LMFDB - Embedded newform 961.2.d.b.628.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(374,961)] 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("961.374"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.d (of order $5$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-3,-1,3] 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:	$7.67362363425$
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 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			628.1
Root			$-0.309017 + 0.951057i$ of defining polynomial
Character	$\chi$	$=$	961.628
Dual form			961.2.d.b.531.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.190983 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} -2.61803 q^{5} -0.618034 q^{6} +(-2.42705 - 1.76336i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(1.61803 - 1.17557i) q^{9} +(0.500000 - 1.53884i) q^{10} +(-0.618034 - 0.449028i) q^{11} +(-0.500000 + 1.53884i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(1.50000 - 1.08981i) q^{14} +(-0.809017 - 2.48990i) q^{15} +(0.572949 + 1.76336i) q^{16} +(0.190983 - 0.138757i) q^{17} +(0.381966 + 1.17557i) q^{18} +(1.54508 - 4.75528i) q^{19} +(-3.42705 - 2.48990i) q^{20} +(0.927051 - 2.85317i) q^{21} +(0.381966 - 0.277515i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(-1.80902 - 1.31433i) q^{24} +1.85410 q^{25} +3.00000 q^{26} +(4.04508 + 2.93893i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(2.66312 - 8.19624i) q^{29} +1.61803 q^{30} -5.61803 q^{32} +(0.236068 - 0.726543i) q^{33} +(0.0450850 + 0.138757i) q^{34} +(6.35410 + 4.61653i) q^{35} +3.23607 q^{36} -0.236068 q^{37} +(2.50000 + 1.81636i) q^{38} +(3.92705 - 2.85317i) q^{39} +(4.73607 - 3.44095i) q^{40} +(2.00000 - 6.15537i) q^{41} +(1.50000 + 1.08981i) q^{42} +(1.42705 - 4.39201i) q^{43} +(-0.381966 - 1.17557i) q^{44} +(-4.23607 + 3.07768i) q^{45} +(-1.04508 - 3.21644i) q^{46} +(-1.04508 - 3.21644i) q^{47} +(-1.50000 + 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(-0.354102 + 1.08981i) q^{50} +(0.190983 + 0.138757i) q^{51} +(2.42705 - 7.46969i) q^{52} +(-10.2812 + 7.46969i) q^{53} +(-2.50000 + 1.81636i) q^{54} +(1.61803 + 1.17557i) q^{55} +6.70820 q^{56} +5.00000 q^{57} +(4.30902 + 3.13068i) q^{58} +(2.92705 + 9.00854i) q^{59} +(1.30902 - 4.02874i) q^{60} +6.94427 q^{61} -6.00000 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(3.92705 + 12.0862i) q^{65} +(0.381966 + 0.277515i) q^{66} -4.23607 q^{67} +0.381966 q^{68} +(-4.42705 - 3.21644i) q^{69} +(-3.92705 + 2.85317i) q^{70} +(-0.0729490 + 0.0530006i) q^{71} +(-1.38197 + 4.25325i) q^{72} +(-6.92705 - 5.03280i) q^{73} +(0.0450850 - 0.138757i) q^{74} +(0.572949 + 1.76336i) q^{75} +(6.54508 - 4.75528i) q^{76} +(0.708204 + 2.17963i) q^{77} +(0.927051 + 2.85317i) q^{78} +(-1.50000 - 4.61653i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.23607 + 2.35114i) q^{82} +(1.26393 - 3.88998i) q^{83} +(3.92705 - 2.85317i) q^{84} +(-0.500000 + 0.363271i) q^{85} +(2.30902 + 1.67760i) q^{86} +8.61803 q^{87} +1.70820 q^{88} +(-5.16312 - 3.75123i) q^{89} +(-1.00000 - 3.07768i) q^{90} +(-4.50000 + 13.8496i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(-4.04508 + 12.4495i) q^{95} +(-1.73607 - 5.34307i) q^{96} +(4.28115 + 3.11044i) q^{97} -1.23607 q^{98} -1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 3 q^{2} - q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 6 q^{14} - q^{15} + 9 q^{16} + 3 q^{17} + 6 q^{18} - 5 q^{19} - 7 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) $ 4 * q - 3 * q^2 - q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 - 5 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 6 * q^14 - q^15 + 9 * q^16 + 3 * q^17 + 6 * q^18 - 5 * q^19 - 7 * q^20 - 3 * q^21 + 6 * q^22 - 11 * q^23 - 5 * q^24 - 6 * q^25 + 12 * q^26 + 5 * q^27 - 6 * q^28 - 5 * q^29 + 2 * q^30 - 18 * q^32 - 8 * q^33 - 11 * q^34 + 12 * q^35 + 4 * q^36 + 8 * q^37 + 10 * q^38 + 9 * q^39 + 10 * q^40 + 8 * q^41 + 6 * q^42 - q^43 - 6 * q^44 - 8 * q^45 + 7 * q^46 + 7 * q^47 - 6 * q^48 - 2 * q^49 + 12 * q^50 + 3 * q^51 + 3 * q^52 - 21 * q^53 - 10 * q^54 + 2 * q^55 + 20 * q^57 + 15 * q^58 + 5 * q^59 + 3 * q^60 - 8 * q^61 - 24 * q^63 - 7 * q^64 + 9 * q^65 + 6 * q^66 - 8 * q^67 + 6 * q^68 - 11 * q^69 - 9 * q^70 - 7 * q^71 - 10 * q^72 - 21 * q^73 - 11 * q^74 + 9 * q^75 + 15 * q^76 - 24 * q^77 - 3 * q^78 - 6 * q^80 - q^81 + 4 * q^82 + 14 * q^83 + 9 * q^84 - 2 * q^85 + 7 * q^86 + 30 * q^87 - 20 * q^88 - 5 * q^89 - 4 * q^90 - 18 * q^91 - 22 * q^92 - 14 * q^94 - 5 * q^95 + 2 * q^96 - 3 * q^97 + 4 * q^98 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	−0.995597	−	0.0937362i	$-0.970119\pi$
$2$	−0.190983	+	0.587785i	−0.135045	+	0.415627i	0.860552	+	0.509363i	$0.170119\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	0.999773	−	0.0213149i	$-0.00678525\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	−0.821362	+	0.570408i	$0.806785\pi$
$4$	1.30902	+	0.951057i	0.654508	+	0.475528i
$5$	−2.61803			−1.17082			−0.585410	−	0.810737i	$-0.699067\pi$
$5$	−2.61803			−1.17082			−0.585410	+	0.810737i	$0.699067\pi$
$6$	−0.618034			−0.252311
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	0.0255212	−	0.999674i	$-0.491875\pi$
$7$	−2.42705	−	1.76336i	−0.917339	−	0.666486i	−0.942860	+	0.333188i	$0.891875\pi$
$8$	−1.80902	+	1.31433i	−0.639584	+	0.464685i
$9$	1.61803	−	1.17557i	0.539345	−	0.391857i
$10$	0.500000	−	1.53884i	0.158114	−	0.486624i
$11$	−0.618034	−	0.449028i	−0.186344	−	0.135387i	0.490702	−	0.871327i	$-0.336740\pi$
$11$	−0.618034	−	0.449028i	−0.186344	−	0.135387i	−0.677046	+	0.735940i	$0.736740\pi$
$12$	−0.500000	+	1.53884i	−0.144338	+	0.444225i
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	−0.911331	−	0.411675i	$-0.864944\pi$
$13$	−1.50000	−	4.61653i	−0.416025	−	1.28039i	0.495306	−	0.868719i	$-0.335056\pi$
$14$	1.50000	−	1.08981i	0.400892	−	0.291265i
$15$	−0.809017	−	2.48990i	−0.208887	−	0.642889i
$16$	0.572949	+	1.76336i	0.143237	+	0.440839i
$17$	0.190983	−	0.138757i	0.0463202	−	0.0336536i	−0.564384	−	0.825512i	$-0.690886\pi$
$17$	0.190983	−	0.138757i	0.0463202	−	0.0336536i	0.610704	+	0.791859i	$0.290886\pi$
$18$	0.381966	+	1.17557i	0.0900303	+	0.277085i
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	−0.601851	−	0.798608i	$-0.705570\pi$
$19$	1.54508	−	4.75528i	0.354467	−	1.09094i	0.956318	−	0.292328i	$-0.0944300\pi$
$20$	−3.42705	−	2.48990i	−0.766312	−	0.556758i
$21$	0.927051	−	2.85317i	0.202299	−	0.622613i
$22$	0.381966	−	0.277515i	0.0814354	−	0.0591663i
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	−0.944295	−	0.329101i	$-0.893254\pi$
$23$	−4.42705	+	3.21644i	−0.923104	+	0.670674i	0.0211907	+	0.999775i	$0.493254\pi$
$24$	−1.80902	−	1.31433i	−0.369264	−	0.268286i
$25$	1.85410			0.370820
$26$	3.00000			0.588348
$27$	4.04508	+	2.93893i	0.778477	+	0.565597i
$28$	−1.50000	−	4.61653i	−0.283473	−	0.872441i
$29$	2.66312	−	8.19624i	0.494529	−	1.52200i	−0.323161	−	0.946344i	$-0.604746\pi$
$29$	2.66312	−	8.19624i	0.494529	−	1.52200i	0.817690	−	0.575659i	$-0.195254\pi$
$30$	1.61803			0.295411
$31$		0			0
$31$		0			0
$32$	−5.61803			−0.993137
$33$	0.236068	−	0.726543i	0.0410942	−	0.126475i
$34$	0.0450850	+	0.138757i	0.00773201	+	0.0237967i
$35$	6.35410	+	4.61653i	1.07404	+	0.780335i
$36$	3.23607			0.539345
$37$	−0.236068			−0.0388093			−0.0194047	−	0.999812i	$-0.506177\pi$
$37$	−0.236068			−0.0388093			−0.0194047	+	0.999812i	$0.506177\pi$
$38$	2.50000	+	1.81636i	0.405554	+	0.294652i
$39$	3.92705	−	2.85317i	0.628831	−	0.456873i
$40$	4.73607	−	3.44095i	0.748838	−	0.544063i
$41$	2.00000	−	6.15537i	0.312348	−	0.961307i	−0.664485	−	0.747302i	$-0.731349\pi$
$41$	2.00000	−	6.15537i	0.312348	−	0.961307i	0.976833	−	0.214005i	$-0.0686510\pi$
$42$	1.50000	+	1.08981i	0.231455	+	0.168162i
$43$	1.42705	−	4.39201i	0.217623	−	0.669775i	−0.781334	−	0.624113i	$-0.785460\pi$
$43$	1.42705	−	4.39201i	0.217623	−	0.669775i	0.998957	−	0.0456620i	$-0.0145397\pi$
$44$	−0.381966	−	1.17557i	−0.0575835	−	0.177224i
$45$	−4.23607	+	3.07768i	−0.631476	+	0.458794i
$46$	−1.04508	−	3.21644i	−0.154089	−	0.474238i
$47$	−1.04508	−	3.21644i	−0.152441	−	0.469166i	0.845451	−	0.534052i	$-0.179332\pi$
$47$	−1.04508	−	3.21644i	−0.152441	−	0.469166i	−0.997893	+	0.0648863i	$0.979332\pi$
$48$	−1.50000	+	1.08981i	−0.216506	+	0.157301i
$49$	0.618034	+	1.90211i	0.0882906	+	0.271730i
$50$	−0.354102	+	1.08981i	−0.0500776	+	0.154123i
$51$	0.190983	+	0.138757i	0.0267430	+	0.0194299i
$52$	2.42705	−	7.46969i	0.336571	−	1.03586i
$53$	−10.2812	+	7.46969i	−1.41222	+	1.02604i	−0.419231	+	0.907880i	$0.637700\pi$
$53$	−10.2812	+	7.46969i	−1.41222	+	1.02604i	−0.992994	+	0.118162i	$0.962300\pi$
$54$	−2.50000	+	1.81636i	−0.340207	+	0.247175i
$55$	1.61803	+	1.17557i	0.218176	+	0.158514i
$56$	6.70820			0.896421
$57$	5.00000			0.662266
$58$	4.30902	+	3.13068i	0.565802	+	0.411079i
$59$	2.92705	+	9.00854i	0.381070	+	1.17281i	0.939292	+	0.343120i	$0.111484\pi$
$59$	2.92705	+	9.00854i	0.381070	+	1.17281i	−0.558222	+	0.829692i	$0.688516\pi$
$60$	1.30902	−	4.02874i	0.168993	−	0.520108i
$61$	6.94427			0.889123			0.444561	−	0.895748i	$-0.353360\pi$
$61$	6.94427			0.889123			0.444561	+	0.895748i	$0.353360\pi$
$62$		0			0
$63$	−6.00000			−0.755929
