LMFDB - Embedded newform 363.2.e.g.202.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,2,Mod(124,363)] 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("363.124"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.e (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,1,1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 33)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			202.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	363.202
Dual form			363.2.e.g.124.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.23607 - 3.80423i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +2.00000 q^{10} +1.00000 q^{12} +(-1.61803 - 1.17557i) q^{13} +(1.23607 - 3.80423i) q^{14} +(0.618034 + 1.90211i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.61803 + 1.17557i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.61803 - 1.17557i) q^{20} +4.00000 q^{21} +8.00000 q^{23} +(2.42705 + 1.76336i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-0.618034 - 1.90211i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.23607 + 2.35114i) q^{28} +(1.85410 + 5.70634i) q^{29} +(-0.618034 + 1.90211i) q^{30} +(6.47214 + 4.70228i) q^{31} -5.00000 q^{32} -2.00000 q^{34} +(-6.47214 - 4.70228i) q^{35} +(-0.309017 + 0.951057i) q^{36} +(1.85410 + 5.70634i) q^{37} +(1.61803 - 1.17557i) q^{39} +(-1.85410 - 5.70634i) q^{40} +(0.618034 - 1.90211i) q^{41} +(3.23607 + 2.35114i) q^{42} -2.00000 q^{45} +(6.47214 + 4.70228i) q^{46} +(2.47214 - 7.60845i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-7.28115 + 5.29007i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.618034 - 1.90211i) q^{51} +(-0.618034 + 1.90211i) q^{52} +(-4.85410 - 3.52671i) q^{53} +1.00000 q^{54} -12.0000 q^{56} +(-1.85410 + 5.70634i) q^{58} +(-1.23607 - 3.80423i) q^{59} +(1.61803 - 1.17557i) q^{60} +(4.85410 - 3.52671i) q^{61} +(2.47214 + 7.60845i) q^{62} +(-1.23607 + 3.80423i) q^{63} +(-5.66312 - 4.11450i) q^{64} -4.00000 q^{65} -4.00000 q^{67} +(1.61803 + 1.17557i) q^{68} +(-2.47214 + 7.60845i) q^{69} +(-2.47214 - 7.60845i) q^{70} +(-2.42705 + 1.76336i) q^{72} +(4.32624 + 13.3148i) q^{73} +(-1.85410 + 5.70634i) q^{74} +(-0.809017 - 0.587785i) q^{75} +2.00000 q^{78} +(-3.23607 - 2.35114i) q^{79} +(0.618034 - 1.90211i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.61803 - 1.17557i) q^{82} +(9.70820 - 7.05342i) q^{83} +(-1.23607 - 3.80423i) q^{84} +(-1.23607 + 3.80423i) q^{85} -6.00000 q^{87} -6.00000 q^{89} +(-1.61803 - 1.17557i) q^{90} +(-2.47214 + 7.60845i) q^{91} +(-2.47214 - 7.60845i) q^{92} +(-6.47214 + 4.70228i) q^{93} +(6.47214 - 4.70228i) q^{94} +(1.54508 - 4.75528i) q^{96} +(-1.61803 - 1.17557i) q^{97} -9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 3 q^{8} - q^{9} + 8 q^{10} + 4 q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 2 q^{20} + 16 q^{21} + 32 q^{23} + 3 q^{24}+ \cdots - 36 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^3 + q^4 + 2 * q^5 - q^6 + 4 * q^7 - 3 * q^8 - q^9 + 8 * q^10 + 4 * q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 + q^16 - 2 * q^17 + q^18 - 2 * q^20 + 16 * q^21 + 32 * q^23 + 3 * q^24 + q^25 + 2 * q^26 + q^27 - 4 * q^28 - 6 * q^29 + 2 * q^30 + 8 * q^31 - 20 * q^32 - 8 * q^34 - 8 * q^35 + q^36 - 6 * q^37 + 2 * q^39 + 6 * q^40 - 2 * q^41 + 4 * q^42 - 8 * q^45 + 8 * q^46 - 8 * q^47 - q^48 - 9 * q^49 - q^50 + 2 * q^51 + 2 * q^52 - 6 * q^53 + 4 * q^54 - 48 * q^56 + 6 * q^58 + 4 * q^59 + 2 * q^60 + 6 * q^61 - 8 * q^62 + 4 * q^63 - 7 * q^64 - 16 * q^65 - 16 * q^67 + 2 * q^68 + 8 * q^69 + 8 * q^70 - 3 * q^72 - 14 * q^73 + 6 * q^74 - q^75 + 8 * q^78 - 4 * q^79 - 2 * q^80 - q^81 + 2 * q^82 + 12 * q^83 + 4 * q^84 + 4 * q^85 - 24 * q^87 - 24 * q^89 - 2 * q^90 + 8 * q^91 + 8 * q^92 - 8 * q^93 + 8 * q^94 - 5 * q^96 - 2 * q^97 - 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	0.835853	−	0.548953i	$-0.184973\pi$
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	−0.263792	+	0.964580i	$0.584973\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	−0.163928	−	0.986472i	$-0.552416\pi$
$5$	1.61803	−	1.17557i	0.723607	−	0.525731i	0.887535	+	0.460741i	$0.152416\pi$
$6$	−0.809017	+	0.587785i	−0.330280	+	0.239962i
$7$	−1.23607	−	3.80423i	−0.467190	−	1.43786i	−0.856208	−	0.516632i	$-0.827186\pi$
$7$	−1.23607	−	3.80423i	−0.467190	−	1.43786i	0.389018	−	0.921230i	$-0.372814\pi$
$8$	0.927051	−	2.85317i	0.327762	−	1.00875i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	2.00000			0.632456
$11$		0			0
$11$		0			0
$12$	1.00000			0.288675
$13$	−1.61803	−	1.17557i	−0.448762	−	0.326045i	0.340345	−	0.940301i	$-0.389456\pi$
$13$	−1.61803	−	1.17557i	−0.448762	−	0.326045i	−0.789107	+	0.614256i	$0.789456\pi$
$14$	1.23607	−	3.80423i	0.330353	−	1.01672i
$15$	0.618034	+	1.90211i	0.159576	+	0.491123i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$	−1.61803	+	1.17557i	−0.392431	+	0.285118i	−0.766451	−	0.642303i	$-0.777979\pi$
$17$	−1.61803	+	1.17557i	−0.392431	+	0.285118i	0.374020	+	0.927421i	$0.377979\pi$
$18$	−0.309017	−	0.951057i	−0.0728360	−	0.224166i
$19$		0			0		−0.951057	−	0.309017i	$-0.900000\pi$
$19$		0			0		0.951057	+	0.309017i	$0.100000\pi$
$20$	−1.61803	−	1.17557i	−0.361803	−	0.262866i
$21$	4.00000			0.872872
$22$		0			0
$23$	8.00000			1.66812			0.834058	−	0.551677i	$-0.186012\pi$
$23$	8.00000			1.66812			0.834058	+	0.551677i	$0.186012\pi$
$24$	2.42705	+	1.76336i	0.495420	+	0.359943i
$25$	−0.309017	+	0.951057i	−0.0618034	+	0.190211i
$26$	−0.618034	−	1.90211i	−0.121206	−	0.373035i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	−3.23607	+	2.35114i	−0.611559	+	0.444324i
$29$	1.85410	+	5.70634i	0.344298	+	1.05964i	0.961958	+	0.273196i	$0.0880806\pi$
$29$	1.85410	+	5.70634i	0.344298	+	1.05964i	−0.617660	+	0.786445i	$0.711919\pi$
$30$	−0.618034	+	1.90211i	−0.112837	+	0.347277i
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.990083	−	0.140482i	$-0.0448651\pi$
$31$	6.47214	+	4.70228i	1.16243	+	0.844555i	0.172347	+	0.985036i	$0.444865\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$	−2.00000			−0.342997
$35$	−6.47214	−	4.70228i	−1.09399	−	0.794831i
$36$	−0.309017	+	0.951057i	−0.0515028	+	0.158509i
$37$	1.85410	+	5.70634i	0.304812	+	0.938116i	0.979747	+	0.200239i	$0.0641718\pi$
$37$	1.85410	+	5.70634i	0.304812	+	0.938116i	−0.674935	+	0.737878i	$0.735828\pi$
$38$		0			0
$39$	1.61803	−	1.17557i	0.259093	−	0.188242i
$40$	−1.85410	−	5.70634i	−0.293159	−	0.902251i
$41$	0.618034	−	1.90211i	0.0965207	−	0.297060i	−0.891126	−	0.453755i	$-0.850084\pi$
$41$	0.618034	−	1.90211i	0.0965207	−	0.297060i	0.987647	+	0.156695i	$0.0500840\pi$
$42$	3.23607	+	2.35114i	0.499336	+	0.362789i
$43$		0			0			−	1.00000i	$-0.5\pi$
$43$		0			0				1.00000i	$0.5\pi$
$44$		0			0
$45$	−2.00000			−0.298142
$46$	6.47214	+	4.70228i	0.954264	+	0.693314i
$47$	2.47214	−	7.60845i	0.360598	−	1.10981i	−0.592094	−	0.805869i	$-0.701699\pi$
$47$	2.47214	−	7.60845i	0.360598	−	1.10981i	0.952692	−	0.303938i	$-0.0983015\pi$
$48$	0.309017	+	0.951057i	0.0446028	+	0.137273i
$49$	−7.28115	+	5.29007i	−1.04016	+	0.755724i
$50$	−0.809017	+	0.587785i	−0.114412	+	0.0831254i
$51$	−0.618034	−	1.90211i	−0.0865421	−	0.266349i
$52$	−0.618034	+	1.90211i	−0.0857059	+	0.263776i
$53$	−4.85410	−	3.52671i	−0.666762	−	0.484431i	0.202178	−	0.979349i	$-0.435198\pi$
$53$	−4.85410	−	3.52671i	−0.666762	−	0.484431i	−0.868940	+	0.494918i	$0.835198\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	−12.0000			−1.60357
$57$		0			0
$58$	−1.85410	+	5.70634i	−0.243456	+	0.749279i
$59$	−1.23607	−	3.80423i	−0.160922	−	0.495268i	0.837790	−	0.545992i	$-0.183847\pi$
$59$	−1.23607	−	3.80423i	−0.160922	−	0.495268i	−0.998713	+	0.0507240i	$0.983847\pi$
$60$	1.61803	−	1.17557i	0.208887	−	0.151765i
$61$	4.85410	−	3.52671i	0.621504	−	0.451549i	−0.231942	−	0.972730i	$-0.574508\pi$
$61$	4.85410	−	3.52671i	0.621504	−	0.451549i	0.853447	+	0.521180i	$0.174508\pi$
$62$	2.47214	+	7.60845i	0.313962	+	0.966274i
$63$	−1.23607	+	3.80423i	−0.155730	+	0.479287i
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$	−4.00000			−0.496139
$66$		0			0
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$	1.61803	+	1.17557i	0.196215	+	0.142559i
$69$	−2.47214	+	7.60845i	−0.297610	+	0.915950i
$70$	−2.47214	−	7.60845i	−0.295477	−	0.909384i
