LMFDB - Embedded newform 675.2.ba.c.443.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [675,2,Mod(32,675)] 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("675.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(675, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([10, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.ba (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [288] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$24$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			443.18
Character	$\chi$	$=$	675.443
Dual form			675.2.ba.c.32.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.140766 + 1.60897i) q^{2} +(-1.63374 + 0.575232i) q^{3} +(-0.599344 + 0.105680i) q^{4} +(-1.15550 - 2.54766i) q^{6} +(-0.784107 - 1.11982i) q^{7} +(0.581640 + 2.17071i) q^{8} +(2.33822 - 1.87956i) q^{9} +(-1.36918 - 3.76179i) q^{11} +(0.918381 - 0.517416i) q^{12} +(-6.44387 - 0.563766i) q^{13} +(1.69138 - 1.41923i) q^{14} +(-4.55450 + 1.65770i) q^{16} +(1.63825 - 6.11402i) q^{17} +(3.35329 + 3.49753i) q^{18} +(-0.488800 - 0.282209i) q^{19} +(1.92518 + 1.37845i) q^{21} +(5.85987 - 2.73250i) q^{22} +(-1.38722 - 0.971342i) q^{23} +(-2.19891 - 3.21180i) q^{24} -10.4473i q^{26} +(-2.73886 + 4.41573i) q^{27} +(0.588292 + 0.588292i) q^{28} +(-5.06125 - 4.24689i) q^{29} +(0.238769 + 1.35412i) q^{31} +(-1.40882 - 3.02123i) q^{32} +(4.40079 + 5.35820i) q^{33} +(10.0679 + 1.77524i) q^{34} +(-1.20276 + 1.37361i) q^{36} +(6.49160 + 1.73942i) q^{37} +(0.385258 - 0.826189i) q^{38} +(10.8519 - 2.78567i) q^{39} +(-1.33886 - 1.59560i) q^{41} +(-1.94688 + 3.29160i) q^{42} +(-3.12602 - 1.45769i) q^{43} +(1.21816 + 2.10991i) q^{44} +(1.36758 - 2.36872i) q^{46} +(1.10135 - 0.771171i) q^{47} +(6.48731 - 5.32815i) q^{48} +(1.75497 - 4.82173i) q^{49} +(0.840508 + 10.9311i) q^{51} +(3.92167 - 0.343102i) q^{52} +(7.66637 - 7.66637i) q^{53} +(-7.49030 - 3.78515i) q^{54} +(1.97474 - 2.35340i) q^{56} +(0.960908 + 0.179883i) q^{57} +(6.12066 - 8.74120i) q^{58} +(6.76439 + 2.46204i) q^{59} +(-1.59070 + 9.02132i) q^{61} +(-2.14513 + 0.574786i) q^{62} +(-3.93818 - 1.14461i) q^{63} +(-3.73216 + 2.15476i) q^{64} +(-8.00168 + 7.83498i) q^{66} +(-0.487878 + 5.57647i) q^{67} +(-0.335740 + 3.83753i) q^{68} +(2.82510 + 0.788948i) q^{69} +(0.594251 - 0.343091i) q^{71} +(5.43998 + 3.98237i) q^{72} +(-7.02013 + 1.88104i) q^{73} +(-1.88487 + 10.6896i) q^{74} +(0.322783 + 0.117483i) q^{76} +(-3.13895 + 4.48288i) q^{77} +(6.00964 + 17.0682i) q^{78} +(-8.21845 + 9.79437i) q^{79} +(1.93452 - 8.78963i) q^{81} +(2.37879 - 2.37879i) q^{82} +(-16.5771 + 1.45031i) q^{83} +(-1.29952 - 0.622713i) q^{84} +(1.90533 - 5.23485i) q^{86} +(10.7117 + 4.02693i) q^{87} +(7.36939 - 5.16010i) q^{88} +(0.301153 - 0.521612i) q^{89} +(4.42137 + 7.65803i) q^{91} +(0.934073 + 0.435565i) q^{92} +(-1.16902 - 2.07494i) q^{93} +(1.39582 + 1.66348i) q^{94} +(4.03955 + 4.12550i) q^{96} +(6.91688 - 14.8333i) q^{97} +(8.00504 + 2.14495i) q^{98} +(-10.2720 - 6.22243i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) $ 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.140766	+	1.60897i	0.0995368	+	1.13771i	0.867575	+	0.497307i	$0.165678\pi$
$2$	0.140766	+	1.60897i	0.0995368	+	1.13771i	−0.768038	+	0.640404i	$0.778767\pi$
$3$	−1.63374	+	0.575232i	−0.943241	+	0.332110i
$3$	−1.63374	+	0.575232i	−0.943241	+	0.332110i
$4$	−0.599344	+	0.105680i	−0.299672	+	0.0528402i
$5$		0			0
$5$		0			0
$6$	−1.15550	−	2.54766i	−0.471733	−	1.04008i
$7$	−0.784107	−	1.11982i	−0.296365	−	0.423252i	0.643161	−	0.765731i	$-0.277623\pi$
$7$	−0.784107	−	1.11982i	−0.296365	−	0.423252i	−0.939526	+	0.342478i	$0.888734\pi$
$8$	0.581640	+	2.17071i	0.205641	+	0.767462i
$9$	2.33822	−	1.87956i	0.779406	−	0.626520i
$10$		0			0
$11$	−1.36918	−	3.76179i	−0.412823	−	1.13422i	−0.955682	−	0.294399i	$-0.904880\pi$
$11$	−1.36918	−	3.76179i	−0.412823	−	1.13422i	0.542859	−	0.839824i	$-0.317342\pi$
$12$	0.918381	−	0.517416i	0.265114	−	0.149365i
$13$	−6.44387	−	0.563766i	−1.78721	−	0.156360i	−0.855082	−	0.518493i	$-0.826493\pi$
$13$	−6.44387	−	0.563766i	−1.78721	−	0.156360i	−0.932127	+	0.362133i	$0.882049\pi$
$14$	1.69138	−	1.41923i	0.452040	−	0.379306i
$15$		0			0
$16$	−4.55450	+	1.65770i	−1.13863	+	0.414426i
$17$	1.63825	−	6.11402i	0.397333	−	1.48287i	−0.420436	−	0.907322i	$-0.638123\pi$
$17$	1.63825	−	6.11402i	0.397333	−	1.48287i	0.817770	−	0.575546i	$-0.195210\pi$
$18$	3.35329	+	3.49753i	0.790378	+	0.824377i
$19$	−0.488800	−	0.282209i	−0.112138	−	0.0647432i	0.442882	−	0.896580i	$-0.353956\pi$
$19$	−0.488800	−	0.282209i	−0.112138	−	0.0647432i	−0.555020	+	0.831837i	$0.687289\pi$
$20$		0			0
$21$	1.92518	+	1.37845i	0.420109	+	0.300803i
$22$	5.85987	−	2.73250i	1.24933	−	0.582571i
$23$	−1.38722	−	0.971342i	−0.289255	−	0.202539i	0.419938	−	0.907553i	$-0.362052\pi$
$23$	−1.38722	−	0.971342i	−0.289255	−	0.202539i	−0.709193	+	0.705014i	$0.750941\pi$
$24$	−2.19891	−	3.21180i	−0.448851	−	0.655606i
$25$		0			0
$26$		−	10.4473i		−	2.04889i
$27$	−2.73886	+	4.41573i	−0.527094	+	0.849807i
$28$	0.588292	+	0.588292i	0.111177	+	0.111177i
$29$	−5.06125	−	4.24689i	−0.939851	−	0.788628i	0.0377087	−	0.999289i	$-0.487994\pi$
$29$	−5.06125	−	4.24689i	−0.939851	−	0.788628i	−0.977559	+	0.210660i	$0.932439\pi$
$30$		0			0
$31$	0.238769	+	1.35412i	0.0428841	+	0.243208i	0.998713	−	0.0507153i	$-0.0161501\pi$
$31$	0.238769	+	1.35412i	0.0428841	+	0.243208i	−0.955829	+	0.293923i	$0.905039\pi$
$32$	−1.40882	−	3.02123i	−0.249047	−	0.534082i
$33$	4.40079	+	5.35820i	0.766079	+	0.932742i
$34$	10.0679	+	1.77524i	1.72662	+	0.304451i
$35$		0			0
$36$	−1.20276	+	1.37361i	−0.200460	+	0.228934i
$37$	6.49160	+	1.73942i	1.06721	+	0.285959i	0.749348	−	0.662177i	$-0.230367\pi$
$37$	6.49160	+	1.73942i	1.06721	+	0.285959i	0.317866	+	0.948136i	$0.397034\pi$
$38$	0.385258	−	0.826189i	0.0624971	−	0.134026i
$39$	10.8519	−	2.78567i	1.73770	−	0.446065i
$40$		0			0
$41$	−1.33886	−	1.59560i	−0.209095	−	0.249190i	0.651296	−	0.758824i	$-0.274226\pi$
$41$	−1.33886	−	1.59560i	−0.209095	−	0.249190i	−0.860392	+	0.509633i	$0.829781\pi$
$42$	−1.94688	+	3.29160i	−0.300411	+	0.507904i
$43$	−3.12602	−	1.45769i	−0.476713	−	0.222295i	0.169384	−	0.985550i	$-0.445822\pi$
$43$	−3.12602	−	1.45769i	−0.476713	−	0.222295i	−0.646097	+	0.763255i	$0.723600\pi$
$44$	1.21816	+	2.10991i	0.183644	+	0.318081i
$45$		0			0
$46$	1.36758	−	2.36872i	0.201639	−	0.349249i
$47$	1.10135	−	0.771171i	0.160648	−	0.112487i	−0.490488	−	0.871448i	$-0.663182\pi$
$47$	1.10135	−	0.771171i	0.160648	−	0.112487i	0.651136	+	0.758961i	$0.274293\pi$
$48$	6.48731	−	5.32815i	0.936362	−	0.769052i
$49$	1.75497	−	4.82173i	0.250709	−	0.688819i
$50$		0			0
$51$	0.840508	+	10.9311i	0.117695	+	1.53066i
$52$	3.92167	−	0.343102i	0.543838	−	0.0475797i
$53$	7.66637	−	7.66637i	1.05306	−	1.05306i	0.0545457	−	0.998511i	$-0.482629\pi$
$53$	7.66637	−	7.66637i	1.05306	−	1.05306i	0.998511	−	0.0545457i	$-0.0173711\pi$
$54$	−7.49030	−	3.78515i	−1.01930	−	0.515093i
$55$		0			0
$56$	1.97474	−	2.35340i	0.263886	−	0.314487i
$57$	0.960908	+	0.179883i	0.127275	+	0.0238261i
$58$	6.12066	−	8.74120i	0.803682	−	1.14778i
$59$	6.76439	+	2.46204i	0.880648	+	0.320530i	0.742471	−	0.669878i	$-0.233654\pi$
$59$	6.76439	+	2.46204i	0.880648	+	0.320530i	0.138177	+	0.990408i	$0.455876\pi$
$60$		0			0
$61$	−1.59070	+	9.02132i	−0.203669	+	1.15506i	0.695852	+	0.718185i	$0.255027\pi$
$61$	−1.59070	+	9.02132i	−0.203669	+	1.15506i	−0.899521	+	0.436877i	$0.856084\pi$
$62$	−2.14513	+	0.574786i	−0.272432	+	0.0729979i
$63$	−3.93818	−	1.14461i	−0.496164	−	0.144207i
$64$	−3.73216	+	2.15476i	−0.466520	+	0.269346i
$65$		0			0
$66$	−8.00168	+	7.83498i	−0.984939	+	0.964419i
$67$	−0.487878	+	5.57647i	−0.0596038	+	0.681274i	0.906345	+	0.422539i	$0.138861\pi$
$67$	−0.487878	+	5.57647i	−0.0596038	+	0.681274i	−0.965948	+	0.258735i	$0.916694\pi$
$68$	−0.335740	+	3.83753i	−0.0407145	+	0.465369i
$69$	2.82510	+	0.788948i	0.340102	+	0.0949781i
$70$		0			0
$71$	0.594251	−	0.343091i	0.0705246	−	0.0407174i	−0.464323	−	0.885666i	$-0.653702\pi$
$71$	0.594251	−	0.343091i	0.0705246	−	0.0407174i	0.534848	+	0.844949i	$0.320369\pi$
$72$	5.43998	+	3.98237i	0.641108	+	0.469326i
$73$	−7.02013	+	1.88104i	−0.821644	+	0.220159i	−0.645065	−	0.764128i	$-0.723170\pi$
$73$	−7.02013	+	1.88104i	−0.821644	+	0.220159i	−0.176579	+	0.984287i	$0.556503\pi$
$74$	−1.88487	+	10.6896i	−0.219112	+	1.24264i
$75$		0			0
