LMFDB - Embedded newform 546.2.p.d.239.7

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			239.7
Root			$0.831607 + 1.51935i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.d.281.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(-0.486309 - 1.66238i) q^{3} +1.00000i q^{4} +(2.72859 + 2.72859i) q^{5} +(0.831607 - 1.51935i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52701 + 1.61686i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(-0.486309 - 1.66238i) q^{3} +1.00000i q^{4} +(2.72859 + 2.72859i) q^{5} +(0.831607 - 1.51935i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52701 + 1.61686i) q^{9} +3.85881i q^{10} +(-0.0114588 + 0.0114588i) q^{11} +(1.66238 - 0.486309i) q^{12} +(1.73087 + 3.16292i) q^{13} +1.00000i q^{14} +(3.20901 - 5.86288i) q^{15} -1.00000 q^{16} -5.61037 q^{17} +(-2.93016 - 0.643571i) q^{18} +(-0.157765 + 0.157765i) q^{19} +(-2.72859 + 2.72859i) q^{20} +(0.831607 - 1.51935i) q^{21} -0.0162051 q^{22} +2.57099 q^{23} +(1.51935 + 0.831607i) q^{24} +9.89038i q^{25} +(-1.01261 + 3.46044i) q^{26} +(3.91674 + 3.41455i) q^{27} +(-0.707107 + 0.707107i) q^{28} -7.70551i q^{29} +(6.41480 - 1.87657i) q^{30} +(6.66648 - 6.66648i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.0246213 + 0.0134763i) q^{33} +(-3.96713 - 3.96713i) q^{34} +3.85881i q^{35} +(-1.61686 - 2.52701i) q^{36} +(7.86287 + 7.86287i) q^{37} -0.223113 q^{38} +(4.41624 - 4.41552i) q^{39} -3.85881 q^{40} +(-5.18774 - 5.18774i) q^{41} +(1.66238 - 0.486309i) q^{42} +5.09898i q^{43} +(-0.0114588 - 0.0114588i) q^{44} +(-11.3069 - 2.48342i) q^{45} +(1.81796 + 1.81796i) q^{46} +(3.31273 - 3.31273i) q^{47} +(0.486309 + 1.66238i) q^{48} +1.00000i q^{49} +(-6.99356 + 6.99356i) q^{50} +(2.72837 + 9.32656i) q^{51} +(-3.16292 + 1.73087i) q^{52} -2.49125i q^{53} +(0.355103 + 5.18400i) q^{54} -0.0625325 q^{55} -1.00000 q^{56} +(0.338988 + 0.185543i) q^{57} +(5.44862 - 5.44862i) q^{58} +(-2.10029 + 2.10029i) q^{59} +(5.86288 + 3.20901i) q^{60} +1.82875 q^{61} +9.42782 q^{62} +(-2.93016 - 0.643571i) q^{63} -1.00000i q^{64} +(-3.90748 + 13.3531i) q^{65} +(0.00788071 + 0.0269391i) q^{66} +(8.61829 - 8.61829i) q^{67} -5.61037i q^{68} +(-1.25029 - 4.27396i) q^{69} +(-2.72859 + 2.72859i) q^{70} +(2.76005 + 2.76005i) q^{71} +(0.643571 - 2.93016i) q^{72} +(-9.83977 - 9.83977i) q^{73} +11.1198i q^{74} +(16.4416 - 4.80978i) q^{75} +(-0.157765 - 0.157765i) q^{76} -0.0162051 q^{77} +(6.24500 + 0.000504619i) q^{78} -5.90280 q^{79} +(-2.72859 - 2.72859i) q^{80} +(3.77153 - 8.17163i) q^{81} -7.33658i q^{82} +(-11.9527 - 11.9527i) q^{83} +(1.51935 + 0.831607i) q^{84} +(-15.3084 - 15.3084i) q^{85} +(-3.60552 + 3.60552i) q^{86} +(-12.8095 + 3.74726i) q^{87} -0.0162051i q^{88} +(-5.15703 + 5.15703i) q^{89} +(-6.23915 - 9.75123i) q^{90} +(-1.01261 + 3.46044i) q^{91} +2.57099i q^{92} +(-14.3242 - 7.84024i) q^{93} +4.68491 q^{94} -0.860951 q^{95} +(-0.831607 + 1.51935i) q^{96} +(5.94479 - 5.94479i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(0.0104292 - 0.0474836i) 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
$3$	−0.486309	−	1.66238i	−0.280771	−	0.959775i
$3$	−0.486309	−	1.66238i	−0.280771	−	0.959775i
$4$			1.00000i			0.500000i
$5$	2.72859	+	2.72859i	1.22026	+	1.22026i	0.967539	+	0.252723i	$0.0813260\pi$
$5$	2.72859	+	2.72859i	1.22026	+	1.22026i	0.252723	+	0.967539i	$0.418674\pi$
$6$	0.831607	−	1.51935i	0.339502	−	0.620273i
$7$	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
$9$	−2.52701	+	1.61686i	−0.842336	+	0.538953i
$10$			3.85881i			1.22026i
$11$	−0.0114588	+	0.0114588i	−0.00345495	+	0.00345495i	−0.708832	−	0.705377i	$-0.750778\pi$
$11$	−0.0114588	+	0.0114588i	−0.00345495	+	0.00345495i	0.705377	+	0.708832i	$0.250778\pi$
$12$	1.66238	−	0.486309i	0.479887	−	0.140385i
$13$	1.73087	+	3.16292i	0.480058	+	0.877237i
$13$	1.73087	+	3.16292i	0.480058	+	0.877237i
$14$			1.00000i			0.267261i
$15$	3.20901	−	5.86288i	0.828563	−	1.51379i
$16$	−1.00000			−0.250000
$17$	−5.61037			−1.36071			−0.680357	−	0.732881i	$-0.738175\pi$
$17$	−5.61037			−1.36071			−0.680357	+	0.732881i	$0.738175\pi$
$18$	−2.93016	−	0.643571i	−0.690644	−	0.151691i
$19$	−0.157765	+	0.157765i	−0.0361938	+	0.0361938i	−0.724972	−	0.688778i	$-0.758147\pi$
$19$	−0.157765	+	0.157765i	−0.0361938	+	0.0361938i	0.688778	+	0.724972i	$0.258147\pi$
$20$	−2.72859	+	2.72859i	−0.610131	+	0.610131i
$21$	0.831607	−	1.51935i	0.181472	−	0.331550i
$22$	−0.0162051			−0.00345495
$23$	2.57099			0.536088			0.268044	−	0.963407i	$-0.413623\pi$
$23$	2.57099			0.536088			0.268044	+	0.963407i	$0.413623\pi$
$24$	1.51935	+	0.831607i	0.310136	+	0.169751i
$25$			9.89038i			1.97808i
$26$	−1.01261	+	3.46044i	−0.198590	+	0.678647i
$27$	3.91674	+	3.41455i	0.753777	+	0.657130i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$		−	7.70551i		−	1.43088i	−0.698675	−	0.715439i	$-0.746227\pi$
$29$		−	7.70551i		−	1.43088i	0.698675	−	0.715439i	$-0.253773\pi$
$30$	6.41480	−	1.87657i	1.17118	−	0.342614i
$31$	6.66648	−	6.66648i	1.19733	−	1.19733i	0.222373	−	0.974962i	$-0.428620\pi$
$31$	6.66648	−	6.66648i	1.19733	−	1.19733i	0.974962	−	0.222373i	$-0.0713802\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	0.0246213	+	0.0134763i	0.00428602	+	0.00234592i
$34$	−3.96713	−	3.96713i	−0.680357	−	0.680357i
$35$			3.85881i			0.652257i
$36$	−1.61686	−	2.52701i	−0.269477	−	0.421168i
$37$	7.86287	+	7.86287i	1.29265	+	1.29265i	0.933144	+	0.359503i	$0.117054\pi$
$37$	7.86287	+	7.86287i	1.29265	+	1.29265i	0.359503	+	0.933144i	$0.382946\pi$
$38$	−0.223113			−0.0361938
$39$	4.41624	−	4.41552i	0.707164	−	0.707050i
$40$	−3.85881			−0.610131
$41$	−5.18774	−	5.18774i	−0.810189	−	0.810189i	0.174473	−	0.984662i	$-0.444178\pi$
$41$	−5.18774	−	5.18774i	−0.810189	−	0.810189i	−0.984662	+	0.174473i	$0.944178\pi$
$42$	1.66238	−	0.486309i	0.256511	−	0.0750391i
$43$			5.09898i			0.777587i	0.921325	+	0.388793i	$0.127108\pi$
$43$			5.09898i			0.777587i	−0.921325	+	0.388793i	$0.872892\pi$
$44$	−0.0114588	−	0.0114588i	−0.00172747	−	0.00172747i
$45$	−11.3069	−	2.48342i	−1.68553	−	0.370206i
$46$	1.81796	+	1.81796i	0.268044	+	0.268044i
$47$	3.31273	−	3.31273i	0.483211	−	0.483211i	−0.422944	−	0.906156i	$-0.639003\pi$
$47$	3.31273	−	3.31273i	0.483211	−	0.483211i	0.906156	+	0.422944i	$0.139003\pi$
$48$	0.486309	+	1.66238i	0.0701927	+	0.239944i
$49$			1.00000i			0.142857i
$50$	−6.99356	+	6.99356i	−0.989038	+	0.989038i
$51$	2.72837	+	9.32656i	0.382049	+	1.30598i
$52$	−3.16292	+	1.73087i	−0.438618	+	0.240029i
$53$		−	2.49125i		−	0.342200i	−0.985254	−	0.171100i	$-0.945268\pi$
$53$		−	2.49125i		−	0.342200i	0.985254	−	0.171100i	$-0.0547321\pi$
$54$	0.355103	+	5.18400i	0.0483234	+	0.705454i
$55$	−0.0625325			−0.00843188
$56$	−1.00000			−0.133631
$57$	0.338988	+	0.185543i	0.0449000	+	0.0245757i
$58$	5.44862	−	5.44862i	0.715439	−	0.715439i
$59$	−2.10029	+	2.10029i	−0.273435	+	0.273435i	−0.830481	−	0.557047i	$-0.811934\pi$
$59$	−2.10029	+	2.10029i	−0.273435	+	0.273435i	0.557047	+	0.830481i	$0.311934\pi$
$60$	5.86288	+	3.20901i	0.756895	+	0.414281i
$61$	1.82875			0.234148			0.117074	−	0.993123i	$-0.462649\pi$
$61$	1.82875			0.234148			0.117074	+	0.993123i	$0.462649\pi$
$62$	9.42782			1.19733
$63$	−2.93016	−	0.643571i	−0.369165	−	0.0810823i
$64$		−	1.00000i		−	0.125000i
$65$	−3.90748	+	13.3531i	−0.484663	+	1.65625i
$66$	0.00788071	+	0.0269391i	0.000970048	+	0.00331597i
$67$	8.61829	−	8.61829i	1.05289	−	1.05289i	0.0543710	−	0.998521i	$-0.482685\pi$
$67$	8.61829	−	8.61829i	1.05289	−	1.05289i	0.998521	−	0.0543710i	$-0.0173154\pi$
$68$		−	5.61037i		−	0.680357i
$69$	−1.25029	−	4.27396i	−0.150518	−	0.514524i
$70$	−2.72859	+	2.72859i	−0.326129	+	0.326129i
$71$	2.76005	+	2.76005i	0.327557	+	0.327557i	0.851657	−	0.524100i	$-0.175598\pi$
$71$	2.76005	+	2.76005i	0.327557	+	0.327557i	−0.524100	+	0.851657i	$0.675598\pi$
$72$	0.643571	−	2.93016i	0.0758456	−	0.345322i
$73$	−9.83977	−	9.83977i	−1.15166	−	1.15166i	−0.986220	−	0.165438i	$-0.947096\pi$
$73$	−9.83977	−	9.83977i	−1.15166	−	1.15166i	−0.165438	−	0.986220i	$-0.552904\pi$
$74$			11.1198i			1.29265i
$75$	16.4416	−	4.80978i	1.89851	−	0.555386i
$76$	−0.157765	−	0.157765i	−0.0180969	−	0.0180969i
$77$	−0.0162051			−0.00184675
$78$	6.24500		0.000504619i	0.707107		5.71369e-5i
$79$	−5.90280			−0.664117			−0.332058	−	0.943259i	$-0.607743\pi$
$79$	−5.90280			−0.664117			−0.332058	+	0.943259i	$0.607743\pi$
$80$	−2.72859	−	2.72859i	−0.305065	−	0.305065i