$71$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$71$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$72$	−2.42705	+	1.76336i	−0.286031	+	0.207813i
$73$	4.32624	+	13.3148i	0.506348	+	1.55838i	0.798493	+	0.602004i	$0.205631\pi$
$73$	4.32624	+	13.3148i	0.506348	+	1.55838i	−0.292145	+	0.956374i	$0.594369\pi$
$74$	−1.85410	+	5.70634i	−0.215535	+	0.663348i
$75$	−0.809017	−	0.587785i	−0.0934172	−	0.0678716i
$76$		0			0
$77$		0			0
$78$	2.00000			0.226455
$79$	−3.23607	−	2.35114i	−0.364086	−	0.264524i	0.390668	−	0.920532i	$-0.372244\pi$
$79$	−3.23607	−	2.35114i	−0.364086	−	0.264524i	−0.754754	+	0.656007i	$0.772244\pi$
$80$	0.618034	−	1.90211i	0.0690983	−	0.212663i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.61803	−	1.17557i	0.178682	−	0.129820i
$83$	9.70820	−	7.05342i	1.06561	−	0.774214i	0.0904951	−	0.995897i	$-0.471155\pi$
$83$	9.70820	−	7.05342i	1.06561	−	0.774214i	0.975119	+	0.221683i	$0.0711551\pi$
$84$	−1.23607	−	3.80423i	−0.134866	−	0.415075i
$85$	−1.23607	+	3.80423i	−0.134070	+	0.412626i
$86$		0			0
$87$	−6.00000			−0.643268
$88$		0			0
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−1.61803	−	1.17557i	−0.170556	−	0.123916i
$91$	−2.47214	+	7.60845i	−0.259150	+	0.797582i
$92$	−2.47214	−	7.60845i	−0.257738	−	0.793236i
$93$	−6.47214	+	4.70228i	−0.671129	+	0.487604i
$94$	6.47214	−	4.70228i	0.667550	−	0.485003i
$95$		0			0
$96$	1.54508	−	4.75528i	0.157695	−	0.485334i
$97$	−1.61803	−	1.17557i	−0.164286	−	0.119361i	0.502604	−	0.864517i	$-0.332375\pi$
$97$	−1.61803	−	1.17557i	−0.164286	−	0.119361i	−0.666891	+	0.745155i	$0.732375\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$	1.00000			0.100000
$101$	1.61803	+	1.17557i	0.161000	+	0.116974i	0.665368	−	0.746515i	$-0.268274\pi$
$101$	1.61803	+	1.17557i	0.161000	+	0.116974i	−0.504368	+	0.863489i	$0.668274\pi$
$102$	0.618034	−	1.90211i	0.0611945	−	0.188337i
$103$	2.47214	+	7.60845i	0.243587	+	0.749683i	0.995866	+	0.0908382i	$0.0289546\pi$
$103$	2.47214	+	7.60845i	0.243587	+	0.749683i	−0.752279	+	0.658845i	$0.771045\pi$
$104$	−4.85410	+	3.52671i	−0.475984	+	0.345823i
$105$	6.47214	−	4.70228i	0.631616	−	0.458896i
$106$	−1.85410	−	5.70634i	−0.180086	−	0.554249i
$107$	3.70820	−	11.4127i	0.358486	−	1.10331i	−0.595475	−	0.803374i	$-0.703036\pi$
$107$	3.70820	−	11.4127i	0.358486	−	1.10331i	0.953961	−	0.299932i	$-0.0969638\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	2.00000			0.191565			0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000			0.191565			0.0957826	+	0.995402i	$0.469465\pi$
$110$		0			0
$111$	−6.00000			−0.569495
$112$	−3.23607	−	2.35114i	−0.305780	−	0.222162i
$113$	−1.85410	+	5.70634i	−0.174419	+	0.536807i	−0.999606	−	0.0280521i	$-0.991070\pi$
$113$	−1.85410	+	5.70634i	−0.174419	+	0.536807i	0.825187	+	0.564859i	$0.191070\pi$
$114$		0			0
$115$	12.9443	−	9.40456i	1.20706	−	0.876980i
$116$	4.85410	−	3.52671i	0.450692	−	0.327447i
$117$	0.618034	+	1.90211i	0.0571373	+	0.175850i
$118$	1.23607	−	3.80423i	0.113789	−	0.350207i
$119$	6.47214	+	4.70228i	0.593300	+	0.431057i
$120$	6.00000			0.547723
$121$		0			0
$122$	6.00000			0.543214
$123$	1.61803	+	1.17557i	0.145893	+	0.105998i
$124$	2.47214	−	7.60845i	0.222004	−	0.683259i
$125$	3.70820	+	11.4127i	0.331672	+	1.02078i
$126$	−3.23607	+	2.35114i	−0.288292	+	0.209456i
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	−0.722032	−	0.691860i	$-0.756792\pi$
$127$	−3.23607	+	2.35114i	−0.287155	+	0.208630i	0.434877	+	0.900490i	$0.356792\pi$
$128$	0.927051	+	2.85317i	0.0819405	+	0.252187i
$129$		0			0
$130$	−3.23607	−	2.35114i	−0.283822	−	0.206209i
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$		0			0
$134$	−3.23607	−	2.35114i	−0.279554	−	0.203108i
$135$	0.618034	−	1.90211i	0.0531919	−	0.163708i
$136$	1.85410	+	5.70634i	0.158988	+	0.489315i
$137$	−1.61803	+	1.17557i	−0.138238	+	0.100436i	−0.654755	−	0.755841i	$-0.727228\pi$
$137$	−1.61803	+	1.17557i	−0.138238	+	0.100436i	0.516517	+	0.856277i	$0.327228\pi$
$138$	−6.47214	+	4.70228i	−0.550945	+	0.400285i
$139$	2.47214	+	7.60845i	0.209684	+	0.645340i	0.999488	+	0.0319820i	$0.0101819\pi$
$139$	2.47214	+	7.60845i	0.209684	+	0.645340i	−0.789805	+	0.613359i	$0.789818\pi$
$140$	−2.47214	+	7.60845i	−0.208934	+	0.643032i
$141$	6.47214	+	4.70228i	0.545052	+	0.396004i
$142$		0			0
$143$		0			0
$144$	−1.00000			−0.0833333
$145$	9.70820	+	7.05342i	0.806222	+	0.585755i
$146$	−4.32624	+	13.3148i	−0.358042	+	1.10194i
$147$	−2.78115	−	8.55951i	−0.229386	−	0.705976i
$148$	4.85410	−	3.52671i	0.399005	−	0.289894i
$149$	−17.7984	+	12.9313i	−1.45810	+	1.05937i	−0.474247	+	0.880392i	$0.657280\pi$
$149$	−17.7984	+	12.9313i	−1.45810	+	1.05937i	−0.983853	+	0.178979i	$0.942720\pi$
$150$	−0.309017	−	0.951057i	−0.0252311	−	0.0776534i
$151$	−6.18034	+	19.0211i	−0.502949	+	1.54792i	0.301243	+	0.953548i	$0.402599\pi$
$151$	−6.18034	+	19.0211i	−0.502949	+	1.54792i	−0.804192	+	0.594370i	$0.797401\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$		0			0
$155$	16.0000			1.28515
$156$	−1.61803	−	1.17557i	−0.129546	−	0.0941210i
$157$	4.32624	−	13.3148i	0.345271	−	1.06264i	−0.616167	−	0.787616i	$-0.711315\pi$
$157$	4.32624	−	13.3148i	0.345271	−	1.06264i	0.961438	−	0.275020i	$-0.0886846\pi$
$158$	−1.23607	−	3.80423i	−0.0983363	−	0.302648i
$159$	4.85410	−	3.52671i	0.384955	−	0.279686i
$160$	−8.09017	+	5.87785i	−0.639584	+	0.464685i
$161$	−9.88854	−	30.4338i	−0.779326	−	2.39852i
$162$	−0.309017	+	0.951057i	−0.0242787	+	0.0747221i
$163$	−3.23607	−	2.35114i	−0.253468	−	0.184156i	0.453794	−	0.891107i	$-0.350070\pi$
$163$	−3.23607	−	2.35114i	−0.253468	−	0.184156i	−0.707263	+	0.706951i	$0.750070\pi$
$164$	−2.00000			−0.156174
$165$		0			0
$166$	12.0000			0.931381
$167$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$167$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$168$	3.70820	−	11.4127i	0.286094	−	0.880507i
$169$	−2.78115	−	8.55951i	−0.213935	−	0.658424i
$170$	−3.23607	+	2.35114i	−0.248195	+	0.180324i
$171$		0			0
$172$		0			0
$173$	1.85410	−	5.70634i	0.140965	−	0.433845i	−0.855505	−	0.517794i	$-0.826753\pi$
$173$	1.85410	−	5.70634i	0.140965	−	0.433845i	0.996470	+	0.0839492i	$0.0267533\pi$
$174$	−4.85410	−	3.52671i	−0.367989	−	0.267359i
$175$	4.00000			0.302372
$176$		0			0
$177$	4.00000			0.300658
$178$	−4.85410	−	3.52671i	−0.363830	−	0.264338i
$179$	3.70820	−	11.4127i	0.277164	−	0.853024i	−0.711474	−	0.702712i	$-0.751972\pi$
$179$	3.70820	−	11.4127i	0.277164	−	0.853024i	0.988639	−	0.150312i	$-0.0480277\pi$
$180$	0.618034	+	1.90211i	0.0460655	+	0.141775i
$181$	−17.7984	+	12.9313i	−1.32294	+	0.961174i	−0.323052	+	0.946381i	$0.604709\pi$
$181$	−17.7984	+	12.9313i	−1.32294	+	0.961174i	−0.999891	+	0.0147930i	$0.995291\pi$
$182$	−6.47214	+	4.70228i	−0.479747	+	0.348556i
$183$	1.85410	+	5.70634i	0.137059	+	0.421825i
$184$	7.41641	−	22.8254i	0.546745	−	1.68271i
$185$	9.70820	+	7.05342i	0.713761	+	0.518578i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−8.00000			−0.583460
$189$	−3.23607	−	2.35114i	−0.235389	−	0.171020i
$190$		0			0
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	0.999789	−	0.0205267i	$-0.00653431\pi$
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	−0.820912	+	0.571055i	$0.806534\pi$
$192$	5.66312	−	4.11450i	0.408700	−	0.296938i
$193$	−11.3262	+	8.22899i	−0.815280	+	0.592336i	−0.915357	−	0.402644i	$-0.868091\pi$
$193$	−11.3262	+	8.22899i	−0.815280	+	0.592336i	0.100076	+	0.994980i	$0.468091\pi$
$194$	−0.618034	−	1.90211i	−0.0443723	−	0.136564i
$195$	1.23607	−	3.80423i	0.0885167	−	0.272426i
$196$	7.28115	+	5.29007i	0.520082	+	0.377862i
$197$	14.0000			0.997459			0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000			0.997459			0.498729	+	0.866758i	$0.333800\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	2.42705	+	1.76336i	0.171618	+	0.124688i
$201$	1.23607	−	3.80423i	0.0871855	−	0.268329i
$202$	0.618034	+	1.90211i	0.0434847	+	0.133832i
$203$	19.4164	−	14.1068i	1.36276	−	0.990106i
$204$	−1.61803	+	1.17557i	−0.113285	+	0.0823064i
$205$	−1.23607	−	3.80423i	−0.0863307	−	0.265699i
$206$	−2.47214	+	7.60845i	−0.172242	+	0.530106i
$207$	−6.47214	−	4.70228i	−0.449845	−	0.326831i
$208$	−2.00000			−0.138675
$209$		0			0
$210$	8.00000			0.552052
