LMFDB - Embedded newform 465.2.k.a.218.27

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(32,465)] 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("465.32"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.k (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,0,0,0,0,-4,0,0,0,-32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(10)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$30$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.27
Character	$\chi$	$=$	465.218
Dual form			465.2.k.a.32.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.50249 + 1.50249i) q^{2} +(-0.884514 - 1.48917i) q^{3} +2.51495i q^{4} +(0.967939 + 2.01571i) q^{5} +(0.908494 - 3.56644i) q^{6} +(-2.29931 + 2.29931i) q^{7} +(-0.773713 + 0.773713i) q^{8} +(-1.43527 + 2.63439i) q^{9} +(-1.57427 + 4.48291i) q^{10} +1.64801i q^{11} +(3.74520 - 2.22451i) q^{12} +(0.884592 + 0.884592i) q^{13} -6.90938 q^{14} +(2.14559 - 3.22435i) q^{15} +2.70492 q^{16} +(0.210964 + 0.210964i) q^{17} +(-6.11462 + 1.80166i) q^{18} +2.54829i q^{19} +(-5.06942 + 2.43432i) q^{20} +(5.45784 + 1.39030i) q^{21} +(-2.47611 + 2.47611i) q^{22} +(2.86717 - 2.86717i) q^{23} +(1.83655 + 0.467832i) q^{24} +(-3.12619 + 3.90217i) q^{25} +2.65818i q^{26} +(5.19257 - 0.192786i) q^{27} +(-5.78265 - 5.78265i) q^{28} -2.52760 q^{29} +(8.06828 - 1.62084i) q^{30} +1.00000 q^{31} +(5.61153 + 5.61153i) q^{32} +(2.45417 - 1.45768i) q^{33} +0.633944i q^{34} +(-6.86033 - 2.40915i) q^{35} +(-6.62536 - 3.60964i) q^{36} +(6.52469 - 6.52469i) q^{37} +(-3.82879 + 3.82879i) q^{38} +(0.534876 - 2.09974i) q^{39} +(-2.30849 - 0.810675i) q^{40} +1.27873i q^{41} +(6.11144 + 10.2893i) q^{42} +(-4.59068 - 4.59068i) q^{43} -4.14466 q^{44} +(-6.69942 - 0.343165i) q^{45} +8.61579 q^{46} +(-8.06085 - 8.06085i) q^{47} +(-2.39254 - 4.02809i) q^{48} -3.57364i q^{49} +(-10.5600 + 1.16591i) q^{50} +(0.127562 - 0.500764i) q^{51} +(-2.22471 + 2.22471i) q^{52} +(-1.18368 + 1.18368i) q^{53} +(8.09145 + 7.51213i) q^{54} +(-3.32191 + 1.59517i) q^{55} -3.55801i q^{56} +(3.79485 - 2.25400i) q^{57} +(-3.79769 - 3.79769i) q^{58} +6.21291 q^{59} +(8.10910 + 5.39605i) q^{60} +3.86559 q^{61} +(1.50249 + 1.50249i) q^{62} +(-2.75714 - 9.35740i) q^{63} +11.4527i q^{64} +(-0.926851 + 2.63931i) q^{65} +(5.87752 + 1.49720i) q^{66} +(6.83911 - 6.83911i) q^{67} +(-0.530566 + 0.530566i) q^{68} +(-6.80576 - 1.73366i) q^{69} +(-6.68786 - 13.9273i) q^{70} -13.3036i q^{71} +(-0.927772 - 3.14875i) q^{72} +(11.4996 + 11.4996i) q^{73} +19.6066 q^{74} +(8.57617 + 1.20391i) q^{75} -6.40884 q^{76} +(-3.78928 - 3.78928i) q^{77} +(3.95849 - 2.35120i) q^{78} -3.25032i q^{79} +(2.61819 + 5.45233i) q^{80} +(-4.88000 - 7.56212i) q^{81} +(-1.92127 + 1.92127i) q^{82} +(9.54347 - 9.54347i) q^{83} +(-3.49653 + 13.7262i) q^{84} +(-0.221043 + 0.629444i) q^{85} -13.7949i q^{86} +(2.23569 + 3.76403i) q^{87} +(-1.27508 - 1.27508i) q^{88} -7.12419 q^{89} +(-9.55021 - 10.5814i) q^{90} -4.06790 q^{91} +(7.21080 + 7.21080i) q^{92} +(-0.884514 - 1.48917i) q^{93} -24.2227i q^{94} +(-5.13662 + 2.46659i) q^{95} +(3.39306 - 13.3200i) q^{96} +(-5.73716 + 5.73716i) q^{97} +(5.36936 - 5.36936i) q^{98} +(-4.34149 - 2.36534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) $ 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.50249	+	1.50249i	1.06242	+	1.06242i	0.997917	+	0.0645035i	$0.0205464\pi$
$2$	1.50249	+	1.50249i	1.06242	+	1.06242i	0.0645035	+	0.997917i	$0.479454\pi$
$3$	−0.884514	−	1.48917i	−0.510674	−	0.859774i
$3$	−0.884514	−	1.48917i	−0.510674	−	0.859774i
$4$			2.51495i			1.25748i
$5$	0.967939	+	2.01571i	0.432876	+	0.901454i
$5$	0.967939	+	2.01571i	0.432876	+	0.901454i
$6$	0.908494	−	3.56644i	0.370891	−	1.45599i
$7$	−2.29931	+	2.29931i	−0.869057	+	0.869057i	−0.992368	−	0.123311i	$-0.960649\pi$
$7$	−2.29931	+	2.29931i	−0.869057	+	0.869057i	0.123311	+	0.992368i	$0.460649\pi$
$8$	−0.773713	+	0.773713i	−0.273549	+	0.273549i
$9$	−1.43527	+	2.63439i	−0.478424	+	0.878129i
$10$	−1.57427	+	4.48291i	−0.497827	+	1.41762i
$11$			1.64801i			0.496893i	0.968646	+	0.248446i	$0.0799200\pi$
$11$			1.64801i			0.496893i	−0.968646	+	0.248446i	$0.920080\pi$
$12$	3.74520	−	2.22451i	1.08115	−	0.642161i
$13$	0.884592	+	0.884592i	0.245342	+	0.245342i	0.819056	−	0.573714i	$-0.194498\pi$
$13$	0.884592	+	0.884592i	0.245342	+	0.245342i	−0.573714	+	0.819056i	$0.694498\pi$
$14$	−6.90938			−1.84661
$15$	2.14559	−	3.22435i	0.553988	−	0.832525i
$16$	2.70492			0.676229
$17$	0.210964	+	0.210964i	0.0511664	+	0.0511664i	0.732227	−	0.681061i	$-0.238481\pi$
$17$	0.210964	+	0.210964i	0.0511664	+	0.0511664i	−0.681061	+	0.732227i	$0.738481\pi$
$18$	−6.11462	+	1.80166i	−1.44123	+	0.424656i
$19$			2.54829i			0.584619i	0.956324	+	0.292309i	$0.0944237\pi$
$19$			2.54829i			0.584619i	−0.956324	+	0.292309i	$0.905576\pi$
$20$	−5.06942	+	2.43432i	−1.13356	+	0.544331i
$21$	5.45784	+	1.39030i	1.19100	+	0.303388i
$22$	−2.47611	+	2.47611i	−0.527909	+	0.527909i
$23$	2.86717	−	2.86717i	0.597846	−	0.597846i	−0.341893	−	0.939739i	$-0.611068\pi$
$23$	2.86717	−	2.86717i	0.597846	−	0.597846i	0.939739	+	0.341893i	$0.111068\pi$
$24$	1.83655	+	0.467832i	0.374885	+	0.0954959i
$25$	−3.12619	+	3.90217i	−0.625237	+	0.780435i
$26$			2.65818i			0.521312i
$27$	5.19257	−	0.192786i	0.999311	−	0.0371017i
$28$	−5.78265	−	5.78265i	−1.09282	−	1.09282i
$29$	−2.52760			−0.469363			−0.234682	−	0.972072i	$-0.575405\pi$
$29$	−2.52760			−0.469363			−0.234682	+	0.972072i	$0.575405\pi$
$30$	8.06828	−	1.62084i	1.47306	−	0.295923i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	5.61153	+	5.61153i	0.991989	+	0.991989i
$33$	2.45417	−	1.45768i	0.427216	−	0.253750i
$34$			0.633944i			0.108721i
$35$	−6.86033	−	2.40915i	−1.15961	−	0.407221i
$36$	−6.62536	−	3.60964i	−1.10423	−	0.601607i
$37$	6.52469	−	6.52469i	1.07265	−	1.07265i	0.0755078	−	0.997145i	$-0.475942\pi$
$37$	6.52469	−	6.52469i	1.07265	−	1.07265i	0.997145	−	0.0755078i	$-0.0240578\pi$
$38$	−3.82879	+	3.82879i	−0.621111	+	0.621111i
$39$	0.534876	−	2.09974i	0.0856487	−	0.336228i
$40$	−2.30849	−	0.810675i	−0.365004	−	0.128179i
$41$			1.27873i			0.199704i	0.995002	+	0.0998518i	$0.0318369\pi$
$41$			1.27873i			0.199704i	−0.995002	+	0.0998518i	$0.968163\pi$
$42$	6.11144	+	10.2893i	0.943016	+	1.58767i
$43$	−4.59068	−	4.59068i	−0.700072	−	0.700072i	0.264354	−	0.964426i	$-0.414841\pi$
$43$	−4.59068	−	4.59068i	−0.700072	−	0.700072i	−0.964426	+	0.264354i	$0.914841\pi$
$44$	−4.14466			−0.624831
$45$	−6.69942	−	0.343165i	−0.998691	−	0.0511560i
$46$	8.61579			1.27033
$47$	−8.06085	−	8.06085i	−1.17580	−	1.17580i	−0.980805	−	0.194991i	$-0.937532\pi$
$47$	−8.06085	−	8.06085i	−1.17580	−	1.17580i	−0.194991	−	0.980805i	$-0.562468\pi$
$48$	−2.39254	−	4.02809i	−0.345333	−	0.581404i
$49$		−	3.57364i		−	0.510520i
$50$	−10.5600	+	1.16591i	−1.49342	+	0.164885i
$51$	0.127562	−	0.500764i	0.0178622	−	0.0701209i
$52$	−2.22471	+	2.22471i	−0.308511	+	0.308511i
$53$	−1.18368	+	1.18368i	−0.162591	+	0.162591i	−0.783714	−	0.621122i	$-0.786677\pi$
$53$	−1.18368	+	1.18368i	−0.162591	+	0.162591i	0.621122	+	0.783714i	$0.286677\pi$
$54$	8.09145	+	7.51213i	1.10111	+	1.02227i
$55$	−3.32191	+	1.59517i	−0.447926	+	0.215093i
$56$		−	3.55801i		−	0.475459i
$57$	3.79485	−	2.25400i	0.502640	−	0.298550i
$58$	−3.79769	−	3.79769i	−0.498661	−	0.498661i
$59$	6.21291			0.808852			0.404426	−	0.914571i	$-0.367471\pi$
$59$	6.21291			0.808852			0.404426	+	0.914571i	$0.367471\pi$
$60$	8.10910	+	5.39605i	1.04688	+	0.696627i
$61$	3.86559			0.494938			0.247469	−	0.968896i	$-0.420401\pi$
$61$	3.86559			0.494938			0.247469	+	0.968896i	$0.420401\pi$
$62$	1.50249	+	1.50249i	0.190816	+	0.190816i
$63$	−2.75714	−	9.35740i	−0.347367	−	1.17892i
$64$			11.4527i			1.43159i
$65$	−0.926851	+	2.63931i	−0.114962	+	0.327366i
$66$	5.87752	+	1.49720i	0.723473	+	0.184293i
$67$	6.83911	−	6.83911i	0.835530	−	0.835530i	−0.152737	−	0.988267i	$-0.548809\pi$
$67$	6.83911	−	6.83911i	0.835530	−	0.835530i	0.988267	+	0.152737i	$0.0488086\pi$
$68$	−0.530566	+	0.530566i	−0.0643406	+	0.0643406i
$69$	−6.80576	−	1.73366i	−0.819317	−	0.208708i
$70$	−6.68786	−	13.9273i	−0.799352	−	1.66463i
$71$		−	13.3036i		−	1.57885i	−0.613846	−	0.789426i	$-0.710379\pi$
$71$		−	13.3036i		−	1.57885i	0.613846	−	0.789426i	$-0.289621\pi$
$72$	−0.927772	−	3.14875i	−0.109339	−	0.371083i
$73$	11.4996	+	11.4996i	1.34593	+	1.34593i	0.890036	+	0.455889i	$0.150679\pi$
$73$	11.4996	+	11.4996i	1.34593	+	1.34593i	0.455889	+	0.890036i	$0.349321\pi$
$74$	19.6066			2.27922
$75$	8.57617	+	1.20391i	0.990290	+	0.139015i
