41059	−	0.202256i	−0.0504103	−	0.00722806i
$784$			4.39351i			0.156911i
$785$	−21.2783	+	3.76750i	−0.759457	+	0.134468i
$786$	4.11234	+	8.57796i	0.146682	+	0.305966i
$787$	39.2475	+	27.4814i	1.39902	+	0.979605i	0.997979	+	0.0635454i	$0.0202408\pi$
$787$	39.2475	+	27.4814i	1.39902	+	0.979605i	0.401042	+	0.916060i	$0.368648\pi$
$788$	9.76033	−	4.55132i	0.347697	−	0.162134i
$789$	9.87520	+	9.66598i	0.351567	+	0.344118i
$790$	10.0754	+	11.9901i	0.358466	+	0.426589i
$791$	20.4262	+	11.7931i	0.726274	+	0.419314i
$792$	−0.261607	+	0.391180i	−0.00929579	+	0.0139000i
$793$	11.2238	−	41.8877i	0.398568	−	1.48748i
$794$	4.46093	−	1.62365i	0.158312	−	0.0576210i
$795$	17.2065	−	14.7759i	0.610252	−	0.524048i
$796$	0.367380	−	0.308268i	0.0130214	−	0.0109263i
$797$	33.4856	+	2.92961i	1.18612	+	0.103772i	0.663088	−	0.748541i	$-0.269245\pi$
$797$	33.4856	+	2.92961i	1.18612	+	0.103772i	0.523032	+	0.852313i	$0.324801\pi$
$798$	27.4778	−	10.3356i	0.972702	−	0.365875i
$799$	−2.06721	−	5.67962i	−0.0731327	−	0.200930i
$800$	0.428718	−	4.98159i	0.0151575	−	0.176126i
$801$	2.71059	−	17.5638i	0.0957740	−	0.620587i
$802$	−4.23223	−	15.7949i	−0.149445	−	0.557737i
$803$	−1.19478	−	1.70633i	−0.0421630	−	0.0602150i
$804$	2.62957	+	9.40956i	0.0927379	+	0.331850i
$805$	14.6743	−	54.9208i	0.517200	−	1.93570i
$806$	70.2314	−	12.3837i	2.47379	−	0.436197i
$807$	40.6418	−	7.61576i	1.43066	−	0.268087i
$808$	0.208861	+	2.38729i	0.00734771	+	0.0839847i
$809$	39.5234			1.38957			0.694784	−	0.719218i	$-0.255500\pi$
$809$	39.5234			1.38957			0.694784	+	0.719218i	$0.255500\pi$
$810$	10.8113	+	16.9740i	0.379869	+	0.596405i
$811$	−21.1540			−0.742818			−0.371409	−	0.928469i	$-0.621125\pi$
$811$	−21.1540			−0.742818			−0.371409	+	0.928469i	$0.621125\pi$
$812$	−0.0806793	−	0.922169i	−0.00283129	−	0.0323618i
$813$	23.4043	−	4.38568i	0.820825	−	0.153812i
$814$	−0.347205	+	0.0612217i	−0.0121695	+	0.00214582i
$815$	15.9963	+	27.6611i	0.560326	+	0.968927i
$816$	−1.28527	−	4.59915i	−0.0449934	−	0.161003i
$817$	−10.1812	−	14.5402i	−0.356195	−	0.508699i
$818$	0.781662	+	2.91720i	0.0273302	+	0.101998i
$819$	55.6402	+	44.6929i	1.94422	+	1.56170i
$820$	−8.53760	−	12.1746i	−0.298146	−	0.425155i
$821$	−14.3479	−	39.4206i	−0.500745	−	1.37579i	−0.890548	−	0.454889i	$-0.849679\pi$
$821$	−14.3479	−	39.4206i	−0.500745	−	1.37579i	0.389803	−	0.920898i	$-0.372543\pi$
$822$	−25.0366	+	9.41733i	−0.873251	+	0.328467i
$823$	46.0512	+	4.02896i	1.60524	+	0.140441i	0.854248	−	0.519866i	$-0.174018\pi$
