LMFDB - Embedded newform 539.2.f.d.344.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [539,2,Mod(148,539)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(539, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("539.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 539 = 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	539.f (of order $5$, 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:	$4.30393666895$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.159390625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 6x^{6} - 11x^{5} + 21x^{4} - 5x^{3} + 10x^{2} + 25x + 25 $ x^8 - x^7 + 6x^6 - 11x^5 + 21x^4 - 5x^3 + 10x^2 + 25x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			344.2
Root			$0.453245 - 1.39494i$ of defining polynomial
Character	$\chi$	$=$	539.344
Dual form			539.2.f.d.246.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.18661 - 0.862123i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(1.91998 + 1.39494i) q^{6} +(0.837913 + 2.57883i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})$	\(q+(1.18661 - 0.862123i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(1.91998 + 1.39494i) q^{6} +(0.837913 + 2.57883i) q^{8} +(0.309017 - 0.224514i) q^{9} +0.684570 q^{10} +(-2.22899 + 2.45593i) q^{11} +0.244812 q^{12} +(-1.28012 + 0.930062i) q^{13} +(-0.233366 + 0.718226i) q^{15} +(3.46236 + 2.51555i) q^{16} +(4.22899 + 3.07254i) q^{17} +(0.173124 - 0.532822i) q^{18} +(-1.30464 - 4.01528i) q^{19} +(0.0571308 - 0.0415079i) q^{20} +(-0.527635 + 4.83590i) q^{22} -1.80505 q^{23} +(-3.54946 + 2.57883i) q^{24} +(-1.47777 - 4.54811i) q^{25} +(-0.717177 + 2.20724i) q^{26} +(4.42705 + 3.21644i) q^{27} +(0.840363 - 2.58637i) q^{29} +(0.342285 + 1.05345i) q^{30} +(1.04675 - 0.760512i) q^{31} +0.854102 q^{32} +(-4.89378 - 2.20210i) q^{33} +7.66708 q^{34} +(-0.0178588 - 0.0549637i) q^{36} +(-0.600175 + 1.84715i) q^{37} +(-5.00978 - 3.63982i) q^{38} +(-2.07128 - 1.50487i) q^{39} +(-0.391081 + 1.20362i) q^{40} +(0.321724 + 0.990166i) q^{41} +8.70820 q^{43} +(0.249184 + 0.435572i) q^{44} +0.178276 q^{45} +(-2.14190 + 1.55618i) q^{46} +(1.97626 + 6.08229i) q^{47} +(-2.13986 + 6.58580i) q^{48} +(-5.67457 - 4.12281i) q^{50} +(-2.61366 + 8.04402i) q^{51} +(0.0739811 + 0.227690i) q^{52} +(10.6826 - 7.76137i) q^{53} +8.02616 q^{54} +(-1.51541 + 0.315846i) q^{55} +(5.52656 - 4.01528i) q^{57} +(-1.23259 - 3.79351i) q^{58} +(2.65875 - 8.18278i) q^{59} +(0.0924396 + 0.0671613i) q^{60} +(-12.3295 - 8.95793i) q^{61} +(0.586436 - 1.80486i) q^{62} +(-5.91123 + 4.29476i) q^{64} -0.738517 q^{65} +(-7.70550 + 1.60600i) q^{66} -4.67583 q^{67} +(0.639856 - 0.464883i) q^{68} +(-0.902527 - 2.77769i) q^{69} +(-7.88234 - 5.72685i) q^{71} +(0.837913 + 0.608780i) q^{72} +(4.11611 - 12.6681i) q^{73} +(0.880296 + 2.70927i) q^{74} +(6.25993 - 4.54811i) q^{75} -0.638786 q^{76} -3.75519 q^{78} +(-2.89815 + 2.10563i) q^{79} +(0.617255 + 1.89971i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(1.23541 + 0.897575i) q^{82} +(-13.9627 - 10.1445i) q^{83} +(0.753927 + 2.32035i) q^{85} +(10.3333 - 7.50755i) q^{86} +4.40020 q^{87} +(-8.20113 - 3.69034i) q^{88} +8.91982 q^{89} +(0.211544 - 0.153696i) q^{90} +(-0.0843952 + 0.259742i) q^{92} +(1.69369 + 1.23053i) q^{93} +(7.58873 + 5.51353i) q^{94} +(0.608919 - 1.87406i) q^{95} +(0.427051 + 1.31433i) q^{96} +(-2.18727 + 1.58915i) q^{97} +(-0.137407 + 1.25936i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9	$ 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9} + 28 q^{10} + 5 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{15} - 3 q^{16} + 11 q^{17} + 4 q^{18} + 9 q^{19} - 21 q^{20} - q^{22} - 16 q^{23} - 21 q^{24} + 5 q^{25} - 21 q^{26} + 22 q^{27} - 9 q^{29} + 14 q^{30} + 11 q^{31} - 20 q^{32} - 10 q^{33} + 24 q^{34} - 2 q^{36} + 6 q^{37} - 35 q^{38} - 5 q^{39} + 16 q^{40} + 22 q^{41} + 16 q^{43} + 29 q^{44} - 18 q^{45} + 29 q^{46} - 7 q^{47} - 4 q^{48} - 34 q^{50} + 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 26 q^{55} - 3 q^{57} - 39 q^{58} - 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + q^{64} + 24 q^{65} - 18 q^{66} - 30 q^{67} - 8 q^{68} - 8 q^{69} - 14 q^{71} + 3 q^{72} - 3 q^{73} - 9 q^{74} - 5 q^{75} + 52 q^{76} - 18 q^{78} - 9 q^{79} + 33 q^{80} - 28 q^{81} - 31 q^{82} - 23 q^{83} - 10 q^{85} - 17 q^{86} - 12 q^{87} - 7 q^{88} + 34 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 10 q^{96} - 30 q^{97}+O(q^{100}) $ 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9 + 28 * q^10 + 5 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^15 - 3 * q^16 + 11 * q^17 + 4 * q^18 + 9 * q^19 - 21 * q^20 - q^22 - 16 * q^23 - 21 * q^24 + 5 * q^25 - 21 * q^26 + 22 * q^27 - 9 * q^29 + 14 * q^30 + 11 * q^31 - 20 * q^32 - 10 * q^33 + 24 * q^34 - 2 * q^36 + 6 * q^37 - 35 * q^38 - 5 * q^39 + 16 * q^40 + 22 * q^41 + 16 * q^43 + 29 * q^44 - 18 * q^45 + 29 * q^46 - 7 * q^47 - 4 * q^48 - 34 * q^50 + 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 26 * q^55 - 3 * q^57 - 39 * q^58 - 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + q^64 + 24 * q^65 - 18 * q^66 - 30 * q^67 - 8 * q^68 - 8 * q^69 - 14 * q^71 + 3 * q^72 - 3 * q^73 - 9 * q^74 - 5 * q^75 + 52 * q^76 - 18 * q^78 - 9 * q^79 + 33 * q^80 - 28 * q^81 - 31 * q^82 - 23 * q^83 - 10 * q^85 - 17 * q^86 - 12 * q^87 - 7 * q^88 + 34 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 + 30 * q^94 + 24 * q^95 - 10 * q^96 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/539\mathbb{Z}\right)^\times$.

$n$	$199$	$442$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.18661	−	0.862123i	0.839061	−	0.609613i	−0.0830475	−	0.996546i	$-0.526465\pi$
$2$	1.18661	−	0.862123i	0.839061	−	0.609613i	0.922108	+	0.386932i	$0.126465\pi$
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	0.985273	+	0.170989i	$0.0546962\pi$
$3$	0.500000	+	1.53884i	0.288675	+	0.888451i	−0.696598	+	0.717462i	$0.745304\pi$
$4$	0.0467549	−	0.143897i	0.0233775	−	0.0719485i
$5$	0.377594	+	0.274338i	0.168865	+	0.122688i	0.669008	−	0.743255i	$-0.266719\pi$
$5$	0.377594	+	0.274338i	0.168865	+	0.122688i	−0.500143	+	0.865943i	$0.666719\pi$
$6$	1.91998	+	1.39494i	0.783827	+	0.569484i
$7$		0			0
$7$		0			0
$8$	0.837913	+	2.57883i	0.296247	+	0.911755i
$9$	0.309017	−	0.224514i	0.103006	−	0.0748380i
$10$	0.684570			0.216480
$11$	−2.22899	+	2.45593i	−0.672067	+	0.740490i
$11$	−2.22899	+	2.45593i	−0.672067	+	0.740490i
$12$	0.244812			0.0706712
$13$	−1.28012	+	0.930062i	−0.355042	+	0.257953i	−0.750981	−	0.660324i	$-0.770419\pi$
$13$	−1.28012	+	0.930062i	−0.355042	+	0.257953i	0.395939	+	0.918277i	$0.370419\pi$
$14$		0			0
$15$	−0.233366	+	0.718226i	−0.0602548	+	0.185445i
$16$	3.46236	+	2.51555i	0.865590	+	0.628888i
$17$	4.22899	+	3.07254i	1.02568	+	0.745201i	0.967440	−	0.253101i	$-0.0814505\pi$
$17$	4.22899	+	3.07254i	1.02568	+	0.745201i	0.0582418	+	0.998303i	$0.481451\pi$
$18$	0.173124	−	0.532822i	0.0408058	−	0.125587i
$19$	−1.30464	−	4.01528i	−0.299306	−	0.921169i	−0.981741	−	0.190223i	$-0.939079\pi$
$19$	−1.30464	−	4.01528i	−0.299306	−	0.921169i	0.682435	−	0.730946i	$-0.260921\pi$
$20$	0.0571308	−	0.0415079i	0.0127748	−	0.00928146i
$21$		0			0
$22$	−0.527635	+	4.83590i	−0.112492	+	1.03102i
$23$	−1.80505			−0.376380			−0.188190	−	0.982133i	$-0.560262\pi$
$23$	−1.80505			−0.376380			−0.188190	+	0.982133i	$0.560262\pi$
$24$	−3.54946	+	2.57883i	−0.724530	+	0.526402i
$25$	−1.47777	−	4.54811i	−0.295554	−	0.909621i
$26$	−0.717177	+	2.20724i	−0.140650	+	0.432876i
$27$	4.42705	+	3.21644i	0.851986	+	0.619004i
$28$		0			0
$29$	0.840363	−	2.58637i	0.156051	−	0.480277i	−0.842215	−	0.539143i	$-0.818748\pi$
$29$	0.840363	−	2.58637i	0.156051	−	0.480277i	0.998266	+	0.0588657i	$0.0187484\pi$
$30$	0.342285	+	1.05345i	0.0624924	+	0.192332i
$31$	1.04675	−	0.760512i	0.188003	−	0.136592i	−0.489803	−	0.871833i	$-0.662931\pi$
$31$	1.04675	−	0.760512i	0.188003	−	0.136592i	0.677805	+	0.735241i	$0.262931\pi$
$32$	0.854102			0.150985
$33$	−4.89378	−	2.20210i	−0.851898	−	0.383337i
$34$	7.66708			1.31489
$35$		0			0
$36$	−0.0178588	−	0.0549637i	−0.00297647	−	0.00916062i
$37$	−0.600175	+	1.84715i	−0.0986682	+	0.303669i	−0.988192	−	0.153219i	$-0.951036\pi$
$37$	−0.600175	+	1.84715i	−0.0986682	+	0.303669i	0.889524	+	0.456888i	$0.151036\pi$
$38$	−5.00978	−	3.63982i	−0.812693	−	0.590456i
$39$	−2.07128	−	1.50487i	−0.331670	−	0.240972i
$40$	−0.391081	+	1.20362i	−0.0618353	+	0.190309i
$41$	0.321724	+	0.990166i	0.0502449	+	0.154638i	0.973031	−	0.230675i	$-0.0740935\pi$
$41$	0.321724	+	0.990166i	0.0502449	+	0.154638i	−0.922786	+	0.385313i	$0.874093\pi$
$42$		0			0
$43$	8.70820			1.32799			0.663994	−	0.747738i	$-0.268860\pi$
$43$	8.70820			1.32799			0.663994	+	0.747738i	$0.268860\pi$
$44$	0.249184	+	0.435572i	0.0375659	+	0.0656650i
$45$	0.178276			0.0265758
$46$	−2.14190	+	1.55618i	−0.315805	+	0.229446i
$47$	1.97626	+	6.08229i	0.288266	+	0.887193i	0.985401	+	0.170252i	$0.0544582\pi$
$47$	1.97626	+	6.08229i	0.288266	+	0.887193i	−0.697134	+	0.716941i	$0.745542\pi$
