LMFDB - Embedded newform 546.2.p.c.239.2

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			239.2
Root			$0.831607 + 1.51935i$ of defining polynomial
Character	$\chi$	$=$	546.239
Dual form			546.2.p.c.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 0.707107i) q^{2} +(-0.486309 + 1.66238i) q^{3} +1.00000i q^{4} +(-2.72859 - 2.72859i) q^{5} +(1.51935 - 0.831607i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.52701 - 1.61686i) q^{9} +O(q^{10})$	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.486309 + 1.66238i) q^{3} +1.00000i q^{4} +(-2.72859 - 2.72859i) q^{5} +(1.51935 - 0.831607i) 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} +(5.86288 - 3.20901i) q^{15} -1.00000 q^{16} +5.61037 q^{17} +(0.643571 + 2.93016i) q^{18} +(-0.157765 + 0.157765i) q^{19} +(2.72859 - 2.72859i) q^{20} +(-1.51935 + 0.831607i) q^{21} -0.0162051 q^{22} -2.57099 q^{23} +(0.831607 + 1.51935i) 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} +(0.0134763 + 0.0246213i) 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} +(-6.09972 + 1.33921i) 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} +(2.48342 + 11.3069i) 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} +(-5.18400 - 0.355103i) q^{54} -0.0625325 q^{55} +1.00000 q^{56} +(-0.185543 - 0.338988i) q^{57} +(5.44862 - 5.44862i) q^{58} +(2.10029 - 2.10029i) q^{59} +(3.20901 + 5.86288i) q^{60} +1.82875 q^{61} -9.42782 q^{62} +(-0.643571 - 2.93016i) 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} +(-2.93016 + 0.643571i) 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} +(5.26011 + 3.36619i) 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} +(-0.831607 - 1.51935i) 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} +(7.84024 + 14.3242i) q^{93} +4.68491 q^{94} +0.860951 q^{95} +(-1.51935 + 0.831607i) q^{96} +(5.94479 - 5.94479i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-0.0474836 + 0.0104292i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	$ 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) $ 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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	$-0.918674\pi$
$5$	−2.72859	−	2.72859i	−1.22026	−	1.22026i	−0.252723	−	0.967539i	$-0.581326\pi$
$6$	1.51935	−	0.831607i	0.620273	−	0.339502i
$7$	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	−0.705377	−	0.708832i	$-0.749222\pi$
$11$	0.0114588	−	0.0114588i	0.00345495	−	0.00345495i	0.708832	+	0.705377i	$0.249222\pi$
$12$	−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
$15$	5.86288	−	3.20901i	1.51379	−	0.828563i
$16$	−1.00000			−0.250000
$17$	5.61037			1.36071			0.680357	−	0.732881i	$-0.261825\pi$
$17$	5.61037			1.36071			0.680357	+	0.732881i	$0.261825\pi$
$18$	0.643571	+	2.93016i	0.151691	+	0.690644i
$19$	−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
$21$	−1.51935	+	0.831607i	−0.331550	+	0.181472i
$22$	−0.0162051			−0.00345495
$23$	−2.57099			−0.536088			−0.268044	−	0.963407i	$-0.586377\pi$
$23$	−2.57099			−0.536088			−0.268044	+	0.963407i	$0.586377\pi$
$24$	0.831607	+	1.51935i	0.169751	+	0.310136i
$25$			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	$0.253773\pi$
$29$			7.70551i			1.43088i	−0.698675	+	0.715439i	$0.746227\pi$
$30$	−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
$33$	0.0134763	+	0.0246213i	0.00234592	+	0.00428602i
$34$	−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
$39$	−6.09972	+	1.33921i	−0.976736	+	0.214445i
$40$	−3.85881			−0.610131
$41$	5.18774	+	5.18774i	0.810189	+	0.810189i	0.984662	−	0.174473i	$-0.0558221\pi$
$41$	5.18774	+	5.18774i	0.810189	+	0.810189i	−0.174473	+	0.984662i	$0.555822\pi$
$42$	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
$45$	2.48342	+	11.3069i	0.370206	+	1.68553i
$46$	1.81796	+	1.81796i	0.268044	+	0.268044i
$47$	−3.31273	+	3.31273i	−0.483211	+	0.483211i	−0.906156	−	0.422944i	$-0.860997\pi$
$47$	−3.31273	+	3.31273i	−0.483211	+	0.483211i	0.422944	+	0.906156i	$0.360997\pi$
$48$	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	$0.0547321\pi$
$53$			2.49125i			0.342200i	−0.985254	+	0.171100i	$0.945268\pi$
$54$	−5.18400	−	0.355103i	−0.705454	−	0.0483234i
$55$	−0.0625325			−0.00843188
$56$	1.00000			0.133631
$57$	−0.185543	−	0.338988i	−0.0245757	−	0.0449000i
$58$	5.44862	−	5.44862i	0.715439	−	0.715439i
$59$	2.10029	−	2.10029i	0.273435	−	0.273435i	−0.557047	−	0.830481i	$-0.688066\pi$
$59$	2.10029	−	2.10029i	0.273435	−	0.273435i	0.830481	+	0.557047i	$0.188066\pi$
$60$	3.20901	+	5.86288i	0.414281	+	0.756895i
$61$	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
$63$	−0.643571	−	2.93016i	−0.0810823	−	0.369165i
$64$		−	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	0.524100	−	0.851657i	$-0.324402\pi$
$71$	−2.76005	−	2.76005i	−0.327557	−	0.327557i	−0.851657	+	0.524100i	$0.824402\pi$
