LMFDB - Embedded newform 650.2.t.h.643.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(7,650)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(650, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 11]))

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

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

chi := DirichletCharacter("650.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.t (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:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 294x^{12} + 1516x^{10} + 4147x^{8} + 6012x^{6} + 4338x^{4} + 1296x^{2} + 81 $ x^16 + 28x^14 + 294x^12 + 1516x^10 + 4147x^8 + 6012x^6 + 4338x^4 + 1296*x^2 + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			643.3
Root			$1.77906i$ of defining polynomial
Character	$\chi$	$=$	650.643
Dual form			650.2.t.h.557.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(1.71844 - 0.460454i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.71844 + 0.460454i) q^{6} +(0.386889 + 0.670111i) q^{7} +1.00000i q^{8} +(0.142931 - 0.0825211i) q^{9} +(2.36760 - 0.634396i) q^{11} +(1.25798 + 1.25798i) q^{12} +(3.22410 - 1.61406i) q^{13} +0.773777i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.325938 + 1.21642i) q^{17} +0.165042 q^{18} +(-0.0463847 + 0.173110i) q^{19} +(0.973399 + 0.973399i) q^{21} +(2.36760 + 0.634396i) q^{22} +(-0.0925293 - 0.345324i) q^{23} +(0.460454 + 1.71844i) q^{24} +(3.59918 + 0.214229i) q^{26} +(-3.56633 + 3.56633i) q^{27} +(-0.386889 + 0.670111i) q^{28} +(0.581688 + 0.335838i) q^{29} +(2.01980 - 2.01980i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.77646 - 2.18034i) q^{33} +(-0.890480 + 0.890480i) q^{34} +(0.142931 + 0.0825211i) q^{36} +(-4.27996 + 7.41311i) q^{37} +(-0.126725 + 0.126725i) q^{38} +(4.79721 - 4.25821i) q^{39} +(-2.60617 - 9.72634i) q^{41} +(0.356289 + 1.32969i) q^{42} +(-0.194605 - 0.0521443i) q^{43} +(1.73320 + 1.73320i) q^{44} +(0.0925293 - 0.345324i) q^{46} -9.78940 q^{47} +(-0.460454 + 1.71844i) q^{48} +(3.20063 - 5.54366i) q^{49} +2.24042i q^{51} +(3.00987 + 1.98512i) q^{52} +(-0.918640 - 0.918640i) q^{53} +(-4.87170 + 1.30537i) q^{54} +(-0.670111 + 0.386889i) q^{56} +0.318837i q^{57} +(0.335838 + 0.581688i) q^{58} +(-0.742719 - 0.199011i) q^{59} +(-7.31689 - 12.6732i) q^{61} +(2.75910 - 0.739298i) q^{62} +(0.110597 + 0.0638529i) q^{63} -1.00000 q^{64} +4.36068 q^{66} +(-0.894801 - 0.516614i) q^{67} +(-1.21642 + 0.325938i) q^{68} +(-0.318011 - 0.550812i) q^{69} +(4.58286 + 1.22797i) q^{71} +(0.0825211 + 0.142931i) q^{72} +12.2960i q^{73} +(-7.41311 + 4.27996i) q^{74} +(-0.173110 + 0.0463847i) q^{76} +(1.34111 + 1.34111i) q^{77} +(6.28361 - 1.28912i) q^{78} -8.67104i q^{79} +(-4.73394 + 8.19943i) q^{81} +(2.60617 - 9.72634i) q^{82} -8.94673 q^{83} +(-0.356289 + 1.32969i) q^{84} +(-0.142461 - 0.142461i) q^{86} +(1.15423 + 0.309275i) q^{87} +(0.634396 + 2.36760i) q^{88} +(3.34657 + 12.4896i) q^{89} +(2.32897 + 1.53604i) q^{91} +(0.252795 - 0.252795i) q^{92} +(2.54087 - 4.40092i) q^{93} +(-8.47787 - 4.89470i) q^{94} +(-1.25798 + 1.25798i) q^{96} +(9.71868 - 5.61108i) q^{97} +(5.54366 - 3.20063i) q^{98} +(0.286051 - 0.286051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33}+ \cdots + 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	1.71844	−	0.460454i	0.992140	−	0.265843i	0.273991	−	0.961732i	$-0.411656\pi$
$3$	1.71844	−	0.460454i	0.992140	−	0.265843i	0.718149	+	0.695889i	$0.244990\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.71844	+	0.460454i	0.701549	+	0.187979i
$7$	0.386889	+	0.670111i	0.146230	+	0.253278i	0.929831	−	0.367986i	$-0.119953\pi$
$7$	0.386889	+	0.670111i	0.146230	+	0.253278i	−0.783601	+	0.621264i	$0.786619\pi$
$8$			1.00000i			0.353553i
$9$	0.142931	−	0.0825211i	0.0476436	−	0.0275070i
$10$		0			0
$11$	2.36760	−	0.634396i	0.713858	−	0.191278i	0.116428	−	0.993199i	$-0.462855\pi$
$11$	2.36760	−	0.634396i	0.713858	−	0.191278i	0.597429	+	0.801922i	$0.296189\pi$
$12$	1.25798	+	1.25798i	0.363148	+	0.363148i
$13$	3.22410	−	1.61406i	0.894204	−	0.447660i
$13$	3.22410	−	1.61406i	0.894204	−	0.447660i
$14$			0.773777i			0.206801i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.325938	+	1.21642i	−0.0790516	+	0.295025i	−0.994121	−	0.108271i	$-0.965469\pi$
$17$	−0.325938	+	1.21642i	−0.0790516	+	0.295025i	0.915070	+	0.403295i	$0.132135\pi$
$18$	0.165042			0.0389008
$19$	−0.0463847	+	0.173110i	−0.0106414	+	0.0397142i	−0.971042	−	0.238907i	$-0.923211\pi$
$19$	−0.0463847	+	0.173110i	−0.0106414	+	0.0397142i	0.960401	+	0.278621i	$0.0898775\pi$
$20$		0			0
$21$	0.973399	+	0.973399i	0.212413	+	0.212413i
$22$	2.36760	+	0.634396i	0.504774	+	0.135254i
$23$	−0.0925293	−	0.345324i	−0.0192937	−	0.0720050i	0.955608	−	0.294642i	$-0.0952003\pi$
$23$	−0.0925293	−	0.345324i	−0.0192937	−	0.0720050i	−0.974901	+	0.222637i	$0.928534\pi$
$24$	0.460454	+	1.71844i	0.0939897	+	0.350774i
$25$		0			0
$26$	3.59918	+	0.214229i	0.705858	+	0.0420138i
$27$	−3.56633	+	3.56633i	−0.686340	+	0.686340i
$28$	−0.386889	+	0.670111i	−0.0731151	+	0.126639i
$29$	0.581688	+	0.335838i	0.108017	+	0.0623635i	0.553035	−	0.833158i	$-0.313470\pi$
$29$	0.581688	+	0.335838i	0.108017	+	0.0623635i	−0.445018	+	0.895521i	$0.646803\pi$
$30$		0			0
$31$	2.01980	−	2.01980i	0.362767	−	0.362767i	−0.502064	−	0.864831i	$-0.667426\pi$
$31$	2.01980	−	2.01980i	0.362767	−	0.362767i	0.864831	+	0.502064i	$0.167426\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	3.77646	−	2.18034i	0.657397	−	0.379548i
$34$	−0.890480	+	0.890480i	−0.152716	+	0.152716i
$35$		0			0
$36$	0.142931	+	0.0825211i	0.0238218	+	0.0137535i
$37$	−4.27996	+	7.41311i	−0.703621	+	1.21871i	0.263566	+	0.964641i	$0.415101\pi$
$37$	−4.27996	+	7.41311i	−0.703621	+	1.21871i	−0.967187	+	0.254066i	$0.918232\pi$
$38$	−0.126725	+	0.126725i	−0.0205576	+	0.0205576i
$39$	4.79721	−	4.25821i	0.768168	−	0.681860i
$40$		0			0
$41$	−2.60617	−	9.72634i	−0.407015	−	1.51900i	−0.800309	−	0.599587i	$-0.795331\pi$
$41$	−2.60617	−	9.72634i	−0.407015	−	1.51900i	0.393295	−	0.919412i	$-0.371335\pi$
$42$	0.356289	+	1.32969i	0.0549765	+	0.205175i
$43$	−0.194605	−	0.0521443i	−0.0296770	−	0.00795193i	0.243950	−	0.969788i	$-0.421557\pi$
$43$	−0.194605	−	0.0521443i	−0.0296770	−	0.00795193i	−0.273627	+	0.961836i	$0.588223\pi$
$44$	1.73320	+	1.73320i	0.261290	+	0.261290i
$45$		0			0
$46$	0.0925293	−	0.345324i	0.0136427	−	0.0509152i
$47$	−9.78940			−1.42793			−0.713965	−	0.700181i	$-0.753103\pi$
$47$	−9.78940			−1.42793			−0.713965	+	0.700181i	$0.753103\pi$
$48$	−0.460454	+	1.71844i	−0.0664608	+	0.248035i
$49$	3.20063	−	5.54366i	0.457233	−	0.791952i
$50$		0			0
$51$			2.24042i			0.313721i
$52$	3.00987	+	1.98512i	0.417394	+	0.275286i
$53$	−0.918640	−	0.918640i	−0.126185	−	0.126185i	0.641194	−	0.767379i	$-0.278439\pi$
$53$	−0.918640	−	0.918640i	−0.126185	−	0.126185i	−0.767379	+	0.641194i	$0.778439\pi$
$54$	−4.87170	+	1.30537i	−0.662954	+	0.177638i
$55$		0			0
$56$	−0.670111	+	0.386889i	−0.0895473	+	0.0517002i
$57$			0.318837i			0.0422310i
$58$	0.335838	+	0.581688i	0.0440976	+	0.0763793i
$59$	−0.742719	−	0.199011i	−0.0966937	−	0.0259090i	0.210148	−	0.977670i	$-0.432605\pi$
$59$	−0.742719	−	0.199011i	−0.0966937	−	0.0259090i	−0.306842	+	0.951761i	$0.599272\pi$
$60$		0			0
$61$	−7.31689	−	12.6732i	−0.936831	−	1.62264i	−0.771335	−	0.636429i	$-0.780411\pi$
$61$	−7.31689	−	12.6732i	−0.936831	−	1.62264i	−0.165496	−	0.986211i	$-0.552922\pi$
$62$	2.75910	−	0.739298i	0.350406	−	0.0938909i
$63$	0.110597	+	0.0638529i	0.0139339	+	0.00804471i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	4.36068			0.536762
$67$	−0.894801	−	0.516614i	−0.109317	−	0.0631144i	0.444344	−	0.895856i	$-0.353437\pi$
$67$	−0.894801	−	0.516614i	−0.109317	−	0.0631144i	−0.553662	+	0.832742i	$0.686770\pi$
$68$	−1.21642	+	0.325938i	−0.147512	+	0.0395258i
$69$	−0.318011	−	0.550812i	−0.0382841	−	0.0663099i
$70$		0			0
$71$	4.58286	+	1.22797i	0.543885	+	0.145734i	0.520293	−	0.853988i	$-0.325823\pi$
$71$	4.58286	+	1.22797i	0.543885	+	0.145734i	0.0235925	+	0.999722i	$0.492490\pi$
$72$	0.0825211	+	0.142931i	0.00972520	+	0.0168445i
$73$			12.2960i			1.43913i	0.694424	+	0.719566i	$0.255659\pi$
$73$			12.2960i			1.43913i	−0.694424	+	0.719566i	$0.744341\pi$
$74$	−7.41311	+	4.27996i	−0.861756	+	0.497535i
$75$		0			0
