LMFDB - Embedded newform 465.2.k.a.218.4

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			218.4
Character	$\chi$	$=$	465.218
Dual form			465.2.k.a.32.4

$q$-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} +(-1.48917 - 0.884514i) 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} +(2.22451 - 3.74520i) q^{12} +(0.884592 + 0.884592i) q^{13} +6.90938 q^{14} +(-0.341496 + 3.85790i) q^{15} +2.70492 q^{16} +(-0.210964 - 0.210964i) q^{17} +(1.80166 - 6.11462i) 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} +(0.192786 - 5.19257i) q^{27} +(-5.78265 - 5.78265i) q^{28} +2.52760 q^{29} +(6.30955 - 5.28336i) q^{30} +1.00000 q^{31} +(-5.61153 - 5.61153i) q^{32} +(-1.45768 + 2.45417i) 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} +(-10.2893 - 6.11144i) q^{42} +(-4.59068 - 4.59068i) q^{43} +4.14466 q^{44} +(3.92091 - 5.44302i) q^{45} +8.61579 q^{46} +(8.06085 + 8.06085i) q^{47} +(-4.02809 - 2.39254i) 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} +(2.25400 - 3.79485i) q^{57} +(-3.79769 - 3.79769i) q^{58} -6.21291 q^{59} +(-9.70244 - 0.858847i) q^{60} +3.86559 q^{61} +(-1.50249 - 1.50249i) q^{62} +(-9.35740 - 2.75714i) 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} +(3.14875 + 0.927772i) q^{72} +(11.4996 + 11.4996i) q^{73} -19.6066 q^{74} +(8.10696 - 3.04585i) q^{75} -6.40884 q^{76} +(3.78928 + 3.78928i) q^{77} +(-2.35120 + 3.95849i) 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} +(-3.76403 - 2.23569i) q^{87} +(-1.27508 - 1.27508i) q^{88} +7.12419 q^{89} +(-14.0692 + 2.28695i) q^{90} -4.06790 q^{91} +(-7.21080 - 7.21080i) q^{92} +(-1.48917 - 0.884514i) 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	$-0.979454\pi$
$2$	−1.50249	−	1.50249i	−1.06242	−	1.06242i	−0.0645035	−	0.997917i	$-0.520546\pi$
$3$	−1.48917	−	0.884514i	−0.859774	−	0.510674i
$3$	−1.48917	−	0.884514i	−0.859774	−	0.510674i
$4$			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	$-0.920080\pi$
$11$		−	1.64801i		−	0.496893i	0.968646	−	0.248446i	$-0.0799200\pi$
$12$	2.22451	−	3.74520i	0.642161	−	1.08115i
$13$	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
$15$	−0.341496	+	3.85790i	−0.0881739	+	0.996105i
$16$	2.70492			0.676229
$17$	−0.210964	−	0.210964i	−0.0511664	−	0.0511664i	0.681061	−	0.732227i	$-0.261519\pi$
$17$	−0.210964	−	0.210964i	−0.0511664	−	0.0511664i	−0.732227	+	0.681061i	$0.761519\pi$
$18$	1.80166	−	6.11462i	0.424656	−	1.44123i
$19$			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	−0.939739	−	0.341893i	$-0.888932\pi$
$23$	−2.86717	+	2.86717i	−0.597846	+	0.597846i	0.341893	+	0.939739i	$0.388932\pi$
$24$	−1.83655	+	0.467832i	−0.374885	+	0.0954959i
$25$	−3.12619	+	3.90217i	−0.625237	+	0.780435i
$26$		−	2.65818i		−	0.521312i
$27$	0.192786	−	5.19257i	0.0371017	−	0.999311i
$28$	−5.78265	−	5.78265i	−1.09282	−	1.09282i
$29$	2.52760			0.469363			0.234682	−	0.972072i	$-0.424595\pi$
$29$	2.52760			0.469363			0.234682	+	0.972072i	$0.424595\pi$
$30$	6.30955	−	5.28336i	1.15196	−	0.964605i
$31$	1.00000			0.179605
$31$	1.00000			0.179605
$32$	−5.61153	−	5.61153i	−0.991989	−	0.991989i
$33$	−1.45768	+	2.45417i	−0.253750	+	0.427216i
$34$			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	$-0.968163\pi$
$41$		−	1.27873i		−	0.199704i	0.995002	−	0.0998518i	$-0.0318369\pi$
$42$	−10.2893	−	6.11144i	−1.58767	−	0.943016i
$43$	−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
$45$	3.92091	−	5.44302i	0.584495	−	0.811397i
$46$	8.61579			1.27033
$47$	8.06085	+	8.06085i	1.17580	+	1.17580i	0.980805	+	0.194991i	$0.0624679\pi$
$47$	8.06085	+	8.06085i	1.17580	+	1.17580i	0.194991	+	0.980805i	$0.437532\pi$
$48$	−4.02809	−	2.39254i	−0.581404	−	0.345333i
$49$		−	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	−0.621122	−	0.783714i	$-0.713323\pi$
$53$	1.18368	−	1.18368i	0.162591	−	0.162591i	0.783714	+	0.621122i	$0.213323\pi$
$54$	−8.09145	+	7.51213i	−1.10111	+	1.02227i
$55$	−3.32191	+	1.59517i	−0.447926	+	0.215093i
$56$			3.55801i			0.475459i
$57$	2.25400	−	3.79485i	0.298550	−	0.502640i
$58$	−3.79769	−	3.79769i	−0.498661	−	0.498661i
$59$	−6.21291			−0.808852			−0.404426	−	0.914571i	$-0.632529\pi$
$59$	−6.21291			−0.808852			−0.404426	+	0.914571i	$0.632529\pi$
$60$	−9.70244	−	0.858847i	−1.25258	−	0.110877i
$61$	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
$63$	−9.35740	−	2.75714i	−1.17892	−	0.347367i
$64$			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	$0.289621\pi$
$71$			13.3036i			1.57885i	−0.613846	+	0.789426i	$0.710379\pi$
$72$	3.14875	+	0.927772i	0.371083	+	0.109339i
$73$	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
$75$	8.10696	−	3.04585i	0.936111	−	0.351705i
$76$	−6.40884			−0.735144
$77$	3.78928	+	3.78928i	0.431828	+	0.431828i
$78$	−2.35120	+	3.95849i	−0.266221	+	0.448211i
