LMFDB - Embedded newform 546.2.p.d.239.9

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			239.9
Root			$1.72939 + 0.0958811i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.d.281.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(1.15507 - 1.29067i) q^{3} +1.00000i q^{4} +(-0.616653 - 0.616653i) q^{5} +(1.72939 - 0.0958811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.331633 - 2.98161i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(1.15507 - 1.29067i) q^{3} +1.00000i q^{4} +(-0.616653 - 0.616653i) q^{5} +(1.72939 - 0.0958811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.331633 - 2.98161i) q^{9} -0.872079i q^{10} +(2.63014 - 2.63014i) q^{11} +(1.29067 + 1.15507i) q^{12} +(1.08413 + 3.43870i) q^{13} +1.00000i q^{14} +(-1.50817 + 0.0836158i) q^{15} -1.00000 q^{16} +5.36595 q^{17} +(1.87382 - 2.34282i) q^{18} +(3.60391 - 3.60391i) q^{19} +(0.616653 - 0.616653i) q^{20} +(1.72939 - 0.0958811i) q^{21} +3.71958 q^{22} -2.67136 q^{23} +(0.0958811 + 1.72939i) q^{24} -4.23948i q^{25} +(-1.66493 + 3.19813i) q^{26} +(-4.23132 - 3.01594i) q^{27} +(-0.707107 + 0.707107i) q^{28} +3.00014i q^{29} +(-1.12556 - 1.00731i) q^{30} +(-6.60062 + 6.60062i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.356638 - 6.43263i) q^{33} +(3.79430 + 3.79430i) q^{34} -0.872079i q^{35} +(2.98161 - 0.331633i) q^{36} +(4.44970 + 4.44970i) q^{37} +5.09669 q^{38} +(5.69046 + 2.57268i) q^{39} +0.872079 q^{40} +(-8.43789 - 8.43789i) q^{41} +(1.29067 + 1.15507i) q^{42} +0.610209i q^{43} +(2.63014 + 2.63014i) q^{44} +(-1.63412 + 2.04312i) q^{45} +(-1.88894 - 1.88894i) q^{46} +(-3.46010 + 3.46010i) q^{47} +(-1.15507 + 1.29067i) q^{48} +1.00000i q^{49} +(2.99776 - 2.99776i) q^{50} +(6.19805 - 6.92565i) q^{51} +(-3.43870 + 1.08413i) q^{52} +0.464507i q^{53} +(-0.859404 - 5.12459i) q^{54} -3.24377 q^{55} -1.00000 q^{56} +(-0.488676 - 8.81419i) q^{57} +(-2.12142 + 2.12142i) q^{58} +(-8.93448 + 8.93448i) q^{59} +(-0.0836158 - 1.50817i) q^{60} -8.37831 q^{61} -9.33468 q^{62} +(1.87382 - 2.34282i) q^{63} -1.00000i q^{64} +(1.45195 - 2.78902i) q^{65} +(4.29637 - 4.80074i) q^{66} +(1.77932 - 1.77932i) q^{67} +5.36595i q^{68} +(-3.08561 + 3.44784i) q^{69} +(0.616653 - 0.616653i) q^{70} +(0.00980127 + 0.00980127i) q^{71} +(2.34282 + 1.87382i) q^{72} +(11.1380 + 11.1380i) q^{73} +6.29283i q^{74} +(-5.47175 - 4.89689i) q^{75} +(3.60391 + 3.60391i) q^{76} +3.71958 q^{77} +(2.20460 + 5.84292i) q^{78} +6.11811 q^{79} +(0.616653 + 0.616653i) q^{80} +(-8.78004 + 1.97760i) q^{81} -11.9330i q^{82} +(3.29926 + 3.29926i) q^{83} +(0.0958811 + 1.72939i) q^{84} +(-3.30893 - 3.30893i) q^{85} +(-0.431483 + 0.431483i) q^{86} +(3.87217 + 3.46536i) q^{87} +3.71958i q^{88} +(-8.90085 + 8.90085i) q^{89} +(-2.60020 + 0.289210i) q^{90} +(-1.66493 + 3.19813i) q^{91} -2.67136i q^{92} +(0.895019 + 16.1433i) q^{93} -4.89332 q^{94} -4.44472 q^{95} +(-1.72939 + 0.0958811i) q^{96} +(-5.41720 + 5.41720i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-8.71431 - 6.96983i) 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} - 16 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} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 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} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 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} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 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 - 16 * 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 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * 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 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * 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 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	1.15507	−	1.29067i	0.666879	−	0.745166i
$3$	1.15507	−	1.29067i	0.666879	−	0.745166i
$4$			1.00000i			0.500000i
$5$	−0.616653	−	0.616653i	−0.275775	−	0.275775i	0.555645	−	0.831420i	$-0.312472\pi$
$5$	−0.616653	−	0.616653i	−0.275775	−	0.275775i	−0.831420	+	0.555645i	$0.812472\pi$
$6$	1.72939	−	0.0958811i	0.706023	−	0.0391433i
$7$	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
$9$	−0.331633	−	2.98161i	−0.110544	−	0.993871i
$10$		−	0.872079i		−	0.275775i
$11$	2.63014	−	2.63014i	0.793018	−	0.793018i	−0.188966	−	0.981984i	$-0.560514\pi$
$11$	2.63014	−	2.63014i	0.793018	−	0.793018i	0.981984	+	0.188966i	$0.0605135\pi$
$12$	1.29067	+	1.15507i	0.372583	+	0.333440i
$13$	1.08413	+	3.43870i	0.300684	+	0.953724i
$13$	1.08413	+	3.43870i	0.300684	+	0.953724i
$14$			1.00000i			0.267261i
$15$	−1.50817	+	0.0836158i	−0.389407	+	0.0215895i
$16$	−1.00000			−0.250000
$17$	5.36595			1.30144			0.650718	−	0.759320i	$-0.274468\pi$
$17$	5.36595			1.30144			0.650718	+	0.759320i	$0.274468\pi$
$18$	1.87382	−	2.34282i	0.441664	−	0.552208i
$19$	3.60391	−	3.60391i	0.826793	−	0.826793i	−0.160279	−	0.987072i	$-0.551239\pi$
$19$	3.60391	−	3.60391i	0.826793	−	0.826793i	0.987072	+	0.160279i	$0.0512394\pi$
$20$	0.616653	−	0.616653i	0.137888	−	0.137888i
$21$	1.72939	−	0.0958811i	0.377385	−	0.0209230i
$22$	3.71958			0.793018
$23$	−2.67136			−0.557018			−0.278509	−	0.960434i	$-0.589840\pi$
$23$	−2.67136			−0.557018			−0.278509	+	0.960434i	$0.589840\pi$
$24$	0.0958811	+	1.72939i	0.0195716	+	0.353011i
$25$		−	4.23948i		−	0.847896i
$26$	−1.66493	+	3.19813i	−0.326520	+	0.627204i
$27$	−4.23132	−	3.01594i	−0.814318	−	0.580418i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$			3.00014i			0.557111i	0.960420	+	0.278556i	$0.0898556\pi$
$29$			3.00014i			0.557111i	−0.960420	+	0.278556i	$0.910144\pi$
$30$	−1.12556	−	1.00731i	−0.205498	−	0.183909i
$31$	−6.60062	+	6.60062i	−1.18551	+	1.18551i	−0.207209	+	0.978297i	$0.566438\pi$
$31$	−6.60062	+	6.60062i	−1.18551	+	1.18551i	−0.978297	+	0.207209i	$0.933562\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.356638	−	6.43263i	−0.0620827	−	1.11978i
$34$	3.79430	+	3.79430i	0.650718	+	0.650718i
$35$		−	0.872079i		−	0.147408i
$36$	2.98161	−	0.331633i	0.496936	−	0.0552721i
$37$	4.44970	+	4.44970i	0.731527	+	0.731527i	0.970922	−	0.239395i	$-0.0769492\pi$
$37$	4.44970	+	4.44970i	0.731527	+	0.731527i	−0.239395	+	0.970922i	$0.576949\pi$
$38$	5.09669			0.826793
$39$	5.69046	+	2.57268i	0.911202	+	0.411959i
$40$	0.872079			0.137888
$41$	−8.43789	−	8.43789i	−1.31778	−	1.31778i	−0.915532	−	0.402245i	$-0.868230\pi$
$41$	−8.43789	−	8.43789i	−1.31778	−	1.31778i	−0.402245	−	0.915532i	$-0.631770\pi$
$42$	1.29067	+	1.15507i	0.199154	+	0.178231i
$43$			0.610209i			0.0930560i	0.998917	+	0.0465280i	$0.0148157\pi$
$43$			0.610209i			0.0930560i	−0.998917	+	0.0465280i	$0.985184\pi$
$44$	2.63014	+	2.63014i	0.396509	+	0.396509i
$45$	−1.63412	+	2.04312i	−0.243600	+	0.304571i
$46$	−1.88894	−	1.88894i	−0.278509	−	0.278509i
$47$	−3.46010	+	3.46010i	−0.504707	+	0.504707i	−0.912897	−	0.408190i	$-0.866160\pi$
$47$	−3.46010	+	3.46010i	−0.504707	+	0.504707i	0.408190	+	0.912897i	$0.366160\pi$
$48$	−1.15507	+	1.29067i	−0.166720	+	0.186291i
$49$			1.00000i			0.142857i
$50$	2.99776	−	2.99776i	0.423948	−	0.423948i
$51$	6.19805	−	6.92565i	0.867900	−	0.969785i
$52$	−3.43870	+	1.08413i	−0.476862	+	0.150342i
$53$			0.464507i			0.0638049i	0.999491	+	0.0319024i	$0.0101566\pi$
$53$			0.464507i			0.0638049i	−0.999491	+	0.0319024i	$0.989843\pi$
$54$	−0.859404	−	5.12459i	−0.116950	−	0.697368i
$55$	−3.24377			−0.437390
$56$	−1.00000			−0.133631
$57$	−0.488676	−	8.81419i	−0.0647268	−	1.16747i
$58$	−2.12142	+	2.12142i	−0.278556	+	0.278556i
$59$	−8.93448	+	8.93448i	−1.16317	+	1.16317i	−0.179393	+	0.983778i	$0.557413\pi$
$59$	−8.93448	+	8.93448i	−1.16317	+	1.16317i	−0.983778	+	0.179393i	$0.942587\pi$
$60$	−0.0836158	−	1.50817i	−0.0107948	−	0.194704i
$61$	−8.37831			−1.07273			−0.536367	−	0.843985i	$-0.680204\pi$
$61$	−8.37831			−1.07273			−0.536367	+	0.843985i	$0.680204\pi$
$62$	−9.33468			−1.18551
$63$	1.87382	−	2.34282i	0.236079	−	0.295167i
$64$		−	1.00000i		−	0.125000i
$65$	1.45195	−	2.78902i	0.180092	−	0.345935i
$66$	4.29637	−	4.80074i	0.528847	−	0.590930i
$67$	1.77932	−	1.77932i	0.217379	−	0.217379i	−0.590014	−	0.807393i	$-0.700878\pi$
$67$	1.77932	−	1.77932i	0.217379	−	0.217379i	0.807393	+	0.590014i	$0.200878\pi$
$68$			5.36595i			0.650718i
$69$	−3.08561	+	3.44784i	−0.371464	+	0.415071i
$70$	0.616653	−	0.616653i	0.0737041	−	0.0737041i
$71$	0.00980127	+	0.00980127i	0.00116320	+	0.00116320i	0.707688	−	0.706525i	$-0.249738\pi$
$71$	0.00980127	+	0.00980127i	0.00116320	+	0.00116320i	−0.706525	+	0.707688i	$0.749738\pi$
$72$	2.34282	+	1.87382i	0.276104	+	0.220832i
$73$	11.1380	+	11.1380i	1.30360	+	1.30360i	0.925948	+	0.377650i	$0.123268\pi$