$211$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$211$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$212$	−1.85410	+	5.70634i	−0.127340	+	0.391913i
$213$		0			0
$214$	9.70820	−	7.05342i	0.663639	−	0.482162i
$215$		0			0
$216$	−0.927051	−	2.85317i	−0.0630778	−	0.194134i
$217$	9.88854	−	30.4338i	0.671278	−	2.06598i
$218$	1.61803	+	1.17557i	0.109587	+	0.0796197i
$219$	−14.0000			−0.946032
$220$		0			0
$221$	4.00000			0.269069
$222$	−4.85410	−	3.52671i	−0.325786	−	0.236697i
$223$	4.94427	−	15.2169i	0.331093	−	1.01900i	−0.637522	−	0.770432i	$-0.720040\pi$
$223$	4.94427	−	15.2169i	0.331093	−	1.01900i	0.968615	−	0.248567i	$-0.0799596\pi$
$224$	6.18034	+	19.0211i	0.412941	+	1.27090i
$225$	0.809017	−	0.587785i	0.0539345	−	0.0391857i
$226$	−4.85410	+	3.52671i	−0.322890	+	0.234593i
$227$	−3.70820	−	11.4127i	−0.246122	−	0.757486i	−0.995450	−	0.0952867i	$-0.969623\pi$
$227$	−3.70820	−	11.4127i	−0.246122	−	0.757486i	0.749328	−	0.662199i	$-0.230377\pi$
$228$		0			0
$229$	−4.85410	−	3.52671i	−0.320768	−	0.233052i	0.415735	−	0.909486i	$-0.363524\pi$
$229$	−4.85410	−	3.52671i	−0.320768	−	0.233052i	−0.736503	+	0.676434i	$0.763524\pi$
$230$	16.0000			1.05501
$231$		0			0
$232$	18.0000			1.18176
$233$	24.2705	+	17.6336i	1.59001	+	1.15521i	0.903921	+	0.427698i	$0.140675\pi$
$233$	24.2705	+	17.6336i	1.59001	+	1.15521i	0.686092	+	0.727514i	$0.259325\pi$
$234$	−0.618034	+	1.90211i	−0.0404021	+	0.124345i
$235$	−4.94427	−	15.2169i	−0.322529	−	0.992641i
$236$	−3.23607	+	2.35114i	−0.210650	+	0.153046i
$237$	3.23607	−	2.35114i	0.210205	−	0.152723i
$238$	2.47214	+	7.60845i	0.160245	+	0.493183i
$239$	−7.41641	+	22.8254i	−0.479728	+	1.47645i	0.359747	+	0.933050i	$0.382863\pi$
$239$	−7.41641	+	22.8254i	−0.479728	+	1.47645i	−0.839474	+	0.543400i	$0.817137\pi$
$240$	1.61803	+	1.17557i	0.104444	+	0.0758827i
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$	−4.85410	−	3.52671i	−0.310752	−	0.225775i
$245$	−5.56231	+	17.1190i	−0.355363	+	1.09369i
$246$	0.618034	+	1.90211i	0.0394044	+	0.121274i
$247$		0			0
$248$	19.4164	−	14.1068i	1.23294	−	0.895786i
$249$	3.70820	+	11.4127i	0.234998	+	0.723249i
$250$	−3.70820	+	11.4127i	−0.234527	+	0.721801i
$251$	−3.23607	−	2.35114i	−0.204259	−	0.148403i	0.480953	−	0.876746i	$-0.340291\pi$
$251$	−3.23607	−	2.35114i	−0.204259	−	0.148403i	−0.685212	+	0.728343i	$0.740291\pi$
$252$	4.00000			0.251976
$253$		0			0
$254$	−4.00000			−0.250982
$255$	−3.23607	−	2.35114i	−0.202650	−	0.147234i
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$	−4.32624	−	13.3148i	−0.269863	−	0.830554i	−0.990533	−	0.137275i	$-0.956166\pi$
$257$	−4.32624	−	13.3148i	−0.269863	−	0.830554i	0.720670	−	0.693279i	$-0.243834\pi$
$258$		0			0
$259$	19.4164	−	14.1068i	1.20648	−	0.876557i
$260$	1.23607	+	3.80423i	0.0766577	+	0.235928i
$261$	1.85410	−	5.70634i	0.114766	−	0.353214i
$262$	9.70820	+	7.05342i	0.599775	+	0.435762i
$263$	16.0000			0.986602			0.493301	−	0.869859i	$-0.335790\pi$
$263$	16.0000			0.986602			0.493301	+	0.869859i	$0.335790\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$	1.85410	−	5.70634i	0.113469	−	0.349222i
$268$	1.23607	+	3.80423i	0.0755049	+	0.232380i
$269$	1.61803	−	1.17557i	0.0986533	−	0.0716758i	−0.537365	−	0.843350i	$-0.680580\pi$
$269$	1.61803	−	1.17557i	0.0986533	−	0.0716758i	0.636018	+	0.771674i	$0.280580\pi$
$270$	1.61803	−	1.17557i	0.0984704	−	0.0715429i
$271$	−6.18034	−	19.0211i	−0.375429	−	1.15545i	−0.943189	−	0.332257i	$-0.892190\pi$
$271$	−6.18034	−	19.0211i	−0.375429	−	1.15545i	0.567760	−	0.823194i	$-0.307810\pi$
$272$	−0.618034	+	1.90211i	−0.0374738	+	0.115333i
$273$	−6.47214	−	4.70228i	−0.391711	−	0.284595i
$274$	−2.00000			−0.120824
$275$		0			0
$276$	8.00000			0.481543
$277$	−21.0344	−	15.2824i	−1.26384	−	0.918231i	−0.264898	−	0.964277i	$-0.585338\pi$
$277$	−21.0344	−	15.2824i	−1.26384	−	0.918231i	−0.998939	+	0.0460451i	$0.985338\pi$
$278$	−2.47214	+	7.60845i	−0.148269	+	0.456325i
$279$	−2.47214	−	7.60845i	−0.148003	−	0.455506i
$280$	−19.4164	+	14.1068i	−1.16035	+	0.843045i
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	−0.930242	−	0.366947i	$-0.880403\pi$
$281$	−14.5623	+	10.5801i	−0.868714	+	0.631158i	0.0615273	+	0.998105i	$0.480403\pi$
$282$	2.47214	+	7.60845i	0.147214	+	0.453077i
$283$	−4.94427	+	15.2169i	−0.293906	+	0.904551i	0.689680	+	0.724114i	$0.257751\pi$
$283$	−4.94427	+	15.2169i	−0.293906	+	0.904551i	−0.983587	+	0.180437i	$0.942249\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−8.00000			−0.472225
$288$	4.04508	+	2.93893i	0.238359	+	0.173178i
$289$	−4.01722	+	12.3637i	−0.236307	+	0.727279i
$290$	3.70820	+	11.4127i	0.217753	+	0.670176i
$291$	1.61803	−	1.17557i	0.0948508	−	0.0689132i
$292$	11.3262	−	8.22899i	0.662818	−	0.481565i
$293$	1.85410	+	5.70634i	0.108318	+	0.333368i	0.990495	−	0.137550i	$-0.0439228\pi$
$293$	1.85410	+	5.70634i	0.108318	+	0.333368i	−0.882177	+	0.470918i	$0.843923\pi$
$294$	2.78115	−	8.55951i	0.162200	−	0.499201i
$295$	−6.47214	−	4.70228i	−0.376822	−	0.273777i
$296$	18.0000			1.04623
$297$		0			0
$298$	−22.0000			−1.27443
$299$	−12.9443	−	9.40456i	−0.748587	−	0.543880i
$300$	−0.309017	+	0.951057i	−0.0178411	+	0.0549093i
$301$		0			0
$302$	−16.1803	+	11.7557i	−0.931074	+	0.676465i
$303$	−1.61803	+	1.17557i	−0.0929536	+	0.0675348i
$304$		0			0
$305$	3.70820	−	11.4127i	0.212331	−	0.653488i
$306$	1.61803	+	1.17557i	0.0924968	+	0.0672029i
$307$	−32.0000			−1.82634			−0.913168	−	0.407583i	$-0.866372\pi$
$307$	−32.0000			−1.82634			−0.913168	+	0.407583i	$0.866372\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$	12.9443	+	9.40456i	0.735185	+	0.534143i
$311$	−7.41641	+	22.8254i	−0.420546	+	1.29431i	0.486649	+	0.873597i	$0.338219\pi$
$311$	−7.41641	+	22.8254i	−0.420546	+	1.29431i	−0.907195	+	0.420710i	$0.861781\pi$
$312$	−1.85410	−	5.70634i	−0.104968	−	0.323058i
$313$	17.7984	−	12.9313i	1.00602	−	0.730919i	0.0426523	−	0.999090i	$-0.486419\pi$
$313$	17.7984	−	12.9313i	1.00602	−	0.730919i	0.963371	+	0.268171i	$0.0864192\pi$
$314$	11.3262	−	8.22899i	0.639177	−	0.464389i
$315$	2.47214	+	7.60845i	0.139289	+	0.428688i
$316$	−1.23607	+	3.80423i	−0.0695343	+	0.214004i
$317$	−17.7984	−	12.9313i	−0.999656	−	0.726293i	−0.0376418	−	0.999291i	$-0.511985\pi$
$317$	−17.7984	−	12.9313i	−0.999656	−	0.726293i	−0.962014	+	0.272999i	$0.911985\pi$
$318$	6.00000			0.336463
$319$		0			0
$320$	−14.0000			−0.782624
$321$	9.70820	+	7.05342i	0.541859	+	0.393684i
$322$	9.88854	−	30.4338i	0.551067	−	1.69601i
$323$		0			0
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	1.61803	−	1.17557i	0.0897524	−	0.0652089i
$326$	−1.23607	−	3.80423i	−0.0684595	−	0.210697i
$327$	−0.618034	+	1.90211i	−0.0341774	+	0.105187i
$328$	−4.85410	−	3.52671i	−0.268023	−	0.194730i
$329$	−32.0000			−1.76422
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	−9.70820	−	7.05342i	−0.532807	−	0.387107i
$333$	1.85410	−	5.70634i	0.101604	−	0.312705i
$334$		0			0
$335$	−6.47214	+	4.70228i	−0.353611	+	0.256913i
$336$	3.23607	−	2.35114i	0.176542	−	0.128265i
$337$	6.79837	+	20.9232i	0.370331	+	1.13976i	0.946575	+	0.322484i	$0.104518\pi$
$337$	6.79837	+	20.9232i	0.370331	+	1.13976i	−0.576244	+	0.817278i	$0.695482\pi$
$338$	2.78115	−	8.55951i	0.151275	−	0.465576i
$339$	−4.85410	−	3.52671i	−0.263639	−	0.191545i
$340$	4.00000			0.216930
$341$		0			0
$342$		0			0
$343$	6.47214	+	4.70228i	0.349462	+	0.253899i
$344$		0			0
$345$	4.94427	+	15.2169i	0.266191	+	0.819251i
$346$	4.85410	−	3.52671i	0.260958	−	0.189597i
$347$	3.23607	−	2.35114i	0.173721	−	0.126216i	−0.497527	−	0.867448i	$-0.665758\pi$
$347$	3.23607	−	2.35114i	0.173721	−	0.126216i	0.671248	+	0.741233i	$0.265758\pi$
$348$	1.85410	+	5.70634i	0.0993903	+	0.305892i
$349$	−1.85410	+	5.70634i	−0.0992478	+	0.305453i	−0.988337	−	0.152280i	$-0.951338\pi$
$349$	−1.85410	+	5.70634i	−0.0992478	+	0.305453i	0.889090	+	0.457733i	$0.151338\pi$
$350$	3.23607	+	2.35114i	0.172975	+	0.125674i
$351$	−2.00000			−0.106752
$352$		0			0
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$	3.23607	+	2.35114i	0.171995	+	0.124962i
$355$		0			0
$356$	1.85410	+	5.70634i	0.0982672	+	0.302435i
$357$	−6.47214	+	4.70228i	−0.342542	+	0.248871i
$358$	9.70820	−	7.05342i	0.513095	−	0.372785i