$79$		−	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	$0.515514\pi$
$83$	−9.54347	+	9.54347i	−1.04753	+	1.04753i	−0.998812	+	0.0487197i	$0.984486\pi$
$84$	3.49653	+	13.7262i	0.381503	+	1.49765i
$85$	−0.221043	+	0.629444i	−0.0239755	+	0.0682728i
$86$			13.7949i			1.48754i
$87$	−3.76403	−	2.23569i	−0.403546	−	0.239692i
$88$	−1.27508	−	1.27508i	−0.135924	−	0.135924i
$89$	7.12419			0.755163			0.377581	−	0.925976i	$-0.376756\pi$
$89$	7.12419			0.755163			0.377581	+	0.925976i	$0.376756\pi$
$90$	−14.0692	+	2.28695i	−1.48303	+	0.241066i
$91$	−4.06790			−0.426432
$92$	−7.21080	−	7.21080i	−0.751778	−	0.751778i
$93$	−1.48917	−	0.884514i	−0.154420	−	0.0917198i
$94$		−	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	$-0.879221\pi$
$101$		−	7.44491i		−	0.740796i	0.928873	−	0.370398i	$-0.120779\pi$
$102$	0.560732	−	0.944052i	0.0555208	−	0.0934751i
$103$	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
$105$	−8.08529	−	9.65570i	−0.789044	−	0.942300i
$106$	−3.55694			−0.345480
$107$	13.6220	+	13.6220i	1.31689	+	1.31689i	0.916228	+	0.400658i	$0.131218\pi$
$107$	13.6220	+	13.6220i	1.31689	+	1.31689i	0.400658	+	0.916228i	$0.368782\pi$
$108$	13.0591	+	0.484848i	1.25661	+	0.0466545i
$109$			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	−0.890195	−	0.455579i	$-0.849432\pi$
$113$	−4.62004	+	4.62004i	−0.434617	+	0.434617i	0.455579	+	0.890195i	$0.349432\pi$
$114$	−9.08834	+	2.31511i	−0.851201	+	0.216830i
$115$	8.55463	+	3.00414i	0.797723	+	0.280138i
$116$			6.35679i			0.590213i
$117$	−1.06073	+	3.59999i	−0.0980644	+	0.332819i
$118$	9.33483	+	9.33483i	0.859341	+	0.859341i
$119$	0.970145			0.0889330
$120$	2.72069	+	3.24913i	0.248363	+	0.296603i
$121$	8.28407			0.753098
$122$	−5.80801	−	5.80801i	−0.525832	−	0.525832i
$123$	−1.13105	+	1.90424i	−0.101983	+	0.171700i
$124$			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	$-0.931435\pi$
$131$		−	4.89277i		−	0.427484i	0.976890	−	0.213742i	$-0.0685651\pi$
$132$	−6.17212	−	3.66601i	−0.537214	−	0.319085i
$133$	−5.85931	−	5.85931i	−0.508067	−	0.508067i
$134$	−20.5514			−1.77537
$135$	−10.6533	+	4.63750i	−0.916893	+	0.399132i
$136$	−0.326452			−0.0279930
$137$	5.21531	+	5.21531i	0.445574	+	0.445574i	0.893880	−	0.448306i	$-0.147973\pi$
$137$	5.21531	+	5.21531i	0.445574	+	0.445574i	−0.448306	+	0.893880i	$0.647973\pi$
$138$	−12.8304	−	7.62078i	−1.09220	−	0.648724i
$139$			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
$147$	−3.16093	+	5.32177i	−0.260709	+	0.438932i
$148$	16.4093	+	16.4093i	1.34884	+	1.34884i
$149$	−17.2070			−1.40965			−0.704825	−	0.709381i	$-0.748975\pi$
$149$	−17.2070			−1.40965			−0.704825	+	0.709381i	$0.748975\pi$
$150$	−16.7570	−	7.60426i	−1.36820	−	0.620885i
$151$	−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
$153$	0.252971	−	0.858553i	0.0204515	−	0.0694099i
$154$		−	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
$162$	18.6942	−	4.02986i	1.46875	−	0.316616i
$163$	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
$165$	6.35784	+	0.562788i	0.494957	+	0.0438130i
$166$	28.6779			2.22584
$167$	1.39709	+	1.39709i	0.108110	+	0.108110i	0.759093	−	0.650982i	$-0.225643\pi$
$167$	1.39709	+	1.39709i	0.108110	+	0.108110i	−0.650982	+	0.759093i	$0.725643\pi$
$168$	3.14711	−	5.29849i	0.242805	−	0.408787i
$169$		−	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	−0.203369	−	0.979102i	$-0.565189\pi$
$173$	10.2032	−	10.2032i	0.775734	−	0.775734i	0.979102	+	0.203369i	$0.0651890\pi$
$174$	2.29631	+	9.01453i	0.174083	+	0.683389i
$175$	−1.78423	−	16.1604i	−0.134875	−	1.22161i
$176$		−	4.45772i		−	0.336013i
$177$	9.25209	+	5.49540i	0.695430	+	0.413060i
$178$	−10.7040	−	10.7040i	−0.802301	−	0.802301i
$179$	9.82107			0.734061			0.367031	−	0.930209i	$-0.380374\pi$
$179$	9.82107			0.734061			0.367031	+	0.930209i	$0.380374\pi$
$180$	13.6889	+	9.86091i	1.02031	+	0.734989i
$181$	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
$183$	−5.75653	−	3.41917i	−0.425535	−	0.252752i
$184$			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	$-0.724110\pi$
$191$		−	21.0682i		−	1.52444i	0.647319	−	0.762220i	$-0.275890\pi$
$192$	10.1301	−	17.0551i	0.731076	−	1.23084i
$193$	−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
$195$	−3.71475	+	3.11058i	−0.266019	+	0.222753i
$196$	8.98754			0.641967
$197$	−9.01815	−	9.01815i	−0.642517	−	0.642517i	0.308657	−	0.951173i	$-0.400121\pi$
$197$	−9.01815	−	9.01815i	−0.642517	−	0.642517i	−0.951173	+	0.308657i	$0.900121\pi$
$198$	−10.0769	−	2.96915i	−0.716137	−	0.211008i
$199$			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
$207$	−11.6684	−	3.43807i	−0.811010	−	0.238962i
$208$	2.39275	+	2.39275i	0.165907	+	0.165907i
$209$	4.19961			0.290493
$210$	−2.35952	+	26.6557i	−0.162823	+	1.83942i
$211$	−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
$213$	11.7672	−	19.8114i	0.806279	−	1.35746i