$76$	0.322783	+	0.117483i	0.0370258	+	0.0134763i
$77$	−3.13895	+	4.48288i	−0.357716	+	0.510872i
$78$	6.00964	+	17.0682i	0.680457	+	1.93260i
$79$	−8.21845	+	9.79437i	−0.924648	+	1.10195i	0.0698876	+	0.997555i	$0.477736\pi$
$79$	−8.21845	+	9.79437i	−0.924648	+	1.10195i	−0.994536	+	0.104398i	$0.966709\pi$
$80$		0			0
$81$	1.93452	−	8.78963i	0.214946	−	0.976626i
$82$	2.37879	−	2.37879i	0.262694	−	0.262694i
$83$	−16.5771	+	1.45031i	−1.81958	+	0.159192i	−0.945293	−	0.326223i	$-0.894224\pi$
$83$	−16.5771	+	1.45031i	−1.81958	+	0.159192i	−0.874283	+	0.485416i	$0.838668\pi$
$84$	−1.29952	−	0.622713i	−0.141789	−	0.0679435i
$85$		0			0
$86$	1.90533	−	5.23485i	0.205457	−	0.564488i
$87$	10.7117	+	4.02693i	1.14842	+	0.431732i
$88$	7.36939	−	5.16010i	0.785580	−	0.550069i
$89$	0.301153	−	0.521612i	0.0319221	−	0.0552908i	−0.849623	−	0.527391i	$-0.823170\pi$
$89$	0.301153	−	0.521612i	0.0319221	−	0.0552908i	0.881545	+	0.472100i	$0.156504\pi$
$90$		0			0
$91$	4.42137	+	7.65803i	0.463485	+	0.802780i
$92$	0.934073	+	0.435565i	0.0973838	+	0.0454108i
$93$	−1.16902	−	2.07494i	−0.121222	−	0.215161i
$94$	1.39582	+	1.66348i	0.143968	+	0.171574i
$95$		0			0
$96$	4.03955	+	4.12550i	0.412285	+	0.421057i
$97$	6.91688	−	14.8333i	0.702302	−	1.50609i	−0.153146	−	0.988204i	$-0.548940\pi$
$97$	6.91688	−	14.8333i	0.702302	−	1.50609i	0.855448	−	0.517888i	$-0.173282\pi$
$98$	8.00504	+	2.14495i	0.808632	+	0.216672i
$99$	−10.2720	−	6.22243i	−1.03237	−	0.625378i
$100$		0			0
$101$	−9.25810	−	1.63245i	−0.921215	−	0.162435i	−0.307124	−	0.951670i	$-0.599366\pi$
$101$	−9.25810	−	1.63245i	−0.921215	−	0.162435i	−0.614092	+	0.789235i	$0.710478\pi$
$102$	−17.4695	+	2.89108i	−1.72973	+	0.286260i
$103$	−7.65736	−	16.4213i	−0.754502	−	1.61803i	−0.785767	−	0.618523i	$-0.787731\pi$
$103$	−7.65736	−	16.4213i	−0.754502	−	1.61803i	0.0312651	−	0.999511i	$-0.490046\pi$
$104$	−2.52424	−	14.3157i	−0.247522	−	1.40377i
$105$		0			0
$106$	13.4141	+	11.2558i	1.30289	+	1.09326i
$107$	−1.55188	−	1.55188i	−0.150026	−	0.150026i	0.628104	−	0.778130i	$-0.283831\pi$
$107$	−1.55188	−	1.55188i	−0.150026	−	0.150026i	−0.778130	+	0.628104i	$0.783831\pi$
$108$	1.17486	−	2.93598i	0.113051	−	0.282515i
$109$			2.31464i			0.221703i	0.993837	+	0.110851i	$0.0353577\pi$
$109$			2.31464i			0.221703i	−0.993837	+	0.110851i	$0.964642\pi$
$110$		0			0
$111$	−11.6062	+	0.892415i	−1.10161	+	0.0847043i
$112$	5.42754	+	3.80041i	0.512855	+	0.359105i
$113$	0.613289	−	0.285981i	0.0576934	−	0.0269029i	−0.393557	−	0.919300i	$-0.628756\pi$
$113$	0.613289	−	0.285981i	0.0576934	−	0.0269029i	0.451251	+	0.892397i	$0.350978\pi$
$114$	−0.154162	+	1.57139i	−0.0144386	+	0.147174i
$115$		0			0
$116$	3.48224	+	2.01047i	0.323318	+	0.186668i
$117$	−16.1268	+	10.7934i	−1.49092	+	0.997853i
$118$	−3.00913	+	11.2302i	−0.277013	+	1.03383i
$119$	−8.13117	+	2.95950i	−0.745383	+	0.271297i
$120$		0			0
$121$	−3.84994	+	3.23048i	−0.349995	+	0.293680i
$122$	−14.7389	−	1.28949i	−1.33440	−	0.116745i
$123$	3.10519	+	1.83663i	0.279986	+	0.165604i
$124$	−0.286209	−	0.786352i	−0.0257023	−	0.0706165i
$125$		0			0
$126$	1.28727	−	6.49752i	0.114679	−	0.578845i
$127$	1.10450	+	4.12205i	0.0980085	+	0.365773i	0.997458	−	0.0712511i	$-0.0226992\pi$
$127$	1.10450	+	4.12205i	0.0980085	+	0.365773i	−0.899450	+	0.437024i	$0.856033\pi$
$128$	−7.81640	−	11.1630i	−0.690879	−	0.986677i
$129$	5.94561	+	0.583296i	0.523481	+	0.0513564i
$130$		0			0
$131$	10.6271	−	1.87385i	0.928496	−	0.163719i	0.311105	−	0.950375i	$-0.399301\pi$
$131$	10.6271	−	1.87385i	0.928496	−	0.163719i	0.617391	+	0.786656i	$0.288190\pi$
$132$	−3.20384	−	2.74632i	−0.278859	−	0.239037i
$133$	0.0672482	+	0.768651i	0.00583116	+	0.0666505i
$134$	−9.04103			−0.781026
$135$		0			0
$136$	14.2246			1.21975
$137$	−1.42197	−	16.2532i	−0.121487	−	1.38860i	−0.775131	−	0.631801i	$-0.782316\pi$
$137$	−1.42197	−	16.2532i	−0.121487	−	1.38860i	0.653643	−	0.756803i	$-0.273240\pi$
$138$	−0.871711	+	4.65655i	−0.0742050	+	0.396392i
$139$	−17.7679	+	3.13296i	−1.50705	+	0.265734i	−0.865330	−	0.501202i	$-0.832891\pi$
$139$	−17.7679	+	3.13296i	−1.50705	+	0.265734i	−0.641723	+	0.766937i	$0.721780\pi$
$140$		0			0
$141$	−1.35571	+	1.89342i	−0.114172	+	0.159455i
$142$	0.635672	+	0.907834i	0.0533444	+	0.0761837i
$143$	6.70205	+	25.0124i	0.560454	+	2.09164i
$144$	−7.53366	+	12.4365i	−0.627805	+	1.03638i
$145$		0			0
$146$	−4.01472	−	11.0304i	−0.332261	−	0.912879i
$147$	−0.0935477	+	8.88697i	−0.00771568	+	0.732985i
$148$	−4.07452	−	0.356475i	−0.334924	−	0.0293020i
$149$	7.44284	−	6.24528i	0.609741	−	0.511633i	−0.284819	−	0.958581i	$-0.591934\pi$
$149$	7.44284	−	6.24528i	0.609741	−	0.511633i	0.894560	+	0.446948i	$0.147489\pi$
$150$		0			0
$151$	2.08611	−	0.759282i	0.169765	−	0.0617895i	−0.255739	−	0.966746i	$-0.582319\pi$
$151$	2.08611	−	0.759282i	0.169765	−	0.0617895i	0.425505	+	0.904956i	$0.360097\pi$
$152$	0.328288	−	1.22519i	0.0266277	−	0.0993759i
$153$	−7.66108	−	17.3751i	−0.619362	−	1.40469i
$154$	−7.65467	−	4.41943i	−0.616831	−	0.356127i
$155$		0			0
$156$	−6.20963	+	2.81641i	−0.497168	+	0.225493i
$157$	−16.4399	+	7.66606i	−1.31205	+	0.611818i	−0.947616	−	0.319412i	$-0.896515\pi$
$157$	−16.4399	+	7.66606i	−1.31205	+	0.611818i	−0.364432	+	0.931230i	$0.618737\pi$
$158$	−16.9157	−	11.8445i	−1.34574	−	0.942298i
$159$	−8.11492	+	16.9348i	−0.643555	+	1.34302i
$160$		0			0
$161$			2.31507i			0.182453i
$162$	14.4145	+	1.87529i	1.13251	+	0.147337i
$163$	14.0631	+	14.0631i	1.10151	+	1.10151i	0.994229	+	0.107281i	$0.0342144\pi$
$163$	14.0631	+	14.0631i	1.10151	+	1.10151i	0.107281	+	0.994229i	$0.465786\pi$
$164$	0.971063	+	0.814818i	0.0758273	+	0.0636266i
$165$		0			0
$166$	−4.66700	−	26.4679i	−0.362230	−	2.05431i
$167$	−8.17550	−	17.5324i	−0.632639	−	1.35670i	−0.917348	−	0.398086i	$-0.869675\pi$
$167$	−8.17550	−	17.5324i	−0.632639	−	1.35670i	0.284709	−	0.958614i	$-0.408103\pi$
$168$	−1.87246	+	4.98078i	−0.144463	+	0.384276i
$169$	28.4031	+	5.00824i	2.18486	+	0.385249i
$170$		0			0
$171$	−1.67335	+	0.258863i	−0.127964	+	0.0197958i
$172$	2.02761	+	0.543295i	0.154604	+	0.0414259i
$173$	−6.87190	+	14.7368i	−0.522461	+	1.12042i	0.451200	+	0.892423i	$0.350996\pi$
$173$	−6.87190	+	14.7368i	−0.522461	+	1.12042i	−0.973661	+	0.227999i	$0.926782\pi$
$174$	−4.97135	+	17.8017i	−0.376877	+	1.34954i
$175$		0			0
$176$	12.4719	+	14.8634i	0.940102	+	1.12037i
$177$	−12.4675	−	0.131238i	−0.937114	−	0.00986443i
$178$	0.881649	+	0.411119i	0.0660824	+	0.0308147i
$179$	5.29497	+	9.17116i	0.395765	+	0.685485i	0.993199	−	0.116433i	$-0.0371462\pi$
$179$	5.29497	+	9.17116i	0.395765	+	0.685485i	−0.597434	+	0.801918i	$0.703813\pi$
$180$		0			0
$181$	5.21970	−	9.04078i	0.387977	−	0.671996i	−0.604200	−	0.796833i	$-0.706507\pi$
$181$	5.21970	−	9.04078i	0.387977	−	0.671996i	0.992177	+	0.124836i	$0.0398406\pi$
$182$	−11.6991	+	8.19183i	−0.867198	+	0.607219i
$183$	−2.59056	−	15.6535i	−0.191499	−	1.15714i
$184$	1.30164	−	3.57622i	0.0959581	−	0.263643i
$185$		0			0
$186$	3.17395	−	2.17300i	0.232725	−	0.159332i
$187$	−25.2427	+	2.20845i	−1.84593	+	0.161498i
$188$	−0.578587	+	0.578587i	−0.0421978	+	0.0421978i
$189$	7.09238	−	0.395373i	0.515895	−	0.0287591i
$190$		0			0
$191$	−4.58915	+	5.46914i	−0.332060	+	0.395733i	−0.906079	−	0.423108i	$-0.860939\pi$
$191$	−4.58915	+	5.46914i	−0.332060	+	0.395733i	0.574019	+	0.818842i	$0.305383\pi$
$192$	4.85789	−	5.66718i	0.350588	−	0.408994i
$193$	6.24300	−	8.91592i	0.449381	−	0.641782i	−0.528993	−	0.848626i	$-0.677430\pi$
$193$	6.24300	−	8.91592i	0.449381	−	0.641782i	0.978374	+	0.206844i	$0.0663192\pi$
$194$	24.8399	+	9.04099i	1.78340	+	0.649106i
$195$		0			0
$196$	−0.542265	+	3.07534i	−0.0387332	+	0.219667i
$197$	0.930429	−	0.249308i	0.0662904	−	0.0177624i	−0.225521	−	0.974238i	$-0.572409\pi$
$197$	0.930429	−	0.249308i	0.0662904	−	0.0177624i	0.291812	+	0.956476i	$0.405742\pi$
$198$	8.56574	−	17.4031i	0.608741	−	1.23679i
$199$	−13.5074	+	7.79853i	−0.957517	+	0.552823i	−0.895408	−	0.445247i	$-0.853116\pi$
$199$	−13.5074	+	7.79853i	−0.957517	+	0.552823i	−0.0621092	+	0.998069i	$0.519783\pi$
$200$		0			0
$201$	−2.41070	−	9.39115i	−0.170037	−	0.662401i
$202$	1.32333	−	15.1258i	0.0931094	−	1.06425i
$203$	−0.787198	+	8.99771i	−0.0552504	+	0.631515i
$204$	−1.65896	−	6.46266i	−0.116150	−	0.452476i
$205$		0			0
$206$	25.3434	−	14.6320i	1.76575	−	1.01946i
$207$	−5.06931	+	0.336153i	−0.352342	+	0.0233643i
$208$	30.2832	−	8.11435i	2.09976	−	0.562629i
