LMFDB - Embedded newform 1710.2.n.h.647.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1710,2,Mod(647,1710)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1710, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1710.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1710.n (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:	$13.6544187456$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 2 x^{14} + 24 x^{13} + 2 x^{12} - 48 x^{11} + 88 x^{10} - 72 x^{9} + 18 x^{8} + \cdots + 1 $ x^16 - 4x^15 - 2x^14 + 24x^13 + 2x^12 - 48x^11 + 88x^10 - 72x^9 + 18x^8 - 20x^7 + 66x^6 + 84x^5 + 40x^4 + 24x^3 + 20x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.2
Root			$-1.97269 + 0.817117i$ of defining polynomial
Character	$\chi$	$=$	1710.647
Dual form			1710.2.n.h.1673.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.379071 - 2.20370i) q^{5} +(2.44579 + 2.44579i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.379071 - 2.20370i) q^{5} +(2.44579 + 2.44579i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.82630 + 1.29021i) q^{10} +1.85425i q^{11} +(-2.11651 + 2.11651i) q^{13} -3.45887 q^{14} -1.00000 q^{16} +(-2.29031 + 2.29031i) q^{17} +1.00000i q^{19} +(-2.20370 + 0.379071i) q^{20} +(-1.31116 - 1.31116i) q^{22} +(-2.39238 - 2.39238i) q^{23} +(-4.71261 + 1.67072i) q^{25} -2.99319i q^{26} +(2.44579 - 2.44579i) q^{28} -6.09689 q^{29} +1.81940 q^{31} +(0.707107 - 0.707107i) q^{32} -3.23898i q^{34} +(4.46266 - 6.31691i) q^{35} +(4.38577 + 4.38577i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(1.29021 - 1.82630i) q^{40} -4.05224i q^{41} +(-7.27490 + 7.27490i) q^{43} +1.85425 q^{44} +3.38333 q^{46} +(1.44384 - 1.44384i) q^{47} +4.96375i q^{49} +(2.15094 - 4.51370i) q^{50} +(2.11651 + 2.11651i) q^{52} +(1.03342 + 1.03342i) q^{53} +(4.08622 - 0.702894i) q^{55} +3.45887i q^{56} +(4.31116 - 4.31116i) q^{58} -3.94173 q^{59} -2.18060 q^{61} +(-1.28651 + 1.28651i) q^{62} +1.00000i q^{64} +(5.46646 + 3.86184i) q^{65} +(4.80291 + 4.80291i) q^{67} +(2.29031 + 2.29031i) q^{68} +(1.31116 + 7.62231i) q^{70} -2.06683i q^{71} +(-9.58606 + 9.58606i) q^{73} -6.20242 q^{74} +1.00000 q^{76} +(-4.53511 + 4.53511i) q^{77} +1.43010i q^{79} +(0.379071 + 2.20370i) q^{80} +(2.86537 + 2.86537i) q^{82} +(2.48070 + 2.48070i) q^{83} +(5.91534 + 4.17896i) q^{85} -10.2883i q^{86} +(-1.31116 + 1.31116i) q^{88} -13.4176 q^{89} -10.3530 q^{91} +(-2.39238 + 2.39238i) q^{92} +2.04189i q^{94} +(2.20370 - 0.379071i) q^{95} +(4.00000 + 4.00000i) q^{97} +(-3.50990 - 3.50990i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q + 4 q^{10} + 8 q^{13} - 16 q^{16} + 24 q^{22} - 16 q^{25} - 32 q^{31} + 40 q^{37} + 4 q^{40} + 24 q^{43} - 8 q^{46} - 8 q^{52} - 16 q^{55} + 24 q^{58} - 96 q^{61} + 48 q^{67} - 24 q^{70} + 32 q^{73} + 16 q^{76} + 40 q^{82} - 88 q^{85} + 24 q^{88} - 64 q^{91} + 64 q^{97}+O(q^{100}) $ 16 * q + 4 * q^10 + 8 * q^13 - 16 * q^16 + 24 * q^22 - 16 * q^25 - 32 * q^31 + 40 * q^37 + 4 * q^40 + 24 * q^43 - 8 * q^46 - 8 * q^52 - 16 * q^55 + 24 * q^58 - 96 * q^61 + 48 * q^67 - 24 * q^70 + 32 * q^73 + 16 * q^76 + 40 * q^82 - 88 * q^85 + 24 * q^88 - 64 * q^91 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times$.

$n$	$191$	$1027$	$1351$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	−0.379071	−	2.20370i	−0.169526	−	0.985526i
$5$	−0.379071	−	2.20370i	−0.169526	−	0.985526i
$6$		0			0
$7$	2.44579	+	2.44579i	0.924421	+	0.924421i	0.997338	−	0.0729174i	$-0.0232309\pi$
$7$	2.44579	+	2.44579i	0.924421	+	0.924421i	−0.0729174	+	0.997338i	$0.523231\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$		0			0
$10$	1.82630	+	1.29021i	0.577526	+	0.408000i
$11$			1.85425i			0.559078i	0.960134	+	0.279539i	$0.0901817\pi$
$11$			1.85425i			0.559078i	−0.960134	+	0.279539i	$0.909818\pi$
$12$		0			0
$13$	−2.11651	+	2.11651i	−0.587013	+	0.587013i	−0.936821	−	0.349808i	$-0.886247\pi$
$13$	−2.11651	+	2.11651i	−0.587013	+	0.587013i	0.349808	+	0.936821i	$0.386247\pi$
$14$	−3.45887			−0.924421
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−2.29031	+	2.29031i	−0.555481	+	0.555481i	−0.928017	−	0.372537i	$-0.878488\pi$
$17$	−2.29031	+	2.29031i	−0.555481	+	0.555481i	0.372537	+	0.928017i	$0.378488\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−2.20370	+	0.379071i	−0.492763	+	0.0847628i
$21$		0			0
$22$	−1.31116	−	1.31116i	−0.279539	−	0.279539i
$23$	−2.39238	−	2.39238i	−0.498845	−	0.498845i	0.412233	−	0.911078i	$-0.364749\pi$
$23$	−2.39238	−	2.39238i	−0.498845	−	0.498845i	−0.911078	+	0.412233i	$0.864749\pi$
$24$		0			0
$25$	−4.71261	+	1.67072i	−0.942522	+	0.334144i
$26$		−	2.99319i		−	0.587013i
$27$		0			0
$28$	2.44579	−	2.44579i	0.462210	−	0.462210i
$29$	−6.09689			−1.13216			−0.566082	−	0.824349i	$-0.691542\pi$
$29$	−6.09689			−1.13216			−0.566082	+	0.824349i	$0.691542\pi$
$30$		0			0
$31$	1.81940			0.326774			0.163387	−	0.986562i	$-0.447758\pi$
$31$	1.81940			0.326774			0.163387	+	0.986562i	$0.447758\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$		0			0
$34$		−	3.23898i		−	0.555481i
$35$	4.46266	−	6.31691i	0.754327	−	1.06775i
$36$		0			0
$37$	4.38577	+	4.38577i	0.721016	+	0.721016i	0.968812	−	0.247796i	$-0.0797063\pi$
$37$	4.38577	+	4.38577i	0.721016	+	0.721016i	−0.247796	+	0.968812i	$0.579706\pi$
$38$	−0.707107	−	0.707107i	−0.114708	−	0.114708i
$39$		0			0
$40$	1.29021	−	1.82630i	0.204000	−	0.288763i
$41$		−	4.05224i		−	0.632854i	−0.948617	−	0.316427i	$-0.897517\pi$
$41$		−	4.05224i		−	0.632854i	0.948617	−	0.316427i	$-0.102483\pi$
$42$		0			0
$43$	−7.27490	+	7.27490i	−1.10941	+	1.10941i	−0.116185	+	0.993228i	$0.537066\pi$
$43$	−7.27490	+	7.27490i	−1.10941	+	1.10941i	−0.993228	+	0.116185i	$0.962934\pi$
$44$	1.85425			0.279539
$45$		0			0
$46$	3.38333			0.498845
$47$	1.44384	−	1.44384i	0.210605	−	0.210605i	−0.593919	−	0.804524i	$-0.702420\pi$
$47$	1.44384	−	1.44384i	0.210605	−	0.210605i	0.804524	+	0.593919i	$0.202420\pi$
$48$		0			0
$49$			4.96375i			0.709107i
$50$	2.15094	−	4.51370i	0.304189	−	0.638333i
$51$		0			0
$52$	2.11651	+	2.11651i	0.293507	+	0.293507i
$53$	1.03342	+	1.03342i	0.141951	+	0.141951i	0.774511	−	0.632560i	$-0.217996\pi$
$53$	1.03342	+	1.03342i	0.141951	+	0.141951i	−0.632560	+	0.774511i	$0.717996\pi$
$54$		0			0
$55$	4.08622	−	0.702894i	0.550986	−	0.0947781i
$56$			3.45887i			0.462210i
$57$		0			0
$58$	4.31116	−	4.31116i	0.566082	−	0.566082i
$59$	−3.94173			−0.513170			−0.256585	−	0.966522i	$-0.582597\pi$
$59$	−3.94173			−0.513170			−0.256585	+	0.966522i	$0.582597\pi$
$60$		0			0
$61$	−2.18060			−0.279197			−0.139599	−	0.990208i	$-0.544581\pi$
$61$	−2.18060			−0.279197			−0.139599	+	0.990208i	$0.544581\pi$
$62$	−1.28651	+	1.28651i	−0.163387	+	0.163387i
$63$		0			0
$64$			1.00000i			0.125000i
$65$	5.46646	+	3.86184i	0.678030	+	0.479003i
$66$		0			0
$67$	4.80291	+	4.80291i	0.586769	+	0.586769i	0.936755	−	0.349986i	$-0.113814\pi$
$67$	4.80291	+	4.80291i	0.586769	+	0.586769i	−0.349986	+	0.936755i	$0.613814\pi$