$48$	−2.13986	+	6.58580i	−0.308862	+	0.950578i
$49$		0			0
$50$	−5.67457	−	4.12281i	−0.802505	−	0.583054i
$51$	−2.61366	+	8.04402i	−0.365986	+	1.12639i
$52$	0.0739811	+	0.227690i	0.0102593	+	0.0315750i
$53$	10.6826	−	7.76137i	1.46737	−	1.06611i	0.486004	−	0.873957i	$-0.338454\pi$
$53$	10.6826	−	7.76137i	1.46737	−	1.06611i	0.981366	−	0.192149i	$-0.0615458\pi$
$54$	8.02616			1.09222
$55$	−1.51541	+	0.315846i	−0.204338	+	0.0425887i
$56$		0			0
$57$	5.52656	−	4.01528i	0.732011	−	0.531837i
$58$	−1.23259	−	3.79351i	−0.161847	−	0.498112i
$59$	2.65875	−	8.18278i	0.346139	−	1.06531i	−0.614832	−	0.788658i	$-0.710776\pi$
$59$	2.65875	−	8.18278i	0.346139	−	1.06531i	0.960971	−	0.276649i	$-0.0892239\pi$
$60$	0.0924396	+	0.0671613i	0.0119339	+	0.00867048i
$61$	−12.3295	−	8.95793i	−1.57864	−	1.14695i	−0.918237	−	0.396031i	$-0.870387\pi$
$61$	−12.3295	−	8.95793i	−1.57864	−	1.14695i	−0.660399	−	0.750915i	$-0.729613\pi$
$62$	0.586436	−	1.80486i	0.0744774	−	0.229218i
$63$		0			0
$64$	−5.91123	+	4.29476i	−0.738904	+	0.536845i
$65$	−0.738517			−0.0916018
$66$	−7.70550	+	1.60600i	−0.948482	+	0.197685i
$67$	−4.67583			−0.571243			−0.285622	−	0.958342i	$-0.592200\pi$
$67$	−4.67583			−0.571243			−0.285622	+	0.958342i	$0.592200\pi$
$68$	0.639856	−	0.464883i	0.0775939	−	0.0563753i
$69$	−0.902527	−	2.77769i	−0.108651	−	0.334395i
$70$		0			0
$71$	−7.88234	−	5.72685i	−0.935461	−	0.679652i	0.0118626	−	0.999930i	$-0.496224\pi$
$71$	−7.88234	−	5.72685i	−0.935461	−	0.679652i	−0.947324	+	0.320277i	$0.896224\pi$
$72$	0.837913	+	0.608780i	0.0987490	+	0.0717454i
$73$	4.11611	−	12.6681i	0.481754	−	1.48269i	−0.354873	−	0.934915i	$-0.615476\pi$
$73$	4.11611	−	12.6681i	0.481754	−	1.48269i	0.836627	−	0.547773i	$-0.184524\pi$
$74$	0.880296	+	2.70927i	0.102332	+	0.314947i
$75$	6.25993	−	4.54811i	0.722835	−	0.525170i
$76$	−0.638786			−0.0732737
$77$		0			0
$78$	−3.75519			−0.425191
$79$	−2.89815	+	2.10563i	−0.326068	+	0.236902i	−0.738760	−	0.673968i	$-0.764588\pi$
$79$	−2.89815	+	2.10563i	−0.326068	+	0.236902i	0.412692	+	0.910870i	$0.364588\pi$
$80$	0.617255	+	1.89971i	0.0690112	+	0.212395i
$81$	−2.38197	+	7.33094i	−0.264663	+	0.814549i
$82$	1.23541	+	0.897575i	0.136428	+	0.0991206i
$83$	−13.9627	−	10.1445i	−1.53261	−	1.11351i	−0.954766	−	0.297357i	$-0.903895\pi$
$83$	−13.9627	−	10.1445i	−1.53261	−	1.11351i	−0.577842	−	0.816148i	$-0.696105\pi$
$84$		0			0
$85$	0.753927	+	2.32035i	0.0817748	+	0.251677i
$86$	10.3333	−	7.50755i	1.11426	−	0.809559i
$87$	4.40020			0.471750
$88$	−8.20113	−	3.69034i	−0.874243	−	0.393392i
$89$	8.91982			0.945499			0.472750	−	0.881197i	$-0.343262\pi$
$89$	8.91982			0.945499			0.472750	+	0.881197i	$0.343262\pi$
$90$	0.211544	−	0.153696i	0.0222987	−	0.0162009i
$91$		0			0
$92$	−0.0843952	+	0.259742i	−0.00879881	+	0.0270799i
$93$	1.69369	+	1.23053i	0.175627	+	0.127600i
$94$	7.58873	+	5.51353i	0.782718	+	0.568678i
$95$	0.608919	−	1.87406i	0.0624738	−	0.192275i
$96$	0.427051	+	1.31433i	0.0435857	+	0.134143i
$97$	−2.18727	+	1.58915i	−0.222084	+	0.161353i	−0.693264	−	0.720684i	$-0.743828\pi$
$97$	−2.18727	+	1.58915i	−0.222084	+	0.161353i	0.471180	+	0.882037i	$0.343828\pi$
$98$		0			0
$99$	−0.137407	+	1.25936i	−0.0138099	+	0.126571i
$100$	−0.723551			−0.0723551
$101$	0.144637	−	0.105085i	0.0143919	−	0.0104563i	−0.580566	−	0.814213i	$-0.697169\pi$
$101$	0.144637	−	0.105085i	0.0143919	−	0.0104563i	0.594958	+	0.803757i	$0.297169\pi$
$102$	3.83354	+	11.7984i	0.379577	+	1.16822i
$103$	−5.21535	+	16.0512i	−0.513884	+	1.58157i	0.271420	+	0.962461i	$0.412507\pi$
$103$	−5.21535	+	16.0512i	−0.513884	+	1.58157i	−0.785304	+	0.619111i	$0.787493\pi$
$104$	−3.47110	−	2.52190i	−0.340370	−	0.247293i
$105$		0			0
$106$	5.98484	−	18.4195i	0.581299	−	1.78906i
$107$	−4.78241	−	14.7188i	−0.462333	−	1.42292i	−0.862305	−	0.506389i	$-0.830980\pi$
$107$	−4.78241	−	14.7188i	−0.462333	−	1.42292i	0.399972	−	0.916527i	$-0.369020\pi$
$108$	0.669822	−	0.486655i	0.0644537	−	0.0468284i
$109$	11.0349			1.05695			0.528476	−	0.848948i	$-0.322764\pi$
$109$	11.0349			1.05695			0.528476	+	0.848948i	$0.322764\pi$
$110$	−1.52590	+	1.68126i	−0.145489	+	0.160301i
$111$	−3.14256			−0.298278
$112$		0			0
$113$	0.546984	+	1.68344i	0.0514559	+	0.158365i	0.973482	−	0.228762i	$-0.0734676\pi$
$113$	0.546984	+	1.68344i	0.0514559	+	0.158365i	−0.922027	+	0.387127i	$0.873468\pi$
$114$	3.09621	−	9.52916i	0.289987	−	0.892488i
$115$	−0.681577	−	0.495195i	−0.0635574	−	0.0461772i
$116$	−0.332880	−	0.241851i	−0.0309071	−	0.0224553i
$117$	−0.186767	+	0.574810i	−0.0172666	+	0.0531412i
$118$	−3.89967	−	12.0019i	−0.358994	−	1.10487i
$119$		0			0
$120$	−2.04773			−0.186931
$121$	−1.06317	−	10.9485i	−0.0966521	−	0.995318i
$122$	−22.3532			−2.02376
$123$	−1.36285	+	0.990166i	−0.122884	+	0.0892802i
$124$	−0.0604944	−	0.186183i	−0.00543255	−	0.0167197i
$125$	1.41086	−	4.34219i	0.126191	−	0.388377i
$126$		0			0
$127$	6.90919	+	5.01982i	0.613092	+	0.445437i	0.850502	−	0.525972i	$-0.176298\pi$
$127$	6.90919	+	5.01982i	0.613092	+	0.445437i	−0.237410	+	0.971410i	$0.576298\pi$
$128$	−3.83958	+	11.8170i	−0.339374	+	1.04449i
$129$	4.35410	+	13.4005i	0.383357	+	1.17985i
$130$	−0.876333	+	0.636693i	−0.0768595	+	0.0558417i
$131$	9.66708			0.844617			0.422308	−	0.906452i	$-0.361220\pi$
$131$	9.66708			0.844617			0.422308	+	0.906452i	$0.361220\pi$
$132$	−0.545685	+	0.601241i	−0.0474957	+	0.0523313i
$133$		0			0
$134$	−5.54839	+	4.03114i	−0.479308	+	0.348237i
$135$	0.789236	+	2.42902i	0.0679266	+	0.209057i
$136$	−4.38004	+	13.4804i	−0.375586	+	1.15593i
$137$	11.3350	+	8.23535i	0.968413	+	0.703593i	0.955089	−	0.296318i	$-0.0957589\pi$
$137$	11.3350	+	8.23535i	0.968413	+	0.703593i	0.0133236	+	0.999911i	$0.495759\pi$
$138$	−3.46566	−	2.51795i	−0.295017	−	0.214342i
$139$	−2.95966	+	9.10889i	−0.251035	+	0.772606i	0.743550	+	0.668680i	$0.233140\pi$
$139$	−2.95966	+	9.10889i	−0.251035	+	0.772606i	−0.994585	+	0.103926i	$0.966860\pi$
$140$		0			0
$141$	−8.37155	+	6.08229i	−0.705012	+	0.512221i
$142$	−14.2905			−1.19923
$143$	0.569215	−	5.21699i	0.0476001	−	0.436267i
$144$	1.63470			0.136225
$145$	1.02686	−	0.746054i	0.0852757	−	0.0619564i
$146$	−6.03723	−	18.5807i	−0.499645	−	1.53775i
$147$		0			0
$148$	0.237738	+	0.172727i	0.0195419	+	0.0141980i
$149$	−12.1049	−	8.79474i	−0.991674	−	0.720493i	−0.0313866	−	0.999507i	$-0.509992\pi$
$149$	−12.1049	−	8.79474i	−0.991674	−	0.720493i	−0.960287	+	0.279014i	$0.909992\pi$
$150$	3.50707	−	10.7937i	0.286351	−	0.881299i
$151$	−0.887599	−	2.73175i	−0.0722318	−	0.222307i	0.908423	−	0.418053i	$-0.137287\pi$
$151$	−0.887599	−	2.73175i	−0.0722318	−	0.222307i	−0.980655	+	0.195746i	$0.937287\pi$
$152$	9.26156	−	6.72892i	0.751212	−	0.545787i
$153$	1.99666			0.161420
$154$		0			0
$155$	0.603886			0.0485053
$156$	−0.313389	+	0.227690i	−0.0250912	+	0.0182298i
$157$	5.83496	+	17.9582i	0.465680	+	1.43322i	0.858125	+	0.513441i	$0.171630\pi$
$157$	5.83496	+	17.9582i	0.465680	+	1.43322i	−0.392444	+	0.919776i	$0.628370\pi$
$158$	−1.62367	+	4.99713i	−0.129172	+	0.397551i
$159$	17.2848	+	12.5582i	1.37078	+	0.995927i
$160$	0.322504	+	0.234313i	0.0254962	+	0.0185240i
$161$		0			0
$162$	3.49371	+	10.7525i	0.274491	+	0.844798i
$163$	−9.38067	+	6.81545i	−0.734751	+	0.533827i	−0.891063	−	0.453880i	$-0.850039\pi$
$163$	−9.38067	+	6.81545i	−0.734751	+	0.533827i	0.156312	+	0.987708i	$0.450039\pi$
$164$	0.157524			0.0123006
$165$	−1.24374	−	2.17405i	−0.0968252	−	0.169250i
$166$	−25.3142			−1.96476
$167$	5.11696	−	3.71769i	0.395963	−	0.287684i	−0.371932	−	0.928260i	$-0.621305\pi$
$167$	5.11696	−	3.71769i	0.395963	−	0.287684i	0.767894	+	0.640576i	$0.221305\pi$
$168$		0			0
$169$	−3.24353	+	9.98255i	−0.249502	+	0.767889i
$170$	2.89504	+	2.10337i	0.222040	+	0.161321i
$171$	−1.30464	−	0.947880i	−0.0997687	−	0.0724862i
$172$	0.407152	−	1.25308i	0.0310450	−	0.0955467i
$173$	−0.413793	−	1.27352i	−0.0314601	−	0.0968243i	0.934093	−	0.357029i	$-0.116210\pi$
$173$	−0.413793	−	1.27352i	−0.0314601	−	0.0968243i	−0.965554	+	0.260204i	$0.916210\pi$
$174$	5.22132	−	3.79351i	0.395827	−	0.287585i
$175$		0			0
$176$	−13.8956	+	2.89616i	−1.04742	+	0.218306i
$177$	13.9214			1.04639
$178$	10.5844	−	7.68999i	0.793331	−	0.576389i
$179$	5.49705	+	16.9182i	0.410868	+	1.26452i	0.915895	+	0.401419i	$0.131483\pi$
$179$	5.49705	+	16.9182i	0.410868	+	1.26452i	−0.505026	+	0.863104i	$0.668517\pi$
$180$	0.00833527	−	0.0256533i	0.000621274	−	0.00191209i
$181$	−0.779712	−	0.566494i	−0.0579555	−	0.0421072i	0.558430	−	0.829551i	$-0.311404\pi$
$181$	−0.779712	−	0.566494i	−0.0579555	−	0.0421072i	−0.616386	+	0.787444i	$0.711404\pi$
$182$		0			0
$183$	7.62007	−	23.4522i	0.563292	−	1.73363i
$184$	−1.51248	−	4.65493i	−0.111501	−	0.343166i
$185$	−0.733366	+	0.532822i	−0.0539181	+	0.0391738i
$186$	3.07062			0.225149
$187$	−16.9724	+	3.53743i	−1.24114	+	0.258682i
$188$	0.967622			0.0705711
$189$		0			0
$190$	−0.893121	−	2.74874i	−0.0647938	−	0.199415i
$191$	−4.97173	+	15.3014i	−0.359742	+	1.10717i	0.593467	+	0.804858i	$0.297759\pi$
