LMFDB - Embedded newform 450.2.p.a.293.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [450,2,Mod(257,450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(450, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 3]))

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

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

chi := DirichletCharacter("450.257");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 450 = 2 \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	450.p (of order $12$, degree $4$, 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:	$3.59326809096$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			293.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	450.293
Dual form			450.2.p.a.407.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-1.10721 + 1.33195i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(1.05902 + 0.283763i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.548188 - 2.94949i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.10721 + 1.33195i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(1.05902 + 0.283763i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.548188 - 2.94949i) q^{9} +(-5.44949 + 3.14626i) q^{11} +(1.62484 - 0.599900i) q^{12} +(-3.34607 + 0.896575i) q^{13} +(-0.548188 + 0.949490i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.14626 - 3.14626i) q^{17} +(2.99087 + 0.233875i) q^{18} -1.55051i q^{19} +(-1.55051 + 1.09638i) q^{21} +(-1.62863 - 6.07812i) q^{22} +(-0.258819 - 0.965926i) q^{23} +(0.158919 + 1.72474i) q^{24} -3.46410i q^{26} +(4.53553 + 2.53553i) q^{27} +(-0.775255 - 0.775255i) q^{28} +(-1.57313 - 2.72474i) q^{29} +(2.22474 - 3.85337i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.84304 - 10.7420i) q^{33} +(3.85337 - 2.22474i) q^{34} +(-1.00000 + 2.82843i) q^{36} +(3.00000 - 3.00000i) q^{37} +(1.49768 + 0.401302i) q^{38} +(2.51059 - 5.44949i) q^{39} +(-3.39898 - 1.96240i) q^{41} +(-0.657717 - 1.78144i) q^{42} +(-0.896575 + 3.34607i) q^{43} +6.29253 q^{44} +1.00000 q^{46} +(-2.32937 + 8.69333i) q^{47} +(-1.70711 - 0.292893i) q^{48} +(-5.02118 - 2.89898i) q^{49} +(7.67423 - 0.707107i) q^{51} +(3.34607 + 0.896575i) q^{52} +(-6.61037 + 6.61037i) q^{53} +(-3.62302 + 3.72474i) q^{54} +(0.949490 - 0.548188i) q^{56} +(2.06520 + 1.71673i) q^{57} +(3.03906 - 0.814313i) q^{58} +(-5.90326 + 10.2247i) q^{59} +(2.72474 + 4.71940i) q^{61} +(3.14626 + 3.14626i) q^{62} +(0.256415 - 3.27912i) q^{63} -1.00000i q^{64} +(9.89898 + 4.56048i) q^{66} +(-0.978838 - 3.65307i) q^{67} +(1.15161 + 4.29788i) q^{68} +(1.57313 + 0.724745i) q^{69} -0.635674i q^{71} +(-2.47323 - 1.69798i) q^{72} +(-2.89898 - 2.89898i) q^{73} +(2.12132 + 3.67423i) q^{74} +(-0.775255 + 1.34278i) q^{76} +(-6.66390 + 1.78559i) q^{77} +(4.61401 + 3.83548i) q^{78} +(2.12132 - 1.22474i) q^{79} +(-8.39898 + 3.23375i) q^{81} +(2.77526 - 2.77526i) q^{82} +(0.531752 + 0.142483i) q^{83} +(1.89097 - 0.174235i) q^{84} +(-3.00000 - 1.73205i) q^{86} +(5.37101 + 0.921519i) q^{87} +(-1.62863 + 6.07812i) q^{88} -2.36773 q^{89} -3.79796 q^{91} +(-0.258819 + 0.965926i) q^{92} +(2.66925 + 7.22973i) q^{93} +(-7.79423 - 4.50000i) q^{94} +(0.724745 - 1.57313i) q^{96} +(-10.7902 - 2.89123i) q^{97} +(4.09978 - 4.09978i) q^{98} +(12.2672 + 14.3485i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7}+O(q^{10}) $ 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7	$ 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7} - 24 q^{11} + 4 q^{12} + 4 q^{16} + 8 q^{18} - 32 q^{21} + 8 q^{22} + 8 q^{27} - 16 q^{28} + 8 q^{31} - 16 q^{33} - 8 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{41} - 20 q^{42} + 8 q^{46} - 8 q^{48} + 32 q^{51} - 12 q^{56} - 28 q^{57} + 4 q^{58} + 12 q^{61} + 32 q^{63} + 40 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{72} + 16 q^{73} - 16 q^{76} - 24 q^{77} + 24 q^{78} - 28 q^{81} + 32 q^{82} - 12 q^{83} - 24 q^{86} + 8 q^{87} + 8 q^{88} + 48 q^{91} + 20 q^{93} - 4 q^{96} - 12 q^{97}+O(q^{100}) $ 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7 - 24 * q^11 + 4 * q^12 + 4 * q^16 + 8 * q^18 - 32 * q^21 + 8 * q^22 + 8 * q^27 - 16 * q^28 + 8 * q^31 - 16 * q^33 - 8 * q^36 + 24 * q^37 - 12 * q^38 + 12 * q^41 - 20 * q^42 + 8 * q^46 - 8 * q^48 + 32 * q^51 - 12 * q^56 - 28 * q^57 + 4 * q^58 + 12 * q^61 + 32 * q^63 + 40 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^72 + 16 * q^73 - 16 * q^76 - 24 * q^77 + 24 * q^78 - 28 * q^81 + 32 * q^82 - 12 * q^83 - 24 * q^86 + 8 * q^87 + 8 * q^88 + 48 * q^91 + 20 * q^93 - 4 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/450\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	−1.10721	+	1.33195i	−0.639246	+	0.769002i
$3$	−1.10721	+	1.33195i	−0.639246	+	0.769002i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.00000	−	1.41421i	−0.408248	−	0.577350i
$7$	1.05902	+	0.283763i	0.400271	+	0.107252i	0.453338	−	0.891339i	$-0.350233\pi$
$7$	1.05902	+	0.283763i	0.400271	+	0.107252i	−0.0530669	+	0.998591i	$0.516900\pi$
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−0.548188	−	2.94949i	−0.182729	−	0.983163i
$10$		0			0
$11$	−5.44949	+	3.14626i	−1.64308	+	0.948634i	−0.663354	+	0.748305i	$0.730868\pi$
$11$	−5.44949	+	3.14626i	−1.64308	+	0.948634i	−0.979729	+	0.200329i	$0.935799\pi$
$12$	1.62484	−	0.599900i	0.469052	−	0.173176i
$13$	−3.34607	+	0.896575i	−0.928032	+	0.248665i	−0.691015	−	0.722840i	$-0.742836\pi$
$13$	−3.34607	+	0.896575i	−0.928032	+	0.248665i	−0.237016	+	0.971506i	$0.576170\pi$
$14$	−0.548188	+	0.949490i	−0.146509	+	0.253762i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−3.14626	−	3.14626i	−0.763081	−	0.763081i	0.213797	−	0.976878i	$-0.431417\pi$
$17$	−3.14626	−	3.14626i	−0.763081	−	0.763081i	−0.976878	+	0.213797i	$0.931417\pi$
$18$	2.99087	+	0.233875i	0.704955	+	0.0551249i
$19$		−	1.55051i		−	0.355711i	−0.984057	−	0.177856i	$-0.943084\pi$
$19$		−	1.55051i		−	0.355711i	0.984057	−	0.177856i	$-0.0569160\pi$
$20$		0			0
$21$	−1.55051	+	1.09638i	−0.338349	+	0.239249i
$22$	−1.62863	−	6.07812i	−0.347224	−	1.29586i
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	0.933678	−	0.358113i	$-0.116580\pi$
$23$	−0.258819	−	0.965926i	−0.0539675	−	0.201409i	−0.987646	+	0.156704i	$0.949913\pi$
$24$	0.158919	+	1.72474i	0.0324391	+	0.352062i
$25$		0			0
$26$		−	3.46410i		−	0.679366i
$27$	4.53553	+	2.53553i	0.872864	+	0.487964i
$28$	−0.775255	−	0.775255i	−0.146509	−	0.146509i
$29$	−1.57313	−	2.72474i	−0.292123	−	0.505972i	0.682188	−	0.731177i	$-0.261028\pi$
$29$	−1.57313	−	2.72474i	−0.292123	−	0.505972i	−0.974312	+	0.225204i	$0.927695\pi$
$30$		0			0
$31$	2.22474	−	3.85337i	0.399576	−	0.692086i	−0.594098	−	0.804393i	$-0.702491\pi$
$31$	2.22474	−	3.85337i	0.399576	−	0.692086i	0.993674	+	0.112307i	$0.0358240\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	1.84304	−	10.7420i	0.320832	−	1.86995i
$34$	3.85337	−	2.22474i	0.660848	−	0.381541i
$35$		0			0
$36$	−1.00000	+	2.82843i	−0.166667	+	0.471405i
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	−0.416115	−	0.909312i	$-0.636609\pi$
$37$	3.00000	−	3.00000i	0.493197	−	0.493197i	0.909312	+	0.416115i	$0.136609\pi$
$38$	1.49768	+	0.401302i	0.242955	+	0.0650997i
$39$	2.51059	−	5.44949i	0.402016	−	0.872617i
$40$		0			0
$41$	−3.39898	−	1.96240i	−0.530831	−	0.306476i	0.210524	−	0.977589i	$-0.432483\pi$
$41$	−3.39898	−	1.96240i	−0.530831	−	0.306476i	−0.741355	+	0.671113i	$0.765816\pi$
$42$	−0.657717	−	1.78144i	−0.101488	−	0.274882i
$43$	−0.896575	+	3.34607i	−0.136726	+	0.510270i	0.863258	+	0.504762i	$0.168420\pi$
$43$	−0.896575	+	3.34607i	−0.136726	+	0.510270i	−0.999985	+	0.00550783i	$0.998247\pi$
$44$	6.29253			0.948634
$45$		0			0
$46$	1.00000			0.147442
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	0.558827	+	0.829285i	$0.311252\pi$
$47$	−2.32937	+	8.69333i	−0.339774	+	1.26805i	−0.898600	+	0.438768i	$0.855415\pi$
$48$	−1.70711	−	0.292893i	−0.246400	−	0.0422755i
$49$	−5.02118	−	2.89898i	−0.717311	−	0.414140i
$50$		0			0
$51$	7.67423	−	0.707107i	1.07461	−	0.0990148i
$52$	3.34607	+	0.896575i	0.464016	+	0.124333i
$53$	−6.61037	+	6.61037i	−0.908004	+	0.908004i	−0.996111	−	0.0881074i	$-0.971918\pi$
$53$	−6.61037	+	6.61037i	−0.908004	+	0.908004i	0.0881074	+	0.996111i	$0.471918\pi$
$54$	−3.62302	+	3.72474i	−0.493031	+	0.506874i
$55$		0			0
$56$	0.949490	−	0.548188i	0.126881	−	0.0732547i
$57$	2.06520	+	1.71673i	0.273543	+	0.227387i
$58$	3.03906	−	0.814313i	0.399048	−	0.106925i
$59$	−5.90326	+	10.2247i	−0.768539	+	1.33115i	0.169816	+	0.985476i	$0.445683\pi$
$59$	−5.90326	+	10.2247i	−0.768539	+	1.33115i	−0.938355	+	0.345673i	$0.887651\pi$
$60$		0			0