$209$	−0.392356	+	2.22516i	−0.0271398	+	0.153918i
$210$		0			0
$211$	4.84666	+	1.76404i	0.333658	+	0.121442i	0.503416	−	0.864044i	$-0.332076\pi$
$211$	4.84666	+	1.76404i	0.333658	+	0.121442i	−0.169758	+	0.985486i	$0.554299\pi$
$212$	−3.78460	+	5.40497i	−0.259928	+	0.371215i
$213$	−0.773495	+	0.902353i	−0.0529990	+	0.0618282i
$214$	2.27847	−	2.71538i	0.155753	−	0.185619i
$215$		0			0
$216$	−11.1783	−	3.37690i	−0.760587	−	0.229769i
$217$	1.32916	−	1.32916i	0.0902290	−	0.0902290i
$218$	−3.72418	+	0.325824i	−0.252233	+	0.0220676i
$219$	10.3870	−	7.11133i	0.701891	−	0.480539i
$220$		0			0
$221$	−14.0035	+	38.4744i	−0.941979	+	2.58807i
$222$	−3.06962	−	18.5483i	−0.206020	−	1.24488i
$223$	−19.0798	+	13.3598i	−1.27768	+	0.894638i	−0.997858	−	0.0654150i	$-0.979163\pi$
$223$	−19.0798	+	13.3598i	−1.27768	+	0.894638i	−0.279818	+	0.960053i	$0.590274\pi$
$224$	−2.27857	+	3.94659i	−0.152243	+	0.263693i
$225$		0			0
$226$	0.546465	+	0.946505i	0.0363503	+	0.0629606i
$227$	5.88846	+	2.74583i	0.390831	+	0.182247i	0.608093	−	0.793866i	$-0.291935\pi$
$227$	5.88846	+	2.74583i	0.390831	+	0.182247i	−0.217262	+	0.976113i	$0.569713\pi$
$228$	−0.594924	−	0.00626240i	−0.0393998	−	0.000414738i
$229$	−12.2060	−	14.5465i	−0.806595	−	0.961263i	0.193207	−	0.981158i	$-0.438111\pi$
$229$	−12.2060	−	14.5465i	−0.806595	−	0.961263i	−0.999802	+	0.0198953i	$0.993667\pi$
$230$		0			0
$231$	2.54953	−	9.12949i	0.167747	−	0.600677i
$232$	6.27495	−	13.4567i	0.411971	−	0.883474i
$233$	22.6295	+	6.06355i	1.48251	+	0.397236i	0.907199	−	0.420701i	$-0.138216\pi$
$233$	22.6295	+	6.06355i	1.48251	+	0.397236i	0.575307	+	0.817937i	$0.304882\pi$
$234$	−19.6364	−	24.4281i	−1.28367	−	1.59692i
$235$		0			0
$236$	−4.31438	−	0.760742i	−0.280842	−	0.0495201i
$237$	7.79279	−	20.7290i	0.506196	−	1.34649i
$238$	−5.90634	−	12.6662i	−0.382851	−	0.821026i
$239$	−0.177210	−	1.00501i	−0.0114627	−	0.0650084i	0.978540	−	0.206058i	$-0.0660635\pi$
$239$	−0.177210	−	1.00501i	−0.0114627	−	0.0650084i	−0.990003	+	0.141049i	$0.954952\pi$
$240$		0			0
$241$	3.23680	+	2.71599i	0.208500	+	0.174953i	0.741058	−	0.671441i	$-0.234324\pi$
$241$	3.23680	+	2.71599i	0.208500	+	0.174953i	−0.532557	+	0.846394i	$0.678769\pi$
$242$	−5.73968	−	5.73968i	−0.368961	−	0.368961i
$243$	1.89558	+	15.4728i	0.121601	+	0.992579i
$244$		−	5.57498i		−	0.356901i
$245$		0			0
$246$	−2.51797	+	5.25469i	−0.160540	+	0.335027i
$247$	2.99067	+	2.09409i	0.190292	+	0.133244i
$248$	−2.80053	+	1.30591i	−0.177834	+	0.0829254i
$249$	26.2485	−	11.9051i	1.66343	−	0.754456i
$250$		0			0
$251$	−20.9072	−	12.0708i	−1.31965	−	0.761900i	−0.335977	−	0.941870i	$-0.609066\pi$
$251$	−20.9072	−	12.0708i	−1.31965	−	0.761900i	−0.983672	+	0.179970i	$0.942400\pi$
$252$	2.48129	+	0.269825i	0.156306	+	0.0169974i
$253$	−1.75463	+	6.54837i	−0.110313	+	0.411693i
$254$	−6.47677	+	2.35735i	−0.406388	+	0.147913i
$255$		0			0
$256$	10.2580	−	8.60748i	0.641125	−	0.537968i
$257$	20.4386	+	1.78815i	1.27493	+	0.111542i	0.704439	−	0.709765i	$-0.251199\pi$
$257$	20.4386	+	1.78815i	1.27493	+	0.111542i	0.570487	+	0.821306i	$0.306754\pi$
$258$	−0.101563	+	9.64839i	−0.00632302	+	0.600683i
$259$	−3.14227	−	8.63332i	−0.195251	−	0.536449i
$260$		0			0
$261$	−19.8166	−	0.417240i	−1.22662	−	0.0258265i
$262$	4.51090	+	16.8349i	0.278685	+	1.04006i
$263$	−2.57249	−	3.67390i	−0.158627	−	0.226542i	0.731969	−	0.681337i	$-0.238601\pi$
$263$	−2.57249	−	3.67390i	−0.158627	−	0.226542i	−0.890596	+	0.454795i	$0.849712\pi$
$264$	−9.07142	+	12.6694i	−0.558307	+	0.779747i
$265$		0			0
$266$	−1.22727	+	0.216400i	−0.0752486	+	0.0132684i
$267$	−0.191958	+	1.02541i	−0.0117476	+	0.0627542i
$268$	−0.296917	−	3.39378i	−0.0181371	−	0.207308i
$269$	7.32723			0.446749			0.223374	−	0.974733i	$-0.428293\pi$
$269$	7.32723			0.446749			0.223374	+	0.974733i	$0.428293\pi$
$270$		0			0
$271$	19.5478			1.18745			0.593723	−	0.804669i	$-0.297657\pi$
$271$	19.5478			1.18745			0.593723	+	0.804669i	$0.297657\pi$
$272$	2.67383	+	30.5620i	0.162125	+	1.85310i
$273$	−11.6285	−	9.96793i	−0.703789	−	0.603286i
$274$	25.9507	−	4.57580i	1.56774	−	0.276434i
$275$		0			0
$276$	−1.77658	−	0.174292i	−0.106938	−	0.0104912i
$277$	11.9695	+	17.0942i	0.719177	+	1.02709i	0.997774	+	0.0666833i	$0.0212417\pi$
$277$	11.9695	+	17.0942i	0.719177	+	1.02709i	−0.278597	+	0.960408i	$0.589869\pi$
$278$	−7.54195	−	28.1469i	−0.452336	−	1.68814i
$279$	3.10345	+	2.71746i	0.185799	+	0.162690i
$280$		0			0
$281$	−1.84144	−	5.05932i	−0.109851	−	0.301814i	0.872571	−	0.488488i	$-0.162451\pi$
$281$	−1.84144	−	5.05932i	−0.109851	−	0.301814i	−0.982422	+	0.186674i	$0.940229\pi$
$282$	−3.23730	−	1.91477i	−0.192778	−	0.114023i
$283$	8.09174	+	0.707935i	0.481004	+	0.0420824i	0.325080	−	0.945687i	$-0.394609\pi$
$283$	8.09174	+	0.707935i	0.481004	+	0.0420824i	0.155924	+	0.987769i	$0.450164\pi$
$284$	−0.319902	+	0.268430i	−0.0189827	+	0.0159284i
$285$		0			0
$286$	−39.3007	+	14.3043i	−2.32390	+	0.845830i
$287$	−0.736969	+	2.75040i	−0.0435019	+	0.162351i
$288$	−8.97270	−	4.41632i	−0.528722	−	0.260234i
$289$	−19.9750	−	11.5325i	−1.17500	−	0.678385i
$290$		0			0
$291$	−2.76780	+	28.2125i	−0.162252	+	1.65385i
$292$	4.00868	−	1.86928i	0.234590	−	0.109391i
$293$	−4.72431	−	3.30800i	−0.275997	−	0.193255i	0.427380	−	0.904072i	$-0.359437\pi$
$293$	−4.72431	−	3.30800i	−0.275997	−	0.193255i	−0.703377	+	0.710817i	$0.748326\pi$
$294$	−14.3120	+	1.10047i	−0.834693	+	0.0641808i
$295$		0			0
$296$			15.1031i			0.877851i
$297$	20.3610	+	4.25709i	1.18147	+	0.247021i
$298$	11.0961	+	11.0961i	0.642783	+	0.642783i
$299$	8.39145	+	7.04127i	0.485290	+	0.407207i
$300$		0			0
$301$	0.818784	+	4.64356i	0.0471940	+	0.267650i
$302$	1.51531	+	3.24960i	0.0871966	+	0.186994i
$303$	16.0644	−	2.65855i	0.922874	−	0.152730i
$304$	2.69406	+	0.475035i	0.154515	+	0.0272451i
$305$		0			0
$306$	26.8775	−	14.7723i	1.53649	−	0.844474i
$307$	9.73795	+	2.60928i	0.555774	+	0.148919i	0.525764	−	0.850630i	$-0.323779\pi$
$307$	9.73795	+	2.60928i	0.555774	+	0.148919i	0.0300101	+	0.999550i	$0.490446\pi$
$308$	1.40756	−	3.01851i	0.0802029	−	0.171996i
$309$	21.9562	+	22.4233i	1.24904	+	1.27562i
$310$		0			0
$311$	13.2713	+	15.8161i	0.752548	+	0.896851i	0.997352	−	0.0727212i	$-0.0231683\pi$
$311$	13.2713	+	15.8161i	0.752548	+	0.896851i	−0.244805	+	0.969572i	$0.578724\pi$
$312$	12.3588	+	21.9361i	0.699679	+	1.24189i
$313$	13.1567	+	6.13505i	0.743658	+	0.346773i	0.757242	−	0.653134i	$-0.226546\pi$
$313$	13.1567	+	6.13505i	0.743658	+	0.346773i	−0.0135841	+	0.999908i	$0.504324\pi$
$314$	−14.6486	−	25.3722i	−0.826670	−	1.43183i
$315$		0			0
$316$	3.89060	−	6.73872i	0.218863	−	0.379083i
$317$	24.5968	−	17.2229i	1.38150	−	0.967334i	0.382437	−	0.923982i	$-0.375085\pi$
$317$	24.5968	−	17.2229i	1.38150	−	0.967334i	0.999060	−	0.0433528i	$-0.0138039\pi$
$318$	−28.3898	−	10.6728i	−1.59202	−	0.598500i
$319$	−9.04617	+	24.8541i	−0.506488	+	1.39156i
$320$		0			0
$321$	3.42806	+	1.64268i	0.191336	+	0.0916854i
$322$	−3.72487	+	0.325884i	−0.207579	+	0.0181608i
$323$	−2.52621	+	2.52621i	−0.140562	+	0.140562i
$324$	−0.230548	+	5.47245i	−0.0128082	+	0.304025i
$325$		0			0
$326$	−20.6475	+	24.6067i	−1.14356	+	1.36284i
$327$	−1.33146	−	3.78153i	−0.0736297	−	0.209119i
$328$	2.68484	−	3.83435i	0.148245	−	0.211717i
$329$	−1.72715	−	0.628630i	−0.0952207	−	0.0346575i
$330$		0			0
$331$	5.01737	−	28.4549i	0.275779	−	1.56402i	−0.460695	−	0.887558i	$-0.652400\pi$
$331$	5.01737	−	28.4549i	0.275779	−	1.56402i	0.736475	−	0.676465i	$-0.236489\pi$
$332$	9.78212	−	2.62111i	0.536864	−	0.143852i
$333$	18.4481	−	8.13421i	1.01095	−	0.445752i
$334$	27.0582	−	15.6221i	1.48056	−	0.854803i
$335$		0			0
$336$	−11.0533	−	3.08678i	−0.603008	−	0.168398i
$337$	−1.50984	+	17.2575i	−0.0822462	+	0.940078i	0.837209	+	0.546883i	$0.184186\pi$
$337$	−1.50984	+	17.2575i	−0.0822462	+	0.940078i	−0.919455	+	0.393195i	$0.871370\pi$
$338$	−4.05989	+	46.4047i	−0.220829	+	2.52408i
$339$	−0.837450	+	0.820003i	−0.0454840	+	0.0445364i
$340$		0			0
$341$	4.76702	−	2.75224i	0.258148	−	0.149042i
$342$	−0.652053	−	2.65592i	−0.0352590	−	0.143616i
$343$	−16.0188	+	4.29223i	−0.864935	+	0.231759i
$344$	1.34600	−	7.63352i	0.0725713	−	0.411572i
$345$		0			0
$346$	−24.6784	−	8.98221i	−1.32672	−	0.482887i
$347$	−7.07573	+	10.1052i	−0.379845	+	0.542475i	−0.962865	−	0.269983i	$-0.912982\pi$
$347$	−7.07573	+	10.1052i	−0.379845	+	0.542475i	0.583020	+	0.812458i	$0.301871\pi$
$348$	−6.84557	−	1.28150i	−0.366961	−	0.0686954i
