LMFDB - Embedded newform 546.2.bw.a.527.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			527.21
Character	$\chi$	$=$	546.527
Dual form			546.2.bw.a.431.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{2} +(-1.71416 - 0.248275i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.203302 + 0.758733i) q^{5} +(-1.59150 - 0.683474i) q^{6} +(-0.313922 - 2.62706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.87672 + 0.851169i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{2} +(-1.71416 - 0.248275i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.203302 + 0.758733i) q^{5} +(-1.59150 - 0.683474i) q^{6} +(-0.313922 - 2.62706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.87672 + 0.851169i) q^{9} +0.785498i q^{10} +(0.607479 + 0.607479i) q^{11} +(-1.36037 - 1.07209i) q^{12} +(2.66316 + 2.43055i) q^{13} +(0.376709 - 2.61880i) q^{14} +(-0.160118 - 1.35107i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.01144 - 5.21597i) q^{17} +(2.55840 + 1.56672i) q^{18} +(-1.00138 - 1.00138i) q^{19} +(-0.203302 + 0.758733i) q^{20} +(-0.114121 + 4.58115i) q^{21} +(0.429553 + 0.744007i) q^{22} +(3.59349 + 6.22411i) q^{23} +(-1.03654 - 1.38765i) q^{24} +(3.79578 - 2.19150i) q^{25} +(1.94334 + 3.03701i) q^{26} +(-4.71984 - 2.17326i) q^{27} +(1.04167 - 2.43206i) q^{28} +(7.77979 + 4.49166i) q^{29} +(0.195020 - 1.34647i) q^{30} +(1.05134 - 3.92364i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.890497 - 1.19214i) q^{33} +(4.25882 - 4.25882i) q^{34} +(1.92942 - 0.772269i) q^{35} +(2.06573 + 2.17549i) q^{36} +(-3.78403 - 1.01393i) q^{37} +(-0.708082 - 1.22643i) q^{38} +(-3.96165 - 4.82756i) q^{39} +(-0.392749 + 0.680261i) q^{40} +(0.830563 + 3.09970i) q^{41} +(-1.29592 + 4.39552i) q^{42} +(-3.17968 + 1.83579i) q^{43} +(0.222353 + 0.829832i) q^{44} +(-0.0609676 + 2.35570i) q^{45} +(1.86013 + 6.94209i) q^{46} +(4.80000 - 1.28616i) q^{47} +(-0.642070 - 1.60865i) q^{48} +(-6.80291 + 1.64938i) q^{49} +(4.23365 - 1.13440i) q^{50} +(-6.45710 + 8.19336i) q^{51} +(1.09109 + 3.43650i) q^{52} +(9.26822 - 5.35101i) q^{53} +(-3.99654 - 3.32080i) q^{54} +(-0.337413 + 0.584416i) q^{55} +(1.63564 - 2.07959i) q^{56} +(1.46791 + 1.96515i) q^{57} +(6.35217 + 6.35217i) q^{58} +(-13.7375 + 3.68096i) q^{59} +(0.536867 - 1.25012i) q^{60} -10.0652 q^{61} +(2.03103 - 3.51784i) q^{62} +(1.33301 - 7.82452i) q^{63} +1.00000i q^{64} +(-1.30271 + 2.51476i) q^{65} +(-0.551606 - 1.38200i) q^{66} +(-7.26892 - 7.26892i) q^{67} +(5.21597 - 3.01144i) q^{68} +(-4.61454 - 11.5613i) q^{69} +(2.06355 - 0.246585i) q^{70} +(1.26314 + 0.338458i) q^{71} +(1.43228 + 2.63601i) q^{72} +(-1.49555 - 0.400732i) q^{73} +(-3.39267 - 1.95876i) q^{74} +(-7.05069 + 2.81419i) q^{75} +(-0.366530 - 1.36791i) q^{76} +(1.40518 - 1.78659i) q^{77} +(-2.57720 - 5.68841i) q^{78} +(2.32723 - 4.03088i) q^{79} +(-0.555431 + 0.555431i) q^{80} +(7.55102 + 4.89715i) q^{81} +3.20905i q^{82} +(1.36936 - 1.36936i) q^{83} +(-2.38941 + 3.91034i) q^{84} +(4.56976 + 1.22446i) q^{85} +(-3.54648 + 0.950276i) q^{86} +(-12.2207 - 9.63098i) q^{87} +0.859106i q^{88} +(0.800997 - 2.98936i) q^{89} +(-0.668591 + 2.25966i) q^{90} +(5.54918 - 7.75929i) q^{91} +7.18698i q^{92} +(-2.77631 + 6.46475i) q^{93} +4.96933 q^{94} +(0.556197 - 0.963362i) q^{95} +(-0.203843 - 1.72001i) q^{96} +(-1.64679 + 6.14592i) q^{97} +(-6.99799 - 0.167541i) q^{98} +(1.23048 + 2.26461i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$2$	0.965926	+	0.258819i	0.683013	+	0.183013i
$3$	−1.71416	−	0.248275i	−0.989673	−	0.143342i
$3$	−1.71416	−	0.248275i	−0.989673	−	0.143342i
$4$	0.866025	+	0.500000i	0.433013	+	0.250000i
$5$	0.203302	+	0.758733i	0.0909193	+	0.339316i	0.996369	−	0.0851376i	$-0.0271330\pi$
$5$	0.203302	+	0.758733i	0.0909193	+	0.339316i	−0.905450	+	0.424453i	$0.860466\pi$
$6$	−1.59150	−	0.683474i	−0.649726	−	0.279027i
$7$	−0.313922	−	2.62706i	−0.118651	−	0.992936i
$7$	−0.313922	−	2.62706i	−0.118651	−	0.992936i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.87672	+	0.851169i	0.958906	+	0.283723i
$10$			0.785498i			0.248396i
$11$	0.607479	+	0.607479i	0.183162	+	0.183162i	0.792732	−	0.609570i	$-0.208658\pi$
$11$	0.607479	+	0.607479i	0.183162	+	0.183162i	−0.609570	+	0.792732i	$0.708658\pi$
$12$	−1.36037	−	1.07209i	−0.392706	−	0.309487i
$13$	2.66316	+	2.43055i	0.738628	+	0.674113i
$13$	2.66316	+	2.43055i	0.738628	+	0.674113i
$14$	0.376709	−	2.61880i	0.100680	−	0.699903i
$15$	−0.160118	−	1.35107i	−0.0413423	−	0.348844i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	3.01144	−	5.21597i	0.730382	−	1.26506i	−0.226339	−	0.974049i	$-0.572676\pi$
$17$	3.01144	−	5.21597i	0.730382	−	1.26506i	0.956720	−	0.291009i	$-0.0939911\pi$
$18$	2.55840	+	1.56672i	0.603020	+	0.369278i
$19$	−1.00138	−	1.00138i	−0.229732	−	0.229732i	0.582849	−	0.812581i	$-0.301938\pi$
$19$	−1.00138	−	1.00138i	−0.229732	−	0.229732i	−0.812581	+	0.582849i	$0.801938\pi$
$20$	−0.203302	+	0.758733i	−0.0454597	+	0.169658i
$21$	−0.114121	+	4.58115i	−0.0249033	+	0.999690i
$22$	0.429553	+	0.744007i	0.0915810	+	0.158623i
$23$	3.59349	+	6.22411i	0.749295	+	1.29782i	0.948161	+	0.317790i	$0.102941\pi$
$23$	3.59349	+	6.22411i	0.749295	+	1.29782i	−0.198866	+	0.980027i	$0.563726\pi$
$24$	−1.03654	−	1.38765i	−0.211583	−	0.283254i
$25$	3.79578	−	2.19150i	0.759157	−	0.438299i
$26$	1.94334	+	3.03701i	0.381121	+	0.595606i
$27$	−4.71984	−	2.17326i	−0.908335	−	0.418244i
$28$	1.04167	−	2.43206i	0.196857	−	0.459617i
$29$	7.77979	+	4.49166i	1.44467	+	0.834081i	0.998156	−	0.0606952i	$-0.0193318\pi$
$29$	7.77979	+	4.49166i	1.44467	+	0.834081i	0.446515	+	0.894776i	$0.352665\pi$
$30$	0.195020	−	1.34647i	0.0356056	−	0.245831i
$31$	1.05134	−	3.92364i	0.188826	−	0.704707i	−0.804953	−	0.593338i	$-0.797810\pi$
$31$	1.05134	−	3.92364i	0.188826	−	0.704707i	0.993779	−	0.111369i	$-0.0355236\pi$
$32$	0.258819	+	0.965926i	0.0457532	+	0.170753i
$33$	−0.890497	−	1.19214i	−0.155016	−	0.207525i
$34$	4.25882	−	4.25882i	0.730382	−	0.730382i
$35$	1.92942	−	0.772269i	0.326131	−	0.130537i
$36$	2.06573	+	2.17549i	0.344288	+	0.362582i
$37$	−3.78403	−	1.01393i	−0.622090	−	0.166689i	−0.0660125	−	0.997819i	$-0.521028\pi$
$37$	−3.78403	−	1.01393i	−0.622090	−	0.166689i	−0.556078	+	0.831130i	$0.687694\pi$
$38$	−0.708082	−	1.22643i	−0.114866	−	0.198954i
$39$	−3.96165	−	4.82756i	−0.634372	−	0.773028i
$40$	−0.392749	+	0.680261i	−0.0620991	+	0.107559i
$41$	0.830563	+	3.09970i	0.129712	+	0.484092i	0.999964	−	0.00851511i	$-0.00271048\pi$
$41$	0.830563	+	3.09970i	0.129712	+	0.484092i	−0.870252	+	0.492608i	$0.836044\pi$
$42$	−1.29592	+	4.39552i	−0.199965	+	0.678243i
$43$	−3.17968	+	1.83579i	−0.484897	+	0.279956i	−0.722455	−	0.691418i	$-0.756986\pi$
$43$	−3.17968	+	1.83579i	−0.484897	+	0.279956i	0.237558	+	0.971373i	$0.423653\pi$
$44$	0.222353	+	0.829832i	0.0335210	+	0.125102i
$45$	−0.0609676	+	2.35570i	−0.00908851	+	0.351168i
$46$	1.86013	+	6.94209i	0.274261	+	1.02356i
$47$	4.80000	−	1.28616i	0.700152	−	0.187605i	0.108854	−	0.994058i	$-0.465282\pi$
$47$	4.80000	−	1.28616i	0.700152	−	0.187605i	0.591299	+	0.806453i	$0.298615\pi$
$48$	−0.642070	−	1.60865i	−0.0926748	−	0.232188i
$49$	−6.80291	+	1.64938i	−0.971844	+	0.235626i
$50$	4.23365	−	1.13440i	0.598728	−	0.160429i
$51$	−6.45710	+	8.19336i	−0.904175	+	1.14730i
$52$	1.09109	+	3.43650i	0.151307	+	0.476557i
$53$	9.26822	−	5.35101i	1.27309	−	0.735017i	0.297519	−	0.954716i	$-0.403841\pi$
$53$	9.26822	−	5.35101i	1.27309	−	0.735017i	0.975568	+	0.219698i	$0.0705074\pi$
$54$	−3.99654	−	3.32080i	−0.543860	−	0.451903i
$55$	−0.337413	+	0.584416i	−0.0454967	+	0.0788027i
$56$	1.63564	−	2.07959i	0.218571	−	0.277897i
$57$	1.46791	+	1.96515i	0.194430	+	0.260290i
$58$	6.35217	+	6.35217i	0.834081	+	0.834081i
$59$	−13.7375	+	3.68096i	−1.78847	+	0.479220i	−0.992085	−	0.125567i	$-0.959925\pi$
$59$	−13.7375	+	3.68096i	−1.78847	+	0.479220i	−0.796388	+	0.604786i	$0.793258\pi$
$60$	0.536867	−	1.25012i	0.0693093	−	0.161390i
$61$	−10.0652			−1.28871			−0.644357	−	0.764724i	$-0.722875\pi$
$61$	−10.0652			−1.28871			−0.644357	+	0.764724i	$0.722875\pi$
$62$	2.03103	−	3.51784i	0.257941	−	0.446767i
$63$	1.33301	−	7.82452i	0.167943	−	0.985797i
$64$			1.00000i			0.125000i
$65$	−1.30271	+	2.51476i	−0.161581	+	0.311918i
$66$	−0.551606	−	1.38200i	−0.0678979	−	0.170112i
$67$	−7.26892	−	7.26892i	−0.888039	−	0.888039i	0.106295	−	0.994335i	$-0.466101\pi$
$67$	−7.26892	−	7.26892i	−0.888039	−	0.888039i	−0.994335	+	0.106295i	$0.966101\pi$
$68$	5.21597	−	3.01144i	0.632529	−	0.365191i
$69$	−4.61454	−	11.5613i	−0.555526	−	1.39182i
$70$	2.06355	−	0.246585i	0.246642	−	0.0294725i
$71$	1.26314	+	0.338458i	0.149908	+	0.0401676i	0.332992	−	0.942930i	$-0.391942\pi$
$71$	1.26314	+	0.338458i	0.149908	+	0.0401676i	−0.183085	+	0.983097i	$0.558608\pi$
$72$	1.43228	+	2.63601i	0.168796	+	0.310657i
$73$	−1.49555	−	0.400732i	−0.175041	−	0.0469021i	0.170234	−	0.985404i	$-0.445548\pi$
$73$	−1.49555	−	0.400732i	−0.175041	−	0.0469021i	−0.345275	+	0.938502i	$0.612214\pi$
$74$	−3.39267	−	1.95876i	−0.394390	−	0.227701i
$75$	−7.05069	+	2.81419i	−0.814144	+	0.324954i
$76$	−0.366530	−	1.36791i	−0.0420439	−	0.156910i
$77$	1.40518	−	1.78659i	0.160136	−	0.203600i