$61$	2.72474	+	4.71940i	0.348868	+	0.604257i	0.986049	−	0.166458i	$-0.0532329\pi$
$61$	2.72474	+	4.71940i	0.348868	+	0.604257i	−0.637181	+	0.770714i	$0.719900\pi$
$62$	3.14626	+	3.14626i	0.399576	+	0.399576i
$63$	0.256415	−	3.27912i	0.0323053	−	0.413130i
$64$		−	1.00000i		−	0.125000i
$65$		0			0
$66$	9.89898	+	4.56048i	1.21848	+	0.561356i
$67$	−0.978838	−	3.65307i	−0.119584	−	0.446294i	0.880005	−	0.474965i	$-0.157539\pi$
$67$	−0.978838	−	3.65307i	−0.119584	−	0.446294i	−0.999589	+	0.0286709i	$0.990873\pi$
$68$	1.15161	+	4.29788i	0.139654	+	0.521194i
$69$	1.57313	+	0.724745i	0.189383	+	0.0872490i
$70$		0			0
$71$		−	0.635674i		−	0.0754407i	−0.999288	−	0.0377203i	$-0.987990\pi$
$71$		−	0.635674i		−	0.0754407i	0.999288	−	0.0377203i	$-0.0120096\pi$
$72$	−2.47323	−	1.69798i	−0.291473	−	0.200108i
$73$	−2.89898	−	2.89898i	−0.339300	−	0.339300i	0.516804	−	0.856104i	$-0.327122\pi$
$73$	−2.89898	−	2.89898i	−0.339300	−	0.339300i	−0.856104	+	0.516804i	$0.827122\pi$
$74$	2.12132	+	3.67423i	0.246598	+	0.427121i
$75$		0			0
$76$	−0.775255	+	1.34278i	−0.0889279	+	0.154028i
$77$	−6.66390	+	1.78559i	−0.759422	+	0.203487i
$78$	4.61401	+	3.83548i	0.522434	+	0.434282i
$79$	2.12132	−	1.22474i	0.238667	−	0.137795i	−0.375897	−	0.926662i	$-0.622665\pi$
$79$	2.12132	−	1.22474i	0.238667	−	0.137795i	0.614564	+	0.788867i	$0.289332\pi$
$80$		0			0
$81$	−8.39898	+	3.23375i	−0.933220	+	0.359306i
$82$	2.77526	−	2.77526i	0.306476	−	0.306476i
$83$	0.531752	+	0.142483i	0.0583674	+	0.0156395i	0.287885	−	0.957665i	$-0.407048\pi$
$83$	0.531752	+	0.142483i	0.0583674	+	0.0156395i	−0.229517	+	0.973305i	$0.573715\pi$
$84$	1.89097	−	0.174235i	0.206322	−	0.0190106i
$85$		0			0
$86$	−3.00000	−	1.73205i	−0.323498	−	0.186772i
$87$	5.37101	+	0.921519i	0.575833	+	0.0987973i
$88$	−1.62863	+	6.07812i	−0.173612	+	0.647929i
$89$	−2.36773			−0.250978			−0.125489	−	0.992095i	$-0.540050\pi$
$89$	−2.36773			−0.250978			−0.125489	+	0.992095i	$0.540050\pi$
$90$		0			0
$91$	−3.79796			−0.398134
$92$	−0.258819	+	0.965926i	−0.0269838	+	0.100705i
$93$	2.66925	+	7.22973i	0.276788	+	0.749688i
$94$	−7.79423	−	4.50000i	−0.803913	−	0.464140i
$95$		0			0
$96$	0.724745	−	1.57313i	0.0739690	−	0.160557i
$97$	−10.7902	−	2.89123i	−1.09558	−	0.293560i	−0.334616	−	0.942355i	$-0.608607\pi$
$97$	−10.7902	−	2.89123i	−1.09558	−	0.293560i	−0.760963	+	0.648795i	$0.775273\pi$
$98$	4.09978	−	4.09978i	0.414140	−	0.414140i
$99$	12.2672	+	14.3485i	1.23290	+	1.44208i
$100$		0			0
$101$	1.10102	−	0.635674i	0.109556	−	0.0632520i	−0.444221	−	0.895917i	$-0.646519\pi$
$101$	1.10102	−	0.635674i	0.109556	−	0.0632520i	0.553777	+	0.832665i	$0.313186\pi$
$102$	−1.30323	+	7.59575i	−0.129039	+	0.752092i
$103$	3.96008	−	1.06110i	0.390198	−	0.104553i	−0.0583855	−	0.998294i	$-0.518595\pi$
$103$	3.96008	−	1.06110i	0.390198	−	0.104553i	0.448584	+	0.893741i	$0.351929\pi$
$104$	−1.73205	+	3.00000i	−0.169842	+	0.294174i
$105$		0			0
$106$	−4.67423	−	8.09601i	−0.454002	−	0.786354i
$107$	−3.71051	−	3.71051i	−0.358708	−	0.358708i	0.504628	−	0.863337i	$-0.331630\pi$
$107$	−3.71051	−	3.71051i	−0.358708	−	0.358708i	−0.863337	+	0.504628i	$0.831630\pi$
$108$	−2.66012	−	4.46360i	−0.255970	−	0.429510i
$109$			20.3485i			1.94903i	0.224323	+	0.974515i	$0.427983\pi$
$109$			20.3485i			1.94903i	−0.224323	+	0.974515i	$0.572017\pi$
$110$		0			0
$111$	0.674235	+	7.31747i	0.0639955	+	0.694544i
$112$	0.283763	+	1.05902i	0.0268131	+	0.100068i
$113$	3.57117	+	13.3278i	0.335948	+	1.25377i	0.902838	+	0.429981i	$0.141480\pi$
$113$	3.57117	+	13.3278i	0.335948	+	1.25377i	−0.566890	+	0.823793i	$0.691854\pi$
$114$	−2.19275	+	1.55051i	−0.205370	+	0.145219i
$115$		0			0
$116$			3.14626i			0.292123i
$117$	4.47871	+	9.37769i	0.414057	+	0.866968i
$118$	−8.34847	−	8.34847i	−0.768539	−	0.768539i
$119$	−2.43916	−	4.22474i	−0.223597	−	0.387282i
$120$		0			0
$121$	14.2980	−	24.7648i	1.29981	−	2.25134i
$122$	−5.26380	+	1.41043i	−0.476562	+	0.127694i
$123$	6.37720	−	2.35449i	0.575012	−	0.212297i
$124$	−3.85337	+	2.22474i	−0.346043	+	0.199788i
$125$		0			0
$126$	3.10102	+	1.09638i	0.276261	+	0.0976730i
$127$	−14.1237	+	14.1237i	−1.25328	+	1.25328i	−0.299036	+	0.954242i	$0.596665\pi$
$127$	−14.1237	+	14.1237i	−1.25328	+	1.25328i	−0.954242	+	0.299036i	$0.903335\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	−3.46410	−	4.89898i	−0.304997	−	0.431331i
$130$		0			0
$131$	9.12372	+	5.26758i	0.797143	+	0.460231i	0.842471	−	0.538741i	$-0.181100\pi$
$131$	9.12372	+	5.26758i	0.797143	+	0.460231i	−0.0453278	+	0.998972i	$0.514433\pi$
$132$	−6.96713	+	8.38134i	−0.606411	+	0.729502i
$133$	0.439978	−	1.64202i	0.0381509	−	0.142381i
$134$	3.78194			0.326710
$135$		0			0
$136$	−4.44949			−0.381541
$137$	0.569930	−	2.12701i	0.0486924	−	0.181723i	−0.937297	−	0.348533i	$-0.886680\pi$
$137$	0.569930	−	2.12701i	0.0486924	−	0.181723i	0.985989	+	0.166810i	$0.0533467\pi$
$138$	−1.10721	+	1.33195i	−0.0942517	+	0.113383i
$139$	11.1708	+	6.44949i	0.947499	+	0.547039i	0.892303	−	0.451437i	$-0.149088\pi$
$139$	11.1708	+	6.44949i	0.947499	+	0.547039i	0.0551956	+	0.998476i	$0.482422\pi$
$140$		0			0
$141$	−9.00000	−	12.7279i	−0.757937	−	1.07188i
$142$	0.614014	+	0.164525i	0.0515269	+	0.0138066i
$143$	15.4135	−	15.4135i	1.28894	−	1.28894i
$144$	2.28024	−	1.94949i	0.190020	−	0.162457i
$145$		0			0
$146$	3.55051	−	2.04989i	0.293842	−	0.169650i
$147$	9.42078	−	3.47820i	0.777013	−	0.286877i
$148$	−4.09808	+	1.09808i	−0.336860	+	0.0902613i
$149$	6.45145	−	11.1742i	0.528523	−	0.915429i	−0.470924	−	0.882174i	$-0.656079\pi$
$149$	6.45145	−	11.1742i	0.528523	−	0.915429i	0.999447	−	0.0332550i	$-0.0105874\pi$
$150$		0			0
$151$	10.7980	+	18.7026i	0.878725	+	1.52200i	0.852741	+	0.522335i	$0.174939\pi$
$151$	10.7980	+	18.7026i	0.878725	+	1.52200i	0.0259849	+	0.999662i	$0.491728\pi$
$152$	−1.09638	−	1.09638i	−0.0889279	−	0.0889279i
$153$	−7.55513	+	11.0046i	−0.610796	+	0.889671i
$154$		−	6.89898i		−	0.555936i
$155$		0			0
$156$	−4.89898	+	3.46410i	−0.392232	+	0.277350i
$157$	−1.59165	−	5.94012i	−0.127028	−	0.474073i	0.872876	−	0.487942i	$-0.162252\pi$
$157$	−1.59165	−	5.94012i	−0.127028	−	0.474073i	−0.999904	+	0.0138684i	$0.995585\pi$
$158$	0.633975	+	2.36603i	0.0504363	+	0.188231i
$159$	−1.48565	−	16.1237i	−0.117819	−	1.27869i
$160$		0			0
$161$		−	1.09638i		−	0.0864066i
$162$	−0.949747	−	8.94975i	−0.0746192	−	0.703159i
$163$	0.449490	+	0.449490i	0.0352068	+	0.0352068i	0.724491	−	0.689284i	$-0.242075\pi$
$163$	0.449490	+	0.449490i	0.0352068	+	0.0352068i	−0.689284	+	0.724491i	$0.742075\pi$
$164$	1.96240	+	3.39898i	0.153238	+	0.265416i
$165$		0			0
$166$	−0.275255	+	0.476756i	−0.0213639	+	0.0370034i
$167$	10.4300	−	2.79472i	0.807100	−	0.216262i	0.168401	−	0.985719i	$-0.446140\pi$
$167$	10.4300	−	2.79472i	0.807100	−	0.216262i	0.638699	+	0.769457i	$0.279473\pi$
$168$	−0.321121	+	1.87163i	−0.0247750	+	0.144400i
$169$	−0.866025	+	0.500000i	−0.0666173	+	0.0384615i
$170$		0			0
$171$	−4.57321	+	0.849971i	−0.349722	+	0.0649989i
$172$	2.44949	−	2.44949i	0.186772	−	0.186772i
$173$	−2.99536	−	0.802603i	−0.227733	−	0.0610208i	0.143148	−	0.989701i	$-0.454277\pi$
$173$	−2.99536	−	0.802603i	−0.227733	−	0.0610208i	−0.370881	+	0.928680i	$0.620944\pi$
$174$	−2.28024	+	4.94949i	−0.172864	+	0.375220i
$175$		0			0
$176$	−5.44949	−	3.14626i	−0.410771	−	0.237159i
$177$	−7.08274	−	19.1838i	−0.532371	−	1.44194i
$178$	0.612812	−	2.28705i	0.0459322	−	0.171421i
$179$	−17.6062			−1.31595			−0.657976	−	0.753039i	$-0.728587\pi$
$179$	−17.6062			−1.31595			−0.657976	+	0.753039i	$0.728587\pi$
$180$		0			0
$181$	−10.5505			−0.784213			−0.392107	−	0.919920i	$-0.628254\pi$
$181$	−10.5505			−0.784213			−0.392107	+	0.919920i	$0.628254\pi$
$182$	0.982984	−	3.66855i	0.0728636	−	0.271931i
$183$	−9.30286	−	1.59612i	−0.687687	−	0.117988i
$184$	−0.866025	−	0.500000i	−0.0638442	−	0.0368605i
$185$		0			0
$186$	−7.67423	+	0.707107i	−0.562702	+	0.0518476i
$187$	27.0445	+	7.24656i	1.97769	+	0.529921i
$188$	6.36396	−	6.36396i	0.464140	−	0.464140i
$189$	4.08372	+	3.97219i	0.297047	+	0.288935i
$190$		0			0
$191$	−2.87628	+	1.66062i	−0.208120	+	0.120158i	−0.600437	−	0.799672i	$-0.705007\pi$
$191$	−2.87628	+	1.66062i	−0.208120	+	0.120158i	0.392317	+	0.919830i	$0.371673\pi$
$192$	1.33195	+	1.10721i	0.0961253	+	0.0799057i
$193$	16.7303	−	4.48288i	1.20428	−	0.322685i	0.399762	−	0.916619i	$-0.369093\pi$
$193$	16.7303	−	4.48288i	1.20428	−	0.322685i	0.804513	+	0.593934i	$0.202426\pi$
$194$	5.58542	−	9.67423i	0.401010	−	0.694570i
$195$		0			0
$196$	2.89898	+	5.02118i	0.207070	+	0.358656i
$197$	−6.92820	−	6.92820i	−0.493614	−	0.493614i	0.415829	−	0.909443i	$-0.363492\pi$
$197$	−6.92820	−	6.92820i	−0.493614	−	0.493614i	−0.909443	+	0.415829i	$0.863492\pi$