$214$		−	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
$222$	29.1976	+	17.3423i	1.95961	+	1.16394i
$223$	−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
$225$	−14.7668	−	2.63491i	−0.984451	−	0.175661i
$226$	13.8831			0.923492
$227$	18.4147	+	18.4147i	1.22223	+	1.22223i	0.966838	+	0.255391i	$0.0822042\pi$
$227$	18.4147	+	18.4147i	1.22223	+	1.22223i	0.255391	+	0.966838i	$0.417796\pi$
$228$	9.54387	+	5.66871i	0.632058	+	0.375419i
$229$			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	−0.946287	−	0.323328i	$-0.895198\pi$
$233$	−9.50905	+	9.50905i	−0.622959	+	0.622959i	0.323328	+	0.946287i	$0.395198\pi$
$234$	7.00268	−	3.81521i	0.457779	−	0.249408i
$235$	8.44594	−	24.0508i	0.550952	−	1.56890i
$236$		−	15.6252i		−	1.01711i
$237$	−2.87495	+	4.84029i	−0.186748	+	0.314410i
$238$	−1.45763	−	1.45763i	−0.0944843	−	0.0944843i
$239$	−21.4806			−1.38947			−0.694733	−	0.719268i	$-0.744477\pi$
$239$	−21.4806			−1.38947			−0.694733	+	0.719268i	$0.744477\pi$
$240$	−0.923718	+	10.4353i	−0.0596257	+	0.673595i
$241$	−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
$243$	13.9560	−	6.94488i	0.895275	−	0.445514i
$244$			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	$0.308154\pi$
$251$			26.1031i			1.64762i	−0.566870	+	0.823808i	$0.691846\pi$
$252$	6.93408	−	23.5334i	0.436806	−	1.48247i
$253$	4.72511	+	4.72511i	0.297065	+	0.297065i
$254$	−9.96444			−0.625225
$255$	0.885923	−	0.741836i	0.0554787	−	0.0464556i
$256$	4.92204			0.307628
$257$	11.6728	+	11.6728i	0.728130	+	0.728130i	0.970247	−	0.242117i	$-0.0778418\pi$
$257$	11.6728	+	11.6728i	0.728130	+	0.728130i	−0.242117	+	0.970247i	$0.577842\pi$
$258$	12.2018	−	20.5430i	0.759650	−	1.27895i
$259$			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	−0.792864	−	0.609398i	$-0.791411\pi$
$263$	−2.97531	+	2.97531i	−0.183466	+	0.183466i	0.609398	+	0.792864i	$0.291411\pi$
$264$	0.770991	+	3.02665i	0.0474512	+	0.186277i
$265$	−3.53169	−	1.24023i	−0.216950	−	0.0761866i
$266$			17.6071i			1.07956i
$267$	−10.6091	−	6.30144i	−0.649269	−	0.385642i
$268$	17.2000	+	17.2000i	1.05066	+	1.05066i
$269$	24.4322			1.48966			0.744829	−	0.667255i	$-0.232531\pi$
$269$	24.4322			1.48966			0.744829	+	0.667255i	$0.232531\pi$
$270$	22.9743	+	9.03875i	1.39817	+	0.550081i
$271$	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
$273$	6.05780	+	3.59811i	0.366635	+	0.217768i
$274$		−	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	$-0.918596\pi$
$281$		−	8.48072i		−	0.505917i	0.967477	−	0.252959i	$-0.0814037\pi$
$282$	−21.4253	+	36.0718i	−1.27586	+	2.14804i
$283$	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
$285$	−9.83106	−	0.870232i	−0.582342	−	0.0515481i
$286$	−4.38070			−0.259036
$287$	2.94019	+	2.94019i	0.173554	+	0.173554i
$288$	6.72889	−	22.8370i	0.396503	−	1.34568i
$289$		−	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	−0.963910	−	0.266229i	$-0.914222\pi$
$293$	−11.9424	+	11.9424i	−0.697681	+	0.697681i	0.266229	+	0.963910i	$0.414222\pi$
$294$	12.7452	−	3.24663i	0.743313	−	0.189347i
$295$	6.01372	+	12.5234i	0.350132	+	0.729142i
$296$		−	10.0965i		−	0.586846i
$297$	−8.55740	−	0.317713i	−0.496551	−	0.0184356i
$298$	25.8533	+	25.8533i	1.49764	+	1.49764i
$299$	−5.07255			−0.293353
$300$	7.66018	+	20.3886i	0.442261	+	1.17714i
$301$	21.1108			1.21680
$302$	25.7969	+	25.7969i	1.48445	+	1.48445i
$303$	−6.58513	+	11.0868i	−0.378306	+	0.636918i
$304$			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	$-0.931835\pi$
$311$		−	7.49544i		−	0.425027i	0.977158	−	0.212514i	$-0.0681650\pi$
$312$	−2.03844	−	1.21076i	−0.115404	−	0.0685457i
$313$	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
$315$	3.49980	+	21.5306i	0.197191	+	1.21311i
$316$	8.17440			0.459846
$317$	−13.7470	−	13.7470i	−0.772109	−	0.772109i	0.206366	−	0.978475i	$-0.433836\pi$
$317$	−13.7470	−	13.7470i	−0.772109	−	0.772109i	−0.978475	+	0.206366i	$0.933836\pi$
$318$	5.29689	+	3.14616i	0.297035	+	0.176428i
$319$		−	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
$327$	15.6329	−	26.3197i	0.864503	−	1.45548i
$328$	−0.989367	−	0.989367i	−0.0546287	−	0.0546287i
$329$	−37.0688			−2.04367
$330$	−8.70701	−	10.3982i	−0.479305	−	0.572401i
$331$	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
$333$	26.5533	+	7.82387i	1.45511	+	0.428745i
$334$		−	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
$342$	15.5818	+	4.59116i	0.842570	+	0.248262i
$343$	−7.87826	−	7.87826i	−0.425386	−	0.425386i
$344$	−7.10373			−0.383008
$345$	−10.0821	−	12.0404i	−0.542803	−	0.648232i
$346$	−30.6604			−1.64831
$347$	8.98969	+	8.98969i	0.482592	+	0.482592i	0.905958	−	0.423367i	$-0.139152\pi$
$347$	8.98969	+	8.98969i	0.482592	+	0.482592i	−0.423367	+	0.905958i	$0.639152\pi$
$348$	5.62267	−	9.46636i	0.301407	−	0.507450i
