LMFDB - Embedded newform 546.2.p.c.281.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(239,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 0, 3]))

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

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

chi := DirichletCharacter("546.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + \cdots + 59049 $ x^20 - 4x^19 + 8x^18 - 20x^17 + 56x^16 - 140x^15 + 288x^14 - 532x^13 + 1065x^12 - 2080x^11 + 3712x^10 - 6240x^9 + 9585x^8 - 14364x^7 + 23328x^6 - 34020x^5 + 40824x^4 - 43740x^3 + 52488x^2 - 78732*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			281.1
Root			$0.0557032 - 1.73115i$ of defining polynomial
Character	$\chi$	$=$	546.281
Dual form			546.2.p.c.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.18472 - 1.26350i) q^{3} -1.00000i q^{4} +(2.80148 - 2.80148i) q^{5} +(1.73115 + 0.0557032i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.192862 + 2.99379i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.18472 - 1.26350i) q^{3} -1.00000i q^{4} +(2.80148 - 2.80148i) q^{5} +(1.73115 + 0.0557032i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.192862 + 2.99379i) q^{9} +3.96189i q^{10} +(3.20912 + 3.20912i) q^{11} +(-1.26350 + 1.18472i) q^{12} +(3.52656 - 0.750597i) q^{13} +1.00000i q^{14} +(-6.85864 - 0.220690i) q^{15} -1.00000 q^{16} +3.46154 q^{17} +(-1.98056 - 2.25331i) q^{18} +(-1.81073 - 1.81073i) q^{19} +(-2.80148 - 2.80148i) q^{20} +(-1.73115 - 0.0557032i) q^{21} -4.53838 q^{22} -0.728379 q^{23} +(0.0557032 - 1.73115i) q^{24} -10.6966i q^{25} +(-1.96290 + 3.02440i) q^{26} +(4.01115 - 3.30314i) q^{27} +(-0.707107 - 0.707107i) q^{28} +6.96800i q^{29} +(5.00584 - 4.69374i) q^{30} +(-7.26840 - 7.26840i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.252802 - 7.85664i) q^{33} +(-2.44768 + 2.44768i) q^{34} -3.96189i q^{35} +(2.99379 + 0.192862i) q^{36} +(-1.56147 + 1.56147i) q^{37} +2.56075 q^{38} +(-5.12637 - 3.56655i) q^{39} +3.96189 q^{40} +(3.59240 - 3.59240i) q^{41} +(1.26350 - 1.18472i) q^{42} +7.44129i q^{43} +(3.20912 - 3.20912i) q^{44} +(7.84675 + 8.92735i) q^{45} +(0.515041 - 0.515041i) q^{46} +(7.17522 + 7.17522i) q^{47} +(1.18472 + 1.26350i) q^{48} -1.00000i q^{49} +(7.56361 + 7.56361i) q^{50} +(-4.10096 - 4.37365i) q^{51} +(-0.750597 - 3.52656i) q^{52} -11.8689i q^{53} +(-0.500638 + 5.17198i) q^{54} +17.9806 q^{55} +1.00000 q^{56} +(-0.142642 + 4.43306i) q^{57} +(-4.92712 - 4.92712i) q^{58} +(-7.33162 - 7.33162i) q^{59} +(-0.220690 + 6.85864i) q^{60} -0.300726 q^{61} +10.2791 q^{62} +(1.98056 + 2.25331i) q^{63} +1.00000i q^{64} +(7.77679 - 11.9824i) q^{65} +(5.37672 + 5.73424i) q^{66} +(-3.02964 - 3.02964i) q^{67} -3.46154i q^{68} +(0.862927 + 0.920306i) q^{69} +(2.80148 + 2.80148i) q^{70} +(-3.36041 + 3.36041i) q^{71} +(-2.25331 + 1.98056i) q^{72} +(-6.89498 + 6.89498i) q^{73} -2.20825i q^{74} +(-13.5151 + 12.6725i) q^{75} +(-1.81073 + 1.81073i) q^{76} +4.53838 q^{77} +(6.14683 - 1.10296i) q^{78} -5.87555 q^{79} +(-2.80148 + 2.80148i) q^{80} +(-8.92561 - 1.15478i) q^{81} +5.08041i q^{82} +(-7.55138 + 7.55138i) q^{83} +(-0.0557032 + 1.73115i) q^{84} +(9.69742 - 9.69742i) q^{85} +(-5.26178 - 5.26178i) q^{86} +(8.80407 - 8.25516i) q^{87} +4.53838i q^{88} +(0.819132 + 0.819132i) q^{89} +(-11.8611 - 0.764097i) q^{90} +(1.96290 - 3.02440i) q^{91} +0.728379i q^{92} +(-0.572577 + 17.7947i) q^{93} -10.1473 q^{94} -10.1454 q^{95} +(-1.73115 - 0.0557032i) q^{96} +(1.37504 + 1.37504i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-10.2264 + 8.98852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.18472	−	1.26350i	−0.684000	−	0.729482i
$3$	−1.18472	−	1.26350i	−0.684000	−	0.729482i
$4$		−	1.00000i		−	0.500000i
$5$	2.80148	−	2.80148i	1.25286	−	1.25286i	0.298426	−	0.954433i	$-0.403538\pi$
$5$	2.80148	−	2.80148i	1.25286	−	1.25286i	0.954433	−	0.298426i	$-0.0964617\pi$
$6$	1.73115	+	0.0557032i	0.706741	+	0.0227407i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	−0.192862	+	2.99379i	−0.0642873	+	0.997931i
$10$			3.96189i			1.25286i
$11$	3.20912	+	3.20912i	0.967586	+	0.967586i	0.999491	−	0.0319052i	$-0.0101575\pi$
$11$	3.20912	+	3.20912i	0.967586	+	0.967586i	−0.0319052	+	0.999491i	$0.510157\pi$
$12$	−1.26350	+	1.18472i	−0.364741	+	0.342000i
$13$	3.52656	−	0.750597i	0.978091	−	0.208178i
$13$	3.52656	−	0.750597i	0.978091	−	0.208178i
$14$			1.00000i			0.267261i
$15$	−6.85864	−	0.220690i	−1.77089	−	0.0569819i
$16$	−1.00000			−0.250000
$17$	3.46154			0.839546			0.419773	−	0.907629i	$-0.362110\pi$
$17$	3.46154			0.839546			0.419773	+	0.907629i	$0.362110\pi$
$18$	−1.98056	−	2.25331i	−0.466822	−	0.531109i
$19$	−1.81073	−	1.81073i	−0.415409	−	0.415409i	0.468209	−	0.883618i	$-0.344899\pi$
$19$	−1.81073	−	1.81073i	−0.415409	−	0.415409i	−0.883618	+	0.468209i	$0.844899\pi$
$20$	−2.80148	−	2.80148i	−0.626430	−	0.626430i
$21$	−1.73115	−	0.0557032i	−0.377769	−	0.0121554i
$22$	−4.53838			−0.967586
$23$	−0.728379			−0.151877			−0.0759387	−	0.997112i	$-0.524195\pi$
$23$	−0.728379			−0.151877			−0.0759387	+	0.997112i	$0.524195\pi$
$24$	0.0557032	−	1.73115i	0.0113704	−	0.353371i
$25$		−	10.6966i		−	2.13931i
$26$	−1.96290	+	3.02440i	−0.384956	+	0.593134i
$27$	4.01115	−	3.30314i	0.771945	−	0.635689i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$			6.96800i			1.29393i	0.762521	+	0.646963i	$0.223961\pi$
$29$			6.96800i			1.29393i	−0.762521	+	0.646963i	$0.776039\pi$
$30$	5.00584	−	4.69374i	0.913938	−	0.856956i
$31$	−7.26840	−	7.26840i	−1.30544	−	1.30544i	−0.924668	−	0.380775i	$-0.875657\pi$
$31$	−7.26840	−	7.26840i	−1.30544	−	1.30544i	−0.380775	−	0.924668i	$-0.624343\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.252802	−	7.85664i	0.0440072	−	1.36766i
$34$	−2.44768	+	2.44768i	−0.419773	+	0.419773i
$35$		−	3.96189i		−	0.669681i
$36$	2.99379	+	0.192862i	0.498966	+	0.0321436i
$37$	−1.56147	+	1.56147i	−0.256703	+	0.256703i	−0.823712	−	0.567009i	$-0.808101\pi$
$37$	−1.56147	+	1.56147i	−0.256703	+	0.256703i	0.567009	+	0.823712i	$0.308101\pi$
$38$	2.56075			0.415409
$39$	−5.12637	−	3.56655i	−0.820877	−	0.571106i
$40$	3.96189			0.626430
$41$	3.59240	−	3.59240i	0.561038	−	0.561038i	−0.368564	−	0.929602i	$-0.620151\pi$
$41$	3.59240	−	3.59240i	0.561038	−	0.561038i	0.929602	+	0.368564i	$0.120151\pi$
$42$	1.26350	−	1.18472i	0.194962	−	0.182807i
$43$			7.44129i			1.13479i	0.823447	+	0.567393i	$0.192048\pi$
$43$			7.44129i			1.13479i	−0.823447	+	0.567393i	$0.807952\pi$
$44$	3.20912	−	3.20912i	0.483793	−	0.483793i
$45$	7.84675	+	8.92735i	1.16972	+	1.33081i
$46$	0.515041	−	0.515041i	0.0759387	−	0.0759387i
$47$	7.17522	+	7.17522i	1.04661	+	1.04661i	0.998859	+	0.0477542i	$0.0152064\pi$
$47$	7.17522	+	7.17522i	1.04661	+	1.04661i	0.0477542	+	0.998859i	$0.484794\pi$
$48$	1.18472	+	1.26350i	0.171000	+	0.182370i
$49$		−	1.00000i		−	0.142857i
$50$	7.56361	+	7.56361i	1.06966	+	1.06966i
$51$	−4.10096	−	4.37365i	−0.574250	−	0.612434i
$52$	−0.750597	−	3.52656i	−0.104089	−	0.489045i
$53$		−	11.8689i		−	1.63031i	−0.579240	−	0.815157i	$-0.696651\pi$
$53$		−	11.8689i		−	1.63031i	0.579240	−	0.815157i	$-0.303349\pi$
$54$	−0.500638	+	5.17198i	−0.0681282	+	0.703817i
$55$	17.9806			2.42450
$56$	1.00000			0.133631
$57$	−0.142642	+	4.43306i	−0.0188934	+	0.587173i
$58$	−4.92712	−	4.92712i	−0.646963	−	0.646963i
$59$	−7.33162	−	7.33162i	−0.954495	−	0.954495i	0.0445134	−	0.999009i	$-0.485826\pi$
$59$	−7.33162	−	7.33162i	−0.954495	−	0.954495i	−0.999009	+	0.0445134i	$0.985826\pi$
$60$	−0.220690	+	6.85864i	−0.0284910	+	0.885447i
$61$	−0.300726			−0.0385040			−0.0192520	−	0.999815i	$-0.506128\pi$
$61$	−0.300726			−0.0385040			−0.0192520	+	0.999815i	$0.506128\pi$
$62$	10.2791			1.30544
$63$	1.98056	+	2.25331i	0.249527	+	0.283890i
$64$			1.00000i			0.125000i
$65$	7.77679	−	11.9824i	0.964592	−	1.48623i
$66$	5.37672	+	5.73424i	0.661829	+	0.705836i
$67$	−3.02964	−	3.02964i	−0.370130	−	0.370130i	0.497395	−	0.867524i	$-0.334290\pi$
$67$	−3.02964	−	3.02964i	−0.370130	−	0.370130i	−0.867524	+	0.497395i	$0.834290\pi$
$68$		−	3.46154i		−	0.419773i
$69$	0.862927	+	0.920306i	0.103884	+	0.110792i
$70$	2.80148	+	2.80148i	0.334841	+	0.334841i
$71$	−3.36041	+	3.36041i	−0.398807	+	0.398807i	−0.877812	−	0.479005i	$-0.840998\pi$
$71$	−3.36041	+	3.36041i	−0.398807	+	0.398807i	0.479005	+	0.877812i	$0.340998\pi$
$72$	−2.25331	+	1.98056i	−0.265555	+	0.233411i
$73$	−6.89498	+	6.89498i	−0.806996	+	0.806996i	−0.984178	−	0.177182i	$-0.943302\pi$