$73$	11.1380	+	11.1380i	1.30360	+	1.30360i	0.377650	+	0.925948i	$0.376732\pi$
$74$			6.29283i			0.731527i
$75$	−5.47175	−	4.89689i	−0.631823	−	0.565444i
$76$	3.60391	+	3.60391i	0.413396	+	0.413396i
$77$	3.71958			0.423886
$78$	2.20460	+	5.84292i	0.249622	+	0.661581i
$79$	6.11811			0.688341			0.344170	−	0.938907i	$-0.388160\pi$
$79$	6.11811			0.688341			0.344170	+	0.938907i	$0.388160\pi$
$80$	0.616653	+	0.616653i	0.0689439	+	0.0689439i
$81$	−8.78004	+	1.97760i	−0.975560	+	0.219733i
$82$		−	11.9330i		−	1.31778i
$83$	3.29926	+	3.29926i	0.362141	+	0.362141i	0.864601	−	0.502460i	$-0.167572\pi$
$83$	3.29926	+	3.29926i	0.362141	+	0.362141i	−0.502460	+	0.864601i	$0.667572\pi$
$84$	0.0958811	+	1.72939i	0.0104615	+	0.188692i
$85$	−3.30893	−	3.30893i	−0.358904	−	0.358904i
$86$	−0.431483	+	0.431483i	−0.0465280	+	0.0465280i
$87$	3.87217	+	3.46536i	0.415140	+	0.371526i
$88$			3.71958i			0.396509i
$89$	−8.90085	+	8.90085i	−0.943489	+	0.943489i	−0.998486	−	0.0549979i	$-0.982485\pi$
$89$	−8.90085	+	8.90085i	−0.943489	+	0.943489i	0.0549979	+	0.998486i	$0.482485\pi$
$90$	−2.60020	+	0.289210i	−0.274085	+	0.0304854i
$91$	−1.66493	+	3.19813i	−0.174532	+	0.335255i
$92$		−	2.67136i		−	0.278509i
$93$	0.895019	+	16.1433i	0.0928092	+	1.67399i
$94$	−4.89332			−0.504707
$95$	−4.44472			−0.456018
$96$	−1.72939	+	0.0958811i	−0.176506	+	0.00978582i
$97$	−5.41720	+	5.41720i	−0.550033	+	0.550033i	−0.926450	−	0.376417i	$-0.877156\pi$
$97$	−5.41720	+	5.41720i	−0.550033	+	0.550033i	0.376417	+	0.926450i	$0.377156\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	−8.71431	−	6.96983i	−0.875821	−	0.700494i
$100$	4.23948			0.423948
$101$	−9.74113			−0.969278			−0.484639	−	0.874714i	$-0.661049\pi$
$101$	−9.74113			−0.969278			−0.484639	+	0.874714i	$0.661049\pi$
$102$	9.27985	−	0.514494i	0.918842	−	0.0509424i
$103$		−	13.8659i		−	1.36625i	−0.730302	−	0.683124i	$-0.760621\pi$
$103$		−	13.8659i		−	1.36625i	0.730302	−	0.683124i	$-0.239379\pi$
$104$	−3.19813	−	1.66493i	−0.313602	−	0.163260i
$105$	−1.12556	−	1.00731i	−0.109844	−	0.0983035i
$106$	−0.328456	+	0.328456i	−0.0319024	+	0.0319024i
$107$		−	2.77130i		−	0.267911i	−0.990987	−	0.133956i	$-0.957232\pi$
$107$		−	2.77130i		−	0.267911i	0.990987	−	0.133956i	$-0.0427680\pi$
$108$	3.01594	−	4.23132i	0.290209	−	0.407159i
$109$	2.22915	−	2.22915i	0.213513	−	0.213513i	−0.592245	−	0.805758i	$-0.701758\pi$
$109$	2.22915	−	2.22915i	0.213513	−	0.213513i	0.805758	+	0.592245i	$0.201758\pi$
$110$	−2.29369	−	2.29369i	−0.218695	−	0.218695i
$111$	10.8828	−	0.603364i	1.03295	−	0.0572687i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$			13.7999i			1.29818i	0.760710	+	0.649091i	$0.224851\pi$
$113$			13.7999i			1.29818i	−0.760710	+	0.649091i	$0.775149\pi$
$114$	5.88703	−	6.57812i	0.551371	−	0.616098i
$115$	1.64730	+	1.64730i	0.153612	+	0.153612i
$116$	−3.00014			−0.278556
$117$	9.89334	−	4.37285i	0.914640	−	0.404270i
$118$	−12.6353			−1.16317
$119$	3.79430	+	3.79430i	0.347823	+	0.347823i
$120$	1.00731	−	1.12556i	0.0919545	−	0.102749i
$121$		−	2.83530i		−	0.257754i
$122$	−5.92436	−	5.92436i	−0.536367	−	0.536367i
$123$	−20.6368	+	1.14415i	−1.86076	+	0.103164i
$124$	−6.60062	−	6.60062i	−0.592753	−	0.592753i
$125$	−5.69755	+	5.69755i	−0.509604	+	0.509604i
$126$	2.98161	−	0.331633i	0.265623	−	0.0295442i
$127$		−	21.3350i		−	1.89317i	−0.322453	−	0.946585i	$-0.604508\pi$
$127$		−	21.3350i		−	1.89317i	0.322453	−	0.946585i	$-0.395492\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	0.787575	+	0.704833i	0.0693421	+	0.0620571i
$130$	2.99882	−	0.945448i	0.263014	−	0.0829213i
$131$		−	8.16389i		−	0.713282i	−0.934242	−	0.356641i	$-0.883922\pi$
$131$		−	8.16389i		−	0.713282i	0.934242	−	0.356641i	$-0.116078\pi$
$132$	6.43263	−	0.356638i	0.559888	−	0.0310413i
$133$	5.09669			0.441939
$134$	2.51634			0.217379
$135$	0.749468	+	4.46905i	0.0645039	+	0.384634i
$136$	−3.79430	+	3.79430i	−0.325359	+	0.325359i
$137$	9.21910	−	9.21910i	0.787641	−	0.787641i	−0.193466	−	0.981107i	$-0.561973\pi$
$137$	9.21910	−	9.21910i	0.787641	−	0.787641i	0.981107	+	0.193466i	$0.0619729\pi$
$138$	−4.61984	+	0.256133i	−0.393267	+	0.0218035i
$139$	−2.49440			−0.211572			−0.105786	−	0.994389i	$-0.533736\pi$
$139$	−2.49440			−0.211572			−0.105786	+	0.994389i	$0.533736\pi$
$140$	0.872079			0.0737041
$141$	0.469177	+	8.46248i	0.0395118	+	0.712670i
$142$			0.0138611i			0.00116320i
$143$	11.8957	+	6.19285i	0.994768	+	0.517872i
$144$	0.331633	+	2.98161i	0.0276360	+	0.248468i
$145$	1.85004	−	1.85004i	0.153638	−	0.153638i
$146$			15.7514i			1.30360i
$147$	1.29067	+	1.15507i	0.106452	+	0.0952685i
$148$	−4.44970	+	4.44970i	−0.365763	+	0.365763i
$149$	12.3117	+	12.3117i	1.00862	+	1.00862i	0.999963	+	0.00865511i	$0.00275504\pi$
$149$	12.3117	+	12.3117i	1.00862	+	1.00862i	0.00865511	+	0.999963i	$0.497245\pi$
$150$	−0.406486	−	7.33173i	−0.0331894	−	0.598634i
$151$	−3.48920	−	3.48920i	−0.283947	−	0.283947i	0.550734	−	0.834681i	$-0.314348\pi$
$151$	−3.48920	−	3.48920i	−0.283947	−	0.283947i	−0.834681	+	0.550734i	$0.814348\pi$
$152$			5.09669i			0.413396i
$153$	−1.77952	−	15.9992i	−0.143866	−	1.29346i
$154$	2.63014	+	2.63014i	0.211943	+	0.211943i
$155$	8.14057			0.653867
$156$	−2.57268	+	5.69046i	−0.205979	+	0.455601i
$157$	0.911415			0.0727388			0.0363694	−	0.999338i	$-0.488421\pi$
$157$	0.911415			0.0727388			0.0363694	+	0.999338i	$0.488421\pi$
$158$	4.32615	+	4.32615i	0.344170	+	0.344170i
$159$	0.599522	+	0.536537i	0.0475452	+	0.0425502i
$160$			0.872079i			0.0689439i
$161$	−1.88894	−	1.88894i	−0.148869	−	0.148869i
$162$	−7.60680	−	4.81005i	−0.597647	−	0.377913i
$163$	−13.4803	−	13.4803i	−1.05586	−	1.05586i	−0.998345	−	0.0575128i	$-0.981683\pi$
$163$	−13.4803	−	13.4803i	−1.05586	−	1.05586i	−0.0575128	−	0.998345i	$-0.518317\pi$
$164$	8.43789	−	8.43789i	0.658888	−	0.658888i
$165$	−3.74678	+	4.18662i	−0.291686	+	0.325928i
$166$			4.66586i			0.362141i
$167$	−4.56615	+	4.56615i	−0.353339	+	0.353339i	−0.861350	−	0.508011i	$-0.830381\pi$
$167$	−4.56615	+	4.56615i	−0.353339	+	0.353339i	0.508011	+	0.861350i	$0.330381\pi$
$168$	−1.15507	+	1.29067i	−0.0891155	+	0.0995770i
$169$	−10.6493	+	7.45601i	−0.819178	+	0.573539i
$170$		−	4.67953i		−	0.358904i
$171$	−11.9406	−	9.55028i	−0.913122	−	0.730328i
$172$	−0.610209			−0.0465280
$173$	−20.5507			−1.56244			−0.781221	−	0.624255i	$-0.785403\pi$
$173$	−20.5507			−1.56244			−0.781221	+	0.624255i	$0.785403\pi$
$174$	0.287656	+	5.18842i	0.0218072	+	0.393333i
$175$	2.99776	−	2.99776i	0.226610	−	0.226610i
$176$	−2.63014	+	2.63014i	−0.198254	+	0.198254i
$177$	1.21148	+	21.8514i	0.0910606	+	1.64245i
$178$	−12.5877			−0.943489
$179$	12.5336			0.936809			0.468404	−	0.883514i	$-0.344829\pi$
$179$	12.5336			0.936809			0.468404	+	0.883514i	$0.344829\pi$
$180$	−2.04312	−	1.63412i	−0.152285	−	0.121800i
$181$		−	13.2739i		−	0.986643i	−0.869847	−	0.493321i	$-0.835783\pi$
$181$		−	13.2739i		−	0.986643i	0.869847	−	0.493321i	$-0.164217\pi$
$182$	−3.43870	+	1.08413i	−0.254893	+	0.0803612i
$183$	−9.67753	+	10.8136i	−0.715383	+	0.799364i
$184$	1.88894	−	1.88894i	0.139254	−	0.139254i
$185$		−	5.48784i		−	0.403474i
$186$	−10.7822	+	12.0479i	−0.790589	+	0.883398i
$187$	14.1132	−	14.1132i	1.03206	−	1.03206i
$188$	−3.46010	−	3.46010i	−0.252354	−	0.252354i
$189$	−0.859404	−	5.12459i	−0.0625124	−	0.372759i
$190$	−3.14289	−	3.14289i	−0.228009	−	0.228009i
$191$		−	3.21043i		−	0.232299i	−0.993232	−	0.116149i	$-0.962945\pi$
$191$		−	3.21043i		−	0.232299i	0.993232	−	0.116149i	$-0.0370552\pi$
$192$	−1.29067	−	1.15507i	−0.0931457	−	0.0833599i
$193$	16.2407	+	16.2407i	1.16903	+	1.16903i	0.982437	+	0.186594i	$0.0597450\pi$
$193$	16.2407	+	16.2407i	1.16903	+	1.16903i	0.186594	+	0.982437i	$0.440255\pi$
$194$	−7.66107			−0.550033
$195$	−1.92258	−	5.09549i	−0.137679	−	0.364895i
$196$	−1.00000			−0.0714286
$197$	−14.8966	−	14.8966i	−1.06134	−	1.06134i	−0.997992	−	0.0633475i	$-0.979822\pi$
$197$	−14.8966	−	14.8966i	−1.06134	−	1.06134i	−0.0633475	−	0.997992i	$-0.520178\pi$
$198$	−1.23353	−	11.0904i	−0.0876635	−	0.788158i
$199$		−	15.1640i		−	1.07495i	−0.843281	−	0.537473i	$-0.819379\pi$
$199$		−	15.1640i		−	1.07495i	0.843281	−	0.537473i	$-0.180621\pi$
$200$	2.99776	+	2.99776i	0.211974	+	0.211974i
$201$	−0.241270	−	4.35175i	−0.0170178	−	0.306949i
$202$	−6.88802	−	6.88802i	−0.484639	−	0.484639i
$203$	−2.12142	+	2.12142i	−0.148894	+	0.148894i
$204$	6.92565	+	6.19805i	0.484892	+	0.433950i
$205$			10.4065i			0.726821i
$206$	9.80468	−	9.80468i	0.683124	−	0.683124i
$207$	0.885911	+	7.96498i	0.0615751	+	0.553604i
$208$	−1.08413	−	3.43870i	−0.0751710	−	0.238431i
$209$		−	18.9576i		−	1.31132i
$210$	−0.0836158	−	1.50817i	−0.00577004	−	0.104073i
