LMFDB - Embedded newform 1053.2.e.g.703.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1053,2,Mod(352,1053)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1053, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1053.352"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1053 = 3^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1053.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-1,0,1,-3,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$8.40824733284$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 351)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			703.1
Root			$0.809017 - 1.40126i$ of defining polynomial
Character	$\chi$	$=$	1053.703
Dual form			1053.2.e.g.352.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(-1.11803 + 1.93649i) q^{7} -2.23607 q^{8} +4.23607 q^{10} +(0.427051 - 0.739674i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.80902 - 3.13331i) q^{14} +(2.42705 - 4.20378i) q^{16} +4.61803 q^{17} -4.09017 q^{19} +(-0.809017 + 1.40126i) q^{20} +(0.690983 + 1.19682i) q^{22} +(-3.42705 - 5.93583i) q^{23} +(-0.927051 + 1.60570i) q^{25} -1.61803 q^{26} +1.38197 q^{28} +(2.35410 - 4.07742i) q^{29} +(4.23607 + 7.33708i) q^{31} +(1.69098 + 2.92887i) q^{32} +(-3.73607 + 6.47106i) q^{34} +5.85410 q^{35} +6.23607 q^{37} +(3.30902 - 5.73139i) q^{38} +(2.92705 + 5.06980i) q^{40} +(0.118034 + 0.204441i) q^{41} +(5.66312 - 9.80881i) q^{43} -0.527864 q^{44} +11.0902 q^{46} +(-0.545085 + 0.944115i) q^{47} +(1.00000 + 1.73205i) q^{49} +(-1.50000 - 2.59808i) q^{50} +(0.309017 - 0.535233i) q^{52} +2.14590 q^{53} -2.23607 q^{55} +(2.50000 - 4.33013i) q^{56} +(3.80902 + 6.59741i) q^{58} +(3.11803 + 5.40059i) q^{59} +(7.59017 - 13.1466i) q^{61} -13.7082 q^{62} +4.23607 q^{64} +(1.30902 - 2.26728i) q^{65} +(-2.54508 - 4.40822i) q^{67} +(-1.42705 - 2.47172i) q^{68} +(-4.73607 + 8.20311i) q^{70} -0.291796 q^{71} +3.38197 q^{73} +(-5.04508 + 8.73834i) q^{74} +(1.26393 + 2.18919i) q^{76} +(0.954915 + 1.65396i) q^{77} +(-1.66312 + 2.88061i) q^{79} -12.7082 q^{80} -0.381966 q^{82} +(6.97214 - 12.0761i) q^{83} +(-6.04508 - 10.4704i) q^{85} +(9.16312 + 15.8710i) q^{86} +(-0.954915 + 1.65396i) q^{88} +17.2361 q^{89} -2.23607 q^{91} +(-2.11803 + 3.66854i) q^{92} +(-0.881966 - 1.52761i) q^{94} +(5.35410 + 9.27358i) q^{95} +(-1.23607 + 2.14093i) q^{97} -3.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} + q^{4} - 3 q^{5} + 8 q^{10} - 5 q^{11} + 2 q^{13} - 5 q^{14} + 3 q^{16} + 14 q^{17} + 6 q^{19} - q^{20} + 5 q^{22} - 7 q^{23} + 3 q^{25} - 2 q^{26} + 10 q^{28} - 4 q^{29} + 8 q^{31} + 9 q^{32}+ \cdots - 4 q^{98}+O(q^{100}) $ 4 * q - q^2 + q^4 - 3 * q^5 + 8 * q^10 - 5 * q^11 + 2 * q^13 - 5 * q^14 + 3 * q^16 + 14 * q^17 + 6 * q^19 - q^20 + 5 * q^22 - 7 * q^23 + 3 * q^25 - 2 * q^26 + 10 * q^28 - 4 * q^29 + 8 * q^31 + 9 * q^32 - 6 * q^34 + 10 * q^35 + 16 * q^37 + 11 * q^38 + 5 * q^40 - 4 * q^41 + 7 * q^43 - 20 * q^44 + 22 * q^46 + 9 * q^47 + 4 * q^49 - 6 * q^50 - q^52 + 22 * q^53 + 10 * q^56 + 13 * q^58 + 8 * q^59 + 8 * q^61 - 28 * q^62 + 8 * q^64 + 3 * q^65 + q^67 + q^68 - 10 * q^70 - 28 * q^71 + 18 * q^73 - 9 * q^74 + 14 * q^76 + 15 * q^77 + 9 * q^79 - 24 * q^80 - 6 * q^82 + 10 * q^83 - 13 * q^85 + 21 * q^86 - 15 * q^88 + 60 * q^89 - 4 * q^92 - 8 * q^94 + 8 * q^95 + 4 * q^97 - 4 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1053\mathbb{Z}\right)^\times$.

$n$	$326$	$730$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	0.424293	+	0.905525i	$0.360523\pi$
$2$	−0.809017	+	1.40126i	−0.572061	+	0.990839i	−0.996354	+	0.0853143i	$0.972811\pi$
$3$		0			0
$3$		0			0
$4$	−0.309017	−	0.535233i	−0.154508	−	0.267617i
$5$	−1.30902	−	2.26728i	−0.585410	−	1.01396i	−0.994824	−	0.101611i	$-0.967600\pi$
$5$	−1.30902	−	2.26728i	−0.585410	−	1.01396i	0.409414	−	0.912349i	$-0.365733\pi$
$6$		0			0
$7$	−1.11803	+	1.93649i	−0.422577	+	0.731925i	−0.996191	−	0.0872010i	$-0.972208\pi$
$7$	−1.11803	+	1.93649i	−0.422577	+	0.731925i	0.573614	+	0.819126i	$0.305541\pi$
$8$	−2.23607			−0.790569
$9$		0			0
$10$	4.23607			1.33956
$11$	0.427051	−	0.739674i	0.128761	−	0.223020i	−0.794436	−	0.607348i	$-0.792233\pi$
$11$	0.427051	−	0.739674i	0.128761	−	0.223020i	0.923197	+	0.384328i	$0.125567\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−1.80902	−	3.13331i	−0.483480	−	0.837412i
$15$		0			0
$16$	2.42705	−	4.20378i	0.606763	−	1.05094i
$17$	4.61803			1.12004			0.560019	−	0.828480i	$-0.310794\pi$
$17$	4.61803			1.12004			0.560019	+	0.828480i	$0.310794\pi$
$18$		0			0
$19$	−4.09017			−0.938349			−0.469175	−	0.883105i	$-0.655449\pi$
$19$	−4.09017			−0.938349			−0.469175	+	0.883105i	$0.655449\pi$
$20$	−0.809017	+	1.40126i	−0.180902	+	0.313331i
$21$		0			0
$22$	0.690983	+	1.19682i	0.147318	+	0.255162i
$23$	−3.42705	−	5.93583i	−0.714590	−	1.23771i	−0.963118	−	0.269081i	$-0.913280\pi$
$23$	−3.42705	−	5.93583i	−0.714590	−	1.23771i	0.248528	−	0.968625i	$-0.420053\pi$
$24$		0			0
$25$	−0.927051	+	1.60570i	−0.185410	+	0.321140i
$26$	−1.61803			−0.317323
$27$		0			0
$28$	1.38197			0.261167
$29$	2.35410	−	4.07742i	0.437146	−	0.757159i	−0.560322	−	0.828275i	$-0.689323\pi$
$29$	2.35410	−	4.07742i	0.437146	−	0.757159i	0.997468	+	0.0711160i	$0.0226561\pi$
$30$		0			0
$31$	4.23607	+	7.33708i	0.760820	+	1.31778i	0.942428	+	0.334408i	$0.108536\pi$
$31$	4.23607	+	7.33708i	0.760820	+	1.31778i	−0.181608	+	0.983371i	$0.558130\pi$
$32$	1.69098	+	2.92887i	0.298926	+	0.517756i
$33$		0			0
$34$	−3.73607	+	6.47106i	−0.640730	+	1.10978i
$35$	5.85410			0.989524
$36$		0			0
$37$	6.23607			1.02520			0.512602	−	0.858627i	$-0.328682\pi$
$37$	6.23607			1.02520			0.512602	+	0.858627i	$0.328682\pi$
$38$	3.30902	−	5.73139i	0.536793	−	0.929754i
$39$		0			0
$40$	2.92705	+	5.06980i	0.462807	+	0.801606i
$41$	0.118034	+	0.204441i	0.0184338	+	0.0319283i	0.875095	−	0.483951i	$-0.160799\pi$
$41$	0.118034	+	0.204441i	0.0184338	+	0.0319283i	−0.856661	+	0.515879i	$0.827465\pi$
$42$		0			0
$43$	5.66312	−	9.80881i	0.863618	−	1.49583i	−0.00479580	−	0.999989i	$-0.501527\pi$
$43$	5.66312	−	9.80881i	0.863618	−	1.49583i	0.868413	−	0.495841i	$-0.165140\pi$
$44$	−0.527864			−0.0795785
$45$		0			0
$46$	11.0902			1.63516
$47$	−0.545085	+	0.944115i	−0.0795088	+	0.137713i	−0.903038	−	0.429560i	$-0.858669\pi$
$47$	−0.545085	+	0.944115i	−0.0795088	+	0.137713i	0.823529	+	0.567274i	$0.192002\pi$
$48$		0			0
$49$	1.00000	+	1.73205i	0.142857	+	0.247436i
$50$	−1.50000	−	2.59808i	−0.212132	−	0.367423i
$51$		0			0
$52$	0.309017	−	0.535233i	0.0428529	−	0.0742235i
$53$	2.14590			0.294762			0.147381	−	0.989080i	$-0.452916\pi$
$53$	2.14590			0.294762			0.147381	+	0.989080i	$0.452916\pi$
$54$		0			0
$55$	−2.23607			−0.301511
$56$	2.50000	−	4.33013i	0.334077	−	0.578638i
$57$		0			0
$58$	3.80902	+	6.59741i	0.500148	+	0.866282i
$59$	3.11803	+	5.40059i	0.405933	+	0.703097i	0.994430	−	0.105403i	$-0.0336131\pi$
$59$	3.11803	+	5.40059i	0.405933	+	0.703097i	−0.588496	+	0.808500i	$0.700280\pi$
$60$		0			0
$61$	7.59017	−	13.1466i	0.971822	−	1.68324i	0.281774	−	0.959481i	$-0.409077\pi$
$61$	7.59017	−	13.1466i	0.971822	−	1.68324i	0.690048	−	0.723764i	$-0.257589\pi$
$62$	−13.7082			−1.74094
$63$		0			0
$64$	4.23607			0.529508
$65$	1.30902	−	2.26728i	0.162364	−	0.281222i