$76$	−6.40884			−0.735144
$77$	−3.78928	−	3.78928i	−0.431828	−	0.431828i
$78$	3.95849	−	2.35120i	0.448211	−	0.266221i
$79$		−	3.25032i		−	0.365689i	−0.983142	−	0.182845i	$-0.941469\pi$
$79$		−	3.25032i		−	0.365689i	0.983142	−	0.182845i	$-0.0585306\pi$
$80$	2.61819	+	5.45233i	0.292723	+	0.609589i
$81$	−4.88000	−	7.56212i	−0.542222	−	0.840235i
$82$	−1.92127	+	1.92127i	−0.212169	+	0.212169i
$83$	9.54347	−	9.54347i	1.04753	−	1.04753i	0.0487197	−	0.998812i	$-0.484486\pi$
$83$	9.54347	−	9.54347i	1.04753	−	1.04753i	0.998812	−	0.0487197i	$-0.0155141\pi$
$84$	−3.49653	+	13.7262i	−0.381503	+	1.49765i
$85$	−0.221043	+	0.629444i	−0.0239755	+	0.0682728i
$86$		−	13.7949i		−	1.48754i
$87$	2.23569	+	3.76403i	0.239692	+	0.403546i
$88$	−1.27508	−	1.27508i	−0.135924	−	0.135924i
$89$	−7.12419			−0.755163			−0.377581	−	0.925976i	$-0.623244\pi$
$89$	−7.12419			−0.755163			−0.377581	+	0.925976i	$0.623244\pi$
$90$	−9.55021	−	10.5814i	−1.00668	−	1.11538i
$91$	−4.06790			−0.426432
$92$	7.21080	+	7.21080i	0.751778	+	0.751778i
$93$	−0.884514	−	1.48917i	−0.0917198	−	0.154420i
$94$		−	24.2227i		−	2.49838i
$95$	−5.13662	+	2.46659i	−0.527007	+	0.253067i
$96$	3.39306	−	13.3200i	0.346303	−	1.35947i
$97$	−5.73716	+	5.73716i	−0.582520	+	0.582520i	−0.935595	−	0.353075i	$-0.885136\pi$
$97$	−5.73716	+	5.73716i	−0.582520	+	0.582520i	0.353075	+	0.935595i	$0.385136\pi$
$98$	5.36936	−	5.36936i	0.542387	−	0.542387i
$99$	−4.34149	−	2.36534i	−0.436336	−	0.237725i
$100$	−9.81378	−	7.86222i	−0.981378	−	0.786222i
$101$			7.44491i			0.740796i	0.928873	+	0.370398i	$0.120779\pi$
$101$			7.44491i			0.740796i	−0.928873	+	0.370398i	$0.879221\pi$
$102$	0.944052	−	0.560732i	0.0934751	−	0.0555208i
$103$	7.28888	+	7.28888i	0.718194	+	0.718194i	0.968235	−	0.250041i	$-0.0804440\pi$
$103$	7.28888	+	7.28888i	0.718194	+	0.718194i	−0.250041	+	0.968235i	$0.580444\pi$
$104$	−1.36884			−0.134226
$105$	2.48042	+	12.3472i	0.242064	+	1.20496i
$106$	−3.55694			−0.345480
$107$	−13.6220	−	13.6220i	−1.31689	−	1.31689i	−0.916228	−	0.400658i	$-0.868782\pi$
$107$	−13.6220	−	13.6220i	−1.31689	−	1.31689i	−0.400658	−	0.916228i	$-0.631218\pi$
$108$	0.484848	+	13.0591i	0.0466545	+	1.25661i
$109$			17.6740i			1.69287i	0.532496	+	0.846433i	$0.321254\pi$
$109$			17.6740i			1.69287i	−0.532496	+	0.846433i	$0.678746\pi$
$110$	−7.38786	−	2.59440i	−0.704405	−	0.247367i
$111$	−15.4876	−	3.94521i	−1.47002	−	0.374463i
$112$	−6.21943	+	6.21943i	−0.587681	+	0.587681i
$113$	4.62004	−	4.62004i	0.434617	−	0.434617i	−0.455579	−	0.890195i	$-0.650568\pi$
$113$	4.62004	−	4.62004i	0.434617	−	0.434617i	0.890195	+	0.455579i	$0.150568\pi$
$114$	9.08834	+	2.31511i	0.851201	+	0.216830i
$115$	8.55463	+	3.00414i	0.797723	+	0.280138i
$116$		−	6.35679i		−	0.590213i
$117$	−3.59999	+	1.06073i	−0.332819	+	0.0980644i
$118$	9.33483	+	9.33483i	0.859341	+	0.859341i
$119$	−0.970145			−0.0889330
$120$	0.834655	+	4.15479i	0.0761933	+	0.379279i
$121$	8.28407			0.753098
$122$	5.80801	+	5.80801i	0.525832	+	0.525832i
$123$	1.90424	−	1.13105i	0.171700	−	0.101983i
$124$			2.51495i			0.225850i
$125$	−10.8916	−	2.52442i	−0.974176	−	0.225791i
$126$	9.91683	−	18.2020i	0.883461	−	1.62156i
$127$	3.31598	−	3.31598i	0.294245	−	0.294245i	−0.544509	−	0.838755i	$-0.683284\pi$
$127$	3.31598	−	3.31598i	0.294245	−	0.294245i	0.838755	+	0.544509i	$0.183284\pi$
$128$	−5.98453	+	5.98453i	−0.528963	+	0.528963i
$129$	−2.77580	+	10.8968i	−0.244395	+	0.959413i
$130$	−5.35813	+	2.57296i	−0.469939	+	0.225663i
$131$			4.89277i			0.427484i	0.976890	+	0.213742i	$0.0685651\pi$
$131$			4.89277i			0.427484i	−0.976890	+	0.213742i	$0.931435\pi$
$132$	3.66601	+	6.17212i	0.319085	+	0.537214i
$133$	−5.85931	−	5.85931i	−0.508067	−	0.508067i
$134$	20.5514			1.77537
$135$	5.41470	+	10.2801i	0.466023	+	0.884773i
$136$	−0.326452			−0.0279930
$137$	−5.21531	−	5.21531i	−0.445574	−	0.445574i	0.448306	−	0.893880i	$-0.352027\pi$
$137$	−5.21531	−	5.21531i	−0.445574	−	0.445574i	−0.893880	+	0.448306i	$0.852027\pi$
$138$	−7.62078	−	12.8304i	−0.648724	−	1.09220i
$139$			18.7388i			1.58940i	0.607001	+	0.794701i	$0.292372\pi$
$139$			18.7388i			1.58940i	−0.607001	+	0.794701i	$0.707628\pi$
$140$	6.05891	−	17.2534i	0.512071	−	1.45818i
$141$	−4.87407	+	19.1339i	−0.410470	+	1.61137i
$142$	19.9886	−	19.9886i	1.67740	−	1.67740i
$143$	−1.45781	+	1.45781i	−0.121908	+	0.121908i
$144$	−3.88229	+	7.12580i	−0.323524	+	0.593816i
$145$	−2.44656	−	5.09491i	−0.203176	−	0.423109i
$146$			34.5561i			2.85988i
$147$	−5.32177	+	3.16093i	−0.438932	+	0.260709i
$148$	16.4093	+	16.4093i	1.34884	+	1.34884i
$149$	17.2070			1.40965			0.704825	−	0.709381i	$-0.251025\pi$
$149$	17.2070			1.40965			0.704825	+	0.709381i	$0.251025\pi$
$150$	11.0767	+	14.6945i	0.904413	+	1.19980i
$151$	−17.1695			−1.39723			−0.698615	−	0.715497i	$-0.746200\pi$
$151$	−17.1695			−1.39723			−0.698615	+	0.715497i	$0.746200\pi$
$152$	−1.97165	−	1.97165i	−0.159922	−	0.159922i
$153$	−0.858553	+	0.252971i	−0.0694099	+	0.0204515i
$154$		−	11.3867i		−	0.917567i
$155$	0.967939	+	2.01571i	0.0777468	+	0.161906i
$156$	5.28076	+	1.34519i	0.422799	+	0.107701i
$157$	6.68820	−	6.68820i	0.533776	−	0.533776i	−0.387918	−	0.921694i	$-0.626805\pi$
$157$	6.68820	−	6.68820i	0.533776	−	0.533776i	0.921694	+	0.387918i	$0.126805\pi$
$158$	4.88357	−	4.88357i	0.388516	−	0.388516i
$159$	2.80969	+	0.715723i	0.222823	+	0.0567605i
$160$	−5.87961	+	16.7429i	−0.464824	+	1.32364i
$161$			13.1850i			1.03912i
$162$	4.02986	−	18.6942i	0.316616	−	1.46875i
$163$	3.18880	+	3.18880i	0.249766	+	0.249766i	0.820875	−	0.571108i	$-0.193486\pi$
$163$	3.18880	+	3.18880i	0.249766	+	0.249766i	−0.571108	+	0.820875i	$0.693486\pi$
$164$	−3.21594			−0.251123
$165$	5.31376	+	3.53594i	0.413675	+	0.275273i
$166$	28.6779			2.22584
$167$	−1.39709	−	1.39709i	−0.108110	−	0.108110i	0.650982	−	0.759093i	$-0.274357\pi$
$167$	−1.39709	−	1.39709i	−0.108110	−	0.108110i	−0.759093	+	0.650982i	$0.774357\pi$
$168$	−5.29849	+	3.14711i	−0.408787	+	0.242805i
$169$		−	11.4350i		−	0.879615i
$170$	−1.27785	+	0.613619i	−0.0980065	+	0.0470625i
$171$	−6.71319	−	3.65749i	−0.513371	−	0.279695i
$172$	11.5453	−	11.5453i	0.880324	−	0.880324i
$173$	−10.2032	+	10.2032i	−0.775734	+	0.775734i	−0.979102	−	0.203369i	$-0.934811\pi$
$173$	−10.2032	+	10.2032i	−0.775734	+	0.775734i	0.203369	+	0.979102i	$0.434811\pi$
$174$	−2.29631	+	9.01453i	−0.174083	+	0.683389i
$175$	−1.78423	−	16.1604i	−0.134875	−	1.22161i
$176$			4.45772i			0.336013i
$177$	−5.49540	−	9.25209i	−0.413060	−	0.695430i
$178$	−10.7040	−	10.7040i	−0.802301	−	0.802301i
$179$	−9.82107			−0.734061			−0.367031	−	0.930209i	$-0.619626\pi$
$179$	−9.82107			−0.734061			−0.367031	+	0.930209i	$0.619626\pi$
$180$	0.863043	−	16.8487i	0.0643274	−	1.25583i
$181$	5.56207			0.413426			0.206713	−	0.978402i	$-0.433723\pi$
$181$	5.56207			0.413426			0.206713	+	0.978402i	$0.433723\pi$
$182$	−6.11198	−	6.11198i	−0.453050	−	0.453050i
$183$	−3.41917	−	5.75653i	−0.252752	−	0.425535i
$184$			4.43673i			0.327080i
$185$	19.4674	+	6.83639i	1.43127	+	0.502622i
$186$	0.908494	−	3.56644i	0.0666140	−	0.261504i
$187$	−0.347671	+	0.347671i	−0.0254242	+	0.0254242i
$188$	20.2727	−	20.2727i	1.47854	−	1.47854i
$189$	−11.4961	+	12.3826i	−0.836215	+	0.900702i
$190$	−11.4238	−	4.01170i	−0.828767	−	0.291039i
$191$			21.0682i			1.52444i	0.647319	+	0.762220i	$0.275890\pi$
$191$			21.0682i			1.52444i	−0.647319	+	0.762220i	$0.724110\pi$
$192$	17.0551	−	10.1301i	1.23084	−	0.731076i
$193$	−0.456311	−	0.456311i	−0.0328460	−	0.0328460i	0.690493	−	0.723339i	$-0.257394\pi$
$193$	−0.456311	−	0.456311i	−0.0328460	−	0.0328460i	−0.723339	+	0.690493i	$0.757394\pi$
$194$	−17.2401			−1.23776
$195$	4.75020	−	0.954268i	0.340169	−	0.0683365i
$196$	8.98754			0.641967
$197$	9.01815	+	9.01815i	0.642517	+	0.642517i	0.951173	−	0.308657i	$-0.0998795\pi$
$197$	9.01815	+	9.01815i	0.642517	+	0.642517i	−0.308657	+	0.951173i	$0.599879\pi$
$198$	−2.96915	−	10.0769i	−0.211008	−	0.716137i
$199$			12.8681i			0.912197i	0.889929	+	0.456098i	$0.150753\pi$
$199$			12.8681i			0.912197i	−0.889929	+	0.456098i	$0.849247\pi$
$200$	−0.600390	−	5.43793i	−0.0424540	−	0.384520i
$201$	−16.2339	−	4.13533i	−1.14505	−	0.291684i
$202$	−11.1859	+	11.1859i	−0.787038	+	0.787038i
$203$	5.81173	−	5.81173i	0.407903	−	0.407903i
$204$	1.25940	+	0.320811i	0.0881754	+	0.0224613i
$205$	−2.57754	+	1.23773i	−0.180024	+	0.0864468i
$206$			21.9029i			1.52605i
$207$	3.43807	+	11.6684i	0.238962	+	0.811010i
$208$	2.39275	+	2.39275i	0.165907	+	0.165907i
$209$	−4.19961			−0.290493
$210$	−14.8247	+	22.2783i	−1.02300	+	1.53735i
