LMFDB - Embedded newform 1053.2.e.k.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,-3,0,3] 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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			703.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	1053.703
Dual form			1053.2.e.k.352.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.309017 + 0.535233i) q^{2} +(0.809017 + 1.40126i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(0.190983 - 0.330792i) q^{7} -2.23607 q^{8} +1.61803 q^{10} +(2.92705 - 5.06980i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.118034 + 0.204441i) q^{14} +(-0.927051 + 1.60570i) q^{16} -4.23607 q^{17} -7.47214 q^{19} +(2.11803 - 3.66854i) q^{20} +(1.80902 + 3.13331i) q^{22} +(0.427051 + 0.739674i) q^{23} +(-0.927051 + 1.60570i) q^{25} -0.618034 q^{26} +0.618034 q^{28} +(-2.92705 + 5.06980i) q^{29} +(-4.16312 - 7.21073i) q^{31} +(-2.80902 - 4.86536i) q^{32} +(1.30902 - 2.26728i) q^{34} -1.00000 q^{35} -6.09017 q^{37} +(2.30902 - 3.99933i) q^{38} +(2.92705 + 5.06980i) q^{40} +(-3.30902 - 5.73139i) q^{41} +(5.11803 - 8.86469i) q^{43} +9.47214 q^{44} -0.527864 q^{46} +(3.73607 - 6.47106i) q^{47} +(3.42705 + 5.93583i) q^{49} +(-0.572949 - 0.992377i) q^{50} +(-0.809017 + 1.40126i) q^{52} -0.291796 q^{53} -15.3262 q^{55} +(-0.427051 + 0.739674i) q^{56} +(-1.80902 - 3.13331i) q^{58} +(-2.73607 - 4.73901i) q^{59} +(4.04508 - 7.00629i) q^{61} +5.14590 q^{62} -0.236068 q^{64} +(1.30902 - 2.26728i) q^{65} +(4.54508 + 7.87232i) q^{67} +(-3.42705 - 5.93583i) q^{68} +(0.309017 - 0.535233i) q^{70} -5.00000 q^{71} +11.1803 q^{73} +(1.88197 - 3.25966i) q^{74} +(-6.04508 - 10.4704i) q^{76} +(-1.11803 - 1.93649i) q^{77} +(-1.11803 + 1.93649i) q^{79} +4.85410 q^{80} +4.09017 q^{82} +(-3.59017 + 6.21836i) q^{83} +(5.54508 + 9.60437i) q^{85} +(3.16312 + 5.47868i) q^{86} +(-6.54508 + 11.3364i) q^{88} +0.381966 q^{89} +0.381966 q^{91} +(-0.690983 + 1.19682i) q^{92} +(2.30902 + 3.99933i) q^{94} +(9.78115 + 16.9415i) q^{95} +(3.23607 - 5.60503i) q^{97} -4.23607 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + q^{4} - 3 q^{5} + 3 q^{7} + 2 q^{10} + 5 q^{11} + 2 q^{13} - 4 q^{14} + 3 q^{16} - 8 q^{17} - 12 q^{19} + 4 q^{20} + 5 q^{22} - 5 q^{23} + 3 q^{25} + 2 q^{26} - 2 q^{28} - 5 q^{29} - q^{31}+ \cdots - 8 q^{98}+O(q^{100}) $ 4 * q + q^2 + q^4 - 3 * q^5 + 3 * q^7 + 2 * q^10 + 5 * q^11 + 2 * q^13 - 4 * q^14 + 3 * q^16 - 8 * q^17 - 12 * q^19 + 4 * q^20 + 5 * q^22 - 5 * q^23 + 3 * q^25 + 2 * q^26 - 2 * q^28 - 5 * q^29 - q^31 - 9 * q^32 + 3 * q^34 - 4 * q^35 - 2 * q^37 + 7 * q^38 + 5 * q^40 - 11 * q^41 + 16 * q^43 + 20 * q^44 - 20 * q^46 + 6 * q^47 + 7 * q^49 - 9 * q^50 - q^52 - 28 * q^53 - 30 * q^55 + 5 * q^56 - 5 * q^58 - 2 * q^59 + 5 * q^61 + 34 * q^62 + 8 * q^64 + 3 * q^65 + 7 * q^67 - 7 * q^68 - q^70 - 20 * q^71 + 12 * q^74 - 13 * q^76 + 6 * q^80 - 6 * q^82 + 8 * q^83 + 11 * q^85 - 3 * q^86 - 15 * q^88 + 6 * q^89 + 6 * q^91 - 5 * q^92 + 7 * q^94 + 19 * q^95 + 4 * q^97 - 8 * 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 $

$2$	−0.309017	+	0.535233i	−0.218508	+	0.378467i	−0.954352	−	0.298684i	$-0.903452\pi$
$2$	−0.309017	+	0.535233i	−0.218508	+	0.378467i	0.735844	+	0.677151i	$0.236786\pi$
$3$		0			0
$3$		0			0
$4$	0.809017	+	1.40126i	0.404508	+	0.700629i
$5$	−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
$7$	0.190983	−	0.330792i	0.0721848	−	0.125028i	−0.827674	−	0.561210i	$-0.810336\pi$
$7$	0.190983	−	0.330792i	0.0721848	−	0.125028i	0.899859	+	0.436182i	$0.143670\pi$
$8$	−2.23607			−0.790569
$9$		0			0
$10$	1.61803			0.511667
$11$	2.92705	−	5.06980i	0.882539	−	1.52860i	0.0340306	−	0.999421i	$-0.489166\pi$
$11$	2.92705	−	5.06980i	0.882539	−	1.52860i	0.848509	−	0.529182i	$-0.177501\pi$
$12$		0			0
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	0.118034	+	0.204441i	0.0315459	+	0.0546391i
$15$		0			0
$16$	−0.927051	+	1.60570i	−0.231763	+	0.401425i
$17$	−4.23607			−1.02740			−0.513699	−	0.857971i	$-0.671725\pi$
$17$	−4.23607			−1.02740			−0.513699	+	0.857971i	$0.671725\pi$
$18$		0			0
$19$	−7.47214			−1.71423			−0.857113	−	0.515129i	$-0.827744\pi$
$19$	−7.47214			−1.71423			−0.857113	+	0.515129i	$0.827744\pi$
$20$	2.11803	−	3.66854i	0.473607	−	0.820311i
$21$		0			0
$22$	1.80902	+	3.13331i	0.385684	+	0.668024i
$23$	0.427051	+	0.739674i	0.0890463	+	0.154233i	0.907108	−	0.420897i	$-0.138285\pi$
$23$	0.427051	+	0.739674i	0.0890463	+	0.154233i	−0.818062	+	0.575130i	$0.804951\pi$
$24$		0			0
$25$	−0.927051	+	1.60570i	−0.185410	+	0.321140i
$26$	−0.618034			−0.121206
$27$		0			0
$28$	0.618034			0.116797
$29$	−2.92705	+	5.06980i	−0.543540	+	0.941438i	0.455158	+	0.890411i	$0.349583\pi$
$29$	−2.92705	+	5.06980i	−0.543540	+	0.941438i	−0.998697	+	0.0510275i	$0.983750\pi$
$30$		0			0
$31$	−4.16312	−	7.21073i	−0.747718	−	1.29509i	−0.948914	−	0.315535i	$-0.897816\pi$
$31$	−4.16312	−	7.21073i	−0.747718	−	1.29509i	0.201196	−	0.979551i	$-0.435517\pi$
$32$	−2.80902	−	4.86536i	−0.496569	−	0.860082i
$33$		0			0
$34$	1.30902	−	2.26728i	0.224495	−	0.388836i
$35$	−1.00000			−0.169031
$36$		0			0
$37$	−6.09017			−1.00122			−0.500609	−	0.865674i	$-0.666891\pi$
$37$	−6.09017			−1.00122			−0.500609	+	0.865674i	$0.666891\pi$
$38$	2.30902	−	3.99933i	0.374572	−	0.648778i
$39$		0			0
$40$	2.92705	+	5.06980i	0.462807	+	0.801606i
$41$	−3.30902	−	5.73139i	−0.516782	−	0.895092i	−0.999810	−	0.0194874i	$-0.993797\pi$
$41$	−3.30902	−	5.73139i	−0.516782	−	0.895092i	0.483028	−	0.875605i	$-0.339537\pi$
$42$		0			0
$43$	5.11803	−	8.86469i	0.780493	−	1.35185i	−0.151162	−	0.988509i	$-0.548302\pi$
$43$	5.11803	−	8.86469i	0.780493	−	1.35185i	0.931655	−	0.363344i	$-0.118365\pi$
$44$	9.47214			1.42798
$45$		0			0
$46$	−0.527864			−0.0778293
$47$	3.73607	−	6.47106i	0.544962	−	0.943901i	−0.453648	−	0.891181i	$-0.649878\pi$
$47$	3.73607	−	6.47106i	0.544962	−	0.943901i	0.998609	−	0.0527200i	$-0.0167891\pi$
$48$		0			0
$49$	3.42705	+	5.93583i	0.489579	+	0.847975i
$50$	−0.572949	−	0.992377i	−0.0810272	−	0.140343i
$51$		0			0
$52$	−0.809017	+	1.40126i	−0.112190	+	0.194320i
$53$	−0.291796			−0.0400813			−0.0200406	−	0.999799i	$-0.506380\pi$
$53$	−0.291796			−0.0400813			−0.0200406	+	0.999799i	$0.506380\pi$
$54$		0			0
$55$	−15.3262			−2.06659
$56$	−0.427051	+	0.739674i	−0.0570671	+	0.0988431i
$57$		0			0
$58$	−1.80902	−	3.13331i	−0.237536	−	0.411424i
$59$	−2.73607	−	4.73901i	−0.356206	−	0.616966i	0.631118	−	0.775687i	$-0.282596\pi$
$59$	−2.73607	−	4.73901i	−0.356206	−	0.616966i	−0.987324	+	0.158721i	$0.949263\pi$
$60$		0			0
$61$	4.04508	−	7.00629i	0.517920	−	0.897064i	−0.481863	−	0.876246i	$-0.660040\pi$
$61$	4.04508	−	7.00629i	0.517920	−	0.897064i	0.999783	−	0.0208174i	$-0.00662687\pi$
$62$	5.14590			0.653530
$63$		0			0
$64$	−0.236068			−0.0295085
$65$	1.30902	−	2.26728i	0.162364	−	0.281222i
$66$		0			0
$67$	4.54508	+	7.87232i	0.555271	+	0.961757i	0.997882	+	0.0650435i	$0.0207186\pi$
$67$	4.54508	+	7.87232i	0.555271	+	0.961757i	−0.442612	+	0.896713i	$0.645948\pi$
$68$	−3.42705	−	5.93583i	−0.415591	−	0.719825i
$69$		0			0
$70$	0.309017	−	0.535233i	0.0369346	−	0.0639726i