$349$			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	−0.956916	−	0.290364i	$-0.906224\pi$
$353$	−12.5234	+	12.5234i	−0.666552	+	0.666552i	0.290364	+	0.956916i	$0.406224\pi$
$354$	−5.64439	−	22.1580i	−0.299996	−	1.17768i
$355$	26.8163	−	12.8771i	1.42326	−	0.683446i
$356$			17.9170i			0.949599i
$357$	−1.44471	−	0.858107i	−0.0764623	−	0.0454158i
$358$	−14.7561	−	14.7561i	−0.779882	−	0.779882i
$359$	−22.5376			−1.18949			−0.594744	−	0.803915i	$-0.702747\pi$
$359$	−22.5376			−1.18949			−0.594744	+	0.803915i	$0.702747\pi$
$360$	−1.17767	−	7.24499i	−0.0620689	−	0.381845i
$361$	12.5062			0.658221
$362$	−8.35696	−	8.35696i	−0.439232	−	0.439232i
$363$	−12.3364	−	7.32738i	−0.647494	−	0.384588i
$364$		−	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
$372$	2.22451	−	3.74520i	0.115336	−	0.194180i
$373$	−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
$375$	−13.9866	−	13.3931i	−0.722265	−	0.691616i
$376$	12.4736			0.643275
$377$	2.23589	+	2.23589i	0.115154	+	0.115154i
$378$	1.33203	−	35.8775i	0.0685123	−	1.84534i
$379$			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	−0.227121	−	0.973866i	$-0.572931\pi$
$383$	14.6141	−	14.6141i	0.746745	−	0.746745i	0.973866	+	0.227121i	$0.0729314\pi$
$384$	−14.2054	+	3.61860i	−0.724916	+	0.184661i
$385$	3.97030	−	11.3059i	0.202345	−	0.576201i
$386$			1.37121i			0.0697926i
$387$	5.50476	−	18.6825i	0.279823	−	0.949685i
$388$	−14.4287	−	14.4287i	−0.732506	−	0.732506i
$389$	12.3238			0.624840			0.312420	−	0.949944i	$-0.398860\pi$
$389$	12.3238			0.624840			0.312420	+	0.949944i	$0.398860\pi$
$390$	10.2550	+	0.907758i	0.519282	+	0.0459661i
$391$	1.20974			0.0611793
$392$	−2.76497	−	2.76497i	−0.139652	−	0.139652i
$393$	−4.32773	+	7.28619i	−0.218305	+	0.367539i
$394$			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	$0.211386\pi$
$401$			24.6845i			1.23268i	−0.787478	+	0.616342i	$0.788614\pi$
$402$	30.6046	+	18.1780i	1.52642	+	0.906636i
$403$	0.884592	+	0.884592i	0.0440646	+	0.0440646i
$404$	18.7236			0.931534
$405$	19.9666	+	2.51699i	0.992148	+	0.125070i
$406$	17.4641			0.866730
$407$	−10.7527	−	10.7527i	−0.532994	−	0.532994i
$408$	0.486143	+	0.288751i	0.0240677	+	0.0142953i
$409$		−	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
$417$	16.5747	−	27.9053i	0.811667	−	1.36653i
$418$	−6.30987	−	6.30987i	−0.308626	−	0.308626i
$419$	15.0668			0.736061			0.368030	−	0.929814i	$-0.380032\pi$
$419$	15.0668			0.736061			0.368030	+	0.929814i	$0.380032\pi$
$420$	24.2836	−	20.3341i	1.18492	−	0.992204i
$421$	−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
$423$	−9.66591	+	32.8049i	−0.469972	+	1.59503i
$424$		−	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	$-0.977772\pi$
$431$		−	2.89707i		−	0.139547i	0.997563	−	0.0697735i	$-0.0222277\pi$
$432$	0.521470	−	14.0455i	0.0250892	−	0.675763i
$433$	−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
$435$	−0.863164	+	9.75121i	−0.0413856	+	0.467535i
$436$	−44.4494			−2.12874
$437$	−7.30639	−	7.30639i	−0.349512	−	0.349512i
$438$	−30.5653	+	51.4599i	−1.46047	+	2.45885i
$439$			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	−0.793383	−	0.608723i	$-0.791682\pi$
$443$	−3.88666	+	3.88666i	−0.184661	+	0.184661i	0.608723	+	0.793383i	$0.291682\pi$
$444$	−9.92203	−	38.9505i	−0.470879	−	1.84851i
$445$	−6.89578	−	14.3603i	−0.326891	−	0.680744i
$446$			58.0550i			2.74898i
$447$	25.6242	+	15.2198i	1.21198	+	0.719872i
$448$	−26.3333	−	26.3333i	−1.24413	−	1.24413i
$449$	3.08994			0.145823			0.0729117	−	0.997338i	$-0.476771\pi$
$449$	3.08994			0.145823			0.0729117	+	0.997338i	$0.476771\pi$
$450$	18.2280	+	26.1458i	0.859275	+	1.23253i
$451$	−2.10735			−0.0992313
$452$	−11.6192	−	11.6192i	−0.546520	−	0.546520i
$453$	25.5683	+	15.1866i	1.20130	+	0.713530i
$454$		−	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	$0.170103\pi$
$461$			21.8712i			1.01864i	−0.860577	+	0.509321i	$0.829897\pi$
$462$	−10.0717	+	16.9568i	−0.468578	+	0.788900i
$463$	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
$465$	−0.341496	+	3.85790i	−0.0158365	+	0.178906i
$466$	28.5745			1.32369
$467$	−14.8096	−	14.8096i	−0.685305	−	0.685305i	0.275886	−	0.961190i	$-0.411029\pi$
$467$	−14.8096	−	14.8096i	−0.685305	−	0.685305i	−0.961190	+	0.275886i	$0.911029\pi$
$468$	−9.05380	−	2.66768i	−0.418512	−	0.123314i
$469$			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
$477$	4.81718	+	1.41937i	0.220563	+	0.0649886i
$478$	32.2744	+	32.2744i	1.47620	+	1.47620i
$479$	−10.5791			−0.483372			−0.241686	−	0.970355i	$-0.577700\pi$
$479$	−10.5791			−0.483372			−0.241686	+	0.970355i	$0.577700\pi$
$480$	23.5650	−	19.7324i	1.07559	−	0.900657i
$481$	11.5434			0.526333
$482$	6.88938	+	6.88938i	0.313803	+	0.313803i
$483$	−11.6623	+	19.6348i	−0.530654	+	0.893412i
$484$			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	$0.127541\pi$