$211$	2.49834			0.171993			0.0859965	−	0.996295i	$-0.472593\pi$
$211$	2.49834			0.171993			0.0859965	+	0.996295i	$0.472593\pi$
$212$	−0.464507			−0.0319024
$213$	0.0239713	−	0.00132902i	0.00164249	−	9.10627e-5i
$214$	1.95960	−	1.95960i	0.133956	−	0.133956i
$215$	0.376287	−	0.376287i	0.0256626	−	0.0256626i
$216$	5.12459	−	0.859404i	0.348684	−	0.0584750i
$217$	−9.33468			−0.633679
$218$	3.15249			0.213513
$219$	27.2405	−	1.51027i	1.84074	−	0.102054i
$220$		−	3.24377i		−	0.218695i
$221$	5.81740	+	18.4519i	0.391321	+	1.24121i
$222$	8.12194	+	7.26865i	0.545109	+	0.487840i
$223$	6.63646	−	6.63646i	0.444410	−	0.444410i	−0.449081	−	0.893491i	$-0.648249\pi$
$223$	6.63646	−	6.63646i	0.444410	−	0.444410i	0.893491	+	0.449081i	$0.148249\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−12.6405	+	1.40595i	−0.842699	+	0.0937299i
$226$	−9.75798	+	9.75798i	−0.649091	+	0.649091i
$227$	8.75850	+	8.75850i	0.581322	+	0.581322i	0.935266	−	0.353944i	$-0.115160\pi$
$227$	8.75850	+	8.75850i	0.581322	+	0.581322i	−0.353944	+	0.935266i	$0.615160\pi$
$228$	8.81419	−	0.488676i	0.583734	−	0.0323634i
$229$	4.24481	+	4.24481i	0.280505	+	0.280505i	0.833310	−	0.552805i	$-0.186443\pi$
$229$	4.24481	+	4.24481i	0.280505	+	0.280505i	−0.552805	+	0.833310i	$0.686443\pi$
$230$			2.32964i			0.153612i
$231$	4.29637	−	4.80074i	0.282681	−	0.315865i
$232$	−2.12142	−	2.12142i	−0.139278	−	0.139278i
$233$	−5.81776			−0.381134			−0.190567	−	0.981674i	$-0.561033\pi$
$233$	−5.81776			−0.381134			−0.190567	+	0.981674i	$0.561033\pi$
$234$	10.0877	+	3.90358i	0.659455	+	0.255185i
$235$	4.26736			0.278372
$236$	−8.93448	−	8.93448i	−0.581585	−	0.581585i
$237$	7.06683	−	7.89643i	0.459040	−	0.512928i
$238$			5.36595i			0.347823i
$239$	6.19473	+	6.19473i	0.400704	+	0.400704i	0.878481	−	0.477777i	$-0.158557\pi$
$239$	6.19473	+	6.19473i	0.400704	+	0.400704i	−0.477777	+	0.878481i	$0.658557\pi$
$240$	1.50817	−	0.0836158i	0.0973518	−	0.00539738i
$241$	19.2493	+	19.2493i	1.23996	+	1.23996i	0.960018	+	0.279940i	$0.0903144\pi$
$241$	19.2493	+	19.2493i	1.23996	+	1.23996i	0.279940	+	0.960018i	$0.409686\pi$
$242$	2.00486	−	2.00486i	0.128877	−	0.128877i
$243$	−7.58913	+	13.6164i	−0.486843	+	0.873490i
$244$		−	8.37831i		−	0.536367i
$245$	0.616653	−	0.616653i	0.0393965	−	0.0393965i
$246$	−15.4015	−	13.7834i	−0.981962	−	0.878798i
$247$	16.2999	+	8.48564i	1.03714	+	0.539928i
$248$		−	9.33468i		−	0.592753i
$249$	8.06911	−	0.447367i	0.511359	−	0.0283508i
$250$	−8.05755			−0.509604
$251$	21.2530			1.34148			0.670738	−	0.741694i	$-0.265977\pi$
$251$	21.2530			1.34148			0.670738	+	0.741694i	$0.265977\pi$
$252$	2.34282	+	1.87382i	0.147584	+	0.118040i
$253$	−7.02607	+	7.02607i	−0.441725	+	0.441725i
$254$	15.0861	−	15.0861i	0.946585	−	0.946585i
$255$	−8.09276	+	0.448679i	−0.506788	+	0.0280974i
$256$	1.00000			0.0625000
$257$	−13.2098			−0.824005			−0.412002	−	0.911183i	$-0.635170\pi$
$257$	−13.2098			−0.824005			−0.412002	+	0.911183i	$0.635170\pi$
$258$	0.0585075	+	1.05529i	0.00364252	+	0.0656996i
$259$			6.29283i			0.391018i
$260$	2.78902	+	1.45195i	0.172967	+	0.0900461i
$261$	8.94524	−	0.994943i	0.553697	−	0.0615854i
$262$	5.77274	−	5.77274i	0.356641	−	0.356641i
$263$		−	15.8036i		−	0.974493i	−0.873264	−	0.487247i	$-0.838001\pi$
$263$		−	15.8036i		−	0.974493i	0.873264	−	0.487247i	$-0.161999\pi$
$264$	4.80074	+	4.29637i	0.295465	+	0.264424i
$265$	0.286439	−	0.286439i	0.0175958	−	0.0175958i
$266$	3.60391	+	3.60391i	0.220970	+	0.220970i
$267$	1.20692	+	21.7691i	0.0738625	+	1.33225i
$268$	1.77932	+	1.77932i	0.108689	+	0.108689i
$269$			7.86513i			0.479545i	0.970829	+	0.239773i	$0.0770729\pi$
$269$			7.86513i			0.479545i	−0.970829	+	0.239773i	$0.922927\pi$
$270$	−2.63014	+	3.69005i	−0.160065	+	0.224569i
$271$	7.27480	+	7.27480i	0.441913	+	0.441913i	0.892654	−	0.450742i	$-0.148840\pi$
$271$	7.27480	+	7.27480i	0.441913	+	0.441913i	−0.450742	+	0.892654i	$0.648840\pi$
$272$	−5.36595			−0.325359
$273$	2.20460	+	5.84292i	0.133428	+	0.353630i
$274$	13.0378			0.787641
$275$	−11.1504	−	11.1504i	−0.672396	−	0.672396i
$276$	−3.44784	−	3.08561i	−0.207535	−	0.185732i
$277$			15.2302i			0.915091i	0.889186	+	0.457546i	$0.151271\pi$
$277$			15.2302i			0.915091i	−0.889186	+	0.457546i	$0.848729\pi$
$278$	−1.76381	−	1.76381i	−0.105786	−	0.105786i
$279$	21.8695	+	17.4915i	1.30929	+	1.04719i
$280$	0.616653	+	0.616653i	0.0368520	+	0.0368520i
$281$	19.8714	−	19.8714i	1.18543	−	1.18543i	0.207110	−	0.978318i	$-0.433594\pi$
$281$	19.8714	−	19.8714i	1.18543	−	1.18543i	0.978318	−	0.207110i	$-0.0664057\pi$
$282$	−5.65212	+	6.31564i	−0.336579	+	0.376091i
$283$			11.9364i			0.709548i	0.934952	+	0.354774i	$0.115442\pi$
$283$			11.9364i			0.709548i	−0.934952	+	0.354774i	$0.884558\pi$
$284$	−0.00980127	+	0.00980127i	−0.000581598	+	0.000581598i
$285$	−5.13395	+	5.73664i	−0.304109	+	0.339809i
$286$	4.03252	+	12.7905i	0.238448	+	0.756320i
$287$		−	11.9330i		−	0.704381i
$288$	−1.87382	+	2.34282i	−0.110416	+	0.138052i
$289$	11.7935			0.693733
$290$	2.61635			0.153638
$291$	0.734552	+	13.2490i	0.0430602	+	0.776672i
$292$	−11.1380	+	11.1380i	−0.651799	+	0.651799i
$293$	−12.0322	+	12.0322i	−0.702931	+	0.702931i	−0.965039	−	0.262108i	$-0.915582\pi$
$293$	−12.0322	+	12.0322i	−0.702931	+	0.702931i	0.262108	+	0.965039i	$0.415582\pi$
$294$	0.0958811	+	1.72939i	0.00559190	+	0.100860i
$295$	11.0189			0.641548
$296$	−6.29283			−0.365763
$297$	−19.0613	+	3.19662i	−1.10605	+	0.185487i
$298$			17.4114i			1.00862i
$299$	−2.89611	−	9.18602i	−0.167486	−	0.531241i
$300$	4.89689	−	5.47175i	0.282722	−	0.315911i
$301$	−0.431483	+	0.431483i	−0.0248703	+	0.0248703i
$302$		−	4.93447i		−	0.283947i
$303$	−11.2517	+	12.5725i	−0.646392	+	0.722273i
$304$	−3.60391	+	3.60391i	−0.206698	+	0.206698i
$305$	5.16651	+	5.16651i	0.295833	+	0.295833i
$306$	10.0548	−	12.5715i	0.574796	−	0.718662i
$307$	−8.97229	−	8.97229i	−0.512076	−	0.512076i	0.403086	−	0.915162i	$-0.367937\pi$
$307$	−8.97229	−	8.97229i	−0.512076	−	0.512076i	−0.915162	+	0.403086i	$0.867937\pi$
$308$			3.71958i			0.211943i
$309$	−17.8962	−	16.0161i	−1.01808	−	0.911123i
$310$	5.75626	+	5.75626i	0.326933	+	0.326933i
$311$	27.6299			1.56675			0.783373	−	0.621551i	$-0.213497\pi$
$311$	27.6299			1.56675			0.783373	+	0.621551i	$0.213497\pi$
$312$	−5.84292	+	2.20460i	−0.330790	+	0.124811i
$313$	14.2907			0.807757			0.403878	−	0.914813i	$-0.367662\pi$
$313$	14.2907			0.807757			0.403878	+	0.914813i	$0.367662\pi$
$314$	0.644468	+	0.644468i	0.0363694	+	0.0363694i
$315$	−2.60020	+	0.289210i	−0.146505	+	0.0162951i
$316$			6.11811i			0.344170i
$317$	−2.71639	−	2.71639i	−0.152568	−	0.152568i	0.626696	−	0.779264i	$-0.284407\pi$
$317$	−2.71639	−	2.71639i	−0.152568	−	0.152568i	−0.779264	+	0.626696i	$0.784407\pi$
$318$	0.0445374	+	0.803315i	0.00249753	+	0.0450477i
$319$	7.89078	+	7.89078i	0.441799	+	0.441799i
$320$	−0.616653	+	0.616653i	−0.0344719	+	0.0344719i
$321$	−3.57682	−	3.20104i	−0.199638	−	0.178665i
$322$		−	2.67136i		−	0.148869i
$323$	19.3384	−	19.3384i	1.07602	−	1.07602i
$324$	−1.97760	−	8.78004i	−0.109867	−	0.487780i
$325$	14.5783	−	4.59616i	0.808658	−	0.254949i
$326$		−	19.0640i		−	1.05586i
$327$	−0.302264	−	5.45190i	−0.0167152	−	0.301491i
$328$	11.9330			0.658888
$329$	−4.89332			−0.269777
$330$	−5.60976	+	0.311016i	−0.308807	+	0.0171209i
$331$	−10.6402	+	10.6402i	−0.584837	+	0.584837i	−0.936229	−	0.351392i	$-0.885709\pi$
$331$	−10.6402	+	10.6402i	−0.584837	+	0.584837i	0.351392	+	0.936229i	$0.385709\pi$
$332$	−3.29926	+	3.29926i	−0.181070	+	0.181070i
$333$	11.7916	−	14.7430i	0.646178	−	0.807910i
$334$	−6.45750			−0.353339
$335$	−2.19445			−0.119895
$336$	−1.72939	+	0.0958811i	−0.0943462	+	0.00523074i
$337$		−	26.4051i		−	1.43838i	−0.694816	−	0.719188i	$-0.744514\pi$
$337$		−	26.4051i		−	1.43838i	0.694816	−	0.719188i	$-0.255486\pi$
$338$	−12.8024	−	2.25801i	−0.696359	−	0.122819i
$339$	17.8110	+	15.9398i	0.967361	+	0.865731i
$340$	3.30893	−	3.30893i	0.179452	−	0.179452i
$341$			34.7211i			1.88025i
$342$	−1.69023	−	15.1964i	−0.0913971	−	0.821725i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−0.431483	−	0.431483i	−0.0232640	−	0.0232640i
$345$	4.02887	−	0.223368i	0.216907	−	0.0120257i
$346$	−14.5316	−	14.5316i	−0.781221	−	0.781221i
$347$		−	10.1701i		−	0.545960i	−0.962020	−	0.272980i	$-0.911991\pi$
$347$		−	10.1701i		−	0.545960i	0.962020	−	0.272980i	$-0.0880092\pi$
$348$	−3.46536	+	3.87217i	−0.185763	+	0.207570i
$349$	0.699211	+	0.699211i	0.0374279	+	0.0374279i	0.725573	−	0.688145i	$-0.241575\pi$
$349$	0.699211	+	0.699211i	0.0374279	+	0.0374279i	−0.688145	+	0.725573i	$0.741575\pi$
$350$	4.23948			0.226610
$351$	5.78361	−	17.8199i	0.308706	−	0.951157i