$71$	−5.00000			−0.593391			−0.296695	−	0.954972i	$-0.595885\pi$
$71$	−5.00000			−0.593391			−0.296695	+	0.954972i	$0.595885\pi$
$72$		0			0
$73$	11.1803			1.30856			0.654280	−	0.756252i	$-0.272972\pi$
$73$	11.1803			1.30856			0.654280	+	0.756252i	$0.272972\pi$
$74$	1.88197	−	3.25966i	0.218774	−	0.378928i
$75$		0			0
$76$	−6.04508	−	10.4704i	−0.693419	−	1.20104i
$77$	−1.11803	−	1.93649i	−0.127412	−	0.220684i
$78$		0			0
$79$	−1.11803	+	1.93649i	−0.125789	+	0.217872i	−0.922041	−	0.387092i	$-0.873479\pi$
$79$	−1.11803	+	1.93649i	−0.125789	+	0.217872i	0.796252	+	0.604965i	$0.206813\pi$
$80$	4.85410			0.542705
$81$		0			0
$82$	4.09017			0.451684
$83$	−3.59017	+	6.21836i	−0.394072	+	0.682553i	−0.992982	−	0.118263i	$-0.962267\pi$
$83$	−3.59017	+	6.21836i	−0.394072	+	0.682553i	0.598910	+	0.800816i	$0.295601\pi$
$84$		0			0
$85$	5.54508	+	9.60437i	0.601449	+	1.04174i
$86$	3.16312	+	5.47868i	0.341088	+	0.590782i
$87$		0			0
$88$	−6.54508	+	11.3364i	−0.697708	+	1.20847i
$89$	0.381966			0.0404883			0.0202442	−	0.999795i	$-0.493556\pi$
$89$	0.381966			0.0404883			0.0202442	+	0.999795i	$0.493556\pi$
$90$		0			0
$91$	0.381966			0.0400409
$92$	−0.690983	+	1.19682i	−0.0720400	+	0.124777i
$93$		0			0
$94$	2.30902	+	3.99933i	0.238157	+	0.412500i
$95$	9.78115	+	16.9415i	1.00353	+	1.73816i
$96$		0			0
$97$	3.23607	−	5.60503i	0.328573	−	0.569105i	−0.653656	−	0.756792i	$-0.726766\pi$
$97$	3.23607	−	5.60503i	0.328573	−	0.569105i	0.982229	+	0.187687i	$0.0600990\pi$
$98$	−4.23607			−0.427907
$99$		0			0
$100$	−3.00000			−0.300000
$101$	2.11803	−	3.66854i	0.210752	−	0.365034i	−0.741198	−	0.671287i	$-0.765742\pi$
$101$	2.11803	−	3.66854i	0.210752	−	0.365034i	0.951950	+	0.306253i	$0.0990753\pi$
$102$		0			0
$103$	5.19098	+	8.99105i	0.511483	+	0.885914i	0.999911	+	0.0133103i	$0.00423692\pi$
$103$	5.19098	+	8.99105i	0.511483	+	0.885914i	−0.488429	+	0.872604i	$0.662430\pi$
$104$	−1.11803	−	1.93649i	−0.109632	−	0.189889i
$105$		0			0
$106$	0.0901699	−	0.156179i	0.00875808	−	0.0151694i
$107$	−3.38197			−0.326947			−0.163473	−	0.986548i	$-0.552270\pi$
$107$	−3.38197			−0.326947			−0.163473	+	0.986548i	$0.552270\pi$
$108$		0			0
$109$	0.763932			0.0731714			0.0365857	−	0.999331i	$-0.488352\pi$
$109$	0.763932			0.0731714			0.0365857	+	0.999331i	$0.488352\pi$
$110$	4.73607	−	8.20311i	0.451566	−	0.782136i
$111$		0			0
$112$	0.354102	+	0.613323i	0.0334595	+	0.0579535i
$113$	−8.94427	−	15.4919i	−0.841406	−	1.45736i	−0.888706	−	0.458478i	$-0.848395\pi$
$113$	−8.94427	−	15.4919i	−0.841406	−	1.45736i	0.0472996	−	0.998881i	$-0.484938\pi$
$114$		0			0
$115$	1.11803	−	1.93649i	0.104257	−	0.180579i
$116$	−9.47214			−0.879466
$117$		0			0
$118$	3.38197			0.311335
$119$	−0.809017	+	1.40126i	−0.0741625	+	0.128453i
$120$		0			0
$121$	−11.6353	−	20.1529i	−1.05775	−	1.83208i
$122$	2.50000	+	4.33013i	0.226339	+	0.392031i
$123$		0			0
$124$	6.73607	−	11.6672i	0.604917	−	1.04775i
$125$	−8.23607			−0.736656
$126$		0			0
$127$	12.6525			1.12273			0.561363	−	0.827570i	$-0.310277\pi$
$127$	12.6525			1.12273			0.561363	+	0.827570i	$0.310277\pi$
$128$	5.69098	−	9.85707i	0.503017	−	0.871250i
$129$		0			0
$130$	0.809017	+	1.40126i	0.0709555	+	0.122899i
$131$	−1.92705	−	3.33775i	−0.168367	−	0.291621i	0.769479	−	0.638672i	$-0.220516\pi$
$131$	−1.92705	−	3.33775i	−0.168367	−	0.291621i	−0.937846	+	0.347052i	$0.887183\pi$
$132$		0			0
$133$	−1.42705	+	2.47172i	−0.123741	+	0.214326i
$134$	−5.61803			−0.485324
$135$		0			0
$136$	9.47214			0.812229
$137$	−11.3090	+	19.5878i	−0.966195	+	1.67350i	−0.259824	+	0.965656i	$0.583664\pi$
$137$	−11.3090	+	19.5878i	−0.966195	+	1.67350i	−0.706371	+	0.707842i	$0.749669\pi$
$138$		0			0
$139$	−4.39919	−	7.61962i	−0.373134	−	0.646287i	0.616912	−	0.787032i	$-0.288384\pi$
$139$	−4.39919	−	7.61962i	−0.373134	−	0.646287i	−0.990046	+	0.140745i	$0.955050\pi$
$140$	−0.809017	−	1.40126i	−0.0683744	−	0.118428i
$141$		0			0
$142$	1.54508	−	2.67617i	0.129661	−	0.224579i
$143$	5.85410			0.489545
$144$		0			0
$145$	15.3262			1.27277
$146$	−3.45492	+	5.98409i	−0.285931	+	0.495247i
$147$		0			0
$148$	−4.92705	−	8.53390i	−0.405001	−	0.701482i
$149$	0.381966	+	0.661585i	0.0312919	+	0.0541991i	0.881247	−	0.472656i	$-0.156705\pi$
$149$	0.381966	+	0.661585i	0.0312919	+	0.0541991i	−0.849955	+	0.526855i	$0.823371\pi$
$150$		0			0
$151$	5.78115	−	10.0133i	0.470464	−	0.814867i	−0.528966	−	0.848643i	$-0.677420\pi$
$151$	5.78115	−	10.0133i	0.470464	−	0.814867i	0.999429	+	0.0337763i	$0.0107534\pi$
$152$	16.7082			1.35521
$153$		0			0
$154$	1.38197			0.111362
$155$	−10.8992	+	18.8779i	−0.875444	+	1.51631i
$156$		0			0
$157$	2.57295	+	4.45648i	0.205344	+	0.355666i	0.950242	−	0.311512i	$-0.100835\pi$
$157$	2.57295	+	4.45648i	0.205344	+	0.355666i	−0.744898	+	0.667178i	$0.767502\pi$
$158$	−0.690983	−	1.19682i	−0.0549717	−	0.0952137i
$159$		0			0
$160$	−7.35410	+	12.7377i	−0.581393	+	1.00700i
$161$	0.326238			0.0257112
$162$		0			0
$163$	−9.52786			−0.746280			−0.373140	−	0.927775i	$-0.621719\pi$
$163$	−9.52786			−0.746280			−0.373140	+	0.927775i	$0.621719\pi$
$164$	5.35410	−	9.27358i	0.418085	−	0.724145i
$165$		0			0
$166$	−2.21885	−	3.84316i	−0.172216	−	0.298287i
$167$	1.02786	+	1.78031i	0.0795385	+	0.137765i	0.903051	−	0.429534i	$-0.141322\pi$
$167$	1.02786	+	1.78031i	0.0795385	+	0.137765i	−0.823512	+	0.567298i	$0.807989\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−6.85410			−0.525686
$171$		0			0
$172$	16.5623			1.26286
$173$	−2.26393	+	3.92125i	−0.172124	+	0.298127i	−0.939162	−	0.343474i	$-0.888396\pi$
$173$	−2.26393	+	3.92125i	−0.172124	+	0.298127i	0.767039	+	0.641601i	$0.221730\pi$
$174$		0			0
$175$	0.354102	+	0.613323i	0.0267676	+	0.0463628i
$176$	5.42705	+	9.39993i	0.409079	+	0.708546i
$177$		0			0
$178$	−0.118034	+	0.204441i	−0.00884702	+	0.0153235i
$179$	7.90983			0.591208			0.295604	−	0.955310i	$-0.404479\pi$
$179$	7.90983			0.591208			0.295604	+	0.955310i	$0.404479\pi$
$180$		0			0
$181$	−18.1246			−1.34719			−0.673596	−	0.739100i	$-0.735251\pi$
$181$	−18.1246			−1.34719			−0.673596	+	0.739100i	$0.735251\pi$
$182$	−0.118034	+	0.204441i	−0.00874926	+	0.0151542i
$183$		0			0
$184$	−0.954915	−	1.65396i	−0.0703973	−	0.121932i
$185$	7.97214	+	13.8081i	0.586123	+	1.01519i
$186$		0			0
$187$	−12.3992	+	21.4760i	−0.906718	+	1.57048i
$188$	12.0902			0.881766
$189$		0			0
$190$	−12.0902			−0.877113
$191$	−1.19098	+	2.06284i	−0.0861765	+	0.149262i	−0.905892	−	0.423509i	$-0.860798\pi$
$191$	−1.19098	+	2.06284i	−0.0861765	+	0.149262i	0.819715	+	0.572771i	$0.194132\pi$
$192$		0			0
$193$	−0.0278640	−	0.0482619i	−0.00200570	−	0.00347397i	0.865021	−	0.501736i	$-0.167305\pi$
$193$	−0.0278640	−	0.0482619i	−0.00200570	−	0.00347397i	−0.867027	+	0.498262i	$0.833972\pi$
$194$	2.00000	+	3.46410i	0.143592	+	0.248708i
$195$		0			0
$196$	−5.54508	+	9.60437i	−0.396077	+	0.686026i
$197$	11.0000			0.783718			0.391859	−	0.920025i	$-0.371832\pi$
$197$	11.0000			0.783718			0.391859	+	0.920025i	$0.371832\pi$
$198$		0			0
$199$	−13.1803			−0.934330			−0.467165	−	0.884170i	$-0.654725\pi$
$199$	−13.1803			−0.934330			−0.467165	+	0.884170i	$0.654725\pi$