$349$	−8.50408	+	10.1348i	−0.455213	+	0.542502i	−0.944019	−	0.329891i	$-0.892988\pi$
$349$	−8.50408	+	10.1348i	−0.455213	+	0.542502i	0.488806	+	0.872392i	$0.337433\pi$
$350$		0			0
$351$	20.1383	−	26.9103i	1.07490	−	1.43637i
$352$	−9.43630	+	9.43630i	−0.502956	+	0.502956i
$353$	21.7758	−	1.90514i	1.15901	−	0.101400i	0.508613	−	0.860995i	$-0.330159\pi$
$353$	21.7758	−	1.90514i	1.15901	−	0.101400i	0.650396	+	0.759595i	$0.274603\pi$
$354$	−1.54385	−	20.0783i	−0.0820545	−	1.06715i
$355$		0			0
$356$	−0.125370	+	0.344451i	−0.00664459	+	0.0182559i
$357$	11.5818	−	9.51236i	0.612975	−	0.503448i
$358$	−14.0107	+	9.81043i	−0.740491	+	0.518497i
$359$	−2.83192	+	4.90502i	−0.149463	+	0.258877i	−0.931029	−	0.364945i	$-0.881088\pi$
$359$	−2.83192	+	4.90502i	−0.149463	+	0.258877i	0.781566	+	0.623822i	$0.214421\pi$
$360$		0			0
$361$	−9.34072	−	16.1786i	−0.491617	−	0.851505i
$362$	15.2811	+	7.12568i	0.803156	+	0.374518i
$363$	4.43153	−	7.49238i	0.232595	−	0.393248i
$364$	−3.45922	−	4.12254i	−0.181312	−	0.216080i
$365$		0			0
$366$	24.8213	−	6.37161i	1.29743	−	0.333049i
$367$	−0.650455	+	1.39490i	−0.0339535	+	0.0728134i	−0.922553	−	0.385870i	$-0.873901\pi$
$367$	−0.650455	+	1.39490i	−0.0339535	+	0.0728134i	0.888600	+	0.458684i	$0.151679\pi$
$368$	7.92829	+	2.12438i	0.413290	+	0.110741i
$369$	−6.12957	−	1.21438i	−0.319093	−	0.0632179i
$370$		0			0
$371$	−14.5962	−	2.57371i	−0.757798	−	0.133620i
$372$	0.919926	+	1.12006i	0.0476959	+	0.0580724i
$373$	7.18493	+	15.4081i	0.372021	+	0.797802i	0.999811	+	0.0194197i	$0.00618187\pi$
$373$	7.18493	+	15.4081i	0.372021	+	0.797802i	−0.627790	+	0.778383i	$0.716040\pi$
$374$	−7.10666	−	40.3038i	−0.367476	−	2.08406i
$375$		0			0
$376$	2.31458	+	1.94216i	0.119365	+	0.100159i
$377$	30.2198	+	30.2198i	1.55640	+	1.55640i
$378$	1.63451	+	11.3557i	0.0840701	+	0.584077i
$379$		−	37.4048i		−	1.92136i	−0.277663	−	0.960679i	$-0.589560\pi$
$379$		−	37.4048i		−	1.92136i	0.277663	−	0.960679i	$-0.410440\pi$
$380$		0			0
$381$	−4.17560	−	6.09902i	−0.213922	−	0.312462i
$382$	−9.44567	−	6.61393i	−0.483282	−	0.338398i
$383$	21.8049	−	10.1678i	1.11418	−	0.519550i	0.223738	−	0.974649i	$-0.428174\pi$
$383$	21.8049	−	10.1678i	1.11418	−	0.519550i	0.890441	+	0.455099i	$0.150396\pi$
$384$	19.1913	+	13.7412i	0.979351	+	0.701226i
$385$		0			0
$386$	15.2242	+	8.78971i	0.774893	+	0.447385i
$387$	−10.0491	+	2.46715i	−0.510825	+	0.125412i
$388$	−2.57800	+	9.62121i	−0.130878	+	0.488443i
$389$	5.94474	−	2.16371i	0.301410	−	0.109704i	−0.186888	−	0.982381i	$-0.559840\pi$
$389$	5.94474	−	2.16371i	0.301410	−	0.109704i	0.488298	+	0.872677i	$0.337618\pi$
$390$		0			0
$391$	−8.21141	+	6.89019i	−0.415269	+	0.348452i
$392$	11.4873	+	1.00501i	0.580198	+	0.0507608i
$393$	−16.2841	+	9.17444i	−0.821423	+	0.462789i
$394$	0.532101	+	1.46194i	0.0268069	+	0.0736513i
$395$		0			0
$396$	6.81402	+	2.64383i	0.342417	+	0.132857i
$397$	−7.91207	−	29.5283i	−0.397095	−	1.48198i	−0.818182	−	0.574960i	$-0.805018\pi$
$397$	−7.91207	−	29.5283i	−0.397095	−	1.48198i	0.421086	−	0.907021i	$-0.361649\pi$
$398$	−14.4490	−	20.6353i	−0.724261	−	1.03435i
$399$	−0.552018	−	1.21709i	−0.0276355	−	0.0609308i
$400$		0			0
$401$	−2.27324	+	0.400833i	−0.113520	+	0.0200167i	−0.230120	−	0.973162i	$-0.573912\pi$
$401$	−2.27324	+	0.400833i	−0.113520	+	0.0200167i	0.116599	+	0.993179i	$0.462801\pi$
$402$	14.7707	−	5.20069i	0.736696	−	0.259387i
$403$	−0.775186	−	8.86041i	−0.0386147	−	0.441369i
$404$	5.72130			0.284645
$405$		0			0
$406$	−14.5878			−0.723982
$407$	−2.34484	−	26.8017i	−0.116229	−	1.32851i
$408$	−23.2394	+	8.18246i	−1.15052	+	0.405092i
$409$	−13.8912	+	2.44939i	−0.686874	+	0.121114i	−0.506184	−	0.862426i	$-0.668944\pi$
$409$	−13.8912	+	2.44939i	−0.686874	+	0.121114i	−0.180690	+	0.983540i	$0.557833\pi$
$410$		0			0
$411$	11.6725	+	25.7355i	0.575761	+	1.26944i
$412$	6.32479	+	9.03274i	0.311600	+	0.445011i
$413$	−2.54696	−	9.50540i	−0.125328	−	0.467730i
$414$	−1.25445	−	8.10904i	−0.0616528	−	0.398537i
$415$		0			0
$416$	7.37500	+	20.2626i	0.361589	+	0.993458i
$417$	27.2260	−	15.3391i	1.33326	−	0.751159i
$418$	−3.63544	−	0.318060i	−0.177815	−	0.0155568i
$419$	−22.4508	+	18.8385i	−1.09679	+	0.920320i	−0.997205	−	0.0747090i	$-0.976197\pi$
$419$	−22.4508	+	18.8385i	−1.09679	+	0.920320i	−0.0995889	+	0.995029i	$0.531753\pi$
$420$		0			0
$421$	−19.6404	+	7.14853i	−0.957216	+	0.348398i	−0.772942	−	0.634477i	$-0.781216\pi$
$421$	−19.6404	+	7.14853i	−0.957216	+	0.348398i	−0.184274	+	0.982875i	$0.558993\pi$
$422$	−2.15604	+	8.04644i	−0.104954	+	0.391694i
$423$	1.12573	−	3.87321i	0.0547347	−	0.188322i
$424$	21.1005	+	12.1824i	1.02473	+	0.591630i
$425$		0			0
$426$	−1.56074	−	1.11751i	−0.0756180	−	0.0541434i
$427$	11.3495	−	5.29238i	0.549243	−	0.256116i
$428$	1.09411	+	0.766106i	0.0528859	+	0.0370311i
$429$	−25.3373	−	37.0085i	−1.22330	−	1.78679i
$430$		0			0
$431$		−	22.4642i		−	1.08206i	−0.841003	−	0.541030i	$-0.818034\pi$
$431$		−	22.4642i		−	1.08206i	0.841003	−	0.541030i	$-0.181966\pi$
$432$	5.15417	−	24.6516i	0.247980	−	1.18605i
$433$	−7.75200	−	7.75200i	−0.372537	−	0.372537i	0.495863	−	0.868401i	$-0.334852\pi$
$433$	−7.75200	−	7.75200i	−0.372537	−	0.372537i	−0.868401	+	0.495863i	$0.834852\pi$
$434$	2.32567	+	1.95147i	0.111636	+	0.0936734i
$435$		0			0
$436$	−0.244612	−	1.38727i	−0.0117148	−	0.0664380i
$437$	0.403952	+	0.866278i	0.0193236	+	0.0414397i
$438$	12.9040	+	15.7114i	0.616579	+	0.750718i
$439$	26.6574	+	4.70041i	1.27229	+	0.224338i	0.768702	−	0.639608i	$-0.220903\pi$
$439$	26.6574	+	4.70041i	1.27229	+	0.224338i	0.503585	+	0.863946i	$0.332014\pi$
$440$		0			0
$441$	−4.95923	−	14.5728i	−0.236154	−	0.693944i
$442$	−63.8752	−	17.1153i	−3.03823	−	0.814092i
$443$	17.4674	−	37.4589i	0.829901	−	1.77973i	0.243090	−	0.970004i	$-0.421839\pi$
$443$	17.4674	−	37.4589i	0.829901	−	1.77973i	0.586810	−	0.809724i	$-0.300383\pi$
$444$	6.86177	−	1.76141i	0.325645	−	0.0835927i
$445$		0			0
$446$	−24.1813	−	28.8181i	−1.14502	−	1.36458i
$447$	−8.56718	+	14.4845i	−0.405214	+	0.685094i
$448$	5.33936	+	2.48979i	0.252261	+	0.117631i
$449$	−5.23440	−	9.06624i	−0.247027	−	0.427862i	0.715673	−	0.698436i	$-0.246120\pi$
$449$	−5.23440	−	9.06624i	−0.247027	−	0.427862i	−0.962699	+	0.270573i	$0.912787\pi$
$450$		0			0
$451$	−4.16915	+	7.22119i	−0.196318	+	0.340032i
$452$	−0.337348	+	0.236214i	−0.0158675	+	0.0111106i
$453$	−2.97140	+	2.44047i	−0.139609	+	0.114663i
$454$	−3.58906	+	9.86086i	−0.168443	+	0.462793i
$455$		0			0
$456$	0.168429	+	2.19048i	0.00788743	+	0.102579i
$457$	−34.6748	+	3.03365i	−1.62202	+	0.141908i	−0.861622	−	0.507550i	$-0.830551\pi$
$457$	−34.6748	+	3.03365i	−1.62202	+	0.141908i	−0.760397	+	0.649458i	$0.774996\pi$
$458$	21.6867	−	21.6867i	1.01335	−	1.01335i
$459$	22.5109	+	23.9795i	1.05072	+	1.11927i
$460$		0			0
$461$	20.9800	−	25.0030i	0.977135	−	1.16450i	−0.00923458	−	0.999957i	$-0.502939\pi$
$461$	20.9800	−	25.0030i	0.977135	−	1.16450i	0.986369	−	0.164546i	$-0.0526161\pi$
$462$	15.0479	+	2.81699i	0.700093	+	0.131058i
$463$	−3.37708	+	4.82297i	−0.156946	+	0.224143i	−0.889923	−	0.456112i	$-0.849242\pi$
$463$	−3.37708	+	4.82297i	−0.156946	+	0.224143i	0.732976	+	0.680254i	$0.238131\pi$
$464$	30.0916	+	10.9524i	1.39697	+	0.508454i
$465$		0			0
$466$	−6.57058	+	37.2636i	−0.304376	+	1.72620i
$467$	−19.7683	+	5.29691i	−0.914769	+	0.245112i	−0.685348	−	0.728216i	$-0.740350\pi$
$467$	−19.7683	+	5.29691i	−0.914769	+	0.245112i	−0.229421	+	0.973327i	$0.573683\pi$
$468$	8.52484	−	8.17326i	0.394061	−	0.377809i
$469$	6.62720	−	3.82621i	0.306015	−	0.176678i
$470$		0			0
$471$	22.4488	−	21.9811i	1.03439	−	1.01284i
$472$	−1.40993	+	16.1155i	−0.0648972	+	0.741778i
$473$	−1.20343	+	13.7553i	−0.0553337	+	0.632467i
$474$	34.4492	+	9.62039i	1.58230	+	0.441879i
$475$		0			0
$476$	4.56060	−	2.63306i	0.209035	−	0.120686i
$477$	3.51624	−	32.3350i	0.160998	−	1.48052i
$478$	1.59208	−	0.426596i	0.0728199	−	0.0195120i
$479$	−1.10017	+	6.23936i	−0.0502679	+	0.285083i	−0.999571	−	0.0292779i	$-0.990679\pi$
$479$	−1.10017	+	6.23936i	−0.0502679	+	0.285083i	0.949303	+	0.314361i	$0.101790\pi$
$480$		0			0
$481$	−40.8504	−	14.8683i	−1.86262	−	0.677938i
$482$	−3.91431	+	5.59022i	−0.178292	+	0.254627i
$483$	−1.33170	−	3.78223i	−0.0605946	−	0.172097i
$484$	1.96604	−	2.34303i	0.0893654	−	0.106501i
$485$		0			0
$486$	−24.6283	+	5.22796i	−1.11716	+	0.237145i
$487$	4.69365	−	4.69365i	0.212690	−	0.212690i	−0.592719	−	0.805409i	$-0.701946\pi$