$191$	−4.97173	+	15.3014i	−0.359742	+	1.10717i	−0.953209	+	0.302313i	$0.902241\pi$
$192$	−9.56458	−	6.94907i	−0.690264	−	0.501506i
$193$	−9.82750	−	7.14010i	−0.707399	−	0.513955i	0.174935	−	0.984580i	$-0.444029\pi$
$193$	−9.82750	−	7.14010i	−0.707399	−	0.513955i	−0.882333	+	0.470625i	$0.844029\pi$
$194$	−1.22540	+	3.77140i	−0.0879787	+	0.270771i
$195$	−0.369259	−	1.13646i	−0.0264432	−	0.0813837i
$196$		0			0
$197$	−2.30179			−0.163996			−0.0819978	−	0.996633i	$-0.526130\pi$
$197$	−2.30179			−0.163996			−0.0819978	+	0.996633i	$0.526130\pi$
$198$	0.922679	+	1.61284i	0.0655719	+	0.114619i
$199$	−20.2797			−1.43759			−0.718795	−	0.695222i	$-0.755306\pi$
$199$	−20.2797			−1.43759			−0.718795	+	0.695222i	$0.755306\pi$
$200$	10.4906	−	7.62184i	0.741794	−	0.538945i
$201$	−2.33791	−	7.19536i	−0.164904	−	0.507521i
$202$	0.0810316	−	0.249390i	0.00570136	−	0.0175470i
$203$		0			0
$204$	1.03531	+	0.752196i	0.0724861	+	0.0526642i
$205$	−0.150159	+	0.462142i	−0.0104876	+	0.0322774i
$206$	7.64952	+	23.5428i	0.532967	+	1.64030i
$207$	−0.557792	+	0.405260i	−0.0387692	+	0.0281675i
$208$	−6.77186			−0.469544
$209$	12.7693	+	5.74593i	0.883271	+	0.397454i
$210$		0			0
$211$	−4.34062	+	3.15364i	−0.298820	+	0.217106i	−0.727085	−	0.686548i	$-0.759125\pi$
$211$	−4.34062	+	3.15364i	−0.298820	+	0.217106i	0.428264	+	0.903654i	$0.359125\pi$
$212$	−0.617372	−	1.90008i	−0.0424013	−	0.130498i
$213$	4.87155	−	14.9931i	0.333793	−	1.02731i
$214$	−18.3642	−	13.3424i	−1.25535	−	0.912068i
$215$	3.28817	+	2.38899i	0.224251	+	0.162928i
$216$	−4.58517	+	14.1117i	−0.311982	+	0.960181i
$217$		0			0
$218$	13.0941	−	9.51344i	0.886847	−	0.644332i
$219$	21.5522			1.45637
$220$	−0.0254036	+	0.232830i	−0.00171271	+	0.0156974i
$221$	−8.27128			−0.556387
$222$	−3.72899	+	2.70927i	−0.250274	+	0.181834i
$223$	7.85614	+	24.1787i	0.526086	+	1.61913i	0.762158	+	0.647391i	$0.224140\pi$
$223$	7.85614	+	24.1787i	0.526086	+	1.61913i	−0.236072	+	0.971736i	$0.575860\pi$
$224$		0			0
$225$	−1.47777	−	1.07366i	−0.0985179	−	0.0715775i
$226$	2.10039	+	1.52602i	0.139716	+	0.101510i
$227$	6.70869	−	20.6472i	0.445271	−	1.37040i	−0.436915	−	0.899503i	$-0.643929\pi$
$227$	6.70869	−	20.6472i	0.445271	−	1.37040i	0.882186	−	0.470901i	$-0.156071\pi$
$228$	−0.319393	−	0.982990i	−0.0211523	−	0.0651001i
$229$	16.6097	−	12.0676i	1.09760	−	0.797451i	0.116931	−	0.993140i	$-0.462694\pi$
$229$	16.6097	−	12.0676i	1.09760	−	0.797451i	0.980666	+	0.195689i	$0.0626943\pi$
$230$	−1.23569			−0.0814787
$231$		0			0
$232$	7.37396			0.484124
$233$	−0.561503	+	0.407956i	−0.0367853	+	0.0267261i	−0.606026	−	0.795445i	$-0.707237\pi$
$233$	−0.561503	+	0.407956i	−0.0367853	+	0.0267261i	0.569241	+	0.822171i	$0.307237\pi$
$234$	0.273937	+	0.843092i	0.0179078	+	0.0551147i
$235$	−0.922381	+	2.83880i	−0.0601695	+	0.185183i
$236$	−1.05317	−	0.765171i	−0.0685554	−	0.0498084i
$237$	−4.68931	−	3.40699i	−0.304604	−	0.221307i
$238$		0			0
$239$	0.107093	+	0.329599i	0.00692728	+	0.0213200i	0.954460	−	0.298338i	$-0.0964321\pi$
$239$	0.107093	+	0.329599i	0.00692728	+	0.0213200i	−0.947533	+	0.319658i	$0.896432\pi$
$240$	−2.61473	+	1.89971i	−0.168780	+	0.122626i
$241$	10.4372			0.672317			0.336158	−	0.941806i	$-0.390872\pi$
$241$	10.4372			0.672317			0.336158	+	0.941806i	$0.390872\pi$
$242$	−10.7005	−	12.0750i	−0.687856	−	0.776212i
$243$	3.94427			0.253025
$244$	−1.86549	+	1.35536i	−0.119426	+	0.0867677i
$245$		0			0
$246$	−0.763523	+	2.34988i	−0.0486805	+	0.149823i
$247$	5.40457	+	3.92665i	0.343884	+	0.249847i
$248$	2.83832	+	2.06216i	0.180234	+	0.130947i
$249$	8.62944	−	26.5587i	0.546869	−	1.68309i
$250$	−2.06936	−	6.36882i	−0.130878	−	0.402800i
$251$	−5.65909	+	4.11157i	−0.357199	+	0.259520i	−0.751883	−	0.659297i	$-0.770854\pi$
$251$	−5.65909	+	4.11157i	−0.357199	+	0.259520i	0.394684	+	0.918817i	$0.370854\pi$
$252$		0			0
$253$	4.02345	−	4.43308i	0.252952	−	0.278706i
$254$	12.5262			0.785965
$255$	−3.19369	+	2.32035i	−0.199996	+	0.145306i
$256$	1.11586	+	3.43426i	0.0697412	+	0.214641i
$257$	3.07423	−	9.46152i	0.191765	−	0.590193i	−0.808234	−	0.588862i	$-0.799576\pi$
$257$	3.07423	−	9.46152i	0.191765	−	0.590193i	0.999999	−	0.00133144i	$-0.000423809\pi$
$258$	16.7196	+	12.1475i	1.04091	+	0.756268i
$259$		0			0
$260$	−0.0345293	+	0.106270i	−0.00214142	+	0.00659061i
$261$	−0.320990	−	0.987905i	−0.0198688	−	0.0611498i
$262$	11.4711	−	8.33422i	0.708685	−	0.514890i
$263$	14.1803			0.874397			0.437199	−	0.899365i	$-0.355971\pi$
$263$	14.1803			0.874397			0.437199	+	0.899365i	$0.355971\pi$
$264$	1.57829	−	14.4654i	0.0971371	−	0.890285i
$265$	6.16293			0.378586
$266$		0			0
$267$	4.45991	+	13.7262i	0.272942	+	0.840029i
$268$	−0.218618	+	0.672837i	−0.0133542	+	0.0411001i
$269$	−14.8884	−	10.8171i	−0.907762	−	0.659528i	0.0326859	−	0.999466i	$-0.489594\pi$
$269$	−14.8884	−	10.8171i	−0.907762	−	0.659528i	−0.940448	+	0.339938i	$0.889594\pi$
$270$	3.03063	+	2.20188i	0.184438	+	0.134002i
$271$	−0.225765	+	0.694833i	−0.0137142	+	0.0422081i	−0.957679	−	0.287837i	$-0.907064\pi$
$271$	−0.225765	+	0.694833i	−0.0137142	+	0.0422081i	0.943965	+	0.330045i	$0.107064\pi$
$272$	6.91316	+	21.2765i	0.419172	+	1.29008i
$273$		0			0
$274$	20.5501			1.24148
$275$	14.4638	+	6.50840i	0.872198	+	0.392472i
$276$	−0.441899			−0.0265992
$277$	−12.1874	+	8.85463i	−0.732267	+	0.532023i	−0.890280	−	0.455414i	$-0.849491\pi$
$277$	−12.1874	+	8.85463i	−0.732267	+	0.532023i	0.158013	+	0.987437i	$0.449491\pi$
$278$	4.34102	+	13.3603i	0.260357	+	0.801297i
$279$	0.152719	−	0.470022i	0.00914308	−	0.0281395i
$280$		0			0
$281$	8.65334	+	6.28702i	0.516215	+	0.375052i	0.815176	−	0.579213i	$-0.196640\pi$
$281$	8.65334	+	6.28702i	0.516215	+	0.375052i	−0.298961	+	0.954265i	$0.596640\pi$
$282$	−4.69009	+	14.4346i	−0.279291	+	0.859569i
$283$	−2.81481	−	8.66308i	−0.167323	−	0.514967i	0.831877	−	0.554960i	$-0.187266\pi$
$283$	−2.81481	−	8.66308i	−0.167323	−	0.514967i	−0.999200	+	0.0399931i	$0.987266\pi$
$284$	−1.19261	+	0.866485i	−0.0707687	+	0.0514164i
$285$	3.18834			0.188861
$286$	−3.82225	−	6.68127i	−0.226014	−	0.395072i
$287$		0			0
$288$	0.263932	−	0.191758i	0.0155523	−	0.0112994i
$289$	3.19057	+	9.81958i	0.187681	+	0.577622i
$290$	0.575287	−	1.77055i	0.0337820	−	0.103970i
$291$	−3.53908	−	2.57129i	−0.207465	−	0.150732i
$292$	−1.63045	−	1.18459i	−0.0954149	−	0.0693230i
$293$	−3.67390	+	11.3071i	−0.214632	+	0.660569i	0.784548	+	0.620068i	$0.212895\pi$
$293$	−3.67390	+	11.3071i	−0.214632	+	0.660569i	−0.999180	+	0.0405002i	$0.987105\pi$
$294$		0			0
$295$	3.24878	−	2.36037i	0.189151	−	0.137426i
$296$	−5.26638			−0.306102
$297$	−17.7672	+	3.70310i	−1.03096	+	0.214875i
$298$	−21.9460			−1.27130
$299$	2.31069	−	1.67881i	0.133630	−	0.0970882i
$300$	−0.361776	−	1.11343i	−0.0208871	−	0.0642840i
$301$		0			0
$302$	−3.40834	−	2.47630i	−0.196128	−	0.142495i
$303$	0.234027	+	0.170031i	0.0134445	+	0.00976802i
$304$	5.58350	−	17.1843i	0.320236	−	0.985585i
$305$	−2.19806	−	6.76492i	−0.125860	−	0.387358i
$306$	2.36926	−	1.72137i	0.135442	−	0.0984040i
$307$	−2.22072			−0.126743			−0.0633716	−	0.997990i	$-0.520185\pi$
$307$	−2.22072			−0.126743			−0.0633716	+	0.997990i	$0.520185\pi$
$308$		0			0
$309$	−27.3079			−1.55349
$310$	0.716577	−	0.520624i	0.0406989	−	0.0295695i
$311$	6.61685	+	20.3646i	0.375207	+	1.15477i	0.943339	+	0.331831i	$0.107666\pi$
$311$	6.61685	+	20.3646i	0.375207	+	1.15477i	−0.568132	+	0.822937i	$0.692334\pi$
$312$	2.14526	−	6.60243i	0.121451	−	0.373789i
$313$	−25.5283	−	18.5474i	−1.44295	−	1.04836i	−0.987416	−	0.158142i	$-0.949450\pi$
$313$	−25.5283	−	18.5474i	−1.44295	−	1.04836i	−0.455531	−	0.890220i	$-0.650550\pi$
$314$	22.4060	+	16.2789i	1.26444	+	0.918671i
$315$		0			0
$316$	0.167491	+	0.515484i	0.00942211	+	0.0289983i
$317$	10.6796	−	7.75915i	0.599824	−	0.435798i	−0.245992	−	0.969272i	$-0.579114\pi$
$317$	10.6796	−	7.75915i	0.599824	−	0.435798i	0.845816	+	0.533474i	$0.179114\pi$
$318$	31.3370			1.75729
$319$	4.47878	+	7.82887i	0.250763	+	0.438333i
$320$	−3.41026			−0.190639
$321$	20.2586	−	14.7188i	1.13073	−	0.821521i
$322$		0			0
$323$	6.81980	−	20.9892i	0.379464	−	1.16787i
$324$	0.943531	+	0.685515i	0.0524184	+	0.0380842i
$325$	6.12174	+	4.44771i	0.339573	+	0.246714i
$326$	−5.25544	+	16.1746i	−0.291072	+	0.895827i
$327$	5.51745	+	16.9810i	0.305116	+	0.939050i
$328$	−2.28389	+	1.65935i	−0.126107	+	0.0916220i
$329$		0			0
$330$	−3.35014	−	1.50750i	−0.184419	−	0.0829849i
$331$	9.47653			0.520877			0.260439	−	0.965490i	$-0.416133\pi$
$331$	9.47653			0.520877			0.260439	+	0.965490i	$0.416133\pi$
$332$	−2.11259	+	1.53489i	−0.115944	+	0.0842379i
$333$	0.229247	+	0.705548i	0.0125626	+	0.0386638i
$334$	2.86674	−	8.82291i	0.156861	−	0.482768i
$335$	−1.76556	−	1.28276i	−0.0964631	−	0.0700845i
$336$		0			0
$337$	−5.93346	+	18.2613i	−0.323216	+	0.994758i	0.649023	+	0.760769i	$0.275178\pi$
$337$	−5.93346	+	18.2613i	−0.323216	+	0.994758i	−0.972239	+	0.233989i	$0.924822\pi$
$338$	4.75738	+	14.6417i	0.258768	+	0.796405i
$339$	−2.31706	+	1.68344i	−0.125845	+	0.0914321i