$73$	−6.89498	+	6.89498i	−0.806996	+	0.806996i	0.177182	+	0.984178i	$0.443302\pi$
$74$		−	2.20825i		−	0.256703i
$75$	−13.5151	+	12.6725i	−1.56059	+	1.46329i
$76$	−1.81073	+	1.81073i	−0.207704	+	0.207704i
$77$	4.53838			0.517196
$78$	6.14683	−	1.10296i	0.695991	−	0.124885i
$79$	−5.87555			−0.661051			−0.330525	−	0.943797i	$-0.607226\pi$
$79$	−5.87555			−0.661051			−0.330525	+	0.943797i	$0.607226\pi$
$80$	−2.80148	+	2.80148i	−0.313215	+	0.313215i
$81$	−8.92561	−	1.15478i	−0.991734	−	0.128309i
$82$			5.08041i			0.561038i
$83$	−7.55138	+	7.55138i	−0.828872	+	0.828872i	−0.987361	−	0.158489i	$-0.949338\pi$
$83$	−7.55138	+	7.55138i	−0.828872	+	0.828872i	0.158489	+	0.987361i	$0.449338\pi$
$84$	−0.0557032	+	1.73115i	−0.00607772	+	0.188884i
$85$	9.69742	−	9.69742i	1.05183	−	1.05183i
$86$	−5.26178	−	5.26178i	−0.567393	−	0.567393i
$87$	8.80407	−	8.25516i	0.943895	−	0.885046i
$88$			4.53838i			0.483793i
$89$	0.819132	+	0.819132i	0.0868278	+	0.0868278i	0.749187	−	0.662359i	$-0.230445\pi$
$89$	0.819132	+	0.819132i	0.0868278	+	0.0868278i	−0.662359	+	0.749187i	$0.730445\pi$
$90$	−11.8611	−	0.764097i	−1.25027	−	0.0805429i
$91$	1.96290	−	3.02440i	0.205768	−	0.317044i
$92$			0.728379i			0.0759387i
$93$	−0.572577	+	17.7947i	−0.0593735	+	1.84522i
$94$	−10.1473			−1.04661
$95$	−10.1454			−1.04090
$96$	−1.73115	−	0.0557032i	−0.176685	−	0.00568519i
$97$	1.37504	+	1.37504i	0.139614	+	0.139614i	0.773460	−	0.633846i	$-0.218525\pi$
$97$	1.37504	+	1.37504i	0.139614	+	0.139614i	−0.633846	+	0.773460i	$0.718525\pi$
$98$	0.707107	+	0.707107i	0.0714286	+	0.0714286i
$99$	−10.2264	+	8.98852i	−1.02779	+	0.903381i
$100$	−10.6966			−1.06966
$101$	1.04374			0.103856			0.0519282	−	0.998651i	$-0.483463\pi$
$101$	1.04374			0.103856			0.0519282	+	0.998651i	$0.483463\pi$
$102$	5.99246	+	0.192819i	0.593342	+	0.0190919i
$103$		−	8.39105i		−	0.826795i	−0.910551	−	0.413398i	$-0.864342\pi$
$103$		−	8.39105i		−	0.826795i	0.910551	−	0.413398i	$-0.135658\pi$
$104$	3.02440	+	1.96290i	0.296567	+	0.192478i
$105$	−5.00584	+	4.69374i	−0.488520	+	0.458062i
$106$	8.39255	+	8.39255i	0.815157	+	0.815157i
$107$			14.3199i			1.38435i	0.721728	+	0.692176i	$0.243348\pi$
$107$			14.3199i			1.38435i	−0.721728	+	0.692176i	$0.756652\pi$
$108$	−3.30314	−	4.01115i	−0.317844	−	0.385973i
$109$	−0.311497	−	0.311497i	−0.0298360	−	0.0298360i	0.692031	−	0.721867i	$-0.256716\pi$
$109$	−0.311497	−	0.311497i	−0.0298360	−	0.0298360i	−0.721867	+	0.692031i	$0.756716\pi$
$110$	−12.7142	+	12.7142i	−1.21225	+	1.21225i
$111$	3.82282	+	0.123006i	0.362846	+	0.0116753i
$112$	−0.707107	+	0.707107i	−0.0668153	+	0.0668153i
$113$		−	4.65219i		−	0.437641i	−0.975765	−	0.218821i	$-0.929779\pi$
$113$		−	4.65219i		−	0.437641i	0.975765	−	0.218821i	$-0.0702209\pi$
$114$	−3.03378	−	3.23551i	−0.284140	−	0.303033i
$115$	−2.04054	+	2.04054i	−0.190281	+	0.190281i
$116$	6.96800			0.646963
$117$	1.56699	+	10.7025i	0.144869	+	0.989451i
$118$	10.3685			0.954495
$119$	2.44768	−	2.44768i	0.224378	−	0.224378i
$120$	−4.69374	−	5.00584i	−0.428478	−	0.456969i
$121$			9.59688i			0.872444i
$122$	0.212645	−	0.212645i	0.0192520	−	0.0192520i
$123$	−8.79498	−	0.282995i	−0.793017	−	0.0255168i
$124$	−7.26840	+	7.26840i	−0.652721	+	0.652721i
$125$	−15.9588	−	15.9588i	−1.42740	−	1.42740i
$126$	−2.99379	−	0.192862i	−0.266708	−	0.0171815i
$127$			8.51785i			0.755837i	0.925839	+	0.377918i	$0.123360\pi$
$127$			8.51785i			0.755837i	−0.925839	+	0.377918i	$0.876640\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	9.40206	−	8.81586i	0.827805	−	0.776194i
$130$	2.97378	+	13.9718i	0.260818	+	1.22541i
$131$			1.65007i			0.144167i	0.997399	+	0.0720837i	$0.0229649\pi$
$131$			1.65007i			0.144167i	−0.997399	+	0.0720837i	$0.977035\pi$
$132$	−7.85664	−	0.252802i	−0.683832	−	0.0220036i
$133$	−2.56075			−0.222045
$134$	4.28456			0.370130
$135$	1.98347	−	20.4908i	0.170710	−	1.76357i
$136$	2.44768	+	2.44768i	0.209887	+	0.209887i
$137$	9.11987	+	9.11987i	0.779163	+	0.779163i	0.979689	−	0.200525i	$-0.0642648\pi$
$137$	9.11987	+	9.11987i	0.779163	+	0.779163i	−0.200525	+	0.979689i	$0.564265\pi$
$138$	−1.26094	−	0.0405730i	−0.107338	−	0.00345381i
$139$	−19.2565			−1.63331			−0.816656	−	0.577125i	$-0.804175\pi$
$139$	−19.2565			−1.63331			−0.816656	+	0.577125i	$0.804175\pi$
$140$	−3.96189			−0.334841
$141$	0.565237	−	17.5665i	0.0476015	−	1.47937i
$142$		−	4.75234i		−	0.398807i
$143$	13.7259	+	8.90839i	1.14782	+	0.744957i
$144$	0.192862	−	2.99379i	0.0160718	−	0.249483i
$145$	19.5207	+	19.5207i	1.62111	+	1.62111i
$146$		−	9.75097i		−	0.806996i
$147$	−1.26350	+	1.18472i	−0.104212	+	0.0977143i
$148$	1.56147	+	1.56147i	0.128352	+	0.128352i
$149$	15.7466	−	15.7466i	1.29001	−	1.29001i	0.355233	−	0.934778i	$-0.384401\pi$
$149$	15.7466	−	15.7466i	1.29001	−	1.29001i	0.934778	−	0.355233i	$-0.115599\pi$
$150$	0.595833	−	18.5174i	0.0486495	−	1.51194i
$151$	13.5912	−	13.5912i	1.10604	−	1.10604i	0.112374	−	0.993666i	$-0.464155\pi$
$151$	13.5912	−	13.5912i	1.10604	−	1.10604i	0.993666	−	0.112374i	$-0.0358454\pi$
$152$		−	2.56075i		−	0.207704i
$153$	−0.667599	+	10.3631i	−0.0539721	+	0.837810i
$154$	−3.20912	+	3.20912i	−0.258598	+	0.258598i
$155$	−40.7245			−3.27107
$156$	−3.56655	+	5.12637i	−0.285553	+	0.410438i
$157$	1.54786			0.123533			0.0617665	−	0.998091i	$-0.480327\pi$
$157$	1.54786			0.123533			0.0617665	+	0.998091i	$0.480327\pi$
$158$	4.15464	−	4.15464i	0.330525	−	0.330525i
$159$	−14.9963	+	14.0613i	−1.18928	+	1.11514i
$160$		−	3.96189i		−	0.313215i
$161$	−0.515041	+	0.515041i	−0.0405910	+	0.0405910i
$162$	7.12791	−	5.49481i	0.560021	−	0.431713i
$163$	0.281966	−	0.281966i	0.0220853	−	0.0220853i	−0.695978	−	0.718063i	$-0.745029\pi$
$163$	0.281966	−	0.281966i	0.0220853	−	0.0220853i	0.718063	+	0.695978i	$0.245029\pi$
$164$	−3.59240	−	3.59240i	−0.280519	−	0.280519i
$165$	−21.3020	−	22.7184i	−1.65836	−	1.76863i
$166$		−	10.6793i		−	0.828872i
$167$	13.9826	+	13.9826i	1.08201	+	1.08201i	0.996322	+	0.0856865i	$0.0273083\pi$
$167$	13.9826	+	13.9826i	1.08201	+	1.08201i	0.0856865	+	0.996322i	$0.472692\pi$
$168$	−1.18472	−	1.26350i	−0.0914034	−	0.0974811i
$169$	11.8732	−	5.29404i	0.913324	−	0.407234i
$170$			13.7142i			1.05183i
$171$	5.77016	−	5.07172i	0.441255	−	0.387844i
$172$	7.44129			0.567393
$173$	−4.63785			−0.352609			−0.176304	−	0.984336i	$-0.556414\pi$
$173$	−4.63785			−0.352609			−0.176304	+	0.984336i	$0.556414\pi$
$174$	−0.388140	+	12.0627i	−0.0294248	+	0.914471i
$175$	−7.56361	−	7.56361i	−0.571755	−	0.571755i
$176$	−3.20912	−	3.20912i	−0.241896	−	0.241896i
$177$	−0.577557	+	17.9494i	−0.0434119	+	1.34916i
$178$	−1.15843			−0.0868278
$179$	−7.59068			−0.567354			−0.283677	−	0.958920i	$-0.591554\pi$
$179$	−7.59068			−0.567354			−0.283677	+	0.958920i	$0.591554\pi$
$180$	8.92735	−	7.84675i	0.665405	−	0.584862i
$181$			17.9019i			1.33064i	0.746558	+	0.665320i	$0.231705\pi$
$181$			17.9019i			1.33064i	−0.746558	+	0.665320i	$0.768295\pi$
$182$	0.750597	+	3.52656i	0.0556379	+	0.261406i
$183$	0.356277	+	0.379967i	0.0263367	+	0.0280879i
$184$	−0.515041	−	0.515041i	−0.0379694	−	0.0379694i
$185$			8.74882i			0.643226i
$186$	−12.1779	−	12.9876i	−0.892923	−	0.952297i
$187$	11.1085	+	11.1085i	0.812333	+	0.812333i
$188$	7.17522	−	7.17522i	0.523307	−	0.523307i
$189$	0.500638	−	5.17198i	0.0364160	−	0.376206i
$190$	7.17389	−	7.17389i	0.520449	−	0.520449i
$191$			9.21892i			0.667058i	0.942740	+	0.333529i	$0.108239\pi$
$191$			9.21892i			0.667058i	−0.942740	+	0.333529i	$0.891761\pi$
$192$	1.26350	−	1.18472i	0.0911852	−	0.0855000i
$193$	−0.100044	+	0.100044i	−0.00720135	+	0.00720135i	−0.710698	−	0.703497i	$-0.751621\pi$
$193$	−0.100044	+	0.100044i	−0.00720135	+	0.00720135i	0.703497	+	0.710698i	$0.251621\pi$
$194$	−1.94460			−0.139614
$195$	−24.3530	+	4.36980i	−1.74396	+	0.312928i
$196$	−1.00000			−0.0714286
$197$	−8.24868	+	8.24868i	−0.587694	+	0.587694i	−0.937006	−	0.349312i	$-0.886415\pi$
$197$	−8.24868	+	8.24868i	−0.587694	+	0.587694i	0.349312	+	0.937006i	$0.386415\pi$
$198$	0.875280	−	13.5870i	0.0622034	−	0.965584i
$199$			7.57896i			0.537258i	0.963244	+	0.268629i	$0.0865706\pi$
$199$			7.57896i			0.537258i	−0.963244	+	0.268629i	$0.913429\pi$
$200$	7.56361	−	7.56361i	0.534828	−	0.534828i
$201$	−0.238664	+	7.41724i	−0.0168341	+	0.523172i
$202$	−0.738039	+	0.738039i	−0.0519282	+	0.0519282i
$203$	4.92712	+	4.92712i	0.345816	+	0.345816i
$204$	−4.37365	+	4.10096i	−0.306217	+	0.287125i
$205$		−	20.1280i		−	1.40580i