$211$	−23.4797			−1.61641			−0.808203	−	0.588904i	$-0.799560\pi$
$211$	−23.4797			−1.61641			−0.808203	+	0.588904i	$0.799560\pi$
$212$	−2.97690	−	2.97690i	−0.204454	−	0.204454i
$213$	−19.8114	+	11.7672i	−1.35746	+	0.806279i
$214$		−	40.9338i		−	2.79817i
$215$	4.80999	−	13.6970i	0.328038	−	0.934127i
$216$	−3.86840	+	4.16672i	−0.263211	+	0.283510i
$217$	−2.29931	+	2.29931i	−0.156087	+	0.156087i
$218$	−26.5551	+	26.5551i	−1.79854	+	1.79854i
$219$	6.95333	−	27.2964i	0.469863	−	1.84452i
$220$	−4.01178	−	8.35444i	−0.270474	−	0.563256i
$221$			0.373235i			0.0251065i
$222$	−17.3423	−	29.1976i	−1.16394	−	1.95961i
$223$	−19.3196	−	19.3196i	−1.29374	−	1.29374i	−0.932458	−	0.361277i	$-0.882341\pi$
$223$	−19.3196	−	19.3196i	−1.29374	−	1.29374i	−0.361277	−	0.932458i	$-0.617659\pi$
$224$	−25.8053			−1.72419
$225$	−5.79291	−	13.8363i	−0.386194	−	0.922418i
$226$	13.8831			0.923492
$227$	−18.4147	−	18.4147i	−1.22223	−	1.22223i	−0.966838	−	0.255391i	$-0.917796\pi$
$227$	−18.4147	−	18.4147i	−1.22223	−	1.22223i	−0.255391	−	0.966838i	$-0.582204\pi$
$228$	5.66871	+	9.54387i	0.375419	+	0.632058i
$229$			3.62523i			0.239562i	0.992800	+	0.119781i	$0.0382193\pi$
$229$			3.62523i			0.239562i	−0.992800	+	0.119781i	$0.961781\pi$
$230$	8.33956	+	17.3669i	0.549894	+	1.14514i
$231$	−2.29122	+	8.99455i	−0.150751	+	0.591798i
$232$	1.95563	−	1.95563i	0.128394	−	0.128394i
$233$	9.50905	−	9.50905i	0.622959	−	0.622959i	−0.323328	−	0.946287i	$-0.604802\pi$
$233$	9.50905	−	9.50905i	0.622959	−	0.622959i	0.946287	+	0.323328i	$0.104802\pi$
$234$	−7.00268	−	3.81521i	−0.457779	−	0.249408i
$235$	8.44594	−	24.0508i	0.550952	−	1.56890i
$236$			15.6252i			1.01711i
$237$	−4.84029	+	2.87495i	−0.314410	+	0.186748i
$238$	−1.45763	−	1.45763i	−0.0944843	−	0.0944843i
$239$	21.4806			1.38947			0.694733	−	0.719268i	$-0.255523\pi$
$239$	21.4806			1.38947			0.694733	+	0.719268i	$0.255523\pi$
$240$	5.80363	−	8.72160i	0.374623	−	0.562977i
$241$	−4.58531			−0.295366			−0.147683	−	0.989035i	$-0.547181\pi$
$241$	−4.58531			−0.295366			−0.147683	+	0.989035i	$0.547181\pi$
$242$	12.4467	+	12.4467i	0.800107	+	0.800107i
$243$	−6.94488	+	13.9560i	−0.445514	+	0.895275i
$244$			9.72178i			0.622373i
$245$	7.20343	−	3.45907i	0.460210	−	0.220992i
$246$	4.56050	+	1.16172i	0.290767	+	0.0740683i
$247$	−2.25420	+	2.25420i	−0.143431	+	0.143431i
$248$	−0.773713	+	0.773713i	−0.0491308	+	0.0491308i
$249$	−22.6532	−	5.77055i	−1.43559	−	0.365693i
$250$	−12.5716	−	20.1575i	−0.795099	−	1.27487i
$251$		−	26.1031i		−	1.64762i	−0.566870	−	0.823808i	$-0.691846\pi$
$251$		−	26.1031i		−	1.64762i	0.566870	−	0.823808i	$-0.308154\pi$
$252$	23.5334	−	6.93408i	1.48247	−	0.436806i
$253$	4.72511	+	4.72511i	0.297065	+	0.297065i
$254$	9.96444			0.625225
$255$	1.13287	−	0.227581i	0.0709429	−	0.0142517i
$256$	4.92204			0.307628
$257$	−11.6728	−	11.6728i	−0.728130	−	0.728130i	0.242117	−	0.970247i	$-0.422158\pi$
$257$	−11.6728	−	11.6728i	−0.728130	−	0.728130i	−0.970247	+	0.242117i	$0.922158\pi$
$258$	−20.5430	+	12.2018i	−1.27895	+	0.759650i
$259$			30.0046i			1.86439i
$260$	−6.63775	−	2.33099i	−0.411656	−	0.144562i
$261$	3.62779	−	6.65867i	0.224554	−	0.412161i
$262$	−7.35135	+	7.35135i	−0.454168	+	0.454168i
$263$	2.97531	−	2.97531i	0.183466	−	0.183466i	−0.609398	−	0.792864i	$-0.708589\pi$
$263$	2.97531	−	2.97531i	0.183466	−	0.183466i	0.792864	+	0.609398i	$0.208589\pi$
$264$	−0.770991	+	3.02665i	−0.0474512	+	0.186277i
$265$	−3.53169	−	1.24023i	−0.216950	−	0.0761866i
$266$		−	17.6071i		−	1.07956i
$267$	6.30144	+	10.6091i	0.385642	+	0.649269i
$268$	17.2000	+	17.2000i	1.05066	+	1.05066i
$269$	−24.4322			−1.48966			−0.744829	−	0.667255i	$-0.767469\pi$
$269$	−24.4322			−1.48966			−0.744829	+	0.667255i	$0.767469\pi$
$270$	−7.31026	+	23.5813i	−0.444888	+	1.43511i
$271$	16.8165			1.02153			0.510764	−	0.859721i	$-0.329363\pi$
$271$	16.8165			1.02153			0.510764	+	0.859721i	$0.329363\pi$
$272$	0.570641	+	0.570641i	0.0346002	+	0.0346002i
$273$	3.59811	+	6.05780i	0.217768	+	0.366635i
$274$		−	15.6719i		−	0.946774i
$275$	−6.43081	−	5.15198i	−0.387792	−	0.310676i
$276$	4.36007	−	17.1162i	0.262446	−	1.03027i
$277$	2.12323	−	2.12323i	0.127572	−	0.127572i	−0.640438	−	0.768010i	$-0.721247\pi$
$277$	2.12323	−	2.12323i	0.127572	−	0.127572i	0.768010	+	0.640438i	$0.221247\pi$
$278$	−28.1548	+	28.1548i	−1.68861	+	1.68861i
$279$	−1.43527	+	2.63439i	−0.0859274	+	0.157717i
$280$	7.17192	−	3.44394i	0.428604	−	0.205815i
$281$			8.48072i			0.505917i	0.967477	+	0.252959i	$0.0814037\pi$
$281$			8.48072i			0.505917i	−0.967477	+	0.252959i	$0.918596\pi$
$282$	−36.0718	+	21.4253i	−2.14804	+	1.27586i
$283$	6.79771	+	6.79771i	0.404082	+	0.404082i	0.879669	−	0.475587i	$-0.157764\pi$
$283$	6.79771	+	6.79771i	0.404082	+	0.404082i	−0.475587	+	0.879669i	$0.657764\pi$
$284$	33.4580			1.98537
$285$	8.21660	+	5.46759i	0.486709	+	0.323872i
$286$	−4.38070			−0.259036
$287$	−2.94019	−	2.94019i	−0.173554	−	0.173554i
$288$	−22.8370	+	6.72889i	−1.34568	+	0.396503i
$289$		−	16.9110i		−	0.994764i
$290$	3.97911	−	11.3310i	0.233662	−	0.665378i
$291$	13.6182	+	3.46902i	0.798314	+	0.203358i
$292$	−28.9209	+	28.9209i	−1.69247	+	1.69247i
$293$	11.9424	−	11.9424i	0.697681	−	0.697681i	−0.266229	−	0.963910i	$-0.585778\pi$
$293$	11.9424	−	11.9424i	0.697681	−	0.697681i	0.963910	+	0.266229i	$0.0857778\pi$
$294$	−12.7452	−	3.24663i	−0.743313	−	0.189347i
$295$	6.01372	+	12.5234i	0.350132	+	0.729142i
$296$			10.0965i			0.586846i
$297$	0.317713	+	8.55740i	0.0184356	+	0.496551i
$298$	25.8533	+	25.8533i	1.49764	+	1.49764i
$299$	5.07255			0.293353
$300$	−3.02777	+	21.5687i	−0.174808	+	1.24527i
$301$	21.1108			1.21680
$302$	−25.7969	−	25.7969i	−1.48445	−	1.48445i
$303$	11.0868	−	6.58513i	0.636918	−	0.378306i
$304$			6.89292i			0.395336i
$305$	3.74165	+	7.79191i	0.214247	+	0.446164i
$306$	−1.67005	−	0.909882i	−0.0954707	−	0.0520145i
$307$	−12.1969	+	12.1969i	−0.696116	+	0.696116i	−0.963570	−	0.267455i	$-0.913817\pi$
$307$	−12.1969	+	12.1969i	−0.696116	+	0.696116i	0.267455	+	0.963570i	$0.413817\pi$
$308$	9.52985	−	9.52985i	0.543014	−	0.543014i
$309$	4.40729	−	17.3015i	0.250722	−	0.984249i
$310$	−1.57427	+	4.48291i	−0.0894124	+	0.254612i
$311$			7.49544i			0.425027i	0.977158	+	0.212514i	$0.0681650\pi$
$311$			7.49544i			0.425027i	−0.977158	+	0.212514i	$0.931835\pi$
$312$	1.21076	+	2.03844i	0.0685457	+	0.115404i
$313$	6.57532	+	6.57532i	0.371659	+	0.371659i	0.868081	−	0.496422i	$-0.165353\pi$
$313$	6.57532	+	6.57532i	0.371659	+	0.371659i	−0.496422	+	0.868081i	$0.665353\pi$
$314$	20.0979			1.13419
$315$	16.1931	−	14.6150i	0.912376	−	0.823462i
$316$	8.17440			0.459846
$317$	13.7470	+	13.7470i	0.772109	+	0.772109i	0.978475	−	0.206366i	$-0.0661637\pi$
$317$	13.7470	+	13.7470i	0.772109	+	0.772109i	−0.206366	+	0.978475i	$0.566164\pi$
$318$	3.14616	+	5.29689i	0.176428	+	0.297035i
$319$		−	4.16550i		−	0.233223i
$320$	−23.0854	+	11.0855i	−1.29051	+	0.619700i
$321$	−8.23665	+	32.3343i	−0.459725	+	1.80472i
$322$	−19.8103	+	19.8103i	−1.10399	+	1.10399i
$323$	−0.537599	+	0.537599i	−0.0299128	+	0.0299128i
$324$	19.0184	−	12.2730i	1.05658	−	0.681831i
$325$	−6.21723	+	0.686431i	−0.344870	+	0.0380763i
$326$			9.58229i			0.530714i
$327$	26.3197	−	15.6329i	1.45548	−	0.864503i
$328$	−0.989367	−	0.989367i	−0.0546287	−	0.0546287i
$329$	37.0688			2.04367
$330$	2.67115	+	13.2966i	0.147042	+	0.731953i
$331$	8.94775			0.491813			0.245906	−	0.969294i	$-0.420914\pi$
$331$	8.94775			0.491813			0.245906	+	0.969294i	$0.420914\pi$
$332$	24.0014	+	24.0014i	1.31725	+	1.31725i
$333$	7.82387	+	26.5533i	0.428745	+	1.45511i
$334$		−	4.19824i		−	0.229717i
$335$	20.4055	+	7.16583i	1.11487	+	0.391511i
$336$	14.7630	+	3.76064i	0.805387	+	0.205160i
$337$	7.69837	−	7.69837i	0.419357	−	0.419357i	−0.465625	−	0.884982i	$-0.654170\pi$
$337$	7.69837	−	7.69837i	0.419357	−	0.419357i	0.884982	+	0.465625i	$0.154170\pi$
$338$	17.1810	−	17.1810i	0.934521	−	0.934521i
$339$	−10.9665	−	2.79355i	−0.595620	−	0.151725i
$340$	−1.58302	−	0.555912i	−0.0858515	−	0.0301486i
$341$			1.64801i			0.0892446i
$342$	−4.59116	−	15.5818i	−0.248262	−	0.842570i
$343$	−7.87826	−	7.87826i	−0.425386	−	0.425386i
$344$	7.10373			0.383008
$345$	−3.09301	−	15.3965i	−0.166522	−	0.828921i
$346$	−30.6604			−1.64831
$347$	−8.98969	−	8.98969i	−0.482592	−	0.482592i	0.423367	−	0.905958i	$-0.360848\pi$
$347$	−8.98969	−	8.98969i	−0.482592	−	0.482592i	−0.905958	+	0.423367i	$0.860848\pi$
$348$	−9.46636	+	5.62267i	−0.507450	+	0.301407i
$349$			6.12166i			0.327685i	0.986487	+	0.163843i	$0.0523889\pi$
$349$			6.12166i			0.327685i	−0.986487	+	0.163843i	$0.947611\pi$