$76$	−0.173110	+	0.0463847i	−0.0198571	+	0.00532069i
$77$	1.34111	+	1.34111i	0.152834	+	0.152834i
$78$	6.28361	−	1.28912i	0.711478	−	0.145964i
$79$		−	8.67104i		−	0.975569i	−0.872964	−	0.487784i	$-0.837805\pi$
$79$		−	8.67104i		−	0.975569i	0.872964	−	0.487784i	$-0.162195\pi$
$80$		0			0
$81$	−4.73394	+	8.19943i	−0.525994	+	0.911048i
$82$	2.60617	−	9.72634i	0.287803	−	1.07409i
$83$	−8.94673			−0.982031			−0.491015	−	0.871151i	$-0.663374\pi$
$83$	−8.94673			−0.982031			−0.491015	+	0.871151i	$0.663374\pi$
$84$	−0.356289	+	1.32969i	−0.0388743	+	0.145081i
$85$		0			0
$86$	−0.142461	−	0.142461i	−0.0153619	−	0.0153619i
$87$	1.15423	+	0.309275i	0.123747	+	0.0331578i
$88$	0.634396	+	2.36760i	0.0676268	+	0.252387i
$89$	3.34657	+	12.4896i	0.354735	+	1.32389i	0.880817	+	0.473456i	$0.156994\pi$
$89$	3.34657	+	12.4896i	0.354735	+	1.32389i	−0.526082	+	0.850434i	$0.676339\pi$
$90$		0			0
$91$	2.32897	+	1.53604i	0.244142	+	0.161021i
$92$	0.252795	−	0.252795i	0.0263557	−	0.0263557i
$93$	2.54087	−	4.40092i	0.263476	−	0.456354i
$94$	−8.47787	−	4.89470i	−0.874425	−	0.504850i
$95$		0			0
$96$	−1.25798	+	1.25798i	−0.128392	+	0.128392i
$97$	9.71868	−	5.61108i	0.986783	−	0.569719i	0.0824718	−	0.996593i	$-0.473719\pi$
$97$	9.71868	−	5.61108i	0.986783	−	0.569719i	0.904311	+	0.426874i	$0.140385\pi$
$98$	5.54366	−	3.20063i	0.559994	−	0.323313i
$99$	0.286051	−	0.286051i	0.0287492	−	0.0287492i
$100$		0			0
$101$	−8.25395	−	4.76542i	−0.821299	−	0.474177i	0.0295654	−	0.999563i	$-0.490588\pi$
$101$	−8.25395	−	4.76542i	−0.821299	−	0.474177i	−0.850864	+	0.525386i	$0.823921\pi$
$102$	−1.12021	+	1.94026i	−0.110917	+	0.192114i
$103$	−12.2537	+	12.2537i	−1.20740	+	1.20740i	−0.235529	+	0.971867i	$0.575682\pi$
$103$	−12.2537	+	12.2537i	−1.20740	+	1.20740i	−0.971867	+	0.235529i	$0.924318\pi$
$104$	1.61406	+	3.22410i	0.158272	+	0.316149i
$105$		0			0
$106$	−0.336246	−	1.25489i	−0.0326591	−	0.121885i
$107$	−4.96534	−	18.5309i	−0.480018	−	1.79145i	−0.601519	−	0.798859i	$-0.705438\pi$
$107$	−4.96534	−	18.5309i	−0.480018	−	1.79145i	0.121501	−	0.992591i	$-0.461229\pi$
$108$	−4.87170	−	1.30537i	−0.468779	−	0.125609i
$109$	−1.18050	−	1.18050i	−0.113071	−	0.113071i	0.648308	−	0.761379i	$-0.275477\pi$
$109$	−1.18050	−	1.18050i	−0.113071	−	0.113071i	−0.761379	+	0.648308i	$0.775477\pi$
$110$		0			0
$111$	−3.94145	+	14.7097i	−0.374106	+	1.39618i
$112$	−0.773777			−0.0731151
$113$	−1.02288	+	3.81745i	−0.0962246	+	0.359115i	−0.997202	−	0.0747503i	$-0.976184\pi$
$113$	−1.02288	+	3.81745i	−0.0962246	+	0.359115i	0.900978	+	0.433866i	$0.142851\pi$
$114$	−0.159418	+	0.276121i	−0.0149309	+	0.0258611i
$115$		0			0
$116$			0.671675i			0.0623635i
$117$	0.327628	−	0.496755i	0.0302892	−	0.0459250i
$118$	−0.543708	−	0.543708i	−0.0500524	−	0.0500524i
$119$	−0.941237	+	0.252204i	−0.0862830	+	0.0231195i
$120$		0			0
$121$	−4.32322	+	2.49601i	−0.393020	+	0.226910i
$122$		−	14.6338i		−	1.32488i
$123$	−8.95706	−	15.5141i	−0.807631	−	1.39886i
$124$	2.75910	+	0.739298i	0.247774	+	0.0663909i
$125$		0			0
$126$	0.0638529	+	0.110597i	0.00568847	+	0.00985272i
$127$	11.1303	−	2.98237i	0.987659	−	0.264642i	0.271392	−	0.962469i	$-0.412516\pi$
$127$	11.1303	−	2.98237i	0.987659	−	0.264642i	0.716267	+	0.697827i	$0.245849\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	−0.358427			−0.0315577
$130$		0			0
$131$	9.63004			0.841380			0.420690	−	0.907204i	$-0.361788\pi$
$131$	9.63004			0.841380			0.420690	+	0.907204i	$0.361788\pi$
$132$	3.77646	+	2.18034i	0.328698	+	0.189774i
$133$	−0.133949	+	0.0358915i	−0.0116148	+	0.00311218i
$134$	−0.516614	−	0.894801i	−0.0446286	−	0.0772991i
$135$		0			0
$136$	−1.21642	−	0.325938i	−0.104307	−	0.0279490i
$137$	0.452627	+	0.783972i	0.0386705	+	0.0669793i	0.884713	−	0.466136i	$-0.154354\pi$
$137$	0.452627	+	0.783972i	0.0386705	+	0.0669793i	−0.846042	+	0.533116i	$0.821021\pi$
$138$		−	0.636023i		−	0.0541418i
$139$	1.75329	−	1.01226i	0.148712	−	0.0858588i	−0.423798	−	0.905757i	$-0.639303\pi$
$139$	1.75329	−	1.01226i	0.148712	−	0.0858588i	0.572510	+	0.819898i	$0.305970\pi$
$140$		0			0
$141$	−16.8225	+	4.50757i	−1.41671	+	0.379606i
$142$	3.35488	+	3.35488i	0.281536	+	0.281536i
$143$	6.60941	−	5.86681i	0.552707	−	0.490607i
$144$			0.165042i			0.0137535i
$145$		0			0
$146$	−6.14798	+	10.6486i	−0.508810	+	0.881285i
$147$	2.94749	−	11.0002i	0.243105	−	0.907279i
$148$	−8.55992			−0.703621
$149$	−3.77908	+	14.1037i	−0.309594	+	1.15542i	0.619324	+	0.785136i	$0.287407\pi$
$149$	−3.77908	+	14.1037i	−0.309594	+	1.15542i	−0.928918	+	0.370286i	$0.879260\pi$
$150$		0			0
$151$	12.7324	+	12.7324i	1.03615	+	1.03615i	0.999322	+	0.0368303i	$0.0117261\pi$
$151$	12.7324	+	12.7324i	1.03615	+	1.03615i	0.0368303	+	0.999322i	$0.488274\pi$
$152$	−0.173110	−	0.0463847i	−0.0140411	−	0.00376230i
$153$	0.0537935	+	0.200760i	0.00434895	+	0.0162305i
$154$	0.490881	+	1.83199i	0.0395563	+	0.147626i
$155$		0			0
$156$	6.08632	+	2.02540i	0.487296	+	0.162161i
$157$	2.87854	−	2.87854i	0.229732	−	0.229732i	−0.582849	−	0.812581i	$-0.698062\pi$
$157$	2.87854	−	2.87854i	0.229732	−	0.229732i	0.812581	+	0.582849i	$0.198062\pi$
$158$	4.33552	−	7.50934i	0.344916	−	0.597411i
$159$	−2.00162	−	1.15563i	−0.158739	−	0.0916477i
$160$		0			0
$161$	0.195607	−	0.195607i	0.0154160	−	0.0154160i
$162$	−8.19943	+	4.73394i	−0.644208	+	0.371934i
$163$	12.0420	−	6.95243i	0.943199	−	0.544556i	0.0522375	−	0.998635i	$-0.483365\pi$
$163$	12.0420	−	6.95243i	0.943199	−	0.544556i	0.890962	+	0.454078i	$0.150031\pi$
$164$	7.12018	−	7.12018i	0.555992	−	0.555992i
$165$		0			0
$166$	−7.74809	−	4.47336i	−0.601369	−	0.347200i
$167$	−7.09421	+	12.2875i	−0.548966	+	0.950838i	0.449379	+	0.893341i	$0.351645\pi$
$167$	−7.09421	+	12.2875i	−0.548966	+	0.950838i	−0.998346	+	0.0574967i	$0.981688\pi$
$168$	−0.973399	+	0.973399i	−0.0750993	+	0.0750993i
$169$	7.78960	−	10.4078i	0.599200	−	0.800599i
$170$		0			0
$171$	0.00765543	+	0.0285705i	0.000585426	+	0.00218484i
$172$	−0.0521443	−	0.194605i	−0.00397596	−	0.0148385i
$173$	−10.8608	−	2.91015i	−0.825733	−	0.221254i	−0.178881	−	0.983871i	$-0.557248\pi$
$173$	−10.8608	−	2.91015i	−0.825733	−	0.221254i	−0.646851	+	0.762616i	$0.723915\pi$
$174$	0.844956	+	0.844956i	0.0640559	+	0.0640559i
$175$		0			0
$176$	−0.634396	+	2.36760i	−0.0478194	+	0.178464i
$177$	−1.36795			−0.102821
$178$	−3.34657	+	12.4896i	−0.250836	+	0.936132i
$179$	2.87010	−	4.97117i	0.214522	−	0.371562i	−0.738603	−	0.674141i	$-0.764514\pi$
$179$	2.87010	−	4.97117i	0.214522	−	0.371562i	0.953124	+	0.302578i	$0.0978474\pi$
$180$		0			0
$181$			7.97888i			0.593065i	0.955023	+	0.296533i	$0.0958303\pi$
$181$			7.97888i			0.593065i	−0.955023	+	0.296533i	$0.904170\pi$
$182$	1.24893	+	2.49473i	0.0925765	+	0.184922i
$183$	−18.4090	−	18.4090i	−1.36084	−	1.36084i
$184$	0.345324	−	0.0925293i	0.0254576	−	0.00682135i
$185$		0			0
$186$	4.40092	−	2.54087i	0.322691	−	0.186306i
$187$			3.08676i			0.225726i
$188$	−4.89470	−	8.47787i	−0.356983	−	0.618312i
$189$	−3.76961	−	1.01006i	−0.274199	−	0.0734713i
$190$		0			0
$191$	−11.3313	−	19.6263i	−0.819901	−	1.42011i	−0.905754	−	0.423803i	$-0.860695\pi$
$191$	−11.3313	−	19.6263i	−0.819901	−	1.42011i	0.0858531	−	0.996308i	$-0.472638\pi$
$192$	−1.71844	+	0.460454i	−0.124017	+	0.0332304i
$193$	22.1356	+	12.7800i	1.59335	+	0.919924i	0.992726	+	0.120396i	$0.0384164\pi$
$193$	22.1356	+	12.7800i	1.59335	+	0.919924i	0.600629	+	0.799528i	$0.294917\pi$
$194$	11.2222			0.805705
$195$		0			0
$196$	6.40127			0.457233
$197$	−10.6183	−	6.13049i	−0.756524	−	0.436779i	0.0715225	−	0.997439i	$-0.477214\pi$
$197$	−10.6183	−	6.13049i	−0.756524	−	0.436779i	−0.828046	+	0.560660i	$0.810548\pi$
$198$	0.390753	−	0.104702i	0.0277696	−	0.00744085i
$199$	−10.6245	−	18.4021i	−0.753149	−	1.30449i	−0.946289	−	0.323322i	$-0.895200\pi$
$199$	−10.6245	−	18.4021i	−0.753149	−	1.30449i	0.193140	−	0.981171i	$-0.438133\pi$
$200$		0			0
$201$	−1.77554	−	0.475753i	−0.125237	−	0.0335571i
$202$	−4.76542	−	8.25395i	−0.335294	−	0.580746i
$203$			0.519727i			0.0364777i
$204$	−1.94026	+	1.12021i	−0.135845	+	0.0784303i
$205$		0			0
$206$	−16.7389	+	4.48518i	−1.16626	+	0.312497i
$207$	−0.0417218	−	0.0417218i	−0.00289986	−	0.00289986i
$208$	−0.214229	+	3.59918i	−0.0148541	+	0.249558i
$209$			0.439282i			0.0303857i
$210$		0			0