$64$	−0.0729490	+	0.224514i	−0.00911863	+	0.0280642i
$65$	3.92705	+	12.0862i	0.487091	+	1.49911i
$66$	0.381966	+	0.277515i	0.0470168	+	0.0341597i
$67$	−4.23607			−0.517518			−0.258759	−	0.965942i	$-0.583314\pi$
$67$	−4.23607			−0.517518			−0.258759	+	0.965942i	$0.583314\pi$
$68$	0.381966			0.0463202
$69$	−4.42705	−	3.21644i	−0.532954	−	0.387214i
$70$	−3.92705	+	2.85317i	−0.469372	+	0.341019i
$71$	−0.0729490	+	0.0530006i	−0.00865746	+	0.00629001i	−0.592106	−	0.805860i	$-0.701703\pi$
$71$	−0.0729490	+	0.0530006i	−0.00865746	+	0.00629001i	0.583448	+	0.812150i	$0.301703\pi$
$72$	−1.38197	+	4.25325i	−0.162866	+	0.501251i
$73$	−6.92705	−	5.03280i	−0.810750	−	0.589044i	0.103298	−	0.994650i	$-0.467060\pi$
$73$	−6.92705	−	5.03280i	−0.810750	−	0.589044i	−0.914048	+	0.405606i	$0.867060\pi$
$74$	0.0450850	−	0.138757i	0.00524102	−	0.0161302i
$75$	0.572949	+	1.76336i	0.0661585	+	0.203615i
$76$	6.54508	−	4.75528i	0.750773	−	0.545468i
$77$	0.708204	+	2.17963i	0.0807073	+	0.248392i
$78$	0.927051	+	2.85317i	0.104968	+	0.323058i
$79$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$79$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$80$	−1.50000	−	4.61653i	−0.167705	−	0.516143i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	3.23607	+	2.35114i	0.357364	+	0.259640i
$83$	1.26393	−	3.88998i	0.138735	−	0.426981i	−0.857418	−	0.514621i	$-0.827933\pi$
$83$	1.26393	−	3.88998i	0.138735	−	0.426981i	0.996152	+	0.0876401i	$0.0279326\pi$
$84$	3.92705	−	2.85317i	0.428476	−	0.311306i
$85$	−0.500000	+	0.363271i	−0.0542326	+	0.0394023i
$86$	2.30902	+	1.67760i	0.248988	+	0.180900i
$87$	8.61803			0.923950
$88$	1.70820			0.182095
$89$	−5.16312	−	3.75123i	−0.547290	−	0.397629i	0.279496	−	0.960147i	$-0.409833\pi$
$89$	−5.16312	−	3.75123i	−0.547290	−	0.397629i	−0.826785	+	0.562518i	$0.809833\pi$
$90$	−1.00000	−	3.07768i	−0.105409	−	0.324416i
$91$	−4.50000	+	13.8496i	−0.471728	+	1.45183i
$92$	−8.85410			−0.923104
$93$		0			0
$94$	2.09017			0.215585
$95$	−4.04508	+	12.4495i	−0.415017	+	1.27729i
$96$	−1.73607	−	5.34307i	−0.177187	−	0.545325i
$97$	4.28115	+	3.11044i	0.434685	+	0.315817i	0.783520	−	0.621367i	$-0.213422\pi$
$97$	4.28115	+	3.11044i	0.434685	+	0.315817i	−0.348834	+	0.937184i	$0.613422\pi$
$98$	−1.23607			−0.124862
$99$	−1.52786			−0.153556
$100$	2.42705	+	1.76336i	0.242705	+	0.176336i
$101$	−3.85410	+	2.80017i	−0.383497	+	0.278627i	−0.762786	−	0.646651i	$-0.776169\pi$
$101$	−3.85410	+	2.80017i	−0.383497	+	0.278627i	0.379288	+	0.925279i	$0.376169\pi$
$102$	−0.118034	+	0.0857567i	−0.0116871	+	0.00849118i
$103$	−0.0450850	+	0.138757i	−0.00444235	+	0.0136722i	−0.953253	−	0.302173i	$-0.902288\pi$
$103$	−0.0450850	+	0.138757i	−0.00444235	+	0.0136722i	0.948811	+	0.315845i	$0.102288\pi$
$104$	8.78115	+	6.37988i	0.861063	+	0.625599i
$105$	−2.42705	+	7.46969i	−0.236856	+	0.728968i
$106$	−2.42705	−	7.46969i	−0.235736	−	0.725521i
$107$	−0.881966	+	0.640786i	−0.0852629	+	0.0619471i	−0.629600	−	0.776919i	$-0.716781\pi$
$107$	−0.881966	+	0.640786i	−0.0852629	+	0.0619471i	0.544337	+	0.838867i	$0.316781\pi$
$108$	2.50000	+	7.69421i	0.240563	+	0.740376i
$109$	−2.60081	−	8.00448i	−0.249113	−	0.766690i	−0.994933	−	0.100543i	$-0.967942\pi$
$109$	−2.60081	−	8.00448i	−0.249113	−	0.766690i	0.745820	−	0.666147i	$-0.232058\pi$
$110$	−1.00000	+	0.726543i	−0.0953463	+	0.0692731i
$111$	−0.0729490	−	0.224514i	−0.00692401	−	0.0213099i
$112$	1.71885	−	5.29007i	0.162416	−	0.499864i
$113$	1.50000	+	1.08981i	0.141108	+	0.102521i	0.656100	−	0.754674i	$-0.272205\pi$
$113$	1.50000	+	1.08981i	0.141108	+	0.102521i	−0.514992	+	0.857195i	$0.672205\pi$
$114$	−0.954915	+	2.93893i	−0.0894360	+	0.275256i
$115$	11.5902	−	8.42075i	1.08079	−	0.785239i
$116$	11.2812	−	8.19624i	1.04743	−	0.761002i
$117$	−7.85410	−	5.70634i	−0.726112	−	0.527551i
$118$	−5.85410			−0.538914
$119$	−0.708204			−0.0649209
$120$	4.73607	+	3.44095i	0.432342	+	0.314115i
$121$	−3.21885	−	9.90659i	−0.292622	−	0.900599i
$122$	−1.32624	+	4.08174i	−0.120072	+	0.369543i
$123$	6.47214			0.583573
$124$		0			0
$125$	8.23607			0.736656
$126$	1.14590	−	3.52671i	0.102085	−	0.314184i
$127$	−3.16312	−	9.73508i	−0.280681	−	0.863849i	−0.987660	−	0.156614i	$-0.949942\pi$
$127$	−3.16312	−	9.73508i	−0.280681	−	0.863849i	0.706979	−	0.707235i	$-0.250058\pi$
$128$	−9.20820	−	6.69015i	−0.813898	−	0.591331i
$129$	4.61803			0.406595
$130$	−7.85410			−0.688850
$131$	−0.0729490	−	0.0530006i	−0.00637359	−	0.00463068i	0.584594	−	0.811326i	$-0.301254\pi$
$131$	−0.0729490	−	0.0530006i	−0.00637359	−	0.00463068i	−0.590967	+	0.806695i	$0.701254\pi$
$132$	1.00000	−	0.726543i	0.0870388	−	0.0632374i
$133$	−12.1353	+	8.81678i	−1.05226	+	0.764512i
$134$	0.809017	−	2.48990i	0.0698884	−	0.215094i
$135$	−10.5902	−	7.69421i	−0.911457	−	0.662212i
$136$	−0.163119	+	0.502029i	−0.0139873	+	0.0430486i
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	0.999421	−	0.0340275i	$-0.0108334\pi$
$137$	2.00000	+	6.15537i	0.170872	+	0.525888i	−0.828549	+	0.559916i	$0.810833\pi$
$138$	2.73607	−	1.98787i	0.232910	−	0.169219i
$139$	−1.80902	−	5.56758i	−0.153439	−	0.472236i	0.844561	−	0.535460i	$-0.179862\pi$
$139$	−1.80902	−	5.56758i	−0.153439	−	0.472236i	−0.997999	+	0.0632239i	$0.979862\pi$
$140$	3.92705	+	12.0862i	0.331896	+	1.02147i
$141$	2.73607	−	1.98787i	0.230418	−	0.167409i
$142$	−0.0172209	−	0.0530006i	−0.00144515	−	0.00444771i
$143$	−1.14590	+	3.52671i	−0.0958248	+	0.294918i
$144$	3.00000	+	2.17963i	0.250000	+	0.181636i
$145$	−6.97214	+	21.4580i	−0.579004	+	1.78199i
$146$	4.28115	−	3.11044i	0.354311	−	0.257422i
$147$	−1.61803	+	1.17557i	−0.133453	+	0.0969594i
$148$	−0.309017	−	0.224514i	−0.0254010	−	0.0184549i
$149$	−17.0344			−1.39552			−0.697758	−	0.716334i	$-0.745819\pi$
$149$	−17.0344			−1.39552			−0.697758	+	0.716334i	$0.745819\pi$
$150$	−1.14590			−0.0935622
$151$	−15.7812	−	11.4657i	−1.28425	−	0.933064i	−0.284579	−	0.958652i	$-0.591854\pi$
$151$	−15.7812	−	11.4657i	−1.28425	−	0.933064i	−0.999673	+	0.0255888i	$0.991854\pi$
$152$	3.45492	+	10.6331i	0.280231	+	0.862461i
$153$	0.145898	−	0.449028i	0.0117952	−	0.0363018i
$154$	−1.41641			−0.114137
$155$		0			0
$156$	7.85410			0.628831
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	−0.757077	−	0.653325i	$-0.773373\pi$
$157$	3.00000	−	9.23305i	0.239426	−	0.736878i	0.996503	−	0.0835524i	$-0.0266266\pi$
$158$		0			0
$159$	−10.2812	−	7.46969i	−0.815348	−	0.592385i
$160$	14.7082			1.16279
$161$	16.4164			1.29379
$162$	0.500000	+	0.363271i	0.0392837	+	0.0285413i
$163$	10.2812	−	7.46969i	0.805282	−	0.585072i	−0.107177	−	0.994240i	$-0.534181\pi$
$163$	10.2812	−	7.46969i	0.805282	−	0.585072i	0.912459	+	0.409168i	$0.134181\pi$
$164$	8.47214	−	6.15537i	0.661563	−	0.480653i
$165$	−0.618034	+	1.90211i	−0.0481139	+	0.148079i
$166$	2.04508	+	1.48584i	0.158729	+	0.115324i
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	−0.777829	−	0.628476i	$-0.783679\pi$
$167$	2.85410	−	8.78402i	0.220857	−	0.679728i	0.998686	−	0.0512518i	$-0.0163211\pi$
$168$	2.07295	+	6.37988i	0.159931	+	0.492219i
$169$	−8.54508	+	6.20837i	−0.657314	+	0.477567i
$170$	−0.118034	−	0.363271i	−0.00905279	−	0.0278616i
$171$	−3.09017	−	9.51057i	−0.236311	−	0.727291i
$172$	6.04508	−	4.39201i	0.460933	−	0.334888i
$173$	0.281153	+	0.865300i	0.0213757	+	0.0657875i	0.961175	−	0.275938i	$-0.0889886\pi$
$173$	0.281153	+	0.865300i	0.0213757	+	0.0657875i	−0.939800	+	0.341726i	$0.888989\pi$
$174$	−1.64590	+	5.06555i	−0.124775	+	0.384019i
$175$	−4.50000	−	3.26944i	−0.340168	−	0.247147i
$176$	0.437694	−	1.34708i	0.0329924	−	0.101540i
$177$	−7.66312	+	5.56758i	−0.575995	+	0.418485i
$178$	3.19098	−	2.31838i	0.239174	−	0.173770i
$179$	16.0172	+	11.6372i	1.19718	+	0.869805i	0.994005	−	0.109337i	$-0.0348728\pi$
$179$	16.0172	+	11.6372i	1.19718	+	0.869805i	0.203179	+	0.979142i	$0.434873\pi$
$180$	−8.47214			−0.631476
$181$	−17.0000			−1.26360			−0.631800	−	0.775131i	$-0.717684\pi$
$181$	−17.0000			−1.26360			−0.631800	+	0.775131i	$0.717684\pi$
$182$	−7.28115	−	5.29007i	−0.539715	−	0.392126i
$183$	2.14590	+	6.60440i	0.158629	+	0.488211i
$184$	3.78115	−	11.6372i	0.278750	−	0.857905i
$185$	0.618034			0.0454388
$186$		0			0
$187$	−0.180340			−0.0131878
$188$	1.69098	−	5.20431i	0.123328	−	0.379563i
$189$	−4.63525	−	14.2658i	−0.337165	−	1.03769i
$190$	−6.54508	−	4.75528i	−0.474830	−	0.344984i
$191$	−16.0902			−1.16424			−0.582122	−	0.813102i	$-0.697777\pi$
$191$	−16.0902			−1.16424			−0.582122	+	0.813102i	$0.697777\pi$
$192$	−0.236068			−0.0170367
$193$	1.92705	+	1.40008i	0.138712	+	0.100780i	0.654977	−	0.755648i	$-0.272678\pi$
$193$	1.92705	+	1.40008i	0.138712	+	0.100780i	−0.516265	+	0.856429i	$0.672678\pi$
$194$	−2.64590	+	1.92236i	−0.189964	+	0.138017i
$195$	−10.2812	+	7.46969i	−0.736249	+	0.534916i
$196$	−1.00000	+	3.07768i	−0.0714286	+	0.219835i
$197$	13.2812	+	9.64932i	0.946243	+	0.687486i	0.949915	−	0.312507i	$-0.101169\pi$
$197$	13.2812	+	9.64932i	0.946243	+	0.687486i	−0.00367232	+	0.999993i	$0.501169\pi$
$198$	0.291796	−	0.898056i	0.0207370	−	0.0638221i
$199$	8.25329	+	25.4010i	0.585060	+	1.80063i	0.599029	+	0.800728i	$0.295554\pi$
$199$	8.25329	+	25.4010i	0.585060	+	1.80063i	−0.0139686	+	0.999902i	$0.504446\pi$
$200$	−3.35410	+	2.43690i	−0.237171	+	0.172315i
$201$	−1.30902	−	4.02874i	−0.0923309	−	0.284165i