$350$	21.6000	−	26.9616i	1.15457	−	1.44116i
$351$	4.76385	+	4.42277i	0.254275	+	0.236070i
$352$	−9.24785	+	9.24785i	−0.492912	+	0.492912i
$353$	12.5234	−	12.5234i	0.666552	−	0.666552i	−0.290364	−	0.956916i	$-0.593776\pi$
$353$	12.5234	−	12.5234i	0.666552	−	0.666552i	0.956916	+	0.290364i	$0.0937764\pi$
$354$	5.64439	−	22.1580i	0.299996	−	1.17768i
$355$	26.8163	−	12.8771i	1.42326	−	0.683446i
$356$		−	17.9170i		−	0.949599i
$357$	0.858107	+	1.44471i	0.0454158	+	0.0764623i
$358$	−14.7561	−	14.7561i	−0.779882	−	0.779882i
$359$	22.5376			1.18949			0.594744	−	0.803915i	$-0.297253\pi$
$359$	22.5376			1.18949			0.594744	+	0.803915i	$0.297253\pi$
$360$	5.44894	−	4.91792i	0.287184	−	0.259197i
$361$	12.5062			0.658221
$362$	8.35696	+	8.35696i	0.439232	+	0.439232i
$363$	−7.32738	−	12.3364i	−0.384588	−	0.647494i
$364$		−	10.2306i		−	0.536228i
$365$	−12.0490	+	34.3108i	−0.630671	+	1.79591i
$366$	3.51186	−	13.7864i	0.183568	−	0.720626i
$367$	−19.8260	+	19.8260i	−1.03491	+	1.03491i	−0.0355402	+	0.999368i	$0.511315\pi$
$367$	−19.8260	+	19.8260i	−1.03491	+	1.03491i	−0.999368	+	0.0355402i	$0.988685\pi$
$368$	7.75545	−	7.75545i	0.404281	−	0.404281i
$369$	−3.36866	−	1.83532i	−0.175366	−	0.0955429i
$370$	18.9780	+	39.5212i	0.986618	+	2.05461i
$371$		−	5.44329i		−	0.282602i
$372$	3.74520	−	2.22451i	0.194180	−	0.115336i
$373$	−24.3780	−	24.3780i	−1.26225	−	1.26225i	−0.950002	−	0.312243i	$-0.898920\pi$
$373$	−24.3780	−	24.3780i	−1.26225	−	1.26225i	−0.312243	−	0.950002i	$-0.601080\pi$
$374$	−1.04474			−0.0540224
$375$	5.87448	+	18.4524i	0.303357	+	0.952877i
$376$	12.4736			0.643275
$377$	−2.23589	−	2.23589i	−0.115154	−	0.115154i
$378$	−35.8775	+	1.33203i	−1.84534	+	0.0685123i
$379$			12.2181i			0.627601i	0.949489	+	0.313800i	$0.101602\pi$
$379$			12.2181i			0.627601i	−0.949489	+	0.313800i	$0.898398\pi$
$380$	−6.20337	−	12.9184i	−0.318226	−	0.662699i
$381$	−7.87109	−	2.00503i	−0.403248	−	0.102721i
$382$	−31.6547	+	31.6547i	−1.61960	+	1.61960i
$383$	−14.6141	+	14.6141i	−0.746745	+	0.746745i	−0.973866	−	0.227121i	$-0.927069\pi$
$383$	−14.6141	+	14.6141i	−0.746745	+	0.746745i	0.227121	+	0.973866i	$0.427069\pi$
$384$	14.2054	+	3.61860i	0.724916	+	0.184661i
$385$	3.97030	−	11.3059i	0.202345	−	0.576201i
$386$		−	1.37121i		−	0.0697926i
$387$	18.6825	−	5.50476i	0.949685	−	0.279823i
$388$	−14.4287	−	14.4287i	−0.732506	−	0.732506i
$389$	−12.3238			−0.624840			−0.312420	−	0.949944i	$-0.601140\pi$
$389$	−12.3238			−0.624840			−0.312420	+	0.949944i	$0.601140\pi$
$390$	8.57091	+	5.70336i	0.434005	+	0.288801i
$391$	1.20974			0.0611793
$392$	2.76497	+	2.76497i	0.139652	+	0.139652i
$393$	7.28619	−	4.32773i	0.367539	−	0.218305i
$394$			27.0994i			1.36525i
$395$	6.55170	−	3.14611i	0.329652	−	0.158298i
$396$	5.94871	−	10.9186i	0.298934	−	0.548683i
$397$	−22.4047	+	22.4047i	−1.12446	+	1.12446i	−0.133399	+	0.991062i	$0.542589\pi$
$397$	−22.4047	+	22.4047i	−1.12446	+	1.12446i	−0.991062	+	0.133399i	$0.957411\pi$
$398$	−19.3342	+	19.3342i	−0.969137	+	0.969137i
$399$	−3.54289	+	13.9082i	−0.177366	+	0.696279i
$400$	−8.45607	+	10.5550i	−0.422804	+	0.527752i
$401$		−	24.6845i		−	1.23268i	−0.787478	−	0.616342i	$-0.788614\pi$
$401$		−	24.6845i		−	1.23268i	0.787478	−	0.616342i	$-0.211386\pi$
$402$	−18.1780	−	30.6046i	−0.906636	−	1.52642i
$403$	0.884592	+	0.884592i	0.0440646	+	0.0440646i
$404$	−18.7236			−0.931534
$405$	10.5195	−	17.1563i	0.522719	−	0.852505i
$406$	17.4641			0.866730
$407$	10.7527	+	10.7527i	0.532994	+	0.532994i
$408$	0.288751	+	0.486143i	0.0142953	+	0.0240677i
$409$		−	26.9114i		−	1.33068i	−0.746539	−	0.665341i	$-0.768286\pi$
$409$		−	26.9114i		−	1.33068i	0.746539	−	0.665341i	$-0.231714\pi$
$410$	−5.73241	−	2.01306i	−0.283104	−	0.0994179i
$411$	−3.15348	+	12.3795i	−0.155550	+	0.610636i
$412$	−18.3312	+	18.3312i	−0.903113	+	0.903113i
$413$	−14.2854	+	14.2854i	−0.702938	+	0.702938i
$414$	−12.3660	+	22.6973i	−0.607755	+	1.11551i
$415$	28.4744	+	9.99939i	1.39775	+	0.490851i
$416$			9.92783i			0.486752i
$417$	27.9053	−	16.5747i	1.36653	−	0.811667i
$418$	−6.30987	−	6.30987i	−0.308626	−	0.308626i
$419$	−15.0668			−0.736061			−0.368030	−	0.929814i	$-0.619968\pi$
$419$	−15.0668			−0.736061			−0.368030	+	0.929814i	$0.619968\pi$
$420$	−31.0525	+	6.23813i	−1.51521	+	0.304390i
$421$	−23.6558			−1.15291			−0.576456	−	0.817128i	$-0.695565\pi$
$421$	−23.6558			−1.15291			−0.576456	+	0.817128i	$0.695565\pi$
$422$	−35.2780	−	35.2780i	−1.71730	−	1.71730i
$423$	32.8049	−	9.66591i	1.59503	−	0.469972i
$424$		−	1.83166i		−	0.0889532i
$425$	−1.48273	+	0.163706i	−0.0719232	+	0.00794088i
$426$	−47.4466	−	12.0863i	−2.29880	−	0.585582i
$427$	−8.88818	+	8.88818i	−0.430129	+	0.430129i
$428$	34.2586	−	34.2586i	1.65595	−	1.65595i
$429$	3.46039	+	0.881480i	0.167069	+	0.0425582i
$430$	27.8065	−	13.3526i	1.34095	−	0.643921i
$431$			2.89707i			0.139547i	0.997563	+	0.0697735i	$0.0222277\pi$
$431$			2.89707i			0.139547i	−0.997563	+	0.0697735i	$0.977772\pi$
$432$	14.0455	−	0.521470i	0.675763	−	0.0250892i
$433$	−3.41970	−	3.41970i	−0.164340	−	0.164340i	0.620146	−	0.784486i	$-0.287073\pi$
$433$	−3.41970	−	3.41970i	−0.164340	−	0.164340i	−0.784486	+	0.620146i	$0.787073\pi$
$434$	−6.90938			−0.331661
$435$	−5.42318	+	8.14987i	−0.260022	+	0.390756i
$436$	−44.4494			−2.12874
$437$	7.30639	+	7.30639i	0.349512	+	0.349512i
$438$	51.4599	−	30.5653i	2.45885	−	1.46047i
$439$			22.5629i			1.07687i	0.842667	+	0.538435i	$0.180984\pi$
$439$			22.5629i			1.07687i	−0.842667	+	0.538435i	$0.819016\pi$
$440$	1.33600	−	3.80441i	0.0636912	−	0.181368i
$441$	9.41435	+	5.12914i	0.448302	+	0.244245i
$442$	−0.560782	+	0.560782i	−0.0266737	+	0.0266737i
$443$	3.88666	−	3.88666i	0.184661	−	0.184661i	−0.608723	−	0.793383i	$-0.708318\pi$
$443$	3.88666	−	3.88666i	0.184661	−	0.184661i	0.793383	+	0.608723i	$0.208318\pi$
$444$	9.92203	−	38.9505i	0.470879	−	1.84851i
$445$	−6.89578	−	14.3603i	−0.326891	−	0.680744i
$446$		−	58.0550i		−	2.74898i
$447$	−15.2198	−	25.6242i	−0.719872	−	1.21198i
$448$	−26.3333	−	26.3333i	−1.24413	−	1.24413i
$449$	−3.08994			−0.145823			−0.0729117	−	0.997338i	$-0.523229\pi$
$449$	−3.08994			−0.145823			−0.0729117	+	0.997338i	$0.523229\pi$
$450$	12.0851	−	29.4926i	0.569695	−	1.39030i
$451$	−2.10735			−0.0992313
$452$	11.6192	+	11.6192i	0.546520	+	0.546520i
$453$	15.1866	+	25.5683i	0.713530	+	1.20130i
$454$		−	55.3359i		−	2.59704i
$455$	−3.93748	−	8.19971i	−0.184592	−	0.384408i
$456$	−1.19217	+	4.68007i	−0.0558287	+	0.219164i
$457$	8.80890	−	8.80890i	0.412063	−	0.412063i	−0.470394	−	0.882457i	$-0.655888\pi$
$457$	8.80890	−	8.80890i	0.412063	−	0.412063i	0.882457	+	0.470394i	$0.155888\pi$
$458$	−5.44688	+	5.44688i	−0.254516	+	0.254516i
$459$	1.13612	+	1.05478i	0.0530295	+	0.0492328i
$460$	−7.55527	+	21.5145i	−0.352266	+	1.00312i
$461$		−	21.8712i		−	1.01864i	−0.860577	−	0.509321i	$-0.829897\pi$
$461$		−	21.8712i		−	1.01864i	0.860577	−	0.509321i	$-0.170103\pi$
$462$	−16.9568	+	10.0717i	−0.788900	+	0.468578i
$463$	8.84979	+	8.84979i	0.411285	+	0.411285i	0.882186	−	0.470901i	$-0.156071\pi$
$463$	8.84979	+	8.84979i	0.411285	+	0.411285i	−0.470901	+	0.882186i	$0.656071\pi$
$464$	−6.83694			−0.317397
$465$	2.14559	−	3.22435i	0.0994992	−	0.149526i
$466$	28.5745			1.32369
$467$	14.8096	+	14.8096i	0.685305	+	0.685305i	0.961190	−	0.275886i	$-0.0889711\pi$
$467$	14.8096	+	14.8096i	0.685305	+	0.685305i	−0.275886	+	0.961190i	$0.588971\pi$
$468$	−2.66768	−	9.05380i	−0.123314	−	0.418512i
$469$			31.4504i			1.45225i
$470$	48.8260	−	23.4461i	2.25218	−	1.08149i
$471$	−15.8757	−	4.04408i	−0.731513	−	0.186341i
$472$	−4.80701	+	4.80701i	−0.221260	+	0.221260i
$473$	7.56547	−	7.56547i	0.347861	−	0.347861i
$474$	−11.5921	−	2.95290i	−0.532441	−	0.135631i
$475$	−9.94388	−	7.96644i	−0.456257	−	0.365525i
$476$		−	2.43987i		−	0.111831i
$477$	−1.41937	−	4.81718i	−0.0649886	−	0.220563i
$478$	32.2744	+	32.2744i	1.47620	+	1.47620i
$479$	10.5791			0.483372			0.241686	−	0.970355i	$-0.422300\pi$
$479$	10.5791			0.483372			0.241686	+	0.970355i	$0.422300\pi$
$480$	30.1336	−	6.05353i	1.37540	−	0.276305i
$481$	11.5434			0.526333
$482$	−6.88938	−	6.88938i	−0.313803	−	0.313803i
$483$	19.6348	−	11.6623i	0.893412	−	0.530654i
$484$			20.8341i			0.947003i
$485$	−17.1177	−	6.01124i	−0.777274	−	0.272956i
$486$	−31.4033	+	10.5341i	−1.42448	+	0.477835i
$487$	18.8854	−	18.8854i	0.855780	−	0.855780i	−0.135058	−	0.990838i	$-0.543122\pi$
$487$	18.8854	−	18.8854i	0.855780	−	0.855780i	0.990838	+	0.135058i	$0.0431219\pi$
$488$	−2.99086	+	2.99086i	−0.135390	+	0.135390i
$489$	1.92814	−	7.56922i	0.0871934	−	0.342292i