$206$	5.93337	+	5.93337i	0.413398	+	0.413398i
$207$	0.140476	−	2.18062i	0.00976379	−	0.151563i
$208$	−3.52656	+	0.750597i	−0.244523	+	0.0520445i
$209$		−	11.6217i		−	0.803887i
$210$	0.220690	−	6.85864i	0.0152291	−	0.473291i
$211$	11.7943			0.811951			0.405976	−	0.913884i	$-0.366932\pi$
$211$	11.7943			0.811951			0.405976	+	0.913884i	$0.366932\pi$
$212$	−11.8689			−0.815157
$213$	8.22703	+	0.264720i	0.563707	+	0.0181383i
$214$	−10.1257	−	10.1257i	−0.692176	−	0.692176i
$215$	20.8466	+	20.8466i	1.42173	+	1.42173i
$216$	5.17198	+	0.500638i	0.351909	+	0.0340641i
$217$	−10.2791			−0.697789
$218$	0.440523			0.0298360
$219$	16.8804	+	0.543161i	1.14067	+	0.0367034i
$220$		−	17.9806i		−	1.21225i
$221$	12.2073	−	2.59822i	0.821153	−	0.174775i
$222$	−2.79012	+	2.61616i	−0.187260	+	0.175585i
$223$	5.27800	+	5.27800i	0.353441	+	0.353441i	0.861388	−	0.507947i	$-0.169595\pi$
$223$	5.27800	+	5.27800i	0.353441	+	0.353441i	−0.507947	+	0.861388i	$0.669595\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	32.0233	+	2.06296i	2.13489	+	0.137531i
$226$	3.28959	+	3.28959i	0.218821	+	0.218821i
$227$	12.0460	−	12.0460i	0.799522	−	0.799522i	−0.183498	−	0.983020i	$-0.558742\pi$
$227$	12.0460	−	12.0460i	0.799522	−	0.799522i	0.983020	+	0.183498i	$0.0587420\pi$
$228$	4.43306	+	0.142642i	0.293587	+	0.00944671i
$229$	−12.4724	+	12.4724i	−0.824200	+	0.824200i	−0.986707	−	0.162507i	$-0.948042\pi$
$229$	−12.4724	+	12.4724i	−0.824200	+	0.824200i	0.162507	+	0.986707i	$0.448042\pi$
$230$		−	2.88575i		−	0.190281i
$231$	−5.37672	−	5.73424i	−0.353762	−	0.377285i
$232$	−4.92712	+	4.92712i	−0.323481	+	0.323481i
$233$	−17.2708			−1.13144			−0.565722	−	0.824596i	$-0.691403\pi$
$233$	−17.2708			−1.13144			−0.565722	+	0.824596i	$0.691403\pi$
$234$	−8.67588	−	6.45981i	−0.567160	−	0.422291i
$235$	40.2024			2.62252
$236$	−7.33162	+	7.33162i	−0.477248	+	0.477248i
$237$	6.96090	+	7.42375i	0.452159	+	0.482224i
$238$			3.46154i			0.224378i
$239$	3.19200	−	3.19200i	0.206473	−	0.206473i	−0.596293	−	0.802767i	$-0.703360\pi$
$239$	3.19200	−	3.19200i	0.206473	−	0.206473i	0.802767	+	0.596293i	$0.203360\pi$
$240$	6.85864	+	0.220690i	0.442723	+	0.0142455i
$241$	−9.64002	+	9.64002i	−0.620968	+	0.620968i	−0.945779	−	0.324811i	$-0.894699\pi$
$241$	−9.64002	+	9.64002i	−0.620968	+	0.620968i	0.324811	+	0.945779i	$0.394699\pi$
$242$	−6.78602	−	6.78602i	−0.436222	−	0.436222i
$243$	9.11532	+	12.6456i	0.584748	+	0.811215i
$244$			0.300726i			0.0192520i
$245$	−2.80148	−	2.80148i	−0.178980	−	0.178980i
$246$	6.41910	−	6.01888i	0.409267	−	0.383750i
$247$	−7.74475	−	5.02650i	−0.492787	−	0.319829i
$248$		−	10.2791i		−	0.652721i
$249$	18.4875	+	0.594870i	1.17160	+	0.0376983i
$250$	22.5691			1.42740
$251$	−10.4429			−0.659151			−0.329576	−	0.944129i	$-0.606906\pi$
$251$	−10.4429			−0.659151			−0.329576	+	0.944129i	$0.606906\pi$
$252$	2.25331	−	1.98056i	0.141945	−	0.124763i
$253$	−2.33745	−	2.33745i	−0.146954	−	0.146954i
$254$	−6.02303	−	6.02303i	−0.377918	−	0.377918i
$255$	−23.7415	−	0.763927i	−1.48675	−	0.0478389i
$256$	1.00000			0.0625000
$257$	−24.8464			−1.54987			−0.774937	−	0.632039i	$-0.782218\pi$
$257$	−24.8464			−1.54987			−0.774937	+	0.632039i	$0.782218\pi$
$258$	−0.414504	+	12.8820i	−0.0258059	+	0.801999i
$259$			2.20825i			0.137214i
$260$	−11.9824	−	7.77679i	−0.743114	−	0.482296i
$261$	−20.8608	−	1.34386i	−1.29125	−	0.0831830i
$262$	−1.16678	−	1.16678i	−0.0720837	−	0.0720837i
$263$			13.4778i			0.831079i	0.909575	+	0.415540i	$0.136407\pi$
$263$			13.4778i			0.831079i	−0.909575	+	0.415540i	$0.863593\pi$
$264$	5.73424	−	5.37672i	0.352918	−	0.330914i
$265$	−33.2504	−	33.2504i	−2.04255	−	2.04255i
$266$	1.81073	−	1.81073i	0.111023	−	0.111023i
$267$	0.0645281	−	2.00542i	0.00394906	−	0.122729i
$268$	−3.02964	+	3.02964i	−0.185065	+	0.185065i
$269$		−	0.0472472i		−	0.00288071i	−0.999999	−	0.00144036i	$-0.999542\pi$
$269$		−	0.0472472i		−	0.00288071i	0.999999	−	0.00144036i	$-0.000458480\pi$
$270$	13.0867	+	15.8917i	0.796429	+	0.967139i
$271$	9.20531	−	9.20531i	0.559183	−	0.559183i	−0.369892	−	0.929075i	$-0.620605\pi$
$271$	9.20531	−	9.20531i	0.559183	−	0.559183i	0.929075	+	0.369892i	$0.120605\pi$
$272$	−3.46154			−0.209887
$273$	−6.14683	+	1.10296i	−0.372023	+	0.0667541i
$274$	−12.8974			−0.779163
$275$	34.3265	−	34.3265i	2.06997	−	2.06997i
$276$	0.920306	−	0.862927i	0.0553959	−	0.0519421i
$277$			7.05593i			0.423950i	0.977275	+	0.211975i	$0.0679895\pi$
$277$			7.05593i			0.423950i	−0.977275	+	0.211975i	$0.932010\pi$
$278$	13.6164	−	13.6164i	0.816656	−	0.816656i
$279$	23.1619	−	20.3583i	1.38667	−	1.21882i
$280$	2.80148	−	2.80148i	0.167420	−	0.167420i
$281$	10.2852	+	10.2852i	0.613563	+	0.613563i	0.943873	−	0.330309i	$-0.107153\pi$
$281$	10.2852	+	10.2852i	0.613563	+	0.613563i	−0.330309	+	0.943873i	$0.607153\pi$
$282$	12.0217	+	12.8211i	0.715884	+	0.763485i
$283$		−	1.95168i		−	0.116015i	−0.998316	−	0.0580076i	$-0.981525\pi$
$283$		−	1.95168i		−	0.116015i	0.998316	−	0.0580076i	$-0.0184748\pi$
$284$	3.36041	+	3.36041i	0.199404	+	0.199404i
$285$	12.0195	+	12.8187i	0.711974	+	0.759316i
$286$	−16.0049	+	3.40649i	−0.946387	+	0.201430i
$287$		−	5.08041i		−	0.299887i
$288$	1.98056	+	2.25331i	0.116706	+	0.132777i
$289$	−5.01775			−0.295162
$290$	−27.6065			−1.62111
$291$	0.108320	−	3.36640i	0.00634984	−	0.197342i
$292$	6.89498	+	6.89498i	0.403498	+	0.403498i
$293$	17.6386	+	17.6386i	1.03046	+	1.03046i	0.999521	+	0.0309390i	$0.00984977\pi$
$293$	17.6386	+	17.6386i	1.03046	+	1.03046i	0.0309390	+	0.999521i	$0.490150\pi$
$294$	0.0557032	−	1.73115i	0.00324868	−	0.100963i
$295$	−41.0787			−2.39170
$296$	−2.20825			−0.128352
$297$	23.4724	+	2.27208i	1.36201	+	0.131840i
$298$			22.2690i			1.29001i
$299$	−2.56867	+	0.546718i	−0.148550	+	0.0316175i
$300$	12.6725	+	13.5151i	0.731645	+	0.780294i
$301$	5.26178	+	5.26178i	0.303284	+	0.303284i
$302$			19.2209i			1.10604i
$303$	−1.23655	−	1.31877i	−0.0710378	−	0.0757614i
$304$	1.81073	+	1.81073i	0.103852	+	0.103852i
$305$	−0.842476	+	0.842476i	−0.0482401	+	0.0482401i
$306$	−6.85578	−	7.79991i	−0.391919	−	0.445891i
$307$	20.4024	−	20.4024i	1.16443	−	1.16443i	0.180931	−	0.983496i	$-0.442089\pi$
$307$	20.4024	−	20.4024i	1.16443	−	1.16443i	0.983496	−	0.180931i	$-0.0579110\pi$
$308$		−	4.53838i		−	0.258598i
$309$	−10.6021	+	9.94108i	−0.603132	+	0.565528i
$310$	28.7966	−	28.7966i	1.63554	−	1.63554i
$311$	21.1901			1.20158			0.600790	−	0.799407i	$-0.294853\pi$
$311$	21.1901			1.20158			0.600790	+	0.799407i	$0.294853\pi$
$312$	−1.10296	−	6.14683i	−0.0624427	−	0.347996i
$313$	25.8039			1.45852			0.729262	−	0.684235i	$-0.239864\pi$
$313$	25.8039			1.45852			0.729262	+	0.684235i	$0.239864\pi$
$314$	−1.09450	+	1.09450i	−0.0617665	+	0.0617665i
$315$	11.8611	+	0.764097i	0.668296	+	0.0430520i
$316$			5.87555i			0.330525i
$317$	14.4728	−	14.4728i	0.812873	−	0.812873i	−0.172190	−	0.985064i	$-0.555084\pi$
$317$	14.4728	−	14.4728i	0.812873	−	0.812873i	0.985064	+	0.172190i	$0.0550844\pi$
$318$	0.661134	−	20.5468i	0.0370746	−	1.15221i
$319$	−22.3612	+	22.3612i	−1.25198	+	1.25198i
$320$	2.80148	+	2.80148i	0.156607	+	0.156607i
$321$	18.0931	−	16.9651i	1.00986	−	0.946898i
$322$		−	0.728379i		−	0.0405910i
$323$	−6.26790	−	6.26790i	−0.348755	−	0.348755i
$324$	−1.15478	+	8.92561i	−0.0641543	+	0.495867i
$325$	−8.02880	−	37.7220i	−0.445358	−	2.09244i
$326$			0.398760i			0.0220853i
$327$	−0.0245385	+	0.762613i	−0.00135698	+	0.0421726i
$328$	5.08041			0.280519
$329$	10.1473			0.559438
$330$	31.1271	+	1.00157i	1.71349	+	0.0551349i
$331$	0.263725	+	0.263725i	0.0144956	+	0.0144956i	0.714317	−	0.699822i	$-0.246737\pi$
$331$	0.263725	+	0.263725i	0.0144956	+	0.0144956i	−0.699822	+	0.714317i	$0.746737\pi$
$332$	7.55138	+	7.55138i	0.414436	+	0.414436i
$333$	−4.37356	−	4.97585i	−0.239670	−	0.272675i
$334$	−19.7744			−1.08201
$335$	−16.9750			−0.927441
$336$	1.73115	+	0.0557032i	0.0944422	+	0.00303886i
$337$		−	5.07335i		−	0.276363i	−0.990407	−	0.138181i	$-0.955874\pi$
$337$		−	5.07335i		−	0.276363i	0.990407	−	0.138181i	$-0.0441257\pi$
$338$	−4.65217	+	12.1391i	−0.253045	+	0.660279i
$339$	−5.87804	+	5.51156i	−0.319251	+	0.299347i
$340$	−9.69742	−	9.69742i	−0.525917	−	0.525917i
$341$		−	46.6503i		−	2.52626i
$342$	−0.493871	+	7.66637i	−0.0267055	+	0.414550i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−5.26178	+	5.26178i	−0.283696	+	0.283696i
$345$	4.99569	+	0.160746i	0.268959	+	0.00865427i
$346$	3.27945	−	3.27945i	0.176304	−	0.176304i