$202$	−0.909830	−	2.80017i	−0.0640154	−	0.197019i
$203$	−20.9164	+	15.1967i	−1.46804	+	1.06660i
$204$	0.118034	+	0.363271i	0.00826403	+	0.0254341i
$205$	−5.23607	+	16.1150i	−0.365703	+	1.12552i
$206$	−0.0729490	−	0.0530006i	−0.00508260	−	0.00369272i
$207$	−3.38197	+	10.4086i	−0.235063	+	0.723449i
$208$	7.28115	−	5.29007i	0.504857	−	0.366800i
$209$	−3.09017	+	2.24514i	−0.213752	+	0.155300i
$210$	−3.92705	−	2.85317i	−0.270992	−	0.196887i
$211$	−8.00000			−0.550743			−0.275371	−	0.961338i	$-0.588801\pi$
$211$	−8.00000			−0.550743			−0.275371	+	0.961338i	$0.588801\pi$
$212$	−20.5623			−1.41222
$213$	−0.0729490	−	0.0530006i	−0.00499838	−	0.00363154i
$214$	−0.208204	−	0.640786i	−0.0142325	−	0.0438032i
$215$	−3.73607	+	11.4984i	−0.254798	+	0.784187i
$216$	−11.1803			−0.760726
$217$		0			0
$218$	5.20163			0.352299
$219$	2.64590	−	8.14324i	0.178793	−	0.550269i
$220$	1.00000	+	3.07768i	0.0674200	+	0.207497i
$221$	−0.927051	−	0.673542i	−0.0623602	−	0.0453073i
$222$	0.145898			0.00979203
$223$	−0.708204			−0.0474248			−0.0237124	−	0.999719i	$-0.507549\pi$
$223$	−0.708204			−0.0474248			−0.0237124	+	0.999719i	$0.507549\pi$
$224$	13.6353	+	9.90659i	0.911044	+	0.661912i
$225$	3.00000	−	2.17963i	0.200000	−	0.145309i
$226$	−0.927051	+	0.673542i	−0.0616665	+	0.0448033i
$227$	−6.40983	+	19.7274i	−0.425435	+	1.30936i	0.477141	+	0.878827i	$0.341673\pi$
$227$	−6.40983	+	19.7274i	−0.425435	+	1.30936i	−0.902577	+	0.430529i	$0.858327\pi$
$228$	6.54508	+	4.75528i	0.433459	+	0.314926i
$229$	2.23607	−	6.88191i	0.147764	−	0.454769i	−0.849592	−	0.527440i	$-0.823152\pi$
$229$	2.23607	−	6.88191i	0.147764	−	0.454769i	0.997356	+	0.0726703i	$0.0231521\pi$
$230$	2.73607	+	8.42075i	0.180411	+	0.555248i
$231$	−1.85410	+	1.34708i	−0.121991	+	0.0886316i
$232$	5.95492	+	18.3273i	0.390959	+	1.20325i
$233$	5.80902	+	17.8783i	0.380561	+	1.17125i	0.939649	+	0.342139i	$0.111151\pi$
$233$	5.80902	+	17.8783i	0.380561	+	1.17125i	−0.559088	+	0.829108i	$0.688849\pi$
$234$	4.85410	−	3.52671i	0.317323	−	0.230548i
$235$	2.73607	+	8.42075i	0.178481	+	0.549309i
$236$	−4.73607	+	14.5761i	−0.308292	+	0.948824i
$237$		0			0
$238$	0.135255	−	0.416272i	0.00876727	−	0.0269829i
$239$	−10.8541	+	7.88597i	−0.702093	+	0.510101i	−0.880613	−	0.473836i	$-0.842869\pi$
$239$	−10.8541	+	7.88597i	−0.702093	+	0.510101i	0.178520	+	0.983936i	$0.442869\pi$
$240$	3.92705	−	2.85317i	0.253490	−	0.184171i
$241$	−6.89919	−	5.01255i	−0.444416	−	0.322887i	0.342971	−	0.939346i	$-0.388567\pi$
$241$	−6.89919	−	5.01255i	−0.444416	−	0.322887i	−0.787387	+	0.616459i	$0.788567\pi$
$242$	6.43769			0.413831
$243$	16.0000			1.02640
$244$	9.09017	+	6.60440i	0.581938	+	0.422803i
$245$	−1.61803	−	4.97980i	−0.103372	−	0.318148i
$246$	−1.23607	+	3.80423i	−0.0788088	+	0.242549i
$247$	−24.2705			−1.54430
$248$		0			0
$249$	4.09017			0.259204
$250$	−1.57295	+	4.84104i	−0.0994820	+	0.306174i
$251$	−0.291796	−	0.898056i	−0.0184180	−	0.0566848i	0.941425	−	0.337222i	$-0.109487\pi$
$251$	−0.291796	−	0.898056i	−0.0184180	−	0.0566848i	−0.959843	+	0.280537i	$0.909487\pi$
$252$	−7.85410	−	5.70634i	−0.494762	−	0.359466i
$253$	4.18034			0.262816
$254$	6.32624			0.396943
$255$	−0.500000	−	0.363271i	−0.0313112	−	0.0227489i
$256$	5.30902	−	3.85723i	0.331814	−	0.241077i
$257$	−1.14590	+	0.832544i	−0.0714792	+	0.0519326i	−0.622951	−	0.782261i	$-0.714066\pi$
$257$	−1.14590	+	0.832544i	−0.0714792	+	0.0519326i	0.551472	+	0.834194i	$0.314066\pi$
$258$	−0.881966	+	2.71441i	−0.0549088	+	0.168992i
$259$	0.572949	+	0.416272i	0.0356013	+	0.0258659i
$260$	−6.35410	+	19.5559i	−0.394065	+	1.21281i
$261$	−5.32624	−	16.3925i	−0.329686	−	1.01467i
$262$	0.0450850	−	0.0327561i	0.00278536	−	0.00202368i
$263$	3.33688	+	10.2699i	0.205761	+	0.633267i	0.999681	+	0.0252452i	$0.00803665\pi$
$263$	3.33688	+	10.2699i	0.205761	+	0.633267i	−0.793920	+	0.608022i	$0.791963\pi$
$264$	0.527864	+	1.62460i	0.0324878	+	0.0999871i
$265$	26.9164	−	19.5559i	1.65346	−	1.20131i
$266$	−2.86475	−	8.81678i	−0.175649	−	0.540591i
$267$	1.97214	−	6.06961i	0.120693	−	0.371454i
$268$	−5.54508	−	4.02874i	−0.338720	−	0.246094i
$269$	0.427051	−	1.31433i	0.0260378	−	0.0801360i	−0.937193	−	0.348811i	$-0.886586\pi$
$269$	0.427051	−	1.31433i	0.0260378	−	0.0801360i	0.963231	+	0.268675i	$0.0865856\pi$
$270$	6.54508	−	4.75528i	0.398321	−	0.289397i
$271$	7.73607	−	5.62058i	0.469933	−	0.341426i	−0.327482	−	0.944857i	$-0.606200\pi$
$271$	7.73607	−	5.62058i	0.469933	−	0.341426i	0.797415	+	0.603431i	$0.206200\pi$
$272$	0.354102	+	0.257270i	0.0214706	+	0.0155993i
$273$	−14.5623			−0.881351
$274$	−4.00000			−0.241649
$275$	−1.14590	−	0.832544i	−0.0691003	−	0.0502043i
$276$	−2.73607	−	8.42075i	−0.164692	−	0.506870i
$277$	−4.11803	+	12.6740i	−0.247429	+	0.761507i	0.747799	+	0.663925i	$0.231111\pi$
$277$	−4.11803	+	12.6740i	−0.247429	+	0.761507i	−0.995228	+	0.0975818i	$0.968889\pi$
$278$	3.61803			0.216995
$279$		0			0
$280$	−17.5623			−1.04955
$281$	5.88197	−	18.1028i	0.350889	−	1.07992i	−0.607466	−	0.794345i	$-0.707814\pi$
$281$	5.88197	−	18.1028i	0.350889	−	1.07992i	0.958355	−	0.285579i	$-0.0921859\pi$
$282$	0.645898	+	1.98787i	0.0384627	+	0.118376i
$283$	−5.30902	−	3.85723i	−0.315588	−	0.229288i	0.418702	−	0.908124i	$-0.362485\pi$
$283$	−5.30902	−	3.85723i	−0.315588	−	0.229288i	−0.734291	+	0.678835i	$0.762485\pi$
$284$	−0.145898			−0.00865746
$285$	−13.0902			−0.775395
$286$	−1.85410	−	1.34708i	−0.109635	−	0.0796547i
$287$	−15.7082	+	11.4127i	−0.927226	+	0.673669i
$288$	−9.09017	+	6.60440i	−0.535643	+	0.389168i
$289$	−5.23607	+	16.1150i	−0.308004	+	0.947939i
$290$	−11.2812	−	8.19624i	−0.662452	−	0.481300i
$291$	−1.63525	+	5.03280i	−0.0958603	+	0.295028i
$292$	−4.28115	−	13.1760i	−0.250536	−	0.771069i
$293$	6.66312	−	4.84104i	0.389264	−	0.282817i	−0.375890	−	0.926664i	$-0.622663\pi$
$293$	6.66312	−	4.84104i	0.389264	−	0.282817i	0.765154	+	0.643848i	$0.222663\pi$
$294$	−0.381966	−	1.17557i	−0.0222767	−	0.0685607i
$295$	−7.66312	−	23.5847i	−0.446164	−	1.37315i
$296$	0.427051	−	0.310271i	0.0248218	−	0.0180341i
$297$	−1.18034	−	3.63271i	−0.0684903	−	0.210791i
$298$	3.25329	−	10.0126i	0.188458	−	0.580014i
$299$	21.4894	+	15.6129i	1.24276	+	0.902919i
$300$	−0.927051	+	2.85317i	−0.0535233	+	0.164728i
$301$	−11.2082	+	8.14324i	−0.646030	+	0.469368i
$302$	9.75329	−	7.08618i	0.561239	−	0.407764i
$303$	−3.85410	−	2.80017i	−0.221412	−	0.160866i
$304$	9.27051			0.531700
$305$	−18.1803			−1.04100
$306$	0.236068	+	0.171513i	0.0134951	+	0.00980477i
$307$	1.88197	+	5.79210i	0.107409	+	0.330572i	0.990288	−	0.139028i	$-0.0443979\pi$
$307$	1.88197	+	5.79210i	0.107409	+	0.330572i	−0.882879	+	0.469601i	$0.844398\pi$
$308$	−1.14590	+	3.52671i	−0.0652936	+	0.200953i
$309$	−0.145898			−0.00829985
$310$		0			0
$311$	16.4721			0.934049			0.467025	−	0.884244i	$-0.345326\pi$
$311$	16.4721			0.934049			0.467025	+	0.884244i	$0.345326\pi$
$312$	−3.35410	+	10.3229i	−0.189889	+	0.584417i
$313$	−0.381966	−	1.17557i	−0.0215900	−	0.0664472i	0.939681	−	0.342052i	$-0.111122\pi$
$313$	−0.381966	−	1.17557i	−0.0215900	−	0.0664472i	−0.961271	+	0.275605i	$0.911122\pi$
$314$	4.85410	+	3.52671i	0.273933	+	0.199024i
$315$	15.7082			0.885057
$316$		0			0
$317$	−20.9443	−	15.2169i	−1.17635	−	0.854666i	−0.184593	−	0.982815i	$-0.559097\pi$
$317$	−20.9443	−	15.2169i	−1.17635	−	0.854666i	−0.991755	+	0.128149i	$0.959097\pi$
$318$	6.35410	−	4.61653i	0.356320	−	0.258882i
$319$	−5.32624	+	3.86974i	−0.298212	+	0.216664i
$320$	0.190983	−	0.587785i	0.0106763	−	0.0328582i
$321$	−0.881966	−	0.640786i	−0.0492265	−	0.0357652i
$322$	−3.13525	+	9.64932i	−0.174721	+	0.537736i
$323$	−0.364745	−	1.12257i	−0.0202950	−	0.0624615i
$324$	1.30902	−	0.951057i	0.0727232	−	0.0528365i
$325$	−2.78115	−	8.55951i	−0.154271	−	0.474796i
$326$	2.42705	+	7.46969i	0.134422	+	0.413708i
$327$	6.80902	−	4.94704i	0.376540	−	0.273572i
$328$	4.47214	+	13.7638i	0.246932	+	0.759980i
$329$	−3.13525	+	9.64932i	−0.172852	+	0.531984i
$330$	−1.00000	−	0.726543i	−0.0550482	−	0.0399948i
$331$	−3.48278	+	10.7189i	−0.191431	+	0.589164i	0.808569	+	0.588402i	$0.200243\pi$
$331$	−3.48278	+	10.7189i	−0.191431	+	0.589164i	−1.00000		0.000762014i	$0.999757\pi$
$332$	5.35410	−	3.88998i	0.293845	−	0.213491i
$333$	−0.381966	+	0.277515i	−0.0209316	+	0.0152077i
$334$	4.61803	+	3.35520i	0.252688	+	0.183588i
$335$	11.0902			0.605921
$336$	5.56231			0.303449
$337$	15.3541	+	11.1554i	0.836391	+	0.607674i	0.921360	−	0.388710i	$-0.127079\pi$
$337$	15.3541	+	11.1554i	0.836391	+	0.607674i	−0.0849690	+	0.996384i	$0.527079\pi$
$338$	−2.01722	−	6.20837i	−0.109722	−	0.337691i
$339$	−0.572949	+	1.76336i	−0.0311183	+	0.0957723i
$340$	−1.00000			−0.0542326
$341$		0			0
$342$	6.18034			0.334195
$343$	−4.63525	+	14.2658i	−0.250280	+	0.770283i
$344$	3.19098	+	9.82084i	0.172046	+	0.529504i
$345$	11.5902	+	8.42075i	0.623994	+	0.453358i
$346$	−0.562306			−0.0302298
$347$	−8.12461			−0.436152			−0.218076	−	0.975932i	$-0.569978\pi$
$347$	−8.12461			−0.436152			−0.218076	+	0.975932i	$0.569978\pi$
$348$	11.2812	+	8.19624i	0.604733	+	0.439364i
$349$	13.5172	−	9.82084i	0.723560	−	0.525697i	−0.163959	−	0.986467i	$-0.552427\pi$
$349$	13.5172	−	9.82084i	0.723560	−	0.525697i	0.887520	+	0.460770i	$0.152427\pi$
$350$	2.78115	−	2.02063i	0.148659	−	0.108007i