$81$	3.77153	−	8.17163i	0.419059	−	0.907959i
$82$		−	7.33658i		−	0.810189i
$83$	−11.9527	−	11.9527i	−1.31197	−	1.31197i	−0.919958	−	0.392017i	$-0.871778\pi$
$83$	−11.9527	−	11.9527i	−1.31197	−	1.31197i	−0.392017	−	0.919958i	$-0.628222\pi$
$84$	1.51935	+	0.831607i	0.165775	+	0.0907358i
$85$	−15.3084	−	15.3084i	−1.66043	−	1.66043i
$86$	−3.60552	+	3.60552i	−0.388793	+	0.388793i
$87$	−12.8095	+	3.74726i	−1.37332	+	0.401749i
$88$		−	0.0162051i		−	0.00172747i
$89$	−5.15703	+	5.15703i	−0.546645	+	0.546645i	−0.925469	−	0.378824i	$-0.876329\pi$
$89$	−5.15703	+	5.15703i	−0.546645	+	0.546645i	0.378824	+	0.925469i	$0.376329\pi$
$90$	−6.23915	−	9.75123i	−0.657664	−	1.02787i
$91$	−1.01261	+	3.46044i	−0.106151	+	0.362752i
$92$			2.57099i			0.268044i
$93$	−14.3242	−	7.84024i	−1.48535	−	0.812995i
$94$	4.68491			0.483211
$95$	−0.860951			−0.0883318
$96$	−0.831607	+	1.51935i	−0.0848755	+	0.155068i
$97$	5.94479	−	5.94479i	0.603602	−	0.603602i	−0.337665	−	0.941266i	$-0.609637\pi$
$97$	5.94479	−	5.94479i	0.603602	−	0.603602i	0.941266	+	0.337665i	$0.109637\pi$
$98$	−0.707107	+	0.707107i	−0.0714286	+	0.0714286i
$99$	0.0104292	−	0.0474836i	0.00104817	−	0.00477228i
$100$	−9.89038			−0.989038
$101$	4.06932			0.404913			0.202456	−	0.979291i	$-0.435108\pi$
$101$	4.06932			0.404913			0.202456	+	0.979291i	$0.435108\pi$
$102$	−4.66562	+	8.52412i	−0.461965	+	0.844014i
$103$		−	17.5417i		−	1.72843i	−0.503118	−	0.864217i	$-0.667814\pi$
$103$		−	17.5417i		−	1.72843i	0.503118	−	0.864217i	$-0.332186\pi$
$104$	−3.46044	−	1.01261i	−0.339324	−	0.0992948i
$105$	6.41480	−	1.87657i	0.626020	−	0.183135i
$106$	1.76158	−	1.76158i	0.171100	−	0.171100i
$107$			0.228357i			0.0220761i	0.999939	+	0.0110381i	$0.00351360\pi$
$107$			0.228357i			0.0220761i	−0.999939	+	0.0110381i	$0.996486\pi$
$108$	−3.41455	+	3.91674i	−0.328565	+	0.376889i
$109$	−8.58774	+	8.58774i	−0.822556	+	0.822556i	−0.986474	−	0.163918i	$-0.947587\pi$
$109$	−8.58774	+	8.58774i	−0.822556	+	0.822556i	0.163918	+	0.986474i	$0.447587\pi$
$110$	−0.0442171	−	0.0442171i	−0.00421594	−	0.00421594i
$111$	9.24728	−	16.8948i	0.877713	−	1.60359i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$		−	2.22102i		−	0.208936i	−0.994528	−	0.104468i	$-0.966686\pi$
$113$		−	2.22102i		−	0.208936i	0.994528	−	0.104468i	$-0.0333140\pi$
$114$	0.108502	+	0.370899i	0.0101622	+	0.0347379i
$115$	7.01517	+	7.01517i	0.654168	+	0.654168i
$116$	7.70551			0.715439
$117$	−9.48793	−	5.19415i	−0.877159	−	0.480199i
$118$	−2.97026			−0.273435
$119$	−3.96713	−	3.96713i	−0.363666	−	0.363666i
$120$	1.87657	+	6.41480i	0.171307	+	0.585588i
$121$			10.9997i			0.999976i
$122$	1.29312	+	1.29312i	0.117074	+	0.117074i
$123$	−6.10115	+	11.1468i	−0.550122	+	1.00508i
$124$	6.66648	+	6.66648i	0.598667	+	0.598667i
$125$	−13.3438	+	13.3438i	−1.19351	+	1.19351i
$126$	−1.61686	−	2.52701i	−0.144041	−	0.225124i
$127$		−	4.31508i		−	0.382901i	−0.981502	−	0.191451i	$-0.938681\pi$
$127$		−	4.31508i		−	0.382901i	0.981502	−	0.191451i	$-0.0613192\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	8.47643	−	2.47968i	0.746308	−	0.218324i
$130$	−12.2051	+	6.67910i	−1.07046	+	0.585796i
$131$			0.111141i			0.00971047i	0.999988	+	0.00485524i	$0.00154548\pi$
$131$			0.111141i			0.00971047i	−0.999988	+	0.00485524i	$0.998455\pi$
$132$	−0.0134763	+	0.0246213i	−0.00117296	+	0.00214301i
$133$	−0.223113			−0.0193464
$134$	12.1881			1.05289
$135$	1.37027	+	20.0041i	0.117934	+	1.72168i
$136$	3.96713	−	3.96713i	0.340178	−	0.340178i
$137$	−1.03778	+	1.03778i	−0.0886637	+	0.0886637i	−0.750048	−	0.661384i	$-0.769969\pi$
$137$	−1.03778	+	1.03778i	−0.0886637	+	0.0886637i	0.661384	+	0.750048i	$0.269969\pi$
$138$	2.13805	−	3.90624i	0.182003	−	0.332521i
$139$	−13.8241			−1.17254			−0.586271	−	0.810115i	$-0.699405\pi$
$139$	−13.8241			−1.17254			−0.586271	+	0.810115i	$0.699405\pi$
$140$	−3.85881			−0.326129
$141$	−7.11802	−	3.89600i	−0.599446	−	0.328102i
$142$			3.90330i			0.327557i
$143$	−0.0560768	−	0.0164095i	−0.00468938	−	0.00137223i
$144$	2.52701	−	1.61686i	0.210584	−	0.134738i
$145$	21.0252	−	21.0252i	1.74605	−	1.74605i
$146$		−	13.9155i		−	1.15166i
$147$	1.66238	−	0.486309i	0.137111	−	0.0401101i
$148$	−7.86287	+	7.86287i	−0.646324	+	0.646324i
$149$	−9.29931	−	9.29931i	−0.761829	−	0.761829i	0.214823	−	0.976653i	$-0.431082\pi$
$149$	−9.29931	−	9.29931i	−0.761829	−	0.761829i	−0.976653	+	0.214823i	$0.931082\pi$
$150$	15.0270	+	8.22491i	1.22695	+	0.671561i
$151$	0.393892	+	0.393892i	0.0320545	+	0.0320545i	0.722952	−	0.690898i	$-0.242785\pi$
$151$	0.393892	+	0.393892i	0.0320545	+	0.0320545i	−0.690898	+	0.722952i	$0.742785\pi$
$152$		−	0.223113i		−	0.0180969i
$153$	14.1774	−	9.07118i	1.14618	−	0.733361i
$154$	−0.0114588	−	0.0114588i	−0.000923373	−	0.000923373i
$155$	36.3801			2.92212
$156$	4.41552	+	4.41624i	0.353525	+	0.353582i
$157$	10.2524			0.818233			0.409117	−	0.912482i	$-0.365837\pi$
$157$	10.2524			0.818233			0.409117	+	0.912482i	$0.365837\pi$
$158$	−4.17391	−	4.17391i	−0.332058	−	0.332058i
$159$	−4.14140	+	1.21152i	−0.328435	+	0.0960797i
$160$		−	3.85881i		−	0.305065i
$161$	1.81796	+	1.81796i	0.143276	+	0.143276i
$162$	8.44509	−	3.11134i	0.663509	−	0.244450i
$163$	3.68210	+	3.68210i	0.288404	+	0.288404i	0.836449	−	0.548045i	$-0.184628\pi$
$163$	3.68210	+	3.68210i	0.288404	+	0.288404i	−0.548045	+	0.836449i	$0.684628\pi$
$164$	5.18774	−	5.18774i	0.405095	−	0.405095i
$165$	0.0304101	+	0.103953i	0.00236742	+	0.00809270i
$166$		−	16.9036i		−	1.31197i
$167$	−0.964267	+	0.964267i	−0.0746173	+	0.0746173i	−0.743430	−	0.668813i	$-0.766803\pi$
$167$	−0.964267	+	0.964267i	−0.0746173	+	0.0746173i	0.668813	+	0.743430i	$0.266803\pi$
$168$	0.486309	+	1.66238i	0.0375196	+	0.128255i
$169$	−7.00816	+	10.9492i	−0.539089	+	0.842249i
$170$		−	21.6493i		−	1.66043i
$171$	0.143589	−	0.653757i	0.0109806	−	0.0499941i
$172$	−5.09898			−0.388793
$173$	11.1981			0.851378			0.425689	−	0.904870i	$-0.360032\pi$
$173$	11.1981			0.851378			0.425689	+	0.904870i	$0.360032\pi$
$174$	−11.7074	−	6.40796i	−0.887535	−	0.485786i
$175$	−6.99356	+	6.99356i	−0.528663	+	0.528663i
$176$	0.0114588	−	0.0114588i	0.000863737	−	0.000863737i
$177$	4.51287	+	2.47009i	0.339208	+	0.185663i
$178$	−7.29315			−0.546645
$179$	4.63389			0.346354			0.173177	−	0.984891i	$-0.444597\pi$
$179$	4.63389			0.346354			0.173177	+	0.984891i	$0.444597\pi$
$180$	2.48342	−	11.3069i	0.185103	−	0.842767i
$181$			15.3210i			1.13880i	0.822060	+	0.569401i	$0.192825\pi$
$181$			15.3210i			1.13880i	−0.822060	+	0.569401i	$0.807175\pi$
$182$	−3.16292	+	1.73087i	−0.234451	+	0.128301i
$183$	−0.889340	−	3.04008i	−0.0657419	−	0.224729i
$184$	−1.81796	+	1.81796i	−0.134022	+	0.134022i
$185$			42.9090i			3.15473i
$186$	−4.58483	−	15.6726i	−0.336176	−	1.14917i
$187$	0.0642879	−	0.0642879i	0.00470119	−	0.00470119i
$188$	3.31273	+	3.31273i	0.241606	+	0.241606i
$189$	0.355103	+	5.18400i	0.0258299	+	0.377081i
$190$	−0.608785	−	0.608785i	−0.0441659	−	0.0441659i
$191$		−	12.6760i		−	0.917203i	−0.888642	−	0.458601i	$-0.848351\pi$
$191$		−	12.6760i		−	0.917203i	0.888642	−	0.458601i	$-0.151649\pi$
$192$	−1.66238	+	0.486309i	−0.119972	+	0.0350963i
$193$	5.53338	+	5.53338i	0.398301	+	0.398301i	0.877634	−	0.479332i	$-0.159121\pi$
$193$	5.53338	+	5.53338i	0.398301	+	0.398301i	−0.479332	+	0.877634i	$0.659121\pi$
$194$	8.40720			0.603602
$195$	24.0982	+	0.00194723i	1.72571	+	0.000139444i
$196$	−1.00000			−0.0714286
$197$	17.4414	+	17.4414i	1.24265	+	1.24265i	0.958899	+	0.283747i	$0.0915776\pi$
$197$	17.4414	+	17.4414i	1.24265	+	1.24265i	0.283747	+	0.958899i	$0.408422\pi$
$198$	0.0409505	−	0.0262014i	0.00291022	−	0.00186206i
$199$			16.2501i			1.15194i	0.817471	+	0.575970i	$0.195376\pi$
$199$			16.2501i			1.15194i	−0.817471	+	0.575970i	$0.804624\pi$
$200$	−6.99356	−	6.99356i	−0.494519	−	0.494519i
$201$	−18.5180	−	10.1357i	−1.30616	−	0.714918i
$202$	2.87744	+	2.87744i	0.202456	+	0.202456i
$203$	5.44862	−	5.44862i	0.382418	−	0.382418i
$204$	−9.32656	+	2.72837i	−0.652990	+	0.191024i
$205$		−	28.3104i		−	1.97729i
$206$	12.4039	−	12.4039i	0.864217	−	0.864217i
$207$	−6.49690	+	4.15693i	−0.451566	+	0.288926i
$208$	−1.73087	−	3.16292i	−0.120014	−	0.219309i
$209$		−	0.00361558i		−	0.000250095i
$210$	5.86288	+	3.20901i	0.404577	+	0.221443i
$211$	12.6989			0.874230			0.437115	−	0.899406i	$-0.356000\pi$
$211$	12.6989			0.874230			0.437115	+	0.899406i	$0.356000\pi$
$212$	2.49125			0.171100
$213$	3.24601	−	5.93048i	0.222413	−	0.406350i