$211$	−7.59324	+	13.1519i	−0.522740	+	0.905413i	0.476909	+	0.878952i	$0.341757\pi$
$211$	−7.59324	+	13.1519i	−0.522740	+	0.905413i	−0.999650	+	0.0264606i	$0.991576\pi$
$212$	0.336246	−	1.25489i	0.0230935	−	0.0861859i
$213$	8.44077			0.578352
$214$	4.96534	−	18.5309i	0.339424	−	1.26675i
$215$		0			0
$216$	−3.56633	−	3.56633i	−0.242658	−	0.242658i
$217$	2.13493	+	0.572052i	0.144928	+	0.0388334i
$218$	−0.432091	−	1.61259i	−0.0292649	−	0.109218i
$219$	5.66172	+	21.1298i	0.382583	+	1.42782i
$220$		0			0
$221$	0.912519	+	4.44793i	0.0613827	+	0.299200i
$222$	−10.7682	+	10.7682i	−0.722716	+	0.722716i
$223$	3.07093	−	5.31901i	0.205645	−	0.356188i	−0.744693	−	0.667407i	$-0.767404\pi$
$223$	3.07093	−	5.31901i	0.205645	−	0.356188i	0.950338	+	0.311220i	$0.100737\pi$
$224$	−0.670111	−	0.386889i	−0.0447737	−	0.0258501i
$225$		0			0
$226$	−2.79457	+	2.79457i	−0.185892	+	0.185892i
$227$	13.2304	−	7.63857i	0.878132	−	0.506990i	0.00808986	−	0.999967i	$-0.497425\pi$
$227$	13.2304	−	7.63857i	0.878132	−	0.506990i	0.870042	+	0.492978i	$0.164092\pi$
$228$	−0.276121	+	0.159418i	−0.0182865	+	0.0105577i
$229$	3.10587	−	3.10587i	0.205242	−	0.205242i	−0.597000	−	0.802242i	$-0.703641\pi$
$229$	3.10587	−	3.10587i	0.205242	−	0.205242i	0.802242	+	0.597000i	$0.203641\pi$
$230$		0			0
$231$	2.92214	+	1.68710i	0.192263	+	0.111003i
$232$	−0.335838	+	0.581688i	−0.0220488	+	0.0381897i
$233$	−15.7484	+	15.7484i	−1.03171	+	1.03171i	−0.0322328	+	0.999480i	$0.510262\pi$
$233$	−15.7484	+	15.7484i	−1.03171	+	1.03171i	−0.999480	+	0.0322328i	$0.989738\pi$
$234$	0.532112	−	0.266388i	0.0347852	−	0.0174144i
$235$		0			0
$236$	−0.199011	−	0.742719i	−0.0129545	−	0.0483469i
$237$	−3.99261	−	14.9006i	−0.259348	−	0.967901i
$238$	−0.941237	−	0.252204i	−0.0610113	−	0.0163479i
$239$	−3.91466	−	3.91466i	−0.253219	−	0.253219i	0.569070	−	0.822289i	$-0.307303\pi$
$239$	−3.91466	−	3.91466i	−0.253219	−	0.253219i	−0.822289	+	0.569070i	$0.807303\pi$
$240$		0			0
$241$	−0.0415022	+	0.154888i	−0.00267339	+	0.00997724i	−0.967250	−	0.253827i	$-0.918311\pi$
$241$	−0.0415022	+	0.154888i	−0.00267339	+	0.00997724i	0.964576	+	0.263804i	$0.0849773\pi$
$242$	−4.99202			−0.320899
$243$	−0.443423	+	1.65488i	−0.0284456	+	0.106160i
$244$	7.31689	−	12.6732i	0.468416	−	0.811320i
$245$		0			0
$246$		−	17.9141i		−	1.14216i
$247$	0.129862	+	0.632992i	0.00826291	+	0.0402763i
$248$	2.01980	+	2.01980i	0.128257	+	0.128257i
$249$	−15.3744	+	4.11955i	−0.974312	+	0.261066i
$250$		0			0
$251$	24.0672	−	13.8952i	1.51911	−	0.877057i	0.519360	−	0.854556i	$-0.326170\pi$
$251$	24.0672	−	13.8952i	1.51911	−	0.877057i	0.999747	−	0.0225011i	$-0.00716292\pi$
$252$			0.127706i			0.00804471i
$253$	−0.438144	−	0.758888i	−0.0275459	−	0.0477109i
$254$	11.1303	+	2.98237i	0.698380	+	0.187130i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.64080	−	0.975550i	0.227107	−	0.0608531i	−0.143471	−	0.989655i	$-0.545826\pi$
$257$	3.64080	−	0.975550i	0.227107	−	0.0608531i	0.370578	+	0.928801i	$0.379160\pi$
$258$	−0.310407	−	0.179213i	−0.0193251	−	0.0111573i
$259$	−6.62347			−0.411563
$260$		0			0
$261$	0.110855			0.00686173
$262$	8.33986	+	4.81502i	0.515238	+	0.297473i
$263$	16.8872	−	4.52492i	1.04131	−	0.279019i	0.302655	−	0.953100i	$-0.402127\pi$
$263$	16.8872	−	4.52492i	1.04131	−	0.279019i	0.738657	+	0.674082i	$0.235460\pi$
$264$	2.18034	+	3.77646i	0.134191	+	0.232425i
$265$		0			0
$266$	−0.133949	−	0.0358915i	−0.00821292	−	0.00220065i
$267$	11.5017	+	19.9216i	0.703894	+	1.21918i
$268$		−	1.03323i		−	0.0631144i
$269$	−22.5481	+	13.0181i	−1.37478	+	0.793729i	−0.991525	−	0.129914i	$-0.958530\pi$
$269$	−22.5481	+	13.0181i	−1.37478	+	0.793729i	−0.383254	+	0.923643i	$0.625197\pi$
$270$		0			0
$271$	0.804227	−	0.215492i	0.0488533	−	0.0130902i	−0.234310	−	0.972162i	$-0.575283\pi$
$271$	0.804227	−	0.215492i	0.0488533	−	0.0130902i	0.283163	+	0.959072i	$0.408616\pi$
$272$	−0.890480	−	0.890480i	−0.0539933	−	0.0539933i
$273$	4.70946	+	1.56721i	0.285029	+	0.0948516i
$274$			0.905253i			0.0546884i
$275$		0			0
$276$	0.318011	−	0.550812i	0.0191420	−	0.0331550i
$277$	−1.85586	+	6.92616i	−0.111508	+	0.416153i	−0.999002	−	0.0446663i	$-0.985778\pi$
$277$	−1.85586	+	6.92616i	−0.111508	+	0.416153i	0.887494	+	0.460819i	$0.152444\pi$
$278$	2.02452			0.121423
$279$	0.122015	−	0.455367i	0.00730486	−	0.0272621i
$280$		0			0
$281$	16.3268	+	16.3268i	0.973977	+	0.973977i	0.999670	−	0.0256932i	$-0.00817929\pi$
$281$	16.3268	+	16.3268i	0.973977	+	0.973977i	−0.0256932	+	0.999670i	$0.508179\pi$
$282$	−16.8225	−	4.50757i	−1.00176	−	0.268422i
$283$	6.46878	+	24.1418i	0.384529	+	1.43508i	0.838908	+	0.544273i	$0.183195\pi$
$283$	6.46878	+	24.1418i	0.384529	+	1.43508i	−0.454379	+	0.890809i	$0.650139\pi$
$284$	1.22797	+	4.58286i	0.0728668	+	0.271942i
$285$		0			0
$286$	8.65732	−	1.77610i	0.511918	−	0.105023i
$287$	5.50943	−	5.50943i	0.325212	−	0.325212i
$288$	−0.0825211	+	0.142931i	−0.00486260	+	0.00842227i
$289$	13.3490	+	7.70705i	0.785235	+	0.453356i
$290$		0			0
$291$	14.1173	−	14.1173i	0.827571	−	0.827571i
$292$	−10.6486	+	6.14798i	−0.623163	+	0.359783i
$293$	17.3578	−	10.0215i	1.01405	−	0.585464i	0.101677	−	0.994817i	$-0.467579\pi$
$293$	17.3578	−	10.0215i	1.01405	−	0.585464i	0.912376	+	0.409354i	$0.134246\pi$
$294$	8.05269	−	8.05269i	0.469642	−	0.469642i
$295$		0			0
$296$	−7.41311	−	4.27996i	−0.430878	−	0.248768i
$297$	−6.18117	+	10.7061i	−0.358668	+	0.621231i
$298$	−10.3246	+	10.3246i	−0.598090	+	0.598090i
$299$	−0.855698	−	0.964010i	−0.0494863	−	0.0557501i
$300$		0			0
$301$	−0.0403481	−	0.150581i	−0.00232562	−	0.00867935i
$302$	4.66040	+	17.3928i	0.268176	+	1.00085i
$303$	−16.3781	−	4.38851i	−0.940900	−	0.252113i
$304$	−0.126725	−	0.126725i	−0.00726820	−	0.00726820i
$305$		0			0
$306$	−0.0537935	+	0.200760i	−0.00307517	+	0.0114767i
$307$	18.0635			1.03094			0.515469	−	0.856908i	$-0.327618\pi$
$307$	18.0635			1.03094			0.515469	+	0.856908i	$0.327618\pi$
$308$	−0.490881	+	1.83199i	−0.0279706	+	0.104388i
$309$	−15.4150	+	26.6996i	−0.876928	+	1.51888i
$310$		0			0
$311$		−	26.0358i		−	1.47635i	−0.674608	−	0.738177i	$-0.735687\pi$
$311$		−	26.0358i		−	1.47635i	0.674608	−	0.738177i	$-0.264313\pi$
$312$	4.25821	+	4.79721i	0.241074	+	0.271588i
$313$	9.77762	+	9.77762i	0.552664	+	0.552664i	0.927209	−	0.374545i	$-0.122201\pi$
$313$	9.77762	+	9.77762i	0.552664	+	0.552664i	−0.374545	+	0.927209i	$0.622201\pi$
$314$	3.93215	−	1.05362i	0.221904	−	0.0594591i
$315$		0			0
$316$	7.50934	−	4.33552i	0.422434	−	0.243892i
$317$			27.2186i			1.52875i	0.644771	+	0.764376i	$0.276953\pi$
$317$			27.2186i			1.52875i	−0.644771	+	0.764376i	$0.723047\pi$
$318$	−1.15563	−	2.00162i	−0.0648047	−	0.112245i
$319$	1.59026	+	0.426108i	0.0890373	+	0.0238575i
$320$		0			0
$321$	−17.0652	−	29.5579i	−0.952489	−	1.64976i
$322$	0.267204	−	0.0715970i	0.0148907	−	0.00398995i
$323$	−0.195456	−	0.112846i	−0.0108755	−	0.00627894i
$324$	−9.46789			−0.525994
$325$		0			0
$326$	13.9049			0.770119
$327$	−2.57217	−	1.48504i	−0.142241	−	0.0821231i
$328$	9.72634	−	2.60617i	0.537047	−	0.143901i
$329$	−3.78741	−	6.55998i	−0.208807	−	0.361664i
$330$		0			0
$331$	32.2610	+	8.64431i	1.77323	+	0.475135i	0.989322	−	0.145747i	$-0.0465586\pi$
$331$	32.2610	+	8.64431i	1.77323	+	0.475135i	0.783904	+	0.620882i	$0.213225\pi$
$332$	−4.47336	−	7.74809i	−0.245508	−	0.425232i
$333$			1.41275i			0.0774181i
$334$	−12.2875	+	7.09421i	−0.672344	+	0.388178i
$335$		0			0
$336$	−1.32969	+	0.356289i	−0.0725404	+	0.0194371i
$337$	4.14484	+	4.14484i	0.225784	+	0.225784i	0.810929	−	0.585145i	$-0.198962\pi$
$337$	4.14484	+	4.14484i	0.225784	+	0.225784i	−0.585145	+	0.810929i	$0.698962\pi$
$338$	11.9499	−	5.11861i	0.649988	−	0.278416i
$339$			7.03103i			0.381873i
$340$		0			0
$341$	3.50072	−	6.06342i	0.189575	−	0.328353i
$342$	−0.00765543	+	0.0285705i	−0.000413958	+	0.00154491i
$343$	10.3696			0.559906
$344$	0.0521443	−	0.194605i	0.00281143	−	0.0104924i
$345$		0			0
$346$	−7.95067	−	7.95067i	−0.427431	−	0.427431i
$347$	4.79055	+	1.28362i	0.257170	+	0.0689085i	0.385101	−	0.922875i	$-0.374167\pi$
$347$	4.79055	+	1.28362i	0.257170	+	0.0689085i	−0.127930	+	0.991783i	$0.540833\pi$
$348$	0.309275	+	1.15423i	0.0165789	+	0.0618733i
$349$	8.15741	+	30.4439i	0.436656	+	1.62962i	0.737072	+	0.675814i	$0.236208\pi$
$349$	8.15741	+	30.4439i	0.436656	+	1.62962i	−0.300416	+	0.953808i	$0.597126\pi$