$491$			17.2857i			0.780091i	−0.920796	+	0.390046i	$0.872459\pi$
$492$	−4.78909	−	2.84454i	−0.215909	−	0.128242i
$493$	−0.533233	−	0.533233i	−0.0240156	−	0.0240156i
$494$	6.77382			0.304769
$495$	−8.97013	−	6.46169i	−0.403178	−	0.290431i
$496$	2.70492			0.121454
$497$	−30.5892	−	30.5892i	−1.37211	−	1.37211i
$498$	−42.7064	−	25.3660i	−1.91372	−	1.13668i
$499$		−	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	−0.524285	−	0.851543i	$-0.675667\pi$
$503$	7.33962	−	7.33962i	0.327257	−	0.327257i	0.851543	+	0.524285i	$0.175667\pi$
$504$	−9.37317	+	5.10671i	−0.417514	+	0.227471i
$505$	−15.0068	+	7.20622i	−0.667794	+	0.320673i
$506$		−	14.1989i		−	0.631217i
$507$	−10.1144	+	17.0287i	−0.449197	+	0.756270i
$508$	8.33953	+	8.33953i	0.370007	+	0.370007i
$509$	4.20821			0.186526			0.0932629	−	0.995642i	$-0.470270\pi$
$509$	4.20821			0.186526			0.0932629	+	0.995642i	$0.470270\pi$
$510$	−2.44569	−	0.216489i	−0.108297	−	0.00958631i
$511$	−52.8822			−2.33937
$512$	−19.3644	−	19.3644i	−0.855793	−	0.855793i
$513$	13.2322	+	0.491276i	0.584216	+	0.0216904i
$514$		−	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	$0.197050\pi$
$521$			26.4895i			1.16053i	−0.814429	+	0.580263i	$0.802950\pi$
$522$	4.55387	−	15.4553i	0.199318	−	0.676460i
$523$	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
$525$	−11.6370	+	25.6438i	−0.507882	+	1.11919i
$526$	8.94076			0.389836
$527$	−0.210964	−	0.210964i	−0.00918976	−	0.00918976i
$528$	−3.94291	+	6.63831i	−0.171593	+	0.288896i
$529$			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
$537$	−14.6253	−	8.68687i	−0.631127	−	0.374866i
$538$	−36.7092	−	36.7092i	−1.58264	−	1.58264i
$539$	−5.88938			−0.253674
$540$	−11.6631	−	26.7927i	−0.501899	−	1.15297i
$541$	−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
$543$	−8.28289	−	4.91973i	−0.355453	−	0.211126i
$544$			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
$552$	3.92435	−	6.60706i	0.167031	−	0.281215i
$553$	7.47348	+	7.47348i	0.317805	+	0.317805i
$554$	−6.38026			−0.271071
$555$	22.9434	+	27.3998i	0.973895	+	1.16306i
$556$	−47.1272			−1.99864
$557$	26.8281	+	26.8281i	1.13674	+	1.13674i	0.989030	+	0.147713i	$0.0471912\pi$
$557$	26.8281	+	26.8281i	1.13674	+	1.13674i	0.147713	+	0.989030i	$0.452809\pi$
$558$	1.80166	−	6.11462i	0.0762704	−	0.258853i
$559$		−	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	−0.768108	−	0.640320i	$-0.778802\pi$
$563$	−3.03211	+	3.03211i	−0.127788	+	0.127788i	0.640320	+	0.768108i	$0.278802\pi$
$564$	48.1210	−	12.2581i	2.02626	−	0.516157i
$565$	13.7846	+	4.84075i	0.579922	+	0.203652i
$566$		−	20.4270i		−	0.858611i
$567$	−6.16703	−	28.6083i	−0.258991	−	1.20143i
$568$	10.2932	+	10.2932i	0.431893	+	0.431893i
$569$	20.6457			0.865511			0.432756	−	0.901511i	$-0.357541\pi$
$569$	20.6457			0.865511			0.432756	+	0.901511i	$0.357541\pi$
$570$	13.4636	+	16.0786i	0.563926	+	0.673458i
$571$	−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
$573$	−18.6351	+	31.3741i	−0.778492	+	1.31067i
$574$		−	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
$582$	−25.6734	−	15.2491i	−1.06420	−	0.632094i
$583$	−1.95071	−	1.95071i	−0.0807903	−	0.0807903i
$584$	17.7948			0.736353
$585$	8.28325	−	1.34644i	0.342470	−	0.0556686i
$586$	35.8866			1.48246
$587$	−14.5277	−	14.5277i	−0.599621	−	0.599621i	0.340590	−	0.940212i	$-0.389373\pi$
$587$	−14.5277	−	14.5277i	−0.599621	−	0.599621i	−0.940212	+	0.340590i	$0.889373\pi$
$588$	−13.3840	−	7.94960i	−0.551947	−	0.327836i
$589$			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	−0.533391	−	0.845869i	$-0.679082\pi$
$593$	7.60934	−	7.60934i	0.312478	−	0.312478i	0.845869	+	0.533391i	$0.179082\pi$
$594$	12.3800	+	13.3348i	0.507960	+	0.547132i
$595$	−0.939041	−	1.95553i	−0.0384969	−	0.0801690i
$596$		−	43.2748i		−	1.77260i
$597$	11.3820	−	19.1628i	0.465835	−	0.784283i
$598$	7.62145	+	7.62145i	0.311664	+	0.311664i
$599$	1.13006			0.0461730			0.0230865	−	0.999733i	$-0.492651\pi$
$599$	1.13006			0.0461730			0.0230865	+	0.999733i	$0.492651\pi$
$600$	3.91584	−	8.62907i	0.159864	−	0.352280i
$601$	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
$603$	27.8328	+	8.20089i	1.13344	+	0.333966i
$604$		−	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
$612$	2.15922	+	0.636211i	0.0872814	+	0.0257173i
$613$	−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
$615$	4.93320	+	0.436680i	0.198926	+	0.0176086i
$616$	5.86362			0.236252
$617$	19.9288	+	19.9288i	0.802302	+	0.802302i	0.983455	−	0.181153i	$-0.0579828\pi$
$617$	19.9288	+	19.9288i	0.802302	+	0.802302i	−0.181153	+	0.983455i	$0.557983\pi$
$618$	−19.3734	+	32.6173i	−0.779314	+	1.31206i
$619$		−	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
$627$	−6.25394	−	3.71461i	−0.249758	−	0.148347i
$628$	16.8205	+	16.8205i	0.671212	+	0.671212i
$629$	−2.75296			−0.109768