$347$		−	5.56263i		−	0.298618i	−0.988791	−	0.149309i	$-0.952295\pi$
$347$		−	5.56263i		−	0.298618i	0.988791	−	0.149309i	$-0.0477049\pi$
$348$	−8.25516	−	8.80407i	−0.442523	−	0.471948i
$349$	−13.8464	+	13.8464i	−0.741180	+	0.741180i	−0.972805	−	0.231625i	$-0.925596\pi$
$349$	−13.8464	+	13.8464i	−0.741180	+	0.741180i	0.231625	+	0.972805i	$0.425596\pi$
$350$	10.6966			0.571755
$351$	11.6662	−	14.6595i	0.622696	−	0.782464i
$352$	4.53838			0.241896
$353$	−25.3196	+	25.3196i	−1.34762	+	1.34762i	−0.459389	+	0.888235i	$0.651932\pi$
$353$	−25.3196	+	25.3196i	−1.34762	+	1.34762i	−0.888235	+	0.459389i	$0.848068\pi$
$354$	−12.2838	−	13.1006i	−0.652875	−	0.696287i
$355$			18.8282i			0.999298i
$356$	0.819132	−	0.819132i	0.0434139	−	0.0434139i
$357$	−5.99246	−	0.192819i	−0.317155	−	0.0102051i
$358$	5.36742	−	5.36742i	0.283677	−	0.283677i
$359$	2.81055	+	2.81055i	0.148335	+	0.148335i	0.777374	−	0.629039i	$-0.216551\pi$
$359$	2.81055	+	2.81055i	0.148335	+	0.148335i	−0.629039	+	0.777374i	$0.716551\pi$
$360$	−0.764097	+	11.8611i	−0.0402714	+	0.625134i
$361$		−	12.4425i		−	0.654871i
$362$	−12.6586	−	12.6586i	−0.665320	−	0.665320i
$363$	12.1257	−	11.3697i	0.636432	−	0.596752i
$364$	−3.02440	−	1.96290i	−0.158522	−	0.102884i
$365$			38.6323i			2.02211i
$366$	−0.520603	−	0.0167514i	−0.0272123	−	0.000875609i
$367$	−11.1457			−0.581803			−0.290902	−	0.956753i	$-0.593955\pi$
$367$	−11.1457			−0.581803			−0.290902	+	0.956753i	$0.593955\pi$
$368$	0.728379			0.0379694
$369$	10.0621	+	11.4477i	0.523810	+	0.595945i
$370$	−6.18635	−	6.18635i	−0.321613	−	0.321613i
$371$	−8.39255	−	8.39255i	−0.435720	−	0.435720i
$372$	17.7947	+	0.572577i	0.922610	+	0.0296867i
$373$	15.2818			0.791262			0.395631	−	0.918409i	$-0.370526\pi$
$373$	15.2818			0.791262			0.395631	+	0.918409i	$0.370526\pi$
$374$	−15.7098			−0.812333
$375$	−1.25717	+	39.0707i	−0.0649201	+	2.01760i
$376$			10.1473i			0.523307i
$377$	5.23016	+	24.5731i	0.269367	+	1.26558i
$378$	3.30314	+	4.01115i	0.169895	+	0.206311i
$379$	−13.4151	−	13.4151i	−0.689088	−	0.689088i	0.272943	−	0.962030i	$-0.412003\pi$
$379$	−13.4151	−	13.4151i	−0.689088	−	0.689088i	−0.962030	+	0.272943i	$0.912003\pi$
$380$			10.1454i			0.520449i
$381$	10.7623	−	10.0913i	0.551369	−	0.516992i
$382$	−6.51876	−	6.51876i	−0.333529	−	0.333529i
$383$	1.21551	−	1.21551i	0.0621098	−	0.0621098i	−0.675370	−	0.737479i	$-0.736016\pi$
$383$	1.21551	−	1.21551i	0.0621098	−	0.0621098i	0.737479	+	0.675370i	$0.236016\pi$
$384$	−0.0557032	+	1.73115i	−0.00284259	+	0.0883426i
$385$	12.7142	−	12.7142i	0.647974	−	0.647974i
$386$		−	0.141484i		−	0.00720135i
$387$	−22.2777	−	1.43514i	−1.13244	−	0.0729523i
$388$	1.37504	−	1.37504i	0.0698069	−	0.0698069i
$389$	−27.2012			−1.37915			−0.689577	−	0.724212i	$-0.742204\pi$
$389$	−27.2012			−1.37915			−0.689577	+	0.724212i	$0.742204\pi$
$390$	14.1303	−	20.3101i	0.715515	−	1.02844i
$391$	−2.52131			−0.127508
$392$	0.707107	−	0.707107i	0.0357143	−	0.0357143i
$393$	2.08486	−	1.95488i	0.105167	−	0.0986105i
$394$		−	11.6654i		−	0.587694i
$395$	−16.4602	+	16.4602i	−0.828203	+	0.828203i
$396$	8.98852	+	10.2264i	0.451690	+	0.513894i
$397$	13.1240	−	13.1240i	0.658677	−	0.658677i	−0.296390	−	0.955067i	$-0.595783\pi$
$397$	13.1240	−	13.1240i	0.658677	−	0.658677i	0.955067	+	0.296390i	$0.0957829\pi$
$398$	−5.35913	−	5.35913i	−0.268629	−	0.268629i
$399$	3.03378	+	3.23551i	0.151879	+	0.161978i
$400$			10.6966i			0.534828i
$401$	0.204321	+	0.204321i	0.0102033	+	0.0102033i	0.712190	−	0.701987i	$-0.247703\pi$
$401$	0.204321	+	0.204321i	0.0102033	+	0.0102033i	−0.701987	+	0.712190i	$0.747703\pi$
$402$	−5.07602	−	5.41354i	−0.253169	−	0.270003i
$403$	−31.0881	−	20.1768i	−1.54861	−	1.00508i
$404$		−	1.04374i		−	0.0519282i
$405$	−28.2400	+	21.7698i	−1.40326	+	1.08175i
$406$	−6.96800			−0.345816
$407$	−10.0219			−0.496765
$408$	0.192819	−	5.99246i	0.00954596	−	0.296671i
$409$	3.12131	+	3.12131i	0.154339	+	0.154339i	0.780053	−	0.625714i	$-0.215192\pi$
$409$	3.12131	+	3.12131i	0.154339	+	0.154339i	−0.625714	+	0.780053i	$0.715192\pi$
$410$	14.2327	+	14.2327i	0.702901	+	0.702901i
$411$	0.718430	−	22.3275i	0.0354375	−	1.10133i
$412$	−8.39105			−0.413398
$413$	−10.3685			−0.510199
$414$	1.44260	+	1.64126i	0.0708997	+	0.0806635i
$415$			42.3101i			2.07692i
$416$	1.96290	−	3.02440i	0.0962391	−	0.148284i
$417$	22.8136	+	24.3305i	1.11719	+	1.19147i
$418$	8.21776	+	8.21776i	0.401944	+	0.401944i
$419$		−	10.6945i		−	0.522459i	−0.965277	−	0.261229i	$-0.915872\pi$
$419$		−	10.6945i		−	0.522459i	0.965277	−	0.261229i	$-0.0841279\pi$
$420$	4.69374	+	5.00584i	0.229031	+	0.244260i
$421$	−9.86237	−	9.86237i	−0.480663	−	0.480663i	0.424681	−	0.905343i	$-0.360386\pi$
$421$	−9.86237	−	9.86237i	−0.480663	−	0.480663i	−0.905343	+	0.424681i	$0.860386\pi$
$422$	−8.33981	+	8.33981i	−0.405976	+	0.405976i
$423$	−22.8650	+	20.0973i	−1.11173	+	0.977164i
$424$	8.39255	−	8.39255i	0.407578	−	0.407578i
$425$		−	37.0265i		−	1.79605i
$426$	−6.00457	+	5.63020i	−0.290923	+	0.272784i
$427$	−0.212645	+	0.212645i	−0.0102906	+	0.0102906i
$428$	14.3199			0.692176
$429$	−5.00564	−	27.8966i	−0.241675	−	1.34686i
$430$	−29.4815			−1.42173
$431$	−12.4189	+	12.4189i	−0.598196	+	0.598196i	−0.939832	−	0.341636i	$-0.889019\pi$
$431$	−12.4189	+	12.4189i	−0.598196	+	0.598196i	0.341636	+	0.939832i	$0.389019\pi$
$432$	−4.01115	+	3.30314i	−0.192986	+	0.158922i
$433$		−	29.3877i		−	1.41228i	−0.708070	−	0.706142i	$-0.750434\pi$
$433$		−	29.3877i		−	1.41228i	0.708070	−	0.706142i	$-0.249566\pi$
$434$	7.26840	−	7.26840i	0.348894	−	0.348894i
$435$	1.53777	−	47.7910i	0.0737304	−	2.29141i
$436$	−0.311497	+	0.311497i	−0.0149180	+	0.0149180i
$437$	1.31889	+	1.31889i	0.0630912	+	0.0630912i
$438$	−12.3204	+	11.5522i	−0.588689	+	0.551986i
$439$		−	35.4420i		−	1.69155i	−0.533537	−	0.845776i	$-0.679138\pi$
$439$		−	35.4420i		−	1.69155i	0.533537	−	0.845776i	$-0.320862\pi$
$440$	12.7142	+	12.7142i	0.606124	+	0.606124i
$441$	2.99379	+	0.192862i	0.142562	+	0.00918390i
$442$	−6.79466	+	10.4691i	−0.323189	+	0.497964i
$443$		−	10.2171i		−	0.485431i	−0.970097	−	0.242716i	$-0.921962\pi$
$443$		−	10.2171i		−	0.485431i	0.970097	−	0.242716i	$-0.0780382\pi$
$444$	0.123006	−	3.82282i	0.00583763	−	0.181423i
$445$	4.58956			0.217566
$446$	−7.46422			−0.353441
$447$	−38.5512	−	1.24046i	−1.82341	−	0.0586716i
$448$	0.707107	+	0.707107i	0.0334077	+	0.0334077i
$449$	10.2744	+	10.2744i	0.484877	+	0.484877i	0.906685	−	0.421808i	$-0.138604\pi$
$449$	10.2744	+	10.2744i	0.484877	+	0.484877i	−0.421808	+	0.906685i	$0.638604\pi$
$450$	−24.1026	+	21.1852i	−1.13621	+	0.998678i
$451$	23.0568			1.08570
$452$	−4.65219			−0.218821
$453$	−33.2744	−	1.07067i	−1.56337	−	0.0503043i
$454$			17.0356i			0.799522i
$455$	−2.97378	−	13.9718i	−0.139413	−	0.655009i
$456$	−3.23551	+	3.03378i	−0.151517	+	0.142070i
$457$	20.4058	+	20.4058i	0.954543	+	0.954543i	0.999011	−	0.0444681i	$-0.0141593\pi$
$457$	20.4058	+	20.4058i	0.954543	+	0.954543i	−0.0444681	+	0.999011i	$0.514159\pi$
$458$		−	17.6387i		−	0.824200i
$459$	13.8847	−	11.4339i	0.648084	−	0.533690i
$460$	2.04054	+	2.04054i	0.0951405	+	0.0951405i
$461$	−9.03208	+	9.03208i	−0.420666	+	0.420666i	−0.885433	−	0.464767i	$-0.846138\pi$
$461$	−9.03208	+	9.03208i	−0.420666	+	0.420666i	0.464767	+	0.885433i	$0.346138\pi$
$462$	7.85664	+	0.252802i	0.365524	+	0.0117614i
$463$	−1.89548	+	1.89548i	−0.0880905	+	0.0880905i	−0.749779	−	0.661688i	$-0.769840\pi$
$463$	−1.89548	+	1.89548i	−0.0880905	+	0.0880905i	0.661688	+	0.749779i	$0.269840\pi$
$464$		−	6.96800i		−	0.323481i
$465$	48.2473	+	51.4554i	2.23741	+	2.38619i
$466$	12.2123	−	12.2123i	0.565722	−	0.565722i
$467$	−3.05929			−0.141567			−0.0707834	−	0.997492i	$-0.522550\pi$
$467$	−3.05929			−0.141567			−0.0707834	+	0.997492i	$0.522550\pi$
$468$	10.7025	−	1.56699i	0.494725	−	0.0724343i
$469$	−4.28456			−0.197843
$470$	−28.4274	+	28.4274i	−1.31126	+	1.31126i
$471$	−1.83379	−	1.95572i	−0.0844966	−	0.0901150i
$472$		−	10.3685i		−	0.477248i
$473$	−23.8800	+	23.8800i	−1.09800	+	1.09800i
$474$	−10.1715	−	0.327287i	−0.467192	−	0.0150328i
$475$	−19.3685	+	19.3685i	−0.888689	+	0.888689i
$476$	−2.44768	−	2.44768i	−0.112189	−	0.112189i
$477$	35.5329	+	2.28905i	1.62694	+	0.104808i
$478$			4.51417i			0.206473i
$479$	−13.5200	−	13.5200i	−0.617747	−	0.617747i	0.327206	−	0.944953i	$-0.393893\pi$
$479$	−13.5200	−	13.5200i	−0.617747	−	0.617747i	−0.944953	+	0.327206i	$0.893893\pi$
$480$	−5.00584	+	4.69374i	−0.228484	+	0.214239i
