LMFDB - Embedded newform 650.2.w.h.193.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [650,2,Mod(193,650)]

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([9, 7]))

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

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

chi := DirichletCharacter("650.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.w (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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			193.3
Root			$1.77906i$ of defining polynomial
Character	$\chi$	$=$	650.193
Dual form			650.2.w.h.357.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(0.460454 - 1.71844i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.71844 - 0.460454i) q^{6} +(0.670111 + 0.386889i) q^{7} -1.00000 q^{8} +(-0.142931 - 0.0825211i) q^{9} +(2.36760 + 0.634396i) q^{11} +(1.25798 + 1.25798i) q^{12} +(1.61406 - 3.22410i) q^{13} +0.773777i q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.21642 - 0.325938i) q^{17} -0.165042i q^{18} +(0.0463847 + 0.173110i) q^{19} +(0.973399 - 0.973399i) q^{21} +(0.634396 + 2.36760i) q^{22} +(0.345324 + 0.0925293i) q^{23} +(-0.460454 + 1.71844i) q^{24} +(3.59918 - 0.214229i) q^{26} +(3.56633 - 3.56633i) q^{27} +(-0.670111 + 0.386889i) q^{28} +(-0.581688 + 0.335838i) q^{29} +(2.01980 + 2.01980i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.18034 - 3.77646i) q^{33} +(0.890480 + 0.890480i) q^{34} +(0.142931 - 0.0825211i) q^{36} +(7.41311 - 4.27996i) q^{37} +(-0.126725 + 0.126725i) q^{38} +(-4.79721 - 4.25821i) q^{39} +(-2.60617 + 9.72634i) q^{41} +(1.32969 + 0.356289i) q^{42} +(0.0521443 + 0.194605i) q^{43} +(-1.73320 + 1.73320i) q^{44} +(0.0925293 + 0.345324i) q^{46} -9.78940i q^{47} +(-1.71844 + 0.460454i) q^{48} +(-3.20063 - 5.54366i) q^{49} -2.24042i q^{51} +(1.98512 + 3.00987i) q^{52} +(0.918640 + 0.918640i) q^{53} +(4.87170 + 1.30537i) q^{54} +(-0.670111 - 0.386889i) q^{56} +0.318837 q^{57} +(-0.581688 - 0.335838i) q^{58} +(0.742719 - 0.199011i) q^{59} +(-7.31689 + 12.6732i) q^{61} +(-0.739298 + 2.75910i) q^{62} +(-0.0638529 - 0.110597i) q^{63} +1.00000 q^{64} +4.36068 q^{66} +(-0.516614 - 0.894801i) q^{67} +(-0.325938 + 1.21642i) q^{68} +(0.318011 - 0.550812i) q^{69} +(4.58286 - 1.22797i) q^{71} +(0.142931 + 0.0825211i) q^{72} -12.2960 q^{73} +(7.41311 + 4.27996i) q^{74} +(-0.173110 - 0.0463847i) q^{76} +(1.34111 + 1.34111i) q^{77} +(1.28912 - 6.28361i) q^{78} -8.67104i q^{79} +(-4.73394 - 8.19943i) q^{81} +(-9.72634 + 2.60617i) q^{82} +8.94673i q^{83} +(0.356289 + 1.32969i) q^{84} +(-0.142461 + 0.142461i) q^{86} +(0.309275 + 1.15423i) q^{87} +(-2.36760 - 0.634396i) q^{88} +(-3.34657 + 12.4896i) q^{89} +(2.32897 - 1.53604i) q^{91} +(-0.252795 + 0.252795i) q^{92} +(4.40092 - 2.54087i) q^{93} +(8.47787 - 4.89470i) q^{94} +(-1.25798 - 1.25798i) q^{96} +(-5.61108 + 9.71868i) q^{97} +(3.20063 - 5.54366i) q^{98} +(-0.286051 - 0.286051i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) $ 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Character values

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

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.460454	−	1.71844i	0.265843	−	0.992140i	−0.695889	−	0.718149i	$-0.744990\pi$
$3$	0.460454	−	1.71844i	0.265843	−	0.992140i	0.961732	−	0.273991i	$-0.0883438\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.71844	−	0.460454i	0.701549	−	0.187979i
$7$	0.670111	+	0.386889i	0.253278	+	0.146230i	0.621264	−	0.783601i	$-0.286619\pi$
$7$	0.670111	+	0.386889i	0.253278	+	0.146230i	−0.367986	+	0.929831i	$0.619953\pi$
$8$	−1.00000			−0.353553
$9$	−0.142931	−	0.0825211i	−0.0476436	−	0.0275070i
$10$		0			0
$11$	2.36760	+	0.634396i	0.713858	+	0.191278i	0.597429	−	0.801922i	$-0.296189\pi$
$11$	2.36760	+	0.634396i	0.713858	+	0.191278i	0.116428	+	0.993199i	$0.462855\pi$
$12$	1.25798	+	1.25798i	0.363148	+	0.363148i
$13$	1.61406	−	3.22410i	0.447660	−	0.894204i
$13$	1.61406	−	3.22410i	0.447660	−	0.894204i
$14$			0.773777i			0.206801i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.21642	−	0.325938i	0.295025	−	0.0790516i	−0.108271	−	0.994121i	$-0.534531\pi$
$17$	1.21642	−	0.325938i	0.295025	−	0.0790516i	0.403295	+	0.915070i	$0.367865\pi$
$18$		−	0.165042i		−	0.0389008i
$19$	0.0463847	+	0.173110i	0.0106414	+	0.0397142i	0.971042	−	0.238907i	$-0.0767892\pi$
$19$	0.0463847	+	0.173110i	0.0106414	+	0.0397142i	−0.960401	+	0.278621i	$0.910123\pi$
$20$		0			0
$21$	0.973399	−	0.973399i	0.212413	−	0.212413i
$22$	0.634396	+	2.36760i	0.135254	+	0.504774i
$23$	0.345324	+	0.0925293i	0.0720050	+	0.0192937i	0.294642	−	0.955608i	$-0.404800\pi$
$23$	0.345324	+	0.0925293i	0.0720050	+	0.0192937i	−0.222637	+	0.974901i	$0.571466\pi$
$24$	−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
$28$	−0.670111	+	0.386889i	−0.126639	+	0.0731151i
$29$	−0.581688	+	0.335838i	−0.108017	+	0.0623635i	−0.553035	−	0.833158i	$-0.686530\pi$
$29$	−0.581688	+	0.335838i	−0.108017	+	0.0623635i	0.445018	+	0.895521i	$0.353197\pi$
$30$		0			0
$31$	2.01980	+	2.01980i	0.362767	+	0.362767i	0.864831	−	0.502064i	$-0.167426\pi$
$31$	2.01980	+	2.01980i	0.362767	+	0.362767i	−0.502064	+	0.864831i	$0.667426\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	2.18034	−	3.77646i	0.379548	−	0.657397i
$34$	0.890480	+	0.890480i	0.152716	+	0.152716i
$35$		0			0
$36$	0.142931	−	0.0825211i	0.0238218	−	0.0137535i
$37$	7.41311	−	4.27996i	1.21871	−	0.703621i	0.254066	−	0.967187i	$-0.418232\pi$
$37$	7.41311	−	4.27996i	1.21871	−	0.703621i	0.964641	+	0.263566i	$0.0848986\pi$
$38$	−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	0.393295	+	0.919412i	$0.371335\pi$
$41$	−2.60617	+	9.72634i	−0.407015	+	1.51900i	−0.800309	+	0.599587i	$0.795331\pi$
$42$	1.32969	+	0.356289i	0.205175	+	0.0549765i
$43$	0.0521443	+	0.194605i	0.00795193	+	0.0296770i	0.969788	−	0.243950i	$-0.0784433\pi$
$43$	0.0521443	+	0.194605i	0.00795193	+	0.0296770i	−0.961836	+	0.273627i	$0.911777\pi$
$44$	−1.73320	+	1.73320i	−0.261290	+	0.261290i
$45$		0			0
$46$	0.0925293	+	0.345324i	0.0136427	+	0.0509152i
$47$		−	9.78940i		−	1.42793i	−0.700181	−	0.713965i	$-0.746897\pi$
$47$		−	9.78940i		−	1.42793i	0.700181	−	0.713965i	$-0.253103\pi$
$48$	−1.71844	+	0.460454i	−0.248035	+	0.0664608i
$49$	−3.20063	−	5.54366i	−0.457233	−	0.791952i
$50$		0			0
$51$		−	2.24042i		−	0.313721i
$52$	1.98512	+	3.00987i	0.275286	+	0.417394i
$53$	0.918640	+	0.918640i	0.126185	+	0.126185i	0.767379	−	0.641194i	$-0.221561\pi$
$53$	0.918640	+	0.918640i	0.126185	+	0.126185i	−0.641194	+	0.767379i	$0.721561\pi$
$54$	4.87170	+	1.30537i	0.662954	+	0.177638i
$55$		0			0
$56$	−0.670111	−	0.386889i	−0.0895473	−	0.0517002i
$57$	0.318837			0.0422310
$58$	−0.581688	−	0.335838i	−0.0763793	−	0.0440976i
$59$	0.742719	−	0.199011i	0.0966937	−	0.0259090i	−0.210148	−	0.977670i	$-0.567395\pi$
$59$	0.742719	−	0.199011i	0.0966937	−	0.0259090i	0.306842	+	0.951761i	$0.400728\pi$
$60$		0			0
$61$	−7.31689	+	12.6732i	−0.936831	+	1.62264i	−0.165496	+	0.986211i	$0.552922\pi$
$61$	−7.31689	+	12.6732i	−0.936831	+	1.62264i	−0.771335	+	0.636429i	$0.780411\pi$
$62$	−0.739298	+	2.75910i	−0.0938909	+	0.350406i
$63$	−0.0638529	−	0.110597i	−0.00804471	−	0.0139339i
$64$	1.00000			0.125000
$65$		0			0
$66$	4.36068			0.536762
$67$	−0.516614	−	0.894801i	−0.0631144	−	0.109317i	0.832742	−	0.553662i	$-0.186770\pi$
$67$	−0.516614	−	0.894801i	−0.0631144	−	0.109317i	−0.895856	+	0.444344i	$0.853437\pi$
$68$	−0.325938	+	1.21642i	−0.0395258	+	0.147512i