$66$		0			0
$67$	−2.54508	−	4.40822i	−0.310932	−	0.538549i	0.667633	−	0.744491i	$-0.267308\pi$
$67$	−2.54508	−	4.40822i	−0.310932	−	0.538549i	−0.978564	+	0.205941i	$0.933974\pi$
$68$	−1.42705	−	2.47172i	−0.173055	−	0.299741i
$69$		0			0
$70$	−4.73607	+	8.20311i	−0.566068	+	0.980459i
$71$	−0.291796			−0.0346298			−0.0173149	−	0.999850i	$-0.505512\pi$
$71$	−0.291796			−0.0346298			−0.0173149	+	0.999850i	$0.505512\pi$
$72$		0			0
$73$	3.38197			0.395829			0.197915	−	0.980219i	$-0.436583\pi$
$73$	3.38197			0.395829			0.197915	+	0.980219i	$0.436583\pi$
$74$	−5.04508	+	8.73834i	−0.586479	+	1.01581i
$75$		0			0
$76$	1.26393	+	2.18919i	0.144983	+	0.251118i
$77$	0.954915	+	1.65396i	0.108823	+	0.188486i
$78$		0			0
$79$	−1.66312	+	2.88061i	−0.187116	+	0.324094i	−0.944287	−	0.329122i	$-0.893247\pi$
$79$	−1.66312	+	2.88061i	−0.187116	+	0.324094i	0.757172	+	0.653216i	$0.226581\pi$
$80$	−12.7082			−1.42082
$81$		0			0
$82$	−0.381966			−0.0421811
$83$	6.97214	−	12.0761i	0.765291	−	1.32552i	−0.174801	−	0.984604i	$-0.555928\pi$
$83$	6.97214	−	12.0761i	0.765291	−	1.32552i	0.940092	−	0.340920i	$-0.110738\pi$
$84$		0			0
$85$	−6.04508	−	10.4704i	−0.655682	−	1.13567i
$86$	9.16312	+	15.8710i	0.988085	+	1.71141i
$87$		0			0
$88$	−0.954915	+	1.65396i	−0.101794	+	0.176313i
$89$	17.2361			1.82702			0.913510	−	0.406817i	$-0.133361\pi$
$89$	17.2361			1.82702			0.913510	+	0.406817i	$0.133361\pi$
$90$		0			0
$91$	−2.23607			−0.234404
$92$	−2.11803	+	3.66854i	−0.220820	+	0.382472i
$93$		0			0
$94$	−0.881966	−	1.52761i	−0.0909678	−	0.157561i
$95$	5.35410	+	9.27358i	0.549319	+	0.951449i
$96$		0			0
$97$	−1.23607	+	2.14093i	−0.125504	+	0.217379i	−0.921930	−	0.387357i	$-0.873388\pi$
$97$	−1.23607	+	2.14093i	−0.125504	+	0.217379i	0.796426	+	0.604736i	$0.206721\pi$
$98$	−3.23607			−0.326892
$99$		0			0
$100$	1.14590			0.114590
$101$	−9.59017	+	16.6107i	−0.954258	+	1.65282i	−0.218200	+	0.975904i	$0.570018\pi$
$101$	−9.59017	+	16.6107i	−0.954258	+	1.65282i	−0.736058	+	0.676918i	$0.763315\pi$
$102$		0			0
$103$	−9.39919	−	16.2799i	−0.926129	−	1.60410i	−0.789735	−	0.613449i	$-0.789782\pi$
$103$	−9.39919	−	16.2799i	−0.926129	−	1.60410i	−0.136395	−	0.990655i	$-0.543552\pi$
$104$	−1.11803	−	1.93649i	−0.109632	−	0.189889i
$105$		0			0
$106$	−1.73607	+	3.00696i	−0.168622	+	0.292062i
$107$	−6.38197			−0.616968			−0.308484	−	0.951230i	$-0.599822\pi$
$107$	−6.38197			−0.616968			−0.308484	+	0.951230i	$0.599822\pi$
$108$		0			0
$109$	13.7984			1.32164			0.660822	−	0.750542i	$-0.270208\pi$
$109$	13.7984			1.32164			0.660822	+	0.750542i	$0.270208\pi$
$110$	1.80902	−	3.13331i	0.172483	−	0.298749i
$111$		0			0
$112$	5.42705	+	9.39993i	0.512808	+	0.888210i
$113$	−0.0278640	−	0.0482619i	−0.00262123	−	0.00454010i	0.864712	−	0.502268i	$-0.167501\pi$
$113$	−0.0278640	−	0.0482619i	−0.00262123	−	0.00454010i	−0.867333	+	0.497728i	$0.834168\pi$
$114$		0			0
$115$	−8.97214	+	15.5402i	−0.836656	+	1.44913i
$116$	−2.90983			−0.270171
$117$		0			0
$118$	−10.0902			−0.928875
$119$	−5.16312	+	8.94278i	−0.473302	+	0.819784i
$120$		0			0
$121$	5.13525	+	8.89452i	0.466841	+	0.808593i
$122$	12.2812	+	21.2716i	1.11188	+	1.92584i
$123$		0			0
$124$	2.61803	−	4.53457i	0.235106	−	0.407216i
$125$	−8.23607			−0.736656
$126$		0			0
$127$	1.47214			0.130631			0.0653155	−	0.997865i	$-0.479195\pi$
$127$	1.47214			0.130631			0.0653155	+	0.997865i	$0.479195\pi$
$128$	−6.80902	+	11.7936i	−0.601838	+	1.04241i
$129$		0			0
$130$	2.11803	+	3.66854i	0.185764	+	0.321752i
$131$	−6.50000	−	11.2583i	−0.567908	−	0.983645i	−0.996773	−	0.0802763i	$-0.974420\pi$
$131$	−6.50000	−	11.2583i	−0.567908	−	0.983645i	0.428865	−	0.903369i	$-0.358914\pi$
$132$		0			0
$133$	4.57295	−	7.92058i	0.396525	−	0.686801i
$134$	8.23607			0.711488
$135$		0			0
$136$	−10.3262			−0.885468
$137$	−6.09017	+	10.5485i	−0.520318	+	0.901218i	0.479403	+	0.877595i	$0.340853\pi$
$137$	−6.09017	+	10.5485i	−0.520318	+	0.901218i	−0.999721	+	0.0236227i	$0.992480\pi$
$138$		0			0
$139$	2.11803	+	3.66854i	0.179649	+	0.311162i	0.941760	−	0.336285i	$-0.109170\pi$
$139$	2.11803	+	3.66854i	0.179649	+	0.311162i	−0.762111	+	0.647446i	$0.775837\pi$
$140$	−1.80902	−	3.13331i	−0.152890	−	0.264813i
$141$		0			0
$142$	0.236068	−	0.408882i	0.0198104	−	0.0343126i
$143$	0.854102			0.0714236
$144$		0			0
$145$	−12.3262			−1.02364
$146$	−2.73607	+	4.73901i	−0.226439	+	0.392203i
$147$		0			0
$148$	−1.92705	−	3.33775i	−0.158403	−	0.274361i
$149$	2.80902	+	4.86536i	0.230124	+	0.398586i	0.957844	−	0.287288i	$-0.0927536\pi$
$149$	2.80902	+	4.86536i	0.230124	+	0.398586i	−0.727721	+	0.685874i	$0.759420\pi$
$150$		0			0
$151$	6.35410	−	11.0056i	0.517089	−	0.895625i	−0.482714	−	0.875778i	$-0.660349\pi$
$151$	6.35410	−	11.0056i	0.517089	−	0.895625i	0.999803	−	0.0198470i	$-0.00631790\pi$
$152$	9.14590			0.741830
$153$		0			0
$154$	−3.09017			−0.249013
$155$	11.0902	−	19.2087i	0.890784	−	1.54288i
$156$		0			0
$157$	−7.57295	−	13.1167i	−0.604387	−	1.04683i	−0.992148	−	0.125069i	$-0.960085\pi$
$157$	−7.57295	−	13.1167i	−0.604387	−	1.04683i	0.387761	−	0.921760i	$-0.373249\pi$
$158$	−2.69098	−	4.66092i	−0.214083	−	0.370803i
$159$		0			0
$160$	4.42705	−	7.66788i	0.349989	−	0.606199i
$161$	15.3262			1.20788
$162$		0			0
$163$	−10.6180			−0.831669			−0.415834	−	0.909440i	$-0.636510\pi$
$163$	−10.6180			−0.831669			−0.415834	+	0.909440i	$0.636510\pi$
$164$	0.0729490	−	0.126351i	0.00569636	−	0.00986639i
$165$		0			0
$166$	11.2812	+	19.5395i	0.875587	+	1.51656i
$167$	−5.11803	−	8.86469i	−0.396045	−	0.685971i	0.597189	−	0.802101i	$-0.296284\pi$
$167$	−5.11803	−	8.86469i	−0.396045	−	0.685971i	−0.993234	+	0.116130i	$0.962951\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	19.5623			1.50036
$171$		0			0
$172$	−7.00000			−0.533745
$173$	−6.19098	+	10.7231i	−0.470692	+	0.815262i	−0.999438	−	0.0335179i	$-0.989329\pi$
$173$	−6.19098	+	10.7231i	−0.470692	+	0.815262i	0.528746	+	0.848780i	$0.322662\pi$
$174$		0			0
$175$	−2.07295	−	3.59045i	−0.156700	−	0.271413i
$176$	−2.07295	−	3.59045i	−0.156254	−	0.270641i
$177$		0			0
$178$	−13.9443	+	24.1522i	−1.04517	+	1.81028i
$179$	−4.79837			−0.358647			−0.179324	−	0.983790i	$-0.557391\pi$
$179$	−4.79837			−0.358647			−0.179324	+	0.983790i	$0.557391\pi$
$180$		0			0
$181$	13.5623			1.00808			0.504039	−	0.863681i	$-0.331847\pi$
$181$	13.5623			1.00808			0.504039	+	0.863681i	$0.331847\pi$
$182$	1.80902	−	3.13331i	0.134093	−	0.232256i
$183$		0			0
$184$	7.66312	+	13.2729i	0.564933	+	0.978492i
$185$	−8.16312	−	14.1389i	−0.600164	−	1.03952i
$186$		0			0
$187$	1.97214	−	3.41584i	0.144217	−	0.249791i
$188$	0.673762			0.0491391
$189$		0			0
$190$	−17.3262			−1.25698
$191$	10.8713	−	18.8297i	0.786621	−	1.36247i	−0.141404	−	0.989952i	$-0.545162\pi$
$191$	10.8713	−	18.8297i	0.786621	−	1.36247i	0.928026	−	0.372516i	$-0.121505\pi$
$192$		0			0
$193$	−3.89919	−	6.75359i	−0.280670	−	0.486134i	0.690880	−	0.722969i	$-0.257223\pi$
$193$	−3.89919	−	6.75359i	−0.280670	−	0.486134i	−0.971550	+	0.236835i	$0.923890\pi$
$194$	−2.00000	−	3.46410i	−0.143592	−	0.248708i
$195$		0			0
$196$	0.618034	−	1.07047i	0.0441453	−	0.0764619i
$197$	−11.7082			−0.834175			−0.417087	−	0.908866i	$-0.636949\pi$
$197$	−11.7082			−0.834175			−0.417087	+	0.908866i	$0.636949\pi$