$481$	−4.33457	+	6.67863i	−0.197639	+	0.304519i
$482$		−	13.6330i		−	0.620968i
$483$	1.26094	+	0.0405730i	0.0573746	+	0.00184614i
$484$	9.59688			0.436222
$485$	7.70427			0.349833
$486$	−15.3873	−	2.49628i	−0.697981	−	0.113234i
$487$	12.0429	+	12.0429i	0.545716	+	0.545716i	0.925199	−	0.379483i	$-0.123898\pi$
$487$	12.0429	+	12.0429i	0.545716	+	0.545716i	−0.379483	+	0.925199i	$0.623898\pi$
$488$	−0.212645	−	0.212645i	−0.00962599	−	0.00962599i
$489$	−0.690315	−	0.0222122i	−0.0312171	−	0.00100447i
$490$	3.96189			0.178980
$491$	−22.3159			−1.00710			−0.503551	−	0.863965i	$-0.667973\pi$
$491$	−22.3159			−1.00710			−0.503551	+	0.863965i	$0.667973\pi$
$492$	−0.282995	+	8.79498i	−0.0127584	+	0.396508i
$493$			24.1200i			1.08631i
$494$	9.03064	−	1.92209i	0.406308	−	0.0864790i
$495$	−3.46776	+	53.8301i	−0.155864	+	2.41948i
$496$	7.26840	+	7.26840i	0.326361	+	0.326361i
$497$			4.75234i			0.213171i
$498$	−13.4932	+	12.6520i	−0.604647	+	0.566949i
$499$	27.8917	+	27.8917i	1.24860	+	1.24860i	0.956337	+	0.292267i	$0.0944097\pi$
$499$	27.8917	+	27.8917i	1.24860	+	1.24860i	0.292267	+	0.956337i	$0.405590\pi$
$500$	−15.9588	+	15.9588i	−0.713698	+	0.713698i
$501$	1.10150	−	34.2326i	0.0492114	−	1.52940i
$502$	7.38426	−	7.38426i	0.329576	−	0.329576i
$503$		−	18.1161i		−	0.807758i	−0.914813	−	0.403879i	$-0.867662\pi$
$503$		−	18.1161i		−	0.807758i	0.914813	−	0.403879i	$-0.132338\pi$
$504$	−0.192862	+	2.99379i	−0.00859075	+	0.133354i
$505$	2.92403	−	2.92403i	0.130117	−	0.130117i
$506$	3.30566			0.146954
$507$	−20.7555	−	8.72982i	−0.921784	−	0.387705i
$508$	8.51785			0.377918
$509$	−7.75052	+	7.75052i	−0.343536	+	0.343536i	−0.857695	−	0.514159i	$-0.828104\pi$
$509$	−7.75052	+	7.75052i	−0.343536	+	0.343536i	0.514159	+	0.857695i	$0.328104\pi$
$510$	17.3279	−	16.2476i	0.767293	−	0.719454i
$511$			9.75097i			0.431358i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−13.2442	−	1.28201i	−0.584744	−	0.0566021i
$514$	17.5690	−	17.5690i	0.774937	−	0.774937i
$515$	−23.5074	−	23.5074i	−1.03586	−	1.03586i
$516$	−8.81586	−	9.40206i	−0.388097	−	0.413903i
$517$			46.0523i			2.02538i
$518$	−1.56147	−	1.56147i	−0.0686069	−	0.0686069i
$519$	5.49456	+	5.85992i	0.241185	+	0.257222i
$520$	13.9718	−	2.97378i	0.612705	−	0.130409i
$521$		−	2.45446i		−	0.107532i	−0.998554	−	0.0537659i	$-0.982878\pi$
$521$		−	2.45446i		−	0.107532i	0.998554	−	0.0537659i	$-0.0171225\pi$
$522$	15.7010	−	13.8005i	0.687216	−	0.604033i
$523$	−29.1475			−1.27453			−0.637265	−	0.770645i	$-0.719934\pi$
$523$	−29.1475			−1.27453			−0.637265	+	0.770645i	$0.719934\pi$
$524$	1.65007			0.0720837
$525$	−0.595833	+	18.5174i	−0.0260043	+	0.808166i
$526$	−9.53027	−	9.53027i	−0.415540	−	0.415540i
$527$	−25.1598	−	25.1598i	−1.09598	−	1.09598i
$528$	−0.252802	+	7.85664i	−0.0110018	+	0.341916i
$529$	−22.4695			−0.976933
$530$	47.0231			2.04255
$531$	23.3633	−	20.5354i	1.01388	−	0.891159i
$532$			2.56075i			0.111023i
$533$	9.97235	−	15.3652i	0.431950	−	0.665542i
$534$	1.37242	+	1.46367i	0.0593902	+	0.0633393i
$535$	40.1168	+	40.1168i	1.73440	+	1.73440i
$536$		−	4.28456i		−	0.185065i
$537$	8.99286	+	9.59082i	0.388070	+	0.413875i
$538$	0.0334088	+	0.0334088i	0.00144036	+	0.00144036i
$539$	3.20912	−	3.20912i	0.138227	−	0.138227i
$540$	−20.4908	−	1.98347i	−0.881784	−	0.0853550i
$541$	−22.0191	+	22.0191i	−0.946673	+	0.946673i	−0.998648	−	0.0519752i	$-0.983448\pi$
$541$	−22.0191	+	22.0191i	−0.946673	+	0.946673i	0.0519752	+	0.998648i	$0.483448\pi$
$542$			13.0183i			0.559183i
$543$	22.6191	−	21.2088i	0.970678	−	0.910158i
$544$	2.44768	−	2.44768i	0.104943	−	0.104943i
$545$	−1.74530			−0.0747605
$546$	3.56655	−	5.12637i	0.152634	−	0.219388i
$547$	12.6981			0.542930			0.271465	−	0.962448i	$-0.412492\pi$
$547$	12.6981			0.542930			0.271465	+	0.962448i	$0.412492\pi$
$548$	9.11987	−	9.11987i	0.389582	−	0.389582i
$549$	0.0579985	−	0.900311i	0.00247532	−	0.0384243i
$550$			48.5450i			2.06997i
$551$	12.6171	−	12.6171i	0.537508	−	0.537508i
$552$	−0.0405730	+	1.26094i	−0.00172690	+	0.0536690i
$553$	−4.15464	+	4.15464i	−0.176673	+	0.176673i
$554$	−4.98930	−	4.98930i	−0.211975	−	0.211975i
$555$	11.0541	−	10.3649i	0.469222	−	0.439967i
$556$			19.2565i			0.816656i
$557$	10.0740	+	10.0740i	0.426849	+	0.426849i	0.887554	−	0.460705i	$-0.152403\pi$
$557$	10.0740	+	10.0740i	0.426849	+	0.426849i	−0.460705	+	0.887554i	$0.652403\pi$
$558$	−1.98244	+	30.7734i	−0.0839234	+	1.30274i
$559$	5.58540	+	26.2421i	0.236237	+	1.10992i
$560$			3.96189i			0.167420i
$561$	0.875085	−	27.1960i	0.0369461	−	1.14822i
$562$	−14.5455			−0.613563
$563$	−10.5842			−0.446073			−0.223036	−	0.974810i	$-0.571597\pi$
$563$	−10.5842			−0.446073			−0.223036	+	0.974810i	$0.571597\pi$
$564$	−17.5665	−	0.565237i	−0.739685	−	0.0238008i
$565$	−13.0330	−	13.0330i	−0.548303	−	0.548303i
$566$	1.38004	+	1.38004i	0.0580076	+	0.0580076i
$567$	−7.12791	+	5.49481i	−0.299344	+	0.230760i
$568$	−4.75234			−0.199404
$569$	−22.5816			−0.946669			−0.473334	−	0.880883i	$-0.656950\pi$
$569$	−22.5816			−0.946669			−0.473334	+	0.880883i	$0.656950\pi$
$570$	−17.5633	−	0.565132i	−0.735645	−	0.0236708i
$571$		−	6.83794i		−	0.286159i	−0.989711	−	0.143079i	$-0.954300\pi$
$571$		−	6.83794i		−	0.286159i	0.989711	−	0.143079i	$-0.0457004\pi$
$572$	8.90839	−	13.7259i	0.372478	−	0.573908i
$573$	11.6481	−	10.9219i	0.486606	−	0.456268i
$574$	3.59240	+	3.59240i	0.149944	+	0.149944i
$575$			7.79114i			0.324913i
$576$	−2.99379	−	0.192862i	−0.124741	−	0.00803591i
$577$	20.7633	+	20.7633i	0.864388	+	0.864388i	0.991844	−	0.127456i	$-0.0406812\pi$
$577$	20.7633	+	20.7633i	0.864388	+	0.864388i	−0.127456	+	0.991844i	$0.540681\pi$
$578$	3.54809	−	3.54809i	0.147581	−	0.147581i
$579$	0.244931	+	0.00788112i	0.0101790	+	0.000327528i
$580$	19.5207	−	19.5207i	0.810553	−	0.810553i
$581$			10.6793i			0.443051i
$582$	2.30381	+	2.45699i	0.0954959	+	0.101846i
$583$	38.0886	−	38.0886i	1.57747	−	1.57747i
$584$	−9.75097			−0.403498
$585$	34.3729	+	25.5931i	1.42114	+	1.05814i
$586$	−24.9448			−1.03046
$587$	18.8625	−	18.8625i	0.778540	−	0.778540i	−0.201042	−	0.979583i	$-0.564433\pi$
$587$	18.8625	−	18.8625i	0.778540	−	0.778540i	0.979583	+	0.201042i	$0.0644328\pi$
$588$	1.18472	+	1.26350i	0.0488572	+	0.0521058i
$589$			26.3222i			1.08459i
$590$	29.0471	−	29.0471i	1.19585	−	1.19585i
$591$	20.1946	+	0.649800i	0.830695	+	0.0267292i
$592$	1.56147	−	1.56147i	0.0641758	−	0.0641758i
$593$	10.7560	+	10.7560i	0.441694	+	0.441694i	0.892581	−	0.450887i	$-0.148892\pi$
$593$	10.7560	+	10.7560i	0.441694	+	0.441694i	−0.450887	+	0.892581i	$0.648892\pi$
$594$	−18.2041	+	14.9909i	−0.746923	+	0.615084i
$595$		−	13.7142i		−	0.562229i
$596$	−15.7466	−	15.7466i	−0.645006	−	0.645006i
$597$	9.57601	−	8.97897i	0.391920	−	0.367485i
$598$	1.42973	−	2.20291i	0.0584662	−	0.0900837i
$599$		−	6.53963i		−	0.267202i	−0.991035	−	0.133601i	$-0.957346\pi$
$599$		−	6.53963i		−	0.267202i	0.991035	−	0.133601i	$-0.0426541\pi$
$600$	−18.5174	−	0.595833i	−0.755970	−	0.0243248i
$601$	−15.8483			−0.646465			−0.323232	−	0.946320i	$-0.604770\pi$
$601$	−15.8483			−0.646465			−0.323232	+	0.946320i	$0.604770\pi$
$602$	−7.44129			−0.303284
$603$	9.65443	−	8.48583i	0.393159	−	0.345570i
$604$	−13.5912	−	13.5912i	−0.553020	−	0.553020i
$605$	26.8855	+	26.8855i	1.09305	+	1.09305i
$606$	1.80688	+	0.0581399i	0.0733996	+	0.00236177i
$607$	33.8692			1.37471			0.687354	−	0.726323i	$-0.258772\pi$
$607$	33.8692			1.37471			0.687354	+	0.726323i	$0.258772\pi$
$608$	−2.56075			−0.103852
$609$	0.388140	−	12.0627i	0.0157282	−	0.488805i
$610$		−	1.19144i		−	0.0482401i
$611$	30.6895	+	19.9181i	1.24156	+	0.805801i
$612$	10.3631	+	0.667599i	0.418905	+	0.0269861i
$613$	−31.6180	−	31.6180i	−1.27704	−	1.27704i	−0.942316	−	0.334724i	$-0.891357\pi$
$613$	−31.6180	−	31.6180i	−1.27704	−	1.27704i	−0.334724	−	0.942316i	$-0.608643\pi$
$614$			28.8534i			1.16443i
$615$	−25.4318	+	23.8461i	−1.02551	+	0.961570i
$616$	3.20912	+	3.20912i	0.129299	+	0.129299i
$617$	1.92767	−	1.92767i	0.0776053	−	0.0776053i	−0.667239	−	0.744844i	$-0.732524\pi$
$617$	1.92767	−	1.92767i	0.0776053	−	0.0776053i	0.744844	+	0.667239i	$0.232524\pi$
$618$	0.467409	−	14.5262i	0.0188019	−	0.584330i
$619$	3.42808	−	3.42808i	0.137786	−	0.137786i	−0.634850	−	0.772636i	$-0.718938\pi$
$619$	3.42808	−	3.42808i	0.137786	−	0.137786i	0.772636	+	0.634850i	$0.218938\pi$
$620$			40.7245i			1.63554i
$621$	−2.92163	+	2.40593i	−0.117241	+	0.0965468i