$78$	−2.57720	−	5.68841i	−0.291810	−	0.644086i
$79$	2.32723	−	4.03088i	0.261834	−	0.453509i	−0.704896	−	0.709311i	$-0.749006\pi$
$79$	2.32723	−	4.03088i	0.261834	−	0.453509i	0.966729	+	0.255802i	$0.0823395\pi$
$80$	−0.555431	+	0.555431i	−0.0620991	+	0.0620991i
$81$	7.55102	+	4.89715i	0.839003	+	0.544128i
$82$			3.20905i			0.354380i
$83$	1.36936	−	1.36936i	0.150307	−	0.150307i	−0.627948	−	0.778255i	$-0.716105\pi$
$83$	1.36936	−	1.36936i	0.150307	−	0.150307i	0.778255	+	0.627948i	$0.216105\pi$
$84$	−2.38941	+	3.91034i	−0.260706	+	0.426653i
$85$	4.56976	+	1.22446i	0.495660	+	0.132812i
$86$	−3.54648	+	0.950276i	−0.382426	+	0.102471i
$87$	−12.2207	−	9.63098i	−1.31019	−	1.03255i
$88$			0.859106i			0.0915810i
$89$	0.800997	−	2.98936i	0.0849055	−	0.316872i	−0.910391	−	0.413750i	$-0.864219\pi$
$89$	0.800997	−	2.98936i	0.0849055	−	0.316872i	0.995296	+	0.0968777i	$0.0308856\pi$
$90$	−0.668591	+	2.25966i	−0.0704757	+	0.238189i
$91$	5.54918	−	7.75929i	0.581712	−	0.813395i
$92$			7.18698i			0.749295i
$93$	−2.77631	+	6.46475i	−0.287890	+	0.670363i
$94$	4.96933			0.512547
$95$	0.556197	−	0.963362i	0.0570646	−	0.0988388i
$96$	−0.203843	−	1.72001i	−0.0208046	−	0.175548i
$97$	−1.64679	+	6.14592i	−0.167207	+	0.624024i	0.830542	+	0.556956i	$0.188031\pi$
$97$	−1.64679	+	6.14592i	−0.167207	+	0.624024i	−0.997748	+	0.0670675i	$0.978636\pi$
$98$	−6.99799	−	0.167541i	−0.706904	−	0.0169242i
$99$	1.23048	+	2.26461i	0.123668	+	0.227602i
$100$	4.38299			0.438299
$101$	−17.3738			−1.72876			−0.864381	−	0.502837i	$-0.832290\pi$
$101$	−17.3738			−1.72876			−0.864381	+	0.502837i	$0.832290\pi$
$102$	−8.35768	+	6.24296i	−0.827533	+	0.618145i
$103$	−3.24085	−	1.87110i	−0.319330	−	0.184365i	0.331764	−	0.943362i	$-0.392356\pi$
$103$	−3.24085	−	1.87110i	−0.319330	−	0.184365i	−0.651094	+	0.758997i	$0.725690\pi$
$104$	0.164482	+	3.60180i	0.0161288	+	0.353185i
$105$	−3.49907	+	0.844770i	−0.341475	+	0.0824411i
$106$	10.3374	−	2.76988i	1.00405	−	0.269035i
$107$	4.10838	−	2.37198i	0.397172	−	0.229308i	−0.288091	−	0.957603i	$-0.593020\pi$
$107$	4.10838	−	2.37198i	0.397172	−	0.229308i	0.685263	+	0.728295i	$0.259687\pi$
$108$	−3.00087	−	4.24202i	−0.288759	−	0.408189i
$109$	−2.96384	+	11.0612i	−0.283884	+	1.05947i	0.665767	+	0.746160i	$0.268105\pi$
$109$	−2.96384	+	11.0612i	−0.283884	+	1.05947i	−0.949651	+	0.313310i	$0.898562\pi$
$110$	−0.477174	+	0.477174i	−0.0454967	+	0.0454967i
$111$	6.23471	+	2.67752i	0.591773	+	0.254139i
$112$	2.11814	−	1.58539i	0.200146	−	0.149806i
$113$	−7.21357	+	4.16476i	−0.678596	+	0.391787i	−0.799326	−	0.600898i	$-0.794810\pi$
$113$	−7.21357	+	4.16476i	−0.678596	+	0.391787i	0.120730	+	0.992685i	$0.461476\pi$
$114$	0.909276	+	2.27811i	0.0851615	+	0.213364i
$115$	−3.99187	+	3.99187i	−0.372244	+	0.372244i
$116$	4.49166	+	7.77979i	0.417041	+	0.722335i
$117$	5.59236	+	9.25881i	0.517014	+	0.855977i
$118$	−14.2221			−1.30925
$119$	−14.6480	−	6.27384i	−1.34278	−	0.575122i
$120$	0.842128	−	1.06857i	0.0768754	−	0.0975466i
$121$		−	10.2619i		−	0.932903i
$122$	−9.72222	−	2.60506i	−0.880209	−	0.235851i
$123$	−0.654142	−	5.51961i	−0.0589820	−	0.497687i
$124$	2.87231	−	2.87231i	0.257941	−	0.257941i
$125$	5.21160	+	5.21160i	0.466140	+	0.466140i
$126$	3.31272	−	7.21290i	0.295121	−	0.642576i
$127$	−13.3542	−	7.71003i	−1.18499	−	0.684155i	−0.227827	−	0.973702i	$-0.573162\pi$
$127$	−13.3542	−	7.71003i	−1.18499	−	0.684155i	−0.957164	+	0.289547i	$0.906495\pi$
$128$	−0.258819	+	0.965926i	−0.0228766	+	0.0853766i
$129$	5.90628	−	2.35741i	0.520019	−	0.207559i
$130$	−1.90919	+	2.09191i	−0.167447	+	0.183472i
$131$	6.14853	+	3.54985i	0.537199	+	0.310152i	0.743943	−	0.668243i	$-0.232953\pi$
$131$	6.14853	+	3.54985i	0.537199	+	0.310152i	−0.206744	+	0.978395i	$0.566287\pi$
$132$	−0.175123	−	1.47767i	−0.0152425	−	0.128615i
$133$	−2.31633	+	2.94504i	−0.200851	+	0.255367i
$134$	−5.13990	−	8.90257i	−0.444020	−	0.769065i
$135$	0.689372	−	4.02293i	0.0593317	−	0.346239i
$136$	5.81766	−	1.55884i	0.498860	−	0.133669i
$137$	−18.0143	+	4.82693i	−1.53907	+	0.412392i	−0.925965	−	0.377610i	$-0.876746\pi$
$137$	−18.0143	+	4.82693i	−1.53907	+	0.412392i	−0.613104	+	0.790002i	$0.710079\pi$
$138$	−1.46502	−	12.3617i	−0.124710	−	1.05230i
$139$	9.91806	+	17.1786i	0.841239	+	1.45707i	0.888848	+	0.458202i	$0.151506\pi$
$139$	9.91806	+	17.1786i	0.841239	+	1.45707i	−0.0476095	+	0.998866i	$0.515160\pi$
$140$	2.05706	+	0.295904i	0.173853	+	0.0250084i
$141$	−8.54731	+	1.01296i	−0.719814	+	0.0853068i
$142$	1.13250	+	0.653851i	0.0950375	+	0.0548700i
$143$	0.141308	+	3.09432i	0.0118167	+	0.258760i
$144$	0.701225	+	2.91690i	0.0584355	+	0.243075i
$145$	−1.82633	+	6.81595i	−0.151668	+	0.566033i
$146$	−1.34087	−	0.774154i	−0.110972	−	0.0640695i
$147$	12.0708	−	1.13832i	0.995583	−	0.0938870i
$148$	−2.77010	−	2.77010i	−0.227701	−	0.227701i
$149$	−8.04973	+	8.04973i	−0.659459	+	0.659459i	−0.955252	−	0.295793i	$-0.904416\pi$
$149$	−8.04973	+	8.04973i	−0.659459	+	0.659459i	0.295793	+	0.955252i	$0.404416\pi$
$150$	−7.53881	+	0.893442i	−0.615541	+	0.0729493i
$151$	−5.39810	−	1.44642i	−0.439291	−	0.117708i	0.0323931	−	0.999475i	$-0.489687\pi$
$151$	−5.39810	−	1.44642i	−0.439291	−	0.117708i	−0.471684	+	0.881767i	$0.656354\pi$
$152$		−	1.41616i		−	0.114866i
$153$	13.1027	−	12.4416i	1.05929	−	1.00585i
$154$	1.81971	−	1.36202i	0.146636	−	0.109755i
$155$	3.19074			0.256286
$156$	−1.01711	−	6.16161i	−0.0814342	−	0.493324i
$157$	6.20541	+	10.7481i	0.495245	+	0.857790i	0.999985	−	0.00548153i	$-0.00174483\pi$
$157$	6.20541	+	10.7481i	0.495245	+	0.857790i	−0.504740	+	0.863272i	$0.668411\pi$
$158$	3.29120	−	3.29120i	0.261834	−	0.261834i
$159$	−17.2158	+	6.87144i	−1.36530	+	0.544940i
$160$	−0.680261	+	0.392749i	−0.0537794	+	0.0310495i
$161$	15.2230	−	11.3942i	1.19974	−	0.897989i
$162$	6.02625	+	6.68463i	0.473467	+	0.525194i
$163$	9.32490	−	9.32490i	0.730382	−	0.730382i	−0.240313	−	0.970695i	$-0.577250\pi$
$163$	9.32490	−	9.32490i	0.730382	−	0.730382i	0.970695	+	0.240313i	$0.0772501\pi$
$164$	−0.830563	+	3.09970i	−0.0648561	+	0.242046i
$165$	0.723477	−	0.918014i	0.0563226	−	0.0714673i
$166$	1.67712	−	0.968287i	0.130170	−	0.0751537i
$167$	19.6766	−	5.27232i	1.52262	−	0.407984i	0.602016	−	0.798484i	$-0.294364\pi$
$167$	19.6766	−	5.27232i	1.52262	−	0.407984i	0.920603	+	0.390500i	$0.127698\pi$
$168$	−3.32006	+	3.15867i	−0.256148	+	0.243697i
$169$	1.18486	+	12.9459i	0.0911434	+	0.995838i
$170$	4.09713	+	2.36548i	0.314236	+	0.181424i
$171$	−2.02834	−	3.73303i	−0.155111	−	0.285472i
$172$	−3.67158			−0.279956
$173$	11.1891			0.850690			0.425345	−	0.905031i	$-0.360153\pi$
$173$	11.1891			0.850690			0.425345	+	0.905031i	$0.360153\pi$
$174$	−9.31158	−	12.4658i	−0.705909	−	0.945026i
$175$	−6.94877	−	9.28380i	−0.525278	−	0.701789i
$176$	−0.222353	+	0.829832i	−0.0167605	+	0.0625510i
$177$	24.4623	−	2.89908i	1.83870	−	0.217908i
$178$	1.54741	−	2.68019i	0.115983	−	0.200889i
$179$	−2.55873			−0.191249			−0.0956243	−	0.995417i	$-0.530485\pi$
$179$	−2.55873			−0.191249			−0.0956243	+	0.995417i	$0.530485\pi$
$180$	−1.23065	+	2.00962i	−0.0917274	+	0.149788i
$181$		−	14.6075i		−	1.08577i	−0.839808	−	0.542884i	$-0.817332\pi$
$181$		−	14.6075i		−	1.08577i	0.839808	−	0.542884i	$-0.182668\pi$
$182$	7.36835	−	6.05867i	0.546178	−	0.449098i
$183$	17.2534	+	2.49894i	1.27541	+	0.184727i
$184$	−1.86013	+	6.94209i	−0.137130	+	0.511778i
$185$		−	3.07720i		−	0.226240i
$186$	−4.35491	+	5.52591i	−0.319317	+	0.405179i
$187$	4.99798	−	1.33920i	0.365489	−	0.0979324i
$188$	4.80000	+	1.28616i	0.350076	+	0.0938026i
$189$	−4.22763	+	13.0816i	−0.307515	+	0.951543i
$190$	0.786581	−	0.786581i	0.0570646	−	0.0570646i
$191$		−	0.552155i		−	0.0399525i	−0.999800	−	0.0199763i	$-0.993641\pi$
$191$		−	0.552155i		−	0.0399525i	0.999800	−	0.0199763i	$-0.00635906\pi$
$192$	0.248275	−	1.71416i	0.0179177	−	0.123709i
$193$	18.5552	−	18.5552i	1.33563	−	1.33563i	0.435386	−	0.900244i	$-0.356612\pi$
$193$	18.5552	−	18.5552i	1.33563	−	1.33563i	0.900244	−	0.435386i	$-0.143388\pi$
$194$	−3.18136	+	5.51028i	−0.228409	+	0.395615i
$195$	2.85741	−	3.98729i	0.204624	−	0.285536i
$196$	−6.71618	−	1.97305i	−0.479727	−	0.140932i
$197$	−1.08744	−	4.05837i	−0.0774766	−	0.289147i	0.916307	−	0.400477i	$-0.131156\pi$
$197$	−1.08744	−	4.05837i	−0.0774766	−	0.289147i	−0.993783	+	0.111330i	$0.964489\pi$
$198$	0.602427	+	2.50592i	0.0428126	+	0.178088i
$199$	−9.69661	−	5.59834i	−0.687375	−	0.396856i	0.115253	−	0.993336i	$-0.463232\pi$
$199$	−9.69661	−	5.59834i	−0.687375	−	0.396856i	−0.802628	+	0.596480i	$0.796565\pi$
$200$	4.23365	+	1.13440i	0.299364	+	0.0802143i
$201$	10.6554	+	14.2648i	0.751576	+	1.00616i
$202$	−16.7818	−	4.49668i	−1.18077	−	0.316385i
$203$	9.35764	−	21.8480i	0.656777	−	1.53343i
$204$	−9.68869	+	3.86711i	−0.678344	+	0.270752i
$205$	−2.18299	+	1.26035i	−0.152467	+	0.0880267i
$206$	−2.64614	−	2.64614i	−0.184365	−	0.184365i
$207$	5.03970	+	20.9637i	0.350283	+	1.45708i
$208$	−0.773336	+	3.52164i	−0.0536212	+	0.244182i
$209$		−	1.21663i		−	0.0841564i
$210$	−3.59849	−	0.0896419i	−0.248319	−	0.00618588i
$211$	−6.06686	+	10.5081i	−0.417660	+	0.723408i	−0.995704	−	0.0925979i	$-0.970483\pi$
$211$	−6.06686	+	10.5081i	−0.417660	+	0.723408i	0.578044	+	0.816006i	$0.303816\pi$
