LMFDB - Embedded newform 784.2.x.o.373.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [784,2,Mod(165,784)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("784.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(784, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([0, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,-4,0,-4,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			373.10
Character	$\chi$	$=$	784.373
Dual form			784.2.x.o.557.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.945375 - 1.05179i) q^{2} +(0.0543752 + 0.0145698i) q^{3} +(-0.212530 - 1.98868i) q^{4} +(-1.25781 + 0.337028i) q^{5} +(0.0667293 - 0.0434174i) q^{6} +(-2.29259 - 1.65651i) q^{8} +(-2.59533 - 1.49842i) q^{9} +(-0.834616 + 1.64157i) q^{10} +(-0.402875 + 1.50355i) q^{11} +(0.0174182 - 0.111231i) q^{12} +(-1.59615 + 1.59615i) q^{13} -0.0733039 q^{15} +(-3.90966 + 0.845308i) q^{16} +(-1.46910 - 2.54455i) q^{17} +(-4.02958 + 1.31318i) q^{18} +(-2.05021 - 7.65147i) q^{19} +(0.937562 + 2.42974i) q^{20} +(1.20055 + 1.84516i) q^{22} +(-3.91784 - 2.26197i) q^{23} +(-0.100525 - 0.123475i) q^{24} +(-2.86164 + 1.65217i) q^{25} +(0.169855 + 3.18777i) q^{26} +(-0.238706 - 0.238706i) q^{27} +(2.06234 - 2.06234i) q^{29} +(-0.0692997 + 0.0771004i) q^{30} +(3.14025 + 5.43908i) q^{31} +(-2.80701 + 4.91128i) q^{32} +(-0.0438128 + 0.0758861i) q^{33} +(-4.06519 - 0.860373i) q^{34} +(-2.42828 + 5.47973i) q^{36} +(5.24787 - 1.40616i) q^{37} +(-9.98597 - 5.07713i) q^{38} +(-0.110046 + 0.0635352i) q^{39} +(3.44193 + 1.31090i) q^{40} +7.34101i q^{41} +(-1.99391 - 1.99391i) q^{43} +(3.07570 + 0.481638i) q^{44} +(3.76943 + 1.01002i) q^{45} +(-6.08295 + 1.98235i) q^{46} +(-0.979430 + 1.69642i) q^{47} +(-0.224904 - 0.0109992i) q^{48} +(-0.967587 + 4.57177i) q^{50} +(-0.0428089 - 0.159765i) q^{51} +(3.51345 + 2.83499i) q^{52} +(3.00493 - 11.2146i) q^{53} +(-0.476736 + 0.0254021i) q^{54} -2.02696i q^{55} -0.445921i q^{57} +(-0.219466 - 4.11884i) q^{58} +(-0.793411 + 2.96105i) q^{59} +(0.0155793 + 0.145778i) q^{60} +(-2.60480 - 9.72123i) q^{61} +(8.68949 + 1.83908i) q^{62} +(2.51197 + 7.59540i) q^{64} +(1.46970 - 2.54559i) q^{65} +(0.0383967 + 0.117823i) q^{66} +(-2.11517 - 0.566758i) q^{67} +(-4.74806 + 3.46236i) q^{68} +(-0.180077 - 0.180077i) q^{69} -7.26378i q^{71} +(3.46790 + 7.73444i) q^{72} +(12.2392 - 7.06631i) q^{73} +(3.48222 - 6.84902i) q^{74} +(-0.179674 + 0.0481435i) q^{75} +(-14.7806 + 5.70337i) q^{76} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 + 1.66547i) q^{79} +(4.63270 - 2.38090i) q^{80} +(4.48574 + 7.76954i) q^{81} +(7.72121 + 6.94001i) q^{82} +(-8.82731 + 8.82731i) q^{83} +(2.70543 + 2.70543i) q^{85} +(-3.98217 + 0.212184i) q^{86} +(0.142188 - 0.0820924i) q^{87} +(3.41427 - 2.77967i) q^{88} +(-11.5526 - 6.66987i) q^{89} +(4.62586 - 3.00981i) q^{90} +(-3.66566 + 8.27206i) q^{92} +(0.0915056 + 0.341503i) q^{93} +(0.858354 + 2.63391i) q^{94} +(5.15752 + 8.93309i) q^{95} +(-0.224188 + 0.226154i) q^{96} +9.69578 q^{97} +(3.29854 - 3.29854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.945375	−	1.05179i	0.668481	−	0.743729i
$2$	0.945375	−	1.05179i	0.668481	−	0.743729i
$3$	0.0543752	+	0.0145698i	0.0313935	+	0.00841187i	0.274482	−	0.961592i	$-0.411494\pi$
$3$	0.0543752	+	0.0145698i	0.0313935	+	0.00841187i	−0.243088	+	0.970004i	$0.578160\pi$
$4$	−0.212530	−	1.98868i	−0.106265	−	0.994338i
$5$	−1.25781	+	0.337028i	−0.562508	+	0.150724i	−0.528858	−	0.848710i	$-0.677380\pi$
$5$	−1.25781	+	0.337028i	−0.562508	+	0.150724i	−0.0336497	+	0.999434i	$0.510713\pi$
$6$	0.0667293	−	0.0434174i	0.0272421	−	0.0177251i
$7$		0			0
$7$		0			0
$8$	−2.29259	−	1.65651i	−0.810554	−	0.585664i
$9$	−2.59533	−	1.49842i	−0.865111	−	0.499472i
$10$	−0.834616	+	1.64157i	−0.263929	+	0.519109i
$11$	−0.402875	+	1.50355i	−0.121472	+	0.453338i	−0.999689	−	0.0249229i	$-0.992066\pi$
$11$	−0.402875	+	1.50355i	−0.121472	+	0.453338i	0.878218	+	0.478261i	$0.158733\pi$
$12$	0.0174182	−	0.111231i	0.00502820	−	0.0321097i
$13$	−1.59615	+	1.59615i	−0.442691	+	0.442691i	−0.892916	−	0.450224i	$-0.851344\pi$
$13$	−1.59615	+	1.59615i	−0.442691	+	0.442691i	0.450224	+	0.892916i	$0.351344\pi$
$14$		0			0
$15$	−0.0733039			−0.0189270
$16$	−3.90966	+	0.845308i	−0.977415	+	0.211327i
$17$	−1.46910	−	2.54455i	−0.356309	−	0.617145i	0.631032	−	0.775757i	$-0.282632\pi$
$17$	−1.46910	−	2.54455i	−0.356309	−	0.617145i	−0.987341	+	0.158612i	$0.949298\pi$
$18$	−4.02958	+	1.31318i	−0.949782	+	0.309520i
$19$	−2.05021	−	7.65147i	−0.470350	−	1.75537i	−0.638514	−	0.769610i	$-0.720451\pi$
$19$	−2.05021	−	7.65147i	−0.470350	−	1.75537i	0.168165	−	0.985759i	$-0.446216\pi$
$20$	0.937562	+	2.42974i	0.209645	+	0.543306i
$21$		0			0
$22$	1.20055	+	1.84516i	0.255959	+	0.393390i
$23$	−3.91784	−	2.26197i	−0.816927	−	0.471653i	0.0324286	−	0.999474i	$-0.489676\pi$
$23$	−3.91784	−	2.26197i	−0.816927	−	0.471653i	−0.849356	+	0.527821i	$0.823009\pi$
$24$	−0.100525	−	0.123475i	−0.0205196	−	0.0252043i
$25$	−2.86164	+	1.65217i	−0.572328	+	0.330434i
$26$	0.169855	+	3.18777i	0.0333114	+	0.625173i
$27$	−0.238706	−	0.238706i	−0.0459390	−	0.0459390i
$28$		0			0
$29$	2.06234	−	2.06234i	0.382968	−	0.382968i	−0.489203	−	0.872170i	$-0.662712\pi$
$29$	2.06234	−	2.06234i	0.382968	−	0.382968i	0.872170	+	0.489203i	$0.162712\pi$
$30$	−0.0692997	+	0.0771004i	−0.0126523	+	0.0140765i
$31$	3.14025	+	5.43908i	0.564006	+	0.976887i	0.997141	+	0.0755580i	$0.0240738\pi$
$31$	3.14025	+	5.43908i	0.564006	+	0.976887i	−0.433136	+	0.901329i	$0.642593\pi$
$32$	−2.80701	+	4.91128i	−0.496214	+	0.868200i
$33$	−0.0438128	+	0.0758861i	−0.00762684	+	0.0132101i
$34$	−4.06519	−	0.860373i	−0.697174	−	0.147553i
$35$		0			0
$36$	−2.42828	+	5.47973i	−0.404713	+	0.913289i
$37$	5.24787	−	1.40616i	0.862745	−	0.231172i	0.199797	−	0.979837i	$-0.435972\pi$
$37$	5.24787	−	1.40616i	0.862745	−	0.231172i	0.662948	+	0.748666i	$0.269305\pi$
$38$	−9.98597	−	5.07713i	−1.61994	−	0.823619i
$39$	−0.110046	+	0.0635352i	−0.0176215	+	0.0101738i
$40$	3.44193	+	1.31090i	0.544216	+	0.207271i
$41$			7.34101i			1.14647i	0.819390	+	0.573236i	$0.194312\pi$
$41$			7.34101i			1.14647i	−0.819390	+	0.573236i	$0.805688\pi$
$42$		0			0
$43$	−1.99391	−	1.99391i	−0.304068	−	0.304068i	0.538535	−	0.842603i	$-0.318978\pi$
$43$	−1.99391	−	1.99391i	−0.304068	−	0.304068i	−0.842603	+	0.538535i	$0.818978\pi$
$44$	3.07570	+	0.481638i	0.463679	+	0.0726097i
$45$	3.76943	+	1.01002i	0.561914	+	0.150564i
$46$	−6.08295	+	1.98235i	−0.896882	+	0.292281i
$47$	−0.979430	+	1.69642i	−0.142865	+	0.247449i	−0.928574	−	0.371147i	$-0.878965\pi$
$47$	−0.979430	+	1.69642i	−0.142865	+	0.247449i	0.785710	+	0.618596i	$0.212298\pi$
$48$	−0.224904	−	0.0109992i	−0.0324622	−	0.00158759i
$49$		0			0
$50$	−0.967587	+	4.57177i	−0.136837	+	0.646545i
$51$	−0.0428089	−	0.159765i	−0.00599444	−	0.0223716i
$52$	3.51345	+	2.83499i	0.487228	+	0.393142i
$53$	3.00493	−	11.2146i	0.412759	−	1.54044i	−0.376522	−	0.926408i	$-0.622880\pi$
$53$	3.00493	−	11.2146i	0.412759	−	1.54044i	0.789282	−	0.614031i	$-0.210453\pi$
$54$	−0.476736	+	0.0254021i	−0.0648756	+	0.00345679i
$55$		−	2.02696i		−	0.273315i
$56$		0			0
$57$		−	0.445921i		−	0.0590637i
$58$	−0.219466	−	4.11884i	−0.0288173	−	0.540831i
$59$	−0.793411	+	2.96105i	−0.103293	+	0.385496i	−0.998146	−	0.0608657i	$-0.980614\pi$
$59$	−0.793411	+	2.96105i	−0.103293	+	0.385496i	0.894853	+	0.446362i	$0.147281\pi$
$60$	0.0155793	+	0.145778i	0.00201128	+	0.0188198i
$61$	−2.60480	−	9.72123i	−0.333510	−	1.24468i	−0.905476	−	0.424398i	$-0.860486\pi$
$61$	−2.60480	−	9.72123i	−0.333510	−	1.24468i	0.571966	−	0.820277i	$-0.306181\pi$
$62$	8.68949	+	1.83908i	1.10357	+	0.233563i
$63$		0			0
$64$	2.51197	+	7.59540i	0.313996	+	0.949424i
$65$	1.46970	−	2.54559i	0.182293	−	0.315742i
$66$	0.0383967	+	0.117823i	0.00472631	+	0.0145030i
$67$	−2.11517	−	0.566758i	−0.258409	−	0.0692405i	0.127289	−	0.991866i	$-0.459373\pi$
$67$	−2.11517	−	0.566758i	−0.258409	−	0.0692405i	−0.385698	+	0.922625i	$0.626039\pi$
$68$	−4.74806	+	3.46236i	−0.575787	+	0.419872i
$69$	−0.180077	−	0.180077i	−0.0216787	−	0.0216787i
$70$		0			0
$71$		−	7.26378i		−	0.862052i	−0.902340	−	0.431026i	$-0.858152\pi$
$71$		−	7.26378i		−	0.862052i	0.902340	−	0.431026i	$-0.141848\pi$
$72$	3.46790	+	7.73444i	0.408696	+	0.911513i
$73$	12.2392	−	7.06631i	1.43249	−	0.827049i	0.435181	−	0.900343i	$-0.356684\pi$
$73$	12.2392	−	7.06631i	1.43249	−	0.827049i	0.997310	+	0.0732936i	$0.0233510\pi$
$74$	3.48222	−	6.84902i	0.404800	−	0.796182i
$75$	−0.179674	+	0.0481435i	−0.0207469	+	0.00555913i
$76$	−14.7806	+	5.70337i	−1.69545	+	0.654221i
$77$		0			0
$78$	−0.0372092	+	0.175810i	−0.00421311	+	0.0199066i
$79$	−0.961559	+	1.66547i	−0.108184	+	0.187380i	−0.915035	−	0.403376i	$-0.867837\pi$