$622$	−14.9836	+	14.9836i	−0.600790	+	0.600790i
$623$	1.15843			0.0464114
$624$	5.12637	+	3.56655i	0.205219	+	0.142776i
$625$	−35.9336			−1.43734
$626$	−18.2461	+	18.2461i	−0.729262	+	0.729262i
$627$	−14.6840	+	13.7685i	−0.586421	+	0.549859i
$628$		−	1.54786i		−	0.0617665i
$629$	−5.40507	+	5.40507i	−0.215514	+	0.215514i
$630$	−8.92735	+	7.84675i	−0.355674	+	0.312622i
$631$	−16.8098	+	16.8098i	−0.669188	+	0.669188i	−0.957528	−	0.288340i	$-0.906897\pi$
$631$	−16.8098	+	16.8098i	−0.669188	+	0.669188i	0.288340	+	0.957528i	$0.406897\pi$
$632$	−4.15464	−	4.15464i	−0.165263	−	0.165263i
$633$	−13.9730	−	14.9021i	−0.555375	−	0.592304i
$634$			20.4676i			0.812873i
$635$	23.8626	+	23.8626i	0.946957	+	0.946957i
$636$	14.0613	+	14.9963i	0.557568	+	0.594642i
$637$	−0.750597	−	3.52656i	−0.0297397	−	0.139727i
$638$		−	31.6234i		−	1.25198i
$639$	−9.41228	−	10.7085i	−0.372344	−	0.423620i
$640$	−3.96189			−0.156607
$641$	−37.3693			−1.47600			−0.738000	−	0.674801i	$-0.764229\pi$
$641$	−37.3693			−1.47600			−0.738000	+	0.674801i	$0.764229\pi$
$642$	−0.797662	+	24.7899i	−0.0314812	+	0.978379i
$643$	−23.3585	−	23.3585i	−0.921171	−	0.921171i	0.0759411	−	0.997112i	$-0.475804\pi$
$643$	−23.3585	−	23.3585i	−0.921171	−	0.921171i	−0.997112	+	0.0759411i	$0.975804\pi$
$644$	0.515041	+	0.515041i	0.0202955	+	0.0202955i
$645$	1.64222	−	51.0371i	0.0646622	−	2.00958i
$646$	8.86414			0.348755
$647$	12.8059			0.503453			0.251727	−	0.967798i	$-0.419002\pi$
$647$	12.8059			0.503453			0.251727	+	0.967798i	$0.419002\pi$
$648$	−5.49481	−	7.12791i	−0.215856	−	0.280011i
$649$		−	47.0561i		−	1.84711i
$650$	32.3507	+	20.9963i	1.26890	+	0.823542i
$651$	12.1779	+	12.9876i	0.477288	+	0.509024i
$652$	−0.281966	−	0.281966i	−0.0110426	−	0.0110426i
$653$			15.8484i			0.620194i	0.950705	+	0.310097i	$0.100362\pi$
$653$			15.8484i			0.620194i	−0.950705	+	0.310097i	$0.899638\pi$
$654$	−0.521898	−	0.556600i	−0.0204078	−	0.0217648i
$655$	4.62264	+	4.62264i	0.180621	+	0.180621i
$656$	−3.59240	+	3.59240i	−0.140259	+	0.140259i
$657$	−19.3124	−	21.9719i	−0.753447	−	0.857207i
$658$	−7.17522	+	7.17522i	−0.279719	+	0.279719i
$659$			14.8247i			0.577488i	0.957406	+	0.288744i	$0.0932377\pi$
$659$			14.8247i			0.577488i	−0.957406	+	0.288744i	$0.906762\pi$
$660$	−22.7184	+	21.3020i	−0.884313	+	0.829178i
$661$	0.547620	−	0.547620i	0.0212999	−	0.0212999i	−0.696377	−	0.717677i	$-0.745206\pi$
$661$	0.547620	−	0.547620i	0.0212999	−	0.0212999i	0.717677	+	0.696377i	$0.245206\pi$
$662$	−0.372963			−0.0144956
$663$	−17.7451	−	12.3458i	−0.689164	−	0.479470i
$664$	−10.6793			−0.414436
$665$	−7.17389	+	7.17389i	−0.278192	+	0.278192i
$666$	6.61103	+	0.425886i	0.256172	+	0.0165028i
$667$		−	5.07535i		−	0.196518i
$668$	13.9826	−	13.9826i	0.541004	−	0.541004i
$669$	0.415781	−	12.9217i	0.0160750	−	0.499583i
$670$	12.0031	−	12.0031i	0.463720	−	0.463720i
$671$	−0.965064	−	0.965064i	−0.0372559	−	0.0372559i
$672$	−1.26350	+	1.18472i	−0.0487406	+	0.0457017i
$673$		−	17.2387i		−	0.664502i	−0.943191	−	0.332251i	$-0.892192\pi$
$673$		−	17.2387i		−	0.664502i	0.943191	−	0.332251i	$-0.107808\pi$
$674$	3.58740	+	3.58740i	0.138181	+	0.138181i
$675$	−35.3322	−	42.9055i	−1.35994	−	1.65143i
$676$	−5.29404	−	11.8732i	−0.203617	−	0.456662i
$677$		−	16.5049i		−	0.634333i	−0.948370	−	0.317167i	$-0.897269\pi$
$677$		−	16.5049i		−	0.634333i	0.948370	−	0.317167i	$-0.102731\pi$
$678$	0.259142	−	8.05366i	0.00995229	−	0.309299i
$679$	1.94460			0.0746267
$680$	13.7142			0.525917
$681$	−29.4913	−	0.948940i	−1.13011	−	0.0363635i
$682$	32.9867	+	32.9867i	1.26313	+	1.26313i
$683$	9.73430	+	9.73430i	0.372473	+	0.372473i	0.868377	−	0.495904i	$-0.165163\pi$
$683$	9.73430	+	9.73430i	0.372473	+	0.372473i	−0.495904	+	0.868377i	$0.665163\pi$
$684$	−5.07172	−	5.77016i	−0.193922	−	0.220628i
$685$	51.0983			1.95236
$686$	1.00000			0.0381802
$687$	30.5352	+	0.982530i	1.16499	+	0.0374859i
$688$		−	7.44129i		−	0.283696i
$689$	−8.90873	−	41.8562i	−0.339396	−	1.59460i
$690$	−3.64615	+	3.41882i	−0.138807	+	0.130152i
$691$	−27.4763	−	27.4763i	−1.04525	−	1.04525i	−0.998927	−	0.0463224i	$-0.985250\pi$
$691$	−27.4763	−	27.4763i	−1.04525	−	1.04525i	−0.0463224	−	0.998927i	$-0.514750\pi$
$692$			4.63785i			0.176304i
$693$	−0.875280	+	13.5870i	−0.0332491	+	0.516126i
$694$	3.93338	+	3.93338i	0.149309	+	0.149309i
$695$	−53.9466	+	53.9466i	−2.04631	+	2.04631i
$696$	12.0627	+	0.388140i	0.457235	+	0.0147124i
$697$	12.4352	−	12.4352i	0.471017	−	0.471017i
$698$		−	19.5818i		−	0.741180i
$699$	20.4611	+	21.8216i	0.773908	+	0.825368i
$700$	−7.56361	+	7.56361i	−0.285878	+	0.285878i
$701$	−13.3217			−0.503153			−0.251576	−	0.967837i	$-0.580949\pi$
$701$	−13.3217			−0.503153			−0.251576	+	0.967837i	$0.580949\pi$
$702$	2.11654	+	18.6151i	0.0798837	+	0.702580i
$703$	5.65477			0.213274
$704$	−3.20912	+	3.20912i	−0.120948	+	0.120948i
$705$	−47.6288	−	50.7958i	−1.79380	−	1.91308i
$706$		−	35.8073i		−	1.34762i
$707$	0.738039	−	0.738039i	0.0277568	−	0.0277568i
$708$	17.9494	+	0.577557i	0.674581	+	0.0217059i
$709$	−18.7138	+	18.7138i	−0.702813	+	0.702813i	−0.965013	−	0.262200i	$-0.915552\pi$
$709$	−18.7138	+	18.7138i	−0.702813	+	0.702813i	0.262200	+	0.965013i	$0.415552\pi$
$710$	−13.3136	−	13.3136i	−0.499649	−	0.499649i
$711$	1.13317	−	17.5902i	0.0424971	−	0.659683i
$712$			1.15843i			0.0434139i
$713$	5.29415	+	5.29415i	0.198267	+	0.198267i
$714$	4.37365	−	4.10096i	0.163680	−	0.153475i
$715$	63.4094	−	13.4961i	2.37138	−	0.504727i
$716$			7.59068i			0.283677i
$717$	−7.81472	−	0.251454i	−0.291846	−	0.00939071i
$718$	−3.97472			−0.148335
$719$	31.8959			1.18952			0.594759	−	0.803904i	$-0.297247\pi$
$719$	31.8959			1.18952			0.594759	+	0.803904i	$0.297247\pi$
$720$	−7.84675	−	8.92735i	−0.292431	−	0.332703i
$721$	−5.93337	−	5.93337i	−0.220970	−	0.220970i
$722$	8.79821	+	8.79821i	0.327435	+	0.327435i
$723$	23.6009	+	0.759405i	0.877727	+	0.0282426i
$724$	17.9019			0.665320
$725$	74.5337			2.76811
$726$	−0.534577	+	16.6137i	−0.0198400	+	0.616592i
$727$			14.0190i			0.519935i	0.965617	+	0.259967i	$0.0837118\pi$
$727$			14.0190i			0.519935i	−0.965617	+	0.259967i	$0.916288\pi$
$728$	3.52656	−	0.750597i	0.130703	−	0.0278190i
$729$	5.17857	−	26.4987i	0.191799	−	0.981434i
$730$	−27.3171	−	27.3171i	−1.01105	−	1.01105i
$731$			25.7583i			0.952705i
$732$	0.379967	−	0.356277i	0.0140440	−	0.0131684i
$733$	−24.3910	−	24.3910i	−0.900902	−	0.900902i	0.0946120	−	0.995514i	$-0.469839\pi$
$733$	−24.3910	−	24.3910i	−0.900902	−	0.900902i	−0.995514	+	0.0946120i	$0.969839\pi$
$734$	7.88123	−	7.88123i	0.290902	−	0.290902i
$735$	−0.220690	+	6.85864i	−0.00814027	+	0.252985i
$736$	−0.515041	+	0.515041i	−0.0189847	+	0.0189847i
$737$		−	19.4450i		−	0.716265i
$738$	−15.2097	−	0.979818i	−0.559877	−	0.0360676i
$739$	24.7933	−	24.7933i	0.912037	−	0.912037i	−0.0843950	−	0.996432i	$-0.526896\pi$
$739$	24.7933	−	24.7933i	0.912037	−	0.912037i	0.996432	+	0.0843950i	$0.0268957\pi$
$740$	8.74882			0.321613
$741$	2.82440	+	15.7405i	0.103757	+	0.578242i
$742$	11.8689			0.435720
$743$	26.9802	−	26.9802i	0.989806	−	0.989806i	−0.0101427	−	0.999949i	$-0.503229\pi$
$743$	26.9802	−	26.9802i	0.989806	−	0.989806i	0.999949	+	0.0101427i	$0.00322858\pi$
$744$	−12.9876	+	12.1779i	−0.476148	+	0.446462i
$745$		−	88.2275i		−	3.23240i
$746$	−10.8059	+	10.8059i	−0.395631	+	0.395631i
$747$	−21.1509	−	24.0637i	−0.773871	−	0.880443i
$748$	11.1085	−	11.1085i	0.406166	−	0.406166i
$749$	10.1257	+	10.1257i	0.369984	+	0.369984i
$750$	−26.7382	−	28.5161i	−0.976340	−	1.04126i
$751$			31.4776i			1.14864i	0.818633	+	0.574318i	$0.194733\pi$
$751$			31.4776i			1.14864i	−0.818633	+	0.574318i	$0.805267\pi$
$752$	−7.17522	−	7.17522i	−0.261653	−	0.261653i
$753$	12.3720	+	13.1946i	0.450860	+	0.480839i
$754$	−21.0741	−	13.6775i	−0.767472	−	0.498105i
$755$		−	76.1511i		−	2.77142i
$756$	−5.17198	−	0.500638i	−0.188103	−	0.0182080i
$757$	−40.9867			−1.48969			−0.744843	−	0.667240i	$-0.767476\pi$
$757$	−40.9867			−1.48969			−0.744843	+	0.667240i	$0.767476\pi$
$758$	18.9718			0.689088
$759$	−0.184136	+	5.72261i	−0.00668371	+	0.207717i
$760$	−7.17389	−	7.17389i	−0.260224	−	0.260224i
$761$	14.0359	+	14.0359i	0.508801	+	0.508801i	0.914158	−	0.405357i	$-0.132853\pi$
$761$	14.0359	+	14.0359i	0.508801	+	0.508801i	−0.405357	+	0.914158i	$0.632853\pi$
$762$	−0.474472	+	14.7457i	−0.0171883	+	0.534181i
$763$	−0.440523			−0.0159480
$764$	9.21892			0.333529
$765$	27.1618	+	30.9024i	0.982038	+	1.11728i