$69$	0.318011	−	0.550812i	0.0382841	−	0.0663099i
$70$		0			0
$71$	4.58286	−	1.22797i	0.543885	−	0.145734i	0.0235925	−	0.999722i	$-0.492490\pi$
$71$	4.58286	−	1.22797i	0.543885	−	0.145734i	0.520293	+	0.853988i	$0.325823\pi$
$72$	0.142931	+	0.0825211i	0.0168445	+	0.00972520i
$73$	−12.2960			−1.43913			−0.719566	−	0.694424i	$-0.755659\pi$
$73$	−12.2960			−1.43913			−0.719566	+	0.694424i	$0.755659\pi$
$74$	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
$78$	1.28912	−	6.28361i	0.145964	−	0.711478i
$79$		−	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
$82$	−9.72634	+	2.60617i	−1.07409	+	0.287803i
$83$			8.94673i			0.982031i	0.871151	+	0.491015i	$0.163374\pi$
$83$			8.94673i			0.982031i	−0.871151	+	0.491015i	$0.836626\pi$
$84$	0.356289	+	1.32969i	0.0388743	+	0.145081i
$85$		0			0
$86$	−0.142461	+	0.142461i	−0.0153619	+	0.0153619i
$87$	0.309275	+	1.15423i	0.0331578	+	0.123747i
$88$	−2.36760	−	0.634396i	−0.252387	−	0.0676268i
$89$	−3.34657	+	12.4896i	−0.354735	+	1.32389i	0.526082	+	0.850434i	$0.323661\pi$
$89$	−3.34657	+	12.4896i	−0.354735	+	1.32389i	−0.880817	+	0.473456i	$0.843006\pi$
$90$		0			0
$91$	2.32897	−	1.53604i	0.244142	−	0.161021i
$92$	−0.252795	+	0.252795i	−0.0263557	+	0.0263557i
$93$	4.40092	−	2.54087i	0.456354	−	0.263476i
$94$	8.47787	−	4.89470i	0.874425	−	0.504850i
$95$		0			0
$96$	−1.25798	−	1.25798i	−0.128392	−	0.128392i
$97$	−5.61108	+	9.71868i	−0.569719	+	0.986783i	0.426874	+	0.904311i	$0.359615\pi$
$97$	−5.61108	+	9.71868i	−0.569719	+	0.986783i	−0.996593	+	0.0824718i	$0.973719\pi$
$98$	3.20063	−	5.54366i	0.323313	−	0.559994i
$99$	−0.286051	−	0.286051i	−0.0287492	−	0.0287492i
$100$		0			0
$101$	−8.25395	+	4.76542i	−0.821299	+	0.474177i	−0.850864	−	0.525386i	$-0.823921\pi$
$101$	−8.25395	+	4.76542i	−0.821299	+	0.474177i	0.0295654	+	0.999563i	$0.490588\pi$
$102$	1.94026	−	1.12021i	0.192114	−	0.110917i
$103$	−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
$107$	−18.5309	−	4.96534i	−1.79145	−	0.480018i	−0.798859	−	0.601519i	$-0.794562\pi$
$107$	−18.5309	−	4.96534i	−1.79145	−	0.480018i	−0.992591	+	0.121501i	$0.961229\pi$
$108$	1.30537	+	4.87170i	0.125609	+	0.468779i
$109$	1.18050	−	1.18050i	0.113071	−	0.113071i	−0.648308	−	0.761379i	$-0.724523\pi$
$109$	1.18050	−	1.18050i	0.113071	−	0.113071i	0.761379	+	0.648308i	$0.224523\pi$
$110$		0			0
$111$	−3.94145	−	14.7097i	−0.374106	−	1.39618i
$112$		−	0.773777i		−	0.0731151i
$113$	−3.81745	+	1.02288i	−0.359115	+	0.0962246i	−0.433866	−	0.900978i	$-0.642851\pi$
$113$	−3.81745	+	1.02288i	−0.359115	+	0.0962246i	0.0747503	+	0.997202i	$0.476184\pi$
$114$	0.159418	+	0.276121i	0.0149309	+	0.0258611i
$115$		0			0
$116$		−	0.671675i		−	0.0623635i
$117$	−0.496755	+	0.327628i	−0.0459250	+	0.0302892i
$118$	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
$122$	−14.6338			−1.32488
$123$	15.5141	+	8.95706i	1.39886	+	0.807631i
$124$	−2.75910	+	0.739298i	−0.247774	+	0.0663909i
$125$		0			0
$126$	0.0638529	−	0.110597i	0.00568847	−	0.00985272i
$127$	−2.98237	+	11.1303i	−0.264642	+	0.987659i	0.697827	+	0.716267i	$0.254151\pi$
$127$	−2.98237	+	11.1303i	−0.264642	+	0.987659i	−0.962469	+	0.271392i	$0.912516\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	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	$0.361788\pi$
$132$	2.18034	+	3.77646i	0.189774	+	0.328698i
$133$	−0.0358915	+	0.133949i	−0.00311218	+	0.0116148i
$134$	0.516614	−	0.894801i	0.0446286	−	0.0772991i
$135$		0			0
$136$	−1.21642	+	0.325938i	−0.104307	+	0.0279490i
$137$	0.783972	+	0.452627i	0.0669793	+	0.0386705i	0.533116	−	0.846042i	$-0.321021\pi$
$137$	0.783972	+	0.452627i	0.0669793	+	0.0386705i	−0.466136	+	0.884713i	$0.654354\pi$
$138$	0.636023			0.0541418
$139$	−1.75329	−	1.01226i	−0.148712	−	0.0858588i	0.423798	−	0.905757i	$-0.360697\pi$
$139$	−1.75329	−	1.01226i	−0.148712	−	0.0858588i	−0.572510	+	0.819898i	$0.694030\pi$
$140$		0			0
$141$	−16.8225	−	4.50757i	−1.41671	−	0.379606i
$142$	3.35488	+	3.35488i	0.281536	+	0.281536i
$143$	5.86681	−	6.60941i	0.490607	−	0.552707i
$144$			0.165042i			0.0137535i
$145$		0			0
$146$	−6.14798	−	10.6486i	−0.508810	−	0.881285i
$147$	−11.0002	+	2.94749i	−0.907279	+	0.243105i
$148$			8.55992i			0.703621i
$149$	3.77908	+	14.1037i	0.309594	+	1.15542i	0.928918	+	0.370286i	$0.120740\pi$
$149$	3.77908	+	14.1037i	0.309594	+	1.15542i	−0.619324	+	0.785136i	$0.712593\pi$
$150$		0			0
$151$	12.7324	−	12.7324i	1.03615	−	1.03615i	0.0368303	−	0.999322i	$-0.488274\pi$
$151$	12.7324	−	12.7324i	1.03615	−	1.03615i	0.999322	−	0.0368303i	$-0.0117261\pi$
$152$	−0.0463847	−	0.173110i	−0.00376230	−	0.0140411i
$153$	−0.200760	−	0.0537935i	−0.0162305	−	0.00434895i
$154$	−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	−0.812581	−	0.582849i	$-0.801938\pi$
$157$	−2.87854	+	2.87854i	−0.229732	+	0.229732i	0.582849	+	0.812581i	$0.301938\pi$
$158$	7.50934	−	4.33552i	0.597411	−	0.344916i
$159$	2.00162	−	1.15563i	0.158739	−	0.0916477i
$160$		0			0
$161$	0.195607	+	0.195607i	0.0154160	+	0.0154160i
$162$	4.73394	−	8.19943i	0.371934	−	0.644208i
$163$	6.95243	−	12.0420i	0.544556	−	0.943199i	−0.454078	−	0.890962i	$-0.650031\pi$
$163$	6.95243	−	12.0420i	0.544556	−	0.943199i	0.998635	−	0.0522375i	$-0.0166353\pi$
$164$	−7.12018	−	7.12018i	−0.555992	−	0.555992i
$165$		0			0
$166$	−7.74809	+	4.47336i	−0.601369	+	0.347200i
$167$	12.2875	−	7.09421i	0.950838	−	0.548966i	0.0574967	−	0.998346i	$-0.481688\pi$
$167$	12.2875	−	7.09421i	0.950838	−	0.548966i	0.893341	+	0.449379i	$0.148355\pi$
$168$	−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
$172$	−0.194605	−	0.0521443i	−0.0148385	−	0.00397596i
$173$	2.91015	+	10.8608i	0.221254	+	0.825733i	0.983871	+	0.178881i	$0.0572478\pi$
$173$	2.91015	+	10.8608i	0.221254	+	0.825733i	−0.762616	+	0.646851i	$0.776085\pi$
$174$	−0.844956	+	0.844956i	−0.0640559	+	0.0640559i
$175$		0			0
$176$	−0.634396	−	2.36760i	−0.0478194	−	0.178464i
$177$		−	1.36795i		−	0.102821i
$178$	−12.4896	+	3.34657i	−0.936132	+	0.250836i
$179$	−2.87010	−	4.97117i	−0.214522	−	0.371562i	0.738603	−	0.674141i	$-0.235486\pi$
$179$	−2.87010	−	4.97117i	−0.214522	−	0.371562i	−0.953124	+	0.302578i	$0.902153\pi$
$180$		0			0
$181$		−	7.97888i		−	0.593065i	−0.955023	−	0.296533i	$-0.904170\pi$
$181$		−	7.97888i		−	0.593065i	0.955023	−	0.296533i	$-0.0958303\pi$
$182$	2.49473	+	1.24893i	0.184922	+	0.0925765i
$183$	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
$187$	3.08676			0.225726
$188$	8.47787	+	4.89470i	0.618312	+	0.356983i
$189$	3.76961	−	1.01006i	0.274199	−	0.0734713i
$190$		0			0
$191$	−11.3313	+	19.6263i	−0.819901	+	1.42011i	0.0858531	+	0.996308i	$0.472638\pi$
$191$	−11.3313	+	19.6263i	−0.819901	+	1.42011i	−0.905754	+	0.423803i	$0.860695\pi$
$192$	0.460454	−	1.71844i	0.0332304	−	0.124017i
$193$	−12.7800	−	22.1356i	−0.919924	−	1.59335i	−0.799528	−	0.600629i	$-0.794917\pi$
$193$	−12.7800	−	22.1356i	−0.919924	−	1.59335i	−0.120396	−	0.992726i	$-0.538416\pi$
$194$	−11.2222			−0.805705
$195$		0			0
$196$	6.40127			0.457233
$197$	−6.13049	−	10.6183i	−0.436779	−	0.756524i	0.560660	−	0.828046i	$-0.310548\pi$
$197$	−6.13049	−	10.6183i	−0.436779	−	0.756524i	−0.997439	+	0.0715225i	$0.977214\pi$
$198$	0.104702	−	0.390753i	0.00744085	−	0.0277696i
$199$	10.6245	−	18.4021i	0.753149	−	1.30449i	−0.193140	−	0.981171i	$-0.561867\pi$
$199$	10.6245	−	18.4021i	0.753149	−	1.30449i	0.946289	−	0.323322i	$-0.104800\pi$
$200$		0			0
$201$	−1.77554	+	0.475753i	−0.125237	+	0.0335571i
$202$	−8.25395	−	4.76542i	−0.580746	−	0.335294i
$203$	−0.519727			−0.0364777