$351$	7.50000	−	23.0826i	0.400320	−	1.23206i
$352$	3.47214	+	2.52265i	0.185065	+	0.134458i
$353$	10.0066	−	30.7971i	0.532596	−	1.63916i	−0.216190	−	0.976351i	$-0.569363\pi$
$353$	10.0066	−	30.7971i	0.532596	−	1.63916i	0.748786	−	0.662812i	$-0.230637\pi$
$354$	−1.80902	−	5.56758i	−0.0961482	−	0.295914i
$355$	0.190983	−	0.138757i	0.0101363	−	0.00736447i
$356$	−3.19098	−	9.82084i	−0.169122	−	0.520503i
$357$	−0.218847	−	0.673542i	−0.0115826	−	0.0356476i
$358$	−9.89919	+	7.19218i	−0.523188	+	0.380119i
$359$	−7.82624	−	24.0867i	−0.413053	−	1.27125i	−0.913981	−	0.405757i	$-0.867008\pi$
$359$	−7.82624	−	24.0867i	−0.413053	−	1.27125i	0.500928	−	0.865489i	$-0.332992\pi$
$360$	3.61803	−	11.1352i	0.190687	−	0.586875i
$361$	−4.85410	−	3.52671i	−0.255479	−	0.185616i
$362$	3.24671	−	9.99235i	0.170643	−	0.525186i
$363$	8.42705	−	6.12261i	0.442305	−	0.321354i
$364$	−19.0623	+	13.8496i	−0.999136	+	0.725915i
$365$	18.1353	+	13.1760i	0.949243	+	0.689665i
$366$	−4.29180			−0.224336
$367$	36.2705			1.89331			0.946653	−	0.322256i	$-0.104441\pi$
$367$	36.2705			1.89331			0.946653	+	0.322256i	$0.104441\pi$
$368$	−8.20820	−	5.96361i	−0.427882	−	0.310875i
$369$	−4.00000	−	12.3107i	−0.208232	−	0.640871i
$370$	−0.118034	+	0.363271i	−0.00613629	+	0.0188856i
$371$	38.1246			1.97933
$372$		0			0
$373$	−0.347524			−0.0179941			−0.00899706	−	0.999960i	$-0.502864\pi$
$373$	−0.347524			−0.0179941			−0.00899706	+	0.999960i	$0.502864\pi$
$374$	0.0344419	−	0.106001i	0.00178095	−	0.00548119i
$375$	2.54508	+	7.83297i	0.131428	+	0.404493i
$376$	6.11803	+	4.44501i	0.315514	+	0.229234i
$377$	−41.8328			−2.15450
$378$	9.27051			0.476824
$379$	14.8992	+	10.8249i	0.765320	+	0.556037i	0.900537	−	0.434779i	$-0.143173\pi$
$379$	14.8992	+	10.8249i	0.765320	+	0.556037i	−0.135218	+	0.990816i	$0.543173\pi$
$380$	−17.1353	+	12.4495i	−0.879020	+	0.638645i
$381$	8.28115	−	6.01661i	0.424256	−	0.308240i
$382$	3.07295	−	9.45756i	0.157226	−	0.483891i
$383$	−13.6353	−	9.90659i	−0.696729	−	0.506203i	0.182136	−	0.983273i	$-0.441699\pi$
$383$	−13.6353	−	9.90659i	−0.696729	−	0.506203i	−0.878865	+	0.477070i	$0.841699\pi$
$384$	3.51722	−	10.8249i	0.179487	−	0.552406i
$385$	−1.85410	−	5.70634i	−0.0944938	−	0.290822i
$386$	−1.19098	+	0.865300i	−0.0606194	+	0.0440426i
$387$	−2.85410	−	8.78402i	−0.145082	−	0.446517i
$388$	2.64590	+	8.14324i	0.134325	+	0.413410i
$389$	−23.5172	+	17.0863i	−1.19237	+	0.866308i	−0.993513	−	0.113721i	$-0.963723\pi$
$389$	−23.5172	+	17.0863i	−1.19237	+	0.866308i	−0.198858	+	0.980028i	$0.563723\pi$
$390$	−2.42705	−	7.46969i	−0.122899	−	0.378243i
$391$	−0.399187	+	1.22857i	−0.0201878	+	0.0621315i
$392$	−3.61803	−	2.62866i	−0.182738	−	0.132767i
$393$	0.0278640	−	0.0857567i	0.00140556	−	0.00432585i
$394$	−8.20820	+	5.96361i	−0.413523	+	0.300442i
$395$		0			0
$396$	−2.00000	−	1.45309i	−0.100504	−	0.0730203i
$397$	16.2918			0.817662			0.408831	−	0.912610i	$-0.365937\pi$
$397$	16.2918			0.817662			0.408831	+	0.912610i	$0.365937\pi$
$398$	−16.5066			−0.827400
$399$	−12.1353	−	8.81678i	−0.607523	−	0.441391i
$400$	1.06231	+	3.26944i	0.0531153	+	0.163472i
$401$	9.21885	−	28.3727i	0.460367	−	1.41686i	−0.404349	−	0.914605i	$-0.632502\pi$
$401$	9.21885	−	28.3727i	0.460367	−	1.41686i	0.864717	−	0.502260i	$-0.167498\pi$
$402$	2.61803			0.130576
$403$		0			0
$404$	−7.70820			−0.383497
$405$	−0.809017	+	2.48990i	−0.0402004	+	0.123724i
$406$	−4.93769	−	15.1967i	−0.245054	−	0.754198i
$407$	0.145898	+	0.106001i	0.00723190	+	0.00525428i
$408$	−0.527864			−0.0261332
$409$	6.18034			0.305598			0.152799	−	0.988257i	$-0.451171\pi$
$409$	6.18034			0.305598			0.152799	+	0.988257i	$0.451171\pi$
$410$	−8.47214	−	6.15537i	−0.418409	−	0.303992i
$411$	−5.23607	+	3.80423i	−0.258276	+	0.187649i
$412$	−0.190983	+	0.138757i	−0.00940906	+	0.00683608i
$413$	8.78115	−	27.0256i	0.432092	−	1.32984i
$414$	−5.47214	−	3.97574i	−0.268941	−	0.195397i
$415$	−3.30902	+	10.1841i	−0.162433	+	0.499918i
$416$	8.42705	+	25.9358i	0.413170	+	1.27161i
$417$	4.73607	−	3.44095i	0.231926	−	0.168504i
$418$	−0.729490	−	2.24514i	−0.0356805	−	0.109813i
$419$	1.38197	+	4.25325i	0.0675135	+	0.207785i	0.979122	−	0.203275i	$-0.0651586\pi$
$419$	1.38197	+	4.25325i	0.0675135	+	0.207785i	−0.911608	+	0.411060i	$0.865159\pi$
$420$	−10.2812	+	7.46969i	−0.501669	+	0.364484i
$421$	4.56231	+	14.0413i	0.222353	+	0.684333i	0.998549	+	0.0538414i	$0.0171466\pi$
$421$	4.56231	+	14.0413i	0.222353	+	0.684333i	−0.776196	+	0.630491i	$0.782853\pi$
$422$	1.52786	−	4.70228i	0.0743753	−	0.228904i
$423$	−5.47214	−	3.97574i	−0.266064	−	0.193307i
$424$	8.78115	−	27.0256i	0.426450	−	1.31248i
$425$	0.354102	−	0.257270i	0.0171765	−	0.0124794i
$426$	0.0450850	−	0.0327561i	0.00218437	−	0.00158704i
$427$	−16.8541	−	12.2452i	−0.815627	−	0.592588i
$428$	−1.76393			−0.0852629
$429$	−3.70820			−0.179034
$430$	−6.04508	−	4.39201i	−0.291520	−	0.211802i
$431$	9.03444	+	27.8052i	0.435174	+	1.33933i	0.892908	+	0.450238i	$0.148661\pi$
$431$	9.03444	+	27.8052i	0.435174	+	1.33933i	−0.457735	+	0.889089i	$0.651339\pi$
$432$	−2.86475	+	8.81678i	−0.137830	+	0.424197i
$433$	−0.583592			−0.0280456			−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592			−0.0280456			−0.0140228	+	0.999902i	$0.504464\pi$
$434$		0			0
$435$	−22.5623			−1.08178
$436$	4.20820	−	12.9515i	0.201536	−	0.620265i
$437$	8.45492	+	26.0216i	0.404453	+	1.24478i
$438$	4.28115	+	3.11044i	0.204561	+	0.148623i
$439$	41.8328			1.99657			0.998286	−	0.0585295i	$-0.0186412\pi$
$439$	41.8328			1.99657			0.998286	+	0.0585295i	$0.0186412\pi$
$440$	−4.47214			−0.213201
$441$	3.23607	+	2.35114i	0.154098	+	0.111959i
$442$	0.572949	−	0.416272i	0.0272524	−	0.0198000i
$443$	33.2705	−	24.1724i	1.58073	−	1.14847i	0.664877	−	0.746953i	$-0.268484\pi$
$443$	33.2705	−	24.1724i	1.58073	−	1.14847i	0.915853	−	0.401514i	$-0.131516\pi$
$444$	0.118034	−	0.363271i	0.00560165	−	0.0172401i
$445$	13.5172	+	9.82084i	0.640778	+	0.465552i
$446$	0.135255	−	0.416272i	0.00640451	−	0.0197110i
$447$	−5.26393	−	16.2007i	−0.248975	−	0.766268i
$448$	0.572949	−	0.416272i	0.0270693	−	0.0196670i
$449$	−7.43769	−	22.8909i	−0.351006	−	1.08029i	−0.958289	−	0.285801i	$-0.907740\pi$
$449$	−7.43769	−	22.8909i	−0.351006	−	1.08029i	0.607283	−	0.794486i	$-0.292260\pi$
$450$	0.708204	+	2.17963i	0.0333851	+	0.102749i
$451$	−4.00000	+	2.90617i	−0.188353	+	0.136846i
$452$	0.927051	+	2.85317i	0.0436048	+	0.134202i
$453$	6.02786	−	18.5519i	0.283214	−	0.871642i
$454$	−10.3713	−	7.53521i	−0.486750	−	0.353645i
$455$	11.7812	−	36.2587i	0.552309	−	1.69983i
$456$	−9.04508	+	6.57164i	−0.423575	+	0.307745i
$457$	−12.7361	+	9.25330i	−0.595768	+	0.432851i	−0.844374	−	0.535754i	$-0.820028\pi$
$457$	−12.7361	+	9.25330i	−0.595768	+	0.432851i	0.248606	+	0.968605i	$0.420028\pi$
$458$	3.61803	+	2.62866i	0.169060	+	0.122829i
$459$	1.18034			0.0550935
$460$	23.1803			1.08079
$461$	8.69098	+	6.31437i	0.404779	+	0.294089i	0.771485	−	0.636248i	$-0.219514\pi$
$461$	8.69098	+	6.31437i	0.404779	+	0.294089i	−0.366705	+	0.930337i	$0.619514\pi$
$462$	−0.437694	−	1.34708i	−0.0203634	−	0.0626720i
$463$	9.61803	−	29.6013i	0.446988	−	1.37569i	−0.433301	−	0.901249i	$-0.642651\pi$
$463$	9.61803	−	29.6013i	0.446988	−	1.37569i	0.880289	−	0.474438i	$-0.157349\pi$
$464$	15.9787			0.741793
$465$		0			0
$466$	−11.6180			−0.538195
$467$	−10.1287	+	31.1729i	−0.468699	+	1.44251i	0.385571	+	0.922678i	$0.374005\pi$
$467$	−10.1287	+	31.1729i	−0.468699	+	1.44251i	−0.854270	+	0.519830i	$0.825995\pi$
$468$	−4.85410	−	14.9394i	−0.224381	−	0.690574i
$469$	10.2812	+	7.46969i	0.474740	+	0.344918i
$470$	−5.47214			−0.252411
$471$	9.70820			0.447330
$472$	−17.1353	−	12.4495i	−0.788714	−	0.573034i
$473$	−2.85410	+	2.07363i	−0.131232	+	0.0953454i
$474$		0			0
$475$	2.86475	−	8.81678i	0.131444	−	0.404542i
$476$	−0.927051	−	0.673542i	−0.0424913	−	0.0308717i
$477$	−7.85410	+	24.1724i	−0.359615	+	1.10678i
$478$	−2.56231	−	7.88597i	−0.117197	−	0.360696i
$479$	7.23607	−	5.25731i	0.330624	−	0.240213i	−0.410071	−	0.912054i	$-0.634496\pi$
$479$	7.23607	−	5.25731i	0.330624	−	0.240213i	0.740696	+	0.671841i	$0.234496\pi$
$480$	4.54508	+	13.9883i	0.207454	+	0.638477i
$481$	0.354102	+	1.08981i	0.0161457	+	0.0496912i
$482$	4.26393	−	3.09793i	0.194217	−	0.141107i
$483$	5.07295	+	15.6129i	0.230827	+	0.710413i
$484$	5.20820	−	16.0292i	0.236737	−	0.728600i
$485$	−11.2082	−	8.14324i	−0.508938	−	0.369765i
$486$	−3.05573	+	9.40456i	−0.138611	+	0.426600i
$487$	18.5451	−	13.4738i	0.840358	−	0.610556i	−0.0821126	−	0.996623i	$-0.526167\pi$
$487$	18.5451	−	13.4738i	0.840358	−	0.610556i	0.922471	+	0.386067i	$0.126167\pi$
$488$	−12.5623	+	9.12705i	−0.568669	+	0.413162i
$489$	10.2812	+	7.46969i	0.464930	+	0.337791i
$490$	3.23607			0.146191
$491$	27.5967			1.24542			0.622712	−	0.782451i	$-0.286031\pi$
$491$	27.5967			1.24542			0.622712	+	0.782451i	$0.286031\pi$
$492$	8.47214	+	6.15537i	0.381953	+	0.277505i
$493$	−0.628677	−	1.93487i	−0.0283142	−	0.0871421i
$494$	4.63525	−	14.2658i	0.208550	−	0.641851i
$495$	4.00000			0.179787
$496$		0			0
$497$	0.270510			0.0121340
$498$	−0.781153	+	2.40414i	−0.0350043	+	0.107732i
$499$	−1.28115	−	3.94298i	−0.0573523	−	0.176512i	0.918277	−	0.395940i	$-0.129581\pi$
$499$	−1.28115	−	3.94298i	−0.0573523	−	0.176512i	−0.975629	+	0.219427i	$0.929581\pi$