$352$	−3.71958			−0.198254
$353$	1.42912	+	1.42912i	0.0760646	+	0.0760646i	0.744116	−	0.668051i	$-0.232871\pi$
$353$	1.42912	+	1.42912i	0.0760646	+	0.0760646i	−0.668051	+	0.744116i	$0.732871\pi$
$354$	−14.5946	+	16.3079i	−0.775694	+	0.866755i
$355$		−	0.0120880i		−	0.000641562i
$356$	−8.90085	−	8.90085i	−0.471744	−	0.471744i
$357$	9.27985	−	0.514494i	0.491142	−	0.0272299i
$358$	8.86263	+	8.86263i	0.468404	+	0.468404i
$359$	−9.15856	+	9.15856i	−0.483370	+	0.483370i	−0.906206	−	0.422836i	$-0.861035\pi$
$359$	−9.15856	+	9.15856i	−0.483370	+	0.483370i	0.422836	+	0.906206i	$0.361035\pi$
$360$	−0.289210	−	2.60020i	−0.0152427	−	0.137043i
$361$		−	6.97627i		−	0.367172i
$362$	9.38608	−	9.38608i	0.493321	−	0.493321i
$363$	−3.65942	−	3.27497i	−0.192070	−	0.171891i
$364$	−3.19813	−	1.66493i	−0.167627	−	0.0872661i
$365$		−	13.7365i		−	0.719001i
$366$	−14.4894	+	0.803322i	−0.757374	+	0.0419903i
$367$	34.3663			1.79391			0.896953	−	0.442125i	$-0.145775\pi$
$367$	34.3663			1.79391			0.896953	+	0.442125i	$0.145775\pi$
$368$	2.67136			0.139254
$369$	−22.3602	+	27.9568i	−1.16403	+	1.45537i
$370$	3.88049	−	3.88049i	0.201737	−	0.201737i
$371$	−0.328456	+	0.328456i	−0.0170526	+	0.0170526i
$372$	−16.1433	+	0.895019i	−0.836994	+	0.0464046i
$373$	−27.8414			−1.44157			−0.720787	−	0.693157i	$-0.756219\pi$
$373$	−27.8414			−1.44157			−0.720787	+	0.693157i	$0.756219\pi$
$374$	19.9591			1.03206
$375$	0.772567	+	13.9347i	0.0398952	+	0.719584i
$376$		−	4.89332i		−	0.252354i
$377$	−10.3166	+	3.25254i	−0.531330	+	0.167515i
$378$	3.01594	−	4.23132i	0.155123	−	0.217636i
$379$	−0.998941	+	0.998941i	−0.0513121	+	0.0513121i	−0.732297	−	0.680985i	$-0.761552\pi$
$379$	−0.998941	+	0.998941i	−0.0513121	+	0.0513121i	0.680985	+	0.732297i	$0.261552\pi$
$380$		−	4.44472i		−	0.228009i
$381$	−27.5363	−	24.6433i	−1.41073	−	1.26252i
$382$	2.27012	−	2.27012i	0.116149	−	0.116149i
$383$	10.4955	+	10.4955i	0.536296	+	0.536296i	0.922439	−	0.386143i	$-0.126193\pi$
$383$	10.4955	+	10.4955i	0.536296	+	0.536296i	−0.386143	+	0.922439i	$0.626193\pi$
$384$	−0.0958811	−	1.72939i	−0.00489291	−	0.0882528i
$385$	−2.29369	−	2.29369i	−0.116897	−	0.116897i
$386$			22.9678i			1.16903i
$387$	1.81941	−	0.202365i	0.0924857	−	0.0102868i
$388$	−5.41720	−	5.41720i	−0.275017	−	0.275017i
$389$	24.1159			1.22273			0.611363	−	0.791350i	$-0.290621\pi$
$389$	24.1159			1.22273			0.611363	+	0.791350i	$0.290621\pi$
$390$	2.24358	−	4.96253i	0.113608	−	0.251287i
$391$	−14.3344			−0.724923
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	−10.5368	−	9.42985i	−0.531513	−	0.475673i
$394$		−	21.0670i		−	1.06134i
$395$	−3.77275	−	3.77275i	−0.189827	−	0.189827i
$396$	6.96983	−	8.71431i	0.350247	−	0.437911i
$397$	0.284448	+	0.284448i	0.0142760	+	0.0142760i	0.714209	−	0.699933i	$-0.246787\pi$
$397$	0.284448	+	0.284448i	0.0142760	+	0.0142760i	−0.699933	+	0.714209i	$0.746787\pi$
$398$	10.7226	−	10.7226i	0.537473	−	0.537473i
$399$	5.88703	−	6.57812i	0.294720	−	0.329318i
$400$			4.23948i			0.211974i
$401$	4.67831	−	4.67831i	0.233623	−	0.233623i	−0.580580	−	0.814203i	$-0.697174\pi$
$401$	4.67831	−	4.67831i	0.233623	−	0.233623i	0.814203	+	0.580580i	$0.197174\pi$
$402$	2.90655	−	3.24775i	0.144965	−	0.161983i
$403$	−29.8535	−	15.5416i	−1.48711	−	0.774182i
$404$		−	9.74113i		−	0.484639i
$405$	6.63373	+	4.19474i	0.329633	+	0.208438i
$406$	−3.00014			−0.148894
$407$	23.4067			1.16023
$408$	0.514494	+	9.27985i	0.0254712	+	0.459421i
$409$	−20.7469	+	20.7469i	−1.02587	+	1.02587i	−0.0262127	+	0.999656i	$0.508345\pi$
$409$	−20.7469	+	20.7469i	−1.02587	+	1.02587i	−0.999656	+	0.0262127i	$0.991655\pi$
$410$	−7.35850	+	7.35850i	−0.363411	+	0.363411i
$411$	−1.25008	−	22.5475i	−0.0616617	−	1.11218i
$412$	13.8659			0.683124
$413$	−12.6353			−0.621741
$414$	−5.00565	+	6.25852i	−0.246014	+	0.307590i
$415$		−	4.06899i		−	0.199739i
$416$	1.66493	−	3.19813i	0.0816299	−	0.156801i
$417$	−2.88120	+	3.21943i	−0.141093	+	0.157656i
$418$	13.4050	−	13.4050i	0.655661	−	0.655661i
$419$		−	19.4610i		−	0.950732i	−0.879788	−	0.475366i	$-0.842316\pi$
$419$		−	19.4610i		−	0.950732i	0.879788	−	0.475366i	$-0.157684\pi$
$420$	1.00731	−	1.12556i	0.0491517	−	0.0549218i
$421$	−12.3696	+	12.3696i	−0.602858	+	0.602858i	−0.941070	−	0.338212i	$-0.890178\pi$
$421$	−12.3696	+	12.3696i	−0.602858	+	0.602858i	0.338212	+	0.941070i	$0.390178\pi$
$422$	1.76660	+	1.76660i	0.0859965	+	0.0859965i
$423$	11.4642	+	9.16920i	0.557407	+	0.445822i
$424$	−0.328456	−	0.328456i	−0.0159512	−	0.0159512i
$425$		−	22.7488i		−	1.10348i
$426$	0.0178900	+	0.0160105i	0.000866774	+	0.000775711i
$427$	−5.92436	−	5.92436i	−0.286700	−	0.286700i
$428$	2.77130			0.133956
$429$	21.7332	−	8.20019i	1.04929	−	0.395909i
$430$	0.532150			0.0256626
$431$	−8.30885	−	8.30885i	−0.400223	−	0.400223i	0.478088	−	0.878312i	$-0.341330\pi$
$431$	−8.30885	−	8.30885i	−0.400223	−	0.400223i	−0.878312	+	0.478088i	$0.841330\pi$
$432$	4.23132	+	3.01594i	0.203580	+	0.145105i
$433$			9.90076i			0.475800i	0.971290	+	0.237900i	$0.0764591\pi$
$433$			9.90076i			0.475800i	−0.971290	+	0.237900i	$0.923541\pi$
$434$	−6.60062	−	6.60062i	−0.316840	−	0.316840i
$435$	−0.250859	−	4.52471i	−0.0120278	−	0.216943i
$436$	2.22915	+	2.22915i	0.106757	+	0.106757i
$437$	−9.62734	+	9.62734i	−0.460538	+	0.460538i
$438$	20.3298	+	18.1940i	0.971397	+	0.869343i
$439$		−	16.7403i		−	0.798972i	−0.916739	−	0.399486i	$-0.869189\pi$
$439$		−	16.7403i		−	0.798972i	0.916739	−	0.399486i	$-0.130811\pi$
$440$	2.29369	−	2.29369i	0.109347	−	0.109347i
$441$	2.98161	−	0.331633i	0.141982	−	0.0157920i
$442$	−8.93394	+	17.1610i	−0.424944	+	0.816265i
$443$			7.56632i			0.359487i	0.983714	+	0.179743i	$0.0575267\pi$
$443$			7.56632i			0.359487i	−0.983714	+	0.179743i	$0.942473\pi$
$444$	0.603364	+	10.8828i	0.0286344	+	0.516474i
$445$	10.9775			0.520382
$446$	9.38537			0.444410
$447$	30.1113	−	1.66943i	1.42421	−	0.0789612i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−12.1480	+	12.1480i	−0.573301	+	0.573301i	−0.933049	−	0.359748i	$-0.882863\pi$
$449$	−12.1480	+	12.1480i	−0.573301	+	0.573301i	0.359748	+	0.933049i	$0.382863\pi$
$450$	−9.93233	−	7.94402i	−0.468215	−	0.374485i
$451$	−44.3857			−2.09004
$452$	−13.7999			−0.649091
$453$	−8.53365	+	0.473122i	−0.400946	+	0.0222292i
$454$			12.3864i			0.581322i
$455$	2.99882	−	0.945448i	0.140587	−	0.0443233i
$456$	6.57812	+	5.88703i	0.308049	+	0.275685i
$457$	17.0229	−	17.0229i	0.796296	−	0.796296i	−0.186213	−	0.982509i	$-0.559621\pi$
$457$	17.0229	−	17.0229i	0.796296	−	0.796296i	0.982509	+	0.186213i	$0.0596215\pi$
$458$			6.00307i			0.280505i
$459$	−22.7051	−	16.1834i	−1.05978	−	0.755377i
$460$	−1.64730	+	1.64730i	−0.0768059	+	0.0768059i
$461$	4.28202	+	4.28202i	0.199434	+	0.199434i	0.799757	−	0.600324i	$-0.204962\pi$
$461$	4.28202	+	4.28202i	0.199434	+	0.199434i	−0.600324	+	0.799757i	$0.704962\pi$
$462$	6.43263	−	0.356638i	0.299273	−	0.0165923i
$463$	−14.6083	−	14.6083i	−0.678904	−	0.678904i	0.280848	−	0.959752i	$-0.409384\pi$
$463$	−14.6083	−	14.6083i	−0.678904	−	0.678904i	−0.959752	+	0.280848i	$0.909384\pi$
$464$		−	3.00014i		−	0.139278i
$465$	9.40292	−	10.5068i	0.436050	−	0.487239i
$466$	−4.11378	−	4.11378i	−0.190567	−	0.190567i
$467$	−31.2477			−1.44597			−0.722985	−	0.690864i	$-0.757230\pi$
$467$	−31.2477			−1.44597			−0.722985	+	0.690864i	$0.757230\pi$
$468$	4.37285	+	9.89334i	0.202135	+	0.457320i
$469$	2.51634			0.116194
$470$	3.01748	+	3.01748i	0.139186	+	0.139186i
$471$	1.05275	−	1.17633i	0.0485080	−	0.0542025i
$472$		−	12.6353i		−	0.581585i
$473$	1.60494	+	1.60494i	0.0737951	+	0.0737951i
$474$	10.5806	−	0.586611i	0.485984	−	0.0269439i
$475$	−15.2787	−	15.2787i	−0.701034	−	0.701034i
$476$	−3.79430	+	3.79430i	−0.173912	+	0.173912i
$477$	1.38498	−	0.154046i	0.0634138	−	0.00705326i
$478$			8.76067i			0.400704i
$479$	10.8416	−	10.8416i	0.495365	−	0.495365i	−0.414627	−	0.909992i	$-0.636088\pi$
$479$	10.8416	−	10.8416i	0.495365	−	0.495365i	0.909992	+	0.414627i	$0.136088\pi$
$480$	1.12556	+	1.00731i	0.0513746	+	0.0459772i
$481$	−10.4771	+	20.1253i	−0.477716	+	0.917633i
$482$			27.2226i			1.23996i
$483$	−4.61984	+	0.256133i	−0.210210	+	0.0116545i
$484$	2.83530			0.128877
$485$	6.68106			0.303371
$486$	−14.9945	+	4.26189i	−0.680166	+	0.193323i
$487$	17.7146	−	17.7146i	0.802727	−	0.802727i	−0.180794	−	0.983521i	$-0.557867\pi$
$487$	17.7146	−	17.7146i	0.802727	−	0.802727i	0.983521	+	0.180794i	$0.0578669\pi$
$488$	5.92436	−	5.92436i	0.268183	−	0.268183i
$489$	−32.9692	+	1.82788i	−1.49092	+	0.0826595i
$490$	0.872079			0.0393965
$491$	8.91977			0.402543			0.201272	−	0.979535i	$-0.435493\pi$
$491$	8.91977			0.402543			0.201272	+	0.979535i	$0.435493\pi$