$823$	46.0512	+	4.02896i	1.60524	+	0.140441i	0.750996	+	0.660307i	$0.229574\pi$
$824$	7.89958	−	6.62853i	0.275195	−	0.230916i
$825$	−0.0164698	−	1.35839i	−0.000573404	−	0.0472931i
$826$	30.1393	−	10.9698i	1.04868	−	0.381689i
$827$	12.8454	−	47.9396i	0.446677	−	1.66702i	−0.264792	−	0.964306i	$-0.585303\pi$
$827$	12.8454	−	47.9396i	0.446677	−	1.66702i	0.711469	−	0.702717i	$-0.248030\pi$
$828$	−22.5463	−	1.48691i	−0.783539	−	0.0516737i
$829$	39.6831	+	22.9111i	1.37825	+	0.795734i	0.991949	−	0.126639i	$-0.0404188\pi$
$829$	39.6831	+	22.9111i	1.37825	+	0.795734i	0.386302	+	0.922372i	$0.373752\pi$
$830$	0.263765	−	3.03966i	0.00915542	−	0.105508i
$831$	26.1999	+	25.6448i	0.908865	+	0.889609i
$832$	−6.38741	+	2.97850i	−0.221444	+	0.103261i
$833$	−9.92252	−	6.94782i	−0.343795	−	0.240728i
$834$	−9.29818	−	19.3951i	−0.321970	−	0.671598i
$835$	2.78050	+	15.7039i	0.0962233	+	0.543457i
$836$			0.787686i			0.0272427i
$837$	−35.0732	−	39.1718i	−1.21231	−	1.35397i
$838$	26.4939	+	26.4939i	0.915216	+	0.915216i
$839$	−38.0359	−	31.9159i	−1.31314	−	1.10186i	−0.987711	−	0.156293i	$-0.950045\pi$
$839$	−38.0359	−	31.9159i	−1.31314	−	1.10186i	−0.325433	−	0.945565i	$-0.605510\pi$
$840$	−9.13787	+	9.34890i	−0.315286	+	0.322568i
$841$	−5.02274	−	28.4854i	−0.173198	−	0.982254i
$842$	−4.10198	−	8.79673i	−0.141364	−	0.303155i
$843$	21.4558	+	36.2603i	0.738976	+	1.24887i
$844$	11.4749	+	2.02333i	0.394982	+	0.0696460i
$845$	−74.3396	−	34.6010i	−2.55736	−	1.19031i
$846$	5.76469	+	3.16565i	0.198194	+	0.108837i
$847$	35.7843	+	9.58838i	1.22956	+	0.329460i
$848$	2.47486	−	5.30734i	0.0849869	−	0.182255i
$849$	−13.7741	+	1.35382i	−0.472726	+	0.0464631i
$850$	10.5727	+	8.84604i	0.362641	+	0.303417i
$851$	−10.8811	−	12.9676i	−0.373000	−	0.444524i
$852$	−8.04730	+	9.80163i	−0.275696	+	0.335798i
$853$	−14.0386	−	6.54631i	−0.480673	−	0.224141i	0.167152	−	0.985931i	$-0.446543\pi$
$853$	−14.0386	−	6.54631i	−0.480673	−	0.224141i	−0.647824	+	0.761790i	$0.724321\pi$
$854$	−10.3847	−	17.9868i	−0.355356	−	0.615494i
$855$	30.8362	+	13.5570i	1.05457	+	0.463640i
$856$	−4.56834	+	7.91260i	−0.156143	+	0.270447i
$857$	−18.3150	+	12.8243i	−0.625630	+	0.438071i	−0.842922	−	0.538036i	$-0.819166\pi$
$857$	−18.3150	+	12.8243i	−0.625630	+	0.438071i	0.217292	+	0.976107i	$0.430278\pi$
$858$	−1.64797	+	0.975127i	−0.0562607	+	0.0332903i
$859$	−3.57578	+	9.82439i	−0.122004	+	0.335204i	−0.985627	−	0.168934i	$-0.945967\pi$