$500$	10.7812	+	7.83297i	0.482148	+	0.350301i
$501$	9.23607			0.412637
$502$	0.583592			0.0260470
$503$	−10.6353	−	7.72696i	−0.474203	−	0.344528i	0.324874	−	0.945757i	$-0.394678\pi$
$503$	−10.6353	−	7.72696i	−0.474203	−	0.344528i	−0.799077	+	0.601229i	$0.794678\pi$
$504$	10.8541	−	7.88597i	0.483480	−	0.351269i
$505$	10.0902	−	7.33094i	0.449007	−	0.326222i
$506$	−0.798374	+	2.45714i	−0.0354920	+	0.109233i
$507$	−8.54508	−	6.20837i	−0.379501	−	0.275723i
$508$	5.11803	−	15.7517i	0.227076	−	0.698868i
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	0.963284	−	0.268486i	$-0.0865232\pi$
$509$	0.590170	+	1.81636i	0.0261588	+	0.0805086i	−0.937125	+	0.348994i	$0.886523\pi$
$510$	0.309017	−	0.224514i	0.0136835	−	0.00994165i
$511$	7.93769	+	24.4297i	0.351143	+	1.08071i
$512$	−5.78115	−	17.7926i	−0.255493	−	0.786327i
$513$	20.2254	−	14.6946i	0.892974	−	0.648784i
$514$	−0.270510	−	0.832544i	−0.0119317	−	0.0367219i
$515$	0.118034	−	0.363271i	0.00520120	−	0.0160076i
$516$	6.04508	+	4.39201i	0.266120	+	0.193348i
$517$	−0.798374	+	2.45714i	−0.0351124	+	0.108065i
$518$	−0.354102	+	0.257270i	−0.0155583	+	0.0113038i
$519$	−0.736068	+	0.534785i	−0.0323098	+	0.0234744i
$520$	−22.9894	−	16.7027i	−1.00815	−	0.732464i
$521$	31.0689			1.36115			0.680576	−	0.732677i	$-0.261729\pi$
$521$	31.0689			1.36115			0.680576	+	0.732677i	$0.261729\pi$
$522$	10.6525			0.466246
$523$	27.6074	+	20.0579i	1.20719	+	0.877073i	0.994972	−	0.100150i	$-0.0319324\pi$
$523$	27.6074	+	20.0579i	1.20719	+	0.877073i	0.212215	+	0.977223i	$0.431932\pi$
$524$	−0.0450850	−	0.138757i	−0.00196955	−	0.00606164i
$525$	1.71885	−	5.29007i	0.0750166	−	0.230877i
$526$	−6.67376			−0.290990
$527$		0			0
$528$	1.41641			0.0616412
$529$	2.14590	−	6.60440i	0.0932999	−	0.287148i
$530$	6.35410	+	19.5559i	0.276005	+	0.849455i
$531$	15.3262	+	11.1352i	0.665102	+	0.483225i
$532$	−24.2705			−1.05226
$533$	−31.4164			−1.36080
$534$	3.19098	+	2.31838i	0.138087	+	0.100326i
$535$	2.30902	−	1.67760i	0.0998275	−	0.0725289i
$536$	7.66312	−	5.56758i	0.330996	−	0.240483i
$537$	−6.11803	+	18.8294i	−0.264013	+	0.812547i
$538$	0.690983	+	0.502029i	0.0297904	+	0.0216440i
$539$	0.472136	−	1.45309i	0.0203363	−	0.0625888i
$540$	−6.54508	−	20.1437i	−0.281656	−	0.866847i
$541$	−17.7984	+	12.9313i	−0.765212	+	0.555959i	−0.900504	−	0.434847i	$-0.856803\pi$
$541$	−17.7984	+	12.9313i	−0.765212	+	0.555959i	0.135293	+	0.990806i	$0.456803\pi$
$542$	1.82624	+	5.62058i	0.0784436	+	0.241425i
$543$	−5.25329	−	16.1680i	−0.225440	−	0.693834i
$544$	−1.07295	+	0.779543i	−0.0460023	+	0.0334226i
$545$	6.80902	+	20.9560i	0.291666	+	0.897656i
$546$	2.78115	−	8.55951i	0.119022	−	0.366313i
$547$	19.1803	+	13.9353i	0.820092	+	0.595832i	0.916739	−	0.399487i	$-0.130812\pi$
$547$	19.1803	+	13.9353i	0.820092	+	0.595832i	−0.0966468	+	0.995319i	$0.530812\pi$
$548$	−3.23607	+	9.95959i	−0.138238	+	0.425453i
$549$	11.2361	−	8.16348i	0.479544	−	0.348409i
$550$	0.708204	−	0.514540i	0.0301979	−	0.0219401i
$551$	−34.8607	−	25.3278i	−1.48511	−	1.07900i
$552$	12.2361			0.520802
$553$		0			0
$554$	−6.66312	−	4.84104i	−0.283089	−	0.205676i
$555$	0.190983	+	0.587785i	0.00810678	+	0.0249501i
$556$	2.92705	−	9.00854i	0.124135	−	0.382047i
$557$	−35.8885			−1.52065			−0.760323	−	0.649545i	$-0.774959\pi$
$557$	−35.8885			−1.52065			−0.760323	+	0.649545i	$0.774959\pi$
$558$		0			0
$559$	−22.4164			−0.948113
$560$	−4.50000	+	13.8496i	−0.190160	+	0.585251i
$561$	−0.0557281	−	0.171513i	−0.00235284	−	0.00724130i
$562$	9.51722	+	6.91467i	0.401460	+	0.291678i
$563$	−8.56231			−0.360858			−0.180429	−	0.983588i	$-0.557749\pi$
$563$	−8.56231			−0.360858			−0.180429	+	0.983588i	$0.557749\pi$
$564$	5.47214			0.230418
$565$	−3.92705	−	2.85317i	−0.165212	−	0.120034i
$566$	3.28115	−	2.38390i	0.137917	−	0.100203i
$567$	−2.42705	+	1.76336i	−0.101927	+	0.0740540i
$568$	0.0623059	−	0.191758i	0.00261430	−	0.00804598i
$569$	12.5623	+	9.12705i	0.526639	+	0.382626i	0.819099	−	0.573652i	$-0.194474\pi$
$569$	12.5623	+	9.12705i	0.526639	+	0.382626i	−0.292460	+	0.956278i	$0.594474\pi$
$570$	2.50000	−	7.69421i	0.104713	−	0.322275i
$571$	−2.16312	−	6.65740i	−0.0905237	−	0.278603i	0.895538	−	0.444986i	$-0.146791\pi$
$571$	−2.16312	−	6.65740i	−0.0905237	−	0.278603i	−0.986061	+	0.166383i	$0.946791\pi$
$572$	−4.85410	+	3.52671i	−0.202960	+	0.147459i
$573$	−4.97214	−	15.3027i	−0.207714	−	0.639278i
$574$	−3.70820	−	11.4127i	−0.154777	−	0.476356i
$575$	−8.20820	+	5.96361i	−0.342306	+	0.248700i
$576$	0.145898	+	0.449028i	0.00607908	+	0.0187095i
$577$	12.0451	−	37.0710i	0.501443	−	1.54328i	−0.305225	−	0.952280i	$-0.598732\pi$
$577$	12.0451	−	37.0710i	0.501443	−	1.54328i	0.806669	−	0.591004i	$-0.201268\pi$
$578$	−8.47214	−	6.15537i	−0.352394	−	0.256030i
$579$	−0.736068	+	2.26538i	−0.0305899	+	0.0941462i
$580$	−29.5344	+	21.4580i	−1.22635	+	0.890996i
$581$	−9.92705	+	7.21242i	−0.411843	+	0.299222i
$582$	−2.64590	−	1.92236i	−0.109676	−	0.0796843i
$583$	9.70820			0.402073
$584$	19.1459			0.792263
$585$	20.5623	+	14.9394i	0.850147	+	0.617668i
$586$	1.57295	+	4.84104i	0.0649779	+	0.199981i
$587$	−11.1287	+	34.2505i	−0.459330	+	1.41367i	0.406646	+	0.913586i	$0.366698\pi$
$587$	−11.1287	+	34.2505i	−0.459330	+	1.41367i	−0.865976	+	0.500086i	$0.833302\pi$
$588$	−3.23607			−0.133453
$589$		0			0
$590$	15.3262			0.630971
$591$	−5.07295	+	15.6129i	−0.208673	+	0.642230i
$592$	−0.135255	−	0.416272i	−0.00555894	−	0.0171087i
$593$	−4.94427	−	3.59222i	−0.203037	−	0.147515i	0.481621	−	0.876380i	$-0.340048\pi$
$593$	−4.94427	−	3.59222i	−0.203037	−	0.147515i	−0.684658	+	0.728865i	$0.740048\pi$
$594$	2.36068			0.0968599
$595$	1.85410			0.0760108
$596$	−22.2984	−	16.2007i	−0.913377	−	0.663607i
$597$	−21.6074	+	15.6987i	−0.884332	+	0.642505i
$598$	−13.2812	+	9.64932i	−0.543107	+	0.394590i
$599$	9.20820	−	28.3399i	0.376237	−	1.15794i	−0.566403	−	0.824128i	$-0.691666\pi$
$599$	9.20820	−	28.3399i	0.376237	−	1.15794i	0.942640	−	0.333810i	$-0.108334\pi$
$600$	−3.35410	−	2.43690i	−0.136931	−	0.0994859i
$601$	−6.79837	+	20.9232i	−0.277311	+	0.853477i	0.711287	+	0.702902i	$0.248113\pi$
$601$	−6.79837	+	20.9232i	−0.277311	+	0.853477i	−0.988599	+	0.150575i	$0.951887\pi$
$602$	−2.64590	−	8.14324i	−0.107839	−	0.331894i
$603$	−6.85410	+	4.97980i	−0.279121	+	0.202793i
$604$	−9.75329	−	30.0175i	−0.396856	−	1.22140i
$605$	8.42705	+	25.9358i	0.342608	+	1.05444i
$606$	2.38197	−	1.73060i	0.0967608	−	0.0703008i
$607$	−7.85410	−	24.1724i	−0.318788	−	0.981129i	−0.974167	−	0.225829i	$-0.927491\pi$
$607$	−7.85410	−	24.1724i	−0.318788	−	0.981129i	0.655379	−	0.755300i	$-0.272509\pi$
$608$	−8.68034	+	26.7153i	−0.352034	+	1.08345i
$609$	−20.9164	−	15.1967i	−0.847576	−	0.615800i
$610$	3.47214	−	10.6861i	0.140583	−	0.432669i
$611$	−13.2812	+	9.64932i	−0.537298	+	0.390370i
$612$	0.618034	−	0.449028i	0.0249825	−	0.0181509i
$613$	20.2705	+	14.7274i	0.818718	+	0.594834i	0.916345	−	0.400390i	$-0.131125\pi$
$613$	20.2705	+	14.7274i	0.818718	+	0.594834i	−0.0976269	+	0.995223i	$0.531125\pi$
$614$	−3.76393			−0.151900
$615$	−16.9443			−0.683259
$616$	−4.14590	−	3.01217i	−0.167043	−	0.121364i
$617$	−4.39919	−	13.5393i	−0.177105	−	0.545072i	0.822619	−	0.568593i	$-0.192512\pi$
$617$	−4.39919	−	13.5393i	−0.177105	−	0.545072i	−0.999723	+	0.0235215i	$0.992512\pi$
$618$	0.0278640	−	0.0857567i	0.00112086	−	0.00344964i
$619$	40.0000			1.60774			0.803868	−	0.594808i	$-0.202772\pi$
$619$	40.0000			1.60774			0.803868	+	0.594808i	$0.202772\pi$
$620$		0			0
$621$	−27.3607			−1.09795
$622$	−3.14590	+	9.68208i	−0.126139	+	0.388216i
$623$	5.91641	+	18.2088i	0.237036	+	0.729521i
$624$	7.28115	+	5.29007i	0.291479	+	0.211772i
$625$	−30.8328			−1.23331
$626$	0.763932			0.0305329
$627$	−3.09017	−	2.24514i	−0.123410	−	0.0896623i
$628$	12.7082	−	9.23305i	0.507113	−	0.368439i
$629$	−0.0450850	+	0.0327561i	−0.00179766	+	0.00130607i
$630$	−3.00000	+	9.23305i	−0.119523	+	0.367854i
$631$	−7.06231	−	5.13107i	−0.281146	−	0.204264i	0.438271	−	0.898843i	$-0.355591\pi$
$631$	−7.06231	−	5.13107i	−0.281146	−	0.204264i	−0.719417	+	0.694578i	$0.755591\pi$
$632$		0			0
$633$	−2.47214	−	7.60845i	−0.0982586	−	0.302409i
$634$	12.9443	−	9.40456i	0.514083	−	0.373503i
$635$	8.28115	+	25.4868i	0.328628	+	1.01141i
$636$	−6.35410	−	19.5559i	−0.251957	−	0.775442i
$637$	7.85410	−	5.70634i	0.311191	−	0.226093i
$638$	−1.25735	−	3.86974i	−0.0497791	−	0.153204i
$639$	−0.0557281	+	0.171513i	−0.00220457	+	0.00678497i
$640$	24.1074	+	17.5150i	0.952928	+	0.692343i
$641$	12.6976	−	39.0791i	0.501523	−	1.54353i	−0.305014	−	0.952348i	$-0.598661\pi$
$641$	12.6976	−	39.0791i	0.501523	−	1.54353i	0.806538	−	0.591183i	$-0.201339\pi$
$642$	0.545085	−	0.396027i	0.0215128	−	0.0156300i
$643$	6.59017	−	4.78804i	0.259891	−	0.188822i	−0.450208	−	0.892924i	$-0.648650\pi$
$643$	6.59017	−	4.78804i	0.259891	−	0.188822i	0.710099	+	0.704102i	$0.248650\pi$
$644$	21.4894	+	15.6129i	0.846799	+	0.615236i
$645$	−12.0902			−0.476050
$646$	0.729490			0.0287014
$647$	−24.1803	−	17.5680i	−0.950627	−	0.690671i	0.000327889	−	1.00000i	$-0.499896\pi$
$647$	−24.1803	−	17.5680i	−0.950627	−	0.690671i	−0.950955	+	0.309329i	$0.899896\pi$
$648$	0.690983	+	2.12663i	0.0271444	+	0.0835418i
$649$	2.23607	−	6.88191i	0.0877733	−	0.270139i