$214$	−0.161473	+	0.161473i	−0.0110381	+	0.0110381i
$215$	−13.9130	+	13.9130i	−0.948859	+	0.948859i
$216$	−5.18400	+	0.355103i	−0.352727	+	0.0241617i
$217$	9.42782			0.640002
$218$	−12.1449			−0.822556
$219$	−11.5723	+	21.1426i	−0.781981	+	1.42868i
$220$		−	0.0625325i		−	0.00421594i
$221$	−9.71083	−	17.7452i	−0.653221	−	1.19367i
$222$	18.4853	−	5.40765i	1.24065	−	0.362937i
$223$	0.153697	−	0.153697i	0.0102923	−	0.0102923i	−0.701942	−	0.712234i	$-0.747683\pi$
$223$	0.153697	−	0.153697i	0.0102923	−	0.0102923i	0.712234	+	0.701942i	$0.247683\pi$
$224$		−	1.00000i		−	0.0668153i
$225$	−15.9914	−	24.9931i	−1.06609	−	1.66620i
$226$	1.57050	−	1.57050i	0.104468	−	0.104468i
$227$	−8.19047	−	8.19047i	−0.543620	−	0.543620i	0.380968	−	0.924588i	$-0.375591\pi$
$227$	−8.19047	−	8.19047i	−0.543620	−	0.543620i	−0.924588	+	0.380968i	$0.875591\pi$
$228$	−0.185543	+	0.338988i	−0.0122879	+	0.0224500i
$229$	−5.81934	−	5.81934i	−0.384553	−	0.384553i	0.488186	−	0.872739i	$-0.337659\pi$
$229$	−5.81934	−	5.81934i	−0.384553	−	0.384553i	−0.872739	+	0.488186i	$0.837659\pi$
$230$			9.92094i			0.654168i
$231$	0.00788071	+	0.0269391i	0.000518512	+	0.00177246i
$232$	5.44862	+	5.44862i	0.357720	+	0.357720i
$233$	−9.95377			−0.652093			−0.326047	−	0.945354i	$-0.605717\pi$
$233$	−9.95377			−0.652093			−0.326047	+	0.945354i	$0.605717\pi$
$234$	−3.03616	−	10.3818i	−0.198480	−	0.678679i
$235$	18.0781			1.17929
$236$	−2.10029	−	2.10029i	−0.136717	−	0.136717i
$237$	2.87059	+	9.81269i	0.186465	+	0.637403i
$238$		−	5.61037i		−	0.363666i
$239$	12.3472	+	12.3472i	0.798673	+	0.798673i	0.982886	−	0.184213i	$-0.0589737\pi$
$239$	12.3472	+	12.3472i	0.798673	+	0.798673i	−0.184213	+	0.982886i	$0.558974\pi$
$240$	−3.20901	+	5.86288i	−0.207141	+	0.378447i
$241$	7.54377	+	7.54377i	0.485937	+	0.485937i	0.907022	−	0.421084i	$-0.138350\pi$
$241$	7.54377	+	7.54377i	0.485937	+	0.485937i	−0.421084	+	0.907022i	$0.638350\pi$
$242$	−7.77799	+	7.77799i	−0.499988	+	0.499988i
$243$	−15.4185	−	2.29577i	−0.989096	−	0.147274i
$244$			1.82875i			0.117074i
$245$	−2.72859	+	2.72859i	−0.174323	+	0.174323i
$246$	−12.1962	+	3.56784i	−0.777599	+	0.227477i
$247$	−0.772070	−	0.225928i	−0.0491256	−	0.0143754i
$248$			9.42782i			0.598667i
$249$	−14.0572	+	25.6825i	−0.890836	+	1.62756i
$250$	−18.8710			−1.19351
$251$	−26.2173			−1.65482			−0.827410	−	0.561599i	$-0.810186\pi$
$251$	−26.2173			−1.65482			−0.827410	+	0.561599i	$0.810186\pi$
$252$	0.643571	−	2.93016i	0.0405412	−	0.184583i
$253$	−0.0294603	+	0.0294603i	−0.00185216	+	0.00185216i
$254$	3.05122	−	3.05122i	0.191451	−	0.191451i
$255$	−18.0037	+	32.8929i	−1.12744	+	2.05984i
$256$	1.00000			0.0625000
$257$	−30.7002			−1.91503			−0.957513	−	0.288390i	$-0.906880\pi$
$257$	−30.7002			−1.91503			−0.957513	+	0.288390i	$0.906880\pi$
$258$	7.74714	+	4.24035i	0.482316	+	0.263992i
$259$			11.1198i			0.690949i
$260$	−13.3531	−	3.90748i	−0.828127	−	0.242331i
$261$	12.4587	+	19.4719i	0.771176	+	1.20528i
$262$	−0.0785889	+	0.0785889i	−0.00485524	+	0.00485524i
$263$			14.7267i			0.908089i	0.890979	+	0.454045i	$0.150019\pi$
$263$			14.7267i			0.908089i	−0.890979	+	0.454045i	$0.849981\pi$
$264$	−0.0269391	+	0.00788071i	−0.00165799	+	0.000485024i
$265$	6.79760	−	6.79760i	0.417573	−	0.417573i
$266$	−0.157765	−	0.157765i	−0.00967319	−	0.00967319i
$267$	11.0809	+	6.06503i	0.678138	+	0.371174i
$268$	8.61829	+	8.61829i	0.526446	+	0.526446i
$269$		−	18.3642i		−	1.11969i	−0.828598	−	0.559843i	$-0.810861\pi$
$269$		−	18.3642i		−	1.11969i	0.828598	−	0.559843i	$-0.189139\pi$
$270$	−13.1761	+	15.1139i	−0.801871	+	0.919805i
$271$	−8.96232	−	8.96232i	−0.544422	−	0.544422i	0.380400	−	0.924822i	$-0.375786\pi$
$271$	−8.96232	−	8.96232i	−0.544422	−	0.544422i	−0.924822	+	0.380400i	$0.875786\pi$
$272$	5.61037			0.340178
$273$	6.24500		0.000504619i	0.377964		3.05410e-5i
$274$	−1.46765			−0.0886637
$275$	−0.113332	−	0.113332i	−0.00683415	−	0.00683415i
$276$	4.27396	−	1.25029i	0.257262	−	0.0752589i
$277$		−	13.4939i		−	0.810772i	−0.914146	−	0.405386i	$-0.867137\pi$
$277$		−	13.4939i		−	0.810772i	0.914146	−	0.405386i	$-0.132863\pi$
$278$	−9.77510	−	9.77510i	−0.586271	−	0.586271i
$279$	−6.06747	+	27.6250i	−0.363250	+	1.65386i
$280$	−2.72859	−	2.72859i	−0.163064	−	0.163064i
$281$	18.7437	−	18.7437i	1.11815	−	1.11815i	0.126142	−	0.992012i	$-0.459740\pi$
$281$	18.7437	−	18.7437i	1.11815	−	1.11815i	0.992012	−	0.126142i	$-0.0402596\pi$
$282$	−2.27831	−	7.78809i	−0.135672	−	0.463774i
$283$			0.555789i			0.0330382i	0.999864	+	0.0165191i	$0.00525844\pi$
$283$			0.555789i			0.0330382i	−0.999864	+	0.0165191i	$0.994742\pi$
$284$	−2.76005	+	2.76005i	−0.163779	+	0.163779i
$285$	0.418689	+	1.43123i	0.0248010	+	0.0847786i
$286$	−0.0280490	−	0.0512556i	−0.00165857	−	0.00303081i
$287$		−	7.33658i		−	0.433064i
$288$	2.93016	+	0.643571i	0.172661	+	0.0379228i
$289$	14.4762			0.851542
$290$	29.7341			1.74605
$291$	−12.7735	−	6.99148i	−0.748795	−	0.409848i
$292$	9.83977	−	9.83977i	0.575829	−	0.575829i
$293$	6.73256	−	6.73256i	0.393321	−	0.393321i	−0.482549	−	0.875869i	$-0.660289\pi$
$293$	6.73256	−	6.73256i	0.393321	−	0.393321i	0.875869	+	0.482549i	$0.160289\pi$
$294$	1.51935	+	0.831607i	0.0886104	+	0.0485003i
$295$	−11.4617			−0.667323
$296$	−11.1198			−0.646324
$297$	−0.0840075	+	0.00575449i	−0.00487461	+	0.000333909i
$298$		−	13.1512i		−	0.761829i
$299$	4.45005	+	8.13184i	0.257353	+	0.470276i
$300$	4.80978	+	16.4416i	0.277693	+	0.949254i
$301$	−3.60552	+	3.60552i	−0.207819	+	0.207819i
$302$			0.557047i			0.0320545i
$303$	−1.97895	−	6.76475i	−0.113688	−	0.388625i
$304$	0.157765	−	0.157765i	0.00904845	−	0.00904845i
$305$	4.98992	+	4.98992i	0.285722	+	0.285722i
$306$	16.4393	+	3.61067i	0.939770	+	0.206408i
$307$	−13.6798	−	13.6798i	−0.780748	−	0.780748i	0.199209	−	0.979957i	$-0.436163\pi$
$307$	−13.6798	−	13.6798i	−0.780748	−	0.780748i	−0.979957	+	0.199209i	$0.936163\pi$
$308$		−	0.0162051i		−	0.000923373i
$309$	−29.1609	+	8.53069i	−1.65891	+	0.485294i
$310$	25.7246	+	25.7246i	1.46106	+	1.46106i
$311$	3.04815			0.172845			0.0864225	−	0.996259i	$-0.472457\pi$
$311$	3.04815			0.172845			0.0864225	+	0.996259i	$0.472457\pi$
$312$	−0.000504619		6.24500i	−2.85684e−5		0.353553i
$313$	19.2531			1.08825			0.544124	−	0.839005i	$-0.316862\pi$
$313$	19.2531			1.08825			0.544124	+	0.839005i	$0.316862\pi$
$314$	7.24957	+	7.24957i	0.409117	+	0.409117i
$315$	−6.23915	−	9.75123i	−0.351536	−	0.549419i
$316$		−	5.90280i		−	0.332058i
$317$	12.2211	+	12.2211i	0.686403	+	0.686403i	0.961435	−	0.275032i	$-0.0886885\pi$
$317$	12.2211	+	12.2211i	0.686403	+	0.686403i	−0.275032	+	0.961435i	$0.588688\pi$
$318$	−3.78509	−	2.07174i	−0.212257	−	0.116178i
$319$	0.0882957	+	0.0882957i	0.00494361	+	0.00494361i
$320$	2.72859	−	2.72859i	0.152533	−	0.152533i
$321$	0.379616	−	0.111052i	0.0211881	−	0.00619833i
$322$			2.57099i			0.143276i
$323$	0.885120	−	0.885120i	0.0492494	−	0.0492494i
$324$	8.17163	+	3.77153i	0.453980	+	0.209529i
$325$	−31.2825	+	17.1190i	−1.73524	+	0.949590i
$326$			5.20727i			0.288404i
$327$	18.4524	+	10.0998i	1.02042	+	0.558519i
$328$	7.33658			0.405095
$329$	4.68491			0.258287
$330$	−0.0520024	+	0.0950088i	−0.00286264	+	0.00523006i
$331$	−9.25094	+	9.25094i	−0.508478	+	0.508478i	−0.914059	−	0.405581i	$-0.867069\pi$
$331$	−9.25094	+	9.25094i	−0.508478	+	0.508478i	0.405581	+	0.914059i	$0.367069\pi$
$332$	11.9527	−	11.9527i	0.655987	−	0.655987i
$333$	−32.5827	−	7.15636i	−1.78552	−	0.392166i
$334$	−1.36368			−0.0746173
$335$	47.0315			2.56961
$336$	−0.831607	+	1.51935i	−0.0453679	+	0.0828874i
$337$		−	3.92073i		−	0.213576i	−0.994282	−	0.106788i	$-0.965943\pi$
$337$		−	3.92073i		−	0.213576i	0.994282	−	0.106788i	$-0.0340566\pi$
$338$	−12.6978	+	2.78676i	−0.690669	+	0.151580i
$339$	−3.69218	+	1.08010i	−0.200532	+	0.0586631i
$340$	15.3084	−	15.3084i	0.830213	−	0.830213i
$341$			0.152779i			0.00827345i
$342$	0.563809	−	0.360743i	0.0304873	−	0.0195068i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−3.60552	−	3.60552i	−0.194397	−	0.194397i
$345$	8.25032	−	15.0734i	0.444183	−	0.811525i
$346$	7.91827	+	7.91827i	0.425689	+	0.425689i
$347$		−	11.8159i		−	0.634311i	−0.948374	−	0.317156i	$-0.897272\pi$
$347$		−	11.8159i		−	0.634311i	0.948374	−	0.317156i	$-0.102728\pi$
$348$	−3.74726	−	12.8095i	−0.200874	−	0.686660i
$349$	8.77505	+	8.77505i	0.469717	+	0.469717i	0.901823	−	0.432106i	$-0.142229\pi$
$349$	8.77505	+	8.77505i	0.469717	+	0.469717i	−0.432106	+	0.901823i	$0.642229\pi$