$68$	2.29031	+	2.29031i	0.277740	+	0.277740i
$69$		0			0
$70$	1.31116	+	7.62231i	0.156713	+	0.911040i
$71$		−	2.06683i		−	0.245288i	−0.992451	−	0.122644i	$-0.960863\pi$
$71$		−	2.06683i		−	0.245288i	0.992451	−	0.122644i	$-0.0391373\pi$
$72$		0			0
$73$	−9.58606	+	9.58606i	−1.12196	+	1.12196i	−0.130517	+	0.991446i	$0.541664\pi$
$73$	−9.58606	+	9.58606i	−1.12196	+	1.12196i	−0.991446	+	0.130517i	$0.958336\pi$
$74$	−6.20242			−0.721016
$75$		0			0
$76$	1.00000			0.114708
$77$	−4.53511	+	4.53511i	−0.516824	+	0.516824i
$78$		0			0
$79$			1.43010i			0.160899i	0.996759	+	0.0804495i	$0.0256356\pi$
$79$			1.43010i			0.160899i	−0.996759	+	0.0804495i	$0.974364\pi$
$80$	0.379071	+	2.20370i	0.0423814	+	0.246381i
$81$		0			0
$82$	2.86537	+	2.86537i	0.316427	+	0.316427i
$83$	2.48070	+	2.48070i	0.272293	+	0.272293i	0.830022	−	0.557730i	$-0.188328\pi$
$83$	2.48070	+	2.48070i	0.272293	+	0.272293i	−0.557730	+	0.830022i	$0.688328\pi$
$84$		0			0
$85$	5.91534	+	4.17896i	0.641609	+	0.453272i
$86$		−	10.2883i		−	1.10941i
$87$		0			0
$88$	−1.31116	+	1.31116i	−0.139770	+	0.139770i
$89$	−13.4176			−1.42226			−0.711132	−	0.703059i	$-0.751817\pi$
$89$	−13.4176			−1.42226			−0.711132	+	0.703059i	$0.751817\pi$
$90$		0			0
$91$	−10.3530			−1.08529
$92$	−2.39238	+	2.39238i	−0.249422	+	0.249422i
$93$		0			0
$94$			2.04189i			0.210605i
$95$	2.20370	−	0.379071i	0.226095	−	0.0388919i
$96$		0			0
$97$	4.00000	+	4.00000i	0.406138	+	0.406138i	0.880390	−	0.474251i	$-0.157281\pi$
$97$	4.00000	+	4.00000i	0.406138	+	0.406138i	−0.474251	+	0.880390i	$0.657281\pi$
$98$	−3.50990	−	3.50990i	−0.354553	−	0.354553i
$99$		0			0
$100$	1.67072	+	4.71261i	0.167072	+	0.471261i
$101$			19.4889i			1.93921i	0.244667	+	0.969607i	$0.421321\pi$
$101$			19.4889i			1.93921i	−0.244667	+	0.969607i	$0.578679\pi$
$102$		0			0
$103$	4.23654	−	4.23654i	0.417439	−	0.417439i	−0.466881	−	0.884320i	$-0.654622\pi$
$103$	4.23654	−	4.23654i	0.417439	−	0.417439i	0.884320	+	0.466881i	$0.154622\pi$
$104$	−2.99319			−0.293507
$105$		0			0
$106$	−1.46147			−0.141951
$107$	−1.11330	+	1.11330i	−0.107627	+	0.107627i	−0.758870	−	0.651242i	$-0.774248\pi$
$107$	−1.11330	+	1.11330i	−0.107627	+	0.107627i	0.651242	+	0.758870i	$0.274248\pi$
$108$		0			0
$109$		−	3.40579i		−	0.326215i	−0.986608	−	0.163108i	$-0.947848\pi$
$109$		−	3.40579i		−	0.326215i	0.986608	−	0.163108i	$-0.0521518\pi$
$110$	−2.39238	+	3.38642i	−0.228104	+	0.322882i
$111$		0			0
$112$	−2.44579	−	2.44579i	−0.231105	−	0.231105i
$113$	1.01123	+	1.01123i	0.0951289	+	0.0951289i	0.753070	−	0.657941i	$-0.228572\pi$
$113$	1.01123	+	1.01123i	0.0951289	+	0.0951289i	−0.657941	+	0.753070i	$0.728572\pi$
$114$		0			0
$115$	−4.36520	+	6.17896i	−0.407057	+	0.576191i
$116$			6.09689i			0.566082i
$117$		0			0
$118$	2.78723	−	2.78723i	0.256585	−	0.256585i
$119$	−11.2032			−1.02700
$120$		0			0
$121$	7.56174			0.687431
$122$	1.54192	−	1.54192i	0.139599	−	0.139599i
$123$		0			0
$124$		−	1.81940i		−	0.163387i
$125$	5.46818	+	9.75187i	0.489089	+	0.872234i
$126$		0			0
$127$	−0.919417	−	0.919417i	−0.0815850	−	0.0815850i	0.665137	−	0.746722i	$-0.268373\pi$
$127$	−0.919417	−	0.919417i	−0.0815850	−	0.0815850i	−0.746722	+	0.665137i	$0.768373\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$		0			0
$130$	−6.59610	+	1.13463i	−0.578517	+	0.0995138i
$131$			4.24264i			0.370681i	0.982674	+	0.185341i	$0.0593388\pi$
$131$			4.24264i			0.370681i	−0.982674	+	0.185341i	$0.940661\pi$
$132$		0			0
$133$	−2.44579	+	2.44579i	−0.212077	+	0.212077i
$134$	−6.79234			−0.586769
$135$		0			0
$136$	−3.23898			−0.277740
$137$	−8.15130	+	8.15130i	−0.696413	+	0.696413i	−0.963635	−	0.267222i	$-0.913894\pi$
$137$	−8.15130	+	8.15130i	−0.696413	+	0.696413i	0.267222	+	0.963635i	$0.413894\pi$
$138$		0			0
$139$		−	6.18060i		−	0.524232i	−0.965036	−	0.262116i	$-0.915580\pi$
$139$		−	6.18060i		−	0.524232i	0.965036	−	0.262116i	$-0.0844203\pi$
$140$	−6.31691	−	4.46266i	−0.533877	−	0.377164i
$141$		0			0
$142$	1.46147	+	1.46147i	0.122644	+	0.122644i
$143$	−3.92454	−	3.92454i	−0.328186	−	0.328186i
$144$		0			0
$145$	2.31116	+	13.4357i	0.191931	+	1.11578i
$146$		−	13.5567i		−	1.12196i
$147$		0			0
$148$	4.38577	−	4.38577i	0.360508	−	0.360508i
$149$	−5.71955			−0.468564			−0.234282	−	0.972169i	$-0.575274\pi$
$149$	−5.71955			−0.468564			−0.234282	+	0.972169i	$0.575274\pi$
$150$		0			0
$151$	−16.8191			−1.36872			−0.684358	−	0.729146i	$-0.739918\pi$
$151$	−16.8191			−1.36872			−0.684358	+	0.729146i	$0.739918\pi$
$152$	−0.707107	+	0.707107i	−0.0573539	+	0.0573539i
$153$		0			0
$154$		−	6.41361i		−	0.516824i
$155$	−0.689681	−	4.00942i	−0.0553965	−	0.322044i
$156$		0			0
$157$	−1.82912	−	1.82912i	−0.145979	−	0.145979i	0.630340	−	0.776319i	$-0.282916\pi$
$157$	−1.82912	−	1.82912i	−0.145979	−	0.145979i	−0.776319	+	0.630340i	$0.782916\pi$
$158$	−1.01123	−	1.01123i	−0.0804495	−	0.0804495i
$159$		0			0
$160$	−1.82630	−	1.29021i	−0.144381	−	0.102000i
$161$		−	11.7025i		−	0.922285i
$162$		0			0
$163$	15.5861	−	15.5861i	1.22079	−	1.22079i	0.253444	−	0.967350i	$-0.418437\pi$
$163$	15.5861	−	15.5861i	1.22079	−	1.22079i	0.967350	−	0.253444i	$-0.0815635\pi$
$164$	−4.05224			−0.316427
$165$		0			0
$166$	−3.50824			−0.272293
$167$	−12.1544	+	12.1544i	−0.940537	+	0.940537i	−0.998329	−	0.0577920i	$-0.981594\pi$
$167$	−12.1544	+	12.1544i	−0.940537	+	0.940537i	0.0577920	+	0.998329i	$0.481594\pi$
$168$		0			0
$169$			4.04080i			0.310831i
$170$	−7.13775	+	1.22780i	−0.547440	+	0.0941682i
$171$		0			0
$172$	7.27490	+	7.27490i	0.554706	+	0.554706i
$173$	11.9151	+	11.9151i	0.905885	+	0.905885i	0.995937	−	0.0900517i	$-0.0287032\pi$
$173$	11.9151	+	11.9151i	0.905885	+	0.905885i	−0.0900517	+	0.995937i	$0.528703\pi$
$174$		0			0
$175$	−15.6123	−	7.43982i	−1.18018	−	0.562397i
$176$		−	1.85425i		−	0.139770i
$177$		0			0
$178$	9.48768	−	9.48768i	0.711132	−	0.711132i
$179$	15.8288			1.18310			0.591552	−	0.806267i	$-0.298516\pi$
$179$	15.8288			1.18310			0.591552	+	0.806267i	$0.298516\pi$
$180$		0			0
$181$	−2.63425			−0.195802			−0.0979010	−	0.995196i	$-0.531213\pi$
$181$	−2.63425			−0.195802			−0.0979010	+	0.995196i	$0.531213\pi$
$182$	7.32071	−	7.32071i	0.542647	−	0.542647i
$183$		0			0
$184$		−	3.38333i		−	0.249422i
$185$	8.00241	−	11.3275i	0.588349	−	0.832811i
$186$		0			0
$187$	−4.24681	−	4.24681i	−0.310557	−	0.310557i
$188$	−1.44384	−	1.44384i	−0.105303	−	0.105303i
$189$		0			0
$190$	−1.29021	+	1.82630i	−0.0936016	+	0.132493i
$191$			16.9820i			1.22877i	0.789005	+	0.614387i	$0.210597\pi$
$191$			16.9820i			1.22877i	−0.789005	+	0.614387i	$0.789403\pi$
$192$		0			0
$193$	15.1246	−	15.1246i	1.08869	−	1.08869i	0.0930281	−	0.995663i	$-0.470345\pi$
$193$	15.1246	−	15.1246i	1.08869	−	1.08869i	0.995663	−	0.0930281i	$-0.0296546\pi$
$194$	−5.65685			−0.406138
$195$		0			0
$196$	4.96375			0.354553
$197$	10.3726	−	10.3726i	0.739018	−	0.739018i	−0.233370	−	0.972388i	$-0.574975\pi$
$197$	10.3726	−	10.3726i	0.739018	−	0.739018i	0.972388	+	0.233370i	$0.0749754\pi$