$650$	5.56231			0.218172
$651$		0			0
$652$	20.5623			0.805282
$653$	12.2533	−	37.7117i	0.479508	−	1.47577i	−0.360272	−	0.932847i	$-0.617316\pi$
$653$	12.2533	−	37.7117i	0.479508	−	1.47577i	0.839780	−	0.542927i	$-0.182684\pi$
$654$	1.60739	+	4.94704i	0.0628540	+	0.193445i
$655$	0.190983	+	0.138757i	0.00746232	+	0.00542170i
$656$	12.0000			0.468521
$657$	−17.1246			−0.668095
$658$	−5.07295	−	3.68571i	−0.197764	−	0.143684i
$659$	−18.3541	+	13.3350i	−0.714974	+	0.519459i	−0.884775	−	0.466019i	$-0.845688\pi$
$659$	−18.3541	+	13.3350i	−0.714974	+	0.519459i	0.169800	+	0.985478i	$0.445688\pi$
$660$	−2.61803	+	1.90211i	−0.101907	+	0.0740396i
$661$	−5.13525	+	15.8047i	−0.199738	+	0.614731i	0.800150	+	0.599800i	$0.204753\pi$
$661$	−5.13525	+	15.8047i	−0.199738	+	0.614731i	−0.999889	+	0.0149316i	$0.995247\pi$
$662$	−5.63525	−	4.09425i	−0.219020	−	0.159128i
$663$	0.354102	−	1.08981i	0.0137522	−	0.0423249i
$664$	2.82624	+	8.69827i	0.109679	+	0.337558i
$665$	31.7705	−	23.0826i	1.23201	−	0.895106i
$666$	−0.0901699	−	0.277515i	−0.00349401	−	0.0107535i
$667$	14.5729	+	44.8509i	0.564267	+	1.73663i
$668$	12.0902	−	8.78402i	0.467783	−	0.339864i
$669$	−0.218847	−	0.673542i	−0.00846112	−	0.0260406i
$670$	−2.11803	+	6.51864i	−0.0818268	+	0.251837i
$671$	−4.29180	−	3.11817i	−0.165683	−	0.120376i
$672$	−5.20820	+	16.0292i	−0.200911	+	0.618340i
$673$	−3.57295	+	2.59590i	−0.137727	+	0.100065i	−0.654516	−	0.756049i	$-0.727127\pi$
$673$	−3.57295	+	2.59590i	−0.137727	+	0.100065i	0.516788	+	0.856113i	$0.327127\pi$
$674$	−9.48936	+	6.89442i	−0.365516	+	0.265563i
$675$	7.50000	+	5.44907i	0.288675	+	0.209735i
$676$	−17.0902			−0.657314
$677$	−28.6525			−1.10120			−0.550602	−	0.834768i	$-0.685602\pi$
$677$	−28.6525			−1.10120			−0.550602	+	0.834768i	$0.685602\pi$
$678$	−0.927051	−	0.673542i	−0.0356032	−	0.0258672i
$679$	−4.90576	−	15.0984i	−0.188266	−	0.579423i
$680$	0.427051	−	1.31433i	0.0163767	−	0.0504022i
$681$	−20.7426			−0.794860
$682$		0			0
$683$	10.0557			0.384772			0.192386	−	0.981319i	$-0.438377\pi$
$683$	10.0557			0.384772			0.192386	+	0.981319i	$0.438377\pi$
$684$	5.00000	−	15.3884i	0.191180	−	0.588391i
$685$	−5.23607	−	16.1150i	−0.200060	−	0.615721i
$686$	−7.50000	−	5.44907i	−0.286351	−	0.208046i
$687$	7.23607			0.276073
$688$	8.56231			0.326435
$689$	49.9058	+	36.2587i	1.90126	+	1.38134i
$690$	−7.16312	+	5.20431i	−0.272695	+	0.198125i
$691$	−3.10081	+	2.25287i	−0.117960	+	0.0857033i	−0.645201	−	0.764013i	$-0.723227\pi$
$691$	−3.10081	+	2.25287i	−0.117960	+	0.0857033i	0.527241	+	0.849716i	$0.323227\pi$
$692$	−0.454915	+	1.40008i	−0.0172933	+	0.0532232i
$693$	3.70820	+	2.69417i	0.140863	+	0.102343i
$694$	1.55166	−	4.77553i	0.0589003	−	0.181277i
$695$	4.73607	+	14.5761i	0.179649	+	0.552904i
$696$	−15.5902	+	11.3269i	−0.590944	+	0.429346i
$697$	−0.472136	−	1.45309i	−0.0178834	−	0.0550395i
$698$	3.19098	+	9.82084i	0.120780	+	0.371724i
$699$	−15.2082	+	11.0494i	−0.575227	+	0.417927i
$700$	−2.78115	−	8.55951i	−0.105118	−	0.323519i
$701$	−9.28115	+	28.5645i	−0.350544	+	1.07886i	0.608004	+	0.793934i	$0.291970\pi$
$701$	−9.28115	+	28.5645i	−0.350544	+	1.07886i	−0.958548	+	0.284930i	$0.908030\pi$
$702$	12.1353	+	8.81678i	0.458016	+	0.332768i
$703$	−0.364745	+	1.12257i	−0.0137566	+	0.0423385i
$704$	0.145898	−	0.106001i	0.00549874	−	0.00399507i
$705$	−7.16312	+	5.20431i	−0.269779	+	0.196006i
$706$	16.1910	+	11.7634i	0.609356	+	0.442723i
$707$	14.2918			0.537498
$708$	−15.3262			−0.575995
$709$	3.35410	+	2.43690i	0.125966	+	0.0915196i	0.648984	−	0.760802i	$-0.275194\pi$
$709$	3.35410	+	2.43690i	0.125966	+	0.0915196i	−0.523018	+	0.852321i	$0.675194\pi$
$710$	0.0450850	+	0.138757i	0.00169201	+	0.00520747i
$711$		0			0
$712$	14.2705			0.534810
$713$		0			0
$714$	0.437694			0.0163803
$715$	3.00000	−	9.23305i	0.112194	−	0.345297i
$716$	9.89919	+	30.4666i	0.369950	+	1.13859i
$717$	−10.8541	−	7.88597i	−0.405354	−	0.294507i
$718$	15.6525			0.584145
$719$	41.3820			1.54329			0.771643	−	0.636055i	$-0.219435\pi$
$719$	41.3820			1.54329			0.771643	+	0.636055i	$0.219435\pi$
$720$	−7.85410	−	5.70634i	−0.292705	−	0.212663i
$721$	0.354102	−	0.257270i	0.0131874	−	0.00958124i
$722$	3.00000	−	2.17963i	0.111648	−	0.0811173i
$723$	2.63525	−	8.11048i	0.0980062	−	0.301632i
$724$	−22.2533	−	16.1680i	−0.827037	−	0.600878i
$725$	4.93769	−	15.1967i	0.183381	−	0.564390i
$726$	1.98936	+	6.12261i	0.0738320	+	0.227231i
$727$	19.2812	−	14.0086i	0.715098	−	0.519549i	−0.169716	−	0.985493i	$-0.554285\pi$
$727$	19.2812	−	14.0086i	0.715098	−	0.519549i	0.884814	+	0.465944i	$0.154285\pi$
$728$	−10.0623	−	30.9686i	−0.372934	−	1.14777i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	−11.2082	+	8.14324i	−0.414834	+	0.301395i
$731$	−0.336881	−	1.03681i	−0.0124600	−	0.0383479i
$732$	−3.47214	+	10.6861i	−0.128334	+	0.394971i
$733$	−22.6074	−	16.4252i	−0.835023	−	0.606680i	0.0859529	−	0.996299i	$-0.472607\pi$
$733$	−22.6074	−	16.4252i	−0.835023	−	0.606680i	−0.920976	+	0.389619i	$0.872607\pi$
$734$	−6.92705	+	21.3193i	−0.255682	+	0.786909i
$735$	4.23607	−	3.07768i	0.156250	−	0.113522i
$736$	24.8713	−	18.0701i	0.916769	−	0.666072i
$737$	2.61803	+	1.90211i	0.0964365	+	0.0700652i
$738$	8.00000			0.294484
$739$	−21.7082			−0.798549			−0.399275	−	0.916831i	$-0.630738\pi$
$739$	−21.7082			−0.798549			−0.399275	+	0.916831i	$0.630738\pi$
$740$	0.809017	+	0.587785i	0.0297401	+	0.0216074i
$741$	−7.50000	−	23.0826i	−0.275519	−	0.847961i
$742$	−7.28115	+	22.4091i	−0.267300	+	0.822663i
$743$	3.43769			0.126117			0.0630584	−	0.998010i	$-0.479915\pi$
$743$	3.43769			0.126117			0.0630584	+	0.998010i	$0.479915\pi$
$744$		0			0
$745$	44.5967			1.63390
$746$	0.0663712	−	0.204270i	0.00243002	−	0.00747884i
$747$	−2.52786	−	7.77997i	−0.0924897	−	0.284654i
$748$	−0.236068	−	0.171513i	−0.00863150	−	0.00627115i
$749$	3.27051			0.119502
$750$	−5.09017			−0.185867
$751$	32.2254	+	23.4131i	1.17592	+	0.854358i	0.991706	−	0.128528i	$-0.0410252\pi$
$751$	32.2254	+	23.4131i	1.17592	+	0.854358i	0.184217	+	0.982886i	$0.441025\pi$
$752$	5.07295	−	3.68571i	0.184991	−	0.134404i
$753$	0.763932	−	0.555029i	0.0278392	−	0.0202264i
$754$	7.98936	−	24.5887i	0.290955	−	0.895468i
$755$	41.3156	+	30.0175i	1.50363	+	1.09245i
$756$	7.50000	−	23.0826i	0.272772	−	0.839507i
$757$	−13.3262	−	41.0139i	−0.484350	−	1.49068i	−0.832920	−	0.553394i	$-0.813332\pi$
$757$	−13.3262	−	41.0139i	−0.484350	−	1.49068i	0.348569	−	0.937283i	$-0.386668\pi$
$758$	−9.20820	+	6.69015i	−0.334457	+	0.242997i
$759$	1.29180	+	3.97574i	0.0468892	+	0.144310i
$760$	−9.04508	−	27.8379i	−0.328100	−	1.00979i
$761$	2.83688	−	2.06111i	0.102837	−	0.0747154i	−0.535178	−	0.844739i	$-0.679756\pi$
$761$	2.83688	−	2.06111i	0.102837	−	0.0747154i	0.638015	+	0.770024i	$0.279756\pi$
$762$	1.95492	+	6.01661i	0.0708191	+	0.217959i
$763$	−7.80244	+	24.0134i	−0.282467	+	0.869345i
$764$	−21.0623	−	15.3027i	−0.762007	−	0.553631i
$765$	−0.381966	+	1.17557i	−0.0138100	+	0.0425028i
$766$	8.42705	−	6.12261i	0.304482	−	0.221219i
$767$	37.1976	−	27.0256i	1.34313	−	0.975838i
$768$	5.30902	+	3.85723i	0.191573	+	0.139186i
$769$	−53.7426			−1.93801			−0.969005	−	0.247042i	$-0.920541\pi$
$769$	−53.7426			−1.93801			−0.969005	+	0.247042i	$0.920541\pi$
$770$	3.70820			0.133634
$771$	−1.14590	−	0.832544i	−0.0412685	−	0.0299833i
$772$	1.19098	+	3.66547i	0.0428644	+	0.131923i
$773$	5.89919	−	18.1558i	0.212179	−	0.653020i	−0.787163	−	0.616745i	$-0.788451\pi$
$773$	5.89919	−	18.1558i	0.212179	−	0.653020i	0.999342	−	0.0362746i	$-0.0115491\pi$
$774$	5.70820			0.205177
$775$		0			0
$776$	−11.8328			−0.424773
$777$	−0.218847	+	0.673542i	−0.00785109	+	0.0241632i
$778$	−5.55166	−	17.0863i	−0.199037	−	0.612572i
$779$	−26.1803	−	19.0211i	−0.938008	−	0.681503i
$780$	−20.5623			−0.736249
$781$	0.0688837			0.00246485
$782$	−0.645898	−	0.469272i	−0.0230973	−	0.0167811i
$783$	34.8607	−	25.3278i	1.24582	−	0.905141i
$784$	−3.00000	+	2.17963i	−0.107143	+	0.0778438i
$785$	−7.85410	+	24.1724i	−0.280325	+	0.862751i
$786$	0.0450850	+	0.0327561i	0.00160813	+	0.00116837i
$787$	−9.66970	+	29.7603i	−0.344687	+	1.06084i	0.617063	+	0.786913i	$0.288322\pi$
$787$	−9.66970	+	29.7603i	−0.344687	+	1.06084i	−0.961751	+	0.273926i	$0.911678\pi$
$788$	8.20820	+	25.2623i	0.292405	+	0.899931i
$789$	−8.73607	+	6.34712i	−0.311012	+	0.225964i
$790$		0			0
$791$	−1.71885	−	5.29007i	−0.0611152	−	0.188093i
$792$	2.76393	−	2.00811i	0.0982120	−	0.0713552i
$793$	−10.4164	−	32.0584i	−0.369897	−	1.13843i
$794$	−3.11146	+	9.57608i	−0.110421	+	0.339842i
$795$	26.9164	+	19.5559i	0.954627	+	0.693577i
$796$	−13.3541	+	41.0997i	−0.473324	+	1.45674i
$797$	7.32624	−	5.32282i	0.259509	−	0.188544i	−0.450422	−	0.892816i	$-0.648726\pi$
$797$	7.32624	−	5.32282i	0.259509	−	0.188544i	0.709930	+	0.704272i	$0.248726\pi$
$798$	7.50000	−	5.44907i	0.265497	−	0.192895i
$799$	−0.645898	−	0.469272i	−0.0228502	−	0.0166017i
$800$	−10.4164			−0.368276
$801$	−12.7639			−0.450991
$802$	14.9164	+	10.8374i	0.526717	+	0.382682i
$803$	2.02129	+	6.22088i	0.0713296	+	0.219530i
$804$	2.11803	−	6.51864i	0.0746973	−	0.229895i
$805$	−42.9787			−1.51480
$806$		0			0
$807$	1.38197			0.0486475
$808$	3.29180	−	10.1311i	0.115805	−	0.356411i
$809$	−16.9336	−	52.1164i	−0.595355	−	1.83231i	−0.552953	−	0.833213i	$-0.686499\pi$