$198$	−17.0345	+	8.13557i	−1.21059	+	0.578170i
$199$		−	3.55051i		−	0.251689i	−0.992050	−	0.125844i	$-0.959836\pi$
$199$		−	3.55051i		−	0.251689i	0.992050	−	0.125844i	$-0.0401640\pi$
$200$		0			0
$201$	5.94949	+	2.74094i	0.419645	+	0.193331i
$202$	0.329049	+	1.22803i	0.0231518	+	0.0864038i
$203$	−0.892794	−	3.33195i	−0.0626618	−	0.233857i
$204$	−6.99964	−	3.22474i	−0.490073	−	0.225777i
$205$		0			0
$206$			4.09978i			0.285645i
$207$	−2.70711	+	1.29289i	−0.188157	+	0.0898623i
$208$	−2.44949	−	2.44949i	−0.169842	−	0.169842i
$209$	4.87832	+	8.44949i	0.337440	+	0.584463i
$210$		0			0
$211$	−9.44949	+	16.3670i	−0.650530	+	1.12675i	0.332465	+	0.943116i	$0.392120\pi$
$211$	−9.44949	+	16.3670i	−0.650530	+	1.12675i	−0.982995	+	0.183635i	$0.941214\pi$
$212$	9.02993	−	2.41956i	0.620178	−	0.166176i
$213$	0.846687	+	0.703823i	0.0580141	+	0.0482251i
$214$	4.54442	−	2.62372i	0.310650	−	0.179354i
$215$		0			0
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	3.44949	−	3.44949i	0.234167	−	0.234167i
$218$	−19.6551	−	5.26657i	−1.33121	−	0.356697i
$219$	7.07107	−	0.651531i	0.477818	−	0.0440264i
$220$		0			0
$221$	13.3485	+	7.70674i	0.897915	+	0.518412i
$222$	−7.24264	−	1.24264i	−0.486094	−	0.0834006i
$223$	−2.15087	+	8.02714i	−0.144033	+	0.537537i	0.855764	+	0.517367i	$0.173088\pi$
$223$	−2.15087	+	8.02714i	−0.144033	+	0.537537i	−0.999797	+	0.0201706i	$0.993579\pi$
$224$	−1.09638			−0.0732547
$225$		0			0
$226$	−13.7980			−0.917827
$227$	3.90843	−	14.5865i	0.259412	−	0.968138i	−0.706171	−	0.708041i	$-0.749579\pi$
$227$	3.90843	−	14.5865i	0.259412	−	0.968138i	0.965583	−	0.260096i	$-0.0837543\pi$
$228$	−0.930152	−	2.51934i	−0.0616008	−	0.166847i
$229$	−14.1582	−	8.17423i	−0.935600	−	0.540169i	−0.0470214	−	0.998894i	$-0.514973\pi$
$229$	−14.1582	−	8.17423i	−0.935600	−	0.540169i	−0.888578	+	0.458725i	$0.848306\pi$
$230$		0			0
$231$	5.00000	−	10.8530i	0.328976	−	0.714075i
$232$	−3.03906	−	0.814313i	−0.199524	−	0.0534623i
$233$	−10.9959	+	10.9959i	−0.720363	+	0.720363i	−0.968679	−	0.248316i	$-0.920123\pi$
$233$	−10.9959	+	10.9959i	−0.720363	+	0.720363i	0.248316	+	0.968679i	$0.420123\pi$
$234$	−10.2173	+	1.89898i	−0.667928	+	0.124140i
$235$		0			0
$236$	10.2247	−	5.90326i	0.665574	−	0.384269i
$237$	−0.717439	+	4.18154i	−0.0466027	+	0.271620i
$238$	4.71209	−	1.26260i	0.305439	−	0.0818423i
$239$	8.48528	−	14.6969i	0.548867	−	0.950666i	−0.449485	−	0.893288i	$-0.648393\pi$
$239$	8.48528	−	14.6969i	0.548867	−	0.950666i	0.998353	−	0.0573782i	$-0.0182741\pi$
$240$		0			0
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	−0.990912	−	0.134515i	$-0.957053\pi$
$241$	−9.50000	−	16.4545i	−0.611949	−	1.05993i	0.378963	−	0.925412i	$-0.376281\pi$
$242$	20.2204	+	20.2204i	1.29981	+	1.29981i
$243$	4.99221	−	14.7675i	0.320250	−	0.947333i
$244$		−	5.44949i		−	0.348868i
$245$		0			0
$246$	0.623724	+	6.76928i	0.0397672	+	0.431594i
$247$	1.39015	+	5.18811i	0.0884531	+	0.330111i
$248$	−1.15161	−	4.29788i	−0.0731275	−	0.272915i
$249$	−0.778539	+	0.550510i	−0.0493379	+	0.0348872i
$250$		0			0
$251$		−	11.1708i		−	0.705097i	−0.935793	−	0.352549i	$-0.885315\pi$
$251$		−	11.1708i		−	0.705097i	0.935793	−	0.352549i	$-0.114685\pi$
$252$	−1.86162	+	2.71159i	−0.117271	+	0.170814i
$253$	4.44949	+	4.44949i	0.279737	+	0.279737i
$254$	−9.98698	−	17.2980i	−0.626639	−	1.08537i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	25.1579	−	6.74105i	1.56931	−	0.420495i	0.633713	−	0.773568i	$-0.281530\pi$
$257$	25.1579	−	6.74105i	1.56931	−	0.420495i	0.935596	+	0.353073i	$0.114863\pi$
$258$	5.62863	−	2.07812i	0.350423	−	0.129378i
$259$	4.02834	−	2.32577i	0.250309	−	0.144516i
$260$		0			0
$261$	−7.17423	+	6.13361i	−0.444074	+	0.379661i
$262$	−7.44949	+	7.44949i	−0.460231	+	0.460231i
$263$	−12.2643	−	3.28621i	−0.756249	−	0.202636i	−0.139961	−	0.990157i	$-0.544698\pi$
$263$	−12.2643	−	3.28621i	−0.756249	−	0.202636i	−0.616288	+	0.787521i	$0.711364\pi$
$264$	−6.29253	−	8.89898i	−0.387278	−	0.547694i
$265$		0			0
$266$	1.47219	+	0.849971i	0.0902660	+	0.0521151i
$267$	2.62156	−	3.15369i	0.160437	−	0.193003i
$268$	−0.978838	+	3.65307i	−0.0597920	+	0.223147i
$269$	4.70334			0.286768			0.143384	−	0.989667i	$-0.454202\pi$
$269$	4.70334			0.286768			0.143384	+	0.989667i	$0.454202\pi$
$270$		0			0
$271$	−16.0454			−0.974689			−0.487345	−	0.873210i	$-0.662034\pi$
$271$	−16.0454			−0.974689			−0.487345	+	0.873210i	$0.662034\pi$
$272$	1.15161	−	4.29788i	0.0698268	−	0.260597i
$273$	4.20512	−	5.05870i	0.254506	−	0.306166i
$274$	1.90702	+	1.10102i	0.115208	+	0.0665151i
$275$		0			0
$276$	−1.00000	−	1.41421i	−0.0601929	−	0.0851257i
$277$	−13.7983	−	3.69723i	−0.829057	−	0.222145i	−0.180754	−	0.983528i	$-0.557854\pi$
$277$	−13.7983	−	3.69723i	−0.829057	−	0.222145i	−0.648302	+	0.761383i	$0.724521\pi$
$278$	−9.12096	+	9.12096i	−0.547039	+	0.547039i
$279$	−12.5851	−	4.44949i	−0.753448	−	0.266384i
$280$		0			0
$281$	−0.151531	+	0.0874863i	−0.00903957	+	0.00521900i	−0.504513	−	0.863404i	$-0.668328\pi$
$281$	−0.151531	+	0.0874863i	−0.00903957	+	0.00521900i	0.495473	+	0.868623i	$0.334995\pi$
$282$	14.6236	−	5.39910i	0.870823	−	0.321512i
$283$	6.66112	−	1.78484i	0.395962	−	0.106098i	−0.0553430	−	0.998467i	$-0.517625\pi$
$283$	6.66112	−	1.78484i	0.395962	−	0.106098i	0.451305	+	0.892370i	$0.350959\pi$
$284$	−0.317837	+	0.550510i	−0.0188602	+	0.0326668i
$285$		0			0
$286$	10.8990	+	18.8776i	0.644470	+	1.11626i
$287$	−3.04272	−	3.04272i	−0.179606	−	0.179606i
$288$	1.29289	+	2.70711i	0.0761845	+	0.159518i
$289$			2.79796i			0.164586i
$290$		0			0
$291$	15.7980	−	11.1708i	0.926093	−	0.654846i
$292$	1.06110	+	3.96008i	0.0620962	+	0.231746i
$293$	−5.70577	−	21.2942i	−0.333335	−	1.24402i	−0.905663	−	0.423998i	$-0.860626\pi$
$293$	−5.70577	−	21.2942i	−0.333335	−	1.24402i	0.572329	−	0.820024i	$-0.306040\pi$
$294$	0.921404	+	10.0000i	0.0537374	+	0.583212i
$295$		0			0
$296$		−	4.24264i		−	0.246598i
$297$	−32.6938	+	0.452623i	−1.89709	+	0.0262638i
$298$	9.12372	+	9.12372i	0.528523	+	0.528523i
$299$	1.73205	+	3.00000i	0.100167	+	0.173494i
$300$		0			0
$301$	−1.89898	+	3.28913i	−0.109455	+	0.189582i
$302$	−20.8601	+	5.58943i	−1.20036	+	0.321636i
$303$	−0.372369	+	2.17033i	−0.0213921	+	0.124682i
$304$	1.34278	−	0.775255i	0.0770138	−	0.0444639i
$305$		0			0
$306$	−8.67423	−	10.1459i	−0.495873	−	0.580002i
$307$	−0.674235	+	0.674235i	−0.0384806	+	0.0384806i	−0.726085	−	0.687605i	$-0.758662\pi$
$307$	−0.674235	+	0.674235i	−0.0384806	+	0.0384806i	0.687605	+	0.726085i	$0.258662\pi$
$308$	6.66390	+	1.78559i	0.379711	+	0.101743i
$309$	−2.97129	+	6.44949i	−0.169031	+	0.366899i
$310$		0			0
$311$	−17.8207	−	10.2888i	−1.01052	−	0.583422i	−0.0991741	−	0.995070i	$-0.531620\pi$
$311$	−17.8207	−	10.2888i	−1.01052	−	0.583422i	−0.911343	+	0.411648i	$0.864953\pi$
$312$	−2.07812	−	5.62863i	−0.117650	−	0.318658i
$313$	−1.29958	+	4.85009i	−0.0734564	+	0.274143i	−0.992879	−	0.119128i	$-0.961990\pi$
$313$	−1.29958	+	4.85009i	−0.0734564	+	0.274143i	0.919422	+	0.393271i	$0.128657\pi$
$314$	6.14966			0.347046
$315$		0			0
$316$	−2.44949			−0.137795
$317$	−0.284965	+	1.06350i	−0.0160052	+	0.0597323i	−0.973467	−	0.228829i	$-0.926510\pi$
$317$	−0.284965	+	1.06350i	−0.0160052	+	0.0597323i	0.957461	+	0.288561i	$0.0931770\pi$
$318$	15.9588	+	2.73810i	0.894927	+	0.153545i
$319$	17.1455	+	9.89898i	0.959966	+	0.554236i
$320$		0			0
$321$	9.05051	−	0.833917i	0.505150	−	0.0465447i
$322$	1.05902	+	0.283763i	0.0590168	+	0.0158135i
$323$	−4.87832	+	4.87832i	−0.271437	+	0.271437i
$324$	8.89060	+	1.39898i	0.493922	+	0.0777211i
$325$		0			0
$326$	−0.550510	+	0.317837i	−0.0304899	+	0.0176034i
$327$	−27.1032	−	22.5300i	−1.49881	−	1.24591i
$328$	−3.79107	+	1.01581i	−0.209327	+	0.0560889i
$329$	−4.93369	+	8.54541i	−0.272003	+	0.471124i
$330$		0			0
$331$	2.22474	+	3.85337i	0.122283	+	0.211800i	0.920668	−	0.390347i	$-0.127645\pi$
$331$	2.22474	+	3.85337i	0.122283	+	0.211800i	−0.798385	+	0.602148i	$0.794312\pi$
$332$	−0.389270	−	0.389270i	−0.0213639	−	0.0213639i
$333$	−10.4930	−	7.20390i	−0.575015	−	0.394772i
$334$			10.7980i			0.590838i
$335$		0			0
$336$	−1.72474	−	0.794593i	−0.0940925	−	0.0433486i
$337$	7.97861	+	29.7766i	0.434622	+	1.62203i	0.741968	+	0.670435i	$0.233892\pi$
$337$	7.97861	+	29.7766i	0.434622	+	1.62203i	−0.307346	+	0.951598i	$0.599441\pi$
$338$	−0.258819	−	0.965926i	−0.0140779	−	0.0525394i
$339$	−21.7060	−	10.0000i	−1.17891	−	0.543125i
$340$		0			0
$341$			27.9985i			1.51621i
$342$	0.362626	−	4.63737i	0.0196085	−	0.250760i
$343$	−9.92168	−	9.92168i	−0.535721	−	0.535721i
$344$	1.73205	+	3.00000i	0.0933859	+	0.161749i
$345$		0			0
$346$	1.55051	−	2.68556i	0.0833559	−	0.144377i