$72$	−2.93016	+	0.643571i	−0.345322	+	0.0758456i
$73$	−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
$78$	5.26011	+	3.36619i	0.595590	+	0.381146i
$79$	−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	$0.128222\pi$
$83$	11.9527	+	11.9527i	1.31197	+	1.31197i	0.392017	+	0.919958i	$0.371778\pi$
$84$	−0.831607	−	1.51935i	−0.0907358	−	0.165775i
$85$	−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	−0.378824	−	0.925469i	$-0.623671\pi$
$89$	5.15703	−	5.15703i	0.546645	−	0.546645i	0.925469	+	0.378824i	$0.123671\pi$
$90$	6.23915	−	9.75123i	0.657664	−	1.02787i
$91$	−1.01261	+	3.46044i	−0.106151	+	0.362752i
$92$		−	2.57099i		−	0.268044i
$93$	7.84024	+	14.3242i	0.812995	+	1.48535i
$94$	4.68491			0.483211
$95$	0.860951			0.0883318
$96$	−1.51935	+	0.831607i	−0.155068	+	0.0848755i
$97$	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
$99$	−0.0474836	+	0.0104292i	−0.00477228	+	0.00104817i
$100$	−9.89038			−0.989038
$101$	−4.06932			−0.404913			−0.202456	−	0.979291i	$-0.564892\pi$
$101$	−4.06932			−0.404913			−0.202456	+	0.979291i	$0.564892\pi$
$102$	8.52412	−	4.66562i	0.844014	−	0.461965i
$103$		−	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	$-0.996486\pi$
$107$		−	0.228357i		−	0.0220761i	0.999939	−	0.0110381i	$-0.00351360\pi$
$108$	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
$111$	−16.8948	+	9.24728i	−1.60359	+	0.877713i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$			2.22102i			0.208936i	0.994528	+	0.104468i	$0.0333140\pi$
$113$			2.22102i			0.208936i	−0.994528	+	0.104468i	$0.966686\pi$
$114$	−0.108502	+	0.370899i	−0.0101622	+	0.0347379i
$115$	7.01517	+	7.01517i	0.654168	+	0.654168i
$116$	−7.70551			−0.715439
$117$	0.740077	−	10.7913i	0.0684202	−	0.997657i
$118$	−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
$123$	−11.1468	+	6.10115i	−1.00508	+	0.550122i
$124$	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	$-0.998455\pi$
$131$		−	0.111141i		−	0.00971047i	0.999988	−	0.00485524i	$-0.00154548\pi$
$132$	−0.0246213	+	0.0134763i	−0.00214301	+	0.00117296i
$133$	−0.223113			−0.0193464
$134$	−12.1881			−1.05289
$135$	−20.0041	−	1.37027i	−1.72168	−	0.117934i
$136$	3.96713	−	3.96713i	0.340178	−	0.340178i
$137$	1.03778	−	1.03778i	0.0886637	−	0.0886637i	−0.661384	−	0.750048i	$-0.730031\pi$
$137$	1.03778	−	1.03778i	0.0886637	−	0.0886637i	0.750048	+	0.661384i	$0.230031\pi$
$138$	−3.90624	+	2.13805i	−0.332521	+	0.182003i
$139$	−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
$141$	−3.89600	−	7.11802i	−0.328102	−	0.599446i
$142$			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	0.976653	−	0.214823i	$-0.0689176\pi$
$149$	9.29931	+	9.29931i	0.761829	+	0.761829i	−0.214823	+	0.976653i	$0.568918\pi$
$150$	8.22491	+	15.0270i	0.671561	+	1.22695i
$151$	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
$156$	−1.33921	−	6.09972i	−0.107222	−	0.488368i
$157$	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
$162$	3.11134	−	8.44509i	0.244450	−	0.663509i
$163$	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	−0.668813	−	0.743430i	$-0.733197\pi$
$167$	0.964267	−	0.964267i	0.0746173	−	0.0746173i	0.743430	+	0.668813i	$0.233197\pi$
$168$	−0.486309	+	1.66238i	−0.0375196	+	0.128255i
$169$	−7.00816	+	10.9492i	−0.539089	+	0.842249i
$170$			21.6493i			1.66043i
$171$	0.653757	−	0.143589i	0.0499941	−	0.0109806i
$172$	−5.09898			−0.388793
$173$	−11.1981			−0.851378			−0.425689	−	0.904870i	$-0.639968\pi$
$173$	−11.1981			−0.851378			−0.425689	+	0.904870i	$0.639968\pi$
$174$	6.40796	+	11.7074i	0.485786	+	0.887535i
$175$	−6.99356	+	6.99356i	−0.528663	+	0.528663i
$176$	−0.0114588	+	0.0114588i	−0.000863737	+	0.000863737i
$177$	2.47009	+	4.51287i	0.185663	+	0.339208i
$178$	−7.29315			−0.546645
$179$	−4.63389			−0.346354			−0.173177	−	0.984891i	$-0.555403\pi$
$179$	−4.63389			−0.346354			−0.173177	+	0.984891i	$0.555403\pi$
$180$	−11.3069	+	2.48342i	−0.842767	+	0.185103i
$181$			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
$189$	5.18400	+	0.355103i	0.377081	+	0.0258299i
$190$	−0.608785	−	0.608785i	−0.0441659	−	0.0441659i
$191$			12.6760i			0.917203i	0.888642	+	0.458601i	$0.151649\pi$
$191$			12.6760i			0.917203i	−0.888642	+	0.458601i	$0.848351\pi$
$192$	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
$195$	20.2978	+	12.9895i	1.45355	+	0.930195i
$196$	−1.00000			−0.0714286
$197$	−17.4414	−	17.4414i	−1.24265	−	1.24265i	−0.958899	−	0.283747i	$-0.908422\pi$
$197$	−17.4414	−	17.4414i	−1.24265	−	1.24265i	−0.283747	−	0.958899i	$-0.591578\pi$
$198$	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
$201$	10.1357	+	18.5180i	0.714918	+	1.30616i
$202$	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
$210$	−3.20901	−	5.86288i	−0.221443	−	0.404577i
$211$	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