$809$	−16.9336	−	52.1164i	−0.595355	−	1.83231i	−0.0424020	−	0.999101i	$-0.513501\pi$
$810$	−1.30902	−	0.951057i	−0.0459942	−	0.0334167i
$811$	42.7771			1.50211			0.751053	−	0.660242i	$-0.229546\pi$
$811$	42.7771			1.50211			0.751053	+	0.660242i	$0.229546\pi$
$812$	−41.8328			−1.46804
$813$	7.73607	+	5.62058i	0.271316	+	0.197122i
$814$	−0.0901699	+	0.0655123i	−0.00316045	+	0.00229620i
$815$	−26.9164	+	19.5559i	−0.942841	+	0.685014i
$816$	−0.135255	+	0.416272i	−0.00473487	+	0.0145724i
$817$	−18.6803	−	13.5721i	−0.653542	−	0.474826i
$818$	−1.18034	+	3.63271i	−0.0412696	+	0.127015i
$819$	9.00000	+	27.6992i	0.314485	+	0.967887i
$820$	−22.1803	+	16.1150i	−0.774571	+	0.562759i
$821$	10.0344	+	30.8828i	0.350204	+	1.07782i	0.958738	+	0.284290i	$0.0917580\pi$
$821$	10.0344	+	30.8828i	0.350204	+	1.07782i	−0.608534	+	0.793528i	$0.708242\pi$
$822$	−1.23607	−	3.80423i	−0.0431128	−	0.132688i
$823$	−4.95492	+	3.59996i	−0.172717	+	0.125487i	−0.670786	−	0.741651i	$-0.734043\pi$
$823$	−4.95492	+	3.59996i	−0.172717	+	0.125487i	0.498068	+	0.867138i	$0.334043\pi$
$824$	−0.100813	−	0.310271i	−0.00351199	−	0.0108088i
$825$	0.437694	−	1.34708i	0.0152386	−	0.0468994i
$826$	14.2082	+	10.3229i	0.494367	+	0.359178i
$827$	−0.826238	+	2.54290i	−0.0287311	+	0.0884253i	−0.964394	−	0.264470i	$-0.914803\pi$
$827$	−0.826238	+	2.54290i	−0.0287311	+	0.0884253i	0.935663	+	0.352896i	$0.114803\pi$
$828$	−14.3262	+	10.4086i	−0.497871	+	0.361725i
$829$	−17.5623	+	12.7598i	−0.609964	+	0.443165i	−0.849402	−	0.527747i	$-0.823037\pi$
$829$	−17.5623	+	12.7598i	−0.609964	+	0.443165i	0.239438	+	0.970912i	$0.423037\pi$
$830$	−5.35410	−	3.88998i	−0.185844	−	0.135023i
$831$	−13.3262			−0.462282
$832$	1.14590			0.0397269
$833$	0.381966	+	0.277515i	0.0132343	+	0.00961531i
$834$	1.11803	+	3.44095i	0.0387144	+	0.119151i
$835$	−7.47214	+	22.9969i	−0.258584	+	0.795839i
$836$	−6.18034			−0.213752
$837$		0			0
$838$	−2.76393			−0.0954784
$839$	3.45492	−	10.6331i	0.119277	−	0.367097i	−0.873538	−	0.486756i	$-0.838180\pi$
$839$	3.45492	−	10.6331i	0.119277	−	0.367097i	0.992815	+	0.119659i	$0.0381802\pi$
$840$	−5.42705	−	16.7027i	−0.187251	−	0.576299i
$841$	−36.6246	−	26.6093i	−1.26292	−	0.917563i
$842$	−9.12461			−0.314455
$843$	19.0344			0.655581
$844$	−10.4721	−	7.60845i	−0.360466	−	0.261894i
$845$	22.3713	−	16.2537i	0.769597	−	0.559145i
$846$	3.38197	−	2.45714i	0.116274	−	0.0844783i
$847$	−9.65654	+	29.7198i	−0.331803	+	1.02118i
$848$	−19.0623	−	13.8496i	−0.654602	−	0.475596i
$849$	2.02786	−	6.24112i	0.0695961	−	0.214195i
$850$	0.0835921	+	0.257270i	0.00286719	+	0.00882429i
$851$	1.04508	−	0.759299i	0.0358251	−	0.0260284i
$852$	−0.0450850	−	0.138757i	−0.00154459	−	0.00475375i
$853$	1.23607	+	3.80423i	0.0423222	+	0.130254i	0.969985	−	0.243164i	$-0.0781855\pi$
$853$	1.23607	+	3.80423i	0.0423222	+	0.130254i	−0.927663	+	0.373419i	$0.878185\pi$
$854$	10.4164	−	7.56796i	0.356442	−	0.258970i
$855$	8.09017	+	24.8990i	0.276678	+	0.851527i
$856$	0.753289	−	2.31838i	0.0257469	−	0.0792408i
$857$	6.61803	+	4.80828i	0.226068	+	0.164248i	0.695054	−	0.718958i	$-0.255381\pi$
$857$	6.61803	+	4.80828i	0.226068	+	0.164248i	−0.468986	+	0.883206i	$0.655381\pi$
$858$	0.708204	−	2.17963i	0.0241777	−	0.0744113i
$859$	35.0238	−	25.4463i	1.19500	−	0.868216i	0.201213	−	0.979547i	$-0.435512\pi$
$859$	35.0238	−	25.4463i	1.19500	−	0.868216i	0.993783	+	0.111332i	$0.0355116\pi$
$860$	−15.8262	+	11.4984i	−0.539670	+	0.392093i
$861$	−15.7082	−	11.4127i	−0.535334	−	0.388943i
$862$	−18.0689			−0.615429
$863$	−2.49342			−0.0848771			−0.0424385	−	0.999099i	$-0.513513\pi$
$863$	−2.49342			−0.0848771			−0.0424385	+	0.999099i	$0.513513\pi$
$864$	−22.7254	−	16.5110i	−0.773135	−	0.561715i
$865$	−0.736068	−	2.26538i	−0.0250271	−	0.0770254i
$866$	0.111456	−	0.343027i	0.00378744	−	0.0116565i
$867$	−16.9443			−0.575458
$868$		0			0
$869$		0			0
$870$	4.30902	−	13.2618i	0.146089	−	0.449617i
$871$	6.35410	+	19.5559i	0.215301	+	0.662627i
$872$	15.2254	+	11.0619i	0.515598	+	0.374604i
$873$	10.5836			0.358200
$874$	−16.9098			−0.571984
$875$	−19.9894	−	14.5231i	−0.675764	−	0.490971i
$876$	11.2082	−	8.14324i	0.378690	−	0.275134i
$877$	−13.1803	+	9.57608i	−0.445068	+	0.323361i	−0.787646	−	0.616129i	$-0.788700\pi$
$877$	−13.1803	+	9.57608i	−0.445068	+	0.323361i	0.342577	+	0.939490i	$0.388700\pi$
$878$	−7.98936	+	24.5887i	−0.269628	+	0.829829i
$879$	6.66312	+	4.84104i	0.224741	+	0.163284i
$880$	−1.14590	+	3.52671i	−0.0386282	+	0.118885i
$881$	4.74671	+	14.6089i	0.159921	+	0.492185i	0.998626	−	0.0523999i	$-0.0166870\pi$
$881$	4.74671	+	14.6089i	0.159921	+	0.492185i	−0.838705	+	0.544585i	$0.816687\pi$
$882$	−2.00000	+	1.45309i	−0.0673435	+	0.0489279i
$883$	0.309017	+	0.951057i	0.0103992	+	0.0320056i	0.956121	−	0.292970i	$-0.0946438\pi$
$883$	0.309017	+	0.951057i	0.0103992	+	0.0320056i	−0.945722	+	0.324976i	$0.894644\pi$
$884$	−0.572949	−	1.76336i	−0.0192704	−	0.0593081i
$885$	20.0623	−	14.5761i	0.674387	−	0.489971i
$886$	7.85410	+	24.1724i	0.263864	+	0.812089i
$887$	12.0836	−	37.1895i	0.405727	−	1.24870i	−0.514559	−	0.857455i	$-0.672044\pi$
$887$	12.0836	−	37.1895i	0.405727	−	1.24870i	0.920286	−	0.391245i	$-0.127956\pi$
$888$	0.427051	+	0.310271i	0.0143309	+	0.0104120i
$889$	−9.48936	+	29.2052i	−0.318263	+	0.979512i
$890$	−8.35410	+	6.06961i	−0.280030	+	0.203454i
$891$	−0.618034	+	0.449028i	−0.0207049	+	0.0150430i
$892$	−0.927051	−	0.673542i	−0.0310400	−	0.0225519i
$893$	−16.9098			−0.565866
$894$	10.5279			0.352104
$895$	−41.9336	−	30.4666i	−1.40169	−	1.01838i
$896$	10.5517	+	32.4747i	0.352506	+	1.08490i
$897$	−8.20820	+	25.2623i	−0.274064	+	0.843482i
$898$	14.8754			0.496398
$899$		0			0
$900$	6.00000			0.200000
$901$	−0.927051	+	2.85317i	−0.0308845	+	0.0950529i
$902$	−0.944272	−	2.90617i	−0.0314408	−	0.0967649i
$903$	−11.2082	−	8.14324i	−0.372986	−	0.270990i
$904$	−4.14590			−0.137891
$905$	44.5066			1.47945
$906$	9.75329	+	7.08618i	0.324031	+	0.235423i
$907$	−42.8156	+	31.1074i	−1.42167	+	1.03290i	−0.430175	+	0.902745i	$0.641548\pi$
$907$	−42.8156	+	31.1074i	−1.42167	+	1.03290i	−0.991493	+	0.130157i	$0.958452\pi$
$908$	−27.1525	+	19.7274i	−0.901087	+	0.654678i
$909$	−2.94427	+	9.06154i	−0.0976553	+	0.300552i
$910$	19.0623	+	13.8496i	0.631909	+	0.459109i
$911$	−2.52786	+	7.77997i	−0.0837519	+	0.257762i	−0.984159	−	0.177286i	$-0.943268\pi$
$911$	−2.52786	+	7.77997i	−0.0837519	+	0.257762i	0.900408	+	0.435047i	$0.143268\pi$
$912$	2.86475	+	8.81678i	0.0948612	+	0.291953i
$913$	−2.52786	+	1.83660i	−0.0836601	+	0.0607826i
$914$	−3.00658	−	9.25330i	−0.0994488	−	0.306072i
$915$	−5.61803	−	17.2905i	−0.185726	−	0.571607i
$916$	9.47214	−	6.88191i	0.312968	−	0.227385i
$917$	0.0835921	+	0.257270i	0.00276046	+	0.00849581i
$918$	−0.225425	+	0.693786i	−0.00744013	+	0.0228984i
$919$	−7.98936	−	5.80461i	−0.263545	−	0.191476i	0.448164	−	0.893952i	$-0.352078\pi$
$919$	−7.98936	−	5.80461i	−0.263545	−	0.191476i	−0.711708	+	0.702475i	$0.752078\pi$
$920$	−9.89919	+	30.4666i	−0.326367	+	1.00445i
$921$	−4.92705	+	3.57971i	−0.162352	+	0.117956i
$922$	−5.37132	+	3.90249i	−0.176895	+	0.128522i
$923$	0.354102	+	0.257270i	0.0116554	+	0.00846815i
$924$	−3.70820			−0.121991
$925$	−0.437694			−0.0143913
$926$	15.5623	+	11.3067i	0.511409	+	0.371560i
$927$	0.0901699	+	0.277515i	0.00296157	+	0.00911477i
$928$	−14.9615	+	46.0467i	−0.491135	+	1.51156i
$929$	−33.5410			−1.10045			−0.550223	−	0.835018i	$-0.685457\pi$
$929$	−33.5410			−1.10045			−0.550223	+	0.835018i	$0.685457\pi$
$930$		0			0
$931$	10.0000			0.327737
$932$	−9.39919	+	28.9277i	−0.307881	+	0.947559i
$933$	5.09017	+	15.6659i	0.166645	+	0.512880i
$934$	−16.3885	−	11.9070i	−0.536250	−	0.389608i
$935$	0.472136			0.0154405
$936$	21.7082			0.709555
$937$	−32.7533	−	23.7967i	−1.07000	−	0.777403i	−0.0940905	−	0.995564i	$-0.529994\pi$
$937$	−32.7533	−	23.7967i	−1.07000	−	0.777403i	−0.975913	+	0.218161i	$0.929994\pi$
$938$	−6.35410	+	4.61653i	−0.207469	+	0.150735i
$939$	1.00000	−	0.726543i	0.0326338	−	0.0237098i
$940$	−4.42705	+	13.6251i	−0.144394	+	0.444401i
$941$	23.1246	+	16.8010i	0.753841	+	0.547697i	0.897015	−	0.442000i	$-0.145731\pi$
$941$	23.1246	+	16.8010i	0.753841	+	0.547697i	−0.143174	+	0.989698i	$0.545731\pi$
$942$	−1.85410	+	5.70634i	−0.0604099	+	0.185923i
$943$	10.9443	+	33.6830i	0.356395	+	1.09687i
$944$	−14.2082	+	10.3229i	−0.462438	+	0.335981i
$945$	12.1353	+	37.3485i	0.394760	+	1.21495i
$946$	−0.673762	−	2.07363i	−0.0219059	−	0.0674194i
$947$	17.8541	−	12.9718i	0.580180	−	0.421526i	−0.258609	−	0.965982i	$-0.583264\pi$
$947$	17.8541	−	12.9718i	0.580180	−	0.421526i	0.838789	+	0.544456i	$0.183264\pi$
$948$		0			0
$949$	−12.8435	+	39.5281i	−0.416916	+	1.28314i
$950$	4.63525	+	3.36771i	0.150388	+	0.109263i
$951$	8.00000	−	24.6215i	0.259418	−	0.798406i
$952$	1.28115	−	0.930812i	0.0415224	−	0.0301678i
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.124229	−	0.992254i	$-0.460354\pi$
$953$	34.1525	−	24.8132i	1.10631	−	0.803779i	0.982078	+	0.188474i	$0.0603542\pi$
$954$	−12.7082	−	9.23305i	−0.411443	−	0.298931i
$955$	42.1246			1.36312
$956$	−21.7082			−0.702093
$957$	−5.32624	−	3.86974i	−0.172173	−	0.125091i
$958$	1.70820	+	5.25731i	0.0551896	+	0.169856i
$959$	6.00000	−	18.4661i	0.193750	−	0.596302i
$960$	0.618034			0.0199470