$198$		0			0
$199$		−	22.3411i		−	1.58372i	−0.610703	−	0.791860i	$-0.709113\pi$
$199$		−	22.3411i		−	1.58372i	0.610703	−	0.791860i	$-0.290887\pi$
$200$	−4.51370	−	2.15094i	−0.319166	−	0.152095i
$201$		0			0
$202$	−13.7807	−	13.7807i	−0.969607	−	0.969607i
$203$	−14.9117	−	14.9117i	−1.04660	−	1.04660i
$204$		0			0
$205$	−8.92994	+	1.53609i	−0.623694	+	0.107285i
$206$			5.99137i			0.417439i
$207$		0			0
$208$	2.11651	−	2.11651i	0.146753	−	0.146753i
$209$	−1.85425			−0.128261
$210$		0			0
$211$	−20.6747			−1.42331			−0.711653	−	0.702531i	$-0.752053\pi$
$211$	−20.6747			−1.42331			−0.711653	+	0.702531i	$0.752053\pi$
$212$	1.03342	−	1.03342i	0.0709754	−	0.0709754i
$213$		0			0
$214$		−	1.57445i		−	0.107627i
$215$	18.7894	+	13.2740i	1.28143	+	0.905281i
$216$		0			0
$217$	4.44986	+	4.44986i	0.302076	+	0.302076i
$218$	2.40826	+	2.40826i	0.163108	+	0.163108i
$219$		0			0
$220$	−0.702894	−	4.08622i	−0.0473891	−	0.275493i
$221$		−	9.69489i		−	0.652149i
$222$		0			0
$223$	7.03945	−	7.03945i	0.471397	−	0.471397i	−0.430970	−	0.902366i	$-0.641828\pi$
$223$	7.03945	−	7.03945i	0.471397	−	0.471397i	0.902366	+	0.430970i	$0.141828\pi$
$224$	3.45887			0.231105
$225$		0			0
$226$	−1.43010			−0.0951289
$227$	12.2308	−	12.2308i	0.811790	−	0.811790i	−0.173112	−	0.984902i	$-0.555382\pi$
$227$	12.2308	−	12.2308i	0.811790	−	0.811790i	0.984902	+	0.173112i	$0.0553823\pi$
$228$		0			0
$229$			22.0162i			1.45487i	0.686177	+	0.727434i	$0.259287\pi$
$229$			22.0162i			1.45487i	−0.686177	+	0.727434i	$0.740713\pi$
$230$	−1.28252	−	7.45585i	−0.0845670	−	0.491624i
$231$		0			0
$232$	−4.31116	−	4.31116i	−0.283041	−	0.283041i
$233$	−10.0056	−	10.0056i	−0.655486	−	0.655486i	0.298823	−	0.954309i	$-0.403406\pi$
$233$	−10.0056	−	10.0056i	−0.655486	−	0.655486i	−0.954309	+	0.298823i	$0.903406\pi$
$234$		0			0
$235$	−3.72910	−	2.63447i	−0.243260	−	0.171854i
$236$			3.94173i			0.256585i
$237$		0			0
$238$	7.92186	−	7.92186i	0.513498	−	0.513498i
$239$	−6.74453			−0.436267			−0.218134	−	0.975919i	$-0.569997\pi$
$239$	−6.74453			−0.436267			−0.218134	+	0.975919i	$0.569997\pi$
$240$		0			0
$241$	−24.7353			−1.59334			−0.796670	−	0.604415i	$-0.793407\pi$
$241$	−24.7353			−1.59334			−0.796670	+	0.604415i	$0.793407\pi$
$242$	−5.34696	+	5.34696i	−0.343716	+	0.343716i
$243$		0			0
$244$			2.18060i			0.139599i
$245$	10.9386	−	1.88161i	0.698843	−	0.120212i
$246$		0			0
$247$	−2.11651	−	2.11651i	−0.134670	−	0.134670i
$248$	1.28651	+	1.28651i	0.0816935	+	0.0816935i
$249$		0			0
$250$	−10.7622	−	3.02903i	−0.680661	−	0.191572i
$251$			26.1657i			1.65156i	0.563989	+	0.825782i	$0.309266\pi$
$251$			26.1657i			1.65156i	−0.563989	+	0.825782i	$0.690734\pi$
$252$		0			0
$253$	4.43607	−	4.43607i	0.278893	−	0.278893i
$254$	1.30025			0.0815850
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.39021	+	4.39021i	−0.273854	+	0.273854i	−0.830650	−	0.556796i	$-0.812031\pi$
$257$	−4.39021	+	4.39021i	−0.273854	+	0.273854i	0.556796	+	0.830650i	$0.312031\pi$
$258$		0			0
$259$			21.4533i			1.33304i
$260$	3.86184	−	5.46646i	0.239501	−	0.339015i
$261$		0			0
$262$	−3.00000	−	3.00000i	−0.185341	−	0.185341i
$263$	9.13690	+	9.13690i	0.563405	+	0.563405i	0.930273	−	0.366868i	$-0.119570\pi$
$263$	9.13690	+	9.13690i	0.563405	+	0.563405i	−0.366868	+	0.930273i	$0.619570\pi$
$264$		0			0
$265$	1.88561	−	2.66908i	0.115832	−	0.163960i
$266$		−	3.45887i		−	0.212077i
$267$		0			0
$268$	4.80291	−	4.80291i	0.293384	−	0.293384i
$269$	12.9121			0.787264			0.393632	−	0.919268i	$-0.371218\pi$
$269$	12.9121			0.787264			0.393632	+	0.919268i	$0.371218\pi$
$270$		0			0
$271$	−11.8032			−0.716996			−0.358498	−	0.933531i	$-0.616711\pi$
$271$	−11.8032			−0.716996			−0.358498	+	0.933531i	$0.616711\pi$
$272$	2.29031	−	2.29031i	0.138870	−	0.138870i
$273$		0			0
$274$		−	11.5277i		−	0.696413i
$275$	−3.09794	−	8.73837i	−0.186813	−	0.526944i
$276$		0			0
$277$	10.2184	+	10.2184i	0.613965	+	0.613965i	0.943977	−	0.330012i	$-0.107053\pi$
$277$	10.2184	+	10.2184i	0.613965	+	0.613965i	−0.330012	+	0.943977i	$0.607053\pi$
$278$	4.37034	+	4.37034i	0.262116	+	0.262116i
$279$		0			0
$280$	7.62231	−	1.31116i	0.455520	−	0.0783565i
$281$		−	19.0301i		−	1.13524i	−0.823291	−	0.567620i	$-0.807864\pi$
$281$		−	19.0301i		−	1.13524i	0.823291	−	0.567620i	$-0.192136\pi$
$282$		0			0
$283$	−17.7166	+	17.7166i	−1.05314	+	1.05314i	−0.0546371	+	0.998506i	$0.517400\pi$
$283$	−17.7166	+	17.7166i	−1.05314	+	1.05314i	−0.998506	+	0.0546371i	$0.982600\pi$
$284$	−2.06683			−0.122644
$285$		0			0
$286$	5.55014			0.328186
$287$	9.91092	−	9.91092i	0.585023	−	0.585023i
$288$		0			0
$289$			6.50900i			0.382883i
$290$	−11.1347	−	7.86627i	−0.653854	−	0.461923i
$291$		0			0
$292$	9.58606	+	9.58606i	0.560982	+	0.560982i
$293$	11.0892	+	11.0892i	0.647840	+	0.647840i	0.952471	−	0.304631i	$-0.0985330\pi$
$293$	11.0892	+	11.0892i	0.647840	+	0.647840i	−0.304631	+	0.952471i	$0.598533\pi$
$294$		0			0
$295$	1.49420	+	8.68640i	0.0869954	+	0.505742i
$296$			6.20242i			0.360508i
$297$		0			0
$298$	4.04433	−	4.04433i	0.234282	−	0.234282i
$299$	10.1270			0.585657
$300$		0			0
$301$	−35.5857			−2.05113
$302$	11.8929	−	11.8929i	0.684358	−	0.684358i
$303$		0			0
$304$		−	1.00000i		−	0.0573539i
$305$	0.826602	+	4.80539i	0.0473311	+	0.275156i
$306$		0			0
$307$	16.7304	+	16.7304i	0.954855	+	0.954855i	0.999024	−	0.0441693i	$-0.0140641\pi$
$307$	16.7304	+	16.7304i	0.954855	+	0.954855i	−0.0441693	+	0.999024i	$0.514064\pi$
$308$	4.53511	+	4.53511i	0.258412	+	0.258412i
$309$		0			0
$310$	3.32276	+	2.34741i	0.188720	+	0.133324i
$311$			11.1802i			0.633973i	0.948430	+	0.316987i	$0.102671\pi$
$311$			11.1802i			0.633973i	−0.948430	+	0.316987i	$0.897329\pi$
$312$		0			0
$313$	10.6888	−	10.6888i	0.604169	−	0.604169i	−0.337247	−	0.941416i	$-0.609496\pi$
$313$	10.6888	−	10.6888i	0.604169	−	0.604169i	0.941416	+	0.337247i	$0.109496\pi$
$314$	2.58676			0.145979
$315$		0			0
$316$	1.43010			0.0804495
$317$	16.9307	−	16.9307i	0.950924	−	0.950924i	−0.0479267	−	0.998851i	$-0.515261\pi$
$317$	16.9307	−	16.9307i	0.950924	−	0.950924i	0.998851	+	0.0479267i	$0.0152614\pi$
$318$		0			0
$319$		−	11.3052i		−	0.632969i
$320$	2.20370	−	0.379071i	0.123191	−	0.0211907i
$321$		0			0
$322$	8.27490	+	8.27490i	0.461142	+	0.461142i
$323$	−2.29031	−	2.29031i	−0.127436	−	0.127436i
$324$		0			0
$325$	6.43818	−	13.5104i	0.357126	−	0.749420i
$326$			22.0420i			1.22079i
$327$		0			0
$328$	2.86537	−	2.86537i	0.158213	−	0.158213i
$329$	7.06263			0.389375
$330$		0			0
$331$	3.54526			0.194865			0.0974324	−	0.995242i	$-0.468937\pi$
$331$	3.54526			0.194865			0.0974324	+	0.995242i	$0.468937\pi$
$332$	2.48070	−	2.48070i	0.136146	−	0.136146i
$333$		0			0
$334$		−	17.1889i		−	0.940537i
$335$	8.76354	−	12.4048i	0.478804	−	0.677748i
$336$		0			0
$337$	21.5139	+	21.5139i	1.17194	+	1.17194i	0.981748	+	0.190188i	$0.0609099\pi$
$337$	21.5139	+	21.5139i	1.17194	+	1.17194i	0.190188	+	0.981748i	$0.439090\pi$
$338$	−2.85728	−	2.85728i	−0.155416	−	0.155416i