$359$	2.47214	+	7.60845i	0.130474	+	0.401559i	0.994859	−	0.101273i	$-0.0322915\pi$
$359$	2.47214	+	7.60845i	0.130474	+	0.401559i	−0.864384	+	0.502832i	$0.832292\pi$
$360$	−1.85410	+	5.70634i	−0.0977198	+	0.300750i
$361$	15.3713	+	11.1679i	0.809017	+	0.587785i
$362$	−22.0000			−1.15629
$363$		0			0
$364$	8.00000			0.419314
$365$	22.6525	+	16.4580i	1.18568	+	0.861450i
$366$	−1.85410	+	5.70634i	−0.0969155	+	0.298275i
$367$	−9.88854	−	30.4338i	−0.516178	−	1.58863i	−0.781129	−	0.624370i	$-0.785356\pi$
$367$	−9.88854	−	30.4338i	−0.516178	−	1.58863i	0.264951	−	0.964262i	$-0.414644\pi$
$368$	6.47214	−	4.70228i	0.337383	−	0.245123i
$369$	−1.61803	+	1.17557i	−0.0842315	+	0.0611978i
$370$	3.70820	+	11.4127i	0.192780	+	0.593317i
$371$	−7.41641	+	22.8254i	−0.385041	+	1.18503i
$372$	6.47214	+	4.70228i	0.335565	+	0.243802i
$373$	2.00000			0.103556			0.0517780	−	0.998659i	$-0.483511\pi$
$373$	2.00000			0.103556			0.0517780	+	0.998659i	$0.483511\pi$
$374$		0			0
$375$	−12.0000			−0.619677
$376$	−19.4164	−	14.1068i	−1.00132	−	0.727505i
$377$	3.70820	−	11.4127i	0.190982	−	0.587783i
$378$	−1.23607	−	3.80423i	−0.0635765	−	0.195668i
$379$	−22.6525	+	16.4580i	−1.16358	+	0.845390i	−0.990226	−	0.139470i	$-0.955460\pi$
$379$	−22.6525	+	16.4580i	−1.16358	+	0.845390i	−0.173353	+	0.984860i	$0.555460\pi$
$380$		0			0
$381$	−1.23607	−	3.80423i	−0.0633257	−	0.194896i
$382$	−2.47214	+	7.60845i	−0.126485	+	0.389282i
$383$	12.9443	+	9.40456i	0.661421	+	0.480551i	0.867143	−	0.498060i	$-0.165954\pi$
$383$	12.9443	+	9.40456i	0.661421	+	0.480551i	−0.205721	+	0.978611i	$0.565954\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	−14.0000			−0.712581
$387$		0			0
$388$	−0.618034	+	1.90211i	−0.0313759	+	0.0965652i
$389$	−5.56231	−	17.1190i	−0.282020	−	0.867969i	−0.987276	−	0.159016i	$-0.949168\pi$
$389$	−5.56231	−	17.1190i	−0.282020	−	0.867969i	0.705256	−	0.708953i	$-0.250832\pi$
$390$	3.23607	−	2.35114i	0.163865	−	0.119055i
$391$	−12.9443	+	9.40456i	−0.654620	+	0.475609i
$392$	8.34346	+	25.6785i	0.421408	+	1.29696i
$393$	−3.70820	+	11.4127i	−0.187054	+	0.575693i
$394$	11.3262	+	8.22899i	0.570608	+	0.414571i
$395$	−8.00000			−0.402524
$396$		0			0
$397$	−2.00000			−0.100377			−0.0501886	−	0.998740i	$-0.515982\pi$
$397$	−2.00000			−0.100377			−0.0501886	+	0.998740i	$0.515982\pi$
$398$		0			0
$399$		0			0
$400$	0.309017	+	0.951057i	0.0154508	+	0.0475528i
$401$	−21.0344	+	15.2824i	−1.05041	+	0.763167i	−0.972290	−	0.233777i	$-0.924892\pi$
$401$	−21.0344	+	15.2824i	−1.05041	+	0.763167i	−0.0781195	+	0.996944i	$0.524892\pi$
$402$	3.23607	−	2.35114i	0.161400	−	0.117264i
$403$	−4.94427	−	15.2169i	−0.246292	−	0.758008i
$404$	0.618034	−	1.90211i	0.0307483	−	0.0946337i
$405$	1.61803	+	1.17557i	0.0804008	+	0.0584146i
$406$	24.0000			1.19110
$407$		0			0
$408$	−6.00000			−0.297044
$409$	14.5623	+	10.5801i	0.720060	+	0.523154i	0.886403	−	0.462914i	$-0.153196\pi$
$409$	14.5623	+	10.5801i	0.720060	+	0.523154i	−0.166344	+	0.986068i	$0.553196\pi$
$410$	1.23607	−	3.80423i	0.0610450	−	0.187877i
$411$	−0.618034	−	1.90211i	−0.0304854	−	0.0938243i
$412$	6.47214	−	4.70228i	0.318859	−	0.231665i
$413$	−12.9443	+	9.40456i	−0.636946	+	0.462768i
$414$	−2.47214	−	7.60845i	−0.121499	−	0.373935i
$415$	7.41641	−	22.8254i	0.364057	−	1.12045i
$416$	8.09017	+	5.87785i	0.396653	+	0.288185i
$417$	−8.00000			−0.391762
$418$		0			0
$419$	−4.00000			−0.195413			−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000			−0.195413			−0.0977064	+	0.995215i	$0.531151\pi$
$420$	−6.47214	−	4.70228i	−0.315808	−	0.229448i
$421$	−8.03444	+	24.7275i	−0.391575	+	1.20514i	0.540022	+	0.841651i	$0.318416\pi$
$421$	−8.03444	+	24.7275i	−0.391575	+	1.20514i	−0.931597	+	0.363492i	$0.881584\pi$
$422$		0			0
$423$	−6.47214	+	4.70228i	−0.314686	+	0.228633i
$424$	−14.5623	+	10.5801i	−0.707208	+	0.513817i
$425$	−0.618034	−	1.90211i	−0.0299791	−	0.0922660i
$426$		0			0
$427$	−19.4164	−	14.1068i	−0.939626	−	0.682678i
$428$	−12.0000			−0.580042
$429$		0			0
$430$		0			0
$431$	−19.4164	−	14.1068i	−0.935255	−	0.679503i	0.0120185	−	0.999928i	$-0.496174\pi$
$431$	−19.4164	−	14.1068i	−0.935255	−	0.679503i	−0.947274	+	0.320425i	$0.896174\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	10.5066	+	32.3359i	0.504914	+	1.55397i	0.800915	+	0.598778i	$0.204347\pi$
$433$	10.5066	+	32.3359i	0.504914	+	1.55397i	−0.296001	+	0.955188i	$0.595653\pi$
$434$	25.8885	−	18.8091i	1.24269	−	0.902867i
$435$	−9.70820	+	7.05342i	−0.465473	+	0.338186i
$436$	−0.618034	−	1.90211i	−0.0295985	−	0.0910947i
$437$		0			0
$438$	−11.3262	−	8.22899i	−0.541189	−	0.393197i
$439$	20.0000			0.954548			0.477274	−	0.878755i	$-0.341625\pi$
$439$	20.0000			0.954548			0.477274	+	0.878755i	$0.341625\pi$
$440$		0			0
$441$	9.00000			0.428571
$442$	3.23607	+	2.35114i	0.153924	+	0.111832i
$443$	8.65248	−	26.6296i	0.411092	−	1.26521i	−0.504609	−	0.863348i	$-0.668363\pi$
$443$	8.65248	−	26.6296i	0.411092	−	1.26521i	0.915700	−	0.401862i	$-0.131637\pi$
$444$	1.85410	+	5.70634i	0.0879918	+	0.270811i
$445$	−9.70820	+	7.05342i	−0.460213	+	0.334364i
$446$	12.9443	−	9.40456i	0.612929	−	0.445319i
$447$	−6.79837	−	20.9232i	−0.321552	−	0.989635i
$448$	−8.65248	+	26.6296i	−0.408791	+	1.25813i
$449$	−1.61803	−	1.17557i	−0.0763597	−	0.0554786i	0.548950	−	0.835855i	$-0.315028\pi$
$449$	−1.61803	−	1.17557i	−0.0763597	−	0.0554786i	−0.625310	+	0.780376i	$0.715028\pi$
$450$	1.00000			0.0471405
$451$		0			0
$452$	6.00000			0.282216
$453$	−16.1803	−	11.7557i	−0.760219	−	0.552331i
$454$	3.70820	−	11.4127i	0.174035	−	0.535624i
$455$	4.94427	+	15.2169i	0.231791	+	0.713379i
$456$		0			0
$457$	14.5623	−	10.5801i	0.681196	−	0.494918i	−0.192558	−	0.981286i	$-0.561678\pi$
$457$	14.5623	−	10.5801i	0.681196	−	0.494918i	0.873754	+	0.486368i	$0.161678\pi$
$458$	−1.85410	−	5.70634i	−0.0866365	−	0.266640i
$459$	−0.618034	+	1.90211i	−0.0288474	+	0.0887830i
$460$	−12.9443	−	9.40456i	−0.603530	−	0.438490i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	4.85410	+	3.52671i	0.225346	+	0.163723i
$465$	−4.94427	+	15.2169i	−0.229285	+	0.705667i
$466$	9.27051	+	28.5317i	0.429448	+	1.32171i
$467$	9.70820	−	7.05342i	0.449242	−	0.326393i	−0.340054	−	0.940406i	$-0.610445\pi$
$467$	9.70820	−	7.05342i	0.449242	−	0.326393i	0.789296	+	0.614012i	$0.210445\pi$
$468$	1.61803	−	1.17557i	0.0747936	−	0.0543408i
$469$	4.94427	+	15.2169i	0.228305	+	0.702651i
$470$	4.94427	−	15.2169i	0.228062	−	0.701903i
$471$	11.3262	+	8.22899i	0.521885	+	0.379172i
$472$	−12.0000			−0.552345
$473$		0			0
$474$	4.00000			0.183726
$475$		0			0
$476$	2.47214	−	7.60845i	0.113310	−	0.348733i
$477$	1.85410	+	5.70634i	0.0848935	+	0.261275i
$478$	−19.4164	+	14.1068i	−0.888086	+	0.645232i
$479$	6.47214	−	4.70228i	0.295719	−	0.214853i	−0.430025	−	0.902817i	$-0.641495\pi$
$479$	6.47214	−	4.70228i	0.295719	−	0.214853i	0.725745	+	0.687964i	$0.241495\pi$
$480$	−3.09017	−	9.51057i	−0.141046	−	0.434096i
$481$	3.70820	−	11.4127i	0.169080	−	0.520373i
$482$	−8.09017	−	5.87785i	−0.368497	−	0.267729i
$483$	32.0000			1.45605
$484$		0			0
$485$	−4.00000			−0.181631
$486$	−0.809017	−	0.587785i	−0.0366978	−	0.0266625i
$487$	−4.94427	+	15.2169i	−0.224046	+	0.689544i	0.774341	+	0.632769i	$0.218082\pi$
$487$	−4.94427	+	15.2169i	−0.224046	+	0.689544i	−0.998387	+	0.0567748i	$0.981918\pi$
$488$	−5.56231	−	17.1190i	−0.251794	−	0.774942i
$489$	3.23607	−	2.35114i	0.146340	−	0.106322i
$490$	−14.5623	+	10.5801i	−0.657858	+	0.477962i
$491$	−1.23607	−	3.80423i	−0.0557830	−	0.171682i	0.919283	−	0.393597i	$-0.128769\pi$
$491$	−1.23607	−	3.80423i	−0.0557830	−	0.171682i	−0.975066	+	0.221915i	$0.928769\pi$
$492$	0.618034	−	1.90211i	0.0278631	−	0.0857539i
$493$	−9.70820	−	7.05342i	−0.437236	−	0.317670i
$494$		0			0
$495$		0			0
$496$	8.00000			0.359211
$497$		0			0
$498$	−3.70820	+	11.4127i	−0.166169	+	0.511414i
$499$	−1.23607	−	3.80423i	−0.0553340	−	0.170301i	0.919570	−	0.392926i	$-0.128537\pi$
$499$	−1.23607	−	3.80423i	−0.0553340	−	0.170301i	−0.974904	+	0.222626i	$0.928537\pi$
$500$	9.70820	−	7.05342i	0.434164	−	0.315439i
$501$		0			0
$502$	−1.23607	−	3.80423i	−0.0551684	−	0.169791i
$503$	9.88854	−	30.4338i	0.440908	−	1.35698i	−0.446001	−	0.895033i	$-0.647152\pi$
$503$	9.88854	−	30.4338i	0.440908	−	1.35698i	0.886909	−	0.461944i	$-0.152848\pi$