$212$	10.7020			0.735017
$213$	−2.08120	−	0.893780i	−0.142602	−	0.0612408i
$214$	4.58231	−	1.22783i	0.313240	−	0.0839324i
$215$	−2.03931	−	2.03931i	−0.139080	−	0.139080i
$216$	−1.80071	−	4.87416i	−0.122523	−	0.331645i
$217$	−10.6377	−	1.53021i	−0.722134	−	0.103878i
$218$	−5.72570	+	9.91720i	−0.387793	+	0.671677i
$219$	2.46413	+	1.05823i	0.166510	+	0.0715085i
$220$	−0.584416	+	0.337413i	−0.0394013	+	0.0227484i
$221$	20.6976	−	6.57151i	1.39227	−	0.442048i
$222$	5.32928	+	4.19995i	0.357678	+	0.281882i
$223$	18.4444	−	4.94218i	1.23513	−	0.330953i	0.418556	−	0.908191i	$-0.362536\pi$
$223$	18.4444	−	4.94218i	1.23513	−	0.330953i	0.816576	+	0.577238i	$0.195870\pi$
$224$	2.45630	−	0.983159i	0.164118	−	0.0656900i
$225$	12.7847	−	3.07347i	0.852316	−	0.204898i
$226$	−8.04569	+	2.15584i	−0.535192	+	0.143404i
$227$	2.58579	+	9.65028i	0.171625	+	0.640512i	0.997102	+	0.0760766i	$0.0242394\pi$
$227$	2.58579	+	9.65028i	0.171625	+	0.640512i	−0.825477	+	0.564435i	$0.809094\pi$
$228$	0.288675	+	2.43582i	0.0191180	+	0.161316i
$229$	2.05810	+	7.68092i	0.136003	+	0.507570i	0.999992	+	0.00405883i	$0.00129197\pi$
$229$	2.05810	+	7.68092i	0.136003	+	0.507570i	−0.863989	+	0.503511i	$0.832041\pi$
$230$	−4.88903	+	2.82268i	−0.322373	+	0.186122i
$231$	−2.85228	+	2.71363i	−0.187666	+	0.178544i
$232$	2.32506	+	8.67723i	0.152647	+	0.569688i
$233$	−12.8017	+	22.1731i	−0.838664	+	1.45261i	0.0523476	+	0.998629i	$0.483330\pi$
$233$	−12.8017	+	22.1731i	−0.838664	+	1.45261i	−0.891012	+	0.453980i	$0.850004\pi$
$234$	3.00545	+	10.3907i	0.196472	+	0.679263i
$235$	1.95170	+	3.38044i	0.127315	+	0.220516i
$236$	−13.7375	−	3.68096i	−0.894236	−	0.239610i
$237$	−4.99002	+	6.33179i	−0.324137	+	0.411294i
$238$	−12.5251	−	9.85125i	−0.811883	−	0.638562i
$239$	−17.7067	+	17.7067i	−1.14535	+	1.14535i	−0.157898	+	0.987455i	$0.550472\pi$
$239$	−17.7067	+	17.7067i	−1.14535	+	1.14535i	−0.987455	+	0.157898i	$0.949528\pi$
$240$	1.09000	−	0.814200i	0.0703592	−	0.0525564i
$241$	0.199072	+	0.742948i	0.0128234	+	0.0478575i	0.972041	−	0.234811i	$-0.0754471\pi$
$241$	0.199072	+	0.742948i	0.0128234	+	0.0478575i	−0.959218	+	0.282668i	$0.908780\pi$
$242$	2.65598	−	9.91227i	0.170733	−	0.637185i
$243$	−11.7279	−	10.2692i	−0.752342	−	0.658773i
$244$	−8.71671	−	5.03259i	−0.558030	−	0.322179i
$245$	−2.63448	−	4.82627i	−0.168311	−	0.308339i
$246$	0.796728	−	5.50084i	0.0507975	−	0.350721i
$247$	−0.232934	−	5.10074i	−0.0148212	−	0.324552i
$248$	3.51784	−	2.03103i	0.223383	−	0.128970i
$249$	−2.68730	+	2.00734i	−0.170300	+	0.127210i
$250$	3.68516	+	6.38289i	0.233070	+	0.403689i
$251$	−2.31959	−	4.01766i	−0.146411	−	0.253592i	0.783487	−	0.621408i	$-0.213439\pi$
$251$	−2.31959	−	4.01766i	−0.146411	−	0.253592i	−0.929899	+	0.367816i	$0.880106\pi$
$252$	5.06668	−	6.10973i	0.319171	−	0.384877i
$253$	−1.59805	+	5.96399i	−0.100468	+	0.374953i
$254$	−10.9036	−	10.9036i	−0.684155	−	0.684155i
$255$	−7.52931	−	3.23349i	−0.471504	−	0.202489i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	5.67626	+	9.83157i	0.354075	+	0.613276i	0.986959	−	0.160970i	$-0.0514623\pi$
$257$	5.67626	+	9.83157i	0.354075	+	0.613276i	−0.632884	+	0.774247i	$0.718129\pi$
$258$	6.31517	−	0.748426i	0.393166	−	0.0465950i
$259$	−1.47576	+	10.2592i	−0.0916994	+	0.637474i
$260$	−2.38556	+	1.52649i	−0.147946	+	0.0946691i
$261$	18.5571	+	19.5432i	1.14866	+	1.20969i
$262$	5.02025	+	5.02025i	0.310152	+	0.310152i
$263$		−	17.9208i		−	1.10504i	−0.833499	−	0.552521i	$-0.813666\pi$
$263$		−	17.9208i		−	1.10504i	0.833499	−	0.552521i	$-0.186334\pi$
$264$	0.213295	−	1.47265i	0.0131274	−	0.0906352i
$265$	5.94423	+	5.94423i	0.365151	+	0.365151i
$266$	−2.99964	+	2.24518i	−0.183919	+	0.137661i
$267$	−2.11523	+	4.92539i	−0.129450	+	0.301429i
$268$	−2.66061	−	9.92952i	−0.162522	−	0.606542i
$269$	−3.55080	−	2.05006i	−0.216496	−	0.124994i	0.387831	−	0.921731i	$-0.373225\pi$
$269$	−3.55080	−	2.05006i	−0.216496	−	0.124994i	−0.604327	+	0.796737i	$0.706558\pi$
$270$	1.70709	−	3.70743i	0.103890	−	0.225627i
$271$	−15.7584	−	4.22244i	−0.957252	−	0.256495i	−0.253815	−	0.967253i	$-0.581685\pi$
$271$	−15.7584	−	4.22244i	−0.957252	−	0.256495i	−0.703437	+	0.710758i	$0.748352\pi$
$272$	6.02288			0.365191
$273$	−11.4386	+	11.9230i	−0.692298	+	0.721612i
$274$	−18.6498			−1.12668
$275$	3.63715	+	0.974571i	0.219328	+	0.0587688i
$276$	1.78435	−	12.3197i	0.107405	−	0.741557i
$277$	2.79473	+	1.61354i	0.167919	+	0.0969480i	0.581604	−	0.813472i	$-0.302425\pi$
$277$	2.79473	+	1.61354i	0.167919	+	0.0969480i	−0.413685	+	0.910420i	$0.635759\pi$
$278$	5.13396	+	19.1602i	0.307915	+	1.14915i
$279$	6.36409	−	10.3924i	0.381008	−	0.622174i
$280$	1.91038	+	0.818227i	0.114167	+	0.0488984i
$281$	−13.0111	−	13.0111i	−0.776179	−	0.776179i	0.203000	−	0.979179i	$-0.434931\pi$
$281$	−13.0111	−	13.0111i	−0.776179	−	0.776179i	−0.979179	+	0.203000i	$0.934931\pi$
$282$	−8.51825	−	1.23376i	−0.507254	−	0.0734694i
$283$			9.45845i			0.562247i	0.959672	+	0.281123i	$0.0907070\pi$
$283$			9.45845i			0.562247i	−0.959672	+	0.281123i	$0.909293\pi$
$284$	0.924685	+	0.924685i	0.0548700	+	0.0548700i
$285$	−1.19259	+	1.51327i	−0.0706430	+	0.0896384i
$286$	−0.664377	+	3.02546i	−0.0392855	+	0.178899i
$287$	7.88238	−	3.15500i	0.465282	−	0.186234i
$288$	−0.0776165	+	2.99900i	−0.00457360	+	0.176718i
$289$	−9.63755	−	16.6927i	−0.566915	−	0.981925i
$290$	−3.52819	+	6.11101i	−0.207183	+	0.358851i
$291$	4.34876	−	10.1263i	0.254929	−	0.593612i
$292$	−1.09482	−	1.09482i	−0.0640695	−	0.0640695i
$293$	4.46839	−	16.6763i	0.261046	−	0.974238i	−0.703580	−	0.710616i	$-0.748416\pi$
$293$	4.46839	−	16.6763i	0.261046	−	0.974238i	0.964626	−	0.263622i	$-0.0849171\pi$
$294$	11.9541	+	2.02462i	0.697178	+	0.118078i
$295$	−5.58573	−	9.67476i	−0.325214	−	0.563286i
$296$	−1.95876	−	3.39267i	−0.113850	−	0.197195i
$297$	−1.54700	−	4.18742i	−0.0897659	−	0.242979i
$298$	−9.85886	+	5.69202i	−0.571109	+	0.329730i
$299$	−5.55795	+	25.3100i	−0.321425	+	1.46371i
$300$	−7.51317	−	1.08819i	−0.433773	−	0.0628266i
$301$	5.82091	+	7.77693i	0.335512	+	0.448255i
$302$	−4.83981	−	2.79426i	−0.278499	−	0.160792i
$303$	29.7816	+	4.31350i	1.71091	+	0.247804i
$304$	0.366530	−	1.36791i	0.0210220	−	0.0784550i
$305$	−2.04627	−	7.63679i	−0.117169	−	0.437281i
$306$	15.8764	−	8.62645i	0.907594	−	0.493141i
$307$	−3.21016	+	3.21016i	−0.183214	+	0.183214i	−0.792755	−	0.609541i	$-0.791354\pi$
$307$	−3.21016	+	3.21016i	−0.183214	+	0.183214i	0.609541	+	0.792755i	$0.291354\pi$
$308$	2.11022	−	0.844637i	0.120241	−	0.0481277i
$309$	5.09079	+	4.01200i	0.289605	+	0.228235i
$310$	3.08201	+	0.825823i	0.175047	+	0.0469036i
$311$	10.6649	+	18.4721i	0.604751	+	1.04746i	0.992091	+	0.125522i	$0.0400605\pi$
$311$	10.6649	+	18.4721i	0.604751	+	1.04746i	−0.387340	+	0.921937i	$0.626606\pi$
$312$	0.612287	−	6.21491i	0.0346639	−	0.351850i
$313$	4.51871	−	7.82663i	0.255413	−	0.442387i	−0.709595	−	0.704610i	$-0.751122\pi$
$313$	4.51871	−	7.82663i	0.255413	−	0.442387i	0.965007	+	0.262222i	$0.0844554\pi$
$314$	3.21215	+	11.9879i	0.181272	+	0.676518i
$315$	6.20772	−	0.579341i	0.349765	−	0.0326422i
$316$	4.03088	−	2.32723i	0.226755	−	0.130917i
$317$	−2.62454	−	9.79491i	−0.147409	−	0.550137i	−0.999636	−	0.0269656i	$-0.991416\pi$
$317$	−2.62454	−	9.79491i	−0.147409	−	0.550137i	0.852228	−	0.523171i	$-0.175251\pi$
$318$	−18.4076	+	2.18153i	−1.03225	+	0.122334i
$319$	1.99747	+	7.45466i	0.111837	+	0.417381i
$320$	−0.758733	+	0.203302i	−0.0424144	+	0.0113649i
$321$	−7.63135	+	3.04595i	−0.425940	+	0.170008i
$322$	17.6534	−	7.06594i	0.983784	−	0.393770i
$323$	−8.23876	+	2.20757i	−0.458417	+	0.122832i
$324$	4.09080	+	8.01657i	0.227267	+	0.445365i
$325$	15.4353	+	3.38953i	0.856198	+	0.188017i
$326$	11.4206	−	6.59370i	0.632530	−	0.365191i
$327$	7.82673	−	18.2249i	0.432819	−	1.00784i
$328$	−1.60452	+	2.77912i	−0.0885951	+	0.153451i
$329$	−4.88564	−	12.2062i	−0.269354	−	0.672947i
$330$	0.936425	−	0.699484i	0.0515485	−	0.0385053i
$331$	16.9699	+	16.9699i	0.932751	+	0.932751i	0.997877	−	0.0651256i	$-0.0207448\pi$
$331$	16.9699	+	16.9699i	0.932751	+	0.932751i	−0.0651256	+	0.997877i	$0.520745\pi$
$332$	1.87059	−	0.501222i	0.102662	−	0.0275081i
$333$	−10.0226	−	6.13763i	−0.549233	−	0.336340i
$334$	20.3707			1.11463
$335$	4.03738	−	6.99295i	0.220586	−	0.382066i
$336$	−4.02446	+	2.19175i	−0.219552	+	0.119570i
$337$		−	13.0484i		−	0.710794i	−0.934715	−	0.355397i	$-0.884346\pi$
$337$		−	13.0484i		−	0.710794i	0.934715	−	0.355397i	$-0.115654\pi$
$338$	−2.20615	+	12.8114i	−0.119999	+	0.696850i
$339$	13.3993	−	5.34813i	0.727747	−	0.290470i
$340$	3.34529	+	3.34529i	0.181424	+	0.181424i
$341$	3.02220	−	1.74487i	0.163661	−	0.0944899i
$342$	−0.993050	−	4.13080i	−0.0536980	−	0.223368i
$343$	6.46861	+	17.3539i	0.349272	+	0.937021i
$344$	−3.54648	−	0.950276i	−0.191213	−	0.0512354i
$345$	7.83381	−	5.85164i	0.421758	−	0.315042i
$346$	10.8078	+	2.89595i	0.581032	+	0.155687i
$347$	10.0427	+	5.79814i	0.539119	+	0.311260i	0.744722	−	0.667375i	$-0.232582\pi$
$347$	10.0427	+	5.79814i	0.539119	+	0.311260i	−0.205603	+	0.978636i	$0.565916\pi$
$348$	−5.76792	−	14.4510i	−0.309193	−	0.774655i
$349$	−7.54906	−	28.1735i	−0.404092	−	1.50809i	−0.805725	−	0.592290i	$-0.798224\pi$