$204$	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
$208$	−3.59918	+	0.214229i	−0.249558	+	0.0148541i
$209$			0.439282i			0.0303857i
$210$		0			0
$211$	−7.59324	−	13.1519i	−0.522740	−	0.905413i	−0.999650	−	0.0264606i	$-0.991576\pi$
$211$	−7.59324	−	13.1519i	−0.522740	−	0.905413i	0.476909	−	0.878952i	$-0.341757\pi$
$212$	−1.25489	+	0.336246i	−0.0861859	+	0.0230935i
$213$		−	8.44077i		−	0.578352i
$214$	−4.96534	−	18.5309i	−0.339424	−	1.26675i
$215$		0			0
$216$	−3.56633	+	3.56633i	−0.242658	+	0.242658i
$217$	0.572052	+	2.13493i	0.0388334	+	0.144928i
$218$	1.61259	+	0.432091i	0.109218	+	0.0292649i
$219$	−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
$223$	5.31901	−	3.07093i	0.356188	−	0.205645i	−0.311220	−	0.950338i	$-0.600737\pi$
$223$	5.31901	−	3.07093i	0.356188	−	0.205645i	0.667407	+	0.744693i	$0.267404\pi$
$224$	0.670111	−	0.386889i	0.0447737	−	0.0258501i
$225$		0			0
$226$	−2.79457	−	2.79457i	−0.185892	−	0.185892i
$227$	−7.63857	+	13.2304i	−0.506990	+	0.878132i	0.492978	+	0.870042i	$0.335908\pi$
$227$	−7.63857	+	13.2304i	−0.506990	+	0.878132i	−0.999967	+	0.00808986i	$0.997425\pi$
$228$	−0.159418	+	0.276121i	−0.0105577	+	0.0182865i
$229$	−3.10587	−	3.10587i	−0.205242	−	0.205242i	0.597000	−	0.802242i	$-0.296359\pi$
$229$	−3.10587	−	3.10587i	−0.205242	−	0.205242i	−0.802242	+	0.597000i	$0.796359\pi$
$230$		0			0
$231$	2.92214	−	1.68710i	0.192263	−	0.111003i
$232$	0.581688	−	0.335838i	0.0381897	−	0.0220488i
$233$	−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
$237$	−14.9006	−	3.99261i	−0.967901	−	0.259348i
$238$	0.252204	+	0.941237i	0.0163479	+	0.0610113i
$239$	3.91466	−	3.91466i	0.253219	−	0.253219i	−0.569070	−	0.822289i	$-0.692697\pi$
$239$	3.91466	−	3.91466i	0.253219	−	0.253219i	0.822289	+	0.569070i	$0.192697\pi$
$240$		0			0
$241$	−0.0415022	−	0.154888i	−0.00267339	−	0.00997724i	0.964576	−	0.263804i	$-0.0849773\pi$
$241$	−0.0415022	−	0.154888i	−0.00267339	−	0.00997724i	−0.967250	+	0.253827i	$0.918311\pi$
$242$		−	4.99202i		−	0.320899i
$243$	−1.65488	+	0.443423i	−0.106160	+	0.0284456i
$244$	−7.31689	−	12.6732i	−0.468416	−	0.811320i
$245$		0			0
$246$			17.9141i			1.14216i
$247$	0.632992	+	0.129862i	0.0402763	+	0.00826291i
$248$	−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	0.999747	+	0.0225011i	$0.00716292\pi$
$251$	24.0672	+	13.8952i	1.51911	+	0.877057i	0.519360	+	0.854556i	$0.326170\pi$
$252$	0.127706			0.00804471
$253$	0.758888	+	0.438144i	0.0477109	+	0.0275459i
$254$	−11.1303	+	2.98237i	−0.698380	+	0.187130i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.975550	+	3.64080i	−0.0608531	+	0.227107i	−0.989655	−	0.143471i	$-0.954174\pi$
$257$	−0.975550	+	3.64080i	−0.0608531	+	0.227107i	0.928801	+	0.370578i	$0.120840\pi$
$258$	0.179213	+	0.310407i	0.0111573	+	0.0193251i
$259$	6.62347			0.411563
$260$		0			0
$261$	0.110855			0.00686173
$262$	4.81502	+	8.33986i	0.297473	+	0.515238i
$263$	4.52492	−	16.8872i	0.279019	−	1.04131i	−0.674082	−	0.738657i	$-0.735460\pi$
$263$	4.52492	−	16.8872i	0.279019	−	1.04131i	0.953100	−	0.302655i	$-0.0978729\pi$
$264$	−2.18034	+	3.77646i	−0.134191	+	0.232425i
$265$		0			0
$266$	−0.133949	+	0.0358915i	−0.00821292	+	0.00220065i
$267$	19.9216	+	11.5017i	1.21918	+	0.703894i
$268$	1.03323			0.0631144
$269$	22.5481	+	13.0181i	1.37478	+	0.793729i	0.991525	−	0.129914i	$-0.0414701\pi$
$269$	22.5481	+	13.0181i	1.37478	+	0.793729i	0.383254	+	0.923643i	$0.374803\pi$
$270$		0			0
$271$	0.804227	+	0.215492i	0.0488533	+	0.0130902i	0.283163	−	0.959072i	$-0.408616\pi$
$271$	0.804227	+	0.215492i	0.0488533	+	0.0130902i	−0.234310	+	0.972162i	$0.575283\pi$
$272$	−0.890480	−	0.890480i	−0.0539933	−	0.0539933i
$273$	−1.56721	−	4.70946i	−0.0948516	−	0.285029i
$274$			0.905253i			0.0546884i
$275$		0			0
$276$	0.318011	+	0.550812i	0.0191420	+	0.0331550i
$277$	6.92616	−	1.85586i	0.416153	−	0.111508i	−0.0446663	−	0.999002i	$-0.514222\pi$
$277$	6.92616	−	1.85586i	0.416153	−	0.111508i	0.460819	+	0.887494i	$0.347556\pi$
$278$		−	2.02452i		−	0.121423i
$279$	−0.122015	−	0.455367i	−0.00730486	−	0.0272621i
$280$		0			0
$281$	16.3268	−	16.3268i	0.973977	−	0.973977i	−0.0256932	−	0.999670i	$-0.508179\pi$
$281$	16.3268	−	16.3268i	0.973977	−	0.973977i	0.999670	+	0.0256932i	$0.00817929\pi$
$282$	−4.50757	−	16.8225i	−0.268422	−	1.00176i
$283$	−24.1418	−	6.46878i	−1.43508	−	0.384529i	−0.544273	−	0.838908i	$-0.683195\pi$
$283$	−24.1418	−	6.46878i	−1.43508	−	0.384529i	−0.890809	+	0.454379i	$0.849861\pi$
$284$	−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
$288$	−0.142931	+	0.0825211i	−0.00842227	+	0.00486260i
$289$	−13.3490	+	7.70705i	−0.785235	+	0.453356i
$290$		0			0
$291$	14.1173	+	14.1173i	0.827571	+	0.827571i
$292$	6.14798	−	10.6486i	0.359783	−	0.623163i
$293$	10.0215	−	17.3578i	0.585464	−	1.01405i	−0.409354	−	0.912376i	$-0.634246\pi$
$293$	10.0215	−	17.3578i	0.585464	−	1.01405i	0.994817	−	0.101677i	$-0.0324209\pi$
$294$	−8.05269	−	8.05269i	−0.469642	−	0.469642i
$295$		0			0
$296$	−7.41311	+	4.27996i	−0.430878	+	0.248768i
$297$	10.7061	−	6.18117i	0.621231	−	0.358668i
$298$	−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
$302$	17.3928	+	4.66040i	1.00085	+	0.268176i
$303$	4.38851	+	16.3781i	0.252113	+	0.940900i
$304$	0.126725	−	0.126725i	0.00726820	−	0.00726820i
$305$		0			0
$306$	−0.0537935	−	0.200760i	−0.00307517	−	0.0114767i
$307$			18.0635i			1.03094i	0.856908	+	0.515469i	$0.172382\pi$
$307$			18.0635i			1.03094i	−0.856908	+	0.515469i	$0.827618\pi$
$308$	−1.83199	+	0.490881i	−0.104388	+	0.0279706i
$309$	15.4150	+	26.6996i	0.876928	+	1.51888i
$310$		0			0
$311$			26.0358i			1.47635i	0.674608	+	0.738177i	$0.264313\pi$
$311$			26.0358i			1.47635i	−0.674608	+	0.738177i	$0.735687\pi$
$312$	4.79721	+	4.25821i	0.271588	+	0.241074i
$313$	−9.77762	−	9.77762i	−0.552664	−	0.552664i	0.374545	−	0.927209i	$-0.377799\pi$
$313$	−9.77762	−	9.77762i	−0.552664	−	0.552664i	−0.927209	+	0.374545i	$0.877799\pi$
$314$	−3.93215	−	1.05362i	−0.221904	−	0.0594591i
$315$		0			0
$316$	7.50934	+	4.33552i	0.422434	+	0.243892i
$317$	27.2186			1.52875			0.764376	−	0.644771i	$-0.223047\pi$
$317$	27.2186			1.52875			0.764376	+	0.644771i	$0.223047\pi$
$318$	2.00162	+	1.15563i	0.112245	+	0.0648047i
$319$	−1.59026	+	0.426108i	−0.0890373	+	0.0238575i
$320$		0			0
$321$	−17.0652	+	29.5579i	−0.952489	+	1.64976i
$322$	−0.0715970	+	0.267204i	−0.00398995	+	0.0148907i
$323$	0.112846	+	0.195456i	0.00627894	+	0.0108755i
$324$	9.46789			0.525994
$325$		0			0
$326$	13.9049			0.770119
$327$	−1.48504	−	2.57217i	−0.0821231	−	0.142241i
$328$	2.60617	−	9.72634i	0.143901	−	0.537047i
$329$	3.78741	−	6.55998i	0.208807	−	0.361664i
$330$		0			0
$331$	32.2610	−	8.64431i	1.77323	−	0.475135i	0.783904	−	0.620882i	$-0.213225\pi$
$331$	32.2610	−	8.64431i	1.77323	−	0.475135i	0.989322	+	0.145747i	$0.0465586\pi$
$332$	−7.74809	−	4.47336i	−0.425232	−	0.245508i
$333$	−1.41275			−0.0774181
$334$	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	$0.698962\pi$
$338$	5.11861	−	11.9499i	0.278416	−	0.649988i
$339$			7.03103i			0.381873i
$340$		0			0
$341$	3.50072	+	6.06342i	0.189575	+	0.328353i
$342$	0.0285705	−	0.00765543i	0.00154491	−	0.000413958i
$343$		−	10.3696i		−	0.559906i
$344$	−0.0521443	−	0.194605i	−0.00281143	−	0.0104924i
$345$		0			0
$346$	−7.95067	+	7.95067i	−0.427431	+	0.427431i
$347$	1.28362	+	4.79055i	0.0689085	+	0.257170i	0.991783	−	0.127930i	$-0.0408334\pi$
$347$	1.28362	+	4.79055i	0.0689085	+	0.257170i	−0.922875	+	0.385101i	$0.874167\pi$
$348$	−1.15423	−	0.309275i	−0.0618733	−	0.0165789i