$350$	−9.89038			−0.528663
$351$	−4.02058	+	18.2985i	−0.214603	+	0.976701i
$352$	0.0162051			0.000863737
$353$	−0.431441	−	0.431441i	−0.0229633	−	0.0229633i	0.695532	−	0.718495i	$-0.255169\pi$
$353$	−0.431441	−	0.431441i	−0.0229633	−	0.0229633i	−0.718495	+	0.695532i	$0.755169\pi$
$354$	1.44446	+	4.93770i	0.0767724	+	0.262436i
$355$			15.0621i			0.799411i
$356$	−5.15703	−	5.15703i	−0.273322	−	0.273322i
$357$	−4.66562	+	8.52412i	−0.246931	+	0.451144i
$358$	3.27666	+	3.27666i	0.173177	+	0.173177i
$359$	−1.98976	+	1.98976i	−0.105015	+	0.105015i	−0.757662	−	0.652647i	$-0.773659\pi$
$359$	−1.98976	+	1.98976i	−0.105015	+	0.105015i	0.652647	+	0.757662i	$0.273659\pi$
$360$	9.75123	−	6.23915i	0.513935	−	0.328832i
$361$			18.9502i			0.997380i
$362$	−10.8336	+	10.8336i	−0.569401	+	0.569401i
$363$	18.2857	−	5.34927i	0.959752	−	0.280764i
$364$	−3.46044	−	1.01261i	−0.181376	−	0.0530753i
$365$		−	53.6974i		−	2.81065i
$366$	1.52080	−	2.77852i	0.0794937	−	0.145236i
$367$	−6.88839			−0.359571			−0.179785	−	0.983706i	$-0.557540\pi$
$367$	−6.88839			−0.359571			−0.179785	+	0.983706i	$0.557540\pi$
$368$	−2.57099			−0.134022
$369$	21.4973	+	4.72161i	1.11911	+	0.245797i
$370$	−30.3413	+	30.3413i	−1.57737	+	1.57737i
$371$	1.76158	−	1.76158i	0.0914567	−	0.0914567i
$372$	7.84024	−	14.3242i	0.406498	−	0.742674i
$373$	−7.13093			−0.369225			−0.184613	−	0.982811i	$-0.559103\pi$
$373$	−7.13093			−0.369225			−0.184613	+	0.982811i	$0.559103\pi$
$374$	0.0909168			0.00470119
$375$	28.6717	+	15.6933i	1.48060	+	0.810397i
$376$			4.68491i			0.241606i
$377$	24.3719	−	13.3373i	1.25522	−	0.686904i
$378$	−3.41455	+	3.91674i	−0.175625	+	0.201455i
$379$	26.5110	−	26.5110i	1.36178	−	1.36178i	0.490131	−	0.871649i	$-0.336949\pi$
$379$	26.5110	−	26.5110i	1.36178	−	1.36178i	0.871649	−	0.490131i	$-0.163051\pi$
$380$		−	0.860951i		−	0.0441659i
$381$	−7.17330	+	2.09846i	−0.367499	+	0.107507i
$382$	8.96328	−	8.96328i	0.458601	−	0.458601i
$383$	20.2050	+	20.2050i	1.03243	+	1.03243i	0.999456	+	0.0329712i	$0.0104969\pi$
$383$	20.2050	+	20.2050i	1.03243	+	1.03243i	0.0329712	+	0.999456i	$0.489503\pi$
$384$	−1.51935	−	0.831607i	−0.0775341	−	0.0424378i
$385$	−0.0442171	−	0.0442171i	−0.00225351	−	0.00225351i
$386$			7.82538i			0.398301i
$387$	−8.24433	−	12.8852i	−0.419083	−	0.654989i
$388$	5.94479	+	5.94479i	0.301801	+	0.301801i
$389$	−3.37710			−0.171226			−0.0856128	−	0.996328i	$-0.527285\pi$
$389$	−3.37710			−0.171226			−0.0856128	+	0.996328i	$0.527285\pi$
$390$	17.0386	+	17.0414i	0.862785	+	0.862925i
$391$	−14.4242			−0.729462
$392$	−0.707107	−	0.707107i	−0.0357143	−	0.0357143i
$393$	0.184759	−	0.0540491i	0.00931987	−	0.00272642i
$394$			24.6658i			1.24265i
$395$	−16.1063	−	16.1063i	−0.810396	−	0.810396i
$396$	0.0474836	+	0.0104292i	0.00238614	+	0.000524085i
$397$	−2.62666	−	2.62666i	−0.131828	−	0.131828i	0.638114	−	0.769942i	$-0.279715\pi$
$397$	−2.62666	−	2.62666i	−0.131828	−	0.131828i	−0.769942	+	0.638114i	$0.779715\pi$
$398$	−11.4906	+	11.4906i	−0.575970	+	0.575970i
$399$	0.108502	+	0.370899i	0.00543190	+	0.0185682i
$400$		−	9.89038i		−	0.494519i
$401$	−17.3405	+	17.3405i	−0.865943	+	0.865943i	−0.992020	−	0.126078i	$-0.959761\pi$
$401$	−17.3405	+	17.3405i	−0.865943	+	0.865943i	0.126078	+	0.992020i	$0.459761\pi$
$402$	−5.92719	−	20.2612i	−0.295621	−	1.01054i
$403$	32.6244	+	9.54673i	1.62514	+	0.475557i
$404$			4.06932i			0.202456i
$405$	32.5880	−	12.0061i	1.61931	−	0.596586i
$406$	7.70551			0.382418
$407$	−0.180197			−0.00893205
$408$	−8.52412	−	4.66562i	−0.422007	−	0.230983i
$409$	−12.2005	+	12.2005i	−0.603276	+	0.603276i	−0.941180	−	0.337905i	$-0.890282\pi$
$409$	−12.2005	+	12.2005i	−0.603276	+	0.603276i	0.337905	+	0.941180i	$0.390282\pi$
$410$	20.0185	−	20.0185i	0.988643	−	0.988643i
$411$	2.22987	+	1.22050i	0.109991	+	0.0602030i
$412$	17.5417			0.864217
$413$	−2.97026			−0.146157
$414$	−7.53340	−	1.65461i	−0.370246	−	0.0813198i
$415$		−	65.2278i		−	3.20190i
$416$	1.01261	−	3.46044i	0.0496474	−	0.169662i
$417$	6.72277	+	22.9808i	0.329216	+	1.12538i
$418$	0.00255660	−	0.00255660i	0.000125048	−	0.000125048i
$419$			15.1275i			0.739027i	0.929225	+	0.369514i	$0.120476\pi$
$419$			15.1275i			0.739027i	−0.929225	+	0.369514i	$0.879524\pi$
$420$	1.87657	+	6.41480i	0.0915674	+	0.313010i
$421$	−3.41592	+	3.41592i	−0.166482	+	0.166482i	−0.785431	−	0.618949i	$-0.787559\pi$
$421$	−3.41592	+	3.41592i	−0.166482	+	0.166482i	0.618949	+	0.785431i	$0.287559\pi$
$422$	8.97949	+	8.97949i	0.437115	+	0.437115i
$423$	−3.01507	+	13.7275i	−0.146598	+	0.667454i
$424$	1.76158	+	1.76158i	0.0855499	+	0.0855499i
$425$		−	55.4887i		−	2.69160i
$426$	6.48876	−	1.89821i	0.314381	−	0.0919685i
$427$	1.29312	+	1.29312i	0.0625787	+	0.0625787i
$428$	−0.228357			−0.0110381
$429$	−8.17743e−6		0.101201i	−3.94810e−7		0.00488603i
$430$	−19.6760			−0.948859
$431$	3.91881	+	3.91881i	0.188762	+	0.188762i	0.795161	−	0.606399i	$-0.207386\pi$
$431$	3.91881	+	3.91881i	0.188762	+	0.188762i	−0.606399	+	0.795161i	$0.707386\pi$
$432$	−3.91674	−	3.41455i	−0.188444	−	0.164283i
$433$		−	15.2572i		−	0.733212i	−0.930376	−	0.366606i	$-0.880520\pi$
$433$		−	15.2572i		−	0.733212i	0.930376	−	0.366606i	$-0.119480\pi$
$434$	6.66648	+	6.66648i	0.320001	+	0.320001i
$435$	−45.1765	−	24.7271i	−2.16605	−	1.18557i
$436$	−8.58774	−	8.58774i	−0.411278	−	0.411278i
$437$	−0.405612	+	0.405612i	−0.0194031	+	0.0194031i
$438$	−23.1329	+	6.76725i	−1.10533	+	0.323352i
$439$			13.4437i			0.641632i	0.947141	+	0.320816i	$0.103957\pi$
$439$			13.4437i			0.641632i	−0.947141	+	0.320816i	$0.896043\pi$
$440$	0.0442171	−	0.0442171i	0.00210797	−	0.00210797i
$441$	−1.61686	−	2.52701i	−0.0769933	−	0.120334i
$442$	5.68113	−	19.4143i	0.270224	−	0.923445i
$443$		−	38.0441i		−	1.80753i	−0.428032	−	0.903764i	$-0.640793\pi$
$443$		−	38.0441i		−	1.80753i	0.428032	−	0.903764i	$-0.359207\pi$
$444$	16.8948	+	9.24728i	0.801794	+	0.438856i
$445$	−28.1428			−1.33410
$446$	0.217361			0.0102923
$447$	−10.9366	+	19.9813i	−0.517285	+	0.945084i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	−5.40078	+	5.40078i	−0.254879	+	0.254879i	−0.822967	−	0.568089i	$-0.807683\pi$
$449$	−5.40078	+	5.40078i	−0.254879	+	0.254879i	0.568089	+	0.822967i	$0.307683\pi$
$450$	6.36516	−	28.9804i	0.300057	−	1.36615i
$451$	0.118890			0.00559832
$452$	2.22102			0.104468
$453$	0.463244	−	0.846351i	0.0217651	−	0.0397650i
$454$		−	11.5831i		−	0.543620i
$455$	−12.2051	+	6.67910i	−0.572184	+	0.313121i
$456$	−0.370899	+	0.108502i	−0.0173689	+	0.00508108i
$457$	−23.4514	+	23.4514i	−1.09701	+	1.09701i	−0.102249	+	0.994759i	$0.532604\pi$
$457$	−23.4514	+	23.4514i	−1.09701	+	1.09701i	−0.994759	+	0.102249i	$0.967396\pi$
$458$		−	8.22979i		−	0.384553i
$459$	−21.9744	−	19.1569i	−1.02567	−	0.894166i
$460$	−7.01517	+	7.01517i	−0.327084	+	0.327084i
$461$	21.2145	+	21.2145i	0.988057	+	0.988057i	0.999930	−	0.0118730i	$-0.00377937\pi$
$461$	21.2145	+	21.2145i	0.988057	+	0.988057i	−0.0118730	+	0.999930i	$0.503779\pi$
$462$	−0.0134763	+	0.0246213i	−0.000626974	+	0.00114549i
$463$	23.6011	+	23.6011i	1.09684	+	1.09684i	0.994778	+	0.102059i	$0.0325429\pi$
$463$	23.6011	+	23.6011i	1.09684	+	1.09684i	0.102059	+	0.994778i	$0.467457\pi$
$464$			7.70551i			0.357720i
$465$	−17.6920	−	60.4776i	−0.820446	−	2.80458i
$466$	−7.03838	−	7.03838i	−0.326047	−	0.326047i
$467$	−1.29336			−0.0598496			−0.0299248	−	0.999552i	$-0.509527\pi$
$467$	−1.29336			−0.0598496			−0.0299248	+	0.999552i	$0.509527\pi$
$468$	5.19415	−	9.48793i	0.240100	−	0.438580i
$469$	12.1881			0.562794
$470$	12.7832	+	12.7832i	0.589644	+	0.589644i
$471$	−4.98585	−	17.0434i	−0.229736	−	0.785320i
$472$		−	2.97026i		−	0.136717i
$473$	−0.0584280	−	0.0584280i	−0.00268652	−	0.00268652i
$474$	−4.90881	+	8.96843i	−0.225469	+	0.411934i
$475$	−1.56036	−	1.56036i	−0.0715941	−	0.0715941i
$476$	3.96713	−	3.96713i	0.181833	−	0.181833i
$477$	4.02800	+	6.29541i	0.184430	+	0.288247i
$478$			17.4616i			0.798673i
$479$	14.5097	−	14.5097i	0.662966	−	0.662966i	−0.293112	−	0.956078i	$-0.594691\pi$
$479$	14.5097	−	14.5097i	0.662966	−	0.662966i	0.956078	+	0.293112i	$0.0946909\pi$
$480$	−6.41480	+	1.87657i	−0.292794	+	0.0856534i
$481$	−11.2600	+	38.4793i	−0.513413	+	1.75450i
$482$			10.6685i			0.485937i
$483$	2.13805	−	3.90624i	0.0972847	−	0.177740i
$484$	−10.9997			−0.499988
$485$	32.4417			1.47310
$486$	−9.27916	−	12.5259i	−0.420911	−	0.568185i
$487$	16.4423	−	16.4423i	0.745074	−	0.745074i	−0.228476	−	0.973550i	$-0.573374\pi$