$198$		0			0
$199$	−7.67376			−0.543979			−0.271989	−	0.962300i	$-0.587682\pi$
$199$	−7.67376			−0.543979			−0.271989	+	0.962300i	$0.587682\pi$
$200$	2.07295	−	3.59045i	0.146580	−	0.253883i
$201$		0			0
$202$	−15.5172	−	26.8766i	−1.09179	−	1.89103i
$203$	5.26393	+	9.11740i	0.369456	+	0.639916i
$204$		0			0
$205$	0.309017	−	0.535233i	0.0215827	−	0.0373823i
$206$	30.4164			2.11921
$207$		0			0
$208$	4.85410			0.336571
$209$	−1.74671	+	3.02539i	−0.120823	+	0.209271i
$210$		0			0
$211$	−9.57295	−	16.5808i	−0.659029	−	1.14147i	−0.980867	−	0.194677i	$-0.937634\pi$
$211$	−9.57295	−	16.5808i	−0.659029	−	1.14147i	0.321838	−	0.946795i	$-0.395699\pi$
$212$	−0.663119	−	1.14856i	−0.0455432	−	0.0788831i
$213$		0			0
$214$	5.16312	−	8.94278i	0.352944	−	0.611316i
$215$	−29.6525			−2.02228
$216$		0			0
$217$	−18.9443			−1.28602
$218$	−11.1631	+	19.3351i	−0.756062	+	1.30954i
$219$		0			0
$220$	0.690983	+	1.19682i	0.0465861	+	0.0806894i
$221$	2.30902	+	3.99933i	0.155321	+	0.269024i
$222$		0			0
$223$	−7.57295	+	13.1167i	−0.507122	+	0.878361i	0.492844	+	0.870118i	$0.335957\pi$
$223$	−7.57295	+	13.1167i	−0.507122	+	0.878361i	−0.999966	+	0.00824360i	$0.997376\pi$
$224$	−7.56231			−0.505278
$225$		0			0
$226$	0.0901699			0.00599802
$227$	10.6910	−	18.5173i	0.709585	−	1.22904i	−0.255426	−	0.966829i	$-0.582216\pi$
$227$	10.6910	−	18.5173i	0.709585	−	1.22904i	0.965011	−	0.262209i	$-0.0844511\pi$
$228$		0			0
$229$	−4.80902	−	8.32946i	−0.317789	−	0.550426i	0.662238	−	0.749294i	$-0.269607\pi$
$229$	−4.80902	−	8.32946i	−0.317789	−	0.550426i	−0.980026	+	0.198868i	$0.936274\pi$
$230$	−14.5172	−	25.1446i	−0.957237	−	1.65798i
$231$		0			0
$232$	−5.26393	+	9.11740i	−0.345594	+	0.598586i
$233$	2.70820			0.177420			0.0887102	−	0.996057i	$-0.471726\pi$
$233$	2.70820			0.177420			0.0887102	+	0.996057i	$0.471726\pi$
$234$		0			0
$235$	2.85410			0.186181
$236$	1.92705	−	3.33775i	0.125440	−	0.217269i
$237$		0			0
$238$	−8.35410	−	14.4697i	−0.541516	−	0.937933i
$239$	−9.20820	−	15.9491i	−0.595629	−	1.03166i	−0.993458	−	0.114200i	$-0.963569\pi$
$239$	−9.20820	−	15.9491i	−0.595629	−	1.03166i	0.397829	−	0.917460i	$-0.369764\pi$
$240$		0			0
$241$	14.8090	−	25.6500i	0.953933	−	1.65226i	0.217141	−	0.976140i	$-0.430327\pi$
$241$	14.8090	−	25.6500i	0.953933	−	1.65226i	0.736792	−	0.676119i	$-0.236340\pi$
$242$	−16.6180			−1.06825
$243$		0			0
$244$	−9.38197			−0.600619
$245$	2.61803	−	4.53457i	0.167260	−	0.289703i
$246$		0			0
$247$	−2.04508	−	3.54219i	−0.130126	−	0.225384i
$248$	−9.47214	−	16.4062i	−0.601481	−	1.04180i
$249$		0			0
$250$	6.66312	−	11.5409i	0.421413	−	0.729908i
$251$	21.2705			1.34258			0.671291	−	0.741194i	$-0.265740\pi$
$251$	21.2705			1.34258			0.671291	+	0.741194i	$0.265740\pi$
$252$		0			0
$253$	−5.85410			−0.368044
$254$	−1.19098	+	2.06284i	−0.0747289	+	0.129434i
$255$		0			0
$256$	−6.78115	−	11.7453i	−0.423822	−	0.734081i
$257$	2.89919	+	5.02154i	0.180846	+	0.313235i	0.942169	−	0.335138i	$-0.108783\pi$
$257$	2.89919	+	5.02154i	0.180846	+	0.313235i	−0.761323	+	0.648373i	$0.775450\pi$
$258$		0			0
$259$	−6.97214	+	12.0761i	−0.433227	+	0.750372i
$260$	−1.61803			−0.100346
$261$		0			0
$262$	21.0344			1.29951
$263$	−1.63525	+	2.83234i	−0.100834	+	0.174650i	−0.912029	−	0.410127i	$-0.865484\pi$
$263$	−1.63525	+	2.83234i	−0.100834	+	0.174650i	0.811194	+	0.584777i	$0.198818\pi$
$264$		0			0
$265$	−2.80902	−	4.86536i	−0.172557	−	0.298877i
$266$	7.39919	+	12.8158i	0.453673	+	0.785785i
$267$		0			0
$268$	−1.57295	+	2.72443i	−0.0960832	+	0.166421i
$269$	18.2705			1.11397			0.556986	−	0.830522i	$-0.311958\pi$
$269$	18.2705			1.11397			0.556986	+	0.830522i	$0.311958\pi$
$270$		0			0
$271$	−10.2361			−0.621797			−0.310898	−	0.950443i	$-0.600630\pi$
$271$	−10.2361			−0.621797			−0.310898	+	0.950443i	$0.600630\pi$
$272$	11.2082	−	19.4132i	0.679597	−	1.17710i
$273$		0			0
$274$	−9.85410	−	17.0678i	−0.595308	−	1.03110i
$275$	0.791796	+	1.37143i	0.0477471	+	0.0827004i
$276$		0			0
$277$	−13.5623	+	23.4906i	−0.814880	+	1.41141i	0.0945341	+	0.995522i	$0.469864\pi$
$277$	−13.5623	+	23.4906i	−0.814880	+	1.41141i	−0.909414	+	0.415892i	$0.863469\pi$
$278$	−6.85410			−0.411082
$279$		0			0
$280$	−13.0902			−0.782287
$281$	−8.94427	+	15.4919i	−0.533571	+	0.924171i	0.465661	+	0.884963i	$0.345817\pi$
$281$	−8.94427	+	15.4919i	−0.533571	+	0.924171i	−0.999231	+	0.0392078i	$0.987517\pi$
$282$		0			0
$283$	2.07295	+	3.59045i	0.123224	+	0.213430i	0.921037	−	0.389474i	$-0.127343\pi$
$283$	2.07295	+	3.59045i	0.123224	+	0.213430i	−0.797813	+	0.602905i	$0.794010\pi$
$284$	0.0901699	+	0.156179i	0.00535060	+	0.00926751i
$285$		0			0
$286$	−0.690983	+	1.19682i	−0.0408587	+	0.0707693i
$287$	−0.527864			−0.0311588
$288$		0			0
$289$	4.32624			0.254485
$290$	9.97214	−	17.2722i	0.585584	−	1.01426i
$291$		0			0
$292$	−1.04508	−	1.81014i	−0.0611590	−	0.105930i
$293$	−2.59017	−	4.48631i	−0.151319	−	0.262093i	0.780393	−	0.625289i	$-0.215019\pi$
$293$	−2.59017	−	4.48631i	−0.151319	−	0.262093i	−0.931713	+	0.363196i	$0.881686\pi$
$294$		0			0
$295$	8.16312	−	14.1389i	0.475275	−	0.823201i
$296$	−13.9443			−0.810494
$297$		0			0
$298$	−9.09017			−0.526579
$299$	3.42705	−	5.93583i	0.198191	−	0.343278i
$300$		0			0
$301$	12.6631	+	21.9332i	0.729890	+	1.26421i
$302$	10.2812	+	17.8075i	0.591614	+	1.02471i
$303$		0			0
$304$	−9.92705	+	17.1942i	−0.569355	+	0.986153i
$305$	−39.7426			−2.27566
$306$		0			0
$307$	17.7426			1.01263			0.506313	−	0.862350i	$-0.331008\pi$
$307$	17.7426			1.01263			0.506313	+	0.862350i	$0.331008\pi$
$308$	0.590170	−	1.02220i	0.0336281	−	0.0582455i
$309$		0			0
$310$	17.9443	+	31.0804i	1.01917	+	1.76525i
$311$	15.1631	+	26.2633i	0.859822	+	1.48925i	0.872099	+	0.489330i	$0.162759\pi$
$311$	15.1631	+	26.2633i	0.859822	+	1.48925i	−0.0122771	+	0.999925i	$0.503908\pi$
$312$		0			0
$313$	13.8541	−	23.9960i	0.783080	−	1.35633i	−0.147059	−	0.989128i	$-0.546981\pi$
$313$	13.8541	−	23.9960i	0.783080	−	1.35633i	0.930139	−	0.367207i	$-0.119686\pi$
$314$	24.5066			1.38299
$315$		0			0
$316$	2.05573			0.115644
$317$	14.7812	−	25.6017i	0.830192	−	1.43794i	−0.0676933	−	0.997706i	$-0.521564\pi$
$317$	14.7812	−	25.6017i	0.830192	−	1.43794i	0.897886	−	0.440229i	$-0.145103\pi$
$318$		0			0
$319$	−2.01064	−	3.48254i	−0.112574	−	0.194985i
$320$	−5.54508	−	9.60437i	−0.309980	−	0.536901i
$321$		0			0
$322$	−12.3992	+	21.4760i	−0.690980	+	1.19681i
$323$	−18.8885			−1.05099
$324$		0			0
$325$	−1.85410			−0.102847
$326$	8.59017	−	14.8786i	0.475766	−	0.824050i
$327$		0			0
$328$	−0.263932	−	0.457144i	−0.0145732	−	0.0252415i
$329$	−1.21885	−	2.11111i	−0.0671972	−	0.116389i
$330$		0			0
$331$	−1.88197	+	3.25966i	−0.103442	+	0.179167i	−0.913101	−	0.407734i	$-0.866319\pi$
$331$	−1.88197	+	3.25966i	−0.103442	+	0.179167i	0.809658	+	0.586901i	$0.199652\pi$
$332$	−8.61803			−0.472976
$333$		0			0
$334$	16.5623			0.906249
$335$	−6.66312	+	11.5409i	−0.364045	+	0.630545i
$336$		0			0
$337$	10.2984	+	17.8373i	0.560988	+	0.971660i	0.997411	+	0.0719181i	$0.0229120\pi$
$337$	10.2984	+	17.8373i	0.560988	+	0.971660i	−0.436422	+	0.899742i	$0.643755\pi$
$338$	−0.809017	−	1.40126i	−0.0440047	−	0.0762184i
$339$		0			0
$340$	−3.73607	+	6.47106i	−0.202617	+	0.350942i