$200$	2.07295	−	3.59045i	0.146580	−	0.253883i
$201$		0			0
$202$	1.30902	+	2.26728i	0.0921021	+	0.159526i
$203$	1.11803	+	1.93649i	0.0784706	+	0.135915i
$204$		0			0
$205$	−8.66312	+	15.0050i	−0.605058	+	1.04799i
$206$	−6.41641			−0.447052
$207$		0			0
$208$	−1.85410			−0.128559
$209$	−21.8713	+	37.8822i	−1.51287	+	2.62037i
$210$		0			0
$211$	8.07295	+	13.9828i	0.555765	+	0.962613i	0.997844	+	0.0656366i	$0.0209078\pi$
$211$	8.07295	+	13.9828i	0.555765	+	0.962613i	−0.442079	+	0.896976i	$0.645759\pi$
$212$	−0.236068	−	0.408882i	−0.0162132	−	0.0280821i
$213$		0			0
$214$	1.04508	−	1.81014i	0.0714405	−	0.123739i
$215$	−26.7984			−1.82763
$216$		0			0
$217$	−3.18034			−0.215896
$218$	−0.236068	+	0.408882i	−0.0159885	+	0.0276930i
$219$		0			0
$220$	−12.3992	−	21.4760i	−0.835953	−	1.44791i
$221$	−2.11803	−	3.66854i	−0.142474	−	0.246773i
$222$		0			0
$223$	−9.56231	+	16.5624i	−0.640339	+	1.10910i	0.345018	+	0.938596i	$0.387873\pi$
$223$	−9.56231	+	16.5624i	−0.640339	+	1.10910i	−0.985357	+	0.170504i	$0.945460\pi$
$224$	−2.14590			−0.143379
$225$		0			0
$226$	11.0557			0.735416
$227$	6.32624	−	10.9574i	0.419887	−	0.727266i	−0.576041	−	0.817421i	$-0.695403\pi$
$227$	6.32624	−	10.9574i	0.419887	−	0.727266i	0.995928	+	0.0901552i	$0.0287363\pi$
$228$		0			0
$229$	−6.33688	−	10.9758i	−0.418753	−	0.725301i	0.577061	−	0.816701i	$-0.304199\pi$
$229$	−6.33688	−	10.9758i	−0.418753	−	0.725301i	−0.995814	+	0.0913995i	$0.970866\pi$
$230$	0.690983	+	1.19682i	0.0455621	+	0.0789158i
$231$		0			0
$232$	6.54508	−	11.3364i	0.429706	−	0.744272i
$233$	25.9787			1.70192			0.850961	−	0.525229i	$-0.176020\pi$
$233$	25.9787			1.70192			0.850961	+	0.525229i	$0.176020\pi$
$234$		0			0
$235$	−19.5623			−1.27610
$236$	4.42705	−	7.66788i	0.288176	−	0.499136i
$237$		0			0
$238$	−0.500000	−	0.866025i	−0.0324102	−	0.0561361i
$239$	11.2812	+	19.5395i	0.729717	+	1.26391i	0.957003	+	0.290079i	$0.0936816\pi$
$239$	11.2812	+	19.5395i	0.729717	+	1.26391i	−0.227286	+	0.973828i	$0.572985\pi$
$240$		0			0
$241$	5.39919	−	9.35167i	0.347792	−	0.602394i	−0.638065	−	0.769983i	$-0.720265\pi$
$241$	5.39919	−	9.35167i	0.347792	−	0.602394i	0.985857	+	0.167589i	$0.0535981\pi$
$242$	14.3820			0.924508
$243$		0			0
$244$	13.0902			0.838012
$245$	8.97214	−	15.5402i	0.573209	−	0.992827i
$246$		0			0
$247$	−3.73607	−	6.47106i	−0.237720	−	0.411744i
$248$	9.30902	+	16.1237i	0.591123	+	1.02386i
$249$		0			0
$250$	2.54508	−	4.40822i	0.160965	−	0.278800i
$251$	4.85410			0.306388			0.153194	−	0.988196i	$-0.451044\pi$
$251$	4.85410			0.306388			0.153194	+	0.988196i	$0.451044\pi$
$252$		0			0
$253$	5.00000			0.314347
$254$	−3.90983	+	6.77202i	−0.245325	+	0.424915i
$255$		0			0
$256$	3.28115	+	5.68312i	0.205072	+	0.355195i
$257$	13.1074	+	22.7027i	0.817617	+	1.41615i	0.907434	+	0.420195i	$0.138038\pi$
$257$	13.1074	+	22.7027i	0.817617	+	1.41615i	−0.0898172	+	0.995958i	$0.528628\pi$
$258$		0			0
$259$	−1.16312	+	2.01458i	−0.0722727	+	0.125180i
$260$	4.23607			0.262710
$261$		0			0
$262$	2.38197			0.147158
$263$	−6.57295	+	11.3847i	−0.405305	+	0.702010i	−0.994357	−	0.106086i	$-0.966168\pi$
$263$	−6.57295	+	11.3847i	−0.405305	+	0.702010i	0.589052	+	0.808095i	$0.299501\pi$
$264$		0			0
$265$	0.381966	+	0.661585i	0.0234640	+	0.0406408i
$266$	−0.881966	−	1.52761i	−0.0540768	−	0.0936638i
$267$		0			0
$268$	−7.35410	+	12.7377i	−0.449223	+	0.778078i
$269$	−20.5623			−1.25371			−0.626853	−	0.779138i	$-0.715657\pi$
$269$	−20.5623			−1.25371			−0.626853	+	0.779138i	$0.715657\pi$
$270$		0			0
$271$	27.9443			1.69749			0.848747	−	0.528799i	$-0.177358\pi$
$271$	27.9443			1.69749			0.848747	+	0.528799i	$0.177358\pi$
$272$	3.92705	−	6.80185i	0.238112	−	0.412423i
$273$		0			0
$274$	−6.98936	−	12.1059i	−0.422242	−	0.731345i
$275$	5.42705	+	9.39993i	0.327263	+	0.566837i
$276$		0			0
$277$	8.85410	−	15.3358i	0.531991	−	0.921436i	−0.467311	−	0.884093i	$-0.654777\pi$
$277$	8.85410	−	15.3358i	0.531991	−	0.921436i	0.999302	−	0.0373432i	$-0.0118895\pi$
$278$	5.43769			0.326131
$279$		0			0
$280$	2.23607			0.133631
$281$	−11.8090	+	20.4538i	−0.704467	+	1.22017i	0.262417	+	0.964955i	$0.415481\pi$
$281$	−11.8090	+	20.4538i	−0.704467	+	1.22017i	−0.966884	+	0.255218i	$0.917853\pi$
$282$		0			0
$283$	0.708204	+	1.22665i	0.0420984	+	0.0729165i	0.886307	−	0.463098i	$-0.153262\pi$
$283$	0.708204	+	1.22665i	0.0420984	+	0.0729165i	−0.844208	+	0.536015i	$0.819929\pi$
$284$	−4.04508	−	7.00629i	−0.240032	−	0.415747i
$285$		0			0
$286$	−1.80902	+	3.13331i	−0.106969	+	0.185276i
$287$	−2.52786			−0.149215
$288$		0			0
$289$	0.944272			0.0555454
$290$	−4.73607	+	8.20311i	−0.278111	+	0.481703i
$291$		0			0
$292$	9.04508	+	15.6665i	0.529324	+	0.916815i
$293$	3.32624	+	5.76121i	0.194321	+	0.336574i	0.946678	−	0.322182i	$-0.104416\pi$
$293$	3.32624	+	5.76121i	0.194321	+	0.336574i	−0.752357	+	0.658756i	$0.771083\pi$
$294$		0			0
$295$	−7.16312	+	12.4069i	−0.417053	+	0.722357i
$296$	13.6180			0.791532
$297$		0			0
$298$	−0.472136			−0.0273501
$299$	−0.427051	+	0.739674i	−0.0246970	+	0.0427765i
$300$		0			0
$301$	−1.95492	−	3.38601i	−0.112679	−	0.195166i
$302$	3.57295	+	6.18853i	0.205600	+	0.356110i
$303$		0			0
$304$	6.92705	−	11.9980i	0.397294	−	0.688133i
$305$	−21.1803			−1.21278
$306$		0			0
$307$	6.94427			0.396331			0.198165	−	0.980169i	$-0.436502\pi$
$307$	6.94427			0.396331			0.198165	+	0.980169i	$0.436502\pi$
$308$	1.80902	−	3.13331i	0.103078	−	0.178537i
$309$		0			0
$310$	−6.73607	−	11.6672i	−0.382583	−	0.662653i
$311$	−7.25329	−	12.5631i	−0.411296	−	0.712386i	0.583735	−	0.811944i	$-0.301591\pi$
$311$	−7.25329	−	12.5631i	−0.411296	−	0.712386i	−0.995032	+	0.0995578i	$0.968257\pi$
$312$		0			0
$313$	10.5000	−	18.1865i	0.593495	−	1.02796i	−0.400262	−	0.916401i	$-0.631081\pi$
$313$	10.5000	−	18.1865i	0.593495	−	1.02796i	0.993757	−	0.111563i	$-0.0355857\pi$
$314$	−3.18034			−0.179477
$315$		0			0
$316$	−3.61803			−0.203530
$317$	6.92705	−	11.9980i	0.389062	−	0.673875i	−0.603262	−	0.797543i	$-0.706133\pi$
$317$	6.92705	−	11.9980i	0.389062	−	0.673875i	0.992324	+	0.123668i	$0.0394659\pi$
$318$		0			0
$319$	17.1353	+	29.6791i	0.959390	+	1.66171i
$320$	0.309017	+	0.535233i	0.0172746	+	0.0299204i
$321$		0			0
$322$	−0.100813	+	0.174613i	−0.00561809	+	0.00973082i
$323$	31.6525			1.76119
$324$		0			0
$325$	−1.85410			−0.102847
$326$	2.94427	−	5.09963i	0.163068	−	0.282442i
$327$		0			0
$328$	7.39919	+	12.8158i	0.408552	+	0.707632i
$329$	−1.42705	−	2.47172i	−0.0786759	−	0.136271i
$330$		0			0
$331$	1.88197	−	3.25966i	0.103442	−	0.179167i	−0.809658	−	0.586901i	$-0.800348\pi$
$331$	1.88197	−	3.25966i	0.103442	−	0.179167i	0.913101	+	0.407734i	$0.133681\pi$
$332$	−11.6180			−0.637622
$333$		0			0
$334$	−1.27051			−0.0695192
$335$	11.8992	−	20.6100i	0.650122	−	1.12604i
$336$		0			0
$337$	−4.59017	−	7.95041i	−0.250042	−	0.433086i	0.713495	−	0.700661i	$-0.247111\pi$
$337$	−4.59017	−	7.95041i	−0.250042	−	0.433086i	−0.963537	+	0.267574i	$0.913778\pi$
$338$	−0.309017	−	0.535233i	−0.0168083	−	0.0291128i
$339$		0			0
$340$	−8.97214	+	15.5402i	−0.486582	+	0.842785i
$341$	−48.7426			−2.63956
$342$		0			0