$213$	5.93048	−	3.24601i	0.406350	−	0.222413i
$214$	−0.161473	+	0.161473i	−0.0110381	+	0.0110381i
$215$	13.9130	−	13.9130i	0.948859	−	0.948859i
$216$	0.355103	−	5.18400i	0.0241617	−	0.352727i
$217$	9.42782			0.640002
$218$	12.1449			0.822556
$219$	21.1426	−	11.5723i	1.42868	−	0.781981i
$220$		−	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	0.924588	−	0.380968i	$-0.124409\pi$
$227$	8.19047	+	8.19047i	0.543620	+	0.543620i	−0.380968	+	0.924588i	$0.624409\pi$
$228$	0.338988	−	0.185543i	0.0224500	−	0.0122879i
$229$	−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	$-0.394283\pi$
$233$	9.95377			0.652093			0.326047	+	0.945354i	$0.394283\pi$
$234$	−8.15392	+	7.10729i	−0.533038	+	0.464618i
$235$	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	0.184213	−	0.982886i	$-0.441026\pi$
$239$	−12.3472	−	12.3472i	−0.798673	−	0.798673i	−0.982886	+	0.184213i	$0.941026\pi$
$240$	−5.86288	+	3.20901i	−0.378447	+	0.207141i
$241$	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
$249$	−25.6825	+	14.0572i	−1.62756	+	0.890836i
$250$	−18.8710			−1.19351
$251$	26.2173			1.65482			0.827410	−	0.561599i	$-0.189814\pi$
$251$	26.2173			1.65482			0.827410	+	0.561599i	$0.189814\pi$
$252$	2.93016	−	0.643571i	0.184583	−	0.0405412i
$253$	−0.0294603	+	0.0294603i	−0.00185216	+	0.00185216i
$254$	−3.05122	+	3.05122i	−0.191451	+	0.191451i
$255$	32.8929	−	18.0037i	2.05984	−	1.12744i
$256$	1.00000			0.0625000
$257$	30.7002			1.91503			0.957513	−	0.288390i	$-0.0931201\pi$
$257$	30.7002			1.91503			0.957513	+	0.288390i	$0.0931201\pi$
$258$	4.24035	+	7.74714i	0.263992	+	0.482316i
$259$			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	$-0.849981\pi$
$263$		−	14.7267i		−	0.908089i	0.890979	−	0.454045i	$-0.150019\pi$
$264$	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
$267$	6.06503	+	11.0809i	0.371174	+	0.678138i
$268$	8.61829	+	8.61829i	0.526446	+	0.526446i
$269$			18.3642i			1.11969i	0.828598	+	0.559843i	$0.189139\pi$
$269$			18.3642i			1.11969i	−0.828598	+	0.559843i	$0.810861\pi$
$270$	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
$273$	−5.26011	−	3.36619i	−0.318356	−	0.203731i
$274$	−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
$279$	−27.6250	+	6.06747i	−1.65386	+	0.363250i
$280$	−2.72859	−	2.72859i	−0.163064	−	0.163064i
$281$	−18.7437	+	18.7437i	−1.11815	+	1.11815i	−0.126142	+	0.992012i	$0.540260\pi$
$281$	−18.7437	+	18.7437i	−1.11815	+	1.11815i	−0.992012	+	0.126142i	$0.959740\pi$
$282$	−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
$288$	−0.643571	−	2.93016i	−0.0379228	−	0.172661i
$289$	14.4762			0.851542
$290$	−29.7341			−1.74605
$291$	6.99148	+	12.7735i	0.409848	+	0.748795i
$292$	9.83977	−	9.83977i	0.575829	−	0.575829i
$293$	−6.73256	+	6.73256i	−0.393321	+	0.393321i	−0.875869	−	0.482549i	$-0.839711\pi$
$293$	−6.73256	+	6.73256i	−0.393321	+	0.393321i	0.482549	+	0.875869i	$0.339711\pi$
$294$	0.831607	+	1.51935i	0.0485003	+	0.0886104i
$295$	−11.4617			−0.667323
$296$	11.1198			0.646324
$297$	0.00575449	−	0.0840075i	0.000333909	−	0.00487461i
$298$		−	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
$306$	3.61067	+	16.4393i	0.206408	+	0.939770i
$307$	−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	$-0.527543\pi$
$311$	−3.04815			−0.172845			−0.0864225	+	0.996259i	$0.527543\pi$
$312$	−3.36619	+	5.26011i	−0.190573	+	0.297795i
$313$	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	0.275032	−	0.961435i	$-0.411312\pi$
$317$	−12.2211	−	12.2211i	−0.686403	−	0.686403i	−0.961435	+	0.275032i	$0.911312\pi$
$318$	2.07174	+	3.78509i	0.116178	+	0.212257i
$319$	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
$327$	−10.0998	−	18.4524i	−0.558519	−	1.02042i
$328$	7.33658			0.405095
$329$	−4.68491			−0.258287
$330$	−0.0950088	+	0.0520024i	−0.00523006	+	0.00286264i
$331$	−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
$333$	−7.15636	−	32.5827i	−0.392166	−	1.78552i
$334$	−1.36368			−0.0746173
$335$	−47.0315			−2.56961
$336$	1.51935	−	0.831607i	0.0828874	−	0.0453679i
$337$		−	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
$345$	−15.0734	+	8.25032i	−0.811525	+	0.444183i
$346$	7.91827	+	7.91827i	0.425689	+	0.425689i
$347$			11.8159i			0.634311i	0.948374	+	0.317156i	$0.102728\pi$
$347$			11.8159i			0.634311i	−0.948374	+	0.317156i	$0.897272\pi$
$348$	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
$351$	17.5793	+	6.47820i	0.938315	+	0.345781i
$352$	0.0162051			0.000863737
$353$	0.431441	+	0.431441i	0.0229633	+	0.0229633i	0.718495	−	0.695532i	$-0.244831\pi$
$353$	0.431441	+	0.431441i	0.0229633	+	0.0229633i	−0.695532	+	0.718495i	$0.744831\pi$
$354$	1.44446	−	4.93770i	0.0767724	−	0.262436i
$355$			15.0621i			0.799411i
$356$	5.15703	+	5.15703i	0.273322	+	0.273322i
$357$	−8.52412	+	4.66562i	−0.451144	+	0.246931i
$358$	3.27666	+	3.27666i	0.173177	+	0.173177i