$350$		0			0
$351$	−5.74191	+	17.2545i	−0.306481	+	0.920975i
$352$	−1.73320	+	1.73320i	−0.0923800	+	0.0923800i
$353$	−14.2281	+	24.6438i	−0.757286	+	1.31166i	0.186943	+	0.982371i	$0.440142\pi$
$353$	−14.2281	+	24.6438i	−0.757286	+	1.31166i	−0.944230	+	0.329288i	$0.893191\pi$
$354$	−1.18468	−	0.683975i	−0.0629650	−	0.0363529i
$355$		0			0
$356$	−9.14299	+	9.14299i	−0.484577	+	0.484577i
$357$	−1.50133	+	0.866792i	−0.0794587	+	0.0458755i
$358$	4.97117	−	2.87010i	0.262734	−	0.151690i
$359$	−11.7211	+	11.7211i	−0.618618	+	0.618618i	−0.945177	−	0.326559i	$-0.894111\pi$
$359$	−11.7211	+	11.7211i	−0.618618	+	0.618618i	0.326559	+	0.945177i	$0.394111\pi$
$360$		0			0
$361$	16.4267	+	9.48394i	0.864561	+	0.499155i
$362$	−3.98944	+	6.90991i	−0.209680	+	0.363177i
$363$	−6.27988	+	6.27988i	−0.329608	+	0.329608i
$364$	−0.165766	+	2.78497i	−0.00868848	+	0.145972i
$365$		0			0
$366$	−6.73817	−	25.1472i	−0.352210	−	1.31447i
$367$	5.26220	+	19.6388i	0.274685	+	1.02514i	0.956052	+	0.293196i	$0.0947189\pi$
$367$	5.26220	+	19.6388i	0.274685	+	1.02514i	−0.681368	+	0.731941i	$0.738614\pi$
$368$	0.345324	+	0.0925293i	0.0180013	+	0.00482342i
$369$	−1.17513	−	1.17513i	−0.0611748	−	0.0611748i
$370$		0			0
$371$	0.260179	−	0.971003i	0.0135078	−	0.0504119i
$372$	5.08174			0.263476
$373$	−4.47138	+	16.6874i	−0.231519	+	0.864042i	0.748168	+	0.663510i	$0.230934\pi$
$373$	−4.47138	+	16.6874i	−0.231519	+	0.864042i	−0.979687	+	0.200532i	$0.935733\pi$
$374$	−1.54338	+	2.67322i	−0.0798064	+	0.138229i
$375$		0			0
$376$		−	9.78940i		−	0.504850i
$377$	2.41748	+	0.143892i	0.124507	+	0.00741083i
$378$	−2.75954	−	2.75954i	−0.141936	−	0.141936i
$379$	14.7036	−	3.93982i	0.755273	−	0.202375i	0.139417	−	0.990234i	$-0.455477\pi$
$379$	14.7036	−	3.93982i	0.755273	−	0.202375i	0.615856	+	0.787859i	$0.288810\pi$
$380$		0			0
$381$	17.7536	−	10.2500i	0.909542	−	0.525124i
$382$		−	22.6625i		−	1.15952i
$383$	−12.0951	−	20.9494i	−0.618032	−	1.07046i	−0.989844	−	0.142155i	$-0.954597\pi$
$383$	−12.0951	−	20.9494i	−0.618032	−	1.07046i	0.371812	−	0.928308i	$-0.378737\pi$
$384$	−1.71844	−	0.460454i	−0.0876936	−	0.0234974i
$385$		0			0
$386$	12.7800	+	22.1356i	0.650484	+	1.12667i
$387$	−0.0321180	+	0.00860600i	−0.00163265	+	0.000437468i
$388$	9.71868	+	5.61108i	0.493391	+	0.284860i
$389$	8.26825			0.419217			0.209608	−	0.977785i	$-0.432781\pi$
$389$	8.26825			0.419217			0.209608	+	0.977785i	$0.432781\pi$
$390$		0			0
$391$	0.450217			0.0227685
$392$	5.54366	+	3.20063i	0.279997	+	0.161656i
$393$	16.5486	−	4.43419i	0.834767	−	0.223675i
$394$	−6.13049	−	10.6183i	−0.308850	−	0.534943i
$395$		0			0
$396$	0.390753	+	0.104702i	0.0196361	+	0.00526148i
$397$	−5.26822	−	9.12482i	−0.264404	−	0.457962i	0.703003	−	0.711187i	$-0.251842\pi$
$397$	−5.26822	−	9.12482i	−0.264404	−	0.457962i	−0.967407	+	0.253225i	$0.918509\pi$
$398$		−	21.2490i		−	1.06511i
$399$	−0.213656	+	0.123354i	−0.0106962	+	0.00617544i
$400$		0			0
$401$	−28.3308	+	7.59122i	−1.41477	+	0.379088i	−0.883627	−	0.468192i	$-0.844906\pi$
$401$	−28.3308	+	7.59122i	−1.41477	+	0.379088i	−0.531147	+	0.847279i	$0.678239\pi$
$402$	−1.29978	−	1.29978i	−0.0648273	−	0.0648273i
$403$	3.25194	−	9.77211i	0.161991	−	0.486783i
$404$		−	9.53084i		−	0.474177i
$405$		0			0
$406$	−0.259864	+	0.450097i	−0.0128968	+	0.0223379i
$407$	−5.43038	+	20.2664i	−0.269174	+	1.00457i
$408$	−2.24042			−0.110917
$409$	3.90885	−	14.5880i	0.193280	−	0.721331i	−0.799425	−	0.600765i	$-0.794863\pi$
$409$	3.90885	−	14.5880i	0.193280	−	0.721331i	0.992705	−	0.120565i	$-0.0384708\pi$
$410$		0			0
$411$	1.13879	+	1.13879i	0.0561725	+	0.0561725i
$412$	−16.7389	−	4.48518i	−0.824667	−	0.220969i
$413$	−0.153990	−	0.574699i	−0.00757736	−	0.0282791i
$414$	−0.0152712	−	0.0569930i	−0.000750540	−	0.00280105i
$415$		0			0
$416$	−1.98512	+	3.00987i	−0.0973284	+	0.147571i
$417$	2.54681	−	2.54681i	0.124718	−	0.124718i
$418$	−0.219641	+	0.380429i	−0.0107430	+	0.0186074i
$419$	21.8423	+	12.6107i	1.06707	+	0.616071i	0.927378	−	0.374125i	$-0.122057\pi$
$419$	21.8423	+	12.6107i	1.06707	+	0.616071i	0.139687	+	0.990196i	$0.455390\pi$
$420$		0			0
$421$	1.12596	−	1.12596i	0.0548760	−	0.0548760i	−0.679136	−	0.734012i	$-0.737645\pi$
$421$	1.12596	−	1.12596i	0.0548760	−	0.0548760i	0.734012	+	0.679136i	$0.237645\pi$
$422$	−13.1519	+	7.59324i	−0.640224	+	0.369633i
$423$	−1.39921	+	0.807832i	−0.0680317	+	0.0392781i
$424$	0.918640	−	0.918640i	0.0446131	−	0.0446131i
$425$		0			0
$426$	7.30992	+	4.22039i	0.354167	+	0.204478i
$427$	5.66164	−	9.80625i	0.273986	−	0.474558i
$428$	13.5656	−	13.5656i	0.655716	−	0.655716i
$429$	8.65646	−	13.1251i	0.417938	−	0.633684i
$430$		0			0
$431$	4.71456	+	17.5950i	0.227092	+	0.847520i	0.981555	+	0.191178i	$0.0612307\pi$
$431$	4.71456	+	17.5950i	0.227092	+	0.847520i	−0.754463	+	0.656343i	$0.772103\pi$
$432$	−1.30537	−	4.87170i	−0.0628045	−	0.234390i
$433$	−11.7924	−	3.15977i	−0.566707	−	0.151849i	−0.0359210	−	0.999355i	$-0.511436\pi$
$433$	−11.7924	−	3.15977i	−0.566707	−	0.151849i	−0.530786	+	0.847506i	$0.678103\pi$
$434$	1.56287	+	1.56287i	0.0750204	+	0.0750204i
$435$		0			0
$436$	0.432091	−	1.61259i	0.0206934	−	0.0772289i
$437$	0.0640710			0.00306493
$438$	−5.66172	+	21.1298i	−0.270527	+	1.00962i
$439$	14.7099	−	25.4783i	0.702066	−	1.21601i	−0.265674	−	0.964063i	$-0.585595\pi$
$439$	14.7099	−	25.4783i	0.702066	−	1.21601i	0.967740	−	0.251951i	$-0.0810721\pi$
$440$		0			0
$441$		−	1.05648i		−	0.0503085i
$442$	−1.43370	+	4.30828i	−0.0681943	+	0.204924i
$443$	−15.0828	−	15.0828i	−0.716607	−	0.716607i	0.251302	−	0.967909i	$-0.419141\pi$
$443$	−15.0828	−	15.0828i	−0.716607	−	0.716607i	−0.967909	+	0.251302i	$0.919141\pi$
$444$	−14.7097	+	3.94145i	−0.698090	+	0.187053i
$445$		0			0
$446$	5.31901	−	3.07093i	0.251863	−	0.145413i
$447$			25.9764i			1.22864i
$448$	−0.386889	−	0.670111i	−0.0182788	−	0.0316598i
$449$	−8.07087	−	2.16258i	−0.380888	−	0.102059i	0.0632947	−	0.997995i	$-0.479839\pi$
$449$	−8.07087	−	2.16258i	−0.380888	−	0.102059i	−0.444183	+	0.895936i	$0.646506\pi$
$450$		0			0
$451$	−12.3407	−	21.3747i	−0.581101	−	1.00650i
$452$	−3.81745	+	1.02288i	−0.179558	+	0.0481123i
$453$	27.7426	+	16.0172i	1.30346	+	0.752554i
$454$	15.2771			0.716992
$455$		0			0
$456$	−0.318837			−0.0149309
$457$	−14.6540	−	8.46052i	−0.685487	−	0.395766i	0.116432	−	0.993199i	$-0.462854\pi$
$457$	−14.6540	−	8.46052i	−0.685487	−	0.395766i	−0.801919	+	0.597432i	$0.796188\pi$
$458$	4.24270	−	1.13683i	0.198248	−	0.0531205i
$459$	−3.17574	−	5.50055i	−0.148231	−	0.256744i
$460$		0			0
$461$	3.13394	+	0.839736i	0.145962	+	0.0391104i	0.331060	−	0.943610i	$-0.392594\pi$
$461$	3.13394	+	0.839736i	0.145962	+	0.0391104i	−0.185098	+	0.982720i	$0.559260\pi$
$462$	1.68710	+	2.92214i	0.0784908	+	0.135950i
$463$		−	11.5604i		−	0.537259i	−0.963244	−	0.268630i	$-0.913429\pi$
$463$		−	11.5604i		−	0.537259i	0.963244	−	0.268630i	$-0.0865708\pi$
$464$	−0.581688	+	0.335838i	−0.0270042	+	0.0155909i
$465$		0			0
$466$	−21.5127	+	5.76432i	−0.996558	+	0.267027i
$467$	−12.4293	−	12.4293i	−0.575162	−	0.575162i	0.358405	−	0.933566i	$-0.383321\pi$
$467$	−12.4293	−	12.4293i	−0.575162	−	0.575162i	−0.933566	+	0.358405i	$0.883321\pi$
$468$	0.594016	+	0.0353568i	0.0274584	+	0.00163437i
$469$		−	0.799488i		−	0.0369169i
$470$		0			0
$471$	3.62115	−	6.27201i	0.166854	−	0.288999i
$472$	0.199011	−	0.742719i	0.00916022	−	0.0341864i
$473$	−0.493827			−0.0227062
$474$	3.99261	−	14.9006i	0.183387	−	0.684409i
$475$		0			0
$476$	−0.689033	−	0.689033i	−0.0315818	−	0.0315818i
$477$	−0.207109	−	0.0554947i	−0.00948287	−	0.00254093i
$478$	−1.43287	−	5.34753i	−0.0655378	−	0.244590i
$479$	−5.39239	−	20.1247i	−0.246385	−	0.919520i	−0.972682	−	0.232140i	$-0.925427\pi$
$479$	−5.39239	−	20.1247i	−0.246385	−	0.919520i	0.726298	−	0.687380i	$-0.241239\pi$
$480$		0			0
$481$	−1.83378	+	30.8087i	−0.0836133	+	1.40476i
$482$	−0.113386	+	0.113386i	−0.00516460	+	0.00516460i
$483$	0.246070	−	0.426206i	0.0111966	−	0.0193930i
$484$	−4.32322	−	2.49601i	−0.196510	−	0.113455i
$485$		0			0
$486$	−1.21145	+	1.21145i	−0.0549527	+	0.0549527i
$487$	−1.49645	+	0.863977i	−0.0678107	+	0.0391505i	−0.533522	−	0.845786i	$-0.679132\pi$
$487$	−1.49645	+	0.863977i	−0.0678107	+	0.0391505i	0.465711	+	0.884937i	$0.345799\pi$
$488$	12.6732	−	7.31689i	0.573690	−	0.331220i