$343$	5.29180			0.285730
$344$	−11.4443	+	19.8221i	−0.617034	+	1.06873i
$345$		0			0
$346$	−1.39919	−	2.42346i	−0.0752208	−	0.130286i
$347$	10.9443	+	18.9560i	0.587519	+	1.01761i	0.994556	+	0.104202i	$0.0332287\pi$
$347$	10.9443	+	18.9560i	0.587519	+	1.01761i	−0.407037	+	0.913412i	$0.633438\pi$
$348$		0			0
$349$	−17.5451	+	30.3890i	−0.939167	+	1.62668i	−0.172137	+	0.985073i	$0.555067\pi$
$349$	−17.5451	+	30.3890i	−0.939167	+	1.62668i	−0.767030	+	0.641612i	$0.778266\pi$
$350$	−0.437694			−0.0233957
$351$		0			0
$352$	−32.8885			−1.75297
$353$	16.2082	−	28.0734i	0.862676	−	1.49420i	−0.00666108	−	0.999978i	$-0.502120\pi$
$353$	16.2082	−	28.0734i	0.862676	−	1.49420i	0.869337	−	0.494220i	$-0.164546\pi$
$354$		0			0
$355$	6.54508	+	11.3364i	0.347377	+	0.601675i
$356$	0.309017	+	0.535233i	0.0163779	+	0.0283673i
$357$		0			0
$358$	−2.44427	+	4.23360i	−0.129184	+	0.223753i
$359$	−6.27051			−0.330945			−0.165472	−	0.986214i	$-0.552915\pi$
$359$	−6.27051			−0.330945			−0.165472	+	0.986214i	$0.552915\pi$
$360$		0			0
$361$	36.8328			1.93857
$362$	5.60081	−	9.70089i	0.294372	−	0.509868i
$363$		0			0
$364$	0.309017	+	0.535233i	0.0161969	+	0.0280538i
$365$	−14.6353	−	25.3490i	−0.766044	−	1.32683i
$366$		0			0
$367$	15.3541	−	26.5941i	0.801478	−	1.38820i	−0.117166	−	0.993112i	$-0.537381\pi$
$367$	15.3541	−	26.5941i	0.801478	−	1.38820i	0.918643	−	0.395088i	$-0.129286\pi$
$368$	−1.58359			−0.0825504
$369$		0			0
$370$	−9.85410			−0.512290
$371$	−0.0557281	+	0.0965239i	−0.00289326	+	0.00501127i
$372$		0			0
$373$	−6.28115	−	10.8793i	−0.325226	−	0.563308i	0.656332	−	0.754472i	$-0.272107\pi$
$373$	−6.28115	−	10.8793i	−0.325226	−	0.563308i	−0.981558	+	0.191164i	$0.938774\pi$
$374$	−7.66312	−	13.2729i	−0.396250	−	0.686326i
$375$		0			0
$376$	−8.35410	+	14.4697i	−0.430830	+	0.746219i
$377$	−5.85410			−0.301502
$378$		0			0
$379$	−17.0000			−0.873231			−0.436616	−	0.899648i	$-0.643823\pi$
$379$	−17.0000			−0.873231			−0.436616	+	0.899648i	$0.643823\pi$
$380$	−15.8262	+	27.4118i	−0.811869	+	1.40620i
$381$		0			0
$382$	−0.736068	−	1.27491i	−0.0376605	−	0.0652299i
$383$	8.50000	+	14.7224i	0.434330	+	0.752281i	0.997241	−	0.0742364i	$-0.0236519\pi$
$383$	8.50000	+	14.7224i	0.434330	+	0.752281i	−0.562911	+	0.826518i	$0.690319\pi$
$384$		0			0
$385$	−2.92705	+	5.06980i	−0.149176	+	0.258381i
$386$	0.0344419			0.00175304
$387$		0			0
$388$	10.4721			0.531642
$389$	1.57295	−	2.72443i	0.0797517	−	0.138134i	−0.823391	−	0.567474i	$-0.807921\pi$
$389$	1.57295	−	2.72443i	0.0797517	−	0.138134i	0.903143	+	0.429340i	$0.141254\pi$
$390$		0			0
$391$	−1.80902	−	3.13331i	−0.0914859	−	0.158458i
$392$	−7.66312	−	13.2729i	−0.387046	−	0.670383i
$393$		0			0
$394$	−3.39919	+	5.88756i	−0.171249	+	0.296611i
$395$	5.85410			0.294552
$396$		0			0
$397$	−9.29180			−0.466342			−0.233171	−	0.972436i	$-0.574910\pi$
$397$	−9.29180			−0.466342			−0.233171	+	0.972436i	$0.574910\pi$
$398$	4.07295	−	7.05455i	0.204158	−	0.353613i
$399$		0			0
$400$	−1.71885	−	2.97713i	−0.0859424	−	0.148857i
$401$	−3.02786	−	5.24441i	−0.151204	−	0.261894i	0.780466	−	0.625198i	$-0.214982\pi$
$401$	−3.02786	−	5.24441i	−0.151204	−	0.261894i	−0.931670	+	0.363304i	$0.881648\pi$
$402$		0			0
$403$	4.16312	−	7.21073i	0.207380	−	0.359192i
$404$	6.85410			0.341004
$405$		0			0
$406$	−1.38197			−0.0685858
$407$	−17.8262	+	30.8759i	−0.883614	+	1.53046i
$408$		0			0
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	0.826555	−	0.562856i	$-0.190297\pi$
$409$	−1.50000	−	2.59808i	−0.0741702	−	0.128467i	−0.900725	+	0.434389i	$0.856964\pi$
$410$	−5.35410	−	9.27358i	−0.264420	−	0.457989i
$411$		0			0
$412$	−8.39919	+	14.5478i	−0.413798	+	0.716720i
$413$	−2.09017			−0.102851
$414$		0			0
$415$	18.7984			0.922776
$416$	2.80902	−	4.86536i	0.137723	−	0.238544i
$417$		0			0
$418$	−13.5172	−	23.4125i	−0.661149	−	1.14514i
$419$	−0.236068	−	0.408882i	−0.0115327	−	0.0199752i	0.860201	−	0.509954i	$-0.170338\pi$
$419$	−0.236068	−	0.408882i	−0.0115327	−	0.0199752i	−0.871734	+	0.489979i	$0.837004\pi$
$420$		0			0
$421$	−12.2361	+	21.1935i	−0.596349	+	1.03291i	0.397005	+	0.917816i	$0.370049\pi$
$421$	−12.2361	+	21.1935i	−0.596349	+	1.03291i	−0.993355	+	0.115091i	$0.963284\pi$
$422$	−9.97871			−0.485756
$423$		0			0
$424$	0.652476			0.0316870
$425$	3.92705	−	6.80185i	0.190490	−	0.329938i
$426$		0			0
$427$	−1.54508	−	2.67617i	−0.0747719	−	0.129509i
$428$	−2.73607	−	4.73901i	−0.132253	−	0.229069i
$429$		0			0
$430$	8.28115	−	14.3434i	0.399353	−	0.691699i
$431$	27.2361			1.31192			0.655958	−	0.754798i	$-0.272265\pi$
$431$	27.2361			1.31192			0.655958	+	0.754798i	$0.272265\pi$
$432$		0			0
$433$	7.94427			0.381777			0.190889	−	0.981612i	$-0.438863\pi$
$433$	7.94427			0.381777			0.190889	+	0.981612i	$0.438863\pi$
$434$	0.982779	−	1.70222i	0.0471749	−	0.0817093i
$435$		0			0
$436$	0.618034	+	1.07047i	0.0295985	+	0.0512660i
$437$	−3.19098	−	5.52694i	−0.152645	−	0.264390i
$438$		0			0
$439$	16.7705	−	29.0474i	0.800413	−	1.38636i	−0.118932	−	0.992902i	$-0.537947\pi$
$439$	16.7705	−	29.0474i	0.800413	−	1.38636i	0.919345	−	0.393453i	$-0.128720\pi$
$440$	34.2705			1.63378
$441$		0			0
$442$	2.61803			0.124527
$443$	−13.9164	+	24.1039i	−0.661188	+	1.14521i	0.319115	+	0.947716i	$0.396614\pi$
$443$	−13.9164	+	24.1039i	−0.661188	+	1.14521i	−0.980304	+	0.197496i	$0.936719\pi$
$444$		0			0
$445$	−0.500000	−	0.866025i	−0.0237023	−	0.0410535i
$446$	−5.90983	−	10.2361i	−0.279839	−	0.484695i
$447$		0			0
$448$	−0.0450850	+	0.0780895i	−0.00213006	+	0.00368938i
$449$	−28.5279			−1.34631			−0.673157	−	0.739500i	$-0.735062\pi$
$449$	−28.5279			−1.34631			−0.673157	+	0.739500i	$0.735062\pi$
$450$		0			0
$451$	−38.7426			−1.82432
$452$	14.4721	−	25.0665i	0.680712	−	1.17903i
$453$		0			0
$454$	3.90983	+	6.77202i	0.183497	+	0.317827i
$455$	−0.500000	−	0.866025i	−0.0234404	−	0.0405999i
$456$		0			0
$457$	13.3262	−	23.0817i	0.623375	−	1.07972i	−0.365478	−	0.930820i	$-0.619094\pi$
$457$	13.3262	−	23.0817i	0.623375	−	1.07972i	0.988853	−	0.148897i	$-0.0475724\pi$
$458$	7.83282			0.366003
$459$		0			0
$460$	3.61803			0.168692
$461$	4.40983	−	7.63805i	0.205386	−	0.355739i	−0.744869	−	0.667210i	$-0.767488\pi$
$461$	4.40983	−	7.63805i	0.205386	−	0.355739i	0.950256	+	0.311471i	$0.100822\pi$
$462$		0			0
$463$	15.4164	+	26.7020i	0.716461	+	1.24095i	0.962393	+	0.271660i	$0.0875727\pi$
$463$	15.4164	+	26.7020i	0.716461	+	1.24095i	−0.245932	+	0.969287i	$0.579094\pi$
$464$	−5.42705	−	9.39993i	−0.251945	−	0.436381i
$465$		0			0
$466$	−8.02786	+	13.9047i	−0.371884	+	0.644121i
$467$	6.58359			0.304652			0.152326	−	0.988330i	$-0.451324\pi$
$467$	6.58359			0.304652			0.152326	+	0.988330i	$0.451324\pi$
$468$		0			0
$469$	3.47214			0.160328
$470$	6.04508	−	10.4704i	0.278839	−	0.482963i
$471$		0			0
$472$	6.11803	+	10.5967i	0.281605	+	0.487755i
$473$	−29.9615	−	51.8948i	−1.37763	−	2.38613i
$474$		0			0
$475$	6.92705	−	11.9980i	0.317835	−	0.550506i
$476$	−2.61803			−0.119997
$477$		0			0
$478$	−13.9443			−0.637796
$479$	4.38197	−	7.58979i	0.200217	−	0.346786i	−0.748381	−	0.663269i	$-0.769169\pi$
$479$	4.38197	−	7.58979i	0.200217	−	0.346786i	0.948598	+	0.316483i	$0.102502\pi$