$487$	4.69365	−	4.69365i	0.212690	−	0.212690i	0.805409	+	0.592719i	$0.201946\pi$
$488$	−20.5079	+	1.79421i	−0.928349	+	0.0812200i
$489$	−31.0651	−	14.8860i	−1.40481	−	0.673166i
$490$		0			0
$491$	2.14176	−	5.88443i	0.0966562	−	0.265561i	−0.881936	−	0.471369i	$-0.843760\pi$
$491$	2.14176	−	5.88443i	0.0966562	−	0.265561i	0.978592	+	0.205808i	$0.0659823\pi$
$492$	−2.05517	−	0.772616i	−0.0926544	−	0.0348322i
$493$	−34.2572	+	23.9871i	−1.54287	+	1.08033i
$494$	−2.94833	+	5.10666i	−0.132652	+	0.229759i
$495$		0			0
$496$	−3.33221	−	5.77155i	−0.149620	−	0.259150i
$497$	−0.850156	−	0.396434i	−0.0381347	−	0.0177825i
$498$	22.8498	+	40.5571i	1.02393	+	1.81741i
$499$	15.3830	+	18.3328i	0.688638	+	0.820687i	0.991190	−	0.132446i	$-0.0422831\pi$
$499$	15.3830	+	18.3328i	0.688638	+	0.820687i	−0.302552	+	0.953133i	$0.597839\pi$
$500$		0			0
$501$	23.4419	+	23.9406i	1.04730	+	1.06959i
$502$	16.4784	−	35.3381i	0.735468	−	1.57722i
$503$	7.23333	+	1.93816i	0.322518	+	0.0864185i	0.416446	−	0.909161i	$-0.363276\pi$
$503$	7.23333	+	1.93816i	0.322518	+	0.0864185i	−0.0939277	+	0.995579i	$0.529942\pi$
$504$	0.194010	−	9.21440i	0.00864190	−	0.410442i
$505$		0			0
$506$	−10.7831	−	1.90135i	−0.479368	−	0.0845255i
$507$	−49.2843	+	8.15622i	−2.18879	+	0.362231i
$508$	−1.09759	−	2.35380i	−0.0486979	−	0.104433i
$509$	1.85342	+	10.5113i	0.0821515	+	0.465904i	0.997935	+	0.0642321i	$0.0204598\pi$
$509$	1.85342	+	10.5113i	0.0821515	+	0.465904i	−0.915783	+	0.401672i	$0.868429\pi$
$510$		0			0
$511$	7.61095	+	6.38635i	0.336689	+	0.282515i
$512$	−3.97904	−	3.97904i	−0.175850	−	0.175850i
$513$	2.58491	−	1.38548i	0.114127	−	0.0611704i
$514$			33.1368i			1.46160i
$515$		0			0
$516$	−3.62510	+	0.278739i	−0.159586	+	0.0122708i
$517$	−4.40893	−	3.08717i	−0.193905	−	0.135773i
$518$	13.4484	−	6.27109i	0.590889	−	0.275536i
$519$	2.74981	−	28.0291i	0.120703	−	1.23034i
$520$		0			0
$521$	12.8647	+	7.42744i	0.563613	+	0.325402i	0.754594	−	0.656192i	$-0.227834\pi$
$521$	12.8647	+	7.42744i	0.563613	+	0.325402i	−0.190982	+	0.981594i	$0.561167\pi$
$522$	−2.11818	−	31.9430i	−0.0927103	−	1.39811i
$523$	5.65314	−	21.0978i	0.247194	−	0.922542i	−0.725073	−	0.688672i	$-0.758194\pi$
$523$	5.65314	−	21.0978i	0.247194	−	0.922542i	0.972268	−	0.233870i	$-0.0751391\pi$
$524$	−6.17127	+	2.24616i	−0.269593	+	0.0981239i
$525$		0			0
$526$	5.54906	−	4.65621i	0.241951	−	0.203021i
$527$	8.67030	+	0.758553i	0.377684	+	0.0330431i
$528$	−28.9257	−	17.1087i	−1.25883	−	0.744561i
$529$	−6.88559	−	18.9180i	−0.299373	−	0.822522i
$530$		0			0
$531$	20.4441	−	6.95729i	0.887200	−	0.301921i
$532$	−0.121536	−	0.453579i	−0.00526926	−	0.0196651i
$533$	7.72792	+	11.0366i	0.334734	+	0.478049i
$534$	−1.67687	−	0.164510i	−0.0725654	−	0.00711906i
$535$		0			0
$536$	−12.3887	+	2.18446i	−0.535109	+	0.0943542i
$537$	−13.9262	−	11.9375i	−0.600958	−	0.515140i
$538$	1.03143	+	11.7893i	0.0444680	+	0.508271i
$539$	−20.5412			−0.884773
$540$		0			0
$541$	−4.75367			−0.204376			−0.102188	−	0.994765i	$-0.532584\pi$
$541$	−4.75367			−0.204376			−0.102188	+	0.994765i	$0.532584\pi$
$542$	2.75168	+	31.4518i	0.118195	+	1.35097i
$543$	−3.32709	+	17.7728i	−0.142779	+	0.762705i
$544$	−20.7798	+	3.66405i	−0.890928	+	0.157095i
$545$		0			0
$546$	14.4012	−	20.1130i	0.616313	−	0.860758i
$547$	10.4741	+	14.9586i	0.447840	+	0.639582i	0.978071	−	0.208271i	$-0.0667837\pi$
$547$	10.4741	+	14.9586i	0.447840	+	0.639582i	−0.530231	+	0.847853i	$0.677895\pi$
$548$	2.56989	+	9.59097i	0.109780	+	0.409706i
$549$	13.2367	+	24.0836i	0.564929	+	1.02786i
$550$		0			0
$551$	1.27543	+	3.50421i	0.0543351	+	0.149284i
$552$	−0.0693833	+	6.59137i	−0.00295315	+	0.280547i
$553$	17.4121	+	1.52336i	0.740437	+	0.0647798i
$554$	−25.8191	+	21.6648i	−1.09695	+	0.920449i
$555$		0			0
$556$	10.3180	−	3.75544i	0.437580	−	0.159266i
$557$	−4.50326	+	16.8064i	−0.190809	+	0.712110i	0.802503	+	0.596649i	$0.203501\pi$
$557$	−4.50326	+	16.8064i	−0.190809	+	0.712110i	−0.993312	+	0.115461i	$0.963165\pi$
$558$	−3.93544	+	5.37587i	−0.166600	+	0.227579i
$559$	19.3219	+	11.1555i	0.817227	+	0.471826i
$560$		0			0
$561$	39.9697	−	18.1285i	1.68752	−	0.765384i
$562$	7.88106	−	3.67500i	0.332442	−	0.155020i
$563$	−6.97840	−	4.88633i	−0.294104	−	0.205934i	0.417206	−	0.908812i	$-0.363009\pi$
$563$	−6.97840	−	4.88633i	−0.294104	−	0.205934i	−0.711311	+	0.702878i	$0.751898\pi$
$564$	0.612440	−	1.27808i	0.0257884	−	0.0538170i
$565$		0			0
$566$			13.1190i			0.551432i
$567$	−11.3597	+	4.72570i	−0.477062	+	0.198461i
$568$	1.09039	+	1.09039i	0.0457518	+	0.0457518i
$569$	−1.30840	−	1.09788i	−0.0548512	−	0.0460256i	0.614950	−	0.788566i	$-0.289176\pi$
$569$	−1.30840	−	1.09788i	−0.0548512	−	0.0460256i	−0.669801	+	0.742541i	$0.733621\pi$
$570$		0			0
$571$	−2.38472	−	13.5244i	−0.0997975	−	0.565980i	−0.993171	−	0.116665i	$-0.962779\pi$
$571$	−2.38472	−	13.5244i	−0.0997975	−	0.565980i	0.893374	−	0.449314i	$-0.148332\pi$
$572$	−6.66015	−	14.2827i	−0.278475	−	0.597192i
$573$	4.35147	−	11.5750i	0.181785	−	0.483552i
$574$	−4.52905	−	0.798594i	−0.189039	−	0.0333327i
$575$		0			0
$576$	−4.67660	+	12.0531i	−0.194858	+	0.502213i
$577$	28.7885	+	7.71384i	1.19848	+	0.321131i	0.802232	−	0.597013i	$-0.203646\pi$
$577$	28.7885	+	7.71384i	1.19848	+	0.321131i	0.396247	+	0.918144i	$0.370312\pi$
$578$	15.7437	−	33.7624i	0.654851	−	1.40433i
$579$	−5.07072	+	18.1575i	−0.210732	+	0.754599i
$580$		0			0
$581$	14.6223	+	17.4262i	0.606636	+	0.722961i
$582$	−45.7827	−	0.481926i	−1.89775	−	0.0199765i
$583$	−39.3359	−	18.3427i	−1.62913	−	0.759675i
$584$	−8.16638	−	14.1446i	−0.337927	−	0.585307i
$585$		0			0
$586$	4.65744	−	8.06692i	0.192397	−	0.333241i
$587$	−14.0836	+	9.86144i	−0.581292	+	0.407025i	−0.826904	−	0.562343i	$-0.809900\pi$
$587$	−14.0836	+	9.86144i	−0.581292	+	0.407025i	0.245612	+	0.969368i	$0.421011\pi$
$588$	−0.883112	−	5.33623i	−0.0364189	−	0.220063i
$589$	0.265436	−	0.729279i	0.0109371	−	0.0300494i
$590$		0			0
$591$	−1.37667	+	0.942517i	−0.0566287	+	0.0387700i
$592$	−32.4495	+	2.83896i	−1.33366	+	0.116681i
$593$	3.89096	−	3.89096i	0.159783	−	0.159783i	−0.622688	−	0.782470i	$-0.713959\pi$
$593$	3.89096	−	3.89096i	0.159783	−	0.159783i	0.782470	+	0.622688i	$0.213959\pi$
$594$	−3.98336	+	33.3595i	−0.163439	+	1.36876i
$595$		0			0
$596$	−3.80081	+	4.52963i	−0.155687	+	0.185541i
$597$	17.5817	−	20.5107i	0.719571	−	0.839446i
$598$	−10.1479	+	14.4927i	−0.414980	+	0.592652i
$599$	−8.34437	−	3.03710i	−0.340942	−	0.124093i	0.165874	−	0.986147i	$-0.446955\pi$
$599$	−8.34437	−	3.03710i	−0.340942	−	0.124093i	−0.506816	+	0.862054i	$0.669178\pi$
$600$		0			0
$601$	6.49256	−	36.8211i	0.264837	−	1.50197i	−0.504661	−	0.863317i	$-0.668383\pi$
$601$	6.49256	−	36.8211i	0.264837	−	1.50197i	0.769499	−	0.638649i	$-0.220506\pi$
$602$	−7.35607	+	1.97105i	−0.299811	+	0.0803341i
$603$	9.34054	+	13.9560i	0.380376	+	0.568332i
$604$	−1.17006	+	0.675532i	−0.0476089	+	0.0274870i
$605$		0			0
$606$	6.53884	+	25.4728i	0.265622	+	1.03476i
$607$	2.18141	−	24.9336i	0.0885406	−	1.01202i	−0.813841	−	0.581087i	$-0.802628\pi$
$607$	2.18141	−	24.9336i	0.0885406	−	1.01202i	0.902382	−	0.430937i	$-0.141817\pi$
$608$	−0.163985	+	1.87436i	−0.00665047	+	0.0760153i
$609$	−3.88969	−	15.1527i	−0.157618	−	0.614020i
$610$		0			0
$611$	−7.53170	+	4.34843i	−0.304700	+	0.175919i
$612$	6.42783	+	9.60402i	0.259830	+	0.388219i
$613$	5.98971	−	1.60494i	0.241922	−	0.0648229i	−0.135820	−	0.990733i	$-0.543367\pi$
$613$	5.98971	−	1.60494i	0.241922	−	0.0648229i	0.377743	+	0.925911i	$0.376700\pi$
$614$	−2.82746	+	16.0353i	−0.114107	+	0.647134i
$615$		0			0
$616$	−11.5568	−	4.20633i	−0.465636	−	0.169478i
$617$	−4.90794	+	7.00927i	−0.197586	+	0.282182i	−0.905703	−	0.423913i	$-0.860656\pi$
$617$	−4.90794	+	7.00927i	−0.197586	+	0.282182i	0.708117	+	0.706096i	$0.249545\pi$
$618$	−32.9877	+	38.4832i	−1.32696	+	1.54802i
$619$	−7.05535	+	8.40824i	−0.283579	+	0.337956i	−0.888964	−	0.457976i	$-0.848574\pi$
$619$	−7.05535	+	8.40824i	−0.283579	+	0.337956i	0.605386	+	0.795932i	$0.293019\pi$
$620$		0			0
$621$	8.08858	−	3.46522i	0.324583	−	0.139054i
$622$	−23.5795	+	23.5795i	−0.945452	+	0.945452i
$623$	−0.820248	+	0.0717624i	−0.0328625	+	0.00287510i
$624$	−44.8072	+	30.6766i	−1.79372	+	1.22805i
$625$		0			0
$626$	−8.01907	+	22.0322i	−0.320507	+	0.880585i
$627$	−0.638975	−	3.86103i	−0.0255182	−	0.154195i
$628$	9.04301	−	6.33198i	0.360855	−	0.252674i
$629$	21.2697	−	36.8402i	0.848079	−	1.46892i