$630$	27.0911	−	37.6079i	1.07933	−	1.49833i
$631$	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
$633$	34.9653	+	20.7681i	1.38974	+	0.825457i
$634$			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	$0.162669\pi$
$641$			24.7653i			0.978170i	−0.872236	+	0.489085i	$0.837331\pi$
$642$	−36.2065	+	60.9574i	−1.42896	+	2.40580i
$643$	−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
$645$	19.2781	−	16.1427i	0.759073	−	0.635617i
$646$	−1.61548			−0.0635600
$647$	−34.1074	−	34.1074i	−1.34090	−	1.34090i	−0.895163	−	0.445739i	$-0.852941\pi$
$647$	−34.1074	−	34.1074i	−1.34090	−	1.34090i	−0.445739	−	0.895163i	$-0.647059\pi$
$648$	2.07519	+	9.62662i	0.0815213	+	0.378169i
$649$			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	−0.430925	−	0.902388i	$-0.641813\pi$
$653$	12.0477	−	12.0477i	0.471463	−	0.471463i	0.902388	+	0.430925i	$0.141813\pi$
$654$	−63.0334	+	16.0568i	−2.46480	+	0.627869i
$655$	−9.86242	+	4.73591i	−0.385357	+	0.185047i
$656$		−	3.45885i		−	0.135045i
$657$	−13.7894	+	46.7994i	−0.537974	+	1.82582i
$658$	55.6955	+	55.6955i	2.17124	+	2.17124i
$659$	11.3138			0.440722			0.220361	−	0.975418i	$-0.429276\pi$
$659$	11.3138			0.440722			0.220361	+	0.975418i	$0.429276\pi$
$660$	−1.41539	+	15.9897i	−0.0550938	+	0.622398i
$661$	−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
$663$	−0.330131	+	0.555811i	−0.0128212	+	0.0215859i
$664$			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
$672$	−38.4285	−	22.8251i	−1.48241	−	0.880499i
$673$	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
$675$	19.6596	+	16.9852i	0.756700	+	0.653762i
$676$	28.7585			1.10610
$677$	32.6858	+	32.6858i	1.25622	+	1.25622i	0.952884	+	0.303335i	$0.0981001\pi$
$677$	32.6858	+	32.6858i	1.25622	+	1.25622i	0.303335	+	0.952884i	$0.401900\pi$
$678$	−20.6744	−	12.2798i	−0.793994	−	0.471603i
$679$		−	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	−0.847238	−	0.531214i	$-0.821736\pi$
$683$	−8.25904	+	8.25904i	−0.316023	+	0.316023i	0.531214	+	0.847238i	$0.321736\pi$
$684$	−9.19842	−	16.8834i	−0.351710	−	0.645552i
$685$	5.46445	−	15.5607i	0.208786	−	0.594542i
$686$			23.6740i			0.903878i
$687$	3.20657	−	5.39860i	0.122338	−	0.205969i
$688$	−12.4174	−	12.4174i	−0.473409	−	0.473409i
$689$	2.09415			0.0797807
$690$	−2.94226	+	33.2388i	−0.112010	+	1.26538i
$691$	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
$693$	−4.54379	+	15.4211i	−0.172604	+	0.585798i
$694$		−	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	$-0.972691\pi$
$701$		−	4.53744i		−	0.171377i	0.996322	−	0.0856883i	$-0.0273089\pi$
$702$	−13.8028	−	0.512460i	−0.520953	−	0.0193416i
$703$	16.6268	+	16.6268i	0.627093	+	0.627093i
$704$	18.8742			0.711347
$705$	−33.8507	+	28.3452i	−1.27489	+	1.06754i
$706$	37.6325			1.41632
$707$	17.1181	+	17.1181i	0.643794	+	0.643794i
$708$	−13.8207	+	23.2686i	−0.519413	+	0.874487i
$709$			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
$717$	31.9883	+	18.9999i	1.19463	+	0.709564i
$718$	33.8625	+	33.8625i	1.26374	+	1.26374i
$719$	37.4509			1.39668			0.698341	−	0.715765i	$-0.253922\pi$
$719$	37.4509			1.39668			0.698341	+	0.715765i	$0.253922\pi$
$720$	10.6057	−	14.7229i	0.395252	−	0.548690i
$721$	−33.5188			−1.24830
$722$	−18.7904	−	18.7904i	−0.699308	−	0.699308i
$723$	6.82832	+	4.05577i	0.253948	+	0.150836i
$724$			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
$732$	8.59904	−	14.4774i	0.317830	−	0.535100i
$733$	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
$735$	13.7867	+	1.22038i	0.508531	+	0.0450145i
$736$	32.1784			1.18611
$737$	−11.2709	−	11.2709i	−0.415169	−	0.415169i
$738$	−7.81893	−	2.30383i	−0.287819	−	0.0848052i
$739$		−	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	−0.156244	−	0.987719i	$-0.549938\pi$
$743$	22.6644	−	22.6644i	0.831475	−	0.831475i	0.987719	+	0.156244i	$0.0499385\pi$
$744$	−1.83655	+	0.467832i	−0.0673313	+	0.0171516i
$745$	16.6553	+	34.6843i	0.610203	+	1.27073i
$746$			73.2554i			2.68207i
$747$	−38.8387	−	11.4437i	−1.42103	−	0.418704i
$748$	−0.874376	−	0.874376i	−0.0319704	−	0.0319704i
$749$	−62.6422			−2.28890
$750$	0.891756	+	41.1377i	0.0325623	+	1.50214i
$751$	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
$753$	23.0886	−	38.8721i	0.841395	−	1.41658i
$754$		−	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	$0.234307\pi$
$761$			37.0428i			1.34280i	−0.741095	+	0.671400i	$0.765693\pi$
$762$	14.8388	+	8.81369i	0.537552	+	0.319286i
$763$	−40.6381	−	40.6381i	−1.47120	−	1.47120i
$764$	52.9855			1.91695
$765$	−1.97546	+	0.321111i	−0.0714228	+	0.0116098i
$766$	−43.9151			−1.58672
$767$	−5.49589	−	5.49589i	−0.198445	−	0.198445i
$768$	−7.32977	−	4.35361i	−0.264490	−	0.157097i
$769$		−	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	−0.880536	−	0.473979i	$-0.842817\pi$