$340$	0.369141			0.0200195
$341$	−0.465447	+	4.26593i	−0.0252054	+	0.231013i
$342$	−2.36530			−0.127901
$343$		0			0
$344$	7.29672	+	22.4570i	0.393413	+	1.21080i
$345$	0.421238	−	1.29644i	0.0226787	−	0.0697978i
$346$	−1.58895	−	1.15444i	−0.0854223	−	0.0620629i
$347$	−2.46613	−	1.79175i	−0.132389	−	0.0961862i	0.519620	−	0.854397i	$-0.326074\pi$
$347$	−2.46613	−	1.79175i	−0.132389	−	0.0961862i	−0.652009	+	0.758211i	$0.726074\pi$
$348$	0.205731	−	0.633175i	0.0110283	−	0.0339417i
$349$	−5.99373	−	18.4468i	−0.320837	−	0.987435i	−0.973285	−	0.229601i	$-0.926258\pi$
$349$	−5.99373	−	18.4468i	−0.320837	−	0.987435i	0.652448	−	0.757834i	$-0.273742\pi$
$350$		0			0
$351$	−8.65865			−0.462165
$352$	−1.90379	+	2.09761i	−0.101472	+	0.111803i
$353$	10.7585			0.572619			0.286309	−	0.958137i	$-0.407572\pi$
$353$	10.7585			0.572619			0.286309	+	0.958137i	$0.407572\pi$
$354$	16.5193	−	12.0019i	0.877989	−	0.637896i
$355$	−1.40523	−	4.32485i	−0.0745818	−	0.229539i
$356$	0.417046	−	1.28353i	0.0221034	−	0.0680272i
$357$		0			0
$358$	21.1084	+	15.3361i	1.11561	+	0.810541i
$359$	0.187643	−	0.577506i	0.00990342	−	0.0304796i	−0.945983	−	0.324217i	$-0.894899\pi$
$359$	0.187643	−	0.577506i	0.00990342	−	0.0304796i	0.955886	+	0.293738i	$0.0948992\pi$
$360$	0.149380	+	0.459743i	0.00787299	+	0.0242306i
$361$	0.950914	−	0.690879i	0.0500481	−	0.0363621i
$362$	−1.41360			−0.0742973
$363$	16.3164	−	7.11030i	0.856390	−	0.373194i
$364$		0			0
$365$	5.02956	−	3.65419i	0.263259	−	0.191269i
$366$	−11.1766	−	34.3981i	−0.584211	−	1.79802i
$367$	−8.54829	+	26.3089i	−0.446217	+	1.37332i	0.434926	+	0.900466i	$0.356774\pi$
$367$	−8.54829	+	26.3089i	−0.446217	+	1.37332i	−0.881143	+	0.472849i	$0.843226\pi$
$368$	−6.24975	−	4.54071i	−0.325791	−	0.236701i
$369$	0.321724	+	0.233746i	0.0167483	+	0.0121684i
$370$	−0.410862	+	1.26450i	−0.0213597	+	0.0657384i
$371$		0			0
$372$	0.256258	−	0.186183i	0.0132864	−	0.00965311i
$373$	−29.4513			−1.52493			−0.762465	−	0.647029i	$-0.776011\pi$
$373$	−29.4513			−1.52493			−0.762465	+	0.647029i	$0.776011\pi$
$374$	−17.0899	+	18.8298i	−0.883697	+	0.973666i
$375$	7.38737			0.381482
$376$	−14.0293	+	10.1929i	−0.723504	+	0.525657i
$377$	1.32972	+	4.09246i	0.0684840	+	0.210772i
$378$		0			0
$379$	−20.5034	−	14.8966i	−1.05319	−	0.765188i	−0.0803745	−	0.996765i	$-0.525612\pi$
$379$	−20.5034	−	14.8966i	−1.05319	−	0.765188i	−0.972817	+	0.231577i	$0.925612\pi$
$380$	−0.241202	−	0.175243i	−0.0123734	−	0.00898979i
$381$	−4.27012	+	13.1421i	−0.218765	+	0.673288i
$382$	7.29219	+	22.4431i	0.373101	+	1.14829i
$383$	−25.8337	+	18.7693i	−1.32004	+	0.959065i	−0.320108	+	0.947381i	$0.603719\pi$
$383$	−25.8337	+	18.7693i	−1.32004	+	0.959065i	−0.999932	+	0.0116837i	$0.996281\pi$
$384$	−20.1043			−1.02594
$385$		0			0
$386$	−17.8171			−0.906865
$387$	2.69098	−	1.95511i	0.136790	−	0.0993840i
$388$	0.126407	+	0.389042i	0.00641737	+	0.0197506i
$389$	5.48558	−	16.8829i	0.278130	−	0.855996i	−0.710244	−	0.703955i	$-0.751416\pi$
$389$	5.48558	−	16.8829i	0.278130	−	0.855996i	0.988374	−	0.152040i	$-0.0485844\pi$
$390$	−1.41794	−	1.03019i	−0.0718000	−	0.0521657i
$391$	−7.63356	−	5.54611i	−0.386046	−	0.280479i
$392$		0			0
$393$	4.83354	+	14.8761i	0.243820	+	0.750400i
$394$	−2.73133	+	1.98442i	−0.137602	+	0.0999738i
$395$	−1.67198			−0.0841265
$396$	0.174794	+	0.0786539i	0.00878374	+	0.00395251i
$397$	13.3047			0.667742			0.333871	−	0.942619i	$-0.391645\pi$
$397$	13.3047			0.667742			0.333871	+	0.942619i	$0.391645\pi$
$398$	−24.0641	+	17.4836i	−1.20623	+	0.876374i
$399$		0			0
$400$	6.32443	−	19.4646i	0.316221	−	0.973229i
$401$	2.82317	+	2.05115i	0.140982	+	0.102430i	0.656041	−	0.754725i	$-0.272230\pi$
$401$	2.82317	+	2.05115i	0.140982	+	0.102430i	−0.515059	+	0.857155i	$0.672230\pi$
$402$	−8.97748	−	6.52252i	−0.447756	−	0.325314i
$403$	−0.632649	+	1.94709i	−0.0315145	+	0.0969917i
$404$	−0.00835890	−	0.0257260i	−0.000415871	−	0.00127992i
$405$	−2.91057	+	2.11465i	−0.144627	+	0.105078i
$406$		0			0
$407$	−3.19868	−	5.59127i	−0.158553	−	0.277149i
$408$	−22.9342			−1.13541
$409$	−23.9675	+	17.4134i	−1.18512	+	0.861039i	−0.992740	−	0.120282i	$-0.961620\pi$
$409$	−23.9675	+	17.4134i	−1.18512	+	0.861039i	−0.192379	+	0.981321i	$0.561620\pi$
$410$	0.220243	+	0.677838i	0.0108770	+	0.0334760i
$411$	−7.00540	+	21.5604i	−0.345551	+	1.06350i
$412$	2.06587	+	1.50095i	0.101778	+	0.0739463i
$413$		0			0
$414$	−0.312499	+	0.961771i	−0.0153585	+	0.0472685i
$415$	−2.48922	−	7.66102i	−0.122191	−	0.376065i
$416$	−1.09335	+	0.794368i	−0.0536061	+	0.0389471i
$417$	−15.4970			−0.758890
$418$	20.1059	−	4.19053i	0.983411	−	0.204965i
$419$	11.6452			0.568907			0.284454	−	0.958690i	$-0.408188\pi$
$419$	11.6452			0.568907			0.284454	+	0.958690i	$0.408188\pi$
$420$		0			0
$421$	6.14475	+	18.9116i	0.299477	+	0.921696i	0.981681	+	0.190533i	$0.0610217\pi$
$421$	6.14475	+	18.9116i	0.299477	+	0.921696i	−0.682204	+	0.731162i	$0.738978\pi$
$422$	−2.43179	+	7.48429i	−0.118378	+	0.364330i
$423$	1.97626	+	1.43583i	0.0960888	+	0.0698126i
$424$	28.9664	+	21.0453i	1.40673	+	1.02205i
$425$	7.72478	−	23.7744i	0.374707	−	1.15323i
$426$	−7.14526	−	21.9908i	−0.346189	−	1.06546i
$427$		0			0
$428$	−2.34159			−0.113185
$429$	8.31273	−	1.73256i	0.401342	−	0.0836489i
$430$	5.96138			0.287483
$431$	−24.4698	+	17.7784i	−1.17867	+	0.856354i	−0.992021	−	0.126073i	$-0.959763\pi$
$431$	−24.4698	+	17.7784i	−1.17867	+	0.856354i	−0.186649	+	0.982427i	$0.559763\pi$
$432$	7.23692	+	22.2730i	0.348186	+	1.07161i
$433$	1.76362	−	5.42786i	0.0847542	−	0.260846i	−0.899694	−	0.436521i	$-0.856211\pi$
$433$	1.76362	−	5.42786i	0.0847542	−	0.260846i	0.984448	+	0.175674i	$0.0562106\pi$
$434$		0			0
$435$	1.66149	+	1.20714i	0.0796622	+	0.0578780i
$436$	0.515936	−	1.58789i	0.0247089	−	0.0760461i
$437$	2.35495	+	7.24780i	0.112653	+	0.346709i
$438$	25.5741	−	18.5807i	1.22198	−	0.887820i
$439$	−6.84875			−0.326873			−0.163436	−	0.986554i	$-0.552258\pi$
$439$	−6.84875			−0.326873			−0.163436	+	0.986554i	$0.552258\pi$
$440$	−2.08430	−	3.64333i	−0.0993649	−	0.173689i
$441$		0			0
$442$	−9.81479	+	7.13086i	−0.466842	+	0.339181i
$443$	0.0311165	+	0.0957668i	0.00147839	+	0.00455002i	0.951793	−	0.306741i	$-0.0992386\pi$
$443$	0.0311165	+	0.0957668i	0.00147839	+	0.00455002i	−0.950315	+	0.311291i	$0.899239\pi$
$444$	−0.146930	+	0.452204i	−0.00697300	+	0.0214607i
$445$	3.36807	+	2.44705i	0.159662	+	0.116001i
$446$	30.1672	+	21.9178i	1.42846	+	1.03784i
$447$	7.48125	−	23.0249i	0.353851	−	1.08904i
$448$		0			0
$449$	24.9216	−	18.1066i	1.17612	−	0.854502i	0.184392	−	0.982853i	$-0.440968\pi$
$449$	24.9216	−	18.1066i	1.17612	−	0.854502i	0.991729	+	0.128351i	$0.0409683\pi$
$450$	−2.67917			−0.126297
$451$	−3.14890	−	1.41694i	−0.148276	−	0.0667211i
$452$	0.267817			0.0125970
$453$	3.75993	−	2.73175i	0.176657	−	0.128349i
$454$	−9.83984	−	30.2839i	−0.461807	−	1.42129i
$455$		0			0
$456$	14.9855	+	10.8876i	0.701761	+	0.509859i
$457$	−18.7171	−	13.5987i	−0.875547	−	0.636122i	0.0565223	−	0.998401i	$-0.481999\pi$
$457$	−18.7171	−	13.5987i	−0.875547	−	0.636122i	−0.932070	+	0.362279i	$0.881999\pi$
$458$	9.30542	−	28.6392i	0.434814	−	1.33822i
$459$	8.83932	+	27.2046i	0.412584	+	1.26980i
$460$	−0.103124	+	0.0749241i	−0.00480819	+	0.00349335i
$461$	2.77839			0.129403			0.0647013	−	0.997905i	$-0.479391\pi$
$461$	2.77839			0.129403			0.0647013	+	0.997905i	$0.479391\pi$
$462$		0			0
$463$	−26.0950			−1.21274			−0.606369	−	0.795184i	$-0.707374\pi$
$463$	−26.0950			−1.21274			−0.606369	+	0.795184i	$0.707374\pi$
$464$	9.41578	−	6.84097i	0.437117	−	0.317584i
$465$	0.301943	+	0.929285i	0.0140023	+	0.0430945i
$466$	−0.314577	+	0.968169i	−0.0145725	+	0.0448496i
$467$	−2.15060	−	1.56250i	−0.0995180	−	0.0723041i	0.536913	−	0.843637i	$-0.319590\pi$
$467$	−2.15060	−	1.56250i	−0.0995180	−	0.0723041i	−0.636431	+	0.771333i	$0.719590\pi$
$468$	0.0739811	+	0.0537504i	0.00341978	+	0.00248461i
$469$		0			0
$470$	1.35289	+	4.16375i	0.0624040	+	0.192060i
$471$	−24.7173	+	17.9582i	−1.13891	+	0.827468i
$472$	23.3298			1.07384
$473$	−19.4105	+	21.3867i	−0.892497	+	0.983363i
$474$	−8.50163			−0.390493
$475$	−16.3340	+	11.8673i	−0.749454	+	0.544510i
$476$		0			0
$477$	1.55857	−	4.79679i	0.0713621	−	0.219630i
$478$	0.411233	+	0.298778i	0.0188093	+	0.0136658i
$479$	−6.70047	−	4.86818i	−0.306152	−	0.222433i	0.424091	−	0.905619i	$-0.360593\pi$
$479$	−6.70047	−	4.86818i	−0.306152	−	0.222433i	−0.730244	+	0.683187i	$0.760593\pi$
$480$	−0.199318	+	0.613439i	−0.00909759	+	0.0279995i
$481$	−0.949667	−	2.92277i	−0.0433011	−	0.133267i
$482$	12.3848	−	8.99812i	0.564114	−	0.409853i
$483$		0			0
$484$	−1.62516	−	0.358909i	−0.0738711	−	0.0163141i
$485$	−1.26186			−0.0572983
$486$	4.68032	−	3.40045i	0.212303	−	0.154247i
$487$	−6.05536	−	18.6365i	−0.274395	−	0.844500i	−0.989379	−	0.145360i	$-0.953566\pi$
$487$	−6.05536	−	18.6365i	−0.274395	−	0.844500i	0.714984	−	0.699141i	$-0.246434\pi$
$488$	12.7699	−	39.3018i	0.578067	−	1.77911i
$489$	−15.1782	−	11.0276i	−0.686384	−	0.498687i