$492$	−1.14415	−	20.6368i	−0.0515821	−	0.930380i
$493$			16.0986i			0.725044i
$494$	5.52549	+	17.5260i	0.248603	+	0.788532i
$495$	1.07574	+	9.67166i	0.0483509	+	0.434709i
$496$	6.60062	−	6.60062i	0.296376	−	0.296376i
$497$			0.0138611i			0.000621755i
$498$	6.02206	+	5.38938i	0.269855	+	0.241504i
$499$	−20.1012	+	20.1012i	−0.899854	+	0.899854i	−0.995423	−	0.0955687i	$-0.969533\pi$
$499$	−20.1012	+	20.1012i	−0.899854	+	0.899854i	0.0955687	+	0.995423i	$0.469533\pi$
$500$	−5.69755	−	5.69755i	−0.254802	−	0.254802i
$501$	0.619153	+	11.1676i	0.0276617	+	0.498930i
$502$	15.0281	+	15.0281i	0.670738	+	0.670738i
$503$		−	1.38296i		−	0.0616631i	−0.999525	−	0.0308316i	$-0.990184\pi$
$503$		−	1.38296i		−	0.0616631i	0.999525	−	0.0308316i	$-0.00981554\pi$
$504$	0.331633	+	2.98161i	0.0147721	+	0.132812i
$505$	6.00689	+	6.00689i	0.267303	+	0.267303i
$506$	−9.93636			−0.441725
$507$	−2.67748	+	22.3569i	−0.118911	+	0.992905i
$508$	21.3350			0.946585
$509$	−15.7238	−	15.7238i	−0.696947	−	0.696947i	0.266804	−	0.963751i	$-0.414032\pi$
$509$	−15.7238	−	15.7238i	−0.696947	−	0.696947i	−0.963751	+	0.266804i	$0.914032\pi$
$510$	−6.03971	−	5.40518i	−0.267443	−	0.239346i
$511$			15.7514i			0.696803i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−26.1185	+	4.38012i	−1.15316	+	0.193387i
$514$	−9.34074	−	9.34074i	−0.412002	−	0.412002i
$515$	−8.55045	+	8.55045i	−0.376778	+	0.376778i
$516$	−0.704833	+	0.787575i	−0.0310286	+	0.0346711i
$517$			18.2011i			0.800484i
$518$	−4.44970	+	4.44970i	−0.195509	+	0.195509i
$519$	−23.7375	+	26.5241i	−1.04196	+	1.16428i
$520$	0.945448	+	2.99882i	0.0414607	+	0.131507i
$521$		−	24.0452i		−	1.05344i	−0.850039	−	0.526720i	$-0.823422\pi$
$521$		−	24.0452i		−	1.05344i	0.850039	−	0.526720i	$-0.176578\pi$
$522$	7.02877	+	5.62171i	0.307641	+	0.246056i
$523$	−11.7120			−0.512132			−0.256066	−	0.966659i	$-0.582426\pi$
$523$	−11.7120			−0.512132			−0.256066	+	0.966659i	$0.582426\pi$
$524$	8.16389			0.356641
$525$	−0.406486	−	7.33173i	−0.0177405	−	0.319983i
$526$	11.1748	−	11.1748i	0.487247	−	0.487247i
$527$	−35.4186	+	35.4186i	−1.54286	+	1.54286i
$528$	0.356638	+	6.43263i	0.0155207	+	0.279944i
$529$	−15.8638			−0.689731
$530$	0.405086			0.0175958
$531$	29.6021	+	23.6762i	1.28462	+	1.02746i
$532$			5.09669i			0.220970i
$533$	19.8676	−	38.1632i	0.860561	−	1.65303i
$534$	−14.5397	+	16.2465i	−0.629193	+	0.703055i
$535$	−1.70893	+	1.70893i	−0.0738834	+	0.0738834i
$536$			2.51634i			0.108689i
$537$	14.4772	−	16.1767i	0.624738	−	0.698078i
$538$	−5.56149	+	5.56149i	−0.239773	+	0.239773i
$539$	2.63014	+	2.63014i	0.113288	+	0.113288i
$540$	−4.46905	+	0.749468i	−0.192317	+	0.0322520i
$541$	1.33026	+	1.33026i	0.0571925	+	0.0571925i	0.735125	−	0.677932i	$-0.237124\pi$
$541$	1.33026	+	1.33026i	0.0571925	+	0.0571925i	−0.677932	+	0.735125i	$0.737124\pi$
$542$			10.2881i			0.441913i
$543$	−17.1322	−	15.3323i	−0.735213	−	0.657972i
$544$	−3.79430	−	3.79430i	−0.162679	−	0.162679i
$545$	−2.74922			−0.117764
$546$	−2.57268	+	5.69046i	−0.110101	+	0.243529i
$547$	−13.7724			−0.588865			−0.294433	−	0.955672i	$-0.595131\pi$
$547$	−13.7724			−0.588865			−0.294433	+	0.955672i	$0.595131\pi$
$548$	9.21910	+	9.21910i	0.393821	+	0.393821i
$549$	2.77852	+	24.9809i	0.118584	+	1.06616i
$550$		−	15.7691i		−	0.672396i
$551$	10.8122	+	10.8122i	0.460615	+	0.460615i
$552$	−0.256133	−	4.61984i	−0.0109018	−	0.196634i
$553$	4.32615	+	4.32615i	0.183967	+	0.183967i
$554$	−10.7693	+	10.7693i	−0.457546	+	0.457546i
$555$	−7.08297	−	6.33884i	−0.300655	−	0.269069i
$556$		−	2.49440i		−	0.105786i
$557$	17.7921	−	17.7921i	0.753876	−	0.753876i	−0.221324	−	0.975200i	$-0.571038\pi$
$557$	17.7921	−	17.7921i	0.753876	−	0.753876i	0.975200	+	0.221324i	$0.0710378\pi$
$558$	3.09568	+	27.8324i	0.131051	+	1.17824i
$559$	−2.09833	+	0.661547i	−0.0887497	+	0.0279805i
$560$			0.872079i			0.0368520i
$561$	−1.91370	−	34.5172i	−0.0807965	−	1.45732i
$562$	28.1024			1.18543
$563$	−2.64079			−0.111296			−0.0556480	−	0.998450i	$-0.517722\pi$
$563$	−2.64079			−0.111296			−0.0556480	+	0.998450i	$0.517722\pi$
$564$	−8.46248	+	0.469177i	−0.356335	+	0.0197559i
$565$	8.50973	−	8.50973i	0.358007	−	0.358007i
$566$	−8.44034	+	8.44034i	−0.354774	+	0.354774i
$567$	−7.60680	−	4.81005i	−0.319456	−	0.202003i
$568$	−0.0138611			−0.000581598
$569$	1.57360			0.0659689			0.0329844	−	0.999456i	$-0.489499\pi$
$569$	1.57360			0.0659689			0.0329844	+	0.999456i	$0.489499\pi$
$570$	−7.68667	+	0.426164i	−0.321959	+	0.0178501i
$571$		−	13.0500i		−	0.546126i	−0.961996	−	0.273063i	$-0.911963\pi$
$571$		−	13.0500i		−	0.546126i	0.961996	−	0.273063i	$-0.0880367\pi$
$572$	−6.19285	+	11.8957i	−0.258936	+	0.497384i
$573$	−4.14360	−	3.70827i	−0.173101	−	0.154915i
$574$	8.43789	−	8.43789i	0.352191	−	0.352191i
$575$			11.3252i			0.472293i
$576$	−2.98161	+	0.331633i	−0.124234	+	0.0138180i
$577$	30.4816	−	30.4816i	1.26896	−	1.26896i	0.322340	−	0.946624i	$-0.395531\pi$
$577$	30.4816	−	30.4816i	1.26896	−	1.26896i	0.946624	−	0.322340i	$-0.104469\pi$
$578$	8.33924	+	8.33924i	0.346867	+	0.346867i
$579$	39.7204	−	2.20218i	1.65072	−	0.0915195i
$580$	1.85004	+	1.85004i	0.0768188	+	0.0768188i
$581$			4.66586i			0.193572i
$582$	−8.84907	+	9.88788i	−0.366806	+	0.409866i
$583$	1.22172	+	1.22172i	0.0505984	+	0.0505984i
$584$	−15.7514			−0.651799
$585$	−8.79728	−	3.40423i	−0.363723	−	0.140747i
$586$	−17.0162			−0.702931
$587$	−8.10578	−	8.10578i	−0.334561	−	0.334561i	0.519754	−	0.854316i	$-0.326023\pi$
$587$	−8.10578	−	8.10578i	−0.334561	−	0.334561i	−0.854316	+	0.519754i	$0.826023\pi$
$588$	−1.15507	+	1.29067i	−0.0476342	+	0.0532261i
$589$			47.5760i			1.96033i
$590$	7.79157	+	7.79157i	0.320774	+	0.320774i
$591$	−36.4331	+	2.01992i	−1.49866	+	0.0830886i
$592$	−4.44970	−	4.44970i	−0.182882	−	0.182882i
$593$	−17.6343	+	17.6343i	−0.724154	+	0.724154i	−0.969449	−	0.245295i	$-0.921115\pi$
$593$	−17.6343	+	17.6343i	−0.724154	+	0.724154i	0.245295	+	0.969449i	$0.421115\pi$
$594$	−15.7388	−	11.2180i	−0.645769	−	0.460282i
$595$		−	4.67953i		−	0.191842i
$596$	−12.3117	+	12.3117i	−0.504309	+	0.504309i
$597$	−19.5716	−	17.5154i	−0.801013	−	0.716859i
$598$	4.44764	−	8.54336i	0.181877	−	0.349364i
$599$		−	22.8023i		−	0.931675i	−0.884870	−	0.465838i	$-0.845753\pi$
$599$		−	22.8023i		−	0.931675i	0.884870	−	0.465838i	$-0.154247\pi$
$600$	7.33173	−	0.406486i	0.299317	−	0.0165947i
$601$	10.1241			0.412970			0.206485	−	0.978450i	$-0.433798\pi$
$601$	10.1241			0.412970			0.206485	+	0.978450i	$0.433798\pi$
$602$	−0.610209			−0.0248703
$603$	−5.89533	−	4.71517i	−0.240076	−	0.192017i
$604$	3.48920	−	3.48920i	0.141973	−	0.141973i
$605$	−1.74839	+	1.74839i	−0.0710824	+	0.0710824i
$606$	−16.8463	+	0.933990i	−0.684332	+	0.0379407i
$607$	−30.2863			−1.22928			−0.614642	−	0.788806i	$-0.710699\pi$
$607$	−30.2863			−1.22928			−0.614642	+	0.788806i	$0.710699\pi$
$608$	−5.09669			−0.206698
$609$	0.287656	+	5.18842i	0.0116564	+	0.210245i
$610$			7.30655i			0.295833i
$611$	−15.6494	−	8.14704i	−0.633109	−	0.329594i
$612$	15.9992	−	1.77952i	0.646729	−	0.0719330i
$613$	15.8557	−	15.8557i	0.640406	−	0.640406i	−0.310249	−	0.950655i	$-0.600412\pi$
$613$	15.8557	−	15.8557i	0.640406	−	0.640406i	0.950655	+	0.310249i	$0.100412\pi$
$614$		−	12.6887i		−	0.512076i
$615$	13.4313	+	12.0202i	0.541602	+	0.484702i
$616$	−2.63014	+	2.63014i	−0.105971	+	0.105971i
$617$	9.52955	+	9.52955i	0.383645	+	0.383645i	0.872414	−	0.488768i	$-0.162554\pi$
$617$	9.52955	+	9.52955i	0.383645	+	0.383645i	−0.488768	+	0.872414i	$0.662554\pi$
$618$	−1.32948	−	23.9796i	−0.0534795	−	0.964602i
$619$	8.43686	+	8.43686i	0.339106	+	0.339106i	0.856031	−	0.516925i	$-0.172923\pi$
$619$	8.43686	+	8.43686i	0.339106	+	0.339106i	−0.516925	+	0.856031i	$0.672923\pi$
$620$			8.14057i			0.326933i
$621$	11.3034	+	8.05668i	0.453590	+	0.323303i
$622$	19.5373	+	19.5373i	0.783373	+	0.783373i
$623$	−12.5877			−0.504316
$624$	−5.69046	−	2.57268i	−0.227801	−	0.102990i
$625$	−14.1706			−0.566823
$626$	10.1050	+	10.1050i	0.403878	+	0.403878i
$627$	−24.4679	−	21.8973i	−0.977153	−	0.874494i
$628$			0.911415i			0.0363694i
$629$	23.8769	+	23.8769i	0.952035	+	0.952035i
$630$	−2.04312	−	1.63412i	−0.0813999	−	0.0651048i
$631$	6.47280	+	6.47280i	0.257678	+	0.257678i	0.824109	−	0.566431i	$-0.191676\pi$
$631$	6.47280	+	6.47280i	0.257678	+	0.257678i	−0.566431	+	0.824109i	$0.691676\pi$
$632$	−4.32615	+	4.32615i	−0.172085	+	0.172085i
$633$	2.88576	−	3.22452i	0.114699	−	0.128163i
$634$		−	3.84155i		−	0.152568i
$635$	−13.1563	+	13.1563i	−0.522090	+	0.522090i
$636$	−0.536537	+	0.599522i	−0.0212751	+	0.0237726i
$637$	−3.43870	+	1.08413i	−0.136246	+	0.0429549i
$638$			11.1593i			0.441799i