$859$	−3.57578	+	9.82439i	−0.122004	+	0.335204i	0.863623	+	0.504138i	$0.168190\pi$
$860$	6.84815	+	3.94731i	0.233520	+	0.134602i
$861$	−2.97363	+	38.7646i	−0.101341	+	1.32109i
$862$	−1.47528	+	0.129070i	−0.0502482	+	0.00439615i
$863$	−12.2209	+	12.2209i	−0.416005	+	0.416005i	−0.883824	−	0.467819i	$-0.845040\pi$
$863$	−12.2209	+	12.2209i	−0.416005	+	0.416005i	0.467819	+	0.883824i	$0.345040\pi$
$864$	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
$867$	−15.3559	−	5.40361i	−0.521513	−	0.183516i
$868$	19.5907	−	27.9785i	0.664953	−	0.949651i
$869$	1.03242	+	0.375769i	0.0350223	+	0.0127471i
$870$	0.673400	−	0.821389i	0.0228304	−	0.0278477i
$871$	−6.90330	+	39.1506i	−0.233909	+	1.32657i
$872$	6.02070	−	1.61324i	0.203887	−	0.0546313i
$873$	−0.545186	+	8.26678i	−0.0184518	+	0.279788i
$874$	−32.7532	+	18.9101i	−1.10790	+	0.639644i
$875$	6.47417	−	37.1789i	0.218867	−	1.25688i
$876$	−18.6984	+	13.3933i	−0.631759	+	0.452519i
$877$	−2.91008	+	33.2624i	−0.0982665	+	1.12319i	0.773676	+	0.633582i	$0.218416\pi$
$877$	−2.91008	+	33.2624i	−0.0982665	+	1.12319i	−0.871942	+	0.489609i	$0.837140\pi$
$878$	−0.412517	+	4.71509i	−0.0139218	+	0.159127i
$879$	−20.9947	−	9.51768i	−0.708134	−	0.321024i
$880$	−0.148463	−	0.317792i	−0.00500470	−	0.0107128i
$881$	26.7397	−	15.4382i	0.900882	−	0.520125i	0.0233961	−	0.999726i	$-0.492552\pi$
$881$	26.7397	−	15.4382i	0.900882	−	0.520125i	0.877486	+	0.479602i	$0.159219\pi$
$882$	13.1028	−	1.42963i	0.441193	−	0.0481382i
$883$	−16.2505	+	4.35431i	−0.546874	+	0.146534i	−0.521669	−	0.853148i	$-0.674690\pi$
$883$	−16.2505	+	4.35431i	−0.546874	+	0.146534i	−0.0252047	+	0.999682i	$0.508024\pi$
$884$	3.37416	−	19.1358i	0.113485	−	0.643607i
$885$	33.5288	+	15.1712i	1.12706	+	0.509975i
$886$	−24.4096	−	8.88437i	−0.820057	−	0.298476i
$887$	−11.9273	+	17.0340i	−0.400481	+	0.571946i	−0.967853	−	0.251515i	$-0.919071\pi$
$887$	−11.9273	+	17.0340i	−0.400481	+	0.571946i	0.567372	+	0.823461i	$0.307960\pi$
$888$	0.716995	+	3.82627i	0.0240608	+	0.128401i
$889$	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
$893$	10.9662	−	0.959422i	0.366971	−	0.0321058i
$894$	−10.7764	−	7.37507i	−0.360418	−	0.246659i
$895$	6.04060	+	22.4801i	0.201915	+	0.751427i
$896$	−1.15446	+	3.17186i	−0.0385679	+	0.105965i
$897$	−80.1103	−	45.1151i	−2.67481	−	1.50635i
$898$	5.66701	−	3.96808i	0.189111	−	0.132417i
$899$	−1.38752	+	2.40325i	−0.0462763	+	0.0801529i
$900$	−14.9961	+	0.342424i	−0.499870	+	0.0114141i
$901$	8.07268	+	13.9823i	0.268940	+	0.465818i