$487$	16.4423	−	16.4423i	0.745074	−	0.745074i	0.973550	+	0.228476i	$0.0733742\pi$
$488$	−1.29312	+	1.29312i	−0.0585370	+	0.0585370i
$489$	4.33040	−	7.91168i	0.195828	−	0.357778i
$490$	−3.85881			−0.174323
$491$	−5.23186			−0.236111			−0.118055	−	0.993007i	$-0.537666\pi$
$491$	−5.23186			−0.236111			−0.118055	+	0.993007i	$0.537666\pi$
$492$	−11.1468	−	6.10115i	−0.502538	−	0.275061i
$493$			43.2308i			1.94702i
$494$	−0.386181	−	0.705691i	−0.0173751	−	0.0317505i
$495$	0.158020	−	0.101106i	0.00710247	−	0.00454439i
$496$	−6.66648	+	6.66648i	−0.299334	+	0.299334i
$497$			3.90330i			0.175087i
$498$	−28.1002	+	8.22038i	−1.25920	+	0.368364i
$499$	−21.9429	+	21.9429i	−0.982297	+	0.982297i	−0.999846	−	0.0175490i	$-0.994414\pi$
$499$	−21.9429	+	21.9429i	−0.982297	+	0.982297i	0.0175490	+	0.999846i	$0.494414\pi$
$500$	−13.3438	−	13.3438i	−0.596754	−	0.596754i
$501$	2.07191	+	1.13405i	0.0925661	+	0.0506654i
$502$	−18.5384	−	18.5384i	−0.827410	−	0.827410i
$503$			14.1370i			0.630336i	0.949036	+	0.315168i	$0.102061\pi$
$503$			14.1370i			0.630336i	−0.949036	+	0.315168i	$0.897939\pi$
$504$	2.52701	−	1.61686i	0.112562	−	0.0720207i
$505$	11.1035	+	11.1035i	0.494099	+	0.494099i
$506$	−0.0416632			−0.00185216
$507$	21.6099	+	6.32551i	0.959729	+	0.280926i
$508$	4.31508			0.191451
$509$	−24.6460	−	24.6460i	−1.09241	−	1.09241i	−0.995271	−	0.0971423i	$-0.969030\pi$
$509$	−24.6460	−	24.6460i	−1.09241	−	1.09241i	−0.0971423	−	0.995271i	$-0.530970\pi$
$510$	−35.9894	+	10.5283i	−1.59364	+	0.466199i
$511$		−	13.9155i		−	0.615587i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.15662	+	0.0792282i	−0.0510661	+	0.00349801i
$514$	−21.7083	−	21.7083i	−0.957513	−	0.957513i
$515$	47.8641	−	47.8641i	2.10914	−	2.10914i
$516$	2.47968	+	8.47643i	0.109162	+	0.373154i
$517$			0.0759196i			0.00333894i
$518$	−7.86287	+	7.86287i	−0.345474	+	0.345474i
$519$	−5.44575	−	18.6155i	−0.239042	−	0.817131i
$520$	−6.67910	−	12.2051i	−0.292898	−	0.535229i
$521$			42.9249i			1.88057i	0.340383	+	0.940287i	$0.389443\pi$
$521$			42.9249i			1.88057i	−0.340383	+	0.940287i	$0.610557\pi$
$522$	−4.95905	+	22.5784i	−0.217052	+	0.988228i
$523$	−9.09629			−0.397753			−0.198877	−	0.980025i	$-0.563729\pi$
$523$	−9.09629			−0.397753			−0.198877	+	0.980025i	$0.563729\pi$
$524$	−0.111141			−0.00485524
$525$	15.0270	+	8.22491i	0.655831	+	0.358964i
$526$	−10.4134	+	10.4134i	−0.454045	+	0.454045i
$527$	−37.4014	+	37.4014i	−1.62923	+	1.62923i
$528$	−0.0246213	−	0.0134763i	−0.00107150	−	0.000586481i
$529$	−16.3900			−0.712610
$530$	9.61326			0.417573
$531$	1.91157	−	8.70332i	0.0829552	−	0.377692i
$532$		−	0.223113i		−	0.00967319i
$533$	7.42911	−	25.3877i	0.321790	−	1.09967i
$534$	3.54672	+	12.1240i	0.153482	+	0.524656i
$535$	−0.623093	+	0.623093i	−0.0269386	+	0.0269386i
$536$			12.1881i			0.526446i
$537$	−2.25350	−	7.70329i	−0.0972459	−	0.332421i
$538$	12.9855	−	12.9855i	0.559843	−	0.559843i
$539$	−0.0114588	−	0.0114588i	−0.000493564	−	0.000493564i
$540$	−20.0041	+	1.37027i	−0.860838	+	0.0589671i
$541$	−25.9593	−	25.9593i	−1.11608	−	1.11608i	−0.992312	−	0.123765i	$-0.960503\pi$
$541$	−25.9593	−	25.9593i	−1.11608	−	1.11608i	−0.123765	−	0.992312i	$-0.539497\pi$
$542$		−	12.6746i		−	0.544422i
$543$	25.4693	−	7.45074i	1.09299	−	0.319742i
$544$	3.96713	+	3.96713i	0.170089	+	0.170089i
$545$	−46.8648			−2.00747
$546$	4.41552	+	4.41624i	0.188967	+	0.188998i
$547$	5.50448			0.235355			0.117677	−	0.993052i	$-0.462455\pi$
$547$	5.50448			0.235355			0.117677	+	0.993052i	$0.462455\pi$
$548$	−1.03778	−	1.03778i	−0.0443319	−	0.0443319i
$549$	−4.62127	+	2.95684i	−0.197231	+	0.126195i
$550$		−	0.160275i		−	0.00683415i
$551$	1.21566	+	1.21566i	0.0517889	+	0.0517889i
$552$	3.90624	+	2.13805i	0.166260	+	0.0910015i
$553$	−4.17391	−	4.17391i	−0.177493	−	0.177493i
$554$	9.54165	−	9.54165i	0.405386	−	0.405386i
$555$	71.3311	−	20.8671i	3.02784	−	0.885757i
$556$		−	13.8241i		−	0.586271i
$557$	1.35829	−	1.35829i	0.0575525	−	0.0575525i	−0.677745	−	0.735297i	$-0.737043\pi$
$557$	1.35829	−	1.35829i	0.0575525	−	0.0575525i	0.735297	+	0.677745i	$0.237043\pi$
$558$	−23.8242	+	15.2435i	−1.00856	+	0.645307i
$559$	−16.1277	+	8.82568i	−0.682128	+	0.373287i
$560$		−	3.85881i		−	0.163064i
$561$	−0.138135	−	0.0756070i	−0.00583205	−	0.00319213i
$562$	26.5076			1.11815
$563$	37.6045			1.58484			0.792420	−	0.609976i	$-0.208821\pi$
$563$	37.6045			1.58484			0.792420	+	0.609976i	$0.208821\pi$
$564$	3.89600	−	7.11802i	0.164051	−	0.299723i
$565$	6.06025	−	6.06025i	0.254957	−	0.254957i
$566$	−0.393002	+	0.393002i	−0.0165191	+	0.0165191i
$567$	8.44509	−	3.11134i	0.354660	−	0.130664i
$568$	−3.90330			−0.163779
$569$	−12.8584			−0.539053			−0.269527	−	0.962993i	$-0.586867\pi$
$569$	−12.8584			−0.539053			−0.269527	+	0.962993i	$0.586867\pi$
$570$	−0.715973	+	1.30809i	−0.0299888	+	0.0547898i
$571$		−	30.6551i		−	1.28288i	−0.767174	−	0.641439i	$-0.778338\pi$
$571$		−	30.6551i		−	1.28288i	0.767174	−	0.641439i	$-0.221662\pi$
$572$	0.0164095	−	0.0560768i	0.000686117	−	0.00234469i
$573$	−21.0723	+	6.16445i	−0.880308	+	0.257524i
$574$	5.18774	−	5.18774i	0.216532	−	0.216532i
$575$			25.4280i			1.06042i
$576$	1.61686	+	2.52701i	0.0673692	+	0.105292i
$577$	21.0219	−	21.0219i	0.875155	−	0.875155i	−0.117874	−	0.993029i	$-0.537608\pi$
$577$	21.0219	−	21.0219i	0.875155	−	0.875155i	0.993029	+	0.117874i	$0.0376079\pi$
$578$	10.2362	+	10.2362i	0.425771	+	0.425771i
$579$	6.50764	−	11.8895i	0.270448	−	0.494111i
$580$	21.0252	+	21.0252i	0.873023	+	0.873023i
$581$		−	16.9036i		−	0.701280i
$582$	−4.08850	−	13.9759i	−0.169474	−	0.579322i
$583$	0.0285467	+	0.0285467i	0.00118228	+	0.00118228i
$584$	13.9155			0.575829
$585$	−11.7160	−	40.0613i	−0.484395	−	1.65633i
$586$	9.52128			0.393321
$587$	−19.4406	−	19.4406i	−0.802398	−	0.802398i	0.181072	−	0.983470i	$-0.442043\pi$
$587$	−19.4406	−	19.4406i	−0.802398	−	0.802398i	−0.983470	+	0.181072i	$0.942043\pi$
$588$	0.486309	+	1.66238i	0.0200550	+	0.0685553i
$589$			2.10347i			0.0866721i
$590$	−8.10461	−	8.10461i	−0.333662	−	0.333662i
$591$	20.5123	−	37.4761i	0.843762	−	1.54156i
$592$	−7.86287	−	7.86287i	−0.323162	−	0.323162i
$593$	−23.9101	+	23.9101i	−0.981871	+	0.981871i	−0.999839	−	0.0179672i	$-0.994281\pi$
$593$	−23.9101	+	23.9101i	−0.981871	+	0.981871i	0.0179672	+	0.999839i	$0.494281\pi$
$594$	−0.0634713	−	0.0553332i	−0.00260426	−	0.00227035i
$595$		−	21.6493i		−	0.887535i
$596$	9.29931	−	9.29931i	0.380915	−	0.380915i
$597$	27.0139	−	7.90258i	1.10560	−	0.323431i
$598$	−2.60342	+	8.89674i	−0.106462	+	0.363815i
$599$			30.5039i			1.24636i	0.782080	+	0.623178i	$0.214159\pi$
$599$			30.5039i			1.24636i	−0.782080	+	0.623178i	$0.785841\pi$
$600$	−8.22491	+	15.0270i	−0.335780	+	0.613473i
$601$	32.8095			1.33833			0.669165	−	0.743114i	$-0.266652\pi$
$601$	32.8095			1.33833			0.669165	+	0.743114i	$0.266652\pi$
$602$	−5.09898			−0.207819
$603$	−7.84391	+	35.7130i	−0.319429	+	1.45435i
$604$	−0.393892	+	0.393892i	−0.0160272	+	0.0160272i
$605$	−30.0137	+	30.0137i	−1.22023	+	1.22023i
$606$	3.38408	−	6.18273i	0.137469	−	0.251156i
$607$	−23.8071			−0.966299			−0.483149	−	0.875538i	$-0.660507\pi$
$607$	−23.8071			−0.966299			−0.483149	+	0.875538i	$0.660507\pi$
$608$	0.223113			0.00904845
$609$	−11.7074	−	6.40796i	−0.474407	−	0.259664i
$610$			7.05681i			0.285722i
$611$	16.2118	+	4.74400i	0.655860	+	0.191922i
$612$	9.07118	+	14.1774i	0.366681	+	0.573089i
$613$	2.22797	−	2.22797i	0.0899870	−	0.0899870i	−0.660680	−	0.750667i	$-0.729732\pi$
$613$	2.22797	−	2.22797i	0.0899870	−	0.0899870i	0.750667	+	0.660680i	$0.229732\pi$
$614$		−	19.3462i		−	0.780748i
$615$	−47.0626	+	13.7676i	−1.89775	+	0.555164i
$616$	0.0114588	−	0.0114588i	0.000461687	−	0.000461687i
$617$	9.41224	+	9.41224i	0.378922	+	0.378922i	0.870713	−	0.491791i	$-0.163658\pi$
$617$	9.41224	+	9.41224i	0.378922	+	0.378922i	−0.491791	+	0.870713i	$0.663658\pi$
$618$	−26.6520	−	14.5878i	−1.07210	−	0.586807i
$619$	−30.1524	−	30.1524i	−1.21193	−	1.21193i	−0.970392	−	0.241535i	$-0.922349\pi$
$619$	−30.1524	−	30.1524i	−1.21193	−	1.21193i	−0.241535	−	0.970392i	$-0.577651\pi$
$620$			36.3801i			1.46106i
$621$	10.0699	+	8.77876i	0.404091	+	0.352280i
$622$	2.15537	+	2.15537i	0.0864225	+	0.0864225i
$623$	−7.29315			−0.292194
$624$	−4.41624	+	4.41552i	−0.176791	+	0.176762i
$625$	−23.3677			−0.934709
$626$	13.6140	+	13.6140i	0.544124	+	0.544124i
$627$	−0.00601047	+	0.00175829i	−0.000240035	+	7.02194e-5i