$359$	1.98976	−	1.98976i	0.105015	−	0.105015i	−0.652647	−	0.757662i	$-0.726341\pi$
$359$	1.98976	−	1.98976i	0.105015	−	0.105015i	0.757662	+	0.652647i	$0.226341\pi$
$360$	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
$366$	2.77852	−	1.52080i	0.145236	−	0.0794937i
$367$	−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
$369$	−4.72161	−	21.4973i	−0.245797	−	1.11911i
$370$	−30.3413	+	30.3413i	−1.57737	+	1.57737i
$371$	−1.76158	+	1.76158i	−0.0914567	+	0.0914567i
$372$	−14.3242	+	7.84024i	−0.742674	+	0.406498i
$373$	−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
$375$	15.6933	+	28.6717i	0.810397	+	1.48060i
$376$			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	$-0.989503\pi$
$383$	−20.2050	−	20.2050i	−1.03243	−	1.03243i	−0.0329712	−	0.999456i	$-0.510497\pi$
$384$	−0.831607	−	1.51935i	−0.0424378	−	0.0775341i
$385$	−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	$-0.472715\pi$
$389$	3.37710			0.171226			0.0856128	+	0.996328i	$0.472715\pi$
$390$	−5.16774	−	23.5376i	−0.261679	−	1.19187i
$391$	−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
$396$	−0.0104292	−	0.0474836i	−0.000524085	−	0.00238614i
$397$	−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	−0.126078	−	0.992020i	$-0.540239\pi$
$401$	17.3405	−	17.3405i	0.865943	−	0.865943i	0.992020	+	0.126078i	$0.0402388\pi$
$402$	5.92719	−	20.2612i	0.295621	−	1.01054i
$403$	32.6244	+	9.54673i	1.62514	+	0.475557i
$404$		−	4.06932i		−	0.202456i
$405$	12.0061	−	32.5880i	0.596586	−	1.61931i
$406$	7.70551			0.382418
$407$	0.180197			0.00893205
$408$	4.66562	+	8.52412i	0.230983	+	0.422007i
$409$	−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
$411$	1.22050	+	2.22987i	0.0602030	+	0.109991i
$412$	17.5417			0.864217
$413$	2.97026			0.146157
$414$	−1.65461	−	7.53340i	−0.0813198	−	0.370246i
$415$		−	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	$-0.879524\pi$
$419$		−	15.1275i		−	0.739027i	0.929225	−	0.369514i	$-0.120476\pi$
$420$	−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
$423$	13.7275	−	3.01507i	0.667454	−	0.146598i
$424$	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
$429$	−0.0545495	+	0.0852408i	−0.00263368	+	0.00411547i
$430$	−19.6760			−0.948859
$431$	−3.91881	−	3.91881i	−0.188762	−	0.188762i	0.606399	−	0.795161i	$-0.292614\pi$
$431$	−3.91881	−	3.91881i	−0.188762	−	0.188762i	−0.795161	+	0.606399i	$0.792614\pi$
$432$	−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
$435$	24.7271	+	45.1765i	1.18557	+	2.16605i
$436$	−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	$0.359207\pi$
$443$			38.0441i			1.80753i	−0.428032	+	0.903764i	$0.640793\pi$
$444$	−9.24728	−	16.8948i	−0.438856	−	0.801794i
$445$	−28.1428			−1.33410
$446$	−0.217361			−0.0102923
$447$	−19.9813	+	10.9366i	−0.945084	+	0.517285i
$448$	0.707107	−	0.707107i	0.0334077	−	0.0334077i
$449$	5.40078	−	5.40078i	0.254879	−	0.254879i	−0.568089	−	0.822967i	$-0.692317\pi$
$449$	5.40078	−	5.40078i	0.254879	−	0.254879i	0.822967	+	0.568089i	$0.192317\pi$
$450$	−28.9804	+	6.36516i	−1.36615	+	0.300057i
$451$	0.118890			0.00559832
$452$	−2.22102			−0.104468
$453$	−0.846351	+	0.463244i	−0.0397650	+	0.0217651i
$454$		−	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	0.0118730	−	0.999930i	$-0.496221\pi$
$461$	−21.2145	−	21.2145i	−0.988057	−	0.988057i	−0.999930	+	0.0118730i	$0.996221\pi$
$462$	0.0246213	−	0.0134763i	0.00114549	−	0.000626974i
$463$	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	$-0.490473\pi$
$467$	1.29336			0.0598496			0.0299248	+	0.999552i	$0.490473\pi$
$468$	10.7913	+	0.740077i	0.498828	+	0.0342101i
$469$	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
$474$	−8.96843	+	4.90881i	−0.411934	+	0.225469i
$475$	−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	−0.956078	−	0.293112i	$-0.905309\pi$
$479$	−14.5097	+	14.5097i	−0.662966	+	0.662966i	0.293112	+	0.956078i	$0.405309\pi$
$480$	6.41480	+	1.87657i	0.292794	+	0.0856534i
$481$	−11.2600	+	38.4793i	−0.513413	+	1.75450i
$482$		−	10.6685i		−	0.485937i
$483$	3.90624	−	2.13805i	0.177740	−	0.0972847i
$484$	−10.9997			−0.499988
$485$	−32.4417			−1.47310
$486$	12.5259	+	9.27916i	0.568185	+	0.420911i
$487$	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
$489$	−7.91168	+	4.33040i	−0.357778	+	0.195828i
$490$	−3.85881			−0.174323
$491$	5.23186			0.236111			0.118055	−	0.993007i	$-0.462334\pi$
$491$	5.23186			0.236111			0.118055	+	0.993007i	$0.462334\pi$
$492$	−6.10115	−	11.1468i	−0.275061	−	0.502538i
$493$			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
$501$	1.13405	+	2.07191i	0.0506654	+	0.0925661i
$502$	−18.5384	−	18.5384i	−0.827410	−	0.827410i
$503$		−	14.1370i		−	0.630336i	−0.949036	−	0.315168i	$-0.897939\pi$
$503$		−	14.1370i		−	0.630336i	0.949036	−	0.315168i	$-0.102061\pi$