$349$	−8.15741	+	30.4439i	−0.436656	+	1.62962i	0.300416	+	0.953808i	$0.402874\pi$
$349$	−8.15741	+	30.4439i	−0.436656	+	1.62962i	−0.737072	+	0.675814i	$0.763792\pi$
$350$		0			0
$351$	−5.74191	−	17.2545i	−0.306481	−	0.920975i
$352$	1.73320	−	1.73320i	0.0923800	−	0.0923800i
$353$	−24.6438	+	14.2281i	−1.31166	+	0.757286i	−0.982371	−	0.186943i	$-0.940142\pi$
$353$	−24.6438	+	14.2281i	−1.31166	+	0.757286i	−0.329288	+	0.944230i	$0.606809\pi$
$354$	1.18468	−	0.683975i	0.0629650	−	0.0363529i
$355$		0			0
$356$	−9.14299	−	9.14299i	−0.484577	−	0.484577i
$357$	0.866792	−	1.50133i	0.0458755	−	0.0794587i
$358$	2.87010	−	4.97117i	0.151690	−	0.262734i
$359$	11.7211	+	11.7211i	0.618618	+	0.618618i	0.945177	−	0.326559i	$-0.105889\pi$
$359$	11.7211	+	11.7211i	0.618618	+	0.618618i	−0.326559	+	0.945177i	$0.605889\pi$
$360$		0			0
$361$	16.4267	−	9.48394i	0.864561	−	0.499155i
$362$	6.90991	−	3.98944i	0.363177	−	0.209680i
$363$	−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
$367$	19.6388	+	5.26220i	1.02514	+	0.274685i	0.731941	−	0.681368i	$-0.238614\pi$
$367$	19.6388	+	5.26220i	1.02514	+	0.274685i	0.293196	+	0.956052i	$0.405281\pi$
$368$	−0.0925293	−	0.345324i	−0.00482342	−	0.0180013i
$369$	1.17513	−	1.17513i	0.0611748	−	0.0611748i
$370$		0			0
$371$	0.260179	+	0.971003i	0.0135078	+	0.0504119i
$372$			5.08174i			0.263476i
$373$	−16.6874	+	4.47138i	−0.864042	+	0.231519i	−0.663510	−	0.748168i	$-0.730934\pi$
$373$	−16.6874	+	4.47138i	−0.864042	+	0.231519i	−0.200532	+	0.979687i	$0.564267\pi$
$374$	1.54338	+	2.67322i	0.0798064	+	0.138229i
$375$		0			0
$376$			9.78940i			0.504850i
$377$	0.143892	+	2.41748i	0.00741083	+	0.124507i
$378$	2.75954	+	2.75954i	0.141936	+	0.141936i
$379$	−14.7036	−	3.93982i	−0.755273	−	0.202375i	−0.139417	−	0.990234i	$-0.544523\pi$
$379$	−14.7036	−	3.93982i	−0.755273	−	0.202375i	−0.615856	+	0.787859i	$0.711190\pi$
$380$		0			0
$381$	17.7536	+	10.2500i	0.909542	+	0.525124i
$382$	−22.6625			−1.15952
$383$	20.9494	+	12.0951i	1.07046	+	0.618032i	0.928308	−	0.371812i	$-0.121263\pi$
$383$	20.9494	+	12.0951i	1.07046	+	0.618032i	0.142155	+	0.989844i	$0.454597\pi$
$384$	1.71844	−	0.460454i	0.0876936	−	0.0234974i
$385$		0			0
$386$	12.7800	−	22.1356i	0.650484	−	1.12667i
$387$	0.00860600	−	0.0321180i	0.000437468	−	0.00163265i
$388$	−5.61108	−	9.71868i	−0.284860	−	0.493391i
$389$	−8.26825			−0.419217			−0.209608	−	0.977785i	$-0.567219\pi$
$389$	−8.26825			−0.419217			−0.209608	+	0.977785i	$0.567219\pi$
$390$		0			0
$391$	0.450217			0.0227685
$392$	3.20063	+	5.54366i	0.161656	+	0.279997i
$393$	4.43419	−	16.5486i	0.223675	−	0.834767i
$394$	6.13049	−	10.6183i	0.308850	−	0.534943i
$395$		0			0
$396$	0.390753	−	0.104702i	0.0196361	−	0.00526148i
$397$	−9.12482	−	5.26822i	−0.457962	−	0.264404i	0.253225	−	0.967407i	$-0.418509\pi$
$397$	−9.12482	−	5.26822i	−0.457962	−	0.264404i	−0.711187	+	0.703003i	$0.751842\pi$
$398$	21.2490			1.06511
$399$	0.213656	+	0.123354i	0.0106962	+	0.00617544i
$400$		0			0
$401$	−28.3308	−	7.59122i	−1.41477	−	0.379088i	−0.531147	−	0.847279i	$-0.678239\pi$
$401$	−28.3308	−	7.59122i	−1.41477	−	0.379088i	−0.883627	+	0.468192i	$0.844906\pi$
$402$	−1.29978	−	1.29978i	−0.0648273	−	0.0648273i
$403$	9.77211	−	3.25194i	0.486783	−	0.161991i
$404$		−	9.53084i		−	0.474177i
$405$		0			0
$406$	−0.259864	−	0.450097i	−0.0128968	−	0.0223379i
$407$	20.2664	−	5.43038i	1.00457	−	0.269174i
$408$			2.24042i			0.110917i
$409$	−3.90885	−	14.5880i	−0.193280	−	0.721331i	−0.992705	−	0.120565i	$-0.961529\pi$
$409$	−3.90885	−	14.5880i	−0.193280	−	0.721331i	0.799425	−	0.600765i	$-0.205137\pi$
$410$		0			0
$411$	1.13879	−	1.13879i	0.0561725	−	0.0561725i
$412$	−4.48518	−	16.7389i	−0.220969	−	0.824667i
$413$	0.574699	+	0.153990i	0.0282791	+	0.00757736i
$414$	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
$418$	−0.380429	+	0.219641i	−0.0186074	+	0.0107430i
$419$	−21.8423	+	12.6107i	−1.06707	+	0.616071i	−0.927378	−	0.374125i	$-0.877943\pi$
$419$	−21.8423	+	12.6107i	−1.06707	+	0.616071i	−0.139687	+	0.990196i	$0.544610\pi$
$420$		0			0
$421$	1.12596	+	1.12596i	0.0548760	+	0.0548760i	0.734012	−	0.679136i	$-0.237645\pi$
$421$	1.12596	+	1.12596i	0.0548760	+	0.0548760i	−0.679136	+	0.734012i	$0.737645\pi$
$422$	7.59324	−	13.1519i	0.369633	−	0.640224i
$423$	−0.807832	+	1.39921i	−0.0392781	+	0.0680317i
$424$	−0.918640	−	0.918640i	−0.0446131	−	0.0446131i
$425$		0			0
$426$	7.30992	−	4.22039i	0.354167	−	0.204478i
$427$	−9.80625	+	5.66164i	−0.474558	+	0.273986i
$428$	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	−0.754463	−	0.656343i	$-0.772103\pi$
$431$	4.71456	−	17.5950i	0.227092	−	0.847520i	0.981555	−	0.191178i	$-0.0612307\pi$
$432$	−4.87170	−	1.30537i	−0.234390	−	0.0628045i
$433$	3.15977	+	11.7924i	0.151849	+	0.566707i	0.999355	+	0.0359210i	$0.0114365\pi$
$433$	3.15977	+	11.7924i	0.151849	+	0.566707i	−0.847506	+	0.530786i	$0.821897\pi$
$434$	−1.56287	+	1.56287i	−0.0750204	+	0.0750204i
$435$		0			0
$436$	0.432091	+	1.61259i	0.0206934	+	0.0772289i
$437$			0.0640710i			0.00306493i
$438$	−21.1298	+	5.66172i	−1.00962	+	0.270527i
$439$	−14.7099	−	25.4783i	−0.702066	−	1.21601i	−0.967740	−	0.251951i	$-0.918928\pi$
$439$	−14.7099	−	25.4783i	−0.702066	−	1.21601i	0.265674	−	0.964063i	$-0.414405\pi$
$440$		0			0
$441$			1.05648i			0.0503085i
$442$	4.30828	−	1.43370i	0.204924	−	0.0681943i
$443$	15.0828	+	15.0828i	0.716607	+	0.716607i	0.967909	−	0.251302i	$-0.0808586\pi$
$443$	15.0828	+	15.0828i	0.716607	+	0.716607i	−0.251302	+	0.967909i	$0.580859\pi$
$444$	14.7097	+	3.94145i	0.698090	+	0.187053i
$445$		0			0
$446$	5.31901	+	3.07093i	0.251863	+	0.145413i
$447$	25.9764			1.22864
$448$	0.670111	+	0.386889i	0.0316598	+	0.0182788i
$449$	8.07087	−	2.16258i	0.380888	−	0.102059i	−0.0632947	−	0.997995i	$-0.520161\pi$
$449$	8.07087	−	2.16258i	0.380888	−	0.102059i	0.444183	+	0.895936i	$0.353494\pi$
$450$		0			0
$451$	−12.3407	+	21.3747i	−0.581101	+	1.00650i
$452$	1.02288	−	3.81745i	0.0481123	−	0.179558i
$453$	−16.0172	−	27.7426i	−0.752554	−	1.30346i
$454$	−15.2771			−0.716992
$455$		0			0
$456$	−0.318837			−0.0149309
$457$	−8.46052	−	14.6540i	−0.395766	−	0.685487i	0.597432	−	0.801919i	$-0.296188\pi$
$457$	−8.46052	−	14.6540i	−0.395766	−	0.685487i	−0.993199	+	0.116432i	$0.962854\pi$
$458$	1.13683	−	4.24270i	0.0531205	−	0.198248i
$459$	3.17574	−	5.50055i	0.148231	−	0.256744i
$460$		0			0
$461$	3.13394	−	0.839736i	0.145962	−	0.0391104i	−0.185098	−	0.982720i	$-0.559260\pi$
$461$	3.13394	−	0.839736i	0.145962	−	0.0391104i	0.331060	+	0.943610i	$0.392594\pi$
$462$	2.92214	+	1.68710i	0.135950	+	0.0784908i
$463$	11.5604			0.537259			0.268630	−	0.963244i	$-0.413429\pi$
$463$	11.5604			0.537259			0.268630	+	0.963244i	$0.413429\pi$
$464$	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	$0.883321\pi$
$468$	−0.0353568	−	0.594016i	−0.00163437	−	0.0274584i
$469$		−	0.799488i		−	0.0369169i
$470$		0			0
$471$	3.62115	+	6.27201i	0.166854	+	0.288999i
$472$	−0.742719	+	0.199011i	−0.0341864	+	0.00916022i
$473$			0.493827i			0.0227062i
$474$	−3.99261	−	14.9006i	−0.183387	−	0.684409i
$475$		0			0
$476$	−0.689033	+	0.689033i	−0.0315818	+	0.0315818i
$477$	−0.0554947	−	0.207109i	−0.00254093	−	0.00948287i
$478$	5.34753	+	1.43287i	0.244590	+	0.0655378i
$479$	5.39239	−	20.1247i	0.246385	−	0.919520i	−0.726298	−	0.687380i	$-0.758761\pi$
$479$	5.39239	−	20.1247i	0.246385	−	0.919520i	0.972682	−	0.232140i	$-0.0745727\pi$
$480$		0			0
$481$	−1.83378	−	30.8087i	−0.0836133	−	1.40476i