$480$		0			0
$481$	−3.04508	−	5.27424i	−0.138844	−	0.240485i
$482$	3.33688	+	5.77965i	0.151991	+	0.263256i
$483$		0			0
$484$	18.8262	−	32.6080i	0.855738	−	1.48218i
$485$	−16.9443			−0.769400
$486$		0			0
$487$	−8.34752			−0.378262			−0.189131	−	0.981952i	$-0.560567\pi$
$487$	−8.34752			−0.378262			−0.189131	+	0.981952i	$0.560567\pi$
$488$	−9.04508	+	15.6665i	−0.409452	+	0.709191i
$489$		0			0
$490$	5.54508	+	9.60437i	0.250501	+	0.433881i
$491$	−20.1631	−	34.9235i	−0.909949	−	1.57608i	−0.814133	−	0.580679i	$-0.802787\pi$
$491$	−20.1631	−	34.9235i	−0.909949	−	1.57608i	−0.0958159	−	0.995399i	$-0.530546\pi$
$492$		0			0
$493$	12.3992	−	21.4760i	0.558431	−	0.967231i
$494$	4.61803			0.207775
$495$		0			0
$496$	15.4377			0.693173
$497$	−0.954915	+	1.65396i	−0.0428338	+	0.0741903i
$498$		0			0
$499$	−9.89919	−	17.1459i	−0.443148	−	0.767556i	0.554773	−	0.832002i	$-0.312805\pi$
$499$	−9.89919	−	17.1459i	−0.443148	−	0.767556i	−0.997921	+	0.0644463i	$0.979472\pi$
$500$	−6.66312	−	11.5409i	−0.297984	−	0.516123i
$501$		0			0
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	20.3262			0.906302			0.453151	−	0.891434i	$-0.350300\pi$
$503$	20.3262			0.906302			0.453151	+	0.891434i	$0.350300\pi$
$504$		0			0
$505$	−11.0902			−0.493506
$506$	−1.54508	+	2.67617i	−0.0686874	+	0.118970i
$507$		0			0
$508$	10.2361	+	17.7294i	0.454152	+	0.786614i
$509$	8.51722	+	14.7523i	0.377519	+	0.653882i	0.990701	−	0.136060i	$-0.0434439\pi$
$509$	8.51722	+	14.7523i	0.377519	+	0.653882i	−0.613181	+	0.789942i	$0.710111\pi$
$510$		0			0
$511$	2.13525	−	3.69837i	0.0944581	−	0.163606i
$512$	18.7082			0.826794
$513$		0			0
$514$	−16.2016			−0.714623
$515$	13.5902	−	23.5389i	0.598854	−	1.03725i
$516$		0			0
$517$	−21.8713	−	37.8822i	−0.961900	−	1.66606i
$518$	−0.718847	−	1.24508i	−0.0315843	−	0.0547057i
$519$		0			0
$520$	−2.92705	+	5.06980i	−0.128360	+	0.222325i
$521$	−38.7639			−1.69828			−0.849139	−	0.528169i	$-0.822879\pi$
$521$	−38.7639			−1.69828			−0.849139	+	0.528169i	$0.822879\pi$
$522$		0			0
$523$	−38.4721			−1.68227			−0.841135	−	0.540826i	$-0.818112\pi$
$523$	−38.4721			−1.68227			−0.841135	+	0.540826i	$0.818112\pi$
$524$	3.11803	−	5.40059i	0.136212	−	0.235926i
$525$		0			0
$526$	−4.06231	−	7.03612i	−0.177125	−	0.306789i
$527$	17.6353	+	30.5452i	0.768204	+	1.33057i
$528$		0			0
$529$	11.1353	−	19.2868i	0.484142	−	0.838558i
$530$	−0.472136			−0.0205083
$531$		0			0
$532$	−4.61803			−0.200217
$533$	3.30902	−	5.73139i	0.143329	−	0.248254i
$534$		0			0
$535$	4.42705	+	7.66788i	0.191398	+	0.331511i
$536$	−10.1631	−	17.6030i	−0.438980	−	0.760335i
$537$		0			0
$538$	6.35410	−	11.0056i	0.273945	−	0.474486i
$539$	40.1246			1.72829
$540$		0			0
$541$	33.1246			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$541$	33.1246			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$542$	−8.63525	+	14.9567i	−0.370916	+	0.642445i
$543$		0			0
$544$	11.8992	+	20.6100i	0.510173	+	0.883646i
$545$	−1.00000	−	1.73205i	−0.0428353	−	0.0741929i
$546$		0			0
$547$	14.6180	−	25.3192i	0.625022	−	1.08257i	−0.363515	−	0.931588i	$-0.618423\pi$
$547$	14.6180	−	25.3192i	0.625022	−	1.08257i	0.988537	−	0.150981i	$-0.0482433\pi$
$548$	−36.5967			−1.56334
$549$		0			0
$550$	−6.70820			−0.286039
$551$	21.8713	−	37.8822i	0.931750	−	1.61384i
$552$		0			0
$553$	0.427051	+	0.739674i	0.0181601	+	0.0314541i
$554$	5.47214	+	9.47802i	0.232489	+	0.402682i
$555$		0			0
$556$	7.11803	−	12.3288i	0.301872	−	0.522857i
$557$	17.6180			0.746500			0.373250	−	0.927731i	$-0.378243\pi$
$557$	17.6180			0.746500			0.373250	+	0.927731i	$0.378243\pi$
$558$		0			0
$559$	10.2361			0.432940
$560$	0.927051	−	1.60570i	0.0391751	−	0.0678532i
$561$		0			0
$562$	−7.29837	−	12.6412i	−0.307863	−	0.533235i
$563$	−11.4164	−	19.7738i	−0.481144	−	0.833366i	0.518622	−	0.855004i	$-0.326445\pi$
$563$	−11.4164	−	19.7738i	−0.481144	−	0.833366i	−0.999766	+	0.0216376i	$0.993112\pi$
$564$		0			0
$565$	−23.4164	+	40.5584i	−0.985136	+	1.70631i
$566$	−0.875388			−0.0367953
$567$		0			0
$568$	11.1803			0.469117
$569$	23.1353	−	40.0714i	0.969880	−	1.67988i	0.273992	−	0.961732i	$-0.411656\pi$
$569$	23.1353	−	40.0714i	0.969880	−	1.67988i	0.695888	−	0.718150i	$-0.255011\pi$
$570$		0			0
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	0.913584	−	0.406651i	$-0.133303\pi$
$571$	2.50000	+	4.33013i	0.104622	+	0.181210i	−0.808962	+	0.587861i	$0.799970\pi$
$572$	4.73607	+	8.20311i	0.198025	+	0.342989i
$573$		0			0
$574$	0.781153	−	1.35300i	0.0326047	−	0.0564730i
$575$	−1.58359			−0.0660404
$576$		0			0
$577$	−31.5410			−1.31307			−0.656535	−	0.754296i	$-0.727979\pi$
$577$	−31.5410			−1.31307			−0.656535	+	0.754296i	$0.727979\pi$
$578$	−0.291796	+	0.505406i	−0.0121371	+	0.0210221i
$579$		0			0
$580$	12.3992	+	21.4760i	0.514848	+	0.891743i
$581$	1.37132	+	2.37520i	0.0568921	+	0.0985399i
$582$		0			0
$583$	−0.854102	+	1.47935i	−0.0353733	+	0.0612683i
$584$	−25.0000			−1.03451
$585$		0			0
$586$	−4.11146			−0.169843
$587$	12.5729	−	21.7770i	0.518941	−	0.898832i	−0.480817	−	0.876821i	$-0.659660\pi$
$587$	12.5729	−	21.7770i	0.518941	−	0.898832i	0.999758	−	0.0220112i	$-0.00700696\pi$
$588$		0			0
$589$	31.1074	+	53.8796i	1.28176	+	2.22007i
$590$	−4.42705	−	7.66788i	−0.182259	−	0.315682i
$591$		0			0
$592$	5.64590	−	9.77898i	0.232045	−	0.401914i
$593$	10.8541			0.445725			0.222862	−	0.974850i	$-0.428460\pi$
$593$	10.8541			0.445725			0.222862	+	0.974850i	$0.428460\pi$
$594$		0			0
$595$	4.23607			0.173662
$596$	−0.618034	+	1.07047i	−0.0253157	+	0.0438480i
$597$		0			0
$598$	−0.263932	−	0.457144i	−0.0107930	−	0.0186940i
$599$	16.8262	+	29.1439i	0.687501	+	1.19079i	0.972644	+	0.232302i	$0.0746258\pi$
$599$	16.8262	+	29.1439i	0.687501	+	1.19079i	−0.285142	+	0.958485i	$0.592041\pi$
$600$		0			0
$601$	−9.09017	+	15.7446i	−0.370796	+	0.642237i	−0.989688	−	0.143239i	$-0.954248\pi$
$601$	−9.09017	+	15.7446i	−0.370796	+	0.642237i	0.618892	+	0.785476i	$0.287582\pi$
$602$	2.41641			0.0984854
$603$		0			0
$604$	18.7082			0.761226
$605$	−30.4615	+	52.7609i	−1.23844	+	2.14503i
$606$		0			0
$607$	−2.28115	−	3.95107i	−0.0925891	−	0.160369i	0.816011	−	0.578037i	$-0.196181\pi$
$607$	−2.28115	−	3.95107i	−0.0925891	−	0.160369i	−0.908600	+	0.417668i	$0.862848\pi$
$608$	20.9894	+	36.3546i	0.851231	+	1.47438i
$609$		0			0
$610$	6.54508	−	11.3364i	0.265003	−	0.458998i
$611$	7.47214			0.302290
$612$		0			0
$613$	7.74265			0.312723			0.156361	−	0.987700i	$-0.450024\pi$
$613$	7.74265			0.312723			0.156361	+	0.987700i	$0.450024\pi$
$614$	−2.14590	+	3.71680i	−0.0866014	+	0.149998i
$615$		0			0
$616$	2.50000	+	4.33013i	0.100728	+	0.174466i
$617$	−8.66312	−	15.0050i	−0.348764	−	0.604077i	0.637266	−	0.770644i	$-0.280065\pi$
$617$	−8.66312	−	15.0050i	−0.348764	−	0.604077i	−0.986030	+	0.166567i	$0.946732\pi$
$618$		0			0
$619$	1.76393	−	3.05522i	0.0708984	−	0.122800i	−0.828397	−	0.560142i	$-0.810747\pi$
$619$	1.76393	−	3.05522i	0.0708984	−	0.122800i	0.899295	+	0.437342i	$0.144080\pi$
$620$	−35.2705			−1.41650
$621$		0			0
$622$	8.96556			0.359486
$623$	0.0729490	−	0.126351i	0.00292264	−	0.00506216i