$504$	−2.52701	−	1.61686i	−0.112562	−	0.0720207i
$505$	11.1035	+	11.1035i	0.494099	+	0.494099i
$506$	0.0416632			0.00185216
$507$	−14.7936	−	16.9749i	−0.657008	−	0.753883i
$508$	4.31508			0.191451
$509$	24.6460	+	24.6460i	1.09241	+	1.09241i	0.995271	+	0.0971423i	$0.0309702\pi$
$509$	24.6460	+	24.6460i	1.09241	+	1.09241i	0.0971423	+	0.995271i	$0.469030\pi$
$510$	−35.9894	−	10.5283i	−1.59364	−	0.466199i
$511$		−	13.9155i		−	0.615587i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−0.0792282	+	1.15662i	−0.00349801	+	0.0510661i
$514$	−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	$-0.610557\pi$
$521$		−	42.9249i		−	1.88057i	0.340383	−	0.940287i	$-0.389443\pi$
$522$	−22.5784	+	4.95905i	−0.988228	+	0.217052i
$523$	−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
$525$	−8.22491	−	15.0270i	−0.358964	−	0.655831i
$526$	−10.4134	+	10.4134i	−0.454045	+	0.454045i
$527$	37.4014	−	37.4014i	1.62923	−	1.62923i
$528$	−0.0134763	−	0.0246213i	−0.000586481	−	0.00107150i
$529$	−16.3900			−0.712610
$530$	−9.61326			−0.417573
$531$	−8.70332	+	1.91157i	−0.377692	+	0.0829552i
$532$		−	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
$540$	1.37027	−	20.0041i	0.0589671	−	0.860838i
$541$	−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
$546$	1.33921	+	6.09972i	0.0573128	+	0.261044i
$547$	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
$552$	−2.13805	−	3.90624i	−0.0910015	−	0.166260i
$553$	−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	−0.735297	−	0.677745i	$-0.762957\pi$
$557$	−1.35829	+	1.35829i	−0.0575525	+	0.0575525i	0.677745	+	0.735297i	$0.262957\pi$
$558$	23.8242	+	15.2435i	1.00856	+	0.645307i
$559$	−16.1277	+	8.82568i	−0.682128	+	0.373287i
$560$			3.85881i			0.163064i
$561$	0.0756070	+	0.138135i	0.00319213	+	0.00583205i
$562$	26.5076			1.11815
$563$	−37.6045			−1.58484			−0.792420	−	0.609976i	$-0.791179\pi$
$563$	−37.6045			−1.58484			−0.792420	+	0.609976i	$0.791179\pi$
$564$	7.11802	−	3.89600i	0.299723	−	0.164051i
$565$	6.06025	−	6.06025i	0.254957	−	0.254957i
$566$	0.393002	−	0.393002i	0.0165191	−	0.0165191i
$567$	−3.11134	+	8.44509i	−0.130664	+	0.354660i
$568$	−3.90330			−0.163779
$569$	12.8584			0.539053			0.269527	−	0.962993i	$-0.413133\pi$
$569$	12.8584			0.539053			0.269527	+	0.962993i	$0.413133\pi$
$570$	1.30809	−	0.715973i	0.0547898	−	0.0299888i
$571$		−	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
$579$	−11.8895	+	6.50764i	−0.494111	+	0.270448i
$580$	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
$585$	−31.4644	+	27.4257i	−1.30089	+	1.13391i
$586$	9.52128			0.393321
$587$	19.4406	+	19.4406i	0.802398	+	0.802398i	0.983470	−	0.181072i	$-0.0579566\pi$
$587$	19.4406	+	19.4406i	0.802398	+	0.802398i	−0.181072	+	0.983470i	$0.557957\pi$
$588$	0.486309	−	1.66238i	0.0200550	−	0.0685553i
$589$			2.10347i			0.0866721i
$590$	8.10461	+	8.10461i	0.333662	+	0.333662i
$591$	37.4761	−	20.5123i	1.54156	−	0.843762i
$592$	−7.86287	−	7.86287i	−0.323162	−	0.323162i
$593$	23.9101	−	23.9101i	0.981871	−	0.981871i	−0.0179672	−	0.999839i	$-0.505719\pi$
$593$	23.9101	−	23.9101i	0.981871	−	0.981871i	0.999839	+	0.0179672i	$0.00571946\pi$
$594$	−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	$-0.785841\pi$
$599$		−	30.5039i		−	1.24636i	0.782080	−	0.623178i	$-0.214159\pi$
$600$	−15.0270	+	8.22491i	−0.613473	+	0.335780i
$601$	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
$603$	−35.7130	+	7.84391i	−1.45435	+	0.319429i
$604$	−0.393892	+	0.393892i	−0.0160272	+	0.0160272i
$605$	30.0137	−	30.0137i	1.22023	−	1.22023i
$606$	−6.18273	+	3.38408i	−0.251156	+	0.137469i
$607$	−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
$609$	−6.40796	−	11.7074i	−0.259664	−	0.474407i
$610$			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	0.491791	−	0.870713i	$-0.336342\pi$
$617$	−9.41224	−	9.41224i	−0.378922	−	0.378922i	−0.870713	+	0.491791i	$0.836342\pi$
$618$	−14.5878	−	26.6520i	−0.586807	−	1.07210i
$619$	−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
$624$	6.09972	−	1.33921i	0.244184	−	0.0536112i
$625$	−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
$630$	11.3069	−	2.48342i	0.450478	−	0.0989416i
$631$	−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
$639$	2.51205	+	11.4373i	0.0993751	+	0.452451i
$640$	3.85881			0.152533
$641$	−6.22306			−0.245796			−0.122898	−	0.992419i	$-0.539219\pi$
$641$	−6.22306			−0.245796			−0.122898	+	0.992419i	$0.539219\pi$
$642$	−0.189903	−	0.346955i	−0.00749489	−	0.0136932i
$643$	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
$645$	16.3627	+	29.8947i	0.644279	+	1.17710i
$646$	1.25175			0.0492494
$647$	14.3535			0.564293			0.282147	−	0.959371i	$-0.408954\pi$
$647$	14.3535			0.564293			0.282147	+	0.959371i	$0.408954\pi$
$648$	8.44509	+	3.11134i	0.331754	+	0.122225i
$649$		−	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	$-0.969369\pi$