$773$	−11.3034	+	11.3034i	−0.406556	+	0.406556i	0.473979	+	0.880536i	$0.342817\pi$
$774$	−36.3411	+	19.7994i	−1.30625	+	0.711675i
$775$	−3.12619	+	3.90217i	−0.112296	+	0.140170i
$776$			8.87783i			0.318695i
$777$	26.5395	−	44.6820i	0.952098	−	1.60296i
$778$	−18.5163	−	18.5163i	−0.663843	−	0.663843i
$779$	3.25857			0.116750
$780$	−7.82297	−	9.34242i	−0.280107	−	0.334512i
$781$	21.9245			0.784520
$782$	−1.81762	−	1.81762i	−0.0649981	−	0.0649981i
$783$	0.487286	−	13.1247i	0.0174142	−	0.469040i
$784$		−	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
$792$	1.52897	−	5.18916i	0.0543298	−	0.184389i
$793$	3.41947	+	3.41947i	0.121429	+	0.121429i
$794$	67.3258			2.38930
$795$	4.16230	+	4.97074i	0.147621	+	0.176294i
$796$	−32.3627			−1.14707
$797$	16.8144	+	16.8144i	0.595596	+	0.595596i	0.939138	−	0.343541i	$-0.111627\pi$
$797$	16.8144	+	16.8144i	0.595596	+	0.595596i	−0.343541	+	0.939138i	$0.611627\pi$
$798$	15.5737	−	26.2200i	0.551304	−	0.928179i
$799$		−	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
$807$	−36.3838	−	21.6106i	−1.28077	−	0.760730i
$808$	−5.76022	−	5.76022i	−0.202644	−	0.202644i
$809$	−22.4780			−0.790286			−0.395143	−	0.918620i	$-0.629305\pi$
$809$	−22.4780			−0.790286			−0.395143	+	0.918620i	$0.629305\pi$
$810$	−26.2179	−	33.7814i	−0.921201	−	1.18696i
$811$	−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
$813$	−25.0426	−	14.8744i	−0.878283	−	0.521668i
$814$			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	$-0.916188\pi$
$821$		−	14.9152i		−	0.520543i	0.965535	−	0.260271i	$-0.0838121\pi$
$822$	−13.8620	+	23.3382i	−0.483493	+	0.814012i
$823$	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
$825$	−5.01959	−	13.3603i	−0.174760	−	0.465147i
$826$	−42.9273			−1.49363
$827$	21.5531	+	21.5531i	0.749476	+	0.749476i	0.974381	−	0.224905i	$-0.0722072\pi$
$827$	21.5531	+	21.5531i	0.749476	+	0.749476i	−0.224905	+	0.974381i	$0.572207\pi$
$828$	8.64659	−	29.3455i	0.300490	−	1.01983i
$829$		−	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
$837$	0.192786	−	5.19257i	0.00666366	−	0.179482i
$838$	−22.6377	−	22.6377i	−0.782006	−	0.782006i
$839$	5.16183			0.178206			0.0891031	−	0.996022i	$-0.471600\pi$
$839$	5.16183			0.178206			0.0891031	+	0.996022i	$0.471600\pi$
$840$	−13.7264	−	1.21505i	−0.473607	−	0.0419231i
$841$	−22.6113			−0.779698
$842$	35.5426	+	35.5426i	1.22488	+	1.22488i
$843$	−7.50132	+	12.6293i	−0.258359	+	0.434975i
$844$		−	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
$852$	49.8248	+	29.5941i	1.70697	+	1.01388i
$853$	−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
$855$	13.8704	+	9.99163i	0.474358	+	0.341707i
$856$	21.0790			0.720465
$857$	−20.8116	−	20.8116i	−0.710910	−	0.710910i	0.255816	−	0.966726i	$-0.417656\pi$
$857$	−20.8116	−	20.8116i	−0.710910	−	0.710910i	−0.966726	+	0.255816i	$0.917656\pi$
$858$	6.52362	+	3.87479i	0.222713	+	0.132283i
$859$		−	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	$-0.362042\pi$
$863$	38.9980	−	38.9980i	1.32751	−	1.32751i	0.907540	−	0.419966i	$-0.137958\pi$
$864$	−30.2201	+	28.0565i	−1.02811	+	0.954501i
$865$	−30.4427	−	10.6906i	−1.03508	−	0.363492i
$866$			10.2761i			0.349197i
$867$	−14.9580	+	25.1834i	−0.508000	+	0.855272i
$868$	−5.78265	−	5.78265i	−0.196276	−	0.196276i
$869$	−5.35655			−0.181708
$870$	15.9480	−	13.3542i	0.540688	−	0.452750i
$871$	12.0996			0.409981
$872$	13.6746	+	13.6746i	0.463081	+	0.463081i
$873$	−23.3483	−	6.87952i	−0.790219	−	0.232837i
$874$			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	$-0.858639\pi$
$881$		−	25.5051i		−	0.859289i	0.902998	−	0.429644i	$-0.141361\pi$
$882$	−21.8515	−	6.43849i	−0.735777	−	0.216795i
$883$	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
$885$	2.12168	−	23.9688i	0.0713196	−	0.805701i
$886$	11.6793			0.392375
$887$	−5.17231	−	5.17231i	−0.173669	−	0.173669i	0.614920	−	0.788589i	$-0.289188\pi$
$887$	−5.17231	−	5.17231i	−0.173669	−	0.173669i	−0.788589	+	0.614920i	$0.789188\pi$
$888$	−8.93047	+	15.0354i	−0.299687	+	0.504555i
$889$			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
$897$	7.55390	+	4.48674i	0.252217	+	0.149808i
$898$	−4.64261	−	4.64261i	−0.154926	−	0.154926i
$899$	2.52760			0.0843001
$900$	6.62669	−	37.1377i	0.220890	−	1.23792i
$901$	−0.499429			−0.0166384
$902$	3.16627	+	3.16627i	0.105425	+	0.105425i
$903$	−31.4376	−	18.6728i	−1.04618	−	0.621391i
$904$			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	$0.163307\pi$
$911$			29.6294i			0.981666i	−0.871254	+	0.490833i	$0.836693\pi$
$912$	6.09688	−	10.2647i	0.201888	−	0.339900i
$913$	15.7277	+	15.7277i	0.520511	+	0.520511i
$914$	−26.4706			−0.875568
$915$	−1.32008	+	14.9130i	−0.0436406	+	0.493010i
$916$	−9.11729			−0.301244
$917$	11.2500	+	11.2500i	0.371508	+	0.371508i
$918$	3.29180	+	0.122216i	0.108646	+	0.00403372i