$639$	0.0259732	−	0.0324740i	0.00102748	−	0.00128465i
$640$	−0.872079			−0.0344719
$641$	9.04638			0.357311			0.178655	−	0.983912i	$-0.442825\pi$
$641$	9.04638			0.357311			0.178655	+	0.983912i	$0.442825\pi$
$642$	−0.265715	−	4.79267i	−0.0104869	−	0.189151i
$643$	21.3385	−	21.3385i	0.841508	−	0.841508i	−0.147547	−	0.989055i	$-0.547138\pi$
$643$	21.3385	−	21.3385i	0.841508	−	0.841508i	0.989055	+	0.147547i	$0.0471378\pi$
$644$	1.88894	−	1.88894i	0.0744347	−	0.0744347i
$645$	−0.0510231	−	0.920298i	−0.00200903	−	0.0362367i
$646$	27.3486			1.07602
$647$	−23.9618			−0.942037			−0.471018	−	0.882123i	$-0.656113\pi$
$647$	−23.9618			−0.942037			−0.471018	+	0.882123i	$0.656113\pi$
$648$	4.81005	−	7.60680i	0.188957	−	0.298823i
$649$			46.9979i			1.84483i
$650$	13.5584	+	7.05844i	0.531804	+	0.276855i
$651$	−10.7822	+	12.0479i	−0.422588	+	0.472196i
$652$	13.4803	−	13.4803i	0.527929	−	0.527929i
$653$			16.8655i			0.659997i	0.943981	+	0.329998i	$0.107048\pi$
$653$			16.8655i			0.659997i	−0.943981	+	0.329998i	$0.892952\pi$
$654$	3.64134	−	4.06881i	0.142388	−	0.159103i
$655$	−5.03428	+	5.03428i	−0.196706	+	0.196706i
$656$	8.43789	+	8.43789i	0.329444	+	0.329444i
$657$	29.5154	−	36.9028i	1.15150	−	1.43971i
$658$	−3.46010	−	3.46010i	−0.134889	−	0.134889i
$659$		−	23.3034i		−	0.907773i	−0.891060	−	0.453886i	$-0.850037\pi$
$659$		−	23.3034i		−	0.907773i	0.891060	−	0.453886i	$-0.149963\pi$
$660$	−4.18662	−	3.74678i	−0.162964	−	0.145843i
$661$	−33.0664	−	33.0664i	−1.28613	−	1.28613i	−0.937116	−	0.349019i	$-0.886515\pi$
$661$	−33.0664	−	33.0664i	−1.28613	−	1.28613i	−0.349019	−	0.937116i	$-0.613485\pi$
$662$	−15.0475			−0.584837
$663$	30.5347	+	13.8049i	1.18587	+	0.536138i
$664$	−4.66586			−0.181070
$665$	−3.14289	−	3.14289i	−0.121876	−	0.121876i
$666$	18.7628	−	2.08691i	0.727044	−	0.0808660i
$667$		−	8.01445i		−	0.310321i
$668$	−4.56615	−	4.56615i	−0.176669	−	0.176669i
$669$	−0.899879	−	16.2310i	−0.0347913	−	0.627527i
$670$	−1.55171	−	1.55171i	−0.0599477	−	0.0599477i
$671$	−22.0362	+	22.0362i	−0.850696	+	0.850696i
$672$	−1.29067	−	1.15507i	−0.0497885	−	0.0445577i
$673$			27.1641i			1.04710i	0.851996	+	0.523549i	$0.175392\pi$
$673$			27.1641i			1.04710i	−0.851996	+	0.523549i	$0.824608\pi$
$674$	18.6712	−	18.6712i	0.719188	−	0.719188i
$675$	−12.7860	+	17.9386i	−0.492134	+	0.690457i
$676$	−7.45601	−	10.6493i	−0.286770	−	0.409589i
$677$		−	21.1789i		−	0.813969i	−0.913435	−	0.406985i	$-0.866580\pi$
$677$		−	21.1789i		−	0.813969i	0.913435	−	0.406985i	$-0.133420\pi$
$678$	1.32315	+	23.8654i	0.0508151	+	0.916546i
$679$	−7.66107			−0.294005
$680$	4.67953			0.179452
$681$	21.4210	−	1.18762i	0.820853	−	0.0455097i
$682$	−24.5515	+	24.5515i	−0.940127	+	0.940127i
$683$	−16.6542	+	16.6542i	−0.637256	+	0.637256i	−0.949878	−	0.312622i	$-0.898793\pi$
$683$	−16.6542	+	16.6542i	−0.637256	+	0.637256i	0.312622	+	0.949878i	$0.398793\pi$
$684$	9.55028	−	11.9406i	0.365164	−	0.456561i
$685$	−11.3700			−0.434424
$686$	−1.00000			−0.0381802
$687$	10.3817	−	0.575581i	0.396086	−	0.0219598i
$688$		−	0.610209i		−	0.0232640i
$689$	−1.59730	+	0.503587i	−0.0608522	+	0.0191851i
$690$	3.00678	+	2.69089i	0.114466	+	0.102441i
$691$	−12.0327	+	12.0327i	−0.457746	+	0.457746i	−0.897915	−	0.440169i	$-0.854919\pi$
$691$	−12.0327	+	12.0327i	−0.457746	+	0.457746i	0.440169	+	0.897915i	$0.354919\pi$
$692$		−	20.5507i		−	0.781221i
$693$	−1.23353	−	11.0904i	−0.0468581	−	0.421288i
$694$	7.19135	−	7.19135i	0.272980	−	0.272980i
$695$	1.53818	+	1.53818i	0.0583464	+	0.0583464i
$696$	−5.18842	+	0.287656i	−0.196667	+	0.0109036i
$697$	−45.2773	−	45.2773i	−1.71500	−	1.71500i
$698$			0.988833i			0.0374279i
$699$	−6.71991	+	7.50878i	−0.254170	+	0.284008i
$700$	2.99776	+	2.99776i	0.113305	+	0.113305i
$701$	46.7003			1.76385			0.881923	−	0.471393i	$-0.156249\pi$
$701$	46.7003			1.76385			0.881923	+	0.471393i	$0.156249\pi$
$702$	16.6902	−	8.51097i	0.629932	−	0.321226i
$703$	32.0726			1.20964
$704$	−2.63014	−	2.63014i	−0.0991272	−	0.0991272i
$705$	4.92909	−	5.50773i	0.185640	−	0.207433i
$706$			2.02109i			0.0760646i
$707$	−6.88802	−	6.88802i	−0.259051	−	0.259051i
$708$	−21.8514	+	1.21148i	−0.821224	+	0.0455303i
$709$	−23.8602	−	23.8602i	−0.896089	−	0.896089i	0.0989984	−	0.995088i	$-0.468436\pi$
$709$	−23.8602	−	23.8602i	−0.896089	−	0.896089i	−0.995088	+	0.0989984i	$0.968436\pi$
$710$	0.00854747	−	0.00854747i	0.000320781	−	0.000320781i
$711$	−2.02896	−	18.2418i	−0.0760921	−	0.684122i
$712$		−	12.5877i		−	0.471744i
$713$	17.6326	−	17.6326i	0.660348	−	0.660348i
$714$	6.92565	+	6.19805i	0.259186	+	0.231956i
$715$	−3.51667	−	11.1543i	−0.131516	−	0.417149i
$716$			12.5336i			0.468404i
$717$	15.1507	−	0.839982i	0.565812	−	0.0313697i
$718$	−12.9522			−0.483370
$719$	18.8987			0.704802			0.352401	−	0.935849i	$-0.385365\pi$
$719$	18.8987			0.704802			0.352401	+	0.935849i	$0.385365\pi$
$720$	1.63412	−	2.04312i	0.0609000	−	0.0761427i
$721$	9.80468	−	9.80468i	0.365145	−	0.365145i
$722$	4.93297	−	4.93297i	0.183586	−	0.183586i
$723$	47.0787	−	2.61014i	1.75088	−	0.0970720i
$724$	13.2739			0.493321
$725$	12.7190			0.472372
$726$	−0.271852	−	4.90335i	−0.0100894	−	0.181980i
$727$			9.73860i			0.361185i	0.983558	+	0.180592i	$0.0578015\pi$
$727$			9.73860i			0.361185i	−0.983558	+	0.180592i	$0.942199\pi$
$728$	−1.08413	−	3.43870i	−0.0401806	−	0.127447i
$729$	8.80819	+	25.5228i	0.326229	+	0.945291i
$730$	9.71317	−	9.71317i	0.359500	−	0.359500i
$731$			3.27435i			0.121106i
$732$	−10.8136	−	9.67753i	−0.399682	−	0.357692i
$733$	2.79274	−	2.79274i	0.103152	−	0.103152i	−0.653647	−	0.756799i	$-0.726762\pi$
$733$	2.79274	−	2.79274i	0.103152	−	0.103152i	0.756799	+	0.653647i	$0.226762\pi$
$734$	24.3006	+	24.3006i	0.896953	+	0.896953i
$735$	−0.0836158	−	1.50817i	−0.00308422	−	0.0556296i
$736$	1.88894	+	1.88894i	0.0696272	+	0.0696272i
$737$		−	9.35974i		−	0.344770i
$738$	−35.5795	+	3.95736i	−1.30970	+	0.145673i
$739$	−4.29662	−	4.29662i	−0.158054	−	0.158054i	0.623650	−	0.781704i	$-0.285649\pi$
$739$	−4.29662	−	4.29662i	−0.158054	−	0.158054i	−0.781704	+	0.623650i	$0.785649\pi$
$740$	5.48784			0.201737
$741$	29.7796	−	11.2362i	1.09398	−	0.412771i
$742$	−0.464507			−0.0170526
$743$	26.3150	+	26.3150i	0.965406	+	0.965406i	0.999421	−	0.0340158i	$-0.0108296\pi$
$743$	26.3150	+	26.3150i	0.965406	+	0.965406i	−0.0340158	+	0.999421i	$0.510830\pi$
$744$	−12.0479	−	10.7822i	−0.441699	−	0.395295i
$745$		−	15.1841i		−	0.556304i
$746$	−19.6868	−	19.6868i	−0.720787	−	0.720787i
$747$	8.74297	−	10.9313i	0.319889	−	0.399954i
$748$	14.1132	+	14.1132i	0.516031	+	0.516031i
$749$	1.95960	−	1.95960i	0.0716023	−	0.0716023i
$750$	−9.30703	+	10.3996i	−0.339845	+	0.379740i
$751$		−	39.0092i		−	1.42347i	−0.702450	−	0.711733i	$-0.747910\pi$
$751$		−	39.0092i		−	1.42347i	0.702450	−	0.711733i	$-0.252090\pi$
$752$	3.46010	−	3.46010i	0.126177	−	0.126177i
$753$	24.5487	−	27.4305i	0.894603	−	0.999623i
$754$	−9.59481	−	4.99502i	−0.349422	−	0.181908i
$755$			4.30325i			0.156611i
$756$	5.12459	−	0.859404i	0.186380	−	0.0312562i
$757$	−25.7810			−0.937025			−0.468513	−	0.883457i	$-0.655210\pi$
$757$	−25.7810			−0.937025			−0.468513	+	0.883457i	$0.655210\pi$
$758$	−1.41272			−0.0513121
$759$	0.952709	+	17.1839i	0.0345812	+	0.623736i
$760$	3.14289	−	3.14289i	0.114005	−	0.114005i
$761$	16.8635	−	16.8635i	0.611300	−	0.611300i	−0.331985	−	0.943285i	$-0.607718\pi$
$761$	16.8635	−	16.8635i	0.611300	−	0.611300i	0.943285	+	0.331985i	$0.107718\pi$
$762$	−2.04562	−	36.8966i	−0.0741049	−	1.33662i
$763$	3.15249			0.114128
$764$	3.21043			0.116149
$765$	−8.76860	+	10.9633i	−0.317029	+	0.396379i
$766$			14.8429i			0.536296i
$767$	−40.4092	−	21.0368i	−1.45909	−	0.759596i
$768$	1.15507	−	1.29067i	0.0416800	−	0.0465729i
$769$	−29.5659	+	29.5659i	−1.06617	+	1.06617i	−0.0685256	+	0.997649i	$0.521829\pi$
$769$	−29.5659	+	29.5659i	−1.06617	+	1.06617i	−0.997649	+	0.0685256i	$0.978171\pi$
$770$		−	3.24377i		−	0.116897i
$771$	−15.2582	+	17.0494i	−0.549512	+	0.614020i
$772$	−16.2407	+	16.2407i	−0.584516	+	0.584516i
$773$	−16.1450	−	16.1450i	−0.580696	−	0.580696i	0.354398	−	0.935095i	$-0.384686\pi$
$773$	−16.1450	−	16.1450i	−0.580696	−	0.580696i	−0.935095	+	0.354398i	$0.884686\pi$
$774$	1.42961	+	1.14342i	0.0513862	+	0.0410994i
$775$	27.9832	+	27.9832i	1.00519	+	1.00519i
$776$		−	7.66107i		−	0.275017i
$777$	8.12194	+	7.26865i	0.291373	+	0.260762i
$778$	17.0525	+	17.0525i	0.611363	+	0.611363i
$779$	−60.8187			−2.17906
$780$	5.09549	−	1.92258i	0.182448	−	0.0688395i
$781$	0.0515575			0.00184487
$782$	−10.1360	−	10.1360i	−0.362461	−	0.362461i
$783$	9.04824	−	12.6945i	0.323358	−	0.453666i
$784$		−	1.00000i		−	0.0357143i
$785$	−0.562026	−	0.562026i	−0.0200596	−	0.0200596i