$653$		−	4.91046i		−	0.192161i	0.995374	−	0.0960805i	$-0.0306306\pi$
$654$	−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
$657$	8.95564	+	40.7747i	0.349393	+	1.59077i
$658$	3.31273	+	3.31273i	0.129144	+	0.129144i
$659$		−	29.9426i		−	1.16640i	−0.812329	−	0.583199i	$-0.801801\pi$
$659$		−	29.9426i		−	1.16640i	0.812329	−	0.583199i	$-0.198199\pi$
$660$	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
$663$	−34.2216	+	7.51344i	−1.32906	+	0.291798i
$664$	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
$669$	0.180759	+	0.330248i	0.00698854	+	0.0127681i
$670$	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	$0.143258\pi$
$677$			22.6377i			0.870037i	−0.900421	+	0.435019i	$0.856742\pi$
$678$	1.84702	+	3.37451i	0.0709342	+	0.129597i
$679$	8.40720			0.322639
$680$	−21.6493			−0.830213
$681$	−17.5988	+	9.63256i	−0.674386	+	0.369121i
$682$	−0.108031	+	0.108031i	−0.00413673	+	0.00413673i
$683$	28.9868	−	28.9868i	1.10915	−	1.10915i	0.115885	−	0.993263i	$-0.463029\pi$
$683$	28.9868	−	28.9868i	1.10915	−	1.10915i	0.993263	−	0.115885i	$-0.0369705\pi$
$684$	0.143589	+	0.653757i	0.00549028	+	0.0249970i
$685$	−5.66336			−0.216386
$686$	1.00000			0.0381802
$687$	12.5040	−	6.84395i	0.477056	−	0.261113i
$688$		−	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
$696$	−11.7074	+	6.40796i	−0.443767	+	0.242893i
$697$	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	$-0.489035\pi$
$701$	1.82380			0.0688840			0.0344420	+	0.999407i	$0.489035\pi$
$702$	−7.84969	−	17.0112i	−0.296267	−	0.642048i
$703$	−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
$708$	−4.51287	+	2.47009i	−0.169604	+	0.0928316i
$709$	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
$717$	26.5302	−	14.5212i	0.990790	−	0.542302i
$718$	−2.81394			−0.105015
$719$	10.2208			0.381172			0.190586	−	0.981670i	$-0.438961\pi$
$719$	10.2208			0.381172			0.190586	+	0.981670i	$0.438961\pi$
$720$	−2.48342	−	11.3069i	−0.0925514	−	0.421383i
$721$	12.4039	−	12.4039i	0.461944	−	0.461944i
$722$	13.3998	−	13.3998i	0.498690	−	0.498690i
$723$	−16.2092	+	8.87200i	−0.602827	+	0.329953i
$724$	−15.3210			−0.569401
$725$	−76.2105			−2.83039
$726$	9.14746	+	16.7125i	0.339494	+	0.620258i
$727$		−	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
$735$	3.20901	+	5.86288i	0.118366	+	0.216256i
$736$	−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
$741$	0.751042	−	1.17360i	0.0275902	−	0.0431133i
$742$	2.49125			0.0914567
$743$	3.43994	+	3.43994i	0.126199	+	0.126199i	0.767385	−	0.641186i	$-0.221557\pi$
$743$	3.43994	+	3.43994i	0.126199	+	0.126199i	−0.641186	+	0.767385i	$0.721557\pi$
$744$	15.6726	+	4.58483i	0.574586	+	0.168088i
$745$		−	50.7480i		−	1.85926i
$746$	5.04233	+	5.04233i	0.184613	+	0.184613i
$747$	−10.8787	−	49.5302i	−0.398030	−	1.81222i
$748$	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
$756$	−0.355103	+	5.18400i	−0.0129150	+	0.188540i
$757$	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
$759$	−0.0346474	−	0.0633011i	−0.00125762	−	0.00229768i
$760$	0.608785	−	0.608785i	0.0220829	−	0.0220829i
$761$	21.2949	−	21.2949i	0.771940	−	0.771940i	−0.206506	−	0.978445i	$-0.566209\pi$
$761$	21.2949	−	21.2949i	0.771940	−	0.771940i	0.978445	+	0.206506i	$0.0662092\pi$
$762$	−3.58845	−	6.55612i	−0.129996	−	0.237503i
$763$	−12.1449			−0.439675
$764$	−12.6760			−0.458601
$765$	13.9329	+	63.4359i	0.503744	+	2.29353i
$766$			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	$-0.901435\pi$
$773$	−34.9528	−	34.9528i	−1.25717	−	1.25717i	−0.304727	−	0.952440i	$-0.598565\pi$
$774$	−14.9408	+	3.28156i	−0.537036	+	0.117953i
$775$	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
$780$	−12.9895	+	20.2978i	−0.465097	+	0.726776i
$781$	−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
$786$	−0.0924260	−	0.168863i	−0.00329673	−	0.00602314i
$787$	−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
$795$	7.99445	+	14.6059i	0.283534	+	0.518018i
$796$	−16.2501			−0.575970
$797$	15.7976			0.559581			0.279791	−	0.960061i	$-0.409735\pi$
$797$	15.7976			0.559581			0.279791	+	0.960061i	$0.409735\pi$
$798$	−0.338988	+	0.185543i	−0.0120000	+	0.00656814i
$799$	−18.5856	+	18.5856i	−0.657512	+	0.657512i
$800$	−6.99356	+	6.99356i	−0.247260	+	0.247260i
$801$	−21.3701	+	4.69366i	−0.755074	+	0.165842i
$802$	−24.5232			−0.865943
$803$	−0.225503			−0.00795784
$804$	−18.5180	+	10.1357i	−0.653080	+	0.357459i
$805$			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	$0.101756\pi$
$809$			17.8770i			0.628520i	−0.949337	+	0.314260i	$0.898244\pi$
$810$	−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
$813$	19.2572	−	10.5403i	0.675381	−	0.369665i
$814$	−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
$819$	8.15392	−	7.10729i	0.284921	−	0.248349i
$820$	28.3104			0.988643