$919$		−	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
$927$	−8.74022	+	29.6632i	−0.287066	+	0.974269i
$928$	−14.1837	−	14.1837i	−0.465603	−	0.465603i
$929$	−41.0325			−1.34623			−0.673116	−	0.739537i	$-0.735045\pi$
$929$	−41.0325			−1.34623			−0.673116	+	0.739537i	$0.735045\pi$
$930$	6.30955	−	5.28336i	0.206898	−	0.173248i
$931$	9.10668			0.298459
$932$	−23.9148	−	23.9148i	−0.783356	−	0.783356i
$933$	−6.62982	+	11.1620i	−0.217051	+	0.365428i
$934$			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	$0.170510\pi$
$941$			31.3149i			1.02084i	−0.859926	+	0.510419i	$0.829490\pi$
$942$	29.9293	+	17.7769i	0.975148	+	0.579202i
$943$	3.66633	+	3.66633i	0.119392	+	0.119392i
$944$	−16.8054			−0.546969
$945$	13.8323	−	35.1583i	0.449964	−	1.14370i
$946$	22.7341			0.739149
$947$	−31.5744	−	31.5744i	−1.02603	−	1.02603i	−0.999652	−	0.0263795i	$-0.991602\pi$
$947$	−31.5744	−	31.5744i	−1.02603	−	1.02603i	−0.0263795	−	0.999652i	$-0.508398\pi$
$948$	−12.1731	−	7.23037i	−0.395364	−	0.234831i
$949$			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	−0.793443	−	0.608645i	$-0.791713\pi$
$953$	−5.70484	+	5.70484i	−0.184798	+	0.184798i	0.608645	+	0.793443i	$0.291713\pi$
$954$	−5.10517	−	9.37035i	−0.165286	−	0.303376i
$955$	−42.4674	+	20.3927i	−1.37421	+	0.659893i
$956$		−	54.0227i		−	1.74722i
$957$	−3.68444	+	6.20315i	−0.119101	+	0.200519i
$958$	15.8950	+	15.8950i	0.513544	+	0.513544i
$959$	−23.9832			−0.774458
$960$	−44.1834	−	3.91106i	−1.42601	−	0.126229i
$961$	1.00000			0.0322581
$962$	−17.3438	−	17.3438i	−0.559187	−	0.559187i
$963$	−16.3343	+	55.4368i	−0.526367	+	1.78642i
$964$		−	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	$-0.946457\pi$
$971$		−	10.4338i		−	0.334835i	0.985886	−	0.167418i	$-0.0535429\pi$
$972$	17.4660	+	35.0986i	0.560224	+	1.12579i
$973$	−43.0862	−	43.0862i	−1.38128	−	1.38128i
$974$	−56.7503			−1.81840
$975$	9.86568	+	4.47701i	0.315955	+	0.143379i
$976$	10.4561			0.334691
$977$	−10.4553	−	10.4553i	−0.334495	−	0.334495i	0.519796	−	0.854291i	$-0.326008\pi$
$977$	−10.4553	−	10.4553i	−0.334495	−	0.334495i	−0.854291	+	0.519796i	$0.826008\pi$
$978$	−8.47567	+	14.2697i	−0.271022	+	0.456294i
$979$		−	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	−0.262530	−	0.964924i	$-0.584557\pi$
$983$	22.0220	−	22.0220i	0.702394	−	0.702394i	0.964924	+	0.262530i	$0.0845568\pi$
$984$	0.598230	+	2.34845i	0.0190709	+	0.0748658i
$985$	−9.44897	+	26.9070i	−0.301069	+	0.857329i
$986$			1.60236i			0.0510294i
$987$	55.2018	+	32.7878i	1.75709	+	1.04365i
$988$	−5.66921	−	5.66921i	−0.180361	−	0.180361i
$989$	26.3245			0.837071
$990$	3.76891	+	23.1862i	0.119784	+	0.736905i
$991$	−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
$993$	−13.3247	−	7.91441i	−0.422848	−	0.251156i
$994$			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.218.4	yes	60
3.2	odd	2	inner	465.2.k.a.218.27	yes	60
5.2	odd	4	inner	465.2.k.a.32.27	yes	60
15.2	even	4	inner	465.2.k.a.32.4	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.k.a.32.4	✓	60	15.2	even	4	inner
465.2.k.a.32.27	yes	60	5.2	odd	4	inner
465.2.k.a.218.4	yes	60	1.1	even	1	trivial
465.2.k.a.218.27	yes	60	3.2	odd	2	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50249 - 1.50249i) q^{2} +(-1.48917 - 0.884514i) 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} +(2.22451 - 3.74520i) q^{12} +(0.884592 + 0.884592i) q^{13} +6.90938 q^{14} +(-0.341496 + 3.85790i) q^{15} +2.70492 q^{16} +(-0.210964 - 0.210964i) q^{17} +(1.80166 - 6.11462i) 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} +(0.192786 - 5.19257i) q^{27} +(-5.78265 - 5.78265i) q^{28} +2.52760 q^{29} +(6.30955 - 5.28336i) q^{30} +1.00000 q^{31} +(-5.61153 - 5.61153i) q^{32} +(-1.45768 + 2.45417i) 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} +(-10.2893 - 6.11144i) q^{42} +(-4.59068 - 4.59068i) q^{43} +4.14466 q^{44} +(3.92091 - 5.44302i) q^{45} +8.61579 q^{46} +(8.06085 + 8.06085i) q^{47} +(-4.02809 - 2.39254i) 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} +(2.25400 - 3.79485i) q^{57} +(-3.79769 - 3.79769i) q^{58} -6.21291 q^{59} +(-9.70244 - 0.858847i) q^{60} +3.86559 q^{61} +(-1.50249 - 1.50249i) q^{62} +(-9.35740 - 2.75714i) 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} +(3.14875 + 0.927772i) q^{72} +(11.4996 + 11.4996i) q^{73} -19.6066 q^{74} +(8.10696 - 3.04585i) q^{75} -6.40884 q^{76} +(3.78928 + 3.78928i) q^{77} +(-2.35120 + 3.95849i) 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} +(-3.76403 - 2.23569i) q^{87} +(-1.27508 - 1.27508i) q^{88} +7.12419 q^{89} +(-14.0692 + 2.28695i) q^{90} -4.06790 q^{91} +(-7.21080 - 7.21080i) q^{92} +(-1.48917 - 0.884514i) 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

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Groups

Database

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