$902$	−0.945414	−	0.440854i	−0.0314788	−	0.0146788i
$903$	−7.27591	−	19.3435i	−0.242127	−	0.643711i
$904$	4.49156	+	5.35283i	0.149387	+	0.178032i
$905$	1.49755	−	1.49967i	0.0497801	−	0.0498507i
$906$	8.05685	+	11.2481i	0.267671	+	0.373694i
$907$	9.66469	−	20.7260i	0.320911	−	0.688195i	−0.677990	−	0.735071i	$-0.737149\pi$
$907$	9.66469	−	20.7260i	0.320911	−	0.688195i	0.998901	+	0.0468760i	$0.0149266\pi$
$908$	2.88651	+	0.773438i	0.0957922	+	0.0256675i
$909$	7.05166	−	1.39970i	0.233889	−	0.0464252i
$910$	−49.9731	+	18.2288i	−1.65659	+	0.604280i
$911$	−9.67975	−	1.70680i	−0.320705	−	0.0565489i	0.0109786	−	0.999940i	$-0.496505\pi$
$911$	−9.67975	−	1.70680i	−0.320705	−	0.0565489i	−0.331683	+	0.943391i	$0.607616\pi$
$912$	8.69686	−	0.0931154i	0.287982	−	0.00308336i
$913$	−0.0904573	−	0.193986i	−0.00299370	−	0.00642001i
$914$	−2.94259	−	16.6883i	−0.0973323	−	0.551999i
$915$	5.90472	−	23.0877i	0.195204	−	0.763257i
$916$	10.0725	+	8.45187i	0.332806	+	0.279258i
$917$	13.1087	+	13.1087i	0.432888	+	0.432888i
$918$	−13.2978	+	5.32961i	−0.438894	+	0.175903i
$919$			4.32140i			0.142550i	0.997457	+	0.0712749i	$0.0227067\pi$
$919$			4.32140i			0.142550i	−0.997457	+	0.0712749i	$0.977293\pi$
$920$	9.65013	−	13.8026i	0.318155	−	0.455059i
$921$	−18.8936	−	1.44933i	−0.622565	−	0.0477570i
$922$	−31.7628	−	22.2405i	−1.04605	−	0.732453i
$923$	−46.7680	+	21.8083i	−1.53939	+	0.717828i
$924$	−0.227865	+	0.888339i	−0.00749620	+	0.0292242i
$925$	−7.95753	−	7.93500i	−0.261642	−	0.260901i
$926$	20.4431	+	11.8029i	0.671803	+	0.387866i
$927$	−22.3388	−	21.4020i	−0.733702	−	0.702935i
$928$	0.0709796	−	0.264900i	0.00233002	−	0.00869575i
$929$	29.4359	−	10.7138i	0.965761	−	0.351508i	0.189473	−	0.981886i	$-0.439322\pi$
$929$	29.4359	−	10.7138i	0.965761	−	0.351508i	0.776289	+	0.630378i	$0.217100\pi$
$930$	38.5145	−	7.24540i	1.26294	−	0.237586i
$931$	16.9002	−	14.1810i	0.553882	−	0.464762i
$932$	−9.79218	−	0.856705i	−0.320753	−	0.0280623i
$933$	4.56394	+	3.74707i	0.149417	+	0.122674i
$934$	−5.84848	−	16.0686i	−0.191368	−	0.525779i
$935$	0.952496	+	0.167255i	0.0311500	+	0.00546982i
$936$	10.9612	+	18.0800i	0.358278	+	0.590963i
$937$	−6.78666	−	25.3282i	−0.221711	−	0.827435i	−0.983696	−	0.179841i	$-0.942442\pi$
$937$	−6.78666	−	25.3282i	−0.221711	−	0.827435i	0.761985	−	0.647595i	$-0.224225\pi$
$938$	10.9209	+	15.5966i	0.356579	+	0.509248i
$939$	13.8994	+	3.56529i	0.453590	+	0.116349i
$940$	−4.24351	+	2.45400i	−0.138408	+	0.0800407i