$79$	−0.961559	+	1.66547i	−0.108184	+	0.187380i	0.806851	+	0.590755i	$0.201170\pi$
$80$	4.63270	−	2.38090i	0.517952	−	0.266193i
$81$	4.48574	+	7.76954i	0.498416	+	0.863282i
$82$	7.72121	+	6.94001i	0.852665	+	0.766396i
$83$	−8.82731	+	8.82731i	−0.968923	+	0.968923i	−0.999531	−	0.0306086i	$-0.990255\pi$
$83$	−8.82731	+	8.82731i	−0.968923	+	0.968923i	0.0306086	+	0.999531i	$0.490255\pi$
$84$		0			0
$85$	2.70543	+	2.70543i	0.293445	+	0.293445i
$86$	−3.98217	+	0.212184i	−0.429408	+	0.0228803i
$87$	0.142188	−	0.0820924i	0.0152442	−	0.00880123i
$88$	3.41427	−	2.77967i	0.363963	−	0.296313i
$89$	−11.5526	−	6.66987i	−1.22457	−	0.707005i	−0.258680	−	0.965963i	$-0.583287\pi$
$89$	−11.5526	−	6.66987i	−1.22457	−	0.707005i	−0.965888	+	0.258959i	$0.916621\pi$
$90$	4.62586	−	3.00981i	0.487608	−	0.317262i
$91$		0			0
$92$	−3.66566	+	8.27206i	−0.382172	+	0.862422i
$93$	0.0915056	+	0.341503i	0.00948869	+	0.0354123i
$94$	0.858354	+	2.63391i	0.0885325	+	0.271667i
$95$	5.15752	+	8.93309i	0.529151	+	0.916516i
$96$	−0.224188	+	0.226154i	−0.0228811	+	0.0230818i
$97$	9.69578			0.984458			0.492229	−	0.870466i	$-0.336182\pi$
$97$	9.69578			0.984458			0.492229	+	0.870466i	$0.336182\pi$
$98$		0			0
$99$	3.29854	−	3.29854i	0.331516	−	0.331516i
$100$	3.89381	+	5.33974i	0.389381	+	0.533974i
$101$	2.73526	−	10.2081i	0.272168	−	1.01575i	−0.685547	−	0.728029i	$-0.740437\pi$
$101$	2.73526	−	10.2081i	0.272168	−	1.01575i	0.957715	−	0.287718i	$-0.0928966\pi$
$102$	−0.208510	−	0.106012i	−0.0206456	−	0.0104967i
$103$	2.96542	+	1.71209i	0.292192	+	0.168697i	0.638930	−	0.769265i	$-0.279377\pi$
$103$	2.96542	+	1.71209i	0.292192	+	0.168697i	−0.346738	+	0.937962i	$0.612711\pi$
$104$	6.30334	−	1.01529i	0.618094	−	0.0995570i
$105$		0			0
$106$	−8.95459	−	13.7625i	−0.869747	−	1.33674i
$107$	−11.0668	+	2.96534i	−1.06987	+	0.286670i	−0.750439	−	0.660940i	$-0.770158\pi$
$107$	−11.0668	+	2.96534i	−1.06987	+	0.286670i	−0.319429	+	0.947610i	$0.603491\pi$
$108$	−0.423977	+	0.525441i	−0.0407972	+	0.0505606i
$109$	3.02860	+	0.811511i	0.290087	+	0.0777287i	0.400928	−	0.916110i	$-0.368688\pi$
$109$	3.02860	+	0.811511i	0.290087	+	0.0777287i	−0.110841	+	0.993838i	$0.535354\pi$
$110$	−2.13194	−	1.91624i	−0.203272	−	0.182706i
$111$	0.305841			0.0290292
$112$		0			0
$113$	4.67963			0.440223			0.220111	−	0.975475i	$-0.429358\pi$
$113$	4.67963			0.440223			0.220111	+	0.975475i	$0.429358\pi$
$114$	−0.469016	−	0.421563i	−0.0439274	−	0.0394830i
$115$	5.69024	+	1.52469i	0.530617	+	0.142178i
$116$	−4.53964	−	3.66302i	−0.421495	−	0.340103i
$117$	6.53422	−	1.75084i	0.604089	−	0.161865i
$118$	2.36434	+	3.63381i	0.217655	+	0.334519i
$119$		0			0
$120$	0.168056	+	0.121428i	0.0153413	+	0.0110848i
$121$	7.42792	+	4.28851i	0.675265	+	0.389865i
$122$	−12.6872	−	6.45051i	−1.14865	−	0.584002i
$123$	−0.106957	+	0.399168i	−0.00964398	+	0.0359918i
$124$	10.1492	−	7.40091i	0.911421	−	0.664621i
$125$	7.64645	−	7.64645i	0.683919	−	0.683919i
$126$		0			0
$127$	5.63308			0.499855			0.249928	−	0.968265i	$-0.419593\pi$
$127$	5.63308			0.499855			0.249928	+	0.968265i	$0.419593\pi$
$128$	10.3635	+	4.53844i	0.916015	+	0.401145i
$129$	−0.0793683	−	0.137470i	−0.00698799	−	0.0121035i
$130$	−1.28801	−	3.95235i	−0.112966	−	0.346644i
$131$	−0.537304	−	2.00524i	−0.0469444	−	0.175199i	0.938473	−	0.345352i	$-0.112240\pi$
$131$	−0.537304	−	2.00524i	−0.0469444	−	0.175199i	−0.985418	+	0.170153i	$0.945574\pi$
$132$	0.160224	+	0.0710014i	0.0139457	+	0.00617988i
$133$		0			0
$134$	−2.59574	+	1.68892i	−0.224238	+	0.145900i
$135$	0.380697	+	0.219795i	0.0327652	+	0.0189170i
$136$	−0.847027	+	8.26720i	−0.0726319	+	0.708906i
$137$	2.68685	−	1.55125i	0.229553	−	0.132532i	−0.380813	−	0.924652i	$-0.624356\pi$
$137$	2.68685	−	1.55125i	0.229553	−	0.132532i	0.610366	+	0.792120i	$0.291022\pi$
$138$	−0.359644	+	0.0191631i	−0.0306149	+	0.00163127i
$139$	−12.7451	−	12.7451i	−1.08103	−	1.08103i	−0.996414	−	0.0846114i	$-0.973035\pi$
$139$	−12.7451	−	12.7451i	−1.08103	−	1.08103i	−0.0846114	−	0.996414i	$-0.526965\pi$
$140$		0			0
$141$	−0.0779732	+	0.0779732i	−0.00656653	+	0.00656653i
$142$	−7.63998	−	6.86700i	−0.641133	−	0.576266i
$143$	−1.75684	−	3.04294i	−0.146914	−	0.254463i
$144$	11.4135	+	3.66444i	0.951124	+	0.305370i
$145$	−1.89896	+	3.28910i	−0.157700	+	0.273145i
$146$	4.13836	−	19.5534i	0.342493	−	1.61825i
$147$		0			0
$148$	−3.91173	−	10.1375i	−0.321543	−	0.833294i
$149$	14.5303	−	3.89339i	1.19037	−	0.318959i	0.391338	−	0.920247i	$-0.372012\pi$
$149$	14.5303	−	3.89339i	1.19037	−	0.318959i	0.799032	+	0.601288i	$0.205346\pi$
$150$	−0.119222	+	0.234493i	−0.00973446	+	0.0191463i
$151$	15.7545	−	9.09588i	1.28209	−	0.740212i	0.304856	−	0.952398i	$-0.401392\pi$
$151$	15.7545	−	9.09588i	1.28209	−	0.740212i	0.977229	+	0.212186i	$0.0680584\pi$
$152$	−7.97444	+	20.9379i	−0.646812	+	1.69829i
$153$			8.80528i			0.711865i
$154$		0			0
$155$	−5.78295	−	5.78295i	−0.464498	−	0.464498i
$156$	0.149739	+	0.205343i	0.0119887	+	0.0164406i
$157$	−9.39175	−	2.51651i	−0.749544	−	0.200840i	−0.136228	−	0.990678i	$-0.543498\pi$
$157$	−9.39175	−	2.51651i	−0.749544	−	0.200840i	−0.613316	+	0.789838i	$0.710165\pi$
$158$	0.842692	+	2.58585i	0.0670410	+	0.205719i
$159$	0.326788	−	0.566013i	0.0259159	−	0.0448877i
$160$	1.87543	−	7.12348i	0.148266	−	0.563161i
$161$		0			0
$162$	12.4126	+	2.62706i	0.975230	+	0.206402i
$163$	−3.36548	−	12.5602i	−0.263605	−	0.983787i	−0.963099	−	0.269148i	$-0.913258\pi$
$163$	−3.36548	−	12.5602i	−0.263605	−	0.983787i	0.699494	−	0.714639i	$-0.253409\pi$
$164$	14.5989	−	1.56019i	1.13998	−	0.121830i
$165$	0.0295323	−	0.110216i	0.00229909	−	0.00858031i
$166$	0.939366	+	17.6296i	0.0729090	+	1.36832i
$167$		−	16.5417i		−	1.28004i	−0.768360	−	0.640018i	$-0.778927\pi$
$167$		−	16.5417i		−	1.28004i	0.768360	−	0.640018i	$-0.221073\pi$
$168$		0			0
$169$			7.90463i			0.608049i
$170$	5.40319	−	0.287901i	0.414406	−	0.0220810i
$171$	−6.14412	+	22.9302i	−0.469853	+	1.75351i
$172$	−3.54147	+	4.38900i	−0.270035	+	0.334658i
$173$	5.59219	+	20.8703i	0.425166	+	1.58674i	0.763559	+	0.645738i	$0.223450\pi$
$173$	5.59219	+	20.8703i	0.425166	+	1.58674i	−0.338393	+	0.941005i	$0.609883\pi$
$174$	0.0480771	−	0.227160i	0.00364472	−	0.0172210i
$175$		0			0
$176$	0.304142	−	6.21893i	0.0229256	−	0.468770i
$177$	−0.0862837	+	0.149448i	−0.00648548	+	0.0112332i
$178$	−17.9368	+	5.84534i	−1.34442	+	0.438127i
$179$	−18.3264	−	4.91053i	−1.36978	−	0.367031i	−0.502379	−	0.864647i	$-0.667542\pi$
$179$	−18.3264	−	4.91053i	−1.36978	−	0.367031i	−0.867397	+	0.497617i	$0.834209\pi$
$180$	1.20748	−	7.71084i	0.0899999	−	0.574732i
$181$	−6.44222	−	6.44222i	−0.478846	−	0.478846i	0.425916	−	0.904763i	$-0.359952\pi$
$181$	−6.44222	−	6.44222i	−0.478846	−	0.478846i	−0.904763	+	0.425916i	$0.859952\pi$
$182$		0			0
$183$		−	0.566545i		−	0.0418802i
$184$	5.23505	+	11.6757i	0.385933	+	0.860745i
$185$	−6.12689	+	3.53736i	−0.450458	+	0.260072i
$186$	0.445698	+	0.226604i	0.0326801	+	0.0166154i
$187$	4.41773	−	1.18373i	0.323057	−	0.0865627i
$188$	3.58179	+	1.58723i	0.261229	+	0.115760i
$189$		0			0
$190$	14.2716	+	3.02049i	1.03537	+	0.219129i
$191$	−12.9567	+	22.4417i	−0.937515	+	1.62382i	−0.167429	+	0.985884i	$0.553546\pi$
$191$	−12.9567	+	22.4417i	−0.937515	+	1.62382i	−0.770086	+	0.637940i	$0.779787\pi$
$192$	0.0259253	+	0.449600i	0.00187100	+	0.0324471i
$193$	−6.27389	−	10.8667i	−0.451604	−	0.782202i	0.546881	−	0.837210i	$-0.315815\pi$
$193$	−6.27389	−	10.8667i	−0.451604	−	0.782202i	−0.998486	+	0.0550082i	$0.982481\pi$
$194$	9.16616	−	10.1979i	0.658092	−	0.732170i
$195$	0.117004	−	0.117004i	0.00837881	−	0.00837881i
$196$		0			0
$197$	−8.31651	−	8.31651i	−0.592527	−	0.592527i	0.345786	−	0.938313i	$-0.387612\pi$
$197$	−8.31651	−	8.31651i	−0.592527	−	0.592527i	−0.938313	+	0.345786i	$0.887612\pi$
$198$	−0.351017	−	6.58774i	−0.0249457	−	0.468170i
$199$	−16.6783	+	9.62922i	−1.18229	+	0.682597i	−0.956544	−	0.291589i	$-0.905816\pi$
$199$	−16.6783	+	9.62922i	−1.18229	+	0.682597i	−0.225749	+	0.974186i	$0.572483\pi$
$200$	9.29740	+	0.952578i	0.657426	+	0.0673574i
$201$	−0.106755	−	0.0616352i	−0.00752993	−	0.00434741i
$202$	−8.15097	−	12.5274i	−0.573501	−	0.881427i
$203$		0			0
$204$	−0.308623	+	0.119088i	−0.0216079	+	0.00833782i
$205$	−2.47413	−	9.23356i	−0.172800	−	0.644900i
$206$	4.60419	−	1.50044i	0.320789	−	0.104541i
$207$	6.77874	+	11.7411i	0.471155	+	0.816064i
$208$	4.89116	−	7.58963i	0.339141	−	0.526246i
$209$	12.3304			0.852909
$210$		0			0
$211$	−8.62222	+	8.62222i	−0.593578	+	0.593578i	−0.938596	−	0.345018i	$-0.887873\pi$
$211$	−8.62222	+	8.62222i	−0.593578	+	0.593578i	0.345018	+	0.938596i	$0.387873\pi$
$212$	−22.9408	−	3.59240i	−1.57558	−	0.246727i