$482$	0.113386	−	0.113386i	0.00516460	−	0.00516460i
$483$	0.426206	−	0.246070i	0.0193930	−	0.0111966i
$484$	4.32322	−	2.49601i	0.196510	−	0.113455i
$485$		0			0
$486$	−1.21145	−	1.21145i	−0.0549527	−	0.0549527i
$487$	0.863977	−	1.49645i	0.0391505	−	0.0678107i	−0.845786	−	0.533522i	$-0.820868\pi$
$487$	0.863977	−	1.49645i	0.0391505	−	0.0678107i	0.884937	+	0.465711i	$0.154201\pi$
$488$	7.31689	−	12.6732i	0.331220	−	0.573690i
$489$	−17.4921	−	17.4921i	−0.791019	−	0.791019i
$490$		0			0
$491$	0.747027	−	0.431296i	0.0337129	−	0.0194641i	−0.483049	−	0.875593i	$-0.660471\pi$
$491$	0.747027	−	0.431296i	0.0337129	−	0.0194641i	0.516762	+	0.856129i	$0.327137\pi$
$492$	−15.5141	+	8.95706i	−0.699429	+	0.403816i
$493$	−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
$497$	3.54611	+	0.950178i	0.159065	+	0.0426213i
$498$	4.11955	+	15.3744i	0.184602	+	0.688943i
$499$	−4.24329	+	4.24329i	−0.189956	+	0.189956i	−0.795677	−	0.605721i	$-0.792885\pi$
$499$	−4.24329	+	4.24329i	−0.189956	+	0.189956i	0.605721	+	0.795677i	$0.292885\pi$
$500$		0			0
$501$	−6.53311	−	24.3819i	−0.291878	−	1.08930i
$502$			27.7904i			1.24035i
$503$	−1.12001	+	0.300105i	−0.0499387	+	0.0133810i	−0.283702	−	0.958913i	$-0.591563\pi$
$503$	−1.12001	+	0.300105i	−0.0499387	+	0.0133810i	0.233763	+	0.972294i	$0.424896\pi$
$504$	0.0638529	+	0.110597i	0.00284424	+	0.00492636i
$505$		0			0
$506$			0.876288i			0.0389558i
$507$	−21.4719	+	8.59363i	−0.953600	+	0.381657i
$508$	−8.14798	−	8.14798i	−0.361508	−	0.361508i
$509$	17.3274	+	4.64287i	0.768024	+	0.205792i	0.621499	−	0.783415i	$-0.286524\pi$
$509$	17.3274	+	4.64287i	0.768024	+	0.205792i	0.146526	+	0.989207i	$0.453191\pi$
$510$		0			0
$511$	−8.23965	−	4.75717i	−0.364501	−	0.210445i
$512$	−1.00000			−0.0441942
$513$	0.782791	+	0.451945i	0.0345611	+	0.0199538i
$514$	−3.64080	+	0.975550i	−0.160589	+	0.0430297i
$515$		0			0
$516$	−0.179213	+	0.310407i	−0.00788943	+	0.0136649i
$517$	6.21036	−	23.1774i	0.273131	−	1.01934i
$518$	3.31174	+	5.73610i	0.145509	+	0.252030i
$519$	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	$0.645532\pi$
$522$	0.0554273	+	0.0960030i	0.00242599	+	0.00420194i
$523$	4.56062	−	17.0205i	0.199422	−	0.744252i	−0.791656	−	0.610967i	$-0.790781\pi$
$523$	4.56062	−	17.0205i	0.199422	−	0.744252i	0.991078	−	0.133285i	$-0.0425526\pi$
$524$	−4.81502	+	8.33986i	−0.210345	+	0.364328i
$525$		0			0
$526$	16.8872	−	4.52492i	0.736318	−	0.197296i
$527$	3.11525	+	1.79859i	0.135702	+	0.0783478i
$528$	−4.36068			−0.189774
$529$	−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
$533$	27.1522	+	24.1015i	1.17609	+	1.04395i
$534$			23.0034i			0.995457i
$535$		0			0
$536$	0.516614	+	0.894801i	0.0223143	+	0.0386495i
$537$	−9.86418	+	2.64310i	−0.425671	+	0.114058i
$538$			26.0363i			1.12250i
$539$	−4.06094	−	15.1556i	−0.174917	−	0.652799i
$540$		0			0
$541$	−8.75869	+	8.75869i	−0.376566	+	0.376566i	−0.869862	−	0.493296i	$-0.835792\pi$
$541$	−8.75869	+	8.75869i	−0.376566	+	0.376566i	0.493296	+	0.869862i	$0.335792\pi$
$542$	0.215492	+	0.804227i	0.00925617	+	0.0345445i
$543$	−13.7112	−	3.67390i	−0.588404	−	0.157662i
$544$	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	$0.582818\pi$
$547$	−28.6176	+	28.6176i	−1.22360	+	1.22360i	−0.966343	+	0.257256i	$0.917182\pi$
$548$	−0.783972	+	0.452627i	−0.0334896	+	0.0193353i
$549$	2.09161	−	1.20759i	0.0892679	−	0.0515389i
$550$		0			0
$551$	−0.0851183	−	0.0851183i	−0.00362616	−	0.00362616i
$552$	−0.318011	+	0.550812i	−0.0135355	+	0.0234441i
$553$	3.35473	−	5.81056i	0.142658	−	0.247090i
$554$	5.07030	+	5.07030i	0.215416	+	0.215416i
$555$		0			0
$556$	1.75329	−	1.01226i	0.0743559	−	0.0429294i
$557$	−0.503539	+	0.290718i	−0.0213356	+	0.0123181i	−0.510630	−	0.859801i	$-0.670588\pi$
$557$	−0.503539	+	0.290718i	−0.0213356	+	0.0123181i	0.489294	+	0.872119i	$0.337254\pi$
$558$	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
$562$	22.3029	+	5.97603i	0.940789	+	0.252084i
$563$	−1.83523	−	6.84916i	−0.0773456	−	0.288658i	0.916409	−	0.400242i	$-0.131074\pi$
$563$	−1.83523	−	6.84916i	−0.0773456	−	0.288658i	−0.993755	+	0.111585i	$0.964407\pi$
$564$	12.3149	−	12.3149i	0.518551	−	0.518551i
$565$		0			0
$566$	−6.46878	−	24.1418i	−0.271903	−	1.01476i
$567$		−	7.32604i		−	0.307665i
$568$	−4.58286	+	1.22797i	−0.192292	+	0.0515246i
$569$	11.4714	+	19.8690i	0.480904	+	0.832950i	0.999760	−	0.0219115i	$-0.00697519\pi$
$569$	11.4714	+	19.8690i	0.480904	+	0.832950i	−0.518856	+	0.854862i	$0.673642\pi$
$570$		0			0
$571$			10.3285i			0.432233i	0.976368	+	0.216117i	$0.0693391\pi$
$571$			10.3285i			0.432233i	−0.976368	+	0.216117i	$0.930661\pi$
$572$	2.79051	+	8.38551i	0.116677	+	0.350616i
$573$	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
$577$	−0.576251			−0.0239897			−0.0119948	−	0.999928i	$-0.503818\pi$
$577$	−0.576251			−0.0239897			−0.0119948	+	0.999928i	$0.503818\pi$
$578$	−13.3490	−	7.70705i	−0.555245	−	0.320571i
$579$	−43.9232	+	11.7692i	−1.82539	+	0.489111i
$580$		0			0
$581$	−3.46139	+	5.99530i	−0.143603	+	0.248727i
$582$	−5.16729	+	19.2846i	−0.214191	+	0.799372i
$583$	1.59219	+	2.75775i	0.0659418	+	0.114214i
$584$	12.2960			0.508810
$585$		0			0
$586$	20.0431			0.827971
$587$	−10.8879	−	18.8584i	−0.449392	−	0.778370i	0.548954	−	0.835852i	$-0.315026\pi$
$587$	−10.8879	−	18.8584i	−0.449392	−	0.778370i	−0.998347	+	0.0574823i	$0.981693\pi$
$588$	2.94749	−	11.0002i	0.121552	−	0.453640i
$589$	−0.255960	+	0.443336i	−0.0105466	+	0.0182673i
$590$		0			0
$591$	−21.0697	+	5.64561i	−0.866692	+	0.232229i
$592$	−7.41311	−	4.27996i	−0.304677	−	0.175905i
$593$	−3.64436			−0.149656			−0.0748280	−	0.997196i	$-0.523841\pi$
$593$	−3.64436			−0.149656			−0.0748280	+	0.997196i	$0.523841\pi$
$594$	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
$598$	1.26271	+	0.259051i	0.0516359	+	0.0105934i
$599$		−	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	0.945793	−	0.324770i	$-0.105287\pi$
$601$	4.69804	+	8.13724i	0.191637	+	0.331925i	−0.754156	+	0.656695i	$0.771954\pi$
$602$	−0.150581	+	0.0403481i	−0.00613723	+	0.00164446i
$603$			0.170526i			0.00694436i
$604$	4.66040	+	17.3928i	0.189629	+	0.707705i
$605$		0			0
$606$	−11.9896	+	11.9896i	−0.487046	+	0.487046i
$607$	−1.69659	−	6.33176i	−0.0688624	−	0.256998i	0.922909	−	0.385018i	$-0.125805\pi$
$607$	−1.69659	−	6.33176i	−0.0688624	−	0.256998i	−0.991772	+	0.128020i	$0.959138\pi$
$608$	0.173110	+	0.0463847i	0.00702054	+	0.00188115i
$609$	−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
$613$	−4.63368	+	2.67526i	−0.187153	+	0.108053i	−0.590649	−	0.806929i	$-0.701128\pi$
$613$	−4.63368	+	2.67526i	−0.187153	+	0.108053i	0.403496	+	0.914981i	$0.367795\pi$
$614$	−15.6435	+	9.03175i	−0.631319	+	0.364492i
$615$		0			0
$616$	−1.34111	−	1.34111i	−0.0540350	−	0.0540350i
$617$	−3.64259	+	6.30916i	−0.146645	+	0.253997i	−0.929986	−	0.367596i	$-0.880181\pi$
$617$	−3.64259	+	6.30916i	−0.146645	+	0.253997i	0.783340	+	0.621593i	$0.213514\pi$
$618$	−15.4150	+	26.6996i	−0.620082	+	1.07401i
$619$	29.6086	+	29.6086i	1.19007	+	1.19007i	0.977047	+	0.213022i	$0.0683305\pi$
$619$	29.6086	+	29.6086i	1.19007	+	1.19007i	0.213022	+	0.977047i	$0.431669\pi$
$620$		0			0
$621$	1.56153	−	0.901549i	0.0626620	−	0.0361779i
$622$	−22.5476	+	13.0179i	−0.904078	+	0.521970i
$623$	−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
$627$	0.754878	+	0.202269i	0.0301469	+	0.00807784i
$628$	−1.05362	−	3.93215i	−0.0420439	−	0.156910i
$629$	7.62244	−	7.62244i	0.303926	−	0.303926i
$630$		0			0