$766$			1.71899i			0.0621098i
$767$	−31.3585	−	20.3523i	−1.13229	−	0.734878i
$768$	−1.18472	−	1.26350i	−0.0427500	−	0.0455926i
$769$	−0.689254	−	0.689254i	−0.0248551	−	0.0248551i	0.694570	−	0.719425i	$-0.255595\pi$
$769$	−0.689254	−	0.689254i	−0.0248551	−	0.0248551i	−0.719425	+	0.694570i	$0.755595\pi$
$770$			17.9806i			0.647974i
$771$	29.4361	+	31.3934i	1.06011	+	1.13060i
$772$	0.100044	+	0.100044i	0.00360067	+	0.00360067i
$773$	2.82339	−	2.82339i	0.101550	−	0.101550i	−0.654506	−	0.756057i	$-0.727123\pi$
$773$	2.82339	−	2.82339i	0.101550	−	0.101550i	0.756057	+	0.654506i	$0.227123\pi$
$774$	16.7675	−	14.7379i	0.602695	−	0.529743i
$775$	−77.7468	+	77.7468i	−2.79275	+	2.79275i
$776$			1.94460i			0.0698069i
$777$	2.79012	−	2.61616i	0.100095	−	0.0938542i
$778$	19.2341	−	19.2341i	0.689577	−	0.689577i
$779$	−13.0097			−0.466120
$780$	4.36980	+	24.3530i	0.156464	+	0.871979i
$781$	−21.5679			−0.771760
$782$	1.78284	−	1.78284i	0.0637541	−	0.0637541i
$783$	23.0163	+	27.9497i	0.822534	+	0.998840i
$784$			1.00000i			0.0357143i
$785$	4.33630	−	4.33630i	0.154769	−	0.154769i
$786$	−0.0919143	+	2.85653i	−0.00327847	+	0.101889i
$787$	8.83760	−	8.83760i	0.315026	−	0.315026i	−0.531827	−	0.846853i	$-0.678494\pi$
$787$	8.83760	−	8.83760i	0.315026	−	0.315026i	0.846853	+	0.531827i	$0.178494\pi$
$788$	8.24868	+	8.24868i	0.293847	+	0.293847i
$789$	17.0292	−	15.9675i	0.606257	−	0.568458i
$790$		−	23.2783i		−	0.828203i
$791$	−3.28959	−	3.28959i	−0.116964	−	0.116964i
$792$	−13.5870	−	0.875280i	−0.482792	−	0.0311017i
$793$	−1.06053	+	0.225724i	−0.0376604	+	0.00801568i
$794$			18.5602i			0.658677i
$795$	−2.61934	+	81.4043i	−0.0928984	+	2.88711i
$796$	7.57896			0.268629
$797$	49.1094			1.73954			0.869772	−	0.493453i	$-0.164266\pi$
$797$	49.1094			1.73954			0.869772	+	0.493453i	$0.164266\pi$
$798$	−4.43306	−	0.142642i	−0.156929	−	0.00504948i
$799$	24.8373	+	24.8373i	0.878680	+	0.878680i
$800$	−7.56361	−	7.56361i	−0.267414	−	0.267414i
$801$	−2.61029	+	2.29433i	−0.0922301	+	0.0810662i
$802$	−0.288953			−0.0102033
$803$	−44.2536			−1.56168
$804$	7.41724	+	0.238664i	0.261586	+	0.00841703i
$805$			2.88575i			0.101709i
$806$	36.2497	−	7.71543i	1.27684	−	0.271765i
$807$	−0.0596968	+	0.0559748i	−0.00210143	+	0.00197041i
$808$	0.738039	+	0.738039i	0.0259641	+	0.0259641i
$809$		−	14.6228i		−	0.514111i	−0.966397	−	0.257056i	$-0.917248\pi$
$809$		−	14.6228i		−	0.514111i	0.966397	−	0.257056i	$-0.0827524\pi$
$810$	4.57510	−	35.3623i	0.160753	−	1.24250i
$811$	−8.49248	−	8.49248i	−0.298211	−	0.298211i	0.542102	−	0.840313i	$-0.317629\pi$
$811$	−8.49248	−	8.49248i	−0.298211	−	0.298211i	−0.840313	+	0.542102i	$0.817629\pi$
$812$	4.92712	−	4.92712i	0.172908	−	0.172908i
$813$	−22.5366	−	0.725160i	−0.790395	−	0.0254325i
$814$	7.08652	−	7.08652i	0.248383	−	0.248383i
$815$		−	1.57984i		−	0.0553394i
$816$	4.10096	+	4.37365i	0.143562	+	0.153108i
$817$	13.4741	−	13.4741i	0.471400	−	0.471400i
$818$	−4.41420			−0.154339
$819$	8.67588	+	6.45981i	0.303160	+	0.225724i
$820$	−20.1280			−0.702901
$821$	−24.1550	+	24.1550i	−0.843016	+	0.843016i	−0.989250	−	0.146234i	$-0.953285\pi$
$821$	−24.1550	+	24.1550i	−0.843016	+	0.843016i	0.146234	+	0.989250i	$0.453285\pi$
$822$	15.2799	+	16.2959i	0.532948	+	0.568385i
$823$			53.6160i			1.86894i	0.356045	+	0.934469i	$0.384125\pi$
$823$			53.6160i			1.86894i	−0.356045	+	0.934469i	$0.615875\pi$
$824$	5.93337	−	5.93337i	0.206699	−	0.206699i
$825$	−84.0390	−	2.70412i	−2.92586	−	0.0941452i
$826$	7.33162	−	7.33162i	0.255100	−	0.255100i
$827$	14.6303	+	14.6303i	0.508746	+	0.508746i	0.914141	−	0.405395i	$-0.132866\pi$
$827$	14.6303	+	14.6303i	0.508746	+	0.508746i	−0.405395	+	0.914141i	$0.632866\pi$
$828$	−2.18062	−	0.140476i	−0.0757816	−	0.00488189i
$829$			11.9834i			0.416199i	0.978108	+	0.208100i	$0.0667278\pi$
$829$			11.9834i			0.416199i	−0.978108	+	0.208100i	$0.933272\pi$
$830$	−29.9177	−	29.9177i	−1.03846	−	1.03846i
$831$	8.91517	−	8.35933i	0.309264	−	0.289982i
$832$	0.750597	+	3.52656i	0.0260223	+	0.122261i
$833$		−	3.46154i		−	0.119935i
$834$	−33.3359	−	1.07265i	−1.15433	−	0.0371427i
$835$	78.3441			2.71121
$836$	−11.6217			−0.401944
$837$	−53.1631	−	5.14609i	−1.83759	−	0.177875i
$838$	7.56212	+	7.56212i	0.261229	+	0.261229i
$839$	9.43893	+	9.43893i	0.325868	+	0.325868i	0.851013	−	0.525145i	$-0.175989\pi$
$839$	9.43893	+	9.43893i	0.325868	+	0.325868i	−0.525145	+	0.851013i	$0.675989\pi$
$840$	−6.85864	−	0.220690i	−0.236646	−	0.00761453i
$841$	−19.5531			−0.674244
$842$	13.9475			0.480663
$843$	0.810229	−	25.1805i	0.0279058	−	0.867261i
$844$		−	11.7943i		−	0.405976i
$845$	18.4314	−	48.0937i	0.634059	−	1.65447i
$846$	1.95703	−	30.3789i	0.0672839	−	1.04445i
$847$	6.78602	+	6.78602i	0.233170	+	0.233170i
$848$			11.8689i			0.407578i
$849$	−2.46594	+	2.31220i	−0.0846310	+	0.0793544i
$850$	26.1817	+	26.1817i	0.898026	+	0.898026i
$851$	1.13734	−	1.13734i	0.0389874	−	0.0389874i
$852$	0.264720	−	8.22703i	0.00906917	−	0.281853i
$853$	0.386062	−	0.386062i	0.0132185	−	0.0132185i	−0.700467	−	0.713685i	$-0.747025\pi$
$853$	0.386062	−	0.386062i	0.0132185	−	0.0132185i	0.713685	+	0.700467i	$0.247025\pi$
$854$		−	0.300726i		−	0.0102906i
$855$	1.95666	−	30.3733i	0.0669165	−	1.03874i
$856$	−10.1257	+	10.1257i	−0.346088	+	0.346088i
$857$	3.54962			0.121253			0.0606264	−	0.998161i	$-0.480690\pi$
$857$	3.54962			0.121253			0.0606264	+	0.998161i	$0.480690\pi$
$858$	23.2654	+	16.1864i	0.794268	+	0.552594i
$859$	−25.4195			−0.867303			−0.433652	−	0.901081i	$-0.642775\pi$
$859$	−25.4195			−0.867303			−0.433652	+	0.901081i	$0.642775\pi$
$860$	20.8466	−	20.8466i	0.710863	−	0.710863i
$861$	−6.41910	+	6.01888i	−0.218762	+	0.205123i
$862$		−	17.5629i		−	0.598196i
$863$	2.46097	−	2.46097i	0.0837722	−	0.0837722i	−0.663979	−	0.747751i	$-0.731134\pi$
$863$	2.46097	−	2.46097i	0.0837722	−	0.0837722i	0.747751	+	0.663979i	$0.231134\pi$
$864$	0.500638	−	5.17198i	0.0170320	−	0.175954i
$865$	−12.9928	+	12.9928i	−0.441769	+	0.441769i
$866$	20.7803	+	20.7803i	0.706142	+	0.706142i
$867$	5.94465	+	6.33993i	0.201891	+	0.215315i
$868$			10.2791i			0.348894i
$869$	−18.8553	−	18.8553i	−0.639623	−	0.639623i
$870$	32.7060	+	34.8807i	1.10884	+	1.18257i
$871$	−12.9582	−	8.41017i	−0.439073	−	0.284968i
$872$		−	0.440523i		−	0.0149180i
$873$	−4.38177	+	3.85138i	−0.148300	+	0.130350i
$874$	−1.86520			−0.0630912
$875$	−22.5691			−0.762976
$876$	0.543161	−	16.8804i	0.0183517	−	0.570337i
$877$	5.56917	+	5.56917i	0.188057	+	0.188057i	0.794856	−	0.606798i	$-0.207546\pi$
$877$	5.56917	+	5.56917i	0.188057	+	0.188057i	−0.606798	+	0.794856i	$0.707546\pi$
$878$	25.0613	+	25.0613i	0.845776	+	0.845776i
$879$	1.38951	−	43.1833i	0.0468669	−	1.45654i
$880$	−17.9806			−0.606124
$881$	18.6076			0.626906			0.313453	−	0.949604i	$-0.398514\pi$
$881$	18.6076			0.626906			0.313453	+	0.949604i	$0.398514\pi$
$882$	−2.25331	+	1.98056i	−0.0758728	+	0.0666889i
$883$			10.7533i			0.361877i	0.983494	+	0.180938i	$0.0579135\pi$
$883$			10.7533i			0.361877i	−0.983494	+	0.180938i	$0.942087\pi$
$884$	−2.59822	−	12.2073i	−0.0873875	−	0.410576i
$885$	48.6669	+	51.9030i	1.63592	+	1.74470i
$886$	7.22461	+	7.22461i	0.242716	+	0.242716i
$887$		−	0.411411i		−	0.0138138i	−0.999976	−	0.00690691i	$-0.997801\pi$
$887$		−	0.411411i		−	0.0138138i	0.999976	−	0.00690691i	$-0.00219855\pi$
$888$	2.61616	+	2.79012i	0.0877926	+	0.0936302i
$889$	6.02303	+	6.02303i	0.202006	+	0.202006i
$890$	−3.24531	+	3.24531i	−0.108783	+	0.108783i
$891$	−24.9375	−	32.3492i	−0.835438	−	1.08374i
$892$	5.27800	−	5.27800i	0.176721	−	0.176721i
$893$		−	25.9847i		−	0.869545i
$894$	28.1369	−	26.3827i	0.941040	−	0.882368i
$895$	−21.2651	+	21.2651i	−0.710815	+	0.710815i
$896$	−1.00000			−0.0334077
$897$	3.73394	+	2.59780i	0.124673	+	0.0867381i
$898$	−14.5301			−0.484877
$899$	50.6462	−	50.6462i	1.68915	−	1.68915i
$900$	2.06296	−	32.0233i	0.0687653	−	1.06744i
$901$		−	41.0845i		−	1.36872i
$902$	−16.3037	+	16.3037i	−0.542852	+	0.542852i
$903$	0.414504	−	12.8820i	0.0137938	−	0.428687i
$904$	3.28959	−	3.28959i	0.109410	−	0.109410i
$905$	50.1519	+	50.1519i	1.66711	+	1.66711i
$906$	24.2856	−	22.7715i	0.806836	−	0.756531i
$907$		−	17.9157i		−	0.594881i	−0.954740	−	0.297440i	$-0.903867\pi$
$907$		−	17.9157i		−	0.594881i	0.954740	−	0.297440i	$-0.0961330\pi$
$908$	−12.0460	−	12.0460i	−0.399761	−	0.399761i
$909$	−0.201298	+	3.12476i	−0.00667665	+	0.103642i
$910$	11.9824	+	7.77679i	0.397211	+	0.257798i