$628$			10.2524i			0.409117i
$629$	−44.1136	−	44.1136i	−1.75892	−	1.75892i
$630$	2.48342	−	11.3069i	0.0989416	−	0.450478i
$631$	−17.9690	−	17.9690i	−0.715334	−	0.715334i	0.252312	−	0.967646i	$-0.418809\pi$
$631$	−17.9690	−	17.9690i	−0.715334	−	0.715334i	−0.967646	+	0.252312i	$0.918809\pi$
$632$	4.17391	−	4.17391i	0.166029	−	0.166029i
$633$	−6.17560	−	21.1104i	−0.245458	−	0.839064i
$634$			17.2832i			0.686403i
$635$	11.7741	−	11.7741i	0.467240	−	0.467240i
$636$	−1.21152	−	4.14140i	−0.0480398	−	0.164217i
$637$	−3.16292	+	1.73087i	−0.125320	+	0.0685797i
$638$			0.124869i			0.00494361i
$639$	−11.4373	−	2.51205i	−0.452451	−	0.0993751i
$640$	3.85881			0.152533
$641$	6.22306			0.245796			0.122898	−	0.992419i	$-0.460781\pi$
$641$	6.22306			0.245796			0.122898	+	0.992419i	$0.460781\pi$
$642$	0.346955	+	0.189903i	0.0136932	+	0.00749489i
$643$	2.90196	−	2.90196i	0.114442	−	0.114442i	−0.647567	−	0.762009i	$-0.724213\pi$
$643$	2.90196	−	2.90196i	0.114442	−	0.114442i	0.762009	+	0.647567i	$0.224213\pi$
$644$	−1.81796	+	1.81796i	−0.0716378	+	0.0716378i
$645$	29.8947	+	16.3627i	1.17710	+	0.644279i
$646$	1.25175			0.0492494
$647$	−14.3535			−0.564293			−0.282147	−	0.959371i	$-0.591046\pi$
$647$	−14.3535			−0.564293			−0.282147	+	0.959371i	$0.591046\pi$
$648$	3.11134	+	8.44509i	0.122225	+	0.331754i
$649$		−	0.0481335i		−	0.00188940i
$650$	−34.2250	−	10.0151i	−1.34242	−	0.392826i
$651$	−4.58483	−	15.6726i	−0.179694	−	0.614258i
$652$	−3.68210	+	3.68210i	−0.144202	+	0.144202i
$653$			4.91046i			0.192161i	0.995374	+	0.0960805i	$0.0306306\pi$
$653$			4.91046i			0.192161i	−0.995374	+	0.0960805i	$0.969369\pi$
$654$	5.90617	+	20.1894i	0.230950	+	0.789469i
$655$	−0.303259	+	0.303259i	−0.0118493	+	0.0118493i
$656$	5.18774	+	5.18774i	0.202547	+	0.202547i
$657$	40.7747	+	8.95564i	1.59077	+	0.349393i
$658$	3.31273	+	3.31273i	0.129144	+	0.129144i
$659$			29.9426i			1.16640i	0.812329	+	0.583199i	$0.198199\pi$
$659$			29.9426i			1.16640i	−0.812329	+	0.583199i	$0.801801\pi$
$660$	−0.103953	+	0.0304101i	−0.00404635	+	0.00118371i
$661$	5.12233	+	5.12233i	0.199236	+	0.199236i	0.799672	−	0.600437i	$-0.205007\pi$
$661$	5.12233	+	5.12233i	0.199236	+	0.199236i	−0.600437	+	0.799672i	$0.705007\pi$
$662$	−13.0828			−0.508478
$663$	−24.7767	+	24.7727i	−0.962248	+	0.962092i
$664$	16.9036			0.655987
$665$	−0.608785	−	0.608785i	−0.0236077	−	0.0236077i
$666$	−17.9791	−	28.0997i	−0.696676	−	1.08884i
$667$		−	19.8108i		−	0.767077i
$668$	−0.964267	−	0.964267i	−0.0373086	−	0.0373086i
$669$	−0.330248	−	0.180759i	−0.0127681	−	0.00698854i
$670$	33.2563	+	33.2563i	1.28480	+	1.28480i
$671$	−0.0209553	+	0.0209553i	−0.000808969	+	0.000808969i
$672$	−1.66238	+	0.486309i	−0.0641277	+	0.0187598i
$673$		−	0.955996i		−	0.0368509i	−0.999830	−	0.0184255i	$-0.994135\pi$
$673$		−	0.955996i		−	0.0368509i	0.999830	−	0.0184255i	$-0.00586534\pi$
$674$	2.77238	−	2.77238i	0.106788	−	0.106788i
$675$	−33.7712	+	38.7381i	−1.29985	+	1.49103i
$676$	−10.9492	−	7.00816i	−0.421124	−	0.269545i
$677$		−	22.6377i		−	0.870037i	−0.900421	−	0.435019i	$-0.856742\pi$
$677$		−	22.6377i		−	0.870037i	0.900421	−	0.435019i	$-0.143258\pi$
$678$	−3.37451	−	1.84702i	−0.129597	−	0.0709342i
$679$	8.40720			0.322639
$680$	21.6493			0.830213
$681$	−9.63256	+	17.5988i	−0.369121	+	0.674386i
$682$	−0.108031	+	0.108031i	−0.00413673	+	0.00413673i
$683$	−28.9868	+	28.9868i	−1.10915	+	1.10915i	−0.115885	+	0.993263i	$0.536971\pi$
$683$	−28.9868	+	28.9868i	−1.10915	+	1.10915i	−0.993263	+	0.115885i	$0.963029\pi$
$684$	0.653757	+	0.143589i	0.0249970	+	0.00549028i
$685$	−5.66336			−0.216386
$686$	−1.00000			−0.0381802
$687$	−6.84395	+	12.5040i	−0.261113	+	0.477056i
$688$		−	5.09898i		−	0.194397i
$689$	7.87964	−	4.31204i	0.300190	−	0.164276i
$690$	16.4924	−	4.82464i	0.627854	−	0.183671i
$691$	14.1906	−	14.1906i	0.539837	−	0.539837i	−0.383644	−	0.923481i	$-0.625331\pi$
$691$	14.1906	−	14.1906i	0.539837	−	0.539837i	0.923481	+	0.383644i	$0.125331\pi$
$692$			11.1981i			0.425689i
$693$	0.0409505	−	0.0262014i	0.00155558	−	0.000995310i
$694$	8.35511	−	8.35511i	0.317156	−	0.317156i
$695$	−37.7202	−	37.7202i	−1.43081	−	1.43081i
$696$	6.40796	−	11.7074i	0.242893	−	0.443767i
$697$	29.1051	+	29.1051i	1.10244	+	1.10244i
$698$			12.4098i			0.469717i
$699$	4.84061	+	16.5469i	0.183089	+	0.625863i
$700$	−6.99356	−	6.99356i	−0.264332	−	0.264332i
$701$	−1.82380			−0.0688840			−0.0344420	−	0.999407i	$-0.510965\pi$
$701$	−1.82380			−0.0688840			−0.0344420	+	0.999407i	$0.510965\pi$
$702$	−15.7820	+	10.0960i	−0.595652	+	0.381049i
$703$	−2.48097			−0.0935716
$704$	0.0114588	+	0.0114588i	0.000431868	+	0.000431868i
$705$	−8.79157	−	30.0527i	−0.331110	−	1.13185i
$706$		−	0.610149i		−	0.0229633i
$707$	2.87744	+	2.87744i	0.108217	+	0.108217i
$708$	−2.47009	+	4.51287i	−0.0928316	+	0.169604i
$709$	13.5253	+	13.5253i	0.507953	+	0.507953i	0.913898	−	0.405945i	$-0.133057\pi$
$709$	13.5253	+	13.5253i	0.507953	+	0.507953i	−0.405945	+	0.913898i	$0.633057\pi$
$710$	−10.6505	+	10.6505i	−0.399706	+	0.399706i
$711$	14.9164	−	9.54400i	0.559409	−	0.357928i
$712$		−	7.29315i		−	0.273322i
$713$	17.1394	−	17.1394i	0.641877	−	0.641877i
$714$	−9.32656	+	2.72837i	−0.349038	+	0.102107i
$715$	−0.108236	−	0.197785i	−0.00404779	−	0.00739675i
$716$			4.63389i			0.173177i
$717$	14.5212	−	26.5302i	0.542302	−	0.990790i
$718$	−2.81394			−0.105015
$719$	−10.2208			−0.381172			−0.190586	−	0.981670i	$-0.561039\pi$
$719$	−10.2208			−0.381172			−0.190586	+	0.981670i	$0.561039\pi$
$720$	11.3069	+	2.48342i	0.421383	+	0.0925514i
$721$	12.4039	−	12.4039i	0.461944	−	0.461944i
$722$	−13.3998	+	13.3998i	−0.498690	+	0.498690i
$723$	8.87200	−	16.2092i	0.329953	−	0.602827i
$724$	−15.3210			−0.569401
$725$	76.2105			2.83039
$726$	16.7125	+	9.14746i	0.620258	+	0.339494i
$727$		−	43.8339i		−	1.62571i	−0.582466	−	0.812855i	$-0.697912\pi$
$727$		−	43.8339i		−	1.62571i	0.582466	−	0.812855i	$-0.302088\pi$
$728$	−1.73087	−	3.16292i	−0.0641504	−	0.117226i
$729$	3.68171	+	26.7478i	0.136360	+	0.990659i
$730$	37.9698	−	37.9698i	1.40532	−	1.40532i
$731$		−	28.6071i		−	1.05807i
$732$	3.04008	−	0.889340i	0.112365	−	0.0328709i
$733$	−8.47954	+	8.47954i	−0.313199	+	0.313199i	−0.846148	−	0.532949i	$-0.821084\pi$
$733$	−8.47954	+	8.47954i	−0.313199	+	0.313199i	0.532949	+	0.846148i	$0.321084\pi$
$734$	−4.87082	−	4.87082i	−0.179785	−	0.179785i
$735$	5.86288	+	3.20901i	0.216256	+	0.118366i
$736$	−1.81796	−	1.81796i	−0.0670110	−	0.0670110i
$737$			0.197510i			0.00727537i
$738$	11.8622	+	18.5396i	0.436654	+	0.682451i
$739$	−23.8959	−	23.8959i	−0.879025	−	0.879025i	0.114409	−	0.993434i	$-0.463503\pi$
$739$	−23.8959	−	23.8959i	−0.879025	−	0.879025i	−0.993434	+	0.114409i	$0.963503\pi$
$740$	−42.9090			−1.57737
$741$	−0.000112587		1.39334i	−4.13600e−6		0.0511857i
$742$	2.49125			0.0914567
$743$	−3.43994	−	3.43994i	−0.126199	−	0.126199i	0.641186	−	0.767385i	$-0.278443\pi$
$743$	−3.43994	−	3.43994i	−0.126199	−	0.126199i	−0.767385	+	0.641186i	$0.778443\pi$
$744$	15.6726	−	4.58483i	0.574586	−	0.168088i
$745$		−	50.7480i		−	1.85926i
$746$	−5.04233	−	5.04233i	−0.184613	−	0.184613i
$747$	49.5302	+	10.8787i	1.81222	+	0.398030i
$748$	0.0642879	+	0.0642879i	0.00235060	+	0.00235060i
$749$	−0.161473	+	0.161473i	−0.00590009	+	0.00590009i
$750$	9.17715	+	31.3708i	0.335102	+	1.14550i
$751$			9.39451i			0.342810i	0.985201	+	0.171405i	$0.0548307\pi$
$751$			9.39451i			0.342810i	−0.985201	+	0.171405i	$0.945169\pi$
$752$	−3.31273	+	3.31273i	−0.120803	+	0.120803i
$753$	12.7497	+	43.5830i	0.464625	+	1.58825i
$754$	26.6644	+	7.80270i	0.971062	+	0.284158i
$755$			2.14954i			0.0782297i
$756$	−5.18400	+	0.355103i	−0.188540	+	0.0129150i
$757$	35.0626			1.27437			0.637187	−	0.770709i	$-0.280098\pi$
$757$	35.0626			1.27437			0.637187	+	0.770709i	$0.280098\pi$
$758$	37.4923			1.36178
$759$	0.0633011	+	0.0346474i	0.00229768	+	0.00125762i
$760$	0.608785	−	0.608785i	0.0220829	−	0.0220829i
$761$	−21.2949	+	21.2949i	−0.771940	+	0.771940i	−0.978445	−	0.206506i	$-0.933791\pi$
$761$	−21.2949	+	21.2949i	−0.771940	+	0.771940i	0.206506	+	0.978445i	$0.433791\pi$
$762$	−6.55612	−	3.58845i	−0.237503	−	0.129996i
$763$	−12.1449			−0.439675
$764$	12.6760			0.458601
$765$	63.4359	+	13.9329i	2.29353	+	0.503744i
$766$			28.5742i			1.03243i
$767$	−10.2784	−	3.00772i	−0.371131	−	0.108603i
$768$	−0.486309	−	1.66238i	−0.0175482	−	0.0599859i
$769$	−10.2910	+	10.2910i	−0.371104	+	0.371104i	−0.867879	−	0.496775i	$-0.834517\pi$