$490$	16.0203	+	5.62586i	0.723723	+	0.254151i
$491$		−	17.2857i		−	0.780091i	−0.920796	−	0.390046i	$-0.872459\pi$
$491$		−	17.2857i		−	0.780091i	0.920796	−	0.390046i	$-0.127541\pi$
$492$	2.84454	+	4.78909i	0.128242	+	0.215909i
$493$	−0.533233	−	0.533233i	−0.0240156	−	0.0240156i
$494$	−6.77382			−0.304769
$495$	0.565538	−	11.0407i	0.0254190	−	0.496242i
$496$	2.70492			0.121454
$497$	30.5892	+	30.5892i	1.37211	+	1.37211i
$498$	−25.3660	−	42.7064i	−1.13668	−	1.91372i
$499$		−	32.8327i		−	1.46979i	−0.678179	−	0.734896i	$-0.737231\pi$
$499$		−	32.8327i		−	1.46979i	0.678179	−	0.734896i	$-0.262769\pi$
$500$	6.34881	−	27.3919i	0.283927	−	1.22500i
$501$	−0.844765	+	3.31626i	−0.0377413	+	0.148160i
$502$	39.2197	−	39.2197i	1.75046	−	1.75046i
$503$	−7.33962	+	7.33962i	−0.327257	+	0.327257i	−0.851543	−	0.524285i	$-0.824333\pi$
$503$	−7.33962	+	7.33962i	−0.327257	+	0.327257i	0.524285	+	0.851543i	$0.324333\pi$
$504$	9.37317	+	5.10671i	0.417514	+	0.227471i
$505$	−15.0068	+	7.20622i	−0.667794	+	0.320673i
$506$			14.1989i			0.631217i
$507$	−17.0287	+	10.1144i	−0.756270	+	0.449197i
$508$	8.33953	+	8.33953i	0.370007	+	0.370007i
$509$	−4.20821			−0.186526			−0.0932629	−	0.995642i	$-0.529730\pi$
$509$	−4.20821			−0.186526			−0.0932629	+	0.995642i	$0.529730\pi$
$510$	2.04406	+	1.36018i	0.0905125	+	0.0602299i
$511$	−52.8822			−2.33937
$512$	19.3644	+	19.3644i	0.855793	+	0.855793i
$513$	0.491276	+	13.2322i	0.0216904	+	0.584216i
$514$		−	35.0766i		−	1.54716i
$515$	−7.63708	+	21.7475i	−0.336530	+	0.958308i
$516$	−27.4050	−	6.98100i	−1.20644	−	0.307321i
$517$	13.2843	−	13.2843i	0.584245	−	0.584245i
$518$	−45.0816	+	45.0816i	−1.98077	+	1.98077i
$519$	24.2192	+	6.16945i	1.06310	+	0.270809i
$520$	−1.32495	−	2.75919i	−0.0581031	−	0.120998i
$521$		−	26.4895i		−	1.16053i	−0.814429	−	0.580263i	$-0.802950\pi$
$521$		−	26.4895i		−	1.16053i	0.814429	−	0.580263i	$-0.197050\pi$
$522$	15.4553	−	4.55387i	0.676460	−	0.199318i
$523$	15.6242	+	15.6242i	0.683199	+	0.683199i	0.960720	−	0.277520i	$-0.0895126\pi$
$523$	15.6242	+	15.6242i	0.683199	+	0.683199i	−0.277520	+	0.960720i	$0.589513\pi$
$524$	−12.3051			−0.537551
$525$	−22.4874	+	16.9511i	−0.981431	+	0.739807i
$526$	8.94076			0.389836
$527$	0.210964	+	0.210964i	0.00918976	+	0.00918976i
$528$	6.63831	−	3.94291i	0.288896	−	0.171593i
$529$			6.55869i			0.285160i
$530$	−3.44290	−	7.16976i	−0.149550	−	0.311434i
$531$	−8.91720	+	16.3672i	−0.386974	+	0.710276i
$532$	14.7359	−	14.7359i	0.638882	−	0.638882i
$533$	−1.13115	+	1.13115i	−0.0489956	+	0.0489956i
$534$	−6.47228	+	25.4080i	−0.280083	+	1.09951i
$535$	14.2727	−	40.6432i	0.617064	−	1.75716i
$536$			10.5830i			0.457117i
$537$	8.68687	+	14.6253i	0.374866	+	0.631127i
$538$	−36.7092	−	36.7092i	−1.58264	−	1.58264i
$539$	5.88938			0.253674
$540$	−25.8540	+	13.6177i	−1.11258	+	0.586013i
$541$	−8.08661			−0.347670			−0.173835	−	0.984775i	$-0.555616\pi$
$541$	−8.08661			−0.347670			−0.173835	+	0.984775i	$0.555616\pi$
$542$	25.2666	+	25.2666i	1.08529	+	1.08529i
$543$	−4.91973	−	8.28289i	−0.211126	−	0.355453i
$544$			2.36767i			0.101513i
$545$	−35.6258	+	17.1074i	−1.52604	+	0.732800i
$546$	−3.69566	+	14.5079i	−0.158160	+	0.620882i
$547$	19.1539	−	19.1539i	0.818962	−	0.818962i	−0.166996	−	0.985958i	$-0.553407\pi$
$547$	19.1539	−	19.1539i	0.818962	−	0.818962i	0.985958	+	0.166996i	$0.0534066\pi$
$548$	13.1163	−	13.1163i	0.560299	−	0.560299i
$549$	−5.54817	+	10.1835i	−0.236790	+	0.434619i
$550$	−1.92143	−	17.4030i	−0.0819301	−	0.742067i
$551$		−	6.44106i		−	0.274398i
$552$	6.60706	−	3.92435i	0.281215	−	0.167031i
$553$	7.47348	+	7.47348i	0.317805	+	0.317805i
$554$	6.38026			0.271071
$555$	−7.03862	−	35.0372i	−0.298773	−	1.48725i
$556$	−47.1272			−1.99864
$557$	−26.8281	−	26.8281i	−1.13674	−	1.13674i	−0.989030	−	0.147713i	$-0.952809\pi$
$557$	−26.8281	−	26.8281i	−1.13674	−	1.13674i	−0.147713	−	0.989030i	$-0.547191\pi$
$558$	−6.11462	+	1.80166i	−0.258853	+	0.0762704i
$559$		−	8.12175i		−	0.343514i
$560$	−18.5566	−	6.51655i	−0.784160	−	0.275375i
$561$	0.825262	+	0.210222i	0.0348426	+	0.00887559i
$562$	−12.7422	+	12.7422i	−0.537497	+	0.537497i
$563$	3.03211	−	3.03211i	0.127788	−	0.127788i	−0.640320	−	0.768108i	$-0.721198\pi$
$563$	3.03211	−	3.03211i	0.127788	−	0.127788i	0.768108	+	0.640320i	$0.221198\pi$
$564$	−48.1210	−	12.2581i	−2.02626	−	0.516157i
$565$	13.7846	+	4.84075i	0.579922	+	0.203652i
$566$			20.4270i			0.858611i
$567$	28.6083	+	6.16703i	1.20143	+	0.258991i
$568$	10.2932	+	10.2932i	0.431893	+	0.431893i
$569$	−20.6457			−0.865511			−0.432756	−	0.901511i	$-0.642459\pi$
$569$	−20.6457			−0.865511			−0.432756	+	0.901511i	$0.642459\pi$
$570$	4.13037	+	20.5604i	0.173002	+	0.861178i
$571$	−4.54635			−0.190259			−0.0951294	−	0.995465i	$-0.530326\pi$
$571$	−4.54635			−0.190259			−0.0951294	+	0.995465i	$0.530326\pi$
$572$	−3.66633	−	3.66633i	−0.153297	−	0.153297i
$573$	31.3741	−	18.6351i	1.31067	−	0.778492i
$574$		−	8.83520i		−	0.368774i
$575$	2.22488	+	20.1515i	0.0927840	+	0.840375i
$576$	−30.1709	−	16.4378i	−1.25712	−	0.684906i
$577$	−13.2514	+	13.2514i	−0.551662	+	0.551662i	−0.926920	−	0.375259i	$-0.877554\pi$
$577$	−13.2514	+	13.2514i	−0.551662	+	0.551662i	0.375259	+	0.926920i	$0.377554\pi$
$578$	25.4086	−	25.4086i	1.05686	−	1.05686i
$579$	−0.275913	+	1.08314i	−0.0114665	+	0.0450138i
$580$	12.8135	−	6.15299i	0.532050	−	0.255489i
$581$			43.8868i			1.82073i
$582$	15.2491	+	25.6734i	0.632094	+	1.06420i
$583$	−1.95071	−	1.95071i	−0.0807903	−	0.0807903i
$584$	−17.7948			−0.736353
$585$	−5.62269	−	6.22981i	−0.232470	−	0.257571i
$586$	35.8866			1.48246
$587$	14.5277	+	14.5277i	0.599621	+	0.599621i	0.940212	−	0.340590i	$-0.110627\pi$
$587$	14.5277	+	14.5277i	0.599621	+	0.599621i	−0.340590	+	0.940212i	$0.610627\pi$
$588$	−7.94960	−	13.3840i	−0.327836	−	0.551947i
$589$			2.54829i			0.105001i
$590$	−9.78078	+	27.8519i	−0.402668	+	1.14664i
$591$	5.45290	−	21.4063i	0.224303	−	0.880536i
$592$	17.6487	−	17.6487i	0.725359	−	0.725359i
$593$	−7.60934	+	7.60934i	−0.312478	+	0.312478i	−0.845869	−	0.533391i	$-0.820918\pi$
$593$	−7.60934	+	7.60934i	−0.312478	+	0.312478i	0.533391	+	0.845869i	$0.320918\pi$
$594$	−12.3800	+	13.3348i	−0.507960	+	0.547132i
$595$	−0.939041	−	1.95553i	−0.0384969	−	0.0801690i
$596$			43.2748i			1.77260i
$597$	19.1628	−	11.3820i	0.784283	−	0.465835i
$598$	7.62145	+	7.62145i	0.311664	+	0.311664i
$599$	−1.13006			−0.0461730			−0.0230865	−	0.999733i	$-0.507349\pi$
$599$	−1.13006			−0.0461730			−0.0230865	+	0.999733i	$0.507349\pi$
$600$	−7.56697	+	5.70401i	−0.308920	+	0.232865i
$601$	16.0741			0.655677			0.327839	−	0.944734i	$-0.393680\pi$
$601$	16.0741			0.655677			0.327839	+	0.944734i	$0.393680\pi$
$602$	31.7187	+	31.7187i	1.29276	+	1.29276i
$603$	8.20089	+	27.8328i	0.333966	+	1.13344i
$604$		−	43.1804i		−	1.75699i
$605$	8.01848	+	16.6983i	0.325998	+	0.678883i
$606$	26.5518	+	6.76366i	1.07859	+	0.274755i
$607$	−15.1618	+	15.1618i	−0.615399	+	0.615399i	−0.944348	−	0.328948i	$-0.893306\pi$
$607$	−15.1618	+	15.1618i	−0.615399	+	0.615399i	0.328948	+	0.944348i	$0.393306\pi$
$608$	−14.2998	+	14.2998i	−0.579935	+	0.579935i
$609$	−13.7952	−	3.51411i	−0.559010	−	0.142399i
$610$	−6.08547	+	17.3291i	−0.246394	+	0.701634i
$611$		−	14.2611i		−	0.576943i
$612$	−0.636211	−	2.15922i	−0.0257173	−	0.0872814i
$613$	−20.0523	−	20.0523i	−0.809904	−	0.809904i	0.174715	−	0.984619i	$-0.444100\pi$
$613$	−20.0523	−	20.0523i	−0.809904	−	0.809904i	−0.984619	+	0.174715i	$0.944100\pi$
$614$	−36.6515			−1.47914
$615$	4.12307	+	2.74362i	0.166258	+	0.110633i
$616$	5.86362			0.236252
$617$	−19.9288	−	19.9288i	−0.802302	−	0.802302i	0.181153	−	0.983455i	$-0.442017\pi$
$617$	−19.9288	−	19.9288i	−0.802302	−	0.802302i	−0.983455	+	0.181153i	$0.942017\pi$
$618$	32.6173	−	19.3734i	1.31206	−	0.779314i
$619$		−	30.7552i		−	1.23616i	−0.786117	−	0.618078i	$-0.787912\pi$
$619$		−	30.7552i		−	1.23616i	0.786117	−	0.618078i	$-0.212088\pi$
$620$	−5.06942	+	2.43432i	−0.203593	+	0.0977647i
$621$	14.3352	−	15.4407i	0.575253	−	0.619616i
$622$	−11.2618	+	11.2618i	−0.451558	+	0.451558i
$623$	16.3807	−	16.3807i	0.656279	−	0.656279i
$624$	1.44679	−	5.67963i	0.0579182	−	0.227367i
$625$	−5.45391	−	24.3978i	−0.218156	−	0.975914i
$626$			19.7587i			0.789717i
$627$	3.71461	+	6.25394i	0.148347	+	0.249758i
$628$	16.8205	+	16.8205i	0.671212	+	0.671212i
$629$	2.75296			0.109768
$630$	46.2888	+	2.37105i	1.84419	+	0.0944651i
$631$	21.7543			0.866025			0.433012	−	0.901388i	$-0.357451\pi$
$631$	21.7543			0.866025			0.433012	+	0.901388i	$0.357451\pi$