$630$		0			0
$631$	17.7048	+	30.6656i	0.704816	+	1.22078i	0.966758	+	0.255694i	$0.0823038\pi$
$631$	17.7048	+	30.6656i	0.704816	+	1.22078i	−0.261942	+	0.965084i	$0.584363\pi$
$632$	−26.0409	−	12.1431i	−1.03585	−	0.483026i
$633$	−8.93292	−	0.0940314i	−0.355052	−	0.00373741i
$634$	31.1735	+	37.1511i	1.23806	+	1.47546i
$635$		0			0
$636$	3.07395	−	11.0074i	0.121890	−	0.436470i
$637$	−14.0271	+	30.0812i	−0.555774	+	1.19186i
$638$	−41.2629	−	11.0564i	−1.63361	−	0.437725i
$639$	0.744628	−	1.91915i	0.0294570	−	0.0759204i
$640$		0			0
$641$	−14.4883	−	2.55468i	−0.572254	−	0.100904i	−0.119970	−	0.992778i	$-0.538280\pi$
$641$	−14.4883	−	2.55468i	−0.572254	−	0.100904i	−0.452285	+	0.891874i	$0.649391\pi$
$642$	−2.16046	+	5.74687i	−0.0852666	+	0.226811i
$643$	−4.29031	−	9.20060i	−0.169193	−	0.362836i	0.803368	−	0.595483i	$-0.203039\pi$
$643$	−4.29031	−	9.20060i	−0.169193	−	0.362836i	−0.972561	+	0.232647i	$0.925261\pi$
$644$	−0.244658	−	1.38752i	−0.00964087	−	0.0546761i
$645$		0			0
$646$	−4.42019	−	3.70898i	−0.173910	−	0.145928i
$647$	−2.41506	−	2.41506i	−0.0949459	−	0.0949459i	0.658038	−	0.752984i	$-0.271386\pi$
$647$	−2.41506	−	2.41506i	−0.0949459	−	0.0949459i	−0.752984	+	0.658038i	$0.771386\pi$
$648$	20.2049	−	0.913126i	0.793725	−	0.0358710i
$649$		−	28.8172i		−	1.13117i
$650$		0			0
$651$	−1.40692	+	2.93607i	−0.0551417	+	0.115074i
$652$	−9.91484	−	6.94245i	−0.388295	−	0.271887i
$653$	29.0939	−	13.5667i	1.13853	−	0.530907i	0.240419	−	0.970669i	$-0.422715\pi$
$653$	29.0939	−	13.5667i	1.13853	−	0.530907i	0.898114	+	0.439763i	$0.144937\pi$
$654$	5.89692	−	2.67458i	0.230588	−	0.104584i
$655$		0			0
$656$	8.74288	+	5.04770i	0.341352	+	0.197080i
$657$	−12.8791	+	17.5930i	−0.502460	+	0.686369i
$658$	0.768321	−	2.86741i	0.0299523	−	0.111783i
$659$	−1.04455	+	0.380185i	−0.0406898	+	0.0148099i	−0.362285	−	0.932067i	$-0.618003\pi$
$659$	−1.04455	+	0.380185i	−0.0406898	+	0.0148099i	0.321595	+	0.946877i	$0.395781\pi$
$660$		0			0
$661$	−2.09875	+	1.76106i	−0.0816318	+	0.0684972i	−0.682690	−	0.730708i	$-0.739190\pi$
$661$	−2.09875	+	1.76106i	−0.0816318	+	0.0684972i	0.601059	+	0.799205i	$0.294746\pi$
$662$	46.4893	+	4.06728i	1.80686	+	0.158080i
$663$	0.746452	−	70.9124i	0.0289898	−	2.75401i
$664$	−12.7901	−	35.1406i	−0.496353	−	1.36372i
$665$		0			0
$666$	15.6846	+	28.5374i	0.607764	+	1.10580i
$667$	2.89588	+	10.8076i	0.112129	+	0.418471i
$668$	6.75277	+	9.64395i	0.261272	+	0.373136i
$669$	23.4864	−	32.8017i	0.908037	−	1.26819i
$670$		0			0
$671$	36.1143	−	6.36793i	1.39418	−	0.245831i
$672$	1.45238	−	7.75841i	0.0560268	−	0.299287i
$673$	1.79638	+	20.5328i	0.0692455	+	0.791479i	0.948840	+	0.315756i	$0.102258\pi$
$673$	1.79638	+	20.5328i	0.0692455	+	0.791479i	−0.879595	+	0.475723i	$0.842186\pi$
$674$	−27.9793			−1.07772
$675$		0			0
$676$	−17.5525			−0.675097
$677$	−0.452063	−	5.16710i	−0.0173742	−	0.198588i	−0.999921	−	0.0125721i	$-0.995998\pi$
$677$	−0.452063	−	5.16710i	−0.0173742	−	0.198588i	0.982547	−	0.186016i	$-0.0595575\pi$
$678$	−1.43724	−	1.23200i	−0.0551970	−	0.0473147i
$679$	−22.0342	+	3.88522i	−0.845595	+	0.149101i
$680$		0			0
$681$	−11.1997	−	1.09875i	−0.429174	−	0.0421043i
$682$	5.09930	+	7.28255i	0.195262	+	0.278863i
$683$	1.09208	+	4.07571i	0.0417874	+	0.155953i	0.983667	−	0.179998i	$-0.0576091\pi$
$683$	1.09208	+	4.07571i	0.0417874	+	0.155953i	−0.941880	+	0.335951i	$0.890942\pi$
$684$	0.975554	−	0.331988i	0.0373013	−	0.0126939i
$685$		0			0
$686$	−9.16097	−	25.1696i	−0.349767	−	0.960978i
$687$	28.3091	+	16.7440i	1.08006	+	0.638824i
$688$	16.6538	+	1.45702i	0.634922	+	0.0555485i
$689$	−53.7231	+	45.0791i	−2.04669	+	1.71738i
$690$		0			0
$691$	−5.69285	+	2.07203i	−0.216566	+	0.0788236i	−0.448025	−	0.894021i	$-0.647872\pi$
$691$	−5.69285	+	2.07203i	−0.216566	+	0.0788236i	0.231459	+	0.972845i	$0.425650\pi$
$692$	2.56124	−	9.55866i	0.0973636	−	0.363366i
$693$	1.08630	+	16.3818i	0.0412651	+	0.622293i
$694$	−17.2549	−	9.96215i	−0.654989	−	0.378158i
$695$		0			0
$696$	−2.51094	+	25.5943i	−0.0951768	+	0.970148i
$697$	−11.9489	+	5.57186i	−0.452597	+	0.211049i
$698$	−17.5036	−	12.2562i	−0.662521	−	0.463902i
$699$	−40.4587	+	3.11092i	−1.53029	+	0.117666i
$700$		0			0
$701$		−	31.6966i		−	1.19716i	−0.801062	−	0.598581i	$-0.795731\pi$
$701$		−	31.6966i		−	1.19716i	0.801062	−	0.598581i	$-0.204269\pi$
$702$	46.1326	+	28.6138i	1.74116	+	1.07996i
$703$	−2.68222	−	2.68222i	−0.101162	−	0.101162i
$704$	13.2158	+	11.0894i	0.498088	+	0.417946i
$705$		0			0
$706$	6.13060	+	34.7684i	0.230728	+	1.30852i
$707$	5.43129	+	11.6474i	0.204265	+	0.438047i
$708$	7.48618	−	1.23891i	0.281348	−	0.0465612i
$709$	−20.0118	−	3.52862i	−0.751559	−	0.132520i	−0.215270	−	0.976555i	$-0.569063\pi$
$709$	−20.0118	−	3.52862i	−0.751559	−	0.132520i	−0.536289	+	0.844035i	$0.680174\pi$
$710$		0			0
$711$	−0.807430	+	38.3484i	−0.0302810	+	1.43818i
$712$	1.30743	+	0.350325i	0.0489981	+	0.0131290i
$713$	0.984093	−	2.11039i	0.0368546	−	0.0790348i
$714$	16.9354	+	17.2957i	0.633792	+	0.647277i
$715$		0			0
$716$	−4.14272	−	4.93710i	−0.154821	−	0.184508i
$717$	0.867626	+	1.53998i	0.0324021	+	0.0575117i
$718$	−8.29065	−	3.86600i	−0.309404	−	0.144278i
$719$	5.78147	+	10.0138i	0.215612	+	0.373452i	0.953462	−	0.301514i	$-0.0974919\pi$
$719$	5.78147	+	10.0138i	0.215612	+	0.373452i	−0.737849	+	0.674965i	$0.764159\pi$
$720$		0			0
$721$	−12.3847	+	21.4509i	−0.461229	+	0.798872i
$722$	24.7160	−	17.3063i	0.919833	−	0.644074i
$723$	−6.85041	−	2.57532i	−0.254770	−	0.0957773i
$724$	−2.17296	+	5.97016i	−0.0807574	+	0.221879i
$725$		0			0
$726$	12.6788	+	6.07551i	0.470554	+	0.225483i
$727$	19.4967	−	1.70574i	0.723094	−	0.0632625i	0.280334	−	0.959903i	$-0.409555\pi$
$727$	19.4967	−	1.70574i	0.723094	−	0.0632625i	0.442760	+	0.896640i	$0.353999\pi$
$728$	−14.0517	+	14.0517i	−0.520792	+	0.520792i
$729$	−11.9973	−	24.1881i	−0.444345	−	0.895856i
$730$		0			0
$731$	−14.0335	+	16.7245i	−0.519048	+	0.618577i
$732$	3.20690	+	9.10807i	0.118531	+	0.336644i
$733$	−14.0049	+	20.0010i	−0.517282	+	0.738755i	−0.989784	−	0.142575i	$-0.954462\pi$
$733$	−14.0049	+	20.0010i	−0.517282	+	0.738755i	0.472502	+	0.881329i	$0.343351\pi$
$734$	−2.33592	−	0.850204i	−0.0862203	−	0.0313816i
$735$		0			0
$736$	−0.980299	+	5.55955i	−0.0361343	+	0.204928i
$737$	21.6455	−	5.79990i	0.797323	−	0.213642i
$738$	1.09105	−	10.0332i	0.0401622	−	0.369328i
$739$	3.92364	−	2.26531i	0.144333	−	0.0833310i	−0.426094	−	0.904679i	$-0.640111\pi$
$739$	3.92364	−	2.26531i	0.144333	−	0.0833310i	0.570428	+	0.821348i	$0.306777\pi$
$740$		0			0
$741$	−6.09056	−	1.70087i	−0.223742	−	0.0624830i
$742$	2.08635	−	23.8471i	0.0765924	−	0.875455i
$743$	−3.85745	+	44.0909i	−0.141516	+	1.61754i	0.510875	+	0.859655i	$0.329321\pi$
$743$	−3.85745	+	44.0909i	−0.141516	+	1.61754i	−0.652391	+	0.757882i	$0.726234\pi$
$744$	3.82415	−	3.74448i	0.140200	−	0.137279i
$745$		0			0
$746$	−23.7798	+	13.7293i	−0.870639	+	0.502664i
$747$	−36.0350	+	34.5488i	−1.31845	+	1.26408i
$748$	14.8957	−	3.99128i	0.544640	−	0.145936i
$749$	−0.520987	+	2.95467i	−0.0190365	+	0.107961i
$750$		0			0
$751$	21.6380	+	7.87559i	0.789582	+	0.287384i	0.705162	−	0.709046i	$-0.250874\pi$
$751$	21.6380	+	7.87559i	0.789582	+	0.287384i	0.0844197	+	0.996430i	$0.473096\pi$
$752$	−3.73771	+	5.33801i	−0.136300	+	0.194657i
$753$	41.1004	+	7.69403i	1.49778	+	0.280386i
$754$	−44.3687	+	52.8766i	−1.61581	+	1.92565i
$755$		0			0
$756$	−4.20899	+	0.986490i	−0.153079	+	0.0358783i
$757$	−7.64204	+	7.64204i	−0.277755	+	0.277755i	−0.832212	−	0.554457i	$-0.812926\pi$
$757$	−7.64204	+	7.64204i	−0.277755	+	0.277755i	0.554457	+	0.832212i	$0.312926\pi$
$758$	60.1831	−	5.26534i	2.18595	−	0.191246i
$759$	−0.900219	−	11.7077i	−0.0326759	−	0.424961i
$760$		0			0
$761$	7.73791	−	21.2597i	0.280499	−	0.770664i	−0.716804	−	0.697274i	$-0.754396\pi$
$761$	7.73791	−	21.2597i	0.280499	−	0.770664i	0.997303	−	0.0733901i	$-0.0233818\pi$
$762$	9.22533	−	7.57694i	0.334199	−	0.274484i
$763$	2.59198	−	1.81493i	0.0938361	−	0.0657048i
$764$	2.17250	−	3.76288i	0.0785983	−	0.136136i
$765$		0			0
$766$	19.4291	+	33.6521i	0.702000	+	1.21590i
$767$	−42.2008	−	19.6786i	−1.52378	−	0.710552i
$768$	−11.8076	+	19.9631i	−0.426071	+	0.720357i
$769$	−19.5257	−	23.2698i	−0.704115	−	0.839132i	0.288870	−	0.957368i	$-0.406720\pi$
$769$	−19.5257	−	23.2698i	−0.704115	−	0.839132i	−0.992985	+	0.118236i	$0.962276\pi$
$770$		0			0
$771$	−34.4200	+	8.83557i	−1.23961	+	0.318205i