$504$	9.70820	+	7.05342i	0.432438	+	0.314184i
$505$	4.00000			0.177998
$506$		0			0
$507$	9.00000			0.399704
$508$	3.23607	+	2.35114i	0.143577	+	0.104315i
$509$	9.27051	−	28.5317i	0.410908	−	1.26465i	−0.504952	−	0.863147i	$-0.668490\pi$
$509$	9.27051	−	28.5317i	0.410908	−	1.26465i	0.915860	−	0.401498i	$-0.131510\pi$
$510$	−1.23607	−	3.80423i	−0.0547340	−	0.168454i
$511$	45.3050	−	32.9160i	2.00417	−	1.45612i
$512$	−8.89919	+	6.46564i	−0.393292	+	0.285744i
$513$		0			0
$514$	4.32624	−	13.3148i	0.190822	−	0.587290i
$515$	12.9443	+	9.40456i	0.570393	+	0.414415i
$516$		0			0
$517$		0			0
$518$	24.0000			1.05450
$519$	4.85410	+	3.52671i	0.213071	+	0.154805i
$520$	−3.70820	+	11.4127i	−0.162615	+	0.500479i
$521$	−9.27051	−	28.5317i	−0.406148	−	1.25000i	−0.919933	−	0.392077i	$-0.871757\pi$
$521$	−9.27051	−	28.5317i	−0.406148	−	1.25000i	0.513784	−	0.857920i	$-0.328243\pi$
$522$	4.85410	−	3.52671i	0.212458	−	0.154360i
$523$	−12.9443	+	9.40456i	−0.566013	+	0.411233i	−0.833655	−	0.552286i	$-0.813756\pi$
$523$	−12.9443	+	9.40456i	−0.566013	+	0.411233i	0.267641	+	0.963519i	$0.413756\pi$
$524$	−3.70820	−	11.4127i	−0.161994	−	0.498565i
$525$	−1.23607	+	3.80423i	−0.0539464	+	0.166030i
$526$	12.9443	+	9.40456i	0.564397	+	0.410058i
$527$	−16.0000			−0.696971
$528$		0			0
$529$	41.0000			1.78261
$530$	−9.70820	−	7.05342i	−0.421697	−	0.306381i
$531$	−1.23607	+	3.80423i	−0.0536408	+	0.165089i
$532$		0			0
$533$	−3.23607	+	2.35114i	−0.140170	+	0.101839i
$534$	4.85410	−	3.52671i	0.210058	−	0.152616i
$535$	−7.41641	−	22.8254i	−0.320639	−	0.986826i
$536$	−3.70820	+	11.4127i	−0.160170	+	0.492953i
$537$	9.70820	+	7.05342i	0.418940	+	0.304378i
$538$	2.00000			0.0862261
$539$		0			0
$540$	−2.00000			−0.0860663
$541$	37.2148	+	27.0381i	1.59999	+	1.16246i	0.887535	+	0.460740i	$0.152416\pi$
$541$	37.2148	+	27.0381i	1.59999	+	1.16246i	0.712453	+	0.701719i	$0.247584\pi$
$542$	6.18034	−	19.0211i	0.265468	−	0.817028i
$543$	−6.79837	−	20.9232i	−0.291746	−	0.897902i
$544$	8.09017	−	5.87785i	0.346863	−	0.252011i
$545$	3.23607	−	2.35114i	0.138618	−	0.100712i
$546$	−2.47214	−	7.60845i	−0.105798	−	0.325612i
$547$	−2.47214	+	7.60845i	−0.105701	+	0.325314i	−0.989894	−	0.141807i	$-0.954709\pi$
$547$	−2.47214	+	7.60845i	−0.105701	+	0.325314i	0.884193	+	0.467121i	$0.154709\pi$
$548$	1.61803	+	1.17557i	0.0691190	+	0.0502179i
$549$	−6.00000			−0.256074
$550$		0			0
$551$		0			0
$552$	19.4164	+	14.1068i	0.826417	+	0.600427i
$553$	−4.94427	+	15.2169i	−0.210252	+	0.647089i
$554$	−8.03444	−	24.7275i	−0.341351	−	1.05057i
$555$	−9.70820	+	7.05342i	−0.412090	+	0.299401i
$556$	6.47214	−	4.70228i	0.274480	−	0.199421i
$557$	4.32624	+	13.3148i	0.183309	+	0.564166i	0.999915	−	0.0130289i	$-0.00414735\pi$
$557$	4.32624	+	13.3148i	0.183309	+	0.564166i	−0.816607	+	0.577195i	$0.804147\pi$
$558$	2.47214	−	7.60845i	0.104654	−	0.322091i
$559$		0			0
$560$	−8.00000			−0.338062
$561$		0			0
$562$	−18.0000			−0.759284
$563$	−35.5967	−	25.8626i	−1.50022	−	1.08998i	−0.970292	−	0.241936i	$-0.922217\pi$
$563$	−35.5967	−	25.8626i	−1.50022	−	1.08998i	−0.529932	−	0.848040i	$-0.677783\pi$
$564$	2.47214	−	7.60845i	0.104096	−	0.320374i
$565$	3.70820	+	11.4127i	0.156005	+	0.480135i
$566$	−12.9443	+	9.40456i	−0.544088	+	0.395303i
$567$	3.23607	−	2.35114i	0.135902	−	0.0987386i
$568$		0			0
$569$	12.9787	−	39.9444i	0.544096	−	1.67456i	−0.179034	−	0.983843i	$-0.557297\pi$
$569$	12.9787	−	39.9444i	0.544096	−	1.67456i	0.723130	−	0.690712i	$-0.242703\pi$
$570$		0			0
$571$	16.0000			0.669579			0.334790	−	0.942293i	$-0.391335\pi$
$571$	16.0000			0.669579			0.334790	+	0.942293i	$0.391335\pi$
$572$		0			0
$573$	−8.00000			−0.334205
$574$	−6.47214	−	4.70228i	−0.270142	−	0.196269i
$575$	−2.47214	+	7.60845i	−0.103095	+	0.317294i
$576$	2.16312	+	6.65740i	0.0901300	+	0.277391i
$577$	24.2705	−	17.6336i	1.01039	−	0.734095i	0.0461028	−	0.998937i	$-0.485320\pi$
$577$	24.2705	−	17.6336i	1.01039	−	0.734095i	0.964292	+	0.264842i	$0.0853198\pi$
$578$	−10.5172	+	7.64121i	−0.437459	+	0.317832i
$579$	−4.32624	−	13.3148i	−0.179792	−	0.553344i
$580$	3.70820	−	11.4127i	0.153975	−	0.473886i
$581$	−38.8328	−	28.2137i	−1.61106	−	1.17050i
$582$	2.00000			0.0829027
$583$		0			0
$584$	42.0000			1.73797
$585$	3.23607	+	2.35114i	0.133795	+	0.0972077i
$586$	−1.85410	+	5.70634i	−0.0765922	+	0.235727i
$587$	8.65248	+	26.6296i	0.357126	+	1.09912i	0.954767	+	0.297356i	$0.0961050\pi$
$587$	8.65248	+	26.6296i	0.357126	+	1.09912i	−0.597641	+	0.801764i	$0.703895\pi$
$588$	−7.28115	+	5.29007i	−0.300270	+	0.218159i
$589$		0			0
$590$	−2.47214	−	7.60845i	−0.101776	−	0.313235i
$591$	−4.32624	+	13.3148i	−0.177958	+	0.547697i
$592$	4.85410	+	3.52671i	0.199502	+	0.144947i
$593$	−38.0000			−1.56047			−0.780236	−	0.625485i	$-0.784901\pi$
$593$	−38.0000			−1.56047			−0.780236	+	0.625485i	$0.784901\pi$
$594$		0			0
$595$	16.0000			0.655936
$596$	17.7984	+	12.9313i	0.729050	+	0.529686i
$597$		0			0
$598$	−4.94427	−	15.2169i	−0.202186	−	0.622265i
$599$	6.47214	−	4.70228i	0.264444	−	0.192130i	−0.447660	−	0.894204i	$-0.647742\pi$
$599$	6.47214	−	4.70228i	0.264444	−	0.192130i	0.712104	+	0.702074i	$0.247742\pi$
$600$	−2.42705	+	1.76336i	−0.0990839	+	0.0719887i
$601$	−8.03444	−	24.7275i	−0.327732	−	1.00865i	−0.970192	−	0.242336i	$-0.922086\pi$
$601$	−8.03444	−	24.7275i	−0.327732	−	1.00865i	0.642461	−	0.766319i	$-0.277914\pi$
$602$		0			0
$603$	3.23607	+	2.35114i	0.131783	+	0.0957459i
$604$	20.0000			0.813788
$605$		0			0
$606$	−2.00000			−0.0812444
$607$	−3.23607	−	2.35114i	−0.131348	−	0.0954299i	0.520171	−	0.854062i	$-0.325868\pi$
$607$	−3.23607	−	2.35114i	−0.131348	−	0.0954299i	−0.651519	+	0.758632i	$0.725868\pi$
$608$		0			0
$609$	7.41641	+	22.8254i	0.300528	+	0.924930i
$610$	9.70820	−	7.05342i	0.393074	−	0.285585i
$611$	−12.9443	+	9.40456i	−0.523669	+	0.380468i
$612$	−0.618034	−	1.90211i	−0.0249825	−	0.0768884i
$613$	−4.32624	+	13.3148i	−0.174735	+	0.537779i	−0.999621	−	0.0275195i	$-0.991239\pi$
$613$	−4.32624	+	13.3148i	−0.174735	+	0.537779i	0.824886	+	0.565299i	$0.191239\pi$
$614$	−25.8885	−	18.8091i	−1.04478	−	0.759075i
$615$	4.00000			0.161296
$616$		0			0
$617$	−30.0000			−1.20775			−0.603877	−	0.797077i	$-0.706378\pi$
$617$	−30.0000			−1.20775			−0.603877	+	0.797077i	$0.706378\pi$
$618$	−6.47214	−	4.70228i	−0.260347	−	0.189154i
$619$	13.5967	−	41.8465i	0.546499	−	1.68195i	−0.170898	−	0.985289i	$-0.554667\pi$
$619$	13.5967	−	41.8465i	0.546499	−	1.68195i	0.717398	−	0.696664i	$-0.245333\pi$
$620$	−4.94427	−	15.2169i	−0.198567	−	0.611126i
$621$	6.47214	−	4.70228i	0.259718	−	0.188696i
$622$	−19.4164	+	14.1068i	−0.778527	+	0.565633i
$623$	7.41641	+	22.8254i	0.297132	+	0.914479i
$624$	0.618034	−	1.90211i	0.0247412	−	0.0761455i
$625$	15.3713	+	11.1679i	0.614853	+	0.446717i
$626$	22.0000			0.879297
$627$		0			0
$628$	−14.0000			−0.558661
$629$	−9.70820	−	7.05342i	−0.387091	−	0.281238i
$630$	−2.47214	+	7.60845i	−0.0984923	+	0.303128i
$631$	4.94427	+	15.2169i	0.196828	+	0.605775i	0.999950	+	0.00996082i	$0.00317068\pi$
$631$	4.94427	+	15.2169i	0.196828	+	0.605775i	−0.803122	+	0.595815i	$0.796829\pi$
$632$	−9.70820	+	7.05342i	−0.386172	+	0.280570i
$633$		0			0
$634$	−6.79837	−	20.9232i	−0.269998	−	0.830968i
$635$	−2.47214	+	7.60845i	−0.0981037	+	0.301932i
$636$	−4.85410	−	3.52671i	−0.192478	−	0.139843i
$637$	18.0000			0.713186
$638$		0			0
$639$		0			0
$640$	4.85410	+	3.52671i	0.191875	+	0.139406i
$641$	5.56231	−	17.1190i	0.219698	−	0.676161i	−0.779089	−	0.626914i	$-0.784318\pi$
$641$	5.56231	−	17.1190i	0.219698	−	0.676161i	0.998787	−	0.0492469i	$-0.0156821\pi$
$642$	3.70820	+	11.4127i	0.146351	+	0.450422i
$643$	−16.1803	+	11.7557i	−0.638090	+	0.463600i	−0.859194	−	0.511651i	$-0.829034\pi$
$643$	−16.1803	+	11.7557i	−0.638090	+	0.463600i	0.221103	+	0.975250i	$0.429034\pi$
$644$	−25.8885	+	18.8091i	−1.02015	+	0.741183i
$645$		0			0
$646$		0			0
$647$	−6.47214	−	4.70228i	−0.254446	−	0.184866i	0.453249	−	0.891384i	$-0.350265\pi$
$647$	−6.47214	−	4.70228i	−0.254446	−	0.184866i	−0.707695	+	0.706518i	$0.750265\pi$
$648$	3.00000			0.117851
$649$		0			0
$650$	2.00000			0.0784465
$651$	25.8885	+	18.8091i	1.01465	+	0.737188i
$652$	−1.23607	+	3.80423i	−0.0484082	+	0.148985i
$653$	−0.618034	−	1.90211i	−0.0241855	−	0.0744354i	0.938235	−	0.345998i	$-0.112460\pi$