$341$	7.23607			0.391855
$342$		0			0
$343$	−20.1246			−1.08663
$344$	−12.6631	+	21.9332i	−0.682750	+	1.18256i
$345$		0			0
$346$	−10.0172	−	17.3503i	−0.538529	−	0.932760i
$347$	4.02786	+	6.97647i	0.216227	+	0.374516i	0.953651	−	0.300913i	$-0.0972915\pi$
$347$	4.02786	+	6.97647i	0.216227	+	0.374516i	−0.737424	+	0.675430i	$0.763958\pi$
$348$		0			0
$349$	1.54508	−	2.67617i	0.0827065	−	0.143252i	−0.821705	−	0.569913i	$-0.806977\pi$
$349$	1.54508	−	2.67617i	0.0827065	−	0.143252i	0.904412	+	0.426661i	$0.140310\pi$
$350$	6.70820			0.358569
$351$		0			0
$352$	2.88854			0.153960
$353$	−2.35410	+	4.07742i	−0.125296	+	0.217019i	−0.921849	−	0.387550i	$-0.873321\pi$
$353$	−2.35410	+	4.07742i	−0.125296	+	0.217019i	0.796552	+	0.604569i	$0.206655\pi$
$354$		0			0
$355$	0.381966	+	0.661585i	0.0202727	+	0.0351133i
$356$	−5.32624	−	9.22531i	−0.282290	−	0.488941i
$357$		0			0
$358$	3.88197	−	6.72376i	0.205168	−	0.355362i
$359$	−34.4164			−1.81643			−0.908214	−	0.418505i	$-0.862554\pi$
$359$	−34.4164			−1.81643			−0.908214	+	0.418505i	$0.862554\pi$
$360$		0			0
$361$	−2.27051			−0.119501
$362$	−10.9721	+	19.0043i	−0.576683	+	0.998844i
$363$		0			0
$364$	0.690983	+	1.19682i	0.0362174	+	0.0627303i
$365$	−4.42705	−	7.66788i	−0.231722	−	0.401355i
$366$		0			0
$367$	−0.354102	+	0.613323i	−0.0184840	+	0.0320152i	−0.875119	−	0.483907i	$-0.839217\pi$
$367$	−0.354102	+	0.613323i	−0.0184840	+	0.0320152i	0.856635	+	0.515922i	$0.172551\pi$
$368$	−33.2705			−1.73435
$369$		0			0
$370$	26.4164			1.37332
$371$	−2.39919	+	4.15551i	−0.124560	+	0.215744i
$372$		0			0
$373$	1.92705	+	3.33775i	0.0997789	+	0.172822i	0.911593	−	0.411094i	$-0.134853\pi$
$373$	1.92705	+	3.33775i	0.0997789	+	0.172822i	−0.811814	+	0.583916i	$0.801520\pi$
$374$	3.19098	+	5.52694i	0.165002	+	0.285792i
$375$		0			0
$376$	1.21885	−	2.11111i	0.0628572	−	0.108872i
$377$	4.70820			0.242485
$378$		0			0
$379$	−14.7082			−0.755510			−0.377755	−	0.925906i	$-0.623304\pi$
$379$	−14.7082			−0.755510			−0.377755	+	0.925906i	$0.623304\pi$
$380$	3.30902	−	5.73139i	0.169749	−	0.294014i
$381$		0			0
$382$	17.5902	+	30.4671i	0.899991	+	1.55883i
$383$	−4.70820	−	8.15485i	−0.240578	−	0.416693i	0.720301	−	0.693662i	$-0.244004\pi$
$383$	−4.70820	−	8.15485i	−0.240578	−	0.416693i	−0.960879	+	0.276968i	$0.910670\pi$
$384$		0			0
$385$	2.50000	−	4.33013i	0.127412	−	0.220684i
$386$	12.6180			0.642241
$387$		0			0
$388$	1.52786			0.0775655
$389$	3.85410	−	6.67550i	0.195411	−	0.338461i	−0.751624	−	0.659591i	$-0.770729\pi$
$389$	3.85410	−	6.67550i	0.195411	−	0.338461i	0.947035	+	0.321130i	$0.104063\pi$
$390$		0			0
$391$	−15.8262	−	27.4118i	−0.800367	−	1.38628i
$392$	−2.23607	−	3.87298i	−0.112938	−	0.195615i
$393$		0			0
$394$	9.47214	−	16.4062i	0.477199	−	0.826533i
$395$	8.70820			0.438157
$396$		0			0
$397$	−12.1246			−0.608517			−0.304258	−	0.952590i	$-0.598409\pi$
$397$	−12.1246			−0.608517			−0.304258	+	0.952590i	$0.598409\pi$
$398$	6.20820	−	10.7529i	0.311189	−	0.538995i
$399$		0			0
$400$	4.50000	+	7.79423i	0.225000	+	0.389711i
$401$	2.61803	+	4.53457i	0.130738	+	0.226446i	0.923961	−	0.382486i	$-0.124932\pi$
$401$	2.61803	+	4.53457i	0.130738	+	0.226446i	−0.793223	+	0.608931i	$0.791599\pi$
$402$		0			0
$403$	−4.23607	+	7.33708i	−0.211014	+	0.365486i
$404$	11.8541			0.589764
$405$		0			0
$406$	−17.0344			−0.845405
$407$	2.66312	−	4.61266i	0.132006	−	0.228641i
$408$		0			0
$409$	−10.4164	−	18.0417i	−0.515058	−	0.892107i	−0.999847	−	0.0174759i	$-0.994437\pi$
$409$	−10.4164	−	18.0417i	−0.515058	−	0.892107i	0.484789	−	0.874631i	$-0.338896\pi$
$410$	0.500000	+	0.866025i	0.0246932	+	0.0427699i
$411$		0			0
$412$	−5.80902	+	10.0615i	−0.286190	+	0.495695i
$413$	−13.9443			−0.686153
$414$		0			0
$415$	−36.5066			−1.79204
$416$	−1.69098	+	2.92887i	−0.0829073	+	0.143600i
$417$		0			0
$418$	−2.82624	−	4.89519i	−0.138236	−	0.239431i
$419$	9.18034	+	15.9008i	0.448489	+	0.776806i	0.998288	−	0.0584914i	$-0.0186290\pi$
$419$	9.18034	+	15.9008i	0.448489	+	0.776806i	−0.549799	+	0.835297i	$0.685296\pi$
$420$		0			0
$421$	15.0902	−	26.1369i	0.735450	−	1.27384i	−0.219076	−	0.975708i	$-0.570304\pi$
$421$	15.0902	−	26.1369i	0.735450	−	1.27384i	0.954526	−	0.298129i	$-0.0963625\pi$
$422$	30.9787			1.50802
$423$		0			0
$424$	−4.79837			−0.233030
$425$	−4.28115	+	7.41517i	−0.207666	+	0.359689i
$426$		0			0
$427$	16.9721	+	29.3966i	0.821339	+	1.42260i
$428$	1.97214	+	3.41584i	0.0953268	+	0.165111i
$429$		0			0
$430$	23.9894	−	41.5508i	1.15687	−	2.00376i
$431$	−18.8885			−0.909829			−0.454915	−	0.890535i	$-0.650330\pi$
$431$	−18.8885			−0.909829			−0.454915	+	0.890535i	$0.650330\pi$
$432$		0			0
$433$	24.0344			1.15502			0.577511	−	0.816383i	$-0.304024\pi$
$433$	24.0344			1.15502			0.577511	+	0.816383i	$0.304024\pi$
$434$	15.3262	−	26.5458i	0.735683	−	1.27424i
$435$		0			0
$436$	−4.26393	−	7.38535i	−0.204205	−	0.353694i
$437$	14.0172	+	24.2785i	0.670535	+	1.16140i
$438$		0			0
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	0.0137020	+	0.999906i	$0.495638\pi$
$439$	−18.0000	+	31.1769i	−0.859093	+	1.48799i	−0.872795	+	0.488087i	$0.837695\pi$
$440$	5.00000			0.238366
$441$		0			0
$442$	−7.47214			−0.355413
$443$	−8.06231	+	13.9643i	−0.383052	+	0.663465i	−0.991497	−	0.130131i	$-0.958460\pi$
$443$	−8.06231	+	13.9643i	−0.383052	+	0.663465i	0.608445	+	0.793596i	$0.291794\pi$
$444$		0			0
$445$	−22.5623	−	39.0791i	−1.06956	−	1.85253i
$446$	−12.2533	−	21.2233i	−0.580210	−	1.00495i
$447$		0			0
$448$	−4.73607	+	8.20311i	−0.223758	+	0.387561i
$449$	31.4721			1.48526			0.742631	−	0.669701i	$-0.233578\pi$
$449$	31.4721			1.48526			0.742631	+	0.669701i	$0.233578\pi$
$450$		0			0
$451$	0.201626			0.00949420
$452$	−0.0172209	+	0.0298275i	−0.000810004	+	0.00140297i
$453$		0			0
$454$	17.2984	+	29.9617i	0.811853	+	1.40617i
$455$	2.92705	+	5.06980i	0.137222	+	0.237676i
$456$		0			0
$457$	0.590170	−	1.02220i	0.0276070	−	0.0478167i	−0.851892	−	0.523718i	$-0.824545\pi$
$457$	0.590170	−	1.02220i	0.0276070	−	0.0478167i	0.879499	+	0.475901i	$0.157878\pi$
$458$	15.5623			0.727179
$459$		0			0
$460$	11.0902			0.517082
$461$	−0.809017	+	1.40126i	−0.0376797	+	0.0652631i	−0.884250	−	0.467013i	$-0.845330\pi$
$461$	−0.809017	+	1.40126i	−0.0376797	+	0.0652631i	0.846571	+	0.532276i	$0.178663\pi$
$462$		0			0
$463$	15.2812	+	26.4677i	0.710175	+	1.23006i	0.964791	+	0.263018i	$0.0847177\pi$
$463$	15.2812	+	26.4677i	0.710175	+	1.23006i	−0.254616	+	0.967042i	$0.581949\pi$
$464$	−11.4271	−	19.7922i	−0.530488	−	0.918831i
$465$		0			0
$466$	−2.19098	+	3.79489i	−0.101495	+	0.175795i
$467$	30.1246			1.39400			0.697000	−	0.717071i	$-0.254518\pi$
$467$	30.1246			1.39400			0.697000	+	0.717071i	$0.254518\pi$
$468$		0			0
$469$	11.3820			0.525570
$470$	−2.30902	+	3.99933i	−0.106507	+	0.184476i
$471$		0			0
$472$	−6.97214	−	12.0761i	−0.320919	−	0.555847i
$473$	−4.83688	−	8.37772i	−0.222400	−	0.385208i
$474$		0			0
$475$	3.79180	−	6.56758i	0.173980	−	0.301341i
$476$	6.38197			0.292517
$477$		0			0
$478$	29.7984			1.36295
$479$	−7.89919	+	13.6818i	−0.360923	+	0.625137i	−0.988113	−	0.153729i	$-0.950872\pi$
$479$	−7.89919	+	13.6818i	−0.360923	+	0.625137i	0.627190	+	0.778866i	$0.284205\pi$
$480$		0			0
$481$	3.11803	+	5.40059i	0.142170	+	0.246246i