$631$	−8.22180	−	30.6842i	−0.327305	−	1.22152i	−0.911975	−	0.410247i	$-0.865443\pi$
$631$	−8.22180	−	30.6842i	−0.327305	−	1.22152i	0.584670	−	0.811271i	$-0.301224\pi$
$632$			8.67104i			0.344916i
$633$	−26.0970	+	6.99267i	−1.03726	+	0.277934i
$634$	13.6093	+	23.5720i	0.540495	+	0.936165i
$635$		0			0
$636$			2.31127i			0.0916477i
$637$	−23.0393	+	1.37134i	−0.912851	+	0.0543344i
$638$	−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	0.775009	−	0.631950i	$-0.217745\pi$
$641$	15.5764	+	8.99301i	0.615229	+	0.355203i	−0.159780	+	0.987153i	$0.551079\pi$
$642$	−34.1305			−1.34702
$643$	12.8469	+	7.41717i	0.506633	+	0.292505i	0.731449	−	0.681897i	$-0.238845\pi$
$643$	12.8469	+	7.41717i	0.506633	+	0.292505i	−0.224816	+	0.974401i	$0.572178\pi$
$644$	−0.267204	+	0.0715970i	−0.0105293	+	0.00282132i
$645$		0			0
$646$	−0.112846	+	0.195456i	−0.00443988	+	0.00769011i
$647$	5.74551	−	21.4425i	0.225879	−	0.842993i	−0.756171	−	0.654374i	$-0.772932\pi$
$647$	5.74551	−	21.4425i	0.225879	−	0.842993i	0.982050	−	0.188619i	$-0.0604011\pi$
$648$	4.73394	+	8.19943i	0.185967	+	0.322104i
$649$	1.88471			0.0739814
$650$		0			0
$651$	3.93214			0.154113
$652$	6.95243	+	12.0420i	0.272278	+	0.471600i
$653$	−3.79373	+	14.1584i	−0.148460	+	0.554060i	0.851117	+	0.524976i	$0.175926\pi$
$653$	−3.79373	+	14.1584i	−0.148460	+	0.554060i	−0.999577	+	0.0290840i	$0.990741\pi$
$654$	1.48504	−	2.57217i	0.0580698	−	0.100580i
$655$		0			0
$656$	9.72634	−	2.60617i	0.379750	−	0.101754i
$657$	1.75747	+	1.01467i	0.0685654	+	0.0395862i
$658$	7.57482			0.295297
$659$	26.6381	+	15.3795i	1.03767	+	0.599101i	0.919174	−	0.393853i	$-0.128858\pi$
$659$	26.6381	+	15.3795i	1.03767	+	0.599101i	0.118500	+	0.992954i	$0.462191\pi$
$660$		0			0
$661$	−23.6815	−	6.34545i	−0.921105	−	0.246809i	−0.233047	−	0.972465i	$-0.574870\pi$
$661$	−23.6815	−	6.34545i	−0.921105	−	0.246809i	−0.688057	+	0.725656i	$0.741536\pi$
$662$	23.6167	+	23.6167i	0.917889	+	0.917889i
$663$	−7.22332	−	3.61617i	−0.280531	−	0.140441i
$664$		−	8.94673i		−	0.347200i
$665$		0			0
$666$	−0.706374	−	1.22347i	−0.0273714	−	0.0474087i
$667$	−0.231945	+	0.0621496i	−0.00898096	+	0.00240644i
$668$			14.1884i			0.548966i
$669$	−2.82805	−	10.5544i	−0.109339	−	0.408057i
$670$		0			0
$671$	−25.3633	+	25.3633i	−0.979139	+	0.979139i
$672$	−0.356289	−	1.32969i	−0.0137441	−	0.0512938i
$673$	25.3811	+	6.80086i	0.978371	+	0.262154i	0.712358	−	0.701816i	$-0.247627\pi$
$673$	25.3811	+	6.80086i	0.978371	+	0.262154i	0.266013	+	0.963970i	$0.414294\pi$
$674$	−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	$0.606691\pi$
$677$	−33.1300	+	33.1300i	−1.27329	+	1.27329i	−0.944352	+	0.328938i	$0.893309\pi$
$678$	−6.08905	+	3.51552i	−0.233849	+	0.135013i
$679$	−7.52010	+	4.34173i	−0.288595	+	0.166620i
$680$		0			0
$681$	19.2184	+	19.2184i	0.736450	+	0.736450i
$682$	−3.50072	+	6.06342i	−0.134049	+	0.232180i
$683$	−1.40920	+	2.44081i	−0.0539216	+	0.0933950i	−0.891726	−	0.452575i	$-0.850505\pi$
$683$	−1.40920	+	2.44081i	−0.0539216	+	0.0933950i	0.837805	+	0.545970i	$0.183839\pi$
$684$	0.0209150	+	0.0209150i	0.000799706	+	0.000799706i
$685$		0			0
$686$	8.98034	−	5.18480i	0.342871	−	0.197957i
$687$	−6.76736	+	3.90714i	−0.258191	+	0.149067i
$688$	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	−0.949007	−	0.315254i	$-0.897910\pi$
$691$	0.801327	−	2.99059i	0.0304839	−	0.113768i	0.979491	+	0.201486i	$0.0645771\pi$
$692$	−10.8608	−	2.91015i	−0.412866	−	0.110627i
$693$	−0.0810161	−	0.302356i	−0.00307755	−	0.0114856i
$694$	−3.50692	+	3.50692i	−0.133121	+	0.133121i
$695$		0			0
$696$	−0.309275	−	1.15423i	−0.0117231	−	0.0437510i
$697$			12.6807i			0.480318i
$698$	−30.4439	+	8.15741i	−1.15232	+	0.308762i
$699$	19.8112	+	34.3141i	0.749330	+	1.29788i
$700$		0			0
$701$		−	22.6870i		−	0.856875i	−0.903571	−	0.428438i	$-0.859064\pi$
$701$		−	22.6870i		−	0.856875i	0.903571	−	0.428438i	$-0.140936\pi$
$702$	12.0719	−	13.5999i	0.455623	−	0.513294i
$703$	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
$707$	−7.37475			−0.277356
$708$	1.18468	+	0.683975i	0.0445230	+	0.0257054i
$709$	7.63472	−	2.04572i	0.286728	−	0.0768285i	−0.112589	−	0.993642i	$-0.535914\pi$
$709$	7.63472	−	2.04572i	0.286728	−	0.0768285i	0.399316	+	0.916813i	$0.369248\pi$
$710$		0			0
$711$	−0.715544	+	1.23936i	−0.0268350	+	0.0464796i
$712$	3.34657	−	12.4896i	0.125418	−	0.468066i
$713$	0.510594	+	0.884375i	0.0191219	+	0.0331201i
$714$	1.73358			0.0648778
$715$		0			0
$716$	5.74021			0.214522
$717$	−4.92458	−	8.52962i	−0.183912	−	0.318545i
$718$	−4.29023	+	16.0114i	−0.160110	+	0.597539i
$719$	9.22690	−	15.9815i	0.344105	−	0.596008i	−0.641086	−	0.767469i	$-0.721516\pi$
$719$	9.22690	−	15.9815i	0.344105	−	0.596008i	0.985191	+	0.171462i	$0.0548490\pi$
$720$		0			0
$721$	−12.9522	+	3.47053i	−0.482365	+	0.129249i
$722$	16.4267	+	9.48394i	0.611337	+	0.352956i
$723$	−0.285276			−0.0106095
$724$	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	$0.909977\pi$
$728$	−2.32897	+	1.53604i	−0.0863173	+	0.0569294i
$729$		−	25.3557i		−	0.939099i
$730$		0			0
$731$	0.126859	+	0.219725i	0.00469203	+	0.00812684i
$732$	−25.1472	+	6.73817i	−0.929468	+	0.249050i
$733$		−	11.9202i		−	0.440282i	−0.975468	−	0.220141i	$-0.929348\pi$
$733$		−	11.9202i		−	0.440282i	0.975468	−	0.220141i	$-0.0706517\pi$
$734$	5.26220	+	19.6388i	0.194231	+	0.724882i
$735$		0			0
$736$	0.252795	−	0.252795i	0.00931813	−	0.00931813i
$737$	−0.655475	−	2.44627i	−0.0241447	−	0.0901094i
$738$	1.60526	+	0.430127i	0.0590903	+	0.0158332i
$739$	2.47875	−	9.25081i	0.0911822	−	0.340297i	−0.905231	−	0.424920i	$-0.860302\pi$
$739$	2.47875	−	9.25081i	0.0911822	−	0.340297i	0.996413	+	0.0846236i	$0.0269688\pi$
$740$		0			0
$741$	0.514623	−	1.02796i	0.0189051	−	0.0377631i
$742$	−0.710823	+	0.710823i	−0.0260951	+	0.0260951i
$743$	−29.6828	+	17.1373i	−1.08895	+	0.628708i	−0.933298	−	0.359103i	$-0.883083\pi$
$743$	−29.6828	+	17.1373i	−1.08895	+	0.628708i	−0.155657	+	0.987811i	$0.549749\pi$
$744$	−4.40092	+	2.54087i	−0.161346	+	0.0931529i
$745$		0			0
$746$	−12.2160	−	12.2160i	−0.447261	−	0.447261i
$747$	0.738293	−	1.27876i	0.0270127	−	0.0467874i
$748$	−1.54338	+	2.67322i	−0.0564316	+	0.0977424i
$749$	−10.4967	−	10.4967i	−0.383542	−	0.383542i
$750$		0			0
$751$	−27.4571	+	15.8524i	−1.00193	+	0.578462i	−0.908817	−	0.417194i	$-0.863014\pi$
$751$	−27.4571	+	15.8524i	−1.00193	+	0.578462i	−0.0931081	+	0.995656i	$0.529680\pi$
$752$	−8.47787	+	4.89470i	−0.309156	+	0.178491i
$753$	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
$757$	38.1732	+	10.2285i	1.38743	+	0.371760i	0.873814	−	0.486261i	$-0.161640\pi$
$757$	38.1732	+	10.2285i	1.38743	+	0.371760i	0.513614	+	0.858021i	$0.328306\pi$
$758$	−3.93982	−	14.7036i	−0.143101	−	0.534059i
$759$	1.10236	−	1.10236i	0.0400130	−	0.0400130i
$760$		0			0
$761$	6.83854	+	25.5218i	0.247897	+	0.925164i	0.971905	+	0.235373i	$0.0756310\pi$
$761$	6.83854	+	25.5218i	0.247897	+	0.925164i	−0.724008	+	0.689791i	$0.757702\pi$
$762$			20.5000i			0.742638i
$763$	1.24778	−	0.334343i	0.0451728	−	0.0121040i
$764$	−11.3313	−	19.6263i	−0.409951	−	0.710055i
$765$		0			0
$766$			24.1903i			0.874030i
$767$	0.557164	−	2.71581i	0.0201180	−	0.0980623i
$768$	1.25798	+	1.25798i	0.0453935	+	0.0453935i
$769$	−12.1496	−	3.25549i	−0.438127	−	0.117396i	0.0330114	−	0.999455i	$-0.489490\pi$
$769$	−12.1496	−	3.25549i	−0.438127	−	0.117396i	−0.471139	+	0.882059i	$0.656157\pi$
$770$		0			0
$771$	5.80729	+	3.35284i	0.209145	+	0.120750i
$772$	25.5600			0.919924
$773$	−27.2999	−	15.7616i	−0.981907	−	0.566905i	−0.0790620	−	0.996870i	$-0.525193\pi$