$339$		0			0
$340$	4.17896	−	5.91534i	0.226636	−	0.320804i
$341$			3.37363i			0.182692i
$342$		0			0
$343$	4.98024	−	4.98024i	0.268908	−	0.268908i
$344$	−10.2883			−0.554706
$345$		0			0
$346$	−16.8504			−0.905885
$347$	−19.8400	+	19.8400i	−1.06507	+	1.06507i	−0.0673389	+	0.997730i	$0.521451\pi$
$347$	−19.8400	+	19.8400i	−1.06507	+	1.06507i	−0.997730	+	0.0673389i	$0.978549\pi$
$348$		0			0
$349$		−	25.3808i		−	1.35860i	−0.733859	−	0.679302i	$-0.762283\pi$
$349$		−	25.3808i		−	1.35860i	0.733859	−	0.679302i	$-0.237717\pi$
$350$	16.3003	−	5.77879i	0.871287	−	0.308889i
$351$		0			0
$352$	1.31116	+	1.31116i	0.0698848	+	0.0698848i
$353$	12.0280	+	12.0280i	0.640187	+	0.640187i	0.950601	−	0.310414i	$-0.100468\pi$
$353$	12.0280	+	12.0280i	0.640187	+	0.640187i	−0.310414	+	0.950601i	$0.600468\pi$
$354$		0			0
$355$	−4.55469	+	0.783477i	−0.241738	+	0.0415826i
$356$			13.4176i			0.711132i
$357$		0			0
$358$	−11.1927	+	11.1927i	−0.591552	+	0.591552i
$359$	−4.14510			−0.218770			−0.109385	−	0.993999i	$-0.534888\pi$
$359$	−4.14510			−0.218770			−0.109385	+	0.993999i	$0.534888\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	1.86269	−	1.86269i	0.0979010	−	0.0979010i
$363$		0			0
$364$			10.3530i			0.542647i
$365$	24.7586	+	17.4910i	1.29593	+	0.915522i
$366$		0			0
$367$	−17.5236	−	17.5236i	−0.914725	−	0.914725i	0.0819148	−	0.996639i	$-0.473896\pi$
$367$	−17.5236	−	17.5236i	−0.914725	−	0.914725i	−0.996639	+	0.0819148i	$0.973896\pi$
$368$	2.39238	+	2.39238i	0.124711	+	0.124711i
$369$		0			0
$370$	2.35116	+	13.6683i	0.122231	+	0.710580i
$371$			5.05504i			0.262444i
$372$		0			0
$373$	14.4452	−	14.4452i	0.747946	−	0.747946i	−0.226147	−	0.974093i	$-0.572613\pi$
$373$	14.4452	−	14.4452i	0.747946	−	0.747946i	0.974093	+	0.226147i	$0.0726130\pi$
$374$	6.00589			0.310557
$375$		0			0
$376$	2.04189			0.105303
$377$	12.9041	−	12.9041i	0.664596	−	0.664596i
$378$		0			0
$379$		−	8.12491i		−	0.417349i	−0.977985	−	0.208674i	$-0.933085\pi$
$379$		−	8.12491i		−	0.417349i	0.977985	−	0.208674i	$-0.0669149\pi$
$380$	−0.379071	−	2.20370i	−0.0194459	−	0.113048i
$381$		0			0
$382$	−12.0081	−	12.0081i	−0.614387	−	0.614387i
$383$	−23.6409	−	23.6409i	−1.20799	−	1.20799i	−0.971676	−	0.236315i	$-0.924060\pi$
$383$	−23.6409	−	23.6409i	−1.20799	−	1.20799i	−0.236315	−	0.971676i	$-0.575940\pi$
$384$		0			0
$385$	11.7132	+	8.27490i	0.596958	+	0.421728i
$386$			21.3894i			1.08869i
$387$		0			0
$388$	4.00000	−	4.00000i	0.203069	−	0.203069i
$389$	8.51622			0.431789			0.215895	−	0.976417i	$-0.430733\pi$
$389$	8.51622			0.431789			0.215895	+	0.976417i	$0.430733\pi$
$390$		0			0
$391$	10.9585			0.554197
$392$	−3.50990	+	3.50990i	−0.177277	+	0.177277i
$393$		0			0
$394$			14.6691i			0.739018i
$395$	3.15152	−	0.542110i	0.158570	−	0.0272765i
$396$		0			0
$397$	18.7675	+	18.7675i	0.941912	+	0.941912i	0.998403	−	0.0564911i	$-0.0179913\pi$
$397$	18.7675	+	18.7675i	0.941912	+	0.941912i	−0.0564911	+	0.998403i	$0.517991\pi$
$398$	15.7976	+	15.7976i	0.791860	+	0.791860i
$399$		0			0
$400$	4.71261	−	1.67072i	0.235631	−	0.0835360i
$401$		−	34.6647i		−	1.73107i	−0.500845	−	0.865537i	$-0.666977\pi$
$401$		−	34.6647i		−	1.73107i	0.500845	−	0.865537i	$-0.333023\pi$
$402$		0			0
$403$	−3.85077	+	3.85077i	−0.191821	+	0.191821i
$404$	19.4889			0.969607
$405$		0			0
$406$	21.0883			1.04660
$407$	−8.13233	+	8.13233i	−0.403105	+	0.403105i
$408$		0			0
$409$		−	17.4825i		−	0.864455i	−0.901765	−	0.432227i	$-0.857728\pi$
$409$		−	17.4825i		−	0.864455i	0.901765	−	0.432227i	$-0.142272\pi$
$410$	5.22824	−	7.40060i	0.258204	−	0.365489i
$411$		0			0
$412$	−4.23654	−	4.23654i	−0.208719	−	0.208719i
$413$	−9.64064	−	9.64064i	−0.474385	−	0.474385i
$414$		0			0
$415$	4.52637	−	6.40710i	0.222191	−	0.314512i
$416$			2.99319i			0.146753i
$417$		0			0
$418$	1.31116	−	1.31116i	0.0641307	−	0.0641307i
$419$	28.3156			1.38331			0.691653	−	0.722230i	$-0.256883\pi$
$419$	28.3156			1.38331			0.691653	+	0.722230i	$0.256883\pi$
$420$		0			0
$421$	20.8666			1.01698			0.508488	−	0.861069i	$-0.330205\pi$
$421$	20.8666			1.01698			0.508488	+	0.861069i	$0.330205\pi$
$422$	14.6192	−	14.6192i	0.711653	−	0.711653i
$423$		0			0
$424$			1.46147i			0.0709754i
$425$	6.96686	−	14.6198i	0.337942	−	0.709163i
$426$		0			0
$427$	−5.33328	−	5.33328i	−0.258096	−	0.258096i
$428$	1.11330	+	1.11330i	0.0538136	+	0.0538136i
$429$		0			0
$430$	−22.6723	+	3.89998i	−1.09335	+	0.188074i
$431$			16.8849i			0.813317i	0.913580	+	0.406659i	$0.133306\pi$
$431$			16.8849i			0.813317i	−0.913580	+	0.406659i	$0.866694\pi$
$432$		0			0
$433$	19.3819	−	19.3819i	0.931435	−	0.931435i	−0.0663604	−	0.997796i	$-0.521139\pi$
$433$	19.3819	−	19.3819i	0.931435	−	0.931435i	0.997796	+	0.0663604i	$0.0211387\pi$
$434$	−6.29306			−0.302076
$435$		0			0
$436$	−3.40579			−0.163108
$437$	2.39238	−	2.39238i	0.114443	−	0.114443i
$438$		0			0
$439$		−	21.6631i		−	1.03392i	−0.856008	−	0.516962i	$-0.827063\pi$
$439$		−	21.6631i		−	1.03392i	0.856008	−	0.516962i	$-0.172937\pi$
$440$	3.38642	+	2.39238i	0.161441	+	0.114052i
$441$		0			0
$442$	6.85532	+	6.85532i	0.326074	+	0.326074i
$443$	1.39602	+	1.39602i	0.0663269	+	0.0663269i	0.739492	−	0.673165i	$-0.235066\pi$
$443$	1.39602	+	1.39602i	0.0663269	+	0.0663269i	−0.673165	+	0.739492i	$0.735066\pi$
$444$		0			0
$445$	5.08622	+	29.5684i	0.241110	+	1.40168i
$446$			9.95529i			0.471397i
$447$		0			0
$448$	−2.44579	+	2.44579i	−0.115553	+	0.115553i
$449$	−27.2531			−1.28615			−0.643076	−	0.765803i	$-0.722342\pi$
$449$	−27.2531			−1.28615			−0.643076	+	0.765803i	$0.722342\pi$
$450$		0			0
$451$	7.51388			0.353815
$452$	1.01123	−	1.01123i	0.0475645	−	0.0475645i
$453$		0			0
$454$			17.2970i			0.811790i
$455$	3.92454	+	22.8150i	0.183985	+	1.06959i
$456$		0			0
$457$	−2.83134	−	2.83134i	−0.132444	−	0.132444i	0.637777	−	0.770221i	$-0.279854\pi$
$457$	−2.83134	−	2.83134i	−0.132444	−	0.132444i	−0.770221	+	0.637777i	$0.779854\pi$
$458$	−15.5678	−	15.5678i	−0.727434	−	0.727434i
$459$		0			0
$460$	6.17896	+	4.36520i	0.288096	+	0.203529i
$461$		−	11.3251i		−	0.527464i	−0.964596	−	0.263732i	$-0.915047\pi$
$461$		−	11.3251i		−	0.527464i	0.964596	−	0.263732i	$-0.0849535\pi$
$462$		0			0
$463$	−12.1265	+	12.1265i	−0.563565	+	0.563565i	−0.930318	−	0.366753i	$-0.880469\pi$
$463$	−12.1265	+	12.1265i	−0.563565	+	0.563565i	0.366753	+	0.930318i	$0.380469\pi$
$464$	6.09689			0.283041
$465$		0			0
$466$	14.1500			0.655486
$467$	−23.4660	+	23.4660i	−1.08588	+	1.08588i	−0.0899279	+	0.995948i	$0.528664\pi$
$467$	−23.4660	+	23.4660i	−1.08588	+	1.08588i	−0.995948	+	0.0899279i	$0.971336\pi$
$468$		0			0
$469$			23.4938i			1.08484i
$470$	4.49972	−	0.774022i	0.207557	−	0.0357030i
$471$		0			0
$472$	−2.78723	−	2.78723i	−0.128292	−	0.128292i
$473$	−13.4895	−	13.4895i	−0.620249	−	0.620249i
$474$		0			0
$475$	−1.67072	−	4.71261i	−0.0766578	−	0.216229i
$476$			11.2032i			0.513498i
$477$		0			0
$478$	4.76910	−	4.76910i	0.218134	−	0.218134i
$479$	5.29439			0.241907			0.120953	−	0.992658i	$-0.461405\pi$