$653$	−0.618034	−	1.90211i	−0.0241855	−	0.0744354i	−0.962421	+	0.271563i	$0.912460\pi$
$654$	−1.61803	+	1.17557i	−0.0632701	+	0.0459684i
$655$	19.4164	−	14.1068i	0.758662	−	0.551200i
$656$	−0.618034	−	1.90211i	−0.0241302	−	0.0742650i
$657$	4.32624	−	13.3148i	0.168783	−	0.519459i
$658$	−25.8885	−	18.8091i	−1.00924	−	0.733256i
$659$	−4.00000			−0.155818			−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000			−0.155818			−0.0779089	+	0.996960i	$0.524824\pi$
$660$		0			0
$661$	−26.0000			−1.01128			−0.505641	−	0.862744i	$-0.668744\pi$
$661$	−26.0000			−1.01128			−0.505641	+	0.862744i	$0.668744\pi$
$662$	−16.1803	−	11.7557i	−0.628867	−	0.456898i
$663$	−1.23607	+	3.80423i	−0.0480049	+	0.147744i
$664$	−11.1246	−	34.2380i	−0.431719	−	1.32869i
$665$		0			0
$666$	4.85410	−	3.52671i	0.188093	−	0.136657i
$667$	14.8328	+	45.6507i	0.574329	+	1.76760i
$668$		0			0
$669$	12.9443	+	9.40456i	0.500454	+	0.363601i
$670$	−8.00000			−0.309067
$671$		0			0
$672$	−20.0000			−0.771517
$673$	−37.2148	−	27.0381i	−1.43452	−	1.04224i	−0.989152	−	0.146898i	$-0.953071\pi$
$673$	−37.2148	−	27.0381i	−1.43452	−	1.04224i	−0.445373	−	0.895345i	$-0.646929\pi$
$674$	−6.79837	+	20.9232i	−0.261864	+	0.805933i
$675$	0.309017	+	0.951057i	0.0118941	+	0.0366062i
$676$	−7.28115	+	5.29007i	−0.280044	+	0.203464i
$677$	14.5623	−	10.5801i	0.559675	−	0.406628i	−0.271665	−	0.962392i	$-0.587574\pi$
$677$	14.5623	−	10.5801i	0.559675	−	0.406628i	0.831340	+	0.555764i	$0.187574\pi$
$678$	−1.85410	−	5.70634i	−0.0712064	−	0.219151i
$679$	−2.47214	+	7.60845i	−0.0948719	+	0.291986i
$680$	9.70820	+	7.05342i	0.372293	+	0.270486i
$681$	12.0000			0.459841
$682$		0			0
$683$	20.0000			0.765279			0.382639	−	0.923898i	$-0.375015\pi$
$683$	20.0000			0.765279			0.382639	+	0.923898i	$0.375015\pi$
$684$		0			0
$685$	−1.23607	+	3.80423i	−0.0472277	+	0.145352i
$686$	2.47214	+	7.60845i	0.0943866	+	0.290492i
$687$	4.85410	−	3.52671i	0.185196	−	0.134552i
$688$		0			0
$689$	3.70820	+	11.4127i	0.141271	+	0.434788i
$690$	−4.94427	+	15.2169i	−0.188225	+	0.579298i
$691$	22.6525	+	16.4580i	0.861741	+	0.626091i	0.928358	−	0.371687i	$-0.121221\pi$
$691$	22.6525	+	16.4580i	0.861741	+	0.626091i	−0.0666172	+	0.997779i	$0.521221\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	4.00000			0.151838
$695$	12.9443	+	9.40456i	0.491004	+	0.356735i
$696$	−5.56231	+	17.1190i	−0.210839	+	0.648895i
$697$	1.23607	+	3.80423i	0.0468194	+	0.144095i
$698$	−4.85410	+	3.52671i	−0.183730	+	0.133488i
$699$	−24.2705	+	17.6336i	−0.917995	+	0.666962i
$700$	−1.23607	−	3.80423i	−0.0467190	−	0.143786i
$701$	−15.4508	+	47.5528i	−0.583571	+	1.79605i	0.0213660	+	0.999772i	$0.493198\pi$
$701$	−15.4508	+	47.5528i	−0.583571	+	1.79605i	−0.604936	+	0.796274i	$0.706802\pi$
$702$	−1.61803	−	1.17557i	−0.0610688	−	0.0443690i
$703$		0			0
$704$		0			0
$705$	16.0000			0.602595
$706$	14.5623	+	10.5801i	0.548060	+	0.398189i
$707$	2.47214	−	7.60845i	0.0929742	−	0.286145i
$708$	−1.23607	−	3.80423i	−0.0464543	−	0.142972i
$709$	−30.7426	+	22.3358i	−1.15456	+	0.838840i	−0.989081	−	0.147373i	$-0.952918\pi$
$709$	−30.7426	+	22.3358i	−1.15456	+	0.838840i	−0.165483	+	0.986213i	$0.552918\pi$
$710$		0			0
$711$	1.23607	+	3.80423i	0.0463562	+	0.142670i
$712$	−5.56231	+	17.1190i	−0.208456	+	0.641562i
$713$	51.7771	+	37.6183i	1.93907	+	1.40881i
$714$	−8.00000			−0.299392
$715$		0			0
$716$	−12.0000			−0.448461
$717$	−19.4164	−	14.1068i	−0.725119	−	0.526830i
$718$	−2.47214	+	7.60845i	−0.0922593	+	0.283945i
$719$	7.41641	+	22.8254i	0.276585	+	0.851242i	0.988796	+	0.149276i	$0.0476943\pi$
$719$	7.41641	+	22.8254i	0.276585	+	0.851242i	−0.712210	+	0.701966i	$0.752306\pi$
$720$	−1.61803	+	1.17557i	−0.0603006	+	0.0438109i
$721$	25.8885	−	18.8091i	0.964140	−	0.700489i
$722$	5.87132	+	18.0701i	0.218508	+	0.672499i
$723$	3.09017	−	9.51057i	0.114925	−	0.353702i
$724$	17.7984	+	12.9313i	0.661471	+	0.480587i
$725$	−6.00000			−0.222834
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	19.4164	+	14.1068i	0.719620	+	0.522834i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	8.65248	+	26.6296i	0.320242	+	0.985605i
$731$		0			0
$732$	4.85410	−	3.52671i	0.179413	−	0.130351i
$733$	−9.27051	−	28.5317i	−0.342414	−	1.05384i	−0.962954	−	0.269667i	$-0.913086\pi$
$733$	−9.27051	−	28.5317i	−0.342414	−	1.05384i	0.620540	−	0.784175i	$-0.286914\pi$
$734$	9.88854	−	30.4338i	0.364993	−	1.12333i
$735$	−14.5623	−	10.5801i	−0.537139	−	0.390254i
$736$	−40.0000			−1.47442
$737$		0			0
$738$	−2.00000			−0.0736210
$739$	6.47214	+	4.70228i	0.238081	+	0.172976i	0.700428	−	0.713723i	$-0.252992\pi$
$739$	6.47214	+	4.70228i	0.238081	+	0.172976i	−0.462347	+	0.886699i	$0.652992\pi$
$740$	3.70820	−	11.4127i	0.136316	−	0.419538i
$741$		0			0
$742$	−19.4164	+	14.1068i	−0.712799	+	0.517879i
$743$	32.3607	−	23.5114i	1.18720	−	0.862550i	0.194233	−	0.980955i	$-0.437778\pi$
$743$	32.3607	−	23.5114i	1.18720	−	0.862550i	0.992965	+	0.118405i	$0.0377783\pi$
$744$	7.41641	+	22.8254i	0.271899	+	0.836818i
$745$	−13.5967	+	41.8465i	−0.498146	+	1.53314i
$746$	1.61803	+	1.17557i	0.0592404	+	0.0430407i
$747$	−12.0000			−0.439057
$748$		0			0
$749$	−48.0000			−1.75388
$750$	−9.70820	−	7.05342i	−0.354493	−	0.257555i
$751$	−2.47214	+	7.60845i	−0.0902095	+	0.277636i	−0.985976	−	0.166889i	$-0.946628\pi$
$751$	−2.47214	+	7.60845i	−0.0902095	+	0.277636i	0.895766	+	0.444526i	$0.146628\pi$
$752$	−2.47214	−	7.60845i	−0.0901495	−	0.277452i
$753$	3.23607	−	2.35114i	0.117929	−	0.0856803i
$754$	9.70820	−	7.05342i	0.353552	−	0.256871i
$755$	12.3607	+	38.0423i	0.449851	+	1.38450i
$756$	−1.23607	+	3.80423i	−0.0449554	+	0.138358i
$757$	8.09017	+	5.87785i	0.294042	+	0.213634i	0.725019	−	0.688729i	$-0.241831\pi$
$757$	8.09017	+	5.87785i	0.294042	+	0.213634i	−0.430977	+	0.902363i	$0.641831\pi$
$758$	−28.0000			−1.01701
$759$		0			0
$760$		0			0
$761$	4.85410	+	3.52671i	0.175961	+	0.127843i	0.672280	−	0.740297i	$-0.265315\pi$
$761$	4.85410	+	3.52671i	0.175961	+	0.127843i	−0.496319	+	0.868140i	$0.665315\pi$
$762$	1.23607	−	3.80423i	0.0447780	−	0.137813i
$763$	−2.47214	−	7.60845i	−0.0894973	−	0.275444i
$764$	6.47214	−	4.70228i	0.234154	−	0.170123i
$765$	3.23607	−	2.35114i	0.117000	−	0.0850057i
$766$	4.94427	+	15.2169i	0.178644	+	0.549809i
$767$	−2.47214	+	7.60845i	−0.0892637	+	0.274725i
$768$	−13.7533	−	9.99235i	−0.496279	−	0.360568i
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$	14.0000			0.504198
$772$	11.3262	+	8.22899i	0.407640	+	0.296168i
$773$	1.85410	−	5.70634i	0.0666874	−	0.205243i	−0.912160	−	0.409834i	$-0.865587\pi$
$773$	1.85410	−	5.70634i	0.0666874	−	0.205243i	0.978847	+	0.204591i	$0.0655866\pi$
$774$		0			0
$775$	−6.47214	+	4.70228i	−0.232486	+	0.168911i
$776$	−4.85410	+	3.52671i	−0.174252	+	0.126602i
$777$	7.41641	+	22.8254i	0.266062	+	0.818855i
$778$	5.56231	−	17.1190i	0.199418	−	0.613747i
$779$		0			0
$780$	−4.00000			−0.143223
$781$		0			0
$782$	−16.0000			−0.572159
$783$	4.85410	+	3.52671i	0.173471	+	0.126034i
$784$	−2.78115	+	8.55951i	−0.0993269	+	0.305697i
$785$	−8.65248	−	26.6296i	−0.308820	−	0.950451i
$786$	−9.70820	+	7.05342i	−0.346280	+	0.251587i
$787$	−6.47214	+	4.70228i	−0.230707	+	0.167618i	−0.697133	−	0.716942i	$-0.745541\pi$
$787$	−6.47214	+	4.70228i	−0.230707	+	0.167618i	0.466426	+	0.884560i	$0.345541\pi$
$788$	−4.32624	−	13.3148i	−0.154116	−	0.474320i
$789$	−4.94427	+	15.2169i	−0.176021	+	0.541736i
$790$	−6.47214	−	4.70228i	−0.230268	−	0.167300i
$791$	24.0000			0.853342
$792$		0			0
$793$	−12.0000			−0.426132
$794$	−1.61803	−	1.17557i	−0.0574219	−	0.0417194i
$795$	3.70820	−	11.4127i	0.131516	−	0.404766i
$796$		0			0
$797$	8.09017	−	5.87785i	0.286569	−	0.208204i	−0.435209	−	0.900330i	$-0.643325\pi$
$797$	8.09017	−	5.87785i	0.286569	−	0.208204i	0.721777	+	0.692125i	$0.243325\pi$
$798$		0			0
$799$	4.94427	+	15.2169i	0.174916	+	0.538335i
$800$	1.54508	−	4.75528i	0.0546270	−	0.168125i
$801$	4.85410	+	3.52671i	0.171511	+	0.124610i
$802$	−26.0000			−0.918092
$803$		0			0
$804$	−4.00000			−0.141069
$805$	−51.7771	−	37.6183i	−1.82490	−	1.32587i
$806$	4.94427	−	15.2169i	0.174155	−	0.535993i
$807$	0.618034	+	1.90211i	0.0217558	+	0.0669575i
$808$	4.85410	−	3.52671i	0.170767	−	0.124069i