$786$	−0.782762	−	14.1186i	−0.0279202	−	0.503593i
$787$	11.6387	+	11.6387i	0.414876	+	0.414876i	0.883433	−	0.468557i	$-0.155226\pi$
$787$	11.6387	+	11.6387i	0.414876	+	0.414876i	−0.468557	+	0.883433i	$0.655226\pi$
$788$	14.8966	−	14.8966i	0.530670	−	0.530670i
$789$	−20.3972	−	18.2543i	−0.726159	−	0.649869i
$790$		−	5.33547i		−	0.189827i
$791$	−9.75798	+	9.75798i	−0.346954	+	0.346954i
$792$	11.0904	−	1.23353i	0.394079	−	0.0438318i
$793$	−9.08320	−	28.8105i	−0.322554	−	1.02309i
$794$			0.402270i			0.0142760i
$795$	−0.0388401	−	0.700554i	−0.00137752	−	0.0248461i
$796$	15.1640			0.537473
$797$	−35.2474			−1.24853			−0.624264	−	0.781214i	$-0.714601\pi$
$797$	−35.2474			−1.24853			−0.624264	+	0.781214i	$0.714601\pi$
$798$	8.81419	−	0.488676i	0.312019	−	0.0172990i
$799$	−18.5667	+	18.5667i	−0.656844	+	0.656844i
$800$	−2.99776	+	2.99776i	−0.105987	+	0.105987i
$801$	29.4907	+	23.5871i	1.04200	+	0.833409i
$802$	6.61612			0.233623
$803$	58.5888			2.06755
$804$	4.35175	−	0.241270i	0.153474	−	0.00850892i
$805$			2.32964i			0.0821090i
$806$	−10.1200	−	32.0992i	−0.356463	−	1.13064i
$807$	10.1512	+	9.08477i	0.357341	+	0.319799i
$808$	6.88802	−	6.88802i	0.242320	−	0.242320i
$809$			52.9887i			1.86298i	0.363761	+	0.931492i	$0.381492\pi$
$809$			52.9887i			1.86298i	−0.363761	+	0.931492i	$0.618508\pi$
$810$	1.72462	+	7.65688i	0.0605971	+	0.269035i
$811$	4.32230	−	4.32230i	0.151777	−	0.151777i	−0.627134	−	0.778911i	$-0.715772\pi$
$811$	4.32230	−	4.32230i	0.151777	−	0.151777i	0.778911	+	0.627134i	$0.215772\pi$
$812$	−2.12142	−	2.12142i	−0.0744471	−	0.0744471i
$813$	17.7922	−	0.986437i	0.624001	−	0.0345958i
$814$	16.5510	+	16.5510i	0.580114	+	0.580114i
$815$			16.6253i			0.582359i
$816$	−6.19805	+	6.92565i	−0.216975	+	0.242446i
$817$	2.19914	+	2.19914i	0.0769380	+	0.0769380i
$818$	−29.3406			−1.02587
$819$	10.0877	+	3.90358i	0.352493	+	0.136402i
$820$	−10.4065			−0.363411
$821$	16.6689	+	16.6689i	0.581747	+	0.581747i	0.935383	−	0.353636i	$-0.115055\pi$
$821$	16.6689	+	16.6689i	0.581747	+	0.581747i	−0.353636	+	0.935383i	$0.615055\pi$
$822$	15.0595	−	16.8274i	0.525261	−	0.586923i
$823$		−	2.89381i		−	0.100872i	−0.998727	−	0.0504359i	$-0.983939\pi$
$823$		−	2.89381i		−	0.100872i	0.998727	−	0.0504359i	$-0.0160611\pi$
$824$	9.80468	+	9.80468i	0.341562	+	0.341562i
$825$	−27.2710	+	1.51196i	−0.949454	+	0.0526396i
$826$	−8.93448	−	8.93448i	−0.310870	−	0.310870i
$827$	22.3134	−	22.3134i	0.775914	−	0.775914i	−0.203219	−	0.979133i	$-0.565140\pi$
$827$	22.3134	−	22.3134i	0.775914	−	0.775914i	0.979133	+	0.203219i	$0.0651404\pi$
$828$	−7.96498	+	0.885911i	−0.276802	+	0.0307875i
$829$			41.7444i			1.44984i	0.688831	+	0.724922i	$0.258124\pi$
$829$			41.7444i			1.44984i	−0.688831	+	0.724922i	$0.741876\pi$
$830$	2.87721	−	2.87721i	0.0998695	−	0.0998695i
$831$	19.6570	+	17.5919i	0.681895	+	0.610255i
$832$	3.43870	−	1.08413i	0.119215	−	0.0375855i
$833$			5.36595i			0.185919i
$834$	−4.31380	+	0.239166i	−0.149375	+	0.00828163i
$835$	5.63145			0.194884
$836$	18.9576			0.655661
$837$	47.8364	−	8.02226i	1.65347	−	0.277290i
$838$	13.7610	−	13.7610i	0.475366	−	0.475366i
$839$	−35.6454	+	35.6454i	−1.23061	+	1.23061i	−0.266887	+	0.963728i	$0.585995\pi$
$839$	−35.6454	+	35.6454i	−1.23061	+	1.23061i	−0.963728	+	0.266887i	$0.914005\pi$
$840$	1.50817	−	0.0836158i	0.0520367	−	0.00288502i
$841$	19.9992			0.689627
$842$	−17.4933			−0.602858
$843$	−2.69449	−	48.6001i	−0.0928031	−	1.67388i
$844$			2.49834i			0.0859965i
$845$	11.1647	+	1.96916i	0.384077	+	0.0677411i
$846$	1.62278	+	14.5900i	0.0557925	+	0.501614i
$847$	2.00486	−	2.00486i	0.0688878	−	0.0688878i
$848$		−	0.464507i		−	0.0159512i
$849$	15.4060	+	13.7874i	0.528731	+	0.473183i
$850$	16.0859	−	16.0859i	0.551741	−	0.551741i
$851$	−11.8868	−	11.8868i	−0.407474	−	0.407474i
$852$	0.00132902	+	0.0239713i	4.55313e−5	+	0.000821243i
$853$	5.75295	+	5.75295i	0.196977	+	0.196977i	0.798703	−	0.601726i	$-0.205520\pi$
$853$	5.75295	+	5.75295i	0.196977	+	0.196977i	−0.601726	+	0.798703i	$0.705520\pi$
$854$		−	8.37831i		−	0.286700i
$855$	1.47401	+	13.2524i	0.0504102	+	0.453223i
$856$	1.95960	+	1.95960i	0.0669778	+	0.0669778i
$857$	23.4108			0.799697			0.399849	−	0.916581i	$-0.369063\pi$
$857$	23.4108			0.799697			0.399849	+	0.916581i	$0.369063\pi$
$858$	21.1661	+	9.56931i	0.722600	+	0.326691i
$859$	56.2528			1.91932			0.959660	−	0.281162i	$-0.0907198\pi$
$859$	56.2528			1.91932			0.959660	+	0.281162i	$0.0907198\pi$
$860$	0.376287	+	0.376287i	0.0128313	+	0.0128313i
$861$	−15.4015	−	13.7834i	−0.524881	−	0.469737i
$862$		−	11.7505i		−	0.400223i
$863$	11.3466	+	11.3466i	0.386244	+	0.386244i	0.873345	−	0.487101i	$-0.161946\pi$
$863$	11.3466	+	11.3466i	0.386244	+	0.386244i	−0.487101	+	0.873345i	$0.661946\pi$
$864$	0.859404	+	5.12459i	0.0292375	+	0.174342i
$865$	12.6727	+	12.6727i	0.430883	+	0.430883i
$866$	−7.00089	+	7.00089i	−0.237900	+	0.237900i
$867$	13.6223	−	15.2214i	0.462636	−	0.516946i
$868$		−	9.33468i		−	0.316840i
$869$	16.0915	−	16.0915i	0.545866	−	0.545866i
$870$	3.02207	−	3.37684i	0.102458	−	0.114485i
$871$	8.04757	+	4.18953i	0.272682	+	0.141957i
$872$			3.15249i			0.106757i
$873$	17.9485	+	14.3555i	0.607465	+	0.485859i
$874$	−13.6151			−0.460538
$875$	−8.05755			−0.272395
$876$	1.51027	+	27.2405i	0.0510271	+	0.920370i
$877$	24.5954	−	24.5954i	0.830527	−	0.830527i	−0.157062	−	0.987589i	$-0.550202\pi$
$877$	24.5954	−	24.5954i	0.830527	−	0.830527i	0.987589	+	0.157062i	$0.0502022\pi$
$878$	11.8372	−	11.8372i	0.399486	−	0.399486i
$879$	1.63153	+	29.4277i	0.0550301	+	0.992570i
$880$	3.24377			0.109347
$881$	−1.28707			−0.0433624			−0.0216812	−	0.999765i	$-0.506902\pi$
$881$	−1.28707			−0.0433624			−0.0216812	+	0.999765i	$0.506902\pi$
$882$	2.34282	+	1.87382i	0.0788868	+	0.0630948i
$883$		−	31.8432i		−	1.07161i	−0.844342	−	0.535804i	$-0.820009\pi$
$883$		−	31.8432i		−	1.07161i	0.844342	−	0.535804i	$-0.179991\pi$
$884$	−18.4519	+	5.81740i	−0.620605	+	0.195660i
$885$	12.7276	−	14.2218i	0.427835	−	0.478059i
$886$	−5.35019	+	5.35019i	−0.179743	+	0.179743i
$887$			31.2740i			1.05008i	0.851078	+	0.525039i	$0.175949\pi$
$887$			31.2740i			1.05008i	−0.851078	+	0.525039i	$0.824051\pi$
$888$	−7.26865	+	8.12194i	−0.243920	+	0.272554i
$889$	15.0861	−	15.0861i	0.505971	−	0.505971i
$890$	7.76224	+	7.76224i	0.260191	+	0.260191i
$891$	−17.8914	+	28.2941i	−0.599384	+	0.947889i
$892$	6.63646	+	6.63646i	0.222205	+	0.222205i
$893$			24.9397i			0.834577i
$894$	22.4723	+	20.1114i	0.751587	+	0.672626i
$895$	−7.72891	−	7.72891i	−0.258349	−	0.258349i
$896$	1.00000			0.0334077
$897$	−15.2013	−	6.87257i	−0.507556	−	0.229469i
$898$	−17.1799			−0.573301
$899$	−19.8027	−	19.8027i	−0.660458	−	0.660458i
$900$	−1.40595	−	12.6405i	−0.0468650	−	0.421350i
$901$			2.49252i			0.0830379i
$902$	−31.3854	−	31.3854i	−1.04502	−	1.04502i
$903$	0.0585075	+	1.05529i	0.00194701	+	0.0351179i
$904$	−9.75798	−	9.75798i	−0.324546	−	0.324546i
$905$	−8.18540	+	8.18540i	−0.272092	+	0.272092i
$906$	−6.36875	−	5.69965i	−0.211587	−	0.189358i
$907$			31.7804i			1.05525i	0.849477	+	0.527626i	$0.176918\pi$
$907$			31.7804i			1.05525i	−0.849477	+	0.527626i	$0.823082\pi$
$908$	−8.75850	+	8.75850i	−0.290661	+	0.290661i
$909$	3.23047	+	29.0443i	0.107148	+	0.963338i
$910$	2.78902	+	1.45195i	0.0924550	+	0.0481317i
$911$			27.7211i			0.918441i	0.888322	+	0.459220i	$0.151871\pi$
$911$			27.7211i			0.918441i	−0.888322	+	0.459220i	$0.848129\pi$
$912$	0.488676	+	8.81419i	0.0161817	+	0.291867i
$913$	17.3550			0.574368
$914$	24.0740			0.796296
$915$	12.6359	−	0.700560i	0.417730	−	0.0231598i
$916$	−4.24481	+	4.24481i	−0.140252	+	0.140252i
$917$	5.77274	−	5.77274i	0.190633	−	0.190633i
$918$	−4.61152	−	27.4983i	−0.152203	−	0.907580i
$919$	−11.8757			−0.391742			−0.195871	−	0.980630i	$-0.562753\pi$
$919$	−11.8757			−0.391742			−0.195871	+	0.980630i	$0.562753\pi$
$920$	−2.32964			−0.0768059
$921$	−21.9438	+	1.21661i	−0.723074	+	0.0400887i
$922$			6.05569i			0.199434i
$923$	−0.0230777	+	0.0443295i	−0.000759613	+	0.00145912i
$924$	4.80074	+	4.29637i	0.157933	+	0.141340i
$925$	18.8644	−	18.8644i	0.620259	−	0.620259i
$926$		−	20.6592i		−	0.678904i
$927$	−41.3428	+	4.59839i	−1.35787	+	0.151031i
$928$	2.12142	−	2.12142i	0.0696389	−	0.0696389i
$929$	−7.35645	−	7.35645i	−0.241357	−	0.241357i	0.576054	−	0.817411i	$-0.304592\pi$
$929$	−7.35645	−	7.35645i	−0.241357	−	0.241357i	−0.817411	+	0.576054i	$0.804592\pi$
$930$	14.0783	−	0.780527i	0.461645	−	0.0255945i
$931$	3.60391	+	3.60391i	0.118113	+	0.118113i
$932$		−	5.81776i		−	0.190567i
$933$	31.9144	−	35.6609i	1.04483	−	1.16749i
$934$	−22.0954	−	22.0954i	−0.722985	−	0.722985i
$935$	−17.4059			−0.569234