$213$	0.105832	−	0.394969i	0.00725147	−	0.0270628i
$214$	−7.34336	+	14.4433i	−0.501982	+	0.987325i
$215$	3.17995	+	1.83595i	0.216871	+	0.125211i
$216$	0.151838	+	0.942675i	0.0103312	+	0.0641409i
$217$		0			0
$218$	3.71670	−	2.41827i	0.251727	−	0.163786i
$219$	0.768464	−	0.205909i	0.0519280	−	0.0139141i
$220$	−4.03096	+	0.430790i	−0.271767	+	0.0290439i
$221$	6.40638	+	1.71658i	0.430940	+	0.115470i
$222$	0.289135	−	0.321681i	0.0194055	−	0.0215898i
$223$	22.4402			1.50271			0.751354	−	0.659899i	$-0.229401\pi$
$223$	22.4402			1.50271			0.751354	+	0.659899i	$0.229401\pi$
$224$		0			0
$225$	9.90254			0.660169
$226$	4.42401	−	4.92200i	0.294281	−	0.327406i
$227$	2.25930	+	0.605377i	0.149955	+	0.0401803i	0.333016	−	0.942921i	$-0.391934\pi$
$227$	2.25930	+	0.605377i	0.149955	+	0.0401803i	−0.183061	+	0.983102i	$0.558600\pi$
$228$	−0.886793	+	0.0947718i	−0.0587293	+	0.00627642i
$229$	18.9832	−	5.08653i	1.25444	−	0.336127i	0.430393	−	0.902642i	$-0.358375\pi$
$229$	18.9832	−	5.08653i	1.25444	−	0.336127i	0.824052	+	0.566514i	$0.191708\pi$
$230$	6.98307	−	4.54353i	0.460450	−	0.299592i
$231$		0			0
$232$	−8.14440	+	1.31183i	−0.534706	+	0.0861256i
$233$	−3.35515	−	1.93710i	−0.219803	−	0.126903i	0.386056	−	0.922475i	$-0.373837\pi$
$233$	−3.35515	−	1.93710i	−0.219803	−	0.126903i	−0.605859	+	0.795572i	$0.707171\pi$
$234$	4.33577	−	8.52784i	0.283438	−	0.557482i
$235$	0.660191	−	2.46387i	0.0430661	−	0.160725i
$236$	6.05719	+	0.948524i	0.394290	+	0.0617437i
$237$	−0.0765505	+	0.0765505i	−0.00497249	+	0.00497249i
$238$		0			0
$239$	−6.56774			−0.424832			−0.212416	−	0.977179i	$-0.568133\pi$
$239$	−6.56774			−0.424832			−0.212416	+	0.977179i	$0.568133\pi$
$240$	0.286593	−	0.0619643i	0.0184995	−	0.00399978i
$241$	−6.62647	−	11.4774i	−0.426849	−	0.739323i	0.569742	−	0.821823i	$-0.307043\pi$
$241$	−6.62647	−	11.4774i	−0.426849	−	0.739323i	−0.996591	+	0.0824998i	$0.973710\pi$
$242$	11.5328	−	3.75837i	0.741356	−	0.241597i
$243$	0.392830	+	1.46606i	0.0252001	+	0.0940479i
$244$	−18.7788	+	7.24615i	−1.20219	+	0.463887i
$245$		0			0
$246$	0.318728	+	0.489860i	0.0203213	+	0.0312324i
$247$	15.4853	+	8.94045i	0.985306	+	0.568867i
$248$	1.81055	−	17.6714i	0.114970	−	1.12214i
$249$	−0.608598	+	0.351374i	−0.0385683	+	0.0222674i
$250$	−0.813704	−	15.2712i	−0.0514632	−	0.965838i
$251$	3.80916	+	3.80916i	0.240432	+	0.240432i	0.817029	−	0.576597i	$-0.195620\pi$
$251$	3.80916	+	3.80916i	0.240432	+	0.240432i	−0.576597	+	0.817029i	$0.695620\pi$
$252$		0			0
$253$	4.97939	−	4.97939i	0.313052	−	0.313052i
$254$	5.32538	−	5.92483i	0.334144	−	0.371757i
$255$	0.107691	+	0.186526i	0.00674385	+	0.0116807i
$256$	14.5709	−	6.60974i	0.910682	−	0.413109i
$257$	−11.8190	+	20.4712i	−0.737251	+	1.27696i	0.216477	+	0.976288i	$0.430543\pi$
$257$	−11.8190	+	20.4712i	−0.737251	+	1.27696i	−0.953729	+	0.300669i	$0.902790\pi$
$258$	−0.219622	−	0.0464818i	−0.0136731	−	0.00289383i
$259$		0			0
$260$	−5.37471	−	2.38174i	−0.333325	−	0.147709i
$261$	−8.44271	+	2.26222i	−0.522591	+	0.140028i
$262$	−2.61705	−	1.33058i	−0.161682	−	0.0822033i
$263$	−15.4301	+	8.90857i	−0.951460	+	0.549326i	−0.893534	−	0.448995i	$-0.851782\pi$
$263$	−15.4301	+	8.90857i	−0.951460	+	0.549326i	−0.0579260	+	0.998321i	$0.518449\pi$
$264$	0.226151	−	0.101400i	0.0139186	−	0.00624071i
$265$			15.1185i			0.928722i
$266$		0			0
$267$	−0.530993	−	0.530993i	−0.0324963	−	0.0324963i
$268$	−0.677560	+	4.32684i	−0.0413886	+	0.264304i
$269$	6.16728	+	1.65252i	0.376026	+	0.100756i	0.441882	−	0.897073i	$-0.354311\pi$
$269$	6.16728	+	1.65252i	0.376026	+	0.100756i	−0.0658559	+	0.997829i	$0.520978\pi$
$270$	0.591080	−	0.192624i	0.0359720	−	0.0117228i
$271$	−3.98703	+	6.90574i	−0.242195	+	0.419494i	−0.961339	−	0.275367i	$-0.911201\pi$
$271$	−3.98703	+	6.90574i	−0.242195	+	0.419494i	0.719144	+	0.694861i	$0.244534\pi$
$272$	7.89461	+	8.70650i	0.478681	+	0.527909i
$273$		0			0
$274$	0.908486	−	4.29252i	0.0548836	−	0.259320i
$275$	−1.33124	−	4.96824i	−0.0802765	−	0.299596i
$276$	−0.319843	+	0.396387i	−0.0192523	+	0.0238597i
$277$	3.31607	−	12.3757i	0.199243	−	0.743586i	−0.791884	−	0.610671i	$-0.790900\pi$
$277$	3.31607	−	12.3757i	0.199243	−	0.743586i	0.991127	−	0.132915i	$-0.0424337\pi$
$278$	−25.4541	+	1.35628i	−1.52664	+	0.0813444i
$279$		−	18.8216i		−	1.12682i
$280$		0			0
$281$			13.0438i			0.778126i	0.921211	+	0.389063i	$0.127201\pi$
$281$			13.0438i			0.778126i	−0.921211	+	0.389063i	$0.872799\pi$
$282$	0.00829759	+	0.155726i	0.000494115	+	0.00927332i
$283$	4.98843	−	18.6171i	0.296531	−	1.10667i	−0.643462	−	0.765478i	$-0.722503\pi$
$283$	4.98843	−	18.6171i	0.296531	−	1.10667i	0.939994	−	0.341192i	$-0.110831\pi$
$284$	−14.4453	+	1.54377i	−0.857171	+	0.0916061i
$285$	0.150288	+	0.560883i	0.00890229	+	0.0332238i
$286$	−4.86141	−	1.02889i	−0.287461	−	0.0608395i
$287$		0			0
$288$	14.6443	−	8.54034i	0.862922	−	0.503244i
$289$	4.18350	−	7.24603i	0.246088	−	0.426237i
$290$	1.66421	+	5.10674i	0.0977259	+	0.299878i
$291$	0.527210	+	0.141265i	0.0309056	+	0.00828113i
$292$	−16.6538	−	22.8380i	−0.974590	−	1.33649i
$293$	−12.7021	−	12.7021i	−0.742067	−	0.742067i	0.230908	−	0.972975i	$-0.425830\pi$
$293$	−12.7021	−	12.7021i	−0.742067	−	0.742067i	−0.972975	+	0.230908i	$0.925830\pi$
$294$		0			0
$295$		−	3.99183i		−	0.232413i
$296$	−14.3605	−	5.46938i	−0.834690	−	0.317901i
$297$	0.455076	−	0.262738i	0.0264062	−	0.0152456i
$298$	9.64158	−	18.9636i	0.558522	−	1.09853i
$299$	9.86389	−	2.64302i	0.570443	−	0.152850i
$300$	0.133928	+	0.347081i	0.00773233	+	0.0200387i
$301$		0			0
$302$	5.32697	−	25.1695i	0.306533	−	1.44834i
$303$	0.297460	−	0.515217i	0.0170887	−	0.0295984i
$304$	14.4835	+	28.1816i	0.830684	+	1.61633i
$305$	6.55265	+	11.3495i	0.375204	+	0.649872i
$306$	9.26132	+	8.32430i	0.529434	+	0.475868i
$307$	−15.5180	+	15.5180i	−0.885657	+	0.885657i	−0.994102	−	0.108446i	$-0.965413\pi$
$307$	−15.5180	+	15.5180i	−0.885657	+	0.885657i	0.108446	+	0.994102i	$0.465413\pi$
$308$		0			0
$309$	0.136300	+	0.136300i	0.00775386	+	0.00775386i
$310$	−11.5495	+	0.615398i	−0.655968	+	0.0349523i
$311$	−3.14576	+	1.81621i	−0.178380	+	0.102988i	−0.586531	−	0.809927i	$-0.699507\pi$
$311$	−3.14576	+	1.81621i	−0.178380	+	0.102988i	0.408151	+	0.912914i	$0.366174\pi$
$312$	0.357538	+	0.0366320i	0.0202416	+	0.00207388i
$313$	−3.24479	−	1.87338i	−0.183406	−	0.105890i	0.405486	−	0.914101i	$-0.367102\pi$
$313$	−3.24479	−	1.87338i	−0.183406	−	0.105890i	−0.588892	+	0.808212i	$0.700436\pi$
$314$	−11.5256	+	7.49912i	−0.650426	+	0.423200i
$315$		0			0
$316$	3.51644	+	1.55827i	0.197815	+	0.0876593i
$317$	6.36774	+	23.7647i	0.357648	+	1.33476i	0.877119	+	0.480272i	$0.159462\pi$
$317$	6.36774	+	23.7647i	0.357648	+	1.33476i	−0.519472	+	0.854488i	$0.673871\pi$
$318$	−0.286390	−	0.878807i	−0.0160600	−	0.0492810i
$319$	2.26997	+	3.93171i	0.127094	+	0.220133i
$320$	−5.71943	−	8.70693i	−0.319726	−	0.486732i
$321$	−0.644963			−0.0359983
$322$		0			0
$323$	−16.4576	+	16.4576i	−0.915727	+	0.915727i
$324$	14.4977	−	10.5720i	0.805430	−	0.587331i
$325$	1.93049	−	7.20470i	0.107084	−	0.399645i
$326$	−16.3923	−	8.33427i	−0.907886	−	0.461593i
$327$	0.152857	+	0.0882521i	0.00845302	+	0.00488035i
$328$	12.1604	−	16.8299i	0.671448	−	0.929278i
$329$		0			0
$330$	−0.0880053	−	0.135257i	−0.00484453	−	0.00744568i
$331$	9.79479	−	2.62451i	0.538370	−	0.144256i	0.0206195	−	0.999787i	$-0.493436\pi$
$331$	9.79479	−	2.62451i	0.538370	−	0.144256i	0.517751	+	0.855532i	$0.326769\pi$
$332$	19.4307	+	15.6786i	1.06640	+	0.860474i
$333$	−15.7270	−	4.21403i	−0.861833	−	0.230928i
$334$	−17.3984	−	15.6381i	−0.952000	−	0.855680i
$335$	2.85149			0.155793
$336$		0			0
$337$	−5.30745			−0.289115			−0.144558	−	0.989496i	$-0.546176\pi$
$337$	−5.30745			−0.289115			−0.144558	+	0.989496i	$0.546176\pi$
$338$	8.31402	+	7.47284i	0.452223	+	0.406469i
$339$	0.254456	+	0.0681812i	0.0138201	+	0.00370309i
$340$	4.80523	−	5.95520i	0.260600	−	0.322966i
$341$	−9.44306	+	2.53026i	−0.511370	+	0.137021i
$342$	18.3093	+	28.1400i	0.990051	+	1.52163i
$343$		0			0
$344$	1.26830	+	7.87414i	0.0683819	+	0.424545i
$345$	0.287193	+	0.165811i	0.0154620	+	0.00892696i
$346$	27.2380	+	13.8485i	1.46432	+	0.744499i
$347$	1.06753	−	3.98409i	0.0573082	−	0.213877i	−0.931334	−	0.364166i	$-0.881354\pi$
$347$	1.06753	−	3.98409i	0.0573082	−	0.213877i	0.988642	+	0.150290i	$0.0480206\pi$
$348$	−0.193474	−	0.265319i	−0.0103713	−	0.0142226i
$349$	−11.4637	+	11.4637i	−0.613639	+	0.613639i	−0.943892	−	0.330253i	$-0.892866\pi$
$349$	−11.4637	+	11.4637i	−0.613639	+	0.613639i	0.330253	+	0.943892i	$0.392866\pi$
$350$		0			0
$351$	0.762020			0.0406736
$352$	−6.25349	−	6.19912i	−0.333312	−	0.330414i
$353$	−1.93371	−	3.34929i	−0.102921	−	0.178265i	0.809966	−	0.586477i	$-0.199486\pi$