$624$		0			0
$625$	15.4164	+	26.7020i	0.616656	+	1.06808i
$626$	6.48936	+	11.2399i	0.259367	+	0.449237i
$627$		0			0
$628$	−4.16312	+	7.21073i	−0.166127	+	0.287740i
$629$	25.7984			1.02865
$630$		0			0
$631$	0.381966			0.0152058			0.00760291	−	0.999971i	$-0.497580\pi$
$631$	0.381966			0.0152058			0.00760291	+	0.999971i	$0.497580\pi$
$632$	2.50000	−	4.33013i	0.0994447	−	0.172243i
$633$		0			0
$634$	4.28115	+	7.41517i	0.170026	+	0.294494i
$635$	−16.5623	−	28.6868i	−0.657255	−	1.13840i
$636$		0			0
$637$	−3.42705	+	5.93583i	−0.135785	+	0.235186i
$638$	−21.1803			−0.838538
$639$		0			0
$640$	−29.7984			−1.17788
$641$	9.37132	−	16.2316i	0.370145	−	0.641110i	−0.619443	−	0.785042i	$-0.712641\pi$
$641$	9.37132	−	16.2316i	0.370145	−	0.641110i	0.989588	+	0.143932i	$0.0459747\pi$
$642$		0			0
$643$	2.54508	+	4.40822i	0.100368	+	0.173843i	0.911836	−	0.410554i	$-0.134665\pi$
$643$	2.54508	+	4.40822i	0.100368	+	0.173843i	−0.811468	+	0.584397i	$0.801331\pi$
$644$	0.263932	+	0.457144i	0.0104004	+	0.0180140i
$645$		0			0
$646$	−9.78115	+	16.9415i	−0.384834	+	0.666553i
$647$	23.6738			0.930712			0.465356	−	0.885124i	$-0.345926\pi$
$647$	23.6738			0.930712			0.465356	+	0.885124i	$0.345926\pi$
$648$		0			0
$649$	−32.0344			−1.25746
$650$	0.572949	−	0.992377i	0.0224729	−	0.0389242i
$651$		0			0
$652$	−7.70820	−	13.3510i	−0.301877	−	0.522866i
$653$	2.54508	+	4.40822i	0.0995969	+	0.172507i	0.911518	−	0.411261i	$-0.134911\pi$
$653$	2.54508	+	4.40822i	0.0995969	+	0.172507i	−0.811921	+	0.583767i	$0.801578\pi$
$654$		0			0
$655$	−5.04508	+	8.73834i	−0.197128	+	0.341435i
$656$	12.2705			0.479083
$657$		0			0
$658$	1.76393			0.0687652
$659$	12.5451	−	21.7287i	0.488687	−	0.846431i	−0.511228	−	0.859445i	$-0.670809\pi$
$659$	12.5451	−	21.7287i	0.488687	−	0.846431i	0.999915	+	0.0130141i	$0.00414263\pi$
$660$		0			0
$661$	−10.8541	−	18.7999i	−0.422176	−	0.731230i	0.573976	−	0.818872i	$-0.305400\pi$
$661$	−10.8541	−	18.7999i	−0.422176	−	0.731230i	−0.996152	+	0.0876422i	$0.972067\pi$
$662$	1.16312	+	2.01458i	0.0452059	+	0.0782989i
$663$		0			0
$664$	8.02786	−	13.9047i	0.311542	−	0.539606i
$665$	7.47214			0.289757
$666$		0			0
$667$	−5.00000			−0.193601
$668$	−1.66312	+	2.88061i	−0.0643480	+	0.111454i
$669$		0			0
$670$	7.35410	+	12.7377i	0.284114	+	0.492099i
$671$	−23.6803	−	41.0156i	−0.914169	−	1.58339i
$672$		0			0
$673$	−24.6803	+	42.7476i	−0.951357	+	1.64780i	−0.208865	+	0.977945i	$0.566977\pi$
$673$	−24.6803	+	42.7476i	−0.951357	+	1.64780i	−0.742492	+	0.669854i	$0.766356\pi$
$674$	5.67376			0.218545
$675$		0			0
$676$	−1.61803			−0.0622321
$677$	22.8156	−	39.5178i	0.876875	−	1.51879i	0.0221221	−	0.999755i	$-0.492958\pi$
$677$	22.8156	−	39.5178i	0.876875	−	1.51879i	0.854752	−	0.519036i	$-0.173709\pi$
$678$		0			0
$679$	−1.23607	−	2.14093i	−0.0474359	−	0.0821615i
$680$	−12.3992	−	21.4760i	−0.475487	−	0.823568i
$681$		0			0
$682$	15.0623	−	26.0887i	0.576766	−	0.998987i
$683$	−45.6869			−1.74816			−0.874081	−	0.485781i	$-0.838535\pi$
$683$	−45.6869			−1.74816			−0.874081	+	0.485781i	$0.838535\pi$
$684$		0			0
$685$	59.2148			2.26248
$686$	−1.63525	+	2.83234i	−0.0624343	+	0.108139i
$687$		0			0
$688$	9.48936	+	16.4360i	0.361778	+	0.626618i
$689$	−0.145898	−	0.252703i	−0.00555827	−	0.00962721i
$690$		0			0
$691$	4.16312	−	7.21073i	0.158373	−	0.274309i	−0.775909	−	0.630844i	$-0.782709\pi$
$691$	4.16312	−	7.21073i	0.158373	−	0.274309i	0.934282	+	0.356535i	$0.116042\pi$
$692$	−7.32624			−0.278502
$693$		0			0
$694$	−13.5279			−0.513511
$695$	−11.5172	+	19.9484i	−0.436873	+	0.756686i
$696$		0			0
$697$	14.0172	+	24.2785i	0.530940	+	0.919615i
$698$	−10.8435	−	18.7814i	−0.410431	−	0.710887i
$699$		0			0
$700$	−0.572949	+	0.992377i	−0.0216554	+	0.0375083i
$701$	−43.9787			−1.66105			−0.830527	−	0.556979i	$-0.811960\pi$
$701$	−43.9787			−1.66105			−0.830527	+	0.556979i	$0.811960\pi$
$702$		0			0
$703$	45.5066			1.71631
$704$	−0.690983	+	1.19682i	−0.0260424	+	0.0451068i
$705$		0			0
$706$	10.0172	+	17.3503i	0.377003	+	0.652988i
$707$	−0.809017	−	1.40126i	−0.0304262	−	0.0526998i
$708$		0			0
$709$	14.3992	−	24.9401i	0.540773	−	0.936646i	−0.458087	−	0.888907i	$-0.651465\pi$
$709$	14.3992	−	24.9401i	0.540773	−	0.936646i	0.998860	−	0.0477387i	$-0.0152015\pi$
$710$	−8.09017			−0.303619
$711$		0			0
$712$	−0.854102			−0.0320088
$713$	3.55573	−	6.15870i	0.133163	−	0.230645i
$714$		0			0
$715$	−7.66312	−	13.2729i	−0.286584	−	0.496379i
$716$	6.39919	+	11.0837i	0.239149	+	0.414218i
$717$		0			0
$718$	1.93769	−	3.35618i	0.0723141	−	0.125252i
$719$	41.0000			1.52904			0.764521	−	0.644599i	$-0.222976\pi$
$719$	41.0000			1.52904			0.764521	+	0.644599i	$0.222976\pi$
$720$		0			0
$721$	3.96556			0.147685
$722$	−11.3820	+	19.7141i	−0.423593	+	0.733684i
$723$		0			0
$724$	−14.6631	−	25.3973i	−0.544951	−	0.943882i
$725$	−5.42705	−	9.39993i	−0.201556	−	0.349105i
$726$		0			0
$727$	11.1631	−	19.3351i	0.414017	−	0.717099i	−0.581308	−	0.813684i	$-0.697459\pi$
$727$	11.1631	−	19.3351i	0.414017	−	0.717099i	0.995325	+	0.0965852i	$0.0307920\pi$
$728$	−0.854102			−0.0316551
$729$		0			0
$730$	18.0902			0.669547
$731$	−21.6803	+	37.5515i	−0.801876	+	1.38889i
$732$		0			0
$733$	−11.0279	−	19.1008i	−0.407323	−	0.705505i	0.587265	−	0.809394i	$-0.300204\pi$
$733$	−11.0279	−	19.1008i	−0.407323	−	0.705505i	−0.994589	+	0.103890i	$0.966871\pi$
$734$	9.48936	+	16.4360i	0.350259	+	0.606666i
$735$		0			0
$736$	2.39919	−	4.15551i	0.0884352	−	0.153174i
$737$	53.2148			1.96019
$738$		0			0
$739$	25.8885			0.952325			0.476163	−	0.879357i	$-0.342027\pi$
$739$	25.8885			0.952325			0.476163	+	0.879357i	$0.342027\pi$
$740$	−12.8992	+	22.3420i	−0.474184	+	0.821310i
$741$		0			0
$742$	−0.0344419	−	0.0596550i	−0.00126440	−	0.00219001i
$743$	9.64590	+	16.7072i	0.353874	+	0.612927i	0.986925	−	0.161183i	$-0.0515309\pi$
$743$	9.64590	+	16.7072i	0.353874	+	0.612927i	−0.633051	+	0.774110i	$0.718198\pi$
$744$		0			0
$745$	1.00000	−	1.73205i	0.0366372	−	0.0634574i
$746$	7.76393			0.284258
$747$		0			0
$748$	−40.1246			−1.46710
$749$	−0.645898	+	1.11873i	−0.0236006	+	0.0408774i
$750$		0			0
$751$	−4.42705	−	7.66788i	−0.161545	−	0.279805i	0.773878	−	0.633335i	$-0.218314\pi$
$751$	−4.42705	−	7.66788i	−0.161545	−	0.279805i	−0.935423	+	0.353530i	$0.884981\pi$
$752$	6.92705	+	11.9980i	0.252604	+	0.437522i
$753$		0			0
$754$	1.80902	−	3.13331i	0.0658805	−	0.114108i
$755$	−30.2705			−1.10166
$756$		0			0
$757$	−44.3951			−1.61357			−0.806784	−	0.590846i	$-0.798794\pi$
$757$	−44.3951			−1.61357			−0.806784	+	0.590846i	$0.798794\pi$
$758$	5.25329	−	9.09896i	0.190808	−	0.330489i
$759$		0			0
$760$	−21.8713	−	37.8822i	−0.793356	−	1.37413i
$761$	−12.5729	−	21.7770i	−0.455769	−	0.789415i	0.542963	−	0.839757i	$-0.317302\pi$
$761$	−12.5729	−	21.7770i	−0.455769	−	0.789415i	−0.998732	+	0.0503415i	$0.983969\pi$
$762$		0			0
$763$	0.145898	−	0.252703i	0.00528186	−	0.00914846i
$764$	−3.85410			−0.139437
$765$		0			0
$766$	−10.5066			−0.379618
$767$	2.73607	−	4.73901i	0.0987937	−	0.171116i
$768$		0			0
$769$	−12.0000	−	20.7846i	−0.432731	−	0.749512i	0.564376	−	0.825518i	$-0.309117\pi$