$482$	23.9615	+	41.5025i	1.09142	+	1.89039i
$483$		0			0
$484$	3.17376	−	5.49712i	0.144262	−	0.249869i
$485$	6.47214			0.293885
$486$		0			0
$487$	25.3050			1.14668			0.573338	−	0.819319i	$-0.305648\pi$
$487$	25.3050			1.14668			0.573338	+	0.819319i	$0.305648\pi$
$488$	−16.9721	+	29.3966i	−0.768292	+	1.33072i
$489$		0			0
$490$	4.23607	+	7.33708i	0.191366	+	0.331456i
$491$	9.60739	+	16.6405i	0.433575	+	0.750975i	0.997178	−	0.0750712i	$-0.0239184\pi$
$491$	9.60739	+	16.6405i	0.433575	+	0.750975i	−0.563603	+	0.826046i	$0.690585\pi$
$492$		0			0
$493$	10.8713	−	18.8297i	0.489620	−	0.848046i
$494$	6.61803			0.297759
$495$		0			0
$496$	41.1246			1.84655
$497$	0.326238	−	0.565061i	0.0146338	−	0.0253464i
$498$		0			0
$499$	12.1910	+	21.1154i	0.545743	+	0.945255i	0.998560	+	0.0536514i	$0.0170860\pi$
$499$	12.1910	+	21.1154i	0.545743	+	0.945255i	−0.452816	+	0.891604i	$0.649581\pi$
$500$	2.54508	+	4.40822i	0.113820	+	0.197141i
$501$		0			0
$502$	−17.2082	+	29.8055i	−0.768040	+	1.33028i
$503$	−4.23607			−0.188877			−0.0944385	−	0.995531i	$-0.530106\pi$
$503$	−4.23607			−0.188877			−0.0944385	+	0.995531i	$0.530106\pi$
$504$		0			0
$505$	50.2148			2.23453
$506$	4.73607	−	8.20311i	0.210544	−	0.364673i
$507$		0			0
$508$	−0.454915	−	0.787936i	−0.0201836	−	0.0349590i
$509$	−0.909830	−	1.57587i	−0.0403275	−	0.0698493i	0.845157	−	0.534518i	$-0.179507\pi$
$509$	−0.909830	−	1.57587i	−0.0403275	−	0.0698493i	−0.885485	+	0.464669i	$0.846173\pi$
$510$		0			0
$511$	−3.78115	+	6.54915i	−0.167268	+	0.289717i
$512$	−5.29180			−0.233867
$513$		0			0
$514$	−9.38197			−0.413821
$515$	−24.6074	+	42.6213i	−1.08433	+	1.87812i
$516$		0			0
$517$	0.465558	+	0.806370i	0.0204752	+	0.0354641i
$518$	−11.2812	−	19.5395i	−0.495665	−	0.858518i
$519$		0			0
$520$	−2.92705	+	5.06980i	−0.128360	+	0.222325i
$521$	34.2361			1.49991			0.749955	−	0.661489i	$-0.230075\pi$
$521$	34.2361			1.49991			0.749955	+	0.661489i	$0.230075\pi$
$522$		0			0
$523$	21.0344			0.919772			0.459886	−	0.887978i	$-0.347890\pi$
$523$	21.0344			0.919772			0.459886	+	0.887978i	$0.347890\pi$
$524$	−4.01722	+	6.95803i	−0.175493	+	0.303963i
$525$		0			0
$526$	−2.64590	−	4.58283i	−0.115367	−	0.199821i
$527$	19.5623	+	33.8829i	0.852147	+	1.47596i
$528$		0			0
$529$	−11.9894	+	20.7662i	−0.521276	+	0.902877i
$530$	9.09017			0.394852
$531$		0			0
$532$	−5.65248			−0.245066
$533$	−0.118034	+	0.204441i	−0.00511262	+	0.00885532i
$534$		0			0
$535$	8.35410	+	14.4697i	0.361179	+	0.625581i
$536$	5.69098	+	9.85707i	0.245813	+	0.425761i
$537$		0			0
$538$	−14.7812	+	25.6017i	−0.637261	+	1.10377i
$539$	1.70820			0.0735776
$540$		0			0
$541$	20.1459			0.866140			0.433070	−	0.901360i	$-0.357430\pi$
$541$	20.1459			0.866140			0.433070	+	0.901360i	$0.357430\pi$
$542$	8.28115	−	14.3434i	0.355706	−	0.616101i
$543$		0			0
$544$	7.80902	+	13.5256i	0.334809	+	0.579906i
$545$	−18.0623	−	31.2848i	−0.773704	−	1.34009i
$546$		0			0
$547$	6.16312	−	10.6748i	0.263516	−	0.456423i	−0.703658	−	0.710539i	$-0.748451\pi$
$547$	6.16312	−	10.6748i	0.263516	−	0.456423i	0.967174	+	0.254116i	$0.0817845\pi$
$548$	7.52786			0.321574
$549$		0			0
$550$	−2.56231			−0.109257
$551$	−9.62868	+	16.6774i	−0.410195	+	0.710479i
$552$		0			0
$553$	−3.71885	−	6.44123i	−0.158141	−	0.273909i
$554$	−21.9443	−	38.0086i	−0.932323	−	1.61483i
$555$		0			0
$556$	1.30902	−	2.26728i	0.0555147	−	0.0961543i
$557$	−38.2361			−1.62011			−0.810057	−	0.586351i	$-0.800564\pi$
$557$	−38.2361			−1.62011			−0.810057	+	0.586351i	$0.800564\pi$
$558$		0			0
$559$	11.3262			0.479049
$560$	14.2082	−	24.6093i	0.600406	−	1.03993i
$561$		0			0
$562$	−14.4721	−	25.0665i	−0.610470	−	1.05737i
$563$	−6.50000	−	11.2583i	−0.273942	−	0.474482i	0.695925	−	0.718114i	$-0.254994\pi$
$563$	−6.50000	−	11.2583i	−0.273942	−	0.474482i	−0.969868	+	0.243632i	$0.921661\pi$
$564$		0			0
$565$	−0.0729490	+	0.126351i	−0.00306899	+	0.00531564i
$566$	−6.70820			−0.281967
$567$		0			0
$568$	0.652476			0.0273773
$569$	−18.0623	+	31.2848i	−0.757211	+	1.31153i	0.187056	+	0.982349i	$0.440105\pi$
$569$	−18.0623	+	31.2848i	−0.757211	+	1.31153i	−0.944267	+	0.329179i	$0.893228\pi$
$570$		0			0
$571$	6.29180	+	10.8977i	0.263303	+	0.456055i	0.967118	−	0.254329i	$-0.0818546\pi$
$571$	6.29180	+	10.8977i	0.263303	+	0.456055i	−0.703814	+	0.710384i	$0.748521\pi$
$572$	−0.263932	−	0.457144i	−0.0110356	−	0.0191141i
$573$		0			0
$574$	0.427051	−	0.739674i	0.0178248	−	0.0308734i
$575$	12.7082			0.529969
$576$		0			0
$577$	−7.27051			−0.302675			−0.151338	−	0.988482i	$-0.548358\pi$
$577$	−7.27051			−0.302675			−0.151338	+	0.988482i	$0.548358\pi$
$578$	−3.50000	+	6.06218i	−0.145581	+	0.252153i
$579$		0			0
$580$	3.80902	+	6.59741i	0.158161	+	0.273943i
$581$	15.5902	+	27.0030i	0.646789	+	1.12027i
$582$		0			0
$583$	0.916408	−	1.58726i	0.0379537	−	0.0657378i
$584$	−7.56231			−0.312930
$585$		0			0
$586$	8.38197			0.346256
$587$	1.63525	−	2.83234i	0.0674942	−	0.116903i	−0.830303	−	0.557312i	$-0.811833\pi$
$587$	1.63525	−	2.83234i	0.0674942	−	0.116903i	0.897798	+	0.440408i	$0.145166\pi$
$588$		0			0
$589$	−17.3262	−	30.0099i	−0.713915	−	1.23654i
$590$	13.2082	+	22.8773i	0.543773	+	0.941843i
$591$		0			0
$592$	15.1353	−	26.2150i	0.622055	−	1.07743i
$593$	−16.6869			−0.685250			−0.342625	−	0.939472i	$-0.611316\pi$
$593$	−16.6869			−0.685250			−0.342625	+	0.939472i	$0.611316\pi$
$594$		0			0
$595$	27.0344			1.10830
$596$	1.73607	−	3.00696i	0.0711121	−	0.123170i
$597$		0			0
$598$	5.54508	+	9.60437i	0.226755	+	0.392752i
$599$	1.90983	+	3.30792i	0.0780335	+	0.135158i	0.902401	−	0.430896i	$-0.141803\pi$
$599$	1.90983	+	3.30792i	0.0780335	+	0.135158i	−0.824368	+	0.566054i	$0.808469\pi$
$600$		0			0
$601$	3.10081	−	5.37077i	0.126485	−	0.219078i	−0.795828	−	0.605523i	$-0.792964\pi$
$601$	3.10081	−	5.37077i	0.126485	−	0.219078i	0.922312	+	0.386445i	$0.126297\pi$
$602$	−40.9787			−1.67017
$603$		0			0
$604$	−7.85410			−0.319579
$605$	13.4443	−	23.2862i	0.546587	−	0.946717i
$606$		0			0
$607$	5.57295	+	9.65263i	0.226199	+	0.391788i	0.956678	−	0.291146i	$-0.0940367\pi$
$607$	5.57295	+	9.65263i	0.226199	+	0.391788i	−0.730479	+	0.682935i	$0.760703\pi$
$608$	−6.91641	−	11.9796i	−0.280497	−	0.485836i
$609$		0			0
$610$	32.1525	−	55.6897i	1.30182	−	2.25481i
$611$	−1.09017			−0.0441036
$612$		0			0
$613$	−24.5967			−0.993453			−0.496727	−	0.867907i	$-0.665465\pi$
$613$	−24.5967			−0.993453			−0.496727	+	0.867907i	$0.665465\pi$
$614$	−14.3541	+	24.8620i	−0.579284	+	1.00335i
$615$		0			0
$616$	−2.13525	−	3.69837i	−0.0860319	−	0.149012i
$617$	−11.5172	−	19.9484i	−0.463666	−	0.803093i	0.535474	−	0.844551i	$-0.320133\pi$
$617$	−11.5172	−	19.9484i	−0.463666	−	0.803093i	−0.999140	+	0.0414587i	$0.986800\pi$
$618$		0			0
$619$	0.236068	−	0.408882i	0.00948837	−	0.0164343i	−0.861242	−	0.508195i	$-0.830313\pi$
$619$	0.236068	−	0.408882i	0.00948837	−	0.0164343i	0.870731	+	0.491760i	$0.163646\pi$
$620$	−13.7082			−0.550535
$621$		0			0
$622$	−49.0689			−1.96748
$623$	−19.2705	+	33.3775i	−0.772057	+	1.33724i
$624$		0			0
$625$	15.4164	+	26.7020i	0.616656	+	1.06808i
$626$	22.4164	+	38.8264i	0.895940	+	1.55181i
$627$		0			0
$628$	−4.68034	+	8.10659i	−0.186766	+	0.323488i
$629$	28.7984			1.14827
$630$		0			0