$936$	−3.90358	+	10.0877i	−0.127592	+	0.329727i
$937$	11.7655			0.384363			0.192182	−	0.981359i	$-0.438444\pi$
$937$	11.7655			0.384363			0.192182	+	0.981359i	$0.438444\pi$
$938$	1.77932	+	1.77932i	0.0580969	+	0.0580969i
$939$	16.5067	−	18.4445i	0.538676	−	0.601913i
$940$			4.26736i			0.139186i
$941$	6.67209	+	6.67209i	0.217504	+	0.217504i	0.807446	−	0.589942i	$-0.200849\pi$
$941$	6.67209	+	6.67209i	0.217504	+	0.217504i	−0.589942	+	0.807446i	$0.700849\pi$
$942$	1.57620	−	0.0873875i	0.0513553	−	0.00284724i
$943$	22.5407	+	22.5407i	0.734025	+	0.734025i
$944$	8.93448	−	8.93448i	0.290793	−	0.290793i
$945$	−2.63014	+	3.69005i	−0.0855584	+	0.120037i
$946$			2.26972i			0.0737951i
$947$	36.4072	−	36.4072i	1.18308	−	1.18308i	0.204133	−	0.978943i	$-0.434562\pi$
$947$	36.4072	−	36.4072i	1.18308	−	1.18308i	0.978943	−	0.204133i	$-0.0654376\pi$
$948$	7.89643	+	7.06683i	0.256464	+	0.229520i
$949$	−26.2251	+	50.3751i	−0.851301	+	1.63524i
$950$		−	21.6073i		−	0.701034i
$951$	−6.64356	+	0.368332i	−0.215432	+	0.0119440i
$952$	−5.36595			−0.173912
$953$	−8.94193			−0.289657			−0.144829	−	0.989457i	$-0.546263\pi$
$953$	−8.94193			−0.289657			−0.144829	+	0.989457i	$0.546263\pi$
$954$	1.08825	+	0.870402i	0.0352336	+	0.0281803i
$955$	−1.97972	+	1.97972i	−0.0640623	+	0.0640623i
$956$	−6.19473	+	6.19473i	−0.200352	+	0.200352i
$957$	19.2988	−	1.06996i	0.623840	−	0.0345869i
$958$	15.3323			0.495365
$959$	13.0378			0.421012
$960$	0.0836158	+	1.50817i	0.00269869	+	0.0486759i
$961$		−	56.1363i		−	1.81085i
$962$	−21.6392	+	6.82226i	−0.697675	+	0.219959i
$963$	−8.26294	+	0.919052i	−0.266269	+	0.0296160i
$964$	−19.2493	+	19.2493i	−0.619979	+	0.619979i
$965$		−	20.0297i		−	0.644780i
$966$	−3.44784	−	3.08561i	−0.110932	−	0.0992778i
$967$	27.9937	−	27.9937i	0.900216	−	0.900216i	−0.0952382	−	0.995455i	$-0.530361\pi$
$967$	27.9937	−	27.9937i	0.900216	−	0.900216i	0.995455	+	0.0952382i	$0.0303613\pi$
$968$	2.00486	+	2.00486i	0.0644386	+	0.0644386i
$969$	−2.62221	−	47.2966i	−0.0842377	−	1.51938i
$970$	4.72422	+	4.72422i	0.151686	+	0.151686i
$971$			1.42350i			0.0456822i	0.999739	+	0.0228411i	$0.00727119\pi$
$971$			1.42350i			0.0456822i	−0.999739	+	0.0228411i	$0.992729\pi$
$972$	−13.6164	−	7.58913i	−0.436745	−	0.243421i
$973$	−1.76381	−	1.76381i	−0.0565451	−	0.0565451i
$974$	25.0523			0.802727
$975$	10.9068	−	24.1246i	0.349298	−	0.772605i
$976$	8.37831			0.268183
$977$	12.1408	+	12.1408i	0.388418	+	0.388418i	0.874123	−	0.485705i	$-0.161437\pi$
$977$	12.1408	+	12.1408i	0.388418	+	0.388418i	−0.485705	+	0.874123i	$0.661437\pi$
$978$	−24.6052	−	22.0202i	−0.786789	−	0.704129i
$979$			46.8210i			1.49641i
$980$	0.616653	+	0.616653i	0.0196982	+	0.0196982i
$981$	−7.38571	−	5.90720i	−0.235808	−	0.188602i
$982$	6.30723	+	6.30723i	0.201272	+	0.201272i
$983$	12.3019	−	12.3019i	0.392371	−	0.392371i	−0.483161	−	0.875532i	$-0.660511\pi$
$983$	12.3019	−	12.3019i	0.392371	−	0.392371i	0.875532	+	0.483161i	$0.160511\pi$
$984$	13.7834	−	15.4015i	0.439399	−	0.490981i
$985$			18.3721i			0.585382i
$986$	−11.3834	+	11.3834i	−0.362522	+	0.362522i
$987$	−5.65212	+	6.31564i	−0.179909	+	0.201029i
$988$	−8.48564	+	16.2999i	−0.269964	+	0.518568i
$989$		−	1.63009i		−	0.0518339i
$990$	−6.07824	+	7.59956i	−0.193179	+	0.241530i
$991$	−1.40127			−0.0445127			−0.0222564	−	0.999752i	$-0.507085\pi$
$991$	−1.40127			−0.0445127			−0.0222564	+	0.999752i	$0.507085\pi$
$992$	9.33468			0.296376
$993$	1.44277	+	26.0230i	0.0457849	+	0.825816i
$994$	−0.00980127	+	0.00980127i	−0.000310877	+	0.000310877i
$995$	−9.35091	+	9.35091i	−0.296444	+	0.296444i
$996$	0.447367	+	8.06911i	0.0141754	+	0.255679i
$997$	−36.0164			−1.14065			−0.570325	−	0.821419i	$-0.693183\pi$
$997$	−36.0164			−1.14065			−0.570325	+	0.821419i	$0.693183\pi$
$998$	−28.4274			−0.899854
$999$	−5.40809	−	32.2482i	−0.171104	−	1.02029i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.d.239.9	yes	20
3.2	odd	2		546.2.p.c.239.4	✓	20
13.8	odd	4		546.2.p.c.281.4	yes	20
39.8	even	4	inner	546.2.p.d.281.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.4	✓	20	3.2	odd	2
546.2.p.c.281.4	yes	20	13.8	odd	4
546.2.p.d.239.9	yes	20	1.1	even	1	trivial
546.2.p.d.281.9	yes	20	39.8	even	4	inner

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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.15507 - 1.29067i) q^{3} +1.00000i q^{4} +(-0.616653 - 0.616653i) q^{5} +(1.72939 - 0.0958811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.331633 - 2.98161i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(1.15507 - 1.29067i) q^{3} +1.00000i q^{4} +(-0.616653 - 0.616653i) q^{5} +(1.72939 - 0.0958811i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-0.331633 - 2.98161i) q^{9} -0.872079i q^{10} +(2.63014 - 2.63014i) q^{11} +(1.29067 + 1.15507i) q^{12} +(1.08413 + 3.43870i) q^{13} +1.00000i q^{14} +(-1.50817 + 0.0836158i) q^{15} -1.00000 q^{16} +5.36595 q^{17} +(1.87382 - 2.34282i) q^{18} +(3.60391 - 3.60391i) q^{19} +(0.616653 - 0.616653i) q^{20} +(1.72939 - 0.0958811i) q^{21} +3.71958 q^{22} -2.67136 q^{23} +(0.0958811 + 1.72939i) q^{24} -4.23948i q^{25} +(-1.66493 + 3.19813i) q^{26} +(-4.23132 - 3.01594i) q^{27} +(-0.707107 + 0.707107i) q^{28} +3.00014i q^{29} +(-1.12556 - 1.00731i) q^{30} +(-6.60062 + 6.60062i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.356638 - 6.43263i) q^{33} +(3.79430 + 3.79430i) q^{34} -0.872079i q^{35} +(2.98161 - 0.331633i) q^{36} +(4.44970 + 4.44970i) q^{37} +5.09669 q^{38} +(5.69046 + 2.57268i) q^{39} +0.872079 q^{40} +(-8.43789 - 8.43789i) q^{41} +(1.29067 + 1.15507i) q^{42} +0.610209i q^{43} +(2.63014 + 2.63014i) q^{44} +(-1.63412 + 2.04312i) q^{45} +(-1.88894 - 1.88894i) q^{46} +(-3.46010 + 3.46010i) q^{47} +(-1.15507 + 1.29067i) q^{48} +1.00000i q^{49} +(2.99776 - 2.99776i) q^{50} +(6.19805 - 6.92565i) q^{51} +(-3.43870 + 1.08413i) q^{52} +0.464507i q^{53} +(-0.859404 - 5.12459i) q^{54} -3.24377 q^{55} -1.00000 q^{56} +(-0.488676 - 8.81419i) q^{57} +(-2.12142 + 2.12142i) q^{58} +(-8.93448 + 8.93448i) q^{59} +(-0.0836158 - 1.50817i) q^{60} -8.37831 q^{61} -9.33468 q^{62} +(1.87382 - 2.34282i) q^{63} -1.00000i q^{64} +(1.45195 - 2.78902i) q^{65} +(4.29637 - 4.80074i) q^{66} +(1.77932 - 1.77932i) q^{67} +5.36595i q^{68} +(-3.08561 + 3.44784i) q^{69} +(0.616653 - 0.616653i) q^{70} +(0.00980127 + 0.00980127i) q^{71} +(2.34282 + 1.87382i) q^{72} +(11.1380 + 11.1380i) q^{73} +6.29283i q^{74} +(-5.47175 - 4.89689i) q^{75} +(3.60391 + 3.60391i) q^{76} +3.71958 q^{77} +(2.20460 + 5.84292i) q^{78} +6.11811 q^{79} +(0.616653 + 0.616653i) q^{80} +(-8.78004 + 1.97760i) q^{81} -11.9330i q^{82} +(3.29926 + 3.29926i) q^{83} +(0.0958811 + 1.72939i) q^{84} +(-3.30893 - 3.30893i) q^{85} +(-0.431483 + 0.431483i) q^{86} +(3.87217 + 3.46536i) q^{87} +3.71958i q^{88} +(-8.90085 + 8.90085i) q^{89} +(-2.60020 + 0.289210i) q^{90} +(-1.66493 + 3.19813i) q^{91} -2.67136i q^{92} +(0.895019 + 16.1433i) q^{93} -4.89332 q^{94} -4.44472 q^{95} +(-1.72939 + 0.0958811i) q^{96} +(-5.41720 + 5.41720i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(-8.71431 - 6.96983i) 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	\( 20 q + 4 q^{5} + 4 q^{6} - 8 q^{9} + 16 q^{11} + 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} - 12 q^{17} - 16 q^{18} + 12 q^{19} - 4 q^{20} + 4 q^{21} - 12 q^{22} + 4 q^{23} - 4 q^{24} + 24 q^{27} - 12 q^{30} - 8 q^{31} + 16 q^{33} - 4 q^{34} + 32 q^{37} + 4 q^{38} + 8 q^{39} - 4 q^{40} - 8 q^{41} + 8 q^{42} + 16 q^{44} - 32 q^{45} - 8 q^{46} - 32 q^{50} + 8 q^{51} - 8 q^{52} + 20 q^{54} + 28 q^{55} - 20 q^{56} + 36 q^{57} - 4 q^{58} - 20 q^{59} - 4 q^{60} - 4 q^{61} - 48 q^{62} - 16 q^{63} - 52 q^{65} - 36 q^{67} - 68 q^{69} - 4 q^{70} + 28 q^{71} - 8 q^{72} - 24 q^{73} + 76 q^{75} + 12 q^{76} - 12 q^{77} + 56 q^{78} - 64 q^{79} - 4 q^{80} + 32 q^{81} + 24 q^{83} - 4 q^{84} + 24 q^{85} - 4 q^{86} + 4 q^{87} + 4 q^{89} + 8 q^{90} + 16 q^{93} - 40 q^{94} + 76 q^{95} - 4 q^{96} + 32 q^{97} - 36 q^{99}+O(q^{100}) \) 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 - 16 * 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 + 16 * q^33 - 4 * q^34 + 32 * q^37 + 4 * q^38 + 8 * q^39 - 4 * q^40 - 8 * q^41 + 8 * q^42 + 16 * q^44 - 32 * q^45 - 8 * q^46 - 32 * q^50 + 8 * q^51 - 8 * q^52 + 20 * 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 - 16 * q^63 - 52 * q^65 - 36 * q^67 - 68 * q^69 - 4 * q^70 + 28 * q^71 - 8 * q^72 - 24 * q^73 + 76 * q^75 + 12 * q^76 - 12 * q^77 + 56 * 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 + 16 * q^93 - 40 * q^94 + 76 * q^95 - 4 * q^96 + 32 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more