$353$	−1.93371	−	3.34929i	−0.102921	−	0.178265i	−0.912887	+	0.408212i	$0.866152\pi$
$354$	0.0756174	+	0.232037i	0.00401902	+	0.0123326i
$355$	2.44810	+	9.13642i	0.129932	+	0.484911i
$356$	−10.8089	+	24.3918i	−0.572873	+	1.29276i
$357$		0			0
$358$	−22.4901	+	14.6332i	−1.18864	+	0.773389i
$359$	−13.6977	−	7.90839i	−0.722938	−	0.417389i	0.0928949	−	0.995676i	$-0.470388\pi$
$359$	−13.6977	−	7.90839i	−0.722938	−	0.417389i	−0.815833	+	0.578287i	$0.803721\pi$
$360$	−6.96867	−	8.55965i	−0.367281	−	0.451133i
$361$	−37.8872	+	21.8742i	−1.99407	+	1.15127i
$362$	−12.8662	+	0.685555i	−0.676232	+	0.0360320i
$363$	0.341412	+	0.341412i	0.0179195	+	0.0179195i
$364$		0			0
$365$	−13.0130	+	13.0130i	−0.681132	+	0.681132i
$366$	−0.595887	−	0.535597i	−0.0311475	−	0.0279961i
$367$	−2.37345	−	4.11093i	−0.123893	−	0.214589i	0.797407	−	0.603442i	$-0.206205\pi$
$367$	−2.37345	−	4.11093i	−0.123893	−	0.214589i	−0.921300	+	0.388853i	$0.872871\pi$
$368$	17.2295	+	5.53175i	0.898150	+	0.288362i
$369$	10.9999	−	19.0523i	0.572631	−	0.991826i
$370$	−2.07164	+	9.78834i	−0.107700	+	0.508872i
$371$		0			0
$372$	0.659692	−	0.254555i	0.0342034	−	0.0131980i
$373$	22.0083	−	5.89711i	1.13955	−	0.305341i	0.360779	−	0.932651i	$-0.382511\pi$
$373$	22.0083	−	5.89711i	1.13955	−	0.305341i	0.778769	+	0.627310i	$0.215844\pi$
$374$	2.93138	−	5.76560i	0.151578	−	0.298132i
$375$	0.527184	−	0.304370i	0.0272237	−	0.0157176i
$376$	5.05557	−	2.26677i	0.260721	−	0.116900i
$377$			6.58360i			0.339073i
$378$		0			0
$379$	20.1030	+	20.1030i	1.03262	+	1.03262i	0.999450	+	0.0331705i	$0.0105604\pi$
$379$	20.1030	+	20.1030i	1.03262	+	1.03262i	0.0331705	+	0.999450i	$0.489440\pi$
$380$	16.6689	−	12.1552i	0.855096	−	0.623549i
$381$	0.306300	+	0.0820728i	0.0156922	+	0.00420472i
$382$	11.3550	+	34.8436i	0.580973	+	1.78275i
$383$	−11.7252	+	20.3087i	−0.599131	+	1.03773i	0.393819	+	0.919188i	$0.371154\pi$
$383$	−11.7252	+	20.3087i	−0.599131	+	1.03773i	−0.992950	+	0.118537i	$0.962180\pi$
$384$	0.497394	+	0.397773i	0.0253825	+	0.0202987i
$385$		0			0
$386$	−17.3607	−	3.67428i	−0.883635	−	0.187016i
$387$	2.18715	+	8.16255i	0.111179	+	0.414926i
$388$	−2.06065	−	19.2818i	−0.104614	−	0.978883i
$389$	2.77356	−	10.3510i	0.140625	−	0.524819i	−0.859286	−	0.511495i	$-0.829092\pi$
$389$	2.77356	−	10.3510i	0.140625	−	0.524819i	0.999911	−	0.0133242i	$-0.00424136\pi$
$390$	−0.0124511	−	0.233676i	−0.000630484	−	0.0118326i
$391$			13.2922i			0.672216i
$392$		0			0
$393$		−	0.116864i		−	0.00589500i
$394$	−16.6095	+	0.885009i	−0.836773	+	0.0445861i
$395$	0.648145	−	2.41891i	0.0326117	−	0.121709i
$396$	−7.26077	−	5.85869i	−0.364867	−	0.294410i
$397$	−1.71548	−	6.40226i	−0.0860975	−	0.321320i	0.909422	−	0.415874i	$-0.136524\pi$
$397$	−1.71548	−	6.40226i	−0.0860975	−	0.321320i	−0.995520	+	0.0945536i	$0.969858\pi$
$398$	−5.63932	+	26.6453i	−0.282674	+	1.33561i
$399$		0			0
$400$	9.79145	−	8.87838i	0.489572	−	0.443919i
$401$	−15.8657	+	27.4802i	−0.792294	+	1.37229i	0.132250	+	0.991216i	$0.457780\pi$
$401$	−15.8657	+	27.4802i	−0.792294	+	1.37229i	−0.924543	+	0.381077i	$0.875553\pi$
$402$	−0.165751	+	0.0540159i	−0.00826691	+	0.00269407i
$403$	−13.6939	−	3.66926i	−0.682140	−	0.182779i
$404$	−20.8820	−	3.27001i	−1.03892	−	0.162689i
$405$	−8.26075	−	8.26075i	−0.410480	−	0.410480i
$406$		0			0
$407$			8.45695i			0.419196i
$408$	−0.166509	+	0.437189i	−0.00824340	+	0.0216441i
$409$	1.11952	−	0.646353i	0.0553565	−	0.0319601i	−0.472066	−	0.881563i	$-0.656492\pi$
$409$	1.11952	−	0.646353i	0.0553565	−	0.0319601i	0.527423	+	0.849603i	$0.323158\pi$
$410$	−12.0508	−	6.12692i	−0.595145	−	0.302587i
$411$	0.168699	−	0.0452028i	0.00832131	−	0.00222969i
$412$	2.77454	−	6.26113i	0.136692	−	0.308464i
$413$		0			0
$414$	18.7577	+	3.96995i	0.921889	+	0.195112i
$415$	8.12799	−	14.0781i	0.398987	−	0.691066i
$416$	−3.35873	−	12.3195i	−0.164675	−	0.604015i
$417$	−0.507324	−	0.878710i	−0.0248437	−	0.0430306i
$418$	11.6568	−	12.9690i	0.570154	−	0.634333i
$419$	−17.2788	+	17.2788i	−0.844124	+	0.844124i	−0.989392	−	0.145269i	$-0.953595\pi$
$419$	−17.2788	+	17.2788i	−0.844124	+	0.844124i	0.145269	+	0.989392i	$0.453595\pi$
$420$		0			0
$421$	3.36245	+	3.36245i	0.163876	+	0.163876i	0.784281	−	0.620405i	$-0.213032\pi$
$421$	3.36245	+	3.36245i	0.163876	+	0.163876i	−0.620405	+	0.784281i	$0.713032\pi$
$422$	0.917541	+	17.2200i	0.0446652	+	0.838257i
$423$	5.08389	−	2.93519i	0.247187	−	0.142714i
$424$	−25.4661	+	20.7327i	−1.23674	+	1.00687i
$425$	8.40806	+	4.85440i	0.407851	+	0.235473i
$426$	−0.315374	−	0.484707i	−0.0152799	−	0.0234841i
$427$		0			0
$428$	8.24913	+	21.3780i	0.398737	+	1.03335i
$429$	−0.0511936	−	0.191057i	−0.00247165	−	0.00922432i
$430$	4.93728	−	1.60899i	0.238097	−	0.0775923i
$431$	−5.58722	−	9.67735i	−0.269127	−	0.466141i	0.699510	−	0.714623i	$-0.253402\pi$
$431$	−5.58722	−	9.67735i	−0.269127	−	0.466141i	−0.968637	+	0.248482i	$0.920068\pi$
$432$	1.13504	+	0.731480i	0.0546097	+	0.0351934i
$433$	17.3943			0.835916			0.417958	−	0.908466i	$-0.362746\pi$
$433$	17.3943			0.835916			0.417958	+	0.908466i	$0.362746\pi$
$434$		0			0
$435$	−0.151178	+	0.151178i	−0.00724842	+	0.00724842i
$436$	0.970163	−	6.19537i	0.0464624	−	0.296705i
$437$	−9.27500	+	34.6148i	−0.443684	+	1.65585i
$438$	0.509913	−	1.00293i	0.0243646	−	0.0479216i
$439$	32.5115	+	18.7705i	1.55169	+	0.895867i	0.998005	+	0.0631399i	$0.0201114\pi$
$439$	32.5115	+	18.7705i	1.55169	+	0.895867i	0.553683	+	0.832727i	$0.313222\pi$
$440$	−3.35767	+	4.64699i	−0.160071	+	0.221536i
$441$		0			0
$442$	7.86192	−	5.11536i	0.373953	−	0.243313i
$443$	6.88186	−	1.84399i	0.326967	−	0.0876106i	−0.0916015	−	0.995796i	$-0.529199\pi$
$443$	6.88186	−	1.84399i	0.326967	−	0.0876106i	0.418569	+	0.908185i	$0.362532\pi$
$444$	−0.0650006	−	0.608219i	−0.00308479	−	0.0288648i
$445$	16.7788	+	4.49587i	0.795392	+	0.213125i
$446$	21.2144	−	23.6024i	1.00453	−	1.11761i
$447$	0.846815			0.0400530
$448$		0			0
$449$	−7.84005			−0.369995			−0.184997	−	0.982739i	$-0.559228\pi$
$449$	−7.84005			−0.369995			−0.184997	+	0.982739i	$0.559228\pi$
$450$	9.36161	−	10.4154i	0.441311	−	0.490987i
$451$	−11.0376	−	2.95751i	−0.519739	−	0.139264i
$452$	−0.994564	−	9.30627i	−0.0467803	−	0.437730i
$453$	0.989180	−	0.265050i	0.0464757	−	0.0124531i
$454$	2.77262	−	1.80400i	0.130125	−	0.0846660i
$455$		0			0
$456$	−0.738672	+	1.02232i	−0.0345915	+	0.0478743i
$457$	−22.2821	−	12.8646i	−1.04231	−	0.601780i	−0.121826	−	0.992551i	$-0.538875\pi$
$457$	−22.2821	−	12.8646i	−1.04231	−	0.601780i	−0.920488	+	0.390771i	$0.872208\pi$
$458$	12.5963	−	24.7750i	0.588585	−	1.15766i
$459$	−0.256718	+	0.958084i	−0.0119826	+	0.0447195i
$460$	1.82277	−	11.6401i	0.0849873	−	0.542721i
$461$	13.1661	−	13.1661i	0.613207	−	0.613207i	−0.330573	−	0.943780i	$-0.607242\pi$
$461$	13.1661	−	13.1661i	0.613207	−	0.613207i	0.943780	+	0.330573i	$0.107242\pi$
$462$		0			0
$463$	6.88821			0.320122			0.160061	−	0.987107i	$-0.448831\pi$
$463$	6.88821			0.320122			0.160061	+	0.987107i	$0.448831\pi$
$464$	−6.31975	+	9.80638i	−0.293387	+	0.455250i
$465$	−0.230193	−	0.398705i	−0.0106749	−	0.0184895i
$466$	−5.20930	+	1.69763i	−0.241316	+	0.0786414i
$467$	−10.2399	−	38.2159i	−0.473847	−	1.76842i	−0.625749	−	0.780025i	$-0.715206\pi$
$467$	−10.2399	−	38.2159i	−0.473847	−	1.76842i	0.151902	−	0.988396i	$-0.451460\pi$
$468$	−4.87057	−	12.6223i	−0.225142	−	0.583468i
$469$		0			0
$470$	−1.96735	−	3.02366i	−0.0907469	−	0.139471i
$471$	−0.474013	−	0.273672i	−0.0218414	−	0.0126101i
$472$	6.72397	−	5.47419i	0.309496	−	0.251970i
$473$	3.80124	−	2.19465i	0.174781	−	0.100910i
$474$	0.00814619	+	0.152884i	0.000374167	+	0.00702220i
$475$	18.5085	+	18.5085i	0.849227	+	0.849227i
$476$		0			0
$477$	−24.6029	+	24.6029i	−1.12649	+	1.12649i
$478$	−6.20898	+	6.90790i	−0.283992	+	0.315960i
$479$	−0.261991	−	0.453782i	−0.0119707	−	0.0207338i	0.859978	−	0.510331i	$-0.170477\pi$
$479$	−0.261991	−	0.453782i	−0.0119707	−	0.0207338i	−0.871949	+	0.489597i	$0.837144\pi$
$480$	0.205765	−	0.360016i	0.00939183	−	0.0164324i
$481$	−6.13193	+	10.6208i	−0.279592	+	0.484267i
$482$	−18.3363	−	3.88077i	−0.835197	−	0.176764i
$483$		0			0
$484$	6.94980	−	15.6832i	0.315900	−	0.712871i
$485$	−12.1954	+	3.26775i	−0.553765	+	0.148381i
$486$	1.91336	+	0.972804i	0.0867920	+	0.0441273i
$487$	2.46586	−	1.42366i	0.111739	−	0.0645124i	−0.443089	−	0.896478i	$-0.646117\pi$
$487$	2.46586	−	1.42366i	0.111739	−	0.0645124i	0.554828	+	0.831965i	$0.312784\pi$
$488$	−10.1316	+	26.6017i	−0.458634	+	1.20420i
$489$		−	0.731995i		−	0.0331019i
$490$		0			0
$491$	−17.4826	−	17.4826i	−0.788977	−	0.788977i	0.192349	−	0.981327i	$-0.438389\pi$
$491$	−17.4826	−	17.4826i	−0.788977	−	0.788977i	−0.981327	+	0.192349i	$0.938389\pi$
$492$	0.816548	+	0.127867i	0.0368128	+	0.00576469i