$631$	−4.52786			−0.180251			−0.0901257	−	0.995930i	$-0.528727\pi$
$631$	−4.52786			−0.180251			−0.0901257	+	0.995930i	$0.528727\pi$
$632$	3.71885	−	6.44123i	0.147928	−	0.256218i
$633$		0			0
$634$	23.9164	+	41.4244i	0.949842	+	1.64517i
$635$	−1.92705	−	3.33775i	−0.0764727	−	0.132455i
$636$		0			0
$637$	−1.00000	+	1.73205i	−0.0396214	+	0.0686264i
$638$	6.50658			0.257598
$639$		0			0
$640$	35.6525			1.40929
$641$	−18.1803	+	31.4893i	−0.718080	+	1.24375i	0.243679	+	0.969856i	$0.421646\pi$
$641$	−18.1803	+	31.4893i	−0.718080	+	1.24375i	−0.961759	+	0.273896i	$0.911688\pi$
$642$		0			0
$643$	19.1525	+	33.1731i	0.755300	+	1.30822i	0.945225	+	0.326419i	$0.105842\pi$
$643$	19.1525	+	33.1731i	0.755300	+	1.30822i	−0.189925	+	0.981799i	$0.560825\pi$
$644$	−4.73607	−	8.20311i	−0.186627	−	0.323248i
$645$		0			0
$646$	15.2812	−	26.4677i	0.601229	−	1.04136i
$647$	32.5066			1.27797			0.638983	−	0.769221i	$-0.279356\pi$
$647$	32.5066			1.27797			0.638983	+	0.769221i	$0.279356\pi$
$648$		0			0
$649$	5.32624			0.209073
$650$	1.50000	−	2.59808i	0.0588348	−	0.101905i
$651$		0			0
$652$	3.28115	+	5.68312i	0.128500	+	0.222568i
$653$	−12.7984	−	22.1674i	−0.500839	−	0.867479i	−1.00000		0.000969148i	$-0.999692\pi$
$653$	−12.7984	−	22.1674i	−0.500839	−	0.867479i	0.499160	−	0.866510i	$-0.333642\pi$
$654$		0			0
$655$	−17.0172	+	29.4747i	−0.664918	+	1.15167i
$656$	1.14590			0.0447398
$657$		0			0
$658$	3.94427			0.153764
$659$	11.9721	−	20.7363i	0.466368	−	0.807773i	−0.532894	−	0.846182i	$-0.678896\pi$
$659$	11.9721	−	20.7363i	0.466368	−	0.807773i	0.999262	+	0.0384086i	$0.0122289\pi$
$660$		0			0
$661$	8.64590	+	14.9751i	0.336286	+	0.582465i	0.983731	−	0.179647i	$-0.0574956\pi$
$661$	8.64590	+	14.9751i	0.336286	+	0.582465i	−0.647445	+	0.762112i	$0.724162\pi$
$662$	−3.04508	−	5.27424i	−0.118351	−	0.204989i
$663$		0			0
$664$	−15.5902	+	27.0030i	−0.605016	+	1.04792i
$665$	−23.9443			−0.928519
$666$		0			0
$667$	−32.2705			−1.24952
$668$	−3.16312	+	5.47868i	−0.122385	+	0.211977i
$669$		0			0
$670$	−10.7812	−	18.6735i	−0.416512	−	0.721420i
$671$	−6.48278	−	11.2285i	−0.250265	−	0.433472i
$672$		0			0
$673$	−7.09017	+	12.2805i	−0.273306	+	0.473380i	−0.969706	−	0.244274i	$-0.921450\pi$
$673$	−7.09017	+	12.2805i	−0.273306	+	0.473380i	0.696400	+	0.717653i	$0.254784\pi$
$674$	−33.3262			−1.28368
$675$		0			0
$676$	0.618034			0.0237705
$677$	2.40983	−	4.17395i	0.0926173	−	0.160418i	−0.815994	−	0.578060i	$-0.803810\pi$
$677$	2.40983	−	4.17395i	0.0926173	−	0.160418i	0.908612	+	0.417642i	$0.137143\pi$
$678$		0			0
$679$	−2.76393	−	4.78727i	−0.106070	−	0.183719i
$680$	13.5172	+	23.4125i	0.518362	+	0.897829i
$681$		0			0
$682$	−5.85410	+	10.1396i	−0.224165	+	0.388265i
$683$	−18.2918			−0.699916			−0.349958	−	0.936765i	$-0.613804\pi$
$683$	−18.2918			−0.699916			−0.349958	+	0.936765i	$0.613804\pi$
$684$		0			0
$685$	31.8885			1.21840
$686$	16.2812	−	28.1998i	0.621617	−	1.07667i
$687$		0			0
$688$	−27.4894	−	47.6130i	−1.04802	−	1.81523i
$689$	1.07295	+	1.85840i	0.0408761	+	0.0707995i
$690$		0			0
$691$	−8.38197	+	14.5180i	−0.318865	+	0.552290i	−0.980252	−	0.197755i	$-0.936635\pi$
$691$	−8.38197	+	14.5180i	−0.318865	+	0.552290i	0.661386	+	0.750045i	$0.269968\pi$
$692$	7.65248			0.290903
$693$		0			0
$694$	−13.0344			−0.494781
$695$	5.54508	−	9.60437i	0.210337	−	0.364314i
$696$		0			0
$697$	0.545085	+	0.944115i	0.0206466	+	0.0357609i
$698$	2.50000	+	4.33013i	0.0946264	+	0.163898i
$699$		0			0
$700$	−1.28115	+	2.21902i	−0.0484230	+	0.0838711i
$701$	−6.41641			−0.242344			−0.121172	−	0.992632i	$-0.538665\pi$
$701$	−6.41641			−0.242344			−0.121172	+	0.992632i	$0.538665\pi$
$702$		0			0
$703$	−25.5066			−0.961999
$704$	1.80902	−	3.13331i	0.0681799	−	0.118091i
$705$		0			0
$706$	−3.80902	−	6.59741i	−0.143354	−	0.248297i
$707$	−21.4443	−	37.1426i	−0.806495	−	1.39689i
$708$		0			0
$709$	15.1631	−	26.2633i	0.569463	−	0.986339i	−0.427156	−	0.904178i	$-0.640485\pi$
$709$	15.1631	−	26.2633i	0.569463	−	0.986339i	0.996619	−	0.0821608i	$-0.0261821\pi$
$710$	−1.23607			−0.0463888
$711$		0			0
$712$	−38.5410			−1.44439
$713$	29.0344	−	50.2891i	1.08735	−	1.88334i
$714$		0			0
$715$	−1.11803	−	1.93649i	−0.0418121	−	0.0724207i
$716$	1.48278	+	2.56825i	0.0554141	+	0.0959800i
$717$		0			0
$718$	27.8435	−	48.2263i	1.03911	−	1.79979i
$719$	4.87539			0.181821			0.0909106	−	0.995859i	$-0.471022\pi$
$719$	4.87539			0.181821			0.0909106	+	0.995859i	$0.471022\pi$
$720$		0			0
$721$	42.0344			1.56544
$722$	1.83688	−	3.18157i	0.0683616	−	0.118406i
$723$		0			0
$724$	−4.19098	−	7.25900i	−0.155757	−	0.269778i
$725$	4.36475	+	7.55996i	0.162103	+	0.280770i
$726$		0			0
$727$	−8.17376	+	14.1574i	−0.303148	+	0.525068i	−0.976847	−	0.213938i	$-0.931371\pi$
$727$	−8.17376	+	14.1574i	−0.303148	+	0.525068i	0.673699	+	0.739006i	$0.264704\pi$
$728$	5.00000			0.185312
$729$		0			0
$730$	14.3262			0.530238
$731$	26.1525	−	45.2974i	0.967284	−	1.67539i
$732$		0			0
$733$	21.2361	+	36.7819i	0.784372	+	1.35857i	0.929373	+	0.369141i	$0.120348\pi$
$733$	21.2361	+	36.7819i	0.784372	+	1.35857i	−0.145001	+	0.989431i	$0.546319\pi$
$734$	−0.572949	−	0.992377i	−0.0211479	−	0.0366293i
$735$		0			0
$736$	11.5902	−	20.0748i	0.427219	−	0.739966i
$737$	−4.34752			−0.160143
$738$		0			0
$739$	−3.61803			−0.133092			−0.0665458	−	0.997783i	$-0.521198\pi$
$739$	−3.61803			−0.133092			−0.0665458	+	0.997783i	$0.521198\pi$
$740$	−5.04508	+	8.73834i	−0.185461	+	0.321228i
$741$		0			0
$742$	−3.88197	−	6.72376i	−0.142511	−	0.246837i
$743$	−6.78115	−	11.7453i	−0.248776	−	0.430893i	0.714410	−	0.699727i	$-0.246695\pi$
$743$	−6.78115	−	11.7453i	−0.248776	−	0.430893i	−0.963187	+	0.268834i	$0.913362\pi$
$744$		0			0
$745$	7.35410	−	12.7377i	0.269433	−	0.466672i
$746$	−6.23607			−0.228319
$747$		0			0
$748$	−2.43769			−0.0891309
$749$	7.13525	−	12.3586i	0.260717	−	0.451574i
$750$		0			0
$751$	−0.635255	−	1.10029i	−0.0231808	−	0.0401503i	0.854202	−	0.519941i	$-0.174046\pi$
$751$	−0.635255	−	1.10029i	−0.0231808	−	0.0401503i	−0.877383	+	0.479790i	$0.840713\pi$
$752$	2.64590	+	4.58283i	0.0964860	+	0.167119i
$753$		0			0
$754$	−3.80902	+	6.59741i	−0.138716	+	0.240264i
$755$	−33.2705			−1.21084
$756$		0			0
$757$	−29.5623			−1.07446			−0.537230	−	0.843436i	$-0.680529\pi$
$757$	−29.5623			−1.07446			−0.537230	+	0.843436i	$0.680529\pi$
$758$	11.8992	−	20.6100i	0.432198	−	0.748589i
$759$		0			0
$760$	−11.9721	−	20.7363i	−0.434275	−	0.752186i
$761$	−5.29180	−	9.16566i	−0.191827	−	0.332255i	0.754028	−	0.656842i	$-0.228108\pi$
$761$	−5.29180	−	9.16566i	−0.191827	−	0.332255i	−0.945856	+	0.324587i	$0.894775\pi$
$762$		0			0
$763$	−15.4271	+	26.7204i	−0.558497	+	0.967345i
$764$	−13.4377			−0.486159
$765$		0			0
$766$	15.2361			0.550502
$767$	−3.11803	+	5.40059i	−0.112586	+	0.195004i
$768$		0			0
$769$	−2.91641	−	5.05137i	−0.105168	−	0.182157i	0.808639	−	0.588306i	$-0.200205\pi$
$769$	−2.91641	−	5.05137i	−0.105168	−	0.182157i	−0.913807	+	0.406149i	$0.866871\pi$
$770$	4.04508	+	7.00629i	0.145775	+	0.252489i
$771$		0			0
$772$	−2.40983	+	4.17395i	−0.0867317	+	0.150224i
$773$	−45.5066			−1.63676			−0.818379	−	0.574679i	$-0.805127\pi$
$773$	−45.5066			−1.63676			−0.818379	+	0.574679i	$0.805127\pi$
$774$		0			0
$775$	−15.7082			−0.564255