$489$	17.4921	−	17.4921i	0.791019	−	0.791019i
$490$		0			0
$491$	0.747027	+	0.431296i	0.0337129	+	0.0194641i	0.516762	−	0.856129i	$-0.327137\pi$
$491$	0.747027	+	0.431296i	0.0337129	+	0.0194641i	−0.483049	+	0.875593i	$0.660471\pi$
$492$	8.95706	−	15.5141i	0.403816	−	0.699429i
$493$	−0.598113	+	0.598113i	−0.0269377	+	0.0269377i
$494$	−0.204032	+	0.613118i	−0.00917985	+	0.0275855i
$495$		0			0
$496$	0.739298	+	2.75910i	0.0331954	+	0.123887i
$497$	0.950178	+	3.54611i	0.0426213	+	0.159065i
$498$	−15.3744	−	4.11955i	−0.688943	−	0.184602i
$499$	4.24329	+	4.24329i	0.189956	+	0.189956i	0.795677	−	0.605721i	$-0.207115\pi$
$499$	4.24329	+	4.24329i	0.189956	+	0.189956i	−0.605721	+	0.795677i	$0.707115\pi$
$500$		0			0
$501$	−6.53311	+	24.3819i	−0.291878	+	1.08930i
$502$	27.7904			1.24035
$503$	−0.300105	+	1.12001i	−0.0133810	+	0.0499387i	−0.972294	−	0.233763i	$-0.924896\pi$
$503$	−0.300105	+	1.12001i	−0.0133810	+	0.0499387i	0.958913	+	0.283702i	$0.0915626\pi$
$504$	−0.0638529	+	0.110597i	−0.00284424	+	0.00492636i
$505$		0			0
$506$		−	0.876288i		−	0.0389558i
$507$	8.59363	−	21.4719i	0.381657	−	0.953600i
$508$	8.14798	+	8.14798i	0.361508	+	0.361508i
$509$	−17.3274	+	4.64287i	−0.768024	+	0.205792i	−0.621499	−	0.783415i	$-0.713476\pi$
$509$	−17.3274	+	4.64287i	−0.768024	+	0.205792i	−0.146526	+	0.989207i	$0.546809\pi$
$510$		0			0
$511$	−8.23965	+	4.75717i	−0.364501	+	0.210445i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.451945	−	0.782791i	−0.0199538	−	0.0345611i
$514$	3.64080	+	0.975550i	0.160589	+	0.0430297i
$515$		0			0
$516$	−0.179213	−	0.310407i	−0.00788943	−	0.0136649i
$517$	−23.1774	+	6.21036i	−1.01934	+	0.273131i
$518$	−5.73610	−	3.31174i	−0.252030	−	0.145509i
$519$	−20.0036			−0.878061
$520$		0			0
$521$	−20.1521			−0.882878			−0.441439	−	0.897291i	$-0.645532\pi$
$521$	−20.1521			−0.882878			−0.441439	+	0.897291i	$0.645532\pi$
$522$	0.0960030	+	0.0554273i	0.00420194	+	0.00242599i
$523$	17.0205	−	4.56062i	0.744252	−	0.199422i	0.133285	−	0.991078i	$-0.457447\pi$
$523$	17.0205	−	4.56062i	0.744252	−	0.199422i	0.610967	+	0.791656i	$0.290781\pi$
$524$	4.81502	+	8.33986i	0.210345	+	0.364328i
$525$		0			0
$526$	16.8872	+	4.52492i	0.736318	+	0.197296i
$527$	1.79859	+	3.11525i	0.0783478	+	0.135702i
$528$			4.36068i			0.189774i
$529$	19.8079	−	11.4361i	0.861213	−	0.497222i
$530$		0			0
$531$	−0.122580	+	0.0328452i	−0.00531951	+	0.00142536i
$532$	−0.0980573	−	0.0980573i	−0.00425132	−	0.00425132i
$533$	−24.1015	−	27.1522i	−1.04395	−	1.17609i
$534$			23.0034i			0.995457i
$535$		0			0
$536$	0.516614	−	0.894801i	0.0223143	−	0.0386495i
$537$	2.64310	−	9.86418i	0.114058	−	0.425671i
$538$	−26.0363			−1.12250
$539$	4.06094	−	15.1556i	0.174917	−	0.652799i
$540$		0			0
$541$	−8.75869	−	8.75869i	−0.376566	−	0.376566i	0.493296	−	0.869862i	$-0.335792\pi$
$541$	−8.75869	−	8.75869i	−0.376566	−	0.376566i	−0.869862	+	0.493296i	$0.835792\pi$
$542$	0.804227	+	0.215492i	0.0345445	+	0.00925617i
$543$	3.67390	+	13.7112i	0.157662	+	0.588404i
$544$	−0.325938	−	1.21642i	−0.0139745	−	0.0521535i
$545$		0			0
$546$	3.29491	+	3.71197i	0.141009	+	0.158858i
$547$	28.6176	−	28.6176i	1.22360	−	1.22360i	0.257256	−	0.966343i	$-0.417182\pi$
$547$	28.6176	−	28.6176i	1.22360	−	1.22360i	0.966343	−	0.257256i	$-0.0828183\pi$
$548$	−0.452627	+	0.783972i	−0.0193353	+	0.0334896i
$549$	−2.09161	−	1.20759i	−0.0892679	−	0.0515389i
$550$		0			0
$551$	−0.0851183	+	0.0851183i	−0.00362616	+	0.00362616i
$552$	0.550812	−	0.318011i	0.0234441	−	0.0135355i
$553$	5.81056	−	3.35473i	0.247090	−	0.142658i
$554$	−5.07030	+	5.07030i	−0.215416	+	0.215416i
$555$		0			0
$556$	1.75329	+	1.01226i	0.0743559	+	0.0429294i
$557$	0.290718	−	0.503539i	0.0123181	−	0.0213356i	−0.859801	−	0.510630i	$-0.829412\pi$
$557$	0.290718	−	0.503539i	0.0123181	−	0.0213356i	0.872119	+	0.489294i	$0.162746\pi$
$558$	0.333352	−	0.333352i	0.0141119	−	0.0141119i
$559$	−0.711590	+	0.145987i	−0.0300970	+	0.00617458i
$560$		0			0
$561$	1.42131	+	5.30441i	0.0600078	+	0.223952i
$562$	5.97603	+	22.3029i	0.252084	+	0.940789i
$563$	6.84916	+	1.83523i	0.288658	+	0.0773456i	0.400242	−	0.916409i	$-0.368926\pi$
$563$	6.84916	+	1.83523i	0.288658	+	0.0773456i	−0.111585	+	0.993755i	$0.535593\pi$
$564$	−12.3149	−	12.3149i	−0.518551	−	0.518551i
$565$		0			0
$566$	−6.46878	+	24.1418i	−0.271903	+	1.01476i
$567$	−7.32604			−0.307665
$568$	−1.22797	+	4.58286i	−0.0515246	+	0.192292i
$569$	−11.4714	+	19.8690i	−0.480904	+	0.832950i	−0.999760	−	0.0219115i	$-0.993025\pi$
$569$	−11.4714	+	19.8690i	−0.480904	+	0.832950i	0.518856	+	0.854862i	$0.326358\pi$
$570$		0			0
$571$		−	10.3285i		−	0.432233i	−0.976368	−	0.216117i	$-0.930661\pi$
$571$		−	10.3285i		−	0.432233i	0.976368	−	0.216117i	$-0.0693391\pi$
$572$	8.38551	+	2.79051i	0.350616	+	0.116677i
$573$	−28.5091	−	28.5091i	−1.19098	−	1.19098i
$574$	7.52602	−	2.01659i	0.314130	−	0.0841709i
$575$		0			0
$576$	−0.142931	+	0.0825211i	−0.00595544	+	0.00343838i
$577$		−	0.576251i		−	0.0239897i	−0.999928	−	0.0119948i	$-0.996182\pi$
$577$		−	0.576251i		−	0.0239897i	0.999928	−	0.0119948i	$-0.00381816\pi$
$578$	7.70705	+	13.3490i	0.320571	+	0.555245i
$579$	43.9232	+	11.7692i	1.82539	+	0.489111i
$580$		0			0
$581$	−3.46139	−	5.99530i	−0.143603	−	0.248727i
$582$	19.2846	−	5.16729i	0.799372	−	0.214191i
$583$	−2.75775	−	1.59219i	−0.114214	−	0.0659418i
$584$	−12.2960			−0.508810
$585$		0			0
$586$	20.0431			0.827971
$587$	−18.8584	−	10.8879i	−0.778370	−	0.449392i	0.0574823	−	0.998347i	$-0.481693\pi$
$587$	−18.8584	−	10.8879i	−0.778370	−	0.449392i	−0.835852	+	0.548954i	$0.815026\pi$
$588$	11.0002	−	2.94749i	0.453640	−	0.121552i
$589$	0.255960	+	0.443336i	0.0105466	+	0.0182673i
$590$		0			0
$591$	−21.0697	−	5.64561i	−0.866692	−	0.232229i
$592$	−4.27996	−	7.41311i	−0.175905	−	0.304677i
$593$			3.64436i			0.149656i	0.997196	+	0.0748280i	$0.0238408\pi$
$593$			3.64436i			0.149656i	−0.997196	+	0.0748280i	$0.976159\pi$
$594$	−10.7061	+	6.18117i	−0.439276	+	0.253616i
$595$		0			0
$596$	−14.1037	+	3.77908i	−0.577711	+	0.154797i
$597$	−26.7308	−	26.7308i	−1.09402	−	1.09402i
$598$	−0.259051	−	1.26271i	−0.0105934	−	0.0516359i
$599$		−	39.9829i		−	1.63366i	−0.576881	−	0.816828i	$-0.695730\pi$
$599$		−	39.9829i		−	1.63366i	0.576881	−	0.816828i	$-0.304270\pi$
$600$		0			0
$601$	4.69804	−	8.13724i	0.191637	−	0.331925i	−0.754156	−	0.656695i	$-0.771954\pi$
$601$	4.69804	−	8.13724i	0.191637	−	0.331925i	0.945793	+	0.324770i	$0.105287\pi$
$602$	0.0403481	−	0.150581i	0.00164446	−	0.00613723i
$603$	−0.170526			−0.00694436
$604$	−4.66040	+	17.3928i	−0.189629	+	0.707705i
$605$		0			0
$606$	−11.9896	−	11.9896i	−0.487046	−	0.487046i
$607$	−6.33176	−	1.69659i	−0.256998	−	0.0688624i	0.128020	−	0.991772i	$-0.459138\pi$
$607$	−6.33176	−	1.69659i	−0.256998	−	0.0688624i	−0.385018	+	0.922909i	$0.625805\pi$
$608$	−0.0463847	−	0.173110i	−0.00188115	−	0.00702054i
$609$	0.239310	+	0.893118i	0.00969734	+	0.0361910i
$610$		0			0
$611$	−31.5620	+	15.8007i	−1.27686	+	0.639228i
$612$	−0.146967	+	0.146967i	−0.00594078	+	0.00594078i
$613$	−2.67526	+	4.63368i	−0.108053	+	0.187153i	−0.914981	−	0.403496i	$-0.867795\pi$
$613$	−2.67526	+	4.63368i	−0.108053	+	0.187153i	0.806929	+	0.590649i	$0.201128\pi$
$614$	15.6435	+	9.03175i	0.631319	+	0.364492i
$615$		0			0
$616$	−1.34111	+	1.34111i	−0.0540350	+	0.0540350i
$617$	6.30916	−	3.64259i	0.253997	−	0.146645i	−0.367596	−	0.929986i	$-0.619819\pi$
$617$	6.30916	−	3.64259i	0.253997	−	0.146645i	0.621593	+	0.783340i	$0.286486\pi$
$618$	−26.6996	+	15.4150i	−1.07401	+	0.620082i
$619$	−29.6086	+	29.6086i	−1.19007	+	1.19007i	−0.213022	+	0.977047i	$0.568331\pi$
$619$	−29.6086	+	29.6086i	−1.19007	+	1.19007i	−0.977047	+	0.213022i	$0.931669\pi$
$620$		0			0
$621$	1.56153	+	0.901549i	0.0626620	+	0.0361779i
$622$	13.0179	−	22.5476i	0.521970	−	0.904078i
$623$	−7.07464	+	7.07464i	−0.283439	+	0.283439i
$624$	1.28912	+	6.28361i	0.0516060	+	0.251546i
$625$		0			0
$626$	3.57886	+	13.3565i	0.143040	+	0.533832i
$627$	0.202269	+	0.754878i	0.00807784	+	0.0301469i
$628$	3.93215	+	1.05362i	0.156910	+	0.0420439i
$629$	−7.62244	−	7.62244i	−0.303926	−	0.303926i
$630$		0			0
$631$	−8.22180	+	30.6842i	−0.327305	+	1.22152i	0.584670	+	0.811271i	$0.301224\pi$
$631$	−8.22180	+	30.6842i	−0.327305	+	1.22152i	−0.911975	+	0.410247i	$0.865443\pi$