$773$	−27.2999	−	15.7616i	−0.981907	−	0.566905i	−0.902845	+	0.429965i	$0.858526\pi$
$774$	0.0321180	−	0.00860600i	0.00115446	−	0.000309336i
$775$		0			0
$776$	5.61108	−	9.71868i	0.201426	−	0.348880i
$777$	3.04980	−	11.3820i	0.109411	−	0.408328i
$778$	−4.13412	−	7.16051i	−0.148216	−	0.256717i
$779$	−1.80462			−0.0646571
$780$		0			0
$781$	11.6294			0.416132
$782$	0.225109	+	0.389899i	0.00804986	+	0.0139428i
$783$	−0.876783	+	3.27220i	−0.0313337	+	0.116939i
$784$	−3.20063	+	5.54366i	−0.114308	+	0.197988i
$785$		0			0
$786$	16.5486	−	4.43419i	0.590269	−	0.158162i
$787$	−14.8066	−	8.54859i	−0.527798	−	0.304724i	0.212321	−	0.977200i	$-0.431898\pi$
$787$	−14.8066	−	8.54859i	−0.527798	−	0.304724i	−0.740119	+	0.672475i	$0.765231\pi$
$788$	12.2610			0.436779
$789$	−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
$793$	29.0498	+	44.0457i	1.03159	+	1.56411i
$794$		−	10.5364i		−	0.373924i
$795$		0			0
$796$	10.6245	+	18.4021i	0.376575	+	0.652246i
$797$	38.0990	−	10.2086i	1.34954	−	0.361607i	0.489573	−	0.871962i	$-0.337153\pi$
$797$	38.0990	−	10.2086i	1.34954	−	0.361607i	0.859964	+	0.510355i	$0.170486\pi$
$798$			0.246709i			0.00873340i
$799$	−3.19074	−	11.9080i	−0.112880	−	0.421275i
$800$		0			0
$801$	1.50898	−	1.50898i	0.0533171	−	0.0533171i
$802$	−7.59122	−	28.3308i	−0.268055	−	1.00040i
$803$	−29.1119	−	7.80050i	−1.02734	−	0.275274i
$804$	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
$808$	8.25395	−	4.76542i	0.290373	−	0.167647i
$809$	19.7531	−	11.4045i	0.694483	−	0.400960i	−0.110806	−	0.993842i	$-0.535343\pi$
$809$	19.7531	−	11.4045i	0.694483	−	0.400960i	0.805289	+	0.592882i	$0.202010\pi$
$810$		0			0
$811$	23.0864	+	23.0864i	0.810674	+	0.810674i	0.984735	−	0.174061i	$-0.0556890\pi$
$811$	23.0864	+	23.0864i	0.810674	+	0.810674i	−0.174061	+	0.984735i	$0.555689\pi$
$812$	0.259864	−	0.450097i	0.00911942	−	0.0157953i
$813$	0.740618	−	1.28279i	0.0259746	−	0.0449893i
$814$	14.8361	+	14.8361i	0.520004	+	0.520004i
$815$		0			0
$816$	−1.94026	+	1.12021i	−0.0679226	+	0.0392151i
$817$	−0.0312694	+	0.0180534i	−0.00109398	+	0.000631609i
$818$	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	−0.999967	−	0.00814199i	$-0.997408\pi$
$821$	−3.72201	+	13.8907i	−0.129899	+	0.484790i	0.870068	+	0.492932i	$0.164075\pi$
$822$	1.55562	+	0.416827i	0.0542585	+	0.0145385i
$823$	−11.0499	−	41.2386i	−0.385174	−	1.43749i	−0.837893	−	0.545835i	$-0.816212\pi$
$823$	−11.0499	−	41.2386i	−0.385174	−	1.43749i	0.452719	−	0.891653i	$-0.350454\pi$
$824$	12.2537	−	12.2537i	0.426879	−	0.426879i
$825$		0			0
$826$	0.153990	+	0.574699i	0.00535800	+	0.0199963i
$827$		−	50.0663i		−	1.74098i	−0.492189	−	0.870488i	$-0.663803\pi$
$827$		−	50.0663i		−	1.74098i	0.492189	−	0.870488i	$-0.336197\pi$
$828$	0.0569930	−	0.0152712i	0.00198064	−	0.000530712i
$829$	−18.8278	−	32.6107i	−0.653916	−	1.13262i	−0.982164	−	0.188025i	$-0.939792\pi$
$829$	−18.8278	−	32.6107i	−0.653916	−	1.13262i	0.328248	−	0.944592i	$-0.393542\pi$
$830$		0			0
$831$		−	12.7567i		−	0.442525i
$832$	1.61406	−	3.22410i	0.0559576	−	0.111775i
$833$	−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
$837$	14.4065			0.497963
$838$	−21.8423	−	12.6107i	−0.754529	−	0.435628i
$839$	−27.1992	+	7.28802i	−0.939022	+	0.251610i	−0.695698	−	0.718335i	$-0.744905\pi$
$839$	−27.1992	+	7.28802i	−0.939022	+	0.251610i	−0.243325	+	0.969945i	$0.578238\pi$
$840$		0			0
$841$	−14.2744	+	24.7240i	−0.492222	+	0.852553i
$842$	−0.412130	+	1.53809i	−0.0142029	+	0.0530061i
$843$	−20.5389	−	35.5744i	−0.707396	−	1.22525i
$844$	15.1865			0.522740
$845$		0			0
$846$	−1.61566			−0.0555477
$847$	−1.93136	−	3.34521i	−0.0663622	−	0.114943i
$848$	0.336246	−	1.25489i	0.0115467	−	0.0430930i
$849$	−22.2324	+	38.5076i	−0.763013	+	1.32158i
$850$		0			0
$851$	2.95594	−	0.792043i	0.101328	−	0.0271509i
$852$	7.30992	+	4.22039i	0.250434	+	0.144588i
$853$	32.0153			1.09618			0.548091	−	0.836419i	$-0.315355\pi$
$853$	32.0153			1.09618			0.548091	+	0.836419i	$0.315355\pi$
$854$	−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	$0.561342\pi$
$858$	7.03841	−	14.0592i	0.240287	−	0.479975i
$859$			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
$862$	17.5950	−	4.71456i	0.599287	−	0.160579i
$863$			21.5671i			0.734153i	0.930191	+	0.367077i	$0.119641\pi$
$863$			21.5671i			0.734153i	−0.930191	+	0.367077i	$0.880359\pi$
$864$	−1.30537	−	4.87170i	−0.0444095	−	0.165738i
$865$		0			0
$866$	−8.63264	+	8.63264i	−0.293349	+	0.293349i
$867$	7.09748	+	26.4881i	0.241043	+	0.899584i
$868$	−2.13493	−	0.572052i	−0.0724641	−	0.0194167i
$869$	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
$873$	1.60399	−	0.926065i	0.0542869	−	0.0313426i
$874$	−0.0554871	+	0.0320355i	−0.00187688	+	0.00108362i
$875$		0			0
$876$	−15.4681	−	15.4681i	−0.522619	−	0.522619i
$877$	−4.29469	+	7.43862i	−0.145021	+	0.251184i	−0.929381	−	0.369122i	$-0.879658\pi$
$877$	−4.29469	+	7.43862i	−0.145021	+	0.251184i	0.784360	+	0.620306i	$0.212992\pi$
$878$	14.7099	−	25.4783i	0.496436	−	0.859852i
$879$	−25.2138	−	25.2138i	−0.850441	−	0.850441i
$880$		0			0
$881$	24.3217	−	14.0421i	0.819419	−	0.473092i	−0.0307970	−	0.999526i	$-0.509805\pi$
$881$	24.3217	−	14.0421i	0.819419	−	0.473092i	0.850216	+	0.526434i	$0.176471\pi$
$882$	−0.914938	+	0.528239i	−0.0308076	+	0.0177867i
$883$	−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
$887$	10.8956	+	2.91948i	0.365840	+	0.0980266i	0.437056	−	0.899434i	$-0.356021\pi$
$887$	10.8956	+	2.91948i	0.365840	+	0.0980266i	−0.0712157	+	0.997461i	$0.522688\pi$
$888$	3.94145	+	14.7097i	0.132266	+	0.493625i
$889$	−6.30472	+	6.30472i	−0.211454	+	0.211454i
$890$		0			0
$891$	−6.00639	−	22.4162i	−0.201222	−	0.750969i
$892$			6.14187i			0.205645i
$893$	1.69464	−	0.454079i	0.0567091	−	0.0151952i
$894$	12.9882	+	22.4963i	0.434391	+	0.752387i
$895$		0			0
$896$			0.773777i			0.0258501i
$897$	−1.26258	−	1.91434i	−0.0421563	−	0.0639181i
$898$	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
$902$	−24.6814			−0.821801
$903$	0.240186	+	0.138671i	0.00799288	+	0.00461469i
$904$	3.81745	−	1.02288i	0.126966	−	0.0340205i
$905$		0			0
$906$	16.0172	−	27.7426i	0.532136	−	0.921686i
$907$	5.14882	−	19.2157i	0.170964	−	0.638045i	−0.826240	−	0.563318i	$-0.809525\pi$
$907$	5.14882	−	19.2157i	0.170964	−	0.638045i	0.997204	−	0.0747275i	$-0.0238087\pi$
$908$	−7.63857	−	13.2304i	−0.253495	−	0.439066i
$909$	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	$0.606959\pi$
$912$	−0.159418	−	0.276121i	−0.00527887	−	0.00914327i
$913$	−5.67577	+	21.1823i	−0.187840	+	0.701030i
$914$	8.46052	−	14.6540i	0.279849	−	0.484713i
$915$		0			0
$916$	4.24270	−	1.13683i	0.140183	−	0.0375619i
$917$	6.45319	+	3.72575i	0.213103	+	0.123035i
$918$	6.35149			0.209630
$919$	24.2229	+	13.9851i	0.799039	+	0.461325i	0.843135	−	0.537702i	$-0.180707\pi$
$919$	24.2229	+	13.9851i	0.799039	+	0.461325i	−0.0440961	+	0.999027i	$0.514041\pi$
$920$		0			0
$921$	31.0410	+	8.31741i	1.02284	+	0.274068i
$922$	2.29420	+	2.29420i	0.0755555	+	0.0755555i
$923$	3.43792	−	16.7576i	0.113160	−	0.551583i
$924$			3.37419i			0.111003i
$925$		0			0
$926$	5.78022	+	10.0116i	0.189950	+	0.329003i
$927$	2.76263	−	0.740243i	0.0907366	−	0.0243128i
$928$			0.671675i			0.0220488i
$929$	−9.06611	−	33.8352i	−0.297449	−	1.11010i	−0.939253	−	0.343227i	$-0.888480\pi$
$929$	−9.06611	−	33.8352i	−0.297449	−	1.11010i	0.641803	−	0.766869i	$-0.278187\pi$
$930$		0			0
$931$	0.811204	−	0.811204i	0.0265861	−	0.0265861i