$490$		0			0
$491$	−8.86312	+	27.2779i	−0.399987	+	1.23103i	0.525022	+	0.851089i	$0.324057\pi$
$491$	−8.86312	+	27.2779i	−0.399987	+	1.23103i	−0.925009	+	0.379945i	$0.875943\pi$
$492$	0.0787620	+	0.242405i	0.00355087	+	0.0109284i
$493$	11.5006	−	8.35569i	0.517962	−	0.376321i
$494$	9.79837			0.440850
$495$	−0.397375	+	0.437832i	−0.0178607	+	0.0196791i
$496$	5.53735			0.248634
$497$		0			0
$498$	−12.6571	−	38.9545i	−0.567177	−	1.74559i
$499$	8.63700	−	26.5819i	0.386645	−	1.18997i	−0.548635	−	0.836062i	$-0.684852\pi$
$499$	8.63700	−	26.5819i	0.386645	−	1.18997i	0.935280	−	0.353909i	$-0.115148\pi$
$500$	−0.558863	−	0.406037i	−0.0249931	−	0.0181585i
$501$	8.27942	+	6.01535i	0.369897	+	0.268746i
$502$	−3.17046	+	9.75767i	−0.141505	+	0.435506i
$503$	2.50222	+	7.70104i	0.111568	+	0.343373i	0.991216	−	0.132254i	$-0.0422214\pi$
$503$	2.50222	+	7.70104i	0.111568	+	0.343373i	−0.879647	+	0.475626i	$0.842221\pi$
$504$		0			0
$505$	0.0834428			0.00371316
$506$	0.952410	−	8.72906i	0.0423398	−	0.388054i
$507$	−16.9833			−0.754256
$508$	1.04538	−	0.759510i	0.0463811	−	0.0336978i
$509$	−5.03702	−	15.5024i	−0.223262	−	0.687130i	−0.998463	−	0.0554159i	$-0.982352\pi$
$509$	−5.03702	−	15.5024i	−0.223262	−	0.687130i	0.775201	−	0.631714i	$-0.217648\pi$
$510$	−1.78924	+	5.50670i	−0.0792287	+	0.243841i
$511$		0			0
$512$	−15.8195	−	11.4935i	−0.699129	−	0.507947i
$513$	7.13919	−	21.9722i	0.315203	−	0.970096i
$514$	−4.50908	−	13.8775i	−0.198887	−	0.612111i
$515$	−6.37274	+	4.63007i	−0.280816	+	0.204025i
$516$	2.13187			0.0938505
$517$	−19.3427	−	8.70384i	−0.850692	−	0.382795i
$518$		0			0
$519$	1.75286	−	1.27352i	0.0769419	−	0.0559015i
$520$	−0.618813	−	1.90451i	−0.0271368	−	0.0835184i
$521$	−2.37512	+	7.30987i	−0.104056	+	0.320251i	−0.989508	−	0.144480i	$-0.953849\pi$
$521$	−2.37512	+	7.30987i	−0.104056	+	0.320251i	0.885452	+	0.464731i	$0.153849\pi$
$522$	−1.23259	−	0.895526i	−0.0539488	−	0.0391961i
$523$	21.1339	+	15.3547i	0.924121	+	0.671413i	0.944546	−	0.328378i	$-0.106502\pi$
$523$	21.1339	+	15.3547i	0.924121	+	0.671413i	−0.0204256	+	0.999791i	$0.506502\pi$
$524$	0.451984	−	1.39106i	0.0197450	−	0.0607689i
$525$		0			0
$526$	16.8265	−	12.2252i	0.733672	−	0.533044i
$527$	6.76343			0.294619
$528$	−11.4045	−	19.9350i	−0.496318	−	0.867561i
$529$	−19.7418			−0.858338
$530$	7.31300	−	5.31320i	0.317656	−	0.230791i
$531$	−1.01555	−	3.12554i	−0.0440712	−	0.135637i
$532$		0			0
$533$	−1.33276	−	0.968308i	−0.0577283	−	0.0419421i
$534$	17.1258	+	12.4427i	0.741108	+	0.538446i
$535$	2.23210	−	6.86971i	0.0965023	−	0.297004i
$536$	−3.91794	−	12.0582i	−0.169229	−	0.520834i
$537$	−23.2859	+	16.9182i	−1.00486	+	0.730073i
$538$	−26.9924			−1.16372
$539$		0			0
$540$	0.386429			0.0166292
$541$	20.9355	−	15.2105i	0.900086	−	0.653951i	−0.0384021	−	0.999262i	$-0.512227\pi$
$541$	20.9355	−	15.2105i	0.900086	−	0.653951i	0.938488	+	0.345312i	$0.112227\pi$
$542$	0.331137	+	1.01913i	0.0142235	+	0.0437756i
$543$	0.481889	−	1.48310i	0.0206798	−	0.0636459i
$544$	3.61199	+	2.62427i	0.154863	+	0.112514i
$545$	4.16671	+	3.02729i	0.178482	+	0.129675i
$546$		0			0
$547$	−11.7726	−	36.2322i	−0.503359	−	1.54918i	−0.803513	−	0.595288i	$-0.797038\pi$
$547$	−11.7726	−	36.2322i	−0.503359	−	1.54918i	0.300154	−	0.953891i	$-0.402962\pi$
$548$	1.71501	−	1.24603i	0.0732615	−	0.0532276i
$549$	−5.82122			−0.248444
$550$	22.7739	−	4.74660i	0.971083	−	0.202396i
$551$	−11.4814			−0.489123
$552$	6.40696	−	4.65493i	0.272698	−	0.198127i
$553$		0			0
$554$	−6.82786	+	21.0140i	−0.290088	+	0.892799i
$555$	−1.18661	−	0.862123i	−0.0503688	−	0.0365951i
$556$	1.17236	+	0.851771i	0.0497192	+	0.0361231i
$557$	10.6741	−	32.8516i	0.452277	−	1.39197i	−0.422026	−	0.906584i	$-0.638681\pi$
$557$	10.6741	−	32.8516i	0.452277	−	1.39197i	0.874303	−	0.485381i	$-0.161319\pi$
$558$	−0.223999	−	0.689397i	−0.00948261	−	0.0291845i
$559$	−11.1476	+	8.09917i	−0.471491	+	0.342558i
$560$		0			0
$561$	−13.9297	−	24.3490i	−0.588113	−	1.02802i
$562$	15.6883			0.661773
$563$	15.7612	−	11.4512i	0.664256	−	0.482610i	−0.203842	−	0.979004i	$-0.565343\pi$
$563$	15.7612	−	11.4512i	0.664256	−	0.482610i	0.868098	+	0.496394i	$0.165343\pi$
$564$	0.483811	+	1.48902i	0.0203721	+	0.0626990i
$565$	−0.255295	+	0.785717i	−0.0107403	+	0.0330553i
$566$	−10.8087	−	7.85300i	−0.454325	−	0.330086i
$567$		0			0
$568$	8.16387	−	25.1258i	0.342549	−	1.05426i
$569$	5.29308	+	16.2904i	0.221897	+	0.682930i	0.998592	+	0.0530524i	$0.0168950\pi$
$569$	5.29308	+	16.2904i	0.221897	+	0.682930i	−0.776694	+	0.629878i	$0.783105\pi$
$570$	3.78332	−	2.74874i	0.158466	−	0.115132i
$571$	−3.85581			−0.161360			−0.0806802	−	0.996740i	$-0.525709\pi$
$571$	−3.85581			−0.161360			−0.0806802	+	0.996740i	$0.525709\pi$
$572$	−0.724095	−	0.325828i	−0.0302759	−	0.0136236i
$573$	−26.0323			−1.08751
$574$		0			0
$575$	2.66745	+	8.20958i	0.111240	+	0.342363i
$576$	−0.862437	+	2.65431i	−0.0359349	+	0.110596i
$577$	−7.91368	−	5.74963i	−0.329451	−	0.239360i	0.410747	−	0.911750i	$-0.365268\pi$
$577$	−7.91368	−	5.74963i	−0.329451	−	0.239360i	−0.740198	+	0.672389i	$0.765268\pi$
$578$	12.2517	+	8.90135i	0.509602	+	0.370247i
$579$	6.07373	−	18.6930i	0.252416	−	0.776855i
$580$	−0.0593443	−	0.182643i	−0.00246414	−	0.00758384i
$581$		0			0
$582$	−6.41628			−0.265964
$583$	−4.75010	+	43.5358i	−0.196729	+	1.80307i
$584$	36.1178			1.49457
$585$	−0.228214	+	0.165807i	−0.00943551	+	0.00685530i
$586$	5.38863	+	16.5845i	0.222602	+	0.685099i
$587$	1.88467	−	5.80041i	0.0777886	−	0.239409i	−0.904599	−	0.426264i	$-0.859830\pi$
$587$	1.88467	−	5.80041i	0.0777886	−	0.239409i	0.982387	+	0.186855i	$0.0598295\pi$
$588$		0			0
$589$	−4.41932	−	3.21082i	−0.182095	−	0.132300i
$590$	1.82010	−	5.60169i	0.0749323	−	0.230618i
$591$	−1.15089	−	3.54209i	−0.0473414	−	0.145702i
$592$	−6.72462	+	4.88572i	−0.276380	+	0.200802i
$593$	−13.2330			−0.543413			−0.271706	−	0.962380i	$-0.587588\pi$
$593$	−13.2330			−0.543413			−0.271706	+	0.962380i	$0.587588\pi$
$594$	−17.8903	+	19.7117i	−0.734046	+	0.808780i
$595$		0			0
$596$	−1.83150	+	1.33066i	−0.0750212	+	0.0545061i
$597$	−10.1399	−	31.2073i	−0.414997	−	1.27723i
$598$	1.29454	−	3.98419i	0.0529378	−	0.162926i
$599$	4.79355	+	3.48271i	0.195859	+	0.142300i	0.681393	−	0.731918i	$-0.261375\pi$
$599$	4.79355	+	3.48271i	0.195859	+	0.142300i	−0.485534	+	0.874218i	$0.661375\pi$
$600$	16.9741	+	12.3324i	0.692964	+	0.503468i
$601$	−3.93712	+	12.1172i	−0.160599	+	0.494272i	−0.998685	−	0.0512657i	$-0.983674\pi$
$601$	−3.93712	+	12.1172i	−0.160599	+	0.494272i	0.838086	+	0.545538i	$0.183674\pi$
$602$		0			0
$603$	−1.44491	+	1.04979i	−0.0588413	+	0.0427507i
$604$	−0.434590			−0.0176832
$605$	2.60214	−	4.42576i	0.105792	−	0.179933i
$606$	0.424287			0.0172355
$607$	6.76452	−	4.91471i	0.274563	−	0.199482i	−0.441979	−	0.897025i	$-0.645724\pi$
$607$	6.76452	−	4.91471i	0.274563	−	0.199482i	0.716543	+	0.697543i	$0.245724\pi$
$608$	−1.11430	−	3.42946i	−0.0451908	−	0.139083i
$609$		0			0
$610$	−8.44044	−	6.13234i	−0.341743	−	0.248291i
$611$	−8.18675	−	5.94802i	−0.331201	−	0.240631i
$612$	0.0933537	−	0.287313i	0.00377360	−	0.0116139i
$613$	−2.06514	−	6.35585i	−0.0834102	−	0.256710i	0.900650	−	0.434545i	$-0.143091\pi$
$613$	−2.06514	−	6.35585i	−0.0834102	−	0.256710i	−0.984060	+	0.177835i	$0.943091\pi$
$614$	−2.63513	+	1.91453i	−0.106345	+	0.0772643i
$615$	−0.786243			−0.0317044
$616$		0			0
$617$	11.8669			0.477741			0.238871	−	0.971051i	$-0.423223\pi$
$617$	11.8669			0.477741			0.238871	+	0.971051i	$0.423223\pi$
$618$	−32.4039	+	23.5428i	−1.30348	+	0.947031i
$619$	−6.37213	−	19.6114i	−0.256118	−	0.788249i	−0.993607	−	0.112891i	$-0.963989\pi$
$619$	−6.37213	−	19.6114i	−0.256118	−	0.788249i	0.737490	−	0.675358i	$-0.236011\pi$
$620$	0.0282346	−	0.0868973i	0.00113393	−	0.00348988i
$621$	−7.99107	−	5.80585i	−0.320670	−	0.232981i
$622$	25.4084	+	18.4603i	1.01878	+	0.740189i
$623$		0			0
$624$	−3.38593	−	10.4208i	−0.135546	−	0.417167i
$625$	−17.6203	+	12.8019i	−0.704812	+	0.512076i
$626$	−46.2824			−1.84982
$627$	−2.45743	+	22.5229i	−0.0981402	+	0.899478i
$628$	2.85694			0.114004
$629$	−8.21358	+	5.96752i	−0.327497	+	0.237941i
$630$		0			0
$631$	−4.78342	+	14.7219i	−0.190425	+	0.586068i	−1.00000		0.000949112i	$-0.999698\pi$
$631$	−4.78342	+	14.7219i	−0.190425	+	0.586068i	0.809575	+	0.587017i	$0.199698\pi$
$632$	−7.85847	−	5.70952i	−0.312593	−	0.227112i
$633$	−7.02326	−	5.10270i	−0.279150	−	0.202814i
$634$	5.98314	−	18.4142i	0.237621	−	0.731321i
$635$	1.23174	+	3.79091i	0.0488801	+	0.150438i
$636$	2.61523	−	1.90008i	0.103701	−	0.0753430i
$637$		0			0
$638$	12.0640	+	5.42857i	0.477619	+	0.214919i
$639$	−3.72153			−0.147222
$640$	−4.69166	+	3.40869i	−0.185454	+	0.134740i
$641$	−7.28615	−	22.4245i	−0.287786	−	0.885713i	−0.985550	−	0.169385i	$-0.945822\pi$
$641$	−7.28615	−	22.4245i	−0.287786	−	0.885713i	0.697764	−	0.716327i	$-0.254178\pi$
$642$	11.3497	−	34.9309i	0.447938	−	1.37861i
$643$	23.2031	+	16.8581i	0.915042	+	0.664817i	0.942285	−	0.334812i	$-0.108673\pi$