$493$	−8.27753	−	2.21796i	−0.372801	−	0.0998918i
$494$	24.0429	−	7.83523i	1.08174	−	0.352524i
$495$	−3.03722	+	5.26063i	−0.136513	+	0.236448i
$496$	−16.8750	−	18.6105i	−0.757711	−	0.835635i
$497$		0			0
$498$	−0.205781	+	0.972299i	−0.00922128	+	0.0435698i
$499$	0.350599	+	1.30845i	0.0156949	+	0.0585743i	0.973329	−	0.229413i	$-0.0736806\pi$
$499$	0.350599	+	1.30845i	0.0156949	+	0.0585743i	−0.957634	+	0.287987i	$0.907014\pi$
$500$	−16.8314	−	13.5812i	−0.752724	−	0.607370i
$501$	0.241009	−	0.899458i	0.0107675	−	0.0401848i
$502$	7.60752	−	0.405355i	0.339540	−	0.0180919i
$503$			15.4389i			0.688388i	0.938899	+	0.344194i	$0.111848\pi$
$503$			15.4389i			0.688388i	−0.938899	+	0.344194i	$0.888152\pi$
$504$		0			0
$505$			13.7617i			0.612388i
$506$	−0.529886	−	9.94467i	−0.0235563	−	0.442095i
$507$	−0.115169	+	0.429816i	−0.00511482	+	0.0190888i
$508$	−1.19720	−	11.2024i	−0.0531172	−	0.497025i
$509$	2.23550	+	8.34301i	0.0990869	+	0.369797i	0.997607	−	0.0691342i	$-0.0220237\pi$
$509$	2.23550	+	8.34301i	0.0990869	+	0.369797i	−0.898520	+	0.438932i	$0.855357\pi$
$510$	0.297994	+	0.0630687i	0.0131954	+	0.00279273i
$511$		0			0
$512$	6.82291	−	21.5742i	0.301533	−	0.953456i
$513$	−1.33706	+	2.31585i	−0.0590325	+	0.102247i
$514$	10.3580	+	31.7841i	0.456871	+	1.40194i
$515$	−4.30694	−	1.15404i	−0.189787	−	0.0508532i
$516$	−0.256515	+	0.187054i	−0.0112924	+	0.00823461i
$517$	−2.15607	−	2.15607i	−0.0948239	−	0.0948239i
$518$		0			0
$519$			1.21631i			0.0533899i
$520$	−7.58620	+	3.40144i	−0.332677	+	0.149163i
$521$	−3.08690	+	1.78222i	−0.135240	+	0.0780807i	−0.566093	−	0.824341i	$-0.691546\pi$
$521$	−3.08690	+	1.78222i	−0.135240	+	0.0780807i	0.430854	+	0.902422i	$0.358213\pi$
$522$	−5.60215	+	11.0186i	−0.245200	+	0.482272i
$523$	−19.5332	+	5.23389i	−0.854125	+	0.228862i	−0.659211	−	0.751958i	$-0.729110\pi$
$523$	−19.5332	+	5.23389i	−0.854125	+	0.228862i	−0.194914	+	0.980820i	$0.562443\pi$
$524$	−3.87359	+	1.49470i	−0.169218	+	0.0652962i
$525$		0			0
$526$	−5.21728	+	24.6512i	−0.227484	+	1.07484i
$527$	9.22668	−	15.9811i	0.401920	−	0.696147i
$528$	0.107146	−	0.333724i	0.00466294	−	0.0145235i
$529$	−1.26700	−	2.19451i	−0.0550869	−	0.0954133i
$530$	15.9015	+	14.2927i	0.690717	+	0.620833i
$531$	6.49605	−	6.49605i	0.281905	−	0.281905i
$532$		0			0
$533$	−11.7173	−	11.7173i	−0.507534	−	0.507534i
$534$	−1.06048	+	0.0565062i	−0.0458916	+	0.00244526i
$535$	12.9205	−	7.45964i	0.558601	−	0.322508i
$536$	3.91039	+	4.80314i	0.168903	+	0.207464i
$537$	−0.924954	−	0.534022i	−0.0399147	−	0.0230448i
$538$	7.56850	−	4.92444i	0.326301	−	0.212308i
$539$		0			0
$540$	0.356192	−	0.803796i	0.0153281	−	0.0345899i
$541$	−1.90773	−	7.11973i	−0.0820195	−	0.306101i	0.912714	−	0.408600i	$-0.133983\pi$
$541$	−1.90773	−	7.11973i	−0.0820195	−	0.306101i	−0.994733	+	0.102499i	$0.967316\pi$
$542$	3.49416	+	10.7220i	0.150087	+	0.460551i
$543$	−0.256435	−	0.444159i	−0.0110047	−	0.0190607i
$544$	16.6208	−	0.0725695i	0.712611	−	0.00311139i
$545$	−4.08289			−0.174892
$546$		0			0
$547$	17.8464	−	17.8464i	0.763058	−	0.763058i	−0.213816	−	0.976874i	$-0.568589\pi$
$547$	17.8464	−	17.8464i	0.763058	−	0.763058i	0.976874	+	0.213816i	$0.0685893\pi$
$548$	−3.65597	−	5.01358i	−0.156175	−	0.214169i
$549$	−7.80613	+	29.1329i	−0.333158	+	1.24336i
$550$	−6.48407	−	3.29667i	−0.276482	−	0.140570i
$551$	−20.0082	−	11.5517i	−0.852378	−	0.492121i
$552$	0.114544	+	0.711142i	0.00487533	+	0.0302682i
$553$		0			0
$554$	−9.88177	−	15.1875i	−0.419836	−	0.645257i
$555$	−0.384689	+	0.103077i	−0.0163291	+	0.00437538i
$556$	−22.6372	+	28.0546i	−0.960029	+	1.18978i
$557$	−14.4174	−	3.86313i	−0.610884	−	0.163686i	−0.0599038	−	0.998204i	$-0.519079\pi$
$557$	−14.4174	−	3.86313i	−0.610884	−	0.163686i	−0.550980	+	0.834518i	$0.685746\pi$
$558$	−19.7964	−	17.7935i	−0.838049	−	0.753258i
$559$	6.36514			0.269217
$560$		0			0
$561$	0.257462			0.0108700
$562$	13.7193	+	12.3313i	0.578715	+	0.520163i
$563$	−7.71786	−	2.06799i	−0.325269	−	0.0871556i	0.0924895	−	0.995714i	$-0.470518\pi$
$563$	−7.71786	−	2.06799i	−0.325269	−	0.0871556i	−0.417759	+	0.908558i	$0.637184\pi$
$564$	0.171635	+	0.138492i	0.00722714	+	0.00583156i
$565$	−5.88607	+	1.57717i	−0.247629	+	0.0663519i
$566$	−14.8653	−	22.8469i	−0.624837	−	0.960327i
$567$		0			0
$568$	−12.0325	+	16.6529i	−0.504873	+	0.698740i
$569$	−12.1275	−	7.00179i	−0.508409	−	0.293530i	0.223770	−	0.974642i	$-0.428163\pi$
$569$	−12.1275	−	7.00179i	−0.508409	−	0.293530i	−0.732180	+	0.681112i	$0.761497\pi$
$570$	0.732010	+	0.372173i	0.0306605	+	0.0155886i
$571$	−0.488992	+	1.82494i	−0.0204637	+	0.0763715i	−0.975403	−	0.220431i	$-0.929254\pi$
$571$	−0.488992	+	1.82494i	−0.0204637	+	0.0763715i	0.954939	+	0.296802i	$0.0959203\pi$
$572$	−5.67803	+	4.14050i	−0.237411	+	0.173123i
$573$	−1.03149	+	1.03149i	−0.0430913	+	0.0430913i
$574$		0			0
$575$	14.9486			0.623400
$576$	4.86167	−	23.4765i	0.202570	−	0.978189i
$577$	8.81809	+	15.2734i	0.367102	+	0.635839i	0.989111	−	0.147171i	$-0.0470167\pi$
$577$	8.81809	+	15.2734i	0.367102	+	0.635839i	−0.622009	+	0.783010i	$0.713683\pi$
$578$	−3.66634	−	11.2504i	−0.152500	−	0.467954i
$579$	−0.182818	−	0.682288i	−0.00759767	−	0.0283549i
$580$	6.94453	+	3.07738i	0.288356	+	0.127781i
$581$		0			0
$582$	0.646993	−	0.420966i	0.0268187	−	0.0174496i
$583$	15.6511	+	9.03615i	0.648201	+	0.374239i
$584$	−39.7649	−	4.07417i	−1.64548	−	0.168590i
$585$	−7.62870	+	4.40443i	−0.315408	+	0.182101i
$586$	−25.3683	+	1.35171i	−1.04795	+	0.0558386i
$587$	−18.5150	−	18.5150i	−0.764194	−	0.764194i	0.212883	−	0.977078i	$-0.431715\pi$
$587$	−18.5150	−	18.5150i	−0.764194	−	0.764194i	−0.977078	+	0.212883i	$0.931715\pi$
$588$		0			0
$589$	35.1788	−	35.1788i	1.44952	−	1.44952i
$590$	−4.19857	−	3.77378i	−0.172852	−	0.155364i
$591$	−0.331042	−	0.573382i	−0.0136172	−	0.0235858i
$592$	−19.3288	+	9.93369i	−0.794407	+	0.408272i
$593$	3.95463	−	6.84963i	0.162397	−	0.281281i	−0.773331	−	0.634003i	$-0.781411\pi$
$593$	3.95463	−	6.84963i	0.162397	−	0.281281i	0.935728	+	0.352722i	$0.114744\pi$
$594$	0.153872	−	0.727031i	0.00631344	−	0.0298305i
$595$		0			0
$596$	−10.8308	−	28.0686i	−0.443648	−	1.14974i
$597$	−1.04718	+	0.280591i	−0.0428582	+	0.0114838i
$598$	6.54517	−	12.8734i	0.267652	−	0.526432i
$599$	18.5333	−	10.7002i	0.757251	−	0.437199i	−0.0710572	−	0.997472i	$-0.522637\pi$
$599$	18.5333	−	10.7002i	0.757251	−	0.437199i	0.828308	+	0.560273i	$0.189304\pi$
$600$	0.491669	+	0.187258i	0.0200723	+	0.00764476i
$601$		−	0.974684i		−	0.0397582i	−0.999802	−	0.0198791i	$-0.993672\pi$
$601$		−	0.974684i		−	0.0397582i	0.999802	−	0.0198791i	$-0.00632813\pi$
$602$		0			0
$603$	4.64033	+	4.64033i	0.188969	+	0.188969i
$604$	−21.4371	−	29.3975i	−0.872262	−	1.19617i
$605$	−10.7882	−	2.89070i	−0.438604	−	0.117524i
$606$	−0.260689	−	0.799939i	−0.0105897	−	0.0324953i
$607$	3.01261	−	5.21800i	0.122278	−	0.211792i	−0.798388	−	0.602144i	$-0.794313\pi$
$607$	3.01261	−	5.21800i	0.122278	−	0.211792i	0.920666	+	0.390352i	$0.127647\pi$
$608$	43.3335	+	11.4086i	1.75741	+	0.462681i
$609$		0			0
$610$	18.1321	+	3.83754i	0.734146	+	0.155378i
$611$	−1.14443	−	4.27106i	−0.0462985	−	0.172788i
$612$	17.5108	−	1.87139i	0.707834	−	0.0756465i
$613$	−0.426012	+	1.58990i	−0.0172065	+	0.0642155i	−0.973995	−	0.226568i	$-0.927249\pi$
$613$	−0.426012	+	1.58990i	−0.0172065	+	0.0642155i	0.956789	+	0.290784i	$0.0939160\pi$
$614$	1.65136	+	30.9920i	0.0666434	+	1.25073i
$615$		−	0.538124i		−	0.0216993i
$616$		0			0
$617$		−	34.0864i		−	1.37227i	−0.727476	−	0.686134i	$-0.759307\pi$
$617$		−	34.0864i		−	1.37227i	0.727476	−	0.686134i	$-0.240693\pi$
$618$	0.272215	−	0.0145045i	0.0109501	−	0.000583458i
$619$	8.65485	−	32.3004i	0.347868	−	1.29826i	−0.541358	−	0.840792i	$-0.682090\pi$
$619$	8.65485	−	32.3004i	0.347868	−	1.29826i	0.889226	−	0.457469i	$-0.151244\pi$
$620$	−10.2714	+	12.7295i	−0.412508	+	0.511228i
$621$	0.395268	+	1.47516i	0.0158615	+	0.0591961i
$622$	−1.06366	+	5.02568i	−0.0426487	+	0.201512i
$623$		0			0
$624$	0.376537	−	0.341424i	0.0150735	−	0.0136679i
$625$	1.22016	−	2.11337i	0.0488063	−	0.0845349i
$626$	−5.03795	+	1.64179i	−0.201357	+	0.0656193i
$627$	0.670466	+	0.179651i	0.0267758	+	0.00717456i
$628$	−3.00849	+	19.2120i	−0.120052	+	0.766642i
$629$	−11.2877	−	11.2877i	−0.450070	−	0.450070i
$630$		0			0
$631$			4.58799i			0.182645i	0.995821	+	0.0913225i	$0.0291094\pi$
$631$			4.58799i			0.182645i	−0.995821	+	0.0913225i	$0.970891\pi$
$632$	4.96333	−	2.22541i	0.197430	−	0.0885222i
$633$	−0.594458	+	0.343211i	−0.0236276	+	0.0136414i
$634$	31.0154	+	15.7691i	1.23178	+	0.626269i
$635$	−7.08533	+	1.89851i	−0.281173	+	0.0753400i
$636$	−1.19507	−	0.529580i	−0.0473875	−	0.0209992i
$637$		0			0