$479$	5.29439			0.241907			0.120953	+	0.992658i	$0.461405\pi$
$480$		0			0
$481$	−18.5650			−0.846492
$482$	17.4905	−	17.4905i	0.796670	−	0.796670i
$483$		0			0
$484$		−	7.56174i		−	0.343716i
$485$	7.29853	−	10.3311i	0.331409	−	0.469111i
$486$		0			0
$487$	−15.8077	−	15.8077i	−0.716316	−	0.716316i	0.251533	−	0.967849i	$-0.419065\pi$
$487$	−15.8077	−	15.8077i	−0.716316	−	0.716316i	−0.967849	+	0.251533i	$0.919065\pi$
$488$	−1.54192	−	1.54192i	−0.0697993	−	0.0697993i
$489$		0			0
$490$	−6.40428	+	9.06528i	−0.289316	+	0.409527i
$491$			11.1535i			0.503349i	0.967812	+	0.251675i	$0.0809812\pi$
$491$			11.1535i			0.503349i	−0.967812	+	0.251675i	$0.919019\pi$
$492$		0			0
$493$	13.9637	−	13.9637i	0.628896	−	0.628896i
$494$	2.99319			0.134670
$495$		0			0
$496$	−1.81940			−0.0816935
$497$	5.05504	−	5.05504i	0.226749	−	0.226749i
$498$		0			0
$499$		−	26.8109i		−	1.20022i	−0.799917	−	0.600111i	$-0.795123\pi$
$499$		−	26.8109i		−	1.20022i	0.799917	−	0.600111i	$-0.204877\pi$
$500$	9.75187	−	5.46818i	0.436117	−	0.244545i
$501$		0			0
$502$	−18.5019	−	18.5019i	−0.825782	−	0.825782i
$503$	2.38661	+	2.38661i	0.106414	+	0.106414i	0.758309	−	0.651895i	$-0.226026\pi$
$503$	2.38661	+	2.38661i	0.106414	+	0.106414i	−0.651895	+	0.758309i	$0.726026\pi$
$504$		0			0
$505$	42.9477	−	7.38766i	1.91115	−	0.328747i
$506$			6.27355i			0.278893i
$507$		0			0
$508$	−0.919417	+	0.919417i	−0.0407925	+	0.0407925i
$509$	34.5225			1.53018			0.765092	−	0.643921i	$-0.222694\pi$
$509$	34.5225			1.53018			0.765092	+	0.643921i	$0.222694\pi$
$510$		0			0
$511$	−46.8909			−2.07433
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$		0			0
$514$		−	6.20870i		−	0.273854i
$515$	−10.9420	−	7.73013i	−0.482163	−	0.340630i
$516$		0			0
$517$	2.67724	+	2.67724i	0.117745	+	0.117745i
$518$	−15.1698	−	15.1698i	−0.666522	−	0.666522i
$519$		0			0
$520$	1.13463	+	6.59610i	0.0497569	+	0.289258i
$521$		−	37.3357i		−	1.63570i	−0.575428	−	0.817852i	$-0.695165\pi$
$521$		−	37.3357i		−	1.63570i	0.575428	−	0.817852i	$-0.304835\pi$
$522$		0			0
$523$	22.0356	−	22.0356i	0.963549	−	0.963549i	−0.0358094	−	0.999359i	$-0.511401\pi$
$523$	22.0356	−	22.0356i	0.963549	−	0.963549i	0.999359	+	0.0358094i	$0.0114009\pi$
$524$	4.24264			0.185341
$525$		0			0
$526$	−12.9215			−0.563405
$527$	−4.16698	+	4.16698i	−0.181517	+	0.181517i
$528$		0			0
$529$		−	11.5531i		−	0.502308i
$530$	0.554002	+	3.22065i	0.0240643	+	0.139896i
$531$		0			0
$532$	2.44579	+	2.44579i	0.106038	+	0.106038i
$533$	8.57660	+	8.57660i	0.371494	+	0.371494i
$534$		0			0
$535$	2.87541	+	2.03137i	0.124315	+	0.0878238i
$536$			6.79234i			0.293384i
$537$		0			0
$538$	−9.13023	+	9.13023i	−0.393632	+	0.393632i
$539$	−9.20405			−0.396446
$540$		0			0
$541$	−10.8429			−0.466175			−0.233087	−	0.972456i	$-0.574883\pi$
$541$	−10.8429			−0.466175			−0.233087	+	0.972456i	$0.574883\pi$
$542$	8.34615	−	8.34615i	0.358498	−	0.358498i
$543$		0			0
$544$			3.23898i			0.138870i
$545$	−7.50534	+	1.29103i	−0.321494	+	0.0553019i
$546$		0			0
$547$	1.13652	+	1.13652i	0.0485942	+	0.0485942i	0.730986	−	0.682392i	$-0.239060\pi$
$547$	1.13652	+	1.13652i	0.0485942	+	0.0485942i	−0.682392	+	0.730986i	$0.739060\pi$
$548$	8.15130	+	8.15130i	0.348206	+	0.348206i
$549$		0			0
$550$	8.36954	+	3.98839i	0.356878	+	0.170066i
$551$		−	6.09689i		−	0.259736i
$552$		0			0
$553$	−3.49772	+	3.49772i	−0.148738	+	0.148738i
$554$	−14.4510			−0.613965
$555$		0			0
$556$	−6.18060			−0.262116
$557$	5.70866	−	5.70866i	0.241884	−	0.241884i	−0.575745	−	0.817629i	$-0.695288\pi$
$557$	5.70866	−	5.70866i	0.241884	−	0.241884i	0.817629	+	0.575745i	$0.195288\pi$
$558$		0			0
$559$		−	30.7948i		−	1.30248i
$560$	−4.46266	+	6.31691i	−0.188582	+	0.266938i
$561$		0			0
$562$	13.4563	+	13.4563i	0.567620	+	0.567620i
$563$	−9.42883	−	9.42883i	−0.397378	−	0.397378i	0.479929	−	0.877307i	$-0.340662\pi$
$563$	−9.42883	−	9.42883i	−0.397378	−	0.397378i	−0.877307	+	0.479929i	$0.840662\pi$
$564$		0			0
$565$	1.84513	−	2.61179i	0.0776252	−	0.109879i
$566$		−	25.0551i		−	1.05314i
$567$		0			0
$568$	1.46147	−	1.46147i	0.0613220	−	0.0613220i
$569$	−14.8826			−0.623912			−0.311956	−	0.950097i	$-0.600984\pi$
$569$	−14.8826			−0.623912			−0.311956	+	0.950097i	$0.600984\pi$
$570$		0			0
$571$	−15.0430			−0.629529			−0.314765	−	0.949170i	$-0.601926\pi$
$571$	−15.0430			−0.629529			−0.314765	+	0.949170i	$0.601926\pi$
$572$	−3.92454	+	3.92454i	−0.164093	+	0.164093i
$573$		0			0
$574$			14.0162i			0.585023i
$575$	15.2713	+	7.27735i	0.636858	+	0.303486i
$576$		0			0
$577$	−16.9500	−	16.9500i	−0.705636	−	0.705636i	0.259979	−	0.965614i	$-0.416285\pi$
$577$	−16.9500	−	16.9500i	−0.705636	−	0.705636i	−0.965614	+	0.259979i	$0.916285\pi$
$578$	−4.60256	−	4.60256i	−0.191441	−	0.191441i
$579$		0			0
$580$	13.4357	−	2.31116i	0.557889	−	0.0959655i
$581$			12.1345i			0.503426i
$582$		0			0
$583$	−1.91622	+	1.91622i	−0.0793616	+	0.0793616i
$584$	−13.5567			−0.560982
$585$		0			0
$586$	−15.6825			−0.647840
$587$	17.9345	−	17.9345i	0.740237	−	0.740237i	−0.232387	−	0.972623i	$-0.574653\pi$
$587$	17.9345	−	17.9345i	0.740237	−	0.740237i	0.972623	+	0.232387i	$0.0746535\pi$
$588$		0			0
$589$			1.81940i			0.0749671i
$590$	−7.19877	−	5.08566i	−0.296369	−	0.209373i
$591$		0			0
$592$	−4.38577	−	4.38577i	−0.180254	−	0.180254i
$593$	19.6576	+	19.6576i	0.807242	+	0.807242i	0.984216	−	0.176974i	$-0.0566308\pi$
$593$	19.6576	+	19.6576i	0.807242	+	0.807242i	−0.176974	+	0.984216i	$0.556631\pi$
$594$		0			0
$595$	4.24681	+	24.6885i	0.174102	+	1.01213i
$596$			5.71955i			0.234282i
$597$		0			0
$598$	−7.16084	+	7.16084i	−0.292828	+	0.292828i
$599$	2.58990			0.105820			0.0529102	−	0.998599i	$-0.483150\pi$
$599$	2.58990			0.105820			0.0529102	+	0.998599i	$0.483150\pi$
$600$		0			0
$601$	15.9918			0.652321			0.326160	−	0.945314i	$-0.394245\pi$
$601$	15.9918			0.652321			0.326160	+	0.945314i	$0.394245\pi$
$602$	25.1629	−	25.1629i	1.02556	−	1.02556i
$603$		0			0
$604$			16.8191i			0.684358i
$605$	−2.86644	−	16.6638i	−0.116537	−	0.677481i
$606$		0			0
$607$	8.09219	+	8.09219i	0.328452	+	0.328452i	0.851998	−	0.523546i	$-0.175391\pi$
$607$	8.09219	+	8.09219i	0.328452	+	0.328452i	−0.523546	+	0.851998i	$0.675391\pi$
$608$	0.707107	+	0.707107i	0.0286770	+	0.0286770i
$609$		0			0
$610$	−3.98242	−	2.81343i	−0.161244	−	0.113912i
$611$			6.11177i			0.247256i
$612$		0			0
$613$	16.5239	−	16.5239i	0.667395	−	0.667395i	−0.289717	−	0.957112i	$-0.593561\pi$
$613$	16.5239	−	16.5239i	0.667395	−	0.667395i	0.957112	+	0.289717i	$0.0935612\pi$
$614$	−23.6604			−0.954855
$615$		0			0
$616$	−6.41361			−0.258412
$617$	5.82216	−	5.82216i	0.234391	−	0.234391i	−0.580132	−	0.814523i	$-0.696999\pi$
$617$	5.82216	−	5.82216i	0.234391	−	0.234391i	0.814523	+	0.580132i	$0.196999\pi$
$618$		0			0
$619$		−	25.4343i		−	1.02229i	−0.859494	−	0.511146i	$-0.829221\pi$
$619$		−	25.4343i		−	1.02229i	0.859494	−	0.511146i	$-0.170779\pi$
$620$	−4.00942	+	0.689681i	−0.161022	+	0.0276983i
$621$		0			0