$769$	−10.2910	+	10.2910i	−0.371104	+	0.371104i	0.496775	+	0.867879i	$0.334517\pi$
$770$		−	0.0625325i		−	0.00225351i
$771$	14.9298	+	51.0354i	0.537683	+	1.83799i
$772$	−5.53338	+	5.53338i	−0.199151	+	0.199151i
$773$	34.9528	+	34.9528i	1.25717	+	1.25717i	0.952440	+	0.304727i	$0.0985651\pi$
$773$	34.9528	+	34.9528i	1.25717	+	1.25717i	0.304727	+	0.952440i	$0.401435\pi$
$774$	3.28156	−	14.9408i	0.117953	−	0.537036i
$775$	65.9340	+	65.9340i	2.36842	+	2.36842i
$776$			8.40720i			0.301801i
$777$	18.4853	−	5.40765i	0.663155	−	0.193998i
$778$	−2.38797	−	2.38797i	−0.0856128	−	0.0856128i
$779$	1.63689			0.0586476
$780$	−0.00194723	+	24.0982i	−6.97219e−5	+	0.862855i
$781$	−0.0632535			−0.00226339
$782$	−10.1994	−	10.1994i	−0.364731	−	0.364731i
$783$	26.3109	−	30.1805i	0.940273	−	1.07856i
$784$		−	1.00000i		−	0.0357143i
$785$	27.9747	+	27.9747i	0.998459	+	0.998459i
$786$	0.168863	+	0.0924260i	0.00602314	+	0.00329673i
$787$	−16.6540	−	16.6540i	−0.593651	−	0.593651i	0.344965	−	0.938616i	$-0.387891\pi$
$787$	−16.6540	−	16.6540i	−0.593651	−	0.593651i	−0.938616	+	0.344965i	$0.887891\pi$
$788$	−17.4414	+	17.4414i	−0.621323	+	0.621323i
$789$	24.4814	−	7.16174i	0.871561	−	0.254965i
$790$		−	22.7778i		−	0.810396i
$791$	1.57050	−	1.57050i	0.0558405	−	0.0558405i
$792$	0.0262014	+	0.0409505i	0.000931028	+	0.00145511i
$793$	3.16534	+	5.78421i	0.112405	+	0.205403i
$794$		−	3.71466i		−	0.131828i
$795$	−14.6059	−	7.99445i	−0.518018	−	0.283534i
$796$	−16.2501			−0.575970
$797$	−15.7976			−0.559581			−0.279791	−	0.960061i	$-0.590265\pi$
$797$	−15.7976			−0.559581			−0.279791	+	0.960061i	$0.590265\pi$
$798$	−0.185543	+	0.338988i	−0.00656814	+	0.0120000i
$799$	−18.5856	+	18.5856i	−0.657512	+	0.657512i
$800$	6.99356	−	6.99356i	0.247260	−	0.247260i
$801$	4.69366	−	21.3701i	0.165842	−	0.755074i
$802$	−24.5232			−0.865943
$803$	0.225503			0.00795784
$804$	10.1357	−	18.5180i	0.357459	−	0.653080i
$805$			9.92094i			0.349667i
$806$	16.3184	+	29.8195i	0.574789	+	1.05035i
$807$	−30.5283	+	8.93069i	−1.07465	+	0.314375i
$808$	−2.87744	+	2.87744i	−0.101228	+	0.101228i
$809$		−	17.8770i		−	0.628520i	−0.949337	−	0.314260i	$-0.898244\pi$
$809$		−	17.8770i		−	0.628520i	0.949337	−	0.314260i	$-0.101756\pi$
$810$	31.5327	+	14.5536i	1.10795	+	0.511361i
$811$	−35.1746	+	35.1746i	−1.23515	+	1.23515i	−0.273184	+	0.961962i	$0.588077\pi$
$811$	−35.1746	+	35.1746i	−1.23515	+	1.23515i	−0.961962	+	0.273184i	$0.911923\pi$
$812$	5.44862	+	5.44862i	0.191209	+	0.191209i
$813$	−10.5403	+	19.2572i	−0.369665	+	0.675381i
$814$	−0.127419	−	0.127419i	−0.00446603	−	0.00446603i
$815$			20.0939i			0.703857i
$816$	−2.72837	−	9.32656i	−0.0955121	−	0.326495i
$817$	−0.804441	−	0.804441i	−0.0281438	−	0.0281438i
$818$	−17.2541			−0.603276
$819$	−3.03616	−	10.3818i	−0.106092	−	0.362769i
$820$	28.3104			0.988643
$821$	24.3906	+	24.3906i	0.851239	+	0.851239i	0.990286	−	0.139047i	$-0.0444039\pi$
$821$	24.3906	+	24.3906i	0.851239	+	0.851239i	−0.139047	+	0.990286i	$0.544404\pi$
$822$	0.713729	+	2.43978i	0.0248942	+	0.0850972i
$823$		−	2.34426i		−	0.0817159i	−0.999165	−	0.0408580i	$-0.986991\pi$
$823$		−	2.34426i		−	0.0817159i	0.999165	−	0.0408580i	$-0.0130091\pi$
$824$	12.4039	+	12.4039i	0.432109	+	0.432109i
$825$	−0.133286	+	0.243514i	−0.00464041	+	0.00847807i
$826$	−2.10029	−	2.10029i	−0.0730785	−	0.0730785i
$827$	24.7349	−	24.7349i	0.860116	−	0.860116i	−0.131235	−	0.991351i	$-0.541894\pi$
$827$	24.7349	−	24.7349i	0.860116	−	0.860116i	0.991351	+	0.131235i	$0.0418943\pi$
$828$	−4.15693	−	6.49690i	−0.144463	−	0.225783i
$829$			31.4236i			1.09139i	0.837985	+	0.545694i	$0.183734\pi$
$829$			31.4236i			1.09139i	−0.837985	+	0.545694i	$0.816266\pi$
$830$	46.1230	−	46.1230i	1.60095	−	1.60095i
$831$	−22.4320	+	6.56222i	−0.778158	+	0.227641i
$832$	3.16292	−	1.73087i	0.109655	−	0.0600072i
$833$		−	5.61037i		−	0.194388i
$834$	−11.4962	+	21.0036i	−0.398081	+	0.727296i
$835$	−5.26218			−0.182105
$836$	0.00361558			0.000125048
$837$	48.8739	−	3.34785i	1.68933	−	0.115718i
$838$	−10.6968	+	10.6968i	−0.369514	+	0.369514i
$839$	−37.5413	+	37.5413i	−1.29607	+	1.29607i	−0.365103	+	0.930967i	$0.618966\pi$
$839$	−37.5413	+	37.5413i	−1.29607	+	1.29607i	−0.930967	+	0.365103i	$0.881034\pi$
$840$	−3.20901	+	5.86288i	−0.110721	+	0.202289i
$841$	−30.3749			−1.04741
$842$	−4.83084			−0.166482
$843$	−40.2743	−	22.0439i	−1.38712	−	0.759232i
$844$			12.6989i			0.437115i
$845$	−48.9983	+	10.7535i	−1.68559	+	0.369933i
$846$	−11.8388	+	7.57484i	−0.407026	+	0.260428i
$847$	−7.77799	+	7.77799i	−0.267255	+	0.267255i
$848$			2.49125i			0.0855499i
$849$	0.923932	−	0.270285i	0.0317093	−	0.00927617i
$850$	39.2364	−	39.2364i	1.34580	−	1.34580i
$851$	20.2153	+	20.2153i	0.692973	+	0.692973i
$852$	5.93048	+	3.24601i	0.203175	+	0.111206i
$853$	3.28483	+	3.28483i	0.112471	+	0.112471i	0.761102	−	0.648632i	$-0.224658\pi$
$853$	3.28483	+	3.28483i	0.112471	+	0.112471i	−0.648632	+	0.761102i	$0.724658\pi$
$854$			1.82875i			0.0625787i
$855$	2.17563	−	1.39204i	0.0744050	−	0.0476067i
$856$	−0.161473	−	0.161473i	−0.00551903	−	0.00551903i
$857$	24.3448			0.831603			0.415802	−	0.909455i	$-0.363501\pi$
$857$	24.3448			0.831603			0.415802	+	0.909455i	$0.363501\pi$
$858$	−0.0715657	+	0.0715542i	−0.00244321	+	0.00244282i
$859$	−34.0749			−1.16262			−0.581310	−	0.813682i	$-0.697460\pi$
$859$	−34.0749			−1.16262			−0.581310	+	0.813682i	$0.697460\pi$
$860$	−13.9130	−	13.9130i	−0.474430	−	0.474430i
$861$	−12.1962	+	3.56784i	−0.415644	+	0.121592i
$862$			5.54203i			0.188762i
$863$	−3.76370	−	3.76370i	−0.128118	−	0.128118i	0.640140	−	0.768258i	$-0.278876\pi$
$863$	−3.76370	−	3.76370i	−0.128118	−	0.128118i	−0.768258	+	0.640140i	$0.778876\pi$
$864$	−0.355103	−	5.18400i	−0.0120808	−	0.176363i
$865$	30.5551	+	30.5551i	1.03890	+	1.03890i
$866$	10.7884	−	10.7884i	0.366606	−	0.366606i
$867$	−7.03992	−	24.0650i	−0.239088	−	0.817289i
$868$			9.42782i			0.320001i
$869$	0.0676388	−	0.0676388i	0.00229449	−	0.00229449i
$870$	−14.4600	−	49.4293i	−0.490238	−	1.67581i
$871$	42.1761	+	12.3418i	1.42908	+	0.418187i
$872$		−	12.1449i		−	0.411278i
$873$	−5.41063	+	24.6344i	−0.183122	+	0.833748i
$874$	−0.573622			−0.0194031
$875$	−18.8710			−0.637957
$876$	−21.1426	−	11.5723i	−0.714342	−	0.390990i
$877$	−2.36669	+	2.36669i	−0.0799174	+	0.0799174i	−0.745936	−	0.666018i	$-0.767997\pi$
$877$	−2.36669	+	2.36669i	−0.0799174	+	0.0799174i	0.666018	+	0.745936i	$0.267997\pi$
$878$	−9.50612	+	9.50612i	−0.320816	+	0.320816i
$879$	−14.4662	−	7.91797i	−0.487932	−	0.267066i
$880$	0.0625325			0.00210797
$881$	25.9887			0.875580			0.437790	−	0.899077i	$-0.355761\pi$
$881$	25.9887			0.875580			0.437790	+	0.899077i	$0.355761\pi$
$882$	0.643571	−	2.93016i	0.0216702	−	0.0986635i
$883$		−	10.0316i		−	0.337589i	−0.985651	−	0.168795i	$-0.946013\pi$
$883$		−	10.0316i		−	0.337589i	0.985651	−	0.168795i	$-0.0539875\pi$
$884$	17.7452	−	9.71083i	0.596834	−	0.326611i
$885$	5.57391	+	19.0536i	0.187365	+	0.640480i
$886$	26.9012	−	26.9012i	0.903764	−	0.903764i
$887$			14.6493i			0.491875i	0.969286	+	0.245937i	$0.0790958\pi$
$887$			14.6493i			0.491875i	−0.969286	+	0.245937i	$0.920904\pi$
$888$	5.40765	+	18.4853i	0.181469	+	0.620325i
$889$	3.05122	−	3.05122i	0.102335	−	0.102335i
$890$	−19.9000	−	19.9000i	−0.667049	−	0.667049i
$891$	0.0504198	+	0.136854i	0.00168913	+	0.00458478i
$892$	0.153697	+	0.153697i	0.00514617	+	0.00514617i
$893$			1.04527i			0.0349785i
$894$	−21.8623	+	6.39556i	−0.731185	+	0.213899i
$895$	12.6440	+	12.6440i	0.422642	+	0.422642i
$896$	1.00000			0.0334077
$897$	11.3541	−	11.3523i	0.379102	−	0.379041i
$898$	−7.63786			−0.254879
$899$	−51.3686	−	51.3686i	−1.71324	−	1.71324i
$900$	24.9931	−	15.9914i	0.833102	−	0.533045i
$901$			13.9768i			0.465636i
$902$	0.0840681	+	0.0840681i	0.00279916	+	0.00279916i
$903$	7.74714	+	4.24035i	0.257809	+	0.141110i
$904$	1.57050	+	1.57050i	0.0522340	+	0.0522340i
$905$	−41.8047	+	41.8047i	−1.38964	+	1.38964i
$906$	0.926024	−	0.270897i	0.0307651	−	0.00899996i
$907$		−	30.9250i		−	1.02685i	−0.858136	−	0.513423i	$-0.828377\pi$
$907$		−	30.9250i		−	1.02685i	0.858136	−	0.513423i	$-0.171623\pi$
$908$	8.19047	−	8.19047i	0.271810	−	0.271810i
$909$	−10.2832	+	6.57952i	−0.341072	+	0.218229i
$910$	−13.3531	−	3.90748i	−0.442653	−	0.129532i
$911$			13.6991i			0.453871i	0.973910	+	0.226935i	$0.0728707\pi$
$911$			13.6991i			0.453871i	−0.973910	+	0.226935i	$0.927129\pi$
$912$	−0.338988	−	0.185543i	−0.0112250	−	0.00614393i