$941$	22.1394	−	3.90377i	0.721722	−	0.127259i	0.199291	−	0.979940i	$-0.436136\pi$
$941$	22.1394	−	3.90377i	0.721722	−	0.127259i	0.522432	+	0.852681i	$0.325025\pi$
$942$	10.8960	+	12.7065i	0.355010	+	0.414000i
$943$	−4.36529	−	49.8955i	−0.142153	−	1.62482i
$944$	9.50209			0.309267
$945$	30.8547	+	24.2098i	1.00370	+	0.787544i
$946$	0.554507			0.0180286
$947$	3.16785	+	36.2086i	0.102941	+	1.17662i	0.855394	+	0.517977i	$0.173315\pi$
$947$	3.16785	+	36.2086i	0.102941	+	1.17662i	−0.752453	+	0.658646i	$0.771130\pi$
$948$	4.02682	−	11.4433i	0.130785	−	0.371663i
$949$	−92.1663	+	16.2514i	−2.99184	+	0.527543i
$950$	−20.5461	+	14.4300i	−0.666604	+	0.468171i
$951$	−37.7574	+	38.5747i	−1.22437	+	1.25087i
$952$	−5.33785	−	7.62324i	−0.173001	−	0.247071i
$953$	−1.93111	−	7.20699i	−0.0625547	−	0.233457i	0.927569	−	0.373651i	$-0.121894\pi$
$953$	−1.93111	−	7.20699i	−0.0625547	−	0.233457i	−0.990124	+	0.140194i	$0.955227\pi$
$954$	−16.6334	−	5.65377i	−0.538526	−	0.183048i
$955$	3.43916	−	2.41176i	0.111289	−	0.0780427i
$956$	−2.65701	−	7.30007i	−0.0859338	−	0.236101i
$957$	0.0121525	−	0.0735140i	0.000392833	−	0.00237637i
$958$	−32.8814	−	2.87675i	−1.06235	−	0.0929435i
$959$	−39.9330	+	33.5078i	−1.28950	+	1.08202i
$960$	−3.49120	+	1.67675i	−0.112678	+	0.0541170i
$961$	−67.0855	+	24.4171i	−2.16405	+	0.787650i
$962$	−4.09972	+	15.3003i	−0.132180	+	0.493303i
$963$	25.0843	+	11.0494i	0.808329	+	0.356063i
$964$	−11.8829	−	6.86058i	−0.382722	−	0.220965i
$965$	−14.1147	+	11.8607i	−0.454368	+	0.381809i
$966$	−42.4089	+	11.8515i	−1.36449	+	0.381316i
$967$	−48.9510	+	22.8262i	−1.57416	+	0.734042i	−0.996607	−	0.0823126i	$-0.973769\pi$
$967$	−48.9510	+	22.8262i	−1.57416	+	0.734042i	−0.577551	+	0.816354i	$0.695992\pi$
$968$	8.99052	+	6.29523i	0.288966	+	0.202336i
$969$	−13.5428	+	19.7887i	−0.435057	+	0.635704i
$970$	−5.06084	−	3.53829i	−0.162494	−	0.113608i
$971$			31.5940i			1.01390i	0.861975	+	0.506951i	$0.169227\pi$
$971$			31.5940i			1.01390i	−0.861975	+	0.506951i	$0.830773\pi$
$972$	7.06073	−	13.8977i	0.226473	−	0.445769i
$973$	−29.6393	−	29.6393i	−0.950194	−	0.950194i
$974$	4.89123	+	4.10423i	0.156725	+	0.131508i
$975$	−55.6252	−	25.1220i	−1.78143	−	0.804548i
$976$	−1.06847	−	6.05962i	−0.0342010	−	0.193964i
$977$	4.92366	+	10.5588i	0.157522	+	0.337807i	0.969191	−	0.246311i	$-0.0792184\pi$
$977$	4.92366	+	10.5588i	0.157522	+	0.337807i	−0.811669	+	0.584118i	$0.801441\pi$
$978$	12.1453	−	21.5663i	0.388364	−	0.689613i