$821$	−24.3906	−	24.3906i	−0.851239	−	0.851239i	0.139047	−	0.990286i	$-0.455596\pi$
$821$	−24.3906	−	24.3906i	−0.851239	−	0.851239i	−0.990286	+	0.139047i	$0.955596\pi$
$822$	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
$825$	−0.243514	+	0.133286i	−0.00847807	+	0.00464041i
$826$	−2.10029	−	2.10029i	−0.0730785	−	0.0730785i
$827$	−24.7349	+	24.7349i	−0.860116	+	0.860116i	−0.991351	−	0.131235i	$-0.958106\pi$
$827$	−24.7349	+	24.7349i	−0.860116	+	0.860116i	0.131235	+	0.991351i	$0.458106\pi$
$828$	−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
$834$	−21.0036	+	11.4962i	−0.727296	+	0.398081i
$835$	−5.26218			−0.182105
$836$	−0.00361558			−0.000125048
$837$	3.34785	−	48.8739i	0.115718	−	1.68933i
$838$	−10.6968	+	10.6968i	−0.369514	+	0.369514i
$839$	37.5413	−	37.5413i	1.29607	−	1.29607i	0.365103	−	0.930967i	$-0.381034\pi$
$839$	37.5413	−	37.5413i	1.29607	−	1.29607i	0.930967	−	0.365103i	$-0.118966\pi$
$840$	5.86288	−	3.20901i	0.202289	−	0.110721i
$841$	−30.3749			−1.04741
$842$	4.83084			0.166482
$843$	−22.0439	−	40.2743i	−0.759232	−	1.38712i
$844$			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
$852$	3.24601	+	5.93048i	0.111206	+	0.203175i
$853$	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	$-0.636499\pi$
$857$	−24.3448			−0.831603			−0.415802	+	0.909455i	$0.636499\pi$
$858$	0.0988467	−	0.0217020i	0.00337457	−	0.000740895i
$859$	−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	0.768258	−	0.640140i	$-0.221124\pi$
$863$	3.76370	+	3.76370i	0.128118	+	0.128118i	−0.640140	+	0.768258i	$0.721124\pi$
$864$	5.18400	+	0.355103i	0.176363	+	0.0120808i
$865$	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
$873$	−24.6344	+	5.41063i	−0.833748	+	0.183122i
$874$	−0.573622			−0.0194031
$875$	18.8710			0.637957
$876$	11.5723	+	21.1426i	0.390990	+	0.714342i
$877$	−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
$879$	−7.91797	−	14.4662i	−0.267066	−	0.487932i
$880$	0.0625325			0.00210797
$881$	−25.9887			−0.875580			−0.437790	−	0.899077i	$-0.644239\pi$
$881$	−25.9887			−0.875580			−0.437790	+	0.899077i	$0.644239\pi$
$882$	−2.93016	+	0.643571i	−0.0986635	+	0.0216702i
$883$		−	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	$-0.920904\pi$
$887$		−	14.6493i		−	0.491875i	0.969286	−	0.245937i	$-0.0790958\pi$
$888$	−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
$891$	0.136854	+	0.0504198i	0.00458478	+	0.00168913i
$892$	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
$897$	15.6823	−	3.44309i	0.523617	−	0.114961i
$898$	−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
$903$	−4.24035	−	7.74714i	−0.141110	−	0.257809i
$904$	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	$-0.927129\pi$
$911$		−	13.6991i		−	0.453871i	0.973910	−	0.226935i	$-0.0728707\pi$
$912$	0.185543	+	0.338988i	0.00614393	+	0.0112250i
$913$	0.273925			0.00906561
$914$	33.1652			1.09701
$915$	10.7218	−	5.86849i	0.354451	−	0.194006i
$916$	5.81934	−	5.81934i	0.192277	−	0.192277i
$917$	0.0785889	−	0.0785889i	0.00259523	−	0.00259523i
$918$	−29.0842	−	1.99226i	−0.959921	−	0.0657543i
$919$	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
$921$	29.3936	−	16.0884i	0.968553	−	0.530131i
$922$			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	0.846690	−	0.532087i	$-0.178592\pi$
$929$	9.58896	+	9.58896i	0.314603	+	0.314603i	−0.532087	+	0.846690i	$0.678592\pi$
$930$	−55.2742	+	30.2540i	−1.81251	+	0.992067i
$931$	−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
$936$	−7.10729	−	8.15392i	−0.232309	−	0.266519i
$937$	−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	0.522241	−	0.852798i	$-0.325096\pi$
$941$	−10.1401	−	10.1401i	−0.330557	−	0.330557i	−0.852798	+	0.522241i	$0.825096\pi$
$942$	15.5771	−	8.52600i	0.507528	−	0.277792i
$943$	−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	−0.143119	−	0.989705i	$-0.545713\pi$
$947$	26.0523	−	26.0523i	0.846587	−	0.846587i	0.989705	+	0.143119i	$0.0457132\pi$
$948$	9.81269	+	2.87059i	0.318701	+	0.0932323i
$949$	14.0911	−	48.1538i	0.457415	−	1.56314i
$950$			2.20668i			0.0715941i
$951$	26.2592	−	14.3728i	0.851514	−	0.466070i
$952$	5.61037			0.181833
$953$	38.1006			1.23420			0.617100	−	0.786885i	$-0.288307\pi$
$953$	38.1006			1.23420			0.617100	+	0.786885i	$0.288307\pi$
$954$	−7.29976	+	1.60330i	−0.236338	+	0.0519087i
$955$	34.5876	−	34.5876i	1.11923	−	1.11923i
$956$	12.3472	−	12.3472i	0.399337	−	0.399337i
$957$	−0.189720	+	0.103842i	−0.00613277	+	0.00335673i
$958$	20.5198			0.662966
$959$	1.46765			0.0473927
$960$	−3.20901	−	5.86288i	−0.103570	−	0.189224i
$961$		−	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
$969$	−1.04096	−	1.90185i	−0.0334405	−	0.0610961i
$970$	22.9398	+	22.9398i	0.736552	+	0.736552i
$971$			28.2363i			0.906145i	0.891474	+	0.453072i	$0.149672\pi$
$971$			28.2363i			0.906145i	−0.891474	+	0.453072i	$0.850328\pi$