$809$	43.6869	−	31.7404i	1.53595	−	1.11593i	0.583138	−	0.812373i	$-0.301825\pi$
$809$	43.6869	−	31.7404i	1.53595	−	1.11593i	0.952812	−	0.303560i	$-0.0981753\pi$
$810$	0.618034	+	1.90211i	0.0217155	+	0.0668334i
$811$	17.3050	−	53.2592i	0.607659	−	1.87018i	0.130298	−	0.991475i	$-0.458407\pi$
$811$	17.3050	−	53.2592i	0.607659	−	1.87018i	0.477361	−	0.878707i	$-0.341593\pi$
$812$	−19.4164	−	14.1068i	−0.681382	−	0.495053i
$813$	20.0000			0.701431
$814$		0			0
$815$	−8.00000			−0.280228
$816$	−1.61803	−	1.17557i	−0.0566425	−	0.0411532i
$817$		0			0
$818$	5.56231	+	17.1190i	0.194481	+	0.598552i
$819$	6.47214	−	4.70228i	0.226155	−	0.164311i
$820$	−3.23607	+	2.35114i	−0.113008	+	0.0821054i
$821$	4.32624	+	13.3148i	0.150987	+	0.464689i	0.997732	−	0.0673088i	$-0.0214413\pi$
$821$	4.32624	+	13.3148i	0.150987	+	0.464689i	−0.846745	+	0.531998i	$0.821441\pi$
$822$	0.618034	−	1.90211i	0.0215564	−	0.0663438i
$823$	−19.4164	−	14.1068i	−0.676813	−	0.491734i	0.195486	−	0.980707i	$-0.437372\pi$
$823$	−19.4164	−	14.1068i	−0.676813	−	0.491734i	−0.872299	+	0.488973i	$0.837372\pi$
$824$	24.0000			0.836080
$825$		0			0
$826$	−16.0000			−0.556711
$827$	16.1803	+	11.7557i	0.562646	+	0.408786i	0.832426	−	0.554136i	$-0.186951\pi$
$827$	16.1803	+	11.7557i	0.562646	+	0.408786i	−0.269781	+	0.962922i	$0.586951\pi$
$828$	−2.47214	+	7.60845i	−0.0859127	+	0.264412i
$829$	−0.618034	−	1.90211i	−0.0214652	−	0.0660631i	0.939750	−	0.341862i	$-0.111058\pi$
$829$	−0.618034	−	1.90211i	−0.0214652	−	0.0660631i	−0.961215	+	0.275799i	$0.911058\pi$
$830$	19.4164	−	14.1068i	0.673953	−	0.489656i
$831$	21.0344	−	15.2824i	0.729677	−	0.530141i
$832$	4.32624	+	13.3148i	0.149985	+	0.461607i
$833$	5.56231	−	17.1190i	0.192722	−	0.593139i
$834$	−6.47214	−	4.70228i	−0.224112	−	0.162827i
$835$		0			0
$836$		0			0
$837$	8.00000			0.276520
$838$	−3.23607	−	2.35114i	−0.111788	−	0.0812188i
$839$	−17.3050	+	53.2592i	−0.597433	+	1.83871i	−0.0552123	+	0.998475i	$0.517584\pi$
$839$	−17.3050	+	53.2592i	−0.597433	+	1.83871i	−0.542221	+	0.840236i	$0.682416\pi$
$840$	−7.41641	−	22.8254i	−0.255890	−	0.787550i
$841$	−5.66312	+	4.11450i	−0.195280	+	0.141879i
$842$	−21.0344	+	15.2824i	−0.724895	+	0.526667i
$843$	−5.56231	−	17.1190i	−0.191576	−	0.589610i
$844$		0			0
$845$	−14.5623	−	10.5801i	−0.500959	−	0.363968i
$846$	−8.00000			−0.275046
$847$		0			0
$848$	−6.00000			−0.206041
$849$	−12.9443	−	9.40456i	−0.444246	−	0.322764i
$850$	0.618034	−	1.90211i	0.0211984	−	0.0652419i
$851$	14.8328	+	45.6507i	0.508462	+	1.56489i
$852$		0			0
$853$	−27.5066	+	19.9847i	−0.941807	+	0.684263i	−0.948855	−	0.315712i	$-0.897757\pi$
$853$	−27.5066	+	19.9847i	−0.941807	+	0.684263i	0.00704774	+	0.999975i	$0.497757\pi$
$854$	−7.41641	−	22.8254i	−0.253784	−	0.781068i
$855$		0			0
$856$	−29.1246	−	21.1603i	−0.995459	−	0.723243i
$857$	10.0000			0.341593			0.170797	−	0.985306i	$-0.445366\pi$
$857$	10.0000			0.341593			0.170797	+	0.985306i	$0.445366\pi$
$858$		0			0
$859$	−36.0000			−1.22830			−0.614152	−	0.789188i	$-0.710502\pi$
$859$	−36.0000			−1.22830			−0.614152	+	0.789188i	$0.710502\pi$
$860$		0			0
$861$	2.47214	−	7.60845i	0.0842502	−	0.259295i
$862$	−7.41641	−	22.8254i	−0.252604	−	0.777435i
$863$	−38.8328	+	28.2137i	−1.32188	+	0.960405i	−0.321978	+	0.946747i	$0.604348\pi$
$863$	−38.8328	+	28.2137i	−1.32188	+	0.960405i	−0.999907	+	0.0136580i	$0.995652\pi$
$864$	−4.04508	+	2.93893i	−0.137617	+	0.0999843i
$865$	−3.70820	−	11.4127i	−0.126083	−	0.388043i
$866$	−10.5066	+	32.3359i	−0.357028	+	1.09882i
$867$	−10.5172	−	7.64121i	−0.357184	−	0.259509i
$868$	−32.0000			−1.08615
$869$		0			0
$870$	−12.0000			−0.406838
$871$	6.47214	+	4.70228i	0.219300	+	0.159331i
$872$	1.85410	−	5.70634i	0.0627878	−	0.193241i
$873$	0.618034	+	1.90211i	0.0209173	+	0.0643768i
$874$		0			0
$875$	38.8328	−	28.2137i	1.31279	−	0.953797i
$876$	4.32624	+	13.3148i	0.146170	+	0.449865i
$877$	−1.85410	+	5.70634i	−0.0626086	+	0.192689i	−0.977468	−	0.211083i	$-0.932301\pi$
$877$	−1.85410	+	5.70634i	−0.0626086	+	0.192689i	0.914860	+	0.403772i	$0.132301\pi$
$878$	16.1803	+	11.7557i	0.546060	+	0.396736i
$879$	−6.00000			−0.202375
$880$		0			0
$881$	26.0000			0.875962			0.437981	−	0.898984i	$-0.355694\pi$
$881$	26.0000			0.875962			0.437981	+	0.898984i	$0.355694\pi$
$882$	7.28115	+	5.29007i	0.245169	+	0.178126i
$883$	−6.18034	+	19.0211i	−0.207985	+	0.640112i	0.791593	+	0.611049i	$0.209252\pi$
$883$	−6.18034	+	19.0211i	−0.207985	+	0.640112i	−0.999578	+	0.0290628i	$0.990748\pi$
$884$	−1.23607	−	3.80423i	−0.0415735	−	0.127950i
$885$	6.47214	−	4.70228i	0.217558	−	0.158065i
$886$	22.6525	−	16.4580i	0.761025	−	0.552917i
$887$	−2.47214	−	7.60845i	−0.0830062	−	0.255467i	0.900937	−	0.433951i	$-0.142881\pi$
$887$	−2.47214	−	7.60845i	−0.0830062	−	0.255467i	−0.983943	+	0.178484i	$0.942881\pi$
$888$	−5.56231	+	17.1190i	−0.186659	+	0.574477i
$889$	12.9443	+	9.40456i	0.434137	+	0.315419i
$890$	−12.0000			−0.402241
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$	6.79837	−	20.9232i	0.227372	−	0.699778i
$895$	−7.41641	−	22.8254i	−0.247903	−	0.762968i
$896$	9.70820	−	7.05342i	0.324328	−	0.235638i
$897$	12.9443	−	9.40456i	0.432197	−	0.314009i
$898$	−0.618034	−	1.90211i	−0.0206241	−	0.0634743i
$899$	−14.8328	+	45.6507i	−0.494702	+	1.52254i
$900$	−0.809017	−	0.587785i	−0.0269672	−	0.0195928i
$901$	12.0000			0.399778
$902$		0			0
$903$		0			0
$904$	14.5623	+	10.5801i	0.484335	+	0.351890i
$905$	−13.5967	+	41.8465i	−0.451971	+	1.39102i
$906$	−6.18034	−	19.0211i	−0.205328	−	0.631935i
$907$	−9.70820	+	7.05342i	−0.322356	+	0.234205i	−0.737180	−	0.675696i	$-0.763843\pi$
$907$	−9.70820	+	7.05342i	−0.322356	+	0.234205i	0.414824	+	0.909902i	$0.363843\pi$
$908$	−9.70820	+	7.05342i	−0.322178	+	0.234076i
$909$	−0.618034	−	1.90211i	−0.0204989	−	0.0630891i
$910$	−4.94427	+	15.2169i	−0.163901	+	0.504435i
$911$	−19.4164	−	14.1068i	−0.643294	−	0.467381i	0.217686	−	0.976019i	$-0.430149\pi$
$911$	−19.4164	−	14.1068i	−0.643294	−	0.467381i	−0.860980	+	0.508638i	$0.830149\pi$
$912$		0			0
$913$		0			0
$914$	18.0000			0.595387
$915$	9.70820	+	7.05342i	0.320943	+	0.233179i
$916$	−1.85410	+	5.70634i	−0.0612613	+	0.188543i
$917$	−14.8328	−	45.6507i	−0.489823	−	1.50752i
$918$	−1.61803	+	1.17557i	−0.0534031	+	0.0387996i
$919$	−16.1803	+	11.7557i	−0.533740	+	0.387785i	−0.821755	−	0.569841i	$-0.807005\pi$
$919$	−16.1803	+	11.7557i	−0.533740	+	0.387785i	0.288015	+	0.957626i	$0.407005\pi$
$920$	−14.8328	−	45.6507i	−0.489023	−	1.50506i
$921$	9.88854	−	30.4338i	0.325839	−	1.00283i
$922$	24.2705	+	17.6336i	0.799307	+	0.580730i
$923$		0			0
$924$		0			0
$925$	−6.00000			−0.197279
$926$	12.9443	+	9.40456i	0.425375	+	0.309053i
$927$	2.47214	−	7.60845i	0.0811956	−	0.249894i
$928$	−9.27051	−	28.5317i	−0.304319	−	0.936599i
$929$	4.85410	−	3.52671i	0.159258	−	0.115708i	−0.505302	−	0.862942i	$-0.668619\pi$
$929$	4.85410	−	3.52671i	0.159258	−	0.115708i	0.664560	+	0.747235i	$0.268619\pi$
$930$	−12.9443	+	9.40456i	−0.424459	+	0.308388i
$931$		0			0
$932$	9.27051	−	28.5317i	0.303666	−	0.934587i
$933$	−19.4164	−	14.1068i	−0.635665	−	0.461837i
$934$	12.0000			0.392652
$935$		0			0
$936$	6.00000			0.196116
$937$	21.0344	+	15.2824i	0.687165	+	0.499255i	0.875727	−	0.482807i	$-0.160383\pi$
$937$	21.0344	+	15.2824i	0.687165	+	0.499255i	−0.188562	+	0.982061i	$0.560383\pi$
$938$	−4.94427	+	15.2169i	−0.161436	+	0.496850i
$939$	6.79837	+	20.9232i	0.221857	+	0.682804i
$940$	−12.9443	+	9.40456i	−0.422196	+	0.306743i
$941$	−43.6869	+	31.7404i	−1.42415	+	1.03471i	−0.433084	+	0.901353i	$0.642575\pi$
$941$	−43.6869	+	31.7404i	−1.42415	+	1.03471i	−0.991068	+	0.133354i	$0.957425\pi$
$942$	4.32624	+	13.3148i	0.140956	+	0.433819i
$943$	4.94427	−	15.2169i	0.161008	−	0.495531i
$944$	−3.23607	−	2.35114i	−0.105325	−	0.0765231i
$945$	−8.00000			−0.260240
$946$		0			0
$947$	12.0000			0.389948			0.194974	−	0.980808i	$-0.437538\pi$
$947$	12.0000			0.389948			0.194974	+	0.980808i	$0.437538\pi$
$948$	−3.23607	−	2.35114i	−0.105103	−	0.0763615i
$949$	8.65248	−	26.6296i	0.280871	−	0.864433i
$950$		0			0
$951$	17.7984	−	12.9313i	0.577152	−	0.419325i
$952$	19.4164	−	14.1068i	0.629289	−	0.457206i
$953$	−6.79837	−	20.9232i	−0.220221	−	0.677770i	−0.998742	−	0.0501514i	$-0.984030\pi$