$638$	6.28131	+	1.32940i	0.248680	+	0.0526315i
$639$	−10.8842	+	18.8519i	−0.430571	+	0.745770i
$640$	−14.5649	−	2.21567i	−0.575728	−	0.0875822i
$641$	24.9135	+	43.1515i	0.984025	+	1.70438i	0.646190	+	0.763177i	$0.276361\pi$
$641$	24.9135	+	43.1515i	0.984025	+	1.70438i	0.337835	+	0.941205i	$0.390305\pi$
$642$	−0.609732	+	0.678367i	−0.0240642	+	0.0267730i
$643$	31.1050	−	31.1050i	1.22666	−	1.22666i	0.261443	−	0.965219i	$-0.415802\pi$
$643$	31.1050	−	31.1050i	1.22666	−	1.22666i	0.965219	−	0.261443i	$-0.0841985\pi$
$644$		0			0
$645$	0.146161	+	0.146161i	0.00575509	+	0.00575509i
$646$	1.75135	+	32.8686i	0.0689061	+	1.29320i
$647$	25.4255	−	14.6794i	0.999579	−	0.577107i	0.0914555	−	0.995809i	$-0.470848\pi$
$647$	25.4255	−	14.6794i	0.999579	−	0.577107i	0.908124	+	0.418702i	$0.137515\pi$
$648$	2.58631	−	25.2431i	0.101600	−	0.991641i
$649$	−4.13245	−	2.38587i	−0.162213	−	0.0936536i
$650$	−5.75280	−	8.84162i	−0.225643	−	0.346797i
$651$		0			0
$652$	−24.2628	+	9.36227i	−0.950205	+	0.366655i
$653$	−3.93761	−	14.6954i	−0.154091	−	0.575075i	−0.999181	−	0.0404516i	$-0.987120\pi$
$653$	−3.93761	−	14.6954i	−0.154091	−	0.575075i	0.845091	−	0.534623i	$-0.179546\pi$
$654$	0.237330	−	0.0773424i	0.00928034	−	0.00302433i
$655$	1.35165	+	2.34112i	0.0528132	+	0.0914752i
$656$	−6.20541	−	28.7008i	−0.242281	−	1.12058i
$657$	−42.3531			−1.65235
$658$		0			0
$659$	−8.45620	+	8.45620i	−0.329407	+	0.329407i	−0.852361	−	0.522954i	$-0.824830\pi$
$659$	−8.45620	+	8.45620i	−0.329407	+	0.329407i	0.522954	+	0.852361i	$0.324830\pi$
$660$	−0.225461	−	0.0353059i	−0.00877604	−	0.00137428i
$661$	3.50720	−	13.0890i	0.136414	−	0.509105i	−0.863574	−	0.504222i	$-0.831779\pi$
$661$	3.50720	−	13.0890i	0.136414	−	0.509105i	0.999988	−	0.00488232i	$-0.00155410\pi$
$662$	6.49932	−	12.7832i	0.252603	−	0.496834i
$663$	0.323338	+	0.186679i	0.0125574	+	0.00725001i
$664$	34.8599	−	5.61492i	1.35283	−	0.217901i
$665$		0			0
$666$	−19.3002	+	12.5577i	−0.747867	+	0.486599i
$667$	−12.7449	+	3.41498i	−0.493484	+	0.132229i
$668$	−32.8961	+	3.51562i	−1.27279	+	0.136023i
$669$	1.22019	+	0.326949i	0.0471753	+	0.0126406i
$670$	2.69573	−	2.99917i	0.104145	−	0.115868i
$671$	15.6658			0.604771
$672$		0			0
$673$	−15.5552			−0.599610			−0.299805	−	0.954000i	$-0.596922\pi$
$673$	−15.5552			−0.599610			−0.299805	+	0.954000i	$0.596922\pi$
$674$	−5.01753	+	5.58233i	−0.193268	+	0.215023i
$675$	1.07747	+	0.288708i	0.0414720	+	0.0111124i
$676$	15.7197	−	1.67997i	0.604606	−	0.0646144i
$677$	39.5868	−	10.6072i	1.52144	−	0.407669i	0.601226	−	0.799079i	$-0.294679\pi$
$677$	39.5868	−	10.6072i	1.52144	−	0.407669i	0.920217	+	0.391410i	$0.128012\pi$
$678$	0.312269	−	0.203178i	0.0119926	−	0.00780299i
$679$		0			0
$680$	−1.72088	−	10.6840i	−0.0659929	−	0.409713i
$681$	0.114030	+	0.0658350i	0.00436962	+	0.00252280i
$682$	−6.26593	+	12.3242i	−0.239935	+	0.471917i
$683$	3.19786	−	11.9346i	0.122363	−	0.456664i	−0.877369	−	0.479816i	$-0.840704\pi$
$683$	3.19786	−	11.9346i	0.122363	−	0.456664i	0.999732	+	0.0231521i	$0.00737021\pi$
$684$	46.9065	+	7.34531i	1.79351	+	0.280855i
$685$	−2.85672	+	2.85672i	−0.109150	+	0.109150i
$686$		0			0
$687$	1.10632			0.0422089
$688$	9.48097	+	6.11004i	0.361459	+	0.232943i
$689$	13.1038	+	22.6964i	0.499214	+	0.864664i
$690$	0.445904	−	0.145314i	0.0169753	−	0.00553199i
$691$	1.44023	+	5.37500i	0.0547888	+	0.204475i	0.987894	−	0.155128i	$-0.0495789\pi$
$691$	1.44023	+	5.37500i	0.0547888	+	0.204475i	−0.933106	+	0.359603i	$0.882912\pi$
$692$	40.3158	−	15.5566i	1.53258	−	0.591375i
$693$		0			0
$694$	−3.18121	−	4.88928i	−0.120757	−	0.185594i
$695$	20.3263	+	11.7354i	0.771021	+	0.445149i
$696$	−0.461966	−	0.0473314i	−0.0175108	−	0.00179409i
$697$	18.6796	−	10.7847i	0.707540	−	0.408498i
$698$	1.21992	+	22.8950i	0.0461748	+	0.866587i
$699$	−0.154214	−	0.154214i	−0.00583290	−	0.00583290i
$700$		0			0
$701$	22.0458	−	22.0458i	0.832657	−	0.832657i	−0.155223	−	0.987880i	$-0.549609\pi$
$701$	22.0458	−	22.0458i	0.832657	−	0.832657i	0.987880	+	0.155223i	$0.0496095\pi$
$702$	0.720395	−	0.801486i	0.0271896	−	0.0302502i
$703$	−21.5184	−	37.2710i	−0.811583	−	1.40570i
$704$	−12.4321	+	0.716872i	−0.468552	+	0.0270181i
$705$	0.0717960	−	0.124354i	0.00270399	−	0.00468346i
$706$	−5.35084	−	1.13247i	−0.201381	−	0.0426212i
$707$		0			0
$708$	0.315541	+	0.139828i	0.0118588	+	0.00525506i
$709$	−11.9661	+	3.20632i	−0.449398	+	0.120416i	−0.476417	−	0.879219i	$-0.658065\pi$
$709$	−11.9661	+	3.20632i	−0.449398	+	0.120416i	0.0270200	+	0.999635i	$0.491398\pi$
$710$	11.9240	+	6.06246i	0.447499	+	0.227520i
$711$	4.99113	−	2.88163i	0.187182	−	0.108070i
$712$	15.4366	+	34.4282i	0.578511	+	1.29025i
$713$		−	28.4126i		−	1.06406i
$714$		0			0
$715$	3.23532	+	3.23532i	0.120994	+	0.120994i
$716$	−5.87055	+	37.4888i	−0.219393	+	1.40102i
$717$	−0.357122	−	0.0956906i	−0.0133370	−	0.00357363i
$718$	−21.2675	+	6.93076i	−0.793695	+	0.258654i
$719$	7.64439	−	13.2405i	0.285088	−	0.493786i	−0.687543	−	0.726144i	$-0.741311\pi$
$719$	7.64439	−	13.2405i	0.285088	−	0.493786i	0.972630	+	0.232358i	$0.0746440\pi$
$720$	−15.5910	−	0.762491i	−0.581042	−	0.0284164i
$721$		0			0
$722$	−12.8106	+	60.5288i	−0.476760	+	2.25265i
$723$	−0.193093	−	0.720631i	−0.00718119	−	0.0268006i
$724$	−11.4423	+	14.1807i	−0.425250	+	0.527020i
$725$	−2.49434	+	9.30902i	−0.0926376	+	0.345728i
$726$	0.681856	−	0.0363317i	0.0253061	−	0.00134839i
$727$		−	23.7860i		−	0.882173i	−0.897465	−	0.441086i	$-0.854593\pi$
$727$		−	23.7860i		−	0.882173i	0.897465	−	0.441086i	$-0.145407\pi$
$728$		0			0
$729$		−	26.8290i		−	0.993668i
$730$	1.38479	+	25.9892i	0.0512534	+	0.961902i
$731$	−2.14436	+	8.00285i	−0.0793119	+	0.295996i
$732$	−1.12667	+	0.120408i	−0.0416431	+	0.00445041i
$733$	−5.32874	−	19.8871i	−0.196822	−	0.734548i	−0.991788	−	0.127894i	$-0.959178\pi$
$733$	−5.32874	−	19.8871i	−0.196822	−	0.734548i	0.794966	−	0.606654i	$-0.207489\pi$
$734$	−6.56764	−	1.39000i	−0.242416	−	0.0513059i
$735$		0			0
$736$	22.1066	−	12.8923i	0.814860	−	0.475215i
$737$	1.70430	−	2.95194i	0.0627787	−	0.108736i
$738$	−9.64008	−	29.5812i	−0.354856	−	1.08890i
$739$	26.3224	+	7.05306i	0.968284	+	0.259451i	0.708103	−	0.706109i	$-0.249551\pi$
$739$	26.3224	+	7.05306i	0.968284	+	0.259451i	0.260181	+	0.965560i	$0.416218\pi$
$740$	8.33681	+	11.4326i	0.306467	+	0.420271i
$741$	0.711756	+	0.711756i	0.0261470	+	0.0261470i
$742$		0			0
$743$			12.8386i			0.471002i	0.971874	+	0.235501i	$0.0756731\pi$
$743$			12.8386i			0.471002i	−0.971874	+	0.235501i	$0.924327\pi$
$744$	0.355918	−	0.934508i	0.0130486	−	0.0342607i
$745$	−16.9641	+	9.79426i	−0.621518	+	0.358834i
$746$	14.6036	−	28.7232i	0.534676	−	1.05163i
$747$	36.1368	−	9.68282i	1.32218	−	0.354276i
$748$	−3.29295	−	8.53386i	−0.120402	−	0.312029i
$749$		0			0
$750$	0.178253	−	0.842232i	0.00650889	−	0.0307539i
$751$	7.23318	−	12.5282i	0.263942	−	0.457162i	−0.703344	−	0.710850i	$-0.748310\pi$
$751$	7.23318	−	12.5282i	0.263942	−	0.457162i	0.967286	+	0.253688i	$0.0816438\pi$
$752$	2.39524	−	7.46036i	0.0873455	−	0.272051i
$753$	0.151625	+	0.262622i	0.00552552	+	0.00957048i
$754$	6.92458	+	6.22398i	0.252178	+	0.226664i
$755$	−16.7506	+	16.7506i	−0.609616	+	0.609616i
$756$		0			0
$757$	−2.16062	−	2.16062i	−0.0785291	−	0.0785291i	0.666751	−	0.745280i	$-0.267684\pi$
$757$	−2.16062	−	2.16062i	−0.0785291	−	0.0785291i	−0.745280	+	0.666751i	$0.767684\pi$
$758$	40.1490	−	2.13928i	1.45828	−	0.0777020i
$759$	0.343304	−	0.198207i	0.0124611	−	0.00719444i
$760$	2.97363	−	29.0234i	0.107865	−	1.05279i
$761$	−2.04136	−	1.17858i	−0.0739994	−	0.0427236i	0.462544	−	0.886596i	$-0.346937\pi$
$761$	−2.04136	−	1.17858i	−0.0739994	−	0.0427236i	−0.536543	+	0.843873i	$0.680270\pi$
$762$	0.375892	−	0.244574i	0.0136171	−	0.00885998i
$763$		0			0
$764$	47.3829	+	20.9972i	1.71425	+	0.759651i
$765$	−2.96763	−	11.0753i	−0.107295	−	0.400430i
$766$	10.2758	+	31.5318i	0.371278	+	1.13929i
$767$	−3.45987	−	5.99267i	−0.124929	−	0.216383i
$768$	0.888598	−	0.147111i	0.0320645	−	0.00530840i
$769$	−7.96868			−0.287358			−0.143679	−	0.989624i	$-0.545893\pi$
$769$	−7.96868			−0.287358			−0.143679	+	0.989624i	$0.545893\pi$
$770$		0			0
$771$	−0.940923	+	0.940923i	−0.0338865	+	0.0338865i
$772$	−20.2769	+	14.7862i	−0.729783	+	0.532168i
$773$	5.69575	−	21.2568i	0.204862	−	0.764555i	−0.784630	−	0.619965i	$-0.787147\pi$
$773$	5.69575	−	21.2568i	0.204862	−	0.764555i	0.989492	−	0.144590i	$-0.0461865\pi$
$774$	10.6530	+	5.41625i	0.382914	+	0.194683i
$775$	−17.9725	−	10.3764i	−0.645592	−	0.372733i
$776$	−22.2285	−	16.0611i	−0.797956	−	0.576561i
$777$		0			0
$778$	−8.26509	−	12.7028i	−0.296318	−	0.455418i
$779$	56.1695	−	15.0506i	2.01248	−	0.539243i
$780$	−0.257549	−	0.207816i	−0.00922174	−	0.00744099i