$776$	2.76393	−	4.78727i	0.0992194	−	0.171853i
$777$		0			0
$778$	6.23607	+	10.8012i	0.223574	+	0.387241i
$779$	−0.482779	−	0.836198i	−0.0172974	−	0.0299599i
$780$		0			0
$781$	−0.124612	+	0.215834i	−0.00445896	+	0.00772315i
$782$	51.2148			1.83144
$783$		0			0
$784$	9.70820			0.346722
$785$	−19.8262	+	34.3401i	−0.707629	+	1.22565i
$786$		0			0
$787$	−4.02786	−	6.97647i	−0.143578	−	0.248684i	0.785264	−	0.619162i	$-0.212527\pi$
$787$	−4.02786	−	6.97647i	−0.143578	−	0.248684i	−0.928841	+	0.370477i	$0.879194\pi$
$788$	3.61803	+	6.26662i	0.128887	+	0.223239i
$789$		0			0
$790$	−7.04508	+	12.2024i	−0.250653	+	0.434144i
$791$	0.124612			0.00443069
$792$		0			0
$793$	15.1803			0.539070
$794$	9.80902	−	16.9897i	0.348109	−	0.602942i
$795$		0			0
$796$	2.37132	+	4.10725i	0.0840493	+	0.145578i
$797$	−20.5344	−	35.5667i	−0.727367	−	1.25984i	−0.957992	−	0.286794i	$-0.907410\pi$
$797$	−20.5344	−	35.5667i	−0.727367	−	1.25984i	0.230625	−	0.973043i	$-0.425923\pi$
$798$		0			0
$799$	−2.51722	+	4.35995i	−0.0890529	+	0.154244i
$800$	−6.27051			−0.221696
$801$		0			0
$802$	−8.47214			−0.299162
$803$	1.44427	−	2.50155i	0.0509672	−	0.0882779i
$804$		0			0
$805$	−20.0623	−	34.7489i	−0.707103	−	1.22474i
$806$	−6.85410	−	11.8717i	−0.241425	−	0.418161i
$807$		0			0
$808$	21.4443	−	37.1426i	0.754407	−	1.30667i
$809$	11.6180			0.408468			0.204234	−	0.978922i	$-0.434530\pi$
$809$	11.6180			0.408468			0.204234	+	0.978922i	$0.434530\pi$
$810$		0			0
$811$	24.5279			0.861290			0.430645	−	0.902521i	$-0.358286\pi$
$811$	24.5279			0.861290			0.430645	+	0.902521i	$0.358286\pi$
$812$	3.25329	−	5.63486i	0.114168	−	0.197745i
$813$		0			0
$814$	4.30902	+	7.46344i	0.151031	+	0.261593i
$815$	13.8992	+	24.0741i	0.486867	+	0.843279i
$816$		0			0
$817$	−23.1631	+	40.1197i	−0.810375	+	1.40361i
$818$	33.7082			1.17858
$819$		0			0
$820$	−0.381966			−0.0133388
$821$	12.9098	−	22.3605i	0.450556	−	0.780386i	−0.547864	−	0.836567i	$-0.684559\pi$
$821$	12.9098	−	22.3605i	0.450556	−	0.780386i	0.998421	+	0.0561809i	$0.0178924\pi$
$822$		0			0
$823$	−12.2082	−	21.1452i	−0.425551	−	0.737076i	0.570921	−	0.821005i	$-0.306586\pi$
$823$	−12.2082	−	21.1452i	−0.425551	−	0.737076i	−0.996472	+	0.0839290i	$0.973253\pi$
$824$	21.0172	+	36.4029i	0.732170	+	1.26815i
$825$		0			0
$826$	11.2812	−	19.5395i	0.392522	−	0.679867i
$827$	19.0000			0.660695			0.330347	−	0.943859i	$-0.392834\pi$
$827$	19.0000			0.660695			0.330347	+	0.943859i	$0.392834\pi$
$828$		0			0
$829$	−34.3607			−1.19340			−0.596698	−	0.802466i	$-0.703521\pi$
$829$	−34.3607			−1.19340			−0.596698	+	0.802466i	$0.703521\pi$
$830$	29.5344	−	51.1552i	1.02516	−	1.77562i
$831$		0			0
$832$	2.11803	+	3.66854i	0.0734296	+	0.127184i
$833$	4.61803	+	7.99867i	0.160005	+	0.277137i
$834$		0			0
$835$	−13.3992	+	23.2081i	−0.463698	+	0.803148i
$836$	2.15905			0.0746724
$837$		0			0
$838$	−29.7082			−1.02625
$839$	0.809017	−	1.40126i	0.0279304	−	0.0483768i	−0.851722	−	0.523993i	$-0.824442\pi$
$839$	0.809017	−	1.40126i	0.0279304	−	0.0483768i	0.879653	+	0.475617i	$0.157775\pi$
$840$		0			0
$841$	3.41641	+	5.91739i	0.117807	+	0.204048i
$842$	24.4164	+	42.2905i	0.841445	+	1.45743i
$843$		0			0
$844$	−5.91641	+	10.2475i	−0.203651	+	0.352734i
$845$	2.61803			0.0900631
$846$		0			0
$847$	−22.9656			−0.789106
$848$	5.20820	−	9.02087i	0.178850	−	0.309778i
$849$		0			0
$850$	−6.92705	−	11.9980i	−0.237596	−	0.411528i
$851$	−21.3713	−	37.0162i	−0.732600	−	1.26890i
$852$		0			0
$853$	0.836881	−	1.44952i	0.0286543	−	0.0496306i	−0.851343	−	0.524610i	$-0.824211\pi$
$853$	0.836881	−	1.44952i	0.0286543	−	0.0496306i	0.879997	+	0.474979i	$0.157544\pi$
$854$	−54.9230			−1.87943
$855$		0			0
$856$	14.2705			0.487756
$857$	14.4336	−	24.9998i	0.493043	−	0.853976i	−0.506925	−	0.861990i	$-0.669218\pi$
$857$	14.4336	−	24.9998i	0.493043	−	0.853976i	0.999968	+	0.00801429i	$0.00255105\pi$
$858$		0			0
$859$	−20.5344	−	35.5667i	−0.700626	−	1.21352i	−0.968247	−	0.249996i	$-0.919571\pi$
$859$	−20.5344	−	35.5667i	−0.700626	−	1.21352i	0.267621	−	0.963524i	$-0.413763\pi$
$860$	9.16312	+	15.8710i	0.312460	+	0.541196i
$861$		0			0
$862$	15.2812	−	26.4677i	0.520478	−	0.901495i
$863$	1.34752			0.0458703			0.0229351	−	0.999737i	$-0.492699\pi$
$863$	1.34752			0.0458703			0.0229351	+	0.999737i	$0.492699\pi$
$864$		0			0
$865$	32.4164			1.10219
$866$	−19.4443	+	33.6785i	−0.660743	+	1.14444i
$867$		0			0
$868$	5.85410	+	10.1396i	0.198701	+	0.344161i
$869$	1.42047	+	2.46033i	0.0481863	+	0.0834610i
$870$		0			0
$871$	2.54508	−	4.40822i	0.0862369	−	0.149367i
$872$	−30.8541			−1.04485
$873$		0			0
$874$	−45.3607			−1.53435
$875$	9.20820	−	15.9491i	0.311294	−	0.539177i
$876$		0			0
$877$	14.2984	+	24.7655i	0.482822	+	0.836272i	0.999805	−	0.0197234i	$-0.00627856\pi$
$877$	14.2984	+	24.7655i	0.482822	+	0.836272i	−0.516984	+	0.855995i	$0.672945\pi$
$878$	−29.1246	−	50.4453i	−0.982908	−	1.70245i
$879$		0			0
$880$	−5.42705	+	9.39993i	−0.182946	+	0.316872i
$881$	22.2361			0.749152			0.374576	−	0.927196i	$-0.377788\pi$
$881$	22.2361			0.749152			0.374576	+	0.927196i	$0.377788\pi$
$882$		0			0
$883$	13.7426			0.462477			0.231238	−	0.972897i	$-0.425722\pi$
$883$	13.7426			0.462477			0.231238	+	0.972897i	$0.425722\pi$
$884$	1.42705	−	2.47172i	0.0479969	−	0.0831331i
$885$		0			0
$886$	−13.0451	−	22.5947i	−0.438258	−	0.759085i
$887$	−5.35410	−	9.27358i	−0.179773	−	0.311376i	0.762030	−	0.647542i	$-0.224203\pi$
$887$	−5.35410	−	9.27358i	−0.179773	−	0.311376i	−0.941803	+	0.336166i	$0.890870\pi$
$888$		0			0
$889$	−1.64590	+	2.85078i	−0.0552016	+	0.0956121i
$890$	73.0132			2.44741
$891$		0			0
$892$	9.36068			0.313419
$893$	2.22949	−	3.86159i	0.0746070	−	0.129223i
$894$		0			0
$895$	6.28115	+	10.8793i	0.209956	+	0.363654i
$896$	−15.2254	−	26.3712i	−0.508646	−	0.881000i
$897$		0			0
$898$	−25.4615	+	44.1006i	−0.849661	+	1.47166i
$899$	39.8885			1.33036
$900$		0			0
$901$	9.90983			0.330144
$902$	−0.163119	+	0.282530i	−0.00543127	+	0.00940723i
$903$		0			0
$904$	0.0623059	+	0.107917i	0.00207226	+	0.00358927i
$905$	−17.7533	−	30.7496i	−0.590139	−	1.02215i
$906$		0			0
$907$	−4.29180	+	7.43361i	−0.142507	+	0.246829i	−0.928440	−	0.371482i	$-0.878850\pi$
$907$	−4.29180	+	7.43361i	−0.142507	+	0.246829i	0.785933	+	0.618311i	$0.212183\pi$
$908$	−13.2148			−0.438548
$909$		0			0
$910$	−9.47214			−0.313998
$911$	−1.57295	+	2.72443i	−0.0521141	+	0.0902643i	−0.890906	−	0.454188i	$-0.849929\pi$
$911$	−1.57295	+	2.72443i	−0.0521141	+	0.0902643i	0.838792	+	0.544453i	$0.183263\pi$
$912$		0			0
$913$	−5.95492	−	10.3142i	−0.197079	−	0.341351i
$914$	0.954915	+	1.65396i	0.0315858	+	0.0547082i
$915$		0			0
$916$	−2.97214	+	5.14789i	−0.0982021	+	0.170091i
$917$	29.0689			0.959939
$918$		0			0
$919$	−17.0557			−0.562617			−0.281308	−	0.959617i	$-0.590768\pi$
$919$	−17.0557			−0.562617			−0.281308	+	0.959617i	$0.590768\pi$
$920$	20.0623	−	34.7489i	0.661435	−	1.14564i
$921$		0			0
$922$	−1.30902	−	2.26728i	−0.0431102	−	0.0746690i
$923$	−0.145898	−	0.252703i	−0.00480229	−	0.00831781i
$924$		0			0
$925$	−5.78115	+	10.0133i	−0.190083	+	0.329234i
$926$	−49.4508			−1.62506
$927$		0			0
$928$	15.9230			0.522698
$929$	−10.9721	+	19.0043i	−0.359984	+	0.623511i	−0.987958	−	0.154724i	$-0.950551\pi$