$643$	23.2031	+	16.8581i	0.915042	+	0.664817i	−0.0272428	+	0.999629i	$0.508673\pi$
$644$		0			0
$645$	−2.03220	+	6.25446i	−0.0800177	+	0.246269i
$646$	−10.0028	−	30.7855i	−0.393556	−	1.21124i
$647$	4.39104	−	3.19028i	0.172630	−	0.125423i	−0.498115	−	0.867111i	$-0.665974\pi$
$647$	4.39104	−	3.19028i	0.172630	−	0.125423i	0.670745	+	0.741688i	$0.265974\pi$
$648$	−20.9011			−0.821074
$649$	14.1700	+	24.7691i	0.556221	+	0.972271i
$650$	11.0986			0.435323
$651$		0			0
$652$	0.542130	+	1.66851i	0.0212315	+	0.0653437i
$653$	−3.81392	+	11.7380i	−0.149250	+	0.459344i	−0.997533	−	0.0701988i	$-0.977637\pi$
$653$	−3.81392	+	11.7380i	−0.149250	+	0.459344i	0.848283	+	0.529543i	$0.177637\pi$
$654$	21.1868	+	15.3931i	0.828468	+	0.601917i
$655$	3.65023	+	2.65205i	0.142626	+	0.103624i
$656$	−1.37689	+	4.23762i	−0.0537584	+	0.165451i
$657$	−1.57221	−	4.83878i	−0.0613379	−	0.188779i
$658$		0			0
$659$	16.2115			0.631512			0.315756	−	0.948840i	$-0.397742\pi$
$659$	16.2115			0.631512			0.315756	+	0.948840i	$0.397742\pi$
$660$	−0.370991	+	0.0773229i	−0.0144408	+	0.00300979i
$661$	−43.7050			−1.69993			−0.849964	−	0.526840i	$-0.823377\pi$
$661$	−43.7050			−1.69993			−0.849964	+	0.526840i	$0.823377\pi$
$662$	11.2450	−	8.16994i	0.437048	−	0.317534i
$663$	−4.13564	−	12.7282i	−0.160615	−	0.494322i
$664$	14.4614	−	44.5078i	0.561213	−	1.72724i
$665$		0			0
$666$	0.880296	+	0.639573i	0.0341108	+	0.0247829i
$667$	−1.51690	+	4.66854i	−0.0587346	+	0.180766i
$668$	−0.295721	−	0.910136i	−0.0114418	−	0.0352142i
$669$	−33.2792	+	24.1787i	−1.28665	+	0.934803i
$670$	−3.20093			−0.123663
$671$	49.4825	−	10.3133i	1.91025	−	0.398140i
$672$		0			0
$673$	4.74166	−	3.44502i	0.182778	−	0.132796i	−0.492634	−	0.870237i	$-0.663966\pi$
$673$	4.74166	−	3.44502i	0.182778	−	0.132796i	0.675412	+	0.737441i	$0.263966\pi$
$674$	8.70280	+	26.7845i	0.335219	+	1.03170i
$675$	8.08655	−	24.8879i	0.311252	−	0.957934i
$676$	1.28481	+	0.933467i	0.0494157	+	0.0359026i
$677$	−16.6074	−	12.0660i	−0.638275	−	0.463734i	0.220982	−	0.975278i	$-0.429074\pi$
$677$	−16.6074	−	12.0660i	−0.638275	−	0.463734i	−0.859257	+	0.511544i	$0.829074\pi$
$678$	−1.29811	+	3.99519i	−0.0498538	+	0.153434i
$679$		0			0
$680$	−5.35206	+	3.88850i	−0.205242	+	0.149117i
$681$	35.1271			1.34607
$682$	3.12546	+	5.46327i	0.119680	+	0.209200i
$683$	38.7055			1.48103			0.740513	−	0.672042i	$-0.234583\pi$
$683$	38.7055			1.48103			0.740513	+	0.672042i	$0.234583\pi$
$684$	−0.197396	+	0.143416i	−0.00754761	+	0.00548366i
$685$	2.02075	+	6.21923i	0.0772090	+	0.237625i
$686$		0			0
$687$	26.8750	+	19.5258i	1.02535	+	0.744957i
$688$	30.1509	+	21.9059i	1.14949	+	0.835156i
$689$	−6.45647	+	19.8710i	−0.245972	+	0.757024i
$690$	−0.617843	−	1.90153i	−0.0235209	−	0.0723898i
$691$	−18.7126	+	13.5955i	−0.711860	+	0.517197i	−0.883773	−	0.467916i	$-0.845005\pi$
$691$	−18.7126	+	13.5955i	−0.711860	+	0.517197i	0.171913	+	0.985112i	$0.445005\pi$
$692$	−0.202603			−0.00770182
$693$		0			0
$694$	−4.47105			−0.169719
$695$	−3.61646	+	2.62751i	−0.137180	+	0.0996673i
$696$	3.68698	+	11.3474i	0.139755	+	0.430121i
$697$	−1.68176	+	5.17592i	−0.0637011	+	0.196052i
$698$	−23.0156	−	16.7218i	−0.871155	−	0.632931i
$699$	−0.908531	−	0.660086i	−0.0343638	−	0.0249668i
$700$		0			0
$701$	10.9734	+	33.7727i	0.414460	+	1.27558i	0.912733	+	0.408557i	$0.133968\pi$
$701$	10.9734	+	33.7727i	0.414460	+	1.27558i	−0.498273	+	0.867020i	$0.666032\pi$
$702$	−10.2744	+	7.46482i	−0.387784	+	0.281742i
$703$	8.19985			0.309263
$704$	2.62847	−	24.0906i	0.0990643	−	0.907947i
$705$	−4.82965			−0.181895
$706$	12.7662	−	9.27518i	0.480462	−	0.349076i
$707$		0			0
$708$	0.650893	−	2.00324i	0.0244621	−	0.0752865i
$709$	−35.4386	−	25.7476i	−1.33092	−	0.966972i	−0.999726	−	0.0234107i	$-0.992547\pi$
$709$	−35.4386	−	25.7476i	−1.33092	−	0.966972i	−0.331197	−	0.943562i	$-0.607453\pi$
$710$	−5.39601	−	3.92043i	−0.202509	−	0.147131i
$711$	−0.422835	+	1.30135i	−0.0158576	+	0.0488045i
$712$	7.47403	+	23.0027i	0.280101	+	0.862063i
$713$	−1.88945	+	1.37277i	−0.0707604	+	0.0514105i
$714$		0			0
$715$	1.64615	−	1.81375i	0.0615625	−	0.0678303i
$716$	2.69149			0.100586
$717$	−0.453654	+	0.329599i	−0.0169420	+	0.0123091i
$718$	−0.275222	−	0.847046i	−0.0102712	−	0.0316115i
$719$	−4.90115	+	15.0842i	−0.182782	+	0.562546i	−0.999903	−	0.0139205i	$-0.995569\pi$
$719$	−4.90115	+	15.0842i	−0.182782	+	0.562546i	0.817121	+	0.576466i	$0.195569\pi$
$720$	0.617255	+	0.448462i	0.0230037	+	0.0167132i
$721$		0			0
$722$	0.532741	−	1.63961i	0.0198266	−	0.0610199i
$723$	5.21858	+	16.0611i	0.194081	+	0.597320i
$724$	−0.117972	+	0.0857118i	−0.00438440	+	0.00318545i
$725$	−13.0049			−0.482992
$726$	13.2313	−	22.5039i	0.491059	−	0.835199i
$727$	−13.7719			−0.510770			−0.255385	−	0.966839i	$-0.582202\pi$
$727$	−13.7719			−0.510770			−0.255385	+	0.966839i	$0.582202\pi$
$728$		0			0
$729$	9.11803	+	28.0624i	0.337705	+	1.03935i
$730$	2.81777	−	8.67220i	0.104290	−	0.320972i
$731$	36.8269	+	26.7563i	1.36209	+	0.989619i
$732$	−3.01842	−	2.19301i	−0.111564	−	0.0810560i
$733$	6.04675	−	18.6100i	0.223342	−	0.687376i	−0.775114	−	0.631822i	$-0.782307\pi$
$733$	6.04675	−	18.6100i	0.223342	−	0.687376i	0.998456	−	0.0555542i	$-0.0176926\pi$
$734$	12.5380	+	38.5881i	0.462788	+	1.42431i
$735$		0			0
$736$	−1.54170			−0.0568278
$737$	10.4224	−	11.4835i	0.383914	−	0.423000i
$738$	0.583280			0.0214708
$739$	9.02392	−	6.55626i	0.331950	−	0.241176i	−0.409307	−	0.912397i	$-0.634230\pi$
$739$	9.02392	−	6.55626i	0.331950	−	0.241176i	0.741258	+	0.671220i	$0.234230\pi$
$740$	0.0423829	+	0.130441i	0.00155803	+	0.00479511i
$741$	−3.34021	+	10.2801i	−0.122706	+	0.377649i
$742$		0			0
$743$	−16.7102	−	12.1407i	−0.613038	−	0.445398i	0.237445	−	0.971401i	$-0.423690\pi$
$743$	−16.7102	−	12.1407i	−0.613038	−	0.445398i	−0.850483	+	0.526003i	$0.823690\pi$
$744$	−1.75418	+	5.39881i	−0.0643113	+	0.197930i
$745$	−2.15801	−	6.64168i	−0.0790635	−	0.243332i
$746$	−34.9472	+	25.3907i	−1.27951	+	0.929618i
$747$	−6.59231			−0.241200
$748$	−0.284517	+	2.60766i	−0.0104030	+	0.0953455i
$749$		0			0
$750$	8.76593	−	6.36882i	0.320087	−	0.232557i
$751$	8.21957	+	25.2972i	0.299936	+	0.923109i	0.981518	+	0.191367i	$0.0612922\pi$
$751$	8.21957	+	25.2972i	0.299936	+	0.923109i	−0.681582	+	0.731742i	$0.738708\pi$
$752$	−8.45780	+	26.0304i	−0.308424	+	0.949233i
$753$	−9.15661	−	6.65266i	−0.333685	−	0.242437i
$754$	5.10606	+	3.70977i	0.185952	+	0.135102i
$755$	0.414271	−	1.27499i	0.0150769	−	0.0464018i
$756$		0			0
$757$	−17.0702	+	12.4022i	−0.620427	+	0.450767i	−0.853071	−	0.521796i	$-0.825262\pi$
$757$	−17.0702	+	12.4022i	−0.620427	+	0.450767i	0.232644	+	0.972562i	$0.425262\pi$
$758$	−37.1723			−1.35016
$759$	8.83354	+	3.97492i	0.320637	+	0.144280i
$760$	5.34311			0.193815
$761$	−6.47006	+	4.70077i	−0.234539	+	0.170403i	−0.698847	−	0.715271i	$-0.746303\pi$
$761$	−6.47006	+	4.70077i	−0.234539	+	0.170403i	0.464308	+	0.885674i	$0.346303\pi$
$762$	6.26311	+	19.2759i	0.226889	+	0.698292i
$763$		0			0
$764$	1.96937	+	1.43083i	0.0712494	+	0.0517657i
$765$	0.753927	+	0.547760i	0.0272583	+	0.0198043i
$766$	−14.4731	+	44.5436i	−0.522935	+	1.60943i
$767$	4.20698	+	12.9477i	0.151905	+	0.467516i
$768$	−4.72685	+	3.43426i	−0.170566	+	0.123923i
$769$	52.0476			1.87689			0.938443	−	0.345435i	$-0.112269\pi$
$769$	52.0476			1.87689			0.938443	+	0.345435i	$0.112269\pi$
$770$		0			0
$771$	16.0969			0.579716
$772$	−1.48692	+	1.08031i	−0.0535155	+	0.0388813i
$773$	0.488554	+	1.50361i	0.0175721	+	0.0540812i	0.959458	−	0.281851i	$-0.0909485\pi$
$773$	0.488554	+	1.50361i	0.0175721	+	0.0540812i	−0.941886	+	0.335933i	$0.890949\pi$
$774$	1.50760	−	4.63992i	0.0541896	−	0.166778i
$775$	−5.00575	−	3.63689i	−0.179812	−	0.130641i
$776$	−5.93089	−	4.30904i	−0.212906	−	0.154686i
$777$		0			0
$778$	−8.04587	−	24.7626i	−0.288458	−	0.887784i
$779$	3.55606	−	2.58363i	0.127409	−	0.0925681i
$780$	−0.180798			−0.00647361
$781$	31.6344	−	6.59334i	1.13197	−	0.235928i
$782$	−13.8395			−0.494899
$783$	12.0392	−	8.74702i	0.430247	−	0.312593i
$784$		0			0
$785$	−2.72336	+	8.38164i	−0.0972009	+	0.299154i
$786$	18.5606	+	13.4850i	0.662034	+	0.480996i
$787$	18.9235	+	13.7487i	0.674549	+	0.490089i	0.871545	−	0.490316i	$-0.163118\pi$
$787$	18.9235	+	13.7487i	0.674549	+	0.490089i	−0.196996	+	0.980404i	$0.563118\pi$
$788$	−0.107620	+	0.331220i	−0.00383380	+	0.0117992i
$789$	7.09017	+	21.8213i	0.252417	+	0.776859i
$790$	−1.98399	+	1.44145i	−0.0705872	+	0.0512846i
$791$		0			0
$792$	−3.36282	+	0.700889i	−0.119493	+	0.0249050i
$793$	24.1147			0.856339
$794$	15.7875	−	11.4703i	0.560276	−	0.407064i
$795$	3.08146	+	9.48377i	0.109288	+	0.336355i
$796$	−0.948177	+	2.91819i	−0.0336072	+	0.103432i
$797$	−37.3376	−	27.1274i	−1.32257	−	0.960900i	−0.999896	−	0.0143887i	$-0.995420\pi$
$797$	−37.3376	−	27.1274i	−1.32257	−	0.960900i	−0.322669	−	0.946512i	$-0.604580\pi$
$798$		0			0
$799$	−10.3305	+	31.7941i	−0.365468	+	1.12479i
$800$	−1.26217	−	3.88455i	−0.0446243	−	0.137339i
$801$	2.75638	−	2.00262i	0.0973918	−	0.0707593i