$632$	2.51481	+	2.51481i	0.100034	+	0.100034i
$633$	20.7681	+	34.9653i	0.825457	+	1.38974i
$634$			41.3095i			1.64061i
$635$	9.89372	+	3.47439i	0.392620	+	0.137877i
$636$	−1.80001	+	7.06623i	−0.0713751	+	0.280194i
$637$	3.16121	−	3.16121i	0.125252	−	0.125252i
$638$	6.25862	−	6.25862i	0.247781	−	0.247781i
$639$	35.0469	+	19.0943i	1.38644	+	0.755360i
$640$	−17.8558	−	6.27043i	−0.705811	−	0.247860i
$641$		−	24.7653i		−	0.978170i	−0.872236	−	0.489085i	$-0.837331\pi$
$641$		−	24.7653i		−	0.978170i	0.872236	−	0.489085i	$-0.162669\pi$
$642$	−60.9574	+	36.2065i	−2.40580	+	1.42896i
$643$	−20.9759	−	20.9759i	−0.827207	−	0.827207i	0.159922	−	0.987130i	$-0.448876\pi$
$643$	−20.9759	−	20.9759i	−0.827207	−	0.827207i	−0.987130	+	0.159922i	$0.948876\pi$
$644$	−33.1597			−1.30667
$645$	−24.6517	+	4.95227i	−0.970659	+	0.194995i
$646$	−1.61548			−0.0635600
$647$	34.1074	+	34.1074i	1.34090	+	1.34090i	0.895163	+	0.445739i	$0.147059\pi$
$647$	34.1074	+	34.1074i	1.34090	+	1.34090i	0.445739	+	0.895163i	$0.352941\pi$
$648$	9.62662	+	2.07519i	0.378169	+	0.0815213i
$649$			10.2389i			0.401913i
$650$	−10.3727	−	8.30997i	−0.406850	−	0.325944i
$651$	5.45784	+	1.39030i	0.213910	+	0.0544901i
$652$	−8.01969	+	8.01969i	−0.314075	+	0.314075i
$653$	−12.0477	+	12.0477i	−0.471463	+	0.471463i	−0.902388	−	0.430925i	$-0.858187\pi$
$653$	−12.0477	+	12.0477i	−0.471463	+	0.471463i	0.430925	+	0.902388i	$0.358187\pi$
$654$	63.0334	+	16.0568i	2.46480	+	0.627869i
$655$	−9.86242	+	4.73591i	−0.385357	+	0.185047i
$656$			3.45885i			0.135045i
$657$	−46.7994	+	13.7894i	−1.82582	+	0.537974i
$658$	55.6955	+	55.6955i	2.17124	+	2.17124i
$659$	−11.3138			−0.440722			−0.220361	−	0.975418i	$-0.570724\pi$
$659$	−11.3138			−0.440722			−0.220361	+	0.975418i	$0.570724\pi$
$660$	−8.89273	+	13.3639i	−0.346149	+	0.520187i
$661$	−36.7813			−1.43063			−0.715314	−	0.698803i	$-0.753716\pi$
$661$	−36.7813			−1.43063			−0.715314	+	0.698803i	$0.753716\pi$
$662$	13.4439	+	13.4439i	0.522512	+	0.522512i
$663$	0.555811	−	0.330131i	0.0215859	−	0.0128212i
$664$			14.7678i			0.573102i
$665$	6.13923	−	17.4821i	0.238069	−	0.677928i
$666$	−28.1407	+	51.6513i	−1.09043	+	2.00145i
$667$	−7.24705	+	7.24705i	−0.280607	+	0.280607i
$668$	3.51363	−	3.51363i	0.135946	−	0.135946i
$669$	−11.6818	+	45.8587i	−0.451643	+	1.77300i
$670$	19.8925	+	41.4257i	0.768514	+	1.60041i
$671$			6.37052i			0.245931i
$672$	22.8251	+	38.4285i	0.880499	+	1.48241i
$673$	21.0059	+	21.0059i	0.809716	+	0.809716i	0.984591	−	0.174875i	$-0.0559520\pi$
$673$	21.0059	+	21.0059i	0.809716	+	0.809716i	−0.174875	+	0.984591i	$0.555952\pi$
$674$	23.1335			0.891068
$675$	−15.4807	+	20.8650i	−0.595851	+	0.803095i
$676$	28.7585			1.10610
$677$	−32.6858	−	32.6858i	−1.25622	−	1.25622i	−0.952884	−	0.303335i	$-0.901900\pi$
$677$	−32.6858	−	32.6858i	−1.25622	−	1.25622i	−0.303335	−	0.952884i	$-0.598100\pi$
$678$	−12.2798	−	20.6744i	−0.471603	−	0.793994i
$679$		−	26.3830i		−	1.01249i
$680$	−0.315986	−	0.658033i	−0.0121175	−	0.0252344i
$681$	−11.1346	+	43.7108i	−0.426680	+	1.67500i
$682$	−2.47611	+	2.47611i	−0.0948153	+	0.0948153i
$683$	8.25904	−	8.25904i	0.316023	−	0.316023i	−0.531214	−	0.847238i	$-0.678264\pi$
$683$	8.25904	−	8.25904i	0.316023	−	0.316023i	0.847238	+	0.531214i	$0.178264\pi$
$684$	9.19842	−	16.8834i	0.351710	−	0.645552i
$685$	5.46445	−	15.5607i	0.208786	−	0.594542i
$686$		−	23.6740i		−	0.903878i
$687$	5.39860	−	3.20657i	0.205969	−	0.122338i
$688$	−12.4174	−	12.4174i	−0.473409	−	0.473409i
$689$	−2.09415			−0.0797807
$690$	18.4859	−	27.7803i	0.703747	−	1.05758i
$691$	15.8013			0.601111			0.300555	−	0.953764i	$-0.402828\pi$
$691$	15.8013			0.601111			0.300555	+	0.953764i	$0.402828\pi$
$692$	−25.6605	−	25.6605i	−0.975467	−	0.975467i
$693$	15.4211	−	4.54379i	0.585798	−	0.172604i
$694$		−	27.0138i		−	1.02543i
$695$	−37.7720	+	18.1380i	−1.43277	+	0.688014i
$696$	−4.64206	−	1.18249i	−0.175957	−	0.0448222i
$697$	−0.269766	+	0.269766i	−0.0102181	+	0.0102181i
$698$	−9.19774	+	9.19774i	−0.348139	+	0.348139i
$699$	−22.5715	−	5.74973i	−0.853733	−	0.217475i
$700$	40.6426	−	4.48726i	1.53614	−	0.169602i
$701$			4.53744i			0.171377i	0.996322	+	0.0856883i	$0.0273089\pi$
$701$			4.53744i			0.171377i	−0.996322	+	0.0856883i	$0.972691\pi$
$702$	0.512460	+	13.8028i	0.0193416	+	0.520953i
$703$	16.6268	+	16.6268i	0.627093	+	0.627093i
$704$	−18.8742			−0.711347
$705$	−43.2863	+	8.69578i	−1.63026	+	0.327502i
$706$	37.6325			1.41632
$707$	−17.1181	−	17.1181i	−0.643794	−	0.643794i
$708$	23.2686	−	13.8207i	0.874487	−	0.519413i
$709$			18.1480i			0.681563i	0.940143	+	0.340781i	$0.110692\pi$
$709$			18.1480i			0.681563i	−0.940143	+	0.340781i	$0.889308\pi$
$710$	59.6390	+	20.9435i	2.23821	+	0.785995i
$711$	8.56260	+	4.66509i	0.321123	+	0.174954i
$712$	5.51208	−	5.51208i	0.206574	−	0.206574i
$713$	2.86717	−	2.86717i	0.107376	−	0.107376i
$714$	−0.881371	+	3.45996i	−0.0329845	+	0.129486i
$715$	−4.34961	−	1.52746i	−0.162666	−	0.0571236i
$716$		−	24.6995i		−	0.923065i
$717$	−18.9999	−	31.9883i	−0.709564	−	1.19463i
$718$	33.8625	+	33.8625i	1.26374	+	1.26374i
$719$	−37.4509			−1.39668			−0.698341	−	0.715765i	$-0.746078\pi$
$719$	−37.4509			−1.39668			−0.698341	+	0.715765i	$0.746078\pi$
$720$	−18.1214	−	0.928231i	−0.675343	−	0.0345931i
$721$	−33.5188			−1.24830
$722$	18.7904	+	18.7904i	0.699308	+	0.699308i
$723$	4.05577	+	6.82832i	0.150836	+	0.253948i
$724$			13.9884i			0.519873i
$725$	7.90174	−	9.86312i	0.293463	−	0.366307i
$726$	7.52603	−	29.5447i	0.279317	−	1.09650i
$727$	17.1314	−	17.1314i	0.635368	−	0.635368i	−0.314041	−	0.949409i	$-0.601683\pi$
$727$	17.1314	−	17.1314i	0.635368	−	0.635368i	0.949409	+	0.314041i	$0.101683\pi$
$728$	3.14738	−	3.14738i	0.116650	−	0.116650i
$729$	26.9257	−	2.00211i	0.997247	−	0.0741523i
$730$	−69.6551	+	33.4482i	−2.57805	+	1.23797i
$731$		−	1.93694i		−	0.0716403i
$732$	14.4774	−	8.59904i	0.535100	−	0.317830i
$733$	24.4852	+	24.4852i	0.904380	+	0.904380i	0.995811	−	0.0914312i	$-0.0291442\pi$
$733$	24.4852	+	24.4852i	0.904380	+	0.904380i	−0.0914312	+	0.995811i	$0.529144\pi$
$734$	−59.5767			−2.19902
$735$	−11.5227	−	7.66755i	−0.425020	−	0.282822i
$736$	32.1784			1.18611
$737$	11.2709	+	11.2709i	0.415169	+	0.415169i
$738$	−2.30383	−	7.81893i	−0.0848052	−	0.287819i
$739$		−	16.5036i		−	0.607094i	−0.952816	−	0.303547i	$-0.901829\pi$
$739$		−	16.5036i		−	0.607094i	0.952816	−	0.303547i	$-0.0981710\pi$
$740$	−17.1932	+	48.9596i	−0.632035	+	1.79979i
$741$	5.35076	+	1.36302i	0.196565	+	0.0500718i
$742$	8.17850	−	8.17850i	0.300242	−	0.300242i
$743$	−22.6644	+	22.6644i	−0.831475	+	0.831475i	−0.987719	−	0.156244i	$-0.950062\pi$
$743$	−22.6644	+	22.6644i	−0.831475	+	0.831475i	0.156244	+	0.987719i	$0.450062\pi$
$744$	1.83655	+	0.467832i	0.0673313	+	0.0171516i
$745$	16.6553	+	34.6843i	0.610203	+	1.27073i
$746$		−	73.2554i		−	2.68207i
$747$	11.4437	+	38.8387i	0.418704	+	1.42103i
$748$	−0.874376	−	0.874376i	−0.0319704	−	0.0319704i
$749$	62.6422			2.28890
$750$	−18.8982	+	36.5509i	−0.690064	+	1.33465i
$751$	21.8657			0.797892			0.398946	−	0.916974i	$-0.369376\pi$
$751$	21.8657			0.797892			0.398946	+	0.916974i	$0.369376\pi$
$752$	−21.8039	−	21.8039i	−0.795107	−	0.795107i
$753$	−38.8721	+	23.0886i	−1.41658	+	0.841395i
$754$		−	6.71881i		−	0.244685i
$755$	−16.6190	−	34.6087i	−0.604827	−	1.25954i
$756$	−31.1417	−	28.9120i	−1.13261	−	1.05152i
$757$	7.98728	−	7.98728i	0.290303	−	0.290303i	−0.546897	−	0.837200i	$-0.684191\pi$
$757$	7.98728	−	7.98728i	0.290303	−	0.290303i	0.837200	+	0.546897i	$0.184191\pi$
$758$	−18.3575	+	18.3575i	−0.666776	+	0.666776i
$759$	2.85708	−	11.2159i	0.103706	−	0.407113i
$760$	2.06584	−	5.88271i	0.0749358	−	0.213388i
$761$		−	37.0428i		−	1.34280i	−0.741095	−	0.671400i	$-0.765693\pi$
$761$		−	37.0428i		−	1.34280i	0.741095	−	0.671400i	$-0.234307\pi$
$762$	−8.81369	−	14.8388i	−0.319286	−	0.537552i
$763$	−40.6381	−	40.6381i	−1.47120	−	1.47120i
$764$	−52.9855			−1.91695
$765$	−1.34094	−	1.48574i	−0.0484819	−	0.0537169i
$766$	−43.9151			−1.58672
$767$	5.49589	+	5.49589i	0.198445	+	0.198445i
$768$	−4.35361	−	7.32977i	−0.157097	−	0.264490i
$769$		−	1.88177i		−	0.0678583i	−0.999424	−	0.0339291i	$-0.989198\pi$
$769$		−	1.88177i		−	0.0678583i	0.999424	−	0.0339291i	$-0.0108021\pi$
$770$	22.9523	−	11.0216i	0.827144	−	0.397192i
$771$	−7.05807	+	27.7076i	−0.254190	+	0.997864i
$772$	1.14760	−	1.14760i	0.0413031	−	0.0413031i
$773$	11.3034	−	11.3034i	0.406556	−	0.406556i	−0.473979	−	0.880536i	$-0.657183\pi$
$773$	11.3034	−	11.3034i	0.406556	−	0.406556i	0.880536	+	0.473979i	$0.157183\pi$
$774$	36.3411	+	19.7994i	1.30625	+	0.711675i