$347$	4.05886	−	1.08757i	0.217891	−	0.0583837i	−0.148222	−	0.988954i	$-0.547355\pi$
$347$	4.05886	−	1.08757i	0.217891	−	0.0583837i	0.366113	+	0.930570i	$0.380688\pi$
$348$	−4.19067	−	3.48356i	−0.224644	−	0.186739i
$349$	13.0297	−	7.52270i	0.697464	−	0.402681i	−0.108938	−	0.994049i	$-0.534745\pi$
$349$	13.0297	−	7.52270i	0.697464	−	0.402681i	0.806402	+	0.591367i	$0.201412\pi$
$350$		0			0
$351$	−17.4495	−	4.41761i	−0.931385	−	0.235795i
$352$	4.44949	−	4.44949i	0.237159	−	0.237159i
$353$	33.1244	+	8.87564i	1.76303	+	0.472403i	0.987328	−	0.158694i	$-0.0507284\pi$
$353$	33.1244	+	8.87564i	1.76303	+	0.472403i	0.775704	+	0.631097i	$0.217395\pi$
$354$	20.3632	−	1.87628i	1.08229	−	0.0997229i
$355$		0			0
$356$	2.05051	+	1.18386i	0.108677	+	0.0627446i
$357$	8.32780	+	1.42883i	0.440754	+	0.0756215i
$358$	4.55683	−	17.0063i	0.240836	−	0.898812i
$359$	17.4634			0.921682			0.460841	−	0.887483i	$-0.347548\pi$
$359$	17.4634			0.921682			0.460841	+	0.887483i	$0.347548\pi$
$360$		0			0
$361$	16.5959			0.873469
$362$	2.73067	−	10.1910i	0.143521	−	0.535628i
$363$	17.1547	+	46.4639i	0.900388	+	2.43872i
$364$	3.28913	+	1.89898i	0.172397	+	0.0995336i
$365$		0			0
$366$	3.94949	−	8.57277i	0.206443	−	0.448106i
$367$	9.42418	+	2.52520i	0.491938	+	0.131814i	0.496256	−	0.868176i	$-0.334708\pi$
$367$	9.42418	+	2.52520i	0.491938	+	0.131814i	−0.00431778	+	0.999991i	$0.501374\pi$
$368$	0.707107	−	0.707107i	0.0368605	−	0.0368605i
$369$	−3.92480	+	11.1010i	−0.204317	+	0.577896i
$370$		0			0
$371$	−8.87628	+	5.12472i	−0.460833	+	0.266062i
$372$	1.30323	−	7.59575i	0.0675691	−	0.393822i
$373$	19.6004	−	5.25190i	1.01487	−	0.271933i	0.287206	−	0.957869i	$-0.407273\pi$
$373$	19.6004	−	5.25190i	1.01487	−	0.271933i	0.727662	+	0.685935i	$0.240607\pi$
$374$	−13.9993	+	24.2474i	−0.723885	+	1.25381i
$375$		0			0
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	7.70674	+	7.70674i	0.396917	+	0.396917i
$378$	−4.89379	+	2.91649i	−0.251709	+	0.150008i
$379$			6.65153i			0.341666i	0.985300	+	0.170833i	$0.0546459\pi$
$379$			6.65153i			0.341666i	−0.985300	+	0.170833i	$0.945354\pi$
$380$		0			0
$381$	−3.17423	−	34.4500i	−0.162621	−	1.76493i
$382$	−0.859599	−	3.20807i	−0.0439809	−	0.164139i
$383$	−7.19464	−	26.8508i	−0.367629	−	1.37201i	−0.863822	−	0.503798i	$-0.831936\pi$
$383$	−7.19464	−	26.8508i	−0.367629	−	1.37201i	0.496193	−	0.868212i	$-0.334731\pi$
$384$	−1.41421	+	1.00000i	−0.0721688	+	0.0510310i
$385$		0			0
$386$			17.3205i			0.881591i
$387$	10.3607	+	0.810167i	0.526663	+	0.0411831i
$388$	7.89898	+	7.89898i	0.401010	+	0.401010i
$389$	−2.81237	−	4.87117i	−0.142593	−	0.246978i	0.785879	−	0.618380i	$-0.212211\pi$
$389$	−2.81237	−	4.87117i	−0.142593	−	0.246978i	−0.928472	+	0.371402i	$0.878877\pi$
$390$		0			0
$391$	−2.22474	+	3.85337i	−0.112510	+	0.194873i
$392$	−5.60040	+	1.50062i	−0.282863	+	0.0757929i
$393$	−17.1180	+	6.32005i	−0.863489	+	0.318804i
$394$	8.48528	−	4.89898i	0.427482	−	0.246807i
$395$		0			0
$396$	−3.44949	−	18.5597i	−0.173343	−	0.932662i
$397$	−15.4495	+	15.4495i	−0.775388	+	0.775388i	−0.979043	−	0.203655i	$-0.934718\pi$
$397$	−15.4495	+	15.4495i	−0.775388	+	0.775388i	0.203655	+	0.979043i	$0.434718\pi$
$398$	3.42953	+	0.918940i	0.171907	+	0.0460623i
$399$	1.69994	+	2.40408i	0.0851036	+	0.120355i
$400$		0			0
$401$	22.3485	+	12.9029i	1.11603	+	0.644340i	0.940384	−	0.340114i	$-0.110466\pi$
$401$	22.3485	+	12.9029i	1.11603	+	0.644340i	0.175645	+	0.984454i	$0.443799\pi$
$402$	−4.18739	+	5.03736i	−0.208848	+	0.251241i
$403$	−3.98930	+	14.8883i	−0.198721	+	0.741638i
$404$	−1.27135			−0.0632520
$405$		0			0
$406$	3.44949			0.171195
$407$	−6.90968	+	25.7873i	−0.342500	+	1.27823i
$408$	4.92650	−	5.92650i	0.243898	−	0.293406i
$409$	−16.5420	−	9.55051i	−0.817948	−	0.472242i	0.0317605	−	0.999496i	$-0.489889\pi$
$409$	−16.5420	−	9.55051i	−0.817948	−	0.472242i	−0.849708	+	0.527253i	$0.823222\pi$
$410$		0			0
$411$	2.20204	+	3.11416i	0.108619	+	0.153610i
$412$	−3.96008	−	1.06110i	−0.195099	−	0.0522767i
$413$	−9.15306	+	9.15306i	−0.450393	+	0.450393i
$414$	−0.548188	−	2.94949i	−0.0269420	−	0.144960i
$415$		0			0
$416$	3.00000	−	1.73205i	0.147087	−	0.0849208i
$417$	−20.9588	+	7.73810i	−1.02636	+	0.378937i
$418$	−9.42418	+	2.52520i	−0.460952	+	0.123512i
$419$	−5.97469	+	10.3485i	−0.291883	+	0.505556i	−0.974255	−	0.225449i	$-0.927615\pi$
$419$	−5.97469	+	10.3485i	−0.291883	+	0.505556i	0.682372	+	0.731005i	$0.260948\pi$
$420$		0			0
$421$	7.44949	+	12.9029i	0.363066	+	0.628849i	0.988464	−	0.151457i	$-0.0483966\pi$
$421$	7.44949	+	12.9029i	0.363066	+	0.628849i	−0.625398	+	0.780306i	$0.715063\pi$
$422$	−13.3636	−	13.3636i	−0.650530	−	0.650530i
$423$	26.9178	+	2.10488i	1.30879	+	0.102343i
$424$			9.34847i			0.454002i
$425$		0			0
$426$	−0.898979	+	0.635674i	−0.0435557	+	0.0307985i
$427$	1.54636	+	5.77111i	0.0748338	+	0.279284i
$428$	1.35814	+	5.06865i	0.0656482	+	0.245002i
$429$	3.46410	+	37.5959i	0.167248	+	1.81515i
$430$		0			0
$431$		−	15.5563i		−	0.749323i	−0.927162	−	0.374661i	$-0.877759\pi$
$431$		−	15.5563i		−	0.749323i	0.927162	−	0.374661i	$-0.122241\pi$
$432$	0.0719302	+	5.19565i	0.00346074	+	0.249976i
$433$	−8.55051	−	8.55051i	−0.410911	−	0.410911i	0.471145	−	0.882056i	$-0.343841\pi$
$433$	−8.55051	−	8.55051i	−0.410911	−	0.410911i	−0.882056	+	0.471145i	$0.843841\pi$
$434$	2.43916	+	4.22474i	0.117083	+	0.202794i
$435$		0			0
$436$	10.1742	−	17.6223i	0.487257	−	0.843955i
$437$	−1.49768	+	0.401302i	−0.0716436	+	0.0191969i
$438$	−1.20080	+	6.99876i	−0.0573763	+	0.334413i
$439$	−8.83523	+	5.10102i	−0.421682	+	0.243458i	−0.695797	−	0.718239i	$-0.744949\pi$
$439$	−8.83523	+	5.10102i	−0.421682	+	0.243458i	0.274114	+	0.961697i	$0.411615\pi$
$440$		0			0
$441$	−5.79796	+	16.3991i	−0.276093	+	0.780910i
$442$	−10.8990	+	10.8990i	−0.518412	+	0.518412i
$443$	−0.531752	−	0.142483i	−0.0252643	−	0.00676955i	0.246165	−	0.969228i	$-0.420830\pi$
$443$	−0.531752	−	0.142483i	−0.0252643	−	0.00676955i	−0.271429	+	0.962458i	$0.587496\pi$
$444$	3.07483	−	6.67423i	0.145925	−	0.316745i
$445$		0			0
$446$	−7.19694	−	4.15515i	−0.340785	−	0.196752i
$447$	7.74045	+	20.9652i	0.366111	+	0.991620i
$448$	0.283763	−	1.05902i	0.0134065	−	0.0500339i
$449$	−21.7060			−1.02437			−0.512185	−	0.858875i	$-0.671164\pi$
$449$	−21.7060			−1.02437			−0.512185	+	0.858875i	$0.671164\pi$
$450$		0			0
$451$	24.6969			1.16293
$452$	3.57117	−	13.3278i	0.167974	−	0.626887i
$453$	−36.8665	−	6.32530i	−1.73214	−	0.297188i
$454$	13.0779	+	7.55051i	0.613775	+	0.354363i
$455$		0			0
$456$	2.67423	−	0.246405i	0.125233	−	0.0115390i
$457$	5.94012	+	1.59165i	0.277867	+	0.0744543i	0.395061	−	0.918655i	$-0.370723\pi$
$457$	5.94012	+	1.59165i	0.277867	+	0.0744543i	−0.117194	+	0.993109i	$0.537390\pi$
$458$	11.5601	−	11.5601i	0.540169	−	0.540169i
$459$	−6.29253	−	22.2474i	−0.293710	−	1.03842i
$460$		0			0
$461$	16.3763	−	9.45485i	0.762719	−	0.440356i	−0.0675520	−	0.997716i	$-0.521519\pi$
$461$	16.3763	−	9.45485i	0.762719	−	0.440356i	0.830271	+	0.557360i	$0.188186\pi$
$462$	9.18910	+	7.63859i	0.427516	+	0.355380i
$463$	−31.8946	+	8.54613i	−1.48227	+	0.397172i	−0.907118	−	0.420876i	$-0.861723\pi$
$463$	−31.8946	+	8.54613i	−1.48227	+	0.397172i	−0.575150	+	0.818048i	$0.695056\pi$
$464$	1.57313	−	2.72474i	0.0730308	−	0.126493i
$465$		0			0
$466$	−7.77526	−	13.4671i	−0.360182	−	0.623853i
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	0.769514	−	0.638630i	$-0.220499\pi$
$467$	2.82843	+	2.82843i	0.130884	+	0.130884i	−0.638630	+	0.769514i	$0.720499\pi$
$468$	0.810167	−	10.3607i	0.0374500	−	0.478922i
$469$		−	4.14643i		−	0.191464i
$470$		0			0
$471$	9.67423	+	4.45694i	0.445765	+	0.205365i
$472$	3.05575	+	11.4042i	0.140652	+	0.524922i
$473$	−5.64173	−	21.0552i	−0.259407	−	0.968120i
$474$	−3.85337	−	1.77526i	−0.176991	−	0.0815402i
$475$		0			0
$476$			4.87832i			0.223597i
$477$	23.1209	+	15.8735i	1.05863	+	0.726797i
$478$	12.0000	+	12.0000i	0.548867	+	0.548867i
$479$	3.53553	+	6.12372i	0.161543	+	0.279800i	0.935422	−	0.353533i	$-0.115020\pi$
$479$	3.53553	+	6.12372i	0.161543	+	0.279800i	−0.773879	+	0.633333i	$0.781686\pi$
$480$		0			0
$481$	−7.34847	+	12.7279i	−0.335061	+	0.580343i
$482$	18.3526	−	4.91756i	0.835938	−	0.223989i
$483$	1.46032	+	1.21391i	0.0664469	+	0.0552350i
$484$	−24.7648	+	14.2980i	−1.12567	+	0.649907i
$485$		0			0
$486$	12.9722	+	8.64420i	0.588431	+	0.392109i
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	−0.380861	−	0.924632i	$-0.624372\pi$
$487$	12.0000	−	12.0000i	0.543772	−	0.543772i	0.924632	+	0.380861i	$0.124372\pi$
$488$	5.26380	+	1.41043i	0.238281	+	0.0638472i
$489$	−1.09638	+	0.101021i	−0.0495799	+	0.00456831i
$490$		0			0