$913$	0.273925			0.00906561
$914$	−33.1652			−1.09701
$915$	5.86849	−	10.7218i	0.194006	−	0.354451i
$916$	5.81934	−	5.81934i	0.192277	−	0.192277i
$917$	−0.0785889	+	0.0785889i	−0.00259523	+	0.00259523i
$918$	−1.99226	−	29.0842i	−0.0657543	−	0.959921i
$919$	44.5040			1.46805			0.734025	−	0.679122i	$-0.237639\pi$
$919$	44.5040			1.46805			0.734025	+	0.679122i	$0.237639\pi$
$920$	−9.92094			−0.327084
$921$	−16.0884	+	29.3936i	−0.530131	+	0.968553i
$922$			30.0018i			0.988057i
$923$	−3.95253	+	13.5071i	−0.130099	+	0.444592i
$924$	−0.0269391	+	0.00788071i	−0.000886231	+	0.000259256i
$925$	−77.7667	+	77.7667i	−2.55695	+	2.55695i
$926$			33.3770i			1.09684i
$927$	28.3625	+	44.3280i	0.931546	+	1.45592i
$928$	−5.44862	+	5.44862i	−0.178860	+	0.178860i
$929$	−9.58896	−	9.58896i	−0.314603	−	0.314603i	0.532087	−	0.846690i	$-0.321408\pi$
$929$	−9.58896	−	9.58896i	−0.314603	−	0.314603i	−0.846690	+	0.532087i	$0.821408\pi$
$930$	30.2540	−	55.2742i	0.992067	−	1.81251i
$931$	−0.157765	−	0.157765i	−0.00517054	−	0.00517054i
$932$		−	9.95377i		−	0.326047i
$933$	−1.48235	−	5.06719i	−0.0485298	−	0.165892i
$934$	−0.914545	−	0.914545i	−0.0299248	−	0.0299248i
$935$	0.350830			0.0114734
$936$	10.3818	−	3.03616i	0.339340	−	0.0992400i
$937$	−17.4053			−0.568605			−0.284303	−	0.958735i	$-0.591762\pi$
$937$	−17.4053			−0.568605			−0.284303	+	0.958735i	$0.591762\pi$
$938$	8.61829	+	8.61829i	0.281397	+	0.281397i
$939$	−9.36295	−	32.0059i	−0.305548	−	1.04447i
$940$			18.0781i			0.589644i
$941$	10.1401	+	10.1401i	0.330557	+	0.330557i	0.852798	−	0.522241i	$-0.174904\pi$
$941$	10.1401	+	10.1401i	0.330557	+	0.330557i	−0.522241	+	0.852798i	$0.674904\pi$
$942$	8.52600	−	15.5771i	0.277792	−	0.507528i
$943$	−13.3376	−	13.3376i	−0.434333	−	0.434333i
$944$	2.10029	−	2.10029i	0.0683586	−	0.0683586i
$945$	−13.1761	+	15.1139i	−0.428618	+	0.491656i
$946$		−	0.0826296i		−	0.00268652i
$947$	−26.0523	+	26.0523i	−0.846587	+	0.846587i	−0.989705	−	0.143119i	$-0.954287\pi$
$947$	−26.0523	+	26.0523i	−0.846587	+	0.846587i	0.143119	+	0.989705i	$0.454287\pi$
$948$	−9.81269	+	2.87059i	−0.318701	+	0.0932323i
$949$	14.0911	−	48.1538i	0.457415	−	1.56314i
$950$		−	2.20668i		−	0.0715941i
$951$	14.3728	−	26.2592i	0.466070	−	0.851514i
$952$	5.61037			0.181833
$953$	−38.1006			−1.23420			−0.617100	−	0.786885i	$-0.711693\pi$
$953$	−38.1006			−1.23420			−0.617100	+	0.786885i	$0.711693\pi$
$954$	−1.60330	+	7.29976i	−0.0519087	+	0.236338i
$955$	34.5876	−	34.5876i	1.11923	−	1.11923i
$956$	−12.3472	+	12.3472i	−0.399337	+	0.399337i
$957$	0.103842	−	0.189720i	0.00335673	−	0.00613277i
$958$	20.5198			0.662966
$959$	−1.46765			−0.0473927
$960$	−5.86288	−	3.20901i	−0.189224	−	0.103570i
$961$		−	57.8838i		−	1.86722i
$962$	−35.1710	+	19.2469i	−1.13396	+	0.620545i
$963$	−0.369222	−	0.577060i	−0.0118980	−	0.0185955i
$964$	−7.54377	+	7.54377i	−0.242969	+	0.242969i
$965$			30.1966i			0.972064i
$966$	4.27396	−	1.25029i	0.137512	−	0.0402276i
$967$	−14.0113	+	14.0113i	−0.450574	+	0.450574i	−0.895545	−	0.444971i	$-0.853214\pi$
$967$	−14.0113	+	14.0113i	−0.450574	+	0.450574i	0.444971	+	0.895545i	$0.353214\pi$
$968$	−7.77799	−	7.77799i	−0.249994	−	0.249994i
$969$	−1.90185	−	1.04096i	−0.0610961	−	0.0334405i
$970$	22.9398	+	22.9398i	0.736552	+	0.736552i
$971$		−	28.2363i		−	0.906145i	−0.891474	−	0.453072i	$-0.850328\pi$
$971$		−	28.2363i		−	0.906145i	0.891474	−	0.453072i	$-0.149672\pi$
$972$	2.29577	−	15.4185i	0.0736368	−	0.494548i
$973$	−9.77510	−	9.77510i	−0.313375	−	0.313375i
$974$	23.2530			0.745074
$975$	43.6712	+	43.6783i	1.39860	+	1.39882i
$976$	−1.82875			−0.0585370
$977$	−5.23687	−	5.23687i	−0.167542	−	0.167542i	0.618356	−	0.785898i	$-0.287799\pi$
$977$	−5.23687	−	5.23687i	−0.167542	−	0.167542i	−0.785898	+	0.618356i	$0.787799\pi$
$978$	8.65646	−	2.53234i	0.276803	−	0.0809754i
$979$		−	0.118186i		−	0.00377726i
$980$	−2.72859	−	2.72859i	−0.0871615	−	0.0871615i
$981$	7.81610	−	35.5864i	0.249549	−	1.13619i
$982$	−3.69948	−	3.69948i	−0.118055	−	0.118055i
$983$	−21.8072	+	21.8072i	−0.695542	+	0.695542i	−0.963446	−	0.267904i	$-0.913669\pi$
$983$	−21.8072	+	21.8072i	−0.695542	+	0.695542i	0.267904	+	0.963446i	$0.413669\pi$
$984$	−3.56784	−	12.1962i	−0.113739	−	0.388800i
$985$			95.1806i			3.03271i
$986$	−30.5688	+	30.5688i	−0.973508	+	0.973508i
$987$	−2.27831	−	7.78809i	−0.0725195	−	0.247898i
$988$	0.225928	−	0.772070i	0.00718771	−	0.0245628i
$989$			13.1094i			0.416855i
$990$	0.183230	+	0.0402441i	0.00582343	+	0.00127904i
$991$	−47.1491			−1.49774			−0.748870	−	0.662716i	$-0.769403\pi$
$991$	−47.1491			−1.49774			−0.748870	+	0.662716i	$0.769403\pi$
$992$	−9.42782			−0.299334
$993$	19.8774	+	10.8798i	0.630790	+	0.345259i
$994$	−2.76005	+	2.76005i	−0.0875434	+	0.0875434i
$995$	−44.3399	+	44.3399i	−1.40567	+	1.40567i
$996$	−25.6825	−	14.0572i	−0.813782	−	0.445418i
$997$	48.3285			1.53058			0.765289	−	0.643687i	$-0.222596\pi$
$997$	48.3285			1.53058			0.765289	+	0.643687i	$0.222596\pi$
$998$	−31.0319			−0.982297
$999$	3.94866	+	57.6449i	0.124930	+	1.82381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.p.d.239.7	yes	20
3.2	odd	2		546.2.p.c.239.2	✓	20
13.8	odd	4		546.2.p.c.281.2	yes	20
39.8	even	4	inner	546.2.p.d.281.7	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.p.c.239.2	✓	20	3.2	odd	2
546.2.p.c.281.2	yes	20	13.8	odd	4
546.2.p.d.239.7	yes	20	1.1	even	1	trivial
546.2.p.d.281.7	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)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.486309 - 1.66238i) q^{3} +1.00000i q^{4} +(2.72859 + 2.72859i) q^{5} +(0.831607 - 1.51935i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52701 + 1.61686i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(-0.486309 - 1.66238i) q^{3} +1.00000i q^{4} +(2.72859 + 2.72859i) q^{5} +(0.831607 - 1.51935i) q^{6} +(0.707107 + 0.707107i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.52701 + 1.61686i) q^{9} +3.85881i q^{10} +(-0.0114588 + 0.0114588i) q^{11} +(1.66238 - 0.486309i) q^{12} +(1.73087 + 3.16292i) q^{13} +1.00000i q^{14} +(3.20901 - 5.86288i) q^{15} -1.00000 q^{16} -5.61037 q^{17} +(-2.93016 - 0.643571i) q^{18} +(-0.157765 + 0.157765i) q^{19} +(-2.72859 + 2.72859i) q^{20} +(0.831607 - 1.51935i) q^{21} -0.0162051 q^{22} +2.57099 q^{23} +(1.51935 + 0.831607i) q^{24} +9.89038i q^{25} +(-1.01261 + 3.46044i) q^{26} +(3.91674 + 3.41455i) q^{27} +(-0.707107 + 0.707107i) q^{28} -7.70551i q^{29} +(6.41480 - 1.87657i) q^{30} +(6.66648 - 6.66648i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(0.0246213 + 0.0134763i) q^{33} +(-3.96713 - 3.96713i) q^{34} +3.85881i q^{35} +(-1.61686 - 2.52701i) q^{36} +(7.86287 + 7.86287i) q^{37} -0.223113 q^{38} +(4.41624 - 4.41552i) q^{39} -3.85881 q^{40} +(-5.18774 - 5.18774i) q^{41} +(1.66238 - 0.486309i) q^{42} +5.09898i q^{43} +(-0.0114588 - 0.0114588i) q^{44} +(-11.3069 - 2.48342i) q^{45} +(1.81796 + 1.81796i) q^{46} +(3.31273 - 3.31273i) q^{47} +(0.486309 + 1.66238i) q^{48} +1.00000i q^{49} +(-6.99356 + 6.99356i) q^{50} +(2.72837 + 9.32656i) q^{51} +(-3.16292 + 1.73087i) q^{52} -2.49125i q^{53} +(0.355103 + 5.18400i) q^{54} -0.0625325 q^{55} -1.00000 q^{56} +(0.338988 + 0.185543i) q^{57} +(5.44862 - 5.44862i) q^{58} +(-2.10029 + 2.10029i) q^{59} +(5.86288 + 3.20901i) q^{60} +1.82875 q^{61} +9.42782 q^{62} +(-2.93016 - 0.643571i) q^{63} -1.00000i q^{64} +(-3.90748 + 13.3531i) q^{65} +(0.00788071 + 0.0269391i) q^{66} +(8.61829 - 8.61829i) q^{67} -5.61037i q^{68} +(-1.25029 - 4.27396i) q^{69} +(-2.72859 + 2.72859i) q^{70} +(2.76005 + 2.76005i) q^{71} +(0.643571 - 2.93016i) q^{72} +(-9.83977 - 9.83977i) q^{73} +11.1198i q^{74} +(16.4416 - 4.80978i) q^{75} +(-0.157765 - 0.157765i) q^{76} -0.0162051 q^{77} +(6.24500 + 0.000504619i) q^{78} -5.90280 q^{79} +(-2.72859 - 2.72859i) q^{80} +(3.77153 - 8.17163i) q^{81} -7.33658i q^{82} +(-11.9527 - 11.9527i) q^{83} +(1.51935 + 0.831607i) q^{84} +(-15.3084 - 15.3084i) q^{85} +(-3.60552 + 3.60552i) q^{86} +(-12.8095 + 3.74726i) q^{87} -0.0162051i q^{88} +(-5.15703 + 5.15703i) q^{89} +(-6.23915 - 9.75123i) q^{90} +(-1.01261 + 3.46044i) q^{91} +2.57099i q^{92} +(-14.3242 - 7.84024i) q^{93} +4.68491 q^{94} -0.860951 q^{95} +(-0.831607 + 1.51935i) q^{96} +(5.94479 - 5.94479i) q^{97} +(-0.707107 + 0.707107i) q^{98} +(0.0104292 - 0.0474836i) 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

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