$781$	10.9215	+	2.92640i	0.390801	+	0.104715i
$782$	13.9806	+	12.5661i	0.499947	+	0.449364i
$783$	−0.984588			−0.0351863
$784$		0			0
$785$	12.6611			0.451896
$786$	−0.122916	−	0.110480i	−0.00438428	−	0.00394070i
$787$	27.7816	+	7.44405i	0.990306	+	0.265352i	0.717379	−	0.696683i	$-0.245342\pi$
$787$	27.7816	+	7.44405i	0.990306	+	0.265352i	0.272927	+	0.962035i	$0.412008\pi$
$788$	−14.7713	+	18.3064i	−0.526207	+	0.652137i
$789$	−0.968810	+	0.259592i	−0.0344905	+	0.00924171i
$790$	−1.93145	−	2.96849i	−0.0687178	−	0.105614i
$791$		0			0
$792$	−13.0263	+	2.09815i	−0.462868	+	0.0745547i
$793$	19.6741	+	11.3589i	0.698649	+	0.403365i
$794$	−8.35562	−	4.24821i	−0.296530	−	0.150764i
$795$	−0.220273	+	0.822071i	−0.00781229	+	0.0291558i
$796$	22.6940	+	31.1212i	0.804369	+	1.10306i
$797$	22.0411	−	22.0411i	0.780736	−	0.780736i	−0.199219	−	0.979955i	$-0.563840\pi$
$797$	22.0411	−	22.0411i	0.780736	−	0.780736i	0.979955	+	0.199219i	$0.0638405\pi$
$798$		0			0
$799$	5.75552			0.203616
$800$	−0.0816127	−	18.6920i	−0.00288544	−	0.660861i
$801$	19.9885	+	34.6210i	0.706258	+	1.22327i
$802$	13.9044	+	42.6664i	0.490980	+	1.50660i
$803$	5.69369	+	21.2491i	0.200926	+	0.749866i
$804$	−0.0998836	+	0.225401i	−0.00352262	+	0.00794928i
$805$		0			0
$806$	−16.8051	+	10.9343i	−0.591936	+	0.385143i
$807$	0.311270	+	0.179712i	0.0109572	+	0.00632616i
$808$	−23.1807	+	18.8721i	−0.815493	+	0.663918i
$809$	25.9855	−	15.0027i	0.913600	−	0.527467i	0.0320125	−	0.999487i	$-0.489808\pi$
$809$	25.9855	−	15.0027i	0.913600	−	0.527467i	0.881588	+	0.472020i	$0.156475\pi$
$810$	−16.4981	+	0.879076i	−0.579684	+	0.0308876i
$811$	20.2976	+	20.2976i	0.712746	+	0.712746i	0.967109	−	0.254363i	$-0.0818658\pi$
$811$	20.2976	+	20.2976i	0.712746	+	0.712746i	−0.254363	+	0.967109i	$0.581866\pi$
$812$		0			0
$813$	−0.317411	+	0.317411i	−0.0111321	+	0.0111321i
$814$	8.89495	+	7.99500i	0.311768	+	0.280224i
$815$	8.46625	+	14.6640i	0.296560	+	0.513657i
$816$	0.302419	+	0.588440i	0.0105868	+	0.0205995i
$817$	−11.1684	+	19.3443i	−0.390733	+	0.676770i
$818$	0.378535	−	1.78854i	0.0132351	−	0.0625349i
$819$		0			0
$820$	−17.8367	+	6.88265i	−0.622886	+	0.240352i
$821$	−53.0609	+	14.2176i	−1.85184	+	0.496199i	−0.999635	−	0.0270111i	$-0.991401\pi$
$821$	−53.0609	+	14.2176i	−1.85184	+	0.496199i	−0.852204	+	0.523210i	$0.824734\pi$
$822$	0.111940	−	0.220170i	0.00390436	−	0.00767931i
$823$	20.1906	−	11.6571i	0.703800	−	0.406339i	−0.104961	−	0.994476i	$-0.533472\pi$
$823$	20.1906	−	11.6571i	0.703800	−	0.406339i	0.808761	+	0.588137i	$0.200138\pi$
$824$	−3.96242	−	8.83736i	−0.138037	−	0.307864i
$825$		−	0.289545i		−	0.0100807i
$826$		0			0
$827$	4.26358	+	4.26358i	0.148259	+	0.148259i	0.777340	−	0.629081i	$-0.216568\pi$
$827$	4.26358	+	4.26358i	0.148259	+	0.148259i	−0.629081	+	0.777340i	$0.716568\pi$
$828$	21.9086	−	15.9761i	0.761376	−	0.555206i
$829$	40.5325	+	10.8606i	1.40775	+	0.377206i	0.881122	−	0.472889i	$-0.156789\pi$
$829$	40.5325	+	10.8606i	1.40775	+	0.377206i	0.526630	+	0.850095i	$0.323455\pi$
$830$	−7.12321	−	21.8580i	−0.247250	−	0.758703i
$831$	0.360624	−	0.624619i	0.0125099	−	0.0216678i
$832$	−16.1328	−	8.11390i	−0.559305	−	0.281299i
$833$		0			0
$834$	−1.40383	−	0.297113i	−0.0486107	−	0.0102882i
$835$	5.57502	+	20.8063i	0.192932	+	0.720030i
$836$	−2.62058	−	24.5211i	−0.0906346	−	0.848080i
$837$	0.548743	−	2.04794i	0.0189673	−	0.0707871i
$838$	1.83874	+	34.5086i	0.0635181	+	1.19208i
$839$			46.6970i			1.61216i	0.591806	+	0.806081i	$0.298415\pi$
$839$			46.6970i			1.61216i	−0.591806	+	0.806081i	$0.701585\pi$
$840$		0			0
$841$			20.4935i			0.706672i
$842$	6.71538	−	0.357819i	0.231427	−	0.0123312i
$843$	−0.190045	+	0.709257i	−0.00654549	+	0.0244281i
$844$	18.9793	+	15.3143i	0.653294	+	0.527140i
$845$	−2.66408	−	9.94249i	−0.0916472	−	0.342032i
$846$	1.71898	−	8.12205i	0.0590999	−	0.279242i
$847$		0			0
$848$	−2.26851	+	46.3853i	−0.0779010	+	1.59288i
$849$	0.542493	−	0.939626i	0.0186183	−	0.0322479i
$850$	13.0546	−	4.25430i	0.447769	−	0.145921i
$851$	−23.7410	−	6.36139i	−0.813832	−	0.218066i
$852$	−0.807958	−	0.126522i	−0.0276802	−	0.00433457i
$853$	14.9036	+	14.9036i	0.510289	+	0.510289i	0.914615	−	0.404326i	$-0.132494\pi$
$853$	14.9036	+	14.9036i	0.510289	+	0.510289i	−0.404326	+	0.914615i	$0.632494\pi$
$854$		0			0
$855$		−	30.9125i		−	1.05718i
$856$	30.2838	+	11.5339i	1.03508	+	0.394221i
$857$	−12.5881	+	7.26772i	−0.430000	+	0.248261i	−0.699347	−	0.714783i	$-0.746526\pi$
$857$	−12.5881	+	7.26772i	−0.430000	+	0.248261i	0.269347	+	0.963043i	$0.413192\pi$
$858$	−0.249349	−	0.126776i	−0.00851265	−	0.00432805i
$859$	−37.9861	+	10.1784i	−1.29607	+	0.347281i	−0.839963	−	0.542644i	$-0.817423\pi$
$859$	−37.9861	+	10.1784i	−1.29607	+	0.347281i	−0.456107	+	0.889925i	$0.650757\pi$
$860$	2.97527	−	6.71409i	0.101456	−	0.228949i
$861$		0			0
$862$	−15.4606	−	3.27214i	−0.526589	−	0.111449i
$863$	6.49230	−	11.2450i	0.221000	−	0.382784i	−0.734112	−	0.679029i	$-0.762401\pi$
$863$	6.49230	−	11.2450i	0.221000	−	0.382784i	0.955112	+	0.296245i	$0.0957345\pi$
$864$	1.84240	−	0.502303i	0.0626799	−	0.0170887i
$865$	−14.0678	−	24.3661i	−0.478319	−	0.828473i
$866$	16.4441	−	18.2952i	0.558795	−	0.621695i
$867$	0.333052	−	0.333052i	0.0113110	−	0.0113110i
$868$		0			0
$869$	−2.11673	−	2.11673i	−0.0718052	−	0.0718052i
$870$	0.0160877	+	0.301927i	0.000545425	+	0.0102363i
$871$	4.28075	−	2.47149i	0.145048	−	0.0837434i
$872$	−5.59907	−	6.87736i	−0.189609	−	0.232897i
$873$	−25.1638	−	14.5283i	−0.851665	−	0.491709i
$874$	27.6392	+	42.4793i	0.934909	+	1.43689i
$875$		0			0
$876$	−0.572809	−	1.48446i	−0.0193534	−	0.0501554i
$877$	5.80637	+	21.6697i	0.196067	+	0.731733i	0.991988	+	0.126332i	$0.0403205\pi$
$877$	5.80637	+	21.6697i	0.196067	+	0.731733i	−0.795921	+	0.605401i	$0.793013\pi$
$878$	50.4782	−	16.4501i	1.70356	−	0.555164i
$879$	−0.505614	−	0.875749i	−0.0170539	−	0.0295383i
$880$	1.71340	+	7.92472i	0.0577588	+	0.267142i
$881$	8.65332			0.291538			0.145769	−	0.989319i	$-0.453434\pi$
$881$	8.65332			0.291538			0.145769	+	0.989319i	$0.453434\pi$
$882$		0			0
$883$	30.6837	−	30.6837i	1.03259	−	1.03259i	0.0331374	−	0.999451i	$-0.489450\pi$
$883$	30.6837	−	30.6837i	1.03259	−	1.03259i	0.999451	−	0.0331374i	$-0.0105499\pi$
$884$	2.05218	−	13.1050i	0.0690222	−	0.440770i
$885$	0.0581601	−	0.217056i	0.00195503	−	0.00729627i
$886$	4.56645	−	8.98155i	0.153413	−	0.301741i
$887$	−24.7803	−	14.3069i	−0.832042	−	0.480380i	0.0225091	−	0.999747i	$-0.492835\pi$
$887$	−24.7803	−	14.3069i	−0.832042	−	0.480380i	−0.854551	+	0.519367i	$0.826168\pi$
$888$	−0.701170	−	0.506628i	−0.0235297	−	0.0170013i
$889$		0			0
$890$	20.5910	−	13.3975i	0.690211	−	0.449086i
$891$	−13.4891	+	3.61439i	−0.451902	+	0.121087i
$892$	−4.76923	−	44.6263i	−0.159686	−	1.49420i
$893$	14.9882	+	4.01607i	0.501560	+	0.134393i
$894$	0.800558	−	0.890672i	0.0267747	−	0.0297885i
$895$	24.7060			0.825830
$896$		0			0
$897$	0.574859			0.0191940
$898$	−7.41179	+	8.24610i	−0.247335	+	0.275176i
$899$	17.6935	+	4.74096i	0.590112	+	0.158120i
$900$	−2.10459	−	19.6929i	−0.0701530	−	0.656431i
$901$	−32.9506	+	8.82909i	−1.09774	+	0.294140i
$902$	−13.5453	+	8.81328i	−0.451011	+	0.293450i
$903$		0			0
$904$	−10.7285	−	7.75184i	−0.356824	−	0.257822i
$905$	10.2743	+	5.93185i	0.341528	+	0.197182i
$906$	0.656369	−	1.29098i	0.0218064	−	0.0428900i
$907$	4.82227	−	17.9969i	0.160121	−	0.597579i	−0.838492	−	0.544915i	$-0.816562\pi$
$907$	4.82227	−	17.9969i	0.160121	−	0.597579i	0.998612	−	0.0526640i	$-0.0167712\pi$
$908$	0.723729	−	4.62167i	0.0240178	−	0.153376i
$909$	−22.3949	+	22.3949i	−0.742793	+	0.742793i
$910$		0			0
$911$	−12.2041			−0.404341			−0.202170	−	0.979350i	$-0.564799\pi$
$911$	−12.2041			−0.404341			−0.202170	+	0.979350i	$0.564799\pi$
$912$	0.376941	+	1.74340i	0.0124818	+	0.0577298i
$913$	−9.71601	−	16.8286i	−0.321553	−	0.556946i
$914$	−34.5958	+	11.2743i	−1.14433	+	0.372920i
$915$	0.190942	+	0.712603i	0.00631233	+	0.0235579i
$916$	−14.1500	−	36.6704i	−0.467528	−	1.21162i
$917$		0			0
$918$	0.765009	+	1.17576i	0.0252491	+	0.0388059i
$919$	−3.57056	−	2.06146i	−0.117782	−	0.0680014i	0.439952	−	0.898021i	$-0.354996\pi$
$919$	−3.57056	−	2.06146i	−0.117782	−	0.0680014i	−0.557734	+	0.830020i	$0.688329\pi$
$920$	−10.5197	−	12.9214i	−0.346825	−	0.426007i
$921$	−1.06989	+	0.617699i	−0.0352539	+	0.0203539i
$922$	−1.40109	−	26.2949i	−0.0461423	−	0.865978i
$923$	11.5941	+	11.5941i	0.381623	+	0.381623i
$924$		0			0
$925$	−12.6943	+	12.6943i	−0.417386	+	0.417386i
$926$	6.51195	−	7.24496i	0.213996	−	0.238084i
$927$	−5.13083	−	8.88686i	−0.168519	−	0.291883i
$928$	4.33973	+	15.9178i	0.142459	+	0.522526i
$929$	22.7002	−	39.3180i	0.744771	−	1.28998i	−0.205531	−	0.978651i	$-0.565892\pi$