$972$	−2.29577	−	15.4185i	−0.0736368	−	0.494548i
$973$	−9.77510	−	9.77510i	−0.313375	−	0.313375i
$974$	−23.2530			−0.745074
$975$	−13.2453	−	60.3285i	−0.424188	−	1.93206i
$976$	−1.82875			−0.0585370
$977$	5.23687	+	5.23687i	0.167542	+	0.167542i	0.785898	−	0.618356i	$-0.212201\pi$
$977$	5.23687	+	5.23687i	0.167542	+	0.167542i	−0.618356	+	0.785898i	$0.712201\pi$
$978$	8.65646	+	2.53234i	0.276803	+	0.0809754i
$979$		−	0.118186i		−	0.00377726i
$980$	2.72859	+	2.72859i	0.0871615	+	0.0871615i
$981$	35.5864	−	7.81610i	1.13619	−	0.249549i
$982$	−3.69948	−	3.69948i	−0.118055	−	0.118055i
$983$	21.8072	−	21.8072i	0.695542	−	0.695542i	−0.267904	−	0.963446i	$-0.586331\pi$
$983$	21.8072	−	21.8072i	0.695542	−	0.695542i	0.963446	+	0.267904i	$0.0863309\pi$
$984$	−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
$990$	−0.0402441	−	0.183230i	−0.00127904	−	0.00582343i
$991$	−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
$993$	−10.8798	−	19.8774i	−0.345259	−	0.630790i
$994$	−2.76005	+	2.76005i	−0.0875434	+	0.0875434i
$995$	44.3399	−	44.3399i	1.40567	−	1.40567i
$996$	−14.0572	−	25.6825i	−0.445418	−	0.813782i
$997$	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
$999$	57.6449	+	3.94866i	1.82381	+	0.124930i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.486309 + 1.66238i) q^{3} +1.00000i q^{4} +(-2.72859 - 2.72859i) q^{5} +(1.51935 - 0.831607i) q^{6} +(0.707107 + 0.707107i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.52701 - 1.61686i) q^{9} +O(q^{10})\)	\(q+(-0.707107 - 0.707107i) q^{2} +(-0.486309 + 1.66238i) q^{3} +1.00000i q^{4} +(-2.72859 - 2.72859i) q^{5} +(1.51935 - 0.831607i) 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} +(5.86288 - 3.20901i) q^{15} -1.00000 q^{16} +5.61037 q^{17} +(0.643571 + 2.93016i) q^{18} +(-0.157765 + 0.157765i) q^{19} +(2.72859 - 2.72859i) q^{20} +(-1.51935 + 0.831607i) q^{21} -0.0162051 q^{22} -2.57099 q^{23} +(0.831607 + 1.51935i) 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} +(0.0134763 + 0.0246213i) 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} +(-6.09972 + 1.33921i) 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} +(2.48342 + 11.3069i) 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} +(-5.18400 - 0.355103i) q^{54} -0.0625325 q^{55} +1.00000 q^{56} +(-0.185543 - 0.338988i) q^{57} +(5.44862 - 5.44862i) q^{58} +(2.10029 - 2.10029i) q^{59} +(3.20901 + 5.86288i) q^{60} +1.82875 q^{61} -9.42782 q^{62} +(-0.643571 - 2.93016i) 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} +(-2.93016 + 0.643571i) 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} +(5.26011 + 3.36619i) 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} +(-0.831607 - 1.51935i) 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} +(7.84024 + 14.3242i) q^{93} +4.68491 q^{94} +0.860951 q^{95} +(-1.51935 + 0.831607i) q^{96} +(5.94479 - 5.94479i) q^{97} +(0.707107 - 0.707107i) q^{98} +(-0.0474836 + 0.0104292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9}+O(q^{10}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9	\( 20 q - 4 q^{5} - 4 q^{6} - 8 q^{9} - 16 q^{11} - 8 q^{12} + 4 q^{13} - 4 q^{15} - 20 q^{16} + 12 q^{17} - 8 q^{18} + 12 q^{19} + 4 q^{20} + 4 q^{21} - 12 q^{22} - 4 q^{23} + 4 q^{24} + 24 q^{27} + 12 q^{30} - 8 q^{31} - 48 q^{33} - 4 q^{34} + 32 q^{37} - 4 q^{38} - 16 q^{39} - 4 q^{40} + 8 q^{41} + 8 q^{42} - 16 q^{44} + 16 q^{45} - 8 q^{46} + 32 q^{50} - 8 q^{51} - 8 q^{52} + 28 q^{54} + 28 q^{55} + 20 q^{56} + 36 q^{57} - 4 q^{58} + 20 q^{59} - 4 q^{60} - 4 q^{61} + 48 q^{62} + 8 q^{63} + 52 q^{65} - 36 q^{67} + 68 q^{69} - 4 q^{70} - 28 q^{71} - 16 q^{72} - 24 q^{73} - 76 q^{75} + 12 q^{76} + 12 q^{77} + 40 q^{78} - 64 q^{79} + 4 q^{80} + 32 q^{81} - 24 q^{83} - 4 q^{84} + 24 q^{85} + 4 q^{86} + 4 q^{87} - 4 q^{89} - 8 q^{90} - 32 q^{93} - 40 q^{94} - 76 q^{95} + 4 q^{96} + 32 q^{97} - 4 q^{99}+O(q^{100}) \) 20 * q - 4 * q^5 - 4 * q^6 - 8 * q^9 - 16 * q^11 - 8 * q^12 + 4 * q^13 - 4 * q^15 - 20 * q^16 + 12 * q^17 - 8 * q^18 + 12 * q^19 + 4 * q^20 + 4 * q^21 - 12 * q^22 - 4 * q^23 + 4 * q^24 + 24 * q^27 + 12 * q^30 - 8 * q^31 - 48 * q^33 - 4 * q^34 + 32 * q^37 - 4 * q^38 - 16 * q^39 - 4 * q^40 + 8 * q^41 + 8 * q^42 - 16 * q^44 + 16 * q^45 - 8 * q^46 + 32 * q^50 - 8 * q^51 - 8 * q^52 + 28 * q^54 + 28 * q^55 + 20 * q^56 + 36 * q^57 - 4 * q^58 + 20 * q^59 - 4 * q^60 - 4 * q^61 + 48 * q^62 + 8 * q^63 + 52 * q^65 - 36 * q^67 + 68 * q^69 - 4 * q^70 - 28 * q^71 - 16 * q^72 - 24 * q^73 - 76 * q^75 + 12 * q^76 + 12 * q^77 + 40 * q^78 - 64 * q^79 + 4 * q^80 + 32 * q^81 - 24 * q^83 - 4 * q^84 + 24 * q^85 + 4 * q^86 + 4 * q^87 - 4 * q^89 - 8 * q^90 - 32 * q^93 - 40 * q^94 - 76 * q^95 + 4 * q^96 + 32 * q^97 - 4 * q^99

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