$772$	−2.79946	+	6.00346i	−0.100755	+	0.216069i
$773$	−44.6289	−	11.9583i	−1.60519	−	0.430109i	−0.658585	−	0.752506i	$-0.728845\pi$
$773$	−44.6289	−	11.9583i	−1.60519	−	0.430109i	−0.946604	+	0.322397i	$0.895511\pi$
$774$	−5.38413	−	15.8214i	−0.193529	−	0.568688i
$775$		0			0
$776$	36.2219	+	6.38690i	1.30029	+	0.229276i
$777$	10.0998	+	12.2971i	0.362329	+	0.441155i
$778$	4.31816	+	9.26032i	0.154813	+	0.331999i
$779$	0.204146	+	1.15777i	0.00731427	+	0.0414813i
$780$		0			0
$781$	−2.10427	−	1.76569i	−0.0752968	−	0.0631815i
$782$	−12.2420	−	12.2420i	−0.437772	−	0.437772i
$783$	32.6152	−	10.7175i	1.16557	−	0.383011i
$784$			24.8698i			0.888207i
$785$		0			0
$786$	−17.0536	−	24.9091i	−0.608283	−	0.888477i
$787$	−2.49588	−	1.74764i	−0.0889687	−	0.0622965i	0.528246	−	0.849092i	$-0.322850\pi$
$787$	−2.49588	−	1.74764i	−0.0889687	−	0.0622965i	−0.617214	+	0.786795i	$0.711739\pi$
$788$	−0.531300	+	0.247749i	−0.0189268	+	0.00882570i
$789$	6.31613	+	4.52242i	0.224860	+	0.161002i
$790$		0			0
$791$	−0.801132	−	0.462534i	−0.0284850	−	0.0164458i
$792$	7.53252	−	25.9167i	0.267656	−	0.920908i
$793$	15.3362	−	57.2355i	0.544604	−	2.03249i
$794$	46.3962	−	16.8868i	1.64654	−	0.599292i
$795$		0			0
$796$	7.27145	−	6.10147i	0.257730	−	0.216261i
$797$	28.8623	+	2.52513i	1.02236	+	0.0894446i	0.585985	−	0.810322i	$-0.300708\pi$
$797$	28.8623	+	2.52513i	1.02236	+	0.0894446i	0.436372	+	0.899767i	$0.356263\pi$
$798$	1.88056	−	1.05950i	0.0665709	−	0.0375061i
$799$	−2.91068	−	7.99703i	−0.102972	−	0.282914i
$800$		0			0
$801$	−0.276240	−	1.78568i	−0.00976045	−	0.0630938i
$802$	−0.964923	−	3.60114i	−0.0340726	−	0.127161i
$803$	16.6879	+	23.8328i	0.588903	+	0.841041i
$804$	2.43730	+	5.37376i	0.0859568	+	0.189518i
$805$		0			0
$806$	14.1470	−	2.49450i	0.498306	−	0.0878649i
$807$	−11.9708	+	4.21485i	−0.421392	+	0.148370i
$808$	−1.84130	−	21.0462i	−0.0647767	−	0.740401i
$809$	7.83479			0.275456			0.137728	−	0.990470i	$-0.456020\pi$
$809$	7.83479			0.275456			0.137728	+	0.990470i	$0.456020\pi$
$810$		0			0
$811$	33.4667			1.17517			0.587587	−	0.809161i	$-0.300078\pi$
$811$	33.4667			1.17517			0.587587	+	0.809161i	$0.300078\pi$
$812$	−0.479080	−	5.47591i	−0.0168124	−	0.192167i
$813$	−31.9361	+	11.2445i	−1.12005	+	0.394363i
$814$	42.7929	−	7.54554i	1.49989	−	0.264471i
$815$		0			0
$816$	−21.9486	−	48.3924i	−0.768355	−	1.69407i
$817$	1.11663	+	1.59471i	0.0390658	+	0.0557917i
$818$	−5.89639	−	22.0056i	−0.206163	−	0.769409i
$819$	24.7318	+	9.59592i	0.864200	+	0.335309i
$820$		0			0
$821$	15.4155	+	42.3537i	0.538004	+	1.47815i	0.849336	+	0.527853i	$0.177003\pi$
$821$	15.4155	+	42.3537i	0.538004	+	1.47815i	−0.311332	+	0.950301i	$0.600775\pi$
$822$	−39.7645	+	22.4033i	−1.38695	+	0.781406i
$823$	27.4152	+	2.39852i	0.955633	+	0.0836071i	0.554293	−	0.832322i	$-0.312989\pi$
$823$	27.4152	+	2.39852i	0.955633	+	0.0836071i	0.401341	+	0.915929i	$0.368544\pi$
$824$	31.1920	−	26.1732i	1.08662	−	0.911785i
$825$		0			0
$826$	14.9353	−	5.43602i	0.519667	−	0.189143i
$827$	−14.6669	+	54.7376i	−0.510018	+	1.90341i	−0.0898754	+	0.995953i	$0.528647\pi$
$827$	−14.6669	+	54.7376i	−0.510018	+	1.90341i	−0.420142	+	0.907458i	$0.638020\pi$
$828$	3.00274	−	0.737199i	0.104352	−	0.0256194i
$829$	12.0181	+	6.93865i	0.417405	+	0.240989i	0.693967	−	0.720007i	$-0.255862\pi$
$829$	12.0181	+	6.93865i	0.417405	+	0.240989i	−0.276561	+	0.960996i	$0.589195\pi$
$830$		0			0
$831$	−29.3882	−	21.0423i	−1.01946	−	0.729948i
$832$	25.2643	−	11.7810i	0.875884	−	0.408431i
$833$	−26.6051	−	18.6291i	−0.921812	−	0.645460i
$834$	28.5126	+	41.6464i	0.987310	+	1.44210i
$835$		0			0
$836$		−	1.37510i		−	0.0475588i
$837$	−6.63340	−	2.65442i	−0.229284	−	0.0917501i
$838$	−33.4708	−	33.4708i	−1.15623	−	1.15623i
$839$	16.4142	+	13.7731i	0.566679	+	0.475501i	0.880542	−	0.473968i	$-0.157179\pi$
$839$	16.4142	+	13.7731i	0.566679	+	0.475501i	−0.313863	+	0.949468i	$0.601623\pi$
$840$		0			0
$841$	2.54436	+	14.4298i	0.0877364	+	0.497578i
$842$	−14.2665	−	30.5945i	−0.491655	−	1.05436i
$843$	5.91872	+	7.20636i	0.203851	+	0.248200i
$844$	−3.09124	−	0.545069i	−0.106405	−	0.0187620i
$845$		0			0
$846$	6.39034	+	1.26604i	0.219704	+	0.0435273i
$847$	6.63633	+	1.77820i	0.228027	+	0.0610996i
$848$	−22.2079	+	47.6250i	−0.762623	+	1.63545i
$849$	−13.6270	+	3.49804i	−0.467678	+	0.120052i
$850$		0			0
$851$	−7.31571	−	8.71852i	−0.250779	−	0.298867i
$852$	0.368228	−	0.622563i	0.0126153	−	0.0213287i
$853$	1.81138	+	0.844662i	0.0620206	+	0.0289207i	0.453381	−	0.891317i	$-0.350218\pi$
$853$	1.81138	+	0.844662i	0.0620206	+	0.0289207i	−0.391361	+	0.920237i	$0.627995\pi$
$854$	10.1129	+	17.5161i	0.346056	+	0.599387i
$855$		0			0
$856$	2.46605	−	4.27132i	0.0842877	−	0.145991i
$857$	−18.9321	+	13.2564i	−0.646709	+	0.452830i	−0.850352	−	0.526215i	$-0.823611\pi$
$857$	−18.9321	+	13.2564i	−0.646709	+	0.452830i	0.203643	+	0.979045i	$0.434722\pi$
$858$	55.9789	−	45.9765i	1.91109	−	1.56961i
$859$	7.86080	−	21.5974i	0.268207	−	0.736893i	−0.730344	−	0.683079i	$-0.760640\pi$
$859$	7.86080	−	21.5974i	0.268207	−	0.736893i	0.998551	−	0.0538131i	$-0.0171375\pi$
$860$		0			0
$861$	−0.378104	−	4.91738i	−0.0128858	−	0.167584i
$862$	36.1441	−	3.16220i	1.23107	−	0.107705i
$863$	2.45592	−	2.45592i	0.0836006	−	0.0836006i	−0.664070	−	0.747671i	$-0.731172\pi$
$863$	2.45592	−	2.45592i	0.0836006	−	0.0836006i	0.747671	+	0.664070i	$0.231172\pi$
$864$	17.1995	+	2.05374i	0.585138	+	0.0698697i
$865$		0			0
$866$	11.3815	−	13.5639i	0.386759	−	0.460921i
$867$	39.2678	+	7.35096i	1.33360	+	0.249652i
$868$	−0.656155	+	0.937087i	−0.0222714	+	0.0318068i
$869$	48.0969	+	17.5059i	1.63158	+	0.593845i
$870$		0			0
$871$	6.28765	−	35.6590i	0.213049	−	1.20826i
$872$	−5.02442	+	1.34629i	−0.170148	+	0.0455911i
$873$	−11.7069	−	47.6841i	−0.396218	−	1.61386i
$874$	−1.33695	+	0.771888i	−0.0452230	+	0.0261095i
$875$		0			0
$876$	−5.47387	+	5.35983i	−0.184945	+	0.181092i
$877$	−1.07474	+	12.2844i	−0.0362915	+	0.414814i	0.956219	+	0.292653i	$0.0945381\pi$
$877$	−1.07474	+	12.2844i	−0.0362915	+	0.414814i	−0.992510	+	0.122161i	$0.961017\pi$
$878$	−3.81035	+	43.5525i	−0.128593	+	1.46982i
$879$	9.62117	+	2.68684i	0.324514	+	0.0906248i
$880$		0			0
$881$	−26.2526	+	15.1569i	−0.884473	+	0.510651i	−0.872131	−	0.489273i	$-0.837262\pi$
$881$	−26.2526	+	15.1569i	−0.884473	+	0.510651i	−0.0123422	+	0.999924i	$0.503929\pi$
$882$	22.7491	−	10.0306i	0.766001	−	0.337748i
$883$	5.54478	−	1.48572i	0.186597	−	0.0499984i	−0.164311	−	0.986409i	$-0.552540\pi$
$883$	5.54478	−	1.48572i	0.186597	−	0.0499984i	0.350907	+	0.936410i	$0.385873\pi$
$884$	4.32693	−	24.5393i	0.145531	−	0.825345i
$885$		0			0
$886$	62.7290	+	22.8315i	2.10742	+	0.767039i
$887$	0.819982	−	1.17106i	0.0275323	−	0.0393202i	−0.805150	−	0.593071i	$-0.797915\pi$
$887$	0.819982	−	1.17106i	0.0275323	−	0.0393202i	0.832682	+	0.553751i	$0.186804\pi$
$888$	−8.68779	−	24.6746i	−0.291543	−	0.828024i
$889$	3.74991	−	4.46897i	0.125768	−	0.149884i
$890$		0			0
$891$	−35.7135	+	4.75734i	−1.19645	+	0.159377i
$892$	10.0235	−	10.0235i	0.335610	−	0.335610i
$893$	−0.755970	+	0.0661388i	−0.0252976	+	0.00221325i
$894$	−24.5111	−	11.7454i	−0.819773	−	0.392824i
$895$		0			0
$896$	−6.37164	+	17.5059i	−0.212862	+	0.584832i
$897$	−17.7598	−	6.67657i	−0.592983	−	0.222924i
$898$	13.8505	−	9.69819i	0.462196	−	0.323633i
$899$	4.54235	−	7.86759i	0.151496	−	0.262399i
$900$		0			0
$901$	−34.3129	−	59.4318i	−1.14313	−	1.97996i
$902$	−12.2055	−	5.69153i	−0.406400	−	0.189507i
$903$	−4.00880	−	7.11538i	−0.133405	−	0.236785i
$904$	0.977497	+	1.16494i	0.0325111	+	0.0387452i
$905$		0			0
$906$	−4.34491	−	4.43735i	−0.144350	−	0.147421i
$907$	7.83856	−	16.8099i	0.260275	−	0.558162i	−0.732131	−	0.681164i	$-0.761474\pi$
$907$	7.83856	−	16.8099i	0.260275	−	0.558162i	0.992406	+	0.123002i	$0.0392520\pi$
$908$	−3.81939	−	1.02340i	−0.126751	−	0.0339628i
$909$	−24.7157	+	13.5841i	−0.819769	+	0.450557i
$910$		0			0
$911$	19.9191	+	3.51228i	0.659950	+	0.116367i	0.493585	−	0.869697i	$-0.335686\pi$
$911$	19.9191	+	3.51228i	0.659950	+	0.116367i	0.166364	+	0.986064i	$0.446797\pi$
$912$	−4.67465	+	0.773624i	−0.154793	+	0.0256172i
$913$	28.1528	+	60.3740i	0.931723	+	1.99809i
$914$	−9.76209	−	55.3636i	−0.322901	−	1.83126i
$915$		0			0
$916$	8.85287	+	7.42844i	0.292507	+	0.245443i
$917$	−10.4312	−	10.4312i	−0.344468	−	0.344468i
$918$	−35.4134	+	39.5948i	−1.16882	+	1.30682i
$919$		−	5.56015i		−	0.183412i	−0.995786	−	0.0917062i	$-0.970768\pi$