$769$	−12.0000	−	20.7846i	−0.432731	−	0.749512i	−0.997107	+	0.0760054i	$0.975783\pi$
$770$	−1.80902	−	3.13331i	−0.0651924	−	0.112917i
$771$		0			0
$772$	0.0450850	−	0.0780895i	0.00162264	−	0.00281050i
$773$	3.18034			0.114389			0.0571944	−	0.998363i	$-0.481785\pi$
$773$	3.18034			0.114389			0.0571944	+	0.998363i	$0.481785\pi$
$774$		0			0
$775$	15.4377			0.554538
$776$	−7.23607	+	12.5332i	−0.259760	+	0.449917i
$777$		0			0
$778$	0.972136	+	1.68379i	0.0348528	+	0.0603668i
$779$	24.7254	+	42.8257i	0.885880	+	1.53439i
$780$		0			0
$781$	−14.6353	+	25.3490i	−0.523691	+	0.907059i
$782$	2.23607			0.0799616
$783$		0			0
$784$	−12.7082			−0.453864
$785$	6.73607	−	11.6672i	0.240421	−	0.416421i
$786$		0			0
$787$	−5.96149	−	10.3256i	−0.212504	−	0.368068i	0.739993	−	0.672614i	$-0.234829\pi$
$787$	−5.96149	−	10.3256i	−0.212504	−	0.368068i	−0.952498	+	0.304546i	$0.901495\pi$
$788$	8.89919	+	15.4138i	0.317020	+	0.549095i
$789$		0			0
$790$	−1.80902	+	3.13331i	−0.0643619	+	0.111478i
$791$	−6.83282			−0.242947
$792$		0			0
$793$	8.09017			0.287290
$794$	2.87132	−	4.97328i	0.101899	−	0.176495i
$795$		0			0
$796$	−10.6631	−	18.4691i	−0.377944	−	0.654619i
$797$	2.80902	+	4.86536i	0.0995005	+	0.172340i	0.911478	−	0.411349i	$-0.134942\pi$
$797$	2.80902	+	4.86536i	0.0995005	+	0.172340i	−0.811978	+	0.583689i	$0.801609\pi$
$798$		0			0
$799$	−15.8262	+	27.4118i	−0.559892	+	0.969761i
$800$	10.4164			0.368276
$801$		0			0
$802$	3.74265			0.132157
$803$	32.7254	−	56.6821i	1.15486	−	2.00027i
$804$		0			0
$805$	−0.427051	−	0.739674i	−0.0150516	−	0.0260701i
$806$	2.57295	+	4.45648i	0.0906283	+	0.156973i
$807$		0			0
$808$	−4.73607	+	8.20311i	−0.166614	+	0.288584i
$809$	−41.7771			−1.46880			−0.734402	−	0.678715i	$-0.762537\pi$
$809$	−41.7771			−1.46880			−0.734402	+	0.678715i	$0.762537\pi$
$810$		0			0
$811$	−27.5066			−0.965887			−0.482943	−	0.875652i	$-0.660432\pi$
$811$	−27.5066			−0.965887			−0.482943	+	0.875652i	$0.660432\pi$
$812$	−1.80902	+	3.13331i	−0.0634841	+	0.109958i
$813$		0			0
$814$	−11.0172	−	19.0824i	−0.386153	−	0.668837i
$815$	12.4721	+	21.6024i	0.436880	+	0.756698i
$816$		0			0
$817$	−38.2426	+	66.2382i	−1.33794	+	2.31738i
$818$	1.85410			0.0648272
$819$		0			0
$820$	−28.0344			−0.979005
$821$	−15.0066	+	25.9922i	−0.523733	+	0.907132i	0.475885	+	0.879507i	$0.342128\pi$
$821$	−15.0066	+	25.9922i	−0.523733	+	0.907132i	−0.999618	+	0.0276251i	$0.991206\pi$
$822$		0			0
$823$	3.50000	+	6.06218i	0.122002	+	0.211314i	0.920557	−	0.390608i	$-0.127735\pi$
$823$	3.50000	+	6.06218i	0.122002	+	0.211314i	−0.798555	+	0.601922i	$0.794402\pi$
$824$	−11.6074	−	20.1046i	−0.404363	−	0.700377i
$825$		0			0
$826$	0.645898	−	1.11873i	0.0224737	−	0.0389255i
$827$	25.8328			0.898295			0.449148	−	0.893458i	$-0.351728\pi$
$827$	25.8328			0.898295			0.449148	+	0.893458i	$0.351728\pi$
$828$		0			0
$829$	−27.8673			−0.967870			−0.483935	−	0.875104i	$-0.660793\pi$
$829$	−27.8673			−0.967870			−0.483935	+	0.875104i	$0.660793\pi$
$830$	−5.80902	+	10.0615i	−0.201634	+	0.349240i
$831$		0			0
$832$	−0.118034	−	0.204441i	−0.00409209	−	0.00708771i
$833$	−14.5172	−	25.1446i	−0.502992	−	0.871208i
$834$		0			0
$835$	2.69098	−	4.66092i	0.0931253	−	0.161298i
$836$	−70.7771			−2.44788
$837$		0			0
$838$	0.291796			0.0100799
$839$	−5.55573	+	9.62280i	−0.191805	+	0.332216i	−0.945848	−	0.324608i	$-0.894767\pi$
$839$	−5.55573	+	9.62280i	−0.191805	+	0.332216i	0.754043	+	0.656825i	$0.228101\pi$
$840$		0			0
$841$	−2.63525	−	4.56440i	−0.0908709	−	0.157393i
$842$	−7.56231	−	13.0983i	−0.260614	−	0.451397i
$843$		0			0
$844$	−13.0623	+	22.6246i	−0.449623	+	0.778770i
$845$	2.61803			0.0900631
$846$		0			0
$847$	−8.88854			−0.305414
$848$	0.270510	−	0.468537i	0.00928935	−	0.0160896i
$849$		0			0
$850$	2.42705	+	4.20378i	0.0832472	+	0.144188i
$851$	−2.60081	−	4.50474i	−0.0891547	−	0.154421i
$852$		0			0
$853$	−25.7533	+	44.6060i	−0.881776	+	1.52728i	−0.0324108	+	0.999475i	$0.510318\pi$
$853$	−25.7533	+	44.6060i	−0.881776	+	1.52728i	−0.849365	+	0.527806i	$0.823015\pi$
$854$	1.90983			0.0653530
$855$		0			0
$856$	7.56231			0.258474
$857$	1.51722	−	2.62790i	0.0518273	−	0.0897675i	−0.838948	−	0.544212i	$-0.816829\pi$
$857$	1.51722	−	2.62790i	0.0518273	−	0.0897675i	0.890775	+	0.454444i	$0.150162\pi$
$858$		0			0
$859$	−9.95492	−	17.2424i	−0.339657	−	0.588304i	0.644711	−	0.764426i	$-0.276978\pi$
$859$	−9.95492	−	17.2424i	−0.339657	−	0.588304i	−0.984368	+	0.176123i	$0.943644\pi$
$860$	−21.6803	−	37.5515i	−0.739293	−	1.28049i
$861$		0			0
$862$	−8.41641	+	14.5776i	−0.286664	+	0.496517i
$863$	−18.7984			−0.639904			−0.319952	−	0.947434i	$-0.603667\pi$
$863$	−18.7984			−0.639904			−0.319952	+	0.947434i	$0.603667\pi$
$864$		0			0
$865$	11.8541			0.403052
$866$	−2.45492	+	4.25204i	−0.0834214	+	0.144490i
$867$		0			0
$868$	−2.57295	−	4.45648i	−0.0873316	−	0.151263i
$869$	6.54508	+	11.3364i	0.222027	+	0.384562i
$870$		0			0
$871$	−4.54508	+	7.87232i	−0.154004	+	0.266743i
$872$	−1.70820			−0.0578471
$873$		0			0
$874$	3.94427			0.133417
$875$	−1.57295	+	2.72443i	−0.0531754	+	0.0921025i
$876$		0			0
$877$	14.8156	+	25.6614i	0.500287	+	0.866523i	1.00000		0.000331534i	$0.000105530\pi$
$877$	14.8156	+	25.6614i	0.500287	+	0.866523i	−0.499713	+	0.866191i	$0.666561\pi$
$878$	10.3647	+	17.9523i	0.349793	+	0.605860i
$879$		0			0
$880$	14.2082	−	24.6093i	0.478958	−	0.829580i
$881$	−9.47214			−0.319124			−0.159562	−	0.987188i	$-0.551008\pi$
$881$	−9.47214			−0.319124			−0.159562	+	0.987188i	$0.551008\pi$
$882$		0			0
$883$	40.3607			1.35825			0.679123	−	0.734025i	$-0.262360\pi$
$883$	40.3607			1.35825			0.679123	+	0.734025i	$0.262360\pi$
$884$	3.42705	−	5.93583i	0.115264	−	0.199643i
$885$		0			0
$886$	−8.60081	−	14.8970i	−0.288950	−	0.500476i
$887$	17.3541	+	30.0582i	0.582694	+	1.00926i	0.995159	+	0.0982816i	$0.0313346\pi$
$887$	17.3541	+	30.0582i	0.582694	+	1.00926i	−0.412465	+	0.910973i	$0.635332\pi$
$888$		0			0
$889$	2.41641	−	4.18534i	0.0810437	−	0.140372i
$890$	0.618034			0.0207165
$891$		0			0
$892$	−30.9443			−1.03609
$893$	−27.9164	+	48.3526i	−0.934187	+	1.61806i
$894$		0			0
$895$	−10.3541	−	17.9338i	−0.346099	−	0.599462i
$896$	−2.17376	−	3.76507i	−0.0726203	−	0.125782i
$897$		0			0
$898$	8.81559	−	15.2691i	0.294180	−	0.509535i
$899$	48.7426			1.62566
$900$		0			0
$901$	1.23607			0.0411794
$902$	11.9721	−	20.7363i	0.398629	−	0.690445i
$903$		0			0
$904$	20.0000	+	34.6410i	0.665190	+	1.15214i
$905$	23.7254	+	41.0936i	0.788660	+	1.36600i
$906$		0			0
$907$	9.42705	−	16.3281i	0.313020	−	0.542167i	−0.665995	−	0.745957i	$-0.731993\pi$
$907$	9.42705	−	16.3281i	0.313020	−	0.542167i	0.979015	+	0.203790i	$0.0653259\pi$
$908$	20.4721			0.679392
$909$		0			0
$910$	0.618034			0.0204876
$911$	−23.7082	+	41.0638i	−0.785488	+	1.36050i	0.143219	+	0.989691i	$0.454255\pi$
$911$	−23.7082	+	41.0638i	−0.785488	+	1.36050i	−0.928707	+	0.370814i	$0.879079\pi$
$912$		0			0
$913$	21.0172	+	36.4029i	0.695568	+	1.20476i
$914$	8.23607	+	14.2653i	0.272425	+	0.471854i
$915$		0			0
$916$	10.2533	−	17.7592i	0.338778	−	0.586781i
$917$	−1.47214			−0.0486142
$918$		0			0