$932$	−5.76432	−	21.5127i	−0.188817	−	0.704673i
$933$	44.7408	+	11.9883i	1.46475	+	0.392478i
$934$	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	−0.588377	−	0.808587i	$-0.700233\pi$
$937$	6.74074	−	6.74074i	0.220210	−	0.220210i	0.808587	+	0.588377i	$0.200233\pi$
$938$	0.692377	−	0.399744i	0.0226069	−	0.0130521i
$939$	−21.3044	+	12.3001i	−0.695242	+	0.401398i
$940$		0			0
$941$	26.4463	+	26.4463i	0.862126	+	0.862126i	0.991585	−	0.129459i	$-0.0413240\pi$
$941$	26.4463	+	26.4463i	0.862126	+	0.862126i	−0.129459	+	0.991585i	$0.541324\pi$
$942$	−3.62115	+	6.27201i	−0.117983	+	0.204353i
$943$	−1.79994	+	3.11759i	−0.0586142	+	0.101523i
$944$	−0.543708	−	0.543708i	−0.0176962	−	0.0176962i
$945$		0			0
$946$	−0.427667	+	0.246913i	−0.0139046	+	0.00802785i
$947$	−5.60757	+	3.23753i	−0.182222	+	0.105206i	−0.588336	−	0.808617i	$-0.700217\pi$
$947$	−5.60757	+	3.23753i	−0.182222	+	0.105206i	0.406114	+	0.913822i	$0.366883\pi$
$948$	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
$952$	−0.941237	−	0.252204i	−0.0305057	−	0.00817397i
$953$	4.94244	+	18.4454i	0.160101	+	0.597506i	0.998614	+	0.0526246i	$0.0167587\pi$
$953$	4.94244	+	18.4454i	0.160101	+	0.597506i	−0.838513	+	0.544881i	$0.816575\pi$
$954$	0.151614	−	0.151614i	0.00490870	−	0.00490870i
$955$		0			0
$956$	1.43287	+	5.34753i	0.0463422	+	0.172951i
$957$			2.92896i			0.0946798i
$958$	20.1247	−	5.39239i	0.650199	−	0.174220i
$959$	0.350232	+	0.606620i	0.0113096	+	0.0195888i
$960$		0			0
$961$		−	22.8408i		−	0.736801i
$962$	25.7642	−	16.9925i	0.830672	−	0.547859i
$963$	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
$967$	49.8566			1.60328			0.801640	−	0.597807i	$-0.203961\pi$
$967$	49.8566			1.60328			0.801640	+	0.597807i	$0.203961\pi$
$968$	4.32322	+	2.49601i	0.138953	+	0.0802248i
$969$	0.387839	−	0.103921i	0.0124592	−	0.00333843i
$970$		0			0
$971$	6.30588	−	10.9221i	0.202365	−	0.350507i	−0.746925	−	0.664908i	$-0.768471\pi$
$971$	6.30588	−	10.9221i	0.202365	−	0.350507i	0.949290	+	0.314402i	$0.101804\pi$
$972$	0.443423	−	1.65488i	0.0142228	−	0.0530802i
$973$	−0.783265	−	1.35665i	−0.0251103	−	0.0434923i
$974$	1.72795			0.0553672
$975$		0			0
$976$	14.6338			0.468416
$977$	15.9106	+	27.5579i	0.509024	+	0.881655i	0.999945	+	0.0104514i	$0.00332685\pi$
$977$	15.9106	+	27.5579i	0.509024	+	0.881655i	−0.490921	+	0.871204i	$0.663340\pi$
$978$	6.40254	−	23.8946i	0.204731	−	0.764066i
$979$	−15.8466	+	27.4472i	−0.506461	+	0.877216i
$980$		0			0
$981$	−0.266145	+	0.0713133i	−0.00849735	+	0.00227686i
$982$	0.747027	+	0.431296i	0.0238386	+	0.0137632i
$983$	−27.3031			−0.870835			−0.435417	−	0.900229i	$-0.643399\pi$
$983$	−27.3031			−0.870835			−0.435417	+	0.900229i	$0.643399\pi$
$984$	−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
$988$	−0.428960	+	0.483256i	−0.0136470	+	0.0153744i
$989$			0.0720267i			0.00229031i
$990$		0			0
$991$	−26.1930	−	45.3676i	−0.832048	−	1.44115i	−0.896411	−	0.443223i	$-0.853835\pi$
$991$	−26.1930	−	45.3676i	−0.832048	−	1.44115i	0.0643633	−	0.997927i	$-0.479498\pi$
$992$	2.75910	−	0.739298i	0.0876014	−	0.0234727i
$993$		−	59.4188i		−	1.88560i
$994$	0.950178	+	3.54611i	0.0301378	+	0.112476i
$995$		0			0
$996$	−11.2548	+	11.2548i	−0.356623	+	0.356623i
$997$	11.8247	+	44.1303i	0.374491	+	1.39762i	0.854087	+	0.520131i	$0.174117\pi$
$997$	11.8247	+	44.1303i	0.374491	+	1.39762i	−0.479595	+	0.877490i	$0.659217\pi$
$998$	−5.79644	−	1.55315i	−0.183483	−	0.0491642i
$999$	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.w.h.193.3	yes	16
5.2	odd	4		650.2.t.f.557.2	✓	16
5.3	odd	4		650.2.t.h.557.3	yes	16
5.4	even	2		650.2.w.f.193.2	yes	16
13.6	odd	12		650.2.t.f.643.2	yes	16
65.19	odd	12		650.2.t.h.643.3	yes	16
65.32	even	12	inner	650.2.w.h.357.3	yes	16
65.58	even	12		650.2.w.f.357.2	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
650.2.t.f.557.2	✓	16	5.2	odd	4
650.2.t.f.643.2	yes	16	13.6	odd	12
650.2.t.h.557.3	yes	16	5.3	odd	4
650.2.t.h.643.3	yes	16	65.19	odd	12
650.2.w.f.193.2	yes	16	5.4	even	2
650.2.w.f.357.2	yes	16	65.58	even	12
650.2.w.h.193.3	yes	16	1.1	even	1	trivial
650.2.w.h.357.3	yes	16	65.32	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.460454 - 1.71844i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(1.71844 - 0.460454i) q^{6} +(0.670111 + 0.386889i) q^{7} -1.00000 q^{8} +(-0.142931 - 0.0825211i) q^{9} +(2.36760 + 0.634396i) q^{11} +(1.25798 + 1.25798i) q^{12} +(1.61406 - 3.22410i) q^{13} +0.773777i q^{14} +(-0.500000 - 0.866025i) q^{16} +(1.21642 - 0.325938i) q^{17} -0.165042i q^{18} +(0.0463847 + 0.173110i) q^{19} +(0.973399 - 0.973399i) q^{21} +(0.634396 + 2.36760i) q^{22} +(0.345324 + 0.0925293i) q^{23} +(-0.460454 + 1.71844i) q^{24} +(3.59918 - 0.214229i) q^{26} +(3.56633 - 3.56633i) q^{27} +(-0.670111 + 0.386889i) q^{28} +(-0.581688 + 0.335838i) q^{29} +(2.01980 + 2.01980i) q^{31} +(0.500000 - 0.866025i) q^{32} +(2.18034 - 3.77646i) q^{33} +(0.890480 + 0.890480i) q^{34} +(0.142931 - 0.0825211i) q^{36} +(7.41311 - 4.27996i) q^{37} +(-0.126725 + 0.126725i) q^{38} +(-4.79721 - 4.25821i) q^{39} +(-2.60617 + 9.72634i) q^{41} +(1.32969 + 0.356289i) q^{42} +(0.0521443 + 0.194605i) q^{43} +(-1.73320 + 1.73320i) q^{44} +(0.0925293 + 0.345324i) q^{46} -9.78940i q^{47} +(-1.71844 + 0.460454i) q^{48} +(-3.20063 - 5.54366i) q^{49} -2.24042i q^{51} +(1.98512 + 3.00987i) q^{52} +(0.918640 + 0.918640i) q^{53} +(4.87170 + 1.30537i) q^{54} +(-0.670111 - 0.386889i) q^{56} +0.318837 q^{57} +(-0.581688 - 0.335838i) q^{58} +(0.742719 - 0.199011i) q^{59} +(-7.31689 + 12.6732i) q^{61} +(-0.739298 + 2.75910i) q^{62} +(-0.0638529 - 0.110597i) q^{63} +1.00000 q^{64} +4.36068 q^{66} +(-0.516614 - 0.894801i) q^{67} +(-0.325938 + 1.21642i) q^{68} +(0.318011 - 0.550812i) q^{69} +(4.58286 - 1.22797i) q^{71} +(0.142931 + 0.0825211i) q^{72} -12.2960 q^{73} +(7.41311 + 4.27996i) q^{74} +(-0.173110 - 0.0463847i) q^{76} +(1.34111 + 1.34111i) q^{77} +(1.28912 - 6.28361i) q^{78} -8.67104i q^{79} +(-4.73394 - 8.19943i) q^{81} +(-9.72634 + 2.60617i) q^{82} +8.94673i q^{83} +(0.356289 + 1.32969i) q^{84} +(-0.142461 + 0.142461i) q^{86} +(0.309275 + 1.15423i) q^{87} +(-2.36760 - 0.634396i) q^{88} +(-3.34657 + 12.4896i) q^{89} +(2.32897 - 1.53604i) q^{91} +(-0.252795 + 0.252795i) q^{92} +(4.40092 - 2.54087i) q^{93} +(8.47787 - 4.89470i) q^{94} +(-1.25798 - 1.25798i) q^{96} +(-5.61108 + 9.71868i) q^{97} +(3.20063 - 5.54366i) q^{98} +(-0.286051 - 0.286051i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 8 q^{4} + 12 q^{7} - 16 q^{8} - 24 q^{9} - 4 q^{11} + 8 q^{13} - 8 q^{16} - 8 q^{17} + 16 q^{19} - 4 q^{21} + 4 q^{22} - 4 q^{23} + 4 q^{26} + 36 q^{27} - 12 q^{28} + 36 q^{29} - 8 q^{31}+ \cdots - 36 q^{99}+O(q^{100}) \) 16 * q + 8 * q^2 - 8 * q^4 + 12 * q^7 - 16 * q^8 - 24 * q^9 - 4 * q^11 + 8 * q^13 - 8 * q^16 - 8 * q^17 + 16 * q^19 - 4 * q^21 + 4 * q^22 - 4 * q^23 + 4 * q^26 + 36 * q^27 - 12 * q^28 + 36 * q^29 - 8 * q^31 + 8 * q^32 - 16 * q^34 + 24 * q^36 - 36 * q^37 - 4 * q^38 + 32 * q^41 - 8 * q^42 - 36 * q^43 + 8 * q^44 + 4 * q^46 + 16 * q^49 - 4 * q^52 + 44 * q^53 + 36 * q^54 - 12 * q^56 - 48 * q^57 + 36 * q^58 - 24 * q^59 - 20 * q^61 + 8 * q^62 - 36 * q^63 + 16 * q^64 - 12 * q^67 - 8 * q^68 + 24 * q^69 + 16 * q^71 + 24 * q^72 - 36 * q^74 - 20 * q^76 + 16 * q^77 + 60 * q^78 + 16 * q^81 + 16 * q^82 - 4 * q^84 - 36 * q^86 + 12 * q^87 + 4 * q^88 - 28 * q^89 - 44 * q^91 + 8 * q^92 - 24 * q^93 + 24 * q^94 - 8 * q^97 - 16 * q^98 - 36 * q^99

Introduction

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