$919$		−	5.56015i		−	0.183412i	0.995786	−	0.0917062i	$-0.0292320\pi$
$920$		0			0
$921$	−17.4102	+	1.33870i	−0.573687	+	0.0441116i
$922$	43.1822	+	30.2365i	1.42213	+	0.995786i
$923$	−4.02270	+	1.87581i	−0.132409	+	0.0617432i
$924$	−0.563237	+	5.74114i	−0.0185291	+	0.188870i
$925$		0			0
$926$	−8.23538	−	4.75470i	−0.270631	−	0.156249i
$927$	−48.7693	−	24.0040i	−1.60179	−	0.788395i
$928$	−5.70043	+	21.2743i	−0.187126	+	0.698363i
$929$	−10.4908	+	3.81834i	−0.344192	+	0.125276i	−0.508331	−	0.861162i	$-0.669737\pi$
$929$	−10.4908	+	3.81834i	−0.344192	+	0.125276i	0.164140	+	0.986437i	$0.447515\pi$
$930$		0			0
$931$	−2.21856	+	1.86160i	−0.0727105	+	0.0610113i
$932$	−14.2036	−	1.24266i	−0.465255	−	0.0407046i
$933$	−30.7798	−	18.2054i	−1.00769	−	0.596018i
$934$	−11.3053	−	31.0610i	−0.369920	−	1.01635i
$935$		0			0
$936$	−32.8094	−	28.7287i	−1.07241	−	0.939028i
$937$	0.849536	+	3.17051i	0.0277531	+	0.103576i	0.978413	−	0.206659i	$-0.0662590\pi$
$937$	0.849536	+	3.17051i	0.0277531	+	0.103576i	−0.950660	+	0.310235i	$0.899592\pi$
$938$	7.08914	+	10.1243i	0.231469	+	0.330571i
$939$	−25.0236	−	2.45495i	−0.816615	−	0.0801144i
$940$		0			0
$941$	−35.8375	+	6.31912i	−1.16827	+	0.205997i	−0.723938	−	0.689865i	$-0.757670\pi$
$941$	−35.8375	+	6.31912i	−1.16827	+	0.205997i	−0.444331	+	0.895863i	$0.646559\pi$
$942$	38.5269	+	33.0252i	1.25527	+	1.07602i
$943$	0.307430	+	3.51394i	0.0100113	+	0.114429i
$944$	−34.8897			−1.13556
$945$		0			0
$946$	−22.3012			−0.725073
$947$	−4.48539	−	51.2682i	−0.145756	−	1.66599i	−0.619248	−	0.785196i	$-0.712562\pi$
$947$	−4.48539	−	51.2682i	−0.145756	−	1.66599i	0.473492	−	0.880798i	$-0.342993\pi$
$948$	−2.47991	+	13.2473i	−0.0805437	+	0.430253i
$949$	46.2973	−	8.16346i	1.50287	−	0.264997i
$950$		0			0
$951$	−30.2777	+	42.2866i	−0.981822	+	1.37124i
$952$	−11.1536	−	15.9290i	−0.361491	−	0.516263i
$953$	5.10731	+	19.0607i	0.165442	+	0.617438i	0.997983	+	0.0634751i	$0.0202183\pi$
$953$	5.10731	+	19.0607i	0.165442	+	0.617438i	−0.832541	+	0.553963i	$0.813115\pi$
$954$	52.5210	+	1.10583i	1.70043	+	0.0358027i
$955$		0			0
$956$	0.212419	+	0.583616i	0.00687012	+	0.0188755i
$957$	0.482202	−	45.8089i	0.0155874	−	1.48079i
$958$	−10.1938	−	0.891840i	−0.329346	−	0.0288141i
$959$	−17.0857	+	14.3366i	−0.551725	+	0.462953i
$960$		0			0
$961$	27.3538	−	9.95598i	0.882382	−	0.321161i
$962$	18.1723	−	67.8200i	0.585899	−	2.18660i
$963$	−6.54548	−	0.711782i	−0.210925	−	0.0229369i
$964$	−2.22698	−	1.28575i	−0.0717262	−	0.0414111i
$965$		0			0
$966$	5.89802	−	2.67508i	0.189766	−	0.0860692i
$967$	−7.39431	+	3.44802i	−0.237785	+	0.110881i	−0.537859	−	0.843035i	$-0.680767\pi$
$967$	−7.39431	+	3.44802i	−0.237785	+	0.110881i	0.300074	+	0.953916i	$0.402989\pi$
$968$	−9.25173	−	6.47813i	−0.297362	−	0.208215i
$969$	2.67401	−	5.58032i	0.0859017	−	0.179266i
$970$		0			0
$971$		−	0.500263i		−	0.0160542i	−0.999968	−	0.00802710i	$-0.997445\pi$
$971$		−	0.500263i		−	0.0160542i	0.999968	−	0.00802710i	$-0.00255513\pi$
$972$	−2.77127	−	9.07318i	−0.0888885	−	0.291022i
$973$	17.4403	+	17.4403i	0.559110	+	0.559110i
$974$	8.21264	+	6.89122i	0.263150	+	0.220809i
$975$		0			0
$976$	−7.70982	−	43.7245i	−0.246785	−	1.39959i
$977$	−5.65025	−	12.1170i	−0.180767	−	0.387657i	0.794955	−	0.606669i	$-0.207494\pi$
$977$	−5.65025	−	12.1170i	−0.180767	−	0.387657i	−0.975722	+	0.219012i	$0.929717\pi$
$978$	19.5781	−	52.0781i	0.626038	−	1.66527i
$979$	−2.37453	−	0.418693i	−0.0758903	−	0.0133815i
$980$		0			0
$981$	4.35051	+	5.41214i	0.138901	+	0.172796i
$982$	9.76934	+	2.61769i	0.311752	+	0.0835337i
$983$	−9.10955	+	19.5355i	−0.290549	+	0.623085i	−0.996353	−	0.0853218i	$-0.972808\pi$
$983$	−9.10955	+	19.5355i	−0.290549	+	0.623085i	0.705804	+	0.708407i	$0.250586\pi$
$984$	−2.18069	+	7.80874i	−0.0695180	+	0.248933i
$985$		0			0
$986$	−43.4168	−	51.7421i	−1.38267	−	1.64780i
$987$	3.18332	+	0.0335089i	0.101326	+	0.00106660i
$988$	−2.01374	−	0.939023i	−0.0640656	−	0.0298743i
$989$	2.92056	+	5.05856i	0.0928684	+	0.160853i
$990$		0			0
$991$	12.2325	−	21.1872i	0.388577	−	0.673035i	−0.603681	−	0.797226i	$-0.706300\pi$
$991$	12.2325	−	21.1872i	0.388577	−	0.673035i	0.992258	+	0.124191i	$0.0396334\pi$
$992$	3.75473	−	2.62909i	0.119213	−	0.0834738i
$993$	8.17109	+	49.3741i	0.259302	+	1.56684i
$994$	0.518176	−	1.42368i	0.0164356	−	0.0451563i
$995$		0			0
$996$	−14.4737	+	9.90921i	−0.458617	+	0.313985i
$997$	45.1132	−	3.94689i	1.42875	−	0.124999i	0.653629	−	0.756815i	$-0.273246\pi$
$997$	45.1132	−	3.94689i	1.42875	−	0.124999i	0.775119	+	0.631816i	$0.217690\pi$
$998$	−27.3314	+	27.3314i	−0.865160	+	0.865160i
$999$	−25.4604	+	23.9011i	−0.805531	+	0.756198i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.ba.c.443.18	yes	288
5.2	odd	4	inner	675.2.ba.c.632.7	yes	288
5.3	odd	4	inner	675.2.ba.c.632.18	yes	288
5.4	even	2	inner	675.2.ba.c.443.7	yes	288
27.5	odd	18	inner	675.2.ba.c.518.7	yes	288
135.32	even	36	inner	675.2.ba.c.32.18	yes	288
135.59	odd	18	inner	675.2.ba.c.518.18	yes	288
135.113	even	36	inner	675.2.ba.c.32.7	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
675.2.ba.c.32.7	✓	288	135.113	even	36	inner
675.2.ba.c.32.18	yes	288	135.32	even	36	inner
675.2.ba.c.443.7	yes	288	5.4	even	2	inner
675.2.ba.c.443.18	yes	288	1.1	even	1	trivial
675.2.ba.c.518.7	yes	288	27.5	odd	18	inner
675.2.ba.c.518.18	yes	288	135.59	odd	18	inner
675.2.ba.c.632.7	yes	288	5.2	odd	4	inner
675.2.ba.c.632.18	yes	288	5.3	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.ba (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.140766 + 1.60897i) q^{2} +(-1.63374 + 0.575232i) q^{3} +(-0.599344 + 0.105680i) q^{4} +(-1.15550 - 2.54766i) q^{6} +(-0.784107 - 1.11982i) q^{7} +(0.581640 + 2.17071i) q^{8} +(2.33822 - 1.87956i) q^{9} +(-1.36918 - 3.76179i) q^{11} +(0.918381 - 0.517416i) q^{12} +(-6.44387 - 0.563766i) q^{13} +(1.69138 - 1.41923i) q^{14} +(-4.55450 + 1.65770i) q^{16} +(1.63825 - 6.11402i) q^{17} +(3.35329 + 3.49753i) q^{18} +(-0.488800 - 0.282209i) q^{19} +(1.92518 + 1.37845i) q^{21} +(5.85987 - 2.73250i) q^{22} +(-1.38722 - 0.971342i) q^{23} +(-2.19891 - 3.21180i) q^{24} -10.4473i q^{26} +(-2.73886 + 4.41573i) q^{27} +(0.588292 + 0.588292i) q^{28} +(-5.06125 - 4.24689i) q^{29} +(0.238769 + 1.35412i) q^{31} +(-1.40882 - 3.02123i) q^{32} +(4.40079 + 5.35820i) q^{33} +(10.0679 + 1.77524i) q^{34} +(-1.20276 + 1.37361i) q^{36} +(6.49160 + 1.73942i) q^{37} +(0.385258 - 0.826189i) q^{38} +(10.8519 - 2.78567i) q^{39} +(-1.33886 - 1.59560i) q^{41} +(-1.94688 + 3.29160i) q^{42} +(-3.12602 - 1.45769i) q^{43} +(1.21816 + 2.10991i) q^{44} +(1.36758 - 2.36872i) q^{46} +(1.10135 - 0.771171i) q^{47} +(6.48731 - 5.32815i) q^{48} +(1.75497 - 4.82173i) q^{49} +(0.840508 + 10.9311i) q^{51} +(3.92167 - 0.343102i) q^{52} +(7.66637 - 7.66637i) q^{53} +(-7.49030 - 3.78515i) q^{54} +(1.97474 - 2.35340i) q^{56} +(0.960908 + 0.179883i) q^{57} +(6.12066 - 8.74120i) q^{58} +(6.76439 + 2.46204i) q^{59} +(-1.59070 + 9.02132i) q^{61} +(-2.14513 + 0.574786i) q^{62} +(-3.93818 - 1.14461i) q^{63} +(-3.73216 + 2.15476i) q^{64} +(-8.00168 + 7.83498i) q^{66} +(-0.487878 + 5.57647i) q^{67} +(-0.335740 + 3.83753i) q^{68} +(2.82510 + 0.788948i) q^{69} +(0.594251 - 0.343091i) q^{71} +(5.43998 + 3.98237i) q^{72} +(-7.02013 + 1.88104i) q^{73} +(-1.88487 + 10.6896i) q^{74} +(0.322783 + 0.117483i) q^{76} +(-3.13895 + 4.48288i) q^{77} +(6.00964 + 17.0682i) q^{78} +(-8.21845 + 9.79437i) q^{79} +(1.93452 - 8.78963i) q^{81} +(2.37879 - 2.37879i) q^{82} +(-16.5771 + 1.45031i) q^{83} +(-1.29952 - 0.622713i) q^{84} +(1.90533 - 5.23485i) q^{86} +(10.7117 + 4.02693i) q^{87} +(7.36939 - 5.16010i) q^{88} +(0.301153 - 0.521612i) q^{89} +(4.42137 + 7.65803i) q^{91} +(0.934073 + 0.435565i) q^{92} +(-1.16902 - 2.07494i) q^{93} +(1.39582 + 1.66348i) q^{94} +(4.03955 + 4.12550i) q^{96} +(6.91688 - 14.8333i) q^{97} +(8.00504 + 2.14495i) q^{98} +(-10.2720 - 6.22243i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 24 q^{6} + 36 q^{11} + 48 q^{21} - 192 q^{36} - 180 q^{41} - 60 q^{51} - 288 q^{56} + 72 q^{61} + 144 q^{71} + 216 q^{76} + 24 q^{81} - 36 q^{91} - 168 q^{96}+O(q^{100}) \) 288 * q + 24 * q^6 + 36 * q^11 + 48 * q^21 - 192 * q^36 - 180 * q^41 - 60 * q^51 - 288 * q^56 + 72 * q^61 + 144 * q^71 + 216 * q^76 + 24 * q^81 - 36 * q^91 - 168 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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