$349$	−7.54906	−	28.1735i	−0.404092	−	1.50809i	0.401633	−	0.915801i	$-0.368443\pi$
$350$	−4.30918	−	10.7659i	−0.230335	−	0.575464i
$351$	−7.28749	−	17.2596i	−0.388978	−	0.921247i
$352$	−0.429553	+	0.744007i	−0.0228952	+	0.0396557i
$353$	−21.2732	+	21.2732i	−1.13226	+	1.13226i	−0.142459	+	0.989801i	$0.545501\pi$
$353$	−21.2732	+	21.2732i	−1.13226	+	1.13226i	−0.989801	+	0.142459i	$0.954499\pi$
$354$	24.3791	+	3.53100i	1.29573	+	0.187671i
$355$			1.02720i			0.0545180i
$356$	2.18837	−	2.18837i	0.115983	−	0.115983i
$357$	23.5515	+	14.3911i	1.24648	+	0.761659i
$358$	−2.47155	−	0.662249i	−0.130625	−	0.0350009i
$359$	−24.3528	+	6.52531i	−1.28529	+	0.344393i	−0.835870	−	0.548927i	$-0.815036\pi$
$359$	−24.3528	+	6.52531i	−1.28529	+	0.344393i	−0.449421	+	0.893320i	$0.648370\pi$
$360$	−1.70885	+	1.62262i	−0.0900641	+	0.0855198i
$361$		−	16.9945i		−	0.894446i
$362$	3.78070	−	14.1098i	0.198709	−	0.741594i
$363$	−2.54778	+	17.5906i	−0.133724	+	0.923270i
$364$	8.68538	−	3.94516i	0.455237	−	0.206782i
$365$		−	1.21619i		−	0.0636585i
$366$	16.0187	+	6.87929i	0.837312	+	0.359586i
$367$	−22.0280			−1.14985			−0.574926	−	0.818205i	$-0.694969\pi$
$367$	−22.0280			−1.14985			−0.574926	+	0.818205i	$0.694969\pi$
$368$	−3.59349	+	6.22411i	−0.187324	+	0.324454i
$369$	−0.249075	+	9.62393i	−0.0129663	+	0.501002i
$370$	0.796438	−	2.97235i	0.0414048	−	0.154525i
$371$	−16.9669	−	22.6684i	−0.880878	−	1.17688i
$372$	−5.63673	+	4.21048i	−0.292251	+	0.218303i
$373$	−3.42592			−0.177388			−0.0886938	−	0.996059i	$-0.528269\pi$
$373$	−3.42592			−0.177388			−0.0886938	+	0.996059i	$0.528269\pi$
$374$	5.17429			0.267556
$375$	−7.63963	−	10.2275i	−0.394509	−	0.528144i
$376$	4.30356	+	2.48466i	0.221939	+	0.128137i
$377$	9.80163	+	30.8712i	0.504810	+	1.58995i
$378$	−7.46933	+	11.5416i	−0.384181	+	0.593637i
$379$	−32.6977	+	8.76132i	−1.67957	+	0.450039i	−0.967665	−	0.252239i	$-0.918833\pi$
$379$	−32.6977	+	8.76132i	−1.67957	+	0.450039i	−0.711903	+	0.702278i	$0.752166\pi$
$380$	0.963362	−	0.556197i	0.0494194	−	0.0285323i
$381$	20.9770	+	16.5318i	1.07469	+	0.846948i
$382$	0.142908	−	0.533340i	0.00731182	−	0.0272881i
$383$	−10.7733	+	10.7733i	−0.550490	+	0.550490i	−0.926582	−	0.376092i	$-0.877268\pi$
$383$	−10.7733	+	10.7733i	−0.550490	+	0.550490i	0.376092	+	0.926582i	$0.377268\pi$
$384$	0.683474	−	1.59150i	0.0348784	−	0.0812158i
$385$	1.64122	+	0.702943i	0.0836442	+	0.0358253i
$386$	22.7253	−	13.1205i	1.15669	−	0.667815i
$387$	−10.7096	+	2.57461i	−0.544401	+	0.130875i
$388$	−4.49913	+	4.49913i	−0.228409	+	0.228409i
$389$	13.2965	+	23.0303i	0.674161	+	1.16768i	0.976713	+	0.214548i	$0.0688280\pi$
$389$	13.2965	+	23.0303i	0.674161	+	1.16768i	−0.302552	+	0.953133i	$0.597839\pi$
$390$	3.79204	−	3.11187i	0.192017	−	0.157576i
$391$	43.2864			2.18908
$392$	−5.97667	−	3.64409i	−0.301867	−	0.184054i
$393$	−9.65824	−	7.61156i	−0.487194	−	0.383952i
$394$		−	4.20153i		−	0.211670i
$395$	3.53149	+	0.946259i	0.177688	+	0.0476115i
$396$	−0.0666808	+	2.57645i	−0.00335083	+	0.129472i
$397$	−0.471077	+	0.471077i	−0.0236427	+	0.0236427i	−0.718829	−	0.695187i	$-0.755322\pi$
$397$	−0.471077	+	0.471077i	−0.0236427	+	0.0236427i	0.695187	+	0.718829i	$0.255322\pi$
$398$	−7.91725	−	7.91725i	−0.396856	−	0.396856i
$399$	4.70175	−	4.47319i	0.235382	−	0.223940i
$400$	3.79578	+	2.19150i	0.189789	+	0.109575i
$401$	4.60614	−	17.1904i	0.230020	−	0.858446i	−0.750311	−	0.661085i	$-0.770096\pi$
$401$	4.60614	−	17.1904i	0.230020	−	0.858446i	0.980331	−	0.197361i	$-0.0632371\pi$
$402$	6.60035	+	16.5366i	0.329195	+	0.824769i
$403$	12.3365	−	7.89398i	0.614524	−	0.393227i
$404$	−15.0462	−	8.68692i	−0.748576	−	0.432191i
$405$	−2.18049	+	6.72481i	−0.108349	+	0.334158i
$406$	14.6935	−	18.6816i	0.729224	−	0.927154i
$407$	−1.68278	−	2.91466i	−0.0834123	−	0.144474i
$408$	−10.3594	+	1.22772i	−0.512869	+	0.0607813i
$409$	−12.0013	+	3.21575i	−0.593428	+	0.159009i	−0.543020	−	0.839720i	$-0.682719\pi$
$409$	−12.0013	+	3.21575i	−0.593428	+	0.159009i	−0.0504088	+	0.998729i	$0.516052\pi$
$410$	−2.43481	+	0.652406i	−0.120247	+	0.0322200i
$411$	32.0779	−	3.80163i	1.58229	−	0.187521i
$412$	−1.87110	−	3.24085i	−0.0921827	−	0.159665i
$413$	13.9826	+	34.9338i	0.688039	+	1.71898i
$414$	−0.557829	+	21.5537i	−0.0274158	+	1.05931i
$415$	1.31738	+	0.760588i	0.0646675	+	0.0373358i
$416$	−1.65845	+	3.20149i	−0.0813123	+	0.156966i
$417$	−12.7362	−	31.9093i	−0.623693	−	1.56261i
$418$	0.314888	−	1.17518i	0.0154017	−	0.0574799i
$419$	0.381763	+	0.220411i	0.0186503	+	0.0107678i	0.509296	−	0.860591i	$-0.329906\pi$
$419$	0.381763	+	0.220411i	0.0186503	+	0.0107678i	−0.490646	+	0.871359i	$0.663239\pi$
$420$	−3.45267	−	1.01794i	−0.168473	−	0.0496706i
$421$	−1.57133	−	1.57133i	−0.0765819	−	0.0765819i	0.667778	−	0.744360i	$-0.267245\pi$
$421$	−1.57133	−	1.57133i	−0.0765819	−	0.0765819i	−0.744360	+	0.667778i	$0.767245\pi$
$422$	−8.57983	+	8.57983i	−0.417660	+	0.417660i
$423$	14.9030	+	0.385702i	0.724608	+	0.0187535i
$424$	10.3374	+	2.76988i	0.502026	+	0.134517i
$425$		−	26.3982i		−	1.28050i
$426$	−1.77896	−	1.40198i	−0.0861910	−	0.0679262i
$427$	3.15968	+	26.4419i	0.152908	+	1.27961i
$428$	4.74395			0.229308
$429$	0.526019	−	5.33926i	0.0253965	−	0.257782i
$430$	−1.44201	−	2.49764i	−0.0695399	−	0.120447i
$431$	−4.37023	+	4.37023i	−0.210507	+	0.210507i	−0.804483	−	0.593976i	$-0.797557\pi$
$431$	−4.37023	+	4.37023i	−0.210507	+	0.210507i	0.593976	+	0.804483i	$0.297557\pi$
$432$	−0.477823	−	5.17414i	−0.0229893	−	0.248941i
$433$	5.21036	−	3.00820i	0.250394	−	0.144565i	−0.369551	−	0.929211i	$-0.620488\pi$
$433$	5.21036	−	3.00820i	0.250394	−	0.144565i	0.619945	+	0.784646i	$0.287155\pi$
$434$	−9.87918	−	4.23131i	−0.474216	−	0.203109i
$435$	4.82286	−	11.2302i	0.231238	−	0.538448i
$436$	−8.09736	+	8.09736i	−0.387793	+	0.387793i
$437$	2.63425	−	9.83114i	0.126013	−	0.470287i
$438$	2.10628	+	1.65993i	0.100642	+	0.0793147i
$439$	13.1314	−	7.58141i	0.626727	−	0.361841i	−0.152756	−	0.988264i	$-0.548815\pi$
$439$	13.1314	−	7.58141i	0.626727	−	0.361841i	0.779484	+	0.626423i	$0.215482\pi$
$440$	−0.651831	+	0.174658i	−0.0310748	+	0.00832648i
$441$	−20.9740	−	1.04561i	−0.998760	−	0.0497911i
$442$	21.6932	−	0.990658i	1.03184	−	0.0471208i
$443$	−26.3260	−	15.1993i	−1.25079	−	0.722141i	−0.279520	−	0.960140i	$-0.590175\pi$
$443$	−26.3260	−	15.1993i	−1.25079	−	0.722141i	−0.971265	+	0.237999i	$0.923509\pi$
$444$	4.06066	+	5.43616i	0.192710	+	0.257989i
$445$	2.43097			0.115239
$446$	19.0951			0.904179
$447$	15.7971	−	11.8000i	0.747177	−	0.558121i
$448$	2.62706	−	0.313922i	0.124117	−	0.0148314i
$449$	3.15104	−	11.7598i	0.148707	−	0.554981i	−0.850856	−	0.525400i	$-0.823916\pi$
$449$	3.15104	−	11.7598i	0.148707	−	0.554981i	0.999562	−	0.0295816i	$-0.00941748\pi$
$450$	13.1446	+	0.340193i	0.619641	+	0.0160368i
$451$	−1.37846	+	2.38756i	−0.0649090	+	0.112426i
$452$	−8.32951			−0.391787
$453$	8.89412	+	3.81961i	0.417882	+	0.179461i
$454$			9.99071i			0.468887i
$455$	7.01539	+	2.63286i	0.328886	+	0.123431i
$456$	−0.351598	+	2.42754i	−0.0164651	+	0.113680i
$457$	1.00277	−	3.74239i	0.0469076	−	0.175062i	−0.938498	−	0.345285i	$-0.887782\pi$
$457$	1.00277	−	3.74239i	0.0469076	−	0.175062i	0.985405	+	0.170223i	$0.0544489\pi$
$458$			7.95188i			0.371567i
$459$	−25.5492	+	18.0739i	−1.19253	+	0.843618i
$460$	−5.45300	+	1.46113i	−0.254247	+	0.0681254i
$461$	−24.1876	−	6.48104i	−1.12653	−	0.301852i	−0.353006	−	0.935621i	$-0.614840\pi$
$461$	−24.1876	−	6.48104i	−1.12653	−	0.301852i	−0.773522	+	0.633769i	$0.781507\pi$
$462$	−3.45743	+	1.88294i	−0.160854	+	0.0876023i
$463$	0.0726544	−	0.0726544i	0.00337653	−	0.00337653i	−0.705416	−	0.708793i	$-0.749240\pi$
$463$	0.0726544	−	0.0726544i	0.00337653	−	0.00337653i	0.708793	+	0.705416i	$0.249240\pi$
$464$			8.98333i			0.417041i
$465$	−5.46945	−	0.792181i	−0.253640	−	0.0367365i
$466$	−18.1043	+	18.1043i	−0.838664	+	0.838664i
$467$	6.92117	−	11.9878i	0.320273	−	0.554730i	−0.660271	−	0.751027i	$-0.729559\pi$
$467$	6.92117	−	11.9878i	0.320273	−	0.554730i	0.980544	+	0.196298i	$0.0628919\pi$
$468$	0.213723	+	10.8145i	0.00987935	+	0.499902i
$469$	−16.8140	+	21.3778i	−0.776399	+	0.987133i
$470$	1.01027	+	3.77039i	0.0466004	+	0.173915i
$471$	−7.96860	−	19.9646i	−0.367174	−	0.919921i
$472$	−12.3167	−	7.11106i	−0.566923	−	0.327313i
$473$	−3.04680	−	0.816387i	−0.140092	−	0.0375375i
$474$	−6.45878	+	4.82453i	−0.296661	+	0.221598i
$475$	−5.99554	−	1.60650i	−0.275094	−	0.0737113i
$476$	−9.54865	−	12.7573i	−0.437661	−	0.584731i
$477$	31.2167	−	7.50452i	1.42931	−	0.343609i
$478$	−21.6862	+	12.5206i	−0.991905	+	0.572677i
$479$	−24.5353	−	24.5353i	−1.12105	−	1.12105i	−0.991584	−	0.129461i	$-0.958675\pi$
$479$	−24.5353	−	24.5353i	−1.12105	−	1.12105i	−0.129461	−	0.991584i	$-0.541325\pi$
$480$	1.26359	−	0.504344i	0.0576747	−	0.0230201i
$481$	−7.61308	−	11.8975i	−0.347127	−	0.542480i
$482$			0.769157i			0.0350341i
$483$	−28.9237	+	15.7520i	−1.31607	+	0.716743i
$484$	5.13097	−	8.88710i	0.233226	−	0.403959i
$485$	−4.99791			−0.226943
$486$	−8.67036	−	12.9547i	−0.393296	−	0.587638i
$487$	−1.09169	+	0.292518i	−0.0494693	+	0.0132553i	−0.283469	−	0.958981i	$-0.591485\pi$
$487$	−1.09169	+	0.292518i	−0.0494693	+	0.0132553i	0.234000	+	0.972237i	$0.424819\pi$