$919$	3.18034			0.104910			0.0524549	−	0.998623i	$-0.483295\pi$
$919$	3.18034			0.104910			0.0524549	+	0.998623i	$0.483295\pi$
$920$	−2.50000	+	4.33013i	−0.0824226	+	0.142760i
$921$		0			0
$922$	2.72542	+	4.72057i	0.0897571	+	0.155464i
$923$	−2.50000	−	4.33013i	−0.0822885	−	0.142528i
$924$		0			0
$925$	5.64590	−	9.77898i	0.185636	−	0.321531i
$926$	−19.0557			−0.626210
$927$		0			0
$928$	32.8885			1.07962
$929$	−7.68034	+	13.3027i	−0.251984	+	0.436449i	−0.964072	−	0.265641i	$-0.914416\pi$
$929$	−7.68034	+	13.3027i	−0.251984	+	0.436449i	0.712088	+	0.702090i	$0.247750\pi$
$930$		0			0
$931$	−25.6074	−	44.3533i	−0.839248	−	1.45362i
$932$	21.0172	+	36.4029i	0.688442	+	1.19242i
$933$		0			0
$934$	−2.03444	+	3.52376i	−0.0665690	+	0.115301i
$935$	64.9230			2.12321
$936$		0			0
$937$	−27.8885			−0.911079			−0.455540	−	0.890216i	$-0.650554\pi$
$937$	−27.8885			−0.911079			−0.455540	+	0.890216i	$0.650554\pi$
$938$	−1.07295	+	1.85840i	−0.0350330	+	0.0606790i
$939$		0			0
$940$	−15.8262	−	27.4118i	−0.516195	−	0.894076i
$941$	1.68034	+	2.91043i	0.0547775	+	0.0948774i	0.892114	−	0.451811i	$-0.149222\pi$
$941$	1.68034	+	2.91043i	0.0547775	+	0.0948774i	−0.837336	+	0.546688i	$0.815888\pi$
$942$		0			0
$943$	2.82624	−	4.89519i	0.0920350	−	0.159409i
$944$	10.1459			0.330221
$945$		0			0
$946$	37.0344			1.20409
$947$	10.4271	−	18.0602i	0.338834	−	0.586877i	−0.645380	−	0.763862i	$-0.723301\pi$
$947$	10.4271	−	18.0602i	0.338834	−	0.586877i	0.984214	+	0.176985i	$0.0566343\pi$
$948$		0			0
$949$	5.59017	+	9.68246i	0.181465	+	0.314306i
$950$	4.28115	+	7.41517i	0.138899	+	0.240580i
$951$		0			0
$952$	1.80902	−	3.13331i	0.0586306	−	0.101551i
$953$	−3.34752			−0.108437			−0.0542185	−	0.998529i	$-0.517267\pi$
$953$	−3.34752			−0.108437			−0.0542185	+	0.998529i	$0.517267\pi$
$954$		0			0
$955$	6.23607			0.201794
$956$	−18.2533	+	31.6156i	−0.590354	+	1.02252i
$957$		0			0
$958$	2.70820	+	4.69075i	0.0874981	+	0.151551i
$959$	4.31966	+	7.48187i	0.139489	+	0.241602i
$960$		0			0
$961$	−19.1631	+	33.1915i	−0.618165	+	1.07069i
$962$	3.76393			0.121354
$963$		0			0
$964$	17.4721			0.562740
$965$	−0.0729490	+	0.126351i	−0.00234831	+	0.00406740i
$966$		0			0
$967$	6.94427	+	12.0278i	0.223313	+	0.386789i	0.955812	−	0.293979i	$-0.0949796\pi$
$967$	6.94427	+	12.0278i	0.223313	+	0.386789i	−0.732499	+	0.680768i	$0.761646\pi$
$968$	26.0172	+	45.0631i	0.836225	+	1.44838i
$969$		0			0
$970$	5.23607	−	9.06914i	0.168120	−	0.291192i
$971$	−9.36068			−0.300399			−0.150199	−	0.988656i	$-0.547992\pi$
$971$	−9.36068			−0.300399			−0.150199	+	0.988656i	$0.547992\pi$
$972$		0			0
$973$	−3.36068			−0.107738
$974$	2.57953	−	4.46787i	0.0826534	−	0.143160i
$975$		0			0
$976$	7.50000	+	12.9904i	0.240069	+	0.415812i
$977$	−10.6525	−	18.4506i	−0.340803	−	0.590288i	0.643779	−	0.765211i	$-0.277366\pi$
$977$	−10.6525	−	18.4506i	−0.340803	−	0.590288i	−0.984582	+	0.174923i	$0.944032\pi$
$978$		0			0
$979$	1.11803	−	1.93649i	0.0357325	−	0.0618905i
$980$	29.0344			0.927471
$981$		0			0
$982$	24.9230			0.795324
$983$	−10.8885	+	18.8595i	−0.347291	+	0.601525i	−0.985767	−	0.168116i	$-0.946232\pi$
$983$	−10.8885	+	18.8595i	−0.347291	+	0.601525i	0.638477	+	0.769641i	$0.279565\pi$
$984$		0			0
$985$	−14.3992	−	24.9401i	−0.458796	−	0.794658i
$986$	7.66312	+	13.2729i	0.244043	+	0.422696i
$987$		0			0
$988$	6.04508	−	10.4704i	0.192320	−	0.333108i
$989$	8.74265			0.278000
$990$		0			0
$991$	38.3607			1.21857			0.609284	−	0.792952i	$-0.291457\pi$
$991$	38.3607			1.21857			0.609284	+	0.792952i	$0.291457\pi$
$992$	−23.3885	+	40.5101i	−0.742587	+	1.28620i
$993$		0			0
$994$	−0.590170	−	1.02220i	−0.0187191	−	0.0324224i
$995$	17.2533	+	29.8836i	0.546966	+	0.947373i
$996$		0			0
$997$	4.22542	−	7.31865i	0.133821	−	0.231784i	−0.791326	−	0.611395i	$-0.790609\pi$
$997$	4.22542	−	7.31865i	0.133821	−	0.231784i	0.925146	+	0.379611i	$0.123942\pi$
$998$	12.2361			0.387326
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1053.2.e.k.703.1		4
3.2	odd	2		1053.2.e.h.703.2		4
9.2	odd	6		1053.2.a.f.1.1	yes	2
9.4	even	3	inner	1053.2.e.k.352.1		4
9.5	odd	6		1053.2.e.h.352.2		4
9.7	even	3		1053.2.a.e.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1053.2.a.e.1.2	✓	2	9.7	even	3
1053.2.a.f.1.1	yes	2	9.2	odd	6
1053.2.e.h.352.2		4	9.5	odd	6
1053.2.e.h.703.2		4	3.2	odd	2
1053.2.e.k.352.1		4	9.4	even	3	inner
1053.2.e.k.703.1		4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.535233i) q^{2} +(0.809017 + 1.40126i) q^{4} +(-1.30902 - 2.26728i) q^{5} +(0.190983 - 0.330792i) q^{7} -2.23607 q^{8} +1.61803 q^{10} +(2.92705 - 5.06980i) q^{11} +(0.500000 + 0.866025i) q^{13} +(0.118034 + 0.204441i) q^{14} +(-0.927051 + 1.60570i) q^{16} -4.23607 q^{17} -7.47214 q^{19} +(2.11803 - 3.66854i) q^{20} +(1.80902 + 3.13331i) q^{22} +(0.427051 + 0.739674i) q^{23} +(-0.927051 + 1.60570i) q^{25} -0.618034 q^{26} +0.618034 q^{28} +(-2.92705 + 5.06980i) q^{29} +(-4.16312 - 7.21073i) q^{31} +(-2.80902 - 4.86536i) q^{32} +(1.30902 - 2.26728i) q^{34} -1.00000 q^{35} -6.09017 q^{37} +(2.30902 - 3.99933i) q^{38} +(2.92705 + 5.06980i) q^{40} +(-3.30902 - 5.73139i) q^{41} +(5.11803 - 8.86469i) q^{43} +9.47214 q^{44} -0.527864 q^{46} +(3.73607 - 6.47106i) q^{47} +(3.42705 + 5.93583i) q^{49} +(-0.572949 - 0.992377i) q^{50} +(-0.809017 + 1.40126i) q^{52} -0.291796 q^{53} -15.3262 q^{55} +(-0.427051 + 0.739674i) q^{56} +(-1.80902 - 3.13331i) q^{58} +(-2.73607 - 4.73901i) q^{59} +(4.04508 - 7.00629i) q^{61} +5.14590 q^{62} -0.236068 q^{64} +(1.30902 - 2.26728i) q^{65} +(4.54508 + 7.87232i) q^{67} +(-3.42705 - 5.93583i) q^{68} +(0.309017 - 0.535233i) q^{70} -5.00000 q^{71} +11.1803 q^{73} +(1.88197 - 3.25966i) q^{74} +(-6.04508 - 10.4704i) q^{76} +(-1.11803 - 1.93649i) q^{77} +(-1.11803 + 1.93649i) q^{79} +4.85410 q^{80} +4.09017 q^{82} +(-3.59017 + 6.21836i) q^{83} +(5.54508 + 9.60437i) q^{85} +(3.16312 + 5.47868i) q^{86} +(-6.54508 + 11.3364i) q^{88} +0.381966 q^{89} +0.381966 q^{91} +(-0.690983 + 1.19682i) q^{92} +(2.30902 + 3.99933i) q^{94} +(9.78115 + 16.9415i) q^{95} +(3.23607 - 5.60503i) q^{97} -4.23607 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + q^{4} - 3 q^{5} + 3 q^{7} + 2 q^{10} + 5 q^{11} + 2 q^{13} - 4 q^{14} + 3 q^{16} - 8 q^{17} - 12 q^{19} + 4 q^{20} + 5 q^{22} - 5 q^{23} + 3 q^{25} + 2 q^{26} - 2 q^{28} - 5 q^{29} - q^{31}+ \cdots - 8 q^{98}+O(q^{100}) \) 4 * q + q^2 + q^4 - 3 * q^5 + 3 * q^7 + 2 * q^10 + 5 * q^11 + 2 * q^13 - 4 * q^14 + 3 * q^16 - 8 * q^17 - 12 * q^19 + 4 * q^20 + 5 * q^22 - 5 * q^23 + 3 * q^25 + 2 * q^26 - 2 * q^28 - 5 * q^29 - q^31 - 9 * q^32 + 3 * q^34 - 4 * q^35 - 2 * q^37 + 7 * q^38 + 5 * q^40 - 11 * q^41 + 16 * q^43 + 20 * q^44 - 20 * q^46 + 6 * q^47 + 7 * q^49 - 9 * q^50 - q^52 - 28 * q^53 - 30 * q^55 + 5 * q^56 - 5 * q^58 - 2 * q^59 + 5 * q^61 + 34 * q^62 + 8 * q^64 + 3 * q^65 + 7 * q^67 - 7 * q^68 - q^70 - 20 * q^71 + 12 * q^74 - 13 * q^76 + 6 * q^80 - 6 * q^82 + 8 * q^83 + 11 * q^85 - 3 * q^86 - 15 * q^88 + 6 * q^89 + 6 * q^91 - 5 * q^92 + 7 * q^94 + 19 * q^95 + 4 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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