$491$	0.247449	+	0.142865i	0.0111672	+	0.00644739i	0.505573	−	0.862784i	$-0.331281\pi$
$491$	0.247449	+	0.142865i	0.0111672	+	0.00644739i	−0.494406	+	0.869231i	$0.664614\pi$
$492$	−6.70006	−	1.14955i	−0.302062	−	0.0518256i
$493$	−3.62328	+	13.5223i	−0.163184	+	0.609012i
$494$	−5.37113			−0.241658
$495$		0			0
$496$	4.44949			0.199788
$497$	0.180381	−	0.673191i	0.00809119	−	0.0301967i
$498$	−0.330251	−	0.894494i	−0.0147989	−	0.0400832i
$499$	−7.70674	−	4.44949i	−0.345001	−	0.199187i	0.317480	−	0.948265i	$-0.397163\pi$
$499$	−7.70674	−	4.44949i	−0.345001	−	0.199187i	−0.662481	+	0.749078i	$0.730497\pi$
$500$		0			0
$501$	−7.82577	+	16.9866i	−0.349629	+	0.758906i
$502$	10.7902	+	2.89123i	0.481590	+	0.129042i
$503$	−16.7563	+	16.7563i	−0.747125	+	0.747125i	−0.973938	−	0.226813i	$-0.927169\pi$
$503$	−16.7563	+	16.7563i	−0.747125	+	0.747125i	0.226813	+	0.973938i	$0.427169\pi$
$504$	−2.13737	−	2.50000i	−0.0952062	−	0.111359i
$505$		0			0
$506$	−5.44949	+	3.14626i	−0.242259	+	0.139869i
$507$	0.292893	−	1.70711i	0.0130078	−	0.0758153i
$508$	19.2934	−	5.16964i	0.856005	−	0.229366i
$509$	19.8150	−	34.3207i	0.878286	−	1.52124i	0.0250662	−	0.999686i	$-0.492020\pi$
$509$	19.8150	−	34.3207i	0.878286	−	1.52124i	0.853220	−	0.521551i	$-0.174646\pi$
$510$		0			0
$511$	−2.24745	−	3.89270i	−0.0994213	−	0.172203i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	3.93137	−	7.03239i	0.173574	−	0.310488i
$514$			26.0454i			1.14881i
$515$		0			0
$516$	0.550510	+	5.97469i	0.0242349	+	0.263021i
$517$	−14.6576	−	54.7030i	−0.644642	−	2.40584i
$518$	1.20390	+	4.49303i	0.0528965	+	0.197413i
$519$	4.38551	−	3.10102i	0.192502	−	0.136120i
$520$		0			0
$521$		−	29.4449i		−	1.29000i	−0.764181	−	0.645001i	$-0.776857\pi$
$521$		−	29.4449i		−	1.29000i	0.764181	−	0.645001i	$-0.223143\pi$
$522$	−4.06778	−	8.51727i	−0.178042	−	0.372791i
$523$	−1.77526	−	1.77526i	−0.0776265	−	0.0776265i	0.667228	−	0.744854i	$-0.267481\pi$
$523$	−1.77526	−	1.77526i	−0.0776265	−	0.0776265i	−0.744854	+	0.667228i	$0.767481\pi$
$524$	−5.26758	−	9.12372i	−0.230116	−	0.398572i
$525$		0			0
$526$	6.34847	−	10.9959i	0.276806	−	0.479443i
$527$	−19.1234	+	5.12409i	−0.833027	+	0.223209i
$528$	10.2244	−	3.77489i	0.444959	−	0.164281i
$529$	19.0526	−	11.0000i	0.828372	−	0.478261i
$530$		0			0
$531$	33.3939	+	11.8065i	1.44917	+	0.512359i
$532$	−1.20204	+	1.20204i	−0.0521151	+	0.0521151i
$533$	13.1326	+	3.51888i	0.568838	+	0.152420i
$534$	2.36773	+	3.34847i	0.102461	+	0.144902i
$535$		0			0
$536$	−3.27526	−	1.89097i	−0.141469	−	0.0816774i
$537$	19.4937	−	23.4506i	0.841217	−	1.01197i
$538$	−1.21731	+	4.54308i	−0.0524822	+	0.195866i
$539$	36.4838			1.57147
$540$		0			0
$541$	−25.9444			−1.11544			−0.557718	−	0.830030i	$-0.688323\pi$
$541$	−25.9444			−1.11544			−0.557718	+	0.830030i	$0.688323\pi$
$542$	4.15286	−	15.4987i	0.178380	−	0.665725i
$543$	11.6816	−	14.0528i	0.501305	−	0.603062i
$544$	3.85337	+	2.22474i	0.165212	+	0.0953851i
$545$		0			0
$546$	3.79796	+	5.37113i	0.162538	+	0.229863i
$547$	−20.6594	−	5.53567i	−0.883332	−	0.236688i	−0.211488	−	0.977381i	$-0.567831\pi$
$547$	−20.6594	−	5.53567i	−0.883332	−	0.236688i	−0.671844	+	0.740693i	$0.734498\pi$
$548$	−1.55708	+	1.55708i	−0.0665151	+	0.0665151i
$549$	12.4261	−	10.6237i	0.530335	−	0.453410i
$550$		0			0
$551$	−4.22474	+	2.43916i	−0.179980	+	0.103912i
$552$	1.62484	−	0.599900i	0.0691580	−	0.0255335i
$553$	2.59405	−	0.695075i	0.110310	−	0.0295576i
$554$	7.14250	−	12.3712i	0.303456	−	0.525601i
$555$		0			0
$556$	−6.44949	−	11.1708i	−0.273519	−	0.473749i
$557$	16.3670	+	16.3670i	0.693492	+	0.693492i	0.962999	−	0.269507i	$-0.0868606\pi$
$557$	16.3670	+	16.3670i	0.693492	+	0.693492i	−0.269507	+	0.962999i	$0.586861\pi$
$558$	7.55513	−	11.0046i	0.319834	−	0.465863i
$559$		−	12.0000i		−	0.507546i
$560$		0			0
$561$	−39.5959	+	27.9985i	−1.67174	+	1.18210i
$562$	−0.0452863	−	0.169011i	−0.00191029	−	0.00712928i
$563$	8.89004	+	33.1781i	0.374670	+	1.39829i	0.853826	+	0.520559i	$0.174276\pi$
$563$	8.89004	+	33.1781i	0.374670	+	1.39829i	−0.479155	+	0.877730i	$0.659057\pi$
$564$	1.43027	+	15.5227i	0.0602251	+	0.653624i
$565$		0			0
$566$			6.89610i			0.289864i
$567$	−9.81229	+	1.04128i	−0.412077	+	0.0437297i
$568$	−0.449490	−	0.449490i	−0.0188602	−	0.0188602i
$569$	13.0458	+	22.5959i	0.546907	+	0.947270i	0.998484	+	0.0550383i	$0.0175281\pi$
$569$	13.0458	+	22.5959i	0.546907	+	0.947270i	−0.451578	+	0.892232i	$0.649139\pi$
$570$		0			0
$571$	−13.5505	+	23.4702i	−0.567071	+	0.982196i	0.429782	+	0.902932i	$0.358590\pi$
$571$	−13.5505	+	23.4702i	−0.567071	+	0.982196i	−0.996854	+	0.0792637i	$0.974743\pi$
$572$	−21.0552	+	5.64173i	−0.880363	+	0.235892i
$573$	0.972768	−	5.66971i	0.0406380	−	0.236855i
$574$	3.72656	−	2.15153i	0.155544	−	0.0898032i
$575$		0			0
$576$	−2.94949	+	0.548188i	−0.122895	+	0.0228412i
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	−0.258336	−	0.966055i	$-0.583174\pi$
$577$	17.0000	−	17.0000i	0.707719	−	0.707719i	0.966055	+	0.258336i	$0.0831741\pi$
$578$	−2.70262	−	0.724165i	−0.112414	−	0.0301213i
$579$	−12.5529	+	27.2474i	−0.521683	+	1.13237i
$580$		0			0
$581$	0.522704	+	0.301783i	0.0216854	+	0.0125201i
$582$	6.70139	+	18.1509i	0.277782	+	0.752378i
$583$	15.2252	−	56.8211i	0.630562	−	2.35329i
$584$	−4.09978			−0.169650
$585$		0			0
$586$	22.0454			0.910687
$587$	−8.03514	+	29.9876i	−0.331646	+	1.23772i	0.575814	+	0.817581i	$0.304685\pi$
$587$	−8.03514	+	29.9876i	−0.331646	+	1.23772i	−0.907460	+	0.420138i	$0.861981\pi$
$588$	−9.89774	−	1.69818i	−0.408176	−	0.0700319i
$589$	−5.97469	−	3.44949i	−0.246183	−	0.142134i
$590$		0			0
$591$	16.8990	−	1.55708i	0.695131	−	0.0640496i
$592$	4.09808	+	1.09808i	0.168430	+	0.0451307i
$593$	10.0745	−	10.0745i	0.413709	−	0.413709i	−0.469320	−	0.883028i	$-0.655501\pi$
$593$	10.0745	−	10.0745i	0.413709	−	0.413709i	0.883028	+	0.469320i	$0.155501\pi$
$594$	8.02458	−	31.6969i	0.329252	−	1.30054i
$595$		0			0
$596$	−11.1742	+	6.45145i	−0.457714	+	0.264262i
$597$	4.72911	+	3.93115i	0.193549	+	0.160891i
$598$	−3.34607	+	0.896575i	−0.136831	+	0.0366637i
$599$	−16.8991	+	29.2702i	−0.690480	+	1.19595i	0.281201	+	0.959649i	$0.409267\pi$
$599$	−16.8991	+	29.2702i	−0.690480	+	1.19595i	−0.971681	+	0.236297i	$0.924066\pi$
$600$		0			0
$601$	−17.3485	−	30.0484i	−0.707659	−	1.22570i	−0.965723	−	0.259573i	$-0.916418\pi$
$601$	−17.3485	−	30.0484i	−0.707659	−	1.22570i	0.258065	−	0.966128i	$-0.416915\pi$
$602$	−2.68556	−	2.68556i	−0.109455	−	0.109455i
$603$	−10.2381	+	4.88964i	−0.416928	+	0.199122i
$604$		−	21.5959i		−	0.878725i
$605$		0			0
$606$	−2.00000	−	0.921404i	−0.0812444	−	0.0374295i
$607$	−5.73717	−	21.4114i	−0.232864	−	0.869062i	−0.979100	−	0.203380i	$-0.934807\pi$
$607$	−5.73717	−	21.4114i	−0.232864	−	0.869062i	0.746235	−	0.665682i	$-0.231859\pi$
$608$	0.401302	+	1.49768i	0.0162749	+	0.0607389i
$609$	5.42650	+	2.50000i	0.219893	+	0.101305i
$610$		0			0
$611$		−	31.1769i		−	1.26128i
$612$	12.0452	−	5.75272i	0.486900	−	0.232540i
$613$	12.7980	+	12.7980i	0.516905	+	0.516905i	0.916633	−	0.399729i	$-0.130896\pi$
$613$	12.7980	+	12.7980i	0.516905	+	0.516905i	−0.399729	+	0.916633i	$0.630896\pi$
$614$	−0.476756	−	0.825765i	−0.0192403	−	0.0333252i
$615$		0			0
$616$	−3.44949	+	5.97469i	−0.138984	+	0.240727i
$617$	−6.85906	+	1.83788i	−0.276135	+	0.0739902i	−0.394229	−	0.919012i	$-0.628988\pi$
$617$	−6.85906	+	1.83788i	−0.276135	+	0.0739902i	0.118094	+	0.993002i	$0.462322\pi$
$618$	−5.46070	−	4.53930i	−0.219662	−	0.182597i
$619$	−21.4275	+	12.3712i	−0.861244	+	0.497239i	−0.864429	−	0.502756i	$-0.832320\pi$
$619$	−21.4275	+	12.3712i	−0.861244	+	0.497239i	0.00318471	+	0.999995i	$0.498986\pi$
$620$		0			0
$621$	1.27526	−	5.03723i	0.0511742	−	0.202137i
$622$	14.5505	−	14.5505i	0.583422	−	0.583422i
$623$	−2.50746	−	0.671873i	−0.100459	−	0.0269180i
$624$	5.97469	−	0.550510i	0.239179	−	0.0220380i
$625$		0			0
$626$	−4.34847	−	2.51059i	−0.173800	−	0.100343i
$627$	−16.6556	−	2.85765i	−0.665161	−	0.114124i
$628$	−1.59165	+	5.94012i	−0.0635138	+	0.237037i
$629$	−18.8776			−0.752699
$630$		0			0
$631$	−12.8990			−0.513500			−0.256750	−	0.966478i	$-0.582652\pi$
$631$	−12.8990			−0.513500			−0.256750	+	0.966478i	$0.582652\pi$
$632$	0.633975	−	2.36603i	0.0252182	−	0.0941154i
$633$	−11.3375	−	30.7079i	−0.450625	−	1.22053i
$634$	−0.953512	−	0.550510i	−0.0378688	−	0.0218636i
$635$		0			0
$636$	−6.77526	+	14.7064i	−0.268656	+	0.583146i
$637$	19.4003	+	5.19831i	0.768670	+	0.205964i
$638$	−13.9993	+	13.9993i	−0.554236	+	0.554236i
$639$	−1.87492	+	0.348469i	−0.0741705	+	0.0137852i
$640$		0			0
$641$	−7.74745	+	4.47299i	−0.306006	+	0.176673i	−0.645138	−	0.764066i	$-0.723200\pi$