$802$	5.11834			0.180735
$803$	21.9371	+	38.3460i	0.774145	+	1.35320i
$804$	−1.14470			−0.0403704
$805$		0			0
$806$	0.927927	+	2.85587i	0.0326848	+	0.100594i
$807$	9.20154	−	28.3194i	0.323910	−	0.996891i
$808$	0.392189	+	0.284942i	0.0137972	+	0.0100242i
$809$	−27.3044	−	19.8378i	−0.959972	−	0.697461i	−0.00682787	−	0.999977i	$-0.502173\pi$
$809$	−27.3044	−	19.8378i	−0.959972	−	0.697461i	−0.953144	+	0.302516i	$0.902173\pi$
$810$	−1.63062	+	5.01854i	−0.0572943	+	0.176334i
$811$	9.50690	+	29.2592i	0.333833	+	1.02743i	0.967294	+	0.253657i	$0.0816334\pi$
$811$	9.50690	+	29.2592i	0.333833	+	1.02743i	−0.633462	+	0.773774i	$0.718367\pi$
$812$		0			0
$813$	−1.18212			−0.0414588
$814$	−8.61596	−	3.87701i	−0.301989	−	0.135889i
$815$	−5.41182			−0.189568
$816$	−29.2846	+	21.2765i	−1.02517	+	0.744827i
$817$	−11.3611	−	34.9659i	−0.397475	−	1.22330i
$818$	−13.4276	+	41.3259i	−0.469485	+	1.44493i
$819$		0			0
$820$	0.0594801	+	0.0432148i	0.00207714	+	0.00150913i
$821$	3.73242	−	11.4872i	0.130262	−	0.400906i	−0.864561	−	0.502528i	$-0.832403\pi$
$821$	3.73242	−	11.4872i	0.130262	−	0.400906i	0.994823	+	0.101622i	$0.0324033\pi$
$822$	10.2750	+	31.6233i	0.358383	+	1.10299i
$823$	20.0787	−	14.5880i	0.699900	−	0.508507i	−0.179999	−	0.983667i	$-0.557610\pi$
$823$	20.0787	−	14.5880i	0.699900	−	0.508507i	0.879900	+	0.475159i	$0.157610\pi$
$824$	−45.7634			−1.59424
$825$	−2.78352	+	25.5116i	−0.0969098	+	0.888201i
$826$		0			0
$827$	−4.18529	+	3.04079i	−0.145537	+	0.105739i	−0.658171	−	0.752868i	$-0.728670\pi$
$827$	−4.18529	+	3.04079i	−0.145537	+	0.105739i	0.512634	+	0.858607i	$0.328670\pi$
$828$	0.0322361	+	0.0992125i	0.00112028	+	0.00344787i
$829$	−9.75057	+	30.0092i	−0.338651	+	1.04226i	0.626244	+	0.779627i	$0.284591\pi$
$829$	−9.75057	+	30.0092i	−0.338651	+	1.04226i	−0.964895	+	0.262635i	$0.915409\pi$
$830$	−9.55847	−	6.94464i	−0.331779	−	0.241052i
$831$	−19.7196	−	14.3271i	−0.684064	−	0.497001i
$832$	3.57270	−	10.9956i	0.123861	−	0.381205i
$833$		0			0
$834$	−18.3889	+	13.3603i	−0.636755	+	0.462629i
$835$	2.95204			0.102160
$836$	1.42385	−	1.56881i	0.0492449	−	0.0542585i
$837$	7.08018			0.244727
$838$	13.8184	−	10.0396i	0.477348	−	0.346813i
$839$	1.80355	+	5.55077i	0.0622656	+	0.191634i	0.977350	−	0.211628i	$-0.0678765\pi$
$839$	1.80355	+	5.55077i	0.0622656	+	0.191634i	−0.915085	+	0.403262i	$0.867876\pi$
$840$		0			0
$841$	17.4784	+	12.6988i	0.602703	+	0.437889i
$842$	23.5956	+	17.1432i	0.813157	+	0.590793i
$843$	−5.34806	+	16.4596i	−0.184197	+	0.566900i
$844$	0.250854	+	0.772050i	0.00863475	+	0.0265750i
$845$	−3.96333	+	2.87953i	−0.136343	+	0.0990588i
$846$	3.58291			0.123183
$847$		0			0
$848$	56.5112			1.94060
$849$	11.9237	−	8.66308i	0.409221	−	0.297316i
$850$	−11.3302	−	34.8707i	−0.388622	−	1.19606i
$851$	1.08335	−	3.33420i	0.0371367	−	0.114295i
$852$	−1.92969	−	1.40200i	−0.0661101	−	0.0480318i
$853$	−16.4604	−	11.9592i	−0.563593	−	0.409475i	0.269179	−	0.963090i	$-0.413248\pi$
$853$	−16.4604	−	11.9592i	−0.563593	−	0.409475i	−0.832772	+	0.553616i	$0.813248\pi$
$854$		0			0
$855$	−0.232586	−	0.715828i	−0.00795429	−	0.0244808i
$856$	33.9499	−	24.6661i	1.16039	−	0.843069i
$857$	15.1087			0.516104			0.258052	−	0.966131i	$-0.416919\pi$
$857$	15.1087			0.516104			0.258052	+	0.966131i	$0.416919\pi$
$858$	8.37029	−	9.22247i	0.285757	−	0.314850i
$859$	33.9641			1.15884			0.579420	−	0.815029i	$-0.303279\pi$
$859$	33.9641			1.15884			0.579420	+	0.815029i	$0.303279\pi$
$860$	0.497507	−	0.361460i	0.0169648	−	0.0123257i
$861$		0			0
$862$	−13.7090	+	42.1920i	−0.466931	+	1.43707i
$863$	2.24691	+	1.63248i	0.0764859	+	0.0555702i	0.625371	−	0.780327i	$-0.284948\pi$
$863$	2.24691	+	1.63248i	0.0764859	+	0.0555702i	−0.548885	+	0.835898i	$0.684948\pi$
$864$	3.78115	+	2.74717i	0.128637	+	0.0934606i
$865$	0.193130	−	0.594395i	0.00656663	−	0.0202100i
$866$	−2.58676	−	7.96122i	−0.0879016	−	0.270533i
$867$	−13.5155	+	9.81958i	−0.459010	+	0.333490i
$868$		0			0
$869$	1.28869	−	11.8111i	0.0437156	−	0.400664i
$870$	3.01224			0.102125
$871$	5.98562	−	4.34881i	0.202815	−	0.147354i
$872$	9.24629	+	28.4571i	0.313119	+	0.963681i
$873$	−0.319119	+	0.982147i	−0.0108005	+	0.0332406i
$874$	9.04292	+	6.57006i	0.305881	+	0.222236i
$875$		0			0
$876$	1.00767	−	3.10130i	0.0340461	−	0.104783i
$877$	15.3514	+	47.2469i	0.518381	+	1.59541i	0.777044	+	0.629446i	$0.216718\pi$
$877$	15.3514	+	47.2469i	0.518381	+	1.59541i	−0.258662	+	0.965968i	$0.583282\pi$
$878$	−8.12680	+	5.90446i	−0.274266	+	0.199266i
$879$	−19.2368			−0.648841
$880$	−6.04142	−	2.71852i	−0.203656	−	0.0916412i
$881$	27.3064			0.919975			0.459988	−	0.887925i	$-0.347854\pi$
$881$	27.3064			0.919975			0.459988	+	0.887925i	$0.347854\pi$
$882$		0			0
$883$	−5.50388	−	16.9392i	−0.185220	−	0.570049i	0.814732	−	0.579838i	$-0.196884\pi$
$883$	−5.50388	−	16.9392i	−0.185220	−	0.570049i	−0.999952	+	0.00978852i	$0.996884\pi$
$884$	−0.386723	+	1.19021i	−0.0130069	+	0.0400312i
$885$	5.25663	+	3.81916i	0.176700	+	0.128380i
$886$	0.119486	+	0.0868116i	0.00401421	+	0.00291649i
$887$	5.09040	−	15.6666i	0.170919	−	0.526034i	−0.828505	−	0.559982i	$-0.810808\pi$
$887$	5.09040	−	15.6666i	0.170919	−	0.526034i	0.999424	+	0.0339479i	$0.0108080\pi$
$888$	−2.63319	−	8.10413i	−0.0883641	−	0.271957i
$889$		0			0
$890$	6.10625			0.204682
$891$	−12.6949	−	22.1906i	−0.425294	−	0.743412i
$892$	3.84656			0.128792
$893$	21.8438	−	15.8705i	0.730975	−	0.531084i
$894$	−10.9730	−	33.7714i	−0.366992	−	1.12948i
$895$	−2.56565	+	7.89625i	−0.0857601	+	0.263942i
$896$		0			0
$897$	3.73877	+	2.71638i	0.124834	+	0.0906971i
$898$	13.9621	−	42.9709i	0.465921	−	1.43396i
$899$	−1.08731	−	3.34640i	−0.0362639	−	0.111609i
$900$	−0.223590	+	0.162447i	−0.00745299	+	0.00541491i
$901$	69.0238			2.29952
$902$	−4.95809	+	1.03338i	−0.165086	+	0.0344078i
$903$		0			0
$904$	−3.88299	+	2.82116i	−0.129146	+	0.0938304i
$905$	−0.139004	−	0.427809i	−0.00462064	−	0.0142209i
$906$	2.10647	−	6.48305i	0.0699828	−	0.215385i
$907$	−23.0470	−	16.7446i	−0.765264	−	0.555997i	0.135257	−	0.990811i	$-0.456814\pi$
$907$	−23.0470	−	16.7446i	−0.765264	−	0.555997i	−0.900520	+	0.434814i	$0.856814\pi$
$908$	−2.65741	−	1.93072i	−0.0881891	−	0.0640731i
$909$	0.0211022	−	0.0649460i	0.000699917	−	0.00215412i
$910$		0			0
$911$	9.08955	−	6.60394i	0.301150	−	0.218798i	−0.426940	−	0.904280i	$-0.640408\pi$
$911$	9.08955	−	6.60394i	0.301150	−	0.218798i	0.728090	+	0.685482i	$0.240408\pi$
$912$	29.2356			0.968088
$913$	56.0371	−	11.6794i	1.85456	−	0.386532i
$914$	−33.9337			−1.12243
$915$	9.31112	−	6.76492i	0.307816	−	0.223641i
$916$	−0.959910	−	2.95430i	−0.0317163	−	0.0976128i
$917$		0			0
$918$	33.9426	+	24.6607i	1.12027	+	0.813925i
$919$	−0.631403	−	0.458741i	−0.0208281	−	0.0151325i	0.577323	−	0.816516i	$-0.304098\pi$
$919$	−0.631403	−	0.458741i	−0.0208281	−	0.0151325i	−0.598151	+	0.801384i	$0.704098\pi$
$920$	0.705922	−	2.17260i	0.0232735	−	0.0716286i
$921$	−1.11036	−	3.41734i	−0.0365876	−	0.112605i
$922$	3.29687	−	2.39532i	0.108577	−	0.0788856i
$923$	15.4167			0.507446
$924$		0			0
$925$	9.28795			0.305386
$926$	−30.9646	+	22.4971i	−1.01756	+	0.739301i
$927$	1.99209	+	6.13101i	0.0654287	+	0.201369i
$928$	0.717755	−	2.20902i	0.0235615	−	0.0725148i
$929$	21.5169	+	15.6329i	0.705946	+	0.512899i	0.881863	−	0.471505i	$-0.156289\pi$
$929$	21.5169	+	15.6329i	0.705946	+	0.512899i	−0.175918	+	0.984405i	$0.556289\pi$
$930$	1.15945	+	0.842387i	0.0380198	+	0.0276230i
$931$		0			0
$932$	0.0324505	+	0.0998725i	0.00106295	+	0.00327143i
$933$	−28.0294	+	20.3646i	−0.917642	+	0.666706i
$934$	−3.89900			−0.127579
$935$	−7.37911	−	3.32045i	−0.241323	−	0.108590i
$936$	−1.63883			−0.0535669
$937$	33.9542	−	24.6691i	1.10923	−	0.805906i	0.126691	−	0.991942i	$-0.459564\pi$
$937$	33.9542	−	24.6691i	1.10923	−	0.805906i	0.982543	+	0.186036i	$0.0595642\pi$
$938$		0			0
$939$	15.7774	−	48.5578i	0.514875	−	1.58462i
$940$	0.365368	+	0.265456i	0.0119170	+	0.00865821i
$941$	−39.6685	−	28.8209i	−1.29316	−	0.939533i	−0.293292	−	0.956023i	$-0.594751\pi$
$941$	−39.6685	−	28.8209i	−1.29316	−	0.939533i	−0.999864	+	0.0164899i	$0.994751\pi$
$942$	−13.8477	+	42.6187i	−0.451181	+	1.38859i
$943$	−0.580730	−	1.78730i	−0.0189112	−	0.0582026i
$944$	29.7897	−	21.6435i	0.969574	−	0.704437i
$945$		0			0
$946$	−4.59475	+	42.1120i	−0.149388	+	1.36918i
$947$	−27.2953			−0.886978			−0.443489	−	0.896280i	$-0.646259\pi$
$947$	−27.2953			−0.886978			−0.443489	+	0.896280i	$0.646259\pi$
$948$	−0.709503	+	0.515484i	−0.0230436	+	0.0167422i
$949$	6.51299	+	20.0449i	0.211421	+	0.650686i
$950$	−9.15097	+	28.1638i	−0.296897	+	0.913754i
$951$	17.2799	+	12.5546i	0.560339	+	0.407110i
$952$		0			0
$953$	6.10023	−	18.7746i	0.197606	−	0.608169i	−0.802330	−	0.596880i	$-0.796407\pi$
$953$	6.10023	−	18.7746i	0.197606	−	0.608169i	0.999936	−	0.0112883i	$-0.00359326\pi$
$954$	−2.28601	−	7.03561i	−0.0740122	−	0.227786i
$955$	−6.07505	+	4.41378i	−0.196584	+	0.142827i
$956$	0.0524354			0.00169588
$957$	−9.80801	+	10.8066i	−0.317048	+	0.349327i
$958$	−12.1478			−0.392478