$929$	22.7002	−	39.3180i	0.744771	−	1.28998i	0.950302	−	0.311330i	$-0.100775\pi$
$930$	−0.636973	−	0.134812i	−0.0208872	−	0.00442064i
$931$		0			0
$932$	−3.13919	+	7.08400i	−0.102827	+	0.232044i
$933$	−0.197513	+	0.0529235i	−0.00646629	+	0.00173264i
$934$	−49.8757	−	25.3581i	−1.63198	−	0.829743i
$935$	−5.15770	+	2.97780i	−0.168675	+	0.0973845i
$936$	−17.8806	−	6.81003i	−0.584445	−	0.222593i
$937$		−	8.69727i		−	0.284127i	−0.989858	−	0.142064i	$-0.954626\pi$
$937$		−	8.69727i		−	0.284127i	0.989858	−	0.142064i	$-0.0453738\pi$
$938$		0			0
$939$	−0.149141	−	0.149141i	−0.00486704	−	0.00486704i
$940$	−5.04014	−	0.789260i	−0.164391	−	0.0257428i
$941$	11.6093	+	3.11071i	0.378454	+	0.101406i	0.443031	−	0.896506i	$-0.353903\pi$
$941$	11.6093	+	3.11071i	0.378454	+	0.101406i	−0.0645772	+	0.997913i	$0.520570\pi$
$942$	−0.735966	+	0.239841i	−0.0239791	+	0.00781443i
$943$	16.6051	−	28.7609i	0.540737	−	0.936584i
$944$	0.598969	−	12.2474i	0.0194948	−	0.398618i
$945$		0			0
$946$	1.28529	−	6.07288i	0.0417883	−	0.197446i
$947$	−14.8879	−	55.5623i	−0.483791	−	1.80553i	−0.585443	−	0.810713i	$-0.699080\pi$
$947$	−14.8879	−	55.5623i	−0.483791	−	1.80553i	0.101652	−	0.994820i	$-0.467587\pi$
$948$	0.168503	+	0.135965i	0.00547273	+	0.00441593i
$949$	−8.25671	+	30.8145i	−0.268024	+	1.00028i
$950$	36.9645	−	1.96960i	1.19929	−	0.0639021i
$951$			1.38499i			0.0449113i
$952$		0			0
$953$		−	8.69133i		−	0.281540i	−0.990042	−	0.140770i	$-0.955042\pi$
$953$		−	8.69133i		−	0.281540i	0.990042	−	0.140770i	$-0.0449578\pi$
$954$	2.61814	+	49.1361i	0.0847654	+	1.59084i
$955$	8.73356	−	32.5941i	0.282611	−	1.05472i
$956$	1.39585	+	13.0611i	0.0451449	+	0.422427i
$957$	0.0661460	+	0.246860i	0.00213820	+	0.00797986i
$958$	−0.724965	−	0.153434i	−0.0234225	−	0.00495724i
$959$		0			0
$960$	−0.184137	−	0.556772i	−0.00594299	−	0.0179697i
$961$	−4.22236	+	7.31334i	−0.136205	+	0.235914i
$962$	5.37390	+	16.4902i	0.173262	+	0.531664i
$963$	33.1653	+	8.88662i	1.06874	+	0.286367i
$964$	−21.4165	+	15.6172i	−0.689778	+	0.502996i
$965$	11.5537	+	11.5537i	0.371927	+	0.371927i
$966$		0			0
$967$			28.1636i			0.905681i	0.891592	+	0.452840i	$0.149589\pi$
$967$			28.1636i			0.905681i	−0.891592	+	0.452840i	$0.850411\pi$
$968$	−9.92525	−	22.1362i	−0.319009	−	0.711485i
$969$	−1.13467	+	0.655102i	−0.0364509	+	0.0210449i
$970$	−8.09225	+	15.9163i	−0.259827	+	0.511041i
$971$	−10.1276	+	2.71368i	−0.325010	+	0.0870862i	−0.417635	−	0.908615i	$-0.637141\pi$
$971$	−10.1276	+	2.71368i	−0.325010	+	0.0870862i	0.0926248	+	0.995701i	$0.470474\pi$
$972$	2.83203	−	1.09279i	0.0908375	−	0.0350514i
$973$		0			0
$974$	0.833765	−	3.93947i	0.0267155	−	0.126229i
$975$	0.209942	−	0.363630i	0.00672352	−	0.0116455i
$976$	18.4013	+	35.8049i	0.589011	+	1.14609i
$977$	−17.3812	−	30.1051i	−0.556073	−	0.963147i	−0.997819	−	0.0660068i	$-0.978974\pi$
$977$	−17.3812	−	30.1051i	−0.556073	−	0.963147i	0.441746	−	0.897140i	$-0.354359\pi$
$978$	−0.769906	−	0.692010i	−0.0246189	−	0.0221280i
$979$	14.6827	−	14.6827i	0.469262	−	0.469262i
$980$		0			0
$981$	−6.64424	−	6.64424i	−0.212134	−	0.212134i
$982$	−34.9156	+	1.86042i	−1.11420	+	0.0593685i
$983$	−2.48718	+	1.43597i	−0.0793286	+	0.0458004i	−0.539140	−	0.842216i	$-0.681250\pi$
$983$	−2.48718	+	1.43597i	−0.0793286	+	0.0458004i	0.459811	+	0.888017i	$0.347917\pi$
$984$	0.906434	−	0.737956i	0.0288961	−	0.0235252i
$985$	13.2635	+	7.65766i	0.422609	+	0.243993i
$986$	−10.1582	+	6.60943i	−0.323503	+	0.210487i
$987$		0			0
$988$	14.4885	−	32.6954i	0.460942	−	1.04018i
$989$	3.30166	+	12.3220i	0.104987	+	0.391816i
$990$	2.66176	+	8.16779i	0.0845964	+	0.259590i
$991$	15.8744	+	27.4952i	0.504266	+	0.873414i	0.999988	+	0.00493273i	$0.00157014\pi$
$991$	15.8744	+	27.4952i	0.504266	+	0.873414i	−0.495722	+	0.868481i	$0.665097\pi$
$992$	−35.5276	+	0.155120i	−1.12800	+	0.00492506i
$993$	0.570832			0.0181148
$994$		0			0
$995$	17.7327	−	17.7327i	0.562166	−	0.562166i
$996$	0.828115	+	1.13563i	0.0262398	+	0.0359837i
$997$	−5.29788	+	19.7719i	−0.167785	+	0.626184i	0.829883	+	0.557937i	$0.188407\pi$
$997$	−5.29788	+	19.7719i	−0.167785	+	0.626184i	−0.997668	+	0.0682464i	$0.978260\pi$
$998$	1.70767	+	0.868222i	0.0540552	+	0.0274831i
$999$	−1.58836	−	0.917039i	−0.0502534	−	0.0290138i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.373.10		48
7.2	even	3		784.2.m.k.197.1		24
7.3	odd	6		112.2.w.c.53.8	yes	48
7.4	even	3	inner	784.2.x.o.165.8		48
7.5	odd	6		784.2.m.j.197.1		24
7.6	odd	2		112.2.w.c.37.10	✓	48
16.13	even	4	inner	784.2.x.o.765.8		48
28.3	even	6		448.2.ba.c.305.6		48
28.27	even	2		448.2.ba.c.177.7		48
56.3	even	6		896.2.ba.e.865.7		48
56.13	odd	2		896.2.ba.f.737.7		48
56.27	even	2		896.2.ba.e.737.6		48
56.45	odd	6		896.2.ba.f.865.6		48
112.3	even	12		448.2.ba.c.81.7		48
112.13	odd	4		112.2.w.c.93.8	yes	48
112.27	even	4		896.2.ba.e.289.7		48
112.45	odd	12		112.2.w.c.109.10	yes	48
112.59	even	12		896.2.ba.e.417.6		48
112.61	odd	12		784.2.m.j.589.1		24
112.69	odd	4		896.2.ba.f.289.6		48
112.83	even	4		448.2.ba.c.401.6		48
112.93	even	12		784.2.m.k.589.1		24
112.101	odd	12		896.2.ba.f.417.7		48
112.109	even	12	inner	784.2.x.o.557.10		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.10	✓	48	7.6	odd	2
112.2.w.c.53.8	yes	48	7.3	odd	6
112.2.w.c.93.8	yes	48	112.13	odd	4
112.2.w.c.109.10	yes	48	112.45	odd	12
448.2.ba.c.81.7		48	112.3	even	12
448.2.ba.c.177.7		48	28.27	even	2
448.2.ba.c.305.6		48	28.3	even	6
448.2.ba.c.401.6		48	112.83	even	4
784.2.m.j.197.1		24	7.5	odd	6
784.2.m.j.589.1		24	112.61	odd	12
784.2.m.k.197.1		24	7.2	even	3
784.2.m.k.589.1		24	112.93	even	12
784.2.x.o.165.8		48	7.4	even	3	inner
784.2.x.o.373.10		48	1.1	even	1	trivial
784.2.x.o.557.10		48	112.109	even	12	inner
784.2.x.o.765.8		48	16.13	even	4	inner
896.2.ba.e.289.7		48	112.27	even	4
896.2.ba.e.417.6		48	112.59	even	12
896.2.ba.e.737.6		48	56.27	even	2
896.2.ba.e.865.7		48	56.3	even	6
896.2.ba.f.289.6		48	112.69	odd	4
896.2.ba.f.417.7		48	112.101	odd	12
896.2.ba.f.737.7		48	56.13	odd	2
896.2.ba.f.865.6		48	56.45	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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.945375 - 1.05179i) q^{2} +(0.0543752 + 0.0145698i) q^{3} +(-0.212530 - 1.98868i) q^{4} +(-1.25781 + 0.337028i) q^{5} +(0.0667293 - 0.0434174i) q^{6} +(-2.29259 - 1.65651i) q^{8} +(-2.59533 - 1.49842i) q^{9} +(-0.834616 + 1.64157i) q^{10} +(-0.402875 + 1.50355i) q^{11} +(0.0174182 - 0.111231i) q^{12} +(-1.59615 + 1.59615i) q^{13} -0.0733039 q^{15} +(-3.90966 + 0.845308i) q^{16} +(-1.46910 - 2.54455i) q^{17} +(-4.02958 + 1.31318i) q^{18} +(-2.05021 - 7.65147i) q^{19} +(0.937562 + 2.42974i) q^{20} +(1.20055 + 1.84516i) q^{22} +(-3.91784 - 2.26197i) q^{23} +(-0.100525 - 0.123475i) q^{24} +(-2.86164 + 1.65217i) q^{25} +(0.169855 + 3.18777i) q^{26} +(-0.238706 - 0.238706i) q^{27} +(2.06234 - 2.06234i) q^{29} +(-0.0692997 + 0.0771004i) q^{30} +(3.14025 + 5.43908i) q^{31} +(-2.80701 + 4.91128i) q^{32} +(-0.0438128 + 0.0758861i) q^{33} +(-4.06519 - 0.860373i) q^{34} +(-2.42828 + 5.47973i) q^{36} +(5.24787 - 1.40616i) q^{37} +(-9.98597 - 5.07713i) q^{38} +(-0.110046 + 0.0635352i) q^{39} +(3.44193 + 1.31090i) q^{40} +7.34101i q^{41} +(-1.99391 - 1.99391i) q^{43} +(3.07570 + 0.481638i) q^{44} +(3.76943 + 1.01002i) q^{45} +(-6.08295 + 1.98235i) q^{46} +(-0.979430 + 1.69642i) q^{47} +(-0.224904 - 0.0109992i) q^{48} +(-0.967587 + 4.57177i) q^{50} +(-0.0428089 - 0.159765i) q^{51} +(3.51345 + 2.83499i) q^{52} +(3.00493 - 11.2146i) q^{53} +(-0.476736 + 0.0254021i) q^{54} -2.02696i q^{55} -0.445921i q^{57} +(-0.219466 - 4.11884i) q^{58} +(-0.793411 + 2.96105i) q^{59} +(0.0155793 + 0.145778i) q^{60} +(-2.60480 - 9.72123i) q^{61} +(8.68949 + 1.83908i) q^{62} +(2.51197 + 7.59540i) q^{64} +(1.46970 - 2.54559i) q^{65} +(0.0383967 + 0.117823i) q^{66} +(-2.11517 - 0.566758i) q^{67} +(-4.74806 + 3.46236i) q^{68} +(-0.180077 - 0.180077i) q^{69} -7.26378i q^{71} +(3.46790 + 7.73444i) q^{72} +(12.2392 - 7.06631i) q^{73} +(3.48222 - 6.84902i) q^{74} +(-0.179674 + 0.0481435i) q^{75} +(-14.7806 + 5.70337i) q^{76} +(-0.0372092 + 0.175810i) q^{78} +(-0.961559 + 1.66547i) q^{79} +(4.63270 - 2.38090i) q^{80} +(4.48574 + 7.76954i) q^{81} +(7.72121 + 6.94001i) q^{82} +(-8.82731 + 8.82731i) q^{83} +(2.70543 + 2.70543i) q^{85} +(-3.98217 + 0.212184i) q^{86} +(0.142188 - 0.0820924i) q^{87} +(3.41427 - 2.77967i) q^{88} +(-11.5526 - 6.66987i) q^{89} +(4.62586 - 3.00981i) q^{90} +(-3.66566 + 8.27206i) q^{92} +(0.0915056 + 0.341503i) q^{93} +(0.858354 + 2.63391i) q^{94} +(5.15752 + 8.93309i) q^{95} +(-0.224188 + 0.226154i) q^{96} +9.69578 q^{97} +(3.29854 - 3.29854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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