$641$	−7.74745	+	4.47299i	−0.306006	+	0.176673i	0.339132	+	0.940739i	$0.389867\pi$
$642$	−1.53694	+	8.95796i	−0.0606583	+	0.353542i
$643$	−30.6976	+	8.22539i	−1.21059	+	0.324378i	−0.806995	−	0.590558i	$-0.798908\pi$
$643$	−30.6976	+	8.22539i	−1.21059	+	0.324378i	−0.403599	+	0.914936i	$0.632241\pi$
$644$	−0.548188	+	0.949490i	−0.0216016	+	0.0374151i
$645$		0			0
$646$	−3.44949	−	5.97469i	−0.135718	−	0.235071i
$647$	−24.9558	−	24.9558i	−0.981114	−	0.981114i	0.0187105	−	0.999825i	$-0.494044\pi$
$647$	−24.9558	−	24.9558i	−0.981114	−	0.981114i	−0.999825	+	0.0187105i	$0.994044\pi$
$648$	−3.65237	+	8.22558i	−0.143479	+	0.323131i
$649$		−	74.2929i		−	2.91625i
$650$		0			0
$651$	0.775255	+	8.41385i	0.0303846	+	0.329765i
$652$	−0.164525	−	0.614014i	−0.00644328	−	0.0240467i
$653$	5.57768	+	20.8162i	0.218272	+	0.814601i	0.984989	+	0.172616i	$0.0552220\pi$
$653$	5.57768	+	20.8162i	0.218272	+	0.814601i	−0.766718	+	0.641985i	$0.778111\pi$
$654$	28.7771	−	20.3485i	1.12527	−	0.795688i
$655$		0			0
$656$		−	3.92480i		−	0.153238i
$657$	−6.96132	+	10.1397i	−0.271587	+	0.395587i
$658$	−6.97730	−	6.97730i	−0.272003	−	0.272003i
$659$	−5.65685	−	9.79796i	−0.220360	−	0.381674i	0.734557	−	0.678546i	$-0.237390\pi$
$659$	−5.65685	−	9.79796i	−0.220360	−	0.381674i	−0.954917	+	0.296872i	$0.904056\pi$
$660$		0			0
$661$	15.3485	−	26.5843i	0.596986	−	1.03401i	−0.396277	−	0.918131i	$-0.629698\pi$
$661$	15.3485	−	26.5843i	0.596986	−	1.03401i	0.993263	−	0.115880i	$-0.0369687\pi$
$662$	−4.29788	+	1.15161i	−0.167042	+	0.0447587i
$663$	−25.0445	+	9.24656i	−0.972648	+	0.359106i
$664$	0.476756	−	0.275255i	0.0185017	−	0.0106820i
$665$		0			0
$666$	9.67423	−	8.27098i	0.374869	−	0.320494i
$667$	−2.22474	+	2.22474i	−0.0861425	+	0.0861425i
$668$	−10.4300	−	2.79472i	−0.403550	−	0.108131i
$669$	−8.31031	−	11.7526i	−0.321295	−	0.454380i
$670$		0			0
$671$	−29.6969	−	17.1455i	−1.14644	−	0.661896i
$672$	1.21391	−	1.46032i	0.0468278	−	0.0563331i
$673$	4.22778	−	15.7783i	0.162969	−	0.608208i	−0.835322	−	0.549762i	$-0.814719\pi$
$673$	4.22778	−	15.7783i	0.162969	−	0.608208i	0.998291	−	0.0584468i	$-0.0186148\pi$
$674$	−30.8270			−1.18741
$675$		0			0
$676$	1.00000			0.0384615
$677$	−1.65750	+	6.18587i	−0.0637028	+	0.237742i	−0.990435	−	0.137981i	$-0.955939\pi$
$677$	−1.65750	+	6.18587i	−0.0637028	+	0.237742i	0.926732	+	0.375723i	$0.122606\pi$
$678$	15.2772	−	18.3782i	0.586717	−	0.705811i
$679$	−10.6066	−	6.12372i	−0.407044	−	0.235007i
$680$		0			0
$681$	15.1010	+	21.3561i	0.578672	+	0.818366i
$682$	−27.0445	−	7.24656i	−1.03559	−	0.277485i
$683$	13.8564	−	13.8564i	0.530201	−	0.530201i	−0.390431	−	0.920632i	$-0.627674\pi$
$683$	13.8564	−	13.8564i	0.530201	−	0.530201i	0.920632	+	0.390431i	$0.127674\pi$
$684$	4.38551	+	1.55051i	0.167684	+	0.0592852i
$685$		0			0
$686$	12.1515	−	7.01569i	0.463948	−	0.267860i
$687$	26.5637	−	9.80745i	1.01347	−	0.374178i
$688$	−3.34607	+	0.896575i	−0.127568	+	0.0341816i
$689$	16.1920	−	28.0454i	0.616867	−	1.06844i
$690$		0			0
$691$	−16.4722	−	28.5307i	−0.626632	−	1.08536i	−0.988223	−	0.153021i	$-0.951100\pi$
$691$	−16.4722	−	28.5307i	−0.626632	−	1.08536i	0.361591	−	0.932337i	$-0.382234\pi$
$692$	2.19275	+	2.19275i	0.0833559	+	0.0833559i
$693$	8.91964	+	18.6763i	0.338829	+	0.709453i
$694$			4.20204i			0.159507i
$695$		0			0
$696$	4.44949	−	3.14626i	0.168657	−	0.119259i
$697$	4.51985	+	16.8683i	0.171202	+	0.638933i
$698$	3.89404	+	14.5327i	0.147392	+	0.550073i
$699$	−2.47127	−	26.8207i	−0.0934719	−	1.01445i
$700$		0			0
$701$			23.9309i			0.903857i	0.892054	+	0.451928i	$0.149264\pi$
$701$			23.9309i			0.903857i	−0.892054	+	0.451928i	$0.850736\pi$
$702$	8.78335	−	15.7116i	0.331506	−	0.592994i
$703$	−4.65153	−	4.65153i	−0.175436	−	0.175436i
$704$	3.14626	+	5.44949i	0.118579	+	0.205385i
$705$		0			0
$706$	−17.1464	+	29.6985i	−0.645314	+	1.11772i
$707$	1.34638	−	0.360762i	0.0506359	−	0.0135678i
$708$	−3.45805	+	20.1550i	−0.129961	+	0.757471i
$709$	−38.4069	+	22.1742i	−1.44240	+	0.832771i	−0.998010	−	0.0630617i	$-0.979914\pi$
$709$	−38.4069	+	22.1742i	−1.44240	+	0.832771i	−0.444392	+	0.895833i	$0.646580\pi$
$710$		0			0
$711$	−4.77526	−	5.58542i	−0.179086	−	0.209470i
$712$	−1.67423	+	1.67423i	−0.0627446	+	0.0627446i
$713$	−4.29788	−	1.15161i	−0.160957	−	0.0431282i
$714$	−3.53553	+	7.67423i	−0.132314	+	0.287201i
$715$		0			0
$716$	15.2474	+	8.80312i	0.569824	+	0.328988i
$717$	10.1806	+	27.5745i	0.380203	+	1.02979i
$718$	−4.51985	+	16.8683i	−0.168679	+	0.629520i
$719$	−32.5269			−1.21305			−0.606525	−	0.795065i	$-0.707437\pi$
$719$	−32.5269			−1.21305			−0.606525	+	0.795065i	$0.707437\pi$
$720$		0			0
$721$	4.49490			0.167399
$722$	−4.29534	+	16.0304i	−0.159856	+	0.596591i
$723$	32.4350	+	5.56497i	1.20627	+	0.206964i
$724$	9.13701	+	5.27526i	0.339574	+	0.196053i
$725$		0			0
$726$	−49.3207	+	4.54442i	−1.83046	+	0.168659i
$727$	−30.2836	−	8.11447i	−1.12316	−	0.300949i	−0.350996	−	0.936377i	$-0.614157\pi$
$727$	−30.2836	−	8.11447i	−1.12316	−	0.300949i	−0.772160	+	0.635428i	$0.780824\pi$
$728$	−2.68556	+	2.68556i	−0.0995336	+	0.0995336i
$729$	14.1421	+	23.0000i	0.523783	+	0.851852i
$730$		0			0
$731$	13.3485	−	7.70674i	0.493711	−	0.285044i
$732$	7.25845	+	6.03371i	0.268280	+	0.223012i
$733$	−13.8603	+	3.71385i	−0.511941	+	0.137174i	−0.505536	−	0.862805i	$-0.668705\pi$
$733$	−13.8603	+	3.71385i	−0.511941	+	0.137174i	−0.00640470	+	0.999979i	$0.502039\pi$
$734$	−4.87832	+	8.44949i	−0.180062	+	0.311876i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	16.8277	+	16.8277i	0.619856	+	0.619856i
$738$	−9.70695	−	6.66422i	−0.357318	−	0.245313i
$739$			24.9444i			0.917594i	0.888541	+	0.458797i	$0.151720\pi$
$739$			24.9444i			0.917594i	−0.888541	+	0.458797i	$0.848280\pi$
$740$		0			0
$741$	−8.44949	−	3.89270i	−0.310400	−	0.143002i
$742$	−2.65275	−	9.90020i	−0.0973855	−	0.363448i
$743$	−0.0261460	−	0.0975783i	−0.000959205	−	0.00357980i	0.965445	−	0.260609i	$-0.0839232\pi$
$743$	−0.0261460	−	0.0975783i	−0.000959205	−	0.00357980i	−0.966404	+	0.257029i	$0.917257\pi$
$744$	6.99964	+	3.22474i	0.256619	+	0.118225i
$745$		0			0
$746$			20.2918i			0.742936i
$747$	0.128751	−	1.64650i	0.00471074	−	0.0602425i
$748$	−19.7980	−	19.7980i	−0.723885	−	0.723885i
$749$	−2.87659	−	4.98240i	−0.105108	−	0.182053i
$750$		0			0
$751$	4.34847	−	7.53177i	0.158678	−	0.274838i	−0.775714	−	0.631084i	$-0.782610\pi$
$751$	4.34847	−	7.53177i	0.158678	−	0.274838i	0.934392	+	0.356246i	$0.115944\pi$
$752$	−8.69333	+	2.32937i	−0.317013	+	0.0849434i
$753$	14.8790	+	12.3684i	0.542222	+	0.450731i
$754$	−9.43879	+	5.44949i	−0.343741	+	0.198459i
$755$		0			0
$756$	−1.55051	−	5.48188i	−0.0563915	−	0.199374i
$757$	22.0454	−	22.0454i	0.801254	−	0.801254i	−0.182038	−	0.983292i	$-0.558269\pi$
$757$	22.0454	−	22.0454i	0.801254	−	0.801254i	0.983292	+	0.182038i	$0.0582693\pi$
$758$	−6.42489	−	1.72154i	−0.233362	−	0.0625293i
$759$	−10.8530	+	1.00000i	−0.393939	+	0.0362977i
$760$		0			0
$761$	−15.3990	−	8.89060i	−0.558213	−	0.322284i	0.194215	−	0.980959i	$-0.437784\pi$
$761$	−15.3990	−	8.89060i	−0.558213	−	0.322284i	−0.752428	+	0.658675i	$0.771117\pi$
$762$	34.0977	+	5.85024i	1.23523	+	0.211932i
$763$	−5.77414	+	21.5494i	−0.209038	+	0.780141i
$764$	3.32124			0.120158
$765$		0			0
$766$	27.7980			1.00438
$767$	10.5854	−	39.5054i	0.382218	−	1.42646i
$768$	−0.599900	−	1.62484i	−0.0216470	−	0.0586315i
$769$	17.0580	+	9.84847i	0.615129	+	0.355145i	0.774970	−	0.631998i	$-0.217765\pi$
$769$	17.0580	+	9.84847i	0.615129	+	0.355145i	−0.159841	+	0.987143i	$0.551098\pi$
$770$		0			0
$771$	−18.8763	+	40.9729i	−0.679812	+	1.47560i
$772$	−16.7303	−	4.48288i	−0.602138	−	0.161342i
$773$	3.11416	−	3.11416i	0.112008	−	0.112008i	−0.648881	−	0.760890i	$-0.724763\pi$
$773$	3.11416	−	3.11416i	0.112008	−	0.112008i	0.760890	+	0.648881i	$0.224763\pi$
$774$	−3.46410	+	9.79796i	−0.124515	+	0.352180i
$775$		0			0
$776$	−9.67423	+	5.58542i	−0.347285	+	0.200505i
$777$	−1.36240	+	7.94066i	−0.0488759	+	0.284870i
$778$	5.43309	−	1.45579i	0.194786	−	0.0521927i
$779$	−3.04272	+	5.27015i	−0.109017	+	0.188823i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	−3.14626	−	3.14626i	−0.112510	−	0.112510i
$783$	−0.226311	−	16.3469i	−0.00808771	−	0.584191i
$784$		−	5.79796i		−	0.207070i
$785$		0			0
$786$	−1.67423	−	18.1705i	−0.0597180	−	0.648120i
$787$	−1.06110	−	3.96008i	−0.0378241	−	0.141162i	0.944432	−	0.328708i	$-0.106613\pi$
$787$	−1.06110	−	3.96008i	−0.0378241	−	0.141162i	−0.982256	+	0.187546i	$0.939947\pi$
$788$	2.53590	+	9.46410i	0.0903376	+	0.337145i
$789$	17.9562	−	12.6969i	0.639257	−	0.452023i
$790$		0			0
$791$			15.1278i			0.537881i
$792$	18.8201	+	1.47167i	0.668744	+	0.0522933i