$632$	8.67104			0.344916
$633$	−6.99267	+	26.0970i	−0.277934	+	1.03726i
$634$	−13.6093	+	23.5720i	−0.540495	+	0.936165i
$635$		0			0
$636$		−	2.31127i		−	0.0916477i
$637$	1.37134	−	23.0393i	0.0543344	−	0.912851i
$638$	1.16415	+	1.16415i	0.0460891	+	0.0460891i
$639$	0.756364	−	0.202667i	0.0299213	−	0.00801739i
$640$		0			0
$641$	15.5764	−	8.99301i	0.615229	−	0.355203i	−0.159780	−	0.987153i	$-0.551079\pi$
$641$	15.5764	−	8.99301i	0.615229	−	0.355203i	0.775009	+	0.631950i	$0.217745\pi$
$642$		−	34.1305i		−	1.34702i
$643$	−7.41717	−	12.8469i	−0.292505	−	0.506633i	0.681897	−	0.731449i	$-0.261155\pi$
$643$	−7.41717	−	12.8469i	−0.292505	−	0.506633i	−0.974401	+	0.224816i	$0.927822\pi$
$644$	0.267204	+	0.0715970i	0.0105293	+	0.00282132i
$645$		0			0
$646$	−0.112846	−	0.195456i	−0.00443988	−	0.00769011i
$647$	−21.4425	+	5.74551i	−0.842993	+	0.225879i	−0.654374	−	0.756171i	$-0.727068\pi$
$647$	−21.4425	+	5.74551i	−0.842993	+	0.225879i	−0.188619	+	0.982050i	$0.560401\pi$
$648$	−8.19943	−	4.73394i	−0.322104	−	0.185967i
$649$	−1.88471			−0.0739814
$650$		0			0
$651$	3.93214			0.154113
$652$	12.0420	+	6.95243i	0.471600	+	0.272278i
$653$	−14.1584	+	3.79373i	−0.554060	+	0.148460i	−0.524976	−	0.851117i	$-0.675926\pi$
$653$	−14.1584	+	3.79373i	−0.554060	+	0.148460i	−0.0290840	+	0.999577i	$0.509259\pi$
$654$	−1.48504	−	2.57217i	−0.0580698	−	0.100580i
$655$		0			0
$656$	9.72634	+	2.60617i	0.379750	+	0.101754i
$657$	1.01467	+	1.75747i	0.0395862	+	0.0685654i
$658$		−	7.57482i		−	0.295297i
$659$	−26.6381	+	15.3795i	−1.03767	+	0.599101i	−0.919174	−	0.393853i	$-0.871142\pi$
$659$	−26.6381	+	15.3795i	−1.03767	+	0.599101i	−0.118500	+	0.992954i	$0.537809\pi$
$660$		0			0
$661$	−23.6815	+	6.34545i	−0.921105	+	0.246809i	−0.688057	−	0.725656i	$-0.741536\pi$
$661$	−23.6815	+	6.34545i	−0.921105	+	0.246809i	−0.233047	+	0.972465i	$0.574870\pi$
$662$	23.6167	+	23.6167i	0.917889	+	0.917889i
$663$	3.61617	+	7.22332i	0.140441	+	0.280531i
$664$		−	8.94673i		−	0.347200i
$665$		0			0
$666$	−0.706374	+	1.22347i	−0.0273714	+	0.0474087i
$667$	0.0621496	−	0.231945i	0.00240644	−	0.00898096i
$668$	−14.1884			−0.548966
$669$	2.82805	−	10.5544i	0.109339	−	0.408057i
$670$		0			0
$671$	−25.3633	−	25.3633i	−0.979139	−	0.979139i
$672$	−1.32969	−	0.356289i	−0.0512938	−	0.0137441i
$673$	−6.80086	−	25.3811i	−0.262154	−	0.978371i	−0.963970	−	0.266013i	$-0.914294\pi$
$673$	−6.80086	−	25.3811i	−0.262154	−	0.978371i	0.701816	−	0.712358i	$-0.252373\pi$
$674$	1.51712	+	5.66196i	0.0584372	+	0.218090i
$675$		0			0
$676$	12.9082	+	1.54210i	0.496470	+	0.0593115i
$677$	33.1300	−	33.1300i	1.27329	−	1.27329i	0.328938	−	0.944352i	$-0.393309\pi$
$677$	33.1300	−	33.1300i	1.27329	−	1.27329i	0.944352	−	0.328938i	$-0.106691\pi$
$678$	−3.51552	+	6.08905i	−0.135013	+	0.233849i
$679$	7.52010	+	4.34173i	0.288595	+	0.166620i
$680$		0			0
$681$	19.2184	−	19.2184i	0.736450	−	0.736450i
$682$	6.06342	−	3.50072i	0.232180	−	0.134049i
$683$	−2.44081	+	1.40920i	−0.0933950	+	0.0539216i	−0.545970	−	0.837805i	$-0.683839\pi$
$683$	−2.44081	+	1.40920i	−0.0933950	+	0.0539216i	0.452575	+	0.891726i	$0.350505\pi$
$684$	−0.0209150	+	0.0209150i	−0.000799706	+	0.000799706i
$685$		0			0
$686$	8.98034	+	5.18480i	0.342871	+	0.197957i
$687$	3.90714	−	6.76736i	0.149067	−	0.258191i
$688$	0.142461	−	0.142461i	0.00543127	−	0.00543127i
$689$	−4.44453	−	1.47904i	−0.169323	−	0.0563470i
$690$		0			0
$691$	0.801327	+	2.99059i	0.0304839	+	0.113768i	0.979491	−	0.201486i	$-0.0645771\pi$
$691$	0.801327	+	2.99059i	0.0304839	+	0.113768i	−0.949007	+	0.315254i	$0.897910\pi$
$692$	−2.91015	−	10.8608i	−0.110627	−	0.412866i
$693$	0.302356	+	0.0810161i	0.0114856	+	0.00307755i
$694$	3.50692	+	3.50692i	0.133121	+	0.133121i
$695$		0			0
$696$	−0.309275	+	1.15423i	−0.0117231	+	0.0437510i
$697$	12.6807			0.480318
$698$	−8.15741	+	30.4439i	−0.308762	+	1.15232i
$699$	−19.8112	+	34.3141i	−0.749330	+	1.29788i
$700$		0			0
$701$			22.6870i			0.856875i	0.903571	+	0.428438i	$0.140936\pi$
$701$			22.6870i			0.856875i	−0.903571	+	0.428438i	$0.859064\pi$
$702$	−13.5999	+	12.0719i	−0.513294	+	0.455623i
$703$	−1.08476	−	1.08476i	−0.0409125	−	0.0409125i
$704$	−2.36760	+	0.634396i	−0.0892322	+	0.0239097i
$705$		0			0
$706$	−24.6438	+	14.2281i	−0.927483	+	0.535482i
$707$		−	7.37475i		−	0.277356i
$708$	−0.683975	−	1.18468i	−0.0257054	−	0.0445230i
$709$	−7.63472	−	2.04572i	−0.286728	−	0.0768285i	0.112589	−	0.993642i	$-0.464086\pi$
$709$	−7.63472	−	2.04572i	−0.286728	−	0.0768285i	−0.399316	+	0.916813i	$0.630752\pi$
$710$		0			0
$711$	−0.715544	−	1.23936i	−0.0268350	−	0.0464796i
$712$	−12.4896	+	3.34657i	−0.468066	+	0.125418i
$713$	−0.884375	−	0.510594i	−0.0331201	−	0.0191219i
$714$	−1.73358			−0.0648778
$715$		0			0
$716$	5.74021			0.214522
$717$	−8.52962	−	4.92458i	−0.318545	−	0.183912i
$718$	−16.0114	+	4.29023i	−0.597539	+	0.160110i
$719$	−9.22690	−	15.9815i	−0.344105	−	0.596008i	0.641086	−	0.767469i	$-0.278484\pi$
$719$	−9.22690	−	15.9815i	−0.344105	−	0.596008i	−0.985191	+	0.171462i	$0.945151\pi$
$720$		0			0
$721$	−12.9522	−	3.47053i	−0.482365	−	0.129249i
$722$	9.48394	+	16.4267i	0.352956	+	0.611337i
$723$			0.285276i			0.0106095i
$724$	−6.90991	+	3.98944i	−0.256805	+	0.148266i
$725$		0			0
$726$	−8.57847	+	2.29859i	−0.318377	+	0.0853089i
$727$	−18.3675	−	18.3675i	−0.681214	−	0.681214i	0.279060	−	0.960274i	$-0.409977\pi$
$727$	−18.3675	−	18.3675i	−0.681214	−	0.681214i	−0.960274	+	0.279060i	$0.909977\pi$
$728$	−1.53604	+	2.32897i	−0.0569294	+	0.0863173i
$729$		−	25.3557i		−	0.939099i
$730$		0			0
$731$	0.126859	−	0.219725i	0.00469203	−	0.00812684i
$732$	6.73817	−	25.1472i	0.249050	−	0.929468i
$733$	11.9202			0.440282			0.220141	−	0.975468i	$-0.429348\pi$
$733$	11.9202			0.440282			0.220141	+	0.975468i	$0.429348\pi$
$734$	−5.26220	+	19.6388i	−0.194231	+	0.724882i
$735$		0			0
$736$	0.252795	+	0.252795i	0.00931813	+	0.00931813i
$737$	−2.44627	−	0.655475i	−0.0901094	−	0.0241447i
$738$	−0.430127	−	1.60526i	−0.0158332	−	0.0590903i
$739$	−2.47875	−	9.25081i	−0.0911822	−	0.340297i	0.905231	−	0.424920i	$-0.139698\pi$
$739$	−2.47875	−	9.25081i	−0.0911822	−	0.340297i	−0.996413	+	0.0846236i	$0.973031\pi$
$740$		0			0
$741$	0.514623	+	1.02796i	0.0189051	+	0.0377631i
$742$	0.710823	−	0.710823i	0.0260951	−	0.0260951i
$743$	−17.1373	+	29.6828i	−0.628708	+	1.08895i	0.359103	+	0.933298i	$0.383083\pi$
$743$	−17.1373	+	29.6828i	−0.628708	+	1.08895i	−0.987811	+	0.155657i	$0.950251\pi$
$744$	4.40092	+	2.54087i	0.161346	+	0.0931529i
$745$		0			0
$746$	−12.2160	+	12.2160i	−0.447261	+	0.447261i
$747$	−1.27876	+	0.738293i	−0.0467874	+	0.0270127i
$748$	−2.67322	+	1.54338i	−0.0977424	+	0.0564316i
$749$	10.4967	−	10.4967i	0.383542	−	0.383542i
$750$		0			0
$751$	−27.4571	−	15.8524i	−1.00193	−	0.578462i	−0.0931081	−	0.995656i	$-0.529680\pi$
$751$	−27.4571	−	15.8524i	−1.00193	−	0.578462i	−0.908817	+	0.417194i	$0.863014\pi$
$752$	4.89470	−	8.47787i	0.178491	−	0.309156i
$753$	34.9598	−	34.9598i	1.27401	−	1.27401i
$754$	2.02165	+	1.33335i	0.0736243	+	0.0485579i
$755$		0			0
$756$	−1.01006	−	3.76961i	−0.0367357	−	0.137099i
$757$	10.2285	+	38.1732i	0.371760	+	1.38743i	0.858021	+	0.513614i	$0.171694\pi$
$757$	10.2285	+	38.1732i	0.371760	+	1.38743i	−0.486261	+	0.873814i	$0.661640\pi$
$758$	14.7036	+	3.93982i	0.534059	+	0.143101i
$759$	−1.10236	−	1.10236i	−0.0400130	−	0.0400130i
$760$		0			0
$761$	6.83854	−	25.5218i	0.247897	−	0.925164i	−0.724008	−	0.689791i	$-0.757702\pi$
$761$	6.83854	−	25.5218i	0.247897	−	0.925164i	0.971905	−	0.235373i	$-0.0756310\pi$
$762$	20.5000			0.742638
$763$	0.334343	−	1.24778i	0.0121040	−	0.0451728i
$764$	11.3313	−	19.6263i	0.409951	−	0.710055i
$765$		0			0
$766$		−	24.1903i		−	0.874030i
$767$	−2.71581	+	0.557164i	−0.0980623	+	0.0201180i
$768$	−1.25798	−	1.25798i	−0.0453935	−	0.0453935i
$769$	12.1496	−	3.25549i	0.438127	−	0.117396i	−0.0330114	−	0.999455i	$-0.510510\pi$
$769$	12.1496	−	3.25549i	0.438127	−	0.117396i	0.471139	+	0.882059i	$0.343843\pi$
$770$		0			0
$771$	5.80729	−	3.35284i	0.209145	−	0.120750i
$772$			25.5600i			0.919924i
$773$	15.7616	+	27.2999i	0.566905	+	0.981907i	0.996870	+	0.0790620i	$0.0251925\pi$
$773$	15.7616	+	27.2999i	0.566905	+	0.981907i	−0.429965	+	0.902845i	$0.641474\pi$
$774$	−0.0321180	−	0.00860600i	−0.00115446	−	0.000309336i
$775$		0			0