$979$	0.915138	+	0.161363i	0.0292479	+	0.00515720i
$980$	−4.14557	+	8.90667i	−0.132425	+	0.284513i
$981$	−6.77029	−	17.4306i	−0.216159	−	0.556516i
$982$	−1.47871	−	0.396220i	−0.0471877	−	0.0126439i
$983$	−11.4709	+	24.5995i	−0.365865	+	0.784601i	0.634070	+	0.773275i	$0.281383\pi$
$983$	−11.4709	+	24.5995i	−0.365865	+	0.784601i	−0.999936	+	0.0113256i	$0.996395\pi$
$984$	−4.75572	+	10.4905i	−0.151607	+	0.334423i
$985$	24.0810	−	0.0170673i	0.767283	−	0.000543810i
$986$	0.486017	+	0.579212i	0.0154779	+	0.0184459i
$987$	12.6451	+	2.09034i	0.402498	+	0.0665361i
$988$	32.0739	+	14.9563i	1.02041	+	0.475823i
$989$	13.3121	+	23.0573i	0.423301	+	0.733178i
$990$	−0.899443	+	0.546171i	−0.0285862	+	0.0173584i
$991$	21.5210	−	37.2754i	0.683636	−	1.18409i	−0.290227	−	0.956958i	$-0.593731\pi$
$991$	21.5210	−	37.2754i	0.683636	−	1.18409i	0.973863	−	0.227135i	$-0.0729358\pi$
$992$	8.28887	−	5.80393i	0.263172	−	0.184275i
$993$	−0.165557	−	15.4629i	−0.00525381	−	0.490699i
$994$	−8.45288	+	23.2241i	−0.268109	+	0.736623i
$995$	1.03564	−	0.278285i	0.0328319	−	0.00882222i
$996$	−2.13111	+	1.02167i	−0.0675269	+	0.0323729i
$997$	61.6293	−	5.39187i	1.95182	−	0.170762i	0.958412	−	0.285388i	$-0.0921224\pi$
$997$	61.6293	−	5.39187i	1.95182	−	0.170762i	0.993409	+	0.114626i	$0.0365668\pi$
$998$	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.173.1	yes	216
3.2	odd	2		810.2.s.a.683.18		216
5.2	odd	4	inner	270.2.r.a.227.14	yes	216
15.2	even	4		810.2.s.a.197.2		216
27.5	odd	18	inner	270.2.r.a.113.14	✓	216
27.22	even	9		810.2.s.a.773.2		216
135.22	odd	36		810.2.s.a.287.18		216
135.32	even	36	inner	270.2.r.a.167.1	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.r.a.113.14	✓	216	27.5	odd	18	inner
270.2.r.a.167.1	yes	216	135.32	even	36	inner
270.2.r.a.173.1	yes	216	1.1	even	1	trivial
270.2.r.a.227.14	yes	216	5.2	odd	4	inner
810.2.s.a.197.2		216	15.2	even	4
810.2.s.a.287.18		216	135.22	odd	36
810.2.s.a.683.18		216	3.2	odd	2
810.2.s.a.773.2		216	27.22	even	9

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+(-0.0871557 - 0.996195i) q^{2} +(-1.70242 + 0.319012i) q^{3} +(-0.984808 + 0.173648i) q^{4} +(-2.16029 - 0.577206i) q^{5} +(0.466174 + 1.66814i) q^{6} +(1.93607 + 2.76499i) q^{7} +(0.258819 + 0.965926i) q^{8} +(2.79646 - 1.08618i) q^{9} +(-0.386728 + 2.20237i) q^{10} +(0.0536510 + 0.147405i) q^{11} +(1.62116 - 0.609788i) q^{12} +(7.02091 + 0.614250i) q^{13} +(2.58573 - 2.16968i) q^{14} +(3.86185 + 0.293489i) q^{15} +(0.939693 - 