$929$	−10.9721	+	19.0043i	−0.359984	+	0.623511i	0.627974	+	0.778235i	$0.283885\pi$
$930$		0			0
$931$	−4.09017	−	7.08438i	−0.134050	−	0.232181i
$932$	−0.836881	−	1.44952i	−0.0274129	−	0.0474806i
$933$		0			0
$934$	−24.3713	+	42.2124i	−0.797454	+	1.38123i
$935$	−10.3262			−0.337704
$936$		0			0
$937$	−10.3820			−0.339164			−0.169582	−	0.985516i	$-0.554242\pi$
$937$	−10.3820			−0.339164			−0.169582	+	0.985516i	$0.554242\pi$
$938$	−9.20820	+	15.9491i	−0.300659	+	0.520756i
$939$		0			0
$940$	−0.881966	−	1.52761i	−0.0287666	−	0.0498251i
$941$	2.32624	+	4.02916i	0.0758332	+	0.131347i	0.901448	−	0.432887i	$-0.142505\pi$
$941$	2.32624	+	4.02916i	0.0758332	+	0.131347i	−0.825615	+	0.564234i	$0.809172\pi$
$942$		0			0
$943$	0.809017	−	1.40126i	0.0263452	−	0.0456313i
$944$	30.2705			0.985221
$945$		0			0
$946$	15.6525			0.508906
$947$	−15.7705	+	27.3153i	−0.512473	+	0.887629i	0.487423	+	0.873166i	$0.337937\pi$
$947$	−15.7705	+	27.3153i	−0.512473	+	0.887629i	−0.999895	+	0.0144626i	$0.995396\pi$
$948$		0			0
$949$	1.69098	+	2.92887i	0.0548916	+	0.0950751i
$950$	6.13525	+	10.6266i	0.199054	+	0.344772i
$951$		0			0
$952$	11.5451	−	19.9967i	0.374178	−	0.648096i
$953$	−0.472136			−0.0152940			−0.00764699	−	0.999971i	$-0.502434\pi$
$953$	−0.472136			−0.0152940			−0.00764699	+	0.999971i	$0.502434\pi$
$954$		0			0
$955$	−56.9230			−1.84198
$956$	−5.69098	+	9.85707i	−0.184060	+	0.318800i
$957$		0			0
$958$	−12.7812	−	22.1376i	−0.412940	−	0.715234i
$959$	−13.6180	−	23.5871i	−0.439749	−	0.761668i
$960$		0			0
$961$	−20.3885	+	35.3140i	−0.657695	+	1.13916i
$962$	−10.0902			−0.325320
$963$		0			0
$964$	−18.3050			−0.589563
$965$	−10.2082	+	17.6811i	−0.328614	+	0.569176i
$966$		0			0
$967$	−12.0902	−	20.9408i	−0.388794	−	0.673410i	0.603494	−	0.797368i	$-0.293775\pi$
$967$	−12.0902	−	20.9408i	−0.388794	−	0.673410i	−0.992288	+	0.123957i	$0.960441\pi$
$968$	−11.4828	−	19.8888i	−0.369070	−	0.639249i
$969$		0			0
$970$	−5.23607	+	9.06914i	−0.168120	+	0.291192i
$971$	39.3050			1.26136			0.630678	−	0.776045i	$-0.282777\pi$
$971$	39.3050			1.26136			0.630678	+	0.776045i	$0.282777\pi$
$972$		0			0
$973$	−9.47214			−0.303663
$974$	−20.4721	+	35.4588i	−0.655970	+	1.13617i
$975$		0			0
$976$	−36.8435	−	63.8147i	−1.17933	−	2.04266i
$977$	−5.38197	−	9.32184i	−0.172184	−	0.298232i	0.766999	−	0.641648i	$-0.221749\pi$
$977$	−5.38197	−	9.32184i	−0.172184	−	0.298232i	−0.939183	+	0.343416i	$0.888416\pi$
$978$		0			0
$979$	7.36068	−	12.7491i	0.235248	−	0.407462i
$980$	−3.23607			−0.103372
$981$		0			0
$982$	−31.0902			−0.992127
$983$	10.5066	−	18.1979i	0.335108	−	0.580424i	−0.648398	−	0.761302i	$-0.724561\pi$
$983$	10.5066	−	18.1979i	0.335108	−	0.580424i	0.983506	+	0.180878i	$0.0578939\pi$
$984$		0			0
$985$	15.3262	+	26.5458i	0.488335	+	0.845820i
$986$	17.5902	+	30.4671i	0.560185	+	0.970269i
$987$		0			0
$988$	−1.26393	+	2.18919i	−0.0402110	+	0.0696476i
$989$	−77.6312			−2.46853
$990$		0			0
$991$	−18.5279			−0.588557			−0.294278	−	0.955720i	$-0.595079\pi$
$991$	−18.5279			−0.588557			−0.294278	+	0.955720i	$0.595079\pi$
$992$	−14.3262	+	24.8138i	−0.454859	+	0.787838i
$993$		0			0
$994$	0.527864	+	0.914287i	0.0167428	+	0.0289994i
$995$	10.0451	+	17.3986i	0.318451	+	0.551573i
$996$		0			0
$997$	13.9615	−	24.1820i	0.442165	−	0.765852i	−0.555685	−	0.831393i	$-0.687544\pi$
$997$	13.9615	−	24.1820i	0.442165	−	0.765852i	0.997850	+	0.0655408i	$0.0208773\pi$
$998$	−39.4508			−1.24879
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1053.2.e.g.703.1		4
3.2	odd	2		1053.2.e.l.703.2		4
9.2	odd	6		351.2.a.a.1.1	✓	2
9.4	even	3	inner	1053.2.e.g.352.1		4
9.5	odd	6		1053.2.e.l.352.2		4
9.7	even	3		351.2.a.c.1.2	yes	2
36.7	odd	6		5616.2.a.bx.1.2		2
36.11	even	6		5616.2.a.bl.1.1		2
45.29	odd	6		8775.2.a.bb.1.2		2
45.34	even	6		8775.2.a.u.1.1		2
117.25	even	6		4563.2.a.h.1.1		2
117.38	odd	6		4563.2.a.p.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
351.2.a.a.1.1	✓	2	9.2	odd	6
351.2.a.c.1.2	yes	2	9.7	even	3
1053.2.e.g.352.1		4	9.4	even	3	inner
1053.2.e.g.703.1		4	1.1	even	1	trivial
1053.2.e.l.352.2		4	9.5	odd	6
1053.2.e.l.703.2		4	3.2	odd	2
4563.2.a.h.1.1		2	117.25	even	6
4563.2.a.p.1.2		2	117.38	odd	6
5616.2.a.bl.1.1		2	36.11	even	6
5616.2.a.bx.1.2		2	36.7	odd	6
8775.2.a.u.1.1		2	45.34	even	6
8775.2.a.bb.1.2		2	45.29	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1053 = 3^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1053.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 1.40126i) q^{2} +(-0.309017 - 0.535233i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(-1.11803 + 1.93649i) q^{7} -2.23607 q^{8} +4.23607 q^{10} +(0.427051 - 0.739674i) q^{11} +(0.500000 + 0.866025i) q^{13} +(-1.80902 - 3.13331i) q^{14} +(2.42705 - 4.20378i) q^{16} +4.61803 q^{17} -4.09017 q^{19} +(-0.809017 + 1.40126i) q^{20} +(0.690983 + 1.19682i) q^{22} +(-3.42705 - 5.93583i) q^{23} +(-0.927051 + 1.60570i) q^{25} -1.61803 q^{26} +1.38197 q^{28} +(2.35410 - 4.07742i) q^{29} +(4.23607 + 7.33708i) q^{31} +(1.69098 + 2.92887i) q^{32} +(-3.73607 + 6.47106i) q^{34} +5.85410 q^{35} +6.23607 q^{37} +(3.30902 - 5.73139i) q^{38} +(2.92705 + 5.06980i) q^{40} +(0.118034 + 0.204441i) q^{41} +(5.66312 - 9.80881i) q^{43} -0.527864 q^{44} +11.0902 q^{46} +(-0.545085 + 0.944115i) q^{47} +(1.00000 + 1.73205i) q^{49} +(-1.50000 - 2.59808i) q^{50} +(0.309017 - 0.535233i) q^{52} +2.14590 q^{53} -2.23607 q^{55} +(2.50000 - 4.33013i) q^{56} +(3.80902 + 6.59741i) q^{58} +(3.11803 + 5.40059i) q^{59} +(7.59017 - 13.1466i) q^{61} -13.7082 q^{62} +4.23607 q^{64} +(1.30902 - 2.26728i) q^{65} +(-2.54508 - 4.40822i) q^{67} +(-1.42705 - 2.47172i) q^{68} +(-4.73607 + 8.20311i) q^{70} -0.291796 q^{71} +3.38197 q^{73} +(-5.04508 + 8.73834i) q^{74} +(1.26393 + 2.18919i) q^{76} +(0.954915 + 1.65396i) q^{77} +(-1.66312 + 2.88061i) q^{79} -12.7082 q^{80} -0.381966 q^{82} +(6.97214 - 12.0761i) q^{83} +(-6.04508 - 10.4704i) q^{85} +(9.16312 + 15.8710i) q^{86} +(-0.954915 + 1.65396i) q^{88} +17.2361 q^{89} -2.23607 q^{91} +(-2.11803 + 3.66854i) q^{92} +(-0.881966 - 1.52761i) q^{94} +(5.35410 + 9.27358i) q^{95} +(-1.23607 + 2.14093i) q^{97} -3.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} + q^{4} - 3 q^{5} + 8 q^{10} - 5 q^{11} + 2 q^{13} - 5 q^{14} + 3 q^{16} + 14 q^{17} + 6 q^{19} - q^{20} + 5 q^{22} - 7 q^{23} + 3 q^{25} - 2 q^{26} + 10 q^{28} - 4 q^{29} + 8 q^{31} + 9 q^{32}+ \cdots - 4 q^{98}+O(q^{100}) \) 4 * q - q^2 + q^4 - 3 * q^5 + 8 * q^10 - 5 * q^11 + 2 * q^13 - 5 * q^14 + 3 * q^16 + 14 * q^17 + 6 * q^19 - q^20 + 5 * q^22 - 7 * q^23 + 3 * q^25 - 2 * q^26 + 10 * q^28 - 4 * q^29 + 8 * q^31 + 9 * q^32 - 6 * q^34 + 10 * q^35 + 16 * q^37 + 11 * q^38 + 5 * q^40 - 4 * q^41 + 7 * q^43 - 20 * q^44 + 22 * q^46 + 9 * q^47 + 4 * q^49 - 6 * q^50 - q^52 + 22 * q^53 + 10 * q^56 + 13 * q^58 + 8 * q^59 + 8 * q^61 - 28 * q^62 + 8 * q^64 + 3 * q^65 + q^67 + q^68 - 10 * q^70 - 28 * q^71 + 18 * q^73 - 9 * q^74 + 14 * q^76 + 15 * q^77 + 9 * q^79 - 24 * q^80 - 6 * q^82 + 10 * q^83 - 13 * q^85 + 21 * q^86 - 15 * q^88 + 60 * q^89 - 4 * q^92 - 8 * q^94 + 8 * q^95 + 4 * q^97 - 4 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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