$775$	−3.12619	+	3.90217i	−0.112296	+	0.140170i
$776$		−	8.87783i		−	0.318695i
$777$	44.6820	−	26.5395i	1.60296	−	0.952098i
$778$	−18.5163	−	18.5163i	−0.663843	−	0.663843i
$779$	−3.25857			−0.116750
$780$	2.39994	+	11.9465i	0.0859316	+	0.427755i
$781$	21.9245			0.784520
$782$	1.81762	+	1.81762i	0.0649981	+	0.0649981i
$783$	−13.1247	+	0.487286i	−0.469040	+	0.0174142i
$784$		−	9.66639i		−	0.345228i
$785$	19.9553	+	7.00771i	0.712234	+	0.250116i
$786$	17.4498	+	4.44506i	0.622413	+	0.158550i
$787$	−32.4925	+	32.4925i	−1.15823	+	1.15823i	−0.173375	+	0.984856i	$0.555467\pi$
$787$	−32.4925	+	32.4925i	−1.15823	+	1.15823i	−0.984856	+	0.173375i	$0.944533\pi$
$788$	−22.6802	+	22.6802i	−0.807950	+	0.807950i
$789$	−7.06246	−	1.79905i	−0.251430	−	0.0640479i
$790$	14.5709	+	5.11687i	0.518408	+	0.182050i
$791$			21.2458i			0.755413i
$792$	5.18916	−	1.52897i	0.184389	−	0.0543298i
$793$	3.41947	+	3.41947i	0.121429	+	0.121429i
$794$	−67.3258			−2.38930
$795$	1.27691	+	6.35629i	0.0452875	+	0.225435i
$796$	−32.3627			−1.14707
$797$	−16.8144	−	16.8144i	−0.595596	−	0.595596i	0.343541	−	0.939138i	$-0.388373\pi$
$797$	−16.8144	−	16.8144i	−0.595596	−	0.595596i	−0.939138	+	0.343541i	$0.888373\pi$
$798$	−26.2200	+	15.5737i	−0.928179	+	0.551304i
$799$		−	3.40111i		−	0.120323i
$800$	−39.4399	+	4.35447i	−1.39441	+	0.153954i
$801$	10.2251	−	18.7679i	0.361288	−	0.663130i
$802$	37.0882	−	37.0882i	1.30963	−	1.30963i
$803$	−18.9514	+	18.9514i	−0.668781	+	0.668781i
$804$	10.4002	−	40.8275i	0.366785	−	1.43988i
$805$	−26.5772	+	12.7623i	−0.936723	+	0.449812i
$806$			2.65818i			0.0936304i
$807$	21.6106	+	36.3838i	0.760730	+	1.28077i
$808$	−5.76022	−	5.76022i	−0.202644	−	0.202644i
$809$	22.4780			0.790286			0.395143	−	0.918620i	$-0.370695\pi$
$809$	22.4780			0.790286			0.395143	+	0.918620i	$0.370695\pi$
$810$	41.5827	−	9.97177i	1.46107	−	0.350372i
$811$	−34.1717			−1.19993			−0.599966	−	0.800026i	$-0.704819\pi$
$811$	−34.1717			−1.19993			−0.599966	+	0.800026i	$0.704819\pi$
$812$	14.6162	+	14.6162i	0.512929	+	0.512929i
$813$	−14.8744	−	25.0426i	−0.521668	−	0.878283i
$814$			32.3118i			1.13253i
$815$	−3.34114	+	9.51427i	−0.117035	+	0.333270i
$816$	0.345043	−	1.35452i	0.0120789	−	0.0474178i
$817$	11.6984	−	11.6984i	0.409275	−	0.409275i
$818$	40.4341	−	40.4341i	1.41375	−	1.41375i
$819$	5.83854	−	10.7164i	0.204015	−	0.374462i
$820$	−3.11283	−	6.48240i	−0.108705	−	0.226375i
$821$			14.9152i			0.520543i	0.965535	+	0.260271i	$0.0838121\pi$
$821$			14.9152i			0.520543i	−0.965535	+	0.260271i	$0.916188\pi$
$822$	−23.3382	+	13.8620i	−0.814012	+	0.483493i
$823$	22.7439	+	22.7439i	0.792803	+	0.792803i	0.981949	−	0.189146i	$-0.0605719\pi$
$823$	22.7439	+	22.7439i	0.792803	+	0.792803i	−0.189146	+	0.981949i	$0.560572\pi$
$824$	−11.2790			−0.392922
$825$	−1.98405	+	14.1336i	−0.0690756	+	0.492068i
$826$	−42.9273			−1.49363
$827$	−21.5531	−	21.5531i	−0.749476	−	0.749476i	0.224905	−	0.974381i	$-0.427793\pi$
$827$	−21.5531	−	21.5531i	−0.749476	−	0.749476i	−0.974381	+	0.224905i	$0.927793\pi$
$828$	−29.3455	+	8.64659i	−1.01983	+	0.300490i
$829$		−	26.5630i		−	0.922571i	−0.887252	−	0.461286i	$-0.847388\pi$
$829$		−	26.5630i		−	0.922571i	0.887252	−	0.461286i	$-0.152612\pi$
$830$	27.7585	+	57.8065i	0.963512	+	2.00649i
$831$	−5.03988	−	1.28383i	−0.174831	−	0.0445355i
$832$	−10.1310	+	10.1310i	−0.351229	+	0.351229i
$833$	0.753911	−	0.753911i	0.0261215	−	0.0261215i
$834$	66.8307	+	17.0241i	2.31416	+	0.589495i
$835$	1.46384	−	4.16844i	0.0506582	−	0.144255i
$836$		−	10.5618i		−	0.365288i
$837$	5.19257	−	0.192786i	0.179482	−	0.00666366i
$838$	−22.6377	−	22.6377i	−0.782006	−	0.782006i
$839$	−5.16183			−0.178206			−0.0891031	−	0.996022i	$-0.528400\pi$
$839$	−5.16183			−0.178206			−0.0891031	+	0.996022i	$0.528400\pi$
$840$	−11.4723	−	7.63402i	−0.395831	−	0.263399i
$841$	−22.6113			−0.779698
$842$	−35.5426	−	35.5426i	−1.22488	−	1.22488i
$843$	12.6293	−	7.50132i	0.434975	−	0.258359i
$844$		−	59.0502i		−	2.03259i
$845$	23.0497	−	11.0684i	0.792932	−	0.380764i
$846$	63.8120	+	34.7661i	2.19390	+	1.19528i
$847$	−19.0476	+	19.0476i	−0.654485	+	0.654485i
$848$	−3.20176	+	3.20176i	−0.109949	+	0.109949i
$849$	4.11030	−	16.1356i	0.141065	−	0.553774i
$850$	−2.47376	−	1.98183i	−0.0848493	−	0.0679761i
$851$		−	37.4148i		−	1.28256i
$852$	−29.5941	−	49.8248i	−1.01388	−	1.70697i
$853$	−6.34767	−	6.34767i	−0.217340	−	0.217340i	0.590036	−	0.807377i	$-0.299113\pi$
$853$	−6.34767	−	6.34767i	−0.217340	−	0.217340i	−0.807377	+	0.590036i	$0.799113\pi$
$854$	−26.7088			−0.913957
$855$	0.874484	−	17.0721i	0.0299067	−	0.583853i
$856$	21.0790			0.720465
$857$	20.8116	+	20.8116i	0.710910	+	0.710910i	0.966726	−	0.255816i	$-0.0823440\pi$
$857$	20.8116	+	20.8116i	0.710910	+	0.710910i	−0.255816	+	0.966726i	$0.582344\pi$
$858$	3.87479	+	6.52362i	0.132283	+	0.222713i
$859$		−	48.1793i		−	1.64386i	−0.569591	−	0.821929i	$-0.692898\pi$
$859$		−	48.1793i		−	1.64386i	0.569591	−	0.821929i	$-0.307102\pi$
$860$	34.4473	+	12.0969i	1.17464	+	0.412501i
$861$	−1.77781	+	6.97908i	−0.0605876	+	0.237846i
$862$	−4.35282	+	4.35282i	−0.148258	+	0.148258i
$863$	−38.9980	+	38.9980i	−1.32751	+	1.32751i	−0.419966	+	0.907540i	$0.637958\pi$
$863$	−38.9980	+	38.9980i	−1.32751	+	1.32751i	−0.907540	+	0.419966i	$0.862042\pi$
$864$	30.2201	+	28.0565i	1.02811	+	0.954501i
$865$	−30.4427	−	10.6906i	−1.03508	−	0.363492i
$866$		−	10.2761i		−	0.349197i
$867$	−25.1834	+	14.9580i	−0.855272	+	0.508000i
$868$	−5.78265	−	5.78265i	−0.196276	−	0.196276i
$869$	5.35655			0.181708
$870$	−20.3934	+	4.09682i	−0.691400	+	0.138895i
$871$	12.0996			0.409981
$872$	−13.6746	−	13.6746i	−0.463081	−	0.463081i
$873$	−6.87952	−	23.3483i	−0.232837	−	0.790219i
$874$			21.9556i			0.742658i
$875$	30.8476	−	19.2388i	1.04284	−	0.650388i
$876$	68.6493	+	17.4873i	2.31944	+	0.590841i
$877$	−5.40703	+	5.40703i	−0.182582	+	0.182582i	−0.792480	−	0.609898i	$-0.791211\pi$
$877$	−5.40703	+	5.40703i	−0.182582	+	0.182582i	0.609898	+	0.792480i	$0.291211\pi$
$878$	−33.9006	+	33.9006i	−1.14409	+	1.14409i
$879$	−28.3474	−	7.22106i	−0.956136	−	0.243560i
$880$	−8.98548	+	4.31480i	−0.302900	+	0.145452i
$881$			25.5051i			0.859289i	0.902998	+	0.429644i	$0.141361\pi$
$881$			25.5051i			0.859289i	−0.902998	+	0.429644i	$0.858639\pi$
$882$	6.43849	+	21.8515i	0.216795	+	0.735777i
$883$	17.5033	+	17.5033i	0.589031	+	0.589031i	0.937369	−	0.348338i	$-0.113254\pi$
$883$	17.5033	+	17.5033i	0.589031	+	0.589031i	−0.348338	+	0.937369i	$0.613254\pi$
$884$	−0.938668			−0.0315708
$885$	13.3303	−	20.0326i	0.448094	−	0.673389i
$886$	11.6793			0.392375
$887$	5.17231	+	5.17231i	0.173669	+	0.173669i	0.788589	−	0.614920i	$-0.210812\pi$
$887$	5.17231	+	5.17231i	0.173669	+	0.173669i	−0.614920	+	0.788589i	$0.710812\pi$
$888$	15.0354	−	8.93047i	0.504555	−	0.299687i
$889$			15.2489i			0.511432i
$890$	11.2154	−	31.9371i	0.375940	−	1.07053i
$891$	12.4624	−	8.04227i	0.417507	−	0.269426i
$892$	48.5879	−	48.5879i	1.62684	−	1.62684i
$893$	20.5414	−	20.5414i	0.687392	−	0.687392i
$894$	15.6324	−	61.3677i	0.522827	−	2.05244i
$895$	−9.50620	−	19.7964i	−0.317757	−	0.661722i
$896$		−	27.5206i		−	0.919398i
$897$	−4.48674	−	7.55390i	−0.149808	−	0.252217i
$898$	−4.64261	−	4.64261i	−0.154926	−	0.154926i
$899$	−2.52760			−0.0843001
$900$	34.7976	−	14.5689i	1.15992	−	0.485630i
$901$	−0.499429			−0.0166384
$902$	−3.16627	−	3.16627i	−0.105425	−	0.105425i
$903$	−18.6728	−	31.4376i	−0.621391	−	1.04618i
$904$			7.14916i			0.237778i
$905$	5.38375	+	11.2115i	0.178962	+	0.372684i
$906$	−15.5984	+	61.2339i	−0.518221	+	2.03436i
$907$	−37.4130	+	37.4130i	−1.24228	+	1.24228i	−0.283223	+	0.959054i	$0.591404\pi$
$907$	−37.4130	+	37.4130i	−1.24228	+	1.24228i	−0.959054	+	0.283223i	$0.908596\pi$
$908$	46.3122	−	46.3122i	1.53692	−	1.53692i
$909$	−19.6128	−	10.6855i	−0.650515	−	0.354414i
$910$	6.40396	−	18.2360i	0.212289	−	0.604518i
$911$		−	29.6294i		−	0.981666i	−0.871254	−	0.490833i	$-0.836693\pi$
$911$		−	29.6294i		−	0.981666i	0.871254	−	0.490833i	$-0.163307\pi$
$912$	10.2647	−	6.09688i	0.339900	−	0.201888i
$913$	15.7277	+	15.7277i	0.520511	+	0.520511i
$914$	26.4706			0.875568
$915$	8.29396	−	12.4640i	0.274190	−	0.412048i
$916$	−9.11729			−0.301244
$917$	−11.2500	−	11.2500i	−0.371508	−	0.371508i
$918$	0.122216	+	3.29180i	0.00403372	+	0.108646i
$919$		−	20.6711i		−	0.681878i	−0.940085	−	0.340939i	$-0.889255\pi$
$919$		−	20.6711i		−	0.681878i	0.940085	−	0.340939i	$-0.110745\pi$
$920$	−8.94317	+	4.29449i	−0.294848	+	0.141585i
$921$	28.9517	+	7.37498i	0.953991	+	0.243014i
$922$	32.8612	−	32.8612i	1.08223	−	1.08223i