$776$	5.61108	+	9.71868i	0.201426	+	0.348880i
$777$	−11.3820	+	3.04980i	−0.408328	+	0.109411i
$778$	7.16051	+	4.13412i	0.256717	+	0.148216i
$779$	1.80462			0.0646571
$780$		0			0
$781$	11.6294			0.416132
$782$	0.389899	+	0.225109i	0.0139428	+	0.00804986i
$783$	−3.27220	+	0.876783i	−0.116939	+	0.0313337i
$784$	3.20063	+	5.54366i	0.114308	+	0.197988i
$785$		0			0
$786$	16.5486	+	4.43419i	0.590269	+	0.158162i
$787$	−8.54859	−	14.8066i	−0.304724	−	0.527798i	0.672475	−	0.740119i	$-0.265231\pi$
$787$	−8.54859	−	14.8066i	−0.304724	−	0.527798i	−0.977200	+	0.212321i	$0.931898\pi$
$788$		−	12.2610i		−	0.436779i
$789$	26.9361	−	15.5516i	0.958952	−	0.553651i
$790$		0			0
$791$	−2.95385	+	0.791483i	−0.105027	+	0.0281419i
$792$	0.286051	+	0.286051i	0.0101644	+	0.0101644i
$793$	−44.0457	−	29.0498i	−1.56411	−	1.03159i
$794$		−	10.5364i		−	0.373924i
$795$		0			0
$796$	10.6245	−	18.4021i	0.376575	−	0.652246i
$797$	−10.2086	+	38.0990i	−0.361607	+	1.34954i	0.510355	+	0.859964i	$0.329514\pi$
$797$	−10.2086	+	38.0990i	−0.361607	+	1.34954i	−0.871962	+	0.489573i	$0.837153\pi$
$798$	−0.246709			−0.00873340
$799$	3.19074	−	11.9080i	0.112880	−	0.421275i
$800$		0			0
$801$	1.50898	+	1.50898i	0.0533171	+	0.0533171i
$802$	−28.3308	−	7.59122i	−1.00040	−	0.268055i
$803$	7.80050	+	29.1119i	0.275274	+	1.02734i
$804$	−0.475753	−	1.77554i	−0.0167785	−	0.0626183i
$805$		0			0
$806$	7.70232	−	6.83692i	0.271303	−	0.240820i
$807$	−32.7532	+	32.7532i	−1.15297	+	1.15297i
$808$	4.76542	−	8.25395i	0.167647	−	0.290373i
$809$	−19.7531	−	11.4045i	−0.694483	−	0.400960i	0.110806	−	0.993842i	$-0.464657\pi$
$809$	−19.7531	−	11.4045i	−0.694483	−	0.400960i	−0.805289	+	0.592882i	$0.797990\pi$
$810$		0			0
$811$	23.0864	−	23.0864i	0.810674	−	0.810674i	−0.174061	−	0.984735i	$-0.555689\pi$
$811$	23.0864	−	23.0864i	0.810674	−	0.810674i	0.984735	+	0.174061i	$0.0556890\pi$
$812$	−0.450097	+	0.259864i	−0.0157953	+	0.00911942i
$813$	1.28279	−	0.740618i	0.0449893	−	0.0259746i
$814$	−14.8361	+	14.8361i	−0.520004	+	0.520004i
$815$		0			0
$816$	−1.94026	−	1.12021i	−0.0679226	−	0.0392151i
$817$	0.0180534	−	0.0312694i	0.000631609	−	0.00109398i
$818$	10.6792	−	10.6792i	0.373388	−	0.373388i
$819$	0.459637	+	0.0273583i	0.0160610	+	0.000955977i
$820$		0			0
$821$	−3.72201	−	13.8907i	−0.129899	−	0.484790i	0.870068	−	0.492932i	$-0.164075\pi$
$821$	−3.72201	−	13.8907i	−0.129899	−	0.484790i	−0.999967	+	0.00814199i	$0.997408\pi$
$822$	0.416827	+	1.55562i	0.0145385	+	0.0542585i
$823$	41.2386	+	11.0499i	1.43749	+	0.385174i	0.891653	−	0.452719i	$-0.149546\pi$
$823$	41.2386	+	11.0499i	1.43749	+	0.385174i	0.545835	+	0.837893i	$0.316212\pi$
$824$	−12.2537	−	12.2537i	−0.426879	−	0.426879i
$825$		0			0
$826$	0.153990	−	0.574699i	0.00535800	−	0.0199963i
$827$	−50.0663			−1.74098			−0.870488	−	0.492189i	$-0.836197\pi$
$827$	−50.0663			−1.74098			−0.870488	+	0.492189i	$0.836197\pi$
$828$	0.0152712	−	0.0569930i	0.000530712	−	0.00198064i
$829$	18.8278	−	32.6107i	0.653916	−	1.13262i	−0.328248	−	0.944592i	$-0.606458\pi$
$829$	18.8278	−	32.6107i	0.653916	−	1.13262i	0.982164	−	0.188025i	$-0.0602084\pi$
$830$		0			0
$831$			12.7567i			0.442525i
$832$	−3.22410	+	1.61406i	−0.111775	+	0.0559576i
$833$	5.70020	+	5.70020i	0.197500	+	0.197500i
$834$	3.47901	−	0.932199i	0.120468	−	0.0322794i
$835$		0			0
$836$	−0.380429	+	0.219641i	−0.0131574	+	0.00759644i
$837$			14.4065i			0.497963i
$838$	12.6107	+	21.8423i	0.435628	+	0.754529i
$839$	27.1992	+	7.28802i	0.939022	+	0.251610i	0.695698	−	0.718335i	$-0.255095\pi$
$839$	27.1992	+	7.28802i	0.939022	+	0.251610i	0.243325	+	0.969945i	$0.421762\pi$
$840$		0			0
$841$	−14.2744	−	24.7240i	−0.492222	−	0.852553i
$842$	1.53809	−	0.412130i	0.0530061	−	0.0142029i
$843$	35.5744	+	20.5389i	1.22525	+	0.707396i
$844$	−15.1865			−0.522740
$845$		0			0
$846$	−1.61566			−0.0555477
$847$	−3.34521	−	1.93136i	−0.114943	−	0.0663622i
$848$	1.25489	−	0.336246i	0.0430930	−	0.0115467i
$849$	22.2324	+	38.5076i	0.763013	+	1.32158i
$850$		0			0
$851$	2.95594	+	0.792043i	0.101328	+	0.0271509i
$852$	4.22039	+	7.30992i	0.144588	+	0.250434i
$853$		−	32.0153i		−	1.09618i	−0.836419	−	0.548091i	$-0.815355\pi$
$853$		−	32.0153i		−	1.09618i	0.836419	−	0.548091i	$-0.184645\pi$
$854$	9.80625	−	5.66164i	0.335563	−	0.193737i
$855$		0			0
$856$	18.5309	−	4.96534i	0.633373	−	0.169712i
$857$	23.1260	+	23.1260i	0.789968	+	0.789968i	0.981489	−	0.191521i	$-0.0613419\pi$
$857$	23.1260	+	23.1260i	0.789968	+	0.789968i	−0.191521	+	0.981489i	$0.561342\pi$
$858$	14.0592	−	7.03841i	0.479975	−	0.240287i
$859$			17.2021i			0.586927i	0.955970	+	0.293463i	$0.0948079\pi$
$859$			17.2021i			0.586927i	−0.955970	+	0.293463i	$0.905192\pi$
$860$		0			0
$861$	6.93077	−	12.0044i	0.236200	−	0.409111i
$862$	−4.71456	+	17.5950i	−0.160579	+	0.599287i
$863$	−21.5671			−0.734153			−0.367077	−	0.930191i	$-0.619641\pi$
$863$	−21.5671			−0.734153			−0.367077	+	0.930191i	$0.619641\pi$
$864$	1.30537	−	4.87170i	0.0444095	−	0.165738i
$865$		0			0
$866$	−8.63264	−	8.63264i	−0.293349	−	0.293349i
$867$	26.4881	+	7.09748i	0.899584	+	0.241043i
$868$	0.572052	+	2.13493i	0.0194167	+	0.0724641i
$869$	−5.50088	−	20.5295i	−0.186604	−	0.696417i
$870$		0			0
$871$	−3.71877	−	0.221347i	−0.126006	−	0.00750007i
$872$	1.18050	−	1.18050i	0.0399766	−	0.0399766i
$873$	0.926065	−	1.60399i	0.0313426	−	0.0542869i
$874$	0.0554871	+	0.0320355i	0.00187688	+	0.00108362i
$875$		0			0
$876$	−15.4681	+	15.4681i	−0.522619	+	0.522619i
$877$	7.43862	−	4.29469i	0.251184	−	0.145021i	−0.369122	−	0.929381i	$-0.620342\pi$
$877$	7.43862	−	4.29469i	0.251184	−	0.145021i	0.620306	+	0.784360i	$0.287008\pi$
$878$	25.4783	−	14.7099i	0.859852	−	0.496436i
$879$	25.2138	−	25.2138i	0.850441	−	0.850441i
$880$		0			0
$881$	24.3217	+	14.0421i	0.819419	+	0.473092i	0.850216	−	0.526434i	$-0.176471\pi$
$881$	24.3217	+	14.0421i	0.819419	+	0.473092i	−0.0307970	+	0.999526i	$0.509805\pi$
$882$	0.528239	−	0.914938i	0.0177867	−	0.0308076i
$883$	−11.6657	+	11.6657i	−0.392583	+	0.392583i	−0.875607	−	0.483024i	$-0.839538\pi$
$883$	−11.6657	+	11.6657i	−0.392583	+	0.392583i	0.483024	+	0.875607i	$0.339538\pi$
$884$	−3.39577	+	3.01423i	−0.114212	+	0.101380i
$885$		0			0
$886$	−5.52070	−	20.6035i	−0.185472	−	0.692189i
$887$	2.91948	+	10.8956i	0.0980266	+	0.365840i	0.997461	−	0.0712157i	$-0.0226879\pi$
$887$	2.91948	+	10.8956i	0.0980266	+	0.365840i	−0.899434	+	0.437056i	$0.856021\pi$
$888$	−14.7097	−	3.94145i	−0.493625	−	0.132266i
$889$	6.30472	+	6.30472i	0.211454	+	0.211454i
$890$		0			0
$891$	−6.00639	+	22.4162i	−0.201222	+	0.750969i
$892$	6.14187			0.205645
$893$	0.454079	−	1.69464i	0.0151952	−	0.0567091i
$894$	−12.9882	+	22.4963i	−0.434391	+	0.752387i
$895$		0			0
$896$		−	0.773777i		−	0.0258501i
$897$	−1.91434	−	1.26258i	−0.0639181	−	0.0421563i
$898$	−5.90829	−	5.90829i	−0.197162	−	0.197162i
$899$	1.85322	−	0.496568i	0.0618082	−	0.0165615i
$900$		0			0
$901$	1.41687	−	0.818031i	0.0472028	−	0.0272526i
$902$		−	24.6814i		−	0.821801i
$903$	−0.138671	−	0.240186i	−0.00461469	−	0.00799288i
$904$	−3.81745	−	1.02288i	−0.126966	−	0.0340205i
$905$		0			0
$906$	16.0172	+	27.7426i	0.532136	+	0.921686i
$907$	−19.2157	+	5.14882i	−0.638045	+	0.170964i	−0.563318	−	0.826240i	$-0.690475\pi$
$907$	−19.2157	+	5.14882i	−0.638045	+	0.170964i	−0.0747275	+	0.997204i	$0.523809\pi$
$908$	13.2304	+	7.63857i	0.439066	+	0.253495i
$909$	−1.57299			−0.0521728
$910$		0			0
$911$	−19.9046			−0.659468			−0.329734	−	0.944074i	$-0.606959\pi$
$911$	−19.9046			−0.659468			−0.329734	+	0.944074i	$0.606959\pi$
$912$	−0.276121	−	0.159418i	−0.00914327	−	0.00527887i
$913$	−21.1823	+	5.67577i	−0.701030	+	0.187840i
$914$	−8.46052	−	14.6540i	−0.279849	−	0.484713i
$915$		0			0
$916$	4.24270	+	1.13683i	0.140183	+	0.0375619i
$917$	3.72575	+	6.45319i	0.123035	+	0.213103i
$918$		−	6.35149i		−	0.209630i
$919$	−24.2229	+	13.9851i	−0.799039	+	0.461325i	−0.843135	−	0.537702i	$-0.819293\pi$
$919$	−24.2229	+	13.9851i	−0.799039	+	0.461325i	0.0440961	+	0.999027i	$0.485959\pi$
$920$		0			0
$921$	31.0410	−	8.31741i	1.02284	−	0.274068i
$922$	2.29420	+	2.29420i	0.0755555	+	0.0755555i
$923$	16.7576	−	3.43792i	0.551583	−	0.113160i
$924$			3.37419i			0.111003i
$925$		0			0
$926$	5.78022	−	10.0116i	0.189950	−	0.329003i
$927$	−0.740243	+	2.76263i	−0.0243128	+	0.0907366i