$793$	−13.3485	−	13.3485i	−0.474018	−	0.474018i
$794$	−10.9244	−	18.9217i	−0.387694	−	0.671505i
$795$		0			0
$796$	−1.77526	+	3.07483i	−0.0629222	+	0.108985i
$797$	19.5137	−	5.22867i	0.691210	−	0.185209i	0.103920	−	0.994586i	$-0.466861\pi$
$797$	19.5137	−	5.22867i	0.691210	−	0.185209i	0.587290	+	0.809377i	$0.300195\pi$
$798$	−2.76214	+	1.01980i	−0.0977788	+	0.0361004i
$799$	34.6803	−	20.0227i	1.22690	−	0.708352i
$800$		0			0
$801$	1.29796	+	6.98358i	0.0458611	+	0.246753i
$802$	−18.2474	+	18.2474i	−0.644340	+	0.644340i
$803$	24.9189	+	6.67700i	0.879369	+	0.235626i
$804$	−3.78194	−	5.34847i	−0.133379	−	0.188626i
$805$		0			0
$806$	−13.3485	−	7.70674i	−0.470180	−	0.271458i
$807$	−5.20757	+	6.26462i	−0.183315	+	0.220525i
$808$	0.329049	−	1.22803i	0.0115759	−	0.0432019i
$809$	54.0901			1.90171			0.950853	−	0.309644i	$-0.100210\pi$
$809$	54.0901			1.90171			0.950853	+	0.309644i	$0.100210\pi$
$810$		0			0
$811$	43.6413			1.53245			0.766227	−	0.642570i	$-0.222132\pi$
$811$	43.6413			1.53245			0.766227	+	0.642570i	$0.222132\pi$
$812$	−0.892794	+	3.33195i	−0.0313309	+	0.116929i
$813$	17.7656	−	21.3717i	0.623066	−	0.749538i
$814$	−23.1202	−	13.3485i	−0.810364	−	0.467864i
$815$		0			0
$816$	4.44949	+	6.29253i	0.155763	+	0.220283i
$817$	5.18811	+	1.39015i	0.181509	+	0.0486352i
$818$	13.5065	−	13.5065i	0.472242	−	0.472242i
$819$	2.08200	+	11.2020i	0.0727508	+	0.391431i
$820$		0			0
$821$	−22.3207	+	12.8868i	−0.778997	+	0.449754i	−0.836075	−	0.548616i	$-0.815155\pi$
$821$	−22.3207	+	12.8868i	−0.778997	+	0.449754i	0.0570780	+	0.998370i	$0.481822\pi$
$822$	−3.57797	+	1.32101i	−0.124796	+	0.0460754i
$823$	−46.9519	+	12.5807i	−1.63664	+	0.438536i	−0.955829	−	0.293923i	$-0.905039\pi$
$823$	−46.9519	+	12.5807i	−1.63664	+	0.438536i	−0.680811	+	0.732459i	$0.738373\pi$
$824$	2.04989	−	3.55051i	0.0714112	−	0.123688i
$825$		0			0
$826$	−6.47219	−	11.2102i	−0.225196	−	0.390052i
$827$	−27.3235	−	27.3235i	−0.950133	−	0.950133i	0.0486816	−	0.998814i	$-0.484498\pi$
$827$	−27.3235	−	27.3235i	−0.950133	−	0.950133i	−0.998814	+	0.0486816i	$0.984498\pi$
$828$	2.99087	+	0.233875i	0.103940	+	0.00812772i
$829$			15.4495i			0.536583i	0.963338	+	0.268291i	$0.0864590\pi$
$829$			15.4495i			0.536583i	−0.963338	+	0.268291i	$0.913541\pi$
$830$		0			0
$831$	20.2020	−	14.2850i	0.700801	−	0.495541i
$832$	0.896575	+	3.34607i	0.0310832	+	0.116004i
$833$	6.67700	+	24.9189i	0.231344	+	0.863389i
$834$	−2.04989	−	22.2474i	−0.0709818	−	0.770366i
$835$		0			0
$836$		−	9.75663i		−	0.337440i
$837$	19.8608	−	11.8362i	0.686488	−	0.409118i
$838$	−8.44949	−	8.44949i	−0.291883	−	0.291883i
$839$	10.1459	+	17.5732i	0.350275	+	0.606695i	0.986298	−	0.164976i	$-0.0527547\pi$
$839$	10.1459	+	17.5732i	0.350275	+	0.606695i	−0.636022	+	0.771671i	$0.719421\pi$
$840$		0			0
$841$	9.55051	−	16.5420i	0.329328	−	0.570413i
$842$	−14.3913	+	3.85614i	−0.495957	+	0.132891i
$843$	0.0512483	−	0.298697i	0.00176509	−	0.0102877i
$844$	16.3670	−	9.44949i	0.563375	−	0.325265i
$845$		0			0
$846$	−9.00000	+	25.4558i	−0.309426	+	0.875190i
$847$	22.1691	−	22.1691i	0.761740	−	0.761740i
$848$	−9.02993	−	2.41956i	−0.310089	−	0.0830881i
$849$	−4.99791	+	10.8485i	−0.171528	+	0.372319i
$850$		0			0
$851$	−3.67423	−	2.12132i	−0.125951	−	0.0727179i
$852$	−0.381341	−	1.03287i	−0.0130645	−	0.0353856i
$853$	9.60723	−	35.8547i	0.328945	−	1.22764i	−0.581340	−	0.813660i	$-0.697472\pi$
$853$	9.60723	−	35.8547i	0.328945	−	1.22764i	0.910286	−	0.413980i	$-0.135862\pi$
$854$	−5.97469			−0.204450
$855$		0			0
$856$	−5.24745			−0.179354
$857$	−0.982984	+	3.66855i	−0.0335781	+	0.125315i	−0.980680	−	0.195616i	$-0.937329\pi$
$857$	−0.982984	+	3.66855i	−0.0335781	+	0.125315i	0.947102	+	0.320932i	$0.103996\pi$
$858$	−37.2114	−	6.38447i	−1.27038	−	0.217962i
$859$	2.16064	+	1.24745i	0.0737202	+	0.0425624i	0.536407	−	0.843959i	$-0.319781\pi$
$859$	2.16064	+	1.24745i	0.0737202	+	0.0425624i	−0.462687	+	0.886522i	$0.653115\pi$
$860$		0			0
$861$	7.42168	−	0.683837i	0.252930	−	0.0233051i
$862$	15.0263	+	4.02628i	0.511797	+	0.137136i
$863$	27.7842	−	27.7842i	0.945787	−	0.945787i	−0.0528175	−	0.998604i	$-0.516820\pi$
$863$	27.7842	−	27.7842i	0.945787	−	0.945787i	0.998604	+	0.0528175i	$0.0168202\pi$
$864$	−5.03723	−	1.27526i	−0.171370	−	0.0433851i
$865$		0			0
$866$	10.4722	−	6.04612i	0.355860	−	0.205456i
$867$	−3.72674	−	3.09792i	−0.126567	−	0.105211i
$868$	−4.71209	+	1.26260i	−0.159939	+	0.0428555i
$869$	−7.70674	+	13.3485i	−0.261433	+	0.452816i
$870$		0			0
$871$	6.55051	+	11.3458i	0.221956	+	0.384438i
$872$	14.3885	+	14.3885i	0.487257	+	0.487257i
$873$	−2.61258	+	33.4105i	−0.0884225	+	1.13078i
$874$		−	1.55051i		−	0.0524468i
$875$		0			0
$876$	−6.44949	−	2.97129i	−0.217908	−	0.100391i
$877$	−2.10558	−	7.85813i	−0.0711004	−	0.265350i	0.921220	−	0.389041i	$-0.127194\pi$
$877$	−2.10558	−	7.85813i	−0.0711004	−	0.265350i	−0.992321	+	0.123691i	$0.960527\pi$
$878$	−2.64048	−	9.85441i	−0.0891120	−	0.332570i
$879$	34.6803	+	15.9773i	1.16974	+	0.538901i
$880$		0			0
$881$			58.3006i			1.96420i	0.188368	+	0.982098i	$0.439680\pi$
$881$			58.3006i			1.96420i	−0.188368	+	0.982098i	$0.560320\pi$
$882$	−14.3397	−	9.84480i	−0.482843	−	0.331492i
$883$	40.2702	+	40.2702i	1.35520	+	1.35520i	0.879736	+	0.475463i	$0.157719\pi$
$883$	40.2702	+	40.2702i	1.35520	+	1.35520i	0.475463	+	0.879736i	$0.342281\pi$
$884$	−7.70674	−	13.3485i	−0.259206	−	0.448958i
$885$		0			0
$886$	0.275255	−	0.476756i	0.00924738	−	0.0160169i
$887$	−26.8508	+	7.19464i	−0.901561	+	0.241572i	−0.679686	−	0.733503i	$-0.737884\pi$
$887$	−26.8508	+	7.19464i	−0.901561	+	0.241572i	−0.221874	+	0.975075i	$0.571217\pi$
$888$	5.65099	+	4.69748i	0.189635	+	0.157637i
$889$	−18.9651	+	10.9495i	−0.636068	+	0.367234i
$890$		0			0
$891$	35.5959	−	44.0477i	1.19251	−	1.47565i
$892$	5.87628	−	5.87628i	0.196752	−	0.196752i
$893$	13.4791	+	3.61171i	0.451061	+	0.120861i
$894$	−22.2542	+	2.05051i	−0.744292	+	0.0685793i
$895$		0			0
$896$	0.949490	+	0.548188i	0.0317202	+	0.0183137i
$897$	−5.91359	−	1.01461i	−0.197449	−	0.0338769i
$898$	5.61793	−	20.9664i	0.187473	−	0.699658i
$899$	−13.9993			−0.466902
$900$		0			0
$901$	41.5959			1.38576
$902$	−6.39204	+	23.8554i	−0.212832	+	0.794298i
$903$	−2.27840	−	6.17109i	−0.0758203	−	0.205361i
$904$	11.9494	+	6.89898i	0.397431	+	0.229457i
$905$		0			0
$906$	15.6515	−	33.9732i	0.519987	−	1.12869i
$907$	6.38512	+	1.71089i	0.212015	+	0.0568091i	0.363263	−	0.931687i	$-0.381663\pi$
$907$	6.38512	+	1.71089i	0.212015	+	0.0568091i	−0.151248	+	0.988496i	$0.548329\pi$
$908$	−10.6780	+	10.6780i	−0.354363	+	0.354363i
$909$	−2.47848	−	2.89898i	−0.0822061	−	0.0961531i
$910$		0			0
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	−0.395114	−	0.918632i	$-0.629295\pi$
$911$	6.12372	−	3.53553i	0.202888	−	0.117137i	0.598002	+	0.801495i	$0.295962\pi$
$912$	−0.454134	+	2.64689i	−0.0150379	+	0.0876472i
$913$	−3.34607	+	0.896575i	−0.110739	+	0.0296723i
$914$	−3.07483	+	5.32577i	−0.101706	+	0.176161i
$915$		0			0
$916$	8.17423	+	14.1582i	0.270084	+	0.467800i
$917$	8.16744	+	8.16744i	0.269713	+	0.269713i
$918$	23.1180	−	0.320053i	0.763008	−	0.0105633i
$919$		−	27.3485i		−	0.902143i	−0.892488	−	0.451071i	$-0.851042\pi$
$919$		−	27.3485i		−	0.902143i	0.892488	−	0.451071i	$-0.148958\pi$
$920$		0			0
$921$	−0.151531	−	1.64456i	−0.00499311	−	0.0541902i
$922$	4.89419	+	18.2654i	0.161182	+	0.601538i
$923$	0.569930	+	2.12701i	0.0187595	+	0.0700113i
$924$	−9.75663	+	6.89898i	−0.320970	+	0.226960i
$925$		0			0
$926$		−	33.0197i		−	1.08510i
$927$	−5.30057	−	11.0985i	−0.174094	−	0.364524i
$928$	2.22474	+	2.22474i	0.0730308	+	0.0730308i
$929$	23.9309	+	41.4495i	0.785147	+	1.35991i	0.928912	+	0.370302i	$0.120746\pi$
$929$	23.9309	+	41.4495i	0.785147	+	1.35991i	−0.143765	+	0.989612i	$0.545921\pi$
$930$		0			0
$931$	−4.49490	+	7.78539i	−0.147314	+	0.255156i
$932$	15.0206	−	4.02477i	0.492017	−	0.131836i
$933$	33.4353	−	12.3445i	1.09462	−	0.404140i
$934$	−3.46410	+	2.00000i	−0.113349	+	0.0654420i
$935$		0			0
$936$	9.79796	+	3.46410i	0.320256	+	0.113228i
$937$	12.8990	−	12.8990i	0.421391	−	0.421391i	−0.464291	−	0.885683i	$-0.653691\pi$
$937$	12.8990	−	12.8990i	0.421391	−	0.421391i	0.885683	+	0.464291i	$0.153691\pi$
$938$	4.00514	+	1.07317i	0.130773	+	0.0350404i
$939$	−5.02118	−	7.10102i	−0.163860	−	0.231733i
$940$		0			0
$941$	5.47730	+	3.16232i	0.178555	+	0.103089i	0.586613	−	0.809867i	$-0.300461\pi$
$941$	5.47730	+	3.16232i	0.178555	+	0.103089i	−0.408059	+	0.912956i	$0.633794\pi$
$942$	−6.80895	+	8.19105i	−0.221847	+	0.266879i
$943$	−1.01581	+	3.79107i	−0.0330795	+	0.123454i
$944$	−11.8065			−0.384269
$945$		0			0
$946$	21.7980			0.708713