$488$	−7.11716	−	7.11716i	−0.322179	−	0.322179i
$489$	−18.2995	+	13.6693i	−0.827534	+	0.618146i
$490$	−1.29559	−	5.34367i	−0.0585286	−	0.241402i
$491$	−6.38970	+	11.0673i	−0.288363	+	0.499459i	−0.973419	−	0.229031i	$-0.926444\pi$
$491$	−6.38970	+	11.0673i	−0.288363	+	0.499459i	0.685056	+	0.728490i	$0.259778\pi$
$492$	2.19330	−	5.10719i	0.0988817	−	0.230250i
$493$	46.8568	−	27.0528i	2.11032	−	1.21840i
$494$	1.09517	−	4.98722i	0.0492741	−	0.224386i
$495$	−1.46808	+	1.39401i	−0.0659852	+	0.0626559i
$496$	3.92364	−	1.05134i	0.176177	−	0.0472064i
$497$	0.492623	−	3.42460i	0.0220971	−	0.153614i
$498$	−3.11527	+	1.24342i	−0.139598	+	0.0557188i
$499$	11.0593	−	2.96334i	0.495084	−	0.132657i	−0.00263375	−	0.999997i	$-0.500838\pi$
$499$	11.0593	−	2.96334i	0.495084	−	0.132657i	0.497717	+	0.867339i	$0.334172\pi$
$500$	1.90758	+	7.11918i	0.0853096	+	0.318380i
$501$	−35.0379	+	4.15242i	−1.56538	+	0.185516i
$502$	−1.20071	−	4.48111i	−0.0535903	−	0.200002i
$503$	−16.3495	+	9.43940i	−0.728989	+	0.420882i	−0.818052	−	0.575144i	$-0.804946\pi$
$503$	−16.3495	+	9.43940i	−0.728989	+	0.420882i	0.0890630	+	0.996026i	$0.471613\pi$
$504$	6.47535	−	4.59019i	0.288435	−	0.204463i
$505$	−3.53213	−	13.1821i	−0.157178	−	0.586596i
$506$	−3.08719	+	5.34717i	−0.137242	+	0.237711i
$507$	1.18309	−	22.4856i	0.0525430	−	0.998619i
$508$	−7.71003	−	13.3542i	−0.342077	−	0.592495i
$509$	−23.6572	−	6.33892i	−1.04859	−	0.280968i	−0.306918	−	0.951736i	$-0.599298\pi$
$509$	−23.6572	−	6.33892i	−1.04859	−	0.280968i	−0.741667	+	0.670768i	$0.765965\pi$
$510$	−6.43587	−	5.07204i	−0.284985	−	0.224594i
$511$	−0.583261	+	4.05470i	−0.0258020	+	0.179370i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.55010	+	6.90261i	0.112589	+	0.304758i
$514$	2.93825	+	10.9657i	0.129601	+	0.483676i
$515$	0.760797	−	2.83933i	0.0335247	−	0.125116i
$516$	6.29370	+	0.911563i	0.277065	+	0.0401293i
$517$	3.69722	+	2.13459i	0.162603	+	0.0938791i
$518$	−4.08075	+	9.52764i	−0.179298	+	0.418621i
$519$	−19.1799	−	2.77797i	−0.841905	−	0.121939i
$520$	−2.69936	+	0.857050i	−0.118375	+	0.0375841i
$521$	12.9183	−	7.45837i	0.565960	−	0.326757i	−0.189574	−	0.981866i	$-0.560711\pi$
$521$	12.9183	−	7.45837i	0.565960	−	0.326757i	0.755534	+	0.655109i	$0.227377\pi$
$522$	12.8666	+	23.6802i	0.563158	+	1.03645i
$523$	19.8706	+	34.4168i	0.868879	+	1.50494i	0.863143	+	0.504959i	$0.168492\pi$
$523$	19.8706	+	34.4168i	0.868879	+	1.50494i	0.00573599	+	0.999984i	$0.498174\pi$
$524$	3.54985	+	6.14853i	0.155076	+	0.268600i
$525$	9.60640	+	17.6392i	0.419258	+	0.769836i
$526$	4.63824	−	17.3101i	0.202237	−	0.754758i
$527$	−17.2996	−	17.2996i	−0.753581	−	0.753581i
$528$	0.587176	−	1.36726i	0.0255536	−	0.0595025i
$529$	−14.3264	+	24.8140i	−0.622886	+	1.07887i
$530$	4.20320	+	7.28016i	0.182576	+	0.316230i
$531$	−42.6521	−	1.10387i	−1.85094	−	0.0479040i
$532$	−3.47852	+	1.39231i	−0.150813	+	0.0603645i
$533$	−5.32206	+	10.2737i	−0.230524	+	0.445005i
$534$	−3.31794	+	4.21010i	−0.143581	+	0.182189i
$535$	2.63494	+	2.63494i	0.113918	+	0.113918i
$536$		−	10.2798i		−	0.444020i
$537$	4.38609	+	0.635270i	0.189274	+	0.0274139i
$538$	−2.89922	−	2.89922i	−0.124994	−	0.124994i
$539$	−5.13459	−	3.13066i	−0.221162	−	0.134847i
$540$	2.60848	−	3.13927i	0.112251	−	0.135093i
$541$	−0.356759	−	1.33144i	−0.0153383	−	0.0572432i	0.957833	−	0.287327i	$-0.0927666\pi$
$541$	−0.356759	−	1.33144i	−0.0153383	−	0.0572432i	−0.973171	+	0.230084i	$0.926100\pi$
$542$	−14.1286	−	8.15712i	−0.606873	−	0.350378i
$543$	−3.62669	+	25.0397i	−0.155636	+	1.07456i
$544$	5.81766	+	1.55884i	0.249430	+	0.0668346i
$545$	−8.99504			−0.385305
$546$	−14.1348	+	8.55618i	−0.604913	+	0.366171i
$547$	9.32307			0.398626			0.199313	−	0.979936i	$-0.436129\pi$
$547$	9.32307			0.398626			0.199313	+	0.979936i	$0.436129\pi$
$548$	−18.0143	−	4.82693i	−0.769534	−	0.206196i
$549$	−28.9547	−	8.56717i	−1.23576	−	0.365638i
$550$	3.26098	+	1.88273i	0.139049	+	0.0802797i
$551$	−3.29266	−	12.2884i	−0.140272	−	0.523503i
$552$	4.91212	−	11.4381i	0.209074	−	0.486836i
$553$	−11.3199	−	4.84839i	−0.481372	−	0.206175i
$554$	2.28189	+	2.28189i	0.0969480	+	0.0969480i
$555$	−0.763992	+	5.27483i	−0.0324297	+	0.223904i
$556$			19.8361i			0.841239i
$557$	−23.2277	−	23.2277i	−0.984189	−	0.984189i	0.0156877	−	0.999877i	$-0.495006\pi$
$557$	−23.2277	−	23.2277i	−0.984189	−	0.984189i	−0.999877	+	0.0156877i	$0.995006\pi$
$558$	8.83698	−	8.39110i	0.374099	−	0.355224i
$559$	−12.9300	−	2.83937i	−0.546881	−	0.120092i
$560$	1.63351	+	1.28479i	0.0690285	+	0.0542923i
$561$	−8.89985	+	1.05474i	−0.375752	+	0.0445313i
$562$	−9.20026	−	15.9353i	−0.388090	−	0.672191i
$563$	−1.00071	+	1.73327i	−0.0421748	+	0.0730488i	−0.886342	−	0.463031i	$-0.846762\pi$
$563$	−1.00071	+	1.73327i	−0.0421748	+	0.0730488i	0.844167	+	0.536080i	$0.180095\pi$
$564$	−7.90867	−	3.39641i	−0.333015	−	0.143014i
$565$	−4.62647	−	4.62647i	−0.194637	−	0.194637i
$566$	−2.44803	+	9.13616i	−0.102898	+	0.384022i
$567$	10.4947	−	21.3743i	0.440735	−	0.897637i
$568$	0.653851	+	1.13250i	0.0274350	+	0.0475188i
$569$	−8.19471	−	14.1936i	−0.343540	−	0.595029i	0.641547	−	0.767083i	$-0.278293\pi$
$569$	−8.19471	−	14.1936i	−0.343540	−	0.595029i	−0.985087	+	0.172055i	$0.944959\pi$
$570$	−1.54362	+	1.15304i	−0.0646551	+	0.0482956i
$571$	17.2345	−	9.95036i	0.721243	−	0.416410i	−0.0939672	−	0.995575i	$-0.529955\pi$
$571$	17.2345	−	9.95036i	0.721243	−	0.416410i	0.815210	+	0.579166i	$0.196622\pi$
$572$	−1.42479	+	2.75042i	−0.0595733	+	0.115001i
$573$	−0.137086	+	0.946484i	−0.00572686	+	0.0395399i
$574$	8.43037	−	1.00739i	0.351877	−	0.0420476i
$575$	27.2802	+	15.7503i	1.13766	+	0.656831i
$576$	−0.851169	+	2.87672i	−0.0354654	+	0.119863i
$577$	−3.51801	+	13.1294i	−0.146457	+	0.546583i	0.853230	+	0.521535i	$0.174641\pi$
$577$	−3.51801	+	13.1294i	−0.146457	+	0.546583i	−0.999686	+	0.0250480i	$0.992026\pi$
$578$	−4.98876	−	18.6183i	−0.207505	−	0.774420i
$579$	−36.4134	+	27.1998i	−1.51329	+	1.13039i
$580$	−4.98962	+	4.98962i	−0.207183	+	0.207183i
$581$	−4.02728	−	3.16753i	−0.167080	−	0.131411i
$582$	6.82145	−	8.65568i	0.282758	−	0.358789i
$583$	8.88088	+	2.37962i	0.367808	+	0.0985539i
$584$	−0.774154	−	1.34087i	−0.0320347	−	0.0554858i
$585$	−5.88802	+	6.12544i	−0.243440	+	0.253256i
$586$	8.63227	−	14.9515i	0.356596	−	0.617642i
$587$	11.7270	+	43.7657i	0.484025	+	1.80641i	0.584412	+	0.811457i	$0.301325\pi$
$587$	11.7270	+	43.7657i	0.484025	+	1.80641i	−0.100388	+	0.994948i	$0.532008\pi$
$588$	11.0228	+	5.04959i	0.454572	+	0.208241i
$589$	−4.98184	+	2.87627i	−0.205273	+	0.118515i
$590$	−2.89138	−	10.7908i	−0.119036	−	0.444250i
$591$	0.856452	+	7.22669i	0.0352297	+	0.297266i
$592$	−1.01393	−	3.78403i	−0.0416722	−	0.155523i
$593$	−5.74309	+	1.53886i	−0.235841	+	0.0631933i	−0.374803	−	0.927104i	$-0.622290\pi$
$593$	−5.74309	+	1.53886i	−0.235841	+	0.0631933i	0.138963	+	0.990298i	$0.455623\pi$
$594$	−0.410500	−	4.44513i	−0.0168430	−	0.182386i
$595$	1.78219	−	12.3894i	0.0730628	−	0.507917i
$596$	−10.9961	+	2.94641i	−0.450419	+	0.120689i
$597$	15.2317	+	12.0039i	0.623390	+	0.491287i
$598$	−11.9193	+	23.0091i	−0.487415	+	0.940910i
$599$	29.0652	−	16.7808i	1.18757	−	0.685644i	0.229817	−	0.973234i	$-0.426187\pi$
$599$	29.0652	−	16.7808i	1.18757	−	0.685644i	0.957754	+	0.287590i	$0.0928539\pi$
$600$	−6.97552	−	2.99566i	−0.284774	−	0.122297i
$601$	−21.5761	+	37.3709i	−0.880109	+	1.52439i	−0.0288892	+	0.999583i	$0.509197\pi$
$601$	−21.5761	+	37.3709i	−0.880109	+	1.52439i	−0.851219	+	0.524810i	$0.824136\pi$
$602$	3.60975	+	9.01850i	0.147122	+	0.367567i
$603$	−14.7236	−	27.0977i	−0.599589	−	1.10350i
$604$	−3.95168	−	3.95168i	−0.160792	−	0.160792i
$605$	7.78607	−	2.08627i	0.316549	−	0.0848190i
$606$	27.6504	+	11.8746i	1.12322	+	0.482371i
$607$	−4.88660			−0.198341			−0.0991705	−	0.995070i	$-0.531619\pi$
$607$	−4.88660			−0.198341			−0.0991705	+	0.995070i	$0.531619\pi$
$608$	0.708082	−	1.22643i	0.0287165	−	0.0497385i
$609$	−21.4648	+	35.1278i	−0.869800	+	1.42345i
$610$		−	7.90618i		−	0.320112i
$611$	15.9093	+	8.24140i	0.643619	+	0.333411i
$612$	17.5681	−	4.22340i	0.710149	−	0.170721i
$613$	−28.0869	−	28.0869i	−1.13442	−	1.13442i	−0.989434	−	0.144985i	$-0.953687\pi$
$613$	−28.0869	−	28.0869i	−1.13442	−	1.13442i	−0.144985	−	0.989434i	$-0.546313\pi$
$614$	−3.93163	+	2.26993i	−0.158668	+	0.0916069i
$615$	4.05492	−	1.61847i	0.163510	−	0.0652628i
$616$	2.25692	−	0.269692i	0.0909340	−	0.0108662i
$617$	36.8763	+	9.88098i	1.48458	+	0.397793i	0.907904	−	0.419177i	$-0.137681\pi$
$617$	36.8763	+	9.88098i	1.48458	+	0.397793i	0.576680	+	0.816970i	$0.304348\pi$
$618$	3.87895	+	5.19289i	0.156034	+	0.208889i
$619$	−9.85373	−	2.64030i	−0.396055	−	0.106123i	0.0552942	−	0.998470i	$-0.482390\pi$
$619$	−9.85373	−	2.64030i	−0.396055	−	0.106123i	−0.451349	+	0.892348i	$0.649057\pi$
$620$	2.76326	+	1.59537i	0.110975	+	0.0640715i
$621$	−3.43410	−	37.1864i	−0.137806	−	1.49224i
$622$	5.52055	+	20.6030i	0.221354	+	0.826105i
$623$	−8.10469	−	1.16584i	−0.324708	−	0.0467086i
$624$	2.19996	−	5.84467i	0.0880689	−	0.233974i
$625$	8.06280	−	13.9652i	0.322512	−	0.558607i
$626$	6.39042	−	6.39042i	0.255413	−	0.255413i
$627$	−0.302060	+	2.08551i	−0.0120631	+	0.0832873i