$622$	−7.90562	−	7.90562i	−0.316987	−	0.316987i
$623$	−32.8166	−	32.8166i	−1.31477	−	1.31477i
$624$		0			0
$625$	19.4174	−	15.7469i	0.776696	−	0.629876i
$626$			15.1163i			0.604169i
$627$		0			0
$628$	−1.82912	+	1.82912i	−0.0729897	+	0.0729897i
$629$	−20.0895			−0.801021
$630$		0			0
$631$	45.9025			1.82735			0.913675	−	0.406445i	$-0.133232\pi$
$631$	45.9025			1.82735			0.913675	+	0.406445i	$0.133232\pi$
$632$	−1.01123	+	1.01123i	−0.0402248	+	0.0402248i
$633$		0			0
$634$			23.9437i			0.950924i
$635$	−1.67760	+	2.37465i	−0.0665734	+	0.0942349i
$636$		0			0
$637$	−10.5058	−	10.5058i	−0.416255	−	0.416255i
$638$	7.99397	+	7.99397i	0.316484	+	0.316484i
$639$		0			0
$640$	−1.29021	+	1.82630i	−0.0510000	+	0.0721907i
$641$		−	36.1191i		−	1.42662i	−0.700848	−	0.713310i	$-0.747195\pi$
$641$		−	36.1191i		−	1.42662i	0.700848	−	0.713310i	$-0.252805\pi$
$642$		0			0
$643$	−24.8180	+	24.8180i	−0.978726	+	0.978726i	−0.999778	−	0.0210526i	$-0.993298\pi$
$643$	−24.8180	+	24.8180i	−0.978726	+	0.978726i	0.0210526	+	0.999778i	$0.493298\pi$
$644$	−11.7025			−0.461142
$645$		0			0
$646$	3.23898			0.127436
$647$	−29.5857	+	29.5857i	−1.16314	+	1.16314i	−0.179350	+	0.983785i	$0.557399\pi$
$647$	−29.5857	+	29.5857i	−1.16314	+	1.16314i	−0.983785	+	0.179350i	$0.942601\pi$
$648$		0			0
$649$		−	7.30897i		−	0.286902i
$650$	5.00078	+	14.1057i	0.196147	+	0.553273i
$651$		0			0
$652$	−15.5861	−	15.5861i	−0.610397	−	0.610397i
$653$	−7.70050	−	7.70050i	−0.301344	−	0.301344i	0.540196	−	0.841540i	$-0.318350\pi$
$653$	−7.70050	−	7.70050i	−0.301344	−	0.301344i	−0.841540	+	0.540196i	$0.818350\pi$
$654$		0			0
$655$	9.34952	−	1.60826i	0.365316	−	0.0628400i
$656$			4.05224i			0.158213i
$657$		0			0
$658$	−4.99403	+	4.99403i	−0.194688	+	0.194688i
$659$	21.6601			0.843757			0.421879	−	0.906652i	$-0.361371\pi$
$659$	21.6601			0.843757			0.421879	+	0.906652i	$0.361371\pi$
$660$		0			0
$661$	−23.4825			−0.913364			−0.456682	−	0.889630i	$-0.650962\pi$
$661$	−23.4825			−0.913364			−0.456682	+	0.889630i	$0.650962\pi$
$662$	−2.50687	+	2.50687i	−0.0974324	+	0.0974324i
$663$		0			0
$664$			3.50824i			0.136146i
$665$	6.31691	+	4.46266i	0.244959	+	0.173055i
$666$		0			0
$667$	14.5861	+	14.5861i	0.564774	+	0.564774i
$668$	12.1544	+	12.1544i	0.470268	+	0.470268i
$669$		0			0
$670$	2.57478	+	14.9683i	0.0994724	+	0.578276i
$671$		−	4.04339i		−	0.156093i
$672$		0			0
$673$	−28.4974	+	28.4974i	−1.09849	+	1.09849i	−0.103907	+	0.994587i	$0.533134\pi$
$673$	−28.4974	+	28.4974i	−1.09849	+	1.09849i	−0.994587	+	0.103907i	$0.966866\pi$
$674$	−30.4252			−1.17194
$675$		0			0
$676$	4.04080			0.155416
$677$	−15.1954	+	15.1954i	−0.584007	+	0.584007i	−0.936002	−	0.351995i	$-0.885504\pi$
$677$	−15.1954	+	15.1954i	−0.584007	+	0.584007i	0.351995	+	0.936002i	$0.385504\pi$
$678$		0			0
$679$			19.5663i			0.750886i
$680$	1.22780	+	7.13775i	0.0470841	+	0.273720i
$681$		0			0
$682$	−2.38552	−	2.38552i	−0.0913461	−	0.0913461i
$683$	34.6257	+	34.6257i	1.32492	+	1.32492i	0.909742	+	0.415174i	$0.136279\pi$
$683$	34.6257	+	34.6257i	1.32492	+	1.32492i	0.415174	+	0.909742i	$0.363721\pi$
$684$		0			0
$685$	21.0530	+	14.8731i	0.804392	+	0.568273i
$686$			7.04312i			0.268908i
$687$		0			0
$688$	7.27490	−	7.27490i	0.277353	−	0.277353i
$689$	−4.37447			−0.166654
$690$		0			0
$691$	−36.0799			−1.37254			−0.686271	−	0.727346i	$-0.740754\pi$
$691$	−36.0799			−1.37254			−0.686271	+	0.727346i	$0.740754\pi$
$692$	11.9151	−	11.9151i	0.452943	−	0.452943i
$693$		0			0
$694$		−	28.0581i		−	1.06507i
$695$	−13.6202	+	2.34289i	−0.516644	+	0.0888707i
$696$		0			0
$697$	9.28087	+	9.28087i	0.351538	+	0.351538i
$698$	17.9469	+	17.9469i	0.679302	+	0.679302i
$699$		0			0
$700$	−7.43982	+	15.6123i	−0.281199	+	0.590088i
$701$			28.8611i			1.09007i	0.838413	+	0.545035i	$0.183484\pi$
$701$			28.8611i			1.09007i	−0.838413	+	0.545035i	$0.816516\pi$
$702$		0			0
$703$	−4.38577	+	4.38577i	−0.165412	+	0.165412i
$704$	−1.85425			−0.0698848
$705$		0			0
$706$	−17.0102			−0.640187
$707$	−47.6656	+	47.6656i	−1.79265	+	1.79265i
$708$		0			0
$709$		−	3.25277i		−	0.122161i	−0.998133	−	0.0610803i	$-0.980545\pi$
$709$		−	3.25277i		−	0.122161i	0.998133	−	0.0610803i	$-0.0194546\pi$
$710$	2.66665	−	3.77465i	0.100078	−	0.141660i
$711$		0			0
$712$	−9.48768	−	9.48768i	−0.355566	−	0.355566i
$713$	−4.35269	−	4.35269i	−0.163009	−	0.163009i
$714$		0			0
$715$	−7.16084	+	10.1362i	−0.267800	+	0.379072i
$716$		−	15.8288i		−	0.591552i
$717$		0			0
$718$	2.93103	−	2.93103i	0.109385	−	0.109385i
$719$	11.0628			0.412574			0.206287	−	0.978492i	$-0.433862\pi$
$719$	11.0628			0.412574			0.206287	+	0.978492i	$0.433862\pi$
$720$		0			0
$721$	20.7234			0.771778
$722$	0.707107	−	0.707107i	0.0263158	−	0.0263158i
$723$		0			0
$724$			2.63425i			0.0979010i
$725$	28.7323	−	10.1862i	1.06709	−	0.378306i
$726$		0			0
$727$	−24.4444	−	24.4444i	−0.906592	−	0.906592i	0.0894039	−	0.995995i	$-0.471504\pi$
$727$	−24.4444	−	24.4444i	−0.906592	−	0.906592i	−0.995995	+	0.0894039i	$0.971504\pi$
$728$	−7.32071	−	7.32071i	−0.271324	−	0.271324i
$729$		0			0
$730$	−29.8750	+	5.13896i	−1.10572	+	0.190202i
$731$		−	33.3235i		−	1.23251i
$732$		0			0
$733$	−19.8872	+	19.8872i	−0.734549	+	0.734549i	−0.971517	−	0.236968i	$-0.923846\pi$
$733$	−19.8872	+	19.8872i	−0.734549	+	0.734549i	0.236968	+	0.971517i	$0.423846\pi$
$734$	24.7821			0.914725
$735$		0			0
$736$	−3.38333			−0.124711
$737$	−8.90581	+	8.90581i	−0.328050	+	0.328050i
$738$		0			0
$739$			9.06729i			0.333546i	0.985995	+	0.166773i	$0.0533347\pi$
$739$			9.06729i			0.333546i	−0.985995	+	0.166773i	$0.946665\pi$
$740$	−11.3275	−	8.00241i	−0.416405	−	0.294175i
$741$		0			0
$742$	−3.57445	−	3.57445i	−0.131222	−	0.131222i
$743$	−25.6087	−	25.6087i	−0.939493	−	0.939493i	0.0587784	−	0.998271i	$-0.481279\pi$
$743$	−25.6087	−	25.6087i	−0.939493	−	0.939493i	−0.998271	+	0.0587784i	$0.981279\pi$
$744$		0			0
$745$	2.16811	+	12.6042i	0.0794336	+	0.461782i
$746$			20.4287i			0.747946i
$747$		0			0
$748$	−4.24681	+	4.24681i	−0.155279	+	0.155279i
$749$	−5.44581			−0.198986
$750$		0			0
$751$	51.1239			1.86554			0.932769	−	0.360474i	$-0.117385\pi$
$751$	51.1239			1.86554			0.932769	+	0.360474i	$0.117385\pi$
$752$	−1.44384	+	1.44384i	−0.0526513	+	0.0526513i
$753$		0			0
$754$			18.2492i			0.664596i
$755$	6.37562	+	37.0642i	0.232033	+	1.34891i
$756$		0			0
$757$	32.1378	+	32.1378i	1.16807	+	1.16807i	0.982662	+	0.185404i	$0.0593595\pi$
$757$	32.1378	+	32.1378i	1.16807	+	1.16807i	0.185404	+	0.982662i	$0.440641\pi$
$758$	5.74518	+	5.74518i	0.208674	+	0.208674i
$759$		0			0
$760$	1.82630	+	1.29021i	0.0662467	+	0.0468008i
$761$			17.3658i			0.629509i	0.949173	+	0.314754i	$0.101922\pi$
$761$			17.3658i			0.629509i	−0.949173	+	0.314754i	$0.898078\pi$
$762$		0			0
$763$	8.32983	−	8.32983i	0.301560	−	0.301560i
$764$	16.9820			0.614387
$765$		0			0
$766$	33.4332			1.20799
$767$	8.34270	−	8.34270i	0.301237	−	0.301237i
$768$		0			0
$769$			0.768835i			0.0277249i	0.999904	+	0.0138624i	$0.00441270\pi$