$953$	−6.79837	−	20.9232i	−0.220221	−	0.677770i	0.778521	−	0.627619i	$-0.215970\pi$
$954$	−1.85410	+	5.70634i	−0.0600288	+	0.184750i
$955$	12.9443	+	9.40456i	0.418867	+	0.304325i
$956$	24.0000			0.776215
$957$		0			0
$958$	8.00000			0.258468
$959$	6.47214	+	4.70228i	0.208996	+	0.151845i
$960$	4.32624	−	13.3148i	0.139629	−	0.429733i
$961$	10.1976	+	31.3849i	0.328954	+	1.01242i
$962$	9.70820	−	7.05342i	0.313005	−	0.227411i
$963$	−9.70820	+	7.05342i	−0.312842	+	0.227293i
$964$	3.09017	+	9.51057i	0.0995277	+	0.306315i
$965$	−8.65248	+	26.6296i	−0.278533	+	0.857237i
$966$	25.8885	+	18.8091i	0.832950	+	0.605174i
$967$	−4.00000			−0.128631			−0.0643157	−	0.997930i	$-0.520486\pi$
$967$	−4.00000			−0.128631			−0.0643157	+	0.997930i	$0.520486\pi$
$968$		0			0
$969$		0			0
$970$	−3.23607	−	2.35114i	−0.103904	−	0.0754906i
$971$	−16.0689	+	49.4549i	−0.515675	+	1.58708i	0.266375	+	0.963869i	$0.414174\pi$
$971$	−16.0689	+	49.4549i	−0.515675	+	1.58708i	−0.782050	+	0.623215i	$0.785826\pi$
$972$	0.309017	+	0.951057i	0.00991172	+	0.0305052i
$973$	25.8885	−	18.8091i	0.829949	−	0.602993i
$974$	−12.9443	+	9.40456i	−0.414761	+	0.301342i
$975$	0.618034	+	1.90211i	0.0197929	+	0.0609164i
$976$	1.85410	−	5.70634i	0.0593484	−	0.182655i
$977$	4.85410	+	3.52671i	0.155296	+	0.112829i	0.662720	−	0.748867i	$-0.269402\pi$
$977$	4.85410	+	3.52671i	0.155296	+	0.112829i	−0.507423	+	0.861697i	$0.669402\pi$
$978$	4.00000			0.127906
$979$		0			0
$980$	18.0000			0.574989
$981$	−1.61803	−	1.17557i	−0.0516598	−	0.0375331i
$982$	1.23607	−	3.80423i	0.0394445	−	0.121398i
$983$	7.41641	+	22.8254i	0.236547	+	0.728016i	0.996912	+	0.0785207i	$0.0250197\pi$
$983$	7.41641	+	22.8254i	0.236547	+	0.728016i	−0.760366	+	0.649495i	$0.774980\pi$
$984$	4.85410	−	3.52671i	0.154743	−	0.112427i
$985$	22.6525	−	16.4580i	0.721768	−	0.524395i
$986$	−3.70820	−	11.4127i	−0.118093	−	0.363454i
$987$	9.88854	−	30.4338i	0.314756	−	0.968719i
$988$		0			0
$989$		0			0
$990$		0			0
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$	−32.3607	−	23.5114i	−1.02745	−	0.746488i
$993$	6.18034	−	19.0211i	0.196127	−	0.603617i
$994$		0			0
$995$		0			0
$996$	9.70820	−	7.05342i	0.307616	−	0.223496i
$997$	−4.32624	−	13.3148i	−0.137013	−	0.421684i	0.858884	−	0.512169i	$-0.171158\pi$
$997$	−4.32624	−	13.3148i	−0.137013	−	0.421684i	−0.995898	+	0.0904858i	$0.971158\pi$
$998$	1.23607	−	3.80423i	0.0391270	−	0.120421i
$999$	4.85410	+	3.52671i	0.153577	+	0.111580i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.e.g.202.1		4
11.2	odd	10		363.2.e.e.148.1		4
11.3	even	5	inner	363.2.e.g.124.1		4
11.4	even	5	inner	363.2.e.g.130.1		4
11.5	even	5		363.2.a.b.1.1		1
11.6	odd	10		33.2.a.a.1.1	✓	1
11.7	odd	10		363.2.e.e.130.1		4
11.8	odd	10		363.2.e.e.124.1		4
11.9	even	5	inner	363.2.e.g.148.1		4
11.10	odd	2		363.2.e.e.202.1		4
33.5	odd	10		1089.2.a.j.1.1		1
33.17	even	10		99.2.a.b.1.1		1
44.27	odd	10		5808.2.a.t.1.1		1
44.39	even	10		528.2.a.g.1.1		1
55.17	even	20		825.2.c.a.199.2		2
55.28	even	20		825.2.c.a.199.1		2
55.39	odd	10		825.2.a.a.1.1		1
55.49	even	10		9075.2.a.q.1.1		1
77.6	even	10		1617.2.a.j.1.1		1
88.61	odd	10		2112.2.a.bb.1.1		1
88.83	even	10		2112.2.a.j.1.1		1
99.50	even	30		891.2.e.g.298.1		2
99.61	odd	30		891.2.e.e.595.1		2
99.83	even	30		891.2.e.g.595.1		2
99.94	odd	30		891.2.e.e.298.1		2
132.83	odd	10		1584.2.a.o.1.1		1
143.116	odd	10		5577.2.a.a.1.1		1
165.17	odd	20		2475.2.c.d.199.1		2
165.83	odd	20		2475.2.c.d.199.2		2
165.149	even	10		2475.2.a.g.1.1		1
187.50	odd	10		9537.2.a.m.1.1		1
231.83	odd	10		4851.2.a.b.1.1		1
264.83	odd	10		6336.2.a.n.1.1		1
264.149	even	10		6336.2.a.x.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.2.a.a.1.1	✓	1	11.6	odd	10
99.2.a.b.1.1		1	33.17	even	10
363.2.a.b.1.1		1	11.5	even	5
363.2.e.e.124.1		4	11.8	odd	10
363.2.e.e.130.1		4	11.7	odd	10
363.2.e.e.148.1		4	11.2	odd	10
363.2.e.e.202.1		4	11.10	odd	2
363.2.e.g.124.1		4	11.3	even	5	inner
363.2.e.g.130.1		4	11.4	even	5	inner
363.2.e.g.148.1		4	11.9	even	5	inner
363.2.e.g.202.1		4	1.1	even	1	trivial
528.2.a.g.1.1		1	44.39	even	10
825.2.a.a.1.1		1	55.39	odd	10
825.2.c.a.199.1		2	55.28	even	20
825.2.c.a.199.2		2	55.17	even	20
891.2.e.e.298.1		2	99.94	odd	30
891.2.e.e.595.1		2	99.61	odd	30
891.2.e.g.298.1		2	99.50	even	30
891.2.e.g.595.1		2	99.83	even	30
1089.2.a.j.1.1		1	33.5	odd	10
1584.2.a.o.1.1		1	132.83	odd	10
1617.2.a.j.1.1		1	77.6	even	10
2112.2.a.j.1.1		1	88.83	even	10
2112.2.a.bb.1.1		1	88.61	odd	10
2475.2.a.g.1.1		1	165.149	even	10
2475.2.c.d.199.1		2	165.17	odd	20
2475.2.c.d.199.2		2	165.83	odd	20
4851.2.a.b.1.1		1	231.83	odd	10
5577.2.a.a.1.1		1	143.116	odd	10
5808.2.a.t.1.1		1	44.27	odd	10
6336.2.a.n.1.1		1	264.83	odd	10
6336.2.a.x.1.1		1	264.149	even	10
9075.2.a.q.1.1		1	55.49	even	10
9537.2.a.m.1.1		1	187.50	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.e (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(1.61803 - 1.17557i) q^{5} +(-0.809017 + 0.587785i) q^{6} +(-1.23607 - 3.80423i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-0.809017 - 0.587785i) q^{9} +2.00000 q^{10} +1.00000 q^{12} +(-1.61803 - 1.17557i) q^{13} +(1.23607 - 3.80423i) q^{14} +(0.618034 + 1.90211i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.61803 + 1.17557i) q^{17} +(-0.309017 - 0.951057i) q^{18} +(-1.61803 - 1.17557i) q^{20} +4.00000 q^{21} +8.00000 q^{23} +(2.42705 + 1.76336i) q^{24} +(-0.309017 + 0.951057i) q^{25} +(-0.618034 - 1.90211i) q^{26} +(0.809017 - 0.587785i) q^{27} +(-3.23607 + 2.35114i) q^{28} +(1.85410 + 5.70634i) q^{29} +(-0.618034 + 1.90211i) q^{30} +(6.47214 + 4.70228i) q^{31} -5.00000 q^{32} -2.00000 q^{34} +(-6.47214 - 4.70228i) q^{35} +(-0.309017 + 0.951057i) q^{36} +(1.85410 + 5.70634i) q^{37} +(1.61803 - 1.17557i) q^{39} +(-1.85410 - 5.70634i) q^{40} +(0.618034 - 1.90211i) q^{41} +(3.23607 + 2.35114i) q^{42} -2.00000 q^{45} +(6.47214 + 4.70228i) q^{46} +(2.47214 - 7.60845i) q^{47} +(0.309017 + 0.951057i) q^{48} +(-7.28115 + 5.29007i) q^{49} +(-0.809017 + 0.587785i) q^{50} +(-0.618034 - 1.90211i) q^{51} +(-0.618034 + 1.90211i) q^{52} +(-4.85410 - 3.52671i) q^{53} +1.00000 q^{54} -12.0000 q^{56} +(-1.85410 + 5.70634i) q^{58} +(-1.23607 - 3.80423i) q^{59} +(1.61803 - 1.17557i) q^{60} +(4.85410 - 3.52671i) q^{61} +(2.47214 + 7.60845i) q^{62} +(-1.23607 + 3.80423i) q^{63} +(-5.66312 - 4.11450i) q^{64} -4.00000 q^{65} -4.00000 q^{67} +(1.61803 + 1.17557i) q^{68} +(-2.47214 + 7.60845i) q^{69} +(-2.47214 - 7.60845i) q^{70} +(-2.42705 + 1.76336i) q^{72} +(4.32624 + 13.3148i) q^{73} +(-1.85410 + 5.70634i) q^{74} +(-0.809017 - 0.587785i) q^{75} +2.00000 q^{78} +(-3.23607 - 2.35114i) q^{79} +(0.618034 - 1.90211i) q^{80} +(0.309017 + 0.951057i) q^{81} +(1.61803 - 1.17557i) q^{82} +(9.70820 - 7.05342i) q^{83} +(-1.23607 - 3.80423i) q^{84} +(-1.23607 + 3.80423i) q^{85} -6.00000 q^{87} -6.00000 q^{89} +(-1.61803 - 1.17557i) q^{90} +(-2.47214 + 7.60845i) q^{91} +(-2.47214 - 7.60845i) q^{92} +(-6.47214 + 4.70228i) q^{93} +(6.47214 - 4.70228i) q^{94} +(1.54508 - 4.75528i) q^{96} +(-1.61803 - 1.17557i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{3} + q^{4} + 2 q^{5} - q^{6} + 4 q^{7} - 3 q^{8} - q^{9} + 8 q^{10} + 4 q^{12} - 2 q^{13} - 4 q^{14} - 2 q^{15} + q^{16} - 2 q^{17} + q^{18} - 2 q^{20} + 16 q^{21} + 32 q^{23} + 3 q^{24}+ \cdots - 36 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^3 + q^4 + 2 * q^5 - q^6 + 4 * q^7 - 3 * q^8 - q^9 + 8 * q^10 + 4 * q^12 - 2 * q^13 - 4 * q^14 - 2 * q^15 + q^16 - 2 * q^17 + q^18 - 2 * q^20 + 16 * q^21 + 32 * q^23 + 3 * q^24 + q^25 + 2 * q^26 + q^27 - 4 * q^28 - 6 * q^29 + 2 * q^30 + 8 * q^31 - 20 * q^32 - 8 * q^34 - 8 * q^35 + q^36 - 6 * q^37 + 2 * q^39 + 6 * q^40 - 2 * q^41 + 4 * q^42 - 8 * q^45 + 8 * q^46 - 8 * q^47 - q^48 - 9 * q^49 - q^50 + 2 * q^51 + 2 * q^52 - 6 * q^53 + 4 * q^54 - 48 * q^56 + 6 * q^58 + 4 * q^59 + 2 * q^60 + 6 * q^61 - 8 * q^62 + 4 * q^63 - 7 * q^64 - 16 * q^65 - 16 * q^67 + 2 * q^68 + 8 * q^69 + 8 * q^70 - 3 * q^72 - 14 * q^73 + 6 * q^74 - q^75 + 8 * q^78 - 4 * q^79 - 2 * q^80 - q^81 + 2 * q^82 + 12 * q^83 + 4 * q^84 + 4 * q^85 - 24 * q^87 - 24 * q^89 - 2 * q^90 + 8 * q^91 + 8 * q^92 - 8 * q^93 + 8 * q^94 - 5 * q^96 - 2 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more