$923$	11.7683	−	11.7683i	0.387358	−	0.387358i
$924$	−22.6209	−	5.76231i	−0.744173	−	0.189566i
$925$	5.06307	+	45.8579i	0.166473	+	1.50780i
$926$			26.5934i			0.873915i
$927$	−29.6632	+	8.74022i	−0.974269	+	0.287066i
$928$	−14.1837	−	14.1837i	−0.465603	−	0.465603i
$929$	41.0325			1.34623			0.673116	−	0.739537i	$-0.264955\pi$
$929$	41.0325			1.34623			0.673116	+	0.739537i	$0.264955\pi$
$930$	8.06828	−	1.62084i	0.264569	−	0.0531493i
$931$	9.10668			0.298459
$932$	23.9148	+	23.9148i	0.783356	+	0.783356i
$933$	11.1620	−	6.62982i	0.365428	−	0.217051i
$934$			44.5024i			1.45616i
$935$	−1.03733	−	0.364280i	−0.0339243	−	0.0119132i
$936$	1.96466	−	3.60605i	0.0642168	−	0.117868i
$937$	16.1114	−	16.1114i	0.526335	−	0.526335i	−0.393143	−	0.919478i	$-0.628612\pi$
$937$	16.1114	−	16.1114i	0.526335	−	0.526335i	0.919478	+	0.393143i	$0.128612\pi$
$938$	−47.2540	+	47.2540i	−1.54290	+	1.54290i
$939$	3.97583	−	15.6078i	0.129746	−	0.509340i
$940$	60.4866	+	21.2411i	1.97285	+	0.692810i
$941$		−	31.3149i		−	1.02084i	−0.859926	−	0.510419i	$-0.829490\pi$
$941$		−	31.3149i		−	1.02084i	0.859926	−	0.510419i	$-0.170510\pi$
$942$	−17.7769	−	29.9293i	−0.579202	−	0.975148i
$943$	3.66633	+	3.66633i	0.119392	+	0.119392i
$944$	16.8054			0.546969
$945$	−36.0872	−	11.1871i	−1.17392	−	0.363917i
$946$	22.7341			0.739149
$947$	31.5744	+	31.5744i	1.02603	+	1.02603i	0.999652	+	0.0263795i	$0.00839784\pi$
$947$	31.5744	+	31.5744i	1.02603	+	1.02603i	0.0263795	+	0.999652i	$0.491602\pi$
$948$	−7.23037	−	12.1731i	−0.234831	−	0.395364i
$949$			20.3449i			0.660423i
$950$	−2.97108	−	26.9101i	−0.0963947	−	0.873078i
$951$	8.31225	−	32.6311i	0.269543	−	1.05814i
$952$	0.750614	−	0.750614i	0.0243275	−	0.0243275i
$953$	5.70484	−	5.70484i	0.184798	−	0.184798i	−0.608645	−	0.793443i	$-0.708287\pi$
$953$	5.70484	−	5.70484i	0.184798	−	0.184798i	0.793443	+	0.608645i	$0.208287\pi$
$954$	5.10517	−	9.37035i	0.165286	−	0.303376i
$955$	−42.4674	+	20.3927i	−1.37421	+	0.659893i
$956$			54.0227i			1.74722i
$957$	−6.20315	+	3.68444i	−0.200519	+	0.119101i
$958$	15.8950	+	15.8950i	0.513544	+	0.513544i
$959$	23.9832			0.774458
$960$	36.9276	+	24.5728i	1.19183	+	0.793084i
$961$	1.00000			0.0322581
$962$	17.3438	+	17.3438i	0.559187	+	0.559187i
$963$	55.4368	−	16.3343i	1.78642	−	0.526367i
$964$		−	11.5318i		−	0.371416i
$965$	0.478110	−	1.36147i	0.0153909	−	0.0438274i
$966$	47.0236	+	11.9785i	1.51296	+	0.385402i
$967$	−29.9783	+	29.9783i	−0.964038	+	0.964038i	−0.999375	−	0.0353373i	$-0.988749\pi$
$967$	−29.9783	+	29.9783i	−0.964038	+	0.964038i	0.0353373	+	0.999375i	$0.488749\pi$
$968$	−6.40949	+	6.40949i	−0.206009	+	0.206009i
$969$	1.27609	+	0.325064i	0.0409940	+	0.0104426i
$970$	−16.6873	−	34.7510i	−0.535798	−	1.11579i
$971$			10.4338i			0.334835i	0.985886	+	0.167418i	$0.0535429\pi$
$971$			10.4338i			0.334835i	−0.985886	+	0.167418i	$0.946457\pi$
$972$	−35.0986	−	17.4660i	−1.12579	−	0.560224i
$973$	−43.0862	−	43.0862i	−1.38128	−	1.38128i
$974$	56.7503			1.81840
$975$	6.52144	+	8.65137i	0.208853	+	0.277066i
$976$	10.4561			0.334691
$977$	10.4553	+	10.4553i	0.334495	+	0.334495i	0.854291	−	0.519796i	$-0.173992\pi$
$977$	10.4553	+	10.4553i	0.334495	+	0.334495i	−0.519796	+	0.854291i	$0.673992\pi$
$978$	14.2697	−	8.47567i	0.456294	−	0.271022i
$979$		−	11.7407i		−	0.375235i
$980$	8.69939	+	18.1163i	0.277892	+	0.578703i
$981$	−46.5603	−	25.3670i	−1.48655	−	0.809907i
$982$	25.9715	−	25.9715i	0.828785	−	0.828785i
$983$	−22.0220	+	22.0220i	−0.702394	+	0.702394i	−0.964924	−	0.262530i	$-0.915443\pi$
$983$	−22.0220	+	22.0220i	−0.702394	+	0.702394i	0.262530	+	0.964924i	$0.415443\pi$
$984$	−0.598230	+	2.34845i	−0.0190709	+	0.0748658i
$985$	−9.44897	+	26.9070i	−0.301069	+	0.857329i
$986$		−	1.60236i		−	0.0510294i
$987$	−32.7878	−	55.2018i	−1.04365	−	1.75709i
$988$	−5.66921	−	5.66921i	−0.180361	−	0.180361i
$989$	−26.3245			−0.837071
$990$	17.4382	−	15.7388i	0.554224	−	0.500212i
$991$	−5.21618			−0.165698			−0.0828488	−	0.996562i	$-0.526402\pi$
$991$	−5.21618			−0.165698			−0.0828488	+	0.996562i	$0.526402\pi$
$992$	5.61153	+	5.61153i	0.178166	+	0.178166i
$993$	−7.91441	−	13.3247i	−0.251156	−	0.422848i
$994$			91.9198i			2.91552i
$995$	−25.9384	+	12.4556i	−0.822303	+	0.394868i
$996$	14.5127	−	56.9718i	0.459851	−	1.80522i
$997$	−0.518622	+	0.518622i	−0.0164249	+	0.0164249i	−0.715272	−	0.698847i	$-0.753697\pi$
$997$	−0.518622	+	0.518622i	−0.0164249	+	0.0164249i	0.698847	+	0.715272i	$0.253697\pi$
$998$	49.3308	−	49.3308i	1.56154	−	1.56154i
$999$	32.6221	−	35.1378i	1.03212	−	1.11171i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.k.a.218.27	yes	60
3.2	odd	2	inner	465.2.k.a.218.4	yes	60
5.2	odd	4	inner	465.2.k.a.32.4	✓	60
15.2	even	4	inner	465.2.k.a.32.27	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.4	✓	60	5.2	odd	4	inner
465.2.k.a.32.27	yes	60	15.2	even	4	inner
465.2.k.a.218.4	yes	60	3.2	odd	2	inner
465.2.k.a.218.27	yes	60	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.50249 + 1.50249i) q^{2} +(-0.884514 - 1.48917i) q^{3} +2.51495i q^{4} +(0.967939 + 2.01571i) q^{5} +(0.908494 - 3.56644i) q^{6} +(-2.29931 + 2.29931i) q^{7} +(-0.773713 + 0.773713i) q^{8} +(-1.43527 + 2.63439i) q^{9} +(-1.57427 + 4.48291i) q^{10} +1.64801i q^{11} +(3.74520 - 2.22451i) q^{12} +(0.884592 + 0.884592i) q^{13} -6.90938 q^{14} +(2.14559 - 3.22435i) q^{15} +2.70492 q^{16} +(0.210964 + 0.210964i) q^{17} +(-6.11462 + 1.80166i) q^{18} +2.54829i q^{19} +(-5.06942 + 2.43432i) q^{20} +(5.45784 + 1.39030i) q^{21} +(-2.47611 + 2.47611i) q^{22} +(2.86717 - 2.86717i) q^{23} +(1.83655 + 0.467832i) q^{24} +(-3.12619 + 3.90217i) q^{25} +2.65818i q^{26} +(5.19257 - 0.192786i) q^{27} +(-5.78265 - 5.78265i) q^{28} -2.52760 q^{29} +(8.06828 - 1.62084i) q^{30} +1.00000 q^{31} +(5.61153 + 5.61153i) q^{32} +(2.45417 - 1.45768i) q^{33} +0.633944i q^{34} +(-6.86033 - 2.40915i) q^{35} +(-6.62536 - 3.60964i) q^{36} +(6.52469 - 6.52469i) q^{37} +(-3.82879 + 3.82879i) q^{38} +(0.534876 - 2.09974i) q^{39} +(-2.30849 - 0.810675i) q^{40} +1.27873i q^{41} +(6.11144 + 10.2893i) q^{42} +(-4.59068 - 4.59068i) q^{43} -4.14466 q^{44} +(-6.69942 - 0.343165i) q^{45} +8.61579 q^{46} +(-8.06085 - 8.06085i) q^{47} +(-2.39254 - 4.02809i) q^{48} -3.57364i q^{49} +(-10.5600 + 1.16591i) q^{50} +(0.127562 - 0.500764i) q^{51} +(-2.22471 + 2.22471i) q^{52} +(-1.18368 + 1.18368i) q^{53} +(8.09145 + 7.51213i) q^{54} +(-3.32191 + 1.59517i) q^{55} -3.55801i q^{56} +(3.79485 - 2.25400i) q^{57} +(-3.79769 - 3.79769i) q^{58} +6.21291 q^{59} +(8.10910 + 5.39605i) q^{60} +3.86559 q^{61} +(1.50249 + 1.50249i) q^{62} +(-2.75714 - 9.35740i) q^{63} +11.4527i q^{64} +(-0.926851 + 2.63931i) q^{65} +(5.87752 + 1.49720i) q^{66} +(6.83911 - 6.83911i) q^{67} +(-0.530566 + 0.530566i) q^{68} +(-6.80576 - 1.73366i) q^{69} +(-6.68786 - 13.9273i) q^{70} -13.3036i q^{71} +(-0.927772 - 3.14875i) q^{72} +(11.4996 + 11.4996i) q^{73} +19.6066 q^{74} +(8.57617 + 1.20391i) q^{75} -6.40884 q^{76} +(-3.78928 - 3.78928i) q^{77} +(3.95849 - 2.35120i) q^{78} -3.25032i q^{79} +(2.61819 + 5.45233i) q^{80} +(-4.88000 - 7.56212i) q^{81} +(-1.92127 + 1.92127i) q^{82} +(9.54347 - 9.54347i) q^{83} +(-3.49653 + 13.7262i) q^{84} +(-0.221043 + 0.629444i) q^{85} -13.7949i q^{86} +(2.23569 + 3.76403i) q^{87} +(-1.27508 - 1.27508i) q^{88} -7.12419 q^{89} +(-9.55021 - 10.5814i) q^{90} -4.06790 q^{91} +(7.21080 + 7.21080i) q^{92} +(-0.884514 - 1.48917i) q^{93} -24.2227i q^{94} +(-5.13662 + 2.46659i) q^{95} +(3.39306 - 13.3200i) q^{96} +(-5.73716 + 5.73716i) q^{97} +(5.36936 - 5.36936i) q^{98} +(-4.34149 - 2.36534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{6} - 32 q^{10} + 4 q^{13} + 20 q^{15} - 60 q^{16} - 46 q^{18} - 4 q^{21} + 8 q^{22} - 8 q^{25} - 6 q^{27} + 112 q^{28} + 54 q^{30} + 60 q^{31} - 30 q^{33} - 4 q^{36} - 36 q^{37} - 36 q^{40}+ \cdots - 8 q^{97}+O(q^{100}) \) 60 * q - 4 * q^6 - 32 * q^10 + 4 * q^13 + 20 * q^15 - 60 * q^16 - 46 * q^18 - 4 * q^21 + 8 * q^22 - 8 * q^25 - 6 * q^27 + 112 * q^28 + 54 * q^30 + 60 * q^31 - 30 * q^33 - 4 * q^36 - 36 * q^37 - 36 * q^40 + 44 * q^42 + 16 * q^43 + 14 * q^45 + 40 * q^46 - 104 * q^48 - 48 * q^51 - 12 * q^52 - 48 * q^55 + 42 * q^57 + 80 * q^58 + 60 * q^60 - 8 * q^61 - 10 * q^63 - 24 * q^66 - 88 * q^67 - 84 * q^70 + 84 * q^72 + 60 * q^73 + 14 * q^75 + 72 * q^76 - 152 * q^78 - 132 * q^81 - 60 * q^82 - 16 * q^85 + 34 * q^87 + 124 * q^88 + 190 * q^90 + 64 * q^91 - 88 * q^96 - 8 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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