$628$			12.4108i			0.495245i
$629$	−16.6840	+	16.6840i	−0.665234	+	0.665234i
$630$	6.14614	+	1.04708i	0.244868	+	0.0417165i
$631$	−34.8008	−	9.32484i	−1.38540	−	0.371216i	−0.512319	−	0.858795i	$-0.671213\pi$
$631$	−34.8008	−	9.32484i	−1.38540	−	0.371216i	−0.873079	+	0.487579i	$0.837880\pi$
$632$	4.49586	−	1.20466i	0.178836	−	0.0479189i
$633$	13.0085	−	16.5064i	0.517041	−	0.656069i
$634$		−	10.1404i		−	0.402728i
$635$	3.13493	−	11.6997i	0.124406	−	0.464289i
$636$	−18.3450	−	2.65704i	−0.727427	−	0.105359i
$637$	−22.1261	−	12.1422i	−0.876670	−	0.481092i
$638$			7.71763i			0.305544i
$639$	3.34562	+	2.04880i	0.132351	+	0.0810492i
$640$	−0.785498			−0.0310495
$641$	−11.6800	+	20.2303i	−0.461331	+	0.799049i	−0.999028	−	0.0440894i	$-0.985961\pi$
$641$	−11.6800	+	20.2303i	−0.461331	+	0.799049i	0.537696	+	0.843139i	$0.319295\pi$
$642$	−8.15967	+	0.967021i	−0.322036	+	0.0381653i
$643$	8.02234	−	29.9398i	0.316370	−	1.18071i	−0.606337	−	0.795208i	$-0.707362\pi$
$643$	8.02234	−	29.9398i	0.316370	−	1.18071i	0.922707	−	0.385502i	$-0.125972\pi$
$644$	18.8807	−	2.25615i	0.744002	−	0.0889047i
$645$	2.98940	+	4.00202i	0.117708	+	0.157580i
$646$	−8.52939			−0.335584
$647$	5.86753			0.230676			0.115338	−	0.993326i	$-0.463205\pi$
$647$	5.86753			0.230676			0.115338	+	0.993326i	$0.463205\pi$
$648$	1.87657	+	8.80219i	0.0737187	+	0.345783i
$649$	−10.5814	−	6.10915i	−0.415355	−	0.239805i
$650$	14.0321	+	7.26899i	0.550384	+	0.285113i
$651$	17.8548	+	5.26411i	0.699786	+	0.206317i
$652$	12.7380	−	3.41315i	0.498860	−	0.133669i
$653$	−13.9274	+	8.04098i	−0.545021	+	0.314668i	−0.747111	−	0.664699i	$-0.768560\pi$
$653$	−13.9274	+	8.04098i	−0.545021	+	0.314668i	0.202091	+	0.979367i	$0.435226\pi$
$654$	12.2770	−	15.5782i	0.480068	−	0.609154i
$655$	−1.44338	+	5.38678i	−0.0563976	+	0.210479i
$656$	−2.26914	+	2.26914i	−0.0885951	+	0.0885951i
$657$	−3.96119	−	2.42576i	−0.154541	−	0.0946379i
$658$	−1.55998	−	13.0547i	−0.0608143	−	0.508926i
$659$	23.0854	−	13.3284i	0.899279	−	0.519199i	0.0223131	−	0.999751i	$-0.492897\pi$
$659$	23.0854	−	13.3284i	0.899279	−	0.519199i	0.876966	+	0.480552i	$0.159564\pi$
$660$	1.08556	−	0.433285i	0.0422552	−	0.0168656i
$661$	−5.28278	+	5.28278i	−0.205476	+	0.205476i	−0.802342	−	0.596865i	$-0.796413\pi$
$661$	−5.28278	+	5.28278i	−0.205476	+	0.205476i	0.596865	+	0.802342i	$0.296413\pi$
$662$	11.9995	+	20.7838i	0.466376	+	0.807786i
$663$	−37.1107	+	6.12595i	−1.44126	+	0.237912i
$664$	1.93657			0.0751537
$665$	−2.70541	−	1.15874i	−0.104911	−	0.0449342i
$666$	−8.09252	−	8.52253i	−0.313579	−	0.330241i
$667$			64.5630i			2.49989i
$668$	19.6766	+	5.27232i	0.761309	+	0.203992i
$669$	−32.8438	+	3.89240i	−1.26982	+	0.150489i
$670$	5.70972	−	5.70972i	0.220586	−	0.220586i
$671$	−6.11439	−	6.11439i	−0.236043	−	0.236043i
$672$	−4.45459	+	1.07546i	−0.171840	+	0.0414867i
$673$	8.26967	+	4.77450i	0.318772	+	0.184043i	0.650845	−	0.759210i	$-0.274415\pi$
$673$	8.26967	+	4.77450i	0.318772	+	0.184043i	−0.332073	+	0.943254i	$0.607748\pi$
$674$	3.37719	−	12.6038i	0.130084	−	0.485481i
$675$	−22.6782	+	2.09429i	−0.872884	+	0.0806094i
$676$	−5.44682	+	11.8039i	−0.209493	+	0.453996i
$677$	−12.9359	−	7.46857i	−0.497168	−	0.287040i	0.230375	−	0.973102i	$-0.426005\pi$
$677$	−12.9359	−	7.46857i	−0.497168	−	0.287040i	−0.727543	+	0.686062i	$0.759338\pi$
$678$	14.3269	−	1.69791i	0.550221	−	0.0652079i
$679$	16.6627	+	2.39689i	0.639455	+	0.0919844i
$680$	2.36548	+	4.09713i	0.0907120	+	0.157118i
$681$	−2.03654	−	17.1842i	−0.0780402	−	0.658498i
$682$	3.37083	−	0.903210i	0.129076	−	0.0345857i
$683$	12.9722	−	3.47590i	0.496368	−	0.133001i	−0.00194581	−	0.999998i	$-0.500619\pi$
$683$	12.9722	−	3.47590i	0.496368	−	0.133001i	0.498314	+	0.866997i	$0.333953\pi$
$684$	0.109918	−	4.24707i	0.00420281	−	0.162391i
$685$	−7.32469	−	12.6867i	−0.279862	−	0.484735i
$686$	1.75668	+	18.4368i	0.0670704	+	0.703919i
$687$	−1.62093	−	13.6773i	−0.0618425	−	0.521823i
$688$	−3.17968	−	1.83579i	−0.121224	−	0.0699889i
$689$	37.6886	+	8.27625i	1.43582	+	0.315300i
$690$	9.08140	−	3.62471i	0.345723	−	0.137991i
$691$	−2.71793	+	10.1435i	−0.103395	+	0.385876i	−0.998158	−	0.0606655i	$-0.980678\pi$
$691$	−2.71793	+	10.1435i	−0.103395	+	0.385876i	0.894763	+	0.446541i	$0.147344\pi$
$692$	9.69003	+	5.59454i	0.368360	+	0.212672i
$693$	5.56301	−	3.94346i	0.211321	−	0.149800i
$694$	8.19981	+	8.19981i	0.311260	+	0.311260i
$695$	−11.0176	+	11.0176i	−0.417921	+	0.417921i
$696$	−1.83119	−	15.4515i	−0.0694110	−	0.585686i
$697$	18.6692	+	5.00238i	0.707144	+	0.189479i
$698$		−	29.1673i		−	1.10400i
$699$	27.4492	−	34.8300i	1.03822	−	1.31739i
$700$	−1.37592	−	11.5144i	−0.0520047	−	0.435203i
$701$	28.4326			1.07388			0.536942	−	0.843619i	$-0.319580\pi$
$701$	28.4326			1.07388			0.536942	+	0.843619i	$0.319580\pi$
$702$	−2.57207	−	18.5576i	−0.0970767	−	0.700411i
$703$	2.77392	+	4.80457i	0.104620	+	0.181208i
$704$	−0.607479	+	0.607479i	−0.0228952	+	0.0228952i
$705$	−2.50625	−	6.27919i	−0.0943909	−	0.236488i
$706$	−26.0543	+	15.0424i	−0.980566	+	0.566130i
$707$	5.45402	+	45.6422i	0.205120	+	1.71655i
$708$	22.6345	+	9.72045i	0.850656	+	0.365317i
$709$	19.2479	−	19.2479i	0.722871	−	0.722871i	−0.246318	−	0.969189i	$-0.579221\pi$
$709$	19.2479	−	19.2479i	0.722871	−	0.722871i	0.969189	+	0.246318i	$0.0792206\pi$
$710$	−0.265858	+	0.992196i	−0.00997748	+	0.0372365i
$711$	10.1257	−	9.61484i	0.379745	−	0.360585i
$712$	2.68019	−	1.54741i	0.100444	−	0.0579916i
$713$	28.1992	−	7.55595i	1.05607	−	0.282972i
$714$	19.0243	+	19.9963i	0.711966	+	0.748344i
$715$	−2.31904	+	0.736297i	−0.0867271	+	0.0275359i
$716$	−2.21593	−	1.27937i	−0.0828131	−	0.0478122i
$717$	34.7484	−	25.9561i	1.29770	−	0.969349i
$718$	−25.2119			−0.940899
$719$	44.0430			1.64253			0.821263	−	0.570550i	$-0.193270\pi$
$719$	44.0430			1.64253			0.821263	+	0.570550i	$0.193270\pi$
$720$	−2.07058	+	1.12505i	−0.0771661	+	0.0419282i
$721$	−3.89813	+	9.10128i	−0.145174	+	0.338949i
$722$	4.39849	−	16.4154i	0.163695	−	0.610918i
$723$	−0.156787	−	1.32296i	−0.00583098	−	0.0492014i
$724$	7.30376	−	12.6505i	0.271442	−	0.470152i
$725$	39.3739			1.46231
$726$	−7.01377	+	16.3318i	−0.260305	+	0.606132i
$727$		−	12.7727i		−	0.473712i	−0.971545	−	0.236856i	$-0.923883\pi$
$727$		−	12.7727i		−	0.473712i	0.971545	−	0.236856i	$-0.0761169\pi$
$728$	9.41051	−	1.56279i	0.348777	−	0.0579207i
$729$	17.5539	+	20.5149i	0.650143	+	0.759812i
$730$	0.314774	−	1.17475i	0.0116503	−	0.0434795i
$731$			22.1135i			0.817898i
$732$	13.6924	+	10.7908i	0.506086	+	0.398841i
$733$	−3.49207	+	0.935698i	−0.128983	+	0.0345608i	−0.322733	−	0.946490i	$-0.604602\pi$
$733$	−3.49207	+	0.935698i	−0.128983	+	0.0345608i	0.193750	+	0.981051i	$0.437935\pi$
$734$	−21.2774	−	5.70127i	−0.785364	−	0.210438i
$735$	3.31770	+	8.92709i	0.122375	+	0.329281i
$736$	−5.08197	+	5.08197i	−0.187324	+	0.187324i
$737$		−	8.83143i		−	0.325310i
$738$	−2.73144	+	9.23153i	−0.100546	+	0.339817i
$739$	−0.282571	+	0.282571i	−0.0103945	+	0.0103945i	−0.712285	−	0.701890i	$-0.752340\pi$
$739$	−0.282571	+	0.282571i	−0.0103945	+	0.0103945i	0.701890	+	0.712285i	$0.252340\pi$
$740$	1.53860	−	2.66493i	0.0565601	−	0.0979649i
$741$	−0.867099	+	8.80133i	−0.0318537	+	0.323325i
$742$	−10.5218	−	26.2873i	−0.386267	−	0.965038i
$743$	−4.39623	−	16.4070i	−0.161282	−	0.601913i	−0.998485	−	0.0550208i	$-0.982477\pi$
$743$	−4.39623	−	16.4070i	−0.161282	−	0.601913i	0.837203	−	0.546892i	$-0.184189\pi$
$744$	−6.53442	+	2.60812i	−0.239563	+	0.0956184i
$745$	−7.74412	−	4.47107i	−0.283722	−	0.163807i
$746$	−3.30919	−	0.886694i	−0.121158	−	0.0324642i
$747$	5.10484	−	2.77372i	0.186776	−	0.101485i
$748$	4.99798	+	1.33920i	0.182744	+	0.0489662i
$749$	−7.52104	−	10.0484i	−0.274813	−	0.367159i
$750$	−4.73226	−	11.8562i	−0.172798	−	0.432929i
$751$	4.10366	−	2.36925i	0.149745	−	0.0864551i	−0.423256	−	0.906010i	$-0.639113\pi$
$751$	4.10366	−	2.36925i	0.149745	−	0.0864551i	0.573000	+	0.819555i	$0.305779\pi$
$752$	3.51385	+	3.51385i	0.128137	+	0.128137i
$753$	2.97868	+	7.46282i	0.108549	+	0.271960i
$754$	1.47760	+	32.3561i	0.0538110	+	1.17834i
$755$		−	4.38978i		−	0.159760i
$756$	−10.2020	+	9.21515i	−0.371044	+	0.335152i
$757$	1.36225	−	2.35948i	0.0495117	−	0.0857567i	−0.840207	−	0.542265i	$-0.817567\pi$
$757$	1.36225	−	2.35948i	0.0495117	−	0.0857567i	0.889719	+	0.456508i	$0.150900\pi$
$758$	−33.8511			−1.22953
$759$	4.22003	−	9.82651i	0.153177	−	0.356680i
$760$	1.07449	−	0.287909i	0.0389759	−	0.0104435i
$761$	33.9082	+	33.9082i	1.22917	+	1.22917i	0.964277	+	0.264896i	$0.0853376\pi$
$761$	33.9082	+	33.9082i	1.22917	+	1.22917i	0.264896	+	0.964277i	$0.414662\pi$
$762$	15.9835	+	21.3977i	0.579022	+	0.775158i
$763$	29.9889	+	4.31384i	1.08567	+	0.156171i
$764$	0.276077	−	0.478180i	0.00998813	−	0.0172999i
$765$	12.1037	+	7.41207i	0.437610	+	0.267984i
$766$	−13.1946	+	7.61788i	−0.476739	+	0.275245i
$767$	−45.5320	−	23.5867i	−1.64406	−	0.851667i
$768$	1.07209	−	1.36037i	0.0386859	−	0.0490882i
$769$	20.9168	−	5.60464i	0.754279	−	0.202109i	0.138864	−	0.990311i	$-0.455655\pi$
$769$	20.9168	−	5.60464i	0.754279	−	0.202109i	0.615415	+	0.788203i	$0.288988\pi$
$770$	1.40336	+	1.10377i	0.0505736	+	0.0397771i