$961$		0			0
$962$	−0.708204			−0.0228334
$963$	−0.673762	+	2.07363i	−0.0217117	+	0.0668217i
$964$	−4.26393	−	13.1230i	−0.137332	−	0.422664i
$965$	−5.04508	−	3.66547i	−0.162407	−	0.117996i
$966$	−10.1459			−0.326439
$967$	−43.6525			−1.40377			−0.701884	−	0.712291i	$-0.747658\pi$
$967$	−43.6525			−1.40377			−0.701884	+	0.712291i	$0.747658\pi$
$968$	18.8435	+	13.6906i	0.605652	+	0.440032i
$969$	0.954915	−	0.693786i	0.0306763	−	0.0222876i
$970$	6.92705	−	5.03280i	0.222414	−	0.161593i
$971$	−6.35410	+	19.5559i	−0.203913	+	0.627579i	0.795843	+	0.605502i	$0.207028\pi$
$971$	−6.35410	+	19.5559i	−0.203913	+	0.627579i	−0.999756	+	0.0220767i	$0.992972\pi$
$972$	20.9443	+	15.2169i	0.671788	+	0.488082i
$973$	−5.42705	+	16.7027i	−0.173983	+	0.535465i
$974$	4.37790	+	13.4738i	0.140277	+	0.431728i
$975$	7.28115	−	5.29007i	0.233184	−	0.169418i
$976$	3.97871	+	12.2452i	0.127356	+	0.391960i
$977$	−1.87539	−	5.77185i	−0.0599990	−	0.184658i	0.916565	−	0.399886i	$-0.130950\pi$
$977$	−1.87539	−	5.77185i	−0.0599990	−	0.184658i	−0.976564	+	0.215228i	$0.930950\pi$
$978$	−6.35410	+	4.61653i	−0.203182	+	0.147620i
$979$	1.50658	+	4.63677i	0.0481504	+	0.148192i
$980$	2.61803	−	8.05748i	0.0836300	−	0.257387i
$981$	−13.6180	−	9.89408i	−0.434790	−	0.315894i
$982$	−5.27051	+	16.2210i	−0.168189	+	0.517632i
$983$	17.0172	−	12.3637i	0.542765	−	0.394342i	−0.282346	−	0.959313i	$-0.591113\pi$
$983$	17.0172	−	12.3637i	0.542765	−	0.394342i	0.825111	+	0.564971i	$0.191113\pi$
$984$	−11.7082	+	8.50651i	−0.373244	+	0.271178i
$985$	−34.7705	−	25.2623i	−1.10788	−	0.804922i
$986$	1.25735			0.0400423
$987$	−10.1459			−0.322947
$988$	−31.7705	−	23.0826i	−1.01075	−	0.734356i
$989$	7.80902	+	24.0337i	0.248312	+	0.764227i
$990$	−0.763932	+	2.35114i	−0.0242794	+	0.0747242i
$991$	17.2705			0.548616			0.274308	−	0.961642i	$-0.411551\pi$
$991$	17.2705			0.548616			0.274308	+	0.961642i	$0.411551\pi$
$992$		0			0
$993$	−11.2705			−0.357659
$994$	−0.0516628	+	0.159002i	−0.00163864	+	0.00504323i
$995$	−21.6074	−	66.5007i	−0.685000	−	2.10821i
$996$	5.35410	+	3.88998i	0.169651	+	0.123259i
$997$	−27.2492			−0.862992			−0.431496	−	0.902115i	$-0.642014\pi$
$997$	−27.2492			−0.862992			−0.431496	+	0.902115i	$0.642014\pi$
$998$	2.56231			0.0811084
$999$	−0.954915	−	0.693786i	−0.0302122	−	0.0219504i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.d.b.628.1		4
31.2	even	5		961.2.a.e.1.1		2
31.3	odd	30		961.2.g.f.816.1		8
31.4	even	5	inner	961.2.d.b.531.1		4
31.5	even	3		961.2.g.c.448.1		8
31.6	odd	6		961.2.g.b.846.1		8
31.7	even	15		961.2.g.c.547.1		8
31.8	even	5		961.2.d.e.388.1		4
31.9	even	15		961.2.g.g.338.1		8
31.10	even	15		961.2.c.d.521.1		4
31.11	odd	30		961.2.g.b.844.1		8
31.12	odd	30		961.2.c.f.439.1		4
31.13	odd	30		961.2.g.f.732.1		8
31.14	even	15		961.2.g.g.235.1		8
31.15	odd	10		961.2.d.f.374.1		4
31.16	even	5		961.2.d.e.374.1		4
31.17	odd	30		961.2.g.f.235.1		8
31.18	even	15		961.2.g.g.732.1		8
31.19	even	15		961.2.c.d.439.1		4
31.20	even	15		961.2.g.c.844.1		8
31.21	odd	30		961.2.c.f.521.1		4
31.22	odd	30		961.2.g.f.338.1		8
31.23	odd	10		961.2.d.f.388.1		4
31.24	odd	30		961.2.g.b.547.1		8
31.25	even	3		961.2.g.c.846.1		8
31.26	odd	6		961.2.g.b.448.1		8
31.27	odd	10		31.2.d.a.4.1	✓	4
31.28	even	15		961.2.g.g.816.1		8
31.29	odd	10		961.2.a.d.1.1		2
31.30	odd	2		31.2.d.a.8.1	yes	4
93.2	odd	10		8649.2.a.f.1.2		2
93.29	even	10		8649.2.a.g.1.2		2
93.89	even	10		279.2.i.a.190.1		4
93.92	even	2		279.2.i.a.163.1		4
124.27	even	10		496.2.n.b.97.1		4
124.123	even	2		496.2.n.b.225.1		4
155.27	even	20		775.2.bf.a.624.2		8
155.58	even	20		775.2.bf.a.624.1		8
155.89	odd	10		775.2.k.c.376.1		4
155.92	even	4		775.2.bf.a.349.1		8
155.123	even	4		775.2.bf.a.349.2		8
155.154	odd	2		775.2.k.c.101.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.d.a.4.1	✓	4	31.27	odd	10
31.2.d.a.8.1	yes	4	31.30	odd	2
279.2.i.a.163.1		4	93.92	even	2
279.2.i.a.190.1		4	93.89	even	10
496.2.n.b.97.1		4	124.27	even	10
496.2.n.b.225.1		4	124.123	even	2
775.2.k.c.101.1		4	155.154	odd	2
775.2.k.c.376.1		4	155.89	odd	10
775.2.bf.a.349.1		8	155.92	even	4
775.2.bf.a.349.2		8	155.123	even	4
775.2.bf.a.624.1		8	155.58	even	20
775.2.bf.a.624.2		8	155.27	even	20
961.2.a.d.1.1		2	31.29	odd	10
961.2.a.e.1.1		2	31.2	even	5
961.2.c.d.439.1		4	31.19	even	15
961.2.c.d.521.1		4	31.10	even	15
961.2.c.f.439.1		4	31.12	odd	30
961.2.c.f.521.1		4	31.21	odd	30
961.2.d.b.531.1		4	31.4	even	5	inner
961.2.d.b.628.1		4	1.1	even	1	trivial
961.2.d.e.374.1		4	31.16	even	5
961.2.d.e.388.1		4	31.8	even	5
961.2.d.f.374.1		4	31.15	odd	10
961.2.d.f.388.1		4	31.23	odd	10
961.2.g.b.448.1		8	31.26	odd	6
961.2.g.b.547.1		8	31.24	odd	30
961.2.g.b.844.1		8	31.11	odd	30
961.2.g.b.846.1		8	31.6	odd	6
961.2.g.c.448.1		8	31.5	even	3
961.2.g.c.547.1		8	31.7	even	15
961.2.g.c.844.1		8	31.20	even	15
961.2.g.c.846.1		8	31.25	even	3
961.2.g.f.235.1		8	31.17	odd	30
961.2.g.f.338.1		8	31.22	odd	30
961.2.g.f.732.1		8	31.13	odd	30
961.2.g.f.816.1		8	31.3	odd	30
961.2.g.g.235.1		8	31.14	even	15
961.2.g.g.338.1		8	31.9	even	15
961.2.g.g.732.1		8	31.18	even	15
961.2.g.g.816.1		8	31.28	even	15
8649.2.a.f.1.2		2	93.2	odd	10
8649.2.a.g.1.2		2	93.29	even	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:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.190983 + 0.587785i) q^{2} +(0.309017 + 0.951057i) q^{3} +(1.30902 + 0.951057i) q^{4} -2.61803 q^{5} -0.618034 q^{6} +(-2.42705 - 1.76336i) q^{7} +(-1.80902 + 1.31433i) q^{8} +(1.61803 - 1.17557i) q^{9} +(0.500000 - 1.53884i) q^{10} +(-0.618034 - 0.449028i) q^{11} +(-0.500000 + 1.53884i) q^{12} +(-1.50000 - 4.61653i) q^{13} +(1.50000 - 1.08981i) q^{14} +(-0.809017 - 2.48990i) q^{15} +(0.572949 + 1.76336i) q^{16} +(0.190983 - 0.138757i) q^{17} +(0.381966 + 1.17557i) q^{18} +(1.54508 - 4.75528i) q^{19} +(-3.42705 - 2.48990i) q^{20} +(0.927051 - 2.85317i) q^{21} +(0.381966 - 0.277515i) q^{22} +(-4.42705 + 3.21644i) q^{23} +(-1.80902 - 1.31433i) q^{24} +1.85410 q^{25} +3.00000 q^{26} +(4.04508 + 2.93893i) q^{27} +(-1.50000 - 4.61653i) q^{28} +(2.66312 - 8.19624i) q^{29} +1.61803 q^{30} -5.61803 q^{32} +(0.236068 - 0.726543i) q^{33} +(0.0450850 + 0.138757i) q^{34} +(6.35410 + 4.61653i) q^{35} +3.23607 q^{36} -0.236068 q^{37} +(2.50000 + 1.81636i) q^{38} +(3.92705 - 2.85317i) q^{39} +(4.73607 - 3.44095i) q^{40} +(2.00000 - 6.15537i) q^{41} +(1.50000 + 1.08981i) q^{42} +(1.42705 - 4.39201i) q^{43} +(-0.381966 - 1.17557i) q^{44} +(-4.23607 + 3.07768i) q^{45} +(-1.04508 - 3.21644i) q^{46} +(-1.04508 - 3.21644i) q^{47} +(-1.50000 + 1.08981i) q^{48} +(0.618034 + 1.90211i) q^{49} +(-0.354102 + 1.08981i) q^{50} +(0.190983 + 0.138757i) q^{51} +(2.42705 - 7.46969i) q^{52} +(-10.2812 + 7.46969i) q^{53} +(-2.50000 + 1.81636i) q^{54} +(1.61803 + 1.17557i) q^{55} +6.70820 q^{56} +5.00000 q^{57} +(4.30902 + 3.13068i) q^{58} +(2.92705 + 9.00854i) q^{59} +(1.30902 - 4.02874i) q^{60} +6.94427 q^{61} -6.00000 q^{63} +(-0.0729490 + 0.224514i) q^{64} +(3.92705 + 12.0862i) q^{65} +(0.381966 + 0.277515i) q^{66} -4.23607 q^{67} +0.381966 q^{68} +(-4.42705 - 3.21644i) q^{69} +(-3.92705 + 2.85317i) q^{70} +(-0.0729490 + 0.0530006i) q^{71} +(-1.38197 + 4.25325i) q^{72} +(-6.92705 - 5.03280i) q^{73} +(0.0450850 - 0.138757i) q^{74} +(0.572949 + 1.76336i) q^{75} +(6.54508 - 4.75528i) q^{76} +(0.708204 + 2.17963i) q^{77} +(0.927051 + 2.85317i) q^{78} +(-1.50000 - 4.61653i) q^{80} +(0.309017 - 0.951057i) q^{81} +(3.23607 + 2.35114i) q^{82} +(1.26393 - 3.88998i) q^{83} +(3.92705 - 2.85317i) q^{84} +(-0.500000 + 0.363271i) q^{85} +(2.30902 + 1.67760i) q^{86} +8.61803 q^{87} +1.70820 q^{88} +(-5.16312 - 3.75123i) q^{89} +(-1.00000 - 3.07768i) q^{90} +(-4.50000 + 13.8496i) q^{91} -8.85410 q^{92} +2.09017 q^{94} +(-4.04508 + 12.4495i) q^{95} +(-1.73607 - 5.34307i) q^{96} +(4.28115 + 3.11044i) q^{97} -1.23607 q^{98} -1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 3 q^{2} - q^{3} + 3 q^{4} - 6 q^{5} + 2 q^{6} - 3 q^{7} - 5 q^{8} + 2 q^{9} + 2 q^{10} + 2 q^{11} - 2 q^{12} - 6 q^{13} + 6 q^{14} - q^{15} + 9 q^{16} + 3 q^{17} + 6 q^{18} - 5 q^{19} - 7 q^{20}+ \cdots - 24 q^{99}+O(q^{100}) \) 4 * q - 3 * q^2 - q^3 + 3 * q^4 - 6 * q^5 + 2 * q^6 - 3 * q^7 - 5 * q^8 + 2 * q^9 + 2 * q^10 + 2 * q^11 - 2 * q^12 - 6 * q^13 + 6 * q^14 - q^15 + 9 * q^16 + 3 * q^17 + 6 * q^18 - 5 * q^19 - 7 * q^20 - 3 * q^21 + 6 * q^22 - 11 * q^23 - 5 * q^24 - 6 * q^25 + 12 * q^26 + 5 * q^27 - 6 * q^28 - 5 * q^29 + 2 * q^30 - 18 * q^32 - 8 * q^33 - 11 * q^34 + 12 * q^35 + 4 * q^36 + 8 * q^37 + 10 * q^38 + 9 * q^39 + 10 * q^40 + 8 * q^41 + 6 * q^42 - q^43 - 6 * q^44 - 8 * q^45 + 7 * q^46 + 7 * q^47 - 6 * q^48 - 2 * q^49 + 12 * q^50 + 3 * q^51 + 3 * q^52 - 21 * q^53 - 10 * q^54 + 2 * q^55 + 20 * q^57 + 15 * q^58 + 5 * q^59 + 3 * q^60 - 8 * q^61 - 24 * q^63 - 7 * q^64 + 9 * q^65 + 6 * q^66 - 8 * q^67 + 6 * q^68 - 11 * q^69 - 9 * q^70 - 7 * q^71 - 10 * q^72 - 21 * q^73 - 11 * q^74 + 9 * q^75 + 15 * q^76 - 24 * q^77 - 3 * q^78 - 6 * q^80 - q^81 + 4 * q^82 + 14 * q^83 + 9 * q^84 - 2 * q^85 + 7 * q^86 + 30 * q^87 - 20 * q^88 - 5 * q^89 - 4 * q^90 - 18 * q^91 - 22 * q^92 - 14 * q^94 - 5 * q^95 + 2 * q^96 - 3 * q^97 + 4 * q^98 - 24 * q^99

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