$959$		0			0
$960$	−1.70513	−	5.24785i	−0.0550329	−	0.169374i
$961$	−9.06221	+	27.8906i	−0.292329	+	0.899697i
$962$	−3.64668	−	2.64947i	−0.117574	−	0.0854222i
$963$	−4.78241	−	3.47463i	−0.154111	−	0.111968i
$964$	0.487989	−	1.50188i	0.0157171	−	0.0483721i
$965$	−1.75200	−	5.39211i	−0.0563990	−	0.173578i
$966$		0			0
$967$	−12.6734			−0.407551			−0.203775	−	0.979018i	$-0.565321\pi$
$967$	−12.6734			−0.407551			−0.203775	+	0.979018i	$0.565321\pi$
$968$	27.3435	−	11.9156i	0.878853	−	0.382983i
$969$	35.7089			1.14714
$970$	−1.49734	+	1.08788i	−0.0480768	+	0.0349298i
$971$	−5.16170	−	15.8861i	−0.165647	−	0.509809i	0.833436	−	0.552615i	$-0.186370\pi$
$971$	−5.16170	−	15.8861i	−0.165647	−	0.509809i	−0.999083	+	0.0428065i	$0.986370\pi$
$972$	0.184414	−	0.567569i	0.00591509	−	0.0182048i
$973$		0			0
$974$	−23.2523	−	16.8938i	−0.745052	−	0.541312i
$975$	−3.78345	+	11.6443i	−0.121167	+	0.372914i
$976$	−20.1552	−	62.0312i	−0.645151	−	1.98557i
$977$	−22.1227	+	16.0731i	−0.707769	+	0.514224i	−0.882453	−	0.470400i	$-0.844110\pi$
$977$	−22.1227	+	16.0731i	−0.707769	+	0.514224i	0.174684	+	0.984625i	$0.444110\pi$
$978$	−27.5178			−0.879924
$979$	−19.8822	+	21.9064i	−0.635439	+	0.700133i
$980$		0			0
$981$	3.40997	−	2.47749i	0.108872	−	0.0791001i
$982$	12.9998	+	40.0093i	0.414841	+	1.27675i
$983$	16.9979	−	52.3143i	0.542150	−	1.66857i	−0.185521	−	0.982640i	$-0.559397\pi$
$983$	16.9979	−	52.3143i	0.542150	−	1.66857i	0.727671	−	0.685926i	$-0.240603\pi$
$984$	−3.69542	−	2.68488i	−0.117806	−	0.0855908i
$985$	−0.869141	−	0.631468i	−0.0276931	−	0.0201202i
$986$	6.44313	−	19.8299i	0.205191	−	0.631513i
$987$		0			0
$988$	0.817723	−	0.594110i	0.0260152	−	0.0189012i
$989$	−15.7188			−0.499828
$990$	−0.0940645	+	0.862123i	−0.00298957	+	0.0274001i
$991$	53.2327			1.69099			0.845497	−	0.533980i	$-0.179304\pi$
$991$	53.2327			1.69099			0.845497	+	0.533980i	$0.179304\pi$
$992$	0.894035	−	0.649555i	0.0283857	−	0.0206234i
$993$	4.73826	+	14.5829i	0.150364	+	0.462774i
$994$		0			0
$995$	−7.65750	−	5.56350i	−0.242759	−	0.176375i
$996$	−3.41825	−	2.48350i	−0.108311	−	0.0786927i
$997$	−10.1217	+	31.1515i	−0.320558	+	0.986577i	0.652848	+	0.757489i	$0.273574\pi$
$997$	−10.1217	+	31.1515i	−0.320558	+	0.986577i	−0.973406	+	0.229087i	$0.926426\pi$
$998$	−12.6682	−	38.9886i	−0.401004	−	1.23416i
$999$	−8.59825	+	6.24700i	−0.272037	+	0.197646i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	539.2.f.d.344.2		8
7.2	even	3		539.2.q.b.410.1		16
7.3	odd	6		539.2.q.c.520.2		16
7.4	even	3		539.2.q.b.520.2		16
7.5	odd	6		539.2.q.c.410.1		16
7.6	odd	2		77.2.f.a.36.2	yes	8
11.2	odd	10		5929.2.a.bb.1.4		4
11.4	even	5	inner	539.2.f.d.246.2		8
11.9	even	5		5929.2.a.bi.1.1		4
21.20	even	2		693.2.m.g.190.1		8
77.4	even	15		539.2.q.b.422.1		16
77.6	even	10		847.2.f.s.372.2		8
77.13	even	10		847.2.a.k.1.4		4
77.20	odd	10		847.2.a.l.1.1		4
77.26	odd	30		539.2.q.c.312.2		16
77.27	odd	10		847.2.f.p.372.1		8
77.37	even	15		539.2.q.b.312.2		16
77.41	even	10		847.2.f.s.148.2		8
77.48	odd	10		77.2.f.a.15.2	✓	8
77.59	odd	30		539.2.q.c.422.1		16
77.62	even	10		847.2.f.q.323.1		8
77.69	odd	10		847.2.f.p.148.1		8
77.76	even	2		847.2.f.q.729.1		8
231.20	even	10		7623.2.a.ch.1.4		4
231.125	even	10		693.2.m.g.631.1		8
231.167	odd	10		7623.2.a.co.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.15.2	✓	8	77.48	odd	10
77.2.f.a.36.2	yes	8	7.6	odd	2
539.2.f.d.246.2		8	11.4	even	5	inner
539.2.f.d.344.2		8	1.1	even	1	trivial
539.2.q.b.312.2		16	77.37	even	15
539.2.q.b.410.1		16	7.2	even	3
539.2.q.b.422.1		16	77.4	even	15
539.2.q.b.520.2		16	7.4	even	3
539.2.q.c.312.2		16	77.26	odd	30
539.2.q.c.410.1		16	7.5	odd	6
539.2.q.c.422.1		16	77.59	odd	30
539.2.q.c.520.2		16	7.3	odd	6
693.2.m.g.190.1		8	21.20	even	2
693.2.m.g.631.1		8	231.125	even	10
847.2.a.k.1.4		4	77.13	even	10
847.2.a.l.1.1		4	77.20	odd	10
847.2.f.p.148.1		8	77.69	odd	10
847.2.f.p.372.1		8	77.27	odd	10
847.2.f.q.323.1		8	77.62	even	10
847.2.f.q.729.1		8	77.76	even	2
847.2.f.s.148.2		8	77.41	even	10
847.2.f.s.372.2		8	77.6	even	10
5929.2.a.bb.1.4		4	11.2	odd	10
5929.2.a.bi.1.1		4	11.9	even	5
7623.2.a.ch.1.4		4	231.20	even	10
7623.2.a.co.1.1		4	231.167	odd	10

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:	\( N \)	\(=\)	\( 539 = 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	539.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18661 - 0.862123i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(1.91998 + 1.39494i) q^{6} +(0.837913 + 2.57883i) q^{8} +(0.309017 - 0.224514i) q^{9} +O(q^{10})\)	\(q+(1.18661 - 0.862123i) q^{2} +(0.500000 + 1.53884i) q^{3} +(0.0467549 - 0.143897i) q^{4} +(0.377594 + 0.274338i) q^{5} +(1.91998 + 1.39494i) q^{6} +(0.837913 + 2.57883i) q^{8} +(0.309017 - 0.224514i) q^{9} +0.684570 q^{10} +(-2.22899 + 2.45593i) q^{11} +0.244812 q^{12} +(-1.28012 + 0.930062i) q^{13} +(-0.233366 + 0.718226i) q^{15} +(3.46236 + 2.51555i) q^{16} +(4.22899 + 3.07254i) q^{17} +(0.173124 - 0.532822i) q^{18} +(-1.30464 - 4.01528i) q^{19} +(0.0571308 - 0.0415079i) q^{20} +(-0.527635 + 4.83590i) q^{22} -1.80505 q^{23} +(-3.54946 + 2.57883i) q^{24} +(-1.47777 - 4.54811i) q^{25} +(-0.717177 + 2.20724i) q^{26} +(4.42705 + 3.21644i) q^{27} +(0.840363 - 2.58637i) q^{29} +(0.342285 + 1.05345i) q^{30} +(1.04675 - 0.760512i) q^{31} +0.854102 q^{32} +(-4.89378 - 2.20210i) q^{33} +7.66708 q^{34} +(-0.0178588 - 0.0549637i) q^{36} +(-0.600175 + 1.84715i) q^{37} +(-5.00978 - 3.63982i) q^{38} +(-2.07128 - 1.50487i) q^{39} +(-0.391081 + 1.20362i) q^{40} +(0.321724 + 0.990166i) q^{41} +8.70820 q^{43} +(0.249184 + 0.435572i) q^{44} +0.178276 q^{45} +(-2.14190 + 1.55618i) q^{46} +(1.97626 + 6.08229i) q^{47} +(-2.13986 + 6.58580i) q^{48} +(-5.67457 - 4.12281i) q^{50} +(-2.61366 + 8.04402i) q^{51} +(0.0739811 + 0.227690i) q^{52} +(10.6826 - 7.76137i) q^{53} +8.02616 q^{54} +(-1.51541 + 0.315846i) q^{55} +(5.52656 - 4.01528i) q^{57} +(-1.23259 - 3.79351i) q^{58} +(2.65875 - 8.18278i) q^{59} +(0.0924396 + 0.0671613i) q^{60} +(-12.3295 - 8.95793i) q^{61} +(0.586436 - 1.80486i) q^{62} +(-5.91123 + 4.29476i) q^{64} -0.738517 q^{65} +(-7.70550 + 1.60600i) q^{66} -4.67583 q^{67} +(0.639856 - 0.464883i) q^{68} +(-0.902527 - 2.77769i) q^{69} +(-7.88234 - 5.72685i) q^{71} +(0.837913 + 0.608780i) q^{72} +(4.11611 - 12.6681i) q^{73} +(0.880296 + 2.70927i) q^{74} +(6.25993 - 4.54811i) q^{75} -0.638786 q^{76} -3.75519 q^{78} +(-2.89815 + 2.10563i) q^{79} +(0.617255 + 1.89971i) q^{80} +(-2.38197 + 7.33094i) q^{81} +(1.23541 + 0.897575i) q^{82} +(-13.9627 - 10.1445i) q^{83} +(0.753927 + 2.32035i) q^{85} +(10.3333 - 7.50755i) q^{86} +4.40020 q^{87} +(-8.20113 - 3.69034i) q^{88} +8.91982 q^{89} +(0.211544 - 0.153696i) q^{90} +(-0.0843952 + 0.259742i) q^{92} +(1.69369 + 1.23053i) q^{93} +(7.58873 + 5.51353i) q^{94} +(0.608919 - 1.87406i) q^{95} +(0.427051 + 1.31433i) q^{96} +(-2.18727 + 1.58915i) q^{97} +(-0.137407 + 1.25936i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9	\( 8 q - q^{2} + 4 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{8} - 2 q^{9} + 28 q^{10} + 5 q^{11} + 14 q^{12} - 5 q^{13} + 6 q^{15} - 3 q^{16} + 11 q^{17} + 4 q^{18} + 9 q^{19} - 21 q^{20} - q^{22} - 16 q^{23} - 21 q^{24} + 5 q^{25} - 21 q^{26} + 22 q^{27} - 9 q^{29} + 14 q^{30} + 11 q^{31} - 20 q^{32} - 10 q^{33} + 24 q^{34} - 2 q^{36} + 6 q^{37} - 35 q^{38} - 5 q^{39} + 16 q^{40} + 22 q^{41} + 16 q^{43} + 29 q^{44} - 18 q^{45} + 29 q^{46} - 7 q^{47} - 4 q^{48} - 34 q^{50} + 3 q^{51} - 21 q^{52} + 2 q^{53} - 4 q^{54} - 26 q^{55} - 3 q^{57} - 39 q^{58} - 25 q^{59} - 38 q^{60} - 7 q^{61} + 5 q^{62} + q^{64} + 24 q^{65} - 18 q^{66} - 30 q^{67} - 8 q^{68} - 8 q^{69} - 14 q^{71} + 3 q^{72} - 3 q^{73} - 9 q^{74} - 5 q^{75} + 52 q^{76} - 18 q^{78} - 9 q^{79} + 33 q^{80} - 28 q^{81} - 31 q^{82} - 23 q^{83} - 10 q^{85} - 17 q^{86} - 12 q^{87} - 7 q^{88} + 34 q^{89} - 2 q^{90} - 34 q^{92} + 8 q^{93} + 30 q^{94} + 24 q^{95} - 10 q^{96} - 30 q^{97}+O(q^{100}) \) 8 * q - q^2 + 4 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^8 - 2 * q^9 + 28 * q^10 + 5 * q^11 + 14 * q^12 - 5 * q^13 + 6 * q^15 - 3 * q^16 + 11 * q^17 + 4 * q^18 + 9 * q^19 - 21 * q^20 - q^22 - 16 * q^23 - 21 * q^24 + 5 * q^25 - 21 * q^26 + 22 * q^27 - 9 * q^29 + 14 * q^30 + 11 * q^31 - 20 * q^32 - 10 * q^33 + 24 * q^34 - 2 * q^36 + 6 * q^37 - 35 * q^38 - 5 * q^39 + 16 * q^40 + 22 * q^41 + 16 * q^43 + 29 * q^44 - 18 * q^45 + 29 * q^46 - 7 * q^47 - 4 * q^48 - 34 * q^50 + 3 * q^51 - 21 * q^52 + 2 * q^53 - 4 * q^54 - 26 * q^55 - 3 * q^57 - 39 * q^58 - 25 * q^59 - 38 * q^60 - 7 * q^61 + 5 * q^62 + q^64 + 24 * q^65 - 18 * q^66 - 30 * q^67 - 8 * q^68 - 8 * q^69 - 14 * q^71 + 3 * q^72 - 3 * q^73 - 9 * q^74 - 5 * q^75 + 52 * q^76 - 18 * q^78 - 9 * q^79 + 33 * q^80 - 28 * q^81 - 31 * q^82 - 23 * q^83 - 10 * q^85 - 17 * q^86 - 12 * q^87 - 7 * q^88 + 34 * q^89 - 2 * q^90 - 34 * q^92 + 8 * q^93 + 30 * q^94 + 24 * q^95 - 10 * q^96 - 30 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more