$771$	−7.28910	−	18.2622i	−0.262511	−	0.657697i
$772$	25.3468	−	6.79166i	0.912252	−	0.244437i
$773$	0.587641	+	2.19311i	0.0211360	+	0.0788806i	0.975688	−	0.219163i	$-0.0703326\pi$
$773$	0.587641	+	2.19311i	0.0211360	+	0.0788806i	−0.954552	+	0.298044i	$0.903666\pi$
$774$	−11.0111	−	0.284975i	−0.395784	−	0.0102432i
$775$	−4.60800	−	17.1973i	−0.165524	−	0.617746i
$776$	−5.51028	+	3.18136i	−0.197808	+	0.114204i
$777$	5.07680	−	17.2195i	0.182129	−	0.617746i
$778$	6.88279	+	25.6869i	0.246760	+	0.920921i
$779$	2.27227	−	3.93569i	0.0814126	−	0.141011i
$780$	4.46824	−	2.02438i	0.159989	−	0.0724846i
$781$	0.561727	+	0.972940i	0.0201002	+	0.0348145i
$782$	41.8114	+	11.2033i	1.49517	+	0.400630i
$783$	−26.9578	−	38.1075i	−0.963395	−	1.36185i
$784$	−4.82986	−	5.06680i	−0.172495	−	0.180957i
$785$	−6.89335	+	6.89335i	−0.246034	+	0.246034i
$786$	−7.35913	−	9.85194i	−0.262491	−	0.351407i
$787$	−6.30962	−	23.5478i	−0.224914	−	0.839390i	−0.982439	−	0.186584i	$-0.940258\pi$
$787$	−6.30962	−	23.5478i	−0.224914	−	0.839390i	0.757525	−	0.652806i	$-0.226408\pi$
$788$	1.08744	−	4.05837i	0.0387383	−	0.144573i
$789$	−4.44928	+	30.7191i	−0.158399	+	1.09363i
$790$	3.16625	+	1.82803i	0.112650	+	0.0650385i
$791$	13.2056	+	17.6431i	0.469536	+	0.627316i
$792$	−0.731244	+	2.47141i	−0.0259836	+	0.0878176i
$793$	−26.8052	−	24.4639i	−0.951881	−	0.868739i
$794$	−0.576949	+	0.333102i	−0.0204751	+	0.0118213i
$795$	−8.71358	−	11.6652i	−0.309039	−	0.413722i
$796$	−5.59834	−	9.69661i	−0.198428	−	0.343687i
$797$	17.3641	+	30.0756i	0.615069	+	1.06533i	0.990372	+	0.138429i	$0.0442053\pi$
$797$	17.3641	+	30.0756i	0.615069	+	1.06533i	−0.375303	+	0.926902i	$0.622461\pi$
$798$	5.69929	−	3.10387i	0.201753	−	0.109876i
$799$	7.74637	−	28.9098i	0.274047	−	1.02276i
$800$	3.09924	+	3.09924i	0.109575	+	0.109575i
$801$	4.84870	−	7.91777i	0.171320	−	0.279761i
$802$	8.89839	−	15.4125i	0.314213	−	0.544233i
$803$	−0.665080	−	1.15195i	−0.0234702	−	0.0406515i
$804$	2.09546	+	17.6814i	0.0739013	+	0.623575i
$805$	11.7400	+	9.23376i	0.413782	+	0.325447i
$806$	13.9592	−	4.43208i	0.491694	−	0.156113i
$807$	5.57768	+	4.39571i	0.196344	+	0.154736i
$808$	−12.2852	−	12.2852i	−0.432191	−	0.432191i
$809$		−	21.6710i		−	0.761912i	−0.924593	−	0.380956i	$-0.875595\pi$
$809$		−	21.6710i		−	0.761912i	0.924593	−	0.380956i	$-0.124405\pi$
$810$	−3.84670	+	5.93131i	−0.135159	+	0.208405i
$811$	12.6491	+	12.6491i	0.444171	+	0.444171i	0.893411	−	0.449240i	$-0.148305\pi$
$811$	12.6491	+	12.6491i	0.444171	+	0.444171i	−0.449240	+	0.893411i	$0.648305\pi$
$812$	19.0280	−	14.2421i	0.667751	−	0.499801i
$813$	25.9641	+	11.1504i	0.910600	+	0.391060i
$814$	−0.871071	−	3.25088i	−0.0305310	−	0.113943i
$815$	8.97087	+	5.17934i	0.314236	+	0.181424i
$816$	−10.3242	−	1.49533i	−0.361420	−	0.0523471i
$817$	5.02239	+	1.34575i	0.175711	+	0.0470817i
$818$	−12.4247			−0.434420
$819$	22.5679	−	17.5980i	0.788586	−	0.614924i
$820$	−2.52070			−0.0880267
$821$	9.26451	+	2.48242i	0.323333	+	0.0866369i	0.416835	−	0.908982i	$-0.363139\pi$
$821$	9.26451	+	2.48242i	0.323333	+	0.0866369i	−0.0935015	+	0.995619i	$0.529806\pi$
$822$	31.9688	+	4.63029i	1.11504	+	0.161500i
$823$	34.7540	+	20.0652i	1.21145	+	0.699431i	0.963075	−	0.269233i	$-0.0867703\pi$
$823$	34.7540	+	20.0652i	1.21145	+	0.699431i	0.248374	+	0.968664i	$0.420104\pi$
$824$	−0.968554	−	3.61469i	−0.0337412	−	0.125924i
$825$	−5.99271	−	2.57359i	−0.208639	−	0.0896009i
$826$	4.46463	+	37.3624i	0.155344	+	1.30000i
$827$	−2.06307	−	2.06307i	−0.0717399	−	0.0717399i	0.670326	−	0.742066i	$-0.266154\pi$
$827$	−2.06307	−	2.06307i	−0.0717399	−	0.0717399i	−0.742066	+	0.670326i	$0.766154\pi$
$828$	−6.11734	+	20.6749i	−0.212592	+	0.718504i
$829$		−	28.6200i		−	0.994013i	−0.867747	−	0.497006i	$-0.834433\pi$
$829$		−	28.6200i		−	0.994013i	0.867747	−	0.497006i	$-0.165567\pi$
$830$	1.07563	+	1.07563i	0.0373358	+	0.0373358i
$831$	−4.39002	−	3.45973i	−0.152288	−	0.120017i
$832$	−2.43055	+	2.66316i	−0.0842641	+	0.0923285i
$833$	−11.8834	+	40.4508i	−0.411736	+	1.40154i
$834$	−4.04345	−	34.1184i	−0.140013	−	1.18142i
$835$	8.00057	+	13.8574i	0.276871	+	0.479555i
$836$	0.608317	−	1.05364i	0.0210391	−	0.0364408i
$837$	−13.4893	+	16.2342i	−0.466257	+	0.561135i
$838$	0.311708	+	0.311708i	0.0107678	+	0.0107678i
$839$	−12.1258	+	45.2541i	−0.418629	+	1.56234i	0.358826	+	0.933405i	$0.383177\pi$
$839$	−12.1258	+	45.2541i	−0.418629	+	1.56234i	−0.777454	+	0.628939i	$0.783489\pi$
$840$	−3.07156	−	1.87688i	−0.105979	−	0.0647584i
$841$	25.8501	+	44.7737i	0.891383	+	1.54392i
$842$	−1.11110	−	1.92448i	−0.0382910	−	0.0663219i
$843$	19.0729	+	25.5336i	0.656905	+	0.879423i
$844$	−10.5081	+	6.06686i	−0.361704	+	0.208830i
$845$	−9.58159	+	3.53092i	−0.329617	+	0.121467i
$846$	14.2954	+	4.22974i	0.491485	+	0.145421i
$847$	−26.9587	+	3.22144i	−0.926313	+	0.110690i
$848$	9.26822	+	5.35101i	0.318272	+	0.183754i
$849$	2.34830	−	16.2133i	0.0805934	−	0.556440i
$850$	6.83237	−	25.4987i	0.234348	−	0.874600i
$851$	−7.28708	−	27.1958i	−0.249798	−	0.932258i
$852$	−1.35549	−	1.81464i	−0.0464382	−	0.0621685i
$853$	−7.05067	+	7.05067i	−0.241410	+	0.241410i	−0.817433	−	0.576023i	$-0.804604\pi$
$853$	−7.05067	+	7.05067i	−0.241410	+	0.241410i	0.576023	+	0.817433i	$0.304604\pi$
$854$	−3.79164	+	26.3587i	−0.129747	+	0.901975i
$855$	2.42001	−	2.29790i	0.0827625	−	0.0785866i
$856$	4.58231	+	1.22783i	0.156620	+	0.0419662i
$857$	−7.75866	−	13.4384i	−0.265031	−	0.459046i	0.702541	−	0.711643i	$-0.252049\pi$
$857$	−7.75866	−	13.4384i	−0.265031	−	0.459046i	−0.967572	+	0.252597i	$0.918715\pi$
$858$	1.89000	−	5.02119i	0.0645235	−	0.171421i
$859$	−18.4140	+	31.8939i	−0.628276	+	1.08821i	0.359622	+	0.933098i	$0.382906\pi$
$859$	−18.4140	+	31.8939i	−0.628276	+	1.08821i	−0.987898	+	0.155108i	$0.950428\pi$
$860$	−0.746440	−	2.78575i	−0.0254534	−	0.0949933i
$861$	−14.2950	+	3.45120i	−0.487173	+	0.117616i
$862$	−5.35242	+	3.09022i	−0.182304	+	0.105253i
$863$	−2.93983	−	10.9716i	−0.100073	−	0.373477i	0.897667	−	0.440675i	$-0.145261\pi$
$863$	−2.93983	−	10.9716i	−0.100073	−	0.373477i	−0.997740	+	0.0671976i	$0.978594\pi$
$864$	0.877624	−	5.12150i	0.0298574	−	0.174237i
$865$	2.27476	+	8.48952i	0.0773442	+	0.288652i
$866$	5.81140	−	1.55716i	0.197479	−	0.0529145i
$867$	12.3760	+	31.0068i	0.420309	+	1.05305i
$868$	−8.44741	−	6.64405i	−0.286724	−	0.225514i
$869$	3.86242	−	1.03493i	0.131024	−	0.0351077i
$870$	7.56512	−	9.59931i	0.256481	−	0.325447i
$871$	−1.69085	−	37.0258i	−0.0572921	−	1.25457i
$872$	−9.91720	+	5.72570i	−0.335839	+	0.193897i
$873$	−9.96858	+	16.2784i	−0.337385	+	0.550940i
$874$	5.08898	−	8.81436i	0.172137	−	0.298150i
$875$	12.0552	−	15.3272i	0.407539	−	0.518155i
$876$	1.60488	+	2.14852i	0.0542240	+	0.0725917i
$877$	−23.6228	−	23.6228i	−0.797685	−	0.797685i	0.185045	−	0.982730i	$-0.440757\pi$
$877$	−23.6228	−	23.6228i	−0.797685	−	0.797685i	−0.982730	+	0.185045i	$0.940757\pi$
$878$	14.6462	−	3.92443i	0.494284	−	0.132443i
$879$	−11.7999	+	27.4765i	−0.398000	+	0.926759i
$880$	−0.674826			−0.0227484
$881$	1.52869	−	2.64778i	0.0515030	−	0.0892059i	−0.839125	−	0.543939i	$-0.816932\pi$
$881$	1.52869	−	2.64778i	0.0515030	−	0.0892059i	0.890628	+	0.454733i	$0.150265\pi$
$882$	−19.9887	−	6.43844i	−0.673053	−	0.216794i
$883$			42.9063i			1.44391i	0.691938	+	0.721956i	$0.256757\pi$
$883$			42.9063i			1.44391i	−0.691938	+	0.721956i	$0.743243\pi$
$884$	21.2104	+	4.65771i	0.713384	+	0.156656i
$885$	7.17285	+	17.9709i	0.241113	+	0.604086i
$886$	−21.4951	−	21.4951i	−0.722141	−	0.722141i
$887$	37.9962	−	21.9371i	1.27579	−	0.736576i	0.299717	−	0.954028i	$-0.403108\pi$
$887$	37.9962	−	21.9371i	1.27579	−	0.736576i	0.976071	+	0.217452i	$0.0697745\pi$
$888$	2.51532	+	6.30190i	0.0844085	+	0.211478i
$889$	−16.0626	+	37.5026i	−0.538721	+	1.25780i
$890$	2.34814	+	0.629182i	0.0787098	+	0.0210902i
$891$	1.61217	+	7.56201i	0.0540099	+	0.253337i
$892$	18.4444	+	4.94218i	0.617566	+	0.165476i
$893$	−6.09455	−	3.51869i	−0.203946	−	0.117749i
$894$	18.3129	−	7.30934i	0.612475	−	0.244461i
$895$	−0.520195	−	1.94139i	−0.0173882	−	0.0648936i
$896$	2.61880	+	0.376709i	0.0874878	+	0.0125850i
$897$	15.8111	−	42.0056i	0.527917	−	1.40252i
$898$	6.08734	−	10.5436i	0.203137	−	0.351844i
$899$	25.8029	−	25.8029i	0.860574	−	0.860574i
$900$	12.6086	+	3.73067i	0.420288	+	0.124356i
$901$		−	64.4570i		−	2.14737i
$902$	−1.94943	+	1.94943i	−0.0649090	+	0.0649090i
$903$	−8.04718	−	14.7761i	−0.267793	−	0.491719i
$904$	−8.04569	−	2.15584i	−0.267596	−	0.0717021i
$905$	11.0832	−	2.96974i	0.368418	−	0.0987174i
$906$	7.60248	+	5.99143i	0.252575	+	0.199052i
$907$			28.5206i			0.947012i	0.880790	+	0.473506i	$0.157012\pi$
$907$			28.5206i			0.947012i	−0.880790	+	0.473506i	$0.842988\pi$
$908$	−2.58579	+	9.65028i	−0.0858123	+	0.320256i
$909$	−49.9797	−	14.7881i	−1.65772	−	0.490490i
$910$	6.09491	+	4.35887i	0.202044	+	0.144495i
$911$		−	11.5741i		−	0.383466i	−0.981447	−	0.191733i	$-0.938589\pi$
$911$		−	11.5741i		−	0.383466i	0.981447	−	0.191733i	$-0.0614108\pi$
$912$	−0.967911	+	2.25382i	−0.0320507	+	0.0746315i
$913$	1.66372			0.0550612
$914$	1.93720	−	3.35533i	0.0640770	−	0.110985i
$915$	1.61162	+	13.5987i	0.0532785	+	0.449561i
$916$	−2.05810	+	7.68092i	−0.0680015	+	0.253785i