$928$	−0.671675			−0.0220488
$929$	9.06611	−	33.8352i	0.297449	−	1.11010i	−0.641803	−	0.766869i	$-0.721813\pi$
$929$	9.06611	−	33.8352i	0.297449	−	1.11010i	0.939253	−	0.343227i	$-0.111520\pi$
$930$		0			0
$931$	0.811204	+	0.811204i	0.0265861	+	0.0265861i
$932$	−21.5127	−	5.76432i	−0.704673	−	0.188817i
$933$	−11.9883	−	44.7408i	−0.392478	−	1.46475i
$934$	−4.54946	−	16.9788i	−0.148863	−	0.555563i
$935$		0			0
$936$	0.496755	+	0.327628i	0.0162369	+	0.0107089i
$937$	−6.74074	+	6.74074i	−0.220210	+	0.220210i	−0.808587	−	0.588377i	$-0.799767\pi$
$937$	−6.74074	+	6.74074i	−0.220210	+	0.220210i	0.588377	+	0.808587i	$0.299767\pi$
$938$	0.399744	−	0.692377i	0.0130521	−	0.0226069i
$939$	21.3044	+	12.3001i	0.695242	+	0.401398i
$940$		0			0
$941$	26.4463	−	26.4463i	0.862126	−	0.862126i	−0.129459	−	0.991585i	$-0.541324\pi$
$941$	26.4463	−	26.4463i	0.862126	−	0.862126i	0.991585	+	0.129459i	$0.0413240\pi$
$942$	6.27201	−	3.62115i	0.204353	−	0.117983i
$943$	−3.11759	+	1.79994i	−0.101523	+	0.0586142i
$944$	0.543708	−	0.543708i	0.0176962	−	0.0176962i
$945$		0			0
$946$	−0.427667	−	0.246913i	−0.0139046	−	0.00802785i
$947$	3.23753	−	5.60757i	0.105206	−	0.182222i	−0.808617	−	0.588336i	$-0.799783\pi$
$947$	3.23753	−	5.60757i	0.105206	−	0.182222i	0.913822	+	0.406114i	$0.133117\pi$
$948$	10.9080	−	10.9080i	0.354276	−	0.354276i
$949$	19.8464	+	39.6433i	0.644243	+	1.28688i
$950$		0			0
$951$	12.5329	+	46.7735i	0.406408	+	1.51674i
$952$	−0.252204	−	0.941237i	−0.00817397	−	0.0305057i
$953$	−18.4454	−	4.94244i	−0.597506	−	0.160101i	−0.0526246	−	0.998614i	$-0.516759\pi$
$953$	−18.4454	−	4.94244i	−0.597506	−	0.160101i	−0.544881	+	0.838513i	$0.683425\pi$
$954$	−0.151614	−	0.151614i	−0.00490870	−	0.00490870i
$955$		0			0
$956$	1.43287	−	5.34753i	0.0463422	−	0.172951i
$957$	2.92896			0.0946798
$958$	5.39239	−	20.1247i	0.174220	−	0.650199i
$959$	−0.350232	+	0.606620i	−0.0113096	+	0.0195888i
$960$		0			0
$961$			22.8408i			0.736801i
$962$	−16.9925	+	25.7642i	−0.547859	+	0.830672i
$963$	−2.23889	−	2.23889i	−0.0721472	−	0.0721472i
$964$	−0.154888	+	0.0415022i	−0.00498862	+	0.00133670i
$965$		0			0
$966$	0.426206	−	0.246070i	0.0137129	−	0.00791717i
$967$			49.8566i			1.60328i	0.597807	+	0.801640i	$0.296039\pi$
$967$			49.8566i			1.60328i	−0.597807	+	0.801640i	$0.703961\pi$
$968$	−2.49601	−	4.32322i	−0.0802248	−	0.138953i
$969$	−0.387839	−	0.103921i	−0.0124592	−	0.00333843i
$970$		0			0
$971$	6.30588	+	10.9221i	0.202365	+	0.350507i	0.949290	−	0.314402i	$-0.101804\pi$
$971$	6.30588	+	10.9221i	0.202365	+	0.350507i	−0.746925	+	0.664908i	$0.768471\pi$
$972$	−1.65488	+	0.443423i	−0.0530802	+	0.0142228i
$973$	1.35665	+	0.783265i	0.0434923	+	0.0251103i
$974$	−1.72795			−0.0553672
$975$		0			0
$976$	14.6338			0.468416
$977$	27.5579	+	15.9106i	0.881655	+	0.509024i	0.871204	−	0.490921i	$-0.163340\pi$
$977$	27.5579	+	15.9106i	0.881655	+	0.509024i	0.0104514	+	0.999945i	$0.496673\pi$
$978$	23.8946	−	6.40254i	0.764066	−	0.204731i
$979$	15.8466	+	27.4472i	0.506461	+	0.877216i
$980$		0			0
$981$	−0.266145	−	0.0713133i	−0.00849735	−	0.00227686i
$982$	0.431296	+	0.747027i	0.0137632	+	0.0238386i
$983$			27.3031i			0.870835i	0.900229	+	0.435417i	$0.143399\pi$
$983$			27.3031i			0.870835i	−0.900229	+	0.435417i	$0.856601\pi$
$984$	15.5141	−	8.95706i	0.494571	−	0.285541i
$985$		0			0
$986$	−0.817038	+	0.218925i	−0.0260198	+	0.00697198i
$987$	−9.52899	−	9.52899i	−0.303311	−	0.303311i
$988$	−0.483256	+	0.428960i	−0.0153744	+	0.0136470i
$989$			0.0720267i			0.00229031i
$990$		0			0
$991$	−26.1930	+	45.3676i	−0.832048	+	1.44115i	0.0643633	+	0.997927i	$0.479498\pi$
$991$	−26.1930	+	45.3676i	−0.832048	+	1.44115i	−0.896411	+	0.443223i	$0.853835\pi$
$992$	−0.739298	+	2.75910i	−0.0234727	+	0.0876014i
$993$	59.4188			1.88560
$994$	−0.950178	+	3.54611i	−0.0301378	+	0.112476i
$995$		0			0
$996$	−11.2548	−	11.2548i	−0.356623	−	0.356623i
$997$	44.1303	+	11.8247i	1.39762	+	0.374491i	0.877490	−	0.479595i	$-0.159217\pi$
$997$	44.1303	+	11.8247i	1.39762	+	0.374491i	0.520131	+	0.854087i	$0.325883\pi$
$998$	1.55315	+	5.79644i	0.0491642	+	0.183483i
$999$	−11.1738	−	41.7013i	−0.353524	−	1.31937i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.t.h.643.3	yes	16
5.2	odd	4		650.2.w.f.357.2	yes	16
5.3	odd	4		650.2.w.h.357.3	yes	16
5.4	even	2		650.2.t.f.643.2	yes	16
13.11	odd	12		650.2.w.f.193.2	yes	16
65.24	odd	12		650.2.w.h.193.3	yes	16
65.37	even	12	inner	650.2.t.h.557.3	yes	16
65.63	even	12		650.2.t.f.557.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.557.2	✓	16	65.63	even	12
650.2.t.f.643.2	yes	16	5.4	even	2
650.2.t.h.557.3	yes	16	65.37	even	12	inner
650.2.t.h.643.3	yes	16	1.1	even	1	trivial
650.2.w.f.193.2	yes	16	13.11	odd	12
650.2.w.f.357.2	yes	16	5.2	odd	4
650.2.w.h.193.3	yes	16	65.24	odd	12
650.2.w.h.357.3	yes	16	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.t (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(1.71844 - 0.460454i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.71844 + 0.460454i) q^{6} +(0.386889 + 0.670111i) q^{7} +1.00000i q^{8} +(0.142931 - 0.0825211i) q^{9} +(2.36760 - 0.634396i) q^{11} +(1.25798 + 1.25798i) q^{12} +(3.22410 - 1.61406i) q^{13} +0.773777i q^{14} +(-0.500000 + 0.866025i) q^{16} +(-0.325938 + 1.21642i) q^{17} +0.165042 q^{18} +(-0.0463847 + 0.173110i) q^{19} +(0.973399 + 0.973399i) q^{21} +(2.36760 + 0.634396i) q^{22} +(-0.0925293 - 0.345324i) q^{23} +(0.460454 + 1.71844i) q^{24} +(3.59918 + 0.214229i) q^{26} +(-3.56633 + 3.56633i) q^{27} +(-0.386889 + 0.670111i) q^{28} +(0.581688 + 0.335838i) q^{29} +(2.01980 - 2.01980i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(3.77646 - 2.18034i) q^{33} +(-0.890480 + 0.890480i) q^{34} +(0.142931 + 0.0825211i) q^{36} +(-4.27996 + 7.41311i) q^{37} +(-0.126725 + 0.126725i) q^{38} +(4.79721 - 4.25821i) q^{39} +(-2.60617 - 9.72634i) q^{41} +(0.356289 + 1.32969i) q^{42} +(-0.194605 - 0.0521443i) q^{43} +(1.73320 + 1.73320i) q^{44} +(0.0925293 - 0.345324i) q^{46} -9.78940 q^{47} +(-0.460454 + 1.71844i) q^{48} +(3.20063 - 5.54366i) q^{49} +2.24042i q^{51} +(3.00987 + 1.98512i) q^{52} +(-0.918640 - 0.918640i) q^{53} +(-4.87170 + 1.30537i) q^{54} +(-0.670111 + 0.386889i) q^{56} +0.318837i q^{57} +(0.335838 + 0.581688i) q^{58} +(-0.742719 - 0.199011i) q^{59} +(-7.31689 - 12.6732i) q^{61} +(2.75910 - 0.739298i) q^{62} +(0.110597 + 0.0638529i) q^{63} -1.00000 q^{64} +4.36068 q^{66} +(-0.894801 - 0.516614i) q^{67} +(-1.21642 + 0.325938i) q^{68} +(-0.318011 - 0.550812i) q^{69} +(4.58286 + 1.22797i) q^{71} +(0.0825211 + 0.142931i) q^{72} +12.2960i q^{73} +(-7.41311 + 4.27996i) q^{74} +(-0.173110 + 0.0463847i) q^{76} +(1.34111 + 1.34111i) q^{77} +(6.28361 - 1.28912i) q^{78} -8.67104i q^{79} +(-4.73394 + 8.19943i) q^{81} +(2.60617 - 9.72634i) q^{82} -8.94673 q^{83} +(-0.356289 + 1.32969i) q^{84} +(-0.142461 - 0.142461i) q^{86} +(1.15423 + 0.309275i) q^{87} +(0.634396 + 2.36760i) q^{88} +(3.34657 + 12.4896i) q^{89} +(2.32897 + 1.53604i) q^{91} +(0.252795 - 0.252795i) q^{92} +(2.54087 - 4.40092i) q^{93} +(-8.47787 - 4.89470i) q^{94} +(-1.25798 + 1.25798i) q^{96} +(9.71868 - 5.61108i) q^{97} +(5.54366 - 3.20063i) q^{98} +(0.286051 - 0.286051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 4 q^{7} + 24 q^{9} - 4 q^{11} - 12 q^{13} - 8 q^{16} - 8 q^{17} + 8 q^{18} - 16 q^{19} - 4 q^{21} - 4 q^{22} - 4 q^{23} + 4 q^{26} - 36 q^{27} - 4 q^{28} - 36 q^{29} - 8 q^{31} + 48 q^{33}+ \cdots + 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 4 * q^7 + 24 * q^9 - 4 * q^11 - 12 * q^13 - 8 * q^16 - 8 * q^17 + 8 * q^18 - 16 * q^19 - 4 * q^21 - 4 * q^22 - 4 * q^23 + 4 * q^26 - 36 * q^27 - 4 * q^28 - 36 * q^29 - 8 * q^31 + 48 * q^33 + 16 * q^34 + 24 * q^36 - 20 * q^37 - 4 * q^38 + 32 * q^41 - 4 * q^42 - 8 * q^44 + 4 * q^46 + 32 * q^47 - 16 * q^49 - 12 * q^52 - 44 * q^53 - 36 * q^54 - 12 * q^56 - 12 * q^58 + 24 * q^59 - 20 * q^61 - 16 * q^62 + 108 * q^63 - 16 * q^64 + 8 * q^68 - 24 * q^69 + 16 * q^71 + 4 * q^72 + 36 * q^74 - 20 * q^76 + 16 * q^77 + 4 * q^78 + 16 * q^81 - 32 * q^82 - 80 * q^83 + 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 + 28 * q^89 - 44 * q^91 - 8 * q^92 - 24 * q^94 + 96 * q^97 + 12 * q^98 + 36 * q^99

Introduction

L-functions

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