$769$			0.768835i			0.0277249i	−0.999904	+	0.0138624i	$0.995587\pi$
$770$	−14.1337	+	2.43121i	−0.509343	+	0.0876149i
$771$		0			0
$772$	−15.1246	−	15.1246i	−0.544346	−	0.544346i
$773$	−23.4941	−	23.4941i	−0.845023	−	0.845023i	0.144484	−	0.989507i	$-0.453848\pi$
$773$	−23.4941	−	23.4941i	−0.845023	−	0.845023i	−0.989507	+	0.144484i	$0.953848\pi$
$774$		0			0
$775$	−8.57412	+	3.03971i	−0.307992	+	0.109189i
$776$			5.65685i			0.203069i
$777$		0			0
$778$	−6.02187	+	6.02187i	−0.215895	+	0.215895i
$779$	4.05224			0.145187
$780$		0			0
$781$	3.83243			0.137135
$782$	−7.74886	+	7.74886i	−0.277099	+	0.277099i
$783$		0			0
$784$		−	4.96375i		−	0.177277i
$785$	−3.33746	+	4.72419i	−0.119119	+	0.168614i
$786$		0			0
$787$	20.8310	+	20.8310i	0.742545	+	0.742545i	0.973067	−	0.230522i	$-0.0740433\pi$
$787$	20.8310	+	20.8310i	0.742545	+	0.742545i	−0.230522	+	0.973067i	$0.574043\pi$
$788$	−10.3726	−	10.3726i	−0.369509	−	0.369509i
$789$		0			0
$790$	−1.84513	+	2.61179i	−0.0656468	+	0.0929233i
$791$			4.94653i			0.175878i
$792$		0			0
$793$	4.61525	−	4.61525i	0.163892	−	0.163892i
$794$	−26.5412			−0.941912
$795$		0			0
$796$	−22.3411			−0.791860
$797$	−22.4652	+	22.4652i	−0.795757	+	0.795757i	−0.982423	−	0.186666i	$-0.940232\pi$
$797$	−22.4652	+	22.4652i	−0.795757	+	0.795757i	0.186666	+	0.982423i	$0.440232\pi$
$798$		0			0
$799$			6.61365i			0.233974i
$800$	−2.15094	+	4.51370i	−0.0760473	+	0.159583i
$801$		0			0
$802$	24.5117	+	24.5117i	0.865537	+	0.865537i
$803$	−17.7750	−	17.7750i	−0.627266	−	0.627266i
$804$		0			0
$805$	−25.7888	+	4.43607i	−0.908935	+	0.156351i
$806$		−	5.44581i		−	0.191821i
$807$		0			0
$808$	−13.7807	+	13.7807i	−0.484804	+	0.484804i
$809$	−52.9692			−1.86230			−0.931148	−	0.364641i	$-0.881192\pi$
$809$	−52.9692			−1.86230			−0.931148	+	0.364641i	$0.881192\pi$
$810$		0			0
$811$	−36.4459			−1.27979			−0.639895	−	0.768462i	$-0.721022\pi$
$811$	−36.4459			−1.27979			−0.639895	+	0.768462i	$0.721022\pi$
$812$	−14.9117	+	14.9117i	−0.523298	+	0.523298i
$813$		0			0
$814$		−	11.5008i		−	0.403105i
$815$	−40.2553	−	28.4388i	−1.41008	−	0.996168i
$816$		0			0
$817$	−7.27490	−	7.27490i	−0.254517	−	0.254517i
$818$	12.3620	+	12.3620i	0.432227	+	0.432227i
$819$		0			0
$820$	1.53609	+	8.92994i	0.0536425	+	0.311847i
$821$			9.58783i			0.334618i	0.985905	+	0.167309i	$0.0535077\pi$
$821$			9.58783i			0.334618i	−0.985905	+	0.167309i	$0.946492\pi$
$822$		0			0
$823$	−14.9600	+	14.9600i	−0.521473	+	0.521473i	−0.918016	−	0.396543i	$-0.870210\pi$
$823$	−14.9600	+	14.9600i	−0.521473	+	0.521473i	0.396543	+	0.918016i	$0.370210\pi$
$824$	5.99137			0.208719
$825$		0			0
$826$	13.6339			0.474385
$827$	−0.562754	+	0.562754i	−0.0195689	+	0.0195689i	−0.716824	−	0.697255i	$-0.754405\pi$
$827$	−0.562754	+	0.562754i	−0.0195689	+	0.0195689i	0.697255	+	0.716824i	$0.254405\pi$
$828$		0			0
$829$			19.0932i			0.663135i	0.943432	+	0.331567i	$0.107577\pi$
$829$			19.0932i			0.663135i	−0.943432	+	0.331567i	$0.892423\pi$
$830$	1.32987	+	7.73113i	0.0461606	+	0.268351i
$831$		0			0
$832$	−2.11651	−	2.11651i	−0.0733766	−	0.0733766i
$833$	−11.3685	−	11.3685i	−0.393895	−	0.393895i
$834$		0			0
$835$	31.3921	+	22.1773i	1.08637	+	0.767478i
$836$			1.85425i			0.0641307i
$837$		0			0
$838$	−20.0221	+	20.0221i	−0.691653	+	0.691653i
$839$	−6.82673			−0.235685			−0.117842	−	0.993032i	$-0.537598\pi$
$839$	−6.82673			−0.235685			−0.117842	+	0.993032i	$0.537598\pi$
$840$		0			0
$841$	8.17212			0.281797
$842$	−14.7549	+	14.7549i	−0.508488	+	0.508488i
$843$		0			0
$844$			20.6747i			0.711653i
$845$	8.90473	−	1.53175i	0.306332	−	0.0526938i
$846$		0			0
$847$	18.4944	+	18.4944i	0.635476	+	0.635476i
$848$	−1.03342	−	1.03342i	−0.0354877	−	0.0354877i
$849$		0			0
$850$	5.41143	+	15.2641i	0.185610	+	0.523553i
$851$		−	20.9848i		−	0.719350i
$852$		0			0
$853$	−10.1332	+	10.1332i	−0.346955	+	0.346955i	−0.858974	−	0.512019i	$-0.828898\pi$
$853$	−10.1332	+	10.1332i	−0.346955	+	0.346955i	0.512019	+	0.858974i	$0.328898\pi$
$854$	7.54240			0.258096
$855$		0			0
$856$	−1.57445			−0.0538136
$857$	30.6067	−	30.6067i	1.04551	−	1.04551i	0.0465916	−	0.998914i	$-0.485164\pi$
$857$	30.6067	−	30.6067i	1.04551	−	1.04551i	0.998914	−	0.0465916i	$-0.0148359\pi$
$858$		0			0
$859$		−	50.5487i		−	1.72470i	−0.506313	−	0.862350i	$-0.668992\pi$
$859$		−	50.5487i		−	1.72470i	0.506313	−	0.862350i	$-0.331008\pi$
$860$	13.2740	−	18.7894i	0.452640	−	0.640714i
$861$		0			0
$862$	−11.9394	−	11.9394i	−0.406659	−	0.406659i
$863$	−32.9784	−	32.9784i	−1.12260	−	1.12260i	−0.991350	−	0.131247i	$-0.958102\pi$
$863$	−32.9784	−	32.9784i	−1.12260	−	1.12260i	−0.131247	−	0.991350i	$-0.541898\pi$
$864$		0			0
$865$	21.7406	−	30.7739i	0.739203	−	1.04634i
$866$			27.4102i			0.931435i
$867$		0			0
$868$	4.44986	−	4.44986i	0.151038	−	0.151038i
$869$	−2.65177			−0.0899552
$870$		0			0
$871$	−20.3308			−0.688882
$872$	2.40826	−	2.40826i	0.0815538	−	0.0815538i
$873$		0			0
$874$			3.38333i			0.114443i
$875$	−10.4770	+	37.2250i	−0.354187	+	1.25843i
$876$		0			0
$877$	16.8518	+	16.8518i	0.569045	+	0.569045i	0.931861	−	0.362816i	$-0.118185\pi$
$877$	16.8518	+	16.8518i	0.569045	+	0.569045i	−0.362816	+	0.931861i	$0.618185\pi$
$878$	15.3181	+	15.3181i	0.516962	+	0.516962i
$879$		0			0
$880$	−4.08622	+	0.702894i	−0.137747	+	0.0236945i
$881$			26.9178i			0.906883i	0.891286	+	0.453441i	$0.149804\pi$
$881$			26.9178i			0.906883i	−0.891286	+	0.453441i	$0.850196\pi$
$882$		0			0
$883$	16.1164	−	16.1164i	0.542361	−	0.542361i	−0.381859	−	0.924220i	$-0.624716\pi$
$883$	16.1164	−	16.1164i	0.542361	−	0.542361i	0.924220	+	0.381859i	$0.124716\pi$
$884$	−9.69489			−0.326074
$885$		0			0
$886$	−1.97427			−0.0663269
$887$	−7.24427	+	7.24427i	−0.243239	+	0.243239i	−0.818189	−	0.574950i	$-0.805022\pi$
$887$	−7.24427	+	7.24427i	−0.243239	+	0.243239i	0.574950	+	0.818189i	$0.305022\pi$
$888$		0			0
$889$		−	4.49740i		−	0.150838i
$890$	−24.5045	−	17.3115i	−0.821394	−	0.580283i
$891$		0			0
$892$	−7.03945	−	7.03945i	−0.235698	−	0.235698i
$893$	1.44384	+	1.44384i	0.0483161	+	0.0483161i
$894$		0			0
$895$	−6.00025	−	34.8821i	−0.200566	−	1.16598i
$896$		−	3.45887i		−	0.115553i
$897$		0			0
$898$	19.2708	−	19.2708i	0.643076	−	0.643076i
$899$	−11.0927			−0.369962
$900$		0			0
$901$	−4.73368			−0.157702
$902$	−5.31312	+	5.31312i	−0.176907	+	0.176907i
$903$		0			0
$904$			1.43010i			0.0475645i
$905$	0.998566	+	5.80510i	0.0331935	+	0.192968i
$906$		0			0
$907$	−34.9997	−	34.9997i	−1.16215	−	1.16215i	−0.984005	−	0.178140i	$-0.942992\pi$
$907$	−34.9997	−	34.9997i	−1.16215	−	1.16215i	−0.178140	−	0.984005i	$-0.557008\pi$
$908$	−12.2308	−	12.2308i	−0.405895	−	0.405895i
$909$		0			0
$910$	−18.9077	−	13.3576i	−0.626785	−	0.442800i
$911$			24.7981i			0.821599i	0.911726	+	0.410799i	$0.134750\pi$
$911$			24.7981i			0.821599i	−0.911726	+	0.410799i	$0.865250\pi$
$912$		0			0
$913$	−4.59985	+	4.59985i	−0.152233	+	0.152233i
$914$	4.00411			0.132444
$915$		0			0
$916$	22.0162			0.727434