$917$	7.39553	−	17.2669i	0.244222	−	0.570204i
$918$	−29.3565	+	10.8454i	−0.968909	+	0.357953i
$919$	10.0202			0.330535			0.165268	−	0.986249i	$-0.447151\pi$
$919$	10.0202			0.330535			0.165268	+	0.986249i	$0.447151\pi$
$920$	−5.64536			−0.186122
$921$	6.29975	−	4.70574i	0.207584	−	0.155060i
$922$	−21.6860	−	12.5204i	−0.714190	−	0.412338i
$923$	2.54132	+	3.97150i	0.0836484	+	0.130724i
$924$	−3.82696	+	0.923931i	−0.125898	+	0.0303951i
$925$	−16.5854	+	4.44404i	−0.545324	+	0.146119i
$926$	0.0889830	−	0.0513744i	0.00292416	−	0.00168827i
$927$	−7.73038	−	8.14115i	−0.253899	−	0.267390i
$928$	−2.32506	+	8.67723i	−0.0763237	+	0.284844i
$929$	−30.0584	+	30.0584i	−0.986186	+	0.986186i	−0.999906	−	0.0137202i	$-0.995633\pi$
$929$	−30.0584	+	30.0584i	−0.986186	+	0.986186i	0.0137202	+	0.999906i	$0.495633\pi$
$930$	−5.07805	−	2.18078i	−0.166516	−	0.0715108i
$931$	8.46395	+	5.16063i	0.277395	+	0.169133i
$932$	−22.1731	+	12.8017i	−0.726305	+	0.419332i
$933$	−13.6952	−	34.3121i	−0.448361	−	1.12333i
$934$	9.78801	−	9.78801i	0.320273	−	0.320273i
$935$	2.03220	+	3.51987i	0.0664600	+	0.115112i
$936$	−2.59257	+	10.5014i	−0.0847408	+	0.343248i
$937$	−0.804682			−0.0262878			−0.0131439	−	0.999914i	$-0.504184\pi$
$937$	−0.804682			−0.0262878			−0.0131439	+	0.999914i	$0.504184\pi$
$938$	−21.7741	+	16.2975i	−0.710949	+	0.532134i
$939$	−9.68897	+	12.2943i	−0.316188	+	0.401208i
$940$			3.90340i			0.127315i
$941$	29.3918	+	7.87551i	0.958145	+	0.256734i	0.703815	−	0.710383i	$-0.251478\pi$
$941$	29.3918	+	7.87551i	0.958145	+	0.256734i	0.254330	+	0.967117i	$0.418145\pi$
$942$	−2.52986	−	21.3468i	−0.0824272	−	0.695515i
$943$	−16.3083	+	16.3083i	−0.531071	+	0.531071i
$944$	−10.0566	−	10.0566i	−0.327313	−	0.327313i
$945$	−10.7849	−	0.548138i	−0.350833	−	0.0178309i
$946$	−2.73168	−	1.57714i	−0.0888147	−	0.0512772i
$947$	11.6478	−	43.4702i	0.378503	−	1.41259i	−0.469656	−	0.882849i	$-0.655622\pi$
$947$	11.6478	−	43.4702i	0.378503	−	1.41259i	0.848159	−	0.529742i	$-0.177711\pi$
$948$	−7.48738	+	2.98848i	−0.243179	+	0.0970615i
$949$	−3.00890	−	4.70222i	−0.0976730	−	0.152641i
$950$	−5.37545	−	3.10352i	−0.174403	−	0.100691i
$951$	2.06706	+	17.4417i	0.0670289	+	0.565585i
$952$	−5.92145	−	14.7940i	−0.191915	−	0.479476i
$953$	−21.9185	−	37.9640i	−0.710011	−	1.22977i	−0.964853	−	0.262792i	$-0.915357\pi$
$953$	−21.9185	−	37.9640i	−0.710011	−	1.22977i	0.254842	−	0.966983i	$-0.417977\pi$
$954$	32.0953	+	0.830653i	1.03912	+	0.0268934i
$955$	0.418938	−	0.112254i	0.0135565	−	0.00363246i
$956$	−24.1878	+	6.48111i	−0.782291	+	0.209614i
$957$	−1.57318	−	13.2744i	−0.0508538	−	0.429101i
$958$	−17.3491	−	30.0495i	−0.560523	−	0.970854i
$959$	18.3357	+	45.8095i	0.592091	+	1.47927i
$960$	1.35107	−	0.160118i	0.0436055	−	0.00516779i
$961$	12.5571	+	7.24985i	0.405068	+	0.233866i
$962$	−4.27437	−	13.4625i	−0.137811	−	0.434049i
$963$	13.8376	−	3.32658i	0.445911	−	0.107198i
$964$	−0.199072	+	0.742948i	−0.00641169	+	0.0239287i
$965$	17.8507	+	10.3061i	0.574635	+	0.331765i
$966$	−32.0151	+	7.72930i	−1.03007	+	0.248686i
$967$	5.40579	+	5.40579i	0.173838	+	0.173838i	0.788664	−	0.614825i	$-0.210773\pi$
$967$	5.40579	+	5.40579i	0.173838	+	0.173838i	−0.614825	+	0.788664i	$0.710773\pi$
$968$	7.25629	−	7.25629i	0.233226	−	0.233226i
$969$	14.6707	−	1.73866i	0.471290	−	0.0558537i
$970$	−4.82761	−	1.29355i	−0.155005	−	0.0415335i
$971$			8.75580i			0.280987i	0.990082	+	0.140493i	$0.0448689\pi$
$971$			8.75580i			0.280987i	−0.990082	+	0.140493i	$0.955131\pi$
$972$	−5.02200	−	14.7574i	−0.161081	−	0.473342i
$973$	42.0157	−	31.4481i	1.34696	−	1.00818i
$974$	−1.13020			−0.0362140
$975$	−25.6171	−	9.64241i	−0.820405	−	0.308804i
$976$	−5.03259	−	8.71671i	−0.161089	−	0.279015i
$977$	32.0415	−	32.0415i	1.02510	−	1.02510i	0.0254202	−	0.999677i	$-0.491908\pi$
$977$	32.0415	−	32.0415i	1.02510	−	1.02510i	0.999677	−	0.0254202i	$-0.00809237\pi$
$978$	−21.2139	+	8.46723i	−0.678345	+	0.270752i
$979$	2.30257	−	1.32939i	0.0735903	−	0.0424874i
$980$	0.131603	−	5.49691i	0.00420390	−	0.175592i
$981$	−17.9411	+	29.2972i	−0.572814	+	0.935388i
$982$	−9.03640	+	9.03640i	−0.288363	+	0.288363i
$983$	−9.62575	+	35.9238i	−0.307014	+	1.14579i	0.624184	+	0.781277i	$0.285431\pi$
$983$	−9.62575	+	35.9238i	−0.307014	+	1.14579i	−0.931198	+	0.364514i	$0.881235\pi$
$984$	3.44041	−	4.36550i	0.109676	−	0.139167i
$985$	2.85814	−	1.65015i	0.0910678	−	0.0525780i
$986$	52.2619	−	14.0035i	1.66436	−	0.445964i
$987$	5.34430	+	22.1363i	0.170111	+	0.704607i
$988$	2.34864	−	4.53383i	0.0747202	−	0.144240i
$989$	−22.8523	−	13.1938i	−0.726662	−	0.419539i
$990$	−1.77885	+	0.966539i	−0.0565356	+	0.0307186i
$991$	33.5943			1.06716			0.533579	−	0.845750i	$-0.320847\pi$
$991$	33.5943			1.06716			0.533579	+	0.845750i	$0.320847\pi$
$992$	4.06206			0.128970
$993$	−24.8760	−	33.3025i	−0.789417	−	1.05682i
$994$	1.36219	−	3.18041i	0.0432060	−	0.100877i
$995$	2.27631	−	8.49529i	0.0721637	−	0.269319i
$996$	−3.33093	+	0.394757i	−0.105545	+	0.0125084i
$997$	−16.4803	+	28.5447i	−0.521936	+	0.904020i	0.477738	+	0.878502i	$0.341457\pi$
$997$	−16.4803	+	28.5447i	−0.521936	+	0.904020i	−0.999674	+	0.0255174i	$0.991877\pi$
$998$	11.4495			0.362426
$999$	15.6565	+	13.0093i	0.495350	+	0.411595i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.527.21	yes	152
3.2	odd	2	inner	546.2.bw.a.527.2	yes	152
7.4	even	3		546.2.ch.a.137.13	yes	152
13.2	odd	12		546.2.ch.a.275.34	yes	152
21.11	odd	6		546.2.ch.a.137.34	yes	152
39.2	even	12		546.2.ch.a.275.13	yes	152
91.67	odd	12	inner	546.2.bw.a.431.2	✓	152
273.158	even	12	inner	546.2.bw.a.431.21	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.2	✓	152	91.67	odd	12	inner
546.2.bw.a.431.21	yes	152	273.158	even	12	inner
546.2.bw.a.527.2	yes	152	3.2	odd	2	inner
546.2.bw.a.527.21	yes	152	1.1	even	1	trivial
546.2.ch.a.137.13	yes	152	7.4	even	3
546.2.ch.a.137.34	yes	152	21.11	odd	6
546.2.ch.a.275.13	yes	152	39.2	even	12
546.2.ch.a.275.34	yes	152	13.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.71416 - 0.248275i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.203302 + 0.758733i) q^{5} +(-1.59150 - 0.683474i) q^{6} +(-0.313922 - 2.62706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.87672 + 0.851169i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{2} +(-1.71416 - 0.248275i) q^{3} +(0.866025 + 0.500000i) q^{4} +(0.203302 + 0.758733i) q^{5} +(-1.59150 - 0.683474i) q^{6} +(-0.313922 - 2.62706i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.87672 + 0.851169i) q^{9} +0.785498i q^{10} +(0.607479 + 0.607479i) q^{11} +(-1.36037 - 1.07209i) q^{12} +(2.66316 + 2.43055i) q^{13} +(0.376709 - 2.61880i) q^{14} +(-0.160118 - 1.35107i) q^{15} +(0.500000 + 0.866025i) q^{16} +(3.01144 - 5.21597i) q^{17} +(2.55840 + 1.56672i) q^{18} +(-1.00138 - 1.00138i) q^{19} +(-0.203302 + 0.758733i) q^{20} +(-0.114121 + 4.58115i) q^{21} +(0.429553 + 0.744007i) q^{22} +(3.59349 + 6.22411i) q^{23} +(-1.03654 - 1.38765i) q^{24} +(3.79578 - 2.19150i) q^{25} +(1.94334 + 3.03701i) q^{26} +(-4.71984 - 2.17326i) q^{27} +(1.04167 - 2.43206i) q^{28} +(7.77979 + 4.49166i) q^{29} +(0.195020 - 1.34647i) q^{30} +(1.05134 - 3.92364i) q^{31} +(0.258819 + 0.965926i) q^{32} +(-0.890497 - 1.19214i) q^{33} +(4.25882 - 4.25882i) q^{34} +(1.92942 - 0.772269i) q^{35} +(2.06573 + 2.17549i) q^{36} +(-3.78403 - 1.01393i) q^{37} +(-0.708082 - 1.22643i) q^{38} +(-3.96165 - 4.82756i) q^{39} +(-0.392749 + 0.680261i) q^{40} +(0.830563 + 3.09970i) q^{41} +(-1.29592 + 4.39552i) q^{42} +(-3.17968 + 1.83579i) q^{43} +(0.222353 + 0.829832i) q^{44} +(-0.0609676 + 2.35570i) q^{45} +(1.86013 + 6.94209i) q^{46} +(4.80000 - 1.28616i) q^{47} +(-0.642070 - 1.60865i) q^{48} +(-6.80291 + 1.64938i) q^{49} +(4.23365 - 1.13440i) q^{50} +(-6.45710 + 8.19336i) q^{51} +(1.09109 + 3.43650i) q^{52} +(9.26822 - 5.35101i) q^{53} +(-3.99654 - 3.32080i) q^{54} +(-0.337413 + 0.584416i) q^{55} +(1.63564 - 2.07959i) q^{56} +(1.46791 + 1.96515i) q^{57} +(6.35217 + 6.35217i) q^{58} +(-13.7375 + 3.68096i) q^{59} +(0.536867 - 1.25012i) q^{60} -10.0652 q^{61} +(2.03103 - 3.51784i) q^{62} +(1.33301 - 7.82452i) q^{63} +1.00000i q^{64} +(-1.30271 + 2.51476i) q^{65} +(-0.551606 - 1.38200i) q^{66} +(-7.26892 - 7.26892i) q^{67} +(5.21597 - 3.01144i) q^{68} +(-4.61454 - 11.5613i) q^{69} +(2.06355 - 0.246585i) q^{70} +(1.26314 + 0.338458i) q^{71} +(1.43228 + 2.63601i) q^{72} +(-1.49555 - 0.400732i) q^{73} +(-3.39267 - 1.95876i) q^{74} +(-7.05069 + 2.81419i) q^{75} +(-0.366530 - 1.36791i) q^{76} +(1.40518 - 1.78659i) q^{77} +(-2.57720 - 5.68841i) q^{78} +(2.32723 - 4.03088i) q^{79} +(-0.555431 + 0.555431i) q^{80} +(7.55102 + 4.89715i) q^{81} +3.20905i q^{82} +(1.36936 - 1.36936i) q^{83} +(-2.38941 + 3.91034i) q^{84} +(4.56976 + 1.22446i) q^{85} +(-3.54648 + 0.950276i) q^{86} +(-12.2207 - 9.63098i) q^{87} +0.859106i q^{88} +(0.800997 - 2.98936i) q^{89} +(-0.668591 + 2.25966i) q^{90} +(5.54918 - 7.75929i) q^{91} +7.18698i q^{92} +(-2.77631 + 6.46475i) q^{93} +4.96933 q^{94} +(0.556197 - 0.963362i) q^{95} +(-0.203843 - 1.72001i) q^{96} +(-1.64679 + 6.14592i) q^{97} +(-6.99799 - 0.167541i) q^{98} +(1.23048 + 2.26461i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more