$947$	−10.6233	+	39.6468i	−0.345212	+	1.28835i	0.547152	+	0.837033i	$0.315712\pi$
$947$	−10.6233	+	39.6468i	−0.345212	+	1.28835i	−0.892364	+	0.451316i	$0.850955\pi$
$948$	2.71209	−	3.26260i	0.0880846	−	0.105964i
$949$	12.2993	+	7.10102i	0.399253	+	0.230509i
$950$		0			0
$951$	−1.10102	−	1.55708i	−0.0357030	−	0.0504917i
$952$	−4.71209	−	1.26260i	−0.152720	−	0.0409211i
$953$	−19.6561	+	19.6561i	−0.636724	+	0.636724i	−0.949746	−	0.313022i	$-0.898659\pi$
$953$	−19.6561	+	19.6561i	−0.636724	+	0.636724i	0.313022	+	0.949746i	$0.398659\pi$
$954$	−21.3167	+	18.2247i	−0.690155	+	0.590048i
$955$		0			0
$956$	−14.6969	+	8.48528i	−0.475333	+	0.274434i
$957$	−32.1686	+	11.8768i	−1.03986	+	0.383923i
$958$	−6.83013	+	1.83013i	−0.220671	+	0.0591287i
$959$	1.20713	−	2.09082i	0.0389804	−	0.0675159i
$960$		0			0
$961$	5.60102	+	9.70125i	0.180678	+	0.312944i
$962$	−10.3923	−	10.3923i	−0.335061	−	0.335061i
$963$	−8.91005	+	12.9782i	−0.287122	+	0.418215i
$964$			19.0000i			0.611949i
$965$		0			0
$966$	−1.55051	+	1.09638i	−0.0498868	+	0.0352753i
$967$	13.0577	+	48.7319i	0.419907	+	1.56711i	0.774800	+	0.632206i	$0.217850\pi$
$967$	13.0577	+	48.7319i	0.419907	+	1.56711i	−0.354894	+	0.934907i	$0.615483\pi$
$968$	−7.40117	−	27.6215i	−0.237883	−	0.887790i
$969$	−1.09638	−	11.8990i	−0.0352207	−	0.382250i
$970$		0			0
$971$		−	49.2117i		−	1.57928i	−0.613570	−	0.789640i	$-0.710267\pi$
$971$		−	49.2117i		−	1.57928i	0.613570	−	0.789640i	$-0.289733\pi$
$972$	−11.7071	+	10.2929i	−0.375506	+	0.330145i
$973$	10.0000	+	10.0000i	0.320585	+	0.320585i
$974$	8.48528	+	14.6969i	0.271886	+	0.470920i
$975$		0			0
$976$	−2.72474	+	4.71940i	−0.0872170	+	0.151064i
$977$	−41.0469	+	10.9985i	−1.31321	+	0.351873i	−0.846429	−	0.532502i	$-0.821252\pi$
$977$	−41.0469	+	10.9985i	−1.31321	+	0.351873i	−0.466778	+	0.884374i	$0.654585\pi$
$978$	0.186185	−	1.08516i	0.00595353	−	0.0346997i
$979$	12.9029	−	7.44949i	0.412378	−	0.238087i
$980$		0			0
$981$	60.0176	−	11.1548i	1.91621	−	0.356145i
$982$	−0.202041	+	0.202041i	−0.00644739	+	0.00644739i
$983$	−45.2034	−	12.1122i	−1.44176	−	0.386319i	−0.548612	−	0.836077i	$-0.684844\pi$
$983$	−45.2034	−	12.1122i	−1.44176	−	0.386319i	−0.893151	+	0.449757i	$0.851510\pi$
$984$	2.84448	−	6.17423i	0.0906787	−	0.196827i
$985$		0			0
$986$	−12.1237	−	6.99964i	−0.386098	−	0.222914i
$987$	−5.91945	−	16.0330i	−0.188418	−	0.510335i
$988$	1.39015	−	5.18811i	0.0442265	−	0.165056i
$989$	3.46410			0.110152
$990$		0			0
$991$	−56.7423			−1.80248			−0.901240	−	0.433320i	$-0.857342\pi$
$991$	−56.7423			−1.80248			−0.901240	+	0.433320i	$0.857342\pi$
$992$	−1.15161	+	4.29788i	−0.0365637	+	0.136458i
$993$	−7.59575	−	1.30323i	−0.241044	−	0.0413566i
$994$	0.603566	+	0.348469i	0.0191440	+	0.0110528i
$995$		0			0
$996$	0.949490	−	0.0874863i	0.0300857	−	0.00277211i
$997$	−39.9528	−	10.7053i	−1.26532	−	0.339041i	−0.437082	−	0.899422i	$-0.643988\pi$
$997$	−39.9528	−	10.7053i	−1.26532	−	0.339041i	−0.828235	+	0.560381i	$0.810655\pi$
$998$	6.29253	−	6.29253i	0.199187	−	0.199187i
$999$	21.2132	−	6.00000i	0.671156	−	0.189832i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	450.2.p.a.293.1		8
3.2	odd	2		1350.2.q.g.1043.2		8
5.2	odd	4	inner	450.2.p.a.257.1		8
5.3	odd	4		90.2.l.a.77.2	yes	8
5.4	even	2		90.2.l.a.23.2	✓	8
9.2	odd	6	inner	450.2.p.a.443.1		8
9.7	even	3		1350.2.q.g.143.2		8
15.2	even	4		1350.2.q.g.557.2		8
15.8	even	4		270.2.m.a.17.1		8
15.14	odd	2		270.2.m.a.233.1		8
20.3	even	4		720.2.cu.a.257.2		8
20.19	odd	2		720.2.cu.a.113.2		8
45.2	even	12	inner	450.2.p.a.407.1		8
45.4	even	6		810.2.f.b.323.3		8
45.7	odd	12		1350.2.q.g.1007.2		8
45.13	odd	12		810.2.f.b.647.1		8
45.14	odd	6		810.2.f.b.323.2		8
45.23	even	12		810.2.f.b.647.4		8
45.29	odd	6		90.2.l.a.83.2	yes	8
45.34	even	6		270.2.m.a.143.1		8
45.38	even	12		90.2.l.a.47.2	yes	8
45.43	odd	12		270.2.m.a.197.1		8
180.83	odd	12		720.2.cu.a.497.2		8
180.119	even	6		720.2.cu.a.353.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.l.a.23.2	✓	8	5.4	even	2
90.2.l.a.47.2	yes	8	45.38	even	12
90.2.l.a.77.2	yes	8	5.3	odd	4
90.2.l.a.83.2	yes	8	45.29	odd	6
270.2.m.a.17.1		8	15.8	even	4
270.2.m.a.143.1		8	45.34	even	6
270.2.m.a.197.1		8	45.43	odd	12
270.2.m.a.233.1		8	15.14	odd	2
450.2.p.a.257.1		8	5.2	odd	4	inner
450.2.p.a.293.1		8	1.1	even	1	trivial
450.2.p.a.407.1		8	45.2	even	12	inner
450.2.p.a.443.1		8	9.2	odd	6	inner
720.2.cu.a.113.2		8	20.19	odd	2
720.2.cu.a.257.2		8	20.3	even	4
720.2.cu.a.353.2		8	180.119	even	6
720.2.cu.a.497.2		8	180.83	odd	12
810.2.f.b.323.2		8	45.14	odd	6
810.2.f.b.323.3		8	45.4	even	6
810.2.f.b.647.1		8	45.13	odd	12
810.2.f.b.647.4		8	45.23	even	12
1350.2.q.g.143.2		8	9.7	even	3
1350.2.q.g.557.2		8	15.2	even	4
1350.2.q.g.1007.2		8	45.7	odd	12
1350.2.q.g.1043.2		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	450.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.10721 + 1.33195i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(1.05902 + 0.283763i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.548188 - 2.94949i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-1.10721 + 1.33195i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-1.00000 - 1.41421i) q^{6} +(1.05902 + 0.283763i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-0.548188 - 2.94949i) q^{9} +(-5.44949 + 3.14626i) q^{11} +(1.62484 - 0.599900i) q^{12} +(-3.34607 + 0.896575i) q^{13} +(-0.548188 + 0.949490i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-3.14626 - 3.14626i) q^{17} +(2.99087 + 0.233875i) q^{18} -1.55051i q^{19} +(-1.55051 + 1.09638i) q^{21} +(-1.62863 - 6.07812i) q^{22} +(-0.258819 - 0.965926i) q^{23} +(0.158919 + 1.72474i) q^{24} -3.46410i q^{26} +(4.53553 + 2.53553i) q^{27} +(-0.775255 - 0.775255i) q^{28} +(-1.57313 - 2.72474i) q^{29} +(2.22474 - 3.85337i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(1.84304 - 10.7420i) q^{33} +(3.85337 - 2.22474i) q^{34} +(-1.00000 + 2.82843i) q^{36} +(3.00000 - 3.00000i) q^{37} +(1.49768 + 0.401302i) q^{38} +(2.51059 - 5.44949i) q^{39} +(-3.39898 - 1.96240i) q^{41} +(-0.657717 - 1.78144i) q^{42} +(-0.896575 + 3.34607i) q^{43} +6.29253 q^{44} +1.00000 q^{46} +(-2.32937 + 8.69333i) q^{47} +(-1.70711 - 0.292893i) q^{48} +(-5.02118 - 2.89898i) q^{49} +(7.67423 - 0.707107i) q^{51} +(3.34607 + 0.896575i) q^{52} +(-6.61037 + 6.61037i) q^{53} +(-3.62302 + 3.72474i) q^{54} +(0.949490 - 0.548188i) q^{56} +(2.06520 + 1.71673i) q^{57} +(3.03906 - 0.814313i) q^{58} +(-5.90326 + 10.2247i) q^{59} +(2.72474 + 4.71940i) q^{61} +(3.14626 + 3.14626i) q^{62} +(0.256415 - 3.27912i) q^{63} -1.00000i q^{64} +(9.89898 + 4.56048i) q^{66} +(-0.978838 - 3.65307i) q^{67} +(1.15161 + 4.29788i) q^{68} +(1.57313 + 0.724745i) q^{69} -0.635674i q^{71} +(-2.47323 - 1.69798i) q^{72} +(-2.89898 - 2.89898i) q^{73} +(2.12132 + 3.67423i) q^{74} +(-0.775255 + 1.34278i) q^{76} +(-6.66390 + 1.78559i) q^{77} +(4.61401 + 3.83548i) q^{78} +(2.12132 - 1.22474i) q^{79} +(-8.39898 + 3.23375i) q^{81} +(2.77526 - 2.77526i) q^{82} +(0.531752 + 0.142483i) q^{83} +(1.89097 - 0.174235i) q^{84} +(-3.00000 - 1.73205i) q^{86} +(5.37101 + 0.921519i) q^{87} +(-1.62863 + 6.07812i) q^{88} -2.36773 q^{89} -3.79796 q^{91} +(-0.258819 + 0.965926i) q^{92} +(2.66925 + 7.22973i) q^{93} +(-7.79423 - 4.50000i) q^{94} +(0.724745 - 1.57313i) q^{96} +(-10.7902 - 2.89123i) q^{97} +(4.09978 - 4.09978i) q^{98} +(12.2672 + 14.3485i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7}+O(q^{10}) \) 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7	\( 8 q - 4 q^{3} - 8 q^{6} + 8 q^{7} - 24 q^{11} + 4 q^{12} + 4 q^{16} + 8 q^{18} - 32 q^{21} + 8 q^{22} + 8 q^{27} - 16 q^{28} + 8 q^{31} - 16 q^{33} - 8 q^{36} + 24 q^{37} - 12 q^{38} + 12 q^{41} - 20 q^{42} + 8 q^{46} - 8 q^{48} + 32 q^{51} - 12 q^{56} - 28 q^{57} + 4 q^{58} + 12 q^{61} + 32 q^{63} + 40 q^{66} - 4 q^{67} + 12 q^{68} - 8 q^{72} + 16 q^{73} - 16 q^{76} - 24 q^{77} + 24 q^{78} - 28 q^{81} + 32 q^{82} - 12 q^{83} - 24 q^{86} + 8 q^{87} + 8 q^{88} + 48 q^{91} + 20 q^{93} - 4 q^{96} - 12 q^{97}+O(q^{100}) \) 8 * q - 4 * q^3 - 8 * q^6 + 8 * q^7 - 24 * q^11 + 4 * q^12 + 4 * q^16 + 8 * q^18 - 32 * q^21 + 8 * q^22 + 8 * q^27 - 16 * q^28 + 8 * q^31 - 16 * q^33 - 8 * q^36 + 24 * q^37 - 12 * q^38 + 12 * q^41 - 20 * q^42 + 8 * q^46 - 8 * q^48 + 32 * q^51 - 12 * q^56 - 28 * q^57 + 4 * q^58 + 12 * q^61 + 32 * q^63 + 40 * q^66 - 4 * q^67 + 12 * q^68 - 8 * q^72 + 16 * q^73 - 16 * q^76 - 24 * q^77 + 24 * q^78 - 28 * q^81 + 32 * q^82 - 12 * q^83 - 24 * q^86 + 8 * q^87 + 8 * q^88 + 48 * q^91 + 20 * q^93 - 4 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

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