$917$	−10.3766	+	10.3766i	−0.342665	+	0.342665i
$918$		0			0
$919$		−	14.0962i		−	0.464989i	−0.972598	−	0.232495i	$-0.925311\pi$
$919$		−	14.0962i		−	0.464989i	0.972598	−	0.232495i	$-0.0746888\pi$
$920$	−7.45585	+	1.28252i	−0.245812	+	0.0422835i
$921$		0			0
$922$	8.00808	+	8.00808i	0.263732	+	0.263732i
$923$	4.37447	+	4.37447i	0.143987	+	0.143987i
$924$		0			0
$925$	−27.9958	−	13.3410i	−0.920497	−	0.438651i
$926$		−	17.1494i		−	0.563565i
$927$		0			0
$928$	−4.31116	+	4.31116i	−0.141521	+	0.141521i
$929$	35.0100			1.14864			0.574320	−	0.818631i	$-0.305266\pi$
$929$	35.0100			1.14864			0.574320	+	0.818631i	$0.305266\pi$
$930$		0			0
$931$	−4.96375			−0.162680
$932$	−10.0056	+	10.0056i	−0.327743	+	0.327743i
$933$		0			0
$934$		−	33.1859i		−	1.08588i
$935$	−7.74886	+	10.9685i	−0.253415	+	0.358710i
$936$		0			0
$937$	21.4974	+	21.4974i	0.702289	+	0.702289i	0.964901	−	0.262612i	$-0.0845840\pi$
$937$	21.4974	+	21.4974i	0.702289	+	0.702289i	−0.262612	+	0.964901i	$0.584584\pi$
$938$	−16.6126	−	16.6126i	−0.542421	−	0.542421i
$939$		0			0
$940$	−2.63447	+	3.72910i	−0.0859269	+	0.121630i
$941$			58.7403i			1.91488i	0.288632	+	0.957440i	$0.406799\pi$
$941$			58.7403i			1.91488i	−0.288632	+	0.957440i	$0.593201\pi$
$942$		0			0
$943$	−9.69448	+	9.69448i	−0.315696	+	0.315696i
$944$	3.94173			0.128292
$945$		0			0
$946$	19.0771			0.620249
$947$	26.0670	−	26.0670i	0.847062	−	0.847062i	−0.142703	−	0.989765i	$-0.545580\pi$
$947$	26.0670	−	26.0670i	0.847062	−	0.847062i	0.989765	+	0.142703i	$0.0455795\pi$
$948$		0			0
$949$		−	40.5779i		−	1.31721i
$950$	4.51370	+	2.15094i	0.146444	+	0.0697858i
$951$		0			0
$952$	−7.92186	−	7.92186i	−0.256749	−	0.256749i
$953$	10.5093	+	10.5093i	0.340429	+	0.340429i	0.856529	−	0.516099i	$-0.172617\pi$
$953$	10.5093	+	10.5093i	0.340429	+	0.340429i	−0.516099	+	0.856529i	$0.672617\pi$
$954$		0			0
$955$	37.4233	−	6.43738i	1.21099	−	0.208309i
$956$			6.74453i			0.218134i
$957$		0			0
$958$	−3.74370	+	3.74370i	−0.120953	+	0.120953i
$959$	−39.8727			−1.28756
$960$		0			0
$961$	−27.6898			−0.893219
$962$	13.1274	−	13.1274i	0.423246	−	0.423246i
$963$		0			0
$964$			24.7353i			0.796670i
$965$	−39.0634	−	27.5968i	−1.25749	−	0.888372i
$966$		0			0
$967$	18.3338	+	18.3338i	0.589574	+	0.589574i	0.937516	−	0.347942i	$-0.113119\pi$
$967$	18.3338	+	18.3338i	0.589574	+	0.589574i	−0.347942	+	0.937516i	$0.613119\pi$
$968$	5.34696	+	5.34696i	0.171858	+	0.171858i
$969$		0			0
$970$	2.14435	+	12.4660i	0.0688509	+	0.400260i
$971$		−	53.9006i		−	1.72975i	−0.501986	−	0.864876i	$-0.667397\pi$
$971$		−	53.9006i		−	1.72975i	0.501986	−	0.864876i	$-0.332603\pi$
$972$		0			0
$973$	15.1164	−	15.1164i	0.484611	−	0.484611i
$974$	22.3555			0.716316
$975$		0			0
$976$	2.18060			0.0697993
$977$	−6.88644	+	6.88644i	−0.220317	+	0.220317i	−0.808632	−	0.588315i	$-0.799791\pi$
$977$	−6.88644	+	6.88644i	−0.220317	+	0.220317i	0.588315	+	0.808632i	$0.299791\pi$
$978$		0			0
$979$		−	24.8796i		−	0.795157i
$980$	−1.88161	−	10.9386i	−0.0601059	−	0.349422i
$981$		0			0
$982$	−7.88669	−	7.88669i	−0.251675	−	0.251675i
$983$	−16.7893	−	16.7893i	−0.535495	−	0.535495i	0.386708	−	0.922202i	$-0.373612\pi$
$983$	−16.7893	−	16.7893i	−0.535495	−	0.535495i	−0.922202	+	0.386708i	$0.873612\pi$
$984$		0			0
$985$	−26.7901	−	18.9262i	−0.853603	−	0.603039i
$986$			19.7477i			0.628896i
$987$		0			0
$988$	−2.11651	+	2.11651i	−0.0673350	+	0.0673350i
$989$	34.8086			1.10685
$990$		0			0
$991$	20.7844			0.660239			0.330120	−	0.943939i	$-0.392911\pi$
$991$	20.7844			0.660239			0.330120	+	0.943939i	$0.392911\pi$
$992$	1.28651	−	1.28651i	0.0408467	−	0.0408467i
$993$		0			0
$994$			7.14890i			0.226749i
$995$	−49.2332	+	8.46886i	−1.56080	+	0.268481i
$996$		0			0
$997$	17.0505	+	17.0505i	0.539995	+	0.539995i	0.923528	−	0.383532i	$-0.125292\pi$
$997$	17.0505	+	17.0505i	0.539995	+	0.539995i	−0.383532	+	0.923528i	$0.625292\pi$
$998$	18.9582	+	18.9582i	0.600111	+	0.600111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1710.2.n.h.647.2	✓	16
3.2	odd	2	inner	1710.2.n.h.647.7	yes	16
5.3	odd	4	inner	1710.2.n.h.1673.7	yes	16
15.8	even	4	inner	1710.2.n.h.1673.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1710.2.n.h.647.2	✓	16	1.1	even	1	trivial
1710.2.n.h.647.7	yes	16	3.2	odd	2	inner
1710.2.n.h.1673.2	yes	16	15.8	even	4	inner
1710.2.n.h.1673.7	yes	16	5.3	odd	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:	\( N \)	\(=\)	\( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1710.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.379071 - 2.20370i) q^{5} +(2.44579 + 2.44579i) q^{7} +(0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} -1.00000i q^{4} +(-0.379071 - 2.20370i) q^{5} +(2.44579 + 2.44579i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.82630 + 1.29021i) q^{10} +1.85425i q^{11} +(-2.11651 + 2.11651i) q^{13} -3.45887 q^{14} -1.00000 q^{16} +(-2.29031 + 2.29031i) q^{17} +1.00000i q^{19} +(-2.20370 + 0.379071i) q^{20} +(-1.31116 - 1.31116i) q^{22} +(-2.39238 - 2.39238i) q^{23} +(-4.71261 + 1.67072i) q^{25} -2.99319i q^{26} +(2.44579 - 2.44579i) q^{28} -6.09689 q^{29} +1.81940 q^{31} +(0.707107 - 0.707107i) q^{32} -3.23898i q^{34} +(4.46266 - 6.31691i) q^{35} +(4.38577 + 4.38577i) q^{37} +(-0.707107 - 0.707107i) q^{38} +(1.29021 - 1.82630i) q^{40} -4.05224i q^{41} +(-7.27490 + 7.27490i) q^{43} +1.85425 q^{44} +3.38333 q^{46} +(1.44384 - 1.44384i) q^{47} +4.96375i q^{49} +(2.15094 - 4.51370i) q^{50} +(2.11651 + 2.11651i) q^{52} +(1.03342 + 1.03342i) q^{53} +(4.08622 - 0.702894i) q^{55} +3.45887i q^{56} +(4.31116 - 4.31116i) q^{58} -3.94173 q^{59} -2.18060 q^{61} +(-1.28651 + 1.28651i) q^{62} +1.00000i q^{64} +(5.46646 + 3.86184i) q^{65} +(4.80291 + 4.80291i) q^{67} +(2.29031 + 2.29031i) q^{68} +(1.31116 + 7.62231i) q^{70} -2.06683i q^{71} +(-9.58606 + 9.58606i) q^{73} -6.20242 q^{74} +1.00000 q^{76} +(-4.53511 + 4.53511i) q^{77} +1.43010i q^{79} +(0.379071 + 2.20370i) q^{80} +(2.86537 + 2.86537i) q^{82} +(2.48070 + 2.48070i) q^{83} +(5.91534 + 4.17896i) q^{85} -10.2883i q^{86} +(-1.31116 + 1.31116i) q^{88} -13.4176 q^{89} -10.3530 q^{91} +(-2.39238 + 2.39238i) q^{92} +2.04189i q^{94} +(2.20370 - 0.379071i) q^{95} +(4.00000 + 4.00000i) q^{97} +(-3.50990 - 3.50990i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q + 4 q^{10} + 8 q^{13} - 16 q^{16} + 24 q^{22} - 16 q^{25} - 32 q^{31} + 40 q^{37} + 4 q^{40} + 24 q^{43} - 8 q^{46} - 8 q^{52} - 16 q^{55} + 24 q^{58} - 96 q^{61} + 48 q^{67} - 24 q^{70} + 32 q^{73} + 16 q^{76} + 40 q^{82} - 88 q^{85} + 24 q^{88} - 64 q^{91} + 64 q^{97}+O(q^{100}) \) 16 * q + 4 * q^10 + 8 * q^13 - 16 * q^16 + 24 * q^22 - 16 * q^25 - 32 * q^31 + 40 * q^37 + 4 * q^40 + 24 * q^43 - 8 * q^46 - 8 * q^52 - 16 * q^55 + 24 * q^58 - 96 * q^61 + 48 * q^67 - 24 * q^70 + 32 * q^73 + 16 * q^76 + 40 * q^82 - 88 * q^85 + 24 * q^88 - 64 * q^91 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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