$911$			19.1444i			0.634282i	0.948378	+	0.317141i	$0.102723\pi$
$911$			19.1444i			0.634282i	−0.948378	+	0.317141i	$0.897277\pi$
$912$	0.142642	−	4.43306i	0.00472335	−	0.146793i
$913$	−48.4666			−1.60401
$914$	−28.8581			−0.954543
$915$	2.06257	+	0.0663671i	0.0681865	+	0.00219403i
$916$	12.4724	+	12.4724i	0.412100	+	0.412100i
$917$	1.16678	+	1.16678i	0.0385303	+	0.0385303i
$918$	−1.73298	+	17.9030i	−0.0571967	+	0.590887i
$919$	2.51015			0.0828024			0.0414012	−	0.999143i	$-0.486818\pi$
$919$	2.51015			0.0828024			0.0414012	+	0.999143i	$0.486818\pi$
$920$	−2.88575			−0.0951405
$921$	−49.9496	−	1.60723i	−1.64590	−	0.0529599i
$922$		−	12.7733i		−	0.420666i
$923$	−9.32836	+	14.3730i	−0.307047	+	0.473093i
$924$	−5.73424	+	5.37672i	−0.188643	+	0.176881i
$925$	16.7023	+	16.7023i	0.549169	+	0.549169i
$926$		−	2.68061i		−	0.0880905i
$927$	25.1211	+	1.61831i	0.825085	+	0.0531524i
$928$	4.92712	+	4.92712i	0.161741	+	0.161741i
$929$	28.2733	−	28.2733i	0.927616	−	0.927616i	−0.0699358	−	0.997551i	$-0.522279\pi$
$929$	28.2733	−	28.2733i	0.927616	−	0.927616i	0.997551	+	0.0699358i	$0.0222794\pi$
$930$	−70.5004	−	2.26849i	−2.31180	−	0.0743866i
$931$	−1.81073	+	1.81073i	−0.0593441	+	0.0593441i
$932$			17.2708i			0.565722i
$933$	−25.1044	−	26.7737i	−0.821880	−	0.876530i
$934$	2.16324	−	2.16324i	0.0707834	−	0.0707834i
$935$	62.2404			2.03548
$936$	−6.45981	+	8.67588i	−0.211146	+	0.283580i
$937$	52.1046			1.70218			0.851091	−	0.525018i	$-0.175941\pi$
$937$	52.1046			1.70218			0.851091	+	0.525018i	$0.175941\pi$
$938$	3.02964	−	3.02964i	0.0989213	−	0.0989213i
$939$	−30.5705	−	32.6032i	−0.997631	−	1.06397i
$940$		−	40.2024i		−	1.31126i
$941$	−23.9256	+	23.9256i	−0.779954	+	0.779954i	−0.979823	−	0.199869i	$-0.935948\pi$
$941$	−23.9256	+	23.9256i	−0.779954	+	0.779954i	0.199869	+	0.979823i	$0.435948\pi$
$942$	2.67959	+	0.0862210i	0.0873058	+	0.00280923i
$943$	−2.61662	+	2.61662i	−0.0852090	+	0.0852090i
$944$	7.33162	+	7.33162i	0.238624	+	0.238624i
$945$	−13.0867	−	15.8917i	−0.425709	−	0.516957i
$946$		−	33.7714i		−	1.09800i
$947$	35.0019	+	35.0019i	1.13741	+	1.13741i	0.988913	+	0.148496i	$0.0474432\pi$
$947$	35.0019	+	35.0019i	1.13741	+	1.13741i	0.148496	+	0.988913i	$0.452557\pi$
$948$	7.42375	−	6.96090i	0.241112	−	0.226079i
$949$	−19.1402	+	29.4909i	−0.621317	+	0.957315i
$950$		−	27.3912i		−	0.888689i
$951$	−35.4326	−	1.14011i	−1.14898	−	0.0369707i
$952$	3.46154			0.112189
$953$	−38.7861			−1.25640			−0.628202	−	0.778050i	$-0.716209\pi$
$953$	−38.7861			−1.25640			−0.628202	+	0.778050i	$0.716209\pi$
$954$	−26.7442	+	23.5070i	−0.865875	+	0.761067i
$955$	25.8266	+	25.8266i	0.835729	+	0.835729i
$956$	−3.19200	−	3.19200i	−0.103237	−	0.103237i
$957$	54.7451	+	1.76153i	1.76966	+	0.0569421i
$958$	19.1202			0.617747
$959$	12.8974			0.416480
$960$	0.220690	−	6.85864i	0.00712274	−	0.221362i
$961$			74.6592i			2.40836i
$962$	−1.65750	−	7.78751i	−0.0534400	−	0.251079i
$963$	−42.8707	−	2.76175i	−1.38149	−	0.0889963i
$964$	9.64002	+	9.64002i	0.310484	+	0.310484i
$965$			0.560544i			0.0180445i
$966$	−0.920306	+	0.862927i	−0.0296104	+	0.0277642i
$967$	−20.9633	−	20.9633i	−0.674134	−	0.674134i	0.284532	−	0.958666i	$-0.408162\pi$
$967$	−20.9633	−	20.9633i	−0.674134	−	0.674134i	−0.958666	+	0.284532i	$0.908162\pi$
$968$	−6.78602	+	6.78602i	−0.218111	+	0.218111i
$969$	−0.493761	+	15.3452i	−0.0158619	+	0.492959i
$970$	−5.44774	+	5.44774i	−0.174916	+	0.174916i
$971$			10.6662i			0.342294i	0.985245	+	0.171147i	$0.0547473\pi$
$971$			10.6662i			0.342294i	−0.985245	+	0.171147i	$0.945253\pi$
$972$	12.6456	−	9.11532i	0.405608	−	0.292374i
$973$	−13.6164	+	13.6164i	−0.436521	+	0.436521i
$974$	−17.0312			−0.545716
$975$	−38.1499	+	54.8345i	−1.22177	+	1.75611i
$976$	0.300726			0.00962599
$977$	−26.2474	+	26.2474i	−0.839727	+	0.839727i	−0.988823	−	0.149095i	$-0.952364\pi$
$977$	−26.2474	+	26.2474i	−0.839727	+	0.839727i	0.149095	+	0.988823i	$0.452364\pi$
$978$	0.503833	−	0.472420i	0.0161108	−	0.0151063i
$979$			5.25738i			0.168027i
$980$	−2.80148	+	2.80148i	−0.0894899	+	0.0894899i
$981$	0.992633	−	0.872481i	0.0316923	−	0.0278562i
$982$	15.7797	−	15.7797i	0.503551	−	0.503551i
$983$	31.9727	+	31.9727i	1.01977	+	1.01977i	0.999801	+	0.0199710i	$0.00635740\pi$
$983$	31.9727	+	31.9727i	1.01977	+	1.01977i	0.0199710	+	0.999801i	$0.493643\pi$
$984$	−6.01888	−	6.41910i	−0.191875	−	0.204633i
$985$			46.2170i			1.47260i
$986$	−17.0554	−	17.0554i	−0.543155	−	0.543155i
$987$	−12.0217	−	12.8211i	−0.382656	−	0.408100i
$988$	−5.02650	+	7.74475i	−0.159914	+	0.246393i
$989$		−	5.42007i		−	0.172348i
$990$	−35.6115	−	40.5157i	−1.13181	−	1.28767i
$991$	30.6657			0.974129			0.487065	−	0.873366i	$-0.338068\pi$
$991$	30.6657			0.974129			0.487065	+	0.873366i	$0.338068\pi$
$992$	−10.2791			−0.326361
$993$	0.0207753	−	0.645658i	0.000659283	−	0.0204893i
$994$	−3.36041	−	3.36041i	−0.106586	−	0.106586i
$995$	21.2323	+	21.2323i	0.673109	+	0.673109i
$996$	0.594870	−	18.4875i	0.0188492	−	0.585798i
$997$	−31.2469			−0.989600			−0.494800	−	0.869007i	$-0.664759\pi$
$997$	−31.2469			−0.989600			−0.494800	+	0.869007i	$0.664759\pi$
$998$	−39.4448			−1.24860
$999$	−1.10553	+	11.4210i	−0.0349775	+	0.361344i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.c.281.1	yes	20
3.2	odd	2		546.2.p.d.281.6	yes	20
13.5	odd	4		546.2.p.d.239.6	yes	20
39.5	even	4	inner	546.2.p.c.239.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.1	✓	20	39.5	even	4	inner
546.2.p.c.281.1	yes	20	1.1	even	1	trivial
546.2.p.d.239.6	yes	20	13.5	odd	4
546.2.p.d.281.6	yes	20	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.18472 - 1.26350i) q^{3} -1.00000i q^{4} +(2.80148 - 2.80148i) q^{5} +(1.73115 + 0.0557032i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.192862 + 2.99379i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.18472 - 1.26350i) q^{3} -1.00000i q^{4} +(2.80148 - 2.80148i) q^{5} +(1.73115 + 0.0557032i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-0.192862 + 2.99379i) q^{9} +3.96189i q^{10} +(3.20912 + 3.20912i) q^{11} +(-1.26350 + 1.18472i) q^{12} +(3.52656 - 0.750597i) q^{13} +1.00000i q^{14} +(-6.85864 - 0.220690i) q^{15} -1.00000 q^{16} +3.46154 q^{17} +(-1.98056 - 2.25331i) q^{18} +(-1.81073 - 1.81073i) q^{19} +(-2.80148 - 2.80148i) q^{20} +(-1.73115 - 0.0557032i) q^{21} -4.53838 q^{22} -0.728379 q^{23} +(0.0557032 - 1.73115i) q^{24} -10.6966i q^{25} +(-1.96290 + 3.02440i) q^{26} +(4.01115 - 3.30314i) q^{27} +(-0.707107 - 0.707107i) q^{28} +6.96800i q^{29} +(5.00584 - 4.69374i) q^{30} +(-7.26840 - 7.26840i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.252802 - 7.85664i) q^{33} +(-2.44768 + 2.44768i) q^{34} -3.96189i q^{35} +(2.99379 + 0.192862i) q^{36} +(-1.56147 + 1.56147i) q^{37} +2.56075 q^{38} +(-5.12637 - 3.56655i) q^{39} +3.96189 q^{40} +(3.59240 - 3.59240i) q^{41} +(1.26350 - 1.18472i) q^{42} +7.44129i q^{43} +(3.20912 - 3.20912i) q^{44} +(7.84675 + 8.92735i) q^{45} +(0.515041 - 0.515041i) q^{46} +(7.17522 + 7.17522i) q^{47} +(1.18472 + 1.26350i) q^{48} -1.00000i q^{49} +(7.56361 + 7.56361i) q^{50} +(-4.10096 - 4.37365i) q^{51} +(-0.750597 - 3.52656i) q^{52} -11.8689i q^{53} +(-0.500638 + 5.17198i) q^{54} +17.9806 q^{55} +1.00000 q^{56} +(-0.142642 + 4.43306i) q^{57} +(-4.92712 - 4.92712i) q^{58} +(-7.33162 - 7.33162i) q^{59} +(-0.220690 + 6.85864i) q^{60} -0.300726 q^{61} +10.2791 q^{62} +(1.98056 + 2.25331i) q^{63} +1.00000i q^{64} +(7.77679 - 11.9824i) q^{65} +(5.37672 + 5.73424i) q^{66} +(-3.02964 - 3.02964i) q^{67} -3.46154i q^{68} +(0.862927 + 0.920306i) q^{69} +(2.80148 + 2.80148i) q^{70} +(-3.36041 + 3.36041i) q^{71} +(-2.25331 + 1.98056i) q^{72} +(-6.89498 + 6.89498i) q^{73} -2.20825i q^{74} +(-13.5151 + 12.6725i) q^{75} +(-1.81073 + 1.81073i) q^{76} +4.53838 q^{77} +(6.14683 - 1.10296i) q^{78} -5.87555 q^{79} +(-2.80148 + 2.80148i) q^{80} +(-8.92561 - 1.15478i) q^{81} +5.08041i q^{82} +(-7.55138 + 7.55138i) q^{83} +(-0.0557032 + 1.73115i) q^{84} +(9.69742 - 9.69742i) q^{85} +(-5.26178 - 5.26178i) q^{86} +(8.80407 - 8.25516i) q^{87} +4.53838i q^{88} +(0.819132 + 0.819132i) q^{89} +(-11.8611 - 0.764097i) q^{90} +(1.96290 - 3.02440i) q^{91} +0.728379i q^{92} +(-0.572577 + 17.7947i) q^{93} -10.1473 q^{94} -10.1454 q^{95} +(-1.73115 - 0.0557032i) q^{96} +(1.37504 + 1.37504i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-10.2264 + 8.98852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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