0.342020i) q^{16} +(-0.713580 + 2.66312i) q^{17} +(-1.32578 - 2.69115i) q^{18} +(-4.34868 - 2.51071i) q^{19} +(2.22770 + 0.193307i) q^{20} +(-4.17806 - 4.08954i) q^{21} +(0.142168 - 0.0662941i) q^{22} +(6.16966 + 4.32004i) q^{23} +(-0.748761 - 1.56184i) q^{24} +(4.33367 + 2.49386i) q^{25} -7.04772i q^{26} +(-4.41425 + 2.74125i) q^{27} +(-2.38679 - 2.38679i) q^{28} +(0.210083 + 0.176281i) q^{29} +(-0.0442096 - 3.87273i) q^{30} +(1.75712 + 9.96511i) q^{31} +(-0.422618 - 0.906308i) q^{32} +(-0.138361 - 0.233830i) q^{33} +(2.71517 + 0.478758i) q^{34} +(-2.58649 - 7.09067i) q^{35} +(-2.56536 + 1.55528i) q^{36} +(-2.17096 - 0.581708i) q^{37} +(-2.12215 + 4.55096i) q^{38} +(-12.1485 + 1.19404i) q^{39} +(-0.00158481 - 2.23607i) q^{40} +(-4.27452 - 5.09418i) q^{41} +(-3.70984 + 4.51859i) q^{42} +(3.20373 + 1.49392i) q^{43} +(-0.0784326 - 0.135849i) q^{44} +(-6.66811 + 0.732334i) q^{45} +(3.76588 - 6.52270i) q^{46} +(-1.79577 + 1.25741i) q^{47} +(-1.49064 + 0.882035i) q^{48} +(-1.50267 + 4.12855i) q^{49} +(2.10667 - 4.53453i) q^{50} +(0.365246 - 4.76138i) q^{51} +(-7.02091 + 0.614250i) 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} +(8.20422 + 2.88700i) q^{57} +(0.157300 - 0.224648i) q^{58} +(8.92905 + 3.24991i) q^{59} +(-3.85414 + 0.381572i) q^{60} +(1.06847 - 6.05962i) q^{61} +(9.77405 - 2.61895i) q^{62} +(8.41742 + 5.62926i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(-14.8126 - 5.37946i) q^{65} +(-0.220881 + 0.158214i) q^{66} +(-0.491625 + 5.61930i) q^{67} +(0.240294 - 2.74657i) q^{68} +(-11.8815 - 5.38633i) q^{69} +(-6.83826 + 3.19464i) q^{70} +(-6.34096 + 3.66095i) q^{71} +(1.77295 + 2.42005i) q^{72} +(-12.8267 + 3.43691i) q^{73} +(-0.390282 + 2.21340i) q^{74} +(-8.17329 - 2.86310i) q^{75} +(4.71859 + 1.71743i) q^{76} +(-0.303701 + 0.433730i) q^{77} +(2.24831 + 11.9982i) 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} +(-1.35929 + 0.118923i) q^{83} +(4.82473 + 3.30190i) q^{84} +(3.07870 - 5.34121i) q^{85} +(1.20902 - 3.32174i) q^{86} +(-0.413885 - 0.233085i) q^{87} +(-0.128496 + 0.0899741i) q^{88} +(2.96196 - 5.13026i) q^{89} +(1.31071 + 6.57891i) q^{90} +(11.8945 + 20.6019i) q^{91} +(-6.82610 - 3.18306i) q^{92} +(-6.17034 - 16.4043i) q^{93} +(1.40914 + 1.67935i) q^{94} +(7.94519 + 7.93394i) q^{95} +(1.00860 + 1.40810i) q^{96} +(-1.16709 + 2.50284i) q^{97} +(4.24380 + 1.13712i) 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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